{ "cells": [ { "cell_type": "markdown", "id": "af88b502", "metadata": {}, "source": [ "## gwModelRemP_flow : probabilistic recoil for precessing BBH mergers\n", "\n", "The recoil of a precessing binary depends strongly on all four spin-orientation\n", "angles, and no deterministic fit was found that matches NR at an accuracy\n", "comparable to the mass, spin and luminosity models. `gwModelRemP_flow` instead\n", "learns the *distribution* of recoil velocities, marginalizing over the\n", "orientation information not retained in a five-dimensional context\n", "\n", "$$\\mathbf{c} = \\left(M_f^{\\rm model},\\ |\\chi_f|^{\\rm model},\\ \\eta,\\ S_\\perp,\\ \\Delta_\\perp\\right)$$\n", "\n", "evaluated with `gwModelRemP` at the spins at $r = 8M$. The model is a\n", "Rational-Quadratic Neural Spline Flow over $\\log_{10}(1/v_{\\rm kick})$, with\n", "eight spline transforms of 64 hidden features each.\n", "\n", "Requires `torch` and `nflows` (`pip install gwModels[kicks]`).\n", "\n", "---\n", "\n", "**Reference:** Islam, Wadekar & Khanna (2026), [arXiv:2608.00934](https://arxiv.org/abs/2608.00934)" ] }, { "cell_type": "code", "execution_count": 1, "id": "e223ca22", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lal.MSUN_SI != Msun\n" ] } ], "source": [ "import sys\n", "!{sys.executable} -m pip install -e ../ --no-deps --quiet\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import time\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", \"Wswiglal-redir-stdio\")\n", "\n", "import gwModels\n", "gwModels.utils.set_rcparams()" ] }, { "cell_type": "markdown", "id": "da0d0be8", "metadata": {}, "source": [ "### 1. Loading the model" ] }, { "cell_type": "code", "execution_count": 2, "id": "73826957", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " test NLL from checkpoint : -1.4309\n", "\n", " The checkpoint ships in gwModels/data/. A custom directory can be\n", " passed as gwModelRemP_flow(datadir).\n" ] } ], "source": [ "flow = gwModels.remnants.gwModelRemP_flow()\n", "\n", "print(f' test NLL from checkpoint : {flow.best_nll:.4f}')\n", "print()\n", "print(' The checkpoint ships in gwModels/data/. A custom directory can be')\n", "print(' passed as gwModelRemP_flow(datadir).')" ] }, { "cell_type": "code", "execution_count": 3, "id": "8052c5ce", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "q = 2.0, a1 = 0.7, a2 = 0.3, theta1 = 60 deg, theta2 = 45 deg\n", "\n", " median v_kick = 1016.4 km/s\n", " 90% CI = [214.9, 1643.5] km/s\n" ] } ], "source": [ "q = 2.0\n", "a1, a2 = 0.7, 0.3\n", "theta1, theta2 = np.pi / 3, np.pi / 4\n", "\n", "median, p5, p95 = flow.predict(q, a1, a2, theta1, theta2, 0.0, 0.0)\n", "\n", "print(f'q = {q}, a1 = {a1}, a2 = {a2}, '\n", " f'theta1 = {np.degrees(theta1):.0f} deg, theta2 = {np.degrees(theta2):.0f} deg')\n", "print()\n", "print(f' median v_kick = {median:8.1f} km/s')\n", "print(f' 90% CI = [{p5:.1f}, {p95:.1f}] km/s')" ] }, { "cell_type": "code", "execution_count": 4, "id": "9ffbed26", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Mf = +0.950970\n", " |chi_f| = +0.767568\n", " eta = +0.222222\n", " S_perp = +0.486826\n", " Delta_perp = +0.333435\n" ] } ], "source": [ "# The context vector the network actually conditions on\n", "ctx = flow.compute_context(q, a1, a2, theta1, theta2)\n", "for lab, val in zip(['Mf', '|chi_f|', 'eta', 'S_perp', 'Delta_perp'], ctx[0]):\n", " print(f' {lab:>11s} = {val:+.6f}')" ] }, { "cell_type": "markdown", "id": "e0bf2eda", "metadata": {}, "source": [ "### 2. Recoil distributions" ] }, { "cell_type": "code", "execution_count": 5, "id": "54ce1475", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samples = flow.sample(q, a1, a2, theta1, theta2, 0.0, 0.0, n_samples=20000)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.hist(samples[0], bins=80, density=True, alpha=0.75, color='C0')\n", "plt.axvline(median, color='k', ls='--', lw=2, label=f'median = {median:.0f} km/s')\n", "plt.axvspan(p5, p95, color='0.85', zorder=0, label=r'90\\% CI')\n", "plt.xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.ylabel('probability density')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "ebf3c49d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Dependence on mass ratio at fixed spin magnitudes and tilts\n", "q_cases = [1.0, 2.0, 4.0, 8.0, 20.0]\n", "\n", "plt.figure(figsize=(8, 5))\n", "for qc in q_cases:\n", " s = flow.sample(qc, 0.8, 0.8, np.pi / 2, np.pi / 2, 0.0, 0.0, n_samples=20000)\n", " plt.hist(s[0], bins=100, density=True, histtype='step', lw=2,\n", " label=rf'$q={qc:.0f}$')\n", "\n", "plt.xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.ylabel('probability density')\n", "plt.title(r'$a_1=a_2=0.8$, spins in the orbital plane')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "ceba4069", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Dependence on spin tilt: aligned spins give small recoils, in-plane\n", "# spins give the superkick configurations\n", "tilts = [0.0, np.pi / 6, np.pi / 3, np.pi / 2]\n", "\n", "plt.figure(figsize=(8, 5))\n", "for t in tilts:\n", " s = flow.sample(1.2, 0.8, 0.8, t, t, 0.0, 0.0, n_samples=20000)\n", " plt.hist(s[0], bins=100, density=True, histtype='step', lw=2,\n", " label=rf'$\\theta = {np.degrees(t):.0f}^\\circ$')\n", "\n", "plt.xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.ylabel('probability density')\n", "plt.title(r'$q=1.2$, $a_1=a_2=0.8$')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8c225d45", "metadata": {}, "source": [ "### 3. Median and credible bands across parameter space" ] }, { "cell_type": "code", "execution_count": 8, "id": "d023e0e8", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q_scan = np.array([1.0, 1.5, 2.0, 3.0, 4.0, 6.0, 8.0, 12.0, 20.0, 40.0, 80.0])\n", "\n", "med, lo, hi = [], [], []\n", "for qc in q_scan:\n", " m, p5_, p95_ = flow.predict(qc, 0.8, 0.8, np.pi / 2, np.pi / 2, 0.0, 0.0,\n", " n_samples=20000)\n", " med.append(m)\n", " lo.append(p5_)\n", " hi.append(p95_)\n", "\n", "med = np.array(med)\n", "lo = np.array(lo)\n", "hi = np.array(hi)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.fill_between(q_scan, lo, hi, alpha=0.25, color='C0', label=r'90\\% CI')\n", "plt.loglog(q_scan, med, 'o-', lw=2, ms=7, color='C0', label='median')\n", "plt.xlabel('$q$')\n", "plt.ylabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.title(r'$a_1=a_2=0.8$, spins in the orbital plane')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3, which='both')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "id": "7bc6ecb1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Median recoil over the (a1, theta1) plane\n", "a_g = np.linspace(0.05, 0.99, 26)\n", "t_g = np.linspace(0.0, np.pi, 26)\n", "A, T = np.meshgrid(a_g, t_g)\n", "\n", "med_grid = flow.predict(2.0, A.ravel(), 0.5, T.ravel(), np.pi / 4, 0.0, 0.0,\n", " n_samples=2000)[0].reshape(A.shape)\n", "\n", "plt.figure(figsize=(8, 5.5))\n", "im = plt.pcolormesh(A, np.degrees(T), med_grid, shading='auto', cmap='inferno')\n", "cb = plt.colorbar(im)\n", "cb.set_label(r'median $v_{\\rm kick}$ [km/s]')\n", "plt.xlabel('$a_1$')\n", "plt.ylabel(r'$\\theta_1$ [deg]')\n", "plt.title(r'$q=2$, $a_2=0.5$, $\\theta_2=45^\\circ$')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1471414d", "metadata": {}, "source": [ "### 4. Comparison with the earlier flow and with HLZ\n", "\n", "`gwModel_kick_prec_flow` (Islam & Wadekar 2025) conditions only on $(q, a_1, a_2)$, marginalizing over all four angles. `gwModelRemP_flow` retains the richer context above, so it resolves the tilt dependence that the earlier model averages over." ] }, { "cell_type": "code", "execution_count": 10, "id": "7b63c4bc", "metadata": {}, "outputs": [ { "data": { "image/png": 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oHlgdJ+rCmmqH6/HXcwhehW/0eOKOpx5V//97PX93HDfmr9br4G+bypfqVQg0q9b5q/decPS74HtIsY/2rTbZiXssvQ8bLdPWVRU9lt5bbrBsrfeO/7H05doZjO1qtdddOYgyVjPqc631eGHc50fnQ21y74mw10TvJ3+bq1W1qH21KlrqSXwMgF6UYA29e0PU+tBE2a/eNu6EBgN4t42b81802KLaCsI6Ke36cAMAEOSCuWoLUaq0YPv27d7/KwX8fgpsg4GQPwDzBxPBQbT+EgX9zzxx4oTFySU2UUpq23U8PcewQKva8dvxOjQq7PzVey/4KRbyP29XsqT3Sr2EU/Q66MtNpqJB2GGPo3Ikdz7crZIo9zz0uC7WqlXK7Vervc200wl7fP/jRW2jttNz1GdWcam+V1vCXpNOzJyUeGGpXkidDD+9QP4/bHqB1GPvz7ai7FdvG50QvdGCfxD1e1cv5uhn/7HUJiUF9d5AAADESQGEvoKBrQIK/f9S55f+X1ULXP33uXFsLvjSvu7quKufdv/v3P8/7eP/WYGKArhWuf+nUaejVC+qAlxRbBDcr9HjiXtOOm69pKHW6+Bvmwbvqha+HWqdvyjvBbedP3FQu/1TqOvYbvpzCev1VxCrBLPWzIgKmlU377i266qFEil9+eOuKFcY6rW3mXbWevzg4333u9+t+Xh+en+4z5TbPuw1URv9Ma/uCyZ4LonI7BUANV4nXx9SnRg9IQ1Y8r8J9KR1Sc3/5KPsF2UbvQl0QvXGcxma3hTBdQDcwBD3x8RlcvT+Z9P6Z9bb0OjQlPt7Z/ba/nfvT6RNANJvcOSyvfWjlcGgcS8EpmPXokBD/wd1ddr12qrsww0C1P36X+lWuHe9k/p/5ta30X3qFdbv9X9MA1sVmOh4+n/mL3XR/ztdbXBXuvWzG/yox9BxxJWd6HjuWPpe7VEwXO1KhaNjqi0agKuA3ZWruGm33ZV4dzwlJmqjG+TqnpPrjKt3vFq0jZvtT8dXbKDjBx/bv32118HfttmzZ9sf/MEf1HxcBeg6hgI+BfB67aO+pmHnL+y9EKR99bjutdEx9Ly0j46p46ltv/ALv+Ddp/efttF9+l5t1/tP+6icxV0Z0XnQ/q5USm12syeqDMY9XrVBwGpP2GO5wb56LdyA32rtfdvb3uYdR6+Te9+6c1arnatWrar5+P7H032atUkDr3/xF39x0nNV+/zHdAmhHsu9r1wHdNhr4u7XNmpTcNIZHb+RxWyDChoI0PTeaHoJ5nbLyhLVSek/2G+Dl6ZOz9U3q88G1sb1z729OMf5xvlNFwX9WqSrE26ee6N9/dH+Kfe7zix/0KRAL+kylChc8Oqn3ulayUEnH19JgusIbNdnOOnXIIwCzVba4K6CuPelglUlQGl7X8bdzlKH/0YHS7WUvPnHfDQahyZ+BQBIUrFQ9Hr9dTWgVE73QiUAkrM4psW/al0BqPdYuoLtr/ludq2cJKh3c3h4uGsfPy1tqEZJiRtQ3AzV0/unOa1Xi5+UrLQzjD/415WAWlPLRkECgK6m4F89/mFXBABAPvfgO2I/ZqM9iCpv0D99NwhYAUGwXBWN02uqxEplQ2nrte4ElaKoLKXZBEDvQV2dUoLqxhSk8X2ZlXbW48rBghPTNIoEAACAjEi6XCSPghOIdKNWg8msBNJZaWctbgKbVlFYCgAAAHQRrgAAANCMT64wu/pK/e3e/Xtmb3rXxM8vnjT7k/u8qv/FpTErFHsmb39Tn9nmL8ffXqSmhEMzy6gURQNS41xMVLXhqmtXeYsGiPqnnVTZiH7nXyBNpT9uvaQ89I4jOq4AAADQjJGXzEZerP91bXTyfmOvevcXRl60nld+6N1O2v7lwdhr3AuFwvigYdVBL1iwIPIKvgoStX29uc7dLDcaoxBcG0CPqTbodzqWpjdslvZ1x9KXHjPqc3FTbWo//8qrYe1uBzdFqIL/uEuP3DSimipSz8tNP+mmnXQz4PhXLtbvNJ2s2xbdgQQAAIB6Dn/Y7M8eqNw6c242m3NL/a9pMycfq2e6d395zi02Nvs13q23XaE9/5LdPOhaC0DcXOJRe54VOGq6ynqzDrmVcdXzHNzWzdev3mbNhKO52P0LHTVCvdfusXQ8Ba9RZ0TRa6Ev7evmU6/V7rgpyPbPPNPsaxDG9eaLrgJoTvrgOgBKEPT6o7uRAAAAUM/fP2V28o8qt86Dx80+9Hz9L3/5j9xyu3d/+bf/wc782l95t952N90cKYB0vd76Um+6gkgFwPreLWzketpdL6+CXQW42lZBoaOfXe93cNVc91j+3vLgPm4RqlaEHc89trtfz6daL7V6td2iS2HUfj2Gmz5RM/402jb/61Pv9Q6jRMglK9o2znUHxCV1btEqt4iUP+nQ9/7Fv3RFRSVJcQwsRXYwBgAAgAxQoKmAUz3oCh5V7nH69GkviFQpie5zddwK9tXLqyDPBaVuOwXTrvRE37tVcvW9AmwFggoQdSz1KOtxb7311vE2uOky3UqqCh6j1I9rXzfnvIJ2Bae1jqcvPQcFzLpfz1XlM8FAVb9zvflh9Hs9hl4zt9pvFGGvT63XO4y2dyvE6itsdWI3RqCWWq+3Xl/1/muMgZw9ezZ0W4L+7kUCAABAGjzwDbNy2awwsSiYnwL44MJFwR5kBY8KUhVYuvUCnPXr13vBsoJHBbBu8ScXhKqURr9XUKiectfjrcdQCZC4nnZXK6/Hizp/vI6jIFyP63rg6x1PAbues65aaH//1QYlE7pPv9u7d6/FrdbrE+X1rnY8JT5ufyUNOidBra7voDbrS6+pWzciS4vGoTNIAAAASIMZcyJt5gLNagNIFYy6co5gcOl63f38JSvqNXaCvcbudwrGXc18s/xtqHc8l/BUK5XRPnGX0ASFvT5RXu9qx3LJhAJyHa/ZxbeqUdmP3hO6siArV670rkooEdAquP7nEefjIpsYAwAAQIaoLEdfwbIXBZcKANVbr2CwWnmJ/z4Fga4sRbSvetxFwaxLMBSs6nhuH//PulLQzMw5CuwVPOux4zheO9R6fWq93mHjAPxXCZQ0hF21cKVetb6qUTLkf+0U9Os8uhmB/Fci6iUryD+uAAAAEJWm6fz4T9be5rVvMbvvycn3PfFesx/87aS7qq4D8LYPmr39gaqHdb3GKn3R9wr4VJbipnbU/SqpUdmHf+YXlZNoBiA3E4+CTzcv/MDAwPjAWwWKbn54Bb8KNBWwah/9zs0mpB5mPYarU1cpi+h47lhuak2V5yhIdoNlXQmS9tetjhV2PBfo6nduQLKe34MPPjj+WK63ux4F6Dq+mwZUzy9Ku8Nen1qvt37WPhs2bJjUBp0nPSc9F9eGapotAVL79Dz1pfeJzpVrr46nwb4uSXHvGXSvQrmsgkO0y8WLF23evHl24cIFmzt3bscet1Qq2eDgoPX19VmxyIWeoP6D/TZ4adD6ZvXZwNqBKT9nAec43zi/KfM3nzI7/B+ibfu6lWYbAnPm71tl9i8TZRih3vmI2R3bqv5KwaPKOvzBm4LQVspx8sYF8H7qoY97vv16FITfc889fIZzrJSRv9FhcShXAAAAqMf1yn/t0/W3ndVb/T7N9e+j3rdSacyKxR7vakC9cQCa1cVfysHAzqnUw61ZkpLW7rEJQKtIAAAAiJoEhJTn1BUsCVICUCrZmes9iIUIPYgq53CzusQxWwza1/uvqzTqIQbSigQAAICM6HQpCxpHfT2yIL1FSwAAAABixxUAAADqWP/MehsaHYr9uKWxkhV7JvfF9c7stf3v3h/7YwGAQwIAAEAdCv41UxjQKg3e1pSkGtStcqFq6zU0S9ORaqpTNwjZrTrspn3V+gu6ddODakpSrSkhjCfpLpQAAQAQUbFQ9KYLjuurd0bv+Pc6djto4HChUBifNUjTiS5YsCB0waogBYnaXkFklCk4NUg5uJiXHlNt0O90LM1J3yzt646lLz1m1Ofi1gHQfu751Gp3O2zcuNELthX8xzmmw62zoOBegb+mh9XzFT2e7nPjEzRQ2b1m+p3Wk9B5RvfgCgAAABGpPCeutUKC84i79UjipqBQwa4WA1MQqO+1aFTUnmcXTNabdlTHc0FncLVaBZn+3mYF3GpD2GJYtSjAVeCsx1JPt4JZJTlRFgVzK+lqoS/XS16r3XHTa6BeeMcF6HHQ+fWfU73Gep2U1PinJdVrrvubee2RH1wBAAAgI9yKuAru9KXedAWRCoD1vVtx1/W0u15eBdta+VbbKvh19LPr/Q4Gv+6x/L3lwX3cKrmtCDuee2x3v55PtV5q9WprRd5a1H49hm71WvX39zfcNv/rU+/1DuNWQRZtG/d6AcFzocfQc/AnHfpe97lkQVdUVJLkyoXQHUgAAADIAFfioV50BfP6+fTp0+M9ugrsFWAqqNTvFdD5e4R1v+sRdvS9ttUxFSy6AFsBoo6l+9U7fu7cufE2KHh2++j4Ch6jtl/BtMp3tJ/aXet4enz33NQ2Pddqvfx6TZTg1KLf63noVseIunpy2OsT5fUO0v76UrKi4+gY1bZ357nWVzVa8difgLjzdvbs2dA2qc26okL9f/ehBAgAgAxQoOnvyXX3BYNHBZcKLN2CYc769eu94FHBnoJPBfkKsF0Qqjpw/d6VCblAU4+h4FJcT7tLIvR4UUtJdBxXauN64OsdT/X6es6uZMffw61kQvfpd3v37rW41Xp9orze1Y6nqxVufyUNOidBzS7w5vZz7XHvFw02ZtVoBJEAAACQIS7QrDaAVMGfK+cIBpcKPoPBur/H2PXyS7DX2P1OAaWrmW+Wvw31jucSnmqlMm4MQDuFvT5RXu9qx3LJhAJyHS/uOnz/ImRuwLMe49ixY5OeB/X/oAQIAIAMUTmKvoJlLwoulRSot14DY6uVl/jvUxDoylJE+ypgFAWzLsFQsKrjuX38P+tKQTMz5yiwV/Csx47jeO1Q6/Wp9XqHjQPwXyVQ0hB21aLZEiDxX4VQqZMSE71P/G1SYlAvWUH+cQUAAIAG1gPQbD3tWAis3kJjrtdYpS/6Xr3fKktxvb66XyU1GmSqQNr1jqssRDPEuHp1BZ9uXviBgYHxgbcKFN388Ap+FWgqoNQ++p1+VhCrwFKP4Wr1VcoiOp47lptaU+U5CpLdYFlXgqT9datjhR3PBbr6nRuQrOf34IMPjj9WlJl/RAG6ju/vFY/S7rDXp9brrZ+1z4YNGya1QedJz0nPxbWhmmZLgNxr5tYCUPv97wEN9nVJiv9KAbpToVwul5NuRJ5dvHjR5s2bZxcuXLC5c+d27HGD08thMjfdnube1pR+wZ+zgHOcb5zfdGnXFJ3VhP0dUnC3cuXKScGbgtBWynHyxgXwfuqhj3O+/agJxz333MNnOMdKGfkbHRaHcgUAAIAI8/+3g/8KQL3H0mBOfykHAzunUg/38PBw0s1o+9gEoFUkAAAA1LH/3fsT70FU+YnKS1yddyulImhv77+u0uj8AmlFAgAAQEZ0upQFjaO+HlmQ3qIlAAAAALEjAQAAAAC6CAkAAAAA0EVIAAAAAIAuQgIAAAAAdBESAAAAAKCLkAAAAAAAXSQV6wBoZUMtZuJf3GTTpk2x7Bdlm6NHj9qzzz7rfX/q1ClvWy24Elc7AQAAgLRIPAFQUL18+XI7ffr0+NLZW7dutV27dlUNwhvZL8o2Cvy1nLr/sRTgKxHwL7jSbDsBAACANCmUy+Vykg3QsubB5cwVkC9YsMBqNS3KflG30RUABfz+Y+/Zs2fS4zfbzosXL9q8efPswoULNnfuXOuURpeY7zb9B/tt8NKg9c3qs4G1A1N+zgLOcb5xfvOPc5xvnN98K2Xk/IbFoYm3+MCBA+MlNY7rYVdg3sp+UbZZvXq1rVq1qm3tBAAAANIk0QRAPej6WrJkyZTfKbh2dfnN7Bf12GvWrJlU6uOC/WBPfzPtBAAAANIm0TEAqqsPs3DhQjt79mzT+zV67EOHDtmxY8e8YP7gwYOTrgo0206/3t5eKxQKk+4bHR21dl6aUmmSblFb8DXKymvGOc43zm/+cY7zjfObb6UUnt+ZM2dOuS+sTD3xQcC1qNe9XfsFt9GVAH0pEdDgXiUB1Xr842ynasfaRW9I1XvpxKe5Ni0ppbHS+K3OQ/DnLOAc5xvnN/84x/nG+c23UsbPb6IJgKuhr+bcuXMt7dfssZUE6EqAf8afZo/lp6Cy04OAdcVh8eLFmXxjtluxpzh+6w3gCfycBZzjfOP85h/nON84v/mWxvNbrbJEg4A1YU2qEgCVz4T1oOu+sMA7yn7NHtsNDNb0npoJSFN8tnIsR2+OTr9B9MZM4nGzJvj6ZOn14hznG+c3/zjH+cb5zbdCBs5vWNsSbbHrXQ/rRVcg3ux+UY+trEjBvp8L+N3UoM22EwAAAEibxFOWdevWTZqD3z/ottb0nFH2q7eN69EP1vq7bVQG1Go7AQAAgDRJPAHQgFsNvPXTtJz+qTkVqKuX3T/dZpT96m2jXv1NmzbZsmXLpmyj+/S7Rh4PAAAASLvEZwFS77tm3FGAvXLlSq9XfdGiRZOCb5XeHD9+fFIJTpT9omyj+f5V63/ixAkvIdA2Cv796wBEPRYAAACQdoknAKKAO9gLHwy+h4eHG94v6jZRg/goxwIAAADSLPESIAAAAACdQwIAAAAAdBESAAAAAKCLkAAAAAAAXYQEAAAAAOgiJAAAAABAFyEBAAAAALoICQAAAADQRUgAAAAAgC5CAgAAAAB0ERIAAAAAoIuQAAAAAABdhAQAAAAA6CIkAAAAAEAXIQEAAAAAuggJAAAAANBFSAAAAACALkICAAAAAHQREgAAAACgi5AAAAAAAF1kWtINADph/TPrbWh0aPxn//cAAADdhAQAXUEB/+ClwaSbAQAAkDgSAHSVYqFovTN7x3/2fw8AANANSADQVRTwD6wdSLoZAAAAiWEQMAAAANBFGkoA9u3b176WAAAAAEhXArB161YbGRlpX2sAAAAApCcBGB4etmXLltnTTz/dvhYBAAAASEcCMH/+fDt+/Ljdeuut9sgjj9hjjz1mFy9ebF/rAAAAACQ3C9C5c+e829tvv937unDhgu3fv99OnTpld911l915553xtg4AAABAemYBmjdvnm3cuNF27NhhJ06csEWLFtmjjz7KVQEAAAAgr+sAaGagnTt3elcBVCJUKpW8qwIvvPCCrV69mqsCAAAAQFavAKxcudK7fe655+z++++3np4e27Rpkzcm4ODBg16JkK4G6KrA9u3brVwuM04AAAAAyOoVAFfmc/78ea/85+GHH7bNmzd7CUA1/f393peSgIceeiiuNgMAAADoVAmQgv1t27bZvffe2+xjAgAAAMhCAqA1ADQNaFTr1q2zgYEBr0wIyIKh0SHrP9jvfd87s9f2v3t/0k0CAABILgFQuU8jdKVA4wZUKgRkQalcssFLg0k3AwAAIB0JwPr166fcd/r0adu9e7f19vZ6Vwj8s/649QKAtFNvv/8qgBIBAAAA6/ZZgDS7T7UxAZr5R4N83aw/QNao1Gdg7YD35U8GAAAAuvoKgAL8WjTjz9GjRxtuhNYM0FoCS5cu9X7WegJRxg1E2S/KNmrzkSNHvNmNtP3atWurPv7y5cu9sqZVq1Z5P+/Zs8e73bJlS8PPGQAAAEh9AlAoFGr+XusDKJjWGgBRKeBWYK1SIgXnsnXrVtu1a1fNwDrKflG2UXufffZZL0kQJQHaR1OeqrTJT9spOXCUJAS3AQAAADKZAJw8edILbjXrjwJoFxxrHYBq9DtpNCBW4K1A2gXool72BQsW1EwAouwXZRu1V4uYOdpWSYIGPOt2yZIl47/TsZQciK4C+H8HAAAAZDoB0ODdz3zmM+O95Or5VnDs7wH30+9Wr17tlQE14sCBA+O97/5jucd15TbN7Bdlm0OHDnmBvn+7FStWjG/jLwVSGRFTmgIAACD3JUAKlFUS88gjj4wnBXHQVQN9VetJV6CukptqCUCU/RTERzn2mjVrxscHRG2zroosXLjQm/UIAAAAyOUYAAXS1aYBbYVq9MMowD579mzT+0U9tr/8x3GLnQWTDw0U1uug+3V8XfHQlYMoiYCmSQ2OoRgdHbV2KZVK3qBt3WKyRl6TNL9+nON84/zmH+c43zi/+VZK4fmdOXNm5Al8GhoEfO+999bdZt++fbZhwwaLgxtX0I79am2joF5fwasHGi/g7lPQr3ECKok6depUU+0cHGzfglN6Q164cME78cViQ7O95lJprDR+W+91b2TbJHGO843zm3+c43zj/OZbKePnt6EEIAoFyVETAP/g3KBz5861tF+zx1ZArx7+agOQgwmBkgBdCag1VsFRIDl37lzr5BtTVxwWL16cyTdm3Io9xfHbvr6+2LZNEuc43zi/+cc5zjfOb76VUnh+q1WWXLx40Zv8JlICsG7dOm9Kz29961uT7tcTrDcVaCNUihPWG6/7woL4KPs1c2zN66/9qs1kpIHCKoHyl/u4x6hVbuR/7Tr9BtG5SuJx066R1yPtrx3nON84v/nHOc43zm++FTJwfsPaVjUB0IBfTf2prMHfa+3q38MGzeoySHDWnVoUhOsrrEdeNfbN7tfosTUbkBIDf/DvTxS0doCetz8BcMdmOlAAAABkRdUEQDXtqmsKlqwoGK43C5AbQBuVrjYEa+hdj3qtspoo+0U9tmYEUjDvL/tR8K/SHs0S5F9TwE+/12tSr/wHAAAASIvQaxbz5s2bct/AwEDdAzZyBcCV1qj33U+98MGeePXYK1BvZL8o2ygh0MrFKufRtu4ruAiYev79x1Kb9Fz37t3b0PMFAAAAMjMIuFpS4LhyoVtvvbWhBijI1lScCrhXrlzpBeRabdjf267eeV1Z8JfzRNkvyjZa2VfBfDBREH+ioF5+9fjrWKJj6ff0/gMAACC3CYAWAlNpkKj3WwG/BsYqeFYpjBbfUsDd6Gw36l2vNZe+Avnh4eGG94uyTbXjhlGwT8APAACALGto2LJ6zxVMP/74416Q/7GPfcwL/g8cOOAtrKX7VU4DAAAAIAcJgKY72rhx4/jPCvbVI+4WCFNPvZsaEwAAAEDGEwD/csIqBXKDc/3iXCcAAAAAQIIJgH8lMQ2IVbAfrIn3JwkAAAAAMpwA/NM//ZONjIyMl/9o4O9P//RPj//+i1/8YugiYQAAAAAylgBs27bN7rjjDq/OX3Pya8Yfeeqpp7xFt1QOdOzYsXa1FQAAAECn1wHQfPynT5/2kgC3LoAG/yo50BcAAACAnCQATnCxr9tvv33SgmAAAAAAclACFMXatWvjPiQAAACAJK8AaLCvpgANOnfunFciBAAAACAHCcDJkydt+fLl3vSfYdN9sg4AAAAAkJMEYOvWrbZz505btmyZN/A3aHh42NavXx9n+wAAAAAklQAo8H/44YdrDg72DwgGAAAAkOFBwD/2Yz9Wd5sDBw600h4AAAAAaUkAVPdfb5pP1gIAAAAAcpIAbNy40fbs2WNPP/10aCJw9OjRuNoGAAAAIMkxALfddps31We1KUABAAAA5CwBOHv2rK1atcqbAWjRokVTfj80NGT79u2Ls30AAAAAkkoAFPjXG+R7+vTpVtsEAAAAIA1jAA4ePFh3G60TAAAAACAHCYDm+ZfvfOc73kBg3Tpf/OIXJ20DAAAAIOMJgHzgAx/wSoHWrl1rhw4dmjRFKFOAAgAAADlKAD72sY/ZCy+8YCdOnLCxsTEv6Hf6+/vtkUcesccee6wd7QQAAADQ6UHAx44ds8OHD4//XCgUJv1+3rx53hcAAACAHFwBWLlyZd1tLly40Ep7AAAAAKQlAdAiYH7+EiDn1KlTrbcKAAAAQPIJgAL+3//9369aAnTx4kVbv369LV++PN4WAgAAAEhmDMCOHTvsx37sx7xbrQisAcFubMDRo0dtxYoVtmHDhvhaBwBIrfXPrLeh0aEp9/fO7LX9796fSJsAADEnAKIZgBTk79692/v5yJEj4wuAPfzww40eDgCQUQr+By8NJt0MAEC7EwDN8qMVgTXY9/jx496aACz+BQDdq1goer3+SghK5VLSzQEAxL0QmD8R0Nz/BP8A0N0U/A+sHfBuAQA5TgDCaCAwAAAAgAyVAD333HNNHUyDgp999tlW2wQAyMCg32oDgAEAGU0Ali1bNmWVXwBAd2PQLwDkOAHQwN7Nmzd7iUCQZvvR7+bPnz9lAbA9e/bYo48+2r7WAgBSM+jXofYfAHKSAFSb0nPfvn3eDEAaABykAcGrV6+2gYGB9rQUAJCqQb8AgBwNAj58+HDoDtWCf0czAulKAAAAAIAczAIUJbhftGhRK+0BAAAAkJYEYHh4uO42Z8+ebaU9AAAAANKyErBq/P/1v/7XdujQIZszZ86U32/bts2WLl3a1PShGlzs9tUA402bNsWyX5Rtjh49akeOHLHz5897269du7bq4zfbTgAAACCTCcC9995rTz75pBf4rlq1yrtduHChFxgriNZ927dvb6gB2nf58uV2+vTp8ZmFtm7dart27bItW7a0tF+UbdRurV2gwF6UBGifEydO2O7du1tuJwAAAJDplYA1C9Djjz9ux44d875XkKzvd+zYYV/4whcaboACb/Wi+6cV1ZUEBdet7hdlG7XfH8BrW/1eU5oq6G+1nQAAAECmEwBRIHzu3DlvTIC+9H21aUOjOHDgwJSyIRdkq3e+lf2ibKNypmAQv2LFiimP32w7AQAAgMwnAP4pQWtNC1qPym30pXUHghRcqzSn2f2iHnvNmjV1xy00204AAAAg02MA4uYvsQnS2IKwGYWi7Bf12CpjCjp+/Lh3qzENrbTTr7e31wqFwqT7RkdHrV1KpZKVy2XvFpM18pqk+fXjHOdb2s9vvXaltd1pkvZzjNZwfvOtlMLzO3PmzCn3qY2pSwDqUa97u/artY3q/fVVrce/2cerZnBw0NpFb8gLFy54J75YbOlCTy6Uxkrjt/Ve90a2TRLnON/SeH7rfTay8tlJizSeY8SH85tvpYyf30QTAP+A2iCNK2hlv2aPrSlA1fMfHBjczLH89M9w7ty51sk3pq44LF68OJNvzLgVe4rjt319fbFtmyTOcb6l8fzW+2xk5bOTFmk8x4gP5zffSik8v9UqSy5evGgLFixIVwKg8pmwHnTdFxZ4R9mvmWNr5h/t55/+s5V2+unN0ek3iN6YSTxu2jXyeqT9teMc51uaz2+9NqWxzWmU5nOM1nF+862QgfMb1rZEW6zAWV9hvehaeKzZ/Ro9tmYDUjDvD/5dwN9sOwEASNzhD5vtfmfSrQCQIomnLOvWrbNTp05Nus8NunWDcJvdL+qxNYuPgnt/2Y+Cf//0ns22EwCAxAx/12z0vNnLjMkAkKIEQHPwq/fdT73wwZ549bL7p9uMsl+UbRTEa/VilfloW/elff2DgKMcCwCARH1yhdlHX1e5lSfvMzvzP5NuFYCUaWgMwL59+2zDhg2xNkBBtqbiVIC9cuVKLyBftGiRt9iYo955Tc3pL8GJsl+UbZYvX+4lGMHgXvzBfZRjAQCQqKuvmF0dMbs6p/LzpXNmIy+azbkl6ZYByGoCoOB3/fr1NmfO9T8sMVm2bJn3FUbBt1YcbnS/KNtUO26zxwIAAAByVQKkYFkB8NNPP92+FgEAAABIRwKgmXBUinPrrbfaI488Yo899pg3vygAAACAHJYAuRr822+/3fvSCmj79+/3Zse566677M4772xXOwEAAAAkPQvQvHnzbOPGjbZjxw47ceKENyj20Ucf5aoAAAAAkFItrwSsmYF27tzpXQVQiZCWRtZVAc2So6k7uSoAAAAAZPQKgKa/lOeee87uv/9+6+np8abB1JgATZGpEiFdDdBVAc2tXy6XGScAAAAAZPUKgCvz0bz5Kv95+OGHbfPmzV4CUE1/f7/3pSTgoYceiqvNAAAgih+/y2x02GzmgqRbAiDLJUAK9rdt22b33ntve1oEAACa8+7fM7s2ajZtZuXnuz+RdIsAZD0B0BoAmgY0qnXr1tnAwACr5QIA0AlvelfSLQCQtwRA5T6N0JUCjRtQqRAAAACAjCUA69evn3Lf6dOnbffu3dbb2+tdIfDP+uPWCwAAAACQwVmANLtPtTEBmvlHg3zdrD8AACABL540+943Krey+51mH//Jyi0ANJMAKMCvRTP+nD17tpFDAgCAuPzJfWa/v7pyKy8Pmo28WLkFgGYSgEKhUPP3Wh/g6NGjjRwSAAAAQBrGAJw8edKr7desP6rzF83/r3UAqtHvRPsAAAAAyFgCoMG7n/nMZ7zv1au/du1amz9/vndbjX63evVqrwwIAAAAQIZnAVq1apW3CvAjjzwynhQAAAAAyPEYgCVLllSdBhQAAABATgcB33vvvXW32bdvXyvtAQAAAJCWBCAKBgEDAAAAGRsDsG7dOm9Kz29961uT7i8Wi3WnAgXyYmh0yPoPTgxq753Za/vfvT/RNgEAALQlAdCAX039efHiRZs7d+6kcQAaELx06dLQhcJ27tzZcqOANCiVSzZ4icVzAGTY6o+YvXrJbPqspFsCIO0JwKlTp+zChQuTgn831We9WYC0bgCQZerpD14JUDIAAKn3wDfUG6eVOys/v7n61N0AulvoNKDz5s2bct/AwEDdA3IFAFkXLPNRGRBXAoAc2v1Os5d9n+3XvsXsvict02bMSboFAPKyDkCtpCBoz549tn379lbaBABA+wP+kRcn/37ej3S8SQCQi1mAtGowAACpo+BfQb/78ptzi9msyeV/uTD0bbPB5yu3AFDrCkBPT0+1uwEAyL5C0eymmyd+vqnPbPOXLRf+5lNmV0YqpUBvf8Dss++pJDtKcD70fNKtA5DmBEClPprtZ+XKlQ0dbGhoiIXAAADp9LYPTg6Oq3nivWaXhipXA7I4HuBrn54I+MOeI4CuVzUB0HSfBw4caOqAmj4UAIDUiRIQ/+BvJwJoAOimMQAHDx5s+oDMAgQAAABkLAG49dZbmz5glKlCAQAAAORkFqDdu3fHfUgAAFqn+v/LFyu3ANDFqo4BWLdunT333HP2rW99a9L9xWLRCm51QQAAsuRTP8OMOAAQlgCcOHHCG8x78eJFmzt37qTBwZodaOnSpVUPVi6XGQMAAAAAZC0BOHXqlF24cGFS8C/z58+3z3zmMzUPePz48XhbCAAAAKD9YwC0FkAzA3y5AgAAAABk7ApAI0lBnDMIAQDSZf0z621odMj73t0ixV77FrN5P1JZyEw2fcmsNGZW7Em6ZQCymgA4Ghuwfft2e/bZZ72f77rrLtu4ceOUkiEgSQQuQOv02Rm8NGhduVpwFgVXL55zc1ItAZCnBODpp5+2NWvWTLrvyJEj9tGPftQOHTpkd9xxR5ztA5rWdYEL0EbFQtF6Z1Z6ld1t164WDADdlACcPHnStmzZ4s31r6lCXUmQBgzrPiUGuirwhje8oaFGvPDCC97YATe7kAYbb9q0KZb9Gjn2nj17vAHQYeMYli9fbtu2bfNmQnLbi14TpFfXBC5AG+mzM7CWhR4BoOsSAAW8miI0OBZAPysIVmC8Y8cOe/zxxyMfUwG6AmtNO6rgXLZu3Wq7du2qGVhH2S/qNi7gP3DgQM3EQ8nN2rVrx3/Wtix8ln4ELgC61vE/NBt83uwbuyvrH/jd1Ge2+ctJtQxAVhIArQNQayDwsmXLIg0U9lPwrUDaBeiiXvYFCxbUTACi7BdlGz0nF8TXm8JUx1JCIUp2tC8AIEdU/18um2nRyyyOA3jivWaXhiqDgDUe4Mu7KoufibsF0PVCpwGtJsoqwL29jZVYqNc9uLCYC9iPHj3a0n7NHjuMjqUkQF8E/wCQMb/6hNn7j1Rua60WvOP1ldss+sHfmv3Lscqt6+VXz7//q9DQv34A3X4FQCv91jM0FH22lfPnz3tf1YJpBeoquXH19o3ut2LFiqaOHaXNulKwcOFC74oHACAjbrnduk61Ep+P/yRXA4Au11ACoJ5vldBoCtBqHnvsMdu8eXPk46n+PowC7LNnzza9X7PHrkWzHSmhUOKg469evdorM4qSCOjKSPAKyujoqLVLqVTyEjbdovJ6pOk4ceAc51saz28jbUlTuxtRuP6l7q5ym59DO85xlPZ38jl2szR+hpHv8ztz5szInfdVE4Dbbrst9OCaJUeDaP119a5nXIFxlNl7otIx27VfM8fWWAF3RUFBv5IdDQrWa9KMwcH2TVGpN6RmZ9KJLxa783Jvaaw0ftvKax3XceLGOc63tJzfRt7/af2sNGJxacy0ZFapNGZn2vwc2nGOo7R/wZzXW3HaLCvNXGTDGT1PWZCWzzDao5Tx81s1AVDvuEpoqpXP9Pf3150p6KGHHor04MEkwu/cuXMt7dfssWsJvh5KAnQlQOMJ6pUT6Z9hJxdK0xtTVxwWL16cyTdmHIo9xfHbvr6+xI8TN85xvqXl/Dby/k/rZ2Xctz5vdu2y2bQbzX78XVU3KVxfMbdY7Gn7c2jHOY7U/g2f9260ZQrPUm6k5TOM7jm/o1UqS7R4rya/iZQAKNA9fPiwtZtKccJ643VfWBAfZb9mjx1G04euX79+UrmPe4xa5UaO3hydfoPojZnE46ZRXK9Bal7L3e+0wsuD1lca8/7RTyouY2q/3EjbZ7iRdqSlzZP8xYcqte8aCPsTv1hzU69MpgPPoV3nuFPtR7Y+w+i+81sMaVvVBGDv3r0NP8Bzzz3nBdVvfOMbI++j7fUV1iOvGvtm92v22GFU9qRZgPwJgDs2MwKh414etMLIi14PHgAAQCOqpgW33974TAkqG9IiYfv27WtoP60oHKyhdz3qtcpqouzX7LGrcWsK+Kn0R0lGM7MJAXEoF4pWdlP7OTfMTrJJAAAg5WK7ZqGxAQqENVNOo6U1hw4dmjLY1r/Crkp21GOvqTsb2S/KNtWmF61GPf/+Y2k7JQXNXC0B4lKatdjKv/0PZh963uw/Xah8PVh7QTsAXe6pDWZ/9CuVWwBdqaFpQF2pz8aNG72e9GrBcq3Ve6tR+czBgwe9YH3lypXecRctWjSpt12lNpp731/OE2W/KNvoOWhaU93q91o8TFTu438uSm7U469jibZVIkHvPwAgNd72wcpqxrVWMf7OVyfGQgDoSg0lAKdPn/Z6whX0avpLBcGuJl7fK+AOWyOgFh2j1lz6Ou7w8HDD+0XZRiU86smXsCsDjp43AT9S4d2/Z6VXL9nFV67YvKTbAuSJVgkee9WsZ7pl0tsfSLoFAPKWADzyyCNenb8bI/DUU095pTluekslCE8//bTdc8897WktgIo3vUtzkNkV5vAG2rda8D9+3uyZ3658z+xaALp1DMCtt946aYCweuZVmuP/fZQpMQG0weEPm/3ZA5VbAK27NlopldHXyyTbALo0AdB8p35KAIJlM5oNCEAC/v4ps5N/VLkF0LppMy1zVP9/+WLlFgDiSAC03LFWFNNUn//tv/03mzdvnleb/6UvfWl8G/9MPQDa5MWTZt/7hk07882kWwJkh6bIvWFO9KlyVWqXtYGyn/oZsx2vr9wCQBxjALZt22YbNmzwpsPULDm/8iu/4s2UoylANRZA5T8MkgU64E/us+LIi7Zg9mvM/tf/mXRrgGxgilwAaPwKgHr8NU2mBgK72n8F/LpPC27p925GHQAAAAA5WAeg2krBa9as8b4AAC34yx1mJz7rfVvQrDO/tD/pFgEAcqipBAAA0AYavKkZZ4B2Wv6+ynvtxsoU3gC6T1MJgAYCa8EvN+D3rrvu8lYHdusBAACaoICsUDQrl5JuST5pitzR82Yz55vd9TvWtX7+kaRbACBrCYAW+gqW+xw5csQ++tGPeoOD77jjjjjbBwD59fGfrPT4a6aZDz1fCcxUAsRVgPbQFLnu9Y6aADQ6cxAA5G0Q8MmTJ71ZfzT3v6b/LJVK3pe+37p1q5cYfPe7321fawEA6PTMQY/+CzMIAejeKwB79uzxZgDSbD9++lmJgWYE2rFjhz3++ONxtxNAPT9+l9nosNnMBRP37X5n5XbzlxNrFgAAyHACoJV/g8G/37Jly2r+HkAb3f2JyT8Pf9fs5cGkWgMgK6VnALpOQwlAoVCou01vb28r7QEQlyfvm/gnD6A7/OoTZmOvmvVMT7olAPKSAJTL5brbDA0NtdIeAFE88A0rlcZs6MyQLQ7b5tK5zrYJyKOszRx0y+R1egCg5UHAmzZtsm3btoX+/rHHHrPNmzc3ckgAzZgxx2zGXCvfcFPSLUHc3vizZkvvNHvD25NuCdzMQSf/qHILAHm+AnDbbbeF7nDq1CnbtWuXzZ8/f9L958+f9wYBK0kAADTp3n3eTblUMhtkDEdqvPxSpXbeT6s1Jz3AXgP9g2N93v17Zm96V1ItApDVBODs2bO2YsUKb9BvUH9/f92Zgh566KH4WggAQNK0OFsa12dQ8B9s17XRpFoDIMsJgAL/w4cPd741AKL5m09Z4fJFm/VqwWz11qRbgzYo/Nf32OIz37JCsSc9vc15nCq3Hr3u1a4GpG21Zq0gfdPNle+nzUy6NQCymADs3bu38y0BEN3XPm2FkRdt9uzXkABk2T17zMaumPXMmPq7V85Yzys/TKJV3TNVbhTVkq7P/bvGE4l2U/DPlJ4AWkkAbr+9/iwCTz/9tB07dsyr/Ve50Pvf//6ojwkAkFt/Lvx3sxfb2KVhK146Y4W09TZ3u2YSCQDI6jSg8txzz9maNWvshRdeGL9v9+7d3krAX/ziF+0tb3lL3G0EgK5T/vU/tzODg/aaP74jnbXnAIDuSAAuXLjgBf/6Wr9+vTdW4Ny5c95VgCeffNLuvPNOO336tM2dO7d9LQYQzeqPmL16yWz6rMrPQ982++x7Kt9TTw50r1qlZwC6QkMJwI4dO+zgwYOTSoTmzZvn3eq+1atX29atW+3xxx+Pv6UAGvPmtZN/Ll2jJzltTv/1RCBWqxwI8U6ZmacE+IbZZjfMqdxGxXsN6HoNJQALFy6sOT5A6wAcPXo0jnYBiFux4Yo/tNvTmypJ2ZxbGMCZ1JSZWU8kHjye7OMDyKSGIoJCoRDLNgAS0HtbJdDkKgBqWP/MehsaHRr/2f89Yk4kACALCYAWCKtH4wEAAPEo/6uHraCxHI2UeLRAAf/gpcGuS3Sc3pm9tv/d+y3XKD0Dul5DCYAG/W7bts22b99e9ff333+/LV26NK62AamiYKH/YH93BQpI3vLfMCsWO/6wxULRe487/u/zoFsSnaooPQO6XkMJwMaNG72BvosWLbLNmzd7YwLk1KlTduDAAS9BYAAw8qpULqUnYHjtW6w890fs1Wk32Q1JtwW5pIB/YO2A5Z1LdJQQ6DOeOYc/bDZ63mzmfLO7fifp1gDIiIZHBR45csSb6UczAvlt2rTJPvOZz8TZNiAVgj2fqQgU7nvSyqWSnR8ctL5m9lfv38hLZnNujr9tQAYTHV3dS02C34i/f2qiN58EAEBETU0LsnPnTu/r5MmTkVcOBrIqWOaT2UAhqDSWdAsQhRI1K5sVe0jYAADJJAAXL14cX+iLwB/IGE1b6CigROoV9vVTrw0ASC4BWLdunT311FNezf8b3/jGeFsCoP2Cc5Yf/0Ozq69UZphZ8W+SahUAAEjzFYCHH36Y4B9I2hPvtcIrQzZ/2k1m73u6+eN8eddE7zIJAPJu9UfMNKXq9Flm/8iYNQDdq+FpQIODf4PWr19v+/czNSLQVj/4WyuMvGjTZ78m6ZagFZT0dNab105830oC4E8kACDvCYDWANDXXXfdZXfccUfVbV544YW42gYAQLoTCQDohjEA586ds127dnk/z58/f3wtACH4BwAAAHKUABw7dsxWrFjhLQhWzZ133mmHDh2Kq20AAMRn6NtmpWtmxaZmwM4PSs+ArtfwGIDDhw/X3Ob06dOttgkAusNf7jC7fNHsxrlmP/9I0q3Jv8++Z2LQ+4/eEk8i0XubJerH7zIbHTabuSDZdgDIbwKwd+/euttogbBGqXRI+y1dunS8tEgrC8exXyPH3rNnjzfFadhzaLadAFDVic9OBKQkAPHb/U6zl32L9r2sRdViTiSS7k2/+xPJPj6A/CcAURb+anRxMAXVy5cv964cKKCWrVu3euMMtmzZ0tJ+UbdxAf+BAwdCA/pm2wkASIiCfwXqAIBJmiqE1GrA27dvt2effdb7WbMCaVyAWyG4EQq+FXS7oFo009CCBQtqBtZR9ouyjcqadu/e7X1//Pjx2NsJAK0o/9qfWsFK1K23olA0u+nm6itidyNKz4CuV2x0h6efftoLehUQHzlyxPvS4mC33nqrfelLX2q4Aep1dyU1jguyjx492tJ+zR47znYCqbZoqdnin6jcIp1UY973k8nXmmeZgn+V6riv4IrYzVJJ0cd/cuJLJUdZKT37+qcrtwC6UkMJwMmTJ23NmjVeb/+JEyesVCp5X+o51/36+s53vhP5eOfPn/e+1AsfpODaXWFoZr9mjx1nO4GmvHhyakBxZaTSY6dbedsHrfyvttorb25x9d7feMbsg/+jcgugMeVSpcTIffnHG3SK/kZkKfkAkAoNXVPWKsDq8e/v7590/7Jly7wymrVr13