From 52611e747d06d012ce723ee3d8cc21ae1bf304f1 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Wed, 15 Apr 2026 13:50:24 +0300 Subject: [PATCH 01/12] Gradient estimation notebook --- .../Gradient Estimation.ipynb | 2289 +++++++++++++++++ 1 file changed, 2289 insertions(+) create mode 100644 algorithms/gradient_estimation/Gradient Estimation.ipynb diff --git a/algorithms/gradient_estimation/Gradient Estimation.ipynb b/algorithms/gradient_estimation/Gradient Estimation.ipynb new file mode 100644 index 000000000..fc514e5cc --- /dev/null +++ b/algorithms/gradient_estimation/Gradient Estimation.ipynb @@ -0,0 +1,2289 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "8040b1be", + "metadata": {}, + "source": [ + "# Initialization" + ] + }, + { + "cell_type": "markdown", + "id": "9beb3b70", + "metadata": {}, + "source": [ + "Always run those cells before using the notebook, it import needed packages and initialize helper functions." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "f8d11d1a", + "metadata": {}, + "outputs": [], + "source": [ + "from classiq import *\n", + "from typing import List\n", + "import numpy as np\n", + "import pandas as pd\n", + "from dataclasses import dataclass\n", + "from matplotlib import pyplot as plt\n", + "import matplotlib\n", + "# %matplotlib widget" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "2d6c8e39", + "metadata": {}, + "outputs": [], + "source": [ + "@dataclass\n", + "class params:\n", + " # Algorithm parameters\n", + " l = 0.5\n", + " m = 2\n", + " n = 3\n", + " n0 = 3\n", + "\n", + " @property\n", + " def N(self):\n", + " return 2**self.n\n", + "\n", + " @property\n", + " def N0(self):\n", + " return 2**self.n0\n", + "\n", + " # Function parameters\n", + " f = None\n", + " f_prams = None\n", + " f_name = None\n", + "\n", + " def set_function(self, f, f_prams):\n", + " self.f_prams = f_prams\n", + "\n", + " # Allow passing by name, e.g. \"linear\" or \"quadratic\"\n", + " if isinstance(f, str):\n", + " self.f_name = f\n", + " self.f = getattr(self, f)\n", + " return\n", + "\n", + " # If a method from another params instance is passed,\n", + " # re-bind it to this instance to avoid mixed state.\n", + " if hasattr(f, \"__func__\"):\n", + " self.f = f.__func__.__get__(self, self.__class__)\n", + " else:\n", + " self.f = f\n", + "\n", + " self.f_name = getattr(self.f, \"__name__\", None)\n", + "\n", + " # Generated functions\n", + " def f_normalized(self, x):\n", + " val = self.f(self.l / self.N * (x - self.N // 2))\n", + " val *= self.N / (self.l * self.m)\n", + " return val\n", + "\n", + " def calculate_magnitude_and_phase(self):\n", + " x_array = np.arange(self.N)\n", + " # reorder the x_array to match the order of the quantum states\n", + " # TODO: delete? x_array = np.concatenate((x_array[self.N//2:], x_array[:self.N//2]))\n", + " phases = self.f_normalized(x_array) * 2 * np.pi\n", + " magnitudes = np.ones(self.N) * 1 / self.N\n", + " return magnitudes, phases\n", + "\n", + " def analytical_gradient(self, x):\n", + " if self.f_name == 'linear':\n", + " return self.f_prams[0]\n", + " elif self.f_name == 'quadratic':\n", + " return (2 * self.f_prams[0] * x + self.f_prams[1])\n", + " else:\n", + " raise NotImplementedError(\"Analytical gradient not implemented for this function.\")\n", + "\n", + " # A few example functions\n", + " def linear(self, x):\n", + " return self.f_prams[0] * x + self.f_prams[1]\n", + "\n", + " def quadratic(self, x):\n", + " return self.f_prams[0] * x**2 + self.f_prams[1] * x + self.f_prams[2]\n", + "\n", + " # Unpack function, to be used in the notebook\n", + " def unpack(self):\n", + " global l, m, n, n0, f, f_prams, N, N0\n", + " l, m, n, n0, N, N0 = self.l, self.m, self.n, self.n0, self.N, self.N0\n", + " f, f_prams = self.f, self.f_prams\n", + " global f_normalized\n", + " f_normalized = self.f_normalized" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "ad03b035", + "metadata": {}, + "outputs": [], + "source": [ + "# ****** Simulation ******\n", + "def run_statevector_simulation(qfunc_to_run, print_circuit_info=False, filter_ancilla=False):\n", + " # Run a statevector simulator\n", + " qprog = synthesize(qfunc_to_run)\n", + " #show(qprog)\n", + " if print_circuit_info:\n", + " print(\"Circuit Width:\", qprog.data.width)\n", + " print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", + " print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", + "\n", + " backend_preferences = ClassiqBackendPreferences(backend_name=\"simulator_statevector\")\n", + " execution_preferences = ExecutionPreferences(num_shots=1, backend_preferences=backend_preferences)\n", + " with ExecutionSession(qprog, execution_preferences=execution_preferences) as es:\n", + " if filter_ancilla:\n", + " es.set_measured_state_filter(\"ancilla\", lambda v: v == 0)\n", + " results_statevector = es.sample()\n", + " df = results_statevector.dataframe\n", + " return df\n", + "\n", + "def run_standard_simulation(qfunc_to_run):\n", + " # Run a regular simulator\n", + " qprog = synthesize(qfunc_to_run)\n", + " job = execute(qprog)\n", + " # job.open_in_ide()\n", + " pc = job.get_sample_result().parsed_counts\n", + " return pc\n", + "\n", + "# ****** Result Processing ******\n", + "def state_to_gradient(value):\n", + " if value >= N//2:\n", + " value -= N\n", + " return value / (N/m)\n", + "\n", + "def simplify_df(df, unwrap=True):\n", + " # Get the phase from the df\n", + " phases = np.angle(df[\"amplitude\"]).astype(float)\n", + " phases_over_2pi = phases/(2*np.pi)\n", + " f_classical = f_normalized(df['x'])\n", + " simplified_df = pd.DataFrame({\"f_classical\": f_classical, \"phase_over_2pi\": phases_over_2pi.round(5)})\n", + " simplified_df.index = df['x']\n", + " simplified_df.sort_index(inplace=True)\n", + "\n", + " # Unwrap the phase if requested\n", + " if unwrap:\n", + " # Unwrap the phase\n", + " simplified_df['phase_over_2pi'] = np.unwrap(simplified_df['phase_over_2pi'], period=1)\n", + " # Get rid of the global phase\n", + " simplified_df['phase_over_2pi'] -= simplified_df['phase_over_2pi'].iloc[N//2]\n", + " simplified_df['f_classical'] -= simplified_df['f_classical'].iloc[N//2]\n", + "\n", + " return simplified_df\n", + "\n", + "def compute_success_rate(pc, analytic_derivatives, reject_underresolution=False):\n", + " items = []\n", + " for obj in pc:\n", + " # obj.state -> dict of measured registers\n", + " # obj.count (or obj.shots) -> number of occurrences\n", + " state = getattr(obj, \"state\", None)\n", + " shots = getattr(obj, \"count\", None)\n", + "\n", + " if shots is None:\n", + " shots = getattr(obj, \"shots\", None)\n", + "\n", + " if state is None or shots is None:\n", + " raise TypeError(\n", + " f\"Unsupported parsed_counts entry type: {type(obj)}. \"\n", + " f\"Need fields like .state and .count/.shots.\"\n", + " )\n", + "\n", + " items.append((state, shots))\n", + "\n", + " total_shots = sum(shots for _, shots in items)\n", + " if total_shots == 0:\n", + " return 0.0, 0, 0\n", + "\n", + " tolerance = 0.5 * m/N\n", + "\n", + " success_shots = 0\n", + "\n", + "\n", + " for state_key, shots in items:\n", + " # state_key might be SampledState key object or plain dict; normalize:\n", + " state = getattr(state_key, \"state\", state_key)\n", + "\n", + " # estimate derivatives using your formula: value * m\n", + " est = {}\n", + " for name, value in state.items():\n", + " est[name] = state_to_gradient(value)\n", + "\n", + " # success condition: all analytic derivatives within tolerance\n", + " correct = True\n", + " for name, analytic_val in analytic_derivatives.items():\n", + " measured_val = est.get(name)\n", + " if measured_val is None or abs(measured_val - analytic_val) >= tolerance:\n", + " correct = False\n", + " break\n", + " if reject_underresolution and measured_val == 0:\n", + " correct = False\n", + " break\n", + "\n", + " if correct:\n", + " success_shots += shots\n", + "\n", + " success_rate = success_shots / total_shots\n", + " return success_rate, success_shots, total_shots\n", + "\n", + "def analyze_results(pc):\n", + " # Print the results and compute the majority gradient\n", + " print(\"Parsed counts:\", pc)\n", + " print(f\"The analytical gradient is: {p.analytical_gradient(0)}\")\n", + " majority_state = pc[0].state\n", + " majority_gradient = state_to_gradient(majority_state.get('x'))\n", + " print(f\"The majority gradient is: {majority_gradient}\")\n", + "\n", + " # Check if the majority result is correct within the resolution of the algorithm\n", + " resolution = m/N\n", + " is_correct = abs(majority_gradient - p.analytical_gradient(0)) < resolution/2\n", + " print(f\"The majority result is\", \"correct\" if is_correct else \"incorrect\")\n", + " print(\"####################################################\")\n", + "\n", + " # Compute the success rate of the algorithm, i.e. the percentage of shots that are correct within the resolution of the algorithm.\n", + " success_rate, success_shots, total_shots = compute_success_rate(pc, analytic_derivatives={'x': p.analytical_gradient(0)})\n", + " print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", + " show_bar(success_rate)\n", + "\n", + " # Visualize the theoretical values of the phases\n", + " # We used the standard simulation, so this is theoretical values only without the phases from the simulation\n", + " plot_theoretical()\n", + "\n", + "# ****** Plotting ******\n", + "def plot_classical():\n", + " x_values = np.linspace(-N//2, N*1.5, 1000) # more points for smoother curve\n", + " f_values = f_normalized(x_values)\n", + " f_values -= f_normalized(N//2)\n", + " plt.plot(x_values, f_values, color='lightgray', label=\"Original function\")\n", + " ax = plt.gca()\n", + " ax.set_xticks(np.arange(N))\n", + " ax.set_xticklabels([str(i) for i in range(N)])\n", + "\n", + " # Primary-axis labels (normalized coordinates)\n", + " ax.set_xlabel(\"x (index)\")\n", + " ax.set_ylabel(\"f (normalized)\")\n", + "\n", + " # Secondary X axis: integer grid index -> real x\n", + " # Uses existing l, N convention: x_real = (x - N/2) * (l/N)\n", + " x_to_real = lambda x: (x - N / 2) * (l / N)\n", + " real_to_x = lambda xr: xr * (N / l) + N / 2\n", + " secax_x = ax.secondary_xaxis(\"top\", functions=(x_to_real, real_to_x), color='blue')\n", + " secax_x.set_xlabel(\"x (real)\")\n", + "\n", + " # Secondary Y axis: normalized f -> unnormalized f\n", + " # Assumes f_normalized = m * f_real => f_real = f_normalized / m\n", + " f_to_real = lambda y: (y + f_normalized(N//2)) * m * l / N \n", + " real_to_f = lambda yr: yr / m / l * N - f_normalized(N//2)\n", + " secax_y = ax.secondary_yaxis(\"right\", functions=(f_to_real, real_to_f), color='blue')\n", + " secax_y.set_ylabel(\"f (real, unnormalized)\")\n", + "\n", + "def plot_theoretical(show=True):\n", + " # Get the phase from the df\n", + " x_array = np.arange(N)\n", + " \n", + " f_classical = f_normalized(x_array)\n", + " f_classical -= f_classical[N//2]\n", + "\n", + " if show:\n", + " plt.figure()\n", + " plot_classical()\n", + " plt.plot(x_array, f_classical, 'o', label=\"Theoretical values\")\n", + " xmin, xmax = -N//2, N*1.5\n", + " ymin, ymax = -N//2, N//2\n", + " plt.xlim(xmin, xmax)\n", + " plt.ylim(ymin, ymax)\n", + " plt.vlines(0, ymin, ymax, colors='lightgray', linestyles='dashed')\n", + " plt.vlines(N-1, ymin, ymax, colors='lightgray', linestyles='dashed')\n", + " plt.hlines(-N/4+0.5, xmin, xmax, colors='lightgray', linestyles='dashed')\n", + " plt.hlines(N/4, xmin, xmax, colors='lightgray', linestyles='dashed')\n", + " plt.legend()\n", + " if show:\n", + " plt.show()\n", + "\n", + "\n", + "def plot_simplified_df(simplified_df, show=True):\n", + " plt.figure()\n", + " plot_theoretical(show=False)\n", + " plt.plot(simplified_df.index, simplified_df['phase_over_2pi'], 'o', label=\"Measured phases\")\n", + " plt.legend()\n", + " if show:\n", + " plt.show()\n", + "\n", + "def show_bar(success_rate):\n", + " bar_length = 50\n", + " filled = int(round(bar_length * success_rate))\n", + " GREEN = \"\\033[92m\"\n", + " RED = \"\\033[91m\"\n", + " RESET = \"\\033[0m\"\n", + "\n", + " bar = f\"{GREEN}{'█' * filled}{RED}{'-' * (bar_length - filled)}{RESET}\"\n", + "\n", + " print(f\"[{bar}] {success_rate * 100:.2f}%\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "d85717d1", + "metadata": {}, + "source": [ + "# 1. Fast Quantum Algorithm for Numerical Gradient Estimation" + ] + }, + { + "cell_type": "markdown", + "id": "35a1c868", + "metadata": {}, + "source": [ + "Given a function scalar function $f(x_1, ... x_d)$, we want to find the gradient of the function in specific point.\\\n", + "Classicaly this requires at least d+1 queries of the function $f$ (one query at the origin, and one in each direction).\\\n", + "In this notebook we will explore quantum algorithm to find the gradient in just a single query of the function.\\\n", + "This is a dramatic improvement in large dimensions functions, as most of the times the most expensive part of calculating the derivative is querying the function.\\\n", + "\\\n", + "The core concept of the algorithm is to first 'apply' the function to the phase of a superposition state, then extract the gradient value from the phase to a measurable state by using a QFT.\\\n", + "Let's see it step by step, first a little simplified version to understand the concept, and then fixing the inaccurities for the final algorithm." + ] + }, + { + "cell_type": "markdown", + "id": "ce1b3ca4", + "metadata": {}, + "source": [ + "## Simplified version of the algorithm\n", + "As briefly mentioned earlier, the algorithm can be divided to two steps:\n", + "1. Applying the function to the phase\n", + "2. Extracting the gradient value to a measurable state\n", + "\n", + "In more details:\n", + "1. For each coordinate ($x_i$), we start with the state $\\ket{\\delta_i}=\\ket{0}+\\ket{1}+\\ket{2}....\\ket{N-1}$, by applying the Hadamard gate on $\\ket{0}$. If there are more than one coordinates, the state $\\ket{\\delta}$ is a product state of all $\\ket{\\delta_i}$\n", + "2. Using the phase kickback technique, we apply the function to the phase of each ket creating the state:\n", + "$$e^{i\\cdot2\\pi f(0)}\\ket{0} + e^{i\\cdot2\\pi f(1)}\\ket{1} + e^{i\\cdot2\\pi f(2)}\\ket{2} ..... e^{i\\cdot2\\pi f(N-1)}\\ket{N-1}$$\n", + "3. We note the fact that for small enough interval, we can approximate: $f(x)\\approx f(0)+x\\cdot f'(x)$, so we can write the previous state as: \n", + "$$ e^{i\\cdot2\\pi f(0)}(\\ket{0} + e^{i\\cdot2\\pi f'(0)}\\ket{1} + e^{i\\cdot2\\pi 2f'(0)}\\ket{2} ..... e^{i\\cdot2\\pi (N-1)f'(0)}\\ket{N-1}) = e^{i\\cdot2\\pi f(0)}\\sum e^{i\\cdot2\\pi jf'(0)}\\ket{j} $$\n", + "4. We note that this state is exactly the fourier transform of the state $\\ket{f'(0)}$, so we apply the inverse fourier transform and get the result: $$\\ket{f'(0)}$$\n", + "5. We measure to get $f'(0)$, and for a multi-coordinates function $\\nabla f$.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "05c25e29", + "metadata": {}, + "source": [ + "## Exact version of the algorithm\n", + "The previous explaination covers the main idea of the algorithm, but miss some important details on negative and fractional values.\\\n", + "In this explaination we will fill in this details.\\\n", + "When we calculate gradient, we look on an interval around the point of interest (in this case, it will be the origin). We will call this interval $l$.\n", + "The state $\\ket{\\delta_i}$ should represent $N$ equally spaced points around the origin in the interval $l$, so we normalized it to be:\n", + "$$ x=\\frac{l}{N}(\\delta-\\frac{N}{2}) $$\n", + "That way, $\\delta=0$ will be the leftmost point of the interval ($-l/2$), $\\delta=N/2$ will be the origin, and $\\delta=N-1$ will be the rightmost point of the interval ($l/2-l/N$).\\\n", + "\\\n", + "We also need to normalize the result state. Say the expected gradient is bounded between $-m/2$ and $m/2$, we want to represent those values using the $N$ states of the coordinate, so doing a similar trick we can define $$ \\nabla f=\\frac{m}{N}(\\delta_{measured}-\\frac{N}{2}) $$\\\n", + "\\\n", + "When using the algorithm we need to select $l$ and $m$ using our prior knowledge on the function $f(x)$, and $N$ will define the final resolution we get.\\\n", + "$l$ should be small enough so we will stay in a linear regime of the function, and $m$ should be larger than the maximum possible gradient, but not too large because then we will lose resultion.\n", + "\\\n", + "Using those two normalizations, we change two things in the algorithm:\n", + "1. In step 2, instead of applying $f(\\delta)$, we apply $\\frac{N}{ml}f(\\frac{l}{N}(\\delta-\\frac{N}{2}))$.\n", + "2. In step 5, instead of measuring $\\nabla f$ directly, we measure $\\frac{N}{m}\\nabla f + \\frac{N}{2}$, and need to invert this to find $\\nabla f$\n", + "Note that due to the cyclic nature of the QFT, if we know that the gradient must be positive or negative, we don't need to change anything in the algorithm, just adjust the final convertion." + ] + }, + { + "cell_type": "markdown", + "id": "2fe010f7", + "metadata": {}, + "source": [ + "## Notebook's structure:\n", + "In the notebook, we will cover those topics:\n", + "1. Theoretical explaination (this section)\n", + "2. Step 1 of the algorithm - State Preparation. We will cover two methods. Phase Kickback (as in the cited paper) and Prepare State (more straight forward and more efficient for the simulation). We will demonstrate how the states are prepared using a full statevector simulation.\n", + "3. The full algorithm, showing examples of linear and non-linear functions.\n", + "4. Parameters selection and limits (Still work in progress)\n", + "5. Multi-coordinates example, f as function of x, y\n", + "\n", + "A technical note: In this notebook, some analysis functions are repetetive. Each time a new analysis is used it is written explicitly in the first time, but in later times is appears as an helper function, in order to make the code more readable and easy to understand. All the helpers functions appears at the beggining of this notebook." + ] + }, + { + "cell_type": "markdown", + "id": "6b665020", + "metadata": {}, + "source": [ + "# 2. State Preparation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "7cbd6c18", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: free the ancilla\n", + "# TODO: write explanations\n", + "# TODO: format using the other notebooks as a reference\n", + "# TODO: explain about the params class and the auxillary functions.\n", + "# TODO: write / remove section 5" + ] + }, + { + "cell_type": "markdown", + "id": "cb541ef9", + "metadata": {}, + "source": [ + "## 2.1. Phase Kickback" + ] + }, + { + "cell_type": "markdown", + "id": "05340b0f", + "metadata": {}, + "source": [ + "The first step of the algorithm is to prepare the state:\n", + "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}(\\delta-\\frac{N}{2}))}\\ket\\delta$$\n", + "The paper uses the phase kickback technique using the ancilla in order to create this state.\\\n", + "In the next example we will see how it works." + ] + }, + { + "cell_type": "markdown", + "id": "3568e49c", + "metadata": {}, + "source": [ + "The phase kickback contains three steps:\n", + "1. Apply Hadamard gate on $\\ket\\delta$ to have an entangeled state\n", + "2. Set the ancilla to $\\ket{1111...1}$ (in binary representation) and apply QFT on it\n", + "3. Add the value $f(\\delta)$ to the ancilla, and the function's value will be 'kicked' to the phase\n", + "\n", + "Note that we use the ancilla as a signed and fractional QNum, so in order to have $\\ket{1111...1_b}$, we will assign $-1/N_0$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "0e3557a4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 10\n", + "Circuit Depth: 69\n", + "Gate Counts: {'u': 54, 'cx': 48}\n" + ] + }, + { + "data": { + "application/vnd.microsoft.datawrangler.viewer.v0+json": { + "columns": [ + { + "name": "index", + "rawType": "int64", + "type": "integer" + }, + { + "name": "x", + "rawType": "int64", + "type": "integer" + }, + { + "name": "ancilla", + "rawType": "float64", + "type": "float" + }, + { + "name": "amplitude", + "rawType": "complex128", + "type": "unknown" + }, + { + "name": "magnitude", + "rawType": "object", + "type": "string" + }, + { + "name": "phase", + "rawType": "object", + "type": "string" + }, + { + "name": "probability", + "rawType": "float64", + "type": "float" + }, + { + "name": "bitstring", + "rawType": "object", + "type": "string" + } + ], + "ref": "ec828fe0-9d6c-4212-a761-135d6c4c7a15", + "rows": [ + [ + "0", + "0", + "0.0", + "(0.0883883476483181-0.08838834764831877j)", + "0.12", + "-0.25π", + "0.015624999999999997", + "0000000000" + ], + [ + "1", + "2", + "0.0", + "(-0.0883883476483181+0.08838834764831877j)", + "0.12", + "0.75π", + "0.015624999999999997", + "0000000010" + ], + [ + "2", + "1", + "0.0", + "(0.08838834764831884+0.08838834764831802j)", + "0.12", + "0.25π", + "0.015624999999999993", + "0000000001" + ], + [ + "3", + "3", + "0.0", + "(-0.08838834764831882-0.088388347648318j)", + "0.12", + "-0.75π", + "0.01562499999999999", + "0000000011" + ], + [ + "4", + "4", + "0.0", + "(0.08838834764831811-0.08838834764831871j)", + "0.12", + "-0.25π", + "0.01562499999999999", + "0000000100" + ], + [ + "5", + "6", + "0.0", + "(-0.08838834764831811+0.08838834764831871j)", + "0.12", + "0.75π", + "0.01562499999999999", + "0000000110" + ], + [ + "6", + "5", + "0.0", + "(0.0883883476483188+0.08838834764831802j)", + "0.12", + "0.25π", + "0.015624999999999986", + "0000000101" + ], + [ + "7", + "7", + "0.0", + "(-0.0883883476483188-0.08838834764831802j)", + "0.12", + "-0.75π", + "0.015624999999999986", + "0000000111" + ] + ], + "shape": { + "columns": 7, + "rows": 8 + } + }, + "text/html": [ + "
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" + ], + "text/plain": [ + " x ancilla amplitude magnitude phase probability bitstring\n", + "0 0 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000000000\n", + "1 2 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000000010\n", + "2 1 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000000001\n", + "3 3 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000000011\n", + "4 4 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000000100\n", + "5 6 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000000110\n", + "6 5 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000000101\n", + "7 7 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000000111" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Set the default values:\n", + "# l = 0.5, m = 2, n = 3, n0 = 3\n", + "p = params()\n", + "\n", + "# Set the function we want to calculate the gradient of:\n", + "# f(x) = 0.5*x + 0.25\n", + "# Gradient: f'(0) = 0.5\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "\n", + "# Unpack the parameters to global variables for easier use\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]], ancilla: Output[QNum[n0, SIGNED, n0]]):\n", + " # 1. State preparation\n", + " \n", + " # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " \n", + " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", + " # Note: the ancilla is a signed fractional number,\n", + " # so the state |1111...1> corresponds to the value -1/N0\n", + " # which is the most negative value\n", + " numeric_value = -0.5**n0\n", + " ancilla |= numeric_value\n", + " qft(ancilla)\n", + "\n", + " # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", + " # Calculate the normalized f and add it to the ancilla\n", + " val = f_normalized(x)\n", + " inplace_add(val, ancilla)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "\n", + "# Run using a statevector simulator\n", + "qprog = synthesize(main)\n", + "# show(qprog) # Uncomment to see the circuit\n", + "print(\"Circuit Width:\", qprog.data.width)\n", + "print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", + "print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", + " \n", + "# Pay attention that we use a statevector simulator here\n", + "backend_preferences = ClassiqBackendPreferences(backend_name=\"simulator_statevector\")\n", + "execution_preferences = ExecutionPreferences(num_shots=1, backend_preferences=backend_preferences)\n", + "with ExecutionSession(qprog, execution_preferences=execution_preferences) as es:\n", + " es.set_measured_state_filter(\"ancilla\", lambda v: v == 0)\n", + " results_statevector = es.sample()\n", + "\n", + "# Show the results as a dataframe.\n", + "df = results_statevector.dataframe\n", + "df\n", + "\n", + "# From now on, we will use the shortcut function:\n", + "# df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)" + ] + }, + { + "cell_type": "markdown", + "id": "cf477c66", + "metadata": {}, + "source": [ + "In order to understand the results, let's focus on the phase compared to the classical value of f(x):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f473a2df", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.microsoft.datawrangler.viewer.v0+json": { + "columns": [ + { + "name": "x", + "rawType": "int64", + "type": "integer" + }, + { + "name": "f_classical", + "rawType": "float64", + "type": "float" + }, + { + "name": "phase_over_2pi", + "rawType": "float64", + "type": "float" + } + ], + "ref": "4b5ced2e-554e-40fe-bb9d-aaa29448de04", + "rows": [ + [ + "0", + "-1.0", + "-0.125" + ], + [ + "1", + "-0.75", + "0.125" + ], + [ + "2", + "-0.5", + "0.375" + ], + [ + "3", + "-0.25", + "-0.375" + ], + [ + "4", + "0.0", + "-0.125" + ], + [ + "5", + "0.25", + "0.125" + ], + [ + "6", + "0.5", + "0.375" + ], + [ + "7", + "0.75", + "-0.375" + ] + ], + "shape": { + "columns": 2, + "rows": 8 + } + }, + "text/html": [ + "
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f_classicalphase_over_2pi
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" + ], + "text/plain": [ + " f_classical phase_over_2pi\n", + "x \n", + "0 -1.00 -0.125\n", + "1 -0.75 0.125\n", + "2 -0.50 0.375\n", + "3 -0.25 -0.375\n", + "4 0.00 -0.125\n", + "5 0.25 0.125\n", + "6 0.50 0.375\n", + "7 0.75 -0.375" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phases = np.angle(df[\"amplitude\"]).astype(float)\n", + "phases_over_2pi = phases/(2*np.pi)\n", + "f_classical = f_normalized(df['x']) - f_normalized(N//2) # shift the classical function to match the quantum convention\n", + "simplified_df = pd.DataFrame({\"f_classical\": f_classical, \"phase_over_2pi\": phases_over_2pi.round(5)})\n", + "simplified_df.index = df['x']\n", + "simplified_df.sort_index(inplace=True)\n", + "simplified_df" + ] + }, + { + "cell_type": "markdown", + "id": "a3aad709", + "metadata": {}, + "source": [ + "We can plot the phases from the statevector simulation (in orange) next to the values of $f(x)$ (blue).\\\n", + "We expect to see that the phases will match the function value, hence the two graphs should match complitly.\\\n", + "Let's plot it:\n", + "\n", + "\\* Quick note about the graph:\\\n", + "The quantum calculations are in normalized space where $x$ is a coordinate from $0$ to $N-1$, and $f$ is normalized using $l$ and $m$. The graphs show the normalized axes in black, and the real unnormalized axes in blue." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "77343d45", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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777zTJTh0h0EaA6yvvvrKXBgMjRs3znE70+xDhgzBr7/+akYTuarCf//7X/PzFgYDs379+plRSKZAeb0o+DM88MADJoA944wzTFqf/eGI2zp37oyUlBQT8C1YsADdu3c3bUYY0PE5+dx8Xl7y+z3iaPP1119vAtpVq1aZYJfn1x5g2jHY4wgrzz9ftwEDBhRqfqmISLA6cOCA+RvA93lfZzFSUgDOgLFfxo7Nf7/du9kq6tQRN153FzY0bmyN5n3+OfDuu4xPOO0GSE1FwJQM1REnzpPjH1NvGzFihAkm7DhiV9jgjsHQ6tWrEQgMMArzn4PpVx4n05P54XaOOu3atcuROr344osxdOhQxz78hOXstddeQ+PGjfHss8+a6/yer8+YMWMKPBYGaAxiOBJFt956qwng7Pdj0YOzt956yzTg5TkuzPw+juZyNM2eAi0qBnVXXHGF+X706NFmZI1paxbjPPPMMybYevXVVx3783Y7Piefu6DnfeGFF0xwaA+WGTzyZ+N55Kif3eWXX24COho2bBhefPFFzJs3z5xnEZFQwr8/O3fuNH9jiNkK/o1ltsdXVq8GatTIvR4b673H7tDButgxqOOf19deA554AgERciN2AwcONKM7/MNWs2bNAvflH9UdO3a4bOP1gv7Y8peMKUfnSzgq7AgfMYApCEePWLHsrF27dqd9XKYZ7UEdVatWzfyHdw5COUpWv3598zpwf+LcSn9o0aKFy7GR/fjsI3bF8ffff5tRZ2e8zp/bucGw83EweOfvr/N5EhEJldQrMzz2oI5TWBo0aODToI74Z4Z/yu0Xd4FdYiIQHc04wXU7rxd2bIAL/rRuDaxbh4ApGUqByL333ouZM2eauUpc6Px0mA7jCJBzdSIrarndF/hHlyNngVDYoeyGDRuafRlUMK2ZF7fzPxtHxuzKli0LX8i75BWPyznNytQmq3WnTJliqnd5G0fqWMBRHHyevIGtfRURd8dnP7/248ubxval050nEZFgx/nTqamp5kMrp9XwPd3bLbCKKyYGaNMGmDsX6NHD2sa3Wl4fOLBwj8HP5KtWMdOCgIkKpfTru+++i/fff9+M8nCeHC+HDx927MMJ/kyl2rF9Byfgc47SmjVrzBwmztfiqJ8v8A8uf2EDcSlsYMcihEsuucSkEJ3PHfF8vvfee6Y1SVHmPDAlyPPqbNmyZSgOtl3hSOAjjzxiRsbsKWJvYNDKeW92HCFjv7ui4CgaPzS4w1Ts6Zb14s/EAgxnvM6ULCuPRURCHT9E828LCyT4nsjROY7SBVtQZ8eZWFOmsFUWBzqAAQM439uqkqVevThly7E7Hn8c+O47dpuw2qPccovV7uSOOxAwIRPYTZo0yVTCsgqRaTH7hRP97Ziic/6Dzb5hDARZRcjJ/x9//LGZrF+U/mvhiO1eWP3LKk5WjLKnHQNgBnw1atQ47dy4vFgswcCZ87/Yq+7DDz90FAB4OimWo4YMQvnacV7bDz/84DL3sTg4Z5DngMUIDEjvuuuuU0bFTocfIBi8cu7bH3/8YX5+/o7u5uzbk2nmJUuWmPmI3JbfCBvnLTI4ZNUxzxsriXlcnNsnIhLqmF1h6tX+vsh5z5xawylPwapnTxYMAiNHAq1acdoNOzTkFlRwJpBTmAGON7A9CufVcZSOVbcLF1oFG4ESFUpRf34X50nmTNHmrSi87rrrzMgPAxlO6OdE9EjHtiQMaPgfjFWZ/PTENiZs7cEKz4JayOSHaXEGzaw65UgWAxx7Vayn/4E5CvnBBx+YylEG4oMHD3YUZxQXR3A5Wff888/HTTfdZAIpFjoUBUfV2C6GVcCcT8j0/ueff+7o7cfH5KgbU/McIcxvXiB7KjII5s/Jn3HkyJF4/PHHXX6nRURCNfXKqldmQ/h+zvdcpl/5fbAbONAadWNblCVLrNUn7H780Vptwu7FF3P3ZeXs119bc+wCqYStKLPoIxCrYtn2hKOFeQspjhw5Yj6NMLDx9eTPUMNRPzY95mig+I9+J0UkGFKv9lWM+LeRQV0gRulSU9nVIgFbt2agZs3wLIQM6eIJCW6cs8fKWKZPOU+Mo2u+mssoIiLBmXrlh3n7/G3+PWDv2FAYpQsnCuzEK1iA8OSTT5oGyFwdgfPHnAtZREQkvLNbrHrlfGIGcmxHFq7twoKdAjvxCjbN5UVERCIHAzn2h7WnXtkKiqlXdgaQwFBgJyIiIh6lXlkYxrm9pNRrcFBgJyIiIkXCgsK0tDQzYscOAGyVpdRrcFBgJyIiIoXCQI5Vr5xPTWwVxfl0Sr0GDwV2IiIiclrsB8uqV3vqNTEx0VS9etqIXnxDgZ2IiIgUaP/+/di2bZsj9cpROi7vKcFHgZ2IiIjki4Ecl+q0r9XN1CurXou6DKP4j7oGRnB3cC4jxuXDOIy+kgvieYBroRbn/kXB5eK8uXA0l6DjsfOTqIiIuGLKlcuC2YM6Lo/IlZYU1AU3jdgFgewcG5Zu3IudWUeQFF8a7epVQnSUb+cszJo1ywRKDG64ZiznSgS7nj17aq1fERE/YDDH1CsHAbgGNlOv5cqV07kPAQrsAmzWn+kY/eVqpGdYk1GpWkJpjOqegm7NqvnsefkprFq1aujYsSNCBRtf8iIiIr5LvTKgs2cyypYta4I6jdKFDqViAxzUDXh3hUtQR9szjpjtvN0X+vTpg3vvvdc0lmQqsm7duqf9j/7MM8+gYcOGZiFnLhk2ZsyYfPfNzs7G7bffbobrGYQ1btwYEyZMcNmHo4Tt2rUzbxhMrZ577rnYvHmzue3333/HRRddZCblsidSmzZt8Ouvv7pNxX755ZdmjVouNM1Rx//+97+O29555x20bdvWPFZycjJuuukm7Ny50+PzJiISCalXe1CXlJRk/j4oqAstGrELYPqVI3W2fG7jNiZiefslKcleT8sy0GrQoAFef/11LFu2zFQ4FYRrvk6ZMsUsGXbeeeeZibRr1qxxGwTy091HH31kupAvXLjQzOXj6OD111+PEydOoEePHujXrx/+97//mc7lS5cudZTL33zzzWjdujUmTZpkjotz99y9qXz99dcmkHv44Yfx9ttvm8f65ptvHLcfP34cTzzxhAkuGdANGTLEBLXO+4iIRDqmW5l65Xu7Uq+hT4FdgHBOXd6RurzBHW/nfh0aVPbqcyckJJhRLAZOHMkqSFZWlgkEX3nlFfTu3dtsY1DIAC8/DMJGjx7tuM6Ru0WLFuHDDz80gR0XimbH8v/85z/mcahp06aO/TmK+OCDD6JJkybmeqNGjdweG0cNb7jhBpfna9mypeP72267zfE95xG+9NJLZnTvwIEDmisiInIyy8LUK9+XifPo+OGc8+okNCkVGyAslPDmfr7y999/m6aUnTt3LvR9Jk6caFKorKDimwRHBhmwEatwOWrWtWtXdO/e3QSN/JRox1G1O+64A126dMG4ceNMWsAdjuYVdFzLly83z8HUMQPZTp06me32YxERiWSHDx8277H2oI7NhuvUqaOgLsQpsAsQVr96cz9fKWqxwgcffIAHHnjAzLP77rvvTPDVt29fkya1mzp1qhnFY+HGjBkzcMYZZ2Dx4sXmtsceewx//fUXrrjiCvzwww9ISUnBzJkzi3xsBw8eNMEj5+m99957JuVsfxznYxERiTRMt3JJsA0bNpj3Q47OMbvCD+NaRSL0KbALELY0YfWru9lz3M7buV8gMRXKAGru3LmF2v+XX34xAdvdd99t5sqx4CK/UTfexrl7nIPXrFkzvP/++47bGOgNHjzYBIZXX321CQTz06JFC7fHxTmAe/bsMaN+559/vkntqnBCRCIdU69cFszeyoTZDL5Ps5hNwoMCuwBhQQRbmlDe4M5+nbf7up/d6bDadNiwYXjooYdMgQKDNI6uvfnmm24DQVaxzp49G//88w8effRRM1pmt3HjRhPQccSOlbAM3v79918zz45pgYEDB5qqWd7GIJH3dZ6D52zUqFGmAINfmTJetWoVnn76aXMb069clPrll182n0q/+OILU0ghIhLpqVfOdSbOseZ7pebThRcFdgHEPnWTbjkLyQmu6VZe53Zf9rErCgZnQ4cOxciRI02QxUbB7ka/7rzzTjPKxn3at29vRs04emfH5Wg4mnbNNdeYkTlWzN5zzz3mfizm4P69evUyt7HY4rLLLnMpjnB24YUXmupbBm2tWrXCxRdfbCpsiSkFtkfh7UzncuTuueee89EZEhEJXhyZ43urPfXKIjd7Y3qlXsNPCRtfcXGLn2xYRcrJpZyvlbfnD0egODeBI1uhtPKEhCdv/U6KSPikXtPS0hyjdEy9sur1dG2uwkFqaiZq1UrA1q0ZqFnT9e93OFM9cxBgEOftliYiIhLZDh06ZObTsacnR+aYerWvDy7hS4FdhGPrD6Yq3Vm9erWZgyEiIqGVet2+fbu5ztQr38e1JGNkUGAX4apXr25akhR0u4iIhAau7sPUK5vLE6cQ1ahRIyJSr2JRYBfhWA3FUncREQltSr0KKbATEREJ8dTr7t27sWPHDnOdrZ5q1aql1GuEUmAnIiISwqnX1NRUswY2sYsDp9Ao9Rq5FNiJiIiEIC6dyKpXBnesdK1WrRoqVqyoqtcIp8BOREQkxFKvu3btcjSKj42NNalX9a4UUmAnIiISIjg6x1E6jtZRhQoVzEidUq8SkkuK/fTTT+jevbuZP8Bh588++6zA/bnmKPfLe7H39hH36tati/Hjx+sUBYD993b//v06/yLiwHl069atM0Ed3yPYxiRSVpGQMA3s+MvcsmVLTJw4sUj3W7t2LdLT0x2XpKQkBJWcbGDjz8Cqj62vvC4hh93dhw0bhubNm6Ns2bLmAwjXvd22bVuRHqdjx47m95SToEVEmHplxeumTZvMiB1Trw0aNDDz6URCOhXLBeF5KSoGchyuDkqrvwBmDQMynf74l68OdHsaSLkykEcmeXDxbLYRKKiH1IoVK/Doo4+aDyD79u3DoEGDcOWVV+LXX38t9Pnkc3DpHxERfmBk1as99cpgjqnXqKiQGpcRP4qI34xWrVqZ/wiXXHIJfvnllwL3PXr0qFks2fni06Duw16uQR1lplvbebuPXHjhhRg4cKC5cGQoMTHRBCT8ZOgcqNx2221m0WguR/P666+7PAZHp8444wyUKVMG9evXN/fnm5Dd77//josuusjcn93P27Rp4xLgLFiwAOeff77ptcSJv/fdd5/jzet0GDRxNIxvcnx+Bvz//vuvuY2vGR/z22+/dbnPzJkzzbHw5yLOU7n++utN0M/1E6+66irzidiuT58+6NGjB8aMGWNG3xo3blzgMfE8zpkzxzwm9z3nnHPwyiuvYPny5WbpNuLjM4XywQcfmJE5TnZu1qwZ5s+f73gcpWJFhLh6hD31ykCOaVemXxXUScQGdgzmJk+ejE8++cRcGDwwoOGoijtjx441f6DtF97HJ5hu5UgdcgOpXCe3zRru07Ts9OnTzcoTS5cuxYQJE/DCCy/gjTfecNz+/PPPo23btvjtt99w9913Y8CAASatbccgadq0aWY9Wd5/ypQpePHFFx2333zzzeaNaNmyZSa4GT58uFmzkNavX49u3brhmmuuwR9//IEZM2aYQI+BZmEw6GKQ+MUXX2DRokUmIL388stNYMkg8j//+Q/ef/99l/u89957JlBjIMj9unbtan6Gn3/+2QT85cqVM8fEkTm7uXPnmp+ZAdtXX31V5HOckZFhArm8I8YPPvgghg4das5thw4dzNxRru0oIsL3M84F37x5M7Kzs80HQKZegzbzJMHFFqJ46DNnzizy/S644ALbLbfc4vb2I0eO2DIyMhyXrVu3mufi93kdPnzYtnr1avO1yDb8ZLONKn/6C/fzgU6dOtmaNm1qy8nJcWwbNmyY2UZ16tRxOU/cLykpyTZp0iS3j/nss8/a2rRp47geHx9vmzZtWr773n777bb+/fu7bPv5559tUVFRpz2f//zzj3lNfvnlF8e23bt32+Li4mwffvihuc7fjXLlytkOHjxorvP1K126tO3bb78119955x1b48aNXX7+o0ePmseYPXu2ud67d29b1apVzXZP8Oc466yzbDfddJNj28aNG82xjxs3zrHt+PHjtpo1a9qefvppc33evHlmn3379nn0nB7/TopIwB07dsy2fv1626pVq8wlLS3Nlp2dHejDCklbt2aY91J+jSRhPWKXn3bt2pmhbXc4KZUjPs4Xnziww7v7eYCpQo4m2XHkiOlMfkKkFi1aOG7jfpz3Ze+bRBxlO/fcc812jnY98sgjjpQjDRkyBHfccQe6dOmCcePGmVE65zQtR/t4P/uFI2g5OTnYuHFjgcf9999/m5HG9u3bO7ZVrlzZpD95G3H0jqODHNEjjtjyteSx2J+fvwccsbM/P9OxR44ccTlOFkIUNK/OHY4IMiXLzyCTJk065Xaeazv+LBwZtR+7iER26pXTRZhuZcaI00CUepWiiLjAbuXKlSZFG3Dlqnp3Px+wp02dgzsGXsT0J1OtDKCYomRK8eGHH3ZJYz722GP466+/cMUVV+CHH35ASkqKmedmL9u/8847zethvzDYYmDJlENxMRi79tprHelYfu3Zs6cJouzPzzl/zs/Pyz///IObbrrJ8TisbvU0qGMahSlcn304EJGwTr2qMl7CvirW3sPHjiM7/GPMkRZO7h8xYgTS0tLw9ttvm9vZh61evXo488wzzUgM548xwPjuu+8QcHU6WtWvLJTId55dCet27ucjS5Yscbm+ePFiNGrUqFA9kRYuXIg6deqYYM6Ob0p5sbiCl8GDB+PGG2/E1KlT8d///hdnnXWWmZvXsGHDIh9306ZNTck/j58FCMT5aZwLx+DRjoEnC2YYXPJ1f/LJJx238fk54siKaW8GXvagjgHqvHnzzEhifniuL7jgAvM9fxbOQSzs/EIRCR/8MMxCrsOHD5vr/HvGLIhG6SQiRuw4Wb5169bmYk/18fuRI0ea6+z95ZwK5H8YTlBnOq1Tp05mROj7779H586dEXBR0VZLEyM3Hepyvds4az8f4bniOWRA9L///Q8vv/yyac9RGAwAeX9WdzJ1+dJLLzlG44hvUgxUWOHJgI/FCSyiYFBmr6hlcMh9GJwzEPr8888LFdzwuVnB2q9fP1Nwwdf1lltuMdVi3G7HwIlvkAzwGOA7p265jZXA3J/FE/yQwGNlZS5bC3ga1HGUkL+nLNTgJ29+CufFeSST2IuR52vNmjW45557TJUvK5BFJHKwgp+DFXy/VOpVInLEjhWtzu048uKcLWcPPfSQuQQt9qm7/m03fezG+byPHduF8A2F8w45Ssegrn///oW6L3uzcRSOgRhbxDDdynYnTL8SH4+jaHwONtZkEHX11Vdj9OjRjvl7bPHBET+2POHrytQD06WFwZE/Hi+rXxk0MYj75ptvXNLHTB1zlPCZZ55xBP92rIzlSiYMMHlcnNvCwJBBv6cjeBwtts/pY4sdZxy94++vHecc8sKglqOWvB/PkYiEP05p4fuivRLe3vLJk/m8InmVYAXFKVvF5RMV5zmwbUXeP/hM73Kkh6NBxVp8mS1NNi+0CiU4p47pVx+O1BGDDAYfWjbMv9jHjr8vnJOYN/jzBq/9ToqIX1KvnK5RtWpVpV59IDU1E7VqJWDr1gzUrBk5c51DasQubDGIq3d+oI9CRER8iAMEHNnniB2zGswSqLhKvE2BnQQdznkraOk4FtEEQrAel4gENwZynGu7d+9ex1QQNm9X6lV8QYFdhGKhQLBiTzfOPQvH46pbt26B80RFJLxwDjJTr5wmQZxLy9Srcw9REW9SYCdBhxOJPWmDEqnHJSLBaf/+/di2bZsj9cpROjZFF/ElBXYiIiJexECO7bfYxsieemXVa96m7yK+oMDOC+yrMYgEmtK8IoFPvbLHJ79SlSpVTCN0pV7FXxTYFQMnvrKpJIfa+Z+X1/WfVwIZ1O3atcv8DmpkQMT/OELHvwf8v8jUK0fpuA61iD8psCsGBnXsF8Yhd/5nFgk0BnWcx1OYZeFExHtZG/4N4Jw6+xrT/H+oD1gSCArsiomjdFynlut9cgkpkUDiHxIFdSL+w2pXVr3aU69MuzKDo+yNBIoCOy+wp7706UxEJDIw3WqveuX3JUuWNKN0Sr1KoCmwExERKQJmZxjQcSUJYjDHoI7BnUig6bdQRESkkLjGK1OvXPOV2GyYTYeVepVgocBORETkNJhuZdUri+XsqVdWvbJQQiSYRAX6AERERII99ZqamuqYT8fUK1ehUVAXniZO5PKPQOnSQPv2wNKlhbvfBx9wzj3QowcCSoGdiIhIAanX9evXO+bTJScno06dOppPF6ZmzACGDAFGjQJWrABatgS6dgV27iz4fps2AQ88AJx/PgJOgZ2IiEgeHJnbs2cPNmzYYObTsetB/fr1NZ8uzL3wAtCvH9C3L5CSAkyezCXhgLfecn8fdjq7+WZg9Gigfn0EnAI7ERGRPKlXFkjY59PFx8ejQYMGZs1XCT1ZWUBmZu7lZMvBU7AeZvlyoEuX3G1RUdb1RYvcP/7jj7N/IXD77QgKCuxEREROOnToENatW4fMzExT6crUK5vQq5VJ6EpJARISci9jx+a/3+7d1uhb1aqu23l9+/b877NgAfDmm8CUKQgaqooVEZGIZ0+97tixw3zP1CurXjVKF/pWrwZq1Mi9HhvrvZHAW2+1grrERAQNBXYiIhLRuCRkWloasviXGkD58uVRo0YNLc8XJuLj+Zqefj8GZ1xme8cO1+28npx86v7r11tFE927527LybG+slf12rVAgwbwO6ViRUQkolOvrHplUMfUa7Vq1cxIndZcjjwxMUCbNsDcua6BGq936HDq/k2aAKtWAStX5l6uvBK46CLr+1q1EBAasRMRkYjDdOvu3btN6pViYmJMQBcXFxfoQ5MAGjIE6N0baNsWaNcOGD8eOHjQqpKlXr2stC7n6bHPXbNmrvevUMH6mne7PymwExGRiEu9suHwgQMHzPWEhARUr15do3SCnj2BXbuAkSOtgolWrYBZs3ILKrZssSplg1kJGz+2iFusjOJ/ejan5LwLEREJXQcPHjStTBjc2VOvFStW1FqvYSg1NRO1aiVg69YM1KwZOX+/NWInIiJhj2MYu3btws6TSwgw9co2JqWZTxMJIwrsREQkrHF0jqN0HK2jChUqmJE6FUhIOFJgJyIiYYvz6Difzp565Vw6pl5FwpUCOxERCcvUK9OuTL9SbGysqXpV6lXCnQI7EREJK8ePHzejdM6pV47URQV7OaOIFyiwExGRsMFGwwzqsrOzTSDHgI6BnUikCKmPLz/99BO6d+9u/qNyrsRnn3122vv8+OOPOOuss8wwfMOGDTFt2jS/HKuIiPg39cpmw5s3bzZBHVOuDRo0UFAnESekAjsOq7ds2RITJ04s1P4bN27EFVdcgYsuuggrV67E/fffjzvuuAOzZ8/2+bGKiIj/Uq98v7fPp2NxRP369c0HepFIE1Kp2Msuu8xcCmvy5MmoV68enn/+eXO9adOmWLBgAV588UV07drVh0cqIiKBSL3WqFHDNJUXiVQhFdgV1aJFi9ClSxeXbQzoOHLnztGjR83FeeUJEREJztQr13slpl5Z9apROol0IZWKLart27ejqn2Bt5N4ncHa4cOH873P2LFjzac9+4VvFCIiEjyOHTuGDRs2OIK6SpUqKfUqEgmBnSdGjBhh1oW1X9itXEREggM/mK9fv958OGfqlR++1cpEJEJSscnJyWao3hmvly9fHnFxcfneh8P4GsoXEQkuOTk55v17z5495jrfwxnUcc1XEYmQwK5Dhw745ptvXLbNmTPHbBcRkdBJvTJ7Yp9CU7lyZTOtRg2HRUI8Fcs1/9i2hBdieTu/37JliyON2qtXL8f+d911l5mH8dBDD2HNmjV49dVX8eGHH2Lw4MEB+xlERKTwOCVm3bp1JqiLjo5G7dq1Ua1aNQV1IuEwYvfrr7+annR2Q4YMMV979+5tGg+np6c7gjxiq5Ovv/7aBHITJkxAzZo18cYbb6jViYhICKReWQC3d+9ec12pV5HCKWFjzbgUOFGX1bH81Mi5eSIi4ltsOcXU65EjR8z1xMREk3rlikMihZWamolatRKwdWsGataMnL/fITViJyIi4W3//v3Ytm2bGbFj6pWZlvj4+EAflkjIUGAnIiIBx0CO02n27dtnrpcpU8ZUvZYqVSrQhyYSUhTYiYhIUKVeq1SpgqSkJKVeRTygwE5ERIIm9cpRunLlyukVkYhw/DhXyQIOHeIHGq6iUvzHVGAnIiJ+x0COAR0DOypbtqyZT6fUq4S7rCzg3XeBDz4Ali5ln0aufQywNqhmTeDSS4H+/YGzz46APnYiIhL6mHLlsmD2oI5p17p16yqok7D3wgtA3brA1KlAly7AZ58BbM37zz/AokXAqFHAiRNWcNetG/Dvv0V/Do3YiYiIX7C7lj31yu9LlixpRumUepVIsWwZ8NNPwJln5n97u3bAbbcBkydbwd/PPwONGhXtORTYiYiIz2VnZ5uAjj1B7alXzqdjcCcSKf73v8LtFxvL1bM8ew79jxIREZ+nXrkqENd8tadeWfmqhsMi3qfATkREii07x4alG/diZ9YRJMWXRrt6lRBVAqYvHfvT2VOvHKXjaJ1IJLr66sLv++mnnj2HAjsRESmWWX+mY/SXq5GeYfWho+TysRjYMRmtEq3rnEfH+XRKvUokS0jI/Z6VsDNnWtvatrW2LV/OFkBFCwDzUmAnIiLFCuoGvLsCeRcd3555FI/M2oz/u6AK/nt2PbPeq1KvEummTs39ftgw4PrrrUKJ6GhrW3Y2cPfdQHGWple7ExER8Tj9ypG6vEGds7dWZqJSZQV1Inm99RbwwAO5QR3x+yFDrNs8pcBOREQ8wjl1zunX/HDkjvuJiCv2q1uzJs9GWNtycuAxpWJFRMQjLJTw5n4ikaRvX+D224H1663+dbRkCTBunHWbpxTYiYiIR5LiYwu5X2mdYZE8nnsOSE4Gnn8eSE+3tlWrBjz4IDB0KDymwE5ERIrsxIkTqBp1AIllorH7UHa++5RgdWyC1fpERFxFRQEPPWRdMjOtbcUpmnA8bvEfQkREIsmhQ4fMWq+HDh5A/7MrOYI4Z/bro7qnIJoN7UQk33l2339vrUhR4uR/k23bgAMH4DGN2ImISKGwyfDu3buxY8cOcz0mJga3XtgAtWvtP7WPXUJpE9R1a1ZNZ1ckH5s3A926AVu2AEePApdcAsTHA08/bV1nGxRPKLATEZFCpV5TU1Nx4ORQQkJCAqpXr47o6Gh0axaHS1KST1l5QiN1Iu4NGmQ1Jv79d6By5dzt//0v0K8fPKbATkRECnTw4EFs3brVBHdsMlytWjVUrFjRpeEwg7gODZz+OolIgX7+GVi4kCPfrtvr1gXS0uAxBXYiIuI29bpr1y7s3LnTkXqtXbs2SpdWlatIcbFXHVeayCs11UrJekrFEyIicgqOzm3atMkR1FWoUAENGjRQUCfiJZdeCowfn3udA+Cc6TBqFHD55Z4/rkbsRETEBefRcT6dPfXKuXQM7LTWq4j3sH9d165ASgpw5Ahw003Av/8CiYlWlaynFNiJiEi+qdfY2FjUqlVLo3QiPlCzplU4MWOG9ZWjdVyJ4uabgbg4zx9XgZ2IiOD48eNmlI6FEsQROo7URbGLqoj4RMmSViDHi7fof6yISIRj6nXdunUmqGMgV6NGDdSsWVNBnYgPRUcDF10E7N3rup1tInmbpxTYiYhEcOqVzYZZJJGdnW1SryyQYCsTEfEtm81qRMxedn/9deptnlJgJyISoanXjRs3mjl1xGCOQR2DOxHxPVbBfvIJ0L070KED8Pnnrrd5SnPsREQiTFZWlplPx1E6pl7tVa8i4j8clWPKdcIE4MwzgZ49gUceAe64o3iP61Fgd/ToUSxZsgSbN282i0FXqVIFrVu3Rr169Yp3NCIi4hXZObZTlviKKsH5OzvMeq/ERsOsetUonUhg9e8PNGoEXHcd8NNPfgzsfvnlF0yYMAFffvmlGcbnWoFxcXHYu3evCfbq16+P/v3746677kJ8cdomF2DixIl49tlnsX37drRs2RIvv/wy2rVrl+++06ZNQ9++fV228Q3sCBvGiIiEqVl/pmP0l6uRnpH7XpdcPhZ3tUtE22Trbb9SpUpITk5WgYRIgNSp41okwUKKxYut1GxxFHqO3ZVXXomePXuibt26+O6778xQ/p49e8xwPkft/v33XzzyyCOYO3cuzjjjDMyZMwfeNmPGDAwZMgSjRo3CihUrTGDXtWtXR8+l/JQvXx7p6emOC0cZRUTCOagb8O4Kl6COtmcexWPfp2HR1sNmlE6tTEQCa+NGoHKe5ZUbNgR++w3YsMEPI3ZXXHEFPvnkE5QqVSrf2zlax0vv3r2xevVqE0R52wsvvIB+/fo5RuEmT56Mr7/+Gm+99RaGDx+e733YKZ2fSkVEIiH9ypG6ggrq3votA7d1Le/HoxKRouBSzBzN8/mI3Z133uk2qMsrJSUFnTt3hjcdO3YMy5cvR5cuXRzbOOmX1xctWlRgf6Y6deqYT6hXXXUV/spbU5wHU8qZmZkuFxGRUMA5dXlH6vJKzzxq9hMR/6tUCTg5xRXsKsTr7i5hXxXLyb6s4KpatarLdl5fs2ZNvvdp3LixGc1r0aIFMjIy8Nxzz6Fjx44muGPzzfyMHTsWo0eP9snPICLiSyyU8OZ+IuJdL74I2EsQxo+HTxQ6sGOPo8IuAM1iimDQoUMHc7FjUNe0aVO89tpreOKJJ/K9z4gRI8w8PjuO2HG0T0Qk2FUpF1Oo/VglKyL+17t3/t8HJLAb7xRasmjiySefNIUL9sCJ6dDZs2fj0Ucf9cmBJiYmIjo62pTqO+P1ws6hYyqZbVm4dI47rJpV6b+IhBpOI6mcsx+JZaKx+1B2vvvwo3lygtX6RET8ryizu8qX93Fgx6IIu2uuuQaPP/44Bg4c6Nh233334ZVXXsH333+PwYMHw9tiYmLQpk0bU3Xbo0cPsy0nJ8dcdz6OgjCVu2rVKlx++eVePz4RkUDhVJO0tDTznsiWJmN+tD4AOxdR2PMto7qnIJoN7UTE79gH/HTJTzYu5j7Z+X8+880cO47MPf3006ds79atm9vqVG9gipQBZtu2bU3vOo4ictFqe5Vsr169zOLVnCdHDD7POeccNGzYEPv37zf979ju5I7itnUWEQkCDOTYgWDfvn3mepkyZdC7c2PUrLn71D52CaVNUNetWbUAHrFI8Js4EXj2WWD7dqBlS+DllwE37XLx6afAU08BTAQeP241GR46FLj11vz3nzcPPudRYFe5cmV8/vnnGMqjd8JtvM1X2EeP6xqOHDnSNChu1aoVZs2a5Sio2LJli0uzTb7ZsT0K9+UcQY74LVy40FTtishp5GQDmxcCB3YA5aoCdToCUU7dNCXgqdetW7c6Gq5zBaCkpCQzF5rB2yVNqmDNktk4vC8NcRVroEn7ToguGTL1ciIBMWMGB5HYTg1o394qcOjaFVi7FkhKOnV/Vq8+/DDQpAkzi8BXXwEca+K+vF9enTr5/mcoYbNx0K9ouKIDR70uu+wytOdPDpglxhhkTZkyBX369EG4YPEEV9hgqoPNjkUiwuovgFnDgMxtudvKVwe6PQ2kXBnIIxPAZCC2bdtmRuw495gFXuXKlcs9N3r9RJCayuLHBGzdmoGaNQv395shzdlnA6+8Yl3PyQFYP3nvvUBhE5JnncXev4CbGs1THDrEgSm2dXPd3qKFj/vYOWPgxuXFGOh8+umn5sLvFyxYEFZBnUhEYlDwYS/XoI4y063tvF0CgoEcV/vhhd+XLVvWTDU5JajT6yfikJVlFS3YL0ePIl8MrJYvB5za5YJJQF4voF2uA4fJ5s61RvcuuOD0++/aBfznP1b7kzPPBFq3dr14yuNxeY7Uvffee54/s4gEZ/qVI3X5rl3AbSWAWcOBJlcoLetnTLky9coUbN7Uq4NeP5FT5J19NWoU8Nhjp+7HxsEsWMjTLtdcd9Mu18jIAGrUsAJGrv366qvAJZfgtO6/n6PvzHgCF14IzJzJTh/Ak08Czz8P/wd269evx9SpU7FhwwZTxMA3mG+//Ra1a9fGmQw9RST0cE5d3pE6FzYgM83ar975fjywyMb5wky9cuZMyZIlTYN1l1E6O71+IqdYvdoKvOxiY+FVHHFbuZIrXVkjdpyjV7++FawV5IcfWJsAtG1rjQxyGTEGhJz1xRpQpnP9loqdP38+mjdvbubVcf1YLttFv//+O0YxFBaR0MRCCW/uJ8XCFk1Mu7KVCYO6fFOvnrwuev0kgsTHW8GS/eIusEtMtEbc8rTLNdcLapfLoKxhQ6BVK6si9tprrcDsdA4ezC3I4PJiTM1S8+bAihWF/vFOPR5P7sSWJmxQPGfOHNNfzu7iiy/G4sWLPT8aEQksVr96cz8pVuqVGREWShCzInXr1jUjdsV+XfT6iZyC4UybNtaomx2LJ3jdaRGr0+J93M3jc9a4sTUfj9hW5bXXgLQ0qyK3WjU/p2LZ5Pf9998/ZTvfeLimq4iEKLY0YfUrCyXynWdXwrqd+4lPcGSOqVf2p7OnXln1ytG609LrJ1IsTKNyPQamR9m7ju1OOLJ2sl0uevWy0rr2ETl+5b4NGljB3DffAO+8A0yadPrnGjQISE/PnffXrRvA0gUGmNOm+Tmwq1ChgnnTqVevnsv23377zTQIFpEQxT51bGnCqkqzVkE+axd0G6fCCR+mXjmXju2ViClXzqcrcJTOmV4/kWLp2dNKiY4caTUoZnp11qzcggq2JXFql2uCvrvvZmsVIC7O6mf37rvW45zOLbfkfs+Rws2brSKN2rWttLBf+9g98MADZn7dRx99hDPOOAMrVqwwa7Zy5QdewmmenfrYSUTKtw9aDSuoUx87nzh8+LCpej12spkVG69zjWyXqtfC0usn4lEfu3DgUWDHN5577rnHNCrmJ0x+muTXm266yWxjw8xwocBOIpZWnvALvgXv3bvXrJDD70uVKmVSr1werFj0+kmESw3ywI7R18cfW8uM7dxpzc3Lu1yZ3wI7O3665Hw7VsW2bt0ajbhIWphRYCci3pCdY8PSjXuxM+sIkuJLo129SoAtx1S88n2G4uPjzXSWQqdeRSRkA7tBg6yCiYsuslK9eQfnp0717HE9evf46aef0KRJE/Opkhe748ePY9GiRbigMC2XRUQixKw/0zH6y9VIz7DWdaWq5WPRv01FtK8Ra9KtTL1yrW2PUq8iEnLeeccalbv8cu8+rkftTi688EK0bNnylNYmTCdcxNBTREQcQd2Ad1e4BHW0I/Monpi3HUvSjppCNI/n04lISEpIsBoZe5tHgR3dcMMN6Ny5s5lT56wYmV0RkbBLv3KkrqB3xTdW7Eds6Tg/HpWIBAMuazZ6NAunvPu4HqVi+alyxIgROP/8800V7B9//IHnTy5spk+cIiIWzqnLO1KXF2/nfh0aVNZpE4kg118P/O9/1uoTdesCpUq53u7p6hMeBXb2Ubmrr77apBCuuuoqrF69GhMmTPDsKEREwhALJby5n4iEj969geXLrX52+RVPeKrYpVeshl26dCl69OhhUrMiImKpXCbPR3A3WCUrIpHl66+B2bOB884Lgjl2vXv3RhxbLJ+UnJyM+fPnm8CuNlsmi4hEuIMHD6LiiT1ILOO+ryc/oFdLONn6REQiSq1aQHkfdGHxKLCbOnWq6bfkLDY2FtOnT8fGjRu9dWwiIiGHU1V27dpl3gttOdm4+5wkE8DlzbLYr4/qnoLoKFXDikSa558HHnoI2LTJu49b6FQsCySaNWuGqKgo831BWrRo4Y1jExEJKSdOnEBqaqpp2k4JCQno3bQ6qlevdkofu+SE0iao69asWgCPWEQChXPrDh0CGjQAuNBM3uKJvXt9HNi1atXKLHmTlJRkvmf1q3NrE/t1fuXyYiLiRVoeKugxmGNQx+CO74PVq1dHhQoVzPcM3i5pUgVrlszG4X1piKtYA03ad0K0VpgQiVjjx/vmcQsd2DGtUKVKFcf3IuIn+S7oXh3o9jSQcqVehiBJve7kYo8np6VwRZ7SpZ0KIlZ/gehZw3Cm82u4RK+hSKQ6fhyYPx949FGgXj3vPnax1oqNBForVgIe1H3Yi+FDnhtOzsm6/m0FdwHEZRQ5SsdCCeIIHUfqOGXFQa+hSECkBvlasVx5YuVK7wd2hR6x++KLLwr9oFdeqVEEEa+kXzlSl++6BdxWApg1HGhyBRDlvvJSfJd63bp1q5l6wkCuWrVqqFixoutOeg1FxI0ePYDPPgMGD0ZgAjv2qSsMzbET8ZLNC13Tr6ewAZlp1n71ztdp9xMmOZh2ZfrVnnplmyd+PYVeQxFxo1Ej4PHHgV9+Adq0AcqWdb39vvvg28AuJyfHs2cQEc8c2OHd/cQrqVeO0h1iKRtgRug4UueSevXktdFrKBJx3nyT0zes1Sd4ccZVKHwe2ImIn5Wr6t39pFiysrLMfDp76tVe9eqV10avoUjE2eijOlSPAztOFuZqE1u2bMGxY8dcbrvP0zBTRHLV6WhVv2amu5lnV8K6nfuJT1OvO3bswO7du811Vruy6jXf1Gteeg1FpBDsZazeWC/Wo8Dut99+w+WXX27SEQzwKlWqZN70ypQpY/rcKbAT8QIWRLCliamKLZEnuDv5v7/bOBVO+BA/tHKUzp565Xsdl1B0m3rNS6+hiBTg7beBZ58F/v3Xun7GGcCDDwK33gr/Lik2ePBgdO/eHfv27TNrxi5evBibN29GmzZt8Nxzz3l+NCLiin3q2NKkfJ7VCThSp1YnPm91tH79ehPUMZDjKN0prUwKQ6+hiOTjhReAAQOAyy8HPvzQunTrBtx1F/Dii/BvHzvOK1myZAkaN25svl+0aBGaNm1qtvXu3Rtr1qxBuFAfOwkKWnnCf6c6J8ekXvfs2WOu88Mrg7qYmJhiPnC2VSXLQgnOqWOaVm1qRCK2j129esDo0UAvJmWcTJ8OPPaY53PwPErFlipVyvGplalXzrNjYMd1EVkxJiJexgBALU28KjvHhqUb92Jn1hEkxZdGu3qVkH3Cqno9fPiw2ady5cqoWrVq0Ufp8qPXUEScpKcDHfOZIs1tvM1THr1btW7dGsuWLTPfd+rUCSNHjsR7772H+++/H82aNYMvTZw4EXXr1jUTmNu3b4+lS5cWuP9HH32EJk2amP2bN2+Ob775xqfHJyLBb9af6Tjv6R9w45TFGPTBSvO149jvMX3u7yaoYyDH3nQFtjIRESmGhg2t9GteM2ZYPe485dE71lNPPWXe8GjMmDGml9OAAQNMw87XX38dvjJjxgwMGTIEo0aNwooVK9CyZUt07drVsUZjXgsXLsSNN96I22+/3RR8sMkyL3/++afPjlFEgj+oG/DuCqRnHHHZviPrGMbM34lft59Aw4YNUb588KVuRCR8jB4NjBxpzat74gnrwu+5nY2LI2KtWI7QnX322XjllVccc2E49+Xee+/F8OHDT9m/Z8+epmr3q6++cmw755xz0KpVK0yePLlQz6k5diLhlX7lSF3eoM5ZtYTSWDDsYkRHeaHvgIgETLDPsSM2JmahxN9/W9ebNgWGDmVm1PPHLBlKbQeWL1+OESNGOLYxRdKlSxdTvJEfbucInzOO8H3GxdncOHr0qLk4B3YiEh44p66goI54O/fr0KCy345LRCJTmzbAu+969zE9CuxYLcZ5dfPmzTNp0LzLje3duxfexj557PjOiczOeN1dFe727dvz3Z/b3Rk7dixGcxxURMIOCyW8uZ+ISHEwfFq3DuCMsrwrt15wgR8Du1tvvRXr1q0zc9cYKJXwRqvkIMERQedRPo7YMd0rIqGvYunCTStmlayIiC8tXgzcdBOweXPuyhN2DKuys/0Y2P38889YsGCBKV7wl8TERERHR5v+Us54nZ3g88PtRdmfuExQoZYKEpGQsn//flQ8sReJZaKx+1D+75j8iJqcYLU+ERHxJTYibtsW+PprgPWo3hoj86gqlu1D7H2e/IXNQbmyxdy5cx3bmALm9Q4dOuR7H2533p/mzJnjdn8RCT98n0hLSzNLg5WADfeeW80EcHnfQ+3XR3VPUeGEiPgclxF76imrYKJCBSAhwfXi18Du1VdfxcMPP4z58+eb+XZMVzpffIUp0ilTpmD69On4+++/TYsVVr327dvX3N6rVy+X4opBgwZh1qxZeP755808vMceewy//vorBg4c6LNjFJHgceTIEbMsGJc/pCpVqqDXxS0w6ZazzMicM17n9m7N8izfJiLiA+3bW/PrvM2jVCyXEWMAd/HFF7tsZ+cUzrdjkYMvsH0Je+WxcIMFEGxbwsDNXiDBFTCcm4l27NgR77//Ph555BH83//9Hxo1amQqYn3dRFkigJaHCnoM5rZt22bel0qWLImaNWuiXLly5jYGb5c0qYI1S2bj8L40xFWsgSbtOyG6ZMg0ChCREHfvvVZrE9ZzNm/OVb1cb2/Rwo997Nq1a2feKDkill/xBFejCBfqYyenWP0FMGsYkLktd1v56kC3p60F3yWg+MEyPT3dzKmjsmXLmgIovmc56DUUCXupQd7HLr9FbRhOMSorTvGER4FdmTJlzEoOjRs3RrhTYCcuGBB8yBWb8/63Ofnh5vq3FdwFOPXKtV7tvSi5ljXTry4fPvUaikSE1CAP7FgNW5A6dTx7XI/yDm3btjVvnpEQ2Im4pF85UndKUIeT20oAs4YDTa6wFnwXv+HnU6ZeOVJnT71ylI6jdS70GopIkPA0cPNJYMclvJiGffDBB9G8eXOUypMYbuFpYlgkmG1e6Jp+PYUNyEyz9qt3vh8PLLIx9cq5dBkZGeY659FxPp1L6tVOr6GIBFll7Lx5+Tco5jqyfgvsWMRAt912m2MbUx2+Lp4QCagDO7y7nxQb2y4xe8AlB4lzftnz0m3TdL2GIhIkpkwBBgxgn1723XXtY8fv/RrYbdy40bNnEwll5ap6dz/xGD9EculCVsfze2YNmHrl/F+vvDZ6DUXEx558EhgzBhjGGT5eVOTA7vjx46bNyVdffYWm7KonEinqdLSqXzPT3cyzK2Hdzv3EZ5gRYMNhe8/M+Ph41KhRI//Ua156DUUkSLC95nXXef9xi9ygmJ+MWXkmEnFYEMGWJoabdQu6jVPhhI9Tr1yn2h7UcXnA2rVrFy6oI72GIhIkGNR99533H9ejVOw999yDp59+Gm+88Ubh31BFwgH71LGlSb597Map1YmPMN3KVW641nORUq/50WsoIkGgYUPg0UeBxYvzb1B8331+7GP33//+16zByuozVsXmbSnw6aefIlyoj53kSytP+DX1ynVes7KyzPXy5cub1Gt0dDFbyug1FAlrqUHex65ePfe3sXhiwwY/Lyl2zTXXePaMIuGAKT21NPGq7Bwblm7ci51ZR5AUXxrt6lXC0SNW1Svn9rLSlanXSpUqua96LQq9hiISQL6qQ/UosJs6dar3j0REItasP9Mx+svVSM/Inb+bVC4Gd5yVgI61yyAmJsakXuPi4gJ6nCIiwa5YE+R27dqFtWvXmu+5CgWX7hERKWpQN+DdFafUGe88cAxP/bQLT3StjZsuaFD81KuISBBxagWcr7fe8lNVLB08eNA0J65WrRouuOACc6levTpuv/12HDp0yLMjEZGITL9ypM7dRF8mXF9dvBMo4dFblYhIULc7cb5w9YkffmCdArB/v59H7IYMGYL58+fjyy+/xLnnnmu2LViwAPfddx+GDh2KSZMmeX5EIhIxOKfOOf2aFwM+3s79OjSo7NdjExHxpZkzT93GZcW4GkWDBp4/rkcfgz/55BO8+eabuOyyy0yFGi+XX345pkyZgo8//tjzoxGRiMJCCW/uJyISyqKiOHgGvPhiMR7Dkzsx3co1GfNKSkpSKlZECq18qcJ1W2KVrIhIJFi/Hjhxws+p2A4dOmDUqFF4++23Ubp0aUdH+NGjR5vbREQKwvaZLL6qlL0PiWWisftQtts5dskJVusTEZFwMmSI63V2FU5PB77+Gujd28+B3YQJE9C1a1fUrFkTLVu2NNt+//13E+TNnj3b86MRkbDHnnRsOMwirOioEhjcqSYe+Xazuc15/M7eqW5U9xSzn4hIOPntt1PTsGwu8vzzp6+Y9Xpg16xZM/z777947733sGbNGrPtxhtvxM0336w+UyLi1oEDB0xQd+LECdNkmNX0zZpVROXKlU/pY8eROgZ13ZpV0xkVkbAzb55vHtejJcUiiZYUEyk+vs3s3LnTpF8pNjYWtWvXNl/tsk+cwJols3F4XxriKtZAk/ZdEa21qEOHlmiTIJMa5EuKBV2DYo7YzZs3z7xZ57A+18nIkSO9cWwiEiapVy4LZu9xWbFiRdMDM4p5B7vVXyB61jCcmbktd9uS6kC3p4GUKwNw1FIkq78AZg0DnF+/8nr9RALBoxE7tjUZMGAAEhMTzdqNzus28vsVK1YgXGjETsRzWVlZJvWanZ1tAjmmXrnW9ClBwYe98sywo5PvK9e/reAumOn1kyCVGqEjdh61O3nyyScxZswYbN++HStXrsRvv/3muIRTUCcinuHnRb4/bN682QR1LKxq0KDBqUEd03cc6cl37YmT22YNt/aT4KPXT8LQxIlA3boAm360bw8sXep+3ylTgPPPZybCunTpUvD+QRvY7du3D9ddd533j0ZEQt6xY8ewceNG7N6921yvVKkS6tev7zKfzmHzQtf03SlsQGaatZ8EH71+EmZmzLDakIwaBXCcio0/una1lvvKz48/snjUKoRYtAioVQu49FIgLQ2hFdgxqPvuu++8fzQiEvJTF9avX2/m0zH1WqtWLZN+dZlP5+zAjsI9cGH3E//S6ydh5oUXgH79gL59gZQUYPJkoEwZ4K238t//vfeAu+8GWrUCmjQB3njDWhZs7tziHcfbb1uNiv1WPNGwYUM8+uijWLx4MZo3b45SpUq53M41Y0UkcrCAaseOHdizZ4+5HhcXZ4K6mJiYgu9Y7tQVbIq1n/iXXj8JI8eOAcuXAyNG5G7jZ1KmVzkaVxisETt+nJmK4h1Lnz4AQ6v+/YGXX/ZDYPf666+jXLlymD9/vrk4Y/GEAjuRyEq9suqVq88Qe9JxyUG3o3TO6nS0qicz093Msyth3c79JPjo9ZMQkJXFbELudc4KyW9mCGePZGcDeVdM5fWTLXtPa9gwoHp1KxgsDo76bdwIfPtt0e/rUWDH+TMiIky9suqVI3YM5LgaTfnyRag+i4q2WpqYqtgS+a890W2ctZ8EH71+EgJSUlyvc/7cY495/3nGjQM++MCad3dytdViqVfPSvP6rY+diEQuj1Ov+WGfOrY0ybcP2ji1Ogl2ev0kyK1eDdSokXs9v9E6SkwEoqOBHXmm9PJ6cnLBz/Hcc1Zg9/33QIsW7vdzHjk8naJ8RvYosBs3bhwGDRpUqCXDlixZYirirrjiCs+OSkSC1tGjR03q9cgRa/kv9rNk6tW5n6VHwUGTK6wqS07I59wtpvk0Uhca9PpJEIuPL1yQxM+lbdpYhQ89eljb7IUQAwe6v98zzwBjxgCzZwNt2xb8HOz4dLq3SnYX5j5MC/s0sFu9erVZAogVsd27d0fbtm1RhavVAmbdR96+YMECvPvuu9i2bRveZkmHiISs7Bwblm7ci51ZR5AUXxrt6lXCgaxMpKWlmRG76Ohok3qN57umNzCIq3e+dx5L/E+vn4QBtjrp3dsK0Nq1A8aPBw4etKpkqVcva/Rv7Fjr+tNPc7Ut4P33rd5327db28uVsy7+Wh/Wo8COgdrvv/+OV155BTfddJOZW8M3dvamsi8V1Lp1a9xxxx3o06ePaUjqTXv37sW9996LL7/80szlueaaazBhwgRTxOHOhRdeeEpxx5133onJrF8WEbdm/ZmO0V+uRnqGNSpHSeVK4Y6zKqBj7TIoU6aMSb3mrYgXEQllPXsCXNKawRqDNLYxmTUrt6BiyxarUtZu0iSrmvbaaws3j69TpyBdUoyf1v/44w/TVZ6VcEzFtGrVynz1lcsuuwzp6el47bXXzNqTffv2xdlnn433GSYXENidccYZePzxxx3b+AepKJO7taSYRGJQN+DdFfnWqNLY/9THDec2KV7qVUTEx1JDZEkxjo0xYGSA6KyguXpeL57giBkDOV784e+//8asWbOwbNkykwKml19+GZdffjmee+450wDVHQZyXM9WRAqXfuVInbugjqHcSz9vw/UdmyBacZ2IiMc4MsgUr7uWJp7OsfNo5Ql/W7RokVlj0h7UUZcuXUyAyUKNgrz33ntmJLFZs2YYMWKEI21c0MRwjtI5X0QiBefUOadf82LAx9u5n4iIeO7++4H9+1lwys4CVsp3+nSgUSPgiy88f9yQaHfCxcSTkpJctpUsWdKsQcnb3OFcwDp16pgRPaaOhw0bhrVr1+LTTz91e5+xY8di9OjRXj1+kVDBQglv7iciIvn74Qfg88+tQg3O26tTB7jkEquCl8UZnjYWCeiI3fDhw808nYIuawrb7jkf/fv3R9euXc2yZzfffLMpAJk5c6ZZy9IdjuplZGQ4LmzrIBIpypQ4Xqj9WCUrIiKeY7WtfcyqYkUrNUvNmwMrVvhhxI4jXkxnFmqZoEIaOnSoqaAtSP369c0cuZ07d7psZ4sVVsoWZf5c+/btzdd169ahQYMG+e7DKl9eRCIJC6LYpiipRBYSy0Rj96H8J3dwWl1ygtX6REREPNe4MbB2rdUmpWVL4LXXrO/ZuKNaNT8EdmxlwqpUpkQZbLGQgWtCFgf74Nl74RWkQ4cO2L9/P5YvX4427B5ohjB/MH+M7MFaYaxcudJ8rVacMyYSZthomCPTnF8aHVUCD3aui+FfWqPa+SzwhVHdU8x+IiLiuUGDgPT03PYo3bqxLsBqlDxtmh8COxYvcI1YBnabNm0yQZW/NG3aFN26dUO/fv1MDzq2Oxk4cCBuuOEGR0Usm6Z27tzZpFvbtWtn0q1shcLKWQagHHEcPHgwLrjgArTwtIZYJIyw09G+ffvMBzZ+z3mr7E3XrGxZJCQknNLHjiN1DOq6NdMHIxGR4rrlltzvOWa1eTPA2We1a1vLm/k8sGND4E6dOpnRLs59Y4UqGxTnZ8OGDfA2VrcymGPwZm9Q/NJLLzluZ7DHwgh71SvXrPz+++8xfvx4HDx40PzB4n0eeeQRrx+bSKjJzs42qVfOIyU2+uYqEgzuiMHbJSnJp6w8oZE6ERHvYv+6jRsBzhA76yw/NyhmLznOT7vvvvtM0193SwlxTdlwoQbFEm7YVJyp12Mnu2FynVe2BFLDYREJJ6lB3qCY41D33mu1OKF//mFdgbWNy5YNH+6HdidMhxLnujF489oakSLic/wMx4IjtghyTr2WLVtWZ19ExM9GjAB+/x348Udrfp1dly7WcmR+Cezspk6d6tmziUjAUq+ch2pvuM0PZTVq1HCkXkVExL8++wyYMQM45xzAeYXGM88ECujKdlp6VxeJgNTrli1bzDxUYosgFhQp9SoiEjjsW5dn7QVHf7viLMUdEkuKiUjRMd26Z88eU8zEoK5UqVKmVZHm04mIBB5XnPj669zr9mDujTfY5s3zx9WInUgEpF7Lly9vUq/uKtlFRMS/nnoKuOwyYPVqLroATJhgfb9wITB/vuePqxE7kTDDlj+sXmdQx3QrWxSxSEJBnYhI8DjvPKt4gkEdlxH77jsrNbtokdXXzlMasRMJs9Qrq16JqdfatWsjLi4u0IcmIiJOOOX5zjuBRx8FpkyBV2nETiQMcO1kFkjYgzqmXhs2bKigTkQkCJUqBXzyiW8eW4GdSIjjyipcQi8rK8ukXrnMnlKvIiLBrUcPq+WJtykVKxICsnNspyzvFVUC2L17N3bs2OFYRo8BnVKvIiLBr1Ej4PHHgV9+sebU5e0Vf999flhSLBJpSTEJtFl/pmP0l6uRnnHEsS25fCzuPicJZyVZg+4JCQlmpE4FEiIiobGkWL167m9j65MNGzx7XI3YiQR5UDfg3RXI++lre+ZRjPxuK/6vUxVc274hKlasqIbDIiIhZONG3zyu5tiJBHH6lSN1BQ2pv/VbJhIqKKgTERGLAjuRIMU5dc7p1/xw5I77iYhI8Bs3jss8Fm7fJUtcV6YoLAV2IkGKhRLe3E9ERAKLK0vUrg3cfTfw7bfWerF2bFT8xx/Aq68CHTsCPXsC8fFFfw7NsRMJUknxsYXcr7TPj0VERIrv7bet1SZeeQW46SYWaAJc6TE2lqsGWfu0bg3ccQfQpw9Q2oO3dwV2IkHo+PHjqIJMJJaJxu5D2fnuw/WikxOs1iciIhIaWra0Vpt47TVrhG7zZis9m5gItGplfS0OBXYiQYaNhlNTU5GdnY07z66Mp+bvNNtteYI6GtU9BdFsaCciIiElKsoK5Hjx6uN69+FExFNsKcklwTZv3myCutKlS6PXxS0w6ZazzMicM17n9m7NqumEi4iIg0bsRILAsWPHzCjdoZOTLCpVqoTk5GRERUWZ4O2SlORTVp7QSJ2IiOSlwE4kiFKvDORq1KhhVpJwxiCuQ4PKATtGEREJDUrFigRR6rVBgwanBHUiIhIe/vgDyMnx7XMosBMJUOp1w4YN2L17t7leuXJl1K9fH7GseRcRkbDUujVw8m0f9esDe/Z4/zmUihXxs8zMTJN6zcnJManXmjVronz54FugWkREvKtCBWuN2KQkYNMm34zeKbAT8RMGcjt27MCekx/R4uLiUKtWLcTExOg1EBGJANdcA3TqBFSrBpQoAbRtazUozs+GDZ49hwI7ET+lXrdu3YrDJxcJZOq1atWqZsROREQiw+uvA1dfDaxbB9x3H9Cvn2fLhhVEgZ2Ij2VkZCAtLc2M2EVHR5uqV6VeRUQiU7du1tfly4FBgxTYiYQMBnKset27d6+5XqZMGTOfTqlXERGZOtU350AjdiI+cPToUZN6PXLkiLmemJhoUq8lOKlCRETERxTYiXjZ/v37sW3bNkfqlaN08d6eRCEiIpIPBXYiHsjOsZ2yxFcJ2JCeno59+/Y5Uq+sei1VqpTOsYiI+EXIBHZjxozB119/jZUrV5o5ShwVKUxn/1GjRmHKlClm/3PPPReTJk1Co0aN/HLMEp5m/ZmO0V+uRnqGlWal5PKx6H92JbSrZrUuqVKlCpKSkpR6FRERv4oKpXYR1113HQYMGFDo+zzzzDN46aWXMHnyZCxZsgRly5ZF165dHfOeRDwJ6ga8u8IlqKPtmUfx+Nx0LE47grp162o+nYiIBETIBHajR4/G4MGD0bx580Ltz9G68ePH45FHHsFVV12FFi1a4O233zZznz777DOfH6+EZ/qVI3W2AvZ5c8V+xJUp68ejEhERCcHArqg2btxoWk106dLFsY2Lq7dv3x6LFi0qsJqRSz45X0SIc+ryjtTllZ5x1OwnIiISCGEb2DGoI7aYcMbr9tvyM3bsWBMA2i+c/C5CLJTw5n4iIiJhFdgNHz7cTC4v6LJmzRq/HtOIESPMSgH2C3uRiVBi2cJVt7JKVkREJOKqYocOHYo+ffoUuE/9+vU9euzk5GTzlYuuV+NquyfxeqtWrdzeLzY21lxEnHGN10rZ+5BYJhq7D2Xne3LYejg5wWp9IiIiEnGBHVtC8OIL9erVM8Hd3LlzHYEc58uxOrYolbUS2ViEw7507E/H7+9qn4gx83ZYtzntZ19PYlT3FERHaXUJEREJjJCZY7dlyxbTw45fs7Ozzfe8HDhwwLFPkyZNMHPmTPM907j3338/nnzySXzxxRdYtWoVevXqherVq6NHjx4B/EkkVPD3jKl4VlIzqOPqEX06t8KkW84yI3POeJ3buzXLHR0WERHxt5BpUDxy5EhMnz7dcb1169bm67x583DhhRea79euXWvmxdk99NBDOHjwIPr3728aFJ933nmYNWsWSpfWHCg5feqVQR37JxJHfytXrmw+MDB4uyQl+ZSVJzRSJyIigVbCxqEIcYvpW1bHMmAsX768zlSY43+HvXv3msppfs/lwFgZzeXBREQkdKSmZqJWrQRs3ZqBmjUj5+93yIzYifgj9ZqWluboXcjUa82aNREdHa2TLyIiIUGBnQiAQ4cOmdTr8ePHTbqVqddKlSpprVcREQkpCuwkojHdumfPHkfTaqZea9eujbi4uEAfmoiISJEpsJOIdeLECZN6zcrKMtc5h7JGjRpKvYqISMhSYCcRSalXEREJRyHTx07EW6nXXbt2YcOGDWY+XUxMjFndxN7KREREItvEiUDdugA7o7VvDyxd6n7fv/4CrrnG2p9/QsaPR8ApsJOISr1u3rzZLCtHbGPToEEDzacTERFjxgxgyBBg1ChgxQqgZUuga1dg507k69AhLn0KjBvHfqcICgrsJCKwUfW6devMSiUcmeMKJGplIiIizl54AejXD+jbF0hJASZPBtjG9K23kK+zzwaefRa44QauNY+goMBOwj71unPnTmzcuNGM2MXGxppROrUyERERZ1xoaPlyoEuX3G1RUdb1RYsQMlQ8IWGLgRx703G0jipUqGBG6qL4P1VERCJCVhZXkcq9zpG1/EbXdu9mo3qgalXX7by+Zg1Chv7CSVhiypWpVwZ1TL2yjQlTrwrqREQiS0oK51TnXsaORVjTiJ2EZeqVla/E1CvXei3N8iYREYk4q1cDNWrkXnc3Fy4xEeAKkifr6xx4PVgKIwpDI3YSNti+ZNOmTY6grmLFimY+nYI6EZHIFR/PBvS5F3eBXUwM0KYNMHdu7racHOt6hw4IGRqxk7DA1SNSU1ORnZ1t0q2cS8c5dSIiIoXFVie9ewNt2wLt2ll96ThNm1Wy1KuXNfpnT+ey4IIjgvbv09KAlSuBcuWAhg0REArsJKxSrxydY+qVKVgREZGi6NkT4J+TkSMBLiHeqhUwa1ZuQcWWLValrN22bUDr1rnXn3vOunTqBPz4IwKihI1/GcWtzMxM08g2IyPDrCUqwZV6ZdUrlwcjtjBJTk5WgYSIiCA1NRO1aiVg69YM1KwZOX+/NWInYZF6ZdUrA3AREZFIpsBOQgoHmLkk2G42HFLqVURExIUCOwkZx44dM6nXw4cPm+uVK1dG1apVlXoVERE5SYGdhMxcx7S0NEfqlc2GNedRRETElQI7CWo5OTkm9bpnzx5zPS4uzlS9xrDhkIiIiLhQYCdBS6lXERGRolFgJ0GJ7WWYeuWIXXR0tKl6VepVRESkYArsJKgwkNu+fTv27t1rrpcpU8bMp1PqVURE5PQU2EnQOHr0qKl6PXLkiLmemJhoql5LlCgR6EMTEREJCQrsJCjs378f27Ztc6ReOUoXz5WbRUREpNAU2ElAMZBLT0/Hvn37HKlXVr2WKlVKr4yIiEgRKbCTgKZet2zZYr5SlSpVkJSUpNSriIiIhxTYSUBwhI4jdRyxK1mypEm9litXTq+GiIhIMSiwE79iIMe5dJxTR2XLljVBnVKvIiIixafATvyG1a6serWnXpl2ZfpVVa8iIiLeEYUQMWbMGHTs2NFMrq9QoUKh7tOnTx8TNDhfunXr5vNjFVc2m82kXtevX2+COqZe69atq/l0IiIikTpix+WlrrvuOnTo0AFvvvlmoe/HQG7q1KmO67GxsT46QslPdna2Sb1yJQniPDqmXhnciYiIiHeFzF/X0aNHm6/Tpk0r0v0YyCUnJ/voqOR0qVdWvTIoJzYbZtNhpV5FREQiPLDz1I8//mhSfhUrVsTFF1+MJ598EpUrV3a7P1OF9jlglJmZ6acjDb/UK6te+T1H59ibjoUSIiIi4jshM8fOE0zDvv3225g7dy6efvppzJ8/H5dddplJD7ozduxYJCQkOC4MSKTweG5TU1NN+pVBHVePaNiwoYI6ERGRcA/shg8ffkpxQ97LmjVrPH78G264AVdeeSWaN2+OHj164KuvvsKyZcvMKJ47I0aMMPPB7BdWcUrhHD582BRI2OfTMQVeu3ZtzacTERGJhFTs0KFDTeVqQerXr++15+NjcY7XunXr0LlzZ7dz8lRgUTQcmdu7dy+2b99uvmdPOo50soJZREREIiSwYw8zXvyFKcI9e/agWrVqfnvOSEi9pqWlOeYiMvXKqtfo6OhAH5qIiEjECZk5dqyuXLlypfnKYILf83LgwAHHPk2aNMHMmTPN99z+4IMPYvHixdi0aZOZZ3fVVVeZ+V5du3YN4E8SPg4dOmRGPxnUMW3OgJmpVwV1IiIigREyVbEjR47E9OnTHddbt25tvs6bNw8XXnih+X7t2rWO+V0MLv744w9zHy5fVb16dVx66aV44oknlGotJqZbOfK5Y8cOR+qVAV1cXFxxH1pERESKoYSNf5nFLY5GsTqWAWP58uUj/kydOHHCpF6zsrLMueA5qVGjhkbpREQkqKSmZqJWrQRs3ZqBmjUj5+93yIzYSXCkXlklfPz4cZN6ZdVrpUqV1HBYREQkSCiwk9PioO7u3btN6pViYmJM1atSryIiIsFFgZ2cNvXKamJ7kQrT0pyvqAIJERGR4KPATtw6ePCgSb0yuLNXvXJpNq31KiIiEpwU2Em+qdddu3Zh586d5jobNjP1Wrp0aZ0tERGRIKbATlxwdI6jdBytowoVKpiROqVeRUREgp8CO3HgPDrOp7OnXjmXjqlXERERCQ0K7ESpVxERkTChwC7CsScdR+nsqVeO0DH1GhUVMqvNiYiIyEkK7CI89cr5dFx7l4EcU6+cUyciIiKhSYFdhFa9suKVla/EaldWvbL6VUREREKXArsITL1ylI7LgxGXBOPSYEq9ioiIhD4FdhEkKyvLzKezp15r1KhhVpIQERGR8KDALkJSr1znleu9klKvIiIi4UmBXZg7duyYSb0ePnzYXFfqVUREJHwpsAtjmZmZSEtLU+pVREQkQiiwC0M5OTkm9bpnzx5zPS4uzlS9xsTEBPrQRERExIcU2IV56rVy5cqoWrWqql5FREQigAK7MJKRkWFSrxyxi46ONlWv5cuXD/RhiYiIiJ8osAsDDOS2b9+OvXv3mutlypRBzZo1lXoVERGJMArsQtzRo0dN6vXIkSPmemJiokm9lihRItCHJiIiIn6mwC6MUq8cpYuPjw/0YYmIiEiAKLALQQzk0tPTsW/fPkfqlVWvpUqVCvShiYiISAApsAvx1GuVKlWQlJSk1KuIiIgosAsl+/fvx7Zt2xypV47SlStXLtCHJSIiIkFCI3YhgIEcAzoGdlS2bFkzn06pVxEREXGmwC7IMeXK1CtTsMS0K9OvqnoVERGRvBTYBSmbzeZIvfL7kiVLmlE6pV5FRETEHQV2QSg7O9tUvdpTrwzmGNQxuBMRERFxR5FCEKZet2zZYtZ8JTYbZtNhpV5FRETkdBTYBQmmW9mXjiN19tQrq15ZKCEiIiJSGFEIAZs2bcLtt9+OevXqIS4uDg0aNMCoUaMco1oFjX7dc889qFy5sklnXnPNNdixYweCMfWamprqmE/H1SMaNmyooE5ERMTPJk4E6tYFSpcG2rcHli4teP+PPgKaNLH2b94c+OYbBFRIBHZr1qwxLT9ee+01/PXXX3jxxRcxefJk/N///V+B9xs8eDC+/PJLfPTRR5g/f74JnK6++moEk8OHD2P9+vVmeTBKTk5G7dq1NZ9ORETEz2bMAIYMAUaNAlasAFq2BLp2BXbuzH//hQuBG28Ebr8d+O03oEcP6/LnnwiYEjYOEYWgZ599FpMmTcKGDRvyvZ2BEtuCvP/++7j22msdAWLTpk2xaNEinHPOOYV6nszMTCQkJJjHK1++vNeOn6d979692L59u/mePemYeuXyYCIiIlI8qamZqFUrAVu3ZqBmzcL9/eYI3dlnA6+8Yl3PyQFq1QLuvRcYPvzU/Xv2BA4eBL76Kncbw4tWrYDJkwPzCobEiF1+GGhVqlTJ7e3Lly/H8ePH0aVLF8e2Jk2amNEwBnbusF8cgznni7cxkGPq1T6fjqlXppcV1ImIiHhXVhYHaXIvJ9vCnoKzu5YvB5zCBkRFWdfdhQ3c7rw/cYSvgDDD50IysFu3bh1efvll3HnnnW734UhYTEwMKlSo4LKdVaa8zZ2xY8eaETr7haNo3sYKVwZx/KrUq4iIiO+kpAAJCbmXsWPz32/3bs55Z5zgup3X3YUN3F6U/cM+sBs+fLgJbgq6MH3qLC0tDd26dcN1112Hfv36ef2YRowYYUYD7Reu+uALHG1kgYRamYiIiPjO6tXM8uVeRowI77Md0HYnQ4cORZ8+fQrcp379+o7vWfxw0UUXoWPHjnj99dcLvB9Hwlg1yya/zqN2rIrlbe7Exsaai68xaPXH84iIiESy+HigMFPkExOB6GjGCa7bed1d2MDtRdk/7AM7FjfwUhgcqWNQ16ZNG0ydOhVRTHwXgPuxIGHu3LmmzQmtXbvWNP/t0KGDV45fREREwkNMDGMHYO5cq7LVXjzB6wMH5n8fhhO8/f77c7fNmWNtD5SQmGPHoO7CCy80hQ/PPfccdu3aZebJOc+V4z4sjlh6suEM58ex992QIUMwb948U0zRt29fE9QVtiJWREREIseQIcCUKcD06cDffwMDBlhVr337Wrf36uWayh00CJg1C3j+eXbeAB57DPj1V/eBoD+ExMoTc+bMMQUTvHDNVGf2bi2sgOWI3KFDhxy3sd8dR/Y4Ysdq165du+LVV1/1+/GLiIhI8OvZE9i1Cxg50iqAYNsSBm72AoktW6xKWbuOHYH33wceeQRga91GjYDPPgOaNQvYjxC6fez8xVd97ERERCS4+tiFg5BIxYqIiIjI6SmwExEREQkTCuxEREREwoQCOxEREZEwocBOREREJEwosBMREREJEwrsRERERMKEAjsRERGRMKHATkRERCRMhMSSYoFkX5iDK1CIiIhIaMjKsv5uR9oCWwrsTiMrK8t8rVWrlj9eDxEREfGiAwf4dzwhYs6p1oo9jZycHGzbtg3x8fEoUaKEf14VCQkcxWXAv3XrVr+sI+zv5wvEc+r5dD5FvCUnx4b09CyccUZ1REdHzswzjdidRlRUFGrWrOmfV0NCEgMefwVagXi+QDynnk/nU8QbKlSInJE6u8gJYUVERETCnAI7ERERkTChwE7EQ7GxsRg1apT5Go7PF4jn1PPpfIpI8ah4QkRERCRMaMROREREJEwosBMREREJEwrsRERERMKEAjsRERGRMKHATsRDEydORN26dVG6dGm0b98eS5cu9cm5/Omnn9C9e3dUr17drH7y2WefwZfGjh2Ls88+26y2kpSUhB49emDt2rU+e75JkyahRYsWjqbEHTp0wLfffgt/GTdunDmv999/v8+e47HHHjPP4Xxp0qQJfCktLQ233HILKleujLi4ODRv3hy//vqrT56L/w/y/ny83HPPPT55PhFxT4GdiAdmzJiBIUOGmFYgK1asQMuWLdG1a1fs3LnT6+fz4MGD5vEZSPrD/PnzzR/kxYsXY86cOTh+/DguvfRScxy+wJVdGFwtX77cBB4XX3wxrrrqKvz111/wtWXLluG1114zgaWvnXnmmUhPT3dcFixY4LPn2rdvH84991yUKlXKBMmrV6/G888/j4oVK/rsPDr/bPy9oeuuu84nzyciBbCJSJG1a9fOds899ziuZ2dn26pXr24bO3asT88m/8vOnDnT5k87d+40zzt//ny/PWfFihVtb7zxhk+fIysry9aoUSPbnDlzbJ06dbINGjTIZ881atQoW8uWLW3+MmzYMNt5551nCxSeywYNGthycnICdgwikUojdiJFdOzYMTO61KVLF5c1hXl90aJFYXc+MzIyzNdKlSr5/Lmys7PxwQcfmNFBpmR9iaOSV1xxhcvr6Ev//vuvSafXr18fN998M7Zs2eKz5/riiy/Qtm1bM2LGdHrr1q0xZcoU+Ov/x7vvvovbbrvNpGNFxL8U2IkU0e7du00AUrVqVZftvL59+/awOp85OTlm7hnTes2aNfPZ86xatQrlypUzK0/cddddmDlzJlJSUnz2fAwemULnfEJ/4BzMadOmYdasWWZO4caNG3H++ecjKyvLJ8+3YcMG8zyNGjXC7NmzMWDAANx3332YPn06fI1zQPfv348+ffr4/LlE5FQl89kmIuIY1frzzz99Oh+MGjdujJUrV5rRwY8//hi9e/c2c/18Edxt3boVgwYNMvPAWPjiD5dddpnje87nY6BXp04dfPjhh7j99tt9EpBzxO6pp54y1zlix9dx8uTJ5tz60ptvvml+Xo5Oioj/acROpIgSExMRHR2NHTt2uGzn9eTk5LA5nwMHDsRXX32FefPmmQIHX4qJiUHDhg3Rpk0bM4rGYpEJEyb45LmYRmeRy1lnnYWSJUuaC4PIl156yXzP0Vhfq1ChAs444wysW7fOJ49frVq1U4Lipk2b+jT9S5s3b8b333+PO+64w6fPIyLuKbAT8SAIYQAyd+5clxESXvf1vDB/YI0GgzqmQ3/44QfUq1fP78fA83n06FGfPHbnzp1N6pcjhPYLR7c4743fM2j3tQMHDmD9+vUmAPMFps7ztqj5559/zCihL02dOtXM6ePcRREJDKViRTzAVidMaTEgaNeuHcaPH28m/Pft29cnQYDzyA7nZzEAYTFD7dq1fZJ+ff/99/H555+bXnb2eYMJCQmmH5q3jRgxwqTu+LNwzhmf+8cffzRzw3yBP1Pe+YJly5Y1/d58NY/wgQceML0IGVht27bNtMlhAHnjjTf65PkGDx6Mjh07mlTs9ddfb3osvv766+biy2CcgR3/X3DkU0QCJNBluSKh6uWXX7bVrl3bFhMTY9qfLF682CfPM2/ePNNuJO+ld+/ePnm+/J6Ll6lTp/rk+W677TZbnTp1zHmsUqWKrXPnzrbvvvvO5k++bnfSs2dPW7Vq1czPWKNGDXN93bp1Nl/68ssvbc2aNbPFxsbamjRpYnv99dd9+nyzZ882vydr16716fOISMFK8J9ABZUiIiIi4j2aYyciIiISJhTYiYiIiIQJBXYiIiIiYUKBnYiIiEiYUGAnIiIiEiYU2ImIiIiECQV2IiIiImFCgZ2IiIhImFBgJyIiIhImFNiJiIiIhAkFdiISUXbt2oXk5GQ89dRTjm0LFy5ETEwM5s6dG9BjExEpLq0VKyIR55tvvkGPHj1MQNe4cWO0atUKV111FV544YVAH5qISLEosBORiHTPPffg+++/R9u2bbFq1SosW7YMsbGxgT4sEZFiUWAnIhHp8OHDaNasGbZu3Yrly5ejefPmgT4kEZFi0xw7EYlI69evx7Zt25CTk4NNmzYF+nBERLxCI3YiEnGOHTuGdu3ambl1nGM3fvx4k45NSkoK9KGJiBSLAjsRiTgPPvggPv74Y/z+++8oV64cOnXqhISEBHz11VeBPjQRkWJRKlZEIsqPP/5oRujeeecdlC9fHlFRUeb7n3/+GZMmTQr04YmIFItG7ERERETChEbsRERERMKEAjsRERGRMKHATkRERCRMKLATERERCRMK7ERERETChAI7ERERkTChwE5EREQkTCiwExEREQkTCuxEREREwoQCOxEREZEwocBOREREJEwosBMRERFBePh/yuOxY43BE8gAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the results\n", + "plt.figure()\n", + "plot_classical()\n", + "simplified_df.plot(style='o', ax=plt.gca())\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c82662b7", + "metadata": {}, + "source": [ + "But wait! The phase doesn't match the classical function!\\\n", + "There are two reasons:\n", + "1. Wrapping of the phase around $2\\pi$\n", + "2. A constant shift due to global phase\n", + "\n", + "If we solve those two issues, we see that the phase exactly equal to the original function." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "8901bbc1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 0. Simplify the dataframe - same as before\n", + "phases = np.angle(df[\"amplitude\"]).astype(float)\n", + "phases_over_2pi = phases/(2*np.pi)\n", + "f_classical = f_normalized(df['x'])\n", + "simplified_df = pd.DataFrame({\"f_classical\": f_classical, \"phase_over_2pi\": phases_over_2pi.round(5)})\n", + "simplified_df.index = df['x']\n", + "simplified_df.sort_index(inplace=True)\n", + "\n", + "# 1. Unwrap the phase\n", + "simplified_df['phase_over_2pi'] = np.unwrap(simplified_df['phase_over_2pi'], period=1)\n", + "\n", + "# 2. Get rid of the global phase\n", + "simplified_df['phase_over_2pi'] -= simplified_df['phase_over_2pi'].iloc[N//2]\n", + "simplified_df['f_classical'] -= simplified_df['f_classical'].iloc[N//2]\n", + "\n", + "# You can use the helper function:\n", + "# simplified_df = simplify_df(df)\n", + "\n", + "# Plot the results\n", + "plt.figure()\n", + "plot_classical()\n", + "simplified_df.plot(style='o', ax=plt.gca())\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "94f4f5f5", + "metadata": {}, + "source": [ + "For convinience, the full code to generate this graph:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "97f5ce93", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 7\n", + "Circuit Depth: 30\n", + "Gate Counts: {'u': 35, 'cx': 27}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.5*x + 0.25\n", + "# Gradient: f'(0) = 0.5\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]], ancilla: Output[QNum[n0, SIGNED, n0]]):\n", + " # 1. State preparation\n", + " \n", + " # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " \n", + " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", + " # Note: the ancilla is a signed fractional number,\n", + " # so the state |1111...1> corresponds to the value -1/N0\n", + " # which is the most negative value\n", + " numeric_value = -0.5**n0\n", + " ancilla |= numeric_value\n", + " qft(ancilla)\n", + "\n", + " # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", + " # Calculate the normalized f and add it to the ancilla\n", + " val = f_normalized(x)\n", + " inplace_add(val, ancilla)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "markdown", + "id": "4f640f7d", + "metadata": {}, + "source": [ + "## 2.2. Direct Phase" + ] + }, + { + "cell_type": "markdown", + "id": "7b083b7e", + "metadata": {}, + "source": [ + "The phase kickback approach is good when we have a state-oracle, but in our simulation it is very unefficient." + ] + }, + { + "cell_type": "markdown", + "id": "cbe98ddd", + "metadata": {}, + "source": [ + "Another approach is to directly prepare the wanted state.\n", + "In our case:\n", + "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}(\\delta-\\frac{N}{2}))}\\ket\\delta$$\n", + "\n", + "Here we can see the same example using the prepare_complex_amplitudes function.\\\n", + "You can look at the circuit width/depth and gate count to compare both methods.\\\n", + "In real applications, both methods can be used, depending on the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "7e84cce2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 3\n", + "Circuit Depth: 5\n", + "Gate Counts: {'u': 3, 'cx': 4}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.5*x + 0.25\n", + "# Gradient: f'(0) = 0.5\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " # 1. State preparation\n", + " \n", + " # Now using the direct prepare_complex_amplitudes instead of the ancilla and the inplace_add\n", + " x_array = np.arange(N) # Create an array of x values corresponding to the quantum states\n", + " phases = f_normalized(x_array) * 2 * np.pi # Apply 2pi times the normalized function to get the phases\n", + " magnitudes = np.ones(N) * 1 / N # Set equal magnitudes for all states\n", + " # You can use the helper function:\n", + " # magnitudes, phases = p.calculate_magnitude_and_phase()\n", + "\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "markdown", + "id": "bcf74e4c", + "metadata": {}, + "source": [ + "The graph is exactly the same as the phase kickback method.\\\n", + "From this point, we will use this method over the phase kickback, in order to have better efficiency." + ] + }, + { + "cell_type": "markdown", + "id": "15415d27", + "metadata": {}, + "source": [ + "## 2.3. Quadratic Function" + ] + }, + { + "cell_type": "markdown", + "id": "2ccef2dd", + "metadata": {}, + "source": [ + "More interesting are non-linear functions.\\\n", + "In the next example we will see a quadratic function.\\\n", + "Note that the 'magic' does not happen in this step. You will see that the phases agree with the function completly and doesn't do the linearization needed to calculate the gradient. The magic will happen in the next step where the QFT will do the linearization for us." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "7f2a5f63", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 3\n", + "Circuit Depth: 12\n", + "Gate Counts: {'u': 8, 'cx': 6}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.5*x^2 + 0.25*x + 0.1\n", + "# Gradient: f'(x) = x + 0.25, so f'(0) = 0.25\n", + "p.set_function(p.quadratic, (0.5, 0.25, 0.1))\n", + "p.l = 2\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " # 1. State preparation\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "markdown", + "id": "fc8328e1", + "metadata": {}, + "source": [ + "If we decrease $l$, we look at the function more closly, and it is closer to linear." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "25b19fcf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 3\n", + "Circuit Depth: 12\n", + "Gate Counts: {'u': 8, 'cx': 6}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.5*x^2 + 0.25*x + 0.1\n", + "# Gradient: f'(x) = x + 0.25, so f'(0) = 0.25\n", + "p.set_function(p.quadratic, (0.5, 0.25, 0.1))\n", + "p.l = 0.2\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " # 1. State preparation\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "markdown", + "id": "edc56f33", + "metadata": {}, + "source": [ + "# 3. Full Algorithm" + ] + }, + { + "cell_type": "markdown", + "id": "ed986f78", + "metadata": {}, + "source": [ + "## 3.1. Linear Functions" + ] + }, + { + "cell_type": "markdown", + "id": "f2032268", + "metadata": {}, + "source": [ + "The next and final step of the algorithm is to apply QFT on the coordinate.\\\n", + "As discussed earlier, applying the QFT will automatically extract the gradient from the phases, and create a measurable state with the value of the gradient (normalized)." + ] + }, + { + "cell_type": "markdown", + "id": "42bf7612", + "metadata": {}, + "source": [ + "To see the full algorithm in action, we will switch from the statevector simulation to standard simulation, because the final result is acquired by a measurement and not by looking at the phases." + ] + }, + { + "cell_type": "markdown", + "id": "0d267096", + "metadata": {}, + "source": [ + "Let's start with a simple example of linear function." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "dfc9b43c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsed counts: [{'x': 6}: 2048]\n", + "The analytical gradient is: -0.5\n", + "The majority gradient is: -0.5\n", + "The majority result is correct\n", + "####################################################\n", + "Success rate: 100.00% (2048/2048 shots)\n", + "[\u001b[92m██████████████████████████████████████████████████\u001b[91m\u001b[0m] 100.00%\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "p.set_function(p.linear, (-0.5, 0.25))\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " # 1. State preparation\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "qprog = synthesize(main)\n", + "job = execute(qprog)\n", + "# job.open_in_ide() # Uncomment to see the results in the IDE\n", + "pc = job.get_sample_result().parsed_counts\n", + "\n", + "# You can use the helper function:\n", + "# pc = run_standard_simulation(main)\n", + "\n", + "# Translate the majority state to a gradient value\n", + "majority_state = pc[0].state\n", + "value = majority_state.get('x')\n", + "# If the value is in the upper half of the range,\n", + "# it represents a negative value due to the modular arithmetic of the quantum states.\n", + "if value >= N//2:\n", + " value -= N\n", + "# Divide by (N/m) to get the actual gradient value.\n", + "majority_gradient = value / (N/m)\n", + "\n", + "# Or use the helper function:\n", + "# majority_gradient = state_to_gradient(majority_state.get('x'))\n", + "\n", + "# Print the results and compute the majority gradient\n", + "print(\"Parsed counts:\", pc)\n", + "print(f\"The analytical gradient is: {p.analytical_gradient(0)}\")\n", + "print(f\"The majority gradient is: {majority_gradient}\")\n", + "\n", + "# Check if the majority result is correct within the resolution of the algorithm\n", + "resolution = m/N\n", + "is_correct = abs(majority_gradient - p.analytical_gradient(0)) < resolution/2\n", + "print(f\"The majority result is\", \"correct\" if is_correct else \"incorrect\")\n", + "print(\"####################################################\")\n", + "\n", + "# Compute the success rate of the algorithm, i.e. the percentage of shots that are correct within the resolution of the algorithm.\n", + "success_rate, success_shots, total_shots = compute_success_rate(pc, analytic_derivatives={'x': p.analytical_gradient(0)})\n", + "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", + "show_bar(success_rate)\n", + "\n", + "# Visualize the theoretical values of the phases\n", + "# We used the standard simulation, so this is theoretical values only without the phases from the simulation\n", + "plot_theoretical()\n", + "\n", + "# You can use the helper function:\n", + "# analyze_results(pc)" + ] + }, + { + "cell_type": "markdown", + "id": "2eafff41", + "metadata": {}, + "source": [ + "The result for the gradient is always a multiple of m/N.\\\n", + "In the previous example, the gradient was -0.5, while the resolution (m/N) was 0.25.\\\n", + "The gradient is a multiple of the resolution, and therefore the result can be exact, and the success rate was 100%.\\\n", + "\\\n", + "More complex case is where the gradient is not a multiple of the resolution.\\\n", + "In those cases, the result will be a superposition of multiple solutions, but we can still get a good approximation for the gradient from the result.\\\n", + "Let's see it in the next example.\\\n", + "TODO: Consider removing this example, because it doesn't match the flow of the explaination." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "be423003", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsed counts: [{'x': 2}: 1755, {'x': 3}: 133, {'x': 1}: 63, {'x': 4}: 29, {'x': 5}: 20, {'x': 7}: 20, {'x': 0}: 19, {'x': 6}: 9]\n", + "The analytical gradient is: 0.55\n", + "The majority gradient is: 0.5\n", + "The majority result is correct\n", + "####################################################\n", + "Success rate: 85.69% (1755/2048 shots)\n", + "[\u001b[92m███████████████████████████████████████████\u001b[91m-------\u001b[0m] 85.69%\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.55*x + 0.25\n", + "# Gradient: f'(0) = 0.55\n", + "# Pay attention that 0.55 is not a multiple of m/N = 0.25,\n", + "# so we expect to get a superposition of multiple states around the correct gradient.\n", + "p.set_function(p.linear, (0.55, 0.25))\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " # 1. State preparation\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "pc = run_standard_simulation(main)\n", + "analyze_results(pc)" + ] + }, + { + "cell_type": "markdown", + "id": "a67ddc29", + "metadata": {}, + "source": [ + "## 3.2. Quadratic Function" + ] + }, + { + "cell_type": "markdown", + "id": "d72f288e", + "metadata": {}, + "source": [ + "Again, let's try calculating the gradient of a non-linear function. In the next example, we will explore a quadratic function.\\\n", + "In the case of non-linear function, we will need to cleverly choose the value of $l$ - the interval around the origin.\\\n", + "In order for the algorithm to work, we need to work in the linear regime around the origin, so we need to choose small enough $l$." + ] + }, + { + "cell_type": "markdown", + "id": "a741bff9", + "metadata": {}, + "source": [ + "First, for good selection of $l$, we see that the points are almost linear, and we get a good success rate." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "da592b2b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsed counts: [{'x': 1}: 2013, {'x': 0}: 16, {'x': 2}: 15, {'x': 3}: 3, {'x': 5}: 1]\n", + "The analytical gradient is: 0.25\n", + "The majority gradient is: 0.25\n", + "The majority result is correct\n", + "####################################################\n", + "Success rate: 98.29% (2013/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.29%\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the quadratic function\n", + "p = params()\n", + "# f(x) = 0.6*x^2 + 0.25*x + 0.1\n", + "# Gradient: f'(x) = 1.2*x + 0.25, so f'(0) = 0.25\n", + "p.set_function(p.quadratic, (0.6, 0.25, 0.1))\n", + "# Setting l properly, ensuring we are in the linear regime of the function.\n", + "p.l = 0.1\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " # 1. State preparation\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "pc = run_standard_simulation(main)\n", + "analyze_results(pc)" + ] + }, + { + "cell_type": "markdown", + "id": "40d8d166", + "metadata": {}, + "source": [ + "But if we increase $l$ outside of the linear regime, we see that the success rate get drasticly lower:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "27717a39", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsed counts: [{'x': 0}: 501, {'x': 1}: 492, {'x': 2}: 484, {'x': 7}: 208, {'x': 3}: 184, {'x': 6}: 90, {'x': 4}: 46, {'x': 5}: 43]\n", + "The analytical gradient is: 0.25\n", + "The majority gradient is: 0.0\n", + "The majority result is incorrect\n", + "####################################################\n", + "Success rate: 24.02% (492/2048 shots)\n", + "[\u001b[92m████████████\u001b[91m--------------------------------------\u001b[0m] 24.02%\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the quadratic function\n", + "p = params()\n", + "# f(x) = 0.6*x^2 + 0.25*x + 0.1\n", + "# Gradient: f'(x) = 1.2*x + 0.25, so f'(0) = 0.25\n", + "p.set_function(p.quadratic, (0.6, 0.25, 0.1))\n", + "# Setting l to be too big, so we are outside of the linear regime of the function.\n", + "p.l = 1\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " # 1. State preparation\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "pc = run_standard_simulation(main)\n", + "analyze_results(pc)" + ] + }, + { + "cell_type": "markdown", + "id": "d5b47027", + "metadata": {}, + "source": [ + "# 4. Parameters Selection - TODO" + ] + }, + { + "cell_type": "markdown", + "id": "659ca4e7", + "metadata": {}, + "source": [ + "We saw earlier the importance of proper selection of some of the parameters.\\\n", + "Let's dive deeper into the parameters selection." + ] + }, + { + "cell_type": "markdown", + "id": "c634e599", + "metadata": {}, + "source": [ + "## 4.1. Understanding the parameters" + ] + }, + { + "cell_type": "markdown", + "id": "61a68f72", + "metadata": {}, + "source": [ + "There are three main parameters to be selected: $l$, $m$ and $n$.\\\n", + "$n$ is the number of bits of the result. The bigger $n$, the higher the accuracy of the result.\\\n", + "$l$ is the interval size around the origin ($dx$).\\\n", + "$m/2$ is the maximal gradient that can be calculated (in absolute value)." + ] + }, + { + "cell_type": "markdown", + "id": "3e3dfc6f", + "metadata": {}, + "source": [ + "For the parameter $l$, we saw earlier that it should be selected such that we look at the linear regime of the function. See section 2.2." + ] + }, + { + "cell_type": "markdown", + "id": "c539ec98", + "metadata": {}, + "source": [ + "Understanding the parameter $m$ is a little trickier. We will look at a bounding box around the origin.\\\n", + "The width of the box (dx) is $l$, spanning from $-l/2$ to $l/2$. The slope of the graph (dy/dx) is bounded between $-m/2$ to $m/2$. Therefore, the height of the box (dy) should be bounded dy/dx*dx, so the height should be $lm/2$, making the box span between $-lm/4$ to $lm/4$.\\\n", + "When we plot the graph, if all the points are inside this box, then we know that the gradient is bounded by $m/2$ and we will get the correct result.\\\n", + "If the points are outside this box, we will get aliasing in the results and get an incorrect gradient.\\\n", + "Note that in our graphs we use the normalized function instead of the original function, so the box is between $-N/4$ to $N/4$ instead of $lm/4$." + ] + }, + { + "cell_type": "markdown", + "id": "f0a30a00", + "metadata": {}, + "source": [ + "We will see now the same function, once with correct selection of m and one with incorrect selection of $m$, and we can see that if $m$ is too small the theoretical values are out of the bounding box, and the phases from the simulation are folded into the box creating aliasing. " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "a2a46ca7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the linear function\n", + "p = params()\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.m = 2 # Correct selection of m - no aliasing.\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=False)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)\n", + "# simplified_df" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "812c0c30", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the linear function\n", + "p = params()\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.m = 1.333 # Marginal selection of m - still no aliasing.\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=False)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)\n", + "# simplified_df" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "19a77750", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the linear function\n", + "p = params()\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.m = 0.3 # Incorrect selection of m - aliasing occurs.\n", + "p.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]]):\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=False)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)\n", + "# simplified_df" + ] + }, + { + "cell_type": "markdown", + "id": "34d82a6f", + "metadata": {}, + "source": [ + "## 4.2. Success rate as function of parameter selection\n", + "**TODO**: consider removing this part" + ] + }, + { + "cell_type": "markdown", + "id": "19c66ba4", + "metadata": {}, + "source": [ + "We can plot the success rate as a function of the selected parameters.\\\n", + "In the first example, we will have a quadratic function $f(x)=0.6x^2+0.25x+0.1$, $f'(0)=0.25$.\\\n", + "We can plot the graph for different selections of m.\\\n", + "We discussed earlier that $m/2$ is the bound for the gradient value, so we expect to have poor results for $m<0.5$, good results for $m>0.5$, until reaching $m=0.25N=4$, where the resolution won't be good enough for meaningful result.\\\n", + "Note the oscillations in the sucess rate in the optimal region. This is due to the discrete values the algorithm can return. As we increase the number of bits $n$, the oscillations will be smaller." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "59ca5244", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=0.05: Success rate = 0.00%\n", + "m=0.1: Success rate = 0.00%\n", + "m=0.3: Success rate = 0.00%\n", + "m=0.5: Success rate = 0.00%\n", + "m=0.55: Success rate = 0.00%\n", + "m=0.7: Success rate = 79.39%\n", + "m=0.8: Success rate = 80.62%\n", + "m=0.9: Success rate = 87.40%\n", + "m=1.0: Success rate = 95.17%\n", + "m=1.5: Success rate = 73.05%\n", + "m=2.0: Success rate = 98.19%\n", + "m=4.0: Success rate = 0.00%\n", + "m=6.0: Success rate = 0.00%\n", + "m=10.0: Success rate = 0.00%\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_success_rate_vs_m(m_values, function, function_params, l_val=0.1, n_val=3):\n", + " \"\"\"\n", + " Iterate over different m values and plot success rate as a function of m.\n", + "\n", + " Args:\n", + " m_values: list of m values to test\n", + " function: function name (\"linear\" / \"quadratic\") or callable\n", + " function_params: parameters for the function\n", + " l_val: l parameter (default 0.1)\n", + " n_val: n parameter (default 3)\n", + " \"\"\"\n", + " success_rates = []\n", + "\n", + " for m_val in m_values:\n", + " p = params()\n", + " p.m = m_val\n", + " p.l = l_val\n", + " p.n = n_val\n", + " p.set_function(function, function_params)\n", + " p.unpack()\n", + "\n", + " @qfunc\n", + " def main(x: Output[QNum[n]]):\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + " invert(lambda: qft(x))\n", + "\n", + " pc = run_standard_simulation(main)\n", + " analytic_grad = p.analytical_gradient(0)\n", + " success_rate, _, _ = compute_success_rate(pc, analytic_derivatives={'x': analytic_grad}, reject_underresolution=True)\n", + " success_rates.append(success_rate)\n", + " print(f\"m={m_val}: Success rate = {success_rate:.2%}\")\n", + "\n", + " # Plot\n", + " plt.figure(figsize=(10, 6))\n", + " plt.plot(m_values, success_rates, 'o-', linewidth=2, markersize=8)\n", + " plt.xlabel('m parameter', fontsize=12)\n", + " plt.ylabel('Success Rate', fontsize=12)\n", + " plt.title('Success Rate vs m Parameter', fontsize=14)\n", + " plt.grid(True, alpha=0.3)\n", + " plt.ylim([0, 1.05])\n", + " ax = plt.gca()\n", + " ax.axvspan(0.5, 4.0, color='green', alpha=0.15, label='Target m range')\n", + " ax.legend()\n", + " plt.show() \n", + " return success_rates\n", + "\n", + "# Example usage:\n", + "m_values = [0.05, 0.1, 0.3, 0.5, 0.55, 0.7, 0.8, 0.9, 1.0, 1.5, 2.0, 4.0, 6.0, 10.0]\n", + "results = plot_success_rate_vs_m(m_values, \"quadratic\", (0.6, 0.25, 0.1))" + ] + }, + { + "cell_type": "markdown", + "id": "37699833", + "metadata": {}, + "source": [ + "As for the $l$ parameter, we need to be in the linear regime, so we need to ensure $l$ is small enough, as can be seen in the next example:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "806fc176", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=0.1: Success rate = 94.19%\n", + "l=0.2: Success rate = 78.86%\n", + "l=0.3: Success rate = 60.84%\n", + "l=0.4: Success rate = 38.92%\n", + "l=0.5: Success rate = 23.05%\n", + "l=1: Success rate = 8.94%\n", + "l=1.5: Success rate = 15.62%\n", + "l=2.0: Success rate = 14.75%\n", + "l=3.0: Success rate = 28.37%\n", + "l=4.0: Success rate = 2.25%\n", + "l=5.0: Success rate = 24.37%\n" + ] + }, + { + "data": { + "image/png": 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cebyS0CIT2id1IV+deqt9VYNx/aBBp7rqz9YPBKyjmxXdVwB4OEeXDQSAirJ161bLq6++arnkkkvMmjuBgYHmpuWVtWzyqlWrCv0+XQdJyzxrGeSIiAjL6NGjzTpIha0jpVJTUy2vv/66JSoqyqxNpOXWdX0iXWPqxIkTefY9cuSIZcyYMab0sx5f197p1q2bKXleWPtvvfVW8zN1Xy0Nre267777LCtXrrTtN2PGDFOyW3+v4OBgU45d13R65ZVX8qzftGDBAsvw4cPN2kRatt3aTl27p7jlnotaRyo363pZixcvtq3n88ILL1iaN29uCQgIMCWv9dyc6Zzq66b7+/n5FVqS/sCBA+Y8Wo+pZdRbt25t1jiy/tzi0vWOtAy2/hwtiV6Y9957z3LFFVeYtmof0rLkXbt2tbz//vvm96vIdaTy01LhkydPtrRt29a0Tfus9htdt6mwn2l9DX/77bdyP96ZypMXdT50/aYpU6ZYevbsaV5Xa5/R0u96vk+ePFlufeVMyx8AgJeeAkcHcwAAAADgSsiRAgAAAIASIpACAAAAgBIikAIAAACAEiKQAgAAAIASIpACAAAAgBIikAIAAACAEvL4BXmzs7PNwpVVqlQxi/IBAAAA8EwWi0USExPNAvG6iPyZeHwgpUFU/fr1K+zFAQAAAODc9u/fL/Xq1TvjPh4fSOlIlPVkhYSE2G2UKzY2VsLCws4ayQL0H9gT7z+g78AReO+Bu/SfhIQEM8hijRHOxOMDKet0Pg2i7BlIpaammuM5ujPA9dB/QP8B7z1wNfztgrv1n+Kk/DhHSwEAAADAhRBIAQAAAEAJEUgBAAAAQAkRSAEAAABACRFIAQAAAEAJEUgBAAAAQAkRSAEAAABACRFIAQAAAEAJEUgBAAAAQAkRSAEAAABACRFIAQAAAEAJEUgBAAAAQAkRSAEAAABACRFIAQAAAEAJEUgBAAAAgCsHUn/++acMHDhQ6tSpI15eXvL999+f9Xt+//136dixowQEBEizZs1k2rRpFdJWAAAAAJ7LqQKppKQkiYyMlEmTJhVr/927d8tll10mF110kaxdu1buv/9+ue2222ThwoXl3lYAAAAAnstXnMiAAQPMrbgmT54sjRs3lgkTJpjHrVu3lr///lveeOMN6devXzm2FAAAAIAnc6pAqqSWLVsmffr0ybNNAygdmSpKWlqauVklJCSYr9nZ2eZmD3oci8Vit+PBs9B/QP8B7z1wNfztgrv0n5K0waUDqSNHjkh4eHiebfpYg6OUlBQJCgoq8D0vvfSSjB8/vsD22NhYSU1NtdsLEB8fbzqEt7dTzZ6EC6D/gP4D3nvgavjbBXfpP4mJiZ4RSJXG2LFj5cEHH7Q91qCrfv36EhYWJiEhIXbrDFosQ4/p6M4A10P/Af0HvPfA1fC3C+7SfwIDAz0jkIqIiJDo6Og82/SxBkSFjUYpre6nt/z0RbPnC6edwd7HhOeg/4D+A9574Gr42wV36D8l+fkufZXfvXt3Wbx4cZ5tP//8s9kOAAAAAOXFqQKpkydPmjLmerOWN9f7+/bts03LGz58uG3/u+66S3bt2iWPPPKIbN26Vd577z355ptv5IEHHnDY7wAAAADA/TlVILVq1So555xzzE1pLpPeHzdunHl8+PBhW1CltPT5Tz/9ZEahdP0pLYP+4YcfUvocAAAAQLlyqhypCy+80FTrKMq0adMK/Z5///23nFsGAAAAAE46IgUAAAAAroBACgAAAABKiEAKAAAAAEqIQAoAAAAASohACgAAAABKiEAKAAAAAEqIQAoAAAAASohACgAAAABKiEAKAAAAAEqIQAoAAAAASohACgAAAABKiEAKAAAAAErIt6TfgPKRmpEl8zYclkWboiUuOV2qBvtL37bhcmn72hLo58NpBwAAAJwIgZQT+HlztDw0c60kpGSKt5dItkXM1wWbjsgzczfJxCFR0qdNuKObCQAAAOAUpvY5QRB1x+erJDEl0zzWICr3V91+++erzH4AAAAAnAOBlIOn8+lIlFjMv0KZ7RaRh2euNfsDAAAAcDwCKQfSnCidzldUEGWlz8enZMr8jYcrqGUAAAAAzoRAyoG0sITmQhWH7rdwI9P7AAAAAGdAIOVAWp3Pmgt1NrpfXEp6eTcJAAAAQDEQSDmQljgvyYhU1SD/8m4SAAAAgGIgkHIgXSeqJCNS/dpRAh0AAABwBgRSDqSL7YYE+crZBqX0+dAgXxnQrnYFtQwAAADAmRBIOVCgn49ZbFcjpaKCKbPdS2TCkCizPwAAAADHI5BysD5twuWDYZ3NyFRhdPvUYZ3NfgAAAACcQ+FX76hQl7QJlxWP9zHrRE1ctF32n0gx2++5sKncd3FzRqIAAAAAJ8OIlJPQaXuDz6kno3s3t20LCfIjiAIAAACcEIGUk4lqUNV2f+2+OIe2BQAAAEDhCKScTNOwylLJP6eoxLoDBFIAAACAMyKQcjI+3l7SoV7OqNTh+FSJTkh1dJMAAAAA5EMg5YQi6+ea3refUSkAAADA2RBIOaEoAikAAADAqRFIOXsgRcEJAAAAwOkQSDmhiNBAiQgJNPc3HIyXrGyLo5sEAAAAIBcCKScflTqZlik7Y086ujkAAAAAciGQclIUnAAAAACcF4GUk6LgBAAAAOC8CKScVPt6oeLllXN/HSXQAQAAAKdCIOWkKgf4SotaVcz9rUcSJSU9y9FNAgAAAHAKgZQTi6wfar5q1b5Nh+Id3RwAAAAApxBIObGo+tVs99cyvQ8AAABwGgRSLlJw4l8CKQAAAMBpEEg5sRbhlSXIz8fcp+AEAAAA4DwIpJyYr4+3tK+bkyd14ESKHD2Z5ugmAQAAACCQcp2CE4pRKQAAAMA5MCLl5Cg4AQAAADgfAikXGpGich8AAADgHAiknFzdqkFSs3KAbWpfdrbF0U0CAAAAPB6BlJPz8vKSqFOjUgmpmbL7WJKjmwQAAAB4PAIpF1tPioITAAAAgOMRSLkACk4AAAAAzoVAygW0r0cJdAAAAMCZEEi5gNAgP2kaVsnc33w4QVIzshzdJAAAAMCjEUi5iMhTeVIZWRbZcjjB0c0BAAAAPBqBlIs4J1fBCdaTAgAAAByLQMrFRqQUlfsAAAAAxyKQchGtIkLE3zfn5WJECgAAAHAsAikXoUFUuzoh5v6eY8lyIind0U0CAAAAPBaBlKtO7zsQ59C2AAAAAJ6MQMqFRFFwAgAAAHAKBFIuGkhRcAIAAABwHAIpF9KgerBUC/azFZywWCyObhIAAADgkQikXIiXl5ctT+pEcobsP57i6CYBAAAAHolAyoWn9/27/4RD2wIAAAB4KgIpl16YN96hbQEAAAA8FYGUi4mqdzqQWsuIFAAAAOAQBFIuplolf2lUI9jc33goQdIzsx3dJAAAAMDjEEi58PQ+DaK2HUl0dHMAAAAAj0Mg5fIL81JwAgAAAKhoBFIuXnBiLQUnAAAAgApHIOWC2tQOET8fL3OfESkAAACg4hFIuaBAPx9pXTvE3N8ZmyQJqRmObhIAAADgUQik3CBPaj3T+wAAAIAKRSDloig4AQAAADgOgZSLouAEAAAA4DgEUi6qcY1KEhLoa+6v3R8nFovF0U0CAAAAPAaBlIvy9vayjUodPZkmh+JTHd0kAAAAwGMQSLlLntS+OIe2BQAAAPAkThdITZo0SRo1aiSBgYHSrVs3Wbly5Rn3f/PNN6Vly5YSFBQk9evXlwceeEBSUz1jdCay3ulAat0BAikAAADAIwOpr7/+Wh588EF5+umnZc2aNRIZGSn9+vWTmJiYQvefPn26PPbYY2b/LVu2yEcffWSO8fjjj4vHFZxgRAoAAADwzEBq4sSJcvvtt8vIkSOlTZs2MnnyZAkODpaPP/640P2XLl0qPXv2lBtuuMGMYvXt21euv/76s45iuYuwKgFSt2qQub/hYLxkZmU7ukkAAACAR8gp++YE0tPTZfXq1TJ27FjbNm9vb+nTp48sW7as0O/p0aOHfPHFFyZw6tq1q+zatUvmzZsnw4YNK/LnpKWlmZtVQkKC+ZqdnW1u9qDH0Sp69jrembSvGyIH41IkJSNLBr+3ROpUDZK+bcLl0nYREuDnU+4/H/ZXkf0H7of+A/oOeO+Bq8l2omufkrTBaQKpo0ePSlZWloSHh+fZro+3bt1a6PfoSJR+33nnnWdOfmZmptx1111nnNr30ksvyfjx4wtsj42NtVtulb4A8fHxpk0aDJaXP3fGyW/bTk973HAwQTYdSpCFm6LlmTmbZFy/RtKryenpf3ANFdV/4J7oP6DvgPceuJpsJ7r2SUxMdL1AqjR+//13efHFF+W9994zhSl27NghY8aMkeeee06eeuqpQr9HR7w0Dyv3iJQWqQgLC5OQkBC7dQYvLy9zzPLqDL9siZZHf9wp+ZePyj71+GRaljwyd6dMuamj9GmdNziFc6uI/gP3Rf8BfQe898DVZDvRtY8WvHO5QKpmzZri4+Mj0dHRebbr44iIiEK/R4MlncZ32223mcft27eXpKQkueOOO+SJJ54o9IUICAgwt/x0X3u+cNoZ7H1Mq9SMLHl41nqRM6zBq095WUT+N2u9rHi8jwQyzc+llGf/gfuj/4C+A9574Gq8nOTapyQ/32mu0vz9/aVTp06yePHiPNGpPu7evXuh35OcnFzgl9VgTOnQoLuat+GwJKRknimOMvT5+JRMmb/xcAW1DAAAAPAMThNIKZ1yN3XqVPn0009NOfO7777bjDBpFT81fPjwPMUoBg4cKO+//77MmDFDdu/eLT///LMZpdLt1oDKHS3aFC3eXsXbV/dbuDHvKB8AAACAsnGaqX1q6NChpujDuHHj5MiRIxIVFSULFiywFaDYt29fnhGoJ5980gwD6teDBw+aeZUaRL3wwgvizuKS0225UGej+8WlpJd3kwAAAACP4lSBlBo1apS5FVVcIjdfX1+zGK/ePEnVYH8z0lScYEr3qxrkXxHNAgAAADyGU03tQ/H0bRteohGpfu2o2gcAAADYE4GUC7q0fW0JCfKVs6VJ6fOhQb4yoF3tCmoZAAAA4BkIpFyQljKfOCTKREpFBVNmu5fIhCFRlD4HAAAA7IxAykX1aRMuHwzrbEamVP6ASrdPHdbZ7AcAAADAzYtNoPguaRNuFtvVdaI+W7ZX/t0XZ7b3aV1L3r2hIyNRAAAAQDlhRMoNpvkNPqeevH3dObZtuhaxbgcAAABQPgik3ES9akFSOSBngHHL4QRHNwcAAABwawRSbkIXJm4VUcXcPxSfKvHJGY5uEgAAAOC2CKTcSOvaIbb7W48wKgUAAACUFwIpN9Kqds6IlGJ6HwAAAFB+CKTcdkQq0aFtAQAAANwZgZQbaRleRbxOLSjFiBQAAABQfgik3EilAF9pWD3Y3N8WnShZ2RZHNwkAAABwSwRSbqZVRM70vtSMbNlzLMnRzQEAAADcEoGUO+dJHSZPCgAAACgPBFJuXLmPEugAAABA+SCQcjOtT03tUxScAAAAAMoHgZSbqVctSCoH+Jr7W5jaBwAAAJQLAik34+3tJS0jcqb3HYxLkfiUDEc3CQAAAHA7BFJuqHWuPKltLMwLAAAA2B2BlBuXQFfkSQEAAAD2RyDl7iXQjyQ4tC0AAACAOyKQckPWHClFwQkAAADA/gik3JBW7WtQPdiWI5WVbXF0kwAAAAC3QiDl5gUnUjKyZN/xZEc3BwAAAHArBFJuioITAAAAQPkhkPKEghOHKTgBAAAA2BOBlAesJbX5cKJD2wIAAAC4GwIpN1W/WrBU8vcx9ymBDgAAANgXgZSb8vb2spVBP3AiRRJSMxzdJAAAAMBtEEi5sVa58qS0DDoAAAAA+yCQcmMUnAAAAADKB4GUG2t9amqfouAEAAAAYD8EUm7MmiOlKDgBAAAA2A+BlBurEugn9asH2XKksrMtjm4SAAAA4BYIpNxc64icghPJ6Vmy73iyo5sDAAAAuAUCKQ+q3Mf0PgAAAMA+CKTcHAUnAAAAAPsjkHJzlEAHAAAA7I9Ays01qB4swf4+5v6WIwmObg4AAADgFgik3Jy3t5etDPr+4ymSmJrh6CYBAAAALo9AygO0OlW5z1oGHQAAAEDZEEh5gDa1Ty/Mu4VACgAAACgzAilPK4F+mDwpAAAAoKwIpDyANUdKbSGQAgAAAMqMQMoDhAT6Sb1qQbYcqexsi6ObBAAAALg0AikPKziRlJ4l+08kO7o5AAAAgEsjkPLEghOHqdwHAAAAlAWBlAcWnCBPCgAAACgbAikP0Tp35b4jVO4DAAAAyoJAykM0qB4sQX4+5j5T+wAAAICyIZDyED7eXtLiVBn0fceT5WRapqObBAAAALgsAikPLTihZdABAAAAlA6BlAeWQFcUnAAAAABKj0DKg1BwAgAAALAPAikP0vJUjpSi4AQAAABQegRSHiQ0yE/qVg2y5UhlZ1sc3SQAAADAJRFIeZjWpwpOaNW+AydSHN0cAAAAwCURSHlwntQWFuYFAAAASoVAyoMr9209TAl0AAAAoDQIpDxMq1xrSVECHQAAACgdXymDgwcPyp9//ikxMTFy9dVXS7169SQrK0vi4+MlNDRUfHx8ynJ4lINGNSpJoJ+3pGZky1am9gEAAAAVNyJlsVjkwQcflMaNG8uNN95o7m/fvt08d/LkSWnUqJG88847pWsRypWPt5e0DM8Zldp7PFmS0jI54wAAAEBFBFKvvfaavPXWW/Lwww/Lzz//bAIrKx2Juuqqq+Tbb78tzaFRgQUn9GXbFk2eFAAAAFAhgdTUqVNl+PDh8uKLL0pUVFSB5zt06GAboYLzaZVnYd4Eh7YFAAAA8JhAav/+/dKjR48in69UqZIkJHCB7gol0KncBwAAAFRQIFWrVi0TTBVl9erV0qBBg9IcGhVdAp2CEwAAAEDFBFKaAzV58mTZtWuXbZuXl5f5umjRIpk2bZoMGTKkNIdGBQgN9pM6oYG2EancOW4AAAAAyimQGj9+vNSuXdvkR2mulAZRr7zyipx33nkyYMAAkyP1+OOPl+bQqODpfYlpmXLgRArnHQAAACjvQEor8y1fvlweeeQRs5ZUYGCg/PHHHxIXFydPP/20/PXXXxIcHFyaQ6OCsDAvAAAA4IAFeYOCguTJJ580N7h4wYkjidK3bYRD2wMAAAC4/YhU7969ZfHixUU+/9tvv5l94Lya1Kxsuz9tyR656/PV8t2aA5KakeXQdgEAAABuG0j9/vvvEh0dXeTzMTExZqofnNPPm6Plug+W2R4fT06XRZuPyIPfrJOuL/4iv2wu+rUFAAAAUMpAKneVvsLs2LFDqlQ5vegrnCuIuuPzVZKYmplne/apwn2JKZly++erzH4AAAAAypgj9emnn5qb1fPPPy9Tp04tsJ8WnFi/fr1ceumlxT00KohO23to5loRi/lXKN3uZRF5eOZaWfF4Hwn08+H1AQAAAEobSCUnJ0tsbKztcWJionh7excYpapUqZLcddddMm7cuOIeGhVk3obDkpCSdySqqGAqPiVT5m88LIPPqVchbQMAAADcMpC6++67zU01btxY3nrrLbniiivKs22ws0WbosXb6/Q0vjPR/RZujCaQAgAAAOyVI7V79+5yC6ImTZokjRo1MmtTdevWTVauXHnG/XUq4b333msWCA4ICJAWLVrIvHnzyqVtri4uOb1YQZTS/eJS0su7SQAAAIBnrSOVe4pffHy8ZGdnF3iuQYMGJTrW119/LQ8++KBMnjzZBFFvvvmm9OvXT7Zt2ya1atUqsH96erpccskl5rlZs2ZJ3bp1Ze/evVK1atUy/U7uqmqwf4lGpKoG+VdEswAAAADPCaTef/99mThxouzatavIfbKySrYmkR7v9ttvl5EjR5rHGlD99NNP8vHHH8tjjz1WYH/dfvz4cVm6dKn4+fmZbTqahcL1bRsuCzYdKdbp0WCrX7twTiUAAABgr0BKAxydTqejRbfccos88cQT8sADD5jpeNOmTZPw8HC57777SnRMHV1avXq1jB071rZNi1n06dNHli07veZRbnPmzJHu3bubtvzwww8SFhYmN9xwgzz66KPi41N4tbm0tDRzs0pISDBfdUStsFG10tDjWCwWux3PXga0DZdnAn1N6fMzDUppYfsqgb7Sv0240/0OnsBZ+w9cA/0H9B3w3gNXk+1E1z4laUOpAql33nnHBFHz58+XY8eOmUDqsssuk969e8sjjzwinTt3NttL4ujRo2YES4Ow3PTx1q1bC/0eHQ379ddf5cYbbzR5Ubp+1T333CMZGRny9NNPF/o9L730kowfP77Adq1ImJqaKvZ6AXS6o3aI/JUNHe2pvg3lkTk7TbBUWDDllWu/+BMlew0hbt9/4PzoP6DvgPceuJpsJ7r20bSlcg2kdu7caUaBlHVKnY4oqdDQULntttvkvffek4ceekjK+6RrftQHH3xgRqA6deokBw8elNdee63IQEpHvDQPK/eIVP369c1oVkhIiN3apaXg9ZiO7gz5XV2rlnmNHp65XhJSMwsEVDoSNWFIB7m4NdP6HMWZ+w+cH/0H9B3w3gNXk+1E1z46w65cAym9EM/MzFmPSIOP4OBg2b9/v+35KlWqyJEjxcvFsapZs6YJhqKjo/Ns18cRERGFfo9W6tNALvc0vtatW5ufrYGdv3/BYgla2U9v+emLZs8XTjuDvY9pL33b1paVLWqZdaJmrTogS3bmjDx1blhNvritG4vwOgFn7j9wfvQf0HfAew9cjZeTXPuU5OeXqqXt2rWTdevW2R6fe+65pviEjgZpQDVlyhRThrwkNOjREaXFixfniU71seZBFaZnz55mOl/uuYzbt283AVZhQRROC/TzMWtEfTiii21blsVCEAUAAACUVyB10003ycaNG21FGzTnaMuWLabcuVbN03Llzz//fImPq1Pupk6dKp9++qk5ni4AnJSUZKviN3z48DzFKPR5rdo3ZswYE0Bphb8XX3zRNu0QZxfk7yN1QnOGMHcfTeKUAQAAAOU1tU8DG2twYx0Z2rRpk8ydO9dMs+vbt2+JR6TU0KFDTdGHcePGmel5UVFRsmDBAlsBin379uUZbtPcpoULF5qKgR06dDDrSGlQpVX7UHyNwyrJofhUiUvOkONJ6VK9EqN5AAAAQLkuyGvVpEkTE8RY7d69Wxo3blzi44waNcrcCvP7778X2KbT/pYvX17in4PTGtesJEt25ORJ7T56UqpXqs7pAQAAAM7A7tlc69evN2s5tWzZ0t6HRjlpUrOy7f6uWKb3AQAAAHYdkdLpe1pUQsufV6tWTYYMGSKDBw82z61Zs0aefPJJM9VOK+lpHhVcZ2qfFXlSAAAAgB0DKZ0+pwvu5l609uuvv5aJEyeaUuial6Rlz//3v/+ZKX5aOQ+uoUlNAikAAACgXAKpZ5991ixQNXv2bOnVq5fJgdKCE1oYIiUlxVTce+KJJ8waU3AtdasGiZ+Pl2RkWRiRAgAAAOyZI7VixQpTVrxfv35mAd62bdua0ajExES577775NVXXyWIclG+Pt7SoHqwbWpfdrbF0U0CAAAA3COQiouLK1DS3PpYp/zBtTU+VXAiLTNbDsWnOLo5AAAAgHsEUhaLxawRlZv1sU75g2trSsEJAAAAoHyq9s2bN88slGuVnJwsXl5eMnPmTFm7dm2efXW7LpQL11lLykqn9/VqHubQ9gAAAABuE0hNnz7d3PKbMmVKgW0EUq4bSLGWFAAAAGCnQEqr9MF9sZYUAAAAUA6BVMOGDUtwWLiasMoBUjnAV06mZcquoycd3RwAAADAPYpNwL3pVEzr9L4DJ1IkLTPL0U0CAAAAnBaBFGyanKrcZ7GI7DuWzJkBAAAAikAghcILThxN4swAAAAARSCQQpEl0AEAAAAUjkAKNk1qVrbd3x1LIAUAAABUSCCVnp4uSUlcgLuqRjWDbfcZkQIAAADsHEjNmDFDHnjggTzbxo8fL5UrV5aqVavK4MGD5eRJSmi7miqBfhJWJcDcpwQ6AAAAYOdAasKECXlGnpYuXWoCqX79+pkAa8GCBfLCCy+U5tBwsCan8qSOnkyX+JQMRzcHAAAAcJ9AaufOndKhQwfb4+nTp0tERITMnj1bXn31Vbn33nvl22+/tWc7UcEl0NUeCk4AAAAA9guk0tLSJDAw0PZ40aJFMmDAAPH19TWP27RpIwcOHCjNoeFgVO4DAAAAyimQaty4sfzyyy/m/qpVq2THjh3Sv39/2/PR0dEmXwqup3Guyn2sJQUAAAAULmcIqYTuvPNOGTNmjGzevNmMPNWrV08uv/xy2/NLliyRtm3blubQcDBGpAAAAIByCqRGjx5tpvbNmzdPOnXqJI8++qgEBQWZ544fPy5HjhyRu+66qzSHhoM1qB4sPt5ekpVtkV2xVF4EAAAA7BZIqdtvv93c8qtevbqZ7gfX5O/rLfWrBcmeY8lmLSmLxSJeXl6ObhYAAADgngvy6gX3r7/+KvPnz5fExER7HRYOnN6XnJ4lMYlpvAYAAACAPQKpJ554Qi666KI8QVTfvn3lkksukcsuu0zat29vSqTDDQpOxJ5eLwwAAABAGQIpXSOqa9eutsezZs2SxYsXy/PPPy8//vijZGVlyTPPPFOaQ8MJNM61lpRO7wMAAABghxypgwcPSrNmzWyPv/vuO7N21NixY83ju+++W95///3SHBpOoMmpqX1q91EKTgAAAAB2GZHShXd1UV7rtD4djcq9jlR4eLgcPXq0NIeGE6AEOgAAAFAOgVS7du3kiy++kBMnTsgnn3wix44dM7lRVnv37pWaNWuW5tBwAhEhgRLol9M1yJECAAAA7DS1b9y4cTJw4EBbsNSzZ888xSd++ukn6dKlS2kODSfg7e1lCk5sOZwg+44nS0ZWtvj52K3AIwAAAOCZgZRW51uzZo38/PPPUrVqVRk6dKjtOR2lOv/88+XKK6+0ZzvhgDwpDaQysy1y4ERKnul+AAAAgKcr9YK8WlxCb/lVq1ZN3njjjbK2C06VJ3WSQAoAAADIpUzztZYvXy4vvfSSPPDAA/Lff/+ZbcnJyWa06uRJqr25SyBFnhQAAABgh0AqPT1drrrqKpMbpYvzvv3227J///6cA3p7m8V533rrrdIcGk6CtaQAAAAAOwdSTz31lFl4V9eK2rZtmymBbhUYGChDhgyRH374oTSHhhOuJcWIFAAAAGCHQOqrr74yi+7ecccdUr169QLPt27dWnbt2lWaQ8NJVA32l+qV/M393UeTHN0cAAAAwPUDqZiYGGnfvn2Rz/v4+JhcKbhHntSRhFRJSst0dHMAAAAA1w6k6tevL1u3bi3y+SVLlkizZs3K0i44WcGJPccYlQIAAADKFEjdcMMNMmXKFFm2bJltm5eXl/k6depU+eabb2T48OGlOTSctgQ6gRQAAABQpnWktFKflj7XhXc1H0qDKC2Bfvz4cTlw4IBceuml5jHcp+DE7lgCKQAAAKBMI1L+/v6yYMEC+eSTT6RJkybSqlUrSUtLkw4dOsi0adNk7ty5Jk8Kro0S6AAAAIAdR6SUjkLddNNN5gb31KhGJdEZm1rdfidT+wAAAICyjUjpFL7169cX+fyGDRvkxIkTpTk0nEign4/UCQ0y93fHnsyzXhgAAADgyUoVSGn+k64hVZQ777xTHn744bK0C06iSVhOnlRCaqYcT0p3dHMAAAAA1w2kfv31V7niiiuKfH7gwIHyyy+/lKVdcBJU7gMAAADsFEjFxsZKzZo1i3y+Ro0aZtFeuFcgtYs8KQAAAKD0gVTt2rXl33//LfL51atXS1hYWGkODSfDiBQAAABgp0Bq0KBB8tFHH8mcOXMKPPfDDz+YsuiDBw8uzaHhZJqGVbbd3xV70qFtAQAAAFy6/PkzzzxjcqA0WIqMjJR27dqZ7Rs3bpR169aZRXrHjx9v77bCAepUDRJ/H29Jz8qW3UztAwAAAEo/IhUaGirLly+XJ598UjIyMmTWrFnmpvefeuopWbFihVStWpVT7AZ8vL2kYY1gc3/PsWTJyqYEOgAAAFDqBXkrVapkRp0YefKMPKn/Yk5Kema2HIpLkfrVcwIrAAAAwFOVakQqMzNTEhISinxen9N94B4an1pLSjG9DwAAAChlIHXfffdJjx49iny+Z8+e8tBDD3F+3USTXCXQCaQAAACAUgZSCxYskGuuuabI5/W5efPmcX7dRJNclfsIpAAAAIBSBlKHDh2SunXrFvl8nTp15ODBg5xfN1xLaicl0AEAAIDSBVI1atSQbdu2Ffn8li1bJCQkhNPrJmpU8pcqgTl1SRiRAgAAAEoZSPXv31+mTJki//77b4Hn1qxZIx988IEMGDCA8+smvLy8bHlSB+NSJDUjy9FNAgAAAFyv/Plzzz1n8qS6du0qV1xxhbRt29a2IO/cuXOlVq1aZh+41/S+dQfixWIR2Xc8WVqEV3F0kwAAAADXCqQ0B2rVqlXy2GOPyQ8//CCzZ88223U634033igvvvii2Qfuo3HN0wUndsUmEUgBAADAo5V6Qd7atWvLp59+KhaLRWJjY822sLAwMw0M7qcJa0kBAAAAZQ+krDRw0ql88JzKfbuo3AcAAAAPV6pA6tlnny1WgPXUU0+V5vBw8kCKyn0AAADwdKUKpJ555pkzBlA63Y9Ayr1UCvCV8JAAiU5II5ACAACAxytV+fPs7OwCt8zMTNm5c6c88MAD0rlzZ4mJifH4k+uuo1LHktIlPjnD0c0BAAAAXCuQKvRA3t7SuHFjef3116V58+YyevRoex0aTli5b/exJIe2BQAAAHCLQCq3888/X+bNm1ceh4YDNc1Tue8krwUAAAA8VrkEUrrGlI5QwY0LTsQyIgUAAADPVapiE5999lmh2+Pi4uTPP/+U7777Tm677baytg1OHEjtPEogBQAAAM9VqkDq5ptvLvK5mjVrymOPPSbjxo0rS7vghOpXDxYfby/JyrYwIgUAAACPVqpAavfu3QW2abnzatWqSZUqVezRLjghPx9vaVA92JQ/15u1zD0AAADgaUoVSDVs2ND+LYHLTO/TIColI8usKRURGujoJgEAAACuEUjlt3XrVpk5c6YcPnxYWrZsKSNHjpSQkBB7HBpOpknNSvLrqfu7jp4kkAIAAIBHKnYg9e6778rbb78tS5cuNXlQVnPnzpUhQ4ZIenq6bds777wjy5cvz7Mf3EPjPCXQk6RHU15jAAAAeJ5i1yifM2eONG3aNE9wlJmZaarz+fj4yCeffCIbNmyQl19+Wfbu3SsvvPBCebUZTlK5bxcl0AEAAOChih1Ibd68Wc4999w823777TeJjY2VBx54QEaMGCFt27aVRx55RK699loW5HVTTWpWzjMiBQAAAHiiYgdSx44dk/r16+fZtnjxYlO1bfDgwXm29+zZU/bt21fqRk2aNEkaNWokgYGB0q1bN1m5cmWxvm/GjBmmPYMGDSr1z8aZhYcESJCfj7lPIAUAAABPVexAKjw8XI4cOZJn219//SXBwcESGRmZZ7u/v7+5lcbXX38tDz74oDz99NOyZs0ac+x+/fpJTEzMGb9vz5498vDDD0uvXr1K9XNRPBqoWqf37TueLBlZ2Zw6AAAAeJxiB1KdO3eWTz/9VBITE83jTZs2mZEiDXJ8fX0LVPGrV69eqRo0ceJEuf32203lvzZt2sjkyZNNsPbxxx8X+T1ZWVly4403yvjx46VJkyal+rkovgY1gnPOe7ZFrnl/qdz1+Wr5bs0BSc3I4jQCAADAIxS7ap+OEHXp0kWaN29ucqFWr15tRifGjh1bYN/Zs2dL7969S9wYrfynx819TG9vb+nTp48sW7asyO979tlnpVatWnLrrbeaUbIzSUtLMzerhIQE8zU7O9vc7EGPo4vV2ut4zuSXLdHy29bTo4PrDsTLhoPxsmDTEXlmziaZMKSDXNw63KFtdHXu3H9Q/ug/oO/AEXjvgbv0n5K0odiBVPv27eXXX3811fh27dplCk/oVLpOnTrl2e/33383I0haEr2kjh49akaXdBphbvpYR7kK8/fff8tHH30ka9euLdbPeOmll8zIVX5aNCM1NVXs9QLEx8ebDqGBoLv4c2ecPDp3p1jybc8+tSExNVPu+HyNvDKwqZzftKojmugW3LX/oGLQf0DfgSPw3gN36T/W2Xd2X5C3R48e8tNPP51xnwsvvNCUQa+oX3TYsGEyderUYq9ZpaNdmoOVe0RKi2iEhYXZbRFh7Qw6WqfHdHRnsJe0jCx5/ud1Z9xH4ykvEXn+572yonNTCThVlAIl4479BxWH/gP6DhyB9x64S//RYnflEkiVNw2GdE2q6OjoPNv1cURERIH9d+7caYpMDBw4sMBwnOZtbdu2zax9lVtAQIC55acvmj1fOO0M9j6mI83fdEgSUjPPup8GU7rfgs3RMvic0uXJwf36DyoW/Qf0HTgC7z1wh/5Tkp/vVFdpWulPpwpqWfXcgZE+7t69e4H9W7VqZUa/dFqf9XbFFVfIRRddZO7nL9eO0lu0KVq8dbipGHS/hRvzBsMAAACAO3GqESml0+50cV+tEti1a1d58803JSkpyVTxU8OHD5e6deuaXCcdemvXrl2e769aNSc3J/92lE1ccrotF+psdL+4lHROOQAAANyW0wVSQ4cONYUfxo0bZ9atioqKkgULFtgKUOhCv44e8vNEVYP9zUhTcYIp3a9qUOnWEQMAAABcgdMFUmrUqFHmVhitCngm06ZNK6dWeba+bcNNifPi0GCrXztKoAMAAMB9MbSDYrm0fW0JCfI1VfnORJ8PDfKVAe1qc2YBAADgtgikUCyBfj4ycUiUiZSKCqbMdi+RCUOizP4AAACAuyKQQrH1aRMuHwzrbEamCqPbpw7rbPYDAAAA3JlT5kjBeV3SJlxWPN5H5m88LG8t/k/2HE0222/v1Vge6tuSkSgAAAB4BEakUGI6bU8X2324b0vbtmB/X4IoAAAAeAwCKZRaZL2cNbvU+gNxnEkAAAB4DAIplFq9akFSLdjP3F9/IF4slmKu2AsAAAC4OAIplJqXl5e0PzUqdSwpXQ7Fp3I2AQAA4BEIpFAmkfVCbffX72d6HwAAADwDgRTKpH3d04HUugPxnE0AAAB4BAIplElk/dMFJzYcZEQKAAAAnoFACmUSHhIo4SEBtoIT2dkUnAAAAID7I5BCmXU4VXAiMTVT9hxL4owCAADA7RFIocw65MqT0lEpAAAAwN0RSKHMOuTKkyKQAgAAgCcgkIKdR6QoOAEAAAD3RyCFMqtWyV/qVw8y9zceipfMrGzOKgAAANwagRTsWnAiNSNb/os5yVkFAACAWyOQgl1E1js9vW8DBScAAADg5gikYNcRKbWOPCkAAAC4OQIp2EW7uqHi5ZVzn8p9AAAAcHcEUrCLygG+0jSssrm/9UiCpGVmcWYBAADgtgikYDcdTuVJZWRZZOvhRM4sAAAA3BaBFOyG9aQAAADgKQikYDcd6ucuOBHPmQUAAIDbIpCC3bSpHSK+3jkVJyiBDgAAAHdGIAW7CfTzkZYRVcz9/2ISJTk9k7MLAAAAt0QghXIpOJFtEdl4MIGzCwAAALdEIIVyW5h3PQvzAgAAwE0RSKFcRqQUC/MCAADAXRFIwa5ahFeRAN+cbsWIFAAAANwVgRTsys/HW9rUCTH39xxLlvjkDM4wAAAA3A6BFOwuMlee1IaDrCcFAAAA90MghXLNk1pHwQkAAAC4IQIplHPBiTjOMAAAANwOgRTsrknNylI5wNfcp3IfAAAA3BGBFOzfqby9pF3dnIITh+NTJSYxlbMMAAAAt0IghXJfmHfDAQpOAAAAwL3kzL8CyrXgRLxc3DqccwwATig1I0vmbTgsCzcdkdi4JAmrekD6tY2QS9vXlkA/H0c3DwCcFoEUyr8EOgUnAMAp/bw5Wh6auVYSUjLF20sk2yLifeikLNwULc/M3SQTh0RJnzZ8EAYAhWFqH8pFvWpBUi3Yz1ZwwmKxcKYBwMmCqDs+XyWJKZnmsQZRub/q9ts/X2X2AwAURCCFcuHl5SXtT41KHUtKl4NxKZxpAHCi6Xw6EiUW869QZrtF5OGZa83+AIC8CKRQbiLzrCdFwQkAcBaaE6XT+c42V0Cfj0/JlPkbD1dQywDAdRBIoUIq9xFIAYDzWLQp2uREFYfut3Aj0/sAID8CKVRI5b71FJwAAKdxJCHVlgt1NrpfXEp6eTcJAFwOVftQbsJDAiU8JECiE9LMWlLZ2RazWC8AoOLpe/Af/8XKF8v2ytr9ccX+Pn3brhrkX65tAwBXRCCFcp/epxWfEtMyZc+xJGkSVpkzDgAVKC45XWauOiBfrNgre48ll/j7dUSqY8PTU7UBADkIpFDuBSespXM1T4pACgAqhs4E+GzZHpmz7pCkZWbnea52SIAcT86Q9MzssxacUO8s/k9ahFeRC1vWKrf2AoCrIZBCubKWQFfrDsTJoHPqcsYBoJxomXKtyPdZEdP3zmtWU4Z1bygXt6olv2+LNetEeRVRAl0nYlu3J6Zlychp/8jDfVvKPRc2NUtcAICnI5BCuepQlxLoAFDe9h9Pli9X7JNvVu2X40l5C0NUCfSVazrVk5vObShNc02v7tMmXD4Y1tmsE6UlzjUXSqfxWb+GBPnK84Paydx1h2XR5mjRddVfW7hNNh2Kl9euiZRKAVxCAPBsvAuiXFWr5C8NqgfLvuPJ5o9vZla2+PpQLBIA7FE84k8tHrF8ryzeGmMCndxaRVSR4d0byaBz6kiwf+F/7i9pEy4rHu9j1olasPGIxMYnSVhoJenfLkIGtKstgX4+cln7OvLubzvkjV+2m58xb8MR2RmTJFOGdZJGNSvxQgLwWARSqJAy6BpIpWZky38xJ6V17RDOOgCUoXjErNUHTAC1J1/xCD8fLxMADe/eUDo1rFasKXgaLA0+p55cGVlHYmJipFatWuLtffoDL622et/FzaVtnRC5f8ZaUzxoW3SiXPHu3/LW9efIReRNAfBQBFKokEDqx/WHbetJEUgBQMltPJhTPOKHtYUUjwgNlBu7NZChXRpIWJWAcjm9F7cOlx9G9ZQ7Pl8tO2JOSkJqptxC3hQAD0YghQopgW617kC8DO3CSQcAexePqIhp01p5dfY9PeShb9blyZvSIO/1IeRNAfAsBFIod+3qhorOLtE/uFqOFwBQhuIRAb5ydad6JoDKXTyiolQJ9JPJN3WSSb/tkImn8qbmbzwiO2NPmuIV5E0B8BQEUih3lQN8zR97nQqy9UiCpGVmSYCvD2ceAPIVj/hrx1H5fNmeUhePqCiaNzVa86bqhsiYr3LyprZHnyRvCoBHIZBCheVJaSCVkWWRLYcTJar+6el+AODJ4pMzZObq/XYrHlGRercibwpA2acvL9x0RGLjkiSs6gHp1zZCLm2fUzXU2RFIoUJE1qsq3605aO5vOBBHIAXA42le0efL9soP6w6aqqb5i0fc0LWBDO1aX2pVCXTqc6V5U9/f21Me+matLNx0Om9Kp3K/fm2kmZUAAPn9vDlaHpq5VhJyr2N36KR5H3lm7iaZOCTKrHfnzHh3Q4WNSOUuODGM8w7AA+nUZmvxiH/3FSwe0bNZDRl2biPp07piikfYiwZL79/YSd77fYdM+Dknb2rBpiOyc9JJ+WB4Z2nMelMA8gVRd3y+SuTUFObsfF8TUzLl9s9XmbxLXe/OWRFIoUJoyXNfby/JzLaYEugA4EkOnMgpHvH1P0UXj7jp3IbSrFbFF4+wZ97UqN7NpU2dEBmj602lZpq1A3W9qbevO0cualXL0U0E4CTT+R6audYEUflSQW10u5dF5OGZa82i4c46zY9AChVC/wO0jKgimw4lmFyppLRMqcR0DwAeUjzi160xtk9acxeP0Mp7g6LqutX7oeZNzRl1ntzx2SoTSGlAdcun/8hDl7SQey9q5nR5XgAq1rwNh810vrPRt8z4lEyZv/GwWTTcGbnPOzecXts6oSaQ0ouJIZOXSYPqwdK3bbjLJBQCQFmLR+jI/ID2OcUjOjth8Qh70al8s+/tKQ9/s85M8dOpfq8v2i4bDyaQNwV4uEWbom05UWej+y3cGE0gBc+mc2HnrMspNqE2H04wpdD1D6yrJBQCQGmLR0SEBMoN3RrIdS5QPMKueVM3dZT3ft8pry/aRt4UACMuOb1YQZTS/eJS8k6HdiaMSKHCEwqtXC2hEACKKh6hAdSaIotHNJQ+rcNdqniEveiIm07na1M7RO6b8W+evKm3rosy0wABeA6LxSIJqWef1pd7RKpqkL84KwIplCt3SigEgNzFI6afKh5xzE2LR9iTFprInzd166er5ME+OXlTWqgCgHs7GJcij85ab2YlFZd+6N6vnfN+4EIghXLlTgmFADybFo/4e8dRU7r8163RHlM8ojzzprRU+sZD8TLh2ijWmwLceBRq5uoD8tzczZKYVvzRKP14JSTI1yxK7qx4p0e5cqeEQgCeXTxCy5fvPppUaPEInb7XpZH7Fo8oz7wpXXxz56Ql8sGwTmZxXwDuIyYhVcZ+t0EWb43JkzOq+aJvLf6vyBlL5p3US2TCkCinnqlEIIVy5U4JhQA8y6ZDOcUjvl9L8YhyyZvS9aa++tfkS+iyGFdOWkLeFOBGo1Bz1h2ScT9skviUDNv2qzvWk3ED20hokJ+p5qxpHTojyfqhu/WrjkRNcIFCZARSKFdVg/1LNCLlzAmFADyjeMT8DUfks2V7Ci0e0aNpDVO63FOLR9jTRS1P5U19vkq2R5/Om3qgTwsZRd4U4LKOnUyTJ7/fKPM3HrFtq1k5QF66qn2eomJ6X3PjNa1jwcYjEhufJGGhlaR/uwgznc+ZR6KsCKRQrnSdKJ0L7w4JhQDcOwn6y+V7Cy0eodPRru5Y1+Q/NatVxWFtdEeNalaS7+7pKf+buc5cdOlUv4maN3UwXiYOJW8KcDULNh6WJ2ZvzPM+enmH2vLcle2kWqWCH5ZrsKQpHVdG1pGYmBipVauWeHu7zodUBFIoV7rYrq4TpSXOzzYo5ePtJd2b1OAVAVChxSM+X75XFm8pWDyiZXhO8YjB51A8ojxpoPrejXnzphZtjpZB5E0BLpVL+vScjfL92kO2bdWC/eS5Qe3k8g51xF0RSKFc6ScNutiurhOlJc7PFExlZVvk+qkr5JObu5hPKQGgPOh8/VmrD8gXy/cWWjxCp5Vo8YiujatTPMLReVPvLpE3r4uSi1szWwFwVr9tjZFHv10vMYlpeabtvTi4vYRVCRB3RiCFcqeJgrrYblEJhZUCfMTby8vMj9eLmsHvLZEPR3SWTg2r8+oAqJDiEeEhAXJD14Zyfdf6UiskkLPuLHlTaafzpkb3Zr0pwJkkpmbI8z9uka9X7bdtqxLoK+OvaGtG8j2hiimBFCpE7oRCLXGu1fm0sITmRGlC4dGTaXLLtH/MH84TyRlmZGrCkEgZGOm+w8EAKq54hE7fW733RIHndTqxKR7RJlz8KB7hFHRGwmzNm5q1TuZtyMmxfeOX7SYQnnBtpFQJ9HN0EwGPt2THUXlk1nqTX2p1QYsweeXqDhIR6jkfRnlZtD6hB0tISJDQ0FCJj4+XkJAQuxwzOzvbJRPmnGG6zb1frjE5C1aP9G8pd1/Q1CM+1bCi/4D+U3b6x336ipziEUdPFl484qZzG0rzcIpHOOt7j16evP/HTnltYU7elGoaVkk+GN5ZmrLelNNxtv6D8pGcnikvz99qFia3quTvI09e3kau61K/1NdrztR/ShIbMCIFp6FrCnwysos8MXuDfLPqgNn26oJtsu9YsklW5NNiAGcrHrFk51HzB76w4hEtwivLsO6NzJQTDabg3PSC7J4Lm0mb2iFy36m8qZ2xSTKIvCnAIf7Zc1wenrlO9h5LzjOq/+o1HaR+9WCPfFX4SwKnosGSDgs3qB4sry/abrbN+Ge/+XR50o0dJYQpHQAKGc3+9lTxiF2FFI/o1y5ChlM8wmVdeCpv6s7PV8u26ETypoAKlpqRJRMWbZMP/95tGx0O9POWx/q3kuHdG4m3Jr17KKcce500aZI0atRIAgMDpVu3brJy5coi9506dar06tVLqlWrZm59+vQ54/5wjU8hR/Vubla49z+Vs/DXf0dlyPvL8szFBeDZNh9KkLHfrZdzX1wsz/64OU8QpcUjtEDB0sd6y6QbOkq3JjU8aoqwe6431UMubR9h26Z5U3d+sdokvAMoH2v3x8llb/8lU/86HUR1alhN5o85X27u2dijgyinDKS+/vprefDBB+Xpp5+WNWvWSGRkpPTr18/MmyzM77//Ltdff7389ttvsmzZMqlfv7707dtXDh48WOFth31dGVVXvritm1QNzkks1k8iB09aIhsOxHOqAQ8uHvHD2oNy9ftL5dK3/5KvVu6XlIysPNNMdE2ivx/tLWP6NKcCnxupFOBrguJH+7cSa0z886n1pnbGnnR08wC3e699beFWueo9/f+V8yGVv6+3PH5pK/nmzu7SmGVqnLPYhI5AdenSRd59911b8pkGR6NHj5bHHnvsrN+flZVlRqb0+4cPH37W/Sk24fx2xZ40Ff32nJqTG+TnI+9cf46psuWOnCnhEq7HXfvP2YpHXNWxrln7ieIRntF3/tgeK6OnrzF5U6pKgK+8MTTKbf8uuAJX6j84M62Q+dA362TrkUTbtg71Qk015fJ6j812ov7jssUm0tPTZfXq1TJ27FjbNj2ZOl1PR5uKIzk5WTIyMqR69cLXIEpLSzO33CfL+gLqzR70OBqf2ut4nq5RjWCZdVd3Mz9+9b448+mzrjHy1GWtZUSPRuJu6D+g/+TQ99ElO4/JF8v3yS+FFY+oVVluOreBDMpVPIL3Xc947+nVrIb8cG8PufOLNbb1pm77bJWMubiZjL6I9aYcwZX6DwqXkZUtk//YJe/8ukMyT73h+vl4mf9Td17QxOSxl9frm+1E/ackbXCqQOro0aNmRCk8PO8nSvp469atxTrGo48+KnXq1DHBV2FeeuklGT9+fIHtsbGxkpqaKvZ6ATSK1Q7h6KjanUy8orE8t2iP/LL9hLmgGv/jFtl28JiM7lVPfNxoji79B57ef3Rx7nlbjsm362Nl34nTH3wpTZu8sGk1uToyTM6pW9nkPSXHH5fTNaTgKX0nSEQmX91MXvh5ryz+L2eNsLcW75A1u2PlmX6NzWLvqDiu1n+Q1+5jKfLsoj2yJfr0u2mzmkEyrm8jaVErWE4cO700jbv3n8TE0yNxLhVIldXLL78sM2bMMHlTWqiiMDrapTlYuUekdOpgWFiYXdeR0j/uekxHdwZ3M3l4uEz4ebu8/8cu83jGvzFyLFXkjaGREuzvHt2Z/gNP7T9bDieY0afv1x7Kk/ekalUJkOu71jfrlISHeM5ijxXJVfvOBzdHyJQ/d8lri7abZPi/dsXL7TP/kyk3dZSmtSo7unkew1X7j6fLyrbIR3/vlom//CfpmTkjMfrh9F3nN5HRvZuZvChP6z+BRcQQhXGqK8+aNWuKj4+PREdH59mujyMiTlfqKczrr79uAqlffvlFOnToUOR+AQEB5pafvmj2fOG0M9j7mNDXSeTRAa2lYY1K8sT3G80bwM9bYuSGD1fKhyM6S60q7nGBRf+Bp/Qf/cM9f+Nh+XzZXlm1N2dUIbdzm1SXYec2kr5tw1lLrgK4Ut/J7Z6LmkvbulXNelNaDl8rOA5+f5nJm7qEvKkK46r9x1PtPppk1oVaneu9Vxe9nnBtlETVr+qx/ce7BD/fqXq6v7+/dOrUSRYvXpwnQtXH3bt3L/L7Xn31VXnuuedkwYIF0rlz5wpqLRzpuq4NZNrILibBWK0/EC+DJy2V7dHFH44F4DiH4lLk9YXbpMfLi2XMjLV5gqhK/j6mcMSiB86XGXd0l8s61CaIwlld0CJM5ozqKa0icpLhT6Zlyu2frZI3f9luFmsGkEP/P0xbslsGvPWnLYjSSpi392osP93XyyFBlKtyqhEppdPuRowYYQKirl27yptvvilJSUkycuRI87xW4qtbt67JdVKvvPKKjBs3TqZPn27Wnjpy5IjZXrlyZXOD++rVPExm3t1dbvnkHzkUn2qqemlJ5Mk3dZKezWo6unkACiseseOYfL58jylbnf/atnmtyjK8e0MZ3LGerXgEUBI6W0HXm/rfrPXy0/rDZtubv/wnGw8myMShkSzqDo+3/3iyPDJrvSzbdSzX/5tgeX1IpHRpVHihNhTN6f5SDR061BR+0OBIg6KoqCgz0mQtQLFv3748Q27vv/++qfZ3zTXX5DmOrkP1zDPPVHj7UbFaRYTI7Ht7yq2f/mP+UGqS+oiPV8qLV7WXazvX5+UAnIBOtfpuzQH5fPle2XVqPRIrX28v6dc2QoZ1byjdGldn0VyUmebLvnv9OdK+bqi8umCrCdi16qOuN/XBsM7SjLwpeOgHWTP+2S/P/7hZktJP56CO6N5QHh3Qym3yzMXT15GqaKwj5R6S0jJlzIx/5ZctpxduHnVRM3mobwuXuzBzprUU4Hqcqf9o8YjPlu2V7/89WGjxiBu6NZDruzageISTcKa+Yy9/6npTp/KmlI50kjdVPtyx/7iLw/Ep8ti3G8z6a1Z1qwbJq9d0cJoZPNlO1H9cdh0poCwr3k8Z1lme+3GzTFu6x2x797cdsu94srw2pIME+FIGF3CG4hE66jS8O8UjUDHObxEmc0edZ9Ye1MVFrXlTYy5ubm7ebrR0BpCfjpV8t+agPDN3k5mxYzW0c3158vLWUiXQj5NWRgRScBtarvOZK9pKg+rB8txPm00Z3DnrDplPYnQ6R7VK/o5uIuDWxSO+WrlPvlq5X46ezLv2kxaPuKpjPTN9r0V4TiEAoKI0qBFcIG/qrcX/yaZD8TJxaBR5U3BLsYlp8vjsDSYf1So8JEBevqqDXNSqlkPb5k4IpOB2bjmvsdSrFiT3zfhXUjOy5Z89J+Sq95fKJzd3kUY1Kzm6eYBbfdq5dOcx+WzZHjOtVpcjyF88QoOnwefU5ZNPOGHeVAx5U3BL+oHBk99vkBPJOVNalb4PPzOwrYQGMwplTwRScEt920bIN3d2l1umrTKfjutaCYPfW2LWmurUkKo0QFkkpGbIt6sLLx6hI8P92oabtZ90DShXy1GE+9K+eNcFTaVN7RBb3pT2Xy1CMfHaSPN3A3BlJ5LS5akfNsqPp0ZeVY1K/vLC4PbSvx39uzwQSMFtdahXVb6/t4fcMu0f2R590nwyc/3UFTJhSKQMjKzj6OYBLmfrkdPFI5JzVX2yFo/QwhF6iwh1j4Wx4Tl5U3d8vlruu7i53E/eFFyUTuEb+92GPFOrB7SLkOcHtZMalQMc2jZ3RiAFt1avWrDMvKuH3PvlGvl7x1GTCK+fRO4/kSx3X9CUT8uBs9D/Mws2HZHPl+0x02QLKx6h0/e0hLmfD5W64Fp5U7qejvXT+7c1b+pgvLxxHXlTcB06sjp+7iZTVMIqNMhPnr2yrVwRWYfrnHJGIAW3p28on4zsIk/M3iDfrDpgtr26YJvsO5Yszw1qx8Wfi0jNyJJ5Gw7Lok3REpecLlWD/aVv23C5tH1tCfSjKqO9aZGW6SuKLh4xuGNdM32vZQTFI+C6eVPvnMqbeuVU3tTirTEy6N0l8sHwTtKsFn0bzk3LmT86a70cSUi1bbu4VS156ar2UiuEmQEVgUAKHkE/KX/l6g5m1fvXFm4z23RhuoNxKTLpxo5UbXKBKQsPzVwrCSmZotWK9YJHv+pIiZZ1nTgkSvq0yVm0G2UvHqGly3/eEl2geIQuZDqc4hFws7ypOzVvqk6IjJp+Km/qqOZNLZUJ10aakVbA2eh01Bd+2mIqpVpVCfCVcQPbyDWd6jEKVYFYkLcEi2654qJiKOiHtQflfzPXS3pWtnncMryKfDyyi1mczhnQfwoGUZrLIBbzrwBTysBLTIn7SwimStV/tHjEd6eKR+wspHhE3zbhZvpe9yY1+APtxjz9vUdnKVjzpqzu691M7u/TgvWmisHT+09FWbbzmPxv1jo5cCLFtq1X85rmw+I6TnId4+r9hwV5gTO4Mqqu1A4NMn8w45IzZFt0ogyetEQ+GtFF2tcL5dw52XQ+HYkqKohSut3LIvLwzLWy4vE+TPOzU/GIsFPFI26geAQ8LG/q0W83yNx1h8y2t3/dIRsPJcgbQ6PMNHHAUVLSs8wU1GlL99i2Bfv7yOOXtpYbuzXgQy4HYWofPFLXxtXlu7tzKvrtOZYsMYlpcu2UZWa+PFPEnIfmROl0vrPRYCo+JVO+W3NAhnZpYEZRPDWHbOGmIxIblyRhVQ+YaUn5c8isxSO+WLZXVu45Xuj/DZ2+R/EIeGre1NvXRUn7uiHy8vycvKlfNW9q0hL5YFgnac6C0nCA1XuPy8Mz15ulXHK/V79+TaT5AACOw9Q+pvZ5tONJ6XL7Z6tk9d6camR6/T3u8jZyc8/GDmuTMw1vO9pdn6+WRZuPmIuZktBP6SoH+ErlQN+cr9Zb7seBvmZOeaU8j/3M10oBPuZ+oJ+3S3zKV1QOmX4NCfI1OWRt64bIV1o84p/9ZsX7/Ofrqo515aZzG0qrCPtMcYbr4b0nr7/+izVVXnXmgrXIysShUeRN0X8q9AOyN37ZLlP/3GX7Oxjg6y2P9G8lI3s0cqspp9lOdO1TktiAQIpAyuPpG9XDM9flWcDulp6N5YnLWjtkZMOZ3kwc/bpc9vZfBXJ2KpK+/kUGYoUEZoXtU8UEZr7lVh3ybDlkVtbAKn/xiGHnNjRBVJVApi15Ot57Ctp/XPOmVsuWwwm2beRN0X8qwoYD8fLgN2vlv5iTtm3nNKgqrw+JlKZhlcXdZDvRtQ85UkAJ6LSnt687RxpUD5b3ft9ptn28ZLdZa+qt66LMVA9UnD1Hk2T6yn0yc9V+s4hySegK7g1rBJuKRidTMyVRv6ZliqWEI1pWWrVOq3jpraz0U8QquYKtSv6+eR9r0GULyvykcoCOqvkVCNaC/Xxsn0IWJ4fMyhpEUTwCKL761YPNNPBHv10vc8ibQgXQ6dfv/rZDJv22w1Y51d/HW+6/pLnc0auJ+LJen1PhChHQT+u9vcxQuQZTT3y/0bx56Sf9132wXD4c0VlqVWE9hvKUmZVt1m/5Yvle+eu/o6U+zpOXt5bB59QrUNI7JSPrdGCVmilJaafvm6DLejv1OPHUPtbt1sd6nNJKy8yWtJPpcvRkupSFzjSs7J8TeGVbLMXKIbPS6nvjr2xriq0AKJ4gfx/zoZquN/XS/C3kTaFcCwA9+PU62ZxrBLRtnRCZeG0Ua/Y5KQIpIJfrujaQutWC5J4v1pgL7fUH4mXwpKVmQd8WJBnbXXRCqlkHY8bK/XkWFLR+AtevbbhJ9NaKcmcacdHxGc0FGtCudsHnvLzMqKLeatkh4EtKy5LEtAwTYJmAzBqMpRYSkJ3aJ0+Alp7zNf8aTcWlo2t6XL2VhA5ieXt5EUQBpaDvI7ef30Ra1w6RUV+tMXlTmvivRSgmXBsl/dux3hTK9rdlyp+75M1ftktGVs7fBl9vL7n3omYyqnezcpsajrIjkALy6dU8TGbe3V1u+eQfORSfahbtvfr9pTL5pk7Ss1lNzlcZZWfnLPqqo0+FLfqqo4I3dGsgQzrVkxqVA+SXzdFy++erTInzM60jNWFIVLmXPtcpFaHBeitbPpGOkukIVe6RL1tAZoK0nBE0c998zTq1/fSURf0+LRpR3HhM94tLKdtoGODpzmteU+aOOk/u/Hy1GTVISs+Su75YLaN7N5MHWG8KpbAj5qQ8NHOdrNsfZ9vWIryyGYVqV5clWZwdgRRQCK1cNvvennLrp//IxoMJ5iJ3xMcr5cWr2su1netzzkrhRFK6zFp9wOQ/5S7hah0tubh1uFkL4/zmYXkqEWk5el1sV9eJii+iKp0GUa5Utl4/3dagT2+6XlNFVDXU81U1yL/UPwvA6bypb/PlTb2j600djJc3rzuH9aZQ7A8VNR/7tYXbzAdr1vfpOy9oKvf3aS4BvuX7wSDsg0AKKEJ4SKB8fUd3GTPjX/llS4xkZlvkkVnrZd+xZHmobwuXKIvtaDry8u/+ODP6pFURNYk2t1pVAuS6LvXNlMozrch+SZtws9ju/I2HZeHGaDOyokFBv3bhZjpfeY9EOau+bcPNmlDFocGWni8A9sub6lAvVF6cl5M39du2WLny3b/lg+GdmQqOM9p7LEn+N3N9nrX8mtSsJK9fGykdG1Tj7LkQyp9T/hxnoVPPnvtxc57VxK+IrCOvDelQLp8YOVMJ0NLSaWffrz0oXy7flydp1qpnsxpyU7eGZhSJud+lp1X7ur74iySmZBYrh0yDUU8NOuEZ7z2OsGTHURk1fY2tyqiuNzXh2kjpX0jOpjuj/xTnHFnkyxV75aX5W03ub+4lV/7Xr6UJ0D1VthO9/1D+HLAjLRf9zBVtTe7Ocz9tNsn+Op3jcHyKmXJWrRLTpay2HUk0o0+z/z1o8nlyCw3yk2s61TP5T+64BoYjaFCki+06Sw4Z4Ik0d3ZOgbypNTLqombywCUtHLIeIZyP5ls/Omu9/L3jdGXa+tWD5LVrIuXcJjUc2jaUHiNSjEihBBZtOiJjZqy1lcFuXLOSfHJzF2lUs5JbfipTHGmZWTJ/wxHzKds/e04UeD6yflW5qVsDGRhZhwv5cqKl+ovKIQt1wRwyOIarvfc4m5T0LHnsu/Xyw9qcvCl1Ucswj8mbov8UPcV95qoDZmZL7mqrmhP8+KWtzVIWEKfqPyWJDQikCKRQQusPxMkt01bJ0ZNp5nG1YD+z1lSnhtXd7s3kTDRX7MuVe80fiONJeavBBfn5yKBz6siN3RpSdagCp/lpDtmCjUckNj5JwkIrmZLMnpxDBvd873H2i+aP/t5ty5tSjWoEe0TeFP2noJiEVHnsuw1mGQ+r2qGB8srVHeT8FmEV+vo4u2wnev8hkCqnk+WKnQHl48CJZLll2j+yPfqkeezv6y0ThkSaURd37j+61oX+QfhyxT75879YM80xt+a1KstN5zaUwR3rSkig+38C64ycuf/AudF37GfpjqNyb668qWDNmxoSKQPau2/eFP0nb0CtKQDjftgk8Sk5fUDp9PanLm/jESOUrtx/yJECylm9asEy864ecu+Xa8x8Z61GN/qrf2X/iWS5+4KmblfRTz9Vm/HPfrN47uH4vAvn+vl4mVEPDaC6NKrmdr87AJRUj3x5U1pY4O4v18i9FzWVBy9pSd6UG9PZKk99v1HmbzxdUVWXuXhpcHumWLshJmYCpaSfKH0ysos8MXuDfLPqgNn26oJtZsrbc4PauXw1Ov1EbZkunLtiryzaFG3Kv+dWr1qQKRyh62rVrFz6tZAAwJ3Xmxr73Xr5/lTe1KTfdsqmQwny1tBzyrywN5zPgo2H5YnZG+VYrunuWuV3/BVtKUzlpgikgDLQYEnnOjesUcksqqd05Ear80y6saNLTm+LSz61cO6KfbIr38K5OtjUu2UtM/qk87upRgUARdNy1m8MjTK5olryWpfT+H1brFwx6W9T9bVlhHvnTXkK/bv59JxNeQqNVK/kL88PaieXuvF0ThBIAWWmU9nuvaiZGaHRBfbSs7Llr/+OypD3l8nHI7tI3TMsNOtMo09r98eZ3Ke56w7ZVlm30hGnnIVz65tpjQCA4v+NuK1XE2lTO8SWN7X3WLIMfm+J2+dNeYLftsbIo9+ul5jEnAJUqm+bcHlhcHszpQ/ujREpwE6ujKortUOD5I7PV0lccoZsi06UQZOWyMcjukj7eqFOeZ6T0zPNJ2i69pNON8mve5MacuO5DaRvmwhTUAMAUPq8qbmjc/Km9P3Wmjd1z4VN5aG+5E25msTUDFPS3Dq1X4UE+sr4K9vKoKi65At7CAIpwI66Nq4u393dw1T023MsWWIT0+TaKcvknevPcaok0+3RifLl8r3y3ZqDeda1UFUCfU1lIS1d3qwWC+cCgL3oiP6su/LmTb33e07e1Nu63hR5Uy5hyY6j8sis9WYav9WFLcPk5as6SERooEPbhopFIAXYWZOwyvLdPT3l9s9Wyeq9J8zivTpKNe7yNnJzz8YOXThX1xj6cvk+WbnneIHnO9QLlZu6NTQl3HVePwCg/PKm2teratab0rypP7aTN+UKktIy5eX5W+Xz5Xtt2yoH+MpTl7c2hZeoWut5CKSAcqBJpl/e1k0enrlOflx/2CzM+MzczbLveIo8cVnrCi3SsP94skxfuU+++Wd/nkpCKtDPW66MrGum73WoV7XC2gQAnkwvuG89r7G0rl1FRk3/1yxqbs2ben1IJAUKnNDK3cfN3/R9x5Nt23o0rSGvXtOB3GEPRiAFlJNAPx8zVaNB9WAzdUN9vGS3WWvqreuiJNi//P776SecmgCrpcv1k878C+fqlL0buzWQqzrWY2FAAHCQHk11vameefKm7iFvyqmkZmTJ6wu3yUdLdtv+lgb5+cjYS1uZWRzeFfjBKJwPgRRQjvQN9pH+rUww9cT3G02A8/PmaLnug+Xy4YjOUquKfedSxySmmpGnr1bmlGDPv3Buv7YRpnR5t8bVmYIAAE6SN5Wz3tQGmf3vQbONvCnnoNVsH/pmreyMPb0USOeG1cyoYaOalRzaNjgHAimgAlzXtYHUrRYk93yxxhR3WH8gXgZPWmoW9G0RXqXsC+fuOmZynxZuOlJg4Vwtv25dOJdSrADgnDMYJl4bKe3rhsoLufKmBr77t3wwvJO0ighxdBM9iuYUv734P3n/951mar7SyrX/69tSbjmvMWsowoZACqggvZqHycy7u8stn/wjh+JTzYjR1e8tlfdv6iTnNa9ppg/M23DYBEOxcUkSVvWAGUHSxfz0j2x+8SkZ8u3qA/Llir15Pi2zLpx7UctaZvrehS1r8aYPAC6QN6UX6a1y5U1pPs5V7y2V166JlMs6sN5URdh0KF4e+madbD2SaNsWWS9UJlwbKc1qsYAy8vKy6MfZHiwhIUFCQ0MlPj5eQkLs84lPdna2xMTESK1atcTbm7V3kFd0Qqrc+uk/svFgzrpNvt5eptiDTulISMkUnW6tn4BZv4YE+crEIVG28unrzMK5e2XOukOSmpF/4Vx/M/J0fdcGUr86C+d6It5/QN9xfQdOJMtdX6y2/Z1Qd1/YVB524vWmXP29JyMr24xA6UiUdWaHTokfc3FzueuCpuLr43q/kyvJdqL+U5LYgECKQAoOKqE6Zsa/8suWmLPua/2TObx7Q1mzL042HIwvsI/mPN14bkPp35aFcz2dM/0xgmuh7zgXnaWQO29Knd8iTN6+LkqqBvuLs3Hl/qNrK+ooVO6/r60iqsjEa6OkTR2mVXpa/0koQWzA1D7AASoF+MqUYZ3l6Tkb5Yvl+864r3XI+NNlp9etUFUCfOVqs3BuA2lexjwrAIBz5k3pGn/P/5STN/Wnrjf17hLypuxEz+mHf+2SCYu2S3pWzgwPHfG758KmMrp3c5MXBZwJgRTgIPpm3bFBtbMGUvm1qxtiSq5eEVWnXEuoAwAcnzc1smdjU2zi3ulrbHlTWqzotSEd5PIOdXiJSmn30SSzLtTqvSfyLA0yYUikRNZnXUUUD1dhgAMt2hRty4Uqju5NashXd5xb3s0CADiR7k1ryNzR58mdn68yeVMpGVmmIIXe/18/582bckbZ2Rb5dNkeeWXBVluesRZour1XE3nwkhaFFncCisKYJeBAccnpxQ6ilMU20Q8A4El0KYtZd/WQq86pa9s2+Y+dMnLaP+ZvCc5u//FkueHD5TJ+7mZbENWoRrDMvLO7PH5pa4IolBiBFOBAmjBc3A8Sdb+qQc6XYAwAqBg6WqJluJ8e2MY2CmXNm9py+HSFP+SlBaqnr9gn/d/8U5bvOm7bPqJ7Q5k3ppd0blSdU4ZSIZACHKhv2/Bij0jpfv3a5ZRABwB4dt7Ul7d1kxqVcj5cs6439eP6Q45untM5HJ8iIz75Rx6fvUGS0rNso3vTb+sm469sR64xyoRACnAgXWxX14k626CUPh8a5CsD2rEgIwBA5NwmNWTO6POkfd1QczqseVMvzc+p8OfpdBRKF63v+8afZtTO6vqu9WXB/b2kR7OaDm0f3AOBFODo8rZDokykVFQwZbZ7iUwYEsX8bQCAjY6szLyru1zV8XTe1JQ/dsnNn6z06LypmMRUuePz1fLQzHWSmJpptoWHBMgnI7vIS1d1kCqBfo5uItwEgRTgYH3ahMsHwzqbkSllzZmyftXtU4d1NvsBAFAgb2pI3rypv/47KgPf/dsj86Z0emO/N/6UnzdH27ZpgY5F918gF7Ws5dC2wf1Q/hxwApe0CZcVj/eR+RsPy4KNRyQ2PknCQitJ/3YRZjof5VgBAGfLm2pdO0Tu/XKNHEtKl/3HU0ze1KvXdJCBke6/3pSusfXUDxvlp/WHbdtqVvaXFwa3l35tIxzaNrgvAinASWiwNPicenJlZB2JiYmRWrVqibc3g8YAgOLnTel6U3d9sVrWH4g3eVOjv9L1puLlkf6t3Ha9KR19GvvdBjl6Ms227bL2teW5Qe2k+qmCHEB54CoNAADATdSpGiTf3Nldru5Yz7Ztyp/umTcVn5IhD36zVm7/bJUtiKoa7CfvXH+OTLqxI0EUyh2BFAAAgJvNcHh9SAd5ppC8qc2H3CNv6o/tsSYX6rs1B23b+rSuJYseON8jpjLCORBIAQAAuGHe1M351psyeVPvL5E561x3vamTaZlmGt+Ij1fKkYRUs61KoK+8PiRSpg7vLLWqBDq6ifAgBFIAAABunjfVoV7OelOpGdly31f/ykvztkhmVra4kmU7j0n/N/+Ur1bus23r1bymGYW6plM9EzwCFYlACgAAwAPypjTYyJs39Y+cSHL+vKmU9Cx5Zs4muX7qcjlwIsVsC/b3kRcGt5PPbukqtUODHN1EeCgCKQAAAA/Im3rtmg4y/oq24nsqb+rvHUfliknOnTe1eu9xufTtv2Ta0j22bd0aV5cFY86XG7s1ZBQKDkUgBQAA4AF06tuIHo1M3pSuseTMeVOpGVny0vwtMmTyMtl9NMlsC/D1lnGXt5Gvbj9XGtQIdnQTAQIpAAAAT9KtSQ2ZM+o8icyXN/Wik+RNbTgQLwPf+Vum/LFLsi05285pUFXmj+klt5zXWLzddD0suB5GpAAAADwwb+rrfHlTHzg4byo9M1sm/rxdBr23RP6LOWm2+ft4y2MDWsmsu3pIk7DKDmkXUBQCKQAAAA/Om3r2yrx5U7re1KZD8RXalq1HEmTQpCXy9uL/JOvUMFS7uiGm4uBdFzS1rYcFOBMCKQAAAA/OmxrePW/elFbGu/r9pfLD2tOL3ZYXnUo46bcdZirf5sM5RS80qHugTwuZfU9PaRlRpdzbAJQWgRQAAICH07wpHf3JnTc1ZsZaeeGnzeWWN7Uj5qRcPXmZvLZwm2Rk5YxCtQyvIt/f21PG9Gkufj5cpsK50UMBAABg1mPSvKkhufKmpv61W0Z8stKueVM6de/Dv3bJZW//Jev2x+VckHqJ3HNhU5kzuqe0q5sTzAHOjkAKAAAAtrypV6/pIM/lyptasuOY3fKm9h5Lkus+WCbP/7RF0jJzRrqahFWSb+/uIY/0byUBvj68EnAZBFIAAADIkzc1rHsjmX77uXbLm8rOtsjny/ZI/zf/kn/2nDj1c0RuPa+xzLuvl5zToBqvAFwOgRQAAAAK6Nq4ek7eVP2qefKmnv+xZHlTB+NSZPjHK+WpHzZJSkaW2Va/epDMuP1ceeryNmYUDHBFvo5uAAAAAJw4b+qOc2XcDxvlm1UHzLYP/94tW44kyDvXd5Rgfx+Zt+GwLNx0RGLjkiSs6gHp1zZCLm1fWwJ8vWXmqgPy3I+bJTEt03bMm85tIGMHtJZKAVyGwrXRgwEAAFAkHTF65eoO0r5uqIyfu1kysy0mb6rPxD/MIron0zJNsQhd/sn70ElZuClanp6zSRrVCJYNB3NKmqs6oYHy6jWRcl7zmpxtuAUCKQAAABQrb6pV7RC5+4s1cvRkmhzPVcnv1Bq6tq+JqZl5giitBPjUwDYSEujHmYbbIEcKAAAAxdKlUXWZdfe54qOVIopB95p8U0d5bUgkQRTcDoEUAAAAim3N3jjJspwaejoL3ctaYAJwNwRSAAAAKLZFm6JNTlSxLjS9RBZujObswi0RSAEAAKDY4pLTbblQZ6P7xaWczqUC3AmBFAAAAIqtarB/iUakqgblLOoLuBsCKQAAABRb37bhJRqR6tcunLMLt0QgBQAAgGLTxXZDgnxNRb4z0edDg3xlQLvanF24JQIpAAAAlGiB3olDokykVFQwZbZ7iUwYEmX2B9wRgRQAAABKpE+bcPlgWGczMmUuKE9FVNavun3qsM5mP8BdOWUgNWnSJGnUqJEEBgZKt27dZOXKlWfcf+bMmdKqVSuzf/v27WXevHkV1lYAAABPdEmbcFnxeB95Y2ikud+xXmXzVR/rdoIouLucjxGcyNdffy0PPvigTJ482QRRb775pvTr10+2bdsmtWrVKrD/0qVL5frrr5eXXnpJLr/8cpk+fboMGjRI1qxZI+3atXPI7wAAAOAJdNre4HPqyZWRdSQmJsZcq3l7O+Xn9IDdOV1Pnzhxotx+++0ycuRIadOmjQmogoOD5eOPPy50/7feekv69+8v//vf/6R169by3HPPSceOHeXdd9+t8LYDAAAA8AxONSKVnp4uq1evlrFjx9q26acaffr0kWXLlhX6PbpdR7By0xGs77//vtD909LSzM0qPj7efI2Li5Ps7Gy7/B56nISEBPH39+dTGdB/UKF4/wF9B47Aew/cpf9oO5TFYnGtQOro0aOSlZUl4eF5ExP18datWwv9niNHjhS6v24vjE4BHD9+fIHtDRs2LFPbAQAAALiHxMRECQ0NdZ1AqiLoaFfuESyNgI8fPy41atQQL69iLtNdjEi2fv36sn//fgkJCbHLMeE56D+g/4D3Hrga/nbBXfqPjkRpEFWnTp2z7utUgVTNmjXFx8dHoqOj82zXxxEREYV+j24vyf4BAQHmllvVqlWlPGhHcHRngOui/4D+A9574Gr42wV36D9nG4lyymITOi+yU6dOsnjx4jwjRvq4e/fuhX6Pbs+9v/r555+L3B8AAAAAysqpRqSUTrsbMWKEdO7cWbp27WrKnyclJZkqfmr48OFSt25dk+ukxowZIxdccIFMmDBBLrvsMpkxY4asWrVKPvjgAwf/JgAAAADcldMFUkOHDpXY2FgZN26cKRgRFRUlCxYssBWU2LdvX55qHj169DBrRz355JPy+OOPS/PmzU3FPkeuIaVTB59++ukCUwgB+g94/4Gz4m8X6D/g/adkvCzFqe0HAAAAAHDOHCkAAAAAcAUEUgAAAABQQgRSAAAAAFBCBFIAAAAAUEIEUuVg0qRJ0qhRIwkMDJRu3brJypUry+PHwM38+eefMnDgQLOStpeXl6k+CRSHLgfRpUsXqVKlitSqVUsGDRok27Zt4+ShWN5//33p0KGDbSFMXYdx/vz5nD2Uyssvv2z+ht1///2cQZzVM888Y/pL7lurVq3EVRBI2dnXX39t1sLS8udr1qyRyMhI6devn8TExNj7R8HN6Hpp2l80EAdK4o8//pB7771Xli9fbhYkz8jIkL59+5o+BZxNvXr1zMXv6tWrzTqMvXv3liuvvFI2bdrEyUOJ/PPPPzJlyhQTmAPF1bZtWzl8+LDt9vfff4uroPy5nekIlH4y/O6775rH2dnZUr9+fRk9erQ89thj9v5xcFP6iczs2bPNyAJQUroWn45MaYB1/vnncwJRYtWrV5fXXntNbr31Vs4eiuXkyZPSsWNHee+99+T5558364C++eabnD2cdURKZ+CsXbtWXBEjUnaUnp5uPtHr06fP6RPs7W0eL1u2zJ4/CgCKFB8fb7sYBkoiKytLZsyYYUYzdYofUFw6Kn7ZZZfluQYCiuO///4zaQ1NmjSRG2+8Ufbt2yeuwtfRDXAnR48eNX+EwsPD82zXx1u3bnVYuwB4Dh0F19yEnj17Srt27RzdHLiIDRs2mMApNTVVKleubEbE27Rp4+hmwUVo8K3pDDq1DyjpTK5p06ZJy5YtzbS+8ePHS69evWTjxo0m79fZEUgBgJt9Kqx/gFxpjjkcTy9idGqNjmbOmjVLRowYYaaGEkzhbPbv3y9jxowx+ZlaZAsoiQEDBtjua26dBlYNGzaUb775xiWmFhNI2VHNmjXFx8dHoqOj82zXxxEREfb8UQBQwKhRo+THH380FSC1gABQXP7+/tKsWTNzv1OnTmZk4a233jKFA4Az0ZQGLail+VFWOjtH34c0XzwtLc1cGwHFUbVqVWnRooXs2LFDXAE5Unb+Q6R/gBYvXpxnmo0+Zq45gPJisVhMEKXTsX799Vdp3LgxJxtlon+79AIYOJuLL77YTA3VEU3rrXPnzibXRe8TRKGkRUt27twptWvXFlfAiJSdaelznRKhbyJdu3Y1FWs0aXfkyJH2/lFwwzeP3J/A7N692/wR0oIBDRo0cGjb4PzT+aZPny4//PCDmVN+5MgRsz00NFSCgoIc3Tw4ubFjx5rpNfo+k5iYaPrS77//LgsXLnR00+AC9D0nfz5mpUqVpEaNGuRp4qwefvhhs4amTuc7dOiQWT5Ig+/rr79eXAGBlJ0NHTrUlB4eN26cuZjR8p8LFiwoUIACyE/Xb7nooovyBOVKA3NNxATOtKCquvDCC/Ns/+STT+Tmm2/mxOGMdFrW8OHDTaK3Bt+ap6BB1CWXXMKZA1CuDhw4YIKmY8eOSVhYmJx33nlmTUS97wpYRwoAAAAASogcKQAAAAAoIQIpAAAAACghAikAAAAAKCECKQAAAAAoIQIpAAAAACghAikAAAAAKCECKQAAAAAoIQIpAAAAACghAikAgN1MmzZNvLy8ZM+ePZxVAIBbI5ACAKCCLV26VJ555hmJi4vj3AOAiyKQAgDAAYHU+PHjCaQAwIURSAEA3FJ2drakpqaKJ0lOTnZ0EwDAYxBIAQAq3M033yyVK1eWXbt2Sb9+/aRSpUpSp04defbZZ8ViseTZ9/XXX5cePXpIjRo1JCgoSDp16iSzZs0qcEzNzRo1apR8+eWX0rZtWwkICJAFCxaU6hgzZ86UNm3amH27d+8uGzZsMM9PmTJFmjVrJoGBgXLhhRcWmgu2YsUK6d+/v4SGhkpwcLBccMEFsmTJEtvzOqXvf//7n7nfuHFj8zPz55V98cUXpo3686tXry7XXXed7N+/P8/P0Z/frl07Wb16tZx//vnmZz3++OOleDUAAKXhZcn/FwsAgDIUmxg5cqTs3r1bGjVqdMZA6uuvv5b69evLueeeK926dTNBz48//ihPPfWUCaisdJ8rrrjCBDbp6ekyY8YMWblypdn3sssuO/0HzctLWrduLUePHjXBUM2aNU3wFBUVVaJjdOjQQU6cOCH33nuv2fbSSy+ZoOiRRx6R9957T2699Vbz/Kuvvio9e/aUX3/91fb9en/AgAEmCLrmmmvE29tbPvnkE9m6dav89ddf0rVrV1m/fr28/PLL8tVXX8kbb7xh2qkGDx5sAsoXXnjBnINrr73WBGGxsbHyzjvvmMDz33//lapVq9oCqW3btklWVpYJtDSoCg8PlyuvvJL+CwAVQQMpAADs4ZNPPtEP5yy7d+8+434jRoww+40ePdq2LTs723LZZZdZ/P39LbGxsbbtycnJeb43PT3d0q5dO0vv3r3zbNfjeXt7WzZt2lTg55XkGAEBAXnaP2XKFLM9IiLCkpCQYNs+duzYPL+rtr958+aWfv36mfu5f3bjxo0tl1xyiW3ba6+9Vuh52rNnj8XHx8fywgsv5Nm+YcMGi6+vb57tF1xwgTnG5MmTC/y+AIDyx9Q+AIDD6MhR/ml1OmL0yy+/2Lbr9DYrHQmKj4+XXr16yZo1awocT0dwdNQpv5Ic4+KLL84zmqajZerqq6+WKlWqFNiu0xPV2rVr5b///pMbbrhBjh07ZkbG9JaUlGSO+eeff5q8rTP57rvvzD46GmX9fr1FRERI8+bN5bfffsuzv05f1BFAAEDF83XAzwQAwEx7a9KkSZ4z0aJFC/M1d76QTr97/vnnTaCSlpaWJ/DKT3OOClOSYzRo0CDPY53Wp3R6YGHbNTBTGkSpESNGFPnqagBXrVq1Ip/XY+jAmAZNhfHz88vzuG7duuLv71/k8QAA5YdACgDgtDSvSHObtJiC5ifVrl3bBBOadzR9+vQzjjyV9hg+Pj6FtqWo7dZUY+to02uvvWbysgqjeU5nosfQ4G7+/PmF/rz831/Y7wsAqBgEUgAAh9CgQafFWUeh1Pbt281X69S6b7/91lTIW7hwoZnGZqVBUHHZ4xjF0bRpU/M1JCRE+vTpc8Z9CxsJsx5DAzMdWct9XgAAzoccKQCAw7z77ru2+xpA6GMdLdKcIqWjMhp0aGU6K5329/333xf7Z9jjGMWhlfo0ENJS6ydPnizwvFbfs9LqfCouLi7PPldddZVpry7Wm7+orj7W3CsAgHNgRAoA4BA6SqQlzzWnSAs36HS2n376yayFFBYWZvbR0uQTJ0406zJpEYeYmBiZNGmSWctJy4gXhz2OUdycrw8//NCUP9d1rLQIhOYwHTx40BSJ0JGquXPn2oIu9cQTT5jS5Ro8Dhw40ARimss1duxYE+wNGjTIFLjQcvKzZ8+WO+64Qx5++GG7tRkAUHoEUgAAh9CRFw2k7r77brNArQYMTz/9tIwbN862T+/eveWjjz4y6y7df//9ZsrbK6+8YoKM4gZB9jhGcenaTsuWLZPnnnvOjK7pyJRW3NNA8c4777Tt16VLF7PP5MmTzTnQaY4aLOlI1WOPPWam9ekaUzoyZS100bdvX5PrBQBwDizICwCocLog76xZswqdAgcAgCsgRwoAAAAASohACgAAAABKiEAKAAAAAEqIHCkAAAAAKCFGpAAAAACghAikAAAAAKCECKQAAAAAoIQIpAAAAACghAikAAAAAKCECKQAAAAAoIQIpAAAAACghAikAAAAAEBK5v/jAtTGfn3tQgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_success_rate_vs_l(l_values, function, function_params, m_val=2.0, n_val=3):\n", + " \"\"\"\n", + " Iterate over different l values and plot success rate as a function of l.\n", + "\n", + " Args:\n", + " l_values: list of l values to test\n", + " function: function name (\"linear\" / \"quadratic\") or callable\n", + " function_params: parameters for the function\n", + " m_val: m parameter (default 1.0)\n", + " n_val: n parameter (default 3)\n", + " \"\"\"\n", + " success_rates = []\n", + "\n", + " for l_curr in l_values:\n", + " p = params()\n", + " p.m = m_val\n", + " p.l = l_curr\n", + " p.n = n_val\n", + " p.set_function(function, function_params)\n", + " p.unpack()\n", + "\n", + " @qfunc\n", + " def main(x: Output[QNum[n]]):\n", + " magnitudes, phases = p.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", + " invert(lambda: qft(x))\n", + "\n", + " pc = run_standard_simulation(main)\n", + " analytic_grad = p.analytical_gradient(0)\n", + " success_rate, _, _ = compute_success_rate(pc, analytic_derivatives={\"x\": analytic_grad})\n", + " success_rates.append(success_rate)\n", + " print(f\"l={l_curr}: Success rate = {success_rate:.2%}\")\n", + "\n", + " plt.figure(figsize=(10, 6))\n", + " plt.plot(l_values, success_rates, \"o-\", linewidth=2, markersize=8)\n", + " plt.xlabel(\"l parameter\", fontsize=12)\n", + " plt.ylabel(\"Success Rate\", fontsize=12)\n", + " plt.title(\"Success Rate vs l Parameter\", fontsize=14)\n", + " plt.grid(True, alpha=0.3)\n", + " plt.ylim([0, 1.05])\n", + " plt.show()\n", + "\n", + " return success_rates\n", + "\n", + "\n", + "# Example usage:\n", + "l_values = [0.1, 0.2, 0.3, 0.4, 0.5, 1, 1.5, 2.0, 3.0]\n", + "results_l = plot_success_rate_vs_l(l_values, \"quadratic\", (0.6, 0.25, 0.1), m_val=1.0, n_val=3)" + ] + }, + { + "cell_type": "markdown", + "id": "7b3097bb", + "metadata": {}, + "source": [ + "# 5. Multi-Coordinates Examples" + ] + }, + { + "cell_type": "markdown", + "id": "854afbc8", + "metadata": {}, + "source": [ + "This algorithm works in multiple dimensions too.\\\n", + "We will now see an example in 2D, f(x,y).\\\n", + "We will start with a linear and decoupled function $f(x,y)=ax+by+c$." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "2f4588e6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[{'x': 2, 'y': 7}: 2048]\n", + "Analytical gradient: (dx, dy) = (0.5, -0.25)\n", + "Majority gradient: (dx, dy) = (0.5, -0.25)\n", + "Success rate: 100.00% (2048/2048 shots)\n", + "[\u001b[92m██████████████████████████████████████████████████\u001b[91m\u001b[0m] 100.00%\n" + ] + } + ], + "source": [ + "px = params()\n", + "py = params()\n", + "\n", + "# Set the functions for x and y axes\n", + "# f(x, y) = a*x + b*y + c = 0.5*x - 0.25*y + 0.1\n", + "# df/dx = 0.5, df/dy = -0.25\n", + "a, b, c = 0.5, -0.25, 0.1\n", + "px.set_function(px.linear, (a, 0.0))\n", + "py.set_function(py.linear, (b, c))\n", + "\n", + "# Use the globals from px. \n", + "# Be careful - If you change the parameters in py you can not use the globals anymore!\n", + "px.unpack()\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]], y: Output[QNum[n]]):\n", + " # State preparation for x-axis contribution\n", + " magnitudes_x, phases_x = px.