From c086becd86d3cae67b9ae18dcce0160d4a17d7b2 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 26 May 2026 16:44:35 -0700
Subject: [PATCH 01/31] bridget nb

---
 calculations/step_size/choose_step_size.ipynb | 10665 ++++++++++++++++
 1 file changed, 10665 insertions(+)
 create mode 100644 calculations/step_size/choose_step_size.ipynb

diff --git a/calculations/step_size/choose_step_size.ipynb b/calculations/step_size/choose_step_size.ipynb
new file mode 100644
index 0000000..0d28670
--- /dev/null
+++ b/calculations/step_size/choose_step_size.ipynb
@@ -0,0 +1,10665 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "8bd8026f",
+   "metadata": {},
+   "source": [
+    "# Choosing PATH `step_size`\n",
+    "\n",
+    "The `step_size` parameter in PATH controls how finely the grid is sampled when calculating the likelihood `p(w|Oi)`. This needs to be small enough to finely sample both the localization size (`a` and `b`) and the galaxy angular size (`ang_size`). In this notebook, I try to figure out some method of choosing `step_size` to properly sample the convolution of the localization and galaxy size.\n",
+    "\n",
+    "The relevant code snippets are [here](https://github.com/FRBs/astropath/blob/d73ad5d552fc2694a8333e3b0815c9396ac0d427/astropath/run.py#L179) (setting the `step_size` parameter) and [here](https://github.com/FRBs/astropath/blob/d73ad5d552fc2694a8333e3b0815c9396ac0d427/astropath/bayesian.py#L189) (actually using `step_size` to calculate the likelihood grid). Note that, when calculating the likelihood, the original `step_size` is scaled by each galaxy size. Here's the relevant code snippet:\n",
+    "```\n",
+    "phi_cand = cand_ang_size[icand]   # arcsec\n",
+    "step_size_phi = phi_cand * step_size        # arcsec\n",
+    "box_hwidth = phi_cand * theta_prior['max']  # arcsec\n",
+    "\n",
+    "# Grid around the galaxy\n",
+    "ngrid = int(np.round(2 * box_hwidth / step_size_phi))\n",
+    "x = np.linspace(-box_hwidth, box_hwidth, ngrid)\n",
+    "xcoord, ycoord = np.meshgrid(x,x)\n",
+    "theta = np.sqrt(xcoord**2 + ycoord**2)\n",
+    "# p(w|O)\n",
+    "p_wOi = pw_Oi(theta, phi_cand, theta_prior)\n",
+    "```\n",
+    "So, we want `step_size` to be *small*. Currently, it is set as:\n",
+    "```\n",
+    "step_size_max = 2 * 3 * np.nanmin([a, b]) / np.nanmax(cut_catalog['ang_size'])\n",
+    "step_size = np.nanmin([0.1, step_size_max])\n",
+    "```\n",
+    "But that doesn't seem quite right..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "a32b7c85",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import matplotlib.pylab as pylab\n",
+    "params = {'axes.labelsize':20,\n",
+    "         'axes.titlesize':20,\n",
+    "         'xtick.labelsize':20,\n",
+    "         'ytick.labelsize':20}\n",
+    "pylab.rcParams.update(params)\n",
+    "import pandas as pd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "13470608",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import matplotlib.patches as mpatches\n",
+    "from matplotlib.gridspec import GridSpec\n",
+    "from scipy.stats import norm"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "06e2ed84",
+   "metadata": {},
+   "source": [
+    "## Question 1: How many samples do you need to smoothly integrate over a Gaussian distribution?\n",
+    "The convolution of the galaxy and localization will be roughly Gaussian. How fine does the sampling need to be to get a small error on the integral under the curve?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "608f7d3d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def pw_Oi(theta, phi, theta_prior):\n",
+    "    \"\"\"\n",
+    "    p(w|O_i) with corrected exp normalisation.\n",
+    "    The fix: norm uses max/scale as the upper limit in units of phi_eff,\n",
+    "    so the truncation (ok_w, in original-phi units) and the norm are consistent.\n",
+    "    \"\"\"\n",
+    "    p    = np.zeros_like(theta, dtype=float)\n",
+    "    ok_w = theta < theta_prior['max'] * phi          # cutoff at max·phi_orig\n",
+    " \n",
+    "    if theta_prior['PDF'] == 'core':\n",
+    "        term0    = -phi**2 * np.log(phi)\n",
+    "        term_max = phi * (theta_prior['max']*phi\n",
+    "                         - phi * np.log(phi + theta_prior['max']*phi))\n",
+    "        norm = 2*np.pi*(term_max - term0)\n",
+    "        if np.any(ok_w):\n",
+    "            p[ok_w] = phi / (theta[ok_w] + phi) / norm\n",
+    " \n",
+    "    elif theta_prior['PDF'] == 'uniform':\n",
+    "        norm = np.pi * (phi * theta_prior['max'])**2\n",
+    "        if np.any(ok_w):\n",
+    "            p[ok_w] = 1.0 / norm\n",
+    " \n",
+    "    elif theta_prior['PDF'] == 'exp':\n",
+    "        phi_eff     = phi * theta_prior['scale']\n",
+    "        max_in_eff  = theta_prior['max'] / theta_prior['scale']   # ← fix\n",
+    "        norm = 2*np.pi * phi_eff**2 * (\n",
+    "            1 - (1 + max_in_eff) * np.exp(-max_in_eff))\n",
+    "        if np.any(ok_w):\n",
+    "            p[ok_w] = np.exp(-theta[ok_w] / phi_eff) / norm\n",
+    "    else:\n",
+    "        raise IOError(\"Bad theta PDF\")\n",
+    " \n",
+    "    if norm == 0:\n",
+    "        raise ValueError(\"Normalisation is zero!\")\n",
+    "    return p\n",
+    " \n",
+    "def gaussian_localiz(xcoord, ycoord, r, a, b, pa_deg=0.):\n",
+    "    \"\"\"\n",
+    "    2D Gaussian L(x-w) centred at (r, 0) with semi-axes a, b.\n",
+    " \n",
+    "    pa_deg : position angle of major axis, East-of-North (degrees).\n",
+    "             Here East = +x, North = +y, so PA rotates from y toward x.\n",
+    "    \"\"\"\n",
+    "    pa  = np.deg2rad(pa_deg)\n",
+    "    dx  = xcoord - r\n",
+    "    dy  = ycoord\n",
+    " \n",
+    "    # Rotate into ellipse frame\n",
+    "    dx_r =  dx * np.cos(pa) + dy * np.sin(pa)\n",
+    "    dy_r = -dx * np.sin(pa) + dy * np.cos(pa)\n",
+    " \n",
+    "    return np.exp(-0.5 * (dx_r**2/a**2 + dy_r**2/b**2)) / (2*np.pi*a*b)\n",
+    " \n",
+    "def build_grids(phi_cand, r, a, b, theta_prior, step_size, pa_deg=0.):\n",
+    "    \"\"\"\n",
+    "    Two grids:\n",
+    "      integration_grid  — strict PATH convention (box_hwidth = max·phi_cand)\n",
+    "      plot_grid         — extended to show the full Gaussian even when r is large\n",
+    "    \"\"\"\n",
+    "    step_size_phi = phi_cand * step_size\n",
+    "    box_hwidth    = phi_cand * theta_prior['max']            # PATH integration box\n",
+    " \n",
+    "    # --- integration grid (matches px_Oi_local exactly) ---\n",
+    "    ngrid_int = int(np.round(2 * box_hwidth / step_size_phi))\n",
+    "    x_int     = np.linspace(-box_hwidth, box_hwidth, ngrid_int)\n",
+    "    xc_int, yc_int = np.meshgrid(x_int, x_int)\n",
+    "    theta_int = np.sqrt(xc_int**2 + yc_int**2)\n",
+    " \n",
+    "    p_wOi_int = pw_Oi(theta_int.ravel(), phi_cand, theta_prior\n",
+    "                      ).reshape(ngrid_int, ngrid_int)\n",
+    "    L_int     = gaussian_localiz(xc_int, yc_int, r, a, b, pa_deg)\n",
+    "    integ_int = p_wOi_int * L_int\n",
+    " \n",
+    "    p_xOi = np.nansum(integ_int) * step_size_phi**2          # ← the integral\n",
+    " \n",
+    "    # sanity checks\n",
+    "    check_pw  = np.nansum(p_wOi_int) * step_size_phi**2\n",
+    "    check_L   = np.nansum(L_int)     * step_size_phi**2\n",
+    " \n",
+    "    # --- plot grid (extended) ---\n",
+    "    box_plot  = max(box_hwidth, r + 4*max(a, b))\n",
+    "    ngrid_plt = int(np.round(2 * box_plot / step_size_phi))\n",
+    "    x_plt     = np.linspace(-box_plot, box_plot, ngrid_plt)\n",
+    "    xc_plt, yc_plt = np.meshgrid(x_plt, x_plt)\n",
+    "    theta_plt = np.sqrt(xc_plt**2 + yc_plt**2)\n",
+    " \n",
+    "    p_wOi_plt = pw_Oi(theta_plt.ravel(), phi_cand, theta_prior\n",
+    "                      ).reshape(ngrid_plt, ngrid_plt)\n",
+    "    L_plt     = gaussian_localiz(xc_plt, yc_plt, r, a, b, pa_deg)\n",
+    "    integ_plt = p_wOi_plt * L_plt\n",
+    " \n",
+    "    return dict(\n",
+    "        # integration result\n",
+    "        p_xOi     = p_xOi,\n",
+    "        check_pw  = check_pw,\n",
+    "        check_L   = check_L,\n",
+    "        # integration grid\n",
+    "        x_int=x_int, p_wOi_int=p_wOi_int, L_int=L_int, integ_int=integ_int,\n",
+    "        step_size_phi=step_size_phi, box_hwidth=box_hwidth,\n",
+    "        # plot grid\n",
+    "        x_plt=x_plt, p_wOi_plt=p_wOi_plt, L_plt=L_plt, integ_plt=integ_plt,\n",
+    "        box_plot=box_plot,\n",
+    "    )\n",
+    " \n",
+    "def plot_convolution(phi_cand, r, a, b, theta_prior,\n",
+    "                     step_size=0.05, pa_deg=0., outfile=None):\n",
+    " \n",
+    "    g = build_grids(phi_cand, r, a, b, theta_prior, step_size, pa_deg)\n",
+    " \n",
+    "    print(f\"\\n{'='*55}\")\n",
+    "    print(f\"  phi_cand = {phi_cand}\\\"   r = {r}\\\"   a = {a}\\\"  b = {b}\\\"\")\n",
+    "    print(f\"  step_size = {step_size}  (step_size_phi = {g['step_size_phi']:.3f}\\\")\")\n",
+    "    print(f\"  Integration box half-width: {g['box_hwidth']:.1f}\\\"\")\n",
+    "    print(f\"  ∫ p(w|O_i) dA  = {g['check_pw']:.6f}  (should = 1)\")\n",
+    "    print(f\"  ∫ L(x-w)   dA  = {g['check_L']:.6f}  (should ≈ 1)\")\n",
+    "    print(f\"  p(x|O_i)       = {g['p_xOi']:.6f}\")\n",
+    "    print(f\"{'='*55}\\n\")\n",
+    " \n",
+    "    BG = '#0d0d0d'\n",
+    "    fig = plt.figure(figsize=(15, 10), facecolor=BG)\n",
+    "    gs  = GridSpec(2, 3, figure=fig, wspace=0.38, hspace=0.45,\n",
+    "                   left=0.07, right=0.97, top=0.91, bottom=0.08)\n",
+    " \n",
+    "    xp  = g['x_plt']\n",
+    "    ext = [-g['box_plot'], g['box_plot'], -g['box_plot'], g['box_plot']]\n",
+    " \n",
+    "    panels = [\n",
+    "        (g['p_wOi_plt'], r'$p(w\\,|\\,O_i)$',\n",
+    "         'magma',   r'arcsec$^{-2}$'),\n",
+    "        (g['L_plt'],     r'$\\mathcal{L}(x{-}w)$',\n",
+    "         'viridis',  r'arcsec$^{-2}$'),\n",
+    "        (g['integ_plt'], r'$\\mathcal{L}(x{-}w)\\cdot p(w\\,|\\,O_i)$',\n",
+    "         'plasma',   r'arcsec$^{-4}$'),\n",
+    "    ]\n",
+    " \n",
+    "    for col, (data, title, cmap, clabel) in enumerate(panels):\n",
+    "        ax = fig.add_subplot(gs[0, col])\n",
+    "        ax.set_facecolor(BG)\n",
+    " \n",
+    "        vmax = np.nanpercentile(data[data > 0], 99.5) if np.any(data > 0) else 1\n",
+    "        im   = ax.imshow(data, origin='lower', extent=ext,\n",
+    "                         cmap=cmap, vmin=0, vmax=vmax,\n",
+    "                         aspect='equal', interpolation='bilinear')\n",
+    " \n",
+    "        # Galaxy angular-size circle\n",
+    "        ax.add_patch(plt.Circle((0, 0), phi_cand,\n",
+    "                                color='white', fill=False, lw=0.9, ls=':', alpha=0.6))\n",
+    "        # Galaxy prior boundary\n",
+    "        ax.add_patch(plt.Circle((0, 0), phi_cand * theta_prior['max'],\n",
+    "                                color='white', fill=False, lw=0.6, ls='--', alpha=0.35))\n",
+    "        # Localization ellipse (1σ)\n",
+    "        ax.add_patch(mpatches.Ellipse(\n",
+    "            (r, 0), 2*a, 2*b, angle=pa_deg,\n",
+    "            color='cyan', fill=False, lw=0.9, ls='--', alpha=0.7))\n",
+    "        # Centres\n",
+    "        ax.plot(0,  0, '+', color='white', ms=9, mew=1.4, alpha=0.9, zorder=5)\n",
+    "        ax.plot(r,  0, 'x', color='cyan',  ms=9, mew=1.4, alpha=0.9, zorder=5)\n",
+    " \n",
+    "        ax.set_title(title, color='white', fontsize=10, pad=5)\n",
+    "        ax.set_xlabel('ΔRA (arcsec)',  color='#cccccc', fontsize=8)\n",
+    "        if col == 0:\n",
+    "            ax.set_ylabel('ΔDec (arcsec)', color='#cccccc', fontsize=8)\n",
+    "        ax.tick_params(colors='#666666', labelsize=7)\n",
+    "        for sp in ax.spines.values():\n",
+    "            sp.set_edgecolor('#444444')\n",
+    " \n",
+    "        cb = fig.colorbar(im, ax=ax, fraction=0.046, pad=0.03)\n",
+    "        cb.set_label(clabel, color='#aaaaaa', fontsize=6)\n",
+    "        cb.ax.tick_params(labelsize=6, colors='#aaaaaa')\n",
+    "        cb.outline.set_edgecolor('#444444')\n",
+    " \n",
+    "    # ── 1D cuts ───────────────────────────────────────────────────────────────\n",
+    " \n",
+    "    mid   = len(xp) // 2                       # row/col index for y=0 / x=0\n",
+    "    r_idx = int(np.argmin(np.abs(xp - r)))     # column index closest to x=r\n",
+    " \n",
+    "    c_pw    = '#ff7f50'   # coral\n",
+    "    c_L     = '#90ee90'   # light green\n",
+    "    c_prod  = '#87ceeb'   # sky blue\n",
+    " \n",
+    "    def _style_ax(ax, xlabel):\n",
+    "        ax.set_facecolor(BG)\n",
+    "        ax.set_xlabel(xlabel, color='#cccccc', fontsize=9)\n",
+    "        ax.set_ylabel('Probability density', color='#cccccc', fontsize=9)\n",
+    "        ax.tick_params(colors='#888888', labelsize=8)\n",
+    "        for sp in ax.spines.values():\n",
+    "            sp.set_edgecolor('#444444')\n",
+    "        ax.legend(fontsize=8, facecolor='#1a1a1a',\n",
+    "                  labelcolor='white', edgecolor='#444444')\n",
+    "        ax.axhline(0, color='#444444', lw=0.5)\n",
+    " \n",
+    "    # Cut along ΔRA at Dec = 0\n",
+    "    ax1 = fig.add_subplot(gs[1, :2])\n",
+    "    ax1.plot(xp, g['p_wOi_plt'][mid, :], color=c_pw,   lw=1.5,\n",
+    "             label=r'$p(w|O_i)$')\n",
+    "    ax1.plot(xp, g['L_plt'][mid, :],     color=c_L,    lw=1.5,\n",
+    "             label=r'$\\mathcal{L}(x{-}w)$')\n",
+    "    ax1.plot(xp, g['integ_plt'][mid, :], color=c_prod, lw=2.0,\n",
+    "             label=r'$\\mathcal{L}\\cdot p(w|O_i)$')\n",
+    "    ax1.axvline(0, color='white', lw=0.6, ls=':', alpha=0.5)\n",
+    "    ax1.axvline(r, color='cyan',  lw=0.6, ls='--', alpha=0.6)\n",
+    " \n",
+    "    # shade the prior support\n",
+    "    ax1.axvspan(-phi_cand*theta_prior['max'], phi_cand*theta_prior['max'],\n",
+    "                alpha=0.05, color='white')\n",
+    "    ax1.set_title('1D cut: ΔRA axis  (ΔDec = 0)',\n",
+    "                  color='white', fontsize=10)\n",
+    "    _style_ax(ax1, 'ΔRA  (arcsec)')\n",
+    " \n",
+    "    # Cut along ΔDec at RA = r\n",
+    "    ax2 = fig.add_subplot(gs[1, 2])\n",
+    "    ax2.plot(xp, g['p_wOi_plt'][:, r_idx], color=c_pw,   lw=1.5,\n",
+    "             label=r'$p(w|O_i)$')\n",
+    "    ax2.plot(xp, g['L_plt'][:, r_idx],     color=c_L,    lw=1.5,\n",
+    "             label=r'$\\mathcal{L}$')\n",
+    "    ax2.plot(xp, g['integ_plt'][:, r_idx], color=c_prod, lw=2.0,\n",
+    "             label=r'Product')\n",
+    "    ax2.axvline(0, color='white', lw=0.6, ls=':', alpha=0.5)\n",
+    "    ax2.set_title(f'1D cut: ΔDec axis  (ΔRA = {r:.1f}\")',\n",
+    "                  color='white', fontsize=10)\n",
+    "    _style_ax(ax2, 'ΔDec  (arcsec)')\n",
+    " \n",
+    "    # suptitle\n",
+    "    fig.suptitle(\n",
+    "        rf'$\\phi={phi_cand:.1f}$\"   $r={r:.1f}$\"   '\n",
+    "        rf'$a={a:.1f}$\", $b={b:.1f}$\"   '\n",
+    "        rf'$\\Rightarrow\\; p(x|O_i) = {g[\"p_xOi\"]:.5f}$'\n",
+    "        '\\n'\n",
+    "        rf'[white $+$ = galaxy centre, cyan $\\times$ = localisation centre, '\n",
+    "        rf'dotted circle = $\\phi$, dashed circle = max·$\\phi$]',\n",
+    "        color='white', fontsize=11, y=0.995\n",
+    "    )\n",
+    "\n",
+    "#     fn = outfile or '~/frb_convolution.png'\n",
+    "#     fig.savefig(fn, dpi=150, facecolor=BG)\n",
+    "#     plt.close(fig)\n",
+    "#     print(f\"Saved → {fn}\")\n",
+    "    return g['p_xOi']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "id": "e5966ddf",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.01  (step_size_phi = 0.010\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.998334  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.998334  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.237034\n",
+      "=======================================================\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "theta_prior = {'PDF': 'exp', 'scale': 0.5, 'max': 6.}\n",
+    "\n",
+    "phi_cand = 1. # Size of galaxy, arcsec\n",
+    "r = 0.5 # Galactocentric offset of localization, arcsec\n",
+    "a = 0.1 # Semi-major axis of 1sigma localization, arcsec\n",
+    "b = 0.05 # Semi-minor axis of 1sigma localization, arcsec\n",
+    "pa_deg = 10. # PA of localization\n",
+    "theta_prior = theta_prior\n",
+    "step_size = 0.01 # Step-size, as a fraction of phi_cand\n",
+    "\n",
+    "g = build_grids(phi_cand, r, a, b, theta_prior, step_size, pa_deg)\n",
+    "\n",
+    "print(f\"\\n{'='*55}\")\n",
+    "print(f\"  phi_cand = {phi_cand}\\\"   r = {r}\\\"   a = {a}\\\"  b = {b}\\\"\")\n",
+    "print(f\"  step_size = {step_size}  (step_size_phi = {g['step_size_phi']:.3f}\\\")\")\n",
+    "print(f\"  Integration box half-width: {g['box_hwidth']:.1f}\\\"\")\n",
+    "print(f\"  ∫ p(w|O_i) dA  = {g['check_pw']:.6f}  (should = 1)\")\n",
+    "print(f\"  ∫ L(x-w)   dA  = {g['check_L']:.6f}  (should ≈ 1)\")\n",
+    "print(f\"  p(x|O_i)       = {g['p_xOi']:.6f}\")\n",
+    "print(f\"{'='*55}\\n\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "id": "b871debc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(-3.0, 3.0)"
+      ]
+     },
+     "execution_count": 50,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 1600x800 with 8 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(16,8))\n",
+    "cycle = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
+    "\n",
+    "# (left, bottom, width, height)\n",
+    "sep_w = 0.1\n",
+    "sep_h = 0.1\n",
+    "bottom = 0.5\n",
+    "ax_exp = (0., bottom+sep_h, 0.3, 0.5)\n",
+    "ax_loc = (0.3+sep_w, bottom+sep_h, 0.3, 0.5)\n",
+    "ax_comb = (2*(0.3+sep_w), bottom+sep_h, 0.3, 0.5)\n",
+    "ax_racut = (0., 0., 0.5, 0.5)\n",
+    "ax_deccut = (0.5+sep_w, 0., 0.5, 0.5)\n",
+    "\n",
+    "xp  = g['x_plt']\n",
+    "ext = [-g['box_plot'], g['box_plot'], -g['box_plot'], g['box_plot']]\n",
+    "\n",
+    "# Plot PDFs\n",
+    "\n",
+    "ax = plt.axes(ax_exp)\n",
+    "\n",
+    "data = g['p_wOi_plt']\n",
+    "vmax = np.nanpercentile(data[data > 0], 99.5) if np.any(data > 0) else 1\n",
+    "im = ax.imshow(\n",
+    "    data, origin='lower', extent=ext,\n",
+    "    cmap='viridis', vmin=0, vmax=vmax,\n",
+    "    aspect='equal', interpolation='bilinear',\n",
+    ")\n",
+    "# Galaxy angular-size circle\n",
+    "ax.add_patch(plt.Circle((0, 0), phi_cand,\n",
+    "                        color='white', fill=False, lw=2, ls=':', alpha=0.6))\n",
+    "# Galaxy prior boundary\n",
+    "ax.add_patch(plt.Circle((0, 0), phi_cand * theta_prior['max'],\n",
+    "                        color='white', fill=False, lw=2, ls='--', alpha=0.35))\n",
+    "# Localization ellipse (3σ)\n",
+    "ax.add_patch(mpatches.Ellipse(\n",
+    "    (r, 0), 3*a, 3*b, angle=pa_deg,\n",
+    "    color='black', fill=False, lw=0.9, ls='-', alpha=0.7))\n",
+    "cb = fig.colorbar(im, ax=ax, fraction=0.046, pad=0.03)\n",
+    "cb.set_label(r'arcsec$^{-2}$', color='black', fontsize=15)\n",
+    "ax.set_title(r'$p(w\\,|\\,O_i)$', color='black', fontsize=15, pad=5)\n",
+    "ax.set_xlabel('RA Offset (arcsec)',  fontsize=15)\n",
+    "ax.set_ylabel('Dec Offset (arcsec)', color='black', fontsize=15)\n",
+    "\n",
+    "ax = plt.axes(ax_loc)\n",
+    "\n",
+    "data = g['L_plt']\n",
+    "vmax = np.nanpercentile(data[data > 0], 99.5) if np.any(data > 0) else 1\n",
+    "im = ax.imshow(\n",
+    "    data, origin='lower', extent=ext,\n",
+    "    cmap='viridis', vmin=0, vmax=vmax,\n",
+    "    aspect='equal', interpolation='bilinear',\n",
+    ")\n",
+    "# Galaxy angular-size circle\n",
+    "ax.add_patch(plt.Circle((0, 0), phi_cand,\n",
+    "                        color='white', fill=False, lw=2, ls=':', alpha=0.6))\n",
+    "# Galaxy prior boundary\n",
+    "ax.add_patch(plt.Circle((0, 0), phi_cand * theta_prior['max'],\n",
+    "                        color='white', fill=False, lw=2, ls='--', alpha=0.35))\n",
+    "# Localization ellipse (3σ)\n",
+    "ax.add_patch(mpatches.Ellipse(\n",
+    "    (r, 0), 3*a, 3*b, angle=pa_deg,\n",
+    "    color='black', fill=False, lw=0.9, ls='-', alpha=0.7))\n",
+    "cb = fig.colorbar(im, ax=ax, fraction=0.046, pad=0.03)\n",
+    "cb.set_label(r'arcsec$^{-2}$', color='black', fontsize=15)\n",
+    "ax.set_title(r'$L(x{-}w)$', color='black', fontsize=15, pad=5)\n",
+    "ax.set_xlabel('RA Offset (arcsec)',  fontsize=15)\n",
+    "ax.set_ylabel('Dec Offset (arcsec)', color='black', fontsize=15)\n",
+    "\n",
+    "ax = plt.axes(ax_comb)\n",
+    "\n",
+    "data = g['integ_plt']\n",
+    "vmax = np.nanpercentile(data[data > 0], 99.5) if np.any(data > 0) else 1\n",
+    "im = ax.imshow(\n",
+    "    data, origin='lower', extent=ext,\n",
+    "    cmap='viridis', vmin=0, vmax=vmax,\n",
+    "    aspect='equal', interpolation='bilinear',\n",
+    ")\n",
+    "# Galaxy angular-size circle\n",
+    "ax.add_patch(plt.Circle((0, 0), phi_cand,\n",
+    "                        color='white', fill=False, lw=2, ls=':', alpha=0.6))\n",
+    "# Galaxy prior boundary\n",
+    "ax.add_patch(plt.Circle((0, 0), phi_cand * theta_prior['max'],\n",
+    "                        color='white', fill=False, lw=2, ls='--', alpha=0.35))\n",
+    "# Localization ellipse (3σ)\n",
+    "ax.add_patch(mpatches.Ellipse(\n",
+    "    (r, 0), 3*a, 3*b, angle=pa_deg,\n",
+    "    color='black', fill=False, lw=0.9, ls='-', alpha=0.7))\n",
+    "cb = fig.colorbar(im, ax=ax, fraction=0.046, pad=0.03)\n",
+    "cb.set_label(r'arcsec$^{-4}$', color='black', fontsize=15)\n",
+    "ax.set_title(r'$L(x{-}w)\\cdot p(w\\,|\\,O_i)$', color='black', fontsize=15, pad=5)\n",
+    "ax.set_xlabel('RA Offset (arcsec)',  fontsize=15)\n",
+    "ax.set_ylabel('Dec Offset (arcsec)', color='black', fontsize=15)\n",
+    "\n",
+    "# Plot cuts\n",
+    "mid = len(xp) // 2                       # row/col index for y=0 / x=0\n",
+    "r_idx = int(np.argmin(np.abs(xp - r)))     # column index closest to x=r\n",
+    "\n",
+    "ax = plt.axes(ax_racut)\n",
+    "\n",
+    "# Cut along ΔRA at Dec = 0\n",
+    "ax.plot(xp, g['p_wOi_plt'][mid, :] / np.nanmax(g['p_wOi_plt'][mid, :]), color=cycle[0], lw=1.5, label=r'$p(w|O_i)$')\n",
+    "ax.plot(xp, g['L_plt'][mid, :] / np.nanmax(g['L_plt'][mid, :]), color=cycle[1], lw=1.5, label=r'$L(x{-}w)$')\n",
+    "ax.plot(xp, g['integ_plt'][mid, :] / np.nanmax(g['integ_plt'][mid, :]), color=cycle[2], lw=2.0, label=r'$L \\cdot p(w|O_i)$')\n",
+    "ax.set_xlabel('RA Offset (arcsec)', color='black', fontsize=15)\n",
+    "ax.set_ylabel('Arbitrary Norm', color='black', fontsize=15)\n",
+    "ax.legend(fontsize=15)\n",
+    "ax.grid()\n",
+    "ax.set_xlim([-3,3])\n",
+    "\n",
+    "ax = plt.axes(ax_deccut)\n",
+    "\n",
+    "# Cut along ΔRA at Dec = 0\n",
+    "ax.plot(xp, g['p_wOi_plt'][:, r_idx] / np.nanmax(g['p_wOi_plt'][:, r_idx]), color=cycle[0], lw=1.5, label=r'$p(w|O_i)$')\n",
+    "ax.plot(xp, g['L_plt'][:, r_idx] / np.nanmax(g['L_plt'][:, r_idx]), color=cycle[1], lw=1.5, label=r'$L(x{-}w)$')\n",
+    "ax.plot(xp, g['integ_plt'][:, r_idx] / np.nanmax(g['integ_plt'][:, r_idx]), color=cycle[2], lw=2.0, label=r'$L \\cdot p(w|O_i)$')\n",
+    "ax.set_xlabel('Dec Offset (arcsec)', color='black', fontsize=15)\n",
+    "ax.set_ylabel('Arbitrary Norm', color='black', fontsize=15)\n",
+    "ax.legend(fontsize=15)\n",
+    "ax.grid()\n",
+    "ax.set_xlim([-3,3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "id": "78967dca",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04  (step_size_phi = 0.040\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.993339  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.993344  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235850\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.040360360360360364  (step_size_phi = 0.040\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991150  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991131  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235324\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04072072072072072  (step_size_phi = 0.041\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.995340  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995321  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236319\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.041081081081081085  (step_size_phi = 0.041\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992440  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992447  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235636\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04144144144144144  (step_size_phi = 0.041\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.996094  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.996100  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236504\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.041801801801801805  (step_size_phi = 0.042\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992587  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992566  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235665\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04216216216216216  (step_size_phi = 0.042\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.995702  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995680  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236404\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.042522522522522525  (step_size_phi = 0.043\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991483  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991490  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235409\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04288288288288288  (step_size_phi = 0.043\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.994056  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994063  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236020\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.043243243243243246  (step_size_phi = 0.043\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.996392  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.996400  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236575\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0436036036036036  (step_size_phi = 0.044\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991274  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991250  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235352\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.043963963963963966  (step_size_phi = 0.044\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.993070  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.993045  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235779\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04432432432432433  (step_size_phi = 0.044\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.994627  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994602  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236148\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.044684684684684686  (step_size_phi = 0.045\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.995946  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995920  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236461\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04504504504504504  (step_size_phi = 0.045\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989509  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989517  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234941\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04540540540540541  (step_size_phi = 0.045\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990286  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990294  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235125\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04576576576576577  (step_size_phi = 0.046\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990824  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990832  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235253\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04612612612612613  (step_size_phi = 0.046\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991122  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991131  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235324\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04648648648648649  (step_size_phi = 0.046\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991182  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991191  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235338\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04684684684684685  (step_size_phi = 0.047\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991002  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991011  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235296\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04720720720720721  (step_size_phi = 0.047\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990583  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990593  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235196\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04756756756756757  (step_size_phi = 0.048\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989926  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989935  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235040\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04792792792792793  (step_size_phi = 0.048\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989029  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989039  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234827\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.048288288288288295  (step_size_phi = 0.048\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.995953  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995920  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236461\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04864864864864865  (step_size_phi = 0.049\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.994635  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994602  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236148\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04900900900900901  (step_size_phi = 0.049\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.993079  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.993045  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235779\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.04936936936936937  (step_size_phi = 0.049\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991285  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991250  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235352\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.049729729729729735  (step_size_phi = 0.050\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989254  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989218  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234870\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05009009009009009  (step_size_phi = 0.050\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.995250  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995261  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236305\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.050450450450450456  (step_size_phi = 0.050\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992794  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992806  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235722\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05081081081081081  (step_size_phi = 0.051\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990103  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990115  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235083\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.051171171171171176  (step_size_phi = 0.051\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.995719  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995680  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236404\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05153153153153153  (step_size_phi = 0.052\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992606  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992566  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235665\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.051891891891891896  (step_size_phi = 0.052\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989259  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989218  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234870\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05225225225225225  (step_size_phi = 0.052\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.994290  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994302  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236077\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.052612612612612616  (step_size_phi = 0.053\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990520  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990533  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235182\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05297297297297297  (step_size_phi = 0.053\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.995364  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995321  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236319\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05333333333333334  (step_size_phi = 0.053\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991175  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991131  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235324\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0536936936936937  (step_size_phi = 0.054\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986756  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986711  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234275\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05405405405405406  (step_size_phi = 0.054\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990998  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991011  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235296\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.054414414414414414  (step_size_phi = 0.054\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.995248  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995201  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236290\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05477477477477478  (step_size_phi = 0.055\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990222  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990174  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235097\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05513513513513514  (step_size_phi = 0.055\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.994048  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994063  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236020\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0554954954954955  (step_size_phi = 0.055\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988606  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988621  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234728\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.055855855855855854  (step_size_phi = 0.056\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992258  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992208  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235580\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.056216216216216225  (step_size_phi = 0.056\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986405  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986353  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234190\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05657657657657658  (step_size_phi = 0.057\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989621  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989636  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234969\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05693693693693694  (step_size_phi = 0.057\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992859  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992806  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235722\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0572972972972973  (step_size_phi = 0.057\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986408  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986353  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234190\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.057657657657657665  (step_size_phi = 0.058\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989201  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989218  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234870\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05801801801801802  (step_size_phi = 0.058\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992025  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991968  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235523\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05837837837837838  (step_size_phi = 0.058\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.994584  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994602  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236148\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05873873873873874  (step_size_phi = 0.059\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987350  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987367  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234430\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.059099099099099106  (step_size_phi = 0.059\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989756  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989697  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234984\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05945945945945946  (step_size_phi = 0.059\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991890  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991908  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235508\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.05981981981981982  (step_size_phi = 0.060\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.994065  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994004  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236006\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06018018018018018  (step_size_phi = 0.060\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986059  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985996  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234105\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06054054054054055  (step_size_phi = 0.061\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987766  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987784  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234529\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0609009009009009  (step_size_phi = 0.061\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989523  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989459  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234927\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06126126126126127  (step_size_phi = 0.061\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990991  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991010  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235295\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06162162162162163  (step_size_phi = 0.062\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992514  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992448  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235637\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06198198198198199  (step_size_phi = 0.062\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.993743  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.993762  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235949\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.062342342342342344  (step_size_phi = 0.062\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984603  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.984622  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233778\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0627027027027027  (step_size_phi = 0.063\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985710  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985640  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234020\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06306306306306307  (step_size_phi = 0.063\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986510  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986529  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234231\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06342342342342343  (step_size_phi = 0.063\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987382  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987311  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234417\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06378378378378378  (step_size_phi = 0.064\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987942  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987960  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234571\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06414414414414416  (step_size_phi = 0.064\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988579  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988507  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234701\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06450450450450451  (step_size_phi = 0.065\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988896  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988914  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234798\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06486486486486487  (step_size_phi = 0.065\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989298  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989225  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234872\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06522522522522523  (step_size_phi = 0.065\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989374  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989390  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234911\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0655855855855856  (step_size_phi = 0.066\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989540  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989466  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234929\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06594594594594595  (step_size_phi = 0.066\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989372  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989388  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234910\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06630630630630631  (step_size_phi = 0.066\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989304  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989229  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234873\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06666666666666668  (step_size_phi = 0.067\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988894  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988907  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234796\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06702702702702704  (step_size_phi = 0.067\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988589  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988516  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234704\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06738738738738739  (step_size_phi = 0.067\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987938  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987948  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234568\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06774774774774775  (step_size_phi = 0.068\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987399  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987326  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234421\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0681081081081081  (step_size_phi = 0.068\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986504  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986511  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234227\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06846846846846848  (step_size_phi = 0.068\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985731  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985662  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234026\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06882882882882883  (step_size_phi = 0.069\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984596  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.984597  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233772\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06918918918918919  (step_size_phi = 0.069\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983589  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.983523  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233518\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06954954954954956  (step_size_phi = 0.070\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.993861  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.993795  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235957\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.06990990990990992  (step_size_phi = 0.070\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992417  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992411  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235627\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07027027027027027  (step_size_phi = 0.070\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991112  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991052  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235306\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07063063063063063  (step_size_phi = 0.071\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989427  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989412  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234915\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.070990990990991  (step_size_phi = 0.071\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987889  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987837  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234543\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07135135135135136  (step_size_phi = 0.071\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985964  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985937  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234089\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07171171171171171  (step_size_phi = 0.072\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984196  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.984154  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233669\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07207207207207209  (step_size_phi = 0.072\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982030  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.981988  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233152\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07243243243243244  (step_size_phi = 0.072\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991875  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991833  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235489\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0727927927927928  (step_size_phi = 0.073\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989809  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989782  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235006\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07315315315315316  (step_size_phi = 0.073\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987333  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987271  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234406\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07351351351351351  (step_size_phi = 0.074\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985038  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985031  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233878\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07387387387387388  (step_size_phi = 0.074\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982326  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.982239  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233210\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07423423423423424  (step_size_phi = 0.074\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991933  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991845  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235491\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07459459459459461  (step_size_phi = 0.075\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989339  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989357  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234906\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07495495495495497  (step_size_phi = 0.075\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986317  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986198  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234149\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07531531531531532  (step_size_phi = 0.075\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983498  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.983548  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233527\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07567567567567568  (step_size_phi = 0.076\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992932  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992982  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235767\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07603603603603604  (step_size_phi = 0.076\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989598  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989439  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234918\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0763963963963964  (step_size_phi = 0.076\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986484  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986575  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234247\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07675675675675676  (step_size_phi = 0.077\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982916  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.982708  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233319\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07711711711711713  (step_size_phi = 0.077\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992167  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991957  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235515\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07747747747747749  (step_size_phi = 0.077\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988757  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988901  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234800\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07783783783783785  (step_size_phi = 0.078\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984881  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.984609  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233770\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0781981981981982  (step_size_phi = 0.078\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981251  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.981460  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233035\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07855855855855856  (step_size_phi = 0.079\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990316  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990527  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235187\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07891891891891892  (step_size_phi = 0.079\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986131  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985781  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234046\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07927927927927929  (step_size_phi = 0.079\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982209  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.982501  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233283\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.07963963963963964  (step_size_phi = 0.080\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991158  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991453  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235409\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08000000000000002  (step_size_phi = 0.080\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986667  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986219  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234149\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08036036036036037  (step_size_phi = 0.080\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982453  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.982849  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233368\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08072072072072073  (step_size_phi = 0.081\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991284  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991683  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235465\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08108108108108109  (step_size_phi = 0.081\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986485  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985918  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234075\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08144144144144144  (step_size_phi = 0.081\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981983  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.982507  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233288\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08180180180180181  (step_size_phi = 0.082\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990693  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991221  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235358\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08216216216216217  (step_size_phi = 0.082\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985589  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.984875  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233825\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08252252252252254  (step_size_phi = 0.083\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980799  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.981481  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233047\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0828828828828829  (step_size_phi = 0.083\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989384  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990072  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235087\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08324324324324325  (step_size_phi = 0.083\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983978  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.983084  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233397\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08360360360360361  (step_size_phi = 0.084\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992516  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991614  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235422\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08396396396396397  (step_size_phi = 0.084\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987361  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988243  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234656\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08432432432432432  (step_size_phi = 0.084\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981654  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.980541  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.232790\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0846846846846847  (step_size_phi = 0.085\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990062  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988939  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234784\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08504504504504505  (step_size_phi = 0.085\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984625  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985743  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234066\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08540540540540542  (step_size_phi = 0.085\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.992987  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994115  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236054\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08576576576576578  (step_size_phi = 0.086\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986895  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.985505  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233965\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08612612612612613  (step_size_phi = 0.086\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981180  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.982584  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233320\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08648648648648649  (step_size_phi = 0.086\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989407  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990824  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235277\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08684684684684685  (step_size_phi = 0.087\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983018  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.981307  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.232964\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08720720720720722  (step_size_phi = 0.087\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991193  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.989468  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234901\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08756756756756758  (step_size_phi = 0.088\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985118  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986884  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234346\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08792792792792795  (step_size_phi = 0.088\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978436  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.976339  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.231779\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0882882882882883  (step_size_phi = 0.088\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986473  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.984358  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233683\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08864864864864866  (step_size_phi = 0.089\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980126  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.982310  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233265\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08900900900900902  (step_size_phi = 0.089\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988110  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.990312  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235166\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08936936936936937  (step_size_phi = 0.089\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981049  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.978469  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.232279\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.08972972972972973  (step_size_phi = 0.090\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988977  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986376  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234156\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0900900900900901  (step_size_phi = 0.090\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982277  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.984983  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233907\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09045045045045046  (step_size_phi = 0.090\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990151  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.992879  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235782\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09081081081081083  (step_size_phi = 0.091\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982712  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.979554  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.232529\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09117117117117118  (step_size_phi = 0.091\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990527  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987343  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234378\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09153153153153154  (step_size_phi = 0.092\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983478  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986810  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234348\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0918918918918919  (step_size_phi = 0.092\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991237  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994595  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236197\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09225225225225225  (step_size_phi = 0.092\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983424  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.979574  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.232526\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09261261261261262  (step_size_phi = 0.093\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991122  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987242  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234346\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09297297297297298  (step_size_phi = 0.093\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983727  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987805  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234594\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09333333333333335  (step_size_phi = 0.093\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991368  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995477  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236416\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09369369369369371  (step_size_phi = 0.094\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983182  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.978511  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.232264\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09405405405405406  (step_size_phi = 0.094\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990760  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986052  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234054\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09441441441441442  (step_size_phi = 0.094\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983024  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987988  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234647\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09477477477477478  (step_size_phi = 0.095\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990542  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995545  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236442\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09513513513513513  (step_size_phi = 0.095\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981989  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.976344  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.231738\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0954954954954955  (step_size_phi = 0.095\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989442  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.983755  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233497\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09585585585585588  (step_size_phi = 0.096\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981369  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.987382  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234515\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09621621621621623  (step_size_phi = 0.096\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988762  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994820  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236281\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09657657657657659  (step_size_phi = 0.097\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979843  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.973053  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.230945\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09693693693693695  (step_size_phi = 0.097\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987169  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.980328  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.232671\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.0972972972972973  (step_size_phi = 0.097\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978766  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.986012  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234202\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09765765765765766  (step_size_phi = 0.098\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986029  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.993329  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235940\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09801801801801803  (step_size_phi = 0.098\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976750  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.968616  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.229877\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09837837837837839  (step_size_phi = 0.098\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983946  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.975751  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.231571\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09873873873873876  (step_size_phi = 0.099\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991167  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.982912  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.233270\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09909909909909911  (step_size_phi = 0.099\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982348  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991103  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235426\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09945945945945947  (step_size_phi = 0.099\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989505  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.998324  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.237142\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.09981981981981983  (step_size_phi = 0.100\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979776  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.970000  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.230190\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10018018018018018  (step_size_phi = 0.100\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986863  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.977017  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.231855\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10054054054054055  (step_size_phi = 0.101\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977724  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.988174  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.234748\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10090090090090091  (step_size_phi = 0.101\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984746  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995271  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236433\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10126126126126128  (step_size_phi = 0.101\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.991792  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.002393  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.238125\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10162162162162164  (step_size_phi = 0.102\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981615  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.969920  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.230153\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.101981981981982  (step_size_phi = 0.102\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988589  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.976811  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.231788\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10234234234234235  (step_size_phi = 0.102\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979047  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.991552  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.235569\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10270270270270271  (step_size_phi = 0.103\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985954  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.998547  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.237231\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10306306306306307  (step_size_phi = 0.103\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975432  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.961597  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.228157\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10342342342342342  (step_size_phi = 0.103\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982265  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.968334  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.229756\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1037837837837838  (step_size_phi = 0.104\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989122  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.975093  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.231359\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10414414414414416  (step_size_phi = 0.104\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979183  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.994077  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236190\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10450450450450452  (step_size_phi = 0.105\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985971  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.000969  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.237827\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10486486486486488  (step_size_phi = 0.105\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975011  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.958601  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.227424\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10522522522522523  (step_size_phi = 0.105\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981724  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.965201  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.228989\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10558558558558559  (step_size_phi = 0.106\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988459  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.971823  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.230560\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10594594594594595  (step_size_phi = 0.106\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978132  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.995790  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236620\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10630630630630633  (step_size_phi = 0.106\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984797  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.002576  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.238232\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10666666666666669  (step_size_phi = 0.107\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973406  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.954024  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.226312\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10702702702702704  (step_size_phi = 0.107\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979994  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.960481  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.227844\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1073873873873874  (step_size_phi = 0.107\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986604  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.966960  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.229381\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10774774774774776  (step_size_phi = 0.108\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975894  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.996735  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.236870\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10810810810810811  (step_size_phi = 0.108\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982433  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.003414  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.238457\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10846846846846847  (step_size_phi = 0.108\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988993  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.010114  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.240050\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10882882882882883  (step_size_phi = 0.109\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977077  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.954132  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.226309\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10918918918918921  (step_size_phi = 0.109\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983558  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.960461  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.227811\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10954954954954957  (step_size_phi = 0.110\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.990061  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.966811  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.229317\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.10990990990990993  (step_size_phi = 0.110\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978885  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.003532  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.238514\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11027027027027028  (step_size_phi = 0.110\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985314  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.010124  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.240081\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11063063063063064  (step_size_phi = 0.111\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972978  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.946114  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.224376\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.110990990990991  (step_size_phi = 0.111\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979327  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.952287  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.225840\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11135135135135135  (step_size_phi = 0.111\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985697  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.958481  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.227309\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11171171171171174  (step_size_phi = 0.112\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974158  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.002985  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.238415\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1120720720720721  (step_size_phi = 0.112\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980453  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.009466  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.239955\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11243243243243245  (step_size_phi = 0.112\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986768  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.015969  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.241501\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1127927927927928  (step_size_phi = 0.113\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973919  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.942399  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.223460\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11315315315315316  (step_size_phi = 0.113\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980152  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.948430  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.224890\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11351351351351352  (step_size_phi = 0.114\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986405  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.954481  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.226325\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11387387387387388  (step_size_phi = 0.114\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974420  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.008199  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.239688\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11423423423423426  (step_size_phi = 0.114\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980597  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.014590  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.241207\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11459459459459462  (step_size_phi = 0.115\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986794  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.021002  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.242732\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11495495495495497  (step_size_phi = 0.115\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973438  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.936620  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.222052\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11531531531531533  (step_size_phi = 0.115\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979550  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.942501  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.223446\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11567567567567569  (step_size_phi = 0.116\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985682  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.948401  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.224845\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11603603603603604  (step_size_phi = 0.116\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973261  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.012662  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.240785\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1163963963963964  (step_size_phi = 0.116\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979315  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.018961  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.242283\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11675675675675676  (step_size_phi = 0.117\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985389  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.025280  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.243786\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11711711711711714  (step_size_phi = 0.117\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971536  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.928722  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.220138\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1174774774774775  (step_size_phi = 0.117\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977523  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.934446  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.221495\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11783783783783786  (step_size_phi = 0.118\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983530  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.940188  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.222856\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11819819819819821  (step_size_phi = 0.118\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989554  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.945947  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.224221\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11855855855855857  (step_size_phi = 0.119\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976610  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.022639  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.243197\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11891891891891893  (step_size_phi = 0.119\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982556  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.028865  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.244677\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11927927927927928  (step_size_phi = 0.119\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988520  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.035110  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.246162\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.11963963963963967  (step_size_phi = 0.120\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974073  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.924214  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.219024\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12000000000000002  (step_size_phi = 0.120\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979950  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.929790  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.220345\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12036036036036038  (step_size_phi = 0.120\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985844  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.935382  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.221671\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12072072072072074  (step_size_phi = 0.121\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972489  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.025685  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.243962\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1210810810810811  (step_size_phi = 0.121\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978304  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.031818  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.245421\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12144144144144145  (step_size_phi = 0.121\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984135  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.037968  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.246884\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1218018018018018  (step_size_phi = 0.122\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989985  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.044138  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.248351\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12216216216216216  (step_size_phi = 0.122\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974953  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.917161  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.217303\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12252252252252255  (step_size_phi = 0.123\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980714  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.922580  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.218587\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1228828828828829  (step_size_phi = 0.123\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986491  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.928015  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.219875\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12324324324324326  (step_size_phi = 0.123\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972640  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.034199  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.246029\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12360360360360362  (step_size_phi = 0.124\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978336  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.040256  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.247470\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12396396396396397  (step_size_phi = 0.124\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984049  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.046330  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.248915\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12432432432432433  (step_size_phi = 0.124\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.989779  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.052422  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.250365\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12468468468468469  (step_size_phi = 0.125\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974173  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.907501  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.214961\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12504504504504507  (step_size_phi = 0.125\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979813  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.912754  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.216206\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12540540540540543  (step_size_phi = 0.125\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985468  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.918023  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.217454\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12576576576576579  (step_size_phi = 0.126\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971136  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.042029  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.247935\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12612612612612614  (step_size_phi = 0.126\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976710  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.048009  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.249358\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1264864864864865  (step_size_phi = 0.126\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982299  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.054006  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.250785\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12684684684684686  (step_size_phi = 0.127\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987904  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.060021  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.252216\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1272072072072072  (step_size_phi = 0.127\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971733  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.895182  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.211986\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12756756756756757  (step_size_phi = 0.128\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977246  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.900261  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.213189\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12792792792792795  (step_size_phi = 0.128\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982775  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.905354  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.214395\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1282882882882883  (step_size_phi = 0.128\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988320  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.910462  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.215605\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12864864864864867  (step_size_phi = 0.129\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973426  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.055127  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.251096\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12900900900900902  (step_size_phi = 0.129\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978887  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.061047  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.252505\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12936936936936938  (step_size_phi = 0.129\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984364  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.066983  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.253917\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.12972972972972974  (step_size_phi = 0.130\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967641  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.880163  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.208368\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1300900900900901  (step_size_phi = 0.130\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973024  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.885059  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.209527\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13045045045045048  (step_size_phi = 0.130\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978422  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.889969  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.210690\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13081081081081083  (step_size_phi = 0.131\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983835  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.894893  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.211856\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1311711711711712  (step_size_phi = 0.131\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968497  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.061651  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.252694\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13153153153153155  (step_size_phi = 0.132\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973826  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.067493  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.254085\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1318918918918919  (step_size_phi = 0.132\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979169  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.073350  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.255479\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13225225225225226  (step_size_phi = 0.132\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984527  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.079223  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.256877\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13261261261261262  (step_size_phi = 0.133\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967153  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.867123  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.205215\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.132972972972973  (step_size_phi = 0.133\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972417  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.871842  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.206332\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13333333333333336  (step_size_phi = 0.133\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977694  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.876574  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.207452\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13369369369369372  (step_size_phi = 0.134\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982986  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.881318  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.208575\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13405405405405407  (step_size_phi = 0.134\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988293  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.886076  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.209701\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13441441441441443  (step_size_phi = 0.134\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972332  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.079156  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.256912\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13477477477477479  (step_size_phi = 0.135\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977552  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.084950  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.258291\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13513513513513514  (step_size_phi = 0.135\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982787  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.090759  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.259674\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1354954954954955  (step_size_phi = 0.135\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988035  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.096584  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.261061\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13585585585585588  (step_size_phi = 0.136\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969918  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.855495  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.202392\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13621621621621624  (step_size_phi = 0.136\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975071  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.860040  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.203467\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1365765765765766  (step_size_phi = 0.137\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980236  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.864596  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.204545\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13693693693693695  (step_size_phi = 0.137\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985416  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.869165  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.205626\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1372972972972973  (step_size_phi = 0.137\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968948  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.090146  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.259589\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13765765765765767  (step_size_phi = 0.138\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974041  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.095876  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.260954\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13801801801801802  (step_size_phi = 0.138\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979148  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.101621  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.262322\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1383783783783784  (step_size_phi = 0.138\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984268  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.107382  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.263693\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13873873873873876  (step_size_phi = 0.139\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965532  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.836004  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.197703\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13909909909909912  (step_size_phi = 0.139\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970554  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.840352  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.198731\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13945945945945948  (step_size_phi = 0.139\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975589  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.844712  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.199762\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.13981981981981983  (step_size_phi = 0.140\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980638  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.849083  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.200796\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1401801801801802  (step_size_phi = 0.140\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985699  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.853466  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.201832\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14054054054054055  (step_size_phi = 0.141\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968650  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.106173  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.263482\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1409009009009009  (step_size_phi = 0.141\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973623  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.111853  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.264835\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1412612612612613  (step_size_phi = 0.141\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978610  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.117548  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.266192\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14162162162162165  (step_size_phi = 0.142\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983609  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.123257  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.267551\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.141981981981982  (step_size_phi = 0.142\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.988621  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.128980  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.268915\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14234234234234236  (step_size_phi = 0.142\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969057  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.821675  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.194229\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14270270270270272  (step_size_phi = 0.143\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973970  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.825841  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.195214\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14306306306306307  (step_size_phi = 0.143\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978896  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.830017  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.196201\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14342342342342343  (step_size_phi = 0.143\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983833  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.834204  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.197191\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14378378378378381  (step_size_phi = 0.144\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966228  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.121528  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.267235\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14414414414414417  (step_size_phi = 0.144\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971077  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.127157  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.268576\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14450450450450453  (step_size_phi = 0.145\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975939  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.132799  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.269920\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14486486486486488  (step_size_phi = 0.145\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980812  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.138456  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.271268\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14522522522522524  (step_size_phi = 0.145\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985698  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.144127  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.272620\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1455855855855856  (step_size_phi = 0.146\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965437  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.799472  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.188890\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14594594594594595  (step_size_phi = 0.146\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970222  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.803435  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.189826\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14630630630630634  (step_size_phi = 0.146\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975019  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.807407  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.190765\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1466666666666667  (step_size_phi = 0.147\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979828  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.811390  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.191706\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14702702702702705  (step_size_phi = 0.147\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984649  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.815382  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.192649\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1473873873873874  (step_size_phi = 0.147\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966415  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.141900  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.272196\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14774774774774777  (step_size_phi = 0.148\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971147  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.147491  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.273529\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14810810810810812  (step_size_phi = 0.148\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975890  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.153095  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.274864\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14846846846846848  (step_size_phi = 0.148\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980645  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.158713  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.276204\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14882882882882884  (step_size_phi = 0.149\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985411  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.164345  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.277546\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14918918918918922  (step_size_phi = 0.149\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964353  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.777536  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.183612\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14954954954954958  (step_size_phi = 0.150\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969017  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.781296  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.184500\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.14990990990990993  (step_size_phi = 0.150\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973693  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.785066  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.185390\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1502702702702703  (step_size_phi = 0.150\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978379  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.788845  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.186283\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15063063063063065  (step_size_phi = 0.151\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983077  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.792633  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.187177\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.150990990990991  (step_size_phi = 0.151\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964246  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.161762  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.277027\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15135135135135136  (step_size_phi = 0.151\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968854  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.167314  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.278351\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15171171171171174  (step_size_phi = 0.152\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973473  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.172880  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.279678\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1520720720720721  (step_size_phi = 0.152\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978104  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.178458  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.281008\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15243243243243246  (step_size_phi = 0.152\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982745  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.184050  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.282342\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15279279279279281  (step_size_phi = 0.153\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.987397  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.189655  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.283678\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15315315315315317  (step_size_phi = 0.153\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965452  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.755318  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.178271\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15351351351351353  (step_size_phi = 0.154\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970001  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.758876  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.179111\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15387387387387388  (step_size_phi = 0.154\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974560  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.762443  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.179952\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15423423423423424  (step_size_phi = 0.154\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979130  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.766019  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.180796\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15459459459459463  (step_size_phi = 0.155\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983711  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.769602  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.181642\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15495495495495498  (step_size_phi = 0.155\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964209  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.186735  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.283026\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15531531531531534  (step_size_phi = 0.155\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968699  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.192261  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.284344\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1556756756756757  (step_size_phi = 0.156\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973199  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.197800  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.285665\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15603603603603605  (step_size_phi = 0.156\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977710  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.203352  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.286989\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1563963963963964  (step_size_phi = 0.156\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982231  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.208917  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.288316\n",
+      "=======================================================\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15675675675675677  (step_size_phi = 0.157\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986763  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.214494  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.289646\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15711711711711715  (step_size_phi = 0.157\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963952  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.728951  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.171959\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1574774774774775  (step_size_phi = 0.157\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968379  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.732299  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.172748\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15783783783783786  (step_size_phi = 0.158\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972816  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.735654  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.173540\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15819819819819822  (step_size_phi = 0.158\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977263  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.739017  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.174333\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15855855855855858  (step_size_phi = 0.159\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981720  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.742388  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.175128\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15891891891891893  (step_size_phi = 0.159\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986188  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.745766  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.175925\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1592792792792793  (step_size_phi = 0.159\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965955  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.216690  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.290105\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.15963963963963965  (step_size_phi = 0.160\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970330  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.222201  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.291419\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16000000000000003  (step_size_phi = 0.160\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974716  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.227725  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.292736\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1603603603603604  (step_size_phi = 0.160\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979112  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.233262  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.294057\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16072072072072074  (step_size_phi = 0.161\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983517  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.238811  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.295380\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1610810810810811  (step_size_phi = 0.161\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959859  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.698593  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.164719\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16144144144144146  (step_size_phi = 0.161\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964158  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.701722  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.165457\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16180180180180181  (step_size_phi = 0.162\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968467  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.704858  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.166197\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16216216216216217  (step_size_phi = 0.162\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972786  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.708001  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.166938\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16252252252252256  (step_size_phi = 0.163\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977114  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.711151  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.167681\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1628828828828829  (step_size_phi = 0.163\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981452  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.714308  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.168425\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16324324324324327  (step_size_phi = 0.163\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985800  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.717473  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.169171\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16360360360360363  (step_size_phi = 0.164\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964875  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.245705  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.296799\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16396396396396398  (step_size_phi = 0.164\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969131  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.251198  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.298108\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16432432432432434  (step_size_phi = 0.164\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973395  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.256704  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.299420\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1646846846846847  (step_size_phi = 0.165\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977669  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.262222  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.300735\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16504504504504508  (step_size_phi = 0.165\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981952  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.267752  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.302052\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16540540540540544  (step_size_phi = 0.165\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986245  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.273294  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.303373\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1657657657657658  (step_size_phi = 0.166\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961535  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.670296  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.157981\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16612612612612615  (step_size_phi = 0.166\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965720  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.673214  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.158669\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1664864864864865  (step_size_phi = 0.166\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969914  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.676137  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.159358\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16684684684684686  (step_size_phi = 0.167\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974117  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.679068  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.160049\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16720720720720725  (step_size_phi = 0.167\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978330  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.682004  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.160741\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1675675675675676  (step_size_phi = 0.168\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982551  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.684947  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.161434\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16792792792792796  (step_size_phi = 0.168\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960980  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.272918  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.302893\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16828828828828832  (step_size_phi = 0.168\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965109  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.278387  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.304194\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16864864864864867  (step_size_phi = 0.169\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969247  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.283868  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.305498\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16900900900900903  (step_size_phi = 0.169\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973393  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.289360  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.306805\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1693693693693694  (step_size_phi = 0.169\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977549  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.294865  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.308115\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.16972972972972977  (step_size_phi = 0.170\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981713  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.300381  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.309427\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17009009009009013  (step_size_phi = 0.170\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985886  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.305908  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.310743\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17045045045045049  (step_size_phi = 0.170\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960146  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.637674  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.150232\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17081081081081084  (step_size_phi = 0.171\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964210  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.640373  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.150868\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1711711711711712  (step_size_phi = 0.171\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968282  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.643078  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.151505\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17153153153153156  (step_size_phi = 0.172\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972364  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.645788  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.152144\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1718918918918919  (step_size_phi = 0.172\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976454  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.648505  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.152784\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17225225225225227  (step_size_phi = 0.172\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980552  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.651227  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.153425\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17261261261261265  (step_size_phi = 0.173\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984659  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.653954  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.154068\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.172972972972973  (step_size_phi = 0.173\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962285  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.307861  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.310730\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17333333333333337  (step_size_phi = 0.173\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966299  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.313316  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.312026\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17369369369369372  (step_size_phi = 0.174\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970321  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.318783  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.313325\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17405405405405408  (step_size_phi = 0.174\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974351  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.324261  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.314626\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17441441441441444  (step_size_phi = 0.174\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978390  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.329750  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.315930\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1747747747747748  (step_size_phi = 0.175\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982437  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.335250  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.317237\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17513513513513518  (step_size_phi = 0.175\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.986493  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.340762  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.318547\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17549549549549553  (step_size_phi = 0.175\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959636  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.603576  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.142126\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1758558558558559  (step_size_phi = 0.176\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963581  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.606057  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.142710\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17621621621621625  (step_size_phi = 0.176\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967534  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.608543  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.143296\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1765765765765766  (step_size_phi = 0.177\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971496  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.611035  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.143883\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17693693693693696  (step_size_phi = 0.177\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975465  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.613531  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.144470\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17729729729729732  (step_size_phi = 0.177\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979442  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.616033  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.145059\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17765765765765767  (step_size_phi = 0.178\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983428  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.618540  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.145650\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17801801801801806  (step_size_phi = 0.178\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960307  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.337957  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.317521\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17837837837837842  (step_size_phi = 0.178\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964199  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.343380  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.318808\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17873873873873877  (step_size_phi = 0.179\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968099  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.348813  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.320098\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17909909909909913  (step_size_phi = 0.179\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972006  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.354257  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.321390\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17945945945945949  (step_size_phi = 0.179\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975922  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.359712  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.322684\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.17981981981981984  (step_size_phi = 0.180\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979845  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.365179  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.323981\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1801801801801802  (step_size_phi = 0.180\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983776  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.370656  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.325281\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18054054054054058  (step_size_phi = 0.181\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955830  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.565520  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.133056\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18090090090090094  (step_size_phi = 0.181\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959650  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.567779  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.133587\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1812612612612613  (step_size_phi = 0.181\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963477  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.570044  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.134120\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18162162162162165  (step_size_phi = 0.182\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967312  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.572313  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.134654\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.181981981981982  (step_size_phi = 0.182\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971154  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.574586  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.135189\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18234234234234237  (step_size_phi = 0.182\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975004  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.576864  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.135725\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18270270270270272  (step_size_phi = 0.183\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978862  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.579146  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.136262\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1830630630630631  (step_size_phi = 0.183\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982727  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.581433  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.136800\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18342342342342347  (step_size_phi = 0.183\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958820  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.367426  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.324597\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18378378378378382  (step_size_phi = 0.184\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962591  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.372805  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.325874\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18414414414414418  (step_size_phi = 0.184\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966370  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.378193  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.327153\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18450450450450454  (step_size_phi = 0.185\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970156  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.383593  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.328435\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1848648648648649  (step_size_phi = 0.185\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973949  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.389003  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.329719\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18522522522522525  (step_size_phi = 0.185\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977750  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.394423  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.331005\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1855855855855856  (step_size_phi = 0.186\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981558  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.399854  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.332295\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.185945945945946  (step_size_phi = 0.186\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.985374  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.405296  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.333586\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18630630630630635  (step_size_phi = 0.186\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956132  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.528066  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.124071\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1866666666666667  (step_size_phi = 0.187\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959835  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.530110  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.124552\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18702702702702706  (step_size_phi = 0.187\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963544  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.532159  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.125033\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18738738738738742  (step_size_phi = 0.187\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967261  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.534212  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.125515\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18774774774774777  (step_size_phi = 0.188\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970984  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.536268  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.125998\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18810810810810813  (step_size_phi = 0.188\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974715  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.538329  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.126483\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18846846846846851  (step_size_phi = 0.188\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978454  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.540394  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.126968\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18882882882882887  (step_size_phi = 0.189\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982199  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.542462  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.127454\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18918918918918923  (step_size_phi = 0.189\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.957471  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.396455  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.332379\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18954954954954958  (step_size_phi = 0.190\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961122  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.401780  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.333647\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.18990990990990994  (step_size_phi = 0.190\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964780  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.407115  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.334917\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1902702702702703  (step_size_phi = 0.190\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968445  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.412460  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.336189\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19063063063063065  (step_size_phi = 0.191\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972117  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.417816  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.337464\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.190990990990991  (step_size_phi = 0.191\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975796  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.423181  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.338741\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1913513513513514  (step_size_phi = 0.191\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979481  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.428557  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.340020\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19171171171171175  (step_size_phi = 0.192\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983174  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.433942  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.341302\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1920720720720721  (step_size_phi = 0.192\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952675  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.486780  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.114122\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19243243243243247  (step_size_phi = 0.192\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956253  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.488608  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.114551\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19279279279279282  (step_size_phi = 0.193\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959838  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.490440  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.114980\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19315315315315318  (step_size_phi = 0.193\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963429  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.492275  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.115410\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19351351351351354  (step_size_phi = 0.194\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967028  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.494114  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.115841\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19387387387387392  (step_size_phi = 0.194\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970633  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.495956  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.116273\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19423423423423428  (step_size_phi = 0.194\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974244  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.497801  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.116706\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19459459459459463  (step_size_phi = 0.195\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977863  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.499650  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.117139\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.194954954954955  (step_size_phi = 0.195\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981488  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.501502  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.117573\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19531531531531535  (step_size_phi = 0.195\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955914  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.427768  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.341782\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1956756756756757  (step_size_phi = 0.196\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959445  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.433041  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.343045\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19603603603603606  (step_size_phi = 0.196\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962982  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.438324  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.344309\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19639639639639642  (step_size_phi = 0.196\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966526  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.443617  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.345576\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.1967567567567568  (step_size_phi = 0.197\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970076  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.448920  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.346846\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19711711711711716  (step_size_phi = 0.197\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973633  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.454232  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.348117\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19747747747747751  (step_size_phi = 0.197\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977196  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.459554  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.349391\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19783783783783787  (step_size_phi = 0.198\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980765  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.464886  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.350668\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19819819819819823  (step_size_phi = 0.198\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984342  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.470227  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.351946\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19855855855855858  (step_size_phi = 0.199\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952376  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.445478  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.104124\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19891891891891894  (step_size_phi = 0.199\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955836  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.447096  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.104503\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19927927927927933  (step_size_phi = 0.199\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959303  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.448717  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.104882\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.19963963963963968  (step_size_phi = 0.200\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962775  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.450342  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.105261\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20000000000000004  (step_size_phi = 0.200\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966254  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.451969  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.105642\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2003603603603604  (step_size_phi = 0.200\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969739  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.453599  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.106023\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20072072072072075  (step_size_phi = 0.201\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973230  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.455232  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.106404\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2010810810810811  (step_size_phi = 0.201\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976728  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.456868  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.106787\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20144144144144147  (step_size_phi = 0.201\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980232  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.458507  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.107170\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20180180180180185  (step_size_phi = 0.202\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953799  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.467190  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.354112\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2021621621621622  (step_size_phi = 0.202\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.957209  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.472435  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.355378\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20252252252252256  (step_size_phi = 0.203\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960624  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.477689  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.356646\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20288288288288292  (step_size_phi = 0.203\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964046  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.482952  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.357916\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20324324324324328  (step_size_phi = 0.203\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967473  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.488225  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.359189\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20360360360360363  (step_size_phi = 0.204\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970907  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.493507  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.360464\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.203963963963964  (step_size_phi = 0.204\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974347  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.498798  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.361741\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20432432432432435  (step_size_phi = 0.204\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977793  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.504099  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.363020\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20468468468468473  (step_size_phi = 0.205\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981245  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.509409  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.364302\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2050450450450451  (step_size_phi = 0.205\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984703  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.514729  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.365586\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20540540540540544  (step_size_phi = 0.205\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951189  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.402211  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.093677\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2057657657657658  (step_size_phi = 0.206\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954529  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.403623  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.094006\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20612612612612616  (step_size_phi = 0.206\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.957875  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.405038  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.094336\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20648648648648651  (step_size_phi = 0.206\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961227  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.406455  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.094666\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20684684684684687  (step_size_phi = 0.207\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964585  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.407875  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.094997\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20720720720720726  (step_size_phi = 0.207\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967949  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.409298  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.095328\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2075675675675676  (step_size_phi = 0.208\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971319  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.410723  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.095660\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20792792792792797  (step_size_phi = 0.208\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974695  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.412150  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.095992\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20828828828828833  (step_size_phi = 0.208\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978076  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.413580  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.096325\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20864864864864868  (step_size_phi = 0.209\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981463  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.415012  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.096659\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20900900900900904  (step_size_phi = 0.209\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954072  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.528126  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.371940\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2093693693693694  (step_size_phi = 0.209\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.957364  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.533400  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.373224\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.20972972972972975  (step_size_phi = 0.210\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960663  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.538683  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.374509\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21009009009009014  (step_size_phi = 0.210\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963967  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.543976  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.375798\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2104504504504505  (step_size_phi = 0.210\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967277  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.549277  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.377088\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21081081081081085  (step_size_phi = 0.211\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970592  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.554587  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.378380\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2111711711711712  (step_size_phi = 0.211\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973913  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.559906  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.379675\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21153153153153156  (step_size_phi = 0.212\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977240  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.565235  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.380972\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21189189189189192  (step_size_phi = 0.212\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980572  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.570572  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.382271\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21225225225225228  (step_size_phi = 0.212\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983910  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.575919  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.383572\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21261261261261266  (step_size_phi = 0.213\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948761  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.357312  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.082941\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21297297297297302  (step_size_phi = 0.213\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951980  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.358525  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.083223\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21333333333333337  (step_size_phi = 0.213\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955205  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.359739  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.083504\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21369369369369373  (step_size_phi = 0.214\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958434  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.360955  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.083787\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2140540540540541  (step_size_phi = 0.214\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961669  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.362174  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.084070\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21441441441441444  (step_size_phi = 0.214\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964910  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.363394  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.084353\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2147747747747748  (step_size_phi = 0.215\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968156  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.364617  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.084637\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21513513513513516  (step_size_phi = 0.215\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971408  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.365841  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.084921\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21549549549549554  (step_size_phi = 0.215\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974665  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.367068  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.085206\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2158558558558559  (step_size_phi = 0.216\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977927  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.368297  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.085491\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21621621621621626  (step_size_phi = 0.216\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949690  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.607773  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.393257\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2165765765765766  (step_size_phi = 0.217\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952858  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.613137  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.394569\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21693693693693697  (step_size_phi = 0.217\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956031  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.618510  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.395883\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21729729729729733  (step_size_phi = 0.217\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959210  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.623891  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.397200\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21765765765765768  (step_size_phi = 0.218\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962394  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.629282  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.398518\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21801801801801807  (step_size_phi = 0.218\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965584  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.634681  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.399839\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21837837837837842  (step_size_phi = 0.218\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968778  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.640090  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.401162\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21873873873873878  (step_size_phi = 0.219\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971978  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.645507  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.402487\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21909909909909914  (step_size_phi = 0.219\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975183  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.650933  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.403814\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2194594594594595  (step_size_phi = 0.219\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978394  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.656368  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.405144\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.21981981981981985  (step_size_phi = 0.220\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981610  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.661813  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.406475\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2201801801801802  (step_size_phi = 0.220\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.984831  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.667266  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.407809\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2205405405405406  (step_size_phi = 0.221\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947847  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.312459  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.072384\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22090090090090095  (step_size_phi = 0.221\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950947  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.313481  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.072621\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2212612612612613  (step_size_phi = 0.221\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954052  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.314505  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.072858\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22162162162162166  (step_size_phi = 0.222\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.957162  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.315530  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.073095\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22198198198198202  (step_size_phi = 0.222\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960278  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.316557  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.073333\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22234234234234238  (step_size_phi = 0.222\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963398  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.317586  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.073571\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22270270270270273  (step_size_phi = 0.223\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966523  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.318616  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.073810\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2230630630630631  (step_size_phi = 0.223\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969654  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.319648  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.074049\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22342342342342347  (step_size_phi = 0.223\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972789  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.320682  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.074289\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22378378378378383  (step_size_phi = 0.224\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975930  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.321717  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.074528\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2241441441441442  (step_size_phi = 0.224\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979075  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.322754  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.074769\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22450450450450454  (step_size_phi = 0.225\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949814  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.724738  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.420844\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2248648648648649  (step_size_phi = 0.225\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952866  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.730279  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.422196\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22522522522522526  (step_size_phi = 0.225\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955922  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.735829  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.423550\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2255855855855856  (step_size_phi = 0.226\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958984  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.741389  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.424907\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.225945945945946  (step_size_phi = 0.226\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962050  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.746957  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.426265\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22630630630630635  (step_size_phi = 0.226\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965121  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.752533  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.427626\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2266666666666667  (step_size_phi = 0.227\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968197  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.758119  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.428989\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22702702702702707  (step_size_phi = 0.227\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971278  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.763714  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.430354\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22738738738738742  (step_size_phi = 0.227\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974364  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.769317  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.431722\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22774774774774778  (step_size_phi = 0.228\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977455  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.774930  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.433091\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22810810810810814  (step_size_phi = 0.228\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980550  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.780551  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.434463\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2284684684684685  (step_size_phi = 0.228\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983651  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.786181  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.435837\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22882882882882888  (step_size_phi = 0.229\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944757  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.267262  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.061953\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22918918918918924  (step_size_phi = 0.229\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947735  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.268105  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.062148\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2295495495495496  (step_size_phi = 0.230\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950718  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.268949  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.062344\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.22990990990990995  (step_size_phi = 0.230\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953705  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.269794  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.062540\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2302702702702703  (step_size_phi = 0.230\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956697  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.270640  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.062736\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23063063063063066  (step_size_phi = 0.231\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959694  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.271488  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.062932\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23099099099099102  (step_size_phi = 0.231\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962695  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.272337  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.063129\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2313513513513514  (step_size_phi = 0.231\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965701  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.273187  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.063326\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23171171171171176  (step_size_phi = 0.232\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968712  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.274039  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.063524\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23207207207207212  (step_size_phi = 0.232\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971728  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.274892  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.063721\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23243243243243247  (step_size_phi = 0.232\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974748  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.275746  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.063920\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23279279279279283  (step_size_phi = 0.233\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977772  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.276602  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.064118\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2331531531531532  (step_size_phi = 0.233\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947535  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.860125  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.448480\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23351351351351354  (step_size_phi = 0.234\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950467  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.865880  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.449868\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23387387387387393  (step_size_phi = 0.234\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953403  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.871643  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.451257\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23423423423423428  (step_size_phi = 0.234\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956343  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.877415  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.452649\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23459459459459464  (step_size_phi = 0.235\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959288  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.883196  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.454043\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.234954954954955  (step_size_phi = 0.235\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962237  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.888986  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.455439\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23531531531531535  (step_size_phi = 0.235\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965191  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.894785  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.456837\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2356756756756757  (step_size_phi = 0.236\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968149  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.900593  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.458237\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23603603603603607  (step_size_phi = 0.236\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971112  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.906410  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.459640\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23639639639639642  (step_size_phi = 0.236\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974080  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.912235  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.461044\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2367567567567568  (step_size_phi = 0.237\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977052  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.918070  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.462451\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23711711711711717  (step_size_phi = 0.237\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980029  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.923913  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.463860\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23747747747747752  (step_size_phi = 0.237\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983010  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.929765  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.465271\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23783783783783788  (step_size_phi = 0.238\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942002  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.223675  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.052066\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23819819819819824  (step_size_phi = 0.238\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944859  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.224354  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.052224\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2385585585585586  (step_size_phi = 0.239\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947720  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.225033  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.052382\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23891891891891895  (step_size_phi = 0.239\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950585  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.225713  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.052541\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.23927927927927933  (step_size_phi = 0.239\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953455  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.226395  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.052699\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2396396396396397  (step_size_phi = 0.240\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956329  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.227077  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.052858\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24000000000000005  (step_size_phi = 0.240\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959207  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.227761  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.053017\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2403603603603604  (step_size_phi = 0.240\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962090  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.228445  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.053177\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24072072072072076  (step_size_phi = 0.241\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964977  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.229131  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.053336\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24108108108108112  (step_size_phi = 0.241\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967868  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.229817  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.053496\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24144144144144147  (step_size_phi = 0.241\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970764  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.230505  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.053656\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24180180180180183  (step_size_phi = 0.242\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973664  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.231193  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.053816\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24216216216216221  (step_size_phi = 0.242\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976568  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.231883  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.053977\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24252252252252257  (step_size_phi = 0.243\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.945332  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.996253  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.471265\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24288288288288293  (step_size_phi = 0.243\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948143  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.002190  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.472667\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24324324324324328  (step_size_phi = 0.243\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950959  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.008135  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.474070\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24360360360360364  (step_size_phi = 0.244\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953778  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.014090  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.475476\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.243963963963964  (step_size_phi = 0.244\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956602  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.020053  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.476884\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24432432432432435  (step_size_phi = 0.244\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959430  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.026025  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.478294\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24468468468468474  (step_size_phi = 0.245\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962263  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.032006  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.479706\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2450450450450451  (step_size_phi = 0.245\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965099  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.037996  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.481120\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24540540540540545  (step_size_phi = 0.245\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967940  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.043994  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.482536\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2457657657657658  (step_size_phi = 0.246\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970784  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.050002  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.483954\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24612612612612617  (step_size_phi = 0.246\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973633  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.056018  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.485374\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24648648648648652  (step_size_phi = 0.246\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976487  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.062043  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.486797\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24684684684684688  (step_size_phi = 0.247\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979344  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.068077  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.488221\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24720720720720724  (step_size_phi = 0.247\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982205  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.074119  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.489647\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24756756756756762  (step_size_phi = 0.248\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.938877  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.182594  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.042822\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24792792792792798  (step_size_phi = 0.248\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.941612  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.183126  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.042947\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24828828828828833  (step_size_phi = 0.248\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944352  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.183658  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.043072\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2486486486486487  (step_size_phi = 0.249\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947095  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.184192  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.043197\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24900900900900905  (step_size_phi = 0.249\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949842  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.184726  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.043322\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2493693693693694  (step_size_phi = 0.249\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952593  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.185261  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.043448\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.24972972972972976  (step_size_phi = 0.250\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955348  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.185797  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.043573\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25009009009009014  (step_size_phi = 0.250\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958107  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.186334  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.043699\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2504504504504505  (step_size_phi = 0.250\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960871  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.186871  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.043825\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25081081081081086  (step_size_phi = 0.251\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963638  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.187409  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.043951\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2511711711711712  (step_size_phi = 0.251\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966409  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.187948  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.044078\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25153153153153157  (step_size_phi = 0.252\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969184  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.188488  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.044204\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25189189189189193  (step_size_phi = 0.252\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971963  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.189028  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.044331\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2522522522522523  (step_size_phi = 0.252\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974746  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.189569  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.044458\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25261261261261264  (step_size_phi = 0.253\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977533  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.190111  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.044585\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.252972972972973  (step_size_phi = 0.253\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.945209  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.101549  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.482740\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25333333333333335  (step_size_phi = 0.253\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947903  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.107540  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.484117\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2536936936936937  (step_size_phi = 0.254\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950602  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.113540  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.485495\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25405405405405407  (step_size_phi = 0.254\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953305  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.119549  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.486875\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2544144144144144  (step_size_phi = 0.254\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956011  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.125566  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.488257\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2547747747747748  (step_size_phi = 0.255\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958721  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.131592  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.489641\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25513513513513514  (step_size_phi = 0.255\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961435  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.137626  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.491028\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25549549549549555  (step_size_phi = 0.255\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964153  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.143669  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.492416\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2558558558558559  (step_size_phi = 0.256\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966875  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.149720  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.493806\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25621621621621626  (step_size_phi = 0.256\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969600  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.155780  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.495198\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2565765765765766  (step_size_phi = 0.257\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972329  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.161848  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.496592\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.256936936936937  (step_size_phi = 0.257\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975063  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.167925  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.497987\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25729729729729733  (step_size_phi = 0.257\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977800  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.174011  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.499385\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2576576576576577  (step_size_phi = 0.258\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980540  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.180105  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.500785\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25801801801801805  (step_size_phi = 0.258\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983285  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.186207  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.502187\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2583783783783784  (step_size_phi = 0.258\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.937301  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.145266  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.034365\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25873873873873876  (step_size_phi = 0.259\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939917  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.145671  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.034461\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2590990990990991  (step_size_phi = 0.259\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942537  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.146077  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.034557\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2594594594594595  (step_size_phi = 0.259\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.945161  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.146484  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.034653\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.25981981981981983  (step_size_phi = 0.260\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947788  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.146891  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.034750\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2601801801801802  (step_size_phi = 0.260\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950419  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.147299  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.034846\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26054054054054054  (step_size_phi = 0.261\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953054  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.147707  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.034943\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26090090090090096  (step_size_phi = 0.261\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955692  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.148116  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.035039\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2612612612612613  (step_size_phi = 0.261\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958334  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.148526  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.035136\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26162162162162167  (step_size_phi = 0.262\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960979  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.148936  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.035233\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.261981981981982  (step_size_phi = 0.262\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963628  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.149346  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.035330\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2623423423423424  (step_size_phi = 0.262\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966281  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.149757  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.035428\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26270270270270274  (step_size_phi = 0.263\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968938  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.150169  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.035525\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2630630630630631  (step_size_phi = 0.263\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971598  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.150581  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.035623\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26342342342342345  (step_size_phi = 0.263\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974261  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.150994  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.035720\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2637837837837838  (step_size_phi = 0.264\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.940982  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.120286  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.473215\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26414414414414417  (step_size_phi = 0.264\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.943555  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.126084  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.474509\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2645045045045045  (step_size_phi = 0.265\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946131  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.131889  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.475804\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2648648648648649  (step_size_phi = 0.265\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948711  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.137701  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.477102\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26522522522522524  (step_size_phi = 0.265\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951294  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.143522  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.478401\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2655855855855856  (step_size_phi = 0.266\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953881  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.149351  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.479702\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26594594594594595  (step_size_phi = 0.266\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956471  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.155188  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.481004\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26630630630630636  (step_size_phi = 0.266\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959065  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.161032  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.482309\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2666666666666667  (step_size_phi = 0.267\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961662  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.166885  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.483615\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2670270270270271  (step_size_phi = 0.267\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964263  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.172745  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.484923\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26738738738738743  (step_size_phi = 0.267\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966867  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.178613  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.486233\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2677477477477478  (step_size_phi = 0.268\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969475  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.184490  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.487544\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26810810810810815  (step_size_phi = 0.268\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972087  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.190374  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.488857\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2684684684684685  (step_size_phi = 0.268\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974702  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.196266  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.490172\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26882882882882886  (step_size_phi = 0.269\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977320  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.202166  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.491489\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2691891891891892  (step_size_phi = 0.269\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979942  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.208074  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.492808\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26954954954954957  (step_size_phi = 0.270\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982567  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.213990  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.494128\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.26990990990990993  (step_size_phi = 0.270\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.933717  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.111703  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.026582\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2702702702702703  (step_size_phi = 0.270\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.936212  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.112002  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.026653\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27063063063063064  (step_size_phi = 0.271\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.938710  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.112301  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.026724\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.270990990990991  (step_size_phi = 0.271\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.941212  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.112600  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.026795\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2713513513513514  (step_size_phi = 0.271\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.943717  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.112899  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.026866\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27171171171171177  (step_size_phi = 0.272\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946225  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.113200  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.026938\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2720720720720721  (step_size_phi = 0.272\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948737  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.113500  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027009\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2724324324324325  (step_size_phi = 0.272\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951251  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.113801  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027081\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27279279279279284  (step_size_phi = 0.273\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953770  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.114102  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027153\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2731531531531532  (step_size_phi = 0.273\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956291  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.114404  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027224\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27351351351351355  (step_size_phi = 0.274\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958816  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.114706  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027296\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2738738738738739  (step_size_phi = 0.274\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961344  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.115008  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027368\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27423423423423426  (step_size_phi = 0.274\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963876  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.115311  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027440\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2745945945945946  (step_size_phi = 0.275\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966411  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.115614  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027513\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.274954954954955  (step_size_phi = 0.275\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968949  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.115918  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027585\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27531531531531533  (step_size_phi = 0.275\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971490  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.116222  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027657\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2756756756756757  (step_size_phi = 0.276\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974035  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.116527  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.027730\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27603603603603605  (step_size_phi = 0.276\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939694  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.037102  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.444452\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2763963963963964  (step_size_phi = 0.276\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942149  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.042424  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.445613\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2767567567567568  (step_size_phi = 0.277\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944607  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.047753  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.446776\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2771171171171172  (step_size_phi = 0.277\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947069  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.053090  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.447940\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27747747747747753  (step_size_phi = 0.277\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949534  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.058433  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.449106\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2778378378378379  (step_size_phi = 0.278\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952002  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.063783  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.450273\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27819819819819824  (step_size_phi = 0.278\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954473  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.069140  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.451442\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2785585585585586  (step_size_phi = 0.279\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956947  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.074504  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.452612\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27891891891891896  (step_size_phi = 0.279\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959425  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.079875  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.453784\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2792792792792793  (step_size_phi = 0.279\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961905  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.085252  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.454957\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.27963963963963967  (step_size_phi = 0.280\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964389  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.090637  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.456132\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28  (step_size_phi = 0.280\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966876  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.096029  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.457309\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2803603603603604  (step_size_phi = 0.280\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969367  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.101427  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.458486\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28072072072072074  (step_size_phi = 0.281\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971860  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.106833  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.459666\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2810810810810811  (step_size_phi = 0.281\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974357  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.112246  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.460847\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28144144144144145  (step_size_phi = 0.281\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976857  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.117665  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.462029\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2818018018018018  (step_size_phi = 0.282\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979360  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.123092  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.463213\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2821621621621622  (step_size_phi = 0.282\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981866  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.128525  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.464398\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2825225225225226  (step_size_phi = 0.283\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.929809  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.082546  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.019604\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28288288288288294  (step_size_phi = 0.283\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.932182  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.082757  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.019654\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2832432432432433  (step_size_phi = 0.283\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.934559  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.082968  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.019704\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28360360360360365  (step_size_phi = 0.284\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.936938  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.083179  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.019755\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.283963963963964  (step_size_phi = 0.284\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939321  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.083391  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.019805\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28432432432432436  (step_size_phi = 0.284\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.941706  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.083603  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.019855\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2846846846846847  (step_size_phi = 0.285\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944095  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.083815  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.019906\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2850450450450451  (step_size_phi = 0.285\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946486  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.084027  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.019956\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28540540540540543  (step_size_phi = 0.285\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948881  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.084240  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020006\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2857657657657658  (step_size_phi = 0.286\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951279  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.084452  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020057\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28612612612612615  (step_size_phi = 0.286\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953679  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.084666  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020108\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2864864864864865  (step_size_phi = 0.286\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956083  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.084879  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020158\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28684684684684686  (step_size_phi = 0.287\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958490  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.085093  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020209\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2872072072072072  (step_size_phi = 0.287\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960900  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.085307  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020260\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28756756756756763  (step_size_phi = 0.288\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963313  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.085521  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020311\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.287927927927928  (step_size_phi = 0.288\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965728  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.085735  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020362\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28828828828828834  (step_size_phi = 0.288\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968147  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.085950  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020413\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2886486486486487  (step_size_phi = 0.289\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970569  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.086165  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020464\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28900900900900905  (step_size_phi = 0.289\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972994  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.086380  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.020515\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2893693693693694  (step_size_phi = 0.289\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.937646  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.846584  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.401523\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.28972972972972977  (step_size_phi = 0.290\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939982  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.851186  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.402524\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2900900900900901  (step_size_phi = 0.290\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942322  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.855794  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.403526\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2904504504504505  (step_size_phi = 0.290\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944665  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.860407  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.404529\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29081081081081084  (step_size_phi = 0.291\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947010  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.865027  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.405534\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2911711711711712  (step_size_phi = 0.291\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949359  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.869652  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.406539\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29153153153153155  (step_size_phi = 0.292\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951710  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.874282  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.407546\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2918918918918919  (step_size_phi = 0.292\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954064  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.878919  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.408554\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29225225225225226  (step_size_phi = 0.292\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956422  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.883561  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.409564\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2926126126126126  (step_size_phi = 0.293\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958782  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.888209  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.410574\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.292972972972973  (step_size_phi = 0.293\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961145  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.892862  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.411586\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29333333333333333  (step_size_phi = 0.293\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963510  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.897522  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.412599\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2936936936936937  (step_size_phi = 0.294\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965879  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.902187  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.413614\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2940540540540541  (step_size_phi = 0.294\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968251  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.906858  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.414629\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29441441441441446  (step_size_phi = 0.294\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970626  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.911534  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.415646\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2947747747747748  (step_size_phi = 0.295\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973003  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.916217  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.416664\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2951351351351352  (step_size_phi = 0.295\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975384  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.920905  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.417684\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29549549549549553  (step_size_phi = 0.295\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977767  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.925598  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.418704\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2958558558558559  (step_size_phi = 0.296\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980153  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.930298  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.419726\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29621621621621624  (step_size_phi = 0.296\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982542  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.935003  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.420749\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2965765765765766  (step_size_phi = 0.297\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.926780  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.057991  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013577\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29693693693693696  (step_size_phi = 0.297\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.929034  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.058132  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013610\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2972972972972973  (step_size_phi = 0.297\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.931290  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.058274  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013643\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29765765765765767  (step_size_phi = 0.298\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.933549  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.058415  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013676\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.298018018018018  (step_size_phi = 0.298\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.935811  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.058556  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013709\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2983783783783784  (step_size_phi = 0.298\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.938075  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.058698  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013742\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29873873873873874  (step_size_phi = 0.299\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.940343  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.058840  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013775\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2990990990990991  (step_size_phi = 0.299\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942613  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.058982  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013809\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.2994594594594595  (step_size_phi = 0.299\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944885  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.059124  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013842\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.29981981981981987  (step_size_phi = 0.300\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947161  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.059267  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013875\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3001801801801802  (step_size_phi = 0.300\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949439  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.059409  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013909\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3005405405405406  (step_size_phi = 0.301\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951720  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.059552  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013942\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30090090090090094  (step_size_phi = 0.301\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954004  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.059695  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.013975\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3012612612612613  (step_size_phi = 0.301\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956290  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.059838  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.014009\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30162162162162165  (step_size_phi = 0.302\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958579  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.059981  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.014042\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.301981981981982  (step_size_phi = 0.302\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960871  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.060125  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.014076\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30234234234234236  (step_size_phi = 0.302\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963166  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.060268  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.014110\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3027027027027027  (step_size_phi = 0.303\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965463  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.060412  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.014143\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3030630630630631  (step_size_phi = 0.303\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967763  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.060556  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.014177\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30342342342342343  (step_size_phi = 0.303\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970066  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.060700  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.014211\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3037837837837838  (step_size_phi = 0.304\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972372  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.060844  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.014245\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30414414414414415  (step_size_phi = 0.304\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.936042  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.608619  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.362971\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3045045045045045  (step_size_phi = 0.305\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.938262  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.612433  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.363832\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3048648648648649  (step_size_phi = 0.305\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.940484  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.616251  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.364694\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30522522522522527  (step_size_phi = 0.305\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942708  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.620075  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.365556\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30558558558558563  (step_size_phi = 0.306\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944936  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.623902  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.366420\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.305945945945946  (step_size_phi = 0.306\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947166  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.627735  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.367285\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30630630630630634  (step_size_phi = 0.306\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949398  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.631571  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.368150\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3066666666666667  (step_size_phi = 0.307\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951633  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.635412  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.369017\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30702702702702706  (step_size_phi = 0.307\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953871  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.639258  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.369885\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3073873873873874  (step_size_phi = 0.307\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956112  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.643109  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.370754\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30774774774774777  (step_size_phi = 0.308\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958355  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.646963  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.371623\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3081081081081081  (step_size_phi = 0.308\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960600  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.650823  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.372494\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3084684684684685  (step_size_phi = 0.308\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962849  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.654686  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.373366\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30882882882882884  (step_size_phi = 0.309\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965100  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.658555  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.374239\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3091891891891892  (step_size_phi = 0.309\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967353  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.662428  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.375113\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.30954954954954955  (step_size_phi = 0.310\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969610  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.666305  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.375988\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3099099099099099  (step_size_phi = 0.310\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971868  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.670187  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.376864\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3102702702702703  (step_size_phi = 0.310\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974130  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.674073  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.377741\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3106306306306307  (step_size_phi = 0.311\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976394  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.677964  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.378619\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31099099099099103  (step_size_phi = 0.311\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978661  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.681860  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.379498\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3113513513513514  (step_size_phi = 0.311\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980930  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.685760  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.380378\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31171171171171175  (step_size_phi = 0.312\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.921092  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.037934  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008632\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3120720720720721  (step_size_phi = 0.312\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.923223  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038022  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008652\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31243243243243246  (step_size_phi = 0.312\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.925356  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038110  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008672\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3127927927927928  (step_size_phi = 0.313\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.927492  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038198  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008692\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3131531531531532  (step_size_phi = 0.313\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.929630  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038286  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008712\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31351351351351353  (step_size_phi = 0.314\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.931771  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038374  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008732\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3138738738738739  (step_size_phi = 0.314\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.933914  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038463  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008752\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31423423423423424  (step_size_phi = 0.314\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.936060  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038551  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008772\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3145945945945946  (step_size_phi = 0.315\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.938208  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038639  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008792\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31495495495495496  (step_size_phi = 0.315\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.940359  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038728  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008812\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3153153153153153  (step_size_phi = 0.315\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942512  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038817  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008833\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3156756756756757  (step_size_phi = 0.316\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944667  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038905  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008853\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3160360360360361  (step_size_phi = 0.316\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946825  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.038994  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008873\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31639639639639644  (step_size_phi = 0.316\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948986  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039083  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008893\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3167567567567568  (step_size_phi = 0.317\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951149  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039172  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008914\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31711711711711715  (step_size_phi = 0.317\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953314  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039261  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008934\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3174774774774775  (step_size_phi = 0.317\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955482  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039351  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008954\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31783783783783787  (step_size_phi = 0.318\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.957652  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039440  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008975\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3181981981981982  (step_size_phi = 0.318\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959825  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039530  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.008995\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3185585585585586  (step_size_phi = 0.319\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962000  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039619  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.009015\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31891891891891894  (step_size_phi = 0.319\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964178  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039709  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.009036\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3192792792792793  (step_size_phi = 0.319\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966358  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039799  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.009056\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.31963963963963965  (step_size_phi = 0.320\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968541  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039889  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.009077\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32  (step_size_phi = 0.320\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970726  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.039979  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.009097\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32036036036036036  (step_size_phi = 0.320\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.933546  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.436840  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.355405\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3207207207207207  (step_size_phi = 0.321\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.935647  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.440074  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.356205\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32108108108108113  (step_size_phi = 0.321\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.937751  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.443312  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.357006\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3214414414414415  (step_size_phi = 0.321\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939857  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.446554  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.357807\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32180180180180185  (step_size_phi = 0.322\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.941965  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.449799  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.358610\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3221621621621622  (step_size_phi = 0.322\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944076  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.453048  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.359414\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32252252252252256  (step_size_phi = 0.323\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946189  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.456300  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.360218\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3228828828828829  (step_size_phi = 0.323\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948305  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.459556  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.361024\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3232432432432433  (step_size_phi = 0.323\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950423  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.462816  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.361830\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32360360360360363  (step_size_phi = 0.324\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952543  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.466079  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.362637\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.323963963963964  (step_size_phi = 0.324\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954666  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.469346  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.363445\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32432432432432434  (step_size_phi = 0.324\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956791  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.472617  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.364254\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3246846846846847  (step_size_phi = 0.325\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958918  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.475891  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.365064\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32504504504504506  (step_size_phi = 0.325\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961048  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.479169  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.365875\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3254054054054054  (step_size_phi = 0.325\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963180  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.482451  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.366687\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32576576576576577  (step_size_phi = 0.326\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965315  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.485736  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.367499\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3261261261261262  (step_size_phi = 0.326\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967451  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.489025  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.368313\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32648648648648654  (step_size_phi = 0.326\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969591  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.492317  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.369127\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3268468468468469  (step_size_phi = 0.327\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971732  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.495614  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.369943\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32720720720720725  (step_size_phi = 0.327\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973876  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.498913  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.370759\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3275675675675676  (step_size_phi = 0.328\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976022  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.502217  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.371576\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32792792792792796  (step_size_phi = 0.328\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978171  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.505524  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.372394\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3282882882882883  (step_size_phi = 0.328\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980322  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.508834  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.373213\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3286486486486487  (step_size_phi = 0.329\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982475  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.512149  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.374033\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32900900900900903  (step_size_phi = 0.329\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.917748  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.022776  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.004976\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3293693693693694  (step_size_phi = 0.329\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.919760  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.022826  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.004987\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.32972972972972975  (step_size_phi = 0.330\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.921773  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.022876  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.004998\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3300900900900901  (step_size_phi = 0.330\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.923789  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.022926  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005009\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33045045045045046  (step_size_phi = 0.330\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.925807  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.022976  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005020\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3308108108108108  (step_size_phi = 0.331\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.927828  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023026  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005031\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3311711711711712  (step_size_phi = 0.331\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.929850  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023076  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005042\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3315315315315316  (step_size_phi = 0.332\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.931875  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023127  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005053\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33189189189189194  (step_size_phi = 0.332\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.933902  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023177  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005064\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3322522522522523  (step_size_phi = 0.332\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.935931  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023227  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005075\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33261261261261266  (step_size_phi = 0.333\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.937962  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023278  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005086\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.332972972972973  (step_size_phi = 0.333\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939996  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023328  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005097\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33333333333333337  (step_size_phi = 0.333\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942032  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023379  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005108\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3336936936936937  (step_size_phi = 0.334\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944070  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023429  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005119\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3340540540540541  (step_size_phi = 0.334\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946110  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023480  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005130\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33441441441441444  (step_size_phi = 0.334\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948152  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023531  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005141\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3347747747747748  (step_size_phi = 0.335\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950197  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023581  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005152\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33513513513513515  (step_size_phi = 0.335\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952243  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023632  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005163\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3354954954954955  (step_size_phi = 0.335\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954292  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023683  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005174\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33585585585585587  (step_size_phi = 0.336\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956343  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023734  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005185\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3362162162162162  (step_size_phi = 0.336\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958397  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023785  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005196\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3365765765765766  (step_size_phi = 0.337\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960452  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023836  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005207\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.336936936936937  (step_size_phi = 0.337\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962510  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023887  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005219\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33729729729729735  (step_size_phi = 0.337\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964570  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023938  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005230\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3376576576576577  (step_size_phi = 0.338\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966632  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.023989  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005241\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33801801801801806  (step_size_phi = 0.338\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968696  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.024040  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.005252\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3383783783783784  (step_size_phi = 0.338\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.930822  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.482274  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.408381\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3387387387387388  (step_size_phi = 0.339\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.932806  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.485433  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.409251\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33909909909909913  (step_size_phi = 0.339\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.934791  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.488595  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.410122\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3394594594594595  (step_size_phi = 0.339\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.936779  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.491761  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.410994\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.33981981981981985  (step_size_phi = 0.340\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.938769  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.494930  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.411867\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3401801801801802  (step_size_phi = 0.340\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.940761  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.498102  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.412741\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34054054054054056  (step_size_phi = 0.341\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942755  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.501278  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.413616\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3409009009009009  (step_size_phi = 0.341\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944752  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.504457  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.414492\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3412612612612613  (step_size_phi = 0.341\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946750  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.507639  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.415369\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34162162162162163  (step_size_phi = 0.342\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948751  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.510825  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.416246\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.341981981981982  (step_size_phi = 0.342\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950753  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.514014  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.417125\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3423423423423424  (step_size_phi = 0.342\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952758  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.517206  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.418005\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34270270270270276  (step_size_phi = 0.343\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954765  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.520402  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.418885\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3430630630630631  (step_size_phi = 0.343\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956774  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.523601  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.419767\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34342342342342347  (step_size_phi = 0.343\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958785  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.526804  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.420649\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3437837837837838  (step_size_phi = 0.344\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960798  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.530010  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.421532\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3441441441441442  (step_size_phi = 0.344\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962814  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.533219  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.422416\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34450450450450454  (step_size_phi = 0.345\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964831  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.536432  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.423301\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3448648648648649  (step_size_phi = 0.345\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966850  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.539648  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.424187\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34522522522522525  (step_size_phi = 0.345\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.968872  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.542867  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.425074\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3455855855855856  (step_size_phi = 0.346\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.970896  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.546090  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.425962\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34594594594594597  (step_size_phi = 0.346\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.972922  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.549316  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.426851\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3463063063063063  (step_size_phi = 0.346\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974950  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.552545  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.427741\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3466666666666667  (step_size_phi = 0.347\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976980  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.555778  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.428631\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34702702702702704  (step_size_phi = 0.347\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979012  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.559014  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.429523\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3473873873873874  (step_size_phi = 0.347\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981046  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.562254  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.430416\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3477477477477478  (step_size_phi = 0.348\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983083  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.565496  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.431309\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34810810810810816  (step_size_phi = 0.348\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.912746  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012246  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002550\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3484684684684685  (step_size_phi = 0.348\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.914637  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012271  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002555\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3488288288288289  (step_size_phi = 0.349\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.916529  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012297  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002561\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34918918918918923  (step_size_phi = 0.349\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.918424  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012322  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002566\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3495495495495496  (step_size_phi = 0.350\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.920321  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012348  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002571\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.34990990990990994  (step_size_phi = 0.350\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.922219  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012373  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002577\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3502702702702703  (step_size_phi = 0.350\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.924120  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012399  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002582\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35063063063063066  (step_size_phi = 0.351\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.926022  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012424  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002587\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.350990990990991  (step_size_phi = 0.351\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.927927  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012450  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002593\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35135135135135137  (step_size_phi = 0.351\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.929833  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012475  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002598\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3517117117117117  (step_size_phi = 0.352\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.931741  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012501  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002603\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3520720720720721  (step_size_phi = 0.352\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.933652  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012526  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002609\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35243243243243244  (step_size_phi = 0.352\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.935564  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012552  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002614\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3527927927927928  (step_size_phi = 0.353\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.937478  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012578  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002619\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3531531531531532  (step_size_phi = 0.353\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939394  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012604  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002625\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35351351351351357  (step_size_phi = 0.354\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.941312  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012629  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002630\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3538738738738739  (step_size_phi = 0.354\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.943232  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012655  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002635\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3542342342342343  (step_size_phi = 0.354\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.945154  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012681  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002641\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35459459459459464  (step_size_phi = 0.355\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947078  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012707  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002646\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.354954954954955  (step_size_phi = 0.355\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949004  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012732  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002651\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35531531531531535  (step_size_phi = 0.355\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950932  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012758  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002657\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3556756756756757  (step_size_phi = 0.356\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952862  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012784  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002662\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35603603603603606  (step_size_phi = 0.356\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954794  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012810  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002668\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3563963963963964  (step_size_phi = 0.356\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956728  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012836  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002673\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3567567567567568  (step_size_phi = 0.357\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958663  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012862  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002678\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35711711711711713  (step_size_phi = 0.357\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960601  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012888  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002684\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3574774774774775  (step_size_phi = 0.357\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962541  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012914  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002689\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35783783783783785  (step_size_phi = 0.358\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964482  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012940  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002695\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3581981981981982  (step_size_phi = 0.358\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.966426  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.012966  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.002700\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3585585585585586  (step_size_phi = 0.359\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.928110  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.881295  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.544280\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35891891891891897  (step_size_phi = 0.359\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.929976  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.885078  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.545375\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.35927927927927933  (step_size_phi = 0.359\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.931845  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.888865  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.546470\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3596396396396397  (step_size_phi = 0.360\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.933715  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.892656  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.547567\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36000000000000004  (step_size_phi = 0.360\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.935587  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.896451  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.548665\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3603603603603604  (step_size_phi = 0.360\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.937461  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.900250  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.549764\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36072072072072076  (step_size_phi = 0.361\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939337  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.904052  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.550864\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3610810810810811  (step_size_phi = 0.361\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.941215  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.907858  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.551965\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36144144144144147  (step_size_phi = 0.361\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.943094  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.911668  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.553067\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3618018018018018  (step_size_phi = 0.362\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944976  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.915482  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.554171\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3621621621621622  (step_size_phi = 0.362\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946859  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.919300  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.555275\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36252252252252254  (step_size_phi = 0.363\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948744  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.923121  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.556381\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3628828828828829  (step_size_phi = 0.363\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950631  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.926946  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.557488\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36324324324324325  (step_size_phi = 0.363\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952520  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.930775  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.558595\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36360360360360366  (step_size_phi = 0.364\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954411  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.934608  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.559704\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.363963963963964  (step_size_phi = 0.364\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956304  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.938445  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.560814\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3643243243243244  (step_size_phi = 0.364\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958199  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.942285  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.561925\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36468468468468473  (step_size_phi = 0.365\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960095  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.946129  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.563037\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3650450450450451  (step_size_phi = 0.365\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961993  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.949977  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.564151\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36540540540540545  (step_size_phi = 0.365\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963894  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.953829  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.565265\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3657657657657658  (step_size_phi = 0.366\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965796  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.957685  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.566381\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36612612612612616  (step_size_phi = 0.366\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967700  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.961544  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.567497\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3664864864864865  (step_size_phi = 0.366\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969606  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.965407  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.568615\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3668468468468469  (step_size_phi = 0.367\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971513  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.969274  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.569734\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36720720720720723  (step_size_phi = 0.367\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973423  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.973145  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.570853\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3675675675675676  (step_size_phi = 0.368\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.975334  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.977020  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.571974\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36792792792792794  (step_size_phi = 0.368\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.977248  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.980898  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.573096\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3682882882882883  (step_size_phi = 0.368\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.979163  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.984780  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.574220\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36864864864864866  (step_size_phi = 0.369\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.981080  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.988666  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.575344\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.36900900900900907  (step_size_phi = 0.369\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982999  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 1.992556  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.576469\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3693693693693694  (step_size_phi = 0.369\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.906115  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005745  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001141\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3697297297297298  (step_size_phi = 0.370\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.907884  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005757  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001143\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37009009009009014  (step_size_phi = 0.370\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.909655  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005768  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001145\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3704504504504505  (step_size_phi = 0.370\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.911427  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005779  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001147\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37081081081081085  (step_size_phi = 0.371\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.913201  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005790  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001149\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3711711711711712  (step_size_phi = 0.371\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.914977  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005802  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001152\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37153153153153157  (step_size_phi = 0.372\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.916755  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005813  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001154\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3718918918918919  (step_size_phi = 0.372\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.918534  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005824  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001156\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3722522522522523  (step_size_phi = 0.372\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.920315  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005836  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001158\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37261261261261264  (step_size_phi = 0.373\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.922097  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005847  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001161\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.372972972972973  (step_size_phi = 0.373\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.923882  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005858  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001163\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37333333333333335  (step_size_phi = 0.373\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.925668  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005869  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001165\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3736936936936937  (step_size_phi = 0.374\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.927456  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005881  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001167\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37405405405405406  (step_size_phi = 0.374\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.929245  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005892  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001170\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3744144144144145  (step_size_phi = 0.374\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.931037  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005903  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001172\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37477477477477483  (step_size_phi = 0.375\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.932830  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005915  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001174\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3751351351351352  (step_size_phi = 0.375\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.934625  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005926  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001176\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37549549549549555  (step_size_phi = 0.375\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.936421  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005938  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001179\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3758558558558559  (step_size_phi = 0.376\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.938219  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005949  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001181\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37621621621621626  (step_size_phi = 0.376\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.940019  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005960  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001183\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3765765765765766  (step_size_phi = 0.377\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.941821  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005972  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001185\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.376936936936937  (step_size_phi = 0.377\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.943624  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005983  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001188\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37729729729729733  (step_size_phi = 0.377\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.945429  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.005995  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001190\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3776576576576577  (step_size_phi = 0.378\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.947236  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006006  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001192\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37801801801801804  (step_size_phi = 0.378\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949045  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006018  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001195\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3783783783783784  (step_size_phi = 0.378\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.950855  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006029  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001197\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37873873873873876  (step_size_phi = 0.379\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.952667  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006041  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001199\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3790990990990991  (step_size_phi = 0.379\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.954481  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006052  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001201\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.37945945945945947  (step_size_phi = 0.379\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956296  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006064  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001204\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3798198198198199  (step_size_phi = 0.380\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958113  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006075  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001206\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38018018018018024  (step_size_phi = 0.380\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.959932  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006087  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001208\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3805405405405406  (step_size_phi = 0.381\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.961753  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006098  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001211\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38090090090090095  (step_size_phi = 0.381\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.963575  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.006110  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.001213\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3812612612612613  (step_size_phi = 0.381\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.925208  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.716502  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.771735\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38162162162162167  (step_size_phi = 0.382\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.926958  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.721640  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.773194\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.381981981981982  (step_size_phi = 0.382\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.928710  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.726782  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.774655\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3823423423423424  (step_size_phi = 0.382\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.930463  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.731930  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.776117\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38270270270270274  (step_size_phi = 0.383\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.932217  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.737082  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.777581\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3830630630630631  (step_size_phi = 0.383\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.933974  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.742239  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.779046\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38342342342342345  (step_size_phi = 0.383\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.935732  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.747401  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.780513\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3837837837837838  (step_size_phi = 0.384\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.937492  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.752567  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.781980\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38414414414414416  (step_size_phi = 0.384\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.939253  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.757739  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.783450\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3845045045045045  (step_size_phi = 0.385\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.941016  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.762915  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.784920\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3848648648648649  (step_size_phi = 0.385\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.942781  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.768097  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.786392\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3852252252252253  (step_size_phi = 0.385\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.944547  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.773283  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.787865\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38558558558558564  (step_size_phi = 0.386\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.946315  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.778474  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.789340\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.385945945945946  (step_size_phi = 0.386\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.948085  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.783670  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.790816\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38630630630630636  (step_size_phi = 0.386\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.949856  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.788870  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.792294\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3866666666666667  (step_size_phi = 0.387\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.951629  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.794076  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.793773\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38702702702702707  (step_size_phi = 0.387\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.953404  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.799286  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.795253\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3873873873873874  (step_size_phi = 0.387\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.955180  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.804502  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.796734\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3877477477477478  (step_size_phi = 0.388\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.956958  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.809722  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.798217\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38810810810810814  (step_size_phi = 0.388\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.958737  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.814947  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.799702\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3884684684684685  (step_size_phi = 0.388\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.960518  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.820176  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.801188\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38882882882882885  (step_size_phi = 0.389\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.962301  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.825411  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.802675\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3891891891891892  (step_size_phi = 0.389\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.964086  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.830651  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.804163\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.38954954954954957  (step_size_phi = 0.390\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.965872  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.835895  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.805653\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3899099099099099  (step_size_phi = 0.390\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.967660  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.841144  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.807144\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3902702702702703  (step_size_phi = 0.390\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.969449  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.846398  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.808637\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3906306306306307  (step_size_phi = 0.391\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.971240  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.851657  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.810131\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39099099099099105  (step_size_phi = 0.391\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.973033  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.856921  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.811626\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3913513513513514  (step_size_phi = 0.391\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.974828  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.862190  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.813123\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39171171171171176  (step_size_phi = 0.392\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.976624  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.867463  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.814621\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3920720720720721  (step_size_phi = 0.392\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.978421  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.872742  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.816121\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3924324324324325  (step_size_phi = 0.392\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.980221  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.878025  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.817622\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39279279279279283  (step_size_phi = 0.393\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.982022  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.883313  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.819124\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3931531531531532  (step_size_phi = 0.393\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.983825  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 2.888606  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.820628\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39351351351351355  (step_size_phi = 0.394\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.899081  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002245  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000430\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3938738738738739  (step_size_phi = 0.394\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.900728  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002249  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000430\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39423423423423426  (step_size_phi = 0.394\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.902377  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002253  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000431\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3945945945945946  (step_size_phi = 0.395\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.904027  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002257  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000432\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.394954954954955  (step_size_phi = 0.395\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.905679  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002261  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000433\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39531531531531533  (step_size_phi = 0.395\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.907333  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002265  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000434\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39567567567567574  (step_size_phi = 0.396\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.908988  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002269  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000434\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3960360360360361  (step_size_phi = 0.396\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.910644  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002274  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000435\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39639639639639646  (step_size_phi = 0.396\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.912302  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002278  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000436\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3967567567567568  (step_size_phi = 0.397\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.913962  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002282  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000437\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39711711711711717  (step_size_phi = 0.397\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.915623  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002286  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000438\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3974774774774775  (step_size_phi = 0.397\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.917285  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002290  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000438\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3978378378378379  (step_size_phi = 0.398\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.918949  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002294  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000439\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39819819819819824  (step_size_phi = 0.398\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.920615  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002298  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000440\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3985585585585586  (step_size_phi = 0.399\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.922282  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002303  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000441\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39891891891891895  (step_size_phi = 0.399\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.923950  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002307  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000441\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.3992792792792793  (step_size_phi = 0.399\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.925620  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002311  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000442\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.39963963963963967  (step_size_phi = 0.400\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.927292  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002315  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000443\n",
+      "=======================================================\n",
+      "\n",
+      "\n",
+      "=======================================================\n",
+      "  phi_cand = 1.0\"   r = 0.5\"   a = 0.1\"  b = 0.05\"\n",
+      "  step_size = 0.4  (step_size_phi = 0.400\")\n",
+      "  Integration box half-width: 6.0\"\n",
+      "  ∫ p(w|O_i) dA  = 0.928965  (should = 1)\n",
+      "  ∫ L(x-w)   dA  = 0.002319  (should ≈ 1)\n",
+      "  p(x|O_i)       = 0.000444\n",
+      "=======================================================\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Now let's iterate through different step_sizes for this scenario to determine \n",
+    "# the error for each size\n",
+    "# step_sizes = np.logspace(-3, -1, 100)\n",
+    "step_size_max_old = 2 * 3 * np.nanmin([a, b]) / np.nanmax(phi_cand)\n",
+    "step_size_max_new = np.nanmin([a, b]) / np.nanmax(phi_cand)\n",
+    "mmin = step_size_max_new - 0.01\n",
+    "mmax = step_size_max_old + 0.1\n",
+    "step_sizes = np.linspace(mmin, mmax, 1000)\n",
+    "pws = []\n",
+    "Ls = []\n",
+    "p_xOis = []\n",
+    "for step_size in step_sizes:\n",
+    "    g = build_grids(phi_cand, r, a, b, theta_prior, step_size, pa_deg)\n",
+    "    pws.append(g['check_pw'])\n",
+    "    Ls.append(g['check_L'])\n",
+    "    p_xOis.append(g['p_xOi'])\n",
+    "    \n",
+    "    print(f\"\\n{'='*55}\")\n",
+    "    print(f\"  phi_cand = {phi_cand}\\\"   r = {r}\\\"   a = {a}\\\"  b = {b}\\\"\")\n",
+    "    print(f\"  step_size = {step_size}  (step_size_phi = {g['step_size_phi']:.3f}\\\")\")\n",
+    "    print(f\"  Integration box half-width: {g['box_hwidth']:.1f}\\\"\")\n",
+    "    print(f\"  ∫ p(w|O_i) dA  = {g['check_pw']:.6f}  (should = 1)\")\n",
+    "    print(f\"  ∫ L(x-w)   dA  = {g['check_L']:.6f}  (should ≈ 1)\")\n",
+    "    print(f\"  p(x|O_i)       = {g['p_xOi']:.6f}\")\n",
+    "    print(f\"{'='*55}\\n\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "id": "f3ce5489",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5, 1.0, '100 by 50 mas, ang_size = 1.0\"')"
+      ]
+     },
+     "execution_count": 54,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 1000x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(10,6))\n",
+    "cycle = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
+    "\n",
+    "plt.scatter(step_sizes, pws, s=10, color=cycle[0], label=r'$p(w|O_i) \\sim 1$')\n",
+    "plt.scatter(step_sizes, Ls, s=10, color=cycle[1], label=r'$L(x{-}w) \\sim 1$')\n",
+    "plt.scatter(step_sizes, p_xOis, s=10, color=cycle[2], label=r'$p(x|O_i)$')\n",
+    "plt.axvline(x=step_size_max_old, color='black', linestyle='dashed', lw=2, label='step_size_max = 6 * min(a,b) / max(phi)')\n",
+    "plt.axvline(x=step_size_max_new, color='black', lw=2, label='step_size_max = min(a,b) / max(phi)')\n",
+    "plt.grid()\n",
+    "plt.xlabel(r'step_size (fraction of $\\phi$)')\n",
+    "plt.ylabel('Integrated Value')\n",
+    "plt.legend(fontsize=15)\n",
+    "plt.xlim([mmin, mmax])\n",
+    "plt.title(f'{int(1000*a):d} by {int(1000*b):d} mas, ang_size = {phi_cand:.1f}\"')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "id": "5bdb27b9",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.30000000000000004 0.05\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(step_size_max_old, step_size_max_new)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c8a4759d",
+   "metadata": {},
+   "source": [
+    "## Question 2: How should we set `step_size` based on `a`, `b`, and `ang_size`?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1aafaa95",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python (frbs2)",
+   "language": "python",
+   "name": "frbs2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.15"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From 1dd4f220b483ea6b4e32fe7bbfb17062ebef3994 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Wed, 27 May 2026 07:22:12 -0700
Subject: [PATCH 02/31] fussin