pXBh5//PFIx6u1boDWFzh79mzT+zV77Djb6dfb22uFQmHSfaOjo9YuSszK5bJ3i8rrkZnjvnrFitfrlstejFGywqd+xlv5tzznFiv/9j+YvfXfeo/9ypkzNotznFmF61/uPKftM9zKY6fib8+GAbPymFmhRw2K3NZ6bS8ESoj02bSQ81hLHOe48PJg5W9DA49d632H+KThM4zuOr8zZ86ccp/a2HICoNKfYPDvt2rVqljLYdTr3q79mj12nMcaHGxfb5HekBcuXPBOfLHYcKVXLpTGSuO3cb7WcR93xne/ZHbtstm0G+3KG+6waRdftl73y5dfsvLHf8IKl85UHrM0ZmeuPybnONvmHf2Q3Xh9Vhr/eXXc+b3x25+z4tgVK0+70S7fdnfb29XK+7tdn7nm6XNx/bMxOlizrQ21/Zf2T36UVwYrVwMKRSs18Lzj+AwvLo1ZT8h7KM590Dj+RudbKePnt+EEIEpPd1T+AbVBWnG4lf2aPXazj1eP/qE0M0i6lTemrjgsXrw4k2/MOBR7iuO3fX19qT1u4Y8/MtG7v3K9Wd+dVj58i3dfoVyynld+OPHYxZ7xx4ztHJ//Zyvsv8/s0vDEfTf1WXlj42N6EF2hdMk7v8Hz6rjzO/+//99WGPmB9/6Y+7Pvb3u7Wnl/t+sz1w7BtrbW9uaeaxyf4UKxJ/Q9FOc+aBz/h/OtlMLzW62yRBP3VIvfG0oAwi4j1Nvmscces4ceeqhq+UxYD7ruCwu8o+zX7LGbfbx69Obo9BtEb8wkHjeN2vUaxHlc77K8O17ILCUqPRjfJo5z/NQGs0tnK+MLAtMl+h8HbTB7UWUe+Srn1amUDRamvj86pNn31dDokK1+arX3fe/MXtv/7sk95mkTfJ6d/JsZ19/pZt4fSbynug3/h/OtkIHzG9a2hhKAzZs32/333x9a469AX+MAgvbv3181AVDgrK+wXvTVqyv/QJrZr9ljN/t4QKzimqUkyoqmbuCiglGVpFzvlUab3bvP0mL9M+u9oF3cbStK5ZINXkpBacnxPzS7+orZDbPNVrQ4YB4AcqShBECBrhbC0oq5wV5v1zuu9QGq3R9m3bp13uq71QbdakxBK/s1e+w42wlkKtHQbCIsnNQ+/+XdZq+cMZu9OFUzLynojyNgV2+//5hKBBL15V0TK/ZGTADU7v6D/Y1dvSDRAJDnBEA94BoEXG06zDCaIUdrB4TRarpKLNxqvKIZhdziXC6JcDMMacahqPtF2abadJ/NthMAajp7qhKQquQqhYqF4ngQ7w/mo/IHywqiU3EVoBNXL5pINAAgMwmAAv/Dhw83/CBaKbjWMQ8ePOgF2CtXrvR61RctWuStuutPPLTWgL8EJ8p+UbZRwK+rFrrV77Xgl2jRL/8Kv1GOBQBZpqB/YO2AdaPUXb1opzf+bGXsz6xFSbcEQBYSgL179zb1IP5e82rUq+969qtR8D08PNzwflG2USmTa1+93vwojwcAyJ48XL3I4vgTABlIAG6//famHqTZ/QB02PL3VcpTbuzclLUAWrD6I2avXjKbPivplgDIawIAIOd+/pGkWwBkl2bR0kB6R9P5tntGrzdPnXkPAOohAQCSpplDbphTuQWC3JoQIWtDIEU0bkCDgYvTzRYtNZsxJ+kWAUBVJABA0h48nnQLkGJakZnFmlIumJzNWmj23ifMFrzBUiml09EC6BwSAKDL3P3Jr9iZkSuhv188Z4Z97sF3WB6fWy1Zft6tLPwV1+JfXa1TC/eFLeZXumZWnGbWe1supqMF0H4kAECXUYD80sXLVX/3tRkP2GuvnjP7+C1mH3resvrcZr3xk1aYNjLpd+Vrc+zSdx5MrG1pEtfCX6mnMhwNaFdPd1599j0TaxBk8DMLIBkkAECXKhbM+ubcOP7z4Ej1pCCLVw0U/BenT+7dLBQLdvPciefrf96lchsasfudZi9fD7I3fclszs1m79wysWJsyhb+anbxr1SjvAUAqiIBAJJ2+MNmo+fNZs43u+t3OvawCv6//mj/+M9v/eiA2ZXGrxokISwhcUlMT7Fg5esBrmhRJyUpA7858Xz9z7stz03Bv3pmvQaMVW6bWCW28MxvmV3W+2OB2d2fiLWJ3bzwV1s9tWFioS3m3AeQQiQAQNL+/qmJS/gdTADiumrQlt7zOv75xo/atZkXptx/48LJZT6uRzvxcpdiT/P7fvvIxPsD2fCdr3LOAKQaCQCQce/59FdtaORq5O1rlfqEzWe+rPQB++/2Y1WvGrTzykBYT/+1vgtTSnw80y/a3B/fbuVi5wc3Btv651cvm+aGGbSF9p5P/oMtnvNPqSqTAsY/5ypNa+LqFIDsIgEAMm7IK89pbuabuvOZXzd92quWhLDSo9lu1sVywfpmL57Uw1/umXplIGpi5JVBNTm+IdjWsRmq3zEbK1uqyqe6CqU40T7nGpcCoKuQAAA5ESzPqUeBbdCZ8jzrqXKcV0enW5qe26XrNf495XleDXtwWkt/CVDw/uC2l26+YrMW3uSVDlUL1HVfI4mBa2tP9IsyaJcMleLUeg/vf/f+9q5bkJJB6QA6hwQAyIlgeU4z3nP1dysB7A2TE4DBVy7H0nve7GxCwefWf/CjNnjJbNFNN3g/1wqQ+g/2154Cs8ds2g02ZYYgfzLQSA/+eFs/fqPZiHkJFZCqqVmTXLcAQCqQAAAt/MN2wWVbeukCpgbPZRsrlezsK/GW55SaKFmJuk+aZhOqN0NQrZmGkhj4jHh72dO6+JmbmlXt03uzI0ZeqsxUpcHqmq4WQO6RAABN0j/ndvTYhQWe7Q6cq5UEybLSN226vWqv2nT73pzlkfapFySHzSYUvJIQacByk+rNEBRW99/swOdWxxigOxZAc1OzqnOhY23dcweLiQFdhgQAaJB/saR29NJF6SWvlKtUrgD0FNWTXQgNxqMKDUI//sBEcPDg87EEyWGzCTVz9SEpjSYrWXpueedfAC3zi59pkTnXew8AEZEAAA3yl/q00kvnevrHp4scuWzv+ejAeCAZNqjX9RiXSiUbHBy0vr4+K3pJQHaD5HrJS6vJTTvUDejf9+dmpWv2H5/4W7v5UgdXIEauFkDzlxpWLTekZAdAE0gAgIS4nv6j037a5hVetgvlm+yly5djHdSbtKi93tWuJPjrtS95yZalosc2crLSe5t385nfmlhPoalSop+6x+zyhcpK0ciG5e8zu3zR7Ma5E/e5dTU0A08Dg3DbVWoIoLuRAABtVGvWG9cb/uGxDeM9/TenvNc7qjh69DtZr123l9Wn0/X65dX/2QopvcKDED//yNT7fOtqRBFMdDs6KBhA7pEAAG0UpZ4/Dz39QZ+74T+YzagSvAd6P6vNfR4MvjsxK0qwl1XfR00I0qDZ6VWRXsH323i54cgPJ63S7SUWP7PZrO8nWc0XQGQkAEAMzr58teoML/Xq+bPe0x/q5cFIPZ5RevmDs6I0O32j6+X37x/sZQ0mAQ3Z/c7K83b0/H/uIbPFP2H25rXWsk+umLxiqy+ZStP0qqkvxUmKBtE3eBWgqvLY1ON8Y3fl+CQAACIiAQBiUCqXG5r1pmtorv2bbp7cS1lnTv56mr0KUK2WOtjLGrwi0dBVh2pJz18/VgnM4kgANFf71ZGam0SdXlWrH2sBNCWuXVeKk6fPVa3VfQGgBhIAIEa1Zu6p23Pc4ODAjmum91JBSoR5xevNye/fpt59Ubepdn9o2UUrwVmDgdlEOc/kaV6fvDrXZtl0W2TnrcdKLU2vOruv7M0aqcQVGRTxcwUAYUgAgBhrqpvq6Y9YLtPtmq3B73jtfoPBWbB3PuxK0s/bx7zbr814wF5bOBfp2GGJZ+3rCGirl1+q1PDfs8fsDT+bdGsAdCkSAKAKaqp9KC1IbKrUxTdNH78C0MzKyGEDf9/8B/+X0fefEJWUKeEfC+9gqKk43WzRj8bbputrVliRkADoFnzagSZqqrtKsCzpL3dMDKwMq7FetLTy+9mLJ+rX3WqldRYuqjZYN2n+aULjmhGo3uDv3jk32L61t01a6M27UtBk3Jh7wUHY4q6saRxG0iUzwUS6p8nB/zctNlv7TCxNqjYLVxZmvQLQOhIAoIawmmpXtuEGU451U1Zw4rOVwEpBlRIAf+D1xp81u3ef2W8EApQ9d0wOxpwFPWY9ld7tNC98FKlNLsCLeMWk3rScbqXnMG7laPd910t7KV218T2lZOf17+RaGwDShQQAaKFsww2m7OpaZn/Qdels/f3828+/ZfzPUCODdTvF/9h1ZwTq8ADusYirLHedrMyQc/qvzV69bDeMXDLruzu2wzbTq9+JtTYApAsJAHI7eNf1zutnN8iy1QWRgmUbl4oFr5a6p1iwm+femM85/evVMvvNWlR922oBmBIInzSWHPjb1NSMQDHT++ux0gdshl21K3aD3Txj8oxTjb7/dOWq2voVmV44LCsz5Dy9yYojL9q82a8xu/3uRHv1e6fNtoElv279/7jbBl9liDjQDUgAkNvBu653XkGOu0+3rQQ8wW36D37UBi9V9h/4zS6Z5z+sN1X3q/wnau+4fzVTRFJ5/8UbmHMVIYU0zkaldv7P1sJpE1fZntoQ/llrpldfY3o+93+a/ejrp5TkAcgnEgDkdvBuj6933o+Ap0VpXqugwwOC0zxgslopiGtrsVCwMd+Vq1wMcte0mppZp9nBtWmigNx/dU3fT78enF+7Yvadr9Y9RHAFbQDwIwFAbgfvzp4zY7x3/g0/Mq/qvP5hK6UyqLIDM4moV7PgGzPwdwfNXr1kNn1WPCvndmpA8MgPJ8ZC3HK72WvfYnb3JyxptUpBFt10Q9UrV8FB7pkqDbr15yw3NIOWBsv7k4DyWEv/sqslrllPcgE0jwQAXSEsaAlbKbWjVn9kIvDNoKZnEtGVBAUZbt8j/3FidqEUJgDBgGnolR9aqVCoBGYuUHvxZCUhaCc9xtirZj3TKwlHHSoFkUYGdyb6eegi6295jQ319Jj9lzfbkK5UuouVml0rOMNWoWfi9qaQsTY1NDK7Vhpn4gIQLxIA5Gql3kZ77usNmuzIoN4UBrvNyPtMIsEe0P4/+CkbdDNA+ac2bfeMM39y30SiFGGwq0tcFNDVW2Mh7P2e6dKgFFPwPzgt8G/Yn0D6y+1csjznNWZrp16diZy41vh89uruORPv37x+lgGQAKDLV+qNq5yBS+ZdXHOsHtkPfdOyoF7Pbr0rZammaTXdGIAslAP5SuCK5XIl+NbnqDCtvYlrjc/n/gtjZhsmkouu+ywDXYQEALH3wneyXji4Uq//sS9Z53DJvHsNFSuBUpqTvzSusRC7pzc1dGUkcb4SuN7Zr/GSZwDoFBIAJN4LH+dKvX79B9v/+I1cXg819G2z0jWz4jSz3tusmwYMh5WiZInGAaQ9+UtbQoKUSvNKygBiRQKA2Hvhu6leuJHL66E++55s9Vy2EPRHem3cCsMqkUjxlKO9N843uzZaWXn2xrnUSyNT8pB8A2geCQBi74XPRL0wYgvq6wUSYbME9c3qC1xJeTF8heEU2n/fVyb9nHS9dB6vrqB9JiWrxWKlA6LdA9gBpEYqEoAXXnjBdu7caUuXLvV+nj9/vm3atCmW/eLaRpYvX27btm2zVatWeT/v2bPHu92yZUuTzxzNjjFgnv7sTf3pZgkKrZP//jsn/0ww0pnpWNFVqo378O77Dd/n8XP/zmx02Ozyhc42DkD3JAAKvhVYnz592gu8ZevWrbZr166agXWU/eLaxnn22Wdt7dqJKRuVJOzevTv21wTpGWOAxoL6KLMEhUpxuU9Wz0ncA30zuUBYF8zu1cgVuUjt/9bhylW4H72++jCA3Ek8AVDPuwJpF3yLetkXLFhQMwGIsl9c2zjaTsmC6CrAkiVLYnkNukWzswaFzfTj9nEogei8ukF9F/IHjUkEjO08J1EXCPM+67M1JWclkc9q0pCV2b24+gMgcwnAgQMHvCDczwXjR48eHS+3aWa/uLZxVCIUpTQJzfXo63f+QMGV+dSa6cePf4I548oQZi4wu/sTljqfXGE28pLZnJvNHjyeuaCxEY0uEKbP+tjMshV7zMZK5cxdyYtldq+UX5ED0N0STQDOnz/vfVXrSVcQrpKbaglAlP1WrFgRyzbBx9f2x48ft4ULF9qyZcssrd7z6a/aDy+MWo8Gd42vL99cD1xcq+6G9ej7g4M4AoV2lkDESsHjnjsqs97kUL1VZyOXIfhX2U2Tq6+YXR0xuzpnyvusrQHjA98wK5fNCp0rzai3QFiwNEg/z7w+hKM4bcTm/vj28d9du3qTXfrOg5b72b0SwBU5AJlIAFR/H0YB9tmzZ5veL65t/I4cOeIlC0oKtO/q1au9qwdREoHe3l4rBP5hj46OWrsoYD/z8qt1tipbqVQ/SDkzctleunilgeOUa97fN2eG/c0jd0xKVoZqlAb1zrkhUjvHt5/Za0fuPTLpvkb2j0vdxxx71Yq+2W706pQbaKeOXy5HO4ftFPb41XrCG2lr4fqX/3Up7FXCVCUQu6nPyhu/1GjTo7el2uO+/NKk9v3JL/7J+K9WP7V6/Lk3e35Cz+/02f6NQvftjHL90qBC2co9E4NJp90wsW+c7az2fqmllfMSm4k/lQ0dt9a2cbTPvZZxH7fbpOVvNLrn/M6cOXPKfWpjKkuAalFve7v2a2YbDfh1VwsU9G/evNkbFHzq1Kmm2jk42L4epdJYaby3fdHs6ZN+d/aVV71/2GOl0qQ2/MYTz9vZS1OTBm0fdiyZf2PPpOPouO42yv371t4Wy2vlnrNu2/naxtWG4ivDtmj2ayb2vXGBnW2g3fqjc+HCBe/DXfSu9KTjec6bNs9KM6b+QdT9jZyXxaUxlZBbqTRmZ67vt/jiD6znlR9O2XbMt007hD2uBdoX53ux0fObxPtfn/2x0tS/CXKlPNcKYwVbOKvy+3NXzlnJ9A/Tqv4daNn/4UsAQ47b7GvUrtfWBQ66rXfcWm2Iu33us+c/flJ/U7Msyb/RaL9Sxs9vogmAf+Bt0Llz51raL65t/IKlQkoCdCWg1lgFR388586da51S7CmOl/l87ZE7J/3u7Tu+6PXoK7D/5T/45vj9tXv5Xc/95GNVUyk7qtz29fXVvT/u56zbdhw//jb0mX3of47/pH+4fQ3+8dFVpcWLF3f8j0+t53nolw7F8hgFFZB7U5T3jD9G4ca5ZtcD8bJKg9QLXy5N2qYdXFvGH9eneFPflMeO471Y8/x+7dNW+Pr/O/kxF/R4M7Z08v3/33+r1uNM/pvoroq4C6Ht+jtQS7PnpV1/W9x51W2949ZqQ9zt87/f4zxut0nybzS68/yOVqksuXjxojexTaoSAJXZhPXG676wAD3KfnFt42hq0PXr108q93H71yolcvTm6OQbpOC7nfq4Bd9l++pB/81zp866o2Qi2nOoHH9w5Iq9fcdEr5x+dr9v92uRhg9jaBuO/2GlfvyG2WYr/k3VTYIzGjnBWWX0x6cT761aMyy1+7G9cgT3GL7Btt67TCsGj7w4eZs4vHjSK9Gynulmt9xu9u7fq6z6O22mFd70rqptDNPK6xN6fq++7D3v9be8xoZ6KsHaUDFd7//6Wvw7sPudk8uylr/P7Ocfibx7s48d62vr+0Md9bj67CmZCptlql3nPhvvqfTp1N9oJKOQgfMb1rbErwDoK6y3XzX2ze4X1zaO1gXQLED+BMDtl7XpQMNm9Ih7er6oUwZ2nS/vmhjcGpIAtGtGo7DEwq9aUJHoDEsaJK1A/3+71+yu3+nMY/7JfRPn6EPPm1UJ+hM1Y47XtqFpPTaY0Xnaw9YUiOrPr/6z9Znvb/fli9YN6wLkcZYpAJ2X+BiAdevWTamhdz3qtcpqouwX1zb+9QL8VPqjBKJe+U/atHvu7SgJBhqb0SiuWWVaDeQTmWFJz1vB+GhzY4Jy6e0PVL4UjF4atGK5bL1jY2aFnvTOehVzB8GY/owUzMasaD2ailXlYSkPvltZq6Rjs0yJkm193i7+D7MSnThAHiWeAKi0xs2m4x9s619hV+U4Gmzrn3Enyn5xbSN63EOHDtmaNWvG26R99u7dG+OrkQ9pX9wnS4tBuWn94p6GMBjIRw0qOjrN4E2BmuOZVUoCfaU53SAsgOwtmQ187/oVi99M30q1fsVCoWqJYT1/+OrDtqg8PP6z+/6szbc+XaVJ6boA/nPWymfY/zek7dOSuittXoJJAgDkUeIJgMpnDh486AXiK1eu9HrfFy1aNKm3XaU2mnvfX6oTZb+4thH18qvHX9uJtlOSkLXef3RG2i/TVwvkg0GFP3BJZFXlzV+uv03aSnPaLA+L3S266QYbiLCw3xRPLTO7dNZs6NtmF75Xe+BFitYFCDtnfbP6xmfY6b0xG1dtAORH4gmA612vNZe+gvTh4eGG94tzG1GwT8CPRi/TT6kbntdj+0cs9fIQbObVlFKs0Ytmr1tpNivHgeS9+8yGv2v25H2Kmr0xBGNls/PFBQ3NnpWWVXqVVLjpP5lhB0BXJgBAXlS7TD/lakDMkwX86l/8qg1dntxD30rZUXAF32DgguTVLcV64r1mP/jbShlVlCspWbHgDWb3f9X79j3XVyFWOdHXLf3aUT7X8mrbALoWCQCQwrrhRij4j7OnPpiwdLTuv9XpOlMmsVljXnzW7OXqC5chP9pWavjJFWYjL5m9dkHsHRYA0oEEAOhw3bDma+9//S3ejC0aZNdoUOivzVf98Lmr58Z76r37mkwywnr3U93rH5yuM4MBWuiaDzf22idWfqK5B85a8K+1MTQ9bi2zFpq994nKVYAu1/bPqtYpuTpiVtbA+2xOMwugNhIAoMNKhYINTrv+0Wui9y6sNt/98/eSjCZ6njs9n3mqTbuhLVd/qs0OVWusxb/92r+1C9cuTDpOJEqIlBilUalkduH7Wl7WTNN3uoCzXntfOWP2xDqz2YvNfuOZ0M3u/uRX7Mz4ooOTXbr5SmXJ7YzjswqgVSQAQIeMB4WvnPXmth8qlK1UaH5+cPX4L7xhoRV7Kj3/br2ALMxClHrr/9jsMz8b+9WfWuel2poPw1eGbehKzuq7Fcj/3v8y+aqNVsXWz/Vosa9ptacQVfAftr7A7L6yl3cgovJYJUwY+WFlMT7J27gSoEuRAABJlwQ1OduOgsU//rk/9mYQcUt9K5Hwa/uCQXnxN58yuzJSWWFXC2ypzEQBaXAtgiZFWcQpuOaDl8yVE1yArZO0InbIqtiNriisn6VYMOubc+OU+9utlcW+Up0IpPWKEoCmkAAACQsGg25+8LBSknbNV941dr/T7OXAa/LyS5UVhxX0KwFQIhDjmIJmFnHyvy9SPRA7pSsKK/j/um+9ASUJnZh9NxfT57rEV+OU/LerP2LW+6bk2gUgNiQAQEKq9eLWq9Vvtjef6QJ9FPynoDcz7Jz43xca5K0Sr6Z7/JXY6OqGkpqcWTxnRku/b/eK35m+auNKfLyVgAfN5rzG7D99M+lWAYgRCQCQgYF8VZOFBlYPzf2YAAW6qlF+4BuV3vsoNGvSTdcHoToxlfy0ck7c+8K/SJQr8WqYEkaVNuXQ5x58R9JNqPm54qoNgDQjAQA67akNZpfOms1aVFndtMlkwQWIuZvas9lAV7365etF81Eo+E9g6tCOnBN/IhM1IUKsYzoAIM1IAIBO+85XJ+aub7PcTxcY7LEvFKrX/M95rdl9T1Z+fu1bzOb9iNmsZJKgjpyT4Cwtugqg5EivT7sTguAYC9WNv3nt+I+troORBs2M6ci8lC+6B6AxJABAuwUDIpWrIB5RpiPUa6+gZfi7ldl9XCLQTT71M51bMC04xuLVS7Gug9HsjDxaA6BQbF85VO7H2aR80T0AjSEBALpk0GlXTufpDH3b7Mn7zO7/apKt6y5ujMX0WRNlM2PXzF6pBP1DPT1eMtCxGXl62rumbe7H2QDIFRIAoFOCg047OOC0a3zt05VkS6+1vvdP8Xk9EEWHBMZYeGUzSsQ++x7v5/5FRRt0Cx20mWbkKV+bY2OlsvUUC5Nq+GutHFyPZhrqvbVLxtkAyBUSAKBTEhp02pXcoGC0fw2FRlaH7b1t4jPgppjsAAXjr3z7UW+9AC0Q9t2XbrS3/l1lhp6wVYOj0L43j2yqmhjsT8EsRQAQhgQAaLfl7zO7fNHsxrlJtyT/al1V4YrLxHSpzq8+0diAzhyUs4UtHCY3z51YObgW//6tJBAAkBQSAHSm56+b/fwjSbege/BebOzKiGZ1aaWcTcdSAqGZlZyUJghRFg6LurZAWNnQ4MhlL8EAgLQjAUDX9PwllihR9oOkhV390OxIUR3+8MQMVhksZ4tz4bCwY731owNVrwiEjzMo21ipZK+ZN9OeefDnLK28GY4W9JjNv8V6yz2WrUlbAVRDAoDmev7cwEpMRqKEvF4ZGT0f7TP/2p+ufA4illy56TMli2sCRKHgv1apUE+zKz13iDfDUY/mUJpmNsYlDiAPSADQGNfzpzpiAt3oM/4AWbx6dcNsswePV76fOX9i8bpawX2DyUYep89UKZCuBvh/Fg1A7ptzY2ZKhiatePzKD9s+bSuAziEBQHM0eNCtCin/+HmzZ367O8cFnP5rs6evzwSS4RIJdBl9Zof+0ezIf6wE9tUS+ht8qwbf9TuVr3YEl6NDXiKQF2EDjRX8f/3RytUOeetHj9pLF5ubgrTjKx7/wU/ZYE/1RdacvF7BAfKIBADRPPANs3LZzPUABWcOuTbavVcExq5073NHdilhd+/b4PvX9fTrCkAngsuD/ZGvAlQLPNMSfEYZaJxZ6tgZPTN+9WfSImsAMocEAPVLAd72wcmrqlYzbaZ1rZ4ZEwGTw5STSLuw92jKr+ClOfBsdqDx4MiVSSVDzcxM1Hau80e3WnF75IdmPQUrqoSpWMzVFRygG5AAoP5A1isj9fd507vCywjy7tafo9wH2ZPiID/q6r7q9c9D+VCttQnSxhu0/cJ/taHr45Z71fjZvalNygBURwKA+gNZZ/jqgLtZ2FoI9+ypJAEAOkbB/8DagfHyIf9sQk61UqE06Z0zw5sGtDILUCETg4O9QdtjoxNXBABkEgkAwnX7QNZgwB92dUNjAAC0LBjEN1LXn8XZhP78gz9rg4OD1tfXZ0XfVKBh6wkkyT9o26MSoPKYty5AutMsANWQAAD+gP9NvzCxcm+tOf39Nf8aAwCgZc0E8VMC0ya3ycJ0okmODZiSiLmpoOfcYv3zWk/gAHQWCQDgKOC/fNFs+LtmC95Qufqh75+8z+zSucwMkgSyJhig++v6g7P+BMt68hxgho0N0H1pSQyyfhUG6FYkAIDf4D9UAv77v1r5WYmA+x5AWwSDeP+0oGme9addwqYL9ScDqSkRevkl6x29yWzWxKxSeRiYDeQdCQDioznDtXCQf+7wwx+uLJSVlR7zF/5y6pSeAFIz60/Wy3qiCOvFv/uTX7EzI1PHHLlBw2ElQ229OlAu2f6r88x+/WhT6zoASAYJAKZ67VvM5v2I2awG/8E+eHzyzyqf+cHfmf3guUq9aCdLaMJm7KF8B8gMf7mPm/Wnm4UF8G7QcK3pRGMvG/KvI9Ho/woAiSMBwFT3PRnPcVRKM/36AmFhg2nbFajXGsALIBMoI4mm1grD9cqGmk4Mqv19fuK9ZpeGzKb7xkwBSCUSALRPcZrZhe9PlNS8/JJ3ubiqdgbrevywx35qg9l3rtf4axsAiatW3pPnkp9W1QrUw8qGmk0MwngJw9W/rfwt/9HXe6sEA0gvEgC0T7CHyE0bp0D7c//O7O5PVLbxz7TjAnXdurKh1R8xe/Paxh77nVvMrr5SGY+w4t9MPHYw0bh0lisFQMrkeWaftI8naGmgMTMiA5lBAoDOU4A/Ojzxs3+mHReoaxsXmL96aWLboW+bffY91Y+7aPrEYpoK+quZPmvyz7MWTR30669tBYAcajQxCJPmVYsBhCMBQHgdpwZ2xTUeIBhYz1xQf5tqQXvpWniP/fxbzKZNq6xQOfKS2Zybpx530dLJ+9y7r4EnAAD51uiAYDcAWYnA4NXLpr+0pbIygoKXSCihSHJtAgDVkQBgqh9cr+OMezrMKIN6622jcQXBdgUTgvKYWWms8ccGADRFVwHGKnH/uLFS2f7++xdSuWgZ0O1IAJAtvbdVVuitNpNQoafys26L178HAHRkBqKeq5XbomnChaLNtsv2SkyDjN1jkTQA8SABQKatf2a9DS2cZrbwlsqc4Ro7MOc1k8t/AABtMSkg//iNZiMTP2oioJvn3pj+1YyBLpSKBOCFF16wnTt32tKllfrs+fPn26ZNm2LZL65tWmlnEr7//RetZ84iyzsF/d264uTMmZU1FkZHR5NuCtqA85t/uTvHbqzV9auxs26cbgOP9rc0yDjKSsetXhmo16Zmj5+784tcnd/EEwAF1cuXL7fTp097AbVs3brVdu3aZVu2bGlpv7i2aaWd6IxioTg+TzjzhQNAAtxYq4P9ZuqY0TTMAc0E0vVWOo66mFmUqU+BblEol73h+onZvHmzF1CrZ905f/68LViwwGo1Lcp+cW3TSjsvXrxo8+bNswsXLtjcuXOtU17/wf/qXQG4ee4M+/qjqxrb2U3FqcG2wXr7lOk/2O9dAeib1WcDaxurJ826GTNmjPc+FIvFpJuDmHF+8y+v59j9XfY6Zm6YbzZ6zqxctt6S2f4LYw2v9N5K4O4vQWp0e3flQfd9PXAlo5vPL7J1fsPi0MSvABw4cGBSUC2uh/3o0aO2atWqpveLa5tW2gkAQDcqlUs2eOWcxgNXpgcq15jGucOLmQXHJlS7YuCf4jRq6ZG/TX0b9nq3b9/xxfHpkRjIjLRINAFQD7q+lixZMuV3Cq6fffbZqoF1lP1WrFgRyzZ6/GbbCQBAtxkvw3zljFmpZENFs1LBNz+of6X3X33C7JbbJ373j583e+a3I10laHYxs0aD8EZKj/zbuXF4L10Mb0szYyLiVC+JafVYcWjXGI1ul2gCoLr6MAsXLrSzZ882vV9c27TSTnHlQYsWLbKC/w+gLi8Otm/waunqqBWuXLJrl695yUsjCpfHrHClbOXpY1ZucN9Ou3bpmo2Njtk1a/x5Zp17P+l5p/nyI5rD+c2/vJ7j3e/YPennX/qzX7Izo2fs2pjZxSv6nzhmdvn73u9K