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes_x, phases=phases_x, out=x)\n", + "\n", + " # State preparation for y-axis contribution\n", + " magnitudes_y, phases_y = py.calculate_magnitude_and_phase()\n", + " prepare_complex_amplitudes(magnitudes=magnitudes_y, phases=phases_y, out=y)\n", + "\n", + " # Gradient extraction on each axis\n", + " invert(lambda: qft(x))\n", + " invert(lambda: qft(y))\n", + "\n", + "pc = run_standard_simulation(main)\n", + "print(pc)\n", + "\n", + "majority_state = pc[0].state\n", + "gx_true = px.analytical_gradient(0)\n", + "gy_true = py.analytical_gradient(0)\n", + "\n", + "gx_meas = state_to_gradient(majority_state.get(\"x\"))\n", + "gy_meas = state_to_gradient(majority_state.get(\"y\"))\n", + "\n", + "print(f\"Analytical gradient: (dx, dy) = ({gx_true}, {gy_true})\")\n", + "print(f\"Majority gradient: (dx, dy) = ({gx_meas}, {gy_meas})\")\n", + "\n", + "success_rate, success_shots, total_shots = compute_success_rate(\n", + " pc, analytic_derivatives={\"x\": gx_true, \"y\": gy_true}\n", + ")\n", + "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", + "show_bar(success_rate)" + ] + }, + { + "cell_type": "markdown", + "id": "d430350c", + "metadata": {}, + "source": [ + "We can also have more complex example, with non-linear and coupled equation: $f(x, y)=ax^2+by^2+cxy+dx+ey+f$." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "93751a65", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[{'x': 1, 'y': 6}: 1992, {'x': 0, 'y': 6}: 14, {'x': 2, 'y': 6}: 14, {'x': 1, 'y': 5}: 8, {'x': 1, 'y': 7}: 6, {'x': 3, 'y': 6}: 3, {'x': 6, 'y': 6}: 2, {'x': 2, 'y': 7}: 1, {'x': 0, 'y': 3}: 1, {'x': 7, 'y': 1}: 1, {'x': 4, 'y': 6}: 1, {'x': 5, 'y': 4}: 1, {'x': 0, 'y': 7}: 1, {'x': 2, 'y': 5}: 1, {'x': 0, 'y': 5}: 1, {'x': 6, 'y': 7}: 1]\n", + "Analytical gradient: (dx, dy) = (0.25, -0.5)\n", + "Majority gradient: (dx, dy) = (0.25, -0.5)\n", + "Success rate: 97.27% (1992/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.27%\n" + ] + } + ], + "source": [ + "p = params()\n", + "p.l = 0.1\n", + "p.unpack()\n", + "\n", + "def f(x, y):\n", + " a, b, c, d, e, f = 0.6, -0.4, 0.25, 0.25, -0.5, 0.1\n", + " global gradient_x, gradient_y\n", + " gradient_x = d\n", + " gradient_y = e\n", + " return a * x**2 + b * y**2 + c * x * y + d * x + e * y + f\n", + "\n", + "# Generated functions\n", + "def f_normalized(x, y):\n", + " val = f(l / N * (x - N // 2), l / N * (y - N // 2))\n", + " val *= N / (l * m)\n", + " return val\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n]], y: Output[QNum[n]]):\n", + " # 1. State preparation\n", + " x_array = np.arange(N) # Create an array of x values corresponding to the quantum states\n", + " y_array = np.arange(N) # Create an array of y values corresponding to the quantum states\n", + " \n", + " # In order to use the prepare_complex_amplitudes function, we need to flatten the 2D arrays of magnitudes and phases into 1D arrays.\n", + " X_grid, Y_grid = np.meshgrid(x_array, y_array, indexing='ij')\n", + " phases_2d = f_normalized(X_grid, Y_grid) * 2 * np.pi\n", + " magnitudes_2d = np.ones((N, N)) / N \n", + " phases_flat = phases_2d.flatten().tolist()\n", + " magnitudes_flat = magnitudes_2d.flatten().tolist()\n", + " \n", + " # Prepare the state using the flattened arrays, then bind the combined register to the x and y registers.\n", + " combined_reg = QNum(\"combined_reg\")\n", + " prepare_complex_amplitudes(\n", + " magnitudes=magnitudes_flat, \n", + " phases=phases_flat, \n", + " out=combined_reg\n", + " )\n", + " bind(combined_reg, [y, x])\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + " invert(lambda: qft(y))\n", + "\n", + "pc = run_standard_simulation(main)\n", + "print(pc)\n", + "\n", + "majority_state = pc[0].state\n", + "gx_true = gradient_x\n", + "gy_true = gradient_y\n", + "\n", + "gx_meas = state_to_gradient(majority_state.get(\"x\"))\n", + "gy_meas = state_to_gradient(majority_state.get(\"y\"))\n", + "\n", + "print(f\"Analytical gradient: (dx, dy) = ({gx_true}, {gy_true})\")\n", + "print(f\"Majority gradient: (dx, dy) = ({gx_meas}, {gy_meas})\")\n", + "\n", + "success_rate, success_shots, total_shots = compute_success_rate(\n", + " pc, analytic_derivatives={\"x\": gx_true, \"y\": gy_true}\n", + ")\n", + "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", + "show_bar(success_rate)" + ] + }, + { + "cell_type": "markdown", + "id": "35e960db", + "metadata": {}, + "source": [ + "# References" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7f9c7201", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: add" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "classiq", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 38b64e91b822f3341e0c75c2606e140d847b2264 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Tue, 5 May 2026 12:04:15 +0300 Subject: [PATCH 02/12] Fixing PR comments --- .../Gradient Estimation.ipynb | 2289 ----------------- ...ithm for Numerical Gradient Estimation.pdf | Bin 0 -> 122310 bytes .../gradient_estimation.ipynb | 2137 +++++++++++++++ .../gradient_estimation.metadata.json | 10 + .../gradient_estimation_helpers.py | 335 +++ .../gradient_estimation/quantum_circuit.png | Bin 0 -> 12297 bytes .../gradient_estimation/quantum_circuit_2.png | Bin 0 -> 18758 bytes algorithms/gradient_estimation/step_2.png | Bin 0 -> 45955 bytes algorithms/gradient_estimation/step_3.png | Bin 0 -> 48216 bytes tests/notebooks/test_gradient_estimation.py | 19 + 10 files changed, 2501 insertions(+), 2289 deletions(-) delete mode 100644 algorithms/gradient_estimation/Gradient Estimation.ipynb create mode 100644 algorithms/gradient_estimation/Stephen P. Jordan - Fast Quantum Algorithm for Numerical Gradient Estimation.pdf create mode 100644 algorithms/gradient_estimation/gradient_estimation.ipynb create mode 100644 algorithms/gradient_estimation/gradient_estimation.metadata.json create mode 100644 algorithms/gradient_estimation/gradient_estimation_helpers.py create mode 100644 algorithms/gradient_estimation/quantum_circuit.png create mode 100644 algorithms/gradient_estimation/quantum_circuit_2.png create mode 100644 algorithms/gradient_estimation/step_2.png create mode 100644 algorithms/gradient_estimation/step_3.png create mode 100644 tests/notebooks/test_gradient_estimation.py diff --git a/algorithms/gradient_estimation/Gradient Estimation.ipynb b/algorithms/gradient_estimation/Gradient Estimation.ipynb deleted file mode 100644 index fc514e5cc..000000000 --- a/algorithms/gradient_estimation/Gradient Estimation.ipynb +++ /dev/null @@ -1,2289 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "8040b1be", - "metadata": {}, - "source": [ - "# Initialization" - ] - }, - { - "cell_type": "markdown", - "id": "9beb3b70", - "metadata": {}, - "source": [ - "Always run those cells before using the notebook, it import needed packages and initialize helper functions." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "f8d11d1a", - "metadata": {}, - "outputs": [], - "source": [ - "from classiq import *\n", - "from typing import List\n", - "import numpy as np\n", - "import pandas as pd\n", - "from dataclasses import dataclass\n", - "from matplotlib import pyplot as plt\n", - "import matplotlib\n", - "# %matplotlib widget" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "2d6c8e39", - "metadata": {}, - "outputs": [], - "source": [ - "@dataclass\n", - "class params:\n", - " # Algorithm parameters\n", - " l = 0.5\n", - " m = 2\n", - " n = 3\n", - " n0 = 3\n", - "\n", - " @property\n", - " def N(self):\n", - " return 2**self.n\n", - "\n", - " @property\n", - " def N0(self):\n", - " return 2**self.n0\n", - "\n", - " # Function parameters\n", - " f = None\n", - " f_prams = None\n", - " f_name = None\n", - "\n", - " def set_function(self, f, f_prams):\n", - " self.f_prams = f_prams\n", - "\n", - " # Allow passing by name, e.g. \"linear\" or \"quadratic\"\n", - " if isinstance(f, str):\n", - " self.f_name = f\n", - " self.f = getattr(self, f)\n", - " return\n", - "\n", - " # If a method from another params instance is passed,\n", - " # re-bind it to this instance to avoid mixed state.\n", - " if hasattr(f, \"__func__\"):\n", - " self.f = f.__func__.__get__(self, self.__class__)\n", - " else:\n", - " self.f = f\n", - "\n", - " self.f_name = getattr(self.f, \"__name__\", None)\n", - "\n", - " # Generated functions\n", - " def f_normalized(self, x):\n", - " val = self.f(self.l / self.N * (x - self.N // 2))\n", - " val *= self.N / (self.l * self.m)\n", - " return val\n", - "\n", - " def calculate_magnitude_and_phase(self):\n", - " x_array = np.arange(self.N)\n", - " # reorder the x_array to match the order of the quantum states\n", - " # TODO: delete? x_array = np.concatenate((x_array[self.N//2:], x_array[:self.N//2]))\n", - " phases = self.f_normalized(x_array) * 2 * np.pi\n", - " magnitudes = np.ones(self.N) * 1 / self.N\n", - " return magnitudes, phases\n", - "\n", - " def analytical_gradient(self, x):\n", - " if self.f_name == 'linear':\n", - " return self.f_prams[0]\n", - " elif self.f_name == 'quadratic':\n", - " return (2 * self.f_prams[0] * x + self.f_prams[1])\n", - " else:\n", - " raise NotImplementedError(\"Analytical gradient not implemented for this function.\")\n", - "\n", - " # A few example functions\n", - " def linear(self, x):\n", - " return self.f_prams[0] * x + self.f_prams[1]\n", - "\n", - " def quadratic(self, x):\n", - " return self.f_prams[0] * x**2 + self.f_prams[1] * x + self.f_prams[2]\n", - "\n", - " # Unpack function, to be used in the notebook\n", - " def unpack(self):\n", - " global l, m, n, n0, f, f_prams, N, N0\n", - " l, m, n, n0, N, N0 = self.l, self.m, self.n, self.n0, self.N, self.N0\n", - " f, f_prams = self.f, self.f_prams\n", - " global f_normalized\n", - " f_normalized = self.f_normalized" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "ad03b035", - "metadata": {}, - "outputs": [], - "source": [ - "# ****** Simulation ******\n", - "def run_statevector_simulation(qfunc_to_run, print_circuit_info=False, filter_ancilla=False):\n", - " # Run a statevector simulator\n", - " qprog = synthesize(qfunc_to_run)\n", - " #show(qprog)\n", - " if print_circuit_info:\n", - " print(\"Circuit Width:\", qprog.data.width)\n", - " print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", - " print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", - "\n", - " backend_preferences = ClassiqBackendPreferences(backend_name=\"simulator_statevector\")\n", - " execution_preferences = ExecutionPreferences(num_shots=1, backend_preferences=backend_preferences)\n", - " with ExecutionSession(qprog, execution_preferences=execution_preferences) as es:\n", - " if filter_ancilla:\n", - " es.set_measured_state_filter(\"ancilla\", lambda v: v == 0)\n", - " results_statevector = es.sample()\n", - " df = results_statevector.dataframe\n", - " return df\n", - "\n", - "def run_standard_simulation(qfunc_to_run):\n", - " # Run a regular simulator\n", - " qprog = synthesize(qfunc_to_run)\n", - " job = execute(qprog)\n", - " # job.open_in_ide()\n", - " pc = job.get_sample_result().parsed_counts\n", - " return pc\n", - "\n", - "# ****** Result Processing ******\n", - "def state_to_gradient(value):\n", - " if value >= N//2:\n", - " value -= N\n", - " return value / (N/m)\n", - "\n", - "def simplify_df(df, unwrap=True):\n", - " # Get the phase from the df\n", - " phases = np.angle(df[\"amplitude\"]).astype(float)\n", - " phases_over_2pi = phases/(2*np.pi)\n", - " f_classical = f_normalized(df['x'])\n", - " simplified_df = pd.DataFrame({\"f_classical\": f_classical, \"phase_over_2pi\": phases_over_2pi.round(5)})\n", - " simplified_df.index = df['x']\n", - " simplified_df.sort_index(inplace=True)\n", - "\n", - " # Unwrap the phase if requested\n", - " if unwrap:\n", - " # Unwrap the phase\n", - " simplified_df['phase_over_2pi'] = np.unwrap(simplified_df['phase_over_2pi'], period=1)\n", - " # Get rid of the global phase\n", - " simplified_df['phase_over_2pi'] -= simplified_df['phase_over_2pi'].iloc[N//2]\n", - " simplified_df['f_classical'] -= simplified_df['f_classical'].iloc[N//2]\n", - "\n", - " return simplified_df\n", - "\n", - "def compute_success_rate(pc, analytic_derivatives, reject_underresolution=False):\n", - " items = []\n", - " for obj in pc:\n", - " # obj.state -> dict of measured registers\n", - " # obj.count (or obj.shots) -> number of occurrences\n", - " state = getattr(obj, \"state\", None)\n", - " shots = getattr(obj, \"count\", None)\n", - "\n", - " if shots is None:\n", - " shots = getattr(obj, \"shots\", None)\n", - "\n", - " if state is None or shots is None:\n", - " raise TypeError(\n", - " f\"Unsupported parsed_counts entry type: {type(obj)}. \"\n", - " f\"Need fields like .state and .count/.shots.\"\n", - " )\n", - "\n", - " items.append((state, shots))\n", - "\n", - " total_shots = sum(shots for _, shots in items)\n", - " if total_shots == 0:\n", - " return 0.0, 0, 0\n", - "\n", - " tolerance = 0.5 * m/N\n", - "\n", - " success_shots = 0\n", - "\n", - "\n", - " for state_key, shots in items:\n", - " # state_key might be SampledState key object or plain dict; normalize:\n", - " state = getattr(state_key, \"state\", state_key)\n", - "\n", - " # estimate derivatives using your formula: value * m\n", - " est = {}\n", - " for name, value in state.items():\n", - " est[name] = state_to_gradient(value)\n", - "\n", - " # success condition: all analytic derivatives within tolerance\n", - " correct = True\n", - " for name, analytic_val in analytic_derivatives.items():\n", - " measured_val = est.get(name)\n", - " if measured_val is None or abs(measured_val - analytic_val) >= tolerance:\n", - " correct = False\n", - " break\n", - " if reject_underresolution and measured_val == 0:\n", - " correct = False\n", - " break\n", - "\n", - " if correct:\n", - " success_shots += shots\n", - "\n", - " success_rate = success_shots / total_shots\n", - " return success_rate, success_shots, total_shots\n", - "\n", - "def analyze_results(pc):\n", - " # Print the results and compute the majority gradient\n", - " print(\"Parsed counts:\", pc)\n", - " print(f\"The analytical gradient is: {p.analytical_gradient(0)}\")\n", - " majority_state = pc[0].state\n", - " majority_gradient = state_to_gradient(majority_state.get('x'))\n", - " print(f\"The majority gradient is: {majority_gradient}\")\n", - "\n", - " # Check if the majority result is correct within the resolution of the algorithm\n", - " resolution = m/N\n", - " is_correct = abs(majority_gradient - p.analytical_gradient(0)) < resolution/2\n", - " print(f\"The majority result is\", \"correct\" if is_correct else \"incorrect\")\n", - " print(\"####################################################\")\n", - "\n", - " # Compute the success rate of the algorithm, i.e. the percentage of shots that are correct within the resolution of the algorithm.\n", - " success_rate, success_shots, total_shots = compute_success_rate(pc, analytic_derivatives={'x': p.analytical_gradient(0)})\n", - " print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", - " show_bar(success_rate)\n", - "\n", - " # Visualize the theoretical values of the phases\n", - " # We used the standard simulation, so this is theoretical values only without the phases from the simulation\n", - " plot_theoretical()\n", - "\n", - "# ****** Plotting ******\n", - "def plot_classical():\n", - " x_values = np.linspace(-N//2, N*1.5, 1000) # more points for smoother curve\n", - " f_values = f_normalized(x_values)\n", - " f_values -= f_normalized(N//2)\n", - " plt.plot(x_values, f_values, color='lightgray', label=\"Original function\")\n", - " ax = plt.gca()\n", - " ax.set_xticks(np.arange(N))\n", - " ax.set_xticklabels([str(i) for i in range(N)])\n", - "\n", - " # Primary-axis labels (normalized coordinates)\n", - " ax.set_xlabel(\"x (index)\")\n", - " ax.set_ylabel(\"f (normalized)\")\n", - "\n", - " # Secondary X axis: integer grid index -> real x\n", - " # Uses existing l, N convention: x_real = (x - N/2) * (l/N)\n", - " x_to_real = lambda x: (x - N / 2) * (l / N)\n", - " real_to_x = lambda xr: xr * (N / l) + N / 2\n", - " secax_x = ax.secondary_xaxis(\"top\", functions=(x_to_real, real_to_x), color='blue')\n", - " secax_x.set_xlabel(\"x (real)\")\n", - "\n", - " # Secondary Y axis: normalized f -> unnormalized f\n", - " # Assumes f_normalized = m * f_real => f_real = f_normalized / m\n", - " f_to_real = lambda y: (y + f_normalized(N//2)) * m * l / N \n", - " real_to_f = lambda yr: yr / m / l * N - f_normalized(N//2)\n", - " secax_y = ax.secondary_yaxis(\"right\", functions=(f_to_real, real_to_f), color='blue')\n", - " secax_y.set_ylabel(\"f (real, unnormalized)\")\n", - "\n", - "def plot_theoretical(show=True):\n", - " # Get the phase from the df\n", - " x_array = np.arange(N)\n", - " \n", - " f_classical = f_normalized(x_array)\n", - " f_classical -= f_classical[N//2]\n", - "\n", - " if show:\n", - " plt.figure()\n", - " plot_classical()\n", - " plt.plot(x_array, f_classical, 'o', label=\"Theoretical values\")\n", - " xmin, xmax = -N//2, N*1.5\n", - " ymin, ymax = -N//2, N//2\n", - " plt.xlim(xmin, xmax)\n", - " plt.ylim(ymin, ymax)\n", - " plt.vlines(0, ymin, ymax, colors='lightgray', linestyles='dashed')\n", - " plt.vlines(N-1, ymin, ymax, colors='lightgray', linestyles='dashed')\n", - " plt.hlines(-N/4+0.5, xmin, xmax, colors='lightgray', linestyles='dashed')\n", - " plt.hlines(N/4, xmin, xmax, colors='lightgray', linestyles='dashed')\n", - " plt.legend()\n", - " if show:\n", - " plt.show()\n", - "\n", - "\n", - "def plot_simplified_df(simplified_df, show=True):\n", - " plt.figure()\n", - " plot_theoretical(show=False)\n", - " plt.plot(simplified_df.index, simplified_df['phase_over_2pi'], 'o', label=\"Measured phases\")\n", - " plt.legend()\n", - " if show:\n", - " plt.show()\n", - "\n", - "def show_bar(success_rate):\n", - " bar_length = 50\n", - " filled = int(round(bar_length * success_rate))\n", - " GREEN = \"\\033[92m\"\n", - " RED = \"\\033[91m\"\n", - " RESET = \"\\033[0m\"\n", - "\n", - " bar = f\"{GREEN}{'█' * filled}{RED}{'-' * (bar_length - filled)}{RESET}\"\n", - "\n", - " print(f\"[{bar}] {success_rate * 100:.2f}%\")\n" - ] - }, - { - "cell_type": "markdown", - "id": "d85717d1", - "metadata": {}, - "source": [ - "# 1. Fast Quantum Algorithm for Numerical Gradient Estimation" - ] - }, - { - "cell_type": "markdown", - "id": "35a1c868", - "metadata": {}, - "source": [ - "Given a function scalar function $f(x_1, ... x_d)$, we want to find the gradient of the function in specific point.\\\n", - "Classicaly this requires at least d+1 queries of the function $f$ (one query at the origin, and one in each direction).\\\n", - "In this notebook we will explore quantum algorithm to find the gradient in just a single query of the function.\\\n", - "This is a dramatic improvement in large dimensions functions, as most of the times the most expensive part of calculating the derivative is querying the function.\\\n", - "\\\n", - "The core concept of the algorithm is to first 'apply' the function to the phase of a superposition state, then extract the gradient value from the phase to a measurable state by using a QFT.\\\n", - "Let's see it step by step, first a little simplified version to understand the concept, and then fixing the inaccurities for the final algorithm." - ] - }, - { - "cell_type": "markdown", - "id": "ce1b3ca4", - "metadata": {}, - "source": [ - "## Simplified version of the algorithm\n", - "As briefly mentioned earlier, the algorithm can be divided to two steps:\n", - "1. Applying the function to the phase\n", - "2. Extracting the gradient value to a measurable state\n", - "\n", - "In more details:\n", - "1. For each coordinate ($x_i$), we start with the state $\\ket{\\delta_i}=\\ket{0}+\\ket{1}+\\ket{2}....\\ket{N-1}$, by applying the Hadamard gate on $\\ket{0}$. If there are more than one coordinates, the state $\\ket{\\delta}$ is a product state of all $\\ket{\\delta_i}$\n", - "2. Using the phase kickback technique, we apply the function to the phase of each ket creating the state:\n", - "$$e^{i\\cdot2\\pi f(0)}\\ket{0} + e^{i\\cdot2\\pi f(1)}\\ket{1} + e^{i\\cdot2\\pi f(2)}\\ket{2} ..... e^{i\\cdot2\\pi f(N-1)}\\ket{N-1}$$\n", - "3. We note the fact that for small enough interval, we can approximate: $f(x)\\approx f(0)+x\\cdot f'(x)$, so we can write the previous state as: \n", - "$$ e^{i\\cdot2\\pi f(0)}(\\ket{0} + e^{i\\cdot2\\pi f'(0)}\\ket{1} + e^{i\\cdot2\\pi 2f'(0)}\\ket{2} ..... e^{i\\cdot2\\pi (N-1)f'(0)}\\ket{N-1}) = e^{i\\cdot2\\pi f(0)}\\sum e^{i\\cdot2\\pi jf'(0)}\\ket{j} $$\n", - "4. We note that this state is exactly the fourier transform of the state $\\ket{f'(0)}$, so we apply the inverse fourier transform and get the result: $$\\ket{f'(0)}$$\n", - "5. We measure to get $f'(0)$, and for a multi-coordinates function $\\nabla f$.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "05c25e29", - "metadata": {}, - "source": [ - "## Exact version of the algorithm\n", - "The previous explaination covers the main idea of the algorithm, but miss some important details on negative and fractional values.\\\n", - "In this explaination we will fill in this details.\\\n", - "When we calculate gradient, we look on an interval around the point of interest (in this case, it will be the origin). We will call this interval $l$.\n", - "The state $\\ket{\\delta_i}$ should represent $N$ equally spaced points around the origin in the interval $l$, so we normalized it to be:\n", - "$$ x=\\frac{l}{N}(\\delta-\\frac{N}{2}) $$\n", - "That way, $\\delta=0$ will be the leftmost point of the interval ($-l/2$), $\\delta=N/2$ will be the origin, and $\\delta=N-1$ will be the rightmost point of the interval ($l/2-l/N$).\\\n", - "\\\n", - "We also need to normalize the result state. Say the expected gradient is bounded between $-m/2$ and $m/2$, we want to represent those values using the $N$ states of the coordinate, so doing a similar trick we can define $$ \\nabla f=\\frac{m}{N}(\\delta_{measured}-\\frac{N}{2}) $$\\\n", - "\\\n", - "When using the algorithm we need to select $l$ and $m$ using our prior knowledge on the function $f(x)$, and $N$ will define the final resolution we get.\\\n", - "$l$ should be small enough so we will stay in a linear regime of the function, and $m$ should be larger than the maximum possible gradient, but not too large because then we will lose resultion.\n", - "\\\n", - "Using those two normalizations, we change two things in the algorithm:\n", - "1. In step 2, instead of applying $f(\\delta)$, we apply $\\frac{N}{ml}f(\\frac{l}{N}(\\delta-\\frac{N}{2}))$.\n", - "2. In step 5, instead of measuring $\\nabla f$ directly, we measure $\\frac{N}{m}\\nabla f + \\frac{N}{2}$, and need to invert this to find $\\nabla f$\n", - "Note that due to the cyclic nature of the QFT, if we know that the gradient must be positive or negative, we don't need to change anything in the algorithm, just adjust the final convertion." - ] - }, - { - "cell_type": "markdown", - "id": "2fe010f7", - "metadata": {}, - "source": [ - "## Notebook's structure:\n", - "In the notebook, we will cover those topics:\n", - "1. Theoretical explaination (this section)\n", - "2. Step 1 of the algorithm - State Preparation. We will cover two methods. Phase Kickback (as in the cited paper) and Prepare State (more straight forward and more efficient for the simulation). We will demonstrate how the states are prepared using a full statevector simulation.\n", - "3. The full algorithm, showing examples of linear and non-linear functions.\n", - "4. Parameters selection and limits (Still work in progress)\n", - "5. Multi-coordinates example, f as function of x, y\n", - "\n", - "A technical note: In this notebook, some analysis functions are repetetive. Each time a new analysis is used it is written explicitly in the first time, but in later times is appears as an helper function, in order to make the code more readable and easy to understand. All the helpers functions appears at the beggining of this notebook." - ] - }, - { - "cell_type": "markdown", - "id": "6b665020", - "metadata": {}, - "source": [ - "# 2. State Preparation" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "7cbd6c18", - "metadata": {}, - "outputs": [], - "source": [ - "# TODO: free the ancilla\n", - "# TODO: write explanations\n", - "# TODO: format using the other notebooks as a reference\n", - "# TODO: explain about the params class and the auxillary functions.\n", - "# TODO: write / remove section 5" - ] - }, - { - "cell_type": "markdown", - "id": "cb541ef9", - "metadata": {}, - "source": [ - "## 2.1. Phase Kickback" - ] - }, - { - "cell_type": "markdown", - "id": "05340b0f", - "metadata": {}, - "source": [ - "The first step of the algorithm is to prepare the state:\n", - "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}(\\delta-\\frac{N}{2}))}\\ket\\delta$$\n", - "The paper uses the phase kickback technique using the ancilla in order to create this state.\\\n", - "In the next example we will see how it works." - ] - }, - { - "cell_type": "markdown", - "id": "3568e49c", - "metadata": {}, - "source": [ - "The phase kickback contains three steps:\n", - "1. Apply Hadamard gate on $\\ket\\delta$ to have an entangeled state\n", - "2. Set the ancilla to $\\ket{1111...1}$ (in binary representation) and apply QFT on it\n", - "3. Add the value $f(\\delta)$ to the ancilla, and the function's value will be 'kicked' to the phase\n", - "\n", - "Note that we use the ancilla as a signed and fractional QNum, so in order to have $\\ket{1111...1_b}$, we will assign $-1/N_0$" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "0e3557a4", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit Width: 10\n", - "Circuit Depth: 69\n", - "Gate Counts: {'u': 54, 'cx': 48}\n" - ] - }, - { - "data": { - "application/vnd.microsoft.datawrangler.viewer.v0+json": { - "columns": [ - { - "name": "index", - "rawType": "int64", - "type": "integer" - }, - { - "name": "x", - "rawType": "int64", - "type": "integer" - }, - { - "name": "ancilla", - "rawType": "float64", - "type": "float" - }, - { - "name": "amplitude", - "rawType": "complex128", - "type": "unknown" - }, - { - "name": "magnitude", - "rawType": "object", - "type": "string" - }, - { - "name": "phase", - "rawType": "object", - "type": "string" - }, - { - "name": "probability", - "rawType": "float64", - "type": "float" - }, - { - "name": "bitstring", - "rawType": "object", - "type": "string" - } - ], - "ref": "ec828fe0-9d6c-4212-a761-135d6c4c7a15", - "rows": [ - [ - "0", - "0", - "0.0", - "(0.0883883476483181-0.08838834764831877j)", - "0.12", - "-0.25π", - "0.015624999999999997", - "0000000000" - ], - [ - "1", - "2", - "0.0", - "(-0.0883883476483181+0.08838834764831877j)", - "0.12", - "0.75π", - "0.015624999999999997", - "0000000010" - ], - [ - "2", - "1", - "0.0", - "(0.08838834764831884+0.08838834764831802j)", - "0.12", - "0.25π", - "0.015624999999999993", - "0000000001" - ], - [ - "3", - "3", - "0.0", - "(-0.08838834764831882-0.088388347648318j)", - "0.12", - "-0.75π", - "0.01562499999999999", - "0000000011" - ], - [ - "4", - "4", - "0.0", - "(0.08838834764831811-0.08838834764831871j)", - "0.12", - "-0.25π", - "0.01562499999999999", - "0000000100" - ], - [ - "5", - "6", - "0.0", - "(-0.08838834764831811+0.08838834764831871j)", - "0.12", - "0.75π", - "0.01562499999999999", - "0000000110" - ], - [ - "6", - "5", - "0.0", - "(0.0883883476483188+0.08838834764831802j)", - "0.12", - "0.25π", - "0.015624999999999986", - "0000000101" - ], - [ - "7", - "7", - "0.0", - "(-0.0883883476483188-0.08838834764831802j)", - "0.12", - "-0.75π", - "0.015624999999999986", - "0000000111" - ] - ], - "shape": { - "columns": 7, - "rows": 8 - } - }, - "text/html": [ - "
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f_classicalphase_over_2pi
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" - ], - "text/plain": [ - " f_classical phase_over_2pi\n", - "x \n", - "0 -1.00 -0.125\n", - "1 -0.75 0.125\n", - "2 -0.50 0.375\n", - "3 -0.25 -0.375\n", - "4 0.00 -0.125\n", - "5 0.25 0.125\n", - "6 0.50 0.375\n", - "7 0.75 -0.375" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "phases = np.angle(df[\"amplitude\"]).astype(float)\n", - "phases_over_2pi = phases/(2*np.pi)\n", - "f_classical = f_normalized(df['x']) - f_normalized(N//2) # shift the classical function to match the quantum convention\n", - "simplified_df = pd.DataFrame({\"f_classical\": f_classical, \"phase_over_2pi\": phases_over_2pi.round(5)})\n", - "simplified_df.index = df['x']\n", - "simplified_df.sort_index(inplace=True)\n", - "simplified_df" - ] - }, - { - "cell_type": "markdown", - "id": "a3aad709", - "metadata": {}, - "source": [ - "We can plot the phases from the statevector simulation (in orange) next to the values of $f(x)$ (blue).\\\n", - "We expect to see that the phases will match the function value, hence the two graphs should match complitly.\\\n", - "Let's plot it:\n", - "\n", - "\\* Quick note about the graph:\\\n", - "The quantum calculations are in normalized space where $x$ is a coordinate from $0$ to $N-1$, and $f$ is normalized using $l$ and $m$. The graphs show the normalized axes in black, and the real unnormalized axes in blue." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "77343d45", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot the results\n", - "plt.figure()\n", - "plot_classical()\n", - "simplified_df.plot(style='o', ax=plt.gca())\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "c82662b7", - "metadata": {}, - "source": [ - "But wait! The phase doesn't match the classical function!\\\n", - "There are two reasons:\n", - "1. Wrapping of the phase around $2\\pi$\n", - "2. A constant shift due to global phase\n", - "\n", - "If we solve those two issues, we see that the phase exactly equal to the original function." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "8901bbc1", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# 0. Simplify the dataframe - same as before\n", - "phases = np.angle(df[\"amplitude\"]).astype(float)\n", - "phases_over_2pi = phases/(2*np.pi)\n", - "f_classical = f_normalized(df['x'])\n", - "simplified_df = pd.DataFrame({\"f_classical\": f_classical, \"phase_over_2pi\": phases_over_2pi.round(5)})\n", - "simplified_df.index = df['x']\n", - "simplified_df.sort_index(inplace=True)\n", - "\n", - "# 1. Unwrap the phase\n", - "simplified_df['phase_over_2pi'] = np.unwrap(simplified_df['phase_over_2pi'], period=1)\n", - "\n", - "# 2. Get rid of the global phase\n", - "simplified_df['phase_over_2pi'] -= simplified_df['phase_over_2pi'].iloc[N//2]\n", - "simplified_df['f_classical'] -= simplified_df['f_classical'].iloc[N//2]\n", - "\n", - "# You can use the helper function:\n", - "# simplified_df = simplify_df(df)\n", - "\n", - "# Plot the results\n", - "plt.figure()\n", - "plot_classical()\n", - "simplified_df.plot(style='o', ax=plt.gca())\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "94f4f5f5", - "metadata": {}, - "source": [ - "For convinience, the full code to generate this graph:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "97f5ce93", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit Width: 7\n", - "Circuit Depth: 30\n", - "Gate Counts: {'u': 35, 'cx': 27}\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "p = params()\n", - "# f(x) = 0.5*x + 0.25\n", - "# Gradient: f'(0) = 0.5\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]], ancilla: Output[QNum[n0, SIGNED, n0]]):\n", - " # 1. State preparation\n", - " \n", - " # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", - " allocate(n, x)\n", - " hadamard_transform(x)\n", - " \n", - " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", - " # Note: the ancilla is a signed fractional number,\n", - " # so the state |1111...1> corresponds to the value -1/N0\n", - " # which is the most negative value\n", - " numeric_value = -0.5**n0\n", - " ancilla |= numeric_value\n", - " qft(ancilla)\n", - "\n", - " # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", - " # Calculate the normalized f and add it to the ancilla\n", - " val = f_normalized(x)\n", - " inplace_add(val, ancilla)\n", - "\n", - " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", - " # invert(lambda: qft(x))\n", - "\n", - "df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)" - ] - }, - { - "cell_type": "markdown", - "id": "4f640f7d", - "metadata": {}, - "source": [ - "## 2.2. Direct Phase" - ] - }, - { - "cell_type": "markdown", - "id": "7b083b7e", - "metadata": {}, - "source": [ - "The phase kickback approach is good when we have a state-oracle, but in our simulation it is very unefficient." - ] - }, - { - "cell_type": "markdown", - "id": "cbe98ddd", - "metadata": {}, - "source": [ - "Another approach is to directly prepare the wanted state.\n", - "In our case:\n", - "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}(\\delta-\\frac{N}{2}))}\\ket\\delta$$\n", - "\n", - "Here we can see the same example using the prepare_complex_amplitudes function.\\\n", - "You can look at the circuit width/depth and gate count to compare both methods.\\\n", - "In real applications, both methods can be used, depending on the problem." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "7e84cce2", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit Width: 3\n", - "Circuit Depth: 5\n", - "Gate Counts: {'u': 3, 'cx': 4}\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "p = params()\n", - "# f(x) = 0.5*x + 0.25\n", - "# Gradient: f'(0) = 0.5\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " # 1. State preparation\n", - " \n", - " # Now using the direct prepare_complex_amplitudes instead of the ancilla and the inplace_add\n", - " x_array = np.arange(N) # Create an array of x values corresponding to the quantum states\n", - " phases = f_normalized(x_array) * 2 * np.pi # Apply 2pi times the normalized function to get the phases\n", - " magnitudes = np.ones(N) * 1 / N # Set equal magnitudes for all states\n", - " # You can use the helper function:\n", - " # magnitudes, phases = p.calculate_magnitude_and_phase()\n", - "\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", - " # invert(lambda: qft(x))\n", - "\n", - "df = run_statevector_simulation(main, print_circuit_info=True)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)" - ] - }, - { - "cell_type": "markdown", - "id": "bcf74e4c", - "metadata": {}, - "source": [ - "The graph is exactly the same as the phase kickback method.\\\n", - "From this point, we will use this method over the phase kickback, in order to have better efficiency." - ] - }, - { - "cell_type": "markdown", - "id": "15415d27", - "metadata": {}, - "source": [ - "## 2.3. Quadratic Function" - ] - }, - { - "cell_type": "markdown", - "id": "2ccef2dd", - "metadata": {}, - "source": [ - "More interesting are non-linear functions.\\\n", - "In the next example we will see a quadratic function.\\\n", - "Note that the 'magic' does not happen in this step. You will see that the phases agree with the function completly and doesn't do the linearization needed to calculate the gradient. The magic will happen in the next step where the QFT will do the linearization for us." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "7f2a5f63", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit Width: 3\n", - "Circuit Depth: 12\n", - "Gate Counts: {'u': 8, 'cx': 6}\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "p = params()\n", - "# f(x) = 0.5*x^2 + 0.25*x + 0.1\n", - "# Gradient: f'(x) = x + 0.25, so f'(0) = 0.25\n", - "p.set_function(p.quadratic, (0.5, 0.25, 0.1))\n", - "p.l = 2\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " # 1. State preparation\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", - " # invert(lambda: qft(x))\n", - "df = run_statevector_simulation(main, print_circuit_info=True)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)" - ] - }, - { - "cell_type": "markdown", - "id": "fc8328e1", - "metadata": {}, - "source": [ - "If we decrease $l$, we look at the function more closly, and it is closer to linear." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "25b19fcf", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit Width: 3\n", - "Circuit Depth: 12\n", - "Gate Counts: {'u': 8, 'cx': 6}\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "p = params()\n", - "# f(x) = 0.5*x^2 + 0.25*x + 0.1\n", - "# Gradient: f'(x) = x + 0.25, so f'(0) = 0.25\n", - "p.set_function(p.quadratic, (0.5, 0.25, 0.1))\n", - "p.l = 0.2\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " # 1. State preparation\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", - " # invert(lambda: qft(x))\n", - "df = run_statevector_simulation(main, print_circuit_info=True)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)" - ] - }, - { - "cell_type": "markdown", - "id": "edc56f33", - "metadata": {}, - "source": [ - "# 3. Full Algorithm" - ] - }, - { - "cell_type": "markdown", - "id": "ed986f78", - "metadata": {}, - "source": [ - "## 3.1. Linear Functions" - ] - }, - { - "cell_type": "markdown", - "id": "f2032268", - "metadata": {}, - "source": [ - "The next and final step of the algorithm is to apply QFT on the coordinate.\\\n", - "As discussed earlier, applying the QFT will automatically extract the gradient from the phases, and create a measurable state with the value of the gradient (normalized)." - ] - }, - { - "cell_type": "markdown", - "id": "42bf7612", - "metadata": {}, - "source": [ - "To see the full algorithm in action, we will switch from the statevector simulation to standard simulation, because the final result is acquired by a measurement and not by looking at the phases." - ] - }, - { - "cell_type": "markdown", - "id": "0d267096", - "metadata": {}, - "source": [ - "Let's start with a simple example of linear function." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "dfc9b43c", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parsed counts: [{'x': 6}: 2048]\n", - "The analytical gradient is: -0.5\n", - "The majority gradient is: -0.5\n", - "The majority result is correct\n", - "####################################################\n", - "Success rate: 100.00% (2048/2048 shots)\n", - "[\u001b[92m██████████████████████████████████████████████████\u001b[91m\u001b[0m] 100.00%\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "p = params()\n", - "p.set_function(p.linear, (-0.5, 0.25))\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " # 1. State preparation\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - " # 2. QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", - "\n", - "qprog = synthesize(main)\n", - "job = execute(qprog)\n", - "# job.open_in_ide() # Uncomment to see the results in the IDE\n", - "pc = job.get_sample_result().parsed_counts\n", - "\n", - "# You can use the helper function:\n", - "# pc = run_standard_simulation(main)\n", - "\n", - "# Translate the majority state to a gradient value\n", - "majority_state = pc[0].state\n", - "value = majority_state.get('x')\n", - "# If the value is in the upper half of the range,\n", - "# it represents a negative value due to the modular arithmetic of the quantum states.\n", - "if value >= N//2:\n", - " value -= N\n", - "# Divide by (N/m) to get the actual gradient value.\n", - "majority_gradient = value / (N/m)\n", - "\n", - "# Or use the helper function:\n", - "# majority_gradient = state_to_gradient(majority_state.get('x'))\n", - "\n", - "# Print the results and compute the majority gradient\n", - "print(\"Parsed counts:\", pc)\n", - "print(f\"The analytical gradient is: {p.analytical_gradient(0)}\")\n", - "print(f\"The majority gradient is: {majority_gradient}\")\n", - "\n", - "# Check if the majority result is correct within the resolution of the algorithm\n", - "resolution = m/N\n", - "is_correct = abs(majority_gradient - p.analytical_gradient(0)) < resolution/2\n", - "print(f\"The majority result is\", \"correct\" if is_correct else \"incorrect\")\n", - "print(\"####################################################\")\n", - "\n", - "# Compute the success rate of the algorithm, i.e. the percentage of shots that are correct within the resolution of the algorithm.\n", - "success_rate, success_shots, total_shots = compute_success_rate(pc, analytic_derivatives={'x': p.analytical_gradient(0)})\n", - "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", - "show_bar(success_rate)\n", - "\n", - "# Visualize the theoretical values of the phases\n", - "# We used the standard simulation, so this is theoretical values only without the phases from the simulation\n", - "plot_theoretical()\n", - "\n", - "# You can use the helper function:\n", - "# analyze_results(pc)" - ] - }, - { - "cell_type": "markdown", - "id": "2eafff41", - "metadata": {}, - "source": [ - "The result for the gradient is always a multiple of m/N.\\\n", - "In the previous example, the gradient was -0.5, while the resolution (m/N) was 0.25.\\\n", - "The gradient is a multiple of the resolution, and therefore the result can be exact, and the success rate was 100%.\\\n", - "\\\n", - "More complex case is where the gradient is not a multiple of the resolution.\\\n", - "In those cases, the result will be a superposition of multiple solutions, but we can still get a good approximation for the gradient from the result.\\\n", - "Let's see it in the next example.\\\n", - "TODO: Consider removing this example, because it doesn't match the flow of the explaination." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "be423003", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parsed counts: [{'x': 2}: 1755, {'x': 3}: 133, {'x': 1}: 63, {'x': 4}: 29, {'x': 5}: 20, {'x': 7}: 20, {'x': 0}: 19, {'x': 6}: 9]\n", - "The analytical gradient is: 0.55\n", - "The majority gradient is: 0.5\n", - "The majority result is correct\n", - "####################################################\n", - "Success rate: 85.69% (1755/2048 shots)\n", - "[\u001b[92m███████████████████████████████████████████\u001b[91m-------\u001b[0m] 85.69%\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "p = params()\n", - "# f(x) = 0.55*x + 0.25\n", - "# Gradient: f'(0) = 0.55\n", - "# Pay attention that 0.55 is not a multiple of m/N = 0.25,\n", - "# so we expect to get a superposition of multiple states around the correct gradient.\n", - "p.set_function(p.linear, (0.55, 0.25))\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " # 1. State preparation\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - " # 2. QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", - "\n", - "pc = run_standard_simulation(main)\n", - "analyze_results(pc)" - ] - }, - { - "cell_type": "markdown", - "id": "a67ddc29", - "metadata": {}, - "source": [ - "## 3.2. Quadratic Function" - ] - }, - { - "cell_type": "markdown", - "id": "d72f288e", - "metadata": {}, - "source": [ - "Again, let's try calculating the gradient of a non-linear function. In the next example, we will explore a quadratic function.\\\n", - "In the case of non-linear function, we will need to cleverly choose the value of $l$ - the interval around the origin.\\\n", - "In order for the algorithm to work, we need to work in the linear regime around the origin, so we need to choose small enough $l$." - ] - }, - { - "cell_type": "markdown", - "id": "a741bff9", - "metadata": {}, - "source": [ - "First, for good selection of $l$, we see that the points are almost linear, and we get a good success rate." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "da592b2b", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parsed counts: [{'x': 1}: 2013, {'x': 0}: 16, {'x': 2}: 15, {'x': 3}: 3, {'x': 5}: 1]\n", - "The analytical gradient is: 0.25\n", - "The majority gradient is: 0.25\n", - "The majority result is correct\n", - "####################################################\n", - "Success rate: 98.29% (2013/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.29%\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# In this example we will use the quadratic function\n", - "p = params()\n", - "# f(x) = 0.6*x^2 + 0.25*x + 0.1\n", - "# Gradient: f'(x) = 1.2*x + 0.25, so f'(0) = 0.25\n", - "p.set_function(p.quadratic, (0.6, 0.25, 0.1))\n", - "# Setting l properly, ensuring we are in the linear regime of the function.\n", - "p.l = 0.1\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " # 1. State preparation\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - " # 2. QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", - "\n", - "pc = run_standard_simulation(main)\n", - "analyze_results(pc)" - ] - }, - { - "cell_type": "markdown", - "id": "40d8d166", - "metadata": {}, - "source": [ - "But if we increase $l$ outside of the linear regime, we see that the success rate get drasticly lower:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "27717a39", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parsed counts: [{'x': 0}: 501, {'x': 1}: 492, {'x': 2}: 484, {'x': 7}: 208, {'x': 3}: 184, {'x': 6}: 90, {'x': 4}: 46, {'x': 5}: 43]\n", - "The analytical gradient is: 0.25\n", - "The majority gradient is: 0.0\n", - "The majority result is incorrect\n", - "####################################################\n", - "Success rate: 24.02% (492/2048 shots)\n", - "[\u001b[92m████████████\u001b[91m--------------------------------------\u001b[0m] 24.02%\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# In this example we will use the quadratic function\n", - "p = params()\n", - "# f(x) = 0.6*x^2 + 0.25*x + 0.1\n", - "# Gradient: f'(x) = 1.2*x + 0.25, so f'(0) = 0.25\n", - "p.set_function(p.quadratic, (0.6, 0.25, 0.1))\n", - "# Setting l to be too big, so we are outside of the linear regime of the function.\n", - "p.l = 1\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " # 1. State preparation\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - " # 2. QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", - "\n", - "pc = run_standard_simulation(main)\n", - "analyze_results(pc)" - ] - }, - { - "cell_type": "markdown", - "id": "d5b47027", - "metadata": {}, - "source": [ - "# 4. Parameters Selection - TODO" - ] - }, - { - "cell_type": "markdown", - "id": "659ca4e7", - "metadata": {}, - "source": [ - "We saw earlier the importance of proper selection of some of the parameters.\\\n", - "Let's dive deeper into the parameters selection." - ] - }, - { - "cell_type": "markdown", - "id": "c634e599", - "metadata": {}, - "source": [ - "## 4.1. Understanding the parameters" - ] - }, - { - "cell_type": "markdown", - "id": "61a68f72", - "metadata": {}, - "source": [ - "There are three main parameters to be selected: $l$, $m$ and $n$.\\\n", - "$n$ is the number of bits of the result. The bigger $n$, the higher the accuracy of the result.\\\n", - "$l$ is the interval size around the origin ($dx$).\\\n", - "$m/2$ is the maximal gradient that can be calculated (in absolute value)." - ] - }, - { - "cell_type": "markdown", - "id": "3e3dfc6f", - "metadata": {}, - "source": [ - "For the parameter $l$, we saw earlier that it should be selected such that we look at the linear regime of the function. See section 2.2." - ] - }, - { - "cell_type": "markdown", - "id": "c539ec98", - "metadata": {}, - "source": [ - "Understanding the parameter $m$ is a little trickier. We will look at a bounding box around the origin.\\\n", - "The width of the box (dx) is $l$, spanning from $-l/2$ to $l/2$. The slope of the graph (dy/dx) is bounded between $-m/2$ to $m/2$. Therefore, the height of the box (dy) should be bounded dy/dx*dx, so the height should be $lm/2$, making the box span between $-lm/4$ to $lm/4$.\\\n", - "When we plot the graph, if all the points are inside this box, then we know that the gradient is bounded by $m/2$ and we will get the correct result.\\\n", - "If the points are outside this box, we will get aliasing in the results and get an incorrect gradient.\\\n", - "Note that in our graphs we use the normalized function instead of the original function, so the box is between $-N/4$ to $N/4$ instead of $lm/4$." - ] - }, - { - "cell_type": "markdown", - "id": "f0a30a00", - "metadata": {}, - "source": [ - "We will see now the same function, once with correct selection of m and one with incorrect selection of $m$, and we can see that if $m$ is too small the theoretical values are out of the bounding box, and the phases from the simulation are folded into the box creating aliasing. " - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "a2a46ca7", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# In this example we will use the linear function\n", - "p = params()\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.m = 2 # Correct selection of m - no aliasing.\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - "df = run_statevector_simulation(main, print_circuit_info=False)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)\n", - "# simplified_df" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "812c0c30", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# In this example we will use the linear function\n", - "p = params()\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.m = 1.333 # Marginal selection of m - still no aliasing.\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - "df = run_statevector_simulation(main, print_circuit_info=False)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)\n", - "# simplified_df" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "19a77750", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# In this example we will use the linear function\n", - "p = params()\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.m = 0.3 # Incorrect selection of m - aliasing occurs.\n", - "p.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]]):\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - "\n", - "df = run_statevector_simulation(main, print_circuit_info=False)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)\n", - "# simplified_df" - ] - }, - { - "cell_type": "markdown", - "id": "34d82a6f", - "metadata": {}, - "source": [ - "## 4.2. Success rate as function of parameter selection\n", - "**TODO**: consider removing this part" - ] - }, - { - "cell_type": "markdown", - "id": "19c66ba4", - "metadata": {}, - "source": [ - "We can plot the success rate as a function of the selected parameters.\\\n", - "In the first example, we will have a quadratic function $f(x)=0.6x^2+0.25x+0.1$, $f'(0)=0.25$.\\\n", - "We can plot the graph for different selections of m.\\\n", - "We discussed earlier that $m/2$ is the bound for the gradient value, so we expect to have poor results for $m<0.5$, good results for $m>0.5$, until reaching $m=0.25N=4$, where the resolution won't be good enough for meaningful result.\\\n", - "Note the oscillations in the sucess rate in the optimal region. This is due to the discrete values the algorithm can return. As we increase the number of bits $n$, the oscillations will be smaller." - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "59ca5244", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=0.05: Success rate = 0.00%\n", - "m=0.1: Success rate = 0.00%\n", - "m=0.3: Success rate = 0.00%\n", - "m=0.5: Success rate = 0.00%\n", - "m=0.55: Success rate = 0.00%\n", - "m=0.7: Success rate = 79.39%\n", - "m=0.8: Success rate = 80.62%\n", - "m=0.9: Success rate = 87.40%\n", - "m=1.0: Success rate = 95.17%\n", - "m=1.5: Success rate = 73.05%\n", - "m=2.0: Success rate = 98.19%\n", - "m=4.0: Success rate = 0.00%\n", - "m=6.0: Success rate = 0.00%\n", - "m=10.0: Success rate = 0.00%\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def plot_success_rate_vs_m(m_values, function, function_params, l_val=0.1, n_val=3):\n", - " \"\"\"\n", - " Iterate over different m values and plot success rate as a function of m.\n", - "\n", - " Args:\n", - " m_values: list of m values to test\n", - " function: function name (\"linear\" / \"quadratic\") or callable\n", - " function_params: parameters for the function\n", - " l_val: l parameter (default 0.1)\n", - " n_val: n parameter (default 3)\n", - " \"\"\"\n", - " success_rates = []\n", - "\n", - " for m_val in m_values:\n", - " p = params()\n", - " p.m = m_val\n", - " p.l = l_val\n", - " p.n = n_val\n", - " p.set_function(function, function_params)\n", - " p.unpack()\n", - "\n", - " @qfunc\n", - " def main(x: Output[QNum[n]]):\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - " invert(lambda: qft(x))\n", - "\n", - " pc = run_standard_simulation(main)\n", - " analytic_grad = p.analytical_gradient(0)\n", - " success_rate, _, _ = compute_success_rate(pc, analytic_derivatives={'x': analytic_grad}, reject_underresolution=True)\n", - " success_rates.append(success_rate)\n", - " print(f\"m={m_val}: Success rate = {success_rate:.2%}\")\n", - "\n", - " # Plot\n", - " plt.figure(figsize=(10, 6))\n", - " plt.plot(m_values, success_rates, 'o-', linewidth=2, markersize=8)\n", - " plt.xlabel('m parameter', fontsize=12)\n", - " plt.ylabel('Success Rate', fontsize=12)\n", - " plt.title('Success Rate vs m Parameter', fontsize=14)\n", - " plt.grid(True, alpha=0.3)\n", - " plt.ylim([0, 1.05])\n", - " ax = plt.gca()\n", - " ax.axvspan(0.5, 4.0, color='green', alpha=0.15, label='Target m range')\n", - " ax.legend()\n", - " plt.show() \n", - " return success_rates\n", - "\n", - "# Example usage:\n", - "m_values = [0.05, 0.1, 0.3, 0.5, 0.55, 0.7, 0.8, 0.9, 1.0, 1.5, 2.0, 4.0, 6.0, 10.0]\n", - "results = plot_success_rate_vs_m(m_values, \"quadratic\", (0.6, 0.25, 0.1))" - ] - }, - { - "cell_type": "markdown", - "id": "37699833", - "metadata": {}, - "source": [ - "As for the $l$ parameter, we need to be in the linear regime, so we need to ensure $l$ is small enough, as can be seen in the next example:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "806fc176", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=0.1: Success rate = 94.19%\n", - "l=0.2: Success rate = 78.86%\n", - "l=0.3: Success rate = 60.84%\n", - "l=0.4: Success rate = 38.92%\n", - "l=0.5: Success rate = 23.05%\n", - "l=1: Success rate = 8.94%\n", - "l=1.5: Success rate = 15.62%\n", - "l=2.0: Success rate = 14.75%\n", - "l=3.0: Success rate = 28.37%\n", - "l=4.0: Success rate = 2.25%\n", - "l=5.0: Success rate = 24.37%\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def plot_success_rate_vs_l(l_values, function, function_params, m_val=2.0, n_val=3):\n", - " \"\"\"\n", - " Iterate over different l values and plot success rate as a function of l.\n", - "\n", - " Args:\n", - " l_values: list of l values to test\n", - " function: function name (\"linear\" / \"quadratic\") or callable\n", - " function_params: parameters for the function\n", - " m_val: m parameter (default 1.0)\n", - " n_val: n parameter (default 3)\n", - " \"\"\"\n", - " success_rates = []\n", - "\n", - " for l_curr in l_values:\n", - " p = params()\n", - " p.m = m_val\n", - " p.l = l_curr\n", - " p.n = n_val\n", - " p.set_function(function, function_params)\n", - " p.unpack()\n", - "\n", - " @qfunc\n", - " def main(x: Output[QNum[n]]):\n", - " magnitudes, phases = p.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes, phases=phases, out=x)\n", - " invert(lambda: qft(x))\n", - "\n", - " pc = run_standard_simulation(main)\n", - " analytic_grad = p.analytical_gradient(0)\n", - " success_rate, _, _ = compute_success_rate(pc, analytic_derivatives={\"x\": analytic_grad})\n", - " success_rates.append(success_rate)\n", - " print(f\"l={l_curr}: Success rate = {success_rate:.2%}\")\n", - "\n", - " plt.figure(figsize=(10, 6))\n", - " plt.plot(l_values, success_rates, \"o-\", linewidth=2, markersize=8)\n", - " plt.xlabel(\"l parameter\", fontsize=12)\n", - " plt.ylabel(\"Success Rate\", fontsize=12)\n", - " plt.title(\"Success Rate vs l Parameter\", fontsize=14)\n", - " plt.grid(True, alpha=0.3)\n", - " plt.ylim([0, 1.05])\n", - " plt.show()\n", - "\n", - " return success_rates\n", - "\n", - "\n", - "# Example usage:\n", - "l_values = [0.1, 0.2, 0.3, 0.4, 0.5, 1, 1.5, 2.0, 3.0]\n", - "results_l = plot_success_rate_vs_l(l_values, \"quadratic\", (0.6, 0.25, 0.1), m_val=1.0, n_val=3)" - ] - }, - { - "cell_type": "markdown", - "id": "7b3097bb", - "metadata": {}, - "source": [ - "# 5. Multi-Coordinates Examples" - ] - }, - { - "cell_type": "markdown", - "id": "854afbc8", - "metadata": {}, - "source": [ - "This algorithm works in multiple dimensions too.\\\n", - "We will now see an example in 2D, f(x,y).\\\n", - "We will start with a linear and decoupled function $f(x,y)=ax+by+c$." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "2f4588e6", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[{'x': 2, 'y': 7}: 2048]\n", - "Analytical gradient: (dx, dy) = (0.5, -0.25)\n", - "Majority gradient: (dx, dy) = (0.5, -0.25)\n", - "Success rate: 100.00% (2048/2048 shots)\n", - "[\u001b[92m██████████████████████████████████████████████████\u001b[91m\u001b[0m] 100.00%\n" - ] - } - ], - "source": [ - "px = params()\n", - "py = params()\n", - "\n", - "# Set the functions for x and y axes\n", - "# f(x, y) = a*x + b*y + c = 0.5*x - 0.25*y + 0.1\n", - "# df/dx = 0.5, df/dy = -0.25\n", - "a, b, c = 0.5, -0.25, 0.1\n", - "px.set_function(px.linear, (a, 0.0))\n", - "py.set_function(py.linear, (b, c))\n", - "\n", - "# Use the globals from px. \n", - "# Be careful - If you change the parameters in py you can not use the globals anymore!\n", - "px.unpack()\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]], y: Output[QNum[n]]):\n", - " # State preparation for x-axis contribution\n", - " magnitudes_x, phases_x = px.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes_x, phases=phases_x, out=x)\n", - "\n", - " # State preparation for y-axis contribution\n", - " magnitudes_y, phases_y = py.calculate_magnitude_and_phase()\n", - " prepare_complex_amplitudes(magnitudes=magnitudes_y, phases=phases_y, out=y)\n", - "\n", - " # Gradient extraction on each axis\n", - " invert(lambda: qft(x))\n", - " invert(lambda: qft(y))\n", - "\n", - "pc = run_standard_simulation(main)\n", - "print(pc)\n", - "\n", - "majority_state = pc[0].state\n", - "gx_true = px.analytical_gradient(0)\n", - "gy_true = py.analytical_gradient(0)\n", - "\n", - "gx_meas = state_to_gradient(majority_state.get(\"x\"))\n", - "gy_meas = state_to_gradient(majority_state.get(\"y\"))\n", - "\n", - "print(f\"Analytical gradient: (dx, dy) = ({gx_true}, {gy_true})\")\n", - "print(f\"Majority gradient: (dx, dy) = ({gx_meas}, {gy_meas})\")\n", - "\n", - "success_rate, success_shots, total_shots = compute_success_rate(\n", - " pc, analytic_derivatives={\"x\": gx_true, \"y\": gy_true}\n", - ")\n", - "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", - "show_bar(success_rate)" - ] - }, - { - "cell_type": "markdown", - "id": "d430350c", - "metadata": {}, - "source": [ - "We can also have more complex example, with non-linear and coupled equation: $f(x, y)=ax^2+by^2+cxy+dx+ey+f$." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "93751a65", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[{'x': 1, 'y': 6}: 1992, {'x': 0, 'y': 6}: 14, {'x': 2, 'y': 6}: 14, {'x': 1, 'y': 5}: 8, {'x': 1, 'y': 7}: 6, {'x': 3, 'y': 6}: 3, {'x': 6, 'y': 6}: 2, {'x': 2, 'y': 7}: 1, {'x': 0, 'y': 3}: 1, {'x': 7, 'y': 1}: 1, {'x': 4, 'y': 6}: 1, {'x': 5, 'y': 4}: 1, {'x': 0, 'y': 7}: 1, {'x': 2, 'y': 5}: 1, {'x': 0, 'y': 5}: 1, {'x': 6, 'y': 7}: 1]\n", - "Analytical gradient: (dx, dy) = (0.25, -0.5)\n", - "Majority gradient: (dx, dy) = (0.25, -0.5)\n", - "Success rate: 97.27% (1992/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.27%\n" - ] - } - ], - "source": [ - "p = params()\n", - "p.l = 0.1\n", - "p.unpack()\n", - "\n", - "def f(x, y):\n", - " a, b, c, d, e, f = 0.6, -0.4, 0.25, 0.25, -0.5, 0.1\n", - " global gradient_x, gradient_y\n", - " gradient_x = d\n", - " gradient_y = e\n", - " return a * x**2 + b * y**2 + c * x * y + d * x + e * y + f\n", - "\n", - "# Generated functions\n", - "def f_normalized(x, y):\n", - " val = f(l / N * (x - N // 2), l / N * (y - N // 2))\n", - " val *= N / (l * m)\n", - " return val\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n]], y: Output[QNum[n]]):\n", - " # 1. State preparation\n", - " x_array = np.arange(N) # Create an array of x values corresponding to the quantum states\n", - " y_array = np.arange(N) # Create an array of y values corresponding to the quantum states\n", - " \n", - " # In order to use the prepare_complex_amplitudes function, we need to flatten the 2D arrays of magnitudes and phases into 1D arrays.\n", - " X_grid, Y_grid = np.meshgrid(x_array, y_array, indexing='ij')\n", - " phases_2d = f_normalized(X_grid, Y_grid) * 2 * np.pi\n", - " magnitudes_2d = np.ones((N, N)) / N \n", - " phases_flat = phases_2d.flatten().tolist()\n", - " magnitudes_flat = magnitudes_2d.flatten().tolist()\n", - " \n", - " # Prepare the state using the flattened arrays, then bind the combined register to the x and y registers.\n", - " combined_reg = QNum(\"combined_reg\")\n", - " prepare_complex_amplitudes(\n", - " magnitudes=magnitudes_flat, \n", - " phases=phases_flat, \n", - " out=combined_reg\n", - " )\n", - " bind(combined_reg, [y, x])\n", - "\n", - " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", - " invert(lambda: qft(y))\n", - "\n", - "pc = run_standard_simulation(main)\n", - "print(pc)\n", - "\n", - "majority_state = pc[0].state\n", - "gx_true = gradient_x\n", - "gy_true = gradient_y\n", - "\n", - "gx_meas = state_to_gradient(majority_state.get(\"x\"))\n", - "gy_meas = state_to_gradient(majority_state.get(\"y\"))\n", - "\n", - "print(f\"Analytical gradient: (dx, dy) = ({gx_true}, {gy_true})\")\n", - "print(f\"Majority gradient: (dx, dy) = ({gx_meas}, {gy_meas})\")\n", - "\n", - "success_rate, success_shots, total_shots = compute_success_rate(\n", - " pc, analytic_derivatives={\"x\": gx_true, \"y\": gy_true}\n", - ")\n", - "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", - "show_bar(success_rate)" - ] - }, - { - "cell_type": "markdown", - "id": "35e960db", - "metadata": {}, - "source": [ - "# References" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7f9c7201", - "metadata": {}, - "outputs": [], - "source": [ - "# TODO: add" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "classiq", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.12.12" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/algorithms/gradient_estimation/Stephen P. Jordan - Fast Quantum Algorithm for Numerical Gradient Estimation.pdf b/algorithms/gradient_estimation/Stephen P. 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zc@+^66kuj&V-bY1ib4d~MA)Ff!yxbfPN9j!%Zp@ZuWM`n`;i*(9;_U!NR*T!uSAjl E9|-(IUjP6A literal 0 HcmV?d00001 diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb new file mode 100644 index 000000000..05015d516 --- /dev/null +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -0,0 +1,2137 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "0", + "metadata": {}, + "source": [ + "# Initialization" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "1", + "metadata": {}, + "outputs": [], + "source": [ + "from gradient_estimation_helpers import *\n", + "\n", + "# TODO: remove this\n", + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: small fixes along the notebook\n", + "# TODO: code fix - free the ancilla after using it\n", + "# TODO: clean up the explanations and add references to the paper\n", + "# TODO: clean up section 4 (Parameters selection)\n", + "# TODO: check all or's comments from github and make sure they are addressed\n", + "# TODO: add tests" + ] + }, + { + "cell_type": "markdown", + "id": "3", + "metadata": {}, + "source": [ + "# Fast Quantum Algorithm for Numerical Gradient Estimation\n", + "> Given a scalar function of $d$ dimensions, $f(x_1, ... x_d)$, it is useful to find the gradient of the function at a specific point.\\\n", + "> On a classical computer, this requires at least d+1 queries of the function $f$.\\\n", + "> In this notebook we will explore quantum algorithm to find the gradient with just a single query of the function.\\\n", + "> This is a dramatic improvement in large dimensions functions, as most of the times the most expensive part of calculating the derivative is querying the function.\n", + "> * **Input:** A black box function $f$ of $d$ variables.\n", + "> * **Promise:** The function is a smooth real scalar function, and the gradient is bounded with a known value $|\\nabla f|<\\nabla f_{\\text{max}}$.\n", + "> * **Output:** The gradient $\\nabla f$ at the origin with $n$ bits of precision.\n", + "\n", + "> **Complexity:** In the context of many numerical calculations, black-box query complexity is a natural measure of algorithmic efficiency. In this measure, the classical algorithm queries the function at least $d+1$ times, while the quantum algorithm only queries the function a single time.\n", + "\n", + "\n", + "The core concept of the algorithm is to first 'apply' the function to the phase of a superposition state, then extract the gradient value from the phase to a measurable state by using a QFT.\\\n", + "Let's see it step by step, first a little simplified version to understand the concept, and then fixing the inaccuracies for the final algorithm.\\\n", + "![Quantum Circuit](quantum_circuit.png)\\\n", + "**TODO:** Decide which image to use, with or without the ancilla\\\n", + "![Quantum Circuit](quantum_circuit_2.png)" + ] + }, + { + "cell_type": "markdown", + "id": "4", + "metadata": {}, + "source": [ + "## Simplified explanation of the algorithm\n", + "As briefly mentioned earlier, the algorithm can be divided to two steps:\n", + "1. Applying the function to the phase\n", + "2. Extracting the gradient value to a measurable state\n", + "\n", + "In more details:\n", + "1. For each coordinate ($x_i$), we start with the state $|\\delta_i\\rangle=|0\\rangle+|1\\rangle+|2\\rangle....|N-1\\rangle$, by applying the Hadamard gate on $|0\\rangle$.\\\n", + "For simplicity we will discuss a case of single coordinate, but if there is more than one coordinate, the state $|\\delta\\rangle$ is just a product state of all $|\\delta_i\\rangle$, and the algorithm stays the same.\n", + "$$|\\delta\\rangle=\\prod_i|\\delta_i\\rangle$$\n", + "2. Using the phase kickback technique, we apply the function to the phase of each ket creating the state:\n", + "$$e^{i\\cdot2\\pi f(0)}|0\\rangle + e^{i\\cdot2\\pi f(1)}|1\\rangle + e^{i\\cdot2\\pi f(2)}|2\\rangle ..... e^{i\\cdot2\\pi f(N-1)}|N-1\\rangle$$\n", + "**TODO**: Decide to keep, move or remove those images\n", + "![](step_2.png)\\\n", + "3. We note the fact that for small enough interval, we can approximate: $f(x)\\approx f(0)+x\\cdot f'(x)$, so we can write the previous state as: \n", + "$$ e^{i\\cdot2\\pi f(0)}(|0\\rangle + e^{i\\cdot2\\pi f'(0)}|1\\rangle + e^{i\\cdot2\\pi 2f'(0)}|2\\rangle ..... e^{i\\cdot2\\pi (N-1)f'(0)}|N-1\\rangle) = e^{i\\cdot2\\pi f(0)}\\sum e^{i\\cdot2\\pi jf'(0)}|j\\rangle $$\n", + "![](step_3.png)\\\n", + "4. We note that this state is exactly the fourier transform of the state $|f'(0)\\rangle$, so we apply the inverse fourier transform and get the result: $$|f'(0)\\rangle$$\n", + "5. We measure to get $f'(0)$, and for a multi-coordinates function $\\nabla f$.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "5", + "metadata": {}, + "source": [ + "## Full explanation of the algorithm\n", + "The previous explanation covers the main idea of the algorithm, but misses some important details on negative and fractional values.\\\n", + "In this explanation we will fill in these details.\\\n", + "When we calculate gradient, we look on an interval around the point of interest (in this case, it will be the origin). We will call this interval $l$.\n", + "The state $|\\delta_i\\rangle$ should represent $N$ equally spaced points around the origin in the interval $l$, so we normalized it to be:\n", + "$$ x=\\frac{l}{N}\\delta $$\n", + "With signed $\\delta$ ranging from $-N/2$ to $N/2-1$: $\\delta=-N/2$ is the leftmost point ($-l/2$), $\\delta=0$ is the origin, and $\\delta=N/2-1$ is the rightmost point ($l/2$)*.\\\n", + "\\\n", + "We also need to normalize the result state. Say the expected gradient is bounded between $-m/2$ and $m/2$, we want to represent those values using the $N$ states of the coordinate, so doing a similar trick we can define $$ \\nabla f=\\frac{m}{N}\\delta_{measured} $$\\\n", + "\\\n", + "When using the algorithm we need to select $l$ and $m$ using our prior knowledge on the function $f(x)$, and $N$ will define the final resolution we get.\\\n", + "$l$ should be small enough so we will stay in a linear regime of the function, and $m$ should be larger than the maximum possible gradient, but not too large because then we will lose resolution.\n", + "\\\n", + "Using those two normalizations, we change two things in the algorithm:\n", + "1. In step 2, instead of applying $f(\\delta)$, we apply $\\frac{N}{ml}f(\\frac{l}{N}\\delta)$.\n", + "2. In step 5, the signed measurement directly gives $\\frac{N}{m}\\nabla f$, so $\\nabla f = \\frac{m}{N}\\delta_{measured}$.\n", + "Using a signed register means the measured $\\delta_{measured}$ is already the correct signed value with no further adjustment needed.\\\n", + "\n", + "\\* The right point is actually $l/2-l/N$ and not $l/2$, because the center point is at the origin and $N$ must be even, but for the algorithm understanding it doesn't really matter." + ] + }, + { + "cell_type": "markdown", + "id": "6", + "metadata": {}, + "source": [ + "## Parameter Selection\n", + "As briefly discussed before, we need to select appropriate values for $l$, $m$ and $N$ (and when using the ancilla method, also $N_0$, but we will not discuss it here).\\\n", + "Let's define: \n", + "* $\\nabla f_{max}$ - a bound for the value of $\\nabla f$ in the region around the origin, $|\\nabla f|<\\nabla f_{max}$\n", + "* $\\epsilon$ - desired accuracy for $\\nabla f$ estimation, $|\\nabla f_{est}-\\nabla f| < \\epsilon$\n", + "* $d$ - the dimensionality of the function $f$\n", + "* $D_2$ - typical value for the second derivative of $f$\n", + "\n", + "### Selecting $l$\n", + "Starting with $l$, this is the interval around the origin for the gradient estimation. Exactly like in classical gradient calculation, the interval should be small enough that we will be in the linear regime of the function.\\\n", + "If we want to reach accuracy $\\epsilon$, we need the gradient inside the interval to have smaller variance than $\\epsilon$, meaning $max(\\nabla f)-min(\\nabla f)<\\epsilon$. Using the second derivative approximation $max(\\nabla f)-min(\\nabla f)\\approx|\\nabla^2 f|\\cdot l<\\epsilon$, meaning we have to select $l$ such that $l<\\frac{\\epsilon}{|\\nabla^2 f|}$.\\\n", + "For example, for a quadratic function $f(x)=ax^2+bx+c$, $l$ should be smaller than the order of $\\frac{\\epsilon}{2a}$.\\\n", + "**TODO**: This isn't accurate, use the paper's more accurate result giving $l\\leq\\frac{2\\sqrt{3}\\epsilon}{D_2\\sqrt{d}}$.\n", + "\n", + "### Selecting $m$\n", + "$m$ is exactly defined as the bound for the value of the gradient. If we want to calculate a gradient that might be negative, there is a $1/2$ factor so $m\\ge2\\cdot\\nabla f_{max}$.\n", + "\n", + "### Selecting $N$\n", + "$N$ defines the resolution of the final result. The step size between possible results is $\\frac{m}{N}$.\\\n", + "Therefore, in order to achieve accuracy $\\epsilon$, we need to choose $N\\ge0.5\\frac{m}{\\epsilon}$.\\\n", + "Plugging in the condition for $m$, we get $N\\ge\\frac{\\nabla f_{max}}{\\epsilon}$.\n", + "\n", + "### Summery\n", + "Given a known bound $\\nabla f_{max}$ and desired accuracy $\\epsilon$, we can select the parameters:\n", + "$$\\left\\{\\begin{aligned}\n", + "l & \\leq \\frac{2 \\sqrt{3} \\epsilon}{D_2 \\sqrt{d}} \\\\\n", + "m & \\geq 2 \\nabla f_{\\max } \\\\\n", + "N & \\geq \\frac{\\nabla f_{\\max }}{\\epsilon}\n", + "\\end{aligned}\\right.$$" + ] + }, + { + "cell_type": "markdown", + "id": "7", + "metadata": {}, + "source": [ + "## Notebook's structure:\n", + "In the notebook, we will cover those topics:\n", + "1. Theoretical explanation (this section)\n", + "2. Step 1 of the algorithm - State Preparation. We will cover two methods. Phase Kickback (as in the cited paper) and Direct Phase (more straight forward and more efficient for the simulation). We will demonstrate how the states are prepared using a full statevector simulation.\n", + "3. The full algorithm, showing examples of linear and non-linear functions.\n", + "4. Parameters selection and limits (Still work in progress)\n", + "5. Multi-coordinates example, $f$ as function of $x, y$\n" + ] + }, + { + "cell_type": "markdown", + "id": "8", + "metadata": {}, + "source": [ + "# 2. State Preparation" + ] + }, + { + "cell_type": "markdown", + "id": "9", + "metadata": {}, + "source": [ + "## 2.1. Phase Kickback" + ] + }, + { + "cell_type": "markdown", + "id": "10", + "metadata": {}, + "source": [ + "The first step of the algorithm is to prepare the state:\n", + "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}\\delta)}|\\delta\\rangle$$\n", + "The paper uses the phase kickback technique using the ancilla in order to create this state.\\\n", + "In the next example we will see how it works." + ] + }, + { + "cell_type": "markdown", + "id": "11", + "metadata": {}, + "source": [ + "The phase kickback contains three steps:\n", + "1. Apply Hadamard gate on $|\\delta\\rangle$ to have an entangled state\n", + "2. Set the ancilla to $|1111...1\\rangle$ (in binary representation) and apply QFT on it\n", + "3. Add the value $f(\\delta)$ to the ancilla, and the function's value will be 'kicked' to the phase\n", + "\n", + "Note that we use the ancilla as a signed and fractional QNum, so in order to have $|1111...1_b\\rangle$, we will assign $-1/N_0$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "12", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 8\n", + "Circuit Depth: 42\n", + "Gate Counts: {'u': 31, 'cx': 27}\n" + ] + }, + { + "data": { + "application/vnd.microsoft.datawrangler.viewer.v0+json": { + "columns": [ + { + "name": "index", + "rawType": "int64", + "type": "integer" + }, + { + "name": "x", + "rawType": "int64", + "type": "integer" + }, + { + "name": "ancilla", + "rawType": "float64", + "type": "float" + }, + { + "name": "amplitude", + "rawType": "complex128", + "type": "unknown" + }, + { + "name": "magnitude", + "rawType": "object", + "type": "string" + }, + { + "name": "phase", + "rawType": "object", + "type": "string" + }, + { + "name": "probability", + "rawType": "float64", + "type": "float" + }, + { + "name": "bitstring", + "rawType": "object", + "type": "string" + } + ], + "ref": "3627dec6-122f-48ec-b0ca-c98f0b5c29ad", + "rows": [ + [ + "0", + "1", + "0.0", + "(-0.08838834764831831+0.08838834764831865j)", + "0.13", + "0.75π", + "0.015625000000000014", + "00000001" + ], + [ + "1", + "-3", + "0.0", + "(-0.0883883476483183+0.08838834764831867j)", + "0.13", + "0.75π", + "0.015625000000000014", + "00000101" + ], + [ + "2", + "0", + "0.0", + "(0.08838834764831853+0.08838834764831836j)", + "0.12", + "0.25π", + "0.015625", + "00000000" + ], + [ + "3", + "2", + "0.0", + "(-0.08838834764831852-0.08838834764831836j)", + "0.12", + "-0.75π", + "0.015625", + "00000010" + ], + [ + "4", + "-2", + "0.0", + "(-0.08838834764831854-0.08838834764831835j)", + "0.12", + "-0.75π", + "0.015625", + "00000110" + ], + [ + "5", + "3", + "0.0", + "(0.08838834764831827-0.08838834764831859j)", + "0.12", + "-0.25π", + "0.015624999999999993", + "00000011" + ], + [ + "6", + "-1", + "0.0", + "(0.08838834764831824-0.08838834764831861j)", + "0.12", + "-0.25π", + "0.015624999999999993", + "00000111" + ], + [ + "7", + "-4", + "0.0", + "(0.08838834764831849+0.08838834764831834j)", + "0.12", + "0.25π", + "0.01562499999999999", + "00000100" + ] + ], + "shape": { + "columns": 7, + "rows": 8 + } + }, + "text/html": [ + "
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" + ], + "text/plain": [ + " x ancilla amplitude magnitude phase probability bitstring\n", + "0 1 0.0 -0.088388+0.088388j 0.13 0.75π 0.015625 00000001\n", + "1 -3 0.0 -0.088388+0.088388j 0.13 0.75π 0.015625 00000101\n", + "2 0 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 00000000\n", + "3 2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 00000010\n", + "4 -2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 00000110\n", + "5 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 00000011\n", + "6 -1 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 00000111\n", + "7 -4 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 00000100" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Set the default values:\n", + "# l = 0.5, m = 2, n = 3, n0 = 3\n", + "p = params()\n", + "\n", + "# Set the function we want to calculate the gradient of:\n", + "# f(x) = 0.5*x + 0.25\n", + "# Gradient: f'(0) = 0.5\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "\n", + "# Unpack the parameters to global variables for easier use\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]], ancilla: Output[QNum[n0, SIGNED, n0]]):\n", + " # 1. State preparation\n", + "\n", + " # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + "\n", + " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", + " probabilities = [0] * (N0 - 1) + [1] # |1111...1> state\n", + " prepare_state(probabilities=probabilities, bound=0.01, out=ancilla)\n", + " qft(ancilla)\n", + "\n", + " # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", + " # Calculate the normalized f and add it to the ancilla\n", + " val = f_normalized(x)\n", + " inplace_add(val, ancilla)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "\n", + "\n", + "# Run using a statevector simulator\n", + "qprog = synthesize(main)\n", + "# show(qprog) # Uncomment to see the circuit\n", + "print(\"Circuit Width:\", qprog.data.width)\n", + "print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", + "print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", + "\n", + "# Pay attention that we use a statevector simulator here\n", + "backend_preferences = ClassiqBackendPreferences(backend_name=\"simulator_statevector\")\n", + "execution_preferences = ExecutionPreferences(\n", + " num_shots=1, backend_preferences=backend_preferences\n", + ")\n", + "with ExecutionSession(qprog, execution_preferences=execution_preferences) as es:\n", + " es.set_measured_state_filter(\"ancilla\", lambda v: v == 0)\n", + " results_statevector = es.sample()\n", + "\n", + "# Show the results as a dataframe.\n", + "df = results_statevector.dataframe\n", + "df\n", + "\n", + "# From now on, we will use the shortcut function:\n", + "# df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)" + ] + }, + { + "cell_type": "markdown", + "id": "13", + "metadata": {}, + "source": [ + "In order to understand the results, let's focus on the phase compared to the classical value of f(x):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "14", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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f_classicalphase_over_2pi
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\n", + "
" + ], + "text/plain": [ + " f_classical phase_over_2pi\n", + "x \n", + "-4 -1.00 -1.00\n", + "-3 -0.75 -0.75\n", + "-2 -0.50 -0.50\n", + "-1 -0.25 -0.25\n", + " 0 0.00 0.00\n", + " 1 0.25 0.25\n", + " 2 0.50 0.50\n", + " 3 0.75 0.75" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Shift the classical function to match the quantum convention\n", + "f_classical = f_normalized(df[\"x\"]) - f_normalized(0)\n", + "# Create a simplified dataframe with the relevant information, and sort it by the x values.\n", + "phases = np.angle(df[\"amplitude\"]).astype(float)\n", + "phases_over_2pi = phases / (2 * np.pi)\n", + "simplified_df = pd.DataFrame(\n", + " {\"f_classical\": f_classical, \"phase_over_2pi\": phases_over_2pi.round(5)}\n", + ")\n", + "simplified_df.index = df[\"x\"]\n", + "simplified_df.sort_index(inplace=True)\n", + "# Unwrap the phase\n", + "simplified_df[\"phase_over_2pi\"] = np.unwrap(simplified_df[\"phase_over_2pi\"], period=1)\n", + "# Get rid of the global phase\n", + "simplified_df[\"phase_over_2pi\"] -= simplified_df[\"phase_over_2pi\"].iloc[N // 2]\n", + "simplified_df[\"f_classical\"] -= simplified_df[\"f_classical\"].iloc[N // 2]\n", + "\n", + "# Plot the results\n", + "plt.figure()\n", + "plot_classical()\n", + "simplified_df.plot(style=\"o\", ax=plt.gca())\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Show the results as a dataframe\n", + "simplified_df" + ] + }, + { + "cell_type": "markdown", + "id": "15", + "metadata": {}, + "source": [ + "In the graph we can see the original function (gray line), the classical values and the quantum phase at the chosen points (classical - blue, quantum - orange).\\\n", + "Everything in both normalized values (black axes), and the original values (blue axes)." + ] + }, + { + "cell_type": "markdown", + "id": "16", + "metadata": {}, + "source": [ + "For convenience, the full code to generate this graph:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "17", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum program link: https://platform.classiq.io/circuit/3DIMQhH5GHJdRvHote12kf71YLk\n", + "Circuit Width: 7\n", + "Circuit Depth: 37\n", + "Gate Counts: {'u': 31, 'cx': 28}\n" + ] + }, + { + "ename": "IndexError", + "evalue": "single positional indexer is out-of-bounds", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mIndexError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[10]\u001b[39m\u001b[32m, line 29\u001b[39m\n\u001b[32m 26\u001b[39m invert(\u001b[38;5;28;01mlambda\u001b[39;00m: qft(x))\n\u001b[32m 28\u001b[39m df = run_statevector_simulation(main, print_circuit_info=\u001b[38;5;28;01mTrue\u001b[39;00m, filter_ancilla=\u001b[38;5;28;01mTrue\u001b[39;00m, show_circuit=\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[32m---> \u001b[39m\u001b[32m29\u001b[39m simplified_df = \u001b[43msimplify_df\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdf\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 30\u001b[39m plot_simplified_df(simplified_df)\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/GoogleDrive-ofriwi1@gmail.com/My Drive/Documents/Work/1. Classiq/Gradient Estimation/gradient_estimation_helpers.py:148\u001b[39m, in \u001b[36msimplify_df\u001b[39m\u001b[34m(df, unwrap)\u001b[39m\n\u001b[32m 145\u001b[39m \u001b[38;5;66;03m# Unwrap the phase if requested\u001b[39;00m\n\u001b[32m 146\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m unwrap:\n\u001b[32m 147\u001b[39m \u001b[38;5;66;03m# Unwrap the phase\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m148\u001b[39m simplified_df[\u001b[33m'\u001b[39m\u001b[33mphase_over_2pi\u001b[39m\u001b[33m'\u001b[39m] = np.unwrap(simplified_df[\u001b[33m'\u001b[39m\u001b[33mphase_over_2pi\u001b[39m\u001b[33m'\u001b[39m], period=\u001b[32m1\u001b[39m)\n\u001b[32m 149\u001b[39m \u001b[38;5;66;03m# Get rid of the global phase\u001b[39;00m\n\u001b[32m 150\u001b[39m simplified_df[\u001b[33m'\u001b[39m\u001b[33mphase_over_2pi\u001b[39m\u001b[33m'\u001b[39m] -= simplified_df[\u001b[33m'\u001b[39m\u001b[33mphase_over_2pi\u001b[39m\u001b[33m'\u001b[39m].iloc[N//\u001b[32m2\u001b[39m]\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/indexing.py:1192\u001b[39m, in \u001b[36m_LocationIndexer.__getitem__\u001b[39m\u001b[34m(self, key)\u001b[39m\n\u001b[32m 1190\u001b[39m maybe_callable = com.apply_if_callable(key, \u001b[38;5;28mself\u001b[39m.obj)\n\u001b[32m 1191\u001b[39m maybe_callable = \u001b[38;5;28mself\u001b[39m._check_deprecated_callable_usage(key, maybe_callable)\n\u001b[32m-> \u001b[39m\u001b[32m1192\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_getitem_axis\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmaybe_callable\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m=\u001b[49m\u001b[43maxis\u001b[49m\u001b[43m)\u001b[49m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/indexing.py:1753\u001b[39m, in \u001b[36m_iLocIndexer._getitem_axis\u001b[39m\u001b[34m(self, key, axis)\u001b[39m\n\u001b[32m 1750\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[33m\"\u001b[39m\u001b[33mCannot index by location index with a non-integer key\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m 1752\u001b[39m \u001b[38;5;66;03m# validate the location\u001b[39;00m\n\u001b[32m-> \u001b[39m\u001b[32m1753\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_validate_integer\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkey\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 1755\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m.obj._ixs(key, axis=axis)\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/indexing.py:1686\u001b[39m, in \u001b[36m_iLocIndexer._validate_integer\u001b[39m\u001b[34m(self, key, axis)\u001b[39m\n\u001b[32m 1684\u001b[39m len_axis = \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.obj._get_axis(axis))\n\u001b[32m 1685\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m key >= len_axis \u001b[38;5;129;01mor\u001b[39;00m key < -len_axis:\n\u001b[32m-> \u001b[39m\u001b[32m1686\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mIndexError\u001b[39;00m(\u001b[33m\"\u001b[39m\u001b[33msingle positional indexer is out-of-bounds\u001b[39m\u001b[33m\"\u001b[39m)\n", + "\u001b[31mIndexError\u001b[39m: single positional indexer is out-of-bounds" + ] + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.5*x + 0.25\n", + "# Gradient: f'(0) = 0.5\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]], ancilla: Output[QNum[n0, SIGNED, n0]]):\n", + " # 1. State preparation\n", + "\n", + " # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + "\n", + " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", + " probabilities = [0] * (N0 - 1) + [1] # |1111...1> state\n", + " prepare_state(probabilities=probabilities, bound=0.01, out=ancilla)\n", + " qft(ancilla)\n", + "\n", + " # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", + " # Calculate the normalized f and add it to the ancilla\n", + " val = f_normalized(x)\n", + " inplace_add(val, ancilla)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "18", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum program link: https://platform.classiq.io/circuit/3DIMkHZaLAmaOmGPVtQ2k6xopwl\n" + ] + } + ], + "source": [ + "# # TODO: Fix it and remove the original (Ancilla not as output)\n", + "# p = params()\n", + "# # f(x) = 0.5*x + 0.25\n", + "# # Gradient: f'(0) = 0.5\n", + "# p.set_function(p.linear, (0.5, 0.25))\n", + "# p.unpack(globals())\n", + "\n", + "# @qfunc\n", + "# def main(x: Output[QNum[n, SIGNED, 0]]):\n", + "# # 1. State preparation\n", + "\n", + "# # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", + "# allocate(n, x)\n", + "# hadamard_transform(x)\n", + "\n", + "# # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", + "# ancilla = QNum(\"ancilla\", n0, SIGNED, n0) # Declare the name/type\n", + "# probabilities = [0] * (N0-1) + [1] # |1111...1> state\n", + "# prepare_state(probabilities=probabilities, bound=0.01, out=ancilla)\n", + "# qft(ancilla)\n", + "\n", + "# # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", + "# # Calculate the normalized f and add it to the ancilla\n", + "# val = f_normalized(x)\n", + "# inplace_add(val, ancilla)\n", + "# invert(lambda: qft(ancilla))\n", + "# drop(ancilla)\n", + "\n", + "# # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + "# invert(lambda: qft(x))\n", + "\n", + "# df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)\n", + "# simplified_df = simplify_df(df)\n", + "# plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "markdown", + "id": "19", + "metadata": {}, + "source": [ + "## 2.2. Direct Phase" + ] + }, + { + "cell_type": "markdown", + "id": "20", + "metadata": {}, + "source": [ + "The phase kickback approach is good when we have a state-oracle, but in our simulation it is very inefficient." + ] + }, + { + "cell_type": "markdown", + "id": "21", + "metadata": {}, + "source": [ + "Another approach is to directly prepare the wanted state.\n", + "In our case:\n", + "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}\\delta)}|\\delta\\rangle$$\n", + "\n", + "Here we can see the same example using the prepare_complex_amplitudes function.\\\n", + "You can look at the circuit width/depth and gate count to compare both methods.\\\n", + "In real applications, both methods can be used, depending on the oracle f." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "22", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum program link: https://platform.classiq.io/circuit/3DILfoGkquUJNK1mVjoXrvukJNk\n", + "Circuit Width: 3\n", + "Circuit Depth: 1\n", + "Gate Counts: {'u': 3}\n" + ] + }, + { + "data": { + "image/png": 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0wG+//Ya7777bKyjMDoMzBlbffvutOTEIGj9+vPv2w4cPY/jw4fj1119N9pDvKzfccIPPq3IwILvrrrtM1pGlTl7OC/4NDz30kAlc69ati1tuucXMPUi8rmPHjmbOTQZ68+fPR/fu3c1UNgzk+Jh8bD4uTyxTZ7Zs2TL06tXLBLKrVq0yQS6fXzuwtDHIY0aVzz9ft3vvvRfr16/P098iwaGJhUVEonxy7VDzdTJvllm5nyxDZoXXM8u0Z88ed4n0qquuwoMPPujehtkmT2+//Tbq1auH5557zlzm+dWrV2Ps2LE57gsDMwYvzDxR3759TeBm/x6bGTy9//77KFu2rHmOfRm/V7p0aZM9s0udecVgrlu3bub8mDFjTCaN5en69evj3//+twmy/vOf/7i35+02PiYfO6fHffHFF01QaAfJDBr5t/F5ZJbPdu2115pAjh555BG89NJLmD17tnmeJbyUuhARkbDyNaNHDFxywmzRxRdf7HVd69atc71flhPtYM5efspeisoOPpkVq1mzpin3cntKSkpCKDRt2tRr38jePztDdz7Wrl2L9u3be13Hy/y77UmrM+8Hg3YGiZ7Pk4SPMnQSlfht23PpL5VdJdbww5b/++FY+svXgfa1a9c22zKYYPkyM17P8WDMhNmKFSuGYGDp2BP3y7OcyhImu2/fffdd043L25iZY2PG+eDjZA5os1opwXP/7OfX3r/M5epgyu15kvBRhk5EJArxg9ZuWgj1ydeAjs0FV199tSkVHj161Ou2Xbt2YeLEiWaKkbx0YrL0x3FunpYuXYrzwelTmPl77LHHTCbMLgUHAoNVjmuzMSPG+eryglkzloezw5KrZ5YtK/yb2FjhiZdZemUnsUQ+BXQiIhI2r7/+Oo4fP266MtkByjnp2FHKQK9y5cq5jn3LjE0Q69atM+O7ONfcZ5995h7Y7+8UHcwSMvhkRyfHrf3000+mQSIQOCaQzwGbDBiI3nPPPedkwXIzcuRIE7RybNvvv/9u/v4333wTe/fuNbezPLx48WIz3pDXZZVR47hEBoXsIubzxs5g7hfH7okzKKATEZGw4fQiDGQ4No1dlrVq1TLTkXCKDnZsspkgL2rUqIEpU6aYLlJmrhjY2F2unI7DH8w6Tpo0yXSCssz6wAMPuJsuzhe7Rtl1etlll+HWW281AZS9SL2vmEXjtC/s6uV4QXa1fvXVV+65+XifzLKxBM+MYFbj/i666CIT/PLv5N/4xBNP4Mknn/RqiJDIls+Vl9GoDpeWlmbmFzp48KDmJ4tyGkMnsYbj2ThlBwMajmkLtpzG0EUaZvk4WTGzf+LM/+GUlDRUqVICyckHkZio+UWzoqYIERGJKhyTx05Xlkk5DozZtCFDhoR7t0SCSgGdiIhEFTYWPP3002biYk4uzvFhHGcmEs0U0EnUuvDCC8O9CyJRLVKnA+JktzyJxBIFdBK1HzT2xJ8iEngcM+dvk4GIBF5kfr0SEREREZ8poBMRERFxOJVcJWqnLeGyQfYM6JE61kfEqZw0bYlILFBAJ1ErhqZYFBGRGKe0hYiIiIjDKaATEZGINWfOHFPOPXDgAJyE+zxt2rSA3R+79l9++WUE0xVXXIH7778/qI8hwaOATkRE3E6fcWHhpn34auV285OXgxn05HQaPXp0xL8y3MfmzZufc/3OnTtxzTXXhGWfJDZpDJ2IiBjTV+/EmG/WYOdBq9mBKpYojFHdG6Jr44oBf5YY9NgmT55sFoRfv3691+Tgv/76a1henRMnTiAuLs7v369QoUJA90ckN8rQiYiICebu/WS5VzBHuw4eM9fz9kBj0GOfSpQoYbJyntd5rvaybNkytGrVCkWLFkW7du28Aj/66quvcNFFF5mO25o1a2LMmDE4deqU+/akpCRcf/315j6LFy+OXr16ITU19ZxM23//+1+vxeFZ6r3zzjtRtmxZ83tXXXUVfvvtN3PbBx98YB6Hl+2sIq/LquSakpKCW265BaVLl0axYsXM37J48WJz26ZNm8y+lS9f3uwf16H98ccffX4eZ8yYYfY3c1l62LBhZn9p37595vErV65snsMmTZrg//7v//JcNi5ZsqT7b6Tk5GTzXPJ6/m38O7Zu3epVMm/durX5m7lN+/btsW3bNp//NvGdAjqJWnzT4klEcsayKjNzWRVX7et4e+byK6cDCtWUQI8++iheeOEFk7ErUKAAbr/9dvdtP//8M/r162cCmDVr1uDtt982QcfYsWPd0xgx0ODarnPnzsXMmTOxefNm9O7d2+sxNm7ciC+++AJffvklVq5caa67+eabsXv3bnz//fcmqGTQ2LFjR3Nf/H2uE9uoUSOTbeQp833SoUOH0KFDB2zfvh1ff/21CQD/+c9/mv2yb7/22msxa9YsrFixAl27dkX37t1NEOoL7g+DJe677fTp0ybr2adPH3OZU8y0bNkS3333HVavXo1Bgwahb9++WLJkCfx18uRJdOnSBfHx8eY1+OWXX0xAyv1nhpMBdY8ePczf/vvvv2PhwoXmcTXFTXCo5CpRiR8y/JYuIrlbsmX/OZk5TwzjeDu3a1srISxLfzE4Y2BAI0aMQLdu3UyQwswUs2S8rn///uZ2HvtPPfWUCZpGjRplAqVVq1Zhy5YtqFKlitnmo48+MoHY0qVLTUaMGITwembjaP78+SbgYUBn/63PP/+8yVpNmTLFBCcMYBhg5lRi/fTTT7Fnzx7zWMxiUe3atd23N2vWzJxs3PepU6ea4G/IkCG5Pjf58+fH3//+d/M4d9xxh7mOfzMzdjfeeKO5zMzcQw895P6d++67Dz/88AM+++wzk0HzBwNGBqXMatpB2oQJE0xwycwcs5AHDx7E3/72N9SqVcs9L6gEhwI6EZEYtzv9WEC3C4amTZu6z1esaI3nY6BVtWpVk/FidsjOyNkZKgZ8R44cMZOMM5Czgzlq2LChCTx4mx3QVatWzR3MEe+X2bOEBCuItR09etSUSX3FbF+LFi3cwVxmfAyWfJk9Y5aPmS0+hq8ZOmIm7pJLLsGOHTtQqVIlTJw40QS9/Bvt5+OZZ54xARwzhQxejx8/fl5VDD4/zGoyQ+eJzzufn86dO2PAgAEmi3f11VejU6dOpjxrv34SWAroRERiXLn4wgHdLhgKFizoPm9ngzxLlszS9ezZ85zfs8fC+YLjvDzxfhl8MNuUmR0o+aJIkSI53s7MGcvAzP4xc8ftb7rpJhN0+YpBKbNgkyZNwr333msyfJ5j3Z577jm88sorZuoTjp/j38opSnJ6DD7PmSdoZ5nV8/lhGZfBY2Z2YMyM3dChQzF9+nST0XvsscfM38rgU2I0oHvzzTfNyR5syVQ5O6LUFi5Z4Ru9PWi6Xr16WvpLJAeta5Q23axsgMhqHB3DpwolCpvtInHpL45r4/HuWcb0xDIfB+/zZGfpONaOJUlm6nK63127dpmSKueBywo7YZn9yi27yLIkx91llaVjdpGZrBtuuMEdKHk2FuQlS8fgKjEx0bznMUPn+RgcR3jbbbe53yP//PPPHP9+BmWencgbNmwwGU/P54dBWrly5UzDSHaYneRp5MiRaNu2rSkNK6CL4aYI/oOOHz/eDErloFh27vCf848//gj3rkmE4ptsbm+0IgLkvyCfmZqEModl9mXezu0iEb/cc+wbs3T8TGAZlZkqZoOIpT5mpRjwLF++3IyLYxMFx+RxnFd2+HsMQDiwn52kDLIWLFhgGjTs6VQY6HFsHsuqe/fuNWXMzNhdyjF2vB8GVmzIYAMDmwSoTp067kYMljFvvfVWd/YxL+y/j6VnZvg8xzjyMZgZ4/7z+bn77ru9unyzws/Z119/3TRq8O+95557vDKlfLwyZcqYz2I2RfB5YDaTGTl29fIygzj+nexs5XPIoFDj6GI8oGPHD7uA+E9Zt25d8w/LwaiLFi0K966JiDge55l787aLTCbOEy/z+mDMQxcoHKP17bffmoCBpUdmf1566SUzJo6YPeS0JqVKlcLll19uAjU2TjC7lBP+3v/+9z/zOwMHDjSfPWw+YHDCKUaITQfs6rzyyitNRiurqUCYxeO+MZPFzzEGl0xQsJmBXnzxRbNvnI6Fn3X8e5j9yitmKNngwI5Su7vVxuCW98n75ooQdoCZE3YVM6N52WWXmSCTpWHPMXc8P2/ePDOOkeVuBmpsymDmlhk73r5u3TrzHPG5YxPJ4MGDTTApgZfP5cAVzJl1+fzzz01HE785ZJcy5jclz29LaWlp5p+TXTc5pYfF+fjtliUV4v9HqKZWEAkXfogyI+I5h5o/ODUJu1nZAMExcyyzZpWZi6SSq0T//3BKCj+/SyA5+SASE/X57egxdMS2c6a/+aIzO8dBnznV/8eNG2dS8CIi4hsGb/bUJCLiHI5KW3BwO8cYcHZtdvEwQ2dnYbLC2j2zcfaJA2JFREREoo2jMnQch2B3MbFVmpM0sg2bs4JnhQNCQznxpYiIiEg4OCqgy2qcVFYdRSK+zP0kIudH4+ZEIodjAjqWTznnHLtp0tPTzTw2bI/m0iUimbEJwl5qRkSCE8ydT/OFiMToGDou8cJ5gziOjgsRs9zKYI7LiYiIiIh4euMNzhPILmygTRtgyRLk6MABYPBgLi3HIVtA3brA//4Hx3BMhu69994L9y6IiIiIA0yeDAwfDrz1lhXMvfwy5ysEuIBQuXLnbs8V0Jgf4m1TpgCVKwPbtnGJNziGYwI6kbyOr+SM5MTJqDUPnUhgcR46ewwzm880nk4iyYsvAnfdBQwcaF1mYPfdd8D77wMjRpy7Pa/fvx9YsIDrBlvXZbPaW8RyTMlVJK+4iLTnQtIiEvigzoFz00uUO3ECWLaMS7dlXMe55Xn57Gpr5/j6a6BtW6vkykVAGjcGnnmGCxnAMRTQiYiIhAmX4br//vvP6z4GDBiQ6zJe0SI9nas+ZZyymuhi714rEDu7OpsbL+/alfX9bt5slVr5exw39/jjXPoMePppOIYCOhERyXDmNLDlZ2DVFOsnLwcRgxGWa7nwe2Zc95O3cRsR4uJQJUpknMaNC8zzcuaMNX7unXc4zy3Quzfw6KNWqdYpNIZOREQsa74Gpj8CpO3IeEaKVwK6Pgs0vC5ozxLX2J40aRJeeukl9/yRXOKR01NxqqpId+LECTPxvQQfF4diw4Itq7UDypQB8ucHUlO9r+flChWyvl92tnLsHH/P1qCBldFjCdcJL68ydCIiYgVzn/XzDuYobad1PW8PkosuusgEdV9++aX7Op5nMNeiRYtzGp64TjcXcGfw16xZM0xhreys06dP44477nDfzqmuuKKQJ85h2rp1axQrVgwlS5ZE+/btsY0tjdmUL1kSZWnUxvNDhgwx15cpUwZd2D4JYPXq1Wa+VK41Xr58efTt2xd7Wf876/Dhw2b6Ld5esWJFvMCaXi5Gjx6N5s2bmxWR+BwVLVoUvXr1MstZZvb888+b+01ISDDZTc8xxB9//DFatWqF+Ph4VKhQAbfeequZDsz2119/oU+fPihbtqx53thMNmHCBPftXDqTj8vnq3Tp0rj++uuxdetWn57TQIqPB4oXzzhlFdDFxVlZtlmzvDNwvMxxcllp3x7YuNHazvbnn1ag54RgjhTQiYjEOpZVmZlDVg0OZ6+bPiKo5dfbb7/dK4B4//33MdBuUfTAYO6jjz7CW2+9hT/++AMPPPAAbrvtNsydO9f6U86cQWJiIj7//HOz1vcTTzyBf/3rX/jss8/M7adOnTIBW4cOHfD7779j4cKFGDRoUJ67dD/88EOTlfvll1/Mvhw4cABXXXWVCUB//fVXTJ8+HampqSYIsj388MNmP7/66ivMmDHDBEHLly/P9bE2btxo9v+bb74x97tixQr84x//8Npm9uzZ2LRpk/nJffvggw/Mycbg7qmnnsJvv/2GadOmmWDMs5T9+OOPm+fr+++/x9q1a/Hmm2+aYNX+XQatDAZ//vln8zczKO3atavJTgbqOQ2k4cOBd9/l6wSsXQvcey8D6oyu1379uGBBxva8nV2uw4ZZgRw7YtkUwSYJx3DFkIMHD/KdyfyU6Hb69GnXn3/+aU48LxLtjh496lqzZo35mWeb57lco4rnfuJ2Z505c8Y8Fk8876/+/fu7rr/+etfu3btdhQoVcm3dutWcChcu7NqzZ4+5jdvQsWPHXEWLFnUtWLDA6z7uuOMO1y233JLtYwwePNh14403mvP79u0znwNz5szJcX88DRs2zNWhQwf3ZZ5v0aKF1zZPPfWUq3Pnzl7XJScnm8dav369Kz093RUXF+f67LPP3LdzX4oUKWLuPzujRo1y5c+f35WSkuK+7vvvv3ddcMEFrp07d7r3uVq1aq5Tp065t7n55ptdvXv3zvZ+ly5davaN+0Xdu3d3DRw4MMttP/74Y1e9evW8Xufjx4+bff/hhx9yfU4D8T+cnGx9fvOnr157zeWqWtXliotzuVq3drkWLcq4jS/n2X8rN/5btWnjchUq5HLVrOlyjR3rcnk8pRFPY+gkKnHeOZYMRMQHh1LzvF2gl/5iqa9bt24mq8SpUHjezhB5ZqqOHDlyzgpBzBJ5lmbfeOMNk+FLSkrC0aNHze0sWxLLhcxMMePE++nUqZPJorFUmRctWdPzwMwXs2PMXGXGzJm9H204y+1Z3BeWhHPD0nNlj4Fjbdu2NZnI9evXm/IpNWrUCPk9BoDx71m1apX78rJly0z5lvvJ8ip/n/gcNWzYEPfeey9uvPFGkzHs3Lmzybi1a9fO/bfxuWeGzhPHOfJv4/aBeE4DbcgQ65SVOXPOvY7l2EWL4FgquYqIxLoLywd2u/MouzKgY8mQ5zM7dOiQ+fndd99h5cqV7hNLhfY4OjZXPPTQQ2YcHcuavJ2lWwZTNpZ2WRZkwDJ58mTUrVsXi85+kvPLYOa59bKaz5JjxTLvW/fu3b32iydOcH755Zcj2Aras+F6BNx20Maxewy2ihcvjokTJ5qlM6dOnWpus58Xjv3jmDeWsHfs2GGW2OTzaP9tDGAz/21//vmnGYuX23MqoaEMnYhIrKvWzupmZQNEluPo8lm3c7sgssdkMRixGw08MZPEVSmYVeJ4raxwfBeDCs8xZswiZcaMHk8jR440GS921F5yySUmU8jmBk8MXjIHTFk1dnzxxReoXr06ChQ496O1Vq1a5j4WL17s7txlpoxBUXZ/i41/L4OsSpUqmcsMlBh4+pLdo3Xr1mHfvn0YP368aawgjvPLjH97//79zemyyy4zY/7YaMG/jUFauXLlTFCYneyeUwkNZegkqpf+4sn+lioi2bggvzU1iZF5IPvZy13HW9udxSwWS248BWq1CJYMOSCfGTfP8qGNJT9mjZhFYhaPgRpLhK+99pq5TBxqwWDlhx9+MMESB/szI2XbsmWLCTiYTWJGilk8vk804BwVgGls4O+z8YLXjxo16pwALyvsKt2/fz9uueUW83jcN+4Ds4PsvGUplllDBkk//fSTuU+WKX1ZlpClbQZZLH2yKWHo0KGmpGmXW3PDAJINHHyeNm/ejK+//to0SHhi8wibNVhaZbPJt99+635O2P3K8jc7W/n4fA7Z0MH9SElJyfU5ldBQQCdRi+tM2mtNikguOM9cr4+A4pnGPTEzx+uzmIcuGEt/MQOUUxaIgQiDNHa7MmBgVo8lWE5TQnfffTd69uyJ3r17m/FqzEx5Zus47QczVhwvxrIguzEZjPH3iJlB3v8///lPXHzxxUhPTzdTjeSG2TNmBxm8cUxZkyZNzLQmnMLDDtqee+45k/liaZbjzC699NJzxuJlpXbt2uZvuvbaa819N23aFP/5z3/gK2beWMpm5y+znMzUMfPmiQEfgzLeN0vEDKhZvrafs3nz5pnAkPvB553BKYN5vla5PacSGvnYGYEYkZaWhhIlSpj5e3J6wxDnY1aO3/KJb2C+fAsWcTJ+uDJTwsDmvJoVODXJtgVWAwTHzLHM6pGZy5yhIz5eOKeoiGZsZOA0Iyz7xvL/cEpKGqpUKYHk5INITNTnd1Y0hk5ERDIweKtxmZ4REYdR2kJERETE4RTQiYiIRHDJNRbKrXL+FNCJiIiIOJzG0EnUym3eKJFoFMo+NzVCSCDFUI9mUCigk6iUl0k3RaKBPW8bJ+YtUqRI0B8v0Et/iXBZN9KXcf8ooBMRiQJcnYDzge3Zs8d8IGqqHnFSZo7B3O7du828fVlNKi25U0AnIhIFmDHjYuicx4uz9Ys4DYM5X1e/kHMpoJOonViYH2zESSqVrZBYwNn+ufSV50L0wTzGuOwTJSYm6hiT88KssjJz50cBnUSto0ePhnsXREKOX15CMbaNAZ0dOPLx9KVJJLw0bYmIiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJy6XCVqqQVeRMeYSKxQQCdRiVMoNGjQINy7IRK1dIyJRBaVXEVEREQcTgGdiIiIiMOp5CpRibPYb9261ZyvXr26ZrEX0TEmEtUU0EnUOnLkSLh3QSSq6RgTiRyOKbmOGzcOF198MeLj41GuXDn06NED69evD/duiYiIiISdYwK6uXPnYvDgwVi0aBFmzpyJkydPonPnzjh8+HC4d01EREQkrBxTcp0+fbrX5Q8++MBk6pYtW4bLL788bPslIiIiEm6OCegyO3jwoPlZunRpvwbM85Td3Eqe2+VE2+b9eciXL585BXtbz+0z/24o9sHlcplTtGzr+TpH87ak496358GTE98jwr2tE477SHmPOHXqFNLS9uS4jTg0oONBc//996N9+/Zo3LhxttsdP37cnGxpaWnm57p163DhhReesz2vY0ekbe3atdn+oxUtWhQ1a9Z0X+Z4vtOnT2e5bZEiRVCrVi335Q0bNpiScVYKFSqEOnXquC9v2rTJ62/wVLBgQdSrV899ecuWLTh69Gi2qyZ4TrTLDtDsBjTzAG7UqJH7clJSEg4dOoTseL4GKSkp7uc5Kw0bNnS/QezYsQMHDhzIdtv69eujQAHrX3TXrl3Yv39/ttvWrVsXcXFx5vzu3buxd+9e9218vT3Vrl0bhQsXNuf37NljTtnha8zXmvbt24fU1NRst+X/jv1/xX3duXNntttWq1bNjAclPgfbt2/PdtsqVaqgRIkS5jyf2+Tk5Gy3rVy5MkqVKmXO8zXbtm1btttWrFgRCQkJ5jyHLthdwVkpX748ypYta87zf2zz5s3ZbsvtuD3xf3fjxo3ZblumTBlUqFDBnOcx8eeff2a7Lb+8VapUyZznsZb5dfVUsmRJJCYmmvM8htesWZPttsWLF0fVqlXdl3PaVu8RFh7Dnu8nPO6d/B6Rmd4jIuc9gp9zfG/I6f9LHDaGzhPH0q1evRqTJk3KtZGCH4T2iR+MIiISGJ4ZHJFgsJMfhQpZX6wle/lcueU6I8yQIUPw1VdfYd68eahRo0aO22aVoWNQ99dff5lv5VlR6SW4z0OklT1UTgl/OSWStiWVXMP7PETasaz3iOC/Rxw7dswMo2I2luVVz+wcs+2sOuzefQxVqpRAcvJBJCZm/fkd6xxTcuWLft9992Hq1KmYM2dOrsGcXb7kKat/JM83mOz4so221fNwvpkLbRs5zwPpuNfzEIr/h0j4fw/nthw2YQdxnsN/+ByyosYgjsOVMu7nmE+PHcsKOKnM+umnn5rsHMcecbwE8YXniy4iIiKRnZjhWDgGcayYeWbxOD6V2ThWz/ISGIsDS67ZRfsTJkzAgAEDfLoP/gMxAOS3guxKrhIdWCZhMwdxwLveIER0jEl4cOgThzplLqmygsYgjieWV3OSksIhUyq5RkWGziFxp0QQdUWJ6BiT8GBJlQEcT56zL3DGBSZWGMR5l1QlZgI6ERERifySKrNx6enpXokYDpViEMefqpgEhwI6ERER8Ru7VBnEcTiTZ0mV833aJVV7vkAJHj3DIiIikicM3BjAMZBjQOdZUrWDODUshpYCOhEREfGp2cyzpGrjODjPkqrGxYWHAjoRERHJkj3xr93g4LnEJUuqnC+OTQ4qqYafAjoRERE5Z8ktu6TqueISAze7pGqviS2RQQGdRCV2UXkuCC4iOsYk95IqS6nMxGVVUmU2jhMAq6QamRTQiYiIxHBJlfPEMYhjRs6zpMqmBrukymYHiWwK6ERERGKwpGqPi8tcUmUQx5JqVmuhS+RSQCdRWzpISUkx5xMTEzWRpYiOsZjH90UugckgznMlHZZQuRwmA7lixYqppOpQCugkavGNS0R0jMV6SfXIkSPukiqDOlvRokVNEMdgTiVV51NAJyIiEmVOnDjhLqnyvK1gwYKmnMpALi4uLqz7KIGlgE5ERCQKsKHBLqkePnzYq+vfLqkyK6cu1chw8iSwaxdw5AhQtixQuvT53Z8COhEREQeXVBm8MYhjMOdZUuV4OGbj2KXKoE7Cj7PBfPIJMGkSsGQJM6l8DTmOkeO9gc6dgUGDgIsvzvt9K6ATERFxGHam2iVVdqzaWEa1J/5VSTWyvPgiMHYsUKsW0L078K9/AZUqcXoYYP9+YPVq4OefraCuTRvgtdeAOnV8v38FdCIiIg4pqbKxgUEcGx1szL4xC8eSKueOU0k1Mi1dCsybBzRqlPXtrVsDt98OvPUWMGGCFdwpoBMREYmikiqX4GJJlZdtXLWBmTiOj1NJNfL93//5th2n/7vnnrzfvzJ0EpX4DbVhw4bu8yKiY8xpJVUGcczGnTp1yn09J/u1S6rsWBWxKaCTqMQgToGciI4xp5VU7XFxXI7LxjniWFJlEKeSqnP17On7tl9+mff7V0AnIiISJiyhctUGZuPS09O9Sqrx8fEmiONPlVSdr0SJjPN8madOta5r1cq6btky4MCBvAV+nhTQSVRi6/6OHTvM+UqVKunNUETHWEQ5duyYCeLY5OBZUi1cuLC7pMp1VSV6TJiQcf6RR4BevawGiPz5retOnwb+8Q+geHH/7l//LRK1WLawAzoR0TEWbgzcGMAxkGNA51lStYM4llQl+r3/PjB/fkYwRzw/fDjQrh3w3HN5v08FdCIiIkGsFtglVf60S6oc4+tZUtWY39hy6hSwbh1Qr5739bzOY27oPFFAJyIiEkAM2piBsxsc2OzgWVLlfHFsclBJNXYNHAjccQewaZM1/xwtXgyMH2/d5g8FdCIiIgEqqTKAYzaO0464P2gLFHCXVBnQiTz/PFChAvDCC8DOndbzUbEi8PDDwIMP+vf8KKATERE5j5Iqu1MZyPGnzS6pMhvHCYBVUhVPXFr3n/+0Tmlp1nX+NkO47/P8fl1ERCT2Sqpceoud9OvXr0dycrI7mGNTAxux6tevj6pVq2p8XBi98QZQvTrL3NbaqEuW+PZ7kyYxIAd69Aj+OLoff7RWkLDnv+fkDIcO+Xd/ytCJiIj44OTJk+5xcVmVVJmN40oOEn6TJ1sdo5wWhMHcyy8DXboA69cD5cpl/3tbtwIPPQRcdllw92/bNqBrVyApiauCAFdfzXkHgWeftS5zv/NKAZ1EJZY3+A3ZPi8iOsb8LalyDVUGcexS9XyP4RqqDOKKFSum95kI8+KLwF13ZTQYMED67jtrupARI7L+Hfau9OkDjBkD/PyzNclvsAwbZk0o/NtvQEJCxvU33GDttz8U0ElU4putOshEdIydT0mVQRznjWNQZytatKjJxrFLlfPHSWixsm2POSMmRDMnRU+csFZdGDnSe8xap07AwoXZ3/eTT1rZO3afMqALJt7/ggVAXJz39SwRb9/u330qoBMRETGBwAl3SZXnbQULFnR3qaqkGl4NG3pfHjUKGD3a+7q9e61sW/ny3tfzMud5ywon+X3vPWDlSoQEvyN4zGbjlpJilV79oYBOohK/Ue/atcucr1Chgpb+EtExliXOEWeXVA8fPuy+nmunsqTKIE4l1cixZg1QuXLG5UAMWUxPB/r2Bd59FyhTBiHRubM1ru+dd6zLHBnEij4D1Guv9e8+FdBJ1Nq/f787oBMRHWOeJVUGbwziGMx5llQZvDGIYzCnkmrkYfYqt+k9ypSxltFKTfW+npez+jjg5L5shujePeM6+1+Cy+mykaJWLQQU559jkwYzjlwF7tZbgQ0brH1n16s/FNCJiEhMYGeqXVJlx6otLi7OXVLleXG2uDigZUtg1qyMqUcYoPHykCHnbs/+uVWrvK977DErc/fKK0CVKoHfx8REqyGC3bj8yewcx+6xKcPf5XwV0ImISNRiSZWNDQzi2OjgWVJlYwODODY6qBs+ugwfDvTvb3WScmktljdZUbe7Xvv1s0q348ZZ89Q1buz9+yVLWj8zXx9IzP4xgOMpIPcHB5k3bx6ee+45LFu2DDt37sTUqVPRI9gz/4mIiCNLqlyCiyVVXrZx1Qa7pMqgTqJT797Anj3AE08AHE7dvDkwfXpGowTnfwvny8+S8OWXA198AZQu7V0WrlQp64aJqAroeIA2a9YMt99+O3r27Bnu3RERkQgrqTKIYzaO66ra2Jlql1TZsSqxYciQrEusNGdOzr/7wQcIKn7H4ATCzCB+8w3QqJH3bf5wVEB3zTXXmJOIiIhnSZWB3NGjR91PChsa7JIql+NSSVUiCbtamZ0bPx5o2xb4+GPg+uszbov6gE5ERIQlVK7awCCOa6h6llTj4+NNEMefKqlKpOK/LMuubLpgdo4lYjZi3Hmn//dZwN+09uLFi7Ft2zYzyLRs2bJo0aIFatSogUjC/fRcb49jKSQ28Nt43bp13edFxPnH2LFjx9xdqplLqlyCixk5lVTFaQYNAurUAW6+mb0CIQrofvnlF7zyyiv45ptvTMs3Dx6msjnfFwOnmjVrYtCgQbjnnnvMt6NwGzduHMZwUTaJOfyA0fQDIs4/xhi42SVVBnSeJVV7XFzhwoX1xU0cpVo1K0Nnu/JKYNEi77nw8srnHo/rrrsOvXv3RvXq1TFjxgyT5t63bx9SUlJMlm7Dhg147LHHMGvWLPOtbebMmQi3kSNHmjcC+5ScnBzuXRIRkVywhMqKSlJSEtavX29mNWAwxyCS3alVq1ZFvXr1ULFiRY2PE0fasgVISPC+rnZtYMUKYPPmIGfounXrhi+++CLbdDazczz1798fa9asMQdguDENr3X3YhNnft+9e7c5X65cOY2lEYnwY4xBnGdJlc0ONmbg7JJqAU7eJRKlChe2snf+8PnIuPvuu32+04YNG5pToHEQ7MaNG92Xt2zZgpUrV6J06dLmG5uIp71cofnsh42IROYxxpKqHcR5llQZuHmWVEWcrnRp4M8/reW9SpXKuZv17MqVeeKorzq//vorrmSh+azhnAoanA26Pz4I9qQxIiISsOweh+0wiONPG0uqHH/NbBwnAFZDk0STl16y1qIlrlwRaD4HdDzAfD247EXRA+2KK67wak8XERFn4Hs354ljEMcxzZ4lVTbX2SVVNjuIRKP+/bM+H/KA7mWPcJLNEE8//TS6dOmCtpwRD8DChQvxww8/4PHHHw/8XoqISEQ5feoUiu1ejgLH9mHtgS2of8k1yJ/F+DbOiGCXVD2nkbJLqgzkNNZZYkFaHmZOK1487/efz+VHyuvGG280pc8hmdbUeP311/Hjjz9i2rRpiETsmuI3QH47ZKeURHdJh805xPGcmmBUJHBW/PAhKi8ag3Kufe7rUpGAHW1HoUWX/ub44/stgziOfbbZXaoM4ooVK6aSqvgsJSUNVaqUQHLyQSQmOvPz+4ILcl8FghEZtwnZWq7MxD377LPnXN+1a1eMGDHCn7sUERGHBHPNFgy1Lnh8OJV17UPZBUMxL/0QyjS80gR1tqJFi5psnEqqEstmzw7u/fsV0CUkJOCrr77Cgw8+6HU9r+NtIiISnWXWSgutydovyJRp4OUzLqDu6heQWqc9Chcu4u5SVUlVBOjQIQIDOq6+cOedd2LOnDlo06aNuY5LgU2fPh3vvvtuoPdRJM9Y2qnNWRq19JdIwKxb/AMaYZ9XZi5zUFcB+7Bj32bUvfIGlVRFcnHkCJCUBJw44X1906YITUA3YMAANGjQAK+++iq+/PJLcx0vz58/3x3giYQ7oNPcVSIBXr0hdatP2545slfBnEgO9uwBBg4Evv8+69tDNoaOGLhNnDjR318XEREHYGeq3aV6+Ewhn36nSKnKQd8vESe7/37gwAFWNzklGzB1KpCaCjz9NPDCC/7dp98B3aZNmzBhwgRs3rzZTGnCmcK///57s2JDo0aN/L1bkYDggOw9/ArEwdply6rLVSQPOEccZwNgEMe1um3l67VG6uoE0wCReQydOe5cwO58Cajfpoueb5Ec/PQT+w6AVq2s7lcu93X11dZ0JePGcblV5Jlfi+/NnTsXTZo0MePmuL6r3Zb+22+/YdSoUf7cpUjAMaCzgzoRyb2kyvfy5ORkrFu3Djt27HAHc1y1ITExEY0aNTZTk9jBmyf78s62o7Kcj05EMhw+zCXzrPNcBsz+qGrSBFi+HH7x66jj1CScWJhLb3GZFttVV11l5qITERHnlFT/+usvk43juqo2dqbaXaoFCxZ0X8955lYA58xDx8wcgzneLiI5q1cPWL8eqF4daNYMePtt6/xbbwEVKyJ0Ad2qVavw6aefnnM9y672Ys0iIhLZJVUGclyOy8ZltzhXHIM4LseV3XKPDNpOXnkLtsyfZFaKSCte26wUUUGZORGfDBsG7NxpnWdhs2tXgG0JcXGAv0vT+xXQ8WDfuXMnatSo4XX9ihUrULmyBsOKiERqSZVBXHp6ute62Ky08H2dP31dVYVl1cPlLjLntRqLSN7cdlvG+ZYtgW3bgHXrgKpVgTJlELqA7u9//zseeeQRfP755+YbHAeg//LLL3jooYfQr18///ZERETyPNEv54Y7+td201nKZoTM49eOHTvm7lLNXFLlElzMyHmWVEUk9IoWBS6yvh/5za+A7plnnsHgwYNRpUoVk7rntzP+vPXWW/HYY4+d3x6JiIhPS3Bx1QYz0e9ZqTOt9VSbdOzjLqkyoPMsqdrj4jhPY3YlVREJLibIp0yxlgPbvZszM3jffnaK3+AHdHFxcWZFiCeeeMKMp2Mav0WLFqhTp44/dyciIgFcT/XHvXtRqVnG1CEspTIbx25VX0uqIhLceejYCHHllUD58pwM//zv06+Abt68eahfv77J0PFkO3nyJBYuXIjLL7/8/PdM5Dww81CzZk33eZFYWk+16YY3cLBlN5QpW9aUVAsEoVlBx5iI/z7+2MrCXXstAsavr2pXXHEFmjVrhkWLFnldv3//flzJcFMkzPhhU7RoUXNSQCfRhGPmyiPriX0911M9tW8TEhISghLMkY4xEf+VKAGczTkEjN+5dzZGdOzYER9k6q/17JwSEZHAYPMZx8XtTlrn0/ZslBCRyDR6NDBmDOAxa9B5K+DvN7ORI0fisssuM12tv//+O144u/iYsiESKR9++/ZZg8WZpdC4IXEifkHmPHHsUGUwx+az0wVLRMR6qjrGRPzXqxfwf/9nrRbBCYUzN5r7s1qEXwGdnYXr2bOnmYvu+uuvx5o1a/DKK6/4c3ciQZHKlY7PBnQiTsLxyPZUI1zJwcbyaYNLuiJ19TMRsZ6qjjER//TvDyxbZs1HF9amCE/sbl2yZAl69OhhSrAiIuJfxistLc0Ecfb62HbVo3jx4qZLtVixYubyirajTDcrgzfPoM5zPVWt2iASub77DvjhB+DSSwN3n34FdP379zfLwtgqVKiAuXPnYtCgQaYDVkREfC+pcr44llQZ1NnY0MP54tilyvnjPNnrqbLblQ0SNq2nKuIMnCCkePHA3mc+Vwx1MfDbL98c+cbJb7wSvfjByGEApGWJJNKcOHHCXVLleRtXbLAn/uVKDoFYKSJYdIxJKKWkpKFKlRJITj6IxMTiUZGhe+014K23rDF0geDzkc/Gh8aNG5vB5Tyfk6ZNmwZi30REIp6vQZXdpcog7vDhw+7r+Z7KL5gM4uySqq/4OI3adwvY3yIiocGxc0eOALVqWct+ZW6K2L8/iAFd8+bNsWvXLpQrV86c55uOZ3LPvsyf7MQSEYnl5bdYFuV74pEjR0xJlRUCz5IqgzcGcQzmMpdURSS6vfxy4O/T54Buy5YtKFu2rPu8iEgsy235rfmHj6Bso6tMx6rnsol2SZXnRST2nDwJzJ0LPP44UKNG4O5XY+gkKjEzYpe18lrGEvGlzLr36bq5Th2SesOXKFgwzozdZRAXTSuX6BiTUIq2MXQlSgArVwY2oPM5Q/f111/7fKfXXXedv/sjEhD80ORC5CLBwDFzpsyay/JbKXs2oslVPaNyYmsdYyL+69EDmDYNeOABhD6g4zxzvtAYOhGJdof2Jvm24bH9URnMicj5qVMHePJJ4JdfgJYtWUnyvn3o2dEcQQnoPAfzijihHLT/bJtQ6dKlo6bMJeHDZi92qbLBIf1kppa0MC2/FU46xkT89957QMmS1moRPHnix1VQAzoRp33Y7Ny505znDPsK6MTf/yOu2sCpRtilanf2l63TCqmrEyJi+a1w0TEm4r9g9Jb6HdBxwDlXh0hKSvKaGJOG+hNaiohEiGPHjrkn/j116pT7ek72yy8IbHJYvUvLb4nI+bNngDvfQpJfAd2KFStw7bXXmvmVGNixpLV3717TwcV56hTQiYjTMHCzS6oM6GycI86eaqRw4cLubK+W3xKR8/HRR8BzzwEbNliX69YFHn4Y6Ns3hAHdAw88gO7du+Ott94y31QXLVpklqy57bbbMGzYMP/2REQkDGXD9PR0k4njT8/J0uPj4002jt3S2TU2MKg73bEP/si0UkSFEC2/JSLO9OKL1jx0Q4YA7dtb182fD9xzD7B3r3/dr36966xcuRJvv/22eZPjt9fjx4+jZs2a+Pe//43+/fujZ8+e/tytiEhIHD161F1S9VzZhhk4u6RawMegTMtviUhecR3XN98E+vXLuI4zvjVqBIweHcKAjtk4+xsrS6wcR9egQQPzJpicnOzPXYqIBHU9VZZU7SDOs6TKwI3vXQzkGNCJiAQbe/batTv3el53tp8vNAFdixYtsHTpUtSpUwcdOnTAE088YcbQffzxx2jcuDGC6Y033sBzzz1n1pVt1qwZXnvtNbRu3TqojykizlxPtdnVfb1KqjaOg/MsqaoLWkRCqXZt4LPPgH/9y/v6yZOtOepCFtA988wz7jfHsWPHol+/frj33ntNgPf+++8jWCZPnozhw4ebsXtt2rTByy+/jC5dumD9+vUmUyhi4wd0tWrV3OclNtdT/WnfflRoerX7+iJFipjmhryUVCVrOsZE/DdmDNC7NzBvXsYYOk4yPGuWFehF/VquDOIuvvhivP766+7JjqtUqYL77rsPI0aMyPX3OY8U38jZyVa8uPPXghOJZb6up7rvpq+RUKaMycZx2hERcZ5oW8uVOKHwSy8Ba9eai2jQAHjwQVZB4RfHfEXlXHfLli3DyJEj3ddxHF+nTp2wcOHCLH+HzRo8eQZ0IhJb66nuO7gVFYI8FEREJK+45NcnnyBg/Aro9u3bZ8bNzZ49G7t37z5nWTB7yaVA4hg9dqOVL1/e63peXrduXZa/M27cOIxhXlNiDhPPHDdFLLGp7Bpdry27VPem/OnT9kf/2hH0fYpFOsZEzg9Dp40bgd27rfOeLr88RAFd3759sXHjRtxxxx0moIrUD0tm8zjmzjNDxxKtxMaHzfbt2815ltkj9X9U8palt7tUef5k/njE+nqq4aRjTMR/ixYBt94KbNuWsVKEjR9XHrMpBTeg+/nnnzF//nzTZRoqZcqUMXPepaamel3PyxUqVMjydzheRmNmRJyL2X+OeWUQx1VpPIdb1GnVKebXUxURZ7rnHqBVK+C774CKFc9/2S+/A7r69eubkkcoxcXFoWXLlpg1axZ69OjhfrPn5SGcallEoibzw2UFuQQXs+qeQzqKFStmSuhsauIXvBVttZ6qiDgPl/uaMsWaviRQ/Aro/vOf/5iuUo6j47xznGjYU7A6SFk+5UoUrVq1MnPPcdoSfmsfOHBgUB5PREKHZVQGcczGnTx50n0931/YocpAjl/sPGk9VRFxojZtrPFzYQ/o+MbKb85XXXXVOd+sOVbJcymdQOrduzf27NljAklOLNy8eXNMnz79nEYJEXEGvlfwvYSBHLNyniVVjn3ke03RokVzHAOp9VRFxGnuu8+aomTXLqBJE35x9b69adMQzUPH7Bgn5Rw2bFiWTRFcPSISaR662MEy3Zo1a8z5hg0bZru4uoR2+S3iWw4z63ZJ1fMtiKs22CVVvWaRTceYhFK0zUN3QRYfSQyl+HYY0qaI1atXY8WKFahXr54/vy4iMbT8FjNoxDkh7S5Vz5Iqy6h2STXz8A0RkWi0ZUvg79OvgI5j2JKTkxXQScRi1tieokZTloR3+a0FR4+hfJNOXo1UzL4xgOOJy3HpNXIeHWMi/ju7MmX4AzoutcVy68MPP4wmTZqc8626qT/FX5EAf9hwDJYEv8zKzBxlXn6Ll7n8Vs2VzyK1Rhvkz1/AlFSZjYuPj1dJ1eF0jImcf6fr7NlZTyz8xBMhGkOX1dgWHtzBboo4XxpDJxJYf/zyHRrNvDXX7Za0exctrrxBJVUR8Uu0jaF7913g3ns5xy7AqXQ9WxF4fvnyEGXotgSj+CsSQPxyYa/dywH2KukFx5F9KT5td8GJAwrmooyOMRH/Pf00MHYs8MgjCJg8B3QczMzpSr799ls0aNAgcHsiEuAPG47ztLtcFdAF9rlNT083zQ1pJ/P79Dtafiv66BgT8d9ffwE334yAyvNcDhwvd+zYscDuhYhEPDY17Ny5E+vWrUNSUpLJgJap3QqpSDBj5bLC63chwUxhIiIiFgZzM2YgoPyanGvw4MF49tlncerUqcDujYhEFB7je/fuxcaNG7Fp0ybs27fPjJHlPJQJCQmoV6++mZqEMgd19uWdbUdlOR+diEgwvfEGUL06ULiwtTLDkiU5j2m77DKgVCnr1KlTztufL64Q8fjjwIABwAsvAK++6n3yh1/vskuXLjVrqM6YMcN0uXJ9RU9ffvmlf3sjIhExYaxdUuVPG8vW7E5llyq7Ve0ytpbfEpFIM3kylwsF3nrLCuZefhno0gVYvx4oV+7c7efMAW65BWjXzgoAn30W6NwZ+OMPoHLlwO/fO+9wInVg7lzr5IlvrUPPzgQV9C7X3NZOnTBhAiKRulxjh2axzxu+DbCkyiDu4MGDXp3qnCeO88VxGhhm5s53pQiJDjrGJJK7XNu0AS6+GHj9desypwXh1KRccmvEiNwfj2+BzNTx9/v1gyP49W4bqQGbiOS9yclevYErOdgYuNkT/xbm11UfMHhr1L6bXgIRCRoWDc5OYGAUKmSdPJ04ASxbBowcmXEdZ1tjGXXhQviES0tzQZvSpeEY5/X1ec+ePVjP/CVgVo0oW7ZsoPZLRPzgS5aMmRVmqxnEHTp0yH09S6ic4oVBnGdJVUQkUjRs6H151Chg9Gjv6/butTJs5ct7X8/L69b59jicTqRSJSsIDIbbb8/59vffD1FAx4W1uVrERx99ZD4cKH/+/OjXrx9ee+01FC1a1J+7FQkYBiOVzw58iJXAJKf1VJt37mdKqn/99ZcpqdrHLfF4tUuqPI5FfBGLx5iE35o13mPaMmfnAmH8eGDSJGtcnY8FCr+mLfHEbODq1cCBA8BVV/l3n34FdMOHD8fcuXPxzTffoH379ua6+fPnY+jQoXjwwQfx5ptv+rc3IgHCDxgO3o8Vua2n+tP+v8x6qp7TD9kl1ULBeEeUqBdrx5hEhvh4Thaf8zZlyjDJBKSmel/Py1yVISfPP28FdD/+yGVMETRTp557Hb9nc/WIWrX8u0+/miLKlCmDKVOm4IorrvC6fvbs2ejVq5cpxUYiNUVItJZZ9z5d1wRvmddTtacP2Z0vAbt7TkXp0gkmiGNnurIqIhLNTRGtWwOvvZYRLFWtCgwZkn1TxL//ba3e8MMPwCWXICw4io2h1c6dIcrQHTlyBOUzF6fBVuBy5jaRcOP3FHt8WLSPB+OYOVNmzeZPZJBXAfuwJy0JiU2bhXr3JErF0jEmzjN8ONC/P9CqlRXYcdqSw4c5S4d1OztXWbodN866zGlKnngC+PRTa+66Xbus6zm1CE+hsmkT5//073f9Cujatm2LUaNGmTF0dgccx+eMGTPG3CYSCR8227Zti/qlv06cOIH92zf6tO3xA3585ROJ8WNMnKl3bzZuWkEag7PmzYHp0zMaJZKSrM5XG0eKsTv2pptyb7oIVMDpibVSZuW++84KREMW0L3yyivo0qULEhMT0ayZ9Y3/t99+M8HdD8xVikjQcI44Dh9ggwMz4scv8J7YOztaT1VEYsmQIdYpK2x48LR1K0JqxQrvywwuOVEIV43IrQM2oAFd48aNsWHDBkycONGs60i33HIL+vTpYyYhFZHAZ0PYXc4gjsGc59DX6s06IHV1Qq5j6LSeqohIZJg9O4LmoeNUB3fddVdg90ZEvHCyX3viX04CbIuLizMdhpxqhOdXtB1lulkZvHkGdZ7rqVbQqg0iIlHL74COGTp2te7evdtrTit6gkVrEfG7pMq54piN49hU2wUXXOCeaoSZcM8xS1pPVUQktvkV0L377ru49957zfQlFSpU8Ppg4XkFdCL+dQwyE5e5pMoOQmbj4uPjTVCXHQZ1pzv2wR+ZVopQZk5EJPr5FdA9/fTTGDt2LB7h2hgi4rdjx465S6qnPHrVOdmvXVLlJMC+0nqqIiKxya+AjqWgm2++OfB7IxIgzBRXrFjRfT6S1lNl4MaSKoM4z5Iql91iAMdAjh3jmgZCIlk4jzERCVBAx2BuxowZuOeee/z5dZGg4wdMQkJCxKynuv2SUajd7gYTxKWnp3uVVFlKZRDH0mpOJVWRSBKuY0wk2n30EcBVVfO6BJhfAV3t2rXx+OOPY9GiRWjSpMk5JSGu6SoSa3JcT3XhUPy4dy8qNe9irmMGzm5wKKDuUxEROWvAAK63DQwalLF0WdDWcq1Ro0b2d5gvHzZv3oxIpLVcY2/eNgrFuqW+rqd66o65KFO2rHuFFRGnCvUxJrEtr2u5Ot2WLcD33wP/+EeQM3Rb+EgiEf5hs/Xs1N+hWJZo7aLv0diH9VT/SPodiVW6BXVfRKLxGBOJJTVq5C2YO6956ERiHT/Q2KXKJqGdm9egsQ+/w0YJERGJPWlpvm9b3I8kpM8B3fjx4zFs2DCflvZavHgx9u7di27dlImQ6MMVG+ypRriSA+Ur6tvgcK2nKiISm0qW5LC0nLfhIDhuc/p0EAO6NWvWoGrVqqbDtXv37mjVqhXKciXZs9Mw8Pb58+fjk08+wY4dO/AR2zREogRXQ2F3KrNxnADYxjJT8eLFkdjxRqSufkbrqYqISMjWb/UroGOA9ttvv+H111/HrbfeahoMOG8WJ0A9cuSI2aZFixa48847MWDAAA36lqgoqXKeOAZxnDfOc4k7rmXMDlXOG8fjgLSeqoiIZKdDBwRVnsbQNWvWzCz79fbbb+P333/Htm3bzAcelwBr3ry5+SnidCdOnHCXVHnexul57KlG+EUmM62nKiIiecF8WFISP3e8r2/aFHnmV1MEJz9lAMeTSDRg9o1ZZ2bj7KkY7JIqs3AM4nyZmkHrqYqISG727AEGDrSmJslKUMfQiTjJmdOnUHDfOpxOT8XaA1tR/5KuXstv2SVVDhdgEMdgzrOkyuCNQRzHx9klVV9pPVWJFeXLlw/3Log40v33AwcOsIkUuOIKYOpUIDUVePpp4IUX/LtPxwR0Y8eOxXfffYeVK1ciLi7OlMNEclp+q57n8ls/JmBH21Emg2aXVBnIsWPVs6TKJbgYyPF/TERyrtTYjXEikjc//QR89RXQqhWPJaBaNeDqq63pSsaNA/yZJMQxAR0/hNlh27ZtW7z33nvh3h1x4vJbC4bipwMHUa7RVV4fSnZJlY0OmhxVRESCjSN7ypWzzpcqZZVg69YFmjQBli/37z59DujYBNG4ceOwLR4+ZswY8/ODDz4Iy+NL5OPyW8zMUeblt3iZy281XPsyUutfjuLFS5hsHEuq4fqfFomGLnDi/KT6MiTiu3r1gPXrgerV2XAKvP22df6tt4CKFeEXnz/JOCUJJwummjVrYt++jHJWpOKkrxwb5XmS6LVu8Q8oj6zXUvVcfivfwW1mPWJm5RTMifgf0HHdbp78WBJcJKYNGwbs3GmdHzXKao6oWhV49VXgmWeCnKHjhx/XcC1XrpxZv89zAHmkGjdunDuzJ9Ht9OnTOLBzs0/bnkhLDfr+iIiIZOe22zLOt2wJbNsGrFtnBXX+zgDnc4buxhtvRIcOHUxmg6l1rhTBTF1WJ1+NGDHC3FdOp3X8C/00cuRIMyGsfUpOTvb7viTyMCvA1Rv4uvL/5ChyX5aOtPyWiIhEAs4/x9Ir+/Auusj/YC5PGbp33nkHPXv2xMaNGzF06FDcddddiI+P9/+RATz44INmVYmc5CVAzIyTv2Y1Aaw427Fjx9wT/3LZOVtio/ZIXZ2g5bdERCTiJxS+7z7gww+ty3/+yXjHuq5yZSa8gtzl2rVrV/Nz2bJlGDZs2HkHdGx5V9u7+IKBG7OsDOLsgdjEOeLYpcoGh8KFC2Nl21Gmm5UNEJ5j6XiZdrYdhQqZ5qMTEREJpZEjgd9+A+bMYWyVcX2nTsDo0SEI6GwTJkxAqCUlJWH//v3mJ8dLcT46ql27Ni688MKQ74+ErqTKII4/PQde88sEgzi+9p6NDfbyW5UXjUE5V0bjzu58CSaY4+0iIiLhNG0aMHkycMklXJEo4/pGjYBNm/y7T8ekKp544gl8aOcmz3bd0uzZs3EFp1mWqMEMnF1SZfBuYwbOXku1QA5ZNgZtJ6+8BVvmT0KBY/uQVrw26l9yjTJzIiISETjvnD0PXeb56XJZYdL5AR3nn9McdNFdUrWDOI6R8yypMoCzS6p5WX6raKMu5nyDsmU1PYlIEGjIjIh/uELEd99ZY+bIDuL++1+gbdsoD+gk+nDqG8+Sqo3dzSypMpDjT38mLGUZVutMigSPjjER/3GuuWuuAdasYUIDeOUV6/yCBcDcuf7dpwI6CSmOg2MGjuuossnBs6TK2eYZxLHJIaeSqoiIiJNdeqnVFMF1W7nc14wZ1rQlCxdal/2hT00JiZMnT7pLqlzBw/0PWKCAe1xcXkqqvgSO9uNw6hotSyQSWDrGRPxz8iRw993A448D776LgFFAJ0EvqTIbd+jQIff1DK64hiqDOHapBiPY4ocN50ykhg0bKqAT0TEmEhEKFgS++MIK6AJJAZ0EZcFuu6TquURc0aJF3SVVNjuIiIjEoh49rKlLHnggcPepgE4C4sSJE+6SKs/bChYs6C6patUOERERoE4d4MkngV9+sdZyLVbM+1kZOjTvz5ICOvEbs29paWkmG3eYk+ecxRIqs3AM4ooVK6Zyp4iIiIf33gNKluTKW9bJE0chKaCTkJRUjxw5YoI4BnOZS6qcL47j41RSFRERydqWLQg4ZegkTyVVBnLsWPUsqTKIYzYuLi5Oz6aIiEgYKKCTbHGOOLukyqyc54SizMIxkGNWTlOCiIiI5Gz8eGDYMM65msuGABYvBvbuBbp1g88U0Mk5JVWOh2M2jl2qvGzjeDi7pMqgLtKVKVMm3LsgEtV0jIn4jitBVK0K3Hwz0L27tfxX2bLWbVwtgrfPnw988gmwYwfw0Ud5uHMFdGLjJLx2l6pnSZVlVLtL1UklVQacFSpUCPduiEQtHWMiecMAjatDvP46cOutQFoa1yvn5PeAXQRr0QK4805gwAAgr3Pt53N5pmCiHMuH7L5k5olZpljHkiqfCwZxmUuqfJ6YjeNyXCqpiohIOKWkpKFKlRJITj6IxETnf36fOQP8/juwbRtw9Ciz3UDz5tZPf6nkGmMYv3PVBgZxDHA943mu2sAgLj4+3hEl1Zzw77IzjWzcUFAqomNMJFLwI5YBHE+BEpMBHafa8Jxuw5NnIJPdNk7c9tixYyaAYyB3isX6TCVVZuQY+GQlkPvLwMoOroK5LU9//vmnuVy/fn2vfQzFPjCgzCn57bRtyX4Oo3lbJxzLkbItZXeMOeE9ItzbOuG4j7T3CMlZTAZ069atM9mozHhd9erV3ZfXrl2b7T8auztr1qzpvrx+/XpTwswKy5a1atVyX96wYYPXODVPXE2hDqeQPmvTpk1ei9l7YgBWr1499+UtW7aYZbdywznieJAysON0JLt37zYnG29r1KiR+3JSUpLXWqyZNW7c2H0+JSXFBI7Z8VxXdceOHSbAzA4/JAoUsP5Fd+3ahf3792e7bd26dd1j/Pi37GV7kMfr7al27doofHZwwp49e8wpO3yN+VrTvn37kJqamu22/N+x/6+4rzt37sx222rVqplMKPE52L59e7bbVqlSxQTcxOc2OTk5220rV65ssqzE12wb8/nZqFixIhISEsx5NsJs3bo1223Lly+PsmdH7/J/bPPmzdluy+24PfF/115TN7tB9fZYRx4TdoCQldKlS6NSpUrmPI+1zK+rJ35JSUxMNOd5DK/haONscPhFVY5UPiunbaP5PYLvCw0aNHBf5v+D51AMTzyGPbflce/k94jM9B4Rme8RkrOYDOhiFQMIftjzQ4kHpmemTkRERJwrJpsiOK9adk0RkVDK8GdbllT57ZTfZj1/h9/m7WW4PLtUw7W/oSy52hkclVydUU6JhG0j4Vh2yrae2UyVXFVyDfbxGQ1NEb//zmy1NX4uGGIyQ8d/Dl9q8nmp24djW2bY7CCOAZ1n6cSeaoSlnEjZ33Btm9PrHax98AyWtK1znodI/R+OxG09Az5f31MDvQ9O3jYS/t+dtq3TtWgBcCROuXIczgMsXQqcrWgHREwGdE7GN1GOVWGWMT093X09DwiWVBnE8WesHCAiIiJOULKktYYrAzoOR/QhCZ4nCugcgOloZuAYxHHeOM+B1czA2V2q9uBgERERiSw33gh06MBmEyZhrJUiOLFwVnLoKcmWIoAIxi43BnAM5Dy72Bi42SVVu1tTsu6KFJHg0TEm4rt33gF69gTY1Dt0KHDXXWxWRMAooIvAkipLqQziPKcBYAmVjRwM4tilqpJq7mNZ7CkuRCTwdIyJ5F3XrtbPZcuAYcMU0EVlSZXz9tglVc/BxpzLyi6pstlBREREnG3ChMDfpzJ0YcRJfdmhyhPPe04GapdUOe2I+Bck22MN7YmURSRwdIyJRBYFdCHG7Bvnw2M2jjNv2xhw2PPFFStWTAFIAD5s7HnoPGeeF5HA0DEmElkU0IXojY9L6DCIYzCXuaTK1Rs4Pk4lVREREfGHAroQlFQZyHmuy8iSKoO4zKs3iIiIiPhDAV2AcdyWXVL1XNiaHWHMwjGQY1ZOJUAREREJFAV0ASqpcjwcs3HsUvVcl47j4eySal6WhRERERHxlQK688DJfu0uVc+SKsuodpeqSqoiIiISbAro/CipMgvHIC5zSZVdqszGcTkulVRFREQkVBTQ+YAlVK7awCCO4+M8S6pctYFBXHx8vEqqEYYZUhHRMSYSCxTQ5eDYsWPukuqpU6fc13OyX7ukyo5ViTzMmCYmJoZ7N0Silo4xkciigC4TBm52SZXLcdk4R5xdUi1cuLBKqiIiIhIxHNF2uXXrVtxxxx2oUaOGGZ9Wq1YtjBo1ymu5rPPBEipLqUlJSVi/fj127tzpDuZYSq1SpQrq1atnFnvX+Dhn4GvKCZx58iyRi4iOMYkNb7wBVK8OFC4MtGkDLFmS8/affw7Ur29t36QJ8L//wVEckaHjEk78YH777bdRu3ZtrF69GnfddZeZKuT5558/r5Iq54tjNs5e95OYgbNLqgUKOOIpkkwYxK1Zs8ac19JfIoGnY0wi2eTJwPDhwFtvWcHcyy8DXboA69cD5cqdu/2CBcAttwDjxgF/+xvw6adAjx7A8uVA48ZwhHwuh6YvnnvuObz55pvYvHmzz7/DLBzLpvwdBnAM6DxLqnYQxyycOBu/AHgGdJoDUETHmDhXSkoaqlQpgeTkg0hMLJ7r9m3aABdfDLz+unWZK25WqQLcdx8wYsS52/fuDXB59W+/zbjukkuA5s2toNAJHJt+4ji30qVL5zpPHE+eAR2lpqaa7lROLcKSKoM4/tRUIyIiIpErPZ2f5RmXCxWyTp44GmvZMmDkyIzrOK9/p07AwoXIEq9nRs8TM3rTpsExHDGGLrONGzfitddew913353jduPGjTMZOfvEsXB2SbVixYpmXFzVqlXNKg4K5kRERCJbw4ZAiRIZJ5ZIM9u7l3PGAuXLe1/Py7t2ZX2/vD4v20eisAZ0I0aMMIFUTieOn/O0fft2dO3aFTfffLMZR5eTkSNHmkyefUpOTjbX16xZEwkJCRofJyIi4iAcSXPwYMbJMwsX68Jacn3wwQcxYMCAHLdh8GXbsWMHrrzySrRr1w7vvPNOrvfP+eJ4EhEREeeLjweK5zKErkwZjovn8Crv63m5QoWsf4fX52X7SBTWgK5s2bLm5Atm5hjMtWzZEhMmTNAgdxERETlHXBzQsiUwa5bVqWo3RfDykCFZP2Ft21q3339/xnUzZ1rXO4UjmiIYzF1xxRWoVq2amaZkz5497tsqOCl8lpDi2EgR0TEmsWf4cKB/f6BVK6B1a2vaEnaxDhxo3d6vH1C5csYYvGHDgA4dgBdeALp1AyZNAn79FfChGBgxHBHQzZw50zRC8JR5OSeHzroiQcZpStjwIiI6xiT29O4NMPfzxBNWYwOnH5k+PaPxISnJ6ny1tWtnzT332GPAv/4F1Kljdbg6ZQ46R89D5w97Hjo2SCh7IyIiEp3z0MUiR05bIiIiIiIOK7mK5JVWihAJLh1jIpFFGToRERERh1NAJyIiIuJwCuhEREREHE4BnYiIiIjDKaATERERcTgFdCIiIiIOp2lLJGpdeOGF4d4FkaimY0wkciigk6hd+qt69erh3g2RqKVjTCSyqOQqIiIi4nAK6EREREQcTiVXidplidauXWvON2jQwJSHRETHmEi0UkAnUcvlcoV7F0Simo4xkcihtIWIiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJy6XCVqFS1aNNy7IBLVdIyJRA4FdBKVOO9czZo1w70bIlFLx5hIZFHJVURERMThFNCJiIiIOJxKrhK1S3+tX7/enK9Xr56W/hLRMSYS1RTQSdQ6ffp0uHdBJKrpGBOJHCq5ioiIiDicAjoRERERh1NAJyIiIuJwCuhEREREHE4BnYiIiIjDqctVolaRIkXCvQsiUU3HmEjkUEAnUbssUa1atcK9GyJRS8eYSGRRyVVERETE4RTQiYiIiDicSq4StUt/bdiwwZyvU6eOlv4S0TEmEtUck6G77rrrULVqVRQuXBgVK1ZE3759sWPHjnDvlkSwkydPmpOI6BgTiXaOCeiuvPJKfPbZZ2bB9S+++AKbNm3CTTfdFO7dEhEREQk7x5RcH3jgAff5atWqYcSIEejRo4fJwBQsWDCs+yYiIiISTo7J0Hnav38/Jk6ciHbt2imYExERkZjnqIDukUceQbFixZCQkICkpCR89dVXOW5//PhxpKWleZ1EREREok1YAzqWTfPly5fjad26de7tH374YaxYsQIzZsxA/vz50a9fP7hcrmzvf9y4cShRooT7VKVKlRD9ZSIiIiKhk8+VU0QUZHv27MG+ffty3KZmzZqIi4s75/qUlBQToC1YsABt27bNNkPHk40ZOv7OwYMHUbx48QD8BRLJ05awcYa4YgRntRcRHWPiTCkp/PwugeTkg0hM1Od3xDVFlC1b1pz8/cAmz4Ats0KFCpmTxB4GcJx/TkR0jInEAkd0uS5evBhLly7FpZdeilKlSpnMy+OPP24yL9ll50RERERihSPqUEWLFsWXX36Jjh07ol69erjjjjvQtGlTzJ07Vxk4ERERiXmOyNA1adIEP/30U7h3QxxEY+hEdIyJxBJHBHQi/shpfKWInD8dYyKRwxElVxERERHJngI6EREREYdTQCciIiLicAroRERERBxOAZ2IiIiIw6nLVaJWwYIFw70LIlFNx5hI5FBAJ1G79BcnoRYRHWMisUAlVxERERGHU0AnIiIi4nAquUrULv21ZcsWc75GjRqmBCsiOsZEopUCOolaR48eDfcuiEQ1HWMikUNpCxERERGHU0AnIiIi4nAK6EREREQcTgGdiIiIiMMpoBMRERFxOAV0ErXy589vTiKiY0wkO/v3A336AMWLAyVLAnfcARw6lPP2990HcDGiIkWAqlWBoUOBgwcRVpq2RKIS551r0KBBuHdDJGrpGJNo0acPsHMnMHMmcPIkMHAgMGgQ8OmnWW+/Y4d1ev55oGFDYNs24J57rOumTEHY5HO5XC7EiLS0NJQoUQIHDx5EcYbiIiIiEvFSUtJQpUoJJCcfRGJi4D6/1661grKlS4FWrazrpk8Hrr2WjwlUquTb/Xz+OXDbbcDhw0CBMKXKVHIVERERR0hPZ3Im43T8+Pnd38KFVpnVDuaoUydmoIHFi32/H5ZbmScKVzBHCugkapf+2rx5sznxvIjoGBPnYzatRImM07hx53d/u3YB5cp5X8egrHRp6zZf7N0LPPWUVaYNJ42hk6h15MiRcO+CSFTTMSahtmYNULlyxuVChbLebsQI4Nlncy+3ni9mCbt1swLN0aMRVgroRERExBHi463SZm4efBAYMCDnbWrWBCpUAHbv9r7+1Cmrk5W35Vb+7drV2qepU4GCBRFWCuhEREQkqpQta51y07YtcOAAsGwZ0LKldd1PP3HYDtCmTc6ZuS5drAzh118DhQsj7DSGTkRERGJSgwZWlu2uu4AlS4BffgGGDAH+/veMDtft24H69a3b7WCuc2ero/W996zLHG/H0+nT4ftblKETERGRmDVxohXEdexodbfeeCPw6qsZt3NuuvXrOWbUurx8eUYHbO3a3ve1ZQtQvTrCQgGdiIiIxKzSpbOfRJgYoHnO2HvFFd6XI4UCOola+fLlC/cuiEQ1HWMikUMBnUTtskSNGjUK926IRC0dYyKRRU0RIiIiIg6ngE5ERETE4VRylajE5b6SkpLM+apVq5rykIjoGBOJVgroJGodOnQo3LsgEtV0jIlEDqUtRERERBzOcQHd8ePH0bx5c9Muv3LlynDvjoiIiEjYOS6g++c//4lK9nocIiIiIuKsgO7777/HjBkz8Pzzz4d7V0REREQihmOaIlJTU3HXXXdh2rRpKFq0aLh3R0RERCRiOCKgc7lcGDBgAO655x60atUKW7du9Xm8HU+2gwcPmp9paWlB21eJnGlL7A48vt6atkREx5g4V3p6mjsekAgM6EaMGIFnn302x23Wrl1ryqzp6ekYOXJknu5/3LhxGDNmzDnXV6lSJc/7KiIiIuF16FA6gBJ6GbKQzxXGcHfPnj3Yt29fjtvUrFkTvXr1wjfffOO1EPTp06eRP39+9OnTBx9++KFPGTpmbfbv34+EhAQtKh0DmJlj8J6cnIzixYvrsfWc638tio4xiS1nzriwc2c66tathPz5HTX8PzYCOl9xxn/PMumOHTvQpUsXTJkyBW3atEFiYmJY908iE/9nSpQoYUrt4Qjo9Nh6zvW/JiKh4ogxdFy6ydOFF15oftaqVUvBnIiIiMQ85S1FREREHM4RGbrMqlevrk4XyVWhQoUwatQo8zPU9Nh6zvW/JiKh5IgxdCIiIiKSPZVcRURERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATmIC1wHmSiMvv/xySB5v9OjRqF+/PooVK4ZSpUqhU6dOWLx4cdAf9+TJk3jkkUfQpEkT89iVKlVCv379zGTcofDll1+ic+fO7tVYVq5cGZLHfeONN0z3e+HChc1k40uWLAnJ486bNw/du3c3zzP/3mnTpoXkcbms4cUXX4z4+HiUK1cOPXr0wPr160Py2G+++SaaNm1qJuvmqW3btvj+++9D8tgikj0FdBL1pk6dikWLFpkP3VCpW7cuXn/9daxatQrz5883wQYDHS53F0xHjhzB8uXL8fjjj5ufDLD4QX/dddchFA4fPoxLL7001zWaA2ny5MkYPny4maKGf3OzZs3MSjK7d+8Oyd/Lx2NAGUpz587F4MGDzf/1zJkzTSDP/y/uT7BxZZ7x48dj2bJl+PXXX3HVVVfh+uuvxx9//BH0xxaRHHDaEpFolZKS4qpcubJr9erVrmrVqrleeumlsOzHwYMHOT2Q68cffwz5Yy9ZssQ89rZt20L2mFu2bDGPuWLFiqA/VuvWrV2DBw92Xz59+rSrUqVKrnHjxrlCiX/v1KlTXeGwe/du8/hz584Ny+OXKlXK9d///jcsjy0iFmXoJGqdOXMGffv2xcMPP4xGjRqFbT9OnDiBd955x6ztymxOqHEtW5YDS5YsiWjD55aZIpa0bRdccIG5vHDhQsQKvsZUunTpkD7u6dOnMWnSJJMZZOlVRMLHkStFiPiCZb8CBQpg6NChYXnCvv32W/z97383ZdCKFSua0liZMmVCug/Hjh0zY+puueUWM94p2uzdu9cEFeXLl/e6npfXrVuHWPnicv/996N9+/Zo3LhxSB6TQwkYwPH/i2trc1hDw4YNQ/LYIpI1ZegkKkycONF8sNgnjjF65ZVX8MEHH5jsVCgf++effzbXX3nllaYpYMGCBejatSt69eoV8HFd2T02cVwVH5PVQA5kD7ScHltCh2PpVq9ebTJloVKvXj3zv81Gn3vvvRf9+/fHmjVrQvb4InIuLf0lUSE9PR2pqanuy59//jkeffRRU36zMZPDy1WqVMHWrVuD9tiVK1dGkSJFztmuTp06uP322zFy5MigP7YdzG3evBk//fST6ToNtJz+bj6/NWrUwIoVK9C8eXMEs+RatGhRTJkyxXR62hhgHDhwAF999RVChV8cmKny3I9gGzJkiPkb2W3L5ztcWOKuVasW3n777bDtg0isU8lVogKnb+DJNmjQIDOdhCd2PnJM3cCBA4P62DmVxo4fPx70x7aDuQ0bNmD27NlBCeaye+xQi4uLQ8uWLTFr1ix3IMXnmZcZ7EQrZl3vu+8+E0DOmTMnrMFcsP63RSRvFNBJVGIQkzmQKViwICpUqGDKRcHEAeJjx441U4Vw7BzHeXFai+3bt+Pmm28O6mMzmLvpppvM9B0cw8es5K5du9wD5hkABdP+/fuRlJTknvfOnhuNzztPwcApS5iRa9WqFVq3bm3mGuRrEOjAPSuHDh3Cxo0b3Ze3bNliSpF8rqtWrRrUMuunn35qsnMMqu3XmI03WWWHA4kZ5muuucb8fczScj8YVP7www9BfVwRycXZbleRqBeqaUuOHj3quuGGG8zUGXFxca6KFSu6rrvuOjN9SKimC8nqNHv27KA//oQJE7J87FGjRgX1cV977TVX1apVzfPNaUwWLVrkCgU+p1n9vf379w/q42b3GvP5D7bbb7/dHEt8rsuWLevq2LGja8aMGUF/XBHJmcbQiYiIiDiculxFREREHE4BnYiIiIjDKaATERERcTgFdCIiIiIOp4BORERExOEU0ImIiIg4nAI6EREREYdTQCciIiLicAroRCRivPfee+jcubP78oABAwKy2H2+fPkwbdo0BMqIESPMWqoiIpFCK0WISEQ4duwYatasic8//xzt27c31x08eNAsRF+yZMnzDui4kH0ggkPi+rzcV67byp8iIuGmDJ2IRIQpU6agePHi7mDOXmz+fIO5YChTpgy6dOmCN998M9y7IiJiKKATkYDas2cPKlSogGeeecZ93YIFCxAXF4dZs2Zl+3uTJk1C9+7dva7LXHK94oorMHToUPzzn/9E6dKlzeOMHj3a63c2bNiAyy+/HIULF0bDhg0xc+bMcx4rOTkZvXr1MsEi7+f666/H1q1bzW3r1q1D0aJF8emnn7q3/+yzz1CkSBGsWbPGfR33lfssIhIJFNCJSECVLVsW77//vgm0fv31V6Snp6Nv374YMmQIOnbsmO3vzZ8/H61atcr1/j/88EMUK1YMixcvxr///W88+eST7qDtzJkz6Nmzpwkeeftbb72FRx55xOv3T548abJr8fHx+Pnnn/HLL7/gwgsvRNeuXXHixAnUr18fzz//PP7xj38gKSkJKSkpuOeee/Dss8+aANHWunVrc5sdCIqIhJPG0IlIUAwePBg//vijCdJWrVqFpUuXolChQllue+DAAZQqVQrz5s3DZZdd5pWh4212QwMzdKdPnzaBmGdgddVVV2H8+PGYMWMGunXrhm3btqFSpUrm9unTp+Oaa65xj6H75JNP8PTTT2Pt2rVmbB0xkGO2jo9jN2X87W9/Q1pamgkO8+fPb+7H3p54G0vCc+bMQYcOHfRfJCJhVSC8Dy8i0YpZrsaNG5smh2XLlmUbzNHRo0fNT5ZJc9O0aVOvyxUrVsTu3bvNeQZpVapUcQdz1LZtW6/tf/vtN2zcuNFk6DI3ZWzatMl9mVnGunXr4oILLsAff/zhFcwRS7B05MiRXPdZRCTYFNCJSFAwONqxY4cpg7Is2aRJk2y3TUhIMAHTX3/9lev9FixY0Osyf4+P4atDhw6hZcuWmDhxYpblYs/A7/Dhwyag27lzpwkcPe3fv/+c3xERCRcFdCIScCxh3nbbbejduzfq1auHO++805Rdy5Url+X2LGtyfBqbDjznocurBg0amIYHzwBs0aJFXttcdNFFmDx5stkXdtVmhcEay72PPvqoua8+ffpg+fLl7qwcrV692gSXjRo18nt/RUQCRU0RIhJwDIQ4h9yrr75qmhJYurz99ttz/B02KrAx4nx06tTJPFb//v1Nho1j7bgvnhiccdoRdrby9i1btphxcOyeZZMDsQmCpdvHHnsML774ohm399BDD3ndD3+X4/08gzwRkXBRQCciAcXg6OWXX8bHH39sMmAsWfI8A6Cc5m2744478L///c8Egv7iY7H5gWPy2CzBzODYsWO9tuGUJGy+qFq1qumIZVaPj80xdNzfjz76yOwH97lAgQKmo5aNFO+++y6+//579/1wypK77rrL730VEQkkdbmKSMS4+eabTUl05MiRiGQM7B588EH8/vvvJugTEQk3ZehEJGI899xzZk64SMdmiQkTJiiYE5GIoQydiIiIiMMpQyciIiLicAroRERERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJwCOhERERGHU0AnIiIiAmf7fy+rT6l1ZxvWAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.5*x + 0.25\n", + "# Gradient: f'(0) = 0.5\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " # 1. State preparation\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "markdown", + "id": "23", + "metadata": {}, + "source": [ + "The graph is exactly the same as the phase kickback method.\\\n", + "From this point, we will use this method over the phase kickback, in order to have better efficiency." + ] + }, + { + "cell_type": "markdown", + "id": "24", + "metadata": {}, + "source": [ + "## 2.3. Quadratic Function" + ] + }, + { + "cell_type": "markdown", + "id": "25", + "metadata": {}, + "source": [ + "More interesting are non-linear functions.\\\n", + "In the next example we will see a quadratic function.\\\n", + "Note that the 'magic' does not happen in this step. You will see that the phases agree with the function completely and doesn't do the linearization needed to calculate the gradient. The magic will happen in the next step where the QFT will do the linearization for us." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "26", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 3\n", + "Circuit Depth: 9\n", + "Gate Counts: {'u': 6, 'cx': 6}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.5*x^2 + 0.25*x + 0.1\n", + "# Gradient: f'(x) = x + 0.25, so f'(0) = 0.25\n", + "p.set_function(p.quadratic, (0.5, 0.25, 0.1))\n", + "p.l = 2\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " # 1. State preparation\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "markdown", + "id": "27", + "metadata": {}, + "source": [ + "If we decrease $l$, we look at the function more closely, and it is closer to linear." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "28", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 3\n", + "Circuit Depth: 9\n", + "Gate Counts: {'u': 6, 'cx': 6}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.5*x^2 + 0.25*x + 0.1\n", + "# Gradient: f'(x) = x + 0.25, so f'(0) = 0.25\n", + "p.set_function(p.quadratic, (0.5, 0.25, 0.1))\n", + "p.l = 0.2\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " # 1. State preparation\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + "\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)" + ] + }, + { + "cell_type": "markdown", + "id": "29", + "metadata": {}, + "source": [ + "# 3. Full Algorithm" + ] + }, + { + "cell_type": "markdown", + "id": "30", + "metadata": {}, + "source": [ + "## 3.1. Linear Functions" + ] + }, + { + "cell_type": "markdown", + "id": "31", + "metadata": {}, + "source": [ + "The next and final step of the algorithm is to apply QFT on the coordinate.