---
 astropath/bayesian.py                         |   4 +-
 calculations/step_size/Steps_big_galaxy.ipynb | 459 ++++++++++++++++++
 .../step_size/Steps_small_galaxy.ipynb        | 403 +++++++++++++++
 calculations/step_size/choose_step_size.ipynb |   6 +-
 docs/nb/FRB_example.ipynb                     |   2 +-
 5 files changed, 869 insertions(+), 5 deletions(-)
 create mode 100644 calculations/step_size/Steps_big_galaxy.ipynb
 create mode 100644 calculations/step_size/Steps_small_galaxy.ipynb

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index bd5dd7e..be055c1 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -66,7 +66,7 @@ def pw_Oi(theta, phi, theta_prior):
 
 def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords, 
                     cand_ang_size, theta_prior, step_size=0.1, 
-                    return_grids=False):
+                    return_grids=False, return_debug:bool=False):
     """
     Calculate p(x|O_i), the primary piece of the analysis
 
@@ -147,6 +147,8 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
     # Return
     if return_grids:
         return np.array(p_xOis), grids
+    elif return_debug:
+        return L_wx, p_wOi, grid_p, p_xOis[0]
     else:
         return np.array(p_xOis)
 
diff --git a/calculations/step_size/Steps_big_galaxy.ipynb b/calculations/step_size/Steps_big_galaxy.ipynb
new file mode 100644
index 0000000..e968deb
--- /dev/null
+++ b/calculations/step_size/Steps_big_galaxy.ipynb
@@ -0,0 +1,459 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d7d37368-c3bf-409a-baed-92aa8ae7e4da",
+   "metadata": {},
+   "source": [
+    "# Experimenting with step size for a galaxy bigger than the localization"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "437a70b4-3383-4150-bd32-5cf699eaf30b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# imports\n",
+    "from importlib import reload\n",
+    "import os\n",
+    "from importlib.resources import files as resource_files\n",
+    "\n",
+    "import numpy as np\n",
+    "\n",
+    "import pandas\n",
+    "\n",
+    "from astropy.coordinates import SkyCoord\n",
+    "from astropy.coordinates import offset_by\n",
+    "from astropy import units\n",
+    "#from astropy.io import fits\n",
+    "\n",
+    "from astropath import path\n",
+    "from astropath import localization\n",
+    "from astropath import bayesian"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fc737260-332c-4826-9175-43651e1b94fe",
+   "metadata": {},
+   "source": [
+    "# Convenience class"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "f3eb095d-fe29-423a-915b-da42129781e3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Path = path.PATH()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b33b8175-ba4d-498f-a771-d3ab84506125",
+   "metadata": {},
+   "source": [
+    "# Faux FRB"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "bca3fbb6-6452-4d56-b6ab-8a95242a7899",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<SkyCoord (ICRS): (ra, dec) in deg\n",
+       "    (326.10522917, -40.90002778)>"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "## FRB Coord\n",
+    "frb_coord = SkyCoord('21h44m25.255s -40d54m00.10s', frame='icrs')\n",
+    "frb_coord"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6bcba1af-5912-4e0f-ac65-d34fe7ad13dc",
+   "metadata": {},
+   "source": [
+    "# Prior"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "e6fb9982-fc3d-435c-a2ed-1852c72bac51",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "theta_prior = dict(max=6., PDF='exp', scale=1.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e104c1a9-2030-4280-bdf4-29a08eacca6e",
+   "metadata": {},
+   "source": [
+    "# Localization"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "id": "73d77df6-8227-4041-914a-a8128291ac9a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Small, but not tiny\n",
+    "eellipse = dict(a=0.5, b=0.5, theta=0.)\n",
+    "# Tiny\n",
+    "tiny_eellipse = dict(a=0.1, b=0.1, theta=0.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a961b5e7-32b5-4c87-9461-4def50dbc1d6",
+   "metadata": {},
+   "source": [
+    "## Build it"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "f6caf5ba-364a-48dd-9ef0-8750cf39f966",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Path.init_localization('eellipse', center_coord=frb_coord, eellipse=eellipse)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "5eaa3ff1-c8f8-40c8-849d-6e16ae5c7429",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'type': 'eellipse',\n",
+       " 'center_coord': <SkyCoord (ICRS): (ra, dec) in deg\n",
+       "     (326.10522917, -40.90002778)>,\n",
+       " 'eellipse': {'a': 0.5, 'b': 0.5, 'theta': 0.0}}"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Path.localiz"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fdcc22c3-f73f-4bf0-9dbb-76dba0905559",
+   "metadata": {},
+   "source": [
+    "# Galaxy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "133449b0-e2e5-4890-a5f0-6c982871997c",
+   "metadata": {},
+   "source": [
+    "## Position"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "8e95410a-225b-4d51-b106-100dd8977a1b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(<SkyCoord (ICRS): (ra, dec) in deg\n",
+       "     (326.10522917, -40.89988889)>,\n",
+       " <Angle 0.5 arcsec>)"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 0.5\" North\n",
+    "gal_coord = frb_coord.directional_offset_by(0.*units.deg, 0.5*units.arcsec)\n",
+    "gal_coord, gal_coord.separation(frb_coord).to('arcsec')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cdcbeee-d802-4df8-9b1b-b3fbb19abca8",
+   "metadata": {},
+   "source": [
+    "## Size"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "9aa4a92b-ac36-443c-b3b2-fb483b72b4f1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Medium (5\")\n",
+    "gal_size = np.array([5.]) # arcsec\n",
+    "box_hwidth = 50."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe49b2ec-ecd6-4617-aa25-b3cf76b7cd7f",
+   "metadata": {},
+   "source": [
+    "# Calculate"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c570e983-2743-4f8a-ac90-5b33a2942ebf",
+   "metadata": {},
+   "source": [
+    "## Tiny step_size"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "23333cb5-ccb0-4e95-bdc1-88723d227ab5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "reload(bayesian)\n",
+    "step_size = 0.05\n",
+    "L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(box_hwidth, Path.localiz, np.array([gal_coord]),\n",
+    "                    gal_size, theta_prior, step_size=step_size, return_debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "id": "c2b453a6-c164-45d1-9c0c-8c8aa08d682c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "L_wx: 0.9990002500065099\n",
+      "p_wO: 0.9989995728142178\n",
+      "p_xO: 0.005565669003159662\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f'L_wx: {np.sum(L_wx) * step_size**2}')\n",
+    "print(f'p_wO: {np.sum(p_wOi) * step_size**2}')\n",
+    "print(f'p_xO: {p_xOis}')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b385ce97-f46c-44ee-aaac-27580cf666d0",
+   "metadata": {},
+   "source": [
+    "## Vary it"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "id": "8c9bb78e-89f0-4707-af8e-103145d77e6b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "================================================\n",
+      "step: 0.05\n",
+      "L_wx: 0.9990002500065099\n",
+      "p_wO: 0.9989995728142178\n",
+      "p_xO_corr: 0.005571238849162845\n",
+      "p_xO: 0.005565669003159662\n",
+      "================================================\n",
+      "step: 0.1\n",
+      "L_wx: 0.9980009999805872\n",
+      "p_wO: 0.9980024191155251\n",
+      "p_xO_corr: 0.005576787526152111\n",
+      "p_xO: 0.005565639527779072\n",
+      "================================================\n",
+      "step: 0.25\n",
+      "L_wx: 0.9950062499888919\n",
+      "p_wO: 0.9950197864401361\n",
+      "p_xO_corr: 0.005593068199721013\n",
+      "p_xO: 0.005565137815336528\n",
+      "================================================\n",
+      "step: 0.5\n",
+      "L_wx: 0.9900249871353524\n",
+      "p_wO: 0.9899999465857889\n",
+      "p_xO_corr: 0.0056171414167946665\n",
+      "p_xO: 0.005561110358899594\n",
+      "================================================\n",
+      "step: 1.0\n",
+      "L_wx: 0.9492423957451299\n",
+      "p_wO: 0.9801137413800345\n",
+      "p_xO_corr: 0.005598644562157263\n",
+      "p_xO: 0.005314470777107605\n",
+      "================================================\n",
+      "step: 5.0\n",
+      "L_wx: 5.936931936520572e-11\n",
+      "p_wO: 0.8927383033791967\n",
+      "p_xO_corr: 0.003407067919875997\n",
+      "p_xO: 2.0227530343406521e-13\n"
+     ]
+    }
+   ],
+   "source": [
+    "Path.init_localization('eellipse', center_coord=frb_coord, eellipse=eellipse)\n",
+    "Path.localiz\n",
+    "for step_size in [0.05, 0.1, 0.25, 0.5, 1., 5.]:\n",
+    "    L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(box_hwidth, Path.localiz, np.array([gal_coord]),\n",
+    "                    gal_size, theta_prior, step_size=step_size, return_debug=True)\n",
+    "    print('================================================')\n",
+    "    print(f'step: {step_size}')\n",
+    "    print(f'L_wx: {np.sum(L_wx) * step_size**2}')\n",
+    "    print(f'p_wO: {np.sum(p_wOi) * step_size**2}')\n",
+    "    print(f'p_xO_corr: {p_xOis/np.sum(L_wx)/step_size**2}')\n",
+    "    print(f'p_xO: {p_xOis}')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0bf9d0b-2b25-4214-a99c-82309657d956",
+   "metadata": {},
+   "source": [
+    "# Tiny localization, 5\" galaxy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "id": "6cf80d82-8175-4276-a7a8-d11dead4ddd0",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "================================================\n",
+      "step: 0.02\n",
+      "L_wx: 0.9996000399631986\n",
+      "p_wO: 0.9995974938858885\n",
+      "p_xO: 0.005851396503041362\n",
+      "p_xO_corr: 0.005853737764212962\n",
+      "================================================\n",
+      "step: 0.05\n",
+      "L_wx: 0.9990002500317912\n",
+      "p_wO: 0.9989995728142178\n",
+      "p_xO: 0.005851396502948485\n",
+      "p_xO_corr: 0.005857252290739943\n",
+      "================================================\n",
+      "step: 0.1\n",
+      "L_wx: 0.9980009889120542\n",
+      "p_wO: 0.9980024191155251\n",
+      "p_xO: 0.00585139640804566\n",
+      "p_xO_corr: 0.00586311684362599\n",
+      "================================================\n",
+      "step: 0.25\n",
+      "L_wx: 0.8306016683369597\n",
+      "p_wO: 0.9950197864401361\n",
+      "p_xO: 0.00487868135693966\n",
+      "p_xO_corr: 0.0058736715117702724\n",
+      "================================================\n",
+      "step: 0.5\n",
+      "L_wx: 0.028849033861050546\n",
+      "p_wO: 0.9899999465857889\n",
+      "p_xO: 0.0001685103560061478\n",
+      "p_xO_corr: 0.0058411091621912445\n",
+      "================================================\n",
+      "step: 1.0\n",
+      "L_wx: 5.32193597973942e-10\n",
+      "p_wO: 0.9801137413800345\n",
+      "p_xO: 2.9945296714021977e-12\n",
+      "p_xO_corr: 0.005626767557524847\n",
+      "================================================\n",
+      "step: 5.0\n",
+      "L_wx: 2.7788932288980924e-298\n",
+      "p_wO: 0.8927383033791967\n",
+      "p_xO: 9.465433682953108e-301\n",
+      "p_xO_corr: 0.0034061883286917115\n"
+     ]
+    }
+   ],
+   "source": [
+    "Path.init_localization('eellipse', center_coord=frb_coord, eellipse=tiny_eellipse)\n",
+    "Path.localiz\n",
+    "for step_size in [0.02, 0.05, 0.1, 0.25, 0.5, 1., 5.]:\n",
+    "    L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(box_hwidth, Path.localiz, np.array([gal_coord]),\n",
+    "                    gal_size, theta_prior, step_size=step_size, return_debug=True)\n",
+    "    print('================================================')\n",
+    "    print(f'step: {step_size}')\n",
+    "    print(f'L_wx: {np.sum(L_wx) * step_size**2}')\n",
+    "    print(f'p_wO: {np.sum(p_wOi) * step_size**2}')\n",
+    "    print(f'p_xO: {p_xOis}')\n",
+    "    print(f'p_xO_corr: {p_xOis/np.sum(L_wx)/step_size**2}')\n",
+    "    #print(f'p_xO_norm_norm: {p_xOis/np.sum(L_wx)/np.sum(p_wOi)/step_size**4}')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "96193089-8446-4a6c-911b-d10b1fe40347",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.14.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/calculations/step_size/Steps_small_galaxy.ipynb b/calculations/step_size/Steps_small_galaxy.ipynb
new file mode 100644
index 0000000..876ae6c
--- /dev/null
+++ b/calculations/step_size/Steps_small_galaxy.ipynb
@@ -0,0 +1,403 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d7d37368-c3bf-409a-baed-92aa8ae7e4da",
+   "metadata": {},
+   "source": [
+    "# Experimenting with step size for a galaxy smaller than the ellipse"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "437a70b4-3383-4150-bd32-5cf699eaf30b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# imports\n",
+    "from importlib import reload\n",
+    "import os\n",
+    "from importlib.resources import files as resource_files\n",
+    "\n",
+    "import numpy as np\n",
+    "\n",
+    "import pandas\n",
+    "\n",
+    "from astropy.coordinates import SkyCoord\n",
+    "from astropy.coordinates import offset_by\n",
+    "from astropy import units\n",
+    "#from astropy.io import fits\n",
+    "\n",
+    "from astropath import path\n",
+    "from astropath import localization\n",
+    "from astropath import bayesian"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fc737260-332c-4826-9175-43651e1b94fe",
+   "metadata": {},
+   "source": [
+    "# Convenience class"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "f3eb095d-fe29-423a-915b-da42129781e3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Path = path.PATH()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b33b8175-ba4d-498f-a771-d3ab84506125",
+   "metadata": {},
+   "source": [
+    "# Faux FRB"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "bca3fbb6-6452-4d56-b6ab-8a95242a7899",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<SkyCoord (ICRS): (ra, dec) in deg\n",
+       "    (326.10522917, -40.90002778)>"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "## FRB Coord\n",
+    "frb_coord = SkyCoord('21h44m25.255s -40d54m00.10s', frame='icrs')\n",
+    "frb_coord"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6bcba1af-5912-4e0f-ac65-d34fe7ad13dc",
+   "metadata": {},
+   "source": [
+    "# Prior"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "e6fb9982-fc3d-435c-a2ed-1852c72bac51",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "theta_prior = dict(max=6., PDF='exp', scale=1.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e104c1a9-2030-4280-bdf4-29a08eacca6e",
+   "metadata": {},
+   "source": [
+    "# Localization"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "73d77df6-8227-4041-914a-a8128291ac9a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Small, but not tiny\n",
+    "eellipse = dict(a=5, b=5, theta=0.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a961b5e7-32b5-4c87-9461-4def50dbc1d6",
+   "metadata": {},
+   "source": [
+    "## Build it"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "f6caf5ba-364a-48dd-9ef0-8750cf39f966",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Path.init_localization('eellipse', center_coord=frb_coord, eellipse=eellipse)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "5eaa3ff1-c8f8-40c8-849d-6e16ae5c7429",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'type': 'eellipse',\n",
+       " 'center_coord': <SkyCoord (ICRS): (ra, dec) in deg\n",
+       "     (326.10522917, -40.90002778)>,\n",
+       " 'eellipse': {'a': 5, 'b': 5, 'theta': 0.0}}"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Path.localiz"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fdcc22c3-f73f-4bf0-9dbb-76dba0905559",
+   "metadata": {},
+   "source": [
+    "# Galaxy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "133449b0-e2e5-4890-a5f0-6c982871997c",
+   "metadata": {},
+   "source": [
+    "## Position"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "8e95410a-225b-4d51-b106-100dd8977a1b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(<SkyCoord (ICRS): (ra, dec) in deg\n",
+       "     (326.10522917, -40.89975)>,\n",
+       " <Angle 1. arcsec>)"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 1.0\" North\n",
+    "gal_coord = frb_coord.directional_offset_by(0.*units.deg, 1.0*units.arcsec)\n",
+    "gal_coord, gal_coord.separation(frb_coord).to('arcsec')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cdcbeee-d802-4df8-9b1b-b3fbb19abca8",
+   "metadata": {},
+   "source": [
+    "## Size"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "9aa4a92b-ac36-443c-b3b2-fb483b72b4f1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "small_gal_size = np.array([1.]) # arcsec\n",
+    "tiny_gal_size = np.array([0.2]) # arcsec\n",
+    "box_hwidth = 50."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe49b2ec-ecd6-4617-aa25-b3cf76b7cd7f",
+   "metadata": {},
+   "source": [
+    "# Calculate"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b385ce97-f46c-44ee-aaac-27580cf666d0",
+   "metadata": {},
+   "source": [
+    "## Small galaxy (1\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "8c9bb78e-89f0-4707-af8e-103145d77e6b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "================================================\n",
+      "step: 0.01\n",
+      "L_wx: 0.9998000103183573\n",
+      "p_wO: 0.9997974697127257\n",
+      "p_xO: 0.005678161376930544\n",
+      "p_xO_corr: 0.005679311609542346\n",
+      "================================================\n",
+      "step: 0.1\n",
+      "L_wx: 0.998001000318597\n",
+      "p_wO: 0.9980224620716001\n",
+      "p_xO: 0.005678195745918647\n",
+      "p_xO_corr: 0.005689446842841982\n",
+      "================================================\n",
+      "step: 0.25\n",
+      "L_wx: 0.995006250316858\n",
+      "p_wO: 0.9949216063486281\n",
+      "p_xO: 0.0056773558179761905\n",
+      "p_xO_corr: 0.005706334832562478\n",
+      "================================================\n",
+      "step: 0.5\n",
+      "L_wx: 0.9900250003138782\n",
+      "p_wO: 0.9886994904374402\n",
+      "p_xO: 0.0056697174162953674\n",
+      "p_xO_corr: 0.005734520419128423\n",
+      "================================================\n",
+      "step: 1.0\n",
+      "L_wx: 0.9801000003123983\n",
+      "p_wO: 0.9702169732356216\n",
+      "p_xO: 0.00561310714089473\n",
+      "p_xO_corr: 0.005785414289522599\n",
+      "================================================\n",
+      "step: 5.0\n",
+      "L_wx: 0.9024999341095425\n",
+      "p_wO: 0.457497692474131\n",
+      "p_xO: 0.0024463480206865554\n",
+      "p_xO_corr: 0.005347235758626002\n"
+     ]
+    }
+   ],
+   "source": [
+    "for step_size in [0.01, 0.1, 0.25, 0.5, 1., 5.]:\n",
+    "    L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(box_hwidth, Path.localiz, np.array([gal_coord]),\n",
+    "                    small_gal_size, theta_prior, step_size=step_size, return_debug=True)\n",
+    "    print('================================================')\n",
+    "    print(f'step: {step_size}')\n",
+    "    print(f'L_wx: {np.sum(L_wx) * step_size**2}')\n",
+    "    print(f'p_wO: {np.sum(p_wOi) * step_size**2}')\n",
+    "    print(f'p_xO: {p_xOis}')\n",
+    "    print(f'p_xO_corr: {p_xOis/np.sum(p_wOi)/step_size**2}')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0bf9d0b-2b25-4214-a99c-82309657d956",
+   "metadata": {},
+   "source": [
+    "# Tiny galaxy (0.2\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "6cf80d82-8175-4276-a7a8-d11dead4ddd0",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "================================================\n",
+      "step: 0.01\n",
+      "L_wx: 0.9998000103183573\n",
+      "p_wO: 0.9998049191069248\n",
+      "p_xO: 0.006214941133239931\n",
+      "p_xO_corr: 0.006216153786072012\n",
+      "================================================\n",
+      "step: 0.05\n",
+      "L_wx: 0.9990002503180448\n",
+      "p_wO: 0.998734557460303\n",
+      "p_xO: 0.00621326369200773\n",
+      "p_xO_corr: 0.00622113618237816\n",
+      "================================================\n",
+      "step: 0.1\n",
+      "L_wx: 0.998001000318597\n",
+      "p_wO: 0.9963147603287327\n",
+      "p_xO: 0.00620441779104315\n",
+      "p_xO_corr: 0.006227367131443492\n",
+      "================================================\n",
+      "step: 0.25\n",
+      "L_wx: 0.995006250316858\n",
+      "p_wO: 0.9775937336096671\n",
+      "p_xO: 0.006105245905153129\n",
+      "p_xO_corr: 0.006245177004776943\n",
+      "================================================\n",
+      "step: 0.5\n",
+      "L_wx: 0.9900250003138782\n",
+      "p_wO: 0.8572364100422724\n",
+      "p_xO: 0.005378097137839817\n",
+      "p_xO_corr: 0.006273761910759962\n",
+      "================================================\n",
+      "step: 1.0\n",
+      "L_wx: 0.9801000003123983\n",
+      "p_wO: 0.455664596376793\n",
+      "p_xO: 0.002873215741084444\n",
+      "p_xO_corr: 0.006305549660717017\n"
+     ]
+    }
+   ],
+   "source": [
+    "for step_size in [0.01, 0.05, 0.1, 0.25, 0.5, 1.]:#, 5.]:\n",
+    "    L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(box_hwidth, Path.localiz, np.array([gal_coord]),\n",
+    "                    tiny_gal_size, theta_prior, step_size=step_size, return_debug=True)\n",
+    "    print('================================================')\n",
+    "    print(f'step: {step_size}')\n",
+    "    print(f'L_wx: {np.sum(L_wx) * step_size**2}')\n",
+    "    print(f'p_wO: {np.sum(p_wOi) * step_size**2}')\n",
+    "    print(f'p_xO: {p_xOis}')\n",
+    "    print(f'p_xO_corr: {p_xOis/np.sum(p_wOi)/step_size**2}')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "96193089-8446-4a6c-911b-d10b1fe40347",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.14.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/calculations/step_size/choose_step_size.ipynb b/calculations/step_size/choose_step_size.ipynb
index 0d28670..11c97d9 100644
--- a/calculations/step_size/choose_step_size.ipynb
+++ b/calculations/step_size/choose_step_size.ipynb
@@ -10643,9 +10643,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python (frbs2)",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
-   "name": "frbs2"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -10657,7 +10657,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.15"
+   "version": "3.14.5"
   }
  },
  "nbformat": 4,
diff --git a/docs/nb/FRB_example.ipynb b/docs/nb/FRB_example.ipynb
index bfc0c0d..4b26f17 100644
--- a/docs/nb/FRB_example.ipynb
+++ b/docs/nb/FRB_example.ipynb
@@ -709,7 +709,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.5"
+   "version": "3.14.5"
   }
  },
  "nbformat": 4,

From 6e18ed207d8921e499331ce5251f92ac0ae7a066 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 28 May 2026 10:51:19 -0700
Subject: [PATCH 03/31] mo

---
 calculations/step_size/Steps_small_galaxy.ipynb | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/calculations/step_size/Steps_small_galaxy.ipynb b/calculations/step_size/Steps_small_galaxy.ipynb
index 876ae6c..e8ef066 100644
--- a/calculations/step_size/Steps_small_galaxy.ipynb
+++ b/calculations/step_size/Steps_small_galaxy.ipynb
@@ -244,7 +244,9 @@
    "cell_type": "code",
    "execution_count": 24,
    "id": "8c9bb78e-89f0-4707-af8e-103145d77e6b",
-   "metadata": {},
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "name": "stdout",

From 9d85c3bd085aef62edee20803d629074f87c2419 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 05:20:25 -0700
Subject: [PATCH 04/31] profile

---
 astropath/bayesian.py                  |   2 +-
 calculations/step_size/Profiling.ipynb | 459 +++++++++++++++++++++++++
 2 files changed, 460 insertions(+), 1 deletion(-)
 create mode 100644 calculations/step_size/Profiling.ipynb

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index be055c1..1406cf5 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -119,7 +119,7 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
     ra = localiz['center_coord'].ra.deg + \
         xcoord/3600. / np.cos(localiz['center_coord'].dec).value
     dec = localiz['center_coord'].dec.deg + ycoord/3600.
-    L_wx = localization.calc_LWx(ra, dec, localiz) 
+    L_wx = localization.calc_LWx(ra, dec, localiz)
 
     p_xOis, grids = [], []
     # TODO -- multiprocess this
diff --git a/calculations/step_size/Profiling.ipynb b/calculations/step_size/Profiling.ipynb
new file mode 100644
index 0000000..baff2a6
--- /dev/null
+++ b/calculations/step_size/Profiling.ipynb
@@ -0,0 +1,459 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d7d37368-c3bf-409a-baed-92aa8ae7e4da",
+   "metadata": {},
+   "source": [
+    "# Profiling for PATH"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "437a70b4-3383-4150-bd32-5cf699eaf30b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# imports\n",
+    "from importlib import reload\n",
+    "import os\n",
+    "from importlib.resources import files as resource_files\n",
+    "\n",
+    "import numpy as np\n",
+    "\n",
+    "import pandas\n",
+    "\n",
+    "from astropy.coordinates import SkyCoord\n",
+    "from astropy.coordinates import offset_by\n",
+    "from astropy import units\n",
+    "#from astropy.io import fits\n",
+    "\n",
+    "from astropath import path\n",
+    "from astropath import localization\n",
+    "from astropath import bayesian"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fc737260-332c-4826-9175-43651e1b94fe",
+   "metadata": {},
+   "source": [
+    "# Convenience class"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "f3eb095d-fe29-423a-915b-da42129781e3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Path = path.PATH()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b33b8175-ba4d-498f-a771-d3ab84506125",
+   "metadata": {},
+   "source": [
+    "# Faux FRB"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "bca3fbb6-6452-4d56-b6ab-8a95242a7899",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<SkyCoord (ICRS): (ra, dec) in deg\n",
+       "    (326.10522917, -40.90002778)>"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "## FRB Coord\n",
+    "frb_coord = SkyCoord('21h44m25.255s -40d54m00.10s', frame='icrs')\n",
+    "frb_coord"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6bcba1af-5912-4e0f-ac65-d34fe7ad13dc",
+   "metadata": {},
+   "source": [
+    "# Prior"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "e6fb9982-fc3d-435c-a2ed-1852c72bac51",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "theta_prior = dict(max=6., PDF='exp', scale=1.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e104c1a9-2030-4280-bdf4-29a08eacca6e",
+   "metadata": {},
+   "source": [
+    "# Localization"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "73d77df6-8227-4041-914a-a8128291ac9a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Small, but not tiny\n",
+    "eellipse = dict(a=5, b=5, theta=0.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a961b5e7-32b5-4c87-9461-4def50dbc1d6",
+   "metadata": {},
+   "source": [
+    "## Build it"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "f6caf5ba-364a-48dd-9ef0-8750cf39f966",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Path.init_localization('eellipse', center_coord=frb_coord, eellipse=eellipse)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "5eaa3ff1-c8f8-40c8-849d-6e16ae5c7429",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'type': 'eellipse',\n",
+       " 'center_coord': <SkyCoord (ICRS): (ra, dec) in deg\n",
+       "     (326.10522917, -40.90002778)>,\n",
+       " 'eellipse': {'a': 5, 'b': 5, 'theta': 0.0}}"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Path.localiz"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fdcc22c3-f73f-4bf0-9dbb-76dba0905559",
+   "metadata": {},
+   "source": [
+    "# Galaxies"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "133449b0-e2e5-4890-a5f0-6c982871997c",
+   "metadata": {},
+   "source": [
+    "## Positions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "8e95410a-225b-4d51-b106-100dd8977a1b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# 1.0\" North, 1.0\" East\n",
+    "gal_coord1 = frb_coord.directional_offset_by(0.*units.deg, 1.0*units.arcsec)\n",
+    "gal_coord2 = frb_coord.directional_offset_by(90.*units.deg, 1.0*units.arcsec)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cdcbeee-d802-4df8-9b1b-b3fbb19abca8",
+   "metadata": {},
+   "source": [
+    "# Sizes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "9aa4a92b-ac36-443c-b3b2-fb483b72b4f1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "small_gal_size = np.array([1.]) # arcsec\n",
+    "tiny_gal_size = np.array([0.2]) # arcsec\n",
+    "box_hwidth = 50."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "4f4e6d7f-978c-41a9-adac-838689d5be67",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "box_hwidth = 90. # arcsec\n",
+    "step_size = 0.5 / 20 # arcsize"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe49b2ec-ecd6-4617-aa25-b3cf76b7cd7f",
+   "metadata": {},
+   "source": [
+    "# Calculate"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "96193089-8446-4a6c-911b-d10b1fe40347",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Set Equinox (for spherical offsets)\n",
+    "localiz = Path.localiz.copy()\n",
+    "localiz['center_coord'].equinox = gal_coord1.equinox"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8dada471-1d7d-45b8-8472-e7d5fb740295",
+   "metadata": {},
+   "source": [
+    "## Init the main grid :: $\\sim 0.1$s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "6106617f-b5cf-48ca-9079-76b58bcbb90b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "125 ms ± 3.72 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "# Build the fixed grid around the transient\n",
+    "ngrid = int(np.round(2*box_hwidth / step_size))\n",
+    "x = np.linspace(-box_hwidth, box_hwidth, ngrid)\n",
+    "xcoord, ycoord = np.meshgrid(x,x)\n",
+    "\n",
+    "# Grid spacing\n",
+    "grid_spacing_arcsec = x[1]-x[0]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a35631b4-0163-4a84-9cc8-0cdd020a4411",
+   "metadata": {},
+   "source": [
+    "## $L(w,x)$ ::  $\\sim 10$s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "3bad0ff5-c09a-4b6e-b7c0-ec2f9137beea",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "8.48 s ± 113 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "# #####################\n",
+    "# L(w-x) -- 2D Gaussian, normalized to 1 when integrating over x not omega\n",
+    "# Approximate as flat sky\n",
+    "#  Warning:  RA increases in x for these grids!!\n",
+    "ra = localiz['center_coord'].ra.deg + \\\n",
+    "    xcoord/3600. / np.cos(localiz['center_coord'].dec).value\n",
+    "dec = localiz['center_coord'].dec.deg + ycoord/3600.\n",
+    "L_wx = localization.calc_LWx(ra, dec, localiz)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bc9064b9-e017-4691-ba85-56a01e0c9044",
+   "metadata": {},
+   "source": [
+    "## Offsets :: $\\sim 0.5$s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "3f6b489c-04cd-44a0-8f5f-fc86a5b0226f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "474 ms ± 6.39 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "# Offsets from the transient (approximate + flat sky)\n",
+    "cand_coord = gal_coord1\n",
+    "theta = 3600*np.sqrt(np.cos(cand_coord.dec).value**2 * (\n",
+    "    ra-cand_coord.ra.deg)**2 + (dec-cand_coord.dec.deg)**2)  # arc sec"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "30595b71-0151-4a9d-9abc-8d60b9c2cac6",
+   "metadata": {},
+   "source": [
+    "## $p(w,O_i)$ :: $\\sim 0.1$s\n",
+    "\n",
+    "### This step could be sped up by cutting out a portion of the full grid"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "b6b2b319-2921-415e-8f9f-14ccdcd8fd9d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "110 ms ± 3.15 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "# p(w|O_i)\n",
+    "p_wOi = bayesian.pw_Oi(theta,\n",
+    "      0.2, # arcsec\n",
+    "      theta_prior)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "57242588-22bf-45dc-8fc7-102a7051d3d1",
+   "metadata": {},
+   "source": [
+    "## Product :: $\\sim 0.1$s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "43c2d0db-2b2e-4a1f-a804-0bf9ff2b212f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "109 ms ± 782 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "# Product\n",
+    "grid_p = L_wx * p_wOi"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b965a5d5-9e99-45bd-a2f7-aa1a78db18fb",
+   "metadata": {},
+   "source": [
+    "## Sum :: $\\sim 0.3$s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "c71355e9-4572-4fa5-a2a5-361e255b3fb4",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "26.3 ms ± 552 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "tsum = np.sum(grid_p)*grid_spacing_arcsec**2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "71061bb3-9c10-45f7-bd98-3b476421e56c",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.14.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From 3e27e38e8dea6d45774ac77f0a2075ff79f0cbb5 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 05:31:37 -0700
Subject: [PATCH 05/31] localization

---
 calculations/step_size/Profiling.ipynb | 166 ++++++++++++++++++++++++-
 1 file changed, 164 insertions(+), 2 deletions(-)

diff --git a/calculations/step_size/Profiling.ipynb b/calculations/step_size/Profiling.ipynb
index baff2a6..6f62dcc 100644
--- a/calculations/step_size/Profiling.ipynb
+++ b/calculations/step_size/Profiling.ipynb
@@ -404,7 +404,7 @@
    "id": "b965a5d5-9e99-45bd-a2f7-aa1a78db18fb",
    "metadata": {},
    "source": [
-    "## Sum :: $\\sim 0.3$s"
+    "## Sum :: $\\sim 0.03$s"
    ]
   },
   {
@@ -426,10 +426,172 @@
     "tsum = np.sum(grid_p)*grid_spacing_arcsec**2"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "71061bb3-9c10-45f7-bd98-3b476421e56c",
+   "metadata": {},
+   "source": [
+    "----"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7c090381-6b31-4c39-9add-d0d6a2df96f8",
+   "metadata": {},
+   "source": [
+    "# Profile the Localization step"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "13b39f5c-d739-4f84-bba4-74f6605d0a92",
+   "metadata": {},
+   "source": [
+    "## Setup the coords ($\\sim 0.8$s)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "08873c16-9049-4abe-b6f8-a4dd0b016d68",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "771 ms ± 31.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "# Setup\n",
+    "eellipse = localiz['eellipse']  # convenience\n",
+    "pa_ee = eellipse['theta'] # PA of error ellipse on the sky; deg\n",
+    "dtheta = 90. - pa_ee  # Rotation to place the semi-major axis \"a\" of the ellipse along the x-axis we define\n",
+    "#\n",
+    "coord = SkyCoord(ra=ra, dec=dec, unit='deg')\n",
+    "coord.equinox = localiz['center_coord'].equinox"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "826a62ef-3086-4cfa-9407-74bdef72d4f5",
+   "metadata": {},
+   "source": [
+    "## Separation ($\\sim 3$s)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "7f0e8ddc-eb34-469a-b5c9-529914ce40e6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2.87 s ± 38.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "# Rotate to the transient frame\n",
+    "sep_box = localiz['center_coord'].separation(coord).to('arcsec')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bbd2f0bd-486e-47fa-8ee2-c4ded1907aca",
+   "metadata": {},
+   "source": [
+    "## PA ($\\sim 3$s)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "id": "ae199478-ce4f-4dff-9ab2-7d6389d514f8",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "3.01 s ± 34 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "pa_box = localiz['center_coord'].position_angle(coord).to('deg')\n",
+    "new_pa_box = pa_box + dtheta * units.deg"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1aa3a417-6aec-40a4-be53-b426e929ada0",
+   "metadata": {},
+   "source": [
+    "## $x,y$ ($\\sim 0.9$s)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "9fb79f71-3385-4581-9700-a275184f608e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "868 ms ± 8.78 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "# x, y of the box in transient frame with x along major axis\n",
+    "x_box = -sep_box.value * np.sin(new_pa_box).value\n",
+    "y_box = sep_box.value * np.cos(new_pa_box).value"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4d550d29-c411-4237-9985-95aa7365f591",
+   "metadata": {},
+   "source": [
+    "## $L(w,x)$ ($\\sim 0.7$s)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "b1ab4b00-081e-408b-8aca-f12f77383698",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "673 ms ± 18.7 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "L_wx = np.exp(-x_box ** 2 / (2 * eellipse['a'] ** 2)) * np.exp(\n",
+    "    -y_box ** 2 / (2 * eellipse['b'] ** 2)) / (2*np.pi*eellipse['a']*eellipse['b'])"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "71061bb3-9c10-45f7-bd98-3b476421e56c",
+   "id": "386b39a8-fed9-444a-821b-cace96066cff",
    "metadata": {},
    "outputs": [],
    "source": []

From 55c8e589dbe85aa77b43ff1bf303bddc65d42958 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 05:38:20 -0700
Subject: [PATCH 06/31] mo

---
 calculations/step_size/Profiling.ipynb | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/calculations/step_size/Profiling.ipynb b/calculations/step_size/Profiling.ipynb
index 6f62dcc..cd3ee98 100644
--- a/calculations/step_size/Profiling.ipynb
+++ b/calculations/step_size/Profiling.ipynb
@@ -275,6 +275,27 @@
     "grid_spacing_arcsec = x[1]-x[0]"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "id": "2e926add-37d1-419d-9271-d47a7c47b846",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "7200"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x.size"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "a35631b4-0163-4a84-9cc8-0cdd020a4411",

From 0a48005ac8fb32bab68441d1b3c178faeb4a0264 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 07:11:35 -0700
Subject: [PATCH 07/31] big loc

---
 calculations/step_size/test_accuracy.py | 128 ++++++++++++++++++++++++
 1 file changed, 128 insertions(+)
 create mode 100644 calculations/step_size/test_accuracy.py

diff --git a/calculations/step_size/test_accuracy.py b/calculations/step_size/test_accuracy.py
new file mode 100644
index 0000000..359cd80
--- /dev/null
+++ b/calculations/step_size/test_accuracy.py
@@ -0,0 +1,128 @@
+""" Test the accuracy of the step size for the 
+localization and galaxy convolution. 
+"""
+
+# imports
+import os
+
+import numpy as np
+import matplotlib.pyplot as plt
+#import pandas
+
+from astropy.coordinates import SkyCoord
+from astropy.coordinates import offset_by
+from astropy import units
+#from astropy.io import fits
+
+from astropath import path
+from astropath import localization
+from astropath import bayesian
+
+theta_prior = dict(max=6., PDF='exp', scale=1.)
+
+
+def set_fontsize(ax, fsz):
+    """
+    Set the fontsize throughout an Axis
+
+    Args:
+        ax (Matplotlib Axis):
+        fsz (float): Font size
+
+    Returns:
+
+    """
+    for item in ([ax.title, ax.xaxis.label, ax.yaxis.label] +
+                 ax.get_xticklabels() + ax.get_yticklabels()):
+        item.set_fontsize(fsz)
+
+def init_localization(a, b):
+
+    Path = path.PATH()
+    frb_coord = SkyCoord('21h44m25.255s -40d54m00.10s', frame='icrs')
+    eellipse = dict(a=a, b=b, theta=0.)
+
+    Path.init_localization('eellipse', 
+                           center_coord=frb_coord, 
+                           eellipse=eellipse)
+
+    return Path
+
+
+def big_localization():
+
+    # FRB:  10" circle
+    frb_local = 20. # arcsec
+    path = init_localization(frb_local, frb_local)
+    box_hwidth = 5 * frb_local # arcsec
+
+    # Galaxy
+    gal_coord = path.localiz['center_coord'].directional_offset_by(
+        0.*units.deg, 1.0*units.arcsec)
+
+    # Loop on galaxy size
+    gal_sizes = np.array([0.1, 0.5, 1.0])
+
+    #step_sizes = np.array([0.01, 0.05, 0.1, 0.2, 0.5, 1.])
+    step_sizes = np.array([0.05, 0.1, 0.2, 0.5, 1., 2.]) # fast
+
+    raw_pxO = np.zeros((len(gal_sizes), len(step_sizes)))
+    cor_pxO = np.zeros((len(gal_sizes), len(step_sizes)))
+
+    for ss, gal_size in enumerate(gal_sizes):
+
+        # Loop on step size
+        for ii, step_size in enumerate(step_sizes):
+            print(f'Galaxy size: {gal_size}, Step size: {step_size}')
+
+            # Calculate
+            L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(
+                box_hwidth, path.localiz, np.array([gal_coord]),
+                np.array([gal_size]), theta_prior, step_size=step_size, 
+                return_debug=True)
+
+            # Save
+            raw_pxO[ss, ii] = p_xOis
+            cor_pxO[ss, ii] = p_xOis / np.sum(p_wOi) / step_size**2
+            #assert (np.sum(L_wx) * step_size**2) > 0.98, f'L_wx: {np.sum(L_wx) * step_size**2}'
+
+    # Normalize by the first step size
+    for ss in range(len(gal_sizes)):
+        cor_pxO[ss, :] /= cor_pxO[ss, 0]
+        raw_pxO[ss, :] /= raw_pxO[ss, 0]
+
+    # Plot me
+    fig = plt.figure(figsize=(10, 5))
+    ax = plt.gca()
+
+    clrs = ['red', 'green', 'blue']
+    for ss, gal_size in enumerate(gal_sizes):
+        ax.plot(step_sizes, cor_pxO[ss, :], color=clrs[ss],
+                label=f'Galaxy size: {gal_size}')
+        ax.plot(step_sizes, raw_pxO[ss, :], ls=':', color=clrs[ss])
+
+    ax.legend(fontsize=15.)
+    ax.set_xlabel('Step size (arcsec)')
+    ax.set_ylabel('Normalized p_xO')
+
+    ax.set_title(f'Big Localization, {frb_local}"')
+    ax.set_xscale('log')
+    #ax.set_yscale('log')
+    #ax.grid(True)
+    ax.grid(which='major', linewidth=0.8, alpha=0.7)
+    ax.grid(which='minor', linewidth=0.5, alpha=0.3)
+    set_fontsize(ax, 15.)
+
+    # Vertical line at FRB local / 20
+    ax.axvline(x=frb_local / 20., color='black', 
+               linewidth=0.8)
+
+    ax.set_ylim(0.9, 1.1)
+
+    plt.tight_layout()
+    plt.savefig('big_localization.png', dpi=300)
+    print(f'Saved to big_localization.png')
+
+# Command line
+if __name__ == '__main__':
+    big_localization()
\ No newline at end of file

From 026e8362b722221e10da140ae07661c29e6ead38 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 07:39:34 -0700
Subject: [PATCH 08/31] mo

---
 calculations/step_size/test_accuracy.py | 147 +++++++++++++++++++++---
 1 file changed, 134 insertions(+), 13 deletions(-)

diff --git a/calculations/step_size/test_accuracy.py b/calculations/step_size/test_accuracy.py
index 359cd80..5718b4a 100644
--- a/calculations/step_size/test_accuracy.py
+++ b/calculations/step_size/test_accuracy.py
@@ -49,10 +49,65 @@ def init_localization(a, b):
     return Path
 
 
-def big_localization():
+def big_galaxy(galaxy_size:float=20.):
 
-    # FRB:  10" circle
-    frb_local = 20. # arcsec
+    box_hwidth = 6 * galaxy_size # arcsec
+
+    # FRB  
+    frb_coord = SkyCoord('21h44m25.255s -40d54m00.10s', frame='icrs')
+
+    # Galaxy
+    gal_coord = frb_coord.directional_offset_by(
+        0.*units.deg, 3.0*units.arcsec)
+
+    # Loop on FRB sizes
+    frb_sizes = np.array([0.1, 0.5, 1.0, 5.])
+
+    #step_sizes = np.array([0.01, 0.05, 0.1, 0.2, 0.5, 1.])
+    step_sizes = np.array([0.05, 0.1, 0.2, 0.5, 1., 2.]) # fast
+
+    raw_pxO = np.zeros((len(frb_sizes), len(step_sizes)))
+    cor_pxO = np.zeros((len(frb_sizes), len(step_sizes)))
+
+    for ss, frb_size in enumerate(frb_sizes):
+
+        # Loop on step size
+        for ii, step_size in enumerate(step_sizes):
+            print(f'FRB size: {frb_size}, Step size: {step_size}')
+
+            # FRB
+            path = init_localization(frb_size, frb_size)
+
+            # Calculate
+            L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(
+                box_hwidth, path.localiz, np.array([gal_coord]),
+                np.array([galaxy_size]), theta_prior, 
+                step_size=step_size, 
+                return_debug=True)
+
+            # Save
+            raw_pxO[ss, ii] = p_xOis
+            cor_pxO[ss, ii] = p_xOis / np.sum(L_wx) / step_size**2
+            # Another correction
+            #cor_pxO[ss, ii] = cor_pxO[ss,ii] / np.sum(p_wOi) / step_size**2
+            
+            #assert (np.sum(L_wx) * step_size**2) > 0.98, f'L_wx: {np.sum(L_wx) * step_size**2}'
+
+    # Normalize by the first step size
+    for ss in range(len(frb_sizes)):
+        cor_pxO[ss, :] /= cor_pxO[ss, 0]
+        raw_pxO[ss, :] /= raw_pxO[ss, 0]
+
+    # Plot
+    outfile = 'big_galaxy.png'
+    title = f'Big Galaxy, {galaxy_size}"'
+    plot_results(outfile, raw_pxO, cor_pxO, 
+                 frb_sizes, step_sizes, galaxy_size/20,
+                 var_name='FRB size', title=title)
+
+def big_localization(frb_local:float=20.):
+
+    # FRB  
     path = init_localization(frb_local, frb_local)
     box_hwidth = 5 * frb_local # arcsec
 
@@ -61,7 +116,7 @@ def big_localization():
         0.*units.deg, 1.0*units.arcsec)
 
     # Loop on galaxy size
-    gal_sizes = np.array([0.1, 0.5, 1.0])
+    gal_sizes = np.array([0.1, 0.5, 1.0, 5.])
 
     #step_sizes = np.array([0.01, 0.05, 0.1, 0.2, 0.5, 1.])
     step_sizes = np.array([0.05, 0.1, 0.2, 0.5, 1., 2.]) # fast
@@ -91,21 +146,84 @@ def big_localization():
         cor_pxO[ss, :] /= cor_pxO[ss, 0]
         raw_pxO[ss, :] /= raw_pxO[ss, 0]
 
+    # Plot
+    outfile = 'big_localization.png'
+    title = f'Big Localization, {frb_local}"'
+    plot_results(outfile, raw_pxO, cor_pxO, 
+                 gal_sizes, step_sizes, frb_local/20,
+                 var_name='Galaxy size', title=title)
+
+
+def gbo_localization(a=20., b=0.2):
+
+    # FRB  
+    path = init_localization(a, b)
+    box_hwidth = 5 * a # arcsec
+
+    # Galaxy
+    gal_coord = path.localiz['center_coord'].directional_offset_by(
+        0.*units.deg, 3.0*units.arcsec)
+
+    # Loop on galaxy size
+    gal_sizes = np.array([0.1, 0.5, 1.0, 5.])
+
+    step_sizes = np.array([0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.])
+    #step_sizes = np.array([0.05, 0.1, 0.2, 0.5, 1., 2.]) # fast
+
+    raw_pxO = np.zeros((len(gal_sizes), len(step_sizes)))
+    cor_pxO = np.zeros((len(gal_sizes), len(step_sizes)))
+
+    for ss, gal_size in enumerate(gal_sizes):
+
+        # Loop on step size
+        for ii, step_size in enumerate(step_sizes):
+            print(f'Galaxy size: {gal_size}, Step size: {step_size}')
+
+            # Calculate
+            L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(
+                box_hwidth, path.localiz, np.array([gal_coord]),
+                np.array([gal_size]), theta_prior, step_size=step_size, 
+                return_debug=True)
+
+            # Save
+            raw_pxO[ss, ii] = p_xOis
+            cor_pxO[ss, ii] = p_xOis / np.sum(p_wOi) / step_size**2
+            #assert (np.sum(L_wx) * step_size**2) > 0.98, f'L_wx: {np.sum(L_wx) * step_size**2}'
+
+    # Normalize by the first step size
+    for ss in range(len(gal_sizes)):
+        cor_pxO[ss, :] /= cor_pxO[ss, 0]
+        raw_pxO[ss, :] /= raw_pxO[ss, 0]
+
+    # Plot
+    outfile = 'gbo_localization.png'
+    title = f'GBO Localization, a={a}", b={b}"'
+    plot_results(outfile, raw_pxO, cor_pxO, 
+                 gal_sizes, step_sizes, 0.1, 
+                 var_name='Galaxy size', title=title)
+
+def plot_results(outfile:str, raw_pxO, cor_pxO, 
+                 var_sizes, step_sizes, 
+                 pref_step_size:float,
+                 var_name:str='Galaxy size',
+                 title:str=None):
+
     # Plot me
     fig = plt.figure(figsize=(10, 5))
     ax = plt.gca()
 
-    clrs = ['red', 'green', 'blue']
-    for ss, gal_size in enumerate(gal_sizes):
+    clrs = ['red', 'green', 'blue', 'purple']
+    for ss, var_size in enumerate(var_sizes):
         ax.plot(step_sizes, cor_pxO[ss, :], color=clrs[ss],
-                label=f'Galaxy size: {gal_size}')
+                label=f'{var_name}: {var_size}')
         ax.plot(step_sizes, raw_pxO[ss, :], ls=':', color=clrs[ss])
 
     ax.legend(fontsize=15.)
     ax.set_xlabel('Step size (arcsec)')
     ax.set_ylabel('Normalized p_xO')
 
-    ax.set_title(f'Big Localization, {frb_local}"')
+    if title is not None:
+        ax.set_title(title, fontsize=15.)
     ax.set_xscale('log')
     #ax.set_yscale('log')
     #ax.grid(True)
@@ -113,16 +231,19 @@ def big_localization():
     ax.grid(which='minor', linewidth=0.5, alpha=0.3)
     set_fontsize(ax, 15.)
 
-    # Vertical line at FRB local / 20
-    ax.axvline(x=frb_local / 20., color='black', 
+    # Vertical line 
+    ax.axvline(x=pref_step_size, color='black', 
                linewidth=0.8)
 
     ax.set_ylim(0.9, 1.1)
 
     plt.tight_layout()
-    plt.savefig('big_localization.png', dpi=300)
-    print(f'Saved to big_localization.png')
+    plt.savefig(outfile, dpi=300)
+    print(f'Saved to {outfile}')
 
 # Command line
 if __name__ == '__main__':
-    big_localization()
\ No newline at end of file
+
+    #big_localization()
+    #big_galaxy()
+    gbo_localization()
\ No newline at end of file

From aacd16d3f60c3488271c17cd4c1d501da1ec302b Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 08:02:56 -0700
Subject: [PATCH 09/31] ok

---
 calculations/step_size/test_accuracy.py | 63 ++++++++++++++++++++++++-
 1 file changed, 62 insertions(+), 1 deletion(-)

diff --git a/calculations/step_size/test_accuracy.py b/calculations/step_size/test_accuracy.py
index 5718b4a..e3a57d1 100644
--- a/calculations/step_size/test_accuracy.py
+++ b/calculations/step_size/test_accuracy.py
@@ -48,6 +48,60 @@ def init_localization(a, b):
 
     return Path
 
+def single_case(outfile:str, a, b, galaxy_size, 
+                gal_offset:float=3., step_sizes=None,
+                gal_pa:float=0.):
+
+    box_hwidth = max(5 * a, gal_offset + 6 * galaxy_size) # arcsec
+
+    # FRB
+    path = init_localization(a, b)
+
+    # Galaxy
+    gal_coord = path.localiz['center_coord'].directional_offset_by(
+        gal_pa*units.deg, gal_offset*units.arcsec)
+
+    # Step sizes
+    if step_sizes is None:
+        step_sizes = np.array([0.02, 0.05, 0.1, 0.2, 0.5, 1., 2.]) # fast
+
+    raw_pxO = np.zeros((1, len(step_sizes)))
+    cor_pxO = np.zeros((1, len(step_sizes)))
+
+    # Prescription
+    best_step = max(b, galaxy_size)/20.
+
+    for ss in [0]:
+
+        # Loop on step size
+        for ii, step_size in enumerate(step_sizes):
+            print(f'Step size: {step_size}')
+
+            # Calculate
+            L_wx, p_wOi, grid_p, p_xOis = bayesian.px_Oi_fixedgrid(
+                box_hwidth, path.localiz, np.array([gal_coord]),
+                np.array([galaxy_size]), theta_prior, step_size=step_size, 
+                return_debug=True)
+
+            # Save
+            raw_pxO[ss, ii] = p_xOis
+
+            # Correction
+            if b > galaxy_size:
+                cor_pxO[ss, ii] = p_xOis / np.sum(p_wOi) / step_size**2
+            else:
+                cor_pxO[ss, ii] = p_xOis / np.sum(L_wx) / step_size**2
+            #assert (np.sum(L_wx) * step_size**2) > 0.98, f'L_wx: {np.sum(L_wx) * step_size**2}'
+
+    # Normalize by the first step size
+    for ss in [0]:
+        cor_pxO[ss, :] /= cor_pxO[ss, 0]
+        raw_pxO[ss, :] /= raw_pxO[ss, 0]
+
+    title = f'Localization, a={a}", b={b}; offset by {gal_offset}"; PA={gal_pa}"'
+    plot_results(outfile, raw_pxO, cor_pxO, 
+                 np.array([galaxy_size]), step_sizes, best_step,
+                 var_name='Galaxy size', title=title)
 
 def big_galaxy(galaxy_size:float=20.):
 
@@ -246,4 +300,11 @@ def plot_results(outfile:str, raw_pxO, cor_pxO,
 
     #big_localization()
     #big_galaxy()
-    gbo_localization()
\ No newline at end of file
+    #gbo_localization()
+
+    # ############
+    # Individual cases
+    #single_case('single_case.png', 
+    #            5., 5., 2., gal_offset=7.)
+    single_case('single_case.png', 
+                20., 0.2, 2., gal_offset=2., gal_pa=90.)
\ No newline at end of file

From fbd295505c04d326ebec00f09fb8e43787874432 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 20:05:03 -0700
Subject: [PATCH 10/31] Lwx

---
 astropath/localization.py        |  44 +++++--
 astropath/tests/test_speed_up.py | 182 ++++++++++++++++++++++++++
 prompts/speed_up.md              | 211 +++++++++++++++++++++++++++++++
 3 files changed, 427 insertions(+), 10 deletions(-)
 create mode 100644 astropath/tests/test_speed_up.py
 create mode 100644 prompts/speed_up.md

diff --git a/astropath/localization.py b/astropath/localization.py
index 996d7ff..3e22d79 100644
--- a/astropath/localization.py
+++ b/astropath/localization.py
@@ -63,18 +63,42 @@ def calc_LWx(ra:np.ndarray, dec:np.ndarray, localiz:dict):
     if localiz['type'] == 'eellipse':
         # Setup
         eellipse = localiz['eellipse']  # convenience
-        pa_ee = eellipse['theta'] # PA of error ellipse on the sky; deg
-        dtheta = 90. - pa_ee  # Rotation to place the semi-major axis "a" of the ellipse along the x-axis we define
+        pa_ee = eellipse['theta']  # PA of error ellipse on the sky; deg
+        # Rotation to place the semi-major axis "a" of the ellipse along
+        # the x-axis we define
+        dtheta = 90. - pa_ee
         #
-        coord = SkyCoord(ra=ra, dec=dec, unit='deg')
-        coord.equinox = localiz['center_coord'].equinox
-        # Rotate to the transient frame
-        sep_box = localiz['center_coord'].separation(coord).to('arcsec')
-        pa_box = localiz['center_coord'].position_angle(coord).to('deg')
-        new_pa_box = pa_box + dtheta * units.deg
+        # Pure-numpy replacement for the astropy SkyCoord/separation/
+        # position_angle calls (see Logs in prompts/speed_up.md).  We
+        # reproduce astropy.coordinates.angle_utilities exactly with
+        # numpy, avoiding SkyCoord construction and Quantity overhead.
+        # Equinox is irrelevant: ICRS separation/PA do not depend on it.
+        ra0 = np.radians(localiz['center_coord'].ra.deg)   # center RA, rad
+        dec0 = np.radians(localiz['center_coord'].dec.deg)  # center Dec, rad
+        ra_r = np.radians(ra)   # grid RA, rad
+        dec_r = np.radians(dec)  # grid Dec, rad
+        # Trig terms shared by the separation and position-angle formulae
+        dlon = ra_r - ra0
+        sdlon = np.sin(dlon)
+        cdlon = np.cos(dlon)
+        sl1 = np.sin(dec0)
+        cl1 = np.cos(dec0)
+        sl2 = np.sin(dec_r)
+        cl2 = np.cos(dec_r)
+        # Vincenty angular separation (rad) -> arcsec.  Matches
+        # SkyCoord.separation to ~1e-10 arcsec.
+        sep = np.arctan2(
+            np.hypot(cl2 * sdlon, cl1 * sl2 - sl1 * cl2 * cdlon),
+            sl1 * sl2 + cl1 * cl2 * cdlon)
+        sep_box = np.degrees(sep) * 3600.  # arcsec
+        # Position angle East of North (rad).  Matches
+        # SkyCoord.position_angle to ~1e-8 deg.
+        pa_box = np.arctan2(sdlon * cl2, sl2 * cl1 - cl2 * sl1 * cdlon)
+        # Rotate to the transient frame (dtheta given in deg)
+        new_pa_box = pa_box + np.radians(dtheta)
         # x, y of the box in transient frame with x along major axis
-        x_box = -sep_box.value * np.sin(new_pa_box).value
-        y_box = sep_box.value * np.cos(new_pa_box).value
+        x_box = -sep_box * np.sin(new_pa_box)
+        y_box = sep_box * np.cos(new_pa_box)
 
         # Calculate
         L_wx = np.exp(-x_box ** 2 / (2 * eellipse['a'] ** 2)) * np.exp(
diff --git a/astropath/tests/test_speed_up.py b/astropath/tests/test_speed_up.py
new file mode 100644
index 0000000..710305b
--- /dev/null
+++ b/astropath/tests/test_speed_up.py
@@ -0,0 +1,182 @@
+""" Test the numpy speed-up of localization.calc_LWx (eellipse type).
+
+The eellipse branch of localization.calc_LWx was re-implemented in pure
+numpy (replacing astropy SkyCoord / separation / position_angle).  These
+tests:
+
+  1. Verify the new numpy code reproduces the original astropy code to
+     within tight numerical tolerances.
+  2. Time both implementations and report the speed-up, including a large
+     7200x7200 pixel grid.
+
+See prompts/speed_up.md for the analysis behind the change.
+"""
+
+import time
+
+import numpy as np
+
+from astropy.coordinates import SkyCoord
+from astropy import units
+
+from astropath import localization
+
+import pytest
+
+
+def _calc_LWx_eellipse_astropy(ra, dec, localiz):
+    """Original (astropy-based) eellipse implementation of calc_LWx.
+
+    Frozen here as the reference for regression/speed comparison.  This
+    is a verbatim copy of the eellipse branch of localization.calc_LWx
+    as it existed before the numpy rewrite.
+
+    Args:
+        ra (np.ndarray): RA grid (ICRS), deg.
+        dec (np.ndarray): Dec grid (ICRS), deg.
+        localiz (dict): Localization dict (eellipse type).
+
+    Returns:
+        np.ndarray: L(w-x) grid, same shape as ra/dec.
+    """
+    eellipse = localiz['eellipse']  # convenience
+    pa_ee = eellipse['theta']  # PA of error ellipse on the sky; deg
+    # Rotation to place the semi-major axis "a" along the x-axis
+    dtheta = 90. - pa_ee
+    #
+    coord = SkyCoord(ra=ra, dec=dec, unit='deg')
+    coord.equinox = localiz['center_coord'].equinox
+    # Rotate to the transient frame
+    sep_box = localiz['center_coord'].separation(coord).to('arcsec')
+    pa_box = localiz['center_coord'].position_angle(coord).to('deg')
+    new_pa_box = pa_box + dtheta * units.deg
+    # x, y of the box in transient frame with x along major axis
+    x_box = -sep_box.value * np.sin(new_pa_box).value
+    y_box = sep_box.value * np.cos(new_pa_box).value
+    # Calculate
+    L_wx = np.exp(-x_box ** 2 / (2 * eellipse['a'] ** 2)) * np.exp(
+        -y_box ** 2 / (2 * eellipse['b'] ** 2)) / (
+        2 * np.pi * eellipse['a'] * eellipse['b'])
+    return L_wx
+
+
+def _build_grid(cent_ra, cent_dec, box_hwidth, ngrid):
+    """Build an ra/dec grid around a center (flat-sky), as the callers do.
+
+    Args:
+        cent_ra (float): Central RA, deg.
+        cent_dec (float): Central Dec, deg.
+        box_hwidth (float): Half-width of the grid, arcsec.
+        ngrid (int): Number of pixels per side.
+
+    Returns:
+        tuple: (ra, dec) numpy arrays of shape (ngrid, ngrid), deg.
+    """
+    x = np.linspace(-box_hwidth, box_hwidth, ngrid)
+    xcoord, ycoord = np.meshgrid(x, x)
+    # RA increases in x; flat-sky scaling by cos(dec)
+    ra = cent_ra + xcoord / 3600. / np.cos(np.radians(cent_dec))
+    dec = cent_dec + ycoord / 3600.
+    return ra, dec
+
+
+def _eellipse_localiz(cent_ra, cent_dec, a=1.0, b=0.5, theta=45.):
+    """Construct an eellipse localization dict for testing.
+
+    Args:
+        cent_ra (float): Central RA, deg.
+        cent_dec (float): Central Dec, deg.
+        a (float): Semi-major axis, arcsec.
+        b (float): Semi-minor axis, arcsec.
+        theta (float): Position angle of the ellipse, deg (E of N).
+
+    Returns:
+        dict: Localization dict (eellipse type).
+    """
+    center = SkyCoord(ra=cent_ra, dec=cent_dec, unit='deg')
+    return dict(type='eellipse',
+                center_coord=center,
+                eellipse=dict(a=a, b=b, theta=theta))
+
+
+def test_eellipse_matches_astropy():
+    """numpy calc_LWx must match the frozen astropy implementation."""
+    cent_ra, cent_dec = 120.0, 32.0
+    localiz = _eellipse_localiz(cent_ra, cent_dec)
+    # Modest grid; box_hwidth=10", step_size=0.1" -> 200x200
+    ra, dec = _build_grid(cent_ra, cent_dec, box_hwidth=10., ngrid=200)
+
+    L_new = localization.calc_LWx(ra, dec, localiz)
+    L_ref = _calc_LWx_eellipse_astropy(ra, dec, localiz)
+
+    # Tight tolerance: the two should agree to roundoff
+    assert np.allclose(L_new, L_ref, rtol=1e-8, atol=1e-12)
+    # Sanity: L_wx peaks at the center pixel region and is finite
+    assert np.all(np.isfinite(L_new))
+
+
+def test_eellipse_matches_astropy_offcenter():
+    """Match also at a southern, high-PA case to exercise the geometry."""
+    cent_ra, cent_dec = 263.667, -50.768
+    localiz = _eellipse_localiz(cent_ra, cent_dec, a=2.0, b=0.7, theta=110.)
+    ra, dec = _build_grid(cent_ra, cent_dec, box_hwidth=15., ngrid=150)
+
+    L_new = localization.calc_LWx(ra, dec, localiz)
+    L_ref = _calc_LWx_eellipse_astropy(ra, dec, localiz)
+
+    assert np.allclose(L_new, L_ref, rtol=1e-8, atol=1e-12)
+
+
+def _time_call(func, ra, dec, localiz, reps=3):
+    """Return the best-of-reps wall time (s) for func(ra, dec, localiz).
+
+    Args:
+        func (callable): Implementation to time.
+        ra, dec (np.ndarray): Grid coords.
+        localiz (dict): Localization dict.
+        reps (int): Number of repetitions; the minimum is returned.
+
+    Returns:
+        float: Best wall-clock time in seconds.
+    """
+    best = np.inf
+    for _ in range(reps):
+        t0 = time.perf_counter()
+        func(ra, dec, localiz)
+        best = min(best, time.perf_counter() - t0)
+    return best
+
+
+@pytest.mark.parametrize("ngrid", [200, 1000, 7200])
+def test_eellipse_speed_up(ngrid, capsys):
+    """Time numpy vs astropy and report the speed-up.
+
+    Includes the requested 7200x7200 pixel grid.  Also re-checks
+    correctness on each grid (subsampled for the largest grid to keep
+    memory/time reasonable).
+    """
+    cent_ra, cent_dec = 120.0, 32.0
+    localiz = _eellipse_localiz(cent_ra, cent_dec)
+    # Keep angular scale fixed-ish; box grows with ngrid
+    box_hwidth = 0.05 * ngrid  # arcsec (0.1"/pix)
+    ra, dec = _build_grid(cent_ra, cent_dec, box_hwidth, ngrid)
+
+    t_np = _time_call(localization.calc_LWx, ra, dec, localiz)
+    t_ap = _time_call(_calc_LWx_eellipse_astropy, ra, dec, localiz)
+
+    # Correctness check (single eval)
+    L_new = localization.calc_LWx(ra, dec, localiz)
+    L_ref = _calc_LWx_eellipse_astropy(ra, dec, localiz)
+    assert np.allclose(L_new, L_ref, rtol=1e-8, atol=1e-12)
+
+    speedup = t_ap / t_np if t_np > 0 else np.inf
+    # Report (use -s to see this output)
+    with capsys.disabled():
+        print(
+            "\n  grid %5dx%-5d (%9d pts): "
+            "astropy %8.2f ms  numpy %8.2f ms  speed-up %5.1fx"
+            % (ngrid, ngrid, ngrid * ngrid,
+               t_ap * 1e3, t_np * 1e3, speedup))
+
+    # The numpy path should never be slower than astropy
+    assert t_np <= t_ap
diff --git a/prompts/speed_up.md b/prompts/speed_up.md
new file mode 100644
index 0000000..b829671
--- /dev/null
+++ b/prompts/speed_up.md
@@ -0,0 +1,211 @@
+# Speeding up the PATH calculations
+
+## Goals
+
+This document is a collection of ideas and prompts for speeding up the PATH calculations. 
+
+## Coding
+
+Here are guidelines for coding: 
+
+- Use Python where possible
+- Add inline comments to explain the effort
+- Reuse existing code when possible
+- Place import statements at the top of the file.
+- Include a description of inputs/outputs in the doc string of all methods
+- Use lines of code that are less than 80 characters wide
+
+## Running
+
+If you need to run python, use the "astro14" environment.  
+
+## Development
+
+### calc_LWx
+
+We wish to speed up the calculation of L(w-x) for a given localization. 
+
+1. Speed up the code in localization.py:calc_LWx that calculates the grid of L(w-x) values for a given localization with the eellipse type.  Please:
+
+- Examine the code
+- Identify the bottlenecks
+- Figure out how to replace all astropy calculations 
+- Log your work in the "Logs" section below.
+- Make recommendations 
+- Do not generate any new code yet
+- If you have any questions, ask them in the Logs and I will clarify at my next prompt
+
+2. Write new code to replace the astropy calculations with numpy calculations. Please:
+
+- Replace the astropy calculations with numpy calculations as described in the Logs.
+- Keep the existing astropy code as a test case.
+- Stick with calc_Lwx for now;  we will revisit px_Oi_local later.
+- Generate a new test case to verify the new code.  Make a test_speed_up.py module and model it after the other modules in astropath/tests.
+- Have the tests also compare and report the speed up
+- Include the timing for a grid that is 7200x7200 pixels
+- Log your work in the "Logs" section below.
+
+### px_Oi_fixedgrid
+
+We wish to speed up the calculation of p(x|O_i) for a given localization using the fixed grid method.  
+
+1. Similar to the calc_LWx bottlenecks, we need to identify the bottlenecks and replace the astropy calculations with numpy calculations.  Please:
+
+- Examine the code
+- Identify the bottlenecks
+- Figure out how to replace all astropy calculations 
+- If it would help to store ra, dec in radians and not deg consider it
+- Log your work in the "Logs" section below.
+- Make recommendations 
+- Do not generate any new code yet
+- If you have any questions, ask them in the Logs and I will clarify at my next prompt
+
+## Prompts
+
+1. Read this doc.  Proceed with the 1st item under Development/calc_LWx
+2. Read this doc.  Proceed with the 2nd item under Development/calc_LWx
+3. Read this doc.  Proceed with the 1st item under Development/px_Oi_fixedgrid
+
+
+## Logging
+
+The "Logs" section will record Claude's work.  Please use the following format:
+
+### <Date> (Short summary of the work)
+
+<Detailed description of the work and what you learned>
+
+### <Date> (Short summary of the work)
+
+<Detailed description of the work and what you learned>
+
+...
+
+
+## Logs
+
+### 2026-06-09 (Analysis of calc_LWx eellipse bottlenecks)
+
+**Code examined:** `astropath/localization.py:calc_LWx`, the `eellipse`
+branch (lines 63-81), plus its two callers in
+`astropath/bayesian.py`: `px_Oi_fixedgrid` (line 122, called once per
+analysis) and `px_Oi_local` (line 209, called **once per candidate**
+inside the galaxy loop).
+
+**What the eellipse branch does:**
+1. `SkyCoord(ra=ra, dec=dec, unit='deg')` — builds a SkyCoord from the
+   whole grid (lines 69-70).
+2. `center.separation(coord)` — Vincenty angular separation (line 72).
+3. `center.position_angle(coord)` — position angle E of N (line 73).
+4. Rotates into the ellipse frame and evaluates a 2D Gaussian (74-81).
+
+**Bottleneck identified:** steps 1-3 are the cost. They are pure
+astropy and dominate the branch. The arithmetic in steps 1-3 is
+trivial; the expense is astropy's per-call machinery — SkyCoord object
+construction, `Quantity`/unit wrapping, and `.to('arcsec')` /
+`.to('deg')` conversions. I confirmed this with two benchmarks
+(grid mimicking `box_hwidth=10"`, `step_size=0.1"`):
+
+| grid        | pts   | astropy   | numpy     | speedup |
+|-------------|-------|-----------|-----------|---------|
+| 20x20       | 400   | 0.342 ms  | 0.018 ms  | ~19x    |
+| 60x60       | 3600  | 0.509 ms  | 0.112 ms  | ~4.5x   |
+| 200x200     | 40000 | 3.13 ms   | 1.13 ms   | ~2.8x   |
+
+The speedup grows as the grid shrinks because astropy's overhead is
+largely fixed per call. This matters most in `px_Oi_local`, which
+calls `calc_LWx` once per candidate on small per-galaxy grids — the
+regime where the win is ~19x.
+
+**How to replace all astropy calculations:** astropy's `separation` and
+`position_angle` are just closed-form spherical formulas
+(`astropy.coordinates.angle_utilities`). They can be reproduced exactly
+in numpy. Working from the center (ra0, dec0) and grid (ra, dec), all
+in radians:
+
+```
+dlon = ra - ra0
+sdlon, cdlon = sin(dlon), cos(dlon)
+sl1, cl1 = sin(dec0), cos(dec0)
+sl2, cl2 = sin(dec), cos(dec)
+# separation (Vincenty), radians:
+sep = arctan2(hypot(cl2*sdlon, cl1*sl2 - sl1*cl2*cdlon),
+              sl1*sl2 + cl1*cl2*cdlon)
+# position angle E of N, radians:
+pa  = arctan2(sdlon*cl2, sl2*cl1 - cl2*sl1*cdlon)
+```
+
+I verified these against astropy on the 200x200 grid: max separation
+diff ~7e-11 arcsec, max PA diff ~1e-8 deg — i.e. bit-for-bit
+equivalent for our purposes. `sep` then goes to arcsec via
+`degrees(sep)*3600`, `pa` to degrees via `degrees(pa)` (no need to
+wrap to [0,360) since the result is fed straight into `sin`/`cos`).
+
+The center RA/Dec come from `localiz['center_coord'].ra.deg` /
+`.dec.deg` (read once, cheap). The `coord.equinox =
+localiz['center_coord'].equinox` line (70) is a no-op for the
+math — ICRS separation/PA don't depend on equinox — and can be
+dropped in the numpy path.
+
+**Recommendations (no code written yet):**
+1. Replace the SkyCoord/separation/position_angle block in the
+   `eellipse` branch with the numpy formulas above. Identical results,
+   ~3-19x faster depending on grid size.
+2. Bigger structural win: in `px_Oi_local` the localization mapping is
+   rebuilt per candidate. `px_Oi_fixedgrid` already computes `L_wx`
+   once (good). Worth revisiting `px_Oi_local` after step 1.
+3. Keep the spherical (not flat-sky) formula so numerical results are
+   unchanged; only the implementation changes.
+
+**Question for next prompt:** Should I prioritize (a) just the in-place
+numpy swap inside `calc_LWx`'s eellipse branch (lowest risk, drop-in,
+identical output), or also (b) vectorize/cache across the candidate
+loop in `px_Oi_local`? And is exact equivalence with astropy required,
+or is the existing flat-sky approximation already accepted such that I
+could simplify further?
+
+### 2026-06-09 (Implemented numpy calc_LWx + speed-up tests)
+
+**Code changed:** `astropath/localization.py:calc_LWx`, eellipse branch.
+Replaced the astropy block (`SkyCoord` build, `.separation()`,
+`.position_angle()`, and `units`-based rotation) with the pure-numpy
+Vincenty separation + position-angle formulas worked out in the prior
+log entry. The rest of the branch (rotation into the ellipse frame, the
+2D-Gaussian evaluation) is unchanged, so output is numerically
+identical. The `coord.equinox = ...` line was dropped (no-op for ICRS
+separation/PA). Note: the `from astropy import units` import in
+localization.py is now unused (a Hint-level lint); left in place since
+it is harmless and `units` is a common re-export — can remove if
+desired.
+
+**Tests added:** `astropath/tests/test_speed_up.py`, modeled on
+`tests/test_localization.py`. It freezes the original astropy eellipse
+code as `_calc_LWx_eellipse_astropy()` (the requested "keep the astropy
+code as a test case") and:
+- `test_eellipse_matches_astropy` — 200x200 grid, asserts
+  `np.allclose(rtol=1e-8, atol=1e-12)` against the astropy reference.
+- `test_eellipse_matches_astropy_offcenter` — southern, high-PA case
+  (dec=-50.8, theta=110) to exercise the geometry.
+- `test_eellipse_speed_up[200|1000|7200]` — times both implementations,
+  re-checks correctness, prints the speed-up, and asserts numpy is not
+  slower. Includes the requested **7200x7200** grid.
+
+**Measured results** (astro14 env, best-of-3, run with `pytest -s`):
+
+| grid        | pts        | astropy    | numpy      | speed-up |
+|-------------|------------|------------|------------|----------|
+| 200x200     | 40,000     | 2.95 ms    | 2.39 ms    | 1.2x     |
+| 1000x1000   | 1,000,000  | 141.3 ms   | 85.0 ms    | 1.7x     |
+| 7200x7200   | 51,840,000 | 11,984.9 ms| 6,092.0 ms | 2.0x     |
+
+For very large grids the win plateaus at ~2x (memory-bandwidth-bound on
+the shared trig terms, no longer astropy-overhead-bound). The big-grid
+gains are smaller than the small-grid microbenchmark in the previous
+entry (~19x at 20x20) precisely because the per-call astropy overhead
+is fixed — it dominates only when the grids are small, i.e. the
+`px_Oi_local` per-candidate regime (to be revisited later).
+
+**Verification:** all 5 new tests pass; the existing
+`test_path.py`, `test_localization.py`, and `test_bayesian.py` suites
+(7 tests) still pass, confirming the eellipse path is unchanged
+downstream.
\ No newline at end of file

From 139027c9adbbf529c5ec7ebee356a17434e8303e Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 20:32:30 -0700
Subject: [PATCH 11/31] profiling

---
 astropath/bayesian.py            |  31 +++--
 astropath/profiling.py           | 229 +++++++++++++++++++++++++++++++
 astropath/tests/test_speed_up.py | 124 +++++++++++++++++
 prompts/speed_up.md              | 222 +++++++++++++++++++++++++++++-
 4 files changed, 596 insertions(+), 10 deletions(-)
 create mode 100644 astropath/profiling.py

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index 1406cf5..337f7d3 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -101,9 +101,6 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
         # 
         raise IOError("To use this method, you need to specfic a center for the fixed grid via center_coord in localiz")
 
-    # Set Equinox (for spherical offsets)
-    localiz['center_coord'].equinox = cand_coords[0].equinox
-
     # Build the fixed grid around the transient
     ngrid = int(np.round(2*box_hwidth / step_size))
     x = np.linspace(-box_hwidth, box_hwidth, ngrid)
@@ -112,22 +109,38 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
     # Grid spacing
     grid_spacing_arcsec = x[1]-x[0]
 
+    # Extract the center coordinate once as plain numpy floats.  Avoids
+    # repeated astropy attribute/Quantity access.  The previous
+    # equinox-setting line was dropped: it is a no-op for the numpy
+    # paths (offsets here are flat-sky; calc_LWx ignores equinox).
+    center_ra = localiz['center_coord'].ra.deg     # deg
+    center_dec = localiz['center_coord'].dec.deg   # deg
+    cos_center_dec = np.cos(np.radians(center_dec))  # flat-sky scaling
+
     # #####################
     # L(w-x) -- 2D Gaussian, normalized to 1 when integrating over x not omega
     # Approximate as flat sky
     #  Warning:  RA increases in x for these grids!!
-    ra = localiz['center_coord'].ra.deg + \
-        xcoord/3600. / np.cos(localiz['center_coord'].dec).value
-    dec = localiz['center_coord'].dec.deg + ycoord/3600.
+    ra = center_ra + xcoord/3600. / cos_center_dec
+    dec = center_dec + ycoord/3600.
     L_wx = localization.calc_LWx(ra, dec, localiz)
 
+    # Pre-extract candidate coordinates to numpy arrays ONCE (numpy
+    # only).  Iterating a SkyCoord array and reading .ra/.dec per
+    # candidate is the dominant astropy overhead in this loop; pulling
+    # them out here removes it.  Working with plain arrays/floats also
+    # keeps the inner loop numba-friendly for a future @njit speed-up.
+    cand_ra = cand_coords.ra.deg      # deg, shape (N,)
+    cand_dec = cand_coords.dec.deg    # deg, shape (N,)
+    cos_cand_dec = np.cos(np.radians(cand_dec))  # flat-sky scaling
+
     p_xOis, grids = [], []
     # TODO -- multiprocess this
-    for icand, cand_coord in enumerate(cand_coords):
+    for icand in range(cand_ra.size):
 
         # Offsets from the transient (approximate + flat sky)
-        theta = 3600*np.sqrt(np.cos(cand_coord.dec).value**2 * (
-            ra-cand_coord.ra.deg)**2 + (dec-cand_coord.dec.deg)**2)  # arc sec
+        theta = 3600*np.sqrt(cos_cand_dec[icand]**2 * (
+            ra-cand_ra[icand])**2 + (dec-cand_dec[icand])**2)  # arc sec
 
         # p(w|O_i)
         p_wOi = pw_Oi(theta,
diff --git a/astropath/profiling.py b/astropath/profiling.py
new file mode 100644
index 0000000..051a6a8
--- /dev/null
+++ b/astropath/profiling.py
@@ -0,0 +1,229 @@
+""" Profiling utilities for the PATH calculations.
+
+This module times the two core PATH steps that were targeted for the
+numpy speed-up work (see prompts/speed_up.md):
+
+  * ``localization.calc_LWx`` -- the localization term L(w-x)
+  * ``bayesian.px_Oi_fixedgrid`` -- the fixed-grid p(x|O_i)
+
+It is modeled on the ``calculations/step_size/Profiling.ipynb``
+notebook: a faux FRB, a circular error ellipse, and a couple of
+candidate galaxies.  Rather than timing each sub-step interactively, it
+sweeps a range of grid sizes (by varying ``step_size``), builds a table
+of timings, prints it, and writes a figure.
+
+Run from the command line::
+
+    python -m astropath.profiling
+
+or import and call :func:`run_profiling` directly.
+"""
+import os
+import time
+
+import numpy as np
+import pandas
+
+import matplotlib
+matplotlib.use('Agg')  # headless-safe; no interactive display needed
+import matplotlib.pyplot as plt  # noqa: E402
+
+from astropy.coordinates import SkyCoord
+from astropy import units
+
+from astropath import localization
+from astropath import bayesian
+
+
+# Faux FRB and analysis defaults (mirroring the Profiling notebook)
+FRB_RADEC = '21h44m25.255s -40d54m00.10s'
+BOX_HWIDTH = 90.  # arcsec; half-width of the analysis box
+# step_size sweep (arcsec).  ngrid = 2*box_hwidth/step_size, so with
+# box_hwidth=90 these give side lengths of 360 ... 7200 pixels.
+DEFAULT_STEP_SIZES = [0.5, 0.25, 0.1, 0.05, 0.025]
+
+
+def default_setup():
+    """Build the faux-FRB profiling scenario.
+
+    Mirrors calculations/step_size/Profiling.ipynb: a circular 5"
+    error ellipse and two candidate galaxies 1" from the transient.
+
+    Args:
+        None
+
+    Returns:
+        tuple: (localiz, cand_coords, cand_ang_size, theta_prior)
+            localiz (dict): eellipse localization dict.
+            cand_coords (SkyCoord): candidate host coordinates.
+            cand_ang_size (np.ndarray): candidate angular sizes, arcsec.
+            theta_prior (dict): offset-prior parameters.
+    """
+    frb_coord = SkyCoord(FRB_RADEC, frame='icrs')
+    # Small but not tiny, circular error ellipse
+    eellipse = dict(a=5., b=5., theta=0.)
+    localiz = dict(type='eellipse',
+                   center_coord=frb_coord,
+                   eellipse=eellipse)
+    # Two candidates: 1" North and 1" East of the transient
+    gal1 = frb_coord.directional_offset_by(0. * units.deg,
+                                           1.0 * units.arcsec)
+    gal2 = frb_coord.directional_offset_by(90. * units.deg,
+                                           1.0 * units.arcsec)
+    cand_coords = SkyCoord([gal1.ra, gal2.ra], [gal1.dec, gal2.dec])
+    cand_ang_size = np.array([1.0, 0.2])  # arcsec
+    theta_prior = dict(max=6., PDF='exp', scale=1.)
+    return localiz, cand_coords, cand_ang_size, theta_prior
+
+
+def _time_call(func, args, npix):
+    """Time a single callable, returning the best wall time in seconds.
+
+    The number of repetitions is scaled down for large grids to keep
+    the overall sweep fast.
+
+    Args:
+        func (callable): Function to time.
+        args (tuple): Positional arguments passed to ``func``.
+        npix (int): Number of grid pixels (used to pick repetitions).
+
+    Returns:
+        float: Best-of-reps wall-clock time, seconds.
+    """
+    # Fewer reps for big grids (they are slow and stable)
+    if npix > 1_000_000:
+        reps = 1
+    elif npix > 100_000:
+        reps = 2
+    else:
+        reps = 3
+    best = np.inf
+    for _ in range(reps):
+        t0 = time.perf_counter()
+        func(*args)
+        best = min(best, time.perf_counter() - t0)
+    return best
+
+
+def _build_grid(localiz, box_hwidth, step_size):
+    """Build the fixed ra/dec grid the same way px_Oi_fixedgrid does.
+
+    Args:
+        localiz (dict): eellipse localization dict (needs center_coord).
+        box_hwidth (float): Half-width of the analysis box, arcsec.
+        step_size (float): Grid step size, arcsec.
+
+    Returns:
+        tuple: (ra, dec, ngrid) with ra/dec numpy arrays in deg and
+            ngrid the number of pixels per side.
+    """
+    ngrid = int(np.round(2 * box_hwidth / step_size))
+    x = np.linspace(-box_hwidth, box_hwidth, ngrid)
+    xcoord, ycoord = np.meshgrid(x, x)
+    # Flat-sky; RA increases in x
+    center = localiz['center_coord']
+    cos_dec = np.cos(np.radians(center.dec.deg))
+    ra = center.ra.deg + xcoord / 3600. / cos_dec
+    dec = center.dec.deg + ycoord / 3600.
+    return ra, dec, ngrid
+
+
+def run_profiling(step_sizes=None, box_hwidth=BOX_HWIDTH):
+    """Profile calc_LWx and px_Oi_fixedgrid over a range of grid sizes.
+
+    Args:
+        step_sizes (list, optional): Grid step sizes (arcsec) to sweep.
+            Defaults to :data:`DEFAULT_STEP_SIZES`.
+        box_hwidth (float, optional): Analysis-box half-width, arcsec.
+
+    Returns:
+        pandas.DataFrame: One row per step size with columns
+            ``step_size``, ``ngrid``, ``n_pixels``, ``calc_LWx_s`` and
+            ``px_Oi_fixedgrid_s`` (times in seconds).
+    """
+    if step_sizes is None:
+        step_sizes = DEFAULT_STEP_SIZES
+    localiz, cand_coords, cand_ang_size, theta_prior = default_setup()
+
+    rows = []
+    for step_size in step_sizes:
+        # Grid for the standalone calc_LWx timing
+        ra, dec, ngrid = _build_grid(localiz, box_hwidth, step_size)
+        npix = ngrid * ngrid
+
+        # Time calc_LWx (localization term only)
+        t_lwx = _time_call(localization.calc_LWx,
+                           (ra, dec, localiz), npix)
+
+        # Time the full fixed-grid p(x|O_i)
+        t_pxoi = _time_call(
+            bayesian.px_Oi_fixedgrid,
+            (box_hwidth, localiz, cand_coords, cand_ang_size,
+             theta_prior, step_size), npix)
+
+        rows.append(dict(step_size=step_size, ngrid=ngrid,
+                         n_pixels=npix, calc_LWx_s=t_lwx,
+                         px_Oi_fixedgrid_s=t_pxoi))
+
+    return pandas.DataFrame(rows)
+
+
+def plot_results(df, outfile):
+    """Plot the timing results vs grid size on log-log axes.
+
+    Args:
+        df (pandas.DataFrame): Output of :func:`run_profiling`.
+        outfile (str): Path to write the PNG figure.
+
+    Returns:
+        str: The path the figure was written to.
+    """
+    fig, ax = plt.subplots(figsize=(7, 5))
+    ax.plot(df['n_pixels'], df['calc_LWx_s'], 'o-',
+            label='calc_LWx')
+    ax.plot(df['n_pixels'], df['px_Oi_fixedgrid_s'], 's-',
+            label='px_Oi_fixedgrid')
+    ax.set_xscale('log')
+    ax.set_yscale('log')
+    ax.set_xlabel('Grid size (pixels)')
+    ax.set_ylabel('Time (s)')
+    ax.set_title('PATH profiling: numpy implementations')
+    ax.grid(True, which='both', alpha=0.3)
+    ax.legend()
+    fig.tight_layout()
+    fig.savefig(outfile, dpi=120)
+    plt.close(fig)
+    return outfile
+
+
+def main():
+    """Run the profiling sweep, print the table, and save the figure.
+
+    Args:
+        None
+
+    Returns:
+        pandas.DataFrame: The timing table (also printed to screen).
+    """
+    df = run_profiling()
+
+    # Print a readable table (times in ms for legibility)
+    show = df.copy()
+    show['calc_LWx_ms'] = show['calc_LWx_s'] * 1e3
+    show['px_Oi_fixedgrid_ms'] = show['px_Oi_fixedgrid_s'] * 1e3
+    cols = ['step_size', 'ngrid', 'n_pixels',
+            'calc_LWx_ms', 'px_Oi_fixedgrid_ms']
+    print('\nPATH profiling results (best-of-reps):')
+    print(show[cols].to_string(index=False,
+                               float_format=lambda v: '%.3f' % v))
+
+    # Save the figure next to this module
+    outfile = os.path.join(os.path.dirname(__file__),
+                           'profiling_timing.png')
+    plot_results(df, outfile)
+    print('\nFigure written to: %s' % outfile)
+    return df
+
+
+if __name__ == '__main__':
+    main()
diff --git a/astropath/tests/test_speed_up.py b/astropath/tests/test_speed_up.py
index 710305b..6d137b4 100644
--- a/astropath/tests/test_speed_up.py
+++ b/astropath/tests/test_speed_up.py
@@ -20,6 +20,7 @@
 from astropy import units
 
 from astropath import localization
+from astropath import bayesian
 
 import pytest
 
@@ -180,3 +181,126 @@ def test_eellipse_speed_up(ngrid, capsys):
 
     # The numpy path should never be slower than astropy
     assert t_np <= t_ap
+
+
+# ---------------------------------------------------------------------------
+# px_Oi_fixedgrid: replaced per-candidate / center astropy access with numpy
+# (pre-extracted arrays).  Reference below freezes the original astropy
+# implementation for regression + speed comparison.
+# ---------------------------------------------------------------------------
+
+
+def _px_Oi_fixedgrid_astropy(box_hwidth, localiz, cand_coords,
+                             cand_ang_size, theta_prior, step_size=0.1):
+    """Original (astropy-based) px_Oi_fixedgrid implementation.
+
+    Verbatim copy of the loop/grid logic as it existed before the numpy
+    rewrite (iterates the SkyCoord array, reads .ra/.dec per candidate,
+    sets equinox).  Kept here as the reference for the tests.  Returns
+    only the p(x|O_i) array (the only output the tests need).
+
+    Args:
+        box_hwidth (float): Half-width of the analysis box, arcsec.
+        localiz (dict): Localization dict (must have center_coord).
+        cand_coords (SkyCoord): Candidate host coordinates.
+        cand_ang_size (np.ndarray): Candidate angular sizes, arcsec.
+        theta_prior (dict): Offset-prior parameters.
+        step_size (float): Grid step size, arcsec.
+
+    Returns:
+        np.ndarray: p(x|O_i) for each candidate.
+    """
+    # Set Equinox (for spherical offsets)
+    localiz['center_coord'].equinox = cand_coords[0].equinox
+    # Build the fixed grid around the transient
+    ngrid = int(np.round(2 * box_hwidth / step_size))
+    x = np.linspace(-box_hwidth, box_hwidth, ngrid)
+    xcoord, ycoord = np.meshgrid(x, x)
+    grid_spacing_arcsec = x[1] - x[0]
+    # L(w-x); RA increases in x (flat-sky)
+    ra = localiz['center_coord'].ra.deg + \
+        xcoord / 3600. / np.cos(localiz['center_coord'].dec).value
+    dec = localiz['center_coord'].dec.deg + ycoord / 3600.
+    L_wx = localization.calc_LWx(ra, dec, localiz)
+    p_xOis = []
+    for icand, cand_coord in enumerate(cand_coords):
+        # Offsets from the transient (flat sky)
+        theta = 3600 * np.sqrt(np.cos(cand_coord.dec).value**2 * (
+            ra - cand_coord.ra.deg)**2
+            + (dec - cand_coord.dec.deg)**2)  # arcsec
+        p_wOi = bayesian.pw_Oi(theta, cand_ang_size[icand], theta_prior)
+        grid_p = L_wx * p_wOi
+        p_xOis.append(np.sum(grid_p) * grid_spacing_arcsec**2)
+    return np.array(p_xOis)
+
+
+def _make_candidates(cent_ra, cent_dec, ncand=10, spread=8.):
+    """Build a SkyCoord of candidates scattered around a center.
+
+    Args:
+        cent_ra (float): Central RA, deg.
+        cent_dec (float): Central Dec, deg.
+        ncand (int): Number of candidates.
+        spread (float): Half-spread of the scatter, arcsec.
+
+    Returns:
+        tuple: (cand_coords SkyCoord, cand_ang_size ndarray arcsec).
+    """
+    # Deterministic offsets (no RNG) spanning +/- spread arcsec
+    off = np.linspace(-spread, spread, ncand)
+    cand_ra = cent_ra + off / 3600. / np.cos(np.radians(cent_dec))
+    cand_dec = cent_dec + off[::-1] / 3600.
+    cand_coords = SkyCoord(ra=cand_ra, dec=cand_dec, unit='deg')
+    # Angular sizes 0.5-2.0 arcsec
+    cand_ang_size = np.linspace(0.5, 2.0, ncand)
+    return cand_coords, cand_ang_size
+
+
+def test_px_Oi_fixedgrid_matches_astropy():
+    """numpy px_Oi_fixedgrid must match the frozen astropy version."""
+    cent_ra, cent_dec = 120.0, 32.0
+    localiz = _eellipse_localiz(cent_ra, cent_dec, a=1.0, b=0.6, theta=30.)
+    cand_coords, cand_ang_size = _make_candidates(cent_ra, cent_dec)
+    theta_prior = dict(PDF='exp', max=6., scale=0.5)
+
+    p_new = bayesian.px_Oi_fixedgrid(
+        10., localiz, cand_coords, cand_ang_size, theta_prior)
+    p_ref = _px_Oi_fixedgrid_astropy(
+        10., localiz, cand_coords, cand_ang_size, theta_prior)
+
+    # Same math, only coordinate extraction changed -> agree to roundoff
+    assert np.allclose(p_new, p_ref, rtol=1e-10, atol=1e-15)
+
+
+def test_px_Oi_fixedgrid_speed_up(capsys):
+    """Time numpy vs astropy px_Oi_fixedgrid and report the speed-up."""
+    cent_ra, cent_dec = 120.0, 32.0
+    localiz = _eellipse_localiz(cent_ra, cent_dec, a=1.0, b=0.6, theta=30.)
+    # Many candidates: the per-candidate astropy overhead is the target
+    cand_coords, cand_ang_size = _make_candidates(
+        cent_ra, cent_dec, ncand=50)
+    theta_prior = dict(PDF='exp', max=6., scale=0.5)
+
+    def _np(*_):
+        return bayesian.px_Oi_fixedgrid(
+            10., localiz, cand_coords, cand_ang_size, theta_prior)
+
+    def _ap(*_):
+        return _px_Oi_fixedgrid_astropy(
+            10., localiz, cand_coords, cand_ang_size, theta_prior)
+
+    # _time_call signature is (func, ra, dec, localiz); pass dummies
+    t_np = _time_call(_np, None, None, None)
+    t_ap = _time_call(_ap, None, None, None)
+
+    assert np.allclose(_np(), _ap(), rtol=1e-10, atol=1e-15)
+
+    speedup = t_ap / t_np if t_np > 0 else np.inf
+    with capsys.disabled():
+        print(
+            "\n  px_Oi_fixedgrid (50 cand, 200x200): "
+            "astropy %8.2f ms  numpy %8.2f ms  speed-up %5.1fx"
+            % (t_ap * 1e3, t_np * 1e3, speedup))
+
+    # numpy path should not be slower
+    assert t_np <= t_ap
diff --git a/prompts/speed_up.md b/prompts/speed_up.md
index b829671..e786bea 100644
--- a/prompts/speed_up.md
+++ b/prompts/speed_up.md
@@ -60,11 +60,36 @@ We wish to speed up the calculation of p(x|O_i) for a given localization using t
 - Do not generate any new code yet
 - If you have any questions, ask them in the Logs and I will clarify at my next prompt
 
+2. Write new code to replace the astropy calculations with numpy calculations. Please:
+
+- Replace the astropy calculations with numpy calculations as described in the Logs.
+- Generate new tests and add them to the test_speed_up.py module.
+- Only implement items 1 and 2 in the Logs; no vectorization or other optimizations yet
+- We may try to speed things up further with numba.  Consider that in your programming
+- Log your work in the "Logs" section below.
+
+## Profiling
+
+1. Generate a module to profile the code.  Call it profiling.py and place it in the astropath directory.  At this stage, we wish to profile the code for the calc_LWx and px_Oi_fixedgrid methods.  Please:
+
+- Model the code after the Profiling.ipynb notebook in the astropath/calculations/step_size directory
+- Run on a range of grid sizes by varying the step_size
+- Generate a table of the timing results.  Print these to the screen
+- Generate a figure of the timing results 
+- Log your work in the "Logs" section below.
+
+2. Modify the profiling.py tests to:
+
+- Run on N=50 candidates instead of only 2.  Have the galaxies have a range of anuglar sizes and locations
+- 
+
 ## Prompts
 
 1. Read this doc.  Proceed with the 1st item under Development/calc_LWx
 2. Read this doc.  Proceed with the 2nd item under Development/calc_LWx
 3. Read this doc.  Proceed with the 1st item under Development/px_Oi_fixedgrid
+4. Read this doc.  Proceed with the 2nd item under Development/px_Oi_fixedgrid
+5. Read this doc.  Proceed with the 1st item under Development/Profiling
 
 
 ## Logging
@@ -208,4 +233,199 @@ is fixed — it dominates only when the grids are small, i.e. the
 **Verification:** all 5 new tests pass; the existing
 `test_path.py`, `test_localization.py`, and `test_bayesian.py` suites
 (7 tests) still pass, confirming the eellipse path is unchanged
-downstream.
\ No newline at end of file
+downstream.
+
+### 2026-06-09 (Analysis of px_Oi_fixedgrid bottlenecks)
+
+**Code examined:** `astropath/bayesian.py:px_Oi_fixedgrid`
+(lines 67-153), plus the `pw_Oi` it calls (15-64).
+
+**Astropy usage in the function:**
+1. Line 105 — `localiz['center_coord'].equinox = cand_coords[0].equinox`
+   (one-time; sets an attribute).
+2. Lines 119-120 — `localiz['center_coord'].ra.deg`,
+   `np.cos(localiz['center_coord'].dec).value` to build the grid
+   (one-time, scalar; cheap).
+3. Line 122 — `calc_LWx` (now pure numpy for eellipse; one call).
+4. **Lines 126-130 (the per-candidate loop)** —
+   `for cand_coord in cand_coords` plus, *each iteration*,
+   `np.cos(cand_coord.dec).value`, `cand_coord.ra.deg`,
+   `cand_coord.dec.deg`.
+
+**Bottleneck identified:** the per-candidate loop (item 4). Two costs:
+- Iterating a SkyCoord array (`for cand_coord in cand_coords`) builds a
+  fresh *scalar* SkyCoord object every candidate — expensive astropy
+  object construction.
+- The three attribute accesses per candidate each go through astropy's
+  `Longitude`/`Latitude`/`Quantity` machinery.
+
+Together this is ~100 us per candidate of pure astropy overhead that
+has nothing to do with the actual math. I benchmarked it (N=50
+candidates, 200x200 grid, best of 20):
+
+| approach                              | time/call |
+|---------------------------------------|-----------|
+| iterate SkyCoord + attr per candidate | 8.75 ms   |
+| pre-extract arrays once + index       | 3.12 ms   |
+| (pure astropy attr access alone)      | 5.06 ms   |
+
+So ~5.6 ms/call (2.8x on the theta-build slice) is removed simply by
+pulling the candidate coordinates out of the SkyCoord *once* before the
+loop. The saving is fixed per candidate, so it grows with the number of
+candidates and dominates when grids are small.
+
+Note: the genuinely heavy numeric work — building `theta`, `pw_Oi`
+(`exp`/`log`), the `L_wx * p_wOi` product and `np.sum` over ngrid^2,
+done N_cand times — is already pure numpy. That is O(N_cand * ngrid^2)
+and is the floor for large grids; the astropy cleanup does not touch it.
+
+**How to replace all astropy calculations:**
+1. Before the loop, extract candidate coords to plain numpy arrays once:
+   `cand_ra = cand_coords.ra.deg`, `cand_dec = cand_coords.dec.deg`,
+   and precompute `cos_cand_dec = np.cos(np.radians(cand_dec))`. Inside
+   the loop, index with `cand_ra[icand]` etc. — no scalar SkyCoord, no
+   per-iteration astropy attribute access.
+2. Extract the center once with numpy too: `center_ra = ...ra.deg`,
+   `center_dec = ...dec.deg`, `cos_center_dec =
+   np.cos(np.radians(center_dec))` (replaces the astropy
+   `np.cos(...).value` on line 120).
+3. Drop the equinox line (105). It is a no-op for the numpy paths
+   (calc_LWx eellipse ignores equinox; healpix/wcs never used it) and
+   the offsets here are computed flat-sky, not via spherical frames.
+
+**On storing ra/dec in radians (the doc's hint):** modest, situational.
+- The flat-sky `theta` (lines 129-130) uses *degree differences* scaled
+  by 3600 to arcsec; in radians it would be `206265 * sqrt(...)`.
+  Mathematically identical, no speed difference — not worth changing.
+- The real redundancy is that `calc_LWx`'s eellipse branch now does
+  `np.radians(ra)` and `np.radians(dec)` over the *whole* grid on every
+  call. In `px_Oi_fixedgrid` that is a single call, so it is a one-time
+  cost — minor here (it matters more for `px_Oi_local`, deferred). If we
+  ever want to shave it, the clean move is to build the grid in radians
+  up front and let `calc_LWx` accept radians (or cache the radian grid),
+  rather than threading radians through the theta loop.
+
+**Recommendations (no code written yet):**
+1. Pre-extract candidate and center coordinates to numpy arrays once;
+   index by `icand` in the loop. Biggest, safest win; output identical.
+2. Remove the equinox-setting line.
+3. (Optional, separate change) Vectorize the candidate loop with
+   broadcasting — compute `theta`/`p_wOi` for all candidates at once as
+   an (N, ngrid, ngrid) array. Fast for moderate sizes but memory grows
+   as N_cand * ngrid^2 (e.g. 50 cands x 7200^2 x 8 B ~ 20 GB). Must keep
+   the per-candidate loop for very large grids, or chunk it; flag the
+   trade-off rather than vectorize unconditionally.
+4. (Optional) `pw_Oi` already masks to `theta < max*phi`; `theta`
+   itself is still computed over the full grid. Could restrict the
+   sqrt/exp to the in-support region, but that complicates the code for
+   limited gain — lower priority than items 1-2.
+
+**Question for next prompt:** For item 1, confirm `cand_coords` is
+always an array-valued SkyCoord (it is built that way in `path.py`) so
+`cand_coords.ra.deg` returns an array — any single-candidate call sites
+I should guard against? And do you want me to implement just items 1-2
+(safe, identical output), or also pursue the vectorization in item 3
+with a memory guard?
+
+### 2026-06-09 (Implemented numpy px_Oi_fixedgrid items 1-2 + tests)
+
+**Scope:** implemented only items 1 and 2 from the recommendations
+above (pre-extract coords; drop equinox). No vectorization (item 3) or
+`pw_Oi` masking (item 4), per the prompt.
+
+**Code changed:** `astropath/bayesian.py:px_Oi_fixedgrid`.
+- Item 2: removed `localiz['center_coord'].equinox = cand_coords[0]
+  .equinox` (no-op for the numpy/flat-sky paths).
+- Item 1 (center): extract `center_ra`, `center_dec` as plain floats
+  once and precompute `cos_center_dec = np.cos(np.radians(center_dec))`,
+  replacing the astropy `np.cos(...).value` in the grid construction.
+- Item 1 (candidates): before the loop, pull
+  `cand_ra = cand_coords.ra.deg`, `cand_dec = cand_coords.dec.deg`, and
+  `cos_cand_dec = np.cos(np.radians(cand_dec))` as numpy arrays. The
+  loop is now `for icand in range(cand_ra.size)` and indexes those
+  arrays — no per-candidate scalar `SkyCoord` construction, no
+  per-candidate astropy attribute access. Output is numerically
+  identical (same flat-sky formula, just float vs Quantity extraction).
+
+**numba consideration:** I kept the inner loop operating purely on
+numpy arrays and scalar floats (`cand_ra[icand]`, `cos_cand_dec[icand]`,
+`cand_ang_size[icand]`) with no astropy objects or dict access on the
+hot path's coordinate math. That is exactly the shape `@njit` wants.
+The remaining numba blocker is `pw_Oi`, which branches on the
+`theta_prior` dict (string `PDF` key) — to jit the loop later that
+PDF selection would need to be hoisted out (resolve the PDF + its
+scalar norm once, pass plain floats in), but no restructuring was done
+now since the prompt limited scope to items 1-2.
+
+**Tests added** to `astropath/tests/test_speed_up.py`:
+- `_px_Oi_fixedgrid_astropy(...)` — frozen verbatim copy of the original
+  astropy loop/grid logic (returns the p(x|O_i) array), used as the
+  regression + speed reference.
+- `_make_candidates(...)` — deterministic helper (no RNG) building a
+  candidate `SkyCoord` + angular sizes around a center.
+- `test_px_Oi_fixedgrid_matches_astropy` — 10 candidates, asserts
+  `np.allclose(rtol=1e-10, atol=1e-15)` vs the astropy reference.
+- `test_px_Oi_fixedgrid_speed_up` — 50 candidates, 200x200 grid; times
+  both, re-checks equality, prints the speed-up, asserts numpy is not
+  slower.
+
+**Measured result** (astro14 env, best-of-3, `pytest -s`):
+
+| case                          | astropy  | numpy    | speed-up |
+|-------------------------------|----------|----------|----------|
+| 50 cand, 200x200 grid         | 17.19 ms | 10.23 ms | 1.7x     |
+
+The ~1.7x reflects removing the fixed per-candidate astropy overhead;
+the residual time is the genuine numpy compute (theta/pw_Oi/product/sum
+over the grid, x50), which is unchanged and would be the next target
+for numba or vectorization.
+
+**Verification:** the 2 new tests pass (plus the 4 existing
+test_speed_up tests); `test_path.py`, `test_bayesian.py`,
+`test_localization.py` (7 tests) still pass — the fixed-grid posteriors
+are unchanged downstream.
+
+### 2026-06-09 (Profiling module for calc_LWx + px_Oi_fixedgrid)
+
+**Code added:** `astropath/profiling.py`, modeled on
+`calculations/step_size/Profiling.ipynb`. It reuses the notebook's
+faux-FRB scenario: FRB at 21h44m25.255s -40d54m00.10s, a circular 5"
+error ellipse, two candidate galaxies 1" away, `theta_prior =
+dict(max=6, PDF='exp', scale=1)`, `box_hwidth=90"`.
+
+Structure:
+- `default_setup()` — builds the localiz / candidates / prior.
+- `_build_grid()` — constructs the fixed ra/dec grid exactly as
+  `px_Oi_fixedgrid` does (so `calc_LWx` is timed on a realistic grid).
+- `_time_call()` — best-of-reps wall timer; reps scale down for big
+  grids (1 rep > 1e6 px, 2 reps > 1e5, else 3) to keep the sweep quick.
+- `run_profiling()` — sweeps `step_size` and returns a pandas table.
+- `plot_results()` — log-log figure of time vs grid pixels.
+- `main()` / `python -m astropath.profiling` — prints the table and
+  writes `astropath/profiling_timing.png`.
+
+**Sweep:** `step_size` in [0.5, 0.25, 0.1, 0.05, 0.025] arcsec which,
+with box_hwidth=90", gives side lengths 360 -> 7200 px (the notebook's
+max grid). Both `calc_LWx` and `px_Oi_fixedgrid` are timed at each size.
+
+**Results** (astro14 env, printed to screen):
+
+| step_size | ngrid | n_pixels   | calc_LWx (ms) | px_Oi_fixedgrid (ms) |
+|-----------|-------|------------|---------------|----------------------|
+| 0.500     | 360   | 129,600    | 8.37          | 10.24                |
+| 0.250     | 720   | 518,400    | 40.16         | 52.89                |
+| 0.100     | 1800  | 3,240,000  | 286.60        | 393.87               |
+| 0.050     | 3600  | 12,960,000 | 1516.86       | 2337.06              |
+| 0.025     | 7200  | 51,840,000 | 6230.52       | 9482.16              |
+
+Both scale linearly with pixel count (slope ~1 on the log-log figure),
+as expected for elementwise grid ops. `calc_LWx` is the bulk of
+`px_Oi_fixedgrid`'s cost; the gap between the two curves is the
+per-candidate theta/pw_Oi/product/sum work (here 2 candidates). Figure
+saved to `astropath/profiling_timing.png`.
+
+**Note:** with the prior astropy implementation the notebook recorded
+the localization step at ~8.5 s for the 7200 grid (separation ~2.9 s +
+PA ~3 s + coord setup/x,y/L_wx); the numpy `calc_LWx` now does the same
+7200 grid in ~6.2 s end-to-end — consistent with the ~2x large-grid
+speed-up measured earlier, and the astropy separation/PA cost is gone.
\ No newline at end of file

From 37506303fa6d405386db2d166662b1c9440a618a Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Tue, 9 Jun 2026 20:41:48 -0700
Subject: [PATCH 12/31] mo

---
 astropath/profiling.py | 38 ++++++++++++++++++++++++--------------
 prompts/speed_up.md    | 39 +++++++++++++++++++++++++++++++++++++--
 2 files changed, 61 insertions(+), 16 deletions(-)

diff --git a/astropath/profiling.py b/astropath/profiling.py
index 051a6a8..75b858d 100644
--- a/astropath/profiling.py
+++ b/astropath/profiling.py
@@ -43,14 +43,19 @@
 DEFAULT_STEP_SIZES = [0.5, 0.25, 0.1, 0.05, 0.025]
 
 
-def default_setup():
+NCAND = 50  # number of candidate galaxies in the profiling scenario
+
+
+def default_setup(ncand=NCAND):
     """Build the faux-FRB profiling scenario.
 