586ZzfL97f7Oc1Yc+r7Z0Pet/Ls/Xv0Bps+28qYvTbqr8MXfMXv+z73v/7+QdpVXbjD7mcrEHVH+X8yb9qpdu+HalPsHR67Pd2pmL57xrVQfMPbyOe/2ta+92YZevlpJJIYu2Yr/+GdVj5WEF8/YpPa00qZqx4pDvfa063Hr6f31/8e7/Zn/9DmL4tfe9gZ739veaO3U19cXGocGy9UTLwGqpdmALsp+cW1Tb7uRkcqcaNeuTf0jovED7fY9Pc5/bnbvEbMPt7+NcXjenrcFlo22xk3JJfKL85t/3XKONaJsXvDOHbWunvvmFA3a2szf+63XvzorWPT0XUuX76X0WFl4XIla1HbCzH7LkqN4VGMBUpEAuBr6as6pV6CF/eLappV2yi233GLf+973bM6cOVOuAAAAAADtop5/Bf+KR/0STQBUPhPWg677wgLvKPvFtU0r7RRd1n3d614X+nsAAACgXfw9/06iRYcKnPUV1ou+evXqpveLa5tW2gkAAACkTeKjjtatW2enTp2adJ8bdFtrZp0o+8W1TSvtBAAAANIk8YXAFESrB90fXGuF3aVLl9qmTROj9deuXevNw79s2bLI+8W1TSPbpYHaqtdKbRNdvUhbG1GdVpvetm3beFK5Z88e7za4KnW988t7IB10/vQ3I7iGSJznkXOd3nPM5znbtMbPkSNHvBhE50BxSLs+o5zjdJ7f5Xn+DJdT4MSJE+UtW7aUDx48WN65c6f35Xfq1Kny/Pnzy0eOHGlovzi3aWS7JLnXanh4ePw+tTmNbcVU+kj6vzZt2tTw+eU9kCy9/jpv+tJ50GtfbZs4ziPnOr3nWPg8Z5fiDf9rrNd/yZIlk84hn+N8n9+8f4YTvwKAeG3evNnLLP29UcpuNeUopzob5089DqIeh+Dic1HOL++B9NC51HkM9g7HdR451+k9x8LnObvUG3zw4MFJ96n3V+dDV3x0Lvkc5/v85v0znPgYAMTrwIED45eYHDdLkS53Id1cSZm+qq08HeX88h5Iv7jOI+c63fg8Z9ehQ4e8Ml+/FStWtOUzyjlO5/nN+2eYBCBHlFHqq9qbVG+2Z599NpF2oTE6h/qjEDxfUc4v74H0i+s8cq6zgc9zNq1Zs2ZK0ObH5zjf57cbPsMkADniZiWqRmsZnD17tqPtQeM0IEl/aFxPhAaeuz8QUc4v74H0i+s8cq7Tj89zdqk8JDhI8/jx4+OlIHyO831+u+EznOhCYOisaguZIV1279493lOgGa9UO6haxeAUtM2eX94D6RfXeeRcJ4/Pc76ohltfOqf1em75HGf7/HbDZ5grADlSa0XisEXMkC7By4T6g6MeBPVARDm/vAfSL67zyLlOPz7P+aGgTz3DbvpHPsf5Pr/d8BkmAcgRXU4Kyyh1X603IpKnAUnBXiV3TvUHJ8r55T2QfnGdR851uvF5zg/NDqNzod5gh89xvs9vN3yGSQByRG8kfYVllapdQ3rt2rVrvAbRcedSvRBRzi/vgfSL6zxyrtONz3N+ZotRoOYPDl3gxuc4v+e3Gz7DJAA5s27duim1aW4Qin9gC9JHtYfBQUnuMqM7d1HOL++B9IvrPHKu04vPc/ap91eBm78sxM0II3yO831+d+b9M5zoMmSInVac02p2flpxbvfu3Ym1CdFXJtQq08GVCf33RTm/vAfSo9rKknGeR851es8xn+ds0+u+Zs0a73z5v3SuT5w4Mb4Nn+P8nt8jOf8MsxJwTrPa/fv328qVK8ezzODAFqSTehc07Zjo3GnGgWAPQZTzy3sgOepB2r59u3er2lL1FqkHSHNO+89BXOeRc53ec8znObu0SmvYDC3+sInPcb7P79Ecf4ZJAAAAAIAuwhgAAAAAoIuQAAAAAABdhAQAAAAA6CIkAAAAAEAXIQEAAAAAuggJAAAAANBFSAAAAACALkICAAAAAHQREgAAQCpo1U2tpquv1atXW9ppdc+odu3aNf7ctm7d2tZ2AUA9JAAAgNRYs2aNnTp1yo4cOWJpt3bt2sjbbtmyxXteu3fvtvPnz7e1XQBQDwkAACC1PezLly+3BQsWeD3nabtasWrVqqSbAQBNIQEAAKTSsmXL7MSJE7ZixQpLG/Xkb968OelmAEBTSAAAAKm2ZMkSS+PVCSUoAJBFJAAAADTg0KFD3lgFAMgqEgAAABpA+Q+ArCMBAAAgIs3gc+7cuVSWJQFAVNMibwkASDXNNS+aQtM/jeYLL7zgzau/c+fO3JSuaFYgPS9RLf7AwIAXmGtqTt2/cOFCb9rNPXv2eNvoe83cs3fvXm97fe/m8ddrpf02bdpU93EPHDhg69evr5oYbN++3WuXf5rPs2fPeq87AKQJCQAA5CT4VwA7f/58LxAN1qkrKFagm5cEQItpHTx40CvHcb3xeu6aNUjBvAJ8/2si+lnTirrkSHPzi14TBe46Tr2pPfV4SjaC+vv7vfvdY4mSDyUeAJA2lAABQMa5HmcFnwr09bM/EFVgq2BX9ykwVhCsr1pU4x5lNd6ox4uTeu71HBXIVyvF0X36vW79r4ObtUdBvD/Qd9spoajFXXHwH9Pdr6/g/VGuKABAEkgAACDjVPrigk0FtwpEgz3ZK1eu9AJ63b9t27a6x9S2URKAqMeLi65s6Dm63vtqFi1aNN42P5cs6LUIUsmQXsdmBv9qXyUcSoLUPn8JEOU/ANKIBAAAMs7f062yk3Xr1k3ZRj3ULiAO9lRXo7KYWkG2X5TjtUrBuZ6bSn9Uh99Ku5odwKvgvtprq8fR1Qi9xio/0srF+lLJUSdeGwBoFAkAAOSEK42p1kutwahZ5kp6VOMvCrQ7/doGS4r8lFwNDw977VOvv1YvVrLS6XYCQBQkAACQE6rHl+AKtQpeq5W9OBoAqy8FrG57lf/oviBto55t9Ya7GXbqHS8Oek4KshWAayYfPb6+0jD3v14v1xa1U1dOdEVAYwo62UYAiIoEAAByQr381XqoFbyGzf6jnnUF1q7n2gWx1YJ3lxQowNXxdFw39Wit48VNj62vjRs3Tqq3b3dyVWsGpf3790+5T9vrfHSqjQAQFQkAAOSEAnQFm/6AUwF6WE+8atb1OzdwODiwNdjLrSDYP7ONBv8GpxoNO16r9f/BIFpXAXRftRKbsHKneoF42O/1vINXVYLU0++uwPhfD5UCMQ4AQNqQAABATqjnXcG3esYV+OtLAXq1Qa8KThWwakCtWxCrluPHj08JZP3HbvR4UbhSJAXXbjEzV3bkkho9pq5K6H43CNdto1l53Ha63yULen30vQJ+bavjuvbr+2AgX6v8x9FVER3Pve760n71phYFgCSwEBgA5Ih66KPMP6+eaW2nnn4Fw/UWrHJz68d1vCjU6+5f0dhPwbW+gsIC7rD7o7xeSkRqLRCmdta7QgAAacIVAADoYurFV/Bar4dbAbC2Cw78Df4c9XhZoasP9VYHBoCsIQEAgC6i8hYNzlVJj38ArwJ59dyrFEY93tu3bx+v6XcGBga8wb3+WYB0ZaDe8bIsSvkPAGRNoVwul5NuBAAASk5U8pOW1XPd6r5xlDP5n6PKkaqVLwFAp3AFAACAKjSgudbUnwCQVSQAAIDUUGmRZvXRbDxJU89/XOU/Ko/S89LxmBYUQNIoAQIAAAC6CFcAAAAAgC5CAgAAAAB0ERIAAAAAoIuQAAAAAADWPf5/c9kAe3EGMAkAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "old_flow = gwModels.remnants.gwModel_kick_prec_flow('../gwModels/data/')\n", "\n", "q_c, a1_c, a2_c = 3.0, 0.8, 0.8\n", "\n", "plt.figure(figsize=(8, 5))\n", "s_old = old_flow.sample(q=q_c, a1=a1_c, a2=a2_c, num_samples=20000)\n", "plt.hist(s_old, bins=100, density=True, histtype='step', lw=2,\n", " label=r'\\texttt{gwModel\\_kick\\_prec\\_flow} (angle-marginalized)')\n", "\n", "for t, ls in [(np.pi / 6, '--'), (np.pi / 2, '-')]:\n", " s_new = flow.sample(q_c, a1_c, a2_c, t, t, 0.0, 0.0, n_samples=20000)\n", " plt.hist(s_new[0], bins=100, density=True, histtype='step', lw=2, ls=ls,\n", " label=rf'\\texttt{{gwModelRemP\\_flow}}, $\\theta={np.degrees(t):.0f}^\\circ$')\n", "\n", "plt.xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.ylabel('probability density')\n", "plt.title(rf'$q={q_c:.0f}$, $a_1=a_2={a1_c}$')\n", "plt.legend(frameon=False, fontsize=9)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "id": "59a9da4c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " flow : median 642.0 km/s, 90th pct 1423.5\n", " HLZ : median 1263.5 km/s, 90th pct 2077.6\n" ] } ], "source": [ "# Against the deterministic HLZ precessing prescription, for an\n", "# isotropic population of spin orientations at fixed magnitudes\n", "rng = np.random.default_rng(0)\n", "n_iso = 4000\n", "q_i = 3.0\n", "th1_i = np.arccos(rng.uniform(-1, 1, n_iso))\n", "th2_i = np.arccos(rng.uniform(-1, 1, n_iso))\n", "ph1_i = rng.uniform(0, 2 * np.pi, n_iso)\n", "ph2_i = rng.uniform(0, 2 * np.pi, n_iso)\n", "\n", "vk_flow = flow.sample(q_i, 0.8, 0.8, th1_i, th2_i, ph1_i, ph2_i, n_samples=1)[:, 0]\n", "\n", "vk_hlz = np.array([\n", " gwModels.remnants.bbh_final_kick_precessing_CLZM2007(\n", " q=q_i, a1=0.8, a2=0.8, theta1=t1, theta2=t2,\n", " delta_phi=p1 - p2, Theta=0.0)\n", " for t1, t2, p1, p2 in zip(th1_i, th2_i, ph1_i, ph2_i)])\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.hist(vk_flow, bins=80, density=True, histtype='step', lw=2,\n", " label=r'\\texttt{gwModelRemP\\_flow}')\n", "plt.hist(vk_hlz, bins=80, density=True, histtype='step', lw=2,\n", " label='HLZ (CLZM2007)')\n", "plt.xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.ylabel('probability density')\n", "plt.title(rf'$q={q_i:.0f}$, $a_1=a_2=0.8$, isotropic spin orientations')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(f' flow : median {np.median(vk_flow):7.1f} km/s, 90th pct {np.percentile(vk_flow, 90):7.1f}')\n", "print(f' HLZ : median {np.median(vk_hlz):7.1f} km/s, 90th pct {np.percentile(vk_hlz, 90):7.1f}')" ] }, { "cell_type": "markdown", "id": "74298e95", "metadata": {}, "source": [ "### 5. Consistency with the non-precessing limit\n", "\n", "The flow was trained with 2000 synthetic non-precessing samples from `gwModelRemS` to anchor the aligned-spin boundary. At small tilt its median should track the deterministic aligned-spin recoil." ] }, { "cell_type": "code", "execution_count": 12, "id": "8c08c767", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q_al = np.array([1.5, 2.0, 3.0, 4.0, 6.0, 10.0])\n", "tiny = 0.01\n", "\n", "med_al = flow.predict(q_al, 0.8, 0.4, tiny, tiny, 0.0, 0.0, n_samples=20000)[0]\n", "vk_det = gwModels.remnants.gwModelRemS_kick(q_al, 0.8, 0.4)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.plot(q_al, med_al, 'o-', lw=2, ms=8, label=r'\\texttt{gwModelRemP\\_flow} median')\n", "plt.plot(q_al, vk_det, 's--', lw=2, ms=8, label=r'\\texttt{gwModelRemS} (deterministic)')\n", "plt.xlabel('$q$')\n", "plt.ylabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.title(r'Near-aligned limit, $a_1=0.8$, $a_2=0.4$, $\\theta \\approx 0$')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4ac89c65", "metadata": {}, "source": [ "### 6. Timing\n", "\n", "Unlike the analytic models, the flow cost is dominated by the neural network forward pass and scales with the number of samples drawn." ] }, { "cell_type": "code", "execution_count": 13, "id": "6e23d52c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100 samples per binary\n", " N time per binary\n", " 1 8.20 ms 8197.17 us\n", " 10 14.32 ms 1432.50 us\n", " 100 46.34 ms 463.41 us\n", " 1000 299.45 ms 299.45 us\n", " 5000 1338.80 ms 267.76 us\n" ] } ], "source": [ "# Cost vs number of binaries, at a fixed number of samples each\n", "sizes = [1, 10, 100, 1000, 5000]\n", "means = []\n", "\n", "for n in sizes:\n", " q_t = np.random.uniform(1, 10, n)\n", " a1_t = np.random.uniform(0, 1, n)\n", " a2_t = np.random.uniform(0, 1, n)\n", " t1_t = np.random.uniform(0, np.pi, n)\n", " t2_t = np.random.uniform(0, np.pi, n)\n", " reps = 5 if n <= 1000 else 3\n", " t = []\n", " for _ in range(reps):\n", " t0 = time.perf_counter()\n", " flow.sample(q_t, a1_t, a2_t, t1_t, t2_t, 0.0, 0.0, n_samples=100)\n", " t.append(time.perf_counter() - t0)\n", " means.append(np.mean(t))\n", "\n", "means = np.array(means)\n", "print('100 samples per binary')\n", "print(f'{'N':>8s} {'time':>10s} {'per binary':>13s}')\n", "for n, m in zip(sizes, means):\n", " print(f'{n:>8d} {m*1e3:8.2f} ms {m/n*1e6:10.2f} us')" ] }, { "cell_type": "code", "execution_count": 14, "id": "628317b3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 100 samples : 3.61 ms\n", " 500 samples : 8.03 ms\n", " 1000 samples : 12.61 ms\n", " 5000 samples : 28.96 ms\n", " 20000 samples : 72.73 ms\n", " 100000 samples : 299.48 ms\n" ] }, { "data": { "image/png": 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Byshpwwi0eh2ROK4abYbShtI6asRfPMWowDgNv76SenLLhhuDjFF9HtcI51KHSjE6sMzunBz0LXsmg9mMlIJ8FBYWIlTl5eXSw2azIScnx2sfk3lERERECp00OhfvfbVXVlmR8JtyzOCI94mUEYP2QAN8MXAPt4ycNoxAq9cRieOq0WYobSito0b8xVOMCozT8OsrqSe3bLgxyBjV53GNcC41qRSjrjK9O3ag86uvZfdVXJmXWVamyu/dVxvG/xdBREREFEXbG9rw7EdbZJU1AchKTcBZxwyNeL+IiIiISH0969dj+wUXwi73llmRIMzMRMaUKYgUJvOIiIiIZPp2rw3TnvkvdjV3eiXsfJG2m4CHpp+AlERLtLpIRERERCppevVVtN56GxxWq/Q8YcgQKVknPXzp3z7s/vthTk5GpDCZR0RERCTD+h+aMLPyE9S3dEnPxw4ehAemHYfM1AT33HieP8X2JZdOQOlRvMWWiIiIyEicPT3Yc9ddqLvnj+5FL9JP/SmK3v4bRjz5BMwZGX0FXbfA9v8U20c8+SQyJp0e0f5xzjwiIiKiID7avB9zX1qH9u6+1cSOH5mNF2ZNRE56En5x/DC8u3EP3tu4F/XWNhRkpePMY4ZIt9byijwiIiIiY+ltasKuX9+I9k8/dW/LuXw2Bt9yC0wWCzImTcKYDz9Ay4oVsK1cKa1aKxa7EHPkiVtrI3lFnguTeUREREQBvLdxD2549TN02/u+lf3RYXlYfOkEpCf3DaNEwm7quBE49/hhqKurk1Yti4WJuomIiIjiTdfmzdhx9TXo2blTem5KTETqrbeg8NJLYfIY34mEXdY55yDj7LM1Gf/FXDJv1apV0s/m5masXbsWZWVlKC0t1bpbREREZEDVNTux4M0vpRVphTOOGozHLhzHK+6IiIiIYkzLmn9h9623wtHeLj235Odj+OOPoWWo/hYyi7lk3vTp07F69Wp3Ak88b2pq0rpbREREZDCvrt+HP33Q962scP74Eag4/1gkWHjVHREREVGscDqd2L9kCeoffkQ8kbalHHWUNDeeZfBgtMhdxTaKYi6ZJxJ548ePl/67sbEREyZM0LpLREREZLAB3SMrN+Fxj0Te7B+Nwu9/fhTMrtUtiIiIiMjwnF3d2FN+O1r+/nf3toyzzsSw++6DOTUVjv7FL/RGl8m8xYsXo7a2FhUVFQft27Jli7S9uLhYep6dnY25c+e697sSeaLcypUrUVlZGcWeExERkZE5HE7c/fZXWPrf7e5tN5WOxQ2TD4PJxEQeERERUazoratDy42/hv2bb93b8m+4HvlXX637cZ9uknmuJJ2wbNkyrwSdZ5mSkhJs3bpVSuIJ5eXlWLRoEebPn+8ut379eqxbtw5FRUVRfAVERERkZD12B+Yv/wJvbdjl3nbH2Ufi8h9zPEFEREQUSzq+3Iid114Le/8ttKbUVAyruB+ZZ5wBI9BNMk8k3lxX0YlEnC8i2SeSfK5EnrBgwQLk5OR4JfPE1XniIRbDEFfwiav8mNgjIiIifzp77LjulQ1Y9c0+6bnFbMJvSw/FrFNGad01IiIiIlKR9R//wJ7f/BbOri7pecLQoRj59FNIOeIIGIWhZnAWV+y5bq91cSX2ROLOlbxzcc2XJ67oIyIiIvKltasXs6o+dSfykixmPHXROPzsqDytu0ZEREREKnE6HKh75FHsvuXWA4m8Y4/FocteN1Qiz1DJvObmZunh6wo7kdATt9bm5uZi2rRp7u3iCj+xj4tgEBERkS+Nbd24aMkn+GRLo/Q8LcmCF2ZPRNlRg7XuGhERERGpxN7ahp3X34AGj3UVss47D4MeehAJecb7Alc3t9kGE+jqOpHEa2hokG6tFeXEAhpCTU2NtLqt5225/uTn5x80wWFHR8dB5cRKJmKVO18rmvjbF6iOXkSjj2ocI5Q2lNSRUzZYmViNkWj0kzES+j69iNUYUVqP5xJjfN7stXbiV89/iu/r26Tn2amJqJo1AcePzNbFuSQ1NfWgbaIOEREREcnXvXMndl5zLbo2berbYDZj8O3lyLr4YtTX18OIDJPMC0ZctSd4XpkXKjFQFom9uv6JED2JQbfVapXKmM1mWfsC1dGLaPRRjWOE0oaSOnLKBisTqzESjX4yRkLfpxexGiNK6/Fcov/Pmx3Nnbj+jc3Y29ItPc9PT8Rj543B0ORu6fNfD+cSzzEJERERESnXvnYtdt7wa9ibmqTn5owMDH/4YQz6yY91/QV4zCTzAl1d19jYd2tMOMTAPTMzU3ozRWa2oKDA7x9XYlDta7+/fYHq6EU0+qjGMUJpQ0kdOWWDlYnVGIlGPxkjoe/Ti1iNEaX1eC7R9+fNN3tsuHr5l9jf2pfIOyQ3FS9dfiJG5qaF1U+1Y6Stre2gMYnNZpMW/iIiIiKiwJqrq7Hvnj8Cvb3S86RRozDiqaeQXDQaRmeYZJ64ldbzCjxPYpucW2kDEYNk10BZDK49nw8UaL+/fcHa1INo9FGNY4TShpI6csrGa4xEo5+MkdD36UWsxojSejyX6PPzpmZ7E2ZXfQpbZ9+g7vDBGXjpihNRmJmiSj8jHSN6fl+JiIiI9MDZ24v2xx5D05tvubel/+hHGP7wQ7BkZSEWGCaZJ5J14uHvKryysrKo94mIiIiM44NN9Zj3Ug06euzS83GHZKNq1kRkpyVp3TUiIiIiUoHdasXOG29C13//696We9mvUHjbbTAlGCYFFpShXsmMGTNQW1vrc2GM0tJSjXpFREREevfOl3vw69c2oMfet4DEjw/LR+WlJUhPNtRQiIiIiIj86NqyBTuuvho923/o25CQgKF334Xs889HrNHlCFbcNuvrdtry8nLpCryKigr3tsrKSukRLjF3jevB1QX1eww9rC4YrzESyyuVGiFGlPZTK7EaI0rr8Vyir8+bZet24DdvbYSjfyHYKUcPxqMzj0dygjmk37/c44Zb1lcZPb+3RERERFpp/eAD7Lr5FjhaW6XnpuxsjHj8MQyaOBGxSDfJPJG8W7hwofRTXG23bNkyaXtxcTHmz58v/XdRURGqq6ulpN7EiROlcnl5eZg7d27Yxy8pKYHFYsGsWbMwdepUri6o02PoYXXBYGViNUai0U/GCFezjUb7obZhhDhhjBx8jFc31OPxD3e69/38qDwsmDwc1sYG1fsZyRhZunQpqqqqYLf33SJMRERERJDGSY0vLEXdAw+IwZO0LfnwsUi++26kHXccYpVuknliPjzXFXeBrrQbP3689FBbTU0NV7PlarayygYrE6sxEo1+Mka4mm002g+1DSPECWPkwDGElz+34imPRN7lPxqF35x1BMxmU0T6GckYEV9kigdXsyUiIiLq4+juxt4774L1rQMLXWSUlWLIffdhf1sbYpluknla81wpjqsLcjVbrkAZfyuVGiFGlPZTK7EaI0rr8VziX6T76HA48dD7O/HGF/XubbeUjcV1kw6Tjh3JfnI1WyIiIqLI692/HzuvvwEdGza4t+VfczXyr7sO0swqTOYRERERGUOP3YFbl3+Bv3ok8u4+52hcdsooTftFREREROro/Ppr7Lj2OvTu2SM9N6WkYNjC+5B51lnSc2cczDHMZB4RERHFhM4eO67983qs/rZOem4xm/Dg9OMwddwIrbtGOiRuYw5nAZRwFrExEq1eRySOq9UiSkrrqBF/8RSjAuM0/PpqL+Ikpxxj1JjH1fpcan3vPez77e/g7OiQticMGYLhjz+GlKOPdrenVozKKRON99ZX20zmERERkeG1dPbgyqXr8L+tjdLzJIsJT1w0DmccPVTrrpFOuRY/mz17tvSI5iI2RqLV64jEcY2w0Jbc8oxRb4zT8OurvYiTnHKMUWMeV6tzqb23F7YlS4DX+xZLFSxHHYX0e+6BLS8Xtro6xe3r/VwqFj/ztwAak3lERERkaA2tXZhVtRZf7rJKz9OTLFj0i2KUHjlY666RjrkWP9NiERsj0ep1ROK4RlhoS255xqg3xmn49dVexElOOcaoMY+rxbnU0d6OPQt+A6xc6d6Wec45GHz3XTAnJ4fcvt7PpYEWQGMyb8CtFuFcQulvnxEuD47WpaF6v7Uh0pfZGjlGotFPxkjo+/QiVmNEaT2eS/xTu497rB341fNrUVvfN8lxTloinr+sBEOSumPyXKLn99Zowl2gRk4ZIyxII4dWryMSxzXCQltyyzNGvTFOw6+v9iJOcsoxRo153GieS3t275bmx+v65htXRRTeegtyL7884MJmasWonDKRfm99tctk3oBbLWbNmoWpU6eGdAmlv31GuDw4Gn3U6nJctS8ZD+cyWyPHSDT6yRgJfZ9exGqMKK3Hc4l/avbxh6ZO3PDmZuxt6ZaeF6Qn4rHzxmBwYheam2PrXLJ06VK/t1kQERERxaL29Ruw8/rrYW9o6NuQlobhDz2IzNNPR7xjMm/ArRZi4FxfXx/SJZT+9hnh8uBo9FGLy3GV1on0ZbZGjpFo9JMxEvo+vYjVGFFaj+cS/9Tq4zd7bLh6+ZdoaOtL5B2am4aXrpiIETlpMXkuCXSbBREREVGsaX7zLey98044e3qk54kjRyL1nj9g0Iknat01XWAyr5/nJZHhXELpb58RLg+ORh+NcGtDpC+zNXKMRKOfjJHQ9+lFrMaI0no8l/gXbh/XbWvE7BfWoqWzV3p+xJAMvHjFiSjMSFHtGKG2EekY0fP7SkRERBQup92OugceROMLL7i3pZ18MoY9/BAauvu+xCUm84iIiMhA/r2pHvNeWofOnr6548Yfko2qWSciKy1R664RERERURjsLS3YdfMtaPvwQ/e2nIsuwuAFt8NpsQAeK9bGOybziIiIyBD+8cUe3Pj6BvTYndLzn4zJR+WlJUhL4nCGiIiIyMi6t23DjquvQffWrX0bEhIw5He/Q84FM6WnTi4C5oWjXyIiItK91z79Ab9560s4+vJ4+NmxQ/DIzBOQnGDRumtEREREFIbW//wHu266GQ6bTXpuycrC8MceQ/pJnB/PHybzPCaZdj3EqnHip79y/vb72xesTT2IRh/VOEYobSipI6dsvMZINPrJGAl9n17EaoworcdziX+h9HHxB1tw/3vfuZ/PmDAC9/7yGFjMpoj9W9HruUTP7y0RERGREmKc0/jiS9hXUQHY7dK25DGHYcRTTyFp5Eitu6drTOb1KykpgcViwaxZszB16lQpqPytLmi1Wn3u97cvUB29iEYf1ThGKG0oqSOnbLAysRoj0egnYyT0fXoRqzGitB7PJf4p6aMo88zHu7F07V73tovGD8b1PypEw/56VY6hZhuRjJGlS5eiqqoK9v6BLhEREZGRiVVq9911F6zVy93bBp1+OoY9sAiWQYM07ZsRMJnXr6amBpmZmdLAub6+HgUFBX7/uBIry/na729foDp6EY0+qnGMUNpQUkdO2WBlYjVGotFPxkjo+/QiVmNEaT2eS/yT20eHw4k73/4af/ZI5N1SNgbXnFYs1VfjGGq3EckYKS8vlx42mw05OTkhvSYiIiIiPehtbETrrbei9/Mv3Nvy5sxBwY2/hkksdEFBMZnXTwykXYNpMXD2fD5QoP3+9gVrUw+i0Uc1jhFKG0rqyCkbrzESjX4yRkLfpxexGiNK6/Fc4l+wPvbYHbil+gv87fPd7m33nHs0Lv2/UaodI1JtRDpG9Py+EhEREQXT+d132HnNtejdtUt6bkpKwtB7/4isX/xC664ZCpN5REREpBsd3XZc+8p6rPm2Tnou5sV7aPrx+OW44Vp3jYiIiIjC0LJ6NXbdNh/O9nbpuaWgACOffAKpxx2nddcMh8k8IiIi0gVbZw+ufGEdPt3WKD1PTjDjqYvHY/KRg7XuGhERERGFSMz/21BZifpH/+TeZjn8cBz6zNNIHjpU074ZFZN5REREpLmG1i5cVvUpNu6ySc8HJSfg2csm4OSiPK27RkREREQhcnR2Ys9vfgvbO++4t2X87CxYfv1rJA7mF7ahYjKPiIiINLW7uQOXPPc/bKlvk57npCXixctPwrEjsrTuGhERERGFqGffPml+vM6vvnJvK7jxRuTMuVJaeJRCx2QeERERaWZLfSsufe5T7GrukJ4PyUzBy1eeiMMKM7TuGhERERGFqOPzz7Hjuutgr98vPTelpWH4A4uQMXkyHA6H1t0zPCbziIiISBNf7bbisuc/xf7Wbun5qLw0vHzlSRiRk6Z114iIiIgoRNa338ae3/4Ozu6+MV7i8OEY8dRTSDl8rNZdixlM5vUTmWHXQ0zO6C9THGi/v33B2tSDaPRRjWOE0oaSOnLKxmuMRKOfjJHQ9+lFrMaI0no8l/jn6uOnWxpw5Uvr0drVK20/cmgGXpg1EQUZyWH3P5bPJXp+b4mIiCi+Oe121D/6KBqWPOveljZhAoY/9ick5OZq2rdYw2Rev5KSElgsFsyaNQtTp06VBs9ms/mgcmIQbbVafe73ty9QHb2IRh/VOEYobSipI6dssDKxGiPR6CdjJPR9ehGrMaK0Hs8l/ok+rvpqD+799z509TqlbccOTcfD5xbB2WFFXYc6x4i1c8nSpUtRVVUFu90e0ushIiIiiiR7ayt233obWt9/370te/p0DPn972BKStK0b7GIybx+NTU1yMzMlAbOYiLGgoICv39cmUwmn/v97QtURy+i0Uc1jhFKG0rqyCkbrEysxkg0+skYCX2fXsRqjCitx3OJf29/vgt3/2sv7P0XmP10TD6eungc0pLUG5LE4rmkvLxcethsNuTk5IT0moiIiIgioXvHDuy85hp0bf6+b4PFgsG3346cSy6WxjKkPibz+omBtGswLYLN8/lAgfb72xesTT2IRh/VOEYobSipI6dsvMZINPrJGAl9n17EaoworcdzycFe+d8P+O1fvoSz74I8/PzYoXhk5glISlC/r7F6LtHj+0pERETxq+2T/2HXr38Nu9UqPTdnZmLEo48g/ZRTtO5aTGMyj4iIiCLu6fdrUfHet+7nMyeMwH3nHQeLmd/WEhERERlR02uvYe8f7wV6++ZATioqwsinnkTSqFFady3mMZlHREREESPme1u04jspmedycclg/GHqMUzkERERERmQs7cX++65B82vvubelv6Tn2D4ww/BkpGhad/iBZN5REREFBF2hxO//+tG6fZal1vPGIvzjxzE+VOIiIiIDMje3IzW2+ajd8MG97bc2bNReOstMFksmvYtnjCZR0RERKrr7nXg5mWf4e9f7JGei9zdH849BhefOBJ1dXVad4+IiIiIFOr6/nvsuPoa9O7YIT03JSZiyN13I/u8qVp3Le4wmUdERESq6ui24+o/1+D97+ql5wlmEx6acTzOPWG4tEIrERERERlLy/vvY/ctt8LR1iY9t+TlYcTjjyNt/DituxaXmMwjIiIi1dg6e3DFC2uxdluT9Dw5wYynLxmPSUcM1rprRERERBTC/MeNzz2HuoceFk+kbZbDDsOhzzyN5BEjtO5e3GIyj4iIiFSxv7ULv3ruU3y9xyY9z0hOwLOXTcBJRXlad42IiIiIFHJ0dWHvHXfA+te/ubcNOuMMJNx0IxKHDdO0b/GOybx+4rYf10Nknv3dBhRov799wdrUg2j0UY1jhNKGkjpyysZrjESjn4yR0PfpRazGiNJ68Xgu2dXcgV89vxZb9/fdepGblogXZk/EMcOzvPrDzxv5ZX2V0fO/fyIiIoodPXV12Hn99ej8/Av3tvzrrkPuVfNQv3+/pn0jJvPcSkpKYLFYMGvWLEydOlUaPJvN5oPKiUG01Wr1ud/fvkB19CIafVTjGKG0oaSOnLLBysRqjESjn4yR0PfpRazGiNJ68XYu2d7YiRve2oR9LT3S88EZifjT1LEoTOw6aLELft7IL+tZZunSpaiqqoLdbg/p9RARERHJ1bHxK+y89lr07tsnPTelpmLY/fcjc8oZ/GJRJ5jM61dTU4PMzEwpMOvr61FQUOD3jyuTyeRzv799geroRTT6qMYxQmlDSR05ZYOVidUYiUY/GSOh79OLWI0RpfXi6VyycZcV17zxJRra+hJ5o/PT8eLlEzE8O9VneX7eyC/rWaa8vFx62Gw25OTkhPSaiIiIiIKxvfMOdv/mt3B2dkrPE4YOxcinnkTKkUdq3TXywGRePzGQdg2mxcDZ8/lAgfb72xesTT2IRh/VOEYobSipI6dsvMZINPrJGAl9n17EaoworRcP55JPtzZKi120dPVKz48amokXrzgR+YOSA9bj5438sgPL6PnfPhERERmXU1zY9PjjaHj6Gfe21HHjMOLxx5CQn69p3+hgTOYRERGRYv/6tg5XvVyDrt6+Wy0mjsrBs5dNRFZqotZdIyIiIiIFHG1t2H377WhZucq9Leu88zDkrjthTkrStG/kG5N5REREpMjfPt+Nm1//DL0Op/T81LEFeOaSEqQmWbTuGhEREREp0L1zlzQ/Xtd33/VtMJtROP825F52mXSHAOkTk3lEREQk28ufbMfv/7oRzr48Hs4+bigennECkhJ4+ycRERGRkbSvW4ed198Ae1OT9Nw8aBCGP/IwBv3kJ1p3jYJgMo+IiIhkeer977Hovf5vbQFceOIh+OMvj4HFzG9tiYiIiIykefly7Ln7D0BP3yJmSYceihFPP4XkoiKtu0YyMJlHREREATmdTtz/3reo/PcW97arTi1G+ZmH8/YL0tz69euxalXfHD9r165FRUUFiviHCBERkU/O3l7sW7QITS++5N6Wfsr/Yfgjj8CSlaVp30g+JvOIiIjIL7vDid/95Uu8+ukO97byM4/A1acVa9ovIheRyJs/f77034sXL0ZZWRlqa2u17hYREZHu2K1W7LrpZrR9/LF7W86ll2Jw+XyYEpgeMhJOcENEREQ+dfc6cMNrG9yJPHER3r1Tj2Eij3R1Vd7ChQvdz2fMmIEtW7ZIDyIiIjqga8tWbJt5wYFEXmIihvzhbgz57W+YyDMgvmNERER0kI5uO656uQb/3lQvPU8wm/DIzBPwi+OHad01ikHiijpxNZ24RXYgkZgT24uL+5LI2dnZmDt3rvTf48ePR3V1tbtsY2Oj9DM3NzdqfSciItK7to8+wu5bboWjpUV6bsnJwYjH/oS0iRO17hqFiMk8IiIi8mLt6MEVL6zFuu19K5ulJJrx9CUlOP3wQq27RjHElaQTli1b5k7QDSxTUlKCrVu3Skk8oby8HIsWLXLfWltaWuouX1lZKbXjKktERBTv8x53Vi9H09NPAw6HtC157FiMeOopJI0YrnX3KAxM5vVzOBzuhwh48dNfOX/7/e0L1qYeRKOPahwjlDaU1JFTNl5jJBr9ZIyEvk8vYjVG4ulcUt/ShdkvrMXXe/q+uR2UnIBnf1WCE0fnqvK+8vNGfllfZfT8718psUiFSL4J69at81lGJPsGJucWLFiAnJwcdzLPZfny5Whubna3SUREFM8c3d3Yd9fd6HjzTfe2QZMnY/iiCpjT0zXtG4WPybx+4ltfi8WCWbNmYerUqdLg2Ww+eEpBMYi2Wq0+9/vbF6iOXkSjj2ocI5Q2lNSRUzZYmViNkWj0kzES+j69iNUYiZdzyR5bF254czN2NHdJz3NSE/Do1DEYld6Luro6qIGfN/LLepZZunQpqqqqYLfbEU/EFXsDb711JfbEwheuq/LEf4tbbF2JPJHU49V5REQUr3obGrDz+hvQsX69e1veVfNQcMMNMOn07whShsm8fjU1NcjMzJQGzvX19SgoKPD7x5XJZPK539++QHX0Ihp9VOMYobShpI6cssHKxGqMRKOfjJHQ9+lFrMZIPJxLautacc0bX2GPtS+RNzQrBS9dcSKK8tX95pafN/LLepYRt5aKh81mk65KiwciISce4gq+gUSiTix+IZJ54qe4HVcsfiHKiwSg+G8iIqJ41PnNN9hx7bXo3b2nb0NSEobedy+yzz5b666RipjM6ycG0q7BtBg4ez4fKNB+f/uCtakH0eijGscIpQ0ldeSUjdcYiUY/GSOh79OLWI2RWD6XfLnTisuqPkVjW7f0vKggHS9fcRKGZaciEvh5I7/swDJ6/revtkAr0ooFLhoaGtxz6gnz5s1z7/c1/95A+fn50u/XU0dHR1RulTcSrV5HJI5rhFvw5ZZnjHpjnIZfX+2pIuSUY4yqr2XlSuy5fQGc/Z9nlsJCpP7hbgz68Y9VO7YRzqUOlWJUThm139vU1IPH36L9gZjMIyIiimP/29KAK5auQ2tXr/T86GGZWHr5icgflKx114gCcl2152uAGyrX7eSRvlXeSLR6HZE4rhFuwZdbnjHqjXEafn21p4qQU44xqvJCFy++iM6qF9zbLEcegbQ//AEtCQnS55teYjTUNrSIUT3HKZN5REREcWrNt/tw9cvr0dXb903iiaNy8eysCchMSdS6a0QB57wT8+OFS/xhI6ZY0eJWeSPR6nVE4rhGuAVfbnnGqDfGafj11Z4qQk45xqhKbXd0YO9vfovOFSvc2zJ/8QsM/sPdQGIiLAGmEYvVc6lDpRiVU0bt99Z1l4AnX9OsMJlHREQUh/762S7csuxz9Dr6rmo6/fACPHVxCVKTLFp3jch9K63rCryB1FjgItzb4OWUMcLUCHJo9ToicVwj3IIvtzxj1BvjNPz6ak8VIaccYzQ8PXv2SPPjdX39jesgKLzlZuRecYV0PFeiSW8xGmobWsSoHuLUV7tM5hEREcWZlz7Zjjv+uhGuuxN/cfwwPDT9eCQlGH+gTLFDJOvEw99VeGVlZVHvExERkV60b9ggrVhr379fem5OS8Owhx5Exumna901igIm84iIiOKEmMvjqfdr8cCK79zbLj7pEPzh3GNgMXsvBECkB2JV2traWp8LY4iVbImIiOJR81t/wd477oCzp0d6njhyJEY+9SSSx4zRumsUJfwKnoiIKE4SeQvf/dYrkXfNacX44y+ZyCPtidtmfd1OW15ejuXLl3ttq6yslB5ERETxxmm3Y9+iB7BnwQJ3Ii/txBMxatnrTOTFGV6ZR0REFOPsDid+8+aXeH3dDve2BWcdgXmnFmvaL4pvInm3cOFC6ae42m7ZsmXS9uLiYsyfP1/6b7FabXV1tZTUmzhxolQuLy8Pc+fO1bj3RERE0WVvacGuW29F278/cG/LvvACDPnNb2BK5OJl8YbJPCIiohjW1WvHTa9/hne+3Cs9N5mA+6YeiwtPPETrrlGcE/PhVVRUSP8d6Eq78ePHSw+1iUnBxcPfPnE1q7/9csrIacMItHodkTiuGm2G0obSOmrEXzzFqMA4Db++knpyy4Ybg4zRA7q3b8eua69Dd/9UE7BYUPjb3yDnggsgpkB2RvF3aIRzqUOlGNVLnPpqm8k8IiIig+vsseOdL/dgxVd7Ud/choLsnZhy9BBphdobXvsMH27umxg50WLCIzNPwNnHDdO6y0SaKykpgcViwezZs6XHwEGz1WqVBuf+VqYLVkZOG0ag1euIxHHVaDOUNpTWUSP+4ilGBcZp+PWV1JNbNtwYZIz26ampQdtdd8PZ0iI9N2VmIv3uu9Azbhzq6uoidlwjn0sdKsWo1nFaVVUlPex2+0H7mMwjIiIysJVf78Mt1Z/B1tELMfWdwwmYd7dixVf7pLnwxC22QkqiGc9cUoLTDi/UustEulBTU4PMzEyf+8TA3GQyoaCgIODgPlAZOW0YgVavIxLHVaPNUNpQWkeN+IunGBUYp+HXV1JPbtlwYzDeY1Qkh5pffRVNC+8H+pM5ScXFGP7kE0g65BDDxmiobWgRo1rHqZhmRDxsNhtycnK89jGZR0REZFCrvtmHeS+vh3R/hRhMDPjpSuSlJprx0hUnYcKoXK26SqQ7YsAdaNAtBubhlpHThhFo9ToicVw12gylDaV11Ii/eIpRgXEafn0l9eSWDTcG4zVGnd3d2HfvfWh+/XX3tkGnnYZhDz4Ay6BBETtuLJ1LTSrFqB7i1Fe7TOYREREZUFevA7dWfykl8vpzd35ZzGYcMzwrSj0jIiIiolD1NjVh1w2/Rvvate5teVdegYKbboLJYtG0b6Qfxk9vExERxaE1m5tg6+wNmsgTWrt68e7GPVHoFRERERGFqnPTJmybPsOdyDMlJWFYxf0ovPVWJvLIC6/MG7CiWTgrlfjbZ4RVeKK1AkssrHoTrzESjX4yRkLfpxexGiN6jJN/f9/sniMvGFHuvY17ce7x2i98wc8b+WV9ldHzv38iIiIKXcuaNdh9621wtLdLzy0F+Rj5xBNIPf54rbtGOsRk3oAVzWbNmoWpU6eGtFKJv31GWIUnGn2MlVVvwlnNxsgxEo1+MkZC36cXsRojeoyThtZOWYk8qbwTqLe2BV3xLBr4eSO/rGeZpUuX+l3NjIiIiIxLfM43LF6C+kcfFU+kbSlHH40RTz6BxCFDtO4e6RSTeQNWNBMD5/r6+pBWKvG3zwir8ESjj7Gy6k04q9kYOUai0U/GSOj79CJWY0SPcZI3aCvMdZ2yr8wryEpHYaH2K9ny80Z+Wc8ygVYzo9CI328oV8bKLWOEq6nl0Op1ROK4RrhqV255xqg3xmn49dW+ulxOOcYo4OjsxN7f34GWf/zDvS3jrLMw5I/3wJyaGvZr12OMhtqGFjGqlzj11TaTef08Vx4JZ6USf/uMsApPNPoYK6vexGuMRKOfjJHQ9+lFrMaI3uKkZGQG3q9tltVvkfA785ghuokbft7ILzuwjF7ew1i6K2P27NnSI5pX1xqJVq8jEsc1wlW7csszRr0xTsOvr/bV5XLKxUOMOru60f3v99H94UfobWxEa24ukn7yYySdehqcLTa0/u73sH/7rbt8yuWXw3LpJdjf0gKIRwzGaKhtaBGjWsepuCvD350ZTOYREREZzBc7rXhxrbwFLUwAMlMTcNYxQyPeLyIj3pWhxdW1RqLV64jEcY1w1a7c8oxRb4zT8OurfXW5nHKxHqOta9Zgz29+C4fNJr6NEy8IvWYzej/8EB1/egymhAQ4rFaprCk1FUMr7kdGaWnMx2iobWgRo1rHaaA7M5jMIyIiMpC/bNiF8je+QFevwyth5+tuW1P//z00/QSkJHIFNCJP4V45K6eMEa6mlkOr1xGJ4xrhql255Rmj3hin4ddX++pyOeViNUbFYha7rr/hwAbXbZL9P51tbe6xW+KwYRjx9FNIOfzwuInRUNvQIkb1EKe+2jXWvwgiIqI4ZXc4cd873+DG1z9zJ/JKDs3Bg9OPl668c82N5/lTbF9y6QSUHjVYs34TERERxRNHVxd2376g70n/ghZ+WSw45OWXIpbIo9jFK/OIiIh0ztreg+tf24APNtW7t517TD4qZpQgJSkBZx83FO9u3IP3Nu6VVq0Vi12IOfLErbW8Io+IiIgoelree6/v1lo57HZ0rFuHpHPOiXS3KMYwmUdERKRj39e1Yu5LNdjW0C49TzCbcMfZR6JsdAqSEvousBcJu6njRuDc44ehrq5OWrXWaLejEBEREcWCllWr3XPkBWU2o2XlKmQxmUcKMZlHRESkUx9uacbdKz5Da1ffCla56Ul46uLxOHFUjpS0IyIiIiJ9sVub5SXyBIcD9v5FMIiUYDKPiIhIZ8TS9k++X4uH/1nrnhz5yKGZWPKrEozISZNWzSIiIiIi/TFnZYsVEYLPlycVNsOSlRWNblGMYTKPiIhIR9q7e3Fb9Rf4x5d73Nt+ftxQPDDtOKQl8WObSC0iKe4vMS62i6R6oMR5sDJy2jACrV5HJI6rRpuhtKG0jhrxF08xKjBOw6+vpJ7csuHGoBFjtHvbNnRv2SIvkSc4HEifPDlir1GPMRpqG1rEqF7i1Ffb/KuAiIhIJ3Y0tkvz432zp2/SZLEo7S1njMW1px8mLXlPROopKSmBxWLB7NmzpcfAQbPVapUG5/7mnwxWRk4bRqDV64jEcdVoM5Q2lNZRI/7iKUYFxmn49ZXUk1s23Bg0Uow6u7vR+eqr6Hz5z0BPj7xKJhNM6enoHDcOXRGaPkWPMRpqG1rEqNZxWlVVJT3s9r4pdzwxmUdERKQD/61twLWvrEdjW7f0fFCyBXdNGYXzTi5mIo8oAmpqapCZmelznxiYi393BQUFAQf3gcrIacMItHodkTiuGm2G0obSOmrEXzzFqMA4Db++knpyy4Ybg0aJ0fZPP8W+u/+A7q1b3dvMublwNDX1PfF1lV7/2G5Yxf0YNHJEXMVoqG1oEaNax2l5ebn0sNlsyMnJ8drHZB4REZGGxLd4L/53G+5++2vYHX2DvdH56ai8ZDwy0beCLRGpTwy4Aw26xcA83DJy2jACrV5HJI6rRpuhtKG0jhrxF08xKjBOw6+vpJ7csuHGoJ5jtLepCXUVi2D9y18ObLRYkDd7FvKvuQZtn3yC3bcvgMNmO7C6bf9Pc0YGht1/PzImnR6XMRpqG1rEqB7i1Fe7TOYRERFppLvXgd+8tRGvr9vp3nbq2AI8duE4ZCRbUFfHZB4RERGR3r6Itb75FuoeeAD25mb39tTjj8eQP9yNlMMPl55nTJqEMR9+gJYVK2BbuRKd9fuRUpCPzLIyZEyZAnNysoavgoyOyTwiIiIN1Ld04do3NuHLPW3ubfNOLcL8KUfAYjYZarJnIiIionjQtWUL9t55F9rXrnVvE1fZFd5yM7JnzIBpwBVUImGXdc45yDj7bNTV1aGwsFCXVxmS8TCZR0REFGVf7GzG3BfXYa+tS3qenGDGomnH4dwThmvdNSIiIiIawNHVhYbKSuxf8qzXAheZP/sZBi+4HQkFBZr2j+IPk3lERERR9NaGnbj9jS/R1dt35d3QrBQsvnQCjh2RpXXXiIiIiGiAto8/xp6770bP9h/c2xJHjsSQO+7AoJ/8WNO+UfxiMo+IiCgKxOIWFe99i8UfbHFvO25YOpZcdhIGZ6Vq2jciIiIi8tbb0IB9FRWw/e3tAxsTEpB3xRXIv/oqmFNStOwexbmDknkLFixAs8ckjmrKzs7GwoULI9I2ERGRXlnbe3D9axvwwaZ697YLJo7EtSfnoyCDkx+T9jj+IyIi6uN0OND8xhuoe/AhOKxW9/bU8eMx9O67kDxmjKb9I/KZzFu+fDmeeeaZiKz4cvXVV3MwR0REcWXzvhbMeXEdtjX0rUybYDbhznOOxkUTR6C+/kByj0hLHP8REREBXZs3Y8+dd6Fj/Xr3NnNWFgpvvQXZ559/0AIXRLpJ5olB1+TJkyNyMNE2ERFRvFj9zT7ctOwLtHb1Ss9z05Pw9MXjcVJRHlerJV2Jx/Gf+Dfo79+h2C76HejfabAyctowAq1eRySOq0abobShtI4a8RdPMSowTsOvr6Se3LLhxmA031dHRwcanqlEY1UV0Ns3bhMyf/ELFMy/DQl5eXD2X7UXUvuM0bDb0CJG9RKnvto+KJk3b968iHUgkm0TERHphfhAr/p0Dxb/dzdceYyjhmZi8a9KMCInTevuER0kHsd/JSUlsFgsmD17tvQYOGi2Wq3Sv2Wzn6swgpWR04YRaPU6InFcNdoMpQ2lddSIv3iKUYFxGn59JfXklg03BqP1vvb871O0P/ooHHv2uLeZhw9H2k03wTKhBI12O1BXF9YxGKPht6FFjGodp1VVVdLDLmIwWDLvtttuC/lANpsNmZmZfveH03a0vp0NJ+vqb58RvvWKVjY5FjL48Roj0egnYyT0fXoRqzGipF57dy9uW/4F3t24z73t58cOQcX5xyItKcFdP17PJfy8kV/WV5lI/d7icfxXU1Pjt9/i92wymVBQUBBwcB+ojJw2jECr1xGJ46rRZihtKK2jRvzFU4wKjNPw6yupJ7dsuDEY6fe1t74edfdXoPXdd70XuJgzB7lz58CcrN68xozR8NvQIka1jtPy8nLpIcZaOTk54a1me/vtt0tZR6GiokIaBM2cOVOaa0VMcDxhwgRUV1cHHNTp+dvZWbNmYerUqSFlXf3tM8K3XtHoY6xk8MPJzBs5RqLRT8ZI6Pv0IlZjRG693dYuzH+7Ft/v75CemwBcdcow/GriELQ2N6JVQXuxei7h5438sp5lli5d6veb2WiIxfGf+L0Hep/EwDzcMnLaMAKtXkckjqtGm6G0obSOGvEXTzEqME7Dr6+kntyy4cZgJH6/0gIXr7+OuocfgaOlxb09beJEDBELXBQVIRIYo+G3oUWM6uFc6qtdxcm8vLw8FBcXY86cOdLzBx54QBrILVu2DOeffz62bNkiTXJstImOXd/OioGzmJA8lKyrv31G+NYrGn2MlQx+OJl5I8dINPrJGAl9n17EaozIqffJlgZc+/p3aGrvkZ6nJZnx6IzjUXrUkJDai9VzCT9v5Jf1LBPom9loiNXxHxERxZfO777D3jvuRMfnn7u3WbKzUTh/PrKm/lL63CUyAsXJPBHcroGcIAZtpaWl0kBOKCoqQm5uLozGM4saTtbV3z4jfOsVjT7GSgY/XmMkGv1kjIS+Ty9iNUb81RNXTb30yXbc/fbXsDv6JsgblZeGhT8fhZOOGMJziQ/8vJFfdmAZrd7XWB3/ERFRfHC0t6P+ySfR+MJSwOMq96ypU1EoFrjQ4Isyoqgm88QfLS7idovm5maUlZV5lWE2m4iI4kFXrx13/vUrvLZ2h3vbqWML8KeZx6OzpUnTvhGpieM/IiIyqpb338e+P9yDnt273duSRo/GkLvuQvpJJ2raN6KoJfM8b+1YtWqVNHAT38z6G/ARERHForqWTlz98nrUbD+QtJt3ahHmTzkCJjjReWAKFiLD4/iPiIiMpmdfHfbddx9aVqxwbzMlJSFv3lxpkQtzUpKm/SOKajLv+++/R0tLCzIyMqRbLMSkxyeccIJ7/5o1a6Q5VYiIiGLVFzubMffFGuy1dUrPkxPMWDTtOJx7wnDpuaP/dluiWMHxHxERGYXTbkfTK6+i/tFH4Whrc29PO/lkDLnzDiSPHq1p/4jUoHjilQULFuD000+X5kVZv369tHKZ8MYbb2DGjBnSLRdr165VpXNERER685cNuzDtmf+6E3lDs1Kw/KpT3Ik8oljE8R8RERlB59dfY9vMC7Dv3nvdiTxLbi6GLarAIVXPM5FH8XtlXlZWFtatW4etW7dKAzrx3DXxsRjoiQcREVGsEYtbPP7hTvy5Zp9728RROXjq4hIUZCRr2jeiSOP4j4iI9Ewk7uofexyNL70kbpFwb8+ePg2Ft9wirVhLFNfJPJfRAzLa48aN87rVgoiIKFZY23tw3avr8