\\\n", + "As discussed earlier, applying the QFT will automatically extract the gradient from the phases, and create a measurable state with the value of the gradient (normalized)." + ] + }, + { + "cell_type": "markdown", + "id": "32", + "metadata": {}, + "source": [ + "To see the full algorithm in action, we will switch from the statevector simulation to standard simulation, because the final result is acquired by a measurement and not by looking at the phases." + ] + }, + { + "cell_type": "markdown", + "id": "33", + "metadata": {}, + "source": [ + "Let's start with a simple example of linear function." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "34", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum program link: https://platform.classiq.io/circuit/3DILrogdwroL6Ht6yyRhhAQotSH\n", + "Parsed counts: [{'x': -2}: 2048]\n", + "The analytical gradient is: -0.5\n", + "The majority gradient is: -0.5\n", + "The majority result is correct\n", + "####################################################\n", + "Success rate: 100.00% (2048/2048 shots)\n", + "[\u001b[92m██████████████████████████████████████████████████\u001b[91m\u001b[0m] 100.00%\n" + ] + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_circuit = True # Set to True to show the circuit\n", + "\n", + "p = params()\n", + "p.set_function(p.linear, (-0.5, 0.25))\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " # 1. State preparation\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "\n", + "qprog = synthesize(main)\n", + "if show_circuit:\n", + " show(qprog)\n", + "job = execute(qprog)\n", + "# job.open_in_ide() # Uncomment to see the results in the IDE\n", + "pc = job.get_sample_result().parsed_counts\n", + "df = job.get_sample_result().dataframe\n", + "\n", + "# You can use the helper function:\n", + "# pc, df = run_standard_simulation(main)\n", + "\n", + "# Translate the majority state to a gradient value\n", + "majority_state = dict(df.iloc[0])\n", + "value = majority_state.get(\"x\")\n", + "# Divide by (N/m) to get the actual gradient value.\n", + "majority_gradient = value / (N / m)\n", + "analytical_gradient = p.analytical_gradient(0)\n", + "\n", + "# Or use the helper function:\n", + "# majority_gradient = state_to_gradient(majority_state.get('x'), p)\n", + "\n", + "# Print the results and compute the majority gradient\n", + "print(\"Parsed counts:\", pc)\n", + "print(f\"The analytical gradient is: {analytical_gradient}\")\n", + "print(f\"The majority gradient is: {majority_gradient}\")\n", + "\n", + "# Check if the majority result is correct within the resolution of the algorithm\n", + "resolution = m / N\n", + "is_correct = abs(majority_gradient - analytical_gradient) < resolution / 2\n", + "print(f\"The majority result is\", \"correct\" if is_correct else \"incorrect\")\n", + "print(\"####################################################\")\n", + "\n", + "# Compute the success rate of the algorithm, i.e. the percentage of shots that are correct within the resolution of the algorithm.\n", + "success_rate, success_shots, total_shots = compute_success_rate(\n", + " df, analytic_derivatives={\"x\": analytical_gradient}, p=p\n", + ")\n", + "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", + "show_bar(success_rate)\n", + "\n", + "# Visualize the theoretical values of the phases\n", + "# We used the standard simulation, so this is theoretical values only without the phases from the simulation\n", + "plot_theoretical()\n", + "\n", + "# Plot histogram of the results\n", + "plot_histogram(df, analytical_gradient=analytical_gradient)\n", + "\n", + "# You can use the helper function:\n", + "# analyze_results(pc, df, p)" + ] + }, + { + "cell_type": "markdown", + "id": "35", + "metadata": {}, + "source": [ + "The result for the gradient is always a multiple of m/N.\\\n", + "In the previous example, the gradient was -0.5, while the resolution (m/N) was 0.25.\\\n", + "The gradient is a multiple of the resolution, and therefore the result can be exact, and the success rate was 100%.\\\n", + "\\\n", + "More complex case is where the gradient is not a multiple of the resolution.\\\n", + "In those cases, the result will be a superposition of multiple solutions, but we can still get a good approximation for the gradient from the result.\\\n", + "Let's see it in the next example.\\\n", + "TODO: Consider removing this example, because it doesn't match the flow of the explanation." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "36", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum program link: https://platform.classiq.io/circuit/3DINMWkHQwj0urBbWT2H9OD79eG\n", + "Parsed counts: [{'x': 2}: 1765, {'x': 3}: 136, {'x': 1}: 57, {'x': -4}: 28, {'x': 0}: 20, {'x': -1}: 16, {'x': -3}: 16, {'x': -2}: 10]\n", + "The analytical gradient is: 0.55\n", + "The majority gradient is: 0.5\n", + "The majority result is correct\n", + "####################################################\n", + "Success rate: 86.18% (1765/2048 shots)\n", + "[\u001b[92m███████████████████████████████████████████\u001b[91m-------\u001b[0m] 86.18%\n" + ] + }, + { + "data": { + "image/png": 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/Hffee69XUJgVBmcMrL766itzYhA0btw49+1HjhzB0KFD8euvv5rsId9Xrr/++lyvysGA7J577jFZRw518nJe8G949NFHTeBav3593Hrrrab3IPG6Tp06mZ6bDPQWLFiA7t27m1Y2DOT4mHxsPi5PHKbOaPny5ejZs6cJZP/8808T5PL5tQNLG4M8ZlT5/PN1u//++7Fu3bo8/S0SGGosLCIS4c21gy23zbw5zMr95DBkZng9s0wpKSnuIdLLL78cjzzyiHsbZps8vfnmm2jQoAGef/55c5nnV61ahWeeeSbbfWFgxuCFmSfq06ePCdzs32Mxg6d3330X8fHx5jnOzfy9ChUqmOyZPdSZVwzmunXrZs6PGTPGZNI4PN2wYUP8+9//NkHW//3f/7m35+02PiYfO7vHfemll0xQaAfJDBr5t/F5ZJbPdvXVV5tAjoYNG4aXX34ZP/74o3meJbSUuhARkZDKbUaPGLhkh9miCy+80Ou61q1b53i/HE60gzl7+Sl7KSo7+GRWrHbt2ma4l9vT1q1bEQzNmzf32jey98/O0OXHmjVrcPHFF3tdx8v8u+2m1Rn3g0E7g0TP50lCRxk6iUj8tu259JeGXSXa8MOW//uhWPortxPt69ata7ZlMMHhy4x4PeeDMRNmK1WqFAKBQ8eeuF+ew6kcwmT17cSJE001Lm9jZo6FGfnBx8kY0Ga2UoLn/tnPr71/GYerAymn50lCRxk6EZEIxA9au2gh2KfcBnQsLrjiiivMUOGxY8e8btu1axcmT55sWozkpRKTQ3+c5+Zp2bJlyA+2T2Hm74knnjCZMHso2B8YrHJem40ZMfarywtmzTg8nBUOuXpm2TLDv4mFFZ54mUOvrCSW8KeATkREQmb8+PE4ceKEqcpkBSh70rGilIFe1apVc5z7lhGLINauXWvmd7HX3Mcff+ye2O9riw5mCRl8sqKT89Z++OEHUyDhD5wTyOeARQYMRO+7775zsmA5GTFihAlaObftjz/+MH//hAkTsHfvXnM7h4eXLFli5hvyuswyapyXyKCQVcR83lgZzP3i3D1xBgV0IiISMmwvwkCGc9NYZVmnTh3TjoQtOlixyWKCvKhVqxamT59uqkiZuWJgY1e5sh2HL5h1nDp1qqkE5TDrww8/7C66yC9WjbLq9NJLL8Vtt91mAih7kfrcYhaNbV9Y1cv5gqxq/fzzz929+XifzLJxCJ4Zwczm/V1wwQUm+OXfyb9x5MiReOqpp7wKIiS8FXDlZTaqwx06dMj0F0pNTVV/sginOXQSbTifjS07GNBwTlugZTeHLtwwy8dmxcz+iTP/h7dtO4TExBgkJ6eiWjX1F82MiiJERCSicE4eK105TMp5YMymDRo0KNS7JRJQCuhERCSisLDg6aefNo2L2Vyc88M4z0wkkimgk4hVunTpUO+CSEQL13ZAbHbLk0g0UUAnEftBYzf+FBH/45w5X4sMRMT/wvPrlYiIiIjkmgI6EREREYfTkKtEbNsSLhtkd0AP17k+Ik7lpLYlItFAAZ1ErChqsSgiIlFOaQsRERERh1NAJyIiYeunn34yw7kHDx6Ek3CfZ86c6bf7Y9X+K6+8gkDq0KEDHnrooYA+hgSOAjoREXE7fcaFRRv34fPftpufvBzIoCe70+jRo8P+leE+tmjR4pzrd+7ciauuuiok+yTRSXPoRETEmLVqJ8Z8uRo7U61iB6ocUxyjujdG16aV/f4sMeixTZs2zSwIv27dOq/m4L/++mtIXp2TJ0+iaNGiPv9+QkKCX/dHJCfK0ImIiAnm7v9ohVcwR7tSj5vrebu/MeixTzExMSYr53md52ovy5cvR6tWrVCyZEm0a9fOK/Cjzz//HBdccIGpuK1duzbGjBmDv//+23371q1bcd1115n7LFu2LHr27Indu3efk2l7++23vRaH51Dv3Xffjfj4ePN7l19+OX7//Xdz23vvvWceh5ftrCKvy2zIddu2bbj11ltRoUIFlCpVyvwtS5YsMbdt3LjR7FulSpXM/nEd2u+//z7Xz+Ps2bPN/mYclh4yZIjZX9q3b595/KpVq5rnsFmzZvjvf/+b52HjcuXKuf9GSk5ONs8lr+ffxr9j8+bNXkPmrVu3Nn8zt7n44ouxZcuWXP9tknsK6CRi8U2LJxHJHodVmZnLbHDVvo63Zxx+ZTugYLUEevzxx/Hiiy+ajF3hwoVx5513um/7+eef0bdvXxPArF69Gm+++aYJOp555hl3GyMGGlzbdd68eZgzZw42bdqEXr16eT3Ghg0b8Omnn+Kzzz7Db7/9Zq67+eabsWfPHnz77bcmqGTQ2KlTJ3Nf/H2uE9ukSROTbeQp433S4cOH0b59e2zfvh1ffPGFCQD/+c9/mv2yb7/66qsxd+5crFy5El27dkX37t1NEJob3B8GS9x32+nTp03Ws3fv3uYyW8y0bNkSX3/9NVatWoUBAwagT58+WLp0KXx16tQpdOnSBWXKlDGvwS+//GICUu4/M5wMqHv06GH+9j/++AOLFi0yj6sWN4GhIVeJSPyQ4bd0EcnZ0qT952TmPDGM4+3crm2d2JAs/cXgjIEBDR8+HN26dTNBCjNTzJLxun79+pnbeez/61//MkHTqFGjTKD0559/IikpCYmJiWabDz74wARiy5YtMxkxYhDC65mNowULFpiAhwGd/be+8MILJms1ffp0E5wwgGGAmd0Q65QpU5CSkmIei1ksqlu3rvv28847z5xs3PcZM2aY4G/QoEE5PjeFChXCLbfcYh7nrrvuMtfxb2bG7sYbbzSXmZl79NFH3b/z4IMP4rvvvsPHH39sMmi+YMDIoJRZTTtImzRpkgkumZljFjI1NRXXXHMN6tSp4+4LKoGhgE5EJMrtSTvu1+0CoXnz5u7zlStb8/kYaFWvXt1kvJgdsjNydoaKAd/Ro0dNk3EGcnYwR40bNzaBB2+zA7oaNWq4gzni/TJ7FhtrBbG2Y8eOmWHS3GK27/zzz3cHcxnxMTjky+wZs3zMbPExcpuhI2biLrroIuzYsQNVqlTB5MmTTdDLv9F+Pp599lkTwDFTyOD1xIkT+RrF4PPDrCYzdJ74vPP5ufLKK9G/f3+TxbviiivQuXNnMzxrv37iXwroRESiXMUyxf26XSAUKVLEfd7OBnkOWTJLd8MNN5zze/ZcuNzgPC9PvF8GH8w2ZWQHSrlRokSJbG9n5ozDwMz+MXPH7W+66SYTdOUWg1JmwaZOnYr777/fZPg857o9//zzePXVV03rE86f49/KFiXZPQaf54wN2jnM6vn8cBiXwWNGdmDMjN3gwYMxa9Ysk9F74oknzN/K4FOiNKCbMGGCOdmTLZkqZ0WUysIlM3yjtydNN2jQQEt/iWSjda0KppqVBRCZzaNj+JQQU9xsF45Lf3FeG493z2FMTxzm4+R9nuwsHefacUiSmbrs7nfXrl1mSJV94DLDSlhmv3LKLnJYkvPuMsvSMbvITNb111/vDpQ8CwvykqVjcFWtWjXznscMnedjcB7h7bff7n6P/Ouvv7L9+xmUeVYir1+/3mQ8PZ8fBmkVK1Y0BSNZYXaSpxEjRqBt27ZmaFgBXRQXRfAfdNy4cWZSKifFsnKH/5z/+9//Qr1rEqb4JpvTG62IAIUKFjCtSShjWGZf5u3cLhzxyz3nvjFLx88EDqMyU8VsEHGoj1kpBjwrVqww8+JYRME5eZznlRX+HgMQTuxnJSmDrIULF5oCDbudCgM9zs3jsOrevXvNMGZGrC7lHDveDwMrFmSwgIFFAlSvXj13IQaHMW+77TZ39jEv7L+PQ8/M8HnOceRjMDPG/efzc++993pV+WaGn7Pjx483hRr8e++77z6vTCkfLy4uznwWsyiCzwOzmczIsaqXlxnE8e9kZSufQwaFmkcX5QEdK35YBcR/yvr165t/WE5GXbx4cah3TUTE8dhnbsLtF5hMnCde5vWB6EPnL5yj9dVXX5mAgUOPzP68/PLLZk4cMXvItibly5fHZZddZgI1Fk4wu5Qd/t4333xjfueOO+4wnz0sPmBwwhYjxKIDVnV27NjRZLQyawXCLB73jZksfo4xuGSCgsUM9NJLL5l9YzsWftbx72H2K6+YoWSBAytK7epWG4Nb3ifvmytC2AFmdlhVzIzmpZdeaoJMDg17zrnj+fnz55t5jBzuZqDGogxmbpmx4+1r1641zxGfOxaRDBw40AST4n8FXA5cwZxZl08++cRUNPGbQ1YpY35T8vy2dOjQIfPPyaqb7NLD4nz8dsshFeL/R7BaK4iECj9EmRHx7KHmC7YmYTUrCyA4Z47DrJll5sJpyFUi/3942zZ+fscgOTkV1arp89vRc+iIZedMf/NFZ3aOkz6zG/8fO3asScGLiEjuMHizW5OIiHM4Km3Bye2cY8Du2qziYYbOzsJkhmP3zMbZJ06IFREREYk0jsrQcR6CXcXEUmk2aWQZNruCZ4YTQoPZ+FJEREQkFBwV0GU2TyqziiKR3PR+EpH80bw5kfDhmICOw6fsOcdqmrS0NNPHhuXRXLpEJCMWQdhLzYhEk2DVuTGYy0/xhUhGDqzRDCuOmUPHJV7YN4jz6LgQMYdbGcxxORERkWhnt8DIy+oCIuHEblrs2esuP15/nX0CWYUNtGkDLF2a/fYHDwIDB3JpOU7ZAurXB775Bo7hmAzdO++8E+pdEBEJW1zNgH2/uAg8PxDVqkeclJljMMfEDZdUs7+c5Me0acDQocAbb1jB3CuvsF8hwAWEKlY8d3t+D2J+iLdNnw5UrQps2cIl3uAYjuxD5yv2oYuJiVEfuijA+ZXsSE5sRq0PN4kGzM6xj5cvqwzkFT86uIi8HUxqPp3kF4M5NjzO7H8pr33o2rTh+rbA+PHWZR4SXPXtwQeB4cPP3Z6B3/PPA2vXMkPozNfSMRk6kbzyXERaJBqwEwC/wARj2JVB44YNG9zLX+lLk+QHs8r+yMwR//2XL+fce7ixt3znzsDZ1dbO8cUXQNu21pDr559zHVvgttuAYcM4nQGOoIBORCSCMLAKRrECAzo7iOPjKaCTYEhL42hb+mXOdcvYnWzvXq4oBZxdnc2Nl5mBy8ymTcAPP3B9WmveHL+rPPAAEwPAqFFwBMcURYiIiEh04+JQMTHpp7Fj/XO/Z85Y8+feeot9boFevYDHH7eGYp1CGToRERFxBC4OxYIFW2ZrB8TFWcOku3d7X8/LCQmZ3y8rWzl3znN4tVEjYNcuawi3aFGEPWXoRERExBHKlAHKlk0/ZRbQFS1qZdnmzvXOwPEy58ll5uKLrWFWz3qiv/6yAj0nBHOkgE5EREQiytChwMSJwPvvA2vWAPffDxw5Atxxh3V7377eRRO8ff9+YMgQK5D7+mvg2WetIgmn0JCrRCyt4yuiY0yiU69eQEoKMHKkNWzaogUwa1Z6ocTWrVblq40tTbjw1MMPA82bW8O6DO5Y5eoU6kMnIiIiYS2vfeiikYZcRURERBxOAZ2IiIiIw2kOnUQkNj3duHGjOV+nTh01PRXRMSYS0RTQScQ6ceJEqHdBJKLpGBMJHxpyFREREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJwCOhERERGHU5WrRKwiRYqEehdEIpqOMZHwoYBOIlLBggXRoEGDUO+GSMTSMSYSXjTkKiIiIuJwCuhEREREHE5DrhKxS38lJSWZ87Vq1dLSXyI6xkQimgI6iVjHjh0L9S6IRDQdYyLhQ0OuIiIiIg6ngE5ERETE4RTQiYiIiDicAjoRERERh1NAJyIiIuJwqnKViFWoUKFQ74JIRNMxJoHmcrlw6NAhpKRs0ZOdAwV0ErHLEjVq1CjUuyESsXSMSSCdOnUK+/fvx4EDB/D333/jxImjesJzoIBOREREwiIbd/jwYRPIpaWleWWCy5SJC+m+OYECOhEREQkZZuAOHjxoArmTJ0+6ry9ZsiRiY2NRpkwZ7NhxWK9QDhTQScQu/bV582ZzvmbNmlr6S0THmIRZNo4rjezbt8/MkeNleyi/XLlyqFChAooXLx7q3XQUBXQSsY4e1ZwLER1jEk5Onz6N1NRUk407fvy4+3oGbwziGMwxqJO8c8yzNnbsWFx44YUm9VqxYkX06NED69atC/VuiYiISA4YvO3YscN8bvMnLxcoUMAEcLVr10adOnVMQKdgLgoydPPmzcPAgQNNUMfx9sceewxXXnklVq9ejVKlSoV690RERCTD1BcOpzIb5zliUrRoURO8lS9fXq1vojGgmzVrltfl9957z2Tqli9fjssuuyxk+yUiIiLpWNhgtxzhEKutbNmyJpBjEobZOYnSgC4jjsET/zl8+dbAU2Y8071ZbaNtfX8eeBDbB3Igt/XcPuPvBmMfOMHXnuQbCdt6vs6RvC3puM/d8+DJie8Rod7WCcd9XrblbUeOHDGBHFuPeLYcsefGFSlSxL2tL+89EoEBHQ+ahx56CBdffDGaNm2a5XYnTpwwJxtTv7R27VqULl36nO15HSsibWvWrMnyH43l1Bz3t3FegOc3EU8lSpQw8wNs69evN00TM1OsWDHUq1fPfXnjxo1ef4MnHhwNGjRwX05KSjJVQ5nhQeXZaJcVoFkVDfBAa9Kkifvy1q1bvQ7QjDxfg23btrmf58w0btzYfSBzHgVL1bPSsGFDFC5s/Yvu2rXLvFFkpX79+iaNT3v27MHevXvdt/H19lS3bl139VRKSoo5ZYWvMV9rYjXW7t27s9yW/zv2/xX3defOnVluW6NGDTMflPgcbN++PcttExMTERMTY87zuU1OTs5y26pVq5phDOJrtmVL1t3VK1eubFoCEN+I7argzFSqVAnx8fHmPP/HNm3alOW23I7bE/93N2zYkOW2cXFxSEhIMOd5TPz1119ZbssPhSpVqpjzPNYyvq6e+OFRrVo1c57HMKdmZIVZg+rVq7svZ7et3iMsPIY930943Dv5PSIjvUfk/T2CQVdmAS2P1Yzvs76+R0j2HBn2ci7dqlWrMHXq1BwLKfhBaJ/4wSgiIv7hmcGR6MZgjokDBmCeX5AkeAq4csp1hplBgwbh888/x/z581GrVq1st80sQ8egjuP6/FaeGQ29BPZ5CLdhDw2naMg1r//D2jawz0O4Hct6j0h/j2BBIj8/efIcZeIoFDPoTJzwtQ7ElIht2/j5HYPk5FRUq5b553e0c8yQK1/wBx98EDNmzMBPP/2UYzBnD1/ylNk/R27G5PMybq9t9Tz4mrnQtuHzPJCOZT0Pwfh/CIf/99xuy+k5HM7m3PXcNAAO5PEpERDQcZh1ypQpJjvHuUecL0H8RsBvByIiIuIfzEzay3Fl1gCYn70cYpXw4Zgh16wi+EmTJqF///65ug8OufKfkN8yshpylch5M2IxB3E+h6qkRHSMSc4YvDGIYzBnDzfz85efmSyQYAIlFBk1DblGUIbOIXGnhJHsqu5ERMeYWBi4paWlmUr+jA2AWTXPk11NLOFLr5CIiEiUNgC2ixxY8GDjtCYOq7JNj+a3OYcCOhERkSjB0S6OXnBYlVk5GzNwzMQxkLMbAIuzKKATERGJcHbLEQZyni1HuAwXgzjOkVM2ztkU0ImIiERoNs5uOcKiQHsuOqtT7ZYjmbX2EmdSQCciIhJBuNyW3XLEs7l+xgbAElkU0ImIiEQArrNsNwD2bDliZ+PUszWyKaCTiMRvn54LgouIjrFIxMCNARwDOQZ0Ng6lMohjMKcGwNFBAZ2IiIjDcCjVbgDMIVbPBsAM5EqWLKkihyijgE5ERMQBWNTA4gYGckeOHHFfzzYjDOLUADi6KaCTiB2G2LZtmzlfrVo1TQAW0THmWGwzwiBODYAlOwroJGLxm6yI6BiLpAbAnA9nZ+O4NJeITQGdiIhIGDUAtluOcGkuG+fExcbGmmW51HJEMqOATkREJMTZOFao7tu3z6sBMAM3u+VI8eLF9RpFmFOngF27gKNHgfh4oEKF/N2fAjoREZEQYHWq3XLk+PHj7usZvNktR5SNiyxpacBHHwFTpwJLlwJMwjJ+L1CA872BK68EBgwALrww7/etgE5ERCSIGLzZLUc8GwBzBQe7AbDWVY08L70EPPMMUKcO0L078NhjQJUqXMED2L8fWLUK+PlnK6hr0wZ47TWgXr3c378COhERkQBj4Ga3HOH6qjYWNthFDmoAHNmWLQPmzweaNMn89tatgTvvBN54A5g0yQruFNCJiIiEARY22C1H7AbAZDcALlWqlLJxUeK//83ddsWKAffdl/f7V4ZOIhKHKxo3buw+LyI6xoKFRQ1sNcJAjq1HbIULF3Zn49gMWMSfFNBJRGIQp0BORMdYsBsAMxPHQI7tR2ylS5c2gRxbjuh9KXrdcEPut/3ss7zfvwI6ERGRfGTjuAwXgzjPZuacD8dMHE/FOIYmUS8mxvP/BpgxA+a6Vq2s65YvBw4ezFvg50kBnUTsBOQdO3aY81WqVFHpv4iOMb/ifDg7G5exATCzcZwjp5Yj4omFDrZhw4CePa0CiEKFrOs4xfKBBzi/Ej5RQCcRiy0B7IBORHSM+QMrVBnEsX+cGgCLr959F1iwID2YI54fOhRo1w54/vm836cCOhERkRwy/vZyXJk1AGb/OLUckbzgFMu1a4EGDbyv53VnWxPmmQI6ERGRPDQA5nAq11VVA2Dx1R13AHfdBWzcaPWfoyVLgHHjrNt8oYBORETkLAZubDnCdVUzNgC2ixzYfkQkP154AUhIAF58Edi507qucmXgH/8AHnnEt/vUf6WIiEQ9FjawyIEnz5YjbDXCYVW2HlHLEfGXggWBf/7TOtnF0b4WQ7jv0y97JiIi4tAGwFu2bMFff/2FlJQUE8wxAxcfH48GDRqgRo0a6h/nUK+/DtSsybmO1tqoS5fm7vemTuXQOtCjR2D3j98bvv/eWkHC7n/P5gwevajzRBk6ERGJKgza7JYjbAZs4zJcdssRZeOcbdo0q2KUbUEYzL3yCtClC7BuHVCxYta/t3kz8OijwKWXBnb/tmwBunYFtm4FTpwArriC2WDgueesy9zvvFJAJxGJb8YNGzZ0nxeR6D7GmI2zW46wAbDdcoTVqeXKlTOBnBoAR46XXgLuuSe9wIAB0tdfW+1Chg/P/HfYB653b2DMGODnn60mv4EyZIjVUPj334HY2PTrr7/e2m9fKKCTiMQPGE1cFtExxgbAdsuRE0x9nMUKVbvliBoAO0daWvqcM+IiHBkX4jh50lp1YcQI7zlrnTsDixZlfd9PPWVl71h9yoAukHj/Cxey2Mb7eg4Rb9/u230qoBMRkYhz7NgxdwNgz5YjdjaOAZ04T+PG3pdHjQJGj/a+bu9eK9tWqZL39bzMPm+ZYZPfd94BfvsNQcF/Se5jRtu2WUOvvlBAJxGJb+C7du0y5xMSEvQNXCQKjjHuEwM4BnIM6GwcSmUQx2BODYCdbfVqoGrV9Mv+WCY3LQ3o0weYOBGIi0NQXHmlNa/vrbesy5y1wGIIBqhXX+3bfSqgk4jFN3X7w0ZEIvcY41Cq3QCYQ6yeDYAZyHF9VSfM85OcMXuVU3uPuDhrGa3du72v5+XM/lXZ3JfFEN27p19nr9bAloMspKhTx7+vDvvPsUiDGUcuPnLbbcD69da+s+rVFwroRETEcVjUwOIGBnJHjhxxX1+kSBETxKkBcPQqWhRo2RKYOze99QgDNF4eNOjc7Vnb8+ef3tc98YSVuXv1VSAx0f/7WK2aVRDBalz+ZHaOc/dYlOHrbAAFdCIi4hhsM8IgTg2AJTtDhwL9+lmVpFxai8ObjPvtqte+fa2h27FjrT51TZt6/365ctbPjNf7E7N/DOB48ofQT3rIg/nz56N79+6oUqWKSZ/PnDkz1LskIiJBbAC8bt06dwNgzodjA+D69eurAbB46dXLWl5r5EigRQur2GHWrPRCCfZ/s5fcCgUOCXfsyGkL5w4L87aIz9AxrX7eeefhzjvvxA033BDq3RERkQBi0Ga3HOHSXDbOiYuNjTUrOIRDMYaEp0GDMh9ipZ9+yv5333sPAcU2iOyiwwzil18CTZp43xbxAd1VV11lTiIiErnZOFao7tu3z6sBMAM3u+VIcY6RiThYgQLAp58C48YBbdsCH34IXHdd+m0RH9CJiEhkYnWq3XLkOMv+zmLwZrccUTZOIoXLZQ2tsuiC2TkOEbMQ4+67fb/Pwr6WiC9ZssTMZ+BSKpzDcP7556NWrVoIJ9xPz87g/LYn0YFzLDmvxj4vIuF5jDF4s1uOeDYA5goOdgNgHcMSyQYMAOrVA26+mbUCQQrofvnlF7z66qv48ssvTaURDzgebPaSKrVr18aAAQNw3333mbkNoTZ27FiM4aJsEnX4AVA045oqIhIWxxgDN7vlCJMCNt6f3XJEDYAlktWo4V38wAKJxYu9e+HlVa5nk1577bXo1asXatasidmzZ5uKI85x2LZtmzkg169fjyeeeAJz584139rmzJmDUBsxYoRJ4dun5OTkUO+SiEjUYmEDV5dgpar92UFsAMzPlnr16iEuLk7BnES8pCQgNtb7urp1gZUrgU2bApyh69atGz799FPTtDEzzM7x1K9fP6xevRo7Q1kP7LHcC08SfZgB2LNnjzlfsWJFzb0RCdExZrccYTbuMLunnlW4cGF3Ni6rzxWRaFO8uJW9C2hAd++99+b6Ths3bmxO/sY3gw0bNrgvJyUl4bfffjNvCtWrV/f744mz7eUKzWc/bETEv06fcbmPsaTDhdC6dhwKFUyfS8dpOWz+y0CO7UdspUuXNu/ZnJajuXESTSpUAP76y1req3z57KtZM/ani7gq119//RUdOdB81lC2gga7QffDe4FuGiMiIsasVTsx9pvVeP1qq0tr/0nLUKF0MYy8pjEurVXGBHGeRWicD8dMHE8aNZFo9fLL1lq0xJUr/C3XAR0PxNx+m7IXbPa3Dh06uHsSiYhIaIK5+z9agaKFvD8PdqYex/2TV+Cxy+LRrnpJdwNgZuM4R04tRyTa9euX+fmgB3SveISTLIZ4+umn0aVLF7RlRzwAixYtwnfffYcnn3zS/3spIiJhMcw65svVyO5r9Vu/7sdVzasiPi5WDYBFPOSlc1rZsghcQMdhTduNN96Ip556CoM81tQYPHgwxo8fj++//x4PP/xw3vdERETC2tKk/SYTl529R09j24niSNRqDiJeypXLeRUIDkJym9OnEZw5dMzEPffcc+dc37VrVwwfPtyXuxQRkTDGBsDrtuaue8GetOyDPpFo9OOPgb1/nwI6Lor8+eef45FHHvG6ntfxNhERiYzWJHbPUfaMK3o6d4FaxTJaa1Uko/btEX4BHVdfuPvuu/HTTz+hTZs25jouBTZr1ixMnDjR3/sokmcs4KnLLo1a+kvEpwbAbDnCk2fLkYvqxKHSkgPYk3YSJ0+78MCXO6ztT1uz6jialBBTHK1rVdCzLpIL7K29dSuPOe/rmzdHcAK6/v37o1GjRvjPf/6Dzz77zFzHywsWLHAHeCKhDui4qLeI5A47CLDXJ7sUMCvn2QCYXQ5YrcoGwGOuK2aqXGlr6qn0Y+7sz1HdG3v1oxORc6WkAHfcAXz7bRYFSMGaQ0cM3CZPnuzrr4uISBhgBs5uAMxmwLZSpUq5W454tqzq2rQyJtx+gal29SyQYGaOwRxvF5HsPfQQcPAgRzfZkg2YMQPYvRt4+mngxRfhE58Duo0bN2LSpEnYtGmTaWnCbvzffvutWbGhSZMmvt6tiN/m/qTwKxCA+Ph49cASyZCN45w4uwGw3d+TDYDLlStnArnsGgAzaOvcqCJ+X5+MIyf/RpGS5dC6dqwycyK59MMPrDsAWrUCuGoel/u64gqrXcnYsVxuFXmW+eJ7OZg3bx6aNWtm5s1xfVd7fb7ff/8do0aN8uUuRfyOAZ0d1IkIh3FOmwIHLqHIpRNTU1NNMFeiRAlUrVoVDRo0QOXKlXO1mkPBAgVQ7O/DqFDwONrUrqBgTiQPjhzhspTWeS4DZn9UNWsGrLBmNAQnoGNrEjYWnjNnDooWLeq+/vLLL8fixYt92xMREQmIY8eOYfv27Vi3bh127tyJEydOmGFUzo2rU6eOOfG8VnMQCY4GDYB166zz550HvPkmsH078MYbQOXKQRxy/fPPPzFlypRzruewq71Ys4iIBH7lBjb7Zd83tgphdaldkMBpB8zAcViVAZ2N2TcOqXJolUOsIhJ8Q4YAO8+2deTAZteuAMsSmCPzdWl6nwI6vhHwW16tWrW8rl+5cqVJ24uISODXVM1YmFA5pjge61ofrRIK4+DBg2aIlZiNY3EDAzmur5rbdblFJDBuvz39fMuWwJYtwNq1QPXqQFxcEIdcb7nlFgwbNgy7du0ybwz8JvjLL7/g0UcfRd++fX3bExERyXUwx9YhGZfh4uUHp/2BL1cmm2CObUYqVapk5sYlJiaaylUFcyLhp2RJ4IILfA/mfM7QPfvssxg4cKB5g+CbRuPGjc3P2267DU888YTveyMiIjkOszIzZ9WlZu7tFQfR8+KGiClbRgGcSBhiYfn06dZyYHv2cIqE9+1nW/wGPqBjIQRXhBg5cqSZT8cq1/PPPx/16tXz5e5ERCSXlibtOyczl9Gew6ewZu8ptI3R0KpIuPahYyFEx45ApUqcFpH/+/QpoJs/fz4aNmxoMnQ82diUctGiRbjsssvyv2ci+cBhpdq1a7vPi0RCA2DOi/vjry252p6FEoGkY0zEdx9+aGXhrr4afuNTQNehQwczL2PGjBm46KKL3Nezmqpjx47uibgiocIPG07+FnEy9ohjhSp7x9kNgMsUyW6wNR2rXgNJx5iI72JigLM5B7/xqSjCLozo1KkT3stQX2t3HBcREd/wSzG/IHNFHq7GYzcA5vrEV7SohYSyxd1rp2ZU4Gy1K1uYiEh4Gj0aGDOGPSJDnKHjN7MRI0bg0ksvNVWtf/zxB148u/iYhrckHLDymlkNio2NVcNUcYTjx4+bQI5Dq/wftt9TY2JiTMsRrujAy6OvbWyqXBm8eX6FtoM8rqlq96MLFB1jIr7r2RP473+t1SJq1gSKFPG+3ZfVInwK6Ows3A033GB60V133XVYvXo1Xn31VV/uTiQgdnOl47MBnUi4YmDE4VQGclxf1bP4zG4AXLhw4XPWUp1w+wXn9KFLiClugjneHgw6xkR8068fsHy51Y8upEURnljdunTpUvTo0cMMwYqISM5OnjxpgrgDBw54zTu2GwDn1DOOQdsVjROyXClCRMLX118D330HXHKJ/+7Tp4CuX79+JvVvS0hIwLx58zBgwABTASsiIpmPbqSlpZlAju2e3G/EhQubII7rqbIZcG4xeGtbRxloEadhg5CyZf17nz4FdJMmTTrnOq4P+P777/tjn0REImI9Vc+WTszEMZBj+xFb6dKlTSBXpowaAItEkxdfBP75T+CNN6w5dEEN6Fj40LRpUzO5nOez07x5c3/sm4iII9dT5Ty2Lk0ScOTIERPEcY6crVChQiYTxxO/CItI9Ln9doBTZuvUsZb9ypiY378/gAFdixYtzNqtFStWNOc5t8OzRYl9mT/Vh05EomU91YyNmnalHsd9H63AyMsro3WVou7r2ReR2TjOkeMXYxGJXq+84v/7zHVAl5SUhPj4ePd5EZFold16qvZ1/7d4Dy68IRGxFcqbQI495ERETp0C5s0DnnwSqFUrBAFdjRo1Mj0vEo6YKa55dmKCeiOKv3HOXE7rqe49ehqHisWjWZWKEfkC6BgT8Q2HVz/91Aro/CnXAd0XX3yR6zu99tprfd0fEb992HDCuUggbN+flqvt9h45FbEvgI4xEd/16AHMnAk8/DCCH9Cxz1xuaA6diERqA2C2HOEKJCdT94fFeqoi4kz16gFPPQX88gvQsiVQqpT37YMHBzCgs5ehEXECFuiwupA4f0nDrpKfBsBsOcKT3XKkScViiC9VGHuP/J3pPLoCZ1dtiOT1VHWMifjunXeAcuWs1SJ48sR+4gEN6ESc9mGzc+dOc57tIRTQSV7/f9j4l18KmJXzbABstxz5V8G4kK+nGko6xkR8F4jaUp8DOvZX4uoQW7duNd9gPQ32JbQUEQkxZuDsBsBsBmzjMlx2yxH7y0G4rKcqIs5md4DL73quPgV0K1euxNVXX20WkmZgxze6vXv3mj5L7FOngE5EnJRp4nuZ3QDY7q/JBsDlypUz729ZNQDWeqoi4qsPPgCefx5Yv966XL8+8I9/AH36BDGge/jhh9G9e3e88cYbiImJweLFi836g7fffjuGDBni256IiAQRG6AfPHjQBHInTpxwX891qhnE8b0tNw2AtZ6qiOTVSy9ZbUsGDQIuvti6bsEC4L77gL17fat+9Smg++233/Dmm2+aNzt+i+WbYe3atfHvf/8b/fr1ww033ODL3YqIBNyxY8dMEMdgzs7GcRjVzsYxoBMRCaTXXgMmTAD69k2/jh3fmjQBRo8OYkDHbJz9zZVDrJxH16hRI/ONNjk52Ze7FBHJ18oNbPa7J+24aRXC6lLPggRW6aempppAjgGdjUOpDOIYzPHLqYhIMLBmr127c6/ndWfr+YIT0J1//vlYtmwZ6tWrh/bt22PkyJFmDt2HH36Ipk2bIpBef/11PP/882Zd2fPOOw+vvfYaWrduHdDHFJHwXlM1Y2FC5bOFCR3rVXBn4+w1ppmNY3EDAznO+1UFtIgEW926wMcfA4895n39tGlWjzpfFHDZYw558Ouvv5pS/o4dO2LPnj3o27cvFi5caAK8d9991wRagTBt2jTzWJy716ZNG7zyyiv45JNPsG7dOpMpzAknPDOLyG/qfEOXyG87QVwxQh/akRvMsXVIxjcxu5XIY5fFo131ku6RBQZxbDnC9iOSPzrGJJi2bTuExESOAqaiWjXnf35/+inQqxfQuXP6HDo2GZ471wr0rr8+SAFdqDCIu/DCCzF+/Hj3MEpiYiIefPBBDB8+PMffV0AnElnDrJc890O2a6rGlSyEj/s0RHxcrAJ7EQeLtICO2FD45ZeBNWvMRTRqBDzyCEdB4RPHfE1lr7vly5djxIgR7us4j69z585YtGhRpr/DYg3P6jUGdCISGThnLrtgjvYePY3dZ8qgdpkyQdsvEZHc4JJfH30Ev/EpoONahpw39+OPP5oh14zLgtlLLvkT5+hxDkylSpW8rufltWvXZvo7Y8eOxZgxY/y+LxL+mHjmvCnihHcNuUZeA+CNO1JytS0LJcT/dIyJ5A9Dpw0bgD17rPOeLrssSAFdnz59sGHDBtx1110moArXD0tm84YOHeqVoeMQrUTHh8327dvNec6bDNf/Ucnba8oKVX6h5LFc8ER6tWp2WPUq/qdjTMR3ixcDt90GbNmSvlKEjR9XZ2u4Ah/Q/fzzz1iwYEHAih8yExcXZ9oK7N692+t6Xk5ISMj0d9iSIKsO7yLiDMzM2y1Hjh9Pz7a1rB6DimUOICXt5DlFEVTg7DJcbGEiIhJO2EC4VSvg66+BypXzv+wX5dwGPRMNGzb06uUUDEWLFkXLli0xlyUgZ3Gol5fbtm0b1H0RkcBj8LZjxw5Txc6fvGw3AGYj8/r16uKp66w2SRnfC+3LbF3i2Y9ORCQccLmvZ5+1CiHKleNIkvfJFz5l6P7v//7PVJVyHh37zrEdgKdAtQTh8ClXomjVqpXpPce2JVxL9o477gjI44lIcPFLGodTmY3j+qqeX+jsBsCeLUe4luqE2y84pw8dM3MM5ni7iEi4adPGmj/HfnT+4lNAxzdVvulefvnl58yp4Ddou4Gnv/Xq1QspKSkmkGRj4RYtWmDWrFnnFEqIiLOwGv3AgQPm5Pn+YTcALlWqVJbzIBm0XdE4IduVIkREwsmDD1otSnbtApo1Y59M79ubNw9SQNe7d2+TlZsyZUrQiyIGDRpkTiLibPwCyAblzMbZTaCJGTi7AXDG7H9WGLy1rRMbwL0VEfGfG2+0ft55Z/p1DKVYIBHUoohVq1Zh5cqVaNCggS+/LiJR7NSpUyYTx0CO7UdsXNGDgVyZMmVUlSwiES0pyf/36VNAxzlsycnJCugkbDFrbLeoUcuS4K3ckNWwJ7NxnO/KIM6zwTcr15mJ40kV6c6iY0zEdzVqIDwCOi61NWTIEPzjH/9As2bNzhkWae7L4K+Inz9s2H9OgremasbChMoxxfFkt4ZoXaWYCeS42outZMmSJhvHOXJc8UWcR8eYSP4rXX/8MfPGwiNHBmkt18zegHlwB7ooIr+0lqtIYIK5+z9akWkvOHrssni0q17SvG+woIqBXPHiavYrItG7luvEicD997PHLsBWup6lCDy/YkWQMnRJgRj8FfEjfrmwh/aYBdKwa+CGWZmZy+5b4cTlB3B96zqoUL6cGWKVyKBjTMR3Tz8NPPMMMGwY/KawLxOa2a7kq6++QiN2xBMJ0w8bzvOkxo0bK6ALEM6Z8xxmzUzKkb+xIRVoG6dgLpLoGBPx3YEDwM03w6/yPHmF8+U8l98RkehsAMzluFZt3Jqr7VkoISIiFgZzs2fDr3wach04cCCee+45vP32215d20UksrGwwW4AzJYjpQrmbr4sq15FRILp9deB55+3mvdy6fnXXgNat856TtsHH7Atm3W5ZUtraa6sts8vrhDx5JPA4sWZNxYePDjv9+lTNLZs2TKzhurs2bNNlSu7uHv67LPPfLlbEQnToTU2/mWlKhsB2/hlrkOTakhYehC7D53IdB5dgbPLcLGFiYhIsEybxuVCgTfesJbZeuUVoEsXYN06oGLFc7f/6Sfg1luBdu0A1mw99xxw5ZXA//4HVK3q//176y323gTmzbNOnlgUEbSAjpVqN9ptjkUkIjEDZzcA5txZG7/A2S1HWGwy+lqXqXJl8OYZ1NlFW1xTVctwiUgwvfQScM89gL3UOwO7r78G3n0XGD783O0nT/a+/PbbwKefAnPnAn37RnBj4UmTJvl/T0QkLLJxR48edTcAtrsasTrVbjmSsQEw11KdcPsF5/ShY2aOwRxvFxHxBw4SePQmB9+OMrwlgS0vly8HRoxIv47d1jp3BhYtyt3jHD3KIlCggoMGF/I1AS4lJQXrmL8EzKoR8fHx/tovEQki9o48ePCgCeROnDjhvr5EiRImiGOT5uwaADNou6JxQpYrRYiI+EPjxt6XR40CRo/2vm7vXmst1EqVvK/n5bVrc/c4bCdSpYoVBAaC5xqumWEmMSgBHZfw4WoRH3zwgal2s7/B9+3bF6+99prpAi8SShwKrHp24oN60GXt2LFjJohjMGdn4/h82dk4BnS5xeCtbZ3YfL924gw6xiQUVq/2ntOWMTvnD+PGAVOnWvPqAtUDnW1LPDEbyIKMgweByy/37T59CuiGDh2KefPm4csvv8TFF19srluwYAEGDx6MRx55BBMmTPBtb0T8+GHD9UGjTXbrqWZsOcJAjgGdjUOpDOIYzKkBsOQkWo8xCa0yZdgsPvtt4uKYZAJ27/a+npe5KkN2XnjBCui+/57LmCJgZsw49zrmx7h6RJ06vt2nT0t/xcXFYfr06ejQoYPX9T/++CN69uxphmLDkZb+kmhcT9Wex8ahVDsbZy/Pxw9lFjcwkGNmXdlMEYmEpb/atLFajrBViR0sVa8ODBqUeVEE/fvf1uoN330HXHQRQoKz2Bha7dwZpAwdJ01Xyjg4zV5TFSua20TCpdUGlS5dOuIDlazWU92VetxcP/qKamhZqZBXg3AGccywqJek+CLajjFxlqFDgX79gFatrMCObUuOHEmvemXlKodux461LrNNyciRwJQpQM2aVu86YmsRnoJl40Z2GPDtd30K6Nq2bYtRo0aZOXT2ItscuhkzZoy5TSQcPmy2bNkSFUt/Zbeeqn3da7/sxDs9qqJcjJWN0wew5Fc0HWPiPL16sXDTCtIYnLVoAcyalV4osXWrVflq40wxVsfedFPORRf+Cjg9cayUWTm2VmEgGrSA7tVXX0WXLl1QrVo1nMf2ywB+//13E9x9x1yliITVeqp7j57GoWLxOK9GDhNIREQixKBB1ikzLHjwtHkzgmrlSu/LDC7ZKOTFF3OugPVrQNe0aVOsX78ekydPxtqzNcC33norevfunaeqOBHJv10HczfNYf+x3C3TJSIigfXjj2HUh44TqO9hG2YRCclwF6c57Nu3D8cPZijlyoLWUxURiVw+B3TM0LGqdc+ePe5edLaRHLQWEb9jdardcuT4cWuYtXF8McSVKox9R/7WeqoiIlHKp4Bu4sSJuP/++037koSEBK/JsDyvgE7Evxi82S1H7C9QPNa4ggOLHP7VIw4PTNZ6qiIi0cqngO7pp5/GM888g2FcG0NEAoKBG3snMpDzbAdUtGhRdwNgu+XIVc1Kaj1VEZEo5lNAd+DAAdx8883+3xsRP2H2qnJla1F4p7VTYANgHmM82Q2AyW4AXKpUqUz/Jq2nKsHk5GNMJBL5FNAxmJs9ezbuu+8+/++RiB/wAyY2NtZRRQ5paWkmG2c3ayVm4OwGwGwGnBOtpyrB4rRjTMQpPvgA4KqqeV0CzKeArm7dunjyySexePFiNGvW7JwPGq7pKiI5O3XqlMnEMZD726M9OBv/MpArU6aMsh8iIlGkf3+u5gMMGJC+dFnA1nKtVatW1ndYoAA2bdqEcKS1XKMH/62PcJ0XIMshykCu3MBmv3vSjptWIa1rVTCZs4z7xiCO/5O2QoUKmUwcT8WKFQva/oo47RiT6JPXtVydLikJ+PZb4IEHApyhS+IjiYT5h83ms62/g7ksEddU5TJcnis3VI4pjlHdG+OKRhXd2biTXGPGo6cjs3GcI1fQcy0akTAWqmNMJBrUqpW3YC5ffehE5Nxg7v6PVpzTC25X6nHc99EKPNY+Hu0SS5rrGLixSpWBnL0esoiIRK5D6QMyOSrrQxIy1wHduHHjMGTIkFwt7bVkyRLs3bsX3bp1y/seiTgQh1mZmcts/oJ93VvL9qN9nfKIj4s1/eM4xCoiItGhXDlOS8t+G06C4zYeDQ78H9CtXr0a1atXNxWu3bt3R6tWrRDPlWQBM5mbty9YsAAfffQRduzYgQ9YpiESJThnznOYNTN7j57G/kLl0aBChaDtl4iIRO76rT4FdAzQfv/9d4wfPx633XabmczNDAMnb9tNT88//3zcfffd6N+/v4aRJKoaAG/ZfSBX2+5JOxHw/RERkfDTvn1g7z9Pc+jOO+88s+zXm2++iT/++ANbtmwxC4RzCbAWLVqYnyLRgoUNdgPgM0fTe8dlh1WvIiIixHzY1q38PIGX5s2RZz4VRXBCNwM4nkSirbKPjX9ZqcpGwLbzqpRCxdJFkHL4VKbz6DhtIiHGamEiIiLRLSUFuOMOqzVJZnyZQ6ceCRKxKlWqZE7+wHmiKSkp+Ouvv0xm2g7m2H8rMTERjRs1xFM9mpnrMs55tS+zdYlnPzoRp/PnMSYSTR56CDh4kEWkAGtNZ80C3n8fqFcP+OIL3+7TMW1LnnnmGXz99df47bffzOLkB/lMiGSTRbaLdvKTjeP8ULsBsN2Dm3NH7ZYjng2AuZbqhNsvOKcPHTNzDOZ4u0ik8McxJhKtfvgB+PxzoFUrHktAjRrAFVdY7UrGjgV8aRJS2EnzlVhh27ZtW7zzzjuh3h2JYKdPnzZfGBjInTiRXsTAlj0M4thyJKsGwAzarmickO1KESIiEt2OHAEqVrTOly9vDcHWrw80awasWOHbfeY6oGMRRNOmTUPWyX7MmDHm53vvvReSxxdnYTaNBTt2IJabLvbcnkEcgzk7G8ffs7NxuenBSAze2tbRouUS2Xw5xkTE0qABsG4dULMmC06BN9+0zr/xBlC5coADOrYk2blzJypWrIjatWtj2bJliI0N7w8tZlc8Myye62ZK5H/Y2GsKZ7csEVuOpKammkDO/nAiDqUyiGMwpwbAIr4fYyJyriFDgJ07rfOjRgFduwKTJwNFizJxhcAGdPxg4xquDOi4fh8/CMPd2LFj3Zk9ib6VG2xLNu1D69pxXsOeDPTtbByHWIkfSFxPlYEc11fVB5SIiATC7benn2/ZEtiyBVi7FqheHfC1A1yuA7obb7wR7du3R+XKlc0HHVeKyCpzYX9ry8nw4cPx3HPPZbvNmjVr0LBhQ/hixIgRGDp0qFeGjhWJEvlrqo79ZjVev9qqvus/aRkqlC6Gkdc0RrvqJU0gd4QTGM4qUqSICeLKly+PwoUdM61UREQc7uRJICkJqFMHuOCC/N1Xrj+93nrrLdxwww3YsGEDBg8ejHvuuQdlypTJ14M/8sgjZlWJ7HB411ccNvOsQpToCObu/2gFihbyHv5h1en9k1fgscviTVBH/P9lIFe6dGll40REJKgNhR980GpVQn/9xXjHuq5qVSa88n6feUpHdOUgL4Dly5djyJAh+Q7oWPKusnfx5zArW4Zk1tjXNvHX/ejWIhHxcbGm/Y2IiEiwjRgB/P478NNP1vw5W+fOwOjRQQjobJMmTUKwbd261QyV8SfnPLEfHdWtW9dkWETYKsSz/1tmUo6extZjRVFVwZyIiITIzJnAtGnARRdx/nb69U2aABs3+nafjpkwNHLkSLxv5ybPVt3Sjz/+iA4dOoRwzyRc2ies3bw9V9uzP5yIiEiosO+c3YfOE6d3+1ow7piAjv3n1INOPDFTa7ccOX78OIq50lc3Pu1yYcofB93nPbHZr4jkn6bMiPiGK0R8/bU1Z47sIO7tt4G2bSM8oBOxMXizW47Y7XNYeX1x/UqotPQg9hw6gb/PAFP+SPV60gqcXYaLKzeISP6wybzWcRXxzbPPAlddBaxezbXCgVdftc4vXAjMm+fbfYZm2QeRPGLgxgCOLXFYac2AjtexsCEhIQENGjRAjeqJGHNtE7N9xoy1fZlrqmoZLhERCaVLLrGKIhjMcbmv2bOtIdhFi6y+dL5Qhk7CGhsAHzhwwJzsBsBkNwAuVaqUV8sRrqU64fYL8NSXq1EY1vbJqadMZo7BHG8XEf/MXbVX4mF7KDXiFsmdU6eAe+8FnnwSmDgRflPAZS9aGQXYWJgLq3PeFQMCCU/8l0xLSzNZuMOHD7uvZ9NfuwEwmwFn59Tfp7Fu7RpzPq14pXNWihCR/GGGfDXHiM4u/RWqdb4lOmzbxoUBYpCcnIpq1Zz/+R0TA7BZR61a/rtPZegkbJw6dcpk4hjI/c089FlsS8NAjn0Pc5sF8Aze2tSORUEFcyIiEiZ69LBalzz8sP/uUwGdhDwbx2W4GMQxg2rjsnLMxPGk1T5ERCSS1KsHPPUU8Msv1py5UqW8bx88OO/3qYBOQoLz4exs3EkuZndWyZIlTTaOQ+IawhERkUj0zjtAuXJcecs6eeJAlAI6cUQDYAZxnMdoT99k4FauXDkTyBUvrh5xIiIS2ZKS/H+fytBJ0FqO2A2AbQzeGMSxUIVDrCIiIuIbBXQS9AbAHE6NjY1FiRIl1OpARESiwrhxwJAhQIkSOW+7ZAmwdy/QrVvu718BnfgVAze2HNm3bx+OHj3qvp5tRuyWI2w/EgxxcXFBeRyRaKVjTCT32OWnenXg5puB7t2t5b/i463b2NiBty9YAHz0EbBjB/DBB3m4cwV04i8sbLCLHDwbALPVCAM5th4JZuNRzsvjChIiomNMJBwwQOPqEOPHA7fdxt647OjAxtyAnf84/3zg7ruB/v05LSlv96/GwuIzFjWw8S+DOGblbMzA2S1HuDSXiIhIfkRaY+EzZ4A//gC2bAGOHWO2G2jRwvrpKw25Sp6x6a+djWMzYBuX4bJbjoR6GSAGm/a+cbg31PsjEml0jIn4jgurMIDjyV8KR+s8L3uSfkaevc+y2iYat+WbN+fEMZDzbADM7ZiJYyDHBsD2tlmtKMfAyg6uctqH/GzL019//WUuN2zY0OvvCcY+ZPccOHFbsp/DSN42nI65cN+WsjrG8nO/wXqPCPW2Tjjuw+09QrIXlQHd2rVrzZyujHhdzZo13ZfXrFmT5T8aG+DWrl3bfXndunVec8c8sZqzTp067svr16/3ymx5YlBUjy2kz9q4caN7AeyMmHlq0KCB+3JSUpLp85YZtgVp1KiR+/LmzZu9ihY88QBu0qSJOc+/adOmTVnuA9/AKldOX/B+27ZtXgFfRlzz0X6D2LFjh6mAzQo/JOwCil27dpmMYFbq16/vHt7ds2cP9rI8yOP19lS3bl13v7uUlBRzygpfY77WxEKP3bt3Z7kt/3fs/yvu686dO7PctkaNGmZ+IfE52L59e5bbJiYmmtYuxOc2OTk5y22rVq1qAmzicPgW5vOzwNeN1cbE1Tr4P5GVSpUqIf7s7F3+j/F/IivcjtsT/282bNiQ7aR6e64jjwk7QMgMvzRUqVLF/X+Z8XX1xL6G1apVM+d5DNtrjmaGGeXqnKl8Vnbb6j3CwmPY8/2Ex73nussZNW3aNKzfIzLSe0R4vkdI9qIyoJOc2Q2A+Waa07cnERERCa2oLIrgsCG/lYfrUEaotuV1XMGBz49nA2B+q2XWh1mPzBoAh+NwCk92BkdDrs4YTgmHbcP5+Ay3bT2zmRpy1ZBroI/PSCiK+OMPZqut+XOBEJUZOv5z5GZMPi/j9k7elilvOxtnDxvbDYA5zMUhx9wWFYTb32Zfzur3A7UPnsGStnXO8xCu/8PhuK1nwJfb91R/74OTtw2H/3enbet0558PcCZOxYqczgMsWwacHdH2i6gM6MT6VsSMJQM5zo0IZQNgERGRSFeunLWGKwM6TkfMRRI8T/SJHWU48ZxBHIdV2X4k1A2ARUREosGNNwLt27PYhJlJa6WIrJYxz6amJEsK6KK4ATDnw9ktRyKxATD/LhHRMSYSDt56C7jhBoBFvYMHA/fcw2SK/+5fAV0UNADmiUtz2Tgnzm4AHKn9ffh32S0uRETHmEg46NrV+rl8OTBkiAI6ySEbx5Yj7JnGOXJ29RADHFapMpCze7CJiIhI8E2a5P/7VIYuQrA6lS1HOKzq2XKEwRuDOAZzkZqNywwDWbtil0PLmhcoomNMJJIpoHM4Bm92yxG7jQCDF/bbYyDHVSqiMZhhQGf3ofPsPC8iOsZEIpECOgdi4Ga3HPFcvouFDXY2Ti1HREREoocCOgdhA2C7yMFz3Vi7AXCpUqWUiRIREYlCCugcMHTIViPMxnkufs0MnN0AmM2ARUREJHopoAvjBsDMxDGQ82wAzMa/DOTYCFjzwkRERIQU0IVZNo7LcDGI4xy5jA2AeSpWrFhI91FERETCjwK6MMD5cHY2LtoaAIuIiEj+KaALcQNgBnHsH6cGwP7Hal8RCRwdYyLhQwFdCFqOsGdcVg2A2T+OQ6ySP8xoVqtWTU+jSIDoGBMJLwroQtwAmMOpsbGxUdsAWERERPLPEROzNm/ejLvuugu1atUygU+dOnUwatQor/lm4YiBG4dTN23ahA0bNpiAjtexzUilSpXQoEEDJCYmmrlyCub8i0PYfK55soezRUTHmESP118HatbkCBjQpg2wdGn223/yCdCwobV9s2bAN9/AURyRoeMSTvxgfvPNN1G3bl2sWrUK99xzj6kIfeGFFxBuGGjaRQ6eDYDZaoTDqmw9ogAusBjErV692pzX0l8iOsYkukybBgwdCrzxhhXMvfIK0KULsG4dULHiudsvXAjceiswdixwzTXAlClAjx7AihVA06ZwhAIuh6Yvnn/+eUyYMMFkv3KLrUA4R41ZMw51+hOfRjb+ZRDHRsCeDYDtliNcmkuCg18APAM6VQmL6BgT59q27RASE2OQnJyKatVy/vxu0wa48EJg/HjrMmc6JSYCDz4IDB9+7va9egFHjgBffZV+3UUXAS1aWEGhEzgiQ5cZBmXMduW0VBZPNs/ebv7Cpr92No7NgG1chstuOaJsnIiISP4xX+L5Uc7WrBnbs548CSxfDowYkX4dO3917gwsWpT5/fJ6ZvQ8MaM3c6ZzXjVHzKHLiPPRXnvtNdx7773Zbjd27FiTkbNPnK/mzwbAycnJWLduHXbv3m2COVanssChXr16Zr4fH1PBnIiIiH80bgzExKSfOESa0d697O8KVKrkfT0v79qV+f3y+rxsH45CGtANHz7cBDzZnTh/ztP27dvRtWtX3HzzzWYeXXZGjBhhMnn2iQFYfnA+3L59+0xAmZSU5O4fx0KNqlWrmiKHypUrazUHERGRAOBMmtTU9JNnFi7ahXTI9ZFHHkH//v2z3aZ27dru8zt27EDHjh3Rrl07vPXWWzneP5fJ8sdSWXYDYLYcsaccMthkU00OqzKgExERkcAqUwbIaQp8XByXzAR27/a+npcTEjL/HV6fl+3DUUgDuvj4eHPKDWbmGMy1bNkSkyZNCvgkd7vlCAM5BnQ2BogM4hjMqQGwiIhIeClaFGjZEpg716pUtYsieHnQoMx/p21b6/aHHkq/bs4c63qncERRBIO5Dh06oEaNGqZNSUpKivu2BD+HzyyisLNxdssRuwEwAzn1jHMOf1cyi4iOMXGGoUOBfv2AVq2A1q2ttiWsYr3jDuv2vn2BqlXT5+ANGQK0bw+8+CLQrRswdSrw669ALgYDw4YjAro5c+aYeWs8ZVzOyR9dV3gfrIBlIMdiBxsbADOIY8sRth8R52AGt3r16qHeDZGIpWNMwlmvXgBzPyNHWoUNbD8ya1Z64cPWrVblq61dO6v33BNPAI89BtSrZ1W4OqUHnaP70PkiYx86VqYyiGPbEbYfsakBsIiIiHP70EWjqEw7sfEvgzjPBsCcD8dMHDNyagAsIiIiThKVAR3bl3D5LeKcOLsBsFYTiBxaKUJEx5hINInKgI6BG4M4nopzFV4RERERB4vKgK5+/fqm7YiIiIhIJHDk0l/5paFVERERiSRRGdCJiIiIRBIFdCIiIiIOp4BORERExOGisihCooPdmkZEdIyJRDoFdBKxhS81a9YM9W6IRCwdYyLhRUOuIiIiIg6ngE5ERETE4TTkKhG79NeaNWvM+UaNGqn3oIiOMZGIpoBOIpbL5Qr1LohENB1jIuFDQ64iIiIiDqeATkRERMThFNCJiIiIOJwCOhERERGHU0AnIiIi4nCqcpWIVbJkyVDvgkhE0zEmEj4U0EnELktUu3btUO+GSMTSMSYSXjTkKiIiIuJwCuhEREREHE5DrhKxS3+tW7fOnG/QoIGW/hLRMSYS0RTQScQ6ffp0qHdBJKLpGBMJHxpyFREREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJwCOhERERGHU5WrRKwSJUqEehdEIpqOMZHwoYBOInZZojp16oR6N0Qilo4xkfCiIVcRERERh1NAJyIiIuJwGnKViF36a/369eZ8vXr1tPSXiI4xkYjmmAzdtddei+rVq6N48eKoXLky+vTpgx07doR6tySMnTp1ypxERMeYSKRzTEDXsWNHfPzxx2bB9U8//RQbN27ETTfdFOrdEhEREQk5xwy5Pvzww+7zNWrUwPDhw9GjRw+TgSlSpEhI901EREQklByTofO0f/9+TJ48Ge3atVMwJyIiIlHPUQHdsGHDUKpUKcTGxmLr1q34/PPPs93+xIkTOHTokNdJREREJNKENKDjsGmBAgWyPa1du9a9/T/+8Q+sXLkSs2fPRqFChdC3b1+4XK4s73/s2LGIiYlxnxITE4P0l4mIiIgETwFXdhFRgKWkpGDfvn3ZblO7dm0ULVr0nOu3bdtmArSFCxeibdu2WWboeLIxQ8ffSU1NRdmyZf3wF0g4ty1h4QxxxQh2tRcRHWPiTNu28fM7BsnJqahWTZ/fYVcUER8fb06+fmCTZ8CWUbFixcxJog8DOPafExEdYyLRwBFVrkuWLMGyZctwySWXoHz58ibz8uSTT5rMS1bZOREREZFo4YhxqJIlS+Kzzz5Dp06d0KBBA9x1111o3rw55s2bpwyciIiIRD1HZOiaNWuGH374IdS7IQ6iOXQiOsZEookjAjoRX2Q3v1JE8k/HmEj4cMSQq4iIiIhkTQGdiIiIiMMpoBMRERFxOAV0IiIiIg6ngE5ERETE4VTlKhGrSJEiod4FkYimY0wkfCigk4hd+otNqEVEx5hINNCQq4iIiIjDKaATERERcTgNuUrELv2VlJRkzteqVcsMwYqIjjGRSKWATiLWsWPHQr0LIhFNx5hI+FDaQkRERMThFNCJiIiIOJwCOhERERGHU0AnIiIi4nAK6EREREQcTgGdRKxChQqZk4joGBPJyv79QO/eQNmyQLlywF13AYcPZ7/9gw8CXIyoRAmgenVg8GAgNRUhpbYlEpHYd65Ro0ah3g2RiKVjTCJF797Azp3AnDnAqVPAHXcAAwYAU6Zkvv2OHdbphReAxo2BLVuA++6zrps+HSFTwOVyuRAlDh06hJiYGKSmpqIsQ3EREREJe9u2HUJiYgySk1NRrZr/Pr/XrLGCsmXLgFatrOtmzQKuvpqPCVSpkrv7+eQT4PbbgSNHgMIhSpVpyFVEREQcIS2NyZn004kT+bu/RYusYVY7mKPOnZmBBpYsyf39cLiVeaJQBXOkgE4idumvTZs2mRPPi4iOMXE+ZtNiYtJPY8fm7/527QIqVvS+jkFZhQrWbbmxdy/wr39Zw7ShpDl0ErGOHj0a6l0QiWg6xiTYVq8GqlZNv1ysWObbDR8OPPdczsOt+cUsYbduVqA5ejRCSgGdiIiIOEKZMtbQZk4eeQTo3z/7bWrXBhISgD17vK//+2+rkpW35TT827WrtU8zZgBFiiCkFNCJiIhIRImPt045adsWOHgQWL4caNnSuu6HHzhtB2jTJvvMXJcuVobwiy+A4sURcppDJyIiIlGpUSMry3bPPcDSpcAvvwCDBgG33JJe4bp9O9CwoXW7HcxdeaVV0frOO9Zlzrfj6fTp0P0tytCJiIhI1Jo82QriOnWyqltvvBH4z3/Sb2dvunXrOGfUurxiRXoFbN263veVlATUrImQUEAnIiIiUatChaybCBMDNM+OvR06eF8OFwroJGIVKFAg1LsgEtF0jImEDwV0ErHLEjVp0iTUuyESsXSMiYQXFUWIiIiIOJwCOhERERGH05CrRCQu97V161Zzvnr16mZ4SER0jIlEKgV0ErEOHz4c6l0QiWg6xkTCh9IWIiIiIg7nuIDuxIkTaNGihSmX/+2330K9OyIiIiIh57iA7p///Ceq2OtxiIiIiIizArpvv/0Ws2fPxgsvvBDqXREREREJG44piti9ezfuuecezJw5EyVLlgz17oiIiIiEDUcEdC6XC/3798d9992HVq1aYfPmzbmeb8eTLTU11fw8dOhQwPZVwqdtiV2Bx9dbbUtEdIyJc6WlHXLHAxKGAd3w4cPx3HPPZbvNmjVrzDBrWloaRowYkaf7Hzt2LMaMGXPO9YmJiXneVxEREQmtw4fTAMToZchEAVcIw92UlBTs27cv221q166Nnj174ssvv/RaCPr06dMoVKgQevfujffffz9XGTpmbfbv34/Y2FgtKh0FmJlj8J6cnIyyZcvqsfWc638tgo4xiS5nzriwc2ca6tevgkKFHDX9PzoCutxix3/PYdIdO3agS5cumD59Otq0aYNq1aqFdP8kPPF/JiYmxgy1hyKg02PrOdf/mogEiyPm0HHpJk+lS5c2P+vUqaNgTkRERKKe8pYiIiIiDueIDF1GNWvWVKWL5KhYsWIYNWqU+Rlsemw95/pfE5FgcsQcOhERERHJmoZcRURERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATqIC1wHmSiOvvPJKUB5v9OjRaNiwIUqVKoXy5cujc+fOWLJkScAf99SpUxg2bBiaNWtmHrtKlSro27evacYdDJ999hmuvPJK92osv/32W1Ae9/XXXzfV78WLFzfNxpcuXRqUx50/fz66d+9unmf+vTNnzgzK43JZwwsvvBBlypRBxYoV0aNHD6xbty4ojz1hwgQ0b97cNOvmqW3btvj222+D8tgikjUFdBLxZsyYgcWLF5sP3WCpX78+xo8fjz///BMLFiwwwQYDHS53F0hHjx7FihUr8OSTT5qfDLD4QX/ttdciGI4cOYJLLrkkxzWa/WnatGkYOnSoaVHDv/m8884zK8ns2bMnKH8vH48BZTDNmzcPAwcONP/Xc+bMMYE8/7+4P4HGlXnGjRuH5cuX49dff8Xll1+O6667Dv/73/8C/tgikg22LRGJVNu2bXNVrVrVtWrVKleNGjVcL7/8ckj2IzU1le2BXN9//33QH3vp0qXmsbds2RK0x0xKSjKPuXLlyoA/VuvWrV0DBw50Xz59+rSrSpUqrrFjx7qCiX/vjBkzXKGwZ88e8/jz5s0LyeOXL1/e9fbbb4fksUXEogydRKwzZ86gT58++Mc//oEmTZqEbD9OnjyJt956y6ztymxOsHEtWw4HlitXDpGGzy0zRRzSthUsWNBcXrRoEaIFX2OqUKFCUB/39OnTmDp1qskMcuhVRELHkStFiOQGh/0KFy6MwYMHh+QJ++qrr3DLLbeYYdDKlSubobG4uLig7sPx48fNnLpbb73VzHeKNHv37jVBRaVKlbyu5+W1a9ciWr64PPTQQ7j44ovRtGnToDwmpxIwgOP/F9fW5rSGxo0bB+WxRSRzytBJRJg8ebL5YLFPnGP06quv4r333jPZqWA+9s8//2yu79ixoykKWLhwIbp27YqePXv6fV5XVo9NnFfFx+RoICey+1t2jy3Bw7l0q1atMpmyYGnQoIH532ahz/33349+/fph9erVQXt8ETmXlv6SiJCWlobdu3e7L3/yySd4/PHHzfCbjZkcXk5MTMTmzZsD9thVq1ZFiRIlztmuXr16uPPOOzFixIiAP7YdzG3atAk//PCDqTr1t+z+bj6/tWrVwsqVK9GiRQsEcsi1ZMmSmD59uqn0tDHAOHjwID7//HMEC784MFPluR+BNmjQIPM3stqWz3eocIi7Tp06ePPNN0O2DyLRTkOuEhHYvoEn24ABA0w7CU+sfOScujvuuCOgj53d0NiJEycC/th2MLd+/Xr8+OOPAQnmsnrsYCtatChatmyJuXPnugMpPs+8zGAnUjHr+uCDD5oA8qeffgppMBeo/20RyRsFdBKRGMRkDGSKFCmChIQEM1wUSJwg/swzz5hWIZw7x3lebGuxfft23HzzzQF9bAZzN910k2nfwTl8zEru2rXLPWGeAVAg7d+/H1u3bnX3vbN7o/F55ykQ2LKEGblWrVqhdevWptcgXwN/B+6ZOXz4MDZs2OC+nJSUZIYi+VxXr149oMOsU6ZMMdk5BtX2a8zCm8yyw/7EDPNVV11l/j5mabkfDCq/++67gD6uiOTgbLWrSMQLVtuSY8eOua6//nrTOqNo0aKuypUru6699lrTPiRY7UIyO/34448Bf/xJkyZl+tijRo0K6OO+9tprrurVq5vnm21MFi9e7AoGPqeZ/b39+vUL6ONm9Rrz+Q+0O++80xxLfK7j4+NdnTp1cs2ePTvgjysi2dMcOhERERGHU5WriIiIiMMpoBMRERFxOAV0IiIiIg6ngE5ERETE4RTQiYiIiDicAjoRERERh1NAJyIiIuJwCuhEREREHE4BnYiEjXfeeQdXXnml+3L//v39sth9gQIFMHPmTPjL8OHDzVqqIiLhQitFiEhYOH78OGrXro1PPvkEF198sbkuNTXVLERfrly5fAd0XMjeH8EhcX1e7ivXbeVPEZFQU4ZORMLC9OnTUbZsWXcwZy82n99gLhDi4uLQpUsXTJgwIdS7IiJiKKATEb9KSUlBQkICnn32Wfd1CxcuRNGiRTF37twsf2/q1Kno3r2713UZh1w7dOiAwYMH45///CcqVKhgHmf06NFev7N+/XpcdtllKF68OBo3bow5c+ac81jJycno2bOnCRZ5P9dddx02b95sblu7di1KliyJKVOmuLf/+OOPUaJECaxevdp9HfeV+ywiEg4U0ImIX8XHx+Pdd981gdavv/6KtLQ09OnTB4MGDUKnTp2y/L0FCxagVatWOd7/+++/j1KlSmHJkiX497//jaeeesodtJ05cwY33HCDCR55+xtvvIFhw4Z5/f6pU6dMdq1MmTL4+eef8csvv6B06dLo2rUrTp48iYYNG+KFF17AAw88gK1bt2Lbtm2477778Nxzz5kA0da6dWtzmx0IioiEkubQiUhADBw4EN9//70J0v78808sW7YMxYoVy3TbgwcPonz58pg/fz4uvfRSrwwdb7MLGpihO336tAnEPAOryy+/HOPGjcPs2bPRrVs3bNmyBVWqVDG3z5o1C1dddZV7Dt1HH32Ep59+GmvWrDFz64iBHLN1fBy7KOOaa67BoUOHTHBYqFAhcz/29sTbOCT8008/oX379vovEpGQKhzahxeRSMUsV9OmTU2Rw/Lly7MM5ujYsWPmJ4dJc9K8eXOvy5UrV8aePXvMeQZpiYmJ7mCO2rZt67X977//jg0bNpgMXcaijI0bN7ovM8tYv359FCxYEP/73/+8gjniECwdPXo0x30WEQk0BXQiEhAMjnbs2GGGQTks2axZsyy3jY2NNQHTgQMHcrzfIkWKeF3m7/Excuvw4cNo2bIlJk+enOlwsWfgd+TIERPQ7dy50wSOnvbv33/O74iIhIoCOhHxOw5h3n777ejVqxcaNGiAu+++2wy7VqxYMdPtOazJ+WksOvDsQ5dXjRo1MgUPngHY4sWLvba54IILMG3aNLMvrKrNDIM1Dvc+/vjj5r569+6NFStWuLNytGrVKhNcNmnSxOf9FRHxFxVFiIjfMRBiD7n//Oc/piiBQ5d33nlntr/DQgUWRuRH586dzWP169fPZNg414774onBGduOsLKVtyclJZl5cKyeZZEDsQiCQ7dPPPEEXnrpJTNv79FHH/W6H/4u5/t5BnkiIqGigE5E/IrB0SuvvIIPP/zQZMA4ZMnzDICy69t211134ZtvvjGBoK/4WCx+4Jw8FkswM/jMM894bcOWJCy+qF69uqmIZVaPj805dNzfDz74wOwH97lw4cKmopaFFBMnTsS3337rvh+2LLnnnnt83lcREX9SlauIhI2bb77ZDImOGDEC4YyB3SOPPII//vjDBH0iIqGmDJ2IhI3nn3/e9IQLdyyWmDRpkoI5EQkbytCJiIiIOJwydCIiIiIOp4BORERExOEU0ImIiIg4nAI6EREREYdTQCciIiLicAroRERERBxOAZ2IiIiIwymgExEREXE4BXQiIiIicLb/B0+U3xkL3FpRAAAAAElFTkSuQmCC", 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LSgvwaaVpTdylgEiL+qnQyT9SrGrVqm6yL60MraHyx48fdytgq0CaEWAAACAkA6AffvjBGjVqFLjtr8vp0KGDG+req1cvN1eQ5vVRpueqq65yw9xjYv4/B2nmVlFW0KPVsFUB3qpVKzd3EAAAGSlH9hzW4ZIOgX2Et5CZBygrqWtNQ+xVDJ1aDZC61Y4dO3bW2waEily5cqV7mCkAZPX1OzWEsGmgwEfdcwqCAK9S8KOuaAVCABDuCIBOQQmynTt3WlRUlBtqx3/A8CIF/7///rv7XVB9HhOGwqvXg7jjcW4/T848/B6EOQKgU9Cw+ri4OFdUnSdPnrPzqQAhqGjRoi4I0u9Ezpw5s7o5wFmn4CffwHxu/1CfQwyDD3N06J9CQkKC+0raH17n/x3w/04AQDgjAEojUv7wOn4HAEQSAiAAAOA5BEA4Y+XLl7fhw4ef0XPMnz/fZRg031NG2LJli3s+TawZKjp27BiYxFMaNmzoJvsEAJx9BEARbvHixW4E24033mihIqUL/5VXXulGGGk+B6+YNm2avfTSS5kaZAEAUkYAFOHeeecde/jhh23hwoVuBE8oF9hq7bdQrzPRcisZRUu+nM4KxgCAM0cAFMG01tpHH31kDzzwgMsAaXmRlLqdtOBs7dq13TB/ZWLWr18feMwvv/xiLVq0sOLFi1u+fPmsTp069tVXX6X6mp06dbKbbropWdBQrFgxF4wpQ7FgwQJ77bXX3GtrU3dVSl1g33zzjcsWqV3nnnuuNW3a1P788093n5ZE0dIoBQsWtMKFC7vXVFvTQxknnZfcuXO7Cf4mTZqUrDtPbRo9erTdfPPNljdvXuvfv78bBdW5c2f3PfreypUru/cTTI/R0i7+9mlZl6STrifNhB09etQef/xxO++889xraUFfnRc/fX56vlmzZrl18PR5aC08vQ954YUXbPz48fbpp58Gzm3w9wM4M1HZo+y2are5TfsIbwRAp+nwscOpbvEn4tP82CPHj6Tpsafj448/tipVqrgL9J133mnvvvtusouwPP300/bqq6+6tdly5MjhgpjgIKpZs2YuSFqxYoW74DZv3ty2bt2a4mvee++9LjjxX5Tliy++cHMptW3b1gUK9erVcwvY6jHaNMFkUqrd0fpu1apVc914ixYtcq/rH4KtNeIUYKjNapsmqLz11lvTNVv33Xff7bJiChKmTp1qb731lu3ZsyfZ4xRY6LlXrVrlzo1eo3Tp0jZ58mRbs2aNPffcc/bUU0+58+2n86mARedcbf/jjz9s+vTp/9gerWmn9/rhhx/aTz/9ZK1bt3bne+PGjYHH6Dy+8sor9v7777usnj4HBU2ir23atAkERdoU0ALIGDE5Ymxy68lu0z7CnNYC87qDBw8qKnBfkzpy5IhvzZo17mswe8FS3ZpNbJbosXn650n1sQ3GNUj02CKDi6T4uNNx5ZVX+oYPH+72jx8/7itSpIhv3rx5gfu1r/f91VdfBY59+eWX7ljS9xvsoosu8o0YMSJwu1y5cr5hw4YFblerVs338ssvB243b97c17Fjx8DtBg0a+Lp3757oOf1t+fPPP93tdu3a+erXr5/m97p37173/atWrXK3N2/e7G6vWLEixcevXbvW3b906dLAsY0bN7pjwe9Ftx999NFTvn63bt18rVq1CtwuWbKkb/DgwYHbOv+lS5f2tWjRIsXz8Ntvv/mioqJ8O3bsSPS811xzja9Pnz5uf9y4ca49mzZtCtw/atQoX/HixQO3O3TokOg1MlJqvwsAEIrX71MhAxSh1I31/fffW7t27dxtZXaUgVE3VFIXX3xxYL9kyZLuqz8TogyQMgvqclH3i7pd1q5dm2oGyJ8FGjdunNvfvXu3zZgxI1FWKS38GaDUKCui93b++ee7BfDUdSX/1K6k50fn5LLLLgscq1ixoutqS0rdg0mNGjXKatWq5WZH1jlR9sj/2lqUT9kXdWH56bVSeh4/ZZeU3brwwgvd8/k3dRcGd+2pO/CCCy5I9HmllLUCAPwzlsI4TZoGPTVJ+4b3PJ76BSp7tsQx6JbuWywjKNDRkgVawsNPCY3o6GgbOXJkotFWwcsa+IuQ/V1JCn7mzJnjul0UIKjm5bbbbnMLxP5T11Lv3r1dd863337ramX+9a9/pav9ep1/ou6wcuXK2dixY917VHurV6/+j+06XarHCaYuKp0XdXOpO0+FzEOGDLHvvvvutF9DgaZG6y1btsx9DaZAyC/pEhT6vFLq1gSQ8VSOwFIYkYMA6DTlzZU3yx+bGgU+EyZMcBfo6667LtF9GiL9wQcfWNeuXdP0XCpEVuGyamD8F2oVLf8TFf3qdZQFUhB0zz33JBvxdarlFJSVUm1P3759k923f/9+l8FR8OMPrFRnkx6qi9J5Ul2TMjmyadOmQJH1qc6JamsefPDBwLHgLI2CS2VmFBBdffXV7pheS8FNcMYpWM2aNd05UTYnvcFies8tAIAAKCKp6FgXco1USjqvTqtWrVx2KK0BUKVKldx8Ncq4KNvw7LPPpqnQWN1gGpmli3GHDh0S3afuKgUHCqSU3dBw8KT69OljNWrUcEGG2qoL+7x581xhsB6vIEvdTgo01PWkjFN6qDi8SZMmdt9997lRXsqs9OzZ02WeTjUUX+dEAaZGYym7pYLkpUuXun2/7t2726BBg9xj9VpDhw79x0ke1fXVvn17lz1T4KqAaO/evS4IVDCY1nmcdG7VLgWIOkf6/Fm4FACSowYoAinA0cU9pUkFFQBp5JRGGaWFLtyqi1HGQ0GQhqKnlsUIptdXcKLHB3fDibqP1M2jEV6qoUmpbkcBwezZs23lypV2+eWXu64mDe9WLY1GfKkbShkVdXv16NHDdUGll4IYDe9XlkYZLo1MU3dWTMw/j+64//77rWXLlq6mSnU+ykgFZ4NEwdRdd93lgj9/N5k/i5YaZcwUAOl7laFSFk2BVdmyZdP8nvQe9L2qN9K5VbYKAJBcNlVCm8fFxsa6YEHFqyqoDRYfH2+bN292/92f6sKI/1FXmeaz0UVdwUI42L59uxuSr3mO/qkA26v4XYDXUQMUXtfvU6EGCBlK3WP79u1z3TgaNaYJBEPVf//7XxeoqatNo7Y0WaG6kPx1OwCAyEUAhAyl7ixlyzRRoCYCVJdVqNIM1ZrA8Ndff3VdVOrmmzhxIjUzAOABoXt1QlhSBiVcelVVn6QNANJCU5w0q9QssI/wRgAEAEAaaPmLL+/4knMVIRgFBgAAPIcACAAAeA4BEAAAaRwGn3dAXrdpH+GNGiAAANIo7ngc5ypCkAECAACeQwAEAAA8hy6w0zRt/U47m1pWLpmux2sF9/Hjx7t1q8aMGZPovm7dutkbb7zh1qnSZIU4fVo4dfr06W7drlD3wgsv2CeffGI//vhjVjcFALIcGaAIpnWttGjokSNHEq3nNGnSpHQtsJlVjh07ltVNAABEKAKgCKZV2xUETZs2LXBM+wp+atasmWwNr4EDB7plLHLnzm2XXHKJTZkyJXB/QkKCde7cOXC/Vhx/7bXXEj3H/Pnz3crtefPmdeuA1a9f33777bdARippluTRRx+1hg0bBm5r/6GHHnLHixQpEpil+eeff7YbbrjB8uXL51Zv1yrrWm8s+Psefvhh931auV6PGTt2rB0+fNjuuecet8xFxYoVbcaMGYlePy3P+8gjj7g1wgoVKmQlSpRwWZTgWa9Fq7wrE+S/ndpCq+3atXPPo/Oj1dq/++67wP2jR4+2Cy64wHLlyuXO7fvvvx+4b8uWLe75gzM3Bw4ccMd0zv3nXrfnzp3rnjtPnjxuaY/169e7+5Xp69u3r61cudI9TpuOadZuvSf9TERHR1upUqXcewaASEcAFOE6derkVmT3e/fdd11QkJSCnwkTJrjustWrV1uPHj3szjvvtAULFgQCJK3vNXnyZFuzZo0999xzbh2tjz/+2N1/4sQJF+A0aNDAfvrpJ1u8eLHdd9997kKbHuq2UxDwzTffuLboQt+4cWMXsP3www82c+ZM2717t7Vp0ybZ9ylo+v77710w9MADD1jr1q1dELB8+XK77rrrXIATF/f3CI70PK8CFgUrgwcPthdffNHmzJnj7lu6dKn7qvOrxVT9t5PSgqs6Lzt27LDPPvvMBSEKqnRORV1o3bt3t549e7qgTN2W+ozmzZtn6fX000+7hWj1nrQOmz5/adu2rXv+iy66yLVVm45NnTrVhg0bZm+++aZt3LjRdZFpcVgAyWXPlt0alGvgNu0jvFEDFOEUxPTp0yeQiVFgoW4xf+ZAjh49agMGDLCvvvrK6tWr546df/75tmjRIndh1MU7Z86cLoPgp0yQghwFQAoaYmNj7eDBg3bTTTe5TIZUrVo13e2tVKmSCzT8+vXr54IUtS84iFNma8OGDXbhhRe6Y8pYPfPMM25f73fQoEEuIOrSpYs7poBNWRYFZ1dccYWNHDkyTc978cUX2/PPPx9om75PWZZrr73WihYt6o4r26XsUGrU5bh3714XICkDJMpI+b3yyisuQ/bggw+624899pgtWbLEHW/UqFG6zl///v3d5yW9e/e2G2+80XV7KmunTJeCouC2avFa3W7SpIn7jJUJUhYPQHK5c+a2+R3/97cT4Y0QNsLpIq2LoLo7lKnQvgKDYJs2bXKZEV3UdZH0b8oI/fLLL4HHjRo1ymrVquWeU/e/9dZb7gIqurDrIq5uq+bNm7vuMWUZ0kvPH0zZEmVCgttVpUoVd19w2xSo+EVFRVnhwoUTZTLUxSV79uw57eeVkiVLBp4jrdR1pWDLH/wktXbtWtddGEy3dTy9gturtso/tVdZMtWIKeBVsKhslLJ5ABDpyAB5gLpBVFvjD2JS6qKRL7/80s4777xE96kuRJQ1evzxx133irJEqqsZMmRIojoWBViqH1F30kcffeQyMuouUsYle/bsyVaJP378eLK2qLspadsUUL388svJHuu/wIuyF8HU9RZ8zN8V5+92OpPn9T9HWin7ciZ07iT4/KV07uSf3nNKlPFSnZCyf/qslIXS56quz6TvHQAiCQGQB1x//fVuRJUuiP7C4mDVqlVzgY6yOf7uk6TUdaZ6Gn83TdJMiZ8yHdrUDaVASd0/CoCUNVJ9S9LMyKkusirkVp2KCozVfZNRMup51X4ViJ8qK/P222/bH3/8kWIWSF2FOr+alsBPt/W5iL+rTRk1f/H66QxlV21VSm1VgKZgUJumSFAmbNWqVe4cAfgfLX9R/rW/Bzts6b7F8uZK/A8bwgtdYB6gLiF1p6h4WftJKZuj7I4Kn1X0q8BGhcMjRoxwt/31LyqsnTVrlquRefbZZxMV/W7evNkFPaoLUr3R7NmzXVGtvw5IBcf6fnWr6bjqapIGRCnRBVmBg0ZQ6fXUNrVBRcKnCjzOxvMqgFJN0K5du+zPP/9M8TF6DdXZqEhcgc2vv/7qgi+dK3niiSdcF6VqlHRuhg4d6kbr6TPxBygKIlXXpM9R2Rl/vVN6qK36nBQ8abSbar/0uu+88477LNSuf//73+71ypUrl+7nB7xgX9w+tyH8EQB5RP78+d2WmpdeeskFNRoNpqBFWSN1ianYWTQyqWXLlm7kUN26dW3//v2JskEadr1u3Tpr1aqVKyDWCDAFGfo+UeZJz6/RT3Xq1LG//vrL7r777lO2W8OyFTQoKNFILtX1aLi7Co/9XUOnI6OeV12C6jpSV1LSqQWCMy8KCIsVK2bNmjVzr6Vgxh+MKjBSzZSKnjVKS4Xn6k4MniJABdqqzVGNlNqp4vD00mejz1WF1coqffDBB+79asoA1RwpU6WusM8//9zVUAFAJMvmS1qY4UEawVSgQAE3iilpkKARNPqvWYFATExMlrURyGr8LsDr1AWWb2A+t3+ozyG6wEL8+n0qZIAAAIDnEAABAADPIQACAACewzB4AADSQMtf1C5VO7CP8EYAlEbUisPr+B2A12kpjKVdUl7zD+GHAOgU/EOVNZHgmc7oC4Qz/Q5ISnNJAWfLtPXpX2InK7Ws/L+Z5RFaCIBOdYJy5HBz3GgxS836eyZzzwDhSstp6HdAvwsZOSM3AGQV/pKdgpaP0NpQmgvIv6I64EUK/rVavH+NMcBrjp6Is+7/+XuC0teazbfoHHmyukk4AwRAaaCZfLUUhL8LAPDq7wEZUHiZZg3eG7c9sI/wRgCURvrDz0zQAABEBgpaAACA5xAAAQAAzyEAAgAAnkMABAAAPIciaAAA0kATQJTOf2FgH+GNAAgAgDTQvD+a/weRgS4wAADgOQRAAADAcwiAAABIx1IY2rSP8EYNEAAAaaDlL7bHbgjsI7yRAQIAAJ5DAAQAADyHAAgAAHgOARAAAPCckA6AEhIS7Nlnn7UKFSpY7ty57YILLrCXXnrJfL7/lZ9p/7nnnrOSJUu6xzRp0sQ2btyYpe0GAAChLaQDoJdfftlGjx5tI0eOtLVr17rbgwcPthEjRgQeo9uvv/66jRkzxr777jvLmzevNW3a1OLj47O07QCAyKLlL4rmKe02lsIIfyE9DP7bb7+1Fi1a2I033uhuly9f3j744AP7/vvvA9mf4cOH2zPPPOMeJxMmTLDixYvbJ598YrfffnuWth8AEFlLYYy5+e/rD8JfSGeArrzySps7d65t2PD3vAsrV660RYsW2Q033OBub9682Xbt2uW6vfwKFChgdevWtcWLF6f6vEePHrXY2NhEGwAA8I6QzgD17t3bBSdVqlSxqKgoVxPUv39/a9++vbtfwY8o4xNMt/33pWTgwIHWt2/fTG49AAAIVSGdAfr4449t4sSJNmnSJFu+fLmNHz/eXnnlFff1TPTp08cOHjwY2LZt25ZhbQYARKajJ45Yr9k3uE37CG8hnQF64oknXBbIX8tTo0YN++2331wGp0OHDlaiRAl3fPfu3W4UmJ9uX3rppak+b3R0tNsAAEgrn/nslz9WBvYR3kI6AxQXF2fZsyduorrCTp486fY1PF5BkOqE/NRlptFg9erVO+vtBQAA4SGkM0DNmzd3NT9ly5a1iy66yFasWGFDhw61Tp06ufuzZctmjz76qPXr188qVarkAiLNG1SqVCm75ZZbsrr5AAAgRIV0AKT5fhTQPPjgg7Znzx4X2Nx///1u4kO/Xr162eHDh+2+++6zAwcO2FVXXWUzZ860mJiYLG07AAAIXdl8wdMqe5S6zTR8XgXR+fPnz+rmAABSMW39ziw7N/En4qz9lIpuf+JtmywmR55Tfk/Lyv+rT0VoXb9DugYIAADAc11gAACEkvzRhbK6CcggBEAAAKSBurzG3foz5ypC0AUGAAA8hwAIAAB4DgEQAABpoOUvnpvbym0shRH+qAECACANtPzF6r2LA/sIb2SAAACA5xAAAQAAzyEAAgAAnkMABAAAPIcACAAAeA6jwAAASKPoqNycqwhBAAQAQBqXwpjU+hfOVYSgCwwAAHgOARAAAPAcusAAAEiDYwnxNmRRF7f/xFVjLVdUDOctjBEAAQCQBid9J235zrmBfYQ3usAAAIDnEAABAADPIQACAACeQwAEAAA8hwAIAAB4TrpGgZ08edIWLFhgX3/9tf32228WFxdnRYsWtZo1a1qTJk2sTJkymddSAACAs5kBOnLkiPXr188FOM2aNbMZM2bYgQMHLCoqyjZt2mTPP/+8VahQwd23ZMmSjGobAAAhtRTG1Nt/d5v24YEM0IUXXmj16tWzsWPH2rXXXms5c+ZM9hhlhCZNmmS33367Pf3009aly9+TRQEAAISabD6fz3eqB61du9aqVq2apic8fvy4bd261S644AILF7GxsVagQAE7ePCg5c+fP6ubAwBIxbT1O8Pq3LSsXDKrmxDRYs/g+p2mDFBagx9Rdiicgh8AANK6FMbrSx5x+49c8TpLYXh1KYwTJ07Ym2++afPnz7eEhASrX7++devWzWJiWBsFABB5tPzF4m1fuP2H6g7P6uYgqwKgRx55xDZs2GAtW7Z03V4TJkywH374wT744IMzbRMAAEBoBEDTp0+3W2+9NXB79uzZtn79ejcSTJo2bWpXXHFF5rQSAAAgKyZCfPfdd+2WW26x33//3d2+7LLLrGvXrjZz5kz7/PPPrVevXlanTp2MbBsAAEDWBkAKctq1a2cNGza0ESNG2FtvveUqrjXk/dlnn3VzBGkYPAAAQETVALVt29Z1dSnbo69jxoyxV199NfNaBwAAEAprgRUsWNBlf4YMGWJ33323PfHEExYfH58ZbQMAAMjaAEiTG7Zp08Zq1Khh7du3t0qVKtmyZcssT548dskll7jlMQAAiFTRUblt4m2b3KZ9eCQAUrYne/bsLvNTrFgxu//++y1XrlzWt29f++STT2zgwIEuQAIAIBJly5bNrQGmTfvwSA2Q5vhZuXKlm+VZ9T9a/DR4puiFCxe6rjEAAICICYBq1aplzz33nHXo0MG++uor1xWW1H333ZfR7QMAICQcTzhqY5Y+6fa71nnZckZFZ3WTcDa6wDTT89GjR61Hjx62Y8cOtwwGAABekeBLsPlbPnab9uGRDFC5cuVsypQpmdsaAACAUMkAHT58OF1Pmt7HAwAAhFwAVLFiRRs0aJDt3Lkz1cf4fD6bM2eO3XDDDfb6669nZBsBAADOfhfY/Pnz7amnnrIXXnjBzflTu3ZtK1WqlMXExNiff/5pa9asscWLF1uOHDmsT58+bog8AABAWAdAlStXtqlTp7rJECdPnmxff/21ffvtt3bkyBErUqSI1axZ08aOHeuyP/7V4QEAACJiLbCyZctaz5493QYAAOCJAAgAAK/S8hfv3rIqsI/wRgAEAEAaaPmLAjGFOVdeXQ0eAAAg3JEBAgAgjUthvLfiBbffseYLLIUR5sgAAQCQBlr+Yuam8W5jKQwPBkAzZ860RYsWBW6PGjXKLr30UrvjjjvcnEAAAAARFwA98cQTFhsb6/ZXrVrlhsQ3a9bMNm/ebI899lhmtBEAACBra4AU6FSrVs3ta3LEm266yQYMGGDLly93gRAAAEDEZYBy5cplcXFxbv+rr76y6667zu0XKlQokBkCAACIqAzQVVdd5bq66tevb99//7199NFH7viGDRusdOnSmdFGAACArM0AjRw50i16OmXKFBs9erSdd9557viMGTPs+uuvz9jWAQAAZIJsPp/PZx6nrrsCBQrYwYMHLX/+/FndHABAKqat35ll5+ak76TtO7zD7RfJe55lz3bqHELLyiXPQsu8K/YMrt/pzgBptfc9e/YkO75//35WggcARCwFPMXylXFbWoIfhLZ0f4KpJYyOHj3qCqQBAAAipgj69ddfDywG9/bbb1u+fPkC9yUkJNjChQutSpUqmdNKAACy2PGEYzZp1SC3f0eN3pYzin/6PREADRs2LJABGjNmTKLuLmV+ypcv744DABCJEnwn7LN1f1/n2lZ/3HIaAZAnAiBNgCiNGjWyadOm2bnnnpuZ7QIAAAidGqB58+YFgh9lgzJ7ENmOHTvszjvvtMKFC1vu3LmtRo0a9sMPPwTu1+s/99xzVrJkSXd/kyZNbOPGjZnaJgAAEN5Oq4x9woQJLhBRwKHt4osvtvfffz/DG6fFVTXhYs6cOd08Q2vWrLFXX301UfZp8ODBrj5J3W/fffed5c2b15o2bWrx8fEZ3h4AAODRmaCHDh1qzz77rD300EMuOBGtDt+1a1fbt2+f9ejRI8Ma9/LLL1uZMmVs3LhxgWMVKlRIlP0ZPny4PfPMM9aiRYtAcFa8eHH75JNP7Pbbb8+wtgAAAA9ngEaMGOFmgFZwcvPNN7tNWZg33ngjMFIso3z22WdWu3Zta926tRUrVsxq1qxpY8eOTVSXtGvXLtft5acJkerWrWuLFy9O9Xk1ZF+TJwVvAADAO9IdAO3cudOuvPLKZMd1TPdlpF9//dUFW5UqVbJZs2bZAw88YI888oiNHz/e3a/gR5TxCabb/vtSMnDgQBco+TdlmQAAgHekOwCqWLGiffzxx8mOa1FUBSoZ6eTJk3bZZZfZgAEDXPbnvvvusy5dupzxcPs+ffq4abP927Zt2zKszQCAyJQrKsaG3TDPbdqHx2qA+vbta23btnUTH/prgL755hubO3duioHRmdDIrmrVqiU6VrVqVZs6darbL1GihPu6e/du91g/3b700ktTfd7o6Gi3AQCQVlr+omyBypwwr2aAWrVq5UZbFSlSxBUaa9P+999/b7feemuGNk4B1vr16xMd27Bhg5UrVy5QEK0gSMGXn+p51L569eplaFsAAICHM0BSq1Yt+/e//22ZTSPKVFukLrA2bdq4IOutt95ym39ZjkcffdT69evnut8UEGmEWqlSpeyWW27J9PYBALy1FMa0NX8P9mlZ7RGWwvBiAKTanE2bNrlV4bUf7Oqrr86otlmdOnVs+vTprmbnxRdfdAGOhr23b98+8JhevXrZ4cOHXX3QgQMH7KqrrrKZM2daTAz9swCAjF0K4+PVQ91+i6oPshRGmMvmS+dUzkuWLLE77rjDfvvtt2SzQCsjo4VRw426zTQaTAXR+fPnz+rmAABSMW19xo42To/4E3HWfkpFtz/xtk0WkyPPKb+nZeX/1acitK7f6c4AacJDzc3z5ZdfusJjBT0AAADhJN0BkNbZmjJlihsODwAA4IlRYJplWfU/AAAAEZ0B+umnnwL7Dz/8sPXs2dPNtKwFUbVQaTAtjAoAABD2AZAmFVStT3DRc6dOnQL7/vvCtQgaAAB4S5oCIC06CgCAl+XMHm0vX/ufwD48EAD5Z14GAMCrorJHWcXCqS+zhAgvgtZK7BoCHzwRYcGCBd2MzZobCAAAIOICIC1LkTt3bre/ePFiGzlypA0ePNitB6alKwAAiNSlMD5Z+4bbtA+PzQO0bdu2wBxAWgj1tttuc8tQaOHShg0bZkYbAQAIiaUw3l/Zz+1fX6kjS2F4LQOUL18+279/v9ufPXu2XXvttW5fa28dOXIk41sIAACQ1RkgBTz33nuv1axZ0zZs2GDNmjVzx1evXm3ly5fP6PYBAABkfQZo1KhRVq9ePdu7d69NnTrVChcu7I4vW7bM2rVrx0cEAAAiLwOkEV8qfE6qb9++GdUmAACA0MoAAQAAhDsCIAAA4Dnp7gIDAMCLtPxF30ZTAvvwQAbos88+s+PHj2d+awAACOGlMKoXv9Jt2ocHAqBbb73VDhw44PajoqJsz549md0uAACArA2AihYtakuWLHH7Pp/PsmXLlnktAgAgBJ04edxmbBznNu3DAzVAXbt2tRYtWrjAR1uJEiVSfWxCQkJGtg8AgJCgoOftZU+7/UYV2lqO7DmzuknI7ADohRdesNtvv902bdpkN998s40bN87NBwQAABDRo8CqVKnitueff95at25tefLkydyWAQAAhMoweAVAoqUw1q9f7/YrV67s6oQAAAAiciLEuLg469Spk5UqVcquvvpqt2m/c+fO7j4AAICIC4B69OhhCxYscHMDaWi8tk8//dQd69mzZ+a0EgAAICu7wLQC/JQpU6xhw4aBY82aNbPcuXNbmzZtbPTo0RnZPgAAgKwPgNTNVbx48WTHixUrRhcYACBi5cyey566ekJgHx7rAqtXr54rhI6Pjw8cO3LkiPXt29fdBwBAJIrKnsNqlWriNu0jvKX7E3zttdesadOmVrp0abvkkkvcsZUrV1pMTIzNmjUrM9oIAACQtQFQ9erVbePGjTZx4kRbt26dO9auXTtr3769qwMCACBSZ4JeuGWa27+6fEtmgg5zp5XD0ySIXbp0yfjWAAAQwgHQqO97uP0ryzYnAPJaDRAAAEC4IwACAACeQwAEAAA8hwAIAAB4zmkFQFr+4u2337Y+ffrYH3/84Y4tX77cduzYkdHtAwAAyPpRYD/99JM1adLEChQoYFu2bHGjwQoVKmTTpk2zrVu32oQJf8+SCQAAEDEZoMcee8w6duzo5gLS5IfB64EtXLgwo9sHAEBI0PIXPa98020sheHBDNDSpUvtzTffTHb8vPPOs127dmVUuwAACCla/kLz/8CjGaDo6GiLjY1NdnzDhg1WtGjRjGoXAABA6ARAN998s7344ot2/Phxdztbtmyu9ufJJ5+0Vq1aZUYbAQDIcgknT9i3Wz93m/bhsQDo1VdftUOHDlmxYsXcKvANGjSwihUr2jnnnGP9+/fPnFYCAJDFjp88Zq9+e7/btA+P1QBp9NecOXNs0aJFbkSYgqHLLrvMjQwDAACI2MVQ5aqrrnIbAABAxAdAr7/+eorHVQukYfHqDrv66qstKioqI9oHAACQ9QHQsGHDbO/evRYXF2fnnnuuO/bnn39anjx5LF++fLZnzx47//zzbd68eVamTJmMbzEAAMDZLoIeMGCA1alTx02EuH//frdpCHzdunXttddecyPCSpQoYT169DjTtgEAAIRGBuiZZ56xqVOn2gUXXBA4pm6vV155xQ2D//XXX23w4MEMiQcAAJETAO3cudNOnEg+/4GO+WeCLlWqlP31118Z00IAAEJAjuw5rdvlwwL78FgXWKNGjez++++3FStWBI5p/4EHHrDGjRu726tWrbIKFSpkbEsBAMhCCnoan9/WbQRAHgyA3nnnHbf6e61atdyyGNpq167tjuk+UTG0JkwEAACIiC4wFThrIsR169a54mepXLmy24KzRAAARBItf/Hjrvlu/9ISDd3iqAhfp/3pValSxW0AAHiBlr8YsPButz/xtk0EQF4MgLZv326fffaZG/J+7Fji9VCGDh2aUW0DAAAIjQBo7ty5bkV4TXaobrDq1avbli1bzOfzuTXBAAAAIq4Iuk+fPvb444+7kV5a+kJzAm3bts2tCt+6devMaSUAAEBWBkBr1661u+/+uw80R44cduTIETfq68UXX7SXX345I9sGAAAQGgFQ3rx5A3U/JUuWtF9++SVw3759+zK2dQAAAKFQA3TFFVfYokWLrGrVqtasWTPr2bOn6w6bNm2auw8AACDiAiCN8jp06JDb79u3r9v/6KOPrFKlSowAAwBELM3+fG+t/oF9hLdsPg3f8rjY2FgrUKCAHTx40PLnz5/VzQEApGLa+p1hdW5aVi6Z1U2IaLFncP1Odw2Qhr/v378/2fEDBw64+wAAAEJdugMgzfmTkJCQ7PjRo0dtx44dlpkGDRpk2bJls0cffTRwLD4+3rp162aFCxd2o9FatWplu3fvztR2AAC8J+Fkgv28+1u3aR8eqQHSzM9+s2bNciknPwVEmiCxfPnyllmWLl1qb775pl188cWJjvfo0cO+/PJLmzx5smvTQw89ZC1btrRvvvkm09oCAPCe4yeP2vPzbgtaCiNPVjcJZyMAuuWWW9xXZWA6dOiQ6L6cOXO64CezVoBXoXX79u1t7Nix1q9fv8Bx9flpBfpJkyZZ48aN3bFx48a5EWpLlixhVBoAADizLrCTJ0+6rWzZsrZnz57AbW3q/lq/fr3ddNNNlhnUxXXjjTdakyZNEh1ftmyZHT9+PNFxLdCqNi5evDjV51N7VTgVvAEAAO9I9zD4zZs329n04Ycf2vLly10XWFK7du2yXLlyWcGCBRMdL168uLsvNQMHDnRD+AEAgDed1mrwqvfR5s8EBXv33Xczqm1ujbHu3bvbnDlz3LpjGUXrmT322GOB28oAlSlTJsOeHwAARFgApMyJ1v2qXbu2WwpDNUGZRV1cCrKCV5lXwfXChQtt5MiRrhhby3JoCH5wFkijwEqUKJHq80ZHR7sNAAB4U7oDoDFjxth7771nd911l2W2a665xi2zEeyee+5xdT5PPvmky9qoAFvZKA1/F9Uibd261erVq5fp7QMAAB4JgJRxufLKK+1sOOecc6x69erJFmPVnD/+4507d3bdWYUKFXKzQD788MMu+GFdMgBARorKlsPuuuSZwD7CW7o/wXvvvdcNO3/22WctFAwbNsyyZ8/uMkAa3dW0aVN74403srpZAIAIkzMql91S9cGsbgayKgDSzMtvvfWWffXVV25SQnVBJV0sNTPNnz8/0W0VR48aNcptAAAAmRIA/fTTT3bppZe6/Z9//jnRfZlZEA0AQFbS8heb//y7LrXCuTUsKnsUH4iXAqB58+ZlTksAAAjxpTCenNPM7bMUhgcXQ/XbtGmTG4Z+5MgRd9vn82VkuwAAAEInANq/f78bnn7hhRdas2bNbOfOnYHRWD179syMNgIAAGRtAKTV11X4rLl28uT530q4bdu2tZkzZ2Zs6wAAAEKhBmj27Nmu66t06dKJjleqVMl+++23jGwbAABAaGSADh8+nCjz4/fHH3+wvAQAAIjMAOhf//qXTZgwIdHQdy2IOnjwYGvUqFFGtw8AACDru8AU6KgI+ocffnDLYvTq1ctWr17tMkDffPNNxrcQAIAQoOUv2lz0WGAf4S3dn6DW4NqwYYNbjV1rdR06dMhatmxp3bp1c6vDAwAQqUthtK3xeFY3AxnktELYAgUK2NNPP51RbQAAAAjtGqBx48bZ5MmTkx3XsfHjx2dUuwAACCknfSdt68H1btM+PBYADRw40IoUKZLseLFixWzAgAEZ1S4AAELKsYR46zGjkdu0D48FQJoAsUKFCsmOlytXzt0HAAAQcQGQMj1aET6plStXWuHChTOqXQAAAKETALVr184eeeQRtyp8QkKC2/773/9a9+7d7fbbb8+cVgIAAGTlKLCXXnrJtmzZ4uYCypHj72/XRIh33303NUAAACDyAiCfz2e7du2y9957z/r162c//vij5c6d22rUqOFqgAAAACIyAKpYsaKb+VmLn2oDAACI6AAoe/bsLujZv38/wQ8AwFO0/MXNVboG9uGxIuhBgwbZE088YT///HPmtAgAgBBdCqPDpc+5TfsIb+kOYVXsHBcXZ5dcconlypXL1QAF06KoAAAAERUADR8+PHNaAgBACNPyF/sO73D7RfKeZ9mzpbsTBeEcAHXo0CFzWgIAQAjT8hcPfFHX7U+8bZPF5MiT1U3CGTit8PWXX36xZ555xk2KuGfPHndsxowZbnQYAABAxAVACxYscPP+fPfddzZt2jQ7dOhQYCmM559/PjPaCAAAkLUBUO/evd0kiHPmzHFF0H6NGze2JUuWZGzrAAAAQiEAWrVqld16660pLpK6b9++jGoXAABA6ARABQsWtJ07dyY7vmLFCjvvvPMyql0AAAChEwBpxfcnn3zSrQmWLVs2txDqN998Y48//ribIwgAACDihsEPGDDAunXrZmXKlLGEhASrVq2a+3rHHXe4kWEAAESiqGxRdn3FDoF9hLdsPq1wehq2bdvm6oE0CqxmzZphvTZYbGysFShQwA4ePGj58+fP6uYAAFIxbX3yEoxQ1rJyyaxuQkSLPYPrd5ozQOrqGjJkiH322Wd27Ngxu+aaa9yw96RLYQAAAERMDVD//v3tqaeesnz58rli59dee811hQEA4AXqMDkYv99tp9l5gnAMgCZMmGBvvPGGzZo1yz755BP7/PPPbeLEiS4zBABApDuacMQ6fVLDbdqHRwKgrVu3WrNmzQK3mzRp4kaB/f7775nVNgAAgKwNgE6cOGExMTGJjuXMmdOOHz+eGe0CAADINGkuglZ/Z8eOHS06OjpwLD4+3rp27Wp58+YNHNP6YAAAABERAHXo8PfcB8HuvPPOjG4PAABA6ARA48aNy9yWAAAAhOpSGAAAAJ5bCgMAAC/S8hcNy7cJ7CO8EQABAJAGOaOi7eErhnOuIgRdYAAAwHPIAAEAkMbpYPwzQEdH5XaTASN8kQECACANFPy0n1LRbSyFEf4IgAAAgOcQAAEAAM8hAAIAAJ5DAAQAADyHAAgAAHgOARAAAPAc5gECACANsmfLbvXK3BTYR3gjAAIAIA1yRcXY4/Xf4lxFCEJYAADgOQRAAADAcwiAAABIg/gTcdbqw1Ju0z7CGwEQAADwHAIgAADgOQRAAADAcwiAAACA5xAAAQAAzyEAAgAAnhPSAdDAgQOtTp06ds4551ixYsXslltusfXr1yd6THx8vHXr1s0KFy5s+fLls1atWtnu3buzrM0AgMik5S8uK3mN21gKI/yFdAC0YMECF9wsWbLE5syZY8ePH7frrrvODh8+HHhMjx497PPPP7fJkye7x//+++/WsmXLLG03ACAyl8J4usH7btM+wls2n8/nszCxd+9elwlSoHP11VfbwYMHrWjRojZp0iS77bbb3GPWrVtnVatWtcWLF9sVV1yRpueNjY21AgUKuOfLnz9/Jr8LAMDpmrZ+Z1idvJaVS2Z1EyJa7Blcv0M6A5SU3qAUKlTIfV22bJnLCjVp0iTwmCpVqljZsmVdAJSao0ePupMWvAEAAO8ImwDo5MmT9uijj1r9+vWtevXq7tiuXbssV65cVrBgwUSPLV68uLvvn2qLFDH6tzJlymR6+wEA4U3LX9wx+QK3sRRG+AubAEi1QD///LN9+OGHZ/xcffr0cdkk/7Zt27YMaSMAILIdTTjiNoS/HBYGHnroIfviiy9s4cKFVrp06cDxEiVK2LFjx+zAgQOJskAaBab7UhMdHe02AADgTSGdAVJ9toKf6dOn23//+1+rUKFCovtr1aplOXPmtLlz5waOaZj81q1brV69elnQYgAAEA5yhHq3l0Z4ffrpp24uIH9dj+p2cufO7b527tzZHnvsMVcYrQrwhx9+2AU/aR0BBgAAvCekA6DRo0e7rw0bNkx0fNy4cdaxY0e3P2zYMMuePbubAFGju5o2bWpvvPFGlrQXAACEh5AOgNIyRVFMTIyNGjXKbQAAAGEfAAEAECqyWTa7qGi9wD7CGwEQAABpEJ0jt714zVTOVYQI6VFgAAAAmYEACAAAeA4BEAAAaaDlL+6ZXt1tLIUR/qgBAgAgjWKP/sG5ihBkgAAAgOcQAAEAAM8hAAIAAJ5DAAQAADyHAAgAAHgOo8AAAEgDLX9xQaFLAvsIbwRAAACkcSmMwdfN4FxFCLrAAACA5xAAAQAAzyEAAgAgDY6eiLOun13uNu0jvFEDBABAGvjMbG/c9sA+whsZIAAA4DkEQAAAwHMIgAAAgOcQAAEAAM8hAAIAAJ7DKDAAANJAi1+Uzn9hYB/hjQAIAIA0iM6Rx15rNp9zFSHoAgMAAJ5DAAQAADyHAAgAgDTQ8hfd/9PQbSyFEf6oAQIAIA20/MX22A2BfYQ3MkAAAMBzCIAAAIDnEAABAADPIQACAACeQwAEAAA8h1FgAACkgZa/KJqndGAf4Y0ACACANC6FMebm7zlXEYIuMAAA4DkEQAAAwHMIgAAASIOjJ45Yr9k3uE37CG/UAAEAkAY+89kvf6wM7CO8kQECAACeQwAEAAA8hwAIAAB4DjVAAACEgGnrd1q4aVm5pIUrMkAAAMBzyAABAJBG+aMLca4iBAEQAABpEJMjj4279WfOVYSgCwwAAHgOARAAAPAcAiAAANJAy188N7eV21gKI/xRAwQAQBpo+YvVexcH9hHeyAABAADPIQACAACeQwAEAAA8hwAIAAB4DgEQAADwHEaBAQCQRtFRuTlXEYIACAAiTLitKh4uK4prKYxJrX/J6mYgg9AFBgAAPIcACAAAeA5dYAAApMGxhHgbsqiL23/iqrGWKyqG8xbGCIAAAEiDk76Ttnzn3MA+whtdYAAAwHMiJgM0atQoGzJkiO3atcsuueQSGzFihF1++eUWThi5AQDA2RERAdBHH31kjz32mI0ZM8bq1q1rw4cPt6ZNm9r69eutWLFiWd08ACGIfzgAb4uIAGjo0KHWpUsXu+eee9xtBUJffvmlvfvuu9a7d++sbh642IQtggQAkSrsA6Bjx47ZsmXLrE+fPoFj2bNntyZNmtjixYuztG3wBoIEAAg/YR8A7du3zxISEqx48eKJjuv2unXrUvyeo0ePus3v4MGD7mtsbKxlpbhDf1k4iY3Nm+bH8t5CB5/b3/iZDB3h8jMZfyLOLP5/7TiZIyFi3tvpSs/7ywz+67bP5/NeAHQ6Bg4caH379k12vEyZMlnSHgBAeOkyqGZWNwFB9u/fbwUKFDBPBUBFihSxqKgo2717d6Ljul2iRIkUv0fdZSqa9jtw4ICVK1fOtm7dmu4TGOoUHSuw27Ztm+XPn98iCe8tPPG5hSc+t/AVyZ/dwYMHrWzZslaoUKF0f2/YB0C5cuWyWrVq2dy5c+2WW25xx06ePOluP/TQQyl+T3R0tNuSUvATaT8cfnpfvLfww+cWnvjcwlMkf26R/v6yZ8/uvQBIlM3p0KGD1a5d2839o2Hwhw8fDowKAwAAiLgAqG3btrZ371577rnn3ESIl156qc2cOTNZYTQAAEDEBECi7q7UurxORd1hzz//fIrdYuGO9xae+NzCE59beIrkzy3S31/0Gby3bL7TGTsGAAAQxlgMFQAAeA4BEAAA8BwCIAAA4DkEQAAAwHMIgJIoX768ZcuWLdE2aNAgiyRaB01TBei9/fjjjxYJbr75ZjcbaExMjJUsWdLuuusu+/333y3cbdmyxTp37mwVKlSw3Llz2wUXXOBGPGgR4EjQv39/u/LKKy1PnjxWsGBBC3ejRo1yf0P0c1i3bl37/vvvLdwtXLjQmjdvbqVKlXJ/Mz755BOLpGWR6tSpY+ecc44VK1bMTaa7fv16iwSjR4+2iy++ODD5Yb169WzGjBkWiQYNGuR+Nh999NF0fR8BUApefPFF27lzZ2B7+OGHLZL06tXL/TGLJI0aNbKPP/7Y/fGaOnWq/fLLL3bbbbdZuNOCvprZ/M0337TVq1fbsGHDbMyYMfbUU09ZJFAg17p1a3vggQcs3H300UduUlYFqMuXL7dLLrnEmjZtanv27LFwpkll9V4U3EWaBQsWWLdu3WzJkiU2Z84cO378uF133XXuPYe70qVLu8Bg2bJl9sMPP1jjxo2tRYsW7u9IJFm6dKn7+6hgL900DB7/U65cOd+wYcMi9pT85z//8VWpUsW3evVqTX/gW7FihS8Sffrpp75s2bL5jh075os0gwcP9lWoUMEXScaNG+crUKCAL5xdfvnlvm7dugVuJyQk+EqVKuUbOHCgL1Lob8b06dN9kWrPnj3uPS5YsMAXic4991zf22+/7YsUf/31l69SpUq+OXPm+Bo0aODr3r17ur6fDFAKFDUXLlzYatasaUOGDLETJ05YJNACsV26dLH333/fdTlEqj/++MMmTpzoulZy5sxpkUaL/53Own/I3EyW/tNu0qRJorWJdHvx4sWc+jD63ZJI+/1KSEiwDz/80GW21BUWKbp162Y33nhjot87T84EnVEeeeQRu+yyy9wvwLfffutWjlc32NChQy2c6Z+3jh07WteuXd2aaaotiTRPPvmkjRw50uLi4uyKK66wL774wiLNpk2bbMSIEfbKK69kdVMQZN++fe4ik3T5Hd1WNyZCn7qaVUNSv359q169ukWCVatWuYAnPj7e8uXLZ9OnT7dq1apZJPjwww9dV7O6wE6XJzJAvXv3TlbYnHTz/5FSH37Dhg1df6KChVdffdVdcFQ4HM7vTe/hr7/+cgFdJH5u8sQTT9iKFSts9uzZFhUVZXfffbcL/CLhvcmOHTvs+uuvdzUzyuSFqtN5b0AoZBN+/vlnd2GNFJUrV3YDXb777jtXZ6dFw9esWWPhbtu2bda9e3eX6deAg9PliaUwtFDq/v37//Ex559/vuXKlSvZcRWM6b8B/cHWD1O4vrc2bdrY559/7i4+fvqPVYFC+/btbfz48RZJn9v27dutTJkyLosXiinf9L43jWhTYK7M1nvvvee6V0LV6Xxuek/67/vAgQMWrl1g6laeMmWKG0nkpwuO3tOnn35qkUB/P5RFCH6PkUDrSOoz0og3jbiMVOoq0khSFQ2HM41EvPXWW931K/h6pp9P/W1UwiL4Pk93gRUtWtRtp0PRs06ohkiG83t7/fXXrV+/foHbuqBqhIpGrmi4bqR9bkpnS6hm7tLz3pT50Si3WrVq2bhx40I6+DnTzy1cKZjT5zN37txAcKCfQd0+3UWakfn0/79G+Sqomz9/fkQHP/6fyVD9m5ge11xzjeveC3bPPfdYlSpVXClEWoIfzwRAaaViRaUKdbHRvBC63aNHD7vzzjvt3HPPtXCmOXKCqT9Y9N+AhkuGM31m6ge+6qqr3OekIfDPPvuse2+hmP1JDwU/yvyUK1fO1f0ou+JXokQJC3dbt251Rev6qv/g/PNSVaxYMfAzGi7Ufa6Mj2rsLr/8chs+fLgrOtUf5nB26NAhV3vmt3nzZvc5qU4y6d+VcOz2mjRpksv+6G/+rl273PECBQq4ebfCmcodbrjhBvcZqfxB71NB3qxZsyzcnXPOOcnqtPLmzesGL6WrfiuzhqeFo2XLlvnq1q3rhuPGxMT4qlat6hswYIAvPj7eF2k2b94cMcPgf/rpJ1+jRo18hQoV8kVHR/vKly/v69q1q2/79u2+SBgers8ppS0SdOjQIcX3Nm/ePF84GjFihK9s2bK+XLlyuWHxS5Ys8YU7fRYpfUb67MJdar9b+r0Ld506dXLTuuhnsWjRor5rrrnGN3v2bF+kanAaw+A9UQMEAAAQLLSLCQAAADIBARAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPIQACAACeQwAEAAA8hwAIQMh755137Lrrrgvc7tixY4YsyKnFE7WwYkbp3bu3W1sKQOhjJmgAIS0+Pt6tHj958mSrX7++O3bw4EG3kGXBggVDanXzffv2ubZqrSx9BRC6yAABCGlTpkyx/PnzB4If/2KVZxr8ZIYiRYpY06ZNbfTo0VndFACnQAAE4KzQSvZawX7AgAGBY99++63lypXL5s6dm+r3ffjhh9a8efNEx5J2gTVs2NAeeeQR69Wrl1ulXK/zwgsvJPqejRs32tVXX20xMTFWrVo1mzNnTrLX2rZtm7Vp08YFV3qeFi1a2JYtW9x969atszx58rhVtf0+/vhjt2r4mjVrAsfUVrUZQGgjAAJwVhQtWtTeffddF5j88MMP9tdff9ldd91lDz30kF1zzTWpft+iRYusdu3ap3z+8ePHW968ee27776zwYMH24svvhgIck6ePGktW7Z0wZbuHzNmjD355JOJvv/48eMue3POOefY119/bd98843ly5fPrr/+ejt27JhVqVLFXnnlFXvwwQdt69attn37duvatau9/PLLLqDyu/zyy919/sAJQGiiBgjAWdWtWzf76quvXFCzatUqW7p0qUVHR6f42AMHDti5555rCxcutH/961+JMkC6z1/ArAxQQkKCC1yCA5HGjRvboEGDbPbs2XbjjTfab7/9ZqVKlXL3z5w502644YZADdC///1v69evn61du9bVBokCH2WD9Dr+IuybbrrJYmNjXTAVFRXlnsf/eNF96qKbP3++NWjQIJPOIoAzleOMnwEA0kFZlOrVq7ui5mXLlqUa/MiRI0fcV3VbncrFF1+c6HbJkiVtz549bl9BTZkyZQLBj9SrVy/R41euXGmbNm1yGaCkRdi//PJL4LayWBdeeKFlz57dVq9enSj4EXWJSVxc3CnbDCDrEAABOKsUTPz++++uW0rdRDVq1Ej1sYULF3YBxp9//nnK582ZM2ei2/o+vUZaHTp0yGrVqmUTJ05MsfsuOFA6fPiwC4B27tzpAq1gf/zxR7LvARB6CIAAnDXqUrrzzjutbdu2VrlyZbv33ntdN1ixYsVSfLy6mVRfoyLj4HmA0qtq1aquwDk4YFmyZEmix1x22WX20UcfubZo1FlKFNyo++3pp592z9W+fXtbvnx5IOsjP//8swvGLrrootNuL4DMRxE0gLNGgYPm8Hn99dddEbK6kjp16vSP36PCZBVCn4kmTZq41+rQoYPL4KhWSG0JpmBGw9g18kv3b9682dXxaHSZippFRc/qSnvmmWds6NChru7o8ccfT/Q8+l7VKwUHRQBCDwEQgLNCwcTw4cPt/fffdxkWdSFpXwHDP82b07lzZ/vPf/7jAqfTpddSsbNqilQcrcxT//79Ez1GQ9xVbF22bFk3YkxZI722aoDU3gkTJrh2qM05cuRwI85UOD127FibMWNG4Hk0BL5Lly6n3VYAZwejwACEvNatW7suqj59+lgoUyDUs2dP++mnn1yQBCB0kQECEPKGDBni5uQJdSqOHjduHMEPEAbIAAEAAM8hAwQAADyHAAgAAHgOARAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPIQACAACeQwAEAAA85/8AxPmENwXnVcQAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = params()\n", + "# f(x) = 0.55*x + 0.25\n", + "# Gradient: f'(0) = 0.55\n", + "# Pay attention that 0.55 is not a multiple of m/N = 0.25,\n", + "# so we expect to get a superposition of multiple states around the correct gradient.\n", + "p.set_function(p.linear, (0.55, 0.25))\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " # 1. State preparation\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "\n", + "pc, df = run_standard_simulation(main, show_circuit=True)\n", + "analyze_results(pc, df, p)" + ] + }, + { + "cell_type": "markdown", + "id": "37", + "metadata": {}, + "source": [ + "## 3.2. Quadratic Function" + ] + }, + { + "cell_type": "markdown", + "id": "38", + "metadata": {}, + "source": [ + "Again, let's try calculating the gradient of a non-linear function. In the next example, we will explore a quadratic function.\\\n", + "In the case of non-linear function, we will need to cleverly choose the value of $l$ - the interval around the origin.\\\n", + "In order for the algorithm to work, we need to work in the linear regime around the origin, so we need to choose small enough $l$." + ] + }, + { + "cell_type": "markdown", + "id": "39", + "metadata": {}, + "source": [ + "First, for good selection of $l$, we see that the points are almost linear, and we get a good success rate." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "40", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsed counts: [{'x': 1}: 2021, {'x': 0}: 13, {'x': 2}: 13, {'x': 3}: 1]\n", + "The analytical gradient is: 0.25\n", + "The majority gradient is: 0.25\n", + "The majority result is correct\n", + "####################################################\n", + "Success rate: 98.68% (2021/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.68%\n" + ] + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the quadratic function\n", + "p = params()\n", + "# f(x) = 0.6*x^2 + 0.25*x + 0.1\n", + "# Gradient: f'(x) = 1.2*x + 0.25, so f'(0) = 0.25\n", + "p.set_function(p.quadratic, (0.6, 0.25, 0.1))\n", + "# Setting l properly, ensuring we are in the linear regime of the function.\n", + "p.l = 0.1\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " # 1. State preparation\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "\n", + "pc, df = run_standard_simulation(main)\n", + "analyze_results(pc, df, p)" + ] + }, + { + "cell_type": "markdown", + "id": "41", + "metadata": {}, + "source": [ + "But if we increase $l$ outside of the linear regime, we see that the success rate get drastically lower:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "42", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsed counts: [{'x': 0}: 517, {'x': 1}: 486, {'x': 2}: 473, {'x': 3}: 206, {'x': -1}: 163, {'x': -4}: 79, {'x': -2}: 78, {'x': -3}: 46]\n", + "The analytical gradient is: 0.25\n", + "The majority gradient is: 0.0\n", + "The majority result is incorrect\n", + "####################################################\n", + "Success rate: 23.73% (486/2048 shots)\n", + "[\u001b[92m████████████\u001b[91m--------------------------------------\u001b[0m] 23.73%\n" + ] + }, + { + "data": { + "image/png": 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", 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the quadratic function\n", + "p = params()\n", + "# f(x) = 0.6*x^2 + 0.25*x + 0.1\n", + "# Gradient: f'(x) = 1.2*x + 0.25, so f'(0) = 0.25\n", + "p.set_function(p.quadratic, (0.6, 0.25, 0.1))\n", + "# Setting l to be too big, so we are outside of the linear regime of the function.\n", + "p.l = 1\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " # 1. State preparation\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "\n", + "pc, df = run_standard_simulation(main)\n", + "analyze_results(pc, df, p)" + ] + }, + { + "cell_type": "markdown", + "id": "43", + "metadata": {}, + "source": [ + "# 4. Parameters Selection - TODO" + ] + }, + { + "cell_type": "markdown", + "id": "44", + "metadata": {}, + "source": [ + "**TODO:** I moved the theoretical explanation to the top, so it will be removed from here.\\\n", + "I'll need to rewrite the functions to use the $\\nabla f_{max}$ and $\\epsilon$ that I defined above." + ] + }, + { + "cell_type": "markdown", + "id": "45", + "metadata": {}, + "source": [ + "## 4.1. Understanding the parameters" + ] + }, + { + "cell_type": "markdown", + "id": "46", + "metadata": {}, + "source": [ + "There are three main parameters to be selected: $l$, $m$ and $n$.\\\n", + "$n$ is the number of bits of the result. The bigger $n$, the higher the accuracy of the result.\\\n", + "$l$ is the interval size around the origin ($dx$).\\\n", + "$m/2$ is the maximal gradient that can be calculated (in absolute value)." + ] + }, + { + "cell_type": "markdown", + "id": "47", + "metadata": {}, + "source": [ + "For the parameter $l$, we saw earlier that it should be selected such that we look at the linear regime of the function. See section 2.2." + ] + }, + { + "cell_type": "markdown", + "id": "48", + "metadata": {}, + "source": [ + "Understanding the parameter $m$ is a little trickier. We will look at a bounding box around the origin.\\\n", + "The width of the box (dx) is $l$, spanning from $-l/2$ to $l/2$. The slope of the graph (dy/dx) is bounded between $-m/2$ to $m/2$. Therefore, the height of the box (dy) should be bounded dy/dx*dx, so the height should be $lm/2$, making the box span between $-lm/4$ to $lm/4$.\\\n", + "When we plot the graph, if all the points are inside this box, then we know that the gradient is bounded by $m/2$ and we will get the correct result.\\\n", + "If the points are outside this box, we will get aliasing in the results and get an incorrect gradient.\\\n", + "Note that in our graphs we use the normalized function instead of the original function, so the box is between $-N/4$ to $N/4$ instead of $lm/4$." + ] + }, + { + "cell_type": "markdown", + "id": "49", + "metadata": {}, + "source": [ + "We will see now the same function, once with correct selection of m and one with incorrect selection of $m$, and we can see that if $m$ is too small the theoretical values are out of the bounding box, and the phases from the simulation are folded into the box creating aliasing. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "50", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'params' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mNameError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m \u001b[38;5;66;03m# In this example we will use the linear function\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m p = \u001b[43mparams\u001b[49m()\n\u001b[32m 3\u001b[39m p.set_function(p.linear, (\u001b[32m0.5\u001b[39m, \u001b[32m0.25\u001b[39m))\n\u001b[32m 4\u001b[39m p.m = \u001b[32m2\u001b[39m \u001b[38;5;66;03m# Correct selection of m - no aliasing.\u001b[39;00m\n", + "\u001b[31mNameError\u001b[39m: name 'params' is not defined" + ] + } + ], + "source": [ + "# In this example we will use the linear function\n", + "p = params()\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.m = 2 # Correct selection of m - no aliasing.\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=False)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)\n", + "# simplified_df" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "51", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the linear function\n", + "p = params()\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.m = 1.333 # Marginal selection of m - still no aliasing.\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=False)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)\n", + "# simplified_df" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "52", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In this example we will use the linear function\n", + "p = params()\n", + "p.set_function(p.linear, (0.5, 0.25))\n", + "p.m = 0.3 # Incorrect selection of m - aliasing occurs.\n", + "p.unpack(globals())\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + "\n", + "\n", + "df = run_statevector_simulation(main, print_circuit_info=False)\n", + "simplified_df = simplify_df(df)\n", + "plot_simplified_df(simplified_df)\n", + "# simplified_df" + ] + }, + { + "cell_type": "markdown", + "id": "53", + "metadata": {}, + "source": [ + "## 4.2. Success rate as function of parameter selection\n", + "**TODO**: consider removing this part" + ] + }, + { + "cell_type": "markdown", + "id": "54", + "metadata": {}, + "source": [ + "We can plot the success rate as a function of the selected parameters.\\\n", + "In the first example, we will have a quadratic function $f(x)=0.6x^2+0.25x+0.1$, $f'(0)=0.25$.\\\n", + "We can plot the graph for different selections of m.\\\n", + "We discussed earlier that $m/2$ is the bound for the gradient value, so we expect to have poor results for $m<0.5$, good results for $m>0.5$, until reaching $m=0.25N=4$, where the resolution won't be good enough for meaningful result.\\\n", + "Note the oscillations in the success rate in the optimal region. This is due to the discrete values the algorithm can return. As we increase the number of bits $n$, the oscillations will be smaller." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "55", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=0.05: Success rate = 0.00%\n", + "m=0.1: Success rate = 0.00%\n", + "m=0.3: Success rate = 0.00%\n", + "m=0.5: Success rate = 8.74%\n", + "m=0.55: Success rate = 39.70%\n", + "m=0.7: Success rate = 86.62%\n", + "m=0.8: Success rate = 79.88%\n", + "m=0.9: Success rate = 92.63%\n", + "m=1.0: Success rate = 94.24%\n", + "m=1.5: Success rate = 73.73%\n", + "m=2.0: Success rate = 98.39%\n", + "m=4.0: Success rate = 0.00%\n", + "m=6.0: Success rate = 0.00%\n", + "m=10.0: Success rate = 0.00%\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_success_rate_vs_m(m_values, function, function_params, l_val=0.1, n_val=3):\n", + " \"\"\"\n", + " Iterate over different m values and plot success rate as a function of m.\n", + "\n", + " Args:\n", + " m_values: list of m values to test\n", + " function: function name (\"linear\" / \"quadratic\") or callable\n", + " function_params: parameters for the function\n", + " l_val: l parameter (default 0.1)\n", + " n_val: n parameter (default 3)\n", + " \"\"\"\n", + " success_rates = []\n", + "\n", + " for m_val in m_values:\n", + " p = params()\n", + " p.m = m_val\n", + " p.l = l_val\n", + " p.n = n_val\n", + " p.set_function(function, function_params)\n", + " p.unpack(globals())\n", + "\n", + " @qfunc\n", + " def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + " invert(lambda: qft(x))\n", + "\n", + " pc, df = run_standard_simulation(main)\n", + " analytic_grad = p.analytical_gradient(0)\n", + " success_rate, _, _ = compute_success_rate(\n", + " df,\n", + " analytic_derivatives={\"x\": analytic_grad},\n", + " p=p,\n", + " tolerance=0.5 * analytic_grad,\n", + " )\n", + " success_rates.append(success_rate)\n", + " print(f\"m={m_val}: Success rate = {success_rate:.2%}\")\n", + "\n", + " # Plot\n", + " plt.figure(figsize=(10, 6))\n", + " plt.plot(m_values, success_rates, \"o-\", linewidth=2, markersize=8)\n", + " plt.xlabel(\"m parameter\", fontsize=12)\n", + " plt.ylabel(\"Success Rate\", fontsize=12)\n", + " plt.title(\"Success Rate vs m Parameter\", fontsize=14)\n", + " plt.grid(True, alpha=0.3)\n", + " plt.ylim([0, 1.05])\n", + " ax = plt.gca()\n", + " ax.axvspan(0.5, 4.0, color=\"green\", alpha=0.15, label=\"Target m range\")\n", + " ax.legend()\n", + " plt.show()\n", + " return success_rates\n", + "\n", + "\n", + "# Example usage:\n", + "m_values = [\n", + " 0.05,\n", + " 0.1,\n", + " 0.3,\n", + " 0.5,\n", + " 0.55,\n", + " 0.7,\n", + " 0.8,\n", + " 0.9,\n", + " 1.0,\n", + " 1.5,\n", + " 2.0,\n", + " 3.0,\n", + " 4.0,\n", + " 6.0,\n", + " 10.0,\n", + "]\n", + "results = plot_success_rate_vs_m(m_values, \"quadratic\", (0.6, 0.25, 0.1))" + ] + }, + { + "cell_type": "markdown", + "id": "56", + "metadata": {}, + "source": [ + "As for the $l$ parameter, we need to be in the linear regime, so we need to ensure $l$ is small enough, as can be seen in the next example:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "57", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=0.1: Success rate = 94.34%\n", + "l=0.2: Success rate = 79.69%\n", + "l=0.3: Success rate = 59.91%\n", + "l=0.4: Success rate = 38.53%\n", + "l=0.5: Success rate = 24.37%\n", + "l=1: Success rate = 11.72%\n", + "l=1.5: Success rate = 14.06%\n", + "l=2.0: Success rate = 14.65%\n", + "l=3.0: Success rate = 26.32%\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_success_rate_vs_l(l_values, function, function_params, m_val=2.0, n_val=3):\n", + " \"\"\"\n", + " Iterate over different l values and plot success rate as a function of l.\n", + "\n", + " Args:\n", + " l_values: list of l values to test\n", + " function: function name (\"linear\" / \"quadratic\") or callable\n", + " function_params: parameters for the function\n", + " m_val: m parameter (default 1.0)\n", + " n_val: n parameter (default 3)\n", + " \"\"\"\n", + " success_rates = []\n", + "\n", + " for l_curr in l_values:\n", + " p = params()\n", + " p.m = m_val\n", + " p.l = l_curr\n", + " p.n = n_val\n", + " p.set_function(function, function_params)\n", + " p.unpack(globals())\n", + "\n", + " @qfunc\n", + " def main(x: Output[QNum[n, SIGNED, 0]]):\n", + " allocate(n, x)\n", + " hadamard_transform(x)\n", + " phase(f_normalized(x), 2 * pi)\n", + " invert(lambda: qft(x))\n", + "\n", + " pc, df = run_standard_simulation(main)\n", + " analytic_grad = p.analytical_gradient(0)\n", + " success_rate, _, _ = compute_success_rate(\n", + " df, analytic_derivatives={\"x\": analytic_grad}, p=p\n", + " )\n", + " success_rates.append(success_rate)\n", + " print(f\"l={l_curr}: Success rate = {success_rate:.2%}\")\n", + "\n", + " plt.figure(figsize=(10, 6))\n", + " plt.plot(l_values, success_rates, \"o-\", linewidth=2, markersize=8)\n", + " plt.xlabel(\"l parameter\", fontsize=12)\n", + " plt.ylabel(\"Success Rate\", fontsize=12)\n", + " plt.title(\"Success Rate vs l Parameter\", fontsize=14)\n", + " plt.grid(True, alpha=0.3)\n", + " plt.ylim([0, 1.05])\n", + " plt.show()\n", + "\n", + " return success_rates\n", + "\n", + "\n", + "# Example usage:\n", + "l_values = [0.1, 0.2, 0.3, 0.4, 0.5, 1, 1.5, 2.0, 3.0]\n", + "results_l = plot_success_rate_vs_l(\n", + " l_values, \"quadratic\", (0.6, 0.25, 0.1), m_val=1.0, n_val=3\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "58", + "metadata": {}, + "source": [ + "# 5. Multi-Coordinates Examples" + ] + }, + { + "cell_type": "markdown", + "id": "59", + "metadata": {}, + "source": [ + "This algorithm works in multiple dimensions too.\\\n", + "We will now see an example in 2D, f(x,y).\\\n", + "We will start with a linear and decoupled function $f(x,y)=ax+by+c$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "60", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'params' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mNameError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[4]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m px = \u001b[43mparams\u001b[49m()\n\u001b[32m 2\u001b[39m py = params()\n\u001b[32m 4\u001b[39m \u001b[38;5;66;03m# Set the functions for x and y axes\u001b[39;00m\n\u001b[32m 5\u001b[39m \u001b[38;5;66;03m# f(x, y) = a*x + b*y + c = 0.5*x - 0.25*y + 0.1\u001b[39;00m\n\u001b[32m 6\u001b[39m \u001b[38;5;66;03m# df/dx = 0.5, df/dy = -0.25\u001b[39;00m\n", + "\u001b[31mNameError\u001b[39m: name 'params' is not defined" + ] + } + ], + "source": [ + "px = params()\n", + "py = params()\n", + "\n", + "# Set the functions for x and y axes\n", + "# f(x, y) = a*x + b*y + c = 0.5*x - 0.25*y + 0.1\n", + "# df/dx = 0.5, df/dy = -0.25\n", + "a, b, c = 0.5, -0.25, 0.1\n", + "px.set_function(px.linear, (a, 0.0))\n", + "py.set_function(py.linear, (b, c))\n", + "\n", + "# Important: we can't use the globals here, because there are two different functions for px and for py.\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[px.n, SIGNED, 0]], y: Output[QNum[py.n, SIGNED, 0]]):\n", + " # State preparation for x-axis contribution\n", + " allocate(px.n, x)\n", + " hadamard_transform(x)\n", + " phase(px.f_normalized(x), 2 * pi)\n", + "\n", + " # State preparation for y-axis contribution\n", + " allocate(py.n, y)\n", + " hadamard_transform(y)\n", + " phase(py.f_normalized(y), 2 * pi)\n", + "\n", + " # Gradient extraction on each axis\n", + " invert(lambda: qft(x))\n", + " invert(lambda: qft(y))\n", + "\n", + "\n", + "pc, df = run_standard_simulation(main)\n", + "print(pc)\n", + "\n", + "majority_state = dict(df.iloc[0])\n", + "gx_true = px.analytical_gradient(0)\n", + "gy_true = py.analytical_gradient(0)\n", + "\n", + "gx_meas = (majority_state.get(\"x\")) / (px.N / px.m)\n", + "gy_meas = (majority_state.get(\"y\")) / (py.N / py.m)\n", + "\n", + "print(f\"Analytical gradient: (dx, dy) = ({gx_true}, {gy_true})\")\n", + "print(f\"Majority gradient: (dx, dy) = ({gx_meas}, {gy_meas})\")\n", + "\n", + "success_rate, success_shots, total_shots = compute_success_rate(\n", + " df, analytic_derivatives={\"x\": gx_true, \"y\": gy_true}, p=px\n", + ")\n", + "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", + "show_bar(success_rate)" + ] + }, + { + "cell_type": "markdown", + "id": "61", + "metadata": {}, + "source": [ + "We can also have more complex example, with non-linear and coupled equation: $f(x, y)=ax^2+by^2+cxy+dx+ey+f$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "62", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[{'x': 1, 'y': -2}: 1996, {'x': 2, 'y': -2}: 14, {'x': 0, 'y': -2}: 13, {'x': 1, 'y': -3}: 12, {'x': 1, 'y': -1}: 4, {'x': 2, 'y': -1}: 3, {'x': -1, 'y': -2}: 1, {'x': 0, 'y': -3}: 1, {'x': 3, 'y': -3}: 1, {'x': 2, 'y': -4}: 1, {'x': 1, 'y': -4}: 1, {'x': -4, 'y': -2}: 1]\n", + "Analytical gradient: (dx, dy) = (0.25, -0.5)\n", + "Majority gradient: (dx, dy) = (0.25, -0.5)\n", + "Success rate: 97.46% (1996/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.46%\n" + ] + } + ], + "source": [ + "p = params()\n", + "p.l = 0.1\n", + "p.unpack(globals())\n", + "\n", + "\n", + "def f(x, y):\n", + " a, b, c, d, e, f = 0.6, -0.4, 0.25, 0.25, -0.5, 0.1\n", + " global gradient_x, gradient_y\n", + " gradient_x = d\n", + " gradient_y = e\n", + " return a * x**2 + b * y**2 + c * x * y + d * x + e * y + f\n", + "\n", + "\n", + "# Generated functions\n", + "def f_normalized(x, y):\n", + " val = f(l / N * x, l / N * y)\n", + " val *= N / (l * m)\n", + " return val\n", + "\n", + "\n", + "@qfunc\n", + "def main(x: Output[QNum[n, SIGNED, 0]], y: Output[QNum[n, SIGNED, 0]]):\n", + " # 1. State preparation\n", + " # Build arrays in two's complement binary order for prepare_complex_amplitudes.\n", + " # Binary index i maps to signed value: i if i < N//2 else i - N\n", + " idx = np.arange(N)\n", + " x_signed = np.where(idx < N // 2, idx, idx - N)\n", + " y_signed = np.where(idx < N // 2, idx, idx - N)\n", + "\n", + " # In order to use the prepare_complex_amplitudes function, we need to flatten the 2D arrays of magnitudes and phases into 1D arrays.\n", + " X_grid, Y_grid = np.meshgrid(x_signed, y_signed, indexing=\"ij\")\n", + " phases_2d = f_normalized(X_grid, Y_grid) * 2 * np.pi\n", + " magnitudes_2d = np.ones((N, N)) / N\n", + " phases_flat = phases_2d.flatten().tolist()\n", + " magnitudes_flat = magnitudes_2d.flatten().tolist()\n", + "\n", + " # Prepare the state using the flattened arrays, then bind the combined register to the x and y registers.\n", + " combined_reg = QNum(\"combined_reg\")\n", + " prepare_complex_amplitudes(\n", + " magnitudes=magnitudes_flat, phases=phases_flat, out=combined_reg\n", + " )\n", + " bind(combined_reg, [y, x])\n", + "\n", + " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + " invert(lambda: qft(y))\n", + "\n", + "\n", + "pc, df = run_standard_simulation(main)\n", + "print(pc)\n", + "\n", + "majority_state = dict(df.iloc[0])\n", + "gx_true = gradient_x\n", + "gy_true = gradient_y\n", + "\n", + "gx_meas = state_to_gradient(majority_state.get(\"x\"), p)\n", + "gy_meas = state_to_gradient(majority_state.get(\"y\"), p)\n", + "\n", + "print(f\"Analytical gradient: (dx, dy) = ({gx_true}, {gy_true})\")\n", + "print(f\"Majority gradient: (dx, dy) = ({gx_meas}, {gy_meas})\")\n", + "\n", + "success_rate, success_shots, total_shots = compute_success_rate(\n", + " df, analytic_derivatives={\"x\": gx_true, \"y\": gy_true}, p=p\n", + ")\n", + "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", + "show_bar(success_rate)" + ] + }, + { + "cell_type": "markdown", + "id": "63", + "metadata": {}, + "source": [ + "# References" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "64", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: add" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "classiq", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 9 +} diff --git a/algorithms/gradient_estimation/gradient_estimation.metadata.json b/algorithms/gradient_estimation/gradient_estimation.metadata.json new file mode 100644 index 000000000..be6f2f983 --- /dev/null +++ b/algorithms/gradient_estimation/gradient_estimation.metadata.json @@ -0,0 +1,10 @@ +{ + "title": "Gradient Estimation", + "subtitle": "Initialization", + "description": "Initialization", + "friendly_name": "Gradient Estimation", + "vertical_tags": [], + "problem_domain_tags": [], + "qmod_type": [], + "level": [] +} diff --git a/algorithms/gradient_estimation/gradient_estimation_helpers.py b/algorithms/gradient_estimation/gradient_estimation_helpers.py new file mode 100644 index 000000000..1d1a79bbd --- /dev/null +++ b/algorithms/gradient_estimation/gradient_estimation_helpers.py @@ -0,0 +1,335 @@ +from classiq import * +from typing import List +import numpy as np +import pandas as pd +from dataclasses import dataclass +from matplotlib import pyplot as plt +from classiq.qmod.symbolic import pi + +# %matplotlib widget + +# Module-level globals populated by params.unpack(globals()). +# Defaults match params class defaults. +l = 0.5 +m = 2 +n = 3 +n0 = 3 +N = 2**n +N0 = 2**n0 +f = None +f_prams = None +f_normalized = None + + +@dataclass +class params: + # Algorithm parameters + l = 0.5 + m = 2 + n = 3 + n0 = 3 + + @property + def N(self): + return 2**self.n + + @property + def N0(self): + return 2**self.n0 + + # Function parameters + f = None + f_prams = None + f_name = None + + def set_function(self, f, f_prams): + self.f_prams = f_prams + + # Allow passing by name, e.g. "linear" or "quadratic" + if isinstance(f, str): + self.f_name = f + self.f = getattr(self, f) + return + + # If a method from another params instance is passed, + # re-bind it to this instance to avoid mixed state. + if hasattr(f, "__func__"): + self.f = f.__func__.__get__(self, self.__class__) + else: + self.f = f + + self.f_name = getattr(self.f, "__name__", None) + + # Generated functions + def f_normalized(self, x): + val = self.f(self.l / self.N * x) + val *= self.N / (self.l * self.m) + return val + + def analytical_gradient(self, x): + if self.f_name == "linear": + return self.f_prams[0] + elif self.f_name == "quadratic": + return 2 * self.f_prams[0] * x + self.f_prams[1] + else: + raise NotImplementedError( + "Analytical gradient not implemented for this function." + ) + + # A few example functions + def linear(self, x): + return self.f_prams[0] * x + self.f_prams[1] + + def quadratic(self, x): + return self.f_prams[0] * x**2 + self.f_prams[1] * x + self.f_prams[2] + + # Unpack function, to be used in the notebook. + # Pass globals() from the notebook cell so variables are injected there too: + # p.unpack(globals()) + def unpack(self, namespace=None): + import sys + + vals = dict( + l=self.l, + m=self.m, + n=self.n, + n0=self.n0, + N=self.N, + N0=self.N0, + f=self.f, + f_prams=self.f_prams, + f_normalized=self.f_normalized, + ) + # Update this module's globals so helper functions (state_to_gradient, etc.) work + vars(sys.modules[self.__class__.__module__]).update(vals) + # Update the notebook's globals if provided + if namespace is not None: + namespace.update(vals) + + +# ****** Simulation ****** +def run_statevector_simulation( + qfunc_to_run, print_circuit_info=False, filter_ancilla=False, show_circuit=False +): + # Run a statevector simulator + qprog = synthesize(qfunc_to_run) + if show_circuit: + show(qprog) + if print_circuit_info: + print("Circuit Width:", qprog.data.width) + print("Circuit Depth:", qprog.transpiled_circuit.depth) + print("Gate Counts:", qprog.transpiled_circuit.count_ops) + + backend_preferences = ClassiqBackendPreferences( + backend_name="simulator_statevector" + ) + execution_preferences = ExecutionPreferences( + num_shots=1, backend_preferences=backend_preferences + ) + with ExecutionSession(qprog, execution_preferences=execution_preferences) as es: + if filter_ancilla: + es.set_measured_state_filter("ancilla", lambda v: v == 0) + results_statevector = es.sample() + df = results_statevector.dataframe + return df + + +def run_standard_simulation(qfunc_to_run, show_circuit=False): + # Run a regular simulator + qprog = synthesize(qfunc_to_run) + if show_circuit: + show(qprog) + job = execute(qprog) + # job.open_in_ide() + pc = job.get_sample_result().parsed_counts + df = job.get_sample_result().dataframe + df.sort_values( + "counts", ascending=False, inplace=True + ) # Verify that the most common state is first, as expected from a statevector simulation + + return pc, df + + +# ****** Result Processing ****** +def state_to_gradient(value, p): + return value / (p.N / p.m) + + +def simplify_df(df, unwrap=True): + # Get the phase from the df + phases = np.angle(df["amplitude"]).astype(float) + phases_over_2pi = phases / (2 * np.pi) + f_classical = f_normalized(df["x"]) + simplified_df = pd.DataFrame( + {"f_classical": f_classical, "phase_over_2pi": phases_over_2pi.round(5)} + ) + simplified_df.index = df["x"] + simplified_df.sort_index(inplace=True) + + # Unwrap the phase if requested + if unwrap: + # Unwrap the phase + simplified_df["phase_over_2pi"] = np.unwrap( + simplified_df["phase_over_2pi"], period=1 + ) + # Get rid of the global phase + simplified_df["phase_over_2pi"] -= simplified_df["phase_over_2pi"].iloc[N // 2] + simplified_df["f_classical"] -= simplified_df["f_classical"].iloc[N // 2] + + return simplified_df + + +def compute_success_rate(df, analytic_derivatives, p, tolerance=None): + total_shots = int(df["counts"].sum()) + if total_shots == 0: + return 0.0, 0, 0 + if tolerance is None: + tolerance = 0.5 * p.m / p.N + + success_shots = 0 + + for _, row in df.iterrows(): + est = {name: state_to_gradient(row[name], p) for name in analytic_derivatives} + + correct = True + for name, analytic_val in analytic_derivatives.items(): + measured_val = est.get(name) + if measured_val is None or abs(measured_val - analytic_val) >= tolerance: + correct = False + break + + if correct: + success_shots += int(row["counts"]) + + success_rate = success_shots / total_shots + return success_rate, success_shots, total_shots + + +def analyze_results(pc, df, p): + analytical_gradient = p.analytical_gradient(0) + + # Print the results and compute the majority gradient + print("Parsed counts:", pc) + print(f"The analytical gradient is: {analytical_gradient}") + majority_state = dict(df.iloc[0]) + majority_gradient = state_to_gradient(majority_state.get("x"), p) + print(f"The majority gradient is: {majority_gradient}") + + # Check if the majority result is correct within the resolution of the algorithm + resolution = m / N + is_correct = abs(majority_gradient - analytical_gradient) < resolution / 2 + print(f"The majority result is", "correct" if is_correct else "incorrect") + print("####################################################") + + # Compute the success rate of the algorithm, i.e. the percentage of shots that are correct within the resolution of the algorithm. + success_rate, success_shots, total_shots = compute_success_rate( + df, analytic_derivatives={"x": analytical_gradient}, p=p + ) + print(f"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)") + show_bar(success_rate) + + # Visualize the theoretical values of the phases + # We used the standard simulation, so this is theoretical values only without the phases from the simulation + plot_theoretical() + + # Plot histogram of the results + plot_histogram(df, analytical_gradient=analytical_gradient) + + +# ****** Plotting ****** +def plot_classical(): + x_values = np.linspace(-N, N, 1000) + f_values = f_normalized(x_values) + f_values -= f_normalized(0) + plt.plot(x_values, f_values, color="lightgray", label="Original function") + ax = plt.gca() + ax.set_xticks(np.arange(-N // 2, N // 2)) + ax.set_xticklabels([str(i) for i in range(-N // 2, N // 2)]) + + # Primary-axis labels (normalized coordinates) + ax.set_xlabel("x (index)") + ax.set_ylabel("f (normalized)") + + # Secondary X axis: signed quantum index -> real x (x_real = x * l/N) + x_to_real = lambda x: x * (l / N) + real_to_x = lambda xr: xr * (N / l) + secax_x = ax.secondary_xaxis("top", functions=(x_to_real, real_to_x), color="blue") + secax_x.set_xlabel("x (real)") + + # Secondary Y axis: normalized f -> unnormalized f + f_to_real = lambda y: (y + f_normalized(0)) * m * l / N + real_to_f = lambda yr: yr / m / l * N - f_normalized(0) + secax_y = ax.secondary_yaxis( + "right", functions=(f_to_real, real_to_f), color="blue" + ) + secax_y.set_ylabel("f (real, unnormalized)") + + +def plot_theoretical(show=True): + x_array = np.arange(-N // 2, N // 2) + + f_classical = f_normalized(x_array) + f_classical -= f_classical[N // 2] # index N//2 in [-N/2..N/2-1] is x=0 + + if show: + plt.figure() + plot_classical() + plt.plot(x_array, f_classical, "o", label="Theoretical values") + xmin, xmax = -N, N + ymin, ymax = -N // 2, N // 2 + plt.xlim(xmin, xmax) + plt.ylim(ymin, ymax) + plt.vlines(-N // 2, ymin, ymax, colors="lightgray", linestyles="dashed") + plt.vlines(N // 2 - 1, ymin, ymax, colors="lightgray", linestyles="dashed") + plt.hlines(-N / 4 + 0.5, xmin, xmax, colors="lightgray", linestyles="dashed") + plt.hlines(N / 4, xmin, xmax, colors="lightgray", linestyles="dashed") + plt.legend() + if show: + plt.show() + + +def plot_histogram(df, analytical_gradient=None, show=True): + plt.figure() + percentage = df["counts"] / df["counts"].sum() * 100 + plt.bar(df["x"], percentage, color="lightblue", label="Measurement counts") + plt.xlabel("x (index)") + plt.ylabel("Percentage of shots (%)") + plt.xlim(-N // 2 - 1, N // 2) + plt.ylim(0, 100) + plt.title("Measurement Histogram") + plt.legend() + # plot the analytical gradient as a vertical line if provided + if analytical_gradient is not None: + x_analytic = analytical_gradient * (N / m) + plt.axvline( + x=x_analytic, color="green", linestyle="dashed", label="Analytical gradient" + ) + plt.legend() + if show: + plt.show() + + +def plot_simplified_df(simplified_df, show=True): + plt.figure() + plot_theoretical(show=False) + plt.plot( + simplified_df.index, + simplified_df["phase_over_2pi"], + "o", + label="Measured phases", + ) + plt.legend() + if show: + plt.show() + + +def show_bar(success_rate): + bar_length = 50 + filled = int(round(bar_length * success_rate)) + GREEN = "\033[92m" + RED = "\033[91m" + RESET = "\033[0m" + + bar = f"{GREEN}{'█' * filled}{RED}{'-' * (bar_length - filled)}{RESET}" + + print(f"[{bar}] {success_rate * 100:.2f}%") diff --git a/algorithms/gradient_estimation/quantum_circuit.png b/algorithms/gradient_estimation/quantum_circuit.png new file mode 100644 index 0000000000000000000000000000000000000000..6ad8c5cb236745eba7c3ddaabe5e3d4903dea010 GIT binary patch literal 12297 zcmZX41ymeM*DW$Q1eXB8-QC^Y-5myZ1`iP2U4jLI1`qBU+})kv?)r1(yZ5g5daa(W z-gTtT?y8=io*k~FAc+Kz3l9bch9oT|rUC{A5%k`cg@u0qM39O00|Nt>0*Z<%NsEdS zDLFe>0By~|z^LMV<3?pfj8Q@eW#eUvsdVb%VDqZtOa*Oz7I*e_Mfkb*=L2(#VzJu8;R2h#5J_3hHrs6!?y%)(EFq6Fjr2T?`XDm8iqjRy2@Ccho7;Zk zAqk=<92-aZ4ObL@2Ns%t8Gq$JLGz z)p9y45#e2dNnNF&>$@>q7s@{H2vfaVYNg)9lkZd!Xr7zw__h{daCp51dv)`I{I)hR zApTU0;<~yOfF8LK)!f{#-NG)_#&new8((g`Vi;O)xcoj}b=a(@*I}$Ll;4!EUgk^B zI2m%EQ0crI6~Oy->KCw*OIo7mj|PHZ^MFthXTO>?=A569rt|)1A|Nm0fTuz zqP_28xe)*Bg$T-p{9hYP_76j0RZ(f__oJ$*v$?swiU{CZ%Tw@alH&=cVl0Opt zv;8$ra}e;~O!h8+m-SvC;~zbY%nVG7|HOWG<@*EWQ38U@ZMDUKcJK7O=Mdmz=lj$A 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a/tests/notebooks/test_gradient_estimation.py b/tests/notebooks/test_gradient_estimation.py new file mode 100644 index 000000000..1d9b15041 --- /dev/null +++ b/tests/notebooks/test_gradient_estimation.py @@ -0,0 +1,19 @@ +from tests.utils_for_testbook import ( + validate_quantum_program_size, + wrap_testbook, +) +from testbook.client import TestbookNotebookClient + + +@wrap_testbook("gradient_estimation", timeout_seconds=60) +def test_notebook(tb: TestbookNotebookClient) -> None: + # test quantum programs + validate_quantum_program_size( + tb.ref_pydantic("qprog"), + expected_width=None, + expected_depth=None, + expected_cx_count=None, + ) + + # test notebook content + pass # Todo From 454b64fa8d4e13c8b5eb9485d65bd1cf2d749d54 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Tue, 5 May 2026 12:15:12 +0300 Subject: [PATCH 03/12] Fixing small error in the notebook --- .../gradient_estimation.ipynb | 339 +++++++++--------- 1 file changed, 162 insertions(+), 177 deletions(-) diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index 05015d516..4cea27dc8 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -24,7 +24,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "2", "metadata": {}, "outputs": [], @@ -205,7 +205,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "id": "12", "metadata": {}, "outputs": [ @@ -213,9 +213,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Circuit Width: 8\n", - "Circuit Depth: 42\n", - "Gate Counts: {'u': 31, 'cx': 27}\n" + "Circuit Width: 7\n", + "Circuit Depth: 30\n", + "Gate Counts: {'u': 25, 'cx': 19}\n" ] }, { @@ -263,87 +263,87 @@ "type": "string" } ], - "ref": "3627dec6-122f-48ec-b0ca-c98f0b5c29ad", + "ref": "2ed188b1-5bb0-4ee9-9817-91350a30d4cd", "rows": [ [ "0", - "1", + "3", "0.0", - "(-0.08838834764831831+0.08838834764831865j)", - "0.13", - "0.75π", - "0.015625000000000014", - "00000001" + "(0.08838834764831856-0.08838834764831835j)", + "0.12", + "-0.25π", + "0.015625", + "0000011" ], [ "1", - "-3", + "1", "0.0", - "(-0.0883883476483183+0.08838834764831867j)", - "0.13", + "(-0.0883883476483185+0.08838834764831836j)", + "0.12", "0.75π", - "0.015625000000000014", - "00000101" + "0.015624999999999997", + "0000001" ], [ "2", - "0", + "-3", "0.0", - "(0.08838834764831853+0.08838834764831836j)", + "(-0.0883883476483185+0.08838834764831836j)", "0.12", - "0.25π", - "0.015625", - "00000000" + "0.75π", + "0.015624999999999997", + "0000101" ], [ "3", - "2", + "-1", "0.0", - "(-0.08838834764831852-0.08838834764831836j)", + "(0.08838834764831853-0.08838834764831834j)", "0.12", - "-0.75π", - "0.015625", - "00000010" + "-0.25π", + "0.015624999999999997", + "0000111" ], [ "4", - "-2", + "2", "0.0", - "(-0.08838834764831854-0.08838834764831835j)", + "(-0.08838834764831827-0.08838834764831852j)", "0.12", "-0.75π", - "0.015625", - "00000110" + "0.015624999999999983", + "0000010" ], [ "5", - "3", + "0", "0.0", - "(0.08838834764831827-0.08838834764831859j)", + "(0.08838834764831827+0.08838834764831847j)", "0.12", - "-0.25π", - "0.015624999999999993", - "00000011" + "0.25π", + "0.015624999999999972", + "0000000" ], [ "6", - "-1", + "-2", "0.0", - "(0.08838834764831824-0.08838834764831861j)", + "(-0.08838834764831822-0.0883883476483185j)", "0.12", - "-0.25π", - "0.015624999999999993", - "00000111" + "-0.75π", + "0.015624999999999972", + "0000110" ], [ "7", "-4", "0.0", - "(0.08838834764831849+0.08838834764831834j)", + "(0.08838834764831822+0.08838834764831847j)", "0.12", "0.25π", - "0.01562499999999999", - "00000100" + "0.015624999999999965", + "0000100" ] ], "shape": { @@ -382,73 +382,73 @@ " \n", " \n", " 0\n", - " 1\n", + " 3\n", " 0.0\n", - " -0.088388+0.088388j\n", - " 0.13\n", - " 0.75π\n", + " 0.088388-0.088388j\n", + " 0.12\n", + " -0.25π\n", " 0.015625\n", - " 00000001\n", + " 0000011\n", " \n", " \n", " 1\n", - " -3\n", + " 1\n", " 0.0\n", " -0.088388+0.088388j\n", - " 0.13\n", + " 0.12\n", " 0.75π\n", " 0.015625\n", - " 00000101\n", + " 0000001\n", " \n", " \n", " 2\n", - " 0\n", + " -3\n", " 0.0\n", - " 0.088388+0.088388j\n", + " -0.088388+0.088388j\n", " 0.12\n", - " 0.25π\n", + " 0.75π\n", " 0.015625\n", - " 00000000\n", + " 0000101\n", " \n", " \n", " 3\n", - " 2\n", + " -1\n", " 0.0\n", - " -0.088388-0.088388j\n", + " 0.088388-0.088388j\n", " 0.12\n", - " -0.75π\n", + " -0.25π\n", " 0.015625\n", - " 00000010\n", + " 0000111\n", " \n", " \n", " 4\n", - " -2\n", + " 2\n", " 0.0\n", " -0.088388-0.088388j\n", " 0.12\n", " -0.75π\n", " 0.015625\n", - " 00000110\n", + " 0000010\n", " \n", " \n", " 5\n", - " 3\n", + " 0\n", " 0.0\n", - " 0.088388-0.088388j\n", + " 0.088388+0.088388j\n", " 0.12\n", - " -0.25π\n", + " 0.25π\n", " 0.015625\n", - " 00000011\n", + " 0000000\n", " \n", " \n", " 6\n", - " -1\n", + " -2\n", " 0.0\n", - " 0.088388-0.088388j\n", + " -0.088388-0.088388j\n", " 0.12\n", - " -0.25π\n", + " -0.75π\n", " 0.015625\n", - " 00000111\n", + " 0000110\n", " \n", " \n", " 7\n", @@ -458,7 +458,7 @@ " 0.12\n", " 0.25π\n", " 0.015625\n", - " 00000100\n", + " 0000100\n", " \n", " \n", "\n", @@ -466,17 +466,17 @@ ], "text/plain": [ " x ancilla amplitude magnitude phase probability bitstring\n", - "0 1 0.0 -0.088388+0.088388j 0.13 0.75π 0.015625 00000001\n", - "1 -3 0.0 -0.088388+0.088388j 0.13 0.75π 0.015625 00000101\n", - "2 0 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 00000000\n", - "3 2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 00000010\n", - "4 -2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 00000110\n", - "5 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 00000011\n", - "6 -1 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 00000111\n", - "7 -4 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 00000100" + "0 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000011\n", + "1 1 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000001\n", + "2 -3 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000101\n", + "3 -1 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000111\n", + "4 2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000010\n", + "5 0 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000000\n", + "6 -2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000110\n", + "7 -4 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000100" ] }, - "execution_count": 2, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -551,7 +551,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "id": "14", "metadata": {}, "outputs": [ @@ -585,7 +585,7 @@ "type": "float" } ], - "ref": "c51b192d-c6bf-4330-b755-745827c97e05", + "ref": "37d53315-ee64-43e9-82c2-55f4fc1ca29e", "rows": [ [ "-4", @@ -719,7 +719,7 @@ " 3 0.75 0.75" ] }, - "execution_count": 3, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -771,7 +771,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "id": "17", "metadata": {}, "outputs": [ @@ -779,26 +779,20 @@ "name": "stdout", "output_type": "stream", "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3DIMQhH5GHJdRvHote12kf71YLk\n", - "Circuit Width: 7\n", - "Circuit Depth: 37\n", - "Gate Counts: {'u': 31, 'cx': 28}\n" + "Circuit Width: 8\n", + "Circuit Depth: 42\n", + "Gate Counts: {'u': 31, 'cx': 27}\n" ] }, { - "ename": "IndexError", - "evalue": "single positional indexer is out-of-bounds", - "output_type": "error", - "traceback": [ - "\u001b[31m---------------------------------------------------------------------------\u001b[39m", - "\u001b[31mIndexError\u001b[39m Traceback (most recent call last)", - "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[10]\u001b[39m\u001b[32m, line 29\u001b[39m\n\u001b[32m 26\u001b[39m invert(\u001b[38;5;28;01mlambda\u001b[39;00m: qft(x))\n\u001b[32m 28\u001b[39m df = run_statevector_simulation(main, print_circuit_info=\u001b[38;5;28;01mTrue\u001b[39;00m, filter_ancilla=\u001b[38;5;28;01mTrue\u001b[39;00m, show_circuit=\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[32m---> \u001b[39m\u001b[32m29\u001b[39m simplified_df = \u001b[43msimplify_df\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdf\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 30\u001b[39m plot_simplified_df(simplified_df)\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/GoogleDrive-ofriwi1@gmail.com/My Drive/Documents/Work/1. Classiq/Gradient Estimation/gradient_estimation_helpers.py:148\u001b[39m, in \u001b[36msimplify_df\u001b[39m\u001b[34m(df, unwrap)\u001b[39m\n\u001b[32m 145\u001b[39m \u001b[38;5;66;03m# Unwrap the phase if requested\u001b[39;00m\n\u001b[32m 146\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m unwrap:\n\u001b[32m 147\u001b[39m \u001b[38;5;66;03m# Unwrap the phase\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m148\u001b[39m simplified_df[\u001b[33m'\u001b[39m\u001b[33mphase_over_2pi\u001b[39m\u001b[33m'\u001b[39m] = np.unwrap(simplified_df[\u001b[33m'\u001b[39m\u001b[33mphase_over_2pi\u001b[39m\u001b[33m'\u001b[39m], period=\u001b[32m1\u001b[39m)\n\u001b[32m 149\u001b[39m \u001b[38;5;66;03m# Get rid of the global phase\u001b[39;00m\n\u001b[32m 150\u001b[39m simplified_df[\u001b[33m'\u001b[39m\u001b[33mphase_over_2pi\u001b[39m\u001b[33m'\u001b[39m] -= simplified_df[\u001b[33m'\u001b[39m\u001b[33mphase_over_2pi\u001b[39m\u001b[33m'\u001b[39m].iloc[N//\u001b[32m2\u001b[39m]\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/indexing.py:1192\u001b[39m, in \u001b[36m_LocationIndexer.__getitem__\u001b[39m\u001b[34m(self, key)\u001b[39m\n\u001b[32m 1190\u001b[39m maybe_callable = com.apply_if_callable(key, \u001b[38;5;28mself\u001b[39m.obj)\n\u001b[32m 1191\u001b[39m maybe_callable = \u001b[38;5;28mself\u001b[39m._check_deprecated_callable_usage(key, maybe_callable)\n\u001b[32m-> \u001b[39m\u001b[32m1192\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_getitem_axis\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmaybe_callable\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m=\u001b[49m\u001b[43maxis\u001b[49m\u001b[43m)\u001b[49m\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/indexing.py:1753\u001b[39m, in \u001b[36m_iLocIndexer._getitem_axis\u001b[39m\u001b[34m(self, key, axis)\u001b[39m\n\u001b[32m 1750\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[33m\"\u001b[39m\u001b[33mCannot index by location index with a non-integer key\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m 1752\u001b[39m \u001b[38;5;66;03m# validate the location\u001b[39;00m\n\u001b[32m-> \u001b[39m\u001b[32m1753\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_validate_integer\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkey\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 1755\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m.obj._ixs(key, axis=axis)\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/indexing.py:1686\u001b[39m, in \u001b[36m_iLocIndexer._validate_integer\u001b[39m\u001b[34m(self, key, axis)\u001b[39m\n\u001b[32m 1684\u001b[39m len_axis = \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.obj._get_axis(axis))\n\u001b[32m 1685\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m key >= len_axis \u001b[38;5;129;01mor\u001b[39;00m key < -len_axis:\n\u001b[32m-> \u001b[39m\u001b[32m1686\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mIndexError\u001b[39;00m(\u001b[33m\"\u001b[39m\u001b[33msingle positional indexer is out-of-bounds\u001b[39m\u001b[33m\"\u001b[39m)\n", - "\u001b[31mIndexError\u001b[39m: single positional indexer is out-of-bounds" - ] + "data": { + "image/png": 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0wG+//Ya7777bKyjMDoMzBlbffvutOTEIGj9+vPv2w4cPY/jw4fj1119N9pDvKzfccIPPq3IwILvrrrtM1pGlTl7OC/4NDz30kAlc69ati1tuucXMPUi8rmPHjmbOTQZ68+fPR/fu3c1UNgzk+Jh8bD4uTyxTZ7Zs2TL06tXLBLKrVq0yQS6fXzuwtDHIY0aVzz9ft3vvvRfr16/P098iwaGJhUVEonxy7VDzdTJvllm5nyxDZoXXM8u0Z88ed4n0qquuwoMPPujehtkmT2+//Tbq1auH5557zlzm+dWrV2Ps2LE57gsDMwYvzDxR3759TeBm/x6bGTy9//77KFu2rHmOfRm/V7p0aZM9s0udecVgrlu3bub8mDFjTCaN5en69evj3//+twmy/vOf/7i35+02PiYfO6fHffHFF01QaAfJDBr5t/F5ZJbPdu2115pAjh555BG89NJLmD17tnmeJbyUuhARkbDyNaNHDFxywmzRxRdf7HVd69atc71flhPtYM5efspeisoOPpkVq1mzpin3cntKSkpCKDRt2tRr38jePztDdz7Wrl2L9u3be13Hy/y77UmrM+8Hg3YGiZ7Pk4SPMnQSlfht23PpL5VdJdbww5b/++FY+svXgfa1a9c22zKYYPkyM17P8WDMhNmKFSuGYGDp2BP3y7OcyhImu2/fffdd043L25iZY2PG+eDjZA5os1opwXP/7OfX3r/M5epgyu15kvBRhk5EJArxg9ZuWgj1ydeAjs0FV199tSkVHj161Ou2Xbt2YeLEiWaKkbx0YrL0x3FunpYuXYrzwelTmPl77LHHTCbMLgUHAoNVjmuzMSPG+eryglkzloezw5KrZ5YtK/yb2FjhiZdZemUnsUQ+BXQiIhI2r7/+Oo4fP266MtkByjnp2FHKQK9y5cq5jn3LjE0Q69atM+O7ONfcZ5995h7Y7+8UHcwSMvhkRyfHrf3000+mQSIQOCaQzwGbDBiI3nPPPedkwXIzcuRIE7RybNvvv/9u/v4333wTe/fuNbezPLx48WIz3pDXZZVR47hEBoXsIubzxs5g7hfH7okzKKATEZGw4fQiDGQ4No1dlrVq1TLTkXCKDnZsspkgL2rUqIEpU6aYLlJmrhjY2F2unI7DH8w6Tpo0yXSCssz6wAMPuJsuzhe7Rtl1etlll+HWW281AZS9SL2vmEXjtC/s6uV4QXa1fvXVV+65+XifzLKxBM+MYFbj/i666CIT/PLv5N/4xBNP4Mknn/RqiJDIls+Vl9GoDpeWlmbmFzp48KDmJ4tyGkMnsYbj2ThlBwMajmkLtpzG0EUaZvk4WTGzf+LM/+GUlDRUqVICyckHkZio+UWzoqYIERGJKhyTx05Xlkk5DozZtCFDhoR7t0SCSgGdiIhEFTYWPP3002biYk4uzvFhHGcmEs0U0EnUuvDCC8O9CyJRLVKnA+JktzyJxBIFdBK1HzT2xJ8iEngcM+dvk4GIBF5kfr0SEREREZ8poBMRERFxOJVcJWqnLeGyQfYM6JE61kfEqZw0bYlILFBAJ1ErhqZYFBGRGKe0hYiIiIjDKaATEZGINWfOHFPOPXDgAJyE+zxt2rSA3R+79l9++WUE0xVXXIH7778/qI8hwaOATkRE3E6fcWHhpn34auV285OXgxn05HQaPXp0xL8y3MfmzZufc/3OnTtxzTXXhGWfJDZpDJ2IiBjTV+/EmG/WYOdBq9mBKpYojFHdG6Jr44oBf5YY9NgmT55sFoRfv3691+Tgv/76a1henRMnTiAuLs7v369QoUJA90ckN8rQiYiICebu/WS5VzBHuw4eM9fz9kBj0GOfSpQoYbJyntd5rvaybNkytGrVCkWLFkW7du28Aj/66quvcNFFF5mO25o1a2LMmDE4deqU+/akpCRcf/315j6LFy+OXr16ITU19ZxM23//+1+vxeFZ6r3zzjtRtmxZ83tXXXUVfvvtN3PbBx98YB6Hl+2sIq/LquSakpKCW265BaVLl0axYsXM37J48WJz26ZNm8y+lS9f3uwf16H98ccffX4eZ8yYYfY3c1l62LBhZn9p37595vErV65snsMmTZrg//7v//JcNi5ZsqT7b6Tk5GTzXPJ6/m38O7Zu3epVMm/durX5m7lN+/btsW3bNp//NvGdAjqJWnzT4klEcsayKjNzWRVX7et4e+byK6cDCtWUQI8++iheeOEFk7ErUKAAbr/9dvdtP//8M/r162cCmDVr1uDtt982QcfYsWPd0xgx0ODarnPnzsXMmTOxefNm9O7d2+sxNm7ciC+++AJffvklVq5caa67+eabsXv3bnz//fcmqGTQ2LFjR3Nf/H2uE9uoUSOTbeQp833SoUOH0KFDB2zfvh1ff/21CQD/+c9/mv2yb7/22msxa9YsrFixAl27dkX37t1NEOoL7g+DJe677fTp0ybr2adPH3OZU8y0bNkS3333HVavXo1Bgwahb9++WLJkCfx18uRJdOnSBfHx8eY1+OWXX0xAyv1nhpMBdY8ePczf/vvvv2PhwoXmcTXFTXCo5CpRiR8y/JYuIrlbsmX/OZk5TwzjeDu3a1srISxLfzE4Y2BAI0aMQLdu3UyQwswUs2S8rn///uZ2HvtPPfWUCZpGjRplAqVVq1Zhy5YtqFKlitnmo48+MoHY0qVLTUaMGITwembjaP78+SbgYUBn/63PP/+8yVpNmTLFBCcMYBhg5lRi/fTTT7Fnzx7zWMxiUe3atd23N2vWzJxs3PepU6ea4G/IkCG5Pjf58+fH3//+d/M4d9xxh7mOfzMzdjfeeKO5zMzcQw895P6d++67Dz/88AM+++wzk0HzBwNGBqXMatpB2oQJE0xwycwcs5AHDx7E3/72N9SqVcs9L6gEhwI6EZEYtzv9WEC3C4amTZu6z1esaI3nY6BVtWpVk/FidsjOyNkZKgZ8R44cMZOMM5Czgzlq2LChCTx4mx3QVatWzR3MEe+X2bOEBCuItR09etSUSX3FbF+LFi3cwVxmfAyWfJk9Y5aPmS0+hq8ZOmIm7pJLLsGOHTtQqVIlTJw40QS9/Bvt5+OZZ54xARwzhQxejx8/fl5VDD4/zGoyQ+eJzzufn86dO2PAgAEmi3f11VejU6dOpjxrv34SWAroRERiXLn4wgHdLhgKFizoPm9ngzxLlszS9ezZ85zfs8fC+YLjvDzxfhl8MNuUmR0o+aJIkSI53s7MGcvAzP4xc8ftb7rpJhN0+YpBKbNgkyZNwr333msyfJ5j3Z577jm88sorZuoTjp/j38opSnJ6DD7PmSdoZ5nV8/lhGZfBY2Z2YMyM3dChQzF9+nST0XvsscfM38rgU2I0oHvzzTfNyR5syVQ5O6LUFi5Z4Ru9PWi6Xr16WvpLJAeta5Q23axsgMhqHB3DpwolCpvtInHpL45r4/HuWcb0xDIfB+/zZGfpONaOJUlm6nK63127dpmSKueBywo7YZn9yi27yLIkx91llaVjdpGZrBtuuMEdKHk2FuQlS8fgKjEx0bznMUPn+RgcR3jbbbe53yP//PPPHP9+BmWencgbNmwwGU/P54dBWrly5UzDSHaYneRp5MiRaNu2rSkNK6CL4aYI/oOOHz/eDErloFh27vCf848//gj3rkmE4ptsbm+0IgLkvyCfmZqEModl9mXezu0iEb/cc+wbs3T8TGAZlZkqZoOIpT5mpRjwLF++3IyLYxMFx+RxnFd2+HsMQDiwn52kDLIWLFhgGjTs6VQY6HFsHsuqe/fuNWXMzNhdyjF2vB8GVmzIYAMDmwSoTp067kYMljFvvfVWd/YxL+y/j6VnZvg8xzjyMZgZ4/7z+bn77ru9unyzws/Z119/3TRq8O+95557vDKlfLwyZcqYz2I2RfB5YDaTGTl29fIygzj+nexs5XPIoFDj6GI8oGPHD7uA+E9Zt25d8w/LwaiLFi0K966JiDge55l787aLTCbOEy/z+mDMQxcoHKP17bffmoCBpUdmf1566SUzJo6YPeS0JqVKlcLll19uAjU2TjC7lBP+3v/+9z/zOwMHDjSfPWw+YHDCKUaITQfs6rzyyitNRiurqUCYxeO+MZPFzzEGl0xQsJmBXnzxRbNvnI6Fn3X8e5j9yitmKNngwI5Su7vVxuCW98n75ooQdoCZE3YVM6N52WWXmSCTpWHPMXc8P2/ePDOOkeVuBmpsymDmlhk73r5u3TrzHPG5YxPJ4MGDTTApgZfP5cAVzJl1+fzzz01HE785ZJcy5jclz29LaWlp5p+TXTc5pYfF+fjtliUV4v9HqKZWEAkXfogyI+I5h5o/ODUJu1nZAMExcyyzZpWZi6SSq0T//3BKCj+/SyA5+SASE/X57egxdMS2c6a/+aIzO8dBnznV/8eNG2dS8CIi4hsGb/bUJCLiHI5KW3BwO8cYcHZtdvEwQ2dnYbLC2j2zcfaJA2JFREREoo2jMnQch2B3MbFVmpM0sg2bs4JnhQNCQznxpYiIiEg4OCqgy2qcVFYdRSK+zP0kIudH4+ZEIodjAjqWTznnHLtp0tPTzTw2bI/m0iUimbEJwl5qRkSCE8ydT/OFiMToGDou8cJ5gziOjgsRs9zKYI7LiYiIiIh4euMNzhPILmygTRtgyRLk6MABYPBgLi3HIVtA3brA//4Hx3BMhu69994L9y6IiIiIA0yeDAwfDrz1lhXMvfwy5ysEuIBQuXLnbs8V0Jgf4m1TpgCVKwPbtnGJNziGYwI6kbyOr+SM5MTJqDUPnUhgcR46ewwzm880nk4iyYsvAnfdBQwcaF1mYPfdd8D77wMjRpy7Pa/fvx9YsIDrBlvXZbPaW8RyTMlVJK+4iLTnQtIiEvigzoFz00uUO3ECWLaMS7dlXMe55Xn57Gpr5/j6a6BtW6vkykVAGjcGnnmGCxnAMRTQiYiIhAmX4br//vvP6z4GDBiQ6zJe0SI9nas+ZZyymuhi714rEDu7OpsbL+/alfX9bt5slVr5exw39/jjXPoMePppOIYCOhERyXDmNLDlZ2DVFOsnLwcRgxGWa7nwe2Zc95O3cRsR4uJQJUpknMaNC8zzcuaMNX7unXc4zy3Quzfw6KNWqdYpNIZOREQsa74Gpj8CpO3IeEaKVwK6Pgs0vC5ozxLX2J40aRJeeukl9/yRXOKR01NxqqpId+LECTPxvQQfF4diw4Itq7UDypQB8ucHUlO9r+flChWyvl92tnLsHH/P1qCBldFjCdcJL68ydCIiYgVzn/XzDuYobad1PW8PkosuusgEdV9++aX7Op5nMNeiRYtzGp64TjcXcGfw16xZM0xhreys06dP44477nDfzqmuuKKQJ85h2rp1axQrVgwlS5ZE+/btsY0tjdmUL1kSZWnUxvNDhgwx15cpUwZd2D4JYPXq1Wa+VK41Xr58efTt2xd7Wf876/Dhw2b6Ld5esWJFvMCaXi5Gjx6N5s2bmxWR+BwVLVoUvXr1MstZZvb888+b+01ISDDZTc8xxB9//DFatWqF+Ph4VKhQAbfeequZDsz2119/oU+fPihbtqx53thMNmHCBPftXDqTj8vnq3Tp0rj++uuxdetWn57TQIqPB4oXzzhlFdDFxVlZtlmzvDNwvMxxcllp3x7YuNHazvbnn1ag54RgjhTQiYjEOpZVmZlDVg0OZ6+bPiKo5dfbb7/dK4B4//33MdBuUfTAYO6jjz7CW2+9hT/++AMPPPAAbrvtNsydO9f6U86cQWJiIj7//HOz1vcTTzyBf/3rX/jss8/M7adOnTIBW4cOHfD7779j4cKFGDRoUJ67dD/88EOTlfvll1/Mvhw4cABXXXWVCUB//fVXTJ8+HampqSYIsj388MNmP7/66ivMmDHDBEHLly/P9bE2btxo9v+bb74x97tixQr84x//8Npm9uzZ2LRpk/nJffvggw/Mycbg7qmnnsJvv/2GadOmmWDMs5T9+OOPm+fr+++/x9q1a/Hmm2+aYNX+XQatDAZ//vln8zczKO3atavJTgbqOQ2k4cOBd9/l6wSsXQvcey8D6oyu1379uGBBxva8nV2uw4ZZgRw7YtkUwSYJx3DFkIMHD/KdyfyU6Hb69GnXn3/+aU48LxLtjh496lqzZo35mWeb57lco4rnfuJ2Z505c8Y8Fk8876/+/fu7rr/+etfu3btdhQoVcm3dutWcChcu7NqzZ4+5jdvQsWPHXEWLFnUtWLDA6z7uuOMO1y233JLtYwwePNh14403mvP79u0znwNz5szJcX88DRs2zNWhQwf3ZZ5v0aKF1zZPPfWUq3Pnzl7XJScnm8dav369Kz093RUXF+f67LPP3LdzX4oUKWLuPzujRo1y5c+f35WSkuK+7vvvv3ddcMEFrp07d7r3uVq1aq5Tp065t7n55ptdvXv3zvZ+ly5davaN+0Xdu3d3DRw4MMttP/74Y1e9evW8Xufjx4+bff/hhx9yfU4D8T+cnGx9fvOnr157zeWqWtXliotzuVq3drkWLcq4jS/n2X8rN/5btWnjchUq5HLVrOlyjR3rcnk8pRFPY+gkKnHeOZYMRMQHh1LzvF2gl/5iqa9bt24mq8SpUHjezhB5ZqqOHDlyzgpBzBJ5lmbfeOMNk+FLSkrC0aNHze0sWxLLhcxMMePE++nUqZPJorFUmRctWdPzwMwXs2PMXGXGzJm9H204y+1Z3BeWhHPD0nNlj4Fjbdu2NZnI9evXm/IpNWrUCPk9BoDx71m1apX78rJly0z5lvvJ8ip/n/gcNWzYEPfeey9uvPFGkzHs3Lmzybi1a9fO/bfxuWeGzhPHOfJv4/aBeE4DbcgQ65SVOXPOvY7l2EWL4FgquYqIxLoLywd2u/MouzKgY8mQ5zM7dOiQ+fndd99h5cqV7hNLhfY4OjZXPPTQQ2YcHcuavJ2lWwZTNpZ2WRZkwDJ58mTUrVsXi85+kvPLYOa59bKaz5JjxTLvW/fu3b32iydOcH755Zcj2Aras+F6BNx20Maxewy2ihcvjokTJ5qlM6dOnWpus58Xjv3jmDeWsHfs2GGW2OTzaP9tDGAz/21//vmnGYuX23MqoaEMnYhIrKvWzupmZQNEluPo8lm3c7sgssdkMRixGw08MZPEVSmYVeJ4raxwfBeDCs8xZswiZcaMHk8jR440GS921F5yySUmU8jmBk8MXjIHTFk1dnzxxReoXr06ChQ496O1Vq1a5j4WL17s7txlpoxBUXZ/i41/L4OsSpUqmcsMlBh4+pLdo3Xr1mHfvn0YP368aawgjvPLjH97//79zemyyy4zY/7YaMG/jUFauXLlTFCYneyeUwkNZegkqpf+4sn+lioi2bggvzU1iZF5IPvZy13HW9udxSwWS248BWq1CJYMOSCfGTfP8qGNJT9mjZhFYhaPgRpLhK+99pq5TBxqwWDlhx9+MMESB/szI2XbsmWLCTiYTWJGilk8vk804BwVgGls4O+z8YLXjxo16pwALyvsKt2/fz9uueUW83jcN+4Ds4PsvGUplllDBkk//fSTuU+WKX1ZlpClbQZZLH2yKWHo0KGmpGmXW3PDAJINHHyeNm/ejK+//to0SHhi8wibNVhaZbPJt99+635O2P3K8jc7W/n4fA7Z0MH9SElJyfU5ldBQQCdRi+tM2mtNikguOM9cr4+A4pnGPTEzx+uzmIcuGEt/MQOUUxaIgQiDNHa7MmBgVo8lWE5TQnfffTd69uyJ3r17m/FqzEx5Zus47QczVhwvxrIguzEZjPH3iJlB3v8///lPXHzxxUhPTzdTjeSG2TNmBxm8cUxZkyZNzLQmnMLDDtqee+45k/liaZbjzC699NJzxuJlpXbt2uZvuvbaa819N23aFP/5z3/gK2beWMpm5y+znMzUMfPmiQEfgzLeN0vEDKhZvrafs3nz5pnAkPvB553BKYN5vla5PacSGvnYGYEYkZaWhhIlSpj5e3J6wxDnY1aO3/KJb2C+fAsWcTJ+uDJTwsDmvJoVODXJtgVWAwTHzLHM6pGZy5yhIz5eOKeoiGZsZOA0Iyz7xvL/cEpKGqpUKYHk5INITNTnd1Y0hk5ERDIweKtxmZ4REYdR2kJERETE4RTQiYiIRHDJNRbKrXL+FNCJiIiIOJzG0EnUym3eKJFoFMo+NzVCSCDFUI9mUCigk6iUl0k3RaKBPW8bJ+YtUqRI0B8v0Et/iXBZN9KXcf8ooBMRiQJcnYDzge3Zs8d8IGqqHnFSZo7B3O7du828fVlNKi25U0AnIhIFmDHjYuicx4uz9Ys4DYM5X1e/kHMpoJOonViYH2zESSqVrZBYwNn+ufSV50L0wTzGuOwTJSYm6hiT88KssjJz50cBnUSto0ePhnsXREKOX15CMbaNAZ0dOPLx9KVJJLw0bYmIiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJy6XCVqqQVeRMeYSKxQQCdRiVMoNGjQINy7IRK1dIyJRBaVXEVEREQcTgGdiIiIiMOp5CpRibPYb9261ZyvXr26ZrEX0TEmEtUU0EnUOnLkSLh3QSSq6RgTiRyOKbmOGzcOF198MeLj41GuXDn06NED69evD/duiYiIiISdYwK6uXPnYvDgwVi0aBFmzpyJkydPonPnzjh8+HC4d01EREQkrBxTcp0+fbrX5Q8++MBk6pYtW4bLL788bPslIiIiEm6OCegyO3jwoPlZunRpvwbM85Td3Eqe2+VE2+b9eciXL585BXtbz+0z/24o9sHlcplTtGzr+TpH87ak496358GTE98jwr2tE477SHmPOHXqFNLS9uS4jTg0oONBc//996N9+/Zo3LhxttsdP37cnGxpaWnm57p163DhhReesz2vY0ekbe3atdn+oxUtWhQ1a9Z0X+Z4vtOnT2e5bZEiRVCrVi335Q0bNpiScVYKFSqEOnXquC9v2rTJ62/wVLBgQdSrV899ecuWLTh69Gi2qyZ4TrTLDtDsBjTzAG7UqJH7clJSEg4dOoTseL4GKSkp7uc5Kw0bNnS/QezYsQMHDhzIdtv69eujQAHrX3TXrl3Yv39/ttvWrVsXcXFx5vzu3buxd+9e9218vT3Vrl0bhQsXNuf37NljTtnha8zXmvbt24fU1NRst+X/jv1/xX3duXNntttWq1bNjAclPgfbt2/PdtsqVaqgRIkS5jyf2+Tk5Gy3rVy5MkqVKmXO8zXbtm1btttWrFgRCQkJ5jyHLthdwVkpX748ypYta87zf2zz5s3ZbsvtuD3xf3fjxo3ZblumTBlUqFDBnOcx8eeff2a7Lb+8VapUyZznsZb5dfVUsmRJJCYmmvM8htesWZPttsWLF0fVqlXdl3PaVu8RFh7Dnu8nPO6d/B6Rmd4jIuc9gp9zfG/I6f9LHDaGzhPH0q1evRqTJk3KtZGCH4T2iR+MIiISGJ4ZHJFgsJMfhQpZX6wle/lcueU6I8yQIUPw1VdfYd68eahRo0aO22aVoWNQ99dff5lv5VlR6SW4z0OklT1UTgl/OSWStiWVXMP7PETasaz3iOC/Rxw7dswMo2I2luVVz+wcs+2sOuzefQxVqpRAcvJBJCZm/fkd6xxTcuWLft9992Hq1KmYM2dOrsGcXb7kKat/JM83mOz4so221fNwvpkLbRs5zwPpuNfzEIr/h0j4fw/nthw2YQdxnsN/+ByyosYgjsOVMu7nmE+PHcsKOKnM+umnn5rsHMcecbwE8YXniy4iIiKRnZjhWDgGcayYeWbxOD6V2ThWz/ISGIsDS67ZRfsTJkzAgAEDfLoP/gMxAOS3guxKrhIdWCZhMwdxwLveIER0jEl4cOgThzplLqmygsYgjieWV3OSksIhUyq5RkWGziFxp0QQdUWJ6BiT8GBJlQEcT56zL3DGBSZWGMR5l1QlZgI6ERERifySKrNx6enpXokYDpViEMefqpgEhwI6ERER8Ru7VBnEcTiTZ0mV833aJVV7vkAJHj3DIiIikicM3BjAMZBjQOdZUrWDODUshpYCOhEREfGp2cyzpGrjODjPkqrGxYWHAjoRERHJkj3xr93g4LnEJUuqnC+OTQ4qqYafAjoRERE5Z8ktu6TqueISAze7pGqviS2RQQGdRCV2UXkuCC4iOsYk95IqS6nMxGVVUmU2jhMAq6QamRTQiYiIxHBJlfPEMYhjRs6zpMqmBrukymYHiWwK6ERERGKwpGqPi8tcUmUQx5JqVmuhS+RSQCdRWzpISUkx5xMTEzWRpYiOsZjH90UugckgznMlHZZQuRwmA7lixYqppOpQCugkavGNS0R0jMV6SfXIkSPukiqDOlvRokVNEMdgTiVV51NAJyIiEmVOnDjhLqnyvK1gwYKmnMpALi4uLqz7KIGlgE5ERCQKsKHBLqkePnzYq+vfLqkyK6cu1chw8iSwaxdw5AhQtixQuvT53Z8COhEREQeXVBm8MYhjMOdZUuV4OGbj2KXKoE7Cj7PBfPIJMGkSsGQJM6l8DTmOkeO9gc6dgUGDgIsvzvt9K6ATERFxGHam2iVVdqzaWEa1J/5VSTWyvPgiMHYsUKsW0L078K9/AZUqcXoYYP9+YPVq4OefraCuTRvgtdeAOnV8v38FdCIiIg4pqbKxgUEcGx1szL4xC8eSKueOU0k1Mi1dCsybBzRqlPXtrVsDt98OvPUWMGGCFdwpoBMREYmikiqX4GJJlZdtXLWBmTiOj1NJNfL93//5th2n/7vnnrzfvzJ0EpX4DbVhw4bu8yKiY8xpJVUGcczGnTp1yn09J/u1S6rsWBWxKaCTqMQgToGciI4xp5VU7XFxXI7LxjniWFJlEKeSqnP17On7tl9+mff7V0AnIiISJiyhctUGZuPS09O9Sqrx8fEmiONPlVSdr0SJjPN8madOta5r1cq6btky4MCBvAV+nhTQSVRi6/6OHTvM+UqVKunNUETHWEQ5duyYCeLY5OBZUi1cuLC7pMp1VSV6TJiQcf6RR4BevawGiPz5retOnwb+8Q+geHH/7l//LRK1WLawAzoR0TEWbgzcGMAxkGNA51lStYM4llQl+r3/PjB/fkYwRzw/fDjQrh3w3HN5v08FdCIiIkGsFtglVf60S6oc4+tZUtWY39hy6hSwbh1Qr5739bzOY27oPFFAJyIiEkAM2piBsxsc2OzgWVLlfHFsclBJNXYNHAjccQewaZM1/xwtXgyMH2/d5g8FdCIiIgEqqTKAYzaO0464P2gLFHCXVBnQiTz/PFChAvDCC8DOndbzUbEi8PDDwIMP+vf8KKATERE5j5Iqu1MZyPGnzS6pMhvHCYBVUhVPXFr3n/+0Tmlp1nX+NkO47/P8fl1ERCT2Sqpceoud9OvXr0dycrI7mGNTAxux6tevj6pVq2p8XBi98QZQvTrL3NbaqEuW+PZ7kyYxIAd69Aj+OLoff7RWkLDnv+fkDIcO+Xd/ytCJiIj44OTJk+5xcVmVVJmN40oOEn6TJ1sdo5wWhMHcyy8DXboA69cD5cpl/3tbtwIPPQRcdllw92/bNqBrVyApiauCAFdfzXkHgWeftS5zv/NKAZ1EJZY3+A3ZPi8iOsb8LalyDVUGcexS9XyP4RqqDOKKFSum95kI8+KLwF13ZTQYMED67jtrupARI7L+Hfau9OkDjBkD/PyzNclvsAwbZk0o/NtvQEJCxvU33GDttz8U0ElU4putOshEdIydT0mVQRznjWNQZytatKjJxrFLlfPHSWixsm2POSMmRDMnRU+csFZdGDnSe8xap07AwoXZ3/eTT1rZO3afMqALJt7/ggVAXJz39SwRb9/u330qoBMRETGBwAl3SZXnbQULFnR3qaqkGl4NG3pfHjUKGD3a+7q9e61sW/ny3tfzMud5ywon+X3vPWDlSoQEvyN4zGbjlpJilV79oYBOohK/Ue/atcucr1Chgpb+EtExliXOEWeXVA8fPuy+nmunsqTKIE4l1cixZg1QuXLG5UAMWUxPB/r2Bd59FyhTBiHRubM1ru+dd6zLHBnEij4D1Guv9e8+FdBJ1Nq/f787oBMRHWOeJVUGbwziGMx5llQZvDGIYzCnkmrkYfYqt+k9ypSxltFKTfW+npez+jjg5L5shujePeM6+1+Cy+mykaJWLQQU559jkwYzjlwF7tZbgQ0brH1n16s/FNCJiEhMYGeqXVJlx6otLi7OXVLleXG2uDigZUtg1qyMqUcYoPHykCHnbs/+uVWrvK977DErc/fKK0CVKoHfx8REqyGC3bj8yewcx+6xKcPf5XwV0ImISNRiSZWNDQzi2OjgWVJlYwODODY6qBs+ugwfDvTvb3WScmktljdZUbe7Xvv1s0q348ZZ89Q1buz9+yVLWj8zXx9IzP4xgOMpIPcHB5k3bx6ee+45LFu2DDt37sTUqVPRI9gz/4mIiCNLqlyCiyVVXrZx1Qa7pMqgTqJT797Anj3AE08AHE7dvDkwfXpGowTnfwvny8+S8OWXA198AZQu7V0WrlQp64aJqAroeIA2a9YMt99+O3r27Bnu3RERkQgrqTKIYzaO66ra2Jlql1TZsSqxYciQrEusNGdOzr/7wQcIKn7H4ATCzCB+8w3QqJH3bf5wVEB3zTXXmJOIiIhnSZWB3NGjR91PChsa7JIql+NSSVUiCbtamZ0bPx5o2xb4+GPg+uszbov6gE5ERIQlVK7awCCOa6h6llTj4+NNEMefKqlKpOK/LMuubLpgdo4lYjZi3Hmn//dZwN+09uLFi7Ft2zYzyLRs2bJo0aIFatSogUjC/fRcb49jKSQ28Nt43bp13edFxPnH2LFjx9xdqplLqlyCixk5lVTFaQYNAurUAW6+mb0CIQrofvnlF7zyyiv45ptvTMs3Dx6msjnfFwOnmjVrYtCgQbjnnnvMt6NwGzduHMZwUTaJOfyA0fQDIs4/xhi42SVVBnSeJVV7XFzhwoX1xU0cpVo1K0Nnu/JKYNEi77nw8srnHo/rrrsOvXv3RvXq1TFjxgyT5t63bx9SUlJMlm7Dhg147LHHMGvWLPOtbebMmQi3kSNHmjcC+5ScnBzuXRIRkVywhMqKSlJSEtavX29mNWAwxyCS3alVq1ZFvXr1ULFiRY2PE0fasgVISPC+rnZtYMUKYPPmIGfounXrhi+++CLbdDazczz1798fa9asMQdguDENr3X3YhNnft+9e7c5X65cOY2lEYnwY4xBnGdJlc0ONmbg7JJqAU7eJRKlChe2snf+8PnIuPvuu32+04YNG5pToHEQ7MaNG92Xt2zZgpUrV6J06dLmG5uIp71cofnsh42IROYxxpKqHcR5llQZuHmWVEWcrnRp4M8/reW9SpXKuZv17MqVeeKorzq//vorrmSh+azhnAoanA26Pz4I9qQxIiISsOweh+0wiONPG0uqHH/NbBwnAFZDk0STl16y1qIlrlwRaD4HdDzAfD247EXRA+2KK67wak8XERFn4Hs354ljEMcxzZ4lVTbX2SVVNjuIRKP+/bM+H/KA7mWPcJLNEE8//TS6dOmCtpwRD8DChQvxww8/4PHHHw/8XoqISEQ5feoUiu1ejgLH9mHtgS2of8k1yJ/F+DbOiGCXVD2nkbJLqgzkNNZZYkFaHmZOK1487/efz+VHyuvGG280pc8hmdbUeP311/Hjjz9i2rRpiETsmuI3QH47ZKeURHdJh805xPGcmmBUJHBW/PAhKi8ag3Kufe7rUpGAHW1HoUWX/ub44/stgziOfbbZXaoM4ooVK6aSqvgsJSUNVaqUQHLyQSQmOvPz+4ILcl8FghEZtwnZWq7MxD377LPnXN+1a1eMGDHCn7sUERGHBHPNFgy1Lnh8OJV17UPZBUMxL/0QyjS80gR1tqJFi5psnEqqEstmzw7u/fsV0CUkJOCrr77Cgw8+6HU9r+NtIiISnWXWSgutydovyJRp4OUzLqDu6heQWqc9Chcu4u5SVUlVBOjQIQIDOq6+cOedd2LOnDlo06aNuY5LgU2fPh3vvvtuoPdRJM9Y2qnNWRq19JdIwKxb/AMaYZ9XZi5zUFcB+7Bj32bUvfIGlVRFcnHkCJCUBJw44X1906YITUA3YMAANGjQAK+++iq+/PJLcx0vz58/3x3giYQ7oNPcVSIBXr0hdatP2545slfBnEgO9uwBBg4Evv8+69tDNoaOGLhNnDjR318XEREHYGeq3aV6+Ewhn36nSKnKQd8vESe7/37gwAFWNzklGzB1KpCaCjz9NPDCC/7dp98B3aZNmzBhwgRs3rzZTGnCmcK///57s2JDo0aN/L1bkYDggOw9/ArEwdply6rLVSQPOEccZwNgEMe1um3l67VG6uoE0wCReQydOe5cwO58Cajfpoueb5Ec/PQT+w6AVq2s7lcu93X11dZ0JePGcblV5Jlfi+/NnTsXTZo0MePmuL6r3Zb+22+/YdSoUf7cpUjAMaCzgzoRyb2kyvfy5ORkrFu3Djt27HAHc1y1ITExEY0aNTZTk9jBmyf78s62o7Kcj05EMhw+zCXzrPNcBsz+qGrSBFi+HH7x66jj1CScWJhLb3GZFttVV11l5qITERHnlFT/+usvk43juqo2dqbaXaoFCxZ0X8955lYA58xDx8wcgzneLiI5q1cPWL8eqF4daNYMePtt6/xbbwEVKyJ0Ad2qVavw6aefnnM9y672Ys0iIhLZJVUGclyOy8ZltzhXHIM4LseV3XKPDNpOXnkLtsyfZFaKSCte26wUUUGZORGfDBsG7NxpnWdhs2tXgG0JcXGAv0vT+xXQ8WDfuXMnatSo4XX9ihUrULmyBsOKiERqSZVBXHp6ute62Ky08H2dP31dVYVl1cPlLjLntRqLSN7cdlvG+ZYtgW3bgHXrgKpVgTJlELqA7u9//zseeeQRfP755+YbHAeg//LLL3jooYfQr18///ZERETyPNEv54Y7+td201nKZoTM49eOHTvm7lLNXFLlElzMyHmWVEUk9IoWBS6yvh/5za+A7plnnsHgwYNRpUoVk7rntzP+vPXWW/HYY4+d3x6JiIhPS3Bx1QYz0e9ZqTOt9VSbdOzjLqkyoPMsqdrj4jhPY3YlVREJLibIp0yxlgPbvZszM3jffnaK3+AHdHFxcWZFiCeeeMKMp2Mav0WLFqhTp44/dyciIgFcT/XHvXtRqVnG1CEspTIbx25VX0uqIhLceejYCHHllUD58pwM//zv06+Abt68eahfv77J0PFkO3nyJBYuXIjLL7/8/PdM5Dww81CzZk33eZFYWk+16YY3cLBlN5QpW9aUVAsEoVlBx5iI/z7+2MrCXXstAsavr2pXXHEFmjVrhkWLFnldv3//flzJcFMkzPhhU7RoUXNSQCfRhGPmyiPriX0911M9tW8TEhISghLMkY4xEf+VKAGczTkEjN+5dzZGdOzYER9k6q/17JwSEZHAYPMZx8XtTlrn0/ZslBCRyDR6NDBmDOAxa9B5K+DvN7ORI0fisssuM12tv//+O144u/iYsiESKR9++/ZZg8WZpdC4IXEifkHmPHHsUGUwx+az0wVLRMR6qjrGRPzXqxfwf/9nrRbBCYUzN5r7s1qEXwGdnYXr2bOnmYvu+uuvx5o1a/DKK6/4c3ciQZHKlY7PBnQiTsLxyPZUI1zJwcbyaYNLuiJ19TMRsZ6qjjER//TvDyxbZs1HF9amCE/sbl2yZAl69OhhSrAiIuJfxistLc0Ecfb62HbVo3jx4qZLtVixYubyirajTDcrgzfPoM5zPVWt2iASub77DvjhB+DSSwN3n34FdP379zfLwtgqVKiAuXPnYtCgQaYDVkREfC+pcr44llQZ1NnY0MP54tilyvnjPNnrqbLblQ0SNq2nKuIMnCCkePHA3mc+Vwx1MfDbL98c+cbJb7wSvfjByGEApGWJJNKcOHHCXVLleRtXbLAn/uVKDoFYKSJYdIxJKKWkpKFKlRJITj6IxMTiUZGhe+014K23rDF0geDzkc/Gh8aNG5vB5Tyfk6ZNmwZi30REIp6vQZXdpcog7vDhw+7r+Z7KL5gM4uySqq/4OI3adwvY3yIiocGxc0eOALVqWct+ZW6K2L8/iAFd8+bNsWvXLpQrV86c55uOZ3LPvsyf7MQSEYnl5bdYFuV74pEjR0xJlRUCz5IqgzcGcQzmMpdURSS6vfxy4O/T54Buy5YtKFu2rPu8iEgsy235rfmHj6Bso6tMx6rnsol2SZXnRST2nDwJzJ0LPP44UKNG4O5XY+gkKjEzYpe18lrGEvGlzLr36bq5Th2SesOXKFgwzozdZRAXTSuX6BiTUIq2MXQlSgArVwY2oPM5Q/f111/7fKfXXXedv/sjEhD80ORC5CLBwDFzpsyay/JbKXs2oslVPaNyYmsdYyL+69EDmDYNeOABhD6g4zxzvtAYOhGJdof2Jvm24bH9URnMicj5qVMHePJJ4JdfgJYtWUnyvn3o2dEcQQnoPAfzijihHLT/bJtQ6dKlo6bMJeHDZi92qbLBIf1kppa0MC2/FU46xkT89957QMmS1moRPHnix1VQAzoRp33Y7Ny505znDPsK6MTf/yOu2sCpRtilanf2l63TCqmrEyJi+a1w0TEm4r9g9Jb6HdBxwDlXh0hKSvKaGJOG+hNaiohEiGPHjrkn/j116pT7ek72yy8IbHJYvUvLb4nI+bNngDvfQpJfAd2KFStw7bXXmvmVGNixpLV3717TwcV56hTQiYjTMHCzS6oM6GycI86eaqRw4cLubK+W3xKR8/HRR8BzzwEbNliX69YFHn4Y6Ns3hAHdAw88gO7du+Ott94y31QXLVpklqy57bbbMGzYMP/2REQkDGXD9PR0k4njT8/J0uPj4002jt3S2TU2MKg73bEP/si0UkSFEC2/JSLO9OKL1jx0Q4YA7dtb182fD9xzD7B3r3/dr36966xcuRJvv/22eZPjt9fjx4+jZs2a+Pe//43+/fujZ8+e/tytiEhIHD161F1S9VzZhhk4u6RawMegTMtviUhecR3XN98E+vXLuI4zvjVqBIweHcKAjtk4+xsrS6wcR9egQQPzJpicnOzPXYqIBHU9VZZU7SDOs6TKwI3vXQzkGNCJiAQbe/batTv3el53tp8vNAFdixYtsHTpUtSpUwcdOnTAE088YcbQffzxx2jcuDGC6Y033sBzzz1n1pVt1qwZXnvtNbRu3TqojykizlxPtdnVfb1KqjaOg/MsqaoLWkRCqXZt4LPPgH/9y/v6yZOtOepCFtA988wz7jfHsWPHol+/frj33ntNgPf+++8jWCZPnozhw4ebsXtt2rTByy+/jC5dumD9+vUmUyhi4wd0tWrV3OclNtdT/WnfflRoerX7+iJFipjmhryUVCVrOsZE/DdmDNC7NzBvXsYYOk4yPGuWFehF/VquDOIuvvhivP766+7JjqtUqYL77rsPI0aMyPX3OY8U38jZyVa8uPPXghOJZb6up7rvpq+RUKaMycZx2hERcZ5oW8uVOKHwSy8Ba9eai2jQAHjwQVZB4RfHfEXlXHfLli3DyJEj3ddxHF+nTp2wcOHCLH+HzRo8eQZ0IhJb66nuO7gVFYI8FEREJK+45NcnnyBg/Aro9u3bZ8bNzZ49G7t37z5nWTB7yaVA4hg9dqOVL1/e63peXrduXZa/M27cOIxhXlNiDhPPHDdFLLGp7Bpdry27VPem/OnT9kf/2hH0fYpFOsZEzg9Dp40bgd27rfOeLr88RAFd3759sXHjRtxxxx0moIrUD0tm8zjmzjNDxxKtxMaHzfbt2815ltkj9X9U8palt7tUef5k/njE+nqq4aRjTMR/ixYBt94KbNuWsVKEjR9XHrMpBTeg+/nnnzF//nzTZRoqZcqUMXPepaamel3PyxUqVMjydzheRmNmRJyL2X+OeWUQx1VpPIdb1GnVKebXUxURZ7rnHqBVK+C774CKFc9/2S+/A7r69eubkkcoxcXFoWXLlpg1axZ69OjhfrPn5SGcallEoibzw2UFuQQXs+qeQzqKFStmSuhsauIXvBVttZ6qiDgPl/uaMsWaviRQ/Aro/vOf/5iuUo6j47xznGjYU7A6SFk+5UoUrVq1MnPPcdoSfmsfOHBgUB5PREKHZVQGcczGnTx50n0931/YocpAjl/sPGk9VRFxojZtrPFzYQ/o+MbKb85XXXXVOd+sOVbJcymdQOrduzf27NljAklOLNy8eXNMnz79nEYJEXEGvlfwvYSBHLNyniVVjn3ke03RokVzHAOp9VRFxGnuu8+aomTXLqBJE35x9b69adMQzUPH7Bgn5Rw2bFiWTRFcPSISaR662MEy3Zo1a8z5hg0bZru4uoR2+S3iWw4z63ZJ1fMtiKs22CVVvWaRTceYhFK0zUN3QRYfSQyl+HYY0qaI1atXY8WKFahXr54/vy4iMbT8FjNoxDkh7S5Vz5Iqy6h2STXz8A0RkWi0ZUvg79OvgI5j2JKTkxXQScRi1tieokZTloR3+a0FR4+hfJNOXo1UzL4xgOOJy3HpNXIeHWMi/ju7MmX4AzoutcVy68MPP4wmTZqc8626qT/FX5EAf9hwDJYEv8zKzBxlXn6Ll7n8Vs2VzyK1Rhvkz1/AlFSZjYuPj1dJ1eF0jImcf6fr7NlZTyz8xBMhGkOX1dgWHtzBboo4XxpDJxJYf/zyHRrNvDXX7Za0exctrrxBJVUR8Uu0jaF7913g3ns5xy7AqXQ9WxF4fvnyEGXotgSj+CsSQPxyYa/dywH2KukFx5F9KT5td8GJAwrmooyOMRH/Pf00MHYs8MgjCJg8B3QczMzpSr799ls0aNAgcHsiEuAPG47ztLtcFdAF9rlNT083zQ1pJ/P79Dtafiv66BgT8d9ffwE334yAyvNcDhwvd+zYscDuhYhEPDY17Ny5E+vWrUNSUpLJgJap3QqpSDBj5bLC63chwUxhIiIiFgZzM2YgoPyanGvw4MF49tlncerUqcDujYhEFB7je/fuxcaNG7Fp0ybs27fPjJHlPJQJCQmoV6++mZqEMgd19uWdbUdlOR+diEgwvfEGUL06ULiwtTLDkiU5j2m77DKgVCnr1KlTztufL64Q8fjjwIABwAsvAK++6n3yh1/vskuXLjVrqM6YMcN0uXJ9RU9ffvmlf3sjIhExYaxdUuVPG8vW7E5llyq7Ve0ytpbfEpFIM3kylwsF3nrLCuZefhno0gVYvx4oV+7c7efMAW65BWjXzgoAn30W6NwZ+OMPoHLlwO/fO+9wInVg7lzr5IlvrUPPzgQV9C7X3NZOnTBhAiKRulxjh2axzxu+DbCkyiDu4MGDXp3qnCeO88VxGhhm5s53pQiJDjrGJJK7XNu0AS6+GHj9desypwXh1KRccmvEiNwfj2+BzNTx9/v1gyP49W4bqQGbiOS9yclevYErOdgYuNkT/xbm11UfMHhr1L6bXgIRCRoWDc5OYGAUKmSdPJ04ASxbBowcmXEdZ1tjGXXhQviES0tzQZvSpeEY5/X1ec+ePVjP/CVgVo0oW7ZsoPZLRPzgS5aMmRVmqxnEHTp0yH09S6ic4oVBnGdJVUQkUjRs6H151Chg9Gjv6/butTJs5ct7X8/L69b59jicTqRSJSsIDIbbb8/59vffD1FAx4W1uVrERx99ZD4cKH/+/OjXrx9ee+01FC1a1J+7FQkYBiOVzw58iJXAJKf1VJt37mdKqn/99ZcpqdrHLfF4tUuqPI5FfBGLx5iE35o13mPaMmfnAmH8eGDSJGtcnY8FCr+mLfHEbODq1cCBA8BVV/l3n34FdMOHD8fcuXPxzTffoH379ua6+fPnY+jQoXjwwQfx5ptv+rc3IgHCDxgO3o8Vua2n+tP+v8x6qp7TD9kl1ULBeEeUqBdrx5hEhvh4Thaf8zZlyjDJBKSmel/Py1yVISfPP28FdD/+yGVMETRTp557Hb9nc/WIWrX8u0+/miLKlCmDKVOm4IorrvC6fvbs2ejVq5cpxUYiNUVItJZZ9z5d1wRvmddTtacP2Z0vAbt7TkXp0gkmiGNnurIqIhLNTRGtWwOvvZYRLFWtCgwZkn1TxL//ba3e8MMPwCWXICw4io2h1c6dIcrQHTlyBOUzF6fBVuBy5jaRcOP3FHt8WLSPB+OYOVNmzeZPZJBXAfuwJy0JiU2bhXr3JErF0jEmzjN8ONC/P9CqlRXYcdqSw4c5S4d1OztXWbodN866zGlKnngC+PRTa+66Xbus6zm1CE+hsmkT5//073f9Cujatm2LUaNGmTF0dgccx+eMGTPG3CYSCR8227Zti/qlv06cOIH92zf6tO3xA3585ROJ8WNMnKl3bzZuWkEag7PmzYHp0zMaJZKSrM5XG0eKsTv2pptyb7oIVMDpibVSZuW++84KREMW0L3yyivo0qULEhMT0ayZ9Y3/t99+M8HdD8xVikjQcI44Dh9ggwMz4scv8J7YOztaT1VEYsmQIdYpK2x48LR1K0JqxQrvywwuOVEIV43IrQM2oAFd48aNsWHDBkycONGs60i33HIL+vTpYyYhFZHAZ0PYXc4gjsGc59DX6s06IHV1Qq5j6LSeqohIZJg9O4LmoeNUB3fddVdg90ZEvHCyX3viX04CbIuLizMdhpxqhOdXtB1lulkZvHkGdZ7rqVbQqg0iIlHL74COGTp2te7evdtrTit6gkVrEfG7pMq54piN49hU2wUXXOCeaoSZcM8xS1pPVUQktvkV0L377ru49957zfQlFSpU8Ppg4XkFdCL+dQwyE5e5pMoOQmbj4uPjTVCXHQZ1pzv2wR+ZVopQZk5EJPr5FdA9/fTTGDt2LB7h2hgi4rdjx465S6qnPHrVOdmvXVLlJMC+0nqqIiKxya+AjqWgm2++OfB7IxIgzBRXrFjRfT6S1lNl4MaSKoM4z5Iql91iAMdAjh3jmgZCIlk4jzERCVBAx2BuxowZuOeee/z5dZGg4wdMQkJCxKynuv2SUajd7gYTxKWnp3uVVFlKZRDH0mpOJVWRSBKuY0wk2n30EcBVVfO6BJhfAV3t2rXx+OOPY9GiRWjSpMk5JSGu6SoSa3JcT3XhUPy4dy8qNe9irmMGzm5wKKDuUxEROWvAAK63DQwalLF0WdDWcq1Ro0b2d5gvHzZv3oxIpLVcY2/eNgrFuqW+rqd66o65KFO2rHuFFRGnCvUxJrEtr2u5Ot2WLcD33wP/+EeQM3Rb+EgiEf5hs/Xs1N+hWJZo7aLv0diH9VT/SPodiVW6BXVfRKLxGBOJJTVq5C2YO6956ERiHT/Q2KXKJqGdm9egsQ+/w0YJERGJPWlpvm9b3I8kpM8B3fjx4zFs2DCflvZavHgx9u7di27dlImQ6MMVG+ypRriSA+Ur6tvgcK2nKiISm0qW5LC0nLfhIDhuc/p0EAO6NWvWoGrVqqbDtXv37mjVqhXKciXZs9Mw8Pb58+fjk08+wY4dO/AR2zREogRXQ2F3KrNxnADYxjJT8eLFkdjxRqSufkbrqYqISMjWb/UroGOA9ttvv+H111/HrbfeahoMOG8WJ0A9cuSI2aZFixa48847MWDAAA36lqgoqXKeOAZxnDfOc4k7rmXMDlXOG8fjgLSeqoiIZKdDBwRVnsbQNWvWzCz79fbbb+P333/Htm3bzAcelwBr3ry5+SnidCdOnHCXVHnexul57KlG+EUmM62nKiIiecF8WFISP3e8r2/aFHnmV1MEJz9lAMeTSDRg9o1ZZ2bj7KkY7JIqs3AM4nyZmkHrqYqISG727AEGDrSmJslKUMfQiTjJmdOnUHDfOpxOT8XaA1tR/5KuXstv2SVVDhdgEMdgzrOkyuCNQRzHx9klVV9pPVWJFeXLlw/3Log40v33AwcOsIkUuOIKYOpUIDUVePpp4IUX/LtPxwR0Y8eOxXfffYeVK1ciLi7OlMNEclp+q57n8ls/JmBH21Emg2aXVBnIsWPVs6TKJbgYyPF/TERyrtTYjXEikjc//QR89RXQqhWPJaBaNeDqq63pSsaNA/yZJMQxAR0/hNlh27ZtW7z33nvh3h1x4vJbC4bipwMHUa7RVV4fSnZJlY0OmhxVRESCjSN7ypWzzpcqZZVg69YFmjQBli/37z59DujYBNG4ceOwLR4+ZswY8/ODDz4Iy+NL5OPyW8zMUeblt3iZy281XPsyUutfjuLFS5hsHEuq4fqfFomGLnDi/KT6MiTiu3r1gPXrgerV2XAKvP22df6tt4CKFeEXnz/JOCUJJwummjVrYt++jHJWpOKkrxwb5XmS6LVu8Q8oj6zXUvVcfivfwW1mPWJm5RTMifgf0HHdbp78WBJcJKYNGwbs3GmdHzXKao6oWhV49VXgmWeCnKHjhx/XcC1XrpxZv89zAHmkGjdunDuzJ9Ht9OnTOLBzs0/bnkhLDfr+iIiIZOe22zLOt2wJbNsGrFtnBXX+zgDnc4buxhtvRIcOHUxmg6l1rhTBTF1WJ1+NGDHC3FdOp3X8C/00cuRIMyGsfUpOTvb7viTyMCvA1Rv4uvL/5ChyX5aOtPyWiIhEAs4/x9Ir+/Auusj/YC5PGbp33nkHPXv2xMaNGzF06FDcddddiI+P9/+RATz44INmVYmc5CVAzIyTv2Y1Aaw427Fjx9wT/3LZOVtio/ZIXZ2g5bdERCTiJxS+7z7gww+ty3/+yXjHuq5yZSa8gtzl2rVrV/Nz2bJlGDZs2HkHdGx5V9u7+IKBG7OsDOLsgdjEOeLYpcoGh8KFC2Nl21Gmm5UNEJ5j6XiZdrYdhQqZ5qMTEREJpZEjgd9+A+bMYWyVcX2nTsDo0SEI6GwTJkxAqCUlJWH//v3mJ8dLcT46ql27Ni688MKQ74+ErqTKII4/PQde88sEgzi+9p6NDfbyW5UXjUE5V0bjzu58CSaY4+0iIiLhNG0aMHkycMklXJEo4/pGjYBNm/y7T8ekKp544gl8aOcmz3bd0uzZs3EFp1mWqMEMnF1SZfBuYwbOXku1QA5ZNgZtJ6+8BVvmT0KBY/uQVrw26l9yjTJzIiISETjvnD0PXeb56XJZYdL5AR3nn9McdNFdUrWDOI6R8yypMoCzS6p5WX6raKMu5nyDsmU1PYlIEGjIjIh/uELEd99ZY+bIDuL++1+gbdsoD+gk+nDqG8+Sqo3dzSypMpDjT38mLGUZVutMigSPjjER/3GuuWuuAdasYUIDeOUV6/yCBcDcuf7dpwI6CSmOg2MGjuuossnBs6TK2eYZxLHJIaeSqoiIiJNdeqnVFMF1W7nc14wZ1rQlCxdal/2hT00JiZMnT7pLqlzBw/0PWKCAe1xcXkqqvgSO9uNw6hotSyQSWDrGRPxz8iRw993A448D776LgFFAJ0EvqTIbd+jQIff1DK64hiqDOHapBiPY4ocN50ykhg0bKqAT0TEmEhEKFgS++MIK6AJJAZ0EZcFuu6TquURc0aJF3SVVNjuIiIjEoh49rKlLHnggcPepgE4C4sSJE+6SKs/bChYs6C6patUOERERoE4d4MkngV9+sdZyLVbM+1kZOjTvz5ICOvEbs29paWkmG3eYk+ecxRIqs3AM4ooVK6Zyp4iIiIf33gNKluTKW9bJE0chKaCTkJRUjxw5YoI4BnOZS6qcL47j41RSFRERydqWLQg4ZegkTyVVBnLsWPUsqTKIYzYuLi5Oz6aIiEgYKKCTbHGOOLukyqyc54SizMIxkGNWTlOCiIiI5Gz8eGDYMM65msuGABYvBvbuBbp1g88U0Mk5JVWOh2M2jl2qvGzjeDi7pMqgLtKVKVMm3LsgEtV0jIn4jitBVK0K3Hwz0L27tfxX2bLWbVwtgrfPnw988gmwYwfw0Ud5uHMFdGLjJLx2l6pnSZVlVLtL1UklVQacFSpUCPduiEQtHWMiecMAjatDvP46cOutQFoa1yvn5PeAXQRr0QK4805gwAAgr3Pt53N5pmCiHMuH7L5k5olZpljHkiqfCwZxmUuqfJ6YjeNyXCqpiohIOKWkpKFKlRJITj6IxETnf36fOQP8/juwbRtw9Ciz3UDz5tZPf6nkGmMYv3PVBgZxDHA943mu2sAgLj4+3hEl1Zzw77IzjWzcUFAqomNMJFLwI5YBHE+BEpMBHafa8Jxuw5NnIJPdNk7c9tixYyaAYyB3isX6TCVVZuQY+GQlkPvLwMoOroK5LU9//vmnuVy/fn2vfQzFPjCgzCn57bRtyX4Oo3lbJxzLkbItZXeMOeE9ItzbOuG4j7T3CMlZTAZ069atM9mozHhd9erV3ZfXrl2b7T8auztr1qzpvrx+/XpTwswKy5a1atVyX96wYYPXODVPXE2hDqeQPmvTpk1ei9l7YgBWr1499+UtW7aYZbdywznieJAysON0JLt37zYnG29r1KiR+3JSUpLXWqyZNW7c2H0+JSXFBI7Z8VxXdceOHSbAzA4/JAoUsP5Fd+3ahf3792e7bd26dd1j/Pi37GV7kMfr7al27doofHZwwp49e8wpO3yN+VrTvn37kJqamu22/N+x/6+4rzt37sx222rVqplMKPE52L59e7bbVqlSxQTcxOc2OTk5220rV65ssqzE12wb8/nZqFixIhISEsx5NsJs3bo1223Lly+PsmdH7/J/bPPmzdluy+24PfF/115TN7tB9fZYRx4TdoCQldKlS6NSpUrmPI+1zK+rJ35JSUxMNOd5DK/haONscPhFVY5UPiunbaP5PYLvCw0aNHBf5v+D51AMTzyGPbflce/k94jM9B4Rme8RkrOYDOhiFQMIftjzQ4kHpmemTkRERJwrJpsiOK9adk0RkVDK8GdbllT57ZTfZj1/h9/m7WW4PLtUw7W/oSy52hkclVydUU6JhG0j4Vh2yrae2UyVXFVyDfbxGQ1NEb//zmy1NX4uGGIyQ8d/Dl9q8nmp24djW2bY7CCOAZ1n6cSeaoSlnEjZ33Btm9PrHax98AyWtK1znodI/R+OxG09Az5f31MDvQ9O3jYS/t+dtq3TtWgBcCROuXIczgMsXQqcrWgHREwGdE7GN1GOVWGWMT093X09DwiWVBnE8WesHCAiIiJOULKktYYrAzoOR/QhCZ4nCugcgOloZuAYxHHeOM+B1czA2V2q9uBgERERiSw33gh06MBmEyZhrJUiOLFwVnLoKcmWIoAIxi43BnAM5Dy72Bi42SVVu1tTsu6KFJHg0TEm4rt33gF69gTY1Dt0KHDXXWxWRMAooIvAkipLqQziPKcBYAmVjRwM4tilqpJq7mNZ7CkuRCTwdIyJ5F3XrtbPZcuAYcMU0EVlSZXz9tglVc/BxpzLyi6pstlBREREnG3ChMDfpzJ0YcRJfdmhyhPPe04GapdUOe2I+Bck22MN7YmURSRwdIyJRBYFdCHG7Bvnw2M2jjNv2xhw2PPFFStWTAFIAD5s7HnoPGeeF5HA0DEmElkU0IXojY9L6DCIYzCXuaTK1Rs4Pk4lVREREfGHAroQlFQZyHmuy8iSKoO4zKs3iIiIiPhDAV2AcdyWXVL1XNiaHWHMwjGQY1ZOJUAREREJFAV0ASqpcjwcs3HsUvVcl47j4eySal6WhRERERHxlQK688DJfu0uVc+SKsuodpeqSqoiIiISbAro/CipMgvHIC5zSZVdqszGcTkulVRFREQkVBTQ+YAlVK7awCCO4+M8S6pctYFBXHx8vEqqEYYZUhHRMSYSCxTQ5eDYsWPukuqpU6fc13OyX7ukyo5ViTzMmCYmJoZ7N0Silo4xkciigC4TBm52SZXLcdk4R5xdUi1cuLBKqiIiIhIxHNF2uXXrVtxxxx2oUaOGGZ9Wq1YtjBo1ymu5rPPBEipLqUlJSVi/fj127tzpDuZYSq1SpQrq1atnFnvX+Dhn4GvKCZx58iyRi4iOMYkNb7wBVK8OFC4MtGkDLFmS8/affw7Ur29t36QJ8L//wVEckaHjEk78YH777bdRu3ZtrF69GnfddZeZKuT5558/r5Iq54tjNs5e95OYgbNLqgUKOOIpkkwYxK1Zs8ac19JfIoGnY0wi2eTJwPDhwFtvWcHcyy8DXboA69cD5cqdu/2CBcAttwDjxgF/+xvw6adAjx7A8uVA48ZwhHwuh6YvnnvuObz55pvYvHmzz7/DLBzLpvwdBnAM6DxLqnYQxyycOBu/AHgGdJoDUETHmDhXSkoaqlQpgeTkg0hMLJ7r9m3aABdfDLz+unWZK25WqQLcdx8wYsS52/fuDXB59W+/zbjukkuA5s2toNAJHJt+4ji30qVL5zpPHE+eAR2lpqaa7lROLcKSKoM4/tRUIyIiIpErPZ2f5RmXCxWyTp44GmvZMmDkyIzrOK9/p07AwoXIEq9nRs8TM3rTpsExHDGGLrONGzfitddew913353jduPGjTMZOfvEsXB2SbVixYpmXFzVqlXNKg4K5kRERCJbw4ZAiRIZJ5ZIM9u7l3PGAuXLe1/Py7t2ZX2/vD4v20eisAZ0I0aMMIFUTieOn/O0fft2dO3aFTfffLMZR5eTkSNHmkyefUpOTjbX16xZEwkJCRofJyIi4iAcSXPwYMbJMwsX68Jacn3wwQcxYMCAHLdh8GXbsWMHrrzySrRr1w7vvPNOrvfP+eJ4EhEREeeLjweK5zKErkwZjovn8Crv63m5QoWsf4fX52X7SBTWgK5s2bLm5Atm5hjMtWzZEhMmTNAgdxERETlHXBzQsiUwa5bVqWo3RfDykCFZP2Ft21q3339/xnUzZ1rXO4UjmiIYzF1xxRWoVq2amaZkz5497tsqOCl8lpDi2EgR0TEmsWf4cKB/f6BVK6B1a2vaEnaxDhxo3d6vH1C5csYYvGHDgA4dgBdeALp1AyZNAn79FfChGBgxHBHQzZw50zRC8JR5OSeHzroiQcZpStjwIiI6xiT29O4NMPfzxBNWYwOnH5k+PaPxISnJ6ny1tWtnzT332GPAv/4F1Kljdbg6ZQ46R89D5w97Hjo2SCh7IyIiEp3z0MUiR05bIiIiIiIOK7mK5JVWihAJLh1jIpFFGToRERERh1NAJyIiIuJwCuhEREREHE4BnYiIiIjDKaATERERcTgFdCIiIiIOp2lLJGpdeOGF4d4FkaimY0wkciigk6hd+qt69erh3g2RqKVjTCSyqOQqIiIi4nAK6EREREQcTiVXidplidauXWvON2jQwJSHRETHmEi0UkAnUcvlcoV7F0Simo4xkcihtIWIiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJy6XCVqFS1aNNy7IBLVdIyJRA4FdBKVOO9czZo1w70bIlFLx5hIZFHJVURERMThFNCJiIiIOJxKrhK1S3+tX7/enK9Xr56W/hLRMSYS1RTQSdQ6ffp0uHdBJKrpGBOJHCq5ioiIiDicAjoRERERh1NAJyIiIuJwCuhEREREHE4BnYiIiIjDqctVolaRIkXCvQsiUU3HmEjkUEAnUbssUa1atcK9GyJRS8eYSGRRyVVERETE4RTQiYiIiDicSq4StUt/bdiwwZyvU6eOlv4S0TEmEtUck6G77rrrULVqVRQuXBgVK1ZE3759sWPHjnDvlkSwkydPmpOI6BgTiXaOCeiuvPJKfPbZZ2bB9S+++AKbNm3CTTfdFO7dEhEREQk7x5RcH3jgAff5atWqYcSIEejRo4fJwBQsWDCs+yYiIiISTo7J0Hnav38/Jk6ciHbt2imYExERkZjnqIDukUceQbFixZCQkICkpCR89dVXOW5//PhxpKWleZ1EREREok1YAzqWTfPly5fjad26de7tH374YaxYsQIzZsxA/vz50a9fP7hcrmzvf9y4cShRooT7VKVKlRD9ZSIiIiKhk8+VU0QUZHv27MG+ffty3KZmzZqIi4s75/qUlBQToC1YsABt27bNNkPHk40ZOv7OwYMHUbx48QD8BRLJ05awcYa4YgRntRcRHWPiTCkp/PwugeTkg0hM1Od3xDVFlC1b1pz8/cAmz4Ats0KFCpmTxB4GcJx/TkR0jInEAkd0uS5evBhLly7FpZdeilKlSpnMy+OPP24yL9ll50RERERihSPqUEWLFsWXX36Jjh07ol69erjjjjvQtGlTzJ07Vxk4ERERiXmOyNA1adIEP/30U7h3QxxEY+hEdIyJxBJHBHQi/shpfKWInD8dYyKRwxElVxERERHJngI6EREREYdTQCciIiLicAroRERERBxOAZ2IiIiIw6nLVaJWwYIFw70LIlFNx5hI5FBAJ1G79BcnoRYRHWMisUAlVxERERGHU0AnIiIi4nAquUrULv21ZcsWc75GjRqmBCsiOsZEopUCOolaR48eDfcuiEQ1HWMikUNpCxERERGHU0AnIiIi4nAK6EREREQcTgGdiIiIiMMpoBMRERFxOAV0ErXy589vTiKiY0wkO/v3A336AMWLAyVLAnfcARw6lPP2990HcDGiIkWAqlWBoUOBgwcRVpq2RKIS551r0KBBuHdDJGrpGJNo0acPsHMnMHMmcPIkMHAgMGgQ8OmnWW+/Y4d1ev55oGFDYNs24J57rOumTEHY5HO5XC7EiLS0NJQoUQIHDx5EcYbiIiIiEvFSUtJQpUoJJCcfRGJi4D6/1661grKlS4FWrazrpk8Hrr2WjwlUquTb/Xz+OXDbbcDhw0CBMKXKVHIVERERR0hPZ3Im43T8+Pnd38KFVpnVDuaoUydmoIHFi32/H5ZbmScKVzBHCugkapf+2rx5sznxvIjoGBPnYzatRImM07hx53d/u3YB5cp5X8egrHRp6zZf7N0LPPWUVaYNJ42hk6h15MiRcO+CSFTTMSahtmYNULlyxuVChbLebsQI4Nlncy+3ni9mCbt1swLN0aMRVgroRERExBHi463SZm4efBAYMCDnbWrWBCpUAHbv9r7+1Cmrk5W35Vb+7drV2qepU4GCBRFWCuhEREQkqpQta51y07YtcOAAsGwZ0LKldd1PP3HYDtCmTc6ZuS5drAzh118DhQsj7DSGTkRERGJSgwZWlu2uu4AlS4BffgGGDAH+/veMDtft24H69a3b7WCuc2ero/W996zLHG/H0+nT4ftblKETERGRmDVxohXEdexodbfeeCPw6qsZt3NuuvXrOWbUurx8eUYHbO3a3ve1ZQtQvTrCQgGdiIiIxKzSpbOfRJgYoHnO2HvFFd6XI4UCOola+fLlC/cuiEQ1HWMikUMBnUTtskSNGjUK926IRC0dYyKRRU0RIiIiIg6ngE5ERETE4VRylajE5b6SkpLM+apVq5rykIjoGBOJVgroJGodOnQo3LsgEtV0jIlEDqUtRERERBzOcQHd8ePH0bx5c9Muv3LlynDvjoiIiEjYOS6g++c//4lK9nocIiIiIuKsgO7777/HjBkz8Pzzz4d7V0REREQihmOaIlJTU3HXXXdh2rRpKFq0aLh3R0RERCRiOCKgc7lcGDBgAO655x60atUKW7du9Xm8HU+2gwcPmp9paWlB21eJnGlL7A48vt6atkREx5g4V3p6mjsekAgM6EaMGIFnn302x23Wrl1ryqzp6ekYOXJknu5/3LhxGDNmzDnXV6lSJc/7KiIiIuF16FA6gBJ6GbKQzxXGcHfPnj3Yt29fjtvUrFkTvXr1wjfffOO1EPTp06eRP39+9OnTBx9++KFPGTpmbfbv34+EhAQtKh0DmJlj8J6cnIzixYvrsfWc638tio4xiS1nzriwc2c66tathPz5HTX8PzYCOl9xxn/PMumOHTvQpUsXTJkyBW3atEFiYmJY908iE/9nSpQoYUrt4Qjo9Nh6zvW/JiKh4ogxdFy6ydOFF15oftaqVUvBnIiIiMQ85S1FREREHM4RGbrMqlevrk4XyVWhQoUwatQo8zPU9Nh6zvW/JiKh5IgxdCIiIiKSPZVcRURERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATmIC1wHmSiMvv/xySB5v9OjRqF+/PooVK4ZSpUqhU6dOWLx4cdAf9+TJk3jkkUfQpEkT89iVKlVCv379zGTcofDll1+ic+fO7tVYVq5cGZLHfeONN0z3e+HChc1k40uWLAnJ486bNw/du3c3zzP/3mnTpoXkcbms4cUXX4z4+HiUK1cOPXr0wPr160Py2G+++SaaNm1qJuvmqW3btvj+++9D8tgikj0FdBL1pk6dikWLFpkP3VCpW7cuXn/9daxatQrz5883wQYDHS53F0xHjhzB8uXL8fjjj5ufDLD4QX/dddchFA4fPoxLL7001zWaA2ny5MkYPny4maKGf3OzZs3MSjK7d+8Oyd/Lx2NAGUpz587F4MGDzf/1zJkzTSDP/y/uT7BxZZ7x48dj2bJl+PXXX3HVVVfh+uuvxx9//BH0xxaRHHDaEpFolZKS4qpcubJr9erVrmrVqrleeumlsOzHwYMHOT2Q68cffwz5Yy9ZssQ89rZt20L2mFu2bDGPuWLFiqA/VuvWrV2DBw92Xz59+rSrUqVKrnHjxrlCiX/v1KlTXeGwe/du8/hz584Ny+OXKlXK9d///jcsjy0iFmXoJGqdOXMGffv2xcMPP4xGjRqFbT9OnDiBd955x6ztymxOqHEtW5YDS5YsiWjD55aZIpa0bRdccIG5vHDhQsQKvsZUunTpkD7u6dOnMWnSJJMZZOlVRMLHkStFiPiCZb8CBQpg6NChYXnCvv32W/z97383ZdCKFSua0liZMmVCug/Hjh0zY+puueUWM94p2uzdu9cEFeXLl/e6npfXrVuHWPnicv/996N9+/Zo3LhxSB6TQwkYwPH/i2trc1hDw4YNQ/LYIpI1ZegkKkycONF8sNgnjjF65ZVX8MEHH5jsVCgf++effzbXX3nllaYpYMGCBejatSt69eoV8HFd2T02cVwVH5PVQA5kD7ScHltCh2PpVq9ebTJloVKvXj3zv81Gn3vvvRf9+/fHmjVrQvb4InIuLf0lUSE9PR2pqanuy59//jkeffRRU36zMZPDy1WqVMHWrVuD9tiVK1dGkSJFztmuTp06uP322zFy5MigP7YdzG3evBk//fST6ToNtJz+bj6/NWrUwIoVK9C8eXMEs+RatGhRTJkyxXR62hhgHDhwAF999RVChV8cmKny3I9gGzJkiPkb2W3L5ztcWOKuVasW3n777bDtg0isU8lVogKnb+DJNmjQIDOdhCd2PnJM3cCBA4P62DmVxo4fPx70x7aDuQ0bNmD27NlBCeaye+xQi4uLQ8uWLTFr1ix3IMXnmZcZ7EQrZl3vu+8+E0DOmTMnrMFcsP63RSRvFNBJVGIQkzmQKViwICpUqGDKRcHEAeJjx441U4Vw7BzHeXFai+3bt+Pmm28O6mMzmLvpppvM9B0cw8es5K5du9wD5hkABdP+/fuRlJTknvfOnhuNzztPwcApS5iRa9WqFVq3bm3mGuRrEOjAPSuHDh3Cxo0b3Ze3bNliSpF8rqtWrRrUMuunn35qsnMMqu3XmI03WWWHA4kZ5muuucb8fczScj8YVP7www9BfVwRycXZbleRqBeqaUuOHj3quuGGG8zUGXFxca6KFSu6rrvuOjN9SKimC8nqNHv27KA//oQJE7J87FGjRgX1cV977TVX1apVzfPNaUwWLVrkCgU+p1n9vf379w/q42b3GvP5D7bbb7/dHEt8rsuWLevq2LGja8aMGUF/XBHJmcbQiYiIiDiculxFREREHE4BnYiIiIjDKaATERERcTgFdCIiIiIOp4BORERExOEU0ImIiIg4nAI6EREREYdTQCciIiLicAroRCRivPfee+jcubP78oABAwKy2H2+fPkwbdo0BMqIESPMWqoiIpFCK0WISEQ4duwYatasic8//xzt27c31x08eNAsRF+yZMnzDui4kH0ggkPi+rzcV67byp8iIuGmDJ2IRIQpU6agePHi7mDOXmz+fIO5YChTpgy6dOmCN998M9y7IiJiKKATkYDas2cPKlSogGeeecZ93YIFCxAXF4dZs2Zl+3uTJk1C9+7dva7LXHK94oorMHToUPzzn/9E6dKlzeOMHj3a63c2bNiAyy+/HIULF0bDhg0xc+bMcx4rOTkZvXr1MsEi7+f666/H1q1bzW3r1q1D0aJF8emnn7q3/+yzz1CkSBGsWbPGfR33lfssIhIJFNCJSECVLVsW77//vgm0fv31V6Snp6Nv374YMmQIOnbsmO3vzZ8/H61atcr1/j/88EMUK1YMixcvxr///W88+eST7qDtzJkz6Nmzpwkeeftbb72FRx55xOv3T548abJr8fHx+Pnnn/HLL7/gwgsvRNeuXXHixAnUr18fzz//PP7xj38gKSkJKSkpuOeee/Dss8+aANHWunVrc5sdCIqIhJPG0IlIUAwePBg//vijCdJWrVqFpUuXolChQllue+DAAZQqVQrz5s3DZZdd5pWh4212QwMzdKdPnzaBmGdgddVVV2H8+PGYMWMGunXrhm3btqFSpUrm9unTp+Oaa65xj6H75JNP8PTTT2Pt2rVmbB0xkGO2jo9jN2X87W9/Q1pamgkO8+fPb+7H3p54G0vCc+bMQYcOHfRfJCJhVSC8Dy8i0YpZrsaNG5smh2XLlmUbzNHRo0fNT5ZJc9O0aVOvyxUrVsTu3bvNeQZpVapUcQdz1LZtW6/tf/vtN2zcuNFk6DI3ZWzatMl9mVnGunXr4oILLsAff/zhFcwRS7B05MiRXPdZRCTYFNCJSFAwONqxY4cpg7Is2aRJk2y3TUhIMAHTX3/9lev9FixY0Osyf4+P4atDhw6hZcuWmDhxYpblYs/A7/Dhwyag27lzpwkcPe3fv/+c3xERCRcFdCIScCxh3nbbbejduzfq1auHO++805Rdy5Url+X2LGtyfBqbDjznocurBg0amIYHzwBs0aJFXttcdNFFmDx5stkXdtVmhcEay72PPvqoua8+ffpg+fLl7qwcrV692gSXjRo18nt/RUQCRU0RIhJwDIQ4h9yrr75qmhJYurz99ttz/B02KrAx4nx06tTJPFb//v1Nho1j7bgvnhiccdoRdrby9i1btphxcOyeZZMDsQmCpdvHHnsML774ohm399BDD3ndD3+X4/08gzwRkXBRQCciAcXg6OWXX8bHH39sMmAsWfI8A6Cc5m2744478L///c8Egv7iY7H5gWPy2CzBzODYsWO9tuGUJGy+qFq1qumIZVaPj80xdNzfjz76yOwH97lAgQKmo5aNFO+++y6+//579/1wypK77rrL730VEQkkdbmKSMS4+eabTUl05MiRiGQM7B588EH8/vvvJugTEQk3ZehEJGI899xzZk64SMdmiQkTJiiYE5GIoQydiIiIiMMpQyciIiLicAroRERERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJwCOhERERGHU0AnIiIiAmf7fy+rT6l1ZxvWAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -838,18 +832,10 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "id": "18", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3DIMkHZaLAmaOmGPVtQ2k6xopwl\n" - ] - } - ], + "outputs": [], "source": [ "# # TODO: Fix it and remove the original (Ancilla not as output)\n", "# p = params()\n", @@ -919,7 +905,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "id": "22", "metadata": {}, "outputs": [ @@ -927,7 +913,6 @@ "name": "stdout", "output_type": "stream", "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3DILfoGkquUJNK1mVjoXrvukJNk\n", "Circuit Width: 3\n", "Circuit Depth: 1\n", "Gate Counts: {'u': 3}\n" @@ -997,7 +982,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "id": "26", "metadata": {}, "outputs": [ @@ -1056,7 +1041,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 9, "id": "28", "metadata": {}, "outputs": [ @@ -1071,7 +1056,7 @@ }, { "data": { - "image/png": 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Paj38Qx8RAEDgaj100fuRdNSm19yitR50NE0OgggAIG1rPbSmwwsesfp6eDOaMrzWHoIInKDtrWPGjAmvA6CMnQ6dzdQLHjq5WOS8HpF9Paj1cAdBBE7Q8KEnCACUsZ7QTqUaOLxOptGzmerU6V7wYISLmwgiAICUHFobq5Op0v4dXnML83q4jyACJ2j16b59+8x6aWkpncQAyljY8ePHw7UesSYU06nTvRqPoF9ALhURROCMyCACILhlTIOG18dDbzWIxBtaSyfT1EcQAQBYrxH1Rrdo+Ige3aL0arWRnUzp1J4+CCIAACv9PLwaDw0h0ZNf6pwe2sxCc0v6I4gAAHylIUObVyKbW6KH1epVa73QweiWYCGIAAB6nQ6jjexgGj2LqTeZWGQ/D5pbgokgAgDoleAR2c8juoOphgzt2+GFD+3zQfAAQQQAcFq0hkMDh7fojKbRmMUUiaBGBE7QX0ZVVVXhdQBulbFEg4fWeHgL83kgEQQROMGrtgXgjxOdnVK/6n05+uUuyS0eJuMvuEIy+/btdup0bzl27Ngp2+jIFq+DqZZf7XAK9BSfGgBIc6veek6GfjRfJsqB8GONi0tk97QH5RtXzOpR8Iis8SB4oDcQROAEHcp34MDXJ8mSkhKmeAd6MYRM+fBnX9+JaJEpDR2Q0g9/JssOtUn5lG/HbGoheCAZCCJwRmNjYziIADhznV99ZWpCVJ+obiF6/0RIZNya30nj2AslM7OvGUIbWeORlZXF2wDfEUQAIA0nENMajv/9x3/K+docE6dvqoaRMjkgu/Zvlon/PpOmFlhBEAGANJkyXefx0P4deqt9Pg7u3prY/z/aTAiBNQQRAEgxGjIig4euR0+ZriPRcgcOFanv/vl0FA1gC0EEAJLYZ2P9ircSHkLr0VlKNXR4S6wRLd6U6d7spTqnR6i6WhpX/sZ0TI3uI6K0j0hTRok5DsAWgggAODKE1mtm0aAR2cwSfZ0WpR1JNXR4wUNHuJwyUVmfPub5dXSMho7IMKL31Z5pD0oZ83/AIoIIAFgeQruivUNGXnB1uMZDw0i8WUu98JHoiBYNOatEZNjy+TI49K8QpDUhe6JCEGBDRijWJ94Rra2tUlhYKC0tLVJQUGD7cOAj/Rjqrz+lJ1umeUc6Ncfsf2hct80jjd971Qyh9ZpZvMDhLfrYmfiqo0M2Lf8vOd6yR/oWVcj4b16ZULMQ4Pf3N59COEGDh04VDaRbp9L/Wfafck4CQ2i37PxCJky7yoSOmM0sZ6hvVpZM+LeZvfqcQG8giABAL87d4TWv6EgWvb+/YWNC/z8n1CYDBw7kvUDgEETgzEm8ubnZrOvJmKYZuDZyJVpHR0d4CK3exhpCq7IKBif0fH4PoaWMwVUEEThBT5J79uwx68XFxQQRWB25Ek0DhjeSxQsfGkSiaT+O3Nxc07zi3U4YP14a/+ch60NoKWNwFUEEQCB0N3JFR5ZoGIlsYvFqOvR+rH792pcjMnTE69vBEFogPoIIgLSXyMXfyj+aL5tGTZPjHR0xQ0dmZuZJoUNv9bGeDKHVYxgSURvDEFqAIAIgALRPyMQERq6s+d9lUjb+m+EmlshF5+04k75LGkY6L71Bvojqn8JkYgg6akQApCWdjdTrz9G0fb1MTOD/5MpRGTt2rGRnZ/vST0k7xU6c/t1ef14glRFEAKTsyBWlzSjacVQ7k2rw8G4jp0XvzC5M6LmKyqtMPw8AyUMQAZASI1e80KEXgIsOHTpxWCwaKrRZZfC/XS2Na/6f9ZErACwFkaeeekoeffRR2bt3r0yZMkWeeOIJOf/885Oxa6QIrQYfMWJEeB3BHrmivNErkYFDb2PN1eFdi0UXDR7eemRn0lUBv/gbZQyu8r3UvfTSS3L33XfLH//4R7ngggvksccekyuuuEI2bNgggwcnNtEP0p+eJAcMGGD7MODAyJWGCTPMyBUNHbFGr+hnJVbo6O5aLEEfuUIZQ2Aveqfh47zzzpMnn3zS3NdfMxUVFXLnnXfKvHnzTtpWf/3oEnnRHN2Wi94Bqe+L//4vmbj4/3S73TuT/sOMXFEaLiIDh96e6XVYerN/CgDHL3qnbbkrV66U2tra8GN6Yrnsssvko48+OmX7uro6mT//619MCBbNwwcPHjTrRUVFNM+kAf3RoT8stGZDl8bt6xIauZLdeViGDx9uQocfo1eCOnKFMgZX+RpE9u/fbzqRDRky5KTH9f769etP2V4DizbjRNeIIBgnyV27dpl1TdH0E/Ffb9YMeKNWIpfI2k11IrsooecqGT7WhFH0LsoYXOVUfaRWuTJ0DnB35Ir+sPCaUCNDR7xRK9pZ1OvDUfbv1zJyBUByg8igQYPMiaixsfGkx/V+WVmZn7sGcAYjV6Z8+8aTAod3G+tCbx5tRvFCh7dEz0Ya9JErAE7la4nXE9PUqVPl3XfflZkzZ4bbjfX+HXfc4eeuAZzByJXPy6ZIZmbs00Pfvn1NzaUGDe82kVErKugjVwCcyvefHtrnY9asWXLuueeauUN0+G5bW5vcfPPNfu8aQNREYGv++3WZmsg1VzZ9KsMmTj8lcOitBpEzwTVXACQ1iPzwhz+Uffv2yQMPPGAmNDv77LPlzTffPKUDKxBEvT2U1BupEr1oCNEwcqBhU0LPU5D9lYwfP963TsNBHbkC4FRJaYzVZhiaYoDem+pcr6MSK3B01YdDm05yisoTehv6l1QwcglAUtArDE7QX97eUO0gDN1NpMPo2ZffZGoydIkOHPFGqSjtIO6NQItctONo9bhx0rhqPtdcCaCglTGkDoIInKAnRp0/JAgS7jBafrb06fOva6VE02ARK3B01YdDm0S0xoWRK8ETpDKG1EIQQeAlY8pvbUrxajY2rHhTvplIh9GNn0j5hGlm9FmswJHIKJVYGLkCwCUEEThBO1LqTLpKr0uQrKrjM+mnES9saD8Nr4OodxvZlNLauD2h5yvI6pCamhpfXgtGrgSPrTIGdIcgAmdOkg0NDWbdry/fM7kkvXeMGjK8fhvRS7zL00fPv5FfWiFS3/3x9R9U6evrwMiVYLFRxoBEEEQQSD25JH3niRPhmo7uLlatYUObUrxFg4d36zWlVFZUSOPH99NhFAAIInApGPRv+kz6Hjsg6w7Wy/hvXuXLpdm11kKbUNZ88Lqck0A/jXc+fjt8SXpPZNCIXhLpt0GHUQD4F2pEYJ02kQxbPl9GhSL6abxzev00NGhozYXXhBJ9qyFE7W/YmNDz6SXphw4dGg4a0ddOOV10GAWArxFEYFVP+2lop08vaMQKHF7Q6IoGiZyisoQvST9w4EDxAx1GAYAgghTop7Fl9HQ58c+Oot11CPWChld7EetWJ/w6UV0tjav+r/V+GnQYBRB01IggKSKbTLxly8p3ZFoi/TRWLzmpn4YGCQ0VkUt00Oiu+YR+GgDgBoIIeqXzpwaLWLfeeqyajENNOxLaR64clZEjR4ZDx+lO5BWNfhoIEg3nw4YNC68DriCIICbti6EhwuuTES9kdHXNk2gaIHR4qxcoDg8ZkdB8GkXlVZKfn+/LO0U/DQSFho/i4mLbhwGcgiASEDr/hVd7kcjS3XwZ0Sc4DRZeyNDbyHXvVptMIpWXXS+Ny39FPw0ACDCCSIoHi8iai8jb6PWehgsvYMQLFZG3WtNxOlW99NMAkkfL/+HDh8261jDSPANXEEQcOUHoEh0o4oUM7996Giwim0e6WrTmIlYNhh+8fho6j8jgiHlEdMTKntOYRwRAbHq+2L796+scMcU7XEIQ6eUw4YWERBavRuN0Q0VkrUVkeIi8jV56q6Nnb9Kw0THjx1L/wYtmZtXWgjFmZtUyH2ZWBQC4hTN9VDOH3kaud/VYdKg43TARGSpiBYquHnMxWJwObaZpG3xO+NdauvxdAIA0CiJerYMXDCKXeI9HbxMrWCQySVZPeEGhu0W/bKPv024LAAiSlAgiGzdulLy8vF4PDNE0BGgY8AJCrNvox6JDBWECAIA0CyLaQTM6hESGBu/LP/J+rMVr+ogXMGgOAAAguVIiiIwaNUqKiopOCRUAACC1pUQQyc3NlZycHNuHAR9psCwvLw+vA6CMIRhSIogg/Wn4KCkpsX0YQNqijMFVjJEEAADWUCMCJ+jQ6ra2NrPev39/mmcAyhgCghoROBNEtm3bZpYznRgOAGUMqYMgAgAArCGIAAAAawgiAADAGoIIAACwhiACAACsIYgAAABrmEcEzhgyZIjtQwDSGmUMLiKIwAl6IcPS0lLbhwGkLcoYAtc08/DDD8uFF14oeXl55sq5AAAASQsix48fl+uvv17mzJnj1y6QRnQ21SNHjpiFmVUByhiCw7emmfnz55vbhQsX+rULpBENH1u3bjXrNTU1XGsGoIwhIJzqI9Le3m4WT2trq9XjAQAAARq+W1dXJ4WFheGloqLC9iEBAABXgsi8efNMlXlXy/r160/7YGpra6WlpSW8NDQ0nPZzAQCANGuaueeee2T27NldblNVVXXaB5OTk2MWAAAQDD0KIjrPA3M9AAAA5zur7tixQ5qbm81tZ2enrF692jw+ZswYyc/P92u3AAAghfgWRB544AF57rnnwve/8Y1vmNv3339fLr74Yr92ixRGbRtAGUPwZIQcnj1Kh+/q6BntuFpQUGD7cAAAQC9/fzs1fBcAAASLUxOaIbi0Ys6bzE5HTulQcACUMaQ/akTgTBDZvHmzWRxuLQRSFmUMriKIAAAAawgiAADAGoIIAACwhiACAACsIYgAAABrCCIAAMAa5hGBMwYNGmT7EIC0RhmDiwgicEKfPn2krKzM9mEAaYsyBlfRNAMAAKyhRgTOzPrY0dFh1rOyspjiHaCMISCoEYEzQWTjxo1mYYp3gDKG4EiJGpETJ06YJV67Z+R2XWHbnr8OevE57wJ0fm4buX30/03GMWj46SoApdq2ke9zOm+rKPeJvQ6RUvEcYXvbVCj3GY6dI9IqiKxfv17y8/NPeVwfGzlyZPj+unXr4r5AeXl5UlVVFb6/YcMG6ezsjLltbm6ujB49Onx/06ZN4WaDaHql2LFjx4bvb9myJXwV2Wja5FBdXR2+X19fL0ePHo25bWZmpkyYMCF8f9u2bXLkyJGY2+oHb+LEieH7O3bskMOHD0s8kyZNCq/v3LlTWltb425bU1MT/mDv3r1bDh48GHfb8ePHS9++X3+k9u7dK83NzXG3HTdunGRnZ5v1pqYm2b9//0nvd6QxY8ZIv379zPq+ffvMEo++x/peqwMHDkhjY2PcbfWz432u9Fj37NkTd9sRI0bIgAEDzLq+Brt27Yq7bUVFhRQWFpp1fW0bGhribjts2DApLi426/qebd++Pe625eXlUlJSYtbb2trMZyKeIUOGSGlpqVnXz9jWrVvjbqvb6fZKP7t64cGuRl14nYq1TGgNVjwDBw6UoUOHmnUta9Hva6SioiIZPny4WdcyvHbt2rjbFhQUSGVlZfh+V9tyjvialuHI84mW+1Q+R0TjHOHmOSJRNM0AAABrMkION8hrCtdfll9++aX5FRQLVbTp0zTj/WLWX02Rx0i1q5vVri5sq2iaSex1iKw9ii5jZ/L6utaEQtNMhhPl0/v+bmlpifv9nVJNM/pHJdLm1JN2KbZ193Xo6v326xgiT2Rsmzqvg6ufYRe3jfyCTvSc2tvHkMrbuvB5z0ixbRNF0wwAALAmJWpEEAzauREAZQzBQhCBE7SK1BthAYAyhuCgaQYAAFhDjQicoL2wvXlddA6V3u4MBQQdZQyuokYEzpwkdfiuLg6PKAdSFmUMriKIAAAAawgiAADAGoIIAACwhiACAACsIYgAAABrCCIAAMAa5hGBM4qKimwfApDWKGNwEUEEzkzxPnz4cNuHAaQtyhhcRdMMAACwhhoRODProzejqk7vzhTvAGUMweBbjci2bdvk1ltvlVGjRklubq6MHj1aHnzwQTl+/Lhfu0QK0xCydu1aszDFO0AZQ3D4ViOi1ww5ceKELFiwQMaMGSNr1qyR2267Tdra2uR3v/udX7sFAAApxLcgcuWVV5rFU1VVJRs2bJCnn36aIAIAAJLfR6SlpUUGDhwY99/b29vN4mltbU3SkQEAgLQeNbN582Z54okn5Kc//Wncberq6qSwsDC8VFRUJOvwAABAKgSRefPmhUc1xFu0f0ikXbt2mWaa66+/3vQTiae2ttbUmnhLQ0PD6f1VAAAgPZtm7rnnHpk9e3aX22h/EM/u3btlxowZcuGFF8ozzzzT5f/LyckxCwAACIYeB5HS0lKzJEJrQjSETJ06VZ599lkzsx8QT0FBAS8O4CPKGALVWVVDyMUXXywjRowwo2T27dsX/reysjK/dosUpSG1srLS9mEAaYsyhsAFkcWLF5sOqrpEX0OECasAAIDyra1E+5F403ZHLwAAAIprzcAJOguvTu+uampq6E8EUMYQEPQeBQAA1hBEAACANQQRAABgDUEEAABYQxABAADWEEQAAIA1DN+FM/Lz820fApDWKGNwEUEEzkw/PXLkSNuHAaQtyhhcRdMMAACwhiACAACsoWkGzkzxvm7dOrM+YcIEpngHKGMICIIInMEFEQHKGIKHphkAAGANQQQAAFhDEAEAANYQRAAAgDUEEQAAYA2jZuCMvLw824cApDXKGFxEEIEz009XVVXZPgwgbVHG4CqaZgAAgDUEEQAAYA1NM3BmivcNGzaY9erqaqZ4ByhjCAiCCJzR2dlp+xCAtEYZg4tomgEAANYQRAAAgDUEEQAAYA1BBAAAWEMQAQAA1jBqBs7Izc21fQhAWqOMwUUEETgz/fTo0aNtHwaQtihjcBVNMwAAwBqCCAAAsIamGTgzxfumTZvM+tixY5niHaCMISAIInBGR0eH7UMA0hplDIFrmrnmmmuksrJS+vXrJ+Xl5XLjjTfK7t27/dwlAABIIb4GkRkzZshf//pXc1XVV155RbZs2SLXXXedn7sEAAApxNemmV/84hfh9REjRsi8efNk5syZpnowKyvLz10DAIAUkLQ+Is3NzfL888/LhRdeGDeEtLe3m8XT2tqarMMDAADpOHz3vvvuk/79+0tJSYns2LFDXnvttbjb1tXVSWFhYXipqKjw+/AAAEAqBRFtXsnIyOhyWb9+fXj7e++9V1atWiVvv/22ZGZmyk033SShUCjmc9fW1kpLS0t4aWhoOLO/DiklJyfHLAAoYwiOjFC8VBDHvn375MCBA11uU1VVJdnZ2ac8vnPnTlPL8eGHH8q0adO63Zc2zWjNiIaSgoKCnhwmAACwpCff3z3uI1JaWmqW0520SkX2AwEAAMHlW2fVFStWyCeffCIXXXSRFBcXm6G7999/v7mwWSK1IQAAIP351lk1Ly9PXn31Vbn00kulurpabr31Vpk8ebIsXbqUfgCIO8W7Ll7NGYDeQxlD4GpEzjrrLHnvvff8enqkIZrsAMoYgoer7wIAAGsIIgAAwBqCCAAAsIYgAgAArCGIAACA9L/oHdAdrsgM+IsyBhcRROCEPn36mPlmAFDGECw0zQAAAGsIIgAAwBqaZuDM9NP19fVmfdSoUaapBgBlDOmPIAJnHD161PYhAGmNMgYX8bMTAABYQxABAADWEEQAAIA1BBEAAGANQQQAAFjDqBk4IzMz0/YhAGmNMgYXEUTgBJ03ZMKECbYPA0hblDG4iqYZAABgDUEEAABYQ9MMnJnifdu2bWZ95MiRTPEOUMYQEAQROOPIkSO2DwFIa5QxuIimGQAAYA1BBAAAWEMQAQAA1hBEAACANQQRAABgDaNm4IyMjAzbhwCkNcoYXEQQgTPTT0+cONH2YQBpizIGV9E0AwAArCGIAAAAa2iagTNTvO/YscOsV1ZWMsU7QBlDQBBE4IzDhw/bPgQgrVHG4CKaZgAAgDUEEQAAYA1BBAAApHcQaW9vl7PPPttMprN69epk7BIAAKSApASRX/7ylzJ06NBk7AoAAKQQ30fNvPHGG/L222/LK6+8Yta7qznRxdPS0mJuW1tb/T5MODB81+vRr++3zgIJgDKG1OR9b4dCIbtBpLGxUW677Tb5+9//Lnl5ed1uX1dXJ/Pnzz/l8YqKCp+OEAAA+OXQoUNSWFjY5TYZoUTiymnQp/3Od74j06dPl1//+teybds2GTVqlKxatcr0F0mkRkR/JTc3N0tJSQkXawpIgtbQ2dDQIAUFBeyb15zPWhqVMQRLKBQyIUS7ZXRXw93jGpF58+bJb3/72y63WbdunWmO0YOora1N+LlzcnLMEqmoqKinh4gUpydIWydJ9s1rzmcN6B3d1YScdhC55557ZPbs2V1uU1VVJe+995589NFHpwSLc889V2644QZ57rnnerprAACQZnocREpLS83SnT/84Q/y0EMPhe/v3r1brrjiCnnppZfkggsu6PmRAgCAtONbZ1W9cFmk/Px8czt69GgZPny4X7tFCtPaswcffPCUWjT2zWvOZy31yxiQ9M6q0RLprAoAAIIlaUEEAAAgGrNGAQAAawgiAADAGoIIAACwhiACAACsIYjASbfffruZ1v+xxx5Lyv5+85vfyPjx46V///5SXFwsl112maxYscL3/XZ0dMh9990nZ511ltm3Tod80003mXl3kuHVV1+Vyy+/PHwZhdWrV0uyPPXUUzJy5Ejp16+fmVvo448/9n2fy5Ytk6uvvtq8zvr36nWwkkWvpXXeeefJgAEDZPDgwTJz5kzZsGFDUvb99NNPy+TJk8MzB0+bNq3bi5ACyUIQgXMWLVoky5cvN18WyTJu3Dh58skn5fPPP5cPPvjAfEHqF/S+fft83e+RI0fks88+k/vvv9/cajDQL6drrrlGkqGtrU0uuuiibi/b0Nt0YsO7777bzGmhf/eUKVPMhIdNTU2+/726Lw1BybZ06VKZO3eu+WwvXrzYhFD9jOkx+U3nbnrkkUdk5cqV8umnn8oll1wi1157rXzxxRe+7xvolg7fBVyxc+fO0LBhw0Jr1qwJjRgxIvT73//eynG0tLTosPbQO++8k/R9f/zxx2bf27dvT9o+6+vrzT5XrVqVlP2df/75oblz54bvd3Z2hoYOHRqqq6sLJYv+vYsWLQrZ0tTUZI5h6dKlVvZfXFwc+vOf/2xl30AkakTgDL3a8o033ij33nuvTJw40dpxHD9+XJ555hlzwSb99ZxsLS0tptkgXS/4qK+v/jLX5i+PXp1T7+v1qYJC32c1cODApO63s7NTXnzxRVMTo000QNpO8Q70lDYP9O3bV372s59ZefFef/11+dGPfmSaS8rLy031+aBBg5J6DMeOHTN9Rn784x+n7WXa9+/fb74MhwwZctLjen/9+vUSlNB91113yfTp02XSpElJ2ac2O2rw0M+YXnJDm0BramqSsm+gK9SIwIrnn3/enAy9RdvPH3/8cVm4cKGpDUjmvv/xj3+Yx2fMmGE6a3744Ydy5ZVXyg9+8INe77MQb99K+wzoPrXVQDsX9rau9o3k0r4ia9asMTUTyVJdXW0+39oJe86cOTJr1ixZu3Zt0vYPxMMU77Di0KFD0tjYGL7/8ssvy69+9StTRe/RX816v6KiwlyryK99Dxs2THJzc0/ZbuzYsXLLLbdIbW2t7/v2QsjWrVvlvffeM6NYeltXf3cyrwWlTTN5eXnyt7/9zYwc8egX48GDB+W1116TZNDAq7UCkceQDHfccYf5G3UEj77mtmhTmF6EdMGCBdaOAVA0zcAKHcKoi+cnP/mJGVYZSUdRaJ+Rm2++2dd9d1V93t7e7vu+vRCyadMmef/9930JIfH2bUN2drZMnTpV3n333XAI0Nda7+uXdLrSmq4777zThJ8lS5ZYDSF+fb6B00EQgRP0yzf6CzgrK0vKyspMlbKftNPeww8/bIbMat8Q7cOgwzt37dol119/va/71hBy3XXXmSGs2kdFa4H27t0b7sSoX9p+am5ulh07doTnLfHmtdDXXRe/6NBdrQE599xz5fzzzzfzxej70NuhM9rhw4dl8+bN4fv19fWmuUJf68rKSt+bY1544QVTG6KB0HuftVN0rBq53qS1eldddZX5G7VmTI9Dw9Bbb73l636BhJw0hgZwSLKG7x49ejT0ve99zwwfzc7ODpWXl4euueYaM4w2WcNmYy3vv/++7/t/9tlnY+77wQcf9H3fTzzxRKiystK85jqcd/ny5b7vU1/TWH/vrFmzfN93vPdZ3wO/3XLLLaY86WtdWloauvTSS0Nvv/227/sFEkEfEQAAYA2jZgAAgDUEEQAAYA1BBAAAWEMQAQAA1hBEAACANQQRAABgDUEEAABYQxABAADWEEQAAIA1BBEAAGANQQQAAIgt/x9YQ0HQoOVdowAAAABJRU5ErkJggg==", + "image/png": 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ADiAxsQSKFMkBpzh82Pp/+3bg0CE4hp63/t5OoPe53udOkJTEGWMP48CB+FT5qrx5rcXdyZPA4sVAv34p6847z2qOZSYvIwzwfv0VWLsWeOkla92mTcCuXdY+bHFxVrMx93nHHYgKURX0jR8/HkuWLDHNu5kxdOhQDGZnNg/16sGR+GvHifS8nUV/b2fR39tZqlTZBqBC8nU233KAprt9+4AzZ4AyZVKvL1MGWLMm/X0nJQHly1v9JnPmBN55B7j6aus2Bnz2Pjz3ad8WDaIm6Nu2bRsee+wxTJ06FfnYKzMT+vXrh95s1D/n4MEkVKpUEatWbUPhwkWCeLQSbmfPnsWOHdbZHR9fG+fxZ56I6ByTqLRz5yE0a5aAFSsKIyEhZb1nli87ChcGli1jNzJg+nSrT2DVqlbTb6yImqBv8eLF2LNnDy644ILkdWfOnMHs2bMxYsQI04ybk6G5m7x585rFU/nyRVCkiIK+WA/6Dh0qZC5XqFBEQZ+IzjGJAXFxOZDR13fJklambvfu1Ot37wbKlk3/fswNVK9uXebo3dWr2WJoBX32/bgPjt513ye3jRZRk/5o1aoVli9fjmXLliUvTZs2NYM6eNkz4BMRERHnyZMHaNLEytbZzp61rjdvnvn98D72sIAqVazAz32f7CPPUbxZ2We4RU2mr3Dhwqhfv36qdQULFkSJEiXSrBcRERHnYtNsly5W7b1mzayRt0ePWqN5qXNnq/8eM3nE/7ktR+4y0PvpJ6tO36hR1u05cgAsC8zxozVqWEFg//7sPgR06ICoETVBn0hWFWWVTREJGp1jEqk6dgT27rWKKXOgBZtgJ09OGYixdavVnGtjQPjII0BiolV4uXZt4NNPrf3Ynn7a2q57d44RAC67zNpnJocZRIQcLhcHJzvDoUOHEBcXh6SkJPXpE5GY7c96kjUrRKJI7ty5fXbTSkw8hISEOGzblmT6aYt/lOkTEYkRDPY2bdpkAj+RaMwcly1b1kyxKsGhoE9iEhPYdhKbHyD6EJFYx/f7zp07TbYkISEh6CPWPRuJdI5Jdt5Lx44dMxU6qJz78FgJKAV9ErMfIqtWrTKX69atqy8kiXmnT582X5zx8fEowPmmQnCO/Xtu0lHWTlXQJ9mRnx3pwLlx96B06dKqyOH0ki0iIpI+1i2lPKxXIRKF7B8rp06dCvehxCwFfSIiMUQZN4lWeu8Gn4I+EREREQdQ0CciIlFr8+bNJkPEmZky68MPPwx4jcHMHAf7XN5yyy2mZBi3Pchib2Eyc+bMsB+DhJ6CPhERCatt27bhvvvuM4NQ2CexUqVKeOyxx7B///4M78uRyhy1nJWZmTp27Ii///4bofbRRx9hzpw5+P33380xs25sKLRs2RKPczoJN5dccklIj0Eig4I+EREJm40bN5p51NetW4fPP/8c69evx+jRozF9+nQ0b94cBw4c8FmXkCVqWNstV65cWRopyhGiobZhwwbUqVPHBKjhrkfH4DrcxyChp6BPYhabULiISHCwFmB26wH26NHDBCBTpkxBixYtULFiRbRv3x7Tpk3D9u3b8eyzzyZvW7lyZfz3v/9F586dzbndvXt3r82q3333HWrUqGFKyVx55ZUmw+belOnZvDto0CA0atQIn3zyiXkMZr/uuOMOHD58OHmbyZMn47LLLjP345zv1113nQnispJte/XVVzF79mxzLLxOvDxp0qRU2/IxeIxkP79vvvnGPBeOcG3YsCHmzZuX6j6//fab2SdvL1asGNq2bYt//vkHXbt2xaxZs/Dmm28m1yzlPr0173799deoV68e8ubNa14HHq87rnvxxRdNVrZw4cLmb/Xee+9l+jWQ8FPQJzGJX0T8QOIS7CK1IpGIdfQ4M0ewFu6fU2dx8XyszM7uySzeL7/8gkceeSS5TpuNWahOnTphwoQJqfY3fPhwE/QsXboU/TnjvQfOSHLrrbeiQ4cO+PPPP/Hggw+mChzTwwCOwdcPP/xgFgZKw4YNS7796NGj6N27NxYtWmSykPxcuemmmzI9+wmDtm7dupnsJZtVeT0r+ByefPJJE9zWrFkTd955p6nNSFzXqlUrU5OUweDcuXNx/fXXmzI+DPb4mHxsPi4XNol7Wrx4MW6//XYT7C5fvtwEwnx97eDTxkCQmVm+/vy7Pfzww1i7dm2WnouEj4ozi4jEeIHyUMtsQXQ26fI42eTpDdczW7V3797k5tirrroKffr0Sd6GWSt37777LmrVqoVXXnnFXOflFStW4IUXXvB5LAzeGOAwg0X33HOPCe7s+3EAhrsxY8agVKlS5jXOTH/C4sWLmyyc3ayaVQz4rr32WnN58ODBJiPHpvDatWvj5ZdfNoHYO++8k7w9b7fxMfnYvh73tddeM4GjHUgzsORz4+vIbKHtmmuuMcEePfPMM3j99dcxY8YM8zpL5FMKREREwiqzmUFicOMLs04XXnhhqnXNmjXLcL9surQDPnsqMHtaMDtAZXatatWqpmmZ29PWrVsRCueff36qYyP7+OxMX3asXr0al156aap1vM7nbRf+9jwOBvYMJN1fJ4lsyvRJTOKvdvdp2NTEK07DL2S+98MxDVtmBwdUr17dbMuAg02lnrie/dOYUbMVLFgQwcBmanc8LvemWzaXclTx+++/b0YZ8zZm+DiYJDv4OJ5Br7cZKdyPz3597ePzbBoPpoxeJ4lsyvSJiMQgfhnbAy1CvWQ26OOAiKuvvto0Sx4/fjzVbbt27cK4ceNMeZWsjDBlMyP73blbuHAhsoOlY5hBfO6550xGzW52DgQGtOxnZ2NmjfX8soLZNzZFp4fNu+7ZOm/4nDgYxB2vs5mXI6QlNijoExGRsBkxYgROnDhhRptyZCtr9nGkLIPB8uXLZ9gXzxMHbqxZs8b0N2Mtvi+++CJ5MIK/5UmYbWSAypGq7Ef366+/mkEdgcA+inwNODCCwepDDz2UJpuWkX79+pnAln3t/vrrL/P8R40ahX379pnb2RS9YMEC0/+R67xl5thPkoEjR0fzdeOIZx4X+xJK7FDQJyIiYcPSKgx22FeOo0erVatmSrGwPAlHonIARFZUqVIFX331lRkdywwYgx979C5LkfiD2cvx48ebEa5s0n3iiSeSB4pkF0fDcjTt5ZdfjrvuussEWRx0kRXMxrHkDUcrs/8iR+t+++23ybULuU9m69jcz8yit36IF1xwgQmQ+Tz5HAcMGIDnn38+1SAOiX45XFnpQRvlDh06ZOovJSUlqX5bjFOfPnEa9q9juRIGPexjF2y++vRFGmYLWfCZWUSJzvdwYuIhJCTEYdu2JFSooPqr/tJADhERiSnsI8gRvGySZb80ZuV69uwZ7sMSCTsFfSIiElM4GGLIkCGm+DMLtLO/Gvu9iTidgj6JWYUKFQr3IYjEtEgthcSCwVxEJDUFfRKzX0Z28VQRCTz24fN3YISIhEdk/kwTERERkYBS0CciIiLiAGrelZgt2cIpnOxK85Ha90gkWkVTyRYRsSjok5jloBKUIiIiGVL6Q0RERMQBFPSJiEjEmjlzpmk6PnjwIKIJj3nSpEkB2x+rEbzxxhsIppYtW+Lxxx8P6mNIeCnoExGRZGfOujBvw358u2y7+Z/XgxkY+VoGDRoU8X8ZHmOjRo3SrN+5cyfat28flmMSSY/69ImIiDF5xU4M/n4VdiZZAzSoXFw+DLy+LtrVLxfwV4mBkW3ChAkYMGAA1q5dm6rA+qJFi8Ly1zl58iTy5Mnj9/3Lli0b0OMRCQRl+kRExAR8D3+6JFXAR7uS/jXreXugMTCyl7i4OJPdc1/nPqvO4sWL0bRpUxQoUACXXHJJquCQvv32W1xwwQVmJHHVqlUxePBgnD59Ovn2rVu34sYbbzT7LFKkCG6//Xbs3r07Tcbugw8+QJUqVcx+iM3KDzzwAEqVKmXud9VVV+HPP/80t3344YfmcXjdzk5ynbfm3cTERNx5550oXrw4ChYsaJ7LggULzG0bNmwwx1amTBlzfJw3eNq0aZl+HadMmWKO17MJ/LHHHjPHS/v37zePX758efMaNmjQAJ9//nmWm6iLFi2a/Bxp27Zt5rXkej43Po/Nmzenap5v1qyZec7c5tJLL8WWLVsy/dwksBT0ScziBxsXEfGNTbjM8HlryLXX8XbPpl6WQgpVOaRnn30Wr776qsn85cqVC/fdd1/ybXPmzEHnzp1NkLNq1Sq8++67JjB54YUXkks4MRjhXLyzZs3C1KlTsXHjRnTs2DHVY6xfvx5ff/01vvnmGyxbtsysu+2227Bnzx78/PPPJvBkYNmqVSuzL96f8/rWq1fPZC25eO6Tjhw5ghYtWmD79u347rvvTJD49NNPm+Oyb7/mmmswffp0LF26FO3atcP1119vAtXM4PEwoOKx286cOWOyp506dTLXWV6nSZMm+PHHH7FixQp0794d99xzD/744w/469SpU2jbti0KFy5s/ga//fabCVp5/MyUMuju0KGDee5//fUX5s2bZx5X5X3CR827EpP4RcRf+yKSsT82HUiT4XPHUI+3c7vm1UqEZRo2BnAMHqhv37649tprTSDDDBezbVzXpUsXczvP/f/+978msBo4cKAJppYvX45NmzYhISHBbPPxxx+bYG3hwoUms0YMVLieWT2aO3euCYoY9NnPdfjw4Sb79dVXX5kAhkEOg1BfzbmfffYZ9u7dax6L2TCqXr168u0NGzY0i43HPnHiRBMg9uzZM8PXJmfOnLjjjjvM49x///1mHZ8zM3+33HKLuc4M35NPPpl8n0cffRS//PILvvjiC5OJ8weDSgauzI7agdzYsWNNAMoMH7OZSUlJuO6661CtWrXkuqkSPgr6REQcbs/hfwO6XTCcf/75yZfLlbP6FzIYq1ixosmcMctkZ/bsTBeDwmPHjplC7Qz27ICP6tata4IT3mYHfZUqVUoO+Ij7ZRauRAkr0LUdP37cNMlmFrOGjRs3Tg74PPEx2LzMLByzhcyQ8TEym+kjZvQuvvhi7NixA/Hx8Rg3bpwJjPkc7dfjxRdfNEEeM44McE+cOJGt1hC+PsyOMtPnjq87X582bdqga9euJht49dVXo3Xr1qYp2P77Segp6BMRcbjShfMFdLtgyJ07d/JlO6vk3jzKbN/NN9+c5n5237zMYL8zd9wvAxRmrTzZwVRm5M+f3+ftzMCxyZlZRGYAuf2tt95qArPMYuDKbNr48ePx8MMPm0yhe9+7V155BW+++aYp+8L+fHyuLM/i6zH4OnsWuWeTrvvrwyZjBpie7OCZmb9evXph8uTJJjP43HPPmefKAFVCL2r69I0aNcr80mNHWi7Nmzc3fSxEfE3DxsX+YhAR75pVKW5G6aY3kRrX83ZuZ2MwwGwUl3DPfsN+dhzYwYDJc2FXDzYpcsABFxv7/rH5kxk/X/vdtWuXab713G/JkiXNNhzhyyyaL/zuYraP/QC9YZaSGbGbbrrJBGRsKnYfDJGVbB8DsO+//948b2b63B+D/Rrvvvtu05TMJvC///7b5/4YuLmPsF63bp3JnLq/PlxXunTpNK8PB+bYmOXs168ffv/9d9SvX980Q4fCyJGsb8jAH7joIsBX98X33wcuvxwoVsxaWrdOu33XrgyEUy/t2iGqRE3QV6FCBQwbNsx0pGVHXo5I4ht45cqV4T40iVD8IM7ow1hEgJzn5TBlWcgz8LOv83ZuF4lY6oV98Zjt43cCf+wx48WsErFZkcEUg6IlS5aYfnoc+ME+gux3lh7ejwkGDkbgCFkGYgxcOKjELiXDosnsK8igbt++fabJ1BNHzTKQ434YfHEQCQddcGAD1ahRI3nwCJtM77rrLr9+rNrPj83czBS697nkYzDDxuPn6/Pggw+mGr3sDb9nR4wYYQaX8Pk+9NBDqTKufDwGv/wu5kAOvg7MijKzx9HKvM5gj8+TI3b5GjJIDEW/vgkTgN69gYEDgSVL2G8SaNuWXQK8b89k7p13AjNmAPyzsCdAmzbA9u2pt2OQxzjYXjIYAB1xoibo40gmjm7iG7dmzZrmTc0OtPPnzw/3oYmIRD3W4Rt19wUoG5e6OZTXuT4YdfoChX3GfvjhBxNUsJmTTYevv/666aNnN1OypEuxYsVwxRVXmGCOmS42N/rC+/3000/mPvfee6/57uGACQYwLK9CHCjB0apXXnmlyYx5K4PCbCCPjRkxfo8xAGUSgwMw6LXXXjPHxlI0/K7j82EWLauYYeOgDI6UtUft2hgAc5/cN2fesINQXzhamv0gL7/8chOIshnavQ8gL8+ePdv0q2TTOoM5DiRhnz62yPH2NWvWmNeIrx0HvvTo0cMEnMH22mtAt27Avfey/yYwejSPFxgzxvv2bKF+5BGAdbZr1wY++IAtRhwQk3o7xtEcs2MvzApGkxyucOfl/cDszZdffmlGavEXSHrpef7icv/VdejQIfMG5mgiviEldvFXMptviO+PUJWVEAkXftEys+JeY84fLMvCUboctME+fGzS9Zbh41cHH5P4eCrDIcF8Dycm8vs7DqtWJaF8+SKpgjDPQeTspsgA76uvAPe4tksX1l1kTceMj+XwYaB0aeDLL4Hrrktp3mXZQtbsZrDHEohDhgAe43wiWlQN5OCQe6ba+cZglo8dVX31xxg6dKhJ94uISOYwwLPLsohEGs+vfDbfes7Wt28fk0PAuWRssjJlgDVrMvc4zzwDxMdbffvcm3Y5VqhKFRbUBv7zH4Az7bE5+FzSNuJFVdBXq1Yt0+eBmTrWSGKmj4U20wv82JegNxv1PTJ9IiIiEn3YgFO+fMr1YJSKHDYMGD/e6ufnnnC8446Uyw0acIAOwPKD3K5VK0SFqAr62C/CLmjJYeIsdMkh6Ky+7g07sYayeKiIiIgED0sCZtQ7iwOrmXnzHKeye7fVD8+X4cOtoI+z4LmVhvSK9f/5WOvXR0/Qd16099vyNlJKhFjrKqP6WCLiP3u+WZFIwj53TZqkHoRhD8po3jz9+738MmdDASZPBnwM6k6WmMg5jVksHFEjajJ9bKpt3769GSV0+PBhU+eHQ8M5jYyIJw7csKf9EZHAY7CXnQEjIsHEnl0cuMHgjbPMvfEGcPSoNZqXOne2momHDrWuv/QSS/9wyjyrtt+uXdb6QoWs5cgRgEMEOKsds4Xs0/f00xwxbZWCiRZRE/Rxuh3WVWKhSBZ9ZLFLBnyc2kVERETE1rEjsHevFcgxgGMplsmTUwZ3cIY796IOo0ZZo35vvdX7QBE2F//1F/DRR9YIYA7yYB0/ZgajqRdZVJZs8RcHcjBgVMkWEYk1gSrZIhLJJVu2bUtChQoquRbzmT6RrPb3ZOV3YkFv1ekTCSzmC+w+1Rwwp759IpFPQZ/ELPeJwUUk8BzUUCQSE6J69K6IiEg045Rojz/+eLb20bVr1wynVBMhBX0iIpLi7Blg0xxg+VfW/7weRAxY2DT80EMPpbmN87TyNm4jItmn5l0REbGs+g6Y/AxwaEfKK1IkHmj3ElD3hqC9Spwpafz48Xj99deTa2uyUz9Lc7FMV6Q7efKkmTxAJNIp0yciIlbA90Xn1AEfHdppreftQXLBBReYwO+bb75JXsfLDPgaN26cZpAW51XnCE8GiA0bNjTTctrOnDmD+++/P/l2Tt/JmZvcscZrs2bNULBgQRQtWhSXXnoptmzZkm5TKZtf2Qxr4+WePXua9SVLlkTbc4XaVqxYYerJcm74MmXK4J577sE+TgR7ztGjR03pMd5erlw5vPrqqxm+NoMGDUKjRo3MzFN8jQoUKIDbb7/dVKHwNHz4cLPfEiVKmCype7/mTz75BE2bNkXhwoVRtmxZ3HXXXaYUmu2ff/5Bp06dUKpUKfO6cQDc2LFjk2/ftm2beVy+XsWLF8eNN96IzZs3Z+o1lcihoE9ExOnYhMsMH7wNzDi3bnLfoDb13nfffamCjDFjxuBeu5KuGwZ8H3/8MUaPHo2VK1fiiSeewN13323mYTdP5exZVKhQAV9++SVWrVqFAQMG4D//+Q+++OILc/vp06dNUNeiRQv89ddfmDdvHrp3757l0ccfffSRye799ttv5lgOHjyIq666ygSpixYtwuTJk7F7924TKNmeeuopc5zffvstpkyZYgKlJUuWZPhY69evN8f//fffm/0uXboUjzzySKptZsyYgQ0bNpj/eWwffvihWWwMAP/73//izz//xKRJk0zA5t5s3r9/f/N6/fzzz1i9ejVGjRplAlr7vgxsGTDOmTPHPGcGru3atTNZzkC9phJ8at6VmKV5l0UyacvvaTN8qbiAQ9ut7apcnrw2kF/qDNw485KdHWJgwSZfBkY2loh58cUXMW3aNDQ/N59W1apVMXfuXJMJY9CRO3duDObUCecw48cghEETAzDWa2WW7LrrrkuetadOnTpZPl5mwl7mvF3nDBkyxAR8PD73wJXZub///hvx8fH43//+h08//RStzk3UyuCMAWpG2NTNQLc8p5AA8Pbbb+Paa681mUJm7ahYsWIYMWIEcubMidq1a5vbp0+fjm7duiUH1Ta+Zm+99RYuvPBCHDlyxARwW7duNcfPbCBV5rQU50yYMMEE0x988EHy35wBOjN6/PvwPoF4TSX4FPRJTGJdPn4oi0gmHNmd5e0CPQ0bmxUZqDA7xVIwvGxnmtwzXseOHUszExOzTe7NwCNHjjQBFwOZ48ePm9vZREpsmmSGi5kr7qd169YmGGSzaFY04eSubphBY5aNAZQnZuDs47jooouS1/NY2PycETZz2wEfMeBlELZ27drkoK9evXom4LPx+Sxfvjz5+uLFi01TMY+TTbm8P/E1qlu3Lh5++GHccsstJvPYpk0bk7m75JJLkp8bX3tm+jyDUT43bh+I11SCT827IiJOV6hMYLfzE7NRDPqYAXPPTNmYlaIff/wRy5YtS17YLGn362N28MknnzT9+tiEytvZTMyAy8YsFbN/DGqYxapZsybmz5+f/IPRs/6gt5qf7LvmeWzXX399quPiwiLxV1xxBYKNGU53DMrtwI59CRmQFSlSBOPGjcPChQsxceJEc5v9urAvIrOsbC7fsWOHyUbydbSfG4Ncz+fGDCb7Bmb0mkrkUKZPRMTpKl1ijdLloA2v/fpyWLdzuyCy+4gxYLEHR7hjRordNpidYlOuN2wWZuDh3ueN2ShPzAxyYZMyM2ccKXzxxRebjCMHZLhjgOMZVHkbjPL111+bZtFcudJ+tbLZk/tYsGBB8ohkZtwYOKX3XGx8vgzE2ERMDKYYnGYmS0hr1qzB/v37MWzYMNPcTOx36InPvUuXLma5/PLLTR9EDg7hc2MgV7p0aRM4pie911QihzJ9EtPTsHGxf+2KSDrOy2mVZTE8++mdu95umLXdOcyGsXmPS6Bm5mDzJAcRMHPn3lRpY/Mis0/MRjEbyGCOzZHs48brxG4dDGh++eUXE1BxgAIzWzbO7cqghFkpZraYDeTnhN0HjYMxeH/2oeP6gQMHpgkCveFo2QMHDuDOO+80j8dj4zEwy8gRxWz2ZfaRgdSvv/5q9skm0cxMEclmdAZibGblQIpevXqZ5lO7aTcjDDI56ISv08aNG/Hdd9+ZQR3uOOCFA0zYjMsBMj/88EPya8JRvWxq54hdPj5fQ/bl43EkJiZm+JpK5FDQJzGLnb7tuUFFJAOsw3f7x0ARj35YzPBxvZc6fQz2Aj0VGzNJvrJJDFYYyHEUL4MKZgfZ3MsBG/Tggw/i5ptvRseOHU3/OWa43LN+LHnCzBf7r7EJkqNMGbDxfsQMI/f/9NNPm4EOhw8fNmVWMsIsHLOMDPDYx61BgwampAsHO9iB3SuvvGIyaGwGZr+3yy67LE3fQG+qV69untM111xj9n3++efjnXfeQWYxg8dmc45oZraUGT9m8NwxKGTgxn2zOZpBN5vK7dds9uzZJnjkcfB1ZwDLgJ9/q4xeU4kcOVwOmjyRo7bi4uLMKCNfHyoS/ZjdY7aA+CGXmV/TItGMX8DMuDD4ydYAC5Zl4ShdDtpgHz426bpl+DwzfcTHU3mO4ODgC5ZYYROzk9/DiYmHkJAQh23bklChgr6//aU+fSIikoIBnltZFhGJHUp/iIiIiDiAgj4REZEIbt51QtOuhIaCPhEREREHUJ8+iVkZ1dUSiUWhHJunwRsSSA4aVxo2CvokJmWlcKlILLDr2rG4cf78+YP+eIGehk2EU+yRfrAHj4I+EZEYwFkgWC9t79695ktTZYokmjJ8DPj27Nlj6hp6K8wtgaGgT0QkBjDzxgnuWeeMsyKIRBsGfJmdZUT8o6BPYrY4M7/8iIU+lfUQJ+CsCpyGjE28oTjHOAUXVahQQeeYZAuz08rwBZ+CPolZx48fD/chiIQcf+CEoq8dgz47uOTj6YeVSORTyRYRERERB1DQJyIiIuIACvpEREREHEBBn4iIiIgDKOgTERERcQCN3pWYpeH/IjrHRCSFgj6JSSwfUadOnXAfhkjM0jkmEn3UvCsiIiLiAAr6RERERBxAzbsSkzhbwObNm83lypUra7YAEZ1jIo6noE9i1rFjx8J9CCIxTeeYSHSJmubdoUOH4sILL0ThwoVRunRpdOjQAWvXrg33YYmIiEgEGjmSLT2cGxq46CLgjz/S3/b994HLLweKFbOW1q3Tbu9yAQMGAOXKAfnzW9usW4eoEjVB36xZs9CjRw/Mnz8fU6dOxalTp9CmTRscPXo03IcmIiIiEWTCBKB3b2DgQGDJEqBhQ6BtW2DPHu/bz5wJ3HknMGMGMG8ekJAAtGkDbN+ess3LLwNvvQWMHg0sWAAULGjt899/ETVyuFyMXaPP3r17TcaPweAVV1yRqfscOnQIcXFxSEpKQpEiRYJ+jBLePn2rVq0yl+vWras+fSI6xySKJSYeQkJCHLZtS0KFChl/fzOzd+GFwIgR1vWzZ61A7tFHgb59M368M2esjB/v37mzleWLjwf69AGefNLaJikJKFMG+PBD4I47EBWitk8fAzcqXry4XwEBl/RqT7lv54u2zfrrkCNHDrMEe1v37T3vG4pj4G8pX7+nom1b979zLG9LOu8z9zq4i8bPiHBvGw3nfaR9RmTWyZPA4sVAv37u+7CaY5nFywx2CT91ijGGdX3TJmDXLmsftrg4K7jkPhX0BRFPrMcffxyXXnop6tevn+52J06cMIt7po/WrFmDQoUKpdme6zjS07Z69ep034wFChRA1apVk6+zf+EZ/jTwIn/+/KhWrVry9XXr1pnmaW/y5s2LGjVqJF/fsGFDqufgLnfu3KhVq1by9U2bNuH48ePpzk7hXqyYI1vT64TNk7xevXrJ17du3YojR44gPe5/g8TExOTX2Rtm3ewPkR07duDgwYPpblu7dm3kymX9Ltm1axcOHDiQ7rY1a9ZEnjx5zOU9e/Zg3759ybfx7+2uevXqyMdOHucyxlzSw78x/9a0f/9+7N69O91t+d6x31c81p07d6a7baVKlUz/VOJrsN29DcFDQkKCyVATX9tt27alu2358uVRjD9PAfM327JlS7rblitXDiVKlDCX2U3CHu3sTZkyZVCqVClzme+xjRs3prstt+P2xPfu+vXr0922ZMmSKFu2rLnMc+Lvv/9Od1v+wIvnT23zK/xMmr+ru6JFi6JChQrmMs9hO+vrDbP+FStWTL7ua1t9Rlh4Drt/nvC8j+bPCE/6jIjMzwg6fJifgym3581rLe74p+XX8bmHcDtGwMfHRirPPGNl9uwgjwGfvQ/Pfdq3RYOo6dPnjn37VqxYgfHjx2c4+INflvbCL08REQkM90yQSCjUrWtl2Oxl6NDAP8awYQDDi4kTrUEgsSTq+vT17NkT3377LWbPno0qVar43NZbpo+B3z///JNunz418wT3dYi0JhY13URO000kbEtq3g3v6xBp57I+IyLjM8Lu07dqVRLKly/iM9PH5l020Hz1FdChQ8r6Ll3YsgJ8+236jzV8ODBkCDBtGtC0acp6Ji7ZYLd0KdCoUcr6Fi2s62++iagQNX36+KZ49NFHMXHiRMycOTPDgM9uKuXi7Q2UmT4CWelHoG31OvibAdG2kfM6kM5lvQ6heD9Ewvs92rYl9orJaBwmW/GbNAGmT08J+hjnT5/OxFH69+Po3BdeAH75JXXARww52MrMfdhBH5uZOYr34YcRNXJFU5PuZ599ZrJ87AvF/hvEZlv2mRMREREhlmthZo/BW7NmwBtvsF8icO+91uvDEbnly6c0D7/0klWD77PPrNp+dj89dtPmwrj08cetLCC73TMI7N/f6vfnnk2MdFET9I0aNcr837Jly1Trx44di65du4bpqCRSsUmGA1CInfSzOvpLRHSOSfTq2JED9axAjgEcs3OTJ6cMxODXg/vXAkMMNgvfemvq/bDO36BB1uWnn7YCx+7drWbiyy6z9hlN/f6irk9fdqhOn3OoTp+IzjFxbp0+8U7pDxEREREHUNAnIiIi4gAK+kREREQcQEGfiIiIiAMo6BMRERFxAAV9IiIiIg4QNXX6RLKCdfncJ3kXkcDSOSYSfZTpExEREXEABX0iIiIiDqDmXYnZGTkSExPN5QoVKmgaNhGdYyKOp6BPYnraPRHROSYiFjXvioiIiDiAMn0iIiIiEebUKWDXLuDYMaBUKaB48ezvU5k+ERERkQhw+DAwahTQogVQpAhQuTJQp44V9FWqBHTrBixc6P/+FfSJiIiIhNlrr1lB3tixQOvWwKRJwLJlwN9/A/PmAQMHAqdPA23aAO3aAevWZf0x1LwrIiIiEmbM4M2eDdSr5/32Zs2A++4DRo+2AsM5c4AaNbL2GAr6RERERMLs888zt13evMBDD/n3GAr6JCblyJEDdevWTb4sIjrHRJxOQZ/EJAZ6CvZEdI6JRIubb878tt98499jaCCHiIiISJjFxaUsHLk7fTqwaFHK7YsXW+t4u7+U6ZOYnYZtx44d5nJ8fLymYRPROSZR6NSpU0hKSsLevdsR68aOTbn8zDPA7bdbgzZy5rTWnTkDPPKIFRD6S0GfxKyDBw8mB30ionNMosPJkyfNNJoM9o4fP27WnThh/e8UY8YAc+emBHzEy717A5dcArzyin/7VdAnIiIiERfo2QoUKICcOQvCSU6fBtasAWrVSr2e686e9X+/CvpEREQk4gK9uLg4FClSBLlz50Zi4iFH/YXuvRe4/35gwwarPh8tWAAMG2bd5i8FfSIiIhISJ06cSA70/v33X5+BnpMNHw6ULQu8+iqwc6e1rlw54KmngD59/N+vgj4REREJCpfLZQI9BnkM9njZnQI97847D3j6aWs5dC7JmZ0BHDYFfSIiIhLQQI/NtQzyuLAZ112hQoVMNo9LrlwKQ3z165s502rivesuax2LUjD4K1QIftGrLSIiItkO9I4dO5Yc6LHUio2F8t0DvZzuQ1LFqy1bgHbtgK1b2SQOXH01ULgw8NJL1nWWcvGHgj6JSfyQqV27dvJlEdE5JoEP9I4cOZIc6J1hIblzzjvvPBPosY8e/1eglzWPPQY0bQr8+SdQokTK+ptuArp1g98U9ElMYqCnZgMRnWMS+ML3dqB3+PDhNIGenc1joMfr4p85c4Dffwfy5Em9vnJlYHs26lQr6BMREZF0MbBjgMdAjwEfAz8bM3h2oFewYEEFegHCl9gtnk6WmGg18/pLQZ/EJH4o7dq1y1wuW7asPohEdI5JFnDwhR3oHT16NNVtbEWxS6tw9K260ARemzbAG28A771nXWcvpSNHgIEDgWuu8X+/CvokZh04cCA56BMRnWOScWkVu3+eZw29vHnzonDhwibQy58/vwK9IGN9vrZtgbp1Af4pOHp33TqgZEng88/936+CPhEREQfyNeKWmMVjkMdgj0GfhE6FCtYgjgkTrP+Z5eMMHZ06Afnz+79fBX0iIiIO4Wsghl1axc7oaTBceLGEIYM8LoESVUNrZs+ejeuvvx7x8fHmzTlp0qRwH5KIiEhEO336NP755x9s2bIFq1evxtatW3Hw4EET8HEgRtGiRZGQkGDKXFWqVAnFixePiYBv5EhrtGu+fMBFFwF//JH+titXArfcYm3P/nPsT+dp0CDrNvflXGWwgGMpwyuvZDel1Ot377Zu81dU/VXZmbRhw4a47777cPPNN4f7cERERCIS++fZAzHYhOuO89razbYccRuLAzHYLNq7t1XEmAEfg7i2bYG1a4HSpdNuz5eoalXgttuAJ55If7/16gHTpqVcD1Zs7HJZRZhZq+/7763Hdb/NEUFf+/btzSIiIiKp++cxMcJAj4vn1Gf58uVLbrbl5VgM9Ny99ppVxPjee63rDP5+/BEYMwbo2zft9hdeaC3k7Xb3IC8UYwP55/n6a2DYMKB5c+CTT4Abb0y5zRFBn4iIiKQ027J/nh3oudfPY1DnPhAjj2eV3xjGeHfxYqBfv5R1rBPdujUwb1729s0RtPHxVpMxg7GhQ4GKFRFwzOaxGffNN60sX8eOwHPPAQ88kL395vI3bbxgwQLTP4Bp41KlSqFx48aoUqUKIgmPk4uNaW5xBn7g1axZM/myiOgci5WyKnaQ59lsy/55DPC4xOrUZ4cP87s85ToHFXsOLN63zypsXKZM6vVlygBr1vj/2Gwm/vBDoFYtYOdOYPBg4PLLgRUrslcwOSPduwM1alhNz7NnhzDo++233/Dmm2/i+++/N0O7WZyR9XpYD41vxKpVq6J79+546KGHzJsu3IYOHYrB/KuI4zDQc9IvW5FQ0zkWGszeMbhLr9mWpVTsbJ4T6uexbp07FivmAItQaO/Wu+z8860gsFIl4IsvrHIqgcT9usfsHNQxfz5w/fUhCvpuuOEGLFmyBHfddRemTJmCpk2bmjeYbePGjZgzZw4+//xzvPbaa/j4449x9dVXI5z69euH3uzJ6Zbp4wglERGRSG62tYM8z2nPGNRx8IWd0XPaj9tVq4Dy5VOueysfyALGDJg40tXd7t2B7Y9XtCjABqX16xFwmzalXVe9OrB0adrnFZSg79prr8XXX39tRv14wywfly5dumDVqlXYydxnmPEXkApKOhM/JPfs2WMuly5dWtOwiegci+hmW86AYQd56TXb2vPbxmKzbWaxEbFIEd/bMA5u0gSYPh3o0MFax7h5+nSgZ8/AHQsLJm/YANxzD0KGfQmZBQx60Pfggw9meqd169Y1S6DxZFjvFlJv2rQJy5YtMzWFKgajJ6VEtX3s2HEu6BMRnWORhDXy7EEY/J/ZPW+jbZ3SbBtobOTr0sUqedKsmVWy5ejRlNG8nTtbGUMOxCC2mjOLaF/evh1YtgwoVMjKsNGTT1rNqwy6duywmpYZf995Z2COuXhx4O+/rUxlsWK+R+l61u+LydG7ixYtwpVs2D7HbrpldvFD9q4UERGJwkEY7rNh8H+nNdsGGke77t0LDBgA7NoFNGoETJ6cMrhj61ZrRK+NQVzjxinXhw+3lhYtgJkzrXWJiVaAt38/UKoUcNllVj87Xg6E119PGRDirTh0IORw8Z2YCcWKFcv0Lw17ovtIwz59HHySlJRk0uQS28277GZAzDqf5352i4jOsRBl89xr53lm89j9yA70WF5Fn1PpS0xkn/w4bNuWhAoV9P3tr0xn+t5wCzv379+PIUOGoG3btmjOQjVg7Zt5+OWXX9C/f3+/D0ZERCTas3l2sy2zee55FTubZwd6yuaJu6xUlfM3b5XpoI9NqLZbbrkFzz//PHq69Yjs1asXRowYgWnTpuEJX3OYiIiIxFg2zw70WM7MHQM7u8mWgzCUzRNfo4EzalDlbwhuwzqEIevTx4zeSy+9lGZ9u3bt0NfX/CUiIiIxMNKWQZ490tYzm2eXVGGgpwoSklkzZiDo/Ar6SpQogW+//RZ9+vRJtZ7reJuIiEisYPbODvK4MLvnjqXM7JG2yuaJvzhoJCKDPs5y8cADD2DmzJm4iCWpATMt2+TJk/H+++8H+hhFsoy/tqufG2evUgcigRfL55g9C4Yd5DGz545NtAzu7P55yuZJsHCQN0cae0zEYmYECVnQ17VrV9SpUwdvvfUWvvnmG7OO1+fOnZscBIqEE7+EWOdKRHSOZWUABhf20fMsbMFaeXaQx8vqmyfBxHIzrCn488/ebw9pnz5icDdu3Dh/7y4iIhI2LJ/iPgDDs5xKrly5koM8LrwuEiqPPw4cPMhWVKBlS2DiRGv6tSFDgFdf9X+/fr+LN2zYgLFjx5o5d1nOhbMe/Pzzz2ZmjHr16vl/RCIBap7Zy59KYOHMUvpVLuLwc8y9yZbB3vHjx9O0DrBWnvsAjFhrtpbo8euvHCdhzSjCU4uzgFx9tVWqhbOIXHttCIO+WbNmoX379rj00ksxe/ZsU7OPQd+ff/6J//3vf/jqq6/8OxqRAHL/QhIRZ51jGY2ydS+OrHIqEmk4ZZw9gyinZOOpVrMm0KABsGSJ//v1K+hjWRYGepwGjb+KbFdddZWp1SciIhJKDOhOnjyZnMnj4jnK1m6ytQdhcNStSCSqVQtYuxaoXBlo2BB4913r8ujRQLlyIQ76li9fjs8++yzNemb77EnuRUREgon98NwHX3gWRnYfZcv/1WQr0eKxx4CdO63LAweyDjLAYRSckvnDD0Mc9BUtWhQ7d+5ElSpVUq1funQpypcv7//RiIiIpIOZO/dSKhxx661fnh3ocZSt+uVJNLr77pTLTZoAW7YAa9YAFSsCJUuGOOi744478Mwzz+DLL780JxQ7yP7222948skn0blzZ/+PRkRExGPwhd1cy8ueWJrJzuSpMLLEqgIFgAsuyP5+/Ar6XnzxRfTo0QMJCQnml1fdunXN/3fddReee+657B+ViIjA6UEeR9h6Dr7gXLbuTbYqpSKxyOUCOCaWU7Pt2cNzI/Xt50okhybo40nHmTcGDBhg+vcxzd64cWPUqFHDv6MQERFHBnkM7NwzeZ5BHoM6O4vHQI/fPyJOqNP37rvAlVcCZcqw60Jg9utX0McyLbVr1zaZPi42dqKdN28errjiisAcnYif2O2gatWqyZdFJLDOnjmD8w6ux6mDO7H64GbUvrgdcmZQwDirQR4XBnk6h8VpPvnEyuZdc01g9+tX0NeyZUuUKVMGEydOxMUXX5y8/sCBA7jyyivTDJMXCTW7Q7eIBN7SXz5C/LzBqIv9yet2TyuBHc0HonHbLsnrGNDZQV56tfJy5syZqk+egjwRIC4OOJe3CCi/Z+TgYI5WrVph5MiRZi5em+cJLSIisRXwNfy9l3XFLYleyrUfpX7vhQUnT6HKRTeYAI8Ls3ueQZ57Jk9lVETSGjQIGDwYGDOG8z4jvEEfsyj9+vXD5Zdfbkbr/vXXX3j13GRwSsNLJOAXzf79VhaiRIkSET9FlEg0OHP6tMnw0XkevSZ4/awLqLT4Reys2BQ5c1pfLwryRLLu9tuBzz+3ZuVgUWbPOuL+zsrhV9BnZ/NuvvlmU6vvxhtvxKpVq/Dmm2/6dxQiQbCbs1OfC/pEJPtWzfsZDdikm043WQZ+ZbEf6xNXoM7F7U0XC5ZUUTJAJGu6dAEWL7bq9YV9IIc7jtr9448/0KFDB9PcKyIisYGD8+wBF/x/58aVaJCJ++VzHdOPLZFs+PFH4JdfgMsuQ0D5FfR16dLFVDq3lS1bFrNmzUL37t3NyF4REYnOuWvdg7w005oVzNxUAPmLaWYmkexgYZQiRRBwOVwOGnlx6NAhxMXFISkpCUWC8WpKRPXpY5cDYvFw9emTWO1jt2bBLzj+z3YTaNW+qG2GZVM8y6fYAy64eKu8wB/49tRmefPkwcFhdc2gDc8+fWafLmBPjhIo9dzfmT4OkcxITDyEhIQ4bNuWhAoVijgi0/f228Do0VafvkDJ9FnJwRr169c3X5687Mv5558fiGMTEZEMyqbUcy+bMjVt2RTb6dOnk4M7ZvH+/fffNNUW2PeOQR4DPAZ6XDgQwx33z1G6DPDcAz9ep53NB6KsAj6RbGFfPs46WK2aNQWb50COAweCHPQ1atQIu3btQunSpc1lfji4f2DY1/m/6vSJiISvbMoSF1C3ZcdUWTw23XqyR9baAR4HXWSUFWdAuRRA+fmDUdqVEnAyw7cznYBTRLLmjTcQFJkO+jZt2oRSpUolXxYRkcgsmxI/fzDWlmuYXDbFxpp4doDHxd9CyAzsTl15JzbNHY9c/+7HoSLVUfvi9srwiQQAu9LOmgX07w9UqYLwBH2VKlXyelkkEvGLrPK5jhAqFyGxZM2CyVaTbgZlU1auX4SqF7RKFeR5NtVmR67cuVGq2c3mcoWCBXWeiQQIm3K//toK+gIt00Hfd999l+md3nDDDf4ej0hAMNDj1E4i0Y7dZewBF/x/x4aVqJeJ+8XlOWvqqAaLzjGR4OnQAZg0CXjiiTAFfazDlxnq0yci4h/2iz5x4kRyPzwGebye6jO2QOaKjecvrrIpItGqRg3g+eeB334DmjQBChZMfXuvc116s0olWyRmvzwPnBveVLx4cTU9SUSWTWEdPPcsHhfPuWopd+7cpnmWI2tZNuXYa43CXjZF55iEktNKtlTxkaRnN9yNG/3brwopSUziF9LOnTvN5WLFiinok7CXTbHr4tkLAz3P4sfE0bN2bTz7/1wewdv6CCibonNMJHiCNV7W708F1nniLBxbt25NUwqgl795RxGRGCmb8sep06jWvENykOfZTOs5otYO8Hg9o8FHdtkUBpxl3AJOlU0RiT2ucz/mAjH/rl9B39KlS3HNNdckF/lk89m+ffvMBxbr+CnoExGnl02puOgFJCY0SVU2hRk7BnfumTx/R9Qy8DvTqhNWejQtqzCySGz4+GPglVeAdeus6zVrAk89BdxzT4iDvieeeALXX389Ro8ebaY1mz9/vulzcvfdd+Oxxx7z/2hERKJgftrlc75H00yUTVm3dTlqNmuTHOjxczKQ2Gev3qXXBnSfIhJ+r71mlWzp2RO49FJr3dy5wEMPAfv2+T+q16+gb9myZXj33XdN3xP+SmWzRdWqVfHyyy+jS5cuuPlmq3aTiEi0B3icrsy9Lx775h3Yvj5T+8if4zjKlCkT9GMVkdjy9tvAqFFA584p61gNr149YNCgEAd9/LVqT9XD5lz266tTp47J+m3bts2/IxERCcMIWvdSKQzq7CCP/3sbScv+dnmLlQMy0dGaxyIiklUch3jJJWnXc925MYp+8T3JYjoaN26MhQsXmsstWrTAgAEDMG7cODz++OOoX78+gmnkyJFmpgXOEXnRRRfhjz/+COrjiUjkD6jYN6Qm6k29C00XPWX+53Wu98YeRcuSPjt27MCGDRuwatUqrF+/Htu3b8f+/ftNf2VuxwCPzbIcAR4fH49q1aqhbt26uOyaTtiNEsmjZdM8hgvYhRIm+BSR8Bg5EuDETPnyARddBPgKF1auBG65xdqeAybSm/s2K/vMjurVgS++SLt+wgSrhp+//Mr0vfjiizh8+LC5/MILL6Bz5854+OGHUaNGDYwZMwbBMmHCBPTu3dv0JWTA98Ybb6Bt27ZYu3atyTiK2PhlbU8XqGnYnDuCdvFZF2pfcVuq7B0Xb9h6wR+TDPLs/9MbScss4o4IKJsSTjrHJJIxOOrdGxg92grOGMS1bQusXcsWyrTbHzsGVK0K3HZb+k2nWd1ndgweDHTsCMyendKnj4Wap0/3HgzGZHFmBnoXXnghRowYYa7zl3hCQgIeffRR9O3bN8P7Hzp0yDRBJyUloUiR2C/uKBLrTbrM6GVUpHj3Td+kGkFL7ItsB3Z2kJcnT54s/0Cw6/S5l01hhm+nlzp9IhK64swMyi68EDgXLoA9NRISgEcfBTIKF5jJe/xxawnUPv2xeDHw+uvA6tXW9Tp1gD592Nrq/z6j5mcoO1QvXrwY/fr1S/XLvHXr1pg3b57X+7CPjnttLAZ9IhLd+GOP5/XK337I1AjaVRuXoNoFrVJl8dgvORAZYJVNEQktNjK6f5XnzWst7lg6mAGTW7gADkNo3RpIJ1zIUDD2mRFOv/bpp4Hdp19BH/u8sB/fjBkzsGfPnjSdne3prwKJdQA58bjnSDheX7Nmjdf7DB06FIOZIxXHYQL74MGD5nLRokXVxBsFgym8/Q1Pnz6d3CRrL/YPuQPbN2RqP0Vyn05u6g8Gp5ZN0Tkm4VC3burrAwdao1ndsaTJmTOMD1KvL1MGSCdcyFAw9pkRhlbr1wN79liX3V1xhX/79OsT+Z577jGdnu+//34TdEVqnylmBdkH0D3Tx+ZgccYXEjvlE5v0I/U96sTpyHxl7zwDPP7Q84bNs/mLx2sEbRjpHJNwWLUKKO82KN4zyxcr5s8H7roL2LIlZUYOG7/O0vloDE7QN2fOHMydOxcNGzZEqJQsWdJ80O/evTvVel4vW7as1/uwEzYXEQnfYApOF2YHfnZpFDvAs//3nMrR23ns3jzLmS3O1qiB3YsHZdinTyNoRWJH4cJARl3yS5bkD0PGB6nX794NpBMuZCgY+/SFRZibNgV+/BEoVy4wU7D5HfTVrl3bjIQLJXaybtKkCaZPn44OHTokZwd4vSdLVotIRE5HVm7eYGyueQVOnT5tgrv0xo7xR50d3Lkvdk3QNNtrBK2IeJEnj9UfjiNdz4ULpnl0+nRrhotI2acvnHrtq6+s0i2B5FfQ984775jRsuzXx7p8nlMLBWtkLJtqOeNH06ZN0axZM1OyhXP/3nvvvUF5PBHxbc2CyVaTbgaDKaYtno6ytS+21p13XqrsHRdeZvYuq83wzCAyk+g5gpYZPo2gFXEu9uzq0sXKljVrZpVXOXoUsMMFznTBZuKhQ63rbGxg07F9mb2Dli0DChVKCbwy2mcgcaQw+/NFRNDHjvHsH3fVVVelWs9f8PzQTq8fTnZ17NgRe/fuNcHmrl270KhRI0yePFnTHIkEaTCF55RkdtOsvWzfsAL1MnH/fGePomLFigEdOWvTCFoR8cQad3v3AgMGALt2AY0aAZMnpwzE2LrVGn1r27EjdSmU4cOtpUULYObMzO0zkFgGhuVZ+DgNGnAmtNS3n39+COv0McvGX+WPPfaY14EcnKUjEqlOn3Ow6Z+zLBBnUEiviTCWeKsZx1kjMjuYwn1AheeSXrPsrjXz0XpFnwz3u/Lqzxw5wjWWOfEck+ip0xftzvNyOjHU4sdwyAdyrFixAkuXLkWtWrX8e1QRCdtgCmIpFG/B3alTp9J9DDPn7LlmWXupUrkydq94UYMpREQCaFMm5vYOWdDHPnXbtm1T0CcRiwGKXZ4n1su1ZHYwxdbaLXH6zBkT3PnqgmEPqPBc0muW/dvh05E5lZPOMZFQC1ZpUb8+iTntGZt2n3rqKTRo0CDNQI7z/W1sFgkQfgmxPl+sY5Pryt9/xPmZGUyxcGryYArieestuGPQl5UvcQ2mcCannGMi4cIRvDNmeC/OzH6FIevT563vBj8Agj2QI7vUp0+ieWYKeyCF+/9cti/6Hm02nRuC5sOcus+jQZsuJrBjCSQGd9EwiERExGl9+t5/H3j4Yas+IOsAuv8O5+UlS/zbr1+fyJuC1dgsEiAMlOy5lllCKFTNT/7OTGGPjvW2sJ+d51SH7nIWKpmpYytevroZeR8sTp2OzKnCdY6JOMGQIcALLwDPPBPY/WY56OMXEEu1/PDDD6hTp05gj0YkgF9I7HdqjywMxRdSRoMpFp91oW7LjukGdhlhdo6Lnamz/69dqxZ2L9dgCon9c0zEKf75B7jttsDvN8tBH/sBcdokkUjGpsaCe5Yg17/7sfrgJtS+uH1QmxozM5ii/ILn8Xd8I+TM6f04+KVpB3aeC887XyUxmEnUYAoRkdhw223AlCnWdGyB5Ne3YI8ePfDSSy/hgw8+MPX6RCIJM27l5w9GFZdbE+u0rNWrSy+zwYwcFzs7Z/+/edkMXJmJwRSrNi5BpfNbeA3s/JmRwqbBFCIisaN6daB/f2D+fO/FmXuda1TKKr8itoULF5o5b6dMmWJG7xYsWDDV7d98841/RyMS4np13oI6z4DO/t9XE+ypQ3sydXxFcp9GtWrVEAyamUJEJDa89541BdysWdbijrmBkAZ97Ax+yy23+PeIImGuV3eg6XU465a1sxeOkM0IM3FsauViN7vy/1N7awKZGN/EUa3BpMEUIiLRb1MkFWceO3Zs4I9ExE/M0LFM0IrffkCjzNSrmzExVb06b0GdHdDZl+3r6TXBnn/5Ddg9q4RmphARkYiVrQ55e/fuxdq1a81lTslWqlSpQB2XiMFSJXYWjot92f1/Lgz89mxek6lX7bwTB02JCTuoc1/87VfHDJsGU4iISCDcd5/v28eMCWHQd/ToUTMrx8cff5xcP4yFXjt37oy3334bBQoU8O9oxDH4vvEVyNn/+6pP5ylXkdKZ2q5M5TqoWLEiAk2DKcRJ+OOofHmru4LKtYgEvmSLO3YpX7ECOHgQuOoq//fr14wcDz74IKZNm4YRI0bg0ksvNevmzp2LXr164eqrr8aoUaMQiTQjR3AxQGMzqx3M+VqyMmuL3eTKLJy3/+3LrrNnsW9IzQybWEs993fQy7doZgoRkcBx2owc3jAHwlk6OBbw6acRuqCvZMmS+Oqrr9CyZctU62fMmIHbb7/dNPtGIgV92cvI+QrgshrI2cFceoEc/7cvsz5dZjMJ7qN33QM/Bnz05yVvZatsi4iIhJ6CPgt71DH02rkTfvEr3XHs2DGUKVMmzfrSpUub2ySyM3HuQVp6/9uX/fhNkBywZbSwS0Cgm4XUxCoSGvxsOHLkiLlcqFAhNfGKhMCGDUAmCk0ENuhr3rw5Bg4caPr05cuXz6w7fvw4Bg8ebG6T0AVv7pc9F89ALiv949wxMGOAFq5Azp/A79SVd2LT3PFmRo5DRaqbGTnKqpC4SECDvi1btpjLmoZNJLB69059nfkXZvd+/BHo0iXEQd+bb76Jtm3bokKFCmjYsKFZ9+eff5oA8JdffvH/aByCwZe9pBe4+Qrm/Mm+ubMDOPf/va2z/89K82qkYJ+9o6UvSP5C8jWFmYiISCRZypkE3PArjAVSXn0145G9AQ/66tevj3Xr1mHcuHFYs8Yqk3HnnXeiU6dOyJ8/P2INgywu7sFaeoFbZtZlN2iz2QGZHbR5Lt6CuGgM4ERERJxkxozg7NfvIYwsy9KtWzdEIw40Yd9DX4GcvdjbBAMDMHvJKIDzXBS8iYiISEiCPmb6OFp3z549aYKiAQMGINKDPvZB9AezZO7BmmfAlt46b7cp4yYiIiIRHfS9//77ePjhh03plrJly6YKXng50oM+zh0cFxfnNYDzXDy3UaAmIiIijgn6hgwZghdeeAHPPPMMolF8fLyZhktERETEKfwK+v755x/cdtttgT8akQBhRrZcuXLJl0UksHSOiUQfv+pYMOCbMmVK4I9GJIBfSCVKlDCLgj6RwNM5JhIeH39sFWkOWaavevXq6N+/P+bPn48GDRqYqbLccQ5eEREREQmsrl0Bhl3duwNvvx2CuXerVKmS/g5z5MDGjRsRiTT3rnPwbX306FFzuWDBgsr2iegckyimuXdT27QJ+Pln4JFHEPxM3yY+mkiEB32bN282lzVFlIjOMZFYwtxbVgO+bNXpExEREZHAOHQo89v6W4Ak0wM5hg0blumCxgsWLMCPnBVYRERERDJUtChQrJjvxd7GX5nO9K1atQoVK1Y0I3evv/56NG3aFKU4+y+A06dPm9vnzp2LTz/9FDt27MDHHF4iIiIiImGbb9evoI9B3J9//okRI0bgrrvuMoMiOJ1Y3rx5zTy21LhxYzzwwAPo2rUr8uXLF8zjFhEREYkZLVoE/zGy1KevYcOGZgq2d999F3/99Re2bNlimnw5HVujRo3M/yIiIiKSfcypbd0KnDyZev355/u3P78GcnAOWgZ5XEREREQkcPbuBe691yrL4s2ZMyGckUMkGpQpU8YsIqJzTCSaPP44cPAgB8YC+fMDkycDH30E1KgBfPed//uNmqDvhRdewCWXXIICBQqgKIeviGSQjeZAIy68LCKBpXNMIt3IkUDlygCHGFx0EfDHH763//JLoHZta/sGDYCffko7Ewancndf2rULzrH/+ivw2mtA06Y814BKlYC77wZefhkYOtT//UbNt+HJkyfNyOGHH3443IciIiIiEWzCBKB3b2DgQGDJEo5JANq2Bfbs8b79778Dd94J3H8/sHQp0KGDtaxYkXo7Bnk7d6Ysn38enOPnhFKlS1uXWaKFzb3EYJTPJ+hBHwdunD17FuEyePBgPPHEE2auX5HMzMjBUeVc/JhpUER0jkkUY5asWzerX1zdusDo0UCBAsCYMd63f/NNK6B76imgTh3gv/8FLrgAGDEi9XZ58wJly6Ys2amZ50utWsDatdZlBqzvvgts3249j3LlQhD0sRzLvn37zOWqVati//79iHQnTpwwpWXcF3EGBnqcA5qLgj4RnWMSGw4ftmausJcTJ9Juw5GuixcDrVunrGMTaevWwLx53vfL9e7bEzODntvPnGll4BiUseExWKHQY49ZmURitpIDOipWBN56C3jxxRAEfexHZ8+5yzlNw5n1y6yhQ4ciLi4ueUlISAj3IYmIiIifmLWLi0tZvPVvY36Ko1s9x/GVKQPs2uV9v1yf0fbMBHLeienTgZdeAmbNAtq3938krS/sv8c+hNSkCbBlC7BwIbBtG9Cxo//7zXTJlltuuQUtWrRAuXLlkCNHDjMjB4sze8PsSmb07dsXL/GV82H16tWozZ6VfujXrx96s1H/HGb6FPiJiIhEp1WrgPLlUze3hsodd6RcZk8z1sqrVs3K/rVqFZzHZNaS+TY+DpubsyvTQd97772Hm2++GevXr0evXr3QrVs3FC5cOFsP3qdPHzN7hy9sSvYXZwvhIiIiItGPYUeRIr634TwRzEnt3p16/e7dVj88b7g+K9sTwxM+1vr1gQ/6WJT50UetMi3099/W43Edg96+fUNQnLndubHJixcvxmOPPZbtoM8uqSEiIiISCHnyWE2ibIblCFxij7Tp04GePb3fp3lz63bWx7NNnWqtT09iotWnLzsDK9LTrx/w559WFtG9LAz7HQ4aFKKgzzZ27FiE2tatW3HgwAHz/5kzZ7Bs2TKzvnr16ihUqFDIj0dEREQiE3t2deli1blr1gx44w2rDApH81LnzlbGzO4TyIETnPv21VeBa68Fxo8HFi1iK6d1+5EjrCLCrm5W9m/DBuDppxmDWAM+Am3SJKvszMUXW/UAbfXqWY/tL7+CvnAYMGAAPrLznOdGE9OMGTPQsmXLMB6ZiIiIRBIOdmBtuwEDrMEYnDV28uSUwRqcz9a9bv8llwCffQY89xzwn/9YM18w8Kpf37qdzcV//WU1t3KmjPh4oE0bq7RLMHqR8djtOn3uGLi6B4FZlcPloHoWHMjBUbxJSUkoklGnAIlqHF2+91w1S83KIaJzTKJbYiIHYsZh27YkVKgQ+9/fV1wB3Hab1YePPekYcFapYl1ft84KYGM60yeS1SmiNO+uSPDoHBMJHtbiYzkYjlY+fdoqHs3LnDmEpWJifho2ERERESe47DJrIAcDPpaHmTLFau5lsWgOUvGXMn0Sk9hrgTOyEMv2sLakiOgcE4l0p04BDz4I9O8PvP9+YPetTJ/EbNDHmpJcHNRtVSRkdI6JBEfu3MDXXwdn3wr6RERERCII6wty9HCgqXlXREREJIKwZMzzzwO//Wb14StYMPXtvXr5t18FfSIiIiIR5H//A4oW5Qxo1uKOXdQV9ImIiIjEgE2bgrNf9ekTERERcQAFfSIiIiJhNmwYcPx45rZdsAD48cesP4b69EnMKlmyZLgPQSSm6RwTCRzOuFGxojX92vXXA02bchpR6zYWaebtc+cCn34K7NgBfPxx1h9DQZ/E7BRRZcuWDfdhiMQsnWMigcUgjrNwjBgB3HUXcOgQkDMnJxgAjh2ztmncGHjgAaBrVyBfvqw/Rg6XgyrXHjp0CHFxcUhKSkKRIrE/YbOIiEgsSEw8hISEOGzbloQKFWL/+/vsWeCvv4AtW6wmXzZcNWpk/Z8dyvRJTOJvmVOcy8ZUN8+tadhEdI6JRI3zzrOCPC6B5Mig7+zZs2ZJr8nCfTtftG3WXwfOgWvPgxvMbbn8/fff5nrt2rVTHWMojoFBp68kerRtS/ZrGMvbks77zL0OlN45Fg2fEeHeNhrO+0j7jJDsc2TQt2bNGhQqVCjNeq6rXLly8vXVq1en+2YsUKAAqlatmnx97dq1OHPmjNdt8+fPj2rVqiVfX7duXXIWylPevHlRg6W4z9mwYQNOnDjhdVtmsGrVqpV8fdOmTTieztCfnDlzok6dOsnXN2/ejGN2JwEPPMnr1auXfH3r1q04cuQI0lO/fv3ky4mJiaYZPT1169ZN/hDZsWMHDh48mO62/CLJlct6i+7atQsHDhxId9uaNWsiT5485vKePXuwb9++VH9vd9WrV0e+c50h9u7da5b08G/MvzXt378fu3fvTndbvnfs9xWPdefOneluW6lSJRQuXNhc5muwffv2dLdNSEgw3RKIr+22bdvS3bZ8+fIoVqyYucy/2Ra2DaSjXLlyKFGihLl89OhR855IT5kyZVDqXI9ivsc2btyY7rbcjtsT37uc/9jXQAC77yXPCTuI8KZ48eKIj483l3muef5d3RUtWhQVKlQwl3kOr2IP6HSwq0dF9p4+x9e2+oyw8Bx2/zzheR/NnxGe9BkRmZ8Rkn0Kn0VEREQcwJEDOf755590B3KomSd2mnftTJCad6Oj6SYStiU172budXDPiqp5V827wT4/nTCQ46+/mBW3+vMFiyObd/kGykwfgaz0I9C2kfs6+Pp7B+sY3AMqbRs9r0OkvocjcVv3oDCzn6mBPoZo3jYS3u/Rtm2sa9wYYK+g0qXZtQhYuBA417oeMGreFREREQmzokVT5txl98lMJNuzzJGZPhEREZFIcsstQIsWHEDDDKg1IweLM3vjY5yMTwr6JGZxtKeI6BwTiQbvvQfcfDPAwcy9egHdugHnijwEjII+iUnsW2OX9xARnWMi0aBdO+v/xYuBxx5T0CciIiIS08aODc5+lemTmMQSAHaxbBam1ugwEZ1jIk6n0bsSs0Ef6/RxcVApSpGQ0TkmEn0U9ImIiIg4gII+EREREQdQ0CciIiLiAAr6RERERBxAQZ+IiIiIAyjoExEREXEA1emTmFWUs1eLiM4xETEU9ElM4jRsFSpUCPdhiMQsnWMi0UfNuyIiIiIOEBVB3+bNm3H//fejSpUqyJ8/P6pVq4aBAwfi5MmT4T40ieDZAs6ePWsWzcghonNMnGfkSKByZSBfPuCii4A//vC9/ZdfArVrW9s3aAD89FPq2zm504ABQLlyQP78QOvWwLp1iCpREfRxKi1+eb/77rtYuXIlXn/9dYwePRr/+c9/wn1oEqEY6K1atcosCvpEdI6Js0yYAPTuDQwcCCxZAjRsCLRtC+zZ4337338H7rwTuP9+YOlSoEMHa1mxImWbl18G3noLGD0aWLAAKFjQ2ue//yJq5HBF6TfiK6+8glGjRmHjxo2Zvs+hQ4cQFxeHpKQkFClSJKjHJ+HFHwkM+Khu3bqm/5GI6ByT6JSYeAgJCXHYti0JFSpk/P3NzN6FFwIjRljXz54FEhKARx8F+vZNu33HjsDRo8APP6Ssu/hioFEjK8hjpBQfD/TpAzz5pHV7UhJQpgzw4YfAHXcgKkTtNyEDt+LFi/vc5sSJEybQc19EREQkOh0+zAROynLiRNpt2PNr8WKr+dXG3/2tWwPz5nnfL9e7b0/M4tnbb9oE7NqVepu4OCu4TG+fkSgqg77169fj7bffxoMPPuhzu6FDh5rMnr0kMMwXERGRqFS3rhVs2cvQoWm32bcPOHPGysK5K1PGCty84Xpf29v/Z2WfkSisQV/fvn2RI0cOnwv787nbvn072rVrh9tuuw3dunXzuf9+/fqZjKC9bNu2LcjPSERERIKFvXbYrGov/frptY6aOn19+vRB165dfW5TtWrV5Ms7duzAlVdeiUsuuQTvvfdehvvPmzevWURERCT6FS4MZNQlv2RJIGdOYPfu1Ot37wbKlvV+H673tb39P9dx9K77Nuz3Fy3CGvSVKlXKLJnBDB8DviZNmmDs2LHqmC8iIiJp5MkDNGkCTJ9ujcC1B3JMnw707On9BWve3Lr98cdT1k2daq2nKlWswI/b2EEe+xRyFO/DD0fPHyEqZuRgwNeyZUtUqlQJw4cPx969e5NvK5te2C6OpxHaIsGlc0wiFcu1dOkCNG0KNGsGvPGGNTr33nut2zt3BsqXT+kT+NhjQIsWwKuvAtdeC4wfDyxaBNiNijlyWAHhkCFAjRpWENi/vzWi1w4so0FUBH1Tp041gze4eE6tFaUVZyTIWKKlYsWKep1FdI6JA7EEC/NDLKbMgRbMzk2enDIQY+tWa0Sv7ZJLgM8+A557DmAJYAZ2kyYB9eunbPP001bg2L07cPAgcNll1j5ZzDlaRG2dPn+oTp+IiEjs1+mTGCrZIiIiIiIx2LwrklWakUMkuHSOiUQfZfpEREREHEBBn4iIiIgDKOgTERERcQAFfSIiIiIOoKBPRERExAEU9ImIiIg4gEq2SMwqVKhQuA9BJKbpHBOJLgr6JGanYatcuXK4D0MkZukcE4k+at4VERERcQAFfSIiIiIOoOZdidkpolavXm0u16lTxzRFiYjOMREnU9AnMcvlcoX7EERims4xkeii9IeIiIiIAyjoExEREXEABX0iIiIiDqCgT0RERMQBFPSJiIiIOIBG70rMKlCgQLgPQSSm6RwTiS4K+iQmsS5f1apVw30YIjFL55hI9FHzroiIiIgDKOgTERERcQA170rMTsO2du1ac7lWrVqahk1E55iI4ynok5h15syZcB+CSEzTOSYSXdS8KyIiIuIACvpEREREHEBBn4iIiIgDKOgTERERcQAFfSIiIiIOoNG7ErPy588f7kMQiWk6x0Sii4I+idkpoqpVqxbuwxCJWTrHRKKPmndFREREHEBBn4iIiIgDqHlXYnYatnXr1pnLNWrU0DRsIjrHRBwvajJ9N9xwAypWrIh8+fKhXLlyuOeee7Bjx45wH5ZEsFOnTplFRHSOiaTnwAGgUyegSBGgaFHg/vuBI0fg07//Aj16ACVKAIUKAbfcAuzenXqbHDnSLuPHI6yiJui78sor8cUXX2Dt2rX4+uuvsWHDBtx6663hPiwRERGJYp06AStXAlOnAj/8AMyeDXTv7vs+TzwBfP898OWXwKxZAHNQN9+cdruxY4GdO1OWDh0QVlHTvPsEX+FzKlWqhL59+6JDhw4mk5M7d+6wHpuIiIhEn9WrgcmTgYULgaZNrXVvvw1ccw0wfDgQH5/2PklJwP/+B3z2GXDVVSnBXZ06wPz5wMUXp2zLzGHZsogYUZPpc3fgwAGMGzcOl1xyiQI+ERER8cu8eVZgZgd81Lo1SxIBCxZ4v8/ixew+ZG1nq10bqFjR2p87NgGXLAk0awaMGQO4XOH9Q0VV0PfMM8+gYMGCKFGiBLZu3Ypvv/3W5/YnTpzAoUOHUi0iIiISnQ4fBvhVbi8nTmRvf7t2AaVLp16XKxdQvLh1W3r3yZPHChbdlSmT+j7PPw988YXVbMw+f488YmURHRv0sYk2R44cPpc1a9Ykb//UU09h6dKlmDJlCnLmzInOnTvD5SNsHjp0KOLi4pKXhISEED0zERERCbS6dYG4uJRl6FDv2/Xt630gRQ63xS28CIr+/YFLLwUaN2bSCnj6aeCVV+DcPn19+vRB165dfW5TtWrV5MslS5Y0S82aNVGnTh0TxM2fPx/Nmzf3et9+/fqhd+/eydeZ6VPg5xx58+YN9yGIxDSdYxJqq1YB5cu7vwe9b9enD5BBeAGGF+xvt2dP6vWnT1sjetPri8f1J08CBw+mzvZx9K6v/nsXXQT8979WdjJcX09hDfpKlSplFn/rsNlNuL4+kPSh5NwpolifT0R0jknsKFzYKq2SEYYWmQkvmje3gjf202vSxFr366+MMawgzRtux/Gj06dbzba0di2wdau1v/QsWwYUKxa+gC9qRu8uWLAACxcuxGWXXYZixYqZci39+/c3c6uml+UTERER8aVOHaBdO6BbN2D0aGuARs+ewB13pIzc3b4daNUK+Phja0AGm5VZy48Niez7xyD00UetgM8euctyLsz88Xq+fFa/vhdfBJ58Mrx/j6gI+goUKIBvvvkGAwcOxNGjR01x5nbt2uG5555TJk9ERET8Nm6cFegxsOOoXWbv3nor5XYGgszkHTuWsu7111O2ZYNj27bAO++k3M5M4MiRVj0/Dj2oXh147TUruAynHC5fIyFiDPv0cUBHUlISimQmPyxRi83/zAgTM8Js7hURnWMSnRIT2Sc/Dtu2JaFCBX1/x3SmT8Qfvvp7ikj26RwTiS5Kf4iIiIg4gII+EREREQdQ0CciIiLiAAr6RERERBxAQZ+IiIiIA2j0rsSs3CyUJCI6x0TEUNAnMYl1+WrVqhXuwxCJWTrHRKKPmndFREREHEBBn4iIiIgDqHlXYnYatk2bNpnLVapU0TRsIjrHRBxPQZ/ErOPHj4f7EERims4xkeii5l0RERERB1DQJyIiIuIACvpEREREHEBBn4iIiIgDKOgTERERcQCN3pWYlTNnznAfgkhM0zkmEl0U9EnMThFVp06dcB+GSMzSOSYSfdS8KyIiIuIACvpEREREHEDNuxKz07Bt3rzZXK5cubKmYRPROSbieAr6JGYdO3Ys3IcgEtN0jolEFzXvioiIiDiAgj4RERERB1DQJyIiIuIACvpEREREHEBBn4iIiIgDaPSuxKwcOXKE+xBEYprOMZHooqBPYnaKqHr16oX7MERils4xkeij5l0RERERB1DQJyIiIuIAat6VmJ2GbevWreZyxYoVNQ2biM4xEcdT0Ccx68iRI+E+BJGYpnNMJLqoeVdERETEAaIu6Dtx4gQaNWpkSgUsW7Ys3IcjIiIiUezAAaBTJ6BIEaBoUeD++5nF9n2f994DWra07sPqYAcPBma/wRZ1Qd/TTz+N+Pj4cB+GiIiIxIBOnYCVK4GpU4EffgBmzwa6d/d9n2PHgHbtgP/8J7D7Dbao6tP3888/Y8qUKfj666/NZRERERF/rV4NTJ4MLFwING1qrXv7beCaa4Dhw4H0ckyPP279P3NmYPcbbFGT6du9eze6deuGTz75BAUKFAj34YiIiEiUmzfPanq1AzNq3ZrFx4EFCyJvv47I9LlcLnTt2hUPPfQQmjZtis2bN2e6/x8XW1JSkvn/0KFDQTtWiZySLfbIQv69OXuAiOgck+h0+LD1vX3okAvuX+F581qLv3btAkqXTr0uVy6geHHrtkjbb1QHfX379sVLL73kc5vVq1ebJt3Dhw+jX79+Wdr/0KFDMXjw4DTrExISsnysIiIiEl716h0GEJd8feBAYNCgtNv17QtkEF6ATbBOE9agr0+fPiaD50vVqlXx66+/Yt68ecjrEc4z69epUyd89NFHXu/LILF3796psj8HDhxAiRIlNFG4AzDDxwB/27ZtKMLhU3psveZ6r8XMOSbOcvasC1u2HEbFivHImTNlfXpZvj59gAzCC1StCpQtC+zZk3r96dPWyFve5q9g7Teqg75SpUqZJSNvvfUWhgwZknx9x44daNu2LSZMmICLLroo3fsxSPQMFIuykV0chV9G4fpC0mPrNdd7TSQwihZNyfBlhKFFJsILNG9ulVtZvBho0sRa9+uvDDIBH+FF2PbriD59nEbLXaFChcz/1apVQ4UKFcJ0VCIiIhLN6tSxSq906waMHg2cOgX07AnccUfKCNvt24FWrYCPPwaaNbPWsV8el/XrrevLlwOFCzNesfrtZWa/4aDe7SIiIuJY48YBtWtbgR1Lqlx2mVV82caAbe1aqzafjYFc48ZWUEdXXGFd/+67zO83HKIi0+epcuXKZkSviC9s2h84cGCaJv5Q0GPrNdd7TSQ6FC8OfPZZ+rdXrswqIqnXcfCItwEkWdlvOORwKXoSERERiXlq3hURERFxAAV9IiIiIg6goE9ERETEART0iYiIiDiAgj5xBM7bnCNHDrzxxhshebxBgwahdu3aKFiwIIoVK4bWrVtjQQhm2T516hSeeeYZNGjQwDx2fHw8OnfubAqah8I333yDNm3aJM96s2zZspA87siRI82o/nz58pmC7X/88UdIHnf27Nm4/vrrzevM5ztp0qSQPC6nmLzwwgtRuHBhlC5dGh06dMBa1pQIgVGjRuH8889PLjzevHlz/PzzzyF5bBHJHgV9EvMmTpyI+fPnmy/mUKlZsyZGjBiB5cuXY+7cuSYgYTC0d+/eoD7usWPHsGTJEvTv39/8zyCMwcANN9yAUDh69Cguu+yyDOfUDiTOzMPpFlmeh8+5YcOGZsaePZ5zIAXp+fLxGHSG0qxZs9CjRw/zvp46daoJ9vn+4vEEGwviDxs2DIsXL8aiRYtw1VVX4cYbb8TKlSuD/tgikk0s2SISqxITE13ly5d3rVixwlWpUiXX66+/HpbjSEpKYpUn17Rp00L+2H/88Yd57C1btoTsMTdt2mQec+nSpUF/rGbNmrl69OiRfP3MmTOu+Ph419ChQ12hxOc7ceJEVzjs2bPHPP6sWbPC8vjFihVzffDBB2F5bBHJPGX6JGadPXsW99xzD5566inUq1cvbMdx8uRJvPfee4iLizNZoVBLSkoyTY+xOO80X1tmnNh8bjvvvPPM9Xnz5sEp+Dem4qwGG0JnzpzB+PHjTYaRzbwiEtmickYOkcxgE2OuXLnQq1evsLxgP/zwA+644w7T5FquXDnTDFeyZMmQHsO///5r+vjdeeedpv9VrNm3b58JPMqUKZNqPa+vWbMGTvlx8/jjj+PSSy9F/fr1Q/KY7LbAII/vL86Fzi4UdevWDclji4j/lOmTmDBu3Djz5WMv7PP05ptv4sMPPzRZrlA+9pw5c8z6K6+80gxk+P3339GuXTvcfvvtAe9nlt5jE/t58THZ8sjO94Hm67EldNi3b8WKFSbjFiq1atUy720OTnr44YfRpUsXrFq1KmSPLyL+0TRsEhMOHz6M3bt3J1//8ssv8eyzz5qmPhszQryekJCAzZs3B+2xy5cvj/z586fZrkaNGrjvvvvQr1+/oD+2HfBt3LgRv/76qxlNG2i+njdf3ypVqmDp0qVo1KgRgtm8W6BAAXz11VdmBKuNQcjBgwfx7bffIlT444IZL/fjCLaePXua58hRxHy9w4XN6dWqVcO7774btmMQkYypeVdiAktXcLF1797dlNJwxxGd7ON37733BvWxfTXDnThxIuiPbQd869atw4wZM4IS8KX32KGWJ08eNGnSBNOnT08Otvg68zoDoljF7O2jjz5qgsyZM2eGNeAL1ntbRAJPQZ/EJAY6nsFO7ty5UbZsWdM0FUzs1P7CCy+YMinsy8d+ZyzpsX37dtx2221BfWwGfLfeeqspXcI+hcxu7tq1K7mTP4OkYDpw4AC2bt2aXBfQrh3H151LMLBcCzN7TZs2RbNmzUwtRv4NAh3ce3PkyBGsX78++fqmTZtMsydf64oVKwa1Sfezzz4zWT4G3vbfmIOFvGWZA4mZ6vbt25vnx2wvj4OB5y+//BLUxxWRAMjCSF+RqBaqki3Hjx933XTTTaZsSJ48eVzlypVz3XDDDaZ0SqhKpXhbZsyYEfTHHzt2rNfHHjhwYFAf9+2333ZVrFjRvN4s4TJ//nxXKPA19fZ8u3TpEtTHTe9vzNc/2O677z5zLvG1LlWqlKtVq1auKVOmBP1xRST71KdPRERExAE0eldERETEART0iYiIiDiAgj4RERERB1DQJyIiIuIACvpEREREHEBBn4iIiIgDKOgTERERcQAFfSIiIiIOoKBPRCLG//73P7Rp0yb5eteuXZPn1M2OHDlyYNKkSQiUvn37mrlvRUSiiWbkEJGI8O+//6Jq1ar48ssvcemll5p1SUlJnCoSRYsWzXbQN3HixIAEkMT5lHmsnGeX/4uIRANl+kQkInz11VcoUqRIcsBHcXFx2Q74gqFkyZJo27YtRo0aFe5DERHJNAV9IhJQe/fuRdmyZfHiiy8mr/v999+RJ08eTJ8+Pd37jR8/Htdff32qdZ7Nuy1btkSvXr3w9NNPo3jx4uZxBg0alOo+69atwxVXXIF8+fKhbt26mDp1aprH2rZtG26//XYTUHI/N954IzZv3mxuW7NmDQoUKIDPPvssefsvvvgC+fPnx6pVq5LX8Vh5zCIi0UJBn4gEVKlSpTBmzBgTjC1atAiHDx/GPffcg549e6JVq1bp3m/u3Llo2rRphvv/6KOPULBgQSxYsAAvv/wynn/++eTA7uzZs7j55ptNgMnbR48ejWeeeSbV/U+dOmWydIULF8acOXPw22+/oVChQmjXrh1OnjyJ2rVrY/jw4XjkkUewdetWJCYm4qGHHsJLL71kgkhbs2bNzG12sCgiEunUp09EgqJHjx6YNm2aCeSWL1+OhQsXIm/evF63PXjwIIoVK4bZs2fj8ssvT5Xp4232IAxm+s6cOWOCNffg66qrrsKwYcMwZcoUXHvttdiyZQvi4+PN7ZMnT0b79u2T+/R9+umnGDJkCFavXm36+hGDPWb9+Dj2QJLrrrsOhw4dMgFkzpw5zX7s7Ym3sfl55syZaNGihd5FIhLxcoX7AEQkNjFbVr9+fTMwY/HixekGfHT8+HHzP5tkM3L++eenul6uXDns2bPHXGYgl5CQkBzwUfPmzVNt/+eff2L9+vUm0+c5kGTDhg3J15mtrFmzJs477zysXLkyVcBHbO6lY8eOZXjMIiKRQEGfiAQFA6gdO3aYJlc2gTZo0CDdbUuUKGGCqn/++SfD/ebOnTvVdd6Pj5FZR44cQZMmTTBu3DivTdPuweHRo0dN0Ldz504TXLo7cOBAmvuIiEQyBX0iEnBsLr377rvRsWNH1KpVCw888IBp4i1durTX7dmEyv5yHCjhXqcvq+rUqWMGabgHafPnz0+1zQUXXIAJEyaYY+FoYW8Y0LFp+dlnnzX76tSpE5YsWZKc3aMVK1aYALRevXp+H6+ISChpIIeIBByDJdbYe+utt8xACjaT3nfffT7vw8EVHMyRHa1btzaP1aVLF5OpY98/Hos7BnAsucIRu7x906ZNpl8eRwVzYAZx4AabiZ977jm89tprph/hk08+mWo/vC/7H7oHgiIikUxBn4gEFAOoN954A5988onJpLF5lJcZJPmqa3f//ffjp59+MsGiv/hYHLDBPoIc4MEM4wsvvJBqG5Zj4YCRihUrmpG+zA7ysdmnj8f78ccfm+PgMefKlcuMFObgj/fffx8///xz8n5YrqVbt25+H6uISKhp9K6IRIzbbrvNNL/269cPkYzBX58+ffDXX3+ZwFBEJBoo0yciEeOVV14xNfMiHQd4jB07VgGfiEQVZfpEREREHECZPhEREREHUNAnIiIi4gAK+kREREQcQEGfiIiIiAMo6BMRERFxAAV9IiIiIg6goE9ERETEART0iYiIiDiAgj4RERERxL7/A2oOPZtpLkmsAAAAAElFTkSuQmCC", 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" ] @@ -1148,7 +1133,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 10, "id": "34", "metadata": {}, "outputs": [ @@ -1156,7 +1141,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3DILrogdwroL6Ht6yyRhhAQotSH\n", + "Quantum program link: https://platform.classiq.io/circuit/3DIb1l6DjflPUfuyaOznk0sDwzs\n", "Parsed counts: [{'x': -2}: 2048]\n", "The analytical gradient is: -0.5\n", "The majority gradient is: -0.5\n", @@ -1273,7 +1258,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 11, "id": "36", "metadata": {}, "outputs": [ @@ -1281,14 +1266,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3DINMWkHQwj0urBbWT2H9OD79eG\n", - "Parsed counts: [{'x': 2}: 1765, {'x': 3}: 136, {'x': 1}: 57, {'x': -4}: 28, {'x': 0}: 20, {'x': -1}: 16, {'x': -3}: 16, {'x': -2}: 10]\n", + "Quantum program link: https://platform.classiq.io/circuit/3DIb2AIHYhra9keJamdJ86vntbo\n", + "Parsed counts: [{'x': 2}: 1781, {'x': 3}: 121, {'x': 1}: 67, {'x': -4}: 21, {'x': 0}: 16, {'x': -2}: 15, {'x': -1}: 15, {'x': -3}: 12]\n", "The analytical gradient is: 0.55\n", "The majority gradient is: 0.5\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 86.18% (1765/2048 shots)\n", - "[\u001b[92m███████████████████████████████████████████\u001b[91m-------\u001b[0m] 86.18%\n" + "Success rate: 86.96% (1781/2048 shots)\n", + "[\u001b[92m███████████████████████████████████████████\u001b[91m-------\u001b[0m] 86.96%\n" ] }, { @@ -1303,7 +1288,7 @@ }, { "data": { - "image/png": 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LSgvwaaVpTdylgEiL+qnQyT9SrGrVqm6yL60MraHyx48fdytgq0CaEWAAACAkA6AffvjBGjVqFLjtr8vp0KGDG+req1cvN1eQ5vVRpueqq65yw9xjYv4/B2nmVlFW0KPVsFUB3qpVKzd3EAAAGSlH9hzW4ZIOgX2Et5CZBygrqWtNQ+xVDJ1aDZC61Y4dO3bW2waEily5cqV7mCkAZPX1OzWEsGmgwEfdcwqCAK9S8KOuaAVCABDuCIBOQQmynTt3WlRUlBtqx3/A8CIF/7///rv7XVB9HhOGwqvXg7jjcW4/T848/B6EOQKgU9Cw+ri4OFdUnSdPnrPzqQAhqGjRoi4I0u9Ezpw5s7o5wFmn4CffwHxu/1CfQwyDD3N06J9CQkKC+0raH17n/x3w/04AQDgjAEojUv7wOn4HAEQSAiAAAOA5BEA4Y+XLl7fhw4ef0XPMnz/fZRg031NG2LJli3s+TawZKjp27BiYxFMaNmzoJvsEAJx9BEARbvHixW4E24033mihIqUL/5VXXulGGGk+B6+YNm2avfTSS5kaZAEAUkYAFOHeeecde/jhh23hwoVuBE8oF9hq7bdQrzPRcisZRUu+nM4KxgCAM0cAFMG01tpHH31kDzzwgMsAaXmRlLqdtOBs7dq13TB/ZWLWr18feMwvv/xiLVq0sOLFi1u+fPmsTp069tVXX6X6mp06dbKbbropWdBQrFgxF4wpQ7FgwQJ77bXX3GtrU3dVSl1g33zzjcsWqV3nnnuuNW3a1P788093n5ZE0dIoBQsWtMKFC7vXVFvTQxknnZfcuXO7Cf4mTZqUrDtPbRo9erTdfPPNljdvXuvfv78bBdW5c2f3PfreypUru/cTTI/R0i7+9mlZl6STrifNhB09etQef/xxO++889xraUFfnRc/fX56vlmzZrl18PR5aC08vQ954YUXbPz48fbpp58Gzm3w9wM4M1HZo+y2are5TfsIbwRAp+nwscOpbvEn4tP82CPHj6Tpsafj448/tipVqrgL9J133mnvvvtusouwPP300/bqq6+6tdly5MjhgpjgIKpZs2YuSFqxYoW74DZv3ty2bt2a4mvee++9LjjxX5Tliy++cHMptW3b1gUK9erVcwvY6jHaNMFkUqrd0fpu1apVc914ixYtcq/rH4KtNeIUYKjNapsmqLz11lvTNVv33Xff7bJiChKmTp1qb731lu3ZsyfZ4xRY6LlXrVrlzo1eo3Tp0jZ58mRbs2aNPffcc/bUU0+58+2n86mARedcbf/jjz9s+vTp/9gerWmn9/rhhx/aTz/9ZK1bt3bne+PGjYHH6Dy+8sor9v7777usnj4HBU2ir23atAkERdoU0ALIGDE5Ymxy68lu0z7CnNYC87qDBw8qKnBfkzpy5IhvzZo17mswe8FS3ZpNbJbosXn650n1sQ3GNUj02CKDi6T4uNNx5ZVX+oYPH+72jx8/7itSpIhv3rx5gfu1r/f91VdfBY59+eWX7ljS9xvsoosu8o0YMSJwu1y5cr5hw4YFblerVs338ssvB243b97c17Fjx8DtBg0a+Lp3757oOf1t+fPPP93tdu3a+erXr5/m97p37173/atWrXK3N2/e7G6vWLEixcevXbvW3b906dLAsY0bN7pjwe9Ftx999NFTvn63bt18rVq1CtwuWbKkb/DgwYHbOv+lS5f2tWjRIsXz8Ntvv/mioqJ8O3bsSPS811xzja9Pnz5uf9y4ca49mzZtCtw/atQoX/HixQO3O3TokOg1MlJqvwsAEIrX71MhAxSh1I31/fffW7t27dxtZXaUgVE3VFIXX3xxYL9kyZLuqz8TogyQMgvqclH3i7pd1q5dm2oGyJ8FGjdunNvfvXu3zZgxI1FWKS38GaDUKCui93b++ee7BfDUdSX/1K6k50fn5LLLLgscq1ixoutqS0rdg0mNGjXKatWq5WZH1jlR9sj/2lqUT9kXdWH56bVSeh4/ZZeU3brwwgvd8/k3dRcGd+2pO/CCCy5I9HmllLUCAPwzlsI4TZoGPTVJ+4b3PJ76BSp7tsQx6JbuWywjKNDRkgVawsNPCY3o6GgbOXJkotFWwcsa+IuQ/V1JCn7mzJnjul0UIKjm5bbbbnMLxP5T11Lv3r1dd863337ramX+9a9/pav9ep1/ou6wcuXK2dixY917VHurV6/+j+06XarHCaYuKp0XdXOpO0+FzEOGDLHvvvvutF9DgaZG6y1btsx9DaZAyC/pEhT6vFLq1gSQ8VSOwFIYkYMA6DTlzZU3yx+bGgU+EyZMcBfo6667LtF9GiL9wQcfWNeuXdP0XCpEVuGyamD8F2oVLf8TFf3qdZQFUhB0zz33JBvxdarlFJSVUm1P3759k923f/9+l8FR8OMPrFRnkx6qi9J5Ul2TMjmyadOmQJH1qc6JamsefPDBwLHgLI2CS2VmFBBdffXV7pheS8FNcMYpWM2aNd05UTYnvcFies8tAIAAKCKp6FgXco1USjqvTqtWrVx2KK0BUKVKldx8Ncq4KNvw7LPPpqnQWN1gGpmli3GHDh0S3afuKgUHCqSU3dBw8KT69OljNWrUcEGG2qoL+7x581xhsB6vIEvdTgo01PWkjFN6qDi8SZMmdt9997lRXsqs9OzZ02WeTjUUX+dEAaZGYym7pYLkpUuXun2/7t2726BBg9xj9VpDhw79x0ke1fXVvn17lz1T4KqAaO/evS4IVDCY1nmcdG7VLgWIOkf6/Fm4FACSowYoAinA0cU9pUkFFQBp5JRGGaWFLtyqi1HGQ0GQhqKnlsUIptdXcKLHB3fDibqP1M2jEV6qoUmpbkcBwezZs23lypV2+eWXu64mDe9WLY1GfKkbShkVdXv16NHDdUGll4IYDe9XlkYZLo1MU3dWTMw/j+64//77rWXLlq6mSnU+ykgFZ4NEwdRdd93lgj9/N5k/i5YaZcwUAOl7laFSFk2BVdmyZdP8nvQe9L2qN9K5VbYKAJBcNlVCm8fFxsa6YEHFqyqoDRYfH2+bN292/92f6sKI/1FXmeaz0UVdwUI42L59uxuSr3mO/qkA26v4XYDXUQMUXtfvU6EGCBlK3WP79u1z3TgaNaYJBEPVf//7XxeoqatNo7Y0WaG6kPx1OwCAyEUAhAyl7ixlyzRRoCYCVJdVqNIM1ZrA8Ndff3VdVOrmmzhxIjUzAOABoXt1QlhSBiVcelVVn6QNANJCU5w0q9QssI/wRgAEAEAaaPmLL+/4knMVIRgFBgAAPIcACAAAeA4BEAAAaRwGn3dAXrdpH+GNGiAAANIo7ngc5ypCkAECAACeQwAEAAA8hy6w0zRt/U47m1pWLpmux2sF9/Hjx7t1q8aMGZPovm7dutkbb7zh1qnSZIU4fVo4dfr06W7drlD3wgsv2CeffGI//vhjVjcFALIcGaAIpnWttGjokSNHEq3nNGnSpHQtsJlVjh07ltVNAABEKAKgCKZV2xUETZs2LXBM+wp+atasmWwNr4EDB7plLHLnzm2XXHKJTZkyJXB/QkKCde7cOXC/Vhx/7bXXEj3H/Pnz3crtefPmdeuA1a9f33777bdARippluTRRx+1hg0bBm5r/6GHHnLHixQpEpil+eeff7YbbrjB8uXL51Zv1yrrWm8s+Psefvhh931auV6PGTt2rB0+fNjuuecet8xFxYoVbcaMGYlePy3P+8gjj7g1wgoVKmQlSpRwWZTgWa9Fq7wrE+S/ndpCq+3atXPPo/Oj1dq/++67wP2jR4+2Cy64wHLlyuXO7fvvvx+4b8uWLe75gzM3Bw4ccMd0zv3nXrfnzp3rnjtPnjxuaY/169e7+5Xp69u3r61cudI9TpuOadZuvSf9TERHR1upUqXcewaASEcAFOE6derkVmT3e/fdd11QkJSCnwkTJrjustWrV1uPHj3szjvvtAULFgQCJK3vNXnyZFuzZo0999xzbh2tjz/+2N1/4sQJF+A0aNDAfvrpJ1u8eLHdd9997kKbHuq2UxDwzTffuLboQt+4cWMXsP3www82c+ZM2717t7Vp0ybZ9ylo+v77710w9MADD1jr1q1dELB8+XK77rrrXIATF/f3CI70PK8CFgUrgwcPthdffNHmzJnj7lu6dKn7qvOrxVT9t5PSgqs6Lzt27LDPPvvMBSEKqnRORV1o3bt3t549e7qgTN2W+ozmzZtn6fX000+7hWj1nrQOmz5/adu2rXv+iy66yLVVm45NnTrVhg0bZm+++aZt3LjRdZFpcVgAyWXPlt0alGvgNu0jvFEDFOEUxPTp0yeQiVFgoW4xf+ZAjh49agMGDLCvvvrK6tWr546df/75tmjRIndh1MU7Z86cLoPgp0yQghwFQAoaYmNj7eDBg3bTTTe5TIZUrVo13e2tVKmSCzT8+vXr54IUtS84iFNma8OGDXbhhRe6Y8pYPfPMM25f73fQoEEuIOrSpYs7poBNWRYFZ1dccYWNHDkyTc978cUX2/PPPx9om75PWZZrr73WihYt6o4r26XsUGrU5bh3714XICkDJMpI+b3yyisuQ/bggw+624899pgtWbLEHW/UqFG6zl///v3d5yW9e/e2G2+80XV7KmunTJeCouC2avFa3W7SpIn7jJUJUhYPQHK5c+a2+R3/97cT4Y0QNsLpIq2LoLo7lKnQvgKDYJs2bXKZEV3UdZH0b8oI/fLLL4HHjRo1ymrVquWeU/e/9dZb7gIqurDrIq5uq+bNm7vuMWUZ0kvPH0zZEmVCgttVpUoVd19w2xSo+EVFRVnhwoUTZTLUxSV79uw57eeVkiVLBp4jrdR1pWDLH/wktXbtWtddGEy3dTy9gturtso/tVdZMtWIKeBVsKhslLJ5ABDpyAB5gLpBVFvjD2JS6qKRL7/80s4777xE96kuRJQ1evzxx133irJEqqsZMmRIojoWBViqH1F30kcffeQyMuouUsYle/bsyVaJP378eLK2qLspadsUUL388svJHuu/wIuyF8HU9RZ8zN8V5+92OpPn9T9HWin7ciZ07iT4/KV07uSf3nNKlPFSnZCyf/qslIXS56quz6TvHQAiCQGQB1x//fVuRJUuiP7C4mDVqlVzgY6yOf7uk6TUdaZ6Gn83TdJMiZ8yHdrUDaVASd0/CoCUNVJ9S9LMyKkusirkVp2KCozVfZNRMup51X4ViJ8qK/P222/bH3/8kWIWSF2FOr+alsBPt/W5iL+rTRk1f/H66QxlV21VSm1VgKZgUJumSFAmbNWqVe4cAfgfLX9R/rW/Bzts6b7F8uZK/A8bwgtdYB6gLiF1p6h4WftJKZuj7I4Kn1X0q8BGhcMjRoxwt/31LyqsnTVrlquRefbZZxMV/W7evNkFPaoLUr3R7NmzXVGtvw5IBcf6fnWr6bjqapIGRCnRBVmBg0ZQ6fXUNrVBRcKnCjzOxvMqgFJN0K5du+zPP/9M8TF6DdXZqEhcgc2vv/7qgi+dK3niiSdcF6VqlHRuhg4d6kbr6TPxBygKIlXXpM9R2Rl/vVN6qK36nBQ8abSbar/0uu+88477LNSuf//73+71ypUrl+7nB7xgX9w+tyH8EQB5RP78+d2WmpdeeskFNRoNpqBFWSN1ianYWTQyqWXLlm7kUN26dW3//v2JskEadr1u3Tpr1aqVKyDWCDAFGfo+UeZJz6/RT3Xq1LG//vrL7r777lO2W8OyFTQoKNFILtX1aLi7Co/9XUOnI6OeV12C6jpSV1LSqQWCMy8KCIsVK2bNmjVzr6Vgxh+MKjBSzZSKnjVKS4Xn6k4MniJABdqqzVGNlNqp4vD00mejz1WF1coqffDBB+79asoA1RwpU6WusM8//9zVUAFAJMvmS1qY4UEawVSgQAE3iilpkKARNPqvWYFATExMlrURyGr8LsDr1AWWb2A+t3+ozyG6wEL8+n0qZIAAAIDnEAABAADPIQACAACewzB4AADSQMtf1C5VO7CP8EYAlEbUisPr+B2A12kpjKVdUl7zD+GHAOgU/EOVNZHgmc7oC4Qz/Q5ISnNJAWfLtPXpX2InK7Ws/L+Z5RFaCIBOdYJy5HBz3GgxS836eyZzzwDhSstp6HdAvwsZOSM3AGQV/pKdgpaP0NpQmgvIv6I64EUK/rVavH+NMcBrjp6Is+7/+XuC0teazbfoHHmyukk4AwRAaaCZfLUUhL8LAPDq7wEZUHiZZg3eG7c9sI/wRgCURvrDz0zQAABEBgpaAACA5xAAAQAAzyEAAgAAnkMABAAAPIciaAAA0kATQJTOf2FgH+GNAAgAgDTQvD+a/weRgS4wAADgOQRAAADAcwiAAABIx1IY2rSP8EYNEAAAaaDlL7bHbgjsI7yRAQIAAJ5DAAQAADyHAAgAAHgOARAAAPCckA6AEhIS7Nlnn7UKFSpY7ty57YILLrCXXnrJfL7/lZ9p/7nnnrOSJUu6xzRp0sQ2btyYpe0GAAChLaQDoJdfftlGjx5tI0eOtLVr17rbgwcPthEjRgQeo9uvv/66jRkzxr777jvLmzevNW3a1OLj47O07QCAyKLlL4rmKe02lsIIfyE9DP7bb7+1Fi1a2I033uhuly9f3j744AP7/vvvA9mf4cOH2zPPPOMeJxMmTLDixYvbJ598YrfffnuWth8AEFlLYYy5+e/rD8JfSGeArrzySps7d65t2PD3vAsrV660RYsW2Q033OBub9682Xbt2uW6vfwKFChgdevWtcWLF6f6vEePHrXY2NhEGwAA8I6QzgD17t3bBSdVqlSxqKgoVxPUv39/a9++vbtfwY8o4xNMt/33pWTgwIHWt2/fTG49AAAIVSGdAfr4449t4sSJNmnSJFu+fLmNHz/eXnnlFff1TPTp08cOHjwY2LZt25ZhbQYARKajJ45Yr9k3uE37CG8hnQF64oknXBbIX8tTo0YN++2331wGp0OHDlaiRAl3fPfu3W4UmJ9uX3rppak+b3R0tNsAAEgrn/nslz9WBvYR3kI6AxQXF2fZsyduorrCTp486fY1PF5BkOqE/NRlptFg9erVO+vtBQAA4SGkM0DNmzd3NT9ly5a1iy66yFasWGFDhw61Tp06ufuzZctmjz76qPXr188qVarkAiLNG1SqVCm75ZZbsrr5AAAgRIV0AKT5fhTQPPjgg7Znzx4X2Nx///1u4kO/Xr162eHDh+2+++6zAwcO2FVXXWUzZ860mJiYLG07AAAIXdl8wdMqe5S6zTR8XgXR+fPnz+rmAABSMW39ziw7N/En4qz9lIpuf+JtmywmR55Tfk/Lyv+rT0VoXb9DugYIAADAc11gAACEkvzRhbK6CcggBEAAAKSBurzG3foz5ypC0AUGAAA8hwAIAAB4DgEQAABpoOUvnpvbym0shRH+qAECACANtPzF6r2LA/sIb2SAAACA5xAAAQAAzyEAAgAAnkMABAAAPIcACAAAeA6jwAAASKPoqNycqwhBAAQAQBqXwpjU+hfOVYSgCwwAAHgOARAAAPAcusAAAEiDYwnxNmRRF7f/xFVjLVdUDOctjBEAAQCQBid9J235zrmBfYQ3usAAAIDnEAABAADPIQACAACeQwAEAAA8hwAIAAB4TrpGgZ08edIWLFhgX3/9tf32228WFxdnRYsWtZo1a1qTJk2sTJkymddSAACAs5kBOnLkiPXr188FOM2aNbMZM2bYgQMHLCoqyjZt2mTPP/+8VahQwd23ZMmSjGobAAAhtRTG1Nt/d5v24YEM0IUXXmj16tWzsWPH2rXXXms5c+ZM9hhlhCZNmmS33367Pf3009aly9+TRQEAAISabD6fz3eqB61du9aqVq2apic8fvy4bd261S644AILF7GxsVagQAE7ePCg5c+fP6ubAwBIxbT1O8Pq3LSsXDKrmxDRYs/g+p2mDFBagx9Rdiicgh8AANK6FMbrSx5x+49c8TpLYXh1KYwTJ07Ym2++afPnz7eEhASrX7++devWzWJiWBsFABB5tPzF4m1fuP2H6g7P6uYgqwKgRx55xDZs2GAtW7Z03V4TJkywH374wT744IMzbRMAAEBoBEDTp0+3W2+9NXB79uzZtn79ejcSTJo2bWpXXHFF5rQSAAAgKyZCfPfdd+2WW26x33//3d2+7LLLrGvXrjZz5kz7/PPPrVevXlanTp2MbBsAAEDWBkAKctq1a2cNGza0ESNG2FtvveUqrjXk/dlnn3VzBGkYPAAAQETVALVt29Z1dSnbo69jxoyxV199NfNaBwAAEAprgRUsWNBlf4YMGWJ33323PfHEExYfH58ZbQMAAMjaAEiTG7Zp08Zq1Khh7du3t0qVKtmyZcssT548dskll7jlMQAAiFTRUblt4m2b3KZ9eCQAUrYne/bsLvNTrFgxu//++y1XrlzWt29f++STT2zgwIEuQAIAIBJly5bNrQGmTfvwSA2Q5vhZuXKlm+VZ9T9a/DR4puiFCxe6rjEAAICICYBq1aplzz33nHXo0MG++uor1xWW1H333ZfR7QMAICQcTzhqY5Y+6fa71nnZckZFZ3WTcDa6wDTT89GjR61Hjx62Y8cOtwwGAABekeBLsPlbPnab9uGRDFC5cuVsypQpmdsaAACAUMkAHT58OF1Pmt7HAwAAhFwAVLFiRRs0aJDt3Lkz1cf4fD6bM2eO3XDDDfb6669nZBsBAADOfhfY/Pnz7amnnrIXXnjBzflTu3ZtK1WqlMXExNiff/5pa9asscWLF1uOHDmsT58+bog8AABAWAdAlStXtqlTp7rJECdPnmxff/21ffvtt3bkyBErUqSI1axZ08aOHeuyP/7V4QEAACJiLbCyZctaz5493QYAAOCJAAgAAK/S8hfv3rIqsI/wRgAEAEAaaPmLAjGFOVdeXQ0eAAAg3JEBAgAgjUthvLfiBbffseYLLIUR5sgAAQCQBlr+Yuam8W5jKQwPBkAzZ860RYsWBW6PGjXKLr30UrvjjjvcnEAAAAARFwA98cQTFhsb6/ZXrVrlhsQ3a9bMNm/ebI899lhmtBEAACBra4AU6FSrVs3ta3LEm266yQYMGGDLly93gRAAAEDEZYBy5cplcXFxbv+rr76y6667zu0XKlQokBkCAACIqAzQVVdd5bq66tevb99//7199NFH7viGDRusdOnSmdFGAACArM0AjRw50i16OmXKFBs9erSdd9557viMGTPs+uuvz9jWAQAAZIJsPp/PZx6nrrsCBQrYwYMHLX/+/FndHABAKqat35ll5+ak76TtO7zD7RfJe55lz3bqHELLyiXPQsu8K/YMrt/pzgBptfc9e/YkO75//35WggcARCwFPMXylXFbWoIfhLZ0f4KpJYyOHj3qCqQBAAAipgj69ddfDywG9/bbb1u+fPkC9yUkJNjChQutSpUqmdNKAACy2PGEYzZp1SC3f0eN3pYzin/6PREADRs2LJABGjNmTKLuLmV+ypcv744DABCJEnwn7LN1f1/n2lZ/3HIaAZAnAiBNgCiNGjWyadOm2bnnnpuZ7QIAAAidGqB58+YFgh9lgzJ7ENmOHTvszjvvtMKFC1vu3LmtRo0a9sMPPwTu1+s/99xzVrJkSXd/kyZNbOPGjZnaJgAAEN5Oq4x9woQJLhBRwKHt4osvtvfffz/DG6fFVTXhYs6cOd08Q2vWrLFXX301UfZp8ODBrj5J3W/fffed5c2b15o2bWrx8fEZ3h4AAODRmaCHDh1qzz77rD300EMuOBGtDt+1a1fbt2+f9ejRI8Ma9/LLL1uZMmVs3LhxgWMVKlRIlP0ZPny4PfPMM9aiRYtAcFa8eHH75JNP7Pbbb8+wtgAAAA9ngEaMGOFmgFZwcvPNN7tNWZg33ngjMFIso3z22WdWu3Zta926tRUrVsxq1qxpY8eOTVSXtGvXLtft5acJkerWrWuLFy9O9Xk1ZF+TJwVvAADAO9IdAO3cudOuvPLKZMd1TPdlpF9//dUFW5UqVbJZs2bZAw88YI888oiNHz/e3a/gR5TxCabb/vtSMnDgQBco+TdlmQAAgHekOwCqWLGiffzxx8mOa1FUBSoZ6eTJk3bZZZfZgAEDXPbnvvvusy5dupzxcPs+ffq4abP927Zt2zKszQCAyJQrKsaG3TDPbdqHx2qA+vbta23btnUTH/prgL755hubO3duioHRmdDIrmrVqiU6VrVqVZs6darbL1GihPu6e/du91g/3b700ktTfd7o6Gi3AQCQVlr+omyBypwwr2aAWrVq5UZbFSlSxBUaa9P+999/b7feemuGNk4B1vr16xMd27Bhg5UrVy5QEK0gSMGXn+p51L569eplaFsAAICHM0BSq1Yt+/e//22ZTSPKVFukLrA2bdq4IOutt95ym39ZjkcffdT69evnut8UEGmEWqlSpeyWW27J9PYBALy1FMa0NX8P9mlZ7RGWwvBiAKTanE2bNrlV4bUf7Oqrr86otlmdOnVs+vTprmbnxRdfdAGOhr23b98+8JhevXrZ4cOHXX3QgQMH7KqrrrKZM2daTAz9swCAjF0K4+PVQ91+i6oPshRGmMvmS+dUzkuWLLE77rjDfvvtt2SzQCsjo4VRw426zTQaTAXR+fPnz+rmAABSMW19xo42To/4E3HWfkpFtz/xtk0WkyPPKb+nZeX/1acitK7f6c4AacJDzc3z5ZdfusJjBT0AAADhJN0BkNbZmjJlihsODwAA4IlRYJplWfU/AAAAEZ0B+umnnwL7Dz/8sPXs2dPNtKwFUbVQaTAtjAoAABD2AZAmFVStT3DRc6dOnQL7/vvCtQgaAAB4S5oCIC06CgCAl+XMHm0vX/ufwD48EAD5Z14GAMCrorJHWcXCqS+zhAgvgtZK7BoCHzwRYcGCBd2MzZobCAAAIOICIC1LkTt3bre/ePFiGzlypA0ePNitB6alKwAAiNSlMD5Z+4bbtA+PzQO0bdu2wBxAWgj1tttuc8tQaOHShg0bZkYbAQAIiaUw3l/Zz+1fX6kjS2F4LQOUL18+279/v9ufPXu2XXvttW5fa28dOXIk41sIAACQ1RkgBTz33nuv1axZ0zZs2GDNmjVzx1evXm3ly5fP6PYBAABkfQZo1KhRVq9ePdu7d69NnTrVChcu7I4vW7bM2rVrx0cEAAAiLwOkEV8qfE6qb9++GdUmAACA0MoAAQAAhDsCIAAA4Dnp7gIDAMCLtPxF30ZTAvvwQAbos88+s+PHj2d+awAACOGlMKoXv9Jt2ocHAqBbb73VDhw44PajoqJsz549md0uAACArA2AihYtakuWLHH7Pp/PsmXLlnktAgAgBJ04edxmbBznNu3DAzVAXbt2tRYtWrjAR1uJEiVSfWxCQkJGtg8AgJCgoOftZU+7/UYV2lqO7DmzuknI7ADohRdesNtvv902bdpkN998s40bN87NBwQAABDRo8CqVKnitueff95at25tefLkydyWAQAAhMoweAVAoqUw1q9f7/YrV67s6oQAAAAiciLEuLg469Spk5UqVcquvvpqt2m/c+fO7j4AAICIC4B69OhhCxYscHMDaWi8tk8//dQd69mzZ+a0EgAAICu7wLQC/JQpU6xhw4aBY82aNbPcuXNbmzZtbPTo0RnZPgAAgKwPgNTNVbx48WTHixUrRhcYACBi5cyey566ekJgHx7rAqtXr54rhI6Pjw8cO3LkiPXt29fdBwBAJIrKnsNqlWriNu0jvKX7E3zttdesadOmVrp0abvkkkvcsZUrV1pMTIzNmjUrM9oIAACQtQFQ9erVbePGjTZx4kRbt26dO9auXTtr3769qwMCACBSZ4JeuGWa27+6fEtmgg5zp5XD0ySIXbp0yfjWAAAQwgHQqO97uP0ryzYnAPJaDRAAAEC4IwACAACeQwAEAAA8hwAIAAB4zmkFQFr+4u2337Y+ffrYH3/84Y4tX77cduzYkdHtAwAAyPpRYD/99JM1adLEChQoYFu2bHGjwQoVKmTTpk2zrVu32oQJf8+SCQAAEDEZoMcee8w6duzo5gLS5IfB64EtXLgwo9sHAEBI0PIXPa98020sheHBDNDSpUvtzTffTHb8vPPOs127dmVUuwAACCla/kLz/8CjGaDo6GiLjY1NdnzDhg1WtGjRjGoXAABA6ARAN998s7344ot2/Phxdztbtmyu9ufJJ5+0Vq1aZUYbAQDIcgknT9i3Wz93m/bhsQDo1VdftUOHDlmxYsXcKvANGjSwihUr2jnnnGP9+/fPnFYCAJDFjp88Zq9+e7/btA+P1QBp9NecOXNs0aJFbkSYgqHLLrvMjQwDAACI2MVQ5aqrrnIbAABAxAdAr7/+eorHVQukYfHqDrv66qstKioqI9oHAACQ9QHQsGHDbO/evRYXF2fnnnuuO/bnn39anjx5LF++fLZnzx47//zzbd68eVamTJmMbzEAAMDZLoIeMGCA1alTx02EuH//frdpCHzdunXttddecyPCSpQoYT169DjTtgEAAIRGBuiZZ56xqVOn2gUXXBA4pm6vV155xQ2D//XXX23w4MEMiQcAAJETAO3cudNOnEg+/4GO+WeCLlWqlP31118Z00IAAEJAjuw5rdvlwwL78FgXWKNGjez++++3FStWBI5p/4EHHrDGjRu726tWrbIKFSpkbEsBAMhCCnoan9/WbQRAHgyA3nnnHbf6e61atdyyGNpq167tjuk+UTG0JkwEAACIiC4wFThrIsR169a54mepXLmy24KzRAAARBItf/Hjrvlu/9ISDd3iqAhfp/3pValSxW0AAHiBlr8YsPButz/xtk0EQF4MgLZv326fffaZG/J+7Fji9VCGDh2aUW0DAAAIjQBo7ty5bkV4TXaobrDq1avbli1bzOfzuTXBAAAAIq4Iuk+fPvb444+7kV5a+kJzAm3bts2tCt+6devMaSUAAEBWBkBr1661u+/+uw80R44cduTIETfq68UXX7SXX345I9sGAAAQGgFQ3rx5A3U/JUuWtF9++SVw3759+zK2dQAAAKFQA3TFFVfYokWLrGrVqtasWTPr2bOn6w6bNm2auw8AACDiAiCN8jp06JDb79u3r9v/6KOPrFKlSowAAwBELM3+fG+t/oF9hLdsPg3f8rjY2FgrUKCAHTx40PLnz5/VzQEApGLa+p1hdW5aVi6Z1U2IaLFncP1Odw2Qhr/v378/2fEDBw64+wAAAEJdugMgzfmTkJCQ7PjRo0dtx44dlpkGDRpk2bJls0cffTRwLD4+3rp162aFCxd2o9FatWplu3fvztR2AAC8J+Fkgv28+1u3aR8eqQHSzM9+s2bNciknPwVEmiCxfPnyllmWLl1qb775pl188cWJjvfo0cO+/PJLmzx5smvTQw89ZC1btrRvvvkm09oCAPCe4yeP2vPzbgtaCiNPVjcJZyMAuuWWW9xXZWA6dOiQ6L6cOXO64CezVoBXoXX79u1t7Nix1q9fv8Bx9flpBfpJkyZZ48aN3bFx48a5EWpLlixhVBoAADizLrCTJ0+6rWzZsrZnz57AbW3q/lq/fr3ddNNNlhnUxXXjjTdakyZNEh1ftmyZHT9+PNFxLdCqNi5evDjV51N7VTgVvAEAAO9I9zD4zZs329n04Ycf2vLly10XWFK7du2yXLlyWcGCBRMdL168uLsvNQMHDnRD+AEAgDed1mrwqvfR5s8EBXv33Xczqm1ujbHu3bvbnDlz3LpjGUXrmT322GOB28oAlSlTJsOeHwAARFgApMyJ1v2qXbu2WwpDNUGZRV1cCrKCV5lXwfXChQtt5MiRrhhby3JoCH5wFkijwEqUKJHq80ZHR7sNAAB4U7oDoDFjxth7771nd911l2W2a665xi2zEeyee+5xdT5PPvmky9qoAFvZKA1/F9Uibd261erVq5fp7QMAAB4JgJRxufLKK+1sOOecc6x69erJFmPVnD/+4507d3bdWYUKFXKzQD788MMu+GFdMgBARorKlsPuuuSZwD7CW7o/wXvvvdcNO3/22WctFAwbNsyyZ8/uMkAa3dW0aVN74403srpZAIAIkzMql91S9cGsbgayKgDSzMtvvfWWffXVV25SQnVBJV0sNTPNnz8/0W0VR48aNcptAAAAmRIA/fTTT3bppZe6/Z9//jnRfZlZEA0AQFbS8heb//y7LrXCuTUsKnsUH4iXAqB58+ZlTksAAAjxpTCenNPM7bMUhgcXQ/XbtGmTG4Z+5MgRd9vn82VkuwAAAEInANq/f78bnn7hhRdas2bNbOfOnYHRWD179syMNgIAAGRtAKTV11X4rLl28uT530q4bdu2tZkzZ2Zs6wAAAEKhBmj27Nmu66t06dKJjleqVMl+++23jGwbAABAaGSADh8+nCjz4/fHH3+wvAQAAIjMAOhf//qXTZgwIdHQdy2IOnjwYGvUqFFGtw8AACDru8AU6KgI+ocffnDLYvTq1ctWr17tMkDffPNNxrcQAIAQoOUv2lz0WGAf4S3dn6DW4NqwYYNbjV1rdR06dMhatmxp3bp1c6vDAwAQqUthtK3xeFY3AxnktELYAgUK2NNPP51RbQAAAAjtGqBx48bZ5MmTkx3XsfHjx2dUuwAACCknfSdt68H1btM+PBYADRw40IoUKZLseLFixWzAgAEZ1S4AAELKsYR46zGjkdu0D48FQJoAsUKFCsmOlytXzt0HAAAQcQGQMj1aET6plStXWuHChTOqXQAAAKETALVr184eeeQRtyp8QkKC2/773/9a9+7d7fbbb8+cVgIAAGTlKLCXXnrJtmzZ4uYCypHj72/XRIh33303NUAAACDyAiCfz2e7du2y9957z/r162c//vij5c6d22rUqOFqgAAAACIyAKpYsaKb+VmLn2oDAACI6AAoe/bsLujZv38/wQ8AwFO0/MXNVboG9uGxIuhBgwbZE088YT///HPmtAgAgBBdCqPDpc+5TfsIb+kOYVXsHBcXZ5dcconlypXL1QAF06KoAAAAERUADR8+PHNaAgBACNPyF/sO73D7RfKeZ9mzpbsTBeEcAHXo0CFzWgIAQAjT8hcPfFHX7U+8bZPF5MiT1U3CGTit8PWXX36xZ555xk2KuGfPHndsxowZbnQYAABAxAVACxYscPP+fPfddzZt2jQ7dOhQYCmM559/PjPaCAAAkLUBUO/evd0kiHPmzHFF0H6NGze2JUuWZGzrAAAAQiEAWrVqld16660pLpK6b9++jGoXAABA6ARABQsWtJ07dyY7vmLFCjvvvPMyql0AAAChEwBpxfcnn3zSrQmWLVs2txDqN998Y48//ribIwgAACDihsEPGDDAunXrZmXKlLGEhASrVq2a+3rHHXe4kWEAAESiqGxRdn3FDoF9hLdsPq1wehq2bdvm6oE0CqxmzZphvTZYbGysFShQwA4ePGj58+fP6uYAAFIxbX3yEoxQ1rJyyaxuQkSLPYPrd5ozQOrqGjJkiH322Wd27Ngxu+aaa9yw96RLYQAAAERMDVD//v3tqaeesnz58rli59dee811hQEA4AXqMDkYv99tp9l5gnAMgCZMmGBvvPGGzZo1yz755BP7/PPPbeLEiS4zBABApDuacMQ6fVLDbdqHRwKgrVu3WrNmzQK3mzRp4kaB/f7775nVNgAAgKwNgE6cOGExMTGJjuXMmdOOHz+eGe0CAADINGkuglZ/Z8eOHS06OjpwLD4+3rp27Wp58+YNHNP6YAAAABERAHXo8PfcB8HuvPPOjG4PAABA6ARA48aNy9yWAAAAhOpSGAAAAJ5bCgMAAC/S8hcNy7cJ7CO8EQABAJAGOaOi7eErhnOuIgRdYAAAwHPIAAEAkMbpYPwzQEdH5XaTASN8kQECACANFPy0n1LRbSyFEf4IgAAAgOcQAAEAAM8hAAIAAJ5DAAQAADyHAAgAAHgOARAAAPAc5gECACANsmfLbvXK3BTYR3gjAAIAIA1yRcXY4/Xf4lxFCEJYAADgOQRAAADAcwiAAABIg/gTcdbqw1Ju0z7CGwEQAADwHAIgAADgOQRAAADAcwiAAACA5xAAAQAAzyEAAgAAnhPSAdDAgQOtTp06ds4551ixYsXslltusfXr1yd6THx8vHXr1s0KFy5s+fLls1atWtnu3buzrM0AgMik5S8uK3mN21gKI/yFdAC0YMECF9wsWbLE5syZY8ePH7frrrvODh8+HHhMjx497PPPP7fJkye7x//+++/WsmXLLG03ACAyl8J4usH7btM+wls2n8/nszCxd+9elwlSoHP11VfbwYMHrWjRojZp0iS77bbb3GPWrVtnVatWtcWLF9sVV1yRpueNjY21AgUKuOfLnz9/Jr8LAMDpmrZ+Z1idvJaVS2Z1EyJa7Blcv0M6A5SU3qAUKlTIfV22bJnLCjVp0iTwmCpVqljZsmVdAJSao0ePupMWvAEAAO8ImwDo5MmT9uijj1r9+vWtevXq7tiuXbssV65cVrBgwUSPLV68uLvvn2qLFDH6tzJlymR6+wEA4U3LX9wx+QK3sRRG+AubAEi1QD///LN9+OGHZ/xcffr0cdkk/7Zt27YMaSMAILIdTTjiNoS/HBYGHnroIfviiy9s4cKFVrp06cDxEiVK2LFjx+zAgQOJskAaBab7UhMdHe02AADgTSGdAVJ9toKf6dOn23//+1+rUKFCovtr1aplOXPmtLlz5waOaZj81q1brV69elnQYgAAEA5yhHq3l0Z4ffrpp24uIH9dj+p2cufO7b527tzZHnvsMVcYrQrwhx9+2AU/aR0BBgAAvCekA6DRo0e7rw0bNkx0fNy4cdaxY0e3P2zYMMuePbubAFGju5o2bWpvvPFGlrQXAACEh5AOgNIyRVFMTIyNGjXKbQAAAGEfAAEAECqyWTa7qGi9wD7CGwEQAABpEJ0jt714zVTOVYQI6VFgAAAAmYEACAAAeA4BEAAAaaDlL+6ZXt1tLIUR/qgBAgAgjWKP/sG5ihBkgAAAgOcQAAEAAM8hAAIAAJ5DAAQAADyHAAgAAHgOo8AAAEgDLX9xQaFLAvsIbwRAAACkcSmMwdfN4FxFCLrAAACA5xAAAQAAzyEAAgAgDY6eiLOun13uNu0jvFEDBABAGvjMbG/c9sA+whsZIAAA4DkEQAAAwHMIgAAAgOcQAAEAAM8hAAIAAJ7DKDAAANJAi1+Uzn9hYB/hjQAIAIA0iM6Rx15rNp9zFSHoAgMAAJ5DAAQAADyHAAgAgDTQ8hfd/9PQbSyFEf6oAQIAIA20/MX22A2BfYQ3MkAAAMBzCIAAAIDnEAABAADPIQACAACeQwAEAAA8h1FgAACkgZa/KJqndGAf4Y0ACACANC6FMebm7zlXEYIuMAAA4DkEQAAAwHMIgAAASIOjJ45Yr9k3uE37CG/UAAEAkAY+89kvf6wM7CO8kQECAACeQwAEAAA8hwAIAAB4DjVAAACEgGnrd1q4aVm5pIUrMkAAAMBzyAABAJBG+aMLca4iBAEQAABpEJMjj4279WfOVYSgCwwAAHgOARAAAPAcAiAAANJAy188N7eV21gKI/xRAwQAQBpo+YvVexcH9hHeyAABAADPIQACAACeQwAEAAA8hwAIAAB4DgEQAADwHEaBAQCQRtFRuTlXEYIACAAiTLitKh4uK4prKYxJrX/J6mYgg9AFBgAAPIcACAAAeA5dYAAApMGxhHgbsqiL23/iqrGWKyqG8xbGCIAAAEiDk76Ttnzn3MA+whtdYAAAwHMiJgM0atQoGzJkiO3atcsuueQSGzFihF1++eUWThi5AQDA2RERAdBHH31kjz32mI0ZM8bq1q1rw4cPt6ZNm9r69eutWLFiWd08ACGIfzgAb4uIAGjo0KHWpUsXu+eee9xtBUJffvmlvfvuu9a7d++sbh642IQtggQAkSrsA6Bjx47ZsmXLrE+fPoFj2bNntyZNmtjixYuztG3wBoIEAAg/YR8A7du3zxISEqx48eKJjuv2unXrUvyeo0ePus3v4MGD7mtsbKxlpbhDf1k4iY3Nm+bH8t5CB5/b3/iZDB3h8jMZfyLOLP5/7TiZIyFi3tvpSs/7ywz+67bP5/NeAHQ6Bg4caH379k12vEyZMlnSHgBAeOkyqGZWNwFB9u/fbwUKFDBPBUBFihSxqKgo2717d6Ljul2iRIkUv0fdZSqa9jtw4ICVK1fOtm7dmu4TGOoUHSuw27Ztm+XPn98iCe8tPPG5hSc+t/AVyZ/dwYMHrWzZslaoUKF0f2/YB0C5cuWyWrVq2dy5c+2WW25xx06ePOluP/TQQyl+T3R0tNuSUvATaT8cfnpfvLfww+cWnvjcwlMkf26R/v6yZ8/uvQBIlM3p0KGD1a5d2839o2Hwhw8fDowKAwAAiLgAqG3btrZ371577rnn3ESIl156qc2cOTNZYTQAAEDEBECi7q7UurxORd1hzz//fIrdYuGO9xae+NzCE59beIrkzy3S31/0Gby3bL7TGTsGAAAQxlgMFQAAeA4BEAAA8BwCIAAA4DkEQAAAwHMIgJIoX768ZcuWLdE2aNAgiyRaB01TBei9/fjjjxYJbr75ZjcbaExMjJUsWdLuuusu+/333y3cbdmyxTp37mwVKlSw3Llz2wUXXOBGPGgR4EjQv39/u/LKKy1PnjxWsGBBC3ejRo1yf0P0c1i3bl37/vvvLdwtXLjQmjdvbqVKlXJ/Mz755BOLpGWR6tSpY+ecc44VK1bMTaa7fv16iwSjR4+2iy++ODD5Yb169WzGjBkWiQYNGuR+Nh999NF0fR8BUApefPFF27lzZ2B7+OGHLZL06tXL/TGLJI0aNbKPP/7Y/fGaOnWq/fLLL3bbbbdZuNOCvprZ/M0337TVq1fbsGHDbMyYMfbUU09ZJFAg17p1a3vggQcs3H300UduUlYFqMuXL7dLLrnEmjZtanv27LFwpkll9V4U3EWaBQsWWLdu3WzJkiU2Z84cO378uF133XXuPYe70qVLu8Bg2bJl9sMPP1jjxo2tRYsW7u9IJFm6dKn7+6hgL900DB7/U65cOd+wYcMi9pT85z//8VWpUsW3evVqTX/gW7FihS8Sffrpp75s2bL5jh075os0gwcP9lWoUMEXScaNG+crUKCAL5xdfvnlvm7dugVuJyQk+EqVKuUbOHCgL1Lob8b06dN9kWrPnj3uPS5YsMAXic4991zf22+/7YsUf/31l69SpUq+OXPm+Bo0aODr3r17ur6fDFAKFDUXLlzYatasaUOGDLETJ05YJNACsV26dLH333/fdTlEqj/++MMmTpzoulZy5sxpkUaL/53Own/I3EyW/tNu0qRJorWJdHvx4sWc+jD63ZJI+/1KSEiwDz/80GW21BUWKbp162Y33nhjot87T84EnVEeeeQRu+yyy9wvwLfffutWjlc32NChQy2c6Z+3jh07WteuXd2aaaotiTRPPvmkjRw50uLi4uyKK66wL774wiLNpk2bbMSIEfbKK69kdVMQZN++fe4ik3T5Hd1WNyZCn7qaVUNSv359q169ukWCVatWuYAnPj7e8uXLZ9OnT7dq1apZJPjwww9dV7O6wE6XJzJAvXv3TlbYnHTz/5FSH37Dhg1df6KChVdffdVdcFQ4HM7vTe/hr7/+cgFdJH5u8sQTT9iKFSts9uzZFhUVZXfffbcL/CLhvcmOHTvs+uuvdzUzyuSFqtN5b0AoZBN+/vlnd2GNFJUrV3YDXb777jtXZ6dFw9esWWPhbtu2bda9e3eX6deAg9PliaUwtFDq/v37//Ex559/vuXKlSvZcRWM6b8B/cHWD1O4vrc2bdrY559/7i4+fvqPVYFC+/btbfz48RZJn9v27dutTJkyLosXiinf9L43jWhTYK7M1nvvvee6V0LV6Xxuek/67/vAgQMWrl1g6laeMmWKG0nkpwuO3tOnn35qkUB/P5RFCH6PkUDrSOoz0og3jbiMVOoq0khSFQ2HM41EvPXWW931K/h6pp9P/W1UwiL4Pk93gRUtWtRtp0PRs06ohkiG83t7/fXXrV+/foHbuqBqhIpGrmi4bqR9bkpnS6hm7tLz3pT50Si3WrVq2bhx40I6+DnTzy1cKZjT5zN37txAcKCfQd0+3UWakfn0/79G+Sqomz9/fkQHP/6fyVD9m5ge11xzjeveC3bPPfdYlSpVXClEWoIfzwRAaaViRaUKdbHRvBC63aNHD7vzzjvt3HPPtXCmOXKCqT9Y9N+AhkuGM31m6ge+6qqr3OekIfDPPvuse2+hmP1JDwU/yvyUK1fO1f0ou+JXokQJC3dbt251Rev6qv/g/PNSVaxYMfAzGi7Ufa6Mj2rsLr/8chs+fLgrOtUf5nB26NAhV3vmt3nzZvc5qU4y6d+VcOz2mjRpksv+6G/+rl273PECBQq4ebfCmcodbrjhBvcZqfxB71NB3qxZsyzcnXPOOcnqtPLmzesGL6WrfiuzhqeFo2XLlvnq1q3rhuPGxMT4qlat6hswYIAvPj7eF2k2b94cMcPgf/rpJ1+jRo18hQoV8kVHR/vKly/v69q1q2/79u2+SBgers8ppS0SdOjQIcX3Nm/ePF84GjFihK9s2bK+XLlyuWHxS5Ys8YU7fRYpfUb67MJdar9b+r0Ld506dXLTuuhnsWjRor5rrrnGN3v2bF+kanAaw+A9UQMEAAAQLLSLCQAAADIBARAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPIQACAACeQwAEAAA8hwAIQMh755137Lrrrgvc7tixY4YsyKnFE7WwYkbp3bu3W1sKQOhjJmgAIS0+Pt6tHj958mSrX7++O3bw4EG3kGXBggVDanXzffv2ubZqrSx9BRC6yAABCGlTpkyx/PnzB4If/2KVZxr8ZIYiRYpY06ZNbfTo0VndFACnQAAE4KzQSvZawX7AgAGBY99++63lypXL5s6dm+r3ffjhh9a8efNEx5J2gTVs2NAeeeQR69Wrl1ulXK/zwgsvJPqejRs32tVXX20xMTFWrVo1mzNnTrLX2rZtm7Vp08YFV3qeFi1a2JYtW9x969atszx58rhVtf0+/vhjt2r4mjVrAsfUVrUZQGgjAAJwVhQtWtTeffddF5j88MMP9tdff9ldd91lDz30kF1zzTWpft+iRYusdu3ap3z+8ePHW968ee27776zwYMH24svvhgIck6ePGktW7Z0wZbuHzNmjD355JOJvv/48eMue3POOefY119/bd98843ly5fPrr/+ejt27JhVqVLFXnnlFXvwwQdt69attn37duvatau9/PLLLqDyu/zyy919/sAJQGiiBgjAWdWtWzf76quvXFCzatUqW7p0qUVHR6f42AMHDti5555rCxcutH/961+JMkC6z1/ArAxQQkKCC1yCA5HGjRvboEGDbPbs2XbjjTfab7/9ZqVKlXL3z5w502644YZADdC///1v69evn61du9bVBokCH2WD9Dr+IuybbrrJYmNjXTAVFRXlnsf/eNF96qKbP3++NWjQIJPOIoAzleOMnwEA0kFZlOrVq7ui5mXLlqUa/MiRI0fcV3VbncrFF1+c6HbJkiVtz549bl9BTZkyZQLBj9SrVy/R41euXGmbNm1yGaCkRdi//PJL4LayWBdeeKFlz57dVq9enSj4EXWJSVxc3CnbDCDrEAABOKsUTPz++++uW0rdRDVq1Ej1sYULF3YBxp9//nnK582ZM2ei2/o+vUZaHTp0yGrVqmUTJ05MsfsuOFA6fPiwC4B27tzpAq1gf/zxR7LvARB6CIAAnDXqUrrzzjutbdu2VrlyZbv33ntdN1ixYsVSfLy6mVRfoyLj4HmA0qtq1aquwDk4YFmyZEmix1x22WX20UcfubZo1FlKFNyo++3pp592z9W+fXtbvnx5IOsjP//8swvGLrrootNuL4DMRxE0gLNGgYPm8Hn99dddEbK6kjp16vSP36PCZBVCn4kmTZq41+rQoYPL4KhWSG0JpmBGw9g18kv3b9682dXxaHSZippFRc/qSnvmmWds6NChru7o8ccfT/Q8+l7VKwUHRQBCDwEQgLNCwcTw4cPt/fffdxkWdSFpXwHDP82b07lzZ/vPf/7jAqfTpddSsbNqilQcrcxT//79Ez1GQ9xVbF22bFk3YkxZI722aoDU3gkTJrh2qM05cuRwI85UOD127FibMWNG4Hk0BL5Lly6n3VYAZwejwACEvNatW7suqj59+lgoUyDUs2dP++mnn1yQBCB0kQECEPKGDBni5uQJdSqOHjduHMEPEAbIAAEAAM8hAwQAADyHAAgAAHgOARAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPIQACAACeQwAEAAA85/8AxPmENwXnVcQAAAAASUVORK5CYII=", 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", 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" ] @@ -1365,7 +1350,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "id": "40", "metadata": {}, "outputs": [ @@ -1373,7 +1358,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Parsed counts: [{'x': 1}: 2021, {'x': 0}: 13, {'x': 2}: 13, {'x': 3}: 1]\n", + "Parsed counts: [{'x': 1}: 2021, {'x': 0}: 14, {'x': 2}: 10, {'x': 3}: 2, {'x': -2}: 1]\n", "The analytical gradient is: 0.25\n", "The majority gradient is: 0.25\n", "The majority result is correct\n", @@ -1394,7 +1379,7 @@ }, { "data": { - "image/png": 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", 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agE8rTWviLgVEWtRPhU7BkWLVqlVzk31pZWgNlT948KBbAVsF0owAAwAAURkA/fDDD9aoUaPQ7WBdTps2bdxQ9y5duri5gjSvjzI9F154oRvmHh///7lYM7eKsoIerYatCvDrr7/ezR0EAH41fvnGTH2+g4n7rWH5lm7/81VbLVfs7kx9/uZV/itzAHw3D1AkqWtNQ+xVDJ1WDZC61Q4cOHDC2wZEi9y5c2d4mCm8EQBlNQIgZOX1O9sVQUcTBT7qnlMQBPiVgh91RSsQAoDsjgDoCJQg27hxo8XGxrqhdvwHDD9S8P/nn3+63wXV5zFhqP/+Du5P3Of242Lz8PnDEwiAjkDD6vfu3euKqvPmzXtiPhUgChUtWtQFQfqdyJUrV6SbgxNIwU/rsZXc/qgbVll8Tv4WIvujQ/8IEhMT3VfS/vC74O9A8HcCALIzAqCjRMoffsfvAAAvIQACAAC+QwCE41a+fHkbOHDgcT3HjBkzXIZB8z1lhjVr1rjn08Sa0eL2228PTeIpDRs2dJN9AgBOPAIgj5szZ44bwXbFFVdYtEjtwn/++ee7EUaaz8Evxo8fb88991yWBlkAgNQRAHncW2+9Zffff7/NmjXLjeCJ5gJbrf0W7XUmWm4ls2jJl2NZwRgAcPwIgDxMa619+OGHds8997gMkJYXSa3bSQvOnnPOOW6YvzIxy5cvDz3mt99+s2uuucaKFy9u+fPnt7p169pXX32V5mu2bdvWrrzyyhRBQ7FixVwwpgzFzJkz7eWXX3avrU3dVal1gX377bcuW6R2nXzyyda0aVP766+/3H1aEkVLoxQqVMiKFCniXlNtzQhlnHRe8uTJ4yb4Gz16dIruPLVpyJAhdvXVV1u+fPmsV69ebhRUu3bt3Pfoe6tUqeLeTzg9Rku7BNunZV2ST7qePBO2f/9+e+SRR+zUU091r6UFfXVegvT56fkmT57s1sHT56G18PQ+5Nlnn7URI0bYJ598Ejq34d8PHKscMTmsfpkr3aZ9wAv4ST5Gew7sSXNLOJRw1I/dd3DfUT32WHz00UdWtWpVd4G+5ZZb7O23305xEZYnnnjCXnrpJbc2W86cOV0QEx5ENWvWzAVJixYtchfcq666ytauXZvqa955550uOAlelOXzzz93cym1atXKBQr169d3C9jqMdo0wWRyqt3R+m7Vq1d33XizZ892rxscgq014hRgqM1qmyaovO666zI0W/dtt93msmIKEsaNG2dvvPGGbdmyJcXjFFjouZcsWeLOjV6jdOnSNmbMGPvll1/s6aeftscff9yd7yCdTwUsOudq+44dO2zChAnptkdr2um9fvDBB/bTTz9ZixYt3PleuXJl6DE6jy+++KK9++67Lqunz0FBk+hry5YtQ0GRNgW0wPHKHRtvj1zwhtu0D3gBEyEeo/x98qd5X7PKzeyLm78I3S72YjHbe3Bvqo9tUK6Bzbj9v//Sy79c3rbt3ZbicYFnMr5kmzIuCnxEF0WtlaLsizIP4ZTVaNCggdvv2rWry4okJCS4RWdr1arltiDVrOhC/umnn7oLdnK64Crg0gVaWQ8ZPny4u5grYxHs7lJWR11eaenXr5/LSr322muhY2eccUZoX4vehlOgoYn6FJDUqFHjiOdm2bJlLpM1f/589zry5ptvWuXKlVM89uabb7Y77rgjybHu3buH9pUJUuCiAEgBiCiL1K1bN2vevLm7PXToUJe5SYsCGZ0nfdWkm8GARsGkjvfu3TuUTdNzVaxY0d3WZ9CjRw+3r/OrjJQySemdWwAAGSDPUjfWvHnz7KabbnK3ldlRBkZBUXJnnnlmaL9kyX9XZQ5mQpQB0oVYXS7qftFF9tdff00zAxTMAumiLZs3b7aJEycmySodjWAGKC3Kiui9nXbaaW4BPHVdSXrtSn5+dE7OPvvs0LFKlSq5rrbkggFSuMGDB1udOnVc0KVzouxR8LUVaCr7oi6sIL1Was8TpOySslunn366e77gpoA1vGtPgWMw+Al+XqllrQAA6SMDdIz+6fZPmvfF5ohNcnvLI2lfoJL3p695cI1lBgU6WrIgmE0QdX/FxcXZoEGDkoy2Cl/WIFiEHOxKUvAzdepU1+2iAEEZhhtuuMEtEJte15IyScqKfPfddy5D8r///S9D7dfrpEfdYeXKlbNhw4a596j2KvOTXruOlepxwqmLSudF3VzqzlMh8wsvvGDff//9Mb+GAk2N1luwYIH7Gi6YOZPkS1Do80qtWxPITAmH9rIUBjyHAOgY5cudL+KPTYsCn5EjR7oL9KWXXprkPg2Rfv/9961Dhw5H9VwqRFbhsmpgghdqFS2nR0W/eh1lgRQEJe8+UhfYkZZTUFZKtT3hXU1B27dvdxkcBT/BwEp1NhmhbjqdJ9U1KZMjq1atChVZH+mcqKvv3nvvDR0Lz9IouFRmRgHRRRdd5I7ptRTchGecwtWuXdudE2VzMhosZvTcAgAIgDxJRce6kGukUvJ5dVQ7o+zQ0QZAqonRfDXKuCjb8NRTTx1VobG6wTQySxfjNm3aJLlP3VUKDhRIKbuh4eDJqX6mZs2aLshQW3Vhnz59uqsl0uMVZKnbSYGGup6UccoIFYc3adLE7rrrLjfKS5mVzp07u8zTkYbi65wowFRNj7JbqndSLZH2gx588EHr27eve6xeq3///ulO8qiur9atW7vsmQJXBURbt251QaCCwaOdx0nnVu1SgKhzpM+fhUsBICVGgXmQAhxd3FObVFABkEZOaZTR0dCFW3UxyngoCNJQ9LSyGOH0+gpO9PjwbjhR95G6eTTCSzU0qdXtKCCYMmWKLV682M4991zX1aTh3aql0YgvdUMpo6Jur06dOrkuqIxSEKPh/crSKMOlkWnqzlLxd3ruvvtuV9ysmirV+SgjFZ4NEgVTt956qwv+gt1kwSxaWpQxUwCk71WGSlk0BVZly5Y96vek96DvVb2Rzq2yVQCAlGICFBDY7t27XbCg4lUV1IbTaKjVq1e7/+6PdGHEf9RVpvlsdFEPjoSKduvXr3dD8jU6LL0CbL/idyH7GL/8v2koskMNUPMq/w6+ADLz+n0k1AAhU6l7bNu2ba4bR6PGNIFgtPr6669doKauNo3a0rB9dSEF63YAAN5FAIRMpe4sZcs0UaAmAlSXVbTSnDqawPD33393XVTq5hs1ahQ1MwDgA9F7dUK2pAxKdulVVX2SNgDp03QdZ5f8t1uYpTDgFQRAAIB0afmLJxq8y1mCpzAKDAAA+A4BEAAA8B0CIADAEYfB3zymotu0D3gBNUAAgCPan7iPswRPIQMEAAB8hwAIAAD4Dl1gUTLVfGZPFa8V3EeMGOHWrRo6dGiS+zp27GivvfaaW6dKkxXi2Gnh1AkTJrh1u6Lds88+ax9//LH9+OOPkW4KAEQcGSAP07pWWjR03759SdZzGj16dIYW2IyUAwcORLoJAACPIgDyMK3ariBo/PjxoWPaV/BTu3btFGt49enTxy1jkSdPHqtVq5aNHTs2dH9iYqK1a9cudL9WHH/55ZeTPMeMGTPcyu358uVz64BdcMEF9scff4QyUsmzJA899JA1bNgwdFv79913nzt+yimnhGZp/vnnn+3yyy+3/Pnzu9Xbtcq61hsL/77777/ffZ9Wrtdjhg0bZnv27LE77rjDLXNRqVIlmzhxYpLXP5rnfeCBB9waYYULF7YSJUq4LEr4rNeiVd6VCQreTmuh1Ztuusk9j86PVmv//vvvQ/cPGTLEKlasaLlz53bn9t13/5t0bs2aNe75wzM3O3fudMd0zoPnXrenTZvmnjtv3rxuaY/ly5e7+5Xp6969uy1evNg9TpuOadZuvSf9TMTFxVmpUqXcewYAryMA8ri2bdu6FdmD3n77bRcUJKfgZ+TIka67bOnSpdapUye75ZZbbObMmaEASet7jRkzxn755Rd7+umn3TpaH330kbv/0KFDLsBp0KCB/fTTTzZnzhy766673IU2I9RtpyDg22+/dW3Rhb5x48YuYPvhhx9s0qRJtnnzZmvZsmWK71PQNG/ePBcM3XPPPdaiRQsXBCxcuNAuvfRSF+Ds3fvvEN6MPK8CFgUr/fr1sx49etjUqVPdffPnz3dfdX61mGrwdnJacFXnZcOGDfbpp5+6IERBlc6pqAvtwQcftM6dO7ugTN2W+oymT59uGfXEE0+4hWj1nrQOmz5/adWqlXv+M844w7VVm46NGzfOBgwYYK+//rqtXLnSdZFpcVggXIzF2BlF67tN+4AXUAPkcQpiunXrFsrEKLBQt1gwcyD79++33r1721dffWX169d3x0477TSbPXu2uzDq4p0rVy6XQQhSJkhBjgIgBQ27d++2Xbt22ZVXXukyGVKtWrUMt7dy5cou0Ajq2bOnC1LUvvAgTpmtFStW2Omnn+6OKWP15JNPun293759+7qAqH379u6YAjZlWRScnXfeeTZo0KCjet4zzzzTnnnmmVDb9H3KslxyySVWtGhRd1zZLmWH0qIux61bt7oASRkgUUYq6MUXX3QZsnvvvdfdfvjhh23u3LnueKNGjTJ0/nr16uU+L+natatdccUVrttTWTtluhQUhbdVi9fqdpMmTdxnrEyQsnhAuLiceazHxeM4KfAUMkAep4u0LoLq7lCmQvsKDMKtWrXKZUZ0UddFMrgpI/Tbb7+FHjd48GCrU6eOe07d/8Ybb7gLqOjCrou4uq2uuuoq1z2mLENG6fnDKVuiTEh4u6pWreruC2+bApWg2NhYK1KkSJJMhrq4ZMuWLcf8vFKyZMnQcxwtdV0p2AoGP8n9+uuvrrswnG7reEaFt1dtlfTaqyyZasQU8CpYVDZK2TwA8DoyQD6gbhDV1gSDmNS6aOSLL76wU089Ncl9qgsRZY0eeeQR172iLJHqal544YUkdSwKsFQ/ou6kDz/80GVk1F2kjEuOHDlSrBJ/8ODBFG1Rd1Pytimgev7551M8NniBF2UvwqnrLfxYsCsu2O10PM8bfI6jpezL8dC5k/Dzl9q5k/Tec2qU8VKdkLJ/+qyUhdLnqq7P5O8dALyEAMgHLrvsMjeiShfEYGFxuOrVq7tAR9mcYPdJcuo6Uz1NsJsmeaYkSJkObeqGUqCk7h8FQMoaqb4leWbkSBdZFXKrTkUFxuq+ySyZ9bxqvwrEj5SVefPNN23Hjh2pZoHUVajzq2kJgnRbn4sEu9qUUQsWrx/LUHbVVqXWVgVoCga1aYoEZcKWLFnizhEgWv7ins/+7RodctU8i8+ZlxODbI8uMB9Ql5C6U1S8rP3klM1RdkeFzyr6VWCjwuFXX33V3Q7Wv6iwdvLkya5G5qmnnkpS9Lt69WoX9KguSPVGU6ZMcUW1wTogFRzr+9WtpuOqq0keEKVGF2QFDhpBpddT29QGFQkfKfA4Ec+rAEo1QZs2bbK//vor1cfoNVRnoyJxBTa///67C750ruTRRx91XZSqUdK56d+/vxutp88kGKAoiFRdkz5HZWeC9U4Zobbqc1LwpNFuqv3S67711lvus1C73nvvPfd65cqVy/Dzw9t279/hNsArCIB8okCBAm5Ly3PPPeeCGo0GU9CirJG6xFTsLBqZ1Lx5czdyqF69erZ9+/Yk2SANu162bJldf/31roBYI8AUZOj7RJknPb9GP9WtW9f+/vtvu+22247Ybg3LVtCgoEQjuVTXo+HuKjwOdg0di8x6XnUJqutIXUnJpxYIz7woICxWrJg1a9bMvZaCmWAwqsBINVMqetYoLRWeqzsxfIoAFWirNkc1UmqnisMzSp+NPlcVViur9P7777v3qykDVHOkTJW6wj777DNXQwUAXhYTSF6Y4UMawVSwYEE3iil5kKARNPqvWYFAfHx8xNoIRBq/C/6dqV5dYK3H/jtycdQNqzK9CyyjM90DR3P9PhIyQAAAwHcIgAAAgO8QAAEAAN9hGDwAIF1a/qJi4VqhfcALCICOErXi8Dt+B/y9FEa/S5MuJgxkd3SBHUFwqLImEgT8LPg7kNpcUgCQ3ZABOtIJypnTzXGjxSw16+/xzD0DZFdaTkO/A/pdyMwZuQEgUvhLdgRaPkJrQ2kuoOCK6oAfKfjXavHBNcbgH/sP7bUHv/x3Ys6Xm82wOJbCgAcQAB0FzeSrpSDoBoPffw/IgPqTZsvdund9aB/wAgKgo6Q//MwEDQCAN1DQAgAAfIcACAAA+A4BEAAA8B0CIAAA4DsUQQMA0qWJD0oXOD20D3gBARAAIF2a90fz/wBeQhcYAADwHQIgAADgOwRAAICjWgpDm/YBL6AGCACQLi1/sX73itA+4AVkgAAAgO8QAAEAAN8hAAIAAL5DAAQAAHwnqgOgxMREe+qpp6xChQqWJ08eq1ixoj333HMWCPxXhqf9p59+2kqWLOke06RJE1u5cmVE2w0AAKJbVAdAzz//vA0ZMsQGDRpkv/76q7vdr18/e/XVV0OP0e1XXnnFhg4dat9//73ly5fPmjZtagkJCRFtOwB4hZa/KJq3tNtYCgNeEdXD4L/77ju75ppr7IorrnC3y5cvb++//77NmzcvlP0ZOHCgPfnkk+5xMnLkSCtevLh9/PHHduONN0a0/QDglaUwhl79799dwCuiOgN0/vnn27Rp02zFin/nn1i8eLHNnj3bLr/8cnd79erVtmnTJtftFVSwYEGrV6+ezZkzJ83n3b9/v+3evTvJBgAA/COqM0Bdu3Z1wUnVqlUtNjbW1QT16tXLWrdu7e5X8CPK+ITT7eB9qenTp4917949i1sPAACiVVRngD766CMbNWqUjR492hYuXGgjRoywF1980X09Ht26dbNdu3aFtnXr1mVamwHAa/Yf2mddplzuNu0DXhDVGaBHH33UZYGCtTw1a9a0P/74w2Vw2rRpYyVKlHDHN2/e7EaBBen2WWedlebzxsXFuQ0AcGQBC9hvOxaH9gEviOoM0N69ey1HjqRNVFfY4cOH3b6GxysIUp1QkLrMNBqsfv36J7y9AAAge4jqDNBVV13lan7Kli1rZ5xxhi1atMj69+9vbdu2dffHxMTYQw89ZD179rTKlSu7gEjzBpUqVcquvfbaSDcfAABEqagOgDTfjwKae++917Zs2eICm7vvvttNfBjUpUsX27Nnj9111122c+dOu/DCC23SpEkWHx8f0bYDAIDoFRMIn1bZp9RtpuHzKoguUKBApJsDAMdl/PKNmXoGEw7ttdZjK7n9UTessviceTP1+ZtX+a+GEzhR1++orgECAADwXRcYACA6FIgrHOkmAJmKAAgAkC51eQ2/7mfOEjyFLjAAAOA7BEAAAMB3CIAAAOnS8hdPT7vebSyFAa+gBggAkC4tf7F065zQPuAFZIAAAIDvEAABAADfIQACAAC+QwAEAAB8hwAIAAD4DqPAAABHFBebh7METyEAAgAccSmM0S1+4yzBU+gCAwAAvkMABAAAfIcuMABAug4kJtgLs9u7/UcvHGa5Y+M5Y8j2CIAAAOk6HDhsCzdOC+0DXkAXGAAA8B0CIAAA4DsEQAAAwHcIgAAAgO8QAAEAAN/J0Ciww4cP28yZM+2bb76xP/74w/bu3WtFixa12rVrW5MmTaxMmTJZ11IAAIATmQHat2+f9ezZ0wU4zZo1s4kTJ9rOnTstNjbWVq1aZc8884xVqFDB3Td37tzMahsAIEqWwhh3459u0z7gmwzQ6aefbvXr17dhw4bZJZdcYrly5UrxGGWERo8ebTfeeKM98cQT1r79v5NmAQAARJuYQCAQONKDfv31V6tWrdpRPeHBgwdt7dq1VrFiRcsudu/ebQULFrRdu3ZZgQIFIt0cADgu45dvzFZnsHmVkpFuArKp47l+H1UG6GiDH1F2KDsFPwCAIy+F8crcB9z+A+e9wlIY8PdSGIcOHbLXX3/dZsyYYYmJiXbBBRdYx44dLT6eNWIAwEu0/MWcdZ+7/fvqDYx0c4DIBkAPPPCArVixwpo3b+66vUaOHGk//PCDvf/++5nTMgAAgEgHQBMmTLDrrrsudHvKlCm2fPlyNxJMmjZtauedd17WtBIAACASEyG+/fbbdu2119qff/7pbp999tnWoUMHmzRpkn322WfWpUsXq1u3bma2DQAAILIBkIKcm266yRo2bGivvvqqvfHGG67iWkPen3rqKTdHkIbBAwAAeKoGqFWrVq6rS9kefR06dKi99NJLWdc6AACAaFgLrFChQi7788ILL9htt91mjz76qCUkJGRF2wAAACIbAGlyw5YtW1rNmjWtdevWVrlyZVuwYIHlzZvXatWq5ZbHAAB4T1xsHht1wyq3aR/wVQCkbE+OHDlc5qdYsWJ29913W+7cua179+728ccfW58+fVyABADwlpiYGLcGmDbtA76qAdIcP4sXL3azPKv+R4ufhs8UPWvWLNc1BgAA4JkAqE6dOvb0009bmzZt7KuvvnJdYcndddddmd0+AECEHUzcb0PnP+b2O9R93nLFxkW6ScCJ6wLTTM/79++3Tp062YYNG9wyGAAA70sMJNqMNR+5TfuArzJA5cqVs7Fjx2ZtawAAAKIlA7Rnz54MPWlGHw8AABB1AVClSpWsb9++tnHjxjQfEwgEbOrUqXb55ZfbK6+8kpltBAAAOPFdYDNmzLDHH3/cnn32WTfnzznnnGOlSpWy+Ph4++uvv+yXX36xOXPmWM6cOa1bt25uiDwAAEC2DoCqVKli48aNc5Mhjhkzxr755hv77rvvbN++fXbKKadY7dq1bdiwYS77E1wdHgAAwBNrgZUtW9Y6d+7sNgAAAF8EQAAA/9HyF29fuyS0D3gBARAAIF1a/qJgfBHOEvy9GjwAAEB2RwYIAHDEpTDeWfSs27+99rMshQFPIAMEAEiXlr+YtGqE21gKA74NgCZNmmSzZ88O3R48eLCdddZZdvPNN7s5gQAAADwXAD366KO2e/dut79kyRI3JL5Zs2a2evVqe/jhh7OijQAAAJGtAVKgU716dbevyRGvvPJK6927ty1cuNAFQgAAAJ7LAOXOndv27t3r9r/66iu79NJL3X7hwoVDmSEAAABPZYAuvPBC19V1wQUX2Lx58+zDDz90x1esWGGlS5fOijYCAABENgM0aNAgt+jp2LFjbciQIXbqqae64xMnTrTLLrssc1sHAACQBWICgUDAfE5ddwULFrRdu3ZZgQIFIt0cADgu45dvzNQzeDhw2Lbt2eD2T8l3quWIydwZVJpXKZmpzwf/2H0c1+8M/xRrtfctW7akOL59+3ZWggcAD1LAUyx/GbdldvADREqGf5LTShjt37/fFUgDAAB4pgj6lVdeCS2K9+abb1r+/PlD9yUmJtqsWbOsatWqWdNKAEDEHEw8YKOX9HX7N9fsarli+WcXPgqABgwYEMoADR06NEl3lzI/5cuXd8cBAN6SGDhkny779+97qxqPWC4jAIKPAiBNgCiNGjWy8ePH28knn5yV7QIAAIieGqDp06eHgh9lg7J6ENmGDRvslltusSJFiliePHmsZs2a9sMPP4Tu1+s//fTTVrJkSXd/kyZNbOXKlVnaJgAAkL0dUzn/yJEjXSCigEPbmWeeae+++26mN06Lq2rCxVy5crl5hn755Rd76aWXkmSf+vXr5+qT1P32/fffW758+axp06aWkJCQ6e0BAAA+nQm6f//+9tRTT9l9993nghPR6vAdOnSwbdu2WadOnTKtcc8//7yVKVPGhg8fHjpWoUKFJNmfgQMH2pNPPmnXXHNNKDgrXry4ffzxx3bjjTdmWlsAAICPM0CvvvqqmwFawcnVV1/tNmVhXnvttdBIsczy6aef2jnnnGMtWrSwYsWKWe3atW3YsGFJ6pI2bdrkur2CNCFSvXr1bM6cOWk+r4bsa/Kk8A0AAPhHhgOgjRs32vnnn5/iuI7pvsz0+++/u2CrcuXKNnnyZLvnnnvsgQcesBEjRrj7FfyIMj7hdDt4X2r69OnjAqXgpiwTAADwjwwHQJUqVbKPPvooxXEtiqpAJTMdPnzYzj77bOvdu7fL/tx1113Wvn374x5u361bNzdtdnBbt25dprUZALwmd2y8Dbh8utu0D/iyBqh79+7WqlUrN/FhsAbo22+/tWnTpqUaGB0PjeyqXr16kmPVqlWzcePGuf0SJUq4r5s3b3aPDdLts846K83njYuLcxsA4Mi0/EXZglU4VfB3Buj66693o61OOeUUV2isTfvz5s2z6667LlMbpwBr+fLlSY6tWLHCypUrFyqIVhCk4CtI9TxqX/369TO1LQAAwMcZIKlTp4699957ltU0oky1ReoCa9mypQuy3njjDbcFl+V46KGHrGfPnq77TQGRRqiVKlXKrr322ixvHwD4ZSmM8b/8O8ilefUHWAoD/g2AVJuzatUqtyq89sNddNFFmdU2q1u3rk2YMMHV7PTo0cMFOBr23rp169BjunTpYnv27HH1QTt37rQLL7zQJk2aZPHx9FMDQGYthfHR0v5u/5pq97IUBjwhJpDBqZznzp1rN998s/3xxx8pZoFWRkYLo2Y36jbTaDAVRBcoUCDSzQGA4zJ+eeaOyE04tNdaj63k9kfdsMric+bN1OdvXuW/Gk7gRF2/M5wB0oSHmpvniy++cIXHCnoAAACykwwHQFpna+zYsW44PAAAgC9GgWmWZdX/AAAAeDoD9NNPP4X277//fuvcubObaVkLomqh0nBaGBUAACDbB0CaVFC1PuFFz23btg3tB+/LrkXQAADAX44qANKiowAAf8qVI86ev+TL0D7gmwAoOPMyAMB/YnPEWqUiaS8vBPiiCForsWsIfPhEhIUKFXIzNmtuIAAAAM8FQFqWIk+ePG5/zpw5NmjQIOvXr59bD0xLVwAAvLcUxse/vuY27QO+nAdo3bp1oTmAtBDqDTfc4Jah0MKlDRs2zIo2AgAivBTGu4t7uv3LKt/OUhjwZwYof/78tn37drc/ZcoUu+SSS9y+1t7at29f5rcQAAAg0hkgBTx33nmn1a5d21asWGHNmjVzx5cuXWrly5fP7PYBAABEPgM0ePBgq1+/vm3dutXGjRtnRYoUcccXLFhgN910Ex8RAADwXgZII75U+Jxc9+7dM6tNAAAA0ZUBAgAAyO4IgAAAgO9kuAsMAOAvWv6ie6OxoX3ANxmgTz/91A4ePJj1rQEAROVSGDWKn+827QO+CYCuu+4627lzp9uPjY21LVu2ZHW7AAAAIhsAFS1a1ObOnev2A4GAxcTEZF2LAABR5dDhgzZx5XC3aR/wTQ1Qhw4d7JprrnGBj7YSJUqk+djExMTMbB8AIMIU9Ly54Am336hCK8uZI1ekmwScmADo2WeftRtvvNFWrVplV199tQ0fPtzNBwQAAODpUWBVq1Z12zPPPGMtWrSwvHnzZm3LAAAAomUYvAIg0VIYy5cvd/tVqlRxdUIAAACenAhx79691rZtWytVqpRddNFFbtN+u3bt3H0AAACeC4A6depkM2fOdHMDaWi8tk8++cQd69y5c9a0EgAAIJJdYFoBfuzYsdawYcPQsWbNmlmePHmsZcuWNmTIkMxsHwAAQOQDIHVzFS9ePMXxYsWK0QUGAB6UK0due/yikaF9wJddYPXr13eF0AkJCaFj+/bts+7du7v7AADeEpsjp9Up1cRt2ge8IMM/yS+//LI1bdrUSpcubbVq1XLHFi9ebPHx8TZ58uSsaCMAAEBkA6AaNWrYypUrbdSoUbZs2TJ37KabbrLWrVu7OiAAgPdmgp61Zrzbv6h8c2aChiccUy5TkyC2b98+81sDAIjKAGjwvE5u//yyVxEAwZ81QAAAANkdARAAAPAdAiAAAOA7BEAAAMB3jikA0vIXb775pnXr1s127Njhji1cuNA2bNiQ2e0DAACI/Ciwn376yZo0aWIFCxa0NWvWuNFghQsXtvHjx9vatWtt5Mh/ZwsFAADwTAbo4Ycftttvv93NBaTJD8PXA5s1a1Zmtw8AEGFa/qLz+a+7jaUw4NsM0Pz58+31119PcfzUU0+1TZs2ZVa7AABRQstfaP4fwNcZoLi4ONu9e3eK4ytWrLCiRYtmVrsAAACiJwC6+uqrrUePHnbw4EF3OyYmxtX+PPbYY3b99ddnRRsBABGUePiQfbf2M7dpH/BlAPTSSy/ZP//8Y8WKFXOrwDdo0MAqVapkJ510kvXq1StrWgkAiJiDhw/YS9/d7TbtA76sAdLor6lTp9rs2bPdiDAFQ2effbYbGQYAAODZxVDlwgsvdBsAAIDnA6BXXnkl1eOqBdKweHWHXXTRRRYbG5sZ7QMAAIh8ADRgwADbunWr7d27104++WR37K+//rK8efNa/vz5bcuWLXbaaafZ9OnTrUyZMpnfYgAAgBNdBN27d2+rW7eumwhx+/btbtMQ+Hr16tnLL7/sRoSVKFHCOnXqdLxtAwAAiI4M0JNPPmnjxo2zihUrho6p2+vFF190w+B///1369evH0PiAQCAdwKgjRs32qFDKeeB0LHgTNClSpWyv//+O3NaCACIqJw5clnHcweE9gFfdoE1atTI7r77blu0aFHomPbvuecea9y4sbu9ZMkSq1ChQua2FAAQEQp6Gp/Wym0EQPBtAPTWW2+51d/r1KnjlsXQds4557hjuk9UDK0JEwEAADzRBaYCZ02EuGzZMlf8LFWqVHFbeJYIAOANWv7ix00z3P5ZJRq6xVGB7O6Yf4qrVq3qNgCAt2n5i96zbnP7o25YRQAE/wZA69evt08//dQNeT9wIOm6MP3798+stgEAAERHADRt2jS3IrwmO1Q3WI0aNWzNmjUWCATcmmAAAACeK4Lu1q2bPfLII26kl5a+0JxA69atc6vCt2jRImtaCQAAEMkA6Ndff7Xbbvu3Lzhnzpy2b98+N+qrR48e9vzzz2dm2wAAAKIjAMqXL1+o7qdkyZL222+/he7btm1b5rYOAAAgGmqAzjvvPJs9e7ZVq1bNmjVrZp07d3bdYePHj3f3AQAAeC4A0iivf/75x+13797d7X/44YdWuXJlRoABgAdp9uc76/QK7QNeEBPQ8C2f2717txUsWNB27dplBQoUiHRzAOC4jF++MVudweZVSka6CfDh9TvDNUAa/r59+/YUx3fu3OnuAwAAiHYZDoA0509iYmKK4/v377cNGzZYVurbt6/FxMTYQw89FDqWkJBgHTt2tCJFirjRaNdff71t3rw5S9sBAH6SeDjRft78ndu0D/iqBkgzPwdNnjzZpZyCFBBpgsTy5ctbVpk/f769/vrrduaZZyY53qlTJ/viiy9szJgxrk333XefNW/e3L799tssawsA+MnBw/vtmek3hC2FkTfSTQJOXAB07bXXuq/KwLRp0ybJfbly5XLBT1atAK9C69atW9uwYcOsZ8+eoePq89MK9KNHj7bGjRu7Y8OHD3cj1ObOncuoNAAAcHxdYIcPH3Zb2bJlbcuWLaHb2tT9tXz5crvyyistK6iL64orrrAmTZokOb5gwQI7ePBgkuNaoFVtnDNnTprPp/aqcCp8AwAA/pHhYfCrV6+2E+mDDz6whQsXui6w5DZt2mS5c+e2QoUKJTlevHhxd19a+vTp44bwAwAAfzqm1eBV76MtmAkK9/bbb2dW29waYw8++KBNnTrVrTuWWbSe2cMPPxy6rQxQmTJlMu35AQCAxwIgZU607tc555zjlsJQTVBWUReXgqzwVeZVcD1r1iwbNGiQK8bWshwagh+eBdIosBIlSqT5vHFxcW4DAAD+lOEAaOjQofbOO+/Yrbfealnt4osvdstshLvjjjtcnc9jjz3msjYqwFY2SsPfRbVIa9eutfr162d5+wAAgE8CIGVczj//fDsRTjrpJKtRo0aKxVg150/weLt27Vx3VuHChd0skPfff78LfliXDAAyR2xMTru11pOhfcALMvyTfOedd7ph50899ZRFgwEDBliOHDlcBkiju5o2bWqvvfZapJsFAJ6RKza3XVvt3kg3A4hsAKSZl9944w376quv3KSE6oJKvlhqVpoxY0aS2yqOHjx4sNsAAACyJAD66aef7KyzznL7P//8c5L7srIgGgAQGVr+YvVf/9ZjVji5psXmiOWjgP8CoOnTp2dNSwAAUbsUxmNTm7l9lsKAbxdDDVq1apUbhr5v3z53OxAIZGa7AAAAoicA2r59uxuefvrpp1uzZs1s48aNodFYnTt3zoo2AgAARDYA0urrKnzWXDt58/63InCrVq1s0qRJmds6AACAaKgBmjJliuv6Kl26dJLjlStXtj/++CMz2wYAABAdGaA9e/YkyfwE7dixg+UlAACANwOg//3vfzZy5MgkQ9+1IGq/fv2sUaNGmd0+AACAyHeBKdBREfQPP/zglsXo0qWLLV261GWAvv3228xvIQAgorT8RcszHg7tA16Q4Z9krcG1YsUKtxq71ur6559/rHnz5taxY0e3OjwAwHtLYbSq+UikmwFkqmMK5QsWLGhPPPFE5rYEAAAgWmuAhg8fbmPGjElxXMdGjBiRWe0CAESJw4HDtnbXcrdpH/BlANSnTx875ZRTUhwvVqyY9e7dO7PaBQCIEgcSE6zTxEZu0z7gywBIEyBWqFAhxfFy5cq5+wAAADwXACnToxXhk1u8eLEVKVIks9oFAAAQPQHQTTfdZA888IBbFT4xMdFtX3/9tT344IN24403Zk0rAQAAIjkK7LnnnrM1a9a4uYBy5vz32zUR4m233UYNEAAA8F4AFAgEbNOmTfbOO+9Yz5497ccff7Q8efJYzZo1XQ0QAACAJwOgSpUquZmftfipNgAAAE8HQDly5HBBz/bt2wl+AMAntPzF1VU7hPYBXxZB9+3b1x599FH7+eefs6ZFAICoWwqjzVlPu037gBdkOJRXsfPevXutVq1aljt3blcDFE6LogIAAHgqABo4cGDWtAQAEJW0/MW2PRvc/in5TrUcMRnuPACyfwDUpk2brGkJACAqafmLez6v5/ZH3bDK4nPmjXSTgON2TGH8b7/9Zk8++aSbFHHLli3u2MSJE93oMAAAAM8FQDNnznTz/nz//fc2fvx4++eff0JLYTzzzDNZ0UYAAIDIBkBdu3Z1kyBOnTrVFUEHNW7c2ObOnZu5rQMAAIiGAGjJkiV23XXXpbpI6rZt2zKrXQAAANETABUqVMg2btyY4viiRYvs1FNPzax2AQAARE8ApBXfH3vsMbcmWExMjFsI9dtvv7VHHnnEzREEAADguWHwvXv3to4dO1qZMmUsMTHRqlev7r7efPPNbmQYAMBbYmNi7bJKbUL7gBfEBLTC6TFYt26dqwfSKLDatWtn67XBdu/ebQULFrRdu3ZZgQIFIt0cADgu45enLFOIZs2rlIx0E+DD6/dRZ4DU1fXCCy/Yp59+agcOHLCLL77YDXtPvhQGAACAZ2qAevXqZY8//rjlz5/fFTu//PLLrisMAOBt6ijYlbDdbcfYaQBk3wBo5MiR9tprr9nkyZPt448/ts8++8xGjRrlMkMAAO/an7jP2n5c023aB3wVAK1du9aaNWsWut2kSRM3CuzPP//MqrYBAABENgA6dOiQxcfHJzmWK1cuO3jwYFa0CwAAIMscdRG0+n1vv/12i4uLCx1LSEiwDh06WL58+ULHtD4YAACAJwKgNm3+nQMi3C233JLZ7QEAAIieAGj48OFZ2xIAAIBoXQoDAADAd0thAAD8RctfNCzfMrQPeAEBEAAgXbli4+z+8wZyluApdIEBAADfIQMEADjiNCjBGaDjYvO4SXCB7I4MEAAgXQp+Wo+t5DaWwoBXEAABAADfIQACAAC+QwAEAAB8hwAIAAD4DgEQAADwHQIgAADgO8wDBABIV46YHFa/zJWhfcALCIAAAOnKHRtvj1zwBmcJnkIoDwAAfIcACAAA+A4BEAAgXQmH9tr1H5Rym/YBLyAAAgAAvkMABAAAfIcACAAA+A4BEAAA8B0CIAAA4DsEQAAAwHeiOgDq06eP1a1b10466SQrVqyYXXvttbZ8+fIkj0lISLCOHTtakSJFLH/+/Hb99dfb5s2bI9ZmAPAaLX9xdsmL3cZSGPCKqA6AZs6c6YKbuXPn2tSpU+3gwYN26aWX2p49e0KP6dSpk3322Wc2ZswY9/g///zTmjdvHtF2A4DXlsJ4osG7btM+4AUxgUAgYNnE1q1bXSZIgc5FF11ku3btsqJFi9ro0aPthhtucI9ZtmyZVatWzebMmWPnnXfeUT3v7t27rWDBgu75ChQokMXvAgCy1vjlG7PVKW5epWSkm4Bs6niu31GdAUpOb1AKFy7svi5YsMBlhZo0aRJ6TNWqVa1s2bIuAErL/v373UkL3wAAgH9kmwDo8OHD9tBDD9kFF1xgNWrUcMc2bdpkuXPntkKFCiV5bPHixd196dUWKWIMbmXKlMny9gNAdqXlL24eU9FtLIUBr8g2AZBqgX7++Wf74IMPjvu5unXr5rJJwW3dunWZ0kYA8Kr9ifvcBnhFTssG7rvvPvv8889t1qxZVrp06dDxEiVK2IEDB2znzp1JskAaBab70hIXF+c2AADgT1GdAVJ9toKfCRMm2Ndff20VKlRIcn+dOnUsV65cNm3atNAxDZNfu3at1a9fPwItBgAA2UHOaO/20givTz75xM0FFKzrUd1Onjx53Nd27drZww8/7AqjVQF+//33u+DnaEeAAQAA/4nqAGjIkCHua8OGDZMcHz58uN1+++1uf8CAAZYjRw43AaJGdzVt2tRee+21iLQXAABkD1EdAB3NFEXx8fE2ePBgtwEAAGT7AAgAEHkxFmNnFK0f2ge8gAAIAJCuuJx5rMfF4zhL8JSoHgUGAACQFQiAAACA7xAAAQDSpeUv7phQw20shQGvoAYIAHBEu/fv4CzBU8gAAQAA3yEAAgAAvkMABAAAfIcACAAA+A4BEAAA8B1GgQEA0qXlLyoWrhXaB7yAAAgAcMSlMPpdOpGzBE+hCwwAAPgOARAAAPAdAiAAQLr2H9prHT49123aB7yAGiAAQLoCZrZ17/rQPuAFZIAAAIDvEAABAADfIQACAAC+QwAEAAB8hwAIAAD4DqPAAADp0uIXpQucHtoHvIAACACQrricee3lZjM4S/AUusAAAIDvEAABAADfIQACAKRLy188+GVDt7EUBryCGiAAQLq0/MX63StC+4AXkAECAAC+QwAEAAB8hwAIAAD4DgEQAADwHQIgAADgO4wCAwCkS8tfFM1bOrQPeAEBEADgiEthDL16HmcJnkIXGAAA8B0CIAAA4DsEQACAdO0/tM+6TLncbdoHvIAaIABAugIWsN92LA7tA15ABggAAPgOARAAAPAdAiAAAOA7BEAAAMB3CIAAAIDvMAoMAHBEBeIKc5bgKQRAAIB0xefMa8Ov+5mzBE+hCwwAAPgOARAAAPAdAiAAQLq0/MXT0653G0thwCuoAQIApEvLXyzdOie0D3gBGSAAAOA7BEAAAMB3CIAAAIDvEAABAADfIQACAAC+wygwAMARxcXm4SzBUwiAAABHXApjdIvfOEvwFLrAAACA7xAAAQAA36ELDACQrgOJCfbC7PZu/9ELh1nu2HjOGLI9AiAAQLoOBw7bwo3TQvuAF9AFBgAAfMczAdDgwYOtfPnyFh8fb/Xq1bN58+ZFukkAACBKeSIA+vDDD+3hhx+2Z555xhYuXGi1atWypk2b2pYtWyLdNAAAEIU8UQPUv39/a9++vd1xxx3u9tChQ+2LL76wt99+27p27Rrp5gGIQuOXb7TspHmVkpFuAuAp2T4AOnDggC1YsMC6desWOpYjRw5r0qSJzZkzJ6JtAwBkLgJXZJZsHwBt27bNEhMTrXjx4kmO6/ayZctS/Z79+/e7LWjXrl3u6+7du7O4tQCixd5//rbsZPfufBF7bwmH9pol/Pfch3Mmeua9ZbWMvLdPV26y7ObqyiUi+vrB63YgEPBfAHQs+vTpY927d09xvEyZMhFpDwBkF+371o50E4AUtm/fbgULFjRfBUCnnHKKxcbG2ubNm5Mc1+0SJVKPTNVdpqLpoJ07d1q5cuVs7dq1GT6B0U7RsQK7devWWYECBcxLeG/ZE59b9sTnln15+bPbtWuXlS1b1goXLpzh7832AVDu3LmtTp06Nm3aNLv22mvdscOHD7vb9913X6rfExcX57bkFPx47YcjSO+L95b98LllT3xu2ZOXPzevv78cOXL4LwASZXPatGlj55xzjp177rk2cOBA27NnT2hUGAAAgOcCoFatWtnWrVvt6aeftk2bNtlZZ51lkyZNSlEYDQAA4JkASNTdlVaX15GoO0yTKKbWLZbd8d6yJz637InPLXvy8ufm9fcXdxzvLSZwLGPHAAAAsjFPLIUBAACQEQRAAADAdwiAAACA7xAAAQAA3yEASqZ8+fIWExOTZOvbt695idZB01QBem8//vijecHVV1/tZgONj4+3kiVL2q233mp//vmnZXdr1qyxdu3aWYUKFSxPnjxWsWJFN+JBiwB7Qa9evez888+3vHnzWqFChSy7Gzx4sPsbop/DevXq2bx58yy7mzVrll111VVWqlQp9zfj448/Ni8ti1S3bl076aSTrFixYm4y3eXLl5sXDBkyxM4888zQ5If169e3iRMnmhf17dvX/Ww+9NBDGfo+AqBU9OjRwzZu3Bja7r//fvOSLl26uD9mXtKoUSP76KOP3B+vcePG2W+//WY33HCDZXda0Fczm7/++uu2dOlSGzBggA0dOtQef/xx8wIFci1atLB77rnHsrsPP/zQTcqqAHXhwoVWq1Yta9q0qW3ZssWyM00qq/ei4M5rZs6caR07drS5c+fa1KlT7eDBg3bppZe695zdlS5d2gUGCxYssB9++MEaN25s11xzjfs74iXz5893fx8V7GWYhsHjP+XKlQsMGDDAs6fkyy+/DFStWjWwdOlSTX8QWLRoUcCLPvnkk0BMTEzgwIEDAa/p169foEKFCgEvGT58eKBgwYKB7Ozcc88NdOzYMXQ7MTExUKpUqUCfPn0CXqG/GRMmTAh41ZYtW9x7nDlzZsCLTj755MCbb74Z8Iq///47ULly5cDUqVMDDRo0CDz44IMZ+n4yQKlQ1FykSBGrXbu2vfDCC3bo0CHzAi0Q2759e3v33Xddl4NX7dixw0aNGuW6VnLlymVeo8X/jmXhP2RtJkv/aTdp0iTJ2kS6PWfOHE59NvrdEq/9fiUmJtoHH3zgMlvqCvOKjh072hVXXJHk986XM0FnlgceeMDOPvts9wvw3XffuZXj1Q3Wv39/y870z9vtt99uHTp0cGumqbbEax577DEbNGiQ7d2718477zz7/PPPzWtWrVplr776qr344ouRbgrCbNu2zV1kki+/o9vqxkT0U1ezakguuOACq1GjhnnBkiVLXMCTkJBg+fPntwkTJlj16tXNCz744APX1awusGPliwxQ165dUxQ2J9+Cf6TUh9+wYUPXn6hg4aWXXnIXHBUOZ+f3pvfw999/u4DOi5+bPProo7Zo0SKbMmWKxcbG2m233eYCPy+8N9mwYYNddtllrmZGmbxodSzvDYiGbMLPP//sLqxeUaVKFTfQ5fvvv3d1dlo0/JdffrHsbt26dfbggw+6TL8GHBwrXyyFoYVSt2/fnu5jTjvtNMudO3eK4yoY038D+oOtH6bs+t5atmxpn332mbv4BOk/VgUKrVu3thEjRpiXPrf169dbmTJlXBYvGlO+GX1vGtGmwFyZrXfeecd1r0SrY/nc9J703/fOnTstu3aBqVt57NixbiRRkC44ek+ffPKJeYH+fiiLEP4evUDrSOoz0og3jbj0KnUVaSSpioazM41EvO6669z1K/x6pp9P/W1UwiL8Pl93gRUtWtRtx0LRs06ohkhm5/f2yiuvWM+ePUO3dUHVCBWNXNFwXa99bkpnS7Rm7jLy3pT50Si3OnXq2PDhw6M6+Dnezy27UjCnz2fatGmh4EA/g7p9rIs0I+vp/3+N8lVQN2PGDE8HP8GfyWj9m5gRF198seveC3fHHXdY1apVXSnE0QQ/vgmAjpaKFZUq1MVG80LodqdOneyWW26xk08+2bIzzZETTv3Bov8GNFwyO9Nnpn7gCy+80H1OGgL/1FNPufcWjdmfjFDwo8xPuXLlXN2PsitBJUqUsOxu7dq1rmhdX/UfXHBeqkqVKoV+RrMLdZ8r46Mau3PPPdcGDhzoik71hzk7++eff1ztWdDq1avd56Q6yeR/V7Jjt9fo0aNd9kd/8zdt2uSOFyxY0M27lZ2p3OHyyy93n5HKH/Q+FeRNnjzZsruTTjopRZ1Wvnz53OClDNVvZdXwtOxowYIFgXr16rnhuPHx8YFq1aoFevfuHUhISAh4zerVqz0zDP6nn34KNGrUKFC4cOFAXFxcoHz58oEOHToE1q9fH/DC8HB9TqltXtCmTZtU39v06dMD2dGrr74aKFu2bCB37txuWPzcuXMD2Z0+i9Q+I3122V1av1v6vcvu2rZt66Z10c9i0aJFAxdffHFgypQpAa9qcAzD4H1RAwQAABAuuosJAAAAsgABEAAA8B0CIAAA4DsEQAAAwHcIgAAAgO8QAAEAAN8hAAIAAL5DAAQAAHyHAAhA1Hvrrbfs0ksvDd2+/fbbM2VBTi2eqIUVM0vXrl3d2lIAoh8zQQOIagkJCW71+DFjxtgFF1zgju3atcstZFmoUKGoWt1827Ztrq1aK0tfAUQvMkAAotrYsWOtQIECoeAnuFjl8QY/WeGUU06xpk2b2pAhQyLdFABHQAAE4ITQSvZawb53796hY999953lzp3bpk2blub3ffDBB3bVVVclOZa8C6xhw4b2wAMPWJcuXdwq5XqdZ599Nsn3rFy50i666CKLj4+36tWr29SpU1O81rp166xly5YuuNLzXHPNNbZmzRp337Jlyyxv3rxuVe2gjz76yK0a/ssvv4SOqa1qM4DoRgAE4IQoWrSovf322y4w+eGHH+zvv/+2W2+91e677z67+OKL0/y+2bNn2znnnHPE5x8xYoTly5fPvv/+e+vXr5/16NEjFOQcPnzYmjdv7oIt3T906FB77LHHknz/wYMHXfbmpJNOsm+++ca+/fZby58/v1122WV24MABq1q1qr344ot277332tq1a239+vXWoUMHe/75511AFXTuuee6+4KBE4DoRA0QgBOqY8eO9tVXX7mgZsmSJTZ//nyLi4tL9bE7d+60k08+2WbNmmX/+9//kmSAdF+wgFkZoMTERBe4hAcijRs3tr59+9qUKVPsiiuusD/++MNKlSrl7p80aZJdfvnloRqg9957z3r27Gm//vqrqw0SBT7KBul1gkXYV155pe3evdsFU7Gxse55go8X3acuuhkzZliDBg2y6CwCOF45j/sZACADlEWpUaOGK2pesGBBmsGP7Nu3z31Vt9WRnHnmmUlulyxZ0rZs2eL2FdSUKVMmFPxI/fr1kzx+8eLFtmrVKpcBSl6E/dtvv4VuK4t1+umnW44cOWzp0qVJgh9Rl5js3bv3iG0GEDkEQABOKAUTf/75p+uWUjdRzZo103xskSJFXIDx119/HfF5c+XKleS2vk+vcbT++ecfq1Onjo0aNSrV7rvwQGnPnj0uANq4caMLtMLt2LEjxfcAiD4EQABOGHUp3XLLLdaqVSurUqWK3Xnnna4brFixYqk+Xt1Mqq9RkXH4PEAZVa1aNVfgHB6wzJ07N8ljzj77bPvwww9dWzTqLDUKbtT99sQTT7jnat26tS1cuDCU9ZGff/7ZBWNnnHHGMbcXQNajCBrACaPAQXP4vPLKK64IWV1Jbdu2Tfd7VJisQujj0aRJE/dabdq0cRkc1QqpLeEUzGgYu0Z+6f7Vq1e7Oh6NLlNRs6joWV1pTz75pPXv39/VHT3yyCNJnkffq3ql8KAIQPQhAAJwQiiYGDhwoL377rsuw6IuJO0rYEhv3px27drZl19+6QKnY6XXUrGzaopUHK3MU69evZI8RkPcVWxdtmxZN2JMWSO9tmqA1N6RI0e6dqjNOXPmdCPOVDg9bNgwmzhxYuh5NAS+ffv2x9xWACcGo8AARL0WLVq4Lqpu3bpZNFMg1LlzZ/vpp59ckAQgepEBAhD1XnjhBTcnT7RTcfTw4cMJfoBsgAwQAADwHTJAAADAdwiAAACA7xAAAQAA3yEAAgAAvkMABAAAfIcACAAA+A4BEAAA8B0CIAAA4DsEQAAAwHf+D7/dhF8ie2n9AAAAAElFTkSuQmCC", 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" ] @@ -1439,7 +1424,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 13, "id": "42", "metadata": {}, "outputs": [ @@ -1447,9 +1432,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Parsed counts: [{'x': 0}: 517, {'x': 1}: 486, {'x': 2}: 473, {'x': 3}: 206, {'x': -1}: 163, {'x': -4}: 79, {'x': -2}: 78, {'x': -3}: 46]\n", + "Parsed counts: [{'x': 2}: 497, {'x': 0}: 488, {'x': 1}: 486, {'x': -1}: 189, {'x': 3}: 188, {'x': -4}: 75, {'x': -2}: 65, {'x': -3}: 60]\n", "The analytical gradient is: 0.25\n", - "The majority gradient is: 0.0\n", + "The majority gradient is: 0.5\n", "The majority result is incorrect\n", "####################################################\n", "Success rate: 23.73% (486/2048 shots)\n", @@ -1468,7 +1453,7 @@ }, { "data": { - "image/png": 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", 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", 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" ] @@ -1569,20 +1554,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "id": "50", "metadata": {}, "outputs": [ { - "ename": "NameError", - "evalue": "name 'params' is not defined", - "output_type": "error", - "traceback": [ - "\u001b[31m---------------------------------------------------------------------------\u001b[39m", - "\u001b[31mNameError\u001b[39m Traceback (most recent call last)", - "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m \u001b[38;5;66;03m# In this example we will use the linear function\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m p = \u001b[43mparams\u001b[49m()\n\u001b[32m 3\u001b[39m p.set_function(p.linear, (\u001b[32m0.5\u001b[39m, \u001b[32m0.25\u001b[39m))\n\u001b[32m 4\u001b[39m p.m = \u001b[32m2\u001b[39m \u001b[38;5;66;03m# Correct selection of m - no aliasing.\u001b[39;00m\n", - "\u001b[31mNameError\u001b[39m: name 'params' is not defined" - ] + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -1608,7 +1592,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "id": "51", "metadata": {}, "outputs": [ @@ -1646,7 +1630,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "id": "52", "metadata": {}, "outputs": [ @@ -1705,7 +1689,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, "id": "55", "metadata": {}, "outputs": [ @@ -1716,14 +1700,15 @@ "m=0.05: Success rate = 0.00%\n", "m=0.1: Success rate = 0.00%\n", "m=0.3: Success rate = 0.00%\n", - "m=0.5: Success rate = 8.74%\n", - "m=0.55: Success rate = 39.70%\n", - "m=0.7: Success rate = 86.62%\n", - "m=0.8: Success rate = 79.88%\n", - "m=0.9: Success rate = 92.63%\n", - "m=1.0: Success rate = 94.24%\n", - "m=1.5: Success rate = 73.73%\n", - "m=2.0: Success rate = 98.39%\n", + "m=0.5: Success rate = 9.47%\n", + "m=0.55: Success rate = 42.58%\n", + "m=0.7: Success rate = 87.74%\n", + "m=0.8: Success rate = 81.30%\n", + "m=0.9: Success rate = 91.70%\n", + "m=1.0: Success rate = 94.68%\n", + "m=1.5: Success rate = 72.41%\n", + "m=2.0: Success rate = 98.54%\n", + "m=3.0: Success rate = 0.00%\n", "m=4.0: Success rate = 0.00%\n", "m=6.0: Success rate = 0.00%\n", "m=10.0: Success rate = 0.00%\n" @@ -1731,7 +1716,7 @@ }, { "data": { - "image/png": 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", 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", 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" ] @@ -1826,7 +1811,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 18, "id": "57", "metadata": {}, "outputs": [ @@ -1835,19 +1820,19 @@ "output_type": "stream", "text": [ "l=0.1: Success rate = 94.34%\n", - "l=0.2: Success rate = 79.69%\n", - "l=0.3: Success rate = 59.91%\n", - "l=0.4: Success rate = 38.53%\n", - "l=0.5: Success rate = 24.37%\n", - "l=1: Success rate = 11.72%\n", - "l=1.5: Success rate = 14.06%\n", - "l=2.0: Success rate = 14.65%\n", - "l=3.0: Success rate = 26.32%\n" + "l=0.2: Success rate = 78.96%\n", + "l=0.3: Success rate = 59.67%\n", + "l=0.4: Success rate = 39.31%\n", + "l=0.5: Success rate = 22.80%\n", + "l=1: Success rate = 10.60%\n", + "l=1.5: Success rate = 14.79%\n", + "l=2.0: Success rate = 14.55%\n", + "l=3.0: Success rate = 26.12%\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -1932,19 +1917,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, "id": "60", "metadata": {}, "outputs": [ { - "ename": "NameError", - "evalue": "name 'params' is not defined", - "output_type": "error", - "traceback": [ - "\u001b[31m---------------------------------------------------------------------------\u001b[39m", - "\u001b[31mNameError\u001b[39m Traceback (most recent call last)", - "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[4]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m px = \u001b[43mparams\u001b[49m()\n\u001b[32m 2\u001b[39m py = params()\n\u001b[32m 4\u001b[39m \u001b[38;5;66;03m# Set the functions for x and y axes\u001b[39;00m\n\u001b[32m 5\u001b[39m \u001b[38;5;66;03m# f(x, y) = a*x + b*y + c = 0.5*x - 0.25*y + 0.1\u001b[39;00m\n\u001b[32m 6\u001b[39m \u001b[38;5;66;03m# df/dx = 0.5, df/dy = -0.25\u001b[39;00m\n", - "\u001b[31mNameError\u001b[39m: name 'params' is not defined" + "name": "stdout", + "output_type": "stream", + "text": [ + "[{'x': 2, 'y': -1}: 2048]\n", + "Analytical gradient: (dx, dy) = (0.5, -0.25)\n", + "Majority gradient: (dx, dy) = (0.5, -0.25)\n", + "Success rate: 100.00% (2048/2048 shots)\n", + "[\u001b[92m██████████████████████████████████████████████████\u001b[91m\u001b[0m] 100.00%\n" ] } ], @@ -2009,7 +1994,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, "id": "62", "metadata": {}, "outputs": [ @@ -2017,11 +2002,11 @@ "name": "stdout", "output_type": "stream", "text": [ - "[{'x': 1, 'y': -2}: 1996, {'x': 2, 'y': -2}: 14, {'x': 0, 'y': -2}: 13, {'x': 1, 'y': -3}: 12, {'x': 1, 'y': -1}: 4, {'x': 2, 'y': -1}: 3, {'x': -1, 'y': -2}: 1, {'x': 0, 'y': -3}: 1, {'x': 3, 'y': -3}: 1, {'x': 2, 'y': -4}: 1, {'x': 1, 'y': -4}: 1, {'x': -4, 'y': -2}: 1]\n", + "[{'x': 1, 'y': -2}: 1993, {'x': 0, 'y': -2}: 18, {'x': 2, 'y': -2}: 9, {'x': 1, 'y': -1}: 8, {'x': 1, 'y': -3}: 4, {'x': -2, 'y': -2}: 4, {'x': 0, 'y': -1}: 3, {'x': 2, 'y': -1}: 2, {'x': 1, 'y': -4}: 1, {'x': -1, 'y': 3}: 1, {'x': 0, 'y': 3}: 1, {'x': 0, 'y': -4}: 1, {'x': -4, 'y': -2}: 1, {'x': 3, 'y': 3}: 1, {'x': -1, 'y': -2}: 1]\n", "Analytical gradient: (dx, dy) = (0.25, -0.5)\n", "Majority gradient: (dx, dy) = (0.25, -0.5)\n", - "Success rate: 97.46% (1996/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.46%\n" + "Success rate: 97.31% (1993/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.31%\n" ] } ], @@ -2104,7 +2089,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "id": "64", "metadata": {}, "outputs": [], From 8e0685af18cecfefd56b30b9ca4688118c4d42eb Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Sat, 23 May 2026 20:06:28 +0300 Subject: [PATCH 04/12] Version 3 --- .../gradient_estimation.ipynb | 989 +++++++++--------- .../gradient_estimation_helpers.py | 15 +- algorithms/gradient_estimation/step_2.png | Bin 45955 -> 53466 bytes algorithms/gradient_estimation/step_3.png | Bin 48216 -> 56070 bytes 4 files changed, 478 insertions(+), 526 deletions(-) diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index 4cea27dc8..c0d0b0be6 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -10,31 +10,44 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "id": "1", "metadata": {}, "outputs": [], "source": [ - "from gradient_estimation_helpers import *\n", - "\n", - "# TODO: remove this\n", - "%load_ext autoreload\n", - "%autoreload 2" + "from gradient_estimation_helpers import *" ] }, { - "cell_type": "code", - "execution_count": 2, + "cell_type": "markdown", "id": "2", "metadata": {}, - "outputs": [], "source": [ - "# TODO: small fixes along the notebook\n", - "# TODO: code fix - free the ancilla after using it\n", - "# TODO: clean up the explanations and add references to the paper\n", - "# TODO: clean up section 4 (Parameters selection)\n", - "# TODO: check all or's comments from github and make sure they are addressed\n", - "# TODO: add tests" + "# Fast Quantum Algorithm for Numerical Gradient Estimation\n", + "> Given a scalar function of $d$ dimensions, $f(x_1, \\ldots, x_d)$, computing its gradient at a specific point is often essential.\n", + ">\n", + "> On a classical computer, this requires at least $d+1$ queries to $f$.\n", + ">\n", + "> This notebook presents a quantum algorithm that computes the gradient with a single query, based on the paper by S. P. Jordan [\\[1\\]](#original_paper).\n", + "> \n", + "> This represents a dramatic speedup for high-dimensional functions, where function evaluation is typically the dominant computational cost.\n", + ">\n", + "> - **Input:** A black-box function $f$ of $d$ dimensions.\n", + "> - **Promise:** The function is smooth and has bounded gradient: $|\\nabla f|<\\nabla f_{\\text{max}}$.\n", + "> - **Output:** The gradient $\\nabla f$ at the origin with $n$ bits of precision, encoded on a quantum register.\n", + "> \n", + "> **Complexity:** In black-box query complexity, the classical algorithm requires at least $d+1$ queries to $f$, while the quantum algorithm requires only one.\n", + ">\n", + "> ---\n", + ">\n", + "> **Keywords:** Foundational quantum algorithms, Gradient, Function evaluation, Oracle problem, Quantum Fourier Transform (QFT)\n", + "\n", + "\n", + "The core idea is to encode the function into the phase of a superposition state, then apply an inverse QFT to extract the gradient as a measurable outcome.\n", + "\n", + "We demonstrate this step by step—first with a simplified version to build intuition, then with refinements for the complete algorithm.\n", + "\n", + "![Quantum Circuit](quantum_circuit_2.png)" ] }, { @@ -42,23 +55,7 @@ "id": "3", "metadata": {}, "source": [ - "# Fast Quantum Algorithm for Numerical Gradient Estimation\n", - "> Given a scalar function of $d$ dimensions, $f(x_1, ... x_d)$, it is useful to find the gradient of the function at a specific point.\\\n", - "> On a classical computer, this requires at least d+1 queries of the function $f$.\\\n", - "> In this notebook we will explore quantum algorithm to find the gradient with just a single query of the function.\\\n", - "> This is a dramatic improvement in large dimensions functions, as most of the times the most expensive part of calculating the derivative is querying the function.\n", - "> * **Input:** A black box function $f$ of $d$ variables.\n", - "> * **Promise:** The function is a smooth real scalar function, and the gradient is bounded with a known value $|\\nabla f|<\\nabla f_{\\text{max}}$.\n", - "> * **Output:** The gradient $\\nabla f$ at the origin with $n$ bits of precision.\n", - "\n", - "> **Complexity:** In the context of many numerical calculations, black-box query complexity is a natural measure of algorithmic efficiency. In this measure, the classical algorithm queries the function at least $d+1$ times, while the quantum algorithm only queries the function a single time.\n", - "\n", - "\n", - "The core concept of the algorithm is to first 'apply' the function to the phase of a superposition state, then extract the gradient value from the phase to a measurable state by using a QFT.\\\n", - "Let's see it step by step, first a little simplified version to understand the concept, and then fixing the inaccuracies for the final algorithm.\\\n", - "![Quantum Circuit](quantum_circuit.png)\\\n", - "**TODO:** Decide which image to use, with or without the ancilla\\\n", - "![Quantum Circuit](quantum_circuit_2.png)" + "# 1. Introduction" ] }, { @@ -66,25 +63,37 @@ "id": "4", "metadata": {}, "source": [ - "## Simplified explanation of the algorithm\n", - "As briefly mentioned earlier, the algorithm can be divided to two steps:\n", - "1. Applying the function to the phase\n", - "2. Extracting the gradient value to a measurable state\n", - "\n", - "In more details:\n", - "1. For each coordinate ($x_i$), we start with the state $|\\delta_i\\rangle=|0\\rangle+|1\\rangle+|2\\rangle....|N-1\\rangle$, by applying the Hadamard gate on $|0\\rangle$.\\\n", - "For simplicity we will discuss a case of single coordinate, but if there is more than one coordinate, the state $|\\delta\\rangle$ is just a product state of all $|\\delta_i\\rangle$, and the algorithm stays the same.\n", + "## 1.1. Simplified explanation of the algorithm\n", + "The algorithm has two main steps:\n", + "1. Encode the function into the phase of a quantum superposition\n", + "2. Extract the gradient as a measurable state\n", + "\n", + "**In detail:**\n", + "\n", + "1. We define an interval $l$ with $N$ points around the origin where we estimate the gradient, establishing a resolution $\\mathrm{dx}=l/N$.\n", + "\n", + "For each dimension ($x_i$), we create the superposition $|\\delta_i\\rangle=|-l\\rangle+|-l+\\mathrm{dx}\\rangle+|-l+2\\mathrm{dx}\\rangle\\cdots|l-\\mathrm{dx}\\rangle$ using Hadamard gates on $|0\\rangle^{\\otimes n}$.\n", + "\n", + "*The actual encoding on qubits is discussed later.*\n", + "\n", + "For simplicity, we consider a single dimension. For $d > 1$, the state $|\\delta\\rangle$ is a tensor product over all dimensions:\n", "$$|\\delta\\rangle=\\prod_i|\\delta_i\\rangle$$\n", - "2. Using the phase kickback technique, we apply the function to the phase of each ket creating the state:\n", - "$$e^{i\\cdot2\\pi f(0)}|0\\rangle + e^{i\\cdot2\\pi f(1)}|1\\rangle + e^{i\\cdot2\\pi f(2)}|2\\rangle ..... e^{i\\cdot2\\pi f(N-1)}|N-1\\rangle$$\n", - "**TODO**: Decide to keep, move or remove those images\n", - "![](step_2.png)\\\n", - "3. We note the fact that for small enough interval, we can approximate: $f(x)\\approx f(0)+x\\cdot f'(x)$, so we can write the previous state as: \n", - "$$ e^{i\\cdot2\\pi f(0)}(|0\\rangle + e^{i\\cdot2\\pi f'(0)}|1\\rangle + e^{i\\cdot2\\pi 2f'(0)}|2\\rangle ..... e^{i\\cdot2\\pi (N-1)f'(0)}|N-1\\rangle) = e^{i\\cdot2\\pi f(0)}\\sum e^{i\\cdot2\\pi jf'(0)}|j\\rangle $$\n", - "![](step_3.png)\\\n", - "4. We note that this state is exactly the fourier transform of the state $|f'(0)\\rangle$, so we apply the inverse fourier transform and get the result: $$|f'(0)\\rangle$$\n", - "5. We measure to get $f'(0)$, and for a multi-coordinates function $\\nabla f$.\n", - "\n" + "\n", + "2. Using a phase oracle or the phase kickback technique, we encode the function as phases:\n", + "$$e^{i\\cdot2\\pi f(-l)}|-l\\rangle + e^{i\\cdot2\\pi f(-l+\\mathrm{dx})}|-l+\\mathrm{dx}\\rangle + e^{i\\cdot2\\pi f(-l+2\\mathrm{dx})}|-l+2\\mathrm{dx}\\rangle \\cdots e^{i\\cdot2\\pi f(l-\\mathrm{dx})}|l-\\mathrm{dx}\\rangle$$\n", + "![](step_2.png)\n", + "\n", + "3. For a sufficiently small interval, we approximate $f(x)\\approx f(0)+x\\cdot f'(0)$, allowing us to factor the state:\n", + "$$\\begin{aligned}\n", + "& e^{i\\cdot2\\pi f(0)}\\left(e^{i\\cdot2\\pi (-l)\\cdot f'(0)}\\lvert-l\\rangle + e^{i\\cdot2\\pi (-l+\\mathrm{dx})f'(0)}\\lvert-l+\\mathrm{dx}\\rangle + e^{i\\cdot2\\pi (-l+2\\mathrm{dx})f'(0)}\\lvert-l+2\\mathrm{dx}\\rangle \\cdots e^{i\\cdot2\\pi (l-\\mathrm{dx})f'(0)}\\lvert l-\\mathrm{dx}\\rangle\\right) \\\\\n", + "&= e^{i\\cdot2\\pi f(0)}\\sum_{-l}^{l-\\mathrm{dx}} e^{i\\cdot2\\pi jf'(0)}|j\\rangle\n", + "\\end{aligned}$$\n", + "![](step_3.png)\n", + "\n", + "4. This state is exactly the QFT of the computational basis state $|f'(0)\\rangle$. Applying the inverse QFT yields:\n", + "$$|f'(0)\\rangle$$\n", + "\n", + "5. Measure the register to obtain $f'(0)$ (or $\\nabla f$ for multi-dimensional functions)." ] }, { @@ -92,25 +101,30 @@ "id": "5", "metadata": {}, "source": [ - "## Full explanation of the algorithm\n", - "The previous explanation covers the main idea of the algorithm, but misses some important details on negative and fractional values.\\\n", - "In this explanation we will fill in these details.\\\n", - "When we calculate gradient, we look on an interval around the point of interest (in this case, it will be the origin). We will call this interval $l$.\n", - "The state $|\\delta_i\\rangle$ should represent $N$ equally spaced points around the origin in the interval $l$, so we normalized it to be:\n", + "## 1.2. Full explanation of the algorithm\n", + "The simplified explanation captures the key idea but omits two important details: handling negative values and fractional representation.\n", + "\n", + "When estimating the gradient, we analyze an interval $l$ around the origin.\n", + "\n", + "The state $|\\delta_i\\rangle$ represents $N$ equally spaced points in this interval, normalized as:\n", "$$ x=\\frac{l}{N}\\delta $$\n", - "With signed $\\delta$ ranging from $-N/2$ to $N/2-1$: $\\delta=-N/2$ is the leftmost point ($-l/2$), $\\delta=0$ is the origin, and $\\delta=N/2-1$ is the rightmost point ($l/2$)*.\\\n", - "\\\n", - "We also need to normalize the result state. Say the expected gradient is bounded between $-m/2$ and $m/2$, we want to represent those values using the $N$ states of the coordinate, so doing a similar trick we can define $$ \\nabla f=\\frac{m}{N}\\delta_{measured} $$\\\n", - "\\\n", - "When using the algorithm we need to select $l$ and $m$ using our prior knowledge on the function $f(x)$, and $N$ will define the final resolution we get.\\\n", - "$l$ should be small enough so we will stay in a linear regime of the function, and $m$ should be larger than the maximum possible gradient, but not too large because then we will lose resolution.\n", - "\\\n", - "Using those two normalizations, we change two things in the algorithm:\n", - "1. In step 2, instead of applying $f(\\delta)$, we apply $\\frac{N}{ml}f(\\frac{l}{N}\\delta)$.\n", + "\n", + "With signed $\\delta$ ranging from $-N/2$ to $N/2-1$: $\\delta=-N/2$ is the leftmost point ($-l/2$), $\\delta=0$ is the origin, and $\\delta=N/2-1$ is the rightmost point ($l/2$)*.\n", + "\n", + "We also normalize the output. Assuming the gradient is bounded between $-m/2$ and $m/2$, we represent those values using the $N$ states:\n", + "$$ \\nabla f=\\frac{m}{N}\\delta_{measured} $$\n", + "\n", + "When applying the algorithm, we choose $l$ and $m$ based on prior knowledge of $f(x)$. The value $N$ determines the final resolution.\n", + "\n", + "$l$ must be small enough to keep the function approximately linear, and $m$ must exceed the maximum expected gradient magnitude while maintaining sufficient resolution.\n", + "\n", + "Using these two normalizations, we modify the algorithm:\n", + "1. In step 2, instead of applying $f(\\delta)$, we apply $\\frac{N}{ml}f\\left(\\frac{l}{N}\\delta\\right)$.\n", "2. In step 5, the signed measurement directly gives $\\frac{N}{m}\\nabla f$, so $\\nabla f = \\frac{m}{N}\\delta_{measured}$.\n", - "Using a signed register means the measured $\\delta_{measured}$ is already the correct signed value with no further adjustment needed.\\\n", "\n", - "\\* The right point is actually $l/2-l/N$ and not $l/2$, because the center point is at the origin and $N$ must be even, but for the algorithm understanding it doesn't really matter." + "Using a signed register means the measured $\\delta_{measured}$ is already the correct signed value with no further adjustment needed.\n", + "\n", + "\\* The rightmost point is actually $l/2-l/N$ rather than $l/2$, because the center is at the origin and $N$ must be even. However, this distinction does not affect the conceptual understanding." ] }, { @@ -118,35 +132,57 @@ "id": "6", "metadata": {}, "source": [ - "## Parameter Selection\n", - "As briefly discussed before, we need to select appropriate values for $l$, $m$ and $N$ (and when using the ancilla method, also $N_0$, but we will not discuss it here).