-    Mirrors calculations/step_size/Profiling.ipynb: a circular 5"
-    error ellipse and two candidate galaxies 1" from the transient.
+    Mirrors calculations/step_size/Profiling.ipynb (circular 5" error
+    ellipse), but scatters ``ncand`` candidate galaxies over a range of
+    locations and angular sizes so the per-candidate loop in
+    ``px_Oi_fixedgrid`` is exercised realistically.
 
     Args:
-        None
+        ncand (int, optional): Number of candidate galaxies.
 
     Returns:
         tuple: (localiz, cand_coords, cand_ang_size, theta_prior)
@@ -65,13 +70,16 @@ def default_setup():
     localiz = dict(type='eellipse',
                    center_coord=frb_coord,
                    eellipse=eellipse)
-    # Two candidates: 1" North and 1" East of the transient
-    gal1 = frb_coord.directional_offset_by(0. * units.deg,
-                                           1.0 * units.arcsec)
-    gal2 = frb_coord.directional_offset_by(90. * units.deg,
-                                           1.0 * units.arcsec)
-    cand_coords = SkyCoord([gal1.ra, gal2.ra], [gal1.dec, gal2.dec])
-    cand_ang_size = np.array([1.0, 0.2])  # arcsec
+    # Scatter the candidates deterministically (no RNG) over a range of
+    # position angles and separations from the transient.  Separations
+    # span 0.5"-10" so some fall well inside the localization and some
+    # near its edge.
+    idx = np.arange(ncand)
+    pa = (idx * 360. / ncand) * units.deg          # spread in PA
+    sep = np.linspace(0.5, 10., ncand) * units.arcsec  # spread in offset
+    cand_coords = frb_coord.directional_offset_by(pa, sep)
+    # Range of angular sizes, 0.2"-3.0"
+    cand_ang_size = np.linspace(0.2, 3.0, ncand)  # arcsec
     theta_prior = dict(max=6., PDF='exp', scale=1.)
     return localiz, cand_coords, cand_ang_size, theta_prior
 
@@ -178,14 +186,16 @@ def plot_results(df, outfile):
     Returns:
         str: The path the figure was written to.
     """
+    # x-axis in sqrt(pixels) = grid side length
+    sqrt_pix = np.sqrt(df['n_pixels'])
     fig, ax = plt.subplots(figsize=(7, 5))
-    ax.plot(df['n_pixels'], df['calc_LWx_s'], 'o-',
+    ax.plot(sqrt_pix, df['calc_LWx_s'], 'o-',
             label='calc_LWx')
-    ax.plot(df['n_pixels'], df['px_Oi_fixedgrid_s'], 's-',
+    ax.plot(sqrt_pix, df['px_Oi_fixedgrid_s'], 's-', color='red',
             label='px_Oi_fixedgrid')
     ax.set_xscale('log')
     ax.set_yscale('log')
-    ax.set_xlabel('Grid size (pixels)')
+    ax.set_xlabel('sqrt(grid pixels)')
     ax.set_ylabel('Time (s)')
     ax.set_title('PATH profiling: numpy implementations')
     ax.grid(True, which='both', alpha=0.3)
diff --git a/prompts/speed_up.md b/prompts/speed_up.md
index e786bea..8edcbd7 100644
--- a/prompts/speed_up.md
+++ b/prompts/speed_up.md
@@ -81,7 +81,8 @@ We wish to speed up the calculation of p(x|O_i) for a given localization using t
 2. Modify the profiling.py tests to:
 
 - Run on N=50 candidates instead of only 2.  Have the galaxies have a range of anuglar sizes and locations
-- 
+- Use red, and not orange for px_Oi_fixedgrid 
+- Instead of pixels, label the x-axis in sqrt(pixels)
 
 ## Prompts
 
@@ -90,6 +91,7 @@ We wish to speed up the calculation of p(x|O_i) for a given localization using t
 3. Read this doc.  Proceed with the 1st item under Development/px_Oi_fixedgrid
 4. Read this doc.  Proceed with the 2nd item under Development/px_Oi_fixedgrid
 5. Read this doc.  Proceed with the 1st item under Development/Profiling
+6. Read this doc.  Proceed with the 2nd item under Development/Profiling
 
 
 ## Logging
@@ -428,4 +430,37 @@ saved to `astropath/profiling_timing.png`.
 the localization step at ~8.5 s for the 7200 grid (separation ~2.9 s +
 PA ~3 s + coord setup/x,y/L_wx); the numpy `calc_LWx` now does the same
 7200 grid in ~6.2 s end-to-end — consistent with the ~2x large-grid
-speed-up measured earlier, and the astropy separation/PA cost is gone.
\ No newline at end of file
+speed-up measured earlier, and the astropy separation/PA cost is gone.
+
+### 2026-06-09 (Profiling: 50 candidates, plot tweaks)
+
+**Code changed:** `astropath/profiling.py`, per the three requests.
+- `default_setup()` now builds `NCAND=50` candidates (was 2) with a
+  *range* of locations and sizes: position angles spread evenly over
+  0-360 deg, separations `np.linspace(0.5, 10., 50)"`, and angular
+  sizes `np.linspace(0.2, 3.0, 50)"`. Built deterministically (no RNG)
+  via `frb_coord.directional_offset_by(pa, sep)` with array arguments.
+  `ncand` is a keyword arg so the count is easy to vary.
+- `plot_results()`: `px_Oi_fixedgrid` is now drawn in **red**
+  (`color='red'`); `calc_LWx` keeps the default color.
+- x-axis now plots `sqrt(n_pixels)` (the grid side length) and is
+  labeled `sqrt(grid pixels)` instead of raw pixel count.
+
+**Results** (astro14 env, 50 candidates):
+
+| step_size | ngrid | n_pixels   | calc_LWx (ms) | px_Oi_fixedgrid (ms) |
+|-----------|-------|------------|---------------|----------------------|
+| 0.500     | 360   | 129,600    | 8.45          | 29.35                |
+| 0.250     | 720   | 518,400    | 39.64         | 159.12               |
+| 0.100     | 1800  | 3,240,000  | 289.45        | 1810.51              |
+| 0.050     | 3600  | 12,960,000 | 1524.50       | 15594.88             |
+| 0.025     | 7200  | 51,840,000 | 6130.72       | 65407.29             |
+
+With 50 candidates the two curves separate clearly (the 2-candidate run
+had them nearly on top of each other): `px_Oi_fixedgrid` is now ~3-10x
+`calc_LWx` because the per-candidate theta/pw_Oi/product/sum loop runs
+50x while `calc_LWx` runs once. This confirms that for many candidates
+the per-candidate grid loop — not the localization term — is the
+dominant cost, making it the prime target for the next optimization
+(numba / vectorization with a memory guard). Figure re-written to
+`astropath/profiling_timing.png`.
\ No newline at end of file

From d23c55890089df78e5d319e34f27a3d4563d2676 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Wed, 10 Jun 2026 05:50:23 -0700
Subject: [PATCH 13/31] not bad

---
 astropath/bayesian.py            | 198 ++++++++++++++++++++++----
 astropath/profiling.py           |  59 ++++++--
 astropath/tests/test_speed_up.py |  88 ++++++++++++
 prompts/speed_up.md              | 235 ++++++++++++++++++++++++++++++-
 4 files changed, 540 insertions(+), 40 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index 337f7d3..fe40a02 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -5,13 +5,86 @@
 
 from astropy import units
 
-from astropath import localization 
+from astropath import localization
 
 from IPython import embed
 
+# Optional numba acceleration.  numba need not be installed; when it is
+# absent HAS_NUMBA is False and njit is a no-op decorator (the jitted
+# kernel is simply never called -- callers fall back to numpy).
+try:
+    from numba import njit
+    HAS_NUMBA = True
+except ImportError:  # numba not installed
+    HAS_NUMBA = False
+
+    def njit(*args, **kwargs):
+        """No-op stand-in for numba.njit when numba is unavailable."""
+        # Support both @njit and @njit(...) usage
+        if len(args) == 1 and callable(args[0]) and not kwargs:
+            return args[0]
+
+        def _wrap(func):
+            return func
+        return _wrap
+
 sqarcsec_steradians = 4 * np.pi * (1 / 3600 / 3600) / (180. / np.pi) ** 2
 
 
+# PDF integer codes shared by pw_Oi and the numba kernel
+_PDF_CORE = 0
+_PDF_UNIFORM = 1
+_PDF_EXP = 2
+
+
+def _resolve_offset_prior(phi, theta_prior):
+    """Resolve the offset prior to plain scalars (single source).
+
+    Centralizes the offset-PDF normalization and parameters so that the
+    pure-numpy ``pw_Oi`` and the numba kernel share one definition.
+
+    Args:
+        phi (float):
+            Angular size of the galaxy in arcsec.
+        theta_prior (dict):
+            Offset-prior parameters (keys: PDF, max, and scale for exp).
+
+    Returns:
+        tuple: (pdf_code, theta_max, kparam, norm)
+            pdf_code (int): One of _PDF_CORE/_PDF_UNIFORM/_PDF_EXP.
+            theta_max (float): Cutoff offset (arcsec); p=0 beyond it.
+            kparam (float): PDF scale param -- phi for core, phi*scale
+                for exp, unused (=phi) for uniform.
+            norm (float): Normalization so the PDF integrates to 1.
+    """
+    pdf = theta_prior['PDF']
+    # Cutoff always uses the ORIGINAL phi (matches the legacy pw_Oi,
+    # where ok_w is computed before phi is rescaled for the exp PDF).
+    theta_max = theta_prior['max'] * phi
+    if pdf == 'core':
+        pdf_code = _PDF_CORE
+        kparam = phi
+        # Wolfram; updated by JXP on 14-Feb-2023
+        term0 = -1 * phi**2 * np.log(phi)
+        term_max = phi * (theta_prior['max']*phi
+                          - phi*np.log(phi+theta_prior['max']*phi))
+        norm = 2*np.pi*(term_max - term0)
+    elif pdf == 'uniform':
+        pdf_code = _PDF_UNIFORM
+        kparam = phi  # unused by the uniform PDF
+        norm = np.pi * (phi*theta_prior['max'])**2
+    elif pdf == 'exp':
+        pdf_code = _PDF_EXP
+        # exp decay length is phi*scale; cutoff stays at max*phi above
+        kparam = phi * theta_prior['scale']
+        # Wolfram; updated by JXP on 14-Feb-2023
+        norm = 2 * np.pi * kparam**2 * (1 - (1+theta_prior['max'])*np.exp(
+            -theta_prior['max']))
+    else:
+        raise IOError("Bad theta PDF")
+    return pdf_code, theta_max, kparam, norm
+
+
 def pw_Oi(theta, phi, theta_prior):
     """
     Calculate p(w|O_i) for a given galaxy
@@ -32,41 +105,80 @@ def pw_Oi(theta, phi, theta_prior):
         np.ndarray: Probability values without grid-size normalization
 
     """
-    p = np.zeros_like(theta)
-    ok_w = theta < theta_prior['max']*phi
-    if theta_prior['PDF'] == 'core':
-        # Wolfram
-        # Updated by JXP on 14-Feb-2023
-        term0 = -1 * phi**2 * np.log(phi)
-        term_max = phi * (theta_prior['max']*phi - phi*np.log(phi+theta_prior['max']*phi))
-        norm = 2*np.pi*(term_max - term0)
-        #
-        if np.any(ok_w):
-            p[ok_w] = phi / (theta[ok_w] + phi) / norm
-    elif theta_prior['PDF'] == 'uniform':
-        norm = np.pi * (phi*theta_prior['max'])**2
-        if np.any(ok_w):
-            p[ok_w] = 1. / norm
-    elif theta_prior['PDF'] == 'exp':
-        # Wolfram
-        phi = phi * theta_prior['scale']
-        # Updated by JXP on 14-Feb-2023
-        norm = 2 * np.pi * phi**2 * (1 - (1+theta_prior['max'])*np.exp(
-            -theta_prior['max']))
-        if np.any(ok_w):
-            p[ok_w] = np.exp(-theta[ok_w]/phi) / norm
-    else:
-        raise IOError("Bad theta PDF")
+    # Resolve PDF code + normalization once (single-sourced, also used
+    # by the numba kernel).  kparam = phi (core) or phi*scale (exp).
+    pdf_code, theta_max, kparam, norm = _resolve_offset_prior(
+        phi, theta_prior)
     #
     if norm == 0:
         raise ValueError("You forgot to normalize!")
+    p = np.zeros_like(theta)
+    ok_w = theta < theta_max
+    if np.any(ok_w):
+        if pdf_code == _PDF_CORE:
+            p[ok_w] = kparam / (theta[ok_w] + kparam) / norm
+        elif pdf_code == _PDF_UNIFORM:
+            p[ok_w] = 1. / norm
+        else:  # _PDF_EXP
+            p[ok_w] = np.exp(-theta[ok_w]/kparam) / norm
     # Return
     return p
 
 
-def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords, 
-                    cand_ang_size, theta_prior, step_size=0.1, 
-                    return_grids=False, return_debug:bool=False):
+@njit(cache=True)
+def px_Oi_numba(ra, dec, L_wx, cand_ra, cand_dec, cos_dec,
+          pdf_code, theta_max, kparam, norm, spacing):
+    """Numba kernel: p(x|O_i) for a SINGLE candidate (fused, 1 pass).
+
+    Computes the flat-sky offset theta, the offset PDF p(w|O_i), the
+    product with L(w-x), and the grid sum in one loop over pixels --
+    avoiding the full-grid temporaries (theta, p_wOi, grid_p) that the
+    numpy path allocates per candidate.  Single-threaded @njit.
+
+    Kept separate from ``px_Oi_fixedgrid`` (which orchestrates the grid,
+    L_wx, and the candidate loop) and from ``pw_Oi`` (pure-numpy PDF).
+
+    Args:
+        ra (np.ndarray): 2D grid of RA (deg).
+        dec (np.ndarray): 2D grid of Dec (deg).
+        L_wx (np.ndarray): 2D localization term on the same grid.
+        cand_ra (float): Candidate RA (deg).
+        cand_dec (float): Candidate Dec (deg).
+        cos_dec (float): cos(candidate Dec) for flat-sky scaling.
+        pdf_code (int): Offset-PDF code (see _resolve_offset_prior).
+        theta_max (float): Cutoff offset (arcsec).
+        kparam (float): PDF scale param (phi or phi*scale).
+        norm (float): PDF normalization.
+        spacing (float): Grid spacing (arcsec); result scales by its
+            square.
+
+    Returns:
+        float: p(x|O_i) for the candidate.
+    """
+    nrow, ncol = ra.shape
+    acc = 0.0
+    for i in range(nrow):
+        for j in range(ncol):
+            dra = ra[i, j] - cand_ra
+            ddec = dec[i, j] - cand_dec
+            # flat-sky offset in arcsec
+            theta = 3600.0 * np.sqrt(
+                cos_dec * cos_dec * dra * dra + ddec * ddec)
+            if theta < theta_max:
+                if pdf_code == _PDF_CORE:
+                    pw = kparam / (theta + kparam) / norm
+                elif pdf_code == _PDF_UNIFORM:
+                    pw = 1.0 / norm
+                else:  # _PDF_EXP
+                    pw = np.exp(-theta / kparam) / norm
+                acc += L_wx[i, j] * pw
+    return acc * spacing * spacing
+
+
+def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
+                    cand_ang_size, theta_prior, step_size=0.1,
+                    return_grids=False, return_debug:bool=False,
+                    use_numba:bool=False):
     """
     Calculate p(x|O_i), the primary piece of the analysis
 
@@ -91,6 +203,14 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
             Step size for grid, in arcsec
         return_grids (bool, optional):
             if True, return the calculation grid
+        return_debug (bool, optional):
+            if True, return intermediate grids for debugging
+        use_numba (bool, optional):
+            if True, evaluate the per-candidate loop with the numba
+            ``px_Oi`` kernel (single-threaded @njit).  Defaults to
+            False.  Silently falls back to the numpy path if numba is
+            not installed, or if return_grids/return_debug is set (the
+            fused kernel does not build per-pixel grids).
 
     Returns:
         np.ndarray or tuple: p(x|O_i) values and the grids if return_grids = True
@@ -134,10 +254,30 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
     cand_dec = cand_coords.dec.deg    # deg, shape (N,)
     cos_cand_dec = np.cos(np.radians(cand_dec))  # flat-sky scaling
 
+    # The fused numba kernel returns only the scalar p(x|O_i); it cannot
+    # build per-pixel grids, so disable it when those are requested.
+    # Warn (don't error) if numba was asked for but isn't installed.
+    use_numba_eff = use_numba and not return_grids and not return_debug
+    if use_numba and not HAS_NUMBA:
+        warnings.warn("use_numba=True but numba is not installed; "
+                      "falling back to numpy.")
+        use_numba_eff = False
+
     p_xOis, grids = [], []
     # TODO -- multiprocess this
     for icand in range(cand_ra.size):
 
+        if use_numba_eff:
+            # Resolve the prior to scalars, then fuse theta/PDF/product/
+            # sum in one numba pass (no full-grid temporaries).
+            pdf_code, theta_max, kparam, norm = _resolve_offset_prior(
+                cand_ang_size[icand], theta_prior)
+            p_xOis.append(px_Oi_numba(
+                ra, dec, L_wx, cand_ra[icand], cand_dec[icand],
+                cos_cand_dec[icand], pdf_code, theta_max, kparam, norm,
+                grid_spacing_arcsec))
+            continue
+
         # Offsets from the transient (approximate + flat sky)
         theta = 3600*np.sqrt(cos_cand_dec[icand]**2 * (
             ra-cand_ra[icand])**2 + (dec-cand_dec[icand])**2)  # arc sec
diff --git a/astropath/profiling.py b/astropath/profiling.py
index 75b858d..dfc5ab5 100644
--- a/astropath/profiling.py
+++ b/astropath/profiling.py
@@ -146,33 +146,63 @@ def run_profiling(step_sizes=None, box_hwidth=BOX_HWIDTH):
 
     Returns:
         pandas.DataFrame: One row per step size with columns
-            ``step_size``, ``ngrid``, ``n_pixels``, ``calc_LWx_s`` and
-            ``px_Oi_fixedgrid_s`` (times in seconds).
+            ``step_size``, ``ngrid``, ``n_pixels``, ``calc_LWx_s``,
+            ``px_Oi_fixedgrid_s`` (numpy) and ``px_Oi_numba_s`` (the
+            numba ``use_numba=True`` path; NaN if numba is unavailable).
     """
     if step_sizes is None:
         step_sizes = DEFAULT_STEP_SIZES
     localiz, cand_coords, cand_ang_size, theta_prior = default_setup()
 
+    print("Starting profiling sweep over %d step sizes, %d candidates"
+          % (len(step_sizes), len(cand_ang_size)))
+
+    # Warm up the numba JIT once (compile cost is paid on the first call
+    # and must not pollute the timings).  Small grid is enough to compile.
+    if bayesian.HAS_NUMBA:
+        print("  Warming up numba JIT...")
+        bayesian.px_Oi_fixedgrid(
+            box_hwidth, localiz, cand_coords, cand_ang_size,
+            theta_prior, step_size=DEFAULT_STEP_SIZES[0], use_numba=True)
+
     rows = []
     for step_size in step_sizes:
         # Grid for the standalone calc_LWx timing
         ra, dec, ngrid = _build_grid(localiz, box_hwidth, step_size)
         npix = ngrid * ngrid
+        print("  step_size=%.4f  grid=%dx%d (%d pix) ..."
+              % (step_size, ngrid, ngrid, npix))
 
         # Time calc_LWx (localization term only)
         t_lwx = _time_call(localization.calc_LWx,
                            (ra, dec, localiz), npix)
+        print("    calc_LWx: %.1f ms" % (t_lwx * 1e3))
 
-        # Time the full fixed-grid p(x|O_i)
+        # Time the full fixed-grid p(x|O_i) -- numpy path
         t_pxoi = _time_call(
             bayesian.px_Oi_fixedgrid,
             (box_hwidth, localiz, cand_coords, cand_ang_size,
              theta_prior, step_size), npix)
+        print("    px_Oi_fixedgrid (numpy): %.1f ms" % (t_pxoi * 1e3))
+
+        # Time the numba path (use_numba=True), if available
+        if bayesian.HAS_NUMBA:
+            t_numba = _time_call(
+                lambda *a: bayesian.px_Oi_fixedgrid(
+                    box_hwidth, localiz, cand_coords, cand_ang_size,
+                    theta_prior, step_size=step_size, use_numba=True),
+                (), npix)
+            print("    px_Oi_fixedgrid (numba): %.1f ms (%.1fx)"
+                  % (t_numba * 1e3, t_pxoi / t_numba))
+        else:
+            t_numba = np.nan
 
         rows.append(dict(step_size=step_size, ngrid=ngrid,
                          n_pixels=npix, calc_LWx_s=t_lwx,
-                         px_Oi_fixedgrid_s=t_pxoi))
+                         px_Oi_fixedgrid_s=t_pxoi,
+                         px_Oi_numba_s=t_numba))
 
+    print("Profiling sweep complete.")
     return pandas.DataFrame(rows)
 
 
@@ -192,13 +222,20 @@ def plot_results(df, outfile):
     ax.plot(sqrt_pix, df['calc_LWx_s'], 'o-',
             label='calc_LWx')
     ax.plot(sqrt_pix, df['px_Oi_fixedgrid_s'], 's-', color='red',
-            label='px_Oi_fixedgrid')
+            label='px_Oi_fixedgrid (numpy)')
+    # numba curve (only if it was timed)
+    if 'px_Oi_numba_s' in df and df['px_Oi_numba_s'].notna().any():
+        ax.plot(sqrt_pix, df['px_Oi_numba_s'], '^-', color='green',
+                label='px_Oi_fixedgrid (numba)')
+    # Reference line at 10 s
+    ax.axhline(10., color='dimgray', linestyle='--', linewidth=1.5)
     ax.set_xscale('log')
     ax.set_yscale('log')
     ax.set_xlabel('sqrt(grid pixels)')
     ax.set_ylabel('Time (s)')
-    ax.set_title('PATH profiling: numpy implementations')
+    ax.set_title('PATH profiling')
     ax.grid(True, which='both', alpha=0.3)
+    ax.set_xlim(None, 10000.)
     ax.legend()
     fig.tight_layout()
     fig.savefig(outfile, dpi=120)
@@ -220,9 +257,13 @@ def main():
     # Print a readable table (times in ms for legibility)
     show = df.copy()
     show['calc_LWx_ms'] = show['calc_LWx_s'] * 1e3
-    show['px_Oi_fixedgrid_ms'] = show['px_Oi_fixedgrid_s'] * 1e3
-    cols = ['step_size', 'ngrid', 'n_pixels',
-            'calc_LWx_ms', 'px_Oi_fixedgrid_ms']
+    show['px_Oi_numpy_ms'] = show['px_Oi_fixedgrid_s'] * 1e3
+    show['px_Oi_numba_ms'] = show['px_Oi_numba_s'] * 1e3
+    # numba speed-up factor over the numpy path
+    show['numba_speedup'] = (show['px_Oi_fixedgrid_s']
+                             / show['px_Oi_numba_s'])
+    cols = ['step_size', 'ngrid', 'n_pixels', 'calc_LWx_ms',
+            'px_Oi_numpy_ms', 'px_Oi_numba_ms', 'numba_speedup']
     print('\nPATH profiling results (best-of-reps):')
     print(show[cols].to_string(index=False,
                                float_format=lambda v: '%.3f' % v))
diff --git a/astropath/tests/test_speed_up.py b/astropath/tests/test_speed_up.py
index 6d137b4..84932bb 100644
--- a/astropath/tests/test_speed_up.py
+++ b/astropath/tests/test_speed_up.py
@@ -304,3 +304,91 @@ def _ap(*_):
 
     # numpy path should not be slower
     assert t_np <= t_ap
+
+
+# ---------------------------------------------------------------------------
+# Optional numba kernel (use_numba=True) for px_Oi_fixedgrid.
+# ---------------------------------------------------------------------------
+
+# Skip the numba tests entirely if numba is not installed
+numba_required = pytest.mark.skipif(
+    not bayesian.HAS_NUMBA, reason='numba not installed')
+
+
+@numba_required
+@pytest.mark.parametrize("pdf", ['exp', 'core', 'uniform'])
+def test_px_Oi_fixedgrid_numba_matches_numpy(pdf):
+    """use_numba=True must match the numpy path for every PDF."""
+    cent_ra, cent_dec = 120.0, 32.0
+    localiz = _eellipse_localiz(cent_ra, cent_dec, a=1.0, b=0.6, theta=30.)
+    cand_coords, cand_ang_size = _make_candidates(cent_ra, cent_dec)
+    theta_prior = dict(PDF=pdf, max=6., scale=0.5)
+
+    p_np = bayesian.px_Oi_fixedgrid(
+        10., localiz, cand_coords, cand_ang_size, theta_prior,
+        use_numba=False)
+    p_nb = bayesian.px_Oi_fixedgrid(
+        10., localiz, cand_coords, cand_ang_size, theta_prior,
+        use_numba=True)
+
+    # Same math, just fused in the kernel -> agree to roundoff
+    assert np.allclose(p_np, p_nb, rtol=1e-10, atol=1e-15)
+
+
+def test_px_Oi_fixedgrid_numba_fallback_without_numba(monkeypatch):
+    """use_numba=True falls back to numpy (with a warning) if numba is
+    unavailable, and still returns the correct result."""
+    cent_ra, cent_dec = 120.0, 32.0
+    localiz = _eellipse_localiz(cent_ra, cent_dec, a=1.0, b=0.6, theta=30.)
+    cand_coords, cand_ang_size = _make_candidates(cent_ra, cent_dec)
+    theta_prior = dict(PDF='exp', max=6., scale=0.5)
+
+    # Pretend numba is absent regardless of the environment
+    monkeypatch.setattr(bayesian, 'HAS_NUMBA', False)
+
+    p_ref = bayesian.px_Oi_fixedgrid(
+        10., localiz, cand_coords, cand_ang_size, theta_prior,
+        use_numba=False)
+    with pytest.warns(UserWarning):
+        p_fb = bayesian.px_Oi_fixedgrid(
+            10., localiz, cand_coords, cand_ang_size, theta_prior,
+            use_numba=True)
+    assert np.allclose(p_ref, p_fb, rtol=1e-10, atol=1e-15)
+
+
+@numba_required
+def test_px_Oi_fixedgrid_numba_speed_up(capsys):
+    """Time numba vs numpy px_Oi_fixedgrid and report the speed-up.
+
+    The first numba call pays JIT-compile time, so the kernel is warmed
+    up once before timing.
+    """
+    cent_ra, cent_dec = 120.0, 32.0
+    localiz = _eellipse_localiz(cent_ra, cent_dec, a=1.0, b=0.6, theta=30.)
+    cand_coords, cand_ang_size = _make_candidates(
+        cent_ra, cent_dec, ncand=50)
+    theta_prior = dict(PDF='exp', max=6., scale=0.5)
+
+    def _np(*_):
+        return bayesian.px_Oi_fixedgrid(
+            10., localiz, cand_coords, cand_ang_size, theta_prior,
+            use_numba=False)
+
+    def _nb(*_):
+        return bayesian.px_Oi_fixedgrid(
+            10., localiz, cand_coords, cand_ang_size, theta_prior,
+            use_numba=True)
+
+    # Warm up the JIT (compile) before timing
+    p_nb = _nb()
+    assert np.allclose(_np(), p_nb, rtol=1e-10, atol=1e-15)
+
+    t_np = _time_call(_np, None, None, None)
+    t_nb = _time_call(_nb, None, None, None)
+
+    speedup = t_np / t_nb if t_nb > 0 else np.inf
+    with capsys.disabled():
+        print(
+            "\n  px_Oi_fixedgrid (50 cand, 200x200): "
+            "numpy %8.2f ms  numba %8.2f ms  speed-up %5.1fx"
+            % (t_np * 1e3, t_nb * 1e3, speedup))
diff --git a/prompts/speed_up.md b/prompts/speed_up.md
index 8edcbd7..e224c41 100644
--- a/prompts/speed_up.md
+++ b/prompts/speed_up.md
@@ -84,6 +84,43 @@ We wish to speed up the calculation of p(x|O_i) for a given localization using t
 - Use red, and not orange for px_Oi_fixedgrid 
 - Instead of pixels, label the x-axis in sqrt(pixels)
 
+3. I have added the px_Oi_numba method to the bayesian.py file.  Please:
+
+- Update the profiling.py tests to use the px_Oi_numba method
+- Report back on the speed up
+- Include a new curve on the figure for when using numba
+- Log your work in the "Logs" section below.
+
+4. Make these changes to profiling.py:
+
+- Add a few print statements to the profiling.py module to report on progress
+- Add a dark grey horiztonal line at 10s on the figure
+- You do not need to Log these changes
+
+## Numba
+
+We will use numba to speed up the code.  This will mainly be for sandbox analyses.
+
+### px_Oi_fixedgrid
+
+1. Examine the code for px_Oi_fixedgrid.  We will use numba ot speed up the main loop.  Please:
+
+- Examine the code
+- Develop a plan to introduce numba 
+- Try to keep the pw_Oi() method separate from px_Oi_fixedgrid()
+- Log your work in the "Logs" section below.
+- If you have any questions, ask them in the Logs and I will clarify at my next prompt
+- Do not generate any new code yet
+
+2. Proceed with generating a numba option for the main loop.  Please:
+
+- Make numba optional.  It need not be installed, although I have just done so in the astro14 environment.
+- Have use_numba be a boolean flag for the method that is set to False by default.
+- It is ok to single-source the *norm*
+- Start with single-threaded @njit
+- Perform your validation plan using the test_speed_up.py module.
+- Log your work in the "Logs" section below.
+
 ## Prompts
 
 1. Read this doc.  Proceed with the 1st item under Development/calc_LWx
@@ -92,7 +129,10 @@ We wish to speed up the calculation of p(x|O_i) for a given localization using t
 4. Read this doc.  Proceed with the 2nd item under Development/px_Oi_fixedgrid
 5. Read this doc.  Proceed with the 1st item under Development/Profiling
 6. Read this doc.  Proceed with the 2nd item under Development/Profiling
-
+7. Read this doc.  Proceed with the 1st item under Numba/px_Oi_fixedgrid
+8. Read this doc.  Proceed with the 2nd item under Numba/px_Oi_fixedgrid
+9. Read this doc.  Proceed with the 3rd item under Development/Profiling
+10. Read this doc.  Proceed with the 4th item under Development/Profiling
 
 ## Logging
 
@@ -463,4 +503,195 @@ had them nearly on top of each other): `px_Oi_fixedgrid` is now ~3-10x
 the per-candidate grid loop — not the localization term — is the
 dominant cost, making it the prime target for the next optimization
 (numba / vectorization with a memory guard). Figure re-written to
-`astropath/profiling_timing.png`.
\ No newline at end of file
+`astropath/profiling_timing.png`.
+
+### 2026-06-10 (Plan: numba for the px_Oi_fixedgrid main loop)
+
+**Code examined:** `astropath/bayesian.py` — `px_Oi_fixedgrid`
+(lines 67-166) and the `pw_Oi` it calls (15-64). No new code written.
+
+**What the per-candidate loop does** (lines 139-158), per candidate i:
+1. `theta = 3600*sqrt(cos_dec_i^2*(ra-ra_i)^2 + (dec-dec_i)^2)` — a
+   full-grid temporary.
+2. `p_wOi = pw_Oi(theta, phi_i, theta_prior)` — another full-grid
+   temporary; internally allocates `p` and the boolean mask `ok_w`.
+3. `grid_p = L_wx * p_wOi` — a third full-grid temporary.
+4. `p_xOi = np.sum(grid_p) * spacing^2` — reduction to a scalar.
+
+So each candidate allocates ~3-4 arrays the size of the grid (at 7200^2
+that is ~415 MB each) and makes ~5 full-grid passes. With N candidates
+that is the cost the profiling showed (px_Oi_fixedgrid ~ N x the inner
+work). This is exactly what numba fuses well: one pass, no temporaries.
+
+**Plan to introduce numba (keeping px_Oi() separate):**
+
+1. **Factor out a per-candidate kernel `px_Oi(...)`.** Currently no
+   `px_Oi()` exists (only `pw_Oi` and `px_Oi_fixedgrid`). Create
+   `px_Oi()` that computes p(x|O_i) for ONE candidate and returns the
+   scalar. `px_Oi_fixedgrid()` stays the orchestrator: builds the grid,
+   computes `L_wx` via `calc_LWx`, pre-extracts candidate arrays, and
+   loops calling `px_Oi()` once per candidate. This is the separation
+   the prompt asks for and keeps the jitted hot path isolated.
+
+2. **Make `px_Oi()` a numba `@njit` fused kernel.** Signature roughly:
+   `px_Oi(ra, dec, L_wx, cand_ra, cand_dec, cos_dec, pdf_code,
+   theta_max, kparam, norm, spacing) -> float`. It runs a single loop
+   over grid pixels accumulating `L_wx[p] * p_offset(theta)` and returns
+   `acc * spacing^2`. No `theta`/`p_wOi`/`grid_p` temporaries — the
+   dominant memory cost disappears. (Optionally `prange` + reduction for
+   multi-threading; start single-thread, add `parallel=True` after it
+   works.)
+
+3. **Hoist the dict/branching out of the jitted code.** numba nopython
+   mode does not handle the `theta_prior` dict or string `PDF`
+   comparisons cleanly. So in `px_Oi_fixedgrid` (plain Python), resolve
+   the prior ONCE into scalars the kernel can take:
+   - `pdf_code` int (0=core, 1=uniform, 2=exp),
+   - `theta_max` cutoff,
+   - `norm` (the per-candidate normalization),
+   - `kparam` (the PDF's scale: `phi` for core, `phi*scale` for exp,
+     unused for uniform).
+   The kernel then branches on the integer `pdf_code`. **Subtlety to
+   preserve:** in `pw_Oi` the cutoff `ok_w = theta < max*phi` uses the
+   ORIGINAL `phi`, while the `exp` decay uses `phi*scale` — these are
+   different, so the kernel must use `theta_max = max*phi_original` for
+   the cutoff and `kparam = phi*scale` for the exponent.
+
+4. **Keep `pw_Oi` as-is.** It is public/tested and used elsewhere
+   (e.g. `px_Oi_local`). The kernel will duplicate the *elementwise*
+   PDF formula (one line per PDF) but reuse `pw_Oi`'s exact norm
+   expressions via a small shared `_offset_norm(pdf, phi, prior)` helper
+   so the normalization stays single-sourced. Flagging the minor
+   duplication of the elementwise formula as a maintenance note.
+
+5. **Fallbacks / optionality.** numba is NOT installed in astro14
+   (confirmed: `import numba` -> ModuleNotFoundError). Since this is
+   "mainly for sandbox analyses", I propose: import numba behind a
+   try/except; if absent (or a `use_numba=False` kwarg), `px_Oi()`
+   falls back to the current pure-numpy path so nothing breaks. Add
+   numba to requirements as optional.
+
+6. **return_grids / return_debug.** The fused kernel returns only the
+   scalar, so it cannot produce per-pixel `grid_p`. Plan: use the
+   jitted kernel only for the common "return p_xOis" case; when
+   `return_grids`/`return_debug` is set, fall back to the numpy path
+   (those are debugging/inspection paths, not the hot loop).
+
+**Validation plan (for the implementation prompt):** reuse
+`tests/test_speed_up.py` — assert the numba `px_Oi_fixedgrid` matches
+the frozen astropy/numpy reference to roundoff, and time numba vs numpy
+across grid sizes (note numba's first call pays JIT-compile time, so
+warm up once before timing).
+
+**Questions for next prompt:**
+1. numba is missing from astro14 — should I (a) make it an optional
+   dependency with a numpy fallback (my recommendation, given "sandbox"
+   use), or (b) require it and add to requirements/setup? If (a), do you
+   want a `use_numba` kwarg on `px_Oi_fixedgrid`, or auto-detect?
+2. OK to single-source the *norm* in a helper while duplicating the
+   one-line elementwise PDF inside the kernel, or would you rather I
+   keep all three PDFs only in `pw_Oi` and have the kernel handle just
+   `exp` first (the PDF used in profiling/most analyses)?
+3. Start single-threaded `@njit`, or go straight to `parallel=True`
+   with `prange`? (Single-thread first is safer for verifying
+   correctness; parallel can be a follow-up.)
+
+### 2026-06-10 (Implemented optional numba kernel for px_Oi_fixedgrid)
+
+Followed the plan above with the user's clarifications: numba optional,
+`use_numba=False` by default, single-source the norm, single-threaded
+`@njit`, validate via `test_speed_up.py`.
+
+**Code changed:** `astropath/bayesian.py`.
+- Optional import: `try: from numba import njit / HAS_NUMBA=True` else
+  `HAS_NUMBA=False` and a no-op `njit` decorator stand-in. numba is not
+  required to import the module.
+- `_resolve_offset_prior(phi, theta_prior)` — new single-source helper
+  returning `(pdf_code, theta_max, kparam, norm)`. Encodes the PDFs as
+  ints (`_PDF_CORE/_PDF_UNIFORM/_PDF_EXP`) and preserves the subtlety
+  that the `exp` cutoff uses the original `phi` (`theta_max=max*phi`)
+  while the decay length is `phi*scale` (`kparam`).
+- `pw_Oi` refactored to call `_resolve_offset_prior` for the norm +
+  params, then apply the elementwise PDF. Behavior is unchanged (all
+  existing `test_bayesian` tests pass); the norm is now single-sourced.
+- `px_Oi(...)` — new single-threaded `@njit(cache=True)` kernel
+  computing p(x|O_i) for ONE candidate in a single fused loop over grid
+  pixels (theta -> PDF -> *L_wx -> sum), with no full-grid temporaries.
+  Kept separate from both `pw_Oi` and `px_Oi_fixedgrid`.
+- `px_Oi_fixedgrid` gained `use_numba=False`. When effective
+  (`use_numba and HAS_NUMBA and not return_grids/return_debug`) the loop
+  resolves the prior to scalars and calls the `px_Oi` kernel per
+  candidate. If `use_numba=True` but numba is absent it `warnings.warn`s
+  and falls back to numpy; `return_grids`/`return_debug` also force the
+  numpy path (the fused kernel produces no per-pixel grids).
+
+**Tests added** to `tests/test_speed_up.py` (skipped if numba absent via
+`pytest.mark.skipif(not bayesian.HAS_NUMBA)`):
+- `test_px_Oi_fixedgrid_numba_matches_numpy[exp|core|uniform]` —
+  numba vs numpy agree to `rtol=1e-10` for all three PDFs.
+- `test_px_Oi_fixedgrid_numba_fallback_without_numba` — monkeypatches
+  `HAS_NUMBA=False`, asserts a `UserWarning` is raised and the result
+  still matches numpy.
+- `test_px_Oi_fixedgrid_numba_speed_up` — warms up the JIT, then times
+  numba vs numpy and prints the speed-up.
+
+**Measured numba vs numpy** (astro14, 20 candidates, JIT warmed up):
+
+| grid        | numpy     | numba     | speed-up |
+|-------------|-----------|-----------|----------|
+| 360x360     | 16.5 ms   | 12.3 ms   | 1.3x     |
+| 720x720     | 92.3 ms   | 62.4 ms   | 1.5x     |
+| 1800x1800   | 879.7 ms  | 446.4 ms  | 2.0x     |
+| 3600x3600   | 7557.0 ms | 2191.3 ms | 3.4x     |
+
+The speed-up grows with grid size, as expected: the numpy path
+allocates ~3-4 full-grid temporaries and makes ~5 passes per candidate,
+while the fused kernel does one pass with no temporaries — so the win is
+largest exactly where memory bandwidth dominates (big grids). For small
+grids the gain is modest (and the first call additionally pays one-time
+JIT compilation, not shown here since it is warmed up). All 25 tests in
+the relevant suites pass.
+
+**Maintenance note:** the elementwise PDF formula now exists in two
+places — `pw_Oi` (numpy) and the `px_Oi` kernel (numba). The
+*normalization* and parameter resolution are single-sourced in
+`_resolve_offset_prior`, but the per-pixel PDF line itself is
+necessarily duplicated for the jitted path; a new PDF must be added to
+both (and `_resolve_offset_prior`).
+
+### 2026-06-10 (Profiling: added numba curve + speed-up report)
+
+**Context:** the user renamed the kernel `px_Oi` -> `px_Oi_numba` in
+`bayesian.py` (call site updated to match). This entry updates
+`astropath/profiling.py` to exercise the `use_numba=True` path.
+
+**Code changed:** `astropath/profiling.py`.
+- `run_profiling()` now warms up the numba JIT once (small grid) before
+  timing, then for each grid size also times
+  `px_Oi_fixedgrid(..., use_numba=True)`. Adds a `px_Oi_numba_s`
+  column (NaN if `bayesian.HAS_NUMBA` is False).
+- `plot_results()` adds a third curve (green triangles) for the numba
+  path, drawn only when numba timings exist; the numpy curve is now
+  labeled "px_Oi_fixedgrid (numpy)". Title -> "numpy vs numba".
+- `main()` table now prints numpy vs numba times side by side plus a
+  `numba_speedup` column.
+
+**Results** (astro14, 50 candidates, box_hwidth=90"):
+
+| step_size | ngrid | calc_LWx (ms) | numpy (ms) | numba (ms) | speed-up |
+|-----------|-------|---------------|------------|------------|----------|
+| 0.500     | 360   | 9.68          | 30.21      | 18.46      | 1.64x    |
+| 0.250     | 720   | 42.58         | 169.26     | 81.11      | 2.09x    |
+| 0.100     | 1800  | 296.46        | 1767.59    | 590.88     | 2.99x    |
+| 0.050     | 3600  | 1507.34       | 15659.78   | 2874.86    | 5.45x    |
+| 0.025     | 7200  | 6092.52       | 65256.18   | 11548.08   | 5.65x    |
+
+**Speed-up report:** numba accelerates the fixed-grid p(x|O_i) by
+~1.6x on small grids up to ~5.7x at 7200x7200 with 50 candidates —
+larger than the 20-candidate run logged earlier (max 3.4x) because more
+candidates mean more passes over the grid, so eliminating the per-pixel
+temporaries pays off more. On the figure the numba curve (green) sits
+between `calc_LWx` (blue) and the numpy `px_Oi_fixedgrid` (red): at the
+largest grid the per-candidate work is no longer dominating — numba
+brings it down toward the cost of the single `calc_LWx` localization
+pass. Figure re-written to `astropath/profiling_timing.png`.
\ No newline at end of file

From 422873776513c3f30765360ea1c58c1fca77ea49 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Wed, 10 Jun 2026 06:00:37 -0700
Subject: [PATCH 14/31] docs

---
 docs/frb_example.rst  |   8 ++-
 docs/index.rst        |   8 +++
 docs/localization.rst |   4 ++
 docs/performance.rst  | 111 ++++++++++++++++++++++++++++++++++++++++++
 prompts/speed_up.md   |  46 ++++++++++++++++-
 5 files changed, 175 insertions(+), 2 deletions(-)
 create mode 100644 docs/performance.rst

diff --git a/docs/frb_example.rst b/docs/frb_example.rst
index c2ba214..e356717 100644
--- a/docs/frb_example.rst
+++ b/docs/frb_example.rst
@@ -94,4 +94,10 @@ Another simple call with the "fixed" approach::
     P_Ox, P_Ux = Path.calc_posteriors('fixed', box_hwidth=30.)
 
 
-And we are all done!
\ No newline at end of file
+And we are all done!
+
+.. note::
+
+   For large grids you can optionally accelerate the fixed-grid
+   calculation with ``numba`` (off by default; falls back to numpy if
+   ``numba`` is not installed). See :doc:`performance` for details.
\ No newline at end of file
diff --git a/docs/index.rst b/docs/index.rst
index 88c81b7..298c026 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -64,6 +64,14 @@ Scripts
 
    scripts
 
+Performance
+-----------
+
+.. toctree::
+   :maxdepth: 2
+
+   performance
+
 Notebooks
 ---------
 
diff --git a/docs/localization.rst b/docs/localization.rst
index e1f7650..7efbdcc 100644
--- a/docs/localization.rst
+++ b/docs/localization.rst
@@ -32,6 +32,10 @@ The last line of code checks against the data model.
 The code then defines the localization PDF as a 2D Gaussian
 with sigma's "a" and "b" and orientation given by "theta".
 
+The error-ellipse evaluation of :math:`L(w-x)`
+(``localization.calc_LWx``) is implemented in pure numpy for speed;
+see :doc:`performance`.
+
 Healpix
 =======
 
diff --git a/docs/performance.rst b/docs/performance.rst
new file mode 100644
index 0000000..59a5752
--- /dev/null
+++ b/docs/performance.rst
@@ -0,0 +1,111 @@
+***********
+Performance
+***********
+
+This doc describes the performance-oriented pieces of *astropath*:
+the numpy-accelerated core calculations, the optional ``numba``
+acceleration for the fixed-grid posterior, and the ``profiling``
+module used to measure them.
+
+numpy-accelerated core
+======================
+
+The two most expensive steps in a PATH analysis have been
+re-implemented in pure numpy:
+
+- ``localization.calc_LWx`` (the localization term :math:`L(w-x)`)
+  for the error-ellipse (``eellipse``) localization now computes the
+  angular separation and position angle with closed-form numpy
+  formulae instead of ``astropy`` ``SkyCoord`` operations. Results are
+  numerically identical (to roundoff) and the routine is several times
+  faster on large grids.
+
+- ``bayesian.px_Oi_fixedgrid`` (the fixed-grid :math:`p(x|O_i)`)
+  pre-extracts the candidate and center coordinates into numpy arrays
+  once, rather than reading ``astropy`` attributes inside the
+  per-candidate loop.
+
+These changes are transparent: you do not need to do anything to
+benefit from them, and the public APIs are unchanged.
+
+Optional numba acceleration
+===========================
+
+The per-candidate loop of ``bayesian.px_Oi_fixedgrid`` can optionally
+be evaluated with a `numba <https://numba.pydata.org/>`_ kernel
+(``bayesian.px_Oi_numba``) that fuses the offset, offset-PDF, product
+with :math:`L(w-x)`, and grid sum into a single pass with no full-grid
+temporaries.
+
+To enable it, pass ``use_numba=True``::
+
+    from astropath import bayesian
+
+    p_xOi = bayesian.px_Oi_fixedgrid(
+        box_hwidth, localiz, cand_coords, cand_ang_size,
+        theta_prior, step_size=0.1, use_numba=True)
+
+Key points:
+
+- **Optional.** ``numba`` need *not* be installed. If it is absent (or
+  if you simply leave ``use_numba=False``, the default), the
+  calculation runs via the standard numpy path. With ``use_numba=True``
+  but ``numba`` not installed, the code emits a warning and falls back
+  to numpy — it never errors.
+
+- **Default is off.** ``use_numba`` defaults to ``False``, so existing
+  code and results are unchanged unless you opt in.
+
+- **Only ``px_Oi_fixedgrid``.** The numba option is available *only*
+  for the fixed-grid method. ``px_Oi_local`` and the other routines are
+  unaffected. The fused kernel returns only the scalar posterior, so it
+  is bypassed (numpy path used) when ``return_grids`` or
+  ``return_debug`` is requested.
+
+- **Primarily for sandbox analyses.** numba is recommended mainly for
+  interactive/sandbox work and large-grid experiments, where its
+  speed-up is largest. The first call pays a one-time JIT compilation
+  cost; the win grows with the grid size and the number of candidates
+  (roughly 1.5x on small grids up to ~5-6x on a 7200x7200 grid with
+  many candidates).
+
+.. note::
+
+   The numba flag is exposed on ``bayesian.px_Oi_fixedgrid`` directly.
+   The high-level ``path.PATH.calc_posteriors`` does not currently
+   forward ``use_numba``; call ``bayesian.px_Oi_fixedgrid`` directly to
+   use it.
+
+Profiling module
+================
+
+The ``astropath.profiling`` module measures these calculations across a
+range of grid sizes. It mirrors the
+``calculations/step_size/Profiling.ipynb`` notebook: a faux FRB, a
+circular error ellipse, and a set of candidate galaxies spread over a
+range of locations and angular sizes.
+
+Run it from the command line::
+
+    python -m astropath.profiling
+
+This sweeps a range of ``step_size`` values (hence grid sizes), prints
+a timing table comparing ``calc_LWx``, the numpy ``px_Oi_fixedgrid``,
+and (if ``numba`` is installed) the numba path with its speed-up
+factor, and writes a figure (``profiling_timing.png``) of the timings
+versus grid size.
+
+You can also import and call it directly::
+
+    from astropath import profiling
+
+    df = profiling.run_profiling()      # returns a pandas DataFrame
+    profiling.plot_results(df, 'timing.png')
+
+API Reference
+=============
+
+.. automodule:: astropath.profiling
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/prompts/speed_up.md b/prompts/speed_up.md
index e224c41..e96a4f6 100644
--- a/prompts/speed_up.md
+++ b/prompts/speed_up.md
@@ -121,6 +121,17 @@ We will use numba to speed up the code.  This will mainly be for sandbox analyse
 - Perform your validation plan using the test_speed_up.py module.
 - Log your work in the "Logs" section below.
 
+## Docs
+
+1. Examine the docs in the astropath/docs directory.  We need to update the documentation to reflect the new code and the numba option.  Please:
+
+- Update the documentation to reflect the new code and the numba option.
+- Emphasize that the numba option is optional and that the code will fall back to the numpy option if numba is not installed or if the user does not set use_numba to True.
+- Comment that the numba option is only available for the px_Oi_fixedgrid method.
+- Add that it is primarily recommended for sandbox analyses.
+- Comment on the profiling.py module too
+- Log your work in the "Logs" section below.
+
 ## Prompts
 
 1. Read this doc.  Proceed with the 1st item under Development/calc_LWx
@@ -133,6 +144,7 @@ We will use numba to speed up the code.  This will mainly be for sandbox analyse
 8. Read this doc.  Proceed with the 2nd item under Numba/px_Oi_fixedgrid
 9. Read this doc.  Proceed with the 3rd item under Development/Profiling
 10. Read this doc.  Proceed with the 4th item under Development/Profiling
+11. Read this doc.  Proceed with the 1st item under Docs
 
 ## Logging
 
@@ -694,4 +706,36 @@ temporaries pays off more. On the figure the numba curve (green) sits
 between `calc_LWx` (blue) and the numpy `px_Oi_fixedgrid` (red): at the
 largest grid the per-candidate work is no longer dominating — numba
 brings it down toward the cost of the single `calc_LWx` localization
-pass. Figure re-written to `astropath/profiling_timing.png`.
\ No newline at end of file
+pass. Figure re-written to `astropath/profiling_timing.png`.
+
+### 2026-06-10 (Documentation: numpy/numba speed-ups + profiling)
+
+**Docs added/updated** under `docs/`.
+- New page `docs/performance.rst` with sections: (1) the transparent
+  numpy acceleration of `calc_LWx` (eellipse) and `px_Oi_fixedgrid`;
+  (2) the optional numba option — how to enable it
+  (`px_Oi_fixedgrid(..., use_numba=True)`) and the key caveats; (3) the
+  `profiling` module (CLI `python -m astropath.profiling` + import use),
+  with an `automodule` API reference.
+- Emphasized per the prompt: numba is **optional** (need not be
+  installed), `use_numba` defaults to **False**, and the code **falls
+  back to numpy** (with a warning) if numba is absent or the flag is not
+  set; the numba option is available **only for `px_Oi_fixedgrid`**
+  (not `px_Oi_local`/others, and bypassed for
+  `return_grids`/`return_debug`); and it is **primarily recommended for
+  sandbox analyses**.
+- Added an honest `.. note::` that `use_numba` is exposed on
+  `bayesian.px_Oi_fixedgrid` directly and is *not* currently forwarded
+  by `path.PATH.calc_posteriors` (verified in `path.py`) — call the
+  bayesian function directly to use it.
+- Linked the new page from `docs/index.rst` (new "Performance"
+  toctree section). Added cross-reference `.. note::` pointers in
+  `docs/frb_example.rst` (posterior step) and `docs/localization.rst`
+  (calc_LWx eellipse) to `:doc:\`performance\``.
+
+**Validation:** sphinx/docutils are not installed in astro14, so I
+could not run `make html` here. Instead I checked that all RST section
+underlines are >= their title length (no would-be build warnings) and
+that every `index.rst` toctree entry resolves to an existing
+`.rst`/`.ipynb` file. Both checks pass. A full `make html` should be
+run in the docs environment to confirm rendering.
\ No newline at end of file

From e9686c061def76ed5d1d20b5e1758245913c273d Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Wed, 10 Jun 2026 08:30:30 -0700
Subject: [PATCH 15/31] correction

---
 astropath/bayesian.py            | 63 +++++++++++++++++++-----
 astropath/path.py                | 24 ++++++---
 astropath/run.py                 | 83 ++++++++++++++++++++++++++------
 astropath/tests/test_bayesian.py |  4 +-
 astropath/tests/test_speed_up.py | 20 ++++++++
 prompts/speed_up.md              | 58 +++++++++++++++++++++-
 6 files changed, 214 insertions(+), 38 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index fe40a02..d3316c5 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -153,10 +153,16 @@ def px_Oi_numba(ra, dec, L_wx, cand_ra, cand_dec, cos_dec,
             square.
 
     Returns:
-        float: p(x|O_i) for the candidate.
+        tuple: (p_xOi, pw_sum)
+            p_xOi (float): UNcorrected p(x|O_i) for the candidate
+                (= sum of L_wx*p(w|O_i) over the grid, times spacing^2).
+            pw_sum (float): Sum of p(w|O_i) over the grid.  Returned so
+                ``px_Oi_fixedgrid`` can apply the optional 'p_wO'
+                correction with the same formula as the numpy path.
     """
     nrow, ncol = ra.shape
     acc = 0.0
+    pw_sum = 0.0  # sum of p(w|O_i) over the grid, for the p_wO correction
     for i in range(nrow):
         for j in range(ncol):
             dra = ra[i, j] - cand_ra
@@ -172,13 +178,15 @@ def px_Oi_numba(ra, dec, L_wx, cand_ra, cand_dec, cos_dec,
                 else:  # _PDF_EXP
                     pw = np.exp(-theta / kparam) / norm
                 acc += L_wx[i, j] * pw
-    return acc * spacing * spacing
+                pw_sum += pw  # p(w|O_i)=0 outside support, so this is
+                #               the full-grid sum
+    return acc * spacing * spacing, pw_sum
 
 
 def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
                     cand_ang_size, theta_prior, step_size=0.1,
                     return_grids=False, return_debug:bool=False,
-                    use_numba:bool=False):
+                    use_numba:bool=False, correction:str=None):
     """
     Calculate p(x|O_i), the primary piece of the analysis
 
@@ -211,6 +219,10 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
             False.  Silently falls back to the numpy path if numba is
             not installed, or if return_grids/return_debug is set (the
             fused kernel does not build per-pixel grids).
+        correction (str, optional): Correction to apply to the posteriors
+            'p_wO' -- Correct p(w|O)
+            'L_wx' -- Correct L(w-x)
+            None -- No correction
 
     Returns:
         np.ndarray or tuple: p(x|O_i) values and the grids if return_grids = True
@@ -241,9 +253,13 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
     # L(w-x) -- 2D Gaussian, normalized to 1 when integrating over x not omega
     # Approximate as flat sky
     #  Warning:  RA increases in x for these grids!!
+    print('Calculating L(w-x)')
     ra = center_ra + xcoord/3600. / cos_center_dec
     dec = center_dec + ycoord/3600.
     L_wx = localization.calc_LWx(ra, dec, localiz)
+    # Prep for correction
+    if correction == 'L_wx':
+        corr_Lwx = np.sum(L_wx) * grid_spacing_arcsec**2
 
     # Pre-extract candidate coordinates to numpy arrays ONCE (numpy
     # only).  Iterating a SkyCoord array and reading .ra/.dec per
@@ -265,17 +281,28 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
 
     p_xOis, grids = [], []
     # TODO -- multiprocess this
+    print('Looping on candidates')
     for icand in range(cand_ra.size):
+        if icand % 50 == 0:
+            print(f'icand: {icand}')
 
         if use_numba_eff:
             # Resolve the prior to scalars, then fuse theta/PDF/product/
             # sum in one numba pass (no full-grid temporaries).
             pdf_code, theta_max, kparam, norm = _resolve_offset_prior(
                 cand_ang_size[icand], theta_prior)
-            p_xOis.append(px_Oi_numba(
+            p_val, pw_sum = px_Oi_numba(
                 ra, dec, L_wx, cand_ra[icand], cand_dec[icand],
                 cos_cand_dec[icand], pdf_code, theta_max, kparam, norm,
-                grid_spacing_arcsec))
+                grid_spacing_arcsec)
+            # Apply the SAME optional correction as the numpy path.
+            # Dividing the grid by a scalar then summing == dividing the
+            # sum, so we correct the scalar p(x|O_i) directly.
+            if correction == 'p_wO':
+                p_val /= np.sum(pw_sum) * grid_spacing_arcsec**2
+            elif correction == 'L_wx':
+                p_val /= corr_Lwx
+            p_xOis.append(p_val)
             continue
 
         # Offsets from the transient (approximate + flat sky)
@@ -290,12 +317,21 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
         # Product
         grid_p = L_wx * p_wOi
 
+
         # Save grids if returning
         if return_grids:
             grids.append(grid_p.copy())
 
         # Sum
-        p_xOis.append(np.sum(grid_p)*grid_spacing_arcsec**2)
+        p_val = np.sum(grid_p)*grid_spacing_arcsec**2
+
+        # Correction
+        if correction == 'p_wO':
+            p_val /= np.sum(p_wOi) * grid_spacing_arcsec**2
+        elif correction == 'L_wx':
+            p_val /= corr_Lwx
+
+        p_xOis.append(p_val)
 
     # Return
     if return_grids:
@@ -372,21 +408,24 @@ def px_Oi_local(localiz, cand_coords, cand_ang_size,
     return np.array(p_xOis)
 
 
-def px_U(box_hwidth):
+def px_U(radius:float):
     """
 
     Args:
-        box_hwidth (float):
-            Half-width of the analysis box, in arcsec
+        radius (float):
+            Radius of the area enclosing the candidates
+            in arcsec
 
     Returns:
-        float: p(x|U)
+        float: p(x|U) in squarearcsec
 
     """
-    box_sqarcsec = (2*box_hwidth)**2
+    #box_sqarcsec = (2*box_hwidth)**2
     #box_steradians = box_sqarcsec * sqarcsec_steradians
+    area = np.pi * radius**2
     #
-    return 1./box_sqarcsec  # box_steradians
+    #return 1./box_sqarcsec  # box_steradians
+    return 1./area  
 
 
 
diff --git a/astropath/path.py b/astropath/path.py
index d9a42a1..3ce3b45 100644
--- a/astropath/path.py
+++ b/astropath/path.py
@@ -163,8 +163,12 @@ def calc_priors(self, ifilter:str='r'):
         # Return them too
         return self.prior_Oi
 
-    def calc_posteriors(self, method:str, step_size=0.1, box_hwidth=None,
-                        max_radius=None, debug:bool=False):
+    def calc_posteriors(self, method:str, step_size:float=0.1, 
+                        box_hwidth=None,
+                        survey_radius:float=None, 
+                        use_numba:bool=False, 
+                        debug:bool=False, 
+                        correction:str=None):
         """Calculate the posteriors
 
         Args:
@@ -173,10 +177,14 @@ def calc_posteriors(self, method:str, step_size=0.1, box_hwidth=None,
                 local -- One grid is generated for each candidate
             step_size (float, optional): [description]. Defaults to 0.1.
             box_hwidth (float, optional): [description]. Defaults to None.
-            max_radius (float, optional): Maximum radius (arcsec)
+            survey_radius (float, optional): Maximum radius (arcsec)
                 allowed for galaxy. Only required for cases
                 where P(U)>0.
+            use_numba (bool, optional): Use numba for calculations. Default False.
             debug (bool, optional):  Debug
+            correction (str, optional): Correction to apply to the posteriors
+                'p_wO' -- Correct p(w|O)
+                'L_wx' -- Correct L(w-x)
 
         Raises:
             IOError: [description]
@@ -205,7 +213,9 @@ def calc_posteriors(self, method:str, step_size=0.1, box_hwidth=None,
                         self.cand_coords,
                         self.candidates['ang_size'].values, 
                         self.theta_prior, 
-                        step_size=step_size)
+                        step_size=step_size,
+                        use_numba=use_numba,
+                        correction=correction)
         elif method == 'local':
             self.p_xOi = bayesian.px_Oi_local(
                         self.localiz, 
@@ -219,14 +229,14 @@ def calc_posteriors(self, method:str, step_size=0.1, box_hwidth=None,
         # P(U|x)
         logging.info("Calculating p(x|U)")
         if self.cand_prior['P_U'] > 0.:
-            if max_radius is None:
-                raise IOError("Set max_radius given that P(U) > 0!!")
+            if survey_radius is None:
+                raise IOError("Set survey_radius given that P(U) > 0!!")
             if self.cand_prior['P_O_method']=='user':
                 # leave unmodified
                 self.p_xU = 1
             else:
                 # downweight by FOV
-                self.p_xU = bayesian.px_U(max_radius)
+                self.p_xU = bayesian.px_U(survey_radius)
         else:
             self.p_xU = 0.
         
diff --git a/astropath/run.py b/astropath/run.py
index 4fc0a15..6d1ba06 100644
--- a/astropath/run.py
+++ b/astropath/run.py
@@ -9,12 +9,12 @@
 from astropy.coordinates import SkyCoord
 from astropy.table import Table
 from astropy import units
-from astropath import catalogs
-
-import pandas
 
+from astropath import catalogs
 from astropath import path
 
+from IPython import embed
+
 
 def run_on_dict(idict: dict,
                 verbose: bool = False,
@@ -22,6 +22,7 @@ def run_on_dict(idict: dict,
                 mag_key: str = None,
                 skip_NGC: bool = False,
                 dust_correct: bool = True,
+                use_local: bool = False,
                 star_galaxy_sep: dict = None):
     """Run PATH on a single FRB, given a dictionary of inputs.
 
@@ -58,6 +59,9 @@ def run_on_dict(idict: dict,
         skip_NGC (bool, optional): Skip adding NGC galaxies when querying. Defaults to False.
         dust_correct (bool, optional): Dust correct magnitudes when querying. Defaults to True.
         star_galaxy_sep (dict, optional): Star/galaxy separation parameters for catalog query.
+        use_local (bool, optional): Use the local method for calculating posteriors. Defaults to False.
+            If True, will use the local method for calculating posteriors.
+            If False, will use the fixed method for calculating posteriors.
 
     Returns:
         tuple: 6 items --
@@ -110,8 +114,18 @@ def run_on_dict(idict: dict,
         return catalog, None, None, None, None, None
 
     # Set boxsize according to the largest galaxy (arcsec)
-    box_hwidth = max(idict['max_box'], 10. * np.max(catalog['ang_size']))
-
+    #  or the survey size, whichever is larger
+    # TODO -- X decided this is not worth the extra compute
+    #cat_coord = SkyCoord(ra=catalog['ra'].data, dec=catalog['dec'].data, unit='deg')
+    #sep = coord.separation(cat_coord).to('arcsec')
+    #max_sep = np.max(sep + 6*catalog['ang_size'].data*units.arcsec)
+    #embed(header='run.py:117')
+
+    #box_hwidth = max(idict['max_box'],  # This should be the survey size
+    #    max_sep.value)
+    box_hwidth = idict['max_box']  # This should be the survey size
+    cut_catalog = catalog
+    '''
     # Cut down the catalog based on box_hwidth
     Ddec_arcsec = np.abs(catalog['dec'].data - coord.dec.deg) * 3600.
     Dra_arcsec = np.abs(catalog['ra'].data - coord.ra.deg) * 3600. * np.cos(coord.dec.rad)
@@ -122,6 +136,7 @@ def run_on_dict(idict: dict,
 
     if len(cut_catalog) == 0:
         return cut_catalog, None, None, None, None, None
+    '''
 
     # Initialize PATH
     Path = path.PATH()
@@ -160,13 +175,13 @@ def run_on_dict(idict: dict,
 
     # Candidate prior
     P_O_method = priors_dict.get('P_O_method', 'inverse')
-    P_U = priors_dict.get('PU', 0.)
+    P_U = priors_dict['PU']
     Path.init_cand_prior(P_O_method, P_U=P_U)
 
     # Offset prior
-    theta_PDF = priors_dict.get('theta_PDF', 'exp')
+    theta_PDF = priors_dict['theta_PDF']
     theta_max = priors_dict.get('theta_max', 6.)
-    scale = priors_dict.get('scale', 0.5)
+    scale = priors_dict['scale']
     Path.init_theta_prior(theta_PDF, theta_max, scale)
 
     # Calculate priors
@@ -174,19 +189,47 @@ def run_on_dict(idict: dict,
 
     # Calculate step size based on localization and galaxy sizes
     if idict['ltype'] == 'eellipse':
-        a = eellipse['a']
-        b = eellipse['b']
-        step_size_max = 2 * 3 * np.nanmin([a, b]) / np.nanmax(cut_catalog['ang_size'])
-        step_size = np.nanmin([0.1, step_size_max])
+        # OLD
+        #a = eellipse['a']
+        #b = eellipse['b']
+        #step_size_max = 2 * 3 * np.nanmin([a, b]) / np.nanmax(cut_catalog['ang_size'])
+        #step_size = np.nanmin([0.1, step_size_max])
+        # New
+        min_ang = np.nanmin(cut_catalog['ang_size'].data)
+        if eellipse['b'] > min_ang:
+            correction = 'p_wO'
+            step_size = eellipse['b'] / 20.
+        else:
+            correction = 'L_wx'
+            step_size = min_ang / 20.
     else:
         # For healpix, use default step size
+        raise ValueError("Healpix localization is not supported yet.")
         step_size = 0.1
 
+    # Add to dict
+    idict['step_size'] = step_size
+
     # Calculate posteriors
-    P_Ox, P_Ux = Path.calc_posteriors('local',
+    if idict['pmode'] == 'local':
+        print(f'Calculating posteriors with local') 
+        P_Ox, P_Ux = Path.calc_posteriors('local',
                                        box_hwidth=box_hwidth,
-                                       max_radius=box_hwidth,
+                                       survey_radius=idict['ssize']*60,
                                        step_size=step_size)
+    elif idict['pmode'] == 'fixed':
+        print(f'Calculating posteriors with fixed and correction: {correction}')
+        P_Ox, P_Ux = Path.calc_posteriors('fixed',
+                                       box_hwidth=box_hwidth,
+                                       survey_radius=idict['ssize']*60,
+                                       step_size=step_size,
+                                       use_numba=idict['use_numba'],
+                                       correction=correction)
+    else:
+        raise ValueError(f"Unsupported posterior mode: {idict['pmode']}. "
+                        f"Supported: 'local', 'fixed'")
+
+    #embed(header='run.py:231')
 
     # Add photo-z columns if available in catalog
     photoz_columns = ['z_phot_median', 'z_phot_l68', 'z_phot_u68',
@@ -217,6 +260,9 @@ def set_anly_sizes(ltype: str, lparam: dict):
     This helper function computes appropriate survey search radius (ssize)
     and maximum analysis box size (max_box) based on localization parameters.
 
+    Note: These are guidelines recommended by the PATH
+    developers.  You should use your own judgement
+
     Args:
         ltype (str): Type of localization ['eellipse', 'healpix']
         lparam (dict): Parameters for localization
@@ -265,6 +311,8 @@ def build_idict(ra: float, dec: float,
                 scale: float = 0.5,
                 theta_PDF: str = 'exp',
                 theta_max: float = 6.0,
+                use_numba: bool = False,
+                pmode: str = 'fixed',
                 survey: str = None,
                 ssize: float = None,
                 max_box: float = None):
@@ -288,6 +336,7 @@ def build_idict(ra: float, dec: float,
         survey (str, optional): Survey name for automatic catalog query.
             Supported: 'Pan-STARRS', 'DECaL'. If None, catalog must be provided
             to run_on_dict().
+        use_numba (bool): Use numba for calculations. Default False.
         ssize (float): Survey search radius in arcmin. If None, auto-computed.
         max_box (float): Maximum analysis box in arcsec. If None, auto-computed.
 
@@ -322,11 +371,13 @@ def build_idict(ra: float, dec: float,
     idict = {
         'ra': ra,
         'dec': dec,
-        'ssize': ssize,
+        'ssize': ssize, # arcmin
         'ltype': ltype,
         'lparam': lparam,
+        'use_numba': use_numba,
+        'pmode': pmode,
         'priors': priors,
-        'max_box': max_box,
+        'max_box': max_box, # arcsec
     }
 
     return idict
diff --git a/astropath/tests/test_bayesian.py b/astropath/tests/test_bayesian.py
index 708ab3d..4e030f3 100644
--- a/astropath/tests/test_bayesian.py
+++ b/astropath/tests/test_bayesian.py
@@ -148,9 +148,9 @@ def test_PU():
     p_xU = bayesian.px_U(box_radius)
     # p(x)
     p_x = np.sum(candidates.P_O * candidates.p_xO) + p_xU * cand_prior['P_U']
-    assert np.isclose(p_x, 0.010006174202053927)
+    assert np.isclose(p_x, 0.010013764189863593)
 
     # P(U|x)
     P_Ux = cand_prior['P_U'] * p_xU / p_x
-    assert np.isclose(P_Ux, 0.0027760637799086035)
+    assert np.isclose(P_Ux, 0.003531915118126432)
 
diff --git a/astropath/tests/test_speed_up.py b/astropath/tests/test_speed_up.py
index 84932bb..05d39cc 100644
--- a/astropath/tests/test_speed_up.py
+++ b/astropath/tests/test_speed_up.py
@@ -335,6 +335,26 @@ def test_px_Oi_fixedgrid_numba_matches_numpy(pdf):
     assert np.allclose(p_np, p_nb, rtol=1e-10, atol=1e-15)
 
 
+@numba_required
+@pytest.mark.parametrize("pdf", ['exp', 'core', 'uniform'])
+@pytest.mark.parametrize("correction", ['p_wO', 'L_wx'])
+def test_px_Oi_fixedgrid_numba_matches_numpy_correction(pdf, correction):
+    """numba must match numpy with the optional correction factor too."""
+    cent_ra, cent_dec = 120.0, 32.0
+    localiz = _eellipse_localiz(cent_ra, cent_dec, a=1.0, b=0.6, theta=30.)
+    cand_coords, cand_ang_size = _make_candidates(cent_ra, cent_dec)
+    theta_prior = dict(PDF=pdf, max=6., scale=0.5)
+
+    p_np = bayesian.px_Oi_fixedgrid(
+        10., localiz, cand_coords, cand_ang_size, theta_prior,
+        use_numba=False, correction=correction)
+    p_nb = bayesian.px_Oi_fixedgrid(
+        10., localiz, cand_coords, cand_ang_size, theta_prior,
+        use_numba=True, correction=correction)
+
+    assert np.allclose(p_np, p_nb, rtol=1e-10, atol=1e-15)
+
+
 def test_px_Oi_fixedgrid_numba_fallback_without_numba(monkeypatch):
     """use_numba=True falls back to numpy (with a warning) if numba is
     unavailable, and still returns the correct result."""
diff --git a/prompts/speed_up.md b/prompts/speed_up.md
index e96a4f6..4b58244 100644
--- a/prompts/speed_up.md
+++ b/prompts/speed_up.md
@@ -97,6 +97,12 @@ We wish to speed up the calculation of p(x|O_i) for a given localization using t
 - Add a dark grey horiztonal line at 10s on the figure
 - You do not need to Log these changes
 
+5. Make these changes to profiling.py:
+
+- Include the JIT warm-up as part of the timing 
+- Have it be the default option to call px_Oi_fixedgrid() with correction='p_wO'
+- Log your work in the "Logs" section below.
+
 ## Numba
 
 We will use numba to speed up the code.  This will mainly be for sandbox analyses.
@@ -121,6 +127,12 @@ We will use numba to speed up the code.  This will mainly be for sandbox analyse
 - Perform your validation plan using the test_speed_up.py module.
 - Log your work in the "Logs" section below.
 
+3. I have made a changes to the px_Oi_fixedgrid method to implement an optional correction factor. Please:
+
+- Update the numba version to implement the same correction factor as the numpy version
+- Test these changes
+- Log your work in the "Logs" section below.
+
 ## Docs
 
 1. Examine the docs in the astropath/docs directory.  We need to update the documentation to reflect the new code and the numba option.  Please:
@@ -145,6 +157,8 @@ We will use numba to speed up the code.  This will mainly be for sandbox analyse
 9. Read this doc.  Proceed with the 3rd item under Development/Profiling
 10. Read this doc.  Proceed with the 4th item under Development/Profiling
 11. Read this doc.  Proceed with the 1st item under Docs
+12. Read this doc.  Proceed with the 3rd item under Numba/px_Oi_fixedgrid
+13. Read this doc.  Proceed with the 5th item under Development/Profiling
 
 ## Logging
 
@@ -738,4 +752,46 @@ could not run `make html` here. Instead I checked that all RST section
 underlines are >= their title length (no would-be build warnings) and
 that every `index.rst` toctree entry resolves to an existing
 `.rst`/`.ipynb` file. Both checks pass. A full `make html` should be
-run in the docs environment to confirm rendering.
\ No newline at end of file
+run in the docs environment to confirm rendering.
+
+### 2026-06-10 (numba: match the optional correction factor)
+
+**Context:** the user added an optional `correction` kwarg to the numpy
+`px_Oi_fixedgrid` (`'p_wO'`, `'L_wx'`, or `None`). For a candidate the
+numpy path does `grid_p = L_wx * p_wOi`, then divides the grid by a
+scalar — `sum(p_wOi)/spacing^2` for `'p_wO'` (candidate-dependent) or
+`sum(L_wx)/spacing^2` for `'L_wx'` (candidate-independent) — before
+summing. This entry makes the numba path apply the identical
+correction.
+
+**Code changed:** `astropath/bayesian.py`.
+- `px_Oi_numba` now also accumulates `pw_sum = sum(p(w|O_i))` over the
+  grid and returns `(p_xOi_uncorrected, pw_sum)`. Since p(w|O_i)=0
+  outside the support (`theta >= theta_max`), accumulating only inside
+  the cutoff gives the full-grid sum, matching numpy's `np.sum(p_wOi)`.
+- In the `use_numba` branch of `px_Oi_fixedgrid`, after the kernel call
+  I apply the SAME correction expressions as the numpy branch. Key
+  identity: dividing the grid by a scalar then summing equals dividing
+  the scalar sum, so correcting the returned scalar p(x|O_i) is exact:
+    - `'p_wO'`: `p_val /= pw_sum / spacing^2`
+    - `'L_wx'`: `p_val /= np.sum(L_wx) / spacing^2`
+  No correction logic was duplicated inside the jitted kernel; only the
+  extra `pw_sum` reduction is. (`return_grids`/`return_debug` still force
+  the numpy path, so the grid-level correction there is unaffected.)
+
+**Tests added** to `tests/test_speed_up.py`:
+- `test_px_Oi_fixedgrid_numba_matches_numpy_correction[p_wO|L_wx]
+  [exp|core|uniform]` — 6 cases asserting numba == numpy to
+  `rtol=1e-10` with each correction. All pass (11 numba tests total).
+
+**Note — unrelated pre-existing test failure:** `test_bayesian.py::
+test_PU` fails in the current working tree, but NOT from this change.
+It is caused by a separate uncommitted user edit to `px_U` (signature
+`box_hwidth`->`radius`, formula `1/(2*box_hwidth)^2` ->
+`1/(pi*radius^2)`); `px_U(30)` changed from `1/3600` to `1/(pi*900)`,
+which breaks `test_PU`'s hard-coded expected `p_x`/`P_Ux`. Verified by
+running `test_PU` on the committed baseline (passes) vs the working
+tree (fails on the `p_x` assertion). Left untouched — it is outside the
+scope of this prompt and reflects an intentional user change; the
+`test_PU` expectations (or `px_U` call sites) likely need updating
+separately.
\ No newline at end of file

From 6cc6d80aad839c70d099590b652a973459291e2b Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Wed, 10 Jun 2026 08:43:26 -0700
Subject: [PATCH 16/31] wip

---
 astropath/bayesian.py  |  6 +++--
 astropath/profiling.py | 53 ++++++++++++++++++++++++------------------
 astropath/run.py       |  2 +-
 prompts/speed_up.md    | 33 +++++++++++++++++++++++++-
 4 files changed, 67 insertions(+), 27 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index d3316c5..a890b65 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -278,9 +278,11 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
         warnings.warn("use_numba=True but numba is not installed; "
                       "falling back to numpy.")
         use_numba_eff = False
+    if use_numba_eff:
+        print('Using numba for the posterior calculation')
 
     p_xOis, grids = [], []
-    # TODO -- multiprocess this
+    # TODO -- multiprocess this?
     print('Looping on candidates')
     for icand in range(cand_ra.size):
         if icand % 50 == 0:
@@ -299,7 +301,7 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
             # Dividing the grid by a scalar then summing == dividing the
             # sum, so we correct the scalar p(x|O_i) directly.
             if correction == 'p_wO':
-                p_val /= np.sum(pw_sum) * grid_spacing_arcsec**2
+                p_val /= pw_sum * grid_spacing_arcsec**2
             elif correction == 'L_wx':
                 p_val /= corr_Lwx
             p_xOis.append(p_val)
diff --git a/astropath/profiling.py b/astropath/profiling.py
index dfc5ab5..9602799 100644
--- a/astropath/profiling.py
+++ b/astropath/profiling.py
@@ -84,27 +84,31 @@ def default_setup(ncand=NCAND):
     return localiz, cand_coords, cand_ang_size, theta_prior
 
 
-def _time_call(func, args, npix):
+def _time_call(func, args, npix, reps=None):
     """Time a single callable, returning the best wall time in seconds.
 
     The number of repetitions is scaled down for large grids to keep
-    the overall sweep fast.
+    the overall sweep fast, unless an explicit ``reps`` is given.
 
     Args:
         func (callable): Function to time.
         args (tuple): Positional arguments passed to ``func``.
         npix (int): Number of grid pixels (used to pick repetitions).
+        reps (int, optional): Force a fixed number of repetitions.
+            Use reps=1 to time a single call (e.g. to *include* the
+            numba JIT compilation cost in the first measurement).
 
     Returns:
         float: Best-of-reps wall-clock time, seconds.
     """
-    # Fewer reps for big grids (they are slow and stable)
-    if npix > 1_000_000:
-        reps = 1
-    elif npix > 100_000:
-        reps = 2
-    else:
-        reps = 3
+    if reps is None:
+        # Fewer reps for big grids (they are slow and stable)
+        if npix > 1_000_000:
+            reps = 1
+        elif npix > 100_000:
+            reps = 2
+        else:
+            reps = 3
     best = np.inf
     for _ in range(reps):
         t0 = time.perf_counter()
@@ -154,16 +158,16 @@ def run_profiling(step_sizes=None, box_hwidth=BOX_HWIDTH):
         step_sizes = DEFAULT_STEP_SIZES
     localiz, cand_coords, cand_ang_size, theta_prior = default_setup()
 
+    # Default correction applied to all px_Oi_fixedgrid timings here
+    correction = 'p_wO'
+
     print("Starting profiling sweep over %d step sizes, %d candidates"
           % (len(step_sizes), len(cand_ang_size)))
-
-    # Warm up the numba JIT once (compile cost is paid on the first call
-    # and must not pollute the timings).  Small grid is enough to compile.
-    if bayesian.HAS_NUMBA:
-        print("  Warming up numba JIT...")
-        bayesian.px_Oi_fixedgrid(
-            box_hwidth, localiz, cand_coords, cand_ang_size,
-            theta_prior, step_size=DEFAULT_STEP_SIZES[0], use_numba=True)
+    print("  using correction=%r" % correction)
+    # NOTE: the numba JIT is intentionally NOT pre-warmed.  Its
+    # compilation cost is included in the first (smallest-grid) numba
+    # timing below, so the reported numba time reflects a realistic
+    # one-off sandbox call.
 
     rows = []
     for step_size in step_sizes:
@@ -180,18 +184,21 @@ def run_profiling(step_sizes=None, box_hwidth=BOX_HWIDTH):
 
         # Time the full fixed-grid p(x|O_i) -- numpy path
         t_pxoi = _time_call(
-            bayesian.px_Oi_fixedgrid,
-            (box_hwidth, localiz, cand_coords, cand_ang_size,
-             theta_prior, step_size), npix)
+            lambda *a: bayesian.px_Oi_fixedgrid(
+                box_hwidth, localiz, cand_coords, cand_ang_size,
+                theta_prior, step_size=step_size, correction=correction),
+            (), npix)
         print("    px_Oi_fixedgrid (numpy): %.1f ms" % (t_pxoi * 1e3))
 
-        # Time the numba path (use_numba=True), if available
+        # Time the numba path (use_numba=True), if available.  reps=1 so
+        # the first call's JIT compilation is counted in the timing.
         if bayesian.HAS_NUMBA:
             t_numba = _time_call(
                 lambda *a: bayesian.px_Oi_fixedgrid(
                     box_hwidth, localiz, cand_coords, cand_ang_size,
-                    theta_prior, step_size=step_size, use_numba=True),
-                (), npix)
+                    theta_prior, step_size=step_size, use_numba=True,
+                    correction=correction),
+                (), npix, reps=1)
             print("    px_Oi_fixedgrid (numba): %.1f ms (%.1fx)"
                   % (t_numba * 1e3, t_pxoi / t_numba))
         else:
diff --git a/astropath/run.py b/astropath/run.py
index 6d1ba06..b6394b5 100644
--- a/astropath/run.py
+++ b/astropath/run.py
@@ -229,7 +229,7 @@ def run_on_dict(idict: dict,
         raise ValueError(f"Unsupported posterior mode: {idict['pmode']}. "
                         f"Supported: 'local', 'fixed'")
 
-    #embed(header='run.py:231')
+    embed(header='run.py:231')
 
     # Add photo-z columns if available in catalog
     photoz_columns = ['z_phot_median', 'z_phot_l68', 'z_phot_u68',
diff --git a/prompts/speed_up.md b/prompts/speed_up.md
index 4b58244..bc4740b 100644
--- a/prompts/speed_up.md
+++ b/prompts/speed_up.md
@@ -794,4 +794,35 @@ running `test_PU` on the committed baseline (passes) vs the working
 tree (fails on the `p_x` assertion). Left untouched — it is outside the
 scope of this prompt and reflects an intentional user change; the
 `test_PU` expectations (or `px_U` call sites) likely need updating
-separately.
\ No newline at end of file
+separately.
+
+### 2026-06-10 (Profiling: time JIT warm-up + default correction='p_wO')
+
+**Code changed:** `astropath/profiling.py`.
+- **JIT warm-up now timed.** Removed the separate, untimed numba
+  warm-up call. The numba path is now timed with `reps=1` (added a
+  `reps` override to `_time_call`), so the *first* (smallest-grid) numba
+  call pays the JIT compilation and that cost is reflected in its
+  reported time — a realistic one-off sandbox cost.
+- **Default `correction='p_wO'`.** All `px_Oi_fixedgrid` timings in the
+  sweep (both numpy and numba) now pass `correction='p_wO'` (set once at
+  the top of `run_profiling`). The numpy timing call was wrapped in a
+  lambda to thread the kwarg through.
+
+**Results** (astro14, 50 candidates, correction='p_wO'):
+
+| step_size | ngrid | calc_LWx (ms) | numpy (ms) | numba (ms) | speed-up |
+|-----------|-------|---------------|------------|------------|----------|
+| 0.500     | 360   | 8.61          | 30.48      | 223.20     | 0.14x    |
+| 0.250     | 720   | 41.62         | 171.61     | 81.18      | 2.11x    |
+| 0.100     | 1800  | 284.20        | 1875.81    | 605.40     | 3.10x    |
+| 0.050     | 3600  | 1534.47       | 15954.46   | 2938.61    | 5.43x    |
+| 0.025     | 7200  | 6452.22       | 68480.97   | 12018.50   | 5.70x    |
+
+The first numba point is now **slower** than numpy (0.14x, 223 ms) —
+that row absorbs the one-time JIT compilation (~0.2 s). From the second
+grid on, the kernel is compiled and the true 2.1x->5.7x speed-ups
+return. On the figure this shows as the leftmost green point sitting
+*above* the red numpy point, then dropping below — i.e. numba only pays
+off once the per-call work exceeds the compile overhead. Figure
+re-written to `astropath/profiling_timing.png`.
\ No newline at end of file

From b4557d3a4781240d2c8669f023c053d5b3a603d6 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Wed, 10 Jun 2026 15:07:14 -0700
Subject: [PATCH 17/31] wip

---
 astropath/bayesian.py |  6 ++++--
 astropath/run.py      | 17 ++++++++---------
 2 files changed, 12 insertions(+), 11 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index a890b65..205e46a 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -333,6 +333,7 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
         elif correction == 'L_wx':
             p_val /= corr_Lwx
 
+        #embed(header='336 of bayesian.py')
         p_xOis.append(p_val)
 
     # Return
@@ -419,7 +420,8 @@ def px_U(radius:float):
             in arcsec
 
     Returns:
-        float: p(x|U) in squarearcsec
+        float: p(x|U) in inverse squarearcsec
+            This is the same convention as p(x|O) as it must
 
     """
     #box_sqarcsec = (2*box_hwidth)**2
@@ -427,7 +429,7 @@ def px_U(radius:float):
     area = np.pi * radius**2
     #
     #return 1./box_sqarcsec  # box_steradians
-    return 1./area  
+    return 1./area
 
 
 
diff --git a/astropath/run.py b/astropath/run.py
index b6394b5..c1f7cdc 100644
--- a/astropath/run.py
+++ b/astropath/run.py
@@ -124,19 +124,15 @@ def run_on_dict(idict: dict,
     #box_hwidth = max(idict['max_box'],  # This should be the survey size
     #    max_sep.value)
     box_hwidth = idict['max_box']  # This should be the survey size
-    cut_catalog = catalog
-    '''
-    # Cut down the catalog based on box_hwidth
-    Ddec_arcsec = np.abs(catalog['dec'].data - coord.dec.deg) * 3600.
-    Dra_arcsec = np.abs(catalog['ra'].data - coord.ra.deg) * 3600. * np.cos(coord.dec.rad)
-
-    # This speeds things up and is required for the P_Ux calculation
-    keep = (Ddec_arcsec < box_hwidth) & (Dra_arcsec < box_hwidth)
+
+    # Cut down the catalog based on ssize (usually this should do nothing)
+    catalog_coord = SkyCoord(ra=catalog['ra'].data, dec=catalog['dec'].data, unit='deg')
+    sep = coord.separation(catalog_coord).to('arcsec')
+    keep = sep < idict['ssize']*60*units.arcsec
     cut_catalog = catalog[keep]
 
     if len(cut_catalog) == 0:
         return cut_catalog, None, None, None, None, None
-    '''
 
     # Initialize PATH
     Path = path.PATH()
@@ -218,6 +214,9 @@ def run_on_dict(idict: dict,
                                        survey_radius=idict['ssize']*60,
                                        step_size=step_size)
     elif idict['pmode'] == 'fixed':
+        # Memory check
+        if idict['ssize']*60 / step_size > 10000:
+            raise ValueError(f"Fixed grid would be {int(idict['ssize']*60 / step_size)} pixels.  \nYour array will need >100Gb RAM.  Try local or reduce your ssize if you can")
         print(f'Calculating posteriors with fixed and correction: {correction}')
         P_Ox, P_Ux = Path.calc_posteriors('fixed',
                                        box_hwidth=box_hwidth,

From f9570a252aaa06a68abcc822e9f5f448dee2cfe7 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Wed, 10 Jun 2026 20:13:42 -0700
Subject: [PATCH 18/31] mo

---
 astropath/tests/tests_local.py             | 243 +++++++++++++++++++++
 prompts/{speed_up.md => speed_up_fixed.md} |   0
 prompts/speed_up_local.md                  | 142 ++++++++++++
 3 files changed, 385 insertions(+)
 create mode 100644 astropath/tests/tests_local.py
 rename prompts/{speed_up.md => speed_up_fixed.md} (100%)
 create mode 100644 prompts/speed_up_local.md

diff --git a/astropath/tests/tests_local.py b/astropath/tests/tests_local.py
new file mode 100644
index 0000000..1a65bc9
--- /dev/null
+++ b/astropath/tests/tests_local.py
@@ -0,0 +1,243 @@
+""" Accuracy tests for bayesian.px_Oi_local.
+
+These tests establish a correctness baseline for ``px_Oi_local`` BEFORE
+we start optimizing it (numpy rewrite, then numba; see
+``prompts/speed_up_local.md``).  Both ``px_Oi_local`` and
+``px_Oi_fixedgrid`` evaluate the same integral
+
+    p(x|O_i) = integral over w of  L(w-x) * p(w|O_i) dw
+
+just discretized on different grids: ``px_Oi_local`` builds a grid
+centered on the galaxy and sized to the offset-prior support
+(phi*max), while ``px_Oi_fixedgrid`` builds a grid centered on the
+transient.  Run with a sufficiently fine step the fixed-grid result is
+effectively the truth, so we use it as the reference and check that the
+(coarser) local method reproduces it.
+
+Empirically the local method's RELATIVE error is ~0.17*step_size (first
+order in the grid spacing): step_size=0.1 -> ~1.7%, 0.05 -> ~0.8%,
+0.02 -> ~0.33%.  The tests below run the local method at step_size=0.02
+and require agreement to better than 1% with the fine fixed grid.
+
+The cases requested in the prompt cover the relevant size regimes:
+  * large galaxy (10") with a small localization (1")
+  * large galaxy (10") with a large localization (10")
+  * small galaxy (1")  with a small localization (1")
+  * small galaxy (1")  with a large localization (10")
+  * small galaxy (0.5") with an ellipse localization (a=10", b=0.2")
+"""
+
+import numpy as np
+
+from astropy.coordinates import SkyCoord
+from astropy import units
+
+from astropath import bayesian
+
+import pytest
+
+# Offset prior shared by every comparison.  Exponential PDF with a hard
+# cutoff at max*phi (matches the priors used elsewhere in the package).
+THETA_PRIOR = dict(max=6., PDF='exp', scale=0.5)
+
+# Reference transient = localization center (mid-declination ICRS so the
+# cos(dec) flat-sky scaling is exercised but not degenerate).
+CENT_RA, CENT_DEC = 120.0, 32.0
+
+# Local-method grid step used for the matching tests.  At this (relative)
+# step the local error is ~0.33%, comfortably inside RTOL below.
+LOCAL_STEP = 0.02
+RTOL = 1.0e-2
+
+# Comparison cases.  Each tuple is:
+#   (label, phi_gal, a, b, pa_ee, gal_offset, gal_pa)
+#     phi_gal    : galaxy angular size (arcsec)
+#     a, b       : localization ellipse semi-axes (arcsec); a==b -> circle
+#     pa_ee      : position angle of the localization ellipse (deg)
+#     gal_offset : galaxy offset from the transient center (arcsec)
+#     gal_pa     : position angle of that offset (deg E of N)
+CASES = [
+    ("large_gal10_small_loc1",  10.,  1.,  1.,  0., 1.0,  0.),
+    ("large_gal10_large_loc10", 10., 10., 10.,  0., 3.0,  0.),
+    ("small_gal1_small_loc1",    1.,  1.,  1.,  0., 1.0,  0.),
+    ("small_gal1_large_loc10",   1., 10., 10.,  0., 3.0,  0.),
+    ("small_gal0p5_ellipse",     0.5, 10., 0.2, 0., 2.0, 90.),
+]
+
+
+def _center():
+    """Return the transient/localization center coordinate.
+
+    Returns:
+        SkyCoord: ICRS center coordinate (CENT_RA, CENT_DEC).
+    """
+    return SkyCoord(ra=CENT_RA, dec=CENT_DEC, unit='deg')
+
+
+def _eellipse_localiz(a, b, pa_ee):
+    """Build an eellipse localization dict centered on the transient.
+
+    Args:
+        a (float): Semi-major axis of the error ellipse, arcsec.
+        b (float): Semi-minor axis of the error ellipse, arcsec.
+        pa_ee (float): Position angle of the ellipse, deg (E of N).
+
+    Returns:
+        dict: Localization dict (eellipse type) with center_coord set.
+    """
+    return dict(type='eellipse',
+                center_coord=_center(),
+                eellipse=dict(a=a, b=b, theta=pa_ee))
+
+
+def _galaxy(offset, gal_pa):
+    """Build a single-candidate SkyCoord offset from the transient.
+
+    Args:
+        offset (float): Angular offset from the center, arcsec.
+        gal_pa (float): Position angle of the offset, deg (E of N).
+
+    Returns:
+        SkyCoord: Length-1 SkyCoord array for the candidate galaxy.
+    """
+    gal = _center().directional_offset_by(
+        gal_pa * units.deg, offset * units.arcsec)
+    # Re-wrap as a length-1 array so it iterates like the real input.
+    return SkyCoord([gal.ra.deg], [gal.dec.deg], unit='deg')
+
+
+def _fine_fixedgrid_reference(phi, a, b, pa_ee, offset, gal_pa):
+    """Accurate p(x|O_i) from px_Oi_fixedgrid on a fine, large-enough grid.
+
+    The integrand L(w-x)*p(w|O_i) is non-zero only within phi*max of the
+    galaxy (the offset prior's hard cutoff), so a box reaching
+    ``offset + phi*max`` from the transient (plus a small margin) fully
+    contains it.  The step resolves the smallest relevant scale
+    (the smaller of the ellipse minor axis and the galaxy size), making
+    the fixed-grid result effectively exact for our purposes.
+
+    Args:
+        phi (float): Galaxy angular size, arcsec.
+        a (float): Localization semi-major axis, arcsec.
+        b (float): Localization semi-minor axis, arcsec.
+        pa_ee (float): Localization ellipse PA, deg.
+        offset (float): Galaxy offset from the transient, arcsec.
+        gal_pa (float): PA of the galaxy offset, deg.
+
+    Returns:
+        float: Reference p(x|O_i) for the single candidate.
+    """
+    localiz = _eellipse_localiz(a, b, pa_ee)
+    cand = _galaxy(offset, gal_pa)
+    cand_ang_size = np.array([phi])
+    # Box must cover the offset-prior support around the galaxy.
+    box_hwidth = offset + phi * THETA_PRIOR['max'] + 3.0  # arcsec
+    # Resolve the smallest scale; floor keeps grids tractable.
+    fine_step = max(min(b, phi) / 30., 0.005)             # arcsec
+    p_ref = bayesian.px_Oi_fixedgrid(
+        box_hwidth, localiz, cand, cand_ang_size,
+        THETA_PRIOR, step_size=fine_step)
+    return p_ref[0]
+
+
+@pytest.mark.parametrize(
+    "label,phi,a,b,pa_ee,offset,gal_pa", CASES,
+    ids=[c[0] for c in CASES])
+def test_local_matches_fine_fixedgrid(
+        label, phi, a, b, pa_ee, offset, gal_pa, capsys):
+    """px_Oi_local must match the fine fixed-grid reference (<1%).
+
+    Runs the local method at step_size=LOCAL_STEP and compares to the
+    accurate fixed-grid value for each size regime.
+    """
+    localiz = _eellipse_localiz(a, b, pa_ee)
+    cand = _galaxy(offset, gal_pa)
+    cand_ang_size = np.array([phi])
+
+    p_ref = _fine_fixedgrid_reference(
+        phi, a, b, pa_ee, offset, gal_pa)
+    p_loc = bayesian.px_Oi_local(
+        localiz, cand, cand_ang_size, THETA_PRIOR,
+        step_size=LOCAL_STEP)[0]
+
+    rel = (p_loc - p_ref) / p_ref
+    with capsys.disabled():
+        print("\n  %-24s local=%11.5e  fixed(fine)=%11.5e  "
+              "reldiff=%+.3e" % (label, p_loc, p_ref, rel))
+
+    assert np.isfinite(p_loc) and p_loc > 0
+    assert np.isclose(p_loc, p_ref, rtol=RTOL, atol=0.0)
+
+
+def test_local_multi_candidate_matches_fixedgrid(capsys):
+    """All cases at once: px_Oi_local on a multi-candidate input.
+
+    Drives the candidate loop with every regime in a single call (a
+    useful guard for future vectorization/numba work) and checks each
+    against its fine fixed-grid reference.
+    """
+    # Build one SkyCoord holding all candidate galaxies + their sizes.
+    ras, decs, sizes, refs = [], [], [], []
+    for label, phi, a, b, pa_ee, offset, gal_pa in CASES:
+        gal = _galaxy(offset, gal_pa)
+        ras.append(gal.ra.deg[0])
+        decs.append(gal.dec.deg[0])
+        sizes.append(phi)
+        refs.append(_fine_fixedgrid_reference(
+            phi, a, b, pa_ee, offset, gal_pa))
+    cand = SkyCoord(ra=ras, dec=decs, unit='deg')
+    cand_ang_size = np.array(sizes)
+    refs = np.array(refs)
+
+    # The localization differs per case, so px_Oi_local cannot be run
+    # once for all candidates; we drive it per candidate but through the
+    # same array-style call signature used in production.
+    p_loc = np.array([
+        bayesian.px_Oi_local(
+            _eellipse_localiz(a, b, pa_ee),
+            SkyCoord([ra], [dec], unit='deg'),
+            np.array([phi]), THETA_PRIOR, step_size=LOCAL_STEP)[0]
+        for (label, phi, a, b, pa_ee, offset, gal_pa), ra, dec
+        in zip(CASES, ras, decs)])
+
+    rel = (p_loc - refs) / refs
+    with capsys.disabled():
+        print("\n  multi-candidate max |reldiff| = %.3e" %
+              np.max(np.abs(rel)))
+
+    assert np.all(np.isfinite(p_loc)) and np.all(p_loc > 0)
+    assert np.allclose(p_loc, refs, rtol=RTOL, atol=0.0)
+
+
+def test_local_convergence_to_fixedgrid():
+    """The local error must shrink ~linearly as step_size decreases.
+
+    Uses the small-galaxy/small-localization case (cheap, well behaved)
+    and confirms the relative error vs the fine fixed grid both (a)
+    decreases monotonically and (b) roughly halves when the step is
+    halved -- i.e. first-order convergence to the same integral.
+    """
+    phi, a, b, pa_ee, offset, gal_pa = 1., 1., 1., 0., 1.0, 0.
+    localiz = _eellipse_localiz(a, b, pa_ee)
+    cand = _galaxy(offset, gal_pa)
+    cand_ang_size = np.array([phi])
+
+    p_ref = _fine_fixedgrid_reference(
+        phi, a, b, pa_ee, offset, gal_pa)
+
+    steps = [0.1, 0.05, 0.025]
+    rel_err = []
+    for ss in steps:
+        p_loc = bayesian.px_Oi_local(
+            localiz, cand, cand_ang_size, THETA_PRIOR,
+            step_size=ss)[0]
+        rel_err.append(abs(p_loc - p_ref) / p_ref)
+    rel_err = np.array(rel_err)
+
+    # Monotonic decrease with finer steps.
+    assert np.all(np.diff(rel_err) < 0)
+    # First-order: halving the step should roughly halve the error.
+    # Allow a generous band around the ideal factor of 2.
+    for i in range(len(steps) - 1):
+        ratio = rel_err[i] / rel_err[i + 1]
+        assert 1.6 < ratio < 2.4
diff --git a/prompts/speed_up.md b/prompts/speed_up_fixed.md
similarity index 100%
rename from prompts/speed_up.md
rename to prompts/speed_up_fixed.md
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
new file mode 100644
index 0000000..4ab42d5
--- /dev/null
+++ b/prompts/speed_up_local.md
@@ -0,0 +1,142 @@
+# Speeding up the PATH calculations
+
+## Goals
+
+This document is a collection of ideas and prompts for speeding up the PATH calculations for the bayesian.px_Oi_local method.  
+
+## Coding
+
+Here are guidelines for coding: 
+
+- Examine the work described in the speed_up_fixed.md document.
+- Use Python where possible
+- Add inline comments to explain the effort
+- Reuse existing code when possible, especially in bayesian.py and localization.py
+- Place import statements at the top of the file.
+- Include a description of inputs/outputs in the doc string of all methods
+- Use lines of code that are less than 80 characters wide
+
+## Running
+
+If you need to run python, use the "astro14" environment.  
+
+## Testing
+
+As we will be making a number of significant changes to the code, we will need to generate a set of tests to verify the code as we develop the new method.  
+
+1.  Generate a new module named tests_local.py in astropath/tests.  In it place a series of tests that compare the current px_Oi_local method against the px_Oi_fixedgrid method run with a fine grid.  For this:
+
+- Draw on examples in the Notebooks in the astropath/calculations/step_size directory.
+- Use a fine enough step size for the px_Oi_fixedgrid method to be considered accurate
+- Generate examples for at least these 3 cases:
+  * A large galaxy (10") with a small localization (1")
+  * A large galaxy (10") with a large localization (10")
+  * A small galaxy (1") with a small localization (1")
+  * A small galaxy (1") with a large localization (10")
+  * A small galaxy (0.5") with an ellipse localization (a=10", b=0.2")
+- Log your work in the "Logs" section below.
+
+## Development
+
+We wish to speed up the calculations in bayesian.py:px_Oi_local.  
+We will begin by removing all astropy calculations and replacing them with numpy calculations.  We will then use numba to speed up the code.
+
+1. Examine the code in bayesian.py:px_Oi_local.  Please:
+
+- Examine the code
+- Identify the bottlenecks
+- Figure out how to replace all astropy calculations 
+- When we test, we will use the tests_local.py module to verify the code.  It will not be necessary to preserve a copy of the original algorithm
+- Log your work in the "Logs" section below.
+- Make recommendations 
+- Do not generate any new code yet
+- If you have any questions, ask them in the Logs and I will clarify at my next prompt
+
+## Profiling
+
+## Docs
+
+## Prompts
+
+1. Read this doc.  Proceed with the 1st item under Testing.
+
+## Logging
+
+The "Logs" section will record Claude's work.  Please use the following format:
+
+### <Date> (Short summary of the work)
+
+<Detailed description of the work and what you learned>
+
+### <Date> (Short summary of the work)
+
+<Detailed description of the work and what you learned>
+
+...
+
+
+## Logs
+
+### 2026-06-10 (Generated tests_local.py: px_Oi_local vs fine fixed grid)
+
+**What I built:** A new test module
+`astropath/tests/tests_local.py`, modeled after `test_speed_up.py` and
+the `calculations/step_size/test_accuracy.py` notebook helpers. It
+verifies that `bayesian.px_Oi_local` reproduces
+`bayesian.px_Oi_fixedgrid` run on a fine, large-enough grid (taken as
+the accurate reference).
+
+**Key insight (why this is a valid comparison):** both methods evaluate
+the same integral `p(x|O_i) = ∫ L(w-x) p(w|O_i) dw`, just discretized on
+different grids. `px_Oi_local` centers a grid on the *galaxy* sized to
+the offset-prior support (`phi*max`); `px_Oi_fixedgrid` centers on the
+*transient*. The integrand is non-zero only within `phi*max` of the
+galaxy (the offset prior has a hard cutoff there), so a fixed-grid box
+of `offset + phi*max + 3"` fully contains it. I confirmed the reference
+value is unchanged when the box is enlarged further, so box size is not
+limiting.
+
+**Convergence measured:** `px_Oi_local`'s relative error vs the fine
+fixed grid is first-order in the (relative) step size, ≈ `0.167 *
+step_size`:
+
+| step_size | reldiff |
+|-----------|---------|
+| 0.100     | -1.67%  |
+| 0.050     | -0.83%  |
+| 0.020     | -0.33%  |
+| 0.010     | -0.17%  |
+| 0.005     | -0.08%  |
+
+So the two methods provably converge to the same number.
+
+**Cases covered** (all 5 from the prompt — the prompt says "at least
+3" but lists 5):
+- large galaxy 10" / small loc 1"
+- large galaxy 10" / large loc 10"
+- small galaxy 1"  / small loc 1"
+- small galaxy 1"  / large loc 10"
+- small galaxy 0.5" / ellipse loc a=10", b=0.2"
+
+**Tests written:**
+1. `test_local_matches_fine_fixedgrid` (parametrized over the 5 cases) —
+   runs the local method at `step_size=0.02` and asserts agreement
+   with the fine fixed grid to `rtol=1e-2`. Observed reldiff is a
+   remarkably consistent ≈ -3.34e-3 across every regime.
+2. `test_local_multi_candidate_matches_fixedgrid` — drives all regimes
+   through the candidate loop (a guard for future vectorization/numba),
+   each checked against its own reference.
+3. `test_local_convergence_to_fixedgrid` — confirms the error decreases
+   monotonically and roughly halves when the step halves (first-order).
+
+**Result:** `pytest astropath/tests/tests_local.py -s` → 7 passed in
+~10s. The reference grids stay tractable (largest is 3840² for the
+10"-galaxy / 1"-loc case, ~3s; the b=0.2" ellipse needs a 0.007" step,
+~1s). These now serve as the regression baseline for the upcoming
+numpy/numba rewrite of `px_Oi_local`.
+
+**Question for next prompt:** the `Development` section says to remove
+astropy from `px_Oi_local`. Should I keep the existing astropy-based
+`px_Oi_local` frozen as a reference (as was done for `calc_LWx` /
+`px_Oi_fixedgrid` in `test_speed_up.py`), or is the fine-fixed-grid
+comparison in `tests_local.py` sufficient as the regression anchor?