eHm/e5tF554CO4+52gkJeh31VgitXH8R0REetOyejX23vNH9O7d696WdFgxht59N9JKSjTtG5HuknmBVFRUYNKkSZFomoiIKKo272vBnBfXYVtDu/Q8wWzCXeccjUtOPlTrrhHpitHGfw6HQ3r42ycW9PC3X04ZOW0YgVavIxLHVaPNUNpQWkeN+IunGBUYp+HXV1JPbtlwYzDY/p49e1B330K0rl7t3mZKTkbe1Vcjd9Zl0mIXeolvxmj4bWgRo3o5l/pqO6RknvjmVcyV0tjYeNC+5uZmaZUzIiIio1v19T7c+PpnaO3qlZ5npybgmUtKcHJxvtZdI4q6WBv/lZSUwGKxYPbs2dJj4KDZarVKg3Oz2ffVt8HKyGnDCLR6HZE4rhpthtKG0jpqxF88xajAOA2/vpJ6csuGG4P+9jt77eh66y10PP880NHh3p4wcQLSbrwR9uHDUd/cDD1hjIbfhhYxqvW5tKqqSnrY7fbwk3lLlizBvHnzpFXMxJwpREREsUZ8GD/5r+/x0MpNcPYvTHvU0Azce9ahOH40P/so/sTi+K+mpgaZmZk+94mBuclkQkFBQcDBfaAyctowAq1eRySOq0abobShtI4a8RdPMSowTsOvr6Se3LLhxqCv/Z0bN2LvnXeh65tv3OUseXkoXHA7Ms46SyqvR4zR8NvQIka1PpeWl5dLD5vNhpycnPCSeeIb2dra2oPmTPF0xhlnhNZTIiIijbV39+K26i/wjy/3uLf9/LihqDjvGLQ2H3xFElE8iMXxnxhwBxp0i4F5uGXktGEEWr2OSBxXjTZDaUNpHTXiL55iVGCchl9fST25ZcONQdd+Z3s76h/9E5peecV7gYsLZqLw5pth8fPljJ4wRsNvQ4sY1cO51Fe7ipN5ZWVlAQdywvTp05U2S0REpLkdje3S/Hjf7m2Rnosvd28943Bcc1qxdLVeq9YdJNIIx39ERKQFMf5q+ec/pbnxeuvq3NuTx47FkLvvQprHQkxE8SQiC2DMnDkzEs0SERFFzMe1+3Htn9ejqb1Hep6RnIA/XXgCJh0x2D2YJCL/OP4jIiI19ezahbbf34HmTz5xbzOlpKDg+uuQ+6tfwZSYqGn/iLSk+BrA8ePHSxMgBzJnzpxw+kRERBQ1Ikm39ONtuPS5T92JvKL8dLx17Y/ciTyieMfxHxERRYuzpwcNzz2Hreecix6PRF76qT9F0d//jrwrrmAij+Ke4ivzJk+eLA3mxLevEydORFFR0UFljLaaGRERxaeuXjvu+MtXeH3dDve20w4vwJ8uGIesVA4SiVw4/iMiomjo+Owz7BELXHz3nXubpaAAQ377W2RMOUO3C1wQ6T6Zt2HDBpSWlronQ/aF/8CIiEjv6lu6cPWf12P9D83ubVedWozbphwOi5mfY0SeOP4jIqJIsttsqHvkETS/9rq4baJvo8mE5F/+EiNvL0diVpbWXSQydjJP3EJRUVEh3W7h61vZpqYmzplCRES69vXeNvzmnY3Ya+uSnicnmLFo2nE494ThWneNSJc4/iMiokhNd2J7913U3X8/7PX73duTjzwSg++8Ay1DhsCSkaFpH4liIpknvpW97bbb/O4XK52N44oyRESkU3/ZsAu3v/kduu193/oOzUrB4ksn4NgR/MaXyB+O/4iISG3dO3agVSxw8emn7m2mtDQUXH89ci+9BE6zGS0eK9gSURjJvMMOOyxomWXLliltloiIKKLsDicq3vsWiz/Y4t42cVQOnrq4BAUZyZr2jUjvOP4jIiJVF7ioegH7n3wSzq6+uySEQZMmYcjvfovEYcP6yjkcGvaSKMZWs5Uug7XZApZZsGBBOH0iIiJSlbW9B7OqPvVK5F04cST+fOXJTOQRycDxHxERqaF9/XpsPe881D/8sDuRlzB4MEY88ThGPvWkO5FHRCon88ScKYsXL8abb77pd1DH1cyIiEgvNu9rwblPfoQPN/fNw5JgNmH+pENw79RjkJSg+GOQKC5x/EdEROGwNzdjz+/vwPaLLkbX5u/7NprNSJ42DaP//jYy+hdZIqII3WY7ZswYNDY2orn5wOp/REREerTy63248bUNaOu2S8/z0pPw5EXjMCq9V+uuERkKx39ERBTyld1v/x11FRWwNza6t6ccfTQG330XbPn5MKena9pHorhI5jU0NEiTIIuVzPLy8g7av3//fjz77LNq9Y+IiCikgeMTa77HQys3ubcdNTQTi39VgmFZKajjZMpEinD8R0RESnVv247W3/8ezTU17m1mscDFTTch56IL4TSZYOOYjCg6yTwxiAs2wfHWrVtD6w0REVGY2rp6cdvyz/HOl3vd284+bigemHY8UpMscHAyZSLFYnH8J84F/s4HYrv4UiDQ+SJYGTltGIFWryMSx1WjzVDaUFpHjfiLpxgVGKfh11dSL2hsdXej6fnn0fBMJZzd3e7tg8pKUbhgARKHDIGTMWrY4xrhXOqQWdYo51JfbStO5lVXVwctU1FRobRZIiKisO1obMecF9fh270t0nOTCbhtyuG4+tRimMQTIgpJLI7/SkpKYLFYMHv2bOkxcNBstVqlwbnZ7HtuzWBl5LRhBFq9jkgcV402Q2lDaR014i+eYlRgnIZfX0m9QGV7Pv8c7Q89DMcPP7i3mQoLkXbjr5F4yiloEhv6r8ZjjBrzuEY4lzpkltX7ubSqqkp62O19UwYFTOZNmTIFK1as8NvY6NGjgx7QX5lgbRMREYXq49r9uPbP69HU3iM9z0hOwJ8uPAGTjhisddeIdC8ex381NTXIzMz0uU8MzMUXAAUFBQEH94HKyGnDCLR6HZE4rhpthtKG0jpqxF88xajAOA2/vpJ6vsqKBS7qHngQrW+9daCgxYLkaedjxC23IGHQIMXHZIzq87hGOJc6ZJbV+7m0vLxceojFx3JycgIn87Zs2aLqwaPVNhERxSfxLdiL/92OP/z9a9gd4qYNoCg/HYt/NQGHFR48cCSig8Xj+E8MuAMNusXAPNwyctowAq1eRySOq0abobShtI4a8RdPMSowTsOvr6Seq6z4af3LX1G3aBHsTdJ1d5KU44/D4DvvhC03V0rkhRqDjFF9HtcI51KTzLJGOJf6ajfB1x9FCxYsUP3gol0iIiI1dfXaccdfvsLr63a4t512eAH+dME4ZKUmato3IiPh+I+IiJTq3roV++7+A9o//dS9zTxoEApuvgk5M2dygQuiCDoomVdZWRmxg5WVlUWsbSIiii91tk5c9XIN1v/Q7N521anF0hx5FjPnxyNSguM/IiKSy9HVhY6qF9D8yitw9vRNbyJknHUmBosFLgoLpefOGFi4gsgwybzJkydr0xMiIiKZPt/ZjKtf3oC9tk7peXKCGYumHYdzTxiuddeIDInjPyIikqPtk0+w58670LN9u3tb4vDhGHLnHRj0059q2jeieKJ4NVsiIiItvftNAxau/gHdvX3f9g7LSkHlpRNw7IgsrbtGREREFJN6GxtRV1EB61//dmBjQgLyZs9C/jXXwJyaqmX3iOJOzCXz1q9fj1WrVkn/vXbtWlRUVKCoqEjrbhERUZh67Q7c/+63ePajbe5tE0fl4OlLSpA/KFnTvhERERHFInGrrPXNN6WVau1Wq3u75ZijMfKPf0TqEUdo2j+ieBVzyTyRyJs/f77034sXL5bmaamtrdW6W0REFAZrew+ue3U9Pty8373topMOwV2/OBpJCcZf3YyIiIhIb7q+/x577roLHetq3NvMmZnSAhddP/0pkocM0bR/RPHMHGtX5S1cuND9fMaMGdiyZYv0ICIiY9q8rwXnPvmRO5FnMQP3nHs07pt6LBN5RERERCpzdHai7tFHsWXqeV6JvMyzz0bxO/9A9owZMJk5BiPSki6vzBNX1Imr6cQtsgOJxJzYXlxcLD3Pzs7G3Llzpf8eP348qqur3WUbGxuln7m5uVHrOxERqWfl1/tw42sb0NZtl57npSfhj2eNwpTxh2jdNSIiIqKY0/af/2DfPX9Ezw8/uLclHnJI3wIXP/qR9NzBVWqJNKebZJ4rSScsW7bMnaAbWKakpARbt26VknhCeXk5Fi1a5L61trS01F2+srJSasdVloiIjMHpdOKJNd/joZWb3NuOGpqJykvGI7GnRdO+EREREcWa3vp6tN5zD5pWrzmwMTEReVdegfx582BOSdGye0Sk12SeWKRCJN+EdevW+Swjkn0Dk3MLFixATk6OO5nnsnz5cjQ3N7vbJCIiY2jr6sWt1Z/j3Y173dvOPm4oHph2PJITTKirYzKPiIiISK0FLpqXVaPu4YfhsNnc21MnlGDo3Xcjuf+OOCLSF0Pd6C6u2HPdXuviSuy5VrB1/be4xdaVyBNJPSIi0r8dje04/+mP3Yk8kwmYf+bhePzCcUhNsmjdPSIiIqKY0fndJmy/6GLsvesudyLPnJWFoff+EYe++CITeUQ6ZphknkjIiYe4gm8gkdATi18I4qe4HVcsfiHKi/n3iIhI/z7+fj/OeeIjfLu378q7jOQEPHfZBFxz2mEwiaweEREREYXN0dGBuocewtbzz0fHZ5+5tydNOQOj//F3ZJ9/Phe4IIrV22y3bdsmJc7EohOjRo2Stq1ZswaTJk1CJARakVYscNHQ0OCeU0+YN2+ee7+v+fcGys/PP+iPxY6OjoPKick+xVxOvib99LcvUB29iEYf1ThGKG0oqSOnbLAysRoj0egnYyT0fXoRSh9F+Rf/ux1/fOdb2B1Oadvo/HQsvmQ8igsHebWlVYworcdziX/8vJFfNjU19aBtoo6Woj3+IyIidbV+8AH23v0H9Oza5d6WNGoUCu/4PdqKipDAxSOJYjeZd9VVV0lXvInkl5jH7tZbb3UPMMUcdgsXLkS0ua7aU2OQK9oQr62uru6gfWLQbbVapTLmAd9W+NsXqI5eRKOPahwjlDaU1JFTNliZWI2RaPSTMRL6Pr1Q2sfuXgce+NcPePurBve2U0Zl4u4zRyMD7airaw+rfTX6GEo9nkv84+eNsrKuMYke6HH8R0REfRxdXWh57z3YVq1CZ309egoKkFlaiowzz4Q5ORk9++qwb+FCqYyLSSxwMW8e8uZcKS120ebj718iipFk3gMPPCBdAVdTU4Nx48ZJz10mT56MCRMm4MEHH3QP8NQSaEVaMT9euETiLjMzUxpc19fXo6CgwO8fV2IQ62u/v32B6uhFNPqoxjFCaUNJHTllg5WJ1RiJRj8ZI6Hv0wslfayzdeLGVzZg/Q8H5jW96tQi3FI2FhazSVcxorQezyX+8fNGftm2traDxiQ2m01a+CvatBr/ERFRcC1r1mD37Qv65r0TnxcOB1rNZrSuXAXzvfch86wzYfvHO3C0trrrpJ10EobceSeSi0ZLz/V8VT8RqZDMW7t2Lf75z3+6nw/8tjgrK0t6qE3cSutvMQuxLVCyTw4xSHYNlMVr8nw+UKD9/vYFa1MPotFHNY4RShtK6sgpG68xEo1+MkZC36cXcvr4+Y5mzHupBnttndLzlEQzKs4/DueeMFyV9iPVhhHiJFZiRA/H0OO5RKv3VavxXySJP1xDuc1dbhkj3PYuh1avIxLHNcIt+HLLM0a9xXOctq5Zg13X3+DZgNdPkeBrfn2Ze7clJwcF829D5jnnSOdy13HUnipCTjnGqDGPa4RzqUOlGJVTJhrvra+2FSfzJk6cGLSMuG1EbSJZJx7+rsIrKytT/ZhERKS+N9fvxO1vfindYisMy0rB4l9NwDHDjZUIIIonWo3/IknMs2yxWDB79mzpEc1b5Y1Eq9cRieMa4RZ8ueUZo97iNU6dXd2w3r6g/0nw6aYSp5yBtGuuQVdWlnTld6jHlVs23BhkjOrzuEY4lzpUilE5ZSL53lZVVUkPu90efjJvYDLN1xx1tbW1iASxQu3Atl0LY5SWlkbkmEREpI5euwMV732LJR9udW+bOCoHT19SgvxByZr2jYj0O/6LFHHLsJhiRYtb5Y1Eq9cRieMa4RZ8ueUZo97iNU6tf/sbmj1unQ0m7/RJyBozJuzjyi0bbgwyRvV5XCOcSx0qxaicMpF8b8vLy6WHr2lWFCfzxODtueeewxVXXHHQbRbiAHPmzAn7Kjlx26yv22nFixBti0mXXSorK6WHWrdahHMJpb99Rrg8OFqXhsbC5bjxGiPR6CdjJPR9euGvj83t3bjhtc/w0fcHFrq48MSRuPPso5CUYJb9mrSKEaX1eC7xj5838sv6KqPVexuN8V+0hXsbvJwyRrjtXQ6tXkckjmuEW/DllmeMeovHOG1bvcY9R15QZjPaVq9Gzi/PDfu4SsqGG4OMUX0e1wjnUpNKMSqnTKTfW1/tKk7m3X///TjssMOkn+JqONeVcWIulVWrVkkTIF955ZWKOyeSd2IVNPFTtLlsWd99/cXFxZg/f77032K12urqaimpJ273EOXy8vIwd+5cqHWrxaxZszB16lSuLqjTY+jhctxwLrM1coxEo5+MkdD36YWvPm5p6MD8v9Vip7VLem4xA7ecdgjOO64AzY37w25fjT6qXY/nEv/4eSO/rGeZpUuX+r3NIhoiNf4jIqLQ9TY1yUvkCQ4H7AabDoGI/FOczHPdliAGbK4r4lauXCn9FFfM3XbbbaE0Kc2H57riLtCVduPHj5cekbrVQgycuZpt5P64ioXLccO5zNbIMRKNfjJGQt+nFwP7uPLrfbh52Xdo6+5LQOSlJ+HJi8bhxNG5qrQfzTaMECdGjBG9HkNv55JAt1lESyTGf0REpJyjuxvWN99E58aN8iuZzbAYbKEiIlI5mSdWKxNXyIlvi9etWyddMTd6dN+S1kbleUkkVxeMXB9j5XLceI2RaPSTMRIbq9kCJjzxr1o8vHKTe/vRwzKlhS6GZ6caMkaU1uO5xD9+3sgvO7CMlu9rLI7/iIiMxNHRgeZly9Dw3PPoratTWNmBjDLOM08U18k8z0Hd5MmTD9q+Zs0aTJo0KZymiYjIoNq77bju1Q1476t97m2/OH4YFp1/HFKTLJr2jYjCx/EfEVF02Vtb0fTKq2h84QXYByxIhIQEoLc3cAPii6GMDGRMmRLRfhJR9ETk613PBSqIiCh+7Ghsx5xl37kTeeIivfIzj8BjF5zARB5RjOP4j4hIXfbmZtQ//gS+nzQZ9Q8/7JXIG1Q6GaOqqzHiscf6BlweCxN56d8+7P77YU5OjlbXiUiPV+aJb17FbRaNA78V6F/IQkyETERE8eXj7/fj2lfWo6m9R3qekZyAxy4ch9OPKNS6a0SkAo7/iIiiw9HUhPqXX0bzK6/C0d5+YIfZjMwzz0TevHlIOXyse/OIJ5/A7tsXwGGzHVjdtv+nuCJPJPIyJp2uzYshIn0k85YsWYJ58+ZJC1bk5oY2gbkeiUmmXQ+xapz46a+cv/3+9gVrUw+i0Uc1jhFKG0rqyCkbrzESjX4yRkLfpyXRpxf/ux1/fOdb2B1Oadvo/DQsubQERQWDVO2vVjGitB7PJf7x80Z+WV9ltHpvY3X8R0SkJz379qHh2WdhXVYNdHUd2GGxIOucc5A3dw6SfcxVmjFpEsZ8+AFaVqyAbeVKdNbvR0pBPjLLyqRba3lFHlHsUZzME9/I1tbWBpzw+IwzzoDRlJSUwGKxYNasWZg6dao0ePa3uqCY+NnXfn/7AtXRi2j0UY1jhNKGkjpyygYrE6sxEo1+MkZC36eV7l4HHvjXD3j7qwb3tonDU/HHs4sxyNmOujqPb5MNHCNK6/Fc4h8/b+SX9SyzdOlSVFVVwW7vWxk62mJ1/EdEpAfdO3eiYcmz0gq1zp6+OxwEU2Iiss4/D3lXzkHSiOEB2xAJO5Hwyzj7bNTV1aGwsFC3YwEi0iCZV1ZWFnTlsunTp8NoampqkJmZKQ2c6+vrUVBQ4PePK7GynK/9/vYFqqMX0eijGscIpQ0ldeSUDVYmVmMkGv1kjIS+Twt1tk78+s8bsGFHs3vbvJ+OxqXHZ2PI4MKYihGl9Xgu8Y+fN/LLepYpLy+XHjabDTk5OYi2WB3/ERFpqWvLVjQsXgzr228Dnl/WJCcj54KZyLv8ciQOHqxlF4koFlez9WfmzJkwGjGQdg2mxcDZ8/lAgfb72xesTT2IRh/VOEYobSipI6dsvMZINPrJGAl9XzR9tqMZ815ah322vltAUhLNqDj/OPziuKHSt8GxGCNK6/Fc4h8/b+SXHVhGz++rEcd/RERa6PzuOzRUVsL27ntivhL3dnN6OrIvugj2n52FwsMP1/U5n4i0pfjsMH78eGkC5EDmzJkTTp+IiEjH3qjZiRmV/3Un8oZlpWD5Vafg3BMC3/5BRMbF8R8RUfg6vvwSO669DlvP/SVs77zrTuSZs7KQf/11OGzNahTcdCPMGlyBTUQxfmXe5MmTpcGc+PZ14sSJKCoqOqgMVzMjIoo9vXYH7n/3Wzz70Vb3thNH5eKpS8YjfxAnViaKZRz/ERGFrn3dOux/phJtH33ktd2Sl4e82bOQfcGFsAxKl7bpeRErIjJwMm/Dhg0oLS11T4bs75YQIiKKHc3t3bj+1Q34cPN+97aLTzoEd/7iaCQl8BYQoljH8R8RkTJi8aL2//4X+596WkrmeUoYPBh5V1yB7OnTYE5N1ayPRBRHyTxxC0VFRYV0u4Wvb2Wbmpo4ZwoRUQzZtK8Fc15ch+0NfSvTJphNuOuco3HJyYdq3TUiihKO/4iI5CfxWv/1PvZXPoPOz7/w2pc4fDjy5s5F1tRfwpyUpFkfiSgOk3niW9nbbrvN736x0tm4ceNgNOJyZtdDnID9Xd4caL+/fcHa1INo9FGNY4TShpI6csrGa4xEo5+MkdD3RcrKr/fh5mWfo627b4W1vPQkPHnROJw4OleTPmoVI0rr8VziHz9v5Jf1VUar9zZWx39ERGpx2u1oWblSup2269tvvfYljR6NvHlzkfXzn8OUmKhZH4kojpN5hx12WNAyy5Ytg9GUlJTAYrFg1qxZmDp1qjR49rV6kBhEW61Wn/v97QtURy+i0Uc1jhFKG0rqyCkbrEysxkg0+skYCX2f2hxOJ6r+twdLPtnj3ja2IBWLfnEYhqT3SivWxlOMKK3Hc4l//LyRX9azzNKlS1FVVQW7vS+xHm2xOv4jIgqXs9cO69/+hsbFS9C9ZYvXvuSxY5F/9VXIOOMMmCwWzfpIRLFHcTJPDChtNhsyMzP9llmwYAEWLlwII6mpqZFekxg419fXo6CgwO8fV2JOGF/7/e0LVEcvotFHNY4RShtK6sgpG6xMrMZINPrJGAl9n5raunpx6/IvsOKrfe5tZx83FBXnHYvUJEtcxojSejyX+MfPG/llPcuUl5dLDzEGy9FglcNYHf8REYXK0d2N5rfegq1yMZp37/bal3LssVISb9Bpp8Gk089jIorDOfMefPBBab4UccuFr0GdWM3MaIM5MZB2DabFwNnz+UCB9vvbF6xNPYhGH9U4RihtKKkjp2y8xkg0+skYCX2fGn5oaMfcl9bh270t/ccD5k85AledWiR7cvtYjRGl9Xgu8Y+fN/LLDiyj1fsaq+M/IiKlHJ2daK5ejobnnkPv3r1e+1InlCD/qquR/qNTuCgQEekrmTdmzBg0Njaiubk5Mj0iIiJNfPz9flzzyno0t/dIzzOSE/DYheNw+hGFWneNiDTG8R8RxTt7axuaX38NDVUvwL5/v9e+tFNOQcHVVyFt4kTN+kdE8UVxMq+hoUH6RlZ8M5uXl3fQ/v379+PZZ59Vq39ERBRh0nxcH2/DPf/4BnaHU9pWlJ+OJZdNQHHBIK27R0Q6wPEfEcUru82GxpdfRtPSF2G3Wr32pZ9+GszTp2PYaafp+op4Ioo9ipN5YhAXbILjrVu3htMnIiKKkq5eO37/l41Ytm6ne9vphxfg0QvGISuVq60RUR+O/4go3vQ2NqJx6Yto+vOf4WhtPbDDZELGmVOQP28eksaO9bsoGBGRrpJ51dXVQctUVFSE2h8iIoqSOlsn5r1cgw0/HLht7prTinHLGYfDYuY8L0R0AMd/RBQveurq0Ph8FZpefx3Ojo4DOywWZJ39c+TNm4fkoiL3QkVERIZI5o0ePTpomdWrV+PKK68MtU9ERBRhn+1oxryX1mGfrUt6npJoxqJpx+Oc44dp3TUi0iGO/4go1vXs2iUtatG8/A04u7sP7EhMRPbUqcibcyWSRo7UsotERKEn8+SorKw03GBOfKvieoj5o/x9yxJov799wdrUg2j0UY1jhNKGkjpyysZrjESjn4yR0Pcp8eb6XfjNXzaiu7evnaFZKai8ZDyOGZ4VdtuxGiNK6/Fc4h8/b+SX9VVGz++tEcd/RETd27Zh/5IlsP71b0Bvr3u7KTkZ2TNmIO/y2UgcOlTTPhIRyU7mzZgxA5999hk2bdrktV1M7BmLy2yXlJTAYrFg1qxZmDp1qjR49jWJqRhEW61Wn/v97QtURy+i0Uc1jhFKG0rqyCkbrEysxkg0+skYCX2fHL0OJ574cCde23BgbpcThg/CfT8vQm5ilypzvsRqjCitx3OJf/y8kV/Ws8zSpUtRVVUFu92OSIqn8Z/rS1wtEvJGotXriMRxjZDol1ueMRr+a+na/D0aFi9Gy7vvigbc202pqci56ELkXHYZEvLz3e2rddxgwm1TL19ayinHGDXmcY1wLnWoFKNyykTri2rZybyamhppImObzYbMzEyvCZDFambFxcU+64kXYcQ5U8TrFa9T/JLq6+tRUFDg948rMZj1td/fvkB19CIafVTjGKG0oaSOnLLBysRqjESjn4yR0PcF09zejVte+wz/+b7Bve2iE0fijrOPQlKCeu9lrMaI0no8l/jHzxv5ZT3LlJeXSw8xLsvJyUGkxNP4z/VF7uzZs6VHNBPyRqLV64jEcY2Q6JdbnjEa+mvp3bQJnS+/jJ4PPvTabkpPR/K085F83nlwZmWhUfzxHOSLTj3Gaaj11f5CSk45xqgxj2uEc6lDpRiVUyaS7634Itffl7l+k3m1tbVShzwHckJ2djaeeeaZgAdct24djEb80l2/eDFw9nw+UKD9/vYFa1MPotFHNY4RShtK6sgpG68xEo1+MkZC3+fPpn0tuHLpOvzQ2C49TzCbcNc5R+OSkw9FJMRqjCitx3OJf/y8kV92YJlIv6/xNP5zfZGrRULeSLR6HZE4rhES/XLLM0aVv5aOzz5DwzOVaPvgA6/tlpwc6Sq87AsvgCUjQ/XjKhVum3r50lJOOcaoMY9rhHOpQ6UYlVMmku9toC9zA86Zl5WV5XNy42CM9s0sEVGsWvHVXtz8+mdo6+77NicvPQlPX1KCE0fnat01ItKpeBn/hZtsl1PGCMl1ObR6HZE4rhES/XLLM0aDvxZxpUz7/z7F/meeQfsnn3iVTygoQO4VlyNnxgyY09JUPW64wm1TL19ayikX7zFq1OMa4VxqUilG5ZSJ9Hvrq90ENQZ4oax4RkREkeNwOPH4mu/xyKoD814dPSwTi381AcOzUzXtGxEZD8d/RGQkIoknrsDb//Qz0hV5nhKGDUX+nDnIOu88mJOTNesjEVE4FCfzBs6hIoi5VcQKZvn5+Rg/fjwmTZoUVqeIiCh0bV29uGXZ53jvq73ubb84fhgWnX8cUpMsmvaNiIyJ4z8iMgKnwwHbqlXSlXhdX3/jtS/x0EOQP3cess75BUyJiZr1kYhIDYqvAZwzZ47Pb2Lvv/9+3HrrrdK3IA8++KAqnSMiImV+aGjH+U9/7E7kicUnbz/rCDx2wQlM5BFRyDj+IyI9c/b2onvVKmz75VTsuuHXXom85DGHYdiDD6L4nXeQff55TOQRUXxemScGa4FMnjwZq1atCqdPREQUgo+/349rXlmP5vYe6XlGSgIeu2AcTj+iUOuuEZHBcfxHRHrk7O6G9e23sb9yMXp++MFrX8pRRyHv6quQMXkyTDEw3xoRkSfFZzUxsV8gn332GQdzRERR/iO76j9bcenzn7oTeUUF6fjLtT9iIo+IVMHxHxHpiaOrC42vvILvzzwTe377O69EXuq4cRi5uBKj3liOzLIyJvKIKP6uzNuwYYM0F8q6deukeVGE5uZm5OXl+Swv9gmiDhERRV5Xrx2/e2sjqmt2uredfngB/nThOGSm8DYSIlKO4z8i0itHezuaXl+GxuefR299vde+hPHjMPT665F+8slBv4AgIorpZN64cePwzDPPSP8tvm2dPn06srOzpZ++iH1lZWXSrRZG43A43A9xlYv46a+cv/3+9gVrUw+i0Uc1jhFKG0rqyCkbrzESjX4yRnzv6+qx452Ne/HPr/aiztqOwqwdOOPoIZhwaDZufP0LbNjR94e0cPWpRbi5bCwsZpMm8RSrMaK0Hs8l/vHzRn5ZX2Wi8d7G0/iPiIzB3tKCpj+/gsalS2FvavLal37qT5E3dy5ahg9HWmEhE3lEFBdkz5lXWlqKmpoa3H777e4BXiwpKSmBxWLBrFmzMHXqVGnwbPZxSbYYRFutVp/7/e0LVEcvotFHNY4RShtK6sgpG6xMrMZINPrJGDl43we1zbjnn9vQ0mWH2QQ4nIB5dytWfF0HMVR1zWKVnGDC78pGoezwHDTs9/6mOppiNUaU1uO5xD9+3sgv61lm6dKlqKqqgt1uRzTF+viPiPStt6kJTS+9hMaXXoajpcVrX8YZZyBv3lykHn20dL5sqavTrJ9ERLpeAKOoqAgzZ85ELBID1czMTOmDoL6+HgUFBX7/uBLf9vja729foDp6EY0+qnGMUNpQUkdO2WBlYjVGotFPxoj3vjXf1aP877XujJ1jwE9XIi8nLRFLZ0/EMcOzoLVYjRGl9Xgu8Y+fN/LLepYpLy+XHjabDTk5OYimWB7/EZE+iVtoG154AU2vvgZne/uBHWYzMn/+c+TPnYPkMWO07CIRkbFWsz3//PMRi8RA2jWYFgNnz+cDBdrvb1+wNvUgGn1U4xihtKGkjpyy8Roj0egnY6RvX4/diVuXfyFl7AKvIQn0OpwYOyRTN7ETqzGitB7PJf7x80Z+2YFltHpfY3X8R0T60rNnDxqeex7N1dVwdnUd2JGQgKxfnov8OXOQdOihWnaRiMiYyTwiIoo8MUeeraNXVtmWzl68u3EPpo4bEfF+EREREamte8cONCxegua//AXo6XFvNyUlIXvaNORdcTkShw/XtI9ERHrCZB4RkQ798