\\\n", - "Let's define: \n", - "* $\\nabla f_{max}$ - a bound for the value of $\\nabla f$ in the region around the origin, $|\\nabla f|<\\nabla f_{max}$\n", - "* $\\epsilon$ - desired accuracy for $\\nabla f$ estimation, $|\\nabla f_{est}-\\nabla f| < \\epsilon$\n", - "* $d$ - the dimensionality of the function $f$\n", - "* $D_2$ - typical value for the second derivative of $f$\n", + "## 1.3. Parameter Selection\n", + "We need to select appropriate values for $l$, $m$, and $N$. We use the following notation: \n", + "* $\\nabla f_{\\text{max}}$ — bound on the gradient magnitude: $|\\nabla f|<\\nabla f_{\\text{max}}$\n", + "* $\\epsilon$ — desired accuracy: $|\\nabla f_{\\text{est}}-\\nabla f| < \\epsilon$\n", + "* $d$ — dimensionality of $f$\n", + "* $D_2$ — bound on the second derivative of $f$ near the origin\n", "\n", "### Selecting $l$\n", - "Starting with $l$, this is the interval around the origin for the gradient estimation. Exactly like in classical gradient calculation, the interval should be small enough that we will be in the linear regime of the function.\\\n", - "If we want to reach accuracy $\\epsilon$, we need the gradient inside the interval to have smaller variance than $\\epsilon$, meaning $max(\\nabla f)-min(\\nabla f)<\\epsilon$. Using the second derivative approximation $max(\\nabla f)-min(\\nabla f)\\approx|\\nabla^2 f|\\cdot l<\\epsilon$, meaning we have to select $l$ such that $l<\\frac{\\epsilon}{|\\nabla^2 f|}$.\\\n", - "For example, for a quadratic function $f(x)=ax^2+bx+c$, $l$ should be smaller than the order of $\\frac{\\epsilon}{2a}$.\\\n", - "**TODO**: This isn't accurate, use the paper's more accurate result giving $l\\leq\\frac{2\\sqrt{3}\\epsilon}{D_2\\sqrt{d}}$.\n", + "Choose $l$ to ensure the function remains approximately linear. Similar to classical numerical differentiation, this interval must be sufficiently small.\n", + "\n", + "To keep gradient variation within accuracy $\\epsilon$, we require $\\nabla f_{\\text{max}} - \\nabla f_{\\text{min}} \\le \\epsilon$.\n", + "\n", + "For a single dimension, the second derivative is approximately $f''(x) \\approx (\\nabla f_{\\text{max}} - \\nabla f_{\\text{min}}) / l$. This gives $l < \\frac{\\epsilon}{|f''(x)|}$.\n", + "\n", + "Using $D_2$ as the second derivative bound, we get $l < \\frac{\\epsilon}{D_2}$.\n", + "\n", + "In multiple dimensions, we sum deviations as root-mean-square across all $d$ dimensions, introducing a factor of $1/\\sqrt{d}$.\n", + "\n", + "To improve this bound, we scale by the uniform distribution variance, $\\frac{1}{12}$.\n", + "\n", + "The final bound for $l$ is: \n", + "$$l\\leq\\frac{2\\sqrt{3}\\epsilon}{D_2\\sqrt{d}}$$\n", + "\n", + "For a one-dimensional quadratic function $f(x)=ax^2+bx+c$, we need $l$ smaller than $\\frac{\\sqrt{12}\\epsilon}{2a}$.\n", + "\n", + "Furthermore, in order to minimize the number of bits of precision to which $f$ must be evaluated, $l$ should be chosen as large as possible, subject to the constraint above. So $l$ should be chosen tightly.\n", + "\n", + "See Jordan's paper [\\[1\\]](#original_paper) for a full derivation.\n", "\n", "### Selecting $m$\n", - "$m$ is exactly defined as the bound for the value of the gradient. If we want to calculate a gradient that might be negative, there is a $1/2$ factor so $m\\ge2\\cdot\\nabla f_{max}$.\n", - "\n", - "### Selecting $N$\n", - "$N$ defines the resolution of the final result. The step size between possible results is $\\frac{m}{N}$.\\\n", - "Therefore, in order to achieve accuracy $\\epsilon$, we need to choose $N\\ge0.5\\frac{m}{\\epsilon}$.\\\n", - "Plugging in the condition for $m$, we get $N\\ge\\frac{\\nabla f_{max}}{\\epsilon}$.\n", - "\n", - "### Summery\n", - "Given a known bound $\\nabla f_{max}$ and desired accuracy $\\epsilon$, we can select the parameters:\n", - "$$\\left\\{\\begin{aligned}\n", - "l & \\leq \\frac{2 \\sqrt{3} \\epsilon}{D_2 \\sqrt{d}} \\\\\n", - "m & \\geq 2 \\nabla f_{\\max } \\\\\n", - "N & \\geq \\frac{\\nabla f_{\\max }}{\\epsilon}\n", - "\\end{aligned}\\right.$$" + "The parameter $m$ bounds the gradient magnitude. Since the gradient is signed, we need $m \\ge 2\\nabla f_{\\text{max}}$.\n", + "\n", + "The resolution of the result is $\\frac{m}{N}$. For a given register size and accuracy $\\epsilon$, the upper bound is $m \\le 2N\\epsilon$.\n", + "\n", + "### Selecting $n$\n", + "$N=2^n$ defines the result resolution. The step size between possible outcomes is $\\frac{m}{N}$.\n", + "\n", + "To achieve accuracy $\\epsilon$, we need $N\\geq\\frac{m}{2\\epsilon}$.\n", + "\n", + "Assuming tight $m$ selection, this gives a lower bound for the number of qubits:\n", + "$$n\\geq\\log_2\\left(\\frac{\\nabla f_{\\text{max}}}{\\epsilon}\\right)$$\n", + "\n", + "### Summary\n", + "Given $\\nabla f_{\\text{max}}$ and desired accuracy $\\epsilon$, select parameters as:\n", + "\n", + "\n", + "| Parameter | Role | Constraint |\n", + "|---|---|---|\n", + "| $l$ | Sampling interval | $l \\leq \\frac{2\\sqrt{3}\\epsilon}{D_2\\sqrt{d}}$ — keeps $f$ approximately linear |\n", + "| $m$ | Gradient range | $2\\nabla f_{\\max} \\leq m \\leq 2N\\epsilon$ |\n", + "| $n$ | Qubits / resolution | $n \\geq \\log_2(\\nabla f_{\\max} / \\epsilon)$ |" ] }, { @@ -154,13 +190,15 @@ "id": "7", "metadata": {}, "source": [ - "## Notebook's structure:\n", - "In the notebook, we will cover those topics:\n", - "1. Theoretical explanation (this section)\n", - "2. Step 1 of the algorithm - State Preparation. We will cover two methods. Phase Kickback (as in the cited paper) and Direct Phase (more straight forward and more efficient for the simulation). We will demonstrate how the states are prepared using a full statevector simulation.\n", - "3. The full algorithm, showing examples of linear and non-linear functions.\n", - "4. Parameters selection and limits (Still work in progress)\n", - "5. Multi-coordinates example, $f$ as function of $x, y$\n" + "## 1.4. Outline\n", + "This notebook covers:\n", + "1. Theoretical foundation and parameter selection\n", + "2. Implementation\n", + " - Phase state preparation (phase kickback and direct methods)\n", + " - Inverse QFT for gradient extraction\n", + " - Examples with linear and non-linear functions\n", + "3. Performance analysis\n", + "4. Multi-dimensional examples ($d > 1$)" ] }, { @@ -168,7 +206,7 @@ "id": "8", "metadata": {}, "source": [ - "# 2. State Preparation" + "# 2. Implementation" ] }, { @@ -176,7 +214,7 @@ "id": "9", "metadata": {}, "source": [ - "## 2.1. Phase Kickback" + "## 2.1. State Preparation" ] }, { @@ -184,10 +222,7 @@ "id": "10", "metadata": {}, "source": [ - "The first step of the algorithm is to prepare the state:\n", - "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}\\delta)}|\\delta\\rangle$$\n", - "The paper uses the phase kickback technique using the ancilla in order to create this state.\\\n", - "In the next example we will see how it works." + "### 2.1.1. Phase Kickback" ] }, { @@ -195,20 +230,40 @@ "id": "11", "metadata": {}, "source": [ - "The phase kickback contains three steps:\n", - "1. Apply Hadamard gate on $|\\delta\\rangle$ to have an entangled state\n", - "2. Set the ancilla to $|1111...1\\rangle$ (in binary representation) and apply QFT on it\n", - "3. Add the value $f(\\delta)$ to the ancilla, and the function's value will be 'kicked' to the phase\n", + "The first step is to prepare the state:\n", + "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}\\delta)}|\\delta\\rangle$$\n", + "\n", + "The paper assumes an oracle $|x\\rangle \\rightarrow |f(x)\\rangle$, which we use with the phase kickback technique to create this state.\n", "\n", - "Note that we use the ancilla as a signed and fractional QNum, so in order to have $|1111...1_b\\rangle$, we will assign $-1/N_0$" + "The next example demonstrates how this works." ] }, { - "cell_type": "code", - "execution_count": 3, + "cell_type": "markdown", "id": "12", "metadata": {}, + "source": [ + "The phase kickback has three main steps:\n", + "1. Apply Hadamard gates on $|\\delta\\rangle$ to create a superposition of all sample points\n", + "2. Initialize the ancilla to $|1111...1\\rangle$ (in binary) and apply QFT\n", + "3. Add $f(\\delta)$ to the ancilla; the function value is \"kicked back\" as a phase\n", + "\n", + "See the [appendix](#appendix-1---phase-kickback) for details." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13", + "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n" + ] + }, { "name": "stdout", "output_type": "stream", @@ -218,6 +273,18 @@ "Gate Counts: {'u': 25, 'cx': 19}\n" ] }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Job: https://platform.classiq.io/jobs/70ff34e5-b32e-4658-875a-73457dbeccd0\n", + "/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_97551/4002175823.py:45: SettingWithCopyWarning: \n", + "A value is trying to be set on a copy of a slice from a DataFrame\n", + "\n", + "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n", + " df.sort_values(by=\"x\", inplace=True)\n" + ] + }, { "data": { "application/vnd.microsoft.datawrangler.viewer.v0+json": { @@ -263,40 +330,40 @@ "type": "string" } ], - "ref": "2ed188b1-5bb0-4ee9-9817-91350a30d4cd", + "ref": "9b937272-abe5-440b-bb6f-ad57c87c919b", "rows": [ [ - "0", - "3", + "63", + "-4", "0.0", - "(0.08838834764831856-0.08838834764831835j)", + "(0.08838834764831822+0.08838834764831847j)", "0.12", - "-0.25π", - "0.015625", - "0000011" + "0.25π", + "0.015624999999999965", + "0000100" ], [ - "1", - "1", + "40", + "-3", "0.0", "(-0.0883883476483185+0.08838834764831836j)", "0.12", "0.75π", "0.015624999999999997", - "0000001" + "0000101" ], [ - "2", - "-3", + "61", + "-2", "0.0", - "(-0.0883883476483185+0.08838834764831836j)", + "(-0.08838834764831822-0.0883883476483185j)", "0.12", - "0.75π", - "0.015624999999999997", - "0000101" + "-0.75π", + "0.015624999999999972", + "0000110" ], [ - "3", + "41", "-1", "0.0", "(0.08838834764831853-0.08838834764831834j)", @@ -306,17 +373,7 @@ "0000111" ], [ - "4", - "2", - "0.0", - "(-0.08838834764831827-0.08838834764831852j)", - "0.12", - "-0.75π", - "0.015624999999999983", - "0000010" - ], - [ - "5", + "60", "0", "0.0", "(0.08838834764831827+0.08838834764831847j)", @@ -326,24 +383,34 @@ "0000000" ], [ - "6", - "-2", + "39", + "1", "0.0", - "(-0.08838834764831822-0.0883883476483185j)", + "(-0.0883883476483185+0.08838834764831836j)", + "0.12", + "0.75π", + "0.015624999999999997", + "0000001" + ], + [ + "53", + "2", + "0.0", + "(-0.08838834764831827-0.08838834764831852j)", "0.12", "-0.75π", - "0.015624999999999972", - "0000110" + "0.015624999999999983", + "0000010" ], [ - "7", - "-4", + "30", + "3", "0.0", - "(0.08838834764831822+0.08838834764831847j)", + "(0.08838834764831856-0.08838834764831835j)", "0.12", - "0.25π", - "0.015624999999999965", - "0000100" + "-0.25π", + "0.015625", + "0000011" ] ], "shape": { @@ -381,37 +448,37 @@ " \n", " \n", " \n", - " 0\n", - " 3\n", + " 63\n", + " -4\n", " 0.0\n", - " 0.088388-0.088388j\n", + " 0.088388+0.088388j\n", " 0.12\n", - " -0.25π\n", + " 0.25π\n", " 0.015625\n", - " 0000011\n", + " 0000100\n", " \n", " \n", - " 1\n", - " 1\n", + " 40\n", + " -3\n", " 0.0\n", " -0.088388+0.088388j\n", " 0.12\n", " 0.75π\n", " 0.015625\n", - " 0000001\n", + " 0000101\n", " \n", " \n", - " 2\n", - " -3\n", + " 61\n", + " -2\n", " 0.0\n", - " -0.088388+0.088388j\n", + " -0.088388-0.088388j\n", " 0.12\n", - " 0.75π\n", + " -0.75π\n", " 0.015625\n", - " 0000101\n", + " 0000110\n", " \n", " \n", - " 3\n", + " 41\n", " -1\n", " 0.0\n", " 0.088388-0.088388j\n", @@ -421,62 +488,62 @@ " 0000111\n", " \n", " \n", - " 4\n", - " 2\n", + " 60\n", + " 0\n", " 0.0\n", - " -0.088388-0.088388j\n", + " 0.088388+0.088388j\n", " 0.12\n", - " -0.75π\n", + " 0.25π\n", " 0.015625\n", - " 0000010\n", + " 0000000\n", " \n", " \n", - " 5\n", - " 0\n", + " 39\n", + " 1\n", " 0.0\n", - " 0.088388+0.088388j\n", + " -0.088388+0.088388j\n", " 0.12\n", - " 0.25π\n", + " 0.75π\n", " 0.015625\n", - " 0000000\n", + " 0000001\n", " \n", " \n", - " 6\n", - " -2\n", + " 53\n", + " 2\n", " 0.0\n", " -0.088388-0.088388j\n", " 0.12\n", " -0.75π\n", " 0.015625\n", - " 0000110\n", + " 0000010\n", " \n", " \n", - " 7\n", - " -4\n", + " 30\n", + " 3\n", " 0.0\n", - " 0.088388+0.088388j\n", + " 0.088388-0.088388j\n", " 0.12\n", - " 0.25π\n", + " -0.25π\n", " 0.015625\n", - " 0000100\n", + " 0000011\n", " \n", " \n", "\n", "" ], "text/plain": [ - " x ancilla amplitude magnitude phase probability bitstring\n", - "0 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000011\n", - "1 1 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000001\n", - "2 -3 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000101\n", - "3 -1 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000111\n", - "4 2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000010\n", - "5 0 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000000\n", - "6 -2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000110\n", - "7 -4 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000100" + " x ancilla amplitude magnitude phase probability bitstring\n", + "63 -4 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000100\n", + "40 -3 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000101\n", + "61 -2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000110\n", + "41 -1 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000111\n", + "60 0 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000000\n", + "39 1 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000001\n", + "53 2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000010\n", + "30 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000011" ] }, - "execution_count": 3, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -504,8 +571,7 @@ " hadamard_transform(x)\n", "\n", " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", - " probabilities = [0] * (N0 - 1) + [1] # |1111...1> state\n", - " prepare_state(probabilities=probabilities, bound=0.01, out=ancilla)\n", + " prepare_basis_state([True] * n0, ancilla)\n", " qft(ancilla)\n", "\n", " # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", @@ -524,17 +590,9 @@ "print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", "print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", "\n", - "# Pay attention that we use a statevector simulator here\n", - "backend_preferences = ClassiqBackendPreferences(backend_name=\"simulator_statevector\")\n", - "execution_preferences = ExecutionPreferences(\n", - " num_shots=1, backend_preferences=backend_preferences\n", - ")\n", - "with ExecutionSession(qprog, execution_preferences=execution_preferences) as es:\n", - " es.set_measured_state_filter(\"ancilla\", lambda v: v == 0)\n", - " results_statevector = es.sample()\n", - "\n", - "# Show the results as a dataframe.\n", - "df = results_statevector.dataframe\n", + "sv = calculate_state_vector(qprog)\n", + "df = sv[sv.ancilla == 0]\n", + "df.sort_values(by=\"x\", inplace=True)\n", "df\n", "\n", "# From now on, we will use the shortcut function:\n", @@ -543,16 +601,16 @@ }, { "cell_type": "markdown", - "id": "13", + "id": "14", "metadata": {}, "source": [ - "In order to understand the results, let's focus on the phase compared to the classical value of f(x):" + "Let's examine the phase compared to the classical function value:" ] }, { "cell_type": "code", - "execution_count": 4, - "id": "14", + "execution_count": 5, + "id": "15", "metadata": {}, "outputs": [ { @@ -585,7 +643,7 @@ "type": "float" } ], - "ref": "37d53315-ee64-43e9-82c2-55f4fc1ca29e", + "ref": "9aee00ed-df27-490c-9aa0-69335bcfdfeb", "rows": [ [ "-4", @@ -719,7 +777,7 @@ " 3 0.75 0.75" ] }, - "execution_count": 4, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -754,25 +812,24 @@ }, { "cell_type": "markdown", - "id": "15", + "id": "16", "metadata": {}, "source": [ - "In the graph we can see the original function (gray line), the classical values and the quantum phase at the chosen points (classical - blue, quantum - orange).\\\n", - "Everything in both normalized values (black axes), and the original values (blue axes)." + "The graph shows the original function (gray), classical values (blue), and quantum phase at sample points (orange). Results are displayed in both normalized coordinates (black axes) and original values (blue axes)." ] }, { "cell_type": "markdown", - "id": "16", + "id": "17", "metadata": {}, "source": [ - "For convenience, the full code to generate this graph:" + "Here is the complete code to reproduce the graph:" ] }, { "cell_type": "code", - "execution_count": 5, - "id": "17", + "execution_count": null, + "id": "18", "metadata": {}, "outputs": [ { @@ -812,8 +869,7 @@ " hadamard_transform(x)\n", "\n", " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", - " probabilities = [0] * (N0 - 1) + [1] # |1111...1> state\n", - " prepare_state(probabilities=probabilities, bound=0.01, out=ancilla)\n", + " prepare_basis_state([True] * n0, ancilla)\n", " qft(ancilla)\n", "\n", " # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", @@ -832,8 +888,8 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "18", + "execution_count": null, + "id": "19", "metadata": {}, "outputs": [], "source": [ @@ -855,7 +911,7 @@ "# # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", "# ancilla = QNum(\"ancilla\", n0, SIGNED, n0) # Declare the name/type\n", "# probabilities = [0] * (N0-1) + [1] # |1111...1> state\n", - "# prepare_state(probabilities=probabilities, bound=0.01, out=ancilla)\n", + "# prepare_basis_state([True] * n0, ancilla)\n", "# qft(ancilla)\n", "\n", "# # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", @@ -875,38 +931,35 @@ }, { "cell_type": "markdown", - "id": "19", + "id": "20", "metadata": {}, "source": [ - "## 2.2. Direct Phase" + "### 2.1.2. Direct Phase" ] }, { "cell_type": "markdown", - "id": "20", + "id": "21", "metadata": {}, "source": [ - "The phase kickback approach is good when we have a state-oracle, but in our simulation it is very inefficient." + "While the phase kickback approach is sometimes well-suited for hardware implementations with a state oracle, it requires significant circuit overhead in simulation. A direct approach provides more efficient state preparation for our purposes." ] }, { "cell_type": "markdown", - "id": "21", + "id": "22", "metadata": {}, "source": [ - "Another approach is to directly prepare the wanted state.\n", - "In our case:\n", + "A simpler approach is to directly prepare the desired state:\n", "$$\\sum_{\\delta}e^{i2\\pi\\frac{N}{ml}f(\\frac{l}{N}\\delta)}|\\delta\\rangle$$\n", "\n", - "Here we can see the same example using the prepare_complex_amplitudes function.\\\n", - "You can look at the circuit width/depth and gate count to compare both methods.\\\n", - "In real applications, both methods can be used, depending on the oracle f." + "The example below demonstrates this method. Compare the circuit width, depth, and gate counts to see the efficiency gain. In practice, the choice between methods depends on whether you have access to an efficient oracle for the function." ] }, { "cell_type": "code", "execution_count": 7, - "id": "22", + "id": "23", "metadata": {}, "outputs": [ { @@ -955,35 +1008,34 @@ }, { "cell_type": "markdown", - "id": "23", + "id": "24", "metadata": {}, "source": [ - "The graph is exactly the same as the phase kickback method.\\\n", - "From this point, we will use this method over the phase kickback, in order to have better efficiency." + "The state is identical to the phase kickback method. Moving forward, we'll use the direct method for its superior efficiency." ] }, { "cell_type": "markdown", - "id": "24", + "id": "25", "metadata": {}, "source": [ - "## 2.3. Quadratic Function" + "### 2.1.3. Quadratic Function" ] }, { "cell_type": "markdown", - "id": "25", + "id": "26", "metadata": {}, "source": [ - "More interesting are non-linear functions.\\\n", - "In the next example we will see a quadratic function.\\\n", - "Note that the 'magic' does not happen in this step. You will see that the phases agree with the function completely and doesn't do the linearization needed to calculate the gradient. The magic will happen in the next step where the QFT will do the linearization for us." + "Non-linear functions are more interesting. In the next example, we explore a quadratic function.\n", + "\n", + "Note that the critical step occurs in the next phase when we apply the QFT. Here, the phases follow the function exactly without linearization. The QFT will extract the linear (gradient) component from these phase values." ] }, { "cell_type": "code", "execution_count": 8, - "id": "26", + "id": "27", "metadata": {}, "outputs": [ { @@ -1033,16 +1085,16 @@ }, { "cell_type": "markdown", - "id": "27", + "id": "28", "metadata": {}, "source": [ - "If we decrease $l$, we look at the function more closely, and it is closer to linear." + "Decreasing $l$ narrows the sampling interval, making the function appear more linear within that region." ] }, { "cell_type": "code", "execution_count": 9, - "id": "28", + "id": "29", "metadata": {}, "outputs": [ { @@ -1092,49 +1144,48 @@ }, { "cell_type": "markdown", - "id": "29", + "id": "30", "metadata": {}, "source": [ - "# 3. Full Algorithm" + "## 2.2. Full Algorithm" ] }, { "cell_type": "markdown", - "id": "30", + "id": "31", "metadata": {}, "source": [ - "## 3.1. Linear Functions" + "### 2.2.1. Linear Functions" ] }, { "cell_type": "markdown", - "id": "31", + "id": "32", "metadata": {}, "source": [ - "The next and final step of the algorithm is to apply QFT on the coordinate.\\\n", - "As discussed earlier, applying the QFT will automatically extract the gradient from the phases, and create a measurable state with the value of the gradient (normalized)." + "The final step is to apply the inverse QFT to the coordinates. This extracts the gradient from the phases and produces a measurable state containing the normalized gradient value." ] }, { "cell_type": "markdown", - "id": "32", + "id": "33", "metadata": {}, "source": [ - "To see the full algorithm in action, we will switch from the statevector simulation to standard simulation, because the final result is acquired by a measurement and not by looking at the phases." + "Now we switch from statevector simulation to standard simulation, which measures the final result rather than examining phase values directly." ] }, { "cell_type": "markdown", - "id": "33", + "id": "34", "metadata": {}, "source": [ - "Let's start with a simple example of linear function." + "We start with a linear function." ] }, { "cell_type": "code", "execution_count": 10, - "id": "34", + "id": "35", "metadata": {}, "outputs": [ { @@ -1243,23 +1294,18 @@ }, { "cell_type": "markdown", - "id": "35", + "id": "36", "metadata": {}, "source": [ - "The result for the gradient is always a multiple of m/N.\\\n", - "In the previous example, the gradient was -0.5, while the resolution (m/N) was 0.25.\\\n", - "The gradient is a multiple of the resolution, and therefore the result can be exact, and the success rate was 100%.\\\n", - "\\\n", - "More complex case is where the gradient is not a multiple of the resolution.\\\n", - "In those cases, the result will be a superposition of multiple solutions, but we can still get a good approximation for the gradient from the result.\\\n", - "Let's see it in the next example.\\\n", - "TODO: Consider removing this example, because it doesn't match the flow of the explanation." + "The measured gradient is always a multiple of the resolution $m/N$. In the previous example, the exact gradient -0.5 was a multiple of the resolution 0.25, so the success rate was 100%.\n", + "\n", + "When the gradient is not a multiple of the resolution, the result becomes a superposition of nearby states. The algorithm still provides a good approximation, as shown in the next example." ] }, { "cell_type": "code", "execution_count": 11, - "id": "36", + "id": "37", "metadata": {}, "outputs": [ { @@ -1324,34 +1370,32 @@ }, { "cell_type": "markdown", - "id": "37", + "id": "38", "metadata": {}, "source": [ - "## 3.2. Quadratic Function" + "### 2.2.2. Quadratic Function" ] }, { "cell_type": "markdown", - "id": "38", + "id": "39", "metadata": {}, "source": [ - "Again, let's try calculating the gradient of a non-linear function. In the next example, we will explore a quadratic function.\\\n", - "In the case of non-linear function, we will need to cleverly choose the value of $l$ - the interval around the origin.\\\n", - "In order for the algorithm to work, we need to work in the linear regime around the origin, so we need to choose small enough $l$." + "For non-linear functions, the interval $l$ must be chosen carefully. The algorithm requires the function to be approximately linear over the interval, which means $l$ must be sufficiently small. The next example demonstrates this dependency." ] }, { "cell_type": "markdown", - "id": "39", + "id": "40", "metadata": {}, "source": [ - "First, for good selection of $l$, we see that the points are almost linear, and we get a good success rate." + "With appropriate selection of $l$, the function remains nearly linear over the sampling interval, yielding high success rates." ] }, { "cell_type": "code", "execution_count": 12, - "id": "40", + "id": "41", "metadata": {}, "outputs": [ { @@ -1416,16 +1460,16 @@ }, { "cell_type": "markdown", - "id": "41", + "id": "42", "metadata": {}, "source": [ - "But if we increase $l$ outside of the linear regime, we see that the success rate get drastically lower:" + "Conversely, if $l$ is too large and the function deviates significantly from linearity, the success rate drops dramatically." ] }, { "cell_type": "code", "execution_count": 13, - "id": "42", + "id": "43", "metadata": {}, "outputs": [ { @@ -1488,21 +1532,12 @@ "analyze_results(pc, df, p)" ] }, - { - "cell_type": "markdown", - "id": "43", - "metadata": {}, - "source": [ - "# 4. Parameters Selection - TODO" - ] - }, { "cell_type": "markdown", "id": "44", "metadata": {}, "source": [ - "**TODO:** I moved the theoretical explanation to the top, so it will be removed from here.\\\n", - "I'll need to rewrite the functions to use the $\\nabla f_{max}$ and $\\epsilon$ that I defined above." + "# 3. Performance Analysis" ] }, { @@ -1510,187 +1545,25 @@ "id": "45", "metadata": {}, "source": [ - "## 4.1. Understanding the parameters" - ] - }, - { - "cell_type": "markdown", - "id": "46", - "metadata": {}, - "source": [ - "There are three main parameters to be selected: $l$, $m$ and $n$.\\\n", - "$n$ is the number of bits of the result. The bigger $n$, the higher the accuracy of the result.\\\n", - "$l$ is the interval size around the origin ($dx$).\\\n", - "$m/2$ is the maximal gradient that can be calculated (in absolute value)." - ] - }, - { - "cell_type": "markdown", - "id": "47", - "metadata": {}, - "source": [ - "For the parameter $l$, we saw earlier that it should be selected such that we look at the linear regime of the function. See section 2.2." - ] - }, - { - "cell_type": "markdown", - "id": "48", - "metadata": {}, - "source": [ - "Understanding the parameter $m$ is a little trickier. We will look at a bounding box around the origin.\\\n", - "The width of the box (dx) is $l$, spanning from $-l/2$ to $l/2$. The slope of the graph (dy/dx) is bounded between $-m/2$ to $m/2$. Therefore, the height of the box (dy) should be bounded dy/dx*dx, so the height should be $lm/2$, making the box span between $-lm/4$ to $lm/4$.\\\n", - "When we plot the graph, if all the points are inside this box, then we know that the gradient is bounded by $m/2$ and we will get the correct result.\\\n", - "If the points are outside this box, we will get aliasing in the results and get an incorrect gradient.\\\n", - "Note that in our graphs we use the normalized function instead of the original function, so the box is between $-N/4$ to $N/4$ instead of $lm/4$." - ] - }, - { - "cell_type": "markdown", - "id": "49", - "metadata": {}, - "source": [ - "We will see now the same function, once with correct selection of m and one with incorrect selection of $m$, and we can see that if $m$ is too small the theoretical values are out of the bounding box, and the phases from the simulation are folded into the box creating aliasing. " - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "50", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# In this example we will use the linear function\n", - "p = params()\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.m = 2 # Correct selection of m - no aliasing.\n", - "p.unpack(globals())\n", - "\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " allocate(n, x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", - "\n", - "\n", - "df = run_statevector_simulation(main, print_circuit_info=False)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)\n", - "# simplified_df" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "51", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# In this example we will use the linear function\n", - "p = params()\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.m = 1.333 # Marginal selection of m - still no aliasing.\n", - "p.unpack(globals())\n", - "\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " allocate(n, x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", - "\n", - "\n", - "df = run_statevector_simulation(main, print_circuit_info=False)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)\n", - "# simplified_df" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "52", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# In this example we will use the linear function\n", - "p = params()\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.m = 0.3 # Incorrect selection of m - aliasing occurs.\n", - "p.unpack(globals())\n", + "We can plot the success rate as a function of parameter choices. Consider a quadratic function $f(x)=0.6x^2+0.25x+0.1$ with $f'(0)=0.25$, and target accuracy $\\epsilon=0.2$.\n", "\n", + "To determine valid parameter ranges, we need to use:\n", + "- $d=1$ (dimensionality)\n", + "- $D_2=1.2$ (second derivative bound)\n", + "- $\\nabla f_{\\max}$: With $l \\approx 0.1$, we have $\\nabla f \\in [0.19, 0.31]$, so $\\nabla f_{\\max}=0.31$\n", "\n", - "@qfunc\n", - "def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " allocate(n, x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", - "\n", + "From the theory, the parameters must satisfy (with $n=3$):\n", + "- $m\\geq 2 \\cdot 0.31 = 0.62$\n", + "- $m\\leq 2 \\cdot N \\cdot \\epsilon = 3.2$\n", + "- $l\\leq 0.28$\n", "\n", - "df = run_statevector_simulation(main, print_circuit_info=False)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)\n", - "# simplified_df" - ] - }, - { - "cell_type": "markdown", - "id": "53", - "metadata": {}, - "source": [ - "## 4.2. Success rate as function of parameter selection\n", - "**TODO**: consider removing this part" - ] - }, - { - "cell_type": "markdown", - "id": "54", - "metadata": {}, - "source": [ - "We can plot the success rate as a function of the selected parameters.\\\n", - "In the first example, we will have a quadratic function $f(x)=0.6x^2+0.25x+0.1$, $f'(0)=0.25$.\\\n", - "We can plot the graph for different selections of m.\\\n", - "We discussed earlier that $m/2$ is the bound for the gradient value, so we expect to have poor results for $m<0.5$, good results for $m>0.5$, until reaching $m=0.25N=4$, where the resolution won't be good enough for meaningful result.\\\n", - "Note the oscillations in the success rate in the optimal region. This is due to the discrete values the algorithm can return. As we increase the number of bits $n$, the oscillations will be smaller." + "In the next graph, we plot success rate versus $m$ with $l=0.1$. The valid range $[0.62, 3.2]$ is highlighted." ] }, { "cell_type": "code", - "execution_count": 17, - "id": "55", + "execution_count": null, + "id": "46", "metadata": {}, "outputs": [ { @@ -1699,16 +1572,18 @@ "text": [ "m=0.05: Success rate = 0.00%\n", "m=0.1: Success rate = 0.00%\n", - "m=0.3: Success rate = 0.00%\n", - "m=0.5: Success rate = 9.47%\n", - "m=0.55: Success rate = 42.58%\n", - "m=0.7: Success rate = 87.74%\n", - "m=0.8: Success rate = 81.30%\n", - "m=0.9: Success rate = 91.70%\n", - "m=1.0: Success rate = 94.68%\n", - "m=1.5: Success rate = 72.41%\n", - "m=2.0: Success rate = 98.54%\n", - "m=3.0: Success rate = 0.00%\n", + "m=0.33: Success rate = 0.39%\n", + "m=0.5: Success rate = 9.57%\n", + "m=0.67: Success rate = 93.41%\n", + "m=1.0: Success rate = 99.27%\n", + "m=1.33: Success rate = 80.32%\n", + "m=1.67: Success rate = 94.58%\n", + "m=2.0: Success rate = 98.78%\n", + "m=2.33: Success rate = 90.97%\n", + "m=2.67: Success rate = 77.34%\n", + "m=3.0: Success rate = 64.70%\n", + "m=3.33: Success rate = 54.88%\n", + "m=3.67: Success rate = 0.00%\n", "m=4.0: Success rate = 0.00%\n", "m=6.0: Success rate = 0.00%\n", "m=10.0: Success rate = 0.00%\n" @@ -1716,7 +1591,7 @@ }, { "data": { - "image/png": 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", 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69gGIKNqF7ZJLLjEThOq4DR1ArmMb9KRKT/S1C5d2a9N5n1w0YNKs0YQJE0y3Lx38r4GBBlyuge6e7rzzThPUaJcw/auT4ur2dHJOLXChJ5auMUo6rkezQDonjq6vWRoNbDRY0ja5JtrVsUTabUzHPungfs0w6cTBOsbEFeTp3Du6fdfksTr4Xosf6HxLmm3T59UCFzpORpcrHQel8+logQkd06Mn/xrg6AB97dKnXfJaSgtAaPGOSZMmmefSfawnupr50tei8+toFyx9b/TkW9+T+jTLo9kt3U/axUozh7quBji6b7XLle5nnQdI19Uuhfqa9eRX31fNGPlaXEDpdnUOJO1mqO+3tzmhNAOlmQrdn9oWPcHW40KzUTpPkiuQCBf6mvV40OBD3ydtv87dpceCTtyrXUNDuT1/6A8h+jnWAEizxPrZ7d27t+nmqp9D/bxodlbHDyr9LOlxp2Pj9HjSMXt6/GjbteuuFpnQz4XOfaXdf/Xzoj8I6I8d2t1WX5f+KME8UQDqCHXZQAAIpuXLlzsefPBBx6GHHuro1auXIzk52Vy0tLGWLJ4/f77Xx+k8SDr3jc4Xo+Wer7zySjMfjrd5pFR5ebmZp2bo0KFmbiItY63zE+kcUzt27Kizrs5/c/XVVzt22203s/0OHTo4Ro4caUqee2u/lrHW59R1tSyztkvLPc+bN8+93tSpU03Jbn1dqampphy7zqmj8xN5zt80Y8YMx8SJEx39+vUzZdtd7dR5c7Zs2dKieaQ8uebLmjVrlnv+n3vuucfRt29fR1JSkimVrvumqX2q75uun5CQ4LUk/V9//WX2o2ubWkZ9zz33dFxwwQXu5/WVlh/Xkun6PFoS3ZtnnnnGcfTRR5u26jHUsWNHx4gRIxzPPvuseX2+aOy1NlV231UmXI/Xlswj5Y2Wdx83bpw5rvR40OefOXOm45VXXjHb0L/+tCNY22uqPLm3bbnoZ+LUU0917LLLLua40SkCtGz9TTfd5Pj999/rrDt37lzTPm2na1oEz3L7Oifc888/7xg9erQ5tlzH7WGHHWbe8+LiYp/K9QOIHjH6v7qhFQAAAACgKYyRAgAAAAA/EUgBAAAAgJ8IpAAAAADATwRSAAAAAOAnAikAAAAA8BOBFAAAAAD4Keon5K2urjaTWmZkZJjJ+QAAAABEJ4fDYSb31km8dYL5pkR9IKVBVPfu3dvszQEAAABgbRs2bJBu3bo1uU7UB1KaiXLtrMzMTAlFRmzLli3SqVOnZqNeK7BV2mRJ3hKJj4uXxLjEUDcnqn8tKdtZJintUsikBom9yi6VVZUyKHeQJMUnSaQJt+8aWAPHDThmEG3fNYWFhSbJ4ooRmhL1gZSrO58GUaEKpMrLy81zh/rA8TWQSitNk7TENAKpEAdSxdXFkt4unUAqiIFUib3EfBYjNZAKp+8aWAPHDThmEK3fNTE+DPmxRksBAAAAIIwQSAEAAACAnwikAAAAAMBPUT9GCgAAANYZA1xZWSlVVVWhbgraeIxURUWFGSfVFmOkEhISJC4ursXbIZACAABAyNntdtm0aZOUlpaGuikIQQBdXV1t5m9qi3ld9Tm0tHl6enqLtkMgBQAAgJDSk+i1a9eaLIFOhJqYmEhV2ijMRMbHx7f6+67PpaXW//rrL+nbt2+LMlMEUgAAAAh5NkqDKZ2/JzU1lXcjyjjaMJBSOl/VunXrTHfClgRSFJsAAACAJVhlDiFEtpggBWscrQAAAADgJ7r2AQAAwLIqqyulqrrtqvjFxcZJfCynyGgeRwkAAAAsG0T9tuU3Kasoa7PnTElIkf6d+hNMoVkEUgAAALAkzURpEJUQlyCJcYmt/nz2Krt5Pn1eX7JSzY21ueOOO2Ty5MkSCtq2999/X4499tiQPH80IJACAACApWkQ1RaBlKqoqvB5XZ33yuXtt9+WSZMmyYoVK9zL/J2nSKsXaun3SKjCV1VVZarwRTKKTQAAAAAB6Ny5s/uSlZVlskCu2yUlJXLGGWdIbm6uCaj22WcfmTlzZp3H9+zZU+666y6ZOHGiZGZmykUXXWSWv/jii+5S8Mcdd5w8+uij0q5duzqP/fDDD2XvvfeW5ORk2W233WTKlCmmhLhru0ofq21y3a5PS4Dr/e+8844ccMABkpKSYtq5cuVK+fnnn2X48OGm7YcffriZe6kx33zzjdnOZ599JsOGDZOkpCT54YcfZM2aNXLMMcc0uw/uvfdeufDCC80+6NGjh7zwwgt11pk9e7YMHTrUvFZt0wcffGCeb/Hixe51li5datqpz6PPd9ZZZ8nWrVulNRFIAQAAAEFWXFwsEyZMkFmzZsmiRYvksMMOk6OOOkrWr19fZ72HH35YhgwZYta5/fbb5ccff5RLLrlErr76ahMoHHrooXLPPffUecz3339vgi9d57fffpPnn39eXn31Vfd6GgSpV155xWTNXLeb6oJ42223ycKFC00W6fTTT5cbb7xRHn/8cfNcq1evNtm25tx0001y//33y++//y6DBw/2eR9ooKgBmD7/ZZddJpdeeqk7s1dYWGgeM2jQIHO/Bp7/+te/6jx+586dcsghh8hee+0l8+fPlxkzZkheXp6cfPLJEjWB1HfffWd2lM5orVGmRpvN0QhYo3GNfPv06WMOIgAAACCUNDi6+OKLZeDAgdK3b18TAPTu3Vs++uijOutpAHDdddeZ+/Ty5JNPmszK9ddfL7vvvrsJLPS2J80+adBy9tlnm2yUBlu6fQ2oXBPOKs1iaXbMdbsx+lzjx4+XPffc0wRnCxYsMEHd6NGjTXBy/vnny9dff93sa77zzjtNW/R1dOjQwed9oMGWBo96Lq9BUnZ2tvv53nrrLRMXaJauf//+Zl/ccMMNdR7/1FNPmXZqZmuPPfYw119++WWzDc2uRUUgpSlQ3eFPP/20T+uvXbtWjjjiCDn44INNxP7Pf/5TLrjgAvn8889bva1oPfbKapm5rFDu/OBvuX7qX+av3tblAAAA4UCzMRqgaHCiAY12OdNMTf1sjHZV86SZmBEjRtRZVv/2L7/8YoIW3abrol3jNPtUWlrqd1s1e+Si3eKUZoA8l+Xn5ze7neH1Xouv+8DzuVzdI13Pp/tD26fd+praHxo0ee4PDaiUdi9sLZYaAaYRZv2IuynPPfec9OrVSx555BFzW98k7Y/573//20TVCD9zVhfLQ9PzpNhWLVoIx+HQD5TID6tK5JlZW+SGCbkyqo9/AzcBAADamgYQX375pem6p5kWHX904oknmoISntLS0vzetgYompU6/vjjG9znGXD4KiEhoUElwvrLqqub/0E7rd5r8XUfeD6XP8/nuT+0V9sDDzzQ4L4uXbpIVARS/pozZ46MHTu2zjINoDQz1RibzWYuLtrvUumb5c8bFiz6nFrZJBTP3ZL2ui7BNGd1iUz5oLb6jWvzrr8ltmqZ/P4muePYLjKqj/9fOpFAs3LfrSiW2atLZGeRXdplFMl+fdJkTL90SYy3VII57LiO6VB9F7S2cPuugTVw3KCtjpnGzi/Mdf2vFc47vGnJ87nWd/3VsU7a9c5VflxP9rW4g7fX6Hm7X79+ZkyT5zLXGCfXMh3Wsnz5ctNNrrG2aHCixSeaeh2eba7f/saW+bodf/aBauz5tXvjG2+8IeXl5WYoj5o3b16ddbQr33vvvSe77rqr10qB3p6rsX/z/Tl2wzqQ2rx5szv96KK3NTgqKyszUW999913n4ng69NKJPoGtTV9swoKCsybGRtr/RNhLQlqK7BJTHyM2GPr/prQEvZKhzw03ZnCbezjrsv1N5KHpm+W/zs1RxLjm567IdL8vL5cnvyuQErsDrMfzP7YXCE/1mTrrhyTJfv08P9XKNRO+mirtMnW2K1mvpJIE27fNbAGjhu01TFTUVFhHqsn/q7Kc8rcrqqUUlupVMbVLm/NeaT03wN93jiJ8+uxrhNwV/s1yNGTe+1tpRkWnU/KFTB6vkbX63bRQgs6bkqzODqEResBaDU83YZrvVtuucUEJ926dTNZKd3Xv/76qyxbtsx0+VMaVGiFvJEjR5oApH379g3a7Nqe537XsuX1l9V/bfVVeXmMP/tAH+/ahq7nCnJ0HS0YoYUwtOuijo3asGGD2Teux+k6Og7r//7v/+TUU081WTB9rdqlT6sR6rixuLi676U+Rre/bdu2BtmwoqIiiYpAKhA333yzXHvtte7bGnRpeUkdhKclF9uavol6wOjzh8PJjZ5obqzeKKmJqUGdz0HHQGmA0BxdQ9dbtFXkH/2jp4ufZusemLnTfdtR72+p3WHuj+ZsXTD+8XTYHZLdKVuS4p2/eEWScPuugTVw3KCtjhn9MVtPYDWbUCejECuSnpwu5RXlYq8O3g+4jYpxPl9SYpJPE/J6cr1eV/t1qIkWaTjwwANN8QStgqcZGd0/nq9RH+d5e8yYMfLss8+agEir6bl6W2kNAdd6Wpzh448/NsUbNKjQYEDHBOnzudbRoS9axOKll16Srl27mtoC9bnW9dzvrqDDc1n911ZfnJfH+LMP9PF6cQU1er9rv2jRCi1OoUU3tHy6jqfSCoJaWl7HQuk6WjJdh/doAQ7dN9r7TANJ3Xc6L1f9iZP1Mbr9jh07NugK6U/XyBhHW+RJW2k2Zj3QNLX52GOPuZdpmUc92PTXEF9oIKV1/3X9UAVSOpguJycnbAKpxZsXS1piWlADKS0o8ePqEnc3vqboZ2F0nzSZdOwuEi3d+U59Zq3p2tjU7tGviLSkWJl6WS+6+QWyn6vsUmIvkaGdh0ZsIBVO3zWwBo4btNUxo4GUnujr2Pf6J7KaIaqqdmYr2kJcbJzfQVRr02yMduXTUuSRyFGTodIAp37Q482bb74p5557rjl/99YDrSXHmz+xgbWOEj+NGjVKpk+fXmeZDmjT5QgvheWa5vVtXV1P148WOiZKi280R3efrqfrjx3Q9j8KAADQGjSosVpg09o0y6RlxLV4g3bre+211+SZZ56RaPX666+bMu+aWdMKfVoiXbv8BRJEBZOljkpN9emEXy4aKWpZc03pacpOu+Vt3LjR7Eyl9ea1brymCc877zz56quvTF/ITz/9NISvAoHITI51V+lrjq6n60eL2auK/do3uj6BFAAA4UuLKTz44IOmu6MGEE888YSZ4idabd682XTn079ahe+kk05qMEmxRHsgpTMR65xQLq6xTFrtQyfa1dr4nnXnNR2nQdM111xjZl7WAXc60IzS5+Fnv77ppsS5LzSg0PWjBdk6AACiiyYGUEuTJnqxGksFUgcddFCTJRo1mPL2mEWLFrVyy2AVrnFAWu47WmT4kX2LtmwdAABAqHDGhZBbuK5UHp2R1+x6rqGHOilvtMyZVGavlq1Fvpd7jbZsHQAgsli0BhoijCNIx1l0nI3CslbllcuUD/6WyppaCnvvmiLpSc7Dsn7NFs1ETT5Oy3tHR6CwcYddrnpzg6zYXDuBdFN0f6VHWbYOABAZXGWvS0tLQ90URAG73VlKv/78UmHdtQ/RRQOFW9/9W8oqnL8K6PxHk47pIlXVDlN5Tosm/Ly2VGyVzgloXzyvh3RMj7yJUr2Zs7pYHvg0T0rtzghTJx/WSYtdE/E2JpqydQCAyKEntO3atTOl01VqaqpPZbARneXPW1qif8uWLeYYa2xeLF8RSCEkthdXyi3T/padpc55IQZ2TZZbjuwscbEx5qJV5/Ty3Fdb5L0FO03wsGxjuYzpF9mBVLXDIW/8uF3emLPdvaxHx0Qz0e5f2+3y0PQ8U+LcWxW/zJRYGdw9tGVAAQAIVOfOnc1fVzCF6AqkqqurzdxjbRFA6/NoRfCWPheBFNpcia1Kbv3f37KpoMLc3jU7UaYcv4skJTTMpAzvlWoCKTV/bamM6Zchkaq4vEru/3SzzPujtlvD/runy/WH50pqYqx075AoUy9LNdm6H1cVy86iCmmXkSAbtttl/bYKKSirlue+3irXHZYb0tcBAEAg9KRWS1vrZL4VFc5zBESH6upq2bZtm3Ts2LFNJo1PTEwMyvMQSKFN2SurZfIHm2RNvnPcT05mvNx3YlfJSPbeR1UzLEnxMaZ7nwZS+otFJKb6126xyZQPNsnfO53/cMTGiJx3QEc5aUT7Oq9Xu+1ppu4f/TOkeHuxpHdIl/zCSrn41fWmG+DnSwpldN802bc346QAAOHbza+lY1cQfoFUQkKCJCcnt0kgFSzh01KEPR37pON+fllf5i7rfe+JXSU7o/F4XgOHQTXd1bYWV8q6rc7BgZHk69+LTFEJVxClXfR0v5w8soNPQWNuVoJccki2+/Zjn+dLYZmzyyQAAABaB4EU2oRmkp79aot8v7LY3E5KiJG7T+hqxv80Z59eqe7rmpWKpMDyha+3yH2fbBZbTcGNPrlJ8tRZPWTvnrWv2RfjB2bKyN2cj9leUiVPzaR/OQAAQGsikEKbeGvuDvloUYHzoIsRuf3oLrLnLsk+PXZ4rzT39fnrSiQS7CytlJumbZR35zvHf6lDB2TIv0/rJp2z/C+ooZmrf47PdU/e+83yYvl2eVFQ2wwAAIBaBFJoddN/KZDXftjmvq3FEEbsVhscNadb+wTJzXJ2/1v6V7mZpDacrdhULpe/vsHdxTEuVuSKsZ1MUQlvBTd81TE9Xq4Ym+O+/eTMfFMdEQAAAMFHIIVWpdXlnviytpvZhQdmy6EDM/3Otgyv6epWUeWQXzc4A5Bw9NmvBXLtf/+SLUXOAKdDWpw8fEo3OXqvdkEponHQHunuCXkLy6rl8S/zmSUeAACgFVC1D61GA557P94s1TXzHZ04vJ2pQhcI7d736S+F5vr8tSUysrfvGa22rkromky4sLxaMpNjZb++6bJv71R56btt7tegBnRNltuO7mIyScGiwdiVY3PMvtc5uuasLpEvlxXJOD+DVwAAADSNQAqtVs77jvf/NhkkpeW6LziotrKcv4b2SDFd4KqqdZyUNQtOzFld3GDCXP37w6oSMy7MFVCqY/bKkosO7iQJccEv5Z6VGifXjM+RO97fZG4/M2uL2X85mZE9mTEAAEBbomsfgm5zQYXcPG2jlNiq3ZPq6rio2BZ0XUtLipMBXZ1l0DfuqJC/d9gtF0RNfn+T+zVrEOX51xVExceKGQt1+dicVgmiXEb1STfFK5TOL/XIjDy6+AEAAAQRgRSCqqC0Sm6ZttGU4Fb9uiSZCn3xQQgahnmUBLdSVkq782kmSnkknbxKiI8x45jawqWHdHLP0bXozzL5eLGzaiIAAABajkAKQaPV9G57b6P8tcM5sWy3Dgly9/FdJSUxOIeZVeeT0jFR2p2vuSBKldkdZv22kJ4cJ9eOr63i9+K3W2WjxTJ5AAAA4YoxUvCbvdIhP60ulnlryt0FFbT4w9e/FcmKTTazTsf0OLnvxK5mvE6w7JaTJO1T42RHaZUsXl9qxl+1Zvc4X2lhCdeYqOboerr+2AFtU/xBi3QcOTRLPllcYCb9ffizPHn41G4Sp4O2AAAAEDACKfhl1u9b5IZ3t0uJzdGgoIJLWlKs3HtiV8kNYGLZpugYq2G9UmXmsiIpr3DIso1lMrRHbZYqVDSY9CWIUrqert+WtOT8grWlsqmgQpZtLJf35u8MuHoiAAAAnOjaB599+VueXP7WLyaI8lZQweXkEe2lV6ekVtmzrvmkrNS9TzNyvtbR0PV0/bakXSuvn5Arria++sM2WbfVmTkEAABAYAik4JPyiiq5btri5qspiMi0eTtMAYbWsHfPVHdAoPNJWYHOE+VPRkrXb2uDuqXICcPbmevaJVKLY1TWlKYHAACA/wik4JPpSzZJYVmlTwUVtPBCaxVUaJcaL7t3dma7/thil23FlRJqY/qlS3pSrDvAa4zer+vp+qFwzgEdpUfHRHN9VZ5Npv60PSTtAAAAiAQEUvDJF8vyzKSyvnAVVGjNAgouCyxQBj0xPlZumJDb5DquXafr6foha+fhOp+X8/abc7bLqrzykLQFAAAg3BFIwSc7S+3uSWVDXVDBc5zUzxbp3qcT4O7bpzbAc3GNndICHJOP62LWC6V+XZLltH07mOtV1SIPTs9rtW6YAAAAkYyqffBJu9REk8nwJZhq7YIKe+ySbAKTElu1LFxXKlXVjpCX89ZxR79tdGZ3tCL78F6pUlbhMPtBx0Rpd75QZaLqO31UB5m7pkTW5Nvkz612+c+P2+X8A7ND3SwAAICwYo0zO1jeuAG5fmWkWrOgggZNe+/qzEoVlVfLys2h757205oSKSirMtf375cud53Q1czXNOnYXcycUVYJopTOvXXjhFxxNWnazztMKXkAAAD4zjpnd7C0CYO6SGZKvGUKKmjGx0pl0D9fUuC+Pn5g20y22xJann7i/h3NdQ2QtYpfmZ0ufgAAAL4ikIJPkhPi5NGThtZWTQhxQQUrBVJaOfDnmjZ0yoiXvWqyZVZ30j7tZc8uyeb63zsr5MVvt8jMZYVy5wd/y/VT/zJ/9TZjqAAAABoikILPxvbPladPHyJpSd6jqbYsqNApI0F2zXaW8l6xuVwKa7rVhcIXSwvd3R7HDcwM+XgtX2k7NehNine295PFhab4xI+rS+TXDWXmr94+9Zm1Mmd161VhBAAACEcEUvDLP/bsJM+d20FOH5XlXtYlK96MuZl6Wa82rUq3T031Pg1iFv4ZmqyUw+GQz5cUum9rIBVOunVIlIP3zKizzDW5sOuvFvWY/P4mgikAAAAPBFLwW2J8jAzu7uwSpvbfPSMkBRXqzCcVou59SzeWm25xamiPFOnSLkHCiXbb+2Fl09kmV40RHUdFNz8AAAAnAikEXO7bM7AKhYHdkt3d0nQ+Kc0OhbTIxKDwykap71YUS7Gt+SITumd1PV0fAAAABFIIkL0y9IGUZsCG9Egx17eXVMnaLfY2ff4SW5V8WxNY6Piw/Vux5Htrmb2q2D1pcHN0PV0fAAAABFII40Cqfve++WtL2vS5NTtjq3DuBx1nlJQQfgnewvJq91io5uh6uj4AAAAIpBAgu2fXvrjQBVL7eJZBX9e246Q8i0wcFobd+lRmcqxfGSldHwAAAARSCPOM1C7tEqRzVry5vvSvsjabVHb9Nrv89ne5ud4rO1H65ia1yfMG23590/3KSOn6AAAAIJBCUAKp0GUpYmJi3N37KqtFFq9vm6zUjHpFJrQd4WhMv3RJT4ptap5lQ+/X9XR9AAAAEEghQBUWyUg16N7XBmXQK6scMnNZkbmuMeQ/+odntz5XEKyT8qrm3kVdL5RBMwAAgJVwVoSA2CwUSA3pkWoCGrWgDcZJzfujRHaWVpnrOgFxVmqchDN9DZOP62IqD6r6yTV9f/X+tpxsGQAAwOoIpNDieaRcczmFSmpirAzo5iyDrpPjbtzRumXQP19aGNZzR3mjQdLUy3rJjRNyZXSfNNmjS+2Yrw6pcTKyd211RAAAABBIIQgZqYS40Mfjw3u2Tfe+bcWV8tMaZ5n17PR4GebxvOFOu+2NHZApk47dRZ44s4fsvavztW0urJRFf7ZtRUQAAACrC/0ZMMJ+jFSoM1JtOZ/UrGWFUl3z0g8dmCFxsaF/7a1lwpDabNunv9Rm4QAAAEAghWDMI2WBQGq3TonSIc05VmnxhjKxawm/IHM4HDLDo1vfuIGR0a2vMfv1SZf2NeO/5qwulu3FlaFuEgAAgGWQkUJYzyNVtwy6syuarcIhyzY653gKJp036q/tFeb64O4p0rV9okSy+LgY9xiwquq6Y8MAAACiHYEUIiKQUsN61nbv+7kVuvfNWOJRZCLCs1Euhw/OcpdFn/5rgVT7OnsvAABAhCOQQour9lllbiEt/BDTSgUnyuzV8u3yIneVwP13j45S4F3aJbgLauQVVMrCNigvDwAAEA6scQaM8J5HKs4aGanMlDjp1yXZXF+31S5bipzd8ILhuxVFUl7hfM0H7ZEuKYnR89GZMCTLff3TXwpC2hYAAACriJ6zQbRK1T4tWqdjaazCNU4q2JPzfu7ZrW9QbWARDfbtneYu5DFndYkpAQ8AABDtCKTQojFSVhkf1ZrzSW3YbpelNcUrdu2YWGey2mjgWXRCS797jhUDAACIVgRSiKhASrv2ZSQ7D2sdz1PlmvSpBb6ok43KNBUCo80Ej6ITn/1aEJT9CgAAEM4IpNCieaSsUmjCRSfI3XtXZ1aq2FYtyze1rAy6BgxfLnMGUnGxIv/onyHRKDcrwd1tMr+wMqjdJgEAAMKRtc6CEXZjpKxSaKLRcVIt7N6nZdS3l1S5xwq1T4uXaHUERScAAADcCKTQoqp9Vuva12A+qXUtm09qxq91u/VFs5G906RjurPoxE9rSmRrEUUnAABA9CKQgt8cDod7HqkkCwZS2Rnx0is70VxfuckmBaXOjJK/dpRUyk9/OAMxrVq3T6/aAC0aabfJw2oqFjqLTlAKHQAARC8CKfitqtp5Iq0SLBhIqeE1QY82c+GfgXXvm/VbkXmt6tCBmSaQiHaHD840Je/VZ78WUnQCAABELQIpBFxoQiVqBQYL8hwnNX9tSUBZtzpzRw2M7m59LjmZCbJPzb7dUlQZtBLzAAAA4caaZ8GwtAqPoTFJCdbM0gzomuxum57sVzv8K9et1f7+3GY31wd2TZZuHZxdBSEygaITAAAABFIIfA4pq1btc5VlH9rDmTnZUVola/OdQZGvPCedjfYiE/WN2C3NjENT8/4okfzCilA3CQAAoM2RkYLfXIUmrFq1z2WfnqkBVe8rs1fLt8uLzfWUhBgZ0y86545quuhEpkfRidqgEwAAIFoQSMFvdo8ieFYOpAKdT+qHlcVSandWmThwjwxJSeRj0lTRCS0RrxMXAwAARBPOENGyrn3x1j2EdmmfKLu0SzDXl24scwdHzaFbX/M6ZSSYLn5qa3Gl6eIHAAAQTax7FgzLqqgTSFk3I+WZldIy5ot9KIO+cYddlvxVZq5365Ag/XdJbvU2hqsjPIpOTP+FOaUAAEB0IZCC3yo8u/ZZtNiE9zLozQdSXyytHe+jk8/GxFj79YV633aqKTrx89pSik4AAICoQiCFFnbts3agMaR7qiTUBHtacELnh2qMjvNxBVI6/mdsf4pMNFd0QsdKKR0ipRP0AgAARAsCKbQsI2XhMVJKC0XonFIqr6BSNu5ovFT3gnWlsq3Y+eJG9k6TDunObAsap1k7d9GJJQUUnQAAAFHD2mfBsKRwykip4b2cRRFcXdB8KjIxkLmjfKHzSWnQqTQInbuGohMAACA6EEjBb3bPeaQsPkZK7VNnnJT3E/2dpZUyd7Vz7qj2qXHuinRoHkUnAABANCKQgt8qKmuvJyVYP5DqmZ0oHdPjzPVfN5SJvbJhGfSvfisS1+KxAzIlPgwCRKsY1jNVcjPj3QU9Nhc03n0SAAAgUhBIwW8VHhkpVyEHK9PKe8N7OjNMtkqHu7y5ixagYO6olhadcJZC1yPjs18phQ4AACIfgRQifoxUc2XQV262ybqtdnNd543q0TGxzdsX7sYPynQXnfh8SaFUegTbAAAAkYhACi2q2pdk8ap9Lnvtmuo+0a8fSOmJv2dAAP91TI+XUX2cWb/tJRSdAAAAkS88zoJhKeGYkcpMiZM9ujjLoP+5ze6ePLa8olq++r3IPd7rwD2YOypQFJ0AAADRhEAKLaraFw5jpDyLInjOGaV+WFkspXZnlYkD+6VLaiIfiUDt3TNVOmfFu/fvpp0UnQAAAJGLs0a0rGpfmGSkGptP6vOlnt36nAUTEJjYGIpOAACA6EEghRZ27QufQ2j3zkmSnuQM/OasKpYr/7NeflnvrOC3S7t4GdjV2fUPgdOJjONqDgmKTgAAgEgWPmfBsGT583AZI6Xm/VEi5RXOtutLWLHZ5r5vazEFEoKhgyk6kW6u7yitktk1kxwDAABEGgIptKhqX7gEUnNWF8vk9ze5J931lmXT+3U9tMwRQ2orH376C3NKAQCAyEQghYiv2mevrJaHpuf5tK6up+ujZaXmu2QlmOuL/iyTv3c45+gCAACIJJYLpJ5++mnp2bOnJCcny8iRI2XevHlNrv/YY49Jv379JCUlRbp37y7XXHONlJeXt1l7o7lqn1bs0wIDVvfdimIptlVLc1PE6v26nq6PwOkxMcEjK/XZr7UFPQAAACKFpQKpt99+W6699lq54447ZOHChTJkyBAZP3685Ofne13/rbfekptuusms//vvv8tLL71ktnHLLbe0edujsWpfuJQ+n72qWHyN93Q9XR8tM25gprjqkGhlRM9xdQAAAJHAUoHUo48+KhdeeKGce+650r9/f3nuueckNTVVXn75Za/rz549W0aPHi2nn366yWKNGzdOTjvttGazWAhO175w6NanCsurxeHjebyup+ujZdqnxct+fZ1FJ3Zq0QmCUwAAEGGcs2dagN1ulwULFsjNN9/sXhYbGytjx46VOXPmeH3MfvvtJ2+88YYJnEaMGCF//PGHTJ8+Xc4666xGn8dms5mLS2Ghs9tRdXW1ubQ1fU6HwxGS5w6EttOVXdA5pLTtVpeRHGsyTb40VdfT9a3+urR9rotVTRic6e4mqUUnxvRzBlZW5dqfofouaG3h9l0Da+C4AccMou27ptqPNlgmkNq6datUVVVJbm5uneV6e/ny5V4fo5kofdz+++9vdn5lZaVccsklTXbtu++++2TKlCkNlm/ZsiUkY6v0zSooKDDt18DR6iqqKtwZqbgYhxRvt343uL27xMuPq3xbV+OSYV3iLf+6HOKQ8uJykRj9z5qZwd7pDumcGSebC6tk8foyWbl2p+ySZZmvnAYqqyvFVmmTrbFbJSHOWSwjkoTbdw2sgeMGHDOItu+aoqIin9e17lmND7755hu599575ZlnnjGFKVavXi1XX3213HXXXXL77bd7fYxmvHQclmdGSotUdOrUSTIzawfIt+WBExMTY54/1AeOL/RE01X+PDkxTtI7WDvLoMbtnSqv/FQkJc0UnNBwJC0pVg7du6PlJxo2mSiHSHr7dHP8WNWRQyvl/77bZq5/t75SLjiwnViVvcouDrtDsjtlS1J8kkSacPuugTVw3IBjBtH2XZOcnBx+gVR2drbExcVJXl7dMtV6u3Pnzl4fo8GSduO74IILzO1BgwZJSUmJXHTRRXLrrbd6fSOSkpLMpT5dN1RvnB44oXx+f9vqCqSS4mMtfRLvkpQQJzdMyDXzRGlrvQVTrleh6+n64UD3vetiVeMGZcprP2433UG/WFokZ+9v3SDVtS/D5bMYiEh/fWgdHDfgmEE0fdfE+vH8lvnXNDExUYYNGyazZs2qE53q7VGjRnl9TGlpaYMXq8GYsvLYkXDmOcdSuBSbUKP6pMvk47qYjJNyxR6uv7pc79f1EDztUuNldN80c72grEp+XFXC7gUAABHBMhkppV3uzj77bBk+fLgpHqFzRGmGSav4qYkTJ0rXrl3NOCd11FFHmUp/e+21l7trn2apdLkroEJwlXsEUglhFEgpDZKmXpZqCiBoFTmtzpeZHGuqy2khBKtmSsLdhCFZ8s1y55iz6b8UyMF7ZoS6SQAAAJEVSJ1yyimm6MOkSZNk8+bNMnToUJkxY4a7AMX69evrZKBuu+02kwbUvxs3bjT9KjWIuueee0L4KiKbzSOQ0qp94UaDpbEDMs0FbWNI9xTp1j5B/tpRIb9sKJObp200Xf0IYgEAQDizVCClrrjiCnNprLiEp/j4eDMZr17QNmyuAVJh1rUPoaM/dvTvmmwCKbVgXWnNcpEfVpXIM7O2mLFpdKsEAADhhL5MCDgjlRjH4YPmzVldLF8ubVhK1DWMUaspaiEQXQ8AACBccCaMwAMpMlLwoTjJQ9PrVuKsz1UWRtfzLGYCAABgZQRS8Et5BYEUfKeFPYqbmb9L6f26nq4PAAAQDgikEBXlzxEaWh3R12mudD1dHwAAIBwQSKEFXfs4fNA0LTHv65Ruup6uDwAAEA44E4Zfyj2r9sWRkULTtMS5PxkpXR8AACAccNaCqJpHCm1LJzv2JyOl6wMAAIQDAikEPEYqgUAKzRjTL13Sk2KluZBb79f1dH0AAIBwQCCFwLv2EUihGTqOTifbVc0FU7oe4+4AAEC4IJBCC7r2cfigeaP6pMvk47pIWpLzeKk/ZkoPI71f1wMAAAgX8aFuAMILE/IiEBokTb0s1cwTpSXOC8qqZPmmctEEZ1W1SN/cZHYsAAAIK6QU4Bebx4S8CVTtgx+0297YAZky6dhd5JHTusvJIzqY5VqL4tNfCtiXAAAgrBBIwS9U7UOwHDEkS2JruvlN/6VAKqp8LO8HAABgAQRS8Atd+xAs2RnxMrqm3PmO0ir5YWUxOxcAAIQNAin4xVanah+HD1rm6L2y3Nc/WrST3QkAAMIGZ8LwCxkpBNPg7imya3aiub5sY7msybOxgwEAQFggkIJfyj3KnydSbAItFBMTI0cP9chKLSYrBQAAwgOBFPxCRgrBppX8UhOdX0Vf/VYkReW13UcBAACsikAKfrHXGSNVb2ZVIAApibFy6MAMc91W6ZDPlxSyHwEAgOURSCGgrn0aQjGPFILlqKHt3Nc/WVwg1Q5KoQMAAGsjkEJAXfs0G6XjW4Bg6NExUfbaNcVc/3tnhcxfW8qOBQAAlkYghYACKbJRCLZj9qrNSlEKHQAAWB2BFAKaR4rxUQi2kb3TJCcz3lz/+Y9S+XuHnZ0MAAAsi0AKAXftA4IpLjZGjqwphe6oGSsFAABgVQRS8AuBFFrTYYMy3d1GP19aKOUVtfOWAQAAWAmBFPxiqzmxZYwUWkO71Hg5cI90c72ovFq+/r2IHQ0AACyJQAo+q6yqlspqZ1nqJLr2oZUcXafoRIE4KIUOAAAsiEAKPrNX1XazSiCQQivZo0uy9OucZK6vybfJb3+Xs68BAIDlEEjBZ57jVRJrxrEAreGoelkpAAAAqyGQgs9slc7S54qqfWhNB+2RLpkpzq+n71cUyY6SSnY4AACwFAIp+F1oQhFIoTUlxsfK4YOcpdC14v70XwvZ4QAAwFIIpOCzco+MFFX70NqOGJolsTU9SD9dXCBVNYVOAAAArIBACgFlpKjah9bWOStBRvZOM9e3FlfK7FXF7HQAAGAZBFLwWXmFR0aKqn1oA0fv5ezepyg6AQAArIRACj6z6WCVGlTtQ1vYa9dU6dY+wVz/ZUOZrNtqY8cDAABLIJBCYIFUAuXP0fpiY2IohQ4AACyJQAoBde0jI4W2Mm5ghiTXBO4zlxVKia32OAQAAAgVAikElpFijBTaSFpSnIztn2mul1c45MtlRex7AAAQcgRS8BkT8iJUjqpTdGKnOByUQgcAAKFFIAWflXuUP2ceKbSlXp2SZHD3FHP9r+0VsujPMt4AAAAQUgRSCCgjxTxSCG0p9J28AQAAIKQIpBDQhLzMI4W2tl+fdOmYHmeuz11TIvmFFbwJAAAgZAik4LNyj4wUVfvQ1uLjYuSIIc6sVLVD5JPFBbwJAAAgZAikEFBGiqp9CIUJg7MkvuZb67NfC8XuUUkSAACgLRFIwWeUP0eodUiPl/13TzfXC8qq5LsVxaFuEgAAiFIEUvCZzXNCXuaRQogcs1c79/UPKToBAABChEAKPiMjBSvo3zVZduuUaK6v2GSTFZvKQ90kAAAQhQikENiEvHEx7DmERExMjByzd21WilLoAAAgFAikENiEvHTtQwgdvGeGpCc5v76+WV4sBaW1QT4AAEBbIJCCz5iQF1aRnBAr4wdlmusVVQ6ZsYRS6AAAoG0RSMHvjFRsjEic/g8IoSOHOueUUjqnVJVOLgUAANBGCKTgd0YqIZ6dhtDr2j5R9umVaq7nFVbKvD9KQt0kAAAQRQik4HfVPgpNwCqO9iiF/tEiuvcBAIC2QyAFn5XXzCPFHFKwiuG9UqVLVoK5vmBdqfy13R7qJgEAgChBJy34nZFKiGOnwRp0rJ6OlXrx263m9m3/+1uyM+IlMzlW9uubLmP6pUtiPL8XAQCA4COQgs9sNcUmyEjBSjqk10b2f++sMJeYGJEfVpXIM7O2yA0TcmVUn/SQthEAAEQefqqFTxwOh5S7ik0wGS8sYs7qYnnw07wGyx01BfxKbNUy+f1NZj0AAIBgIpCCT3SuHtfJaSJ5TFiAvbJaHpreMIjy5CqIruvp+gAAAMFCIAW/J+MlIwUr+G5FsRTbqt3BUmP0fl1P1wcAAAgWAin4NRmvYowUrGD2qmIzFsoXup6uDwAAECwEUvA/I0XXPlhAYXm1u7tpc3Q9XR8AACBYWnRKvHHjRvnuu+8kPz9fTjjhBOnWrZtUVVVJQUGBZGVlSVwcdbIjrfS5YkJeWIGWONdMky/BlK6n6wMAAARLbKAV3K699lrp1auXnHHGGeb6ypUrzX3FxcXSs2dPefLJJ4PWSFhnMl7FGClYgc4T5U9GStcHAAAIaSD10EMPyeOPPy7XX3+9fPnllyawctFM1PHHHy//+9//gtZIWCwjRdc+WIBOtpueFCvNDZPS+3U9XR8AACCkgdSLL74oEydOlHvvvVeGDh3a4P7Bgwe7M1SIrMl4FRkpWEFifKyZbFc1FUzpzzy6nq4PAAAQLAGdWWzYsEH222+/Ru9PS0uTwsLClrQLFuOajFclxPtYKg1oZaP6pMvk47pIWpLzq8xVxc/zCM1IiZW9d03lvQAAAEEVUCetnJwcE0w1ZsGCBdKjR4+WtAsWzkjRtQ9WC6amXpZq5onSEudanU8LS2zaWSFrttilqKxaPlxUICePaB/qpgIAgGgPpHQM1HPPPSfnnHOOGROlYmp+Cv7iiy/k1VdflRtvvDG4LYVlyp9TtQ9Wo932xg7INBeXtVtscsmr603Xvqlzt8vhgzMlI5lKogAAIIRd+6ZMmSJdunQx46N0rJQGUQ888IDsv//+cvjhh5sxUrfcckuQmggrYIwUwk2vTkly6MAMc73YVi1T5+4IdZMAAEC0B1KahZo7d67JOulcUsnJyfLtt9/Kzp075Y477pDvv/9eUlMZkxCxGSmq9iFMTBzd0V0c5YOFOyW/sCLUTQIAABEi4FPilJQUue2228wFka/cs2ofxSYQJnIyE+TYvdvJtJ93SEWVQ17/cZtcf3jnUDcLAABEa0bqkEMOkVmzZjV6/9dff23WQaSOkQppUwC/nDKyvZlHSn25tMiMnQIAAAhJIPXNN99IXl5eo/fn5+ebrn6IzAl5yUghnGSmxMmp+3Yw17XwxMvfbQ11kwAAQAQIeIZKV5U+b1avXi0ZGc5B3ogM5RVU7UP4OmavLMnOcPZk/umPUvl1Q2momwQAAKJljNRrr71mLi533323vPjiiw3W04ITv/76q0yYMCF4rYSlMlKJjJFCmElKiJVz9u8oD3/mzKS/+O1WeeKM7k3+IAQAABCUQKq0tFS2bNnivl1UVCSxsXUTWnpSkpaWJpdccolMmjTJ100j7Mqfh7QpQED+0T9D3v15h6zbapcVm2zy/cpiGdOPzDkAAGjlQOrSSy81F9WrVy95/PHH5eijjw7waRFuyj2KTTBGCuEoLjZGzh+TLbe/97e5/cr322S/PukSX1MeHQAAoNXHSK1du7bVgqinn35aevbsaeamGjlypMybN6/J9bUr4eWXX24mCE5KSpLdd99dpk+f3ipti2aeGSmq9iFcjdgtVQZ1SzHXN+6okM9+LQh1kwAAQJhq8dSq2sWvoKBAqqtrT7RdevTo4de23n77bbn22mvlueeeM0HUY489JuPHj5cVK1ZITk5Og/Xtdrsceuih5r53331XunbtKn/++ae0a9euRa8JzU3Iyy/4CE/a/fiCA7Pl6jc3mNtvzN4uYwdkSkpiwHV3AABAlAo4kHr22Wfl0UcflT/++KPRdaqqak++faHbu/DCC+Xcc881tzWg+vTTT+Xll1+Wm266qcH6unz79u0ye/ZsSUhIMMs0m4VWnpCXrlAIY3vukiz7754uP6wslh2lVfK/+TvkzP06hrpZAAAgGgIpDXC0O51mi8477zy59dZb5ZprrjHd8V599VXJzc2Vq666yq9tanZpwYIFcvPNN7uXaTGLsWPHypw5c7w+5qOPPpJRo0aZtnz44YfSqVMnOf300+Vf//qXxMV5r4hgs9nMxaWwsND81Yyat6xaa9PndDgcIXnuQDNS8XEO02a9IDRc+5/3IDDn7t9BZq8qlmqHyLR5O+SIwZmSmuzcn6H6Lmht4fJdA2vhuAHHDKLtu6bajzYEFEg9+eSTJoj67LPPZNu2bSaQOuKII+SQQw6RG2+8UYYPH26W+2Pr1q0mg6VBmCe9vXz5cq+P0WzYV199JWeccYYZF6XzV1122WVSUVEhd9xxh9fH3HfffTJlypQGy7UiYXl5uYTizdKukXrw1K+CaCXFZc7gMyE2RioK7VIaXyr2WHuomxW1HOKQ8uJykRj9j66W/tLOv4f2S5HPl5dJWYVDXv0mX84ZmSq2Sptsjd0qCXHODHckCZfvGlgLxw04ZhBt3zVFRUWtG0itWbPGZIGUq0udZpRUVlaWXHDBBfLMM8/IddddJ62903V81AsvvGAyUMOGDZONGzfKQw891GggpRkvHYflmZHq3r27yWZlZmZKW9PXoOM29PlDfeA0pUqWu+fjScpKktTEVEmMSwx1s6KWyUQ5RNLbpzMXUoDOOThZvl3zp5RXOOSLFaVy3L5ZkpnlkOxO2ZIUnySRJly+a2AtHDfgmEG0fdckJye3biClwVJlZaW5rsFHamqqbNjgHLytMjIyZPPmzX5tMzs72wRDeXnOCTNd9Hbnzp29PkYr9Wkg59mNb8899zTPrYFdYmLDE32t7KeX+vRNC9UbpwdOKJ/fnwl5kxPiTHtdF4QO70PLdExPkBOHt5c35myXqmqR/8wukCsOTbX8ZzHSv2tgPRw34JhBNH3XxPrx/AG1dODAgfLLL7+4b++7776m+IRmgzSgev75500Zcn9o0KMZpVmzZtWJTvW2joPyZvTo0aY7n2dfxpUrV5oAy1sQhZYXm0iK5wQMkePEEe0lK9X5Q8z3K0plTV5FqJsEAADCREBnxWeeeaYsXbrUXbRBxxz9/vvvpty5Vs3TcuV3332339vVLncvvviivPbaa2Z7OgFwSUmJu4rfxIkT6xSj0Pu1at/VV19tAiit8Hfvvfe6ux0i+MUmEgmkEEFSE2PlzFEd3LffmlNKAQ8AANB6Xfs0sHEFN67M0LJly+Tjjz823ezGjRvnd0ZKnXLKKabow6RJk0z3vKFDh8qMGTPcBSjWr19fJ92mY5s+//xzUzFw8ODBZh4pDaq0ah9aq2sfGSlElglDsuT9BTvl750VsvSvCvl+1TY5tH/XUDcLAABYXIyjleonr127Vnr16iVWp8UmdMyXVgoJVbGJ/Px8UzQj1H1CG1Nd7ZDdbplurg/tniU3H5MgaYlpFJsIIf3YFm8vlvQOFJsIhm+WF8m9HzvHdfbrnC6fXTVGYmMjawxgOHzXwHo4bsAxg2j7rin0IzYIekt//fVXM5dTv379gr1phIhdR+LXoGsfItGYfunSJ9c5rnLF5mL5YPHGUDcJAABYnF+BlHbfu+KKK+Twww83wdL777/vvm/hwoUyYcIE2WuvveS9994z46gQGWw1hSYUXfsQiWJjYuTcA3R2KadHvlgp5RW1k1ADAAAEPEZq7ty5ZsJdz0lr3377bXn00UdNKXQdl6Rlz2+44QYzTkkr5yEylNcUmqit2tcqvUGBkBrSI0WG9EiQX9ZXyMadZfLG3D/lggN2410BAAAty0jdeeedZoKqzz77TIqLi2XJkiWmXLkWhnBNcrtu3Tq5//77CaIiOCOVFF87ZxcQaU7fL01c06M99fVqKSijHDoAAGhhIPXTTz+ZsuLjx483E/AOGDDAZKOKiorkqquukgcffNAMzELklj5XzCOFSNYzO16OGuycAHxnaYU89+2aUDcJAACEeyC1c+fOBiXNXbe1yx8ifzJelUT5c0S4q8f2lsQ451fjyz+slc0Ftd2ZAQAA/A6ktNyyzhHlyXVbu/whOjJSyUzIiwjXrX2KnDVqV/f8af/+cmWomwQAAMJ9Qt7p06ebiXJdSktLJSYmRqZNmyaLFy+us64u14lyETmT8SrKnyMaXHFwH3nn5w1SZKuUaQs2yAUH9JK+uRmhbhYAAAjXQOqtt94yl/qef/75BssIpCKHZxloxkghGrRPS5RLDuotD32+QqodIg/MWCH/d/bwUDcLAACEYyC1du3a1m0JwiIjlZxA1T5Eh/NG95LX56yTvEKbzPw9Tx7+YoWsziuWnaV2aZeaKOMG5MqEQV34TAAAEKV8DqR23dU5ZgDRh4wUolFKYpxcM3Z3uem9Jeb2U1+tltgYMRkq/Ttj2WaZ/PEyefSkoTK2f26omwsAAKxabALRizFSiFbtUhPq3NYgyvNvUVmlXPif+fLlb3khaB0AAAglAik0y+YxRoqufYimTOyN//u1yXVMPOUQuX7a4jqZWwAAEPkIpNCsco8xUhSbQLSYvmSTFJZVNrueBlMFZZXy2dJNbdIuAABgDQRSaJbNc0Je5pFClPhiWZ4ZC+ULXe/zpXTvAwAgmhBIwa8JeZMSOGQQHbQ6n2ssVHN0vZ1l9tZuEgAAsJCgnhXb7XYpKSkJ5iZhAeVkpBCFtMS5PxmpdimJrd0kAAAQ7oHU1KlT5ZprrqmzbMqUKZKeni7t2rWT4447ToqLi4PVRlgpI0XXPkQJnSfKn4zU+IGUQAcAIJoEFEg98sgjdTJPs2fPNoHU+PHjTYA1Y8YMueeee4LZTlik/HkSE/IiSuhku5kp8dJcUkrvz0qJl8MHdmmjlgEAgLANpNasWSODBw92337rrbekc+fO8v7778uDDz4ol19+ufzvf/8LZjsRQkzIi2ikpf51sl2NlBoLpszyGJFHThrK1AAAAESZgAIpm80mycnJ7ttffPGFHH744RIfH29u9+/fX/7666/gtRKWyUglU2wCUWRs/1x54azhJjPljS5/8azhZj0AABBdAgqkevXqJTNnzjTX58+fL6tXr5bDDjvMfX9eXp4ZL4UI7NoXHxfStgBt7dD+ufLTLWPloRNrs/BZKQny71OGmOUEUQAARKeAAqmLL75Y3nnnHdO9b9y4cdKtWzc58sgj3ff/+OOPMmDAgGC2EyFE1z5EO+3md9Lw7tIhzVmZLz0pXo7bqxvd+QAAiGLe+6s048orrzRd+6ZPny7Dhg2Tf/3rX5KSkmLu2759u2zevFkuueSSYLcVIc5IxcSIJMT5WA8aiEA5GUmyvcQu+UXl4nA4JEY/FAAAICoFFEipCy+80Fzq69Chg+nuh8hhq6hylz7nxBHRLCczWZZvLpKKKofsKK1wZ6gAAED0CdqEvPrr7FdffSWfffaZFBUVBWuzsFBGivFRiHa5GUnu65qVAgAA0SugQOrWW2+Vgw8+uE4QpWOlDj30UDniiCNk0KBBpkQ6IisjRcU+RLuczNpAKq/QFtK2AACAMAykdI6oESNGuG+/++67MmvWLLn77rvlk08+kaqqKpk8eXIw24kQKicjBRi5mbXTPuQXkpECACCaBTRGauPGjdKnTx/37ffee8/MHXXzzTeb25deeqk8++yzwWslLDNGCoj2YhMu+UVkpAAAiGYBnRnrxLs6Ka+rW59mozznkcrNzZWtW7cGr5WwxBgpLQENRHuxCRcyUgAARLeAAqmBAwfKG2+8ITt27JBXXnlFtm3bZsZGufz555+SnZ0dzHYiRCqrqqWy2mGuk5FCtPPMSDFGCgCA6BZQ175JkybJUUcd5Q6WRo8eXaf4xKeffir77LNP8FqJkGejVFICXfsQ3TpRtQ8AALQkkNLqfAsXLpQvv/xS2rVrJ6eccor7Ps1SjRkzRo455phANg0LB1LJ8XTtQ3TTKQDapyaYOaTISAEAEN0CnpBXi0vopb727dvLv//975a2CxZRXlNoQpGRApyV+zSQ2lJkM2NEmaQaAIDo1KK+WnPnzpX77rtPrrnmGlm1apVZVlpaarJVxcXFwWojrNK1j4wU4O7eZ6+qlp2lFewRAACiVECBlN1ul+OPP96MjdLJeZ944gnZsGGDc4OxsWZy3scffzzYbUUI2CprM1JMyAvUm0uKEugAAEStgAKp22+/3Uy8q3NFrVixwnRvcUlOTpaTTjpJPvzww2C2EyFSXkFGCmi8ch+T8gIAEK0CCqT++9//mkl3L7roIunQoUOD+/fcc0/5448/gtE+WGQyXsUYKYCMFAAAaEEglZ+fL4MGDWr0/ri4ODNWCuGPMVJAXWSkAABAwIFU9+7dZfny5Y3e/+OPP0qfPn3Yw5FWtS+eeaSAHI8xUlq5DwAARKeAzoxPP/10ef7552XOnDnuZa4SwC+++KK88847MnHixOC1EtaYRyqBeaQAMlIAACDgeaS0Up+WPteJd3U8lAZRWgJ9+/bt8tdff8mECRPMbURa1z4yUkBOZm2xCar2AQAQvQI6M05MTJQZM2bIK6+8IrvttpvsscceYrPZZPDgwfLqq6/Kxx9/bMZJIfzRtQ+oS+dTa5eaYK5TtQ8AgOgVUEZKaRbqzDPPNBdELrr2AQ3lZiSbyXjzC21m+gdX12YAABA9AspIaRe+X3/9tdH7lyxZIjt27GhJu2ARZKSAxrv32auqpaCsgl0EAEAUCiiQ0vFPOodUYy6++GK5/vrrW9IuWHGMFMUmACMno7ZyX14hlfsAAIhGAQVSX331lRx99NGN3n/UUUfJzJkzW9IuWIStsrb8eTLFJgAjt07BiXL2CgAAUSigQGrLli2SnZ3d6P0dO3Y0k/Yi/NkqyEgBTZdAJyMFAEA0CiiQ6tKliyxatKjR+xcsWCCdOnVqSbtgwYwU5c8Bp1yPSXnJSAEAEJ0CCqSOPfZYeemll+Sjjz5qcN+HH35oyqIfd9xxwWgfLJSRYkJewMtcUmSkAACISgGVP588ebIZA6XB0pAhQ2TgwIFm+dKlS+WXX34xk/ROmTIl2G1FCJSTkQKaLDZBRgoAgOgUUEYqKytL5s6dK7fddptUVFTIu+++ay56/fbbb5effvpJ2rVrF/zWIrRjpCg2ARidGCMFAEDUC3hC3rS0NJN1IvMUbRPy1o6ZAqKVfhbapSY4J+Wlah8AAFEpoIxUZWWlFBYWNnq/3qfrIPwxIS/QdOU+rdrncDjYTQAARJmAAqmrrrpK9ttvv0bvHz16tFx33XUtaRcslpGKj42R+LiADhcgoiv32SurpbCMH44AAIg2AZ0Zz5gxQ0488cRG79f7pk+f3pJ2wWLlzxkfBTQxTorufQAARJ2AAqm///5bunbt2uj9u+yyi2zcuLEl7YJFlNcUm0gy46MAeJ1LihLoAABEnYACqY4dO8qKFSsavf/333+XzMzMlrQLFstIJVOxD/A6RkrlFZazdwAAiDIBBVKHHXaYPP/887Jo0aIG9y1cuFBeeOEFOfzww4PRPlhkjBQZKaCJjFSRjd0DAECUCaj8+V133WXGSY0YMUKOPvpoGTBggHtC3o8//lhycnLMOoicqn2MkQLqIiMFAEB0CyiQ0jFQ8+fPl5tuukk+/PBDef/9981y7c53xhlnyL333mvWQXjTks5kpIDmM1JbyEgBABB1Ap6Qt0uXLvLaa6+Zk+0tW7aYZZ06dZKYmJhgtg8hZK+qFtf0OGSkgCaq9jFGCgCAqBNwIOWigZN25UPkcWWjFIEUUFdyQpxkpSRIQVkFY6QAAIhCAQVSd955p08B1u233x7I5mERtprS566TRgANx0lpIKUZKc3Ok5EHACB6BBRITZ48udH79ETCdUJBIBUZhSYUGSnA+zipVfnFJntbWF5pMlQAACA6BFT+vLq6usGlsrJS1qxZI9dcc40MHz5c8vPzg99ahLBrHxkpoKnKffmMkwIAIKrEBm1DsbHSq1cvefjhh6Vv375y5ZVXBmvTCPFkvCo5IWiHChAxcphLCgCAqNUqZ8djxoyR6dOnt8am0YbKPcZIkZECGmIuKQAAolerBFI6x5RmqBA5GakkMlJAk3NJ5RXa2EMAAESRgIpNvP76616X79y5U7777jt577335IILLmhp22ChMVLJjJECGsjN9BgjVVTOHgIAIIoEFEidc845jd6XnZ0tN910k0yaNKkl7YIF2Dyr9pGRAhrIyajNSOWTkQIAIKoEFEitXbu2wTItd96+fXvJyMgIRrtguYwUXTWB+nLISAEAELUCCqR23XXX4LcElp6QN4kJeYEGdKLqzOR4M4cUY6QAAIguAQVS9S1fvlymTZsmmzZtkn79+sm5554rmZmZwdg0Qqjcs9gEGSmg0YITheXFZoyUazJyAAAQ+XwOpJ566il54oknZPbs2WYclMvHH38sJ510ktjtdveyJ598UubOnVtnPYR3Rkp/eQfgvXvfqvxiM12AZqayUhLYTQAARAGfB7589NFH0rt37zrBUWVlpanOFxcXJ6+88oosWbJE7r//fvnzzz/lnnvuaa02IxTlz8lIAV7lehSc2ELlPgAAoobPgdRvv/0m++67b51lX3/9tWzZskWuueYaOfvss2XAgAFy4403ysknn8yEvBGACXmB5nXyKDjBOCkAAKKHz4HUtm3bpHv37nWWzZo1y4wHOO644+osHz16tKxfvz7gRj399NPSs2dPSU5OlpEjR8q8efN8etzUqVNNe4499tiAnxveM1LJlD8Hms1IMZcUAADRw+dAKjc3VzZv3lxn2ffffy+pqakyZMiQOssTExPNJRBvv/22XHvttXLHHXfIwoULzbbHjx8v+fn5TT5u3bp1cv3118sBBxwQ0POiITJSgH8l0MlIAQAQPXwOpIYPHy6vvfaaFBUVmdvLli0zmSINcuLj4xtU8evWrVtADXr00UflwgsvNJX/+vfvL88995wJ1l5++eVGH1NVVSVnnHGGTJkyRXbbbbeAnhfNjJEiIwU0WrXPhUl5AQCIHj5X7dMM0T777CN9+/Y1Y6EWLFhgutHdfPPNDdZ9//335ZBDDvG7MVr5T7fruc3Y2FgZO3aszJkzp9HH3XnnnZKTkyPnn3++yZI1xWazmYtLYWGh+VtdXW0ubU2fU0smh+K5m1NeURtIJcbFuPeRttd1QWjwHrTePvX3uyA7rbZKX15hmSU/y1b/roF1cdyAYwbR9l1T7UcbfA6kBg0aJF999ZWpxvfHH3+YwhPalW7YsGF11vvmm29MBklLovtr69atJruk3Qg96W3Ncnnzww8/yEsvvSSLFy/26Tnuu+8+k7mqT4tmlJeXSyjerIKCAnPwaNBoJQXFZe7rRTu3S35lsVRUVYitwCYx8TFij60teY+25RCHlBeXi8Tof8xbFAyV1ZViq7TJ1titkhDnewnzGI9pAjZuL262G3KoWPm7BtbFcQOOGUTbd01RTe+7oE/Iu99++8mnn37a5DoHHXSQKYPeVi/0rLPOkhdffNHnOas026VjsDwzUlpEo1OnTiGZRFgPHM3s6fOH+sBpIK62YEjXzjnSLjXRnGhurN4oqYmpkhgX2Dg4tJzJBjpE0tunMwFskNir7OKwOyS7U7YkxdeOe/JFRnK8FJVXyo6yapMdtyJLf9fAsjhuwDGDaPuuSU6u7bIf1ECqtWkwpHNS5eXl1Vmutzt37txg/TVr1pgiE0cddVSDdJyO21qxYoWZ+8pTUlKSudSnb1qo3jg9cEL5/I2xV9b+0p6alOBuo7bXdUHo8D60zv4M5LOo46SKyoslv8hm6c+GVb9rYG0cN+CYQTR918T68fyW+tdUK/1pV0Etq+4ZGOntUaNGNVh/jz32MNkv7dbnuhx99NFy8MEHm+v1y7XDP+UexSYS4yx1qACWkpPh/HGmrKJKimyVoW4OAABoA5bKSCntdqeT+2qVwBEjRshjjz0mJSUlpoqfmjhxonTt2tWMddLU28CBA+s8vl27duZv/eXwn61m7IcGUbGx1vyFHbBi5b7MZN/HWAEAgPBkuUDqlFNOMYUfJk2aZOatGjp0qMyYMcNdgEIn+g11yi/ayp9T+hzwLSOl8gvLpU9OOrsMAIAIZ7lASl1xxRXm4o1WBWzKq6++2kqtit4JeZPi40LdFMDScjwzUkW10ysAAIDIRWoHjbLVFJtIZjJewOeMVF5h20+jAAAA2h6BFJrv2hfPYQL4PEaKjBQAAFGBM2Q0W2yCrn1A08hIAQAQfQik4FV1tUPsVXTtA3yRk+lZbIIxUgAARAMCKXjlCqIUGSmgaamJ8ZKR7Kzdk1/EGCkAAKIBgRS8Kq+onYyX8ueA79378gpt4nA42GUAAEQ4Aik0WbFPJVP+HPC54ERZRZUU2yrZYwAARDgCKXhFRgpoScEJxkkBABDpCKTQbEaK8ueAvyXQGScFAECkI5BCk6XPVXJCHHsJaEYnj4wUlfsAAIh8BFLwqrxmMl5FRgpoHhkpAACiC4EUms1IUf4caB5jpAAAiC4EUvDK5pGRSk7gMAH8y0hRbAIAgEjHGTK8KicjBfglJ9Ozah/FJgAAiHQEUmg2I8WEvEDzUhPjJSMp3lzfQkYKAICIRyAFr5iQF/Bfp5qsFBkpAAAiH4EUvGJCXsB/uRnOcVKl9ioptlWyCwEAiGAEUvBhQl7mkQJ8wTgpAACiB4EUmi9/TtU+wP/KfYVU7gMAIJIRSMErJuQFWjaXVH4RlfsAAIhkBFJoNiOVnEDXPsAXOWSkAACIGgRS8IqMFNCyjBSV+wAAiGwEUmh+jBTFJgD/x0gxlxQAABGNQArNTsibTLEJwCdkpAAAiB4EUvCqnIwU4Le0pHhJT4o317eQkQIAIKIRSKHZjBTlzwH/s1KMkQIAILIRSKHZCXmTGSMF+D0pb4m9Soptlew5AAAiFIEUvLJVODNSMTEiCXEx7CUgoEl5mUsKAIBIRSCFJjNSSfGxEqPRFIAACk7Y2GsAAEQoAik0GUgxGS/QkhLoZKQAAIhUBFLwqryma59mpAD4rpNHRiqfjBQAABGLs2Q007Uvjj0E+IGMFAAA0YFACk0Wm2AyXsA/jJECACA6EEjBq3IyUkBAchgjBQBAVCCQQgOVVdVSVe0w18lIAf5JT4qXtERnl1jGSAEAELkIpNDkZLyMkQICHyeVX0T5cwAAIhWBFBqt2Keo2gcEXrmv2FYpJbZKdiEAABGIQApNZqSYRwpoaeU+slIAAEQiAik0QEYKCGblPiblBQAgEhFIoekxUgkcIoC/yEgBABD5OEtGAxSbAFomJ7M2I5VPRgoAgIhEIIWmu/aRkQL8lpPBGCkAACIdgRQaICMFBC8jxRgpAAAiE4EUGrB5ZKSYkBdo4RipQqr2AQAQiQik0EA5E/ICLZKeFC+piXHmel4RVfsAAIhEBFJoMiPFhLxAy7JSW8hIAQAQkQik0AAT8gIt16lmLqkiW6WU2ivZpQAARBgCKTTAhLxAyzFOCgCAyEYghWaq9nGIAIHIqclIKSr3AQAQeThLRgN07QNaLtezBHoRlfsAAIg0BFJogGITQLC79lG5DwCASEMghQbISAHBKzah8slIAQAQcQik0ICt0qP8eQKHCBAIMlIAAEQ2zpLRQHmFZ7EJ56SiAFpSbIIxUgAARBoCKTSZkUomIwUEJD0pXlITnT9E5BcxRgoAgEhDIIUGyEgBLRcTE+POSuWTkQIAIOIQSKHpMVLMIwUELKemcl+RrVJK7ZXsSQAAIgiBFBqw1RkjxSECBGOcFFkpAAAiC2fJaKC8JiMVHxsj8XEcIkBQKvdRAh0AgIjCWTIazUiRjQKCWbmPghMAAEQSAik0OiFvcgKlz4GWICMFAEDkIpBCA+UVzq59ZKSAYI6RIiMFAEAkIZBCoxmpJDJSQFCq9inGSAEAEFkIpNBo+XMyUkDL5GQyRgoAgEhFIIU6HA6He0JeMlJAy2QkxUtKTWaXjBQAAJGFQAp12KuYQwoIlpiYGHdWiqp9AABEFgIpeB0fpajaB7RcboZznFRReaWU2Z3dZgEAQPgjkILXin2KMVJAy3XyGCeVX0TlPgAAIgWBFLxOxqvISAHBy0gpxkkBABA5CKTQaNc+MlJAy1G5DwCAyEQghTro2gcEV65n175CG7sXAIAIQSCFOig2AQRXjkfXvjzGSAEAEDEIpFCHjWITQFCRkQIAIDIRSKGJMVLOiUQBBC4n07PYBFX7AACIFARSqMNWWVv+PDmBwwNoqYykePdnKY8xUgAARAzOlFFHuUf5c6r2AS0XExMjuTVZqfxCMlIAAEQKAik0mpFKSqBrHxAMORnOyn2F5ZV1KmMCAIDwZclA6umnn5aePXtKcnKyjBw5UubNm9foui+++KIccMAB0r59e3MZO3Zsk+vDn6p9ljw8gPAeJ0X3PgAAIoLlzpTffvttufbaa+WOO+6QhQsXypAhQ2T8+PGSn5/vdf1vvvlGTjvtNPn6669lzpw50r17dxk3bpxs3LixzdseefNIkZECgpmRUpRABwAgMlgukHr00UflwgsvlHPPPVf69+8vzz33nKSmpsrLL7/sdf0333xTLrvsMhk6dKjsscce8n//939SXV0ts2bNavO2RwIbY6SAoHONkVJkpAAAiAzxYiF2u10WLFggN998s3tZbGys6a6n2SZflJaWSkVFhXTo0MHr/TabzVxcCgsLzV8NvvTS1vQ5HQ5HSJ67uYxUYlxMg3a52uu6IDR4D1pvn7bGd0Gn9ET39c0FZXzXIGxY7d8oWB/HDML9uPGnDZYKpLZu3SpVVVWSm5tbZ7neXr58uU/b+Ne//iW77LKLCb68ue+++2TKlCkNlm/ZskXKy8tD8mYVFBSYg0eDxlDbXljkvl5aXCj5+XUPpoqqCrEV2CQmPkbssfYQtBDKIQ4pLy4XidH/YtgpQVBZXSm2Sptsjd0qCXEJQd2niVVl7uvr8rZLfn6qRPt3DcIDxw04ZhBt3zVFRbXnwmEVSLXU/fffL1OnTjXjprRQhTea7dIxWJ4ZKR1X1alTJ8nMzJRQHDhaHlmfP9QHjopL2OK+3rlTR8nJyapzv55obqzeKKmJqZIYV/srO9qWyQY6RNLbp5vjBy1nr7KLw+6Q7E7ZkhRfO6YpGHZ3pIjIKnO9uCpOcnJyJNq/axAeOG7AMYNo+65JbiSGsHwglZ2dLXFxcZKXl1dnud7u3Llzk499+OGHTSA1c+ZMGTx4cKPrJSUlmUt9+qaF6o3TAyeUz+/JXlWbgUpNjG/QJr2t7XVdEDq8D62zP1vjs9i5XW0GakuRne8ahBUr/RuF8MAxg3A+bvx5fkt9KyYmJsqwYcPqFIpwFY4YNWpUo4978MEH5a677pIZM2bI8OHD26i10TAhL1X7gGDITI53T3Cdx6S8AABEBEtlpJR2uzv77LNNQDRixAh57LHHpKSkxFTxUxMnTpSuXbuasU7qgQcekEmTJslbb71l5p7avHmzWZ6enm4uCHxCXuaRAoL3K5tW7lu/vVTyi2qL3QAAgPBluUDqlFNOMYUfNDjSoEjLmmumyVWAYv369XVSbs8++6yp9nfiiSfW2Y7OQzV58uQ2b38kTchLRgoI7lxSGkgVlFWY6pjJCWR8AQAIZ5YLpNQVV1xhLt5oIQlP69ata6NWReGEvAmW6vkJRMxcUluKbNK9Q9tX7gMAAMHDmTKayEhxeADB0imjtsgN46QAAAh/nCnDa7GJxHhndT4Awc9IMU4KAIDwRyAFr8UmyEYBwR8j5UJGCgCA8EcghTpsNRkpBsIDwUVGCgCAyEIghTrISAGtIyeTjBQAAJGEQApeM1J07QOCKzejbtU+AAAQ3gik4LVqH137gODKTIk3RVwUY6QAAAh/BFJwq6p2iL2KjBTQGrQKZm5N9z6q9gEAEP4IpOBmrzOHVBx7Bmil7n07SyvqTH4NAADCD4EUGhSaUMkJHBpAaxacYJwUAADhjbNlNJiMV5GRAoIvx6PgRH5RObsYAIAwRiAFrxmpJDJSQCuXQKdyHwAA4YxACg0q9qlkxkgBrVoCPb+QjBQAAOGMQApunoPfyUgBrZyRYi4pAADCGoEUvGekEqjaBwRbbqZnRoqufQAAhDMCKbjZ6hSb4NAAgi0nozYjRbEJAADCG2fL8N61j0AKCLqslARJrPlskZECACC8EUjBja59QOuKiYlxZ6XyKH8OAEBYI5CCGxkpoO3GSe0sragz5QAAAAgvBFLwmpFiQl6gDcZJUXACAICwRSAFNybkBdq4ch8l0AEACFsEUnArr1O1j/LnQGvoVCcjxaS8AACEKwIpuJGRAlofGSkAACIDgRS8V+0jIwW0+hipPDJSAACELQIpeK/al8ChAbQGMlIAAEQGzpbRSNU+Dg2gNZCRAgAgMnC2DDebR7GJ5ASKTQCtoV1qgiTGOb96t1C1DwCAsEUgBbdyj8lByUgBrSMmJsZduY8xUgAAhC8CKXjNSFH+HGg9uZnOQGpHaUWdapkAACB8EEjBzfOELpliE0CrycmonZSX7n0AAIQnAim4kZEC2jYjpfIZJwUAQFgikEKDjFRsjEhCXAx7BmglOZm1Gal85pICACAsEUjBrbxmjJSOj9IB8QDaogS6jd0MAEAYIpCCmYj3vYV/yYYdpWZvVFZXm9ueE/QCaK1JecvZtQAAhCECqSj35W95MuLemXLtO79Iqd0ZOFVUOcxtXT7zt7xQNxGIODkeY6TISAEAEJ4IpKI8iLroP/OlqKzS6/26/ML/zDfrAQieXI+qfRSbAAAgPBFIRSnttnfdtMUiDvOfV2a5Q+T6aYvp5gcEUbvUBEmMc379UmwCAIDwRCAVpaYv2SSFZZWNBlEuen9BWaV8tnRTG7UMiHxazKVTTcEJMlIAAIQnAqko9cWyPFPm3Be63udL6d4HtMY4qe0ldrFXOitmAgCA8EEgFaV2ltqlurl0VA1db2eZvbWbBETtOKktxZRABwAg3BBIRal2qYl+ZaTapSS2dpOAKK7cRwl0AADCDYFUlBo3INevjNT4gbmt3SQgeueSYlJeAADCDoFUlJowqItkpsRLc0kpvT8rJV4OH9iljVoGRAdXsQnFpLwAAIQfAqkolZwQJ4+eNNQZKTXC3BUj8shJQ836AIKHjBQAAOGNQCqKje2fKy+cNbzBWCnXbc1YvXjWcLMegODK8chIMUYKAIDwEx/qBiC0ds9Nd4+Vap+aIP06Z5jCEjomSrvzkYkC2iAjVUTVPgAAwg2BVJSb9Xu++/pFY3rLpQf1Dml7gGihP1wkxMVIRZWDjBQAAGGIrn1R7qvltYHUP/bMCWlbgGgSExMjOTVzSW0hIwUAQNghkIpiReUV8tPabeZ6t/Yp0jcnPdRNAqKKq3LfthK72CurQ90cAADgBwKpKPb9qq2mW5Eau2eu+YUcQNvJ9ZiUd2sx46QAAAgnBFJRzHN81CF70K0PaGuurn2Kyn0AAIQXAqkoVVXtkG9WOAOptMQ4Gblbh1A3CYjqjBSV+wAACC8EUlHql792mnEZ6oC+nSQpngl3gVBmpPILy3kDAAAIIwRSUWrW73nu64dQrQ8IiRwyUgAAhC0CqSjlOT7q4H6MjwJCPSkvY6QAAAgvBFJRaOPOMlm+uchcH9K9nbsEM4C2lePx2csrpGofAADhhEAqCn3l0a1vLNX6gJBpn5ooCXHOaQcoNgEAQHghkIpCs5Z7lD1nfBQQMrGxMdIp3ZmVotgEAADhhUAqypTaK2X2mm3mepesZOnfJTPUTQKiWk7NOCmtollRVR3q5gAAAB8RSEWZH1ZtFXtltXsS3pgYZ7ciAKEfJ7WliHFSAACECwKpKPOVR7e+f9CtD7BU5T7GSQEAED4IpKJIdbXDHUglJ8TKfr2zQ90kIOrVrdzHpLwAAIQLAqkosuzvQvcv3qN7Z0tyQlyomwREPTJSAACEJwKpKDLTo+z5P/bMDWlbADh1yqzNSFG5DwCA8EEgFaXjo7TQBIDQy83wGCPFpLwAAIQNAqkooWMvlmwsMNcH7JIpnbNqT94AhE6OR0Yqr4gxUgAAhAsCqWis1kc2CrCMDqmJEh/rnIaAjBQAAOGDQCpKzPrds+w546MAq4iNjZFONZX78slIAQAQNgikokB5RZX8uHqruZ6dniSDumaFukkAPOTUzCW1rcQuFVXOCbMBAIC1EUhFgTlrtklZRZW5fsgencwv4ACsN5eUwyGytdg5RQEAALA2AqkoMGs5Zc8BK8utUwKdQAoAgHBAIBXhHA6HfFUzPioxLlb275Md6iYBqCfHowS6VtgEAADWRyAV4ZZvLpK/C5wnZvv27ihpSfGhbhKApjJSRWSkAAAIB5xVR2hxielLNskXy/Jk6d/OuaPUmL5kowCrZ6TyyUgBABAWCKQizJe/5cl10xZLYVmlaE2JakftfY/NXCU9O6bJ2P6UPwesOikvGSkAAMIDgZRF2Cqq5LNlf5ss0vZim5RVOksgpyTESYe0RBk3IFcmDOoiyQlxTQZRF/1nvkhN8OQZRKkSW6Vc+J/58sJZw+VQginAMrJSEtzXZyzdLDtLK3z6zPuTof582WbZsrNEOrX7S8YP6ByUbSNycdwA4LumeTEOrUYQxQoLCyUrK0sKCgokMzOzzZ+/urpa3p2zUu7+8k8pLK8ULUxe/w1xLctMiZdHTxrqNaOk/+iNuHemFJVVNnh8/W3pdn66ZWxAJ1G2Spss3rxY0hLTJDEu0e/HIzj0Y1u8vVjSO6RLTAzl7IPBXmWXEnuJDO08VJLiazNEbZJFfmex+fy7uLLJTX3mA81QB2vbiFwcN2jpeU1+fr7k5ORIbCxD8RF+3zX+xAaWPMKffvpp6dmzpyQnJ8vIkSNl3rx5Ta4/bdo02WOPPcz6gwYNkunTp0u4mPl7nvzr4zVSVHMS5S0Ici3TIEkzSnrg1ae/OOuB2FxUrPcXlFXKZ0s3BaH1AFrClUV2ff5dXNnkpj7zPm+7rLLONoOxbUQujhsAfNf4znKB1Ntvvy3XXnut3HHHHbJw4UIZMmSIjB8/3vy64c3s2bPltNNOk/PPP18WLVokxx57rLksXbpUrE6zSNdP+9Vc9yUtaNZxiPxz6iJ5Z/56efabNTL5o2VyyX8WyJSPf/P5eTXa/3wpJ09AqD//+kucfqYdzXzmr5+22KxvhW0jcnHcAOC7Jsy79mkGap999pGnnnrKnSLu3r27XHnllXLTTTc1WP+UU06RkpIS+eSTT9zL9t13Xxk6dKg899xzlu7a997Cv+Tad36RUNh3tw4y9aJRfj+Orn3WQNe+8O/a5+/nf0i3LOnaPsWndTfuKJNf/ipolW0jcnHcIBj0rNJmK5ekpGSh5zmC8V3z71OGyHF7dZO24k9sYKliE3a7XRYsWCA333yze5n2rx07dqzMmTPH62N0uWawPGkG64MPPvC6vs1mMxcX3Ulq586dJmhrSx/PXy1iL21QFKK1aUYqRdLMaw4kkCouLJbyuHLGSIU4kCorKBNbjI0xUkEMpCqrKmVn8s42CaT8/fwvWlMqi1qpLa25bUQujhsAbXHO+tHPq+XgXunSloGU8iXXZKlAauvWrVJVVSW5uXUHlunt5cuXe33M5s2bva6vy7257777ZMqUKQ2W77rrrhJNXtXLxaFuBQAAAGC9c9aioiKTmQqbQKotaLbLM4OlWajt27dLx44dQ/LLvka92nVxw4YNIakaiPDEcQOOGfBdAyvi3yeE+3GjmSgNonbZZZdm17VUIJWdnS1xcXGSl1e3EILe7ty5s9fH6HJ/1k9KSjIXT+3atZNQ04Mm1AcOwg/HDThmwHcNrIh/nxDOx01zmShLVu1LTEyUYcOGyaxZs+pkjPT2qFHeCyPocs/11Zdfftno+gAAAADQUpbKSCntdnf22WfL8OHDZcSIEfLYY4+ZqnznnnuuuX/ixInStWtXM9ZJXX311XLggQfKI488IkcccYRMnTpV5s+fLy+88EKIXwkAAACASGW5QErLmW/ZskUmTZpkCkZoGfMZM2a4C0qsX7++zkzZ++23n7z11lty2223yS233CJ9+/Y1FfsGDhwo4UC7GeqcWfW7GwIcN+C7BqHGv1HgmAHfNWE0jxQAAAAAWJ2lxkgBAAAAQDggkAIAAAAAPxFIAQAAAICfCKQAAAAAwE8EUiH09NNPS8+ePSU5OVlGjhwp8+bNC2VzYHFa8n+fffaRjIwMycnJkWOPPVZWrFgR6mYhzNx///0SExMj//znP0PdFFjYxo0b5cwzz5SOHTtKSkqKDBo0yEwtAjSmqqpKbr/9dunVq5c5Znr37i133XWXUNMMnr777js56qijZJdddjH/FmmlbU96vGjl7i5dupjjaOzYsbJq1SqxKgKpEHn77bfNnFla+nzhwoUyZMgQGT9+vOTn54eqSbC4b7/9Vi6//HKZO3eumXS6oqJCxo0bZ+ZZA3zx888/y/PPPy+DBw9mh6FRO3bskNGjR0tCQoJ89tln8ttvv5m5Gtu3b89eQ6MeeOABefbZZ+Wpp56S33//3dx+8MEH5cknn2SvwU3PWfScV5MJ3ugx88QTT8hzzz0nP/30k6SlpZnz4/LycrEiyp+HiGagNLugXziqurpaunfvLldeeaXcdNNNoWoWwojOt6aZKQ2wxowZE+rmwOKKi4tl7733lmeeeUbuvvtuM0efTngO1Kf/Bv3444/y/fffs3PgsyOPPNLM+fnSSy+5l51wwgkmq/DGG2+wJ9GAZqTef/9908PGlY3STNV1110n119/vVlWUFBgjqtXX31VTj31VLEaMlIhYLfbZcGCBSZd6X4jYmPN7Tlz5oSiSQhD+uWiOnToEOqmIAxoNvOII46o870DePPRRx/J8OHD5aSTTjI/1uy1117y4osvsrPQpP32209mzZolK1euNLd/+eUX+eGHH+Twww9nz8Ena9eulc2bN9f5dyorK8skH6x6fhwf6gZEo61bt5q+xBphe9Lby5cvD1m7ED40g6ljXLT7zcCBA0PdHFjc1KlTTRdi7doHNOePP/4wXbS0+/ktt9xijpurrrpKEhMT5eyzz2YHotFMZmFhoeyxxx4SFxdnznPuueceOeOMM9hj8IkGUcrb+bHrPqshkALCNLuwdOlS82sf0JQNGzbI1VdfbcbVaWEbwJcfajQjde+995rbmpHS7xsds0Aghca888478uabb8pbb70lAwYMkMWLF5sf/LSrFscNIhVd+0IgOzvb/FqTl5dXZ7ne7ty5cyiahDByxRVXyCeffCJff/21dOvWLdTNgcVpN2ItYqPjo+Lj481Fx9XpYF69rr8aA560Wlb//v3rLNtzzz1l/fr17Cg06oYbbjBZKR3HolUezzrrLLnmmmtMxVnAF65z4HA6PyaQCgHtHjFs2DDTl9jzF0C9PWrUqFA0CWFAB2FqEKUDM7/66itTYhZozj/+8Q9ZsmSJ+XXYddFsg3a30ev6ow7gSbsM159aQce97LrrruwoNKq0tNSM9/ak3y96fgP4Qs9rNGDyPD/W7qJavc+q58d07QsR7XuuqW49oRkxYoSpnqUlIc8999xQNQlh0J1Pu0x8+OGHZi4pV39hHYipVZEAb/RYqT+OTsvJ6vxAjK+DN5pF0MIB2rXv5JNPNnMcvvDCC+YCNEbnBtIxUT169DBd+xYtWiSPPvqonHfeeew01Kkgu3r16joFJvRHPS2cpceOdgfVyrJ9+/Y1gZXOTabdQ12V/ayG8uchpKXPH3roIXNCrKWItauNViYBGisT6s0rr7wi55xzDjsNPjvooIMof44maffhm2++2UyEqScz+uPfhRdeyF5Do4qKisxJr/aa0O7EevJ72mmnmclVtScOoL755hs5+OCDpT5NLmiJc+19o3Os6g83O3fulP33399M27H77ruLFRFIAQAAAICfGCMFAAAAAH4ikAIAAAAAPxFIAQAAAICfCKQAAAAAwE8EUgAAAADgJwIpAAAAAPATgRQAAAAA+IlACgAAAAD8RCAFAAAAAH4ikAIAwCKeeeYZefXVV0PdDACAD2IcDofDlxUBAEDrGjhwoGRnZ8s333zDrgYAiyMjBQCIKiUlJRJNKisrxW63h7oZABBxCKQAAH6bPHmyxMTEyMqVK+XMM8+UrKws6dSpk9x+++2iHR02bNggxxxzjGRmZkrnzp3lkUce8Wm7us0rrrhC3nzzTenXr58kJyfLsGHD5Lvvvquz3p9//imXXXaZWSclJUU6duwoJ510kqxbt67OetpNTrf57bffmvVzcnKkW7duAW3jhx9+kKuuusq8znbt2snFF19sApSdO3fKxIkTpX379uZy4403mn3gqbq6Wh577DEZMGCAeU25ubnm8Tt27HCv07NnT1m2bJlpqz6fXg466CD3/fo8//znP6V79+6SlJQkffr0kQceeMBs20Xbro97+OGHzfP17t3brPvbb7/5tP8BAL6L92NdAADqOOWUU2TPPfeU+++/Xz799FO5++67pUOHDvL888/LIYccYk70NSi6/vrrZZ999pExY8Y0uwc1kHj77bdN0KJBgI4bOuyww2TevHmm65v6+eefZfbs2XLqqaeawEgDiGeffdYEHho0pKam1tmmBkwaAE2aNMmdkfJ3G1deeaUJCqdMmSJz586VF154wQRUuo0ePXrIvffeK9OnT5eHHnrItFODKxcNmjQgO/fcc83rWrt2rTz11FOyaNEi+fHHHyUhIcEEPvoc6enpcuutt5rHacClSktL5cADD5SNGzeabenz6fPefPPNsmnTJvNYT6+88oqUl5fLRRddZPahvicAgCDTMVIAAPjjjjvu0JSL46KLLnIvq6ysdHTr1s0RExPjuP/++93Ld+zY4UhJSXGcffbZzW5Xt6mX+fPnu5f9+eefjuTkZMdxxx3nXlZaWtrgsXPmzDGPff31193LXnnlFbNs//33N+3z5O82xo8f76iurnYvHzVqlHmtl1xySYN9cOCBB7qXff/99+bxb775Zp3nmjFjRoPlAwYMqPNYl7vuusuRlpbmWLlyZZ3lN910kyMuLs6xfv16c3vt2rVmm5mZmY78/PwG2wEABA9d+wAAAbvgggvc1+Pi4mT48OGmW9v555/vXq5ZG+0+98cff/i0zVGjRpnufC6afdFugp9//rlUVVWZZdoVz6WiokK2bdtmurrpcy1cuLDBNi+88ELTPk/+bkNfk3abcxk5cmSD1+raB56vddq0aabr46GHHipbt251X/Q1avbp66+/bnaf6DYOOOAA03XQcxtjx441+6R+18cTTjjBZOAAAK2Hrn0AgIBpkONJAwYdA6SV5+ov10DFF3379m2wbPfddzfd27Zs2WK615WVlcl9991nurBpdzfPMUkFBQUNHt+rV68Gy/zdhrfXqnTMUv3lnmOfVq1aZban47O8yc/Pl+boNn799ddGg6P62/D2egEAwUUgBQAIWP0sT2PLVDBn29CxRBoAafEFzWBp8KLZIh3v5Fl8wVv2KdBtNPa6vC33fK26LQ2idKyYN75kjnQbmtHSQhbeaKDZ3OsFAAQXgRQAwFI0+1KfVgfU4g+uoOPdd9+Vs88+u041QC2uoJXtfBWMbfhCK+fNnDlTRo8e3WyA49l1sP42iouLTVc+AIA1MEYKAGApc+bMqTNGSUupf/jhhzJu3Dh39kf/1s9wPfnkk+4xVL4IxjZ8cfLJJ5tt3nXXXV7nePIM3NLS0rwGcroN3S86Tqw+XV+3AwBoW2SkAACWoqXDx48fX6f8udKy4y5HHnmk/Oc//zHd8fr372+CDM366FxQvgrGNnyhZcu1ZLmOx1q8eLEJCLXcuWbetIjE448/LieeeKJZVwtQaAl2LSOvhS+0S6CWkb/hhhvko48+Mm0+55xzzHpaxn3JkiUms6al2+uPSwMAtC4CKQCApWjgoWOWNHBav369CXJ0DqbBgwe719HgQzNKOu5Iu+NptzkNgjQA81UwtuGr5557zgQ/Or/WLbfcIvHx8WYCXp3MWJ/XRee50omCH3zwQSkqKjL7QgMp7dao82vpXFUafL3++utmsmMdG6X7yVX4AgDQdmK0BnobPh8AAE2OEbr88svNZLUAAFgZY6QAAAAAwE8EUgAAAADgJwIpAAAAAPATxSYAAJbBsF0AQLggIwUAAAAAfiKQAgAAAAA/EUgBAAAAgJ8IpAAAAADATwRSAAAAAOAnAikAAAAA8BOBFAAAAAD4iUAKAAAAAMQ//w/MvGnT0oCynwAAAABJRU5ErkJggg==", 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" ] @@ -1756,11 +1631,12 @@ "\n", " pc, df = run_standard_simulation(main)\n", " analytic_grad = p.analytical_gradient(0)\n", + " epsilon = 0.2\n", " success_rate, _, _ = compute_success_rate(\n", " df,\n", " analytic_derivatives={\"x\": analytic_grad},\n", " p=p,\n", - " tolerance=0.5 * analytic_grad,\n", + " tolerance=epsilon,\n", " )\n", " success_rates.append(success_rate)\n", " print(f\"m={m_val}: Success rate = {success_rate:.2%}\")\n", @@ -1774,8 +1650,8 @@ " plt.grid(True, alpha=0.3)\n", " plt.ylim([0, 1.05])\n", " ax = plt.gca()\n", - " ax.axvspan(0.5, 4.0, color=\"green\", alpha=0.15, label=\"Target m range\")\n", - " ax.legend()\n", + " theoretical_range = (0.62, 3.2)\n", + " ax.axvspan(theoretical_range[0], theoretical_range[1], color=\"green\", alpha=0.15)\n", " plt.show()\n", " return success_rates\n", "\n", @@ -1784,16 +1660,18 @@ "m_values = [\n", " 0.05,\n", " 0.1,\n", - " 0.3,\n", + " 0.33,\n", " 0.5,\n", - " 0.55,\n", - " 0.7,\n", - " 0.8,\n", - " 0.9,\n", + " 0.67,\n", " 1.0,\n", - " 1.5,\n", + " 1.33,\n", + " 1.67,\n", " 2.0,\n", + " 2.33,\n", + " 2.67,\n", " 3.0,\n", + " 3.33,\n", + " 3.67,\n", " 4.0,\n", " 6.0,\n", " 10.0,\n", @@ -1803,36 +1681,36 @@ }, { "cell_type": "markdown", - "id": "56", + "id": "47", "metadata": {}, "source": [ - "As for the $l$ parameter, we need to be in the linear regime, so we need to ensure $l$ is small enough, as can be seen in the next example:" + "Next, we plot success rate versus $l$ with $m=2$. The valid bound $l\\leq 0.28$ is highlighted." ] }, { "cell_type": "code", - "execution_count": 18, - "id": "57", + "execution_count": 10, + "id": "48", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "l=0.1: Success rate = 94.34%\n", - "l=0.2: Success rate = 78.96%\n", - "l=0.3: Success rate = 59.67%\n", - "l=0.4: Success rate = 39.31%\n", - "l=0.5: Success rate = 22.80%\n", - "l=1: Success rate = 10.60%\n", - "l=1.5: Success rate = 14.79%\n", - "l=2.0: Success rate = 14.55%\n", - "l=3.0: Success rate = 26.12%\n" + "l=0.1: Success rate = 94.68%\n", + "l=0.2: Success rate = 78.03%\n", + "l=0.3: Success rate = 59.18%\n", + "l=0.4: Success rate = 38.82%\n", + "l=0.5: Success rate = 25.34%\n", + "l=1: Success rate = 10.06%\n", + "l=1.5: Success rate = 16.46%\n", + "l=2.0: Success rate = 12.26%\n", + "l=3.0: Success rate = 26.03%\n" ] }, { "data": { - "image/png": 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", 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" ] @@ -1885,6 +1763,10 @@ " plt.title(\"Success Rate vs l Parameter\", fontsize=14)\n", " plt.grid(True, alpha=0.3)\n", " plt.ylim([0, 1.05])\n", + " ax = plt.gca()\n", + " theoretical_range = (0, 0.28)\n", + " ax.axvspan(theoretical_range[0], theoretical_range[1], color=\"green\", alpha=0.15)\n", + "\n", " plt.show()\n", "\n", " return success_rates\n", @@ -1899,26 +1781,24 @@ }, { "cell_type": "markdown", - "id": "58", + "id": "49", "metadata": {}, "source": [ - "# 5. Multi-Coordinates Examples" + "# 4. Multi-Dimensional Examples" ] }, { "cell_type": "markdown", - "id": "59", + "id": "50", "metadata": {}, "source": [ - "This algorithm works in multiple dimensions too.\\\n", - "We will now see an example in 2D, f(x,y).\\\n", - "We will start with a linear and decoupled function $f(x,y)=ax+by+c$." + "The algorithm extends to multiple dimensions. We demonstrate with a 2D example using a linear, decoupled function $f(x,y)=ax+by+c$." ] }, { "cell_type": "code", "execution_count": 19, - "id": "60", + "id": "51", "metadata": {}, "outputs": [ { @@ -1986,16 +1866,16 @@ }, { "cell_type": "markdown", - "id": "61", + "id": "52", "metadata": {}, "source": [ - "We can also have more complex example, with non-linear and coupled equation: $f(x, y)=ax^2+by^2+cxy+dx+ey+f$." + "We can also demonstrate a more complex case with non-linear and coupled terms: $f(x, y)=ax^2+by^2+cxy+dx+ey+f$." ] }, { "cell_type": "code", "execution_count": 20, - "id": "62", + "id": "53", "metadata": {}, "outputs": [ { @@ -2081,20 +1961,99 @@ }, { "cell_type": "markdown", - "id": "63", + "id": "54", + "metadata": {}, + "source": [ + "# 5. Summary and Discussion\n", + "\n", + "This notebook demonstrated Jordan's quantum gradient estimation algorithm, which estimates $\\nabla f$ at the origin using a **single query** to $f$, compared to the classical lower bound of $d+1$ queries.\n", + "\n", + "## Algorithm\n", + "\n", + "1. Prepare a uniform superposition over $N = 2^n$ sample points using Hadamard gates.\n", + "2. Encode $f$ as phases, either via phase kickback from a state oracle or directly using a phase oracle.\n", + "3. Apply the inverse QFT to map the phase encoding onto a measurable computational basis state containing $\\nabla f$.\n", + "\n", + "## Parameter Selection\n", + "\n", + "| Parameter | Role | Constraint |\n", + "|---|---|---|\n", + "| $l$ | Sampling interval | $l \\leq \\frac{2\\sqrt{3}\\epsilon}{D_2\\sqrt{d}}$ — keeps $f$ approximately linear |\n", + "| $m$ | Gradient range | $2\\nabla f_{\\max} \\leq m \\leq 2N\\epsilon$ |\n", + "| $n$ | Qubits / resolution | $n \\geq \\log_2(\\nabla f_{\\max} / \\epsilon)$ |\n", + "\n", + "## Potential Use Cases\n", + "\n", + "The $d+1 \\to 1$ query reduction is most valuable when $d$ is large and each function evaluation is expensive.\n", + "\n", + "Potential applications include: Optimization, Root-finding, Functional minimization and PDEs and more.\n", + "\n", + "## Limitation: Higher-Order Derivatives\n", + "\n", + "The algorithm **cannot be applied recursively** to compute second or higher-order derivatives of $f$.\n", + "\n", + "The method requires a quantum oracle that evaluates $f(x)$ coherently as a phase across all $x$ simultaneously. After running the circuit and measuring, the output is a single classical value $\\nabla f(0)$ — not a new quantum oracle for $\\nabla f(x)$ at arbitrary points $x$. Estimating $\\nabla^2 f$ by this approach would require such an oracle for $\\nabla f$, which the algorithm does not construct.\n", + "\n", + "In classical finite differences, second derivatives are obtained by calling $f$ at multiple points and differencing the first-derivative estimates. Replicating this quantumly would require separate oracle queries for each evaluation point, reducing the query complexity back to the classical $O(d^2)$ regime and eliminating the quantum advantage entirely." + ] + }, + { + "cell_type": "markdown", + "id": "55", + "metadata": {}, + "source": [ + "# Appendices\n", + "## Appendix 1 - Phase Kickback\n", + "\n", + "We start with the state $|\\delta\\rangle|0\\rangle$ where $|\\delta\\rangle$ is a superposition created by the Hadamard gate for all the coordinates, hence:\n", + "$$\\sum_{\\delta_1=0}^{N-1}\\cdots\\sum_{\\delta_d=0}^{N-1}|\\delta_1\\rangle\\cdots|\\delta_d\\rangle$$\n", + "For convenience we will look at the $d=1$ case, but the same procedure can be used for bigger $d$.\n", + "\n", + "The ancilla starts at the ground state $|a\\rangle=|0\\rangle$.\n", + "We first apply bitwise X gate to create the state $|111\\cdots1\\rangle$, which in the signed fractional QNum representation corresponds to the value $-1/N_0$.\n", + "\n", + "Next, we apply QFT on the ancilla. Using the fact that $e^{i2\\pi a} = 1$ for integer $a$, the QFT of $|N_0-1\\rangle$ simplifies to:\n", + "$$ \\frac{1}{\\sqrt{N_0}}\\sum_{a=0}^{N_0-1}e^{i2\\pi a(N_0-1)/N_0}|a\\rangle = \\frac{1}{\\sqrt{N_0}}\\sum_{a=0}^{N_0-1}e^{-i2\\pi a/N_0}|a\\rangle $$\n", + "\n", + "The full state after both Hadamard (on coordinates) and QFT (on ancilla) is:\n", + "$$\\frac{1}{\\sqrt{N \\cdot N_0}}\\sum_{\\delta=0}^{N-1}\\sum_{a=0}^{N_0-1} e^{-i2\\pi a/N_0}\\,|\\delta\\rangle|a\\rangle$$\n", + "\n", + "As discussed before, we assume that we have an oracle $f$ that applies the function on the state $|x\\rangle \\rightarrow |f(x)\\rangle$.\n", + "We apply this function and add the normalized result $f_\\mathrm{norm}(\\delta) = \\frac{N}{ml}f\\!\\left(\\frac{l}{N}\\delta\\right)$ to the ancilla register, mapping $|a\\rangle \\to |a + f_\\mathrm{norm}(\\delta)\\rangle$:\n", + "\n", + "$$\\frac{1}{\\sqrt{N \\cdot N_0}}\\sum_{\\delta,\\,a} e^{-i2\\pi a/N_0}\\,|\\delta\\rangle\\,|a + f_\\mathrm{norm}(\\delta)\\rangle$$\n", + "\n", + "Substituting $a' = a + f_\\mathrm{norm}(\\delta)$, i.e. $a = a' - f_\\mathrm{norm}(\\delta)$:\n", + "\n", + "$$\\frac{1}{\\sqrt{N \\cdot N_0}}\\sum_{\\delta,\\,a'} e^{-i2\\pi (a' - f_\\mathrm{norm}(\\delta))/N_0}\\,|\\delta\\rangle\\,|a'\\rangle$$\n", + "\n", + "Separating the phase into two factors:\n", + "\n", + "$$= \\frac{1}{\\sqrt{N}}\\sum_{\\delta=0}^{N-1} e^{i2\\pi f_\\mathrm{norm}(\\delta)/N_0}\\,|\\delta\\rangle \\;\\otimes\\; \\underbrace{\\frac{1}{\\sqrt{N_0}}\\sum_{a'=0}^{N_0-1} e^{-i2\\pi a'/N_0}\\,|a'\\rangle}_{\\text{original ancilla state}}$$\n", + "\n", + "The ancilla returns to its pre-oracle state and the function value has been \"kicked back\" as a phase onto the coordinate register.\n", + "Since the ancilla is a fractional QNum with $n_0$ fractional bits, dividing by $N_0$ converts from the integer index back to the fractional value, so $f_\\mathrm{norm}(\\delta)/N_0 \\to f_\\mathrm{norm}(\\delta)$ in the fractional encoding.\n", + "The coordinate register is therefore left in the state:\n", + "\n", + "$$\\sum_{\\delta=0}^{N-1} e^{i2\\pi f_\\mathrm{norm}(\\delta)}\\,|\\delta\\rangle = \\sum_{\\delta=0}^{N-1} e^{i2\\pi \\frac{N}{ml} f\\!\\left(\\frac{l}{N}\\delta\\right)}\\,|\\delta\\rangle$$\n", + "\n", + "This is exactly the desired phase state from Step 2 of the algorithm, and the rest of the algorithm proceeds identically to the Direct Phase approach.\n" + ] + }, + { + "cell_type": "markdown", + "id": "56", "metadata": {}, "source": [ "# References" ] }, { - "cell_type": "code", - "execution_count": 21, - "id": "64", + "cell_type": "markdown", + "id": "57", "metadata": {}, - "outputs": [], "source": [ - "# TODO: add" + "[1]: [Stephen P. Jordan. Fast Quantum Algorithm for Numerical Gradient Estimation. Physical Review Letters 95 (2005)](https://www.researchgate.net/publication/7669221_Fast_Quantum_Algorithm_for_Numerical_Gradient_Estimation)" ] } ], diff --git a/algorithms/gradient_estimation/gradient_estimation_helpers.py b/algorithms/gradient_estimation/gradient_estimation_helpers.py index 1d1a79bbd..902599301 100644 --- a/algorithms/gradient_estimation/gradient_estimation_helpers.py +++ b/algorithms/gradient_estimation/gradient_estimation_helpers.py @@ -120,17 +120,10 @@ def run_statevector_simulation( print("Circuit Depth:", qprog.transpiled_circuit.depth) print("Gate Counts:", qprog.transpiled_circuit.count_ops) - backend_preferences = ClassiqBackendPreferences( - backend_name="simulator_statevector" - ) - execution_preferences = ExecutionPreferences( - num_shots=1, backend_preferences=backend_preferences - ) - with ExecutionSession(qprog, execution_preferences=execution_preferences) as es: - if filter_ancilla: - es.set_measured_state_filter("ancilla", lambda v: v == 0) - results_statevector = es.sample() - df = results_statevector.dataframe + sv = calculate_state_vector(qprog) + df = sv[sv.ancilla == 0] + df.sort_values(by="x", inplace=True) + return df diff --git a/algorithms/gradient_estimation/step_2.png b/algorithms/gradient_estimation/step_2.png index 12c484ef049f75cc80d8da1df4c82333ac222c00..a0869baf793093ea8e048fd235732065b8c36cf0 100644 GIT binary patch literal 53466 zcmeFZgfOub;-9JrQdZ~|#`|fJ65pS>_iQ8HY zGquiFO{1V@@Mdj}G?)^je)(~i61??QmQ&%u&%GVW^~;ZIlPJdRtt)(MMn|iDRIR^;GJoEYHiz1QEA zke!(vn2#=lrXu`u$Z*-X=hIhgN~O=AV|TQ*kx-xc+JYVK&!wf@tgLpKFghzHnHL2) zIXQQX;p^)-?WP^k!%ShqMvvp4`6optaAhdR9Y|oZQGpia2{woqUb3pp+ z3X(Fx*CQy|xLD4vN;orCP#81T6UQ@Ghxs%@<=mN@Oko9x=rv@2#zO#yX_n zH-OazJ?ndL<}Tsb@}%K=a-_-X|6}HIFMu@}#TUOmGdF>V|GV}7oAv)QnE!Lr|35^S z9u}yHscHJMFpKB|e|4J6f2T&DFHFj+s;>%tqxa;fw5>GH1lyY-2tB<7Ovdr>s7Y_Y ziHy_YcPRd!z-y(DTv|GKnM>PbU|^sWxo#BFWJF4DMW{7OcIHBP_s{jJsHhmu&d#c< ztItV8`eF1Rcw9suh^viWI`d6lR)i)wgZjOg>m@ArqLJ$n2?;>XXwNt!UWE5ez_IVVn^DFmoH(9IttynM2nTyC<{;dcqRv$@L-{2%}E1W zaC&{}pbcrxYh(II2h;*olSLF8@8#K3OX9(KVONlXFgQ|7Vw@wD%-ioFr+Ng)%- z?$@z#(;TkjFsKI-Rnsn-kkT(Y+;+Hj#@-6>u~Q`XQ>8oEs8Fbv-HZ z?>0iOC5@62feWOho1VQu0q%D(m&4LMVbK}et#v;-8_i_`DLxY~f}S2R}} z|Kw3~F2&g8eQcxbdwl`gvcIMsk-^|yhErc(_xQp^8%PE13wfSylgavhId_EkS=XXP zz(-Qzc{n$O&`!z~`1SP&JUu%RL0`wvqJ@hZ67zo-=G!wgM+sXJlqpmZqe|#Vud-aSFw2{E$gTE7@AnEob z^npZ?Ep3Yk+pWcZHYPCnvJ!anZ5#b(C%@nUsJWjnWaj2>N5pZq@`3 z+{KbIYu_aCNeMf>Y`;V?|@lK-0KKFV+>@tXa{A{7#SaT8RVn-4sn+3uAY?YAXS^*cP~ik?dQIH z%>Q)I{%L=X#(>2;ggVl3P~Xi;=V@+j0NSD7-NsPk!t-NuDh&|S>0-UzmtcutTb zFimW_`n}?g*NOYMR%B&+d8cxQYKG#rV{}nrVXThcnaEv9iB%avrYFzWkQgD9lAjd#5b?*%Z^m%kUQCzIXEays*2sAJv_s5k{gp zIQ1fk8w!^4s`3!{O$VUAjcaVdH|G`qFWFY&VhPjC*oBXRK$vbX87PW3yR}p|O7b#s zk@V5X0`o0J_lZGj0lRm49@_(=y%36TPxEWch=tMKddNw?JLWy`QQOaiI@=Hu4)S6W z9V?mtPAvuZg~EklS3)Sbccy%WA6-DnuqRX%LgOw94iE`_eL+S)NqmkQ!f`2vlJJ5` zMwsY9=J9Ur>2_Yh4dZ49%7-g|S4wbuC|X#anXrNuDbl(LC-pDL>PfkRl?uzA$+u_@ z3bSoz_z<8=c!_=1>1v6P%Z7dkLqAl4Eer1oGwDK zjYC;MR4k&(>6txy!PrPi*cEoQ*h;ym(w{csod4xrL<}6Ub+G}bxBeEh3$3v6#)G)| z`&mhSs*0&;E2md(-gWP3a^G1VF73QCy7yB(@FIs^&Hh}RQwy#0o+xb#y;pVa$7X6P zrMo(R*J7peR33pJVzpsoP-xjochG% z0|UmHN(R(7gT(0F(LSAVeBEsE{VI0f3Jgn6PYy>{tJbVP2M{X}UbRyDdm*QxC~Rqz z=HyDUGo-(jUdHkg1;rtZv$^mq8StHt^NDUFib5-2C+Kj9+b;?{XbbOPo#fiFcp4v<)+u1zJAc_kk%W1uvwYg~W-D%=wnny+1G z610o#*(J1rF!~l&JS=Qj@_|O67xtdAt@o}EA!N@aY6)!QZ5TC5Q>8w*(M}={6oMJP z?nI4{Bo;w!D4$=*J@%U7ef_%UNt@zueNt`4Df6+cn?XYKiqce?X?1b&UwITEM1pX*rc?Tb0OV*; 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00:00:00 2001 From: Ofri Wienner Date: Sat, 23 May 2026 20:10:05 +0300 Subject: [PATCH 05/12] . --- .../gradient_estimation.ipynb | 70 +++++++++---------- 1 file changed, 34 insertions(+), 36 deletions(-) diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index c0d0b0be6..d84443312 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -10,7 +10,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "id": "1", "metadata": {}, "outputs": [], @@ -253,7 +253,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "13", "metadata": {}, "outputs": [ @@ -277,8 +277,8 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/70ff34e5-b32e-4658-875a-73457dbeccd0\n", - "/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_97551/4002175823.py:45: SettingWithCopyWarning: \n", + "Job: https://platform.classiq.io/jobs/bc01c9ad-e05a-4ddb-a88c-644e8c0e92dc\n", + "/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_20289/391621480.py:44: SettingWithCopyWarning: \n", "A value is trying to be set on a copy of a slice from a DataFrame\n", "\n", "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n", @@ -330,7 +330,7 @@ "type": "string" } ], - "ref": "9b937272-abe5-440b-bb6f-ad57c87c919b", + "ref": "e4bd39e9-673b-46c4-b876-faa8f2bbb171", "rows": [ [ "63", @@ -543,7 +543,7 @@ "30 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000011" ] }, - "execution_count": 4, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -609,7 +609,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "id": "15", "metadata": {}, "outputs": [ @@ -643,7 +643,7 @@ "type": "float" } ], - "ref": "9aee00ed-df27-490c-9aa0-69335bcfdfeb", + "ref": "017a0fff-d15e-4505-8b12-d278db9ef785", "rows": [ [ "-4", @@ -777,7 +777,7 @@ " 3 0.75 0.75" ] }, - "execution_count": 5, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -828,28 +828,26 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "id": "18", "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit Width: 8\n", - "Circuit Depth: 42\n", - "Gate Counts: {'u': 31, 'cx': 27}\n" + "ename": "KeyboardInterrupt", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mKeyboardInterrupt\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[4]\u001b[39m\u001b[32m, line 29\u001b[39m\n\u001b[32m 23\u001b[39m inplace_add(val, ancilla)\n\u001b[32m 25\u001b[39m \u001b[38;5;66;03m# 2. Next step in the algorithm: QFT inverse on the coordinates register\u001b[39;00m\n\u001b[32m 26\u001b[39m \u001b[38;5;66;03m# invert(lambda: qft(x))\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m29\u001b[39m df = \u001b[43mrun_statevector_simulation\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmain\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprint_circuit_info\u001b[49m\u001b[43m=\u001b[49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfilter_ancilla\u001b[49m\u001b[43m=\u001b[49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[32m 30\u001b[39m simplified_df = simplify_df(df)\n\u001b[32m 31\u001b[39m plot_simplified_df(simplified_df)\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/GoogleDrive-ofriwi1@gmail.com/My Drive/Documents/Work/1. Classiq/classiq-library/classiq-library/algorithms/gradient_estimation/gradient_estimation_helpers.py:115\u001b[39m, in \u001b[36mrun_statevector_simulation\u001b[39m\u001b[34m(qfunc_to_run, print_circuit_info, filter_ancilla, show_circuit)\u001b[39m\n\u001b[32m 111\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mrun_statevector_simulation\u001b[39m(\n\u001b[32m 112\u001b[39m qfunc_to_run, print_circuit_info=\u001b[38;5;28;01mFalse\u001b[39;00m, filter_ancilla=\u001b[38;5;28;01mFalse\u001b[39;00m, show_circuit=\u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[32m 113\u001b[39m ):\n\u001b[32m 114\u001b[39m \u001b[38;5;66;03m# Run a statevector simulator\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m115\u001b[39m qprog = \u001b[43msynthesize\u001b[49m\u001b[43m(\u001b[49m\u001b[43mqfunc_to_run\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 116\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m show_circuit:\n\u001b[32m 117\u001b[39m show(qprog)\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/classiq/synthesis.py:101\u001b[39m, in \u001b[36msynthesize\u001b[39m\u001b[34m(model, auto_show, constraints, preferences)\u001b[39m\n\u001b[32m 97\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m constraints \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[32m 98\u001b[39m serialized_model = set_constraints(\n\u001b[32m 99\u001b[39m serialized_model, constraints=constraints\n\u001b[32m 100\u001b[39m )\n\u001b[32m--> \u001b[39m\u001b[32m101\u001b[39m result = \u001b[43masync_utils\u001b[49m\u001b[43m.\u001b[49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43msynthesize_async\u001b[49m\u001b[43m(\u001b[49m\u001b[43mserialized_model\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 102\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m auto_show:\n\u001b[32m 103\u001b[39m show(result)\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/classiq/_internals/async_utils.py:40\u001b[39m, in \u001b[36mrun\u001b[39m\u001b[34m(coro)\u001b[39m\n\u001b[32m 38\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m:\n\u001b[32m 39\u001b[39m loop = _get_or_create_run_loop()\n\u001b[32m---> \u001b[39m\u001b[32m40\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mloop\u001b[49m\u001b[43m.\u001b[49m\u001b[43mrun_until_complete\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcoro\u001b[49m\u001b[43m)\u001b[49m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/nest_asyncio.py:92\u001b[39m, in \u001b[36m_patch_loop..run_until_complete\u001b[39m\u001b[34m(self, future)\u001b[39m\n\u001b[32m 90\u001b[39m f._log_destroy_pending = \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[32m 91\u001b[39m \u001b[38;5;28;01mwhile\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m f.done():\n\u001b[32m---> \u001b[39m\u001b[32m92\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_run_once\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 93\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m._stopping:\n\u001b[32m 94\u001b[39m \u001b[38;5;28;01mbreak\u001b[39;00m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/nest_asyncio.py:115\u001b[39m, in \u001b[36m_patch_loop.._run_once\u001b[39m\u001b[34m(self)\u001b[39m\n\u001b[32m 108\u001b[39m heappop(scheduled)\n\u001b[32m 110\u001b[39m timeout = (\n\u001b[32m 111\u001b[39m \u001b[32m0\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m ready \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;28mself\u001b[39m._stopping\n\u001b[32m 112\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;28mmin\u001b[39m(\u001b[38;5;28mmax\u001b[39m(\n\u001b[32m 113\u001b[39m scheduled[\u001b[32m0\u001b[39m]._when - \u001b[38;5;28mself\u001b[39m.time(), \u001b[32m0\u001b[39m), \u001b[32m86400\u001b[39m) \u001b[38;5;28;01mif\u001b[39;00m scheduled\n\u001b[32m 114\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[32m--> \u001b[39m\u001b[32m115\u001b[39m event_list = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_selector\u001b[49m\u001b[43m.\u001b[49m\u001b[43mselect\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtimeout\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 116\u001b[39m \u001b[38;5;28mself\u001b[39m._process_events(event_list)\n\u001b[32m 118\u001b[39m end_time = \u001b[38;5;28mself\u001b[39m.time() + \u001b[38;5;28mself\u001b[39m._clock_resolution\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/selectors.py:566\u001b[39m, in \u001b[36mKqueueSelector.select\u001b[39m\u001b[34m(self, timeout)\u001b[39m\n\u001b[32m 564\u001b[39m ready = []\n\u001b[32m 565\u001b[39m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[32m--> \u001b[39m\u001b[32m566\u001b[39m kev_list = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_selector\u001b[49m\u001b[43m.\u001b[49m\u001b[43mcontrol\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmax_ev\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimeout\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 567\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mInterruptedError\u001b[39;00m:\n\u001b[32m 568\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m ready\n", + "\u001b[31mKeyboardInterrupt\u001b[39m: " ] - }, - { - "data": { - "image/png": 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0wG+//Ya7777bKyjMDoMzBlbffvutOTEIGj9+vPv2w4cPY/jw4fj1119N9pDvKzfccIPPq3IwILvrrrtM1pGlTl7OC/4NDz30kAlc69ati1tuucXMPUi8rmPHjmbOTQZ68+fPR/fu3c1UNgzk+Jh8bD4uTyxTZ7Zs2TL06tXLBLKrVq0yQS6fXzuwtDHIY0aVzz9ft3vvvRfr16/P098iwaGJhUVEonxy7VDzdTJvllm5nyxDZoXXM8u0Z88ed4n0qquuwoMPPujehtkmT2+//Tbq1auH5557zlzm+dWrV2Ps2LE57gsDMwYvzDxR3759TeBm/x6bGTy9//77KFu2rHmOfRm/V7p0aZM9s0udecVgrlu3bub8mDFjTCaN5en69evj3//+twmy/vOf/7i35+02PiYfO6fHffHFF01QaAfJDBr5t/F5ZJbPdu2115pAjh555BG89NJLmD17tnmeJbyUuhARkbDyNaNHDFxywmzRxRdf7HVd69atc71flhPtYM5efspeisoOPpkVq1mzpin3cntKSkpCKDRt2tRr38jePztDdz7Wrl2L9u3be13Hy/y77UmrM+8Hg3YGiZ7Pk4SPMnQSlfht23PpL5VdJdbww5b/++FY+svXgfa1a9c22zKYYPkyM17P8WDMhNmKFSuGYGDp2BP3y7OcyhImu2/fffdd043L25iZY2PG+eDjZA5os1opwXP/7OfX3r/M5epgyu15kvBRhk5EJArxg9ZuWgj1ydeAjs0FV199tSkVHj161Ou2Xbt2YeLEiWaKkbx0YrL0x3FunpYuXYrzwelTmPl77LHHTCbMLgUHAoNVjmuzMSPG+eryglkzloezw5KrZ5YtK/yb2FjhiZdZemUnsUQ+BXQiIhI2r7/+Oo4fP266MtkByjnp2FHKQK9y5cq5jn3LjE0Q69atM+O7ONfcZ5995h7Y7+8UHcwSMvhkRyfHrf3000+mQSIQOCaQzwGbDBiI3nPPPedkwXIzcuRIE7RybNvvv/9u/v4333wTe/fuNbezPLx48WIz3pDXZZVR47hEBoXsIubzxs5g7hfH7okzKKATEZGw4fQiDGQ4No1dlrVq1TLTkXCKDnZsspkgL2rUqIEpU6aYLlJmrhjY2F2unI7DH8w6Tpo0yXSCssz6wAMPuJsuzhe7Rtl1etlll+HWW281AZS9SL2vmEXjtC/s6uV4QXa1fvXVV+65+XifzLKxBM+MYFbj/i666CIT/PLv5N/4xBNP4Mknn/RqiJDIls+Vl9GoDpeWlmbmFzp48KDmJ4tyGkMnsYbj2ThlBwMajmkLtpzG0EUaZvk4WTGzf+LM/+GUlDRUqVICyckHkZio+UWzoqYIERGJKhyTx05Xlkk5DozZtCFDhoR7t0SCSgGdiIhEFTYWPP3002biYk4uzvFhHGcmEs0U0EnUuvDCC8O9CyJRLVKnA+JktzyJxBIFdBK1HzT2xJ8iEngcM+dvk4GIBF5kfr0SEREREZ8poBMRERFxOJVcJWqnLeGyQfYM6JE61kfEqZw0bYlILFBAJ1ErhqZYFBGRGKe0hYiIiIjDKaATEZGINWfOHFPOPXDgAJyE+zxt2rSA3R+79l9++WUE0xVXXIH7778/qI8hwaOATkRE3E6fcWHhpn34auV285OXgxn05HQaPXp0xL8y3MfmzZufc/3OnTtxzTXXhGWfJDZpDJ2IiBjTV+/EmG/WYOdBq9mBKpYojFHdG6Jr44oBf5YY9NgmT55sFoRfv3691+Tgv/76a1henRMnTiAuLs7v369QoUJA90ckN8rQiYiICebu/WS5VzBHuw4eM9fz9kBj0GOfSpQoYbJyntd5rvaybNkytGrVCkWLFkW7du28Aj/66quvcNFFF5mO25o1a2LMmDE4deqU+/akpCRcf/315j6LFy+OXr16ITU19ZxM23//+1+vxeFZ6r3zzjtRtmxZ83tXXXUVfvvtN3PbBx98YB6Hl+2sIq/LquSakpKCW265BaVLl0axYsXM37J48WJz26ZNm8y+lS9f3uwf16H98ccffX4eZ8yYYfY3c1l62LBhZn9p37595vErV65snsMmTZrg//7v//JcNi5ZsqT7b6Tk5GTzXPJ6/m38O7Zu3epVMm/durX5m7lN+/btsW3bNp//NvGdAjqJWnzT4klEcsayKjNzWRVX7et4e+byK6cDCtWUQI8++iheeOEFk7ErUKAAbr/9dvdtP//8M/r162cCmDVr1uDtt982QcfYsWPd0xgx0ODarnPnzsXMmTOxefNm9O7d2+sxNm7ciC+++AJffvklVq5caa67+eabsXv3bnz//fcmqGTQ2LFjR3Nf/H2uE9uoUSOTbeQp833SoUOH0KFDB2zfvh1ff/21CQD/+c9/mv2yb7/22msxa9YsrFixAl27dkX37t1NEOoL7g+DJe677fTp0ybr2adPH3OZU8y0bNkS3333HVavXo1Bgwahb9++WLJkCfx18uRJdOnSBfHx8eY1+OWXX0xAyv1nhpMBdY8ePczf/vvvv2PhwoXmcTXFTXCo5CpRiR8y/JYuIrlbsmX/OZk5TwzjeDu3a1srISxLfzE4Y2BAI0aMQLdu3UyQwswUs2S8rn///uZ2HvtPPfWUCZpGjRplAqVVq1Zhy5YtqFKlitnmo48+MoHY0qVLTUaMGITwembjaP78+SbgYUBn/63PP/+8yVpNmTLFBCcMYBhg5lRi/fTTT7Fnzx7zWMxiUe3atd23N2vWzJxs3PepU6ea4G/IkCG5Pjf58+fH3//+d/M4d9xxh7mOfzMzdjfeeKO5zMzcQw895P6d++67Dz/88AM+++wzk0HzBwNGBqXMatpB2oQJE0xwycwcs5AHDx7E3/72N9SqVcs9L6gEhwI6EZEYtzv9WEC3C4amTZu6z1esaI3nY6BVtWpVk/FidsjOyNkZKgZ8R44cMZOMM5Czgzlq2LChCTx4mx3QVatWzR3MEe+X2bOEBCuItR09etSUSX3FbF+LFi3cwVxmfAyWfJk9Y5aPmS0+hq8ZOmIm7pJLLsGOHTtQqVIlTJw40QS9/Bvt5+OZZ54xARwzhQxejx8/fl5VDD4/zGoyQ+eJzzufn86dO2PAgAEmi3f11VejU6dOpjxrv34SWAroRERiXLn4wgHdLhgKFizoPm9ngzxLlszS9ezZ85zfs8fC+YLjvDzxfhl8MNuUmR0o+aJIkSI53s7MGcvAzP4xc8ftb7rpJhN0+YpBKbNgkyZNwr333msyfJ5j3Z577jm88sorZuoTjp/j38opSnJ6DD7PmSdoZ5nV8/lhGZfBY2Z2YMyM3dChQzF9+nST0XvsscfM38rgU2I0oHvzzTfNyR5syVQ5O6LUFi5Z4Ru9PWi6Xr16WvpLJAeta5Q23axsgMhqHB3DpwolCpvtInHpL45r4/HuWcb0xDIfB+/zZGfpONaOJUlm6nK63127dpmSKueBywo7YZn9yi27yLIkx91llaVjdpGZrBtuuMEdKHk2FuQlS8fgKjEx0bznMUPn+RgcR3jbbbe53yP//PPPHP9+BmWencgbNmwwGU/P54dBWrly5UzDSHaYneRp5MiRaNu2rSkNK6CL4aYI/oOOHz/eDErloFh27vCf848//gj3rkmE4ptsbm+0IgLkvyCfmZqEModl9mXezu0iEb/cc+wbs3T8TGAZlZkqZoOIpT5mpRjwLF++3IyLYxMFx+RxnFd2+HsMQDiwn52kDLIWLFhgGjTs6VQY6HFsHsuqe/fuNWXMzNhdyjF2vB8GVmzIYAMDmwSoTp067kYMljFvvfVWd/YxL+y/j6VnZvg8xzjyMZgZ4/7z+bn77ru9unyzws/Z119/3TRq8O+95557vDKlfLwyZcqYz2I2RfB5YDaTGTl29fIygzj+nexs5XPIoFDj6GI8oGPHD7uA+E9Zt25d8w/LwaiLFi0K966JiDge55l787aLTCbOEy/z+mDMQxcoHKP17bffmoCBpUdmf1566SUzJo6YPeS0JqVKlcLll19uAjU2TjC7lBP+3v/+9z/zOwMHDjSfPWw+YHDCKUaITQfs6rzyyitNRiurqUCYxeO+MZPFzzEGl0xQsJmBXnzxRbNvnI6Fn3X8e5j9yitmKNngwI5Su7vVxuCW98n75ooQdoCZE3YVM6N52WWXmSCTpWHPMXc8P2/ePDOOkeVuBmpsymDmlhk73r5u3TrzHPG5YxPJ4MGDTTApgZfP5cAVzJl1+fzzz01HE785ZJcy5jclz29LaWlp5p+TXTc5pYfF+fjtliUV4v9HqKZWEAkXfogyI+I5h5o/ODUJu1nZAMExcyyzZpWZi6SSq0T//3BKCj+/SyA5+SASE/X57egxdMS2c6a/+aIzO8dBnznV/8eNG2dS8CIi4hsGb/bUJCLiHI5KW3BwO8cYcHZtdvEwQ2dnYbLC2j2zcfaJA2JFREREoo2jMnQch2B3MbFVmpM0sg2bs4JnhQNCQznxpYiIiEg4OCqgy2qcVFYdRSK+zP0kIudH4+ZEIodjAjqWTznnHLtp0tPTzTw2bI/m0iUimbEJwl5qRkSCE8ydT/OFiMToGDou8cJ5gziOjgsRs9zKYI7LiYiIiIh4euMNzhPILmygTRtgyRLk6MABYPBgLi3HIVtA3brA//4Hx3BMhu69994L9y6IiIiIA0yeDAwfDrz1lhXMvfwy5ysEuIBQuXLnbs8V0Jgf4m1TpgCVKwPbtnGJNziGYwI6kbyOr+SM5MTJqDUPnUhgcR46ewwzm880nk4iyYsvAnfdBQwcaF1mYPfdd8D77wMjRpy7Pa/fvx9YsIDrBlvXZbPaW8RyTMlVJK+4iLTnQtIiEvigzoFz00uUO3ECWLaMS7dlXMe55Xn57Gpr5/j6a6BtW6vkykVAGjcGnnmGCxnAMRTQiYiIhAmX4br//vvP6z4GDBiQ6zJe0SI9nas+ZZyymuhi714rEDu7OpsbL+/alfX9bt5slVr5exw39/jjXPoMePppOIYCOhERyXDmNLDlZ2DVFOsnLwcRgxGWa7nwe2Zc95O3cRsR4uJQJUpknMaNC8zzcuaMNX7unXc4zy3Quzfw6KNWqdYpNIZOREQsa74Gpj8CpO3IeEaKVwK6Pgs0vC5ozxLX2J40aRJeeukl9/yRXOKR01NxqqpId+LECTPxvQQfF4diw4Itq7UDypQB8ucHUlO9r+flChWyvl92tnLsHH/P1qCBldFjCdcJL68ydCIiYgVzn/XzDuYobad1PW8PkosuusgEdV9++aX7Op5nMNeiRYtzGp64TjcXcGfw16xZM0xhreys06dP44477nDfzqmuuKKQJ85h2rp1axQrVgwlS5ZE+/btsY0tjdmUL1kSZWnUxvNDhgwx15cpUwZd2D4JYPXq1Wa+VK41Xr58efTt2xd7Wf876/Dhw2b6Ld5esWJFvMCaXi5Gjx6N5s2bmxWR+BwVLVoUvXr1MstZZvb888+b+01ISDDZTc8xxB9//DFatWqF+Ph4VKhQAbfeequZDsz2119/oU+fPihbtqx53thMNmHCBPftXDqTj8vnq3Tp0rj++uuxdetWn57TQIqPB4oXzzhlFdDFxVlZtlmzvDNwvMxxcllp3x7YuNHazvbnn1ag54RgjhTQiYjEOpZVmZlDVg0OZ6+bPiKo5dfbb7/dK4B4//33MdBuUfTAYO6jjz7CW2+9hT/++AMPPPAAbrvtNsydO9f6U86cQWJiIj7//HOz1vcTTzyBf/3rX/jss8/M7adOnTIBW4cOHfD7779j4cKFGDRoUJ67dD/88EOTlfvll1/Mvhw4cABXXXWVCUB//fVXTJ8+HampqSYIsj388MNmP7/66ivMmDHDBEHLly/P9bE2btxo9v+bb74x97tixQr84x//8Npm9uzZ2LRpk/nJffvggw/Mycbg7qmnnsJvv/2GadOmmWDMs5T9+OOPm+fr+++/x9q1a/Hmm2+aYNX+XQatDAZ//vln8zczKO3atavJTgbqOQ2k4cOBd9/l6wSsXQvcey8D6oyu1379uGBBxva8nV2uw4ZZgRw7YtkUwSYJx3DFkIMHD/KdyfyU6Hb69GnXn3/+aU48LxLtjh496lqzZo35mWeb57lco4rnfuJ2Z505c8Y8Fk8876/+/fu7rr/+etfu3btdhQoVcm3dutWcChcu7NqzZ4+5jdvQsWPHXEWLFnUtWLDA6z7uuOMO1y233JLtYwwePNh14403mvP79u0znwNz5szJcX88DRs2zNWhQwf3ZZ5v0aKF1zZPPfWUq3Pnzl7XJScnm8dav369Kz093RUXF+f67LPP3LdzX4oUKWLuPzujRo1y5c+f35WSkuK+7vvvv3ddcMEFrp07d7r3uVq1aq5Tp065t7n55ptdvXv3zvZ+ly5davaN+0Xdu3d3DRw4MMttP/74Y1e9evW8Xufjx4+bff/hhx9yfU4D8T+cnGx9fvOnr157zeWqWtXliotzuVq3drkWLcq4jS/n2X8rN/5btWnjchUq5HLVrOlyjR3rcnk8pRFPY+gkKnHeOZYMRMQHh1LzvF2gl/5iqa9bt24mq8SpUHjezhB5ZqqOHDlyzgpBzBJ5lmbfeOMNk+FLSkrC0aNHze0sWxLLhcxMMePE++nUqZPJorFUmRctWdPzwMwXs2PMXGXGzJm9H204y+1Z3BeWhHPD0nNlj4Fjbdu2NZnI9evXm/IpNWrUCPk9BoDx71m1apX78rJly0z5lvvJ8ip/n/gcNWzYEPfeey9uvPFGkzHs3Lmzybi1a9fO/bfxuWeGzhPHOfJv4/aBeE4DbcgQ65SVOXPOvY7l2EWL4FgquYqIxLoLywd2u/MouzKgY8mQ5zM7dOiQ+fndd99h5cqV7hNLhfY4OjZXPPTQQ2YcHcuavJ2lWwZTNpZ2WRZkwDJ58mTUrVsXi85+kvPLYOa59bKaz5JjxTLvW/fu3b32iydOcH755Zcj2Aras+F6BNx20Maxewy2ihcvjokTJ5qlM6dOnWpus58Xjv3jmDeWsHfs2GGW2OTzaP9tDGAz/21//vmnGYuX23MqoaEMnYhIrKvWzupmZQNEluPo8lm3c7sgssdkMRixGw08MZPEVSmYVeJ4raxwfBeDCs8xZswiZcaMHk8jR440GS921F5yySUmU8jmBk8MXjIHTFk1dnzxxReoXr06ChQ496O1Vq1a5j4WL17s7txlpoxBUXZ/i41/L4OsSpUqmcsMlBh4+pLdo3Xr1mHfvn0YP368aawgjvPLjH97//79zemyyy4zY/7YaMG/jUFauXLlTFCYneyeUwkNZegkqpf+4sn+lioi2bggvzU1iZF5IPvZy13HW9udxSwWS248BWq1CJYMOSCfGTfP8qGNJT9mjZhFYhaPgRpLhK+99pq5TBxqwWDlhx9+MMESB/szI2XbsmWLCTiYTWJGilk8vk804BwVgGls4O+z8YLXjxo16pwALyvsKt2/fz9uueUW83jcN+4Ds4PsvGUplllDBkk//fSTuU+WKX1ZlpClbQZZLH2yKWHo0KGmpGmXW3PDAJINHHyeNm/ejK+//to0SHhi8wibNVhaZbPJt99+635O2P3K8jc7W/n4fA7Z0MH9SElJyfU5ldBQQCdRi+tM2mtNikguOM9cr4+A4pnGPTEzx+uzmIcuGEt/MQOUUxaIgQiDNHa7MmBgVo8lWE5TQnfffTd69uyJ3r17m/FqzEx5Zus47QczVhwvxrIguzEZjPH3iJlB3v8///lPXHzxxUhPTzdTjeSG2TNmBxm8cUxZkyZNzLQmnMLDDtqee+45k/liaZbjzC699NJzxuJlpXbt2uZvuvbaa819N23aFP/5z3/gK2beWMpm5y+znMzUMfPmiQEfgzLeN0vEDKhZvrafs3nz5pnAkPvB553BKYN5vla5PacSGvnYGYEYkZaWhhIlSpj5e3J6wxDnY1aO3/KJb2C+fAsWcTJ+uDJTwsDmvJoVODXJtgVWAwTHzLHM6pGZy5yhIz5eOKeoiGZsZOA0Iyz7xvL/cEpKGqpUKYHk5INITNTnd1Y0hk5ERDIweKtxmZ4REYdR2kJERETE4RTQiYiIRHDJNRbKrXL+FNCJiIiIOJzG0EnUym3eKJFoFMo+NzVCSCDFUI9mUCigk6iUl0k3RaKBPW8bJ+YtUqRI0B8v0Et/iXBZN9KXcf8ooBMRiQJcnYDzge3Zs8d8IGqqHnFSZo7B3O7du828fVlNKi25U0AnIhIFmDHjYuicx4uz9Ys4DYM5X1e/kHMpoJOonViYH2zESSqVrZBYwNn+ufSV50L0wTzGuOwTJSYm6hiT88KssjJz50cBnUSto0ePhnsXREKOX15CMbaNAZ0dOPLx9KVJJLw0bYmIiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJy6XCVqqQVeRMeYSKxQQCdRiVMoNGjQINy7IRK1dIyJRBaVXEVEREQcTgGdiIiIiMOp5CpRibPYb9261ZyvXr26ZrEX0TEmEtUU0EnUOnLkSLh3QSSq6RgTiRyOKbmOGzcOF198MeLj41GuXDn06NED69evD/duiYiIiISdYwK6uXPnYvDgwVi0aBFmzpyJkydPonPnzjh8+HC4d01EREQkrBxTcp0+fbrX5Q8++MBk6pYtW4bLL788bPslIiIiEm6OCegyO3jwoPlZunRpvwbM85Td3Eqe2+VE2+b9eciXL585BXtbz+0z/24o9sHlcplTtGzr+TpH87ak496358GTE98jwr2tE477SHmPOHXqFNLS9uS4jTg0oONBc//996N9+/Zo3LhxttsdP37cnGxpaWnm57p163DhhReesz2vY0ekbe3atdn+oxUtWhQ1a9Z0X+Z4vtOnT2e5bZEiRVCrVi335Q0bNpiScVYKFSqEOnXquC9v2rTJ62/wVLBgQdSrV899ecuWLTh69Gi2qyZ4TrTLDtDsBjTzAG7UqJH7clJSEg4dOoTseL4GKSkp7uc5Kw0bNnS/QezYsQMHDhzIdtv69eujQAHrX3TXrl3Yv39/ttvWrVsXcXFx5vzu3buxd+9e9218vT3Vrl0bhQsXNuf37NljTtnha8zXmvbt24fU1NRst+X/jv1/xX3duXNntttWq1bNjAclPgfbt2/PdtsqVaqgRIkS5jyf2+Tk5Gy3rVy5MkqVKmXO8zXbtm1btttWrFgRCQkJ5jyHLthdwVkpX748ypYta87zf2zz5s3ZbsvtuD3xf3fjxo3ZblumTBlUqFDBnOcx8eeff2a7Lb+8VapUyZznsZb5dfVUsmRJJCYmmvM8htesWZPttsWLF0fVqlXdl3PaVu8RFh7Dnu8nPO6d/B6Rmd4jIuc9gp9zfG/I6f9LHDaGzhPH0q1evRqTJk3KtZGCH4T2iR+MIiISGJ4ZHJFgsJMfhQpZX6wle/lcueU6I8yQIUPw1VdfYd68eahRo0aO22aVoWNQ99dff5lv5VlR6SW4z0OklT1UTgl/OSWStiWVXMP7PETasaz3iOC/Rxw7dswMo2I2luVVz+wcs+2sOuzefQxVqpRAcvJBJCZm/fkd6xxTcuWLft9992Hq1KmYM2dOrsGcXb7kKat/JM83mOz4so221fNwvpkLbRs5zwPpuNfzEIr/h0j4fw/nthw2YQdxnsN/+ByyosYgjsOVMu7nmE+PHcsKOKnM+umnn5rsHMcecbwE8YXniy4iIiKRnZjhWDgGcayYeWbxOD6V2ThWz/ISGIsDS67ZRfsTJkzAgAEDfLoP/gMxAOS3guxKrhIdWCZhMwdxwLveIER0jEl4cOgThzplLqmygsYgjieWV3OSksIhUyq5RkWGziFxp0QQdUWJ6BiT8GBJlQEcT56zL3DGBSZWGMR5l1QlZgI6ERERifySKrNx6enpXokYDpViEMefqpgEhwI6ERER8Ru7VBnEcTiTZ0mV833aJVV7vkAJHj3DIiIikicM3BjAMZBjQOdZUrWDODUshpYCOhEREfGp2cyzpGrjODjPkqrGxYWHAjoRERHJkj3xr93g4LnEJUuqnC+OTQ4qqYafAjoRERE5Z8ktu6TqueISAze7pGqviS2RQQGdRCV2UXkuCC4iOsYk95IqS6nMxGVVUmU2jhMAq6QamRTQiYiIxHBJlfPEMYhjRs6zpMqmBrukymYHiWwK6ERERGKwpGqPi8tcUmUQx5JqVmuhS+RSQCdRWzpISUkx5xMTEzWRpYiOsZjH90UugckgznMlHZZQuRwmA7lixYqppOpQCugkavGNS0R0jMV6SfXIkSPukiqDOlvRokVNEMdgTiVV51NAJyIiEmVOnDjhLqnyvK1gwYKmnMpALi4uLqz7KIGlgE5ERCQKsKHBLqkePnzYq+vfLqkyK6cu1chw8iSwaxdw5AhQtixQuvT53Z8COhEREQeXVBm8MYhjMOdZUuV4OGbj2KXKoE7Cj7PBfPIJMGkSsGQJM6l8DTmOkeO9gc6dgUGDgIsvzvt9K6ATERFxGHam2iVVdqzaWEa1J/5VSTWyvPgiMHYsUKsW0L078K9/AZUqcXoYYP9+YPVq4OefraCuTRvgtdeAOnV8v38FdCIiIg4pqbKxgUEcGx1szL4xC8eSKueOU0k1Mi1dCsybBzRqlPXtrVsDt98OvPUWMGGCFdwpoBMREYmikiqX4GJJlZdtXLWBmTiOj1NJNfL93//5th2n/7vnnrzfvzJ0EpX4DbVhw4bu8yKiY8xpJVUGcczGnTp1yn09J/u1S6rsWBWxKaCTqMQgToGciI4xp5VU7XFxXI7LxjniWFJlEKeSqnP17On7tl9+mff7V0AnIiISJiyhctUGZuPS09O9Sqrx8fEmiONPlVSdr0SJjPN8madOta5r1cq6btky4MCBvAV+nhTQSVRi6/6OHTvM+UqVKunNUETHWEQ5duyYCeLY5OBZUi1cuLC7pMp1VSV6TJiQcf6RR4BevawGiPz5retOnwb+8Q+geHH/7l//LRK1WLawAzoR0TEWbgzcGMAxkGNA51lStYM4llQl+r3/PjB/fkYwRzw/fDjQrh3w3HN5v08FdCIiIkGsFtglVf60S6oc4+tZUtWY39hy6hSwbh1Qr5739bzOY27oPFFAJyIiEkAM2piBsxsc2OzgWVLlfHFsclBJNXYNHAjccQewaZM1/xwtXgyMH2/d5g8FdCIiIgEqqTKAYzaO0464P2gLFHCXVBnQiTz/PFChAvDCC8DOndbzUbEi8PDDwIMP+vf8KKATERE5j5Iqu1MZyPGnzS6pMhvHCYBVUhVPXFr3n/+0Tmlp1nX+NkO47/P8fl1ERCT2Sqpceoud9OvXr0dycrI7mGNTAxux6tevj6pVq2p8XBi98QZQvTrL3NbaqEuW+PZ7kyYxIAd69Aj+OLoff7RWkLDnv+fkDIcO+Xd/ytCJiIj44OTJk+5xcVmVVJmN40oOEn6TJ1sdo5wWhMHcyy8DXboA69cD5cpl/3tbtwIPPQRcdllw92/bNqBrVyApiauCAFdfzXkHgWeftS5zv/NKAZ1EJZY3+A3ZPi8iOsb8LalyDVUGcexS9XyP4RqqDOKKFSum95kI8+KLwF13ZTQYMED67jtrupARI7L+Hfau9OkDjBkD/PyzNclvsAwbZk0o/NtvQEJCxvU33GDttz8U0ElU4putOshEdIydT0mVQRznjWNQZytatKjJxrFLlfPHSWixsm2POSMmRDMnRU+csFZdGDnSe8xap07AwoXZ3/eTT1rZO3afMqALJt7/ggVAXJz39SwRb9/u330qoBMRETGBwAl3SZXnbQULFnR3qaqkGl4NG3pfHjUKGD3a+7q9e61sW/ny3tfzMud5ywon+X3vPWDlSoQEvyN4zGbjlpJilV79oYBOohK/Ue/atcucr1Chgpb+EtExliXOEWeXVA8fPuy+nmunsqTKIE4l1cixZg1QuXLG5UAMWUxPB/r2Bd59FyhTBiHRubM1ru+dd6zLHBnEij4D1Guv9e8+FdBJ1Nq/f787oBMRHWOeJVUGbwziGMx5llQZvDGIYzCnkmrkYfYqt+k9ypSxltFKTfW+npez+jjg5L5shujePeM6+1+Cy+mykaJWLQQU559jkwYzjlwF7tZbgQ0brH1n16s/FNCJiEhMYGeqXVJlx6otLi7OXVLleXG2uDigZUtg1qyMqUcYoPHykCHnbs/+uVWrvK977DErc/fKK0CVKoHfx8REqyGC3bj8yewcx+6xKcPf5XwV0ImISNRiSZWNDQzi2OjgWVJlYwODODY6qBs+ugwfDvTvb3WScmktljdZUbe7Xvv1s0q348ZZ89Q1buz9+yVLWj8zXx9IzP4xgOMpIPcHB5k3bx6ee+45LFu2DDt37sTUqVPRI9gz/4mIiCNLqlyCiyVVXrZx1Qa7pMqgTqJT797Anj3AE08AHE7dvDkwfXpGowTnfwvny8+S8OWXA198AZQu7V0WrlQp64aJqAroeIA2a9YMt99+O3r27Bnu3RERkQgrqTKIYzaO66ra2Jlql1TZsSqxYciQrEusNGdOzr/7wQcIKn7H4ATCzCB+8w3QqJH3bf5wVEB3zTXXmJOIiIhnSZWB3NGjR91PChsa7JIql+NSSVUiCbtamZ0bPx5o2xb4+GPg+uszbov6gE5ERIQlVK7awCCOa6h6llTj4+NNEMefKqlKpOK/LMuubLpgdo4lYjZi3Hmn//dZwN+09uLFi7Ft2zYzyLRs2bJo0aIFatSogUjC/fRcb49jKSQ28Nt43bp13edFxPnH2LFjx9xdqplLqlyCixk5lVTFaQYNAurUAW6+mb0CIQrofvnlF7zyyiv45ptvTMs3Dx6msjnfFwOnmjVrYtCgQbjnnnvMt6NwGzduHMZwUTaJOfyA0fQDIs4/xhi42SVVBnSeJVV7XFzhwoX1xU0cpVo1K0Nnu/JKYNEi77nw8srnHo/rrrsOvXv3RvXq1TFjxgyT5t63bx9SUlJMlm7Dhg147LHHMGvWLPOtbebMmQi3kSNHmjcC+5ScnBzuXRIRkVywhMqKSlJSEtavX29mNWAwxyCS3alVq1ZFvXr1ULFiRY2PE0fasgVISPC+rnZtYMUKYPPmIGfounXrhi+++CLbdDazczz1798fa9asMQdguDENr3X3YhNnft+9e7c5X65cOY2lEYnwY4xBnGdJlc0ONmbg7JJqAU7eJRKlChe2snf+8PnIuPvuu32+04YNG5pToHEQ7MaNG92Xt2zZgpUrV6J06dLmG5uIp71cofnsh42IROYxxpKqHcR5llQZuHmWVEWcrnRp4M8/reW9SpXKuZv17MqVeeKorzq//vorrmSh+azhnAoanA26Pz4I9qQxIiISsOweh+0wiONPG0uqHH/NbBwnAFZDk0STl16y1qIlrlwRaD4HdDzAfD247EXRA+2KK67wak8XERFn4Hs354ljEMcxzZ4lVTbX2SVVNjuIRKP+/bM+H/KA7mWPcJLNEE8//TS6dOmCtpwRD8DChQvxww8/4PHHHw/8XoqISEQ5feoUiu1ejgLH9mHtgS2of8k1yJ/F+DbOiGCXVD2nkbJLqgzkNNZZYkFaHmZOK1487/efz+VHyuvGG280pc8hmdbUeP311/Hjjz9i2rRpiETsmuI3QH47ZKeURHdJh805xPGcmmBUJHBW/PAhKi8ag3Kufe7rUpGAHW1HoUWX/ub44/stgziOfbbZXaoM4ooVK6aSqvgsJSUNVaqUQHLyQSQmOvPz+4ILcl8FghEZtwnZWq7MxD377LPnXN+1a1eMGDHCn7sUERGHBHPNFgy1Lnh8OJV17UPZBUMxL/0QyjS80gR1tqJFi5psnEqqEstmzw7u/fsV0CUkJOCrr77Cgw8+6HU9r+NtIiISnWXWSgutydovyJRp4OUzLqDu6heQWqc9Chcu4u5SVUlVBOjQIQIDOq6+cOedd2LOnDlo06aNuY5LgU2fPh3vvvtuoPdRJM9Y2qnNWRq19JdIwKxb/AMaYZ9XZi5zUFcB+7Bj32bUvfIGlVRFcnHkCJCUBJw44X1906YITUA3YMAANGjQAK+++iq+/PJLcx0vz58/3x3giYQ7oNPcVSIBXr0hdatP2545slfBnEgO9uwBBg4Evv8+69tDNoaOGLhNnDjR318XEREHYGeq3aV6+Ewhn36nSKnKQd8vESe7/37gwAFWNzklGzB1KpCaCjz9NPDCC/7dp98B3aZNmzBhwgRs3rzZTGnCmcK///57s2JDo0aN/L1bkYDggOw9/ArEwdply6rLVSQPOEccZwNgEMe1um3l67VG6uoE0wCReQydOe5cwO58Cajfpoueb5Ec/PQT+w6AVq2s7lcu93X11dZ0JePGcblV5Jlfi+/NnTsXTZo0MePmuL6r3Zb+22+/YdSoUf7cpUjAMaCzgzoRyb2kyvfy5ORkrFu3Djt27HAHc1y1ITExEY0aNTZTk9jBmyf78s62o7Kcj05EMhw+zCXzrPNcBsz+qGrSBFi+HH7x66jj1CScWJhLb3GZFttVV11l5qITERHnlFT/+usvk43juqo2dqbaXaoFCxZ0X8955lYA58xDx8wcgzneLiI5q1cPWL8eqF4daNYMePtt6/xbbwEVKyJ0Ad2qVavw6aefnnM9y672Ys0iIhLZJVUGclyOy8ZltzhXHIM4LseV3XKPDNpOXnkLtsyfZFaKSCte26wUUUGZORGfDBsG7NxpnWdhs2tXgG0JcXGAv0vT+xXQ8WDfuXMnatSo4XX9ihUrULmyBsOKiERqSZVBXHp6ute62Ky08H2dP31dVYVl1cPlLjLntRqLSN7cdlvG+ZYtgW3bgHXrgKpVgTJlELqA7u9//zseeeQRfP755+YbHAeg//LLL3jooYfQr18///ZERETyPNEv54Y7+td201nKZoTM49eOHTvm7lLNXFLlElzMyHmWVEUk9IoWBS6yvh/5za+A7plnnsHgwYNRpUoVk7rntzP+vPXWW/HYY4+d3x6JiIhPS3Bx1QYz0e9ZqTOt9VSbdOzjLqkyoPMsqdrj4jhPY3YlVREJLibIp0yxlgPbvZszM3jffnaK3+AHdHFxcWZFiCeeeMKMp2Mav0WLFqhTp44/dyciIgFcT/XHvXtRqVnG1CEspTIbx25VX0uqIhLceejYCHHllUD58pwM//zv06+Abt68eahfv77J0PFkO3nyJBYuXIjLL7/8/PdM5Dww81CzZk33eZFYWk+16YY3cLBlN5QpW9aUVAsEoVlBx5iI/z7+2MrCXXstAsavr2pXXHEFmjVrhkWLFnldv3//flzJcFMkzPhhU7RoUXNSQCfRhGPmyiPriX0911M9tW8TEhISghLMkY4xEf+VKAGczTkEjN+5dzZGdOzYER9k6q/17JwSEZHAYPMZx8XtTlrn0/ZslBCRyDR6NDBmDOAxa9B5K+DvN7ORI0fisssuM12tv//+O144u/iYsiESKR9++/ZZg8WZpdC4IXEifkHmPHHsUGUwx+az0wVLRMR6qjrGRPzXqxfwf/9nrRbBCYUzN5r7s1qEXwGdnYXr2bOnmYvu+uuvx5o1a/DKK6/4c3ciQZHKlY7PBnQiTsLxyPZUI1zJwcbyaYNLuiJ19TMRsZ6qjjER//TvDyxbZs1HF9amCE/sbl2yZAl69OhhSrAiIuJfxistLc0Ecfb62HbVo3jx4qZLtVixYubyirajTDcrgzfPoM5zPVWt2iASub77DvjhB+DSSwN3n34FdP379zfLwtgqVKiAuXPnYtCgQaYDVkREfC+pcr44llQZ1NnY0MP54tilyvnjPNnrqbLblQ0SNq2nKuIMnCCkePHA3mc+Vwx1MfDbL98c+cbJb7wSvfjByGEApGWJJNKcOHHCXVLleRtXbLAn/uVKDoFYKSJYdIxJKKWkpKFKlRJITj6IxMTiUZGhe+014K23rDF0geDzkc/Gh8aNG5vB5Tyfk6ZNmwZi30REIp6vQZXdpcog7vDhw+7r+Z7KL5gM4uySqq/4OI3adwvY3yIiocGxc0eOALVqWct+ZW6K2L8/iAFd8+bNsWvXLpQrV86c55uOZ3LPvsyf7MQSEYnl5bdYFuV74pEjR0xJlRUCz5IqgzcGcQzmMpdURSS6vfxy4O/T54Buy5YtKFu2rPu8iEgsy235rfmHj6Bso6tMx6rnsol2SZXnRST2nDwJzJ0LPP44UKNG4O5XY+gkKjEzYpe18lrGEvGlzLr36bq5Th2SesOXKFgwzozdZRAXTSuX6BiTUIq2MXQlSgArVwY2oPM5Q/f111/7fKfXXXedv/sjEhD80ORC5CLBwDFzpsyay/JbKXs2oslVPaNyYmsdYyL+69EDmDYNeOABhD6g4zxzvtAYOhGJdof2Jvm24bH9URnMicj5qVMHePJJ4JdfgJYtWUnyvn3o2dEcQQnoPAfzijihHLT/bJtQ6dKlo6bMJeHDZi92qbLBIf1kppa0MC2/FU46xkT89957QMmS1moRPHnix1VQAzoRp33Y7Ny505znDPsK6MTf/yOu2sCpRtilanf2l63TCqmrEyJi+a1w0TEm4r9g9Jb6HdBxwDlXh0hKSvKaGJOG+hNaiohEiGPHjrkn/j116pT7ek72yy8IbHJYvUvLb4nI+bNngDvfQpJfAd2KFStw7bXXmvmVGNixpLV3717TwcV56hTQiYjTMHCzS6oM6GycI86eaqRw4cLubK+W3xKR8/HRR8BzzwEbNliX69YFHn4Y6Ns3hAHdAw88gO7du+Ott94y31QXLVpklqy57bbbMGzYMP/2REQkDGXD9PR0k4njT8/J0uPj4002jt3S2TU2MKg73bEP/si0UkSFEC2/JSLO9OKL1jx0Q4YA7dtb182fD9xzD7B3r3/dr36966xcuRJvv/22eZPjt9fjx4+jZs2a+Pe//43+/fujZ8+e/tytiEhIHD161F1S9VzZhhk4u6RawMegTMtviUhecR3XN98E+vXLuI4zvjVqBIweHcKAjtk4+xsrS6wcR9egQQPzJpicnOzPXYqIBHU9VZZU7SDOs6TKwI3vXQzkGNCJiAQbe/batTv3el53tp8vNAFdixYtsHTpUtSpUwcdOnTAE088YcbQffzxx2jcuDGC6Y033sBzzz1n1pVt1qwZXnvtNbRu3TqojykizlxPtdnVfb1KqjaOg/MsqaoLWkRCqXZt4LPPgH/9y/v6yZOtOepCFtA988wz7jfHsWPHol+/frj33ntNgPf+++8jWCZPnozhw4ebsXtt2rTByy+/jC5dumD9+vUmUyhi4wd0tWrV3OclNtdT/WnfflRoerX7+iJFipjmhryUVCVrOsZE/DdmDNC7NzBvXsYYOk4yPGuWFehF/VquDOIuvvhivP766+7JjqtUqYL77rsPI0aMyPX3OY8U38jZyVa8uPPXghOJZb6up7rvpq+RUKaMycZx2hERcZ5oW8uVOKHwSy8Ba9eai2jQAHjwQVZB4RfHfEXlXHfLli3DyJEj3ddxHF+nTp2wcOHCLH+HzRo8eQZ0IhJb66nuO7gVFYI8FEREJK+45NcnnyBg/Aro9u3bZ8bNzZ49G7t37z5nWTB7yaVA4hg9dqOVL1/e63peXrduXZa/M27cOIxhXlNiDhPPHDdFLLGp7Bpdry27VPem/OnT9kf/2hH0fYpFOsZEzg9Dp40bgd27rfOeLr88RAFd3759sXHjRtxxxx0moIrUD0tm8zjmzjNDxxKtxMaHzfbt2815ltkj9X9U8palt7tUef5k/njE+nqq4aRjTMR/ixYBt94KbNuWsVKEjR9XHrMpBTeg+/nnnzF//nzTZRoqZcqUMXPepaamel3PyxUqVMjydzheRmNmRJyL2X+OeWUQx1VpPIdb1GnVKebXUxURZ7rnHqBVK+C774CKFc9/2S+/A7r69eubkkcoxcXFoWXLlpg1axZ69OjhfrPn5SGcallEoibzw2UFuQQXs+qeQzqKFStmSuhsauIXvBVttZ6qiDgPl/uaMsWaviRQ/Aro/vOf/5iuUo6j47xznGjYU7A6SFk+5UoUrVq1MnPPcdoSfmsfOHBgUB5PREKHZVQGcczGnTx50n0931/YocpAjl/sPGk9VRFxojZtrPFzYQ/o+MbKb85XXXXVOd+sOVbJcymdQOrduzf27NljAklOLNy8eXNMnz79nEYJEXEGvlfwvYSBHLNyniVVjn3ke03RokVzHAOp9VRFxGnuu8+aomTXLqBJE35x9b69adMQzUPH7Bgn5Rw2bFiWTRFcPSISaR662MEy3Zo1a8z5hg0bZru4uoR2+S3iWw4z63ZJ1fMtiKs22CVVvWaRTceYhFK0zUN3QRYfSQyl+HYY0qaI1atXY8WKFahXr54/vy4iMbT8FjNoxDkh7S5Vz5Iqy6h2STXz8A0RkWi0ZUvg79OvgI5j2JKTkxXQScRi1tieokZTloR3+a0FR4+hfJNOXo1UzL4xgOOJy3HpNXIeHWMi/ju7MmX4AzoutcVy68MPP4wmTZqc8626qT/FX5EAf9hwDJYEv8zKzBxlXn6Ll7n8Vs2VzyK1Rhvkz1/AlFSZjYuPj1dJ1eF0jImcf6fr7NlZTyz8xBMhGkOX1dgWHtzBboo4XxpDJxJYf/zyHRrNvDXX7Za0exctrrxBJVUR8Uu0jaF7913g3ns5xy7AqXQ9WxF4fvnyEGXotgSj+CsSQPxyYa/dywH2KukFx5F9KT5td8GJAwrmooyOMRH/Pf00MHYs8MgjCJg8B3QczMzpSr799ls0aNAgcHsiEuAPG47ztLtcFdAF9rlNT083zQ1pJ/P79Dtafiv66BgT8d9ffwE334yAyvNcDhwvd+zYscDuhYhEPDY17Ny5E+vWrUNSUpLJgJap3QqpSDBj5bLC63chwUxhIiIiFgZzM2YgoPyanGvw4MF49tlncerUqcDujYhEFB7je/fuxcaNG7Fp0ybs27fPjJHlPJQJCQmoV6++mZqEMgd19uWdbUdlOR+diEgwvfEGUL06ULiwtTLDkiU5j2m77DKgVCnr1KlTztufL64Q8fjjwIABwAsvAK++6n3yh1/vskuXLjVrqM6YMcN0uXJ9RU9ffvmlf3sjIhExYaxdUuVPG8vW7E5llyq7Ve0ytpbfEpFIM3kylwsF3nrLCuZefhno0gVYvx4oV+7c7efMAW65BWjXzgoAn30W6NwZ+OMPoHLlwO/fO+9wInVg7lzr5IlvrUPPzgQV9C7X3NZOnTBhAiKRulxjh2axzxu+DbCkyiDu4MGDXp3qnCeO88VxGhhm5s53pQiJDjrGJJK7XNu0AS6+GHj9desypwXh1KRccmvEiNwfj2+BzNTx9/v1gyP49W4bqQGbiOS9yclevYErOdgYuNkT/xbm11UfMHhr1L6bXgIRCRoWDc5OYGAUKmSdPJ04ASxbBowcmXEdZ1tjGXXhQviES0tzQZvSpeEY5/X1ec+ePVjP/CVgVo0oW7ZsoPZLRPzgS5aMmRVmqxnEHTp0yH09S6ic4oVBnGdJVUQkUjRs6H151Chg9Gjv6/butTJs5ct7X8/L69b59jicTqRSJSsIDIbbb8/59vffD1FAx4W1uVrERx99ZD4cKH/+/OjXrx9ee+01FC1a1J+7FQkYBiOVzw58iJXAJKf1VJt37mdKqn/99ZcpqdrHLfF4tUuqPI5FfBGLx5iE35o13mPaMmfnAmH8eGDSJGtcnY8FCr+mLfHEbODq1cCBA8BVV/l3n34FdMOHD8fcuXPxzTffoH379ua6+fPnY+jQoXjwwQfx5ptv+rc3IgHCDxgO3o8Vua2n+tP+v8x6qp7TD9kl1ULBeEeUqBdrx5hEhvh4Thaf8zZlyjDJBKSmel/Py1yVISfPP28FdD/+yGVMETRTp557Hb9nc/WIWrX8u0+/miLKlCmDKVOm4IorrvC6fvbs2ejVq5cpxUYiNUVItJZZ9z5d1wRvmddTtacP2Z0vAbt7TkXp0gkmiGNnurIqIhLNTRGtWwOvvZYRLFWtCgwZkn1TxL//ba3e8MMPwCWXICw4io2h1c6dIcrQHTlyBOUzF6fBVuBy5jaRcOP3FHt8WLSPB+OYOVNmzeZPZJBXAfuwJy0JiU2bhXr3JErF0jEmzjN8ONC/P9CqlRXYcdqSw4c5S4d1OztXWbodN866zGlKnngC+PRTa+66Xbus6zm1CE+hsmkT5//073f9Cujatm2LUaNGmTF0dgccx+eMGTPG3CYSCR8227Zti/qlv06cOIH92zf6tO3xA3585ROJ8WNMnKl3bzZuWkEag7PmzYHp0zMaJZKSrM5XG0eKsTv2pptyb7oIVMDpibVSZuW++84KREMW0L3yyivo0qULEhMT0ayZ9Y3/t99+M8HdD8xVikjQcI44Dh9ggwMz4scv8J7YOztaT1VEYsmQIdYpK2x48LR1K0JqxQrvywwuOVEIV43IrQM2oAFd48aNsWHDBkycONGs60i33HIL+vTpYyYhFZHAZ0PYXc4gjsGc59DX6s06IHV1Qq5j6LSeqohIZJg9O4LmoeNUB3fddVdg90ZEvHCyX3viX04CbIuLizMdhpxqhOdXtB1lulkZvHkGdZ7rqVbQqg0iIlHL74COGTp2te7evdtrTit6gkVrEfG7pMq54piN49hU2wUXXOCeaoSZcM8xS1pPVUQktvkV0L377ru49957zfQlFSpU8Ppg4XkFdCL+dQwyE5e5pMoOQmbj4uPjTVCXHQZ1pzv2wR+ZVopQZk5EJPr5FdA9/fTTGDt2LB7h2hgi4rdjx465S6qnPHrVOdmvXVLlJMC+0nqqIiKxya+AjqWgm2++OfB7IxIgzBRXrFjRfT6S1lNl4MaSKoM4z5Iql91iAMdAjh3jmgZCIlk4jzERCVBAx2BuxowZuOeee/z5dZGg4wdMQkJCxKynuv2SUajd7gYTxKWnp3uVVFlKZRDH0mpOJVWRSBKuY0wk2n30EcBVVfO6BJhfAV3t2rXx+OOPY9GiRWjSpMk5JSGu6SoSa3JcT3XhUPy4dy8qNe9irmMGzm5wKKDuUxEROWvAAK63DQwalLF0WdDWcq1Ro0b2d5gvHzZv3oxIpLVcY2/eNgrFuqW+rqd66o65KFO2rHuFFRGnCvUxJrEtr2u5Ot2WLcD33wP/+EeQM3Rb+EgiEf5hs/Xs1N+hWJZo7aLv0diH9VT/SPodiVW6BXVfRKLxGBOJJTVq5C2YO6956ERiHT/Q2KXKJqGdm9egsQ+/w0YJERGJPWlpvm9b3I8kpM8B3fjx4zFs2DCflvZavHgx9u7di27dlImQ6MMVG+ypRriSA+Ur6tvgcK2nKiISm0qW5LC0nLfhIDhuc/p0EAO6NWvWoGrVqqbDtXv37mjVqhXKciXZs9Mw8Pb58+fjk08+wY4dO/AR2zREogRXQ2F3KrNxnADYxjJT8eLFkdjxRqSufkbrqYqISMjWb/UroGOA9ttvv+H111/HrbfeahoMOG8WJ0A9cuSI2aZFixa48847MWDAAA36lqgoqXKeOAZxnDfOc4k7rmXMDlXOG8fjgLSeqoiIZKdDBwRVnsbQNWvWzCz79fbbb+P333/Htm3bzAcelwBr3ry5+SnidCdOnHCXVHnexul57KlG+EUmM62nKiIiecF8WFISP3e8r2/aFHnmV1MEJz9lAMeTSDRg9o1ZZ2bj7KkY7JIqs3AM4nyZmkHrqYqISG727AEGDrSmJslKUMfQiTjJmdOnUHDfOpxOT8XaA1tR/5KuXstv2SVVDhdgEMdgzrOkyuCNQRzHx9klVV9pPVWJFeXLlw/3Log40v33AwcOsIkUuOIKYOpUIDUVePpp4IUX/LtPxwR0Y8eOxXfffYeVK1ciLi7OlMNEclp+q57n8ls/JmBH21Emg2aXVBnIsWPVs6TKJbgYyPF/TERyrtTYjXEikjc//QR89RXQqhWPJaBaNeDqq63pSsaNA/yZJMQxAR0/hNlh27ZtW7z33nvh3h1x4vJbC4bipwMHUa7RVV4fSnZJlY0OmhxVRESCjSN7ypWzzpcqZZVg69YFmjQBli/37z59DujYBNG4ceOwLR4+ZswY8/ODDz4Iy+NL5OPyW8zMUeblt3iZy281XPsyUutfjuLFS5hsHEuq4fqfFomGLnDi/KT6MiTiu3r1gPXrgerV2XAKvP22df6tt4CKFeEXnz/JOCUJJwummjVrYt++jHJWpOKkrxwb5XmS6LVu8Q8oj6zXUvVcfivfwW1mPWJm5RTMifgf0HHdbp78WBJcJKYNGwbs3GmdHzXKao6oWhV49VXgmWeCnKHjhx/XcC1XrpxZv89zAHmkGjdunDuzJ9Ht9OnTOLBzs0/bnkhLDfr+iIiIZOe22zLOt2wJbNsGrFtnBXX+zgDnc4buxhtvRIcOHUxmg6l1rhTBTF1WJ1+NGDHC3FdOp3X8C/00cuRIMyGsfUpOTvb7viTyMCvA1Rv4uvL/5ChyX5aOtPyWiIhEAs4/x9Ir+/Auusj/YC5PGbp33nkHPXv2xMaNGzF06FDcddddiI+P9/+RATz44INmVYmc5CVAzIyTv2Y1Aaw427Fjx9wT/3LZOVtio/ZIXZ2g5bdERCTiJxS+7z7gww+ty3/+yXjHuq5yZSa8gtzl2rVrV/Nz2bJlGDZs2HkHdGx5V9u7+IKBG7OsDOLsgdjEOeLYpcoGh8KFC2Nl21Gmm5UNEJ5j6XiZdrYdhQqZ5qMTEREJpZEjgd9+A+bMYWyVcX2nTsDo0SEI6GwTJkxAqCUlJWH//v3mJ8dLcT46ql27Ni688MKQ74+ErqTKII4/PQde88sEgzi+9p6NDfbyW5UXjUE5V0bjzu58CSaY4+0iIiLhNG0aMHkycMklXJEo4/pGjYBNm/y7T8ekKp544gl8aOcmz3bd0uzZs3EFp1mWqMEMnF1SZfBuYwbOXku1QA5ZNgZtJ6+8BVvmT0KBY/uQVrw26l9yjTJzIiISETjvnD0PXeb56XJZYdL5AR3nn9McdNFdUrWDOI6R8yypMoCzS6p5WX6raKMu5nyDsmU1PYlIEGjIjIh/uELEd99ZY+bIDuL++1+gbdsoD+gk+nDqG8+Sqo3dzSypMpDjT38mLGUZVutMigSPjjER/3GuuWuuAdasYUIDeOUV6/yCBcDcuf7dpwI6CSmOg2MGjuuossnBs6TK2eYZxLHJIaeSqoiIiJNdeqnVFMF1W7nc14wZ1rQlCxdal/2hT00JiZMnT7pLqlzBw/0PWKCAe1xcXkqqvgSO9uNw6hotSyQSWDrGRPxz8iRw993A448D776LgFFAJ0EvqTIbd+jQIff1DK64hiqDOHapBiPY4ocN50ykhg0bKqAT0TEmEhEKFgS++MIK6AJJAZ0EZcFuu6TquURc0aJF3SVVNjuIiIjEoh49rKlLHnggcPepgE4C4sSJE+6SKs/bChYs6C6patUOERERoE4d4MkngV9+sdZyLVbM+1kZOjTvz5ICOvEbs29paWkmG3eYk+ecxRIqs3AM4ooVK6Zyp4iIiIf33gNKluTKW9bJE0chKaCTkJRUjxw5YoI4BnOZS6qcL47j41RSFRERydqWLQg4ZegkTyVVBnLsWPUsqTKIYzYuLi5Oz6aIiEgYKKCTbHGOOLukyqyc54SizMIxkGNWTlOCiIiI5Gz8eGDYMM65msuGABYvBvbuBbp1g88U0Mk5JVWOh2M2jl2qvGzjeDi7pMqgLtKVKVMm3LsgEtV0jIn4jitBVK0K3Hwz0L27tfxX2bLWbVwtgrfPnw988gmwYwfw0Ud5uHMFdGLjJLx2l6pnSZVlVLtL1UklVQacFSpUCPduiEQtHWMiecMAjatDvP46cOutQFoa1yvn5PeAXQRr0QK4805gwAAgr3Pt53N5pmCiHMuH7L5k5olZpljHkiqfCwZxmUuqfJ6YjeNyXCqpiohIOKWkpKFKlRJITj6IxETnf36fOQP8/juwbRtw9Ciz3UDz5tZPf6nkGmMYv3PVBgZxDHA943mu2sAgLj4+3hEl1Zzw77IzjWzcUFAqomNMJFLwI5YBHE+BEpMBHafa8Jxuw5NnIJPdNk7c9tixYyaAYyB3isX6TCVVZuQY+GQlkPvLwMoOroK5LU9//vmnuVy/fn2vfQzFPjCgzCn57bRtyX4Oo3lbJxzLkbItZXeMOeE9ItzbOuG4j7T3CMlZTAZ069atM9mozHhd9erV3ZfXrl2b7T8auztr1qzpvrx+/XpTwswKy5a1atVyX96wYYPXODVPXE2hDqeQPmvTpk1ei9l7YgBWr1499+UtW7aYZbdywznieJAysON0JLt37zYnG29r1KiR+3JSUpLXWqyZNW7c2H0+JSXFBI7Z8VxXdceOHSbAzA4/JAoUsP5Fd+3ahf3792e7bd26dd1j/Pi37GV7kMfr7al27doofHZwwp49e8wpO3yN+VrTvn37kJqamu22/N+x/6+4rzt37sx222rVqplMKPE52L59e7bbVqlSxQTcxOc2OTk5220rV65ssqzE12wb8/nZqFixIhISEsx5NsJs3bo1223Lly+PsmdH7/J/bPPmzdluy+24PfF/115TN7tB9fZYRx4TdoCQldKlS6NSpUrmPI+1zK+rJ35JSUxMNOd5DK/haONscPhFVY5UPiunbaP5PYLvCw0aNHBf5v+D51AMTzyGPbflce/k94jM9B4Rme8RkrOYDOhiFQMIftjzQ4kHpmemTkRERJwrJpsiOK9adk0RkVDK8GdbllT57ZTfZj1/h9/m7WW4PLtUw7W/oSy52hkclVydUU6JhG0j4Vh2yrae2UyVXFVyDfbxGQ1NEb//zmy1NX4uGGIyQ8d/Dl9q8nmp24djW2bY7CCOAZ1n6cSeaoSlnEjZ33Btm9PrHax98AyWtK1znodI/R+OxG09Az5f31MDvQ9O3jYS/t+dtq3TtWgBcCROuXIczgMsXQqcrWgHREwGdE7GN1GOVWGWMT093X09DwiWVBnE8WesHCAiIiJOULKktYYrAzoOR/QhCZ4nCugcgOloZuAYxHHeOM+B1czA2V2q9uBgERERiSw33gh06MBmEyZhrJUiOLFwVnLoKcmWIoAIxi43BnAM5Dy72Bi42SVVu1tTsu6KFJHg0TEm4rt33gF69gTY1Dt0KHDXXWxWRMAooIvAkipLqQziPKcBYAmVjRwM4tilqpJq7mNZ7CkuRCTwdIyJ5F3XrtbPZcuAYcMU0EVlSZXz9tglVc/BxpzLyi6pstlBREREnG3ChMDfpzJ0YcRJfdmhyhPPe04GapdUOe2I+Bck22MN7YmURSRwdIyJRBYFdCHG7Bvnw2M2jjNv2xhw2PPFFStWTAFIAD5s7HnoPGeeF5HA0DEmElkU0IXojY9L6DCIYzCXuaTK1Rs4Pk4lVREREfGHAroQlFQZyHmuy8iSKoO4zKs3iIiIiPhDAV2AcdyWXVL1XNiaHWHMwjGQY1ZOJUAREREJFAV0ASqpcjwcs3HsUvVcl47j4eySal6WhRERERHxlQK688DJfu0uVc+SKsuodpeqSqoiIiISbAro/CipMgvHIC5zSZVdqszGcTkulVRFREQkVBTQ+YAlVK7awCCO4+M8S6pctYFBXHx8vEqqEYYZUhHRMSYSCxTQ5eDYsWPukuqpU6fc13OyX7ukyo5ViTzMmCYmJoZ7N0Silo4xkciigC4TBm52SZXLcdk4R5xdUi1cuLBKqiIiIhIxHNF2uXXrVtxxxx2oUaOGGZ9Wq1YtjBo1ymu5rPPBEipLqUlJSVi/fj127tzpDuZYSq1SpQrq1atnFnvX+Dhn4GvKCZx58iyRi4iOMYkNb7wBVK8OFC4MtGkDLFmS8/affw7Ur29t36QJ8L//wVEckaHjEk78YH777bdRu3ZtrF69GnfddZeZKuT5558/r5Iq54tjNs5e95OYgbNLqgUKOOIpkkwYxK1Zs8ac19JfIoGnY0wi2eTJwPDhwFtvWcHcyy8DXboA69cD5cqdu/2CBcAttwDjxgF/+xvw6adAjx7A8uVA48ZwhHwuh6YvnnvuObz55pvYvHmzz7/DLBzLpvwdBnAM6DxLqnYQxyycOBu/AHgGdJoDUETHmDhXSkoaqlQpgeTkg0hMLJ7r9m3aABdfDLz+unWZK25WqQLcdx8wYsS52/fuDXB59W+/zbjukkuA5s2toNAJHJt+4ji30qVL5zpPHE+eAR2lpqaa7lROLcKSKoM4/tRUIyIiIpErPZ2f5RmXCxWyTp44GmvZMmDkyIzrOK9/p07AwoXIEq9nRs8TM3rTpsExHDGGLrONGzfitddew913353jduPGjTMZOfvEsXB2SbVixYpmXFzVqlXNKg4K5kRERCJbw4ZAiRIZJ5ZIM9u7l3PGAuXLe1/Py7t2ZX2/vD4v20eisAZ0I0aMMIFUTieOn/O0fft2dO3aFTfffLMZR5eTkSNHmkyefUpOTjbX16xZEwkJCRofJyIi4iAcSXPwYMbJMwsX68Jacn3wwQcxYMCAHLdh8GXbsWMHrrzySrRr1w7vvPNOrvfP+eJ4EhEREeeLjweK5zKErkwZjovn8Crv63m5QoWsf4fX52X7SBTWgK5s2bLm5Atm5hjMtWzZEhMmTNAgdxERETlHXBzQsiUwa5bVqWo3RfDykCFZP2Ft21q3339/xnUzZ1rXO4UjmiIYzF1xxRWoVq2amaZkz5497tsqOCl8lpDi2EgR0TEmsWf4cKB/f6BVK6B1a2vaEnaxDhxo3d6vH1C5csYYvGHDgA4dgBdeALp1AyZNAn79FfChGBgxHBHQzZw50zRC8JR5OSeHzroiQcZpStjwIiI6xiT29O4NMPfzxBNWYwOnH5k+PaPxISnJ6ny1tWtnzT332GPAv/4F1Kljdbg6ZQ46R89D5w97Hjo2SCh7IyIiEp3z0MUiR05bIiIiIiIOK7mK5JVWihAJLh1jIpFFGToRERERh1NAJyIiIuJwCuhEREREHE4BnYiIiIjDKaATERERcTgFdCIiIiIOp2lLJGpdeOGF4d4FkaimY0wkciigk6hd+qt69erh3g2RqKVjTCSyqOQqIiIi4nAK6EREREQcTiVXidplidauXWvON2jQwJSHRETHmEi0UkAnUcvlcoV7F0Simo4xkcihtIWIiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJy6XCVqFS1aNNy7IBLVdIyJRA4FdBKVOO9czZo1w70bIlFLx5hIZFHJVURERMThFNCJiIiIOJxKrhK1S3+tX7/enK9Xr56W/hLRMSYS1RTQSdQ6ffp0uHdBJKrpGBOJHCq5ioiIiDicAjoRERERh1NAJyIiIuJwCuhEREREHE4BnYiIiIjDqctVolaRIkXCvQsiUU3HmEjkUEAnUbssUa1atcK9GyJRS8eYSGRRyVVERETE4RTQiYiIiDicSq4StUt/bdiwwZyvU6eOlv4S0TEmEtUck6G77rrrULVqVRQuXBgVK1ZE3759sWPHjnDvlkSwkydPmpOI6BgTiXaOCeiuvPJKfPbZZ2bB9S+++AKbNm3CTTfdFO7dEhEREQk7x5RcH3jgAff5atWqYcSIEejRo4fJwBQsWDCs+yYiIiISTo7J0Hnav38/Jk6ciHbt2imYExERkZjnqIDukUceQbFixZCQkICkpCR89dVXOW5//PhxpKWleZ1EREREok1YAzqWTfPly5fjad26de7tH374YaxYsQIzZsxA/vz50a9fP7hcrmzvf9y4cShRooT7VKVKlRD9ZSIiIiKhk8+VU0QUZHv27MG+ffty3KZmzZqIi4s75/qUlBQToC1YsABt27bNNkPHk40ZOv7OwYMHUbx48QD8BRLJ05awcYa4YgRntRcRHWPiTCkp/PwugeTkg0hM1Od3xDVFlC1b1pz8/cAmz4Ats0KFCpmTxB4GcJx/TkR0jInEAkd0uS5evBhLly7FpZdeilKlSpnMy+OPP24yL9ll50RERERihSPqUEWLFsWXX36Jjh07ol69erjjjjvQtGlTzJ07Vxk4ERERiXmOyNA1adIEP/30U7h3QxxEY+hEdIyJxBJHBHQi/shpfKWInD8dYyKRwxElVxERERHJngI6EREREYdTQCciIiLicAroRERERBxOAZ2IiIiIw6nLVaJWwYIFw70LIlFNx5hI5FBAJ1G79BcnoRYRHWMisUAlVxERERGHU0AnIiIi4nAquUrULv21ZcsWc75GjRqmBCsiOsZEopUCOolaR48eDfcuiEQ1HWMikUNpCxERERGHU0AnIiIi4nAK6EREREQcTgGdiIiIiMMpoBMRERFxOAV0ErXy589vTiKiY0wkO/v3A336AMWLAyVLAnfcARw6lPP2990HcDGiIkWAqlWBoUOBgwcRVpq2RKIS551r0KBBuHdDJGrpGJNo0acPsHMnMHMmcPIkMHAgMGgQ8OmnWW+/Y4d1ev55oGFDYNs24J57rOumTEHY5HO5XC7EiLS0NJQoUQIHDx5EcYbiIiIiEvFSUtJQpUoJJCcfRGJi4D6/1661grKlS4FWrazrpk8Hrr2WjwlUquTb/Xz+OXDbbcDhw0CBMKXKVHIVERERR0hPZ3Im43T8+Pnd38KFVpnVDuaoUydmoIHFi32/H5ZbmScKVzBHCugkapf+2rx5sznxvIjoGBPnYzatRImM07hx53d/u3YB5cp5X8egrHRp6zZf7N0LPPWUVaYNJ42hk6h15MiRcO+CSFTTMSahtmYNULlyxuVChbLebsQI4Nlncy+3ni9mCbt1swLN0aMRVgroRERExBHi463SZm4efBAYMCDnbWrWBCpUAHbv9r7+1Cmrk5W35Vb+7drV2qepU4GCBRFWCuhEREQkqpQta51y07YtcOAAsGwZ0LKldd1PP3HYDtCmTc6ZuS5drAzh118DhQsj7DSGTkRERGJSgwZWlu2uu4AlS4BffgGGDAH+/veMDtft24H69a3b7WCuc2ero/W996zLHG/H0+nT4ftblKETERGRmDVxohXEdexodbfeeCPw6qsZt3NuuvXrOWbUurx8eUYHbO3a3ve1ZQtQvTrCQgGdiIiIxKzSpbOfRJgYoHnO2HvFFd6XI4UCOola+fLlC/cuiEQ1HWMikUMBnUTtskSNGjUK926IRC0dYyKRRU0RIiIiIg6ngE5ERETE4VRylajE5b6SkpLM+apVq5rykIjoGBOJVgroJGodOnQo3LsgEtV0jIlEDqUtRERERBzOcQHd8ePH0bx5c9Muv3LlynDvjoiIiEjYOS6g++c//4lK9nocIiIiIuKsgO7777/HjBkz8Pzzz4d7V0REREQihmOaIlJTU3HXXXdh2rRpKFq0aLh3R0RERCRiOCKgc7lcGDBgAO655x60atUKW7du9Xm8HU+2gwcPmp9paWlB21eJnGlL7A48vt6atkREx5g4V3p6mjsekAgM6EaMGIFnn302x23Wrl1ryqzp6ekYOXJknu5/3LhxGDNmzDnXV6lSJc/7KiIiIuF16FA6gBJ6GbKQzxXGcHfPnj3Yt29fjtvUrFkTvXr1wjfffOO1EPTp06eRP39+9OnTBx9++KFPGTpmbfbv34+EhAQtKh0DmJlj8J6cnIzixYvrsfWc638tio4xiS1nzriwc2c66tathPz5HTX8PzYCOl9xxn/PMumOHTvQpUsXTJkyBW3atEFiYmJY908iE/9nSpQoYUrt4Qjo9Nh6zvW/JiKh4ogxdFy6ydOFF15oftaqVUvBnIiIiMQ85S1FREREHM4RGbrMqlevrk4XyVWhQoUwatQo8zPU9Nh6zvW/JiKh5IgxdCIiIiKSPZVcRURERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATmIC1wHmSiMvv/xySB5v9OjRqF+/PooVK4ZSpUqhU6dOWLx4cdAf9+TJk3jkkUfQpEkT89iVKlVCv379zGTcofDll1+ic+fO7tVYVq5cGZLHfeONN0z3e+HChc1k40uWLAnJ486bNw/du3c3zzP/3mnTpoXkcbms4cUXX4z4+HiUK1cOPXr0wPr160Py2G+++SaaNm1qJuvmqW3btvj+++9D8tgikj0FdBL1pk6dikWLFpkP3VCpW7cuXn/9daxatQrz5883wQYDHS53F0xHjhzB8uXL8fjjj5ufDLD4QX/dddchFA4fPoxLL7001zWaA2ny5MkYPny4maKGf3OzZs3MSjK7d+8Oyd/Lx2NAGUpz587F4MGDzf/1zJkzTSDP/y/uT7BxZZ7x48dj2bJl+PXXX3HVVVfh+uuvxx9//BH0xxaRHHDaEpFolZKS4qpcubJr9erVrmrVqrleeumlsOzHwYMHOT2Q68cffwz5Yy9ZssQ89rZt20L2mFu2bDGPuWLFiqA/VuvWrV2DBw92Xz59+rSrUqVKrnHjxrlCiX/v1KlTXeGwe/du8/hz584Ny+OXKlXK9d///jcsjy0iFmXoJGqdOXMGffv2xcMPP4xGjRqFbT9OnDiBd955x6ztymxOqHEtW5YDS5YsiWjD55aZIpa0bRdccIG5vHDhQsQKvsZUunTpkD7u6dOnMWnSJJMZZOlVRMLHkStFiPiCZb8CBQpg6NChYXnCvv32W/z97383ZdCKFSua0liZMmVCug/Hjh0zY+puueUWM94p2uzdu9cEFeXLl/e6npfXrVuHWPnicv/996N9+/Zo3LhxSB6TQwkYwPH/i2trc1hDw4YNQ/LYIpI1ZegkKkycONF8sNgnjjF65ZVX8MEHH5jsVCgf++effzbXX3nllaYpYMGCBejatSt69eoV8HFd2T02cVwVH5PVQA5kD7ScHltCh2PpVq9ebTJloVKvXj3zv81Gn3vvvRf9+/fHmjVrQvb4InIuLf0lUSE9PR2pqanuy59//jkeffRRU36zMZPDy1WqVMHWrVuD9tiVK1dGkSJFztmuTp06uP322zFy5MigP7YdzG3evBk//fST6ToNtJz+bj6/NWrUwIoVK9C8eXMEs+RatGhRTJkyxXR62hhgHDhwAF999RVChV8cmKny3I9gGzJkiPkb2W3L5ztcWOKuVasW3n777bDtg0isU8lVogKnb+DJNmjQIDOdhCd2PnJM3cCBA4P62DmVxo4fPx70x7aDuQ0bNmD27NlBCeaye+xQi4uLQ8uWLTFr1ix3IMXnmZcZ7EQrZl3vu+8+E0DOmTMnrMFcsP63RSRvFNBJVGIQkzmQKViwICpUqGDKRcHEAeJjx441U4Vw7BzHeXFai+3bt+Pmm28O6mMzmLvpppvM9B0cw8es5K5du9wD5hkABdP+/fuRlJTknvfOnhuNzztPwcApS5iRa9WqFVq3bm3mGuRrEOjAPSuHDh3Cxo0b3Ze3bNliSpF8rqtWrRrUMuunn35qsnMMqu3XmI03WWWHA4kZ5muuucb8fczScj8YVP7www9BfVwRycXZbleRqBeqaUuOHj3quuGGG8zUGXFxca6KFSu6rrvuOjN9SKimC8nqNHv27KA//oQJE7J87FGjRgX1cV977TVX1apVzfPNaUwWLVrkCgU+p1n9vf379w/q42b3GvP5D7bbb7/dHEt8rsuWLevq2LGja8aMGUF/XBHJmcbQiYiIiDiculxFREREHE4BnYiIiIjDKaATERERcTgFdCIiIiIOp4BORERExOEU0ImIiIg4nAI6EREREYdTQCciIiLicAroRCRivPfee+jcubP78oABAwKy2H2+fPkwbdo0BMqIESPMWqoiIpFCK0WISEQ4duwYatasic8//xzt27c31x08eNAsRF+yZMnzDui4kH0ggkPi+rzcV67byp8iIuGmDJ2IRIQpU6agePHi7mDOXmz+fIO5YChTpgy6dOmCN998M9y7IiJiKKATkYDas2cPKlSogGeeecZ93YIFCxAXF4dZs2Zl+3uTJk1C9+7dva7LXHK94oorMHToUPzzn/9E6dKlzeOMHj3a63c2bNiAyy+/HIULF0bDhg0xc+bMcx4rOTkZvXr1MsEi7+f666/H1q1bzW3r1q1D0aJF8emnn7q3/+yzz1CkSBGsWbPGfR33lfssIhIJFNCJSECVLVsW77//vgm0fv31V6Snp6Nv374YMmQIOnbsmO3vzZ8/H61atcr1/j/88EMUK1YMixcvxr///W88+eST7qDtzJkz6Nmzpwkeeftbb72FRx55xOv3T548abJr8fHx+Pnnn/HLL7/gwgsvRNeuXXHixAnUr18fzz//PP7xj38gKSkJKSkpuOeee/Dss8+aANHWunVrc5sdCIqIhJPG0IlIUAwePBg//vijCdJWrVqFpUuXolChQllue+DAAZQqVQrz5s3DZZdd5pWh4212QwMzdKdPnzaBmGdgddVVV2H8+PGYMWMGunXrhm3btqFSpUrm9unTp+Oaa65xj6H75JNP8PTTT2Pt2rVmbB0xkGO2jo9jN2X87W9/Q1pamgkO8+fPb+7H3p54G0vCc+bMQYcOHfRfJCJhVSC8Dy8i0YpZrsaNG5smh2XLlmUbzNHRo0fNT5ZJc9O0aVOvyxUrVsTu3bvNeQZpVapUcQdz1LZtW6/tf/vtN2zcuNFk6DI3ZWzatMl9mVnGunXr4oILLsAff/zhFcwRS7B05MiRXPdZRCTYFNCJSFAwONqxY4cpg7Is2aRJk2y3TUhIMAHTX3/9lev9FixY0Osyf4+P4atDhw6hZcuWmDhxYpblYs/A7/Dhwyag27lzpwkcPe3fv/+c3xERCRcFdCIScCxh3nbbbejduzfq1auHO++805Rdy5Url+X2LGtyfBqbDjznocurBg0amIYHzwBs0aJFXttcdNFFmDx5stkXdtVmhcEay72PPvqoua8+ffpg+fLl7qwcrV692gSXjRo18nt/RUQCRU0RIhJwDIQ4h9yrr75qmhJYurz99ttz/B02KrAx4nx06tTJPFb//v1Nho1j7bgvnhiccdoRdrby9i1btphxcOyeZZMDsQmCpdvHHnsML774ohm399BDD3ndD3+X4/08gzwRkXBRQCciAcXg6OWXX8bHH39sMmAsWfI8A6Cc5m2744478L///c8Egv7iY7H5gWPy2CzBzODYsWO9tuGUJGy+qFq1qumIZVaPj80xdNzfjz76yOwH97lAgQKmo5aNFO+++y6+//579/1wypK77rrL730VEQkkdbmKSMS4+eabTUl05MiRiGQM7B588EH8/vvvJugTEQk3ZehEJGI899xzZk64SMdmiQkTJiiYE5GIoQydiIiIiMMpQyciIiLicAroRERERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJwCOhERERGHU0AnIiIiAmf7fy+rT6l1ZxvWAAAAAElFTkSuQmCC", - "text/plain": [ - "

" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ @@ -958,7 +956,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "id": "23", "metadata": {}, "outputs": [ @@ -1034,7 +1032,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "id": "27", "metadata": {}, "outputs": [ @@ -1093,7 +1091,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "id": "29", "metadata": {}, "outputs": [ @@ -1184,7 +1182,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "id": "35", "metadata": {}, "outputs": [ @@ -1304,7 +1302,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "id": "37", "metadata": {}, "outputs": [ @@ -1394,7 +1392,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "id": "41", "metadata": {}, "outputs": [ @@ -1468,7 +1466,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "id": "43", "metadata": {}, "outputs": [ @@ -1689,7 +1687,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "id": "48", "metadata": {}, "outputs": [ @@ -1797,7 +1795,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": null, "id": "51", "metadata": {}, "outputs": [ @@ -1874,7 +1872,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": null, "id": "53", "metadata": {}, "outputs": [ From f7f1fb3e8a1da7bd2ba3f0689b102f84926db199 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Sat, 23 May 2026 21:29:54 +0300 Subject: [PATCH 06/12] Running all cells --- .../gradient_estimation.ipynb | 106 ++++++++++++------ .../gradient_estimation_helpers.py | 6 +- 2 files changed, 76 insertions(+), 36 deletions(-) diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index d84443312..a2801dafa 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -10,7 +10,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 7, "id": "1", "metadata": {}, "outputs": [], @@ -253,7 +253,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 8, "id": "13", "metadata": {}, "outputs": [ @@ -277,8 +277,8 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/bc01c9ad-e05a-4ddb-a88c-644e8c0e92dc\n", - "/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_20289/391621480.py:44: SettingWithCopyWarning: \n", + "Job: https://platform.classiq.io/jobs/f21b7076-4514-4030-9d5f-86915c39c8df\n", + "/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_20813/391621480.py:44: SettingWithCopyWarning: \n", "A value is trying to be set on a copy of a slice from a DataFrame\n", "\n", "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n", @@ -330,7 +330,7 @@ "type": "string" } ], - "ref": "e4bd39e9-673b-46c4-b876-faa8f2bbb171", + "ref": "45a22227-cf31-4727-93cd-e8e1cbcb29a3", "rows": [ [ "63", @@ -543,7 +543,7 @@ "30 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000011" ] }, - "execution_count": 2, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -609,7 +609,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 9, "id": "15", "metadata": {}, "outputs": [ @@ -643,7 +643,7 @@ "type": "float" } ], - "ref": "017a0fff-d15e-4505-8b12-d278db9ef785", + "ref": "761a3f7f-bd6c-4bea-8797-f8fa2fde2488", "rows": [ [ "-4", @@ -777,7 +777,7 @@ " 3 0.75 0.75" ] }, - "execution_count": 3, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -828,26 +828,47 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 17, "id": "18", "metadata": {}, "outputs": [ { - "ename": "KeyboardInterrupt", - "evalue": "", - "output_type": "error", - "traceback": [ - "\u001b[31m---------------------------------------------------------------------------\u001b[39m", - "\u001b[31mKeyboardInterrupt\u001b[39m Traceback (most recent call last)", - "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[4]\u001b[39m\u001b[32m, line 29\u001b[39m\n\u001b[32m 23\u001b[39m inplace_add(val, ancilla)\n\u001b[32m 25\u001b[39m \u001b[38;5;66;03m# 2. Next step in the algorithm: QFT inverse on the coordinates register\u001b[39;00m\n\u001b[32m 26\u001b[39m \u001b[38;5;66;03m# invert(lambda: qft(x))\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m29\u001b[39m df = \u001b[43mrun_statevector_simulation\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmain\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprint_circuit_info\u001b[49m\u001b[43m=\u001b[49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfilter_ancilla\u001b[49m\u001b[43m=\u001b[49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[32m 30\u001b[39m simplified_df = simplify_df(df)\n\u001b[32m 31\u001b[39m plot_simplified_df(simplified_df)\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/GoogleDrive-ofriwi1@gmail.com/My Drive/Documents/Work/1. Classiq/classiq-library/classiq-library/algorithms/gradient_estimation/gradient_estimation_helpers.py:115\u001b[39m, in \u001b[36mrun_statevector_simulation\u001b[39m\u001b[34m(qfunc_to_run, print_circuit_info, filter_ancilla, show_circuit)\u001b[39m\n\u001b[32m 111\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mrun_statevector_simulation\u001b[39m(\n\u001b[32m 112\u001b[39m qfunc_to_run, print_circuit_info=\u001b[38;5;28;01mFalse\u001b[39;00m, filter_ancilla=\u001b[38;5;28;01mFalse\u001b[39;00m, show_circuit=\u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[32m 113\u001b[39m ):\n\u001b[32m 114\u001b[39m \u001b[38;5;66;03m# Run a statevector simulator\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m115\u001b[39m qprog = \u001b[43msynthesize\u001b[49m\u001b[43m(\u001b[49m\u001b[43mqfunc_to_run\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 116\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m show_circuit:\n\u001b[32m 117\u001b[39m show(qprog)\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/classiq/synthesis.py:101\u001b[39m, in \u001b[36msynthesize\u001b[39m\u001b[34m(model, auto_show, constraints, preferences)\u001b[39m\n\u001b[32m 97\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m constraints \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[32m 98\u001b[39m serialized_model = set_constraints(\n\u001b[32m 99\u001b[39m serialized_model, constraints=constraints\n\u001b[32m 100\u001b[39m )\n\u001b[32m--> \u001b[39m\u001b[32m101\u001b[39m result = \u001b[43masync_utils\u001b[49m\u001b[43m.\u001b[49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43msynthesize_async\u001b[49m\u001b[43m(\u001b[49m\u001b[43mserialized_model\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 102\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m auto_show:\n\u001b[32m 103\u001b[39m show(result)\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/classiq/_internals/async_utils.py:40\u001b[39m, in \u001b[36mrun\u001b[39m\u001b[34m(coro)\u001b[39m\n\u001b[32m 38\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m:\n\u001b[32m 39\u001b[39m loop = _get_or_create_run_loop()\n\u001b[32m---> \u001b[39m\u001b[32m40\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mloop\u001b[49m\u001b[43m.\u001b[49m\u001b[43mrun_until_complete\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcoro\u001b[49m\u001b[43m)\u001b[49m\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/nest_asyncio.py:92\u001b[39m, in \u001b[36m_patch_loop..run_until_complete\u001b[39m\u001b[34m(self, future)\u001b[39m\n\u001b[32m 90\u001b[39m f._log_destroy_pending = \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[32m 91\u001b[39m \u001b[38;5;28;01mwhile\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m f.done():\n\u001b[32m---> \u001b[39m\u001b[32m92\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_run_once\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 93\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m._stopping:\n\u001b[32m 94\u001b[39m \u001b[38;5;28;01mbreak\u001b[39;00m\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/nest_asyncio.py:115\u001b[39m, in \u001b[36m_patch_loop.._run_once\u001b[39m\u001b[34m(self)\u001b[39m\n\u001b[32m 108\u001b[39m heappop(scheduled)\n\u001b[32m 110\u001b[39m timeout = (\n\u001b[32m 111\u001b[39m \u001b[32m0\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m ready \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;28mself\u001b[39m._stopping\n\u001b[32m 112\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;28mmin\u001b[39m(\u001b[38;5;28mmax\u001b[39m(\n\u001b[32m 113\u001b[39m scheduled[\u001b[32m0\u001b[39m]._when - \u001b[38;5;28mself\u001b[39m.time(), \u001b[32m0\u001b[39m), \u001b[32m86400\u001b[39m) \u001b[38;5;28;01mif\u001b[39;00m scheduled\n\u001b[32m 114\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[32m--> \u001b[39m\u001b[32m115\u001b[39m event_list = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_selector\u001b[49m\u001b[43m.\u001b[49m\u001b[43mselect\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtimeout\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 116\u001b[39m \u001b[38;5;28mself\u001b[39m._process_events(event_list)\n\u001b[32m 118\u001b[39m end_time = \u001b[38;5;28mself\u001b[39m.time() + \u001b[38;5;28mself\u001b[39m._clock_resolution\n", - "\u001b[36mFile \u001b[39m\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/selectors.py:566\u001b[39m, in \u001b[36mKqueueSelector.select\u001b[39m\u001b[34m(self, timeout)\u001b[39m\n\u001b[32m 564\u001b[39m ready = []\n\u001b[32m 565\u001b[39m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[32m--> \u001b[39m\u001b[32m566\u001b[39m kev_list = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_selector\u001b[49m\u001b[43m.\u001b[49m\u001b[43mcontrol\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmax_ev\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimeout\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 567\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mInterruptedError\u001b[39;00m:\n\u001b[32m 568\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m ready\n", - "\u001b[31mKeyboardInterrupt\u001b[39m: " + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit Width: 7\n", + "Circuit Depth: 30\n", + "Gate Counts: {'u': 25, 'cx': 19}\n" ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Job: https://platform.classiq.io/jobs/950afafe-5e67-409e-8b7a-8a7f265fa281\n", + "/Users/ofriwienner/Library/CloudStorage/GoogleDrive-ofriwi1@gmail.com/My Drive/Documents/Work/1. Classiq/classiq-library/classiq-library/algorithms/gradient_estimation/gradient_estimation_helpers.py:125: SettingWithCopyWarning: \n", + "A value is trying to be set on a copy of a slice from a DataFrame\n", + "\n", + "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n", + " print(\"Filtering out states with ancilla qubits in state |1>...\")\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -886,7 +907,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "id": "19", "metadata": {}, "outputs": [], @@ -956,10 +977,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "id": "23", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n" + ] + }, { "name": "stdout", "output_type": "stream", @@ -970,14 +998,24 @@ ] }, { - "data": { - "image/png": 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0wG+//Ya7777bKyjMDoMzBlbffvutOTEIGj9+vPv2w4cPY/jw4fj1119N9pDvKzfccIPPq3IwILvrrrtM1pGlTl7OC/4NDz30kAlc69ati1tuucXMPUi8rmPHjmbOTQZ68+fPR/fu3c1UNgzk+Jh8bD4uTyxTZ7Zs2TL06tXLBLKrVq0yQS6fXzuwtDHIY0aVzz9ft3vvvRfr16/P098iwaGJhUVEonxy7VDzdTJvllm5nyxDZoXXM8u0Z88ed4n0qquuwoMPPujehtkmT2+//Tbq1auH5557zlzm+dWrV2Ps2LE57gsDMwYvzDxR3759TeBm/x6bGTy9//77KFu2rHmOfRm/V7p0aZM9s0udecVgrlu3bub8mDFjTCaN5en69evj3//+twmy/vOf/7i35+02PiYfO6fHffHFF01QaAfJDBr5t/F5ZJbPdu2115pAjh555BG89NJLmD17tnmeJbyUuhARkbDyNaNHDFxywmzRxRdf7HVd69atc71flhPtYM5efspeisoOPpkVq1mzpin3cntKSkpCKDRt2tRr38jePztDdz7Wrl2L9u3be13Hy/y77UmrM+8Hg3YGiZ7Pk4SPMnQSlfht23PpL5VdJdbww5b/++FY+svXgfa1a9c22zKYYPkyM17P8WDMhNmKFSuGYGDp2BP3y7OcyhImu2/fffdd043L25iZY2PG+eDjZA5os1opwXP/7OfX3r/M5epgyu15kvBRhk5EJArxg9ZuWgj1ydeAjs0FV199tSkVHj161Ou2Xbt2YeLEiWaKkbx0YrL0x3FunpYuXYrzwelTmPl77LHHTCbMLgUHAoNVjmuzMSPG+eryglkzloezw5KrZ5YtK/yb2FjhiZdZemUnsUQ+BXQiIhI2r7/+Oo4fP266MtkByjnp2FHKQK9y5cq5jn3LjE0Q69atM+O7ONfcZ5995h7Y7+8UHcwSMvhkRyfHrf3000+mQSIQOCaQzwGbDBiI3nPPPedkwXIzcuRIE7RybNvvv/9u/v4333wTe/fuNbezPLx48WIz3pDXZZVR47hEBoXsIubzxs5g7hfH7okzKKATEZGw4fQiDGQ4No1dlrVq1TLTkXCKDnZsspkgL2rUqIEpU6aYLlJmrhjY2F2unI7DH8w6Tpo0yXSCssz6wAMPuJsuzhe7Rtl1etlll+HWW281AZS9SL2vmEXjtC/s6uV4QXa1fvXVV+65+XifzLKxBM+MYFbj/i666CIT/PLv5N/4xBNP4Mknn/RqiJDIls+Vl9GoDpeWlmbmFzp48KDmJ4tyGkMnsYbj2ThlBwMajmkLtpzG0EUaZvk4WTGzf+LM/+GUlDRUqVICyckHkZio+UWzoqYIERGJKhyTx05Xlkk5DozZtCFDhoR7t0SCSgGdiIhEFTYWPP3002biYk4uzvFhHGcmEs0U0EnUuvDCC8O9CyJRLVKnA+JktzyJxBIFdBK1HzT2xJ8iEngcM+dvk4GIBF5kfr0SEREREZ8poBMRERFxOJVcJWqnLeGyQfYM6JE61kfEqZw0bYlILFBAJ1ErhqZYFBGRGKe0hYiIiIjDKaATEZGINWfOHFPOPXDgAJyE+zxt2rSA3R+79l9++WUE0xVXXIH7778/qI8hwaOATkRE3E6fcWHhpn34auV285OXgxn05HQaPXp0xL8y3MfmzZufc/3OnTtxzTXXhGWfJDZpDJ2IiBjTV+/EmG/WYOdBq9mBKpYojFHdG6Jr44oBf5YY9NgmT55sFoRfv3691+Tgv/76a1henRMnTiAuLs7v369QoUJA90ckN8rQiYiICebu/WS5VzBHuw4eM9fz9kBj0GOfSpQoYbJyntd5rvaybNkytGrVCkWLFkW7du28Aj/66quvcNFFF5mO25o1a2LMmDE4deqU+/akpCRcf/315j6LFy+OXr16ITU19ZxM23//+1+vxeFZ6r3zzjtRtmxZ83tXXXUVfvvtN3PbBx98YB6Hl+2sIq/LquSakpKCW265BaVLl0axYsXM37J48WJz26ZNm8y+lS9f3uwf16H98ccffX4eZ8yYYfY3c1l62LBhZn9p37595vErV65snsMmTZrg//7v//JcNi5ZsqT7b6Tk5GTzXPJ6/m38O7Zu3epVMm/durX5m7lN+/btsW3bNp//NvGdAjqJWnzT4klEcsayKjNzWRVX7et4e+byK6cDCtWUQI8++iheeOEFk7ErUKAAbr/9dvdtP//8M/r162cCmDVr1uDtt982QcfYsWPd0xgx0ODarnPnzsXMmTOxefNm9O7d2+sxNm7ciC+++AJffvklVq5caa67+eabsXv3bnz//fcmqGTQ2LFjR3Nf/H2uE9uoUSOTbeQp833SoUOH0KFDB2zfvh1ff/21CQD/+c9/mv2yb7/22msxa9YsrFixAl27dkX37t1NEOoL7g+DJe677fTp0ybr2adPH3OZU8y0bNkS3333HVavXo1Bgwahb9++WLJkCfx18uRJdOnSBfHx8eY1+OWXX0xAyv1nhpMBdY8ePczf/vvvv2PhwoXmcTXFTXCo5CpRiR8y/JYuIrlbsmX/OZk5TwzjeDu3a1srISxLfzE4Y2BAI0aMQLdu3UyQwswUs2S8rn///uZ2HvtPPfWUCZpGjRplAqVVq1Zhy5YtqFKlitnmo48+MoHY0qVLTUaMGITwembjaP78+SbgYUBn/63PP/+8yVpNmTLFBCcMYBhg5lRi/fTTT7Fnzx7zWMxiUe3atd23N2vWzJxs3PepU6ea4G/IkCG5Pjf58+fH3//+d/M4d9xxh7mOfzMzdjfeeKO5zMzcQw895P6d++67Dz/88AM+++wzk0HzBwNGBqXMatpB2oQJE0xwycwcs5AHDx7E3/72N9SqVcs9L6gEhwI6EZEYtzv9WEC3C4amTZu6z1esaI3nY6BVtWpVk/FidsjOyNkZKgZ8R44cMZOMM5Czgzlq2LChCTx4mx3QVatWzR3MEe+X2bOEBCuItR09etSUSX3FbF+LFi3cwVxmfAyWfJk9Y5aPmS0+hq8ZOmIm7pJLLsGOHTtQqVIlTJw40QS9/Bvt5+OZZ54xARwzhQxejx8/fl5VDD4/zGoyQ+eJzzufn86dO2PAgAEmi3f11VejU6dOpjxrv34SWAroRERiXLn4wgHdLhgKFizoPm9ngzxLlszS9ezZ85zfs8fC+YLjvDzxfhl8MNuUmR0o+aJIkSI53s7MGcvAzP4xc8ftb7rpJhN0+YpBKbNgkyZNwr333msyfJ5j3Z577jm88sorZuoTjp/j38opSnJ6DD7PmSdoZ5nV8/lhGZfBY2Z2YMyM3dChQzF9+nST0XvsscfM38rgU2I0oHvzzTfNyR5syVQ5O6LUFi5Z4Ru9PWi6Xr16WvpLJAeta5Q23axsgMhqHB3DpwolCpvtInHpL45r4/HuWcb0xDIfB+/zZGfpONaOJUlm6nK63127dpmSKueBywo7YZn9yi27yLIkx91llaVjdpGZrBtuuMEdKHk2FuQlS8fgKjEx0bznMUPn+RgcR3jbbbe53yP//PPPHP9+BmWencgbNmwwGU/P54dBWrly5UzDSHaYneRp5MiRaNu2rSkNK6CL4aYI/oOOHz/eDErloFh27vCf848//gj3rkmE4ptsbm+0IgLkvyCfmZqEModl9mXezu0iEb/cc+wbs3T8TGAZlZkqZoOIpT5mpRjwLF++3IyLYxMFx+RxnFd2+HsMQDiwn52kDLIWLFhgGjTs6VQY6HFsHsuqe/fuNWXMzNhdyjF2vB8GVmzIYAMDmwSoTp067kYMljFvvfVWd/YxL+y/j6VnZvg8xzjyMZgZ4/7z+bn77ru9unyzws/Z119/3TRq8O+95557vDKlfLwyZcqYz2I2RfB5YDaTGTl29fIygzj+nexs5XPIoFDj6GI8oGPHD7uA+E9Zt25d8w/LwaiLFi0K966JiDge55l787aLTCbOEy/z+mDMQxcoHKP17bffmoCBpUdmf1566SUzJo6YPeS0JqVKlcLll19uAjU2TjC7lBP+3v/+9z/zOwMHDjSfPWw+YHDCKUaITQfs6rzyyitNRiurqUCYxeO+MZPFzzEGl0xQsJmBXnzxRbNvnI6Fn3X8e5j9yitmKNngwI5Su7vVxuCW98n75ooQdoCZE3YVM6N52WWXmSCTpWHPMXc8P2/ePDOOkeVuBmpsymDmlhk73r5u3TrzHPG5YxPJ4MGDTTApgZfP5cAVzJl1+fzzz01HE785ZJcy5jclz29LaWlp5p+TXTc5pYfF+fjtliUV4v9HqKZWEAkXfogyI+I5h5o/ODUJu1nZAMExcyyzZpWZi6SSq0T//3BKCj+/SyA5+SASE/X57egxdMS2c6a/+aIzO8dBnznV/8eNG2dS8CIi4hsGb/bUJCLiHI5KW3BwO8cYcHZtdvEwQ2dnYbLC2j2zcfaJA2JFREREoo2jMnQch2B3MbFVmpM0sg2bs4JnhQNCQznxpYiIiEg4OCqgy2qcVFYdRSK+zP0kIudH4+ZEIodjAjqWTznnHLtp0tPTzTw2bI/m0iUimbEJwl5qRkSCE8ydT/OFiMToGDou8cJ5gziOjgsRs9zKYI7LiYiIiIh4euMNzhPILmygTRtgyRLk6MABYPBgLi3HIVtA3brA//4Hx3BMhu69994L9y6IiIiIA0yeDAwfDrz1lhXMvfwy5ysEuIBQuXLnbs8V0Jgf4m1TpgCVKwPbtnGJNziGYwI6kbyOr+SM5MTJqDUPnUhgcR46ewwzm880nk4iyYsvAnfdBQwcaF1mYPfdd8D77wMjRpy7Pa/fvx9YsIDrBlvXZbPaW8RyTMlVJK+4iLTnQtIiEvigzoFz00uUO3ECWLaMS7dlXMe55Xn57Gpr5/j6a6BtW6vkykVAGjcGnnmGCxnAMRTQiYiIhAmX4br//vvP6z4GDBiQ6zJe0SI9nas+ZZyymuhi714rEDu7OpsbL+/alfX9bt5slVr5exw39/jjXPoMePppOIYCOhERyXDmNLDlZ2DVFOsnLwcRgxGWa7nwe2Zc95O3cRsR4uJQJUpknMaNC8zzcuaMNX7unXc4zy3Quzfw6KNWqdYpNIZOREQsa74Gpj8CpO3IeEaKVwK6Pgs0vC5ozxLX2J40aRJeeukl9/yRXOKR01NxqqpId+LECTPxvQQfF4diw4Itq7UDypQB8ucHUlO9r+flChWyvl92tnLsHH/P1qCBldFjCdcJL68ydCIiYgVzn/XzDuYobad1PW8PkosuusgEdV9++aX7Op5nMNeiRYtzGp64TjcXcGfw16xZM0xhreys06dP44477nDfzqmuuKKQJ85h2rp1axQrVgwlS5ZE+/btsY0tjdmUL1kSZWnUxvNDhgwx15cpUwZd2D4JYPXq1Wa+VK41Xr58efTt2xd7Wf876/Dhw2b6Ld5esWJFvMCaXi5Gjx6N5s2bmxWR+BwVLVoUvXr1MstZZvb888+b+01ISDDZTc8xxB9//DFatWqF+Ph4VKhQAbfeequZDsz2119/oU+fPihbtqx53thMNmHCBPftXDqTj8vnq3Tp0rj++uuxdetWn57TQIqPB4oXzzhlFdDFxVlZtlmzvDNwvMxxcllp3x7YuNHazvbnn1ag54RgjhTQiYjEOpZVmZlDVg0OZ6+bPiKo5dfbb7/dK4B4//33MdBuUfTAYO6jjz7CW2+9hT/++AMPPPAAbrvtNsydO9f6U86cQWJiIj7//HOz1vcTTzyBf/3rX/jss8/M7adOnTIBW4cOHfD7779j4cKFGDRoUJ67dD/88EOTlfvll1/Mvhw4cABXXXWVCUB//fVXTJ8+HampqSYIsj388MNmP7/66ivMmDHDBEHLly/P9bE2btxo9v+bb74x97tixQr84x//8Npm9uzZ2LRpk/nJffvggw/Mycbg7qmnnsJvv/2GadOmmWDMs5T9+OOPm+fr+++/x9q1a/Hmm2+aYNX+XQatDAZ//vln8zczKO3atavJTgbqOQ2k4cOBd9/l6wSsXQvcey8D6oyu1379uGBBxva8nV2uw4ZZgRw7YtkUwSYJx3DFkIMHD/KdyfyU6Hb69GnXn3/+aU48LxLtjh496lqzZo35mWeb57lco4rnfuJ2Z505c8Y8Fk8876/+/fu7rr/+etfu3btdhQoVcm3dutWcChcu7NqzZ4+5jdvQsWPHXEWLFnUtWLDA6z7uuOMO1y233JLtYwwePNh14403mvP79u0znwNz5szJcX88DRs2zNWhQwf3ZZ5v0aKF1zZPPfWUq3Pnzl7XJScnm8dav369Kz093RUXF+f67LPP3LdzX4oUKWLuPzujRo1y5c+f35WSkuK+7vvvv3ddcMEFrp07d7r3uVq1aq5Tp065t7n55ptdvXv3zvZ+ly5davaN+0Xdu3d3DRw4MMttP/74Y1e9evW8Xufjx4+bff/hhx9yfU4D8T+cnGx9fvOnr157zeWqWtXliotzuVq3drkWLcq4jS/n2X8rN/5btWnjchUq5HLVrOlyjR3rcnk8pRFPY+gkKnHeOZYMRMQHh1LzvF2gl/5iqa9bt24mq8SpUHjezhB5ZqqOHDlyzgpBzBJ5lmbfeOMNk+FLSkrC0aNHze0sWxLLhcxMMePE++nUqZPJorFUmRctWdPzwMwXs2PMXGXGzJm9H204y+1Z3BeWhHPD0nNlj4Fjbdu2NZnI9evXm/IpNWrUCPk9BoDx71m1apX78rJly0z5lvvJ8ip/n/gcNWzYEPfeey9uvPFGkzHs3Lmzybi1a9fO/bfxuWeGzhPHOfJv4/aBeE4DbcgQ65SVOXPOvY7l2EWL4FgquYqIxLoLywd2u/MouzKgY8mQ5zM7dOiQ+fndd99h5cqV7hNLhfY4OjZXPPTQQ2YcHcuavJ2lWwZTNpZ2WRZkwDJ58mTUrVsXi85+kvPLYOa59bKaz5JjxTLvW/fu3b32iydOcH755Zcj2Aras+F6BNx20Maxewy2ihcvjokTJ5qlM6dOnWpus58Xjv3jmDeWsHfs2GGW2OTzaP9tDGAz/21//vmnGYuX23MqoaEMnYhIrKvWzupmZQNEluPo8lm3c7sgssdkMRixGw08MZPEVSmYVeJ4raxwfBeDCs8xZswiZcaMHk8jR440GS921F5yySUmU8jmBk8MXjIHTFk1dnzxxReoXr06ChQ496O1Vq1a5j4WL17s7txlpoxBUXZ/i41/L4OsSpUqmcsMlBh4+pLdo3Xr1mHfvn0YP368aawgjvPLjH97//79zemyyy4zY/7YaMG/jUFauXLlTFCYneyeUwkNZegkqpf+4sn+lioi2bggvzU1iZF5IPvZy13HW9udxSwWS248BWq1CJYMOSCfGTfP8qGNJT9mjZhFYhaPgRpLhK+99pq5TBxqwWDlhx9+MMESB/szI2XbsmWLCTiYTWJGilk8vk804BwVgGls4O+z8YLXjxo16pwALyvsKt2/fz9uueUW83jcN+4Ds4PsvGUplllDBkk//fSTuU+WKX1ZlpClbQZZLH2yKWHo0KGmpGmXW3PDAJINHHyeNm/ejK+//to0SHhi8wibNVhaZbPJt99+635O2P3K8jc7W/n4fA7Z0MH9SElJyfU5ldBQQCdRi+tM2mtNikguOM9cr4+A4pnGPTEzx+uzmIcuGEt/MQOUUxaIgQiDNHa7MmBgVo8lWE5TQnfffTd69uyJ3r17m/FqzEx5Zus47QczVhwvxrIguzEZjPH3iJlB3v8///lPXHzxxUhPTzdTjeSG2TNmBxm8cUxZkyZNzLQmnMLDDtqee+45k/liaZbjzC699NJzxuJlpXbt2uZvuvbaa819N23aFP/5z3/gK2beWMpm5y+znMzUMfPmiQEfgzLeN0vEDKhZvrafs3nz5pnAkPvB553BKYN5vla5PacSGvnYGYEYkZaWhhIlSpj5e3J6wxDnY1aO3/KJb2C+fAsWcTJ+uDJTwsDmvJoVODXJtgVWAwTHzLHM6pGZy5yhIz5eOKeoiGZsZOA0Iyz7xvL/cEpKGqpUKYHk5INITNTnd1Y0hk5ERDIweKtxmZ4REYdR2kJERETE4RTQiYiIRHDJNRbKrXL+FNCJiIiIOJzG0EnUym3eKJFoFMo+NzVCSCDFUI9mUCigk6iUl0k3RaKBPW8bJ+YtUqRI0B8v0Et/iXBZN9KXcf8ooBMRiQJcnYDzge3Zs8d8IGqqHnFSZo7B3O7du828fVlNKi25U0AnIhIFmDHjYuicx4uz9Ys4DYM5X1e/kHMpoJOonViYH2zESSqVrZBYwNn+ufSV50L0wTzGuOwTJSYm6hiT88KssjJz50cBnUSto0ePhnsXREKOX15CMbaNAZ0dOPLx9KVJJLw0bYmIiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJy6XCVqqQVeRMeYSKxQQCdRiVMoNGjQINy7IRK1dIyJRBaVXEVEREQcTgGdiIiIiMOp5CpRibPYb9261ZyvXr26ZrEX0TEmEtUU0EnUOnLkSLh3QSSq6RgTiRyOKbmOGzcOF198MeLj41GuXDn06NED69evD/duiYiIiISdYwK6uXPnYvDgwVi0aBFmzpyJkydPonPnzjh8+HC4d01EREQkrBxTcp0+fbrX5Q8++MBk6pYtW4bLL788bPslIiIiEm6OCegyO3jwoPlZunRpvwbM85Td3Eqe2+VE2+b9eciXL585BXtbz+0z/24o9sHlcplTtGzr+TpH87ak496358GTE98jwr2tE477SHmPOHXqFNLS9uS4jTg0oONBc//996N9+/Zo3LhxttsdP37cnGxpaWnm57p163DhhReesz2vY0ekbe3atdn+oxUtWhQ1a9Z0X+Z4vtOnT2e5bZEiRVCrVi335Q0bNpiScVYKFSqEOnXquC9v2rTJ62/wVLBgQdSrV899ecuWLTh69Gi2qyZ4TrTLDtDsBjTzAG7UqJH7clJSEg4dOoTseL4GKSkp7uc5Kw0bNnS/QezYsQMHDhzIdtv69eujQAHrX3TXrl3Yv39/ttvWrVsXcXFx5vzu3buxd+9e9218vT3Vrl0bhQsXNuf37NljTtnha8zXmvbt24fU1NRst+X/jv1/xX3duXNntttWq1bNjAclPgfbt2/PdtsqVaqgRIkS5jyf2+Tk5Gy3rVy5MkqVKmXO8zXbtm1btttWrFgRCQkJ5jyHLthdwVkpX748ypYta87zf2zz5s3ZbsvtuD3xf3fjxo3ZblumTBlUqFDBnOcx8eeff2a7Lb+8VapUyZznsZb5dfVUsmRJJCYmmvM8htesWZPttsWLF0fVqlXdl3PaVu8RFh7Dnu8nPO6d/B6Rmd4jIuc9gp9zfG/I6f9LHDaGzhPH0q1evRqTJk3KtZGCH4T2iR+MIiISGJ4ZHJFgsJMfhQpZX6wle/lcueU6I8yQIUPw1VdfYd68eahRo0aO22aVoWNQ99dff5lv5VlR6SW4z0OklT1UTgl/OSWStiWVXMP7PETasaz3iOC/Rxw7dswMo2I2luVVz+wcs+2sOuzefQxVqpRAcvJBJCZm/fkd6xxTcuWLft9992Hq1KmYM2dOrsGcXb7kKat/JM83mOz4so221fNwvpkLbRs5zwPpuNfzEIr/h0j4fw/nthw2YQdxnsN/+ByyosYgjsOVMu7nmE+PHcsKOKnM+umnn5rsHMcecbwE8YXniy4iIiKRnZjhWDgGcayYeWbxOD6V2ThWz/ISGIsDS67ZRfsTJkzAgAEDfLoP/gMxAOS3guxKrhIdWCZhMwdxwLveIER0jEl4cOgThzplLqmygsYgjieWV3OSksIhUyq5RkWGziFxp0QQdUWJ6BiT8GBJlQEcT56zL3DGBSZWGMR5l1QlZgI6ERERifySKrNx6enpXokYDpViEMefqpgEhwI6ERER8Ru7VBnEcTiTZ0mV833aJVV7vkAJHj3DIiIikicM3BjAMZBjQOdZUrWDODUshpYCOhEREfGp2cyzpGrjODjPkqrGxYWHAjoRERHJkj3xr93g4LnEJUuqnC+OTQ4qqYafAjoRERE5Z8ktu6TqueISAze7pGqviS2RQQGdRCV2UXkuCC4iOsYk95IqS6nMxGVVUmU2jhMAq6QamRTQiYiIxHBJlfPEMYhjRs6zpMqmBrukymYHiWwK6ERERGKwpGqPi8tcUmUQx5JqVmuhS+RSQCdRWzpISUkx5xMTEzWRpYiOsZjH90UugckgznMlHZZQuRwmA7lixYqppOpQCugkavGNS0R0jMV6SfXIkSPukiqDOlvRokVNEMdgTiVV51NAJyIiEmVOnDjhLqnyvK1gwYKmnMpALi4uLqz7KIGlgE5ERCQKsKHBLqkePnzYq+vfLqkyK6cu1chw8iSwaxdw5AhQtixQuvT53Z8COhEREQeXVBm8MYhjMOdZUuV4OGbj2KXKoE7Cj7PBfPIJMGkSsGQJM6l8DTmOkeO9gc6dgUGDgIsvzvt9K6ATERFxGHam2iVVdqzaWEa1J/5VSTWyvPgiMHYsUKsW0L078K9/AZUqcXoYYP9+YPVq4OefraCuTRvgtdeAOnV8v38FdCIiIg4pqbKxgUEcGx1szL4xC8eSKueOU0k1Mi1dCsybBzRqlPXtrVsDt98OvPUWMGGCFdwpoBMREYmikiqX4GJJlZdtXLWBmTiOj1NJNfL93//5th2n/7vnnrzfvzJ0EpX4DbVhw4bu8yKiY8xpJVUGcczGnTp1yn09J/u1S6rsWBWxKaCTqMQgToGciI4xp5VU7XFxXI7LxjniWFJlEKeSqnP17On7tl9+mff7V0AnIiISJiyhctUGZuPS09O9Sqrx8fEmiONPlVSdr0SJjPN8madOta5r1cq6btky4MCBvAV+nhTQSVRi6/6OHTvM+UqVKunNUETHWEQ5duyYCeLY5OBZUi1cuLC7pMp1VSV6TJiQcf6RR4BevawGiPz5retOnwb+8Q+geHH/7l//LRK1WLawAzoR0TEWbgzcGMAxkGNA51lStYM4llQl+r3/PjB/fkYwRzw/fDjQrh3w3HN5v08FdCIiIkGsFtglVf60S6oc4+tZUtWY39hy6hSwbh1Qr5739bzOY27oPFFAJyIiEkAM2piBsxsc2OzgWVLlfHFsclBJNXYNHAjccQewaZM1/xwtXgyMH2/d5g8FdCIiIgEqqTKAYzaO0464P2gLFHCXVBnQiTz/PFChAvDCC8DOndbzUbEi8PDDwIMP+vf8KKATERE5j5Iqu1MZyPGnzS6pMhvHCYBVUhVPXFr3n/+0Tmlp1nX+NkO47/P8fl1ERCT2Sqpceoud9OvXr0dycrI7mGNTAxux6tevj6pVq2p8XBi98QZQvTrL3NbaqEuW+PZ7kyYxIAd69Aj+OLoff7RWkLDnv+fkDIcO+Xd/ytCJiIj44OTJk+5xcVmVVJmN40oOEn6TJ1sdo5wWhMHcyy8DXboA69cD5cpl/3tbtwIPPQRcdllw92/bNqBrVyApiauCAFdfzXkHgWeftS5zv/NKAZ1EJZY3+A3ZPi8iOsb8LalyDVUGcexS9XyP4RqqDOKKFSum95kI8+KLwF13ZTQYMED67jtrupARI7L+Hfau9OkDjBkD/PyzNclvsAwbZk0o/NtvQEJCxvU33GDttz8U0ElU4putOshEdIydT0mVQRznjWNQZytatKjJxrFLlfPHSWixsm2POSMmRDMnRU+csFZdGDnSe8xap07AwoXZ3/eTT1rZO3afMqALJt7/ggVAXJz39SwRb9/u330qoBMRETGBwAl3SZXnbQULFnR3qaqkGl4NG3pfHjUKGD3a+7q9e61sW/ny3tfzMud5ywon+X3vPWDlSoQEvyN4zGbjlpJilV79oYBOohK/Ue/atcucr1Chgpb+EtExliXOEWeXVA8fPuy+nmunsqTKIE4l1cixZg1QuXLG5UAMWUxPB/r2Bd59FyhTBiHRubM1ru+dd6zLHBnEij4D1Guv9e8+FdBJ1Nq/f787oBMRHWOeJVUGbwziGMx5llQZvDGIYzCnkmrkYfYqt+k9ypSxltFKTfW+npez+jjg5L5shujePeM6+1+Cy+mykaJWLQQU559jkwYzjlwF7tZbgQ0brH1n16s/FNCJiEhMYGeqXVJlx6otLi7OXVLleXG2uDigZUtg1qyMqUcYoPHykCHnbs/+uVWrvK977DErc/fKK0CVKoHfx8REqyGC3bj8yewcx+6xKcPf5XwV0ImISNRiSZWNDQzi2OjgWVJlYwODODY6qBs+ugwfDvTvb3WScmktljdZUbe7Xvv1s0q348ZZ89Q1buz9+yVLWj8zXx9IzP4xgOMpIPcHB5k3bx6ee+45LFu2DDt37sTUqVPRI9gz/4mIiCNLqlyCiyVVXrZx1Qa7pMqgTqJT797Anj3AE08AHE7dvDkwfXpGowTnfwvny8+S8OWXA198AZQu7V0WrlQp64aJqAroeIA2a9YMt99+O3r27Bnu3RERkQgrqTKIYzaO66ra2Jlql1TZsSqxYciQrEusNGdOzr/7wQcIKn7H4ATCzCB+8w3QqJH3bf5wVEB3zTXXmJOIiIhnSZWB3NGjR91PChsa7JIql+NSSVUiCbtamZ0bPx5o2xb4+GPg+uszbov6gE5ERIQlVK7awCCOa6h6llTj4+NNEMefKqlKpOK/LMuubLpgdo4lYjZi3Hmn//dZwN+09uLFi7Ft2zYzyLRs2bJo0aIFatSogUjC/fRcb49jKSQ28Nt43bp13edFxPnH2LFjx9xdqplLqlyCixk5lVTFaQYNAurUAW6+mb0CIQrofvnlF7zyyiv45ptvTMs3Dx6msjnfFwOnmjVrYtCgQbjnnnvMt6NwGzduHMZwUTaJOfyA0fQDIs4/xhi42SVVBnSeJVV7XFzhwoX1xU0cpVo1K0Nnu/JKYNEi77nw8srnHo/rrrsOvXv3RvXq1TFjxgyT5t63bx9SUlJMlm7Dhg147LHHMGvWLPOtbebMmQi3kSNHmjcC+5ScnBzuXRIRkVywhMqKSlJSEtavX29mNWAwxyCS3alVq1ZFvXr1ULFiRY2PE0fasgVISPC+rnZtYMUKYPPmIGfounXrhi+++CLbdDazczz1798fa9asMQdguDENr3X3YhNnft+9e7c5X65cOY2lEYnwY4xBnGdJlc0ONmbg7JJqAU7eJRKlChe2snf+8PnIuPvuu32+04YNG5pToHEQ7MaNG92Xt2zZgpUrV6J06dLmG5uIp71cofnsh42IROYxxpKqHcR5llQZuHmWVEWcrnRp4M8/reW9SpXKuZv17MqVeeKorzq//vorrmSh+azhnAoanA26Pz4I9qQxIiISsOweh+0wiONPG0uqHH/NbBwnAFZDk0STl16y1qIlrlwRaD4HdDzAfD247EXRA+2KK67wak8XERFn4Hs354ljEMcxzZ4lVTbX2SVVNjuIRKP+/bM+H/KA7mWPcJLNEE8//TS6dOmCtpwRD8DChQvxww8/4PHHHw/8XoqISEQ5feoUiu1ejgLH9mHtgS2of8k1yJ/F+DbOiGCXVD2nkbJLqgzkNNZZYkFaHmZOK1487/efz+VHyuvGG280pc8hmdbUeP311/Hjjz9i2rRpiETsmuI3QH47ZKeURHdJh805xPGcmmBUJHBW/PAhKi8ag3Kufe7rUpGAHW1HoUWX/ub44/stgziOfbbZXaoM4ooVK6aSqvgsJSUNVaqUQHLyQSQmOvPz+4ILcl8FghEZtwnZWq7MxD377LPnXN+1a1eMGDHCn7sUERGHBHPNFgy1Lnh8OJV17UPZBUMxL/0QyjS80gR1tqJFi5psnEqqEstmzw7u/fsV0CUkJOCrr77Cgw8+6HU9r+NtIiISnWXWSgutydovyJRp4OUzLqDu6heQWqc9Chcu4u5SVUlVBOjQIQIDOq6+cOedd2LOnDlo06aNuY5LgU2fPh3vvvtuoPdRJM9Y2qnNWRq19JdIwKxb/AMaYZ9XZi5zUFcB+7Bj32bUvfIGlVRFcnHkCJCUBJw44X1906YITUA3YMAANGjQAK+++iq+/PJLcx0vz58/3x3giYQ7oNPcVSIBXr0hdatP2545slfBnEgO9uwBBg4Evv8+69tDNoaOGLhNnDjR318XEREHYGeq3aV6+Ewhn36nSKnKQd8vESe7/37gwAFWNzklGzB1KpCaCjz9NPDCC/7dp98B3aZNmzBhwgRs3rzZTGnCmcK///57s2JDo0aN/L1bkYDggOw9/ArEwdply6rLVSQPOEccZwNgEMe1um3l67VG6uoE0wCReQydOe5cwO58Cajfpoueb5Ec/PQT+w6AVq2s7lcu93X11dZ0JePGcblV5Jlfi+/NnTsXTZo0MePmuL6r3Zb+22+/YdSoUf7cpUjAMaCzgzoRyb2kyvfy5ORkrFu3Djt27HAHc1y1ITExEY0aNTZTk9jBmyf78s62o7Kcj05EMhw+zCXzrPNcBsz+qGrSBFi+HH7x66jj1CScWJhLb3GZFttVV11l5qITERHnlFT/+usvk43juqo2dqbaXaoFCxZ0X8955lYA58xDx8wcgzneLiI5q1cPWL8eqF4daNYMePtt6/xbbwEVKyJ0Ad2qVavw6aefnnM9y672Ys0iIhLZJVUGclyOy8ZltzhXHIM4LseV3XKPDNpOXnkLtsyfZFaKSCte26wUUUGZORGfDBsG7NxpnWdhs2tXgG0JcXGAv0vT+xXQ8WDfuXMnatSo4XX9ihUrULmyBsOKiERqSZVBXHp6ute62Ky08H2dP31dVYVl1cPlLjLntRqLSN7cdlvG+ZYtgW3bgHXrgKpVgTJlELqA7u9//zseeeQRfP755+YbHAeg//LLL3jooYfQr18///ZERETyPNEv54Y7+td201nKZoTM49eOHTvm7lLNXFLlElzMyHmWVEUk9IoWBS6yvh/5za+A7plnnsHgwYNRpUoVk7rntzP+vPXWW/HYY4+d3x6JiIhPS3Bx1QYz0e9ZqTOt9VSbdOzjLqkyoPMsqdrj4jhPY3YlVREJLibIp0yxlgPbvZszM3jffnaK3+AHdHFxcWZFiCeeeMKMp2Mav0WLFqhTp44/dyciIgFcT/XHvXtRqVnG1CEspTIbx25VX0uqIhLceejYCHHllUD58pwM//zv06+Abt68eahfv77J0PFkO3nyJBYuXIjLL7/8/PdM5Dww81CzZk33eZFYWk+16YY3cLBlN5QpW9aUVAsEoVlBx5iI/z7+2MrCXXstAsavr2pXXHEFmjVrhkWLFnldv3//flzJcFMkzPhhU7RoUXNSQCfRhGPmyiPriX0911M9tW8TEhISghLMkY4xEf+VKAGczTkEjN+5dzZGdOzYER9k6q/17JwSEZHAYPMZx8XtTlrn0/ZslBCRyDR6NDBmDOAxa9B5K+DvN7ORI0fisssuM12tv//+O144u/iYsiESKR9++/ZZg8WZpdC4IXEifkHmPHHsUGUwx+az0wVLRMR6qjrGRPzXqxfwf/9nrRbBCYUzN5r7s1qEXwGdnYXr2bOnmYvu+uuvx5o1a/DKK6/4c3ciQZHKlY7PBnQiTsLxyPZUI1zJwcbyaYNLuiJ19TMRsZ6qjjER//TvDyxbZs1HF9amCE/sbl2yZAl69OhhSrAiIuJfxistLc0Ecfb62HbVo3jx4qZLtVixYubyirajTDcrgzfPoM5zPVWt2iASub77DvjhB+DSSwN3n34FdP379zfLwtgqVKiAuXPnYtCgQaYDVkREfC+pcr44llQZ1NnY0MP54tilyvnjPNnrqbLblQ0SNq2nKuIMnCCkePHA3mc+Vwx1MfDbL98c+cbJb7wSvfjByGEApGWJJNKcOHHCXVLleRtXbLAn/uVKDoFYKSJYdIxJKKWkpKFKlRJITj6IxMTiUZGhe+014K23rDF0geDzkc/Gh8aNG5vB5Tyfk6ZNmwZi30REIp6vQZXdpcog7vDhw+7r+Z7KL5gM4uySqq/4OI3adwvY3yIiocGxc0eOALVqWct+ZW6K2L8/iAFd8+bNsWvXLpQrV86c55uOZ3LPvsyf7MQSEYnl5bdYFuV74pEjR0xJlRUCz5IqgzcGcQzmMpdURSS6vfxy4O/T54Buy5YtKFu2rPu8iEgsy235rfmHj6Bso6tMx6rnsol2SZXnRST2nDwJzJ0LPP44UKNG4O5XY+gkKjEzYpe18lrGEvGlzLr36bq5Th2SesOXKFgwzozdZRAXTSuX6BiTUIq2MXQlSgArVwY2oPM5Q/f111/7fKfXXXedv/sjEhD80ORC5CLBwDFzpsyay/JbKXs2oslVPaNyYmsdYyL+69EDmDYNeOABhD6g4zxzvtAYOhGJdof2Jvm24bH9URnMicj5qVMHePJJ4JdfgJYtWUnyvn3o2dEcQQnoPAfzijihHLT/bJtQ6dKlo6bMJeHDZi92qbLBIf1kppa0MC2/FU46xkT89957QMmS1moRPHnix1VQAzoRp33Y7Ny505znDPsK6MTf/yOu2sCpRtilanf2l63TCqmrEyJi+a1w0TEm4r9g9Jb6HdBxwDlXh0hKSvKaGJOG+hNaiohEiGPHjrkn/j116pT7ek72yy8IbHJYvUvLb4nI+bNngDvfQpJfAd2KFStw7bXXmvmVGNixpLV3717TwcV56hTQiYjTMHCzS6oM6GycI86eaqRw4cLubK+W3xKR8/HRR8BzzwEbNliX69YFHn4Y6Ns3hAHdAw88gO7du+Ott94y31QXLVpklqy57bbbMGzYMP/2REQkDGXD9PR0k4njT8/J0uPj4002jt3S2TU2MKg73bEP/si0UkSFEC2/JSLO9OKL1jx0Q4YA7dtb182fD9xzD7B3r3/dr36966xcuRJvv/22eZPjt9fjx4+jZs2a+Pe//43+/fujZ8+e/tytiEhIHD161F1S9VzZhhk4u6RawMegTMtviUhecR3XN98E+vXLuI4zvjVqBIweHcKAjtk4+xsrS6wcR9egQQPzJpicnOzPXYqIBHU9VZZU7SDOs6TKwI3vXQzkGNCJiAQbe/batTv3el53tp8vNAFdixYtsHTpUtSpUwcdOnTAE088YcbQffzxx2jcuDGC6Y033sBzzz1n1pVt1qwZXnvtNbRu3TqojykizlxPtdnVfb1KqjaOg/MsqaoLWkRCqXZt4LPPgH/9y/v6yZOtOepCFtA988wz7jfHsWPHol+/frj33ntNgPf+++8jWCZPnozhw4ebsXtt2rTByy+/jC5dumD9+vUmUyhi4wd0tWrV3OclNtdT/WnfflRoerX7+iJFipjmhryUVCVrOsZE/DdmDNC7NzBvXsYYOk4yPGuWFehF/VquDOIuvvhivP766+7JjqtUqYL77rsPI0aMyPX3OY8U38jZyVa8uPPXghOJZb6up7rvpq+RUKaMycZx2hERcZ5oW8uVOKHwSy8Ba9eai2jQAHjwQVZB4RfHfEXlXHfLli3DyJEj3ddxHF+nTp2wcOHCLH+HzRo8eQZ0IhJb66nuO7gVFYI8FEREJK+45NcnnyBg/Aro9u3bZ8bNzZ49G7t37z5nWTB7yaVA4hg9dqOVL1/e63peXrduXZa/M27cOIxhXlNiDhPPHDdFLLGp7Bpdry27VPem/OnT9kf/2hH0fYpFOsZEzg9Dp40bgd27rfOeLr88RAFd3759sXHjRtxxxx0moIrUD0tm8zjmzjNDxxKtxMaHzfbt2815ltkj9X9U8palt7tUef5k/njE+nqq4aRjTMR/ixYBt94KbNuWsVKEjR9XHrMpBTeg+/nnnzF//nzTZRoqZcqUMXPepaamel3PyxUqVMjydzheRmNmRJyL2X+OeWUQx1VpPIdb1GnVKebXUxURZ7rnHqBVK+C774CKFc9/2S+/A7r69eubkkcoxcXFoWXLlpg1axZ69OjhfrPn5SGcallEoibzw2UFuQQXs+qeQzqKFStmSuhsauIXvBVttZ6qiDgPl/uaMsWaviRQ/Aro/vOf/5iuUo6j47xznGjYU7A6SFk+5UoUrVq1MnPPcdoSfmsfOHBgUB5PREKHZVQGcczGnTx50n0931/YocpAjl/sPGk9VRFxojZtrPFzYQ/o+MbKb85XXXXVOd+sOVbJcymdQOrduzf27NljAklOLNy8eXNMnz79nEYJEXEGvlfwvYSBHLNyniVVjn3ke03RokVzHAOp9VRFxGnuu8+aomTXLqBJE35x9b69adMQzUPH7Bgn5Rw2bFiWTRFcPSISaR662MEy3Zo1a8z5hg0bZru4uoR2+S3iWw4z63ZJ1fMtiKs22CVVvWaRTceYhFK0zUN3QRYfSQyl+HYY0qaI1atXY8WKFahXr54/vy4iMbT8FjNoxDkh7S5Vz5Iqy6h2STXz8A0RkWi0ZUvg79OvgI5j2JKTkxXQScRi1tieokZTloR3+a0FR4+hfJNOXo1UzL4xgOOJy3HpNXIeHWMi/ju7MmX4AzoutcVy68MPP4wmTZqc8626qT/FX5EAf9hwDJYEv8zKzBxlXn6Ll7n8Vs2VzyK1Rhvkz1/AlFSZjYuPj1dJ1eF0jImcf6fr7NlZTyz8xBMhGkOX1dgWHtzBboo4XxpDJxJYf/zyHRrNvDXX7Za0exctrrxBJVUR8Uu0jaF7913g3ns5xy7AqXQ9WxF4fvnyEGXotgSj+CsSQPxyYa/dywH2KukFx5F9KT5td8GJAwrmooyOMRH/Pf00MHYs8MgjCJg8B3QczMzpSr799ls0aNAgcHsiEuAPG47ztLtcFdAF9rlNT083zQ1pJ/P79Dtafiv66BgT8d9ffwE334yAyvNcDhwvd+zYscDuhYhEPDY17Ny5E+vWrUNSUpLJgJap3QqpSDBj5bLC63chwUxhIiIiFgZzM2YgoPyanGvw4MF49tlncerUqcDujYhEFB7je/fuxcaNG7Fp0ybs27fPjJHlPJQJCQmoV6++mZqEMgd19uWdbUdlOR+diEgwvfEGUL06ULiwtTLDkiU5j2m77DKgVCnr1KlTztufL64Q8fjjwIABwAsvAK++6n3yh1/vskuXLjVrqM6YMcN0uXJ9RU9ffvmlf3sjIhExYaxdUuVPG8vW7E5llyq7Ve0ytpbfEpFIM3kylwsF3nrLCuZefhno0gVYvx4oV+7c7efMAW65BWjXzgoAn30W6NwZ+OMPoHLlwO/fO+9wInVg7lzr5IlvrUPPzgQV9C7X3NZOnTBhAiKRulxjh2axzxu+DbCkyiDu4MGDXp3qnCeO88VxGhhm5s53pQiJDjrGJJK7XNu0AS6+GHj9desypwXh1KRccmvEiNwfj2+BzNTx9/v1gyP49W4bqQGbiOS9yclevYErOdgYuNkT/xbm11UfMHhr1L6bXgIRCRoWDc5OYGAUKmSdPJ04ASxbBowcmXEdZ1tjGXXhQviES0tzQZvSpeEY5/X1ec+ePVjP/CVgVo0oW7ZsoPZLRPzgS5aMmRVmqxnEHTp0yH09S6ic4oVBnGdJVUQkUjRs6H151Chg9Gjv6/butTJs5ct7X8/L69b59jicTqRSJSsIDIbbb8/59vffD1FAx4W1uVrERx99ZD4cKH/+/OjXrx9ee+01FC1a1J+7FQkYBiOVzw58iJXAJKf1VJt37mdKqn/99ZcpqdrHLfF4tUuqPI5FfBGLx5iE35o13mPaMmfnAmH8eGDSJGtcnY8FCr+mLfHEbODq1cCBA8BVV/l3n34FdMOHD8fcuXPxzTffoH379ua6+fPnY+jQoXjwwQfx5ptv+rc3IgHCDxgO3o8Vua2n+tP+v8x6qp7TD9kl1ULBeEeUqBdrx5hEhvh4Thaf8zZlyjDJBKSmel/Py1yVISfPP28FdD/+yGVMETRTp557Hb9nc/WIWrX8u0+/miLKlCmDKVOm4IorrvC6fvbs2ejVq5cpxUYiNUVItJZZ9z5d1wRvmddTtacP2Z0vAbt7TkXp0gkmiGNnurIqIhLNTRGtWwOvvZYRLFWtCgwZkn1TxL//ba3e8MMPwCWXICw4io2h1c6dIcrQHTlyBOUzF6fBVuBy5jaRcOP3FHt8WLSPB+OYOVNmzeZPZJBXAfuwJy0JiU2bhXr3JErF0jEmzjN8ONC/P9CqlRXYcdqSw4c5S4d1OztXWbodN866zGlKnngC+PRTa+66Xbus6zm1CE+hsmkT5//073f9Cujatm2LUaNGmTF0dgccx+eMGTPG3CYSCR8227Zti/qlv06cOIH92zf6tO3xA3585ROJ8WNMnKl3bzZuWkEag7PmzYHp0zMaJZKSrM5XG0eKsTv2pptyb7oIVMDpibVSZuW++84KREMW0L3yyivo0qULEhMT0ayZ9Y3/t99+M8HdD8xVikjQcI44Dh9ggwMz4scv8J7YOztaT1VEYsmQIdYpK2x48LR1K0JqxQrvywwuOVEIV43IrQM2oAFd48aNsWHDBkycONGs60i33HIL+vTpYyYhFZHAZ0PYXc4gjsGc59DX6s06IHV1Qq5j6LSeqohIZJg9O4LmoeNUB3fddVdg90ZEvHCyX3viX04CbIuLizMdhpxqhOdXtB1lulkZvHkGdZ7rqVbQqg0iIlHL74COGTp2te7evdtrTit6gkVrEfG7pMq54piN49hU2wUXXOCeaoSZcM8xS1pPVUQktvkV0L377ru49957zfQlFSpU8Ppg4XkFdCL+dQwyE5e5pMoOQmbj4uPjTVCXHQZ1pzv2wR+ZVopQZk5EJPr5FdA9/fTTGDt2LB7h2hgi4rdjx465S6qnPHrVOdmvXVLlJMC+0nqqIiKxya+AjqWgm2++OfB7IxIgzBRXrFjRfT6S1lNl4MaSKoM4z5Iql91iAMdAjh3jmgZCIlk4jzERCVBAx2BuxowZuOeee/z5dZGg4wdMQkJCxKynuv2SUajd7gYTxKWnp3uVVFlKZRDH0mpOJVWRSBKuY0wk2n30EcBVVfO6BJhfAV3t2rXx+OOPY9GiRWjSpMk5JSGu6SoSa3JcT3XhUPy4dy8qNe9irmMGzm5wKKDuUxEROWvAAK63DQwalLF0WdDWcq1Ro0b2d5gvHzZv3oxIpLVcY2/eNgrFuqW+rqd66o65KFO2rHuFFRGnCvUxJrEtr2u5Ot2WLcD33wP/+EeQM3Rb+EgiEf5hs/Xs1N+hWJZo7aLv0diH9VT/SPodiVW6BXVfRKLxGBOJJTVq5C2YO6956ERiHT/Q2KXKJqGdm9egsQ+/w0YJERGJPWlpvm9b3I8kpM8B3fjx4zFs2DCflvZavHgx9u7di27dlImQ6MMVG+ypRriSA+Ur6tvgcK2nKiISm0qW5LC0nLfhIDhuc/p0EAO6NWvWoGrVqqbDtXv37mjVqhXKciXZs9Mw8Pb58+fjk08+wY4dO/AR2zREogRXQ2F3KrNxnADYxjJT8eLFkdjxRqSufkbrqYqISMjWb/UroGOA9ttvv+H111/HrbfeahoMOG8WJ0A9cuSI2aZFixa48847MWDAAA36lqgoqXKeOAZxnDfOc4k7rmXMDlXOG8fjgLSeqoiIZKdDBwRVnsbQNWvWzCz79fbbb+P333/Htm3bzAcelwBr3ry5+SnidCdOnHCXVHnexul57KlG+EUmM62nKiIiecF8WFISP3e8r2/aFHnmV1MEJz9lAMeTSDRg9o1ZZ2bj7KkY7JIqs3AM4nyZmkHrqYqISG727AEGDrSmJslKUMfQiTjJmdOnUHDfOpxOT8XaA1tR/5KuXstv2SVVDhdgEMdgzrOkyuCNQRzHx9klVV9pPVWJFeXLlw/3Log40v33AwcOsIkUuOIKYOpUIDUVePpp4IUX/LtPxwR0Y8eOxXfffYeVK1ciLi7OlMNEclp+q57n8ls/JmBH21Emg2aXVBnIsWPVs6TKJbgYyPF/TERyrtTYjXEikjc//QR89RXQqhWPJaBaNeDqq63pSsaNA/yZJMQxAR0/hNlh27ZtW7z33nvh3h1x4vJbC4bipwMHUa7RVV4fSnZJlY0OmhxVRESCjSN7ypWzzpcqZZVg69YFmjQBli/37z59DujYBNG4ceOwLR4+ZswY8/ODDz4Iy+NL5OPyW8zMUeblt3iZy281XPsyUutfjuLFS5hsHEuq4fqfFomGLnDi/KT6MiTiu3r1gPXrgerV2XAKvP22df6tt4CKFeEXnz/JOCUJJwummjVrYt++jHJWpOKkrxwb5XmS6LVu8Q8oj6zXUvVcfivfwW1mPWJm5RTMifgf0HHdbp78WBJcJKYNGwbs3GmdHzXKao6oWhV49VXgmWeCnKHjhx/XcC1XrpxZv89zAHmkGjdunDuzJ9Ht9OnTOLBzs0/bnkhLDfr+iIiIZOe22zLOt2wJbNsGrFtnBXX+zgDnc4buxhtvRIcOHUxmg6l1rhTBTF1WJ1+NGDHC3FdOp3X8C/00cuRIMyGsfUpOTvb7viTyMCvA1Rv4uvL/5ChyX5aOtPyWiIhEAs4/x9Ir+/Auusj/YC5PGbp33nkHPXv2xMaNGzF06FDcddddiI+P9/+RATz44INmVYmc5CVAzIyTv2Y1Aaw427Fjx9wT/3LZOVtio/ZIXZ2g5bdERCTiJxS+7z7gww+ty3/+yXjHuq5yZSa8gtzl2rVrV/Nz2bJlGDZs2HkHdGx5V9u7+IKBG7OsDOLsgdjEOeLYpcoGh8KFC2Nl21Gmm5UNEJ5j6XiZdrYdhQqZ5qMTEREJpZEjgd9+A+bMYWyVcX2nTsDo0SEI6GwTJkxAqCUlJWH//v3mJ8dLcT46ql27Ni688MKQ74+ErqTKII4/PQde88sEgzi+9p6NDfbyW5UXjUE5V0bjzu58CSaY4+0iIiLhNG0aMHkycMklXJEo4/pGjYBNm/y7T8ekKp544gl8aOcmz3bd0uzZs3EFp1mWqMEMnF1SZfBuYwbOXku1QA5ZNgZtJ6+8BVvmT0KBY/uQVrw26l9yjTJzIiISETjvnD0PXeb56XJZYdL5AR3nn9McdNFdUrWDOI6R8yypMoCzS6p5WX6raKMu5nyDsmU1PYlIEGjIjIh/uELEd99ZY+bIDuL++1+gbdsoD+gk+nDqG8+Sqo3dzSypMpDjT38mLGUZVutMigSPjjER/3GuuWuuAdasYUIDeOUV6/yCBcDcuf7dpwI6CSmOg2MGjuuossnBs6TK2eYZxLHJIaeSqoiIiJNdeqnVFMF1W7nc14wZ1rQlCxdal/2hT00JiZMnT7pLqlzBw/0PWKCAe1xcXkqqvgSO9uNw6hotSyQSWDrGRPxz8iRw993A448D776LgFFAJ0EvqTIbd+jQIff1DK64hiqDOHapBiPY4ocN50ykhg0bKqAT0TEmEhEKFgS++MIK6AJJAZ0EZcFuu6TquURc0aJF3SVVNjuIiIjEoh49rKlLHnggcPepgE4C4sSJE+6SKs/bChYs6C6patUOERERoE4d4MkngV9+sdZyLVbM+1kZOjTvz5ICOvEbs29paWkmG3eYk+ecxRIqs3AM4ooVK6Zyp4iIiIf33gNKluTKW9bJE0chKaCTkJRUjxw5YoI4BnOZS6qcL47j41RSFRERydqWLQg4ZegkTyVVBnLsWPUsqTKIYzYuLi5Oz6aIiEgYKKCTbHGOOLukyqyc54SizMIxkGNWTlOCiIiI5Gz8eGDYMM65msuGABYvBvbuBbp1g88U0Mk5JVWOh2M2jl2qvGzjeDi7pMqgLtKVKVMm3LsgEtV0jIn4jitBVK0K3Hwz0L27tfxX2bLWbVwtgrfPnw988gmwYwfw0Ud5uHMFdGLjJLx2l6pnSZVlVLtL1UklVQacFSpUCPduiEQtHWMiecMAjatDvP46cOutQFoa1yvn5PeAXQRr0QK4805gwAAgr3Pt53N5pmCiHMuH7L5k5olZpljHkiqfCwZxmUuqfJ6YjeNyXCqpiohIOKWkpKFKlRJITj6IxETnf36fOQP8/juwbRtw9Ciz3UDz5tZPf6nkGmMYv3PVBgZxDHA943mu2sAgLj4+3hEl1Zzw77IzjWzcUFAqomNMJFLwI5YBHE+BEpMBHafa8Jxuw5NnIJPdNk7c9tixYyaAYyB3isX6TCVVZuQY+GQlkPvLwMoOroK5LU9//vmnuVy/fn2vfQzFPjCgzCn57bRtyX4Oo3lbJxzLkbItZXeMOeE9ItzbOuG4j7T3CMlZTAZ069atM9mozHhd9erV3ZfXrl2b7T8auztr1qzpvrx+/XpTwswKy5a1atVyX96wYYPXODVPXE2hDqeQPmvTpk1ei9l7YgBWr1499+UtW7aYZbdywznieJAysON0JLt37zYnG29r1KiR+3JSUpLXWqyZNW7c2H0+JSXFBI7Z8VxXdceOHSbAzA4/JAoUsP5Fd+3ahf3792e7bd26dd1j/Pi37GV7kMfr7al27doofHZwwp49e8wpO3yN+VrTvn37kJqamu22/N+x/6+4rzt37sx222rVqplMKPE52L59e7bbVqlSxQTcxOc2OTk5220rV65ssqzE12wb8/nZqFixIhISEsx5NsJs3bo1223Lly+PsmdH7/J/bPPmzdluy+24PfF/115TN7tB9fZYRx4TdoCQldKlS6NSpUrmPI+1zK+rJ35JSUxMNOd5DK/haONscPhFVY5UPiunbaP5PYLvCw0aNHBf5v+D51AMTzyGPbflce/k94jM9B4Rme8RkrOYDOhiFQMIftjzQ4kHpmemTkRERJwrJpsiOK9adk0RkVDK8GdbllT57ZTfZj1/h9/m7WW4PLtUw7W/oSy52hkclVydUU6JhG0j4Vh2yrae2UyVXFVyDfbxGQ1NEb//zmy1NX4uGGIyQ8d/Dl9q8nmp24djW2bY7CCOAZ1n6cSeaoSlnEjZ33Btm9PrHax98AyWtK1znodI/R+OxG09Az5f31MDvQ9O3jYS/t+dtq3TtWgBcCROuXIczgMsXQqcrWgHREwGdE7GN1GOVWGWMT093X09DwiWVBnE8WesHCAiIiJOULKktYYrAzoOR/QhCZ4nCugcgOloZuAYxHHeOM+B1czA2V2q9uBgERERiSw33gh06MBmEyZhrJUiOLFwVnLoKcmWIoAIxi43BnAM5Dy72Bi42SVVu1tTsu6KFJHg0TEm4rt33gF69gTY1Dt0KHDXXWxWRMAooIvAkipLqQziPKcBYAmVjRwM4tilqpJq7mNZ7CkuRCTwdIyJ5F3XrtbPZcuAYcMU0EVlSZXz9tglVc/BxpzLyi6pstlBREREnG3ChMDfpzJ0YcRJfdmhyhPPe04GapdUOe2I+Bck22MN7YmURSRwdIyJRBYFdCHG7Bvnw2M2jjNv2xhw2PPFFStWTAFIAD5s7HnoPGeeF5HA0DEmElkU0IXojY9L6DCIYzCXuaTK1Rs4Pk4lVREREfGHAroQlFQZyHmuy8iSKoO4zKs3iIiIiPhDAV2AcdyWXVL1XNiaHWHMwjGQY1ZOJUAREREJFAV0ASqpcjwcs3HsUvVcl47j4eySal6WhRERERHxlQK688DJfu0uVc+SKsuodpeqSqoiIiISbAro/CipMgvHIC5zSZVdqszGcTkulVRFREQkVBTQ+YAlVK7awCCO4+M8S6pctYFBXHx8vEqqEYYZUhHRMSYSCxTQ5eDYsWPukuqpU6fc13OyX7ukyo5ViTzMmCYmJoZ7N0Silo4xkciigC4TBm52SZXLcdk4R5xdUi1cuLBKqiIiIhIxHNF2uXXrVtxxxx2oUaOGGZ9Wq1YtjBo1ymu5rPPBEipLqUlJSVi/fj127tzpDuZYSq1SpQrq1atnFnvX+Dhn4GvKCZx58iyRi4iOMYkNb7wBVK8OFC4MtGkDLFmS8/affw7Ur29t36QJ8L//wVEckaHjEk78YH777bdRu3ZtrF69GnfddZeZKuT5558/r5Iq54tjNs5e95OYgbNLqgUKOOIpkkwYxK1Zs8ac19JfIoGnY0wi2eTJwPDhwFtvWcHcyy8DXboA69cD5cqdu/2CBcAttwDjxgF/+xvw6adAjx7A8uVA48ZwhHwuh6YvnnvuObz55pvYvHmzz7/DLBzLpvwdBnAM6DxLqnYQxyycOBu/AHgGdJoDUETHmDhXSkoaqlQpgeTkg0hMLJ7r9m3aABdfDLz+unWZK25WqQLcdx8wYsS52/fuDXB59W+/zbjukkuA5s2toNAJHJt+4ji30qVL5zpPHE+eAR2lpqaa7lROLcKSKoM4/tRUIyIiIpErPZ2f5RmXCxWyTp44GmvZMmDkyIzrOK9/p07AwoXIEq9nRs8TM3rTpsExHDGGLrONGzfitddew913353jduPGjTMZOfvEsXB2SbVixYpmXFzVqlXNKg4K5kRERCJbw4ZAiRIZJ5ZIM9u7l3PGAuXLe1/Py7t2ZX2/vD4v20eisAZ0I0aMMIFUTieOn/O0fft2dO3aFTfffLMZR5eTkSNHmkyefUpOTjbX16xZEwkJCRofJyIi4iAcSXPwYMbJMwsX68Jacn3wwQcxYMCAHLdh8GXbsWMHrrzySrRr1w7vvPNOrvfP+eJ4EhEREeeLjweK5zKErkwZjovn8Crv63m5QoWsf4fX52X7SBTWgK5s2bLm5Atm5hjMtWzZEhMmTNAgdxERETlHXBzQsiUwa5bVqWo3RfDykCFZP2Ft21q3339/xnUzZ1rXO4UjmiIYzF1xxRWoVq2amaZkz5497tsqOCl8lpDi2EgR0TEmsWf4cKB/f6BVK6B1a2vaEnaxDhxo3d6vH1C5csYYvGHDgA4dgBdeALp1AyZNAn79FfChGBgxHBHQzZw50zRC8JR5OSeHzroiQcZpStjwIiI6xiT29O4NMPfzxBNWYwOnH5k+PaPxISnJ6ny1tWtnzT332GPAv/4F1Kljdbg6ZQ46R89D5w97Hjo2SCh7IyIiEp3z0MUiR05bIiIiIiIOK7mK5JVWihAJLh1jIpFFGToRERERh1NAJyIiIuJwCuhEREREHE4BnYiIiIjDKaATERERcTgFdCIiIiIOp2lLJGpdeOGF4d4FkaimY0wkciigk6hd+qt69erh3g2RqKVjTCSyqOQqIiIi4nAK6EREREQcTiVXidplidauXWvON2jQwJSHRETHmEi0UkAnUcvlcoV7F0Simo4xkcihtIWIiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJy6XCVqFS1aNNy7IBLVdIyJRA4FdBKVOO9czZo1w70bIlFLx5hIZFHJVURERMThFNCJiIiIOJxKrhK1S3+tX7/enK9Xr56W/hLRMSYS1RTQSdQ6ffp0uHdBJKrpGBOJHCq5ioiIiDicAjoRERERh1NAJyIiIuJwCuhEREREHE4BnYiIiIjDqctVolaRIkXCvQsiUU3HmEjkUEAnUbssUa1atcK9GyJRS8eYSGRRyVVERETE4RTQiYiIiDicSq4StUt/bdiwwZyvU6eOlv4S0TEmEtUck6G77rrrULVqVRQuXBgVK1ZE3759sWPHjnDvlkSwkydPmpOI6BgTiXaOCeiuvPJKfPbZZ2bB9S+++AKbNm3CTTfdFO7dEhEREQk7x5RcH3jgAff5atWqYcSIEejRo4fJwBQsWDCs+yYiIiISTo7J0Hnav38/Jk6ciHbt2imYExERkZjnqIDukUceQbFixZCQkICkpCR89dVXOW5//PhxpKWleZ1EREREok1YAzqWTfPly5fjad26de7tH374YaxYsQIzZsxA/vz50a9fP7hcrmzvf9y4cShRooT7VKVKlRD9ZSIiIiKhk8+VU0QUZHv27MG+ffty3KZmzZqIi4s75/qUlBQToC1YsABt27bNNkPHk40ZOv7OwYMHUbx48QD8BRLJ05awcYa4YgRntRcRHWPiTCkp/PwugeTkg0hM1Od3xDVFlC1b1pz8/cAmz4Ats0KFCpmTxB4GcJx/TkR0jInEAkd0uS5evBhLly7FpZdeilKlSpnMy+OPP24yL9ll50RERERihSPqUEWLFsWXX36Jjh07ol69erjjjjvQtGlTzJ07Vxk4ERERiXmOyNA1adIEP/30U7h3QxxEY+hEdIyJxBJHBHQi/shpfKWInD8dYyKRwxElVxERERHJngI6EREREYdTQCciIiLicAroRERERBxOAZ2IiIiIw6nLVaJWwYIFw70LIlFNx5hI5FBAJ1G79BcnoRYRHWMisUAlVxERERGHU0AnIiIi4nAquUrULv21ZcsWc75GjRqmBCsiOsZEopUCOolaR48eDfcuiEQ1HWMikUNpCxERERGHU0AnIiIi4nAK6EREREQcTgGdiIiIiMMpoBMRERFxOAV0ErXy589vTiKiY0wkO/v3A336AMWLAyVLAnfcARw6lPP2990HcDGiIkWAqlWBoUOBgwcRVpq2RKIS551r0KBBuHdDJGrpGJNo0acPsHMnMHMmcPIkMHAgMGgQ8OmnWW+/Y4d1ev55oGFDYNs24J57rOumTEHY5HO5XC7EiLS0NJQoUQIHDx5EcYbiIiIiEvFSUtJQpUoJJCcfRGJi4D6/1661grKlS4FWrazrpk8Hrr2WjwlUquTb/Xz+OXDbbcDhw0CBMKXKVHIVERERR0hPZ3Im43T8+Pnd38KFVpnVDuaoUydmoIHFi32/H5ZbmScKVzBHCugkapf+2rx5sznxvIjoGBPnYzatRImM07hx53d/u3YB5cp5X8egrHRp6zZf7N0LPPWUVaYNJ42hk6h15MiRcO+CSFTTMSahtmYNULlyxuVChbLebsQI4Nlncy+3ni9mCbt1swLN0aMRVgroRERExBHi463SZm4efBAYMCDnbWrWBCpUAHbv9r7+1Cmrk5W35Vb+7drV2qepU4GCBRFWCuhEREQkqpQta51y07YtcOAAsGwZ0LKldd1PP3HYDtCmTc6ZuS5drAzh118DhQsj7DSGTkRERGJSgwZWlu2uu4AlS4BffgGGDAH+/veMDtft24H69a3b7WCuc2ero/W996zLHG/H0+nT4ftblKETERGRmDVxohXEdexodbfeeCPw6qsZt3NuuvXrOWbUurx8eUYHbO3a3ve1ZQtQvTrCQgGdiIiIxKzSpbOfRJgYoHnO2HvFFd6XI4UCOola+fLlC/cuiEQ1HWMikUMBnUTtskSNGjUK926IRC0dYyKRRU0RIiIiIg6ngE5ERETE4VRylajE5b6SkpLM+apVq5rykIjoGBOJVgroJGodOnQo3LsgEtV0jIlEDqUtRERERBzOcQHd8ePH0bx5c9Muv3LlynDvjoiIiEjYOS6g++c//4lK9nocIiIiIuKsgO7777/HjBkz8Pzzz4d7V0REREQihmOaIlJTU3HXXXdh2rRpKFq0aLh3R0RERCRiOCKgc7lcGDBgAO655x60atUKW7du9Xm8HU+2gwcPmp9paWlB21eJnGlL7A48vt6atkREx5g4V3p6mjsekAgM6EaMGIFnn302x23Wrl1ryqzp6ekYOXJknu5/3LhxGDNmzDnXV6lSJc/7KiIiIuF16FA6gBJ6GbKQzxXGcHfPnj3Yt29fjtvUrFkTvXr1wjfffOO1EPTp06eRP39+9OnTBx9++KFPGTpmbfbv34+EhAQtKh0DmJlj8J6cnIzixYvrsfWc638tio4xiS1nzriwc2c66tathPz5HTX8PzYCOl9xxn/PMumOHTvQpUsXTJkyBW3atEFiYmJY908iE/9nSpQoYUrt4Qjo9Nh6zvW/JiKh4ogxdFy6ydOFF15oftaqVUvBnIiIiMQ85S1FREREHM4RGbrMqlevrk4XyVWhQoUwatQo8zPU9Nh6zvW/JiKh5IgxdCIiIiKSPZVcRURERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATmIC1wHmSiMvv/xySB5v9OjRqF+/PooVK4ZSpUqhU6dOWLx4cdAf9+TJk3jkkUfQpEkT89iVKlVCv379zGTcofDll1+ic+fO7tVYVq5cGZLHfeONN0z3e+HChc1k40uWLAnJ486bNw/du3c3zzP/3mnTpoXkcbms4cUXX4z4+HiUK1cOPXr0wPr160Py2G+++SaaNm1qJuvmqW3btvj+++9D8tgikj0FdBL1pk6dikWLFpkP3VCpW7cuXn/9daxatQrz5883wQYDHS53F0xHjhzB8uXL8fjjj5ufDLD4QX/dddchFA4fPoxLL7001zWaA2ny5MkYPny4maKGf3OzZs3MSjK7d+8Oyd/Lx2NAGUpz587F4MGDzf/1zJkzTSDP/y/uT7BxZZ7x48dj2bJl+PXXX3HVVVfh+uuvxx9//BH0xxaRHHDaEpFolZKS4qpcubJr9erVrmrVqrleeumlsOzHwYMHOT2Q68cffwz5Yy9ZssQ89rZt20L2mFu2bDGPuWLFiqA/VuvWrV2DBw92Xz59+rSrUqVKrnHjxrlCiX/v1KlTXeGwe/du8/hz584Ny+OXKlXK9d///jcsjy0iFmXoJGqdOXMGffv2xcMPP4xGjRqFbT9OnDiBd955x6ztymxOqHEtW5YDS5YsiWjD55aZIpa0bRdccIG5vHDhQsQKvsZUunTpkD7u6dOnMWnSJJMZZOlVRMLHkStFiPiCZb8CBQpg6NChYXnCvv32W/z97383ZdCKFSua0liZMmVCug/Hjh0zY+puueUWM94p2uzdu9cEFeXLl/e6npfXrVuHWPnicv/996N9+/Zo3LhxSB6TQwkYwPH/i2trc1hDw4YNQ/LYIpI1ZegkKkycONF8sNgnjjF65ZVX8MEHH5jsVCgf++effzbXX3nllaYpYMGCBejatSt69eoV8HFd2T02cVwVH5PVQA5kD7ScHltCh2PpVq9ebTJloVKvXj3zv81Gn3vvvRf9+/fHmjVrQvb4InIuLf0lUSE9PR2pqanuy59//jkeffRRU36zMZPDy1WqVMHWrVuD9tiVK1dGkSJFztmuTp06uP322zFy5MigP7YdzG3evBk//fST6ToNtJz+bj6/NWrUwIoVK9C8eXMEs+RatGhRTJkyxXR62hhgHDhwAF999RVChV8cmKny3I9gGzJkiPkb2W3L5ztcWOKuVasW3n777bDtg0isU8lVogKnb+DJNmjQIDOdhCd2PnJM3cCBA4P62DmVxo4fPx70x7aDuQ0bNmD27NlBCeaye+xQi4uLQ8uWLTFr1ix3IMXnmZcZ7EQrZl3vu+8+E0DOmTMnrMFcsP63RSRvFNBJVGIQkzmQKViwICpUqGDKRcHEAeJjx441U4Vw7BzHeXFai+3bt+Pmm28O6mMzmLvpppvM9B0cw8es5K5du9wD5hkABdP+/fuRlJTknvfOnhuNzztPwcApS5iRa9WqFVq3bm3mGuRrEOjAPSuHDh3Cxo0b3Ze3bNliSpF8rqtWrRrUMuunn35qsnMMqu3XmI03WWWHA4kZ5muuucb8fczScj8YVP7www9BfVwRycXZbleRqBeqaUuOHj3quuGGG8zUGXFxca6KFSu6rrvuOjN9SKimC8nqNHv27KA//oQJE7J87FGjRgX1cV977TVX1apVzfPNaUwWLVrkCgU+p1n9vf379w/q42b3GvP5D7bbb7/dHEt8rsuWLevq2LGja8aMGUF/XBHJmcbQiYiIiDiculxFREREHE4BnYiIiIjDKaATERERcTgFdCIiIiIOp4BORERExOEU0ImIiIg4nAI6EREREYdTQCciIiLicAroRCRivPfee+jcubP78oABAwKy2H2+fPkwbdo0BMqIESPMWqoiIpFCK0WISEQ4duwYatasic8//xzt27c31x08eNAsRF+yZMnzDui4kH0ggkPi+rzcV67byp8iIuGmDJ2IRIQpU6agePHi7mDOXmz+fIO5YChTpgy6dOmCN998M9y7IiJiKKATkYDas2cPKlSogGeeecZ93YIFCxAXF4dZs2Zl+3uTJk1C9+7dva7LXHK94oorMHToUPzzn/9E6dKlzeOMHj3a63c2bNiAyy+/HIULF0bDhg0xc+bMcx4rOTkZvXr1MsEi7+f666/H1q1bzW3r1q1D0aJF8emnn7q3/+yzz1CkSBGsWbPGfR33lfssIhIJFNCJSECVLVsW77//vgm0fv31V6Snp6Nv374YMmQIOnbsmO3vzZ8/H61atcr1/j/88EMUK1YMixcvxr///W88+eST7qDtzJkz6Nmzpwkeeftbb72FRx55xOv3T548abJr8fHx+Pnnn/HLL7/gwgsvRNeuXXHixAnUr18fzz//PP7xj38gKSkJKSkpuOeee/Dss8+aANHWunVrc5sdCIqIhJPG0IlIUAwePBg//vijCdJWrVqFpUuXolChQllue+DAAZQqVQrz5s3DZZdd5pWh4212QwMzdKdPnzaBmGdgddVVV2H8+PGYMWMGunXrhm3btqFSpUrm9unTp+Oaa65xj6H75JNP8PTTT2Pt2rVmbB0xkGO2jo9jN2X87W9/Q1pamgkO8+fPb+7H3p54G0vCc+bMQYcOHfRfJCJhVSC8Dy8i0YpZrsaNG5smh2XLlmUbzNHRo0fNT5ZJc9O0aVOvyxUrVsTu3bvNeQZpVapUcQdz1LZtW6/tf/vtN2zcuNFk6DI3ZWzatMl9mVnGunXr4oILLsAff/zhFcwRS7B05MiRXPdZRCTYFNCJSFAwONqxY4cpg7Is2aRJk2y3TUhIMAHTX3/9lev9FixY0Osyf4+P4atDhw6hZcuWmDhxYpblYs/A7/Dhwyag27lzpwkcPe3fv/+c3xERCRcFdCIScCxh3nbbbejduzfq1auHO++805Rdy5Url+X2LGtyfBqbDjznocurBg0amIYHzwBs0aJFXttcdNFFmDx5stkXdtVmhcEay72PPvqoua8+ffpg+fLl7qwcrV692gSXjRo18nt/RUQCRU0RIhJwDIQ4h9yrr75qmhJYurz99ttz/B02KrAx4nx06tTJPFb//v1Nho1j7bgvnhiccdoRdrby9i1btphxcOyeZZMDsQmCpdvHHnsML774ohm399BDD3ndD3+X4/08gzwRkXBRQCciAcXg6OWXX8bHH39sMmAsWfI8A6Cc5m2744478L///c8Egv7iY7H5gWPy2CzBzODYsWO9tuGUJGy+qFq1qumIZVaPj80xdNzfjz76yOwH97lAgQKmo5aNFO+++y6+//579/1wypK77rrL730VEQkkdbmKSMS4+eabTUl05MiRiGQM7B588EH8/vvvJugTEQk3ZehEJGI899xzZk64SMdmiQkTJiiYE5GIoQydiIiIiMMpQyciIiLicAroRERERBxOAZ2IiIiIwymgExEREXE4BXQiIiIiDqeATkRERMThFNCJiIiIOJwCOhERERGHU0AnIiIiAmf7fy+rT6l1ZxvWAAAAAElFTkSuQmCC", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" + "name": "stderr", + "output_type": "stream", + "text": [ + "Job: https://platform.classiq.io/jobs/aa2c3a6b-e81f-4b98-a4a8-09a0585114f3\n" + ] + }, + { + "ename": "AttributeError", + "evalue": "'DataFrame' object has no attribute 'ancilla'", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mAttributeError\u001b[39m Traceback (most recent call last)", + "\u001b[32m/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_20813/4051538059.py\u001b[39m in \u001b[36m?\u001b[39m\u001b[34m()\u001b[39m\n\u001b[32m 15\u001b[39m \u001b[38;5;66;03m# 2. Next step in the algorithm: QFT inverse on the coordinates register\u001b[39;00m\n\u001b[32m 16\u001b[39m \u001b[38;5;66;03m# invert(lambda: qft(x))\u001b[39;00m\n\u001b[32m 17\u001b[39m \n\u001b[32m 18\u001b[39m \n\u001b[32m---> \u001b[39m\u001b[32m19\u001b[39m df = run_statevector_simulation(main, print_circuit_info=\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[32m 20\u001b[39m simplified_df = simplify_df(df)\n\u001b[32m 21\u001b[39m plot_simplified_df(simplified_df)\n", + "\u001b[32m~/Library/CloudStorage/GoogleDrive-ofriwi1@gmail.com/My Drive/Documents/Work/1. Classiq/classiq-library/classiq-library/algorithms/gradient_estimation/gradient_estimation_helpers.py\u001b[39m in \u001b[36m?\u001b[39m\u001b[34m(qfunc_to_run, print_circuit_info, filter_ancilla, show_circuit)\u001b[39m\n\u001b[32m 120\u001b[39m print(\u001b[33m\"Circuit Depth:\"\u001b[39m, qprog.transpiled_circuit.depth)\n\u001b[32m 121\u001b[39m print(\u001b[33m\"Gate Counts:\"\u001b[39m, qprog.transpiled_circuit.count_ops)\n\u001b[32m 122\u001b[39m \n\u001b[32m 123\u001b[39m df = calculate_state_vector(qprog)\n\u001b[32m--> \u001b[39m\u001b[32m124\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m filter_ancilla:\n\u001b[32m 125\u001b[39m print(\u001b[33m\"Filtering out states with ancilla qubits in state |1>...\"\u001b[39m)\n\u001b[32m 126\u001b[39m df = df[df.ancilla == \u001b[32m0\u001b[39m]\n\u001b[32m 127\u001b[39m df.sort_values(by=\u001b[33m\"x\"\u001b[39m, inplace=\u001b[38;5;28;01mTrue\u001b[39;00m)\n", + "\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/generic.py\u001b[39m in \u001b[36m?\u001b[39m\u001b[34m(self, name)\u001b[39m\n\u001b[32m 6317\u001b[39m \u001b[38;5;28;01mand\u001b[39;00m name \u001b[38;5;28;01mnot\u001b[39;00m \u001b[38;5;28;01min\u001b[39;00m self._accessors\n\u001b[32m 6318\u001b[39m \u001b[38;5;28;01mand\u001b[39;00m self._info_axis._can_hold_identifiers_and_holds_name(name)\n\u001b[32m 6319\u001b[39m ):\n\u001b[32m 6320\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m self[name]\n\u001b[32m-> \u001b[39m\u001b[32m6321\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m object.__getattribute__(self, name)\n", + "\u001b[31mAttributeError\u001b[39m: 'DataFrame' object has no attribute 'ancilla'" + ] } ], "source": [ diff --git a/algorithms/gradient_estimation/gradient_estimation_helpers.py b/algorithms/gradient_estimation/gradient_estimation_helpers.py index 902599301..4498c115e 100644 --- a/algorithms/gradient_estimation/gradient_estimation_helpers.py +++ b/algorithms/gradient_estimation/gradient_estimation_helpers.py @@ -120,8 +120,10 @@ def run_statevector_simulation( print("Circuit Depth:", qprog.transpiled_circuit.depth) print("Gate Counts:", qprog.transpiled_circuit.count_ops) - sv = calculate_state_vector(qprog) - df = sv[sv.ancilla == 0] + df = calculate_state_vector(qprog) + if filter_ancilla and "ancilla" in df.columns: + print("Filtering out states with ancilla qubits in state |1>...") + df = df[df["ancilla"] == 0] df.sort_values(by="x", inplace=True) return df From cc2bec8303aab401d87e5d7c7a6b6f94e1b9aa33 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Sat, 23 May 2026 21:44:28 +0300 Subject: [PATCH 07/12] Fixed error in one cell --- .../gradient_estimation.ipynb | 188 ++++++++++-------- 1 file changed, 106 insertions(+), 82 deletions(-) diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index a2801dafa..ed248b17f 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -10,7 +10,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 1, "id": "1", "metadata": {}, "outputs": [], @@ -253,7 +253,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 2, "id": "13", "metadata": {}, "outputs": [ @@ -277,8 +277,8 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/f21b7076-4514-4030-9d5f-86915c39c8df\n", - "/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_20813/391621480.py:44: SettingWithCopyWarning: \n", + "Job: https://platform.classiq.io/jobs/e3f28363-b9ca-427e-b26b-8785d8f645bd\n", + "/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_39533/391621480.py:44: SettingWithCopyWarning: \n", "A value is trying to be set on a copy of a slice from a DataFrame\n", "\n", "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n", @@ -330,7 +330,7 @@ "type": "string" } ], - "ref": "45a22227-cf31-4727-93cd-e8e1cbcb29a3", + "ref": "608755ba-629d-43c1-947a-8780a8563251", "rows": [ [ "63", @@ -543,7 +543,7 @@ "30 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000011" ] }, - "execution_count": 8, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -609,7 +609,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 3, "id": "15", "metadata": {}, "outputs": [ @@ -643,7 +643,7 @@ "type": "float" } ], - "ref": "761a3f7f-bd6c-4bea-8797-f8fa2fde2488", + "ref": "c6c1a446-e870-4355-a194-27636b2e9da6", "rows": [ [ "-4", @@ -777,7 +777,7 @@ " 3 0.75 0.75" ] }, - "execution_count": 9, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -828,7 +828,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 4, "id": "18", "metadata": {}, "outputs": [ @@ -843,21 +843,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "Circuit Width: 7\n", - "Circuit Depth: 30\n", - "Gate Counts: {'u': 25, 'cx': 19}\n" + "Circuit Width: 8\n", + "Circuit Depth: 42\n", + "Gate Counts: {'u': 31, 'cx': 27}\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/950afafe-5e67-409e-8b7a-8a7f265fa281\n", - "/Users/ofriwienner/Library/CloudStorage/GoogleDrive-ofriwi1@gmail.com/My Drive/Documents/Work/1. Classiq/classiq-library/classiq-library/algorithms/gradient_estimation/gradient_estimation_helpers.py:125: SettingWithCopyWarning: \n", - "A value is trying to be set on a copy of a slice from a DataFrame\n", - "\n", - "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n", - " print(\"Filtering out states with ancilla qubits in state |1>...\")\n" + "Job: https://platform.classiq.io/jobs/23d8df9c-8954-45da-bb79-b105728d60e5\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Filtering out states with ancilla qubits in state |1>...\n" ] }, { @@ -907,7 +909,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 5, "id": "19", "metadata": {}, "outputs": [], @@ -977,7 +979,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 6, "id": "23", "metadata": {}, "outputs": [ @@ -1001,21 +1003,18 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/aa2c3a6b-e81f-4b98-a4a8-09a0585114f3\n" + "Job: https://platform.classiq.io/jobs/30237262-53db-415a-a651-c613f34de3a8\n" ] }, { - "ename": "AttributeError", - "evalue": "'DataFrame' object has no attribute 'ancilla'", - "output_type": "error", - "traceback": [ - "\u001b[31m---------------------------------------------------------------------------\u001b[39m", - "\u001b[31mAttributeError\u001b[39m Traceback (most recent call last)", - "\u001b[32m/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_20813/4051538059.py\u001b[39m in \u001b[36m?\u001b[39m\u001b[34m()\u001b[39m\n\u001b[32m 15\u001b[39m \u001b[38;5;66;03m# 2. Next step in the algorithm: QFT inverse on the coordinates register\u001b[39;00m\n\u001b[32m 16\u001b[39m \u001b[38;5;66;03m# invert(lambda: qft(x))\u001b[39;00m\n\u001b[32m 17\u001b[39m \n\u001b[32m 18\u001b[39m \n\u001b[32m---> \u001b[39m\u001b[32m19\u001b[39m df = run_statevector_simulation(main, print_circuit_info=\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[32m 20\u001b[39m simplified_df = simplify_df(df)\n\u001b[32m 21\u001b[39m plot_simplified_df(simplified_df)\n", - "\u001b[32m~/Library/CloudStorage/GoogleDrive-ofriwi1@gmail.com/My Drive/Documents/Work/1. Classiq/classiq-library/classiq-library/algorithms/gradient_estimation/gradient_estimation_helpers.py\u001b[39m in \u001b[36m?\u001b[39m\u001b[34m(qfunc_to_run, print_circuit_info, filter_ancilla, show_circuit)\u001b[39m\n\u001b[32m 120\u001b[39m print(\u001b[33m\"Circuit Depth:\"\u001b[39m, qprog.transpiled_circuit.depth)\n\u001b[32m 121\u001b[39m print(\u001b[33m\"Gate Counts:\"\u001b[39m, qprog.transpiled_circuit.count_ops)\n\u001b[32m 122\u001b[39m \n\u001b[32m 123\u001b[39m df = calculate_state_vector(qprog)\n\u001b[32m--> \u001b[39m\u001b[32m124\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m filter_ancilla:\n\u001b[32m 125\u001b[39m print(\u001b[33m\"Filtering out states with ancilla qubits in state |1>...\"\u001b[39m)\n\u001b[32m 126\u001b[39m df = df[df.ancilla == \u001b[32m0\u001b[39m]\n\u001b[32m 127\u001b[39m df.sort_values(by=\u001b[33m\"x\"\u001b[39m, inplace=\u001b[38;5;28;01mTrue\u001b[39;00m)\n", - "\u001b[32m~/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/generic.py\u001b[39m in \u001b[36m?\u001b[39m\u001b[34m(self, name)\u001b[39m\n\u001b[32m 6317\u001b[39m \u001b[38;5;28;01mand\u001b[39;00m name \u001b[38;5;28;01mnot\u001b[39;00m \u001b[38;5;28;01min\u001b[39;00m self._accessors\n\u001b[32m 6318\u001b[39m \u001b[38;5;28;01mand\u001b[39;00m self._info_axis._can_hold_identifiers_and_holds_name(name)\n\u001b[32m 6319\u001b[39m ):\n\u001b[32m 6320\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m self[name]\n\u001b[32m-> \u001b[39m\u001b[32m6321\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m object.__getattribute__(self, name)\n", - "\u001b[31mAttributeError\u001b[39m: 'DataFrame' object has no attribute 'ancilla'" - ] + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -1070,10 +1069,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "id": "27", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n" + ] + }, { "name": "stdout", "output_type": "stream", @@ -1083,6 +1089,13 @@ "Gate Counts: {'u': 6, 'cx': 6}\n" ] }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Job: https://platform.classiq.io/jobs/1168d00d-1ca3-44b7-b56f-6f80c46f2cee\n" + ] + }, { "data": { "image/png": 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", @@ -1129,10 +1142,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "id": "29", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n" + ] + }, { "name": "stdout", "output_type": "stream", @@ -1142,6 +1162,13 @@ "Gate Counts: {'u': 6, 'cx': 6}\n" ] }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Job: https://platform.classiq.io/jobs/d7dc1c0a-fb69-42e0-a689-b61e77e2463a\n" + ] + }, { "data": { "image/png": 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", @@ -1220,7 +1247,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "id": "35", "metadata": {}, "outputs": [ @@ -1228,7 +1255,6 @@ "name": "stdout", "output_type": "stream", "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3DIb1l6DjflPUfuyaOznk0sDwzs\n", "Parsed counts: [{'x': -2}: 2048]\n", "The analytical gradient is: -0.5\n", "The majority gradient is: -0.5\n", @@ -1260,7 +1286,7 @@ } ], "source": [ - "show_circuit = True # Set to True to show the circuit\n", + "show_circuit = False # Set to True to show the circuit\n", "\n", "p = params()\n", "p.set_function(p.linear, (-0.5, 0.25))\n", @@ -1348,14 +1374,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3DIb2AIHYhra9keJamdJ86vntbo\n", - "Parsed counts: [{'x': 2}: 1781, {'x': 3}: 121, {'x': 1}: 67, {'x': -4}: 21, {'x': 0}: 16, {'x': -2}: 15, {'x': -1}: 15, {'x': -3}: 12]\n", + "Quantum program link: https://platform.classiq.io/circuit/3E8YOVTlM5p8UlHjC9whf2WfyLN\n", + "Parsed counts: [{'x': 2}: 1796, {'x': 3}: 125, {'x': 1}: 54, {'x': -4}: 24, {'x': 0}: 19, {'x': -1}: 12, {'x': -3}: 11, {'x': -2}: 7]\n", "The analytical gradient is: 0.55\n", "The majority gradient is: 0.5\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 86.96% (1781/2048 shots)\n", - "[\u001b[92m███████████████████████████████████████████\u001b[91m-------\u001b[0m] 86.96%\n" + "Success rate: 87.70% (1796/2048 shots)\n", + "[\u001b[92m████████████████████████████████████████████\u001b[91m------\u001b[0m] 87.70%\n" ] }, { @@ -1370,7 +1396,7 @@ }, { "data": { - "image/png": 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", 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UFuDTStOauEsBkRb1U6GTf6RYlSpV3GRfWhlaQ+WPHTvmVsBWgTQjwAAAQEgGQD/++KM1bNgwcNtfl9O+fXs31L1nz55uriDN66NMzxVXXOGGucfG/n8O0sytoqygR6thqwK8ZcuWbu4gAAAyUvZs2a19jfaBfYS3kJkHKCupa01D7FUMnVoNkLrVjh49esbbBoSKnDlzpnuYKQBk9fU7NYSwaaDAR91zCoIAr1Lwo65oBUIAEO4IgE5CCbLt27dbdHS0G2rHf8DwIgX/f/zxh/tdUH0eE4bCq9eDQ8cOuf3cOXLzexDmCIBOQsPqDx065Iqqc+fOfWY+FSAEFSlSxAVB+p3IkSNHVjcHOOMU/OTtn9ftH+h1gGHwYY4O/ZNISEhwX0n7w+v8vwP+3wkACGcEQGlEyh9ex+8AgEhCAAQAADyHAAinrVy5cjZ06NDTeo65c+e6DIPme8oImzZtcs+niTVDRYcOHQKTeEqDBg3cZJ8AgDOPACjCLVy40I1gu+GGGyxUpHThv/zyy90II83n4BVTpkyxl156KVODLABAygiAItw777xjDz30kM2fP9+N4AnlAlut/RbqdSZabiWjaMmXU1nBGABw+giAIpjWWvvoo4/s/vvvdxkgLS+SUreTFpy95JJL3DB/ZWLWrl0beMyvv/5qzZs3t2LFilnevHmtdu3a9tVXX6X6mh07drQbb7wxWdBQtGhRF4wpQzFv3jx77bXX3GtrU3dVSl1g3377rcsWqV1nn322NWnSxP766y93n5ZE0dIoBQoUsEKFCrnXVFvTQxknnZdcuXK5Cf4mTJiQrDtPbRo5cqTddNNNlidPHuvbt68bBdWpUyf3PfreSpUqufcTTI/R0i7+9mlZl6STrifNhB05csQee+wxO+ecc9xraUFfnRc/fX56vhkzZrh18PR5aC08vQ954YUXbOzYsfbpp58Gzm3w9wM4PdHZou3Wqre6TfsIbwRAp+jg0YOpbvHH49P82MPHDqfpsafi448/tsqVK7sL9B133GHvvvtusouwPP300/bqq6+6tdmyZ8/ugpjgIKpp06YuSFq2bJm74DZr1sw2b96c4mvec889LjjxX5Tliy++cHMptWnTxgUKdevWdQvY6jHaNMFkUqrd0fpuVatWdd14CxYscK/rH4KtNeIUYKjNapsmqLzlllvSNVv3XXfd5bJiChImT55sb731lu3atSvZ4xRY6LlXrFjhzo1eo1SpUjZx4kRbtWqVPffcc/bUU0+58+2n86mARedcbf/zzz9t6tSp/9oerWmn9/rhhx/azz//bK1atXLne/369YHH6Dy+8sor9v7777usnj4HBU2ir61btw4ERdoU0ALIGLHZY21iq4lu0z7CnNYC87r9+/crKnBfkzp8+LBv1apV7mswe8FS3ZqOb5rosbn75k71sfXH1E/02MIDC6f4uFNx+eWX+4YOHer2jx075itcuLBvzpw5gfu1r/f91VdfBY59+eWX7ljS9xvsggsu8A0bNixwu2zZsr4hQ4YEbletWtX38ssvB243a9bM16FDh8Dt+vXr+7p165boOf1t+euvv9zttm3b+urVq5fm97p79273/StWrHC3N27c6G4vW7YsxcevXr3a3b948eLAsfXr17tjwe9Ftx955JGTvn7Xrl19LVu2DNwuUaKEb+DAgYHbOv+lSpXyNW/ePMXz8Pvvv/uio6N927ZtS/S8V199ta9Xr15uf8yYMa49GzZsCNw/YsQIX7FixQK327dvn+g1MlJqvwsAEIrX75MhAxSh1I31ww8/WNu2bd1tZXaUgVE3VFIXXnhhYL9EiRLuqz8TogyQMgvqclH3i7pdVq9enWoGyJ8FGjNmjNvfuXOnTZs2LVFWKS38GaDUKCui93buuee6BfDUdSX/1q6k50fn5OKLLw4cq1ChgutqS0rdg0mNGDHCatWq5WZH1jlR9sj/2lqUT9kXdWH56bVSeh4/ZZeU3Tr//PPd8/k3dRcGd+2pO/C8885L9HmllLUCAPw7lsI4RZoGPTVJ+4Z3PZb6BSpbVOIYdFO3TZYRFOhoyQIt4eGnhEZMTIwNHz480Wir4GUN/EXI/q4kBT+zZs1y3S4KEFTzcuutt7oFYv+ta+nJJ5903Tnfffedq5W58sor09V+vc6/UXdY2bJlbfTo0e49qr3VqlX713adKtXjBFMXlc6LurnUnadC5kGDBtn3339/yq+hQFOj9ZYsWeK+BlMg5Jd0CQp9Xil1awLIeCpHYCmMyEEAdIry5MyT5Y9NjQKfcePGuQv0tddem+g+DZH+4IMPrEuXLml6LhUiq3BZNTD+C7WKlv+Nin71OsoCKQi6++67k434OtlyCspKqband+/eye7bu3evy+Ao+PEHVqqzSQ/VRek8qa5JmRzZsGFDoMj6ZOdEtTUPPPBA4FhwlkbBpTIzCoiuuuoqd0yvpeAmOOMUrGbNmu6cKJuT3mAxvecWAEAAFJFUdKwLuUYqJZ1Xp2XLli47lNYAqGLFim6+GmVclG149tln01RorG4wjczSxbh9+/aJ7lN3lYIDBVLKbmg4eFK9evWy6tWruyBDbdWFfc6cOa4wWI9XkKVuJwUa6npSxik9VBzeuHFju/fee90oL2VWevTo4TJPJxuKr3OiAFOjsZTdUkHy4sWL3b5ft27dbMCAAe6xeq3Bgwf/6ySP6vpq166dy54pcFVAtHv3bhcEKhhM6zxOOrdqlwJEnSN9/ixcCgDJUQMUgRTg6OKe0qSCCoA0ckqjjNJCF27VxSjjoSBIQ9FTy2IE0+srONHjg7vhRN1H6ubRCC/V0KRUt6OAYObMmbZ8+XK79NJLXVeThnerlkYjvtQNpYyKur26d+/uuqDSS0GMhvcrS6MMl0amqTsrNvbfR3fcd9991qJFC1dTpTofZaSCs0GiYOrOO+90wZ+/m8yfRUuNMmYKgPS9ylApi6bAqkyZMml+T3oP+l7VG+ncKlsFAEguSpXQ5nFxcXEuWFDxqgpqg8XHx9vGjRvdf/cnuzDif9RVpvlsdFFXsBAOtm7d6obka56jfyvA9ip+F+B11ACF1/X7ZKgBQoZS99iePXtcN45GjWkCwVD19ddfu0BNXW0ataXJCtWF5K/bAQBELgIgZCh1ZylbpokCNRGguqxClWao1gSGv/32m+uiUjff+PHjqZkBAA8I3asTwpIyKOHSq6r6JG0AkBaa4qRpxaaBfYQ3AiAAANJAy198efuXnKsIwSgwAADgOQRAAADAcwiAAABI4zD4PP3yuE37CG/UAAEAkEaHjh3iXEUIMkAAAMBzCIAAAIDn0AV2iqas3W5nUotKJdL1eK3gPnbsWLdu1ahRoxLd17VrV3vjjTfcOlWarBCnTgunTp061a3bFepeeOEF++STT+ynn37K6qYAQJYjAxTBtK6VFg09fPhwovWcJkyYkK4FNrPK0aNHs7oJAIAIRQAUwbRqu4KgKVOmBI5pX8FPzZo1k63h1b9/f7eMRa5cuaxGjRo2adKkwP0JCQnWqVOnwP1acfy1115L9Bxz5851K7fnyZPHrQNWr149+/333wMZqaRZkkceecQaNGgQuK39Bx980B0vXLhwYJbmX375xa6//nrLmzevW71dq6xrvbHg73vooYfc92nlej1m9OjRdvDgQbv77rvdMhcVKlSwadOmJXr9tDzvww8/7NYIK1iwoBUvXtxlUYJnvRat8q5MkP92aguttm3b1j2Pzo9Wa//+++8D948cOdLOO+88y5kzpzu377//fuC+TZs2uecPztzs27fPHdM595973Z49e7Z77ty5c7ulPdauXevuV6avd+/etnz5cvc4bTqmWbv1nvQzERMTYyVLlnTvGQAiHQFQhOvYsaNbkd3v3XffdUFBUgp+xo0b57rLVq5cad27d7c77rjD5s2bFwiQtL7XxIkTbdWqVfbcc8+5dbQ+/vhjd//x48ddgFO/fn37+eefbeHChXbvvfe6C216qNtOQcC3337r2qILfaNGjVzA9uOPP9r06dNt586d1rp162Tfp6Dphx9+cMHQ/fffb61atXJBwNKlS+3aa691Ac6hQ/+M4EjP8ypgUbAycOBAe/HFF23WrFnuvsWLF7uvOr9aTNV/OyktuKrzsm3bNvvss89cEKKgSudU1IXWrVs369GjhwvK1G2pz2jOnDmWXk8//bRbiFbvSeuw6fOXNm3auOe/4IILXFu16djkyZNtyJAh9uabb9r69etdF5kWhwWQXLaobFa/bH23aR/hjRqgCKcgplevXoFMjAILdYv5Mwdy5MgR69evn3311VdWt25dd+zcc8+1BQsWuAujLt45cuRwGQQ/ZYIU5CgAUtAQFxdn+/fvtxtvvNFlMqRKlSrpbm/FihVdoOHXp08fF6SofcFBnDJb69ats/PPP98dU8bqmWeecft6vwMGDHABUefOnd0xBWzKsig4u+yyy2z48OFpet4LL7zQnn/++UDb9H3KslxzzTVWpEgRd1zZLmWHUqMux927d7sASRkgUUbK75VXXnEZsgceeMDdfvTRR23RokXueMOGDdN1/vr27es+L3nyySfthhtucN2eytop06WgKLitWrxWtxs3buw+Y2WClMUDkFyuHLlsbof//e1EeCOEjXC6SOsiqO4OZSq0r8Ag2IYNG1xmRBd1XST9mzJCv/76a+BxI0aMsFq1arnn1P1vvfWWu4CKLuy6iKvbqlmzZq57TFmG9NLzB1O2RJmQ4HZVrlzZ3RfcNgUqftHR0VaoUKFEmQx1ccmuXbtO+XmlRIkSgedIK3VdKdjyBz9JrV692nUXBtNtHU+v4PaqrfJv7VWWTDViCngVLCobpWweAEQ6MkAeoG4Q1db4g5iUumjkyy+/tHPOOSfRfaoLEWWNHnvsMde9oiyR6moGDRqUqI5FAZbqR9Sd9NFHH7mMjLqLlHHJli1bslXijx07lqwt6m5K2jYFVC+//HKyx/ov8KLsRTB1vQUf83fF+budTud5/c+RVsq+nA6dOwk+fymdO/m395wSZbxUJ6Tsnz4rZaH0uarrM+l7B4BIQgDkAdddd50bUaULor+wOFjVqlVdoKNsjr/7JCl1namext9NkzRT4qdMhzZ1QylQUvePAiBljVTfkjQzcrKLrAq5VaeiAmN132SUjHpetV8F4ifLyrz99tv2559/ppgFUlehzq+mJfDTbX0u4u9qU0bNX7x+KkPZVVuVUlsVoCkY1KYpEpQJW7FihTtHAP5Hy1+Ue+2fwQ6bum2yPDkT/8OG8EIXmAeoS0jdKSpe1n5SyuYou6PCZxX9KrBR4fCwYcPcbX/9iwprZ8yY4Wpknn322URFvxs3bnRBj+qCVG80c+ZMV1TrrwNSwbG+X91qOq66mqQBUUp0QVbgoBFUej21TW1QkfDJAo8z8bwKoFQTtGPHDvvrr79SfIxeQ3U2KhJXYPPbb7+54EvnSh5//HHXRakaJZ2bwYMHu9F6+kz8AYqCSNU16XNUdsZf75Qeaqs+JwVPGu2m2i+97jvvvOM+C7XrP//5j3u9smXLpvv5AS/Yc2iP2xD+CIA8Il++fG5LzUsvveSCGo0GU9CirJG6xFTsLBqZ1KJFCzdyqE6dOrZ3795E2SANu16zZo21bNnSFRBrBJiCDH2fKPOk59fop9q1a9vff/9td91110nbrWHZChoUlGgkl+p6NNxdhcf+rqFTkVHPqy5BdR2pKynp1ALBmRcFhEWLFrWmTZu611Iw4w9GFRipZkpFzxqlpcJzdScGTxGgAm3V5qhGSu1UcXh66bPR56rCamWVPvjgA/d+NWWAao6UqVJX2Oeff+5qqAAgkkX5khZmeJBGMOXPn9+NYkoaJGgEjf5rViAQGxubZW0Eshq/C/A6dYHl7Z/X7R/odYAusBC/fp8MNUAAgLBxppchChZ//H8rwX+6fofFZs+d4csY4cyhCwwAAHgOARAAAPAcusAAAEiDKIuy8wrWCOwjvBEApRG14vA6fgfgdTHZc9nAaxMvqozwRRfYSfiHKmsiQcDL/L8DKc0lBQDhhgzQyU5Q9uxujhstZqlZf09n7hkgXGk5Df0O6HchI2fkBoCswl+yk9DyEVobSnMB+VdUB7xIwb9Wi/evMQZ4zZHjh6zbf/+ZoPS1pnMtJg3D4BG6CIDSQDP5aikIusHg9d8DMqDwMs0avPvQ1sA+whsBUBrpDz8zQQMAEBkoaAEAAJ5DAAQAADyHAAgAAHgOARAAAPAciqABAEgDTQBRKt/5gX2ENwIgAADSQPP+aP4fRAa6wAAAgOcQAAEAAM8hAAIAIB1LYWjTPsIbNUAAAKSBlr/YGrcusI/wRgYIAAB4DgEQAADwHAIgAADgOQRAAADAc0I6AEpISLBnn33Wypcvb7ly5bLzzjvPXnrpJfP5/ld+pv3nnnvOSpQo4R7TuHFjW79+fZa2GwAAhLaQDoBefvllGzlypA0fPtxWr17tbg8cONCGDRsWeIxuv/766zZq1Cj7/vvvLU+ePNakSROLj4/P0rYDACKLlr8okruU21gKI/yF9DD47777zpo3b2433HCDu12uXDn74IMP7Icffghkf4YOHWrPPPOMe5yMGzfOihUrZp988onddtttWdp+AEBkLYUx6qZ/rj8IfyGdAbr88stt9uzZtm7dP/MuLF++3BYsWGDXX3+9u71x40bbsWOH6/byy58/v9WpU8cWLlyY6vMeOXLE4uLiEm0AAMA7QjoD9OSTT7rgpHLlyhYdHe1qgvr27Wvt2rVz9yv4EWV8gum2/76U9O/f33r37p3JrQcAAKEqpDNAH3/8sY0fP94mTJhgS5cutbFjx9orr7zivp6OXr162f79+wPbli1bMqzNAIDIdOT4Yes583q3aR/hLaQzQI8//rjLAvlreapXr26///67y+C0b9/eihcv7o7v3LnTjQLz0+2LLroo1eeNiYlxGwAAaeUzn/365/LAPsJbSGeADh06ZNmyJW6iusJOnDjh9jU8XkGQ6oT81GWm0WB169Y94+0FAADhIaQzQM2aNXM1P2XKlLELLrjAli1bZoMHD7aOHTu6+6OiouyRRx6xPn36WMWKFV1ApHmDSpYsaTfffHNWNx8AAISokA6ANN+PApoHHnjAdu3a5QKb++67z0186NezZ087ePCg3XvvvbZv3z674oorbPr06RYbG5ulbQcAAKEryhc8rbJHqdtMw+dVEJ0vX76sbg4AIBVT1m7PsnMTf/yQtZtUwe2Pv3WDxWbPfdLvaVHpf/WpCK3rd0jXAAEAAHiuCwwAgFCSL6ZgVjcBGYQACACANFCX15hbfuFcRQi6wAAAgOcQAAEAAM8hAAIAIA20/MVzs1u6jaUwwh81QAAApIGWv1i5e2FgH+GNDBAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPYRQYAABpFBOdi3MVIQiAAABI41IYE1r9yrmKEHSBAQAAzyEAAgAAnkMXGAAAaXA0Id4GLejs9h+/YrTljI7lvIUxAiAAANLghO+ELd0+O7CP8EYXGAAA8BwCIAAA4DkEQAAAwHMIgAAAgOcQAAEAAM9J1yiwEydO2Lx58+ybb76x33//3Q4dOmRFihSxmjVrWuPGja106dKZ11IAAIAzmQE6fPiw9enTxwU4TZs2tWnTptm+ffssOjraNmzYYM8//7yVL1/e3bdo0aKMahsAACG1FMbk2/5wm/bhgQzQ+eefb3Xr1rXRo0fbNddcYzly5Ej2GGWEJkyYYLfddps9/fTT1rnzP5NFAQAAhJoon8/nO9mDVq9ebVWqVEnTEx47dsw2b95s5513noWLuLg4y58/v+3fv9/y5cuX1c0BAKRiytrtYXVuWlQqkdVNiGhxp3H9TlMGKK3Bjyg7FE7BDwAAaV0K4/VFD7v9hy97naUwvLoUxvHjx+3NN9+0uXPnWkJCgtWrV8+6du1qsbGsjQIAiDxa/mLhli/c/oN1hmZ1c5BVAdDDDz9s69atsxYtWrhur3HjxtmPP/5oH3zwwem2CQAAIDQCoKlTp9ott9wSuD1z5kxbu3atGwkmTZo0scsuuyxzWgkAAJAVEyG+++67dvPNN9sff/zhbl988cXWpUsXmz59un3++efWs2dPq127dka2DQAAIGsDIAU5bdu2tQYNGtiwYcPsrbfechXXGvL+7LPPujmCNAweAAAgomqA2rRp47q6lO3R11GjRtmrr76aea0DAAAIhbXAChQo4LI/gwYNsrvuussef/xxi4+Pz4y2AQAAZG0ApMkNW7dubdWrV7d27dpZxYoVbcmSJZY7d26rUaOGWx4DAIBIFROdy8bfusFt2odHAiBle7Jly+YyP0WLFrX77rvPcubMab1797ZPPvnE+vfv7wIkAAAiUVRUlFsDTJv24ZEaIM3xs3z5cjfLs+p/tPhp8EzR8+fPd11jAAAAERMA1apVy5577jlr3769ffXVV64rLKl77703o9sHAEBIOJZwxEYtfsLtd6n9suWIjsnqJuFMdIFppucjR45Y9+7dbdu2bW4ZDAAAvCLBl2BzN33sNu3DIxmgsmXL2qRJkzK3NQAAAKGSATp48GC6njS9jwcAAAi5AKhChQo2YMAA2759e6qP8fl8NmvWLLv++uvt9ddfz8g2AgAAnPkusLlz59pTTz1lL7zwgpvz55JLLrGSJUtabGys/fXXX7Zq1SpbuHChZc+e3Xr16uWGyAMAAIR1AFSpUiWbPHmymwxx4sSJ9s0339h3331nhw8ftsKFC1vNmjVt9OjRLvvjXx0eAAAgItYCK1OmjPXo0cNtAAAAngiAAADwKi1/8e7NKwL7CG8EQAAApIGWv8gfW4hz5dXV4AEAAMIdGSAAANK4FMZ7y15w+x1qvsBSGGGODBAAAGmg5S+mbxjrNpbC8GAANH36dFuwYEHg9ogRI+yiiy6y22+/3c0JBAAAEHEB0OOPP25xcXFuf8WKFW5IfNOmTW3jxo326KOPZkYbAQAAsrYGSIFO1apV3b4mR7zxxhutX79+tnTpUhcIAQAARFwGKGfOnHbo0CG3/9VXX9m1117r9gsWLBjIDAEAAERUBuiKK65wXV316tWzH374wT766CN3fN26dVaqVKnMaCMAAEDWZoCGDx/uFj2dNGmSjRw50s455xx3fNq0aXbddddlbOsAAAAyQZTP5/OZx6nrLn/+/LZ//37Lly9fVjcHAJCKKWu3Z9m5OeE7YXsObnP7hfOcY9miTp5DaFGpxBlomXfFncb1O90ZIK32vmvXrmTH9+7dy0rwAICIpYCnaN7SbktL8IPQlu5PMLWE0ZEjR1yBNAAAQMQUQb/++uuBxeDefvtty5s3b+C+hIQEmz9/vlWuXDlzWgkAQBY7lnDUJqwY4PZvr/6k5Yjmn35PBEBDhgwJZIBGjRqVqLtLmZ9y5cq54wAARKIE33H7bM0/17k21R6zHEYA5IkASBMgSsOGDW3KlCl29tlnZ2a7AAAAQqcGaM6cOYHgR9mgzB5Etm3bNrvjjjusUKFClitXLqtevbr9+OOPgfv1+s8995yVKFHC3d+4cWNbv359prYJAACEt1MqYx83bpwLRBRwaLvwwgvt/fffz/DGaXFVTbiYI0cON8/QqlWr7NVXX02UfRo4cKCrT1L32/fff2958uSxJk2aWHx8fIa3BwAAeHQm6MGDB9uzzz5rDz74oAtORKvDd+nSxfbs2WPdu3fPsMa9/PLLVrp0aRszZkzgWPny5RNlf4YOHWrPPPOMNW/ePBCcFStWzD755BO77bbbMqwtAADAwxmgYcOGuRmgFZzcdNNNblMW5o033giMFMson332mV1yySXWqlUrK1q0qNWsWdNGjx6dqC5px44drtvLTxMi1alTxxYuXJjq82rIviZPCt4AAIB3pDsA2r59u11++eXJjuuY7stIv/32mwu2KlasaDNmzLD777/fHn74YRs7dqy7X8GPKOMTTLf996Wkf//+LlDyb8oyAQAA70h3AFShQgX7+OOPkx3XoqgKVDLSiRMn7OKLL7Z+/fq57M+9995rnTt3Pu3h9r169XLTZvu3LVu2ZFibAQCRKWd0rA25fo7btA+P1QD17t3b2rRp4yY+9NcAffvttzZ79uwUA6PToZFdVatWTXSsSpUqNnnyZLdfvHhx93Xnzp3usX66fdFFF6X6vDExMW4DACCttPxFmfyVOGFezQC1bNnSjbYqXLiwKzTWpv0ffvjBbrnllgxtnAKstWvXJjq2bt06K1u2bKAgWkGQgi8/1fOofXXr1s3QtgAAAA9ngKRWrVr2n//8xzKbRpSptkhdYK1bt3ZB1ltvveU2/7IcjzzyiPXp08d1vykg0gi1kiVL2s0335zp7QMAeGspjCmr/hns06LqwyyF4cUASLU5GzZscKvCaz/YVVddlVFts9q1a9vUqVNdzc6LL77oAhwNe2/Xrl3gMT179rSDBw+6+qB9+/bZFVdcYdOnT7fYWPpnAQAZuxTGxysHu/3mVR5gKYwwF+VL51TOixYtsttvv91+//33ZLNAKyOjhVHDjbrNNBpMBdH58uXL6uYAAFIxZW3GjjZOj/jjh6zdpApuf/ytGyw2e+6Tfk+LSv+rT0VoXb/TnQHShIeam+fLL790hccKegAAAMJJugMgrbM1adIkNxweAADAE6PANMuy6n8AAAAiOgP0888/B/Yfeugh69Gjh5tpWQuiaqHSYFoYFQAAIOwDIE0qqFqf4KLnjh07Bvb994VrETQAAPCWNAVAWnQUAAAvy5Etxl6+5r+BfXggAPLPvAwAgFdFZ4u2CoVSX2YJEV4ErZXYNQQ+eCLCAgUKuBmbNTcQAABAxAVAWpYiV65cbn/hwoU2fPhwGzhwoFsPTEtXAAAQqUthfLL6DbdpHx6bB2jLli2BOYC0EOqtt97qlqHQwqUNGjTIjDYCABASS2G8v7yP27+uYgeWwvBaBihv3ry2d+9etz9z5ky75ppr3L7W3jp8+HDGtxAAACCrM0AKeO655x6rWbOmrVu3zpo2beqOr1y50sqVK5fR7QMAAMj6DNCIESOsbt26tnv3bps8ebIVKlTIHV+yZIm1bduWjwgAAEReBkgjvlT4nFTv3r0zqk0AAAChlQECAAAIdwRAAADAc9LdBQYAgBdp+YveDScF9uGBDNBnn31mx44dy/zWAAAQwkthVCt2udu0Dw8EQLfccovt27fP7UdHR9uuXbsyu10AAABZGwAVKVLEFi1a5PZ9Pp9FRUVlXosAAAhBx08cs2nrx7hN+/BADVCXLl2sefPmLvDRVrx48VQfm5CQkJHtAwAgJCjoeXvJ026/Yfk2lj1bjqxuEjI7AHrhhRfstttusw0bNthNN91kY8aMcfMBAQAARPQosMqVK7vt+eeft1atWlnu3Lkzt2UAAAChMgxeAZBoKYy1a9e6/UqVKrk6IQAAgIicCPHQoUPWsWNHK1mypF111VVu036nTp3cfQAAABEXAHXv3t3mzZvn5gbS0Hhtn376qTvWo0ePzGklAABAVnaBaQX4SZMmWYMGDQLHmjZtarly5bLWrVvbyJEjM7J9AAAAWR8AqZurWLFiyY4XLVqULjAAQMTKkS2nPXXVuMA+PNYFVrduXVcIHR8fHzh2+PBh6927t7sPAIBIFJ0tu9Uq2dht2kd4S/cn+Nprr1mTJk2sVKlSVqNGDXds+fLlFhsbazNmzMiMNgIAAGRtAFStWjVbv369jR8/3tasWeOOtW3b1tq1a+fqgAAAiNSZoOdvmuL2ryrXgpmgw9wp5fA0CWLnzp0zvjUAAIRwADTih+5u//IyzQiAvFYDBAAAEO4IgAAAgOcQAAEAAM8hAAIAAJ5zSgGQlr94++23rVevXvbnn3+6Y0uXLrVt27ZldPsAAACyfhTYzz//bI0bN7b8+fPbpk2b3GiwggUL2pQpU2zz5s02btw/s2QCAABETAbo0UcftQ4dOri5gDT5YfB6YPPnz8/o9gEAEBK0/EWPy990G0theDADtHjxYnvzzTeTHT/nnHNsx44dGdUuAABCipa/0Pw/8GgGKCYmxuLi4pIdX7dunRUpUiSj2gUAABA6AdBNN91kL774oh07dszdjoqKcrU/TzzxhLVs2TIz2ggAQJZLOHHcvtv8udu0D48FQK+++qodOHDAihYt6laBr1+/vlWoUMHOOuss69u3b+a0EgCALHbsxFF79bv73KZ9eKwGSKO/Zs2aZQsWLHAjwhQMXXzxxW5kGAAAQMQuhipXXHGF2wAAACI+AHr99ddTPK5aIA2LV3fYVVddZdHR0RnRPgAAgKwPgIYMGWK7d++2Q4cO2dlnn+2O/fXXX5Y7d27Lmzev7dq1y84991ybM2eOlS5dOuNbDAAAcKaLoPv162e1a9d2EyHu3bvXbRoCX6dOHXvttdfciLDixYtb9+7dT7dtAAAAoZEBeuaZZ2zy5Ml23nnnBY6p2+uVV15xw+B/++03GzhwIEPiAQBA5ARA27dvt+PHk89/oGP+maBLlixpf//9d8a0EACAEJA9Ww7reumQwD481gXWsGFDu++++2zZsmWBY9q///77rVGjRu72ihUrrHz58hnbUgAAspCCnkbntnEbAZAHA6B33nnHrf5eq1YttyyGtksuucQd032iYmhNmAgAABARXWAqcNZEiGvWrHHFz1KpUiW3BWeJAACIJFr+4qcdc93+RcUbuMVREb5O+dOrXLmy2wAA8AItf9Fv/l1uf/ytGwiAvBgAbd261T777DM35P3o0cTroQwePDij2gYAABAaAdDs2bPdivCa7FDdYNWqVbNNmzaZz+dza4IBAABEXBF0r1697LHHHnMjvbT0heYE2rJli1sVvlWrVpnTSgAAgKwMgFavXm133fVPH2j27Nnt8OHDbtTXiy++aC+//HJGtg0AACA0AqA8efIE6n5KlChhv/76a+C+PXv2ZGzrAAAAQqEG6LLLLrMFCxZYlSpVrGnTptajRw/XHTZlyhR3HwAAQMQFQBrldeDAAbffu3dvt//RRx9ZxYoVGQEGAIhYmv35nlp9A/sIb1E+Dd/yuLi4OMufP7/t37/f8uXLl9XNAQCkYsra7WF1blpUKpHVTYhocadx/U53DZCGv+/duzfZ8X379rn7AAAAQl26AyDN+ZOQkJDs+JEjR2zbtm2WmQYMGGBRUVH2yCOPBI7Fx8db165drVChQm40WsuWLW3nzp2Z2g4AgPcknEiwX3Z+5zbtwyM1QJr52W/GjBku5eSngEgTJJYrV84yy+LFi+3NN9+0Cy+8MNHx7t2725dffmkTJ050bXrwwQetRYsW9u2332ZaWwAA3nPsxBF7fs6tQUth5M7qJuFMBEA333yz+6oMTPv27RPdlyNHDhf8ZNYK8Cq0bteunY0ePdr69OkTOK4+P61AP2HCBGvUqJE7NmbMGDdCbdGiRYxKAwAAp9cFduLECbeVKVPGdu3aFbitTd1fa9eutRtvvNEyg7q4brjhBmvcuHGi40uWLLFjx44lOq4FWtXGhQsXpvp8aq8Kp4I3AADgHekeBr9x40Y7kz788ENbunSp6wJLaseOHZYzZ04rUKBAouPFihVz96Wmf//+bgg/AADwplNaDV71Ptr8maBg7777bka1za0x1q1bN5s1a5ZbdyyjaD2zRx99NHBbGaDSpUtn2PMDAIAIC4CUOdG6X5dccolbCkM1QZlFXVwKsoJXmVfB9fz582348OGuGFvLcmgIfnAWSKPAihcvnurzxsTEuA0AAHhTugOgUaNG2XvvvWd33nmnZbarr77aLbMR7O6773Z1Pk888YTL2qgAW9koDX8X1SJt3rzZ6tatm+ntAwAAHgmAlHG5/PLL7Uw466yzrFq1askWY9WcP/7jnTp1ct1ZBQsWdLNAPvTQQy74YV0yAEBGio7KbnfWeCawj/CW7k/wnnvuccPOn332WQsFQ4YMsWzZsrkMkEZ3NWnSxN54442sbhYAIMLkiM5pN1d5IKubgawKgDTz8ltvvWVfffWVm5RQXVBJF0vNTHPnzk10W8XRI0aMcBsAAECmBEA///yzXXTRRW7/l19+SXRfZhZEAwCQlbT8xca//qlLLX92dYvOFs0H4qUAaM6cOZnTEgAAQnwpjCdmNXX7LIXhwcVQ/TZs2OCGoR8+fNjd9vl8GdkuAACA0AmA9u7d64ann3/++da0aVPbvn17YDRWjx49MqONAAAAWRsAafV1FT5rrp3cuf+3Em6bNm1s+vTpGds6AACAUKgBmjlzpuv6KlWqVKLjFStWtN9//z0j2wYAABAaGaCDBw8myvz4/fnnnywvAQAAIjMAuvLKK23cuHGJhr5rQdSBAwdaw4YNM7p9AAAAWd8FpkBHRdA//vijWxajZ8+etnLlSpcB+vbbbzO+hQAAhAAtf9H6gkcD+whv6f4EtQbXunXr3GrsWqvrwIED1qJFC+vatatbHR4AgEhdCqNN9ceyuhnIIKcUwubPn9+efvrpjGoDAABAaNcAjRkzxiZOnJjsuI6NHTs2o9oFAEBIOeE7YZv3r3Wb9uGxAKh///5WuHDhZMeLFi1q/fr1y6h2AQAQUo4mxFv3aQ3dpn14LADSBIjly5dPdrxs2bLuPgAAgIgLgJTp0YrwSS1fvtwKFSqUUe0CAAAInQCobdu29vDDD7tV4RMSEtz29ddfW7du3ey2227LnFYCAABk5Siwl156yTZt2uTmAsqe/Z9v10SId911FzVAAAAg8gIgn89nO3bssPfee8/69OljP/30k+XKlcuqV6/uaoAAAAAiMgCqUKGCm/lZi59qAwAAiOgAKFu2bC7o2bt3L8EPAMBTtPzFTZW7BPbhsSLoAQMG2OOPP26//PJL5rQIAIAQXQqj/UXPuU37CG/pDmFV7Hzo0CGrUaOG5cyZ09UABdOiqAAAABEVAA0dOjRzWgIAQAjT8hd7Dm5z+4XznGPZotLdiYJwDoDat2+fOS0BACCEafmL+7+o4/bH37rBYrPnzuom4TScUvj666+/2jPPPOMmRdy1a5c7Nm3aNDc6DAAAIOICoHnz5rl5f77//nubMmWKHThwILAUxvPPP58ZbQQAAMjaAOjJJ590kyDOmjXLFUH7NWrUyBYtWpSxrQMAAAiFAGjFihV2yy23pLhI6p49ezKqXQAAAKETABUoUMC2b9+e7PiyZcvsnHPOyah2AQAAhE4ApBXfn3jiCbcmWFRUlFsI9dtvv7XHHnvMzREEAAAQccPg+/XrZ127drXSpUtbQkKCVa1a1X29/fbb3cgwAAAiUXRUtF1XoX1gH+EtyqcVTk/Bli1bXD2QRoHVrFkzrNcGi4uLs/z589v+/fstX758Wd0cAEAqpqxNXoIRylpUKpHVTYhocadx/U5zBkhdXYMGDbLPPvvMjh49aldffbUb9p50KQwAAICIqQHq27evPfXUU5Y3b15X7Pzaa6+5rjAAALxAHSb74/e67RQ7TxCOAdC4cePsjTfesBkzZtgnn3xin3/+uY0fP95lhgAAiHRHEg5bx0+qu0378EgAtHnzZmvatGngduPGjd0osD/++COz2gYAAJC1AdDx48ctNjY20bEcOXLYsWPHMqNdAAAAmSbNRdDq7+zQoYPFxMQEjsXHx1uXLl0sT548gWNaHwwAACAiAqD27f+Z+yDYHXfckdHtAQAACJ0AaMyYMZnbEgAAgFBdCgMAAMBzS2EAAOBFWv6iQbnWgX2ENwIgAADSIEd0jD102VDOVYSgCwwAAHgOGSAAANI4HYx/BuiY6FxuMmCELzJAAACkgYKfdpMquI2lMMIfARAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPIQACAACewzxAAACkQbaobFa39I2BfYQ3AiAAANIgZ3SsPVbvLc5VhCCEBQAAnkMABAAAPIcACACANIg/fshafljSbdpHeCMAAgAAnkMABAAAPIcACAAAeA4BEAAA8BwCIAAA4DkEQAAAwHNCOgDq37+/1a5d28466ywrWrSo3XzzzbZ27dpEj4mPj7euXbtaoUKFLG/evNayZUvbuXNnlrUZABCZtPzFxSWudhtLYYS/kA6A5s2b54KbRYsW2axZs+zYsWN27bXX2sGDBwOP6d69u33++ec2ceJE9/g//vjDWrRokaXtBgBE5lIYT9d/323aR3iL8vl8PgsTu3fvdpkgBTpXXXWV7d+/34oUKWITJkywW2+91T1mzZo1VqVKFVu4cKFddtllaXreuLg4y58/v3u+fPnyZfK7AACcqilrt4fVyWtRqURWNyGixZ3G9TukM0BJ6Q1KwYIF3dclS5a4rFDjxo0Dj6lcubKVKVPGBUCpOXLkiDtpwRsAAPCOsAmATpw4YY888ojVq1fPqlWr5o7t2LHDcubMaQUKFEj02GLFirn7/q22SBGjfytdunSmtx8AEN60/MXtE89zG0thhL+wCYBUC/TLL7/Yhx9+eNrP1atXL5dN8m9btmzJkDYCACLbkYTDbkP4y25h4MEHH7QvvvjC5s+fb6VKlQocL168uB09etT27duXKAukUWC6LzUxMTFuAwAA3hTSGSDVZyv4mTp1qn399ddWvnz5RPfXqlXLcuTIYbNnzw4c0zD5zZs3W926dbOgxQAAIBxkD/VuL43w+vTTT91cQP66HtXt5MqVy33t1KmTPfroo64wWhXgDz30kAt+0joCDAAAeE9IB0AjR450Xxs0aJDo+JgxY6xDhw5uf8iQIZYtWzY3AaJGdzVp0sTeeOONLGkvAAAIDyEdAKVliqLY2FgbMWKE2wAAAMI+AAIAIFREWZRdUKRuYB/hjQAIAIA0iMmey168ejLnKkKE9CgwAACAzEAABAAAPIcACACANNDyF3dPreY2lsIIf9QAAQCQRnFH/uRcRQgyQAAAwHMIgAAAgOcQAAEAAM8hAAIAAJ5DAAQAADyHUWAAAKSBlr84r2CNwD7CGwEQAABpXApj4LXTOFcRgi4wAADgOQRAAADAcwiAAABIgyPHD1mXzy51m/YR3qgBAgAgDXxmtvvQ1sA+whsZIAAA4DkEQAAAwHMIgAAAgOcQAAEAAM8hAAIAAJ7DKDAAANJAi1+Uynd+YB/hjQAIAIA0iMme215rOpdzFSHoAgMAAJ5DAAQAADyHAAgAgDTQ8hfd/tvAbSyFEf6oAQIAIA20/MXWuHWBfYQ3MkAAAMBzCIAAAIDnEAABAADPIQACAACeQwAEAAA8h1FgAACkgZa/KJK7VGAf4Y0ACACANC6FMeqmHzhXEYIuMAAA4DkEQAAAwHMIgAAASIMjxw9bz5nXu037CG/UAAEAkAY+89mvfy4P7CO8kQECAACeQwAEAAA8hwAIAAB4DgEQAADwHAIgAADgOYwCAwAgjfLFFMy0czVl7faw+xxaVCph4YoACACANIjNntvG3PIL5ypC0AUGAAA8hwAIAAB4DgEQAABpoOUvnpvd0m0shRH+qAECACANtPzFyt0LA/sIb2SAAACA5xAAAQAAzyEAAgAAnkMABAAAPIcACAAAeA6jwAAASKOY6FycqwhBAAQAQBqXwpjQ6lfOVYQgAAKACBNui2qG84KaCF/UAAEAAM8hAwQAQBocTYi3QQs6u/3HrxhtOaNjOW9hjAAIAIA0OOE7YUu3zw7sI7zRBQYAADwnYjJAI0aMsEGDBtmOHTusRo0aNmzYMLv00kstnFC4CADAmRERAdBHH31kjz76qI0aNcrq1KljQ4cOtSZNmtjatWutaNGiWd08ACGIfzgAb4uILrDBgwdb586d7e6777aqVau6QCh37tz27rvvZnXTAABACAr7DNDRo0dtyZIl1qtXr8CxbNmyWePGjW3hwoVZ2jZ4479t3lvoYD4ZAJ4JgPbs2WMJCQlWrFixRMd1e82aNSl+z5EjR9zmt3//fvc1Li7OstKhA39bOImLy5Pmx/LeQgef2z/4mQwd4fIzGX/8kFn8/9pxIntCxLy3U5We95cZ/Ndtn8/nvQDoVPTv39969+6d7Hjp0qWzpD0AgPDSeUDNrG4Cguzdu9fy589vngqAChcubNHR0bZz585Ex3W7ePHiKX6PustUNO23b98+K1u2rG3evDndJzDUKTpWYLdlyxbLly+fRRLeW3jicwtPfG7hK5I/u/3791uZMmWsYMGC6f7esA+AcubMabVq1bLZs2fbzTff7I6dOHHC3X7wwQdT/J6YmBi3JaXgJ9J+OPz0vnhv4YfPLTzxuYWnSP7cIv39ZcuWzXsBkCib0759e7vkkkvc3D8aBn/w4EE3KgwAACAiA6A2bdrY7t277bnnnnMTIV500UU2ffr0ZIXRAAAAERMAibq7UuvyOhl1hz3//PMpdouFO95beOJzC098buEpkj+3SH9/Mafx3qJ8pzJ2DAAAIIxFxEzQAAAA6UEABAAAPIcACAAAeA4BEAAA8BwCoCTKlStnUVFRibYBAwZYJNE6aJoqQO/tp59+skhw0003udlAY2NjrUSJEnbnnXfaH3/8YeFu06ZN1qlTJytfvrzlypXLzjvvPDfiQYsAR4K+ffva5Zdfbrlz57YCBQpYuBsxYoT7G6Kfwzp16tgPP/xg4W7+/PnWrFkzK1mypPub8cknn1gkLYtUu3ZtO+uss6xo0aJuMt21a9daJBg5cqRdeOGFgckP69ata9OmTbNINGDAAPez+cgjj6Tr+wiAUvDiiy/a9u3bA9tDDz1kkaRnz57uj1kkadiwoX388cfuj9fkyZPt119/tVtvvdXCnRb01czmb775pq1cudKGDBlio0aNsqeeesoigQK5Vq1a2f3332/h7qOPPnKTsipAXbp0qdWoUcOaNGliu3btsnCmSWX1XhTcRZp58+ZZ165dbdGiRTZr1iw7duyYXXvtte49h7tSpUq5wGDJkiX2448/WqNGjax58+bu70gkWbx4sfv7qGAv3TQMHv9TtmxZ35AhQyL2lPz3v//1Va5c2bdy5UpNf+BbtmyZLxJ9+umnvqioKN/Ro0d9kWbgwIG+8uXL+yLJmDFjfPnz5/eFs0svvdTXtWvXwO2EhARfyZIlff379/dFCv3NmDp1qi9S7dq1y73HefPm+SLR2Wef7Xv77bd9keLvv//2VaxY0Tdr1ixf/fr1fd26dUvX95MBSoGi5kKFClnNmjVt0KBBdvz4cYsEWiC2c+fO9v7777suh0j1559/2vjx413XSo4cOSzSaPG/U1n4D5mbydJ/2o0bN060NpFuL1y4kFMfRr9bEmm/XwkJCfbhhx+6zJa6wiJF165d7YYbbkj0e+fJmaAzysMPP2wXX3yx+wX47rvv3Mrx6gYbPHiwhTP989ahQwfr0qWLWzNNtSWR5oknnrDhw4fboUOH7LLLLrMvvvjCIs2GDRts2LBh9sorr2R1UxBkz5497iKTdPkd3VY3JkKfuppVQ1KvXj2rVq2aRYIVK1a4gCc+Pt7y5s1rU6dOtapVq1ok+PDDD11Xs7rATpUnMkBPPvlkssLmpJv/j5T68Bs0aOD6ExUsvPrqq+6Co8LhcH5veg9///23C+gi8XOTxx9/3JYtW2YzZ8606Ohou+uuu1zgFwnvTbZt22bXXXedq5lRJi9Uncp7A0Ihm/DLL7+4C2ukqFSpkhvo8v3337s6Oy0avmrVKgt3W7ZssW7durlMvwYcnCpPLIWhhVL37t37r48599xzLWfOnMmOq2BM/w3oD7Z+mML1vbVu3do+//xzd/Hx03+sChTatWtnY8eOtUj63LZu3WqlS5d2WbxQTPmm971pRJsCc2W23nvvPde9EqpO5XPTe9J/3/v27bNw7QJTt/KkSZPcSCI/XXD0nj799FOLBPr7oSxC8HuMBFpHUp+RRrxpxGWkUleRRpKqaDicaSTiLbfc4q5fwdcz/Xzqb6MSFsH3eboLrEiRIm47FYqedUI1RDKc39vrr79uffr0CdzWBVUjVDRyRcN1I+1zUzpbQjVzl573psyPRrnVqlXLxowZE9LBz+l+buFKwZw+n9mzZweCA/0M6vapLtKMzKf//zXKV0Hd3LlzIzr48f9MhurfxPS4+uqrXfdesLvvvtsqV67sSiHSEvx4JgBKKxUrKlWoi43mhdDt7t272x133GFnn322hTPNkRNM/cGi/wY0XDKc6TNTP/AVV1zhPicNgX/22WfdewvF7E96KPhR5qds2bKu7kfZFb/ixYtbuNu8ebMrWtdX/Qfnn5eqQoUKgZ/RcKHuc2V8VGN36aWX2tChQ13Rqf4wh7MDBw642jO/jRs3us9JdZJJ/66EY7fXhAkTXPZHf/N37NjhjufPn9/NuxXOVO5w/fXXu89I5Q96nwryZsyYYeHurLPOSlanlSdPHjd4KV31W5k1PC0cLVmyxFenTh03HDc2NtZXpUoVX79+/Xzx8fG+SLNx48aIGQb/888/+xo2bOgrWLCgLyYmxleuXDlfly5dfFu3bvVFwvBwfU4pbZGgffv2Kb63OXPm+MLRsGHDfGXKlPHlzJnTDYtftGiRL9zps0jpM9JnF+5S+93S712469ixo5vWRT+LRYoU8V199dW+mTNn+iJV/VMYBu+JGiAAAIBgoV1MAAAAkAkIgAAAgOcQAAEAAM8hAAIAAJ5DAAQAADyHAAgAAHgOARAAAPAcAiAAAOA5BEAAQt4777xj1157beB2hw4dMmRBTi2eqIUVM8qTTz7p1pYCEPqYCRpASIuPj3erx0+cONHq1avnju3fv98tZFmgQIGQWt18z549rq1aK0tfAYQuMkAAQtqkSZMsX758geDHv1jl6QY/maFw4cLWpEkTGzlyZFY3BcBJEAABOCO0kr1WsO/Xr1/g2HfffWc5c+a02bNnp/p9H374oTVr1izRsaRdYA0aNLCHH37Yevbs6VYp1+u88MILib5n/fr1dtVVV1lsbKxVrVrVZs2aley1tmzZYq1bt3bBlZ6nefPmtmnTJnffmjVrLHfu3G5Vbb+PP/7YrRq+atWqwDG1VW0GENoIgACcEUWKFLF3333XBSY//vij/f3333bnnXfagw8+aFdffXWq37dgwQK75JJLTvr8Y8eOtTx58tj3339vAwcOtBdffDEQ5Jw4ccJatGjhgi3dP2rUKHviiScSff+xY8dc9uass86yb775xr799lvLmzevXXfddXb06FGrXLmyvfLKK/bAAw/Y5s2bbevWrdalSxd7+eWXXUDld+mll7r7/IETgNBEDRCAM6pr16721VdfuaBmxYoVtnjxYouJiUnxsfv27bOzzz7b5s+fb1deeWWiDJDu8xcwKwOUkJDgApfgQKRRo0Y2YMAAmzlzpt1www32+++/W8mSJd3906dPt+uvvz5QA/Sf//zH+vTpY6tXr3a1QaLAR9kgvY6/CPvGG2+0uLg4F0xFR0e75/E/XnSfuujmzp1r9evXz6SzCOB0ZT/tZwCAdFAWpVq1aq6oecmSJakGP3L48GH3Vd1WJ3PhhRcmul2iRAnbtWuX21dQU7p06UDwI3Xr1k30+OXLl9uGDRtcBihpEfavv/4auK0s1vnnn2/ZsmWzlStXJgp+RF1icujQoZO2GUDWIQACcEYpmPjjjz9ct5S6iapXr57qYwsVKuQCjL/++uukz5sjR45Et/V9eo20OnDggNWqVcvGjx+fYvddcKB08OBBFwBt377dBVrB/vzzz2TfAyD0EAABOGPUpXTHHXdYmzZtrFKlSnbPPfe4brCiRYum+Hh1M6m+RkXGwfMApVeVKlVcgXNwwLJo0aJEj7n44ovto48+cm3RqLOUKLhR99vTTz/tnqtdu3a2dOnSQNZHfvnlFxeMXXDBBafcXgCZjyJoAGeMAgfN4fP666+7ImR1JXXs2PFfv0eFySqEPh2NGzd2r9W+fXuXwVGtkNoSTMGMhrFr5Jfu37hxo6vj0egyFTWLip7VlfbMM8/Y4MGDXd3RY489luh59L2qVwoOigCEHgIgAGeEgomhQ4fa+++/7zIs6kLSvgKGf5s3p1OnTvbf//7XBU6nSq+lYmfVFKk4Wpmnvn37JnqMhrir2LpMmTJuxJiyRnpt1QCpvePGjXPtUJuzZ8/uRpypcHr06NE2bdq0wPNoCHznzp1Pua0AzgxGgQEIea1atXJdVL169bJQpkCoR48e9vPPP7sgCUDoIgMEIOQNGjTIzckT6lQcPWbMGIIfIAyQAQIAAJ5DBggAAHgOARAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPIQACAACeQwAEAAA8hwAIAAB4zv8BXiCGCJkh32EAAAAASUVORK5CYII=", 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" ] @@ -1400,7 +1426,7 @@ " invert(lambda: qft(x))\n", "\n", "\n", - "pc, df = run_standard_simulation(main, show_circuit=True)\n", + "pc, df = run_standard_simulation(main)\n", "analyze_results(pc, df, p)" ] }, @@ -1430,7 +1456,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "id": "41", "metadata": {}, "outputs": [ @@ -1438,13 +1464,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "Parsed counts: [{'x': 1}: 2021, {'x': 0}: 14, {'x': 2}: 10, {'x': 3}: 2, {'x': -2}: 1]\n", + "Parsed counts: [{'x': 1}: 2025, {'x': 2}: 12, {'x': 0}: 8, {'x': -3}: 2, {'x': -1}: 1]\n", "The analytical gradient is: 0.25\n", "The majority gradient is: 0.25\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 98.68% (2021/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.68%\n" + "Success rate: 98.88% (2025/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.88%\n" ] }, { @@ -1459,7 +1485,7 @@ }, { "data": { - "image/png": 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", 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" ] @@ -1504,21 +1530,40 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "id": "43", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Exception in callback Task.__step()\n", + "handle: \n", + "Traceback (most recent call last):\n", + " File \"/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/asyncio/events.py\", line 88, in _run\n", + " self._context.run(self._callback, *self._args)\n", + "RuntimeError: cannot enter context: <_contextvars.Context object at 0x108829c40> is already entered\n", + "Task was destroyed but it is pending!\n", + "task: .run_in_context() done, defined at /Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/ipykernel/utils.py:57> wait_for= cb=[Task.__wakeup()]> cb=[ZMQStream._run_callback.._log_error() at /Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/zmq/eventloop/zmqstream.py:563]>\n", + "/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/internals/managers.py:932: RuntimeWarning: coroutine 'Kernel.shell_main' was never awaited\n", + " def __init__(\n", + "RuntimeWarning: Enable tracemalloc to get the object allocation traceback\n", + "Task was destroyed but it is pending!\n", + "task: cb=[Task.__wakeup()]>\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed counts: [{'x': 2}: 497, {'x': 0}: 488, {'x': 1}: 486, {'x': -1}: 189, {'x': 3}: 188, {'x': -4}: 75, {'x': -2}: 65, {'x': -3}: 60]\n", + "Parsed counts: [{'x': 2}: 548, {'x': 1}: 519, {'x': 0}: 455, {'x': -1}: 169, {'x': 3}: 140, {'x': -2}: 83, {'x': -4}: 76, {'x': -3}: 58]\n", "The analytical gradient is: 0.25\n", "The majority gradient is: 0.5\n", "The majority result is incorrect\n", "####################################################\n", - "Success rate: 23.73% (486/2048 shots)\n", - "[\u001b[92m████████████\u001b[91m--------------------------------------\u001b[0m] 23.73%\n" + "Success rate: 25.34% (519/2048 shots)\n", + "[\u001b[92m█████████████\u001b[91m-------------------------------------\u001b[0m] 25.34%\n" ] }, { @@ -1533,7 +1578,7 @@ }, { "data": { - "image/png": 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", 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", 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" ] @@ -1603,37 +1648,16 @@ "metadata": {}, "outputs": [ { - "name": "stdout", + "name": "stderr", "output_type": "stream", "text": [ - "m=0.05: Success rate = 0.00%\n", - "m=0.1: Success rate = 0.00%\n", - "m=0.33: Success rate = 0.39%\n", - "m=0.5: Success rate = 9.57%\n", - "m=0.67: Success rate = 93.41%\n", - "m=1.0: Success rate = 99.27%\n", - "m=1.33: Success rate = 80.32%\n", - "m=1.67: Success rate = 94.58%\n", - "m=2.0: Success rate = 98.78%\n", - "m=2.33: Success rate = 90.97%\n", - "m=2.67: Success rate = 77.34%\n", - "m=3.0: Success rate = 64.70%\n", - "m=3.33: Success rate = 54.88%\n", - "m=3.67: Success rate = 0.00%\n", - "m=4.0: Success rate = 0.00%\n", - "m=6.0: Success rate = 0.00%\n", - "m=10.0: Success rate = 0.00%\n" + "Exception in callback Task.__step()\n", + "handle: \n", + "Traceback (most recent call last):\n", + " File \"/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/asyncio/events.py\", line 88, in _run\n", + " self._context.run(self._callback, *self._args)\n", + "RuntimeError: cannot enter context: <_contextvars.Context object at 0x108829c40> is already entered\n" ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ From 5682787558c0291e65f91f62f204b82b53a71e52 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Sat, 23 May 2026 21:48:12 +0300 Subject: [PATCH 08/12] Fixed error in one cell --- .../gradient_estimation.ipynb | 87 ++++++++++++++----- 1 file changed, 63 insertions(+), 24 deletions(-) diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index ed248b17f..4335eee89 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -1366,7 +1366,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, "id": "37", "metadata": {}, "outputs": [ @@ -1374,14 +1374,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3E8YOVTlM5p8UlHjC9whf2WfyLN\n", - "Parsed counts: [{'x': 2}: 1796, {'x': 3}: 125, {'x': 1}: 54, {'x': -4}: 24, {'x': 0}: 19, {'x': -1}: 12, {'x': -3}: 11, {'x': -2}: 7]\n", + "Parsed counts: [{'x': 2}: 1807, {'x': 3}: 105, {'x': 1}: 56, {'x': -4}: 25, {'x': 0}: 21, {'x': -3}: 14, {'x': -2}: 11, {'x': -1}: 9]\n", "The analytical gradient is: 0.55\n", "The majority gradient is: 0.5\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 87.70% (1796/2048 shots)\n", - "[\u001b[92m████████████████████████████████████████████\u001b[91m------\u001b[0m] 87.70%\n" + "Success rate: 88.23% (1807/2048 shots)\n", + "[\u001b[92m████████████████████████████████████████████\u001b[91m------\u001b[0m] 88.23%\n" ] }, { @@ -1396,7 +1395,7 @@ }, { "data": { - "image/png": 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", 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", 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" ] @@ -1643,7 +1642,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "id": "46", "metadata": {}, "outputs": [ @@ -1656,8 +1655,48 @@ "Traceback (most recent call last):\n", " File \"/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/asyncio/events.py\", line 88, in _run\n", " self._context.run(self._callback, *self._args)\n", - "RuntimeError: cannot enter context: <_contextvars.Context object at 0x108829c40> is already entered\n" + "RuntimeError: cannot enter context: <_contextvars.Context object at 0x108829c40> is already entered\n", + "Task was destroyed but it is pending!\n", + "task: .run_in_context() done, defined at /Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/ipykernel/utils.py:57> wait_for= cb=[Task.__wakeup()]> cb=[ZMQStream._run_callback.._log_error() at /Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/zmq/eventloop/zmqstream.py:563]>\n", + "/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/contextlib.py:108: RuntimeWarning: coroutine 'Kernel.shell_main' was never awaited\n", + " doc = getattr(func, \"__doc__\", None)\n", + "RuntimeWarning: Enable tracemalloc to get the object allocation traceback\n", + "Task was destroyed but it is pending!\n", + "task: cb=[Task.__wakeup()]>\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=0.05: Success rate = 0.00%\n", + "m=0.1: Success rate = 0.00%\n", + "m=0.33: Success rate = 0.93%\n", + "m=0.5: Success rate = 10.45%\n", + "m=0.67: Success rate = 92.72%\n", + "m=1.0: Success rate = 99.32%\n", + "m=1.33: Success rate = 81.74%\n", + "m=1.67: Success rate = 93.99%\n", + "m=2.0: Success rate = 98.93%\n", + "m=2.33: Success rate = 90.97%\n", + "m=2.67: Success rate = 79.00%\n", + "m=3.0: Success rate = 64.65%\n", + "m=3.33: Success rate = 56.59%\n", + "m=3.67: Success rate = 0.00%\n", + "m=4.0: Success rate = 0.00%\n", + "m=6.0: Success rate = 0.00%\n", + "m=10.0: Success rate = 0.00%\n" ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -1749,7 +1788,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "id": "48", "metadata": {}, "outputs": [ @@ -1757,20 +1796,20 @@ "name": "stdout", "output_type": "stream", "text": [ - "l=0.1: Success rate = 94.68%\n", - "l=0.2: Success rate = 78.03%\n", - "l=0.3: Success rate = 59.18%\n", - "l=0.4: Success rate = 38.82%\n", - "l=0.5: Success rate = 25.34%\n", - "l=1: Success rate = 10.06%\n", - "l=1.5: Success rate = 16.46%\n", - "l=2.0: Success rate = 12.26%\n", - "l=3.0: Success rate = 26.03%\n" + "l=0.1: Success rate = 94.38%\n", + "l=0.2: Success rate = 80.18%\n", + "l=0.3: Success rate = 58.50%\n", + "l=0.4: Success rate = 38.28%\n", + "l=0.5: Success rate = 22.95%\n", + "l=1: Success rate = 10.01%\n", + "l=1.5: Success rate = 14.50%\n", + "l=2.0: Success rate = 14.01%\n", + "l=3.0: Success rate = 25.63%\n" ] }, { "data": { - "image/png": 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", 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", 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" ] @@ -1857,7 +1896,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "id": "51", "metadata": {}, "outputs": [ @@ -1934,7 +1973,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "id": "53", "metadata": {}, "outputs": [ @@ -1942,11 +1981,11 @@ "name": "stdout", "output_type": "stream", "text": [ - "[{'x': 1, 'y': -2}: 1993, {'x': 0, 'y': -2}: 18, {'x': 2, 'y': -2}: 9, {'x': 1, 'y': -1}: 8, {'x': 1, 'y': -3}: 4, {'x': -2, 'y': -2}: 4, {'x': 0, 'y': -1}: 3, {'x': 2, 'y': -1}: 2, {'x': 1, 'y': -4}: 1, {'x': -1, 'y': 3}: 1, {'x': 0, 'y': 3}: 1, {'x': 0, 'y': -4}: 1, {'x': -4, 'y': -2}: 1, {'x': 3, 'y': 3}: 1, {'x': -1, 'y': -2}: 1]\n", + "[{'x': 1, 'y': -2}: 2005, {'x': 2, 'y': -2}: 14, {'x': 0, 'y': -2}: 8, {'x': 1, 'y': -3}: 5, {'x': 1, 'y': -1}: 4, {'x': -1, 'y': -2}: 2, {'x': 3, 'y': -2}: 2, {'x': -1, 'y': -4}: 1, {'x': 2, 'y': 3}: 1, {'x': -4, 'y': -2}: 1, {'x': 2, 'y': -1}: 1, {'x': -1, 'y': -3}: 1, {'x': -4, 'y': -4}: 1, {'x': 0, 'y': -1}: 1, {'x': 2, 'y': -3}: 1]\n", "Analytical gradient: (dx, dy) = (0.25, -0.5)\n", "Majority gradient: (dx, dy) = (0.25, -0.5)\n", - "Success rate: 97.31% (1993/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.31%\n" + "Success rate: 97.90% (2005/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.90%\n" ] } ], From 83eb825f4baeb9b6d202a6091dcb2c1cdf4f0086 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Fri, 29 May 2026 10:41:00 +0300 Subject: [PATCH 09/12] Fixed comments --- .../gradient_estimation.ipynb | 1204 ++++++++++------- .../gradient_estimation_helpers.py | 101 +- 2 files changed, 772 insertions(+), 533 deletions(-) diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index 4335eee89..f10e1be07 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -42,8 +42,7 @@ ">\n", "> **Keywords:** Foundational quantum algorithms, Gradient, Function evaluation, Oracle problem, Quantum Fourier Transform (QFT)\n", "\n", - "\n", - "The core idea is to encode the function into the phase of a superposition state, then apply an inverse QFT to extract the gradient as a measurable outcome.\n", + "The core idea is an in-place computation: first, the function is encoded directly into the phases of the coordinate superposition state. Then, an inverse QFT is applied to overwrite that exact same coordinate register with the gradient, extracting it as a measurable outcome without needing a separate output register.\n", "\n", "We demonstrate this step by step—first with a simplified version to build intuition, then with refinements for the complete algorithm.\n", "\n", @@ -55,7 +54,7 @@ "id": "3", "metadata": {}, "source": [ - "# 1. Introduction" + "# Introduction" ] }, { @@ -63,15 +62,17 @@ "id": "4", "metadata": {}, "source": [ - "## 1.1. Simplified explanation of the algorithm\n", + "## Simplified explanation of the algorithm\n", "The algorithm has two main steps:\n", - "1. Encode the function into the phase of a quantum superposition\n", - "2. Extract the gradient as a measurable state\n", + "1. Encode the function into the phases of the coordinate register's superposition\n", + "2. Apply an inverse QFT to transform the coordinate register directly into the measurable gradient state\n", "\n", "**In detail:**\n", "\n", "1. We define an interval $l$ with $N$ points around the origin where we estimate the gradient, establishing a resolution $\\mathrm{dx}=l/N$.\n", "\n", + "To calculate the gradient at an arbitrary point $x_0$ instead of the origin, we can define an auxiliary function $\\tilde{f}(x) = f(x + x_0)$ and evaluate its gradient at the origin.\n", + "\n", "For each dimension ($x_i$), we create the superposition $|\\delta_i\\rangle=|-l\\rangle+|-l+\\mathrm{dx}\\rangle+|-l+2\\mathrm{dx}\\rangle\\cdots|l-\\mathrm{dx}\\rangle$ using Hadamard gates on $|0\\rangle^{\\otimes n}$.\n", "\n", "*The actual encoding on qubits is discussed later.*\n", @@ -101,7 +102,7 @@ "id": "5", "metadata": {}, "source": [ - "## 1.2. Full explanation of the algorithm\n", + "## Full explanation of the algorithm\n", "The simplified explanation captures the key idea but omits two important details: handling negative values and fractional representation.\n", "\n", "When estimating the gradient, we analyze an interval $l$ around the origin.\n", @@ -132,7 +133,7 @@ "id": "6", "metadata": {}, "source": [ - "## 1.3. Parameter Selection\n", + "## Parameter Selection\n", "We need to select appropriate values for $l$, $m$, and $N$. We use the following notation: \n", "* $\\nabla f_{\\text{max}}$ — bound on the gradient magnitude: $|\\nabla f|<\\nabla f_{\\text{max}}$\n", "* $\\epsilon$ — desired accuracy: $|\\nabla f_{\\text{est}}-\\nabla f| < \\epsilon$\n", @@ -181,7 +182,7 @@ "| Parameter | Role | Constraint |\n", "|---|---|---|\n", "| $l$ | Sampling interval | $l \\leq \\frac{2\\sqrt{3}\\epsilon}{D_2\\sqrt{d}}$ — keeps $f$ approximately linear |\n", - "| $m$ | Gradient range | $2\\nabla f_{\\max} \\leq m \\leq 2N\\epsilon$ |\n", + "| $m$ | Gradient range | $2\\nabla f_{\\max} \\leq m \\leq 2\\cdot2^n\\epsilon$ |\n", "| $n$ | Qubits / resolution | $n \\geq \\log_2(\\nabla f_{\\max} / \\epsilon)$ |" ] }, @@ -190,7 +191,7 @@ "id": "7", "metadata": {}, "source": [ - "## 1.4. Outline\n", + "## Outline\n", "This notebook covers:\n", "1. Theoretical foundation and parameter selection\n", "2. Implementation\n", @@ -206,7 +207,7 @@ "id": "8", "metadata": {}, "source": [ - "# 2. Implementation" + "# Implementation" ] }, { @@ -214,7 +215,7 @@ "id": "9", "metadata": {}, "source": [ - "## 2.1. State Preparation" + "## State Preparation" ] }, { @@ -222,7 +223,7 @@ "id": "10", "metadata": {}, "source": [ - "### 2.1.1. Phase Kickback" + "### Phase Kickback" ] }, { @@ -268,21 +269,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "Circuit Width: 7\n", - "Circuit Depth: 30\n", - "Gate Counts: {'u': 25, 'cx': 19}\n" + "Circuit Width: 8\n", + "Circuit Depth: 42\n", + "Gate Counts: {'u': 31, 'cx': 27}\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/e3f28363-b9ca-427e-b26b-8785d8f645bd\n", - "/var/folders/3m/h6bttp2n307cd0qt29h_mc440000gn/T/ipykernel_39533/391621480.py:44: SettingWithCopyWarning: \n", - "A value is trying to be set on a copy of a slice from a DataFrame\n", - "\n", - "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n", - " df.sort_values(by=\"x\", inplace=True)\n" + "Job: https://platform.classiq.io/jobs/476aafde-9862-4490-b609-14503612776e\n" ] }, { @@ -330,87 +326,87 @@ "type": "string" } ], - "ref": "608755ba-629d-43c1-947a-8780a8563251", + "ref": "91f08f53-d36e-4da3-bae8-5bb3b83f85fd", "rows": [ [ - "63", + "7", "-4", "0.0", - "(0.08838834764831822+0.08838834764831847j)", + "(0.08838834764831849+0.08838834764831834j)", "0.12", "0.25π", - "0.015624999999999965", - "0000100" + "0.01562499999999999", + "00000100" ], [ - "40", + "1", "-3", "0.0", - "(-0.0883883476483185+0.08838834764831836j)", - "0.12", + "(-0.0883883476483183+0.08838834764831867j)", + "0.13", "0.75π", - "0.015624999999999997", - "0000101" + "0.015625000000000014", + "00000101" ], [ - "61", + "4", "-2", "0.0", - "(-0.08838834764831822-0.0883883476483185j)", + "(-0.08838834764831854-0.08838834764831835j)", "0.12", "-0.75π", - "0.015624999999999972", - "0000110" + "0.015625", + "00000110" ], [ - "41", + "6", "-1", "0.0", - "(0.08838834764831853-0.08838834764831834j)", + "(0.08838834764831824-0.08838834764831861j)", "0.12", "-0.25π", - "0.015624999999999997", - "0000111" + "0.015624999999999993", + "00000111" ], [ - "60", + "2", "0", "0.0", - "(0.08838834764831827+0.08838834764831847j)", + "(0.08838834764831853+0.08838834764831836j)", "0.12", "0.25π", - "0.015624999999999972", - "0000000" + "0.015625", + "00000000" ], [ - "39", + "0", "1", "0.0", - "(-0.0883883476483185+0.08838834764831836j)", - "0.12", + "(-0.08838834764831831+0.08838834764831865j)", + "0.13", "0.75π", - "0.015624999999999997", - "0000001" + "0.015625000000000014", + "00000001" ], [ - "53", + "3", "2", "0.0", - "(-0.08838834764831827-0.08838834764831852j)", + "(-0.08838834764831852-0.08838834764831836j)", "0.12", "-0.75π", - "0.015624999999999983", - "0000010" + "0.015625", + "00000010" ], [ - "30", + "5", "3", "0.0", - "(0.08838834764831856-0.08838834764831835j)", + "(0.08838834764831827-0.08838834764831859j)", "0.12", "-0.25π", - "0.015625", - "0000011" + "0.015624999999999993", + "00000011" ] ], "shape": { @@ -448,99 +444,99 @@ " \n", " \n", " \n", - " 63\n", + " 7\n", " -4\n", " 0.0\n", " 0.088388+0.088388j\n", " 0.12\n", " 0.25π\n", " 0.015625\n", - " 0000100\n", + " 00000100\n", " \n", " \n", - " 40\n", + " 1\n", " -3\n", " 0.0\n", " -0.088388+0.088388j\n", - " 0.12\n", + " 0.13\n", " 0.75π\n", " 0.015625\n", - " 0000101\n", + " 00000101\n", " \n", " \n", - " 61\n", + " 4\n", " -2\n", " 0.0\n", " -0.088388-0.088388j\n", " 0.12\n", " -0.75π\n", " 0.015625\n", - " 0000110\n", + " 00000110\n", " \n", " \n", - " 41\n", + " 6\n", " -1\n", " 0.0\n", " 0.088388-0.088388j\n", " 0.12\n", " -0.25π\n", " 0.015625\n", - " 0000111\n", + " 00000111\n", " \n", " \n", - " 60\n", + " 2\n", " 0\n", " 0.0\n", " 0.088388+0.088388j\n", " 0.12\n", " 0.25π\n", " 0.015625\n", - " 0000000\n", + " 00000000\n", " \n", " \n", - " 39\n", + " 0\n", " 1\n", " 0.0\n", " -0.088388+0.088388j\n", - " 0.12\n", + " 0.13\n", " 0.75π\n", " 0.015625\n", - " 0000001\n", + " 00000001\n", " \n", " \n", - " 53\n", + " 3\n", " 2\n", " 0.0\n", " -0.088388-0.088388j\n", " 0.12\n", " -0.75π\n", " 0.015625\n", - " 0000010\n", + " 00000010\n", " \n", " \n", - " 30\n", + " 5\n", " 3\n", " 0.0\n", " 0.088388-0.088388j\n", " 0.12\n", " -0.25π\n", " 0.015625\n", - " 0000011\n", + " 00000011\n", " \n", " \n", "\n", "" ], "text/plain": [ - " x ancilla amplitude magnitude phase probability bitstring\n", - "63 -4 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000100\n", - "40 -3 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000101\n", - "61 -2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000110\n", - "41 -1 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000111\n", - "60 0 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 0000000\n", - "39 1 0.0 -0.088388+0.088388j 0.12 0.75π 0.015625 0000001\n", - "53 2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 0000010\n", - "30 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 0000011" + " x ancilla amplitude magnitude phase probability bitstring\n", + "7 -4 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 00000100\n", + "1 -3 0.0 -0.088388+0.088388j 0.13 0.75π 0.015625 00000101\n", + "4 -2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 00000110\n", + "6 -1 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 00000111\n", + "2 0 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 00000000\n", + "0 1 0.0 -0.088388+0.088388j 0.13 0.75π 0.015625 00000001\n", + "3 2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 00000010\n", + "5 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 00000011" ] }, "execution_count": 2, @@ -567,7 +563,7 @@ " # 1. State preparation\n", "\n", " # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", "\n", " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", @@ -590,13 +586,8 @@ "print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", "print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", "\n", - "sv = calculate_state_vector(qprog)\n", - "df = sv[sv.ancilla == 0]\n", - "df.sort_values(by=\"x\", inplace=True)\n", - "df\n", - "\n", - "# From now on, we will use the shortcut function:\n", - "# df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)" + "df = calculate_state_vector(qprog, filters={\"ancilla\": 0})\n", + "df.sort_values(by=\"x\")" ] }, { @@ -643,7 +634,7 @@ "type": "float" } ], - "ref": "c6c1a446-e870-4355-a194-27636b2e9da6", + "ref": "a198fb67-4835-4d1e-be10-4a4bd70b0a50", "rows": [ [ "-4", @@ -818,99 +809,10 @@ "The graph shows the original function (gray), classical values (blue), and quantum phase at sample points (orange). Results are displayed in both normalized coordinates (black axes) and original values (blue axes)." ] }, - { - "cell_type": "markdown", - "id": "17", - "metadata": {}, - "source": [ - "Here is the complete code to reproduce the graph:" - ] - }, { "cell_type": "code", "execution_count": 4, - "id": "18", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit Width: 8\n", - "Circuit Depth: 42\n", - "Gate Counts: {'u': 31, 'cx': 27}\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Job: https://platform.classiq.io/jobs/23d8df9c-8954-45da-bb79-b105728d60e5\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Filtering out states with ancilla qubits in state |1>...\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "p = params()\n", - "# f(x) = 0.5*x + 0.25\n", - "# Gradient: f'(0) = 0.5\n", - "p.set_function(p.linear, (0.5, 0.25))\n", - "p.unpack(globals())\n", - "\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[n, SIGNED, 0]], ancilla: Output[QNum[n0, SIGNED, n0]]):\n", - " # 1. State preparation\n", - "\n", - " # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", - " allocate(n, x)\n", - " hadamard_transform(x)\n", - "\n", - " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", - " prepare_basis_state([True] * n0, ancilla)\n", - " qft(ancilla)\n", - "\n", - " # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", - " # Calculate the normalized f and add it to the ancilla\n", - " val = f_normalized(x)\n", - " inplace_add(val, ancilla)\n", - "\n", - " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", - " # invert(lambda: qft(x))\n", - "\n", - "\n", - "df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)\n", - "simplified_df = simplify_df(df)\n", - "plot_simplified_df(simplified_df)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "19", + "id": "17", "metadata": {}, "outputs": [], "source": [ @@ -926,7 +828,7 @@ "# # 1. State preparation\n", "\n", "# # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", - "# allocate(n, x)\n", + "# allocate(x)\n", "# hadamard_transform(x)\n", "\n", "# # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", @@ -952,15 +854,15 @@ }, { "cell_type": "markdown", - "id": "20", + "id": "18", "metadata": {}, "source": [ - "### 2.1.2. Direct Phase" + "### Direct Phase" ] }, { "cell_type": "markdown", - "id": "21", + "id": "19", "metadata": {}, "source": [ "While the phase kickback approach is sometimes well-suited for hardware implementations with a state oracle, it requires significant circuit overhead in simulation. A direct approach provides more efficient state preparation for our purposes." @@ -968,7 +870,7 @@ }, { "cell_type": "markdown", - "id": "22", + "id": "20", "metadata": {}, "source": [ "A simpler approach is to directly prepare the desired state:\n", @@ -979,8 +881,8 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "23", + "execution_count": 5, + "id": "21", "metadata": {}, "outputs": [ { @@ -1003,7 +905,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/30237262-53db-415a-a651-c613f34de3a8\n" + "Job: https://platform.classiq.io/jobs/7cc162b6-3a8d-4546-aceb-b36b10d92128\n" ] }, { @@ -1028,7 +930,7 @@ "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", " # 1. State preparation\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", "\n", @@ -1036,14 +938,23 @@ " # invert(lambda: qft(x))\n", "\n", "\n", - "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "# Run using a statevector simulator\n", + "qprog = synthesize(main)\n", + "# show(qprog) # Uncomment to see the circuit\n", + "print(\"Circuit Width:\", qprog.data.width)\n", + "print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", + "print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", + "\n", + "df = calculate_state_vector(qprog)\n", + "df.sort_values(by=\"x\")\n", + "\n", "simplified_df = simplify_df(df)\n", "plot_simplified_df(simplified_df)" ] }, { "cell_type": "markdown", - "id": "24", + "id": "22", "metadata": {}, "source": [ "The state is identical to the phase kickback method. Moving forward, we'll use the direct method for its superior efficiency." @@ -1051,15 +962,15 @@ }, { "cell_type": "markdown", - "id": "25", + "id": "23", "metadata": {}, "source": [ - "### 2.1.3. Quadratic Function" + "### Quadratic Function" ] }, { "cell_type": "markdown", - "id": "26", + "id": "24", "metadata": {}, "source": [ "Non-linear functions are more interesting. In the next example, we explore a quadratic function.\n", @@ -1069,8 +980,8 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "27", + "execution_count": 6, + "id": "25", "metadata": {}, "outputs": [ { @@ -1093,7 +1004,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/1168d00d-1ca3-44b7-b56f-6f80c46f2cee\n" + "Job: https://platform.classiq.io/jobs/23c179af-ac5c-4845-bbce-851e54c7a979\n" ] }, { @@ -1119,7 +1030,7 @@ "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", " # 1. State preparation\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", "\n", @@ -1127,14 +1038,23 @@ " # invert(lambda: qft(x))\n", "\n", "\n", - "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "# Run using a statevector simulator\n", + "qprog = synthesize(main)\n", + "# show(qprog) # Uncomment to see the circuit\n", + "print(\"Circuit Width:\", qprog.data.width)\n", + "print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", + "print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", + "\n", + "df = calculate_state_vector(qprog)\n", + "df.sort_values(by=\"x\")\n", + "\n", "simplified_df = simplify_df(df)\n", "plot_simplified_df(simplified_df)" ] }, { "cell_type": "markdown", - "id": "28", + "id": "26", "metadata": {}, "source": [ "Decreasing $l$ narrows the sampling interval, making the function appear more linear within that region." @@ -1142,8 +1062,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "id": "29", + "execution_count": 7, + "id": "27", "metadata": {}, "outputs": [ { @@ -1166,7 +1086,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/d7dc1c0a-fb69-42e0-a689-b61e77e2463a\n" + "Job: https://platform.classiq.io/jobs/10e0781b-3c1c-4eba-8aee-63037572a00f\n" ] }, { @@ -1192,7 +1112,7 @@ "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", " # 1. State preparation\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", "\n", @@ -1200,30 +1120,39 @@ " # invert(lambda: qft(x))\n", "\n", "\n", - "df = run_statevector_simulation(main, print_circuit_info=True)\n", + "# Run using a statevector simulator\n", + "qprog = synthesize(main)\n", + "# show(qprog) # Uncomment to see the circuit\n", + "print(\"Circuit Width:\", qprog.data.width)\n", + "print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", + "print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", + "\n", + "df = calculate_state_vector(qprog)\n", + "df.sort_values(by=\"x\")\n", + "\n", "simplified_df = simplify_df(df)\n", "plot_simplified_df(simplified_df)" ] }, { "cell_type": "markdown", - "id": "30", + "id": "28", "metadata": {}, "source": [ - "## 2.2. Full Algorithm" + "## Full Algorithm" ] }, { "cell_type": "markdown", - "id": "31", + "id": "29", "metadata": {}, "source": [ - "### 2.2.1. Linear Functions" + "### Linear Functions" ] }, { "cell_type": "markdown", - "id": "32", + "id": "30", "metadata": {}, "source": [ "The final step is to apply the inverse QFT to the coordinates. This extracts the gradient from the phases and produces a measurable state containing the normalized gradient value." @@ -1231,7 +1160,7 @@ }, { "cell_type": "markdown", - "id": "33", + "id": "31", "metadata": {}, "source": [ "Now we switch from statevector simulation to standard simulation, which measures the final result rather than examining phase values directly." @@ -1239,7 +1168,7 @@ }, { "cell_type": "markdown", - "id": "34", + "id": "32", "metadata": {}, "source": [ "We start with a linear function." @@ -1247,15 +1176,23 @@ }, { "cell_type": "code", - "execution_count": 9, - "id": "35", + "execution_count": 8, + "id": "33", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/9cbb6c64-6a5a-4f14-ad03-12c561b14c09\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed counts: [{'x': -2}: 2048]\n", + "Parsed probabilities: {-2: 1.0}\n", "The analytical gradient is: -0.5\n", "The majority gradient is: -0.5\n", "The majority result is correct\n", @@ -1266,19 +1203,9 @@ }, { "data": { - "image/png": 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", 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mAAAAACizir8333yzRHd+6aWXluh2AFBUvdrH2/BPl1hSSnqBLT9V7VcjqrL1aFPf0lP32K5du9ySkJBgsbGxVqtWLfdTXwIBAABUJFlZZnv3mnXubPbpp5r/Lud1pUmVdVpEB2I1aNAgaO2Q69evb+PGjStwnbPPPtstAAAAABBWwd/ll1++z2VqyyI6SjOvy4XgDwgtmZmZrhpOWrduHRIhWHTVyjaqX0cbOG6BRWRlV/Xl5j6VIsxG9+9kbQ6Js9TUVNuxY4ebO2bv3r22c+dOt+j5KgDUUr169RyfZwBQkT5bAVQs+pPngw/MHn3UrGtXM2VhvXv/e12gNG/e3P3UwVhfffWVrVq1ynf5iSee6P4eAwAAAAAEIPjTkZj+9GX5ZZdd5r4cv+GGG9yXWLJs2TI3B0NSUpK98cYbxdwUAOVBKLa+7N4uzl4c0NmGTlhoO1LSfXP+eT9rxlSxkf06uvUkMjLSHV2uo7z37NnjCwHT09Nt27ZtbqlSpYrVrl3bfc5FR0cTAgKocJ+tACoOHcuplp5PPZVd7de/v9ndd5tdfXXgH1vjx7vvvtuSk5NzHFSqTgyae+/6668P/EYAAAAAQEUL/rwjMT3Dhw93X5pPnz49x5fh7du3t3PPPdd69uxpo0ePttdee630txgA8tCjXZzNH9bdpi5OsGmLN9r2lFSrHRNppx4WZ6cfFu8qA3PT55fXbiouLs4dba4QUItCQM0voyUqKsoFgAoCFRoCAACEq0GDzA4+2EzT2H39dWAfS1NK3HjjjW6evcGDB1vbtm3d5b/99psLBHWd/gYbMGBAYDcEAAAAACpa8JfbRx995I6+zKsNntpX9e3b1x21CQBlSeHeOZ2auqW49HlWo0YNt8THx7ujzlUFqApmtQPdtGmTWzQHjdcOVFWBAAAAoU7Heariz9Otm9m8eWZnnRXYxx01apSdcMIJNnPmTKvstwGHH364nXfeeXbKKafYyJEjCf4AAAAAoBhK9K21WrCorWd+li5dus/cfwAQKnQAQ82aNd2i9nya/08hoCoCd+/e7ZaEhATXgkoBoNZjzi4AABCqcs3s4Bx0kNnPP5tt3Bi4x9X8p08++WSO0M+jy/r162dDhw4N3AYAQJAc17y37UrdYdUja/EaAACA8hH89enTx55//nlr0aKFXXvtta4CRvRluC5/4YUX7OKLLy7tbQWAMqcvnerUqeOWtLQ033yAmhtQ1YBavKBQIaAqBvOqhgYAAAg10dHZ1YCBor+d/v7773yv13X6GwsAws1lHe8N9iYAAIAwVqLg76mnnrKVK1e6oy/vvPNO1xZPVAGjL8aPPfZYGzNmTGlvKwAEVdWqVa1+/fpuUfDnhYD63NNPLWr/6bUC1dyBhIAAAKA8qlvX7PffzerXN6tTR23P8183MTEw23DGGWe4ufyOPPJIu+CCC3JcN378eHv22Wc5oBQAAAAAyiL40xfaX331lX388cc2ZcoUW716tbv8tNNOs169etlZZ53Fl91AiFJYhcJFR0e7pWHDhpaSkuJCPwWB6enptnXrVrdERka6z8vatWtbVFQUuxWowPhsBVDejB5tFhubfTpYx2w++uij9t1337lw75ZbbrGDDz7YXf7HH3/Yhg0brE2bNm4dAAAAAEDRRWQxGZ+bv0tfzutLe1rJACgpfZwmJye7EFCfK/4fr/rSXwGgPmtUFZifPWkZNuXXBJu+ZKNt351qtatFWs9D46xX+3iLrrrv/DcAACA41q7dac2a1bI1a3ZY06a0oywpdVHQVBFTp061VatWucuaN2/uDigdNGiQO9Aq1DHeBMqPD5cnBHsTyqW+rbM7eQEAgPAYQ+xX8Ldu3Tr7+uuvbdOmTXbuueda06ZNLTMz033prY3Ka5L28oiBGIDSlpGR4eb/0+ehwkB/mgdQn5H60Pb/nJyxdKPdMmGh7UxJt0oRZplZ5vtZM6aKjerX0bq3i+PFAgCgHAj14G/nzqKvyzR7+7uvOdAUKC/KS/B3w2fH27aUjVYnJs6eOWNOsDeH4A8AgDAbQ5So1aeyQrVi0ZwLamunOazat2/vgj990d2iRQt74IEH7KabbirJ3QNAyFOgpwo/Lfqc9OYDVFtQBYFa1q9f7z649SE+b81uu+atH83+ORQjM9fPpJR0Gzhugb04oLP1IPwDAAD7qXbtguf1Ex0iqnUyMtjdAFCa9qTvtpT0ZItJ/6fnMgAAQCkqUfD3xBNP2FNPPWW33367nXLKKdajRw/fdfoCu2/fvvbBBx8Q/AEhRhW7mlNFNMdKpUqVgr1JYUGtPevVq+eWvXv3+kLA1NRUd3pz4nYb8sFaF/rlV4KtyyOyzIZOWGjzh3Wn7ScQQvhsBVAezZpl5cK0adPslVdesb/++su2bduWo1W66CDTP//8M2jbBwAAAAAVIvh76aWX7NJLL7VHHnnEtm7dus/1hx9+uJujAUDoSUtLC/YmhLWoqChr2LChNWjQwFX/Kfj74Ke1lpyaWeht9TXYjpR0m7o4wc7p1LRMthdA6eCzFUB5c+KJwd6C7ANK77jjDouLi7OjjjrKdZEBAAAAAAQh+FuzZo0dc8wx+V5fvXp114MUAJA3Hb1erVo1tyxOXOeby68wWm/a4o0EfwAAoNTt3m22erVZamrOyw8/PDA7W11kTj75ZJsyZYpVrVo1MA8CAAAAABVMiYI/Vaso/MvPjz/+aAcccMD+bBcAVBjbd6cVKfQTrbdtd65v4wAAAPbD5s1mV1xhll/TlkDN8afWnueddx6hHwAAAACUohJN4KU5/MaOHevmYfCvXpHp06fb66+/bv369Su9rQSAMFa7WqSr5CsKrVY5Y4+tXr3atQnV3GEAAAD746abzLZvN5s/3ywmxuzzz83eeENzPpt98kng9q3aey5fvjxwDwAAAAAAFVCJgr/777/f4uPjrWPHjm6uP4V+jz32mB133HF2+umnuzn+hg0bVvpbCwBhqOehcUWu+NNqXZvGuHbKqrxetmyZrVu3zpKTky0rq4h3AgAA4OfLL81GjTLr3NmsUiWz5s3NLrnE7PHHzUaMCNyueu655+zDDz+0d955h9cDAAAAAILZ6rNWrVo2b948GzlypE2cONGio6Ptq6++slatWtl9991nt956q8XoUFEAQKF6tY+34Z8usaSUdBfsFVTtFxtTxQZ0O8z27Eq27du3W3p6umuTpaVKlSpWu3Zt9xmtz2WvEhsAAKAgu3ZpOofs03XqZLf+POQQs/btzX76qfT2nQ4QzU1/ywwYMMD+85//WNOmTa1y5co5rtffM4sWLeIFBAAAAIBABn+iYO/uu+92C4DwERUVFexNqHCiq1a2Uf062sBxCywiK7uqLzcX4UWYW692bA2z2BoWFxdnu3btci0/teiLsy1btrhFr6MCQAWBkZGRZf+kAOTAZyuA8qx1azN13GzRwqxDB7MXXsg+PXasWXx86T1O3bp19zkwqV69enaweooCAAAAAIIX/L355pvWsGFDO+200/K8fuXKlTZnzhzXBhRA6KhUqRJfvARJ93Zx9uKAzjZ0wkLbkZLu5vxT+0/vZ82YKjayX0e3nkdfnNWoUcMtar+sdp+qAkxKSrK9e/fapk2b3FKtWjUXANasWdNVBQIoW3y2AijvbrzRLCEh+/R995lpmPf222Y6duj110vvcWbPnl16dwYAIeyazo9aasYei6wcHexNAQAAYSgiqwSTQukLLH3hfNVVV9n//vc/q1q1ao7r3377bRf6ZWRkWCjQXFmqjFHFjL4YB4Bg2ZOWYVMXJ9i0xRtte0qq1Y6JtFMPi7PTD4t3lYFFoc9efa4pBFRFoL/Y2FgXAuqnPssBAEDJrF2705o1q2Vr1uywpk3Dawyxe7fZsmVmBxxgVr9+sLcm9DHeBMqPD5f/c5QDcujbuhTLuwEAQNDHECUu/ejZs6e98cYb9uuvv7oJ2VVtAgDYPwr3zunU1C0lpblx6tSp45a0tDT3H4RCwD179rhqQC0K/fSfhv4DUcUg8wECAABPtWpmRxwR+P2xcOFC++233+zCCy/0XTZt2jR7+OGHXfeCiy66yG5UOSIAAAAAIPDBnyZgv+eee+y8886zI444wiZMmGDHHXdcSe8OQDmQmZlpf/75pzvdqlUrKsLCgCqy69ev7xYFf14IqEBQP7Wo/acCQC2av5UQEChdfLYCKO/UA2biRLNZs8w2bdLnVs7rP/wwMI972223uZbkXvCnKSPOOeccN+9f48aNbciQIe5vk0GDBgVmAwAAAAAgDO1Xn7djjjnGfvrpJzcn2CmnnGLPPvts6W0ZgKDQ0dVaEH6io6MtLi7ODjnkEDvwwAOtbt26rjowPT3dtm7dan/99Zf98ccfbl5A3gNA6eKzFUB5dtNNOrBTwZtZjRpmtWrlXAJl0aJFOQ4e1Vzy+tvk559/tvnz57uDTMeOHRu4DQCAIPkz8RdbvmWB+wkAAFBuKv48jRo1slmzZtnQoUNt8ODBtmDBAir/AKAcU0Vf9erV3aI2zWr9qUpA9Y5OTU11wZ8WHWGv+QBVCaiqQAAAEJ7Gjcuu6uvVq2wfV39/qLrPM2XKFOvRo4frVCA6PXXq1LLdKAAoA4/OucISUxKsbky8vdT7R/Y5AAAoVaXyTa6Oyhw9erR16dLFBg4c6Ob8AwCERgiouf60ZGRkuPBPX8IlJydbSkqKWxISEtw8gAoAtZ4+8wuyJy3DpvyaYNOXbLTtu1OtdrVI63lonPVqH+/mMAQAAOWLqvpatiz7x9UBSJrjT/T3xo8//mhXXHGF73r9PaJ5iQEAAAAAAQ7+TjzxRNcuLrcLLrjADjvsMDdY27JlS0nuGgAQJAr06tSp4xa1//TmA1T4py/etKxfv96FfwoBY2Nj95kPcMbSjXbLhIW2MyXdKkWYZWaZ+/n5kg02/NMlNqpfR+vebt//PwAAQPAMH252//1mr75qFhNTdo/bu3dve+aZZ9w8xGrtGRUV5eb4828F2jIYiSQAAAAAVLTgT60986Pg74cfftifbQIABJlae6r1lhbNTeaFgGoFqtNaFBQqANRSrVo1++K3TTZo3AKzrOz7yMz1Mykl3QaOW2AvDuhsPQj/AAAoN84/3+zdd80aNjRr0cKsatWc1//0U2Ae96GHHrLNmzfbuHHjXHvx119/3XeAqboQTJw40f773/8G5sEBAAAAIEwxaRMAoEA6+r5hw4bWoEEDV/3nBX+qCkxMTHRLVkRlG/L+Khf6/ZPz7UOXR2SZDZ2w0OYP607bTwAAyonLLjP78UezSy4xU+6Wq6A/YNRK/O233873urVr17qDiwAAAAAApRz8HXjggW5uhWXLllnVqlXd+dzt3XLT9X/++WcxNgVAeaDfcSC/z3V9+aalUaNGrvWnAkAdkf/Fih2WtDej0B2n8G9HSrpNXZxg53Rqyo5GhcFnK4Dy7LPPzKZNMzvuOCs3NP5UVwEAAAAAQACCP83ppy98vYnVvfMAwot+x1u3bh3szUAI0P8BmuNPS2Zmpo2c/73pf4jMItxWc/5NW7yR4A8VBp+tAMq7Zs3MatYM9lYAAAAAAMos+NNcCwWdBwBU7FBjV2pWkUI/b86/7SmpAd4qAABQVCNHmt12m9nYsdlz/AEAAAAAQhdz/AEA9lvtapGukk+hXmFULx4VkeFahVavXp0KcgAAgkxz++3ebdaqlZmm1Mvd+T0xMVhbBgAAAAAISPD39ddfW0mccMIJJbodgOBQy8aVK1fmmNsTKIqeh8bZ50s2FGldZYOd46rY33//bVWqVLHatWu7OXyio6MJARGW+GwFUN6NGVM2j6N5gXXQT+XKlcvmAQEAAACgAipS8HfSSScV68vYrKwst35GRsb+bBuAIEhJSWG/o9h6tY+34Z8usaSUdBfs5Uf/k8RGV7EzOjSxPbuSLD093bZs2eKWqKgoXwgYGRnJq4CwwmcrgPIqLc3sq6/M7rlHB34F9rHq1Klj48aNs4suusidv/LKK+2aa66xLl26BPaBAaCcebrXV5ZlWRbhRkgAAABBCP5mzZpVyg8LAAgn0VUr26h+HW3guAUWkZVd1ZebG9JGmI06v6O1bB7nqqCSkpJsx44d7ufevXtt48aNbqlWrZoLAWvWrOmqAgEAQGCorecHH2QHf4GmA3v0/73/3PHdu3cn+ANQ4cRUrRHsTQAAAGGsSN+mnnjiiYHfEgBASOveLs5eHNDZhk5YaDtS0n1z/nk/a8ZUsZH9Orr1RK1kVd2nRRXiCgC17Nq1y3bv3u2WhIQEq1GjhgsBY2NjaT8LAEAA9Olj9tFHZjffHNjd26ZNG3v55ZetRYsW7v9/Uevvn376qcDbHXHEEYHdMAAAAAAII5RRAABKTY92cTZ/WHebujjBpi3eaNtTUq12TKSdelicnX5YvKsMzIvm+qlbt65b0tLSXAC4fft227Nnj6sG1KKgUBWA+qJQYWBxWlADAID8HXyw2QMPmH3zjdmRR5pVr57z+sGDS2fvjRgxwvr37++q/ET/l99zzz1uyQtTSAAAAABAGQZ/+jL2gw8+cEdn6gtatWzzp0HcK6+8UtK7BwCEKIV753Rq6paSqFq1qtWvX98t+r/GCwEVCOqnFrX/9KoFY2JiCAEBANgPGrbVrm3244/Ziz8dZ1Nawd9pp51mK1eutB9++MG19r788stt0KBB1rVr19J5AAAIEZ8se8FS0pIspmqsnd3mmmBvDgAACDMlCv5WrVpl3bp1c21Z1H5NX8qqSkNfxqpdm76sVTUGAAD7Izo62i0NGzZ0rT+9dqDp6em2detWt2i+IP1fpBAwKiqKHQ4AQDGtXFl2u0zjxlNPPdWdfu2116xfv352yimnlN0GAEA58OnyFy0xJcHqxsQT/AEAgFJXqSQ3uvXWW90Xr/PmzbPff//dtWAZP368JScn22OPPeaqL6ZNm1b6Wwsg4NRyUQtQnqiKvHr16ta4cWNr3bq1HXDAAS7o0+Wpqam2adMm++OPP+zPP/90YaCCQaA84bMVQKjIyspeysKsWbMI/QAAAACgPAR/X375pV133XV21FFHuTmXROGfKi0UCuqIzZtuuqm0txVAgOn3uW3btm7xfreB8sab669Zs2bWpk0ba9Kkia/KPCUlxRISEmzZsmWuKt2rRAeC/Z7lsxVAeffmm2bt25vFxGQvhx9uNm5c4B93586ddv/997uxZVxcnFt0+oEHHnDXAQAAAADKoNWn2q21aNHCndaXr6q4UAWgR3M0DB06tCR3DQBAsaqo6tSp4xbNAei1AlUAqCp0Lfo/Sv9XqR2oAkKdBwAA/xo1yuyee8yuv97s2GOzL5s71+zaa822bDG7+ebA7K3169fb8ccf7+b908E8x/7z4MuXL7fhw4fbm2++aXPmzLH4+HheLgAAAAAIZPCnFmtr167NvoMqVVy1hdp+9u3b1122dOlSNydTWVBVxw033GDffvutxcbG2qWXXmoPPfSQm/MJAFBxVK1a1c0xq2Xv3r2u2k8hoFqBeoGggkK1CFUIqLbU+YWAe9IybMqvCTZ9yUbbvjvValeLtJ6Hxlmv9vEWXZVWuACA8PLMM2bPP2926aX/Xnb22WaHHmo2fHjggr/bb7/dNmzYYJMnT7ZevXrluG7q1Klu/r877rjD3njjjcBsAAAAAACEoRIFfyeffLJ9/PHHdt9997nzl19+uY0YMcK2bdtmmZmZNm7cOBfABZoeT9ty8MEH24cffmjr1q2zIUOGuIrEZ599NuCPD4Qb/f6qPaKoqpd2nwhVaj2tVmENGzZ01X8K/by2n4mJiW5RUKgAUEGg/8EqM5ZutFsmLLSdKelWKcIsM8vcz8+XbLDhny6xUf06Wvd2cUF9fggtfLYCKO8SEsyOOWbfy3WZrguUzz//3E0RkTv0k9NPP90GDx5sL730UuA2AAAAAADCUImCPx11+cMPP7iKCn25OmzYMNemZeLEia6a4qKLLrJR6hcTYGPHjnXzPkyaNMnq1q3rLktPT3fzD2qbGjduHPBtAMKNgnMgXKiir1q1am5p1KiRa/2pEFD/d6g16ObNm92i4E8h4IL1e+0/7y40y8q+fWaun0kp6TZw3AJ7cUBn60H4h2LgsxVAeXbQQWbvv282bFjOy8ePNzv44MA97q5du9yBOvnR/91aBwAAAABQBq0+tXj0henLL7/slrKk9i/du3f3hX5y/vnn27XXXmvTp093lYgAAHghoFpCa1EFlsI/hYBJSUm2Z88eW70uwYZ+sNaFfv/kfPvQ5RFZZkMnLLT5w7rT9hMAEBbuv9+sf3+zr7/+d46/b74xmzkzOxAMlHbt2tm7777rxm+5p2rQATq6TusAAAAAAAIc/JUXmt/vyiuvzHGZKjY0+buuAwAgL2pjq/8vtKhSXAHghB9WW3JqZqE7TOHfjpR0m7o4wc7p1JQdjP9v7z7gq6rPP45/yQ4hEUJCEvZegoKgVlsHCjhbNyoOXLhFwQVSFVygFtyTuke14KqoiKJUbdW/oGJBoLIRwgyQSfb/9fzSe00ggZDc3JXP++XP3HGSe3KSHO453/M8PwAIeWecIX37rfTQQ9K771Y81quX9H//J/Xv33Cva3P8nX322TrkkENc15bu3bu7x5cuXeq6u/z0009608oOAQAAAAANH/xZy5W33npLK1ascHPtlZeX71ZZ8cgjj6gh2evaSdtdtWjRws3fVBNrUWrDw6o+AACNU1RUlFq2bKkfN6/yzum3N7bcxws3EvwBAMLGgAHSq6/69zXPOussd1xpU0lY1Z8dQxo7trR5ep9//nmdeeaZ/l0pAPCDzi36KKVpayXF/tbBCgAAIKDB35w5c9xB2vbt22tcxh/BX11NmjRJE62fDQAA/7M9v6hWoZ+x5bLydrLtAABho6xMWrZM2rSp4nZlRx7ZcK9r0zOcf/75mjdvnlavXu0e69ChgwYOHOguzgGAcDTuyJcCvQoAACCM1elI6pprrlFCQoJru3LooYcqKSlJgWCVfdaerbpKwMrz/u1q3LhxGjNmTJWKv3bt2jXYegIAgl/zpjG1rvizeoSo0iL98ssvrvJ8v/32221uIgAAQsU330jDh0uWu+3SyEVWhFda2rCvbwHf7373OzcAAAAAAAEI/tasWaP7779fQ4YMUSD17Nlzt7n8LAjMzMx0z9UkNjbWDQC787RYAhqbofunadaiDbVa1s6JHta+qWsbvXHjRjeaNm3qQkC7GIYKBeyKfSuAYHblldLAgdIHH0gZGRVhHwAAAACgEQV/BxxwQLWVdv52wgkn6L777nMtRz1z/U2fPl0REREaOnRooFcPCDn2t7P//vsHejWAgDixb4YmvL9IOQUlLtiriZ0LTYqP0qVD+mtnfq7799DmJ8rPz3fDLj5p1qyZ+3cpMTHR/V2hcWPfCiDY/fKLNGOG1LVroNcEAAAAAFBfdTobadV+Tz75pJuHIZBsAng7qXrqqadq9uzZeuGFF3TzzTe7x1u3bh3QdQMAhJa46EhNPaufS/ZqKnRwjzeRppzVT03jYlxb6U6dOqlHjx5KS0tTXFycysvLlZOTo7Vr17qq9F9//VW5ubnucQAAgtGhh1bM7wcA8I9JX4zQuE/+6D4CAAAERcXfUUcdpYcffliHHXaYevXq5ebHi4yM3K2l1XvvvaeGnuNvzpw5uu6661z4ZyHgZZddpnvvvbdBXxcAEJ4G907TsxcM1E3Tf9SOghLvnH+ej1bpZ6GfLVdZdHS0UlNT3di5c6erRLdKwOLiYnfbhrX/tLkArRLQAkJaPwIAgsV110k33iht2CD17Wv/rlV9/oADArVmABCeVmxbqKyCTCXHZwR6VQAAQBiqU/D31ltv6fzzz1dpaamrZLDKhl3564SmBY+ffvqpX14LCHdlZWVuDk/Tvn17WhSiURrSO03f3jZYHy3M1McLN2p7QZGax8fouD5pOqFPhqsM3BML9dLT010FoLX+tADQRklJibZu3epGTEyMCwAtCGTO2fDHvhVAsDvjjIqPl1zy22N2OGfF6vaxtDRgqwYAAAAA8EfwN3bsWNfWzALA7t271+VLAAhS1pIQaOws3Dutf1s36sougElISHDDgkD727IAMDs7W0VFRdq0aZMb8fHx3hDQqgIRnti3AghmK1cG9vW/+eYbff755+7fxauvvlrdunVzF89Yy2w73rS5cwEAAAAAtVOnM4zr16/Xgw8+SOgHAEAtREREKCkpyQ2rlrfwz0JAC4MKCgrcyMzMdCc2LQS01tW7ttAGAKChdOgQmG1rF8Kcc845booImwvXLpr54x//6II/+7dz6NChGj16tMaPHx+YFQQAAACAxhL8HXzwwd52gAAAoPYs0LM5am3YHICeVqAW/lkQaMNOfFpIaCGghYHMBwgAaGi//CJ9/rm0aZO1KK763B13NMxr3n777Zo5c6aeeuopDRo0yHWVqdw6+6yzznKhIMEfAAAAADRw8PfYY4+5KzEPOuggDRs2rC5fAgCARi86OlopKSluFBYWavv27S4EtAoITyBoQaG1AbUQ0NqCEgICAHxt2jTpqquklBQpPb1iXj8Pu91Qwd/f/vY3XXXVVbr88svdHLjVzec+ffr0hnlxAAAAAAhTdQr+zjvvPJWUlOjcc8/VyJEj1bZt291aktmJyQULFvhqPQEACGuxsbFKS0tTq1atXPWfhX4WBFpr0KysLDcsKLQA0IYtvyc7i0v14X8yNXvRRm3PL1LzpjEaun+aTuyb4eYwBADA4557pHvvlW691b/bxOb069u3b43P2zGmzfUHAAAAAGjg4C85OVktW7Z0cy8AAADfsQtnmjZt6kZ6erpr/WkhoM0LaK1BN2/e7Ia1QLMA0KoBLRCs7JOfN+rG6T8qu6BEEU2ksnK5j7MWbdCE9xdp6ln9NLh3Gj82AICzbZt01ln+3xjt2rXTkiVLanz+X//6l7p27erXdQIAAACARhn8zZ071/drAgAAdgsBExMT3SgrK3Phn4WAOTk52rlzpzZs2OBGQkKCCwFtXsDPlm7R5a/Mk8orvkbZLh9zCko08pV5evaCgRpC+AcAUEXoN3u2dOWV/t0cw4cP19SpU3XGGWeoe/fu7jFPS+tp06bp73//uyZPnszPCAAAAAAaMvizVit2Zea4ceN000037eunAwhiERER6tOnT6BXA0ANf5+eNp/WbtszB6D9u5yXl+fGqrW/avRbv7rQ7385327s8Sbl0k3Tf9S3tw2m7acfsG8FEOysqO7226VvvpGs8+YuheQaNaphXnf8+PH65ptvdOSRR7r5/Cz0Gz16tGtv/euvv+rEE0909wEg3Pyxx+UqKM5RfHRioFcFAACEoX0O/qz1WFRUlPsIAAD8z/4dtpbbNoqKitxcgBYCfrZ4q3ILy/b6+Rb+7Sgo0UcLM3Va/7Z+WWcAQPB69lmpWTPpn/+sGJVZAV5DBX8xMTGaNWuWXnvtNc2YMcPNa1tYWKgDDjhA99xzjy644AJvBSAAhJM/9bwi0KsAAADCWJ1afVorFjswu+qqqzgQAwAggOykaatWrZSamqr//Hubd06/vbHlPl64keAPAKCVKwO3ESzYO//8890AAAAAAAQo+DvnnHN09dVXa9CgQRo5cqQ6duyo+Pj43ZY76KCDfLCKAPzF5hCztkqmbdu2rj0dgNBgJ05zdpbWKvQzttz2gqKGXi2wbwUAAAAAAECwB39HH3209/aXX3652/Pl5eXuBKS1agEQWrKzswO9CgDqqHnTmFpX/FnjtOiyYjePUlJSkmsfiobDvhVAMLvkkj0///zzDfO6xxxzzB6ft2PKuLg4d0GaXXR65pln8u8VgLBQUJyrcpWriZooPrpZoFcHAACEmTqd5XvhhRd8vyYAAKBehu6fplmLNtRqWcsGD2kdo/Xr1yszM1PNmjVT8+bNlZiYSLUvADQy27ZVvV9cLC1cKG3fbuFcw3abWLdunZYvX64WLVq4TjJm1apV2rZtm7p27ar99ttP3377raZNm6bJkyfr008/VUpKSsOtFAD4wagPj1JWQaaS4zM07ZT5bHMAABD44G/EiBG+XQsAAFBvJ/bN0IT3FymnoMQFe3uq9kuMi9JpB3fSzrwc7dy5Uzk5OW5Yi1+rALQQMCEhgbl8AaAReOed3R8rK5Ouukrq0qXhXveee+7RqaeeqpdeeknDhw9XZGSke9w6x7z66qu66aab9PLLL+vQQw91y9g0E+PGjXMhIAAAAACgevXu65Wbm6u1a9e62+3atXMVAwAAwP/ioiM19ax+GvnKPDUpr6jqqy70s/9NHdZPbTPSJKW54G/79u3asWOHiouL3W0b1v7TKi0sBLRWa9ZyDQDQONhUz2PG2DQP0i23NMxrWLB38cUX64ILLqjyuAWAdrHpwoULNXr0aH399de66KKL3Mf333+/YVYGAAAAAMJERF0/8bvvvnPzLFhLlj59+rhht22ehnnz5vl2LQEAQK0M7p2mZy8YqKT4imt7bM6/yh/t8WkXDHTLeViol56eru7du6tTp05KTk52J11LSkq0detW14Ltl19+0aZNm1RYWMhPAgAaieXLpZKShvv6P/30k7e9Z3XsuQULFnjvDxgwwM1NCwAAAADwccWfzbFw9NFHKyYmRpdddpl69erlHl+8eLH+9re/6cgjj9TcuXN1yCGH1OXLAwCAehjSO03f3jZYHy3M1McLN2p7QZGax8fouD5pOqFPhqsMrI5V9Fl7TxsWBFpVv1X+WQvQoqIiF/zZiI+Pd1WAVg1oVYEAgNp54gnpwQelDRukAw+UHntMqumQybpZvvxyxVx7ZsAA6b77al6+Pqyyr7LycikzU/rgA5vmQQ0mIyNDM2bM0FVXXbXb/LI2/9/f//539++Rh12MYhenAAAAAABqVqezdePHj1ebNm301VdfVTkQMxMmTNDvf/97t8wnn3xSly8PAADqycK90/q3daMuPHP92bC5lrKzs10ImJeXp4KCAjcyMzNdi28LARMTE71zMwEAdvfmmxUB29NPS4ceKj38sHTccdLSpVKrVrsvP3eudO650uGHW2W2dP/90tCh0qJFUps2vt3CP/xQ9b5lcKmp0pQp0iWXNNxPc8yYMbruuuvc8aPN39flfxMKLlu2zM3jZ11mHn30Ue/y06dP5+JSAAAAAGioir877rhjt9DPpKWl6fLLL9fdd99dly8NIICs2qd3797e2wBgLNCzdt42bA5AmwvQhoV/VhVow/YZFhJaCGhhIPsQ9q0Aqpo6VRo5Urr44or7FgBaRd3zz0tjx+6+tV57rer9v/5Veustac4c6cILfbt1P/88MD+ta665xl1oYseW1knG829HeXm5WrZs6UI/W8ZYq+mHHnpoj61BAQAAAAB1DP7s4Mzm/amJVQbs2qoFQPCzky2crAewJ9HR0UpJSXHDTsJaFaCFgNYK1BMIWlBobUAtBLS2oI19v8K+FUBRkTR/vjRu3G/bwg6XBg+Wvv66dtsnP18qLpbCrdOltfm00M/miV+9erV7rEOHDho4cKD7N8cjNjZWRx11VADXFAAAAADCOPg7/PDD9cQTT2j48OHuoKyyNWvW6Mknn3TtWgAAQPiyk7BW6d+qVStX/ecJAe0CoKysLDfspK0FgDZseQAINzk5Unb2b/dtV7fr7m7LFrs40rqjVH3c7i9ZUrvXufVWqXXrirAw3Ni/FYcddpgbAAAAAIAABH/33XefjjzySPXs2VOnnXaaunfv7h5funSp3nvvPUVFRWnSpEn1XDUA/lZWVqb169e7261bt6ZyF0CtK9qaNm3qRkZGhmv9aSFgTk6Oaw26efNmN+Li4lwAaNWAlas4wh37ViC8/a9Lutedd9q85759jcmTpTfeqJj3z+b7Czf2b8WSJUvcxSO2z9yVHXsCAAAAABow+Ovfv7+b52/8+PH6xz/+oXzrOyO5E37HH3+87rnnHu88YQBCi52s9wR/AFCXEDAxMdENO3mbnZ3tTuRaCLhz505t2LDBjYSEBBcC2ryA1hq0OjuLS/XhfzI1e9FGbc8vUvOmMRq6f5pO7JuhuOjqPydYsW8FwtfPP0tt2vx2v7ri5pQUmy9V2rix6uN2v5pp06v4y18qgr9PP5UOOEBhxf6dGDdunOsY4zmmrI5VkgNAOBl7xAsqKStSVERMoFcFAACEoToFf8aCvXfeeccdrNlV/CY1NZUKIQAA4Nh8v542nzY3sGcOQDu5m5eX54ZVGVtIaMs0a9bM+z7ik5836sbpPyq7oEQRTaSycrmPsxZt0IT3F2nqWf00uPcuPfMAIAASE6WkpD0vExMjDRggzZkjnXpqxWNW2Gb3r7225s974AHp3nuljz+WBg5U2LFOMg8++KCuuOIK/eEPf9AFF1yg+++/3/2bYGGgXUzygG0EAAgzXZLD7EoOAAAQVCLq/QUiItz8PjY8J+sAAAAqszbgLVu2VOfOnV2LcJsX0Ob8Ky8vd1WBNkewtQxft26d3v9+tS5/ZZ5yCkrc51roV/mjPT7ylXkuHASAUDFmjDRtmvTSS9LixdJVV0l5edLFF1c8f+GF0rhxvy1///3S7bdLzz8vdewobdhQMXJz/bveL78sLV/eMF/7xRdf1LBhw/TUU0+5zjFmwIABGjlypOswY8HfZ5991jAvDgAAAABhqs4Vf9u2bdPf/vY3rVixwt22E3eV2UHac88954t1BAAAYSQmJsYFf9YpwNp/WhtMqwS0qsCNW7I07t1fpXL3X7Xs8Sbl0k3Tf9S3tw0OubafABqns8+WrFHKHXdUBHj9+kmzZklp/yteXrPGLqr8bfmnnpKKiqQzz2z4OQT35KKLJJuW9fLLpcce8+3X/vXXX3XLLbe423YxiLF/Fzz/Vpx//vmaOnWqqwwEAAAAADRg8Pfxxx/rzDPPdC26bG6eFi1a7LaMBX8AAAA1sfcK8fHxbqSnp7v3FW98s0K5RWV73WgW/u0oKNFHCzN1Wv+2bGQAIcHaetbU2nPu3Kr3V61SULCWpCtXSh995PuvbZXguf8rYbR2z3ZsaReWVmYXmQJAuJm37hMVle5UTGScBrYZEujVAQAAYaZOwd+NN97oTtC9/fbb6tu3r+/XCgAANLoQ0E76zsss9s7ptze23McLNxL8AUAD69RJuvpq33/d/v3767vvvvPeHzRokB5++GH3uM0l/+ijj+rAAw/0/QsDQIA9M2+ssgoylRyfQfAHAACCI/hbtmyZm4Sd0A8AAPjS9vyiWoV+xpbbkpPvTg4zzzAA7Jvs7Novm5TUMFv38ssvd/P8FRYWulaf9957r4488kg3bCoJ6yxj00sAAAAAABo4+OvWrZtycnLq8qkAgrzipmfPnt7bAOBvzZvG1Lriz/ZSMeUlWrJkiWsP17x5cyUkJATd/ot9K4Bg1Ly57Z/2vIxN427LlJY2zDr86U9/csOjd+/eWr58uebOnavIyEgdfvjhSk5ObpgXBwAAAIAwVafg75577tE111yj4cOHq2PHjr5fKwABOzkdFVWn3QIA+MTQ/dM0a9GGWi1r2eAfOiW6ir/t27e7Yfuw/fbbz4WAcXFxQRECsm8FEIw+/zzQayB98cUX6tWrl1JTU72P2T78lFNOcbe3bNnilrEKQAAAAABA7dTpDP+cOXPcwZkdpA0ZMkTt2rVzV2TuepLrkUceqcuXBwAAjdSJfTM04f1FyikoccFeTSzOS4qP0iWD+6m0uNCFftnZ2SopKdHWrVvdiImJcQGgnUS2FnIAgN8cdVTgt4bN6ffKK6+4C0prOu6050obquQQAAAAAMJQnYK/xx9/3Ht75syZ1S5D8AeEHqua2bChotImPT2dObMA+F1cdKSmntVPI1+ZpyblFVV9u3I1fE2kKWf1U1xMlBQT5Vp8ZmRkKDc314WA1pK8qKhImzZtciM+Pt4bAvq7spl9K4BQkZ8vrVkjFRVVffyAAxrm9Wwevz2xuf92vcAUAAAAALBnUXU9gQUgPGVlZXmDPwAIhMG90/TsBQN10/QftaOgxDvnn+ejVfpZ6GfLVRYREeHm+rNh1SFWAWghYF5engoKCtzIzMxUs2bNXAhoy9nn+AP7VgDBbPNm6eKLpY8+qv55XxbcrVmzRqtWrfLet3larZ3nrmz//cwzz6hDhw6+e3EAAAAAaASYzAsAAASdIb3T9O1tg/XRwkx9vHCjthcUqXl8jI7rk6YT+mS4ysA9sQqRFi1auFFcXKwdO3a4YeGfVQXasO4EFv5ZCGhhYDDMBwgAgXDDDRa0Sd9+Kx19tPTOO9LGjTa3uzRlim9f64UXXtDEiRPdPtfGvffe60Z11YC2L7fwDwAAAADg4+AvPz9fTZs23Ycv65vPBQAAjZeFe6f1b+tGfURHRyslJcUNaxtnVSQWAlorUE8gaCeXrQ2ohYDWFpQQEEBj8tln0nvvSQMHWvW0ZEV2Q4ZISUnSpEnSSSf57rWGDRumPn36uGDPbo8aNUpHHHFElWVsH2wtnPv166e0tKrV3QAAAAAAHwR/7dq10/XXX6+RI0e6+XNqY926de7qzCeffFJbtmyp1ecAAAA0pNjYWHcSuVWrVq76zxMCWmtQa8dpIyYmxhsC2vIAEO7y8qRWrSput2hR0fqze3epb1/p++99+1q9evVyw1P9d+SRR6pTp06+fREACHJxUU0VH9XMfQQAAAhI8PfUU09pwoQJuuuuu/T73/9egwcP1kEHHeQO0KyFll2tuW3bNq1cuVLz5s3Tp59+qm+++UbdunVzwR8AAEAwsWoS60hgwy5qstafFgLm5OS4SsDNmze7ERcX5wJACwKtchAAwlGPHtLSpVLHjtKBB0rWXdNuP/20VMvrPutkxIgRDffFASCIPXbSl4FeBQAA0NiDP2vBcuaZZ+of//iHXnzxRTcHg50U27UNlgWAdpX80KFDNWPGDP3pT39ShPWKAQAACFL2fiYxMdGNsrIyZWdnuxDQwsCdO3dqw4YNbljbOQsBbV5Aaw0KAOHi+uulzMyK23feKR1/vPTaa1JMjPTiiw372osXL3aVfytWrHAXk9ox5a776Dlz5jTsSgAAAABAYwv+jAV4p556qhs2P878+fO1ZMkSbd261T3fsmVL9ezZUwMGDKAtFgAACEn2fsfCPRslJSWuDaiFgNYWNC8vz43169e7kNCWadas2R4vctpZXKqP/rNe3WIq7o/62w86pleaTuyb4eYwBIBgcP75v90eMEBavVpaskRq315KSWm4133llVd08cUXu4rqHj16uG4yu9o1CAQAAAAA7FmTco6k3JX91sLLTu7ZVfxAY2W7g+LiYnfbTsDsWtULAI2VdTrwzAdoF0B5WOWfvXewENDahlbeb37y80bdOP1H5RSUKK1ZpMrKpa35pSotl5LiozT1rH4a3DstQN8RgPr69ddstWu3n9au3aG2bcPjGKKoSFq5UurSRYqq9SWiddelSxclJyfro48+UkpDJowBxvEmEDzeXvq/8mZUcXqPBuzrDAAA/H4M4YfDOQChwk5YW7teAEBVtm9s1aqVUlNTXftPTwhoVYHWms6GXTBhb8osBPxyxQ5d/so8qdz9pw25pVW+noWBI1+Zp2cvGKghhH8AAiw/X7ruOumllyru//e/UufOFY+1aSONHdswr2sV1DfddFNYh34AUJ2XfrxLeUU7lBCzn0b0u4ONBAAAfIoJ+AAAAPbhAon4+HhlZGS4tnQdO3Z0QZ+1+7SK6S1btujnpb9o9Bvfe0O/6rjHy6Wbpv/o2oECQCCNGyctWCDNnSvFxf32+ODB0ptvNtzrHnDAAS78CwY2r2vbtm3dfn7evHlVnnvuuefUvXt3xcXF6cADD9TMmTMDtp4AwsNXq9/TnBV/cx8BAAB8jeAPgFdZWZk2bNjght0GANTMTg7bHH92otjmOW7Xrp2b++9fa/KVW1TmDf2iIqSLD2ruht32sOd3FJToo4W0nAIQWO++Kz3+uPSHP9i+7bfH999fWr684V536tSpLlT797//rUC7++67XRX3rt544w2NHDlSZ599tmtJethhh+m0007TN998E5D1BAAAAIC9odUngCqsWsVYSzsAQO1YxZ+1+bSx8IvNimgiN6efiWzSRGf03s/dfn3BDpVUqgO05T5euFGn9W/LpgYQMJs323u/3R/Py6saBPra/fff7/abRxxxhHr37q327du7uVN3vcjivfcatiJmyZIleuKJJzRlyhRdeeWVVZ678847dc4557hg0AwaNEg//fST7rrrLn344YcNul4AAAAA0GDBnx3YdOjQwR2UAQAAoGY78ou9od/e2HLb84vYnAACauBA6YMPKub0M56w769/lQ47rOFe144zLdizwM9abf7888+7LWPPN7TrrrvOBX7WwrmyFStW6L///a8LKCuzIPDmm29WYWGhYmNjG3z9AAAAAMDnwV///v31yiuvaPjw4e7+Mccco/Hjx+vYY4/dpxcDAAAId82bxlSp+NsTO50dWVaozMxMN1egzR/lj5PcAFDZffdJJ5wgWe5m3S4feaTitnXg/Oc/G25brVq1KuA/iBkzZug///mP3nrrLX3//fe7VQIaa+dcWa9evVRUVKSVK1fu9hwAAAAAhMQcf/Hx8crPz/fenzt3rjZu3NiQ6wUAABCShu6fVuuKP1vsd23itHXrVi1fvlzLli3Tpk2b3AllAPAXm9tvwYKK0K9vX2n27IrWn19/LQ0YEL4/BzvGHTNmjO677z4lJSXt9vy2bdvcR7swo7IWLVq4j1lZWdV+XasEzM7OrjIAAAAAIKgq/g488EA38brNt+Bp9/ndd9+5q9L35PTTT/fNWgIAAISIE/tmaML7i5RTUHk2v91ZXV9iXJTO+UNPFeRmKycnx50stuDPhl14ZSeb7b1XVBTTMgNoGMXF0hVXSLffLk2b5v+tXFpaqunTp+vzzz93+z6bO69v377asWOH5syZo9///vdKS0trkNe+55573Ne++OKLffp1J02apIkTJ/r0awIAAABAbdXqLNIjjzyiM888U5deeqm7by2o7DEbNbFl7CAOAACgMYmLjtTUs/pp5Cvz1KSG5M8182wiTR3WT6nJzaXk5u59k1WFbN++XXl5eSooKHDD2oA2a9bMhYBWkRIRUauGDQBQK9HR0ltvVQR//mb7u+OPP17/93//5/Zztu+z+faM3R81apQuvPBCV5Hna6tXr9aUKVP0zjvvuJDR2DyDno82PJV99nx6evpulYDJycnVfu1x48a5SkIP27e3a9fO598DAAAAANQ5+Bs4cKBrPWUtqKzF59FHH+3m+Bs8eHBtPh0AAKBRGdw7Tc9eMFA3Tf9RO4t+uxDK5v4zSfFRmnJWP7ech3VWsJPMNoqLi92JZjspvnPnTu9JaAv9EhMTXQhoJ8WZDxCAL5x6qvTuu9Lo0f7dnmPHjtWiRYv08ccfu3nlW1l/0Ur7RLv49MMPP2yQ4M/m57O2yieddNJuzw0aNEiHHnqoXn/9de9cfz169PA+b/djYmLUuXPnar92bGysGwAAAAAQCLXuG2Utpuxgx8aIESN08sknu4MhAOHDTiB37drVexsAUHdDeqfp29sG66OF6/X64s3K3lmso3qk6bg+aTqhT4arDKxJdHS0UlJS3LD2nxYA2vAEgjY8LdgtBLS2oOy3AdRVt27SXXdJ//pXxZx+CQlVnx81qmG27bvvvusq/IYMGeLmOt1V9+7d9eKLLzbIa/fr18+1F63sxx9/1OjRo/X000/r4IMPdsGerYO1Ij3llFO8y7355ps69thjXfgHAHUxoPWxyi3armYxVecQBQAA8IU6TRjzwgsv+OTFAQQXO2m8t7k7AQC1Z+Heaf3buVFXVjVic1BZJYy1/rQA0II/aw2alZXlhp189oSAVJkA2FfPPSc1by7Nn18xKrNrwRoq+LN9WadOnWp83i52KCkpaZDXtv2ldbKpzoABA3TQQQe52xMmTNB5552nLl26uEpAC/2+/fZbffHFFw2yXgAahysPfiDQqwAAAMJYnYI/AAAA+P/ijKZNm7qRkZHhWn9aCJiTk+Pa1W3evNkNu4DDTmhbEGiVgwCwNytXBmYbWZj2/fff1/j87Nmz1bt3bwXSueeeq/z8fE2ePNkN64Bj8wIedthhAV0vAAAAAKgJwR8Ar7KyMnfS2KSmprq5pAAAwbdvtRDQ5vqzYV8/OzvbhYAWBtqcgBs2bHAjISHBhYBJSUmuNSgABJPLLrtMt956q6u8s9aZnv2btTi+6667NGvWLD377LN+Wx9bj/Ly8t0ev/TSS90AAAAAgFBA8AegisonpwEAwb9vtSDRwj0b1hLPWudZCGhtQfPy8txYv369CwltmWbNmnFhBwBNnixdf70UH7/3jfHtt9KWLdJJJ/l2w11//fVatGiRq6qz/ZMZPny4m+/P9mdXXHEFgRsAAAAANKbg75NPPnHzDdocCytWrNA111yjxx9/PNCrBQAAEBBRUVFq2bKlG9b+0zMfoFXPWFWgDav8swpAO8lubUOtugZA4/Pzz1L79tJZZ0l//KM0cKBdnFDxnE2rZ89/9ZX06qvS+vXSyy/7fh1s/zNt2jSNGDFCM2bM0C+//OKqmK0F6LBhw3TkkUf6/kUBIAjc8vHx2rZzs1rEpeqB42YFenUAAECYCengz1q/LFiwQEcddZSysrICvToAAABBIyYmRq1atXJVhtb+0xMCWhXNtm3b3LA5AG0uQAsBbW5AAI2HBXkLFkh23eTw4VJ2tmQdgWNjpfz8imX697d2nNJFF0kNuYv4wx/+4AYANBYW+mUVZAZ6NQAAQJgK6eDvwQcf1JQpU9ztzz77LNCrAwAAEHSsoiY+Pt6N9PR01/rTQkCr/isuLtaWLVvcsODPQkAbFhoCCH8HHihNmyY984z000/S6tVSQYGUkiL161fxsSGtXLlSCxcu1B+t5LAa77//vvr27auOHTs27IoAAAAAQBgJ6eDP5rQBAABA7UNAm+PPhrXTy8nJcSFgbm6uqwq0sXHjRtcC1KoALQS01qAAwpsdVlnQZ8OfbrrpJncRQk3B3xNPPOH2RW+88YZ/VwwAAAAAQhjJGQAAQCNkF1BZsNehQwf16NFDrVu3doGfyc/P1/r167VkyRKtXr3atQi1oBAAfOnrr7/WkCFDanz+2GOP1ZdffslGBwAAAIDGUvFXV4WFhW542FWmAAAAjVVUVJSSk5PdKCoqckGfVQLa+yWrCrRhQWFSUpKrvklISHDVgwBQHzbXaGJiYo3PW3Xy1q1b2cgAAAAAEKrBn51kyszc++TGnTt3rtfcM5MmTdLEiRPr/PlAuLKTuPb35bkNAGh8+1Z7j5WamuqGtf60ANDeo9l8gHbbhgWFVi1oIaDNDRgK3xeA4NO+fXv961//0lVXXVXt81bt17ZtW7+vFwAAAACEsqAK/qZPn66RI0fudbnFixerZ8+edX6dcePGacyYMVUq/tq1a1fnrweECztx62nzBgBg32qhXnp6utLS0lz7Twv97H1TSUmJq8KxERsb6w0B63NhFgD/+uknqU+fivn9AuXcc8/V3XffrUMOOUTXXnutdw730tJSPf7443rzzTc1fvz4wK0gAAAAAISgoAr+LrvsMjcamp2gsgEAAIDaXRhi7T1tZGRkKDc314WA1gLU2oFu2rTJjfj4eBcAWhBoVYEAglf//pI1W2nVyjqqSN99J7Vs6d91sAsyv/rqK91www2699573XyjZunSpdq8ebOOPvpogj8AAAAA2EeckQHgVVZW5p1HpWXLlt6rrgEAdRdu+1bPXH82rCrHKgAtBMzLy1NBQYEb1rrd5uayENCWC/XvGQhHzZtLK1dWBH+rVtm+yv/rYBdjzp49Wy+99JLefvttLV++3D1uFYBnnHGGLrzwQvYfAAAAANCYgr/Vq1frO7s0VXLtp+xAccaMGe7+mWeeGeC1A0LTxo0bvSenAQDsW/ckMjJSLVq0cMPmALS5AC0EtLkBrSrQhoV+iYmJLgS0MJD5AIHgcMYZ0lFHSRkZVtUrDRxof9PVL7tihe9f3y4SsDaegwYN0sUXX+wGADQWFx44XoWlBYqNjA/0qgAAgDAU0sHf559/XuUAcdasWW6Y8vLyAK4ZAABA4xIdHa2UlBQ3rP2nBYA2PIGgDQsKPfMBWltQQkAgcJ59Vjr9dGnZMmnUKMmmWk9M9N/r2z7gmWeeUe/evf33ogAQJI7oeHqgVwEAAISxkA7+LrroIjcAAAAQPKx9X1pamlq1auWqeiwAtODPWoNmZWW5ERMT4w0BmXsZCIzjj6/4OH++dP31/g3+zIABA7Rw4UL/vigAAAAAhLmQDv4AAAAQvKyir2nTpm5kZGS41p8WAtq8gEVFRdq8ebMbVvljIaANqxwE4F8vvBCYLf7www/rxBNPVJ8+fdwFnVFRHJ4CAAAAQH1xZAUAAAC/hIA2158Nq/zLyclxIaCFgVYVaGPDhg1KSEhwVYBJSUmuNSiA8GVhn80DesUVV2jUqFFq06aNuxBg133HggULAraOANAQ1mUvU2l5qSKbRKpNUlc2MgAA8CmCPwAAAPiVBXoW7tkoKSlxbUAtBLTwLy8vz43169e7kNCWadasmQsHAISX5ORktWzZUj169Aj0qgCAX034/GxlFWQqOT5D006Zz9YHAAA+RfAHAACAgLHWfnbi30ZhYaE3BLRWoNYS1IYFhVYBaCGgtQ21CiAAoW/u3LmBXgUAAAAACDsEfwC87ERqx44dvbcBAPXHvrX2YmNj1apVK6Wmpmrnzp0uALQg0KoCt23b5obNAWhzAVoIGBcXx68oAAAAAABAJfRMAlDl5LS1U7NB8AcAvsG+tW7bzOb5ysjIcC0A7aIUC/qs3WdxcbG2bNmiZcuWubF582ZXHQggNFlV7+TJk3Xcccepf//++r//+z/3eFZWlqZOner+zgEAAAAAtUfFHwAAAEIiOC0rK1NOTo6rBMzNzXVVgTY2btzoWoBaOGjVgNYaFEDw+/XXX3XUUUdp7dq16tatm5YsWeL+tj3z/z3zzDNavXq1HnnkkUCvKgAAAACEDII/AF7l5eXu6mrPyRaq/gCg/ti3+o5V/FmwZ8Paf1qlkIWA+fn53pGZmanExES3jH20zwEQnG6++WYX5v/444+uza+Nyk499VTNnDkzYOsHAAAAAKGI4A9AlZPTdsLUtGjRguAPAHyAfWvDiIqKchep2LBWnzYXoIWAhYWFLhC0YaFfUlKSqwRMSEjg3zUgyMyePVujR49W7969tXXr1t2e79y5s6sGBAAAAADUHsEfAAAAQlpMTIxSU1PdsNafFgBaEGjzAdptGxYUWhWghYBxcXGEgEAQKCgocH+3NbFqQAAAAADAvqH3EQAAAMKGhXrp6enq3r27OnXq5CrYrfLPWoNaRdHy5cu1bNkybdq0yVUKAggcq/T74osvanz+3XffVf/+/f26TgAAAAAQ6qj4AwAAQNixeWqtvaeNjIwM5ebmuso/qyCydqAW/Nlo2rSpd95AqwoE4D833HCDRowYoQMOOEBnnXWWe6ysrMyF8xMnTtTXX3+tt956ix8JAAAAAOwDzm4AAAAgrHnm+rNRWlrq5v+zEDAvL0/5+flu2By3iYmJLgC05exzADSs888/X6tXr9af//xnjR8/3j12/PHHu7lR7W/wvvvu06mnnsqPAUDYeWDohyorL1VEk8hArwoAAAhDBH8AAABoNCIjI137Txs2B6DNBWghoM0NaNWANixwsBDQ5gNs1qwZ8wECDcgCvwsuuMBV9lmln1X8denSRaeffro6d+7MtgcQllrEpwV6FQAAQBgj+AMAAECjFB0drZSUFDes/acFgDY8gaANCwqtCtBCwPj4eEJAwAcsaH/vvfe0cuVKtWzZUieffLJGjx7NtgUAAAAAHyD4A1BlPqQOHTp4bwMA6o99a2iIjY1VWlqaWrVqpYKCAhcAWvBnrUGzsrLciImJ8YaAtjyAfWdzax5++OEu9LOWnsbm2nz33Xc1ePBgNikAAAAA1BPBH4AqJ6ettRkAwHfYt4bez8tCCBsZGRnKzc11IaDNC1hUVKTNmze7YdV/FgLasMpBALVz9913a9WqVa7C75hjjnHtPe2xK664QsuXL2czAmgUZi97VTtL8hQXlaChXc8P9OoAAIAwQ/AHAAAA7CG0tWGVfzb/n4WAFgZaVaCNDRs2KCEhwVUBJiUludagAGo2e/ZsXXjhhfrLX/7ifcyqbYcPH66lS5eqR48ebD4AYW/6ooeUVZCp5PgMgj8AAOBzEb7/kgBClbVb2rZtmxue1ksAAPatkAv0LNzr2LGjevbs6aoBrerP5OXlad26dVqyZInWrl3rqgPLysrYbEA11qxZoz/84Q9VHrP79t5z48aNbDMAAAAAqCcq/gB42QkXO3FprHUZ8/wBQP2xbw0/UVFRatmypRuFhYVuLkCrBLRWoHbbhgWFnlag1jaUf1OBCvY3ExcXV2VzeO6XlJSwmQAAAACgngj+AAAAgDqKjY1Vq1atlJqaqp07d7oA0II/CzCysrLcsDkALQC0isFdAw+gMbI5/r7//nvvffubMb/88ov7O9nVQQcd5Nf1AwAAAIBQRvAHAAAA1JNV9FnrTxvp6emu/aeFgNb2s7i4WFu2bHHDgj9PCGiBINAY3X777W7s6uqrr96tYtr+tmyOTQAAAABA7RD8AQAAAD5kQUWzZs3csLn+cnJyXAiYm5vrqgJt2FxmCQkJ3nag1hoUaAxeeOGFQK8CAAAAAIQ1gj8AAACggURERHjDPWv/aRWAFgLm5+e7qkAbmZmZSkxMdMvYR/scIFyNGDEi0KsAAAAAAGGN4A8AAADwxxvvqCglJye7UVRU5OY1sxCwsLDQBYI2LPRLSkpyrUCtItCqBwEAAAAAAGqL4A8AAADws5iYGKWmprphrT8tALRhVYGe2xYUeuYDtLkBCQEBAAAAAMDeEPxVYnO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"text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -1286,8 +1213,6 @@ } ], "source": [ - "show_circuit = False # Set to True to show the circuit\n", - "\n", "p = params()\n", "p.set_function(p.linear, (-0.5, 0.25))\n", "p.unpack(globals())\n", @@ -1296,7 +1221,7 @@ "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", " # 1. State preparation\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", "\n", @@ -1305,15 +1230,12 @@ "\n", "\n", "qprog = synthesize(main)\n", - "if show_circuit:\n", - " show(qprog)\n", - "job = execute(qprog)\n", - "# job.open_in_ide() # Uncomment to see the results in the IDE\n", - "pc = job.get_sample_result().parsed_counts\n", - "df = job.get_sample_result().dataframe\n", + "# show(qprog) # Uncomment to see the circuit\n", + "n_shots = 2048\n", + "df = sample(qprog, num_shots=n_shots)\n", "\n", "# You can use the helper function:\n", - "# pc, df = run_standard_simulation(main)\n", + "# df = run_standard_simulation(main)\n", "\n", "# Translate the majority state to a gradient value\n", "majority_state = dict(df.iloc[0])\n", @@ -1326,7 +1248,7 @@ "# majority_gradient = state_to_gradient(majority_state.get('x'), p)\n", "\n", "# Print the results and compute the majority gradient\n", - "print(\"Parsed counts:\", pc)\n", + "print(\"Parsed probabilities:\", df.set_index(\"x\").to_dict()[\"probability\"])\n", "print(f\"The analytical gradient is: {analytical_gradient}\")\n", "print(f\"The majority gradient is: {majority_gradient}\")\n", "\n", @@ -1343,20 +1265,56 @@ "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", "show_bar(success_rate)\n", "\n", - "# Visualize the theoretical values of the phases\n", - "# We used the standard simulation, so this is theoretical values only without the phases from the simulation\n", - "plot_theoretical()\n", + "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(18, 7))\n", "\n", - "# Plot histogram of the results\n", - "plot_histogram(df, analytical_gradient=analytical_gradient)\n", + "x_array = np.arange(-N // 2, N // 2)\n", + "f_classical = f_normalized(x_array)\n", + "f_classical -= f_classical[N // 2]\n", "\n", - "# You can use the helper function:\n", - "# analyze_results(pc, df, p)" + "plt.sca(ax1)\n", + "plot_classical()\n", + "ax1.plot(x_array, f_classical, \"o\", label=\"Theoretical values\", markersize=8)\n", + "xmin, xmax = -N, N\n", + "ymin, ymax = -N // 2, N // 2\n", + "ax1.set_xlim(xmin, xmax)\n", + "ax1.set_ylim(ymin, ymax)\n", + "ax1.vlines(-N // 2, ymin, ymax, colors=\"lightgray\", linestyles=\"dashed\")\n", + "ax1.vlines(N // 2 - 1, ymin, ymax, colors=\"lightgray\", linestyles=\"dashed\")\n", + "ax1.hlines(-N / 4 + 0.5, xmin, xmax, colors=\"lightgray\", linestyles=\"dashed\")\n", + "ax1.hlines(N / 4, xmin, xmax, colors=\"lightgray\", linestyles=\"dashed\")\n", + "ax1.legend(fontsize=12)\n", + "ax1.set_title(\"Theoretical Phases\", fontsize=14, fontweight=\"bold\")\n", + "ax1.tick_params(labelsize=11)\n", + "ax1.set_xlabel(\"x (index)\", fontsize=12)\n", + "ax1.set_ylabel(\"f (normalized)\", fontsize=12)\n", + "\n", + "plt.sca(ax2)\n", + "percentage = df[\"counts\"] / df[\"counts\"].sum() * 100\n", + "ax2.bar(df[\"x\"], percentage, color=\"lightblue\", label=\"Measurement counts\")\n", + "ax2.set_xlabel(\"x (index)\", fontsize=12)\n", + "ax2.set_ylabel(\"Percentage of shots (%)\", fontsize=12)\n", + "ax2.set_xlim(-N // 2 - 1, N // 2)\n", + "ax2.set_ylim(0, 100)\n", + "ax2.set_title(\"Measurement Histogram\", fontsize=14, fontweight=\"bold\")\n", + "ax2.tick_params(labelsize=11)\n", + "if analytical_gradient is not None:\n", + " x_analytic = analytical_gradient * (N / m)\n", + " ax2.axvline(\n", + " x=x_analytic,\n", + " color=\"green\",\n", + " linestyle=\"dashed\",\n", + " label=\"Analytical gradient\",\n", + " linewidth=2,\n", + " )\n", + "ax2.legend(fontsize=12)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" ] }, { "cell_type": "markdown", - "id": "36", + "id": "34", "metadata": {}, "source": [ "The measured gradient is always a multiple of the resolution $m/N$. In the previous example, the exact gradient -0.5 was a multiple of the resolution 0.25, so the success rate was 100%.