From 38186a0fc07be5487257a8ed0c64648727b8a877 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 11 Jun 2026 04:55:46 -0700
Subject: [PATCH 19/31] no astropy

---
 astropath/bayesian.py     | 124 +++++++++++++++++++-----
 astropath/profiling.py    |  99 +++++++++++++++++++
 prompts/speed_up_local.md | 193 ++++++++++++++++++++++++++++++++++++++
 3 files changed, 390 insertions(+), 26 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index 205e46a..ac805e9 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -345,13 +345,33 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
         return np.array(p_xOis)
 
 def px_Oi_local(localiz, cand_coords, cand_ang_size,
-                theta_prior, step_size=0.1, debug = False):
+                theta_prior, step_size=0.1, 
+                step_size_mode:str='relative',
+                debug = False):
     """
     Perform the calculation on local grids, one
-    per candidate.  This is likely slower than 
+    per candidate.  This is likely slower than
     the "fixed" method, but best for large localization
     areas which cover a large area of the sky.
-    
+
+    The ``eellipse`` localization type uses a fast pure-numpy, flat-sky
+    path (see notes below); all other types fall back to the generic
+    ``localization.calc_LWx`` lookup.  Either way the only astropy access
+    is a single up-front extraction of the candidate and center
+    coordinates -- the per-candidate loop is pure numpy (and structured
+    so a numba kernel can later replace its body; cf. ``px_Oi_numba``).
+
+    Notes (eellipse fast path):
+        * The per-candidate grid is built ONCE in normalized units.
+          Because ``box_hwidth = phi*max`` and the spacing is
+          ``phi*step_size``, the pixel count ``ngrid = 2*max/step_size``
+          is the SAME for every candidate, so the normalized grid
+          (U, V, R) is reused and merely rescaled by ``phi*max``.
+        * L(w-x) for the error ellipse is evaluated directly in the
+          flat-sky tangent plane (offsets in arcsec, rotated into the
+          ellipse frame), avoiding astropy's spherical separation /
+          position-angle machinery.  This matches calc_LWx's eellipse
+          result to ~1e-5 fractionally at arcsec grid scales.
 
     Args:
         localiz (dict):
@@ -372,41 +392,93 @@ def px_Oi_local(localiz, cand_coords, cand_ang_size,
             If true, hit an embed in the main loop
 
     Returns:
-        np.ndarray or tuple: p(x|O_i) values and the grids if return_grids = True
+        np.ndarray: p(x|O_i) values, one per candidate.
 
     """
+    # Pre-extract candidate coordinates to plain numpy arrays ONCE.
+    # Iterating a SkyCoord and reading .ra/.dec per candidate is the
+    # dominant astropy overhead; pulling them out here removes it and
+    # keeps the loop numba-friendly.
+    cand_ra = cand_coords.ra.deg                     # deg, shape (N,)
+    cand_dec = cand_coords.dec.deg                   # deg, shape (N,)
+    cos_cand_dec = np.cos(np.radians(cand_dec))      # flat-sky scaling
+
+    # Normalized grid, built ONCE.  ngrid depends only on max/step_size
+    # (phi cancels), so the same grid serves every candidate.  U, V span
+    # [-1, 1]; the physical grid is phi*max * (U, V) and theta = phi*max*R.
+    max_theta = theta_prior['max']
+    ngrid = int(np.round(2 * max_theta / step_size))
+    u = np.linspace(-1., 1., ngrid)
+    Ugrid, Vgrid = np.meshgrid(u, u)
+    Rgrid = np.sqrt(Ugrid ** 2 + Vgrid ** 2)         # normalized radius
+
+    # Pre-compute the eellipse constants once (flat-sky fast path).
+    is_eellipse = localiz['type'] == 'eellipse'
+    if is_eellipse:
+        # Pre-extract the localization center once (eellipse only; other
+        # types have no center_coord and resolve L_wx via calc_LWx).
+        center_ra = localiz['center_coord'].ra.deg       # deg
+        center_dec = localiz['center_coord'].dec.deg     # deg
+        cos_center_dec = np.cos(np.radians(center_dec))  # flat-sky scale
+        ell = localiz['eellipse']
+        a = ell['a']
+        b = ell['b']
+        # Rotation that places the ellipse major axis on the x-axis;
+        # identical convention to localization.calc_LWx (dtheta=90-PA).
+        dth = np.radians(90. - ell['theta'])
+        cos_dth = np.cos(dth)
+        sin_dth = np.sin(dth)
+        inv_2a2 = 1. / (2 * a ** 2)
+        inv_2b2 = 1. / (2 * b ** 2)
+        L_norm = 1. / (2 * np.pi * a * b)
+
     # Loop on galaxies
     p_xOis = []
-    # TODO -- parallelize this
-    for icand, cand_coord in enumerate(cand_coords):
-        # Prep
-        phi_cand = cand_ang_size[icand]   # arcsec
-        step_size_phi = phi_cand * step_size        # arcsec
-        box_hwidth = phi_cand * theta_prior['max']  # arcsec
-
-        # Grid around the galaxy
-        ngrid = int(np.round(2 * box_hwidth / step_size_phi))
-        x = np.linspace(-box_hwidth, box_hwidth, ngrid)
-        xcoord, ycoord = np.meshgrid(x,x)
-        theta = np.sqrt(xcoord**2 + ycoord**2)
+    # TODO -- parallelize / numba this per-candidate body
+    for icand in range(cand_ra.size):
+
+        # Dynamic step_size
+        step_size_phi = phi_cand * step_size         # arcsec
+
+        # Prep -- scale the normalized grid to this galaxy's size
+        phi_cand = cand_ang_size[icand]              # arcsec
+        box_hwidth = phi_cand * max_theta            # arcsec
+        xcoord = box_hwidth * Ugrid                  # east offset, arcsec
+        ycoord = box_hwidth * Vgrid                  # north offset, arcsec
+        theta = box_hwidth * Rgrid                   # arcsec
+
         # p(w|O)
         p_wOi = pw_Oi(theta, phi_cand, theta_prior)
 
-        # Generate coords for transient localiation (flat sky)
-        ra = cand_coord.ra.deg + \
-            xcoord/3600. / np.cos(cand_coord.dec).value
-        dec = cand_coord.dec.deg + ycoord/3600.
-
-        # Calculate
-        L_wx = localization.calc_LWx(ra, dec, localiz) 
+        if is_eellipse:
+            # Flat-sky offsets of the galaxy center from the transient
+            # center (arcsec): east scaled by cos(dec), north direct.
+            E0 = (cand_ra[icand] - center_ra) * cos_center_dec * 3600.
+            N0 = (cand_dec[icand] - center_dec) * 3600.
+            # Offsets of every grid point from the transient center
+            E = E0 + xcoord                          # east, arcsec
+            N = N0 + ycoord                          # north, arcsec
+            # Rotate into the ellipse frame (x along the major axis).
+            # Signs are squared below, so they need not match calc_LWx.
+            x_box = E * cos_dth + N * sin_dth
+            y_box = N * cos_dth - E * sin_dth
+            # 2D Gaussian L(w-x), normalized over x (not omega)
+            L_wx = (np.exp(-x_box ** 2 * inv_2a2)
+                    * np.exp(-y_box ** 2 * inv_2b2) * L_norm)
+        else:
+            # Generic fallback (healpix/wcs): build flat-sky coords and
+            # use calc_LWx, which does the type-specific lookup.
+            ra = (cand_ra[icand]
+                  + xcoord / 3600. / cos_cand_dec[icand])
+            dec = cand_dec[icand] + ycoord / 3600.
+            L_wx = localization.calc_LWx(ra, dec, localiz)
 
         # Finish
         grid_p = L_wx * p_wOi
-        #
-        p_xOis.append(np.sum(grid_p)*step_size_phi**2)
+        p_xOis.append(np.sum(grid_p) * step_size_phi ** 2)
         # Debug
         if debug:
-            embed(header='207 of bayesian.py')
+            embed(header='px_Oi_local of bayesian.py')
     # Return
     return np.array(p_xOis)
 
diff --git a/astropath/profiling.py b/astropath/profiling.py
index 9602799..46143ba 100644
--- a/astropath/profiling.py
+++ b/astropath/profiling.py
@@ -213,6 +213,89 @@ def run_profiling(step_sizes=None, box_hwidth=BOX_HWIDTH):
     return pandas.DataFrame(rows)
 
 
+def run_profiling_local(step_sizes=None):
+    """Profile px_Oi_local over a range of (relative) step sizes.
+
+    ``px_Oi_local`` builds one grid per candidate, sized to the offset
+    prior (box_hwidth = phi*max) with spacing phi*step_size.  The
+    per-candidate pixel count is therefore ``ngrid = 2*max/step_size``
+    (independent of phi), so sweeping ``step_size`` sweeps the
+    per-candidate grid size.  The whole multi-candidate call is timed.
+
+    Args:
+        step_sizes (list, optional): Relative step sizes to sweep.
+            Defaults to :data:`DEFAULT_STEP_SIZES`.
+
+    Returns:
+        pandas.DataFrame: One row per step size with columns
+            ``step_size``, ``ngrid`` (per candidate), ``n_pixels``
+            (per candidate), ``ncand``, and ``px_Oi_local_s``.
+    """
+    if step_sizes is None:
+        step_sizes = DEFAULT_STEP_SIZES
+    localiz, cand_coords, cand_ang_size, theta_prior = default_setup()
+    ncand = len(cand_ang_size)
+    max_theta = theta_prior['max']
+
+    print("Starting px_Oi_local profiling over %d step sizes, "
+          "%d candidates" % (len(step_sizes), ncand))
+
+    rows = []
+    for step_size in step_sizes:
+        # Per-candidate grid size (phi cancels out of ngrid)
+        ngrid = int(np.round(2 * max_theta / step_size))
+        npix = ngrid * ngrid
+        print("  step_size=%.4f  per-cand grid=%dx%d (%d pix) ..."
+              % (step_size, ngrid, ngrid, npix))
+
+        # Time the full multi-candidate px_Oi_local call.  Use the total
+        # pixel budget (ncand * npix) to choose the repetition count.
+        t_local = _time_call(
+            lambda *a: bayesian.px_Oi_local(
+                localiz, cand_coords, cand_ang_size, theta_prior,
+                step_size=step_size),
+            (), ncand * npix)
+        print("    px_Oi_local: %.1f ms (%.3f ms/cand)"
+              % (t_local * 1e3, t_local / ncand * 1e3))
+
+        rows.append(dict(step_size=step_size, ngrid=ngrid,
+                         n_pixels=npix, ncand=ncand,
+                         px_Oi_local_s=t_local))
+
+    print("px_Oi_local profiling complete.")
+    return pandas.DataFrame(rows)
+
+
+def plot_local_results(df, outfile):
+    """Plot px_Oi_local timing vs per-candidate grid size (log-log).
+
+    Args:
+        df (pandas.DataFrame): Output of :func:`run_profiling_local`.
+        outfile (str): Path to write the PNG figure.
+
+    Returns:
+        str: The path the figure was written to.
+    """
+    sqrt_pix = np.sqrt(df['n_pixels'])  # per-candidate grid side length
+    fig, ax = plt.subplots(figsize=(7, 5))
+    ax.plot(sqrt_pix, df['px_Oi_local_s'], 'D-', color='purple',
+            label='px_Oi_local (numpy)')
+    # Reference line at 10 s
+    ax.axhline(10., color='dimgray', linestyle='--', linewidth=1.5)
+    ax.set_xscale('log')
+    ax.set_yscale('log')
+    ax.set_xlabel('sqrt(per-candidate grid pixels)')
+    ax.set_ylabel('Time (s)')
+    ax.set_title('px_Oi_local profiling (%d candidates)'
+                 % int(df['ncand'].iloc[0]))
+    ax.grid(True, which='both', alpha=0.3)
+    ax.legend()
+    fig.tight_layout()
+    fig.savefig(outfile, dpi=120)
+    plt.close(fig)
+    return outfile
+
+
 def plot_results(df, outfile):
     """Plot the timing results vs grid size on log-log axes.
 
@@ -280,6 +363,22 @@ def main():
                            'profiling_timing.png')
     plot_results(df, outfile)
     print('\nFigure written to: %s' % outfile)
+
+    # ---- px_Oi_local (the local-grid method) ----
+    df_local = run_profiling_local()
+    show_l = df_local.copy()
+    show_l['px_Oi_local_ms'] = show_l['px_Oi_local_s'] * 1e3
+    show_l['ms_per_cand'] = (show_l['px_Oi_local_s']
+                             / show_l['ncand'] * 1e3)
+    cols_l = ['step_size', 'ngrid', 'n_pixels', 'ncand',
+              'px_Oi_local_ms', 'ms_per_cand']
+    print('\npx_Oi_local profiling results (best-of-reps):')
+    print(show_l[cols_l].to_string(
+        index=False, float_format=lambda v: '%.3f' % v))
+    outfile_local = os.path.join(os.path.dirname(__file__),
+                                 'profiling_local_timing.png')
+    plot_local_results(df_local, outfile_local)
+    print('\nFigure written to: %s' % outfile_local)
     return df
 
 
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
index 4ab42d5..7ba5c68 100644
--- a/prompts/speed_up_local.md
+++ b/prompts/speed_up_local.md
@@ -52,6 +52,16 @@ We will begin by removing all astropy calculations and replacing them with numpy
 - Do not generate any new code yet
 - If you have any questions, ask them in the Logs and I will clarify at my next prompt
 
+2. Write new code to replace the astropy calculations with numpy calculations. Please:
+
+- Here are answers to your questions:
+  * Only consider the ellipse localization type for now.
+  * Flat sky is acceptable
+- Remember that we intend to use numba to speed up the code.  Consider that in your programming
+- Verify using the tests_local.py module that the code is working as expected.
+- Add new code to profiling.py to profile this method
+- Log your work in the "Logs" section below.
+
 ## Profiling
 
 ## Docs
@@ -59,6 +69,8 @@ We will begin by removing all astropy calculations and replacing them with numpy
 ## Prompts
 
 1. Read this doc.  Proceed with the 1st item under Testing.
+2. Read this doc.  Proceed with the 1st item under Development.
+3. Read this doc.  Proceed with the 2nd item under Development.
 
 ## Logging
 
@@ -140,3 +152,184 @@ astropy from `px_Oi_local`. Should I keep the existing astropy-based
 `px_Oi_local` frozen as a reference (as was done for `calc_LWx` /
 `px_Oi_fixedgrid` in `test_speed_up.py`), or is the fine-fixed-grid
 comparison in `tests_local.py` sufficient as the regression anchor?
+
+> Answer (recorded by user in the next prompt): no need to preserve a
+> copy of the original algorithm; `tests_local.py` is the regression
+> anchor.
+
+### 2026-06-10 (Analysis of px_Oi_local: bottlenecks + astropy removal)
+
+**Code examined:** `bayesian.px_Oi_local` (lines 347-411).  It loops
+over candidates; for each it (1) builds a square grid centered on the
+galaxy, sized `box_hwidth = phi*max` with spacing
+`step_size_phi = phi*step_size`, (2) computes `theta = sqrt(x^2+y^2)`
+and `p_wOi = pw_Oi(theta, phi, prior)`, (3) builds flat-sky `ra/dec`
+around the galaxy, (4) calls `localization.calc_LWx(ra, dec, localiz)`,
+(5) accumulates `sum(L_wx * p_wOi) * step_size_phi^2`.
+
+**Astropy inventory (everything in the loop body):**
+- `for icand, cand_coord in enumerate(cand_coords)` -- iterating a
+  SkyCoord array; each item is a scalar SkyCoord (slicing overhead).
+- `cand_coord.ra.deg` (line 396).
+- `np.cos(cand_coord.dec).value` (line 397) -- Angle trig + `.value`.
+- `cand_coord.dec.deg` (line 398).
+- Inside `calc_LWx`: `localiz['center_coord'].ra.deg` / `.dec.deg`
+  (read once per call -> N times).  The eellipse *math* in calc_LWx is
+  already pure numpy (done in the earlier speed_up_fixed.md work).
+- No `units` usage in px_Oi_local itself (the module-level
+  `from astropy import units` is only used by the deprecated
+  `px_Oi_orig`).
+
+**Profile (200 candidates, step_size=0.1, mixed sizes, 3 reps,
+cProfile, cumulative):**
+
+| component | share of runtime |
+|-----------|------------------|
+| `calc_LWx` (numpy Vincenty sep + PA + Gaussian) | ~58% |
+| astropy coordinate access/iteration (SkyCoord, Angle, represent_as) | ~25-30% |
+| `pw_Oi` | ~5% |
+| `np.meshgrid` + grid build | ~3% |
+
+Wall time ~1.0 ms/candidate at step_size=0.1.
+
+**Bottleneck #1 -- `calc_LWx` doing spherical trig on a flat-sky grid.**
+px_Oi_local already *builds* `ra/dec` with a flat-sky tangent-plane
+approximation, then `calc_LWx` (eellipse) runs the FULL Vincenty
+angular separation + position angle (`arctan2`, `hypot`, several
+`sin/cos`) to recover offsets it effectively already knows.  Micro-bench
+on a 120x120 grid: `calc_LWx` (Vincenty) = 601 us/call vs a direct
+flat-sky Gaussian = 100 us/call -- **~6x** -- agreeing to a max
+fractional difference of 1.1e-5 (negligible at arcsec grid scale).
+
+**Bottleneck #2 -- per-candidate astropy coordinate access.**  Same
+issue fixed earlier in `px_Oi_fixedgrid`: iterating a SkyCoord and
+reading `.ra/.dec` per candidate is pure overhead (~25-30% here).
+
+**Key structural finding -- the grid and `p_wOi` are phi-independent.**
+Because `box_hwidth = phi*max` and `step_size_phi = phi*step_size`,
+
+    ngrid = round(2*box_hwidth/step_size_phi) = round(2*max/step_size)
+
+so `ngrid` is the SAME for every candidate (e.g. 120 for max=6,
+step_size=0.1; verified).  Writing the grid as `phi*max * U` for a
+fixed normalized meshgrid `U`, one finds `theta = phi*max*R` and:
+- core: `p_wOi = (1/(max*R+1)) / norm(phi)`
+- exp:  `p_wOi = exp(-max*R/scale) / norm(phi)`
+- uniform: `p_wOi = 1 / norm(phi)`
+
+i.e. the *shape* of `p_wOi` (and the cutoff mask `R<1`) does NOT depend
+on phi -- only the scalar `norm(phi)` and the `step_size_phi^2 =
+(phi*step_size)^2` factor do.  So `meshgrid`, `theta`, `R`, and the
+exp/core grid can be computed ONCE and reused for all candidates.
+
+**Important constraint -- px_Oi_local must stay generic over
+localization type.**  Its docstring ("best for large localization
+areas which cover a large area of the sky") points at healpix maps
+(CHIME baseband), and `calc_LWx` also serves `wcs`.  For healpix/wcs,
+`L_wx` is a pixel lookup that genuinely needs `ra/dec`, so we cannot
+drop `calc_LWx` wholesale -- the flat-sky shortcut (Bottleneck #1)
+applies only to the `eellipse` branch.
+
+**Plan to replace astropy (for the next coding step -- not done yet):**
+1. Pre-extract `cand_ra = cand_coords.ra.deg`,
+   `cand_dec = cand_coords.dec.deg`,
+   `cos_cand_dec = np.cos(np.radians(cand_dec))` ONCE before the loop
+   (mirrors `px_Oi_fixedgrid` lines 269-271).  Index these in the loop
+   instead of touching the SkyCoord.  This removes ALL astropy from the
+   loop body.
+2. Pre-extract `center_ra/center_dec` from `localiz['center_coord']`
+   once, so the per-call astropy read inside `calc_LWx` is avoided for
+   the local method.  (Either compute a flat-sky `L_wx` inline for the
+   eellipse type, or pass scalars; see recommendations.)
+3. After (1)-(2) the only astropy left is constructing the inputs;
+   px_Oi_local's own computation becomes pure numpy.
+
+**Recommendations (ordered by payoff; later items target the numba
+step the doc mentions, NOT this one):**
+- **R1 (biggest, eellipse):** add a flat-sky `L_wx` path for the
+  eellipse type that reuses the rotation/Gaussian already in
+  `calc_LWx` but skips Vincenty -- ~6x on the dominant cost.  Keep
+  calling `calc_LWx` for healpix/wcs.  Consider factoring the eellipse
+  Gaussian into a small numpy helper in `localization.py` so both
+  `calc_LWx` and the local fast path share one definition.
+- **R2:** precompute the phi-independent normalized grid + `p_wOi`
+  shape + cutoff mask once; per candidate only rescale by `norm(phi)`
+  and multiply the sum by `(phi*step_size)^2`.  Removes meshgrid/exp
+  from the per-candidate loop entirely.
+- **R3:** pre-extract candidate/center coordinates (the astropy-removal
+  in the plan above).
+- **R4 (numba step):** with R1-R3 the per-candidate kernel reduces to
+  "offset the fixed grid by the galaxy's center offset, evaluate the
+  eellipse Gaussian, multiply by the cached `p_wOi` shape, sum" -- a
+  tight numeric loop well suited to an `@njit` kernel analogous to
+  `px_Oi_numba`, computing the eellipse `L_wx` inline.
+
+**Questions for the next prompt:**
+1. Should the optimization target ONLY the `eellipse` localization
+   type (with healpix/wcs falling back to the current `calc_LWx`
+   path), or do you also want a fast path for healpix?  (My plan above
+   keeps healpix/wcs on `calc_LWx`.)
+2. The flat-sky `L_wx` for eellipse differs from the current Vincenty
+   result by ~1e-5 fractionally.  Confirm that adopting the flat-sky
+   approximation here is acceptable (it is already used to build the
+   grid, and `px_Oi_fixedgrid` makes the same approximation).
+
+### 2026-06-10 (Rewrote px_Oi_local in numpy; ~6.5x faster)
+
+**Done** (Development item 2). User answers applied: only the
+`eellipse` type gets the fast path; flat-sky is acceptable.
+
+**Changes to `bayesian.px_Oi_local`:**
+- **Astropy removed from the loop (R3):** `cand_coords.ra.deg /
+  .dec.deg` and `cos(dec)` are pre-extracted to numpy arrays ONCE
+  before the loop; the body indexes those arrays instead of iterating
+  the SkyCoord.  For the eellipse path the localization center is also
+  pulled out once.  No astropy remains in the per-candidate loop.
+- **Normalized grid built ONCE (R2, partial):** since `ngrid =
+  2*max/step_size` is phi-independent, the loop now reuses a single
+  normalized meshgrid (U, V, R) rescaled by `phi*max` per candidate
+  instead of rebuilding `np.meshgrid` each time.  (I deliberately did
+  NOT do the full analytic phi-cancellation of `norm(phi)` -- it would
+  obscure the algorithm and is unnecessary for the numba step, which
+  recomputes the PDF per pixel anyway.  `pw_Oi` is still reused as-is.)
+- **Flat-sky eellipse L_wx (R1, the big win):** for `eellipse`, L(w-x)
+  is now evaluated directly in the tangent plane -- galaxy-center
+  offset (E0, N0) plus the grid offsets, rotated into the ellipse frame
+  (same `dtheta = 90-PA` convention as `calc_LWx`), then the 2D
+  Gaussian.  This skips astropy's Vincenty separation / position angle.
+- **Generic fallback preserved:** non-eellipse types (healpix/wcs)
+  still build flat-sky `ra/dec` and call `localization.calc_LWx`, so
+  production GW/healpix runs are unaffected.  (Caught by the existing
+  `test_path.py::test_gw`, which has no `center_coord`; the center
+  extraction is now guarded inside the eellipse branch.)
+- **numba-readiness:** the eellipse per-candidate body is now a tight
+  numeric block (scalars + the fixed normalized grid -> rotation,
+  Gaussian, weighted sum) that maps cleanly onto a future `@njit`
+  kernel analogous to `px_Oi_numba`.
+
+**Verification:** `pytest astropath/tests/tests_local.py -s` -> 8
+passed.  The reldiff vs the fine fixed grid is unchanged from the old
+Vincenty version (e.g. -3.345e-3 vs -3.348e-3 for the large-galaxy/
+small-loc case) -- i.e. the flat-sky approximation contributes <1e-5,
+far below the discretization error and the 1% tolerance.  Full suite
+(`test_bayesian`, `test_path`, `test_speed_up`, `tests_local`) passes.
+
+**Speed-up:** in the 200-candidate / step_size=0.1 / eellipse scenario,
+0.154 ms/candidate vs ~1.000 ms/candidate before -> **~6.5x** (Vincenty
+removal ~6x + per-candidate astropy removal).
+
+**Profiling added** (`astropath/profiling.py`): new
+`run_profiling_local()` sweeps `step_size` (per-candidate grid =
+2*max/step_size) for the 50-candidate eellipse scenario, plus
+`plot_local_results()` (purple curve, x-axis = sqrt(per-candidate
+pixels), 10 s reference line) writing `profiling_local_timing.png`.
+`main()` now runs and reports both the fixed-grid and local sweeps.
+Sample (50 candidates):
+
+| step_size | per-cand grid | total ms | ms/cand |
+|-----------|---------------|----------|---------|
+| 0.500     | 24x24         | 0.9      | 0.018   |
+| 0.250     | 48x48         | 1.8      | 0.035   |
+| 0.100     | 120x120       | 7.8      | 0.155   |
+| 0.050     | 240x240       | 32.8     | 0.655   |
+| 0.025     | 480x480       | 182.9    | 3.659   |

From ca9bd647ba40652276eb17b1a3f70e9590292e3a Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 11 Jun 2026 10:03:28 -0700
Subject: [PATCH 20/31] good to go?

---
 astropath/bayesian.py          | 124 ++++++++++++--
 astropath/run.py               |   2 +-
 astropath/tests/tests_local.py |  41 +++++
 prompts/speed_up_local.md      | 296 +++++++++++++++++++++++++++++++++
 4 files changed, 452 insertions(+), 11 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index ac805e9..5161e34 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -344,8 +344,94 @@ def px_Oi_fixedgrid(box_hwidth, localiz, cand_coords,
     else:
         return np.array(p_xOis)
 
+def _Lwx_correction(E0, N0, a, b, cos_dth, sin_dth, box_hwidth,
+                    ngrid, step_size_phi, max_side:int=5000):
+    """Localization normalization factor for an under-resolved L(w-x).
+
+    Fast companion to ``px_Oi_local`` for the ``b < phi`` regime.  There
+    the galaxy-centered grid (spacing ``step_size_phi``) deliberately
+    UNDER-resolves the sharp localization, so the discrete ``sum(L_wx)``
+    -- and hence the raw p(x|O_i) -- comes out below its true value.
+    This returns the discrete integral of L(w-x), the "total L_wx", on a
+    grid that:
+
+      * is CENTERED ON THE LOCALIZATION (the transient), covering a
+        SQUARE window of half-width ``4*a`` (>= 4 sigma of the major
+        axis, so it captures essentially all of the ellipse);
+      * has EXACTLY the galaxy-grid spacing, and lies ON the galaxy
+        lattice -- it is the galaxy grid shifted by an integer number of
+        cells.  The localization is therefore sampled at the SAME
+        sub-cell phase as the main grid, so the under-resolution aliasing
+        is identical in the raw sum and in this factor.
+
+    The caller divides the raw p(x|O_i) by this factor, which cancels the
+    aliasing bias (accurate to ~1%) -- the same idea as
+    ``px_Oi_fixedgrid``'s ``correction='L_wx'``, but with a coarse,
+    galaxy-aligned grid instead of a fine one.
+
+    Memory guard: the window has ~``8*a/step_size_phi`` cells per side.
+    This only exceeds ``max_side`` when ``step_size_phi`` is very small
+    -- i.e. when the galaxy grid ALREADY resolves L and the raw value
+    needs no correction -- so in that case we skip (return 1.0) rather
+    than allocate a huge array.
+
+    Args:
+        E0 (float): East offset of the galaxy from the localization
+            center, arcsec (flat sky).
+        N0 (float): North offset of the galaxy from the localization
+            center, arcsec.
+        a (float): Localization ellipse semi-major axis, arcsec.
+        b (float): Localization ellipse semi-minor axis, arcsec.
+        cos_dth (float): cos of the ellipse-frame rotation (90 - PA),
+            shared with the main loop.
+        sin_dth (float): sin of the same rotation.
+        box_hwidth (float): Half-width of the galaxy grid, arcsec
+            (= phi*max); recovers the galaxy lattice with ``ngrid``.
+        ngrid (int): Cells per side of the galaxy grid (built as
+            ``linspace(-box_hwidth, box_hwidth, ngrid)``).
+        step_size_phi (float): Galaxy-grid spacing, arcsec
+            (= phi*step_size); used for the area element dA so the factor
+            matches the caller's raw sum.
+        max_side (int, optional): Skip (return 1.0) if the window would
+            exceed this many cells per side.  Default 5000.
+
+    Returns:
+        float: The discrete ``sum(L_wx)*dA`` ("total L_wx"; ~1 when
+            resolved, < 1 when under-resolved), or 1.0 if skipped.
+    """
+    # Exact galaxy-grid spacing (linspace of ngrid points on [-box,box]).
+    h = 2. * box_hwidth / (ngrid - 1)
+    # Half-window in cells to reach 4 sigma along the major axis (4*a).
+    m = int(np.ceil(4. * a / h))
+    # Skip if the window would be huge: that happens when h << a at fine
+    # step, i.e. L is already well resolved on the galaxy grid and the
+    # raw value needs no correction.  Avoids allocating a huge array.
+    if (2 * m + 1) > max_side:
+        return 1.0
+    # Snap the localization onto the galaxy lattice (integer cell shift).
+    # Galaxy-frame lattice points (offsets from the galaxy) are
+    # -box_hwidth + k*h; the transient sits at offset (-E0, -N0).
+    kE = int(np.round((box_hwidth - E0) / h))
+    kN = int(np.round((box_hwidth - N0) / h))
+    idx = np.arange(-m, m + 1)
+    cE = -box_hwidth + (kE + idx) * h        # offsets from galaxy (E)
+    cN = -box_hwidth + (kN + idx) * h        # offsets from galaxy (N)
+    CE, CN = np.meshgrid(cE, cN)
+    # Offset of each cell from the localization center, rotated into the
+    # ellipse frame; same 2D Gaussian L(w-x) as the main loop.
+    E = E0 + CE
+    N = N0 + CN
+    x_box = E * cos_dth + N * sin_dth
+    y_box = N * cos_dth - E * sin_dth
+    L_wx = (np.exp(-x_box ** 2 / (2 * a ** 2))
+            * np.exp(-y_box ** 2 / (2 * b ** 2)) / (2 * np.pi * a * b))
+    # "Total L_wx" -- the discrete integral with the SAME dA as the raw
+    # galaxy-grid sum, so dividing the raw by it cancels the aliasing.
+    return np.sum(L_wx) * step_size_phi ** 2
+
+
 def px_Oi_local(localiz, cand_coords, cand_ang_size,
-                theta_prior, step_size=0.1, 
+                theta_prior, step_size=0.05,
                 step_size_mode:str='relative',
                 debug = False):
     """
@@ -407,10 +493,13 @@ def px_Oi_local(localiz, cand_coords, cand_ang_size,
     # (phi cancels), so the same grid serves every candidate.  U, V span
     # [-1, 1]; the physical grid is phi*max * (U, V) and theta = phi*max*R.
     max_theta = theta_prior['max']
-    ngrid = int(np.round(2 * max_theta / step_size))
-    u = np.linspace(-1., 1., ngrid)
-    Ugrid, Vgrid = np.meshgrid(u, u)
-    Rgrid = np.sqrt(Ugrid ** 2 + Vgrid ** 2)         # normalized radius
+    if step_size_mode == 'relative':
+        ngrid = int(np.round(2 * max_theta / step_size))
+        u = np.linspace(-1., 1., ngrid)
+        Ugrid, Vgrid = np.meshgrid(u, u)
+        Rgrid = np.sqrt(Ugrid ** 2 + Vgrid ** 2)         # normalized radius
+    else:
+        raise ValueError(f"Invalid step_size_mode: {step_size_mode}")
 
     # Pre-compute the eellipse constants once (flat-sky fast path).
     is_eellipse = localiz['type'] == 'eellipse'
@@ -437,12 +526,11 @@ def px_Oi_local(localiz, cand_coords, cand_ang_size,
     # TODO -- parallelize / numba this per-candidate body
     for icand in range(cand_ra.size):
 
-        # Dynamic step_size
-        step_size_phi = phi_cand * step_size         # arcsec
-
         # Prep -- scale the normalized grid to this galaxy's size
         phi_cand = cand_ang_size[icand]              # arcsec
         box_hwidth = phi_cand * max_theta            # arcsec
+        step_size_phi = phi_cand * step_size         # arcsec
+
         xcoord = box_hwidth * Ugrid                  # east offset, arcsec
         ycoord = box_hwidth * Vgrid                  # north offset, arcsec
         theta = box_hwidth * Rgrid                   # arcsec
@@ -465,16 +553,32 @@ def px_Oi_local(localiz, cand_coords, cand_ang_size,
             # 2D Gaussian L(w-x), normalized over x (not omega)
             L_wx = (np.exp(-x_box ** 2 * inv_2a2)
                     * np.exp(-y_box ** 2 * inv_2b2) * L_norm)
+
+            # Correction: when the localization minor axis b is smaller
+            # than the galaxy size phi, the galaxy-centered grid
+            # under-resolves the sharp localization and the raw sum is
+            # biased low.  Divide by the "total L_wx" computed on a
+            # localization-centered, galaxy-aligned grid so the aliasing
+            # cancels (see _Lwx_correction).
+            if b < phi_cand:
+                L_wx_correction = _Lwx_correction(
+                    E0, N0, a, b, cos_dth, sin_dth, box_hwidth,
+                    ngrid, step_size_phi)
+            else:
+                L_wx_correction = 1.0
+
         else:
             # Generic fallback (healpix/wcs): build flat-sky coords and
-            # use calc_LWx, which does the type-specific lookup.
+            # use calc_LWx, which does the type-specific lookup.  No
+            # under-resolution correction here (eellipse only).
             ra = (cand_ra[icand]
                   + xcoord / 3600. / cos_cand_dec[icand])
             dec = cand_dec[icand] + ycoord / 3600.
             L_wx = localization.calc_LWx(ra, dec, localiz)
+            L_wx_correction = 1.0
 
         # Finish
-        grid_p = L_wx * p_wOi
+        grid_p = L_wx * p_wOi / L_wx_correction
         p_xOis.append(np.sum(grid_p) * step_size_phi ** 2)
         # Debug
         if debug:
diff --git a/astropath/run.py b/astropath/run.py
index c1f7cdc..7899d40 100644
--- a/astropath/run.py
+++ b/astropath/run.py
@@ -228,7 +228,7 @@ def run_on_dict(idict: dict,
         raise ValueError(f"Unsupported posterior mode: {idict['pmode']}. "
                         f"Supported: 'local', 'fixed'")
 
-    embed(header='run.py:231')
+    #embed(header='run.py:231')
 
     # Add photo-z columns if available in catalog
     photoz_columns = ['z_phot_median', 'z_phot_l68', 'z_phot_u68',
diff --git a/astropath/tests/tests_local.py b/astropath/tests/tests_local.py
index 1a65bc9..180e0f2 100644
--- a/astropath/tests/tests_local.py
+++ b/astropath/tests/tests_local.py
@@ -169,6 +169,47 @@ def test_local_matches_fine_fixedgrid(
     assert np.isclose(p_loc, p_ref, rtol=RTOL, atol=0.0)
 
 
+# Cases where the localization minor axis is smaller than the galaxy
+# (b < phi) -- these trigger the localization-centered L_wx correction.
+CORR_CASES = [c for c in CASES if c[3] < c[1]]  # b (idx 3) < phi (idx 1)
+
+
+@pytest.mark.parametrize(
+    "label,phi,a,b,pa_ee,offset,gal_pa", CORR_CASES,
+    ids=[c[0] for c in CORR_CASES])
+@pytest.mark.parametrize("coarse_step", [0.05, 0.1])
+def test_local_correction_coarse_step(
+        label, phi, a, b, pa_ee, offset, gal_pa, coarse_step, capsys):
+    """When b < phi, the _Lwx_correction keeps px_Oi_local accurate even
+    at coarse (galaxy-relative) step sizes.
+
+    The fast aligned-grid correction divides the under-resolved raw sum
+    by the discrete "total L_wx"; the aliasing cancels, recovering ~0.1-
+    0.2% accuracy where the UNcorrected raw sum is biased by ~1-2% (the
+    O(step) error).  Tolerance is well below that raw bias but looser
+    than the old fine-grid helper (the new method is ~1%-class by
+    design).
+    """
+    localiz = _eellipse_localiz(a, b, pa_ee)
+    cand = _galaxy(offset, gal_pa)
+    cand_ang_size = np.array([phi])
+
+    p_ref = _fine_fixedgrid_reference(
+        phi, a, b, pa_ee, offset, gal_pa)
+    p_loc = bayesian.px_Oi_local(
+        localiz, cand, cand_ang_size, THETA_PRIOR,
+        step_size=coarse_step)[0]
+
+    rel = (p_loc - p_ref) / p_ref
+    with capsys.disabled():
+        print("\n  %-24s step=%.2f local=%11.5e fixed(fine)=%11.5e "
+              "reldiff=%+.3e" % (label, coarse_step, p_loc, p_ref, rel))
+
+    # Much tighter than the generic RTOL: the correction removes the
+    # bulk of the step-size bias for these cases.
+    assert np.isclose(p_loc, p_ref, rtol=5.0e-3, atol=0.0)
+
+
 def test_local_multi_candidate_matches_fixedgrid(capsys):
     """All cases at once: px_Oi_local on a multi-candidate input.
 
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
index 7ba5c68..c8b8e6b 100644
--- a/prompts/speed_up_local.md
+++ b/prompts/speed_up_local.md
@@ -62,6 +62,34 @@ We will begin by removing all astropy calculations and replacing them with numpy
 - Add new code to profiling.py to profile this method
 - Log your work in the "Logs" section below.
 
+3. I have reduced the default step size to 0.05, relative to the galaxy angular size.  This will not be small enough when the localizatoin error is very small.  In that case, we need to calculate a correction similar to what is done in the fixed method.  The subtlety is that we need to correct it centered on the localization and not at the galaxy.  Please update the code to implement this.  It will mean:
+
+- Checking to see if b is less than the galaxy angular size.  If not, we can ignore the correction.
+- Calculate a new grid roughly centered on the localization but shifted from the galaxy grid.  That is, the localization grid is like an extension of the galaxy grid.  
+- I have put a hook in the code to allow for a correction.  If b < phi_cand, you should calculate the correction and apply it to the grid.
+- Log your work in the "Logs" section below.
+
+4. While your _local_lwx_correction helper works well, it is not exactly what I had in mind.  Let us develop an alternative approach which won't be as accurate but should be much faster.  Here is what the helper function should do:
+
+- Calculate L_wx approximately centered on the localization.  
+- The grid should be large enough to cover most of the ellipse (4 sigma along the major axis) 
+- The grid is spaced exactly the same as the galaxy grid (step_size_phi)
+- The grid should be aligned to the galaxy grid, i.e. only shifted by an integer number of cells in x and y
+- For phi_cand much greater than b, the total L_wx will be significantly less than 1 and we will correct our calculation by this factor
+- We will name this helper _Lwx_correction() 
+- Be careful not to generate any arrays larger than approximately 5000x5000 cells.
+
+The main point is that we will under-resolve the localization in our calculation.  But we can calculate the correction factor and apply it to the grid.  I have found that this is accurate to ~1% for the cases I have tested.
+
+Consider the above and Log a plan in the "Logs" section below.  Do not generate any new code yet.
+
+5. What you describe in the logs looks correct.  Please:
+
+- proeed to generate the code.  
+- Do use a square window for the correction.
+- Log your work in the "Logs" section below.
+
+
 ## Profiling
 
 ## Docs
@@ -71,6 +99,9 @@ We will begin by removing all astropy calculations and replacing them with numpy
 1. Read this doc.  Proceed with the 1st item under Testing.
 2. Read this doc.  Proceed with the 1st item under Development.
 3. Read this doc.  Proceed with the 2nd item under Development.
+4. Read this doc.  Proceed with the 3rd item under Development.
+5. Read this doc.  Proceed with the 4th item under Development.
+6. Read this doc.  Proceed with the 5th item under Development.
 
 ## Logging
 
@@ -333,3 +364,268 @@ Sample (50 candidates):
 | 0.100     | 120x120       | 7.8      | 0.155   |
 | 0.050     | 240x240       | 32.8     | 0.655   |
 | 0.025     | 480x480       | 182.9    | 3.659   |
+
+### 2026-06-11 (Small-localization correction, centered on the loc)
+
+**Done** (Development item 3).  The default step is now 0.05 (relative
+to phi).  That is fine when the localization is comparable to / larger
+than the galaxy, but when the minor axis `b < phi` the galaxy-centered
+grid (spacing `phi*step`) under-resolves the sharp localization and the
+raw sum carries the full O(step) bias (~-0.8% at step 0.05, ~-1.7% at
+0.1).  I filled the existing `if b < phi_cand:` hook with a correction.
+
+**What the correction does** (new helper
+`bayesian._local_lwx_correction`):
+- Builds a SEPARATE grid CENTERED ON THE LOCALIZATION (the transient),
+  not the galaxy -- the galaxy grid shifted/extended onto the
+  localization, in the same flat-sky tangent plane.
+- The grid is tied to the ELLIPSE, not to `step_size`: half-width
+  `6a` (covers the major axis so `sum(L)` captures the full,
+  unit-normalized L) and spacing `b/4` (resolves the minor axis).  It is
+  therefore INDEPENDENT of `step_size`, so coarsening the galaxy step
+  no longer degrades these cases.  `ngrid` is capped at 4000 for extreme
+  axis ratios.
+- Returns `sum(L*p)/sum(L)` -- the L-weighted average of p(w|O_i).  The
+  grid spacing cancels in the ratio and L integrates to 1, so this is
+  the localization-normalized p(x|O_i), exactly the quantity
+  `px_Oi_fixedgrid` produces with `correction='L_wx'`.  This is "similar
+  to the fixed method", but centered on the localization as required.
+- Only the `eellipse` path uses it (per item 2's scope).  For `b >=
+  phi` nothing changes; the generic healpix/wcs path is untouched.
+
+**Why a separate, loc-centered grid (the subtlety):** the ratio's
+denominator `sum(L)` must capture the FULL localization (so it equals
+its analytic norm of 1); a galaxy-centered grid of half-width `phi*max`
+fails this when `a > phi*max` (e.g. the a=10",b=0.2" ellipse), giving
+`sum(L)` over only a sliver and a ratio ~4x too large.  Centering on the
+localization with half-width `6a` fixes it.
+
+**Empirical design** (vs the fine fixed-grid reference, at step 0.05):
+| case (b<phi)            | raw reldiff | corrected | ngrid |
+|-------------------------|-------------|-----------|-------|
+| large gal10 / loc1      | -8.5e-3     | -2.7e-5   | 48    |
+| gal10 / loc0.3          | -1.2e-2     | -1.3e-7*  | 48    |
+| ellipse a10",b0.2"      | -8.4e-3     | -8.0e-5   | 2400  |
+(*with the chosen b/4 spacing; a step-tied spacing under-resolved this
+case, which is why the correction grid is tied to the ellipse.)  A
+galaxy-grid L_wx ratio was also tried but blows up (+3.2) on the ellipse
+because the galaxy box doesn't cover the major axis -- hence the
+loc-centered grid.
+
+**Verification:** `pytest astropath/tests/tests_local.py -s` -> 11
+passed.  Added `test_local_correction_coarse_step` (parametrized over
+the two `b<phi` cases x step_size in {0.05, 0.10}): asserts agreement to
+`rtol=2e-3`, far tighter than the generic 1% -- and the corrected value
+is identical at 0.05 and 0.10, confirming step-independence.
+`test_bayesian` and `test_path` still pass.
+
+**Unrelated note:** `astropath/run.py:231` has a stray
+`embed(header='run.py:231')` (in the committed `wip` state, hit
+unconditionally for both local and fixed modes) that hangs
+`test_run.py::test_run_on_dict_*` under pytest with
+"OSError: reading from stdin while output is captured".  I left it in
+place (it is your WIP debugging, not part of this task); remove that
+line to make those two tests pass.
+
+**Note / possible follow-up:** for very high axis-ratio ellipses
+(`a >> b`) the correction grid is `~6a x 6a` at spacing `b/4`, i.e.
+`~24 a/b` pixels per side (2400 for the test ellipse; the 4000 cap can
+bite for, say, a=60",b=0.2").  An anisotropic grid aligned to the
+ellipse axes (fine along the minor, coarse along the major) would cut
+this by ~100x; I kept the uniform grid for fidelity to "an extension of
+the galaxy grid" and simplicity.  Flag if you want the anisotropic
+version.
+
+### 2026-06-11 (PLAN: faster aligned _Lwx_correction; no code yet)
+
+**Task** (Development item 4): replace the accurate-but-slow
+`_local_lwx_correction` with a faster, ~1%-accurate `_Lwx_correction()`
+that DELIBERATELY under-resolves the localization on the (coarse) galaxy
+grid and divides the raw result by a correction FACTOR.  The hook is
+already stubbed by you:
+```
+if b < phi_cand:
+    L_wx_correction = _Lwx_correction(arguments)
+else:
+    L_wx_correction = 1.0
+...
+grid_p = L_wx * p_wOi / L_wx_correction          # scalar divide
+p_xOis.append(np.sum(grid_p) * step_size_phi**2)
+```
+So `_Lwx_correction()` must return a SCALAR factor; `p(x|O_i)` becomes
+`[sum(L*p)*dA] / factor`.
+
+**What the factor is.**  `factor = sum_over(loc grid) L_wx * dA`, i.e.
+the DISCRETE integral of L ("total L_wx") evaluated on a coarse grid
+centered on the localization.  When `phi >> b` the galaxy-grid spacing
+`step_size_phi` under-samples the sharp ellipse, so this discrete
+integral comes out `< 1` (your observation).  Dividing the raw
+`sum(L*p)*dA` by it renormalizes L back to 1.
+
+**Why this works to ~1% even though L is under-resolved -- the key
+idea is GRID ALIGNMENT.**  The raw numerator `sum_gal L*p*dA` samples L
+on the galaxy lattice at some fixed sub-cell phase relative to the
+ellipse.  If the correction grid is the SAME lattice (same spacing,
+shifted by an integer number of cells), it samples L at the SAME
+sub-cell phase.  Under-resolution then multiplies BOTH the numerator's
+L-weighting and the denominator `sum_loc L*dA` by the same (roughly
+uniform) aliasing factor, so it cancels in the ratio:
+
+    [sum_gal L*p*dA] / [sum_loc L*dA]
+        ~= integral(L*p) / integral(L)  =  integral(L*p)  =  p(x|O_i)
+
+(the last step uses integral(L)=1).  The residual ~1% comes from the
+aliasing factor not being perfectly uniform, the 4-sigma truncation,
+and p varying across the product region.  Alignment is ESSENTIAL: an
+unaligned (differently-phased) correction grid would not cancel and the
+error would be large and noisy.  This is the crucial difference from
+`_local_lwx_correction`, which instead RESOLVED L on a fine (b/4) grid
+-- accurate (~1e-5) but slow.
+
+**Planned `_Lwx_correction()` -- spec.**
+- Purpose: return the scalar `sum(L_wx)*dA` over a coarse,
+  galaxy-grid-aligned grid centered on the localization, so the caller
+  can divide the (under-resolved) raw p(x|O_i) by it.
+- Inputs (all plain floats/arrays, numba-friendly):
+  * `E0, N0` -- flat-sky offsets of the galaxy from the localization
+    center (arcsec); already computed in the loop.
+  * `a, b, cos_dth, sin_dth` -- ellipse semi-axes and the shared
+    rotation into the ellipse frame.
+  * the galaxy-grid lattice description so the correction grid can be
+    built ON the same lattice: pass `box_hwidth` and the shared
+    normalized axis `u` (=`np.linspace(-1,1,ngrid)`), from which
+    `h = box_hwidth*(u[1]-u[0])` is the EXACT galaxy-grid spacing
+    (~`step_size_phi`).  (Using the exact `h`, not the nominal
+    `step_size_phi`, keeps the two grids truly aligned.)
+  * `step_size_phi` -- only for `dA = step_size_phi**2` (kept identical
+    to the caller's `dA` so the scalar divide is consistent; any common
+    dA cancels in the ratio anyway).
+- Grid construction (the three constraints you listed):
+  1. SAME spacing as the galaxy grid: spacing `= h`.
+  2. ALIGNED / integer-cell shift: snap the localization center onto the
+     galaxy lattice -> `iE = round(E0/h)`, `iN = round(N0/h)`; the 1D
+     correction coordinates (offsets from the galaxy) are
+     `(iE + arange(-m, m+1)) * h` and likewise for N, where
+     `m = ceil(4*a / h)`.  These points lie exactly on the galaxy
+     lattice, just translated by `(iE, iN)` cells.
+  3. COVER 4 sigma of the major axis: half-width `4*a` -> the
+     `m = ceil(4a/h)` above.  (A square of half-width 4a covers 4-sigma
+     in every direction, so PA need not be considered for sizing.)
+- Evaluate L on this grid: offset of each correction-grid point from the
+  LOCALIZATION center is `(cE - E0, cN - N0)`; rotate into the ellipse
+  frame (`x_box = E*cos_dth + N*sin_dth`, `y_box = N*cos_dth -
+  E*sin_dth`) and form the same 2D Gaussian
+  `exp(-x_box^2/2a^2)*exp(-y_box^2/2b^2)/(2*pi*a*b)` already used in the
+  main loop.  Reuse, don't duplicate, that expression where practical.
+- Return `np.sum(L_corr) * step_size_phi**2`  (the scalar "total L_wx").
+- Guard: if `b >= phi` the caller never calls this (factor=1.0).  Cap
+  `m` (e.g. `2*m+1 <= ~4000`) so extreme axis ratios stay bounded.
+
+**Cost vs `_local_lwx_correction`.**  New spacing is `h ~ phi*step`
+(coarse) instead of `b/4` (fine).  Correction-grid side length
+`~ 8a/h = 8a/(phi*step)` vs the old `~ 48a/b`.  Ratio
+`new/old ~ b/(6*phi*step)`, i.e. for `phi >> b` (the regime that
+triggers the correction) the new grid is many-fold smaller -- e.g.
+phi=10",b=0.2",step=0.05 -> ~15x fewer points; and it sums only L (no
+p, no product) per point.  For low-phi high-aspect ellipses
+(phi~b, e.g. the a=10",b=0.2",phi=0.5" test case) the two are
+comparable, since there `h` is already small.
+
+**Integration / cleanup.**
+- Implement `_Lwx_correction()` with the spec above; wire its real
+  arguments into your stub (`E0, N0, a, b, cos_dth, sin_dth,
+  box_hwidth, u, step_size_phi`).
+- Delete `_local_lwx_correction` (superseded) -- per your earlier note
+  we need not preserve old algorithms; `tests_local.py` is the anchor.
+
+**Test impact (to handle in the coding step).**
+- `test_local_correction_coarse_step` currently asserts `rtol=2e-3`
+  (true of the fine helper).  The new approach is ~1%, so relax that to
+  ~`1.5e-2` (and drop the "identical at 0.05 vs 0.10" expectation -- the
+  factor now depends on the grid, hence weakly on step).  I will measure
+  the actual reldiff for the two `b<phi` cases at steps {0.05,0.10} and
+  set the tolerance just above the worst observed.
+- `test_local_matches_fine_fixedgrid` runs at step 0.02, where the
+  galaxy grid already resolves L for these cases, so its `rtol=1e-2`
+  should still pass; I will confirm.
+
+**numba note.**  `_Lwx_correction` is a small Gaussian sum over a
+coarse aligned grid -- trivially `@njit`-able later, and (like
+`px_Oi_numba`) it takes only scalars/arrays, no astropy.
+
+**Open question (will proceed with the stated default unless you say
+otherwise):** "4 sigma along the major axis" -> I read this as
+half-width `= 4*a` (with `a` the major-axis sigma).  If you instead
+meant 4 sigma in each axis separately (an anisotropic/elliptical
+window), say so; the square 4a window is simpler, stays aligned, and
+covers the ellipse, so I will use it.
+
+### 2026-06-11 (Implemented fast aligned _Lwx_correction)
+
+**Done** (Development item 5).  Replaced `_local_lwx_correction` with
+the faster `bayesian._Lwx_correction()` and wired it into your stubbed
+hook.  Square 4-sigma window, as you confirmed.
+
+**`_Lwx_correction(E0, N0, a, b, cos_dth, sin_dth, box_hwidth, ngrid,
+step_size_phi, max_side=5000)`** returns a SCALAR "total L_wx" =
+`sum(L_wx)*dA`.  The caller does `grid_p = L_wx*p_wOi /
+L_wx_correction`, i.e. `p(x|O_i) = raw / factor`.  The grid:
+- is centered on the localization (transient), square half-width `4*a`
+  (>= 4 sigma of the major axis);
+- has EXACTLY the galaxy-grid spacing `h = 2*box_hwidth/(ngrid-1)` and
+  lies ON the galaxy lattice (snapped by an integer cell shift `kE, kN`
+  via `round((box_hwidth - E0)/h)`), so L is sampled at the same
+  sub-cell phase as the raw sum -> the under-resolution aliasing cancels
+  in the `raw/factor` ratio;
+- uses `dA = step_size_phi**2` to match the caller's raw sum exactly
+  (so both the aliasing AND the step_size_phi-vs-h convention cancel).
+
+**Memory guard (your <=5000x5000 constraint).**  The window has
+`~8*a/h` cells per side; this only exceeds `max_side=5000` when `h` is
+very small, which is exactly the regime where the galaxy grid ALREADY
+resolves L and the raw value needs no correction.  So when
+`2m+1 > max_side` the helper returns `1.0` (skip) -- provably safe and
+never allocates a large array.  (Found empirically while validating:
+the ellipse at step 0.02 wants a 7987-cell window -> skipped -> raw is
+already -0.33%.)  No striding/coarsening: that would break the
+aliasing/dA cancellation, so skip-when-resolved is the right lever.
+
+**Accuracy measured vs the fine fixed grid** (reldiff; raw = no
+correction):
+
+| case (b<phi)          | step | raw     | corrected | window |
+|-----------------------|------|---------|-----------|--------|
+| gal10", loc 1"        | 0.05 | -0.85%  | -1.7e-4   | 17     |
+| gal10", loc 1"        | 0.10 | -1.85%  | -1.9e-3   | 9      |
+| gal10", loc 1"        | 0.02 | -0.33%  | +7.0e-5   | 41     |
+| ellipse a10",b0.2"    | 0.05 | -0.84%  | -4.1e-6   | 3189   |
+| ellipse a10",b0.2"    | 0.10 | -1.66%  | +3.4e-5   | 1589   |
+| ellipse a10",b0.2"    | 0.02 | -0.33%  | -0.33%(skip)| --    |
+| severe UR phi2 b0.05  | 0.05 | -2.49%  | -1.8e-3   | 9      |
+| severe UR phi2 b0.05  | 0.10 | -60.1%  | -2.1%     | 5      |
+
+So it removes the bulk of the under-resolution bias (dramatically so in
+the severe cases), staying ~0.1-0.2% at the default step 0.05 -- better
+than the ~1% you found.  (The lone outlier, severe under-resolution at
+the very coarse step 0.10 with only 5 window cells, lands ~2%.)
+
+**Cost.**  Common large-galaxy/small-loc case: window ~17-41 cells,
+negligible.  px_Oi_local at step 0.05 with the correction firing on
+ALL 100 candidates (a=1", phi=2-8"): 0.74 ms/candidate.  Much cheaper
+than the old fine-grid helper (which used a b/4 spacing -> e.g. 48-cell
+side even for gal10"/loc1" and 2400 for the ellipse).
+
+**Tests.**  `tests_local.py` -> 11 passed.
+- `test_local_matches_fine_fixedgrid` (step 0.02, rtol 1e-2): the two
+  b<phi cases pass -- gal10"/loc1" via the correction (+7e-5), the
+  ellipse via the skip path (-3.3e-3, raw).  No large array built.
+- `test_local_correction_coarse_step`: relaxed rtol 2e-3 -> 5e-3 (the
+  new method is ~1%-class, not the old ~1e-5) and dropped the
+  step-independence wording (the factor now depends on the galaxy grid).
+  Worst observed: gal10"/loc1" at step 0.10 = -1.9e-3.
+- Removed the obsolete `_local_lwx_correction`.
+- `test_bayesian`, `test_path` still pass.
+
+**numba note.**  `_Lwx_correction` is a small Gaussian sum on a coarse
+aligned grid (scalars + arrays, no astropy) -- ready for an `@njit`
+kernel in the numba step.

From 92b04806ef493bc47b22f7c04ecb4dc141059017 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 11 Jun 2026 10:27:43 -0700
Subject: [PATCH 21/31] ready for PR?

---
 astropath/bayesian.py     |  1 +
 docs/performance.rst      | 81 +++++++++++++++++++++++++++++++++++----
 prompts/speed_up_local.md | 54 ++++++++++++++++++++++++++
 3 files changed, 129 insertions(+), 7 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index 5161e34..693a5e2 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -406,6 +406,7 @@ def _Lwx_correction(E0, N0, a, b, cos_dth, sin_dth, box_hwidth,
     # Skip if the window would be huge: that happens when h << a at fine
     # step, i.e. L is already well resolved on the galaxy grid and the
     # raw value needs no correction.  Avoids allocating a huge array.
+    # TODO -- consider still making a correction but with a smaller window
     if (2 * m + 1) > max_side:
         return 1.0
     # Snap the localization onto the galaxy lattice (integer cell shift).
diff --git a/docs/performance.rst b/docs/performance.rst
index 59a5752..657008c 100644
--- a/docs/performance.rst
+++ b/docs/performance.rst
@@ -25,6 +25,15 @@ re-implemented in pure numpy:
   once, rather than reading ``astropy`` attributes inside the
   per-candidate loop.
 
+- ``bayesian.px_Oi_local`` (the local-grid :math:`p(x|O_i)`, which
+  builds one grid per candidate) has likewise been rewritten in pure
+  numpy for the ``eellipse`` localization: it pre-extracts the
+  coordinates once and evaluates :math:`L(w-x)` directly in a flat-sky
+  tangent plane, removing every ``astropy`` call from the per-candidate
+  loop. Other localization types (``healpix``, ``wcs``) fall back to
+  ``localization.calc_LWx`` as before. See `Local-grid posterior`_
+  below for details.
+
 These changes are transparent: you do not need to do anything to
 benefit from them, and the public APIs are unchanged.
 
@@ -76,6 +85,54 @@ Key points:
    forward ``use_numba``; call ``bayesian.px_Oi_fixedgrid`` directly to
    use it.
 
+Local-grid posterior
+====================
+
+``bayesian.px_Oi_local`` evaluates :math:`p(x|O_i)` on a separate grid
+per candidate, centered on the galaxy and sized to the offset prior
+(``box_hwidth = phi*max``). It is the method of choice for
+localizations that span a large area of sky, where
+a single fixed grid would be prohibitively large.
+
+For the ``eellipse`` localization the calculation is pure numpy and
+flat-sky:
+
+- The per-candidate grid is built once in normalized units and merely
+  rescaled per galaxy — the pixel count ``ngrid = 2*max/step_size`` is
+  the same for every candidate.
+
+- :math:`L(w-x)` is evaluated directly in the tangent plane (offsets
+  rotated into the ellipse frame), matching the spherical ``calc_LWx``
+  to ~1e-5 fractionally at arcsec scales.
+
+Here ``step_size`` is *relative* to the galaxy size (default ``0.05``),
+so the grid spacing is ``phi*step_size``.
+
+.. note::
+
+   ``px_Oi_local`` is **pure numpy and does not require (or use)
+   numba** — for now. The optional numba acceleration described above
+   applies only to ``px_Oi_fixedgrid``. ``px_Oi_local`` is fast on its
+   own because each per-candidate grid is small.
+
+Small-localization correction
+------------------------------
+
+When the localization minor axis :math:`b` is smaller than the galaxy
+angular size :math:`\phi`, the galaxy-centered grid under-resolves the
+sharp localization and the raw sum is biased low. In that case
+``px_Oi_local`` divides the result by a correction factor computed by
+``bayesian._Lwx_correction``: the discrete "total :math:`L(w-x)`" on a
+small grid that is centered on the localization and *aligned to the
+galaxy grid* (same spacing, shifted by an integer number of cells).
+Because the localization is sampled at the same sub-cell phase in the
+raw sum and in this factor, the under-resolution bias cancels in the
+ratio (accurate to ~1%). This is the local analogue of
+``px_Oi_fixedgrid``'s ``correction='L_wx'``. The correction grid is
+bounded (it is skipped when it would exceed ~5000 cells per side, which
+only happens when the localization is already well resolved and no
+correction is needed), so it never allocates a large array.
+
 Profiling module
 ================
 
@@ -89,19 +146,29 @@ Run it from the command line::
 
     python -m astropath.profiling
 
-This sweeps a range of ``step_size`` values (hence grid sizes), prints
-a timing table comparing ``calc_LWx``, the numpy ``px_Oi_fixedgrid``,
-and (if ``numba`` is installed) the numba path with its speed-up
-factor, and writes a figure (``profiling_timing.png``) of the timings
-versus grid size.
+This sweeps a range of ``step_size`` values (hence grid sizes) and
+profiles both posterior methods:
+
+- ``calc_LWx``, the numpy ``px_Oi_fixedgrid``, and (if ``numba`` is
+  installed) the numba path with its speed-up factor — written to
+  ``profiling_timing.png``;
 
-You can also import and call it directly::
+- ``px_Oi_local`` (via ``run_profiling_local``), whose per-candidate
+  grid size is ``2*max/step_size`` — written to
+  ``profiling_local_timing.png``.
+
+Both timing tables are printed to the screen.
+
+You can also import and call the pieces directly::
 
     from astropath import profiling
 
-    df = profiling.run_profiling()      # returns a pandas DataFrame
+    df = profiling.run_profiling()            # fixed-grid (+ numba)
     profiling.plot_results(df, 'timing.png')
 
+    df_local = profiling.run_profiling_local()   # local-grid method
+    profiling.plot_local_results(df_local, 'local.png')
+
 API Reference
 =============
 
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
index c8b8e6b..fe99627 100644
--- a/prompts/speed_up_local.md
+++ b/prompts/speed_up_local.md
@@ -94,6 +94,14 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 
 ## Docs
 
+
+1. Examine the docs in the astropath/docs directory.  We need to update the documentation to reflect the new code.  Please:
+
+- Update the documentation to reflect the new code for the local method
+- Note that it does not require numba (for now)
+- Comment on the profiling.py module too
+- Log your work in the "Logs" section below.
+
 ## Prompts
 
 1. Read this doc.  Proceed with the 1st item under Testing.
@@ -102,6 +110,7 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 4. Read this doc.  Proceed with the 3rd item under Development.
 5. Read this doc.  Proceed with the 4th item under Development.
 6. Read this doc.  Proceed with the 5th item under Development.
+7. Read this doc.  Proceed with the 1st item under Docs
 
 ## Logging
 
@@ -629,3 +638,48 @@ side even for gal10"/loc1" and 2400 for the ellipse).
 **numba note.**  `_Lwx_correction` is a small Gaussian sum on a coarse
 aligned grid (scalars + arrays, no astropy) -- ready for an `@njit`
 kernel in the numba step.
+
+### 2026-06-11 (Docs: documented the local method in performance.rst)
+
+**Done** (Docs item 1).  The docs live in the top-level `docs/`
+directory (not `astropath/docs`).  `docs/performance.rst` already
+documented the numpy-accelerated core, the optional numba path, and the
+`profiling` module (from the earlier fixed-grid work), so it was the
+natural home for the local-method update.
+
+**Edits to `docs/performance.rst`:**
+- Added a third bullet to *numpy-accelerated core* noting that
+  `px_Oi_local` was rewritten in pure numpy for the `eellipse` type
+  (coords pre-extracted once, `L(w-x)` evaluated flat-sky in the tangent
+  plane, no astropy in the per-candidate loop; healpix/wcs still use
+  `calc_LWx`), with a cross-reference to the new section.
+- New *Local-grid posterior* section: what `px_Oi_local` is for (large
+  localizations / healpix), the once-built normalized grid
+  (`ngrid = 2*max/step_size`), the flat-sky `L(w-x)` matching `calc_LWx`
+  to ~1e-5, and that `step_size` is *relative* to the galaxy (default
+  0.05).  Includes a prominent **note that it is pure numpy and does
+  NOT require/use numba** ("for now"); numba remains fixed-grid only.
+- New *Small-localization correction* subsection describing the
+  `b < phi` case and `_Lwx_correction`: the localization-centered,
+  galaxy-aligned "total L_wx" factor, why the aliasing cancels (~1%),
+  the analogy to `px_Oi_fixedgrid`'s `correction='L_wx'`, and that the
+  correction grid is bounded (skipped above ~5000 cells/side, which only
+  happens when no correction is needed) so it never allocates a large
+  array.
+- Updated the *Profiling module* section to say the sweep now profiles
+  BOTH methods: the existing fixed-grid (+numba) curve
+  (`profiling_timing.png`) and the new `run_profiling_local` /
+  `plot_local_results` local-grid curve (`profiling_local_timing.png`),
+  with both tables printed.  Added the import-and-call example for the
+  local profiling.
+
+**Verification:** installed `sphinx`/`sphinx_rtd_theme`/`nbsphinx` in
+astro14 and ran `python -m sphinx -b html . _build/html`.  Build
+succeeded; the 11 warnings are all pre-existing and unrelated (missing
+`nb/*` notebooks, `_static`, `language=None`, the `run.py` docstring
+list, `chime.rst` not in a toctree).  No warning references
+`performance.rst`.  Confirmed in the generated `performance.html` that
+the new *Local-grid posterior* / *Small-localization correction*
+sections, the no-numba note, the profiling mentions, and the
+`Local-grid posterior`_ cross-reference (-> `#local-grid-posterior`) all
+render.

From 53a567919a0a6d6e8cb4886e8c01a381dcd811f0 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 11 Jun 2026 11:13:03 -0700
Subject: [PATCH 22/31] more

---
 astropath/profiling.py    | 115 ++++++++++++++++++++++++++++++--------
 prompts/speed_up_local.md |  97 ++++++++++++++++++++++++++++++++
 2 files changed, 190 insertions(+), 22 deletions(-)

diff --git a/astropath/profiling.py b/astropath/profiling.py
index 46143ba..a0239a0 100644
--- a/astropath/profiling.py
+++ b/astropath/profiling.py
@@ -84,6 +84,44 @@ def default_setup(ncand=NCAND):
     return localiz, cand_coords, cand_ang_size, theta_prior
 
 
+def ellipse_setup(ncand=NCAND):
+    """High-axis-ratio ellipse scenario that exercises _Lwx_correction.
+
+    Unlike :func:`default_setup` (circular localization, where
+    ``b >= phi`` so no correction fires), this uses a long thin error
+    ellipse (a=12.5", b=0.2", axis ratio ~60) with candidate galaxies
+    LARGER than ``b``.  ``px_Oi_local`` therefore triggers the
+    ``_Lwx_correction`` for every candidate.  The galaxy sizes
+    (1.5"-2.5") are chosen so the correction grid is ~1000x1000 cells at
+    the default step (0.05) -- and stays below the ~5000-cell skip
+    threshold across the whole step sweep.
+
+    Args:
+        ncand (int, optional): Number of candidate galaxies.
+
+    Returns:
+        tuple: (localiz, cand_coords, cand_ang_size, theta_prior), same
+            shape as :func:`default_setup`.
+    """
+    frb_coord = SkyCoord(FRB_RADEC, frame='icrs')
+    # Long, thin error ellipse (large axis ratio) -> b < phi below.
+    eellipse = dict(a=12.5, b=0.2, theta=0.)
+    localiz = dict(type='eellipse',
+                   center_coord=frb_coord,
+                   eellipse=eellipse)
+    # Scatter candidates around the transient (some land off the thin
+    # ellipse; that is fine -- we are timing, not validating values).
+    idx = np.arange(ncand)
+    pa = (idx * 360. / ncand) * units.deg
+    sep = np.linspace(0.5, 8., ncand) * units.arcsec
+    cand_coords = frb_coord.directional_offset_by(pa, sep)
+    # Galaxy sizes 1.5"-2.5": all > b=0.2" (correction fires), and sized
+    # so the correction grid is ~1000 cells per side at step 0.05.
+    cand_ang_size = np.linspace(1.5, 2.5, ncand)  # arcsec
+    theta_prior = dict(max=6., PDF='exp', scale=1.)
+    return localiz, cand_coords, cand_ang_size, theta_prior
+
+
 def _time_call(func, args, npix, reps=None):
     """Time a single callable, returning the best wall time in seconds.
 
@@ -222,6 +260,16 @@ def run_profiling_local(step_sizes=None):
     (independent of phi), so sweeping ``step_size`` sweeps the
     per-candidate grid size.  The whole multi-candidate call is timed.
 
+    Two scenarios are timed against this SAME per-candidate galaxy grid
+    (the x-axis of the figure):
+
+    * ``circular`` (:func:`default_setup`) -- ``b >= phi``, so the
+      ``_Lwx_correction`` never fires: pure galaxy-grid cost.
+    * ``ellipse`` (:func:`ellipse_setup`) -- a long thin localization
+      (a=12.5", b=0.2") with ``b < phi``, so the correction fires every
+      candidate on a ~1000x1000 grid (at the default step).  Comparing
+      the two isolates the cost of the L_wx correction.
+
     Args:
         step_sizes (list, optional): Relative step sizes to sweep.
             Defaults to :data:`DEFAULT_STEP_SIZES`.
@@ -229,38 +277,54 @@ def run_profiling_local(step_sizes=None):
     Returns:
         pandas.DataFrame: One row per step size with columns
             ``step_size``, ``ngrid`` (per candidate), ``n_pixels``
-            (per candidate), ``ncand``, and ``px_Oi_local_s``.
+            (per candidate), ``ncand``, ``px_Oi_local_s`` (circular),
+            ``px_Oi_local_ellipse_s`` (ellipse + correction), and
+            ``corr_ngrid`` (representative correction-grid side).
     """
     if step_sizes is None:
         step_sizes = DEFAULT_STEP_SIZES
-    localiz, cand_coords, cand_ang_size, theta_prior = default_setup()
-    ncand = len(cand_ang_size)
+    loc_c, cc_c, sz_c, theta_prior = default_setup()
+    loc_e, cc_e, sz_e, _ = ellipse_setup()
+    ncand = len(sz_c)
     max_theta = theta_prior['max']
+    # Representative correction-grid size uses the ellipse major axis and
+    # a typical galaxy size (mirrors _Lwx_correction's window: ~8a/h).
+    a_e = loc_e['eellipse']['a']
+    phi_mid = float(np.median(sz_e))
 
-    print("Starting px_Oi_local profiling over %d step sizes, "
-          "%d candidates" % (len(step_sizes), ncand))
+    print("Starting px_Oi_local profiling (circular + ellipse) over "
+          "%d step sizes, %d candidates" % (len(step_sizes), ncand))
 
     rows = []
     for step_size in step_sizes:
-        # Per-candidate grid size (phi cancels out of ngrid)
+        # Per-candidate galaxy grid size (phi cancels out of ngrid)
         ngrid = int(np.round(2 * max_theta / step_size))
         npix = ngrid * ngrid
-        print("  step_size=%.4f  per-cand grid=%dx%d (%d pix) ..."
-              % (step_size, ngrid, ngrid, npix))
-
-        # Time the full multi-candidate px_Oi_local call.  Use the total
+        # Representative correction-grid side for the ellipse scenario.
+        h = 2. * (phi_mid * max_theta) / (ngrid - 1)
+        corr_ngrid = 2 * int(np.ceil(4. * a_e / h)) + 1
+        print("  step_size=%.4f  galaxy grid=%dx%d  "
+              "corr grid~%dx%d ..."
+              % (step_size, ngrid, ngrid, corr_ngrid, corr_ngrid))
+
+        # Time both full multi-candidate calls.  Use the total galaxy
         # pixel budget (ncand * npix) to choose the repetition count.
-        t_local = _time_call(
+        t_circ = _time_call(
+            lambda *a: bayesian.px_Oi_local(
+                loc_c, cc_c, sz_c, theta_prior, step_size=step_size),
+            (), ncand * npix)
+        t_ell = _time_call(
             lambda *a: bayesian.px_Oi_local(
-                localiz, cand_coords, cand_ang_size, theta_prior,
-                step_size=step_size),
+                loc_e, cc_e, sz_e, theta_prior, step_size=step_size),
             (), ncand * npix)
-        print("    px_Oi_local: %.1f ms (%.3f ms/cand)"
-              % (t_local * 1e3, t_local / ncand * 1e3))
+        print("    circular: %.1f ms   ellipse(+corr): %.1f ms"
+              % (t_circ * 1e3, t_ell * 1e3))
 
         rows.append(dict(step_size=step_size, ngrid=ngrid,
                          n_pixels=npix, ncand=ncand,
-                         px_Oi_local_s=t_local))
+                         px_Oi_local_s=t_circ,
+                         px_Oi_local_ellipse_s=t_ell,
+                         corr_ngrid=corr_ngrid))
 
     print("px_Oi_local profiling complete.")
     return pandas.DataFrame(rows)
@@ -278,8 +342,16 @@ def plot_local_results(df, outfile):
     """
     sqrt_pix = np.sqrt(df['n_pixels'])  # per-candidate grid side length
     fig, ax = plt.subplots(figsize=(7, 5))
+    # Circular localization (a=b=5"): b >= phi for every candidate, so
+    # the _Lwx_correction never fires (verified: 0 invocations).
     ax.plot(sqrt_pix, df['px_Oi_local_s'], 'D-', color='purple',
-            label='px_Oi_local (numpy)')
+            label='px_Oi_local (circular, b>=phi: no correction)')
+    # Ellipse scenario (b=0.2" < phi): the _Lwx_correction fires for
+    # every candidate on a ~1000x1000 grid.
+    if 'px_Oi_local_ellipse_s' in df:
+        ax.plot(sqrt_pix, df['px_Oi_local_ellipse_s'], 's-',
+                color='darkorange',
+                label='px_Oi_local (ellipse, b<phi: L_wx correction)')
     # Reference line at 10 s
     ax.axhline(10., color='dimgray', linestyle='--', linewidth=1.5)
     ax.set_xscale('log')
@@ -367,11 +439,10 @@ def main():
     # ---- px_Oi_local (the local-grid method) ----
     df_local = run_profiling_local()
     show_l = df_local.copy()
-    show_l['px_Oi_local_ms'] = show_l['px_Oi_local_s'] * 1e3
-    show_l['ms_per_cand'] = (show_l['px_Oi_local_s']
-                             / show_l['ncand'] * 1e3)
-    cols_l = ['step_size', 'ngrid', 'n_pixels', 'ncand',
-              'px_Oi_local_ms', 'ms_per_cand']
+    show_l['circular_ms'] = show_l['px_Oi_local_s'] * 1e3
+    show_l['ellipse_ms'] = show_l['px_Oi_local_ellipse_s'] * 1e3
+    cols_l = ['step_size', 'ngrid', 'ncand', 'corr_ngrid',
+              'circular_ms', 'ellipse_ms']
     print('\npx_Oi_local profiling results (best-of-reps):')
     print(show_l[cols_l].to_string(
         index=False, float_format=lambda v: '%.3f' % v))
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
index fe99627..97a7515 100644
--- a/prompts/speed_up_local.md
+++ b/prompts/speed_up_local.md
@@ -92,6 +92,24 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 
 ## Profiling
 
+1. Please make the following modification to profiling.py:
+
+- Add an additional test for the local method which uses an ellipse localization with a relatively large axis ratio.  Large enough to require an approximately 1000x1000 grid for the L_wx correction.
+- Include this curve in the figure for the local method.
+
+2. The purple curve in the local figure says circular but no correction.  Please:
+
+- check whether there is a correction.  
+- update the figure as needed
+- Log your work in the "Logs" section below.
+
+3. Add one more test to profiling.py for the local method:
+
+- Use a very small localization in both dimenstions (a=0.1", b=0.1")
+- Include galaxy sizes from 0.1" to 20"
+- If necessary, have the test_local.py module include an accuracy test for a small localization too
+- Log your work in the "Logs" section below.
+
 ## Docs
 
 
@@ -111,6 +129,9 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 5. Read this doc.  Proceed with the 4th item under Development.
 6. Read this doc.  Proceed with the 5th item under Development.
 7. Read this doc.  Proceed with the 1st item under Docs
+8. Read this doc.  Proceed with the 1st item under Profiling
+9. Read this doc.  Proceed with the 2nd item under Profiling
+10. Read this doc.  Proceed with the 3rd item under Profiling
 
 ## Logging
 
@@ -683,3 +704,79 @@ the new *Local-grid posterior* / *Small-localization correction*
 sections, the no-numba note, the profiling mentions, and the
 `Local-grid posterior`_ cross-reference (-> `#local-grid-posterior`) all
 render.
+
+### 2026-06-11 (Profiling: ellipse scenario exercising _Lwx_correction)
+
+**Done** (Profiling item 1).  Added a high-axis-ratio ellipse scenario
+to the local-method profiling so the `_Lwx_correction` path is timed on
+a ~1000x1000 grid, and plotted its curve alongside the existing one.
+
+**Edits to `astropath/profiling.py`:**
+- New `ellipse_setup()`: a long thin error ellipse (a=12.5", b=0.2",
+  axis ratio ~62) with 50 candidate galaxies of size 1.5"-2.5" (all
+  `> b`, so the correction fires for every candidate).  The galaxy
+  sizes are tuned so the correction grid is ~1000 cells per side at the
+  default step 0.05, and stays under the ~5000-cell skip threshold
+  across the whole step sweep (so it never short-circuits).
+- `run_profiling_local()` now times BOTH scenarios against the same
+  per-candidate galaxy grid (the figure x-axis): the existing circular
+  case (`b >= phi`, no correction) and the new ellipse case
+  (`b < phi`, correction fires).  Added columns
+  `px_Oi_local_ellipse_s` and `corr_ngrid` (a representative
+  correction-grid side, ~`8a/h`, printed per step), so the table shows
+  the correction grid growing 97 -> 1777 across the sweep
+  (997 at the default 0.05).
+- `plot_local_results()` plots the ellipse curve (orange squares,
+  "ellipse + L_wx corr.") on top of the circular curve (purple
+  diamonds), keeping the 10 s reference line.
+- `main()`'s local table now reports `corr_ngrid`, `circular_ms`, and
+  `ellipse_ms`.
+
+**Measured** (50 candidates; circular vs ellipse+correction):
+
+| step  | galaxy grid | corr grid | circular | ellipse(+corr) |
+|-------|-------------|-----------|----------|----------------|
+| 0.50  | 24x24       | 97        | 1.0 ms   | 6.7 ms         |
+| 0.25  | 48x48       | 197       | 1.9 ms   | 32 ms          |
+| 0.10  | 120x120     | 497       | 7.9 ms   | 361 ms         |
+| 0.05  | 240x240     | 997       | 32 ms    | 1763 ms        |
+| 0.025 | 480x480     | 1777      | 157 ms   | 7059 ms        |
+
+So the L_wx correction dominates the cost for high-axis-ratio ellipses
+(the correction grid `~8a/h` grows faster than the galaxy grid
+`2*max/step`): at step 0.05 the per-candidate correction is a ~1000x1000
+Gaussian sum, ~35 ms/candidate vs ~0.6 ms for the un-corrected circular
+case.  This is the intended demonstration that the cheap-but-not-free
+correction is the bottleneck precisely for long thin localizations --
+useful context for a future numba kernel.
+
+**Verification:** ran `run_profiling_local` and `plot_local_results`;
+confirmed `corr_ngrid=997` at step 0.05, that both data curves render
+(labels "px_Oi_local (circular, no corr.)" and "px_Oi_local (ellipse +
+L_wx corr.)"), and that the largest correction array stays well under
+5000x5000 (max ~2663 per side at step 0.025).
+
+### 2026-06-11 (Profiling: verified the circular curve has no correction)
+
+**Done** (Profiling item 2).  Checked whether the purple (circular)
+curve in the local figure actually applies the `_Lwx_correction`.
+
+**Verification:** wrapped `bayesian._Lwx_correction` with a call
+counter and ran both profiling scenarios at step 0.05:
+- circular (`default_setup`, a=b=5"): the correction fired **0 times**
+  -- `b < phi` is False for every candidate (b=5" vs phi 0.2"-2.5"), so
+  the `else: L_wx_correction = 1.0` branch is always taken.  The
+  "no correction" label is therefore correct.
+- ellipse (`ellipse_setup`, b=0.2"): the correction fired **50 times**
+  (every candidate), with factor ~0.9916.
+
+So the purple curve genuinely has no correction; the difference between
+the two curves IS the correction overhead.
+
+**Figure update:** sharpened both legend labels to state the governing
+condition explicitly, so the figure is self-documenting:
+- ``px_Oi_local (circular, b>=phi: no correction)``
+- ``px_Oi_local (ellipse, b<phi: L_wx correction)``
+and added comments in `plot_local_results` noting the circular case has
+`b >= phi` (0 invocations, verified) while the ellipse case fires the
+correction on a ~1000x1000 grid.

From 08c16348a63d09787b22e4eb7c51e807e1cb63fd Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 11 Jun 2026 11:43:28 -0700
Subject: [PATCH 23/31] go

---
 astropath/bayesian.py          | 13 ++++++
 astropath/profiling.py         | 82 ++++++++++++++++++++++++++++------
 astropath/tests/tests_local.py | 40 +++++++++++++++++
 prompts/speed_up_local.md      | 65 +++++++++++++++++++++++++++
 4 files changed, 186 insertions(+), 14 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index 693a5e2..d27f356 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -565,6 +565,19 @@ def px_Oi_local(localiz, cand_coords, cand_ang_size,
                 L_wx_correction = _Lwx_correction(
                     E0, N0, a, b, cos_dth, sin_dth, box_hwidth,
                     ngrid, step_size_phi)
+                # Degenerate case: the localization is so much smaller
+                # than the grid spacing that even the aligned correction
+                # grid catches no flux -- the factor underflows to 0 and
+                # the raw sum is 0 too (0/0).  Fall back to the
+                # delta-function limit p(x|O_i) = p(w=x|O_i), which is
+                # exact as b -> 0 since L integrates to 1.
+                if not (L_wx_correction > 0.):
+                    theta0 = np.sqrt(E0 ** 2 + N0 ** 2)  # offset, arcsec
+                    p_xOis.append(pw_Oi(
+                        np.array([theta0]), phi_cand, theta_prior)[0])
+                    if debug:
+                        embed(header='px_Oi_local delta-limit')
+                    continue
             else:
                 L_wx_correction = 1.0
 
diff --git a/astropath/profiling.py b/astropath/profiling.py
index a0239a0..decb8d9 100644
--- a/astropath/profiling.py
+++ b/astropath/profiling.py
@@ -122,6 +122,41 @@ def ellipse_setup(ncand=NCAND):
     return localiz, cand_coords, cand_ang_size, theta_prior
 
 
+def small_loc_setup(ncand=NCAND):
+    """Very small (sub-arcsec) circular localization scenario.
+
+    A tiny circular error ellipse (a=b=0.1") with candidate galaxies
+    spanning 0.1"-20".  For every galaxy larger than ``b`` the
+    ``_Lwx_correction`` fires, but because the ellipse major axis is
+    tiny its correction grid (~8a/h cells per side) stays small even as
+    the galaxy grid grows -- the opposite regime to
+    :func:`ellipse_setup` (large axis ratio -> large correction grid).
+    This stresses the deeply under-resolved case (grid spacing
+    ``phi*step`` can be many times ``b``).
+
+    Args:
+        ncand (int, optional): Number of candidate galaxies.
+
+    Returns:
+        tuple: (localiz, cand_coords, cand_ang_size, theta_prior), same
+            shape as :func:`default_setup`.
+    """
+    frb_coord = SkyCoord(FRB_RADEC, frame='icrs')
+    # Very small, circular error ellipse
+    eellipse = dict(a=0.1, b=0.1, theta=0.)
+    localiz = dict(type='eellipse',
+                   center_coord=frb_coord,
+                   eellipse=eellipse)
+    idx = np.arange(ncand)
+    pa = (idx * 360. / ncand) * units.deg
+    sep = np.linspace(0.05, 2.0, ncand) * units.arcsec
+    cand_coords = frb_coord.directional_offset_by(pa, sep)
+    # Wide range of galaxy sizes, 0.1"-20"
+    cand_ang_size = np.linspace(0.1, 20., ncand)  # arcsec
+    theta_prior = dict(max=6., PDF='exp', scale=1.)
+    return localiz, cand_coords, cand_ang_size, theta_prior
+
+
 def _time_call(func, args, npix, reps=None):
     """Time a single callable, returning the best wall time in seconds.
 
@@ -260,15 +295,19 @@ def run_profiling_local(step_sizes=None):
     (independent of phi), so sweeping ``step_size`` sweeps the
     per-candidate grid size.  The whole multi-candidate call is timed.
 
-    Two scenarios are timed against this SAME per-candidate galaxy grid
-    (the x-axis of the figure):
+    Three scenarios are timed against this SAME per-candidate galaxy
+    grid (the x-axis of the figure):
 
     * ``circular`` (:func:`default_setup`) -- ``b >= phi``, so the
       ``_Lwx_correction`` never fires: pure galaxy-grid cost.
     * ``ellipse`` (:func:`ellipse_setup`) -- a long thin localization
       (a=12.5", b=0.2") with ``b < phi``, so the correction fires every
-      candidate on a ~1000x1000 grid (at the default step).  Comparing
-      the two isolates the cost of the L_wx correction.
+      candidate on a ~1000x1000 grid (at the default step).
+    * ``small`` (:func:`small_loc_setup`) -- a tiny circular
+      localization (a=b=0.1") with galaxies 0.1"-20"; the correction
+      fires but its grid stays small (tiny major axis).  Comparing the
+      three isolates how the correction cost scales with the
+      localization size.
 
     Args:
         step_sizes (list, optional): Relative step sizes to sweep.
@@ -278,13 +317,15 @@ def run_profiling_local(step_sizes=None):
         pandas.DataFrame: One row per step size with columns
             ``step_size``, ``ngrid`` (per candidate), ``n_pixels``
             (per candidate), ``ncand``, ``px_Oi_local_s`` (circular),
-            ``px_Oi_local_ellipse_s`` (ellipse + correction), and
-            ``corr_ngrid`` (representative correction-grid side).
+            ``px_Oi_local_ellipse_s`` (ellipse + correction),
+            ``px_Oi_local_smallloc_s`` (small localization), and
+            ``corr_ngrid`` (representative ellipse correction-grid side).
     """
     if step_sizes is None:
         step_sizes = DEFAULT_STEP_SIZES
     loc_c, cc_c, sz_c, theta_prior = default_setup()
     loc_e, cc_e, sz_e, _ = ellipse_setup()
+    loc_s, cc_s, sz_s, _ = small_loc_setup()
     ncand = len(sz_c)
     max_theta = theta_prior['max']
     # Representative correction-grid size uses the ellipse major axis and
@@ -292,8 +333,8 @@ def run_profiling_local(step_sizes=None):
     a_e = loc_e['eellipse']['a']
     phi_mid = float(np.median(sz_e))
 
-    print("Starting px_Oi_local profiling (circular + ellipse) over "
-          "%d step sizes, %d candidates" % (len(step_sizes), ncand))
+    print("Starting px_Oi_local profiling (circular + ellipse + small) "
+          "over %d step sizes, %d candidates" % (len(step_sizes), ncand))
 
     rows = []
     for step_size in step_sizes:
@@ -304,11 +345,11 @@ def run_profiling_local(step_sizes=None):
         h = 2. * (phi_mid * max_theta) / (ngrid - 1)
         corr_ngrid = 2 * int(np.ceil(4. * a_e / h)) + 1
         print("  step_size=%.4f  galaxy grid=%dx%d  "
-              "corr grid~%dx%d ..."
+              "ellipse corr grid~%dx%d ..."
               % (step_size, ngrid, ngrid, corr_ngrid, corr_ngrid))
 
-        # Time both full multi-candidate calls.  Use the total galaxy
-        # pixel budget (ncand * npix) to choose the repetition count.
+        # Time all three full multi-candidate calls.  Use the total
+        # galaxy pixel budget (ncand * npix) to choose the rep count.
         t_circ = _time_call(
             lambda *a: bayesian.px_Oi_local(
                 loc_c, cc_c, sz_c, theta_prior, step_size=step_size),
@@ -317,13 +358,19 @@ def run_profiling_local(step_sizes=None):
             lambda *a: bayesian.px_Oi_local(
                 loc_e, cc_e, sz_e, theta_prior, step_size=step_size),
             (), ncand * npix)
-        print("    circular: %.1f ms   ellipse(+corr): %.1f ms"
-              % (t_circ * 1e3, t_ell * 1e3))
+        t_small = _time_call(
+            lambda *a: bayesian.px_Oi_local(
+                loc_s, cc_s, sz_s, theta_prior, step_size=step_size),
+            (), ncand * npix)
+        print("    circular: %.1f ms   ellipse(+corr): %.1f ms   "
+              "small-loc: %.1f ms"
+              % (t_circ * 1e3, t_ell * 1e3, t_small * 1e3))
 
         rows.append(dict(step_size=step_size, ngrid=ngrid,
                          n_pixels=npix, ncand=ncand,
                          px_Oi_local_s=t_circ,
                          px_Oi_local_ellipse_s=t_ell,
+                         px_Oi_local_smallloc_s=t_small,
                          corr_ngrid=corr_ngrid))
 
     print("px_Oi_local profiling complete.")
@@ -352,6 +399,12 @@ def plot_local_results(df, outfile):
         ax.plot(sqrt_pix, df['px_Oi_local_ellipse_s'], 's-',
                 color='darkorange',
                 label='px_Oi_local (ellipse, b<phi: L_wx correction)')
+    # Small circular localization (a=b=0.1" < phi): correction fires but
+    # its grid is tiny (small major axis).
+    if 'px_Oi_local_smallloc_s' in df:
+        ax.plot(sqrt_pix, df['px_Oi_local_smallloc_s'], '^-',
+                color='seagreen',
+                label='px_Oi_local (small loc a=b=0.1", b<phi)')
     # Reference line at 10 s
     ax.axhline(10., color='dimgray', linestyle='--', linewidth=1.5)
     ax.set_xscale('log')
@@ -441,8 +494,9 @@ def main():
     show_l = df_local.copy()
     show_l['circular_ms'] = show_l['px_Oi_local_s'] * 1e3
     show_l['ellipse_ms'] = show_l['px_Oi_local_ellipse_s'] * 1e3
+    show_l['smallloc_ms'] = show_l['px_Oi_local_smallloc_s'] * 1e3
     cols_l = ['step_size', 'ngrid', 'ncand', 'corr_ngrid',
-              'circular_ms', 'ellipse_ms']
+              'circular_ms', 'ellipse_ms', 'smallloc_ms']
     print('\npx_Oi_local profiling results (best-of-reps):')
     print(show_l[cols_l].to_string(
         index=False, float_format=lambda v: '%.3f' % v))
diff --git a/astropath/tests/tests_local.py b/astropath/tests/tests_local.py
index 180e0f2..9894bfb 100644
--- a/astropath/tests/tests_local.py
+++ b/astropath/tests/tests_local.py
@@ -210,6 +210,46 @@ def test_local_correction_coarse_step(
     assert np.isclose(p_loc, p_ref, rtol=5.0e-3, atol=0.0)
 
 
+# Very small (sub-arcsec) circular localizations -- the deeply
+# under-resolved regime (grid spacing phi*step >> b).  phi is kept <= 1"
+# so the fine fixed-grid reference stays well under 5000 cells per side.
+SMALL_LOC_CASES = [
+    ("small_loc_gal0p3", 0.3, 0.1, 0.1, 0., 0.3, 0.),
+    ("small_loc_gal0p6", 0.6, 0.1, 0.1, 0., 0.3, 0.),
+    ("small_loc_gal1",   1.0, 0.1, 0.1, 0., 0.3, 0.),
+]
+
+
+@pytest.mark.parametrize(
+    "label,phi,a,b,pa_ee,offset,gal_pa", SMALL_LOC_CASES,
+    ids=[c[0] for c in SMALL_LOC_CASES])
+def test_local_small_localization(
+        label, phi, a, b, pa_ee, offset, gal_pa, capsys):
+    """px_Oi_local stays accurate for a very small localization (0.1").
+
+    Here ``b < phi`` so the _Lwx_correction fires, and the galaxy grid
+    badly under-resolves the 0.1" localization (spacing phi*step can be
+    many times b).  The correction must still recover the fine fixed-grid
+    value.  Run at the default step (0.05).
+    """
+    localiz = _eellipse_localiz(a, b, pa_ee)
+    cand = _galaxy(offset, gal_pa)
+    cand_ang_size = np.array([phi])
+
+    p_ref = _fine_fixedgrid_reference(
+        phi, a, b, pa_ee, offset, gal_pa)
+    p_loc = bayesian.px_Oi_local(
+        localiz, cand, cand_ang_size, THETA_PRIOR, step_size=0.05)[0]
+
+    rel = (p_loc - p_ref) / p_ref
+    with capsys.disabled():
+        print("\n  %-18s local=%11.5e  fixed(fine)=%11.5e  "
+              "reldiff=%+.3e" % (label, p_loc, p_ref, rel))
+
+    assert np.isfinite(p_loc) and p_loc > 0
+    assert np.isclose(p_loc, p_ref, rtol=RTOL, atol=0.0)
+
+
 def test_local_multi_candidate_matches_fixedgrid(capsys):
     """All cases at once: px_Oi_local on a multi-candidate input.
 
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
index 97a7515..58db86f 100644
--- a/prompts/speed_up_local.md
+++ b/prompts/speed_up_local.md
@@ -120,6 +120,11 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 - Comment on the profiling.py module too
 - Log your work in the "Logs" section below.
 
+2. Please add the results on accuracy and profiling to the docs/performance.rst file.  And:
+
+- Include the 2 profiling figures (re-generate them first)
+- Tables summarizing the accuracy and profiling results
+
 ## Prompts
 
 1. Read this doc.  Proceed with the 1st item under Testing.
@@ -132,6 +137,7 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 8. Read this doc.  Proceed with the 1st item under Profiling
 9. Read this doc.  Proceed with the 2nd item under Profiling
 10. Read this doc.  Proceed with the 3rd item under Profiling
+11. Read this doc.  Proceed with the 2nd item under Docs
 
 ## Logging
 
@@ -780,3 +786,62 @@ condition explicitly, so the figure is self-documenting:
 and added comments in `plot_local_results` noting the circular case has
 `b >= phi` (0 invocations, verified) while the ellipse case fires the
 correction on a ~1000x1000 grid.
+
+### 2026-06-11 (Profiling: tiny-localization scenario + NaN fix)
+
+**Done** (Profiling item 3).  Added a third local-method profiling
+scenario and an accuracy test; the scenario also surfaced (and I fixed)
+a 0/0 NaN in `px_Oi_local`.
+
+**`ellipse_setup` companion -> new `small_loc_setup()`:** a very small
+circular localization (a=b=0.1") with galaxy sizes 0.1"-20".  For every
+galaxy `> b` the `_Lwx_correction` fires, but because the major axis is
+tiny the correction grid stays small (the opposite of `ellipse_setup`'s
+~1000-cell grid).  This stresses the deeply under-resolved regime
+(galaxy spacing `phi*step` can be many times `b`).
+
+**`run_profiling_local` now times THREE scenarios** against the same
+per-candidate galaxy grid (figure x-axis): circular (no correction),
+ellipse (large correction grid), and small-loc (tiny correction grid).
+Added column `px_Oi_local_smallloc_s`; `plot_local_results` plots the
+new curve (green triangles) and `main()`'s table gains `smallloc_ms`.
+Full sweep (50 candidates):
+
+| step  | galaxy grid | ellipse corr | circular | ellipse | small-loc |
+|-------|-------------|--------------|----------|---------|-----------|
+| 0.50  | 24x24       | 97           | 1.0 ms   | 6.8 ms  | 2.3 ms    |
+| 0.25  | 48x48       | 197          | 1.8 ms   | 32 ms   | 3.3 ms    |
+| 0.10  | 120x120     | 497          | 7.9 ms   | 354 ms  | 11 ms     |
+| 0.05  | 240x240     | 997          | 32 ms    | 1822 ms | 40 ms     |
+| 0.025 | 480x480     | 1997         | 156 ms   | 9721 ms | 184 ms    |
+
+So the correction cost scales with the localization MAJOR axis (a): a
+long thin ellipse (a=12.5") is ~50x the no-correction cost, while a tiny
+round localization (a=0.1") adds only a small overhead.
+
+**Bug found + fixed (0/0 -> NaN).**  The small-loc scenario at coarse
+steps produced NaN: when the grid spacing `phi*step` is many times
+`b` (e.g. step 0.5, phi up to 20", spacing up to 10" vs b=0.1"), the
+0.1" localization falls entirely between grid cells -- the aligned
+`_Lwx_correction` grid catches no flux (factor underflows to 0) and the
+raw sum is 0 too, so `raw/factor` was `0/0`.  This is a real pipeline
+risk (tiny localization + coarse step), so I guarded `px_Oi_local`: when
+the correction factor is not `> 0`, it falls back to the exact
+delta-function limit `p(x|O_i) = pw_Oi(theta_offset)` (correct as
+`b -> 0`, since L integrates to 1).  After the fix the small-loc
+scenario is finite at every step (verified 0.5 -> 0.025, no warnings).
+
+**Accuracy test added** to `tests_local.py`
+(`test_local_small_localization`, 3 cases): a=b=0.1", phi in
+{0.3, 0.6, 1.0}", offset 0.3", compared to the fine fixed grid at the
+default step 0.05.  phi is kept <= 1" so the reference stays well under
+5000 cells per side.  Result: reldiff ~2e-5 to 7e-5 -- the correction
+is essentially exact for very small localizations.  (The earlier ~-2%
+seen against a delta-limit reference was that reference's own bias, not
+the method.)  Full suite: `tests_local.py` 14 passed; with
+`test_bayesian`/`test_path`, 19 passed.
+
+**Note:** the largest array anywhere stays under 5000x5000 -- the
+small-loc correction grids are tiny (small a), the ellipse tops out at
+~2000 (step 0.025), and the NaN guard removed the only pathological
+divide.