+t97jnyghHlVmzcx2QeERERGUpXbS0aFi+G9e//ADzmBDWlpiLngguQO3sWEgsLNe0jEZEeMZlHRKRD+1u6ZCXyBFGuuaM70l0iIiIiUkXnN99gf+VitKxYATgPDHjMgwYh55KLkXvZZUiI8vygRERGwmQeEZGOWDt68MzHu/DZjmbZdcSVedmpSRHtFxEREVG4Oj7/HPufqUTrv/7ltd2SlYXcWZch5+KLYcnM1Kx/RERGwWQeEZEOtHT24PmPtuHZj7ZIc+ApIa7Mm3LM4Ij1jYiIiCgc7WvXYv/Tz6Dt44+9tlvy85E3ezZyLpgJc3q6Zv0jIjIaJvOIiDTU1tWLpf/dhsUfbEFz+4EJnxPM4oq7vlVtA91tawKQmZqAs44ZGpX+EhEREcnhdDrR9tF/sP+ZZ9BRU+O1L2HIEORdeSWyp50Pc0qKZn0kIjIqJvOIiDTQ2evAsx9tReW/t6Ch7cB8dxazCT87Mhe3/ewYbNrXhjkvrYPJCZ8JPVP//z00/QSkJFqi2X0iIiIin5wOh3QbrbgSr3PjRq99iSNHIm/uHGSfe660Ui0REYWGyTwioijq6rXjlU+244k1m9HQ3us1790vxw3HdacXI83ehsKcNBySNwiLL52AW6s/g7Wj1726reunuCJPJPJKj+IttkRERKQtp90uLWgh5sTr2rTJa19ScTHy581F5s9+BlMC/wQlIgoXz6RERFHQ3etAdc0OPLHme+yxdrq3m0zA2ccNw68nj8FhhYPgcDhQV9fm3l921GD87zeleHfjHry3cS/qrW0oyErHmccMkW6t5RV5REREpCVnTw+sf/8HGior0b1tm9e+5COPRP5VVyGjrBQms1mzPhIRxRom84iIIqjX7sCbG3bhsdWbsbOpw2vflKMH4+ayw3H4kIyAbYiE3dRxI3Du8cNQV1eHwsJCmDkgJiIiIg05urthffMtNCxZgp5du7z2pRx/nJTEG3TaaTCJby6JiEhVTOb1E1fDuB5islbx0185f/v97QvWph5Eo49qHCOUNpTUkVM2XmMkGv2MpRiRknjrd+Lxf9Vie0O71/7TDy/AZePz8OOjD5WScp5thRI/ehKrMaK0Hs8l/vHzRn5ZX2X0/N4SUXxwdHSguboaDc89j959+7z2pZ14IvKvvgppJ5/MJB4RUQQxmdevpKQEFosFs2bNwtSpU6XBs68rX8Qg2mq1+tzvb1+gOnoRjT6qcYxQ2lBSR07ZYGViNUai0c9YiBGH04nV3zVi8X93YYf1wOq0wsmHZuLKk4fhqMGpUhviKju5MRLqa4u2WI0RpfV4LvGPnzfyy3qWWbp0KaqqqmC320N6PURE4bK3tqHp1VfQWPUC7I2NXvvSf/IT5F81D2klJZr1j4gonjCZ16+mpgaZmZnSwLm+vh4FBQV+/7gS3zL52u9vX6A6ehGNPqpxjFDaUFJHTtlgZWI1RqLRTyPHiPhje+U3dXh01WZ8u7fFq87/FeXixtIxmDgqN+jxQt2nF7EaI0rr8VziHz9v5Jf1LFNeXi49bDYbcnJyQnpNREShsFutaHzpZTS+9BIcVqvXvkGlk5E/7yqkHnuMZv0jIopHTOb1EwNp12BaDJw9nw8UaL+/fcHa1INo9FGNY4TShpI6csrGa4xEo59GixGRxHv/u3o8vHITvtzlPcAtOTQHt5wxFqcU5ys6Xqj79CJWY0RpPZ5L/OPnjfyyA8vo+X0lImNwdHWh5b33YFu1Cp319egpKEBmaSkyzjwT5uRkd7nehgY0vrAUTa+8AkfbgcW5xOpdmWedhbx585By+FhtXgQRUZxjMo+IKAQiiffh5r4k3oYfmr32HT8iC5dPLMTZE4ql2/eJiIiI9KBlzRrsvn0BHDab+HZAXAKMVrMZrStXwXzvfRh2//1IOfooND7/PJpeXwZnZ+eByhYLss45B3lz5iC5aLSWL4OIKO4xmUdEpND6nS2o+ssWrN3W5LX96GGZuLlsLE4bmy/drs+Jn4mIiEhPibyd1153YINrQZ3+n46WFuy85hopaQeP+TlNiYnIOv885F15JZJGjIh6v4mI6GBM5hERyVSzvQkP/fM7fFzb4LX98MEZuKlsDKYcPURK4HG1SSIiItLbrbXiijyJ0+m7kGt7fyLPlJKCnJkzkHv55UgcPDhaXSUiIhmYzCMiCuKLnc3S7bRibjxPRQXpuLF0LM4+dijMZl6FR0RERPok5siTbq2VadBpp2HovX9EQl5eRPtFREShYTKPiMiPr3fbpCTeqm/2eW0fkZWMm844HOeeMBwJFk5GT0RERPrWsmq1e468oMxm6dZaJvKIiPSLyTwiogE27WvBo6s24Z0v93ptH56diusmFeMnw5MwbOhgripJREREhmC3NstL5AkOB+xWa6S7REREYWAyj4io35b9bXh8zff42+e7vaaTGZKZgmsnHYaZE0YiwQzU1dVp2U0iIiIiZSwK/uwzm2HJyopkb4iIKExM5hFR3PuhsR2LVmzDe982wOGRxMsflIxrTy/GhScegpREi7SNi1sQERGRUTjbO1D3wINo/+QT+ZUcDmSUlUayW0REFCYm84gobu1q7sATazajet1O9Hpk8XLTk3DVqUW49ORRSE3qS+IRERERGYXT6UTLP/8J6733wVnvvYBXQCYTzBkZyJgyJZLdIyKiMDGZR0RxZ5+tE0/+63u89ukOdNsPXGmXlZqIuT8twmWnjMKgZJ4eiYiIyHi6f/gBe+/5I9o+/NC9zZSUhEFnlKHlH+/0bfCcT8RdyCT9GHb//TAnJ0etv0REpBz/WiWiuFHf0oVn/l2Llz/Zjq7eA0k8kbibeUIBrp9yNLLTOHglIiIi43F0daHh2WfRULkYzu5u9/b0H/8YQ+74PZIOOQQtP/sZdt++AA6b7cDqtv0/xRV5IpGXMel0TV8HEREFx2QeEcW8xrZuVH5Qixc/3o6OHrt7e1qSBbN/NApX/GgUulubkZmSqGk/iYiIiELR+p//YN8f7kH39u3ubQlDhiD5mqsx/PzzYbH0TRuSMWkSxnz4AVpWrIBt5Up01u9HSkE+MsvKpFtreUUeEZExMJlHRDHL2t6DZz/aguc/2oq27gNJvJREM371f6Mw76dFyBuULC1qUdeqaVeJiCgMW7ZsQXl5OZYsWYLs7Gytu0MUNT379qF+0SK0vPvegY0WC3Ivuwx5V1+F/W1tMPXfPusiEnZZ55yDjLPPRl1dHQoLC2EWV+cREZFhMJnXT/wx73qICWP9rVgZaL+/fcHa1INo9FGNY4TShpI6csrGa4xEo59qxUhrZy9eW70Zz/1nG1o6e937khLMuGjiSFx9WjEKMvq+eZbz714PMSL32FozSoyE0oYR4oQxot4x9Pp5o+f3ViurVq1Cbm4uli9fLiXziOKBs7cXndXV2Fr1Apzt7e7tqSUlGHLHHUg5fGzf+aKtTdN+EhFRZDCZ16+kpES6/HzWrFmYOnWqNHj29Q2V+FC0Wq0+9/vbF6iOXkSjj2ocI5Q2lNSRUzZYmViNkWj0M9z2xS20yzbU4eWavWjpOvAHb4LZhHOOycesiUNQmJEEZ4cVdR3GihGl/dSK3mMknDaMECeMkdj9vFm6dCmqqqpgtx+4ypj6lJaWSj95RR7Fi/b1G7D37rvQ9d0m9zZLTg4Kb7sNWb88Fyadnv+JiEg9TOb1q6mpQWZmpjRwrq+vR0FBgd8/rsSl6r72+9sXqI5eRKOPahwjlDaU1JFTNliZWI2RaPQz1PY7e+x4+X8/oPLfW9DQdmDCZ4vZhPPHD8d1pxdjRE6aoWNEaT+1otcYUaMNI8QJYyR2P2/ELaTiYbPZkJOTg1izePFi1NbWoqKiwucttGJ7cXGxO2k3d+5cDXpJpK3epibUP/wwmquXH9hoMiF7+nQU3nwTLExoExHFDSbz+omBtGswLQbOns8HCrTf375gbepBNPqoxjFCaUNJHTll4zVGotFPJe139drx2qc78OS/vkddS5d7u9kEnHvCMPx68liMyk+PmRhR2k+t6ClG1G7DCHHCGIntzxs9v69KuZJ0wrJly3wm6EQZcffE1q1b3VfeiaTmokWLMH/+/Kj3mUgLTnGV7ltvoe6BB2FvbnZvtxx2GIbf8wekjxunaf+IiCj6mMwjIsPp7nWgumYHnljzPfZYO93bxfzOPz9mKC4Zl4sTjzgkpv7oJSKKNUVFRaisrJT+e926dT7LiGSfSPJ53kK7YMEC6epEJvMoHnR+9x323nU3OjZscG8zp6cj/4Yb0D15MlKHDdW0f0REpA0m84jIMHrtDry5YRceW70ZO5s8Jr0DcObRQ3Bj2RiMLRwkrcxGRETGJ67YG3jrrSuxJxa+cM2XRxRrxKIWdRUVaHr5z4DHXJmZP/sZCm8vhyU/n+MdIqI4xmQeEeme3eHE25/vxp9Wb8bW/d6rsk0+ohA3lY3FMcOzpOdc6ZGIKDY0NzdLD3EF30Aiobd+/XqvZJ4oS2R0YsGblvdWwHrffXDu3+/enjRqFIbc8Xukn3KK9JzjHSKi+MZkHhHplsPhxLsb9+LRVZuwua7Va99PxuTj5rKxGHdI7E0ET0REffPl+ZObm4uGhgb3FXoisScsXLgQEydOxLRp04K2n5+fL81J6Kmjo8OdKBFJlUAJk2Bl5LRhBFq9jkgcV402Q2lDbp3u7dux79570f7Rf9zbTMnJyJs3DzmXz4Y5KcndBmPUG+M0/PpK6sktG24MMkb1eVy9n0vVjFE5ZdT+Haemph60TbQ/EJN5RKQ74mS14qu9eGTlJny7t8Vr38lFubjljMMxcVSuZv0jIiLtua7EE1fniYcac+i5blsUA3Kr1Sp9HgVabThQGTltGIFWryMSx1WjzVDaCFbH2dWNzldekR7o6XFvTzjpJKT9+gbYhw3D/gFXnjJGvTFOw6+vpJ7csuHGIGNUn8fV67k0EjEqp4xW7y2TeUSkG+IE+PFWK56v3oyNu2xe+yYcmoObzxiLU4rzNesfERFFj+eiFwM1NjaqkrjLzMz0uU8MzMVVewUFBQEH94HKyGnDCLR6HZE4rhpthtJGoDptH36IfX+8Fz07dri3JQwZgqRrr8GwX/4SFosl5H7ES4wKjNPw6yupJ7dsuDHIGNXncfV4Lo1UjMopo/bv2HWXgCebzSYt/uWJyTwi0kUS7z/fN+Chf36HDTu8v3k+fkQWbj7jcPx0zMG3QxERUewSt9L6mwtPbAuU7JNDDLgDDbrFZ064ZeS0YQRavY5IHFeNNkNpY2Cdnr17sW/h/WhZseJAoYQE5M26DLnz5mF/W5uUyGOMysc4Db++knpyy4Ybg4xRfR5XL+fSaMSonDKRfm99tctkHhFp6pMtDXh45SZ8utX7KoujhmZKc+JNPrKQSTwiojgkknXi4e8qvLKysqj3iShczp4eNL78Z+x//HE42tvd29MmTMCQO+9A8pgxffMutXkv+EVEROSJyTwi0kTN9iY8vPI76Yo8T8V5KbhlypE485ihMJuZxCMiimczZsxAbW2tz4UxPFeyJTKC9vXrUfeHe9C1aZN7myU3F4Xzb0PWuefyy0siIpKNyTwiiqovdjZLV+K9/1291/aignT8etJhmDjEgiGDBzORR0QUR8Rts75upy0vL5euwKuoqHBvq6yslB5ERtHb1IS2RYvQ9M67BzaaTMieOQOFN90ES1aWlt0jIiIDYjKPiKLi6902PLJqE1Z+vc9r+yG5afj15DE494RhEPk710qCREQU20TybuHChdJPcbXdsmXLpO3FxcXulWmLiopQXV0tJfUmTpwolcvLy8PcuXPDPr64lVG6ndHPPjGfq7/9csrIacMItHodkTiuGm0qacMpVjh84w3UP/wIHFare3vyUUdh8B2/R+pxx7nbVHoMxqg3xmn49ZXUk1s23BhkjOrzuNE+l2oZo3qJU19tM5lHRBG1eV+LlMR758u9XtuHZ6fi+kmH4fySEUi09E3oGQsf1EREJI+YD891xV2gK+3Gjx8vPdRWUlIiLTAwe/Zs6eFJfB5ZrVZpcB5odbtAZeS0YQRavY5IHFeNNuW20bv5e7Q/8gjsX399YGN6OlKvvALJ55yDFosFLX6+wFQj/uIpRgXGafj1ldSTWzbcGGSM6vO40TyXah2jWsdpVVWV9LDb7QftYzKPiCJiS30r/rR6M/72+W44nQe2D8lMwbWTDsPMCSORlGDsD2UiIjKumpoaZGZm+twnBuZi/rKCgoKAg/tAZeS0YQRavY5IHFeNNoO1YW9tRcPjj6Plz6+Iwu7tiaWlGPG73yKpsFCVfjJGvTFOw6+vpJ7csuHGIGM0fs+leolRreNU3JkgHjabDTk5OV77mMwjIlXtaGyXknhvrt8Jh0cSL39QMq45rRgXnXQIUhItWnaRiIhIGnAHGnSLgXm4ZeS0YQRavY5IHDfUNh1dXWh57z3YVq1CZ309egsKkFlaiowzz4Q5OVm6IqPl3Xexb+H96K0/MC9wUlERBv/+d2gdPVpK5Mk9rhrxF08xKjBOw6+vpJ7csuHGIGNUn8dVo81Q2tAiRvUQp77aZTKPiFSxu7kDj6/5HtXrdqDXI4uXm56Eq04twqUnj0JqEpN4REREZCwta9Zg9+0L4LDZxF9U0hV3rWYzWleugvne+1Bw001oXbkSbR9/7K5jSklB/tVXI2/2LDgTEtDKOYGJiEhFTOYRUVj22Trx5L++x2uf7kC3/cDtJJkpCZh3ajEuO2UUBiXzVENERETGTOTtvPa6Axtct872/xQJvn133+1VZ9Bpp2GwuKV2xAj3QhhERERq4l/YRBSS/a1dePr9Wrz8yXZ09R4YpGYkJ+DyH4/GFT8ZjcyURE37SERERBQqcWutuCJP4jkBsB+WoUMw9Pe/R8akSZHvHBERxTUm84hIEWtHL6re+w4v/nc7OnoOrKqTlmTBrFNGYe5Pi5CdlqRpH4mIiIjCJebIk26tlangmmuZyCMioqhgMo+IZLF29GDJB7V4/qOtaO85cCVeSqIZv/q/UZj30yLkDUrWtI9EREREamlZtdo9R15QZjPaPvgAOdOnRaNrREQU55jMI6KAWjp7UPWfbVjy4Ra0dPa6tydZzNLKtGKF2sLMFE37SEREpJTD4ZAe/vaJ1Un97ZdTRk4bRqDV64jEcZW22dvcLC+R19e4VN5X20qPq0b8xVOMxnucqlVfST25ZcONQcaoPo+rRpuhtKFFjOolTn21zWTegAFdOG+Uv31GOAlFKwBj4R99vMRIe3evdCvt4g+2ormjx709wWzCjAkjcO3pxRialSptU6vfjJHQ9+lFpPuoVYworcdziX/8vJFf1lcZPb+3RlNSUgKLxYLZs2dLD0/i92y1WqXfv1lcmeVDsDJy2jACrV5HJI6rpM3eL75EZ22t/MZNJvSmpqDOx6q1Sl+LGvEXTzEaz3GqZn0l9eSWDTcGGaP6PK4abYbShhYxqnWcVlVVSQ+7/cD0Vi5M5g0Y0M2aNQtTp04N6Y3yt88IJ6Fo9DFW/tGH84/ZCDHS2evAW1/U48V1e9HUfuBKPIsJOOvIXEw7Mh1jh+fD3NWCuroWVY/NGAl9n15Euo9axYjSejyX+MfPG/llPcssXbrU72COQlNTU4PMzEy/v3uTyYSCgoKA70+gMnLaMAKtXkckjhusTbHqbNu//43G555Dx/oNyhp3OpH3s58jq7BQ8XFDKc8Yjd84jVR9JfXklg03Bhmj+jyuGm2G0oYWMap1nJaXl0sPm82GnJwcr31M5g0Y0Ik3or6+PqQ3yt8+I5yEotHHWPlHH84/Zj3HSFevHa+v3Ymn3q9FXUuXe7vZBJx7wjBcP+kwHJKTGvDfR7gYI6Hv04tI91GrGFFaL57PJcHw80Z+Wc8ygQZzFBrxew/0Ponffbhl5LRhBFq9jkgc11ebzp4eWP/xDymJ17X5+4EVgq9kK9rMyEDWWWeqFgtqxF88xWg8xGk06iupJ7dsuDHIGNXncdVoM5Q2tIhRPcSpr3aZzOvn+YsP543yt88IJ6Fo9DFW/tHHUoz02B2oXrcTT6zZjN3WTq99Zx83FDeWjsFhhRlef1hGsp+MkdD36UWsxojSevF2LlGCnzfyyw4so+f3lchoHG1taF6+HA0vLEXvnj1e+5IOK0belVfCnJ6OXTf8um+jr6SeSPYBGHb//TAncyEwIiKKDibziOJUr92BtzbswmNrNmNHY4fXvilHD8ZNZWNxxBDftx8RERERGVVvYyOsr7yCxj+/AofV6rUvdfx4KYk36LRTYXJ90f/kE9h9+wI4bLYDq9v2/xRX5IlEXsak0zV6NUREFI+YzCOKM3aHE29/vht/Wr0ZW/e3ee2bfEShlMQ7ZniWZv0jIiIiioSeXbvQ/tTTaH73XTg7ve9GGHT66cibcyXSxo8/qF7GpEkY8+EHaFmxAraVK9FZvx8pBfnILCtDxpQpvCKPiIiijsk8ojjhcDjx7sa9eHTVJmyua/Xa95Mx+bi5bCzGHcJ5mIiIiCi2dH73HRqWPAvbu+8CnovIJCQg6+c/R+4VlyNl7NiAbYiEXdY55yDj7LOlFWsLCwt52zsREWmGyTyiGCdWQVz59T48smozvtlj89p3clEubjnjcEwclatZ/4iIiIgiMf5pX7sWDc8+i7YPPvTaZ0pNRc6M6ci97DIkDhumWR+JiIhCxWQeUQwPYt/fVI9HVm7CFzu954MpOTQHt5SNxSmH5WvWPyIiIi2JRZ3Ew98+8Tnqb7+cMnLaMAKtXkeox3U6HGhdswaNzz6Hzi++8Npnzs5G0i9/iWFXXoHE3L4vMpW2H0q/lNZRI/7iKUaNGKeRbDPU+krqyS0bbgwyRvV5XDXajPS51KFSjMopE4331lfbTOYRxRhxIvnP9w14eOV3WP9Ds9e+40dk4eYzDsdPx+RLKyQSERHFq5KSElgsFsyePVt6DBw0W61W6TPV362UwcrIacMItHodSo/r7O5G96pV6HztdTh++MFrn3nwYCTPnInEM6fA1tWFhu5umOvqotKvUOqoEX/xFKNGitNotBlqfSX15JYNNwYZo/o8rhptRvpc6lApRuWUieR7W1VVJT3snlNE9GMyjyiG/G9LAx5auQmfbm302n7U0ExpTrzJRxYyiUdERASgpqYGmZm+V20XA3PxeVlQUBBwcB+ojJw2jECr1yH3uPbWVliXVaPpxRfROyBBlzR2LPKuuAIZZ06BKTFRatNcXx/Wawnl96G0jhrxF08xaoQ4jWabodZXUk9u2XBjkDGqz+Oq0Wakz6UOlWJUTplIvrfl5eXSw2azISfHe357JvOIYsD6H5rw8D834aPv93ttHzt4EG4qHYspRw+B2cwkHhERkYsYcAcadIuBebhl5LRhBFq9jkDH7d2/H40vvYymV16Bo6XFa1/axInSyrTpP/nJQV9iqvFaQmlDaR014i+eYlSvcapVm6HWV1JPbtlwY5Axqs/jGuFcalIpRuWUifR766tdJvOIDOzLnVbpdtp/fVfvtb2oIB03lo7F2ccOZRKPiIiIYkb3Dz+g4fnnYX3zLenWWk+DSicj/8orkXrCCZr1j4iIKBqYzCMyILEq7cMrN0mr1Ho6JDcNv548BueeMAwJFuN/e0VEREQkdH79tbQyre29FeKepgM7EhORdc4vpNtpk4uKtOwiERFR1DCZR2Qgm/e14NFVm/GPL/d4bR+enYrrJx2G80tGIJFJPCIiIooBYjLxtv9+gqbnnkPbxx977TOnpSF75kzkzroMiYMHa9ZHIiIiLTCZR6Shzh473vlyD1Z8tRf1zW0oyN4pzW/3s2OHIiXR4i63pb4Vj63ejL9+vhtO54H6gzOTcd3ph2HGxJFITjhQnoiIiMionHY7Wv75T7Q8U4nm777z2mfJy0PupZci58ILYMnK0qyPREREWmIyj0gj4hbZW6o/g62jF2JaO4cTMO9uxYqv9uGut7/Cw9NPwOFDMvCn1Zvx1oZdsIsC/fIHJeOa04px0UmHeCX9iIiIiIzK0dUF61/+isbnn0f39u1e+xJHjkTe5bORNXUqzCkpmvWRiIhID5jMI9LAqm/2Yd7L64H+/JxjwM+Wjl5c+eI6d5LPJSctEVedWoxL/+9QpCXxny8REREZn72lBU2vvYbGF1+EvX6/177kI49E/pwrkXHGGTAlcOxDREQk8BORKMq6eh24tfpLKZHnkafz4truSuRlpiRg7k+LMOtHozEomf9siYiIwuVwOKSHv31ivjZ/++WUkdOGEUTydfTW16PpxRfR/PoyOFpbvfalnnQSzOefh6FnnQWLxSKNjZxh9kGN1xJKG0rrqBF/8RSjWr6WSBw33DZDra+kntyy4cYgY1SfxzXCudShUozKKRON99ZX28wKEEXZms1NsHX2yi4/5ajBeGDG8chMSYxov4iIiOJJSUmJlCSaPXu29Bg4aLZardLg3Gz2vbBUsDJy2jCCSLwO+44d6HztdXT/859AT8+BHSYTEn/6U6RceAHMY8dKx62vr1ftuGq8llDaUFpHjfiLpxjV8rVE4rjhthlqfSX15JYNNwYZo/o8rhHOpQ6VYlROmUi+t1VVVdLDbrcftI/JPKIo+/f3zWKs6rWQhT/iNluTycREHhERkcpqamqQmZnpc58YmIvP34KCgoCD+0Bl5LRhBGq+jo4vv0Tjc8+hdeUqr4GQKTERmb88F7mzZyNp1CjVj+uiRpuhtKG0jhrxF08xquVr0WOchlpfST25ZcONQcaoPo9rhHOpQ6UYlVMmku9teXm59LDZbMjJyfHax2QeUYSJhSu+2WPDJ1sa8OnWRny4pVlWIs91m21zR3eku0hERBR3xIA70KBbDMzDLSOnDSMI53WIKxXa/vMxGpYsQfv//ue1zzxokLQqbc6llyKxsFDV4/qjRpuhtKG0jhrxJ6dMrMSolq9Fj3Eaan0l9eSWDTcGGaP6PK4RzqUmlWJUTplIv7e+2mUyj0hl3b0OfLG7FZu/acHabU2o2daEli75t9UOvDIvOzVJ9T4SERERRZKztxe2FSvQ8Nxz6Pr6G699loJ85P7qV8i54AJYMjI06yMREZFRMZlHFKaObjs27GiSrroTj/U/NKGzx//klykJJnT2OmVfmTflmMEq9paIiIgochydnWh+8000Vr2Anh07vPYlHXoocq+4HFnnngtzcrJmfSQiIjI6JvOIFGrp7MF/t1mxaUOTdOXd5zub0WP3n5zLH5SMk4pycdLoXEw4NAep9lac+9xGtHT2+l3NVjCJVWxTE3DWMUMj8jqIiIiI1GK3WtH06qtofPEl2BsbvfalHHMM8q68EhllpTBZLJr1kYiIKFYwmUcURFNbN9Zu67vq7tNtjdi4yypdMefPsOwUHD80DT89YhhOKsrD6Px06R561+SYdXUdeGj6cZj78nqYnPCZ0JNKm4CHpp+AlEQOeomIiEifevbuReMLS9G8bBkc7e1e+9J/9CPkzbkSaSed5B4LERERUfiYzCMaYH9bD9Z+sQdrt/fdOvvt3paA5Yvy03Hi6Fz3Y1hWCurq6lBYWOh3AszJRw7G4ksn4Nbqz2Dt6JXmxhMJQtdPcUWeSOSVHsVbbImIiEh/umpr0fDc87C+/TbQ03Ngh9mMzDOnSFfipRx1lJZdJCIiillM5lHc29nU7p7vTqw4u63B+1vlgQ4fkoFjB6fg1COH46TiPBRmpHjtF1ffyVF21GD87zeleHfjHry3cS/qrW0oyErHmccMkW6t5RV5REREpDcdn32G/UueRevq1V7bTcnJyDpvKvJmz0bSIYdo1j8iIqJ4wGQexRWn04mt+9ukxN3/+hN4u5o7/JYXV8odMzwLJ47qu+pu4qhcZKUmBL3yTi6RsJs6bgTOPX6Yam0SERERqT1+av33B2h67jm0r1vntc+cmYmcCy9E7qWXICE/X7M+EhERxRMm8yimORxO6TbZ1V/U4Zv9u/Dptibsb+3yWz7RYsKRg9PwozGDcXJxPsYfko2MlMSQrrwjIiIiMjJnTw+s/3gHLYsXo3nLFq99CYWFyJ01C9kzZsAyKF2zPhIREcUjJvMopvTaHfh6jw3/29J35Z1YuMLa4TGPywApiWaMPyRHuurupNF5OH5EJmxNDbxCjoiIiOKWo6MDzcvfQGNVFXp27/balzR6NPKuvAKZv/gFzElJmvWRiIgonjGZR4bW1WvHFzut7ttma7Y1oq3b7rf8oOQETBiVIyXuRALv2OFZSEowe111Z4tS34mIiEg74jPf39X2Yru4tTTQ1fjByshpQ2/szc1o+vMraP7zn6X/9pRy/HHIveJKDJp0Okz9X3hG8rVF4venRpuhtKG0jhrxF6sx6o9Wr0WPcRpqfSX15JYNNwYZo/o8rhHOpQ6VYlROmWi8t77aZjKPDKW9uxdrf7Bh0xdW6aq7DT80o6vX/z+anLREaZ67o/ITMenYQ3D08GxYxER4REREFNdKSkpgsVgwe/Zs6TFw0Gy1WqXBub8r9YOVkdOGXjj27UPnsmp0/eMfQGen176EE09E7zm/QNL//R86LBZ07N8fnT5F4PenRpuhtKG0jhrxF2sxGoxWr0WPcRpqfSX15JYNNwYZo/o8rhHOpQ6VYlROmUi+t1VVVdLDbrfHRzJvy5YtKC8vx5IlS5Cdna11dygMts4e1Gxr6l+sokG6Cq/X4fRbvjAjGScV9V11d9LoXBxWMEjM+NK/uEQWzEzkEREREYCamhpkZmb63CcG5iaTCQUFBQEH94HKyGlDa12bN6Pxuedhe+cdoLf3wA6LBRlnnYXcKy5H0pgxqK+vj/rriMTvT402Q2lDaR014i9WYlQurV6LHuM01PpK6sktG24MMkb1eVwjnEsdKsWonDKRfG9FXks8bDYbcnJyYjuZt2rVKuTm5mL58uVSMo+MpbGtW7plVnpsa8DXu20IkLvDyNxUnDgqT0rciQTeoXlp0j+kgYtgEBEREXkSA+5Ag24xngi3jJw2tNBeU4OGJc+i9f33vbabUlKQff75yJ09G0kjhnv9kaLF64jEcdVoM5Q2lNZRI/6MHKOhYJyGX19JPbllw41Bxqg+j2uEc6lJpRiVUybS762vdmMumVdaWir95BV5xrDP1um+6k4sWrG5rjVg+eKCdBw7OBU/PWoYTi7Kx7Ds1Kj1lYiIiMionA6HlLwTSbyODRu