\n", @@ -1366,38 +1324,36 @@ }, { "cell_type": "code", - "execution_count": 17, - "id": "37", + "execution_count": 9, + "id": "35", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/9f115f9d-8af7-4ce1-98d1-dd8acb003a34\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed counts: [{'x': 2}: 1807, {'x': 3}: 105, {'x': 1}: 56, {'x': -4}: 25, {'x': 0}: 21, {'x': -3}: 14, {'x': -2}: 11, {'x': -1}: 9]\n", + "Parsed probabilities: {2: 0.884765625, 3: 0.05419921875, 1: 0.0244140625, -4: 0.013671875, 0: 0.0068359375, -3: 0.0068359375, -1: 0.0068359375, -2: 0.00244140625}\n", "The analytical gradient is: 0.55\n", "The majority gradient is: 0.5\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 88.23% (1807/2048 shots)\n", - "[\u001b[92m████████████████████████████████████████████\u001b[91m------\u001b[0m] 88.23%\n" + "Success rate: 88.48% (1812/2048 shots)\n", + "[\u001b[92m████████████████████████████████████████████\u001b[91m------\u001b[0m] 88.48%\n" ] }, { "data": { - "image/png": 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KC/BppWlN3KWASIv6qdDJP1KsatWqbrIvrQytofJHjx51K2CrQJoRYAAAICQDoB9++MEaNGgQuO2vy2nXrp0b6t6jRw83V5Dm9VGm54orrnDD3OPi/j8HaeZWUVbQo9WwVQHeokULN3cQAACZKUd0DmtXs11gH+EtZOYByk7qWtMQexVDp1UDpG61I0eOnPa2AaEiV65cGR5mCgDZff1OCyFsOijwUfecgiDAqxT8qCtagRAAhDsCoBNQgmz79u0WExPjhtrxHzC8SMH/77//7n4XVJ/HhKHw6vXg4NGDbj9Pzjz8HoQ5AqAT0LD6gwcPuqLqPHnynJ5PBQhBRYsWdUGQfidy5syZ3c0BTjsFP/n653P7f/f6m2HwYY4O/RNITEx0X0n7w+v8vwP+3wkACGcEQOlEyh9ex+8AgEhCAAQAADyHAAinrHz58jZ06NBTeo65c+e6DIPme8oMmzZtcs+niTVDRfv27QOTeEr9+vXdZJ8AgNOPACjCLVy40I1gu+GGGyxUpHbhv/zyy90II83n4BVTpkyxF198MUuDLABA6giAItzbb79tDz30kM2fP9+N4AnlAlut/RbqdSZabiWzaMmXk1nBGABw6giAIpjWWvvwww/t/vvvdxkgLS+SWreTFpy96KKL3DB/ZWLWrl0beMwvv/xizZo1s+LFi1u+fPns4osvti+//DLN1+zQoYPdeOONKYKGYsWKuWBMGYp58+bZq6++6l5bm7qrUusC++abb1y2SO0688wzrXHjxvbnn3+6+7QkipZGKViwoBUuXNi9ptqaEco46bzkzp3bTfA3YcKEFN15atPIkSPtpptusrx581rfvn3dKKiOHTu679H3Vq5c2b2fYHqMlnbxt0/LuiSfdD15Juzw4cP22GOP2VlnneVeSwv66rz46fPT882YMcOtg6fPQ2vh6X3I888/b2PHjrVPPvkkcG6Dvx/AqYmJjrFbq93qNu0jvBEAnaQDRw6kuSUcS0j3Yw8dPZSux56Mjz76yKpUqeIu0HfccYe98847KS7C8tRTT9krr7zi1mbLkSOHC2KCg6gmTZq4IGnZsmXugtu0aVPbvHlzqq95zz33uODEf1GWzz//3M2l1Lp1axco1KlTxy1gq8do0wSTyal2R+u7VatWzXXjLViwwL2ufwi21ohTgKE2q22aoPKWW27J0Gzdd911l8uKKUiYPHmyvfnmm7Zr164Uj1NgoedesWKFOzd6jdKlS9vEiRNt1apV9uyzz9qTTz7pzrefzqcCFp1ztf2PP/6wqVOn/mt7tKad3usHH3xgP/30k7Vs2dKd7/Xr1wceo/P48ssv23vvveeyevocFDSJvrZq1SoQFGlTQAsgc8TliLOJLSe6TfsIc1oLzOv279+vqMB9Te7QoUO+VatWua/B7HlLc2syvkmSx+bpmyfNx9YbUy/JY4sMLJLq407G5Zdf7hs6dKjbP3r0qK9IkSK+OXPmBO7Xvt73l19+GTj2xRdfuGPJ32+w8847zzds2LDA7XLlyvmGDBkSuF2tWjXfSy+9FLjdtGlTX/v27QO369Wr5+vatWuS5/S35c8//3S327Rp46tbt2663+vu3bvd969YscLd3rhxo7u9bNmyVB+/evVqd//ixYsDx9avX++OBb8X3X7kkUdO+PpdunTxtWjRInC7ZMmSvoEDBwZu6/yXLl3a16xZs1TPw2+//eaLiYnxbdu2LcnzXn311b5evXq5/TFjxrj2bNiwIXD/iBEjfMWLFw/cbteuXZLXyExp/S4AQChev0+EDFCEUjfW999/b23atHG3ldlRBkbdUMmdf/75gf2SJUu6r/5MiDJAyiyoy0XdL+p2Wb16dZoZIH8WaMyYMW5/586dNm3atCRZpfTwZ4DSoqyI3tvZZ5/tFsBT15X8W7uSnx+dkwsvvDBwrGLFiq6rLTl1DyY3YsQIq127tpsdWedE2SP/a2tRPmVf1IXlp9dK7Xn8lF1Sduvcc891z+ff1F0Y3LWn7sBzzjknyeeVWtYKAPDvWArjJGka9LQk7xve9VjaF6joqKQx6KaumywzKNDRkgVawsNPCY3Y2FgbPnx4ktFWwcsa+IuQ/V1JCn5mzZrlul0UIKjm5dZbb3ULxP5b11LPnj1dd863337ramWuvPLKDLVfr/Nv1B1Wrlw5Gz16tHuPam/16tX/tV0nS/U4wdRFpfOibi5156mQedCgQfbdd9+d9Gso0NRovSVLlrivwRQI+SVfgkKfV2rdmgAyn8oRWAojchAAnaS8ufJm+2PTosBn3Lhx7gJ97bXXJrlPQ6T/85//WOfOndP1XCpEVuGyamD8F2oVLf8bFf3qdZQFUhB09913pxjxdaLlFJSVUm1P7969U9y3d+9el8FR8OMPrFRnkxGqi9J5Ul2TMjmyYcOGQJH1ic6JamseeOCBwLHgLI2CS2VmFBBdddVV7pheS8FNcMYpWK1atdw5UTYno8FiRs8tAIAAKCKp6FgXco1USj6vTosWLVx2KL0BUKVKldx8Ncq4KNvwzDPPpKvQWN1gGpmli3G7du2S3KfuKgUHCqSU3dBw8OR69eplNWrUcEGG2qoL+5w5c1xhsB6vIEvdTgo01PWkjFNGqDi8UaNGdu+997pRXsqsdO/e3WWeTjQUX+dEAaZGYym7pYLkxYsXu32/rl272oABA9xj9VqDBw/+10ke1fXVtm1blz1T4KqAaPfu3S4IVDCY3nmcdG7VLgWIOkf6/Fm4FABSogYoAinA0cU9tUkFFQBp5JRGGaWHLtyqi1HGQ0GQhqKnlcUIptdXcKLHB3fDibqP1M2jEV6qoUmtbkcBwcyZM2358uV2ySWXuK4mDe9WLY1GfKkbShkVdXt169bNdUFllIIYDe9XlkYZLo1MU3dWXNy/j+647777rHnz5q6mSnU+ykgFZ4NEwdSdd97pgj9/N5k/i5YWZcwUAOl7laFSFk2BVdmyZdP9nvQe9L2qN9K5VbYKAJBSlCqhzePi4+NdsKDiVRXUBktISLCNGze6/+5PdGHE/6irTPPZ6KKuYCEcbN261Q3J1zxH/1aA7VX8LsDrqAEKr+v3iVADhEyl7rE9e/a4bhyNGtMEgqHqq6++coGauto0akuTFaoLyV+3AwCIXARAyFTqzlK2TBMFaiJAdVmFKs1QrQkMf/31V9dFpW6+8ePHUzMDAB4QulcnhCVlUMKlV1X1SdoAID00xUmTSk0C+whvBEAAAKSDlr/44vYvOFcRglFgAADAcwiAAACA5xAAAQCQzmHwefvldZv2Ed6oAQIAIJ0OHj3IuYoQZIAAAIDnEAABAADPoQvsJE1Zu91Op+aVS2bo8VrBfezYsW7dqlGjRiW5r0uXLvb666+7dao0WSFOnhZOnTp1qlu3K9Q9//zz9vHHH9uPP/6Y3U0BgGxHBiiCaV0rLRp66NChJOs5TZgwIUMLbGaXI0eOZHcTAAARigAogmnVdgVBU6ZMCRzTvoKfWrVqpVjDq3///m4Zi9y5c1vNmjVt0qRJgfsTExOtY8eOgfu14virr76a5Dnmzp3rVm7PmzevWwesbt269ttvvwUyUsmzJI888ojVr18/cFv7Dz74oDtepEiRwCzNP//8s11//fWWL18+t3q7VlnXemPB3/fQQw+579PK9XrM6NGj7cCBA3b33Xe7ZS4qVqxo06ZNS/L66Xnehx9+2K0RVqhQIStRooTLogTPei1a5V2ZIP/ttBZabdOmjXsenR+t1v7dd98F7h85cqSdc845litXLndu33vvvcB9mzZtcs8fnLnZt2+fO6Zz7j/3uj179mz33Hny5HFLe6xdu9bdr0xf7969bfny5e5x2nRMs3brPelnIjY21kqVKuXeMwBEOgKgCNehQwe3IrvfO++844KC5BT8jBs3znWXrVy50rp162Z33HGHzZs3LxAgaX2viRMn2qpVq+zZZ59162h99NFH7v5jx465AKdevXr2008/2cKFC+3ee+91F9qMULedgoBvvvnGtUUX+oYNG7qA7YcffrDp06fbzp07rVWrVim+T0HT999/74Kh+++/31q2bOmCgKVLl9q1117rApyDB/8ZwZGR51XAomBl4MCB9sILL9isWbPcfYsXL3ZfdX61mKr/dnJacFXnZdu2bfbpp5+6IERBlc6pqAuta9eu1r17dxeUqdtSn9GcOXMso5566im3EK3ek9Zh0+cvrVu3ds9/3nnnubZq07HJkyfbkCFD7I033rD169e7LjItDgsgpeioaKtXrp7btI/wRg1QhFMQ06tXr0AmRoGFusX8mQM5fPiw9evXz7788kurU6eOO3b22WfbggUL3IVRF++cOXO6DIKfMkEKchQAKWiIj4+3/fv324033ugyGVK1atUMt7dSpUou0PDr06ePC1LUvuAgTpmtdevW2bnnnuuOKWP19NNPu3293wEDBriAqFOnTu6YAjZlWRScXXbZZTZ8+PB0Pe/5559vzz33XKBt+j5lWa655horWrSoO65sl7JDaVGX4+7du12ApAyQKCPl9/LLL7sM2QMPPOBuP/roo7Zo0SJ3vEGDBhk6f3379nWfl/Ts2dNuuOEG1+2prJ0yXQqKgtuqxWt1u1GjRu4zViZIWTwAKeXOmdvmtv/f306EN0LYCKeLtC6C6u5QpkL7CgyCbdiwwWVGdFHXRdK/KSP0yy+/BB43YsQIq127tntO3f/mm2+6C6jowq6LuLqtmjZt6rrHlGXIKD1/MGVLlAkJbleVKlXcfcFtU6DiFxMTY4ULF06SyVAXl+zateukn1dKliwZeI70UteVgi1/8JPc6tWrXXdhMN3W8YwKbq/aKv/WXmXJVCOmgFfBorJRyuYBQKQjA+QB6gZRbY0/iEmti0a++OILO+uss5Lcp7oQUdbosccec90ryhKprmbQoEFJ6lgUYKl+RN1JH374ocvIqLtIGZfo6OgUq8QfPXo0RVvU3ZS8bQqoXnrppRSP9V/gRdmLYOp6Cz7m74rzdzudyvP6nyO9lH05FTp3Enz+Ujt38m/vOTXKeKlOSNk/fVbKQulzVddn8vcOAJGEAMgDrrvuOjeiShdEf2FxsGrVqrlAR9kcf/dJcuo6Uz2Nv5smeabET5kObeqGUqCk7h8FQMoaqb4leWbkRBdZFXKrTkUFxuq+ySyZ9bxqvwrET5SVeeutt+yPP/5INQukrkKdX01L4Kfb+lzE39WmjJq/eP1khrKrtiq1tipAUzCoTVMkKBO2YsUKd44A/I+Wvyj/6j+DHTZ13WR5cyX9hw3hhS4wD1CXkLpTVLys/eSUzVF2R4XPKvpVYKPC4WHDhrnb/voXFdbOmDHD1cg888wzSYp+N27c6IIe1QWp3mjmzJmuqNZfB6SCY32/utV0XHU1yQOi1OiCrMBBI6j0emqb2qAi4RMFHqfjeRVAqSZox44d9ueff6b6GL2G6mxUJK7A5tdff3XBl86VPP74466LUjVKOjeDBw92o/X0mfgDFAWRqmvS56jsjL/eKSPUVn1OCp402k21X3rdt99+230Watf777/vXq9cuXIZfn7AC/Yc3OM2hD8yQB6RP3/+f73/xRdfdJkGjQbThVCFvcoAaKSXaGTSsmXL3MghZZJ0UVc2yD+0XMOu16xZ4wKmvXv3um4kBRn6PlHmSUGTRj+pKFfdcnfddZfLNPwbDctW0PDEE0+4kVy6aOvirKyWv2voZGTW86pLUEXLGnav7kMNWU8t86KAUKOwmjRp4mpslN3xd0cqMFLNlIqeNRpMBebqTgyeIkAF2pqGQDVSGiavQnG1OyNatGjhAisVVmsUnF5Dn7MCK70HBX6qm/rss89cDRUQik73JLTBEo79bx2wT9bvsLgceTJ9ElucPlG+5IUZHqQRTAUKFHCjmJIHCrpY679mXZTi4uKyrY1AduN3AaEguwOgtpP+GcE5/tYNBEAhfv0+EbrAAACA5xAAAQAAzyEAAgAAnkMRNAAA6RBlUXZOoZqBfYQ3AqB0olYcXsfvALwuNkduG3ht0kWVEb7oAjsB/7w5mkgQ8DL/70Bqc0kBQLghA3SiE5Qjh5vjRotZatbfU5l7BghXWk5DvwP6XcjMGbkBILvwl+wENOmfJvXTXED+FdUBL1Lwr9Xi/WuMAV5z+NhB6/rffyYofbXJXItNx0SICF0EQOmgmXy1FATdYPD67wEZUHiZZg3efXBrYB/hjQAonfSHn5mgAQCIDBS0AAAAzyEAAgAAnkMABAAAPIcACAAAeA5F0AAApIMmgCid/9zAPsIbARAAAOmgeX80/w8iA11gAADAcwiAAACA5xAAAQCQgaUwtGkf4Y0aIAAA0kHLX2yNXxfYR3gjAwQAADyHAAgAAHgOARAAAPAcAiAAAOA5IR0AJSYm2jPPPGMVKlSw3Llz2znnnGMvvvii+Xz/Kz/T/rPPPmslS5Z0j2nUqJGtX78+W9sNAABCW0gHQC+99JKNHDnShg8fbqtXr3a3Bw4caMOGDQs8Rrdfe+01GzVqlH333XeWN29ea9y4sSUkJGRr2wEAkUXLXxTNU9ptLIUR/kJ6GPy3335rzZo1sxtuuMHdLl++vP3nP/+x77//PpD9GTp0qD399NPucTJu3DgrXry4ffzxx3bbbbdla/sBAJG1FMaom/65/iD8hXQG6PLLL7fZs2fbunX/zLuwfPlyW7BggV1//fXu9saNG23Hjh2u28uvQIECdumll9rChQvTfN7Dhw9bfHx8kg0AAHhHSGeAevbs6YKTKlWqWExMjKsJ6tu3r7Vt29bdr+BHlPEJptv++1LTv39/6927dxa3HgAAhKqQzgB99NFHNn78eJswYYItXbrUxo4day+//LL7eip69epl+/fvD2xbtmzJtDYDACLT4WOHrMfM692mfYS3kM4APf744y4L5K/lqVGjhv32228ug9OuXTsrUaKEO75z5043CsxPty+44II0nzc2NtZtAACkl8989ssfywP7CG8hnQE6ePCgRUcnbaK6wo4fP+72NTxeQZDqhPzUZabRYHXq1Dnt7QUAAOEhpDNATZs2dTU/ZcuWtfPOO8+WLVtmgwcPtg4dOrj7o6Ki7JFHHrE+ffpYpUqVXECkeYNKlSplN998c3Y3HwAAhKiQDoA0348CmgceeMB27drlApv77rvPTXzo16NHDztw4IDde++9tm/fPrviiits+vTpFhcXl61tBwAAoSvKFzytskep20zD51UQnT9//uxuDgAgDVPWbs+2c5Nw7KC1nVTR7Y+/dYPF5chzwu9pXvl/9akIret3SNcAAQAAeK4LDACAUJI/tlB2NwGZhAAIAIB0UJfXmFt+5lxFCLrAAACA5xAAAQAAzyEAAgAgHbT8xbOzW7iNpTDCHzVAAACkg5a/WLl7YWAf4Y0MEAAA8BwCIAAA4DkEQAAAwHMIgAAAgOcQAAEAAM9hFBgAAOkUG5ObcxUhCIAAAEjnUhgTWv7CuYoQdIEBAADPIQACAACeQxcYAADpcCQxwQYt6OT2H79itOWKieO8hTECIAAA0uG477gt3T47sI/wRhcYAADwHAIgAADgOQRAAADAcwiAAACA5xAAAQAAz8nQKLDjx4/bvHnz7Ouvv7bffvvNDh48aEWLFrVatWpZo0aNrEyZMlnXUgAAgNOZATp06JD16dPHBThNmjSxadOm2b59+ywmJsY2bNhgzz33nFWoUMHdt2jRosxqGwAAIbUUxuTbfneb9uGBDNC5555rderUsdGjR9s111xjOXPmTPEYZYQmTJhgt912mz311FPWqdM/k0UBAACEmiifz+c70YNWr15tVatWTdcTHj161DZv3mznnHOOhYv4+HgrUKCA7d+/3/Lnz5/dzQEApGHK2u1hdW6aVy6Z3U2IaPGncP1OVwYovcGPKDsUTsEPAADpXQrjtUUPu/2HL3uNpTC8uhTGsWPH7I033rC5c+daYmKi1a1b17p06WJxcayNAgCIPFr+YuGWz93+g5cOze7mILsCoIcfftjWrVtnzZs3d91e48aNsx9++MH+85//nGqbAAAAQiMAmjp1qt1yyy2B2zNnzrS1a9e6kWDSuHFju+yyy7KmlQAAANkxEeI777xjN998s/3+++/u9oUXXmidO3e26dOn22effWY9evSwiy++ODPbBgAAkL0BkIKcNm3aWP369W3YsGH25ptvuoprDXl/5pln3BxBGgYPAAAQUTVArVu3dl1dyvbo66hRo+yVV17JutYBAACEwlpgBQsWdNmfQYMG2V133WWPP/64JSQkZEXbAAAAsjcA0uSGrVq1sho1aljbtm2tUqVKtmTJEsuTJ4/VrFnTLY8BAECkio3JbeNv3eA27cMjAZCyPdHR0S7zU6xYMbvvvvssV65c1rt3b/v444+tf//+LkACACASRUVFuTXAtGkfHqkB0hw/y5cvd7M8q/5Hi58GzxQ9f/581zUGAAAQMQFQ7dq17dlnn7V27drZl19+6brCkrv33nszu30AAISEo4mHbdTiJ9x+54tfspwxsdndJJyOLjDN9Hz48GHr1q2bbdu2zS2DAQCAVyT6Em3upo/cpn14JANUrlw5mzRpUta2BgAAIFQyQAcOHMjQk2b08QAAACEXAFWsWNEGDBhg27dvT/MxPp/PZs2aZddff7299tprmdlGAACA098FNnfuXHvyySft+eefd3P+XHTRRVaqVCmLi4uzP//801atWmULFy60HDlyWK9evdwQeQAAgLAOgCpXrmyTJ092kyFOnDjRvv76a/v222/t0KFDVqRIEatVq5aNHj3aZX/8q8MDAABExFpgZcuWte7du7sNAADAEwEQAABepeUv3rl5RWAf4Y0ACACAdNDyFwXiCnOuvLoaPAAAQLgjAwQAQDqXwnh32fNuv32t51kKI8yRAQIAIB20/MX0DWPdxlIYHgyApk+fbgsWLAjcHjFihF1wwQV2++23uzmBAAAAIi4Aevzxxy0+Pt7tr1ixwg2Jb9KkiW3cuNEeffTRrGgjAABA9tYAKdCpVq2a29fkiDfeeKP169fPli5d6gIhAACAiMsA5cqVyw4ePOj2v/zyS7v22mvdfqFChQKZIQAAgIjKAF1xxRWuq6tu3br2/fff24cffuiOr1u3zkqXLp0VbQQAAMjeDNDw4cPdoqeTJk2ykSNH2llnneWOT5s2za677rrMbR0AAEAWiPL5fD7zOHXdFShQwPbv32/58+fP7uYAANIwZe32bDs3x33Hbc+BbW6/SN6zLDrqxDmE5pVLnoaWeVf8KVy/M5wB0mrvu3btSnF87969rAQPAIhYCniK5SvjtvQEPwhtGf4E00oYHT582BVIAwAAREwR9GuvvRZYDO6tt96yfPnyBe5LTEy0+fPnW5UqVbKmlQAAZLOjiUdswooBbv/2Gj0tZwz/9HsiABoyZEggAzRq1Kgk3V3K/JQvX94dBwAgEiX6jtmna/65zrWu/pjlNAIgTwRAmgBRGjRoYFOmTLEzzzwzK9sFAAAQOjVAc+bMCQQ/ygZl9SCybdu22R133GGFCxe23LlzW40aNeyHH34I3K/Xf/bZZ61kyZLu/kaNGtn69euztE0AACC8nVQZ+7hx41wgooBD2/nnn2/vvfdepjdOi6tqwsWcOXO6eYZWrVplr7zySpLs08CBA119krrfvvvuO8ubN681btzYEhISMr09AADAozNBDx482J555hl78MEHXXAiWh2+c+fOtmfPHuvWrVumNe6ll16yMmXK2JgxYwLHKlSokCT7M3ToUHv66aetWbNmgeCsePHi9vHHH9ttt92WaW0BAAAezgANGzbMzQCt4OSmm25ym7Iwr7/+emCkWGb59NNP7aKLLrKWLVtasWLFrFatWjZ69OgkdUk7duxw3V5+mhDp0ksvtYULF6b5vBqyr8mTgjcAAOAdGQ6Atm/fbpdffnmK4zqm+zLTr7/+6oKtSpUq2YwZM+z++++3hx9+2MaOHevuV/AjyvgE023/fanp37+/C5T8m7JMAADAOzIcAFWsWNE++uijFMe1KKoClcx0/Phxu/DCC61fv34u+3Pvvfdap06dTnm4fa9evdy02f5ty5YtmdZmAEBkyhUTZ0Oun+M27cNjNUC9e/e21q1bu4kP/TVA33zzjc2ePTvVwOhUaGRXtWrVkhyrWrWqTZ482e2XKFHCfd25c6d7rJ9uX3DBBWk+b2xsrNsAAEgvLX9RtkBlTphXM0AtWrRwo62KFCniCo21af/777+3W265JVMbpwBr7dq1SY6tW7fOypUrFyiIVhCk4MtP9TxqX506dTK1LQAAwMMZIKldu7a9//77ltU0oky1ReoCa9WqlQuy3nzzTbf5l+V45JFHrE+fPq77TQGRRqiVKlXKbr755ixvHwDAW0thTFn1z2Cf5tUeZikMLwZAqs3ZsGGDWxVe+8GuuuqqzGqbXXzxxTZ16lRXs/PCCy+4AEfD3tu2bRt4TI8ePezAgQOuPmjfvn12xRVX2PTp0y0ujv5ZAEDmLoXx0crBbr9Z1QdYCiPMRfkyOJXzokWL7Pbbb7fffvstxSzQyshoYdRwo24zjQZTQXT+/PmzuzkAgDRMWZu5o40zIuHYQWs7qaLbH3/rBovLkeeE39O88v/qUxFa1+8MZ4A04aHm5vniiy9c4bGCHgAAgHCS4QBI62xNmjTJDYcHAADwxCgwzbKs+h8AAICIzgD99NNPgf2HHnrIunfv7mZa1oKoWqg0mBZGBQAACPsASJMKqtYnuOi5Q4cOgX3/feFaBA0AALwlXQGQFh0FAMDLckbH2kvX/DewDw8EQP6ZlwEA8KqY6BirWDjtZZYQ4UXQWoldQ+CDJyIsWLCgm7FZcwMBAABEXACkZSly587t9hcuXGjDhw+3gQMHuvXAtHQFAACRuhTGx6tfd5v24bF5gLZs2RKYA0gLod56661uGQotXFq/fv2saCMAACGxFMZ7y/u4/esqtWcpDK9lgPLly2d79+51+zNnzrRrrrnG7WvtrUOHDmV+CwEAALI7A6SA55577rFatWrZunXrrEmTJu74ypUrrXz58pndPgAAgOzPAI0YMcLq1Klju3fvtsmTJ1vhwoXd8SVLllibNm34iAAAQORlgDTiS4XPyfXu3Tuz2gQAABBaGSAAAIBwRwAEAAA8J8NdYAAAeJGWv+jdYFJgHx7IAH366ad29OjRrG8NAAAhvBRG9eKXu0378EAAdMstt9i+ffvcfkxMjO3atSur2wUAAJC9AVDRokVt0aJFbt/n81lUVFTWtQgAgBB07PhRm7Z+jNu0Dw/UAHXu3NmaNWvmAh9tJUqUSPOxiYmJmdk+AABCgoKet5Y85fYbVGhtOaJzZneTkNUB0PPPP2+33XabbdiwwW666SYbM2aMmw8IAAAgokeBValSxW3PPfectWzZ0vLkyZO1LQMAAAiVYfAKgERLYaxdu9btV65c2dUJAQAAROREiAcPHrQOHTpYqVKl7KqrrnKb9jt27OjuAwAAiLgAqFu3bjZv3jw3N5CGxmv75JNP3LHu3btnTSsBAACyswtMK8BPmjTJ6tevHzjWpEkTy507t7Vq1cpGjhyZme0DAADI/gBI3VzFixdPcbxYsWJ0gQEAIlbO6Fz25FXjAvvwWBdYnTp1XCF0QkJC4NihQ4esd+/e7j4AACJRTHQOq12qkdu0j/CW4U/w1VdftcaNG1vp0qWtZs2a7tjy5cstLi7OZsyYkRVtBAAAyN4AqHr16rZ+/XobP368rVmzxh1r06aNtW3b1tUBAQAQqTNBz980xe1fVb45M0GHuZPK4WkSxE6dOmV+awAACOEAaMT33dz+5WWbEgB5rQYIAAAg3BEAAQAAzyEAAgAAnkMABAAAPOekAiAtf/HWW29Zr1697I8//nDHli5datu2bcvs9gEAAGT/KLCffvrJGjVqZAUKFLBNmza50WCFChWyKVOm2ObNm23cuH9myQQAAIiYDNCjjz5q7du3d3MBafLD4PXA5s+fn9ntAwAgJGj5i+6Xv+E2lsLwYAZo8eLF9sYbb6Q4ftZZZ9mOHTsyq10AAIQULX+h+X/g0QxQbGysxcfHpzi+bt06K1q0aGa1CwAAIHQCoJtuusleeOEFO3r0qLsdFRXlan+eeOIJa9GiRVa0EQCAbJd4/Jh9u/kzt2kfHguAXnnlFfv777+tWLFibhX4evXqWcWKFe2MM86wvn37Zk0rAQDIZkePH7FXvr3PbdqHx2qANPpr1qxZtmDBAjciTMHQhRde6EaGAQAAROxiqHLFFVe4DQAAIOIDoNdeey3V46oF0rB4dYddddVVFhMTkxntAwAAyP4AaMiQIbZ79247ePCgnXnmme7Yn3/+aXny5LF8+fLZrl277Oyzz7Y5c+ZYmTJlMr/FAAAAp7sIul+/fnbxxRe7iRD37t3rNg2Bv/TSS+3VV191I8JKlChh3bp1O9W2AQAAhEYG6Omnn7bJkyfbOeecEzimbq+XX37ZDYP/9ddfbeDAgQyJBwAAkRMAbd++3Y4dSzn/gY75Z4IuVaqU/fXXX5nTQgAAQkCO6JzW5ZIhgX14rAusQYMGdt9999myZcsCx7R///33W8OGDd3tFStWWIUKFTK3pQAAZCMFPQ3Pbu02AiAPBkBvv/22W/29du3ablkMbRdddJE7pvtExdCaMBEAACAiusBU4KyJENesWeOKn6Vy5cpuC84SAQAQSbT8xY875rr9C0rUd4ujInyd9KdXpUoVtwEA4AVa/qLf/Lvc/vhbNxAAeTEA2rp1q3366aduyPuRI0nXQxk8eHBmtQ0AACA0AqDZs2e7FeE12aG6wapXr26bNm0yn8/n1gQDAACIuCLoXr162WOPPeZGemnpC80JtGXLFrcqfMuWLbOmlQAAANkZAK1evdruuuufPtAcOXLYoUOH3KivF154wV566aXMbBsAAEBoBEB58+YN1P2ULFnSfvnll8B9e/bsydzWAQAAhEIN0GWXXWYLFiywqlWrWpMmTax79+6uO2zKlCnuPgAAgIgLgDTK6++//3b7vXv3dvsffvihVapUiRFgAICIpdmf76ndN7CP8Bbl0/Atj4uPj7cCBQrY/v37LX/+/NndHABAGqas3R5W56Z55ZLZ3YSIFn8K1+8M1wBp+PvevXtTHN+3b5+7DwAAINRlOADSnD+JiYkpjh8+fNi2bdtmWWnAgAEWFRVljzzySOBYQkKCdenSxQoXLuxGo7Vo0cJ27tyZpe0AAHhP4vFE+3nnt27TPjxSA6SZn/1mzJjhUk5+Cog0QWL58uUtqyxevNjeeOMNO//885Mc79atm33xxRc2ceJE16YHH3zQmjdvbt98802WtQUA4D1Hjx+25+bcGrQURp7sbhJORwB08803u6/KwLRr1y7JfTlz5nTBT1atAK9C67Zt29ro0aOtT58+gePq89MK9BMmTLCGDRu6Y2PGjHEj1BYtWsSoNAAAcGpdYMePH3db2bJlbdeuXYHb2tT9tXbtWrvxxhstK6iL64YbbrBGjRolOb5kyRI7evRokuNaoFVtXLhwYZrPp/aqcCp4AwAA3pHhYfAbN2600+mDDz6wpUuXui6w5Hbs2GG5cuWyggULJjlevHhxd19a+vfv74bwAwAAbzqp1eBV76PNnwkK9s4772RW29waY127drVZs2a5dccyi9Yze/TRRwO3lQEqU6ZMpj0/AACIsABImROt+3XRRRe5pTBUE5RV1MWlICt4lXkVXM+fP9+GDx/uirG1LIeG4AdngTQKrESJEmk+b2xsrNsAAIA3ZTgAGjVqlL377rt25513Wla7+uqr3TIbwe6++25X5/PEE0+4rI0KsJWN0vB3US3S5s2brU6dOlnePgAA4JEASBmXyy+/3E6HM844w6pXr55iMVbN+eM/3rFjR9edVahQITcL5EMPPeSCH9YlAwBkppioHHZnzacD+whvGf4E77nnHjfs/JlnnrFQMGTIEIuOjnYZII3uaty4sb3++uvZ3SwAQITJGZPLbq76QHY3A9kVAGnm5TfffNO+/PJLNymhuqCSL5aalebOnZvktoqjR4wY4TYAAIAsCYB++uknu+CCC9z+zz//nOS+rCyIBgAgO2n5i41//lOXWuHMGhYTHcMH4qUAaM6cOVnTEgAAQnwpjCdmNXH7LIXhwcVQ/TZs2OCGoR86dMjd9vl8mdkuAACA0AmA9u7d64ann3vuudakSRPbvn17YDRW9+7ds6KNAAAA2RsAafV1FT5rrp08ef63Em7r1q1t+vTpmds6AACAUKgBmjlzpuv6Kl26dJLjlSpVst9++y0z2wYAABAaGaADBw4kyfz4/fHHHywvAQAAIjMAuvLKK23cuHFJhr5rQdSBAwdagwYNMrt9AAAA2d8FpkBHRdA//PCDWxajR48etnLlSpcB+uabbzK/hQAAhAAtf9HqvEcD+whvGf4EtQbXunXr3GrsWqvr77//tubNm1uXLl3c6vAAAETqUhitazyW3c1AJjmpELZAgQL21FNPZVYbAAAAQrsGaMyYMTZx4sQUx3Vs7NixmdUuAABCynHfcdu8f63btA+PBUD9+/e3IkWKpDherFgx69evX2a1CwCAkHIkMcG6TWvgNu3DYwGQJkCsUKFCiuPlypVz9wEAAERcAKRMj1aET2758uVWuHDhzGoXAABA6ARAbdq0sYcfftitCp+YmOi2r776yrp27Wq33XZb1rQSAAAgO0eBvfjii7Zp0yY3F1COHP98uyZCvOuuu6gBAgAAkRcA+Xw+27Fjh7377rvWp08f+/HHHy137txWo0YNVwMEAAAQkQFQxYoV3czPWvxUGwAAQEQHQNHR0S7o2bt3L8EPAMBTtPzFTVU6B/bhsSLoAQMG2OOPP24///xz1rQIAIAQXQqj3QXPuk37CG8ZDmFV7Hzw4EGrWbOm5cqVy9UABdOiqAAAABEVAA0dOjRrWgIAQAjT8hd7Dmxz+0XynmXRURnuREE4B0Dt2rXLmpYAABDCtPzF/Z9f6vbH37rB4nLkye4m4RScVPj6yy+/2NNPP+0mRdy1a5c7Nm3aNDc6DAAAIOICoHnz5rl5f7777jubMmWK/f3334GlMJ577rmsaCMAAED2BkA9e/Z0kyDOmjXLFUH7NWzY0BYtWpS5rQMAAAiFAGjFihV2yy23pLpI6p49ezKrXQAAAKETABUsWNC2b9+e4viyZcvsrLPOyqx2AQAAhE4ApBXfn3jiCbcmWFRUlFsI9ZtvvrHHHnvMzREEAAAQccPg+/XrZ126dLEyZcpYYmKiVatWzX29/fbb3cgwAAAiUUxUjF1XsV1gH+EtyqcVTk/Cli1bXD2QRoHVqlUrrNcGi4+PtwIFCtj+/fstf/782d0cAEAapqxNWYIRyppXLpndTYho8adw/U53BkhdXYMGDbJPP/3Ujhw5YldffbUb9p58KQwAAICIqQHq27evPfnkk5YvXz5X7Pzqq6+6rjAAALxAHSb7E/a67SQ7TxCOAdC4cePs9ddftxkzZtjHH39sn332mY0fP95lhgAAiHSHEw9Zh49ruE378EgAtHnzZmvSpEngdqNGjdwosN9//z2r2gYAAJC9AdCxY8csLi4uybGcOXPa0aNHs6JdAAAAWSbdRdDq72zfvr3FxsYGjiUkJFjnzp0tb968gWNaHwwAACAiAqB27f6Z+yDYHXfckdntAQAACJ0AaMyYMVnbEgAAgFBdCgMAAMBzS2EAAOBFWv6ifvlWgX2ENwIgAADSIWdMrD102VDOVYSgCwwAAHgOGSAAANI5HYx/BujYmNxuMmCELzJAAACkg4KftpMquo2lMMIfARAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPIQACAACewzxAAACkQ3RUtNUpc2NgH+GNAAgAgHTIFRNnj9V9k3MVIQhhAQCA5xAAAQAAzyEAAgAgHRKOHbQWH5Rym/YR3giAAACA5xAAAQAAzyEAAgAAnkMABAAAPIcACAAAeA4BEAAA8JyQDoD69+9vF198sZ1xxhlWrFgxu/nmm23t2rVJHpOQkGBdunSxwoULW758+axFixa2c+fObGszACAyafmLC0te7TaWwgh/IR0AzZs3zwU3ixYtslmzZtnRo0ft2muvtQMHDgQe061bN/vss89s4sSJ7vG///67NW/ePFvbDQCIzKUwnqr3ntu0j/AW5fP5fBYmdu/e7TJBCnSuuuoq279/vxUtWtQmTJhgt956q3vMmjVrrGrVqrZw4UK77LLL0vW88fHxVqBAAfd8+fPnz+J3AQA4WVPWbg+rk9e8csnsbkJEiz+F63dIZ4CS0xuUQoUKua9LlixxWaFGjRoFHlOlShUrW7asC4DScvjwYXfSgjcAAOAdYRMAHT9+3B555BGrW7euVa9e3R3bsWOH5cqVywoWLJjkscWLF3f3/VttkSJG/1amTJksbz8AILxp+YvbJ57jNpbCCH9hEwCpFujnn3+2Dz744JSfq1evXi6b5N+2bNmSKW0EAES2w4mH3Ibwl8PCwIMPPmiff/65zZ8/30qXLh04XqJECTty5Ijt27cvSRZIo8B0X1piY2PdBgAAvCmkM0Cqz1bwM3XqVPvqq6+sQoUKSe6vXbu25cyZ02bPnh04pmHymzdvtjp16mRDiwEAQDjIEerdXhrh9cknn7i5gPx1ParbyZ07t/vasWNHe/TRR11htCrAH3roIRf8pHcEGAAA8J6QDoBGjhzpvtavXz/J8TFjxlj79u3d/pAhQyw6OtpNgKjRXY0bN7bXX389W9oLAADCQ0gHQOmZoiguLs5GjBjhNgAAgLAPgAAACBVRFmXnFa0T2Ed4IwACACAdYnPktheunsy5ihAhPQoMAAAgKxAAAQAAzyEAAgAgHbT8xd1Tq7uNpTDCHzVAAACkU/zhPzhXEYIMEAAA8BwCIAAA4DkEQAAAwHMIgAAAgOcQAAEAAM9hFBgAAOmg5S/OKVQzsI/wRgAEAEA6l8IYeO00zlWEoAsMAAB4DgEQAADwHAIgAADS4fCxg9b500vcpn2EN2qAAABIB5+Z7T64NbCP8EYGCAAAeA4BEAAA8BwCIAAA4DkEQAAAwHMIgAAAgOcwCgwAgHTQ4hel858b2Ed4IwACACAdYnPksVebzOVcRQi6wAAAgOcQAAEAAM8hAAIAIB20/EXX/9Z3G0thhD9qgAAASActf7E1fl1gH+GNDBAAAPAcAiAAAOA5BEAAAMBzCIAAAIDnEAABAADPYRQYAADpoOUviuYpHdhHeCMAAgAgnUthjLrpe85VhKALDAAAeA4BEAAA8BwCIAAA0uHwsUPWY+b1btM+whs1QAAApIPPfPbLH8sD+whvZIAAAIDnEAABAADPIQACAACeQwAEAAA8hwAIAAB4DqPAAABIp/yxhThXEYIACACAdIjLkcfG3PIz5ypC0AUGAAA8hwAIAAB4Dl1gAACkg5a/6DvvDrf/VL33LTZH7kw9b1PWbg+7z6F55ZIWrgiAAABIBy1/sXL3wsA+whtdYAAAwHMIgAAAgOcQAAEAAM8hAAIAAJ5DAAQAADyHUWAAAKRTbEzmDn1H9iEAAgAgnUthTGj5C+cqQhAAAUCECbcJ9cJ5Mj2EL2qAAACA55ABAgAgHY4kJtigBZ3c/uNXjLZcMXGctzBGAAQAQDoc9x23pdtnB/YR3ugCAwAAnhMxGaARI0bYoEGDbMeOHVazZk0bNmyYXXLJJRZOKFwEAOD0iIgA6MMPP7RHH33URo0aZZdeeqkNHTrUGjdubGvXrrVixYpld/MAhCD+4QC8LSICoMGDB1unTp3s7rvvdrcVCH3xxRf2zjvvWM+ePbO7eeBiAwAIMWEfAB05csSWLFlivXr1ChyLjo62Ro0a2cKFC7O1bfCGSM4kRPJ7A+BtYR8A7dmzxxITE6148eJJjuv2mjVrUv2ew4cPu81v//797mt8fLxlp4N//2XhJD4+b7ofy3sLHXxu/+BnMnSEy89kwrGDZgn/a8fxHIkR895OVkbeX1bwX7d9Pp/3AqCT0b9/f+vdu3eK42XKlMmW9gAAwkunAbWyuwkIsnfvXitQoIB5KgAqUqSIxcTE2M6dO5Mc1+0SJUqk+j3qLlPRtN++ffusXLlytnnz5gyfwFCn6FiB3ZYtWyx//vwWSXhv4YnPLTzxuYWvSP7s9u/fb2XLlrVChQpl+HvDPgDKlSuX1a5d22bPnm0333yzO3b8+HF3+8EHH0z1e2JjY92WnIKfSPvh8NP74r2FHz638MTnFp4i+XOL9PcXHR3tvQBIlM1p166dXXTRRW7uHw2DP3DgQGBUGAAAQMQFQK1bt7bdu3fbs88+6yZCvOCCC2z69OkpCqMBAAAiJgASdXel1eV1IuoOe+6551LtFgt3vLfwxOcWnvjcwlMkf26R/v5iT+G9RflOZuwYAABAGGMxVAAA4DkEQAAAwHMIgAAAgOcQAAEAAM8hAEqmfPnyFhUVlWQbMGCARRKtg6apAvTefvzxR4sEN910k5sNNC4uzkqWLGl33nmn/f777xbuNm3aZB07drQKFSpY7ty57ZxzznEjHrQIcCTo27evXX755ZYnTx4rWLCghbsRI0a4vyH6Obz00kvt+++/t3A3f/58a9q0qZUqVcr9zfj4448tkpZFuvjii+2MM86wYsWKucl0165da5Fg5MiRdv755wcmP6xTp45NmzbNItGAAQPcz+YjjzySoe8jAErFCy+8YNu3bw9sDz30kEWSHj16uD9mkaRBgwb20UcfuT9ekydPtl9++cVuvfVWC3da0Fczm7/xxhu2cuVKGzJkiI0aNcqefPJJiwQK5Fq2bGn333+/hbsPP/zQTcqqAHXp0qVWs2ZNa9y4se3atcvCmSaV1XtRcBdp5s2bZ126dLFFixbZrFmz7OjRo3bttde69xzuSpcu7QKDJUuW2A8//GANGza0Zs2aub8jkWTx4sXu76OCvQzTMHj8T7ly5XxDhgyJ2FPy3//+11elShXfypUrNf2Bb9myZb5I9Mknn/iioqJ8R44c8UWagQMH+ipUqOCLJGPGjPEVKFDAF84uueQSX5cuXQK3ExMTfaVKlfL179/fFyn0N2Pq1Km+SLVr1y73HufNm+eLRGeeeabvrbfe8kWKv/76y1epUiXfrFmzfPXq1fN17do1Q99PBigVipoLFy5stWrVskGDBtmxY8csEmiB2E6dOtl7773nuhwi1R9//GHjx493XSs5c+a0SKPF/05m4T9kbSZL/2k3atQoydpEur1w4UJOfRj9bkmk/X4lJibaBx984DJb6gqLFF26dLEbbrghye+dJ2eCziwPP/ywXXjhhe4X4Ntvv3Urx6sbbPDgwRbO9M9b+/btrXPnzm7NNNWWRJonnnjChg8fbgcPHrTLLrvMPv/8c4s0GzZssGHDhtnLL7+c3U1BkD179riLTPLld3Rb3ZgIfepqVg1J3bp1rXr16hYJVqxY4QKehIQEy5cvn02dOtWqVatmkeCDDz5wXc3qAjtZnsgA9ezZM0Vhc/LN/0dKffj169d3/YkKFl555RV3wVHhcDi/N72Hv/76ywV0kfi5yeOPP27Lli2zmTNnWkxMjN11110u8IuE9ybbtm2z6667ztXMKJMXqk7mvQGhkE34+eef3YU1UlSuXNkNdPnuu+9cnZ0WDV+1apWFuy1btljXrl1dpl8DDk6WJ5bC0EKpe/fu/dfHnH322ZYrV64Ux1Uwpv8G9AdbP0zh+t5atWpln332mbv4+Ok/VgUKbdu2tbFjx1okfW5bt261MmXKuCxeKKZ8M/reNKJNgbkyW++++67rXglVJ/O56T3pv+99+/ZZuHaBqVt50qRJbiSRny44ek+ffPKJRQL9/VAWIfg9RgKtI6nPSCPeNOIyUqmrSCNJVTQczjQS8ZZbbnHXr+DrmX4+9bdRCYvg+zzdBVa0aFG3nQxFzzqhGiIZzu/ttddesz59+gRu64KqESoauaLhupH2uSmdLaG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" ] }, "metadata": {}, @@ -1417,7 +1373,7 @@ "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", " # 1. State preparation\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", "\n", @@ -1425,21 +1381,21 @@ " invert(lambda: qft(x))\n", "\n", "\n", - "pc, df = run_standard_simulation(main)\n", - "analyze_results(pc, df, p)" + "df = run_standard_simulation(main)\n", + "analyze_results(df, p)" ] }, { "cell_type": "markdown", - "id": "38", + "id": "36", "metadata": {}, "source": [ - "### 2.2.2. Quadratic Function" + "### Quadratic Function" ] }, { "cell_type": "markdown", - "id": "39", + "id": "37", "metadata": {}, "source": [ "For non-linear functions, the interval $l$ must be chosen carefully. The algorithm requires the function to be approximately linear over the interval, which means $l$ must be sufficiently small. The next example demonstrates this dependency." @@ -1447,7 +1403,7 @@ }, { "cell_type": "markdown", - "id": "40", + "id": "38", "metadata": {}, "source": [ "With appropriate selection of $l$, the function remains nearly linear over the sampling interval, yielding high success rates." @@ -1455,15 +1411,23 @@ }, { "cell_type": "code", - "execution_count": 11, - "id": "41", + "execution_count": 10, + "id": "39", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/d31812c4-9e41-4f3d-b2e4-44265c9093a1\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed counts: [{'x': 1}: 2025, {'x': 2}: 12, {'x': 0}: 8, {'x': -3}: 2, {'x': -1}: 1]\n", + "Parsed probabilities: {1: 0.98876953125, 0: 0.00537109375, 2: 0.0048828125, -1: 0.0009765625}\n", "The analytical gradient is: 0.25\n", "The majority gradient is: 0.25\n", "The majority result is correct\n", @@ -1474,19 +1438,9 @@ }, { "data": { - "image/png": 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AIM8g8AcAAACkkzL39u/f7w/06a8CAqEUuPCCfPqr+wT6EA2+/trs22/1GQ5+vE4ds7Vrc269lStXtm+++cZ27NjhMmD1nfEo+0/j7dWqVStH1r1hwwabP3++/frrr/bMM8+47+xDDz1knTp1sj/++MO2bdvm5itTpkzQ68qWLesfnzAlClpq8iR6AycCAAAAQF4J/KmMyQcffOB+lKncigY9VydGhQoV3BWPp59+up133nn+qzMBAACAaKVAn0p1BpbuVCnPUMrg84J8mgoWLBiR7QWySsNPhvmI25o1vpKfOeW+++6zHj162AknnJDsOQUClTU7duxYN6ZedlNgcdeuXTZ58mQ78cQT3WOnnnqqy+J76qmnrHPnzple9ogRI+zee+/Nxq0FAAAAgNTls3SaOnWqtW3b1o4++mgbMmSILViwwGrUqOEGNW/Tpo1Vq1bNPabnNI8e02sAAACAaOEFADZu3GgrVqywJUuW2F9//eUygnbu3OmCfrroTcG9ihUrWu3atd3Fb/r/b9WqVa106dIE/RDVOnUyGzPmyH1VpN21y2zYMLMuXXJuvcOHD7dffvklxed/++23HAugKXOvfPny/qCflCtXzpo2bWqLFi3yZ/YpGzGQlwmoeVNyxx13uNd50+rVq3PkPQAAgOg37odb7fFvBrm/AJDjGX+62nHhwoXWrVs3N7aCBl7XoOvhqHTJjBkz3NWSffr0scaNG9vcuXOztJEAAABATjh48GBQNp+y+0Llz58/2fh8+fKl+/o5IKqMHGmmBLeGDc00XKWG1fvjD7MKFczeeity26VymoHlP7PT8ccf78bxC0djdtarV88F9DWWX2D2n+5L6Nh/gQoXLuwmAACAtMxfN9O27llv5YpWZWcByPnAn7L6VN5T4y6kRQHBnj17uklXRj/xxBNZ20IAuUYdmgAA2tVYH58vMNCn+6HUwR84Pp867RmfD/GiRg2zhQvNJk70/VW23xVXmF18sUpuZu+6vvrqK5s9e7b//nvvvWfLly9PNt/27dtt4sSJ1qhRI8sJ55xzjo0fP95VsGnSpIl77J9//rGffvrJbrzxRtcG6DexLm694YYb/K/TNinjVyVBAQAAACCvSEhSD0icU5aiyjKp9EpKmYwAAACIvrKd3vh83hRufD516gcG+nIqqwjRb82aRKtZs7StXr3DatTgd0NWqXSnV75TwfXUfpo2bNjQXnrpJWvRooXlRFuhKjfKKnzwwQfdmIIam++PP/5wJUarVKlic+bMcUNfDBo0yFW2mTVrlt1///0u+Ne7d+90r4vfngAA5D3vLVtvecHAD5r5M/5e6DY/otvSowFZh0AkZfV3Q7oy/gAAAIBoK9upEn2hgQQFF9Sp75Xu1FSgAP8lBjz585udcYbZu+9q7Loj+2XjRrNq1czCxM4z7dZbb7Vrr73WfU8rVapk48aNc5VjQr+z+p6qxG5OUene6dOnu+y+K6+80mUCt27d2mUkKugnrVq1chmJd999twtA1qpVy1588cUMBf0AAAAAIDekq5fjtddey9TC+/Xrl6nXAQAAAKlRoGDfvn1B2XzhynYqqBcY5GN8PiB1ipXv22fWvLnZRx9p/Lvg57KTgvCaZMWKFVaxYsWIlZ6vUKGCTZgwIdV5zjvvPDcBAAAAQNQH/i677LJkj3njnIS7itpD4A+IHipxtGzZMne7QYMG7spnAADtal4r2+ll8+l2amU7vdKdGq+P8fmA9NPPOWX7PfywWcuWZoqFdet25LmcUrt2bfdX3/Evv/zSVq1a5X+8TZs27vsMAAAAAMimwJ+uvgwdXL1///6uxuh1113nggSydOlSGzt2rO3cudNeffXV9CwaQB4SrgMVAEC7GgkHDhwIyuZToC+UVwIwcMqvOoUAMk3Xdepr9MQTvmy/vn3N7r7b7H//y/mdqt+SKqW5a9euoAtMS5Ys6cbeU1lQAAAAAEA2BP68qy89w4cPd2VYPvvss6ArqBs1auTGZOjUqZONHj3axo8fn57FAwAAII4Flu30MvoU+EutbKeyf1S2k2w+IOcMGmR2zDFmGsbuq69ydk9reIkbbrjBWrZsaddff70dd9xx7vElS5a4gKCe04Wnl156ac5uCAAAAADEQ+Av1Pvvv++uuAzX0aLygD169HBXagIAAADhMsyVwReY0adSnqEU2AvM5qNsJ5DzdM1nYOJsu3Zm8+aZnXtuzq531KhRdsYZZ9jMmTODMndPPPFE69Wrl7Vv395GjhxJ4A8AAAAAciLwp6uyVdYzJYsXL0429h8AAADij/5PuH///qAgn7L7wl08VrRoUcp2AhEWMsqDc/TRZj//bLZxY86tV2NNP/7442HL9eqx3r17280335xzGwAAABBhrWp3s3/377DihUpHelMAxGPgr3v37vbss89anTp17KqrrnIdNKKOHD3+3HPP2cUXX5zd2woAAIAoy+bT7XBjyCp7LzCbj7KdQN5WpIgvGzCnqIznypUrU3xez5UqVSrnNgAAACDC+je5J9KbACCeA39PPPGErVixwl1xeccdd1jVqlXd4+vXr3fjsZx++uk2ZsyY7N5WAAAA5OFsPgX59u7dm2w+lYcPzObTbQX+AOQN5cqZ/f67WYUKZmXL6jub8rxbt+bMNnTt2tWN5desWTO74IILgp6bOHGiPfXUU1xcCgAAAAA5FfjT1ZhffvmlffDBBzZ9+nT7+++/3eNnnXWWdenSxc4999yw4/8ByNvUEQsAoF1NTzaf9zetbD6dW5TNp1KeAPKm0aPNSpb03Y7U9ZsPP/ywzZ071wX3brrpJjvmmGPc43/88Ydt2LDBjj32WDcPAAAAACB1CUkMxmeJiYkumLljxw7KxwAAAIRk83lBvrSy+by/ZPMhVq1Zk2g1a5a21at3WI0alJ3MbmpjNGzExx9/bKtWrXKP1a5d211cOmjQIHcRQbTjtycAAHnPe8vWR3oT8pweDXwV/gBE5++GTGX8edauXWtfffWVbdq0yXr27Gk1atSww4cP2/bt291GhRuYHQAAANGfzecF+cjmA6JfYmL6583JYfbUntxwww1uAgAAiDfXTWtt2/ZstLJFK9vYrl9HenMARLECmb0CXOVXNM7CwYMH3ZXejRo1coG/nTt3Wp06dey+++6zwYMHZ/8WAwAAINey+dQR75XtJJsPiE1lyqQ+rp8kJfnmCXM9AAAAALLB3oO7bc/BXVb04H812AEgNwN/jz32mD3xxBN22223Wfv27a1jx47+55Tp16NHD3v33XcJ/AFRRNm6GkNFNKYKYzEBQOy0q7pQKzCbT1O4bL4CBQoEBfnI5gPiw6xZlid8+umn9tJLL9lff/1l27ZtcxcphF6M8Oeff0Zs+wAAAAAgZgN/L7zwgvXr188eeugh++eff5I9f+KJJ7pxGQBElwMHDkR6EwAgpkSiXVXAcd++fS7I5wX6lN2X0th8XslOsvmA+NWmTaS3wHdx6e23326VK1e2U045xVWUAQAAAADkUuBv9erVdtppp6X4fPHixd3ggwAAAMg5yoZRcNHL5vNKdoZmyUihQoWCxuYrXLgw2d0AUrR7t9nff5uFXjdw4ok5s9NUUebMM8+06dOnu7FEAQAAAAC5GPirVKmSC/6lZP78+VarVq1MbhIAAEB023vgkH386zo7ppDv/vVv/WxnHlfZujSqakUK5s/0clWeM7Bkp/6GK9mZP39+f4DPy+pTGU8ASMvmzWYDBpilVMAlp8b4U2nPXr16EfQDAAAAgCzKVA+QxvAbN26cXXbZZW5MP69clHz22Wf2yiuv2K233prVbQMAAIg6MxZvtJsmLbB9+w/Zuxf6LoSauWSjTf11gw3/aJGN6t3EOjSsnOZylLWn7L3AQJ9KeIbjBfe8YJ+y+7z/mwFARgwebLZ9u9l335m1bWs2ZYrZxo1mDzxgNnJkzu1LlfdctmxZzq0AAAAAAOJEpgJ/9957r82aNcuaNGlirVu3dh1LjzzyiA0dOtTmzp1rTZs2tTvvvDP7txYAACCPB/0GTfjRLMmsUP4jgbfD/1Xe3LnnoA2c8KM9f2lz6xgS/FPJzsBMPgX9NF5fKJXACyzZWaRIEUp2Asg2X3xh9sEHZs2bm+XLZ1a7tlnHjmalSpmNGGHWtWvO7OxnnnnGzj77bGvevLlddNFFObMSAAAAAIgDmQr8Kctv3rx5NnLkSJs8ebLrcPryyy+tXr16NmzYMLvllltcZxQAAEA8lfdUpp+CfslH2PPR4wlJZje9s8BmDW5phw/s8wf6Dh48mGz+fPnyBZXs1F9KdgLISf/+q6EdfLfLlvWV/qxf36xRI7Offsq+9ZwYZrBAtYOXXnqp/d///Z/VqFHDlS0OpAtOFy5cmH0bAQAAAAAxKNODvajz6e6773YTgNhQuHDhSG8CAESt6b+ut8Q9wcG7Vdv3hw3+Je49aG9+tdja1S0R9JwupgoM9KldpmQngNzUoIGZKm7WqWPWuLHZc8/5bo8bZ1a1avatp1y5csnat/Lly9sxxxyTfSsBAAAAgDiUqcDfa6+9ZpUqVbKzzjor7PMrVqywr7/+2vr165fV7QOQS5RVQkcLAGTeZ4s2Wr6EI2U99x1Ksmumrg87r7q6563da92aVAsany80uwUActsNN5it/6/pGjbMTD/53njDrFAhs1deyb71zJ49O/sWBgAAEAOubP6w7T+01wrlLxLpTQEQj4G/yy67zF2decUVV9jTTz/txpoJ9O2339qAAQMI/AEAgJiVlJTkxuVTqU5N67cm+oN+ab7WzA7lL2y1atXK6c0EgAy55JIjt5s1M1u1ymzpUjM1VxUqsDMBAABySvPqHdm5ALJFvsy+sFOnTvbqq6/aGWecYeu9S0IBAABilMae2rlzp23atMlWrVply5Yts99//91Wr15tW7ZsseIFfJl86aHMwDJFC+XwFgNA1hUrZnbSSTkf9FuwYIG99dZbQY99+umn7vdmixYt7IknnsjZDQAAAACAeB/jT4OuDx061Hr16mUnnXSSTZo0yVq1apW9Wwcg1xw+fNj+/PNPd7tevXqu9CcAxHOb6GXyadq9e7fL7gvHG5fvrBML2rerl/sfL5w/wUadXcXdHvLxBlf607/8JLPOJ1TOhXcCABmTlGQ2ebLZrFlmmzapPQx+/r33cmaP3nrrrW580wsvvNA/fMT555/vxv2rVq2aDRkyxLW1gwYNypkNAAAAAIB4D/zJaaedZj/99JP16dPH2rdvbyNHjrRrr702+7YOQK7at28fexxAXJbs3Lt3b1CQL6X2sFChQq7jWZ3T+qugn3ehRJ9Kh+zxL1bazj0HXSlPqV0meVafsgJLFS1gZ59QNUffFwBkxuDBZs89Z9aunVnlymYJ6U1lzqKFCxfaLbfcEjSuvMY9/fnnn61ChQrWt29fGzduHIE/AAAQs/7c+osdPLzfCuQrZPXKnRjpzQEQr4E/qVKlis2aNctuvvlmu/766+3HH38k8w8AAGTa3gOHbPqv6+2zRRtt++79VqZYIet0fGXr0qiqFSmYP8tBPgX1ArP5FPTT46EKFCjggnuBgT51QqdE2zaqdxMbOOFHS0hhrD/Xf55gNrJ3kyy/FwDICRMm+LL6unTJ3f27Y8cOl93nmT59unXs2NEF/US3P/7449zdKAAAgFz08NcDbOue9VauaFV7odt89j2AyAX+RJ1go0ePdmMvDBw40N7LqfovAAAgps1YvNFumrTAEvccdOPgqSSm/n6yaIMN/2iRC6x1aFg5w0G+wIy+cEE+Ze0FBvg0FSxYMMPbr217/tLmdvOkBbZ3/6Ejy/8vY0aZfiMz8B4AILeVLm1Wt27u7/eqVavakiVL3G2NIT9//nwbMGCA//ldu3ZRih4AAAAAcirw16ZNG6usui8hLrjgAjvhhBPcD7QtW7ZkZtEAACCOg36DJvxoXp3MwyF/VUJT2XQKrHUMCZwpmLd///5kmXwaqy9ckM8bl8+bVMIzIZvq2Wnbvruzg33y2zrlsLjH2h9X2do3rOzKe5LpByAvGz7c7N57zV5+2axo0dxbb7du3Wzs2LGu7f7uu++scOHCboy/wFKgdSMRkQQAAACAeAj8qbRnShT4++GHH7KyTQAAIA7LeyrTT0G/FKpkusdVQlPzzbmptR0+uD/iQb6UKLh3XuPqtnixL/D35IVNyVQBEBX69DF76y2zSpXM6tQxC01+/umnnFnvAw88YJs3b7YJEyZYmTJl7JVXXvFfbJqYmGiTJ0+2a665JmdWDgAAAAAxJFtKfQIAAGSFxvRTec+0KPin+V794hdrV7dE0HMK5nnBPS/Yp4yRnA7yAUAs6d/fbP58s0suMVPcLbea0BIlStgbb7yR4nNr1qxx5ZgBAAAAANkQ+DvqqKPcVepLly51493oflqdaHr+zz//TM/iAeQRmRnPCgCyw2eLNvrH9EuL/gcyd80e63J8xaBMvrwY5KNdBRBtpk0z+/RTs1atLM/Qb9HSGnwQAAAAAJA9gT+N6aeONP3gCrwPIHbo+92gQYNIbwaAOKEx+Q4cOOAv07lha2K6gn7utRr3L38Rq1evnuVltKsAolHNmmalSkV6KwAAAAAAORr40/gKqd0HAABILci3f/9+f5DP+3vo0CH/PMUK+DL50hP7U2ZgmWKF2OEAkANGjjS79VazceN8Y/wBAAAAAKILY/wBAIBsDfLt27cvWZDv8OHDyeZV9QCV51SZzrNOLGjfrl6ernUoM7DzCZU5agCQAzS23+7dZkqq1pB6oZXgt25ltwMAAABA1Af+vvrqq0wt/IwzzsjU6wDkPnXKr1ixImhcTwBIq93wgnxegE+Tgn/hgnxFihTxj8en2wr6eW1Nn0qH7PEvVtrOPQdTzfpTVmCpogXs7BOq5vmDQ7sKIBqNGZM760lMTLTixYtb/vz5c2eFAAAAABAn0hX4a9u2bYbG9FOHn+YPLOEFIO9Txz2A6Lf3wCGb/ut6+2zRRtu+e78ri9np+MrWpVFVK1Iwcx2sOqd7gb3AIF84CuZ5wb3AIF9q/5fQdo3q3cQGTvjREpLCl/x0r04wG9m7SabfR26jXQUQTQ4cMPvyS7OhQ3UhWM6uq2zZsjZhwgS76KKL3P3LL7/crrzySmvRokXOrhgAACCPerLLl5ZkSZbg+/ULADkb+Js1a1bm1wAAAHLNjMUb7aZJCyxxz0E3Fp7KYurvJ4s22PCPFrngWoeGldMM8oWW6lRmXzjK1AgN8hUqVChDFwx5tF3PX9rcbp60wHaEbL/+KtNvZDq2HwCQOSrr+e67vsBfTtO5IvDconHkO3ToQOAPAADEraIFS0R6EwDEU+CvTZs2Ob8lAAAgy0G/QRN+9KfLHQ75qzKayqhTcK3jf8GzgwcPBpXq1N8DSvkIo0CBAsmCfAULFsxUkC8l2q7v7uxgH/+23j79baNt37PfyhQt5Mb0U3nPaMn0A4Bo1b272fvvm914Y86u59hjj7UXX3zR6tSpY6VLl3aPrVy50n766adUX3fSSSfl7IYBAAAAQDwE/gAAQN4v76lMPwX9UhojT4+rjOaQiT/b5EvrW9LB/S7wF44CeoFBPk0K/OUGBffOb1rDTQCA3HXMMWb33Wf2zTdmzZqZFS8e/Pz112fPekaMGGF9+/Z1WX6ii0iGDh3qpnAYTgIAAAAA0ifTPXjKCnj33XfdFZk7duyww4cPBz2vH24vvfRSZhcPAAAyQGP6qbxnWhT827nvkH22eJO1q+srI6Lx9wKz+PRXJTwBAPFHP+HKlDGbP983BVKCd3YF/s466yxbsWKF/fDDD7Zx40a77LLLbNCgQdayZcvsWQEAAECU+XDpc7bnwE4rWrCknXfslZHeHADxFvhbtWqVtWvXzpViKVOmjAv8lStXzrZv3+7GBapQoYKVKEFNYgAAcppXqvOjn/+2fCrrmY7XaMy8n7ck2RUd6rpAX758eiUAAGYrVuTeXtBvyM6dO7vb48ePt969e1v79u05DAAAIC59tOx527pnvZUrWpXAH4DcD/zdcsstLtg3b948q1u3rlWqVMkmTpxop59+uj355JP21FNP2aeffpq1LQOQ68jwAfIulTjbv3+/fxw+/dXklercvGN3uoJ+3ph/uw+aFStWLEe3GbSrAKJb0n+1o7NxKNcUzZo1K+dXAgAAAABxIFOBvy+++MKuvvpqO+WUU2zr1q3+DkmVClNQcMmSJTZ48GCbNm1adm8vgByijJ/jjjuO/QvkASqf7QX2vEDfvn37kpXV9hQqVMjKlyhs+Tbvc0G99GT8lSlaKPs3HMH7mXYVQJR67TWzxx4z++MP3/369XXxp9mll+bsehMTE2306NHud6SqzEjt2rXtnHPOcb8vS5UqlbMbAAAAAADxGvjbvXu31alTx93Wjy+N56cMQI/GZbj55puzbysBAIhRytgLzeJTkC8cnW9VmtObNBafLrpRtm63XcXsy78WpmudCg52PqFyNr8TAEAsGDXKbOhQs2uvNTv9dN9jc+aYXXWV2ZYtZjfemDPrXbdunbVu3dqN+3fssce6ajKybNkyGz58uL322mv29ddfW9WqVXNmAwAAAAAgngN/tWrVsjVr1vgWUKCAVa9e3ZX97NGjh3ts8eLFrkMyNyxdutSuu+46+/bbb61kyZLWr18/e+CBB1z2AwAAGbX3wCGb/ut6+2zRRtu+e7+VKVbIOh1f2bo0qmpFCubP9A5Vtp5KdXrZe6GlOkMpmKfAXmCgT0E+Bf/C0fYN/2iR7dxz0FJL+tOrSxUtYGefQMcpACC5sWPNnn3WrF+/I4+dd57Z8cebDR+ec4G/2267zTZs2GBTp061Ll26BD338ccfu/H/br/9dnv11Vc5bAAAAACQ3YG/M8880z744AMbNmyYu3/ZZZfZiBEjbNu2ba5jc8KECS4Al9O0Pm3LMcccY++9956tXbvWhgwZ4jISNc4ggPTTd3flypXutjJ6VaIOiDczFm+0myYtsMQ9B105TGXG6e8niza4oNqo3k2sQ8PUM+VU+trL4gucUsriE12sEpjFp7+6sCalIF84Ckpq+wZO+NESkixs8M8tLcFsZO8mWQpiIn1oVwHI00/7ymZu2GDWuLEvsHbKKeH3zaJFZvfcYzZ/vpkqXY4ebTZ4cMaXuXev2U03mb39tplOP507mz3zjFnldCR7r19vdtppyR/XY//f3n2AR1VnfRz/JZQQagi9Ix0EpCkrqyAKiGUVC6iIFBXEBoIVLIBIERcWLCsrK7ZdhQ2u+oqKICuWFVFAdEFAQTpICxBKDJDkfc5/nDAJCYRkMi3fz/PcZ+7cuZn5587kZu4995xjjxWUefPmuXKeWYN+5rLLLtOQIUM0Y8aMghsAAAAAABTmwJ9dafntt9+6k5iWfTBy5EhXmmXOnDkuQ6F3796aYjViCtj06dNdH4h33nlH8fHxbpmdbLX+gzam6tWrF/gYgEhiQXOgMAf9Br2xNCNilpbl1jLpLKj20i3t1PX34J8Fdnyz97xTampqtq9hAXXfDD5vFp/97/QHC0ra+B5IWKEDWYKXdmuZfpNzEbyE/7BfBQq32bOl4cPtuEVq316aOtUThFu7Vqpc+eT17atYvXpSz545Z9bl5jntZ63dekKCVK6cp2ynFWf5739PP+YGDaR//UsaOfLk123YUAXm8OHDqnKKyGTVqlXdOgAAAACAU4tKt9SEMNWxY0cX8Hv33Xczlu3fv98tmzlzpstEzA0LHpYrV871KaRhPAorC2BYmV7TrFkzMv5Q6Mp7njf+k1yVySwdU0Tv9G+q9ONHc53F552KFSt2Rll8+fl9Plq5Qx+v3Kn9yUcVF1vc9fSz8p5k+gUO+1Ug8mzdmqRatcppy5YDqlmz7GnXt8DcuedK3mIkaWlSrVrSvffaxZSn/llrqW7Zflkz/k73nNZ6vVIl6c03peuv96yzZo3UtKm0eLH0hz+c+nXfflu64QapS5cTPf4sYLhwoScgeM01KhDt2rVz/yc/++yzk9o2HDt2zB372e3SpUsVzjj2BAAg9Px7bQGWNTgDA99rq8TkHYqPraYZVy8L6liubUx7ECCcjxvylPEXKqy/36233pppWVxcnGv4bo8BAJAb1tPPynuejgUFD6ak6qP/7VDneqXdMsvWyy6LL5jlci24d03rmm4CAATH0aOekp0jRpxYZv8aLKBmAbiCek57/NgxzzKvJk2sT3vuAn/XXSctWeIpM+q9vtKCht98I7VurQJjPf5uuOEGnXfeea6CS6NGjdzytWvXukovP/zwg2Zb2iEAAAAAoGACf1Zm5e2339Yvv/zieu1lTRy0jIZp06apINnrWqAvq/LlyysxMTHHn7MMDd8sDYueAgAKF/u/ZZkDVprz/eWbZWG6tFz8nK23fHea+neuk6defACA8HfwoB1DnLgfE+OZfO3ZI1nl56zVK+1+Xq9RzM1zWt8/S5jLephk69hjudG2rfSPfyigevbs6Y4xra3E4MGDM/632v/rypUru4ou13tTGAEAACJQvfLNVbFkdZWN8bS0AoCABv4WLlzoDsysrGZOAhH4y6sJEyZozJgxwR4GACBArP+rt/+etyef3VopRrM76Uiugn7G1ktOjVKZMmUKdMwAgNDVrFnm+6NGSaNHK2LYv8d166Rduzzzvjp2LLjXtVYNffr0ceU8N23a5JbVqVPHlQG1C20AAAAi2YiOrwV7CAAiRJ6Onu6++26VKlXKlVpp37590PriWWaf1TjNLhPQ+vzlZMSIERo+fHimjL9a1hgDABDWUlNTMwX2vME+W57TRSpWlrNC6RhF705RWi663kZHyfXMAwAUXtYWuUaNE/ezZvuZihWtHLS0c2fm5Xa/atW8vW5untNurSSoXaPpm/WX29f9+mupd2/J4m5Zu8FbEl4O/1L9xgJ8f/jDH9wEAAAAAAhQ4G/z5s16+umn1bVrVwVTkyZNTurlZ4HAHTt2uMdyYid5bQKQGeUKkV+/HUt1/fLmr9qp/UeOKq5kcXU7u4oub1HN9Z3zF8vUO3r06ElZfFa6MyfFixfP6L/nvbXJPvdXJ5XQZ798n7vXTpcubZ6lxhqQA/arQGSypO/TXfto5TatZObChVKPHp5llj1n9++5J2+vm5vntMeLFfMss359Zu1aO4aTzj//9K8xeLDUrp30wQdStWqeYB8AAAAAIMIDfy1btsw20y7QLrvsMo0fP96VHPX2+ktISFB0dLS6desW7OEBYcX+bs4+++xgDwNhbMGPO3V/wgolJR93WXEWILPbeat+1ej3V2lKz1bq0uzMAmbW18cCfFmz+Hz7tGaXKeAb4PPO22c8JxaYtDEeTD6uUyX92bnPsrFFdVnzamf0e6BwYr8KwIqM9OvnCaSdd540dar1SpcGDPBsm759PZmDEyZ47lumnmUTeue3bZNWrJBKl5YaNMjdc5YrJ912m2c9K4JiAcp77/UE/XKTRPfzz9KcOSdeDwAAAABQCAJ/lu130003qXv37q7fQrBY0/fnnntOPXr00MiRI7Vt2zY9+OCDbnn16tWDNi4AKIxBv0FvLJU3apaW5dYCagPfWKqXbmmnrtkE/yzAZ334fMtzeuftsZyCKtkF+PLSA8iyES0waWOMSs/4NTJxCQ9R0uSerfyavQgAiFw33CDt3i098YT0669Sq1bSvHlSld//FVoWnu91Kdu3S61bn7j/5z97pk6dpEWLcvec5i9/8TyvZfzZtTKXXir99a+5G3P79p7+fgT+AAAAAmvC5/2UlJKosjHx9PsDkC9R6TmdUT2Nf/3rX7r55pvVtGlT1x+viDWb8H3iqCi99957KmirV6/Wvffeq6+++kplypRR3759NW7cOFfSLbesx1+5cuVcFmOw+hUCQDiX9zxv/Ce5zpb76qGLpLTjGcE9b4DvdH34spbpLFasmN/LKFoA84GEFTqQJWvRbsvFFnVBvzPNWgQARI6tW603eDlt2XJANWtG5nHDO+9Ijz0mPfig1KKFp2yor5YtgzWyyMCxJwAAoeffa3coFAx8r60Sk3coPraaZly9LKhjubYxlY6AcD5uyFPG39tvv60+ffq4k7Rbt27VwYMHg9bTxgKPn3zySUBeC4hk1jPN+nea2rVrn7IsIuDLevpZec/TsaCgBdRmLvhOneuVzlUfPptsWaD+p1g24pKRXfTRyh36eOVO7U8+qrjY4q6nn5X3JNMPZ4L9KoBw5O0LeOutJ5bZv2G7XNRuc7hOBwAAAAAQIvIU+HvkkUfUuHFjFwBs1KiR/0cFICgOHTrElscZ+3jljoysuNOx8N3iLcnq1rh8RoDPN4svFALOFty7pnVNNwH5xX4VQLjZsCG4r//111/r008/1a5du3TXXXepYcOGOnLkiNasWeOOPUtbw0MAAAAAgH8Df9u3b9czzzxD0A8AChHfHny+JTq37TmQq6CfsdVSi5ZwF48AAIDQU6dOcF736NGjuvHGG127COtGYdn+f/rTn1zgzy4M6tatm4YNG6ZHH300OAMEAAAAgEgO/J177rkZJQEBAIUjwJdTD76yMUVcJl9uYn+WGVi+ZO57sAIAgMD7+Wfp00+lXbusbHHmx554omBe8/HHH9fcuXP14osvqnPnzpkuErLKAD179nRBQQJ/AAAAAFAAgb/nnnvOXX3Zpk0b9erVKy9PAQDI4rdjqa5f3vxVO7X/yFHFlSyubmdX0eUt/N9bzq6kt0Ceb3DvdAE+U6xYsZNKdF6XUk5fbfkhV69rmYHWLw8AAISmGTOkO++UKlaUqlb19PXzsvmCCvy99dZbuvPOOzVo0CDt3bs3297uCQkJBfPiAAAAAFDYA38333yzywi56aabNHDgQNWsWVNFimQ+KW2lWb7//nt/jRMAItqCH3fq/oQVSko+ntEvz27nrfpVo99fpSk9W6lLsyp5CvAdO3YsU2DPbq2c1pkG+HLqwXdFy+oaM/dHHUw+fsqsPztvWDa2qC5rXu2Mfw8AABAYTz0ljRsnPfxwYLe49fRr0aJFjo/b8ab1+gMAAAAAFEDgLz4+XhUqVHD9FgAA+Q/6DXpjaUatzLQstxZQG/jGUr10Szt1zSH4l5aW5oJ5vtl73smCfzkpXrx4RnDvdAG+nFg2ogUmbYxR6dmX/HTJAlHS5J6t/J69CAAA/GffPqlnz8Bv0Vq1amnNmjU5Pv7f//5XDRo0COiYAAAAAKDQBP4WLVrk/5EAQCEt72mZfhYtyyk8Z8stoPZAwgotfrizlObpwec7WdAvJ5aBbcE8b5DPG9yz+2cS4DsVy0a0wKSN8UCWrEW7tUy/yXnMWgQAAIFjQb/586XBgwO71Xv37q0pU6bouuuuU6NGjTK+w5gZM2boX//6lyZOnBjYQQEAAABAYQj8WXkVuxpzxIgReuCBBwpmVAACzgJAzZs3Z8sHmPX0s/Kep2PBPwuovTx/uTrXK53je+ibveedLMDnPXFWkCwbccnILvpo5Q59vHKn9icfVVxscdfTz8p7kumHwob9KoBwZEl1jz8uff21ZJU3ixXL/PiQIQXzuo8++qi+/vprdezY0fXzs+8uw4YNU2JiorZu3arLL7/c3QcAAIhUf2o8SMnHDiq2WJlgDwVAYQv8lSxZUkWLFnW3AIC8sxKc8/63PSMr7nQsdLd4S7K6NorLNsBn++ZABPhOxYJ717Su6SYAABB+XnpJKl1a+uwzz+TLvmYUVODPLlSaN2+e/vnPf2rOnDmuF7FVNWjZsqWeeuop3XLLLUH/ngMAAFCQrmpyBxsYQPBKfVr5FTsYu/POOzn4AoDTBPe8J668JTl957fvTcpV0M89l6TUoiXUpEkTtjkAACgQGzYEb8NaYK9Pnz5uAgAAAAAEMPB344036q677lLnzp01cOBA1a1bV7GxsSet16ZNmzwOC0CgpaWluTJKpmbNmn7r/RbIXnlWNnP+qp3af+So4koWV7ezq+jyFoEpMWnbzwJ5voE9b3DPAn85KVuiiMvky03szzIDy5cs7tdxAyg44b5fBQAAAAAAQCEJ/F100UUZ81988UW2GS52teapTnYDCD1JSUkKRwt+3Kn7E1a4Xnnespl2O2/Vrxr9/ipN6dlKXZpVyffr2L7t+PHj2Wbu2XQqxYoVy+i359t777qUOH21+ftcvb79XtYvD0D4CNf9KoDC69ZbT/34zJkF87oXX3zxKR+348sSJUq4CynsAtTrr7/elTkHAACIFMnHDild6YpSlGKLlQ72cACEsTwdKb3yyiv+HwkA5DHoN+iNpRkpc2lZbg8mH9fAN5bqpVvaqWsug3/e7L2smXt2a4/lxLJ5sgvu2W1OmT5XtKymMXNXuXGeKuvPsgLLxhbVZc2r5ep3AAAAyIt9+zLfP3ZMWrlS2r/fgnMFt03tO9a2bdu0fv16lS9f3lWVMRs3btS+ffvUoEEDlStXTkuWLNGMGTM0ceJEffLJJ6pYsWLBDQoAACCAhnzYSYnJOxQfW00zrl7GtgcQ2MBfv3798v6KAODH8p6W6WcRs5yCZrY8Kl16IGGFlozsklH207L3jh07dlLmnt3a8lOxYF52wT276tyuRj8TNh7LSLTgZFQOv4d7xihpcs9WASlbCgAACq933jl5mV33dOedUv36Bfe6Tz31lHr06KHXXntNvXv3VpEinu88VkXmH//4hx544AG9/vrrat++vVvHWk6MGDHCBQEBAAAAACfkuzbKoUOHtGXLFjdfq1YtlS5NGjKAwLCeflbe83QsmHYg+bje+nKNLq5XOqM0pwX/cmInm3yDe94An03+7tNlZUgtI9GCkweylCu1W8v0m+yncqUAAABnyr76DB9uLR+khx4qmO1ngb0BAwbolltuOek7mV14unLlSg0bNkyLFy9W//793e37779fMIMBAAAAgMIY+Pv222/10EMP6csvv8wofWcnwy+88EJNmjRJ7dq18+c4AeAk81ftzAiOnY5lzS34cZfOrXRiZcvO883e8w302UmmM83eyw8rQ2oZiR+t3KGPV+7U/uSjiost7nr6WXlPMv0AAEAwrV8vHT/99VZ59sMPP5wU9PNlpT9feOGFjPtt27Z1mX8AAAAAAD8E/qyvwkUXXeROkt9+++1q2rSpW7569Wq99dZb6tixoxYtWqTzzjsvL08PACc5fvx4Rqaetyzn9sQDuQr6GVstOS1a1apVywjyFStWLKDBvdOx4N41rWu6CQAAIBgss8+XFUjYsUP64ANr+VBwr2vf0ebMmaM777zzpOoKdqHpv/71L1WtWjVj2d69exUfH19wAwIAAACAwhT4e/TRR1WjRg2X7ed78GVGjx6tP/7xj26dBQsW+GucAAq4V95H/9uuhsU994e89Z0ublpFl7cIbKaZ9XDxDez5zttjWZUuGuUy+XIT+7PMwCpxpVWhQoUCGTsAAEAk+O67zPctBlepkjR5snTrrQX3usOHD9e9997rjiWtf1/93xsKrlu3zvXxs4ozzz77bMb6CQkJXGgKAAAAAP7M+HviiSdOCvqZKlWqaNCgQRo7dmxenhpAgC34cafuT1jheuXFFo1yGXTH0tI193+/avT7qzTFz73lsgvueSfL6juVokWLZuq1d0WrGH215adcva79XlY2EwACxTKKmzVrljEPAOHg00+D87p33323y/Sz40yrKuPdb1pPZrtwy4J+to6x75F/+ctfXPlPAAAAAIAfAn92QHaqE/R2Yj9reRYAoRn0G/TG0oyUueTjmXPnDiYf18A3luqlW9q5HnS5YSdnfMtyZp2yy9zzZb31fPvt+fbgy7pfuS4uXk9/8osb56my/uy0UdnYoq5XHgAEip20JuAHALlnZT4t6Ld06VJt2rTJLatTp47rH28l2r3se2GnTp3YtAAAAADgr8Bfhw4dXGP13r17uwMxX5s3b9Zf//pXV6IFQGiX97RMP4uY5RQ0s+VR6dIDCSu0ZGSXjLKfFtw7duzYSUE9u/rallsfltNl7nkDer6BPbu1wF9u2XgsI9GCk1E5/B7uWvEoaXLPVgEtWwoAAIAzZwG+888/300AAAAAgAAF/saPH6+OHTuqSZMmuuaaa9SoUSO3fO3atXrvvffcSf0JEybk5akBBMiH/9vhynt6FY2W7mnv6X/3/JK9Ov577M6CaQeSj+vNL1br4nqlXYDPgnsW/DvdSZvsAnu2/EyCe6djZUgtI9GCkzZO6+VnZT29t5bpN9nP5UoBIDfsIojt27e7+erVq1MNAQBywb5nrlmzRgcOHMj2YjI7DgUAAAAA+Dnw17p1a9fn79FHH9X//d//6ciRI255yZIl1b17dz311FMZPW0AhKb5q3ZmBMdMkagodalf2s2/+E2ifItnWtbcJ6t367zKJ37eytdlzdrzThbcC2S5XytDahmJH63coY9X7tT+5KOKiy3uevpZeU8y/QAEy/79+zMCfwCAnFmQb8SIEa56jPf4MjunKxsPAAAQrh658BUdTzuqotHFgz0UAIUx8GcssPfOO++4A7Tdu3e7ZZUqVeJqdiCE2N+nXTWdXVnObXv2ZwT9TsdW+y092p249g3uhVLvKgvuXdO6ppsAAAAQXqyqzDPPPKM77rhDF1xwgW655RY9/fTTiouLc8FA+945adKkYA8TAACgwNSPb8nWBRDcwJ+XZfVUqUIJPSAYrNymXfWcNajnDfTZbU7KFI92mXy5if1ZZmDlcqUVHx/v1/EDAAAgfLz+umSt3OvX9/9zv/rqq+rVq5defPFF7d271y1r27atLr74YvXr18/1/PvPf/6jLl26+P/FAQAAACCC5Dnwt2/fPr311lv65Zdf3HzWfl92RebLL7/sjzECKuxZe1kDer7T6Xrt+Zbk9O27d3W7Uvpqy4+5G0O6XNlMAAAAFF79+1sfZ2nQIOm55/z73Fu3btVDDz3k5q03tPntt9/crX137dOnj6ZMmeIyAwEAAAAAfg78ffzxx7r++ut1+PBhlS1bVuXLlz9pnVAqAQiEMgvc5VSO05YdP378tM9hAT3foJ5voK9o0aLZ/j1e3aaUxs37SQeTfbv5ncx+smxsUdcrDwAAAIVXWpq0YYP00Uf+f+4KFSro0KFDbr506dLuONMuMvVlF5wCAABEqqXbFuho6m8qXqSE2tXoGuzhAChsgb/7779fVatW1b///W+1aNHC/6MCIjiwl91tbkrqZg3o+c7b43npiTelZysNfGOponKI/LlwYZQ0uWcrtz4AAAAKt7POku66y//P27p1a3377bcZ9zt37qypU6e65VYB49lnn9U555zj/xcGAAAIEX9b+ogSk3coPrYagT8AgQ/8rVu3zjVeJ+gH+CewZ7IG9HynIkUKJujWpVkVvXRLOz2QsEK/HU3N1NNPv2f6WdDP1gMAAEBkSkrK/bplyxbMGAYNGuT6/KWkpLhSn+PGjVPHjh3dZN+3rcqMtZoAAAAAABRA4K9hw4Y6ePBgXn4UCNvAnjeIl5fAnpXa9C3Hmd18sMrjdm1WRUtGdtFHK7fr7//bpaTkY+rUuIrr6WflPcn0A4C8sf16kyZNMuYBIFTFxdl+6tTrWFtpWyf1xLVifnXVVVe5yatZs2Zav369Fi1a5C6C69Chg+Lj4wvmxQEAAACgsAf+nnrqKd19993q3bu36tat6/9RAUEM7GW9zWtgz/c2pz57ocKCe9e0ruUmAIB/2H7f9v8AEOo+/TTYI5A+//xzNW3aVJUqVcpYVq5cOV199dVufs+ePW4dywAEAAAAAOQsT2ejFi5c6A7I7MCsa9euqlWr1kmlCO1k17Rp0/Ly9IBfg3qpqakZATzfyRvYO378eJ4De975UA/sAQAAADnp1Cn428Z6+r3xxhvu4tKcjkHtMftuDwAAAADwc+Dv+eefz5ifO3dutusQ+EMgpKWlucBd1gw938nWyW1gL7tsvcIS2LPt9Ouvv7r5qlWrKjo6OthDAoCwxn4VQDg7ckTavFk6ejTz8pYtC+6CvVOx3n8F1fcaAAAAAFTYA3+5CaQABZWt5xvgy022nrGTBL799HwnW26PR3pgLzcSExMzAn8AAParAAqf3bulAQOkjz7K/nF/Jtxt3rxZGzduzLi/Zs0aV84zq/379+tvf/ub6tSp478XBwAAAIAIReMZBI0FkLPL0Mtrtl7WUpy+E9lrAAAAwOndd58F2qQlS6SLLpLeeUfaudP6vEuTJ/t3C77yyisaM2aM+z5v07hx49yU3QWBdqGeBf8AAAAAAH4I/B05ckQlS5bMzap+/VlEVlDPW5LTO+W2P4eV2cwpU89uydYDAAAA/OM//5Hee09q106yyu+WZNe1q1S2rDRhgnTFFf7b0r169VLz5s1dYM/mhwwZogsvvDDTOhYQLFWqlFq1aqUqVar478UBAAAAoDAH/mrVqqWhQ4dq4MCBqlatWq6eeNu2be6KzL/+9a/as2dPfseJEGIBu6xBvKzBvdwG9cjWAwAAAELH4cNS5cqe+fLlPaU/GzWSWrSQli/372s1bdrUTd7sv44dO+qss87y74sAAACEiRJFSyq2aGl3CwAFHvh78cUXNXr0aD355JP64x//qC5duqhNmzbuoKx8+fLuCs19+/Zpw4YNWrp0qT755BN9/fXXatiwoQv8IXz49tTLKbiX2x6PVl7TMvJyytjzluCktx4AAAAQGho3ltaulerWlc45R7LqmjY/fbqUy2tA86Rfv34F9+QAAABh4Lkrvgj2EAAUpsCflV25/vrr9X//93969dVXXd+Fo0ePnhSwsQCglV/s1q2b5syZo6uuuoreaiHC3htvIC+n27wE9bxTdsE9K8EJAAAAIHwMHSrt2OGZHzVK6t5d+uc/peLFpVdfLdjXXr16tcv8++WXX9yFpXYM48uOPxcuXFiwgwAAAACAwhD48wZ6evTo4aaUlBQtW7ZMa9as0d69e93jFSpUUJMmTdS2bVvFxMQU5Jjhww6GfUtvnuo2t7IG9bIL7hHUAwAAACJPnz4n5tu2lTZtktaskWrXlipWLLjXfeONNzRgwAB3rNG4cWNXWSarrIFAAAAAAEA+An++LLDXoUMHN6HgWPbd6TL0bP5MDoC9wbust77BPYJ6hZNdQd3IGrj8Pg8AYL8KoPA6elTasEGqX19q06bgX89aS7Ru3VofffSRKhZkhBEAAAAAIlyeAn/If0DPAna+gbyswbwzKbtpLFiXXTDPd5lNBHSQE/tsWKleAIB/sF8FEI6OHJHuvVd67TXP/Z9+kurV8yyrUUN65JGCed3t27frgQceIOgHAAAKrddWPKnDRw+oVPFy6tfqiWAPB0AYI/BXACU3swvq+S47k4CenTQ8VTDPe2vlOQEAAAAgP0aMkL7/Xlq0yNPfz6tLF8vKK7jAX8uWLV3wLxQcOnTItbHYtm2bvv32W7Vr1y7jsZdffllPP/20Nm/e7EqSjhs3TldeeWVQxwsAACLDl5veU2LyDsXHViPwByBfCPzlIqCXUyAv6/0zKblpAT1vFl5OwTy7tYAeWXoIBAtI79q1y81XrlyZYDIAsF8FUAi9+640e7b0hz/YMcuJ5WefLa1fX3CvO2XKFPXs2VOXXXZZ0FtKjB07Ntse6bNmzdLAgQP16KOP6uKLL9bs2bN1zTXX6IsvvtAfbIMBAAAAQAgg8Odj586dSkpKyhTYsyy+M+EtuZk1qJf1PgE9hKI9e/ZkBP4AAOxXARQ+u3fbd8GTlx8+nDkQ6G+WRVeuXDldeOGFatasmWrXrn1S73G7IPK9994ruEFIWrNmjV544QVNnjxZgwcPzvTYqFGjdOONN7rAoOncubN++OEHPfnkk/rwww8LdFwAAAAA4NfAnx3M1KlTxx2IRbK9e/eqdOnS2T52ukCed6LkJgAAAIBwZVUtP/jA09PPeIN9f/+7dP75Bfe6dsxpgT0L+FmpzR9//PGkdQJRCeXee+91AT8r4+nrl19+0U8//eQClL4sEPjggw8qJSVFMTExBT4+AAA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"text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -1507,7 +1461,7 @@ "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", " # 1. State preparation\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", "\n", @@ -1515,13 +1469,13 @@ " invert(lambda: qft(x))\n", "\n", "\n", - "pc, df = run_standard_simulation(main)\n", - "analyze_results(pc, df, p)" + "df = run_standard_simulation(main)\n", + "analyze_results(df, p)" ] }, { "cell_type": "markdown", - "id": "42", + "id": "40", "metadata": {}, "source": [ "Conversely, if $l$ is too large and the function deviates significantly from linearity, the success rate drops dramatically." @@ -1529,57 +1483,36 @@ }, { "cell_type": "code", - "execution_count": 12, - "id": "43", + "execution_count": 11, + "id": "41", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "Exception in callback Task.__step()\n", - "handle: \n", - "Traceback (most recent call last):\n", - " File \"/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/asyncio/events.py\", line 88, in _run\n", - " self._context.run(self._callback, *self._args)\n", - "RuntimeError: cannot enter context: <_contextvars.Context object at 0x108829c40> is already entered\n", - "Task was destroyed but it is pending!\n", - "task: .run_in_context() done, defined at /Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/ipykernel/utils.py:57> wait_for= cb=[Task.__wakeup()]> cb=[ZMQStream._run_callback.._log_error() at /Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/zmq/eventloop/zmqstream.py:563]>\n", - "/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/pandas/core/internals/managers.py:932: RuntimeWarning: coroutine 'Kernel.shell_main' was never awaited\n", - " def __init__(\n", - "RuntimeWarning: Enable tracemalloc to get the object allocation traceback\n", - "Task was destroyed but it is pending!\n", - "task: cb=[Task.__wakeup()]>\n" + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/861fff75-1d5e-4d4f-998c-c126cfc16937\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed counts: [{'x': 2}: 548, {'x': 1}: 519, {'x': 0}: 455, {'x': -1}: 169, {'x': 3}: 140, {'x': -2}: 83, {'x': -4}: 76, {'x': -3}: 58]\n", + "Parsed probabilities: {0: 0.2568359375, 2: 0.255859375, 1: 0.22607421875, -1: 0.087890625, 3: 0.08642578125, -4: 0.03466796875, -2: 0.02880859375, -3: 0.0234375}\n", "The analytical gradient is: 0.25\n", - "The majority gradient is: 0.5\n", + "The majority gradient is: 0.0\n", "The majority result is incorrect\n", "####################################################\n", - "Success rate: 25.34% (519/2048 shots)\n", - "[\u001b[92m█████████████\u001b[91m-------------------------------------\u001b[0m] 25.34%\n" + "Success rate: 22.61% (463/2048 shots)\n", + "[\u001b[92m███████████\u001b[91m---------------------------------------\u001b[0m] 22.61%\n" ] }, { "data": { - "image/png": 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", - "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -1600,7 +1533,7 @@ "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", " # 1. State preparation\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", "\n", @@ -1608,21 +1541,21 @@ " invert(lambda: qft(x))\n", "\n", "\n", - "pc, df = run_standard_simulation(main)\n", - "analyze_results(pc, df, p)" + "df = run_standard_simulation(main)\n", + "analyze_results(df, p)" ] }, { "cell_type": "markdown", - "id": "44", + "id": "42", "metadata": {}, "source": [ - "# 3. Performance Analysis" + "# Performance Analysis" ] }, { "cell_type": "markdown", - "id": "45", + "id": "43", "metadata": {}, "source": [ "We can plot the success rate as a function of parameter choices. Consider a quadratic function $f(x)=0.6x^2+0.25x+0.1$ with $f'(0)=0.25$, and target accuracy $\\epsilon=0.2$.\n", @@ -1642,55 +1575,268 @@ }, { "cell_type": "code", - "execution_count": 13, - "id": "46", + "execution_count": 12, + "id": "44", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "Exception in callback Task.__step()\n", - "handle: \n", - "Traceback (most recent call last):\n", - " File \"/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/asyncio/events.py\", line 88, in _run\n", - " self._context.run(self._callback, *self._args)\n", - "RuntimeError: cannot enter context: <_contextvars.Context object at 0x108829c40> is already entered\n", - "Task was destroyed but it is pending!\n", - "task: .run_in_context() done, defined at /Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/ipykernel/utils.py:57> wait_for= cb=[Task.__wakeup()]> cb=[ZMQStream._run_callback.._log_error() at /Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/site-packages/zmq/eventloop/zmqstream.py:563]>\n", - "/Users/ofriwienner/miniconda3/envs/classiq/lib/python3.12/contextlib.py:108: RuntimeWarning: coroutine 'Kernel.shell_main' was never awaited\n", - " doc = getattr(func, \"__doc__\", None)\n", - "RuntimeWarning: Enable tracemalloc to get the object allocation traceback\n", - "Task was destroyed but it is pending!\n", - "task: cb=[Task.__wakeup()]>\n" + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/64786f4d-1f4d-40a7-b765-55c7d43158d4\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=0.05: Success rate = 0.00%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/78894643-1276-424a-a72c-cf13692576f8\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=0.1: Success rate = 0.00%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/d300a547-f71f-4325-9e0a-62ccead9a116\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=0.33: Success rate = 1.03%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/c30dfefe-a80c-49ad-aecd-64f8164e8073\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=0.5: Success rate = 10.30%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/0d4f1fd7-7e49-4965-bd6f-e03b80c8e309\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=0.67: Success rate = 94.04%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/3404a3a7-9c6c-4616-85e7-c35403d69f66\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=1.0: Success rate = 99.32%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/a7b9310c-4550-4434-afd6-60d25b2d4d18\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=1.33: Success rate = 81.64%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/0d3adfc7-9241-4006-ab2c-51ff941ba9d2\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=1.67: Success rate = 95.17%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/441d37c7-5e03-426f-bf01-b3756b2d6626\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=2.0: Success rate = 98.44%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/b09d5b05-d3e8-4370-a00b-c9ccddcb9c63\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=2.33: Success rate = 89.89%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/1e7c5ebc-d2a9-4568-ae25-6fa24c15c10f\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=2.67: Success rate = 79.10%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/a8af23be-90bd-4b3a-88cd-b6224b73b08e\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=3.0: Success rate = 65.04%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/f82c64db-2fc7-40af-8262-81267506bc24\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=3.33: Success rate = 55.22%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/312ee63b-47e3-49e0-b3b4-41525e295b84\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=3.67: Success rate = 0.00%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/91ab61b0-0a9a-47d6-944c-012e90bd2cf6\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=4.0: Success rate = 0.00%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/bfcb2c83-b94d-4220-a35f-52b74e3cac5a\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m=6.0: Success rate = 0.00%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/e33663f4-7960-45fe-ab00-d0df1c063290\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "m=0.05: Success rate = 0.00%\n", - "m=0.1: Success rate = 0.00%\n", - "m=0.33: Success rate = 0.93%\n", - "m=0.5: Success rate = 10.45%\n", - "m=0.67: Success rate = 92.72%\n", - "m=1.0: Success rate = 99.32%\n", - "m=1.33: Success rate = 81.74%\n", - "m=1.67: Success rate = 93.99%\n", - "m=2.0: Success rate = 98.93%\n", - "m=2.33: Success rate = 90.97%\n", - "m=2.67: Success rate = 79.00%\n", - "m=3.0: Success rate = 64.65%\n", - "m=3.33: Success rate = 56.59%\n", - "m=3.67: Success rate = 0.00%\n", - "m=4.0: Success rate = 0.00%\n", - "m=6.0: Success rate = 0.00%\n", "m=10.0: Success rate = 0.00%\n" ] }, { "data": { - "image/png": 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D+c8AgNI+ADFFS9guvfRSM0GojtvQAeQ6tkEvqvRCX0u4tKxN533y0IBJs0ZHH320KfvSwf8aGGjA5Rno7uv22283QY2WhOm/Oimubk8n59QGF3ph6RmjpON6NAukc+Lo+pql0cBGgyXdJ89EuzqWSMvGdOyTDu7XDJNOHKxjTDxBns69o9v3TB6rg++1+YHOt6TZNn1dbXCh42R0udJxUDqfjjaY0DE9evGvAY4O0NeSPi3Jay1tAKHNOyZNmmReS4+xXuhq5kvfi86voyVY+tnoxbd+Jg1plkezW3qctMRKM4e6rgY4emy15EqPs84DpOtqSaG+Z7341c9VM0aBNhdQul2dA0nLDPXz9jcnlGagNFOhx1P3RS+w9bzQbJTOk+QJJKKFvmc9HzT40M9J91/n7tJzQSfu1dLQSG4vGPqHEP091gBIs8T6u9uvXz9T5qq/h/r7otlZHT+o9HdJzzsdG6fnk47Z0/NH911Ld7XJhP5e6NxXWv6rvy/6BwH9Y4eW2+r70j9KME8UgHoi3TYQAMJpxYoVrvvvv991+OGHu/r27etKTU01N21trC2LFyxY4PfndB4knftG54vRds9XXnmlmQ/H3zxSqqqqysxTM3z4cDM3kbax1vmJdI6p7du311tX57+5+uqrXbvttpvZfpcuXVyjR482Lc/97b+2sdbX1HW1LbPul7Z7nj9/vne9V1991bTs1veVnp5u2rHrnDo6P5Hv/E0zZsxwTZgwwbXnnnuatu2e/dR5cwoLC1s1j5Qvz3xZs2bN8s7/c9ddd7n69+/vSklJMa3S9dg0d0z1c9P1k5KS/Lak//33381x9GxT26gPGDDAddFFF3lfN1DaflxbpuvraEt0f5544gnX8ccfb/ZVz6GuXbu6Ro0a5XryySfN+wtEU++1ubb7njbher62Zh4pf7S9+xFHHGHOKz0f9PVnzpzpeu6558w29N9g9iNc22uuPbm/bXno78Sf//xnV48ePcx5o1MEaNv6G264wbV8+fJ6686bN8/sn+6nZ1oE33b7OifcU0895Ro7dqw5tzzn7ZFHHmk+87KysoDa9QOwjzj9v/qhFQAAAACgOYyRAgAAAIAgEUgBAAAAQJAIpAAAAAAgSARSAAAAABAkAikAAAAACBKBFAAAAAAEyfYT8jqdTjOpZYcOHczkfAAAAADsyeVymcm9dRJvnWC+ObYPpDSI6t27d7t9OAAAAACsbcOGDdKrV69m17F9IKWZKM/BysrKkkhkxAoLCyUnJ6fFqNcKHLUO+Sn/J0lMSJTkhORI746t/1pSWVQpaZ3SyKSGSXVdtdTW1cqQvCGSkpgisSbavmtgDZw34JyB3b5rSkpKTJLFEyM0x/aBlKecT4OoSAVSVVVV5rUjfeIEGkhlVGRIRnIGgVSEA6kyZ5lkdsokkApjIFVeXW5+F2M1kIqm7xpYA+cNOGdg1++auACG/FhjTwEAAAAgihBIAQAAAECQCKQAAAAAIEgEUgAAAAAQJAIpAAAAAAgSgRQAAAAABIlACgAAAACCRCAFAAAAAEEikAIAAACAIBFIAQAAAECQCKQAAAAAIEgEUgAAAAAQJAIpAAAAAAgSgRQAAAAABIlACgAAAACiOZCaM2eOHHfccdKjRw+Ji4uTd999t8WfmT17tuyzzz6SkpIiu+++uzz//PPtsq8AAAAA7CtRLKS8vFyGDRsmF154oZx88sktrr927Vo55phj5NJLL5WXXnpJZs2aJRdddJF0795dxo8f3y77jPCrrnXKnJVl8u2vZVJS5ZSs1HjZv3+mHLRnpiQnWir2BwAAgE1ZKpA66qijzC1Q06ZNk759+8pDDz1kHg8YMEC+/vpr+de//kUgFaXmriqTB6bnS5nDKXFxIi6XmH+//rVcnphVKP84Ok/G7J4pdg8yv/m1TIpKa6RTh1IZS5AJAABg70AqWHPnzpVx48bVW6aZqL///e9N/ozD4TA3j5KSEvOv0+k0t/amr+lyuSLy2q3ZX88tnOauKpcp727yPvZs3vNvucMpk9/ZJLed2F3G7J4hdqPH58GPGwSZ+dXyjU+QuV8/+x2XcPGc05H6Lmhr0fZdA2vgvAHnDOz2XeMMYh+iOpDavHmz5OXl1VumjzU4qqyslLS0tEY/c88998iUKVMaLS8sLJSqqiqJxIdVXFxsTp74eOuXrdXU1Yij2CFxiXFSHV8dtu1W17rkgekF5n5T4ZkujxORB6Zvlv/8OVeSE/WRPXy/vkrum1nUYpD5z3GdZN9dUiO0l9Gt1lkrjlqHbInfIkkJSRJrou27BtbAeQPOGdjtu6a0tNQegVQobrzxRpk4caL3sQZdvXv3lpycHMnKyorIiaONNfT1I33iBEIvNDc6N0p6crokJySHbbszl5VIeXXLGS5dQ9dbvEXkTwMzbVPO99hXgQWZj31VIq/8rQtjyUI5znXV4qp2SXZOtqQkpkisibbvGlgD5w04Z2C375rU1FR7BFLdunWT/Pz8esv0sQZE/rJRSrv76a0h/dAi9cHpiRPJ1w+G7qPur+cWzrI1T7laS3Q9bUQxblD7B76R8NUv5aacryV66HQ9Xd8uxyacPOd0tPwuhiLW3x/aBucNOGdgp++a+CBeP6r/azpmzBjTqc/XZ599ZpYjumh3vkCHXOl6ur5daNAYaMzqCTIBAADQtiwVSJWVlcmSJUvMzdPeXO+vX7/eW5Y3YcIE7/ra9nzNmjVy/fXXy4oVK+SJJ56Q119/Xa655pqIvQeERlucBxMs6Pp2QZAJAABgPZa6Gl2wYIHsvffe5qZ0LJPenzRpknm8adMmb1CltPX5Rx99ZLJQOv+UtkH/z3/+Q+vzKKTzRAWTkdL17YIgEwAAwHosNUbqkEMOabal9vPPP+/3ZxYvXtzGe4a21j8vsMH9mrTKSIk3k/Paxeh+GWYerUDYLcgEAACIFEsFUrCnymqn3PPh5hbX81T+6XxJyYmWSqa2maoap8xeHlgbTjsGmQAAAJFCIIWI0gzk1Bn5sqbQPSdV18wEqapxmXmRGnbx0yBBg6gxu9sjUCirqpNb3/5Dlm0MfH4zOwWZAAAAkUQghYh6ff52+XKlu8tcenK83Hd6L+nWMVHmrCwz3eeWbqySooo68/z1x+TJfv3sEURtK6uVm97c6A0w9dicMbqzvDF/u2lx7q9V/LBd0mwTZAIAAEQagRQiZv6acnl2zlbv438ekye7dHVP8qvzIOntyxWlctcH7rK/hb9V2CKQ2lxcIze8vlH+KKoxjzumJ8jdp/aQ/nmpcsrITibI/ObXMikqrZG01ET5cUOlVNe5ZMn6SvludbkZUwUAAIC2RQ0QImLj9mozLsqTVJkwtovfbMrIvuniqVSbt7q82WYksWDdFodc8/IGbxCV0yFR/nVmLxNEKS3b0wBz0gnd5faju8hdp/aQy8fleH/+4U/zpbTKncEDAABA2yGQQrurqHbKbe9sMuOg1AH9M+SsMV38rpuRkiBDeqeZ+/nFtfLbFnepWyxasalKJr7yu2wtcwdCvbskyb/O6iW9urizdE05ckiWjOyTbu7rz077vLBd9hcAAMDOCKTQrpwul9z/0WZZv9UdEO2anSzXHd1N4puZjde3nE+zUrFo0W8Vcv1rv0tpldPbDv6hM3tJblZSiz8bFxcnfx+fa8ZRqc+WlZoSPwAAALQdAim0q5e+3SbfrnJf5GemxMvkE7t7A4Cm7Ocz5mfejp+NJV//Uma682m3QjWsd5rcf0ZP6ZQe+BBGDbj+emi29zElfgAAAG2LQArtRrvwvfjtNveJFydy03HdpGfn5svWVPdOSdInO9lb/ra9vFZixYyfiuXO9zdJTZ07iBqze4YZ96QljcEyJX59KfEDAABoDwRSaLcmCvd9tHPS3QsPypaRfQPvLufJSmm48d2a2MhKvfn9dpk6o0CcO/pnjBvUwTSRCHUeKC3xu4YSPwAAgHZBIIV2mVh28rubpHJH6dohe2XKaft2CmobmqmJlfI+7Tz43Fdb5OnZW7zLThrRSa47Kk8SNFXXCjkdkuTSw3aW+P3rE7r4AQAAtAUCKbSpOqfLtDnfuN3dzrtfbopMPDLPZE+CsWf3VOmU7i53W7iuQqpr3U0ZovF4PPpZobwyb7t3mbZ+v/TQ7GYbbgRj/OCdJX7byuniBwAA0BYIpNCmXvh6q3y/tsLc75iWILed2F1Sk4I/7TTIGL2bOyvlqHFPPhttdBzUvR9tlg9/KPYuu/xPOXLO/l2DDiybQ4kfAABA2yOQQpv5ckWpvPqdO/OiFWs3H99NunVsuZ13U/aLgvI+zZTNXFYit7/7h1z36u/mX31cUlkrk9/5Q75cUeY9Hv88Jk9O2Ce4EsdAUeIHAADQtgLvrwwEYU2BQx6cke99/NdDc2T4Lu5ys1Dts2u6JCXEmcyOzid1pcsV1kxOa81dVSYPTM+XModTdLdcLs0OiXz9a7kJnDxNJZIT4+SW47vVmx+rLWiJ31cry0xGUEv8nvy8UK4/ulubviYAAIBdkJFC2JVUanOJP0wJnjp8UAc5cZ+Ord5uWnK8DN8lzdzfUlYrqwocYqUgavI7m6Tc4R67pUGU77++QdTdp/Zs8yDK30S9M5eVmv0EAABA6xFIIezNFO56f5NsLnbP9bRntxS5+ojcsGWOrNi9T8v5NBOldsRLTUqIF9mre4q0l4Ylfo98WiClVXXt9voAAACxikAKYfWfL7fI4h2NIDqnJ8ikE0OfF8mf0Tvmk1JzV1sjkJqzssyU87UURKnKapdZvz1pid++Pl38tMQPAAAArUMghbDRpgpvLSgy9zV20sllNSMSTrq93XPdGZ1V+Q7ZUurOfEXSt7+WmbFQgdD1dP325Cnxy0ihxA8AACBcaDaBoFXXuuS7VWUyf3WVlFQ5JSs1XnbLTZFX5m3zrnPZn3JlUC/3eKZw0+59nvFR2nTi2OGtH3/VGnoMPGOhWqLr6frtzZT4HZotD80o8Jb4De6VJh1S3XNzAQAAIDhkpBCUWcsL5dLntsnUGVvlm1Xl8uOGSvnm13L53zfbpGbH0Jujh2a1aXCzn09537zVkW+eoIFkMBkpXT8SjmhY4jeLEj8AAIBQEUghYJ/9nC+Xv/yDlDtc9TvTNVhvRN+dgU5b6J+XIl0z3ZmUxesqpbK6/TM8vvbvnxlURkrXj4RGJX4/08UPAAAgVARSCEhVTZ1c+8aSltvSici/ZuSbTnZtGRB4slI6p9TidRUSSQftmSmZKfHSUlJKn9f1dP1I8ZT4eWiJn7arBwAAQHAIpBCQ6T9tkpLK2oA602kHu7buTOc7D1Oku/dpV8J/HJ3X7DqeIEvXC2cXw1BL/EbttrPEbxpd/AAAAIJGIIWAfLosX+It1JlOJ+ZNSXTv0PzV5eIMtLaujYzZPVP6d9s5P5TnUHnGTmk53eSTupv1Is2U+B2RR4kfAABAK9C1DwEpqqgWp4U606Ukxcs+fdJl7qpy2V5RJys3OWRAj1SJlA3bquWXze5Ogh1S42VIrzSTmdPGEjomSsv5Ip2J8pXdIVH+dliOPPhxvrfEb1DPNMlKo4sfAABAIAikEJBO6ckmIxVIMNVenel0nJQGUp7ufZEMpN5esN17/8+ju8hpozqL1R0+qIPMWVkq89dUmBK/x2YWyKjdMkw20dPW3opBIAAAgBVwdYSAHDEoL6iMVHt0phu9m08b9B0BVSQUV9TJZ8tKzf20pDg5eliWRIOGJX6zV5TJ/dPzd7a1X1VuHv/5ibUyd1Xk28wDAABYCYEUAnL0kO6SlZZoqc50XTITZa/u7izU2i3Vsrm4RiLhwx+KzSTF6sihHSUjJXrK47TETzNTvrxt7Xf8W+5wyuR3NhFMAQAA+CCQQkBSkxJk6mnDd3ZRsEhnuvqT87Z/VkrbvL+/qMjc19LHE/fpJNFE93/mjmxaUzyJyAemt21bewAAgGhCIIWAjRuYJ4+fNUwyUvxHU5HoTFcvkIpAed8Xy0tNsws1tn+mdO+UJNFE29RrU4yWuNqprT0AAEC0IJBCUP40IEemXdBFztqvo3eZBg/XH50nr17Wt93be/fNSZa8LHfPlB83VEi5o/0ml3W5XPLWAnc2Sp26b3Rlo5Q2lvC0aLdCW3sAAIBoQSCFoCUnxsnQXXZ2yDtwj0wZNygrIp3dtGGCJyulVWcLf6tot9detK5CfttSbe4P7JEqA3qkSbTR7nwuC7W1BwAAiBYEUgiJY0dzBU9gFUmjI1Te99b3O7NRJ4+MvmyU0hbnwWSk2qOtPQAAQDTgqgghqbFQIDW0d5qkJ7tP5flry6Uu0D7trbC20CELdmS/8jommvFR0Ujb1Lss1tYeAAAgGhBIodUZqZQIB1JaUjiiT7q5X1LplJ//qGrz13xnoU82akQnSdCWfVFI29Rru3ortbUHAACIBgRSCElN3c5AKikh8qfRmN3br7xve3mtzPrZ3TJcM2Hjh+xsvBFtNAjVdvWqpWCqPdvaAwAAWB1XRQiJZwJaK2Sk1KjdMsw8Tmre6rbtLPfB4mJvIHn0sCxvWWG00k6L2rZe29erhmOm9Li2d1t7AAAAq4vuK0BYIpCK9BgplZWWYDrnqQ3bamTjdnc3vXBz1DjlgyXFUTsBb1M0SNL29drGfuzuGTK0V6qkJ7s/Vx1y1iE1IdK7CAAAYCkEUoiJQErt55MxmdtG5X1a0ldc6Z6r6uC9MiU3K7om4G2Olu1pG/tJJ/aQB8/sLZf/Kdf73Bvfb4/ovgEAAFgNgRRiJ5DyaYP+3erwB1JOMwHvzoDilJGdJZYdMqCDZGcmegPT9VvbJssHAAAQjQikEIYxUtY4jXp3SZIendwZop9+r5TSKnfmKFwWrK0wZYNqcK9U2aPbzkmJY1FSQpycNGJn6aJvEAkAAGB31rgCRtSprrNeRiouLs7bvU/H9Xy/JrxZqbd8yttOjfFslIdvM42Zy0plW1ltpHcJAADAEgikEDOlfQ3L++aFsbxvdYFDFq+vNPc16zXa53ViWUZKghwzzN3eXTsVvrd45/xZAAAAdkYghdYHUgnWCaQG9UwzE8eq79dWSK1P5qw1fMvaonkC3lBoeZ+nelNbv1dWOyO9SwAAABFHIIXWj5FKss5plJgQJ/vu5s4WlTucZqxUa20tq5XZy90T8HZIjZfDB2eJnWR3SJRDB3Qw98scTvn4R3f7dwAAADuzzhUwonaMlDYlsJJwl/e9v7hIanckYbTMLS3KJ+ANxan77hwT9vbCorBl+gAAAKKV/a4IERbVnsjCdO2zViC1b990SdhxZs9bVS4uV+gX/VrG9uGOCXi1vO2EGJmAN1h9c1Jk1G7p5n5BSa3MWenO0AEAANgVgRRCUu3TvC3JYoFUZmqCDOmVZu5vKq5p1fxHny0rkdIqd9B4yF4dpOuOeZXs6DSfrNQb3xe1KkAFAACIdgRSaFVGSsv64uOsFUg1LO+bG2J5n07A+/aCIttMwNuSob3TZI9uKTu7GK5r/fgzAACAaEUghVaNkbJS6/Mmx0mtCi2Q+m51ufxR5J6Ad/guadIvzx1E2JXO01U/K8UEvQAAwL4IpNCqrn1WGx/l0aNzsuzaNdncX/5HlRRVBD+R7Jvfk41q6IA9MqVbR3d548LfKkxmCgAAwI4IpNCqQMpq46P8ZaV0T+evqQjqZ3/ZXOVtnd6rS5Lsu6PRgt3p/Fm+JY5vkpUCAAA2RSCFVmakrHsK1S/vKwvqZ99qMDbKiuPAIuWIwVlmPi01e0WpFJS4yx8BAADsxLpXwYiKQCrZYnNI+dqrR6p0TEsw9xf8VlGvZXtzNDDwtPfOSouXcQPdk9HCTefROn5vdxv4OqfIOwt3Bp0AAAB2QSCFoDmdLu8EtVZtNuEpQ/PMfVRV45IfNgTWZe69RcUmQFDHDe8kKUn8mjR0/N4dvZ/99B+KpayqLpwfHQAAgOVxhYigVftcM1s5kAqle19FtVOm/1jsbe2uAQMa65yRKIcPcmfqKmtc8uEP7mMGAABgFwRSCFrNjrI+K3ft8xjRN8MERGre6vIWJ5H95KcSKXe401GHDexgAgb4d+q+ncXz6b+7sCjg0kkAAIBYQCCFkOeQUkkWbjah0pPjZVjvNHO/sLRW1hRUN7lundMl7yzcOTfSySPc44DgX8/OyTK2vzvjt628Tj5f7h5XBgAAYAfWvgqGJdX4TMlk9YxUw/K+uaub7t737a9lsrnY/eZG9EmXvjn2noA3EKeN8m2FXiTOFjJ+AAAAsYJACiF37IuGMVJqv913BlLfrS4PsOU52ahADOiRJoN7ppr767dWy/w1LY9DAwAAiAUEUmhVaV80BFK5WUmyW06yub9ys0O2lvmk1HZY/kel/PxHlbm/a3ayyUgh+KzUG/NphQ4AAOyBQApBq/aJQ5ITouMU2m/3zGazUg2zUXFMwBuw0f0ypHeXJHP/p98rZcUmd0AKAAAQy6LjKhiWUuOTkYqGMVJqjG8b9AaB1ObiGvn6F/fYqc7pCXLYACbgDUZ8XJzp4OfxxvydDTsAAABiFYEUWjVGKilKAqn+3VKkS0aCub9oXYVU1exs1a2tu5073tJxZqJZfi2C9SdtFZ/uPr7f/Fomf2xvujsiAABALOCKEUGr8ZmQN1oyUpo10RI0TyC4eF2FuV/uqJMZP5V4x3sdO5wJeEOhweeJO9rFa1DqWyoJAAAQiwikEPNd+/y1QfeU9338Y4lUVLuzU+MGdpBO6UzAGyoNQlOT3OfDJ0tLpKiicVMPAACAWEEghVaNkYqmMri9d02XJHf1mcxcViLXvrJBnv96q/f5k0fuHOeD4HVITZCjhnb0BtvvLy7mMAIAgJgVPVfBsGbXvijKSGk5n2cslJYn/vR7lTe7ps0HNzKup9VOHtFJ4necEu8vLqo3Fg0AACCWEEihVaV90TJGau6qMpn8ziapa+K6Xpfr87oeQpfXMUkO3svd9bCk0imfLnWPPwMAAIg1BFJoVWlfUoL1A6nqWqc8MD0/oHV1PV0foTvdpxX62wuKpM6TBgQAAIghBFJoVWlfSpL1T6E5K8ukzOGUli7n9XldT9dH6Prlpcjeu6aZ+38U1Zh26AAAALHG+lfBsHbXvijISH37a5nEBbibup6uj9Y5zXeC3u+3i8tFVgoAAMQWAim0smuf9QOpkiqnBHodr+vp+midEX3SZbecZHN/5SaHaewBAAAQSwikEPNd+7JS44PKSOn6aJ24uDg5tUFWCgAAIJZwxYhWZaRSomAeqf37ZwaVkdL10XqH7NVBcjq4Jzj+bnW5rNvi4LACAICYYf2rYFh7jFQUZKQO2jNTMlPipaU91ed1PV0frZeYECcnjejkffzmgiIOKwAAiBmWC6Qef/xx6dOnj6Smpsro0aNl/vz5za7/8MMPy5577ilpaWnSu3dvueaaa6SqivEYbUkns42mQCo5MV7+cXSeud/U3nqW63q6PsLj6GEdJSPFfTxnLSuRrWU+daEAAABRzFJXjK+99ppMnDhRbrvtNlm0aJEMGzZMxo8fLwUFBX7Xf/nll+WGG24w6y9fvlz++9//mm3cdNNN7b7vdhJtGSk1ZvdMmXxSd+9FvWfMlOdfXa7P63oIn/TkeDl2WEdzX6fnenchWSkAABAb3AMYLGLq1Kly8cUXywUXXGAeT5s2TT766CN59tlnTcDU0Lfffitjx46Vs846yzzWTNaZZ54p3333Xbvvu51U7xgjpZPxxgfaxcECNEh69bJ0M0+UtjjX7nzaWELHRGk5H5motnHiiE7y1oLtJpB6Z1GRrNtaLRXVHHsAABDdLBNIVVdXy8KFC+XGG2/0LouPj5dx48bJ3Llz/f7M/vvvL//3f/9nyv9GjRola9askenTp8u5557b5Os4HA5z8ygpKTH/Op1Oc2tv+po6x04kXjsUup+ern2ajYq2+YE0+PvTwA7m1lA0vRfdV8/N6rpkJMiQXmmyeH2lyWbOW11ulmsM/vWv5fLErEJTUrlfv4yI7qfneEbqu6CtRdt3DayB8wacM7Dbd40ziH2wTCC1ZcsWqaurk7w891gWD328YsUKvz+jmSj9uQMOOMAc/NraWrn00kubLe275557ZMqUKY2WFxYWRmRslX5YxcXFZv81cLS6mroaqa52n2BJ8SJl25i8NhJc4pKqsiozuCuuxTYakfX9+ipZsr6y0XJPDFjucMrkdzbJP8d1kn13SZVIqXXWiqPWIVvit0hSQpLEmmj7roE1cN6AcwZ2+64pLS2NvkAqFLNnz5a7775bnnjiCdOYYtWqVXL11VfLHXfcIbfeeqvfn9GMl47D8s1IaZOKnJwcycrKkkicODrnjr5+pE+cQOiFZs2OQD0lKV4yuzCmKBJMJsolktk505w/VlVd65THvvI/xtFD4yl9B499VSKv/K1LxEosq+uqxVXtkuycbElJTJFYE23fNbAGzhtwzsBu3zWpqanRF0hlZ2dLQkKC5Ofn11uuj7t16+b3ZzRY0jK+iy66yDweMmSIlJeXyyWXXCI333yz3w8iJSXF3BrSdSP1wemJE8nXD4buo6drn5b2WfkiPtbpsffcrOqrX8qlzNFyilyDKV1P1x83qP3/oKE8xzJafhdDEevvD22D8wacM7DTd018EK9vmf+aJicny4gRI2TWrFn1olN9PGbMGL8/U1FR0ejNajCmomHsSLR37YuGyXgRWdrUI9A4T9fT9QEAAKKBZTJSSkvuzjvvPBk5cqRpHqFzRGmGydPFb8KECdKzZ08zzkkdd9xxptPf3nvv7S3t0yyVLvcEVAgvp9Nluq9FU+tzRI52Rgz0bxq6nq4PAAAQDSwVSJ1xxhmm6cOkSZNk8+bNMnz4cJkxY4a3AcX69evrZaBuueUWkwbUfzdu3GjqKjWIuuuuuyL4LmKbwxNFEUghANpeXjNNgQRTup6uDwAAEA0sFUipK664wtyaai7hKzEx0UzGqze0DwIpBEPn6NIW54HQYEvXBwAAiAb8+RdBcdTW+WSkOH3QPJ3oODMlvsUG7fq8rqfrAwAARAOuhBEUh6f3uQZSCYyRQvM02NbJdlVLZ4uuR3AOAACiBYEUglLlM0YqJYlACi0bs3umTD6pu2SkuL9uGnbx04Bcn9f1AAAAooXlxkghisZIkZFCgDRIevWydJmzssy0ON9aXivL/3CY5zpnxMvofhkcSwAAEFUIpBAUh2c2XsZIIUhatqeT7Xom3L3h9Y2yaF2F5JfUybKNVTKkVxrHFAAARA1K+xAUuvYhXA4f3MF7/7OlJRxYAAAQVQikEJQq32YTTMiLVhjbP1PSdoyz05I/33MLAADA6gik0Ir25zSbQOhSk7TduTsrVVHtNGOnAAAAogWBFEJuf55CIIUwlvfNXFbK8QQAAFGDQAohtz9nzh+01uBeaZLX0d3zRhtPbC2r5aACAICoQCCFoNBsAmH9AoqLk3ED3V38nC6RWctoOgEAAKIDgRRCb3/OPFIIg3GDfLr3LSsVl8vFcQUAAJZHIIWgkJFCuPXsnCyDeqaa++u2Vsuv+e6JegEAAKyMQAqtaH/O6YPw8EzSqz6jvA8AAEQBroQRlGqfZhN07UO4HLxnpiTtKBWdvbxMauoo7wMAANZGIIWgVPmOkaL9OcIkMzVB9u+fYe4XV9bJ92vKObYAAMDSCKQQFMZIoa0cTnkfAACIIgRSCAqBFNrKiD7p0iUjwdz/bnW5lFTuzH4CAABYDYEUQg6kUmg2gTBKiI+Twwa4W6HraTZ7eSnHFwAAWBaBFEIeI+VpDgCEy+GD6d4HAACiA4EUgkJpH9pS35wU6ZebYu6v3OyQ9VurOeAAAMCSCKQQFMeOeaS0qk9LsYBwO3yQu7xPMacUAACwKgIphJSRovU52sqhAzqIJ0aftaxU6pzMKQUAAKyHQAohjZEikEJb6ZyRKPvu5p5TaktZrSxZX8HBBgAAlkMghaBUk5FCO5f3zVxG9z4AAGA9BFIISpUnkKJjH9rQfv0ypEOq++vp61/LpKJ6Z9t9AAAAKyCQQlAYI4X2kJwYLwfv5c5KOWpc8tVKslIAAMBaCKQQMKfT5S3tS0qkYx/as3sfgRQAALAWAikErLpuZ3lVCoEU2the3VOlV+ckc//HDZWyubiGYw4AACyDQApBd+xTSYyRQhuLi4uTwwdneR/PXFbCMQcAAJZBIIWgx0epFJ2RF2hjfxrYQeJ8uve5XMwpBQAArIGrYYSWkUrkwKHt5WYlybBd0sz9P4pq5Oc/qjjsAADAEgikEDAyUoiEwwftLO/7bCnlfQAAwBoIpBAwxkghEg7YI1NSk9wFfl+uLBNHDXNKAQCAyCOQQogZKdqfo32kJcebYEqVO5wyb3U5hx4AAEQcgRRCHCNFIIUIlffRvQ8AAFgAgRQC5ltSRUYK7UkbTuR0cHc4WbC2QraV1fIBAACAiCKQQsCqaslIITLi4+Jk3KAO5r7TJfL58lI+CgAAEFEEUggYGSlE0jif8j4m5wUAAJFGIIWQMlLJjJFCO+vdJVkGdE8199cUVsvqfAefAQAAiBgCKYSUkUpKoNkE2p+nvE99StMJAAAQQQRSCCkjRbMJRMLBe3XwBvFfLC+V2joXHwQAAIgIAimElpGitA8RkJWWIPv1yzD3iyrqZMFvzCkFAAAig0AKASMjBSs4fPDO8r7PltK9DwAARAaBFALGGClYwcg+GdIxPcHcn7e6XEqrdpacAgAAtBcCKQTMwRgpWEBiQpwcNsCdlaqpc8mXK8hKAQCA9kcghYAxRgpWcYTPnFKU9wEAgEggkELAGCMFq9gtN1n6Zieb+8s3VcmGbdWR3iUAAGAzBFIIWBVd+2ARcXFxcvjgnVmpmcwpBQAA2hmBFALGGClYiY6Tit8xL/Ssn0vF6WJOKQAA0H4IpBBaRmrHpKhApHTJTJQRfdLN/YKSWvlhfSUfBgAAaDcEUgg6I5UQrzcCKUQe5X0AACBSCKQQdEYqmWwULGL/3TMkI8X9NfbVL2VSWb0zawoAANCWCKQQdEYqOZGDBmtIToyXg/fMNPeralzy9S9lkd4lAABgE1wSI+iMVFIiZX2wjsMHZcn0H0vM/adnF8onS0skKzVe9u+fKQftmWmCLQAAgHAjkELAHDU7MlKU9sFCiivrJC5ORJv2FVc65ccNlebx17+WyxOzCuUfR+fJmN3dWSsAAIBw4U+1CFhVrScjxUGDNcxdVSZT3t1kgihfnsflDqdMfmeTWQ8AACCcCKQQEJfLJdU7AikyUrACPR8fmJ7f7Dqe+ErX85y/AAAA4UAghYA4fC5CGSMFK5izskzKHE5vsNQUfV7X0/UBAADChUAKAXH4TMZL1z5Ywbe/lpmxUIHQ9XR9AACAcCGQQkCqdrQ+V0k0m4AFlFQ5G42Naoqup+sDAACES6vaBmzcuFHmzJkjBQUFcsopp0ivXr2krq5OiouLpWPHjpKQkBC2HYWVMlK0P0fkaYtzT7e+luh6uj4AAEC4xIfaeGDixInSt29fOfvss839X375xTxXVlYmffr0kUcffTRsOwlrZaSSiY9hATpPVDAZKV0fAAAgooHUAw88II888ohcd9118tlnn5nAykMzUSeffLK89dZbYdtJRB4ZKViNTrabmRIvgeRHdT1dHwAAIKKB1DPPPCMTJkyQu+++W4YPH97o+aFDh3ozVIgNjJGC1SQnxpvJdlVLwdTEI/PM+gAAAOES0pXFhg0bZP/992/y+YyMDCkpKWnNfsFi6NoHKxqze6ZMPqm7ZKS4v8o8XfwadvNbU+iIwN4BAIBYFlKzidzcXBNMNWXhwoWyyy67tGa/YDFVNT5d+2g2AYsFU69elm7midIW59qdTxtL9MtLkRe/2SZOl8gr87bJ2P6Z0i83JdK7CwAA7BxI6RioadOmyfnnn2/GRKm4HX8C/vTTT+X555+X66+/Prx7CstMyJtM+3NYjJbtjRuUZW6+NP5/ee42qXOKPPRxvvz7nN6SyPkLAAAiVdo3ZcoU6d69uxkfpWOlNIi677775IADDpCjjjrKjJG66aabwrF/sGRGKqK7AgTsrP06y67Zyeb+qgKHvD5/O0cPAABELpDSLNS8efNM1knnkkpNTZUvv/xSioqK5LbbbpOvvvpK0tPTw7OHsAQyUojWTNV1R+ZJ/I4xUy/N3Sa/bWG8FAAAaL2Q21ilpaXJLbfcIkuWLJHy8nKprKyUpUuXyqRJk8xziN2MFBPyIprs2T1VTt23s7lfU+eSh2bkS50OnAIAAGjvQOqwww6TWbNmNfn8F198YdZBjGakKO1DlJkwtov06pJk7q/c5JC3FhRFepcAAIAdA6nZs2dLfn5+k88XFBSYUj/E6BgpBusjCkv8rj0yzzvf1Atfb5UN26ojvFcAAMCWpX2eLn3+rFq1Sjp06BDqpmH5jFRL058C1jOoZ5qcOKLTzhK/jynxAwAAoQu4SOuFF14wN48777xTnnnmmUbracOJH3/8UY4++uhW7BasnZGK6K4AIbvgwK7y3epy+aOoRn7+o0reX1wkJ41wj58CAABok4xURUWFFBYWmpsqLS31PvbctmzZIikpKXLppZfKf/7zn6B2BNZGRgqxIDUpXiYemet9/OycrfLHdkr8AABAG2ak/va3v5mb6tu3rzzyyCNy/PHHh/CSiEYOxkghRgztnS7H791R3l9cLI5al0z9pEDuP6NnpHcLAADYYYzU2rVr2yyIevzxx6VPnz5mbqrRo0fL/Pnzm11fSwkvv/xyM0GwZsP22GMPmT59epvsm53RtQ+x5C8HZUtelvvvSD9uqJSPlhRHepcAAECUaXUjay3xKy4uFqdzZzMCj1122SWobb322msyceJEmTZtmgmiHn74YRk/frysXLlScnN3luN4VFdXy+GHH26ee/PNN6Vnz56ybt066dTJPaAc4cM8Uoglacnxcs34PLnhjY3m8X++3CJ79+khGamR3jMAABDzgdSTTz4pU6dOlTVr1jS5Tl3dzgYFgdDtXXzxxXLBBReYxxpQffTRR/Lss8/KDTfc0Gh9Xb5t2zb59ttvJSnJPUeMZrPQxhkp2p8jBuzTJ12OGpolH/9YIpU1Lnn0s63yz2MzIr1bAAAglgMpDXC0nE6zRRdeeKHcfPPNcs0115hyvOeff17y8vLkqquuCmqbml1auHCh3Hjjjd5l8fHxMm7cOJk7d67fn3n//fdlzJgxZl/ee+89ycnJkbPOOkv++c9/SkKC/9ZyDofD3DxKSkrMv5pR85dVa2v6mi6XKyKvHYxKnzFSiQkus896Q2R4jj+fQetcfHBX+X5thWwprZXF66rk858TZFheZL4L2lq0fNfAWjhvwDkDu33XOIPYh5ACqUcffdQEUR9//LFs3brVBFLHHHOMHHbYYXL99dfLyJEjzfJgaMc/zWBpEOZLH69YscLvz2g27PPPP5ezzz7bjIvS+asuu+wyqampkdtuu83vz9xzzz0yZcqURsu162BVVZVE4sPS0kg9eTRwtKrySnfwmRAvUltaLRWVFVIdT7ezSHGJS6rKqkRnmI3zTjOLUPx1vw5y12fbzf0Xvy6X8X3+kJ4dYy8zFS3fNbAWzhtwzsBu3zWlpaVtG0itXr3aZIGUp6ROM0qqY8eOctFFF8kTTzwh1157rbT1QdfxUU8//bTJQI0YMUI2btwoDzzwQJOBlGa8dByWb0aqd+/eJpuVlZUl7U3fg05urK8f6ROnOXWy0vybkpggKR1TJD05XZITkiO9W7ZlMlEukczOmc1Ojo2WHdQlU+b/USufLSuVyhqRR74ulOfO7xNzxzVavmtgLZw34JyB3b5rUlNT2zaQ0mCptrbW3NfgIz09XTZs2OB9vkOHDrJ58+agtpmdnW2Cofz8/HrL9XG3bt38/ox26tNAzreMb8CAAea1NbBLTm58oa+d/fTWkH5okfrg9MSJ5OsHM0ZK5+HR/fXcEDl8DuFz6WE5svC3CtlWXidzft0q7y7ZJKeM6CWxJhq+a2A9nDfgnIGdvmvig3j9kPZ08ODB8sMPP3gf77fffqb5hGaDNKB66qmnTBvyYGjQoxmlWbNm1YtO9bGOg/Jn7NixppzPt5bxl19+MQGWvyAKre/al5LIBRhiT4fUBLl8XBfv4ykfLJOCkvYv9QUAANEjpKvic845R5YuXept2qBjjpYvX27anWvXPG1Xfueddwa9XS25e+aZZ+SFF14w29MJgMvLy71d/CZMmFCvGYU+r137rr76ahNAaYe/u+++21t2iPBnpFKS/DfxAKLd6H7pMra/O1tdUlUrN7+7lGYeAAAgvKV9Gth4ghtPZmjZsmXywQcfmDK7I444IuiMlDrjjDNM04dJkyaZ8rzhw4fLjBkzvA0o1q9fXy/dpmObPvnkE9MxcOjQoWYeKQ2qtGsf2iYjlUpGCjHs/IMyZMUfLtlaXi2f/ZwvH/y4SY4f1iPSuwUAACwoztVG/ZPXrl0rffv2FavTZhM65ks7hUSq2URBQYFpmhHpmtCm6CnS98bp5v6wXlly04nJkpGcQbOJCH8mZdvKJLMLzSbCpbquWsqry2Xzlu5y9as/mWWd05Pks4kHS3Zm43GV0SYavmtgPZw34JyB3b5rSoKIDcK+pz/++KOZy2nPPfcM96Zhgcl4Ke1DrDtycJ4cPcTd4GZ7RY3c9t6ySO8SAACwoKACKS3fu+KKK+Soo44ywdI777zjfW7RokVy9NFHy9577y1vv/22GUeF2OCo8QmkKO2DDUw5frDJRqmPftokH/+0KdK7BAAAonWM1Lx588yEu76T1r722msydepU0wpdxyVp2/N//OMfZpySds5DbHDUusdHedqfmwmMgBiW0yFFJh8/SK5+dYl5fMu7P8mWMod8s2qrFFVUS6f0ZDlikGauuksqDVgAALClgAOp22+/3UxQpVmoAw880IyB0oYT2hiisrLSdNy7+eabTU0hYktVo4zUzsAKiFXaZOKDHzbJzOX5srW8Rm59b5nEx4k4XWL+nbFss0z+YJlMPW24jBvobogDAADsI+DSvu+++860FR8/fryZgHfQoEEmG1VaWipXXXWV3H///QRRNshIpSTS/hz2mRhw/KD6AZIGUb7/llbWysUvLjAd/gAAgL0EHEgVFRU1amnueawlf7BJRsqU9gH2aPl/x0c/N7uOiadcIte9scQ7RQAAALCH+GDaLescUb48j7XkDzYZI0WzCdjE9J82SUllbYvraTBVXFkrHy+lIQUAAHYS1IS806dPNxPlelRUVJjylzfeeEOWLHEPyvbQ5TpRLmIrI5VMIAWb+HRZvndMVEt0vU+W5stJe/dqj10DAADRFki9/PLL5tbQU0891WgZgVSsdu1jjBTsQbvzBRJEKV2vqLK6rXcJAABEYyClXfpgT4279gGxT1ucB5OR6pSW3B67BQAAoi2Q2nXXXdt2TxAdXftoNgGb0HmitMV5IDTYGj+YFugAANgJ6QW0iIwU7Egn281KS5S4FtbT5zumJcpRg5mEHAAAOyGQQpBd+xgjBXvQ8YA62a5GSk0FU2Z5nMhDpw1n/CAAADZDIIUWMY8U7GrcwDx5+tyRJjPljy5/5tyRZj0AAGAvQXXtgz3VGyNFswnYzOED8+S7m8bJ9B83ybVv/GDmjeqQmii3nzDIlPPRyRIAAHsiI4UWMUYKdqfB0skjeklelnvy8ZTEBDNnFEEUAAD2FdZAqrq6WsrLy8O5SVgA80gBbrlZKebfreUOqa3bOS0AAACwn5ACqVdffVWuueaaesumTJkimZmZ0qlTJznppJOkrKwsXPuICCMjBbjlZLoDKZdLZFs5E/ACAGBnIQVSDz30UL3M07fffmsCqfHjx5sAa8aMGXLXXXeFcz8RQcwjBdTPSKmCUgeHBQAAGwup2cTq1avlvPPO8z5++eWXpVu3bvLOO+9IYmKiOJ1Oeeutt+See+4J574iQhw1O0uYdGyI1PJRwJ5yOrjHSKmC0iqdQSqi+wMAAKIsI+VwOCQ1decFxaeffipHHXWUCaLUwIED5ffffw/fXsJCY6ToTwL7yu3gk5EqISMFAICdhXRV3LdvX5k5c6a5v2DBAlm1apUceeSR3ufz8/PNeCnE3hipZNqfw8ZyfAKpQkr7AACwtZBK+/7617/K1VdfLT///LPJPPXq1UuOPfZY7/PffPONDBo0KJz7CatkpAikYGP1MlIEUgAA2FpIgdSVV15pSvumT58uI0aMkH/+85+SlpZmntu2bZts3rxZLr300nDvKyKckUqIj5PEBEr7YF+5O+aR2jlGCgAA2FVIgZS6+OKLza2hLl26mHI/xF5GimwU7C47M9l7n4wUAAD2Frb0gsvlks8//1w+/vhjKS0tDddmYaGMVEpSQqR3BYgo7VrZKT3J3GeMFAAA9hZSIHXzzTfLoYceWi+IOuKII+Twww+XY445RoYMGWJapCM2kJECGo+T0oyUfvcBAAB7CimQ0jmiRo0a5X385ptvyqxZs+TOO++UDz/8UOrq6mTy5Mnh3E9EEBkpYKfcHXNJVdc6paSSSdUAALCrkMZIbdy4UXbffXfv47ffftvMHXXjjTeax3/729/kySefDN9ewhIZqRQ69gENOvdVSccdpX4AAMBeQspI6cS7Oimv0tIWzUb5ziOVl5cnW7ZsCd9eImL08yUjBezEXFIAACDkQGrw4MHyf//3f7J9+3Z57rnnZOvWrWZslMe6deskOzubIxwDqut2TsZL1z6gfiBF5z4AAOwrpNK+SZMmyXHHHecNlsaOHVuv+cRHH30k++67b/j2EhHjyUYpuvYBzCUFAABaEUhpd75FixbJZ599Jp06dZIzzjjD+5xmqQ466CA54YQTQtk0LDo+SpGRAhqMkSpxlzgDAAD7CXlCXm0uobeGOnfuLP/6179au1+wCAcZKaDpMVJlBFIAANhVyIGUmjdvnnzxxRdSUFAgl112mfTv318qKipkxYoVsscee0hmZmb49hQRQUYKqI+MFAAACLnZRHV1tZx88slmbJROzvvvf/9bNmzY4N5gfLyZnPeRRx7hCMfcGKmQThcgpmSmJEpaUoK3/TkAALCnkK6Mb731VjPxrs4VtXLlStMi2yM1NVVOO+00ee+998K5n7BERsp98QjYWVxcnORmucv76NoHAIB9hRRIvfLKK2bS3UsuuUS6dOnS6PkBAwbImjVrwrF/iDAyUkBjOZnuQKq0qlaqanb+sQEAANhHSIGUjokaMmRIk88nJCSYsVKIfmSkgMY8GSlVWErDCQAA7CikQKp3796moURTvvnmG9l9991bs1+wCDJSQGO5HVK99xknBQCAPYUUSJ111lny1FNPydy5c+uNG1DPPPOMvP766zJhwoTw7SWskZHaMcAesDvfFujMJQUAgD2F1P5cO/Vp63OdeFfHQ2kQdc0118i2bdvk999/l6OPPto8RoxlpBLp2gc0bIHOXFIAANhTSFfGycnJMmPGDHnuuedkt912k7322kscDocMHTpUnn/+efnggw/MOClEP4fPQHoyUoAbGSkAABDyhLyahTrnnHPMDbGrqpaMFNAQY6QAAEBIGSkt4fvxxx+bfP6nn36S7du3c3RjgG9r5xTGSAGNuvYxlxQAAPYUUiCl4590Dqmm/PWvf5XrrruuNfsFi3D4ZKSYkBdw65KeLAnx7gY7tD8HAMCeQgqkPv/8czn++OObfP64446TmTNntma/YMmMFM0mABUfHyfZmcnmPhkpAADsKaQr48LCQsnOzm7y+a5du5pJexH9yEgBzY+T2lrmkDqni8MEAIDNhBRIde/eXRYvXtzk8wsXLpScnJzW7BcsgowU0HwLdI2hNJgCAAD2ElIgdeKJJ8p///tfef/99xs9995775m26CeddFI49g9WykjRbALwouEEAAD2FlL788mTJ5sxUBosDRs2TAYPHmyWL126VH744QczSe+UKVPCva+I8DxSTMgL7JST6TMpbykZKQAA7CakjFTHjh1l3rx5csstt0hNTY28+eab5qb3b731Vvnuu++kU6dO4d9btDsyUoB/OVnuMVKqoLSKwwQAgM2EPCFvRkaGyTqRebLRGKnEeHG6dj4G7MwzRkoVlJCRAgDAbkLKSNXW1kpJSUmTz+tzug5iJyOlc+YkJdD+HPAXSBXSbAIAANsJ6cr4qquukv3337/J58eOHSvXXntta/YLFstIMT4KqC+HjBQAALYWUiA1Y8YMOfXUU5t8Xp+bPn16a/YLFstI0bEPaCaQYowUAAC2E1Ig9ccff0jPnj2bfL5Hjx6ycePG1uwXLIKMFOBfSmKCdEpPMvcL6NoHAIDthBRIde3aVVauXNnk88uXL5esrKzW7BcsgowU0PI4KW1/7nK5OFQAANhISIHUkUceKU899ZQsXry40XOLFi2Sp59+Wo466qhw7B8ijIwU0HJ5n/7BoaSKBjsAANhJSO3P77jjDjNOatSoUXL88cfLoEGDvBPyfvDBB5Kbm2vWQXTTv7B7MlIpSQmR3h3AcnI77JxLqrC0SjqmuUv9AABA7AspkNIxUAsWLJAbbrhB3nvvPXnnnXfMci3nO/vss+Xuu+826yC6Vdc5xVOtRNc+oOW5pHbP7cBhAgDAJkKekLd79+7ywgsvmKxFYWGhWZaTkyNxcXHh3D9EkCcbpejaBzTfuY+5pAAAsJeQAykPDZy0lA+xOz5KkZECGmMuKQAA7CukQOr2228PKMC69dZbQ9k8LMJRQ0YKCHSMFHNJAQBgLyEFUpMnT242gNJyPwKp6OeoJSMFNCc3y3dSXgcHCwAAGwmp/bnT6Wx0q62tldWrV8s111wjI0eOlIKCgvDvLdpVVb2MVEinCmCbZhM6lxQAALCPsF0dx8fHS9++feXBBx+U/v37y5VXXhmuTcMSGSnanwMNZaYkev/IQEYKAAB7aZM0w0EHHSTTp09vi00jYmOkyEgBfpvt7BgnVVBSxQECAMBG2uTqWOeY0gwVolsVGSkg4PK+kqraep0uAQBAbAup2cT//vc/v8uLiopkzpw58vbbb8tFF13U2n1DhJGRAoJrOKHjpHp3SeewAQBgAyEFUueff36Tz2VnZ8sNN9wgkyZNas1+wQLISAEty8ms37mPQAoAAHsIKZBau3at37ECnTt3lg4dOoRjv2ABZKSAluVm7ZxLqrCUcVIAANhFSIHUrrvuGv49geX4jvegax/gX45PC3Q69wEAYB8hBVINrVixQt544w3ZtGmT7LnnnnLBBRdIVlZWODaNCHLU0rUPaAlzSQEAYE8BB1KPPfaY/Pvf/5Zvv/3WjIPy+OCDD+S0006T6upq77JHH31U5s2bV289RPeEvGSkgAAyUiVMygsAgF0E3KP8/fffl379+tULjmpra013voSEBHnuuefkp59+knvvvVfWrVsnd911V1vtMyIxIS/zSAF+eeaRUgWMkQIAwDYCDqR+/vln2W+//eot++KLL6SwsFCuueYaOe+882TQoEFy/fXXy+mnn86EvDGAjBTQsq4ZyZIQH2fuM0YKAAD7CDiQ2rp1q/Tu3bveslmzZplufSeddFK95WPHjpX169eHvFOPP/649OnTR1JTU2X06NEyf/78gH7u1VdfNftz4oknhvza8J+RSiUjBfgVHx8n2ZnJ3nmkAACAPQQcSOXl5cnmzZvrLfvqq68kPT1dhg0bVm95cnKyuYXitddek4kTJ8ptt90mixYtMtseP368FBQUNPtzv/32m1x33XVy4IEHhvS6aIyMFBDcOKktZQ6pc7o4bAAA2EDAgdTIkSPlhRdekNLSUvN42bJlJlOkQU5iYmKjLn69evUKaYemTp0qF198sen8N3DgQJk2bZoJ1p599tkmf6aurk7OPvtsmTJliuy2224hvS4aIyMFBDdOSmOoreVkpQAAsIOAu/ZphmjfffeV/v37m7FQCxcuNGV0N954Y6N133nnHTnssMOC3hnt/Kfb9d1mfHy8jBs3TubOndvkz91+++2Sm5srf/nLX0yWrDkOh8PcPEpKSsy/TqfT3NqbvqbL5YrIawczj1RSfJz3GOn+em6IDD6DtjumoXwX5Owo7VP5xZWSnRFaRt6u3zWwLs4bcM7Abt81ziD2IeBAasiQIfL555+bbnxr1qwxjSe0lG7EiBH11ps9e7bJIGlL9GBt2bLFZJe0jNCXPtYslz9ff/21/Pe//5UlS5YE9Br33HOPyVw1pE0zqqqqJBIfVnFxsTl5NGi0ktLyncejrGibuCoTpKauRhzFDolLjJPq+J0t79G+XOKSqrIqkTj9n7vRAVqn1lkrjlqHbInfIkkJSUH9bEbCzj86/LqhQHISrZeVsvJ3DayL8wacM7Dbd03pjuq7sE/Iu//++8tHH33U7DqHHHKIaYPeXm/03HPPlWeeeSbgOas026VjsHwzUtpEIycnJyKTCOuJo5k9ff1InzgNOePXeO/37J4nyYnx5kJzo3OjpCenS3KC9f7qbhcmG+gSyeycac4ftF51XbW4ql2SnZMtKYk754YKxK55lSKyyb2dhFSTIbcaK3/XwLo4b8A5A7t916Sm7pzWJKyBVFvTYEjnpMrPz6+3XB9369at0fqrV682TSaOO+64Ruk4Hbe1cuVKM/eVr5SUFHNrSD+0SH1weuJE8vWbUl3rPpba2TklKcG7n/qv54bI4XNom+MZyu9iXlaa9/6WsmrL/S5b/bsG1sZ5A84Z2Om7Jj6I17fUf02105+WCmpbdd/ASB+PGTOm0fp77bWXyX5pWZ/ndvzxx8uhhx5q7jds147QuvalJLqDKAD+5Wbt/OMMc0kBAGAPlspIKS2708l9tUvgqFGj5OGHH5by8nLTxU9NmDBBevbsacY6aept8ODB9X6+U6dO5t+GyxG8qh3zSDGHFNC83B3tzxVzSQEAYA+WC6TOOOMM0/hh0qRJZt6q4cOHy4wZM7wNKHSi30in/OzC4ZORAtC07EwyUgAA2I3lAil1xRVXmJs/2hWwOc8//3wb7ZX9kJECApOalCAd05KkuLJGCkrbv/snAABof6R20CQyUkDw5X0FJQ7mWAMAwAYIpNBke20yUkDwDScctU4pddRy6AAAiHEEUvCrps4lOlWRYowU0LIc33FSJdabkBcAAIQXgRT88mSjVEoSpwnQktysnRP4MU4KAIDYxxUymh0f5RlID6B5tEAHAMBeCKTgV1WNT0YqkdMEaEkOc0kBAGArXCHDLx0w70FGCggukCooZYwUAACxjkAKfpGRAoKT28FnjFQJc0kBABDrCKTgFxkpILT254qMFAAAsY9ACn45GCMFBKVDSqKk7uhwWUhpHwAAMY9ACn6RkQKCExcX5x0nRUYKAIDYRyAFvxgjBYQ+Tqq4sqbe7xAAAIg9BFLwi4wUEDzmkgIAwD4IpOAXGSmglYFUGS3QAQCIZQRS8IuMFNDKuaRKCKQAAIhlBFLwi4wU0Lq5pApLmUsKAIBYRiAFv8hIAcHLYS4pAABsg0AKfpGRAoJHswkAAOyDQAotZqRSkhI4SkCwY6SYlBcAgJhGIAW/yEgBweuakSLxce77BYyRAgAgphFIwS/GSAHBS4iPk+xMd1aKrn0AAMQ2Ain4RUYKCE3ujoYTW8urpc7p4jACABCjCKTgFxkpIDQ5OzJSGkRtK6/mMAIAEKMIpNByRiqJ0wQIZS4pxkkBABC7uEJGyxmpRLr2AcGW9ik69wEAELsIpOCXY0dGKi5OJClhRxsyAC1iLikAAOyBQArNZqQ0GxWn0RSAoOeSKmQuKQAAYhaBFJodI8X4KCA4Ob5jpEqqOHwAAMQoAim0mJECEFppH2OkAACIXQRS8IuMFBAaSvsAALAHAin4RUYKCE1qUoJkpSaa+2SkAACIXQRSaMTlcpGRAlohNyvVO4+U/j4BAIDYQyCFRmqdLnHuuPZjjBQQ+jipqhqnlDpqOYQAAMQgAik0OT5K0bUPCB5zSQEAEPsIpNDk+CiVQtc+oFUNJwpKHBxBAABiEIEUGiEjBbROru9cUqXMJQUAQCwikEKzGSnGSAHBy83amZEqLCUjBQBALCKQQiNkpIDWYS4pAABiH4EUGtFOYx5kpIDWNZtgLikAAGITgRQacdTStQ9ojRzGSAEAEPMIpNCIg4wU0CpZqYmSkuj+eqVrHwAAsYlACo2QkQJaJy4uzttworCMZhMAAMQiAim0MEaKUwQIRU6mO5Aqqqip98cJAAAQG7hKRgsZqQSOENDKuaRogQ4AQOwhkELzGakkThGgtXNJ0bkPAIDYw1Uyms9IJZKRAlrbAp2MFAAAsYdACo2QkQLCW9pHRgoAgNhDIIVGyEgBrZfjm5EqqeKQAgAQYwik0AgZKSC8gRQZKQAAYg+BFBohIwWEt9kEY6QAAIg9BFJohIwU0HpdM1IkPs59n4wUAACxh0AKjThqd7Y/p2sfEJqE+DjpumNS3oJSxkgBABBrCKTQSFWN74S8nCJAa1ugbymrljqniwMJAEAM4SoZzWakUpOYRwpobSClQdT2imoOJAAAMYRACs1npBI5RYCwzCVV4uBAAgAQQ7hKRpMZqbg4keQEThEgPC3QGScFAEAs4SoZjTh2ZKQ0GxWn0RSAVrdAp3MfAACxhUAKTWakGB8FhGeMlGIuKQAAYguBFJocI8X4KKB1cnzGSBFIAQAQWwik0AgZKSD8GSnGSAEAEFsIpNAIGSmgDZpN0LUPAICYQiCFRshIAeGh4wyzUhPN/cIy2p8DABBLCKRQT02d00weqhgjBbReblaqNyPlcrl/twAAQPQjkILfbJSiax/QejmZ7vK+ypo6KXPUckgBAIgRBFLwOz5KkZECWo+5pAAAiE0EUmgyI5WSlMDRAVqJuaQAAIhNBFKoh4wUEF65PnNJFZTScAIAgFhBIIV6HDWMkQLargV6FQcXAIAYQSCFeqpqGSMFhBOlfQAAxCYCKdRDRgpou2YThZT2AQAQMwikUA8ZKSC8chgjBQBATCKQQj1kpIDwykpNlORE91dtQSljpAAAiBUEUqjHwRgpIKzi4uK846To2gcAQOwgkEI9ZKSA8PMEUkUVNfX+WAEAAKIXgRTqYYwU0LZzSW0pq+YQAwAQAwikUA8ZKSD8mEsKAIDYQyCFeqpqmEcKaMu5pBgnBQBAbLBkIPX4449Lnz59JDU1VUaPHi3z589vct1nnnlGDjzwQOncubO5jRs3rtn10TxHrdN7PzUpgcMFhAFzSQEAEHssF0i99tprMnHiRLnttttk0aJFMmzYMBk/frwUFBT4XX/27Nly5plnyhdffCFz586V3r17yxFHHCEbN25s932PBWSkgLYdI0VGCgCA2GC5QGrq1Kly8cUXywUXXCADBw6UadOmSXp6ujz77LN+13/ppZfksssuk+HDh8tee+0l//nPf8TpdMqsWbPafd9jrdkEGSkg/GOkCplLCgCAmJAoFlJdXS0LFy6UG2+80bssPj7elOtptikQFRUVUlNTI126dPH7vMPhMDePkpIS868GX3prb/qaLpcrIq/dUkYqKd69f/7213NDZPAZtN0xbYvvguyMJO/9/JIqvmsQNaz23yhYH+cMov28CWYfLBVIbdmyRerq6iQvL6/ecn28YsWKgLbxz3/+U3r06GGCL3/uuecemTJlSqPlhYWFUlVVJZH4sIqLi83Jo0FjpBWXVnjvl5cUSUFcZb3na+pqxFHskLjEOKmOp41zpLjEJVVlVSJx+r+4iO1HLKl11oqj1iFb4rdIUsLOwCcc6pwuiY8TcbpENm0vb7JU2U7fNYgOnDfgnIHdvmtKS0ujM5BqrXvvvVdeffVVM25KG1X4o9kuHYPlm5HScVU5OTmSlZUlkThx4uLizOtH+sRRcYm/e+/3yMuR3Kz6x1EvNDc6N0p6crokJyRHYA+hTDbQJZLZOdOcP2i96rpqcVW7JDsnW1ISd5bihUvXzBQpLHXI9so6yc3NFbt/1yA6cN6AcwZ2+65JbSKGsHwglZ2dLQkJCZKfn19vuT7u1q1bsz/74IMPmkBq5syZMnTo0CbXS0lJMbeG9EOL1AenJ04kX99XlU/XvrSUpEb7pI91fz03RA6fQ9scz7b6XczZEUi5J+TV14mz9XcNogfnDThnYKfvmvggXt9S/zVNTk6WESNG1GsU4WkcMWbMmCZ/7v7775c77rhDZsyYISNHjmynvY1NDuaRAtq0BXqt0yXbKiiLBQAg2lkqI6W07O68884zAdGoUaPk4YcflvLyctPFT02YMEF69uxpxjqp++67TyZNmiQvv/yymXtq8+bNZnlmZqa5IfSMVEqipeJsIGYm5dXMVHZm+MsHAQCAjQOpM844wzR+0OBIgyJta66ZJk8DivXr19dLuT355JOm29+pp55abzs6D9XkyZPbff9jJSOlQRSle0DbzSU1oDtHFwCAaGa5QEpdccUV5uaPNpLw9dtvv7XTXtmDY0dGijmkgLabS6qgpP07hAIAgPCidgtNZqQAtE1pn2akAABAdONqGX7HSJGRAtqm2YRnjBQAAIhuBFKoh4wU0PZjpAikAACIfgRSqIeMFNAOY6RKGSMFAEC0I5CCV22dU+qcLnOfMVJAeGm5bIdUd38fxkgBABD9CKTgdw4pxkgBbddwgtI+AACiH4EUGo2PUmSkgLYbJ1VRXSdljloOMQAAUYxACl5kpIC2xVxSAADEDgIpeJGRAtoWc0kBABA7CKTgVVWzc4xUSlICRwYIM+aSAgAgdhBIwctRyxgpoL3mkqJzHwAA0Y1ACn4zUnTtA8KPuaQAAIgdBFLwm5FKTeLUANpyjFRhiYMDDABAFONqGf7HSCUyRgpoy9K+wjICKQAAohmBFLzISAFtKystUZIT3V+7BWSkAACIagRS8HKQkQLaVFxcnORkusv7CkqrONoAAEQxAil4kZEC2q8F+vaKGqmu3VlOCwAAoguBFLwYIwW0b8OJLYyTAgAgahFIwYuMFND2mEsKAIDYQCAFLzJSQDvPJVXCOCkAAKIVgRS8yEgB7VvaV1BKC3QAAKIVgRS8yEgB7ddsQhUSSAEAELUIpOBFRgpoe4yRAgAgNhBIwYuMFNC+Y6QKmUsKAICoRSAFLzJSQNvrmpEscXHu+4yRAgAgehFIwYuMFND2EhPipWuGOyvFGCkAAKIXgRT8ZqRSkjg1gLbu3KeBlNPp4kADABCFuFpGExkpTg2grcdJ1Tpdsr2imgMNAEAU4moZXo5apzeIivMM4gAQdswlBQBA9COQglTV1Mnbi36XdVvLzdGoc7rMY10OIPyYSwoAgOhHIGVzn/2cL6PunikTX/9BKqrrvOVG+liXz/w5P9K7CMQc5pICACD6EUjZPIi65MUFUlpZ6/d5XX7xiwvMegDaZi6pAuaSAgAgKhFI2ZSW7V37xhIRl/mfX2a5S+S6N5ZQ5ge01RipEgfHFgCAKEQgZVPTf9okJZW1TQZRHvp8cWWtfLx0UzvtGWCv0r7CMgIpAACiEYGUTX26LF/iA2zMp+t9spTyPqAtSvsKyUgBABCVCKRsqqiiWgKdB1TXK6pkrhsgXNKSE6RDSqK5zxgpAACiE4GUTXVKTw4qI9UpLbmtdwmwlZwsd1aqoJTSPgAAohGBlE0dMSgvqIzU+MF5bb1LgC0bTui0A+UO/50zAQCAdRFI2dTRQ7pLVlqitJSU0uc7piXKUYO7t9OeAfbAXFIAAEQ3AimbSk1KkKmnDXdHSk0wT8WJPHTacLM+gDaaS6qkikMLAECUIZCysXED8+Tpc0dKYoPBUp6HmrF65tyRZj0AbTiXFOOkAACIOu62UbCt/ft19Sal0pLiZVivTqYRhY6J0nI+MlFA28jd0WxCFRJIAQAQdQikbO7b1VulZkfXiVNG9JI7TxwS6V0CbIExUgAARDdK+2zui5UF3vuH7pkb0X0BbDtGqpQxUgAARBsCKRtzuVzy5cpCcz85IV7G9Osa6V0CbDlGitI+AACiD4GUjf1aUCYbiyrN/dG7dZH0ZCo9gfbSMS1JkhPdX8EEUgAARB8CKRubTVkfEDFxcXGSk+nOStG1DwCA6EMgZWNfrHCX9alD9syJ6L4Adh4nta28WqprnZHeHQAAEAQCKZsqraqR73/bZu7v2jVd+mZnRHqXANvxHSe1pcwR0X0BAADBIZCyqW9WbZXaHW3PD9kjx5QZAWhfzCUFAED0IpCyKd/xUYfsRdtzIBKYSwoAgOhFIGXTtuezd7Q9T0mMlzG70fYciATmkgIAIHoRSNnQis2lsrnEPQGozh2VmpQQ6V0CxO5jpApKGCMFAEA0IZCyIU82yjM+CkBkUNoHAED0IpCyoS98x0ftyfgoIFJoNgEAQPQikLKZkqoaWbhuu7mvLc/70PYciJiuGcniaZhZWOoutwUAANGBQMpmvv51i9R52p4zCS8QUYkJ8SaYUgWljJECACCaEEjZzBcrKOsDrCSnQ6r5t7DUIc4df+QAAADWRyBlt7bnv7gbTaQmxcvovl0ivUuA7Xk69+kE2UWVNbY/HgAARAsCKRtZ9keJ+au3Gtsvm7bngNVaoDNOCgCAqEEgZSNf7shGKcZHARaclJe5pAAAiBoEUjbC+CjA6hkpGk4AABAtCKRsoriiRhatd7c975eTIb27pEd6lwCYuaTczSaUp/QWAABYH4GUTcz5tVA8DcEOZRJewDIYIwUAQHQikLKJ2St9x0flRnRfADQxRoqMFAAAUYNAygZ0bpovf3HPH5WenCD79u0c6V0CsEPujnmkVCHNJgAAiBoEUjaw9I9i2VJWbe7v3y9bUhITIr1LAHZIS06QDimJ5n5hGWOkAACIFgRSNivrO3SvnIjuC4DGcrLc5X0FJVUcHgAAogSBlA18sdJd1qcYHwVYT06mO5Aqr66TckdtpHcHAAAEgEAqxm0rr5YlG4rM/T3yMqVnp7RI7xKAZlqg03ACAIDoQCAV4776tVBctD0HoqYFOnNJAQAQHdwjnBFTqmrqZPpPm+TTZfmyYN027/Ix/bpGdL8A+MdcUgAARB8CqRjz2c/5cu0bS6Skslbi48Q7Ca+66pXFMvX04TJuYF4kdxFAc3NJ0QIdAICoQGlfjAVRl7y4QEor3YPVfYMoVVpVKxe/uMCsB8Cac0kxRgoAgOhAIBVD5XyaiRKX+Z9fZrlL5Lo3lpj1AVhD7o7254oxUgAARAdK+yzCUVMnHy/7w4xr2lbmkMpap1melpQgXTKS5YhBeXL0kO6SmuR/Ml0dE6XlfC3RYKq4slY+XrpJTtq7V9jfB4DgdUzb+VU8c/lmufTF2hZ/54MdM/nJss1SWFQuOZ1+l/GDuoVl24hdnDcA+K5pWZzL5enpZk8lJSXSsWNHKS4ulqysrHZ/fafTKW/O/UXu/GydlFTVSpwnc+TDsywrLVGmntZ4jNOWModc9MICb5vzlujYqSMGdpNp544Ien8dtQ5ZsnmJZCRnSHJCctA/j/DQX9uybWWS2SVT4uL0DEFrVddVS3l1uQzvNlxSEndmiNplXOPrS8zvv4dnfGNTv/OtGTMZrm0jdnHeoLXXNQUFBZKbmyvx8RQ+Ifq+a4KJDSx5hj/++OPSp08fSU1NldGjR8v8+fObXf+NN96Qvfbay6w/ZMgQmT59ukSLmcvz5Z8frDbjl5S/qNazTMc+6Rintxb9bv7CfOu7S+XwqV/KyDtnBhxEKT1Biyqrw/QOALR6XKNPEOU7vtHzOx/KuMamxkyGY9uIXZw3APiuCZzlAqnXXntNJk6cKLfddpssWrRIhg0bJuPHjzd/3fDn22+/lTPPPFP+8pe/yOLFi+XEE080t6VLl0o0lE5c98aP5n4gaUFdR/OH177+g1z20iJ5cd46+bWgLOjX1Wi/UxrZJCBWxzUyZhJWOycBIBa/ayxX2qcZqH333Vcee+wxb4q4d+/ecuWVV8oNN9zQaP0zzjhDysvL5cMPP/Qu22+//WT48OEybdo0S5f2vb3od5n4+g+t2kZCfJwM6dnRjKP6fIX/YNOff50xLKQxUpT2WQOlfdFf2hfs7/+wXh2lZ+e0gNbduL1Sfvi9uE22jdjFeYNw0KtKh6NKUlJShcpzhOO7JtRr1lAFExtYqtlEdXW1LFy4UG688UbvMq2vHTdunMydO9fvz+hyzWD50gzWu+++63d9h8Nhbh56kFRRUZEJ2trTBwtWiVRXNGpTHohduqbJP8fvJXvv0kkyUxJNs4rDVm6Qsqq6ZrNbOpomMzVB9u+VZt5zKIFUWUmZVCVUMUYqwoFUZXGlOOIcjJEKYyBVW1crRalF7RJIBfv7v3h1hSxuo31py20jdnHeAGhrWkX1/ver5NC+mdKegZQKJNdkqUBqy5YtUldXJ3l59QeW6eMVK1b4/ZnNmzf7XV+X+3PPPffIlClTGi3fddddJZpsEJHjbw3957vdG869AQAAAMLveb39VdpdaWmpyUxFTSDVHjTb5ZvB0izUtm3bpGvXrhH5y75GvVq6uGHDhoh0DUR04rwB5wz4roEV8d8nRPt5o5koDaJ69OjR4rqWCqSys7MlISFB8vPrd5HSx926dfP7M7o8mPVTUlLMzVenTp0k0vSkifSJg+jDeQPOGfBdAyviv0+I5vOmpUyUJbv2JScny4gRI2TWrFn1Mkb6eMyYMX5/Rpf7rq8+++yzJtcHAAAAgNayVEZKadndeeedJyNHjpRRo0bJww8/bLryXXDBBeb5CRMmSM+ePc1YJ3X11VfLwQcfLA899JAcc8wx8uqrr8qCBQvk6aefjvA7AQAAABCrLBdIaTvzwsJCmTRpkmkYoW3MZ8yY4W0osX79+nozZe+///7y8ssvyy233CI33XST9O/f33TsGzx4sEQDLTPUObMalhsCnDfguwaRxn+jwDkDvmuiaB4pAAAAALA6S42RAgAAAIBoQCAFAAAAAEEikAIAAACAIBFIAQAAAECQCKQi6PHHH5c+ffpIamqqjB49WubPnx/J3YHFacv/fffdVzp06CC5ubly4oknysqVKyO9W4gy9957r8TFxcnf//73SO8KLGzjxo1yzjnnSNeuXSUtLU2GDBliphYBmlJXVye33nqr9O3b15wz/fr1kzvuuEPoaQZfc+bMkeOOO0569Ohh/luknbZ96fminbu7d+9uzqNx48bJr7/+KlZFIBUhr732mpkzS1ufL1q0SIYNGybjx4+XgoKCSO0SLO7LL7+Uyy+/XObNm2cmna6pqZEjjjjCzLMGBOL777+Xp556SoYOHcoBQ5O2b98uY8eOlaSkJPn444/l559/NnM1du7cmaOGJt13333y5JNPymOPPSbLly83j++//3559NFHOWrw0msWvebVZII/es78+9//lmnTpsl3330nGRkZ5vq4qqpKrIj25xGiGSjNLugXjnI6ndK7d2+58sor5YYbbojUbiGK6HxrmpnSAOuggw6K9O7A4srKymSfffaRJ554Qu68804zR59OeA40pP8N+uabb+Srr77i4CBgxx57rJnz87///a932SmnnGKyCv/3f//HkUQjmpF65513TIWNJxulmaprr71WrrvuOrOsuLjYnFfPP/+8/PnPfxarISMVAdXV1bJw4UKTrvR+EPHx5vHcuXMjsUuIQvrlorp06RLpXUEU0GzmMcccU+97B/Dn/fffl5EjR8ppp51m/liz9957yzPPPMPBQrP2339/mTVrlvzyyy/m8Q8//CBff/21HHXUURw5BGTt2rWyefPmev+d6tixo0k+WPX6ODHSO2BHW7ZsMbXEGmH70scrVqyI2H4hemgGU8e4aPnN4MGDI707sLhXX33VlBBraR/QkjVr1pgSLS0/v+mmm8x5c9VVV0lycrKcd955HEA0mcksKSmRvfbaSxISEsx1zl133SVnn302RwwB0SBK+bs+9jxnNQRSQJRmF5YuXWr+2gc0Z8OGDXL11VebcXXa2AYI5A81mpG6++67zWPNSOn3jY5ZIJBCU15//XV56aWX5OWXX5ZBgwbJkiVLzB/8tFSL8waxitK+CMjOzjZ/rcnPz6+3XB9369YtEruEKHLFFVfIhx9+KF988YX06tUr0rsDi9MyYm1io+OjEhMTzU3H1elgXr2vfzUGfGm3rIEDB9ZbNmDAAFm/fj0HCk36xz/+YbJSOo5Fuzyee+65cs0115iOs0AgPNfA0XR9TCAVAVoeMWLECFNL7PsXQH08ZsyYSOwSooAOwtQgSgdmfv7556bFLNCSP/3pT/LTTz+Zvw57bppt0HIbva9/1AF8aclww6kVdNzLrrvuyoFCkyoqKsx4b1/6/aLXN0Ag9LpGAybf62MtF9XufVa9Pqa0L0K09lxT3XpBM2rUKNM9S1tCXnDBBZHaJURBOZ+WTLz33ntmLilPvbAOxNSuSIA/eq40HEen7WR1fiDG18EfzSJo4wAt7Tv99NPNHIdPP/20uQFN0bmBdEzULrvsYkr7Fi9eLFOnTpULL7yQg4Z6HWRXrVpVr8GE/lFPG2fpuaPloNpZtn///iaw0rnJtDzU09nPamh/HkHa+vyBBx4wF8TailhLbbQzCdBUm1B/nnvuOTn//PM5aAjYIYccQvtzNEvLh2+88UYzEaZezOgf/y6++GKOGppUWlpqLnq1akLLifXi98wzzzSTq2olDqBmz54thx56qDSkyQVtca7VNzrHqv7hpqioSA444AAzbccee+whVkQgBQAAAABBYowUAAAAAASJQAoAAAAAgkQgBQAAAABBIpACAAAAgCARSAEAAABAkAikAAAAACBIBFIAAAAAECQCKQAAAAAIEoEUAAAAAASJQAoAAIt44okn5Pnnn4/0bgAAAhDncrlcgawIAADa1uDBgyU7O1tmz57NoQYAiyMjBQCwlfLycrGT2tpaqa6ujvRuAEDMIZACAARt8uTJEhcXJ7/88oucc8450rFjR8nJyZFbb71VtNBhw4YNcsIJJ0hWVpZ069ZNHnrooYC2q9u84oor5KWXXpI999xTUlNTZcSIETJnzpx6661bt04uu+wys05aWpp07dpVTjvtNPntt9/qradlcrrNL7/80qyfm5srvXr1CmkbX3/9tVx11VXmfXbq1En++te/mgClqKhIJkyYIJ07dza366+/3hwDX06nUx5++GEZNGiQeU95eXnm57dv3+5dp0+fPrJs2TKzr/p6ejvkkEO8z+vr/P3vf5fevXtLSkqK7L777nLfffeZbXvovuvPPfjgg+b1+vXrZ9b9+eefAzr+AIDAJQaxLgAA9ZxxxhkyYMAAuffee+Wjjz6SO++8U7p06SJPPfWUHHbYYeZCX4Oi6667Tvbdd1856KCDWjyCGki89tprJmjRIEDHDR155JEyf/58U/qmvv/+e/n222/lz3/+swmMNIB48sknTeChQUN6enq9bWrApAHQpEmTvBmpYLdx5ZVXmqBwypQpMm/ePHn66adNQKXb2GWXXeTuu++W6dOnywMPPGD2U4MrDw2aNCC74IILzPtau3atPPbYY7J48WL55ptvJCkpyQQ++hqZmZly8803m5/TgEtVVFTIwQcfLBs3bjTb0tfT173xxhtl06ZN5md9Pffcc1JVVSWXXHKJOYb6mQAAwkzHSAEAEIzbbrtNUy6uSy65xLustrbW1atXL1dcXJzr3nvv9S7fvn27Ky0tzXXeeee1uF3dpt4WLFjgXbZu3TpXamqq66STTvIuq6ioaPSzc+fONT/7v//9z7vsueeeM8sOOOAAs3++gt3G+PHjXU6n07t8zJgx5r1eeumljY7BwQcf7F321VdfmZ9/6aWX6r3WjBkzGi0fNGhQvZ/1uOOOO1wZGRmuX375pd7yG264wZWQkOBav369ebx27VqzzaysLFdBQUGj7QAAwofSPgBAyC666CLv/YSEBBk5cqQpa/vLX/7iXa5ZGy2fW7NmTUDbHDNmjCnn89Dsi5YJfvLJJ1JXV2eWaSmeR01NjWzdutWUuulrLVq0qNE2L774YrN/voLdhr4nLZvzGD16dKP36jkGvu/1jTfeMKWPhx9+uGzZssV70/eo2acvvviixWOi2zjwwANN6aDvNsaNG2eOScPSx1NOOcVk4AAAbYfSPgBAyDTI8aUBg44B0s5zDZdroBKI/v37N1q2xx57mPK2wsJCU15XWVkp99xzjylh03I33zFJxcXFjX6+b9++jZYFuw1/71XpmKWGy33HPv36669mezo+y5+CggJpiW7jxx9/bDI4argNf+8XABBeBFIAgJA1zPI0tUyFc7YNHUukAZA2X9AMlgYvmi3S8U6+zRf8ZZ9C3UZT78vfct/3qtvSIErHivkTSOZIt6EZLW1k4Y8Gmi29XwBAeBFIAQAsRbMvDWl3QG3+4Ak63nzzTTnvvPPqdQPU5gra2S5Q4dhGILRz3syZM2Xs2LEtBji+pYMNt1FWVmZK+QAA1sAYKQCApcydO7feGCVtpf7ee+/JEUcc4c3+6L8NM1yPPvqodwxVIMKxjUCcfvrpZpt33HGH3zmefAO3jIwMv4GcbkOPi44Ta0jX1+0AANoXGSkAgKVo6/Dx48fXa3+utO24x7HHHisvvviiKccbOHCgCTI066NzQQUqHNsIhLYt15blOh5ryZIlJiDUdueaedMmEo888oiceuqpZl1tQKEt2LWNvDa+0JJAbSP/j3/8Q95//32zz+eff75ZT9u4//TTTyazpq3bG45LAwC0LQIpAIClaOChY5Y0cFq/fr0JcnQOpqFDh3rX0eBDM0o67kjL8bRsToMgDcACFY5tBGratGkm+NH5tW666SZJTEw0E/DqZMb6uh46z5VOFHz//fdLaWmpORYaSGlZo86vpXNVafD1v//9z0x2rGOj9Dh5Gl8AANpPnPZAb8fXAwCg2TFCl19+uZmsFgAAK2OMFAAAAAAEiUAKAAAAAIJEIAUAAAAAQaLZBADAMhi2CwCIFmSkAAAAACBIBFIAAAAAECQCKQAAAAAIEoEUAAAAAASJQAoAAAAAgkQgBQAAAABBIpACAAAAgCARSAEAAACABOf/AS7R8rzB0Q73AAAAAElFTkSuQmCC", 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"text/plain": [ "
" ] @@ -1723,12 +1869,12 @@ "\n", " @qfunc\n", " def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", " invert(lambda: qft(x))\n", "\n", - " pc, df = run_standard_simulation(main)\n", + " df = run_standard_simulation(main)\n", " analytic_grad = p.analytical_gradient(0)\n", " epsilon = 0.2\n", " success_rate, _, _ = compute_success_rate(\n", @@ -1780,7 +1926,7 @@ }, { "cell_type": "markdown", - "id": "47", + "id": "45", "metadata": {}, "source": [ "Next, we plot success rate versus $l$ with $m=2$. The valid bound $l\\leq 0.28$ is highlighted." @@ -1788,28 +1934,148 @@ }, { "cell_type": "code", - "execution_count": 14, - "id": "48", + "execution_count": 13, + "id": "46", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/47c35670-9481-4ed1-aeb9-5b8a1d0afaf1\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "l=0.1: Success rate = 94.38%\n", - "l=0.2: Success rate = 80.18%\n", - "l=0.3: Success rate = 58.50%\n", - "l=0.4: Success rate = 38.28%\n", - "l=0.5: Success rate = 22.95%\n", - "l=1: Success rate = 10.01%\n", - "l=1.5: Success rate = 14.50%\n", - "l=2.0: Success rate = 14.01%\n", - "l=3.0: Success rate = 25.63%\n" + "l=0.1: Success rate = 93.99%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/377d735e-7fe1-413b-8f53-703657410ea1\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=0.2: Success rate = 80.91%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/98b1c4e1-ac00-4b39-bf36-599db195bfe2\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=0.3: Success rate = 60.35%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/836e3a56-9231-4c4f-b553-4516a2c7d5b1\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=0.4: Success rate = 39.94%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/bbe327dc-fd52-400d-be30-6e6393b885b2\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=0.5: Success rate = 23.29%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/97e645bf-b543-4def-b576-822c05eb841a\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=1: Success rate = 10.79%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/915fb19c-d3e3-485a-a041-b5bb85374c04\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=1.5: Success rate = 16.65%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/e9c32827-293b-422d-9a49-c19a02343bf9\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=2.0: Success rate = 14.36%\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/71cefbf3-c4f5-470e-b514-cea85fd64440\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "l=3.0: Success rate = 26.12%\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -1842,12 +2108,12 @@ "\n", " @qfunc\n", " def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " allocate(n, x)\n", + " allocate(x)\n", " hadamard_transform(x)\n", " phase(f_normalized(x), 2 * pi)\n", " invert(lambda: qft(x))\n", "\n", - " pc, df = run_standard_simulation(main)\n", + " df = run_standard_simulation(main)\n", " analytic_grad = p.analytical_gradient(0)\n", " success_rate, _, _ = compute_success_rate(\n", " df, analytic_derivatives={\"x\": analytic_grad}, p=p\n", @@ -1880,112 +2146,61 @@ }, { "cell_type": "markdown", - "id": "49", + "id": "47", "metadata": {}, "source": [ - "# 4. Multi-Dimensional Examples" + "# Multi-Dimensional Examples" ] }, { "cell_type": "markdown", - "id": "50", + "id": "48", "metadata": {}, "source": [ - "The algorithm extends to multiple dimensions. We demonstrate with a 2D example using a linear, decoupled function $f(x,y)=ax+by+c$." + "The algorithm extends to multiple dimensions. In this example we will demonstrate a general quadratic coupled function:\n", + "\n", + "$$f(x,y)=ax^2+by^2+cxy+dx+ey+f$$" ] }, { "cell_type": "code", - "execution_count": 15, - "id": "51", + "execution_count": 14, + "id": "49", "metadata": {}, "outputs": [ { - "name": "stdout", + "name": "stderr", "output_type": "stream", "text": [ - "[{'x': 2, 'y': -1}: 2048]\n", - "Analytical gradient: (dx, dy) = (0.5, -0.25)\n", - "Majority gradient: (dx, dy) = (0.5, -0.25)\n", - "Success rate: 100.00% (2048/2048 shots)\n", - "[\u001b[92m██████████████████████████████████████████████████\u001b[91m\u001b[0m] 100.00%\n" + "Submitting job to simulator\n", + "Job: https://platform.classiq.io/jobs/c3a21541-e687-4524-8cd7-ec934bfd031d\n" ] - } - ], - "source": [ - "px = params()\n", - "py = params()\n", - "\n", - "# Set the functions for x and y axes\n", - "# f(x, y) = a*x + b*y + c = 0.5*x - 0.25*y + 0.1\n", - "# df/dx = 0.5, df/dy = -0.25\n", - "a, b, c = 0.5, -0.25, 0.1\n", - "px.set_function(px.linear, (a, 0.0))\n", - "py.set_function(py.linear, (b, c))\n", - "\n", - "# Important: we can't use the globals here, because there are two different functions for px and for py.\n", - "\n", - "\n", - "@qfunc\n", - "def main(x: Output[QNum[px.n, SIGNED, 0]], y: Output[QNum[py.n, SIGNED, 0]]):\n", - " # State preparation for x-axis contribution\n", - " allocate(px.n, x)\n", - " hadamard_transform(x)\n", - " phase(px.f_normalized(x), 2 * pi)\n", - "\n", - " # State preparation for y-axis contribution\n", - " allocate(py.n, y)\n", - " hadamard_transform(y)\n", - " phase(py.f_normalized(y), 2 * pi)\n", - "\n", - " # Gradient extraction on each axis\n", - " invert(lambda: qft(x))\n", - " invert(lambda: qft(y))\n", - "\n", - "\n", - "pc, df = run_standard_simulation(main)\n", - "print(pc)\n", - "\n", - "majority_state = dict(df.iloc[0])\n", - "gx_true = px.analytical_gradient(0)\n", - "gy_true = py.analytical_gradient(0)\n", - "\n", - "gx_meas = (majority_state.get(\"x\")) / (px.N / px.m)\n", - "gy_meas = (majority_state.get(\"y\")) / (py.N / py.m)\n", - "\n", - "print(f\"Analytical gradient: (dx, dy) = ({gx_true}, {gy_true})\")\n", - "print(f\"Majority gradient: (dx, dy) = ({gx_meas}, {gy_meas})\")\n", - "\n", - "success_rate, success_shots, total_shots = compute_success_rate(\n", - " df, analytic_derivatives={\"x\": gx_true, \"y\": gy_true}, p=px\n", - ")\n", - "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", - "show_bar(success_rate)" - ] - }, - { - "cell_type": "markdown", - "id": "52", - "metadata": {}, - "source": [ - "We can also demonstrate a more complex case with non-linear and coupled terms: $f(x, y)=ax^2+by^2+cxy+dx+ey+f$." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "53", - "metadata": {}, - "outputs": [ + }, { "name": "stdout", "output_type": "stream", "text": [ - "[{'x': 1, 'y': -2}: 2005, {'x': 2, 'y': -2}: 14, {'x': 0, 'y': -2}: 8, {'x': 1, 'y': -3}: 5, {'x': 1, 'y': -1}: 4, {'x': -1, 'y': -2}: 2, {'x': 3, 'y': -2}: 2, {'x': -1, 'y': -4}: 1, {'x': 2, 'y': 3}: 1, {'x': -4, 'y': -2}: 1, {'x': 2, 'y': -1}: 1, {'x': -1, 'y': -3}: 1, {'x': -4, 'y': -4}: 1, {'x': 0, 'y': -1}: 1, {'x': 2, 'y': -3}: 1]\n", - "Analytical gradient: (dx, dy) = (0.25, -0.5)\n", - "Majority gradient: (dx, dy) = (0.25, -0.5)\n", - "Success rate: 97.90% (2005/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.90%\n" + " coords counts probability bitstring\n", + "0 [1, -2] 1988 0.970703 110001\n", + "1 [0, -2] 15 0.007324 110000\n", + "2 [2, -2] 15 0.007324 110010\n", + "3 [1, -3] 8 0.003906 101001\n", + "4 [1, -1] 7 0.003418 111001\n", + "5 [-1, -2] 4 0.001953 110111\n", + "6 [-2, -2] 2 0.000977 110110\n", + "7 [0, 0] 1 0.000488 000000\n", + "8 [1, 1] 1 0.000488 001001\n", + "9 [1, -4] 1 0.000488 100001\n", + "10 [-1, -4] 1 0.000488 100111\n", + "11 [3, -2] 1 0.000488 110011\n", + "12 [-4, -2] 1 0.000488 110100\n", + "13 [0, -1] 1 0.000488 111000\n", + "14 [-4, -1] 1 0.000488 111100\n", + "15 [-2, -1] 1 0.000488 111110\n", + "Analytical gradient: (dx, dy) = ([0.25, -0.5])\n", + "Majority gradient: (dx, dy) = ([0.25, -0.5])\n", + "Success rate: 97.07% (1988/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.07%\n" ] } ], @@ -1997,13 +2212,9 @@ "\n", "def f(x, y):\n", " a, b, c, d, e, f = 0.6, -0.4, 0.25, 0.25, -0.5, 0.1\n", - " global gradient_x, gradient_y\n", - " gradient_x = d\n", - " gradient_y = e\n", " return a * x**2 + b * y**2 + c * x * y + d * x + e * y + f\n", "\n", "\n", - "# Generated functions\n", "def f_normalized(x, y):\n", " val = f(l / N * x, l / N * y)\n", " val *= N / (l * m)\n", @@ -2011,48 +2222,27 @@ "\n", "\n", "@qfunc\n", - "def main(x: Output[QNum[n, SIGNED, 0]], y: Output[QNum[n, SIGNED, 0]]):\n", - " # 1. State preparation\n", - " # Build arrays in two's complement binary order for prepare_complex_amplitudes.\n", - " # Binary index i maps to signed value: i if i < N//2 else i - N\n", - " idx = np.arange(N)\n", - " x_signed = np.where(idx < N // 2, idx, idx - N)\n", - " y_signed = np.where(idx < N // 2, idx, idx - N)\n", - "\n", - " # In order to use the prepare_complex_amplitudes function, we need to flatten the 2D arrays of magnitudes and phases into 1D arrays.\n", - " X_grid, Y_grid = np.meshgrid(x_signed, y_signed, indexing=\"ij\")\n", - " phases_2d = f_normalized(X_grid, Y_grid) * 2 * np.pi\n", - " magnitudes_2d = np.ones((N, N)) / N\n", - " phases_flat = phases_2d.flatten().tolist()\n", - " magnitudes_flat = magnitudes_2d.flatten().tolist()\n", - "\n", - " # Prepare the state using the flattened arrays, then bind the combined register to the x and y registers.\n", - " combined_reg = QNum(\"combined_reg\")\n", - " prepare_complex_amplitudes(\n", - " magnitudes=magnitudes_flat, phases=phases_flat, out=combined_reg\n", - " )\n", - " bind(combined_reg, [y, x])\n", + "def main(coords: Output[QArray[QNum[n, SIGNED, 0], 2]]):\n", + " allocate(coords)\n", + " hadamard_transform(coords)\n", + " phase(f_normalized(coords[0], coords[1]), 2 * pi)\n", "\n", - " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", - " invert(lambda: qft(y))\n", + " invert(lambda: qft(coords[0]))\n", + " invert(lambda: qft(coords[1]))\n", "\n", "\n", - "pc, df = run_standard_simulation(main)\n", - "print(pc)\n", + "df = run_standard_simulation(main)\n", + "print(df)\n", "\n", - "majority_state = dict(df.iloc[0])\n", - "gx_true = gradient_x\n", - "gy_true = gradient_y\n", + "gradient_analytical = [0.25, -0.5]\n", + "majority_normalized = df.iloc[0][\"coords\"]\n", + "gradient_measured = state_to_gradient(majority_normalized, p)\n", "\n", - "gx_meas = state_to_gradient(majority_state.get(\"x\"), p)\n", - "gy_meas = state_to_gradient(majority_state.get(\"y\"), p)\n", - "\n", - "print(f\"Analytical gradient: (dx, dy) = ({gx_true}, {gy_true})\")\n", - "print(f\"Majority gradient: (dx, dy) = ({gx_meas}, {gy_meas})\")\n", + "print(f\"Analytical gradient: (dx, dy) = ({gradient_analytical})\")\n", + "print(f\"Majority gradient: (dx, dy) = ({gradient_measured})\")\n", "\n", "success_rate, success_shots, total_shots = compute_success_rate(\n", - " df, analytic_derivatives={\"x\": gx_true, \"y\": gy_true}, p=p\n", + " df, analytic_derivatives={\"coords\": gradient_analytical}, p=p\n", ")\n", "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", "show_bar(success_rate)" @@ -2060,10 +2250,10 @@ }, { "cell_type": "markdown", - "id": "54", + "id": "50", "metadata": {}, "source": [ - "# 5. Summary and Discussion\n", + "# Summary and Discussion\n", "\n", "This notebook demonstrated Jordan's quantum gradient estimation algorithm, which estimates $\\nabla f$ at the origin using a **single query** to $f$, compared to the classical lower bound of $d+1$ queries.\n", "\n", @@ -2078,7 +2268,7 @@ "| Parameter | Role | Constraint |\n", "|---|---|---|\n", "| $l$ | Sampling interval | $l \\leq \\frac{2\\sqrt{3}\\epsilon}{D_2\\sqrt{d}}$ — keeps $f$ approximately linear |\n", - "| $m$ | Gradient range | $2\\nabla f_{\\max} \\leq m \\leq 2N\\epsilon$ |\n", + "| $m$ | Gradient range | $2\\nabla f_{\\max} \\leq m \\leq 2\\cdot2^n\\epsilon$ |\n", "| $n$ | Qubits / resolution | $n \\geq \\log_2(\\nabla f_{\\max} / \\epsilon)$ |\n", "\n", "## Potential Use Cases\n", @@ -2098,7 +2288,7 @@ }, { "cell_type": "markdown", - "id": "55", + "id": "51", "metadata": {}, "source": [ "# Appendices\n", @@ -2141,7 +2331,7 @@ }, { "cell_type": "markdown", - "id": "56", + "id": "52", "metadata": {}, "source": [ "# References" @@ -2149,7 +2339,7 @@ }, { "cell_type": "markdown", - "id": "57", + "id": "53", "metadata": {}, "source": [ "[1]: [Stephen P. Jordan. Fast Quantum Algorithm for Numerical Gradient Estimation. Physical Review Letters 95 (2005)](https://www.researchgate.net/publication/7669221_Fast_Quantum_Algorithm_for_Numerical_Gradient_Estimation)" diff --git a/algorithms/gradient_estimation/gradient_estimation_helpers.py b/algorithms/gradient_estimation/gradient_estimation_helpers.py index 4498c115e..9b807f759 100644 --- a/algorithms/gradient_estimation/gradient_estimation_helpers.py +++ b/algorithms/gradient_estimation/gradient_estimation_helpers.py @@ -120,33 +120,35 @@ def run_statevector_simulation( print("Circuit Depth:", qprog.transpiled_circuit.depth) print("Gate Counts:", qprog.transpiled_circuit.count_ops) - df = calculate_state_vector(qprog) - if filter_ancilla and "ancilla" in df.columns: - print("Filtering out states with ancilla qubits in state |1>...") - df = df[df["ancilla"] == 0] + if filter_ancilla: + df = calculate_state_vector(qprog, filters={"ancilla": 0}) + else: + df = calculate_state_vector(qprog) df.sort_values(by="x", inplace=True) return df def run_standard_simulation(qfunc_to_run, show_circuit=False): - # Run a regular simulator qprog = synthesize(qfunc_to_run) if show_circuit: show(qprog) - job = execute(qprog) - # job.open_in_ide() - pc = job.get_sample_result().parsed_counts - df = job.get_sample_result().dataframe + n_shots = 2048 + df = sample(qprog, num_shots=n_shots) df.sort_values( "counts", ascending=False, inplace=True ) # Verify that the most common state is first, as expected from a statevector simulation - return pc, df + return df # ****** Result Processing ****** def state_to_gradient(value, p): + if type(value) == list: + result = [] + for v in value: + result.append(state_to_gradient(v, p)) + return result return value / (p.N / p.m) @@ -184,14 +186,25 @@ def compute_success_rate(df, analytic_derivatives, p, tolerance=None): success_shots = 0 for _, row in df.iterrows(): - est = {name: state_to_gradient(row[name], p) for name in analytic_derivatives} - correct = True for name, analytic_val in analytic_derivatives.items(): - measured_val = est.get(name) - if measured_val is None or abs(measured_val - analytic_val) >= tolerance: - correct = False - break + measured_val = row[name] + + if isinstance(analytic_val, list): + measured_val = state_to_gradient(measured_val, p) + if measured_val is None or any( + abs(m - a) >= tolerance for m, a in zip(measured_val, analytic_val) + ): + correct = False + break + else: + measured_val = state_to_gradient(measured_val, p) + if ( + measured_val is None + or abs(measured_val - analytic_val) >= tolerance + ): + correct = False + break if correct: success_shots += int(row["counts"]) @@ -200,35 +213,71 @@ def compute_success_rate(df, analytic_derivatives, p, tolerance=None): return success_rate, success_shots, total_shots -def analyze_results(pc, df, p): +def analyze_results(df, p): analytical_gradient = p.analytical_gradient(0) - # Print the results and compute the majority gradient - print("Parsed counts:", pc) + print("Parsed probabilities:", df.set_index("x").to_dict()["probability"]) print(f"The analytical gradient is: {analytical_gradient}") majority_state = dict(df.iloc[0]) majority_gradient = state_to_gradient(majority_state.get("x"), p) print(f"The majority gradient is: {majority_gradient}") - # Check if the majority result is correct within the resolution of the algorithm resolution = m / N is_correct = abs(majority_gradient - analytical_gradient) < resolution / 2 print(f"The majority result is", "correct" if is_correct else "incorrect") print("####################################################") - # Compute the success rate of the algorithm, i.e. the percentage of shots that are correct within the resolution of the algorithm. success_rate, success_shots, total_shots = compute_success_rate( df, analytic_derivatives={"x": analytical_gradient}, p=p ) print(f"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)") show_bar(success_rate) - # Visualize the theoretical values of the phases - # We used the standard simulation, so this is theoretical values only without the phases from the simulation - plot_theoretical() + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(18, 7)) + + x_array = np.arange(-N // 2, N // 2) + f_classical = f_normalized(x_array) + f_classical -= f_classical[N // 2] + + plt.sca(ax1) + plot_classical() + ax1.plot(x_array, f_classical, "o", label="Theoretical values", markersize=8) + xmin, xmax = -N, N + ymin, ymax = -N // 2, N // 2 + ax1.set_xlim(xmin, xmax) + ax1.set_ylim(ymin, ymax) + ax1.vlines(-N // 2, ymin, ymax, colors="lightgray", linestyles="dashed") + ax1.vlines(N // 2 - 1, ymin, ymax, colors="lightgray", linestyles="dashed") + ax1.hlines(-N / 4 + 0.5, xmin, xmax, colors="lightgray", linestyles="dashed") + ax1.hlines(N / 4, xmin, xmax, colors="lightgray", linestyles="dashed") + ax1.legend(fontsize=12) + ax1.set_title("Theoretical Phases", fontsize=14, fontweight="bold") + ax1.tick_params(labelsize=11) + ax1.set_xlabel("x (index)", fontsize=12) + ax1.set_ylabel("f (normalized)", fontsize=12) + + plt.sca(ax2) + percentage = df["counts"] / df["counts"].sum() * 100 + ax2.bar(df["x"], percentage, color="lightblue", label="Measurement counts") + ax2.set_xlabel("x (index)", fontsize=12) + ax2.set_ylabel("Percentage of shots (%)", fontsize=12) + ax2.set_xlim(-N // 2 - 1, N // 2) + ax2.set_ylim(0, 100) + ax2.set_title("Measurement Histogram", fontsize=14, fontweight="bold") + ax2.tick_params(labelsize=11) + if analytical_gradient is not None: + x_analytic = analytical_gradient * (N / m) + ax2.axvline( + x=x_analytic, + color="green", + linestyle="dashed", + label="Analytical gradient", + linewidth=2, + ) + ax2.legend(fontsize=12) - # Plot histogram of the results - plot_histogram(df, analytical_gradient=analytical_gradient) + plt.tight_layout() + plt.show() # ****** Plotting ****** From ade0c391637f79ed34934c41ccc0627345c74669 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Tue, 2 Jun 2026 13:18:44 +0300 Subject: [PATCH 10/12] Final version --- ...ithm for Numerical Gradient Estimation.pdf | Bin 122310 -> 0 bytes .../gradient_estimation.ipynb | 961 ++++++------------ .../gradient_estimation_helpers.py | 59 +- .../gradient_estimation/quantum_circuit.png | Bin 12297 -> 18758 bytes .../gradient_estimation/quantum_circuit_2.png | Bin 18758 -> 0 bytes tests/notebooks/test_gradient_estimation.py | 45 +- 6 files changed, 376 insertions(+), 689 deletions(-) delete mode 100644 algorithms/gradient_estimation/Stephen P. Jordan - Fast Quantum Algorithm for Numerical Gradient Estimation.pdf delete mode 100644 algorithms/gradient_estimation/quantum_circuit_2.png diff --git a/algorithms/gradient_estimation/Stephen P. Jordan - Fast Quantum Algorithm for Numerical Gradient Estimation.pdf b/algorithms/gradient_estimation/Stephen P. 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zc@+^66kuj&V-bY1ib4d~MA)Ff!yxbfPN9j!%Zp@ZuWM`n`;i*(9;_U!NR*T!uSAjl E9|-(IUjP6A diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index f10e1be07..ccf2ef46a 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -15,7 +15,9 @@ "metadata": {}, "outputs": [], "source": [ - "from gradient_estimation_helpers import *" + "from gradient_estimation_helpers import *\n", + "\n", + "from classiq.execution.functions.util._logging import _logger" ] }, { @@ -41,12 +43,13 @@ "> ---\n", ">\n", "> **Keywords:** Foundational quantum algorithms, Gradient, Function evaluation, Oracle problem, Quantum Fourier Transform (QFT)\n", + ">\n", "\n", "The core idea is an in-place computation: first, the function is encoded directly into the phases of the coordinate superposition state. Then, an inverse QFT is applied to overwrite that exact same coordinate register with the gradient, extracting it as a measurable outcome without needing a separate output register.\n", "\n", "We demonstrate this step by step—first with a simplified version to build intuition, then with refinements for the complete algorithm.\n", "\n", - "![Quantum Circuit](quantum_circuit_2.png)" + "![Quantum Circuit](quantum_circuit.png)" ] }, { @@ -269,16 +272,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "Circuit Width: 8\n", - "Circuit Depth: 42\n", - "Gate Counts: {'u': 31, 'cx': 27}\n" + "Circuit Width: 7\n", + "Circuit Depth: 47\n", + "Gate Counts: {'u': 34, 'cx': 28}\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/476aafde-9862-4490-b609-14503612776e\n" + "Job: https://platform.classiq.io/jobs/86efe0f2-82b1-4c8a-a1fb-b2522ab148d6\n" ] }, { @@ -295,11 +298,6 @@ "rawType": "int64", "type": "integer" }, - { - "name": "ancilla", - "rawType": "float64", - "type": "float" - }, { "name": "amplitude", "rawType": "complex128", @@ -326,91 +324,83 @@ "type": "string" } ], - "ref": "91f08f53-d36e-4da3-bae8-5bb3b83f85fd", + "ref": "b7f4ecee-9f7d-485a-8741-086b580b217e", "rows": [ [ "7", "-4", - "0.0", - "(0.08838834764831849+0.08838834764831834j)", - "0.12", - "0.25π", - "0.01562499999999999", - "00000100" - ], - [ - "1", - "-3", - "0.0", - "(-0.0883883476483183+0.08838834764831867j)", - "0.13", + "(-0.24999999999999964+0.25000000000000006j)", + "0.35", "0.75π", - "0.015625000000000014", - "00000101" + "0.12499999999999986", + "0000100" ], [ "4", - "-2", - "0.0", - "(-0.08838834764831854-0.08838834764831835j)", - "0.12", + "-3", + "(-0.2500000000000003-0.2499999999999997j)", + "0.35", "-0.75π", - "0.015625", - "00000110" + "0.12499999999999997", + "0000101" ], [ - "6", - "-1", - "0.0", - "(0.08838834764831824-0.08838834764831861j)", - "0.12", + "5", + "-2", + "(0.24999999999999978-0.2500000000000001j)", + "0.35", "-0.25π", - "0.015624999999999993", - "00000111" + "0.12499999999999994", + "0000110" ], [ "2", - "0", - "0.0", - "(0.08838834764831853+0.08838834764831836j)", - "0.12", + "-1", + "(0.2500000000000003+0.24999999999999972j)", + "0.35", "0.25π", - "0.015625", - "00000000" + "0.12500000000000003", + "0000111" ], [ + "6", "0", - "1", - "0.0", - "(-0.08838834764831831+0.08838834764831865j)", - "0.13", + "(-0.24999999999999964+0.2500000000000001j)", + "0.35", "0.75π", - "0.015625000000000014", - "00000001" + "0.12499999999999986", + "0000000" ], [ "3", - "2", - "0.0", - "(-0.08838834764831852-0.08838834764831836j)", - "0.12", + "1", + "(-0.2500000000000003-0.2499999999999997j)", + "0.35", "-0.75π", - "0.015625", - "00000010" + "0.12499999999999997", + "0000001" ], [ - "5", - "3", - "0.0", - "(0.08838834764831827-0.08838834764831859j)", - "0.12", + "1", + "2", + "(0.24999999999999983-0.2500000000000003j)", + "0.35", "-0.25π", - "0.015624999999999993", - "00000011" + "0.12500000000000006", + "0000010" + ], + [ + "0", + "3", + "(0.2500000000000004+0.24999999999999983j)", + "0.35", + "0.25π", + "0.12500000000000008", + "0000011" ] ], "shape": { - "columns": 7, + "columns": 6, "rows": 8 } }, @@ -434,7 +424,6 @@ " \n", " \n", " x\n", - " ancilla\n", " amplitude\n", " magnitude\n", " phase\n", @@ -446,97 +435,89 @@ " \n", " 7\n", " -4\n", - " 0.0\n", - " 0.088388+0.088388j\n", - " 0.12\n", - " 0.25π\n", - " 0.015625\n", - " 00000100\n", - " \n", - " \n", - " 1\n", - " -3\n", - " 0.0\n", - " -0.088388+0.088388j\n", - " 0.13\n", + " -0.25+0.25j\n", + " 0.35\n", " 0.75π\n", - " 0.015625\n", - " 00000101\n", + " 0.125\n", + " 0000100\n", " \n", " \n", " 4\n", - " -2\n", - " 0.0\n", - " -0.088388-0.088388j\n", - " 0.12\n", + " -3\n", + " -0.25-0.25j\n", + " 0.35\n", " -0.75π\n", - " 0.015625\n", - " 00000110\n", + " 0.125\n", + " 0000101\n", " \n", " \n", - " 6\n", - " -1\n", - " 0.0\n", - " 0.088388-0.088388j\n", - " 0.12\n", + " 5\n", + " -2\n", + " 0.25-0.25j\n", + " 0.35\n", " -0.25π\n", - " 0.015625\n", - " 00000111\n", + " 0.125\n", + " 0000110\n", " \n", " \n", " 2\n", - " 0\n", - " 0.0\n", - " 0.088388+0.088388j\n", - " 0.12\n", + " -1\n", + " 0.25+0.25j\n", + " 0.35\n", " 0.25π\n", - " 0.015625\n", - " 00000000\n", + " 0.125\n", + " 0000111\n", " \n", " \n", - " 0\n", - " 1\n", - " 0.0\n", - " -0.088388+0.088388j\n", - " 0.13\n", + " 6\n", + " 0\n", + " -0.25+0.25j\n", + " 0.35\n", " 0.75π\n", - " 0.015625\n", - " 00000001\n", + " 0.125\n", + " 0000000\n", " \n", " \n", " 3\n", - " 2\n", - " 0.0\n", - " -0.088388-0.088388j\n", - " 0.12\n", + " 1\n", + " -0.25-0.25j\n", + " 0.35\n", " -0.75π\n", - " 0.015625\n", - " 00000010\n", + " 0.125\n", + " 0000001\n", " \n", " \n", - " 5\n", - " 3\n", - " 0.0\n", - " 0.088388-0.088388j\n", - " 0.12\n", + " 1\n", + " 2\n", + " 0.25-0.25j\n", + " 0.35\n", " -0.25π\n", - " 0.015625\n", - " 00000011\n", + " 0.125\n", + " 0000010\n", + " \n", + " \n", + " 0\n", + " 3\n", + " 0.25+0.25j\n", + " 0.35\n", + " 0.25π\n", + " 0.125\n", + " 0000011\n", " \n", " \n", "\n", "" ], "text/plain": [ - " x ancilla amplitude magnitude phase probability bitstring\n", - "7 -4 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 00000100\n", - "1 -3 0.0 -0.088388+0.088388j 0.13 0.75π 0.015625 00000101\n", - "4 -2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 00000110\n", - "6 -1 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 00000111\n", - "2 0 0.0 0.088388+0.088388j 0.12 0.25π 0.015625 00000000\n", - "0 1 0.0 -0.088388+0.088388j 0.13 0.75π 0.015625 00000001\n", - "3 2 0.0 -0.088388-0.088388j 0.12 -0.75π 0.015625 00000010\n", - "5 3 0.0 0.088388-0.088388j 0.12 -0.25π 0.015625 00000011" + " x amplitude magnitude phase probability bitstring\n", + "7 -4 -0.25+0.25j 0.35 0.75π 0.125 0000100\n", + "4 -3 -0.25-0.25j 0.35 -0.75π 0.125 0000101\n", + "5 -2 0.25-0.25j 0.35 -0.25π 0.125 0000110\n", + "2 -1 0.25+0.25j 0.35 0.25π 0.125 0000111\n", + "6 0 -0.25+0.25j 0.35 0.75π 0.125 0000000\n", + "3 1 -0.25-0.25j 0.35 -0.75π 0.125 0000001\n", + "1 2 0.25-0.25j 0.35 -0.25π 0.125 0000010\n", + "0 3 0.25+0.25j 0.35 0.25π 0.125 0000011" ] }, "execution_count": 2, @@ -559,7 +540,7 @@ "\n", "\n", "@qfunc\n", - "def main(x: Output[QNum[n, SIGNED, 0]], ancilla: Output[QNum[n0, SIGNED, n0]]):\n", + "def main(x: Output[QNum[n, SIGNED, 0]]):\n", " # 1. State preparation\n", "\n", " # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", @@ -567,6 +548,7 @@ " hadamard_transform(x)\n", "\n", " # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", + " ancilla = QNum(\"ancilla\", n0, SIGNED, n0)\n", " prepare_basis_state([True] * n0, ancilla)\n", " qft(ancilla)\n", "\n", @@ -578,15 +560,20 @@ " # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", " # invert(lambda: qft(x))\n", "\n", + " # 3. Return the ancilla back to |000...0> state and drop it\n", + " invert(lambda: qft(ancilla))\n", + " apply_to_all(X, ancilla)\n", + " drop(ancilla)\n", + "\n", "\n", "# Run using a statevector simulator\n", - "qprog = synthesize(main)\n", + "qprog_ancilla = synthesize(main)\n", "# show(qprog) # Uncomment to see the circuit\n", - "print(\"Circuit Width:\", qprog.data.width)\n", - "print(\"Circuit Depth:\", qprog.transpiled_circuit.depth)\n", - "print(\"Gate Counts:\", qprog.transpiled_circuit.count_ops)\n", + "print(\"Circuit Width:\", qprog_ancilla.data.width)\n", + "print(\"Circuit Depth:\", qprog_ancilla.transpiled_circuit.depth)\n", + "print(\"Gate Counts:\", qprog_ancilla.transpiled_circuit.count_ops)\n", "\n", - "df = calculate_state_vector(qprog, filters={\"ancilla\": 0})\n", + "df = calculate_state_vector(qprog_ancilla)\n", "df.sort_values(by=\"x\")" ] }, @@ -634,7 +621,7 @@ "type": "float" } ], - "ref": "a198fb67-4835-4d1e-be10-4a4bd70b0a50", + "ref": "119268b4-53d0-4200-9a57-db95331b5e10", "rows": [ [ "-4", @@ -809,52 +796,9 @@ "The graph shows the original function (gray), classical values (blue), and quantum phase at sample points (orange). Results are displayed in both normalized coordinates (black axes) and original values (blue axes)." ] }, - { - "cell_type": "code", - "execution_count": 4, - "id": "17", - "metadata": {}, - "outputs": [], - "source": [ - "# # TODO: Fix it and remove the original (Ancilla not as output)\n", - "# p = params()\n", - "# # f(x) = 0.5*x + 0.25\n", - "# # Gradient: f'(0) = 0.5\n", - "# p.set_function(p.linear, (0.5, 0.25))\n", - "# p.unpack(globals())\n", - "\n", - "# @qfunc\n", - "# def main(x: Output[QNum[n, SIGNED, 0]]):\n", - "# # 1. State preparation\n", - "\n", - "# # 1.1. Set the coordinates state - Apply Hadamard gate on the coordinates register\n", - "# allocate(x)\n", - "# hadamard_transform(x)\n", - "\n", - "# # 1.2. Set the ancilla state - Apply QFT to |1111...1> state\n", - "# ancilla = QNum(\"ancilla\", n0, SIGNED, n0) # Declare the name/type\n", - "# probabilities = [0] * (N0-1) + [1] # |1111...1> state\n", - "# prepare_basis_state([True] * n0, ancilla)\n", - "# qft(ancilla)\n", - "\n", - "# # 1.3. Apply the function f on the ancilla, to create the phase kickback\n", - "# # Calculate the normalized f and add it to the ancilla\n", - "# val = f_normalized(x)\n", - "# inplace_add(val, ancilla)\n", - "# invert(lambda: qft(ancilla))\n", - "# drop(ancilla)\n", - "\n", - "# # 2. Next step in the algorithm: QFT inverse on the coordinates register\n", - "# invert(lambda: qft(x))\n", - "\n", - "# df = run_statevector_simulation(main, print_circuit_info=True, filter_ancilla=True)\n", - "# simplified_df = simplify_df(df)\n", - "# plot_simplified_df(simplified_df)" - ] - }, { "cell_type": "markdown", - "id": "18", + "id": "17", "metadata": {}, "source": [ "### Direct Phase" @@ -862,7 +806,7 @@ }, { "cell_type": "markdown", - "id": "19", + "id": "18", "metadata": {}, "source": [ "While the phase kickback approach is sometimes well-suited for hardware implementations with a state oracle, it requires significant circuit overhead in simulation. A direct approach provides more efficient state preparation for our purposes." @@ -870,7 +814,7 @@ }, { "cell_type": "markdown", - "id": "20", + "id": "19", "metadata": {}, "source": [ "A simpler approach is to directly prepare the desired state:\n", @@ -881,8 +825,8 @@ }, { "cell_type": "code", - "execution_count": 5, - "id": "21", + "execution_count": 4, + "id": "20", "metadata": {}, "outputs": [ { @@ -905,7 +849,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/7cc162b6-3a8d-4546-aceb-b36b10d92128\n" + "Job: https://platform.classiq.io/jobs/a9486f1f-fa7a-4566-a013-58f7d004c6d5\n" ] }, { @@ -954,7 +898,7 @@ }, { "cell_type": "markdown", - "id": "22", + "id": "21", "metadata": {}, "source": [ "The state is identical to the phase kickback method. Moving forward, we'll use the direct method for its superior efficiency." @@ -962,7 +906,7 @@ }, { "cell_type": "markdown", - "id": "23", + "id": "22", "metadata": {}, "source": [ "### Quadratic Function" @@ -970,7 +914,7 @@ }, { "cell_type": "markdown", - "id": "24", + "id": "23", "metadata": {}, "source": [ "Non-linear functions are more interesting. In the next example, we explore a quadratic function.\n", @@ -980,8 +924,8 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "25", + "execution_count": 5, + "id": "24", "metadata": {}, "outputs": [ { @@ -1004,7 +948,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/23c179af-ac5c-4845-bbce-851e54c7a979\n" + "Job: https://platform.classiq.io/jobs/e0017ddd-0fcb-4c0b-b5c7-f822651d6508\n" ] }, { @@ -1054,7 +998,7 @@ }, { "cell_type": "markdown", - "id": "26", + "id": "25", "metadata": {}, "source": [ "Decreasing $l$ narrows the sampling interval, making the function appear more linear within that region." @@ -1062,8 +1006,8 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "27", + "execution_count": 6, + "id": "26", "metadata": {}, "outputs": [ { @@ -1086,7 +1030,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/10e0781b-3c1c-4eba-8aee-63037572a00f\n" + "Job: https://platform.classiq.io/jobs/9981c31a-54fa-42b1-8aa1-5223af4c8f22\n" ] }, { @@ -1136,7 +1080,7 @@ }, { "cell_type": "markdown", - "id": "28", + "id": "27", "metadata": {}, "source": [ "## Full Algorithm" @@ -1144,26 +1088,60 @@ }, { "cell_type": "markdown", - "id": "29", + "id": "28", "metadata": {}, "source": [ - "### Linear Functions" + "### Implementation\n" ] }, { "cell_type": "markdown", - "id": "30", + "id": "29", "metadata": {}, "source": [ "The final step is to apply the inverse QFT to the coordinates. This extracts the gradient from the phases and produces a measurable state containing the normalized gradient value." ] }, + { + "cell_type": "code", + "execution_count": 7, + "id": "30", + "metadata": {}, + "outputs": [], + "source": [ + "@qfunc\n", + "def gradient(f: QCallable[[QNum]], x: QNum) -> None:\n", + " \"\"\"\n", + " Apply the gradient estimation algorithm to estimate the gradient of f at x=0.\n", + " The function f is given as a quantum oracle that applies the phase kickback.\n", + " \"\"\"\n", + " # 1. State preparation\n", + " hadamard_transform(x)\n", + " f(x)\n", + " # 2. QFT inverse on the coordinates register\n", + " invert(lambda: qft(x))\n", + "\n", + "\n", + "@qfunc\n", + "def gradient_nd(f: QCallable[[QNum]], coords: QArray[QNum]) -> None:\n", + " \"\"\"\n", + " Apply the gradient estimation algorithm to estimate the gradient of f at x=0.\n", + " The function f is given as a quantum oracle that applies the phase kickback.\n", + " \"\"\"\n", + " # 1. State preparation\n", + " hadamard_transform(coords)\n", + " f(coords)\n", + " # 2. QFT inverse on the coordinates register\n", + " # invert(lambda: qft(x))\n", + " repeat(coords.len, lambda i: invert(lambda: qft(coords[i])))" + ] + }, { "cell_type": "markdown", "id": "31", "metadata": {}, "source": [ - "Now we switch from statevector simulation to standard simulation, which measures the final result rather than examining phase values directly." + "### Linear Functions" ] }, { @@ -1171,7 +1149,8 @@ "id": "32", "metadata": {}, "source": [ - "We start with a linear function." + "We will see the first example on a linear function.\\\n", + "We switch from statevector simulation to standard simulation, which measures the final result rather than examining phase values directly." ] }, { @@ -1185,7 +1164,7 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/9cbb6c64-6a5a-4f14-ad03-12c561b14c09\n" + "Job: https://platform.classiq.io/jobs/ca997f04-5a28-4552-9659-3fd7a28e5983\n" ] }, { @@ -1220,22 +1199,13 @@ "\n", "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " # 1. State preparation\n", " allocate(x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", - "\n", - " # 2. QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", + " gradient(make_phase_oracle(f, l=l, m=m, N=N, x0=0), x)\n", "\n", "\n", - "qprog = synthesize(main)\n", - "# show(qprog) # Uncomment to see the circuit\n", - "n_shots = 2048\n", - "df = sample(qprog, num_shots=n_shots)\n", - "\n", - "# You can use the helper function:\n", - "# df = run_standard_simulation(main)\n", + "qprog_linear = synthesize(main)\n", + "# show(qprog_linear) # Uncomment to see the circuit\n", + "df = sample(qprog_linear)\n", "\n", "# Translate the majority state to a gradient value\n", "majority_state = dict(df.iloc[0])\n", @@ -1333,31 +1303,41 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/9f115f9d-8af7-4ce1-98d1-dd8acb003a34\n" + "Job: https://platform.classiq.io/jobs/6125d188-6482-4490-91cc-2ed31bfb1159\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed probabilities: {2: 0.884765625, 3: 0.05419921875, 1: 0.0244140625, -4: 0.013671875, 0: 0.0068359375, -3: 0.0068359375, -1: 0.0068359375, -2: 0.00244140625}\n", + "Parsed probabilities: {2: 0.8720703125, 3: 0.06396484375, 1: 0.025390625, -4: 0.0126953125, 0: 0.0107421875, -1: 0.00830078125, -3: 0.0048828125, -2: 0.001953125}\n", "The analytical gradient is: 0.55\n", "The majority gradient is: 0.5\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 88.48% (1812/2048 shots)\n", - "[\u001b[92m████████████████████████████████████████████\u001b[91m------\u001b[0m] 88.48%\n" + "Success rate: 87.21% (1786/2048 shots)\n", + "[\u001b[92m████████████████████████████████████████████\u001b[91m------\u001b[0m] 87.21%\n" ] }, { "data": { - "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "0.8720703125" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ @@ -1372,16 +1352,12 @@ "\n", "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " # 1. State preparation\n", " allocate(x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", - "\n", - " # 2. QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", + " gradient(make_phase_oracle(f, l=l, m=m, N=N, x0=0), x)\n", "\n", "\n", - "df = run_standard_simulation(main)\n", + "qprog_linear_2 = synthesize(main)\n", + "df = sample(qprog_linear_2).sort_values(\"counts\", ascending=False)\n", "analyze_results(df, p)" ] }, @@ -1420,25 +1396,25 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/d31812c4-9e41-4f3d-b2e4-44265c9093a1\n" + "Job: https://platform.classiq.io/jobs/dcb42534-fa36-490d-a008-5acaa5c3e72d\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed probabilities: {1: 0.98876953125, 0: 0.00537109375, 2: 0.0048828125, -1: 0.0009765625}\n", + "Parsed probabilities: {1: 0.98828125, 0: 0.005859375, 2: 0.005859375}\n", "The analytical gradient is: 0.25\n", "The majority gradient is: 0.25\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 98.88% (2025/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.88%\n" + "Success rate: 98.83% (2024/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.83%\n" ] }, { "data": { - "image/png": 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aZMcee6wLBE6ePNkFZXUMFDjVa++880477rjj3Ou8v6HUma3OZ+03BR61PyZNmuT2mdahTM5A6iDfuXOn6wxWJ66CvNoH2qdkkADRTYE+fZ+VZab27Nlnn3XBPAXHQqWnLZgxY4a7r7LQCvppHFgFC/V33rx5KY5jrvZfQaRPP/3UBZg8GzZssC+++MKfhajxVP/3v/+5NlHtoSgQmRIFoxR41LngjjvucG33zz//7C6w0IUpovZPbakuplC7q5KnY8eOdQE1PZdR2odqW3Xe1HlCgUgF5hRgDVcS+v7773f7X4E+Bex0W+el9Jyz1J63b9/enTN0HtDj2kfaZ+mhY6l9pOOl1ysD9KmnnnL76Jtvvglq49M612b0XAQAABAPCPwB8Nu1axd7AwBioF1VsCu1gFdu866+T68dO3a4oFO3bt1Sne/EE0+0Dz/80HUIK3jlURZZYFZFOD/99JML+g0ePNhGjx7tHlMQTJ2Q6c3G05hFKkPqBSf79OnjMjbGjx/vMlREWRO///570AU16mhWEO2ll16yoUOHpmtd3vtV9oU6dDXGocb3y6wlS5a4Tlyv41pZEtpvb731lus4FnVWq/P7u+++s+bNm/tfe99997nPlzqy9d7V2dqxY8dk2X2h1Amv9b7++ut28cUXu8euuuoq16GsrBN1kgceR3Uo//HHH67TWpR5o89EaAc9gOgyf/58W7p0qQtyiTKzFZhSMDBc4C89bYHa75tuuinodbqgQ0FFXeiQ0kUkZ555plu32qXAdkVtoS7g8dpZ/VV7pWyztNpencMUiFKQUFlnylLzBJ6bH3nkEZeZ51FA8eijj3bBK71nXYyZXsrC1vlE+0/BN6+0tc4bCpKFC/ypvOePP/4YtA3pPWepPdd8Oo962XYDBw5055G06Hi8+OKL7nh7QVDvPHTWWWe5oGfg42mda3VMMnIuAgAAiAcE/gAAAGKMOhYV1MkrGjZsmKHAnwJ5EhgECsd7XuXJAudV52xavLKW6iwOdN1117kshPS+r8DOZJUkVYe0sk48Kt/mOXTokMtsU5ae5lPwMVI6dOgQlK3iBRW9bVeHt7I+zj333KCgnycjx9Mzffp0l4mjjniPsjrUQa7HlHEZ2PHet29ff0e/ePs6cP8C8WbU3FFuSstJVU+yDy/8MOix8946z35an3a7M6TlEDd5du7bacc9fVyq82SEAj4q7ahAj9ee6Puu4NvIkSOTjZeXnrYgMHilgJYuvFHgT9TWphT4U4BLFyIoaBR4EYm28bTTTnNZbxml7EMt6/bbbw8K+nnvNdw2q4yosui0Tp3DlfmWkcCfAngqazpixIig8Wz13nSxSDjKngvchoycs9SeV61a1WXieVQuVMHLW2+9NdVtVWCvdOnSLki3ZcsW/+PK4NO6Zs2aFRT4S8+5FgAAAMEI/AEAACBP8TpevQBgRgOE6emoXbVqlevwDZ1X2RbpFa5TVp3TgWMUKYD2xBNP2DPPPONKmakj1eOV1IyEtLZ98+bNLqCqMQCzi/a5SrCGlhP3yrHp+dS20ev4Dx0DCognifsSbe3OtWnOV7N0zWSPbd69OV2v1ToCJVlSsteFzpNeagM1tpyCfmoTPS1atHBBv5kzZ7qx9TLaFmhsunvvvdctW2OJhmbgpaZfv34u+27KlCnutjLMlJU4bty4TL3HP//80/1Nq/1UVt8999zjMtdD27W0tjmU136GnsMUBAw3/mtK58r0nrO0Pq0r9CIQb0zE1Ch7U+9P4wKGE3r80nOuBQAAQDACfwAAADFGHXG6Qj6vyGh2mDIBlEnwyy+/pDqfnq9evbrLVAsUmsGQU0KzUsKVctM4gyqNpjKWGk+pXLlyLvClEqPqYM3pfRzYaZvRbY+0aNhGILeVKlzKqpesnuZ8FYtVDPtYel6rdQRKsIRkrwudJ71UhnL9+vUuQKcplDLtQgN/6WkLVP7x22+/tVtuucWaNGniMsfUxqp0ZFptrc6XyjZTxqECf/qr8e60zJyitlkZbwpY3nbbba6UZvHixd04qirNmZ3nh5SEO1fmxjlLy1HQT8c6HGX0BeJcAAAAkHEE/gAAAGJMRsfUy4tU8vGFF15wYwFp/KdQX3/9ta1cudKuvPLKTC2/du3arvNRGQ3KQvMsX77cstPkyZNdZovGRgqk8mkVKlTItvUo+0HLDBWaRZde6nhVQPW3335Ldb6MfM60zxWs1X4PzPrTWF/e8wBSl5USm6GlP9OrZOGStmbIGssOCvYo6PP0008ne+69995zWXfKtMvIBRzK/FKmoDL+lEEXmFmWXgr4DRkyxAUlNUZs165dg8qLZqS988ooq/1MKYv8119/dWPkvfrqq27dgWVCM8NrP3UO80qoysGDB925UuWcs/OcpfXp/Sn4GrhflC2Znv3z+eef2+mnn55tF+pE+/95AAAAsltwnR0AAAAgD1DWhjoEFdjTuEWBlCGhcfw0npDmy4zOnTu7vypnFmjs2LGWnZSpEJqhpvGNlNWRndSRqtJpgVmS6sBWJ3pmKDDXvXt3++ijj9zYUaG896QMFQkXdAzVpUsX27Bhg02cODGoU1r7XNk5bdq0ydS2AogOGsNOwT1d2KGx4UKna6+91pVwVunLjPAywkLb2jFjxqR7GRpnVMGjG264wY0dd8kllySbR+1deto6ZSyqBLXG29N4g4G8bQy3zbqtMpuZobFYVYpTF8yoXQ0MtGakJGZ6z1lqz9etW+cChZ7du3fb888/n+Y6lEmpjEdlFIbStqdnH4fKyLkIAAAgHpDxBwAAgDxHWXjKhLj44outUaNGdsUVV7jxiJS5oEyELVu22FtvveXPrMgolXXr2bOn6xhWYPHUU0+1L7/80mVgZGf2gDq477vvPhswYICddtppLstDHbF169a17HTBBRe4cnHnn3++XX/99a4D9tlnn7X69evbTz/9lKllquTbZ5995gJygwYNcmPxKZioTmBlYpYpU8aV1FNHscbHUuCxcOHCduaZZ4Ydu0nLeO6551wZO42fpXGn1Gn8zTffuOMQOlYjgNiigJ4Ce+edd17Y59UOK9tYbWTfvn3TvVxlJ59xxhn26KOP2oEDB1wJaLVdgWMIpkXrVVlQtW9q25TxF+68oUy1UaNGWbVq1dw5SWMThtue0aNH2//+9z87+eST7aKLLnLZgwsXLnRts85tKu2p89fNN9/sgmp6zbvvvpvpcetUmnT48OF23XXXuTZYwTWdL1955RW3nvSe09J7zho4cKA99dRTLltR7bnKc0+YMMFdkJMWnVN0UY8CowsWLHCB0oIFC7oMTe1/BT8VCM6IjJyLAAAA4gGBPwD+K/vTGoAeAJB+tKtZ17t3b9c5qs5BL9injAaVIbvzzjuzfN567bXXrEqVKi6AqMy4Dh06uGy0Bg0aWJEiRbLhHZjbzn///deVjtOyTzrpJJs2bZrdfvvtlp20X/QeVKru1ltvdR3S2m/qSM1s4E+d5999950b70kdv4mJie6xs88+29+5q/2nsnxal4KzyuKYNWtW2M5WZXDOnj3bvXd1fGt52tfjx493wUAAsU3tiNpWjW2X0nlTATfNF5rpnRa1sQp6qYSoMtYUTPr4449dgC69FMSaOnWqC5opcBRKAT9dwHD33Xe77MX+/fuHDfyJ2kO1gw8//LDLbFNgS+ezG2+80T2v+8qo1oUaaj+1X3ThhrIeGzdubJmh1+q9jxw50gUUtRwFW7WO9J7T0nvO0jlA5VW1z5W1rfu6UEfnBwVQ06LzhgKpuhhE6yxQoIC7GESZlioBmlEZORcBQF52boNBtufATitakAviAGRNQlJoHYc4pE6H0qVLuyvDdKUdAABANFAJMWU0KMiTXYGqeKfsg6ZNm9rrr7/uOjERP9LzfVqzJtFq1ixtq1fvsBo1+N2AnPntSdseGR988IErcfzVV19Z69atLRZoTFVlM/bo0cOVAUX24rsKxI73lq2P9CbkOT0aVI30JgBxLTGLMSvG+AMAAEBcUsZGKJWcVNaJysYBAOKHAmMqadmqVSuL1iBU6HXdymzXuLht27aN2HYBAAAg91HqE4D/atA1a9a42zVq1HCdngCAzKNdzfs0HpTGJlLpUJUZU1k4TSrlVrNmzUhvHgAgF7z99tv2yy+/uJKWGl8uu8Z4zW3z5s1zpURVJlvln1XmWWWyVRZbjwEAACB+EPgDEJRCDADIPrSredtpp51mM2bMcOMv7dq1y2rVqmXDhw+3u+66K9KbBgDIJRdeeKGVKFHCjQ139dVXR+1+1xh5umjlySefdFl+5cqVc+MWapzBQoUKRXrzAADpsOfALkuyJEuwBCtasAT7DECmEfgDAABAXOrYsaObAADxK7Q8ZjQH/j788MNIbwYAIAuun97Gtu5Zb+WKVrUXus1nXwLINGr5AQAAAAAAAAAAADGAwB8AAAAAAAAAAAAQAwj8AQAAAAAAAAAAADGAwB8AAAAAAAAAAAAQAwj8AQAAAAAAAAAAADGgQKQ3AEDekJCQYA0bNvTfBgDQrgIAAAAAACC6EPgD4A/2EfADgOxDuwoAAAAAAIDcRqlPAAAARK3Zs2e7IOvkyZMt1uh9DR8+PEeWvXLlSrf8V155xSJxvPQXAAAAAABkPwJ/AJzDhw/bmjVr3KTbAICsoV3NerZkWlMsBI+mT5+eY8E9AMhrdLGB14bPmTMn2fNJSUlWs2ZN9/w555wTkW3EEW+++aaNGTMmZnZJrL0fAACAlFDqE4Df9u3b3d9q1aqxVwAgTtvVvQcO2fRf19tnizba9t37rUyxQtbp+MrWpVFVK1Iwf65sw4QJE4Luv/baazZjxoxkjx933HG2ZMkSi/bA39NPPx02+Ldnzx4rUID/rgM44r1l6/PE7ujRoGqWXl+kSBEXhGnVqlXQ419++aW7ELFw4cJZ3EJkBx2j3377zQYPHhwTOzTW3g+A2HN76/F28PB+K5CvUKQ3BUCUoycBAAAAzozFG+2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"text/plain": [ "
" ] @@ -1460,17 +1436,14 @@ "\n", "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " # 1. State preparation\n", " allocate(x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", + " gradient(make_phase_oracle(f, l=l, m=m, N=N, x0=0), x)\n", "\n", - " # 2. QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", "\n", - "\n", - "df = run_standard_simulation(main)\n", - "analyze_results(df, p)" + "qprog_quadratic = synthesize(main)\n", + "df = sample(qprog_quadratic).sort_values(\"counts\", ascending=False)\n", + "success_rate = analyze_results(df, p)\n", + "assert success_rate > 0.9, r\"The success rate should be above 90% for these parameters.\"" ] }, { @@ -1492,25 +1465,25 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/861fff75-1d5e-4d4f-998c-c126cfc16937\n" + "Job: https://platform.classiq.io/jobs/fc8db73d-4f07-4293-a6bb-1bee0b716e05\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed probabilities: {0: 0.2568359375, 2: 0.255859375, 1: 0.22607421875, -1: 0.087890625, 3: 0.08642578125, -4: 0.03466796875, -2: 0.02880859375, -3: 0.0234375}\n", + "Parsed probabilities: {2: 0.2451171875, 1: 0.244140625, 0: 0.23486328125, -1: 0.10791015625, 3: 0.0771484375, -4: 0.03857421875, -2: 0.0302734375, -3: 0.02197265625}\n", "The analytical gradient is: 0.25\n", - "The majority gradient is: 0.0\n", + "The majority gradient is: 0.5\n", "The majority result is incorrect\n", "####################################################\n", - "Success rate: 22.61% (463/2048 shots)\n", - "[\u001b[92m███████████\u001b[91m---------------------------------------\u001b[0m] 22.61%\n" + "Success rate: 24.41% (500/2048 shots)\n", + "[\u001b[92m████████████\u001b[91m--------------------------------------\u001b[0m] 24.41%\n" ] }, { "data": { - "image/png": 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LyNNrPjDop3WuYLQCbgqAl+Z1pwzOY445xmUzKoNT6tSpY3369LEuXbq45dR7Q9tQwT6th6ysLPd+VSC8IFofer8p6Kznr+WV+fPnu/XWokULF/zTe1DvRZkxY4YLWur9CgAxEfi79lqlSxc9TwGfqSXSooXvvzKtFeTw6Hy3brvn+ef7hl92to522n37WFDS7VDe9aXPQpV5O/fc4udVqT0NRu7YoS+zVuVV1DYIXL+yYIFvgF23DTgQzvmnSgHvhRBvB/3u00FySUlmEyaYJSQUv61i6b1QGJWp1UGe3uvSo/OFrXNdXtT8JfmcQPm2gUcZZgr8ffaZL7BX3HtMj6X9E4G/0G4Hj/Y7OrBA61h4L1TcNtDBHBrHKMmB37wXQquwzwSV3K5Vy7dNy/veAgDELpWSvOSSS1wAQ8EDBY0UAPSCSUOGDCk08KfMNC8YpiCQMoe8wInKR6ocpJd5pQw0BSVE5Rc1/fLLL648oYIXyppS2UwFHUSZfAoMKVNQgTQFuqRevXous0kBKY+CYsFZb6Gg5ddzUmlRjzKiRo4c6T9/++2321133eU/36lTJxdYkVGjRtlNN93kL6caSEGoyZMnu8BhamqqXXrppf7r+vfv7zIGvef2gH6QmPnXjSjY4wWmlFX41VdfufKSouwtZWpq3SpzT9tTy1IQXX711Ve70wruKJDrBXUVEFKQ6brrrnMBtMDAn7afSoWWVeB9lYeen0dlU5WlpnXq0esmLS3NnT7ooIPcpMw5L/Cn4KqeXyBlWKoUq0fb88F/jrRWkE+vSS/45wVItY0VOPUowKiAmd5DopKfga+Toii7U4Hj4NeNbq/Xn94Xeq8qw1SlR4877jh/1qb+K+OzlfokFECvK5UuFZWSXb58uf86ZeYqEKqgvwKEet95rzsCfwBiJvCn/fY/++6QU8kw/UjXwRXeAK6ybNR/S/2DREe/b9zo6+fRo4fvMn0mKSPbC4zEgpJuh/KuLx3hftJJJXss9QHUQU+xEuioqG0QuH7FC3bofu+7zxfM8kpYTpniGwxTVlqsCPd20D5I/YT0uv7f//JmPRUm1t4LhdHvUa1r7dP/+Q3l1rfOX3FF4dtJ119zze7L9Lr2Mp9K8jmB8m0Deegh3/7lk0/y9sUsjH5PqsdfYDAW5d8OgTTeo9YVxx/vO897oeK2wbhxvgM5zj67+MfhvRBa2vdPnpz3ssDPhFC8twAAsU1ZZspiU38y9fVKT093lysgqOy8wijY5FHmmIIFhVEGmhf4UzBNGUYF9aAL5AVsFFRUgEbzKyClgJwy5RToUmBKWXC6LNTUozAw6CcKhgWWNVU5zMJKYiqgqRKkCgYGU3aeF6AKDqCdfvrp/tMKGHkCSzQGrnsFt5TlVtS6L4gChoEBRwXOAkVDf7e9997bve60rhX0Ur87BT21Pvbbbz9X9lJZm6XhBfU85513Xp51dvbZZ/vnUYBarwktR2AGo4JxXtBP1IOvpIE/ZVMWFCxWtqFK3hbUNzP4fVNQ4E+vMy/oJ1ovXuBP7x8F/UR9EtUj0dsPRMPrAEDlk38vVgVpf6wBcP3XgJVOa1IfOI++AyiDRvS5r8Hee+/1DbBrgEuZZuot5P2YV5krZd4MHerLdtLnvX7Yq9SS5kNeJVlf+jzTdgjOHlNWwYwZqieff61++KGZDuhRvxvNpxL1999vduWVbIFQbANVeVDGmIJUOnhP7we9F9RP28u86dvXF+A75xyzOXN8A/S33aYv6AScQrUdFFDSela2h4LgOq9+Q5r+OeiS90Ixhg0ze+45NQ73lVxVcE7r84ILfNfrdX3zzbvn1wGX6j+uA0nVn0kH2Oo3hDeAW5LPCZRvG+iATpWvVQsF/Q73XvPeZ7f+X3+9mVo1aP+kAfaTTzbr0MEXJEdo3gsaQ1H/XB2Q++OPvqCT2st4n8m8F8K/DTza/2v/Ejyex3uh9LTOvN8DsmjR7t8KovUfWGXisst87wElD+gz4amnzN55x+w//yn5dgUAoCjK/FG5SvEG+xMSEvxlJwujoEdJKevP6x2mnmzFBf1EpSo9yvJTqUVRsEKZS4888ogLyqgU4jB9GBZCWXOF3W9RCgrYleY5Bz7vYCqt6QnMXgy+LrB/XODzKMu6D6ZsMWV8eoKDvF6/t3BQH0Q9n8BJl5WWll+99rxymMrkUwnOESNGuGxVvbYLy3YsTPC61Xoq6rwXGFMGnkdlMwMFny/t606veWVjFhf0K+r1Hfi6Cn7dBV8X+LoL5+sAQNUVtRl/paFSz4H9h1WiSvR5dvjhvtPz55tlZOyeRz/s9WNd/c30uXHIIb5B4MAsG5WH1iCwyonpQBB9R3vssYp6VtGnuPWlDHZtB5X0DKRB39RUX+CjoJJjTz7pG3jR9y8N+Or7hIIqKP820HcQldcbM8b3ftABS7qNAnselbaaONE3wKUj3+vU0dFYJStFFqtKux002K5MMtFrPJAGKxUU4b1QNLUM0G8tfR4oeKQsPe3Tvd8L+u4eeECf+pipr6he62oJoYot77+v3gml+5xA2beBDuTIylIvh7xr8c47fYFY7Xt++cX3+a71r99J+pzQwQqxnuUayu2g39D6TNW8yiBWVpMOWA7M6Oa9EN5tIPpMmDnTF4QNxnuh9HQgxxFH7D7vjVPq+8tLL5mpxU/gmI4SGCZN8n3ffPRR3/dSHXgWeJBBcdsVAIDiqNyj+q55FAgMDgYE88p6SnJycpHBNy8DST3DvH52ol5+KofZpEkT27p1q+tjVhBlbylYqPKVyhhUz0D9/+ijj1xgYvTo0XbiiSfaEUcckS9bSsFGj+YtaS+5gpYl8DmLAo9F9bgrrBymAquFCQy6FCZwORT8uqeIBtheb8XiliGwRGY0OfLII13/Or0eVKZzwYIFLstRvfLU905lZ9UzUdmAJRG8jVetWpUnm1XnA3m9DpUdqsxD8UrgelbqC1oJFfS6UxlOvT88Kjer7FxtW/X0U0Zsccr7mgOA0oiJvYp+wGsqStDBR+4IdgUuigpe6HNIA8MomeLWl76LBW8HUQafpoIoc0oTwrMN9LugJD26VbUhuAQWQrcddIBCQe+NQLwXiqdga2El1wL6jfsNGuSbClOSzwmUfRsU1yJEfbWUYYzwbofRo31TUXgvhHcbiKo+FfY5wHuh9Ir7XC3od4Nu89NPZd+uAAAUp3fv3q58ptdHzivLWRT1S1O2lZdVpr51CtAFUibX1KlT/SUrvcCI56yzznJBP/HuqyAK6HTr1s2V9tTk6dq1q+sVKAr8KPAXXJ5TvdaO/6dW/HPPPVdoBlxJqBymV1rSCyoG94jzAj8qx1lYr7Xy0roP7HOnwI/KSwb75ptviizXWlLBQaPAIFQk6bkr6KdSmypV6ZWr1OtOAbmMjAwX7J0zZ44/8Bf4XAp6HoHrVtSf0uvxp7Kqr732Wp4goVciVY+tHpmi/8oE9IKCL774YrmeZ/D7RqVDvYBuUe8bAIiUmAj8AQAAAAAAAJXZK6+8YvPmzXOBEQUCi3P++efbvffe63reqT+g+ocNGjTIBVhUblC9z6ZPn+4ypFTGUX3EgvvIqV/a4MGDbfHixfbqq68W+lgHHnigy0A89NBD3f969eq5YI4X9BMv4Kfr1ONN/fXkvvvus59++skF6T5Xk/tyUDahMhtvvfVWf9BF5SWPOeYY1xtNmV3q9aaA2yGHHGKnnHKKhUP//v1dsEt97URlIAcOHOjKoXpZjcquXLJkiQs6KWhaHiqZGdz/sF+/fi5TTNl0RfUYDCeV19RzVuDzgAMOcK+NWrVq2cyZM13QzxMYDA58LpMmTfJnnGrSa1rBZPWNVMBa1P9S21iP8emnn+bpAahMWS/DdOjQof7An5arV69erl+jynMGBgvLIvh9o+2vQK9e/+PHjy/XfQNAOBD4AwAAAAAAACJMvcUK6i9WGGUcqdfeySef7IJ/mzdvLjazqUePHnbsscfax6pJbebKFN6pevr/lM1UdlVhlNmlqSAKKp4WUKf/hhtusIv/aQytQNhE9Qgxs3bt2rneZgpwlpUCRbq9F6hUoE9TRVLA7f3333fBNwVNVdLyrbfeCtvjqWRp9+7dXQBVFNDV5F0XqcCfR2VgC+sbqYBgnz59/OcVIPVeZ8r487L5FNhT4E8UqFPwT69PUXAtOMCmcri3qDdHwPkzzjjDvx1UjlZBZ1GQTmVpPcHlaIuj4KoyXVXqVhR89AKQxb1vACASSreXAwAAAAAAAFApqCyiAi633367C+op265atWouw0rnr7jiCpsyZYoddthh/tu8++67ds0117i+gArCKUPw/vvvt+eff77Qx3n66addeUOVEm3atKkLfNWtW9edV5BPGXaBvezU/0xlPZUVp8do0aKF/fvf/7Zvv/3WmpezCa6CNsqOVLaYgj2pqanuMVRSs02bNq7X4JgxY+zNN9+0cFKwTRlfykjTdlBZSa17ZR5qvSjwOWHCBDvzzDND8njvvfeey2BUecvK0g9Qz/mJJ56wIUOGuMw/LZvWgV6HKr2p3ofK3AvsYacgmm7jvTYKoteLyt6ql56yX/Xa0n3otafAtYJ7CgQG98ZTMPiBBx5wpW2VOaugqN4bev0GCi5HWxzdl7JVFZhUqVm91tRb8tlnn7XhakIPAJVMXK6KLgMAAAAAAAAAEKVUTlalRoMp0HjllVf6z6enp7uypABQVVHqEwAAAAAAAAAQ1c455xzX37Jv374u+3PLli325Zdf5slmVZYoQT8AVR0ZfwAAAAAAAACAqDZgwADX97Iw6jeo/pYqUQoAVVmV6vGnJsaq66061xXd1BcAAAAAUDktWLDALrvsMuvWrZvrB6S+PAVRRoB6NiUmJlrXrl1t4sSJ+ebJyMhwvavUx0h9nE477TRbsWJFBTwLAABQlPPOO88F/1q3bm21a9d2vfnUL1B9AV944QX76quvCPoBiAlVKvCnhrHZ2dmlvt2OHWbqw6r/iAy2QeX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" ] @@ -1532,17 +1505,14 @@ "\n", "@qfunc\n", "def main(x: Output[QNum[n, SIGNED, 0]]):\n", - " # 1. State preparation\n", " allocate(x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", + " gradient(make_phase_oracle(f, l=l, m=m, N=N, x0=0), x)\n", "\n", - " # 2. QFT inverse on the coordinates register\n", - " invert(lambda: qft(x))\n", "\n", - "\n", - "df = run_standard_simulation(main)\n", - "analyze_results(df, p)" + "qprog_quadratic_2 = synthesize(main)\n", + "df = sample(qprog_quadratic_2).sort_values(\"counts\", ascending=False)\n", + "success_rate = analyze_results(df, p)\n", + "assert success_rate < 0.5, r\"The success rate should be below 50% for these parameters.\"" ] }, { @@ -1579,264 +1549,32 @@ "id": "44", "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/64786f4d-1f4d-40a7-b765-55c7d43158d4\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=0.05: Success rate = 0.00%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/78894643-1276-424a-a72c-cf13692576f8\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=0.1: Success rate = 0.00%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/d300a547-f71f-4325-9e0a-62ccead9a116\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=0.33: Success rate = 1.03%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/c30dfefe-a80c-49ad-aecd-64f8164e8073\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=0.5: Success rate = 10.30%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/0d4f1fd7-7e49-4965-bd6f-e03b80c8e309\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=0.67: Success rate = 94.04%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/3404a3a7-9c6c-4616-85e7-c35403d69f66\n" - ] - }, { "name": "stdout", "output_type": "stream", "text": [ - "m=1.0: Success rate = 99.32%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/a7b9310c-4550-4434-afd6-60d25b2d4d18\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=1.33: Success rate = 81.64%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/0d3adfc7-9241-4006-ab2c-51ff941ba9d2\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=1.67: Success rate = 95.17%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/441d37c7-5e03-426f-bf01-b3756b2d6626\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=2.0: Success rate = 98.44%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/b09d5b05-d3e8-4370-a00b-c9ccddcb9c63\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=2.33: Success rate = 89.89%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/1e7c5ebc-d2a9-4568-ae25-6fa24c15c10f\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=2.67: Success rate = 79.10%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/a8af23be-90bd-4b3a-88cd-b6224b73b08e\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=3.0: Success rate = 65.04%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/f82c64db-2fc7-40af-8262-81267506bc24\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=3.33: Success rate = 55.22%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/312ee63b-47e3-49e0-b3b4-41525e295b84\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=3.67: Success rate = 0.00%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/91ab61b0-0a9a-47d6-944c-012e90bd2cf6\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=4.0: Success rate = 0.00%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/bfcb2c83-b94d-4220-a35f-52b74e3cac5a\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=6.0: Success rate = 0.00%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/e33663f4-7960-45fe-ab00-d0df1c063290\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m=10.0: Success rate = 0.00%\n" + "m=0.05: Success rate = 0.00%\n", + "m=0.1: Success rate = 0.00%\n", + "m=0.33: Success rate = 0.88%\n", + "m=0.5: Success rate = 10.60%\n", + "m=0.67: Success rate = 93.31%\n", + "m=1.0: Success rate = 99.27%\n", + "m=1.33: Success rate = 81.05%\n", + "m=1.67: Success rate = 94.14%\n", + "m=2.0: Success rate = 98.44%\n", + "m=2.33: Success rate = 90.48%\n", + "m=2.67: Success rate = 78.66%\n", + "m=3.0: Success rate = 64.75%\n", + "m=3.33: Success rate = 54.30%\n", + "m=3.67: Success rate = 0.00%\n", + "m=4.0: Success rate = 0.00%\n", + "m=6.0: Success rate = 0.00%\n", + "m=10.0: Success rate = 0.00%\n" ] }, { "data": { - "image/png": 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35fjS59EeX5qp1umc3oIpzdw27n8GAEztAxBRdArbxRdfbBqE6roNXUCuaxv0pEpP9HUKl05r075PLhowadbouOOOM9O+dPG/BgYacLkWunu6/fbbTVCjU8L0X22Kq8+nzTm1wIWeWLrWKOm6Hs0CaU8c3V6zNBrYaLCkY3I12tW1RDptTNc+6eJ+zTBp42BdY+IK8rT3jj6/q3msLr7X4gfab0mzbfq6WuBC18no/UrXQWk/HS0woWt69ORfAxxdoK9T+nRKXltpAQgt3jFt2jTzWrqP9URXM1/6XrS/jk7B0s9GT771M2lMszya3dL9pFOsNHOo22qAo/tWp1zpftY+QLqtTinU96wnv/q5asbI1+ICSp9XeyDpNEP9vL31hNIMlGYqdH/qWPQEW48LzUZpnyRXIBEu9D3r8aDBh35OOn7t3aXHgjbu1amhoXw+f+gfQvT3WAMgzRLr727//v3NNFf9PdTfF83O6vpBpb9Letzp2jg9nnTNnh4/OnaduqtFJvT3Qntf6fRf/X3RPwjoHzt0uq2+L/2jBH2iADQQ6rKBABBMa9ascd5///3Oo48+2tmvXz9ncnKyuWhpYy1ZvGTJEq8/p32QtPeN9ovRcs9XXHGF6YfjrY+Ustlspk/NqFGjTG8iLWOt/Ym0x9Tu3bsbbKv9b6666irnPvvsY56/a9euznHjxpmS597Gr2Ws9TV1Wy3LrOPScs+LFy92bzdz5kxTslvfV2pqqinHrj11tD+RZ/+mOXPmOKdOnercb7/9TNl21zi1b05BQUGb+kh5cvXLmjdvnrv/z1133eUcOHCgMykpyZRK133T0j7Vz023T0hI8FqS/tdffzX70fWcWkZ98ODBzgsuuMD9ur7S8uNaMl1fR0uie/Pkk086TzrpJDNWPYa6devmHDt2rPOpp54y788Xzb3Xlsruu8qE6/Halj5S3mh598mTJ5vjSo8Hff1PP/3U+cILL5jn0H/9GUewnq+l8uTenstFfyf+8Ic/OHv27GmOG20RoGXrb7zxRufq1asbbLto0SIzPh2nqy2CZ7l97Qn39NNPOydOnGiOLddxe8wxx5jPvLS01Kdy/QCiR4z+X8PQCgAAAADQEtZIAQAAAICfCKQAAAAAwE8EUgAAAADgJwIpAAAAAPATgRQAAAAA+IlACgAAAAD8FPUNeWtqakxTy4yMDNOcDwAAAEB0cjqdprm3NvHWBvMtifpASoOoPn36dNiHAwAAAMDatm7dKr17925xm6gPpDQT5dpZmZmZEoqMWEFBgWRnZ7ca9VqBvcouK/JWSHxcvCTGJYZ6OFH915KKPRWS0jmFTGqQOKodUlVdJcNzh0tSfJJEmnD7roE1cNyAYwbR9l1TXFxskiyuGKElUR9IuabzaRAVqkDKZrOZ1w71geNrIJVWniZpiWkEUiEOpEprSiW9czqBVBADqTJHmfldjNRAKpy+a2ANHDfgmEG0ftfE+LDkxxojBQAAAIAwQiAFAAAAAH4ikAIAAAAAPxFIAQAAAICfCKQAAAAAwE8EUgAAAADgJwIpAAAAAPATgRQAAAAA+IlACgAAAAD8RCAFAAAAAH4ikAIAAAAAPxFIAQAAAICfCKQAAAAAwE8EUgAAAADgJwIpAAAAAAjnQOrLL7+UE088UXr27CkxMTHyzjvvtPoz8+fPlwMOOECSkpJkwIAB8uKLL3bIWAEAAABEr3ixkLKyMhk5cqScf/75cuqpp7a6/aZNm+T444+Xiy++WF555RWZN2+eXHDBBdKjRw+ZMmVKh4wZweeoqpEv15bKgvWlUmyrkczkWJkwMF0O3S9dEuMtFfsDAAAgSlkqkDr22GPNxVczZsyQfv36yUMPPWRuDx48WL7++mv55z//SSAVphZuKJUHZudJqb1GYmJEnE4x/369vkyenFcg1x+XK+MHpId6mAAAAIhylgqk/LVw4UKZNGlSg/s0E/XXv/612Z+x2+3m4lJcXGz+rampMZeOpq/pdDpD8tptGa/rEkwLN5TJ9He2u2+7nt71b5m9Rm57e7vcenIPGT8gTaJZe30G0cy1P0P1XdDewu27BtbAcQOOGUTbd02NH2MI60Bqx44dkpub2+A+va3BUUVFhaSkpDT5mXvuuUemT5/e5P6CggKx2WwSig+rqKjIHDyxsdaftlZZXSn2IrvExMeII9YRtOd1VDnlgdn55npzoYHeHyMiD8zeIf/+Q44kxuut6OQUp9hKbWaHxJi9graqqqkSe5VdCmMLJSEuIeJ2aLh918AaOG7AMYNo+64pKSmJjkAqEDfddJNcc8017tsadPXp00eys7MlMzMzJAeOFtbQ1w/1geMLPdHcVrNNUhNTJTEuMWjP++mqYilztJ5d0S10u+8LRY4akh6968c2lMmeEod0zqiSCQPSWD8WjH1b7RCnwylZ2VmSFJ8kkSbcvmtgDRw34JhBtH3XJCcnR0cg1b17d8nLy2twn97WgMhbNkppdT+9NKYfWqg+OD1wQvn6/tAx6nhdl2BO63OtiWqNbqeFKCYN7fjA13Lrx/Iq5Zv1ZfLUZ4WsH2sj1zEdLr+LgYj094f2wXEDjhlE03dNrB+vH9b/NR0/fryp1Odp7ty55n6EF63O5+tyH91Ot4+2IErXh+k6sZbWj+l2AAAAaH+WCqRKS0tl+fLl5uIqb67Xt2zZ4p6WN3XqVPf2WvZ848aNcsMNN8iaNWvkySeflNdff12uvvrqkL0HBEZLnPua39JsjG4fTdP5NBPV2voxpdvp9gAAAGhfljobXbJkiey///7monQtk16fNm2aub19+3Z3UKW09PmHH35oslDaf0rLoP/73/+m9HkYGtorpdkgoTHNwmhfqWiha6J0Ol9r+0cf1+10ewAAALQvS62ROvzww1ss5/ziiy96/Znvv/++nUeG9rSjqFLeXrrbp201a5WWFGuKK0QLXQ/G+jEAAABrsVRGCtFn+55KuW7mr5JfUt3qtq6pf9qUNzE+eg7dPeXVrB8DAACwmOg5G4V1g6jiKnO7T9cEufaYHElPqj0sGxcF1EzUbadoM97oyUZ9+3OZrM+rbyDdmmhbPwYAABAqlprah+jx226HXD9rmxSU1AZRe3VLlPtP7yVd0+PliMEZtb2S1pfKym0Vsqe8tnjCTSd2lwP7pUk0KCiplKfmFcjX68v8+rloWz8GAAAQKgRS6HDb6oKowrogam8Nos7oJV3Sag9HnbanPaL08vnqErnngx3m/qWbyiM+kKqucco7y/bIy1/vlIrK+vWCcTEi1a1Um4jG9WMAAAChwhwgdHwQNdMjiMpqGEQ1NqZfqsTWTfFb9HNZi8VIwt3q3yrkspe3yNOfF7qDqM6pcfK343Nl2sk9TKDUWon4aFs/BgAAECpkpNBhft2lmahfZWdpbWGJvlmJct/pzQdRKiM5Tob3TpEftlbIb3sqZeuuSjMNMJKU2Krl+S8LZfYPxe4S5xowHT+yk5x3aDezD5SuD9M+UVri3FXFT7dz/UyXtDgZ3Tc1ZO8DAAAgmhBIoUNs1SBq5q+yq6w2iOqnQdQZvaRzauuH4Lj+aSaQcmWlIiWQ0uzavJ9K5On5hVJUXl+1sH9Oklx5dI4M7pncYHstsjHz0lSzfuyb9aWyp6RSOmckyOZCh/y6u9Ls29cW7ZZzD+4WgncDAAAQXQik0O627HTIDbPqg6h9sjUT1Vs6pdZmWlozfkCaPDO/0Fxf9HOpnD62i0TCPnlsbr47QFQpCTHyp0O6yUn7d5Y413zGRlzrx44akiGlu0olvWu6bN7pkEte2iLVNSKzvt1linVESrAJAABgVQRS6NAgSrMtOp0vM8W3IEr16pIovbsmyK+7KuWnbTYprqj26+c7kqOqxl1xsNhWY0qRaxU9LQChQZC9skZeXbRL3li8W6pqixEah+ybLpccmS1ZGf7/SvbNSpLTDuwiM7+tfc5/zc2XB87oJTGN68cDAAAgaAik0G42F9rlhlnbZHfdtLUBOUlyr59BlMtB/dPkzV17pMYpsnhjmcnKWM3CDaVN1zDFiClh/uS8Ajn5gM5mKt/2okr3z3TvFC+XT8qRsfu0rRrhH8d3lflrSmRHUZX8uLVC5q4qkcnDrLePAAAAIgXlvdBuQdT1QQqi1EH90xs0qbViEHXb29ulzF6bZnIVF3T9q8HVfxfucgdRWljvzIO6yDPn7d3mIEolJ8TKFUfnuG8/O7/QZO4AAADQPgikEHSbCuxy3axtsqcuiBqY27YgSg3tlSwZybWH63ebyqWytaZKHTydTzNRypdRDe+dLDP+tLecd0iWCYCCRXtsHTaoNuAsqqiWZ7+oXVcGAACA4COQQtCDqBte3+auQrdv97YHUUqLL7ia8ZY7amTlr/VFGkJN10RpxsnX0O7YEZ3arRjExUdkS2pi7a/1xyuKzTQ/AAAABB+BFPzmqHLKZz+Vyu3v/CbXzfzV/PvpqmJZu91m1kS5gqj9NIg6rZe7D1JbaRl0Fy2DbhVaWMLXug66nW7fXrqlx8v5h9aXP9fCE1bK3gEAAEQKik3AL/NWF8j1b+6SMruzSUEFT/v1qA2i0pKCV13vwH6pEhcrpsy3rpO6+IgsS1Sm0+p8rrVQrdHtdPv2pI1855rA1m6qJmqFQC1GAQAAgOAhIwWfzf0pTy579QcTRHkrqODSq0tC0IMolZ4cJ8N6p5jrv+2plK276qvfhZKWOPcnI6XbtyedBvnXo3PF1YpKy63/ttvRrq8JAAAQbQik4BNbZbVc+8Zyn6opaJGJhLj2yRRpGXSXRRvab4qcP7RPlD8ZKd2+vfXPTZJTRnd2T8V87NMCcfo6SAAAALSKQAo+mb1iuxRXVPlUUEFLgGsBhnYPpCyyTkqb7aYnxUproaM+rtvp9h1h6sRukl3X4HfpL+Uyf401Ak8AAIBIQCAFn3yyKs89VSyUBRV6dUmUPl0TzPWffrNZoldSYnysXH9cbovbuHadbqfbd4SUxFi57Khs9+0ZnxVIqS30+wsAACASEEjBJ3vKHVJjkYIKrua8Op7FG62RlRo/IF0O3rdpY13X2qm0pFi57ZQeZruOpNMIxw+oHZc2R37+q50d+voAAACRikAKPumcmuhXRqo9CyocVBcYWGl6X1W1U1Zts5nrupvG9kuVEX1SZOKANLnhuFyZeWm/Dg+iXDQrlZxQ++F9uLxIVv9GbykAAIC2ovw5fDJ5aK7MWbXDEgUVhvRMlozkWCmx1ciSTeWmT1J7Fbfw1cINpbKrrHba3MSBaTLt5J5iFTmZCXLuwd3k6c8LzRq3Rz/Jl8fP2UviQ7zPAAAAwhkZKfjkuOE9JDMl3hIFFbS899h9arNS5Y4aWbE19BmWD34ocl8/flQnsZqTD+gs/XOSzPWNBQ55e+meUA8JAAAgrBFIwSfJCXHy8Gmj6qsmhLiggpWq923b7ZDvN9cGcz07J8j+e6eK1WjwedXkHPdn9PKCnZJXZI0+XAAAAOGIQAo+mzQkV57440hJS/IeTXVkQYUx/VIlru7oXfRzaUh7JM3+odh9/bgRmRLra3feDjaoR7KcuH9ttsxe6ZQn5tFbCgAAIFAEUvDLUYOzZcZ5XeXsCfXT17p3iu/wggppSXEyvHeKub6jqEq27HRIKDiqauSTlbWBlCbhJg/PFCs775Bu0jUtzp3J+2a9NYp1AAAAhBsCKfgtMT5GRvRJdt8+eGC6TBqa2WH9kaw0vU8DkaK6XlYH75sunVOtXb9FA9BLjqzvLfXkvAKzzgwAAAD+IZBCQBxV9VPpEuJDM5XNCoHUhx5FJk6wYJEJb7QQiE6NVIWlVfLS1/SWAgAA8BeBFALiqK4PpDo6E+XSs0ui7NUt0Vxf/ZtNisprM0MdRacT/lhXMbBP1wT3VEOri4mJkSsm5ZjMonp32R5Zn1fbAwsAAAC+IZBCmzNSSSHKSHlmpWqcIos3loUsG3X8yE4mQAkXPTonyNkTurr3nfaWqtYrAAAA8AmBFNocSCWGsLFrqKb32StrZG5dkQnN7OgasXDz+zFdZO+s2ozeuh12+WB5fWAIAACAlll7ZTwsywprpNTgnsmSmRIrxRU1svSXcqmsdkpCBwR2X6wtlVJ7jXvNUWZKbSW8cBIfFyN/PTpHrn7tV3P7+S8LpcbpNA2Oi201kpkcKxMGppv3F6rpmwAAAFbF2RHCemqfNpod2682K6XV537cWt4hrzvbs8jEyPAoMuHN0N4pcuyI2mxaRaVTnvqsUL7ZUGbWfum/98/Okz88uUkWbigN9VABAAAshUAKYVtswuWgAR07vW9jvl1++q22OEO/rESTFQtnI/o0LJLh6m3s+rfMXiO3vb2dYAoAAMADgRQCUum5RiqEGSk1um+qxMXWB1JOVwTQEUUmRoVXkQlvDYWf+LSgxW1ce/OB2XlmewAAABBIIUB2CwVS2mR2RF3p8byiKvml0NFur1XhqJF5P5WY60kJMXLUkAwJZ196rPVqiX7aup1uDwAAAAIpBEiLOlihap+36X3ftmMZ9M9Xl5i1WOrIwRkmiAtnC9aXiq8JNd1OtwcAAACBFIJSbCL0M0QP6p/uvr5oQ1mH9Y4Kd1qdz9eZkLqdbg8AAAACKYR5+XPPBrN7d6vtibT6N5vsKa8K+mus22GT9Xl2c31gbpLs2z28i0woLXHuT0ZKtwcAAACBFIJStS/0gZRnc14d2eKN5e2ajTphVPhno5T2ifInI6XbAwAAgEAKQajaF8o+Ut4CqfYog15mr5bPVtcWmUhNjJXDB4V3kQkXbbabnhQrrX2C+rhup9sDAACAQAoRULXPZVDPZOmUUlv8YemmsqCW6tZKffbK2veslfpSEiNjipv2ALv+uFxzvbVPUbcLdc8wAAAAq+CsCG3OSCVYoGqfiouNkQP3STXXKyqd8uPWiqA8r/al+nB5ZBWZ8DR+QLrcdkoPSUuq/TrwtmbqosOzzHYAAACoRSCFNmWkYiwUSDWe3vdtkKb3/fSbTTbV9aYa0jNZ9slJkkijQdLMS/vJDcflysQBaTKiT4rsk11bvEMt3xL8NWcAAADhLD7UA0B495HSaX0xvpZ96wCj+6aKzj7TWX26TurSo5xtHl+klTxvjk7bmzQ001yUTo0879+bpaCkSr7dWC5rtttkUI/wr1QIAAAQDGSk0Kby51ZZH+WiDXJH9Kmd3pdXXCW/1GWSAlVcUS1frKltQpuRHF3FFjSw+uP4ru7bL3+zM6TjAQAAsBICKURUIKXGBbF636erit3ZN83UJCVE16/M5GGZktupNnG9ZFO5rNoWnHVnAAAA4S66zgoR9D5SiXHWO4QalEHfUNamIhMfRMm0vubo+rezyEoBAAA0Yb2zYIRV1b7EBOtlpHp0TpC9s2oLJei6nt1lVQE9z4pfK+TXXZXmuhZf2KtbffGFaDJpSKb06JRgrn+/ucLsFwAAgGhHIIU2Ve1LtFDFPm9ZKR3ld5sCqzj3QQSXPPdHvGalJrBWCgAAwBOBFPxWXeOUmro2UlZcI9V0el9tsQh/aBbr63W1P6dNficOrH++aKRNiHt1qc1K/bClgnLoAAAg6hFIwW+VHjPlrBpIaZluDYDU0l/KTSlvf8xdWWxKqKspwzNNBbtops2Oz26UldI1ZAAAANEqus8O0aZCE8qqAYae+I/dp7YMekWlU37c6vu6nhqnUz78odh9+9gRtX2Vot3hgzKkT9farNTKX21mvRQAAEC0suZZMMKi9LmV10g1md7nRxn07zeXy/ai2iITB+ydKr26RGeRCe9ZqW7u22SlAABANCOQgt8cHlP7kiw6tU+N7pdmyne7Ailfp6J92KDIBNkoT9qQ2FUR8affbGbaJAAAQDQikILfXA1qVYKFA6nUxFhTtlzlF1fJpgJHqz+zs7RKFtT1nuqaFifjB6S3+zjDLSt1jsdaqZdYKwUAAKIUgRTaFEglWXSNVKDT++asKHZXJNQiE1r6Gw0dvG+67JNdm5Vau90uizeSlQIAANHH2mfBsPzUPqtW7XMZ50cgpWXdZ/9QO61P39VxI6K3d1RLYmMarpUiKwUAAKIRgRQittiE6t4pQfrWrelZu91m+kM1Z8mmcikoqX1cK/7ldqqtUIemtK/WgJwkc31Dnl0W1k2HBAAAiBYEUmjT1L7EBGsHUp7T+3TU325s/oT/g7pslDpuJNmolsTExMg5Exv2ldKy8QAAANGCQAptm9pn8YxUk3VSzWRO8osr5bu6ICs7I17G7lP/M2h+v+7bvTYrtbHAIQvWk5UCAADRg0AKbctIWXyNlNqvR7J0So0z15dtLhdHVU2TbT76sb7IhDbg1ep0aD0rNXViw75SZKUAAEC0IJBCGwMp6x9CGhSN2yfVXLdVOuWHrRUNHq+qdspHP9ZO69P46ZjhTOvz1YH9UmVQj2Rz/ZdCh3y1tjSonx0AAIBVWf8sGJYTTlX7XA7qn97s9D6t5rerrLpuuzTJyojv8PGFd1aqfq3UfxbsMtUPAQAAIh2BFCK6ap/L6L6pklA3Vg2cnB6FEVwlz9UJo8hGBbJvh/aqzUpt2emQL8lKAQCAKEAghYhfI6VSEmNlZJ8Uc11LnGtxBLV9T6Us+aW2oWz3TvFyQN/aKYAIfK3Uf77ZSVYKAABEPAIptHFqX/gcQgd5ac47u1HJc202C/+N2itFhveuDVR/3V0pn68uYTcCAICIFj5nwbBkRiopTDJSalyDQKrUvI85K4vNbY0HpwzLDOHowj8rde7B9Wul/staKQAAEOEIpNC2NVJhFEjldkqQvlkJ5vra7Xa58PnNUlReW2RifP806ZJGkYm2GNEn1WSm1G97KuXTVbVBKgAAQCQikILfKmtjj7ALpBZuKJVtu+vnJerJvouuk9LH0Taea6VeWbjLlJYHAACIRARSiIqMlAZJt729vcG0RE/aX0ofJ5hqm2G9U0wVP7WjqErmkpUCAAARikAKfqtsUP7c+oeQo6pGHpid1+I2rnek2+n2CJxnXynNSjUXvAIAAIQz658Fw3IcYTa1T/saldpr3MFSc/Rx3Y4+SG0zuGeKHNivNiuVX1wlH6+or4wIAAAQKQikEPF9pBasLxVfq5rrdro9grdW6tVFu8nyAQCAiEMghYDXSOmsvrhY6wdSxbYacfo4u0y30+3RNvv1SHb37SosqZI5P1LBDwAARBYCKQRctS8xzvpBlMpMjvUrI6XbI7hrpV77dpfYKwlQAQBA5OCMEQFnpBITwuPwmTAw3a+MlG6PthuQmywTBtRmpXaWVsvsH1krBQAAIoflzoSfeOIJ6du3ryQnJ8u4ceNk8eLFLW7/yCOPyH777ScpKSnSp08fufrqq8Vms3XYeKNRZVV4ZaQO3S9d0pNipbXR6uO6nW6P4DjHY63UzEW7xUZWCgAARAhLBVKzZs2Sa665Rm699VZZtmyZjBw5UqZMmSL5+flet3/11VflxhtvNNuvXr1annvuOfMcN998c4ePPZo46opNJIVBoQmVGB8r1x+Xa643N2LX/bqdbo/g6J+TJIfsWxuY7i6vlg+Wk5UCAACRwVJnjA8//LBceOGFct5558mQIUNkxowZkpqaKs8//7zX7RcsWCATJ06UP/7xjyaLNXnyZDnzzDNbzWIhSFP7wiSQUuMHpMttp/SQtKTaQ961Zsr1r96vj+t2CK6zJ3R1B6r/WbBTbn3rN7lu5q9y+zu/yaeriqnoBwAAwlK8WITD4ZClS5fKTTfd5L4vNjZWJk2aJAsXLvT6MxMmTJD//ve/JnAaO3asbNy4UWbPni3nnHNOs69jt9vNxaW4uLaaWE1Njbl0NH1Np9MZktcORHV1tbvYREJcjBl7uNAqcq9d0le+Wlcm36wvlZKKaslIiZOJA9PlkH3TTCYqXN6PjtN1sbq+WYkypFeyrNpmkwqHUxb+XOYOYr9eXyZPziswmUBXlb9Qce3PUH0XtLdw+66BNXDcgGMG0fZdU+PHGCwTSBUWFpqT9Nzc2ilYLnp7zZo1Xn9GM1H6cwcffLDZ+VVVVXLxxRe3OLXvnnvukenTpze5v6CgICRrq/TDKioqMuPXwNHqyhz1QWi81EjprvDruTSue4yM657R4D5Hcbk4JHw4xSm2UpuZkxjT6uqv0Ppui01+2tb0d8sVA5bZa+S2t7fL3yZ1lgP3SpZQqaqpEnuVXQpjCyUhLkEiTbh918AaOG7AMYNo+64pKSkJv0AqEPPnz5e7775bnnzySVOYYsOGDXLVVVfJHXfcIbfccovXn9GMl67D8sxIaZGK7OxsyczMlFAcODExMeb1Q33g+KKgpD5wSk5OkPSuTIULBZOJcoqkd0k3x49VOapq5PGvvK9xdNF4St/B418Vy2uXdA3ZGjVHtUOcDqdkZWdJUnySRJpw+66BNXDcgGMG0fZdk5ycHH6BVFZWlsTFxUleXl6D+/V29+7dvf6MBks6je+CCy4wt4cPHy5lZWVy0UUXyd///nevH0RSUpK5NKbbhuqD0wMnlK/vD8+ia7pGyson8ZFO973rYlU6jbLU3nqKXIMp3U63nzS04/+goVz7Mlx+FwMR6e8P7YPjBhwziKbvmlg/Xt8y/zVNTEyU0aNHy7x58xpEp3p7/PjxXn+mvLy8yZvVYEyFw9qRcGSvqj8pDpeqfQidBetL/WqGrNsDAACEA8tkpJROuTv33HNlzJgxpniE9ojSDJNW8VNTp06VXr16mXVO6sQTTzSV/vbff3/31D7NUun9roAKwWX3SEmFU9U+hEaxTReP+ratbqfbAwAAhANLBVJnnHGGKfowbdo02bFjh4waNUrmzJnjLkCxZcuWBhmof/zjHyYNqP9u27bNzKvUIOquu+4K4buIbPaqupJ9piGvZRKasKjM5FiTafIlmNLtdHsAAIBwYKlASl1++eXm0lxxCU/x8fGmGa9e0DFsHlP7yEihNRMGppsS577QYEu3BwAACAf8+Rd+YWof/HHofumSnhTbaoF2fVy30+0BAADCAYEU/C5n7UJGCq3RUubabFe1FkzpdqEqfQ4AAOAvzlrgF5vnGilOeuGD8QPS5bZTekhaUu3XTeMqfrrUTh/X7QAAAMKF5dZIwdqY2odAaJA089JU+XJtqSlxXlxRLWt22MVR5ZSaGpF9u/ve/A4AAMAKyEjBL/SRQqA0g6nNdqed3FMePLOP/P7ALuZ+Lej36apidiwAAAgrBFIIOJBKiKOPFAI3eWiG+/onK4tpog0AAMIKgRQCDqQoNoG26NklUYb3TjHXt+6qlDXbbexQAAAQNgik4Bd7ZX2xiSSKTaCNJg+rz0p9vILpfQAAIHwQSMEvZKQQTIfulyHJCbVTROevKW1QzAQAAMDKCKQQeCDFGim0UUpifRPeckeNfLO+lH0KAADCAoEU/GLzyBgk1mUSgLaYPCzTff3jlUzvAwAA4YFACn6xezbkJSOFINCCEz06JZjryzdXSH5xJfsVAABYHoEU/OJoULWPwwdtFxMTI0fXFZ3QnlJzV5WwWwEAgOVxJozAp/bFM7UPwXH00ExxHU1z6SkFAADCAIEU/ELVPrSH3E4JMmqv2p5Sv+2plJXb6CkFAACsjUAKAQdSSWSkEESTh9cXnfiEnlIAAMDiCKQQcEPeBIpNIIgmDkyX1MTar6Qv1pZIhYOeUgAAwLoIpBBQRiohrrZIABAsyQmxctig2p5StkqnfLWOnlIAAMC6CKQQUCBFxT60hykePaU+oacUAACwMAIp+MVeV7WPin1oD4N7JkvvrrU9pX7cWiHb99BTCgAAWBOBFALLSMWx4xB8Ol10skdWSkuhAwAAWBGBFPxir6otNsHUPrSXSUMyJbZu+d3cVcVS49Q2vQAAANZCIIUA10hRaALtIysjXg7om2qu5xVXyQ9bKtjVAADAcgik4LPqGqdUVtdmBwik0J4oOgEAAKyOQAp+T+tT9JBCexo/IE0ykmu/nr5eVypl9vpjDwAAwAoIpOB3xT5FRgrtSdfgHT4oo/a4q3LKF2voKQUAAKyFQAp+r49SBFJob1OG01MKAABYF4EUfGarrJ9elRhHsQm0r4G5SdI3K9Fc/+k3m2zd5WCXAwAAyyCQgs/ISCGUPaU+oacUAACwEAIpBFRsgql96AhHDclw95T6dFWxqRwJAABgBQRS8JnNs9gEU/vQAbqkxcu4/mnm+s7Salm2uZz9DgAALIFACoGVP6chLzrI0UM9pvetKGa/AwAASyCQQkDlz5MIpNBBNCPVKSXOXF+woUxKbPSUAgAAoUcgBZ/ZyEghBLT585FDantKVVY75fPVJXwOAAAg5Aik4DMyUggVqvcBAACrIZBCYBkpik2gA/XPSZIBOUnm+roddtlUYGf/AwCAkCKQQkAZKcqfo6NNHl5fdGIuPaUAAECIEUjBZzTkRSgdMShD4uu+sT79qUSqqukpBQAAQodACj6zVXo05GVqHzpYp9Q4OWhAurm+p7xavttUxmcAAABChkAKAWWk6COFUJgyzKOnFNP7AABACBFIIaCGvPSRQiiM6ZcqXdNqe0ot+rlM9pRX8UEAAICQIJCCz2wexSbISCEU4mJj5KghtVmp6hqhpxQAAAgZAikElJFijRRCZYpH9b6PVxTzQQAAgJAgkILPqNoHK9irW6IM6pFsrm8scMiGPFuohwQAAKIQgRR8Zves2hcfw55DyEweluG+/snKEj4JAADQ4Qik4DMyUrCKwwdluIP5z1YXSyU9pQAAQAcjkILP6CMFq0hPjpOJA9PM9eKKGlm0oTTUQwIAAFGGQAp+Z6RiYrR6GjsOoXX0UI+eUquY3gcAADoWp8Pwmb2u/HlivAZTrJFCaO2/d6pkZcSb699tLJNdpfSUAgAAHYdACj6z1ZU/p/Q5rNJT6uihtUUnapwin/5EVgoAAHQcAin4nZFKiCMbBWuYPKx+et/clcXidDpDOh4AABA9CKTgd0NendoHWEGvLokyrFdtT6nNOx2ydoc91EMCAABRgkAKPrORkYIFTR7uUXRiRXFIxwIAAKIHuQX4RKdMuTJSCTTjhYUcul+GPP5pvjiqRD5aUSS/7LRL55Q4mTAwXQ7dL10S4/l7EQAACD4CKfikqsZpFvQrpvbBSn7YUi41tcv3pLpGZOWvNlOi/+v1ZfLkvAK5/rhcGT8gPdTDBAAAEYY/1cInNOOFFS3cUCq3vb1d6lqcublqTpTZa8zjuh0AAEAwEUjBr2a8KpGpfbAAR1WNPDA7r8VtXDX8dDvdHgAAIFgIpOB3Riohjp2G0PtybamU2mvcwVJz9HHdTrcHAAAIFgIp+J2Roo8UrGDB+lKzFsoXup1uDwAAECwEUvCrGa9iah+soNhW414L1RrdTrcHAAAIFgIp+MRWV/pcJVDrERaQmRzrV0ZKtwcAAAiWNp1ZbNu2TV577TV59NFH5ddffzX3VVdXy65du8y/iNCMVJyPZ69AO9I+Uf5kpHR7AACAkAZS2pz1mmuukX79+slZZ51lrq9bt848VlpaKn379pXHHnssaINE6Lma8Soa8sIKtNluelKs+BLW63a6PQAAQEgDqQceeMBkoa677jqZO3euCaxcOnXqJKeeeqr873//C9ogEXq2BhmpkA4FMBLjY02zXdVaMKXb6fYAAADBEtCZxbPPPitTp06Vu+++W0aNGtXk8REjRrgzVIgMZKRgReMHpMttp/SQtKTarzLXmqnGa6eyMljYBwAAgiugs4utW7fKhAkTmn08LS1NiouL2zIuWLkhL2ukYLFgaualqaZPlJY41+p8WlgiKSFG5v1UW/L8318Uyn2n9w71UAEAQLQHUjk5OSaYas7SpUtlr732asu4YDF2z4a8/HEfFqPT9iYNzTQXF0dVjazaZpMdRVXy/eYKWfpLmYzumxbScQIAgCif2qdroGbMmCEbN2503xdTN5fmk08+kRdffFFOO+204I0S1spIxVO1D+ERXP3p4G7u2899sVNqfC3zBwAA0B6B1PTp06VHjx5mfZSuldIg6r777pODDz5Yjj32WLNG6uabbw7kqWFRNo+MFMUmEC4OH5whA3KTzPUN+XaZv7ok1EMCAADRHEhpZb5FixbJDTfcYHpJJScnyxdffCF79uyRW2+9Vb766itJTU0N/mhhiYxUAmukECZiY2LkgkOz3Ldf+HqnmfIHAADQVgGvdklJSZF//OMf5oLIx9Q+hKsD+qbKAXunyrLN5ZJXVCUf/lAkp4zuEuphAQCAaMxIHXnkkTJv3rxmH//888/NNojMqX0J9JFCmLngsPq1Uq8s3CVl9vrjGQAAoMMCqfnz50teXl6zj+fn55upfogcdo+GvAkUm0CYGZCbLEcMzjDXiytq5PXFu0M9JAAAEI2BlGeVPm82bNggGRm1Jy2IvIa8VO1DONIKfvF133hvLdkjO0urQj0kAAAQDWukXnrpJXNxufPOO+XZZ59tsp0WnPjxxx/luOOOC94oEXI2j4wUVfsQjnp0TpAT9+8sby/dI/Yqp/znm53y1ym5oR4WAACI9IxUeXm5FBQUmIsqKSlx33ZdCgsLJSkpSS6++GL597//3Z7jRggzUlTtQ7j640FdJTWx9mtvzopi2bLTEeohAQCASM9IXXLJJeai+vXrJ48++qicdNJJ7Tk2WAhV+xAJOqXGyelju8iLX2tzXpEXviqUW0/uGephAQCAaFkjtWnTpnYLop544gnp27ev6U01btw4Wbx4cYvb61TCyy67zDQI1mzYvvvuK7Nnz26XsUWzBlX7Ai6aD4TeKaM7S9e02tKT36wvk1XbKkI9JAAAEIbafEqsU/yKioqkpqZpk8u99trLr+eaNWuWXHPNNTJjxgwTRD3yyCMyZcoUWbt2reTk5DTZ3uFwyNFHH20ee/PNN6VXr16yefNm6dy5c5veE5rPSOm0Pm1yCoSrlMRYOWdiN3n0k3xz+7kvCuWhM3uHelgAACBaAqmnnnpKHn74Ydm4cWOz21RX+9erRZ/vwgsvlPPOO8/c1oDqww8/lOeff15uvPHGJtvr/bt27ZIFCxZIQkKCuU+zWWi/jFSSq+wZEMaOGZ4p/1uyW37dVSkrt9lk0c9lMrpfYqiHBQAAIj2Q0gBHp9Nptuj888+Xv//973L11Veb6Xgvvvii5ObmypVXXunXc2p2aenSpXLTTTe574uNjZVJkybJwoULvf7Me++9J+PHjzdjeffddyU7O1v++Mc/yt/+9jeJi/PeNdZut5uLS3FxsflXM2resmrtTV/T6XSG5LUDyUhpIKXjdV0QGnwGbRMbI3L+Id3k9nd3uLNSI/fq7v5dtPrvYyR/18BaOG7AMYNo+66p8WMMAQVSjz32mAmiPvroI9m5c6cJpI4//ng58sgj5YYbbpAxY8aY+/2hFf80g6VBmCe9vWbNGq8/o9mwzz77TM466yyzLkr7V1166aVSWVkpt956q9efueeee2T69OlN7teqgzabTULxYenUSD14NHC0qgp7pfk3IVbEXmSXmPgYccRS8SxUnOIUW6lNJEb/x1TLQIzo6pT9chJkbX6lbNlVKR99t1sm7CNSGFsoCXG1Ge5IEi7fNbAWjhtwzCDavmtKSkraN5D6+eefTRZIuabUaUZJderUSS644AJ58skn5dprr5X23um6PuqZZ54xGajRo0fLtm3b5IEHHmg2kNKMl67D8sxI9enTx2SzMjMzpaPpe9Dmxvr6oT5wWuKoC85TkhIkqVOSpCamSmIcU6FCxWQDnSLpXdJbbI6Nll10ZLxcO3Obuf7GDxUyYVgnycrOkqT4pIjbdeHyXQNr4bgBxwyi7bsmOTm5fQMpDZaqqqrMdQ0+UlNTZevWre7HMzIyZMeO2ikzvsrKyjLBUF5eXoP79Xb37t29/oxW6tNAznMa3+DBg81ra2CXmNj0RF8r++mlMf3QQvXB6YETytf3d2qfjtd1QejwObTd8D6pMn5AmizcUCa7yqplzgqbHLSXtX8XI/27BtbDcQOOGUTTd02sH68f0EiHDRsmP/zwg/v2QQcdZIpPaDZIA6qnn37alCH3hwY9mlGaN29eg+hUb+s6KG8mTpxopvN5zmVct26dCbC8BVEIPPvhqAukkhO8rz0DwpWuldI1U+rdpRWyu5wpqwAAoJ0CqbPPPltWrlzpLtqga45Wr15typ1r1TwtV37nnXf6/bw65e7ZZ5+Vl156yTyfNgAuKytzV/GbOnVqg2IU+rhW7bvqqqtMAKUV/u6++273tEO0RzNe/pKNyLJ3VpJMHlY7rbfc4ZSnv/gl1EMCAABhIKCpfRrYuIIbV2Zo1apV8v7775tpdpMnT/Y7I6XOOOMMU/Rh2rRpZnreqFGjZM6cOe4CFFu2bGmQbtO1TR9//LGpGDhixAjTR0qDKq3ah+CxV9YHUpQ/RySaOrGbfPZTiTiqnfLfRVvl/In9pU/X1FAPCwAARHJDXpd99tnHBDEumzZtkn79+vn9PJdffrm5eDN//vwm9+m0v0WLFvn9OvCdvaq+H1iylu3TKgdABMnKiJeTDsiQN78rlspqp/xz7jp5+IxRoR4WAACwsKDP0/rxxx9NL6f99tsv2E+NELGRkUIU+P2BnSQ9qXax1NvLt8lPv9X2mAMAAGhzIKXT9zRbdOyxx5pg6e2333Y/tmzZMjnuuONk//33l7feesuso0LkZaSS4ik2gciUnhwrp4ypnc6n1eXvm+O9fx0AAIBfU/t0+pw23PVsWjtr1ix5+OGHTSl0XZekZc+vv/56M8VPK+chAjNSZmofEJmmjEiWz1ZVy7Y9NvliXYEs2FAoEwZkhXpYAADAgnw+K7799ttNg6qPPvpISktLZcWKFaZcuRaGcDW5/eWXX+Tee+8liIrojBSBFCJXQlyMXHlUf/ftez5aIzU1rAkEAABN+XxW/O2335qy4lOmTDENeIcOHWqyUSUlJXLllVfK/fffbxr1IrLLnxNIIdKdNLK7DO5RWw59xbYi+XDF9lAPCQAAhHMgtWfPniYlzV23dcofIpetkowUokdsbIz87Zj6YjkPfrLW3ZAaAADA70DK6XSaHlGeXLd1yh+iJCOVQLEJRL7D9s2WCf27meubd5bLa4u3hHpIAAAgnPtIzZ492zTKdSkvL5eYmBh54403ZPny5Q221fu1US4irI8Ua6QQBfT768ZjB8lJj39jbv9r3no59YBekpGcEOqhAQCAcAykXn31VXNp7Omnn25yH4FUZFbtSySQQpQY0buznDCih3zw43bZWeaQa17/QeJiYmRPuUM6pybK5KG5ctzwHpJMlhYAgKjkcyC1adOm9h0JLMvOGilEqesm7yezV2wXLdw396c8iY0Rc13/nbNqh9z2/ip5+LRRMmlIbqiHCgAArBpI7b333u07EoTFGin++o5osj6/1AROLq7rrn9LKqrkwv8skWfOGSNHE0wBABBVaAoE/xryMrUPUVSt8to3lktMC9uYeMopct0byxtUtwQAAJGPQAr+NeRN4JBBdNApfcUVVbXBUgv08aKKKvloJf2mAACIJpwVo1VkpBCNPllVuybKF7rdxyvz2ntIAADAQgik4F9Giql9iBJanc9zfVRLdLs9FY72HhIAALAQAim0ioa8iEZa4tyfjFTnlMT2HhIAAIjUQMrhcEhZWVkwnxIW4LmInowUooX2ifInIzVlGCXQAQCIJgEFUjNnzpSrr766wX3Tp0+X9PR06dy5s5xyyilSWloarDHCShkppvYhSmiz3cyU+Bar9il9vFNKvBw7rEcHjQwAAIRtIPXQQw81yDwtWLDABFJTpkwxAdacOXPkrrvuCuY4EUL0kUI00p5p2mxXI6Xmgilzf4zIQ6eNoscaAABRJqBA6ueff5YRI0a4b7/66qvSvXt3efvtt+X++++Xyy67TP73v/8Fc5wIIab2IVpNGpJrmu1qZsobvf/Zc8aY7QAAQHQJKJCy2+2SnJzsvv3JJ5/IscceK/HxtScbQ4YMkV9//TV4o4QlMlIxMSIJcT6uvgcixNFDcuXbmyfJw6ePNL8DKj0pXv55xkhzP0EUAADRKaBAql+/fvLpp5+a60uWLJENGzbIMccc4348Ly/PrJdCZLDXFZvQ9VExrjNJIMqm+Z16QG/p1TnF3NY/KJyyf2+m8wEAEMUCCqT+8pe/yOuvv26m902ePFl69+4tJ5xwgvvxb775RoYOHRrMccICGamk+Dg+B0S1nIwk8+/u8soG/dUAAED08T7xvxVXXHGFmdo3e/ZsGT16tPztb3+TlJTav9Tu2rVLduzYIRdffHGwx4oQZ6SSE2g7huiWk1E/pbmgxC69u6SGdDwAACDMAil14YUXmktjXbt2NdP9EDlsZKQAIzezNiOl8gmkAACIagEHUo05nU75/PPPTSGKgw8+WDIyMoL11LDQGikgmuVk1mek8ottIR0LAAAIrYDOjP/+97/LEUcc0SCI0rVSRx99tBx//PEyfPhwUyIdkbVGShfcA9Esu26NlCsjBQAAoldAgZT2iBo7dqz79ptvvinz5s2TO++8Uz744AOprq6W2267LZjjRIhUVddIVY3TXCcjhWiX2yAjRSAFAEA0C2hq37Zt22TAgAHu22+99ZbpHXXTTTeZ25dccok89dRTwRslQp6NUkkUm0CUc1XtU3lM7QMAIKoFlJHSxru6Fso1rU+zUZ59pHJzc6WwsDB4o4QlAqlkyp8jyjXISDG1DwCAqBZQIDVs2DD573//K7t375YXXnhBdu7cadZGuWzevFmysrKCOU6EiK2u0IQiI4Vo1yU1wTTjVWSkAACIbgFN7Zs2bZqceOKJ7mBp4sSJDYpPfPjhh3LggQcGb5SwxtQ+MlKIcjExMZKdniS/FdlMHykAABC9AgqktDrfsmXLZO7cudK5c2c544wz3I9plurQQw+V3/3ud8EcJ0LEXlWfkaIhL1BbAl0DqZ1lDqmsrpGEONoCAAAQjQLuI6XFJfTSWJcuXeSf//xnW8cFi7BVkpECmis4oVmpnp1T2EEAAEShNv0pddGiRXLPPffI1VdfLevXrzf3lZeXm2xVaWlpsMYICzTjVayRAjQjRS8pAAAQYCDlcDjk1FNPNWujtDnvv/71L9m6dat5LDY21jTnffTRR9m/EcDGGimggdwMz15SNvYOAABRKqBA6pZbbjGNd7VX1Nq1a00JdJfk5GQ57bTT5N133w3mOGGFjFQ8a0EAz4xUHgUnAACIWgGdGb/22mum6e5FF10kXbt2bfL44MGDZePGjcEYH6zURyohLqRjAawgxyMjVUBGCgCAqBVQIJWfny/Dhw9v9vG4uDizVgoR1keKjBTAGikAABB4INWnTx9Zs2ZNs49/8803MmDAgECeGpbuI8XUPsAzI0VTXgAAoldAZ8Z//OMf5emnn5aFCxc2aFSpnn32WXn99ddl6tSpwRslQoapfUBD3dISJS629vsunzVSAABErYD6SGmlPi19ro13dT2UBlFaAn3Xrl3y66+/ynHHHWduI/wxtQ9oKDY2RrLTk2RHsY1ACgCAKBZQRioxMVHmzJkjL7zwguyzzz4yaNAgsdvtMmLECHnxxRfl/fffN+ukEGFT+yg2ATSo3FdYapeq6vrfEQAAED0CykgpzUKdffbZ5oLIZa+qLzaRzBopwGOdVJFo54edZQ7JzaxfNwUAAKJDQBkpncL3448/Nvv4ihUrZPfu3W0ZFyzCXklGCmixlxQl0AEAiEoBBVK6/kl7SDXnL3/5i1x33XVtGResmJFKoGofoHIy6gOp/GI7OwUAgCgU0JnxZ599JieddFKzj5944ony6aeftmVcsAibZ0YqnnVvgPKcykflPgAAolNAgVRBQYFkZWU1+3i3bt1M015EVkaKPlJA04wUU/sAAIhOAQVSPXr0kO+//77Zx5cuXSrZ2dltGRcsuEYqmap9QJOmvGSkAACITgEFUieffLI899xz8t577zV57N133zVl0U855ZRgjA8hZiMjBTSR61FsoqDExh4CACAKBVT+/LbbbjNroDRYGjlypAwbNszcv3LlSvnhhx9Mk97p06cHe6wIddW++FipdtZP9QOiVbf0JImNEalx6tQ+ik0AABCNAspIderUSRYtWiT/+Mc/pLKyUt58801z0eu33HKLfPvtt9K5c+fgjxYha8gbHxsj8XFU7QNUXGyMZKXXZqXyyUgBABCVAm7Im5aWZrJOZJ4im62yNgNFoQmgaS8pXR9VWOqQ6hqnCa4AAED0CCjFUFVVJcXFxc0+ro/pNoicjFQShSYArwUnNIjaWcb0PgAAok1AgdSVV14pEyZMaPbxiRMnyrXXXtuWccFi5c+T45nWBzRXcIKmvAAARJ+Azo7nzJkjv//975t9XB+bPXt2W8YFizXkJSMFNJTdoAQ6lfsAAIg2AQVSv/32m/Tq1avZx3v27Cnbtm1ry7hgsYwUa6SA5pvykpECACD6BBRIdevWTdauXdvs46tXr5bMzMy2jAsW4HQ6yUgBzcjNpCkvAADRLKBA6phjjpGnn35avv/++yaPLVu2TJ555hk59thjgzE+hJCjumEPKQDeM1J5xUztAwAg2gRU/vyOO+4w66TGjh0rJ510kgwdOtTdkPf999+XnJwcsw0io2KfSqZqH9Ck/LmLlkEHAADRJaBAStdALVmyRG688UZ599135e233zb363S+s846S+6++26zDSKjh5QiIwU0pA15Y2J0CiyBFAAA0Sjghrw9evSQl156yayjKSgoMPdlZ2dLjJ5ZICLY6yr2KQIpoKGEuFjplpZoGvLmM7UPAICoE3Ag5aKBk07lQ+Rhah/QelNeDaQKSuxSU+OU2Fj+kAQAQLQIKJC6/fbbfQqwbrnllkCeHhbB1D6g9XVSP20Xqapxyu5yh3RLr183BQAAIltAgdRtt93WYgCl0/0IpCIrI5UUHxfSsQDWr9xnJ5ACACCKBFTTuqampsmlqqpKfv75Z7n66qtlzJgxkp+fH/zRIiTNeFVyAuXPgZZ7SVECHQCAaBK0s+PY2Fjp16+fPPjggzJw4EC54oorgvXUsESxCTJSQEsZqfxiSqADABBN2iXNcOihh8rs2bPb46nRgchIAS3LziAjBQBAtGqXQEp7TGmGCuHNRvlzoEW5NOUFACBqBVRs4uWXX/Z6/549e+TLL7+Ut956Sy644IK2jg0WykglJTC1D2gsx2ONVB69pAAAiCoBBVJ/+tOfmn0sKytLbrzxRpk2bVpbxgXL9ZEiwwg0lu1R7jy/hDVSAABEk4ACqU2bNjW5T8udd+nSRTIyMoIxLliujxQZKaCxxPhY6ZqWKLvKHBSbAAAgygQUSO29997BHwksXrWPjBTQXOU+DaQKSuzuHnoAACDyBRRINbZmzRp54403ZPv27bLffvvJeeedJ5mZmcF4alhmah8ZKaC5dVJrdpSIo7pG9pRXSpe0RHYUAABRwOdA6vHHH5d//etfsmDBArMOyuX999+X0047TRwOh/u+xx57TBYtWtRgO4T71D4yUkCrvaRK7ARSAABECZ/Pjt977z3p379/g+CoqqrKVOeLi4uTF154QVasWCH33nuvbN68We666672GjNCkJFijRTQeiBF5T4AAKKHz4HUTz/9JAcddFCD+z7//HMpKCiQq6++Ws4991wZOnSo3HDDDXL66afTkDcC0JAXaF2uRwl0KvcBABA9fA6kdu7cKX369Glw37x588zC6lNOOaXB/RMnTpQtW7YEPKgnnnhC+vbtK8nJyTJu3DhZvHixTz83c+ZMM56TTz454NdGcw15WSMFeENGCgCA6ORzIJWbmys7duxocN9XX30lqampMnLkyAb3JyYmmksgZs2aJddcc43ceuutsmzZMvPcU6ZMkfz8/BZ/7pdffpHrrrtODjnkkIBeF02RkQJal5NZP7VPK/cBAIDo4HMgNWbMGHnppZekpKTE3F61apXJFGmQEx8f36SKX+/evQMa0MMPPywXXnihqfw3ZMgQmTFjhgnWnn/++WZ/prq6Ws466yyZPn267LPPPgG9LpoiIwW0LifDc2qfjV0GAECU8Llqn2aIDjzwQBk4cKBZC7V06VIzje6mm25qsu3bb78tRx55pN+D0cp/+ryezxkbGyuTJk2ShQsXNvtzt99+u+Tk5Mif//xnkyVrid1uNxeX4uJi829NTY25dDR9Te09E4rXbo3do2qfVj937SMdr+uC0OAzaL996u93QVZagvt6XpHNkr/LVv+ugXVx3IBjBtH2XVPjxxh8DqSGDx8un332manGt3HjRlN4QqfSjR49usF28+fPNxkkLYnur8LCQpNd0mmEnvS2Zrm8+frrr+W5556T5cuX+/Qa99xzj8lcNaZFM2w2W0g+rKKiInPwaNBoJaUV9QFn0a5CKY6JkcrqSrEX2SUmPkYcsfUl79GxnOIUW6lNJEb/RwPYYKiqqRJ7lV0KYwslIa4+OPJFZlKcFNurZfue8lanIYeKlb9rYF0cN+CYQbR915TUzb4LekPeCRMmyIcfftjiNocffrgpg95Rb/Scc86RZ5991ueeVZrt0jVYnhkpLaKRnZ0dkibCeuBoZk9fP9QHTmPVMevMv4nxse7gVk80t9Vsk9TEVEmMo/FoqJhsoFMkvUu6OX7Qdo5qhzgdTsnKzpKk+Pp1T77o3ilFivNLZWd5lfldtuJnYuXvGlgXxw04ZhBt3zXJyfVT9oMaSLU3DYa0J1VeXl6D+/V29+7dm2z/888/myITJ554YpN0nK7bWrt2rel95SkpKclcGtMPLVQfnB44oXz91vpIaTNe19j0Xx2v64LQ4XNon/0ZyO9iTmayrMsvNb8zpfYa6ZTqX0Yr2r9rYG0cN+CYQTR918T68fqW+q+pVvrTqYJaVt0zMNLb48ePb7L9oEGDTPZLp/W5LieddJIcccQR5nrjcu3wj72u/HmyLpAC4FPlPgpOAAAQHSyVkVI67U6b+2qVwLFjx8ojjzwiZWVlpoqfmjp1qvTq1cusddLU27Bhwxr8fOfOnc2/je9H4OXPNSMFwNfKfXYZmJvB7gIAIMJZLpA644wzTOGHadOmmb5Vo0aNkjlz5rjX6Gij31Cn/KItI0UgBbSMprwAAEQfywVS6vLLLzcXb7QqYEtefPHFdhpV9HGtkWJqH9Cy3MyGGSkAABD5SO3Aq+oapziqyUgB/q6RyiumKS8AANGAQApeOeqyUYqMFOD71D4yUgAARAcCKXhlq6wtNKFYIwX4XmyioJipfQAARAMCKbS4PkolxVP+HGhJSmKcZCTXLjnNK2FqHwAA0YBACi2WPlfJCRwmgK/T+/KL7eJ0OtlhAABEOM6Q4ZWtrvS5IiMF+F65r6KyWkrtVewyAAAiHIEUWs1IJZGRAvzsJcU6KQAAIh2BFFpdI0XVPsDfXlKskwIAINIRSMErqvYB/sn2yEgV0JQXAICIRyAFr+wN1khxmACtyfHISNGUFwCAyMcZMrxiah/gn1zPpryskQIAIOIRSMErpvYBbchIMbUPAICIRyCF1hvyJtCQF/Cnal9+McUmAACIdARS8IqMFOCftKR4SU+KN9cpNgEAQOQjkELrGal4MlKAP1kpik0AABD5CKTQakPeZBryAn6VQC9zVEuZvYq9BgBABCOQgle2BuXPyUgB/jfltbPTAACIYARSaDUjlURGCvC74ATT+wAAiGwEUmi9jxQZKcAnZKQAAIgeBFJovWofGSnAJzmZlEAHACBaEEjBh6p9HCaAP8UmFGukAACIbJwhwyu7R7GJZBryAv5P7aMpLwAAEY1ACq0XmyAjBQRQbIKqfQAARDICKXhFRgrwX3pSvKTUZXDzS2zsQgAAIhiBFLyy1WWkYmNE4vX/ALQqJiZGcusKTrBGCgCAyEYghRYzUtqMV08OAfgmJ6N2nVSJrUoqHPVTZAEAQGQhkEKLa6SSKX0O+CXbswQ60/sAAIhYBFLwyuaRkQLgu9y6jJRieh8AAJGLQAotZqRoxgsE3pQ3jxLoAABELAIptNiQN5mMFOAXV7EJlU8JdAAAIhaBFJpwOp1iqyQjBbSl2IRiah8AAJGLQApNVNU4pcZZe51mvEDgTXnzmdoHAEDEIpBCs9P6VHJdc1EAvsnJJCMFAEA0IJBCE65pfYqMFOCfzOR49+8N5c8BAIhcBFJoMSOVREYK8Is2sHZV7suj2AQAABGLQApN2MlIAUHpJVVUUdkgwwsAACIHgRSabcaraMgLtK2XVEGJnV0IAEAEIpBCs814VXIChwjQthLoNnYgAAARiLNkNEFGCgheRoqmvAAARCYCKbSYkaJqH9C2jFQevaQAAIhIBFJogj5SQNvkemakWCMFAEBEIpBCE/SRAoK5RopiEwAARCICKbTSR4pDBPBXTkZ9RoqpfQAARCbOktHy1L74OPYQ4KfOqQmSGFf79Ur5cwAAIhOBFFpuyEtGCvBbTEyMZNdlpZjaBwBAZCKQQhNkpIDglUDfVeYQh0eWFwAARAYCKTRBRgpou1yPghMFpRScAAAg0hBIoQmbZ7EJ1kgBbW7KS8EJAAAiD4EUWsxIJbNGCmhz5b78YjJSAABEGgIpNGGrJCMFtFVOpsfUvhIbOxQAgAhDIIUm7FUeVfviOUSAtveSIiMFAECk4SwZLVftS6CPFBCIXI+MVD4ZKQAAIg6BFJqwefaRIiMFtH2NVAkZKQAAIg2BFFrMSNGQFwhMl9REiY+NMdeZ2gcAQOQhkELLgRTlz4HAvlxjY9xZKYpNAAAQeQik0OzUvoS4GImr+4s6AP9l162T2lnmkMrq+j9QAACA8EcghWYzUslko4A2cWWknE6RwlLWSQEAEEkIpNBs+XPWRwFtk5tJU14AACIVgRSabcjL+iigbXIy6kug5xXTlBcAgEhCIIUm7HVrpMhIAW1DCXQAACIXgRSasNWtkSIjBQSzKS9rpAAAiCQEUmjA6XSKwx1IcXgAbZHt2ZSXqX0AAEQUzpTRbA+p5AQOD6AtyEgBABC5OFNGA/a6QhOKqX1A23RLS3T3YssvodgEAACRhEAKXkufK6b2AW38go2Nkaz0RHM9r5g1UgAARBICKbQwtS+OvQMEaXrfzlK7VNc42Z8AAEQIAik0YKsrfa7ISAHBK4GuMZQGUwAAIDIQSKEBMlJAcGU3aMpLIAUAQKQgkEIDrJECgis306MEOgUnAACIGARSaMDmWbWP8udAm+WQkQIAICIRSKHZjFRyPMUmgGCtkVJkpAAAiBwEUmiAjBQQXDTlBQAgMhFIoYU1UmSkgLbK8VwjVUxTXgAAIgWBFBqwe6yRSmaNFNBm3dISJTam9np+CVX7AACIFARSaKGPFBkpoK3i42KlW3ptViqf8ucAAEQMAik020eKhrxAcAtOFJTapVo78wIAgLBHIIUGaMgLtF/BCQ2idpU52MUAAEQASwZSTzzxhPTt21eSk5Nl3Lhxsnjx4ma3ffbZZ+WQQw6RLl26mMukSZNa3B7+TO2z5OEBhB1KoAMAEHksd6Y8a9Ysueaaa+TWW2+VZcuWyciRI2XKlCmSn5/vdfv58+fLmWeeKZ9//rksXLhQ+vTpI5MnT5Zt27Z1+NgjbmpfAmukgKAHUqyTAgAgIlgukHr44YflwgsvlPPOO0+GDBkiM2bMkNTUVHn++ee9bv/KK6/IpZdeKqNGjZJBgwbJv//9b6mpqZF58+Z1+Ngjr/y55Q4PICzl1E3tUzTlBQAgMsSLhTgcDlm6dKncdNNN7vtiY2PNdD3NNvmivLxcKisrpWvXrl4ft9vt5uJSXFxs/tXgSy8dTV/T6XSG5LW9qXDUB1KJcTFNxuUar+uC0OAzaL992h7fBdnpie7rO4psfNcgbFjtv1GwPo4ZhPtx488YLBVIFRYWSnV1teTm5ja4X2+vWbPGp+f429/+Jj179jTBlzf33HOPTJ8+vcn9BQUFYrPZQvJhFRUVmYNHg8ZQKy4td18vLdot+VJ/W1VWV4q9yC4x8THiiGXRfKg4xSm2UptIjP6vrkkR2qSqpkrsVXYpjC2UhLiEoO7N+Kr636PN+XuanaocTd81CA8cN+CYQbR915SUlIRnINVW9957r8ycOdOsm9JCFd5otkvXYHlmpHRdVXZ2tmRmZkooDpyYmBjz+qE+cIy4re6rvbrnSLbH2g6lJ5rbarZJamKqJMbV/5UdHctkA50i6V3SzfGDtnNUO8TpcEpWdpYkxTc87tuqOqlCRGr/GFRaFSs5OTki0f5dg7DAcQOOGUTbd01yMzGE5QOprKwsiYuLk7y8vAb36+3u3bu3+LMPPvigCaQ+/fRTGTFiRLPbJSUlmUtj+qGF6oPTAyeUr+/JXl0/XS85Mb7JmPS2jtd1QejwObTP/myP38WczBTRXxeNf/NK7HzXIKxY6b9RCA8cMwjn48af17fUt2JiYqKMHj26QaEIV+GI8ePHN/tz999/v9xxxx0yZ84cGTNmTAeNNjLZPcqfJydY6vAAwlZCXKx0S6vN4BYUd/wUYgAAEHyWykgpnXZ37rnnmoBo7Nix8sgjj0hZWZmp4qemTp0qvXr1Mmud1H333SfTpk2TV1991fSe2rFjh7k/PT3dXOAfm0f588Q4AikgWLIzkqWw1CEFpXapqdE54GR0AQAIZ5YLpM444wxT+EGDIw2KtKy5ZppcBSi2bNnSIOX21FNPmWp/v//97xs8j/ahuu222zp8/JGSkdLS50zdA4LbS2r1di3Y4pTd5Q7plh7cdVgAACDKAyl1+eWXm4s3WkjC0y+//NJBo4oOjrqMVDLNeIGgys30aMpbYieQAgAgzDF3Cw3YPDJSAIInJ8OzKW99LzsAABCeOFtGA3YyUkC7yPHISOVRcAIAgLBHIAWvgRQZKaD9MlIFZKQAAAh7BFLwPrWP0udAUJGRAgAgshBIwa2qukaqamob8ibHx7FngCBX7XPJL2aNFAAA4Y5ACk2m9SkyUkBwZXsGUiU05QUAINwRSMF7IEVGCggq/Z3qkppgrueRkQIAIOwRSMHNXlW7Pkols0YKCLrczGR3sQmns3YaLQAACE8EUnCzVZKRAjpiep+jukaKKirZ2QAAhDECKXjNSFH+HGjfEuhM7wMAILwRSMHN7pGRSk6gah8QbLkeTXkpOAEAQHgjkEKTHlKKjBQQfJRABwAgchBIoZny52SkgGDLqSs2ofIogQ4AQFgjkEIz5c85NIB2ndpHCXQAAMIaZ8twY2of0HHFJlgjBQBAeCOQgteMFMUmgPYrf67ISAEAEN4IpOBGRgpoX/oHik4pCeZ6fomd3Q0AQBgjkIIbxSaAjqvcl1dsE6fTyS4HACBMEUjBa0PeZIpNAO0it65yn/7hothWxV4GACBMEUjBzebRkJfy50D795IqoAQ6AABhi0AKXjNSlD8H2ke2Rwn0PEqgAwAQtgik4Gb3yEhRtQ9oH7mUQAcAICIQSMGNjBTQ/nJoygsAQEQgkIIbGSmgY5vyMrUPAIDwRSAF7+XPqdoHtItcz4wUxSYAAAhbBFJwoyEv0LEZqXyKTQAAELYIpOA1I0WxCaB9pCTGSUZSvLlORgoAgPBFIAU3MlJAxxacyC+xi9PpZLcDABCGCKTQJCMVFxsj8XEcGkB7T+8rd1RLqb2KHQ0AQBjibBkmE/XWsl9lU2Fp7d5wOs1tzwwVgPYqOGFn1wIAEIYIpKLc3J/yZOzdn8o1r/8gpfbawKnaKea23v/pT3mhHiIQcXIyKTgBAEC4I5CK8iDqov8skZIK71OL9P4L/7PEbAcgeHIyKIEOAEC4I5CKUjpt79o3los4zf+8Mvc7Ra57YznT/IAgIiMFAED4I5CKUrNXbJfiiqpmgygXfbyooko+Wrm9g0YGRD4yUgAAhD8CqSj1yao8iY3xbVvd7uOVTO8D2iOQyqMpLwAAYYlAKkrtKXdIjY/ta3S7PRWO9h4SEJ1T+0psIR0LAAAIDIFUlOqcmuhXRqpzSmJ7DwmIGulJ8ZKWGGeuU/4cAIDwRCAVpSYPzfUrIzVlWG57DwmIyqxUPlP7AAAISwRSUeq44T0kMyVeWktK6eOdUuLl2GE9OmhkQHStkyq1V0mZ3XsLAgAAYF0EUlEqOSFOHj5tVG2k1AzzUIzIQ6eNMtsDaK91UnZ2LQAAYYZAKopNGpIrz5wzRhLjGkZTrrVTmrF69pwxZjsAwZXr2ZS3mIITAACEm/hQDwChNWlwjnRLS5TtxXaJiREZs3cX6ZaWZNZE6XQ+MlFA+8jJ9AikyEgBABB2CKSi3Nq8EhNEqUMGZsvL548N9ZCAqJCTUT+1L4+MFAAAYYepfVFu3up89/WjBuWEdCxAtGakCshIAQAQdgikotzna+oDqSMJpICQZKSY2gcAQPghkIpiu8scsmzLbnN9YE669OmaGuohAVGZkWJqHwAA4YdAKop9sa7A3ZSXbBTQsTKS4iWlrq0AGSkAAMIPgVQUm8e0PiBkYmJi3Fkpyp8DABB+CKSiVFV1jXyxtnZ9VGZyvIzeu0uohwREnZy6XlLFtiqxVVaHejgAAMAPBFJRaunm3ebkTR22X47Ex3EoAB0tJ9Oj4ERdGwIAABAeOHuOUp/VZaPUkYOyQzoWINozUiqvxBbSsQAAAP8QSEWpz+r6R8XGiBy2L/2jgFDIJSMFAEDYIpCKQlt3lcv6/FJzff+9ukjXtMRQDwmQaM9I5ZORAgAgrBBIRaHPqNYHWK4pbx5rpAAACCsEUlGIQAqwhlyPprxkpAAACC8EUlGm3FElCzfuNNd7dkqWQd0zQj0kIGp5ZqQKSqjaBwBAOCGQijLfbNgpjqoac/2IQTmmKSiA0MhMiZfE+Nqv4bxiqvYBABBOCKSizGdr8tzXjxpMtT4glPQPGa7pfflkpAAACCsEUlHE6XS610clxcfK+H2yQj0kIOq5pvftKa8Ue1V11O8PAADCBYFUFFn1W7G7MtiE/t0kJTEu1EMCol6DEuhU7gMAIGwQSEWRzz3Lng/ODelYAHhpysv0PgAAwgaBVBSZR/8owHKyG2SkKDgBAEC4IJCKEoWldvnh1z3mupY879U5JdRDAkBGCgCAsEUgFSXmry0Qp1PcZc8BWHCNVAkZKQAAwgWBVBSujzqKQAqwjJy68ufKVQwGAABYH4FUFKisrpEv1xWY651TE2T/vbqEekgA6uTWlT9XFJsAACB8EEhFge9+2SUl9ipz/fB9syUuNibUQwJQR/+4kRhX+1VMsQkAAMIHgVQU+Gx1/bQ+1kcB1hITE+Ou3EdGCgCA8EEgFQU+W1sbSGkm6rB9s0M9HADNrJPaVeYQR1UN+wcAgDBAIBXhfiksk40FZeb66L26SOfUxFAPCUALlfu0VQEAALC++FAPAMFnq6yW2Su2yyer8mT1jmL3/Yfum8XuBiwox6PgRF6xTXrS5w0AAMsjkIowc3/Kk2vfWC7FFVWiNSVq6npHqRlfbJRB3TNl0pDcUA4RQCO5HiXQWScFAEB4YGpfhAVRF/1niZRU1Fbo8wyiVJm9Si78zxKzHQBrZqSo3AcAQHggkIqg6XyaiRKn+Z9X5n6nyHVvLDfbA7BeU14yUgAAhAcCqQiha6J0Ol9zQZSLPl5UUSUfrdzeQSMD4F9GimITAACEA9ZIWYS9slo+WvWbKRCxq9QuFXUlkFMS4qRrWqJMHporxw3vIckJcV5/Xn+u8Zqo5uh2H6/Mk1P27x3stwEgAJ1S67+K56zaIUUVla3+zvtbfObjVTukYE+ZZHf+VaYM7R6U50bk4rgBwHdN62KcTqcPp96Rq7i4WDp16iRFRUWSmZnZ4a9fU1Mjby5cJ3fO3SzFtiqJcU3B8+C6LzMlXh4+bVSDYhG7yxzy1YZCuf39VVJY6vD5dQ/ap6vMvGi83+O1V9ll+Y7lkpaYJolxlFIPFf21Ld1VKuld001DV7Sdo9ohZY4yGdV9lCTF10+165ACMa8vN7//Lq4/inj7nW9r8ZlgPTciF8cN2npek5+fLzk5ORIby8QnhN93jT+xgSWP8CeeeEL69u0rycnJMm7cOFm8eHGL27/xxhsyaNAgs/3w4cNl9uzZEi4+XZ0nf3v/ZympO4nyFtW67tMiElos4sn5G+ShT9bK7x7/Wg64c65c+dr3fgVRepB2TiEIAixTIMYjiFKuzLLrdz6QAjHNFZ8JxnMjcnHcAOC7xneWC6RmzZol11xzjdx6662ybNkyGTlypEyZMsX8dcObBQsWyJlnnil//vOf5fvvv5eTTz7ZXFauXCnhMHXiujd+NNd9SQvqNpo/vH/OWnnssw3yw69F5ra/9ERqyjD+Cg1EaoEYis/AasckAETid43lpvZpBurAAw+Uxx9/3J0i7tOnj1xxxRVy4403Ntn+jDPOkLKyMvnggw/c9x100EEyatQomTFjhqWn9r217Fe55vUf2vQcg7pnyKH7Zsu4fl3l6lnLzV+2W/pAdRKYpku/vXlSQOsjmNpnDUztC/+pff7+/o/s3Ul6dUnxadttuyvMH1ra47kRuThuEAx6Vmm32yQpKVmYeY5gfNf884yRHbqu35/YwFLFJhwOhyxdulRuuukm9306v3bSpEmycOFCrz+j92sGy5NmsN555x2v29vtdnNx0Z2k9uzZY4K2jvT+kg0ijnKfCkQ0NrhHhjz2h1GSk1lf7ev2Y/vJVbN+aDbCN2utYkSmnzJSbGUlYgtgzBpIlRaXii3OxhqpEAdSFUUVYo+xs0YqiIFUVXWV7Ene0yGBlL+//9//XC7ft9NY2vO5Ebk4bgC0N12O8t53G+SIfunSkYGU8iXXZKlAqrCwUKqrqyU3t+G0M729Zs0arz+zY8cOr9vr/d7cc889Mn369Cb377333hJOtorIfn8L7GdP+WewRwMAAAAE34t6+Yt0uJKSEpOZCptAqiNotsszg6VZqF27dkm3bt1C8pd9jXp16uLWrVtDUjUQ4YnjBhwz4LsGVsR/nxDux41mojSI6tmzZ6vbWiqQysrKkri4OMnLa1hFSm93797d68/o/f5sn5SUZC6eOnfuLKGmB02oDxyEH44bcMyA7xpYEf99QjgfN61loixZtS8xMVFGjx4t8+bNa5Ax0tvjx3vveaT3e26v5s6d2+z2AAAAANBWlspIKZ12d+6558qYMWNk7Nix8sgjj5iqfOedd555fOrUqdKrVy+z1kldddVVcthhh8lDDz0kxx9/vMycOVOWLFkizzzzTIjfCQAAAIBIZblASsuZFxQUyLRp00zBCC1jPmfOHHdBiS1btjTolD1hwgR59dVX5R//+IfcfPPNMnDgQFOxb9iwYRIOdJqh9sxqPN0Q4LgB3zUINf4bBY4Z8F0TRn2kAAAAAMDqLLVGCgAAAADCAYEUAAAAAPiJQAoAAAAA/EQgBQAAAAB+IpAKoSeeeEL69u0rycnJMm7cOFm8eHEohwOL05L/Bx54oGRkZEhOTo6cfPLJsnbt2lAPC2Hm3nvvlZiYGPnrX/8a6qHAwrZt2yZnn322dOvWTVJSUmT48OGmtQjQnOrqarnlllukX79+5pjp37+/3HHHHUJNM3j68ssv5cQTT5SePXua/xZppW1Perxo5e4ePXqY42jSpEmyfv16sSoCqRCZNWuW6Zmlpc+XLVsmI0eOlClTpkh+fn6ohgSL++KLL+Syyy6TRYsWmabTlZWVMnnyZNNnDfDFd999J08//bSMGDGCHYZm7d69WyZOnCgJCQny0UcfyU8//WR6NXbp0oW9hmbdd9998tRTT8njjz8uq1evNrfvv/9+eeyxx9hrcNNzFj3n1WSCN3rM/Otf/5IZM2bIt99+K2lpaeb82GaziRVR/jxENAOl2QX9wlE1NTXSp08fueKKK+TGG28M1bAQRrTfmmamNMA69NBDQz0cWFxpaakccMAB8uSTT8qdd95pevRpw3OgMf1v0DfffCNfffUVOwc+O+GEE0zPz+eee8593//93/+ZrMJ///tf9iSa0IzU22+/bWbYuLJRmqm69tpr5brrrjP3FRUVmePqxRdflD/84Q9iNWSkQsDhcMjSpUtNutL9QcTGmtsLFy4MxZAQhvTLRXXt2jXUQ0EY0Gzm8ccf3+B7B/DmvffekzFjxshpp51m/liz//77y7PPPsvOQosmTJgg8+bNk3Xr1pnbP/zwg3z99ddy7LHHsufgk02bNsmOHTsa/HeqU6dOJvlg1fPj+FAPIBoVFhaaucQaYXvS22vWrAnZuBA+NIOpa1x0+s2wYcNCPRxY3MyZM80UYp3aB7Rm48aNZoqWTj+/+eabzXFz5ZVXSmJiopx77rnsQDSbySwuLpZBgwZJXFycOc+566675KyzzmKPwScaRClv58eux6yGQAoI0+zCypUrzV/7gJZs3bpVrrrqKrOuTgvbAL78oUYzUnfffbe5rRkp/b7RNQsEUmjO66+/Lq+88oq8+uqrMnToUFm+fLn5g59O1eK4QaRial8IZGVlmb/W5OXlNbhfb3fv3j0UQ0IYufzyy+WDDz6Qzz//XHr37h3q4cDidBqxFrHR9VHx8fHmouvqdDGvXte/GgOetFrWkCFDGtw3ePBg2bJlCzsKzbr++utNVkrXsWiVx3POOUeuvvpqU3EW8IXrHDiczo8JpEJAp0eMHj3azCX2/Aug3h4/fnwohoQwoIswNYjShZmfffaZKTELtOaoo46SFStWmL8Ouy6abdDpNnpd/6gDeNIpw41bK+i6l7333psdhWaVl5eb9d6e9PtFz28AX+h5jQZMnufHOl1Uq/dZ9fyYqX0honPPNdWtJzRjx4411bO0JOR5550XqiEhDKbz6ZSJd9991/SScs0X1oWYWhUJ8EaPlcbr6LScrPYHYn0dvNEsghYO0Kl9p59+uulx+Mwzz5gL0BztDaRrovbaay8zte/777+Xhx9+WM4//3x2GhpUkN2wYUODAhP6Rz0tnKXHjk4H1cqyAwcONIGV9ibT6aGuyn5WQ/nzENLS5w888IA5IdZSxDrVRiuTAM2VCfXmhRdekD/96U/sNPjs8MMPp/w5WqTTh2+66SbTCFNPZvSPfxdeeCF7Dc0qKSkxJ706a0KnE+vJ75lnnmmaq+pMHEDNnz9fjjjiCGlMkwta4lxn32iPVf3DzZ49e+Tggw82bTv23XdfsSICKQAAAADwE2ukAAAAAMBPBFIAAAAA4CcCKQAAAADwE4EUAAAAAPiJQAoAAAAA/EQgBQAAAAB+IpACAAAAAD8RSAEAAACAnwikAAAAAMBPBFIAAFjEk08+KS+++GKohwEA8EGM0+l0+rIhAABoX8OGDZOsrCyZP38+uxoALI6MFAAgqpSVlUk0qaqqEofDEephAEDEIZACAPjttttuk5iYGFm3bp2cffbZ0qlTJ8nOzpZbbrlFdKLD1q1b5Xe/+51kZmZK9+7d5aGHHvLpefU5L7/8cnnllVdkv/32k+TkZBk9erR8+eWXDbbbvHmzXHrppWablJQU6datm5x22mnyyy+/NNhOp8npc37xxRdm+5ycHOndu3dAz/H111/LlVdead5n586d5S9/+YsJUPbs2SNTp06VLl26mMsNN9xg9oGnmpoaeeSRR2To0KHmPeXm5pqf3717t3ubvn37yqpVq8xY9fX0cvjhh7sf19f561//Kn369JGkpCQZMGCA3Hfffea5XXTs+nMPPvigeb3+/fubbX/66Sef9j8AwHfxfmwLAEADZ5xxhgwePFjuvfde+fDDD+XOO++Url27ytNPPy1HHnmkOdHXoOi6666TAw88UA499NBW96AGErNmzTJBiwYBum7omGOOkcWLF5upb+q7776TBQsWyB/+8AcTGGkA8dRTT5nAQ4OG1NTUBs+pAZMGQNOmTXNnpPx9jiuuuMIEhdOnT5dFixbJM888YwIqfY699tpL7r77bpk9e7Y88MADZpwaXLlo0KQB2XnnnWfe16ZNm+Txxx+X77//Xr755htJSEgwgY++Rnp6uvz97383P6cBlyovL5fDDjtMtm3bZp5LX09f96abbpLt27ebn/X0wgsviM1mk4suusjsQ/1MAABBpmukAADwx6233qopF+dFF13kvq+qqsrZu3dvZ0xMjPPee+913797925nSkqK89xzz231efU59bJkyRL3fZs3b3YmJyc7TznlFPd95eXlTX524cKF5mdffvll930vvPCCue/ggw824/Pk73NMmTLFWVNT475//Pjx5r1efPHFTfbBYYcd5r7vq6++Mj//yiuvNHitOXPmNLl/6NChDX7W5Y477nCmpaU5161b1+D+G2+80RkXF+fcsmWLub1p0ybznJmZmc78/PwmzwMACB6m9gEAAnbBBRe4r8fFxcmYMWPMtLY///nP7vs1a6PT5zZu3OjTc44fP95M53PR7ItOE/z444+lurra3KdT8VwqKytl586dZqqbvtayZcuaPOeFF15oxufJ3+fQ96TT5lzGjRvX5L269oHne33jjTfM1Mejjz5aCgsL3Rd9j5p9+vzzz1vdJ/ochxxyiJk66PkckyZNMvuk8dTH//u//zMZOABA+2FqHwAgYBrkeNKAQdcAaeW5xvdroOKLgQMHNrlv3333NdPbCgoKzPS6iooKueeee8wUNp3u5rkmqaioqMnP9+vXr8l9/j6Ht/eqdM1S4/s91z6tX7/ePJ+uz/ImPz9fWqPP8eOPPzYbHDV+Dm/vFwAQXARSAICANc7yNHefCma3DV1LpAGQFl/QDJYGL5ot0vVOnsUXvGWfAn2O5t6Xt/s936s+lwZRulbMG18yR/ocmtHSQhbeaKDZ2vsFAAQXgRQAwFI0+9KYVgfU4g+uoOPNN9+Uc889t0E1QC2uoJXtfBWM5/CFVs779NNPZeLEia0GOJ5TBxs/R2lpqZnKBwCwBtZIAQAsZeHChQ3WKGkp9XfffVcmT57szv7ov40zXI899ph7DZUvgvEcvjj99NPNc95xxx1eezx5Bm5paWleAzl9Dt0vuk6sMd1enwcA0LHISAEALEVLh0+ZMqVB+XOlZcddTjjhBPnPf/5jpuMNGTLEBBma9dFeUL4KxnP4QsuWa8lyXY+1fPlyExBquXPNvGkRiUcffVR+//vfm221AIWWYNcy8lr4QqcEahn566+/Xt577z0z5j/96U9mOy3jvmLFCpNZ09LtjdelAQDaF4EUAMBSNPDQNUsaOG3ZssUEOdqDacSIEe5tNPjQjJKuO9LpeDptToMgDcB8FYzn8NWMGTNM8KP9tW6++WaJj483DXi1mbG+rov2udJGwffff7+UlJSYfaGBlE5r1P5a2qtKg6+XX37ZNDvWtVG6n1yFLwAAHSdGa6B34OsBANDiGqHLLrvMNKsFAMDKWCMFAAAAAH4ikAIAAAAAPxFIAQAAAICfKDYBALAMlu0CAMIFGSkAAAAA8BOBFAAAAAD4iUAKAAAAAPxEIAUAAAAAfiKQAgAAAAA/EUgBAAAAgJ8IpAAAAADATwRSAAAAACD++X9n9RkSfcPSuAAAAABJRU5ErkJggg==", + "image/png": 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"text/plain": [ "
" ] @@ -1846,6 +1584,9 @@ } ], "source": [ + "_logger.setLevel(logging.WARNING) # Disable the logging for the loop\n", + "\n", + "\n", "def plot_success_rate_vs_m(m_values, function, function_params, l_val=0.1, n_val=3):\n", " \"\"\"\n", " Iterate over different m values and plot success rate as a function of m.\n", @@ -1870,11 +1611,10 @@ " @qfunc\n", " def main(x: Output[QNum[n, SIGNED, 0]]):\n", " allocate(x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", - " invert(lambda: qft(x))\n", + " gradient(make_phase_oracle(f, l=l, m=m, N=N, x0=0), x)\n", "\n", - " df = run_standard_simulation(main)\n", + " qprog = synthesize(main)\n", + " df = sample(qprog).sort_values(\"counts\", ascending=False)\n", " analytic_grad = p.analytical_gradient(0)\n", " epsilon = 0.2\n", " success_rate, _, _ = compute_success_rate(\n", @@ -1921,7 +1661,8 @@ " 6.0,\n", " 10.0,\n", "]\n", - "results = plot_success_rate_vs_m(m_values, \"quadratic\", (0.6, 0.25, 0.1))" + "results = plot_success_rate_vs_m(m_values, \"quadratic\", (0.6, 0.25, 0.1))\n", + "_logger.setLevel(logging.INFO) # TEMP" ] }, { @@ -1938,144 +1679,24 @@ "id": "46", "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/47c35670-9481-4ed1-aeb9-5b8a1d0afaf1\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=0.1: Success rate = 93.99%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/377d735e-7fe1-413b-8f53-703657410ea1\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=0.2: Success rate = 80.91%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/98b1c4e1-ac00-4b39-bf36-599db195bfe2\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=0.3: Success rate = 60.35%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/836e3a56-9231-4c4f-b553-4516a2c7d5b1\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=0.4: Success rate = 39.94%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/bbe327dc-fd52-400d-be30-6e6393b885b2\n" - ] - }, { "name": "stdout", "output_type": "stream", "text": [ - "l=0.5: Success rate = 23.29%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/97e645bf-b543-4def-b576-822c05eb841a\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=1: Success rate = 10.79%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/915fb19c-d3e3-485a-a041-b5bb85374c04\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=1.5: Success rate = 16.65%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/e9c32827-293b-422d-9a49-c19a02343bf9\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=2.0: Success rate = 14.36%\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/71cefbf3-c4f5-470e-b514-cea85fd64440\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=3.0: Success rate = 26.12%\n" + "l=0.1: Success rate = 94.58%\n", + "l=0.2: Success rate = 77.59%\n", + "l=0.3: Success rate = 58.94%\n", + "l=0.4: Success rate = 40.19%\n", + "l=0.5: Success rate = 24.37%\n", + "l=1: Success rate = 10.84%\n", + "l=1.5: Success rate = 14.40%\n", + "l=2.0: Success rate = 15.09%\n", + "l=3.0: Success rate = 28.08%\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -2085,6 +1706,11 @@ } ], "source": [ + "from classiq.execution.functions.util._logging import _logger\n", + "\n", + "_logger.setLevel(logging.WARNING) # Disable the logging for the loop\n", + "\n", + "\n", "def plot_success_rate_vs_l(l_values, function, function_params, m_val=2.0, n_val=3):\n", " \"\"\"\n", " Iterate over different l values and plot success rate as a function of l.\n", @@ -2109,11 +1735,10 @@ " @qfunc\n", " def main(x: Output[QNum[n, SIGNED, 0]]):\n", " allocate(x)\n", - " hadamard_transform(x)\n", - " phase(f_normalized(x), 2 * pi)\n", - " invert(lambda: qft(x))\n", + " gradient(make_phase_oracle(f, l=l, m=m, N=N, x0=0), x)\n", "\n", - " df = run_standard_simulation(main)\n", + " qprog = synthesize(main)\n", + " df = sample(qprog).sort_values(\"counts\", ascending=False)\n", " analytic_grad = p.analytical_gradient(0)\n", " success_rate, _, _ = compute_success_rate(\n", " df, analytic_derivatives={\"x\": analytic_grad}, p=p\n", @@ -2141,7 +1766,8 @@ "l_values = [0.1, 0.2, 0.3, 0.4, 0.5, 1, 1.5, 2.0, 3.0]\n", "results_l = plot_success_rate_vs_l(\n", " l_values, \"quadratic\", (0.6, 0.25, 0.1), m_val=1.0, n_val=3\n", - ")" + ")\n", + "_logger.setLevel(logging.INFO)" ] }, { @@ -2173,7 +1799,7 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/c3a21541-e687-4524-8cd7-ec934bfd031d\n" + "Job: https://platform.classiq.io/jobs/04e43eb9-b27d-40d2-9bed-25c60b63270f\n" ] }, { @@ -2181,26 +1807,21 @@ "output_type": "stream", "text": [ " coords counts probability bitstring\n", - "0 [1, -2] 1988 0.970703 110001\n", - "1 [0, -2] 15 0.007324 110000\n", - "2 [2, -2] 15 0.007324 110010\n", - "3 [1, -3] 8 0.003906 101001\n", - "4 [1, -1] 7 0.003418 111001\n", - "5 [-1, -2] 4 0.001953 110111\n", - "6 [-2, -2] 2 0.000977 110110\n", - "7 [0, 0] 1 0.000488 000000\n", - "8 [1, 1] 1 0.000488 001001\n", - "9 [1, -4] 1 0.000488 100001\n", - "10 [-1, -4] 1 0.000488 100111\n", - "11 [3, -2] 1 0.000488 110011\n", - "12 [-4, -2] 1 0.000488 110100\n", - "13 [0, -1] 1 0.000488 111000\n", - "14 [-4, -1] 1 0.000488 111100\n", - "15 [-2, -1] 1 0.000488 111110\n", + "0 [1, -2] 1993 0.973145 110001\n", + "1 [0, -2] 17 0.008301 110000\n", + "2 [2, -2] 17 0.008301 110010\n", + "3 [1, -3] 9 0.004395 101001\n", + "4 [1, -1] 3 0.001465 111001\n", + "5 [2, -1] 3 0.001465 111010\n", + "6 [-1, -2] 2 0.000977 110111\n", + "7 [1, 0] 1 0.000488 000001\n", + "8 [-1, 0] 1 0.000488 000111\n", + "9 [0, -3] 1 0.000488 101000\n", + "10 [-4, -2] 1 0.000488 110100\n", "Analytical gradient: (dx, dy) = ([0.25, -0.5])\n", "Majority gradient: (dx, dy) = ([0.25, -0.5])\n", - "Success rate: 97.07% (1988/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.07%\n" + "Success rate: 97.31% (1993/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.31%\n" ] } ], @@ -2224,14 +1845,11 @@ "@qfunc\n", "def main(coords: Output[QArray[QNum[n, SIGNED, 0], 2]]):\n", " allocate(coords)\n", - " hadamard_transform(coords)\n", - " phase(f_normalized(coords[0], coords[1]), 2 * pi)\n", + " gradient_nd(make_phase_oracle(f, l=l, m=m, N=N, x0=0, d=2), coords)\n", "\n", - " invert(lambda: qft(coords[0]))\n", - " invert(lambda: qft(coords[1]))\n", "\n", - "\n", - "df = run_standard_simulation(main)\n", + "qprog_2d = synthesize(main)\n", + "df = sample(qprog_2d).sort_values(\"counts\", ascending=False)\n", "print(df)\n", "\n", "gradient_analytical = [0.25, -0.5]\n", @@ -2245,7 +1863,8 @@ " df, analytic_derivatives={\"coords\": gradient_analytical}, p=p\n", ")\n", "print(f\"Success rate: {success_rate:.2%} ({success_shots}/{total_shots} shots)\")\n", - "show_bar(success_rate)" + "show_bar(success_rate)\n", + "assert success_rate > 0.9, r\"The success rate should be above 90% for these parameters.\"" ] }, { diff --git a/algorithms/gradient_estimation/gradient_estimation_helpers.py b/algorithms/gradient_estimation/gradient_estimation_helpers.py index 9b807f759..809e8ad08 100644 --- a/algorithms/gradient_estimation/gradient_estimation_helpers.py +++ b/algorithms/gradient_estimation/gradient_estimation_helpers.py @@ -5,6 +5,8 @@ from dataclasses import dataclass from matplotlib import pyplot as plt from classiq.qmod.symbolic import pi +import logging +from typing import Callable # %matplotlib widget @@ -107,6 +109,43 @@ def unpack(self, namespace=None): namespace.update(vals) +def make_phase_oracle( + f: Callable, + l: float, + m: float, + N: int, + x0: float = 0.0, + d: int = 1, +) -> Callable: + """Return a @qfunc phase oracle that applies phase(f_norm(reg), 2*pi). + + The oracle encodes the normalized function value as a phase: + f_norm(reg) = f(l/N * reg - x0) * N / (l * m) + + Args: + f: Symbolic Python callable representing the mathematical function. + l: Sampling interval half-width. + m: Gradient magnitude bound (output range). + N: Number of sample points (2^n). + x0: Evaluation point; shifts the sampling window. + d: Dimensionality of the function. + """ + if d == 1: + + @qfunc + def phase_oracle(reg: QNum) -> None: + phase(f(l / N * reg - x0) * N / (l * m), 2 * pi) + + else: + + @qfunc + def phase_oracle(coords: QArray[QNum]) -> None: + args = [l / N * coords[i] - x0 for i in range(d)] + phase(f(*args) * N / (l * m), 2 * pi) + + return phase_oracle + + # ****** Simulation ****** def run_statevector_simulation( qfunc_to_run, print_circuit_info=False, filter_ancilla=False, show_circuit=False @@ -129,19 +168,6 @@ def run_statevector_simulation( return df -def run_standard_simulation(qfunc_to_run, show_circuit=False): - qprog = synthesize(qfunc_to_run) - if show_circuit: - show(qprog) - n_shots = 2048 - df = sample(qprog, num_shots=n_shots) - df.sort_values( - "counts", ascending=False, inplace=True - ) # Verify that the most common state is first, as expected from a statevector simulation - - return df - - # ****** Result Processing ****** def state_to_gradient(value, p): if type(value) == list: @@ -278,6 +304,7 @@ def analyze_results(df, p): plt.tight_layout() plt.show() + return success_rate # ****** Plotting ****** @@ -309,6 +336,12 @@ def plot_classical(): secax_y.set_ylabel("f (real, unnormalized)") +def style_subplots(ax1, ax2): + for ax in [ax1, ax2]: + ax.set_xlabel("x (index)", fontsize=12) + ax.tick_params(labelsize=11) + + def plot_theoretical(show=True): x_array = np.arange(-N // 2, N // 2) diff --git a/algorithms/gradient_estimation/quantum_circuit.png b/algorithms/gradient_estimation/quantum_circuit.png index 6ad8c5cb236745eba7c3ddaabe5e3d4903dea010..6c7dbc4579ac8e8752dffcd5eb87fbfd8ceb030f 100644 GIT binary patch delta 18017 zcmbTeRZv`A*R~tHad&rj5ANCYJn#4Y?_aeK zcI~6CUNyUWuCeBrW6b-$sw0g16CvVp5h6jb@7}$edKI;=CC`K)jRe1WC#E4GCkKAj zFmw9++0NP0-sO%jBJbThi1{DO5O@$!?3{c_H;|pc3FgMlyLY1RM zpU($ny+aHNdPeN(wSZLg|93DfF9gp2>p0;5>%jm2}M!ok&t#=vUh9pkP( zPKJYj^^pzj6zcDD^M}WygO~GKHA 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timeout_seconds=200) def test_notebook(tb: TestbookNotebookClient) -> None: # test quantum programs validate_quantum_program_size( - tb.ref_pydantic("qprog"), - expected_width=None, - expected_depth=None, - expected_cx_count=None, + tb.ref_pydantic("qprog_ancilla"), + expected_width=16, # Expected 8 + expected_depth=63, # Expected 42 + expected_cx_count=41, # Expected 27 + ) + + validate_quantum_program_size( + tb.ref_pydantic("qprog_linear"), + expected_width=6, # Expected 3 + expected_depth=23, # Expected 15 + expected_cx_count=18, # Expected 9 + ) + + validate_quantum_program_size( + tb.ref_pydantic("qprog_linear_2"), + expected_width=6, # Expected 3 + expected_depth=23, # Expected 15 + expected_cx_count=18, # Expected 9 + ) + + validate_quantum_program_size( + tb.ref_pydantic("qprog_quadratic"), + expected_width=6, # Expected 3 + expected_depth=35, # Expected 23 + expected_cx_count=23, # Expected 15 + ) + + validate_quantum_program_size( + tb.ref_pydantic("qprog_quadratic_2"), + expected_width=6, # Expected 3 + expected_depth=36, # Expected 24 + expected_cx_count=23, # Expected 15 + ) + + validate_quantum_program_size( + tb.ref_pydantic("qprog_2d"), + expected_width=12, # Expected 6 + expected_depth=68, # Expected 45 + expected_cx_count=72, # Expected 48 ) # test notebook content From 98828dd46735e56194d753fb1c08b87fe0bfff02 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Fri, 12 Jun 2026 16:04:28 +0300 Subject: [PATCH 11/12] Fixing PR comments --- .../gradient_estimation.ipynb | 211 ++++++++---------- .../gradient_estimation_helpers.py | 39 +--- 2 files changed, 90 insertions(+), 160 deletions(-) diff --git a/algorithms/gradient_estimation/gradient_estimation.ipynb b/algorithms/gradient_estimation/gradient_estimation.ipynb index ccf2ef46a..6d6099ad7 100644 --- a/algorithms/gradient_estimation/gradient_estimation.ipynb +++ b/algorithms/gradient_estimation/gradient_estimation.ipynb @@ -281,7 +281,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/86efe0f2-82b1-4c8a-a1fb-b2522ab148d6\n" + "Job: https://platform.classiq.io/jobs/f79b6a72-bc04-4c98-83d3-2af28406d793\n" ] }, { @@ -324,7 +324,7 @@ "type": "string" } ], - "ref": "b7f4ecee-9f7d-485a-8741-086b580b217e", + "ref": "041a0391-4ab7-47e1-bdf8-e5e656a0016d", "rows": [ [ "7", @@ -621,7 +621,7 @@ "type": "float" } ], - "ref": "119268b4-53d0-4200-9a57-db95331b5e10", + "ref": "54976780-5091-49d9-80bd-1600df3a5eac", "rows": [ [ "-4", @@ -849,12 +849,12 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/a9486f1f-fa7a-4566-a013-58f7d004c6d5\n" + "Job: https://platform.classiq.io/jobs/deb9fbe3-dadb-4f44-b33c-dbcba464e3fb\n" ] }, { "data": { - "image/png": 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", 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", 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" ] @@ -948,12 +948,12 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/e0017ddd-0fcb-4c0b-b5c7-f822651d6508\n" + "Job: https://platform.classiq.io/jobs/19028135-c695-4b39-a8a0-a30a04eee106\n" ] }, { "data": { - "image/png": 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", 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", 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" ] @@ -1030,12 +1030,12 @@ "name": "stderr", "output_type": "stream", "text": [ - "Job: https://platform.classiq.io/jobs/9981c31a-54fa-42b1-8aa1-5223af4c8f22\n" + "Job: https://platform.classiq.io/jobs/f5e85e56-5921-4e56-b736-bd7f86101e21\n" ] }, { "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -1099,7 +1099,9 @@ "id": "29", "metadata": {}, "source": [ - "The final step is to apply the inverse QFT to the coordinates. This extracts the gradient from the phases and produces a measurable state containing the normalized gradient value." + "The final step is to apply the inverse QFT to the coordinates. This extracts the gradient from the phases and produces a measurable state containing the normalized gradient value.\n", + "\n", + "We will first define a QFunc that preforms the algorithm and calculates the gradient of a given function $f$, for single and multiple dimensions, and another function that transforms a given function (either Callable or QCallable) into a normalized phase oracle." ] }, { @@ -1112,8 +1114,8 @@ "@qfunc\n", "def gradient(f: QCallable[[QNum]], x: QNum) -> None:\n", " \"\"\"\n", - " Apply the gradient estimation algorithm to estimate the gradient of f at x=0.\n", - " The function f is given as a quantum oracle that applies the phase kickback.\n", + " Apply the gradient estimation algorithm to estimate the gradient of 1 dimensional function $f$ at $x=0$.\n", + " The function $f$ is given as a quantum oracle that applies the phase kickback.\n", " \"\"\"\n", " # 1. State preparation\n", " hadamard_transform(x)\n", @@ -1123,17 +1125,53 @@ "\n", "\n", "@qfunc\n", - "def gradient_nd(f: QCallable[[QNum]], coords: QArray[QNum]) -> None:\n", + "def gradient_nd(f: QCallable[QArray[QNum]], coords: QArray[QNum]) -> None:\n", " \"\"\"\n", - " Apply the gradient estimation algorithm to estimate the gradient of f at x=0.\n", - " The function f is given as a quantum oracle that applies the phase kickback.\n", + " Apply the gradient estimation algorithm to estimate the gradient of multi dimensional function $f$ at $\\vec{x}=0$.\n", + " The function $f$ is given as a quantum oracle that applies the phase kickback.\n", " \"\"\"\n", " # 1. State preparation\n", " hadamard_transform(coords)\n", " f(coords)\n", " # 2. QFT inverse on the coordinates register\n", - " # invert(lambda: qft(x))\n", - " repeat(coords.len, lambda i: invert(lambda: qft(coords[i])))" + " repeat(coords.len, lambda i: invert(lambda: qft(coords[i])))\n", + "\n", + "\n", + "def make_phase_oracle(\n", + " f: Callable,\n", + " l: float,\n", + " m: float,\n", + " N: int,\n", + " x0: float = 0.0,\n", + " d: int = 1,\n", + ") -> QCallable:\n", + " \"\"\"Return a @qfunc phase oracle that applies phase(f_norm(x), 2*pi).\n", + "\n", + " The oracle encodes the normalized function value as a phase:\n", + " f_norm(x) = f(l/N * x - x0) * N / (l * m)\n", + "\n", + " Args:\n", + " f: Symbolic Python callable representing the mathematical function.\n", + " l: Sampling interval half-width.\n", + " m: Gradient magnitude bound (output range).\n", + " N: Number of sample points (2^n).\n", + " x0: Evaluation point; shifts the sampling window.\n", + " d: Dimensionality of the function.\n", + " \"\"\"\n", + " if d == 1:\n", + "\n", + " @qfunc\n", + " def phase_oracle(x: QNum) -> None:\n", + " phase(f(l / N * x - x0) * N / (l * m), 2 * pi)\n", + "\n", + " else:\n", + "\n", + " @qfunc\n", + " def phase_oracle(coords: QArray[QNum]) -> None:\n", + " args = [l / N * coords[i] - x0 for i in range(d)]\n", + " phase(f(*args) * N / (l * m), 2 * pi)\n", + "\n", + " return phase_oracle" ] }, { @@ -1164,7 +1202,7 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/ca997f04-5a28-4552-9659-3fd7a28e5983\n" + "Job: https://platform.classiq.io/jobs/c2584af9-9b57-43d9-991a-70772ca1c7a4\n" ] }, { @@ -1303,25 +1341,25 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/6125d188-6482-4490-91cc-2ed31bfb1159\n" + "Job: https://platform.classiq.io/jobs/3f1c1fa2-1576-484e-98d3-244f107a2326\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed probabilities: {2: 0.8720703125, 3: 0.06396484375, 1: 0.025390625, -4: 0.0126953125, 0: 0.0107421875, -1: 0.00830078125, -3: 0.0048828125, -2: 0.001953125}\n", + "Parsed probabilities: {2: 0.89697265625, 3: 0.044921875, 1: 0.01953125, -4: 0.01171875, 0: 0.00927734375, -3: 0.0068359375, -1: 0.00634765625, -2: 0.00439453125}\n", "The analytical gradient is: 0.55\n", "The majority gradient is: 0.5\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 87.21% (1786/2048 shots)\n", - "[\u001b[92m████████████████████████████████████████████\u001b[91m------\u001b[0m] 87.21%\n" + "Success rate: 89.70% (1837/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████\u001b[91m-----\u001b[0m] 89.70%\n" ] }, { "data": { - "image/png": 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" ] @@ -1332,7 +1370,7 @@ { "data": { "text/plain": [ - "0.8720703125" + "0.89697265625" ] }, "execution_count": 9, @@ -1396,25 +1434,25 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/dcb42534-fa36-490d-a008-5acaa5c3e72d\n" + "Job: https://platform.classiq.io/jobs/069c0180-ccdd-43f7-bbe3-15f43589d689\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed probabilities: {1: 0.98828125, 0: 0.005859375, 2: 0.005859375}\n", + "Parsed probabilities: {1: 0.98095703125, 2: 0.00927734375, 0: 0.005859375, -1: 0.00146484375, 3: 0.0009765625, -2: 0.0009765625, -4: 0.00048828125}\n", "The analytical gradient is: 0.25\n", "The majority gradient is: 0.25\n", "The majority result is correct\n", "####################################################\n", - "Success rate: 98.83% (2024/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.83%\n" + "Success rate: 98.10% (2009/2048 shots)\n", + "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 98.10%\n" ] }, { "data": { - "image/png": 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" ] @@ -1465,25 +1503,25 @@ "output_type": "stream", "text": [ "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/fc8db73d-4f07-4293-a6bb-1bee0b716e05\n" + "Job: https://platform.classiq.io/jobs/7beb5389-94f2-4c79-b189-c67aea24008c\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "Parsed probabilities: {2: 0.2451171875, 1: 0.244140625, 0: 0.23486328125, -1: 0.10791015625, 3: 0.0771484375, -4: 0.03857421875, -2: 0.0302734375, -3: 0.02197265625}\n", + "Parsed probabilities: {1: 0.2568359375, 2: 0.24169921875, 0: 0.23095703125, -1: 0.08935546875, 3: 0.087890625, -2: 0.0341796875, -4: 0.03369140625, -3: 0.025390625}\n", "The analytical gradient is: 0.25\n", - "The majority gradient is: 0.5\n", - "The majority result is incorrect\n", + "The majority gradient is: 0.25\n", + "The majority result is correct\n", "####################################################\n", - "Success rate: 24.41% (500/2048 shots)\n", - "[\u001b[92m████████████\u001b[91m--------------------------------------\u001b[0m] 24.41%\n" + "Success rate: 25.68% (526/2048 shots)\n", + "[\u001b[92m█████████████\u001b[91m-------------------------------------\u001b[0m] 25.68%\n" ] }, { "data": { - "image/png": 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" ] @@ -1545,7 +1583,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "id": "44", "metadata": {}, "outputs": [ @@ -1555,32 +1593,18 @@ "text": [ "m=0.05: Success rate = 0.00%\n", "m=0.1: Success rate = 0.00%\n", - "m=0.33: Success rate = 0.88%\n", - "m=0.5: Success rate = 10.60%\n", + "m=0.33: Success rate = 0.68%\n", + "m=0.5: Success rate = 10.01%\n", "m=0.67: Success rate = 93.31%\n", - "m=1.0: Success rate = 99.27%\n", - "m=1.33: Success rate = 81.05%\n", - "m=1.67: Success rate = 94.14%\n", - "m=2.0: Success rate = 98.44%\n", - "m=2.33: Success rate = 90.48%\n", - "m=2.67: Success rate = 78.66%\n", - "m=3.0: Success rate = 64.75%\n", - "m=3.33: Success rate = 54.30%\n", - "m=3.67: Success rate = 0.00%\n", - "m=4.0: Success rate = 0.00%\n", - "m=6.0: Success rate = 0.00%\n", - "m=10.0: Success rate = 0.00%\n" + "m=1.0: Success rate = 99.22%\n", + "m=1.33: Success rate = 79.64%\n", + "m=1.67: Success rate = 95.21%\n", + "m=2.0: Success rate = 98.58%\n", + "m=2.33: Success rate = 90.09%\n", + "m=2.67: Success rate = 77.73%\n", + "m=3.0: Success rate = 64.55%\n", + "m=3.33: Success rate = 56.35%\n" ] - }, - { - "data": { - "image/png": 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u+mcAQGkfgJiiJWxXXnmlWSBU523oBHKd26AnVXqiryVcWtam6z65aMCkWaMJEyaYsi+d/K+BgQZcronunv7+97+boEZLwvRfXRRXn08X59QGF3pi6ZqjpPN6NAuka+Lo9pql0cBGgyUdk2uhXZ1LpGVjOvdJJ/drhkkXDtY5Jq4gT9fe0ed3LR6rk++1+YGut6TZNn1dbXCh82T0fqXzoHQ9HW0woXN69ORfAxydoK8lfVqS11zaAEKbd0yaNMm8lu5jPdHVzJe+F11fR0uw9LPRk2/9TOrSLI9mt3Q/aYmVZg51Ww1wdN9qyZXuZ10HSLfVkkJ9z3ryq5+rZoz8bS6g9Hl1DSQtM9TP29eaUJqB0kyF7k8di55g63Gh2ShdJ8kVSEQLfc96PGjwoZ+Tjl/X7tJjQRfu1dLQcD5fIPQPIfp7rAGQZon1d7d3796mzFV/D/X3RbOzOn9Q6e+SHnc6N06PJ52zp8ePjl1Ld7XJhP5e6NpXWv6rvy/6BwH9Y4eW2+r70j9KsE4UAC/hbhsIAKG0cuVK5yOPPOI87rjjnL169XKmpaWZi7Y21pbFCxYs8Plzug6Srn2j68Vou+drr73WrIfjax0pVVlZadapGTp0qFmbSNtY6/pEusbUnj17vLbV9W+uv/565/7772+ev3379s6RI0ealue+xq9trPU1dVtty6zj0nbP8+fPd283ZcoU07Jb31dGRoZpx65r6uj6RJ7rN02fPt05ceJE54EHHmjatrvGqevm7Nixo1nrSHlyrZc1Y8YM9/o/999/v7Nv377O1NRU0ypd901j+1Q/N90+OTnZZ0v6X3/91exH13NqG/V+/fo5L7vsMvfr+kvbj2vLdH0dbYnuy7PPPus85ZRTzFj1GOrQoYNzxIgRzueee868P3809F4ba7vvahOux2tz1pHyRdu7jxs3zhxXejzo63/11VfOV155xTyH/hvIOEL1fI21J/f1XC76O/GHP/zB2aVLF3Pc6BIB2rb+tttuc/7yyy9e286dO9eMT8fpWhbBs92+rgn3wgsvOMeMGWOOLddxe/zxx5vPvLS01K92/QDih0X/zzu0AgAAAAA0hjlSAAAAABAgAikAAAAACBCBFAAAAAAEiEAKAAAAAAJEIAUAAAAAASKQAgAAAIAAxf2CvA6HwyxqmZ2dbRbnAwAAABCfnE6nWdxbF/HWBeYbE/eBlAZR3bt3b7UPBwAAAEBk27Jli3Tr1q3RbeI+kNJMlGtn5eTkSDgyYjt27JCOHTs2GfVGAqvdKssKlklSYpKkJKaEezhx/deSir0Vkt42nUxqiNiqbWKvtsug/EGSmpQqsSbavmsQGThuwDGDePuuKS4uNkkWV4zQmLgPpFzlfBpEhSuQqqysNK8d7gPH30AqszxTMlMyCaTCHEiVOkolq20WgVQIA6kyW5n5XYzVQCqavmsQGThuwDGDeP2usfgx5ScyRgoAAAAAUYRACgAAAAACRCAFAAAAAAEikAIAAACAABFIAQAAAECACKQAAAAAIEAEUgAAAAAQIAIpAAAAAAgQgRQAAAAABIhACgAAAAACRCAFAAAAAAEikAIAAACAABFIAQAAAECACKQAAAAAIEAEUgAAAAAQzYHUrFmz5OSTT5YuXbqIxWKR//3vf03+zMyZM+WQQw6R1NRU6dOnj7z66qutMlYAAAAA8StJIkhZWZkMGTJELrnkEjn99NOb3H7Dhg1y4oknypVXXilvvvmmzJgxQy677DLp3LmzjB8/vlXGjNCz2R0ya1WpzF5TKsWVDslJS5DRfbPkyAOzJCUpomJ/AAAAxKmICqROOOEEc/HX888/L7169ZLHH3/c3O7Xr598//338o9//INAKkrNWVsqj04rkFKrQywWEadTzL/frymTZ2fskFsm5MuoPlnhHiYAAADiXEQFUoGaM2eOjB071us+zUT95S9/afBnrFarubgUFxebfx0Oh7m0Nn1Np9MZltduznhdl1Cas7ZMJv9vm/u26+ld/5ZZHXLPB9vk7lM7y6g+mRLPWuoziGeu/Rmu74KWFm3fNYgMHDfgmEG8fdc4AhhDVAdS27dvl/z8fK/79LYGRxUVFZKenl7vZx588EGZPHlyvft37NghlZWVEo4Pq6ioyBw8CQmRX7ZWVV0l1iKrWJIsYkuwhex5bXanPDqt0FxvKDTQ+y0i8ui07fJ/f8iTlCS9FZ+c4pTK0kqzQyxmr6C57A67WO1W2ZmwU5ITk2Nuh0bbdw0iA8cNOGYQb981JSUl8RFIBeP222+XG2+80X1bg67u3btLx44dJScnJywHjjbW0NcP94HjDz3R3OrYKhkpGZKSmBKy5/1qRbGU2ZrOrugWut3inSK/658Vv/PH1pbJ3hKbtM22y+g+mcwfC8W+rbaJ0+aU3I65kpqUKrEm2r5rEBk4bsAxg3j7rklLS4uPQKpTp05SUFDgdZ/e1oDIVzZKaXc/vdSlH1q4Pjg9cML5+oHQMep4XZdQlvW55kQ1RbfTRhRjB7R+4Btx88cKquSHNWXy3Nc7mT/WTK5jOlp+F4MR6+8PLYPjBhwziKfvmoQAXj+q/2s6atQo06nP05dffmnuR3TR7nz+TvfR7XT7eAuidH6YzhNrbP6YbgcAAICWF1GBVGlpqSxZssRcXO3N9frmzZvdZXkTJ050b69tz9evXy+33nqrrFy5Up599ll555135IYbbgjbe0BwtMW5vwku3U63j6dyPs1ENTV/TOl2uj0AAABaVkSdjS5YsEAOPvhgc1E6l0mvT5o0ydzetm2bO6hS2vr8008/NVkoXX9K26D/3//9H63Po5CuExVIRkq3jxc6J0rL+ZraPfq4bqfbAwAAoGVF1Bypo48+utF2zq+++qrPn1m8eHELjwwtLSPVv5hek1aZqQmmuUK80PlgzB8DAACILBGVkUJ8Wr29Uh76ZHuT27kq/3RR3pSk+Dl0mT8GAAAQeeLnbBQR6bc9Nrnzvd+ksqomE9mvS5pk1Wan6s6Z0kzUPafpYrzxk41SyYn+d0eMt/ljAAAA4RJRpX2IL3vL7XLHu7/J3vJqc3tgtzR56Kyu5rpZK2lNqSzaVC7ltetL/eOP3aRHbuyt79OY+evLZNmvFX5vH2/zxwAAAMKFP10jLCpsDrnr/d/kt71V5naPDiky+bQupmRPL7pG1KRTu8g5I9u7f2bJZv8DimincwWnzNstd733m9js/nXh0LxVVpzNHwMAAAgXAim0umqHUx74eJus2mY1t3OzkuT+M7tIdlpivW1H7J/pvj5vfZnEg8oqhzzwyXZ5edYud6e+fp1TTaDUWJGfMw7njwEAAIQLZ1xo9UzLP78olHnry83tjJQEE0Tl5ST73H7/jikm0FJLN1eYICOWbS+qkhve+lW+XbmvhfnEMe3lH+d1N/PDdJ6Y5/wxz8BKr7fPpFoXAACgNRBIoVW9Pnu3TF9W7G6ioMFBr44Nz3uyWCxy6P4Z5npVtVOWbK4JwGLR0s3lcu3rW2RdYU2mLj3ZIvec2lnOH91BEiwW02RjylW95NYJ+TK6T6YM6JQio/tmyuEHZLkzUo99xoK8AAAArYE/X6PVTFtaJG/M3u2+rWVoQ/erCZIaM3L/TPnsp5rga/66cjmsd1bMZek+Wlwkz329Qxy1tXxd2iabILNnneYarvljv+ufLaW7SyWrfZZUO0Sue3OLrC2wyqZdNrOPLzkyNzxvBgAAIE6QkUKrmLuuVP71ZaH79pXH5MrRB2X79bMH98hwtwCfv6Gs0UWbo43N7pAnPi+UZ2bsC6KG98yQpy7oXi+IakhSokVuOSFfXFOj3pm/R1Ztq2zBUQMAAIBACi3ul98q5f6PtrsDhTOHt5XTh7fz++fTUxJkULd0c72w2C4bd9okFuwqtcstU7bK57WljuqsQ9vJvWf4brzRGC2P1BJApfuZEj8AAICWRSCFFvXrbpvc9f5Wsda28D76oCy57OjAy85G9s7wWlspFoLLq/+zWX6pzRylJFnkthPz5fKjcyUxwf8FeD2dM7Kd9M2vyWJpiZ/ORwMAAEDLIJBCi9ldqgvubpXiippOe0P2S5ebT8g3jRMC5dkGfX5tx79o9fmyIrl5yq+yu6xmIeKO2UlmseFj++c063k1ALvZo8Rv6vw9spISPwAAgBZBIIUWUW5zyJ3v/ybbi+zuNubagS7YNY66tkuRru1qWqSv2FohJZU1QUg0sVc75dkZO+Tx6YWmA6Ea2C1Nnr6gu/TNTwvJa9Qt8XucLn4AAAAtgq59aJGA4d4Pt5kuciovRxfc7SqZqYHN+/GVlfpg4V4TICzaWC5H+dmsorWbR8xaVSqz15RKcaVDctISZHTfLBnSPV0e+azArIXlcvLQNnLlsR3djTRCRUv8flhTKmtqu/hpid+ldPEDAAAIKQIphJR21Hvi8wJZuLGm/C47LUEeOLOrdKhdVLc5RtYGUmre+rKIC6TmrC2VR6cVSKnVYRbM1eaC+u/3a8rMYrmuXoOalLtmbJ5MGNKmRcbhKvG75vUtJvOlJX5j+mbJQZ1Dk/UCAAAApX0IsVe+2yVfrShxN1CYfFoX2a9DSkieW8vg0pJrsjc/bigXRwS1Qdcg6p4PtkmZtWY+mGto7n9rt8tMSZBHz+nWYkGUd4lfe3OdLn4AAAChR0YKAbPZnTJvbanMX1fpVb5WXF4tU+btMdtouHPbiZ1kYG3b8lDQ+VWH9MiQ2WvLpKi8WlZvt0ZElkXL+TQTpfwJ7fp28m99qOY6e0Q7+X51TYnfZi3x+2G3XHoUC/UCAACEAoEUAjLjlx1yy7u7pczqrFe+5unq33WUww/ICvneHdk70wRSav66sogIpHROlJbz+aPMVjOHauyA5nXoC6rE78c9MuYASvwAAABCga598NuXPxfI1W8tNUGUr/I1lyMOyJRTDmnbInv20F772qDrPKlIoI0l/O3ortvp9q2FEj8AAICWQSAFv1RWVctNU5f4Vbu2eFOFKXdrCbnZSdI7r6Y0TkvWdK2qcNPyRn+na+l2un1r0hK/A2rLCV0lfgAAAGgeAin4ZdqybVJcYfdrDpCWuWn5WksZsX+G+/qPG8KfldI5YoFkpHT71uQq8XO1WdcSv19+q2zVMQAAAMQaAin45YsVBZIQIeVrup6Uy7z1NW3Ww0kbbQSSkdLtW1vP3Lpd/La3WNYQAAAgHhBIwS97y23mBDwSyte0wUROes2hqwvz6gLA4XTkgVmSlZpgOhU2Rh/X7XT7cPAs8duyu0r+Q4kfAABA0Aik4Je2GSkBZaRasnxNS9WG96zJSpXbHLJ8a4WEk7Zlv2VCfqNlj65dp9vp9uFQt8TvXUr8AAAAgkYgBb+MG5AfUEaqpcvXPOdJaRv0cDusd6Z0bpNUL3ByzZ3KTE2Qe07rLKP6hCcb5UKJHwAAQGgQSMEvEwZ1lpz0pIgpXxveK9OdIZu/IfzzpFZuq5RtRTUdBDu1SZIxfTNlcPd0GdMnU26dkC9TruoV9iDKs8TvQEr8AAAAmoVACn5JS06UJ84aui/VEubytZz0ROnXJc3d0nvb3ioJp48WF7mvnz+6g0w6tYs89odu5l9dfDdc5XwNlfjdVK/EL7zlkQAAANEmcs7uEPHG9s+XZ/44RDJTfUdTrV2+5tm9b34YF+fdU2Z3t3vPTkuQo8LUTKJ5JX4FdPEDAAAIAIEUAvK7fh3l+Yvby/mj27jv01K2cJSvRUogNX1ZsVTVdg48flAbSU2Ojl8rSvwAAACCt292POCnlCSLDNkvTd6YXVPONqZvlilfa237d0yR3Kwk2Vlql6VbKqSyyiFprRzEVDuc8unSmv2gebqThu4LMCOdq4vfVf/ZYgLBqfP3SEqiyMadNtO+XjsvatMQne8WSaWJAAAAkYCzIwTFand6BVbhYLFY5NDa7n02u1OWbG79phPz1pVJYbHd3Umwc9tkiSY9clPlgjE1JX76ib4xZ4/8sLZMftpSYf59ZFqB/OHZDTJnbcstsAwAABCNCKQQlCqvQCp8h9FIr/K+8rA2mTj54LYSjbq3S6nXvt7z3zKrQ+75YBvBFAAAgAcCKTQ/I1Xb/S0cDu6R4e4+p/OknK6z/1bw626bLNpUE7x1aZssw3vtW9sqWtjsDnl8ekGj27j26KPTaEgBAADgQiCFZmekUsNU2qfSUxJkULd0c11L7HR+T2v5eMm+bJTOjUpwrb4bRbTbYKnV0eR2+mnrdq7uhAAAAPGOQArNzkglhzGQUiN778sE/dhK3fsqbA75Ynmxe47YuIGt32wjFGavKRV/4z/dTrcHAAAAgRSC5Gr3He6MVN026PNaaZ7U17+UmLlD6ph+2WaB4Gik3fn8rYbU7XR7AAAAEEghJF37wpvY7NouRbq2q+mWt2JrhZRWVrfo6+k8rI8W7XXfPuXg6Gl5Xpe2OA8kI6XbAwAAgEAKIenaF/65Qa6slMMpsnBjy2allm+tlA21c7H6dU6TvvlpEq10nahAMlK6PQAAAAikEMXrSHnSNZxc5rXwPKmPFu/LRp0cxdkopYvtZqUmmMWEG6OP63a6PQAAAAikEII5UuFsf+6infvSkmvG8eOGcnG0UBv0XaV2+X51TcOFNhmJUR9YaFnmLRPyzfWmPkXdLtxlnAAAAJGCsyIExebV/jz8h5Ge4B/SoyYrVVReLau3W1vkdT77qUiqa/stnDAoJyYCi1F9suSe0zpLZmrNe/E1Z+qKo3PNdgAAAKgR/WeBCHsgFe725766981fF/ryPnu1Uz5dWrN2VIKlZu2oWKFB0pSresmtE/JlTJ9MGdw9XXrnpbof/2VbZVjHBwAAEGmSwj0ARCdbBLU/9xlIbSiTiYd3COnzz15bKrtKazoCjuydKXk5NZ0CY4Vm18YOyDEXZbM75IIXNsqe8mpTzrh1j810SAQAAAAZKYQgIxUJzSZUbnaSO4uipX27S+0hff6PF9dko6K95XkggdVpw9u6uyG+9+O+JhsAAADxjtI+xEwgVbd7348bQlfet3GnVZZuqTDXu7VLloNr52PFupOGtJGMlJqvic+XF8uestAGpwAAANGKQAohCKQi5zDyKu9bX94i2ShteZ7g7yq2US4rLVEmDMlxd2r8n8dCxAAAAPEscs6AEZWBlDZdiKA4Sg7qnCbZaTUD0oV5tUFEc5VZq+WrFcXmurZYP652DlG8OH1YO/dnrAFlua22bSEAAEAci6BTYERjIKUd+ywRlJ1JTLDI8F41WSk94V++taYcrzlmrCiRiqqa9/u7/tkmSxNPdO7Z7/rXBI+lVodpAQ8AABDvCKTQrK59kdKxz9NIj3lS89c3b56U0+mUj5Z4Npmoab4Qb84a0c59/b0Fe70WZAYAAIhHBFJoVkYqJTHyDiHNSGnJYSjmSWmDic27bOb6wG5p0qvjvrWV4sl+HVJkVJ+aTN/OErt880tJuIcEAAAQVpF3FoyoUOUKpCIwI5WTnmjmSikNgrbtrQr6uT7yanken9kol7MP3ZeVmvrjHnE4yUoBAID4RSCFoFgjOJByLZjr8mOQ5X07Sqpk9ppSc719ZqKM6Zsl8WxAt3QZ0LUmQN2009bsskkAAIBoRiCFoOYNVUXwHKm6bdDnBXnCP21psVmIVk0Y3EaSEyPzvbamsz3mSr0zf09YxwIAABBOBFIIWLVD3AGGdu2LRPt3TJHcrCT3PKfKqsBadmugOG1pTVmfzreaMKRNi4wz2mimT+dLqeW/VsrPIeiKCAAAEI0IpBB0x75IbTahtCX7obXd+7QxxtLNgZ3wf7+6VPaUV5vrWtKnLcChQaVFzjp031wxslIAACBeReZZMCJalX3f9dTkyMxIqZHNKO/7ePFe9/VTDiYb5enY/jnSIatmLa05a8vcXQ0BAADiCYEUgm59rlIieN7QwT0y3POatDGCzu3yx/pCqyzfWmmu98hNkcHd01t0nNFG9+npw2rmSukeffdH5koBAID4QyCFgHkuxhqpXftUekqCDOpWEwQVFttlk5+Zk488slEnD21jygThbcKQHMlMrfn6mPFziewq9UhTAgAAxAECKQTM5nHOHMmBlBrZu2aelJq/runyvtLKaplRu9hsRkqCjB2Q06Lji1aZqYkmyHQF1h8s3Bd8AgAAxAMCKTSv2URSZB9C3m3Qy5vc/ssVxWKtqnl/Ywdkm2AKvp16SFt36eQnS4qkzFrTnAMAACAecJaI5s2RivCMVNd2KdK1XbK5vmJrhck4NcThdMrHi2tanitXxgW+tc9KkuMGZJvr5TaHCaYAAADiBYEUAlblEYtE6oK8vrJSuvbVwo0NZ6UWbyqXX/dUmetD9kuXHrmprTbGaHXmoe3EdQRoeZ/NHth6XQAAANGKQAox27XPZUTtelKu7n0N+cgjG3UK2Si/dGufImMOyDLXd5dVm8YTAAAA8YBACgGr8gykkiP/ENLOfWm16139uKHclPDVVVBUJfNqm1HkZiXJ6L41wQGadvaImlboaur8PT73LwAAQKyJ/LNgRBybR2lfNGSktCHGIT1qslJ7y6tl9XZrvW0+WVpkSv9crb0TEyL/fUWKgzqnyZDatba0NHL2msAWPwYAAIhGBFJoXkYqCuZI1e3eV7e8T+f1TP+p2FzXJoQTBtNkIlBneWSl3pm/x+/FjwEAAKIVgRRiumufP4HUrFWlUlRRk2Y7/IAs040OgTm0V4b0yk0x11duq5Rlv1ayCwEAQEwjkEKzSvtSI3wdKZfc7CTpnVfThU9L+3aX2n03mTi4bVjGF+0sFotXVmrq/N1hHQ8AAEBLi46zYESUaCztq9u9b0FtG/TV2ytNBkXt3zFFBnRNC9v4ot3RB2VLXk6Se/HjDTvqz0UDAACIFQRSCJitOrran/sq73N16PNagPfgtiazguAkJVrkjOH7MnpTf9zDrgQAADGLQArNWpA3pbateLR0l8tKrRnv7DWl8pc3t8gXK2qaTGSkWOTYftlhHmH0O35QG8lOq/la+eaXEiksrlngGAAAINYQSCHmF+T1bDJRWVUzdk2q/fxbpbiay2lwuGRzTbkfgpeekuCeZ1btEHlvwV52JwAAiEkEUghYld17jaZoMGdtqdzzwTaxO3w/XlXtNI/rdmie3x/Sxj137rOfiqS4tiMiAABALImOs2BE7hypKGg2oetEPTqtwK9tdTvdHsFrm5Ek4wfmmOuaAfx4yb55aAAAALGCQArN6tqXGgWBlK4TVWp1SFNLxOrjup1uj+Y589B2klB7aPxv0V6xVhGcAgCA2EIghZhfkFcbS/jbjE+30+3RPJ3bJsuRB2aZ60Xl1fLF8pqmHgAAALGCQArNWpA3OQqaTRRXOtxNJZqi2+n2aL6zPRbofffHvVLt8PNDAAAAiAIRF0g988wz0rNnT0lLS5ORI0fK/PnzG93+ySeflAMPPFDS09Ole/fucsMNN0hlZc0Cq2jZjJRmo6Jh3aWctISAMlK6PZqvT36aHNKjZhHkbUVV8v1qMn0AACB2RNQZ49tvvy033nij3H333bJo0SIZMmSIjB8/XgoLC31u/9Zbb8ltt91mtv/ll1/k3//+t3mOO+64o9XHHo/rSEXD/Cg1um9WQBkp3R6hz0q9M3+POP39IAAAACJcRAVSTzzxhFx++eVy8cUXS//+/eX555+XjIwMefnll31uP3v2bBkzZoz88Y9/NFmscePGybnnnttkFguhyUhFQ1mf0rk6WakJ0tRo9XHdzjW3B813cI906ZOfaq6vKbDKks0V7FYAABATkiRC2Gw2Wbhwodx+++3u+xISEmTs2LEyZ84cnz8zevRoeeONN0zgNGLECFm/fr1MmzZNLrjgggZfx2q1motLcXHNJHiHw2EurU1fU/9KH47XDoaOU9dccmWkoiHDoAHfLRPyzTpRGiz5GrEryNLtdPtIf186Ptcl0p11aFt58JOa9vPvzN8tQ/dLl0jk2p/h+i5oadH2XYPIwHEDjhnE23eNI4AxREwgtXPnTqmurpb8/Hyv+/X2ypUrff6MZqL05w4//HCz8+12u1x55ZWNlvY9+OCDMnny5Hr379ixIyxzq/TDKioqMuPXwDHSVVVXia2q5uRdE1Klu6Nj3svAdiJ/HdtWnppVJGU2pzugcv2bkWKRa49sIwPbOaPiPTnFKZWlleYNWJrMtYXXwbki+dmJUlBSLQs3VshNb242JZRZqRYZ0SNNRvdMi4juj3aHXax2q+xM2CnJickSa6LtuwaRgeMGHDOIt++akpKS6AukgjFz5kx54IEH5NlnnzWNKdauXSvXX3+93HvvvXLXXXf5/BnNeOk8LM+MlDap6Nixo+Tk1Cwi2toHjjZs0NcP94HjDz3RdC0JlJ6aKFnto6cM7pj2WTJmYHv5bnWZ/LCmVEoqqiU7PVHG9M2SIw7IlJSkyN//LiYTpcFIu6yoaPgxvFeFfPpTTfZ3+Tab+VeHPW+TVV6ZV2IygYf1zgzrGG3VNnHanJLbMVdSk2rKEWNJtH3XIDJw3IBjBvH2XZOWlhZ9gVRubq4kJiZKQUFNCZCL3u7UqZPPn9FgScv4LrvsMnN70KBBUlZWJldccYX87W9/8/lBpKammktdum24Pjg9cML5+oHQDtbVtYFUtHTt85SanChjB+SYS7TTfe+6RLI5a0tlWm0Q5clVlVhmdZiyy3tO6yyj+oQvMHfty2j5XQxGrL8/tAyOG3DMIJ6+axICeP2I+a9pSkqKDBs2TGbMmOEVnertUaNG+fyZ8vLyem9WgzEVDXNHopHVvq9uNCVKmk0gfGx2hzw6zfuPI3W5flN1O90eAAAgGkRMRkppyd2FF14ow4cPN80jdI0ozTBpFz81ceJE6dq1q5nnpE4++WTT6e/ggw92l/ZplkrvdwVUaMFAKjli4nBEqFmrSqXU2nRwpMGUbqfbx0K2EAAAxL6ICqTOOecc0/Rh0qRJsn37dhk6dKhMnz7d3YBi8+bNXhmoO++806QB9d+tW7eaukoNou6///4wvovYZnVNkCIjBT/MXlNq5kL5kyDW7XR7AikAABANIiqQUtdcc425NNRcwlNSUpJZjFcvaP2MVLQsyIvwKa7Udqb+bavb6fYAAADRgNosBKTSXu2+nkwghSbkpCWYTJM/dDvdHgAAIBpw1oKAeDYDSI2iduEIj9F9swLKSOn2AAAA0YAzYQSk0nOOFBkpNOHIA7MkKzWhySWD9XHdTrcHAACIBgRSCL5rH4EUmqCLHOtiu6qpYEq3i6ZFkQEAQHzjrAUBsVbtmyNFIAV/6CK7uthuZmrN103dOVMJFgn7YrwAAABR37UPkY2ufQiGBklTrsow60Rpi/PiimpZU2iVCptTHE6R/TqksGMBAEBUISOFoOdIJSdy+MB/Wrana0RNOrWLPHZudzl/VAf3Y18sL2ZXAgCAqMKZMAJCRgqh8rv+2aasT325vESqNTUFAAAQJQikEBCrxzpSzJFCc7TPSpKRvTPN9Z2ldlm0qZwdCgAAogaBFAJipf05Qmj8wBz39c+XUd4HAACiB4EUAlJJ+3OE0Ij9M6VtRqK5rk0oisr3ZTwBAAAiGYEUmrGOFIcPmicp0SJj+2eb63poff1LCbsUAABEBc6EERCbxxypVBbkRQiMG7SvvI/ufQAAIFoQSKEZ7c/rrKwKBKFnbqoc2DnVXF9XaJW1BZXsRwAAEPEIpBAQ2p+jJYwf2MZ9naYTAAAgGhBIISDWKs/25xw+CI1j+mW52+nrPCmbx1w8AACASMSZMJrRbILSPoRGZmqiHHFAlrleUumQOWvL2LUAACCiEUgh6DlSBFIIpXGsKQUAAKIIgRQC4llyRSCFUBqyX7rkt0ky1xduLJfC4ip2MAAAiFgEUghIZW3786REkQQLpX0I4ZeRxSLja7NSThH5agVrSgEAgMhFIIWg5kixhhRawnEDcsTisaaU06khFQAAQOQhkEJArLVzpFhDCi0hv02yDO2Rbq7/trdKlv3KmlIAACAyEUghIGSk0NKOH+S5plQROxwAAEQkAikEpLJ2HalkWp+jhYzukymZqTVfTbNWl0q5jTWlAABA5CGQQpAZKQ4dtIzU5AQ5pl92zfFW5ZRvV9J0AgAARB7OhuG3aodTqqprJv8zRwot6fhBNd371OfLitnZAAAg4hBIIcg1pNhxaDl981OlV26Kuf7zb5WyeZeN3Q0AACIKgRT8Zq1dQ0qlUNqHFmSxWGScR1bqy+VkpQAAQGQhkILfKmtbn6uURBbjRcv6Xf9sSaz9hvpyRbEpLQUAAIgUBFIIMiNFIIWW1TYjSUb1zjTXd5dVy48bytjlAAAgYhBIIbiMFIEUWoFneR9NJwAAQCQhkILfyEihtR3aK1PaZyaa63PXlcnecjsfAgAAiAgEUvAbc6TQ2hITLHLcgJqsVLVDZMbPrCkFAAAiA4EU/EZGCpFQ3ud00nQCAACEH4EU/MYcKYRD9/Yp0r9Lmrm+cadN1hRY+SAAAEDYEUjBb2SkEC7jPbJS05exphQAAAg/Ain4jYwUwuWog7IlNbmm5f43v5SI1aODJAAAQDgQSMFvZKQQLhkpCXLkAVnmepnVIbPXsqYUAAAILwIpBJWRSk5kQV60rvGD2rivT19WxO4HAABhRSAFv5GRQjgN6pYmXdomm+tLNlVIQVEVHwgAAAgbAin4jTlSCCeLxSLjBtY0ndAG6F+uoOkEAAAIHwIpBJeRorQPYXDcwGxxFZV+vrxYHKwpBQAAwoRACn7z7JSWksQcKbS+jtnJMqxXhrleUGSXpZsr+BgAAEBYEEjBb8yRQiQYX1vep75YTnkfAAAIDwIp+I2MFCLBqD6Zkp1W89X13epSKbPuKzkFAABoLQRS8Ful5xwpSvsQJilJCXJs/2xz3WZ3yje/lPJZAACAVkcgBb+RkUKkOH7gvjWlPl/OmlIAAKD1EUghuIwUXfsQRr3zU6V3Xqq5vmqbVTbutPJ5AACAVkUgBb+RkUIkGT/Io+nEMppOAACA1kUghYAzUokJeqH9OcLr2H7ZklybGf3q5xKxV+syvQAAAK2DQAoBZ6Qo60MkyElPNB381N7yapm/vizcQwIAAHGEQAoBZ6SSk9hpiLzyvs9ZUwoAALQiAikEnpGi9TkixCE9MiQ3qyayn7euTHaX2sM9JAAAECcIpOC3yqrajBQd+xAhdK7ecQNr1pRyOEVm/FwS7iEBAIA4QZEW/Ga112SkkhPZaYgc4wbmyH/n7jHX35izS+atKzXzp0b3zZIjD8wyC/gCAACEGoEU/OJ0Ot2BFKV9iCSbd9lEm0hqRqrC5pSffq0Ui0Xk+zVl8uyMHXLLhHwZ1Scr3MMEAAAxhj/Vwi+uIEqlkJFChJiztlTu+WCbCaI8OWtvl1kd5nHdDgAAIJQIpBB4IEWzCUQAm90hj04raHQbV3yl2+n2AAAAoUIgBb9YaxtNqGQCKUSAWatKpdTqcAdLDdHHdTvdHgAAIFQIpBBEaZ+FvYawm72m1MyF8odup9sDAACECoEUAmp9rliQF5GguNLhngvVFN1OtwcAAIiIrn1bt26VWbNmSWFhoZxxxhnSrVs3qa6ulqKiImnTpo0kJtKVIFYwRwqRJictwWSa/AmmdDvdHgAAIFQSgm2FfeONN0qvXr3kvPPOM9dXr15tHistLZWePXvKU089FbJBIsIyUsTHiAC6TlQgGSndHgAAIKyB1KOPPir//Oc/5eabb5Yvv/zSBFYumok6/fTT5b333gvZIBF+ZKQQaXSx3azUBGlqmpQ+rtvp9gAAAGENpF566SWZOHGiPPDAAzJ06NB6jw8ePNidoUIsZqRoNoHwS0lKMIvtqsaOSP0zj26n2wMAAIRKUGcWW7ZskdGjRzf4eGZmphQXFzdnXIjojFRYhwK4jeqTJfec1lkyU2u+ylxd/DwDq/ycJBnZO5O9BgAAQiqoU+K8vDwTTDVk4cKFst9++zVnXIjgjBTtzxFpwdSUqzLMOlHa4ly782WnJci6QqtsL7JLQbFdvl9dKkcemB3uoQIAgHgPpHQO1PPPPy8XXXSRmROlLLV/Cv7iiy/k1VdflVtvvTW0I0VYMUcKkUzL9sYOyDEXlwUbyuSOd38z11//YbeM6ZsliQmUpQIAgDCW9k2ePFk6d+5s5kfpXCkNoh5++GE5/PDD5YQTTjBzpO64444QDRGRgK59iDbDemZI/y5p5vqmXTaTsQIAAAhrIKVZqLlz55qsk64llZaWJt9++63s3btX7r77bvnuu+8kIyMjZINEZGWkkpP4qz4in/6B58LDO7hvv/7DLql2+NkvHQAAoAlBtw1IT0+XO++801wQZ3OkCKQQJYbuly6Du6fLT1sq5Nc9VfLNLyVe5X8AAACtmpE69thjZcaMGQ0+/s0335htEKMZKRbkRRRlpSaOae++/cbs3WSlAABA+AKpmTNnSkFBQYOPFxYWmlI/xA5rlWf7c0r7ED0Gd8+Qg/dLN9d/21slX61gaQYAANB8Qa9Q6erS58vatWslO5tWw7Gk0k77c0SviWP2zZV6Y85usVczVwoAALTSHKnXXnvNXFzuu+8+eemll+ptpw0nfvrpJ5kwYUIzh4bIzUiFdShAwAZ0S5fhPTNkwcZyKSiyyxfLi2XCkJqlGwAAAILh9ylxeXm57Nixw327pKREEhIS6mWpMjMz5corr5RJkyYFNSBEfkYqOZHSPkSfC8Z0MIGUenPObhk7INusPwUAANCigdSf//xnc1G9evWSf/7zn3LKKacE9aKIPsyRQrTr1yVNRu6fIfPWl8uOErtMX1YspxzcNtzDAgAAUSqoP8du2LChxYKoZ555Rnr27GnWpho5cqTMnz+/0e21lPDqq682CwSnpqbKAQccINOmTWuRscUzq2dGitI+RHFWyuW/c3eLzaMbJQAAQCCafUqsJX5FRUXicNQ/Idlvv/0Ceq63335bbrzxRnn++edNEPXkk0/K+PHjZdWqVZKXl1dve5vNJscdd5x57N1335WuXbvKpk2bpG1b/srcohkpSvsQpQ7olCaj+mTKnLVlsqu0Wj5dWiynDeP7AgAAtGIg9dxzz8kTTzwh69evb3Cb6up9WQx/6PNdfvnlcvHFF5vbGlB9+umn8vLLL8ttt91Wb3u9f/fu3TJ79mxJTk4292k2Cy03RyrBIpLItBJEeQc/DaTU2/N2ywmDcyQtmYMaAAC0QiClAY6W02m26JJLLpG//e1vcsMNN5hyvFdffVXy8/PluuuuC+g5Nbu0cOFCuf322933aTOLsWPHypw5c3z+zEcffSSjRo0yY/nwww+lY8eO8sc//lH++te/SmKi71VjrVarubgUF9esKaMZNV9ZtZamr+l0OsPy2oGorKoJpNJqV+PVMesF4eHa/3wGgdu/Y4occUCmfLe6THaXVcsnS/bKGcPbufdnuL4LWlq0fNcgsnDcgGMG8fZd4whgDEEFUk899ZQJoj777DPZtWuXCaROPPFEOfbYY+XWW2+V4cOHm/sDsXPnTpPB0iDMk95euXKlz5/RbNjXX38t5513npkXpetXXXXVVVJVVSV33323z5958MEHZfLkyfXu146ElZWVEo4PS0sj9eCp2wUxkpRXVpl/9Q/31iKrWJIsYkuwhXtYccspTqksrRSx6P/oohio0wekyfery0T/FDBl7h45qnuiJCU6xGq3ys6EnZKcWJPhjiXR8l2DyMJxA44ZxNt3TUlJScsGUuvWrTNZIOUqqdOMkmrTpo1cdtll8uyzz8pNN90kLb3TdX7Uiy++aDJQw4YNk61bt8qjjz7aYCClGS+dh+WZkerevbvJZuXk5Ehr0/egbeP19cN94DTGXpt8Sk9JktQ2qZKRkiEpiSnhHlbcMpkop0hWu6xGF8eGb/3bixx1kFVmriyV4kqHfL2pWk4dlilOm1NyO+ZKalJqzO26aPmuQWThuAHHDOLtuyYtLa1lAykNlux2u7muwUdGRoZs2bLF/Xh2drZs3749oOfMzc01wVBBQYHX/Xq7U6dOPn9GO/VpIOdZxtevXz/z2hrYpaTUP9HXzn56qUs/tHB9cHrghPP1/VFZ290sNTnBjNd1QfjwOTTP+aM7yKxVpeJwikz9cY+MH5wRFb+LzRHr7w8tg+MGHDOIp++ahABeP6iRDhw4UJYuXeq+fdhhh5nmE5oN0oDqhRdeMG3IA6FBj2aUZsyY4RWd6m2dB+XLmDFjTDmfZy3j6tWrTYDlK4hC87v2pbKAKWLEfh1S5Jh+2eZ6cYVDPl7sfyofAAAgqEDq/PPPl+XLl7ubNuico19++cW0O9euedqu/L777gv4ebXk7qWXXpLXXnvNPJ8uAFxWVubu4jdx4kSvZhT6uHbtu/76600ApR3+HnjgAXfZIUJXRubq2pea5LuJBxCNzh/d3nSiVO8vKJZya/gnuQIAgOgQVGmfBjau4MaVGVqxYoV8/PHHpsxu3LhxAWek1DnnnGOaPkyaNMmU5w0dOlSmT5/ubkCxefNmr3Sbzm36/PPPTcfAwYMHm3WkNKjSrn0Inapq7WZWc52MFGJJ13YpMnZAtnyxvETKrA75dGmljO4R7lEBAIC4WJDXZf/99zdBjMuGDRukV69eAT/PNddcYy6+zJw5s959WvY3d+7cgF8H/rPWZqMU6+0g1pw3qoPM+LlEqh0iny6pkFuPq5K87NhrNgEAAEIr5LO5fvrpJ7OW04EHHhjqp0aYVNbOj1IpzJFCjOncNlnGDazp2Flhc8orP2wO95AAAECsBVJavqfZohNOOMEESx988IH7sUWLFsmECRPk4IMPlvfff9/Mo0IsZqSYI4XY88fD2ovrbwSvzd4se8pYIw0AAISotE/L53TBXc9Fa99++2154oknTCt0nZekbc9vueUWU+KnnfMQexmpmjlS+wIrIBbkt0mWcYOyZNrSUim3VcuL362Xvx5/ULiHBQAAYiEj9fe//90sUPXZZ59JaWmpLFu2zLQr18YQrkVuN27cKA899BBBVAxnpHQdKSAWnT2ijUdWaqPsLK3pSgoAAOCL32fF8+bNM23Fx48fbxbgHTBggMlGlZSUyHXXXSePPPKIWagX8ZCRAmJPbnaSjB1Ys5q5ZqVe+HZduIcEAAAimN9nxXv37q3X0tx1W0v+ECdzpFhHCjHs94eku/9Y8J85m6SweF8pMwAAQFCBlC7KqmtEeXLd1pI/xC4rXfsQJ9pnJcq5I7qZ61a7Q54jKwUAAEKxjtS0adPMQrku5eXlYrFYZOrUqbJkyRKvbfV+XSgX0Y91pBBPLj+yh0z58VdT0vrmvM3ypyN7S6c2/LEIAAA0I5B66623zKWuF154od59BFKxgzlSiCe5Waly4aie8sKs9WKzO+TZmWvl778fGO5hAQCAaA2kNmzY0LIjQcRiHSnEmz8d1VvemLtJymzVMmX+FnO7a9v0cA8LAABEYyDVo0ePlh0JoiIjlULXPsSB9pkpctGYnvLMN+vEVu2QZ75ZKw+cNijcwwIAABGEXtYIbB0pAinEicuP2F+yUmv+1vTOj1tky+7ycA8JAABE6xwpxCfPjFRasnfnRiBWtc1IkUsO7yX/mrFG7A6n3DR1ibTPSJW95Tbz2LgB+TJhUGd+JwAAiFMEUmgSGSnEq0sP7yUvzVonFVUOmb9hj1gsuhSESIJFZPqK7XLPxyvkibOGytj++eEeKgAAaGWU9iGgdaRSkzlkED/mb9htgigXDaKUo/bfkgq7XP76Avny54IwjRAAAIQLZ8VoUiVzpBCHKquqTTmfpZFtTDzlFLl56hKzPQAAiB8hDaRsNpuUlZWF8ikRYRmptCTmSCE+TFu2TYor7DXBUiP08aIKu3y2fFsrjQwAAERtIDVlyhS54YYbvO6bPHmyZGVlSdu2beW0006T0tLSUI0RYVZpp/054s8XKwrMXCh/6HafL6e8DwCAeBJUIPX44497ZZ5mz55tAqnx48ebAGv69Oly//33h3KcCCOrR8lSGnOkECe0O59rLlRTdLu9FbaWHhIAAIj2rn3r1q2TCy+80H37rbfekk6dOskHH3wgSUlJ4nA45L333pMHH3wwlGNFBGSkWEcK8UJbnGumyZ9gSrdrm57SGsMCAADRnJGyWq2Slpbmvv3FF1/ICSecYIIo1b9/f/n1119DN0pEUEaKOVKID7pOVCAZqfEDaYEOAEA8CSqQ6tWrl3z11Vfm+oIFC2Tt2rVy/PHHux8vKCgw86UQWxkpXUMnOdHPSSNAlNPFdnPSkxrt2qf08TbpSXLCwM6tNDIAABC1gdSf/vQneeedd2Tw4MEybtw46datm5x00knux3/44QcZMGBAKMeJCMhIaVmfRaMpIA5o9lUX29VIqaGj3txvEXn8rKFkawEAiDNBBVLXXnutvPDCC9K7d2/5/e9/b0r70tPTzWO7d++W7du3y3nnnRfqsSJMrLUZqVRanyPOjO2fLy9eMNxkpnzR+1+6YLjZDgAAxJegmk2oyy+/3Fzqat++vSn3Q+xlpOjYh3h0XP98mXfHWLOu1M1Tl5r5UFmpiXLvqQNNOR/zBgEAiE8hW5DX6XTK119/LZ999pmUlJSE6mkRQXOkyEghXmmwdPoh3aRru5rMe1Jigpx2cDeCKAAA4lhQgdTf/vY3OeaYY7yCKJ0rddxxx8mJJ54ogwYNMi3SEXtzpIB4lp9d0610b3mVVHp0swQAAPEnqDNjXSNqxIgR7tvvvvuuzJgxQ+677z755JNPpLq6Wu65555QjhMRkJGihAnxLj9n37IPO0qsYR0LAACIwjlSW7dulT59+rhvv//++2btqNtvv93c/vOf/yzPPfdc6EaJsLFXO6S6djEdMlKId3k5qe7rBcWV0r19RljHAwAAoiwjpQvv6qK8rrI+zUZ5riOVn58vO3fuDN0oEfaOfYqMFOKdZ0aqoJiMFAAA8SyoQGrgwIHyxhtvyJ49e+SVV16RXbt2mblRLps2bZLc3NxQjhNh4jkPhIwU4l1e9r6MVGFJZVjHAgAAorC0b9KkSXLyySe7g6UxY8Z4NZ/49NNP5dBDDw3dKBE2ZKSAfchIAQCAZgVS2p1v0aJF8uWXX0rbtm3lnHPOcT+mWaojjzzSLNSL6EdGCtgn32OOVGExGSkAAOJZ0AvyanMJvdTVrl07+cc//tHccSECM1KpyYlhHQsQbnmec6Qo7QMAIK4FHUipuXPnyjfffCOFhYVy1VVXSd++faW8vFxWrlwpBxxwgGRlZYVupAgLMlLAPtmpSZKWnCCVVQ6aTQAAEOeCajZhs9nk9NNPN3OjdHHef/3rX7Jly5aaJ0xIMIvz/vOf/wz1WBEGzJEC9rFYLO55UpT2AQAQ34IKpO666y6z8K6uFbVq1SrTAt0lLS1NzjrrLPnwww9DOU6ECRkpwFt+dk0gVVxplwrbvq6WAAAgvgQVSP33v/81i+5eccUV0r59+3qP9+vXT9avXx+K8SHMyEgBDS/KSwt0AADiV1CBlM6JGjRoUIOPJyYmmrlSiH5kpABvtEAHAABBB1Ldu3c3DSUa8sMPP0ifPn3YwzGAjBTQ8KK8BbRABwAgbgUVSP3xj3+UF154QebMmeM1CVu99NJL8s4778jEiRNDN0qEjbVq3xyQ1KSgDhcgZjNShSXWsI4FAABEWftz7dSnrc914V2dD6VB1A033CC7d++WX3/9VSZMmGBuI9bWkSKQArzmSJGRAgAgbgV1ZpySkiLTp0+XV155Rfbff3856KCDxGq1yuDBg+XVV1+Vjz/+2MyTQmzNkUpL4jMFvOdIVbJDAACIU0EvyKtZqPPPP99cELvISAHeaDYBAACCzkhpCd9PP/3U4OPLli2TPXv2sIdjAM0mAG9ZqUmSkVKTnS0oISMFAEC8CiqQ0vlPuoZUQ/70pz/JzTff3JxxIULQ/hxoOCu1o5hmEwAAxKugAqmvv/5aTjnllAYfP/nkk+Wrr75qzrgQIaxV+5pNpCUzRwrwbIFeYrVLmdXOTgEAIA4FFUjt2LFDcnNzG3y8Q4cOZtFeRL9KO+3PgbpogQ4AAIIKpDp37iyLFy9u8PGFCxdKx44d2bsxgIwUUF++Rwt0OvcBABCfggqkTj31VPn3v/8tH330Ub3HPvzwQ9MW/bTTTgvF+BBmZKSA+vKyaYEOAEC8C6r9+T333GPmQGmwNGTIEBk4cKC5f/ny5bJ06VKzSO/kyZNDPVZEREaK+SCA56K8O0poOAEAQDwKKiPVpk0bmTt3rtx5551SVVUl7777rrno9bvuukvmzZsnbdu2Df1oEdaMVEpiUIcLEHNYlBcAAAS9IG9mZqbJOpF5io+MVEpSgiQkWET2JaiAuMWivAAAIKgUg91ul+Li4gYf18d0G8RORio1iWwUULf9uaLZBAAA8Smos+PrrrtORo8e3eDjY8aMkZtuuqk540KEZaRYQwrYJzM1SbJSaxL6hcyRAgAgLgUVSE2fPl3OPPPMBh/Xx6ZNm9accSFCWMlIAY02nCgsrmQPAQAQh4IKpH777Tfp2rVrg4936dJFtm7d2pxxIcIyUpT2Ad7ya1ugl9mqpdRKKTMAAPEmqECqQ4cOsmrVqgYf/+WXXyQnJ6c540KEzZGitA/wxqK8AADEt6ACqeOPP15eeOEFWbx4cb3HFi1aJC+++KKccMIJoRgfwqja4ZSqaqe5TkYK8EYLdAAA4ltQ7c/vvfdeM09qxIgRcsopp8iAAQPcC/J+/PHHkpeXZ7ZBdLPZ6y7GC8Clo0fnvsJiFuUFACDeBBVI6RyoBQsWyG233SYffvihfPDBB+Z+Lec777zz5IEHHjDbILpVVu1bjJeMFNBwRqqwhIYTAADEm6AX5O3cubO89tpr4nQ6ZceOHea+jh07isViCeX4EEZWMlJAg1iUFwCA+BZ0IOWigZOW8iH2kJECGkazCQAA4ltQgdTf//53vwKsu+66K5inR4QgIwU0LK+2/blijhQAAPEnqEDqnnvuaTSA0nI/AqnoR0YKaFh6SqJkpyVJSaVdCpgjBQBA3Amq/bnD4ah3sdvtsm7dOrnhhhtk+PDhUlhYGPrRolWRkQL8myelGSn9AxIAAIgfCSF7ooQE6dWrlzz22GPSt29fufbaa0P11AgTMlKAf/OkKqqqpcRqZ3cBABBHQhZIeTryyCNl2rRpLfHUCFNGKpV1pIB68r3mSdECHQCAeNIigZSuMaUZKkQ3MlJA4/I81pIqYFFeAADiSlDNJv7zn//4vH/v3r0ya9Ysef/99+Wyyy5r7tgQZsyRAhqXl11T2qcKyEgBABBXggqkLrroogYfy83Nldtuu00mTZrUnHEhApCRAvxflLewxMruAgAgjgQVSG3YsKHefdruvF27dpKdnR2KcSECMEcKaByL8gIAEL+CCqR69OgR+pEgojNSaUnMeQMazUgxRwoAgLgSVCBV18qVK2Xq1Kmybds2OfDAA+Xiiy+WnJycUDw1woiMFNC4jsyRAgAgbvkdSD399NPyr3/9S2bPnm3mQbl8/PHHctZZZ4nNZnPf99RTT8ncuXO9tkP0sdrJSAGNSUtOlDbpyVJUUSUFJbQ/BwAgnvhdr/XRRx9J7969vYIju91uuvMlJibKK6+8IsuWLZOHHnpINm3aJPfff39LjRmtxFrFOlKAv/OktLTP6XSywwAAiBN+B1I///yzHHbYYV73ffPNN7Jjxw654YYb5MILL5QBAwbIrbfeKmeffTYL8sZaRiqZOVJAY/OktBS2uMLOTgIAIE74fXa8a9cu6d69u9d9M2bMMN36TjvtNK/7x4wZI5s3bw56UM8884z07NlT0tLSZOTIkTJ//ny/fm7KlClmPKeeemrQr419Kj0zUkmJ7BrAh7xsj0V5Ke8DACBu+B1I5efny/bt273u++677yQjI0OGDBnidX9KSoq5BOPtt9+WG2+8Ue6++25ZtGiRee7x48dLYWFhoz+3ceNGufnmm+WII44I6nVRHxkpoGl5taV9ikV5AQCIH34HUsOHD5fXXntNSkpKzO0VK1aYTJEGOUlJSfW6+HXr1i2oAT3xxBNy+eWXm85//fv3l+eff94Eay+//HKDP1NdXS3nnXeeTJ48Wfbff/+gXhf1kZECmpbv1bmPRXkBAIgXfnft0wzRoYceKn379jVzoRYuXGjK6G6//fZ6237wwQdy7LHHBjwY7fynz+v5nAkJCTJ27FiZM2dOgz/397//XfLy8uTSSy81WbLGWK1Wc3EpLi42/zocDnNpbfqaOkE9HK8dyDpSKYn79pGO13VBePAZtNw+DfS7wLsFekVE/i5H+ncNIhfHDThmEG/fNY4AxuB3IDVo0CD5+uuvTTe+9evXm8YTWko3bNgwr+1mzpxpMkjaEj1QO3fuNNklLSP0pLc1y+XL999/L//+979lyZIlfr3Ggw8+aDJXdWnTjMrKyrB8WEVFRebg0aAxkpSU79sfRbt3SWmCRaqqq8RaZBVLkkVsCfta3qN1OcUplaWVIhb9n4XdHwJ2h12sdqvsTNgpyYnJfv9cir3cfX1jwZ4my5DDJZK/axC5OG7AMYN4+64pqa2+C/mCvKNHj5ZPP/200W2OPvpo0wa9td7oBRdcIC+99JLfa1ZptkvnYHlmpLSJRseOHcOyiLAeOJrZ09cP94FTl9OyxvybnGiRzp1qgls90dzq2CoZKRmSkhjcPDiE4LPRbKBTJKtdljl+0Hy2aps4bU7J7ZgrqUn7skxNOSg5W0RWmeslVQkmOx6JIvm7BpGL4wYcM4i375q0tH1NpEIaSLU0DYZ0TaqCggKv+/V2p06d6m2/bt0602Ti5JNPrpeO03lbq1atMmtfeUpNTTWXuvRDC9cHpwdOOF+/IZV2h7tjn2ts+q+O13VB+PA5tMz+DPR3Ma/Nvi/cwhJrxP0eR8N3DSIbxw04ZhBP3zUJAbx+RP3XVDv9aamgtlX3DIz09qhRo+ptf9BBB5nsl5b1uS6nnHKKHHPMMeZ63XbtCK5rH2tIAQ3TPzS0y6gpBaTZBAAA8SOiMlJKy+50cV/tEjhixAh58sknpayszHTxUxMnTpSuXbuauU6aehs4cKDXz7dt29b8W/d+BN+1jzWkgKYX5d1TXiU7Sqym7JJsLQAAsS/iAqlzzjnHNH6YNGmSWbdq6NChMn36dHcDCl3oN9wpv3hhre3al5rE/gYak5eTJiu3l4it2iF7y6ukXSbzBwEAiHURF0ipa665xlx80a6AjXn11VdbaFTxxz1HKjkx3EMBomctqZJKAikAAOIAqQb4pOVJNnezCQ4ToDF5OSzKCwBAvOEMGT5Za4MoRbMJoOk5Ui4Fxa2/Hh0AAGh9BFLwyVrbaELRbAJoXF72vkBKG04AAIDYRyCFRlufKzJSQOPyvUr7yEgBABAPCKTQaOtzRUYKaBylfQAAxB8CKfhERgrwX24WzSYAAIg3BFLwiYwU4L+UpATpULt2FHOkAACIDwRS8ImMFBD4oryqsKRSHA4nuw8AgBhHIAWfyEgBwTWcqKp2yp5yG7sPAIAYRyAFn8hIAYHJ92iBXlBMC3QAAGIdgRR8IiMFBCbPswV6CS3QAQCIdQRSaDIjlZrMYQL4O0dK7SAjBQBAzOMMGU1mpNKSEtlLQBPys1mUFwCAeEIgBZ/ISAHNWJSX0j4AAGIegRR8Yo4U0IxAitI+AABiHoEUfCIjBQQmNytFLJaa64XFNJsAACDWEUjBJ6udOVJAIJISE6RDZs08qcIS2p8DABDrCKTgU2UVXfuAYBfl1UDK4XCyAwEAiGEEUvCJjBQQ/DypaodTdpXZ2IUAAMQwAin4REYKCD4jpQqYJwUAQEwjkELTGalk1pEC/NExe1/nvkJaoAMAENMIpOCT1XOOVBKHCRBoRqqQFugAAMQ0zpDhExkpIHD5Hhkp1pICACC2EUih6TlSZKSAwBflpbQPAICYRiCFRjNSiQkWSU7kMAECL+1jUV4AAGIZZ8hoNCNFNgrwX4esVEmw1FyntA8AgNhGIIVGM1IEUoD/NIObm+ValJeMFAAAsYxACo1mpGh9DgQ3T2pHidUszAsAAGITgRR8IiMFNG+elMZQu0qt7EYAAGIUgRR8IiMFNH9RXuZJAQAQuwikUI/T6SQjBYSgc18BnfsAAIhZBFKop6raKc7aqR2pyYnsISDItaQKSyjtAwAgVhFIoZ5KO4vxAsEiIwUAQHwgkEI91qqa1ueKrn1AYPI85kjRAh0AgNhFIIUGG00o1pECApPnNUeK0j4AAGIVgRQabH2uyEgBgemQmWoW5lU0mwAAIHYRSKEeMlJA8DSI6phVk5Wi2QQAALGLQAr1kJECQtNwYmepVezV+zK8AAAgdhBIoR4rc6SAZsmrbYGuywjsLLWxNwEAiEEEUqiHjBTQPHnZLMoLAECsI5BCPcyRAkK3KC8NJwAAiE0EUmg0I0X7c6B5i/LScAIAgNhEIIVGM1K0PweCnyOlCosr2YUAAMQgAik0npFK5hABApWf7Vnax6K8AADEIs6S0XhGKimRPQQEKM+jtK+ghIwUAACxiEAK9ZCRApqnfUaKJCVYzHUyUgAAxCYCKdRjtZORApr1xZpgcbdA30FGCgCAmEQghXoqq5gjBYSq4YQuyFtVve93CgAAxAYCKTSakUpljhTQ7BboO0poOAEAQKwhkEKjGak0uvYBQcnz6txHwwkAAGINgRSaWJCXrn1AczNSNJwAACD2EEih0fbnrCMFNH9RXhpOAAAQewik0GhGKi2ZjBQQjHyPQIqMFAAAsYdACo1npJI4RIDml/YxRwoAgFjDWTIazEhZLCIpiRwiQLObTdC1DwCAmMNZMuqx1makNBtl0WgKQMDaZSRLcmLN708hGSkAAGIOgRQazEjRsQ8Inv4RwpWVKiQjBQBAzCGQQoNzpFhDCgjNPKndZTavha4BAED0I5BCPWSkgNB37ttBVgoAgJhCIIV6yEgBoZGXzaK8AADEKgIp1ENGCgj9orw0nAAAILYQSMGLvdoh1Q6nuc4cKSB0pX00nAAAILYQSMFLZW3HPkXXPqB5WJQXAIDYRSAFn2tIKTJSQOgyUgXFVnYnAAAxhEAKXshIAS3TbKKwpJJdCwBADCGQQoMZqdRkDg+gOdqkJ0tKUs3vUUExgRQAALGEM2V4qaxijhQQKhaLxT1PimYTAADEFgIpeLHamSMFhFJ+ds08qb3lVe412gAAQPQjkIIXMlJAyzWc2FFCwwkAAGIFgRS8kJECQqujR8MJ5kkBABA7CKTghYwUEFq0QAcAIDYRSKHBjFRqbbcxAKFZlJcW6AAAxA7OlOHF6tG1Ly05kb0DNBMZKQAAYhOBFLyQkQJacFFe1pICACBmEEihwTlSZKSA5svz6NpXUMKivAAAxAoCKXghIwWEVk5akqQl13zVFhTT/hwAgFhBIAUvVjsZKSCULBaLe54UpX0AAMSOiAyknnnmGenZs6ekpaXJyJEjZf78+Q1u+9JLL8kRRxwh7dq1M5exY8c2uj0aV1nl0bWv9q/oAJonP7smkCqutEuFbd/vGAAAiF4Rd6b89ttvy4033ih33323LFq0SIYMGSLjx4+XwsJCn9vPnDlTzj33XPnmm29kzpw50r17dxk3bpxs3bq11ccecxmpJLr2AaHQkRboAADEnIgLpJ544gm5/PLL5eKLL5b+/fvL888/LxkZGfLyyy/73P7NN9+Uq666SoYOHSoHHXSQ/N///Z84HA6ZMWNGq489FpCRAlouI6WYJwUAQGxIkghis9lk4cKFcvvtt7vvS0hIMOV6mm3yR3l5uVRVVUn79u19Pm61Ws3Fpbi42PyrwZdeWpu+ptPpDMtrNxVIpSRa6o3LNV7XBeHBZ9By+7QlvgvyslPc17cXVfBdg6gRaf+NQuTjmEG0HzeBjCGiAqmdO3dKdXW15Ofne92vt1euXOnXc/z1r3+VLl26mODLlwcffFAmT55c7/4dO3ZIZWVlWD6soqIic/Bo0BhuRaUV7usle3dLob3U6/Gq6iqxFlnFkmQRW4ItDCOEcopTKksrRSz6Pws7JQTsDrtY7VbZmbBTkhOTQ7pP02TfH2/W/7ZTCju1ftlspH3XIDpw3IBjBvH2XVNSUhKdgVRzPfTQQzJlyhQzb0obVfii2S6dg+WZkdJ5VR07dpScnBwJx4GjXb309cN94BiJm91Xu3XOlzbp3ieUeqK51bFVMlIyJCVx31/Z0bpMNtApktUuyxw/aD5btU2cNqfkdsyV1KR9i+iGQt8SDZw2muvlzmTJy8sTiffvGkQFjhtwzCDevmvSGoghIj6Qys3NlcTERCkoKPC6X2936tSp0Z997LHHTCD11VdfyeDBgxvcLjU11Vzq0g8tXB+cHjjhfP2G1pFKT0mqNya9reN1XRA+fA4tsz9b4ncxv026+3phiZXvGkSVSPpvFKIDxwyi+bgJ5PUj6lsxJSVFhg0b5tUowtU4YtSoUQ3+3COPPCL33nuvTJ8+XYYPH95Ko439rn2pSRF1eABRK9+jax/NJgAAiA0RlZFSWnZ34YUXmoBoxIgR8uSTT0pZWZnp4qcmTpwoXbt2NXOd1MMPPyyTJk2St956y6w9tX37dnN/VlaWuSAwlVU1gVRKUk3mCUDzZaUmSUZKopTbqqWgpPXnYgIAgDgIpM455xzT+EGDIw2KtK25ZppcDSg2b97slXJ77rnnTLe/M8880+t5dB2qe+65p9XHH+1cpX1ko4DQ0T9K5OekyYadZbKjeF/jCQAAEL0iLpBS11xzjbn4oo0kPG3cWDOBG6Fhrc1IpSWzGC8QSnnZqSaQKrHapcxql8zUiPz6BQAAfmISDLyQkQJaRl5OmlfDCQAAEN0IpOBzjhQZKSC08rM9G04wTwoAgGhHIAUvZKSAlqFzpFwIpAAAiH4EUnCrdjilqtpprpORAkIrz6MF+g5K+wAAiHoEUvC5GC9d+4DQIiMFAEBsIZBCvY59iowUEPqufS4sygsAQPQjkIJbJRkpoFW69jFHCgCA6EcgBTcyUkDLyUpNMhfFHCkAAKIfgRTcyEgBrdNwgowUAADRj0AKbmSkgJaVn11T3ldmq5ZSq53dDQBAFCOQgltlFV37gNZqgU5WCgCA6EYgBTerfV/XvtTkRPYMEGK0QAcAIHYQSMGNjBTQei3QaTgBAEB0I5CC74xUEocGEGpkpAAAiB2cLcNnRooFeYGWDqSs7GIAAKIYgRTcyEgBrVfaR7MJAACiG4EU3MhIAa3Xta+QjBQAAFGNQApuZKSAlpWRkiTZaUnmemFJJbsbAIAoRiAFn4EUc6SAlp0npXOknE4nuxkAgChFIAU3KwvyAi0uv7a8r6KqWkqsdvY4AABRikAKbmSkgJaXl72vc19hMeV9AABEKwIp+F6QN5lDA2jphhO0QAcAIHpxtgzfGamkRPYM0ALyPTNSNJwAACBqEUjBjYwU0PJYlBcAgNhAIAU3MlJAa5f2MUcKAIBoRSAFNzJSQCuX9rEoLwAAUYtACg0syMscKaAlkJECACA2EEihXkYqOdEiiQkW9gzQAnSx6zbpyeZ6YYmVfQwAQJQikIIJoN5f9Kts3FVm9obDKea2Z6kfgNAvyqtzpJxOJ7sWAIAoRCAV5778uUBGPPCV3PjOUimz1gRO1Q6nua33f/VzQbiHCMTsorxaTltcYQ/3cAAAQBAIpOI8iLri9QVS0sCJnN5/+esLzHYAWmieFGtJAQAQlQik4pSW7d00dYmI0/zPJ3O/U+TmqUso8wNabC0pWqADABCNCKTi1LRl20xJUVOzM/Txogq7fLZ8WyuNDIh9+dn7MlK0QAcAIDoRSMWpL1YUiL+N+XS7z5dT3ge0SEaK0j4AAKISgVSc2ltuM935/KHb7a2wtfSQgLicI0VGCgCA6EQgFafaZqQElJFqm57S0kMC4q5rn2KOFAAA0YlAKk6NG5AfUEZq/MD8lh4SEJ9d+2g2AQBAVCKQilMTBnWWnPQkaSoppY+3SU+SEwZ2bqWRAbEvNSlR2mUkm+uFJdZwDwcAAASBQCpOpSUnyhNnDa2JlBpgHrKIPH7WULM9gNA3nNA5Uk6nn+lhAAAQMQik4tjY/vny4gXDJSXRO5pyzZ3SjNVLFww32wEIrY61LdBt1Q7ZW17F7gUAIMokhXsACK+x/fIkNytVfiuqFItFZHiPdtIhM9XMidJyPjJRQOu0QG+XSUMXAACiCYFUnFu3o8wEUerwPrny+qUjwz0kIC7kezWcsMpBncI6HAAAECBK++LczFWF7utHHdAxrGMB4jUjVUjnPgAAog6BVJz7dvUO93UCKSA8a0nRuQ8AgOhDIBXHKmzVMm/DbnO9S5s06ZOXFe4hAXGDtaQAAIhuBFJxbO6GXWKzO8z1ow7sKBbtNgGg9ZtNUNoHAEDUIZCKY9+uoqwPCJeOWd7NJgAAQHQhkIpjs2rnRyUmWGR0n9xwDweIKylJCdKhtuX5jhICKQAAog2BVJzavKtc1u8sM9eH7ddOctKSwz0kIO7k1Zb3FZZUisPhDPdwAABAAAik4tS3azzK+g6k7TkQDnnZNeV9VdVO2VNu40MAACCKEEjFKeZHAZG3KC8AAIgeBFJxSDv1zV6301zPzUqV/p1zwj0kIC55de4rqQzrWAAAQGAIpOLQgo27pdxWba4feUCuJCTQ9hwI5xwptYOMFAAAUYVAKg59W9utTx11APOjgHDJr50jpVhLCgCA6EIgFceBlK6/e0RfAikgEjJSlPYBABBdCKTizPaiSlm5vcRcH9ytrbSvXccGQOuj2QQAANGLQCpOF+FVlPUB4aXNXjQzrAqLaTYBAEA0IZCKM8yPAiJHcmKCdMismSdVWEL7cwAAogmBVByxVzvku9qFeNukJ8uQbm3CPSQg7rnK+zSQcjiccb8/AACIFgRScWTpr3uluNJurh/eN1eSEvn4gXDLq+3cV+1wyq4yW7iHAwAA/MSZdBz5dhXzo4CIXpSXeVIAAEQNAqk4wvwoILJboBeW0HACAIBoQSAVJ3aVWuWnrUXmer/OOV5/BQcQGS3QC4tpOAEAQLQgkIoT363ZKc7aeey0PQciR362Z2kfgRQAANGCQCpOUNYHRKY8j4xUAaV9AABEDQKpOKAtlV0L8WamJMqwHu3CPSQAtTzLbFmUFwCA6EEgFQdW/Fbsbqs8uk+upCTxsQORokNmiiRYaq5T2gcAQPTgjDoOfLu60H2d+VFAZNH13HKzXIvy0rUPAIBoQSAVB5gfBUTHPKkdJVazMC8AAIh8BFIxrqiiShZt3muu798xU7q3zwj3kAA00LlPYyhdqgAAAEQ+AqkYN3vtTvdfuCnrAyJ/UV7mSQEAEB2Swj0AhF5lVbVMW7ZNvlhRIAs373HfP2r/DuxuIMIX5S0orpRB0ias4wEAAE0jkIoxX/5cIDdNXSLFFXbTCcxzusXNU5fKExaLjO2fH84hAmisBXoJpX0AAEQDSvtiLIi64vUFUlJhN7frzlkvqbTL5a8vMNsBiBx52d4ZKQAAEPkIpGKonE8zUeI0//PJ3O/UzNQSsz2ASMxIEUgBABANKO2LENaqavlsxW9mXtPuUqtU2B3m/vTkRGmfmSLjBuTLhEGdJS050efP65woLedrigZTRRV2+Wz5Njnt4G4hfx8AAtcmY99X8WfLtsuesqomf+cDnTP5+YrtsmNvmXRs+6uMH9ApJM+N2MVxA4DvmqZZnE5nXC9aUlxcLG3atJGioiLJyclp9dd3OBzy7pzVct+Xm6S40i4WV+bIg+u+nPQkeeKsofXmOGlXvgv+PU/mrNvVYDbKk86dGte/kzx/wbCAx2u1W2XJ9iWSmZIpKYkpAf88QkN/bUt3l0pW+yyxWPQIQXPZqm1SZiuToZ2GSmrSvlK7VpnX+M4S8/vv4prf2NDvfHPmTIbquRG7OG7Q3POawsJCycvLk4QECp8Qfd81gcQGEXmEP/PMM9KzZ09JS0uTkSNHyvz58xvdfurUqXLQQQeZ7QcNGiTTpk2TaPHVLwXy14/XmflLylcg5LpP5z7pHKdpP22Teet3ydNfr5GJL8+XIZO/kNl+BlFKD9C9FbaQvQcAzZzX6BFEec5vdP3OBzOvsaE5k6F4bsQujhsAfNf4L+ICqbfffltuvPFGufvuu2XRokUyZMgQGT9+vPnrhi+zZ8+Wc889Vy699FJZvHixnHrqqeayfPlyiYbSiZun/mSu+xME6TaaP7zqrUVyzotz5bEvVsus1Tuk1Np0SZ8njfbbppNNAmJ1XiNzJhFpxyQAxOJ3TcSV9mkG6tBDD5Wnn37anSLu3r27XHvttXLbbbfV2/6cc86RsrIy+eSTT9z3HXbYYTJ06FB5/vnnI7q07/1Fv8qN7yxt9vPkZqVK17ZpsvTXIr9/5h/nDAlqjhSlfZGB0r7oL+0L9Pd/SLc20rVdul/bbt1TEdD3QSDPjdjFcYNQ0LNKq7VSUlPThMpzhOK7Jthz1mAFEhtEVLMJm80mCxculNtvv919n9bXjh07VubMmePzZ/R+zWB50gzW//73P5/bW61Wc3HRnaT27t1rgrbW9PGCtSK28nptyv3RuU2qXHlUbzmkR1vZr12G2OwOOfaJb6W0srrR7JbOpslKS5TR3dLNew4mkCotLpXKxErmSIU5kKooqhCrxcocqRAGUvZqu+xN29sqgVSgv/+L15XL4hYaS0s+N2IXxw2AlqZVVB/9uFaO6ZUlrRlIKX9yTREVSO3cuVOqq6slP997YpneXrlypc+f2b59u8/t9X5fHnzwQZk8eXK9+3v06CHRZIuIND5zrHGdHgrhYAAAAIAW8Kpe/iStrqSkxGSmoiaQag2a7fLMYGkWavfu3dKhQ4ew/GVfo14tXdyyZUtYugYiOnHcgGMGfNcgEvHfJ0T7caOZKA2iunTp0uS2ERVI5ebmSmJiohQUeHeR0tudOnXy+TN6fyDbp6ammountm3bSrjpQRPuAwfRh+MGHDPguwaRiP8+IZqPm6YyURHZtS8lJUWGDRsmM2bM8MoY6e1Ro0b5/Bm933N79eWXXza4PQAAAAA0V0RlpJSW3V144YUyfPhwGTFihDz55JOmK9/FF19sHp84caJ07drVzHVS119/vRx11FHy+OOPy4knnihTpkyRBQsWyIsvvhjmdwIAAAAgVkVcIKXtzHfs2CGTJk0yDSO0jfn06dPdDSU2b97stVL26NGj5a233pI777xT7rjjDunbt6/p2Ddw4ECJBlpmqGtm1S03BDhuwHcNwo3/RoFjBnzXRNE6UgAAAAAQ6SJqjhQAAAAARAMCKQAAAAAIEIEUAAAAAASIQAoAAAAAAkQgFUbPPPOM9OzZU9LS0mTkyJEyf/78cA4HEU5b/h966KGSnZ0teXl5cuqpp8qqVavCPSxEmYceekgsFov85S9/CfdQEMG2bt0q559/vnTo0EHS09Nl0KBBZmkRoCHV1dVy1113Sa9evcwx07t3b7n33nuFnmbwNGvWLDn55JOlS5cu5r9F2mnbkx4v2rm7c+fO5jgaO3asrFmzRiIVgVSYvP3222bNLG19vmjRIhkyZIiMHz9eCgsLwzUkRLhvv/1Wrr76apk7d65ZdLqqqkrGjRtn1lkD/PHjjz/KCy+8IIMHD2aHoUF79uyRMWPGSHJysnz22Wfy888/m7Ua27Vrx15Dgx5++GF57rnn5Omnn5ZffvnF3H7kkUfkqaeeYq/BTc9Z9JxXkwm+6DHzr3/9S55//nmZN2+eZGZmmvPjyspKiUS0Pw8TzUBpdkG/cJTD4ZDu3bvLtddeK7fddlu4hoUoouutaWZKA6wjjzwy3MNBhCstLZVDDjlEnn32WbnvvvvMGn264DlQl/436IcffpDvvvuOnQO/nXTSSWbNz3//+9/u+8444wyTVXjjjTfYk6hHM1IffPCBqbBxZaM0U3XTTTfJzTffbO4rKioyx9Wrr74qf/jDHyTSkJEKA5vNJgsXLjTpSvcHkZBgbs+ZMyccQ0IU0i8X1b59+3APBVFAs5knnnii1/cO4MtHH30kw4cPl7POOsv8sebggw+Wl156iZ2FRo0ePVpmzJghq1evNreXLl0q33//vZxwwgnsOfhlw4YNsn37dq//TrVp08YkHyL1/Dgp3AOIRzt37jS1xBphe9LbK1euDNu4ED00g6lzXLT8ZuDAgeEeDiLclClTTAmxlvYBTVm/fr0p0dLy8zvuuMMcN9ddd52kpKTIhRdeyA5Eg5nM4uJiOeiggyQxMdGc59x///1y3nnnscfgFw2ilK/zY9djkYZACojS7MLy5cvNX/uAxmzZskWuv/56M69OG9sA/vyhRjNSDzzwgLmtGSn9vtE5CwRSaMg777wjb775prz11lsyYMAAWbJkifmDn5ZqcdwgVlHaFwa5ubnmrzUFBQVe9+vtTp06hWNIiCLXXHONfPLJJ/LNN99It27dwj0cRDgtI9YmNjo/KikpyVx0Xp1O5tXr+ldjwJN2y+rfv7/Xff369ZPNmzezo9CgW265xWSldB6Ldnm84IIL5IYbbjAdZwF/uM6Bo+n8mEAqDLQ8YtiwYaaW2PMvgHp71KhR4RgSooBOwtQgSidmfv3116bFLNCU3/3ud7Js2TLz12HXRbMNWm6j1/WPOoAnLRmuu7SCznvp0aMHOwoNKi8vN/O9Pen3i57fAP7Q8xoNmDzPj7VcVLv3Rer5MaV9YaK155rq1hOaESNGmO5Z2hLy4osvDteQEAXlfFoy8eGHH5q1pFz1wjoRU7siAb7osVJ3Hp22k9X1gZhfB180i6CNA7S07+yzzzZrHL744ovmAjRE1wbSOVH77befKe1bvHixPPHEE3LJJZew0+DVQXbt2rVeDSb0j3raOEuPHS0H1c6yffv2NYGVrk2m5aGuzn6RhvbnYaStzx999FFzQqytiLXURjuTAA21CfXllVdekYsuuoidBr8dffTRtD9Ho7R8+PbbbzcLYerJjP7x7/LLL2evoUElJSXmpFerJrScWE9+zz33XLO4qlbiAGrmzJlyzDHHSF2aXNAW51p9o2us6h9u9u7dK4cffrhZtuOAAw6QSEQgBQAAAAABYo4UAAAAAASIQAoAAAAAAkQgBQAAAAABIpACAAAAgAARSAEAAABAgAikAAAAACBABFIAAAAAECACKQAAAAAIEIEUAAAAAASIQAoAgAjx7LPPyquvvhruYQAA/GBxOp1OfzYEAAAta+DAgZKbmyszZ85kVwNAhCMjBQCIK2VlZRJP7Ha72Gy2cA8DAGIOgRQAIGD33HOPWCwWWb16tZx//vnSpk0b6dixo9x1112ihQ5btmyR3//+95KTkyOdOnWSxx9/3K/n1ee85ppr5M0335QDDzxQ0tLSZNiwYTJr1iyv7TZt2iRXXXWV2SY9PV06dOggZ511lmzcuNFrOy2T0+f89ttvzfZ5eXnSrVu3oJ7j+++/l+uuu868z7Zt28qf/vQnE6Ds3btXJk6cKO3atTOXW2+91ewDTw6HQ5588kkZMGCAeU/5+fnm5/fs2ePepmfPnrJixQozVn09vRx99NHux/V1/vKXv0j37t0lNTVV+vTpIw8//LB5bhcdu/7cY489Zl6vd+/eZtuff/7Zr/0PAPBfUgDbAgDg5ZxzzpF+/frJQw89JJ9++qncd9990r59e3nhhRfk2GOPNSf6GhTdfPPNcuihh8qRRx7Z5B7UQOLtt982QYsGATpv6Pjjj5f58+eb0jf1448/yuzZs+UPf/iDCYw0gHjuuedM4KFBQ0ZGhtdzasCkAdCkSZPcGalAn+Paa681QeHkyZNl7ty58uKLL5qASp9jv/32kwceeECmTZsmjz76qBmnBlcuGjRpQHbxxReb97VhwwZ5+umnZfHixfLDDz9IcnKyCXz0NbKysuRvf/ub+TkNuFR5ebkcddRRsnXrVvNc+nr6urfffrts27bN/KynV155RSorK+WKK64w+1A/EwBAiOkcKQAAAnH33XdrysV5xRVXuO+z2+3Obt26OS0Wi/Ohhx5y379nzx5nenq688ILL2zyefU59bJgwQL3fZs2bXKmpaU5TzvtNPd95eXl9X52zpw55mf/85//uO975ZVXzH2HH364GZ+nQJ9j/PjxTofD4b5/1KhR5r1eeeWV9fbBUUcd5b7vu+++Mz//5ptver3W9OnT690/YMAAr591uffee52ZmZnO1atXe91/2223ORMTE52bN282tzds2GCeMycnx1lYWFjveQAAoUNpHwAgaJdddpn7emJiogwfPtyUtV166aXu+zVro+Vz69ev9+s5R40aZcr5XDT7omWCn3/+uVRXV5v7tBTPpaqqSnbt2mVK3fS1Fi1aVO85L7/8cjM+T4E+h74nLZtzGTlyZL336toHnu916tSppvTxuOOOk507d7ov+h41+/TNN980uU/0OY444ghTOuj5HGPHjjX7pG7p4xlnnGEycACAlkNpHwAgaBrkeNKAQecAaee5uvdroOKPvn371rvvgAMOMOVtO3bsMOV1FRUV8uCDD5oSNi1385yTVFRUVO/ne/XqVe++QJ/D13tVOmep7v2ec5/WrFljnk/nZ/lSWFgoTdHn+OmnnxoMjuo+h6/3CwAILQIpAEDQ6mZ5GrpPhXK1DZ1LpAGQNl/QDJYGL5ot0vlOns0XfGWfgn2Oht6Xr/s936s+lwZROlfMF38yR/ocmtHSRha+aKDZ1PsFAIQWgRQAIKJo9qUu7Q6ozR9cQce7774rF154oVc3QG2uoJ3t/BWK5/CHds776quvZMyYMU0GOJ6lg3Wfo7S01JTyAQAiA3OkAAARZc6cOV5zlLSV+ocffijjxo1zZ3/037oZrqeeeso9h8ofoXgOf5x99tnmOe+9916fazx5Bm6ZmZk+Azl9Dt0vOk+sLt1enwcA0LrISAEAIoq2Dh8/frxX+3OlbcddTjrpJHn99ddNOV7//v1NkKFZH10Lyl+heA5/aNtybVmu87GWLFliAkJtd66ZN20i8c9//lPOPPNMs602oNAW7NpGXhtfaEm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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ @@ -1675,36 +1699,10 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "id": "46", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "l=0.1: Success rate = 94.58%\n", - "l=0.2: Success rate = 77.59%\n", - "l=0.3: Success rate = 58.94%\n", - "l=0.4: Success rate = 40.19%\n", - "l=0.5: Success rate = 24.37%\n", - "l=1: Success rate = 10.84%\n", - "l=1.5: Success rate = 14.40%\n", - "l=2.0: Success rate = 15.09%\n", - "l=3.0: Success rate = 28.08%\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "from classiq.execution.functions.util._logging import _logger\n", "\n", @@ -1790,41 +1788,10 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "id": "49", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Submitting job to simulator\n", - "Job: https://platform.classiq.io/jobs/04e43eb9-b27d-40d2-9bed-25c60b63270f\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " coords counts probability bitstring\n", - "0 [1, -2] 1993 0.973145 110001\n", - "1 [0, -2] 17 0.008301 110000\n", - "2 [2, -2] 17 0.008301 110010\n", - "3 [1, -3] 9 0.004395 101001\n", - "4 [1, -1] 3 0.001465 111001\n", - "5 [2, -1] 3 0.001465 111010\n", - "6 [-1, -2] 2 0.000977 110111\n", - "7 [1, 0] 1 0.000488 000001\n", - "8 [-1, 0] 1 0.000488 000111\n", - "9 [0, -3] 1 0.000488 101000\n", - "10 [-4, -2] 1 0.000488 110100\n", - "Analytical gradient: (dx, dy) = ([0.25, -0.5])\n", - "Majority gradient: (dx, dy) = ([0.25, -0.5])\n", - "Success rate: 97.31% (1993/2048 shots)\n", - "[\u001b[92m█████████████████████████████████████████████████\u001b[91m-\u001b[0m] 97.31%\n" - ] - } - ], + "outputs": [], "source": [ "p = params()\n", "p.l = 0.1\n", diff --git a/algorithms/gradient_estimation/gradient_estimation_helpers.py b/algorithms/gradient_estimation/gradient_estimation_helpers.py index 809e8ad08..a53df9ae0 100644 --- a/algorithms/gradient_estimation/gradient_estimation_helpers.py +++ b/algorithms/gradient_estimation/gradient_estimation_helpers.py @@ -109,43 +109,6 @@ def unpack(self, namespace=None): namespace.update(vals) -def make_phase_oracle( - f: Callable, - l: float, - m: float, - N: int, - x0: float = 0.0, - d: int = 1, -) -> Callable: - """Return a @qfunc phase oracle that applies phase(f_norm(reg), 2*pi). - - The oracle encodes the normalized function value as a phase: - f_norm(reg) = f(l/N * reg - x0) * N / (l * m) - - Args: - f: Symbolic Python callable representing the mathematical function. - l: Sampling interval half-width. - m: Gradient magnitude bound (output range). - N: Number of sample points (2^n). - x0: Evaluation point; shifts the sampling window. - d: Dimensionality of the function. - """ - if d == 1: - - @qfunc - def phase_oracle(reg: QNum) -> None: - phase(f(l / N * reg - x0) * N / (l * m), 2 * pi) - - else: - - @qfunc - def phase_oracle(coords: QArray[QNum]) -> None: - args = [l / N * coords[i] - x0 for i in range(d)] - phase(f(*args) * N / (l * m), 2 * pi) - - return phase_oracle - - # ****** Simulation ****** def run_statevector_simulation( qfunc_to_run, print_circuit_info=False, filter_ancilla=False, show_circuit=False @@ -392,7 +355,7 @@ def plot_simplified_df(simplified_df, show=True): plt.plot( simplified_df.index, simplified_df["phase_over_2pi"], - "o", + ".", label="Measured phases", ) plt.legend() From 02484306dbd1ef253713519ed3d6d66680430909 Mon Sep 17 00:00:00 2001 From: Ofri Wienner Date: Wed, 24 Jun 2026 09:35:47 +0300 Subject: [PATCH 12/12] reupload