From d9df0137715bb799213706b9c83c3df742498f96 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 11 Jun 2026 13:16:15 -0700
Subject: [PATCH 24/31] tests

---
 .gitignore                              |   2 +
 docs/figures/profiling_local_timing.png | Bin 0 -> 76331 bytes
 docs/figures/profiling_timing.png       | Bin 0 -> 65037 bytes
 docs/performance.rst                    | 100 ++++++++++++++++++++++++
 prompts/speed_up_local.md               |  38 ++++++++-
 5 files changed, 139 insertions(+), 1 deletion(-)
 create mode 100644 docs/figures/profiling_local_timing.png
 create mode 100644 docs/figures/profiling_timing.png

diff --git a/.gitignore b/.gitignore
index 9481c69..d8ec7e2 100644
--- a/.gitignore
+++ b/.gitignore
@@ -10,6 +10,8 @@ __pycache__/
 *.png
 *.pdf
 *.csv
+# ...but keep documentation figures (committed for the docs build)
+!docs/figures/*.png
 papers/FRB_I/Analysis/SandBox/
 papers/FRB_I/Resub/
 papers/FRB_I/astroph/
diff --git a/docs/figures/profiling_local_timing.png b/docs/figures/profiling_local_timing.png
new file mode 100644
index 0000000000000000000000000000000000000000..e0ded67d8a650d6ad181423b2b08adf86c39a536
GIT binary patch
literal 76331
zcmd43c|4Zw+BU2-X;P?=sgNO&A#o|9GEbo*A~Fk^XDUT1B}0Z>$()2_PAFt7G9^P~
z3Yljzz1w-OwVvmFe((Ezzwgg){aS0?cZTackK@?)ecQKf+m8TsRk>Z;8MjkVQ0!8W
zKc_)KK`Bo`u~B>57W|F2Y{e}8kK}k>+fmcj)X~Mz-h@KM(DCLCTgMv~Mr_U|_6`=d
zHp2XZ$N9zi*vuUrZ#s|!1g!t-JNRww%><6fHtFEEP~DW*aiE}}aU}k`q05xjm0|-0
zg~B;$E!XJLpDx;Ta;zVxCVn;~ZsT^A&a}Egf5JKN>h)IhM-Lc10tKI$)4j>O{w8Br
zV3F00Oe>LjmO^?y!HSJ{*yIa37O3ryRx)4w_4vAEeINVDyuz91ZEc0*j-L$oI235^
zux<O-pN)#wxBlm!?_A?Ow^d=!Ch33v^hm||a{T+d?o6^aNYniL3(|{EhS;e7^BY#=
z9E1Mzg*|KRB>De*VcYs%W{!XTD(O9U*YEER{?F%>`uzXnV~&69=s0*!=2N`flg8{~
znb?>5Mef6ln(i}`lOM~<%6=FowAV|mD@O{Myv@luAFKXraBwSqx&tdKE8X_ZT&mIE
z6iyDTI;^jGy?OH{Lfj!K^KA9IOBwosGO^d@{<M&WQ><s6u$-2`4~~tI)2B?5E~Q=R
z86H+}bj;2?yZ0{NSz_gmTLp7uT6c(E$+J;eTUp9{_pY?1CG1L$rJ&2W-r>WCA2G)T
zZGSFmZS>=<;g26bj(aZNJfa#cj}HiBzVx0^&}dV7diqY5Q`%ftJKB^+yKPHWO>cU9
z`t)fht0WUOHT9dcwCWfssUr8e-iea+x<|d+J_gWosdLjUE-o6ocZD2LIeh$hP>j!-
zc+<@OyKibre{8^}8;1r3?IAh+Deo!sx3jm8bDR0?>gu|OiRsHH->pmIg%jFuuWj&H
z7*D*>_Kq~78Y4*-yk4RH^2`SI^8)nmTqg9F)>oEhMn1R<)-jKcj%s9+oB5tc)<uh#
z6?-j5ken>zrsjqk%6?r8GWz^rIC1ml%@^Wjca3+KsQGT$HPl%k>@v~yxw|{YYkA&o
zepKhd{$o*HpO5RvJz+WFye%>vKO|z^9-5+=EOhhNnUEU`cdl9fbEdKq8q9}&WU|XW
zW{On^Ir7G!gyr((%S)?2erO+2j`%n`++@+2FL*g!?~vMyQ`5^!(*x`V#hw-0uF986
zt*=nNY!%<geet!{gS?O^6XB+~^AFW|!yG5NPB)l*C@RwQ^!P<BweoRwd4U1z?(qA|
z(<Yy_B{RQW2P;0_rlc*JHhz5S^yxt6I~Qh$8hk0Y?tW`nwxxLK_rdG_?Awm0bsBMP
zlX)NDQ?mB6(8Z!DX%{~~e}C0eUu?GB(6>Y6f$k4(?A`MYOVcLg1rf$wb0e*CvFdM~
z$J(_j-{ChsW)i=XoXjQRJo;^zX@j=5_HpZWk>ZtUrM0C&)`};r88d5@lD?r4-@d6=
zJZ4s^4(80v%>2~W7I{P^>LxzuT&uX_&>jQNsm(SvHrl$nny=Ik;n<~RsX97}>^Q)m
zfL+cnEWB=Q9r*C!j$H>u`|(!8G==j8WW1)o&CmBezkmCsr5)4P*T3=Ot+egZV&1;1
z`8RLxKX&C;Z*QDt#)S(PR%V;jJg2L<ezdjq3=PSTwdb_GGkI8-o1GWVEak2D`24bf
zp=S!u!`M@*(PE!+tvg;_$>DW&cFxbw|5o5&_TsdM=}p}O0{RJdeHCJ2V!!Y^%KUbT
zd(7X6tC!;ZJ=T$Tqa!zv@r0%N+iRcb(n3NfCvSdFzp8}AnY9^XJmq?Pe0-eglxtAQ
z+TWv}J9h5gZQ7Y{7kc#aZV3sA=;-KI>aiQIS3K&$7EIfR3mBLpuC!jMZ#Zz^z>OO>
zxb;7Xb$cx^+jf0u=&)Ha^LxxHrHa_;|9hh$ZnMjHry#xBnKKm363*pVS0-_LbsXFI
zv5s)_m4MT}bo=*L+~3R2t^JlwR8%yS_u_*Bhrzf8^PM(>YpctT7=-<JFTM_vaIry9
z+PSzS+jbYb=kdFHcxaY*dr^3Lc{#P)l;&pI^~wHe%}_(MVE<wrhZ~WC?!9`&T|}=+
zCVf6&;3@s-&gRVA+#`5Otqgr;0|SF16Wu(Uz`(#=M=z%<XWML&UOc0Rgnj7e<}F*M
z+stC7s<~pmWf(}kkn*Yf{q?!U_csg&MQ{A76)4&C5ib&W@T5kvDl>7G()EiT`1(@r
zaXD<)TTX>jKm0vS_w{w{Voz}jtjyKmyinzc<F~&)Kbhq`c4a@G_N~A`6-LEqp+kob
zHNVjb>BzI48BUH7LY~qu@&5Ykn65b@PU#t6tU-x4X+$|%>?s1%(AHKBNsU|U)t>d0
z8EUh-Xv3fHokVW@*mGaPj#(6i&a(L>QbK<n`T1adOqN+aOVml*y6J)1rh)LjleS&N
zy4(N$qEP?hG!+$<VePYHj$`d%X7w+oRu{TQ(j1U9lGI{U)2`$UwWJ=%Fes_0sd+Fo
zWF94AQCc0s#dGmB9Wo8_>mBQk+^K<Z1N*V|6G<x1x3IaGB8PwNt9%kEX4fkh&MElt
zfWYro1E0i;sh675bi-!`>$BWuOw$cY>T;}F-{$5%3tz=&5_!ckCknxe6km;es<8TZ
z&f?ok>DSZ5mjfO@CeptGzsuiQ3;wI`?_No(C@b?teTmj9upd5#qa}WroqeEA*HbYu
z7y<kCMw<{0-;218(T$XpDF!8yPgtcYYHJ^EpxpAZ!93q*U2^94*La`xHAFV$eTg;a
z@lFM-p~a84hZqC>YQqJDQ9yPxiG5s}8Jsh^ldsE#oT`##`gN$gL@Lj=+jM<xRquoA
zQ*78s=nT@j=X{&lrp=oh-slMPUV0;sV{YA^9jlXNTK!D!C@=2=;#sj48nH5)-#d>f
z%FAyH;ZpnEUmdcgwJr1dR;6(MMDNwV&95#{9zA*#$>Q^aeMf&}nNf%HUk$dcw?@9B
zu=@Tc7GEJT&n%L2P;GlACe(12ExL<Oi#z=8?<{awS?qhlblN?%%%A$Y;a->a`3~EX
zhPd-Pn3$O@T3+wlyq%6sOe{jeW&Ew{lu=P%Sw+Pb0Re$JvV@$uIk&2+Do;AAbk#H9
zj=PRD^z_^tXxIXo#5D$s@ZgI3_wUz0P$eQik{3+BL>$_nF<3|DR0vMEUinx-F;Ro}
z>ig{3@t=iSm3wJv*>!Yu6mB_Um5jsdW28zp$tSClgPYuEhwyXPu3dXQ6V9QqG2y+_
z$e)C{v5w0d6HwX|83SciOMKRg`-g_O@e79gT_%4?Qw2Ss<2g(m19!JmUVpXLmQg}T
z896dCG70ZYY8C71>NL)syIbdh)D>J<=<&K{lRQ#PXtQNb^cs$y0=^+QF)?v=vgfS$
z>f%)2GzqKS($SS|(Zq4a^81@eIy`T3iR+Y%y^BjY#qblUwQoAfSZNI-gR6djJbTLn
zXxNZ`PkpW>iHXUdwCVijmVsYE!)D#}K}S_HwM8S-=rhNe_7b0xx@iRK)7lruC(0kO
zoW8O#0Rh6`X>ib>)aU#6?~V9$r}j_|g~rl*J2=lE-@g4c_BHB+(#8aYYa(}Xz2vg;
z#spNi;i82<Ek}8TgfzTYhZ@*<L`5&z7VJBEN&Xfpgw$}t^769Mtptsf1QhF`4<}8(
z&{G9rQ({B9UR_|P3R+oNacp!MYv*hYEGa3e^YCk5X-?7PJY(6KPX6S)Oa8R`>^Gf3
zK$>S=B|aIKi+#6JD`E@(beEK<zMt2Q5VMQxB2CqH=UVF)^=TD$_l0L&Ep(<~!~dw*
z>SpK{2}M*+_LOm+Y0tBb`LwVZ8S`KD*}>l4sPrxs$pSdwsZZq30*B-}k8Yp!(<;wJ
zO`4KalmT|quNE3vTYp6+ZJIq}ck|}kQwi3wGWUY7>K8tmUwZav4>R*u9E`Vld1ilS
zhe>&U`vml(W6%22;O_-WRt_f%XuqYng(FYT#CLejS{n<y#kSTSK<jdb{s*@iKO9$Y
zM{zCQeZr<+&ZMkN&Rs~5-|M%VSy5T}(Wj0>M=!m3<zlk)TFdK;+;rQ2*O8B|3+?{(
z`*#I4e%nXHoh0dZGb727JH~T5K=n$Dq!&g0&7M2a&cDAfY}~l<l|e~y*S?21uNraZ
z0<;E}`>Sbhos02GMQu#Il-8S3vUXTVD7f+oYnJDdJ<@D-D32!nNt@`p>Dbs<iU9p%
z-;(_A-sL#hF;E+h(#(f#H3sBypBStOQyTn}T39H-8>VPmK!o_vP!*EPuHQ|l?vm>(
z4&-cn?#A~{>kHjJ4vUk92#vUt?FJ*?(^62w-kCH`FD%HVXbCy|R`wlh58AkS`;eYO
zvnA52N$oS0Y|ns5DIZCM@|!C;+jVty$qU{qQ*wG&uj-U|7j?N)g>T-eud=D?`ALDv
zSTfa}ATgqGIrQ^lx?bC_G2wPyqQJclNmu7yMAEMUGL~AIq(ppI*4L{|aGW?==rX~w
zckkY5VFoG-+sX$9Cy^q~#;SiqsL>7BjeI|blE`x<`_(DAAeq=-g%ib;^0N$4&D?tV
z$Im~YYfw_V(Y;YC?aD=gV|;v%Zr!4o9;~;$`Ek?Pxu-g>wNm23lg7?f`gqG8d>*UY
z8>+~OIwyazSXx^8OlMlMU$%9}Gaw)hY&HQ#@H@LbXLc<wOjI^D2DfFI&HSAk(He*(
z(iY`Qlu;7-emVa0_GXWaWy|Y(KyAEX+waNT)=23GPzuQXoZVa$`&e5s=6q9b8CH^>
z>EofyG5KJQ?%pWC5I#P>{=PAy$7#vjzjyB^08Tq+=ZgAzYV<f{AEft+_Vz1-;%{)?
zH>#&yIq`R4q8^7nggN)>azV%i>vMa)1h{TdK(amHBa*+EU2@IRr|q!-iWy?n9|6<z
z=TB79;NxsPJ-vQ2y%&;Ric`IxL-f{$o04z!JZ)%vnENH*D)YCb%Jmac92}d>%*=dC
zXt*3v3>iht&)m4dM>HlV;-w7@dlNOPQE-10dE|ZCTBLdO*z%=ieNT&&Ctrev%~Xp-
z#`f{&Tsf9(Q5&R9=6Lpke$3k&t=a4Esd@!MDBS}HjbEc}S)Nm$4}A1Ldd_cNVa4(6
zfQoz}s|IOwHQd0v8dU^4%blj1M<A=|eFvnZO3rl{xwjO>ikit^$rCmz--fhQ6)wQ4
z5+xFQ=Jv+vwI)ffa1DI7bT9`FyUER4o6olASXFivc|;1E?IwcBXMLHK0*IN&8?u3n
z!)de(3{>>Rf6!a=|LbfPxlWZ{`&+WUwu8QSzziwoMtgPuP{GvSIV;3GFLid%6&!f2
z)JuVy$*Oj!_Z$-PSmPcn&ZqYF_FoyT!{>EPt(iGySC$;e18n2Qg52EqtE#Gu)hv^g
zBV~+@6HaZ^_H0U4Gg}z{$+~xSt3_Mhlr2}YqLNnxqnw-^+Z0KG@3bJ=0xXR}%2S*T
z3i8u_#b<m}<$?L8RY<NB8jeR_=Jo{#A7w{DH^K>=-u7V1Hm2EJ<V&=;aGN!UTnB%!
z)f0wHGEnvOOudw5x}G@7ZM;j4XJ17iPmP4(&M@AKy)|J+dGs^RKir>f-f#zy#BOcH
zZGQY`Z7`>jdD}ZqB)~-AT~e)8M_BGZ0c`h>%(iWK96xvW-o4>OEC1{?t(0I@cK{T$
zhn!dly(0H8G^=loK5rLATlkwkn?3g{S>p2AKywg}W)j6WZ0SzsPwB?h!DvhDR{uKr
zUOt~)b{T!3j%uoY5h<7>(fmaeq7~<KXBSQA4|zR{DI`VTvoTz`wzPe}e%(Uj1*{pO
z*4!to#hN6m`yHz}Qk2|aE`~()I`?w1ryIq1SJCs=b4Er+{j?*C@eLP&&5@zj7W=4+
z`YyybRF#ce`M*?EMDM;q%ysfw+*t#w&6_q+e0zQID7kKL`DwY(=BWscsS(MwFwV5l
z-D%^$ew{&GcAXz(pk|d+Zg5`vJ0c*$82G7S!}{8?t#4V9l`W+RU20L$Y2?NM0QF5<
zw<dFsFWUE4Ndw*jC-D>Mt)Zb|i~oFUZYnB65{X*6%7$o`5wwhqH3<qKj*S4M<wz|=
zr;loH?~Z<uEa7tG)T!tbR^QQRNsHe2aVs_TC?Kt{Yhy4CiYS5gHf`GUE%xlzqJqoK
zmM3VBC|^UT)?XX`1OPjkCnogWyLWL`t?AgcYRWz4r#%-5nt?${Nr|kx!+$5k#`0Yk
zZHB^^7cE#=Sn%KueHFXNCYRFnBL8fy2#LFt%5d5}yH3IW+BG)x=E8^o&(*nBo-V-i
zq9Bd{lz#oe@+su3=`~>d%kMwG=mHc9z(%2PwMrbintMYh?y?O{{8*=D%tC+w@-Y~T
z;Y6HwVRR=iPPxgXXe2tO-)ZmYXiC#PiI`13NloAyx7ne+h;W65J>3XgAX;C%1_+Lw
zMGL-n?)2+Y=A6CEHLCZ)b14|h%=!GXA|0Q05Q2LzJ$)5^-l?mj$iwBeH{DQM78hgS
zkp^dSP_8GHgjr8d4=4zKun|R0*)wlBMbDI?U%Zdr0LOld&lxn}fpsm3KpQ`=Nwyy~
z^xKjr?lR6)U_TIte6Z#Eo=rWJ{|X0HkIh41SkQ54zSyb|-!NISzN%Jyg6bNcR<GDI
zaxc4V75nXd-0HWmG&5)#Cy5>h<sV#?#y(%gM5E>TF~^~Aw}C`8v&}DD$u_@@stw+V
z=$$`)Jag*QDS&si2QfN}^ir#{v;e<GJ*D@EjsYj7c82ZVy?dFcJLC;}7*E=K0W1Vh
zwmnfP{Mn$i`&94dWVM(i_qjiB^otm8fkbiu3`U7Mk6&}s-oCdnQ7Kx|D{410=`9YN
zBhOhdG2%XJr?A{2Hl5lpw(@Xr+(iau^!#>O5CD;2B1REi+xPK)`{3q)zU{|*r=tP}
z#m0Ew>N+Z8WpqtIAt=+Dpi|D{<)&t5`zrzuGD&(yn0}42`}OfQ-7ZTCbtEOEwd#g=
zxeKW+BwuQDJQv<OTA((|3^yiLBe&yt_2P9lZP^lh^fJGwP3NodR#bm<gPR-%>jseC
zQQyOe7Q|!0rn9qC8_V~gw$SD$=}${)B|#8@5J<V4!4k|d_3INQ-mx5H!_?&DFW}xp
zJj>{hOkaY)NWFAS|AXtN+mu_mb>11jKRuFX-f&oQc~sbsnzasSk)SFzY}hc`Sr8&n
zym;rd$9#gh1i?-eI*$?Cr-e{Kr&u-i9=yQH-;oSb?cmqv;V5HS7EMQp9u9ezYS*p-
z;9O9L>X}C8QOJ|BRKX1KsK2B@176zLNaNz-0zMP1W7*H2WE3$w@K5^%^dBLRh%$Gx
zrxd|Si<6CrQ$-HcdGE-x=VW6qn(|jVSw|4O+B!PK4?Sj<@WUBG=J;N{j%YgNHhmXZ
zkMYC6#XWa7Jt9@*vu!gyFF~yVRx|-^rxFT#FwP`TTYI}AfKZV4^4Ll8fY0jOWvU=-
z$l>#HawFCg=m5hgEQY?tT0F)<mw$fJ_Su!(8$1JFpI?5LogErYCMRMw<?%SGjxQ1)
zMQl|F<`@P)(fH~@d;*w4g-e$%1&4%$G`}@GJN)aDZ-9+ecd?fSm`@Jijp~{jMPBW<
zFPoE84h|1B#FJ{r+Op(cUrLKIwzU-y7Z+Cm*%Yk$;uKGPW^k~$p@v2hSOx`Tz%cv4
zx??)Jx=N^O!QV3sGV(m_9ZCSM&dbUwqELs`JUe!@?Z*%K`T2Pbv`C3y)admjg?~#6
ziP&CP$t8pD8cYCrsEBU}E-EUTT^fv00u}Of%PvNa4UGs~TAm_FAXMKO-g|z2if8?H
zK7D;L^~gYVh#c|e$nuB61Pt^Uktb(+KR-N|$3RENv5T3c#jBV9*4V=0pEdf^mX-X;
zEh`w<(aHkRq7gvD$zf$>Rb5@J@LE0g&TJXA)DV*rAZX*Q4U`->4b=dBynwhO&ZFAH
zIJ#Rpt{Pcu9nI_;29Vdl!Q<rO;;OEzQ+=&p^gbIUTq|!0J@qiLQGmMw#F}s_JqtCh
ze{l?1|JyHbpM`NU@j3D@Uc3m-$;r_|NwGjgHjcDr&|1eI;MWTR-eVIdkrcPzE4`-M
zk!ALz8C^dQiaXKxhH|N~3?q8N5YSxc$mH~GKz<M~IFZ<3ar^!tCMKqTdTG=<-`VK_
zrJ@g&kC~tU$>rYG7AX_V!9%-z{SI41CKzO*l_I)$gSI_i{K5L8P3G|~W-m;|VFuU4
zB_a|EVlTm*43eZ5bUpUJ(fZo1Lmm$wJcu)IhzsSv8ikZZFTo^TMN=;PkKhp`i=JUi
z41-RQ`w8q|EXYfqaVF``D%axTVj?t=lf{|Y_q|KS!b~ENgv{!guKOR}rsGH8X9y^b
zL#UcsueAbDMlQV37Bsqky}*5r7isheexU`4XRI}Y6&xE6%j+w9f{E@EfG7p~_uo=N
z6%8oWr*XQ4M8}4hZ#ppn79WUJBl}HWUf!viuxo46{nck%)31uVO>>}1a)H)CyV;0D
zkChF7Eqyc_Jtvm%?3Qy!jpZn}>^$zg?M~3ZeKRN(RWzQSo*E*x9|{W#Ke@R}`pvh!
z4m~b%A@v_!N5}tvh(bFX|D*Q&ziLO1jKZtIf{5X9?rq;!3NZVl=ii!>%(Dag_I(D*
zLR-j>R(a)>b--?oBNF&l@KS=#^#2x`t~rBqJCF8J%JN{GZ)i12#HRAG4>%VL;!$so
z9XaBMvkBt&ZFaVZvsh$}UX9J4f#YF|kM_x#4m^Ll6j38d_a)r?dL(;cYnFJZRDA88
zJ$ud|H}*S>Jvl^@k5u;1y$Te@t(*JiX?%4%;N7<E+ac1NsP)!P2rCHv*<5SLJH>GH
z@t2yD>@$L4UfdA^4HZIi&KYJ7+&-pZhfcE??)4S<_iNo@`~R$%Ni!-3aVP*jP0f$#
z;$wq2s(&1c<Oq~K3w#DB!5!9?nqkXta&pc-LeaD00ejZ;*D6nC6V@o&M2&!)oD*)-
z{d=8wx82d9VdkKvJ$SGdIr9Gf`xGBbOE=;>WMYro8z(_xxMpG!c5I~L|FSY72ZA~F
zGBc|f8*_l$r{mYtb_|AQB@yRqY}EC^?d-X8n?Snd7Zey89&)~51ku7WhcQesY^?a@
z*Tm5z{oR@Y_1bpEmx>u8pQMbQbvUd*gQCp=3J(;2kbr^Yb$|3hLFwgr_X4P>spS$i
zp5iYX#0jlY`LRsw$FE;^g(;rb(hAKi+q+3x-i7#J4u#UvQkl-(hq0s)d}wzS6J_EX
z=q2a~){pDo3S>gm;vuy?n;bYv@+ohPt7&*Ir$0(e<dl?@tk^9_1RVa{bv%Nv5|4qC
zZQfm6lzCP`*y$0Y)1&quhX2_w1sdiAEpxD!s8)v&iWR##Rhk7YogIIEdYmqCj*Ew(
ztE&s*nDHWs;m`>?a}h=aW+nPx&9KUUDQ(eWc8BLScypksj_+#Ea-XwAy+soxbY&;2
zlCD3<X;tSo<nJbIkMey*`8o)a5a<A%NM+Oa0|H{zV`catOq5OIp^rP6c1UlhrZxko
z2Mvtwz=3d%60NwnIQrA>BA|LJzkh!Qpk=o>+4E(Wn6HI|TwY$+@A>Z?ZSO*mtM#Kq
ztsel%6Z!=Ag*#8#<!I>Wj7PscG6hxuHyMf)e~?(owJa!3$Q_S@^RR5}vX8F)X-@gz
zv);umh?Sv#-sT)c@cU>V@*M_u@8i{yx7V??wFMWYg#1EqG`wLCz!f-v08@S-dj0bR
zlZ8p1YGc(?_NCs30*hdOfbaj2oeazT`1JCF5V$uXwUGzVKc<J9J_b@cj|`8dM6t!)
z=}+?^P*UjfjMa_rq~yEJ90BJq>`dRLXv9nuEs*DgQsMWz8_A4#G89%J5mxN8rb#Yy
zg6Goo6q;ieDeo_Dbh2o!jsvC>Z8nGqVXN<af9J<)Gp|?Pba635iHxMTt2o{)-dMv=
zPJlE*<Z411;WsG$0!*>^`?;<52UkHf>=NkwV?iF5S5(xDXkWR4v}|4eO1KN9yTE&u
zL?$^Y&b?Pmq&ax-xiMGQqx<*etz3y}gohQrv5d;edF05EvfLO32tt`eexjG1gHm+P
zKg)Yz{A$wYSat5VnVHgw8YbqFNP&bV#^8Q52C0=txMMde=?QcUD$WJK(6JgRLmhb;
z(Wck0pPlF`B3L=K7|E|y$Az^t$n0rf#yKovyz)I3`0-E#n*v!BE0p9Q;a^fBwf){5
zP$a`|q#!8bY=Ur7vwMNcB_<(}1s$S@_91YGko&Cp+RBU?G`l0o$*nWz@G*TLz~XT{
z2{rMZu>vZ7Acul`ZMtsWWBi1XnVEl9mN53N2Yur7GPt!QH2%|RFB28RjA}x8UbR?s
zxB$(T*3{Jey7&^ns-e)u78v3QUJZ1b;m2DW&dJG9`o&1U2B03O3G0IdgxJ~&G0%Ik
zXDi$Irl!hDe;Q83Yk2Qs&n5HLbY`MgcJv6EHsfDeU4;a*;oov+k}|_HKApI{Xn+5$
z$8>Z1fd#cvG&U10`a;QiV%&F0B*&MKsq){y?}hFNuH>JFOo-@zpgddy^8$&2OJym+
z4;ugEuTRjIUx2qjt@aHMKY#;K_-Wv*jLhWxJW;g8#KjwM7>iWXV$FhBBt5w&3KPs@
zTL1Pvk)nrw4D@#dIyJ%hq5B&?R)Q=A$oLSijyN`hbaeOb-Go=8)j2x1AZ9)UyzcGo
zy+bB5<9L|?!jd`~azBG)6ZBqj-A>1S3txev_!*`K4-XG~o;)xT$my48Ue9#SczSz#
zhaS`2fAHWz0tA$Jug<n_LR+=<73%Bm-Mhs|q-h9uHJ7c3HU_xeb!Aa-`@N0#WDfc4
z=X5^BB;ouBy-x_c+-~3t1r*%5_UH3iC)wE8+Prpu18EN%fXdCAHy`{l*t6+Vv^Kp2
z#q~l!7*55|j|~kMxQdXLDD(=Q17+@Q->~Q4K_$?8P|VN_gTa52m}ug+9u>ZyXPC*t
zBHSXcn3=cs3y%`|#mULZYe*u|5-yLyA4Ed@n}lvjVVCDhG*W1EiO)vzD92X=GBN~;
zJQk9$Z#+>iCy~rL3tgy@mx{dJw4f)4b)pKL$uPF@eb|Ly4)ltjr}`>^a!;arBu<3q
z`s%_dkNHRV4b`=O|Niam>pKes7$IUogFYf!%I5{*y&>Q3I#{-*uC5pO{A*@rl}H|t
z91a^A8Y<{>s(eA~%6&OKx~t_jp`0TWXlQ6;uw{hqh!*O4N3Qj`bLWV<J0uE9!5n%l
z+NR$l86`(xOnB8|i4KS8QSqR{AXV7GT|g0Yz=k>w-?vnIqnl%i{(G~>{HP&dG-?i7
zhJ>t9y!udM;ttR>@d*A<J{=(yx7{qKBBI3|@E&FOvi3V;DhP?s)ZT9J+sSZ8Hr^1;
zARgBrEz~!}9un-`q9U)jj@{JMtxKQI#5cUWlzJgWi*$L6@7S?9n<r@MIM9Nbq8~%h
zXF-KSMX9;B;{fr#b?=Z};^dzmCdf`m(F7xh4mm>bx@@osgx>nw`Ly$)^g_nlplA_N
zFyMI4;9w=zz3qcr)`u@BClR0#&?y-s^zF&$kDp4dEwWdqY9kD`ZrzH%kj8c(P_N+$
z5UB4=zcLcLh^%DZk(*X0%BA+=QCQeMAao91UPYS)Xy_sqjd$@qf-n)lj6yL4B%OLW
zgXrUSGLu3<cI@ZZt3psY^%?-bL++1*t>qE3#51g${oJ36L|<C`_s>yaWI|^2Szpat
zVR)*gi@swU8oPKj1#r{sVPL4fvv~*66N6Z6kSNx8Utjd$1E?xtv$}84`Hbh^vTbXt
zsk^i%YUPPBg_xU6hk>x@i=9DZ67o<WxZp%_A8yaaiIG!%j#WSco*se6rFUZD3Gn+T
z>k`i;jfu;R;3+A-ztOoqx&1OI3m6Hw#Kg4CvOh#b(EFC0JJJu621)j7U51OjnQo0w
zW^vJ+XfQ{E^Htr_u6x5Pe=OzUl|UKxU-^sXuDZ+8$i#%xKpX_cH3T)GK7qfuZfN)k
zd0=XO9t5(`8NJo-sh6LC9LR(ckLF1l;EyQZpdkhJv{DI*#6=>}KYRA9^Mf1h{pEdn
zg{m@u7%*_$gk)0C#Hm0N%)$9ybw$WxL9^6}SWu+13iR6ylAdA|5G&B=NPdZtia|mm
znl6yLXwc)JKEKh<l#$#p-kcIrH;;VoL~<i4SY6#?R1!h3s7ud2R#nM^fFvl<;N@XF
zJlZIQj7PvMzrdsofb>V2KX2m!Lk<Tp#KJ^(Z3!>V(#V^2bYkytgu!T4LNVV!xSDVz
zKcl38-mI>LHKVV;Kf&R|7@m;S(ZnJJ{mb56ON;K-hYaMAN&uY9oSd-Mk#Dh-SKm7t
zVq3CpyY<ba!0W!nQW265ZQdaiAbU@!@<28;jEvjMuci@dm1plrZ*M6Cbjauap6{-v
zXmA2>ElyRkw&hqIKnD^Bgg~57;F_jHr31t-%ZtIYhQ|#`{rR3oAQp;#-6fl@57n@J
z9g*^Adnru`f%Gd-igu1=m}(?Qpek@z6bOxDMBV|-=D9qUXU_td9w-|><9k;&USWQb
zI1L{jLq3AHC@4b<Ek~yPfFkTzPvYa*flp0;e~E0)Fo?klR#g&|G(C3h;r?Ta)0Gdw
ziw<S$Sa%#0yUB(g;oSN2f_A;<2x1Fl)2mBqj0p8<>I2w~muS=oq-4E}b2s|4@UqQi
z)GI(BKbTucjzb^ur2TysD7)D6JJ{Za^s5r$=}7I9Etd^4VY(oKQ0DAe1}K{#T?h^g
zycWebd|QE})KWjK{XorUB&WqcsTuv&tIHE5Tb}r1Wr#R_XVuCN8`%SZSwc^Okpd51
zRWEeU-=9+bwH6N{qE5`9D|w4IhjoNMoOnw6<WaD!q{{7{i=9p0zu~5N2M+Mu!jtbo
zht4|cL&jxmb864ER)ULRpcSk43o4yLx@L~$MS`g*kp!m+c0=BtOz4=Sg#>2&Z1P~e
zETtfnM^cj~ghK(wry<Y%#&bf_H4FGx$a&W+EQsFBGLrvAmVbm%K)U8P(*4H;Ye9Y9
zv)yLrN`*LPGffohb=$MNwnATT{FQa2T_An2o(oAR!Sc?J&kqlbIKJxjnC=f)xwp>%
z!nAs73-)EWleCYPwroObMRjs4!Pe#NyX?b5HhcDFXs(Y|lC51_J$nTozj!P^)V*=P
zLDvH}i_DkzR6W~iTgyRe#T=iT=r%ATLmQ4lswDVac-=OD%q?wg4F_9E7>Kar6$s$B
z@7^hjW*{AfDkgdgSy@|?`$@=^zYs+BWUG=zO^u|*k&phgi)a0J6S(zz+VeVRkj0-7
zQf(zZQaEPDK>kEoqh^Wj|6~m&ZZL67-qp=56Q(1Z?&4!Ed@YtaOod@#Vfqq{6*Npt
zk9>W7Rc|21Kxo6bw*yWqcx*)TZF881;QLuRtq=^aP7)LV`-58uTMEo~gr4Bu(NK}J
zDrKnOUecFr)uF!Pgoj>P13eiK7&rjVX`noS_JjM}0}$}lwFh`K?&3ic&1YrC0;tQK
z?xXSQ_iBc;4Ou4I77raM=|uv5P6nPPnP4H}zyvz}X%0Zr&b`rAimV6286~!e0C+o@
z#MJePe-N?lI#vAxdMv=sx0J27&_ZhBP>QDms5F7Me9UrM5e|{go()4y$xl?hJlx#C
zXm3ED69}``WKVuz_v5-4sf?_NT><O9@<8Tz`mpc}XrE}4`mkwn@R1P^4r}4QFrMb1
z>@@N{kkx19DfVFaYEMI>xybZba=WM%cRJcn!sLV8!95`dbd2x+3POAdnjWEicjk8F
zSS2^5XS-R999zrGL|}n@dxdTlMJzmA01$`RZ2W}h(m*&NC%k=o99fGiFS)#C(@=9k
zZv0l($NtEL_Gn)41%EP`?8ygg`V1Y3JuCrk%wxjO{-KfcP_~i3{Q>&m1mw2WU1nZ{
ztE5OQXBlTQE<WCEc|L8W&p?BQ#eqj>5X(w}%f)^6K0$63sKQXob7{1!x&w89d_!MQ
zP>?hQwe>JUFffplk8h_!@RuazsYs1TKu|Sx^*s=o?2C1Zly&T+PH(HF>Q@$(x}}{%
zYN|;%J*Y(8R_tpG=5$g?(ZfS&#V_;<4l3atB3Xc@NAmJRQ+e>i9T3M)6ca&aT^am-
z8giG+xZh;&%0rRL5SqOi>>AAlimq0Mid#<LbOie_@aw!ws3QR+pGnc0CiL4e$I%~8
zyS<kKiIbeH#tLM{u}<0<U?AOCkzBOO&CAPMy@*JWgM!sBWHGU-rV!biL0L6&%4aPa
z@a)&0Kd-Y?;kw-5`gfKGT{r*^oCau~l&0r%wo<eF8X2ht=p~k}&SRpxBz)##ikAIo
z^%z&8M#{`zL^r`X!7*4h!qA@AE|&J@P5%PgLbO0ZPZ+HK!WS?(JKJ0!6K7&*2(N*%
zh`?C)R8x*M_Zq1+!@z8Qv`z25qk`?X&11!_{00f~PwA*jV^?Xuud(`kyn|kC=<}c7
zzmH6`E)Gw1K=U=3nwv``z!-zjU6_)H(nB_=lSDp8!hTJwRGQ1O{yHL;g#rm@uIADQ
zS3Bs%O0KT?b=K}sA4nZv!j2x;vrrZ^Z+lNBHtWgGu<D@2l0ELOu0zdk<DCV!^9S?M
zV7pBn9(RCrtU+2LEOX!t;G2y(x6leK=!&&aeXf%KhC_h>|Bzc`l2uZ)c$fU|p(Ln7
zAS$p%?4PrhKsUc*$BxdQKQHix*+&v0qP8|YWUGLRS8!eE(x425aC8`yil!gaEbWtC
z)&b&HDC#RB!jI&*E$2!gPJ5>x?K7q2rCIQLOErZc#5)zT5G1ZER#IjV=&C}vp43rk
z8PRy}PckOojfri~4Gjgf{PRW=rdQ(`UiFu^>PSzYKIP%pL=%N34er$}9!<|AjU!|G
zIMCV`oHqNXplFt+3RLiE+WGIfudtFHd*?eViL{?L4Cu9UU&51PnwE0?DvG%iZ1C~a
z{~9<ymT?QMr`k;J&(6-94i3VL`jBe+X$KYw;hAmxS?D6xkw-7*W-!;cE5Wk8b3a?p
zeNg;)k)yEFxt}*|$33AX1+ke+Us7lI?jj$rJao{=-g<YwT(3i+dF{Q0nOSm^-OlaX
zd(p&GOrNc6U!e8iXP2~Q-nwZM2g$q=rc0_FJK~XPr=7Ez6GC^+?k%}7)!OhPl&jM(
zmooPBRP%QQAWzz#C1AouEStAM%Y_1V?&;z42&P`-5}0haK-CdvMc(pVx-;&LOnLxk
zyj4f_;6qVSYjGMIr4GrfdU}psSp;xvO48NVMjvK!oMlY1`S-}s(5tNIdFL}wILPkz
zsJTE#7AGKu6J}ntgco3$#s>XBkwP!V4xCS_3`t9~ez4W9!CZu7ElL<iw%#m#M`^G7
zsGFs4aCL3f!+G?_ZICPku&k)?BMK-yoI`IyCYMNOtxuCkQDEuamfPKdBwHRTc@%~|
zfBszcc@`8N37N^BTEgMb|MmHSK-rKRk->3S;RVu29^<?r)xHQ?+i@CB;0h4BJ9a!g
zw-6pHdeEnB@p8$|mOy7_VBG27UyoKk1H)Nll0)7)RvnqE43rMSHq(36-B%E(M>n}E
zXYP5#U28qvBV*Jq?R|&V6r@YXEM{s#xTulHgGR*An2?tBJQC$~ecFXAYy}WHYVXGP
zZQo2#H0AgA20Y^uw9pwuSFSuq%CT&TgVQzT3RjMaMv4|}>Jb+svy~H-+m9YYdYxAA
zx+D;CC?HHh*Bb}bmmH;hO!JJ?HpMjtmotOHhYN%_LfeHB2k)mM+iF3wTsp9{Snq<y
zTi?4|OJvR}s@FtQSf27s<YN;dryxJ%Gj#|$OHSw*0BI*~_d=523nMm!b_NM&KCm7s
zq-%<y+|tm!egId)zkBjWK-2D>PrIlOL&|XIui6Vf*>M`(ar%m6`D$+l?6qFY&T(U7
zDE-if0ke05{A7=r<#e$)#RKjNBNOUegl89|Nlm>?;#M^^HI!e0bxY&>=!0%`-8bRk
z>4uZ*{(}d-gm)Mss{LQ&+$I*s?WbHPZ{eiYW?;s|ZEdCClWrfsUj8kdkb@^}IG{c$
zhVc^0Istacsb{XB|G$ndv${e(&*o~;({+|pt}pXCQ5-U}vO+RCBN)fLL9D%~6Yzu2
z1FCf+rVh@vs#rXCa&b8+mZwwNCwL5*lW11q=1`taryLtALqS!Z4sYmBud}eYuKETc
zHz4FXAj+8?vkMx&YSUk+D>^#J3{LO}0MimQpzLENs`8(~eK74}ll%9MHtG^~#6gwp
z676K;ySWM6THD*-So?A)RPX+-{{E~5@h>uSQ%gtWmX+@~<5Up-k6VOfEl8O7q0tKa
zta$?CeSxuy9)%l!lYB0KhSZ_NJ5H<?7#plqWz-2PM;qM&&m|$)Az$KI!I@n$3-asF
zeXiY>Jwl9v!2gnY?bF7JM-1!&Ct-Z1+kQ{)JC30sNJ|*&+ul2+)@4+*cf8K#Ql5%o
z4S4Xt2)(oYi<CgL`+vSf2%en~|A0O#3t@rXc)4&hSCnNemsawFEq6D#g?F~yk}$io
zQD55Y;}Oi!Gd})UF|ilD8>xPR52mrUX^WAg-aqg9`Jr34JzlX`Uz&KXbR~OTKsOgQ
zTK6h)F~CVJd$dJ(Td|h}TKmrTP7l$SOry0SNKfF^P;)Qo&hm;W)^DxP1bXgAqH%H`
zi8<}@3`OxmfxQXa_@z4ZBuxnlv~Jy>1vE=P9oU)3^+;2qJa7K4lwg3hfT24M3r2{H
z(2ihLv}`8O)e?dxxOC2f`e3Up5CQOa|E`az2lo497UQ+0{A#RT?hOVMQsg*AF4eP6
zK|eBEVC#Vg;2%DQ<n+4E11!p2fBz6T?HEOG+y~|aGD!v<J>7C}EH`H$H!F)>L`0;)
z>t*0E5LjAow4dUv9mnDqWO)JQ!31#*vcN8ulRRyMkUlUJ1wUcVxe<NcJRPs}j3@hi
zg0>v$GhT2PO`O)1r{P&<;2L*0JYQ0O{}I10eZrx8plIaf<?nl@eneO;qP4r7|5S*W
z=Rk)Eue33^K*Em$*)J1}5LUb#nZN1Se!|JP;UJpEU6LFu%*<&E*Sw;5Vq2mv$p@GJ
z9CO*lukqT8=SrHzX2nLXdSmkvb4p4|!f6icLl3|==3H*WP(gUvKrx^g7z3?0g9`yo
zAAc!zYG$SnNn&=iO_N1Ye2sE8fMDzZ8H}+5oyA_y;jH>KI{F2eijames&%6?A5O-U
zlfPsv|8Vq>h!YQ5<q@3zfN3@10`)M<Al|3}%fndT3TPy3!?cQFd$tAPsD!)i8kAo|
zC}Bb*JO*+<34Q<6jXA`Lld8MMK@Z@4!ifU_oD4^{{a;XOVxEh~;gcGCZd)7+{6pYG
zv|<jJ?*NmV;-C?B^V-9^OX$wS5Qo!0UAhTR9@yH?$SY#bqx7)ZC88Y%YVrlUl7-wv
z0c2K#B^WT{>$N@ELpi#OQRE{gED&)GfUKouWjZ;Q`@nGj2A%+&SrkDOq=;dVn3_Zu
z^USg4Tf4>to-Y9}+F9ZggLl%%GF5>O=}<-%f{k$W;#c4~!!!6f@@!$+NfBPj7u`MP
zz^V{N%$<o?eSd^pZ)k0OtbS$|q&nl9vc-`~TZwl6$z5ZYtvv)Cb9g1sjtP6OwL1b6
zAbnK>q!U~#*#FRxY~)#>GR|s}((A7fhL}(;i<ieGu*m1YZP1ID??I3F=4#<H><kJ!
zUwDIhhp3j+6kOL2CB6PmqB*p~)Cds}U=`2;+~_VQL#Fvw?BxM(#wRo`!=M_`2_}Lx
zfR;iy++bbmck4#9mt!=BkO6=lf53qD&P0iPU1fOzWsA_qz~F3w;fLU>kT*a=m7|~1
zEUM2TA_)X&6&U6?rwrzVL!6W^BC-~JMa*qW=o$?mI&1R!qz_fmxv&|vSS|@4j<03g
zVj&-kGd0o~mxWRWII^KUFe<62dkwDFo=R39V@zogydPj$79>JnTJxkZ=S?4A$G(7b
zk06_6k@d~*aHQLQ{{7c9c=pXf&r9t4Tjm`;t{#;;(r(&r?KIibx<-f*Ab-G<`h%T@
z1JMY?k$nNoelp<9;D!yRK78`z$!Gjm6~TZL!Gl2FD&HXedvH(=thEkgHKcepjO9Qi
z5X5Ys>=TwW2Q{!w460wf<@1qrjld5P)G_w(Eg~I0wFq&CBcPYQi8qi>xe4K*nqXoC
zLrNPU5+S10@@#&pr)UB5Oo3mY#uSDyo)NYo6aZq%EdeAWiMk<KWL`~bHI!Hb6#ppE
z)tk$vFuV~$8ewgOJo>?F`59;&!efSp*YSm~LPSPvZmLGgk33se*mkeudtlb01+0M)
zQ33NW10D+p__PThGorGry*&!;KVfXgQ)OiRyi5HyoJZ3SFLK<lbQ9iG1=x1DyF?1b
zxEHYs-H+iBPwf5s+t7R=j#@pWybm^gpFk%-a0sX&Ad85hIi&N9tWo@RqvykrLp&BE
z=<O3x)|6kIiUb|54&e)dnds2M>&;vtV6~DP(&^p8A0E0`Z~NKcyZSOFoeqN;ypCmi
z#3W9GW&(Ok84`|DdNzHq)^jIE$8#xK8W`_{#PbzwJ|TYsR3}4Ko!;iE@Y(d0H_a8;
z!f=-P42q*sS}w4dyoK)6oPJeTpU6AJyd`|XAs7rXw6IWs@seKjM#P6NFQt9+?fSN0
zFvt+iI;Ibs-aA>5z2a62QCvp5OIR`7hWZV0G=VU=VRVF)H<f4_<L~E(5ZjBY5YaFB
zeRt!vp+Y{104aIjOf|i)I*5W0Zl6V|S9NN#d)K%>r)s~_nl?Kp8-D2YRtt6cDXv3%
zg`#tP9f9FFwpz%G-D#;*TvXODm2yZ(EDBCyc3--lU>vl?Axz)IpwRgk4stKtIa^}x
zRhuVeQ{x;zfX@x#5!R&4SsYpcnHJe1$di*lYx=|h;lMEE1nwl>*Poj8$dd9!SuX>V
z6DeMkdh*Xl_3LGi`Dk(LMN@?jO5ZS^uB{xrvgL#A1_lGa{<=)fv!1%fw7j+XM-@y+
z&jhaw${#;X*lmFzr?Vv6T0l$@(lW?#A!qJ8*R;TCd?8DO11<S9iyVL<;`R^j{L!sP
zPxY*1Q<K@1JmUSr7~XZCP^5j@;44BO$DA*{>>^8Dbxq!gdVBKun>UZcxfGzE1PWkS
z$nr8V%i?A%`#a={1%rHP5D;lXt#c!9QO%U#=-Al6Qi#UiYu=_x7ECG3cMli+=WRDn
z4O%HG=+gR%M0_us`OR0@>X7uzpz&pX9#xAtE1fNCb#>IKiw(`ue$#(W(Z%{C-q3t}
zUj3mo<K1$4lb|hU*9uJ|7$}A4gMavzS~MVidP9Xf*G=>p^M~v;Yq(DA+{F^KFVbBc
z>)l*#X#Voim#S7R!fa#yxSVa5o$_#xo5Qo8BjTDh0t(uz9yI=`nwhRMhJWsAZ&fSh
zeSGM(`VMvOmlY41txxXQ-N^Pry2iMDnH^S7%gMDW)XLfrODcszAWXuIF?+}e?IST)
z#lM8Sc%)&W>1a$dD5Db(1*kLy{8P%!-iQeu?SAy7Qfof8fNJN?Q2*ijI>^9OyLZ>+
z`ffFThFxaRUkksizB)x&lU&))QO!>sWhoWM(?qMqy8cC7HoOOD6G8>gRXmILu`lOf
zA7J!6b8Ky!qD<q54<CdEdPb0sM9Ol>m)dm&4_W2y`#(Neyz%kP2xis@HF*if<W~<L
zg<%2C*04?=h-TTkAnGNbmF=%47d!cPe^}V*;iYnS+3~X3&ZPhHX~{U#OwrV-+#XSq
zp6Sk#P*i$#oZ|HpN{N$w6=uf&J^bG$?daNh^XCCG8RbR)S&geNe;Zc~TYUJTe1C|I
zAwW<zQ&_Ie&5_rEr!XbFOsiM;5|a^~#34Z=x<auwFUOoO!9Pcq;%hS=OS^Tj4lGr3
zAJ(s`j*{7>-Wt8dCajM}Xwr3m{0}O3Wm7r{;b5{{vQYTD=fp-!UjKYZHj_5^ux#eT
zke_mwYx&xWUNq@>E0q2nmSjp_y~{fq8_m?G_xP=1-~Bq>lQzchmBk)sHF7(*W!z&3
zc=CiAW}j(pXTqTL{{5e02Uu9(D3W(H7L_(|UU}L4zkSYAoh4Ia$)tDGUqQSB$JG3C
z(Q$@r<DpD!Rc?H$39+3PJSDwtJfX>zah`V4sv%6L)h{pH4kp{F8;^fH!B9j^j*f1$
z*2PChZWDa)v$D1>UNcguO{It_i6(~rbDc;Y`Deg|QOT<DfB!xn{`HaPH!XLr<V>86
z3OuUC`XsKDf{*Wwu;@3A`xi$4<xqm_j>$HrG?MD3)vn2Ik>vfkzvhm4lD5BTn%MrZ
zfL1D*>duD$C;Jh({=a-gS5#-FrW!oz&~Z}Q+D>TMc5A~bcpD}LlwlZ}E@nn3F4GEC
zK=Hf4O$YvzyKEXQuqgU<2ztVV@#qlc2Oml<xlgZqZ(5yTyDdW%Gkd#hgSyr0A*RG&
z9I3VnP?8qy**w6wgxNUm92EdpWE$)7u6#Roh<hgROH}MWe_RNLg7(`~5u(<NaDE6W
zcA3<K#-eDWV1MFX+HogHQSj+ayZvvtw}+eFCh_tYX&)T2+rcP6xx6B~OE8rt??+@7
zIgM@BaJqKGza>-_c1Ce~4$R|2>e!BMixCwpU9X@NbZlF;1uck|M2vn+Poo*C-+y*v
zebkAE!1T!@zJXNer_@d@Kc#x7^!$ViYIr>0C_thtR}s=X=8zbyMjm-Nzw}vO14SQ=
zY~DM}^ZV@HO(6*v%Eof+@|y0QUJZIta-=zuYO^K1fT%DWgR;R4Gi*FEEOFb4$#Eu}
zR0({p_F=(GDzK7Qq2n8BPN9X+8X~uC6r;&_fI$%J$)J%5(v;=m`9uw9A{sfYLLTX1
z<<m&DaEA;4-hYWYaa2Xnsue`jbhqF1cS(^*ZI&caIh7TA>A&SJz?Og&F~7AnXymT6
z-+;>~vEZ~9pC)-L;o${#FZ(6h4WmU`+L&CWnRy4*^_Iu<$z%`icoFk&6u`%rt4I?*
zao))8fm=}d%Be_BWN{#uKR>iZHh2Wpsh!#DsN}6?&wuazZ>@yG$NKz6MH{YbeDUQN
z60A5Szdzx(l2%P<K{(p`a*PWSRUHV0;5<Qr6I=$StNk#c{?8CF&I6xruJYhgSd91I
z04mxegqI#hf~dG975sv`AW<*^x#b&AGJG|V@{Jo46ae|}VR(|}77p4BaN`VI19agk
z9*s0U%Md)uAVa|iH3jc4*jd8S0S-M){|hX}W&k#5w|9WMC%kz-GOxo3y_bTxApj<Y
zez;nQDFDEm_bwB4fH#hQ_fFFJAA-fd96b%#hd;-bN85y95)`}nivrZ6tGoO3SYG#^
z(H&!?slmvG7tNo$^)cB7v3@sx<ECE(um<Ysfxu04kkB${Xlc&^I1nQ_gdqAJ@`owL
zOhIPcgUb8#q^&-o=mLEXn7~De+Zc>N*ssjB8W1ib3<xEul3!<~g*HAr1iciD)H~P+
z(Pj~Y;Zm56fqPc5!TFA_ZyTbG7&`-Afoi4bodI{<2k+G=bRmM6dVxYGOKA6q7j$(k
z4>?6ep8=CW(%lX*Nd=t+#u@ekx`u?GXf}<J@==B10j_Nx#-Chk#mbAM0`a>xo%zy`
zUw?qdATE=j01Fxmv`IAmI}S+h6kf)-32{{j!7u=q5J>@<sG_y?a-A6<GI2M?<{kTS
z9YG1lO!3X0jhacyM5_&>7cq(AK0jIwakXEFNy<AKZ{Yv~2COG3R|`ea@Ft>T134U{
z1~%b3P%7l5J%9=P`XA)6{ye(5e1v$2g(c_};(idvA$1sxBhVONJNv<N)A4HEN5?&d
zHg{O>bc?wN=$rdkoxOYZ+ybu=cJwly^Z<s+!SmkAzuu3n+|ZlOl%`jpA!!3iJY(if
z8^%{Ku|Wl+Svf9iK_M5mXyhO!83f|3ZE>-}HQ;l-{F@sPRRp^QdEMy`xKKhOb)M)V
zkES^ru_T~6dcPp5qs~(AVet&*Qqp2@bW-kDCD)~i0KRsr(EWRuZj@ul{<k#EEWH^^
zLbLJ%v^oM7YWp#NPasg_t3E6oVV(qq4DSJD`PH9<cYqjIhH)_o&b$?99K`(*c;yE4
zm~PJ%n2o7fPW?jjj*Vb%2pIrZavYCOTorKHz-u#FEoBulhn`$82S%gov4O)#Q~!2H
z5qDU?BTrl{;Pw*(s68ViN;or<b90{&DWFyzru!8T$J;+5s50~N1~C)B36mR?$DKg(
zIIxl84yJK-9KZ40xRgV6Jk%0`+#P&({68Ri57GPNb$iFd834jb_{NXp<grTIjP}*%
z$0rtR&HE0b7etS344(wX&)zx?YhbFh1_1%bEI|Mf<Ea>5L^l-}5<&~BlPN@5QU~kt
zYeeGt)Y0+$&{@Apyg4o{DF-Pc?(|3Nwf}1KGedBP7^Yql&q1rz1d<FDBzWi|r9!Y6
z>LEhP2uF@Mqr^oS>uVn52oT`N1=*G@575@(NF2zu`B{Uc1VWye=OSf(d2yP!U&y7~
zi?9vh>V;B#JWRfSZU`IxT*plZE7P?Cr$Ek}rxfFuZwm<)cn7mX5J)y+W^if#EsR4i
zwRj7VN{Ivq*Jhw>85((*R;i)u5f0aDA1PqERDlyB1zIlzSYpKoP*BX^pHgtH+YK)y
zo}HkJP}w-qg>@Ergo8XLM&Kw2Ss7pD27yV-rAm+uFmh>R=${5{#nBp=TU>&?jiJE`
zBy`6=vp6%3P>taYoc?;UTOGm{<Zp9aI00)3v0+4L;q`>zM<o0ofX@Be%jhJLLCui_
zh*@Uvh|wgc2gE%R@JQguo`owe1y{fjU!*{yd8NfmUQG?GL^j9ys-7cm-vM7xgUEGi
zFU~FU!u&2_nZ%O61DQdXK#3k7i|hD@V01vb$aR?o?44ozTs=NBWBlxfZoTbzJZXl#
z#$RH9qq>GlC2XQWi~bQgk=a>xr@)DKji==0Ws=^z%_MD-2Q4nLxCWLg5v4v!&2-I#
z!$Op2dC=g9*R*m4m_A%U(DFJ=^)HN*oM+y9ufC6-hh|&-`SW?p=2uVY_U+@uwE+sm
z{0$u=BQGYAQd%r|NTe$osVxD&^B|Q|1>uB-8|yuO{8$4SexMZ>83dtVX<p2|J7PZb
zLdfJnojo(jF$fGc-JU&c_!XyJC(mf`hG_t+&DG#Knf?-XkVqvtCKE9H8k?DM72z_F
zmP{}W>XtCE>$~HyB%(D}K!*LUFwt3%)!*OGQHkM1?hV1XOyR>L=k<!g@o|1!!F1Mp
zY+^!SLvVO_IJVcrjTIBSni~^<7?grJ6p%7QDTZN94|vuCI)H{P&7ee|YZdV+9Pxq%
zZBsZ!3dW!{K+H0AgU{kP6D8$S+(p7Mdx|p7;pXZpe+#$k9I`;TPD`r3!mJGq+t)~8
zIaLhP1QQN}f`S4C=oX|*jMZF$uRXk@5{?_rGk<Z02j+H-Eg(I~-=d?ZkGN5=fw)hF
zWWgg|(QDNZcTWo^Xvqm6G6B@30xldN-TZZnLm}94pk^O=l}{lU_wgJ-;!@_t=mzn2
zDS(;5@$vDq;L<o|9>O6(+{;l=Sf~WquE9;sV-!?n3NU0a6gWD}QkD2%R#+iLOA+f4
z-jqF-2PWR#jrf6Evxu|d1iYwD4a`%xCd7+83rCSW9>X2R8{#oWe+W_qVSxK}-q>QL
z8%%eOj}IIhvy1<U+Fu-s@{$0eY-BVBF{gM7X@pl?rK8JxY2bkPF*p}%o}bM4RDTNu
zmHaJ7@UcY;y-KYUseF7mP41A5JUh2Duy?dL{E!NE%rD{idZBvIGOFN`#%M!NFx?bs
zX--95cB1SbM&Xn=IgE*Q_w$j&6@#JpP+N)F3x9IGJQwBmnGg$_K@8)5B-q?+gzP&E
zAre^woM3_T7$eey;`D*9cOj8cz}zcuFAkct3(R)!SW-ED2HsFu)U>!(;RHV$OjHqy
zj{q6p%tZj`rEQP<E|x@BmRJ&s9FSPb#Z+80uopS#WXlw8{TjY{5uT^w^NJXsFY!LM
zZq=AT1&bX}5oe1VLt~z;0XbCyV@Q}-k+Gp{*S!nn|M`&DXMpq1)z!qT)NuKqfq{FN
zfW~Q5bMVAQwOX7+{IC(CrS&XY0Pw^+aS<8-lp<s+3|_NA)HZ?#T0yek#?Ua<VI%^6
zQLvAF$T67H(lH|j8J6ac-a=KPoP>PGspAI%pIt#CY1cZq80#fx`CHIGnlOn<80-Ku
zD8!upAYkvnu2MbH*49SgDL4<#!m3D+gW#FsLEtF-b^(~dbv^^BPp2%NkWon;aKPZF
zy#4Uu!xe9EZ~&%H>(-iyYfL_^;B?A>=y7aBVNt|>;BtoV7QQ$U=h7|_2$=FMm`ZSi
z$lc8yHuiY}j07hJR}4&*`E`S`xcB3xqoXll6|e2+=$HYTtj&O%16OXn{v?{Ps^^MN
zf89s3sfYc1(LJdnA8U+mdhy6xp1GZ*by?rbj!|VS^4jyFjCNDM8;*gEJ3oBb;uG^F
z!n#t{xHESb?#jxqvx4#o!&Da&D=@AphDb*{@}3X{0<a^QmvxLPJvTly0^SDLfHiW)
z`cHYUL?FILoa(acPvKwaZz0jfY4KuAUpcs=&}n2pOaOyG=<ei#>@Jt1oUT8X2}8==
zyTpY^NHL~2iTeeTcrxzN<Zgh^9f+AL?=~)5X#{NqrV##c77W<OgNpW?Yq>lvuMf1t
z_K!BTAeedNks6dIjMtGx-}|h46FyW-apHy<sbg2N<)`L>U@{gaeIOOz$`?<<%mIHg
zm*=>G$Hrx3ZMwm52DmF#&=kR~k_d1`01g}y2Y6h`yEP!YIFgQ15LZ{BU&O>t1R-_i
zF&r7_Da*e=str3DJ|xuMr>vVd6^0o?T&nPAS2-bG`*sM0u3=P|0M<A)yVB#WeSs}G
zeAZUn2UL$*7xX?Urm|y>!F_Z!6IT0>=QG%ULsbIAo6SvI)st7MRM~S^L_@A@Zv9h1
z^`51k$cv|<WX59DCBmgczQ!!nDq}J(EdQeN&*^pjM<a^~ckeOxuZr{;DaaZblw<T$
z?>*hZnO=x3Xf9J2g|2ik2s+ZdoLii_PK5f6t)C+RqKQEPlr7~bk$}VJAHX#68Tg4o
z*i<=6cF^9*sYT+`cbh>_>`7?2x3ntNn%}U9C9}-|=@Aw#yl!LaWdR5RWzdCiHI7_-
z194>yI@?_~?3p3oXXCsc8)NITZ?pwtsDc<u#J0+=tqh-BIA>HJ!a4ejQ5Ss&CSrOp
zJ(P@q0;higL<3=YC5jZpc2p@s9Jc)lOR4IMN6SxtLr){D_GV_$5+k%86<^ff%f`n-
z8GFQdqUIOLk7QaA6h*{B6_CGQ1;@6HY!<(|_KTg~Ez@_k;j8B6KVNQ@?&{TlK2+uS
zThTG-UGQJ;6kTs8oo$M3$GgScK8AB?FsQc^HF~i12V8zI0(PaHAubn#X`dJ`!W1oR
zy^wm&J(%IS5Vr|duWNvkFgthuN^@>+i0h?Z31R^RAQXBG5RjHEZT%fwT(<V6zpxNt
zgxgUC{n##>k^kXF@Rg01PP;U+su<1qKMV<CVleFE5-`K4JTeWAJ~7@pJ%UT}aP^xi
z@{rTBR5<kzQf9C;5WOjq^*fA<6W0{}Z!Up_o@ca=uW>8TK-MBLmqS|+GO3|Md@Z5x
z)y_29j4(Cp%(o+~^$=tm(V>z%`m%|e2#by$fW>-iRkm(#<Ma94Gyvuc`8N%hE)hKe
zEoM5g<8HVi0AoQ7x~;%@KpDqj%?D&Bw1q`vj*u^E9y|J=jnZ0Y{3~F70=1$lFfdg}
zB;qkKE2uW_N{sjeZ(}^2%WWS|;$`dX0d(*zsPbV=DD&WDS6=m<JbrvnqK1VKSwi}_
z?vp2_DGif{yR2KpPse^2;cnPK*Q-E(eeVfdj&`>onzbfyD@^pP%K|5)_?2jegUzM|
zKX1+<t~qcV3s6Tc?$0K4Cs>hT5w0VK!GPcy;9Nite?m-7#b_P(FxJC@j2VL%y~_W^
z*LTNrxyFAtD3nn|LMRz!g@}xh5FsrMD`d--O+=ItMF@$K3Q1-mNs>LvCMzK$dwbq@
zoz6MG-*cYlkMruBBj0h~*L_`|&wG7ZJqaopjRjhrV5kU&N~0oPn(CVSv+KUl^RBi9
zEr?vvk4BatoFObjhXf4SA>#D2&lBxhUQ0WAJZyCH?NfB_^Zb%20E-KU)?NHK@`#{$
z&c4!BO>6;Qa5b-258vra?NBFgz#e%NvWz#?#1nxMXLt`cw-SH)OnkQ81Zp6F3pgDQ
zr=B5N)&ec!GEq^foji0sH#pPrpr#kT-Z&~+^l(pe-oPCVa*UugK_dyGQ$lzY5wD33
z$ry-|OIt`#kP)GyXoci;zH4<w5!+V^(pjos`n9?o8(KlLLa^XZo;;zu+fwUsY$St7
zJ%Ch(=qrh0U`NmffOW?r`K!=cu6c4U^KrEVjzwc&6q}huZxP~ccobja4iI5@hB_$c
zpeNilH$Oi(Vs6<+<Tb#1NZ>7X=f0tw0^W23VuwfHoA;lRff^WXf-SNDQI<TI)dAUo
zQWLUbD7J5MC_^s&osXd?b^yFK3V)6rJ~LzR(GVLOjwpvOs362qj7ap?AImLx|H&0x
zG2zeh@sSUkPEQSaUs&_9qG-<U_4Y&bb}Pnbrk83IL@qFuWc%3;D7~x-${%&Rl&{0}
z*aY6)&zH}xRC3F^Y&jb$6mV}NPw-5I1Y%bSx*Tc_fRSZr=7`)=v;^`v+yP?YlN^CI
zg-GjzSRW|>Kx}2vXo(|-g5vrv1-n;(C!^3vy@c+C*d!pUuy%C(1`L-7-2e#*yzz!+
zN@G;p#;|x5?n2*T0>T7PL-@r|gz)GVO5*TE`zVD9jt(Uf6b^)<3u+kE7||eDfoc(o
z0L5RP{oq#ACgH3rPL7U*ZDwK(1B$sO@nU7mA6PJku<`+|xfo|ou7`hx-}M?|;BEn@
zI|=0^Kq<n>4m*A?q0eoL42#;x(=F6G_o`%f4mvsPnS}rD#BcWB`+VwU90I)B`GoDE
z7giAHD}kxKudBO_`wPtlv25HIrn-~kJ$kUC5TTJk7_l-5K#Bl?0c^eXpN~BATuT;Q
zF>NY?B_r5g0zg82(u=K+SL=lrgd#BK)o=`p0=~Mneg8EWxvYm8d0;UiAT*SBO(`K*
z2Ew3giHimQEs9Pe{e$=1%Oh4df2s%e<~YbZTrnvMfl~;=iJ_|4@Ox+w_B&4)7A!nD
zn;uvFfI>M1L_UGj;3R;vR6aNv_Z%E45zR}KF3Clnt2<F{qRI9HV*x)LP_x@${s}V{
zfk5<aizC3YY|9I9FstJG5KA6^^g@Y&T8mma3~{=9;fPN_F$^6Fu|W{&9RNSDMT<3i
z(6*J4Hxw<;T<}1y2I^A<{4#+Rph@gSQA2p>prH#z)Cmp*A{*cwOfba30Rk3}3SsKQ
zGTaV##~PfF-+*Wmb}_V<M2-S-GM;97el|M*r34PtK$LN{fKCYa8ZZVTDFp3s0xpV#
z<!+A)bwZ7o;bWfz1rK3_?#p=guzMTHY0#z9+dVNpJ$Ld)`l|0pB8zSGhj+m@>epXA
zn=cdgNXmD+$K_V$PXfPiFr%GG_v4g!VmI*^*Qv&C1a^6xPy^t@;^-^}oqP{T%*-V~
z5TU)h1gXY^EDTW}0MD4h0|Qo;F!&w*^vwk7gG88oh%yZ|49%7;vS1I0uL-R3%j+g-
zsc*7??1<1AxVYioq6b*v1Lr6(8AE6uC1UddP7;760VMg7)4s^eOvF_IKmy15^_UnY
z0$wJ7I8^6ESS%owS}6H}h4|s2j4|fUYlg4%B*2Rr+{*sE2sW#6FB}NO@<Bgaicf6g
z;6MmnV5ZYfc57X#7ox8Ji~C2lOyI!SI0yxuv!~g>6G+_l3Fy3ei?)c+F+c(^s2Z9N
zd<<lw7IreiMh89zPW9R>^Rp<K_y(A^Y+;WSNXf5@(8n?$kU}6<F(}p%#_<-#W*Ezs
z{e{>tP5=?Y!;EyKFaYx_D=Wm-jKvU!SPqEd9tfX!E=oVL^7%_pLcZ9mE=oKIcYt7j
zSN;AJ3h@NHLx!3_O|C-|58D<nn(}!h_Qs&wsu(jrjxbs5LbkvSK`?vg8oPssAaLmI
z5N{F|BatHP=QdN{PY}F7d^{^o4D=jCxgyRwV&VXfVQyjJ5;O(qwdP=8wQtp2nu*bJ
z-=peeZT%HB6X8V!F_3|P9;Ap86&QFyxNbfU&n+&VgwX*{WGM;{!pZ_$5N^<?3Sx<)
zxviKy-~hZ9n;CDNb0}KI5?qz-z|OJUi6AF*enXX49&2!K_DJ7uCXDaFdGO$NFl>fx
z$f4m;%Z`ob3O5>b33dyb=uzjs!mE%Fu;H-g`3F3Ul+k9rFS09q9E4&%*7vWfpNZb6
z%pTQxvhcE6n=HU6PAD2byXqe5Gh1@~R249DtQ9hK>4mj=Bk4nXQ3bCTyXP~tcM<y$
zBZNx8A?lbo#S^jfN246G{n?{{?c%=a;tNz?;PXD}ZDiZe_?aO1%CK|i0qi=_D|pvU
zSSbF-lK5?U>>sj-n#S@oj65(q_UukzKma>8H`&><O{dgV`I0V1JRi76mfN$D;qqbo
zH+9A;_P*y&7Ux}k_-x2>@4g5b?_2!xwgb&6?1g+J>`cS0S^EHLs7)}q*s&>ZMN~R*
zEP(u@QT>88vH7)AdZ%T?HMXQMPI@cekeG_^Q@PZ!iE`6lpG}UJMx1g8_N|OOkX}c=
z4m5(Qp`qc!qRr1vJ+){2c5d;3!=?IttOm&C<|z!keV2zW&_1S!=MaG$T{)quiuyyi
zUsRjD7jP0`EjI9HCp#C(A^X<qpcMVJ-s4~6hQo8&UrR+_yQj;mLc_wrUNKag;3Ih@
zkR9QxF0?g|6$n;x538);X`Chc;GLBD5q@;f$e)V=vC1YjD_&iS#WKdyN#b;V(cua9
zXEg#@Ltk!1l%LRD#}|Q9f`}8icI_HI;D&UzM@?^#4_8?iqj6yOL^=PPf&w@yH%Q;w
z5z&ED@?A4~(lMx$`ox2_h7*e1z@u<Z`;v6{oiym~PG_yRxS!B^@X0|kUW=`|X9drJ
zlQ%pEjZM_VcvfWOSwG7QG%v4VMGoDX;Y5nY$aN_nVcPBp8Ku?bW@G*Jcl~5P*V)A4
zD<c2nuOxn@fLV5Ho1^XD?K8%D>*<bh4^zg^dl|6zmU1RB5pjgSgE5lcA1%&Ou=d#d
zhI%DbXKK?EDHdDz_80ZnOcCn8I{=G=lk=#6Hr&A)+%HEm8B-p`e%N>DOXPo~p_o{4
zD1(gj=`w0jM(1pnb^g|xd&RfT)P!v)?Vx;8J^zr*m6ywW;*9)BI|)ti^ETv+Zp`=O
z4^?~@N*XY}{hiHd>j+88c@$zG=?3{2SXhDp*O+BV2$xg<q6`~WzFp;4CGwAG;2$#o
zHit3*d!{A+3N=ETv1t<kDqi0Arl*gVPq{>JJda~7>uwd{?QCD5@lWK^-{#5oR4)^&
zLpWtQ=GO;+ocD2C_RGtZ#<Hz-ZLczyB*euLY56qg;?=7M5wuy!6-IGx+Gm&4y+2HU
zM$gCRc&b=Ww)lTL@+(=zXq-?c1qBfU1bTXQwVvDXsnX@lo7`IyAsO7O((K8~j?O2}
z#(SOmz~uUfbcS(<x3ry!F{AbdF0N$zwlfe$2@{4uq#)_!JBnoAV!m5-(d3Gv?~k*(
z-!vWnZ%v3MHyvmU;&KOJ!v${EsIZ}8+{J@-O>$ZBG9PRGbLOuNb=+_K4D_RR8%!K$
zC*JLxAA})u*)$~Uu|!Ww4H}*QQcji<AfH%A1f~Hxi$)4X-S0RPiOCI*Ubzt%3pgc4
z`k4LTkG<f$WIVJvyk}%2sKEX5YJ|C#*(FE`B<$Ytp^^g%hsN)&Y#jnwpWKMFwikTP
zznox~^vd^B$%9$>C(=~6+QqjDMgD(u1Y_}C|5Hb>1=T%7kVIB0Ox;gV(Lk)ET9*$F
z#26JU?5eClDhsMD-5_nY-IxHWD6*Xo#U2Yi;Oy#3izMFFm01}ggQ-Q){^0$e*SE#l
z>~1t&VUm2%c(!(uzj1c`>-M9RCj_bLWItUFmdgE@v5_H&<>+H3?EeJsNqC=8D-a?<
z)S#gRbArPJ@zKedODOH8>nkC(&O}jfm*1JQ&(IRorvWH8*j8?!e>#blxNv2`oCvJ^
zk&l`TGG9i*d!#Ns&q4dJDjyjkXe{3>wZbz(P;><4)+i-QBXmPzLmHpo-8kzn8!x@<
zt?yteZaVv*)aB#3#wY9)ACPy`@-ddd+wHY0Ro7@-Nk?SJEf%%ML`{p0s2d)QK72T$
zR=ZL-?}vi?7nT04ib=xp#}nZnNl>yPjriy-iC%4_YT~SDNIA)ct90)M>i+#mLP1~h
z9_0{xh}3A@3Fw`usLF%W2K)OJV4*|rZ;bjViq2udWpzag|5-EchBVu$otiLl6O7z9
z!0(K4MQnyDVI;HJ?}mh|?KRp{9oAUgeXz{_-I{FTl#tb}Ysxe%Nfv#c#!l}SU0<KL
zH2(7^PAF@{q7V@Uuq8uhLX;tR{fdhD#YNDEgyp$<0R<uQdS3v6qZ=3;9=?f+1>(yF
zCYBedK_Cu^23;PGdZ2u8a9R?|`>{EUvmk=#@wJhdK*a1aEnUBgRsk`8+lZk7=pDf8
z`%|%mb#(!_22#idWUjfjRTJ_p*yF>#v3Db>`Z~5H0@F~Y-n7X8@jIxrAl42-C5UQ<
zh&`PUA|4u`7{E<@0Bs>2MG-)8p9GPqfJ(Il(LDgZ2n;t?l1Qon$;6|bF9OVs$iYV|
zJAvw3<nEqFI)!e^sNYe5Qp05rg2fwZ`|o^6BfW><9W=ymi;KPSs)SS(b?2SF8TD8R
z1$1CMh!n>6B#1hqwMIm&Jzp6LF``S!&d#QTy%j?2#}$siGmfjOZU&itrvV5vfsVr~
z{|!K%a@yF}uU<EAs^q^9JCCeB1}Np(LGkw0#K(iNdo*;cl7Iz~@j##iAmwcre(R8k
z+7cEj!a9K&5~xr6(SB^mnTE0g@^&9U_`n4(6R<*=={w_4wltqX*yHg$oz$_GrP2I0
zNZzbLIpcUO)GJpcc~`C5dN+4+$sLTs62<RtP-%+V3@EUbt(R^;@ARWsAyG#G-3%=>
zszd-c(f1P3A;6_Sjm@G*0!AW)Fkdjo6mS1mYRIR7-=QHPME41^taTJV!Frn-?nhk8
zVJ5(72rM662O+w|%_8K)!^`=j;K6Z_BV&wEs-Pg%1nGqv#wkF=J)y8A28Iy7srl#_
z(XN0gO5!O*D?x0p1t)ZgU}d}-GN`1`(GwQ|%L~XfOKd-o5P2-%6!;wQ_uoTAjH;iQ
zKp^2Xs*0DKN6mY6c9ezSJa~Ckb!LJ4KxO0ysZ1CycO9la5Hv4(ID}>>opcUE{;)Fs
zOAEqQkQqj3YalV{9vP`3K#zzK2xq{5ChHYnBR~LTkQf*k5QuG9r2$k+fKmm)Iiu=7
z3^WXR3Eu4=UV#NBn1sNUJyY07FsLCIsvUgTB)rJx?ShBL%6#uw$*eqB16G_+0}xc7
z@daou?skbOpyh=!h-f7)SKkl7FQQ*EM7Wi58WB&6i}FPC5d~l$LwKNGnKuPv+d6us
zMb~5gI&n*}tM3QEiU<T{K(1E-gz4~NK^8-nfd`rJ8W4ap_AAX(5qJbAp>|JtGk%SY
zW8^bsa~*Sbqrd0sA?lY^q|*aFvn<>lq;x&@T1tnv3VjCp2!<Dha`7xHvU?C@DA+N{
zl5LlL%HvC<#H!y|bnNIn2NA=yl?}YoF)nu`u^?Z*$U|Gr75rQu4tpZqJCGncPe0|@
zhVV2BO3J$^S&-{b$HKyw@_FdUB)rs-Bt%k=iV#2Cj43!sCx!{m6Xj^i-V5&>UOB5r
z2`L!oLHMtPl7oVb454sgFoCi0+&z|pjm*X9mm-V^E$?c5Ig3#QFJTOWp*eo2c@sS^
zcNPLE1UiuRh^|f}4EOK?W)*-$`e=%W{O%fp-h@OVya7G`Z+=+kT+dhuu#sb4Q#dX@
zR<HotS(gMfAvxa-kL_IumG%|QOiqTcF~u%vdmi(QrZ8hf88MdikSFi?YoLOc2(&i^
zqV%4g+qZhMnjS|Ni`t|fuhTE$>FG(XR97@Nos>EYHOI%cUsvfLI@s3bSPrXa5h9}H
zh$PCT^N8Hix<{gfLsI$W(of5d{L@#u_Hgbgv%N$_Ij*fI6hk6GM|Wr8H;_9V2K_-o
z4z>FIgY5Xk$6vzg33~1nmV+tw;Ck%(Q`xM)`0&)!)G4qD6@x$>F*yOO?&q6Ec!nj~
zo&d+}>+gRQzCno~*ecSYa0r9f^XYK$cA=rgz0WYyBLb*;n%xrlpup#8<^`=Vs;SVV
z77FF)<Lxpshm<9xbiz9QFPl7PEM{&!2lY9akVcwGHY0Z7kkoFS9cc?kjuZ{dR2(jt
zGN9(K?~lxAKG%}u60@g6a{K28icgywaLYoghoM*@#$C*eb*Te}TT6u7qceU8SOxm}
z7|862w6`PaB#aLW%(}mR4ehf<o)g>(qIVxDwf--TmWUo=K4|TQT`m)H1i-;?H`K-?
zD;)CN<b{i|<OIA8YpD??7qp-@IB@r#dJ_6{4m}Ov#V;x~QNmofRs(qY*l`R7qyfEB
z#{%kaLbN3ZVz1~BI*g;Xe6Y1>6}Dj?BcfeEoG%c!+mN;Z)RMzisd+l$4q>Ck7KIas
z-!>YB2NWvAzr(~Hh8_ClFLLvG@iXe5v;OQqE2dGsp(rAbsxS^45UCUl{F{kg2=*rH
z=ud!uWD#oB*Myj+so|y&cx<f^N(&B;Dzs-LlJCNql|#S6GMsQ^PAop&yP|Xpj4g2;
zU^fCgFNgDSEpdJVy5L}A^MVe55Q$-D3`$Nme%W>f8GwWZUiU2GfAIw~Kp?_D`z+I9
zb!FK>2gq3rP{7Aen4#}Ga`fodEnB=}W3>anY$0Kf`>2;I$dbmtX4>=Y$8CG(`k3Y{
zb~O(OTe-<aut_ML`&bYek~=jU+sB|vD$kN!sR56BY!lQl+;@)^7;9jsuSC5-Fv-9+
z33ZS9Y3bJB6H9HcH>0a5sjA{T-KJKJCkvy#igX54T^EVRZ0*&#adzY)gSp|zBlN5U
z@QXv~aZ}VLO3LFWZ-sdqi(u1L1|LooK<F%qlae@bUp*PUAr0KIaaa(C1L1lu5V`UC
zfa*R-gn(qi0$PI&!oEkz{9M>1Si(RCfwU&_1FvL=>^9`cAoTjQGYSykVw~fk1c&Z0
z*jFH{RvN%|TO{NR^X0eYouq>i2C&Aaro!Zq5;i2&>1^cZQC62Ex=RasY^=RQeEXS{
zRN4^_(tDtFQ93>baR=09*#2r*__(l2Oc~aReLbqnkFgh=v_SG17tDliAIS*4XnYZw
z!<Tk-57pSjCO)~^wY#)UHr4d2X8qL+@^isZt}COwfq4RnOXs>MWAEMlIHG2@(KG0V
zM@_7ugzTe^z@&w}ngQ*jDbmiq)VeG178|=;=5r`Z41zD6@cD^!SWe6|86Xi`nc2*9
zPH1#J^7@AZ_=(E_(o_YsNWW1SXn7+QGp3(iO(r4%UzFV-7;8+uz<`||TpH3exQWap
zl!GV;5Q!Eu)U2(o4MOJ2g)}@2#5^S&(Zp~tU|^+SNSd=PnQ#t<N1jYMwPBLL7#eyb
zuMkOe0DhqKJON1z>Q!`J1o;g$i*w%GYO+HY$C*`fU8YvnlydddGY!Z~11QgUz>JP~
zWN{!9eFvJk!5@jJ2<e=NO63`?qNdReU3DT=DKL8s0wO0jn8}IY2n1(OkmE|gN636*
zxcO0bXSi9@&qw|DRC0Be94OrjiTEDEkW1uacXSZ?&(6+H(7Idq?R&;iaeF+oT%$6K
zgHe)y>%N!-%MBYh8XzbzE6X8T+CUg`5T!7~KRq)T&Rf2FlZuWEpG!PyW6bx|u8_M^
zYBBVF5odIC!|jREWs@WHSCYTgRtx2C9-KeNfxOoDWn~+|q|G~+m^>*aKL&;ij##0C
zLM=BWv`@y4eJt=OcMP47$Q63l|Kik@Lwt$JrbXjp9k02%tdiVQ>r60q<3+XOM$j+V
z2?4a~L%UQNBNhT8dA*Hpb*mBWV%Fz|hH%tbnfQjNFAT=d92()qEjkdMlPr~>e4LRs
zjp*-)x(m`MwL+|w4G*9fzzu<>1F37>7`j1ZQ*X#|he`-rYx7H^P1rpmD$)vi9@m*@
zvbZ9b4Fsl0?tL^6c<LYF^daO1*m(9Mr4gCyyaQW`R%nIp?DU)maZe=Jdn^ocfy03`
z5bQSyd;5r+o?)@A6O65_2o>WZ;!k2NMplUVWT?6T9NA)J;l5wb%(Q!HsS4Q6oUmd7
z*&S-%^@OEZz#|XssUeVmd5B8-9rh^qVAt=)yGfkA{mRa<RK`Qo#laBl^aR^hbP>j2
zuLzD38_vghGsX19zHoI-H`VQ}P65j08TT9W(XxYU_;@ym7?rTe?O^p9)DkKvBFHHy
zF5wS6+6@^7il~7Uz-E2#EO_0S`n1&nWqkVCU{H*`qoZ*aZH-^9CrtU8dV71rvAnk`
z@#JMr<uHWkSAPk&ly6to#ce|ZIAsTa5^Dhg^Te}!SOLr<CsTQ0d+(`h<AJ?5_STZo
zQ3!_5m{N`KCRT*TIXy6}+EINC3UBn8gfoX27>5i9xKO7fHX)ccLE}56Vl2Iru5{1)
zl8SPEr={*a>#oIV)>ri=PO1jayoWCN5n;Jj(}gg24T{Ieib9NaBqX7zs~Ituj<^LV
zB>HX&6xNDwIX23+h@`K<&VobWUx>9M;oyq%icoVx0}GZlaVc(wgYUp1`!AQUF|IO5
zu~WuLdAJ9RFi}Kiq4--GFQF#tbWFGy(q=!&O*f%r_p|LNN-{~I2t>0u{D^m-0l!g+
ziF9W?Mj;%c-MKSO*v0}`nZ)!PLVD-S@mY=XQJJpJVv%FlIV~;Bx#ZH#t1V1Vz4_`+
zP3;O{A4b&>9xo3Ilo8e?{HnynIz&ZdDH!8_sK!cc149{$Se_D^k!?5TeyW7M2k0|h
zj})^{IAX(Z>F)CohhP@^&*xyZ(0tP0FyDwdMr=q?a9bEmo|xe2@IV$!zXO`V5-6t6
z!IX~jHMD{V5k$P@Vfe-SjQ&xiyX<Da*6kj7|CO7**=!lulKwifJ<6BxY2c(n_WSNr
zd+$~gK_-OB7WUAu0AldgTTyxv-3vq$5QV>V%R0rhh)9l4MXM|OoFoM<=Dr1x18<_%
zOUsiN82svK9}_r8df~!e?ZWj!(f`{X^tQBgPeokrWzwI+Efb&j-0@uUnuu?hSPXNQ
zZT!q7my(`w_UQ|;OMh2@Qd|YFpIB^wqCH$HWlrltTJjS6IA2qUV1{y6AH$MTEA0))
zXX-$_61j@#Vb0}PvFN%_Z@as<^my&eU&Ju_aiYUU{Q|KAF{lqLO(_m$hwR8x?x=W!
zi1}||h6oKB3KIy&zM=aeMkaw5h7jTLq_xYj-{}djtU97`a0#O}0Op_yBf&vTiA05b
z8AauUFeM>Z!3jlpNePt|bO!_@j1VQFy+?D6LU9w$UC8!%s24D-^87r5`6Er9ftdQ{
zHrz=lhoOzT<7V_7YlXla(8pjWBt=h5=v@eX1SF>}Z6bG&#jYe;fOF&dg&gA915s3p
z_YjBr8d#4+Md_+cR=>)20~C2$SQ}_zdq8IZWx)suQ9>{cl}#V@7h+5uG%rLN1kofl
zRpGM0B~e(dx8~<vo|6Q51g5kUN-rB|;~<=#$mIH2f!U?rr=(UN7EIIk#K}g(QA|`D
z$fB_5d=rHVI|J&oSkdP}hYq0XtVFna)B$sPEM_8-42J-`sf4V>K{^v0HIY|Aws~`7
zl&}S8kHhW4c58s64S-Wx1E0S%5fy>7EEklyLM?f>fUck*C1SEb+-PFR5+TG#(LUep
z&-yX;P>$Py4;nE<(TiqM4}}x)fzS?Ppyw8t<r6a103kgAJ_VH|+upqtcnq;=F-p1E
zzqAxinVK_&S`MTX>{hKw6;6kbHmqn|f>-u+o#Q(NZA0E?PTpF&%(o`G)2IW!sA)`Z
zq`T{<r*9fvqx_iRZ(#U4TU3T)yvWxD8EVZ}7Ht#L!UuO~6Ct4RS)eG{fIuX|<^Z&_
zZ#IjIy_MX6eKaZxcd`y<UTkPpc$`n(j|X`NWQZ{15IYuZ%@Di42V=Wk`0{3KdB<jj
zAf6>yYGPC?u%Vx`vt^i(2nEV7vj*=WC{}QMz5@q}VPwo08hQuQ4+>9LpxH-w3lUsE
zRJf>r{&IFVI`eZM0R71grNf16i`(jtM}GVuC|+QBmr(74-X_HDILH|RYLuN;lEkV&
z26+aeuZch~;C2VGMu8_N=SXfv6G>#j5f%ubZR5ypLMA}~q=P7KBq|mb7b|jNf^apk
zbdl63hhN^>QHZXF2x&!DDQHL*WbZ<HQUT4<NvU^wn)syna+H|sppU)|VIuz6d+L#d
zY2UH}4wrC2tuA)0Y9ToSyMHfXDteY)c&u&#TyA3Z@Z6;Eo-eXO9Fme3Jy!OL<Jc!s
z!_fDP1C+wdqPO_8QG)t%fs>gzImu}Dfq%!~kHG@Km`;cU0~=116i6zBz~-F@b+-OT
z9DM{vh&TtO97~F8=g2&RCqe@H^0O$ePj!tX?=^oSLh>}2^g^$y2H!n_>v!5~?Bw$6
zJ1;pQ<RiA*A?uYqI~Viq@{1<%rPz`_D>@x}1v>H6Q{JEE<}Sz5U#25Y0hkRjTnT=e
zD37&|LsQ1&|D?o|PZI4+X(=gIaRJX-X~(t{Xw-KTHyw*hb2?GgOhG{b(f7sRYqyK?
zPS^PE@X7PkeRK-NJj!zTJTDLG&K%clypVg4mcPcQIam4p9y;z%j{Z9ezkavsTO%AI
z{wnh?vQpp0m;<AZqoIJ)M70JU-|&Y9iR=uNwI{J1*uUNzu?-c8fvIVVn12}H>WmZC
zM$*rxd?!!#SJy2r#nUc+RxrtzxIplgTvi#hFQ0$?s)rVpcG*blk>+5PV%Qfq6i&46
zG6fU+H(-7l%7P#kKeq1(jJ>|JS;Mie$kUSuyH{TCBv#DY%P!JM_QqLePxc29Ig1LT
zMOj(jO85!oB8WH^j39~nzWBdLN(91x%-+f3cQUcN|1-5|b!jiBGhgRU9?>rren03{
z<3XrI9Xr(S>~as=6)uoOqEBgZ?9zk*p~2r7P#HS)31RpRz1`ine<-<JV{`LmIQzA6
z`&H&EecG=j$6Jn|Rn;)68nE<ze%wCPm$#y#V&BP~Y_k&+pI%sQLPn5WHr)=g<g$_u
zO4fSbk?w}EVsjF$s5aH3a%Xn^nFTKQ?Z(w@V&m_!N*@FSsGK~1c-})}S@GlTvfQ8K
z>;Cc?%k4m(U(HD_vhqM@2C<8?rBO62GwcO@ks5Xs2N{HQECBmr8`^$dP8Q;}xgHDy
zpizzBP)0=!A^k0uK)oT6jPZeE2Zz^>tt^M?JdtjUTI(!x;JnGT(Cu}yLi+(u5jHp=
z7rn^Gy?(t}ftVjLh;&|TkQg=v(~hX)!D}gD9AwSp$sS%}v(iZe{M1>-UW&9dG9;Tg
zkKK2V*^Yw_0Ul(OlzT)(=&<cU`kWhW2-CsD-RvJ{Wd4hg%d6E9hx-F~ZWvd{Rh=V(
zU&l_4FLGb?7?qEf*MD+=^q3Q=!UxLd9AtyC_Mxh`5S)QsfD__TbPb<!+Q=6;ly^x;
z>_G2i;nZXBU*jG&VFm)o2LSunL%8G>X|}z5(3JDFQESe;#$SYq;feIly_?r;Vgkua
zmIAziQwdz;_wP4|)<}N8Df$9XtKc;Q9~sR=a~1!`90)p+O!^tI`%z>$XMB<ZR5D+9
ze=6y2sM8B?xKT_lHx%$^xO=F}Sl8R@@n45(XcndUk0<!r7JL<EwdU4q94BE<J+iS}
z3Hl$5G{E?dbLW4t!M{oRu))gz7#C6OW>g_czqqqMsFYiv`tX+NqiSF1me)-ihZkq5
zUX+uF8!)VJ2`*#)6klhgR5NJ?qK*UF4#4l9(&gpl(NqXsI&w}I?*nj1DeTV3(M93^
z;E72m@20liI~r7#ICAh}e8AqGsQb*Z!zbVE4ch%7_54M-4fneYpSg&>{q;V$_s4TA
zjs9QV0*10jAYvWH@n4nU|8qh}x<%aw4)W68E{)~=R0_3K)aBKCPBh)S_RwS>v+z}#
zI~FHulm-1KjO`f_zXD(RxlF$*FL1zD^$xPYB88;Tmqyyr|G_$6n->}uompCUe+Q+y
zx|>qPZECZ*hulrHn~c829*cI6O7_Bxlig@}+UWik1vJHMw02=`?^<B5`n2U~a4=JB
zb$zu-0=e8#+CP7Xz4|qSwd2;Myv-u3QmW~%d;@(Rv>tp>VbnfH!cKeRulq0O$iT9J
z!MLPfoMv*g=m_bZQHldx-Y2&t`f-s(DHG%Fv0>3vmLdXsLC~l|!ddQ_rL}?h{TPxh
z0y1v~>PXC1NvyUBbEwJ+8vO|%(Bqe5m8%`O!^bpDe<sp9^eW5VoKG6YoVlKH`+t(l
z(PKUTo&?i!Vy=sI#c?l1)?>MHwFeqI1UO{{*Zz5#Q0<m)*M?{x$jNA&V?4A&R*?Mf
zpRnL3oz%sxb<MZQt|@P6(jfiyF<<UJBt~q`>xp4`zdt!ix6Gg4!sao~`bRJ!xG`g_
zyQAnsupG@x$v^+|<Ipv$l7*+^(#?2Xxd<*~8T@*ck54(sS1wYO`O8}*Wh8DP$^82p
zoI7DC$UM59+HooJ!J2_f4_=TcP<(NksQmby<R1-(@AGeCCtnop^OXv6wbWe`osNh#
z=t<b_t^fOt_ljg#TT$GP*&N2nUzK@4<Q#c++J~UyG?l)8vL6gduf)GyN$+k+$!)@!
zF2;cULE+eF3M~oyo<Co=xUr*)%D>S2Noa0Uno&aO(T~dkCrY-G*a2kueZ?Q|<y@zB
z%Zq7sG4xD=Ok?c&2*(dMRcI>j{dt>v56_C}=|<*?2d{yY<tGJqXLYU(`L!ro+S13h
z&@<s2Bt;kS0PcJYeQs=KCnsK5FPMWojXyAE?sS{@UJa&vZHCz0vL8u$C^RWhm)w9y
zX#yFr1Y(Qn09VJqu7w)w1J&_g_sDL`&mC0Le*Q%t3eIqMX9j3kGIO6MzWYn^I@x31
z(7_YhI$h7@>zI~+j<P3QU0NUPJCu_R&E3D>o+^&nf4#2!oQzF63x)jTw8o1Fo8GOy
z79V)8WB?2JXYvXIYIl4K(Oe6p8-e8H{EHSQig;G(=b4r0>|t~uxHQ{Vu6Vb1=+cE=
z{vKRpxN&IvL8+bD9xDlUryj1iFXEI?yrxHTxkc7xdEo$1?H<s4gmtdm2&2KGU>hgM
zI@JGo`iW8K=xX|n;HO0s(|E21;#edHBO{i$2)-7(rnXq5Z5l{kw^gfIF43sgR;B&H
zW|TS-nQuxl#l($B0K;Xpg`!y+8bqH8?ObbbBD@LOB_ieTFs=yC*)-<Fqd`4H+k%FF
z67_DZ1FS?hF&^Lp{gGc+d(y#4n0a(l-D<2s-vY^bt94C6AA(e9UW#WT1=rG&$TJGp
zwgPs54~-Ek`;svZjS#k0$4ON{VY?O<qJyaB06(hgjH2R42C(R|4|G<LLA@z`<Kt7H
zuR8!`*fIGB!=%KsNUIltT+saAQzdF&yQcvTBW6la-gtej5zPkXJ1AjR5mKJ}(TJh7
zmB^H*Cti+ypR3KbFK7H>p7rRo<;unACKT7`=^L~+lgO^AoT7hy2bMZ<6yXgjO^=rW
zu-mqxD;TUx+=$kb819J5jqA|+S+v#8(?fUF&LeGd4bDvjFu7T5d6@;J8GtwRg9y`T
z_&fIFUt*wZ^T%wM!a43V(LY$~-AEU0vPOh-IKk=%^$h9Z`?MT9uURX;X{?|yb%{G`
zJWQpDFM;FSW$+hQah@Q?K{BMYuHaK4E%(5j4h+Sp=TchZ9$=PF1T>q(RHR+52aNue
z!xDA(%F%BIdlxkXb$Lt;KFy}vNF3T+;TgP^jpvkaBx~twAs@D5q$hgZ*u-0wwM2g%
zH%Q8B_;uVg1c0SSpu5W;;J3)G)$RW)?3n0t&}qt;Ew*Umg#8sl8_Bz<fBVdTRY7`%
zVde&bT#6bjLjk*bNY{iJY-v31QOv1(;60@SPh>}k5oTo_jVvxN=jq74d%*l)ECz|H
z8-FEDMa8y0RK{~9q_q%8D3bIybRin`eSQ5zVzz+SFNxEx3tt}nhw=<_xO^;CStvc1
z$QX=0l=ihSDkMJA(n{_Mxab)6*E>eAOXWnRZZv(Om9Yy_k|w5ii-7AU7JqMWDO)FK
zL_aUoiodK}dweOObOQ}`B0=Yt1qw~HkoTlqMZwI656FVOeAm?#kHrY8Bw=&Kh0XQj
zKP$VvOJDsRGP7UF$JFWq&EcXTp3yW#2RE|7d%5L(kJ`5dSmsmRSMf6OH;wr9nTob2
z6_fmB>38PHhZKAq{N#E;!;ds51^)kWhX;24jypso5^D|fPA%1ae^vt#&GapsbglHO
z{SQm5^A>hzd$;w?cHSLQ)GEz*kg?%s?COb^iy0PF{WZsYM7Y5)*ISx%zDN5FUnP^9
z08BJctg~4i_9OJ^K$w1l=_j<ys5nhQm-@ZO|KlUlHK4CAJ(9_adG8TlzkcOietYTs
ze?JgJ1ow~P{kE~JffFOTYm~CBo-m~znfQ3mF5n0EpXZ?jTPBFutx!iUeYgAZ{9FkS
z%=?LSe8x~EpeICMbLPW_J6?#0biY@!{-&wXp91+(=!S;&?9eLZ9d{xJLKiDTxRX|`
zm~5}ydf2jq*S7C~mBr=1-sQQFk`KmN{W_d!gjDD3=2AC4E%RR+dWW9d?708l-G^_d
zmc8BT%d7sUg3;VPzJ~ex+S}=CZe-1R(KEf^o{Pc}LBg($O6WGyd!*yUZ+#E@`$@pr
zFI;80sYSzr?vrru3GJ9w_7uajIuVOojGNvm^|(rv7|t5BK;n)XVG6%qAOD}fesjoj
zjkr4X;puOjYj)gZev`UD+kL$iq2+#@+)A%9HsATZsL$*u<v0IgP2bns>k|?ZA{iJ9
zGXVCn4^;b9V0wlS(Qt5!cKv@&!h0#GEN3&oaEi+>;YQG!!{NykL!9R2w;O29G15-K
zQ6{1)VTsTtCQrrqikp9V!AO(X{D|6ad)=PYKNY<CtxLwyZS<8FPjNGkQWH5;i}oU)
zqQf<wKJVlBdoW(n_ENQ9X9)YVg#q3lixi#Gfv&N;1w<}v8l?<EJwwL$_vL;iVwO8j
zi|!*#f<INs&Ln@w4_l@KBGAHN=pbXj_R`VbsFEA}|GM{dhj8!p{NBYUNPG{PXi;9n
z@n~E0`3Cs@H&c*qpX;Qz<h3KhM*SylB5FwrSyfZURJ-&48Rv(nCRMw(Yt9)fi)?Df
zMGB0|8@#j>)#c3i*}wGDl2NJIOZ|_pQoH+ThKlDm!G|jUtoC22Pki?RnrFGyLu4Hc
zGVUiK{wrnl;(cB_j-q^w9NhJ5<e=`YOI#c(7=<WZsedH$Ut30CEVhh~Jt!kPtH&2=
za+}Ts*P1YX($syZT6*~iQw1{uv2Z^SxAm)FB{|8VJU(E1P@4JD?%w(d_YHiaUg7@x
zchiy-ll-aBTNM8(F};R*zh(wJpi4$8{P)jGyOQ-h&yu<Bm~EAo5xKDO`Y@9iKYH!J
zUsw9uBCd33<iD=;y(`31cHQLC37va>6Fnkys5w)VR2nHGy)F5DN}Q7K;Cucat*E<s
zlJEPL61QX-yX_M~|E!nIla^R7FE{kRE-Ifd(>s-3y`GIH)p@vI-tgy6ngp*KA&dO~
zx?%c-q*9mejp2sL>pcE@{$hZB;c?us!ILCE4m-S(34B7ch9k26y{NXocAEMNm1N0(
zU9Wpr*v}EKp#NX55D*yPMZ5d!hgIpM)89iLjxzJ|H9Rw)^8O!R<JWM&&=#EzFL&*p
zZwJ@Cu<`q_@4?kWy&v|V)CXqs>-;cu4<l)!FDV~8%(5-=%mYyo-HpN5gP39vt&Ge0
ztJn<9Qh4JhUjVhYP5QQDPo&wcJa+HTxy?qF!XbU&*N*ft|KH`P>?Gyya`ayv!ONWv
zo9|D1Pd2RO;ZMElYVt;MG;cS`KoQ8kcW<FB^^ml?C&Ks7^;V@b$MwF&Ekg6Tc$9l}
z`HI!<O&1y+zU{g@LP}AJJgMmO4}*+?k$Lt_!(;!6=MNNB>0(x(g@5(0wRz$>)}|m;
zjN)sXH{(*D?g_5BWE;Vm^kr+K+8*|U2OD~~{QZcn#upq433)2bAhQw`r8*PD8%jdv
zefZ<itq~+7?<w1573eRBJ)Lbe`)rn;v)rO%snOQyI#`hX+01-+Th1AJo8r`mUV*&&
zDr`*VTeA<dEykUz9t-g%H&|yF)n6Gku<SB@df<Neq<fsOf4QXifTV5|_n9d++ER&l
zdd}la+^KzOGm?#4<5lUNRl9Ez6VAFcH)J#QsAA+M?>Xw?%2keffm#Foa`A6F3q9^<
zg%+vO?c-PG40NF4Q;inYIA5+k;{0TfG+r}yk>1MIOw7$~W8+v(0o5(P;T7tVX6Nma
zOpI&;_g>E}*nE*&5jydlMvjdAy&gBkkA?MalXfrcTOxwqP*`21edp&YD$4GAS=pPz
z7k_8k^qF@}#NpE9>?Vozl~*^|dQ!O@xG1(&&g3qg5?;brBl45O_+Uq^<EI%3Nph=&
zjU1|zCR%c2U2LRb#CtRr*OPWhleVqCc5RtEq*oo!{??gVZxj3bQl;PTP-A|Ogw>N;
z%_^rr)bH(Q0l5za*?B>}H1Ccl9o|a3gYn%$Qe8>1$MkK(3AC0ujS4}t78m8n;yFme
z{O_r9CRfi5-+U$bZ0fM-9;d8<goruGZT_!6IP@PhbEYmOwLf6cJjcB-k%KEKE>kSA
zEIz(zjli4~&%iy`-xnjTx;U!q*`vd@;Y&+yNO3Xq?7%!^OUu-ayC*!(-#hK{;8ob`
z)=3Q&x46I(?cRJ_=BzjV54nn3<#vfl-6(vtb&bklk)X(B@3iiw!v>pbd+O#Ej#clU
z9iQ%fetk(hR^GrMv0<h^R<U_g|G+?ae7w4{GI>-~6jX{dEG#2~FWyAcU%tEZ?<J7j
zW8IXS#;nLUmT)lSl0wn2^VEenIpeJ5JuMQpqF>BcLtca)q~6%%X&ap9pU!H`*EcrA
zyldC}rjMnELSAgx9&|K4j{F?o|Lc;F)@oA5cWgR6Y>__gAvl@yJ$Z?)Ky9q0d4udf
zA3DlMc$Vk)4ZJuu&XpaY+os;8qsZB|WB>bp7ZF}|-#LDsP-1~}OMFvnp5pl7R_J<e
zp~Jc={;f=<oeeqrd(yw|Z_|@D<CwN5mvct4_S0Q1+C1pwEXvRBn@jfB?_UgDx2K}J
z!oRrv@&)?HO=2r7ez&GgOytOHcr@9_*|89uC7AR(LiD;0byV1TZV-+m^(h+Y*(!HK
zI&7UX)(1_s&81ClOYSC5UlmXV_zZV>C5i8(R3T$ukf-3lkL5N8e_ltrN*?1$8d#cb
zF%@LJY)&KDn3+M&enjT?GQZ(%E=?8RNvbH;s>8IT|HZT9y`pULq@kf4*?zX)pW>1p
zl?U1C(pvk*79DD3@0d<+eOf7|NWA*B-w(ofR=bUE(_<QQmu6p9E`EI~<K_8;_?To|
zq3g=!RXJ%n!^<1=uO7&3xm9|p*h17*f-a}w*r-{JJl{{}y;M#?!=G##Cw7`0v*huJ
z@3@|py?sro40FY2frKR9m#MQEU6%j8-}mPW&QoxRmDki5gGZWa3JMBpL@Oq^Ys^?Q
z#?;E{=m|Qk=HXLc{^K34J*2T8=X>WQ9aLSv_VC$C!yU$NeD{cKahr0AzHczvJzREf
z)BI}*{|_IICXZBLO)-3`so|25i4P0gDkLl%aN`D>ghXqDzBBP%)RK4a-TTR0hIhlU
zeR<EMsI%S=q#SHNkhZVvM1|}3X^A00w|TY&`LXp69+X5c+Sxm+Z!r~g5f!Blx2u$L
zTRv#c?s;|q#>Vbf?#=^SzN|^CyHWSOt?1PKVm(1{`~%@-n*Z^-S;6k><J-xr6fM)`
zX=^*i>HXe66TB)a^f~mOSN-<2(*4-4J?2K-^UKW(%ogtSbk8i$O-Sa>oF)tYX<>oY
zEBDtLJJGPE?Q~*qj72)-TI<r)!`1RaIk#!#CV%fiM{<_O-VLm-i>1tNsvER!kYN+8
zNYuyTeEruV7tAXD5dSW&$X=jgf&Joqk>2K+i`b*OFaLh|!qKUnb91g57tCB)Xvmui
zD0;uS5)aWh$?u0i_Yt?o+*Y^gD|&;k_?SGz+vn(gxp0y2H)#I)8;y<|q>EUo+)Z3l
z8%ka!>$eKX3g}Y%(iEyluf2}vP}k0Iy_*ZetNSkssF=vb3MqH<|Jo)K*8TMn-d(!J
zH~(TJ$LrDs(NV|TnRJ?i@5687JDC0c4s+K&P|VFOY7~5)X%!$#TaZ$nI~&!eM8;md
z``1R0;LyKMuVa1fXG2#O;k8yCWuj%cKx7+#zx;V4v+L6#az9rc1S*`jr)h2Q@Q%BQ
zXYiEj?`QC)+K6AsnAgH`c9VCVb;oLPvvXV!@pHA`KUbk6bzELsI4`c1Z&7hnhg|Fp
zseXynj%XUWtLuMXfmD<K`y}#Fl&6(5X<As{wl>%0Vw(SM8!Dbq$@hjr`a)5XEPiK&
zW2&@x=_@a1Cd=C#`g6qoYkxiTJ=o2=dy@5m`5{uTt#Q8n`C=M9$=;=Ai}BVHx)NoQ
z<xL@((USt{DSbbwS2lX(6s<D%8YoWZ$3C;O{x)mI6WY#!=K^}rR$VbsQOye%hKp~!
ziEpuZoR`O_aAJINGWF!S|5(175&UvDS8mq6jQnx4Rk1_vWT$81oWIXfnhj6<!Ln0t
zf4!@xX~U<{)s@S8)OBri)7$d?dLUJ_6}3txCMWUeCnqKOR#vKl?18Xo#$HRO%0e`;
zVGy2T%?|(T&;H{))PCH}=I7v)nBGF})x&VB|C7wuNJr`uSnC%|R+vwc>&jG{RTaH?
z99E?`+p6p7YENzaoUcGf!PbEaa$B{wNR?n~6_ri>{rynyZ-`Y>1f|Kt!-G*wd6y2R
z8;b1MzauD)s$`gPGclIgZ9>cJ|2~sr)28_5dSnH&nsumSZ;U?n{K{~kGt*|Ctt!r7
zZ!b2Vp!uTw<r19;_qUTdOBd4HUJGqB9&Ios)l^U*g$hQ3)opxjX=$leYVfSY@U)AN
zkWlXQmkW6VajqcgZ)N(?qiS$dJS*%rZ@}%I>Dtm)rvL3qvA|p6SaS1w$o-sm=|1Jg
zoLQ}$mA8(c%=ap@ME9+{y>D1cs%dJ<L*yBc70m9$<f4nt{dWnF1G+~7*`QNMC@hQ%
z45V-zZ7+vF>SJb&bcJP3#|QkWa{hd@@B~rtyc+9s#Is&&{c%Qun?6mK%D`&sS3#ur
z^4`2#*BPCz!U*@|XZ*Pxy4i1Bi=QcV>fwzY9Yw`D>}i2p?1yHxuutmx<;*Bdc)BLD
zI$wkMv<8fFZ>Av*T+5TsU-WwFH3+<Q$zFe|$0E0zk_;6QHnS@8;UT@M&gnN<y|hnb
zYA)KkUMUI``M%B+;R(z66n&Usig2YG{G;ydJg?`^Kz!QNM?0inGd%s$qBFd#_w9<_
zry_5n81SWuc6^-W?fGNj*0$@zCZiTv0%ALs1kdqzrnSYS@1o2<yrYuOHYFv+heZcx
zaBW&id^4wqrHrL3OVnnu<@G(U_A@5Z$i?m*RvZ5i95VN!&)i>*+eV4G>9K0>mA1~J
zKIu2}d&4d)kn9b7N5o3}_+bdDy}n8fua>*rj>~OwRj+C6b>yQi%BCgqrGBR;H17^j
zgp3)?&tzFh=F*au7E12(U{;y<W@|J-7dJn!&%Lwj&>@-KtA4C`yG}*gx_D1j=&pnT
z6D5X(zdggO?K+Z$S;#vTPAI9W_Q5p3Auit1BEJbG!q9Z5q=}^c;0UjF?V0u3$FrM0
zXxv*CO6uxwo%5xUE`O>uKUB*f!QiIU9k5I_oTeIAS&(NJb<j;xB9`iAxm@2dvYRtw
z4TZZ^?6odm5Zq3gM%H0;Ux%$=arAY&Z3W*9F}~{?VQXtDS~-B|t)+2)8Di%UL!#g=
z*DbgaB9DL4G)Byf8T%d2=+G21d~SYetK8gkH9H2@NUNS{7S<EzoZc0-n~e8<o2tk&
z{#11<V5gO?)&6r@b^|-2&%|D$a(`W0_fh%Ft2F(Uw#nF?Mf=1H4oi3}9W*F&^bAc0
zH#aq9ALllqyk@7{xU7!Hypb{WJ}f8`mC+i#51D%3+jPyY(>xT2mN>6<dW!VQ*wUTW
z?4yelFTC{VFV}Q0hNp3f+TSRtxxX*?*xBjH5J|n&sJw~+Dt>D*Tx%>YMTGq6y)GCf
zzGj^3Xhu4#sKs{U>WleO53p>zGv94RVdX4A!S3sKN-VZJHI{X9G;aD;jKoNV|8)hM
zroNb5sbMp@B_GM{2`&c<4u7hw>`Tq*?5RF9)>kmwnV6j&5o48KURe0_X&}Zn{`Kko
zJ)b1+#<zH17`->*if)BWg_yyK=QI7im$v4K&0bDZj}5M~{u%aGPsF;yJV(PbH*P5Q
z^YRWEcYTS;uDFnG!;i$ykS8-J5sy8b<yj1}&>?<(`Yi2bIuU+ZUUhdS3AYCqD)-t$
zZaQY3Z&@SeEt+{{`r0~|HmKMR2ublU#i}`#yGI?W{Nduj(6!Q(Bf?@ibe4G_aJNsL
z*XO<x(t7Nc#8@ZzT6X^)meJPqxv7a5>h8};MZEmCb9}X*e++W_((EwKKChMI$yBjP
zI_b^h`ofFp4g0x_cHo`Dc8Wb#UlhuUYM%e3R=7NN#Wck#Lx5U+GZzP^?~pb_QJB4l
zO`qjOA!<z*7m2~aL8%C8Osj(lqH~)(E<4RoLkr2C^x`xbxycjiio1PlpJb;|bqaKT
zj5#Fz?MQ>^;>2MYPpeq#ZBFWix3}CbS$LJ67Qvrg^d^?Cs7=oN_%rwU(EakcOOcV`
z4o>uM6=FoM+S!n(afi0Hwvtg%IWE=^@ACAsmj1rLK;66h6y?YwQ!Fj}Vmnq16}ksR
z9PM@c8Mo4XV4+Pnwy9?JBk`X#)ny4{p?jnC_RBy{y-u5z?#|e)RsE|r;<SZgYYXB#
z3zseqkB-qRcj_>E(^4cMW@jQie#zH!xyf^nv~;1mjNQ_l&B{b%(RjUzfU@EtynpKh
zZfiH%A8tFT+}8|9Z9d+oC75-1Sh=Q@%eVH{?rAP(gEB=ot%+^1m&4uXKYrA27w+f$
zcKM=g=>7-li)QIpjN4eVGe)S}zMFi1ArMk^!|01=<t{827oWni8pd0GI~Bs{19w}?
zc~2o$3GG~saE)XM1Xl#o4od72?6VjWNTP7!NqTzn!-v-}_-7np!!I0$&k(vh6@h}j
zTg=2xUXx*8TzEJ8-IL3az4`B->DL<we&f9APV^HuWO<~WLvtM6KSgfLPJGZDY5acA
zq)&U^MJax2pF-pP4KdlmmKM$)n@9!dYCpFd=}PmuZqJO1R%o>}{XWHTrN`RiHi^l@
zgX_5Hl;FZ4MlHF`b^8-@FLYNIn(Q4MroRU!a8n>A<07#wLYNPaOTt($6IP(y6SX$e
z=1B(brEr68gK_`HL;CgVdM1vu6E_O0B)i5euhT?dKK<Oy?yA^o&dB<iFU+=DPV@Hy
zc*|oe`nH(54=HV|wS9WMs;I3pIMPYaY@~4Ej^G~ebLv&QjI55u&yoiJzJi+J8wzx4
z@Q8oHKgY0p5LVqcZ|-9z<r*lGl#d@bLYf5$$<&B#JT6zlG2=k}Ce{Z(_ynE0g5}0F
zK6;S7^dw;~klgIv=0AG#1X=fVekG?g&tgPVPI|v}hs~m`Oo2C3!)4nmqgA(p7+VIG
z55${%Yg=83h)w_TzTGNYfYqjjEbZz7MOeDZ=vjSx=~TL-0|yIkYJ)ig^+za2t2?uZ
z-HS1B+g@oO?IQoD4#C5hGW92V1y`uX!)4Y{uy07t%MALgpgTTOtuEei{)+BSi_LvA
z&!6QX5@YkGn?sW;J3>TW4i<@KEPn3LlHi-^PfXih`aJpa{)M5s_58P9ecEGLNR;r$
z1+(PJnX>mConEZIkl@pom;KJ<{WdmTeqS0N`=@ykIZhs*hNN`sTR(Rw@Qd1$byegA
z@1uRGe2dk)&g4hK%Fw={mZ`Smbo>JL_mUhcf9$VxF{4ks9AxW4b)KD6Q|1kle3z!v
zJ&oYXUBV-S1E{Nk9UXx6^~Z_X#y4jQ*RgbX7ME_Ph?*^auc-G?>-RIWJ~?FKLvWUx
z<_zCu^Vw~2ec!jV$G8fMJ+2~ocFEJeU(<}b@#Uac47W=rS!sR8NBtj^22s<EyhnAu
z%(hLq0VrCgVP#eK@R0U|Qc#K|5a0Felg`V-M{_(6aChjQB4Z_`WzE{A=zV+VCUvp|
z%D{&&dQEsLa?*`XDkPNT^X#tA6?5VjF6(>H)UqQw>iJ`xnV#?VgQkV^(_(Z*CvROE
z;lK5vhN%YE^tRxh;uLX{D7>fjaB9xFaZCukDoTTGq1xa;iT43KZ7$Dx^L-h!+rEG3
zT<0=>m&bQI^UcqA&M35W#@Y8IQ?*47J4mE4MwSsrJWW^8vxelE`#r-0g^%qWcm^C+
zINfC>B3H}$-y4;Q?{kaqc8H(h<Ksh8{4Ge`PiSZyc6XObFPPb(62Uu|VTol;94#<}
za!yZA8yXq?Y`3c+Eb6lxabM-MC5H5CbQ8uEOr%>2E{<*NWoT=)FY9;Vmj(uhvvK~#
z+`i7{pIgdynE$9)zjUiT%w~_1dS1YL_T_zsPn}LrPG{<#T=8(8m18mNyj|X3^yYp7
zqkQbP!kVA?>jpuKOHNh_b8vEo#l}`)_Yue)fmxN%YKBP7Y$weApp)CL_689ldk8AX
z7ce2ti4!^0j>}t)Mfl{Ux;pFKNmX!~k*5)DH|Qp3f0bC68nEqp{ABg0r)F2Dh3-y9
zx(_|~&GQU;9FCCs&zi@VWwZ1S8y9_hTek5>h5ZJWb557{PcjGxFtYZ(nsdLaLXm{5
z{PCEsC6s-l)(canot~@i@D>;eSb2>5unIyczINo0v~=9ikXcVp4`Mbq=H(TvI;1~%
z;N{fm><`KA&-b+IYpiReW<#T*%4<AkgfaQbqRSBlBr!O=V00j|XlW0A-0pR08#a!u
zf$L7|Hn-Zdt~A?dpW317vAKS9oxuyPhiD!v>-@ss<n_`@b9XBF=T#KCU45@H8t1k<
z$52Q4g{NN8%(;TB=$h3j@ol=Nnj;67rwqGdsw%mRx87}^{nFLbgDUTCM1(Dd2peRb
zk3z~7yd&=|vX37nrdY!>Y+`BIkLh_VwJYn_t-Epa_0*n^ARi3`w_pA0jq8Kdt~|Jx
z=1T=UieY1B6tDkMYJhZr^??eg3O+@(kxR@uEm5toHbxvwQ_1g~ajSbGUjO(4SvOtj
zXaB42i{}duzMy<ozkFC@;l+Mp2R^{#JU6%~o$~Y{_bIFAhQ0Mc%=1Gx-1CaN4p+O2
zS1x%92QY6NtfV91=MMFl$&BB^$XE_RZQY>#W|pC=tG&m?I^IKYd|%3f8v1(9J$tT?
zTbETtI6FJ9K~!<;rldlln5uhKmwD+op+yM}rn+@>_XhbfE|=rSDWM8>)N;hs?KK46
z)$r(0*o{qxRtv@t`~j%dOS{u-w1w2n4=faT7GJ5^cf|gFhQOJnYcC#mUOzCP-*$KR
zg*DYoXXlu++|*2BqeC(ua$BUemM|ScM0$phze9tfkxfls%st6nl(B05mohHB)Dn2X
zRpx%?`7^zSE21_QllvEKiw?`!uI%wQm5Dt%N7m+a@yfjP;LvPsR9W#LX+5HHt1uJ|
z0jU=0%dNDuwBjC1xtabW3HkZa2;19PQNwo#qqmA?=kcIsAew4%m^d;SENIpeHHNr_
zXW@qrAEak9843U|h=_?La#MJC=*%AMcwq8Bn%!>)Jse!gc~<v%pB_s*l+KqX&K*4S
zbGA-&M(vIl_l0Dx`OWld4<c&FQ&0BVh@Pvoc-~q%R8M(I^i*3Ulf6rtYV`YSQ_mQM
z-+wv(8pNpj;wif8yLFlMn<igBY3b;wEEf0}vj1k8;QZ}!UoKyRcYO|ByS0~hLX06{
zsjC)JZI-o_*{$0(7h^1rA3p3wd_{<KnryJ-Mur#n$;cGxhL=cB)ykvAt<`UV0VWS^
z^lx-8zia;utIL^;=<rXSx??8I+oAAp7-RH7S;qO=({8>Vv#fRTb02Iz*OrTLta?3o
z{+fI<*+WmKrA;=bX7l%JB@VC*L{vL=3befKa`HTSTxIr1ees9GRuyjo$Bw@V&V8}s
zUUu?1#iDd`Sq`EePF_#`QL!w)9JTb-kW)r7ib~#p?*uFN*&_en=tDzdjEL!0qDiKf
zn$ieyzyc(81SB1ZyEgBHLk(@@kBm2oi6w=dpAl-^+Dl(zhxK_hv95o=No=v++ZrI5
zA&<`3o^{=67Ep82CfB@uZP2f>xJ9D=fMX5UH8twqZzV}(8Sm8+o}~r9@L~%o@|Szv
zI3b?k5GP%IfY0Gg!Q{y^4DPZjXJ=Vk4diysuOu;P-IIzLe;evC(qNXMnV)~>O5CDf
zbkAg~ry_~qbX|(7tHlo46SCQg!e+;HJmc~vr0l;*$Lg?2VGeV<+hmpG+*hA=n=+O)
zMC?4#^>;0O6T5Tw?oSNalfXCY>FsqbxSO8e>PRlaE_<042uFJ3?<)Ix+Gutj$&t6d
zp4S7Y<>$EDgaq=$bjcEQ{HvLJ(Ki0H85FyhO20T!cY?e<=1^oz{pFsqrXqoXGnsdL
zoC4>+HFa4(ezPcE{@@AQV=3vNH~y1kx9*sC#`R3C8}wtc(!&9<)W;>$efO-++OKJ^
zN99h?LDA*h8zcr<Lj+b8I~SKfcJkWB#=hDo`p{9$OviB?-?2fxirOMS`mal^9xbva
z@Y?8m&Z+C3N1U$mNjzF)H{NrJ_sf0%jK>}8R}!+X8_Vc^p4dq-5(Wsj-TnSHg@p0<
z9-YneTe?osNj$GmR_cx`7u#=VPvsK3^G=}{*^7I;bgKpTs#de27JLRe;ux4J8_OOG
z4Jw9{k!4ElvR#qRvW}a#58vR0)bALWbS9A<XNS${`I&v?<>eQhIvjrCRv(FYxVK{-
zvxjt?`?oDhDq;5Zo0(Q~_{FliSbl84lhT!-?;~QmUGjkRi$VTBds)0yz24xi7enji
zW|p@V<rh#rlkl%f;+xhTWR`Aoyr6Bz_4TTG*7;8P1Z@Jje;u4zYGzcCQSf}Pw)%Y3
z-bDoHKMuM77SFg+2n*$5ckSitjtzE2vGg;k&5GSOuZysb6i%>6iro9LF;n?97p1|A
z+YxE>=gls-EWM$x7RK9Kt0^gw<#ag4sLU*5rPSBf>Wv-Afx9V~B{S==Ti<O(q-p3O
zV}t;)Angl_j^6Phn56<<XEh_Eey;(&9k=W#cOE-->|<r+9ZpKM2ah+3b{zlnq=z5h
z(W;gxu(EGK%JXQGV|`)j!&yb;<((1t6>G~3w@~;#W!u>Ox{uk8`Yh`J6@ZGn9wlwB
zrTa~KosVzbeAMb#Ou2Trm0n|LT*qyJ(supF<Es=c6R-J1Scmy<z4P<mKN4Wt*B<G!
z|9gGTfN8hn<RB;I02n=lsH&lc`s7S&6pH}Zq_ty<PDP6>r%!jBUWRK)3vLv>*Rf;m
zYhADiuMVXoU!ANHOG!`X+PCj!i1flozMMJjKoL`GDs`C`gUWy3F4OwjT$D9yKXtCN
zQ=HvUEYH5kZr>s!#~`$M`S46?y`Ab+8S%3Al5J&q2?bF^i4&r|np9X&UMMLk=vyk@
zG*J-Hw1s7B%h+;stLl%r3Mx^7HdPge*=-3oPHd@kv*i?5u^r#^y{pNZ@4m5gTN2X1
zyt(48Uc)4U7;NA>hqo!nCO7D3Xt~S}7N$IZ{-ePW_E4g5L`g$=6?^~<|6{G6GAn!h
z(j!ai1elvjFP8wkTw?h;u)wnmSbz6b1IjC-bH1}PRu4+r-Oa7!u5NZZo)^$2l)kIE
zX!ZD3iI_tzKPRX}SFMCCliPk&_}^lDN7RJRUuOc9QY)9u4Q|+!1Vc69fg8>3r9x`f
zP-BHQ0YJTPq}X%iYtHcOk<Vi?SFTfq4YX1uZaM3vHjqJcou*aO@#(exwx*X>U1xX)
z4!APPhy<|qRsSE#-ZHA{ENmY(>5}e{lt#LxMOswy(A|x+NJ=Xp4FUoZ(s?KW>F#dn
z?uK_CoN;EJ=UM-?-Vd|p!_4Bh&yG8<>$(klPEA3$q5Z>w!%1;h@2<v;GsBkSG}Djt
zRw?^478c{i6Phn48@*-L^V0Gx5kfbY_M{$%O37Z=F2+0R%3p)0=S)-6JOA`<IYyiF
z&*;ttS<+cNaUjNmD;;Fb_(7Z=h$EW;<aV1?<Zzr(e?O^KoiJE<AXps3?d&Pq(2p75
zsEoy4WxOx<E41rb)?lh?UM%AX@@96{G1RHNzA%ZzYeGay?8LHxZH=w#vRU?}wSt6o
zpS}{Ks_gxGw-?AOaSF~w!C_%WKxndO=KE+Qvr|u&Ul{ZKjOeN1<N)=B!54V^i*b+#
zG4-NzAH(~eOlxCzHBf$&yA)b3bz^%V<^9lRU?u&}`ksZAjGN8pc1-6nYxK^aV;wKK
zCM7dS$r*^8zowE3z4Ha!3hlkp(ejcN7B@PV?+=t^PVf#^LriD{g+BCihe&3PD$Vwt
z$UEb8OWeO*oEr!l->xJ%zuj$s@84K@xxhQn+;dji*KhczNv$>A++!x`Y=e5<h}V}g
zwOmQB3pbJ|#Y#OBSe4pNeU`l>h&@3Ky5EN@JQYr52cCP9*L4>uiDqlp`Z5u0?=;x+
ze_db|&<Y6{J+m!Mw9uX0sVLg$t!6EA#FN}pUWhvjjti+ZW#q$~!p-wL=*p@d6FeGH
zc5re6jB4!dx(h4G5Pa{3z5}fuU~~E1ObQ-DHWS5=Ng)4p2pu7t|10kSKDVz`P6VBf
z1`AFsw{u^)(~YiF2DGFrhirugCqVq*(b3V!a$AZHM+%$kksd8!bwhh3f|r0l*BBqh
zUF0%u<aBLFyBxNy@l#TstR0pPx<iU(kkSue)@7X83BUx60V@^6u`g9s$2Pcpw)AL0
z5|*)k3@eJY+p#)3+dO7P0#yZGVgJ4d;eMcGl-vQus;Rr89Qo`S+CBiO2_eMnt*zp=
zw?AKcaC(MrG8-yIIDVLtFm|<W#R!?6g-Aizf*6wP-ha*gq^X6Ecw+DB?J(<cQUrud
zVCB~}*eC0rDb2OT6mFc@oa(naDw(pLu|2Ow4rxdZlt)Na@@qXQa=%dLBAxmmdXkth
zj<~4$i9ej7RbH}yXl#-6C}87kxnfrF(Dl(9W#>VEwvtxXjcm1$cuupvJ>(-$jRnKu
zXgseEQusNjFa)LXsv8DHrDD7X{^|v1mj@?RkxbV)vtnOAf_&FErrY?oQMfD+^oggs
zTJGeb(1B)L%AZSIwK!$CuD6()R8w@IfBcHfW^6f#Ewa)LyfUh<cXZe^3j6B$KbxJ5
z7N6B~DPNxGVaqu8N4twXWlv6Q2sACvMBBbb%lds$K-cCG4$ji%w5#Bn-io{W>gv-!
z*p)KJqQQ!k$8T>o9+15y@i2B?p>4)^ei18C8dgsx<GY27<gtpf)Nu)V<iBHt3BJj*
zQg`;0S5`}^2c{Qx=`%k#_3f$zx9Bk`{qLfzUcA1lb9K7X#S0MP@r9KLKIO~k4d_P(
zc7Gt*txFR5{oF4qye_z5)$r~58&6R&_+#=!TxmT1mH+NoW-z4N3dN7*%Vhn%q_PVZ
z#}{ojdE@AM-IYM)ljEZgNozDO!n^_S^KX=;7<RU=K6!0k(>iX+9WSL`H!yZV{el0$
z#KPpAyGo(wYlg+T`zIYmvl&@FLz6G#_I{!G8=@0w-jh%Jy-{G8tqunv!Ebe0J)pED
z2pwB<;3M_Av^7TGdi^yx$=>AOW>a9KSsuP6Cw!N|^--9|R^?M>JQ~3;X2ZL1J|C}p
z1-)i?n7b4JprntPw>7Z<x`txCbs6h?l9x3-WD07B9P!mzQ*D=dxrlq{guB-Yn*t4^
zy`J55=*QzRYlnPKagA+Yw%nwpPo#MVNu8(Hy*zjtOF=;QW(QB(y=c_(woM+rVIiu0
zsG{d|^Qita<#eZ`E50+otSbs8^M+>~Xe1}<Xv^V%s?Ji%QbG~kboZl{=8#|IQ4F!d
zYlQFb!E51@OuB{?q+G?{PjL{g|H{7F24x8D^s?pce`4nxZX@FTN=a#c69Q_?HZlH9
zg%=O$JaNQS>`(UJA;j($u<q$1#B9rnBCIH3`@N@Zt||9m(x5-#$xDcjZ3m^Cc9LXC
z2!zDb-`m6S`*~&%>_bf(pxOh==~>#B_i0&-+hQqvIz&u@fsa&5|Am(Yy3aTg-ixz8
zdS;ta(dTOFC*qqV(-RJ{P}EL*>IGEjeQiifh8v+*ld#&+5@$5b!iSl+YPWovssi#=
zs3>`2aj-o6+pk>Xy0rCN5cT=gdw)1lFlgyD#^9y5D>Oww-S5e&0agelIRp9ldm)Y_
zXEpICwN@zahHj6q0yQ5Et`FYq0W&~a!K(EPGe0!=h33VTou#19>hD-3fNH%QtXhBH
z3+}lRHrmwzhPLnprxZ6?8OsUsq5i=A$k@FS0$+4=vR7!LlW-97P*Op{S}o85<dsbS
z2x<=6c9ObD@~x?20dV}KDv>S`a0<xw_fVq#PLkGaOOqtEFI5iRu0!&-zIqhtAv`0v
z5oF{=7nA*LIR)j5Sz$RKN3^C{QJozw<19`yA;~>)m)4gG_HZ#!#CJB(?tGtT9*BZ;
z-&Kokz0>v$wx16fnE}Ywm1@%`>Zb553<kn!*p7;_eOvsFp<ZQ!jV{Z|2jmdjW}H<A
zzC+jACiD5{%OZ9{OkIeqf9!>E^Zclyyv><5VveRy&w#GB6=FyRlOf{P;&uZezP^U4
z#zy(2At}{-_b=k=(nYx}HAuNP3z~IS=fD*;mk@{l!!;E)V_D|Ap4X}q&~KI-SJnN^
zVI_L6znzx8pRS+nj$2?qUTVRhBsejQIC_RF!Y1M{AZ={9;_SSIQ)-j!GAQtzPeLh5
z#@fjiP<1#>O-+BcwD3{V$nkTd4*-3l_O`ZN2Od~YURgzDW%yrPYOQEX_r~G%jd=aV
z!$YZh8%>-@Kf{G|x<y<c?RWOATktAj>7P#&O=1%D@!q)alNaoq#)bwsrS)Aovg?oG
zZ^yZ_tI#O4*c_v8#tcl_maFGQ)ob*?jLIPObjA8Z@dptXHq2Gwzc8^mcf*{`U`Az_
zH!3O$)Yim<f`j3&NG6~3LmY=+*PJaUxPzjsbIZ2-`!1hf#OkqFI)6fmtFR^z6Bab(
z3qQNMK6tZA?m`M`XVZZUyVXB&yquT*K6dV0y`_YvYPC8Krs}Y0{=91UE^*HY{%~o^
zm+%f1{Z)$=eFS3{;kE7u8`j^ZM?IRK(9s8)hAU9+d=$7xc@I7*c)|oY=xmpWM4Lx1
zK;4U-gT${9Pq&w$Z@jN|>YsY_twYXaF8L7N$+g#V9L}TZJXJTPU_IAT8V4&$>+4IR
znW2D&Z2$gauA5P#b@buM82DB=_NxzTvMx4AcXb5|{E_>$XIw&Iedcs54c*Zl-5WDS
z#_7%`DNys)ZM-V43IUk251<XI2047_HG4#mrBNOHS@DJ(*PwU#0wgr5szYB|Se@g?
zkJg#%u6nIag(d`rHB2<=2EDkF+R<fOgnxP|>Lb_+W#K#@h!sJgnCdd~zuE!O^!oR(
z4gX$W>F|azjb|)g$XKF0quI;qGZSZsJKJgs<|@@5E*7g8u=?XcNj?Q5`CCQ(*a^AK
z^GRl|n-in>FwXIqfN%t3U_4m&u0P=W)SNi6r)tSxe0LdzINO4Mj!ZR@<X46*k^C?k
z({E!e%ZdR`=iWW<8T1yGavVupWdYn|4AE+|M4`rwN#TXTeQP$2>Vh}4QsFw%+nQF-
z6TJIbD+^*E-yxfqo$|00r?Y+AX)cvgH16z|EX}MiLH(Vxrf?gQtRx74Du4oEvs(3_
zKped3ZYeA6k3W%oPqQvBB&hDRceQionXy$#fy%w~BKcF5JS@)#sfgu%@~7^$D%VfZ
zKkXXT*@Qg_YV6TBgoPMfDqFUy+@^2oPh{&p5J-=gSAWPuqS^Q%<ONG^j#eNR7gt;p
z^3Gl@sM4g3L$sNnY&`C<HR&lH2K9Ob4E(koN%jE3@dB?pI0D?Mf0?tKKm{dM;@RhK
z*R&A?uA-ahmBo=Pvu|Fw4Y=<j`^$eBbV*?VOTviBT(a-dD=S=EC4Cc<XY2(z88)kx
zZw>i4&L~?SzsL6B&d~5M>f6MgO!*gDOrU~)(x)~nsGwwEM}<X}&^D&gs@MF&-ku$*
zp0pfhuMNB1nJy7E2MBJdFj&mN!PWt}#6S4YaSO?;L6@V%JAY*wQj6>r>60gD{*A(E
zxlFdIh9r)HAciNm<!ay~@u}{-c}!9H#0yx7V_4G4l&nvZDKEr$6<+~%Wv_+sV*ifM
zM;C&UO8W)WkU(OtRojV;i6^J}clobNeR^898|k<xKNBeQkRKhtI)s}PkX9Gyxk|mo
zs*3v_5I(vE;>E$Y^Zs+7^T(&^IjO7Ebm#1)&b<f)`1gu3XMJ?{^;gpeS0{&pd}x6S
zur*cZZC#&;S1r0osZl=VMcta7UU=-&SV_5}j;l};_HAxgBz({n8qIW5?YG5Zm6e;(
zStr0u8wP6)9*w+mI8W}bFSSdAe}Q~<F(d%P7sIU$F>7!`_nqf1FHXb)^xIt{*byrp
zMYE#$;N9q9i@t673;bnOuo2Fc_^X>FWmjZRlCNv}VdrjODy+9_)n4<7d~t3C&y07x
zae3C#sI`+HBr{$;)W2w8ar4)y#K(}2e)K#U&x+N*_l$*Nh@Rr+J_JxZh7edR#SDw3
z(4HU{s*8Ly#`VLvuLv^XR^d~!J8z~AQof?e6&En%3;o=f9NlmBwp7Idz!Z-${LjC7
zmg1uXE)V@hTKgPoK3LyeXgJjtBZJbz{d3B!aD$P-lIL|?YDko+^mY#cj&<sL31ZL<
zItZQ!8K5y6hpgL98VTFJopV!o{&$^x0p7LVLd|~0tG@H5=i*5MJrc~^@`ruqv)~6c
zv6JN<YG(teGSX-N9Jsox0_*YL=?GIpWWKE4h;qquD7`fJ){9%XUNr}?|1`_9z1+TG
z4=>@nk67ombr+g2ggWf^5Ggn^HeWp?LbIx<*YeWgx7YRvNk;``*~>#XtLI4#AoXEq
z=IVd4I6{)6KWNRZ1j|C~Pau-|%OSepJNS-O?mdW(kuYekrnJ)BDR<$)iOuSL#hz+v
zmo}c*Q>?a1yh|}b+%yc)gr0g=hn}hhx-tB=_nYRG_5-Lt{aSepYuGP(3PD40?BJLb
zTjqqxZPALj71l7-n?T44q4dqYMeXM6tiAVOu<%prW^Q%-pfZ`vLTI19Rn7;(!{Tt6
zdfQ4@hq@hwnq+umMk)c;pHK9MqlR|73+hu1BoKqjs#yuWI^P-zat8ahBgzv<Avk}8
zEjclJs}!`m`epiDi`}Xy?hI`EN(+0BG2V7U^PH4vQ=+YnUeEKr0P|JnoM<)7l3o%g
zG4i!@_j-t}tsf*C4v3t;cQCqYW%M^h^~|TD5D-D4LT8JUjg{S>JJR{PZ*n$3WFB%G
zU|j_jl;byT<MnM_@bk%>_y)Y#Wd$ZO(6RA804bLjrraD0Iwt-G)L!t?)T9vh6a_&S
zYpR_E$)c^&GIF;*O%@0jCM{sW6Oi#28hhtBzbRQ8P2kz>zkBgCNlWTH%^~xqe(h&w
z>ph+$w=lx65?WIj=60^@K<<Ach+j<3h_L<D)Cd~wp%?reZD~FgY7V;jfa)7nFZx5e
zm1{baf}k{0=vnJG4GWd<3GZX?tAvvwTf1A>`qoP9u4gh|t1K@2Ea`MpD?C@p%8*Ea
zqhu`^%|>&*Z{1<{i{!e6I?qrSyH;r@!TR9zjqr(>H59&<X`!$W;b6imFXj*GS!?&J
z*<##%XGb)EZ3f6gXHs33C;*-ZZDeX{Y6Bx9pj{~fB*e0s_RaouDn>n3{|a33LVAaS
z>Ne#LLDFWvdX1d(9?h_;Th*S_Z@vTpV0c?du9NxXw+Tn17r$K*W6ktVuc$f>5{zJ5
z&ozB2_-1K;DH_ZD)TdKYZVo+Rrs|hxogg%TedMzcM1pU>`w`cb5mvPJ8?bJWJxoV7
z8wyv4Q0V&~@`qpVA9;1Ex6Kao0)Rh{C5SbAIe(aN=y4DVlK79Z<D-DFP-nl2hG5Bf
z6GdHSy5i~MO_zs!L{RRh{-Vnst2BZ^%ufkaN+G-d+0uNWR>n6Bvv07Ai%m!p(D2gw
zrV%I}vqot=Ezl7GgUL`o(B7nYtsQvIPFE*uLr$I*YyiNbp2tI2I`CTi^>_@?C8}(V
z*JE~1A)hv-kN0~_$^Y77L$sc$EEtO277@B`S-2uGR!<nU-HwK+@LoC`Ea|V1$V`Li
zZT(xy+~B%j04x;XsJ6GL8pR&K`(zM-<9srvH^qiif)-j}kxs`!Vt$X@UHt9IgP|Xm
zYAQ$g%70}hf(JOQ<-{eonaMsnE&J7M7M75}l-d)d-<C<-I?u@ALItyI(dDvd(?OHl
zokrG^_|uBFmXM?$Mh|GU@rOqj72A+#lhXYFDuL;;pkkFUz+$X>Z1FOH=IH!D4RP`9
z4t)LnA9}@w%RQV?`NfWLGTN~{mlZ4etc0#4&NmZR?pK?miDR|^P6u+24l(7}YwJP8
z(8#k1U+ak3O|T7hVXk8bDs=9T>X*0SKlWcVobp>(LKidN!rJmQoQ|dYN^9JC^ylxJ
z%36s>LPH7K(>8ghqJ$#*-pvVZ?Nm2E(z)3=2&QVzQ9RZnm=!odrA4mJqS-}1pxv1l
zfVEj7R9CuUsC+9TU`FT8ZT;z4`-aZ8Rirs8{`*fyVknWM-imRXiU{+X8MNpn;LKA#
zTV^&*2}-={pKDEwGG*+D6O$K3f*x3fR!7YQQC_??j+s7h`M&AqMW!u$!kHxlwVp)|
zM9^7R$b7m*JBSd3L?~_~`j!O-r>>K^tv?;Od^`PV3vu9E-jw3Oa%1XmlGNK>2+;Gx
zSRb%j|CO?&p{iCI_9-#|{K!E3j>b*iuFjhG-{!7`H|&cRRuczaXAoa*l0&*7$A+N4
zC3~^Pu}|7V$@;i(b`dF+8s=-<!?Q^`X8ZwiW&*R-G2Qwd2!6lu(iyS0xf=p*MD{nq
zo}4rm7(O(fUt_EDh>t{tO2J6?n3!26{+$+gp;oNNldv9M72=1@57-uGjaio(o;>h<
zh+?8iQ7Q?;j_;Uc`=`ZxS?%rf%yg^L#xR&d#v=1u<+!!j#F5Qi{yzMwYL#JIQY1Iz
zSVT{K&(u`dy&7KwPlIBXc#SQ!LgaWx2hQaCXbY<7DLrg^CY;S;w#<~y_;olPS<p$)
zK&m@(9|L=-Xczo9<!J|h=M(q#c)<-f*;PJHwnzzH`^v{IPbHh?>Vr^AdG6796(n*x
z=U3@C^HaEgggq?FV)ePcfbz!GvC*)Ng?(_DTBp(AT*{v#%oF40Mt4U`z;2T@+D>DR
zgTg8yDSjgpfl4v?1>vW(uk*neW;DOKPO_k<&W(*{z?D#>$_RXkLcoHPdiylBivw3G
z3nZ*=Rbe%relr*+iIn<`D-X--Jtp@sms%Q5E5nQJK<hjIB1ZW+#dRBj2Yos>M>E4R
z-S#1q9c_d5XXw%~q6#~|A-%U}IU*$K>Y_fkEcj!Iq}^&tz^cW1%^`XsEeINynNxy+
zyj$dOwk>aD!Hou>l)+e3H~C-x2aD>vz@;D^=+Z7P8(~W{^!8TB8-D+_-6eq1{rbU<
zSM(R3n`hPl!&pJsWJ=_QXZb{?&_Aq{DKFRF&E04IA07!^sgx3SkU3h36OgkdVQNfs
zz{B(Qyw*(Oh)Z~B#L8v%;Li8Z?ouri<NHIehQ-_WF*|OQ<W=-XGrZ>bTe?V^x>k$_
z`iACywI%kB-Z0&APWr~i-mZn7xBdU&x1jT(ONcn@VVzHVJ%cqdq1MJqk6ZP+Js+4)
zOg}gccp5PyYsTC2FP@kvzdGOKY2~HH%=86yfO$B79ubyc;zO+b`IaF9kL13xdSIj%
zf{~mqP2u5%1>0Q6+<e1PXjioDzRf6gdzZm8LsNz(m8+IQHENctD79}Yesjvi#eHu%
zWvcgK?d>=f!#)(a`#>s9$c3@&)5W{}LI5qqDL)G~bK=jJsUZZ#K&!4$d<R#!i(GA{
z)^S+lTl067;cZ2+GEN?&W-G1X>~U<L<8qtDcB0*VWl6(BbJ5Z3Rg3Mft4EKKv>3lQ
zr7V)rNvqI&Jb6yKxDqP0lT~jp=zr+9rZpbb@YlBfO}g17wal_)f(C27ABmjqM7<l~
zL@Rra_|wP*W<fI(6Z#xq_wxnSv!`x=D4nq@xm#}0SjUq45g^2UT3GF>W4E{&bV7>3
z<CEPqL*aTlpO5%UFtN1|v5DBTMTdj+X6x*ZU=WoxQ<$#}E$qdvJ7?lMU6X>|UZ)E>
zIXt>gVgUJt6o{a1F-sZ6+YfSsM)pK(dl4bVp>aRc5_vU0NBL=GwHiECn%tf;4#LT8
z^j1Jq+!ehWAmq&0<sU*Ix*cxcekOt@BKDrSGJGb8>PeXID$(u7zN)4!uuob#NY&YB
z;w9XVB=gyGewWg9$?S_?V~+*Rr&pJ1c+`pr0qB4@;dwKwUZ`sy7F0`CN({dG#+rNb
zrZnli=?HD(Q-K@}sDZT1u;SK=%w}CBX;a;ONsQPp1+$z(&HtnLl5BaM_NWBd4nGXN
z2zjm~-J@g{7wa9ko>H#gRnErEaZO&QAY~ed+KBiCLU3j}y$Nn0*QuaCMn9r;ljd?k
zUwOptspB_(Ch-YdO7t)kW}F;N_>lZq8k1GNl%%><v0*>m@d0k%pt!XW;G+Uw7Zq2f
z1xDk6tD)6`1CDBI01@)th~YwLN~!_*A;1_psNx9<#RK3#TODn}yWIwD>X^pof!DBj
zdS0o8ou3W61`U4no!*+(qhteyAn@n!tdwnIi=O5~%V}n2tG$Qa>VCb|4{d@X?&+%m
zB*jLH0&U;wPBH#OPifJHb@do%X%dDfa$5(Zy|j8k0o$=IQXhF1m3F^fY}kSLocx8~
zzw`K$?o73f4yr%Njm%;8z1E{9;|Z&DnPhm^vp`J11Wcpb6w>PHXmoV9{c<O=*+Ls{
z74L`K8an`R1eEHgLkOjgw#|^V=yY~wPxRI{uk{sm49Iy;mLe_`nU&g=m_tPn`nmVF
z#1Poth6a2oKRM%aH4(n=MRcF3mFFb3DD6ay`x*`8ZIw@$k(CkV`Q!P)>pvuVgPXso
zxWyLW*xpYGi<v;kLfa*Q1-+*#i`y|0r39{>RK4JOp_R$9;y!7+eq$2WF1qbB4g-bw
z4J_HQDJb8bRFC>$q8_>PSZ93^KOkgZM^O~vJ01V)hMdQfzWH03+opFxj<)<&)=;U3
zm<CP3aojim4pWx;*jY@{=IH^NdXB~>sL7LLS7d$yFBpJOmj>{CG49g>dROCB+91Fm
z$F?$MW)y|K>oZZ1qVnC<BgtgGuCiv&4XV?zJ_0d(6QzGK`34~@qh7@r73zI!G06rt
z>x+RQB5($E0(5+V(l>k`rr_;AJdZM__fzDDoz6DSXM_`6fNM;UeU^|#i7EQ_30Sc9
zu5P;uha->ts_R*-G-F3{_hJ9|s-s5&w+VSylF@O&gu)ro(yN_sPO5m^Y+*H0`)xIp
zSo#tDhHM~BlL4;(=Ume0<C9O9Vuomx6hGg^F&cr6Swjc1?5gXeZ!RDc5H3J?QW>5N
z?$J11y1?^mk4tOFoshX6db$qaeT@VqQjmv7O|JUx-m(DUTFkuDiBdP^zD=&InE)WZ
zbMYDqD9iP_xpCV-%Vu;T+ifVgOI`EycnYgIbVyQMB&l<L_rUR`szPsgu%9yewhJeA
zMUlx<Fj92ER;j4~Rw;gyID>3xEiyjYXE!z24;t-VIjVp_5D@LRaeB^=1@(XEYa_GF
zh-=Vo<Zx&c)1qs}U39YJ_T+8qJ7tM1;t}d!)Df-<^vc^wqKYOFGK+wT5CEQSpo}^1
z-KCp%1Kjft9~b#*A6?!{%^hb4tX7V!{O=#ogSd;KtH@y<#-gKLl?E^h2Xv?t;VE1t
zN0@&H91PSy?KLUq2C2S<2DU7q!0w$%kD{5m`5tma!7EV{zf1FDjL3H1c7uHfd{`Y@
zzetrep*v<qRe$P}n+h^iY$u)Nh99cG(f{O4!0^cF8eO)t9*Hx*XKsP0ipogVG=0$f
zv(2i4;}gaIa9o3Al(GHNurAbUPh{!@DzCsMoZDZWu1yKen*|_3AbW1Fl(6Z!UlkuH
z@bm8O-NoK;QTYz=B5U5#zot^e+WIh_^{_eb{l%~LVHZaKpK-@u?Ct+X9x+Q+oQq!j
zMDOWmsOMH`SDCiZa=Uf)O~^d>Nu(?E5&8M8m2yQ(n?<!R*yEURFaD2(Bb#rn>v%My
z3GwYRMWcp6<}fK2DtQgzN~9Dhe$F~w#OHcC$E(Y2YS*TGx?xE5tY2i8w^d$js}YX;
zx)BK=7!G|RQkL-lF!A$yQj3cE0rR4Va?|gBv-&<)X~Q-BP3qg9Ko9n|GusZjmxbKF
za{+(uu>**UYn6PgaONG4qlR|UQ97v=vnY4@t69ZE#n|xAIT9)KLawG%F5JHThZZlP
za3QZ!<k}nKUT$q4jtD6rO@Q@iVq;lnmLPNMXd^`jz5L?`=cIf@y}^`y;UPPQtV^j+
zP&!GS8d75Zq1XcA?tBez3#e<Fzw0;oX%fZz2(I&Q-mYC=6*pN4r#hVnmKll0k{-gl
zUoH`z+|aKZZ1~J<Etlcv0(odWUXqw)^#Olj@%{=)#%LU_+-Gs$;C|m=OEnjL%ZOZT
zY@bU+<M28U3I4_<;yoS`&uO+k@uT#|ZCAF;k=rTaimztlncM!zBQOAZrclN+%*Gf8
zt_E*sOUP=N#hp5Kul_&=@++(7YIp8Fovg-a<jq;nReNoc&{tNJ-dv{{5Z2i$YXGcg
zCas}<U$vE}%Db=@G!TUpUnxvx^DC|tS{-txx4Th=M<pot5or<yV2Dn`TAv$?G~dpN
zU(CK2+wrMtvh{cs|DEndHC7{*ASNhtxq(uMHpxUg@H!U!FE<OB`FP&{PC|yM#D78s
zJ`WmZJ$YO7E^RcJwaiJl%@T#}lZV2suTI!L=kdju0W~Cw(&tKZL-Lbb_TbGQ4~A{{
z1c<JmP+T$N^C22!I#c*YCYt3hO$%<Ql^A;zU_qHdOf|e{2jNR)csHzPcq4TIGblkU
z48$W6p`njY<~8j;|H8oEo6e&5!>EI?a7(`y4IFDKjcX{XY*+TMAhgVwRjYHDp{*{Z
z)Pt?Ez=CcYf}pLAuk-*sSU7f;MI>CKYEQ690AAx%3k@b=+4_=N+@L!>M$`iHF!}{V
z!SXC%u#V`Vd>sYi{1zXf&JDeWlEdc4PTr8n!f<(-$&@=tip70J5khmU%@=$Y3RG)X
zki)nV?NnnP#dN^}niRh2CEzF%C+vePSuFH-Cf(R7oO??!F-V{FpxeRDzkl(oTOP*3
z062+8A~h%i&pCm=rFrUtexU<jet4V?L(t25blv=$;O`iX&U8VdfWrriccE7rAb)ce
zn?S)e?4=O23hC4@ie-$d*Omui4e{A>U=uX96d#t)ZfrB&Yt+>K0?_X;Nr4)_v}Z?L
z;9A#vFyIgDCADLUEm(%)4s5?q9Z&wCgpjJnlw|3y3H|U|Lfd98M4#;`jTsNJ{jv>!
zjQGO)R|<R{iGSmC?MTb7H6wDcx4ezRhc9d`0Ae$?^Z0(|6ftRpR5=g<raGYpSdgrC
z%)E!2bSGKyTw-X!a9CUxo0u-wSUdDc$a@Vm4$MGLogsK+PkN1JLUtO$dUXf~<1T;z
zSC;hS@@KtYKf|!FYZRaD@i(hN8IPB|#qPx&vP8Cd(8aWUeIC;axSL$SNh_uwtB+L-
zyunTy+pLt&Y6VIYa+J%DK6%i#%smhHr2`C4Kt)X1ne50(bHq;KnJZ+b5Lm83giu0A
zgEKls+jB5MATW1YzKFH~Dxa{<9*w)#y%wFFBmrfFRA$)E!CjW0JP^;YZk!KqFtgJX
zc32o+391Wd7LE^_P!|o!uaA}h5fki5g2o#e_DLd0Mq-J<;pn!k62~a4BK5ha#gTZ8
zH}uqRem#0+?#u{BVtO#x=Ef8LvlDBH3simwVZjpZ6C~mr+>V)22-~`ajV2jiBe>S*
z(-@KcwNr;l3!vZv*Je>xxHl*N2IsrJ`LI@iqf*18t`r-b3S-FPXG92&#QfN2eb}z8
zt-s7O%JqQQSg=Nt#RA_hN8v7B*{T0X^j803*B5$Kp7!mK$t1@?bA=3U5qB&o?W4-O
zo+Gbp9MRKc<!;Bk@dN6eZAkALF31P6LZ0jE_7H;uTG>a0-0dPUI=<Ftnbe+=Kgu@?
za70wbYy-w6M1tV-VaF&gh3`f?Z79a}fD>WIY>}XfL-7yWq@FwJ1r?kc&y(R>$a{Z+
zbK%I<GX%fk4X$UyXn>QR611St_u&I}Zhc(jk`>k#RPc5<NKFkcIw!}EMj-%f2KX(Z
zu1|4|BES=E%0i0)0T6~2H3$Op4a@?X%q@FyUVFm5DOo(P)YMRlg5tjqaHWw148`FJ
z&OH#a<<YMjijL~)tH!biY_w=g7J7Z@)CZ7@oPr!WU}5%8I+gN*JRm0SbjqF_exMyn
z!@)eXRD?hwZVh{&<Jb(u7ZY!=x3p0qa$y@yQsc|?FRGE#lm)Q>U-$rI!>d0%f#uhq
zuCsJdgQh@G4i8q&ht^=_E=kQ|jfFL{Ej?faU<Nb3mJ@9QAibn#C|$mGD>Tiq4B{YA
z2*6^)#EkNxH`vj&sNGT|qYuTObv&N5muNC>vzGvzMAI#^mBj&T7|r!UfnR==kB{El
zkJmmn!IO91d%H?h8L&jRSS*cCa;w)&R+FXLF?4hQjuEzDdyxy%n86sLhkhUgLy_E&
z27flgS`^lTaHR~X>wkkCT7`J2>9r9AY|WN1q#2fKOm+I^tAuwNDjgGNhR8a19tZ@b
z*}R?Bh2<GHtrw{m%zTYf{*fTXh`ct$Y+!3(4hQUybJ*`V?;Jvc7cRt+c)jtgh$lb1
zz6*Ro`+-P5%+SnZF>|GwyQ`ug7Z=QrAgVlC^ar;Jv`L@1)&{=EL;g0cvQfyq)<Fde
z?JjHfR<C~1Loq~a!8xR{<l*u_8{S}(sNT=SZ9V$fKHZChO0WUMt1*NYpI=FX2%TEH
zzYh?6^2J)a`gs|<;<~%~v8JD<GW>}1Fdn<k+5$wguepFS1FNDoLa<=(P#4R;iW*#8
zd`4hXDq{!TEbMWj>rt6#iANtwHk>w>=Su7iKAY%6qR<3SaCbO0DUWf}Lv(bKMzeiO
zZIo4@QILe~->JCpuR>-!2dXOJ9>WC>EJVV`gSZG3HNjx>-Bk{3>23lnACC^Y5swmF
z>UM$a%5e@iX%0UB<p{p~zRgkP6tb0lPF2{+asCQ$joGHz_Nv^5;)KX{%dC@f;AJ>)
zI22yoIF-QsyYMDYgT;PX`!B&yt-yn&akp7Ih$8GzJ$y;#=;X9N=YzfvXq<h0ea`^9
z77TC@h=Dl8Wr<<+^bPA(JLVtC@$6HhDPZ46sh@g-ox%9-2L&l2a0X0<S@dr&eQxgR
zGz;EHulG@1@PQYr@tO^0wTDH3RS>)KiA}J5h+JYENzC48xi^A63WL(R%}n`Zf3G&I
z^!g?|E>qloVN1%E&1MxW1riGhq_0ANhC@Y7T?C+h0C3p=R1IPJtI^TXzWyBsPFn3|
z{y8ib68#M)4FCh``8?=0B6%$7MkP++>vUz<8Gmqn0ZFc3nl&-8UiMiC&0{|QM2SjE
zQm#P8<?qK^QssH+P$9dDq{FE(eljlvOY`jXGn$~QQ6_d|J=7~R#P=HSPhp0Gbi@by
zxd%2TW+R~0SbBN1k~r@Urd&sXc|fo+@#vB?=MqX^jJTs}9~ycEaJ3RFAqM#k@mu)y
z7e3k7{D{#=-68+FaDL9|VgsDo!EXGGp2lliSX3&L)C2131})XbAjklOR~Qb$siwxK
zg)(%S!6Cv<8L0|=<&yv{L6VjbC4eX|IzD^})G2`6C2W8kHa51Rwsx<1L2V1*yt!IT
zj*qv46?P|B*GU6-xtf}qz{!+7pvW2b*}{g+L7{vtVbNiRTB&Q_EbomLb6a9TlY3b(
zK3NyxNTlaK^yz13L!xkR0kRE~`s3UI&XYI%Pw2fR#!KQ7*gC=geDBpxekRBWkFPyg
zKKE=tLAm$%UhLZ&aXYdOYI@!d%RK-&p?wSSc3AErNOoB!z{J98@98lDEIhm^ComEQ
z#=>nSbqldwY$<X-v$Lw%ljO1(`vF!6Pb}u<#t#S!c(B2{fD3bfCfuf|hi0rESW=QJ
zq}G)n2iE-;;Qm_)J!re2^R@YYUQSc~W@~A%*!paJH(#qF?lX_~Mb`9-`~(_@hk!Z}
zRjVNhi*u&khjbwpl8i3lzdkyu;9gS<L`fpd6V>ED3knCb6ru5zl{`+HV<J{oJ4s$h
zNJudBF>JDlg23K`J7E9Nfs)nbrm?U-7{_&N2`1~c1GxL-hNtIQr}jQzP>pLR$kO04
zYqkL%ABj~J7QHT;$da&SMIXueoi38Fjr2i^txbE0c}kf5Z={W7Gzya6G?rN+<x<&B
z1&!zqXQChOQZ~=XT|N+4eJEHmKn8hydzkRfmkg+z6*p*bu7A(|C6p*L5G`%RFa&UP
zOknL`03|sy^Y*97?^?BlJ`F$aqYLP0<KpADfuR$<ES`JFVWff`Z6C{7+Q96e^}(?>
zxzT_m0(ktbfE&SF&oLybH22F%qr`9D`O8)5;`y9z#Ic8lE(eEHG6SY)rEeM?u_=!!
zOJF(Klhp1Z+ch$QUVuY*QjqPiYO-Ph7?A1U9=v$-8T1dFTakm%^akqXAD=X6KE_<i
zfdbFq0`VSF`I}z1YZI{aFM8eiJi6C&M@P<^%N60hgTc+z15&wY-_0u`PpR2}^Q*9p
z%lEodmgO3&m<4xhYqSC2(R|w?eeOA10>epRh8=n<k-6(Mv*nlx$YP2%RC%kzcdA!~
zdL2vcY3#G&KH*Tq==LAB!XmX=<w9VA+S8r3pZHY0IsjN{RL}WFMFoqDY*zoQ%8*t*
zakXe$FDEDGbaM7uQb&iJjcxis05%Cp)AMYp_FDFq^T)5%&GUAbT&MbVuffx!WBmm^
zzV&_*cRY`?NqhzO&a?Us(2y|vIjpK&AO6Xm;WWjga6E0ys&)|LA1$mX5v4zjERY2*
zZhC0sz3DJRE6Ffp(Z~$~Z1_Iiurzx;P*D9G+g_@qCQB065HV*1<Xc=EC*fm=^{>3Q
zuv2*2PREpd!YbBOv8uJkCFXPeN|UyeJD%-i(K>q4N0P;N1$Ih~?F2^5%3Ni^sCNhd
z6cOq<G|0;;DzGs6?6v%V{CIY8evJ>N&js1-xwY1BWW;Fc0i~_ld~*wnuV4zX_QiqP
zXXbnI?$V0Q)enfZ19~Qw3ZV>7f!qZ0>T@Wn`R@26O9H>Q{7LIN&EIv1z4hF<{|J61
z7VX53xH=`%85<u7Ii*Y~$f#(9TZXs_)1b&0y}W#z`7`SiHi0z@U)~mt*`&Ek?%bkK
z_?c0Ilz`Ay*xlw_IwabPq_3wpLD{EY?==rxRWs0W1(sG1KCkCbim1f6v%bC##}QVj
z)Vbn2a&{~IcUy4S8z4IR=uA2<gn)#UR#LKp_Y3eiFI-jJR#O91D{WGnih(G&9pF#@
z)no6}-&F_ftzTRYOV;Vag-DQqMHU-ss=Ei3%|p%8&rf3s9-N)cpF6)2>@s5KO9}&%
z-3qS0JUIHd8sGhK=jv>qq}Gmcr?0V0uidiqcCNyF*!r8Q7}<hN)1Su0vL-)UY^Ifg
z2%Pa9kCN4{a;;3Uok2Zs!dT1V=v=aVVfm#|_~Lg@L>EL^7ZarHimU~^FLhq#GqOx6
zSn4Z(>6XD8JAFRxp`3!>+uI`s!^vCs0g?C)CMKpPX;WXS7y+MyNx{Y~DR63ITI{N!
zB(k#ZA!-1KA;c(_oSs(`O}8;L=t*RMZ~jddY|!Zw|F29NbD1@8;WulP#t97AMHi<+
zvY(SH-igEcu~`m1U?z%gHk4LFLEe~ke-?>3_;#o6##YscZG4&VDL(4e#ON6zJ<-_p
zfRj@_G~pP!T}_E{4F?d`x8b;b0Q%dTg@IeP;cubG+e!wf2KmyjUxh%&CO$r%n2^(A
zvb?)a>zlY6)24>*hNw#IFf1{U9-ZLp3$1+^(lEWjD7bThCmLAy&C*gwW>||$1-Gco
zj-|{}(7Jnfkf=@m`F!zLMqnU5@;Pw8)y|l*fkO1iR2AI2Gwa?Rm5*QPkZ?8_VDbEw
z`ANEJwRJkO41#`#k8<qg4+Bwue;y_+piPDo&lK_h<jy5_uOx89@&l%5i0ABV|7%bG
zp7pnkd1ADwAvZ!Jd%>2L&|co1SW_TE{fC_(9qHe&Q~kXpX@Qa&#_jno6*TSz%^BU2
zl0?y;pwqDTYi}AvKwYhK88s`?DN{|vjA=HQ_i+>Yaye}`S@->omCNF18C+=y6J*oF
zoP}R&Ld3Fa(LRsTI1JY7e_lo1Tt}92Ex1T?OHc)hSL$ur@f?+7K+);Bn3zv3)-)I~
z$m_I;e<xgE9|1U9Km?2i(@yqbg94S6n}8#8xjGsJ1g>9z*zM@n1@Ihbs6_6?(ms04
zZ=vtL1PwnRJwxz_S=6>*YG^Vg6HGbouh9R1Z>=#FwuPk3Qo8$N;SWsmtF+h+06+F;
z5|)!OWX!1|8alpqI3DPJI)?vDUK1&DQ8|uSIQg`2n>izi$<m?x(4vi16*toFNLZ_P
zzARv?vtyPiD>pYd_r}4oK;q@%ykw9zgV9aUl>?_UcMjVFLVRv7Vglhda+*P0H!)?O
zL491j%zrFjZML+J{F=2n7tZq+FVb>yPU^2;zj_rB74=|@@Tmac_0#}P@X+XJWOQ^h
zOzz5Y6tdD{LJ}Pn1*6{IqMU7dE!Id?>d}F@Up=Yy$<H3pjb0!NdwT4Ym+hQ}l7a}W
zo2}F1O32R5Jy?gwh5xTkU`dPVrit!FKW6!x@puNnLON^3A>kVc2wg4)MqZ|iik+E2
z*ykc_&AEWsLuGv{`<OvG==J>WO2GKu02-Rd@~N!R&u<7cS2mdA!fiA>e3hdfh$o8w
zF?c{G?E@C=OHECI)txad7heVjhKo`NaA&Yc5sdT8M+HjvvtLuc!~M>)%>qC@os4Sw
z&YE*Nkv%(~KF0mpTy11@Mzp^{@qo^HXi%;`rr{CMjU!=^Jt5ZKE~e^smY^+bL&Yv>
z%&zZ%rYvQMNr1iF)pyaQSG;@u>4Zg<*n8{6Cq1R-H3A=#yk?}Q@3x{Prxy^&!SdIs
z#P>6EH7lt<=e{l3i*EduMl>BDhXE+iJP-`6MVpPkxUXnkon}Wk;e}|UG!)(DfWu*&
zLxoiXZ!mCP;S3H8+sju25g(9du7C%=FZmVA2$h_MrX^jQzK7F*4)WTy-SVWiKHOtx
zr=*_CAHN;6>_F!(P%frd9suV!fqb4gyBr}l15{r-efES4df&V+E}ldsAiO31Trh93
z9$oAuRE3AanMt6K=MNTN+iIY1Vz?(v-_YXwL}xi=Gl-7HH-uj5VaD;%M|NVCw8`U3
zy-TV0n00h?B=taNanzXh!xszHydGNmbx9uZ<M|}jO8jYUD%*eFWFTqj$k&DfT{3T+
zTo}qfwc8d`BG-$G<b%B_S?wKV3+7b^orj5u1-PWD#DDZtSvXDmhz^PK_*;6`JvIfD
z<k!}a7+>^$zJ7E!RW^*Q_m}T0nwAU<k|{wE9T|OgCaa!#QCIV}K9x*dtmp)Kf`eMN
z(vfl~Io~`=vQVqL-*1UkIXS|A!*}Hff$HA5pbWINELptX>md-B?N4HMP|a8krAxOi
z<<!7;yf0aQN7I8n_<xJL(h|y-d{0YUxQfOmW=bte&uHcHbiL1u_(Ya}Qj>z3>yZap
zJoN3kU}-EP8103Ax^i`O1?G5@4v7~xmI-)-ogv*?t=|wcP1kfG&^^ezYh^yL`%fEm
zz8sw-CQf~R?xNfXh`r8Ld$r5O-d%G}l~MC$rZfA|jSKhUKQ~%Nj*w3l@ba`;mV*Sr
zjc#gSmvWnC1{uzpw3;Rteee^?LBwNp;=Z@Zd`_T#k$H+DCW+pFulI9kqJC0%059{z
z?Vj2^!GBH=^p*u4l*M?`jd>5>lNy<fXChYBXZX~E$BR3#Q_iUwNW5613gm=<zk%;1
zF5y-gbIc2ox9`;h*!Nh|bQ+uS@iaP$#tTABP`8z{MWtqVL8qoRkd6$|mbL`~#mPXM
za@A=2U8usdv)R<L30sH`$JZHMh7f?U>BWJm&<<5_7L}Q?BrsU2e2}jgIvJBJ82pGM
z99Hv@;Hy-ap85+kk-PV+U;HvP?&wvlNs9&XapDvHLH#QbC`Oc%hjySw6Q8dBkT{`k
z26C5gKVv^n(^%9UI}@G;N}&+~y-pb>heta2ryhp@<-@Ml1q!IWpF0FC@~6bcvyre}
zd!(Z<NSh3$$7K~dXjs^Mc7I?1ZH%(AveUKNT=H-Hs#1GFdM{Ky+nM!dlWt&TQbiQ;
z_<#zaIMu{<Xv%rpP;mLh=LNu?5&+FabX%1KYhj7h`cc=sCSzTa8;>a40}Ar}P0=4Y
z`NzfTCN8{x-Xv%F8DQD~=<b-S0gFb?aq)pFfn{bG>EuI#`>{_Sch6{2usubac2W5v
zM-wS?V1HakL{CJg0g)Wfc`CoXJ#Oc&ddxb2oB0uJ0zfv7#iZQ02s@u?=DjfwFP{am
z*Tjf!v)TH1mBP13bs^f)9w1tYyC1_fn+C5?b{1BydOjuBgNY%wb(ErmN@A+fr{|4(
zRQ`BWw6pV%ug}itb~abx_oGEGOot{yhA((ryn6$Rlqh3~Q#yW~?tN_yYcb&=D#2M_
zcNL0U?6?H+@@Fh2VlB5=F*4FLBNe&uBe52A3Ky-X?G;p5am0x4a5f}_7mbC4BlGi_
z-7a?6>|0q6&f+*YI8o>%=Xw8iIVaqMNd<<NCwu!&COHl%ickom7oj?dvdBy<|8`M)
z)zC2&H{aqW3Gh}kPJcCMtxyFaelSqiqZ!1cWd-OjiiY_s!q(_BREJrnVWz0>MUW?a
z<!7qlM@mnWzOu;DT8a=B5!^SYDcVi)bGPY*zcaPp!epnB6!Y>QCpECFq4{ZY!u=#Y
z?!A200d(Z!f6mgm*|vBs<a?3m5-CXPGqOuo9%Nj@QASFB1?qFbYtrLD-D=Hda_U*-
z)B3vY>LUjR!=2Ac#c94B1@vdzl&{2EP>KYVOL=^B)tcavO8QL<8iaAj^r9Bpa<l*C
zYz~+}`g}A2<r{O!+qAIvdrZGBe+Y%x9U?IEYhcI`etZ$Z_M`hFRMHK?Z@4oalooV^
zLx<a%L-&~N{h`E~0do(Pr`_e3;Iy4jjo`)(Nr3{U?=Hog=8o$@sm+J|+lv>hYOX@8
zM33-a0P#Gmv{oCr2@Xkd)PrZG`ThN4B4-y%QF(OpyU-@p?yw3}e`??H;Iw(=0RCD!
zAf%jX1%t)-whWhZ6@s)dfgyNIy((s+JQ=<Cd=1rrIz->~C09&n$77KD=HViPHzpn+
z;X-b<vJNmzm+YYNv|Hi>njmN!V*Y*+b>vAQ%>-0E&&9K1(!gqAI#r|#`CPO9yZx(C
z$@U))B@xL&n^D<#gK^ch{&@a^dRvD$Iqc-I-VsW-ao4Z0S6R8P(^ld?6`6@Ry|X`H
zfwz^^_m2F6Z)1FK>SKLw3#?!b+Hd0r;ex~(UMThfi`PDS@1NH)MVI=SQfVaz&U~q8
z)@Sp{s1QWz|399R(fRCoMJ>Oc9VSz0%^x>6o3Wq>p0^z5W*)Qg$_KmSL_YDXjNDeI
zhL$^a3om1_g_GO&vZ;KV$3`8?OZ&$MMha|`n&TE@`MZcAUQw{;vwlF|wG~z$ctv?h
z;IU}(X@xqHm9pU)MbSg->Prhwoy<R3l}v(lzfabLyLsGy_M(D^kY9bwv()$d>t^6G
zI<vKwsRmLhJwWXtH2#O-2duUbnHKQC1g4^IbXwV*<Fi#&M8?;j9v4h2sFdj2nxJrg
zddlJl%w0&bAfZn^ha|xG{u7*LbXQbTRg|5L@ci@3Uty)70VJTZO{p(PBI$Tt5X@OB
zdeM-B7mAh2t?YjXU0mOEr=z{RT0uYWmAjfqdk|*F3`2TJ(V%WE+t0RBmqqDX!RWyD
zM<_%>T?c>_%Qy_wh7xZbJ<F{Y8%jr!KOrn>0?;Q*sUTB!$HOt2zTT8}%7Iv+i4jd*
z*;1$Ke6{X3^z}KVI1=U^CIyzxsyleUq&noD7%=weOocA8!Vv-7|8`Z98mRjj-HI&J
z_k$?un3B5ugL>|<&DU##g2{}ZG!xKnYC|^L)3^67FQ<vKFI1V{gjw+EF$B#prI)qX
zE~tyW^S0#<q13m9d%~SHN0u|K52PX*1!0|M1oR^MH=ur+m=tM(E<t;&Uw&+n!bL?F
z@}cQvZ1hvVIDNZ7RFVa6lWD0UdSbw@UBGFM%BRoBfHv#a&U~Xin=pXoo~|<VcjqT!
zOW%N{^4%`g>eb*&V^H7%<|eha>NY^Z3dpikdx<+3S&Yw4<$Vry1tNX5=Q9Vvp!<V0
zsi1gm#ha1)!jx~~SD}`1ADhuJ{!?7T2v-ey7=o^l7OYv%=620^>#UAN8*d2`7%VEf
zNd)XmN4GwuVfJvTwCQ!UIlR9D`b1M~#__atL5=N=k(*Z+T0ttfgYG|zREO3asUUIU
z0If2xob`wpYcusZP|iEWgsDD5u$s-{{u!nKhnWJZbUA`X317={Vy9a>*GdmBD@buM
zWC4r^_Et?lU<IOw+p2n9ulQtzMdr4Af0CbS@tVLew*$E4mCBd!l*S=cmb!%56&aX>
zcxKw15xufyDf*2U{~5#Jx;rLbM40I(J@{MSAiS<+bgaKIAH<${Gp*oXL**xldGbKT
zQ^*xt8S`Zvc$s_sAMg*2R~Ff9`+M&zkkA^3X?T4}25)j<Hy|K;cGmvo$ZDcV%M9OV
z+k=)zm}K{!(Iz>JI316b3lDjQA@0!r8D0P;Ijo9+IS@ijf961F(g^|7bMpFq3&EFN
zBRREEqp#BX?B&x=3-L3PYDJ@BV&zqz1u8Gvlr@0QeoF=*?x^qd=|<MTneIg{N^8Wn
zRBE*9B9>KB3IFe(`#+~n;G@6+<SDIs&losO;g<s&iQ*zHcP1_EL2U#`CG3>)eh_d>
zJm<F(dwrjpL55CEN%W{^opfW-ZlO&zQRKYQA?;K8olSe3D*FH9YrYs-c|cu}DIj>P
z(2HLp3(clx%>g_bR3c03{D`E8_w^|!*9(N-GWF%6@``aJS}RC)ii7~W4VZQV#tw2L
zcUcxUAU8-cbUO>+4q#9Kg}?FY?kz#vJHdKeMG)ENRNz8aGCm0gwmT5bc81!+dcdyO
zZ(ukB=8D=fDFsKQvcxBY(wYfSy7AY&5x|8D^u7f*mcT%m_P{5<+Sc9pSj*v9dOX(h
z?L>b8%+(@}1VNu#NU*fSgr)sV=HD*4*cbFk74yP+A*evvOA8ydlW@7D6||&%og-m*
zN%p_I?`Da(#H*pCRmW<!e#+S7D2bUs6v>CpPu*2(RAvtZ@kx$Iusv0upRL=`kEnc6
zB@Rvt{E0Atml0XT6M5R+<F*W=(f$TU#v8uQ+Z6WrsfDp6REHj!v2uz0$U9XQyZ{h5
zXnyAK*3~UXi(H9^KaB@ymt&8@@Y<ct3_Zw0&;$PNuZyVrmE{Gkz7iZ|W@rS=QTk@W
z3`Ael#0XsZt1Ux&!$%qnCod;Q?6n>Mxy?LZTX6CQkz5wAy3+mr94TXa+KbWcEWo;g
z7v>Ml=v*iiGEhZWLmp@c=f4ml?%?_)2*e#Gk--1zJ&jA`TP$E1Xv`acaUqjFO2v$e
z1Hi_ADnXLsC`-jkSh4Xu-as1?5f!1hphTTfmFY97aQf%P%^V(COBys!y9jWziO&x)
zmeE?T-~oGJ{anewOE{rlB~;S75a**&Fo7#+{$2Ye+c$qpjr={b!-u_IMaKIV4XEre
zLZCy}P=L{*wVt-6Vd}c&M0t?A0NVs=HcoG1N)E(%-Q-EqK<=$yt)qWuys3qamm>Ps
z`8rm_Y+IP7mt=HP?^V5LUu1QT<%M3;1&sW5zLsJ2-!A_+Uv`UiR&{=LL{#LAx>Qfa
zMJ)~*JW^vYYee)`W9jddkAv&DM&IDezmicPz)r!=9tmcZ1A{C`@>yl@uid+dm(rI)
zo(%t72rMA*mb}9Q2jR$k4#q1~@jps`BFY8=@66h!CraJwQfLbzBVsM**y7iQo7&YW
z`9`hp2ZXy)qFkPUAlCSBvmgHw_1G5G5iVwBr(-eiFMj$z(;@;9R^+PZlcZpX^z>e*
zX1m{;W!CEfD)V=MaP3Lj<k9DVaWh>2CFN4VF3K=Nr=~^MeH}$A%+J9Qv?g7?5||m*
zLG_fbt4dmvTu5Qnniv$iK#U0<V(MkB9Umbd@d%MvNJt8IGI-x1wN{Lt-nBP;HY(S@
z$ECp3EvA}o^AP7hoTe-W0FhlJyF|akuzjWgNJ5Z(<NuaSX7m$4$%H2Sx&Ha81+07<
zyE;E0vL)~)IJzS=8uoDuIfAXSu+~1HxEGc164<SVN}^U>l;augVwiYyF6=?rK>y}v
z!c^<SE!C?h#$Of%gkF>@zp{@2omIDKl@}HZ<HwU~vcy8kcZ9uSnzur+a~nU(NzrL3
z$%3#*-JF=Vn)3lZzH<`~c+2db+ix$$mQF#;i-89l!qAxg?@p<*ma_B<i^rh7+|wgn
z8UXN=Y#MImqC}Y3J;3sSbW?BQ8{$uYG+X0SEs_6+^Jn#(c?($hg4o%>P|kb6JT%Yn
znM!z%i$k~9peY*w0Zi#9rOZ47Y@<P`6;_aO?1@RGj-DMSir2ziKfiq8&a_8V9%Jg7
zNo132l1OW;c?&F!1=1#ngqRNAg0Nq(pa=WQD6y}LUXG541F9V`o<QO4Za}WoN}^e|
z{o5q$=pTmZ#j$)(eZGE44GEOlT@R3lNGM^;<0R?z&Yl2hP0kLsgewV*f&l({>6z(+
z)(38MFTo!d<%j)oO+^hAc-jPW%ZG{w;Li`+6`!FD8{ga**fY_{%+k0AqY^awu;a3V
zD!soH%0r7tXuG?P;4t>+m{p2~+Ka909bz&PsvcP?5NWMdWML8Ft;dnWlzBs8lV->a
zi`01s)fK?fa}vyXhhND!mTbLHbhKxpP3Y+x>$h7YIqF{<aecb*X{-68jf2rF!HYLh
ziXaOc%*b-fBjYl}2cp*Ah{3cNfbw?#5lkz)4u<UG$N?@cQqGt-|IT>9B}Y<fW=7p8
z4I*B;m=q8LSZGQoz{QmVC=c6twx0p5FqvTxav!D%d!>ds)#Yp}l29{PO7v#~2+ats
ztTZ_+OsvS%LF2?CAz`X`4Eqc-;16MFwOO#)7iWB?Br)ch9<eDuEt<aPyiKoYeSiRY
z5$J_stK0uGAce`jF|GI73w*2}1vRwMWc92_$th>yQ}ZJS=hBVNn&;}nio-fAL4am@
zqDmHn1>={3Fb^Y|_+i`kK-g>GhheZfK)nXo9@^fS<u}uvufGg39nsNUO%#Y^8Jn13
z+s+#!e<{QVKdtw={yRAmGX9v@H3O3H&P92(@QTW)AnO;~n%4lg{X!-BCD=fHjqoE?
zvV=!6An=2Ij9sYZ_x>#q!y>=`Iqze+juTNa7|2A#f9BJ;JG61r)2F+=e&X45Uo;T8
zWcnO;bkU3Lr?0qPpLUJM@w47`7t<0tzPftr$xLl4GO4Ydd7TAw-f_{hcssBFyUoe}
zueYy&imH3x9RU+06zPx<K^jzAq!dI!5J6f>x=~6(LAoRqm5>q<>24)NQ0eZJW+(w2
zVD5WB{q(oK`@i@8*S&YvVl5cvoH=Koz2DmJ^E`1fN*%?lNHL_6C$=Z(7G`B=2#MSF
zM0@^@$o^GMinZu7LHIwiAUEpM-m)G!O3N8zm7e;lbG@oP<6B4mxgKm;Wzv+^#iwJb
z0>sobauy$neS8QQSa=@tNS$O#8uKR#WjXJ3NaBMhKKiA6LPEMb@iT3$hgf2r%H?59
z`F4rDZZLZE`wwbeS4)u-^lCQKHBu_pX_s<@btduYPc%h48&J4@x|P_L)H36Mdb-8&
zH^TH!eIY7p>exbVv}m;sE65Z8XTcsxATuN5!|7=gMc>KJ-#dLpZnqqwg@t;Rjji2n
zW<}II6bd?8jb^aAJU)1jNXW?ys>W6a(=RH$A0>=Peg5SR>`4whFJpHa6PpjMtnJq6
zZUUYmrNYvn#&1!qPhf@nk0x_wYqJHsAT{O=h@tgm-@_{Havl6*;D0HS0513_4^?nm
zaO2@U2$X`*6R0>m>pGyB<b`%{6WO4-F6D~N+QHkTEQ?<~jA>dGALS*$4`ykZ9!75q
z^E)akyV6zEb+`7sM=k`Wo75bk-Z^zzcNPwYAb>X^`CM&23GSJIAIE$}{`F#hdYfwF
z{CfrQ3u|3s&5GZ88x+%DG+l33?nW1O-+qBQ$0gb~G_#=9U9`DG;qyp_pPBVDn{L=6
z<GTe8Io25&tiqc!5**qgQ&&D_6St9rxvQo0pI%#uLli28WREZ>9KMtO2o_R^ntKzw
zr^5N}wt?P0^!5QtT*zY<tQ;3?PJHZI?;CD*#fCF+HFew>Yw44+*m7X<y&&dYQnUQN
z?d9~zHY-IYds`Mje>@tpS!SU?R_t|g=+>HL3y`!oX78N(vWy@cj|Zm;sd@zTt+OZ;
zb?M#w(Y>yb)gEi<I%r=RZ(sE8(SGlbo%Hkui#+yFQ~@8UH{9nItw9^lh95-0414X*
z0{P`i&m8t@9obFM4vijBKKcDuTb35lWqpI(Xd$EcsZ`8&`u^n9LUsu#PP(H7I8N5u
z#>MBUx%<R!V|!W{HfJV3WuWArK9Y*3PlOn9l0LG%bH3-!AjBpenm3RbawW!)V8?C<
zZiH9^`WQpm{=?yyIEVrnzqR!R^gV(81?$x3<_kqtv8I;O8_B6qcdwC5@*^ZLmR6yu
zVe;)e0^j{`tUB>9?MQNJwE%33LVyj=Vxw`!#D=3fnBmfgLD3MB?%<Qg01eZVpbJnz
zzIYMT=t94LdU9@Rd!tO$<5Sg9GY>$|^moSD!_(5)FO0o%J=NLMGOHQAPIhl7>gAG2
zq8C$+1_!8i9Rtu?C#|+OlK8)=e3R%T!wcoRR-OLE?4iFRjt8yhFF)3Od0%DMbx69;
zVZs2rXCYWTxZ?sr79@H)OJ~Bt!S?q}x6CYTv5R+JGlm<Vb)?xjFz&29+|;yfzy7U6
zbA$`zAxbtmw$Xy8?}zH&6wICR%V5>ezGNP3kVp8l+~B4pJU$gtFP>jES;}ubiKyy$
zJA#&(Z;Z#c=@{(bCYf*4&RrCWEl^HcLS^IYkOgGY6VAcJFf$2XFWkK<YZyA^R+@!Z
zM|^^YE11Yz9`-qNGU|~OaOREjb49@>-4uaYxytj;kZ2Bqx_5pTiDb@zH$PPH7^mU#
z{f*gHq5crkyaid?_>JS!<QFBKn%Tt*$$DC0`93M^u4W>Y8HN64B=m4FVgn*R+O9d^
z5zylIfior#J-O0C?EDHzS%3xa!32{_nai5COKb>CtB__)Oc{<t;r@G0FY_zNW<d)f
zH9$cLHUQe9Qab1}9dBi|&&ihZ`6DO#qR1q8iOLZ<&)8V<#g%>JrNAvgK81~eEsEP`
zKe91&WW7rEfvp21SiI+vF@EJ=!-&zSiT-S&=}(<W=Ult(K{3I~@6zUxz=rj$=Xos3
zVtMEwcnIp%GvV!GU7^Jm-tbqL!se1qY7iSTD8mo~e)u*yOQKbp6id9VhiJc~X7B(*
z#MVA?Iba23gD?_mT@WwL=3LOb@(_-XR+xDG@x3<(a{NBo2g%NVdfAa`6K`%oHJYf*
zGX>mpijO<Mvs>re=-2!2=I64ykqRFY2_Qd@AuEF88Ss!3te)1o*6NSz*0)~xHeHJ*
zxTSO`Ajux<mcy9#-H9JFJgf+p5Mn9TW#9&FWt4&ZA8$oUeBPw!#^XjV;sIoN27J#3
z_zoLsSR7+V|FDcN+IZ#9`{fQlS>XP>-uap90}8<<npep#6i?y8<~BMf)8Qr?G-zoK
z71!x77sQw)z~6Q30Yd6F$4Kkr{i(=h`l`>u{?qXnB<8w{P4+5(16&art>0<NL1TAu
zn8ViqYNKB2khXo-z<>z~#pK@)+p_)Y(%Hi)7fd4JI@s}Vu-mZtupbz<6kO#+m@+9O
z>Q0|fvCagqswy*@R87fmO<-V6DX-!ZS&>qnx|8vGQqc7uJ-<D!!oA&GwW<Ge(DAjB
z_%b^O1Z@AtLsjWp^BG^Ggc>O*(p>sFc6E%UF3l{Cvw+5Uk62wO<QHw@AHtA~F}seO
z3J3-NQ=RJ#gJWPrHAa32{jIPxa2e?0#;UF|TPjgKFu?Wq_g7kQeeE+o-|$<{Z;z1k
zXO@g;M5a0R#eqOlN|6tNo6#aqyUUxX&4%SSrTV+#p$uw({&P!YJ#y{x3&EUmywmsM
zMrzlOtGL~~J3~*3*pnqjq@?cxm29ZssG#3|h1I-{wH9gr8o8YcX(uQd<>=pS+(Bjz
zLyQar%lBgvS<lj27iymn)+D%ze*3E6)whS@N$qofa={FGS8!_Vd~&c!+bWq^^X*PQ
z6?nilBgc2_9`6Uo$D7<M=gVKk%Sh$YB1ovwA*fRfISmKf3fXS@ZuSc_xC&+|HZ#TQ
z(jb|O<ZA@OZ*pt(aDP<7Dt_XV2u|{yeYCYfXfB_z)Ah&2dFim%vG`bm+dNd!*!BCK
z_+)Z`;)Nrtsgca^60oS|2wZ<Xq*un*q3pJ-&nkTCIk3*uD*B(+v%|4HK7QyBK1ItW
zIeU1rAe3|&_GlrvJ3vI`O)%ugtSPUueIU&O{KNM|@#C?_EURP|2ci-@mmZvuB5%`t
z%#7?!LSM8$T<2>o^K0fCQ3-iPjpyjAoOnskalNUJN&wqhRO<?=FtW(LDe#9g!l0aK
zb15yjY`y@4Prm)^b&k^d)T3jsn2E)C<KD?`kV=u;x&L);C)xgIg>)GO)S+i}){GI1
zbaf=2&sTy|hFXW%)RKwGsK37Q!(2YXgp8UK6GRm@UWI+TN2GJ<5XgjtIGAM6inGPN
zWRO4s(=%WV#oSYN4YZ^=WN_6DKvd<L-(~gMqIkMlnngx9ze^!H=HhjgFjt&i2Sj`i
zCJgVPg>MV%?2=O&<^n2bwbqOoFUbg=z3vxJqiExh{p*wD2&TcULuYswT){2{29o;+
zKZ!pHVMf7mmea&EOm$(%sCjEZ!XnKrOeOMqXtL*8=1xmpV8YVlQL#*dN3}l1Z2HK}
z92zBnFOElo#D>Asv;hgFUUy;0mPkf_o{di>fMNH8)_|v7VvD^NtAd6}rs6m<R(HK;
zi3f8c!M>>R5h4EF8@0%n5?9B<4L|Sf9hh-4GMPGTw$TYgDmgAit6_fns=~>$3O~=M
z%dkJZ#T#^(-Z+Y!zb=@ECSWDsdDc?g0?(o5SclNeo86nRAz};rG5X*j-R*_Gg8afl
zKC=#1_th7}JdTT65U$&oYLp79JB26hzns>mC8I4DyU^Go6Oa(5$3S?L^w=v|-n|v;
z5{{Eb@BX7bex(|po0ypR-TFfRGY~fNC8B3RL_ZTuRn^inDC~;)RNN2Lxr~~z8k+bS
zm@nkjg(;-k8%*ro8nxVm4k8eTTgP_IIDpuYEr>L+g~ilDNNPAL*PonjjGxGFM9%Gl
zlY}c59sX`<V08V`kx{1V6ab4MgM&Nv-)!Z6H!co}1_*t-gM)(&@PqT|ReMVqj#H9F
z>_<T`nnQ7Qfdw3--8741>Dro1V8TfBZQriG9QB;&hu3OrYr#qmQdH~?Y0H@`_OPZH
zp&Af)lG4{_1l=}^f#T(d{aos~-XP+!+G7yPYc(MFgj=^MSYYTQ=$S+d*?;x?;4zc(
z)M@k)c~7w|6HwmjIHpwZvC*JDd$?9=1~A_!^S|Nh!sf$4&gJtk(aR;jD?~QPMsSEF
z!oROC&@tus?jR(J|4SFPRaXBAQqm<5Ma#D6<%@F~JB(T^nW6(-*6+Q|?jOE>d9lzB
z*BoJ81yY;ah|JFfC?ne6y2C?J{Pnr{<~G`+x!88Rc=-c$Y-Fr?ETZNX)%R4WOqS0v
zdZDhRM03(Cz?@5iU_asE`Bn`PeHHKS6Y+bG6$5R{q{PG*wX_CK6={Nq%mFW$a8B<k
zIe2)&FzBjy-K{Zl8Znnhkm<t7233ZAb<p=E<g_&6>E1Qy!XDDJy>T&+8G;rH;i?Bn
zKZj}_81Lg0l+!&Lu2*m#%RN>m*tNKaZZ4JLq-EVh4_&)*<;dvhDB-8ol@$~#2S+}+
ztXpeO&&PUtkI&`KtA_{(5OFwz8lR(E>qS*}%?2`CG;JLebdj%l1^}U$9_Pd|iauAc
zx+fW5Vj5d|yZRm{{hDX9DZMyp{~`Rbp4vXM37Q{`Qbc0V=p95W@}vs8jh>j8&{{G!
zGcyx(`;lLhYp)iwtLdAj%S+(>y8&?p-|9x`8`AX7Mo#O2hwn|^wHYP6D)xyeQ&6r*
ze;y&C*q2H03@l+CbY8nFi`qtvAx3K=I<79P*W#WABDoP*H`d|ig8wgSrGJ(;?-Dj`
z>14pgS5(A$dV11*!rfK%U=kIL0WF5LIb$7{nNuKU-8WYXGQLj*D4^y4Eq2+3FiY%y
zgXO1T&Z*6i@l9XMjjAj<^X^B13|JlyeU@6{2wEu%RSsAU-lrcWwL6kaslElKL!ncl
z_`i6;K<wnXSd{B8O7v9~nmrP&U$o-CM74k8ng<R_NJs!Z`1-A()>b`Tv>9l35aW|W
zvlOBfV^#4@6<VpZggx3y*e@eoKc<;xi#eagKM&tCGO-f{@96h}^m0cJtFQjY8^4PV
zS=-qZzdOGEP;~u!jG%dQmpN?of?sIp)aLTI*b_B1HQcbUu#puC&<AOReqdK^<Fi!S
z=N&`gA#R^S>#jj01TkgZTWoaQQd*5a9eGB8{<P#zdKDp}@L#;Re{iV$8Db)0r8m&|
zVrf?u6bLaJ=+v~d2EFfvmi_Z{GUzeb_1e;5;T<<n(cX(K4vktouXvb$`#p~PM%nOk
zBYRfQl*H`({6s;wjsZwFY|q}FI+AJC#<SOYQ<cS-G8AWqQGZKr+4%B+hSP1^-*l~Q
z$r7Ocjst=W<hz>%|2Mi?2U?T$zOM4mK+$H^Ue@4i2=bSyiJ6V5R#W1mKe{<jU!&?M
zv1a%On7`Xuszh36>S`a6oXiX$0vByHB_#=E<zu(aKQ49LP+acPv{us9Ra8|aYrcTt
z0QS;Y>ZH3W%F2>=?yw->2qvbQ$?<O~Uj%wGX=2S+7dYYZLj$4C_8<MTe{mZ9voV`)
z&&tN8H&*LUN={DnL!?lRZnUwn@q#5eU_f$>J^_N|nK>>MO6|Pq=At0}PR_`~<8?T&
z(NQ%aonw~rU*1@XoY(cEUajwdQ7od8r=niinkxi}5TJb$khJ%ut#_$a5HBVvxYDRO
zpZ~5?d!B1T%TWa5;VMy7ir@Mt89Q)|-(A!^1iIDQdr1QD!@Dd=lb7K?`@VG*l{KU4
z$nY0W`iy>RlN<g%DAon;HY}j8Y0v+$8ML5156kH<J>c@vKLi&3r{e`uAvS%LyHI{;
zc`}V96E6MD0j*ftlV(3G=?RI{*lw4-JUODYh}`oM9}>au{$8tY7Z~g7^d>O&$zSB;
zz*a82!HEaxe6GEoc88qfVz1KzV^#mxACvu0D)xUHFD|*#9wFcV&ISK*?JES~zOpaS
zK$ZVTgPPn6>%X6l=_;qorqv5{b+u$_A=8=+<cwWis*;kD<%Rz{gZ%pSYt+lUJo^?*
z8(TmkfeUwH^M%b3T*L?}`u-fzujL>JhN#AR^#RX^RaZ;PJ2hRmx{r^U4j(#%FiLa7
zX5ZMDzM}6a$uDt}z4Y%~(@zm6XYBR{kjKAm-{8i3J@vbrSnX>IVBmoAyJReY-7hGJ
zrlS&KP@QY3?W5_b*?-%$V0$aOMfes_SB|OlV7Msu8)4xpPuNzc;8dWyJ*yT+_}(Bt
zysU5ay8QiJ)~h#@g800|b~~j%6Hrc}k0+oBjQIH}Bo~xid#WX|7vV|z<sn-(0G7|m
z$=RA!t71HVzN<X}nNi1J8tu+4V#%1j!;r-^hCoX9-v0UP=G&$wg~c-T1pv|=CL%KK
z%Qv;?&8=%kgxQx)?tXfcBd_-=SR6okC4w3Yg03sEpK5Ds8=Gl?lR5dFHAPO@6cHBo
z4!ZuIi8|+|N`V~j=)PS}R_|^TQ`1qksvjpnHB3xNNeTGKA=(?7D+G<8Ex>1;W?*>m
z^5scTQE4o_JI7Uu#XU%PT}`bXFap}dNEB&(ayR$Pvi*tq10(dYsi|_h5Yz!jJ+K=d
zC96#$-)rc1Jm23Q`9N)L2-<HIR>MO>P1=rwbrFge<bdgmy&9yNNB2*VA&X8YDK9VL
z#}Aj^(s(6Ew9BEMTdP<0@F5OzDPZ87#{5sCrl+S*!dwAn_gv@IJH89oSdN2Q5H)y3
zq^lq9#W4km`i&-zAo+0?$$u5vacUOYtW7In>>#!obQ}&=NF4_u>8D6%>irl<JAv26
zcw=!eIXRh_j&3nql$)E#6BY?3mwso-S4B-N&#dzdNP-VgzJjkhf$XONq#WM=18atQ
z3Cg}z+Y8o!+$27JT*}0R6(n>(9!tO~SPeez@-e;<F4sf>u#o%q?Gt-)@W6q-ZrmWM
zb4Q#>;RChb_ip6N;ayZyUj520stLv{QDAqWx5R92I=x9xcjXW-;$UESKZuB5E*<;%
zznB=Bb@Z^}jT;d)E1=}q+l|!SD|T67y}xqY%0>m&RkLT6>+5#GB0^B59cecxh3t|K
zCPBEKa0k3ET%(%vaviy;iAlC&qGs7W&iW8q+>ytZ=@?+&B<)6OuFa?<q5%R?Bn4<Y
zAY$eK*e(Atn;u7?3r9E3keUuNL2eib$X=zJH#_G_L2f)eJRGGd<&zrc5>Pbc5(v*e
zH#gU5z1O&8v2<>LA_JLb$o4Q|j*%tP{EtEY!@m9h`js3=l!2Xf1tMrj7hiXQ>Lh3j
zLgLg~X#pTtxG~s(2LuMZ339XpM$66t3aL!u;@I&1$*C!jua7yODH37|ixv^k>~7ww
z!fs%rh3~#G#{uT3Q@hLh(G_|5hUVr}7>Dj}*v)!zL6<dFBJr(kSKQ-I^I@(-c@G}K
zk^^fZ5uNKiZ$Lo6=28vOuJq`sEm2xeXyJ*2b3h4@O-;wyC`(QB38&@<TE_tiSZ)}v
zReg``Io%wM3@%y(*9tu#k)WAGOi4M@mUAGnqJmajd;|M~9?*dc3kwv%mx@B&cx`QM
z5u?4e=vZYiRPG!{c==EQ&aM?vNlr={57!-WgltAhi3Id`?QW=qfM&8NUnV~sje~<D
zO6$|Fo}nr%ER2GTW)14B?KAL8?QNc7w|RN>d=nC|U}H<8HF1P8a9ZS9N{fT`Ad-SU
zj*OHBy;><>LL*50=KBgh>6O7vJ(`#>1Vy}$pFWKP;&~JT%L(|&x3*uTe1?eTVK+mu
zw>OtY@eUqbtry>U3<xJ2o6ehR3GFj9aVdxgS>D(%?s}_EXb|Um2hrt~2_z$-qf>Bj
zI4l0WL2+I;q<I4(I0WMj-{Th$Fcu=RI5ORuMA)z8JQ)RZAlH6M0faqeY;1U{HtV>#
zT!MyN<~UbYRzNKJ&c`r@&(F^V0+4>7a>tA4!pN%^R*YayJv~w35fRQXy@BJhB1Bt5
zqw%JiHgb*{U!tihET+me$a%hp7x9_kcPWG&SVP5k1i>JS70xYCCj0mtc*3DBDJ_ln
z`0?WbS9C?i5M7aRGabBH9nEV1qsq+16#~NSp`bI2IS(y9TbL@W2rB7vXknG()bN?!
zr{nGn)B;w9jgf442M&bC#C+BTg=wAm6KyjNqFYNf<=gB1hK7bnb;LN{?T+ropmErF
z%RXr<tIQgA%<PuEA?OC<?cdMqvSzXaPC~>2`2?(azu@3Wcm~o+q?mgk6UxjC?YV*E
z{ZA2kfpp#NfE<JRV{lUN^hhq>HRpQ&LPSGtTZ%lTfE5i$g-Kt&%y0koDyVf%We?8x
z=I!e*fsKJ(Z@E?z>b}OLnx*rlhDiJ>5EMXB+oCVuKR1_;<=S(+cj;M`jYJ-sQm+)_
zn+!t5K8)7*J`=E}1D6&=Ba~ZzA>M6WeQSH$8QcbFC{Fa5XHB+Vrk@P;*kVE+ovge(
zZZ;MR)rE%7pUX!wuD~Q_WMlIm-dQiQ7%Ytv-&qa?l-MeGu%4ptpfUXAhN4(qqD<iC
zQ;+ZD3h@`d;B%M1d#j$;Q{h@vlc5J!H(*n96wy2!07w}D_4)aS^~Qj&1s!>Qw;v7&
zJRUBmx6qP$t~+ZAE@wX?MCk3~vw~0yw6t9B%F=B{WIS)&I1VT-`yO3@^dnAsb*kC8
zHBkn^(#HdW`f4=K18S?{ec6M2_r9F#wwd@yg6NL{8Wa(YQ?GL0P8m{wU8E<PR(jxi
zx27+PGjehUZw$GH!qh3MF9gZ<aaea-BL~F+Q63T=ehg6wgx&C-(!1=!u_2&wmFIzV
zhx_+f+FES}JyG0?AT3%Iig8>Rs(1l#@;GohkckJ>>5o1$j>|z~%8+XZz6NJd<c2DH
z$!+_93fB$0g@W#5)YS68;R!({5?qnH#aE?QR>o0Vmp_KJw_JgC3yoq|LzpPW(CB8j
zjlu4@W&&E_$fvsQ&k%qjl<bzKlS1_iG}Lnq59{gam9MqQdoIj&L!qQ6-}E?<=n@KK
zO6CX4o`NWR+%{$dI3UovJejb+?~dsoUg5^Ba8FE5wsv&XhR}*2iuLwiKj&DJ1Jkyh
z9pA7!h7*>WQ~WBKq)8;`(IqxRsu4*K2AEuHxU(|_u0;iu6_tcVL>4~j!Z7W>o>@G0
z1d|IT306<OJD(|1GBUpCiKnY(D5H#^WFz*0f>+<$4m5i=ZtcJdxUw%2WXOd$JOGDG
zdXeqS8D&x#r8Dg8C%oRj-1^a7b+5+?w5tQ+<Kt^q*fWbI_eF|hzc-VA{vHEy7pqH!
zPRT-HKPgmDvO)c{4~r=)ITMh$wd5<V^3cmGDg+=@231h_S~mh~aYaijMrsGC?3~!~
zaNVFIHR`P2w>8JbwP7x|j|DgIql`Ae2a>2yVG)K&VNyLu1z1*bPIyGB7*GnZ*>Iee
zlY90y;ZnQg*1-oS+doj%%Xgu4TGVYKZHXmSnEeNbF}|PpIm!lB-0IaZ?sqoFg_?z$
z?c?%3Wmkz!ZJ`XC<HWA0D=LP9nNSZ-(8(hA@bH){&dpUu$=cfHD0dAHbMx}@;#|D9
zI3T27<+#vy3N-=K@JcVZ)BT>%bQ@SYPU)yg#;wDlprBy)eZ?r{ZApnb$e$Wc$J?V4
zmD7@;XK_{-H36pedPqb>MBV%M5*nJCQMs>Pu_&c?s&*F`jogKhIYRj!X5A8GUx}@)
zt!L)uj+2mhy}y0#6(b{<=5j$Hp$3SUBXiQ<zEx>@`t)hwm6Y&!kDcB`ZBx@UR2WD(
zvl{K}>?C&2MH$2@AX?XJubWRYB4F7oCMMI-v&UM!g5~G^{64&|slmM*N++YK`Qpne
zD6w6JFb)jX(cnu-kwhG$xiVSZHLb0-pWVO!d8ejMWl!<*^K*uPw$5GD#hW)zpk5{>
z;;=*<hPpBYw%6T}bqvtl6JSa6P2k!?*VfjQFgMlJ4+Cf6x4CYql-#XVKBvPyBgPfB
z;|IXELQv_YS!6W|j2dJMT3T9&o-bQHRqz4OF)8d}SH5|3KRrD?gs`keFsQdm>?U8k
zWxjdyFgBJJ{9saKTBn)O=L6IO=&GF`__VaN(fr1Qs9T&l`9|gA7ouBDq(NT_eAnpQ
zTzcfe{rlPYO{Jjx%fP{5QG0<h_)<ql$4Ma}${Vk)Dm6+;N#)p#Rx8DudcxUNGc;0Y
z%+FH2)hIXu5rrT~VEb9hU%4`}xEK-{Ns1(dV1cESmBa1aVF4UEdQ?VM)~~Mk6f-mG
zo!|J^(a{G`<%4)2^anv)TpSD!MFAa&*k*BUh@S}!DE=gL&n-i!z`)0M3@mr`%H$^!
z3W`H05U1Xcf-&q&9IW*}9wjWb9}h36jGoV=`NMT7bVjFHf^u4<8_$<7Ux-Q4UA!>D
z(XjMnvbzTdgNKH6CT}IRzWekEN_kqIS5m0HNjbx2>X0j1Y-@8owAg*Sw60`v(JFAf
zA>y>=Le}!yS}iE|CeRcW7BaH3eta_oDs`9U>o01;m=_lp2lcJPgaaqa1y$eR_4RcU
zjO8b%dbjNL^?PgU>&PLqF&TWfEzs%dYFUXzMcsGeL0|h7UT4zsw{MT~^73TVAxQ8P
zaSc6yBd1wjULNV@h#<HxY_Hu2T!njp!tGkN{9)fpGOx+WNd`8y!|&g}kG|k04Ef{Z
zCr^BU2}Yyy#AEC%){QX{LypVLm}o0|?V8Nhs|2tM;tSydM6o0?GBS|GQ>?$(Y7H`8
zKZK%lnPz}3j^L7=79uy8p2u0PzI%Xs(Bcj$H5CWJf-Y3IDu2wfPYQBzHI2pRgiJu5
z=@%I2_2LCJL_#k+%|=H?JR?pkjx7`o7dDOvXnn|gj8lt^>gZ6}TKU9%3$h5XvLj<-
zI54eYgMv4OkRDw;oUvS)wU`2et|-TKKJ8M627T@)4TjZ0l>AG}_4NG~=H|M?o;^Lc
zw2E!^K^5|{r6niio=Xj<<6q|Ild`M6&3@evCVQTeDbYjVfULCi_{8|QS5OcEL^dxW
z!bM^#V4v}Xtm6o*Z`9)bIk9ZKL&Xu-fZ!3tHG^m9nA{?0j~&DDde1Ze9SFVyd%eK<
z))?}!y;v*I;FQLL9IdfvYy5F+tYyx;<?WJq)$~UVhLYg1;f5><w`Wr0p&sE68BQR_
zeI~JH6Y%)0pkaFs*Jgdbm$x7zE35v?3jt1?$OOx>(o!Jv2^|>FdaGNd!&X$_U|!t4
zX!T*Rzn_|r5NITK$~%QLjSSA2wlNFBM%De0oS<RP!ou@l6mETHj1_StMEP7J<b7FM
zN@ZkZ1UdKzf#LhO6*{31_nk@m2p8;*-F6fOWqGWLPd&`)nVA_`MMdNSNT{g;AvsJ(
znTl4$ORwD?r-PZn%SRQgDxX$fQGqP?Wa^NBfa+wqi0c{}0hN^(Qii}MBd8&p0~bvC
z%%Br9*vH35?*@$r#I<DgnuQkoP)0uH5b#`2@BH}XOTlx05|Y6D&O%Tm)_ebOf1{$I
zAu|fG7H6W405^;({~6p3%4i|V`@?YdQwF`_IVP=)`2_`|KwER8(Q2^t(L#SwXqu&m
zhd7j)Uqyns0aMj8D}b^XD({_rUQ=<;k$=&wfC`_C<D!vKO5IKoJgjk;sWsvwtQ}_O
zfTG8*vGIylxswu`IP7rnrSp>k?3gU=J?6)cB~VT_XiJuB#MC@7@6KeS{CWf*UrANf
z2j*>JcJ}qOi097(K0W0&fP7bV!PV8ZwY{Bx{+n+|T3{ePBnNNZ9ZSo~Y)7m2e}*T~
zVSFm_AiZ%I_=IV2XVIe0e9FqoFWYBel0O6%CK{1@1d#6F*cj8xNl5Gi<M_zi8xM4H
z2@ZJe6LDOmxknVv2}KMTI@U91Bpn?E<`)(ohlQcQ2|#+uATCbtOGvA%Y)k~3UfG5X
z$Cz1I#vnGVgP&k>9VdzJ_q5VG6JNeWp(`<58X6j5F);+NF92S3zQ2fwT`jX#)4Jl^
z;xg0`s-dhC79SrP9ZdmQASsw7U_+v~@8-5V>PxS`I8d^*w&tyqRSz-R16cYm%geVi
zpM0)>j2`OG@4?Q3DL)Ld^6(ED@F_`!+T~8X5Jvk#3U-i_lk*ThzLbp2qnjt^zkc<B
z<qGBMadZ{dCqAAYHpeZS?jOa&gAlaFzFEu{I1Kcc$Lbu#7KMa_UT0*~L0Ff4=L;32
zkf7~$8<GyeyR#je2Q0&2nLufUiG}3=B_-uF8eI?BEtF-fa=Oi#D=RCJQ3IYVh>4cL
z=!`)fqo>jh<L8<V`82X3;TgQ{G=ovouM0TA%F22Xl5q!NS}2=kLm~yCH5K^WTKIO@
zEJX@ikcu2UckUddfVs}w+1Wg`_4Q2PX>@dS1l_la!(Vx1!x>Laija`B-#<<g+zM0G
z2zIFx+h=M!I{~^DE0fyZ09j4OEKKB^kPg>^cS%f4L?WJJ<mATuUp9s+TrG#JVR{{-
zpm?3ENf(pp^7Zqx709M;b<oSM4t8`f0}NtpcJ>VTzZJ+A<gBf;I=@w6cU+%|dsGUF
zhy;R%@b>nWy>sVPjF_ux+HrF7)3C8PPL&FR>ynVBo`Q!vHZ#KpiTnyAQLIy;G(wCJ
z|B_t3d>K4U)cm{!gdRCAA4V6&&fYBYlQlO_hq9Y=OiauKOok_K-*TjZ%JaD|@GoQI
z)Z~;D{}(S_6ql9BYiK;*TJN`3WlQ7ME@f^OT@7+_a`G!HD-*@c=e2cp-HAG{Da|Y{
zt_uY+=@e!4lr6eX#YCx<l{&~}Q3YSh*T?`h_y)-1*}&M5eM1qv2pLlKAfgp!h9oz!
z)r6Uc=Q`9gqBh!14(Ozg*N4i3GLE32pkGy070iuW9n{aix?*>>RcGGINN4I+aUmgF
z`%EP1sGFOcvWf~bj6@^m3?HAeoxOcZS(&D($k{KB5)uzS$BAi*ii*~@wkkogZ3r=Y
z<K2U>6t8}5ju)TJJJwoNgZJ1qyFJQpT9@_01v=D+n3mhj;9fydycUw%sG|!oS;4~9
z!G?KB@0KpJkdX7|w6|Dt(6n!DZG8Y{(bW!Hc6YMz1RfsVZ73neNH8*@2E3%D9duow
zn8pjL!s*+W)^1bB=+G8NFat@+mBW>$Tj#BZz}em55oBcCzj2a;WYAaTOs5+rSZv!K
zQe~&_lTRVU@q^+#kmVeO7!P*uH%iSnGC(1GTF3E$-%c~nMeswVipV_g&eSfpn>+$`
z1QZB@tE;Q^u-`dINP_8+Gb68OwnV^%1h2=G5Etye_z|y(yzUTyDMMbLDSmyL7dbV&
t_zXPvK4bU+1tB)PJ_hake|DlgEGnALF@X5x2~rfi<YW}2GbL|7{2#IKKf(Y2

literal 0
HcmV?d00001

diff --git a/docs/figures/profiling_timing.png b/docs/figures/profiling_timing.png
new file mode 100644
index 0000000000000000000000000000000000000000..b2ea4ef05c3a19591df0c0c89cd1555251a8ecf0
GIT binary patch
literal 65037
zcmdSBbyQYs*Efnu3JORoqO?eN3QBhf(w)*E(x8A60uoAtNJ%$H3xae@mxLhQUEf^p
zy`N{l?-^%|Z=C<m9%Gl{eXn(`>zeada|I~KiC@DY!9YPlxh5&`SP2E?k^~CM#iwXj
z;a8rDecyq9@j8k=byT)7aeSd~Z;T?V?`Ugj<7jDaaL38m-of0)nvIc#nURO#j+vvQ
ztphI;lhuEIg3-p_l!;obUmZRL-Bv=~0R;uu5&8SVqzSn*3d*UA<YQqK=lGS07tYE9
zq+d5}!sTeK%wvq-2YXwNNM9FLxO~MJEs_GQ<$#X$ij;aAu8|Les1_QU+#c<n7M&t<
zb<vMO1ivNhy}W$WA6O;dGq)by-{uz#kBD=aba05<S*_U@AQ4r>_q{HHMgjl$So$30
zum3_zCJ4WSj{F)LMI+w-@BdTPcA@K*>+X{1=1f!XqN5o*$=$nmpVqi?kOaRT$X25n
zn;aS<)YY9bvNE^2?|Z$$l~Nd2#9vD+rI+$pKBHgp<HHLYC1&-N&zJk$wX;=od(7A)
zX%#Q})azN}U|>k~E^MET)wpq?bjESX?{RZ@dU`s=P#zo}Zgz4__2j6t37+mKQ_IEs
z2L%P?e!~?(+a$v-!+r>BZY2}XeZ%|Uz_}|)sGF(oq#;kciran;&0)SnvTPMDZKTi;
z6)rN4%Vw*Y+-u`#Isekn#YOYA`<apv)KsK2nHk-YbL@6@c9vsh!D>1#el~TdoFfjm
z_?%KbPmk~)XzWy+8X0NAll(w|9)4Y9PU-CIto8Q#aG{TCt_I7CHLcg!w_+Ir)N9>&
z0zWak?wAQ4udsc1p!tD8*tL>LLgt;48)HV5!veNg$_;YzB>Zj{XXl^O(_wj@tVOx7
zJ=)(%ufR4z=_xXnrhk&<`-%2syIW}9sYa)JX&~F~#S7C0U-Tb&+Hq4}=LwqS)+5ZL
zB~&#w3*}RuDf-`D&vnK{og8lWXDZV$YF9?iaG*zRYS*~FKipnW&eh=1($+Sgtgdj0
zla6BSEjE=8ym|k1L<F9opy1BR2%D%^ZEbBN{Syptj%S0>O!s%Tx213Bip_8B5W#Qo
zyC1xh7d-S0r;?soS&^x*|8)SDrif1^stb2&Gs#b{miIO&2(u~h=Il2dAxc(O)`8<B
z-|KhF!`UQY-*@1877m)R&zHedb%6ad>2>Y_*R#33ZP@aTB1fwtd~>#WjQ+>MXo3DE
zuaiwwWYJx==i|BUUL|>*#b{SK+5P-_fnGHydWPfM>uZKnwH_tUhC<4$#y<5gq8uzF
zc{%@jujU^Z_{rmVPbE()W_zK#*lAV6^Y9m8naxy}G*ivxuN%|f&@nI!CaYak@^uoh
zZ}Fliq=;P$>S7WUOdQPBbU5C#(s5hmAR{9iE-}YT5f7z?znap5eNb^sV7DI}9Q4$A
zdBw-a4_CXey}==;78JZKE-oJQoyPb2o)j)6><kpksoDfgLdK81W*v1aml!n5u)HU0
z+%EOxYH|sl9T=+SJgxs?H``-T?8(vq54E4+hwV&bfXr@%aXUeo<%mHo{&hXLKrC{>
zcwwKbg@(-``1w3eD@4tq<Qa~Oee;~6ioZvSX>e}y>#dHKI<8MnoQ&fLoji<U)c)O@
zg1XR^@F;tLTKb*EkI(w0(pWZAwX(ZQ10!Wtq<MLH-ix037&qxRnh157omQSY^cCAo
z2@){r$oOI0<aYdhJuxv6MJA5(&*mR1w~6a^MW=XdP4m}gN3Z+R+}!Li-Ef7|Y82U<
z>t5$<=S8qu9q<@FKP|j_jf5TLYkPYT*QB!#^3>|ij)I1C+#a+S=BO7_w|nsCiUtw1
zhTrps3w{T?ve;ok?v;;^GUb(f;vq60$S#m^+j_%;>;EY1W7K-%Yt?#f`>QLMXjoX3
z%*^l7W#cs5Z+CC~iqegZxaTe6hp{;yXS20Cq>EfrmTE2r<=T|p?Dv?6dnhzCH0kn5
za<kuqi#e<*d==O#P$khQ?2&`cV%|pyzt`23z-Qi<iazDOEn9@)r0cPJ6H1i(xy&oy
z=JqJ2atVeir&STfNR{(tC>`lXmV-I!ft(3)rgB$9$b}MT4xxahoAJSu(Ubb36w#BY
z;WaonJuM7JL#ZSR3Yz!EhOL99h-D^~$nNq`bG`7H4!!Sn^f^35<U)Q}&&jvxF&EhX
zk}A=7AmF+qv8NTsX+^7)il$j+ISm(wPp8xvn`|OA-QcHeCGXDxN2+rnTxysxS7{7=
z^~Q}GG3adl;fd%{^b{kKm8wq~$dtxtcoVQ~Y;4+5X??FdNp&GzM`9qq?yPNftek};
z7@tXpe?%ldBqU_K!T}YkO56MUR<|s&&W_jXRL0iFD=xjWI9y3>qQj-MjM}Ko@bmRe
z9ZAyoQdM;+a~;p8{-K$fnbR9e-|JaarthForP5DtRSfBR2@J5|T=jVg>r`yegz^0?
zafF4vzO>ukie#?|GZ8$#%O6cTV;7fb^s7n&C00gDF}*cPEsXEBttb|o$ii~U>FM1u
zZi|%M8;8mktdn1^Xe5G`EcmBaN=$zbCOtV^NSf<TN=ouPLMJ4QQYo);KV*IR@+ETG
zp!OO&M0S_KX7W7U9WwGGAz*m=_5FP{=fhu7{o19uiYa0$IZwmBetkHYuPdJ+m(bCj
zt6P@{g+eh|<jNC5UgSXCSIaY6`jJ_EI3G7(tPM@z?Jd5+@4c{sl@hPumhbxAysxUq
zOys;?v)?BZf^xLGEDl%Q{^5bL_N$%mq&7W;hT^<VD-y5)xb0>xBSlO{M~6Y9gm&T-
znj~zWN6_t@_a|PsY<F^Hs$_;&Z0XjzA09v-dZ4s6t`W=eOziyZRK3iS_(_(^^lJIk
z_uk&H2byKjB3_1uhGxwYiukWkCcTDw8V*l${x}dWV!y+R@5S2NH*ZkuPPQ;#tWS1^
zZ1k<>mQNbM<{$rJ=L1y~DV>w9%MY+`^Gl>jy=VQQR^z&h)Xd+5xumE#w~gjIVvwT;
z4Rfno=v*ORN8o;EgFO_6j(8piTL%Zj)^MsE&GHbWDO!z{ZT_skwCy1!f)+Mr9=Y(I
z1-dZBN()r8#fd5|xJfC+M6FaPR#fyVpOM0JuvWEhc`M|)$Z&i-fC1S5FX5W?*hwNv
zVdwi#e|vKYSv}InRKC}j?(P2pOBG*Xj~>DwG@GpEfwJ)nj>HOdTBLiAKFjZ|a4^+;
z1KT|74pN=a!Z1rL1_C2!<cpp!t2Q(=*xK5DgbIOmi#HNJK08mQ3cfvX+$U15u&@w|
zjQbs&2)r9NgnzZYKb#3-GVA&HGWQW4TpDcar~b&#xz^m))z!Ut=~95dzuv*dboJ(U
z(#PWBW4!EtK{;Q)7UEQfjm=Gc*aOg%#|D%C{An}_hC9uP!hs<nCQ#T*%=@o0F)^`|
zT+3F=mwP@oJp5EFn8YtM6bH)jk8HJ2SWbcBb7;vo2nfVr@8n#s`3pfd5ZGJ3ay&ot
zxOnm6!Tyw2rcTWfTlp?@%&vGIsQU@<V3Ye7&Bn?ez(L5gK0nwroOD|kfaB-$=FJ<9
z2ExDYX82)9O(P>G=Le`qf%tR{VfVzH7t^AYwAnYHA0n3!!)D5A(1?a&U|{fBqm&+c
z!OYi}ms-nU&t*XWadvhta9SP3QaeRfqB~IlforCw3k;o5$zZws<L|<!lX6)j=!{=L
zz=}XT<iYkTz=W{7qKQ=#ut@<Y?yOHujnB`_h(PBi=5u1;vL65VH~<%gC|JyO=l4so
z6#dRvju`rYO4IJ!ypF%$O%MGAnZrmeM@s^@rri5YW*3Gp)72p50xr?^#S8gCopNh!
z6uEeAeYtm6v4|c@NT7M0?h;~S$BaEk_pll*p%Wjk!zU+~H!`BUefu^yFYhRCyrc57
z@v^t~tD4L9oClY5bDKjHxOl7?Xv$Zm-Qx2#3_q+t-QD*(J8|KCzGQUfF`{bk@d_Uo
zSEToosB#HS$waLOsrS#HdbLMO_qDXNXcazsyHp9C9r#eo#-@($PgK3Ac(JZiR0ivT
zqL8IR2S-3JjAuApC!dCa0gH(#Uxp^Q?Bn1UD`GXLP^;C=oPj!x&|AsY_Tx|GtjD7E
zxOGdvGfWjOtqW08U;R2?p8R>?b7>gT{g0@>eEAZcgsLnO(K}X3@Ia$6RWd@!gOQar
zyr-uJODtQ^wI=cNXIgww#ep|Jw?A`OYkq$}VW{cG|7<sZ&`|ty92wV#h_SsifiAUN
zmi8ApN5`T5{sm8U)squb2E_o51q27n_9nioudJ*zsayy60jF%i$SR6SH~rBYY}f}s
zS634jYX?N~hf;dYRQA<AEhzq9ET&C+1D0eaavPsSgY1_FbMaRxC@8$mS%y1cb*{t1
zl-lJ19Q8yyD()t9FjQ33s<=>%*)n6T5rMMO=3>=z3jrtJ%2qo=o(e17(OLHal4AGf
ztST>P$Az^;cboHkB6T<{e*Bzi3gUO(xTAiY{OC<bH|Adl)&7l^*VRnr47rY2jv(Xq
z4>3c+fx*GX16faC^LJZ3VV{|u4G0aD-{lci^bZN4rl-g7srT+RE0Mzb@R1e+TESyc
zQRA$YiroLPq&7kO64?U?8h&~4N{@xZ=~U?oJmqFR=8r?mR<{Bt+O3ZJZZBjHM*r(k
z*XtFSdBwa>!Are@NpStf4gI{w<pBJwC#%uFzN2`wv9a+{r^eNBZ9Im>@Vo8)nl^Ok
zW@rp(09yfD69hF)O$n*jzb*-6hl6wX-o4)CU9(aRz+fs4l`KHPt^)FTLPflo{6BWs
zgUOUHU$}1zxHbZmg)ezW*@~UHoBrG_@}KP>9d>nhKmP+jII5Jikrn^^e5U&P`b@zW
ztD_w59v&Bzg<k_gM-X+xw{MxMxg=0()1NO75`-?Uj1;TnYP_Fq4poNcg5Uk-^=n)L
zg4fWI;2u>5P^C3?Tx+x&57|q<TeW{Fa<hCEYMOgi>?TAP*ihrP-;s39d}56DhjgxS
z=&Is>j(~CPz|=WBwa>~K*rr|alDqqJE1zJWV!V3ws;@KwxCWbP7t*)}uh9m;a`1be
z5W&WAcXwBL;dGA!upC*2!08jsT)Q#Wyp`KyqqFMSUYa%Hewc*w^**SL&CS_s>84?V
z7B%J*w||v+n1^mZdDfwnDm-zT{VR)Z_r!!2r6YrWm4XLX#E3jt%ttOmc~>9+YU*RT
zKP_h%{qS1=lxlqso+Dg74(aSb?S@}`dpl|~zGK5HbS4Tm|0*+6s_S8&XlVn(O|Hl!
z>saJ28Hd`B)s{3LW^tHg8f2WEr3Gp;MoiK>!EWQ`;mMpwak(w3*ikszuUkGqQvP7J
zZLKg@AhGnQeAf*h0ML@@8wIXX)!icT{~QRFLS?UW3;3|a6wWu>`}@sPQ&U<^UEjW4
zvawmm9}^W9k6Y&`pcy$8#>2;dJW^z=UTAOy*mcaBxGed&<jB8PsahPJ>bvss%Jrr6
zq2*pP_N?rGU+;gb$~v%TIDaAn;#Q0isyC~Avz}UH<?Jz(W&M8dC}eChZrYUFYevNH
z%#2CEATj89u%Qnip&2m6!PNO#)Jg@E^$1{u#ejlc_tz3uDgfi#|7yEwJyH2S?Mseq
z*6>K#)D9>F0H6k*_~9<53})%<(f(7ap+HP}9Q|~k6+6lkq}3$gwCU<|R%&A0rW9@y
zow+6!a@h~>kQ*CEjb`a!zFE<fJRq9nN7j=dewVH5L`2bdg?Vj%qF`fVuT0emslS4C
zZ5BE|`9^9}9X2tIffNr>M`2+zMxB!9M0an&XI_ENBv`L)7((^=LVnBCn(6nvOz71#
zqT%WsN~y)4KYu<1Tr~_7v1kt{pe^)nAPHi6dU{0*A-4sjWMr^{Nx8bZ6#S45|CqYf
zrin+Zx?bWuKa|;YOjIO-QXFMJ#W1FL_3ouw9;s@I<1D+0%I86~9>-9ke2R<N(xjtI
zetvz~*wh4Q;k*Bhd(N9pgmw-N-zFv!fM^9HhcbH|7}Rzb-?~D9o-h>kOdw_m4|=)+
zUp`-Vem1-Ht9`!g^mu=EZA}gUXJ@NY-vX`<Y5@Rf;39a`G7^L9aN)4*3_8`r28Dl?
z!vAdqn*?XLws9@tYGp?r=01u-qATO{X4m!$_3C9-@-o_}Ocqw9t%JSQF$7fj`=cQw
z9~gTJK&?Z-?*Snp^YGP3JC{q~onBsUhh~YOU1<EX9WiV`uPI5}&DdklJ(hmZLD74i
zl5%go?pzS6$_(rq%aJ0#)(9F?T5C~7B`cfZ0tytj{k1fi7*>?aSFb7oXw`9Dq$0a@
z3mpq96~O)c0(@I@5L2yxuNk5xAgFJ#Kcm0a!_8tKOBBGuqt{r;&=A}=>QU!0%$4Rf
zYfhzOY{C>R9=KWl_k3zb9d@-aO$2`W*xg`S6M5K0BKfW;;6a;vGwEA*2WFycbP*}3
z>|ckxQ2X=kGO=_mqI$!d4ZpudNF3~}q|wr6abq+x(cYhE5n-a(w41u>u;$rNUiHCD
zko)d{+I+Dvx*_!~uirh%w1ExKx@gslQV(~P(`6(Jg^~zg^eseWX_hncCWHWm0kCu-
zx(oODV&4^LnZWYvVSAVj<=xV&<N}E3+G>!<X+;9!P?}o44jHeb|Jmtr%FwcUr6b){
zAK^Cl>}oH%?FX!n{ztX7TxOlR!nRSBFsawl_t!n{l9lqrQ?<FHp16j1J^IuqFz?g6
zIqpTYKfa3p)6<d6hKa|w>e&%}ShWH>Ii60wrDuF1Id)2K%Y0{?3(&AkxP+`R%2nux
z(C1!4Hvs-L*BF2|e;U4V?(6Y<eNq6nN^?*0BRcI$$IAJQoG<;ZIDj9K?t+R<_AsO0
z4o(oGPPIgeSa8pxBfG^9f7rgH33AO%L4<&^Zo`I_8&m@h^|ZpC3hGD(JWMh{_vl~k
zQ8YoCaIbZL?p5Ufaj&CTCyJfI8SVeQ*9sYvHurN<+@|Db`l>;TQ+$i^wO{cK#iVXe
zRlNuWj<f+RA-w|1nGvWn!0P<r0aEb=%>p7aIH!y}#Kyq5=xj12AG)3Mg@Z&k_LSXv
zJQ_3(JOTm}xz{9|mj0^QX~0C`NJWE22~-U2VFb0T(#}AtB;HkQvX%xvO!J9Kj?<%E
zX*I1uO5<9qF&kHj7@Ont!J_7W)jUb9-d;08hKFve8kM>R0o|^2+X*h=cSge61lNd1
z&+2Cnu&4x>@LQwS*d&O9scN94em~fpg`JNB<>7mKJ7%tGJ0O26dwDqvT-;PB1P;It
z9fZ-DCsOc9N!y_YJ_2S7b@4~Ou8=4>5T=#M8d7gy$Q!?V?`_SsMkMtA;V2ve&M26K
z4J#wR=laa5?xKg^ia8K_k7Y$}!`!ELge{UXo9Kq4bb-s16UW?gz<vtwKqFKtXxyn4
zoj?m*fS^Mc5-r+;YJq`I`)+<27lWEV+eTXQvjia#Q42I`^B<qX4tdDQ$)(=YH^E*W
zsq+#7g;IuNGltvl?)lj<Q?W^>!H>_1Z*L34g6iA1REXfdhPJzR_0HT6W-!rkxVY}i
z$(hY0dM*1D2*7Ij@GO<=SpGcjm_w7<zq4!kZu8<b;<N#a#h&C#i1^YHc8_jW0pF1~
zp+e;8E07!lU@r?4uY(lTS7NTLny1wYijMNmGfB`+BN?@0L9Dc$Yq{ZITy^;xDW_3?
zx~$e0TZ)0*P>>iKLHZ&Rbmu1bI$=q2-$I8@h;S%^U}c0njnFb+QOjM{)s1GRVBvAy
z6x~@KOy1uuHFmsvX$~tq*hnpA{erBt!-*?*72~+HVkcDG_M4b}b>@pQp)q0M%}^xt
z0a3F*8+;2KF$osQ4&+tPIl4i0G>5W)JoE1E(5u%-Z09?OLFF_Rd=yzy{i5L<?@RzB
z>sU@Jsa%ax=kwG3&D~upZtiGATn5@_OuGiET&f01wR*7$vYCOm76Sf5Az?RrmxFxZ
z#>9)M3+YC5iw-O-EIUgBK~QhmT(*qfirvGbkuw5Xyt6hD2NwV!IezWb94hQs*=f3|
z7Tva0(hrTj;s4?;)u81wj}nK4PukT)vMMvV*QA0;h`t9ua+$rhBX%!G!%r^bo<JH&
zWM3K!9ErHF%XD$WpE|gr<!&&pXe1aPzk2HSn|D8gfna%czR_)0s;@49NkfV0*(pEq
z0~f7Si5tM<H~05Vp`8Lj@CGd1TlxH1d_n>-k3D5?FX(=!`zHspp+9oeBXm6v{Xj;f
zBE4VAI`t%5)fgD-!SQjiQ7bMmWT?%Q3B1qSY-84e6WKw{#$N>+fZeRe`}H-_B3K~M
z)x|(9j@V677$lWJn(OzFTkTMjMyg&gf%Zm(b=8sg)_v8SkMJ#TiCA6%$x3(g(g=?{
zEVHUxyak18jHdL1K-qt>UD|BlWR-X#m2^w7E61pKXveA@hsDN5N~pibubVw)clgKI
z_o`jyK({<Kgbo(hOZ%brOoCroBxe0DSl;Fq2tq4BIb!-J2|Als?}__-3vk8{HN7ov
z5!GfB*1iN7JxdU!U;2OJ<)J+7M~e8cuimd32IT<V@b&Y{%v&iGX#0oWJRlfa9Wz_#
z5Uz6PiER$;?EHST%i?)NCzY+5-q=E7m=W=Z!h!Dg3Hm;OKk9+0h~gmEkWnpaHsjjj
zHudZ@{fbuvtNkCSLW@Om?cfe}_nC}qMNKkG|NTY9_(Pp>8;1)8?mUg(smr*mFz~29
zTJ_GvJiBGQFBrx;6$46j%T27Sm-g2t*n~JiB5NPR^=y6a;J_BOOn}HCD0jGt1dp*)
z^L$gE{MIO8zG-MS*x^)&p8f8!<QxWQ63%PJL9lrnfo8c~M5HR;O6?kq{`C4-j&~(Q
z!pnoqp8S;R^N;2j!tVrVB};_e1+%F0ggf~tK{cBrNm%N0B$xr<cdg8bDjSqIJ)nHB
z^&>BVjzvo8t>l~x@`vi1n*2aWYdYaB{bTo_g$11+Gsz@iOnIP6M%g)U%PJeFRF$n7
z;Env{DS*1=mLPadIsL1=kZ|8jR|0Q+Mv}<xQdyAfurDP7$}pQuP&FUK#yqhI9{XU|
zDpFXs$|W${CQ`U3nTu&UnlfI-v}#vt5zHg1MI-kyj`P}Ty6n6ae(=>a2UDyR@kaw$
z>0+4f^Cqy0eg?&2xT%%~*?tDOogacsO#Fa|@7_%<Qpj07l3gE$e|sn`H^lt6Bgy%<
zPdB3T&v!Tf%CGC_rqg)9VpAi!)00fp7RAM(u~E!fwI9HMAIGu8W8uK<<>hs9dfJKE
z<ocJKU{Lk@H=z4qi>0p_QL%z3Y_I|T&Dg5N|B%`Y6(K&~%Eet*_|YYTu9E+r4ZCws
zjLVmQ7CnoqknLSmm~_MW_F0iT^8TBQ_usqLJPiIwEEyRYO-F4Q0BS1UJ|GAzy;{on
z<%r)RSd$>|iPt&YQwu{WW4!r4ppSmu<5+LYNJ6QTKwNxd`w^Qfdn~JQONhLKIxVM%
zN7hS9#MA;&*i;dJxQ6uNMVWJXGbj6o;S8Kg7Q>H5l5u`CKV<(HLh$g|XfZ6Otfk&w
zyo5KVt;M{vEN+%0IG3++Gl8Vb5`93ayHr%<vwu<&IT&rko)bWd9s%UFb#!Fc6(6g1
zafs!zvF<(SyI1T`pi(CcjD(#;75u9_PtcgftE;O)wCK|CcA5w2wz0D_7(np|FFu8D
zfo|YMuagVcNE@>Asj0>D@-}+KZFlLv^EfaQJg^w!_R~f-JqegJ_dzPF9~+AUUZhZA
zZ!CB?hZpqZGN0EOKk&my@Gqfw6<dz52JOU=LiGao6->KFpbHm2=N`$DjpK~GuNDFT
zW9-k@3I$$_<9akv*;Dr5<g`3fz($9N16aG>p5?nn2_tVUgQ$p78yvN~RGYCPV_9-$
zo*zJDq6OSI!9OsCM(*tDYQHkfLcpli0zT2#kXwA<Eq!u1hKn$D4vquTV8~7q!)0?D
zv|F}vn~BN+gKY($j+M9tAhp1|v_5*BpAoDM>0l8td*8Sx#teoJbSBefTR51fZ^ed7
zT2<Vq8v`2m+z<7BD-a2iVc-`i+BQr|zKV>{uDH0+HNuM#cMQ@qa#8EG$Ba{+#}7c4
zO6m2l*ZT_16fE67(4XPTOc<ZU!~`;c?0!Y*!)Hf(`?f8zA3s5H1}}Dqe!v#I2~j|=
zwBTDd9hadZhBA<j>5L@LPx48EW!U0q6hGSaymy!N+wi#^s0$~)eT&4uMtb#ddyIiU
zjID*r>8|GC@iC}v-0(EktGBV&*4CWe+}JFKnV}hVj6v(h2p0PWGEqd0=V*yJ><v%o
zWsadd$XzdVcNZDAD@BHac+UveF|)JSpQBqhIiA>i`~qYh1VW(zDtnyL`*VFAC$$<i
z6IcVtj2pnasFzbf;DIkgd{Kun05HM;SX<(_m=3porGO(F56jbZ0It<1;8XC26iO|g
zZ~{=Uh)+&V-uc~o>BWl|faeznvI%MA6J_l3-@zWYwzk%)u=fMUFq}zOu=2%v;(RUW
z%CM|B@Rvi~qV~!IYU<YjLL;C^QZ+e%V-MS)hhNCl)HF*avjH&{Evrf<^S!;j@z-5M
zl7voo@WAc)J}~eeK{-b|<|rQ+wWUByx3#lN2I6=5$`vX%k062vpA}QCiih4#1F!r`
zWu;Q3qxlC0b%RN2Uf$Shmu*(d;R1Y?iE0<T1i7e{@Jg@`6u~wJ2RUkCjfujy<^7K9
z!Jg)4jhmH@k}@IH)zI5*nGcSo?I{^Vy6%ifxV!UjZf??z;tf76Y^0Kjr8!S~bCEWN
zOj!}%+p#IWV3lvZ`cbA*S~L(euk%wb02);K`uYG6uQF5JfIDU*_t?1shEFO8<MDzX
zvEWwrX2_GnV~xn$1WUgW#H-)1ny`kgIuX~~-PUWGfl(pb9=3+u>xIkArd?#Uhx4T1
z&^7|00BIlvoVHe-q>Xi^+JjdKd@uU4)tL6yr$Xg23>W*-EJ0`iG_A1H`n>PiU`{e@
z<m#iPZ1=qpQ+{w}sH8vie6ceG@xnq5t;~9&ZOo=l7LHvE+yU~80p5Y+N<%ti#=Zp>
zm@NoAf(Jh@L3W`LptwlBPL0wEo~UBa@@|RsL@WSEP&KiDKmZbvDYU^CorX*YV(nhI
zbakTvlc~VGpW2~LEQO`>^fN66JSi$h#t;$?i_}VOAS9%mmU<w50LlpkUbVe9W&=W&
zkq+~&%lc6N>ha#H;r4td7706=cemj2Td*Y)ki-H|MK;@?4?(qz0p#Ivw4)C{*{VZ+
z<3{~*ew`fn<**Ex$R4_cirrXW|5DK7=pBtb;z4{x$`3r9a4K_v*nom6omOKR@?b$X
z+nMV4x1*KuuYeSB`j<||LWK2u*H!b4!Tw*$o(B8;fiwG*$D6g{?jEgLOKVjO{I3Uf
z=lUl<FZCNgmoMuq`@%~5w+%6+$NaRUt|J_9EkI2+IJ?`kEiEl7L6<=5nVy?73cJ)e
z-O3ca_=z@#L|JmH(zl5%iE28kPAN^QQ2*Q2ua4)U2oEkYLjU##Cj%}K1tFTSc0Iu1
z5WgOdo@gMxKDa}RA-f$Bb<8!OKEN(wU&E!6`nk5&1=RYPwe*1>U(GCHb&&~q#zSTA
z1z!$>zhZ4fk2&@Ceef$8AXx%#5R1o=W2NI_18^ntsagSG@by6SZ{6wyW{FVEAVMb2
z(Eb{?7vRgcfeF^J3UP{b+vx_x{e^>$Lc(P&Ggf9r_arOQWgLjS{l-sWlkUV$Xe=lQ
z8F5)H9YX1dx<%a~1nyG#q-zj}!LiNqR)XLFnygRO$Rr6SgbJMvkK2IbsI;=2iaXjZ
zP=Qrq)Eb^?y$|)verry$?ZX31gk~cuGCV^z8t%**NUTJMmS-H-*iK)}kWb>Ii2-j2
z_KiP$f&Jc!`nJbIIK~~(EIz<^qsyP*`#}_98w9NFy7N;UZ;)I1J}ce>Q(C;-dIGw1
zDl}Zg97WO&z^~$(b*h{m$i}iKKP@z9o!Q#m{ROnu*Vk9!vqCcdF@^pLNbx~832uyt
z=MUlCyy^FeR#kmKkgN3%o_-b<Jv(EoU6)v`>lyIKwxD7}q2LY<>a`iW?nGLbt%q7<
zsoQM5AC6i7-Z(-vYDrJyJWf)7p#Tekz2g9P0Bary7T{t2lqAT$&^(m1C7;68*SAJ2
zlC!s>O1YLjcizIZs#M7j*=i!3f3tWx-D4rE_8e3R?h&##Si}tw^ck*vejjSX<&SV5
z9Z5n-YZF!dpF}a`68T$oy-r2Xu;K;14mK!Ipd)3j_4|I={?#t7q7vy6=WE1t?>;Y0
zhipbam7BJON2z)LYghud=SwQk9w4}d33ew(bMdnwMu?969xc5;Jv}`?#KXg*2!7t)
z$_Qxf_b4fSfjP2T{GbJd(=k>G^#hvR_Qv$1?JuxzzJWCkpBXm>RLbY-H3Oh2;Dc;u
z4WqN*kg(GZNdE}$T7cw3Lw!BPNEt|HNaW<}*RSlM3zyN!Utht%mv~+UeOw6=0Nb-5
zHqL+;s-V#0FqNOWE~)eYxB-n83ebGipWvlSIpL^_xY^nkxVV86;Nx=%Y6biL^3swN
z=%>V>Z_~)de}s$}QaeG$+&JBz>Myg>{2E!11Z5ml+jM`r=~LMETuGwtv0^Fpt*vwe
z-Pp<2U^2r8Mny$UoP=kq{-xy?<2zU~jB-5d>56_ifArj;cxKket`Y4msK850fzO<p
z-;4fZi^)$lTixH=jQDVghnF|qwb-qJ$r1fretu4JxVV{q)9kiDo9z@y?x4HmozxrK
z{rN6MR^TE<Siw1V0jU=pp4QQ-=gZ$g?LC0J!SAWMy2G5uu2k`gE>OygJd;BB=;;HY
z5yq6aw!|kU#;In@?mm|<?@SbkLy}xGjp(rB#lh$8u+#RmCl<EY|K&|L-EUC}$%9MY
z5H(8uT?b^FjL)fK9M<P~Ai;y!Pj8+2=I-fZqf0)7Sb_4+@lLJe@1cnafe|OB>Wv1r
zeeu5iJIPZ&%I-r9B5)59ZD7=IcI@9@OtX-$J6jaQ3t!7vi0ipcOdOLl(cJt7dN=j6
zY?Vx0y-{+|Umj-<^g-c4Vojj9yKK!(LyqVhkggX~9$cNLS^bNB{A*yylLUXK_ha?l
zr8>DFGFg}Nmt7Y(9c^gvGdurhare)`+{QgzD!m;uc8{Zv4t5l$US%Z;S_F}Qd8#`}
zVL~#R5tI^psbaxzt<JlJHhwD}m32m->bSPL7V?X0L@oHeer*rJ5DF;4Zy*q+&=<ZT
zeFSBuZ=4#07El!dZvVo19RD2rT`sj+K93`Iz*QVVQ5)^22n~RRRjTIXJ3E>K1tr-d
zL0z&to^qV)y^03;2dQvriGE(szRJg}xq|&{s$!7hivTOX2%0D~sy2A0&Y;6~2DmAq
zn_^%}sB1u!YwPz725k&BQxORXgQ|R{x3@5BT!pbSuijsI12<x{HvZO1H%;oO-TnBe
zVQqpKi*_4e$7AS_ouN#+wQr$qD+X9@{HzB@6zKraO}-&9jo&GueFBIp4<+s*074{U
zmzl@14cV+qNY2vKnl%Q}29LnxLEwWqX!mR;9Unnug5U(HH>+_QO8SzCd4lN0{+R2`
ztKAvepr19BK>};0H$@x-$L4WQo>tlX7)5Z@omPg09UUEuik0O<lRo&eF~QlNg+yD2
z3KqI)WTKNm>o4LDj(}NjgA}~tT<N@d_hFIY7r>~9x&sjW17H>h*o^ZKD6&X`Kb`XM
z<wbmkr#<v6ART5s7XLQW#Qcna|Im;^Pb121oZER_pdf|K<gO`b3=PykOrlrp8kmC7
zuUtYwlr{t=m?n9Ahx{FaB|tFDJS6PhiDlNm2!#!C7wEcZ$pl;@fuO}_J;~kz=wfQm
zNz4VsEl;<u3#v~vn<+N1KSV@>gveJ%oUp1YKF|@ROASWABSoQw7!erUdSI12788q2
znkuu3t2hvT1*Z>>oE$Q7?VVPDo0{Ch6d_O|nm<HypIV=ps88l{qH2|sReXGWhbabI
z3Ro!c$Eo?0iEwcZN{dDyFn}21<jqY@g^r6#7z7Mva`t!t-F<R3%UMAktgfkvxHT(z
z3oah8^;0Sx$kGL);^-YY_LG}HW=|%BUd21V?)COU@(UZu5MS9=VoH5HWJ$q*fwun|
z{ANTGLwqoZAztYJlnteG4kCQ>5EH$uSO4k?0tkeJgg~I{_c&Ao<pw&fS2WN&fMzMs
zS|N5|3v>_|Z*X}z*YZ$)ciFR7FV@CeAxsbr{H4@l;G)d3AcxIlJUSjVv(+g3_{4;I
zwKEGui#`JXf*g_`D7W_Tz&(#wxd0M1!vCT~3wrQEfHDO%I3PuD3JREEJIKGMe*$cp
zGjuHZ5$e)lZad_JJAijWS_>Co2Q?%(By?{!{6GK_Vn@K{M9fs!(jx`>kBWR()gcn%
z43^GFtq0$Q3m0MnlcCkUCE*AJuE^^6TLH1)VfWGL*7C!V?^a3b250ZvTVggeZ0vNX
zvnLzhaFEO^Je4%=5LmVE0I){B*xiFwliB62a@%JF9nAnvAVKI8Gzt}pyBBLu`W!iA
z!e<_-<Y6UwVystRqOUlAjK<>=8S(zXv!kDq-CmOPuEuZ3Jr6Dbg%S(B-3e#lJN$nO
zD3u-EIADvxp4)y^h%z}j34ztO@XT0&3}6Lw!43fI_!yoNg7|^CBH$T;N+6LbfN&4d
z*$0Y>ipT=OCT6uB=XP)dv_-^eNd&3uY4CQu7YUa^9#_bD%3{(L-&&ym?Eun-nLxx~
zTXWWx0mMAn>6Zsp0jVXRpgt|NxcPkPha_j2T*fQ}n`c2}Him8gmXr${T!3w2O0d6W
zIwi9Qid?o$fIoJDzedbuO$LpPE#Lh8ZGiaGfc`iM6Iy5?3kirrB9Y&P2y|Y!Cw++c
zl>qKgJ{1Vf$e=;A5AhJP=?Hm2BxT6(w7?rwbfKm)BqcDQrh7%kG(xEu@HHsKoy)cm
zh7Gwva21dGVWtwZoq>V9N-oLC4qm+AHSH=XdrB426r;U0!!SB@<J#_co=32ml=!`N
zm!90&yp3Nf{giJ({e5}3)Ki=#(B?U7hy_yYObIm`-xoOb!!Km&)_Il%CphK>enLc;
zNtcCN)bfdzn`aMrlE71Q0KZHQAn%$dWKLTEV)s{1Wkafx9ris_cx0D+aE*tc|6@R|
zzOP@;tgc$Ay>I#Pms4&7#8jV<N$KZue(wVfqsl2-;am;SF-vT4MovzjwR^<;of7hb
zer_?C6EnZwIwC4iM~p#{vj(Y;*4s4W_vhButZT=+2>@@w#%9p^!aQR9l1CU^)Vk9>
z%~;dWvy*Lkgri2Y7#8ucg8cOA{Ol2*EBlq@K~XM4F<7i}#*?G_WIPvd@fx|=Q$7}J
z5s+xG_Ve?*0Z(*(n>V5B?#=q5XYnh{MlIKG3wg=_uJebW4(tjfoM_&kKE1RQYoflg
zvH{x67W_SG=`IaDg5-FAeIYx)wgE69FiBvG(1Pr>lxTfh{H&)q-!JJ@;%oN_edjRK
zt1MX?P@{<0ufzzOfVl*xWh5xs%|=lE;7JxfNNY}Pa!zKwpRRyOI}Z$!3X}-QBd~a#
zxeLP4G{Vdd%o!^-#euz>4m<<6A@#s+4!BKg6JIVQd0A`B?MhOqdVe|E?L9i4y%P{t
z@CX!N%U|p3p>=h2qDQd;Ze=cZoj*W*7#-jqNd{lZae1(FP=B}-sCoLbOdQZO(A)-b
zB+w`<DQMCD)~eeTODqFCJBS*xR6wWG48NxzMJZeq22fLF2nqIr>Qi;}%u^&GbS0z$
zHbwWuygEx7*IG_UgksrfQW?>I;xFK0(@JF}-4dDDaTU1gbD>7ZW?5lH2Vyr_aqI8z
z|2FA(2<cR_@J1u|-6wAin?JEzng#MO$Oy0q>Hl}5*tAQZMj&LBQpHC4Ix(>%1cL)t
zXJ%$>?d_F1FKqDx#WL(%;pP2bNw?f7$RU0CN6P*5>5~Hf6;#y2rOrT5s0UbeC*I%x
z(i!)r{q;4o@RJbS{;Zog=leo4cxTZ>Bw4Z1Nhbfz58b<amtjy%71D8?)3}Teq-nQT
zr>FIKcTXb!=*ic3`807J%948%|L-K!JpkMh5z7Cp0jSH6&m8bv8xDeNuo9edSm^QC
zBaS8adK@vAQ&H&Qh6SsT{RDGAL&sn{x?k_VmmnY@@Zj%DFoxKHaxQ67L0(|&;JnKR
zU+IhWo(5NU|DAZUI=pSpP6GP%M2_Fx@cu<dZf@?DW77)=>Nl#*kpC7*m)@im!5A}=
ziRXSqH@Y;CRH6D-W9r_20yjJPAMh^!Ge8tE+pNE3H2j67P&Vb|iz%?IK3Y5(YodP4
z8Fm@6?#S%L@d7z`5XRC5ajKXTRo{jS6*9xYR=67{i6ojqnby3;ZzlEj?BHIZY=%#w
zfNX$bg*~_mXrzkWorM1{n)H+zOh5czYSOBMKp2rpgu*kCM~_-TIs}!Ws_6({#D8J5
z97m({)$40`5%<K!e@~G!YP06rP_~A(q`|?g_zv7n3Xbu{-X2szek3>nYEGj8RYZ4^
zP$--d=#a*sLqfmmxO+N(72@Xscr>g~ImXAwEpN${ZSC!)Lq&Z{E;NY*bM1LWUuswV
z{1ugKt~^{j@ndc7vd`7}U+o2sbdii!AchyPR5UV1jW~MZq1>W>USLi(V%6w>qXUQz
zL{HcNsezJ-%wd4QJO{l~uQ}uvgvxuXPZ86z8tpf*V>pN%aa^JHl4nb0kU|dXd~}Vq
z*e1~wj8O1{Ujkj#EYWq_tVbo^002}3aT^$f(nn-zp5RYk%dD<nM>*c7DXaPt-9;2k
zhTar7!YD|g0&a}foO6pE?^#dp&iaMsOvTjKR+rkSr#$v=A!Q2s<1diqL^JyJ*-1cz
zf>Ehnm>=SOvDN|8BORqDY|2GjaCHycNY3Qs<kS;=NRVkBAWa%+TE78~n*I2Eqse}e
za0ipA`XQtu)oWZ!5r3my5x@VJ!-WgBzZDFsva=W8_WIvYNcCTx!4pZF!>!Vy)U$aw
zQ@4Ma-%xrPyj9Q{Y#}v^^eq5jn|pgE!v*?{jg8Uen$Xfg#RZL)+U*oTAq0zvD|HR~
zQYDc{KLT|==j#IV2Ys*!8k>5ZXHA7b%KrMn(GjcN%wrUQrT)N~r>4jyTyP-gQv<s0
zG`Q5VgW{m+z&Fi9kYv8>?-1@gE*l+qCgRW-xZU<F12?$<!N6@nvMw1ofTfH^B1b?^
zj{=f929OOSF9_-ets(u3S_`PqTwGjvS`{LoF|<Z8k%QYH?=bcF@#CKh3vb}Bim9Ev
z*SGNSzJUzgdOyE9e1-?)ci0eSiAfO9LW28%@@2}jHP+Q0K71Is&!60lBnUvem<722
zS{gTyJQP5MX&{3`G3<fE1d&Fi;A5Z<?3TmV)zs9aq8K|tfC(2Mhe(<)I^JjPDo)U-
zkohi185cnEMCJI|K-NtND+o(gPWoRLF?#*!>wM=%pL9>2wt;;l7t>pkE5gFe&puF!
zi=+y}4w``-wEgQj3Td~^Tw?+rXV5~zi%AM-ZwQhAsiO8|tKBF{Z5I?>L^%x=Jn}~p
z%!rx}U-=j;aC2CZ%I_79i@0F1`~=~)apH8bv{u%2Zv{PiO|dNpZ0x?ml*N^C0Jtzk
zVdD(VRcXQrs335wcMweiLW0uI^b4AvG5jJlFO>9GIDo;wfoX+MBY+wXYvVki492fS
z?EwQph!Ut*2vont>-Z7GX)=IuBVWW)!jKUoux3KwV_85~5)lyrVO%ZCZfVz5qug3H
zS;Q}z;~4<}U8k%u$eG63)V2bl{)Q;#k#x#m06NB=3a-MEgTAT=0-{P14i=VC&qrZ|
zE)cVsT!%*trz#=Mtr<xv0S}OYjkmGCzW^KW7w}qBn9FeoYXCvRh|Ub4xewGt{Cr5h
z{e<7o0Fe~Y5MePufBtHOehNQvu#}x|2J;NCd3Zps8;58SFgTD=0`NTsVXn{L-(Lk!
z4~BLKQ*L;k5nBxUa!vWBh|8`XZp92TV_>}M7W5JEvm{Bso|WNm`5XcrR}^3xAYy4-
zEl*1kwynXY9iRJ@aD9@|`SX)n!w<(CL|9T<TJZ+J1xruCE4cX(<XVrSJqUNxc_Rv`
zgQkRp|IDvnX)r$_1p)9U001*18Pt^m-oBN2;SMEO3FQ}r=$uW)LFhxGA|2iPO9Rp%
z+^SSIOY)WjMWcFV1E{eN;E<6O1n{FS(n2gnF;Ax^>q|ui9XvYb=9|RCnPBYE12Xq4
z8k(qZ5Z~O`kQmf~`MWd#TvCr8`&L-NX~uYGi49Ij@kLq~6O=6@hYFdD(uNR~<5aMw
zFg`-ehqsA8X_5>5*cm9pJZFtgKD&9};|q}x)kv$X!=0}Lr}Bydf|U(OAKC#RVblfn
zozG<}^&%}qBjwrBea}GeSN^pa%Jb09$w?K)UQDbtD;+a0(t<>;c$?o@&zhXg<n2Yu
zu`<ZMV0?t&c>6d3DQPyilaJ_BKEJ~yBs85wg<w?ccWfLSH4H+=9N<7SO<F*vKBBZC
zT4UQJYvJI6PeCoHy;PKxjqdLL9Uw8WYHtrL-~4sFeltz#rYK8-5bNo}VkYg`Ss*UK
z2agN)mpno(|1%kI4kse%(9PZ{%<bJu%ZAV!)1@4F6)pT`k&raADQC}n&p!;*chb#1
z`DTHiSwGI{z;;r38Mc|+o--J<NJtII@<7qMpa2mV&@Ci@nIl7QAXn<aaW;qPF<BKA
zd=zM;Zu3s?&sj)Z5yy+p*MN|T*r(p!h{6&2w`40+XEnz8w`9A&KE+kO?8pn<(X>|P
zKFGDe36Yssetv$CYhf7YZ@JcC40e0KUs2B53fb%dR_6^pCrG$k!~>~yU(*7=@&yFg
z!>zLW7l~Mn(12pPtu23RXh3O667tIGuG?z64<_{B$rrFSU>3~*goK5?gb$$JQdd#J
zsdPoDKHVE@4SDao2SYa0W0Q#HODqpbco+)#3ZpDMt~<0K<%(zY$1tt4kpx3Ihv6g8
z;jo)S(oS4tqP_a|HPI*%CG+2`*S*P9o<2EjbYfyU_<iqS<B`PH#2sG=a!Ggs0em#W
zc-76HJZ@j(vFJVP%XUB9YP}uxK$9R>HEzZ;6zC63%4i@m!_oe_JoJ4wcDV+oD)ay)
z4FJ2ek)2Uw$PfaOFoM-8u%6%riPR_$`^Djwu{XQTu)G8=sLL-SkMTZ&YTD{~0|#UQ
zI3A#Y(Tq6#>U+8XdiF~wDMBx9qn`?DC-Rv;`MRUf_vH^Ap&JFmS040|*GFEeN$9P{
z0k~93R$i_Qz?-*#LgwUx!r*OwngP+fO9dvKB#7SvRvHXHaM@_`zQ?UZ-v%d-I5G74
z-Kc=jH#T(~RATbAOenNZuM3_Ht9VcIcoE@?q(ZQPFFYp8!8}1gD$A*NlvpsxXc5EN
z{8WjEgv6pYY91s(m`*4e-I?Ou2U`!t7FaiXIXX5rlDr2f$8+h1=>+WU&iCtZOl4tH
zc6L)yO2H`RHBqIC0M6vmL=GN4K2tMY(+^QmgnCjUO42Qfj79J6n2Wq0+>EddRdYR-
z>3+Ic3afo`asnZ&OGvg31W1vLengmrQW$P<>`R#g${z7;X|you#-{oq-ESr4wyPQj
zZqp6vN)wl^Mq{v`Q4~G?b34+b0I)VI(3K=Z!!4a(Jfco%i-#^vb$tH_1R#KRbo61@
zZu3XOfDJM|3M@C8?*$_mwu+U_nV@>!q*u`c!43c*(}479?b*>Y6dkCA9kSGTphHT4
zVU?*>!HUEKp=vp<42OYiaY-Rvh8P95K%~X<^2?C<xF~bHZ4T{KqHq<8lJm}Q#iC+~
zsED&&7Ca>W2qF@wQ*urOi;J86N|{PjDDYF?p*Tlp62YTSvKXiaeatkgZlS{Cm=lLw
zP{xU0yW082S9h#@7<dGk74(<aM(A21rQb5N-L~50M3k6(ubUJWnnf}C#jsH<F2sh0
zX3|d_ug6Kfz@%Uh$r}EpC$E+#9rS>H6hJKV$SmxaOB*nN7c=(%MfyxvPwON>a2^~-
zD6Q8(C8{49ih?tIgOn6ATFSGks)`NLC`M5xR9_(Bivp8>Y4G#VT3)xbNNjII)tZIv
z)vD7E`909iVAj5(qSK5$-I<9s3#3o5U_tn|v}Pm1n&01Xu^7q=2C^5J<wmSnW~mMX
zGZ6`NSm@}}QM#V3j!E60AQ@d|8FOf-rA3BdG7u!^DY>RCRr-qM-(cUG`C0Fix#t4U
z0jk<(rL@2&1_UC*$<3j?@QmuOUhBC=93D;fp7sKyVBg<ocKi%*>uGena9cgWS;U#H
zJK=4emaV<^q`G83ttzKrKoYP;NWo=mfv3L+!<T?rP-TMhut9@^D~f@}aorp87y$7Y
zVPC`Ktjzu|UBI9qiJs{LXo}~15dv6#c6z!Vz&-NT1<>q}L<c?Q$8-}=Op&4wL?~8T
zGhd@L5Dq<?e#2#m0KW#P3!ZE`nCi#`1XL<yJOELj0V9b)G~{W4-UXEY4EYQ&Ads{t
z*x=V;#sJ(GNGxDLL~`Da&++#|2v8nEPO<{VZ$aKN0LOj)E_zJO{;y!J$&V0kMpC#R
zKi+}Y0d#<v7fxl_4XOYHkZRlD=F!nw#*ehXE7pfbiktz+x^F?G7_n-g`S5t2IHw=E
z6F|8#>4+A#wPl7w^%Jo5PXI0m(Q_xOIXha0n8r&u34M9me8~0(p!^x2bkROlJ%mb}
zXM?%sZc|cR=6Ag;9o6ub`1jhlq~-puU!h^L8dD2J&^ydzF-S{8Si?Qb^eRME!3J{2
zky72s?0w_IrF8!6d7#y^z1E#*bT10|?q$5PQzQrkIy3m!-=X+I1!IE{g9ACa`^E)8
z069+!FN!KE;QPT!ArVm+0d9d|hQqlC`Mz7Tkajd1%pr#Ci2<ZIkVplB2hDo!z@8R`
zxv}u3q%fYez1SZ*rtBmE@b&^o1tBg4<RqfYp8+w0jHxjoyb_zKMEE1UY0`wq3@2=d
zF8C6FYiVH4B99ABP>k*|z{@Sr)tTX$LzQ{-_mB@_m_y`veickFpbYvj%nIk}YObm@
zY;htXPku0~A(Ys}|HiaasB{6zj+~$E3jrVv5=)te2df8TR$$cdb)JTmFo9MN+)@Sx
zYy(Bm13#q_i;K9Oog5+)9>gpLmyygcU}%{H-uJNI>`x9h@$<bZyM4Vf2F`ZKfJ6hm
z{PP9}c;NWpq(D9CFSpU%b`o&gqXZNIbZ`?G2nZ3zND+l1leFS-0ZBi>6qr6NMK}LE
zt|x)g-_uF|N?q*Kz6}wpGD07%aOmZ)5Wo3QHw*tei(wB8OrU#pC~q!!|65DhO&YBE
zHX@s1G!KfcK7etVSoYQvXYd~~RSz*RF~7C8wz}H{jM4?Zs@H>AgtTR*DG)wk+60LM
zjP020y#1b_ZFyq|3A(_+8!3H82*9MhtT3W$z>Hl9l0z^+8o9F2sC24nFF5#ne>POe
z1h6;EWc-ftxQdF32OyHsl49izjD~{C3RuEeI_!Ns1I?PWtO~x1Y98f!Uz%BjO6QNL
z2kkz|j}F&=MYTo=)lGD$<*tYQcO*>6ZI2<pdJ6;Ar*M&K;a@3B9{3$V#ZCX30RuYK
zmy@2R3XZ?T7Y4>f5|*;mbey%+oSQ?C6t<JK&#kQ2(}Vaj0IlslX(pI3F7imCe9Hxq
zl&d(mJAg4MM`D#fKL22n>G|l<BXyX(0FZg=aQwrJ9VXY(jz%bc$o`oR-PqbvT3raK
zX;D08y?b%>)fKb46I|JF5w<o=COslPf;43st(#Z&3z(~7^Z&<_`S)1a?C;;vO9D*j
z=#QNu)yjN9SEKM?p_$;!cEG~KyvNAM*tzhW_ZE~)c!S2<#)S8Ftn?|zY$;HCzQg^P
z_k2XoC{i&1Ya-qd3`BKiloih&xVb{{aFSJB8t*&JE}a5PDBV?F$>NVMOg*+1h4<n8
z1}d7%c~RHezOfl?M*^m<C%PmdUB2qI@1f$`gPPow?zN50W51AL)PEiZ$C27M@@`>V
zO8sVJ-X30n;5I!D5uLQB&Z?cWMsHwfml-q(cuj#C5+zs5BLhOR04KJj#lr>?rHRv%
z0?}-!1PtD(UPPHsFu#Ys*;}obJ9|j~SdJR9&8p~8BpNVpQQR5yEdBd{h_QSz=;b}|
zZV|AGOqQ8JiLNcRv7s+axNY3tP-F})CWDS;mO|7=Ywc*}3!`OMZcgCb|MNzV0!{Sg
z&bdfC&;f@7?yLRGES>LjT)>WGyvD*3V0Dc&7B@vr_kE)T+RgC4<irMz#2gOPhs7r8
zjlX|IQNhrE6Y^#sG(H$w%4+Mwr0B~umhKl2>x>=Y#ie-6EAc9o6;vOXbvYE3Kns&;
zIFbhWsSH~bE$l{ZZGlHsZVKoY-jPy@#2~pqXd7mNvov37py`taenLiH;g`C)x{!=y
z*bSGhVcv@rkFSEg_`WqsNGSBSz+ISo21o$Rp~s>$OCT<lHt^6gO2bel_<u|emkrB<
z%nbv*+1dBO)hRoQhIM{yO>O#41u5syJ(R$k0>S7FAnz>CmtL`-Xh9Qzo63FEdi{To
ztb%|GUh2lqPAbU%PR0Hu*Lg<S2yh5RhJ|>1Qbj;ahRh?#Usku;9GaS&@kmGl%gf7`
zRNFlX{>MiRxUK;5eEI2X+xtb`OOj}ap8qFp?wnY_3}UF~*~nlR8byxGUm0S5(~%ld
z*B$RTF4@pqWDhau(8CP>(QsoAoTIsK2p)Ghy4-qrymy@xlgm0aKeWg=moVvi1N}dr
zJNm1=CzteOJ9M!y`+i5vrAt@61A}PLDT?I&{))?i7qivAy`$LJNY2c4eSWaU=RAES
z?lrY<%WWklRYXv}c!!^C(u4452hxwwAGjSQz=*gR*JWeSe<)jq{fJ-m&l^Xsi>ypw
zuGd64+bD+JEik!OeUxQ2i_0^(`EJ(nBspbq>Qabuio~_CtCSru;(`nk+2<cP6LDe3
za>>ht=y=_dO9-Enc>3h)q<5p&I=b`s4|l8nx>^76#kQMf<3#DQY!hyCGZz7M&37sk
ze9TS3;~9pJZ)MCK16EA47GI#wf0suRc}EFaSQTyH;#LI-$IlIYWso9m=g_c7D4#6(
z4p0fW8CgdZOJx0dn-g3{s6X28(VHhHcX&sCa9T!ZUIz=W?5)fkE~+(|L@BdRyr>e+
z-yh1iGG<CYa{3J?z1a`*8@U&}ts=dB*|*@+n@yaU(|t=Foo)Nru@-g8=kG4lT|xj3
zC?^mWgTaES!RbHpyuglYG;_U*|MbywWzDg&bP+78(P4J>ux$Z<kFN`;f(vQSnOIB~
zh-R?t%&qU6hW&u)J=2Hq8iKzES&*XyPi4_=m)>z5+w0uQb!7#s*rfhvy?uUIL6(0s
z+B|t|H=&o8u(OPFr7mFsjrX;6>jDF#85fvk^+sNQv;i-E8RNVTpCZB^_v!0sY5HSY
z`nDgcrS$Im35(|<PbCj#ZRgJfqFmn0-ykM6w`N+^iG7BXC$PVZZW?B!O*z(D7&QzT
zGd9p^0pLKAi4e{_pxTT|D@#iTz?BWn&8Q%0B6Gh0&x*J}-GVo4h#93W<|uY22DJ9}
zByV&Jg_EIYqkG`DW$+25{TNreymF11Mw}z)$6Q9a*C)^3qs6sn)6;%~7|N-SLIiyN
zek%qtiUVI|3O(E0dU;`?8F($RpgT7b6o*z^Vm0;wN_;Q8ZfONm16eBdVy`+n9t><w
z0Y()x)%@2(I>qKs?=DmxZ!kJwcj?zpU*Ui2WoDf}tNbRQle#a@oexa1ysK(*zKIVb
zLZtbQ2bN4b-!(bR4PVX#R*q!)KvxMN<7t4`OGPd@!7HKWVMR>=F2P*SMejrbHzmkK
zi-nN2LjNgZvqbLQ=(P?E;(^(t#~wSX<91Com-R_DUPHs$<0<{Ym+B0HMbYA$FyXTs
zG-PT}98khI#;eY%Qe|r;w<iQLO3H(Vo5b%7@hHK|2Pn8TzKRGmav3RJ=V$YrgoK1g
zd#mlkg@zS&vsbC4A`47DBa;d(fzO6yOoOp+vkN#my^dj<{)Urw-KXHom|}TMq1RRE
zP(~^-azkqyts)k@IN4O=#Se?T(v&~$H&aV2K0i6IgZDIeS5>(c?LnWp2rsNccX*Ww
zqv6ZDVBEtR!TcAzTm#<3RU`m!TY@*3O?hHoLZzO3rjizzdHq`u(<mon*zCA}b^XGz
z&_cGM?u}>u9OYd5R$ad7cxG#3TDU1>cZX;spasBd*4RbeM8;rfxYG)mZUdWOz8T)$
zfV{8)yp6Pfy<-FBoe&)()--V%=8TDKYIZ-sYvSU#ATTlOu)t>2^3Es}Xz}^@5JENp
zdB>5%*zikans1u}vh8Vrn&*8tK_P;4&Q46eVt+ioD8*kd_1b=;-Vl$A4A4TLR>*-&
zx|^=_OCMjx4<jQvbi*k6CxI}`q;4r^u88jkGz%D+zIE|jeE3>Be2?aehwGr*<w36`
z+|P>(bR4WS5xzWB?y7+LiXo7`@ZA*0LF(PadOuvOtdI}Mwb=V=JtzC*)s`C0%5<u4
zD-(DX^OdOlL(AiM1eQIN@cjsNoL@%i%4un-tU74ac?v*u&)ie)l~qWMZ_+n_pj#CI
zGJQN(L@%?r{jxm6Jj6*cNae`A(6Sz$6n>j(6Ki+w;QK81;By%VIdhK}PnSKUtoWrp
z#rT)2nD0BV5@B^uF!IeEU0wuLhMSKs!|a7i(WgB?P@Pr)jfpkxI6>WM#m!0u#wZ8j
ztJwVD&`=t7_8%vZXg*`3QR@!h;dof7vkh1fTzU&nGKj_4Hgx8i!wYhfft~>`2L<d4
zEV@H;Q4|jqqQK|H_xEqAJIKL<y~oaukBZta9#%RJ`^sVbI1(?kCZ0dTx4W&Npn!}m
zBXxGvQVts%awJ7V2jex;6_kb}6Y)yZFn+sIthDNY0pgNt!>elZf~LZ#4F_k4<Sf+w
znRc)HavtqvASk4B5>~c9ro<q4SSZFn9$MM$u{LHYhi>0y3UXkhLwP%Pg`lwg^XF8Y
zoSdR=GBR%u4?AGg@j4jua)Y3a8Ut=e0*gs*S6j!%#(>yBG6K7&gwo^MySyQwGTbA}
zFjA4^c1a)LGq_S>e^4-tehfP_EA_`K9k+|ajzZqSHMX#mQ`chj%R}mjJNF<wQMfH+
zUs4etg05h9a(XRl+RMo&2^al{PkeE;b#z_%BF8Czn%KNiI5RAWl(={^EXd`NBf<9!
z0kgT9W_h|?xek|Ub#xR8{|{$x8CGTYwR<B<Nr!Z!gmgCu3P^{vbR#9*Akqy|(jbB$
z4bt7+(%qellzQjV`+olUyn7$}vxlr}U2D!U#~5>*zmt-OcX~4=4I)GrA`0$6K6$Es
z_mqP+mRvRnp1!S@M-mPM1(xRq!B-Gt)a~?<EPN*o6l6>}L`hyAJDufxm5`iEoqyvw
zU%qi#!2Wu|C0&VV=u<l85WjEiG_R|hn~-zeUWQ^UO*#v&y6BU-pG<+!izqM%y#npZ
z%sB5&wSZeOa4aXgf=ZkLw{N=KG!H<9Kyi`@T3EQdld4#EQh+04rKY0s^PkBUYP+RW
zKV>6`kP#n$yjWn5JBG)hq2YiIRV=<vHcW8*(Pt=8$STZS<b8PC_tW#u)j_{A{*$bl
zhL_oBVK#henqn3jR+iG`lZR8#=_CLaOTJG_*&QMu&sFpV=Kz3K`2sc=IQERZbfBjJ
z*AMGd5S)AwVA|DkLBt9*Oy%Q3lUaLYdXT2yyFhp2axQ^`HALj_eJ)r&*+c4#a@-0(
zwZva5og54(1%vigDY$8X@V$n10YI|_Ffla>+nvF%&9S^Sd4;KD{;z55|H%3rV^*nS
zNCjSSJJ8NJ?)J<6y1T8p?xAscLT|#<9u+gaTADTSIXz-`&6_3>mnS?N4+|O5Y<RfF
z&QzS6Saw`g<pIOVb&^L{P9%<bH#|@ilT%W*Y6V+^X7e17uCS=|{$E36fWQEUdulq%
zkBAgpMd%V)q5roZBst7p!0u6Gi|>d~&Gh2dy4V_??oo*t@>rvc(hqW)@-FDlLeuVe
zvLM+gaP`a^?$+2#E`MaSR7)aYoLKzoX5A;&AA^Cl(xXc#Su=!VZOc6h?31yALEHZ$
zTZV3#^eYHLn?deT;FJMc85dXAyq%XvuK)ExQCRSYz0L_{=-vzqTv?Qrs?ek8dcui?
zZq)uocR{creyZmT!*9LEQnk&&SKBm|s)#C~xR75z-Wh*5b;|3wg9CnAaNANqM@vhq
zJzG;<&0@bH118tZ=RbS`>6`L+c&G-bi9z?Hr0(ipctC$6mbNj7EuXhz;G4Patvwq1
zmPH~&Z1qVL<u6VP4#bBD0dWeuSyv5f2%p!C<S753>oc_>ZA_C)Wjn=U>Gtj$R6B=1
z^BMfdw-;b~6obIrO)C$}<AUUM>C<RQci#&vkjs%wLjS-!l5On<Zo}k=>{wGeB5|6Z
ze^m@qa>_U;1h5tpPb)o-9`vW7f(nX>Nk0KcOy7CfntDI6J#9&F!^t$2-P7VUTRvMz
znO;TqiD{*uo8(6$Dy5FWO7M#RAZ7lbmtyz^mfN=6&P46kAH#%HaR+2eE6!ALTSfI=
z82y3vylpR_ea!#SiN$eI`FwHC#@gBTeWv%oorm&0)#DmmN(Kg*MnjdkCgsvT<F6s9
zwczdjM&CedA+Rep=-?l^ZVq)>O)%I~1We_~2B&bN8%9$eg&lT*$sC|xohB&%Lc3RA
z8p9mn)iP2iF|c2RR&=RyzUsR}ra&uC5#&28k$FOre{wetzJQR|s2$8-YEzXx(7y$-
zwbD^t<8P#mG6d*9fm+u1VrqhPNb@%TYzlLSx=R*ovN&sZo@l?(6NVOuwZF-T@LS?v
z#o!pcmj3-c7x#iR6mh)jZiwDI{AS1Tl$F)a-p){O-v_0bKjot<vWdHvc{Er|$ET-1
z09#9+OxT<^O1ZRLu%eSuW$)+W-?%Rr;XA~K@Gn|*gXvX7%dJUjlQ?@`?|=XERVPBG
zbMdd%Z<s+Qyaev+H=LYJodYIFdXIj!9S_EwlVz;)tIpp_KjDX_TWe^FiYyMa1v;ry
zTzWA5iB$ghuWIq1Pzk4BC-%70*#9~(x33E<M`+tcH&t)YUvnO?X+so~1HcAo^;NKW
zq`x(RnucT0+=r}M015+3!uS$&_$(i?p}X!_&o?~Ihbc9JP10UM?~X8E?x3}_b+iRw
zn&{NGbVp~rrzGoIUfy{{vUtO@ljfb6S0W@CW%&w_d*U@$<DWb29R5bERcX1-;iH(D
z4v6xbV<pi*xEgQRz(fep$SBkQ%$E4Gf~4CExOcAZ_AX==g;S;V6Z-ezw2)cq7v959
zkiHh$^nlsE^ORy-ECu>?=?k6J*_Yha_bh|;vJbdvY9|?6KICMVr_fICIv4!cCDv!v
z6@EU!C=iGu;(SD|2lgnZ8%LzjCCrZ*Q`J28v_EfNBbavqV`wPB%Vgo$^^qVVTNU1W
z#^#J2-z|+A8dnks79NR&nL}p;6{km6=Wck|EmhD%5%gh!3RyD;Vu+K@a(BhG$DNx7
zv4gx#^zrfDKEEosL}63vkkf|ls3}DNX@c&k^_*342xMpr9#s^Z6zzjjqrfkl#+C|I
zMlHr+Z|j)^y>!TcOuuaaPb2RcYC73vN=7%iy?b=M82*UfquY1qRFQ@g2WoHHocAui
zQSo8`diHvr6&C4X6K>BhdvyG{dYSmH@~T7iJcEQj$tV1?fO@B-FLC>4na8h2CU2SH
za{(c|jHUa%Cx@<wkKsZ+F3Iz*!@h4*s~%%S_60)mab0R`g75jbN#|Iq@cPukM#3e=
zs!VjXNEo9vO&ORh6oyacg{y|6*m$L+9(uTM!TY|A9U9GcI=>{LSAmj@f%ci0*Wh{k
z`|X|v$}32lnr_Qmn`thlOwGtuGRSyo@ukQ8=3Gdvu{HCy;wRSduHiayn-r21EBws$
z)OwQCy|k<!w9O4$>VV`lmQir4Yh@Jqr=js`10RLOo;r*S9f{kb>4weYmJ^5BdUne1
zxnPKQ`zV!kqOBgh^OwWVv(oPICYCX!rv(exG^sJDR6o)XN(t!AFs?4IdSXk^{;KC~
zxot!vNlV<Two82<$|S;4iGPq{iox8$B*7b4@y2D}U1B&8s<*Ia-c*UOmF*n4?Kt4s
z+1tcw4XcHa2khguvY!&7Po^Z&&OH3<FR~JGy=d|}`ik*zy|1m-QQ=zz=z@HQke@$5
zMrSrUZ<+QJk}Kd-8>ypA=emt$QmI?Y7^rEA(5b;2C=*nhet$!K9AG-{8vFVo&U^cu
zh++m03wqv*AZ1<+gdS*c)|@cwMq2IRdo3z!*KZ3sqNt4&7Ek_);alo#gHmqloBTFs
zlB+j}xSV;c2Vm$Xcagk_2Ui+G6TOXumRW;M<#cF|U=4}Fv&WEAhs_;n;r(4+p5F+?
zre2?{4ZM!uuj{PzKK$~uCp5&h_B}o2Mq;tbhl4Yz4<j$?S?zaWq1&v$H@2^v@Ab}?
ziR$qZao+-8qhv3!!FcQlqQDrMV`2gP{Wy9Ud_jSr6wc78N!`FH^)c^ha+<xqu#&1P
z@pkc&y*0K*KFAZrW5tbgyn3CbtQoSAN{6>U2pKV#F{eqBD=xCX&=NP2c1+&SEpH9v
z8VzyMt;%&tS^s>l^1;>{zWiR(DCC_JQY2B_dBz*#3x?Y?v*N|lGBhP7s$KHDP|a1<
zHbT@gv`<#Qp717XlW~hv&G6a}1A6#I4*{j&SPs5wVQb+lq`5L);<|-|L_KB*D(FJg
zw?Wihj3^XsgL_26TRHJ3U5IUzT^<%vL!RX`wrF0D>M39D?s+rJJBQm-1lv0gzjG-U
zSNz3!(lOcR50nHTkyl^H$LKqUD?J}}JdmKlH8^szUukfAw!PTSExq2*;?-nmO!8Gr
zZbGCCdM<!xZSt-l<rkgbJE^X5M0Pv-NWw1zT7Bf?F#FxnW>)G!Eld~2xVf&47o-b@
zVDT{Am{N?`j%=Loz~!$l&ZTqfx?qQk8@3_Fl&>|01#=%kN|PC8-Q$*qB{t3l<oIeQ
z7$p}wvyYEC3YP&9Gu?7;x$rq#wV3O_Fw%zX3}Ryiy}EkAssbspLa}UehK(*FGP@v?
z+92puWha26K_QTT#QC$M9&TtP!-k@Vft^B=i)SY%p@dcB3=XZr3zeSeY=NNQ&Do~n
za>^sZi!5wr#)0&%=!I~pv2qbQ0f;~oY-*Mq{Vs7{>>rN8>(e6&k5f#BxA9XGb=)3T
z*?Abg-Q(60^Cq2l1Pp?;vG|?_r9Obj!d^Q4N;BR%Sf_Xh^Fl*--&z@k{-N*X`JvvI
zPX*@6{bO+#$*~)$2~tsAl3o>qNNd_S(C^W6ygFP#uT`z*wzq9A70c&bX|CRSZvARu
z338hb4MRbkPt!Qf4`x%4WNC)ys$3%k-af)`xTokl*EYT#Np9Z`-#CBlKMz1}48>}Y
z(yeUU*7HAc$c{e?bEDs<)DT<R5dcXRJsv)jp5fxse<Ok^;(>cfKp$EBbm6ml#C057
zF-zmNOH%y1cWqk*yZwc)aSv-+$-cd0p{C=$_+;ZHWTqOQK#wb$KaeP?|A)Da7@a)d
zX!X1uG|RV3<q#e`V0jn2y-2B6OXwA6ew|agu|{~>+1}SP6Km0SnX_uH{v{JNs~ms>
zd0d{wcDNUn9FE=^4OJ8<2cah=tUuFbCK9753kAdwO5~0i=<)1tF#cCQ@=nm2<85We
z?jqSh%(Yl7n=uQBs8aK_IptE~tM+c)Uhn1;CO*wW8gQI~ht9n_YuR^MXoEwYDj6r^
zZNs~cKSk!f?ke{RRNQqxEvOC?_qV!VFrIF-NU1$*o+}!A=d#*CS-;qx@Yo;nU?|Pq
zq_Yy<{Wc=b-@u+ggH{!KG&11i-`)Mr1>eluLbfmuVyL4xcZ&yPBNtr*5#D_JQeEQ{
z(v+@T#azfxx8Y8Ag9V8gGF)8`$B%1ouMW2%3Ya96JNr2PVDzjmRC6)w=Ss*J(bcXf
zzD4951&_e-!gEsu)ct(i42yx*OBbGpw%>KCIqSM&{0;oYx<yN&LCiQ4pkM#w@!uno
zv1#6KO=E)r85mkpQhZ#d_T^OPl0f7@<qGC<pNdWQ^97BZ!}LM<O)pW3WAWsw=M5d7
z#SL?Hs@(#vm3Q4^Ig0Qf-n?I<&Ob+h=qei+tS#>}L(xQ8UXt|?p(bT#6KK)#1JGJ(
zQW$V7-2bML{7w(1Z>m`d^$)c0+2L1KWURu8vNY;&1C_EZvENWnd+3_5Tl8P7rN+oi
zbNiodP9)EAn7LH#)P-5FMSS=FZj$F+(I^pJDn4=0*jW{5eMC-ud{RPrz;tS%lvLy>
z{b_QVuZgtJ+49#f<v+(&Pzux2M>jWmyQ*V`sc1L1vOS-qyeKfISJk^&sSi{8b0Eq6
zR+{1Q*33?ZmaC=p3P*6WaHeA1t)!(6L&jcwb}{NNR}#z0;2<X=<z@96S@?2jO5fjp
z{*BHST{C)H`66BD{k^1E(P*~*JYTNvVx?`crQ_v<KJ>2_<9TyJ3$lg$bJEqMu&jD#
zS0Zs!!TSIKz3nu5OWr3RDI^OIcAg0k{H$jv)S+d_t`&RyXAYhhNU&H89x>>oOig4V
zFsK7Ha%HHrQNAxX8deGS2Vv%Wb8GuyzTtc~=1vaMmm0-oTw#NJfIN_%@gATYp&-Lg
zf@)2%{A85{FS1Vj?e<zLDR=+c+evS}Wmu^3I1ipq&6C74uvP?X>FXW|!JfmH-0nEp
zCudDW3vphv)E=982zpxKrNrTfKjt4?G(JA)Bd#OWx1M~Lq0LG5i}Sgp{x=sOrF+VY
zHT3ikuKEprI2Z!Y5!1nb%*yfZk;UZ4;$qpC*c0DqAJ_RhVS`7X7pWWAm*b;ZC_WR)
zA`JiHCxJ8zXZ8%_zRB`)COv8NTD3%0*3NdrCvvGP^^0Fovg;vOAhJ`%t7A_5M)o5{
zW6#wXK5svo)XnMQBa!(GW7zdEM2Zo)?+uRszFHOZQ<`^uHk|Mf@Zf)vHq)RAXMT2P
zB@#CyiCj7L@V<oC-LLE2@5Z-x7s5ku`^hYJD4tFCd1yKS^RfH0bm&EzUjvwR+nOgj
z5Ug2joy2Rr#U<qW0fK8Sc*8?|-q4?*$>z?=dT8}?ppPRw+m~g;km@I;`hF9bcPtT{
z2)^p}<UvOg#~bG#uTr)rt2yR(;-035*7k-XUxV@_9AH|3zVZGBRYk6N(h$`5yJtg-
z>S7>V{C(wG@#}ZvXy9Gfz-pJ7M5K5EGzGFyLjl*dq@+;~8%@*VXT9LxBo_n60;enP
z9C*2Pvu;Iucb%?!lmhmsWyiobv^Eql$u~v%g%?{+?S`tPh#Os0+^)nn997qDo0+<X
zx_rvaA>~<lmY(k*zwyvEEcgsFx+VY^BMV?gi5%viu568rj3TPhRR7lWf7fKZ{x5Bc
z0m82Ewx;_P*7xMK$apX;wKc~;Y8>QxZ8f}0f#A{gmAdK{g*vrZ_1pSThVa$O6kbY=
zcV~Tgau$(i{`vYX-eTA6IFSK4N2k+aQ}$w(MP}sHMz{BkBL&V&1D#jdqOMz4N|;G;
zXRp4EW89K|-1<=$eW=dAB@DVm2A;-ZgZD;?NPnv0f0+)jc^epK{6A`RZBNC#|HMa&
zMG}dL)V-&e0Yeq-ov?ZZx@2uhoNJ8QN%govY6Et&Lm4{75+eFT4T2s{N9==h(lTKJ
zDT4SXqZk489DX-NS62AOcJXeJ5xS9j+l>}`Jn8ky&TVWur#6~N0mf{q;c|_J;6VBV
zYYIuZ@A;wxcxgO*8)3VK;Fcc{37xpf{<EW24o2G-y>r~d?=IU;)${$2S4RMTY(^`J
z;b}LcurDZN&rB!TjSq2{0(3d5Hl2HhBv6G6Ue8mwRJ%;EwEi$Y7X%&ldAx&Cm!T(U
zy2$KR792;K<CGr51q|aM?x3KLC;zK4GxRMFR5kiTUib5{#PbanZd%`C!8Ku)cxAY>
zddfoXX5H8#E9ieP`RTA!x!1X|g9Q)Yz=7zznNl%Tyr8#MHAca(;OP%>{?ZRNH>1t?
zbMgBeW7;>v0|A&Jb6^w^TF(y{80f9N{wyq93U2n*e{?GciLBut2e?e6X+k@nHCSF9
zb2`lxFjRzLdhZ)rs(IH7o>EXRG|Nj^mpB}%SO*AmRc$(s9_!pHotkSUwH`2Wg(<9o
zu_q`}{hi}R7##th=gcXOuFxBU(*<|vvn!`iL=?+=4gByNtH!k*nA2%5M5Nk@%rNYU
zh^1Acl+aefzoJdExkED;zatkV>r9+QuI3%7Q#4=5S9=^Oz-!vr+W05f=K?KDt3Qaz
z0(9*!Zhz%S@ASr&T3NOl7@U<B@Rf#a`;66)y3Wt(FzB+1bCb$0CVAR6Q%EQ`$iAmx
z3wYwArs2HBhrWs>&6jXwm+d`P=1`<fj3?nZ7f5Nx{HM0!tZ@go(5#GikHMwsYG=#k
zag^^M`I-sqFZ@Qn^C#(WUY&)xZ#T}t%?H7l3rd5<Y3FncLCFB0_{95l9ge<pE#tQ1
z<aQz)`)g#e`Kt^Kf|&+&9E8*f5ZIz$|M?9V?{2VfZe+%HV5H*xDl9T3v6BOyF{~=y
zP{osIcZS`vBL<_fg81-@t*D2`P4zH1X0Rs!Q*)t*2$Nyj-d}iVK}51YG*@jV)Mub?
zv_P~4C2j|olK;;;n$na(2_r>?Y&@%U+=dOs^Oc%_!yKyIzM+QUQ{IVMsoAPFizn7-
z?SIH#bA41)(_nd520hy^zBdGBF>R)hDC79QY(c;Df^eegph}<5<;NjIL?C59pXa4H
zCi}T0{mH8tQw1$R@x2qfU7DP{eV0WlC==R*IL=RMml7fDz;Wx|Yzqd*AG}bu#6iB-
z=-%@!uesl9biIDO@Z|DG&o>9pQhKzR6iEK(mfWMRL=0R2{;i2>SDHuDL?wBLyXtFV
zOshtlj!K0?>1j78pAFp^@;DvJ(bnyVV+2n>xSh%P<M+l_SXolO1ZU>cJ9l}Q`~|I!
zn>NVR${{nNdx{JEx<4#4G%sGrJ3-^K8l-!Lfo-GLR{9pyF8&$+Ub{F{==+Hph5i0=
zubk?fhd@a(sVf`FNeIS?sO4fsQJgmZp>r{sjk9{yC6PR<!*EKunjEpY-)oaKzLp~T
z2;E@i>ilrGV9q<-U9oiI{Kl1dTe%SCut_Ugl++b8A21TB{v1A=LA@LxDuVG5U`pah
zO8}C@f1<hn2KP%w5)D*ZZT&hI1IA7;Qo&gGs>R}xwC&*NAu5ox6862TyM6QH*;9#e
zWHnQ*RofrM!=#1cp&~ZTA1FG`hrU!^!On$-7!S1UdbnT0kCX=6Ub$2cSCul8e1Aes
z&G*SePE+N!hze>6u&CEPH56F!`rnTo^~o21A3HoeQ$x#N|MMw<(tm4MVea<U_I8Kf
z{(AL%-xZJ)Y17icV`7*2CV9c%H{Nn5Gh54@)qH?|aOz%41}^fCN{(bAGjpyMf`att
zNA558wP<Z6r5qEEoiZg-DSv!l^7oZ%Tg^orZ%>H@K>ntCz;O*di+l3F&7l43Df3<E
zQM$yx(Efgxz$oA3-{eZ5rwpb(e9@DP*H-V!1Eg9BI0oGqoHr=qU1H@+>2NX&+`I!;
z5doye4n89qq|&GmLHFwieHU=YUDN#dF|j*EDx)!goH|zT@!-cy`>HxB>o@T~rwf=_
z{|;26P|2okKgDDs5HWxuqCIP&|7Zt4|4Lh8goH-s=|`Q3(FTU$uFl^Q_a;<XSvvKr
z3j0Q`kd<x$piARD#7JdZ3DVc0%R}Tgp*6xpZ^^0)t-?5CJL-x{4wX)7Dsz>CKp;5z
zRIHX%thT%P^)LSdk`C!V$!5Xwo#)mp9+!>yLs~-API(~_ZsQOfgA#TS)Z$4sdQY3T
zZ!V6S9GaN)<Y9;w=Jh(d8HUW1r`!(ELNBz|*TNC)>*Vq?Jsrv5Ip|+zQyx?zD+F2o
zF-Oq{+AWcxv?zt3Oc&eM%>k-KBAbkuwQlQnf)#aJOSm@|vg@ip8SUN8heowRtIy{q
zZ3LR4v7P1A0p_xzV>{fE&nxtqd-40Tg_rhqp;__HyRjL%F>J9%y`baZ-~Gp^2O}Pf
z2pL4<z3E`9RK85zk`Fv$lGl!+Dl4eR1-vx@&`z}ANo`F-y_zdES915D1%Hjx$`uk;
zb88#2#)4N(h3G)pmb%~~S>vGEb&>6+NLbB$+jz7Ns?<n+Ci8;zAUMT>_Wq={`be8Y
zFDHxMulQ}-F4Timdbo~z>r5$o5Dh;JzESX&@qs&R_3v|Xrkn#iNp`8>-QjYEV@83R
z#$Dr?bM3D^wfyvo)`3sMTk5K0hz0{b<fQFS<KHo@9EdhiXK!m(J#|f8pL`X~-xCc+
z<VB7AzciN_9|4BaYFADrpQGM9Ula&8Euc$(ycc<Sc)lsR1!wP$bb;kDbNc4y-R1IE
zd$y`cW}WnM-@zHmpA2=F=Rxb&MJKD#MD6WF1N+90H`YM_-By5>O1!45Zz<Sb{yupq
z%SB&i>I#Fx@Kim^M=?up^yzy$w+(6keS#-cMECRE?eo~Y?#!&qbUUiCrLvtTUWFI7
zPTd3v38_tx56{4QTUSO5cv?}LpKxTP2Z}Mxn)hW&^P+1ef6o8JQo}%S?YTdj)725u
z!oAqs$2`l$bgUKf<!HA<H?hPW7R*n9esAyFppkHKh)62>dq;-~?GL!8@(TE&&bs=W
zS9Luz$*Q#7%_hcqx}C`31s%^`vHkhu1ekaT076l2lE_s2&}ElVy^*+nR0mIdD(wrc
zWkXpUQXS2EQ1sc?CFJ8#5k;)E)slUhq$>tpS(GeA=wD`7u=meuS>A9egr8A?=)V|a
zQ)b-I2a8OB`}f%&bXxoVL9L^&VV6uKWX;DFBC|`<qr0qPwONrWGsWq1%YB|a3zE*u
z>Xt5)d|?!4(`(&Xngu;0NboH5T$Xmu0#y~7Cf_8J95nG-x4K8lz?cBTl>pj0m*?qT
zZMS|k`yiGP*{1$MTVPw3L{6n<1vtl^tNzdoqTGcoMqu-rba6u1=c-z_@9hHjF;}@Q
z5`Z!@!@wo&it}wV(A)ZGywPGV#KqEjXmjrcFbFuZSd-55fF@yx(5eRdNnntT$C=4<
zcA@&g+se;(g(J;0>CJ0BN<ktWXp4OPm)fh-ZpQgFjFE<<0Y6DvL21^)A6W&uJ7GtG
zwgtRq&&NsbXcy*mSkl=&i4t<&HhikC>uzlqHTu(1YlplNOT0T=1=Zj17k{f&OmjYP
z=!3Tp{f!5#n9!I|zOx5Khl?vs6_!B%>MUmD)w@N`Mt+afu48!nx?*Qi5J#lDk~-eo
z{+wnJrPxdUbL_e~?3q1pU$VM4CAIr9cAsjpau94O&@?i)@zwr|ci~-_IU9VshY+Z;
z*_dweIzVxKwcgHn3Qi3*#*M*dlXbH<6^MLv<BYH3{|xmB$d7zEf((Ig?mxIF9C>f;
z?Imzc^*HBii^%SabV5)3NeAL*f>JX)tp)tpSOXW{I;PiG?maU^aS#)|ayyRan~d4D
z{w3spmd9pKy6z{cxEf-o#BGEe$o{qs>vM4!2SO6T{0k$GvE$f5-I-2IlW=g6*ys`|
zR>uU9S1`!44u{vt*YrbAip$otm7j&9eTDXWMF3kXaRrc)ILohfg$jc~iHk*W7r)<O
zEn~?QeX_7_MXW!ug(~jFPtv+Fug2p|(>r&NJ9gy6_$Kdw4Q}2NWD>mTpx*}Sa(NGr
z8wj^DZ-Y)Gm?tluoaKu}`497)ZXN_NiiS-;95In}{~=3W>#~Cl-(-)<dv?`SEwOsm
z;|7<y(b+H?wzOV2`iE2d&K5HDKIxJ3EBUuAb13o*<EdSeUCAo-_`~(E9rZF6_<5cY
z?*tdXUE%F55lX<OO)M%H{iFVS+MVaOb&vv)xDmnM)<Iyd$P10;-)pR(F#4k-{o1BS
zXYeoMh052fd+P5=@49ZVAy*r7-0cLb{rko79&yo*5=tF)k3Y<NeG~84y1M!)=*8oe
zaMTstWVzw&xHO;SZ>GyDoOId6(=Gu<V-4G0kI5Hy)%~9{heKioB+367D*vzUMn=t`
z{HKu@cfWP3)m_OLGu~!@8<8AVcX32oewWtqDNEX=Kwcngv{uF<K!r#g@_1n1P517C
zJU|8E<JDbyvOt*hO}^{#P0^{vUf(RICs_8G;LZdYxjY{XIQ)4?Z+Ut7ztbB6;J!di
zV&A!9^}jk6z2e)Oet6h~p1@?hWlR`O-FH|;%)O0$&J(7AU~;^k$?S@MKRkCQm8gbj
zM*1R^(h(6AwPM!O^{*0T_4sW&LD<H*l-LPtiL1t+5`}BpV()lL(V`#Rb06F}@;MeP
zKKmU}QkdDW#3O)w0&7-4u%!=KODpaE7Z?J@O=1ZS3SJ8J)jjH1)Wvv`pq`Rpo|hxz
z<;o^2%?bC@^<MTr?s0|U)>7&*TfpAEgzS;Twm%Dl)-j-mobBrW5w!IX;{Z7rOi>S3
zy0W7XBLbsH(z@E#SUMI<{M@zTxEc*mQ0S8W`lNwiiiwG>Z*8Mc{~$&;O(t}dQ8}5X
zohS@i0vDsh+Y0j?-{pR^9y~Qu2mzaKdANcley^tWuCM1X`khJ*3mFJO`$|{k{FW5$
z_P<LfO4DD5!uWhRUN@|zg<#%X<13r7C0+u|lK$LF+}rY?p$l)ht=0Cm%m{fB*d&DE
z94(@8YH>ZOh+p2Ge%g2k*|`BO!hG?(vrJ_khbmtTu#uU0%s3r#HNqaq_9-;JZ`?yw
zM~t@qeVTP^;J`KB5rR=?MDMcZoNqK>Y}(7KY$-pyW6Mz8&Ik!wXnLdHvsbCnYlVN<
zc<`fmN@qM+@gp?p+iewuiT#!)?UE8jT*J4s1rmzeq}a}`G0y9cIHE=&zoV&LL<TuN
z3rwZ8tfl+4m3j$G2u`VnIxMtO=4t$xcb#L$zf)P$VAs+s^G+zZO2-AcQ2aWK^d}YQ
zB<%W%n7vLU7G#W!iI}HKdebdPa#4#!p$yaqpvpfV(qnlhV%XIRJ-{f%^hPMRrba4D
z*X=+XK{Z`{09@-=lP0QbLX)wZ<ZFm^ob!nJ{;p05mB@0>0k2!Uge`p0oI5R8TTXwv
z66gDS8X!SMBayP)okTYo<j~fnu@trW3E9uHL7F0J9zV+8I3G>RPMor&oX>ac60t~c
z3V0<TrE3>Ueq!5M31;NuJ-yhVEr`-m7EeBzWO$_P^uAc1^}b9o<k`;nP=YXcXz0Il
zzp24@8=2E-ZFmIAwyxp;vIsuM!tfZ(uHry;8~4tMk(2k1Wl9{Ph!(%sq2KM*wau7D
zmi?woWQ8VB?SAG!I#~lfhniSL*0SYARA_p(*HFH3{>561VA6>A_T5?AbPH%>nhcD)
zkM!T{!g{CF#2ieTeSozd{COOwv>-Z#{rfzbiUil>+-QJpUO!_}@vg)G?q{Ci?35jy
znBtV3Ei$%~>=GE%8rb(g!8MRsWktyqgi({YE}U~>ejd;4thG|tHaS8h+m#X{*B9C`
z&r3*r+&}sJ#Snb95(6Q<p8|LO)7L;+mm=()1{g*_n*;3RV1Ve2TvsUX3Z$KsF_qT-
zcefNgQ>RlsNYrwE@<I<Jt{aT{bO6&pSMAQAwFv3P{+i6bt}36KiYVOZNZPk&H+B;G
z&DzujLHo9|tU=8M-xNmX$qN5Z+D?hW=L+p@{tp(3jX|<S_kH@AfVE;C1{nvlh3}R>
zhK7FWqirBfgvu?UB4yyz0d;8<EFOOcRRKaF45mYAvC(3`KuY{o!YmgI)&q#HrN!Ko
zL$PAERAnfA0%)bBPCBvaUpzva<I%Iea5!FDg(qV#SYSEfojoLbwF=J5%T0LuD%}+?
zhk}|0$t&0}uR<&p4}pFwY4@KdJqPq2o-Ci;B`X=1He|r7y3BCZ;B|lMN78He5jdmq
zQp<d92CyzLUjudZfqJC@VQZAIw-=b*6%a@PbPQV{*o1n30@?KTR4El;du)IK+LCqw
z@YHJ@A+TWb=4D{(d|eI~H}~a@Js=j3c}h^e-A7*Nf+k)-;yo8XL`Me3Wj3?m$(FZQ
z%<GoQUMu3<@m-U#-w6zjU!xD~$A#9i=U6>Uie(0t#1VXqFE!&geK(AGv2f(pR(S-p
zQgc_6b+M=@_SECCzk>1iF(9CWD#LYL*Pjp*r_E>U6q^F6JA+1<ANW^nJeq7~;0q<N
zz9EaxfmmrNX=yQuhRYm)^~@4ajp^)SpeeD$0(Q2@n!Re>w!dw-_9el{`$r3|^;Y=W
z6C_BF4S$hsg7sx>O~0|-OH)Wc+E|OOSqN_Joqw8}D@-(A_+U^ff+vAaQg1Ot0fs4%
z*=7R#8d!Wn`E3Av*ew|*K9+4yCDH1OkW&c@x75d+DUCNKOHMgU+~64tO&+ha7yl=D
zR1B9;1dVed@dU?&Lvi-iA&8~mMS9HusMshNdq=WF=u$}bEFJ*6Y-1x{k>1{Cc5!Pn
zwqW-oG3oeSECx2XW6#z)2iDljN`C6*`gX_P0SX(y--)RiklcKAuX#%_W`rVi<zb1J
z0ypQ0(S|q6d<=>w{50hpd#B-1(0YXDVh#<=$GOFz<nD`STMYREmCYI$8k)~lmnxS7
zGtX#RAyShecyI5qm14cxFzan4mwnFUfcV*zI%l-|`MVp30~-5e-wB^a&TD8JPs(Kq
z2w6u;-QxFaT2DN|wST&L;=#UV$5pNhoQJ@E6>$wls~tlcIp7sX06`h_^O|Fcp|FI#
zxf%evhAI*Oo-M;tgU+4K52I$G)Nr_%j9A#(tze{isfERgu$yeGY#@7BT4shl*zwzB
zrU0FK;n>!eMgt89b>AHBM!6zbELKj%p@}#MAe5*2D-A=;Y7E`Elg}0Ng6dGSutjsj
zJFve3L2x1<nvC7J0LLJxF)F|rC^fh_0_4GmrY2#ar4P>z1fCcA%%s8rk}-M{3@o4T
zKFMcG<-q9@as2?nvAg2PLS}(K5wv~7MO^K~;ZQ-?HWeL1ioIa6Sw#dB4LDxHo`D43
zsWd#N(KQX4w&>zbs=)!q>!Y$1ucUD0qkv7D7yy{|M{-+Ey#N!}fSZB>1Kx`f7=Vr^
zg=&Tx0EgD07|2$0y3o*AOi;pz5P+mBoH3yq)76*G{aeXNyVR+8L(OgK^TVaZ{&c*@
zGxu1;-nyv9(B<q()jFp-N{^oYqv&-VUZ_wNTPg<SMVZUTHDI;27h}==L`)xWm;m^6
z?8XD|SZciQ8?ytS0PA3<=;)jshrak{l?|s@9%oOK^G)ii?V_V{F>>~kJIf6Fg4mzx
zyqm~WLZIeMe^t?XelMhT!yGbn&odMOaUQVJaZSY^{X#sy8`s(+GC_j{<T2o#16a~;
zm?eM?f&hesikc1PiZ?caaEy+8JP3qq=jnO^cr?G+D%nVFZGiL#6IKpNQqwbFbf|CB
zC%t^Do6_Kvb>rM=eU>%v>gl`dpOyL!@t9awpP4JQjliUV0G&)A=&yK%_pyMk^hwQY
zV?K&kztjappfFLJ`r`mzB!JVx1OxwNS69H6AUpxUW=GpJ=K+!K2w1}cDGV4ePXVfV
zC<E$kAk<Lze9;>W2i{y78ocd`&nbUx+&jfo1Xh+JZ8=)M!QJxJZ_$g5O3sr9%m~m~
z4siEM09vFPW!I1CVT&>IxnVQLoB183SZ?AT;~c*)we=H4bT>SHln1n>fb1IvWcSP4
z+dY7?YvIKNA~2AfQ`4{LF$29Q)B+Z&;|G#iC~#<bG+P>s@J>TLbQQ?Nd;mEVAhlcD
zWUbQDSWMBtMApY*Ra{K$mK0z6&({}PUsk|1$$%86;YnYNxzhJwXr-#&5M7L}ZP+p>
z?I#?<UDb3VsxMxV_xh?;2~H6)npaf=ArBz?pp*%*-@4?LQ04;GuPQ*KR1V0v07@eT
zaFAwzSq^~slu*xP@ag~#8!Q?oKupquv7AquIzOLf@fN~id{<s#=bJl4yFrrFwdY$7
z5^0tyZibPl9%lIs<HdxLDObC99M3HU$vVqkZdMZj7`aZCAC2K`<BR#xlR#;TR})58
zaveZ(FX&B0Uw^LgB`XVRxd64>06ts*90el(n|UBOhzHX7W#I7#M2bMUWC$n+J(W<@
z5+MD9-*ay69DEBXn>@cAWCcz=dLLXN8B%fWYq_s6r%E176ep~8hmdv(8i9G4*fh1I
z<GRk|m@Gaa$IGm1vPb7=U&Xd@ozjW-n>^C15=aeN(<l3T6t`hrHRc*{i4Ztr*Ipy)
zV`|7nNyXBNym$cvWH{Si0|3DE8LT?s0nop5lvnG0F9h_@H$dN{T&#1OIQ#4BiWRsG
zKna|HB?kQ2pn5A{PzT`x8BKK^jqa;K;PnMye1D#Kb5FzUCt?74pr5eU*)GEU9Wn|3
z49Aa@J=+_@MxIMJ<3@(I-2E&>PvXZf&RWN>viq2c51c=9t<Ow(8l2j6KXfY;khv&E
zv)wp<2vZN?W4#)9Zh5QwM#sH0cYa6_F_ToIvE3R39>74y#=v+1q-QScaca3L`M7|;
zO$`ivX+uO^TzCL%WEC(~p~m4rxsnWopXFvFl+yha{(vWo1$=(Nisi9edz~akfkr0O
z4{)GEKxq$Ew!;90`d0wc2_xqH1cDsQ(#A$7fbD#0I0sAs06Nlm<^`yiM1Lo@$MOdc
z>E6J{GXvGHCDB_n-2BLOpnPIwd{0=FWt}{mk5kb4bt7i$QdHsx;We|VC;bX*d6kYH
zDEnyTpO3BEj*e8APzYI`!CuX4SrKJmP)dLV=oA<`4(Gk0;j&ri2a6|>&+$0`o6+5U
z%A$P?<h4)$Ilw`r0oX#;xaMZt?DTXZrC5l7a~%L~WQ}b@3EwpXfQ1bx_H0gj>eh4B
zB7hP@3wX5PSDOQ7lYl$(062vu8tw7}+-VWyVsW^NIfdWUtzf)Wf~@7MWE4%Lm0@2d
zw5bbj^FR!LzuJOo?+$nP_>vp43F3Ih*o^n|X}82N!;EJlsIG(Dl@jH?jSsJ9W1(29
z5?X0-SP!b!gabt$!<(-n0M?!P5&^2M0eV5OQ`P}T!7m_5?#$iY{S82zKnWh@A*zzX
zUN<}-Gk$G*r3Dxi51<z7K;G62&|%;djDfQM0HhP3p<BQ?xK~D)4qCPv4jf@brq64m
zj!bXgjq7zh&VADbN+1Qdth9=66VMrY3(U#>edCh^eQ@eI6i<*K6yDOHupYxV3gNf6
zYO4i#q^KtrImWeyS-uG_gPRY6YMzvtZ1F_ZBRhm;Q&Ur+Bx}HQ`Qb2$iwE_HR<<UT
zGpqCDKQ8l!#$e#J0meS)bn1D80Y21T+GDZ7J>fSn3+i7F17NLSz~S3DTOHt#{7o|W
zMDg$U5IsyuR<pyXgnraK_%IzkNUPt{4L~@5?;um(FZUEkMmqI4j#it5*^C!)nEbWb
zsuJEaw@ir}Zfg|MMDR)A_=?uIcwID%<d$41BkEc<_3wAL`&(KhoEjPJKK}W98|iZ+
zzdg9T|A#L$H$DpPK6Clr{gAB25fC~l519ce#OHK*C^Q7{nl4bzn!v6BWVqNJ`{?NC
z4R*_Ong9PQD2p*a|K)?j$X$8i#MzadiDz~b3@BhS_RWQP$Qqm592i$`(!LGXkTA7n
zz4=np@H&kWC7&~_D6V#;z<xu-@AmKl+<2;&98xD7(0Fae_a62yb#|C5bv_L5jM}?q
z17j2aV+{Sz_fS^Nz!zp}Y6@o`h!i(A%MGB6H&8`r%mSGx)bS61^?=8XX`VMH7%l-I
zRWQ7%d`5BkAL4*gLNO7@nEaN|FT?>*I#6?ShmGZAZZDF_)6YvMjeWhS21-E2gh~uB
z^YX@79$b*G)3tX8P`Ng3Tvvk;hSo=>Ho|(H6QRV_SSHr=TN~}exa(WWeFzBJJ6)>Q
z*93pufUhEeAr*iU;_lMZ|Fr)(0~P$%0GedTx!<RC;5VqT)1;6oit}8Vc6<|hgXQ4R
zuXO+Jf0d+ktynMkiTLXE#kW^F?GH2PgcZF)+H1mjaqc!@3u1=1&Rq<&DZh4(`MZb&
zlST%^(!SlhvE2M^6-h+;k)JEhV4G52*M|uf$3#3B=p8MVG(X`HyjP3Sg0Nru{k>>v
zuP3*E9uIuV$NmZs+tAFIRKO*wK%osVUZ7UouZj#gl6oB?i4$G6wR~W6#PsT%;52MH
z4S*u0tAYgDyZ7ZrPns3f79ao<?k{&ypQYOifmtNpW%O0`5@1kDj6yxA_g!W)V|=(l
zM>60CgZu;TGaOqi(KYKDJ`sSJ!iG9Q0_MqvV-%<YGyruHoTXX7OGlOHZ3xE{bl{Qb
z^`C*q&>9!a`DP!pi+y%(f;y)T7WYaz$=*CjW!cY&WY5Wq<)*H5Pj0LWN1<;XD24p7
z`i_C13`EkqSbPG)!vt~t;Hc+hP>5v8y@kqSh;9B!><L$#pZuYK{mszQn?0!4n#S+j
zMjZ2!GC-&Jf3W%v2L{f->KmSJRPQYq4YVc)>jI1hmN5vW)l0`Oak+CP(Oj4i0<K&N
zt8aBYqwMV3harZyl5TS;)!rWyB}~dLCUhVWSK^c5s&~5Zs${Rd5^nHG2@yTb7O!W)
z1oP^mLOe<R!2DMG+BXwcZXrvhl;>h6u#rfpo+(Z=dEKSLzUC#r9jbq?$#-<4K=|h;
z#=x)%bk;J-T;U-3wFOjaC?OnRjX?4ZO%R}-K!63V={98qR9;A4N&)A<hElt2auSc_
zi4l}G0}AwKAWH-%DJw9G1hhu0xaz?)L1`cZ1q2`-mG8=>z4+6h-3zQ!b83lL|MQMm
z!|sL$?IC;yuPrQ$SXK+qd-Ben7z*9N>iWJ3pcAWO+A~<#cC~D%9iKZ`S!!*bd3aTQ
z*M-xY{7W$Z9F#TZTD3#{O-#1O)+=se>&WZtF>3U~^`bsFp*^OrB5nvg;N4S-H4T4{
zdU*pcVz9Q_fU|<-FZZ&Jiz&dlGy@Dh0HFkmKU*LSg=|;B!aW9#(%nER%;*)cVGc;r
z+cSgUm<9if4G75cJ0Tq4cZ803{{1_$?HwC}K9$M9N54M8=Rg5u09PA;nvLk|pHgrC
z2_$gk>jnm;$TX?g58t8df!-3%K!Tm1kh|lF_@lA=%Y>$4YSkS2m4jB$(m4V?30ptn
zYrGk|ZcuV!{;?&8O2r6)`aBq*&H<x^8}y*Xo>T!a<uO2xsJp3yVw|AV6ull4KW=50
zxxNp<ObWQbjj33AH33TGh~PS!vb#CA--C|7OXO{ykUG37P_jHB{uM>wt-VzBhGL`A
zV-U?_xSqk2Fs^f4lBDSrbcWqP$ua}%E`gbJ24HICEf~HjGwM;6wt)5-;QwoJ78RO_
zm-xdJYccf>4Q@<jk1ssJ`FVZY*Z3G(-IDrnsvjxfs&?bBzJI347xdKZ9e<i{DJ~|U
zzm099FOCVP0!-nsa+i-r9E1RtC!aI~e0$MNP3hL@RQ4=^tEIF*$?w@-8bRosGZEXP
zftVG}kbL@1$ru(i0$4s0uzQ}q{WDqpt@Qj<Gb|)8tU@&_+aj(g%$g<XM#`&xuHLTQ
z^gfG6Fdt3J)OCrIw3Avj)$O)}^5!tkF7~un-MBWaWHY^`|DU!EZ)J!!KtDk3Rq#1L
zn|l*1P#}^Pyte_SBw4hRTpt!^M<qoGC25hqVvytHjk;q-hDdaHy*mCtPOiO;^awNh
z%jhHJf-WbVGY{MsZqby2FCIs|cun3AZB%aDD9j~;g7h?MK6QHj+F4ttY-q3%(tl(^
zgU$}=2QD-=2jjh@byGc|S`d>!lB-DO$r^i_-U0@W&-{2r!naR5e>Avd9;G_#AtF66
z8s+R(&3=-tKVGVG$#-nA6&}~bAb@p_nB$Zb(j5>Djz?OC=RfjX-(WW=Hs7z5mu?TC
z7%k>9c=2&teL!j;r1~DsPd?{qT3grK0`CpK+lE`ER>TXzr@ud5AMF_2bGMu*(75ap
zzViX53(I-m(qLh<n!HFrZP*3)tib^IsSg77hECyLM|(RtHMRJj!RGopoUX2J-q?5U
z1|4*NQHnY_&WdP@1*Hw+eaE+Mp7DgbMfTssKf-jFri*YI!sEEQ=0sI-qu4Z|t|K!y
zC!>25CY*k8U=S?9Axpc&SP!scy?ebz^?A`$Xa@er6GJXen|I`huy;J^{?3)pmPIE}
zSxLvcAF>CCe{rt1Y2X{1M}51P;N16*Z_?1vFu<ki`Pnm4@TmDAKw-1%xbJgX=2my!
z)@-Kvk|P2*Ogr%R3jqMN&+Zjmf!cdtX(sEZ^(F3B`y3CHqd&m{*A>e`OS<qbQs0%^
zi%hh#^dj?(%JmyunC75d%qr~-w_`_!`6is*h@zK?jWS`v_{Ze9=ej`=A|w_!DF87@
zNL-f^_^c_VEjm_!6?bp_qxnlsgLcpGfr-Qe>#3c_dbP^x2D^d8E_K&Pn=0)+m?Z$`
z0^asl^1$!y2>@HM5QZZH#1-&o82K>tlbo`Q*!O{Y1L0>uB3e4u4%ml26&5}cWN}>F
ziTr7{#F1WBGZI~0q!NM6XetXsOg)`tw|ynQy5GfaNwr@_l~4rj<Aq))Pff0`;+2OS
zpW7f^GTtTOLmU)W$M2S1G9_rWI8H9b0)o2d7@Q)8=I2QwPxNG783`UAH*bwJXTFRp
zP0)ppXMAX6H~le%ajv}NWT*~r<(j4m0cI_3L%*ZtiMpfNlaM}oGLISNA7r@aZ-W*n
z8Vb|$pBX<fKRzG}z8qSnXHj;@u~(vF{ccLzd4cR(MZ`ab8SPoF?(-GMb%6=P+WNW(
zhTpqG=RI}EGsK9G;CFfU_wQnNU{;~Pr2Tk(G+RO0qZpA<v$@2Y#P9A_wr{HCBK#Ri
zlap3`JsOM`&;3Iu?K%HcI{xE>WoN|<MvTSXg|GYuzuGgrbIlhg*6Xz5Ase{dKioX3
zh2h8!<i#Xw@?v5|9|(*xA;uv1XO&jb!}K}i)DcydFc0+nV_EH2hH86x2?4ZZ1n5h^
zuCK3;FW^0T@Yr9Ji@#ZOszXj^Es2|duiM+BW`JZs*Sp1jM>!V@`vJ^HrQlDchKd}X
zd`lbf;9<i!8Kz1zG%dUFUS_bX;yxs~;ny=sNZgwIN`~{eL)$a3&uZZ&b%A`Ti+%d?
zNP*8z`nmUXjc_}5@%g(jL~rh9g^wvIpZLQJ1nm|Q;`Ksj=_gZM!{Y8Qon||%0k-cF
zET!Y0Z{#xpMFSAN*e;%1V*PV~Nv?ULg#wB=g(8iIVjUW8nO1Ls9mogJb}qTK!Q18a
z+UN0-zADtbF|qyGsOZkHRStt5AnY=fI%C9cb0?1R$WkylczyQM`)!*J`P~fo&%7L1
zf^BQOp=;I5jQ{$=<^emI6>!N4v}#7@Ud}#oDve3|JI-CrP1imF;)&O?oDEKPuz;v#
z(20_3%$07{vT_@0bFDMkscrlIRD||PuUoOii7SL#LdmXlEy140iB~s_(|jw0;N{zu
zOs5tFsbR3Gy3KVpeHpEbwd^-oRToxgt?>9kSn>-DOm<hNr0nf^kRt~tbo+yCA|J2B
zmI~v^Gi@ENUOkSbLQk9JZ+_|4b^Xivfwnup^4^i`TdLTZU@rXPd@wttjc2%EO(?TP
z7O`0u*sQ@AsVf&0^i}!Z8>_AZ5Jr!H1xbq;N0Pf4C1uxB#Ae{8RQOg6SAvwZIf=9R
zV4fl3;1fCG<?<Z5SyQ9n#zD&4-4kSI<^o58nmQfz0FA};)~Go5_LXkHC8+k&pAyUx
z);XB}*nx?u2v?pi0(@mjfeRR*`Gsw!dy@hRVBWFAG&D@u7bgXE-+j$~u-f%d_+E>E
zNQhXy3e9XnrncTPiX3su$(Cs2;BzR|w#3d&4cXxR2kc3?sWpwSU)V^5raUo|&$VAA
z4xXYXJcc`R>7xG3#)H-JBy~F|DEHGe@>js<H2_^(Xaz5q!lSs#7BSTk5wul=AD$z<
zX)^feF|sVHu<+8nv(Go6jEt9dtUNps>Yrvsa96qrVx@`0?nNE1E1WPISmvC%JQA1A
zHg#HeqiPh04Y_c7N_8Q=&UJ3H9XUxBB&wY8&2JhLvnLsRDrl4<flqA%S6fpZ2WXeX
zPtAKcZG^H!?pEI#3qPY4<+LV_b-xIqSRIpZEAgnwd;Mv;KCXOqGQzOs0Pb>M)Hs0;
zod#WIhYhJA>AdyF{@4!3V6Icv&RMEeVLG!2#?fx#u6m;&Qi8p7hf7^&8g${#Ctbrt
z-D!xQQA{4%NSAi($5{*tboPQxobrOz-3L$|h3Wy(QYG!`r3c!lx$eIoh{Glo?O=DZ
z&G5>O_J=0S2MQj1IGd*M6Q75_15yCz(~V~a(<8>0iyimDtfq17;uQq`NF>zFL*wW$
zC99<*j-=&6i_;UASHE_pFemn;+opHp80(1KdG)o1I`Q#GFdq9iuSTGj{o{%1JkgYZ
z$tJ*J_6rsatlCGdi50m*2vASR77bj<gwf7`dxWx95(6y`O9T<Z>K8Gy;S8Uv3BygM
zbzRZ91s)IE4P<<{F+uKk*@Vm$-bm$c1EQ<&;m>;dK0ySJ-7psxlKkd_rws}+li{&{
z1uo|e$}WB7au=qS>^ZxhRkE~oUr%C>ECnBDo$kv4NPWOk5e+am1EA3Tz$zl}eojFM
zOdlb?KOW$-Hm3uivw8^Hd&ua=Tv}Q#tB>DJ<x7gy=fC1*8y=^1Ou1NQU4Br5!*MB^
zw^tu_e$eXC`gCyk2Ev+^fkR(Oz0%Y*s>dNnkIzK-Oy^)6*6_OW#X~$-&#J^2t)?c%
zj=v-G;qm@C?`vaYV_;f<h>qR`T8AUR!r&cIz5*?aaWBsAol?2CfO>Pi_(JK^c7-Nt
z{V_b~WiPEzT3K^Z);%SXzF_Rwp~_dxVa8s)w>*<)*sH>@f}MH&In@{^cBjPa0?y;d
zA=VGKF%7nCSeG*CH!`F+!QyEt{I6b}>7T=z|2o}XNeAq6?Nv60sG#o5Cpe#L$E>Cl
z2zE!|rhXuqP0E2?`8u-_gC4D@ImDM<L0RW%XJ7!T*xUym2ebnQeW&=$aiXK?7UhD4
z#IT!Bz0}CQnw+h>ZJLx{Fqu1^QnDeG<GoG*{u>ujuU?&l?$QU_)eol*V-{*^<V<Mb
z%IpPo0&cfPaM2?RwBnYx*NdXo=0*62;{|xQ=;~oY6rNA}2id~J9|)()bn(B%j*3^C
zPCRHdS@<ki|D@LMq*0fW(w@!T2M2hL9Z&=ZSuURKHh-0D=3Z3pghyc!+|3n3-aaYA
z1j(5tUnP>Q`%08z3PmSBykq;ygHTouOIjSKOUqnO$!YbIUEcO@cp;@5UI(9fe>@8i
zLzr3T!p4-86)F@93fhY%hXKQfK)t=To@lVJ(0sDq9Ljv+Q(Q4jbar|3b2Dh3BsBI0
zhjpR1_zCWruAg`1uW#D8NXOf7F1wSEsbuBp#KEC9q+-;N_BYx|qFH6dgAT7=*(n{u
z=7F1Lh39cl3@IQ)g21V>+ai^zumn7I&$KIKSA7k#K{9cL!G9I$t+tx;^~KpvzJm2E
zbwF68(Bro6DlZf;$S&Ow#9M+6hrA=F1WR9cOJb}JG$b2ZAJ(|!46rNEsgzw4G^W-L
zCg)#et5*mT2&eUaP#8%Z9FX)M5qx>1G^F6dlm8&=0biB?X$~!1jhFY^kiSo)yVcnN
zUjuNPjO;J^AX`aeol~U)p`#aM{Tna$)`Y!MJ2~-}&PODU)XN_ADvb$J1$=<PVbXxz
zKU&T)-doyS#Cjys96`^2G!b3(p87frAKd}DeN8Ur*rD&+@>e@iFP%mQ$pzn;4Ox*y
z(sbg+fI~TxFLQd|!;~K{MOWV8&od%69uS&^B4;pGI&GX#{aduFb5+;_M4(dBA=0&t
zjaFdf0g$v@FE!5t(L>_!YBmM}r+U0^G`qqh1K;hb)1s5%zU;))^*b)CS{f;#xOAwV
zosFqQfH)6z`TTfj&_6kj$L`+WPEVrili#V*y0^3G1QE|?UmAOvQ0jH@3@2XYPI@nD
z;=yMwT3E)L`Rvzf6KlV2t?2$vimxJV)X+or7n_8IuJ_mlApPtc_=6NjBBi4-77HFh
zsW)B4wpxX_;9a>uWS2J9%NaFch`2?0^<Z4Oy7x(H+#cCG^|w@p#wAd?@wpplUYLLO
zxHod)bC>#@dUfNufFA~1N!%2&4z_}h!qrU<Qzq(h=flEby04jjiM{Fn9$$7uN?Qkz
zvx9?(N7B7vvm_px4khW($2I@Vdtu42v_WlU&E`Z6LD|?(31r-?3Sw2Opr>|94N4R=
zZJiuAA1Ygv!g#bN)!qKKDXr_uB5ug$F~qrRx9tl{wIh{Ij@+xKtXC-)PbtedJ35+E
zc$=>eU)E<eYV$9(q5BM;Ut}oROAgA4_ZQ)Nxc-txWZCBqSMn`Q?KE&YoJM?y@zgdT
z-uCVns^#T27MfOphgXdELsJ<N;$Rv+PM;*`nQqi#35Rvx5gJ4sY%t5EcjH3NIgaxl
znsULI^uriANd{|a(N%vGbH`oIS|w{C|IGJ<?uk_W@Eu(LAwOB>Lgpy78HJjibjj(Y
z{pI4eg+YItMtG^Grk=y$#(VpfCKW8qp5W=mxODdeUV)1_dq+*xOoi^EGb&8Q)U~x{
zi_xdKO}CY76Xi4|=Geb8FSdABDs1U<rk2{Q-3(5%j>~Q?D$H4CTt%<*nngRCSi`dj
zBad^_#||JT`6&gLRww)j8^Nz_vQ1+JB{(RT+Jrs|m>v27xTrm<#H**wA7KEP{$~ue
zNKB%6h^q@QZ-FhYH>f=f`rggl*Ts*p(DGeaZ8_i|0N<NsMWh`y=p`tWMxU9AWUs?}
z{J6)OIIR6ZX|*m4j}~SYq=8;3;*ya7%}W%m`c=srfbsR7fyAqGI>rG9-uWTn)s2q!
zP6W~qcDHUB8tjs9VzP+VxsMhyFOJTAs-kt{nLDrj&)Yy`9LX|A-~Loi?yK1BeJ|A(
zVijDisy>}q^wyrNA0Nwyy2$PFSD85iX7t=~t10D|Syn=ya3Y^XcAr*Jm=8;vfgh*T
zs{uJ9R!$C!hL%~g0hjFN>;dkfc33}AqCvgIYLU8t9xFT-nOVX`{^O4yNH*C^PpcrW
z>vgW4PIilvx~%%pp4t$=00%KVbOahoyGIOBPXPijqwcBzhX_!1fZdDbK^j}l2BWdg
zgiclVq}t&zHg+Z<H(GCldq>pq_P0#!S{&|JDIOw}xFLSK_ikCF>8Za^Y_C_|XCH;&
z+x&lweRW(`TetN?BaL)-NQZ!Qh=`(uA|;K0(%nc&mm;Nfi!_LIcT0D-<O5Pt-`bpW
z-h0mb-uvCl?|1$>k9)7Z_gZt!HRc#&F3+Q4o^!QI(q9==oFpedVQ(CoC$ME?QVJ6|
zaA;rgS#<e!pGWoauv5>GXa}+IRQ<RAN@x6<^vB@4M3{{1!NI}O78d!Z)v2kCTvq}r
zfJXY|3%W0D=g&8je}@uI#Of8%PL8$~OFV=LwVvNcxNpOQG53~Y6$$NgJ10l<?92yW
z6`rLIOv$CBjJ*ZJrU$%pGiAai4xfA;HdFgNOOv&-+NF{!d8&TUQ~cIT<VyZ4N7zhK
zv`d--o}3f9cc@(OMQ!&^?3Qx`r`<QtH~)3A0^Zps6nPT8r4QsX1}R%6%H!inLE|J^
zU_=Ota^R2!w81-)$YA96)07)KIv%R&`Tk?%cdy{f%8^u<ZNUUEm~@&qJVsqVEc8BT
zHk2P#!HI{AaINs0#_+gx!C~zU?_8!dLGO+@$v}lCHF?ZVxyU$K7&!FMoH2>G)V%po
z@=54!g;)Y>jz*|J4cC(7!=Y3mHL;dQS&jCypAEF<*IsX^9U8|a3au@_J|FrkO}d8v
ziHmfaj){QY4@lujV(bsHo=F#|P0t*Iy!Or^@Q&oHs~3sX)4~AaQP8GxMy!s82&FCi
zsq)eGt(cg@*fL43D<5IewS^y}_YFB3#bIUceeDzdMvLiAA9!lqGx$kMtj1A1+;~tX
z+g1%{=3B@HoN=4L!R7~9*u=M!+u-PdAk@vyjo_MjpC=plO>nkExsaaCimQ=T1ZeH{
zSB6QgmsNcf#EwlYFS|0~w1;|iX-#{l>z7sm>YNJ_a9_45sna{=TwRFqi!U?6amwB%
zG@9d@iyt&XWp+$J24{d<Wi`$se)vWb;vq@5G%L$JWt~ch*}pR_T`L;Xt_OU73?Jd2
zA+g3X_y7KMqBJ3>bFNql9N<)y^?xc>7~D6`2dpY2z3K9gT-=|8U3VD4!7cQf=}IZA
z%6tZ{RWZ&}*Wqy2!IIU$>8Juc@b;5VL>PKSt@EK{^ASDo7+WWSwHThi1pZs6$q%60
zkOnRO2ZrC9Ec!F|XvJrLO^p%-g(3lC(f3`Op1Dk~SoE6;QBFm!%z4)`?V3;fmwEF}
zIFKvRK>q2vfh7mMP7GD<2&*hrm;#M?V26mH&$F)PprFp=5@^)6mm)lGZtwRA#grf*
zJu&^z+??5?AouL>d5O)5jD<uMnOxI|_romZ#jJDP=30rvA0v6Wtz@4E2BT});`(NT
zRbZd*IvCl?%C5kmfnE|IFAOXB+<ER@8}hyPuN)1rRuyABq{skD+-)q7y0Np<r4dk)
zt<LWn{%)sj7Lr-Q>MKh9X4N)W$E74I`#l)tHvVKqG@*Vovi{as_k>X-0^nIAqdba@
z)n18RTiUs_Uaq^pm!_)6*8Wg7ys`N$=HPdgm$%BwIMn-Qbrd&Owd^si>FG<kp^RFB
z49jM^68~q#9OC20Pf8l4^!vycQm&%~g~(Wkhz&+l^7i|ioRz<D5-$6_#FB&3YRegr
zcX0IR6YkG94DI)i9Xe|1A~X)PkR{!>tf51}#~;PU1Y52o9IgxqNMg7&g<;{;*c>lW
z?>cPj*(o??X*fGj#csd!-Hx*0odbcKgSwdXQs(?oT%!LiU+>vqO(-M1=T-3K7<cA^
z(%Z`sH~07lfEr4bpb@`)UEUbQ)R<r`lRJz6dq>QfI#D?|64vCii6!FUaKXSaQ--(s
zVAHVnzCIdsW!!g?`s0>)1KOO8QF;RgUUm_r<|~_FU4HZ>0#~0;DKi_K%WBTtq*P(L
zn;p#5va%7r&>IevyuO>nB;rmCqh*a@B@-o9REU*YUaiDEyi1CGdhjbQXp+h=)Rm;o
zMPWWxW5f%e+We9<8sl7?-%g-`u*XZO5tpS<=F6A2Vu_=q<J?%>M;18hEJW0MBgk9M
zI*mDK&p*7#Cz9M+Ukn2e*u;L>>~ahyo=>q<RFGnhU*VEorR68xqQEA7Ais<giK(F<
zug&W1nc5PZ{v8sUmMBTnEnuGd<rG`v^)xY{t$vuV74}F>gz;bHcRB9PfV{}!(S&cj
zIPbkUPsOl67k_=-Jy#dz-(+86%t(KslIp+bQo+2#F=}v`tZ=$A(8D^OFcp&*gCRDW
zb&L6zIf5RpDNJs|A^SvklOSYJJYjKS)ng@YV__#-y2E5HySekVcfUr1=PUNZcH(>g
z+<v5~I~a)N)ov3I_<`oSa7Srr1Uoys-ThnBspDHJs;bD+c&TdB{SHxoV%Z5so{BY2
zP38ck8XAJZd_NL|<UDB#SJ(5`O_NeFNSmy9SZKe_ER9#pZb<_4fFU0>S=wB@U&5H@
zg~$fJxuN#6nG&uL$;W4{f<=9C@`_kOB+;k2v>VB?!NxjlZ<4f+yc#xTxbiyG{KBJ>
z1*RkbL-0RyHR(~<J#3Ht$LK-l5s$L)7c>W-%AL5FnNdOE955dqIyl?~wef|mEp|t(
zBe1`xDYGstFEiwEH%<K&;J3=_6Dhx#^m-p04z#^5d5B9oRurh9N~rx)v_9+Ld$DKS
ziNV$G*@Uxk3hANkQPZ#U93zi)xXp0oBXAl96JM`iyW_y}QDv0+WZ^}9wyulkYeo@&
z`RT;_{fF&i{}`nQXzu&xC~?5PDU~rOpA?|^MV0N#s9C}^^`B|SiB6Fcp0{;90`pTu
zKK`e?xVZY8&sg<bQ63wQp38ESi`ylLdSzYvSBb7KRjkan#s_{x%XUl&xO1Z96Bp_^
z@8@{>jEnf%4u_>^CA36YPpDRc1EVD!$#~d9#tOW+zh@op9x*?6la);GKuc8czeUd&
z9R#;H*7g!3uanP<NbOZ>^kw31xzvqs?b{!I<Pq&r=;vsM^7v!>@wWKL8UkGkQXkW5
z0V5+6dirV>a9#PiFgg8YIsLUKsl`h^*>B%A*6blFNn&@dY<mmn^wtDT%$7h$T^<Y}
z3cN4yy@>1f83}v*8Cs1cEKc^aFIan4O3msI3mf(C3ar_vvBT~5)<~y?u#&kBev_Dk
z_`(U@r2aO6kJmNDL|G2s@pf6`*B9CJT}=R4VX#u76r`R;uNxc@md{mQs&X1Ike)|*
zJy`7DN~WdusEV56M7tTyohvnSX2e@M4Mx2+fjk@_OW)b^0?MsBsiB?lY;e<iwZ|u(
zbht$iA@$93{Y$rDV@Dj&%!|T$#~sr=B47HZ>@oM-7Q#vjE?$D!vAT&Z=W(u1u4bVi
ztERGQAM#uFx6v4q%4?#PI|fd&vahV6?WLAd6t(t(&*q|Xvs}iY`s8)j?Nn)`H}++v
zzNLuy_bL(Due5!Z4!XaOfRN~2iD0`yI-&w1xe_=+-Af6scq<;6+1tHiO|=rN*^==?
zv{|ot8$={sXe)GO<wP+w@^PL+u##ZqV#5H~%f{sMshRwIS#{shKy{<dtE^7WKB8q$
zncw<w@3xK6e30gAcI1BZs6FcuzHlwEJNK*8=CPDl5OdQrVvUJ#-Xp`u*F*z5MbzBx
zEHJQ$ih2U5_6y-c-oo}U5)v@(bi4b)f>-7Ew(iR|1*e}$_XtOBS>t#RfQ=~jX^)vg
zRn$vg;|7+6oR6D^`95Xj%jbd1ZOLgigPj>D9QgQ?+#t(gBzs^$7k#+)ssHxuNEQG7
zVxUxw(-4!1@lC>gfmKpt^g-)ATl>rN3OViTdtpK31}FY1ZyyPdZ9i#eL3^fR#pAd(
z{DshE_X_U`B_0BeGfOZ(BR&1YCdA+%#<bHj)6=@&Y^vjI{n3@xh@r#?MRg`3ek-sr
zU;O!`OPoXJ{)aM(zNFTJ#VCg7ZA+UQIcd+PPRIxf=Dd|~GYyaWUjZDf_0-SOkH=m^
z;oWJqLOc~dzA$~qDd)SOmF3@#Kmz-v;VhdEm|GSbAmI@+>*%U6q9eY2^c%(AxxX#g
zoTb$TV2!*DdmgnDiw|C_9$#|MWT-R_<P4Q;pCD(h#)QDZA)MFUg?(l`KMgv2ePA&1
zk(C{zLvPGUL42MKb9IHmGU7<WdSaz74|;G88^?9-)bN;gP*PUfNrjzNof$Y4O}b<q
zvfGSKT$g#^=yo=Nope!E%ZJo_aW6tB;DLe7mYkE9Fde{~DWJW-7NjTJ8o*JB_m#&l
zl~>#v-T?(KMP+RrPJbFeX!bO>6^T)De=?L<>TVsAli!>6!aU5}dI0VGr^_DMq=$z#
z&E|geaMif%A77$xn>+-wycxW5jt+g8S`jK>w*M<#A*FUhZ%?Frb6Dm(Jg#Ik*YA4D
zyZDfIE!(ywv+yHN#yZw%<!_MjIldx}HCR2C_3&K52=l$O_ElwZ9)M6!=6PK19V!DO
z?1QF^+xVJt9%4LhcR}M<V~by}^(XmK4em?j)LfeGNZDEO5pQdGUngGSBFBG41ZaG_
z6M5)lohic)24xUp_5#!*agViI+r>##zVeGtKhA~8Ia!6=@nab59JbY}B*6c$qYvKv
zTGl9{LM+U>UQ-jf{568b%xklD{q;gZ?WX2gOgKC^(g4qj80B%8nIy*HdH=&8=O7SZ
zlIQeWLG02WJ!X7GV&3L*9eV{%p=z(mUSG!%+y+-RgsyzJo|0WA`yU_*F@y?O?|KqI
zW!0)Q?J!BAOF}Ro>4$`#HE-wN2g!nD925ZpF*Su+T^x**df%oJxxG7o1kFa3**}w#
zejF~|p{*kxQY=spf0kpXzVf*u+I7@?wyjOMKLvO7vw$*sc2C#4@0JFDnJbf{m~CwJ
zX)kt8O(EQCtI{>gRm1i*iW-e(I7M}L`a)9>8vZZ~>JCLY8m#8jwc+E(Hz*pv-RUDT
zSAt90=eXiUSP`#ZQ=n%(GdMY4P+a+)WE4sX`b94tcMF&%h_`p!fD-t;K2N-3t$Q0{
z*JIFC29JV*y`GDeRVspNCbjTi$;S7zK=*Fw99BK<D7rI+Qbfj|`d9%8hOVf{n#_kH
zr0Yra<F)s6uf2kGURHa9u$8SVuVBh_m?O)0T54^nj$_e+u1m%i#l}ddD(O_qz*!P7
zDm9$F%9}{m&?FVGQ8Q2-mlB(kfc2X(9URy(^(s^UbF?o(;lmM(7W9vrw=fzF^e`z%
z3I%8LCr_|IA2)m|Ds0e)8?^j=oTOH_dE~}Qh;e#)+WAwVSkSKTWp^#0O?c?J-Rghy
z=8M9xCFtS|tP#5hBuR|gsm1j*8mPHcRKDySyWfnSn~S|Y5Kd#blUv@&k!ztoD^ST!
ze5@0M(6@6f!4B(Wztb_LLjrGGWdA|-#1vbA4JCPN3~Twf;KTbuAhbo3RJ~oFpno_W
zcY_#e{xr%L0NHbg#{ZgeywT0gRc2-$d!zEeFg-V12<8HzMKWjI?8<CgR~!^zbiy6u
zWDch*D=a~?M4{i(@AA$Ss))88MYc%NUoYa}-s2o5D?XFL0HIe-MRPTa2)7)!y*G_>
zaHOMtPaqHXpCjw8&9Ae1DbjxB`9v66RVQmEws$@5f!g(t{7>J`G=czNk;kuR08W7N
z{ZEOP7bO;<G+pjH*{!VRD;gWKyBHI8OKh>$Pg_SXp7G8VRN<Q7TKgYAt;<q~0Q+7T
z*i#4VRC2wQBvF#zk{7q|v-r|3fPyBE^}1MMzZhqGf}3F5$~m)<_KB^Hqf-pe{jJHA
z#Bd=m;lR^hGQ7mp3qDY2)X#$j-m{kj=L$b?u9!{Ow^{gPn%UpH4Pa-QxU0rQDtj9c
z7I~=`sJ*M|)|c9xxYH|BNzJk@y*!f})Pexlp<}m|1MoK&!*cx?cuVaGzPvd0S_=yb
zqKv$xSq$#vdu5kYEKF5t2ZONL!e|}C-sv`qq7x4)f*QqlH6KMCM5sbkICP@aYzk7b
zz+ru%rU4Xyj`X|}J_7C3x5ftd3hx?zTq+P_8(g9p=mVXXrf&7l@{(M~{qi#G)me@J
zDPhw$>fwc*B~BeXHC5H@7PJ~}!{Pc+)?qRP*khD^(6lg~j};Lix%`M3Y>%a$P%4$l
z${i<ylJ~e%vGGFZ5dQQ+$go#)H4LuPz8tP=P1`6g1%l5*Q=TQsK<?$)okyKjD#B=}
z<rs|=xUzI&sXowVg|A71$%t0^7egd!O`6YP88teTSo+gvHb-W)51&&)pu7*vDjtk%
zekP~{=jd|l@OS@xf&u2+rmv~MS35a1*ZBPsk;`}<Z+R!d#b9h-t+K&?M=~!wC}_i~
zM9L1YgFj+<u!u(B(skR`0ezd+Qic&1V4v6GJjNKR>V@)2;cdo*#`^HNwu$|5)QvC^
zm^UJZ*z~Su>#uO>c%^s{p$GJGT{RARgejl)5g0x7)aEsMO?WjZi2j%furcsI7#aGk
z&=T)zYMiZuD1Z5JULhX4OU96%$Ckd>F^}|iVp7@<Go~lqe0GoR_K&YB;8%+$Dqo8{
z0tPZvA`K0${ey6VVtGWjs-r!TtgoG@8<MM-+iSH2;_uN?0xZa<Z0hQ>HQ-v#0&oXs
z!KK|6ejoxnUA(}(XS;(uKrj52Ldd)Fp8lDgl&MH4A`Q*P@>1&cBHF#2tkIn+L4yOy
z>1W!yVUF(O2BV8FSVz<(T1@39@WAT4AJ?t}s$A7}A>}S!5BVgn`H6mqj5#QpG3jpO
zhrlnJ7gw2!a%Kte@gMo4L?NA?Pcrbfm&r#w#PhzsB8lfikyqevBgD|}CDn%;q9-SJ
zdi_!Xu}&tVWJeEFxU*cYf1JCRU%%{R&#QfxZ#tX|VXwafj$^>XvJI2%FV-t)G;AS;
zd~@TKNQb~J%V1{gS;k(lNaf#Z&`wsp9H5^4)pAC&zgU6`mmgsO=ZUhnhOczi2NJk)
zrt9nY#<DProj89~m2DpNl|2&7pHYs$jr0tvth1HpeoV4_f-)D_hD2<naavrRL{)}_
zn&G_{nPt%ST^1x~!EkDWdZ?P0PT_vD8-DO8kt($pND{B!Tusqy?~!c4@)Gj;c3|y4
z_O@Vfs-b*y;Hm(B1%HL7;mK6NlHu^G1G}0ku~dD1<4bD<?mA@Fn4vXOX4DJ>y~Ha-
z-Wo%jJJ(U9xF<Lr=~tmVr91MhM8_osjwPbJm<n%&0}sbTS~Ys)u=m^dS$~E8S|1R=
z#~-9BmMS%>5OsIR%a7uCm1Sa}^fQ^wmfN(595cs6w~z8?+|vZWnW&gY9L|1GmuLlY
zF}Pu4$HS?MURgY353gPK-gyBU)3W{$xbmKI?~VXTi*Ep3qhzDO+ScSR8IH3f%425Z
z&=POd{&+#g+mX&@7(~z{#vctqiK40*p3F!{zswk{vNcWY5eY2QG*wa6J>%|2nL@ny
zbj)(~<h-ogbmp#A&_Sq-`Sn<k1!*vI|I;5tI)i+vOe2pK?{p=JnpP+7MoO|7%~m6r
zkHL~e9>v9xfkW^-_eBH*gKD(%@=~whzjO6mGjQk_R3;_r?CSc!qp<a8fV&M8TK8Mv
zd3aAQNfvf9o7p{Ec&eT4D}~|fQGjPr=rZ!{xudwd1M?P^#QD1E2Hpe$hyiAUFG@5-
z5*&%wO9$vA*r}_ss+LS2J22ggwaxG5&W0_3T3@Dh=BCBRlue80(6IM|z00O1XA<Nq
z*w_$>IT6(gk$({hEuWu#;>vM{Kd7lnw6gxG+dIcgan7|zU?fo}5kG29-0n<<D-@o)
z+1R&EIa$`sM>V!n?Hzfn<Ev)vwovdmw~=2b!C<Hn{ZwdS03=s~vxYvea>gh%pPv}x
z7B#g83dy7?rv{r6+=W~CHW~P}ouEidsXbCFZ{D;R(|ko}8q^a*(QONgV*Rg@bNT8Y
zr^&=CX_PnTW?3s#idKz#8BrzC!t}f>s}s5E(s_Mk5Fi~${Pv1nb;HngGuUnR&;94y
zG>~#o<HtP7vmH_pl}wcYI#_5|hp$KZxXs;*k*+AS6pwPK8ei9o7Q^6*`j7N`8mzV4
zIMMnrzc*-GwcAM`O94<Sh~lYQ?koA}9F)~I=$q9Jj4RAR{?E;%zgC7x^U(6L;0Fr_
zPxx}akf8ZVrBz^KwmOcX%e7tng2i+Ik$@Q{>a5nj+c57StkV%Ov}!B|{{)Y3Fqf#8
zRG*BUd$AJ|tixhxGVp2N@eqm!w~-MV66*shyd)z>5^wXq)#JDBrJlpkk=e;0Wu~W(
zx{b*w>ge_H9A8pmZfOhd1eaTH>>o`|dJaO{yX|*oriolDI^HTgAw5|uIkZfYC=HC4
z&x~glP@6_Wvd69p7Wa0o;g+Sh9y|c`$Nk-!n7HAyb0kpo;;z*vi5rGMhIk!b2xP$1
zuP%|x7}0-{!y7;Bj^j&?{3tQak?K)b+tRgYAc6Wpn?_I(g)R-TKUzA{<R>Vjc%ni3
z;epFN*VN}WEDjijQ-rBc^a3&yGua*tPv)1&_dd$E8<2NX5g7^{f_G#|e)X6e=qqY(
zzEde(Y;@tvir%QM2WDQ+m&#g|T;%phG-57fa=~apN&ZSL7a~9%DBe6}-U!cLQUd6N
z-p;i@iYE!}h^Xoma>2HY8gJ~C8}-WpT@oYg*}L&~c@PJjFnvBw9ful#rsl#1KC)`7
z=}ywqa+Uxro@TR6k`4smW*(8^df7k*fRef5bfUuR;!X_rR_k6!>}_sq8Z8noQ5i~d
zCND4hsOzCP?G=U{Z5UK17T!ne8sdw~r_gjUpMR<0?!ejoD+X84GyRA_W5SCr{URM~
zCcjHVzPX%4%3iGR6Oo2x^S=g}v+mDP%H`kwO~VhK_n?F0m;*O>UmUMh$-n(F4~~7y
z31_7yS_UkFk&6*C|KX}_d)5)+kRBp4Oxum0bd=R@U%D#`&D2Yn&gMZ7#Qv;lIsLPs
zxcI<M#IK3)@B|HTER((F*0^)nS=k%i&*xgYCDqd_Yc;}fBS|AFuWT#1HzdF^s2{RJ
z65Oc^I;!DbkgM9<dzl8ia@8YvLUB7--&+0V>|bil@qV`%bOS54U6xCf@FWMFoIxrd
zHgacDJWD2c4Lc#jwPnqP=Rlg53mp-B%{)TIo1nu_Eu0lIP=9AMZt1jq`QF<dml#`t
z$Jkmf<x&nAuVsZoh%s~I=jG47F_Ity1-j4Xun%Zm#+x<dK>TJ=rg8e^(666ca%b52
z5+&s3N`((}HIqsAD27Nv(KzG=OvIVMd&QDNn7?#Hfhsa?X=-675&JD5nM!-gLlFmZ
z15G5%%o;pG!grv`=5e+f_bg{=pAZ9u++9%4XrTRtRuodULb;XrG=$WFakm*e$Wh%s
zxc&ZpocDF|brGpLTQs^ksoGB1^Ju+j$Cptl64-!ovOW2nY-<z~kZ51e&$+p3c&in)
z1vCgk$x`LpjDz~mTunN~E{%p*X1txeyDWKtbnL`rvRI(k&#>sW>i0PVkwX7?Uu}b+
ztDO;i_pw&QO)jX19BjXbyJ5yvIx4!MM)G3za*!ocDaPfkrbNGKN(Wdm_v|mR6pa&`
z{e3az@5tlF@nXm^t}@fz5xOPGe4(*=NT*9T`ZDUg!nY!{;w*}rRm$(|Fzsq1qq}F5
zT!2qU5fs$3%?m7|=e~60ut+}G-qq0Ns^n;&KCO@jbq=wi1N=a?FxW!xC?bSmQC2Fu
zj`4T)pbQ6mYt1+j2zb1yaqb6l5FCp_DK;*y_EO^>n~fiIloB4KuCA`9pi?w2&?}qu
zn3ZewrbyDHcpj4-931=rRtTWSrosL~(<mBq&HBz#_<6!iB=`?ENii@nkrJdv>DsIS
zH9Cr2>8k1iA0>x4lfImmsDb%f%Xo%1GL;;Y#Y^bA`ns7Ly^%yuO59WA?l^n@*DtEs
zrj%{%h`Qh1U1PxEXZqBd*K6E^ag8wqUL0T$?>4VmJ95NSd9Ox3KJ6%LHAeqzO!mU&
z;w$N)jhc~m15eoQC?ywp%uUuUESSLlzO<~Y#AZ?EuK5@iXi3)rn#NkyY=2S7*q?Qt
zH#k`73JMBp1l$&0k5e1S1E9|Bs8n}|(R^2N7eI^nRDNG2G+yM5)87%w)mn^>{}^O<
zzp7GO&K8v~g#T+f<B8)@L5YpoOsef@^XAB%=XBqkxvk{F#ocA9K(bbtlqER51kOm;
zOqVne;qv3SQV5(m`6*AsfQQ)hnkL~IiA<J5qG4*PY+!j!6ddkD7`^qhtwJle(f%Y*
zf63eC)U9*nN(h8EG!uK2XUfWWe0+RBsS*U3b?Kntxd4~*>Ar!-(Wtt{cMCGWKE{Ea
zjyGKS1KDnGqA&p(4kcdP&S)OV@!q`N@;zvcYilQ-3B7wYpt%#a;r&_`O;$a4EBtqN
z?26{PjbKeFlWTCHtTtE9-JJH=73@Uv_z<Qdo^KMLL&hYjW%Hge$Pjs_tI%Qq%lz|r
zUS$zsO=D3`gY~Q=sMLy+O+{#QWpx!l>n^Cfd4Zul!Ubf-&ZJHCua8hYoOp=xoS7LK
zGVN*tE3jL`(o|mWnzo%!gAcF~0j8gwlarjjzJ5WE=gF+Ia;_>VzeyOWy{&B%Xj#k)
zn(l%obSS{?0tL1`T`^#I7Imq@J{t5ZTsG61QBF1-4~nWiC~@qVIbcyGSpK&6`7Whh
z_@(wsDN_}Ncg|B=b?I<<FRyR=b3Qm|cKEZb<OP>68S)KC@3Kw1to5aRyAK{gF{bQ|
zZolpgq*rq-0QNb6xgCL&E=9>$e{yf#mZ{>vRX0h7+z?vp0DZzeW&#IAAwhN8(NWM(
z4xfzdmXgu{8yrkCL>OSl(h<u$W`R=64Vwb09I2_Hg6euqw=EZb`t)-UijHs|d~s$C
zc!))^>`P0Vaj!-7UeZKFS%ZgfS%CSyb=+5%JFU{WGLauAb8Pv}@4l74k`6PECYL>x
zi{~0X<k!h|E@P?+)uKMxO{{*4ap=_F0-D4H^9qGiFgquNZHi}Sq~$FWAqH}-E%fR2
zFTT<;ww;+7pen)*ZT=w`PFV;QJ3kZ@Pb1!8U_b)8r_m)Lqs`6D(Yd^*+S-&rhu1a^
z`heG4`k})*dwXTo)YM`$?Ckhppr!U?8<U(DH>qWC`Qb75aO!mkCuyY>6`|a49gB=I
zULj|4xP9HrMGr-pn6Z`d$A!TuqhyYT7kkkdOj<4#Qqg*ZT4&{a;&|gl0$RVn*XHmG
zR7|r7)treB9eglLdDQ*1xmg?&-ZyDYD+Pny%T46@zO2!^EkO`2M*iu0T0oW6W&@H!
zxZZSS*QYj(?*g|(Z?kzFd(H^Nk4R!Mhzj}0WqqqkA^9r#^0F|R;a_0TACQZ9JGqt9
zeoXu<v3yommW@;4+m^D>(9qMX*^uDis=UA!@BzO+mOgSuK|ujYdoEo3C6M_3t?pN<
zH7CcQ-Ec`vZELG+Y>EU!j=^B!ZU|d?Go1SR2dn_$+wp6pcNd)8rU-W)+>!59kTuk$
zk2?7HK0Yp}=RwR)Nw_b5mur`Nze4+U)Rnq%dAK+^L#Y8HJ%t>7vuN|L>j3<Hr{j9d
zuL3(ChbMF3tzIcGn1#CqMf&BF6C+6Fvsw~!Dza!!iaZ?m>2X@~N6wVi=!oY(06Rnq
zbLF+QWC!P^vwkkzTF9y&n@aHVQ$$Mts}}vQM2q=q3!4$)`yM$`m7;md@hQ#;DqVAv
zKb^BE|5XgTk>^bR<Q4octnX7*b+t_1s9I=TOib|J%PF8LhPM(ZsRlE#uo$%l;r~H%
zDQdGXzI&teL7<_b(e%7E*3Jg8k4Mdmq=E3juydk<8!Jz(DfcPG=}45i>@Yf(+-U4C
zrs~^_s)?2&ah^CJS6kLT7S`^pp(SR6*_5BM6%y;U^|OoSc}V;a2gM|<VADjatI7F3
z8dSfuDGALw`|{Jt(HwQ7qvBBwH~l+;l=HMs2hXK^J`_AOe4BCxjzC`ycT0ZF`v6$f
zafU)mTw*FE<mvfy<!4sEMU`2-J9f>(#!&<4emtj+laBgkaa8jx;$Il;4e!PBh;$2d
zJp5kr^S(scSg)_IFA$`Rn!&@uuwYW4lU$oUIy$-(_zT|y4W?h;{cgMLX{pLaG-6iX
zXBpXc(BFf!)`v7!fW*d?b6*(`xKKqaN!&8#JV~Cp!_6H|QeEx%U_4tVueIEbGs^yB
zUOA&u=c6w}Q5RF;=9Ny%<WAXYoQWRVo<F)Ph-AcNZ1p~#{}3$Z#F9gL`#8TgXQQK)
z27cZ)4>6RDa4S4WLw|G2)X1HTMa&F=)|Jb7s%%netrZ=7#dhxWr6FwByxDpRUbS#3
z!gNIOJsw11`u}c;0JwLx{%sBCd!X(222C{6K_kz{83FeLaf0^<KE({8dmP-_|Gm}N
z=RPoErho8C|H=cD>Ou>qz|JCwVEKbN^=V8cNK3M66-F^~>?ha1eq$Wq>}$LFb~zDw
zdAf8#QlT@@xAa;$R61yjCeZ3>wWf*Rt0$n4R~H|7gf_4YiMi&OCkV;{D`W<2ByW{5
z(9@^?E}cf)gm=(%i0;+;0p)(sfb@`AIh3dj0>6uzU42t4iy>OhvUSgkd#Zr)r>WwN
z<XxgC2^s|<YE=lL{M<jW48A1$Nfx3!pp1o^x1DcF7*_erC96BjO$alm`Jh=eqGH#_
zk<@ekHB3NA?+g3OTAyFPMiDvA1P~rRJ8aV^j>F8x!RWZZ<D06=w!O6expzRVfqk`e
z@Hp#+&TH}!^(=CL8T+W%?Z|9peLXa3<L%X%X=YXy0*qNP5gnl94qIc`N@8$i(E8TD
zxAzH<p)7v{hQW^?V@O==-_Kj8Bp`U6Wq_1$SH4Hvl^x_;pypi(Eb$3_H~T&A>(ho9
z8Y&;}w`3=%>@Mw1em);YqTX1VMbW9Pfh}e`k`NQ8tLlW<incFy9x({K-OaI=G>|RB
zKhkaBoR#{lo7z@=sb0caQrhJk`0;i|HR@t84gx48e~62FIUn5>@y}2I-X<jf%ao==
zCu$g-eE;Kza%Oh+*y$W_<-j8+$7mdRZ!lNudU|m<04@*+#Hj{A@lGn@@P(+Xfb9<o
z+&v%*2HmBfpQF73Z6Fwggw&mc49BwPTq(kp!7Ng>Uz4&e6HU^>Ue0{P)BnkSAa3|k
zm85mydFd{no5#>{L=QE!Cn*)VBTvt74p*c%o*e_+g9fv^p{LtFj5pY{hTlYEh)wn5
zenflNG(UXMr`stp@sD_BcduQm?2+G0WQhROBN9@~0BbaPpa=Fa+0l`I^eA`Oj*E*6
z%AsO8Uz$w5+eH8`e=qs)YKwbeRNbdRM={U`Db3~D^NUuwjHfks^l#LmisRZBTXqV^
z+)XD+Z>?jGy5Oiod`So?)K8jzQgyL%<kfmC(Cql~80(YH_&+;!tDc%kWO?(?xBHC7
zXfiYHn0K|28Ppsft*jy1ufb?MU^8OysY>2rJEr~9<?NnKi<!;s;TIy~v;Da1UX7q$
z`h%|6Z}np-Jt&eYu?#~+QtiGX4>hfEWtv`cYX9@k0`C-a?ko1sN<IYeaF7KOCS&>(
zX?SBG4Pu$ei#estLD=&gMEi9_YH9%F$t5fcjk`_?1di)3w@`4#g~d?G_qQiBB)5FZ
zi+Re{d@&30pLxE#fDt+=!vILCvZF!!=p9hty%?`0dKf7q{N{G_!^jZc<y2{&eC=D`
zEZ$(m!}nBv;)p8ANdzxzcKC>lAZAR3mxgjVJsJ-!aWJQMVlfHj)pKTfLXH>kA&LBc
z!80|o7PWP;N1=!99{&ozxsfH?hU%hDCH6eqhAiCWs|B5X5B!)E7Jj#p#LRB``l*mo
zVD9+g&N(`Z*smHt0$%U<T=)|rhUQ7*Iw`^&j)6(}OLi9b;v=p_6OfGBh(2<eF(vPe
zpbt2hAv?1WVH_NO_3ZzjZd>J0@^K))+#Vv(1P9~SOn@^{)A+dh&u>4U-jF#v3!gu=
zv`VOGf~`KJkruY5CalW--sdZav<%EN`#+=LIy-9|_=?;)$tfSV+&r4Kx-cxDPB_k5
z$hf@2I{HV|K{ls7enJu}Tug_tFJYTtJ^bu{q{#$;H?GdP*An=2cJs<fm?{9vXQ}Qa
z)oikKZgz85n47(H9Y+)}8}+EFe4Q&;=xZvqwN3N^DGWehAHsjmeV+Y~C#5!86_==)
z!0&qC^gS0CCex@n<(QB4jwJ04KHNzcO=2JbXjO+^%g}uPvLO_Zzn74hU`NVC^868y
z>8k+j649gYZP$XTKPN_8w4_VG!lK`frGISE*!Ohm;>#SM2N+%AlGxl8_@^+BP4nV5
zm`X1I?YNoCX^4;V9xNr8AWg(mD~v1<$KRk0gO<LT@cqJGAeB=ugFprH-bHfIe7{Ku
zuM&ws`-!>FdbNOGnbs{o=}7lCu||3J$(e1gMiPIgiqfR$Y*S(Zd7~e_C<S&bhtG7J
zUI_2~<#tx>Z|GA7EgWM>g@qFaId2aXj!rj}QR^jRP&^-)i-bS(VG%)I@Gtb)w^PZe
zq{VIH>q*$A`Hye&=e*?gL+B2tfcR`7Av6+AUAKM%exzpE!s43A;I4yX8;<Bn_7l@a
z7Bp@nz*J)$Q@b)BTj&gk7v{i7yK=N{RHjJybjZm5ADrCDw*ID)&?F)%F?7)Uhf);C
zQE<h)6I~A%W~<7!4@?4+s`<%L!0{KV07|(@e<E#Y@W(a536?4jrLM2X?yVOuO*v##
z__qu1!6(}yI*0i9eT3#<5?7Uc#N-&Y=UiAV0Zq#AM26C*?jK9{*SObhxiXZ)9w58u
zj{(^JPo{WW3HW9o908x^+=vIZHI4*gh)|KSqZ6vG*Q_c}RrTW`Z=c>}Z8^Hw3pZ-_
z+hwg9Qhx{zIz$D0w6dakM8RRU)RE(TXFcUTeYc6NV1k$uG#cbNPZD&@j~tv|8^U~_
zam;@Xx~5hjpiy64%WR&IFgSHify4ykfNz68O5>G5dv0@Cy@@r*lA_xFSxAUT4p*E}
zM_1MQfw4&bye9(9Zp}NsBz#!vGq!!ezK9oNy?uq9$khKH#KP@cn2f>u!ty2xux?xl
zZ$4(!5MM+<s9!={4kP1HOnE!qv&lGcE_fOi@c3peJ!&}@<)$slJlL~Qj+V^E4VH~>
zsCiR0eL<;d=Ds50EI)V8y0_!6?H}k%ua*ym<#7TAr1>QK((dmkic@?oGi}qDd{4)!
zRf!ky9xpYs^_L#@X&CC}xMvM?yiDpk)2O&+D_jAjh%Gs*_=%cZyXHeMDKa~|ZZp#I
zV>oAw&|s3yTzq84j>5|s-Kw=-qx_4Gb^G^}SSfz5<i?Bc3z!o}r+9G%05Yk*MhW8A
z#g;{#K)RcI=nVgk(CP1h$oJcJ^_AMg0fq4r_YiSqg?wewzKoy7b|-uh{QDdc{mnZ@
z+zwrxGR4mU_m>+W)I#Z9ae8@KC?=0NF(JRH%+8XXdJCKkd#LDq?e`EycgZh6djY!f
z)8vW-)Q_mL3zO#wO`4w80}qNvjyoN9-`CpyZT#Co9U2m7o4a5lO&2>C<%-U34#$){
zq()FHyenWtn-Hy@-tyUReLsca%@2yF1)GT@k83CR3760PTY6sTqNzcX$cy8>{2U*j
zH;_a?8+0+xLfwh?VoO#}=+CTgGv49uT!xp)p{#d=9J8OZdOsAs+x`s{;wPqWsBA%<
zD&XF(Lt8$hc~9epiHJTK78W*cPd5JA%vRXyTmvGYD|ZfTNNT8MVEoZPd9gnJNQzxn
z=s4<T3eywIGd^@bj_1k|wFk^5!*`o@)jyPTOVix|U%!T+Y=5k1-S$fB11avIeH&=j
z$dmeFK}SHJ78*Dq__s8hn~h;)jd6Nv?aeJdC-Z0l*nm&|HSY8mNHtf*j+snDOXQOK
z<HdL=JwJ;uG|oo?*)QNGp+d7)y2LAESh~stI~tQjMnxM7hNrD#;IWKNnxlx4m}KrT
zVeYw4=M<~w?DqDKnw3&}WDXx~{BQ2YSxx^EKo?Ry!FwHzXlHM4xl89{mn6z){r9gw
zJ<O~2^9U|o@`~6)*`hBIhf>OKvMlYfJf4wpOJD{MGirPGQy)+i^fGA=oY1tIePHb7
zVYfnFFZ?0c&M%km*&UyU)4!LqtfcpChf_0I=S^q~S;njGAGH51I+ux48m*Q}NU+BC
z`r?MvJ#Z6IEo#779oGw`qoYR*c#)S%E=G#Y`F?92PUp0y=Ug=x#2u;K1ZW>0)StPw
zTgz|3p3qSG03o4?j-KUdszww+KgFT#U%Cv-Gg9`7n`gksIZxF{!f`p#p%wgo(EC1t
zg2$PQ@Oh5R&bGzmtLp&V68?c|6adjB^*2s8FfG_w1(WVg^in{lj&)_4vcf$p@VXgU
z{_%#Uc-8v1fM_td*PsIjkk}Vys=6nZBawRIkorD9iX)kg?bmM|j20t|j&11~y_IyI
zLMG!`$R167bZ8r}eduC8GvpW<$A&<d;@3{u;9x^P-GUg*vG?<Z{?y$C>$u@GV}<9=
z)lGh2GFvH_@)*t*VxIoe$0!Z$X{&4q<WJtC_N6PJFgW`zYa!~c<1x@N3uKRBjr_Bp
zU))ItQ7*^=gt^kh13UduHvL7Jg?8-cy|YyDLb#xoZDSX8SN!WIFvPqRnvVW=95ZfL
zEHxUTMANrR3}2>`+W&)AS{>~RE(b9T=zC6=aX~3~eL%fkF5<3^;&^7TgR4q`#Dx7V
zQG!w!teJCf_V;hN;#0tpWc01oE{LK4Q}#m^_@{?}s{}Om^+4%GOk`Z0X!V13^B`Sh
zkOJAmb_0X(i!RpeSD-9bxSEWOgNn2tbQY}zUs12FHV$QF8*Z4`uI%E}UJBYAForTv
z*z(npP6~CKb4I{ui(~^c?zj>U1cO0#es)0({@M5D#OllX0NQQ#J%y%^N<ga80y5|)
z(w_>C{jcgh-ni~yLMv$!k68Zp;HJZm&E4HNl}Uguc5e<Z9=6~b$_It`F3vjB{o1p}
z=yaesaudfwMf&AdH<GJL_d*wxVJrB@i`}fJbUgc89=Q%2P7F<(<-%A0eJ6<J<2Emv
zR*Nh_^=ryso@M_}IyqzS7a-uT^x8+5Q7`Z<{YD7WcW{0P|Fy|VCQkn2HSCjh0%*vl
zqJobs{eJd&eZi+VTJ(GI&w_AqvKi>gGLLapm0|m~&lyH$UH<n`{Han};WyvW2AnO3
zX+}d634mf?==n!dyZadk0KYIR1<>Dl6c!_PfKCWhKI8B4CLVM1{|nQZ^mKj60OayE
z3x-^3m$nEjg@i$Hz+RU{b6;A>5}kj^2y>}-XC+5Dowdigq0Ir$ntxmS(XN{Av)|pq
zj*gE7r!|h~QZ%=KO*Qsiatb$--qoILQxeZ>Pvd+?^No2=5`Q3}Iyx#Z*g;5rmYb@U
zXB=0NbtvL-hoq;1dErNvHt$%YX1I#@=fw}KO2|S7E$@mH4LZ(x&1Sc)>Z$RFyw%ZU
zM{4|%vMNTOK?W}W+=e)Aq-~tkMlaZ6CfmQ_63aW7Y87lwKCrcwYFl*xNM2Ad0<+@X
z%L9(Xp3Tmc(^awjiP)gJN0WxVFEW}##qaZGD`8fe69SMB0FJF_1J2FAbx8I%n^a#B
znYXQ8iY3B}cIjNQ^hl@O!NKW+4xl(zoJ?Co0_u6LoR+cy#GY6LY3b~7KFemQn0}z}
z=(Y^Lp^rk#@ZvICrUS@QU|;XP1RT=%dpw9mzc5?=5n4)lK=`1qX-5qHs_=+cN3p_K
z!I(pY9F(#)rq#dZZ*Vc`ayLU4J?a(U%~rXy?=WuSQtow++_ic{BtR}p_Jn7;MjaG)
zgEjz9I{mS+G57#=XC|XPo1i+Y>p41-6!B`$P>om3QmJ_$XNXR9Mk@0e8xJ6HJt4*O
zX`lN(^cd8Tf;xYL;(A^n4Jw!Rm+4XigT_kR#@65$l7}<)jnmfZx{41=otQutfA!%V
zpr$lwsF2<vY79CjUoQ8-M~6Gc2}(oHLD7iVrK?j3OB8=uVO*q*@b;?ez;XIJFwBtJ
zn~UuV?`0EjAOwYk<pc(Gplmx%Jbze23n}jRVL;dgMN)_YkIu@*cR4>?1}djy;uYRz
zv6>nI<uzOjJ@?}P8#)A@W=U?)y&x}(;`SI~hvI**T(WL@bx`Dm0P5sEKF>^L$~*6j
zE%}L)z&D!+qc_<wGp;x<c^z#OzF96YL40+fVhTsOjgXcG8o$UVp^T=35)QUI_rfwb
z+1(Kef<yU&NF|eq|J^@QUi$M!#9)|^P%eL}C@b6WVut6PiEn%KA>F@#R`UyPHcoKs
zCFevy0`wxa!RcByXZVFHPfk@X3POko7dtxQuao%DzqB+(o(5#VMagR*FH<{m;HuX5
z>G`wwdRk{E!}Y-=%(z$&2Y6@zwV|w!!F-QEp=jX0pZQ|#W8qEuUp(p9^?hD3L5JM%
za3VbtLPA;=mJY+MLjh9d@f_k!>;U)v2Y;z9r7Z7<Qvu2>h)Yho2=yY#!2^-T^dLD7
zWf__$GO9+)Ftz7qC6uzVDx4g*?DI6-Jkm7tsOqPR68ii8oYfoJF;U$$Fd+2D`Zr&P
z;t>$roSwSKK77~$+;!{gV{7g{E_gOOT6*#sdUBaG@5so={CZ?_hK|~D;20udN4Djp
z_ux3ZyG#ZjVb{e{>K<wZhW9hg@k3wdfvNM>p{=r!Q@cb_Mz6o`-U^>cB1;^X{|nFs
z7A*j@brkQg$0c;UexQ}6Ji<;A^BARE%W`t31Xi_Dz)uRlEV)~I@{q4^EiMF3{1)6y
z8To3Ei<AwMSkB9I=db7Nr7Gq8&wEik#{oplN3B3^wj7)XI0KBCYtcb)eI<Z?kot6p
z3i&|?qx;bG?`Q$j-``);MDwc<0C%`e`HIclZ%6Tmwz<5I!)!mX^m$9ykB+r(3KV&=
zvWy7C^2a}OQZoC!t?1AZzbDm2fKB`+?L4tw2va}zU(7A+OZ6R0?-K<RD`=x1j6*XX
zIKafj`^SJ^vK2^$omYx3#?*7}UtFfyIP&S(=M9r(J^l#&9L(6xbR0%gBamiX#C&FH
z7t<Mm#3tOo(ES7Xy^x_jcja9}624~RhiGkZXaoIv)g<ydfdD+tO`u~#w{LNkt*B4}
z8Y;wm?+jDa?E?Cs;E9j%OzqkNY_&fa2#wCaN!@p5`D5*-PXU1mpI_OgzeWis{*A#7
z;OHecNFo>g!uA8w^*?`B4Z^4@E`X9CNc*j@=hLt^s*vo9Om~MSLW-N@&!5$_AqH<y
zYj@ZC061i+<KreC^7AKIstfRlr#!a$_kgnT;~!DyMw_$S95Zvfwt?Z+wYU=zY6i$;
z|2Q>dg7|b~A9wHO13`O)tmAtX<&aU)D0tr>pdcgjUg?7vL`LYd?~QuHGXgAj@VFZ|
ze4*XNkmS{NgRlE22G^EqrW!vRD@1lnAF!36SVeCSWDKf)GZd?*`U5B)cC;wQ)!ofs
z06Y(A^qrp8-tc&Xf;a+DZV%2wb|Y{09zb>@R?!r#E|ENX5T`?tPU6qI#)3@%U8+Pa
zGV(;HxxJ1=MI)PJSx1J#@aID82K5^IAA#!?2#_~Q@8Qi%#f&+?%)ZHQJa;gAI{Rud
z6~3MREK->G#*O026yrs+L+);P&}j1u<HTPkt$1oaCi;AMYU}&2-y8z<1^up3#Q%Yc
z_%$h?%cy}k{tr64qGH55vQL43B{bezmZHO(a+<>RXY5q-?J3e$k5+M=-=(m(|3a55
zTGLf#CG70$D>u`9wyOlvsGFtyU1a@{*58-cjW^xl;UVPc29(QFRsWsxTJJklf&G`*
zZTikQ1$?$7PorjwzL4Zin@eSbC^I&C%a5^e0O&LJD0N@H`O}+jer!#w3+X?e@Bc$1
z*R+lV8i$jP!lgQ@NAf-FM9Xv%R*-)Zpn(TGZf@S#%bZEM5!0LI!YvK@KVJOXp}w|5
zJy#V{lLOw64nHZ%g$ExMv|}nv0!@RFHA(G67Jl*$8G<^A=`BdZ^9S$Asp~c2{>ux2
z{F&IG%w9uY>Wxj`TS(3D*XL4%L@Uw-&mPA!K{;<1P_>q_`_k&4S3QC97<)2*!x@lX
zfMfOIC#$}Nbd|{mXgAw1pCqyTD-u9mNY1p#pZM$zbPa~JAVCMqu;p;}{=!=8rXsYg
zo!jS0yVj^`-}?c(3;^)~ZNH6*(UU!5mlAb*mwWb~LDB=n7yCjFOEtZ+)(in%1CUV8
z#O?s_6(UP<pO_(V3%NS>(?QR223CXMx~i50P>Hn`z5|5ubd@E4>NL`67A%Qf#Xo2H
z_b`;(lVM=&H!-3g(7~V>u>&ap{OMACLT|_)_#eapqrNmQQS)8Q^v8X#9KP0gxva*{
z{-?YKQun~&gb5<w{s9L?6+~}Sxa>tTS_s<`$u$u^zeD7bZ)60tQa;%dRzuA4(33g^
zqTKFM)Y82*cg;XHPo?0OmJS67d@6Dyz=XVe@>hT;RR^$yU?EYoL0|tX562Zg2UO`W
z$q7MVANPPZT?OgSh5rx)SH?J<{I+V4E>5Q8vW`=<ou;aV^BCJ8Pa*$7(*+``+W;!~
zRC^O19zfwCOT-V*r8Xl0i+->^x5A+d`m7)BgK(&(uKcwn@SF=|7IDh?qoMF!P7hvi
z4igCk!XYTf!58KO-&6p2+gV7w_r-P6lQPgWHW;~+NtcZsAshK;g^ivbx|Xt*Rimj_
zw*KXAXlI=YSNpU8ym_SQ!v@7BWa4NL0KE`dW&q+Dese>*vftnv+phM`r!OFl#IW#&
z82-S!gc#@rz!t?0ezom@%1|%<IpD;ZkuD?kNm$@njS)z{up)7MZ?x*rJ_26vr*N=%
za65{i#ZwvelCAx|$1IPlGBUN*JSp3smowsc|78v^#3Yk?8$aui*z%qSkXmo=ggioO
zfe%DHO;x$W)C<9UL0_yiXa~h1e3aOWioJqq!BBBE%OPAWi8sybo}AMg4Ab(*%|O!#
z{&sONGetldkyOZv^1JnX1klfZvzjGmS1*(W4H>c&`+kCj5OMfPqh0{tlpmw5G9{3p
z{Rp$8Z1!{0gBGB*2Y(j0&^5M>Ko77sV9x#{^AUl^VV{u8Mq1$es3=5ST-@B@G7O;q
z6}m$KG22>WJa~6E)0^YxIQO6J5d&~D8d?GL({1x6Tb;mT@o;^BL{IW)<as>shzG{@
zkZb%c{;~*3?lt{3u!<DBh>WlkM_o!x(W&1|!uouXQU`5BZl;4}8IZ#QIzx$m6CxIc
zAQrHl2H_NVUD}63OfJZ>3>^n205mHA1i%2${^1i-WM(EK@b;k>6Pw{!?ivL$02im>
z6c@9W6hqq;fWf}ITAVof4STXpgX(MwQhDgp9yhIBbxDefQecvB$pY`@AN8K@+f(IR
z-+Lm+1u*74PpFucl7Ykn-D0kmtR)b)qd!R$SgIGf_osdPMmQjTLJ10>DBRpd?$i(a
z6?2I6+rA?MvxM75z|-q$R2<3-yg|n(h-&gEhW_TsCMUIh2m$vGRNj$MQI`NUXalsQ
z2=Ac+gf%_SBO*|}3)mdaL4sW!6?xH#h>(LaU#kxiTC1`9(NF)&^ONy={fWZ%cqAk&
z^<$e3E=$2Ic+}Lot5KrvAZwyivr=f?g9GXA$H&1yw%c<0)&PCq;lm$*AAL`06=K)q
zB$<zoPdOJLDa}g*Syyj7uVHUn8wwy~wQo<B*{*gI0rxXPSh4kdy-30I>$^*U_W*KN
za7^$(^lx^ecKgatYI~On7bR<T-_B8H{YSuy<fqYznqe=d3E*Bi{IuxV@qqu;$@LVP
zsJ?YNOx=ml1nYDIB&n}?%N>yne0;Zo!}yCOVBm}bOT1?*!}0#78R#L?+1c5+*Kmzf
zJ|*as1mGPgw1DHwE0VZSTQ6Kwv3YT1-0#?}VA&L}p1vSu$6x@4W%)(~P!<XT-EHHW
zkp9Z^JN)I9IJlUUva)jdX`hCh+i#ulxX+(M0RO59JnP%HZw)WT^}HVJ&DEJ-JTWn0
zE-fwn+8XuoBSJjaXxXnzs0g)OFXjUb<0_A|)&H>9FkJmEt2*)kFfP2lVYjwk8NA+I
z=UQ`R0W~{RKLoeBxeE$?=^L#W5Jmm>hn5@E8<^XhQ0?hXTKcGJX<?X}uAAACkdVMH
zYw&O1MqFGgH+B5xw4>G9-adA!`=@N*thVN8Fb!*4u@@CK^SR2V=lVR*eR+P?Z?Jis
z=mur~`3(njc1%yFNB7m|HywqY{mb<RY}Ee&?c9L;>+9<YmifQm59AB*tE;QOE}t@k
zmzMIuJryW`OLj7tTWlpOE3Y6HsIIOqgkelnJAybU=}3NK*s;2k-Sl}~M7@e7w-DrD
zfWr#R`(7O}X;A!^<<9?jbI@JkubY>prqXKHxs_{)0R|TgkCM^?PKk(!h=+%#yzEXM
zj!GWhZn!1kCX5C_W_oy1Z-apto;bsOqK?RdEe6A^d@6m~=+^)G;-SoB1#a;)!Cl!x
z$8qBa0x;%b<>1J_E$OiF{<L14oweYltwT`{wBh4VGSrCs{Q|6vWzaRIDFB<Ib)EK2
zxt7NTykldmU|Pqym|sXi=*_-Ob<NZ`0MV4rI*;UfAs>P{DK@}2_;)Pr=7pC%x-Xuu
zTSpF%EJK!R&_Ido&6_tcZ_qoU8JrhESBVw^B{3h(G7~y}euBlt#nY9KN+9<7;!0lp
z_$l1c+N%0yLVuGPJ8c)yV`ik2eQ+L5&4>b{5fYG@4L^yF)V6NT4+oZO*qH}3z?L|0
zCH(KDXizDYtk?d0m-StZWgjzAT3VX?)29XSI>5rDyL*?=JC_c0x;_L=xl<Upxp8-<
z%3DA~5*~*QWp<O7FFZWNK<^mai&I-*KG>eVrB!!`I5%sXHns{*>m7NQS~J5UU=9FC
z-q@MJ#PUXy3NW%*-IT2MxUCsF*X3GXn!h+~z!w<U)B#^}&<BCcv_G-rbg#>qK1I`=
z<k_=lKffi0hGIf-(6}d7Q!vdPdSV!lfj*;R4#~d*V>8duY7$o5Ztf^#O$%IN|DzfJ
zQfyE!%=F<<%y_osw=QZhwIF}$s_Mxcof60o5(fzK`l^0&8kK#eWO0CXdo&3EVXZ#+
z5a<<=y^@ytjZ(Kzaf5Q|y+1TH@CP{oywN(Ovu!q1^~rP<6IkLIU5fg5mV;XQzf5xf
z9Wc1Dumyh7`uVeM{aPzix!FKgnn2~W0=~&QP8Y?0B<cUR+Wr6GMeqF$DA33VO)CFi
z2YPY}8G=E7jQl`Cc=N}$e_J$Iez2|o_Wxn*f6*QO|4;aT{*?`&PKX1SJ{-~iVP4-b
z0B*ib7Z#wQK!52N{~9@D`2hWWZDht)%N{jDfB^^U+op!ppm8doM*`ws)NFXX^IzUB
zf1C{e+mCVq5(U_o3r|fpj`#W7-7)MiZ+r$h`2=+6-XE}%fDD03)G6BH68!IcuzyaJ
z8e@JIv;;BUG<TRc6kye0@0R;{clWdQ;UDNaI2N{^g5i*Y{yyI=CVlt!ZOS5^9zQLd
z7ykY)MivMjbIU2>?!*iaBV=E_%GB(rdkHcz<VXCp2|3EF`k}+}g{}&p;%+z^nuZq%
zxb716YgmA>WHeUNRp0gR?qu#BRg{3X<MY$9$rt5Wj*ZgaW|8)FL>I5E#OJ>kYInl8
znUcY&sv6VoY@8FkNq2@gBaQ*un>UXC0uuf@kX&3|Lg^alex#6u0RhDydU#{wCjR`*
z0@;82S@_C$joN8hS%D%k`StX7PKaoh`yAY%lpPJ1`rWf!SwQ!m>{t^ACm0i_s|(k=
z)^n8o{r#Xp5;|m&2bjIh5T9iP%u$Qv!Pl~&(-lxQP`ho=^(Kjq=P&2=iIC&t)3LEV
zz9^GPlX7(x1`W8nfrmj*Czhbagg59Qmj-;<=$8*~i_+V@ZfgVlIDG^V?@<B$6CjWv
z^Q&q%F4yAJ^}2LKMnh{E9VLPS^>@o@Gi|4fQ@D+z;{#w_%A?;11O2DQd|yg~RU;XD
zuYGN0MIUsO0FY$4#vGW7ooU9VrbeJi+&$-A%Bc!#uMXpf;pF~A>}m^>rYUWpc^PKR
zWB<jLK%@D3&(T<r8gYhz4A}GB35$#m8N<K%S%MU}v;w$v|0jMl&|)B<qN1Yhzy!Q~
z98T~G$;ik+KyL#I2&<YIa2+@>Z#L+PVuDCv?O|koU}n-XG9rV7G9S(l_D#@2sui?p
zf&+brh8Y2Pfv>t|IwnAR2DPU;J!!bM9IVv@mL~V@|3Acb+x-P;Kx|+Ao-(?1B(JC_
zs8A2W#`k7$rP&&120A(f(5ev7;%V!zew%XuyFFkop00Ta4O$hgBa-Ift5=L-;^KL&
zHBLJiFvyY_mYSOS|BAcva4OR_ep(S@tI1M0mLf$NN_I&?(#TSFGF@YdP$9~x!@=ZW
zG|?DgG&L&O%0aSZpBTjmW0xiSnmV$6zsJnq-#_0U-+Q@S$Lnz3_j&K-ci+!_-#-et
zKX>8oQFcB9-hy*OZ<2<a(qdTVXfJ!lbw#T>T10s>wC3Lt&Nss)f`zk67UZom?c7?f
zk!jA4cuAkZwrv&)!OHQ;$-J-LvAp`LqX_-S#v{6*;VN00J#l%sq3o9t)PuA!3&mZ!
zIy=FrwYy|$baV@%o##C<m5`H1yv8R^ydNL8Q<&`QlPck(KvKcLk!E=b>91$!aV_1W
zequADkwny+Zz3egwee&HSX(E|YeV+Cv|fn0U=;<L%j!)v^9x0|d3p2vjIl<3N4#pz
zA{D291yk@jWOnaft503R4}FXH^=0;eAM^a$GR5eu97ci*;!3T?xNPl}c^6WE2`r0l
zJm^Ztu6&n$i7NcD6}H8J2WLNitWs3dSzS{8iwttwDr*{g_pT6$lVp<vP&`+!2e?~a
zQ8DvcHif!t*CvVJ`P4fj06nkcv5oXKoyuwDxK|*S85$NQb?_jonyqMG7>c4v%I}HC
zhUyc;-|DRHL>ZZDYo^$C1)ET?>)0sSlB;lz{O5jf@%mo}@L^eTm~A4rxONJe+qGlO
zUXU{uH_?kvj{ogVx0OYsBBG<K`>G=Awez6lCMG5sbzpGNP5t&~&*D9M_WTn&K5wfo
zvUGKoGl&wsawg?!f0SxNhOKIy3{txs<l17Zl3-%7i$KaLXO>r&hI9&i2e*Lj)v2p;
zX9KugeP#!YmgbsHolet(BDz1`ieiXGf3V^KtKWAl4Mymk@p%ObIF0%AAlR!LA5&CN
zVAyyrSJ)dGazc<&8(p84OlolP@Kj32Xwv<=uW|s~WxpHY7kJG}3~FrEowzvU^SgZ#
zh$iAgh1Gl?w6%Dsh?3R|inotX>;v7?a@+9Yrt!mP3xyuaAd5pw37^n@hdb(DOG&k%
zpiO_^)va5%4uIYUkFgvfABb^;H3JSri)mP$e}S@N>b`wEnVFfx?X10@C%YnpmlslT
z1AX5>4N+5rCdcax(9GNiPlorUOBF#=#o<JHC=I1F8muC|5GQj}vd`CTKdh#fdMZV`
zdA5V)A%wzI9>g-C495EqKJ7;{4w4MLn_OFW_eSn7(M>$$**iYY1Z(8UYf~*jKf?Hg
zL%1wN@-so`6AtgV^r_VmAu)%Yy?rBseGti&)cWRkhuld>;G)rJbKrfZQzPn7v0s4%
z!zt}A4}_cCS;S&PprNEpFh8CHcU*%z%m2@lX-$%c4sC~gk+sUo+7GrI266?K)?T3C
zqTG<6E#<uFIH^A%7x06aK<tJfu=TAqRh5TwxpoyE#JDuXz}ojT{CQzIH&U+6zYiDI
z@Y@$SH+&NeFa40W0GuMMiTGHn9hXox?CtAYJ~z^o+U&0M-5>lWzo>9c6|+GBn;d18
zVYBYW{3?ttRb9QX{h=$2Urn}i1!)AtfHq;C&HL;M_*Yg|4tmw$DPi7Wj}tBgoSNw~
zr?n}EuP>;C@rbO)Dqu3FZdR)cT(>Le5R%xo4i4gBd=k;I(#QKo(o(8HM;C(UR`&We
z*Z$(U(@`m0oSd(q|I_Gp=mjN9%>%Hps)(X5PEG~;!(c<&<fOj%X}W@scph{u@z}7?
z+nILC1&peOCMK1@;$Deou;m`V&zgSMF<1n?>6o*#WVE=}Eti^T(nZ(jiwKc0daNuj
zDxI&rqkd5pj)Naw))}^f3$}UGvj>IaLWt`^dBxN@Z8EHw7yr&aLZQx0bev&MbiOdB
zP;*@y_2l;KdHl_r{GQ;w6n?+SPHRsw&;kgE2aV^r&xDHy8bTbm!iCFM-@bi&Bm8n_
z;QV?F2Q-${)-Gv3ObG?oRYcZtrm$o|K>_FE$B)mABdI|*e)!~&*U5#?6Zo(3`yCZw
zM>B}om84R2<#1V;h6hQMq42}F_RFWx7Dm!Gsj8|<Dk+)4eI`(Jf#lF!^L@(o-S{kL
zqzx>!^MjWI*WJjbtp+P?7Zj8#!W`YcF~~GGpZ2^{MhBIXegHC%3Xak%Ht`XE!~#I0
z3+}_jL=;*OB(=1PtJy#+w@^P{G+VnDk|Wp;&d5T~qo9foSO?`qPFYr#1IqeTP+6Gg
z?~>~p22A0by}eFKpp1*=5D)mZ+6T832^NYTAA6)Az$dx(7G$M<n1R4K4>zP<d1IYn
z<$~NwpNFihEK^KldqP6O{8(1$B$`gr&ybBu;$P4~7*04CVl-zX=2x)%k@$PSrY&u4
zZGE&2n|UY{bQgZib3xoLjiPuXBO{jA(TcFIVv~~W$9yqZ1sgm>i54gFeLnmtLQ+UX
zOkj)ScCgLO&DT+&h?d%Ejjjy{D@AJntiIR}NiIz!?|gN+)YQ#w4^%i^!Pfj~=2(4g
ztsWv{*2KCSki8ZqTk7G%!jqGemghkANAd2k`k?w{ejdeg-4!5P>>V6ru)Bk@Y8P=)
zm=hRYT1tys^@>hONVwXOBcx~-fpn<8fx&&~J~%Bln<lAS_CKRjfBy6WqdY&8L6fl?
zcBuKvC^{5HfNoQwtgMV+Ccx(qN80kI<eH+y=f^3SI~a-agFy~G#hGV}$x>6AicN5t
zmfdhb1iS(hTJ_Ulwo4}pt}o1$F}Q`M8;?tnEFMgs9>^bZ+?sxOulq1KSoZeq+oBx?
z|9T#^0%Sm#5<23xc^AsimOwtLDpF{}0j)X?UDk;_jE*68a_CCuh{-Vv3ky~b)Tp<w
zk3KLk;9l3dEqyP{LP23+O8}RRo}OM(jnS!7HNag@Dlz_XU2k5!q}KvqR5s{mNmC_^
zOu&1F5W4xQ*cIjFKPDzdBEv{{37c2aCrs|f#PB&>n>jY~{w0zC=`B@!6rvl4YN=B9
zjY&|o^G=zQE;{Yv&Vs6y9uiXJ_ZQl0!a(}mlI0kK*-Jhz>JwF^b#zMKj1^v0vpJbE
z(p{{9w59n&2Fv(i`L9Pp;5g#t*~ekXTgS%ZaSqCu17~7aa?P5VqTz3<nQkr=SX^T4
zf#}Tl+H@JmG@E@q%{0kt@dch{PDLjnYytv$|96f{0MgV|=LyXiVfFyZYu0wOv9ZZG
zu=w)cy?gRmTAG?9N1CA(fNYwgUBL};t-yDM8AN71OEC4^!puzI7Zo>pjRb8cT5Q4h
zz(JDe2)3NQ%nnja*rEsvoS{O(VCPM~Hfv;8c$o{{W5#pp$P=S*UNO}5WM3XRjlAwF
zxLPO+I;kk)R|f?4+2nG*^q;E!QSxZzTi9*Pip>~qdoBy|W{!}u8_+*#2#2icy@H{M
z=%}cwi>1q9-NivJh$}GMD*!x~jc_d;-C38?q4oqm1I<J*nU%<0MgiG5K>?fF<5s&o
zvWmmdwhU5PF(7-KtpKWL78D%Toc%+Za1AHZR<5q4^Wo&OFAbT3vU)2l#?af88saZN
z2quPSnCY_wWAYo2z%bYhk<If4k$q0oVvi^OF`a7R#(M<VPG<5xvIByR?yPdAh;k?~
zd0&aD@OO4~G01B;l#D#U0}lp_3O9l^J-~McxNAADFMiI*sb|Bw*kaa|SEn2?_!rWa
z+3`J)w5<j);`S5DSl4iG<lec!CaZV$?9W7MouP~L$jB3MgOtuZdo?e&j|!ah>>##R
zDrkM^KmGI*YzntCc*x7?o47|iKfHuwlsEo%oH5z;k{f+7dWMD(=w=#~uj^|6u!!gU
zv_;&Ge`9KP_P3l|Tmp#3_UDnlCZTvmdwC?d47~mPwu>IRAa{B6oe?Q2*|KFz<=gJ|
z4;qS!roc?;y%Q4(P`E8-W@hEU0aZR117}~$G8~Eno7V)(P?9r0mlvq`NeH0TItsdq
zET?kFw0}a7TLA7=(6UYyj7JDak9O9!3ljV@K7N5@2X23AZDo11HUR&SwrI@|0Obwc
z_^y9D=yTimjZdwWK_T<IaZzq=ZtWO$J(gzc_Mh`H@V|&?lbE4MY0O&hB@wfX8mJih
zMG}D1od6YF8}DyAZEl|9)uj&5<_w%9_???Xci@=9V{@w1?SllV%h(d(p{;zBuzTtE
z6&~I&RJR+FBPub6sO3A}B965kr-(=Er`GmaNm_-3(>NZj|8KdM|I?ewS2uhrQ}pr6
RonE5gFgj+cpQ-0W{|`({N@f56

literal 0
HcmV?d00001

diff --git a/docs/performance.rst b/docs/performance.rst
index 657008c..af15aee 100644
--- a/docs/performance.rst
+++ b/docs/performance.rst
@@ -169,6 +169,106 @@ You can also import and call the pieces directly::
     df_local = profiling.run_profiling_local()   # local-grid method
     profiling.plot_local_results(df_local, 'local.png')
 
+Benchmark results
+=================
+
+Accuracy
+--------
+
+``px_Oi_local`` is validated against ``px_Oi_fixedgrid`` run on a fine
+grid (the ``astropath/tests/tests_local.py`` module).  Both evaluate the
+same integral :math:`p(x|O_i)=\int L(w-x)\,p(w|O_i)\,dw`; the fine fixed
+grid is taken as truth.  Across the size regimes the local method
+reproduces it to a fraction of a percent (run at ``step_size=0.02``):
+
+.. csv-table:: px_Oi_local vs fine fixed grid (step_size = 0.02)
+   :header: "Case", "localization", "galaxy", "rel. diff"
+   :widths: 30, 18, 10, 12
+
+   "large galaxy / small loc", "a=b=1″", "10″", "+7.0e-5"
+   "large galaxy / large loc", "a=b=10″", "10″", "-3.3e-3"
+   "small galaxy / small loc", "a=b=1″", "1″", "-3.3e-3"
+   "small galaxy / large loc", "a=b=10″", "1″", "-3.3e-3"
+   "small galaxy / ellipse", "a=10″, b=0.2″", "0.5″", "-3.3e-3"
+
+When the localization minor axis is smaller than the galaxy
+(:math:`b<\phi`) the ``_Lwx_correction`` removes the O(step) bias, so the
+result stays accurate even at coarse (galaxy-relative) step sizes where
+the uncorrected sum would be off by ~1-2 %:
+
+.. csv-table:: L_wx correction (b < phi), corrected rel. diff vs raw
+   :header: "Case", "step", "raw (no corr.)", "corrected"
+   :widths: 26, 8, 16, 12
+
+   "gal 10″ / loc a=b=1″", "0.05", "-0.85 %", "-1.7e-4"
+   "gal 10″ / loc a=b=1″", "0.10", "-1.85 %", "-1.9e-3"
+   "ellipse a=10″, b=0.2″", "0.05", "-0.84 %", "-7.1e-6"
+   "ellipse a=10″, b=0.2″", "0.10", "-1.66 %", "+3.4e-5"
+
+Even for a very small (sub-arcsec) localization, where the galaxy grid
+badly under-resolves the localization, the correction recovers the fine
+fixed-grid value (``step_size=0.05``):
+
+.. csv-table:: Very small localization (a=b=0.1")
+   :header: "galaxy", "rel. diff"
+   :widths: 12, 12
+
+   "0.3″", "+6.9e-5"
+   "0.6″", "+2.5e-5"
+   "1.0″", "+4.8e-5"
+
+Profiling
+---------
+
+Timings below were produced by ``python -m astropath.profiling`` (50
+candidate galaxies; absolute times are machine-dependent, the trends and
+ratios are the point).
+
+**Fixed-grid posterior** (``px_Oi_fixedgrid``): the numba path overtakes
+numpy beyond small grids, reaching ~5-6x on the largest grids; the
+one-off JIT cost makes it slower than numpy only on the smallest grid.
+
+.. csv-table:: px_Oi_fixedgrid timing (50 candidates)
+   :header: "step", "grid", "calc_LWx", "numpy", "numba", "numba speed-up"
+   :widths: 8, 12, 10, 12, 10, 14
+
+   "0.50", "360²", "9 ms", "30 ms", "145 ms", "0.2x"
+   "0.25", "720²", "42 ms", "173 ms", "91 ms", "1.9x"
+   "0.10", "1800²", "344 ms", "2.06 s", "670 ms", "3.1x"
+   "0.05", "3600²", "1.67 s", "16.4 s", "2.96 s", "5.6x"
+   "0.025", "7200²", "6.49 s", "68.5 s", "12.4 s", "5.5x"
+
+.. figure:: figures/profiling_timing.png
+   :width: 90 %
+   :align: center
+
+   Fixed-grid timing vs grid side length (sqrt of pixels).  The dashed
+   line marks 10 s.
+
+**Local-grid posterior** (``px_Oi_local``): the cost depends on the
+localization.  With no correction (circular, :math:`b\ge\phi`) or a tiny
+localization (a=b=0.1", small correction grid) the per-candidate cost is
+modest; a long thin ellipse (a=12.5", b=0.2") drives the correction grid
+to ~1000² and dominates the run time -- i.e. the correction cost scales
+with the localization major axis.
+
+.. csv-table:: px_Oi_local timing (50 candidates), milliseconds
+   :header: "step", "galaxy grid", "ellipse corr grid", "circular", "ellipse", "small loc"
+   :widths: 7, 12, 16, 10, 10, 10
+
+   "0.50", "24²", "97²", "0.9", "6.8", "2.3"
+   "0.25", "48²", "197²", "1.8", "22", "3.3"
+   "0.10", "120²", "497²", "7.9", "146", "11"
+   "0.05", "240²", "997²", "31", "1553", "41"
+   "0.025", "480²", "1997²", "155", "9037", "185"
+
+.. figure:: figures/profiling_local_timing.png
+   :width: 90 %
+   :align: center
+
+   Local-grid timing vs per-candidate galaxy-grid side length, for the
+   three localization scenarios.  The dashed line marks 10 s.
+
 API Reference
 =============
 
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
index 58db86f..2327f6d 100644
--- a/prompts/speed_up_local.md
+++ b/prompts/speed_up_local.md
@@ -123,7 +123,7 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 2. Please add the results on accuracy and profiling to the docs/performance.rst file.  And:
 
 - Include the 2 profiling figures (re-generate them first)
-- Tables summarizing the accuracy and profiling results
+- Include tables summarizing the accuracy and profiling results
 
 ## Prompts
 
@@ -845,3 +845,39 @@ the method.)  Full suite: `tests_local.py` 14 passed; with
 small-loc correction grids are tiny (small a), the ellipse tops out at
 ~2000 (step 0.025), and the NaN guard removed the only pathological
 divide.
+
+### 2026-06-11 (Docs: accuracy + profiling results in performance.rst)
+
+**Done** (Docs item 2).  Added the accuracy and profiling results to
+`docs/performance.rst`, with both figures and summary tables.
+
+**Figures.**  Re-generated both via `python -m astropath.profiling`
+(fixed-grid sweep up to 7200²; local sweep with the three scenarios).
+Since `*.png` is globally gitignored, I added a `.gitignore` negation
+`!docs/figures/*.png` and copied both PNGs into a new `docs/figures/`
+so they are tracked and available to the (readthedocs) build:
+`docs/figures/profiling_timing.png` and
+`docs/figures/profiling_local_timing.png`, embedded with `.. figure::`.
+
+**New "Benchmark results" section** in performance.rst (before the API
+Reference), using `csv-table` directives:
+- *Accuracy*: three tables -- (1) px_Oi_local vs the fine fixed grid
+  across the five size regimes (rel. diff +7e-5 ... -3.3e-3 at
+  step 0.02); (2) the `b<phi` L_wx correction at coarse steps, showing
+  raw -0.8%/-1.7% reduced to ~1e-4/1e-3; (3) the very-small-localization
+  cases (a=b=0.1", rel. diff ~few e-5).
+- *Profiling*: the fixed-grid timing table (calc_LWx / numpy / numba /
+  speed-up, 360² -> 7200², numba ~5-6x on large grids) + its figure;
+  and the local-grid timing table (circular / ellipse / small-loc with
+  the ellipse correction grid growing 97² -> 1997²) + its figure.  Noted
+  that absolute times are machine-dependent.
+
+**Build verification:** installed Sphinx earlier; rebuilt with
+`python -m sphinx -b html . _build/html`.  First pass surfaced CSV parse
+errors from `\"`-escaped arcsec marks in the accuracy tables; fixed by
+using the unicode arcsec symbol (″), which renders cleanly (as the ²
+already did in the profiling tables).  Final build: no error or warning
+references `performance.rst`; both figures are copied into
+`_build/html/_images/`; all five tables render.  (The 14 remaining
+warnings are the pre-existing unrelated ones: missing `nb/*` notebooks,
+`_static`, `language=None`, the `run.py` docstring, `chime.rst`.)

From 3ff78eb2c4a547ce5785cd0d9cc223916cfde0e3 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 11 Jun 2026 13:16:23 -0700
Subject: [PATCH 25/31] mo

---
 .github/workflows/ci_tests.yml | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/.github/workflows/ci_tests.yml b/.github/workflows/ci_tests.yml
index 6a3fb24..25d7624 100644
--- a/.github/workflows/ci_tests.yml
+++ b/.github/workflows/ci_tests.yml
@@ -18,8 +18,8 @@ jobs:
     strategy:
       matrix:
         os: [ubuntu-latest]
-        python: ['3.12', '3.13']
-        deps: [current, numpy210, astropydev, numpydev, astropydev-numpydev]
+        python: ['3.12', '3.13', '3.14']
+        deps: [current, numpy224, astropydev, numpydev, astropydev-numpydev]
 
     steps:
     - name: Check out repository
@@ -34,10 +34,10 @@ jobs:
         python -m pip install git+https://github.com/FRBs/frb.git#egg=frb
         python -m pip install git+https://github.com/FRBs/ne2001.git#egg=ne2001
         python -m pip install git+https://github.com/linetools/linetools#egg=linetools
-    - name: Test with numpy = 2.1.0
-      if: "contains(matrix.deps, 'numpy210')"
+    - name: Test with numpy = 2.2.4
+      if: "contains(matrix.deps, 'numpy224')"
       run: |
-        python -m pip install numpy==2.1.0
+        python -m pip install numpy==2.2.4
     - name: Test with dev version of numpy
       if: "contains(matrix.deps, 'numpydev')"
       run: |
@@ -70,7 +70,7 @@ jobs:
     - name: Python codestyle check
       uses: actions/setup-python@v5
       with:
-        python-version: '3.12'
+        python-version: '3.13'
     - name: Install base dependencies
       run: |
         python -m pip install --upgrade pip

From 5e572d1efa0027343c8000859fe5f188cafcc481 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Thu, 11 Jun 2026 13:47:05 -0700
Subject: [PATCH 26/31] test fix

---
 astropath/tests/test_run.py |  9 +++-
 prompts/speed_up_local.md   | 92 +++++++++++++++++++++++++++++++++++++
 2 files changed, 100 insertions(+), 1 deletion(-)

diff --git a/astropath/tests/test_run.py b/astropath/tests/test_run.py
index 4de8351..7cc2215 100644
--- a/astropath/tests/test_run.py
+++ b/astropath/tests/test_run.py
@@ -43,7 +43,11 @@ def test_run_on_dict_eellipse():
         PU=0.,
         scale=1.,
         theta_PDF='exp',
-        theta_max=6.
+        theta_max=6.,
+        # Use the local method: with this tiny a=b=0.1" localization the
+        # fixed grid would be ~15700x15700 (~20 GB peak) and OOM-kill the
+        # CI runner.  The local method gives the same posterior to ~2e-7.
+        pmode='local',
     )
 
     # Run PATH
@@ -87,6 +91,9 @@ def test_run_on_dict_with_PU():
         lparam={'a': 0.1, 'b': 0.1, 'theta': 0.},
         PU=0.1,  # Non-zero unseen prior
         scale=1.,
+        # Local method (see test_run_on_dict_eellipse): avoids the huge
+        # fixed grid that OOM-kills CI for this tiny localization.
+        pmode='local',
     )
 
     # Run PATH
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
index 2327f6d..2a0ab3c 100644
--- a/prompts/speed_up_local.md
+++ b/prompts/speed_up_local.md
@@ -36,6 +36,11 @@ As we will be making a number of significant changes to the code, we will need t
   * A small galaxy (0.5") with an ellipse localization (a=10", b=0.2")
 - Log your work in the "Logs" section below.
 
+2. The test_run.py tests are failing in CI on GitHub Actions.  But they are working fine locally.  Can you investigate?  Log your work and findings in the Logs section below.
+
+3. Proceed with the change to the test_run.py tests that you proposed (pmode="local").  Log your work and findings in the Logs section below.
+ 
+
 ## Development
 
 We wish to speed up the calculations in bayesian.py:px_Oi_local.  
@@ -125,6 +130,7 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 - Include the 2 profiling figures (re-generate them first)
 - Include tables summarizing the accuracy and profiling results
 
+
 ## Prompts
 
 1. Read this doc.  Proceed with the 1st item under Testing.
@@ -138,6 +144,8 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 9. Read this doc.  Proceed with the 2nd item under Profiling
 10. Read this doc.  Proceed with the 3rd item under Profiling
 11. Read this doc.  Proceed with the 2nd item under Docs
+12. Read this doc.  Proceed with the 2nd item under Testing.
+13. Read this doc.  Proceed with the 3rd item under Testing.
 
 ## Logging
 
@@ -881,3 +889,87 @@ references `performance.rst`; both figures are copied into
 `_build/html/_images/`; all five tables render.  (The 14 remaining
 warnings are the pre-existing unrelated ones: missing `nb/*` notebooks,
 `_static`, `language=None`, the `run.py` docstring, `chime.rst`.)
+
+### 2026-06-11 (Investigated test_run.py CI failures: OOM from huge fixed grid)
+
+**Done** (Testing item 2).  Investigated why `test_run.py` fails in CI
+(GitHub Actions) but passes locally.
+
+**Symptom.**  Locally all 7 `test_run.py` tests pass (in ~2 min).  In CI
+they fail.  (Separately, the old `run.py:231` `embed()` that hung pytest
+is now commented out, so that earlier local failure is gone.)
+
+**Root cause: out-of-memory in CI.**  Two tests --
+`test_run_on_dict_eellipse` and `test_run_on_dict_with_PU` -- use a very
+small localization, `a=b=0.1"`, with the `pmode='fixed'` default and the
+frb180924 example catalog.  `run_on_dict` then sets, for `eellipse`:
+`step_size = min_ang/20` (since `b=0.1" < min ang_size=0.459"`) =
+`0.0229"`, with `ssize=3'` so `max_box=180"`.  The fixed grid is
+
+    ngrid = 2*max_box/step_size = 2*180/0.0229 = 15691
+
+i.e. **15691 x 15691 ~ 2.46e8 pixels (~2 GB per float64 array)**.
+`px_Oi_fixedgrid` -> `calc_LWx` allocates ~10+ full-grid temporaries on
+that grid (meshgrid, ra/dec, the eellipse trig intermediates, then
+per-candidate theta/p_wOi/grid_p), so the transient peak is well over
+**~10-20 GB**.  That fits on the local 64 GB box (hence it passes,
+slowly), but exceeds the GitHub-hosted runner's RAM (16 GB, formerly
+7 GB) -> the process is OOM-killed -> the tests fail only in CI.  Both
+failing tests use `a=b=0.1"`; the cheap `test_run.py` tests
+(`test_set_anly_sizes`, `test_build_idict`, `test_empty_catalog`,
+`test_missing_*`) do not allocate big grids and are unaffected.
+
+**Why the existing memory guard misses it.**  `run.py:218` raises only
+when `ssize*60/step_size > 10000`; here that value is `180/0.0229 =
+7845`, just under the threshold.  Two problems: (a) it compares
+`ssize*60/step_size`, which is HALF the true `ngrid`
+(`ngrid = 2*max_box/step_size`), so it under-reports the grid by 2x;
+(b) the threshold/message are miscalibrated -- it warns of ">100Gb RAM"
+at 10000, but 10000^2 is only ~0.8 GB/array (~few GB peak), while the
+real OOM here happens at ngrid=15691 (guard value 7845).
+
+**Validated fix options** (not applied -- investigation only):
+1. **Best / aligned with this work:** run these two tests with
+   `pmode='local'`.  I verified `run_on_dict(..., pmode='local')` on the
+   same inputs gives `P_Ox.max() = 0.98895114` -- identical to the
+   hardcoded fixed value `0.9889513366` to **2e-7** (rtol=1e-3 passes) --
+   in **0.04 s with 35 MB** peak (vs ~2 min and ~10-20 GB for fixed).
+   The tiny-localization regime is exactly what the new local method +
+   `_Lwx_correction` handle well.
+2. Or keep `fixed` but pass an explicit coarser `step_size` / smaller
+   `ssize`/`max_box` so the grid stays small (e.g. cap ngrid ~ few
+   thousand).
+3. Or tighten the `run.py` memory guard: compare the true
+   `ngrid = 2*max_box/step_size` against a CI-realistic cap (~5000-7000
+   px/side) and fix the message.  (This alone would convert the OOM into
+   a raised ValueError -- still needs the test to change to pass.)
+
+**Secondary finding (separate from the failure).**  CI runs
+`pytest --pyargs astropath`, whose default discovery only collects
+`test_*.py`.  The new accuracy module is named `tests_local.py`
+(per the prompt), so it is **not collected in CI**.  If those accuracy
+tests should run in CI, rename to `test_local.py` (or add a discovery
+glob).
+
+### 2026-06-11 (Applied pmode='local' fix to test_run.py)
+
+**Done** (Testing item 3).  Applied the fix proposed in the previous
+investigation: the two `run_on_dict` tests that used the tiny
+`a=b=0.1"` localization now pass `pmode='local'` to `build_idict`
+(`test_run_on_dict_eellipse` and `test_run_on_dict_with_PU`), with a
+short comment explaining why (the fixed grid would be ~15700x15700,
+~20 GB peak, OOM-killing the CI runner).
+
+**No assertion changes needed.**  The hardcoded expected value in
+`test_run_on_dict_eellipse`
+(`P_Ox.max() == 0.9889513366416152`, rtol=1e-3) still passes: the local
+method agrees with the fixed value to ~2e-7, far inside the tolerance.
+
+**Result.**  `pytest astropath/tests/test_run.py` -> **7 passed in
+0.95 s** (was ~118 s, and OOM in CI).  The peak memory for these tests
+drops from ~10-20 GB to ~tens of MB, so they will run comfortably on the
+GitHub Actions runners.
+
+I left the `run.py` memory guard and the `tests_local.py` naming
+(secondary findings from the investigation) unchanged, as they were not
+part of this task.

From 5b0de123bc568d78b917d8c975a537eb859b4cf7 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Fri, 12 Jun 2026 06:51:51 -0700
Subject: [PATCH 27/31] step_size

---
 astropath/run.py | 28 +++++++++++++---------------
 1 file changed, 13 insertions(+), 15 deletions(-)

diff --git a/astropath/run.py b/astropath/run.py
index 7899d40..ec736f3 100644
--- a/astropath/run.py
+++ b/astropath/run.py
@@ -184,31 +184,29 @@ def run_on_dict(idict: dict,
     p_O = Path.calc_priors()
 
     # Calculate step size based on localization and galaxy sizes
+    step_size = None
     if idict['ltype'] == 'eellipse':
-        # OLD
-        #a = eellipse['a']
-        #b = eellipse['b']
-        #step_size_max = 2 * 3 * np.nanmin([a, b]) / np.nanmax(cut_catalog['ang_size'])
-        #step_size = np.nanmin([0.1, step_size_max])
-        # New
-        min_ang = np.nanmin(cut_catalog['ang_size'].data)
-        if eellipse['b'] > min_ang:
-            correction = 'p_wO'
-            step_size = eellipse['b'] / 20.
-        else:
-            correction = 'L_wx'
-            step_size = min_ang / 20.
+        if idict['pmode'] == 'fixed':
+            min_ang = np.nanmin(cut_catalog['ang_size'].data)
+            if eellipse['b'] > min_ang:
+                correction = 'p_wO'
+                step_size = eellipse['b'] / 20.
+            else:
+                correction = 'L_wx'
+                step_size = min_ang / 20.
+        elif idict['pmode'] == 'local':
+            step_size = 0.05
+            correction = None
     else:
         # For healpix, use default step size
         raise ValueError("Healpix localization is not supported yet.")
-        step_size = 0.1
 
     # Add to dict
     idict['step_size'] = step_size
 
     # Calculate posteriors
     if idict['pmode'] == 'local':
-        print(f'Calculating posteriors with local') 
+        print(f'Calculating posteriors with local and step_size: {step_size}') 
         P_Ox, P_Ux = Path.calc_posteriors('local',
                                        box_hwidth=box_hwidth,
                                        survey_radius=idict['ssize']*60,

From 1a96cd95c7b814dde01d1fbe50728c1c57a81870 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Fri, 12 Jun 2026 06:55:21 -0700
Subject: [PATCH 28/31] mo

---
 astropath/run.py | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/astropath/run.py b/astropath/run.py
index ec736f3..a6eb571 100644
--- a/astropath/run.py
+++ b/astropath/run.py
@@ -195,7 +195,8 @@ def run_on_dict(idict: dict,
                 correction = 'L_wx'
                 step_size = min_ang / 20.
         elif idict['pmode'] == 'local':
-            step_size = 0.05
+            assert 'step_size' in idict, "step_size is required for local mode"
+            assert 'step_size_mode' in idict, "step_size_mode is required for local mode"
             correction = None
     else:
         # For healpix, use default step size
@@ -210,7 +211,8 @@ def run_on_dict(idict: dict,
         P_Ox, P_Ux = Path.calc_posteriors('local',
                                        box_hwidth=box_hwidth,
                                        survey_radius=idict['ssize']*60,
-                                       step_size=step_size)
+                                       step_size=step_size,
+                                       step_size_mode=step_size_mode)
     elif idict['pmode'] == 'fixed':
         # Memory check
         if idict['ssize']*60 / step_size > 10000:
@@ -309,7 +311,9 @@ def build_idict(ra: float, dec: float,
                 theta_PDF: str = 'exp',
                 theta_max: float = 6.0,
                 use_numba: bool = False,
-                pmode: str = 'fixed',
+                pmode: str = 'local',
+                step_size_mode: str = 'relative',
+                step_size: float = 0.05,
                 survey: str = None,
                 ssize: float = None,
                 max_box: float = None):
@@ -373,6 +377,8 @@ def build_idict(ra: float, dec: float,
         'lparam': lparam,
         'use_numba': use_numba,
         'pmode': pmode,
+        'step_size_mode': step_size_mode,
+        'step_size': step_size,
         'priors': priors,
         'max_box': max_box, # arcsec
     }

From abc876a679f03c5cbce083ed3f27f7f594aa2215 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Fri, 12 Jun 2026 07:06:22 -0700
Subject: [PATCH 29/31] mo bugs

---
 astropath/path.py |  9 ++++++++-
 astropath/run.py  | 16 +++++++---------
 2 files changed, 15 insertions(+), 10 deletions(-)

diff --git a/astropath/path.py b/astropath/path.py
index 3ce3b45..d209ad0 100644
--- a/astropath/path.py
+++ b/astropath/path.py
@@ -163,9 +163,11 @@ def calc_priors(self, ifilter:str='r'):
         # Return them too
         return self.prior_Oi
 
-    def calc_posteriors(self, method:str, step_size:float=0.1, 
+    def calc_posteriors(self, method:str, 
+                        step_size:float=0.05, 
                         box_hwidth=None,
                         survey_radius:float=None, 
+                        step_size_mode:str=None,
                         use_numba:bool=False, 
                         debug:bool=False, 
                         correction:str=None):
@@ -185,6 +187,9 @@ def calc_posteriors(self, method:str, step_size:float=0.1,
             correction (str, optional): Correction to apply to the posteriors
                 'p_wO' -- Correct p(w|O)
                 'L_wx' -- Correct L(w-x)
+            step_size_mode (str, optional): Mode for step size
+                'relative' -- Step size is relative to the galaxy size
+                'absolute' -- Step size is absolute in arcsec [not recommended]
 
         Raises:
             IOError: [description]
@@ -203,6 +208,7 @@ def calc_posteriors(self, method:str, step_size:float=0.1,
         if 'P_O' not in self.candidates.keys():
             raise ValueError("You need to calculate the candidate priors first!!")
 
+        #embed(header='path.py:211')
         # P(x|O)
         logging.info("Calculating p(x|O)")
         if method == 'fixed':
@@ -223,6 +229,7 @@ def calc_posteriors(self, method:str, step_size:float=0.1,
                         self.candidates['ang_size'].values, 
                         self.theta_prior, 
                         step_size=step_size,
+                        step_size_mode=step_size_mode,
                         debug=debug)
         self.candidates['p_xO'] = self.p_xOi
 
diff --git a/astropath/run.py b/astropath/run.py
index a6eb571..3588b34 100644
--- a/astropath/run.py
+++ b/astropath/run.py
@@ -184,7 +184,6 @@ def run_on_dict(idict: dict,
     p_O = Path.calc_priors()
 
     # Calculate step size based on localization and galaxy sizes
-    step_size = None
     if idict['ltype'] == 'eellipse':
         if idict['pmode'] == 'fixed':
             min_ang = np.nanmin(cut_catalog['ang_size'].data)
@@ -194,6 +193,7 @@ def run_on_dict(idict: dict,
             else:
                 correction = 'L_wx'
                 step_size = min_ang / 20.
+            idict['step_size'] = step_size
         elif idict['pmode'] == 'local':
             assert 'step_size' in idict, "step_size is required for local mode"
             assert 'step_size_mode' in idict, "step_size_mode is required for local mode"
@@ -202,17 +202,15 @@ def run_on_dict(idict: dict,
         # For healpix, use default step size
         raise ValueError("Healpix localization is not supported yet.")
 
-    # Add to dict
-    idict['step_size'] = step_size
 
     # Calculate posteriors
     if idict['pmode'] == 'local':
-        print(f'Calculating posteriors with local and step_size: {step_size}') 
-        P_Ox, P_Ux = Path.calc_posteriors('local',
-                                       box_hwidth=box_hwidth,
-                                       survey_radius=idict['ssize']*60,
-                                       step_size=step_size,
-                                       step_size_mode=step_size_mode)
+        print(f'Calculating posteriors with local and step_size: {idict["step_size"]}') 
+        P_Ox, P_Ux = Path.calc_posteriors(
+            'local',
+            survey_radius=idict['ssize']*60,
+            step_size=idict['step_size'],
+            step_size_mode=idict['step_size_mode'])
     elif idict['pmode'] == 'fixed':
         # Memory check
         if idict['ssize']*60 / step_size > 10000:

From a7a7690219609061f67e725e591a72d654302ed1 Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Sat, 13 Jun 2026 14:35:06 -0700
Subject: [PATCH 30/31] norm bug

---
 astropath/bayesian.py | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/astropath/bayesian.py b/astropath/bayesian.py
index d27f356..e2d959b 100644
--- a/astropath/bayesian.py
+++ b/astropath/bayesian.py
@@ -77,9 +77,10 @@ def _resolve_offset_prior(phi, theta_prior):
         pdf_code = _PDF_EXP
         # exp decay length is phi*scale; cutoff stays at max*phi above
         kparam = phi * theta_prior['scale']
-        # Wolfram; updated by JXP on 14-Feb-2023
-        norm = 2 * np.pi * kparam**2 * (1 - (1+theta_prior['max'])*np.exp(
-            -theta_prior['max']))
+        # Need to also adjust to max/scale for correct normalization
+        max_eff = theta_prior['max'] / theta_prior['scale']
+        norm = 2 * np.pi * kparam**2 * (1 - (1+max_eff)*np.exp(
+            -max_eff))
     else:
         raise IOError("Bad theta PDF")
     return pdf_code, theta_max, kparam, norm

From 6b87fb1158e3b14e62db5d96e38edb4d2c00043c Mon Sep 17 00:00:00 2001
From: "J. Xavier Prochaska" <xavier@ucolick.org>
Date: Mon, 15 Jun 2026 10:30:25 -0700
Subject: [PATCH 31/31] test fix

---
 astropath/path.py            |  2 +-
 astropath/tests/test_path.py |  5 +++-
 prompts/speed_up_local.md    | 55 ++++++++++++++++++++++++++++++++++++
 3 files changed, 60 insertions(+), 2 deletions(-)

diff --git a/astropath/path.py b/astropath/path.py
index d209ad0..53d57c5 100644
--- a/astropath/path.py
+++ b/astropath/path.py
@@ -167,7 +167,7 @@ def calc_posteriors(self, method:str,
                         step_size:float=0.05, 
                         box_hwidth=None,
                         survey_radius:float=None, 
-                        step_size_mode:str=None,
+                        step_size_mode:str='relative',
                         use_numba:bool=False, 
                         debug:bool=False, 
                         correction:str=None):
diff --git a/astropath/tests/test_path.py b/astropath/tests/test_path.py
index fb4cb87..ee84d80 100644
--- a/astropath/tests/test_path.py
+++ b/astropath/tests/test_path.py
@@ -91,5 +91,8 @@ def test_gw():
     P_Ox, P_Ux = Path.calc_posteriors('local', box_hwidth=30.)
 
     # Calculate p(x|O)
-    assert np.isclose(np.max(Path.p_xOi), 0.0002810125426532622)
+    # Reference value at the current default step_size=0.05 (the old
+    # 0.0002810125426532622 was tied to the prior default step_size=0.1;
+    # the finer 0.05 grid is more accurate and converges toward ~2.853e-4).
+    assert np.isclose(np.max(Path.p_xOi), 0.0002833731343742291)
     assert np.isclose(P_Ox.max(), 0.9999929552509278)
\ No newline at end of file
diff --git a/prompts/speed_up_local.md b/prompts/speed_up_local.md
index 2a0ab3c..3978052 100644
--- a/prompts/speed_up_local.md
+++ b/prompts/speed_up_local.md
@@ -40,6 +40,11 @@ As we will be making a number of significant changes to the code, we will need t
 
 3. Proceed with the change to the test_run.py tests that you proposed (pmode="local").  Log your work and findings in the Logs section below.
  
+4. One of the tests in test_path.py is failing.  Please:
+   - Examine the code
+   - Find a fix
+   - Implement it
+   - Log your work in the "Logs" section below.
 
 ## Development
 
@@ -131,6 +136,7 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 - Include tables summarizing the accuracy and profiling results
 
 
+
 ## Prompts
 
 1. Read this doc.  Proceed with the 1st item under Testing.
@@ -146,6 +152,7 @@ Consider the above and Log a plan in the "Logs" section below.  Do not generate
 11. Read this doc.  Proceed with the 2nd item under Docs
 12. Read this doc.  Proceed with the 2nd item under Testing.
 13. Read this doc.  Proceed with the 3rd item under Testing.
+14. Read this doc.  Proceed with the 4th item under Testing.
 
 ## Logging
 
@@ -973,3 +980,51 @@ GitHub Actions runners.
 I left the `run.py` memory guard and the `tests_local.py` naming
 (secondary findings from the investigation) unchanged, as they were not
 part of this task.
+
+### 2026-06-15 (Fixed the failing test_path.py::test_gw)
+
+**Done** (Testing item 4).  `test_path.py::test_gw` was the failing
+test.  It exercises the `local` method on the GW170817 **healpix**
+localization (the generic, non-eellipse `calc_LWx` path).  Two distinct
+problems were nested here; I fixed both.
+
+**Bug 1 -- `step_size_mode=None` crashed every `local` posterior call.**
+`px_Oi_local` (bayesian.py) defaults `step_size_mode='relative'` and
+validates it (`else: raise ValueError`).  But `PATH.calc_posteriors`
+(path.py:170) defaulted `step_size_mode:str=None` and passed it straight
+through, OVERRIDING the function's own default.  So any
+`calc_posteriors('local', ...)` call that did not explicitly set the
+mode reached `px_Oi_local` with `None` and raised
+`ValueError: Invalid step_size_mode: None`.  This was the first error
+surfaced by the test.
+- **Fix:** changed the `calc_posteriors` default to
+  `step_size_mode:str='relative'`, so it matches `px_Oi_local`'s default
+  and the documented behavior in its own docstring ('relative' /
+  'absolute').
+
+**Bug 2 -- stale hardcoded reference value (the second failure once Bug 1
+was fixed).**  With the call working, the test then failed its
+`np.isclose(np.max(Path.p_xOi), 0.0002810125426532622)` assertion,
+getting `0.0002833731343742291` (~+0.8%).  I confirmed this is NOT a
+regression but the expected effect of the **default `step_size` having
+been reduced from 0.1 to 0.05** earlier in this work (Development item
+3).  Convergence run (healpix GW case, varying step):
+
+| step  | max(p_xOi)              |
+|-------|-------------------------|
+| 0.10  | 0.0002810125426532621   |  <- old default == old hardcoded value
+| 0.05  | 0.0002833731343742291   |  <- new default
+| 0.02  | 0.0002848216784445618   |
+| 0.01  | 0.0002852986787862072   |
+
+At step 0.1 the method reproduces the old hardcoded value EXACTLY, proving
+that value was simply baked in at the old default step.  The 0.05 value is
+finer/more accurate and converges toward ~2.853e-4.
+- **Fix:** updated the expected value to the current-default (0.05) result
+  `0.0002833731343742291`, with a comment explaining the provenance.  The
+  `P_Ox.max()` assertion (`0.9999929552509278`) was left untouched -- it
+  is stable across step (max(P_Ox) varies only at the 1e-8 level) and
+  still passes at `np.isclose`'s default rtol.
+
+**Verification:** `pytest astropath/tests/test_path.py` -> 2 passed.
+Wider run (`test_path`, `test_bayesian`, `tests_local`) -> 19 passed.