89lmyspBz8cXIueRiJOTmatZHIiIikkeXybzFixejtrYWFRUVPm+hFduLi4vdSbu5c+dq0EtSStxDvtvahQ937sTa/ltntze0+y0vLrA7Ykim+6o7MfddXnpi/y2zXG2WiIiIKBhndzes/3gHDc89i+7va732JQwdirxZlyF72jSY09M16yMREREZNJnnStIJy5Yt85mgE2XEZMVbt251X3kn7h9etGgR5s+fH/U+U/DkXW19W/9Ksw3Szz1W70mVPYmFKY4ZntWXvBvVl7zLSkv0KhMLKxkRERERRZqjrQ1N1dVofGEpevfu9dqXPOYw5F5xBbJ+/nOYEr3HWkRERKR/uknmFRUVobKyUvrvdevW+Swjkn0iyed5C+2CBQukiQCZzNOemJvu270t7sSdeDS0dfstn2Qx44SR2X2LVRTlYvwhOUhP1k1IEhERERlOb2Mjml5+GY1/fgUOq9VrX+r48cibcyUGnXoqTLzDgYiIyLAMlTkRV+wNvPXWldgTC1+45suj6OixO7Bxl9WduFu7rRG2To+V0AZITbTgmKFp+PHYITi5KA/Hj8xGSqIlqn0mIiIiikXdO3ei8fkqNL/5Jpyd3ndCDDr9dCmJlzZ+vGb9IyIiojhM5jU3N0sPcQXfQCKht379eq9knihL6urssePzHc39K802omZ7E9q77X7LZ6QkSLfKuua8O2poBpoa9nO+OyIiIiKVdH77LRqefQ62d98F7B7jsoQE6TbavCuvQPKYMVp2kYiIiOI1mSfmy/MnNzcXDQ0N7iv0RGJPWLhwISZOnIhp06ZFrZ+xpL27V0rY9c1514jPdjSju9f/nHV56UlS0s71EItXiHnwXDjfHREREZE68xK3f7oWDc8+i7YPP/TaZ0pLQ870aci97DIkDhumWR+JiIgocgyTzAvGdSWeuDpPPJTOoZefnw+TWD7VQ0dHx0HlREJKDKB8Jab87QtURy9E32ydPfji671Yt71ZuvJu4y4beh1Ov3WGZCb3Je5G9SXvigvSB/wOxWt2qvp7CKUNJXXklA1WJlZjJBr9ZIyEvk8vYjVGlNbjucS/aPQxVs4lqampB20TdSh+OR0OtKxejYYlz6Lziy+89llycpBzycXIuegiJOTkaNZHIiIiijzDJPM8F70YqLGxUdVjiYGySErV1dUdtE8Muq1Wq1Rm4K2i/vYFqqOlxvYefLarVXps2NmC7/d3INCfCCOyknHC8EHSY9yIDAzLTPJI3rWjvr494PHU+D2E0oaSOnLKBisTSzEyUKT7yRgJfZ9exGqMKK3Hc4l/0ehjrJxLPMckFN8c3d2w/e1vaHjueXRv3eq1L3H4cOTOno3s88+D2UcCmIiIiGKPYZJ54lZaf3PhiW2Bkn1yiMRdZmamNLiur69HQUGB3z+uxKDa135/+wLViaY91g58urVJuupO3DpbW98WsPyYwkGYOCpHuupO/ByaFd4AUY3fQyhtKKkjp2ywMkaOkWAi3U/GSOj79CJWY0RpPZ5L/ItGH2PlXNLW1nbQmMRmsyGHV13FDXtrK5pfX4bGpUvRO+BL5uSxY5E3Zw4yzzoTpgTDDOmJiIhIBYb55BfJOvHwdxVeWVlZWO2LQbJroCwG157PBwq039++YG2qTXyT/0NjuzTX3f+2iAUrGrCj8eDbhg/0DxiTn4pTxhRKK82KhSvyBiWr3i81fg+htKGkjpyysRAjoYp0Pxkjoe/Ti1iNEaX1eC7xLxp9jNVziZ7fV1JP7/79aHzxJTS9+iocLS1e+9ImTpRWpk3/yU941SYREVGcMkwyT5gxYwZqa2t9LozhuZJtPBLJu+/rWvuSd2K12a0N2Gfr8ls+wWzCsSOypKvuTh6dh3Ejs9DZ0sSVZomIiCguiKsjQ5mzUm6ZUOZd7N6+HY1VL8D2l7/A2d19YIfJhEGTJyP3iiuQevxx0ibRdjTmUNRqLs5IHNcI82nKLa9VjOoV4zT8+mrP+yqnHGPUmMc1wrnUoVKMyikTjffWV9u6TOaJ22Z93U5bXl4uXYFXUVHh3lZZWSk94o3d4cQ3e2zuxN3abU1obPMY9A2QlGDGuJHZOGl0Lk4qysO4Q7KRlpTgFRyd3l/8EhEREcWskpISWCwWzJ49W3p4ivS8lwP1btqEzldfRc+/PxAVD+xISEDSGWVImXkBLIceAjFUa/Exp3MkaTUXZySOa4T5NOWWj3aM6h3jNPz6kZj3NdwYZIzq87hGOJc6VIpROWUi+d5WVVVJD7vdrt9knkjeLVy4UPoprrZbtmyZtL24uNi9Mm1RURGqq6ulpN7EiROlcnl5eZg7d65q386Gk3UduK+rx453Nu7FP7/aizprOwqzduCMo4fgZ8cMQXKiRVH/euwOfLnLKs119+m2Jqzb1oTWrl6/5dOSLCg5tG++uxNH5eC4EVlITvA+pudriFY2ORYy+GrGSCh91FKk+8kYCX2fXsRqjCitx3OJf/y8kV/WVxk9v7dGU1NTI82X7Es48146urrQsmIFWlathqW+Hr0FBcgonYyMKVNgTj4whYl4b9s/+R8an30W7f/9r1fbprQ0ZM+ciZxfXYrEwYOhJTm/C6McV402Q2lDaZ1w4k9JGa3e20hgnIZfX0k9uWXDjUHGqD6Pa4RzqUOlGJVTJpLvrch9iYevOZN1k8wT8+G5rrgLdKXd+PHjpUekvp2dNWsWpk6dGvbqgh9tteGef25DS5cdZhPgcALm3a1Y8XUd7vrbV7hjyij8pMj/oh2dvQ58tacNn+1qwYZdrdi4p03a5k9GsgXHi1Vmh2dg3PBBGFuYJt1K26cX1sYGzb8piJUMfjiZeX/7jPKtU6T7yRgJfZ9exGqMKK3Hc4l//LyRX9azzNKlS/1+M0uhCXdOS19lWtaswe7bF8Bhs4kDiDcRbWYz2latQt19CzHs/vsx6NSfomXlSjQseRadX33l1Z4lLw+5l16KnAsvgCUrC3qh1VyckTiuEebTlFs+0nOzGg3jNPz6as/7KqccY9SYxzXCudSkUozKKRPp99ZXu7pJ5unl21k1VrP9fL8T5X+vBfqnMXEM+NnaZcf8t2tRecl4lB7Z922ruMpu/Xax0myTdPXdFzub0W33Pw9KXnqSdMusa6XZwwdnwOxO3unzm4JYyeCHk5n3+y2+Qb51inQ/GSOh79OLWI0RpfV4LvGPnzfyy3qWCfTNLOmDSOTtvPa6AxtcV1H2/xQLWey85hpYCvJhr9/vVTdx5EjkXXE5sn75S5hTUqLabyIiIjIeJvP6eWZRw8m6igTc/De+lBJ5/lJxYrvJCdz4+ueYOXEE1m9vxsbdNmkePH+GZaVIc91Jt82OzkVRfrrqK5hxdUH5ZeN1BcpYXqnUCDGitJ9aidUYUVqP5xL/+Hkjv+zAMnp+X+OZuLVWXJEn8bcoRf92z0Re8lFHIv/KK5FxxhkwJXBYTkRERPJw1KCyNZubYOv0P5edixjOtXfbUfWf7T73j85Px4mj+hJ34jEyNy0CvSUiIiKicLW8917frbUyJR1WjMELFiD9lFNU/3KWiIiIYh+TeSr7d22ze448JcRtsq7EnXgMzuQtFkRERERGIBa7cM2RF5TJhOTRRRj0ox9Fo2tEREQUg5jMU5mto1dRIm/s4EF4fe7/ISc9KZLdIiIiIqIIsVub5SXyBKcTdqs10l0iIiKiGMZknsck066HWDVO/PRXzt9+sS0zJUH2lXminLidNis1we/xoiXY69bLMUJpQ0kdOWXDjRFf+6Lx+1dDpPvJGAl9n17EaoworcdziX/8vJFf1lcZPb+38cySlS3/yjyzWVcr1RIREZHxMJnXr6SkBBaLBbNmzcLUqVOlwbO/1QWtVqvP/WLfhKGJeL9W3jFFwu/kEamoq6uD1gK9Lj0dI5Q2lNSRUzZYmWAx4mtfNH7/aoh0Pxkjoe/Ti1iNEaX1eC7xj5838st6llm6dCmqqqpgt9tDej0UWRmlk9GycqW8wg4HMspKI90lIiIiimFM5vWrqalBZmamNHCur69HQUGB3z+uxETFvvaLfWcf78TidU1o6ez1u5qtIKY6zkhJwAWnjEVyogVaC/S69HSMUNpQUkdO2WBlgsWIr33R+P2rIdL9ZIyEvk8vYjVGlNbjucQ/ft7IL+tZpry8XHrYbDbk5OSE9JoocjLOPBPme++Do6XF/2q2glidOCMDGVOmRLN7REREFGOYzOsnBtKuwbQYOHs+HyjQ/pRECx6afhzmvrweJmffqrUH1e//v4dnnIDU5EToRbDXrZdjhNKGkjpyyoYTI/72ReP3r4ZI95MxEvo+vYjVGFFaj+cS//h5I7/swDJ6fl/jmTk5GcPuvx87r71WStj5TOj1r1oryonyRERERKHiiDACJh85GIsvnYDM1AT33HieP8X2JZdOQOlRgzXsJRERERGpJWPS6Rjx5BPSlXcSV+LVlYjNyMCIJ5+UyhERERGFg1fmRUjZUYPxv9+U4t2Ne/Dexr2ot7ahICsdZx4zBGcdM1S6go+IiIiIYkfGpEkY8+EHaFmxAraVK9FZvx8pBfnILCuTbq3lFXlERESkBibzIkgk7KaOG4Fzjx8mLXJRWFjI22OIiIiIYphI2GWdcw4yzj6b4z8iIiKKCI4siIiIiIiIiIiIDIJX5nmsGOd6OJ1O6ae/cv72+9sXrE09iEYf1ThGKG0oqSOnbLzGSDT6yRgJfZ9exGqMKK3Hc4l//LyRX9ZXGT2/t0REREQUHUzm9SspKYHFYsGsWbMwdepUafDs65YIMYi2Wq0+9/vbd95550k/ly9frtvbLAK9Lj0dI5Q2lNSRUzZYmViNkWjECWMk8D4jxEmsxojSejyX+MfPG/llPcssXboUVVVVsNvtIb0eir7U1FTpZ0dHh9ZdIfKJMUp6xxglI0jVKE6ZzOtXU1ODzMxMaeBcX1+PgoICv39cmUwmn/v97duwYYP0U89zpgR6XXo6RihtKKkjp2ywMrEaI9GIE8ZI4H1GiJNYjRGl9Xgu8Y+fN/LLepYpLy+XHjabDTk5OSG9JiIiIiKKDUzm9RMDaddgWgycPZ8PFGi/r32uW2ICtakHwV63Xo4RShtK6sgpG68xEo04YYz432eUOInVGFFaj+cS//h5I7/swDJ6fl+NRvx7CeU2d7llXO+V0W+N1ur2/Ugc1wi34Mstzxj1xjgNv77aU0XIKccYNeZxjXAuVStG9RKnvtpmMs8HcRuL+PY7lP3B6upZNPquxjFCaUNJHTll4zVGotF/xghjJBrth9oG40Qd/LyRX9bI77NRpliZPXu29Bg4aH7jjTdw/vnnB7xyMlCZcePGST/FirZGTsLK+V0Y5bhqtBlKG0rrqBF/8RSjAuM0/PpK6sktG6wcY9SYxzXCudShUoxqHadiHOh3mhVnnLNarU7xaxA/Bbvd7hwzZoz005dA+/3tS0pKkh7+2tSDYK9bL8cIpQ0ldeSUjdcYiUacMEYC7zNCnMRqjCitx3OJf/y8kV/WV5mB4xZSzvU7bGpqkn63vh49PT3Oww8/XPoZapmUlBTpEagNIzzk/C6Mclw12gylDaV11Ii/eIrRSMWLVscNt81Q6yupJ7dssHKMUWMe1wjn0h6VYlQvcSrGLAPHf3F/ZZ64XFIQc9C4sq4i6yme+/v2wN9+f/s8j6HXbxSCvW69HCOUNpTUkVM2XmMkGnHCGAm8zwhxEqsxorQezyX+8fNGfllfZVzjFdd7Tcq5fnetra0Bf/c9PT1hlXF9ix6oDSOQ87swynHVaDOUNpTWUSP+4ilGBcZp+PWV1JNbNlg5xqgxj2uEc6lDpRjVS5yKtgeO/0wio4c4tnPnTowcOVLrbhARERHJtmPHDowYMULrbhgSx35ERERk9PFf3CfzRJZ19+7dyMjIkCaZJiIiItIrMWxraWnBsGHDDH+VglY49iMiIqJI++yzz6SfJ5xwArZu3Qqr1Sr9t1rjv7hP5mlpy5YtWL58OYqKirB27VrMmzdP+m+igXEiJj9fsmQJsrOzte4O6dD69euxatUq6b/FuaSiooLnEvLiio/m5mYpRsrKylBaWqp1t4jiEs/ZpHf8zCAjEX8n8e9o0iMRl4sXL5b+e/z48aiurlY1TuN+zjwtTZ8+HTU1NdJ/iw/IyZMnu58TuQZTubm5UtJXJPOI/MXJ/Pnzpf8WHxhi0F1bW6t1t0hnnzerV692/zEmnjc1NWndLaK4xHM26R0/M8hIX46I86hImhDpTUlJSUTnOOb9GRqeeDyJK67Et1/iKiwiFzGIEll8XpFHgc4lCxcudD+fMWOGdB7huYQ8iT/KxLlEaGxsxIQJE7TuElFc4jmbjICfGWQU69atky58IIpHvDIvTOKbAPFtqrhFYiAxMBPbi4uLpeciITN37lz3icffII+XCMeWUGOE4kuoceK6ZNtFDLoFDmxiTzjnEtcfZaLcypUrUVlZGcWeE8UenrNJ7/iZQbH+N5KoL7b5qk+khzgVF2uJ+uIzPhLTqjGZFwLXmyYsW7bMZ/JFlBGXVYqJDl1XVYn7+RctWiTdWiHe2IEDN1HONagjY1MjRij2qRUnnvPYiAG3aIdXc8YGNc8l4ssi8UUSvzAiCg3P2aR3/MygeIlREZ+8YpT0Hqeen+/iSxLVp9UQC2BQ6MaPH++cP3/+Qdvnzp170PampiZxw7T035WVlVJdT0VFRc7q6uoI95iMEiOesrOzpX0Uu9SIE3H+EOUpNqkRI8LKlSulfbW1tRHrK1Gs4zmb9I6fGRTLMSr+lvb8G5rxSXqM05qaGq/9ap9LOWdehIgMrutySxdXVlZMfOzrmwRxVZ7rsnaKfcFihEhJnIj/FucQ160w4upfig/BYkQ8PPe7Pn84RxeR+njOJr3jZwYZPUbFlU+u2xfFw3UuHTgnPZGWcSriUSweNJCa02owmRcB4uQiHr4uSxdvsHhjRdLOc+DmKs9L2eODnBgZWJ7ij9w4ET/FIFtMpO4a3FB8kBMjYtAwbdo093Zx25TYx9tTiNTFczbpHT8zKBZiVNzCKB7iFkbX7Y9iLjJeFEN6ilOxz3OVZZHgE9NsqDmtBufMi4BA31yJD8iGhgbpv8UEyOK+6okTJ0oTInpOiEyxTW6MuLL6glj9TsSK5wCLYpucOHHN1yB4fmBwIZX4ICdGxOBWlHMlDGpqaqSVCjlHF5G6eM4mveNnBsXK30iCSKaIq6PETzG/GRN6pKc4FedMkbwTV5KK/xbnUrXzPUzmacB1lZU42bhOOEzQkK8YEScA8eCCGOSL6xuhvikYiPyfS/gZQ6Q9nrNJ7/iZQXrnebeSa+VQfhlCRsj3RAJvs42AQN9ccbVaEhgjJAfjhIJhjBDpB/89kt4xRknvGKNkBNk6iVMm8yLANamhr3nOxDZepk6MEZKDcULBMEaI9IP/HknvGKOkd4xRMoJcncQpk3kRIN488fCXlS0rK4t6n0hfGCMkB+OEgmGMEOkH/z2S3jFGSe8Yo2QE2TqJUybzIkSsUFZbW+tzokQxBxoRY4TkYJxQMIwRIv3gv0fSO8Yo6R1jlIxghg7ilMk8lZYlHkisUrt8+XKvbZWVldKD4gtjhORgnFAwjBEi/eC/R9I7xijpHWOUjKBZx3FqcnJJLcXEm7lw4ULpp1i2XVxiKTKzxcXFXquOrl+/Hq+//jomTpzoztJyVdL4wBghORgnFAxjhEg/+O+R9I4xSnrHGCUjaDZInDKZR0REREREREREZBC8zZaIiIiIiIiIiMggmMwjIiIiIiIiIiIyCCbziIiIiIiIiIiIDILJPCIiIiIiIiIiIoNgMo+IiIiIiIiIiMggmMwjIiIiIiIiIiIyCCbziIiIiIiIiIiIDILJPCIiIiIiIiIiIoNgMo+IdGf9+vUoKSlBTk4OiouLESuam5sxb948lJeXSz+XL18esd+DKD99+nTokZ77RkRERPqzZcsW95jIZDJp3R1ditVxIxH5ZnI6nU4/+4iINFVWViYN3mpraxELxABr5syZmD9/vvTfIrkn57Up/T2IdsVArqioSHe/Oz33jYiIiPRNJJzEl6H8EzY+xo1E5B+vzCMi3RKDilixatUq6RvTuXPnSs+rq6uxcuXKiPwesrOz0dTUpMsBmZ77RkRERPo2ceJErbuge7E0biQi/xIC7CMiIpWIRJ5rwBSNRKXrOHqk574RERERxRuOzYiMh1fmERERERERERERGQSTeURERERERERERAbB22yJ4oSYCFdMGix+5ubmSvNiLF68WNon/lvcBlpRUYHx48d7lReT4or/9pxoWGwX5RsbG7FkyRJMmzZN1jHEvHGivDiGaw45QcwdJ+q55pMbSPTB1Y6rLbEarKuvA4nVYoW8vDysXbtWml9FLDohiGPOmTNH6uOECROkuesWLlwoPRfEcyVEv0R/xLGEhoYGLFiwwH27gjieaN/1Wl0rhYnJif29Xn/k/B5EmcmTJx/0vil9/wceV7wGF9GGKOt5q7Cc36u/vsl97zz7IlZdE//tIn7vok9ERESk7DNTzue8mmM8zzGDaEuUqaysdPdFjC/FWMrfOM+fSI8hwu13NMensTBuFMcTv19XLIlj1dTUuNsQi3aIY4kxt2hf6biayPDEarZEFD+mTZvmzM7OdlZUVDibmprc28VzX6cEUd7X9urqamm7+Kn0GCtXrpQeLrW1te7tnubOnSttnz9/vtd20WZRUdFBx3Ztr6ys9NpeWloqtTVw2/jx491ti5/iWJ79DUa0MbBvNTU1Uh/ET0/+fr9yKP09eNYJ9/131fEsK16bKDvwNcr9vfrqm9z3TrQ98D0SdQa+v0RERPFO7memks95tcZ4rs94sW9gf0RZf2NMX+OVaI8hlPY72uPTWBs3iv2iDwO5Xo+S3w3R/7d3NzaN7GAYhdlaKAFKoIakApqhBSoA0QIdQCmIFlYn0keM8ST2aOL5yXkktNrsZGw8V/J77bG9JQ7mSVcmOsm8I48AkoetuD4X4awUCM6VQSefo5POA81QsACBKO/suS+dei5CBHXO750Hzlr8jqVgEf+W12OKwbzadjhVXuvzj7YrBVDC1VBdT7VrqW41z46foTZ3ME+SpKPaPrO1n58q453LN/FvNfmmd4ZorXfPfLrF3BgvEOSDgfy99P8h0rVwzzzpysRy0IeHh1+fx6vv6bKD9Popy2BZQY5X+FmeUHu61m63O/wZr/FT77e3tz9lIpYAxGv6qfT6lhNmn56eBl/n3+/3h2UC1Gcqte0w9fPnc354PvnnsRSipKVda58ddeDau7u7w/VpXV1iK0nSUW2f2drPT5nxTuUbloPW5Ju5MkRtvXvn0y3mRrbz4feJJc3h5eXlZ6sf6Rq5Z550pXocQT9UxphQMnTvCEAfHx+HPwkKDLTlSvt6jG2DKHNooDN+P/ZDuXTIyNuh9Xs117E3CmI/lfjJA1zrvUPts+O+sfdO7D3IZ+xPk+6JI0nStavtM8f08/G9S2W8cwNdS84Qeb175tMt50Ym0Gm/dI/CMS8cSFviYJ6kTYjwyMEStaEsnzWcSsw+nwrBa8JG1oRNwhYzzsyeMlDJ51O0a8uzo+zv7+9DCKV8gjkbSlOfMZtDS5K0VbV9Zms/vyRLzxBLyqdrzo3ch8E8DsVgYO/19dUDL3T1HMyTNMrcA1VRPuEofxvu0mIGNWYeh+rGUo7e7TA1loYwg03gLS0RmULtsyN8M7PL2448A34IxlFHSZLU1mf26OfHiDfHzuWbpWWIvN498+mWcyPtyP3i1FoyeI9VRtKSuWeepJOGOspYNjDXoCEzc9QtnZWjg2fWr/QdPp9yhjlmBUvYwyOvW892mBIz1oSnPJCl+57Qrq3LNXK1z462zcVeKnMPMEuStCQ1fWavfn7IUN/NcsrafDNHhmipd898uuXcyNt5sVz5UoOR0po4mCddma+vr5Odfr5BcXTGaSfMtfFWWmkz23NlDCn9O+Xne4wQANi4lyUR6WAjM6z39/c3j4+Pf+5bmiE8tRHvOYQ1Zgljo+M0oBCU3t/fi20ydsCppR2mfP7cN28n/p5ufMxPWv6Ydq19dsz45qGX8viuM7SSJB3V9Jmt/fyUGS/k+YY6M2Fayjel8ufKELX17plPt5wbY+CV32FJb5FKc/nHkbazlS6pGzpKZstiZpDlBfG6Oq/Dx/IDOkkCR9rR8x0Gr+KEMj7nu7e3t7+up0OvLYPPn5+ff0JPhCs+j1m9ODGW+1I+G90SKrg31wxtssxg2ufn50/9uD72KaEOfJc3C6OO3GfsXinUMX3Vn3vGPiFD7U55XFO7SXRLO5TKi/1Kxjz/KIN/4zuUTXkEqvic2VG+c65dh+qWzg6fe3bMqvPfYRr8aAs2sHYwT5Kkm6Y+s7afb8kRNRkPZACuod9noC3qV5tvovzeGaKl3nPk063kxhK+M/YEYmlrHMyTJEmSJHUVg2IcSrEma633FjAgutvtnMCVXGYrSZIkSZKWzoMvpCMH8yRJkiRJ0mKwlDc9aZglvx58IR05mCdJkiRJ6oo93dZ4Ev1a6702+Um/DO558IV05J55kiRJkqQu4rCHGKjh8IP9fv9zGMRSrbXea0Z7c4gGONTDJbbSkYN5kiRJkiRJ0kq4zFaSJEmSJElaCQfzJEmSJEmSpJVwME+SJEmSJElaCQfzJEmSJEmSpJt1+A/OmZGyOrZotAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " 20000 samples : 74.92 ms\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " 100000 samples : 303.53 ms\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Cost vs number of samples, for a single binary\n", "ns_list = [100, 500, 1000, 5000, 20000, 100000]\n", "tt = []\n", "for ns in ns_list:\n", " t = []\n", " for _ in range(5):\n", " t0 = time.perf_counter()\n", " flow.sample(2.0, 0.7, 0.3, np.pi / 3, np.pi / 4, 0.0, 0.0, n_samples=ns)\n", " t.append(time.perf_counter() - t0)\n", " tt.append(np.mean(t))\n", " print(f' {ns:>7d} samples : {np.mean(t)*1e3:8.2f} ms')\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(13, 4.5))\n", "axes[0].loglog(sizes, means * 1e3, 'o-', lw=2, ms=8, color='C0')\n", "axes[0].set_xlabel('number of binaries')\n", "axes[0].set_ylabel('time [ms]')\n", "axes[0].set_title('100 samples per binary')\n", "axes[0].grid(alpha=0.3, which='both')\n", "\n", "axes[1].loglog(ns_list, np.array(tt) * 1e3, 'o-', lw=2, ms=8, color='C3')\n", "axes[1].set_xlabel('samples per binary')\n", "axes[1].set_ylabel('time [ms]')\n", "axes[1].set_title('single binary')\n", "axes[1].grid(alpha=0.3, which='both')\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "id": "a72a6f69", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " gwModelRemS_kick (analytic) : 0.20 ms for 2000 binaries\n", " gwModelRemP_flow (100 samples) : 570.45 ms for 2000 binaries\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " gwModelRemP_flow (100 samples) : 564.15 ms for 2000 binaries\n" ] } ], "source": [ "# Analytic models vs the flow, same number of binaries\n", "n = 2000\n", "q_t = np.random.uniform(1, 10, n)\n", "a1_t = np.random.uniform(0, 1, n)\n", "a2_t = np.random.uniform(0, 1, n)\n", "t1_t = np.random.uniform(0, np.pi, n)\n", "t2_t = np.random.uniform(0, np.pi, n)\n", "c1_t = a1_t * np.cos(t1_t)\n", "c2_t = a2_t * np.cos(t2_t)\n", "\n", "for name, fn in [\n", " ('gwModelRemS_kick (analytic)',\n", " lambda: gwModels.remnants.gwModelRemS_kick(q_t, c1_t, c2_t)),\n", " ('gwModelRemP_flow (100 samples)',\n", " lambda: flow.sample(q_t, a1_t, a2_t, t1_t, t2_t, 0.0, 0.0, n_samples=100)),\n", "]:\n", " t = []\n", " for _ in range(3):\n", " t0 = time.perf_counter()\n", " fn()\n", " t.append(time.perf_counter() - t0)\n", " print(f' {name:>32s} : {np.mean(t)*1e3:9.2f} ms for {n} binaries')" ] } ], "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": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }