{ "cells": [ { "cell_type": "markdown", "id": "e60ddaef", "metadata": {}, "source": [ "# 17 — Generative calibration hooks (MMD)\n", "\n", "Doc page: [generative_calibration_hooks.rst](../../docs/source/algorithms/generative_calibration_hooks.rst).\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "d98275e1", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:06:13.541866Z", "iopub.status.busy": "2026-05-12T14:06:13.541279Z", "iopub.status.idle": "2026-05-12T14:06:14.135078Z", "shell.execute_reply": "2026-05-12T14:06:14.133758Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from optimizr import _core as opt\n", "plt.rcParams['figure.figsize'] = (8.5, 4.5)\n", "plt.rcParams['figure.dpi'] = 110\n", "plt.rcParams['axes.grid'] = True\n", "plt.rcParams['grid.alpha'] = 0.3\n" ] }, { "cell_type": "markdown", "id": "759b0068", "metadata": {}, "source": [ "## Cellule 1 — MMD nulle entre échantillons identiques\n", "\n", "**Théorème (Gretton et al. 2012).** Pour le noyau gaussien\n", "$k(x, y) = \\exp(-(x-y)^2 / 2\\sigma^2)$, la MMD au carré empirique\n", "entre $X = (x_i)$ et $Y = (y_j)$ est\n", "$$\\widehat{\\text{MMD}}^2(X, Y) = \\frac{1}{m^2}\\sum_{ij} k(x_i, x_j)\n", " + \\frac{1}{n^2}\\sum_{ij} k(y_i, y_j)\n", " - \\frac{2}{mn}\\sum_{ij} k(x_i, y_j).$$\n", "\n", "**Équation pivot.** $X = Y \\Rightarrow \\widehat{\\text{MMD}}^2 = 0$.\n", "\n", "**Démonstration.** Les trois sommes coïncident terme à terme. $\\square$\n", "\n", "**Ce que la cellule vérifie.** `mmd_gaussian(X, X, sigma)` retourne $0$\n", "à précision machine.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "c399ff2b", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:06:14.138451Z", "iopub.status.busy": "2026-05-12T14:06:14.138012Z", "iopub.status.idle": "2026-05-12T14:06:14.557121Z", "shell.execute_reply": "2026-05-12T14:06:14.555618Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MMD(X, X) = 0.000e+00 (attendu : 0)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.default_rng(0)\n", "X = rng.standard_normal(200).tolist()\n", "m = float(opt.mmd_gaussian(X, X, sigma=1.0))\n", "print(f\"MMD(X, X) = {m:.3e} (attendu : 0)\")\n", "\n", "fig, ax = plt.subplots()\n", "ax.hist(X, bins=30, density=True, color='C0',\n", " edgecolor='white', alpha=0.85)\n", "ax.set_title(r'Échantillon $X = Y$')\n", "ax.set_xlabel('x'); ax.set_ylabel('densité')\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "01f32911", "metadata": {}, "source": [ "**Résultat attendu.** $\\sim 0$.\n", "\n", "**Lecture du graphique.** Histogramme gaussien standard.\n", "\n", "**Conclusion.** L'auto-MMD nulle est validée.\n" ] }, { "cell_type": "markdown", "id": "6bb48f55", "metadata": {}, "source": [ "## Cellule 2 — MMD entre gaussienne et Laplace\n", "\n", "**Théorème.** Deux distributions de moyenne et variance identiques\n", "mais formes différentes ont une MMD strictement positive.\n", "\n", "**Équation pivot.**\n", "$$\\text{MMD}^2(\\mathcal{N}(0, 1), \\text{Laplace}(0, 1/\\sqrt{2})) > 0.$$\n", "\n", "**Ce que la cellule vérifie.** Sweep en $\\sigma$ : la MMD est\n", "maximale autour de $\\sigma$ commensurable à l'échelle des\n", "distributions.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "a73d2bf4", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:06:14.560906Z", "iopub.status.busy": "2026-05-12T14:06:14.560549Z", "iopub.status.idle": "2026-05-12T14:06:15.607504Z", "shell.execute_reply": "2026-05-12T14:06:15.606471Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MMD min : 1.182e-02, MMD max : 1.603e-01\n", "σ optimal : 0.38\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.default_rng(2)\n", "n = 500\n", "X = rng.standard_normal(n).tolist() # N(0, 1)\n", "Y = rng.laplace(0.0, 1.0 / np.sqrt(2.0), n).tolist() # même variance\n", "\n", "sigmas = np.geomspace(0.1, 10.0, 25)\n", "mmds = [float(opt.mmd_gaussian(X, Y, sigma=s)) for s in sigmas]\n", "print(f\"MMD min : {min(mmds):.3e}, MMD max : {max(mmds):.3e}\")\n", "print(f\"σ optimal : {sigmas[int(np.argmax(mmds))]:.2f}\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "xs = np.linspace(-5, 5, 400)\n", "axes[0].hist(X, bins=40, density=True, alpha=0.5,\n", " label=r'$\\mathcal{N}(0,1)$', color='C0')\n", "axes[0].hist(Y, bins=40, density=True, alpha=0.5,\n", " label='Laplace', color='C3')\n", "axes[0].plot(xs, np.exp(-xs**2/2)/np.sqrt(2*np.pi),\n", " 'C0--', lw=1.5)\n", "axes[0].plot(xs, np.exp(-np.abs(xs)*np.sqrt(2))*np.sqrt(2)/2,\n", " 'C3--', lw=1.5)\n", "axes[0].set_xlabel('x'); axes[0].set_ylabel('densité')\n", "axes[0].set_title(\"Densités comparées\"); axes[0].legend()\n", "axes[1].semilogx(sigmas, mmds, 'o-', lw=2, color='C2')\n", "axes[1].set_xlabel(r'bandwidth $\\sigma$')\n", "axes[1].set_ylabel(r'$\\widehat{\\text{MMD}}^2$')\n", "axes[1].set_title(\"Sensibilité à la bandwidth\")\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "d6403c0a", "metadata": {}, "source": [ "**Résultat attendu.** MMD strictement positive, courbe en cloche.\n", "\n", "**Lecture du graphique.** Gauche : la Laplace est plus pointue ;\n", "droite : MMD maximale lorsque $\\sigma \\sim 1$.\n", "\n", "**Conclusion.** Le choix de bandwidth est crucial ; règle pratique :\n", "$\\sigma \\approx \\text{médiane des distances}$.\n" ] }, { "cell_type": "markdown", "id": "cdf034d4", "metadata": {}, "source": [ "## Cellule 3 — Exemple concret : MMD entre mélange et gaussienne\n", "\n", "**Modèle.** $P = \\mathcal{N}(0, 1)$ vs\n", "$Q_\\mu = \\frac{1}{2}\\mathcal{N}(-\\mu, 1) + \\frac{1}{2}\\mathcal{N}(+\\mu, 1)$.\n", "La MMD doit *croître* avec $\\mu$.\n", "\n", "**Équation pivot.**\n", "$$\\text{MMD}^2(P, Q_\\mu) \\xrightarrow[\\mu \\to 0]{} 0,\n", " \\qquad \\nearrow \\text{ en } \\mu.$$\n", "\n", "**Ce que la cellule vérifie.** Pour $\\mu \\in [0, 2.5]$, la courbe\n", "MMD est croissante.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "45b8aa9b", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:06:15.610838Z", "iopub.status.busy": "2026-05-12T14:06:15.610566Z", "iopub.status.idle": "2026-05-12T14:06:16.202731Z", "shell.execute_reply": "2026-05-12T14:06:16.201441Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "μ = 0.00 -> MMD² = 8.317e-02\n", "μ = 0.25 -> MMD² = 3.606e-02\n", "μ = 0.50 -> MMD² = 9.864e-02\n", "μ = 0.75 -> MMD² = 1.881e-01\n", "μ = 1.00 -> MMD² = 2.075e-01\n", "μ = 1.25 -> MMD² = 3.452e-01\n", "μ = 1.50 -> MMD² = 3.628e-01\n", "μ = 1.75 -> MMD² = 4.763e-01\n", "μ = 2.00 -> MMD² = 5.565e-01\n", "μ = 2.25 -> MMD² = 6.350e-01\n", "μ = 2.50 -> MMD² = 6.936e-01\n" ] }, { "data": { "image/png": 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VlZWQn59faqyXL18WAAhLly4t85gEQRAyMzM1yv7++2/B2NhYmDhxolq5k5OTAEDYsWOHWvmSJUsEAMKRI0fKjL1YXFycYGZmJvj4+AgqlUpt3RdffCEAECIjIysVe1ZWltCyZUuhTZs2auW9evUSrK2thezsbLXy8ePHCwCE27dvi2UdOnQQXFxchKSkJLW6f/zxhyCTyYR58+aJZe+//74AQPjyyy81Ynn6e6I0mzZtEgAIJ06cEMvy8vJK7N8NGzYIAIQff/yx3HZfeOEFwd3dvdx6FTnW4s9jp06dhNzcXLE8NTVVaNasmWBlZSWkpaWJ5RXpn3HjxgkAhDfeeEPje6K0tuLi4gRbW1vB29u7xLZKUtL5/uSTTwQAQmhoqFrdyMhIjZ8rxd/X5ubmGj8HBg8eLBgbG5cYKxER1R7F17cfffSRkJCQICQkJAjXrl0TZs6cKQAQXFxc1H5PlmTs2LGCVCoV7t+/r1a+cOFCAYAQEREhCELFrulK0qlTJwGAxu/5/yq+/irvelgQiq4H3dzcSlxXfA28ZMkStfIpU6YIAITGjRsLqampYvnjx48FU1NTYfTo0WJZTk6O0KhRI6FLly4a53HPnj0CAGHz5s1iWfH1SXR0tFiWnZ1d4nXYxx9/LAAQzp07J5YV92ejRo2E5ORksVypVAru7u6Cg4ODWhs9evQQZDKZcOXKFbXyoKAgAYDQt29fsUwX17xff/21AEA4e/ZsmfWWL18uABD27t2rVp6fny+88MILgouLi1hWfD0jkUiEP/74Q63+5MmTBQDCpk2bxLLKnE8bGxshLi5OrX5lz0fx9frDhw/LPAdEtQkfryaqIEtLS7zxxhv4/vvvkZ+fjzNnzuD69etaPxrdp08ftGrVSnzEuvhRDF9f32eKy9raGkDRiLWyhIeHIyEhAVOnTkXz5s011pf0ePjMmTPVllUqFfbv34/WrVtrzJnz1ltvwdXVFXv37oUgCKXGYWNjg+zsbPzvf/9Texz4acUj006cOIHHjx+XeVyWlpYAih7HTU9PR2JiIho2bIjWrVvjjz/+0Kjv6OiI0aNHq5UVjxAtvrtfnj179iA3Nxf+/v5ISkpCYmKi+FV8B/bIkSPltlMcO1B0Vz0pKQnZ2dnw8PDA9evXkZGRIa739fVFeno69u7dK5ZlZ2dj9+7d6N27tzii8++//8Zff/2FN954AyqVSi225s2bo0WLFmJsKpUKO3bsQPPmzUucE7Syb3M0MTERRzIWFhYiNTUViYmJ8PDwAIAS++W/bGxsEBsbi5MnT5ZapyLH+rRp06apvbypfv36eP/995GRkYGjR4+K5RXpn2IzZ84s8Q72021lZGQgKSkJRkZG6Nq1q1bnoyw//fQTrK2tERwcrFbet29f9O/fH8ePH0dKSorauhEjRmj8HBg4cCAKCgoQHR39TPEQEVHNsGTJEigUCigUCjz33HP49NNP0b9/f4SHh5f5kkOg6LpEpVJh69atauVbtmyBk5MT+vfvD6Bi13QlKb6+Le/txcXrS/rd/F8JCQmwtbUtdb1UKtW4Lip+KmncuHFqsRRfcz59DXns2DE8fvwYvr6+yMjIULs+6dOnDywsLMq9TjQ3NxevwwoKCpCcnIzExETxmrWkawc/Pz+1l65IpVJ4enoiLi5OfNw4Pj4eZ86cgZeXl/jkVrGPPvpIo01dXPPa2NgAKHpR3n8fZX7atm3b4OzsjN69e6vtJy0tDcOGDUN0dLTGtfrAgQPRpUsXtbKPP/4YQNH1UbHKnM9x48aJT6w86/ko/n4rfkSfqC5g0pGoEsaPH4+kpCTs378f3377Lezs7DB8+HCtt/fz80NYWBhiY2Px3XffwdvbW3xMtLKK58sp72Ks+Jd0x44dtWpXoVBovC0uISEBGRkZeP755zXqSyQSPPfcc0hJSdFIcDzt448/RvPmzfHqq6/Czs4OQ4cOxVdffYUnT56IdZycnDB37lwcPXoUjo6OaN++Pd5//321hFCxU6dOiXMH1a9fX7x4/vvvv0ucP7CkhGvxhUBSUlLpJ+QpN27cAAAMGTJE3F/xl5ubGwCoHU9pYmJi8NZbb8HW1hb16tWDnZ0dFAoF1q9fDwBq53HUqFGwsLAQ5/YDgL179yI9PV0tcV0c29N/SDz9dfPmTTG2xMREpKSkoH379pVOMJZmw4YNeOGFF8Q5IhUKhZgY1WZexyVLlsDS0hL9+vVDo0aN8Nprr2HdunVqyfWKHOvT/vuo8dNlT89hVZH+KdaqVasSj+fKlSvw8fGBtbU1rK2txbYOHz6s9TyXpbl79y5atmxZ4gtr2rZtC0EQNBKJuvgcEBFRzebr64ujR4/i2LFj+O233xAfH4/jx4+jRYsW5W7r4eEBJycncR5i4N8pX95++23xBlxFrulK8vR0MGUpXl/WFD9PK+sGuaOjo8bv1OJr4pJ+f8rlcrXfncXXJxMnTtS4NrG3t0d2dna514lKpRKffvop3N3dYWZmBltbWygUCnG+xcpe4969excAxOvVpzk4OGj8PaGLa9433ngDL730EpYuXQq5XI4+ffpg9uzZGvOv37hxAzExMSVe082fP7/EfZV0TWdvbw9bW1u1a7rKnM+Srukqez6Kv9/4aDXVJZzTkagSunbtiueffx4rVqzAX3/9hXfffRcmJiZabz9u3DjMnj0bfn5+uHPnDpYtW/bMMf31118AoPZWbF2wsLDQaXvFXF1dce3aNURGRiIiIgK//vorPvzwQ3zyySc4fPgw+vTpA6DopR/vvPMOwsLC8Ouvv+Knn37CmjVrMHz4cOzbtw8SiQQXLlyAp6cnmjdvjtDQUDRv3hwWFhbi2+RKmpemrDf/lnUB+rTiEZrffvstnJycSqzj6OhYZhuZmZno06cP0tLSMGXKFLRr1w7W1taQSqX47rvvsHPnTrWRoFZWVuJbzh8+fIgmTZpgy5YtsLS0VHsTXvE2QUFBGDZsWIn7Njc31+o4K+vrr7/G1KlTMWDAAKxZs0acNLywsBBeXl6ljnB9WteuXXH79m0cO3YMJ06cwMmTJ7Fnzx7MmTMHp06dgpubW5Uea0X7p1hJn5uHDx+iV69eqFevHj766CO4ubnB0tISUqkUS5YswfHjxysV47PQxeeAiIhqNldXV/HFMRUlkUjw9ttvY+HChThz5gx69OiBLVu2QCKRaDzFo801XWnatm2LCxcu4M8//8SgQYNKrVf8QkRtEqYKhaLMG2xl/Y4sbd3TvzuLrw9CQ0M1RuEV+++N/f/68MMPsXz5cowcORIzZ84UX0YTGxsrjjKtSNyV/d2ui2teExMThIWF4eLFizhy5AhOnz6Nr776CosXL8bnn38uviBIpVKhdevWZb7IsKSBD9qozPks6Zqusuej+PvN3t6+UvET1URMOhJV0vjx4/HBBx+I/6+IRo0a4eWXX8aBAwfg4OAAb2/vZ4olISEB+/btg1wu13jByH8V3627dOlSqQma8igUClhZWeHatWsa6wRBwLVr1yCXy8u9kDI2NsbAgQPFRxquXLmCF198EXPmzFF7IY+TkxMCAwMRGBiIwsJC+Pr6Yvv27Th58iT69euH7du3o7CwEGFhYRp3d5OSkkoc+aWtsi6Ai8+lXC6v9MX68ePHxZeJ+Pn5qa3bsGFDidv4+vpi27Zt2Lp1K9566y0cP34cY8eOVXvBzdN3ZcuLzc7ODnK5HJcvX4ZKpdLZaMctW7bA2dkZR44cUWuz+O6wtiwsLDBs2DDx+/WXX36Bl5cXli5dis2bN1foWJ92/fp1jcnji9+cXvzHSmX6pzR79+5FRkYG9u/fLz5iXqz4EaCnVfQuuKurK27fvo28vDyNx+H+/vtvSCQS8W3sREREujJu3DgsWrQImzdvxgsvvIAff/wRvXv3LnHEXXnXdKV57bXXsHnzZqxbt67UpOPjx49x4MABODk5oVevXuXG/fzzzyMiIgIFBQXlvtiuMoqvT8zMzCp9nbhlyxb07t1bfJFOsbCwsGeKrbhvoqKiNNbFxcVpjCjVxTVvsY4dO4pPXKWkpKBHjx4ICQlBUFAQTExM0KpVKzx48AD9+vUr8yU7Tyu+fntafHw8kpKS0L17d7FMV+ezsufj1q1bsLW1feYn3IhqEj5eTVRJb7/9NubOnYuvvvoKzz33XIW3nzNnDubOnYs1a9Zo/Qu1JE+ePIGPjw8yMzMxd+7cckcmDho0CAqFAsuXL0dMTIzGem1Gn0mlUvj4+CAqKgp79uxRW7d9+3bcuXMHr7zySplJk4SEBI0yd3d3WFpaincB09LSUFBQoFbHyMhITBQV1yu+o/vfu7fr1q3T6vHmshQn8kp63GLUqFEwMzPDvHnzxDlynpaTk1PunEKlxX7lyhXs37+/xG369+8PZ2dnbNmyBVu3boVKpcI777yjVqdDhw5o27YtNm7cWGKSTxAEsQ+kUinGjBmDu3fvYuXKlRp1tfmeKEnxsT29vSAIWLBggdZtlPR9Uvx29eL+r8ixPu3LL79EXl6euJyWlobVq1ejXr16YiK8Mv1TmtLaCgsLw7lz5zTql/W9V5JXXnkFaWlpGn3466+/4vjx4/Dw8Cj3RgAREVFFubq6onfv3vjxxx+xfft2pKena1yXaHtNVxpvb294eHhg3759WL58ucb6zMxMjB49GtnZ2Vi4cKFWN1D79euH3NxcXLx4sdy6lTF48GA0bNgQn3/+eYnzWBYWFpb7O14mk2lcNxQUFGDJkiXPFJu9vT26d++OsLAwXL16VW3d0qVLNerr4po3MTFRo0wul6N58+bIz88Xt3/77beRkpKC0NDQEtsp6dr+6NGjGtdSxdu/8sorYpmuzmdlzkdBQQH+/PNP9OvXj49XU53CkY5EldSgQQPMmzev0ts/fZdPG4Ig4PvvvwdQdJGSlJSEP//8Ez///DPy8vLwySefYMqUKeW2Y2FhgU2bNuGVV15B+/btMX78eLi5uSElJQUnT56El5cXgoKCym1n8eLFOHbsGEaPHo0TJ06gbdu2uHz5MjZs2ICmTZuWeqFQbPDgwbCyskKfPn3QrFkzZGdn44cffkBqaipmz54NoGiy8YCAAIwYMQKtW7eGjY0Nrl+/jnXr1qFx48bincVXXnkFy5Ytg5eXF959911YWFjg9OnTOHLkCFxdXVFYWFju8ZTG1tYWLVq0wA8//ABXV1c0bNgQlpaWGDp0KBo3boz169fDz88PrVu3xrhx49C8eXMkJycjKioKe/fuxf79+8u8c9+zZ084ODhg2rRpuHv3LpydnXHjxg1s2LBBfJTov4ofZVqwYAE+++wzuLi4iBObP13n+++/h4eHBzp27AhfX1+0bdsWBQUFiImJwf79+zFu3Djxe3jRokWIjIzE1KlTceLECfTt2xcmJia4du0abt68iYiIiAqfu9deew0zZ87E4MGDMXLkSGRnZ2Pfvn3Iz8/Xug13d3d07doVXbp0QZMmTZCcnCzOGzVu3LhKHevTevTogTFjxiA/Px+bNm3C/fv3sW7dOvHFTJXpn9J4eXnB0tISb731Ft5//33Y2dnh4sWL2L59O9q2batx0d+tWzesWrUKEydOxMsvvwxjY2N07dq11NGK06dPx08//YTp06fj8uXL6NGjB+7cuYM1a9agfv36WLFihdaxEhERVYSvry/8/Pwwbdo0WFpaYuTIkWrrtb2mK8uuXbswZMgQfPDBB9i3bx+GDRsGuVyO27dvY+vWrYiLi8OCBQvw1ltvaRVz8SO2Bw8eRNeuXSt13GWxsLDAtm3bMHz4cLi7u+Odd96Bm5sbMjIycOfOHezduxdLly4t82WSr732GtauXYuRI0di0KBBSE5Oxvbt23UyRc5XX32Ffv36oXfv3pg4cSKaNGmCiIgIXLp0CXZ2dmqJMV1c8y5atAi//PILhgwZAhcXFxgZGeHkyZM4fPgwhgwZIs47OWXKFERERGDevHk4deoUBg0ahAYNGuDBgwc4c+YM7t69K85JWeyFF17AgAEDMHHiRDRr1gzHjh3Dvn370KtXL7z99ts6P5+VOR/Hjx9HTk6O2nRIRHVC9b4sm6hmOnHihABAWLhwYbl1+/btK8hkMrWyuXPnCgCEX3/9tdztAQienp4abQIQv0xMTASFQiH07NlTmDlzpnDjxo2KHZAgCBcuXBBeffVVQaFQCMbGxoKjo6MwYsQI4cKFC2r7dXJyKrWNBw8eCOPHjxccHBwEIyMjwdHRUQgICBAePXqkVi86OloAIMydO1cs27BhgzB48GDBwcFBPJ4+ffoIu3btEuvcvXtXCAwMFNq0aSNYW1sL5ubmQosWLYSgoCDhwYMHavv4+eefhRdffFGwsLAQ5HK5MHToUOHatWslHoOTk5PQt29fjeMpKU5BEIQ//vhD6NGjh2BhYSEA0Gjv7NmzwsiRI4WGDRsKxsbGQsOGDYXu3bsLCxcuFJKSkko9f8WuXr0qeHt7C3K5XLCwsBC6desmHDhwQPy+iY6O1tjm7t27gkQiKTHepz148EB4//33hebNmwsmJiaCjY2N0LZtW2HKlCnCtWvX1OqmpaUJISEhQqtWrcS6Xbp0EdasWVPuMWzatEkAIJw4cUIsUyqVwqeffiq0bNlSMDU1FRwdHYX33ntPSE5OFgAI48aNK7fdJUuWCH379hXs7e0FY2NjoVGjRsJLL70khIeHV/pYi8/rtWvXhA8++ED8Hmzbtq2wfft2jXYr0j/jxo0TyvrVevr0aaFPnz6CtbW1YGVlJXh4eAinT58ucTulUilMmzZNaNy4sSCVSgUAwqZNm0o934IgCMnJycLUqVMFJycnwdjYWLCzsxPeeOMN4ebNm2r1SvteL6ttIiKqXSpyfVuejIwMwdLSstTf7xW5pitLfn6+sG7dOqF3796CjY2NeG0sk8mEU6dOVTjuoUOHCs2aNRNUKpVaeWnXwMXnrPj3sTbb3LhxQxg3bpzQpEkT8Xdzp06dhI8++ki4f/++WK+k64rs7Gxh5syZgpOTk2BiYiI4OzsLH330kXDjxg2N3+NlxVbaNeXvv/8u9OvXTzA3NxdsbGyE1157Tbh//77QoEEDwcvLS6OdZ7nmPXHihPD6668Lzs7Ogrm5uWBtbS20a9dO+PTTT4Xs7Gy1uoWFhcKaNWuErl27CvXq1RPMzMwEZ2dn4ZVXXlH7W+Hp65kff/xR6NChg2Bqaio0bNhQCAoKEtLT09Xa1dX5rMz5GDNmjNCoUSMhPz+/zPNEVNtIBIEzxRMRUd0xb948zJ8/H9HR0XB2dtZ3OERERPQMVq1ahaCgIPTt2xeHDx+u0EsQL1y4gM6dO2PXrl147bXXqjDKmiMhIQH29vYIDAzE2rVr9R1OmWJiYuDi4oK5c+c+0xNoVe3evXto1aoVli1bhvfff1/f4RBVK87pSERERERERDXSpEmTsHLlSpw8eRLDhg1DTk6O1tt26tQJvr6+mDt3bqXnsK7JSjpXixYtAlA0FRLpxoIFC9CiRQsEBgbqOxSiasc5HYmIiIiIiKjGmjRpEiZNmlSpbb/77jsdR1MzFBYWomnTphg9ejTatGmDrKwshIeH4+jRo+jfvz+GDRum7xBrjY0bN+o7BCK9YdKRiIiIiIiIqA6RyWTw8fHBkSNHsGnTJhQWFsLZ2RmzZ89GSEiIVm8AJyIqD+d0JCIiIiIiIiIiIp3i7QsiIiIiIiIiIiLSKSYdiYiIiIiIiIiISKeYdCQiIiIiIiIiIiKd4otktJCbm4urV69CoVDAyIinjIiIiGq/wsJCJCQkoG3btjAzM9N3OAaH14dERERU11T0+pBXSFq4evUqunTpou8wiIiIiKrduXPn0LlzZ32HYXB4fUhERER1lbbXh0w6akGhUAAoOqkODg5Vth+lUomkpCTY2tpCJpNV2X6o8thHho39Y/jYR4aPfWTYqrN/4uLi0KVLF/E6iNRV1/VhbcSfM/rF869/7AP94vnXP/aBfj3L+a/o9SGTjloofmTGwcEBTZo0qbL9KJVKmJqaQqFQ8INnoNhHho39Y/jYR4aPfWTY9NE/fHS4ZNV1fVgb8eeMfvH86x/7QL94/vWPfaBfujj/2l4f8kUyREREREREREREpFNMOhIREREREREREZFOMelIREREREREREREOlUjJumJiopCUFAQzpw5AysrK7z99ttYtGgRTExMSt0mMjIS/fv3L3Fd69atERUVVVXhEhERERERERHpnSAISExMRG5uLpRKpb7DAVAUU25uLnJyciCRSPQdTp1T0vmXyWQwMzODnZ2dTvvE4JOOKSkp8PDwQMuWLbF3717ExsYiODgY2dnZWLVqVanbdezYEb///rtaWXp6Ory8vODl5VXVYRMRERERERER6Y0gCIiNjUVGRgZMTEwM5qUtEokEpqamTDjqSUnnPz8/H5mZmcjLy0Pjxo111jcGn3Rct24d0tPTsW/fPjRo0AAAUFhYiIkTJyIkJASOjo4lbmdtbY1u3bqplW3evBkqlQpjxoyp8riJiIiIiIiIiPQlMTERGRkZsLe3h62trb7DEQmCgMLCQhgZGTHxqAelnf+kpCTEx8cjMTERCoVCJ/sy+Dkdw8LCMGDAADHhCACjRo2CSqVCeHh4hdrasWMHWrZsic6dO+s6TCIiIiIiIiIig5GbmwsTExODSjiS4bK1tYWJiQlyc3N11qbBj3SMioqCn5+fWpmNjQ0cHBwqNC/jkydPcPz4ccyePVvXIRIRERFVqeyCbByKPoSDdw4iISsBCksFhrgOwcsuL8PC2ELf4REREZEBUiqVBvNINdUMMplMp3N/GnzSMSUlBTY2NhrlcrkcycnJWreza9cuKJVKrR6tTk9PR3p6urgcFxcHoOgDW5UTryqVSqhUKoOZ3JU0sY8MG/vH8LGPDB/7yPDEpMVgQsQEPMl+AgkkECDgYdZDXIy/iPWX12O953o413fW+X75PUBEREREz8Lgk466sn37dnTq1AmtWrUqt+6yZcswf/58jfKkpCSYmppWRXgAAJVKhbS0NACAVGrwT77XSewjw8b+MXzsI8PHPjIsOYU5CDgdgMS8RACAAEHt3/jseASEB2Bjr40wNzLX6b6TkpJ02h4RERER1S0Gn3SUy+XiHz9PS0lJUZvnsSx37tzBuXPnsGzZMq3qBwcHw9/fX1yOi4tDly5dYGtrq7PJNEtSPKLAzs6OQ6ANFPvIsLF/DB/7yPCxjwzLnlt7kJCXUOp6AQIS8hJwPvM8Xm35qk73nZeXp9P2iIiIiKhuMfiko5ubm8bcjWlpaYiLi4Obm5tWbezYsQNSqRRvvPGGVvWtra1hbW2tUS6Tyar8DzCpVFot+6HKYx8ZNvaP4WMfGT72keE4HH1YfKS6NBJIcDjmMEa5jdLpvtn/RERERPQsDP65KS8vLxw7dgypqali2e7duyGVSjFo0CCt2ti5cyf69esHBweHKoqSiIiISLfylfmISY8pM+EIFI12TMrho9BERHXZV0f/0eqLqCabN28eJBKJ+KVQKODh4YFff/1V36Fp2LlzJxQKBdq3by++M6RLly5YvXq1Wr2oqCgMHDgQlpaWaNSoEWbMmIH8/Hyt93P79m0EBgaiQ4cOMDIywvPPP19ivYCAAAQEBFT+gCrJ4Ec6BgYGYuXKlfDx8UFISAhiY2Mxffp0BAYGwtHRUazn6emJe/fu4fbt22rbX7p0CTdu3MC0adOqO3QiIiKiCitQFWD/7f1Yf3k9knPLf2meBBLYmttWQ2RERERUW+gzCT11QMtKb2tubo7jx48DAB4+fIiFCxfC09MTFy9eLDXhVhUyMzORlZWFhg0baqx79OgRDh8+jM8//xwffvgh0tPTERERgZiYGPj5+Yn1UlJS4OHhgZYtW2Lv3r2IjY1FcHAwsrOzsWrVKq3iuHbtGg4dOoSuXbtCpVJBpVKVWG/mzJl47rnnMGPGDLRo0aJyB10JBp90lMvliIiIQFBQEHx8fGBlZQV/f3+Ehoaq1VMqlSgsLNTYfseOHTA1NcWrr+p2niMiIiIiXSpUFeLg3YNYd3kdYjNjtd5OgIAhzYdUYWREREREhkEqlaJbt27icpcuXeDs7Ix169ZpnajThePHjyM8PLzEff74449YsGABXFxc4OvrCwB48803MXr0aJib//viv3Xr1iE9PR379u0T31lSWFiIiRMnIiQkRG2gXWmGDh2K4cOHAwB8fX3x559/llivRYsW6NmzJ1avXo2vvvqqoodbaQb/eDUAuLu749ixY8jOzsaTJ0/w+eefw8TERK1OZGQkYmJiNLb9/PPPkZubCxsbm+oJloiIiKgCVIIKh+8exogDI/DJb5+oJRwtjSxhaWwJaSmXbFJI0dCiIbxdvKsrXCIiIiKD0axZMygUCkRHR1frfi9duoTvv/8e2dnZGuvu3r0LFxcXcTk6Ohq//vorRo4cqVYvLCwMAwYMUHtJ8qhRo6BSqRAeHq5VHFKp9mm91157Ddu3by9xwF5VqRFJRyIiIqLaRhAEHLt3DK/+/Cpm/joTMekx4jpzI3P4t/XHkZFHsPPlnVBYKAAUPUr99L8KCwU2DNoAC2OLao+fiIiISN/S09ORlJRU5qhAQRBQWFhY7ldFXLp0CWlpadixY4daeXx8POzt7dXKIiIiYGRkhC5duqiVR0VFabwg2cbGBg4ODhovVNaFHj16IDExEX/99ZfO2y6NwT9eTURERFSbCIKAUw9PYfVfq3Ej+YbaOlOZKV5v/Tr8nvcT52msb1ofP/v8jMPRh3HwzkHEZ8XD3tIeQ1yHwNvFmwlHIiIiqlOKE4QPHz7EtGnToFQqNUYRPm3Lli145513ym03Ojoazs7OWsUgk8nQsmVLrF69Gv7+/mL5zz//jKFDh6rVPX/+PFq1agVTU1O18pSUlBKfypXL5UhOLn9e74p67rnnIJPJ8Mcff6BDhw46b78kTDoSERERVQNBEPB73O9YfWk1riReUVtnJDXCyJYjEdAuAPYW9hrbWhhbYGSrkRjhOgIJCQlQKBSQyWTVFToRERGRQcjKyoKxsbG4LJfLsWrVKgwePLjUbYYOHYrz58+X27Y2cygCwL1799CyZUv06dMHU6dOxfHjx+Hh4QEAuHLliloSEgDi4uKgUCi0arsqGRkZwcbGBnFxcdW3z2rbExEREVEd9efjP7Hy0kpcjL+oVi6TyODTwgcT2k2AQz0HPUVHREREVDOYm5vj1KlTkEgksLOzQ9OmTcud17BBgwaoX79+uW0bGWmXIjt27BgGDRqErl27YsmSJVi4cCE8PDyQlZWFevXqadTPzc3VGOUIFCVM09LSNMpTUlLU5nnUJVNTU+Tk5FRJ2yVh0pGIiIioilxOuIxVl1bhbNxZtXKpRIohzYcgsF0gmlo31VN0RERERDWLVCrFiy++WKFtdP149alTpzBu3DgYGRnh448/xuTJk3HgwAGoVKoSR1w2aNCgxBcfu7m5aczdmJaWhri4OI25HnUlNTUVtra2VdJ2SZh0JCIiItKx60nXsfqv1Tj18JTGupecX8J7Hd5D8/rN9RAZERERUd2iy8erY2NjYW9vL46KfO+99/Dtt9/i/fffh5eXF9atW6exTevWrXHixAmNci8vLyxevBipqani3I67d++GVCrFoEGDyo2lohISEpCdnY3WrVvrvO3SMOlIREREpCO3Um5hzV9rcOz+MY11ns08MbHDRLSSt9JDZERERER1k62t7TON7vvrr78wdepUbN68GfPmzUNoaKi4zsjICN988w169eoFpVJZ4pzbPXv2xIIFC/Dw4UM0adJELA8MDMTKlSvh4+ODkJAQxMbGYvr06QgMDBQToJGRkejfvz82bdoEX19fjbazs7Nx+PBhAEVzTaanp2PPnj0AgL59+6rNJfnnn38CAHr16lXpc1FRTDoSERERPaPotGis/Wstfon5BQIEtXW9G/fG+y+8j+dsn9NTdERERERUWYWFhfj999/x3HPPYceOHWjcuLHa+q5du2Lu3Llo3759idv369cPtra2CAsLQ0BAgFgul8sRERGBoKAg+Pj4wMrKCv7+/mpJzaysLABAo0aNSmw7Pj4er732mlpZ8fKJEyfQr18/sTwsLAy9e/dGw4YNxTeAVzUmHYmIiIgq6UHGA6y7vA4H7x6ESlCprevq0BWTOkxCB/sO+gmOiIiIqBQfDNTfkxeCIJRfqQTz5s3DvHnzdBuMFl588UXExcXByMgI1tbWJdaZPXt2qdubmJhg3Lhx2Llzp1rSEQDc3d1x7JjmEzLFzp49i+eee67Ut3M7OztrdT4LCwuxZ88eLF26tNy6usSkIxEREVEFPc56jPVX1mP/rf0oFNTvFHe074hJL0xC50ad9RQdEREREenSs75N+sMPP0SLFi1w+fLlUkdEluS3335DSEgIJBLJM+1/x44dqFevHsaMGfNM7VQUk45EREREWkrITsCGqxuw5589KFAVqK1ra9cWkzpMQnfH7s98YUhERAQAXx39R98hEJEOODg4YPPmzUhISKjQdsePH9fJ/qVSKb777jsYGRlVeqRpZTDpSERERFSO5NxkfHf1O/xw8wfkKfPU1rk1cMP7Hd5H3yZ9mWwkIiIiohL9d+7F6jR27Fi97JdJRyIiIqJSpOWlYcu1Lfj+xvfIKcxRW+da3xXvv/A+PJt5QiqR6ilCIiIiIiLDxKQjERER0X9k5mdi2/Vt2Hp9KzILMtXWOVk74b327+El55cgk8r0FCERERERkWFj0pGIiIjo/2UXZGNH1A5svrYZaXlpausa12uMCe0mYKjrUBhJeQlFRERERFQWXjETERFRnZdbmIsfb/6IjX9vRHJusto6ewt7TGg3ASNajICxzFhPERIRERER1SxMOhIREVGdla/Mx0+3fsK3V75FfE682jpbM1sEtAvAyFYjYSoz1VOEREREREQ1E5OOREREVOcUqArw8+2fsf7KesRlxamtszG1gd/zfnjD7Q2YG5nrKUIiIiIiopqNSUciIiKqdbILsnEo+hAO3jmI5NxkNDBrgCGuQ+Dl5IUTD09g7eW1eJDxQG0bKxMr+D7nizfd34SlsaWeIiciIiIiqh2YdCQiIqJaJTotGgHhAXiS/QQSSCBAwL30e7gYfxGhZ0OhFJRq9S2MLPBWm7fw9nNvw9rEWk9RU0VFRUUhKCgIZ86cgZWVFd5++20sWrQIJiYmZW7n7OyMe/fuaZTn5OTAzMysqsIlIiIiqnOk+g6AiIiISFeyC7IREB6AhOwEAIAAQe3fpxOOZjIzvPP8O/jl1V8w6YVJTDjWICkpKfDw8EB+fj727t2LxYsX45tvvkFwcLBW248cORK///672pepKeftJCIiMnTbt29Hjx49YGVlBSsrK/Ts2RM7d+7Uevvc3Fw0bdoUhw4dqsIoK2b9+vUYNGgQGjVqBGtra3Tr1g0HDhzQaluJRKLx1ahRI7U6AQEBCAgIqIrQy8WRjkRERFRrHIo+hCfZT8qt17VRVyztsxR25nbVEBXp2rp165Ceno59+/ahQYMGAIDCwkJMnDgRISEhcHR0LHP7hg0bolu3btURKhERkUFKWLlKb/u2m/R+pbYLCgrC6tWr4efnhzlz5kAikWDPnj148803ceHCBXzxxRfltrF27VrI5XK8/PLLlYqhKoSGhmLw4MF47733UK9ePezevRs+Pj7YvHkzxo0bV+72QUFBGDNmjLj836c+Zs6cieeeew4zZsxAy5YtdR5/WZh0JCIiolrj4J2D4iPVpZFAgkKhkAnHGiwsLAwDBgwQE44AMGrUKAQGBiI8PBy+vr76C46IiIh07ueff8aqVaswd+5czJs3TywfPHgwHB0dsWDBAgwcOBCDBw8utQ1BELBixQpMnjy5GiLW3sWLF2Fn9+916cCBAxETE4MvvvhCq6Rjs2bNyryZ2qJFC/Ts2ROrV6/G8uXLdRGy1vh4NREREdUa8dnxZSYcgaJHrZNykqopIqoKUVFRcHNzUyuzsbGBg4MDoqKiyt1++/btMDU1Rb169eDt7Y2rV69WVahERESkA8uXL4dcLseHH36osW769OmQy+VYtmxZmW2cPHkSMTExGDlypFq5RCLRGCW5fPlySCSSZw9cC08nHIu98MILePTokc728dprr2H79u0oLCzUWZva4EhHIiIiqvEEQcD+2/vxKLP8izMJJLA1t62GqKiqpKSkwMbGRqNcLpcjOTm5zG2HDRuGrl27olmzZrh79y5CQ0PRq1cvXLp0Cc2bNy91u/T0dKSnp4vLcXFxAAClUgmlUlnaZlQCpVIJlUrF86YnPP/6V5E+kAgqne+7rqtLnwFBECCRSCAImjdky7tJW5UEQRC/tFFYWIgzZ87g5ZdfhqWlpcZ2lpaW6N+/P3755RcUFhZCJpOV2M7Ro0fRtGlTNGnSRKON/8ZT/P/yYtQmiSeTySqcwDx9+jTc3d21OkdLlizBRx99BEtLSwwePBifffYZmjVrplane/fuSExMxKVLl9CpU6cyz78gCKV+Pir6uWHSkYiIiGq0xJxEzD8zH5EPI7WqL0DAkOZDqjYoMlgrVqwQ/9+7d28MGjQIbm5u+OKLL7BmzZpSt1u2bBnmz5+vUZ6UlMSX0FSQSqVCWloaAEAq5YNX1Y3nX/8q0gfmyiyd7jshIUGn7dVEdekzkJubC1NT0xITYyqVbhPaFVFYWCgmr7RJxj1+/Bh5eXlo0qRJqUm+Jk2aIDs7G/Hx8VAoFCXWOX/+PNq2bVvq+Xi6vPj8lJVUjImJQatWrcqN/9tvv8Xbb79dbr1iO3fuxJkzZ7B79+5yk5pjx46Ft7c3GjZsiGvXrmHx4sXo3bs3/vzzT8jlcrFe69atIZPJ8Pvvv6N9+/alnn+VSoW8vLxSf1YkJVXsaSEmHYmIiKjGOnrvKBb+vhApeSlimVQiLbp7W8IdfCmkUFgo4O3iXZ1hko7J5XLxD8anpaSkqM3zqA0HBwf06tULFy5cKLNecHAw/P39xeW4uDh06dIFtra2pf5xQyUr/kPHzs6u1NEoVHV4/vWvIn2QI0vV6b7586pufQZycnIgkUhgZKSZ+tFnwrU4HiMjI62SjsX1SzuW4nUAYGxsXGqdx48fo1OnTqWej6fLi89PaW0BRXMpnjt3rtz4XVxcymznaVeuXMGkSZPg6+uLV199tdz6W7duFf/fv39/9OnTB506dcKmTZswY8YMcZ2RkRFsbGzw5MmTMs+/VCqFmZlZqT8r8vLytDoOcb8Vqk1ERERkANLz07H0j6X4393/qZUPaT4EY9zG4IPID/Ak+4n4UpnifxUWCmwYtAEWxhZ6ipx0wc3NTWPuxrS0NMTFxWnM9agr1tbWsLa21iiXyWS1/o/WqiCVSnnu9IjnX/+07QNBotvEEPu8SF35DBQnlEpK7ElQPfMVlkQikah9lUehUMDU1BQPHjwotf6DBw9gampaZmK9eORniefjP7GUde6KmZqa4oUXXig3fm0fr7537x68vb3RpUsXfPPNN5WaU7J9+/Zo3bo1Ll68qLG9qakpcnNzyz3/Eomk1M9GRT8zTDoSERFRjfL7o9/xyW+f4En2E7HMxtQGn3T7BIOcBwEAfvb5GYejD+Pg3YNIykmCrbkthjQfAm8XbyYcawEvLy8sXrwYqamp4tyOu3fvhlQqxaBBgyrU1qNHj3D69Gm89dZbVRApERERPSsjIyP07NkTkZGRyMrKgqWlpdr6rKwsREZGonfv3mW206BBA6Smppa47r+PMWdllT+1QUxMDFxcXMqtt2nTJvj6+pZZJzExEYMHD4a9vT327t0LY2PjctutqNTUVNjaVu+85kw6EhERUY2QU5iD5ReWY0fUDrXyvk36Yl6PebAz//fNfxbGFhjZaiRGthr532aoFggMDMTKlSvh4+ODkJAQxMbGYvr06QgMDISjo6NYz9PTE/fu3cPt27cBFM2RdPDgQXh7e8PR0RF3797FkiVLIJPJMG3aNH0dDhEREZVjypQpGD58OL788kvMmTNHbd2XX36J5ORkTJgwocw2WrdurfGkRLH/lmvz2LSjoyPOnz9fbr3yEpOZmZnw8vJCfn4+Tpw4UeKTFdr666+/cPPmTbzzzjtq5QkJCcjOzkbr1q0r3XZlMOlIREREBu9qwlWEnA5BTHqMWGZhZIGZXWZiRIsRlXr8hGouuVyOiIgIBAUFwcfHB1ZWVvD390doaKhaPaVSqTZywcXFBY8ePcLUqVPFUZIeHh5YsGCBViMViIjK8tXRf7SqN9nDtYojIap9hg0bhkmTJmHevHl48OABXnvtNQDATz/9hA0bNmDcuHEYObLsm809e/bEjz/+iIKCAo2RhD/++COef/55vPDCCzh27BiOHDkCANi2bRveeOONEkcempiY4MUXX3zmY3vllVfw119/4bvvvsO9e/dw7949cV23bt3E/7do0QJOTk6IiIgAAHzxxRe4c+cO+vXrB3t7e/z9998IDQ1F06ZN1eahBoA///wTANCrV69njrcimHQkIiIig1WgKsD6y+vx7dVvoRSUYnlH+44I7RWKJlZN9Bgd6ZO7uzuOHTtWZp3IyEi15W7duuHEiRNVGBURERFVlZUrV6Jr165Ys2YNdu7cKT4CHRoaio8++qjc7YcPH473338fkZGRGDhwoNo6f39/7N27Fx9//DE6dOiAX375BWPHjsXcuXPx2muvVcnjzsWOHj0KACW+4VoQ/n0x4tNv/QaKRm7+9NNP2LVrFzIyMqBQKPDyyy9j0aJF4vQzxcLCwtC7d280bNhQrc2qxqQjERERGaTbKbcRcjoEN5JviGXGUmNM6TgFY93HQiat3ZO/ExEREVUVRdAkve37WZJeY8eOxdixYwEA8fHxePHFF3Hq1CnMmDGj3DdEN2zYEMOGDcPOnTs1ko7NmjXDihUr1MoePnxY6TgrQtvzERMTo7Y8dOhQDB06tNztCgsLsWfPHixdurQy4T0T/b0jvQKioqIwcOBAWFpaolGjRpgxYwby8/O12jY2Nhbjxo2DQqGAubk53N3dsX379iqOmIiIiCpLJaiw5doWvH7wdbWEo3sDd+wasgvjnhvHhCMRERFRHWdvb499+/bh5MmTeO+997Ta5pNPPsGuXbvw5MmT8ivXEjt27EC9evUwZsyYat+3wY90TElJgYeHB1q2bIm9e/ciNjYWwcHByM7OxqpVq8rcNi4uDt27d0fr1q3xzTffwNraGteuXUNeXl41RU9EREQVEZsZi9mnZ+PPJ3+KZVKJFP5t/RHYLhDGsqp7tIWIiIiIapZOnTohJydH6/odOnTA8uXL8eDBAzRs2LAKIzMcUqkU3333XbkjQauCwScd161bh/T0dOzbtw8NGjQAUDQ0dOLEiQgJCVF7Q+F/zZgxA02bNsUvv/wCmaxoRISnp2e1xE1ERETaEwQB+2/vx6fnP0VWQZZY7mTthNBeoWivaK/H6IiIiIiotggICFBbrs45DvWh+HF0fTD4x6vDwsIwYMAAMeEIAKNGjYJKpUJ4eHip26Wnp+PHH3/ExIkTxYQjERERGZ7EnERMPj4Zc87MUUs4jnYbjd1DdzPhSERERERUAxl80jEqKgpubm5qZTY2NnBwcEBUVFSp2128eBH5+fkwNjZG3759YWxsjEaNGmHmzJkoKCio6rCJiIhIC0fvHcUrB15B5MNIsczewh7rB65HSNcQmBuZ6y84IiIiIiKqNIN/vDolJUXjVd8AIJfLkZycXOp2jx8/BlD02vOAgADMmzcP586dw5w5cyCVSrFkyZJSt01PT0d6erq4HBcXBwBQKpVqryfXNaVSCZVKVaX7oGfDPjJs7B/Dxz4yfNXVR+n56fjs/Gc4GH1Qrfxll5cx88WZsDa15vdJCarzM8TzT0REVLPJZDKtX8JLBBRd/5mYmOisPYNPOlaWSqUCAAwYMABffvklAKB///7IyMjAF198gTlz5sDcvOTRE8uWLcP8+fM1ypOSkmBqalqlMaelpQEomuiTDA/7yLCxfwwf+8jwVUcfXUy6iC/+/gIJuQlimbWxNaa0mYI+jfogLz0PCUgoo4W6qzo/Q0lJSVXaPhEREVUtMzMzZGZmIikpCba2tvoOhwxcUlIS8vPzYW1trbM2DT7pKJfLxYvrp6WkpKjN81jSdgDg4eGhVu7p6YnQ0FDcvn0bbdu2LXHb4OBg+Pv7i8txcXHo0qULbG1toVAoKnMYWikeUWBnZ8d5KA0U+8iwsX8MH/vI8FVlH+UU5mDFpRXYeXOnWnmfxn0wp9sc2Jnb6XR/tVF1foby8vKqtH0iIiKqWnZ2dsjLy0N8fDxSU1MN6vpbpVJxEIIe/ff8K5VK5Ofnw8rKCnZ2ursmN/iko5ubm8bcjWlpaYiLi9OY6/Fpbdq0KbPd3NzcUtdZW1uXmNmVyWRV/iGVSqXVsh+qPPaRYWP/GD72keGrij66mnAVIadDEJMeI5ZZGFlgZpeZGNFiBCQSic72VdtV12eIn1EiIqKaTSKRoHHjxkhMTERubq7BTJ0iCALy8vJgZmbGa0A9KOn8m5iYwNraGnZ2djrtE4NPOnp5eWHx4sVITU0V53bcvXs3pFIpBg0aVOp2Tk5OaNu2LY4dO4ZJkyaJ5UePHoW5uXm5SUkiIiJ6dgWqAqy/vB7fXv0WSuHfC92O9h0R2isUTaya6DE6IiIiotpNIpFU6ROblaFUKpGQkACFQsGbnHpQneff4JOOgYGBWLlyJXx8fBASEoLY2FhMnz4dgYGBcHR0FOt5enri3r17uH37tlgWGhqK4cOHY+rUqXj55Zdx/vx5fPHFF5gxYwYsLS31cThERER1xu2U2wg5HYIbyTfEMmOpMaZ0nIKx7mMhk/Iik4iIiIiotjL4pKNcLkdERASCgoLg4+MDKysr+Pv7IzQ0VK2eUqlEYWGhWtnQoUOxc+dOLFy4EGvXroWDgwPmz5+PWbNmVechEBER1SkqQYVt17dhxcUVyFf9+8ZE9wbuCO0VipbylnqMjoiIiIiIqoPBJx0BwN3dHceOHSuzTmRkZInlr7/+Ol5//fUqiIqIiIj+KzYzFrNPz8afT/4Uy6QSKfzb+iOwXSCMZcZ6jI6IiIiIiKpLjUg6EhERkWETBAH7b+/Hp+c/RVZBlljuZO2E0F6haK9or8foiIiIiIioujHpSERERM8kMScR88/MR+TDSLXy0W6j8UGnD2BuZK6fwIiIiIiISG+YdCQiIqJKO3bvGBb8vgApeSlimb2FPRb2XIgejj30GBkREREREekTk45ERERUYen56Vj6x1L87+7/1MqHNB+CWV1mob5pfT1FRkREREREhoBJRyIiIqqQ3x/9jk9++wRPsp+IZTamNvik2ycY5DxIj5EREREREZGhYNKRiIiItJJTmIPlF5ZjR9QOtfK+TfpiXo95sDO301NkRERERERkaJh0JCIionJdTbiKkNMhiEmPEcssjCwws8tMjGgxAhKJRH/BERERERGRwWHSkYiIiEpVoCrA+svr8e3Vb6EUlGJ5R/uOCO0ViiZWTfQYHRERERERGSomHYmIiAjZBdk4FH0IB+8cREJWAhSWCnRt1BXHHxzHzZSbYj1jqTGmdJyCse5jIZPK9BgxEREREREZMiYdiYiI6rjotGgEhAfgSfYTSCCBAAEPsx7iYvxFtXruDdwR2isULeUt9RQpERERERHVFEw6EhER1WHZBdkICA9AQnYCAECAoPZvsXeefwdBHYJgLDOu9hiJiIiIiKjmYdKRiIioDjsUfQhPsp+UW6+ZVTMmHImIiIiISGtSfQdARERE+nPwzkFIUPabpyWQ4ODdg9UUERERERER1QZMOhIREdVhsZmxGo9S/5cAAUk5SdUUERERERER1QZ8vJqIiKgOyi3MxfKLy7V6tFoCCWzNbashKiIiIiIiqi2YdCQiIqpjopKjMOvULNxJu6NVfQEChjQfUsVRERERERFRbcKkIxERUR2hVCmx5foWrLy0EoWqQrHcWGqMQlVhiY9ZSyGFwkIBbxfv6gyViIiIiIhqOM7pSEREVAfEZcbBP9wfX134Skw4GkmN8EGnD7B7yG7YW9gDgPhSmeJ/FRYKbBi0ARbGFvoJnIiIiIiIaiSOdCQiIqrlDt09hNCzocgoyBDLmtdvjqW9l8Ld1h0A8LPPzzgcfRgH7xxEfFY87C3tMcR1CLxdvJlwJCIiIiKiCmPSkYiIqJZKy0tD6B+hCIsOUysf4zYGH3T6AGZGZmKZhbEFRrYaiRGuI5CQkACFQgGZTFbdIRMRERERUS3BpCMREVEtdC7uHD7+7WM8znosltmZ22Fhz4Xo1biXHiMjIiIiIqK6gElHIiKiWiRfmY+Vl1Ziy7Utai+G8Wzmibnd50JuJtdjdEREREREVFcw6UhERFRL3Eq5hVm/zsI/Kf+IZRZGFpjVZRZ8WvhAIpHoMToiIiIiIqpLmHQkIiKq4VSCCttvbMfyC8uRr8oXy9sr2mNJryVoat1Uj9EREREREVFdxKQjERFRDfYk6wlm/zYbZ+POimUyiQyB7QPh39YfRlL+qiciIiIiourHv0SIiIhqqPCYcMz/fT7S89PFsmZWzbC091K0VbTVY2RERERERFTXMelIRERUw2TmZ2LJuSX4+c7PauUjW43E9Benw8LYQk+RERERERERFWHSkYiIqAa5+OQiQk6HIDYzVixrYNYA83vMR7+m/fQXGBERERER0VOYdCQiIqoBCpQFWHt5LTb+vREqQSWW92nSB/N7zIeduZ0eoyMiIiIiIlLHpCMREZGBu5t2Fx/9+hGuJ10Xy8xkZpjeeTpea/UaJBKJHqMjIiIiIiLSJNV3AERERFQyQRCwK2oXXv/f62oJxza2bfDj0B8xqvUoJhypzoqKisLAgQNhaWmJRo0aYcaMGcjPz69QG8uXL4dEIsGQIUOqKEoiIiKiuosjHYmIiAxQYk4i5vw2B7/G/iqWSSVSjH9+PN7r8B6MpcZ6jI5Iv1JSUuDh4YGWLVti7969iI2NRXBwMLKzs7Fq1Sqt2nj8+DHmz58Pe3v7Ko6WiIiIqG6qESMdK3sn29nZGRKJROMrNze3GqImIiKqnBP3T+DVn19VSzg2rtcYm1/ajMkdJzPhSHXeunXrkJ6ejn379mHw4MHw8/PDZ599hnXr1uHRo0datTFjxgwMGzYM7u7uVRwtERERUd1k8CMdn/VO9siRIzFt2jS1MlNT06oKl4iIqNKyC7Lx2fnP8NOtn9TKh7sOx6wus1DPpJ6eIiMyLGFhYRgwYAAaNGgglo0aNQqBgYEIDw+Hr69vmdufPn0a+/fvx82bNzF69OgqjpaIiIiobjL4pOPTd7KLLywLCwsxceJEhISEwNHRscztGzZsiG7dulVHqERERJV2JeEKPvr1I9zPuC+W1Tetjznd5mCQ8yA9RkZkeKKiouDn56dWZmNjAwcHB0RFRZW5rVKpxKRJk/Dxxx/DwcGhKsMkIiIiqtMMPun4rHeyiYiIDFmhqhAbrm7A+svroRSUYnl3h+5Y2HMhGlo21GN0RIYpJSUFNjY2GuVyuRzJycllbrtmzRpkZWXhgw8+qNA+09PTkZ6eLi7HxcUBKEpiKpXK0jajEiiVSqhUKp43PeH5rzoSQaVVvYr0gbZtaov9zs+AIWAf6NeznP+KbmPwScdnuZMNANu3b8eGDRtgbGyMPn364NNPP0Xbtm2rKlwiIiKt3U+/j49Of4QrCVfEMhOpCT7o9AHGuI+BVFIjpl4mqjHi4+MxZ84cbN26FSYmJhXadtmyZZg/f75GeVJSEqfuqSCVSoW0tDQAgFTKn3PVjee/6pgrs7Sql5iYqHUfaNumthISEnTaXk3Ez4D+sQ/061nOf1JSUoXqG3zS8VnuZA8bNgxdu3ZFs2bNcPfuXYSGhqJXr164dOkSmjdvXup2+rqTzWy/4WMfGTb2j+FjHxURBAH77+zHZ39+hpzCHLG8lbwVFvdcjBY2LSCoBChR/eeJfWTYqrN/DPl7QC6XixfLT0tJSVF7Oua/5syZg3bt2qF3795ITU0FUDRtT2FhIVJTU1GvXj0YGZV8eRwcHAx/f39xOS4uDl26dIGtrS0UCsWzHVAdU/y9ZWdnB5lMpudo6h6e/6qTI0vVqp6dnZ34b3l9oG2b2uLPK34GDAH7QL+e5fzn5eVVqL7BJx2fxYoVK8T/9+7dG4MGDYKbmxu++OILrFmzptTt9HUnm9l+w8c+MmzsH8PHPgLS8tPw1bWv8Fv8b2KZBBK85vwaxrUcB5MCE72OQmAfGbbq7J+K3smuTm5ubhpPvKSlpSEuLg5ubm6lbhcVFYVTp05BLpdrrJPL5QgLC8NLL71U4rbW1tawtrbWKJfJZPyDqRKkUinPnR7x/FcNQcsnFGQymdZ9oG2b2mKfF+FnQP/YB/pV2fNf0foGn3Ss7J3skjg4OKBXr164cOFCmfX0dSeb2X7Dxz4ybOwfw1fX++h07GnM+30eEnMTxbJGFo2wsMdCdG7UWY+R/auu95Ghq87+qeid7Ork5eWFxYsXIzU1VXwiZvfu3ZBKpRg0qPQXLy1fvlwc4Vhs6tSpMDc3x5IlS9CuXbsqjJqIiIiobjH4pGNl72Q/C33eyWa23/Cxjwwb+8fw1cU+yinMwbI/l+GHmz+olXu7eOPjbh/D2kTzd44+1cU+qkmqq38Muf8DAwOxcuVK+Pj4ICQkBLGxsZg+fToCAwPh6Ogo1vP09MS9e/dw+/ZtAECHDh002rKxsUG9evXQr1+/aoqeiIiIqG4w+OemvLy8cOzYMbW70trcyS7Jo0ePcPr0aXTubBijSYiIqPa7nnQdrx98XS3haGVshaW9l+LTPp8aXMKRqCaQy+WIiIiAkZERfHx8MGvWLPj7+2PZsmVq9ZRKJQoLC/UUJREREVHdZvAjHSt7J3vnzp04ePAgvL294ejoiLt372LJkiWQyWSYNm2avg6HiIjqCKVKiU3XNmH1pdUoFP5NerzY8EUs7rUYDvUc9BgdUc3n7u6OY8eOlVknMjKy3Ha0qUNEREREFWfwScfiO9lBQUHw8fGBlZUV/P39ERoaqlbvv3eyXVxc8OjRI0ydOlWc78fDwwMLFiyAi4tLdR8GERHVIbGZsQj5NQQX4y+KZUZSI0x+YTLebvM2ZFLDfWyViIiIiIhIFww+6QhU7k52t27dcOLEiSqMioiI6qrsgmwcij6Eg3cOIjk3GQ3MGmCI6xB4O3vj+IPjCP0jFFkFWWJ91/quWNpnKdwaVM1cxERERERERIamRiQdiYiIDEV0WjQCwgPwJPsJJJBAgIB76fdwMf4iPj33KfKU6m/8Hes+FlM6ToGZkZmeIiYiIqL/+uroP1rX/WBgqyqMhIio9mLSkYiISEvZBdkICA9AQnYCAECAoPbv0wlHhbkCi3ouQo/GPao/UCIiIiIiIj1j0pGIiEhLh6IP4Un2k3LruTdwxzcDv4GNmU3VB0VERERERGSApPoOgIiIqKY4eOcgJJCUWUcCCSyMLJhwJCIiIiKiOo1JRyIiIi0l5yaLj1KXRoCApNykaoqIiIiIiIjIMDHpSEREpKUGZg20Guloa25bTREREREREREZJiYdiYiItOTZzFOrkY5Dmg+ppoiIiIiIiIgME18kQ0REpIWU3BTsv72/zDpSSKGwUMDbxbt6giIiIiIiIjJQHOlIRERUjpTcFPiH++NW6i218uJHrYv/VVgosGHQBlgYW1R7jERERERERIaEIx2JiIjKkJybXJRwTPk34TjlhSmwMbPBwbsHkZSTBFtzWwxpPgTeLt5MOBIREREREYFJRyIiolIl5STBP9wft1Nvi2UzOs/AW23eAgCMbDVSX6EREREREREZNCYdiYiISlBSwnFWl1l40/1NPUZFRERERERUMzDpSERE9B+JOYnwP+KPO2l3xDImHImIiIiIiLTHpCMREdFTEnMSMf7IeNxNuyuWhXQNwWi30XqMioiIiIiIqGZh0pGIiOj/JWQnYHz4eESnRYtlH3f9GG+4vaHHqIiIiIiIiGoeJh2JiIhQlHD0O+KHmPQYseyTbp9gVOtR+guKiIiIiIiohpLqOwAiIiJ9i8+OZ8KRiIiIiIhIhzjSkYiI6rQnWU8wPnw87qXfE8vmdJ+D11q9pseoiIiIiIiIajYmHYmIqM4qKeE4r/s8vNrqVT1GRUREREREVPMx6UhERHXS46zHGH9kPO5n3AcASCDB/B7zMaLlCD1HRkREREREVPMx6UhERHXO46zH8DvihwcZDwAw4UhERERERKRrTDoSEVGdEpcZB78jfniY+RBAUcJxQc8F8Gnho9/AiIiIiIiIahEmHYmIqM6Iy4zDO0feQWxmLICihOPCngsxvMVwPUdGRERERERUuzDpSEREdcKjzEfwO+KnlnAM7RWKoa5D9RwZERERERFR7SPVdwBERERVLTYzVi3hKJVImXAkIiIiIiKqQhzpSEREtVpsZiz8fvHDo6xHAIoSjot7LcbLzV/Wc2RERERERES1F5OORERUaz3MeAi/I36Iy4oDUJRwXNJrCbybe+s5MiIiIqoKXx39R98hEBHR/2PSkYiIaqUHGQ/gd8QPj7MeAyhKOC7tvRReLl56joyIiIiIiKj2Y9KRiIhqnQfpD+AX/m/CUSaRYWnvpXjJ5SU9R0ZERERERFQ3MOlIRES1yv30+/A74ocn2U8AFCUcP+3zKQY7D9ZzZERERERERHUH315NRES1xv30+3jnyDtqCcfP+nzGhCORgSgoKMC6deswfvx4DBo0CLdu3QIA7Nq1Czdu3NBzdERERESkS0w6EhFRrXAv/R7e+eUdxGfHAwCMJEb4vO/nGOQ8SM+REdVNd+7cUVu+e/cuWrdujRkzZuD27duIiIhARkYGAODUqVP47LPP9BEmEREREVURJh2JiKjGi0mLKUo45vybcPyi7xcY6DRQz5ER1V2dO3fG0aNHxeXJkydDoVDg7t27iIiIgCAI4rq+ffvi1KlT+giTiIiIiKpIjUg6RkVFYeDAgbC0tESjRo0wY8YM5OfnV6iN5cuXQyKRYMiQIVUUJRER6UN0WjT8jvghIScBwP8nHPt9AU8nTz1HRlS3rV69Gm+++Sa++OILAEBkZCRmz54NOzs7SCQStbqNGjVCXFycPsIkIiIioipS6aRjQUEBvvjiC0yePBnh4eFq66ZNm/bMgRVLSUmBh4cH8vPzsXfvXixevBjffPMNgoODtW7j8ePHmD9/Puzt7XUWFxER6d/dtLvqCUepEb7s9yU8mzHhSKRvo0ePxqVLl8TRjkZGRmqjG5/25MkT1KtXrzrDIyIiIqIqVum3V3t7e8Pe3h6dOnVCcHAwBg0ahGXLlgEATpw4obMA161bh/T0dOzbtw8NGjQAABQWFmLixIkICQmBo6NjuW3MmDEDw4YNw71793QWFxER6dfd1LsYHz4eiTmJAIoSjl/1+wr9mvbTb2BEJGrcuDGOHDkCoOgR6i+//BJeXl6QSovue0skEgiCgG+++QaenrxZQERERFSbVHqkY2xsLLZv347g4GCcP38eMTExeOeddyAIQql3sSsjLCwMAwYMEBOOADBq1CioVCqNEZYlOX36NPbv34+lS5fqLCYiItKvO6l34HfET0w4GkuNsbzfciYciQzYp59+iqtXr6JNmzaYMWMGJBIJVq9eje7du+PixYtYtGiRvkMkIiIiIh2qVNJRpVKpJRbNzc2xZ88eqFQqjBo1CoWFhToLMCoqCm5ubmplNjY2cHBwQFRUVJnbKpVKTJo0CR9//DEcHBx0FhMREelPccIxKTcJwP8nHPsvR9+mffUcGRGVxc3NDRcuXECPHj2wc+dOyGQyHDx4EC1atMC5c+fg6uqq7xCJiIiISIcq9Xj1zZs3cevWLZw/fx6dO3cGAEilUmzZsgXvvfcerl+/rrMAU1JSYGNjo1Eul8uRnJxc5rZr1qxBVlYWPvjggwrtMz09Henp6eJy8cTmSqUSSqWyQm1VhFKphEqlqtJ90LNhHxk29o/he9Y+up16GwFHA5CSlwKgKOG4rO8y9HToyX7XEX6ODFt19k9V7MPFxQVbtmzRebtEREREZHgqlXS8cuUKvvvuOzRr1kxj3dq1a/HWW289c2DPKj4+HnPmzMHWrVthYmJSoW2XLVuG+fPna5QnJSXB1NRUVyFqUKlUSEtLAwBxriMyLOwjw8b+MXzP0kfRGdGY8ecMpOanAihKOM7vMB9uJm5ISEjQdah1Fj9Hhq06+ycpKUmn7Xl4eGDNmjUaT7AAwD///IPAwEAcP35cp/skIiIiIv2pVNLx6tWreP/999GwYcMS1/fo0eOZgnqaXC4XL66flpKSojbP43/NmTMH7dq1Q+/evZGamgqg6AU0hYWFSE1NRb169WBkVPLhBwcHw9/fX1yOi4tDly5dYGtrC4VC8WwHVIbiEQV2dnaQyWRVth+qPPaRYWP/GL7K9tGtlFuYeWGmmHA0kZpgeb/l6OGou983VISfI8NWnf2Tl5en0/YiIyPVniR5Wnp6Ok6dOqXT/RERGaqVEbdgrsxCjiwVgoQ3+Iio9qpU0jEmJkZjjsSYmBh8++23+P333/H48WNIJBI0atQIPXv2xPjx40scFakNNzc3jbkb09LSEBcXV+Kd8mJRUVE4deoU5HK5xjq5XI6wsDC89NJLJW5rbW0Na2trjXKZTFblF/hSqbRa9kOVxz4ybOwfw1fRPrqZfBMBxwKQmpcKADCVmWJF/xXo0ZgJx6rCz5Fhq67+qYr2JRJJieVnzpyBvb29zvdHRERERPpTqaRjbm6u2vKOHTswfvx45OXloXHjxmjatCkEQcDNmzdx/PhxfP7559i8eTNGjRpV4X15eXlh8eLFSE1NFed23L17N6RSKQYNGlTqdsuXLxdHOBabOnUqzM3NsWTJErRr167CsRARUfW6mXwT/uH+6glHjxUc4UhUQyxZsgRLliwBUJRw7N+/v8Zj4Xl5eSgsLMTEiRP1ESIRERERVZEKJx3T0tJgbm4uLkdFRcHPzw+9evXCypUr4e7urlb/2rVrCAoKwrhx49ChQwe0atWqQvsLDAzEypUr4ePjg5CQEMTGxmL69OkIDAyEo6OjWM/T0xP37t3D7du3AQAdOnTQaMvGxgb16tVDv379KhQDERFVv6jkKPiH+yMtr2iKDVOZKVZ6rER3x+56joyItNWjRw9MmzYNgiBgwYIFGD16NJo0aaJWx8TEBO7u7hg6dGiF2o6KikJQUBDOnDkDKysrvP3221i0aFG5c3mPHTsWf/zxBx49egQTExO0bdsWs2fPLvNmNhERERFVXIWTjleuXEHr1q3F5dWrV6N58+Y4fPhwiRd5zz33HMLCwvDCCy9g9erV+Prrryu0P7lcjoiICAQFBcHHxwdWVlbw9/dHaGioWj2lUonCwsKKHg4RERmgG0k3EHA0QEw4msnMsNJzJbo5dNNzZERUEX379kXfvn0BFI109Pf3R+PGjZ+53ZSUFHh4eKBly5bYu3cvYmNjERwcjOzsbKxatarMbfPz8xEcHIyWLVsiNzcXGzduhLe3N06cOIHevXs/c2xEREREVOSZk44nT57Eu+++W+ZdZVNTU7z77rvYtGlTpYJ0d3fHsWPHyqwTGRlZbjva1CEiIv26nnQdAeEBSM8veuGEmcwMqzxXoatDVz1HRkTPYu7cuTpra926dUhPT8e+ffvEFwsWP6IdEhKi9jTMf/34449qy15eXnBxccG2bduYdCQiIiLSoQonHa9evao25879+/fRtm3bcrdr27YtYmJiKro7IiKqQ64lXcO74e+KCUdzI3Os9lyNzo066zkyIqqMYcOG4csvv0TLli0xbNiwMutKJBIcOHBAq3bDwsIwYMAAMeEIAKNGjUJgYCDCw8Ph6+urdYwymQw2NjbIz8/XehsiIiIiKl+Fk45///232kjHjIwMWFlZlbtdvXr1kJmZWdHdERFRHXEt8RoCjgYgIz8DABOORLVBRkYGlEolACA9Pb3Ut1dXVPGc4k+zsbGBg4MDoqKiyt1eEAQolUqkpaVh06ZNuHXrFtavX6+T2IiIiIioSIWTjqmpqTA1NRWXBUHQ2QUkERHVTX8n/o13w99FRsG/Ccc1nmvwYqMX9RwZET2LEydOiP/X5TQ3KSkpsLGx0SiXy+VITk4ud/uNGzciICAAQNGN8V27dqF797JfUpWeno709HRxOS4uDkDRvOLFiVXSjlKphEql4nnTk9p+/iWCSudtanuutN23RFABglAlsZantvZ7RdT2z0BNwD7Qr2c5/xXdpkJJxzt37pQ4+Xf//v0hlUrL3Falqv4fqEREZPiuJlzFhKMT1BKOawesRaeGnfQcGRFVh/z8/HLfOK1rPj4+6NChAxITE7F7926MGjUK+/btg5eXV6nbLFu2DPPnz9coT0pKUrshT+VTqVRISyt6UVh5f0OQ7tX282+uzNJ5mwkJCTretwBTIRdQAUD1DuDR9lhqs9r+GagJ2Af69SznPykpqUL1K5R0vHLlCtzc3NTKdDkpOBER1S1XEq5gwtEJyCwomn7DwsgCawesRceGHfUcGRHp2rZt25CamoqgoCAARVP2jBgxAtHR0ejVqxd+/PFH2Nvba9WWXC4XL5aflpKSojbPY2ns7OxgZ2cHAHjppZeQnJyM6dOnl5l0DA4Ohr+/v7gcFxeHLl26wNbWFgqFQqu4qUjxKAk7OzvIZDI9R1P31PbznyNL1Xmb2n7Gtd130UhHIFdqAUFSvQkX/ryq/Z+BmoB9oF/Pcv7z8vIqVL/CScen53MEmHQkIqLyZRdk41D0IRy8cxAJWQlQWCrQwb4DdkXtQlZh0agACyMLrBu4Di/Yv6DnaImoKnz++eeYMGGCuBwUFAQTExMsX74cK1euREhICL799lut2nJzc9OYuzEtLQ1xcXEaN8i10alTJ4SFhZVZx9raGtbW1hrlMpmMfzBVglQq5bnTo9p8/qsiiaftearQviUSCBJptScda2OfV0Zt/gzUFOwD/ars+a9o/QonHZ9+czUREVF5otOiERAegCfZTyCBBAIEPMx6iIvxF8U6lsaWWDdgHTrYd9BfoERUpWJiYtCmTRsAQGJiIn799VccPHgQL730EhQKBT788EOt2/Ly8sLixYuRmpoqzu24e/duSKVSDBo0qMKxnT59Gs2bN6/wdkRERERUugolHa9evapx9/i/bw4si0QiwcaNGyuySyIiqsGyC7IREB6AhOyi+YMECGr/AoAEEizvt5wJR6JaTiqVIj8/H0DRC2aMjY3Rv39/AICDg0OF5ggKDAzEypUr4ePjg5CQEMTGxmL69OkIDAyEo6OjWM/T0xP37t3D7du3AQCHDh3C1q1bMWTIEDRt2hTJycnYsWMHjhw5gp07d+rwaImIiIhI66RjYWEhYmNjNV4ks3nzZlhZWcHV1RWCIJSydRG+5ZqIqG45FH0IT7KflFlHgICHmQ+rKSIi0pf27dtjzZo1aNKkCVasWAEPDw/xBSz379/Xej5HoGhOx4iICAQFBcHHxwdWVlbw9/dHaGioWj2lUonCwkJx2dXVFXl5eZg1axYSExNhZ2eHdu3aITIyEn379tXNgRIRERERgAokHY2MjGBjY4O0tDTUr19fLO/evTvOnj0LpVKJMWPG4I033oCTk1OVBEtERIavQFmABxkPEJ0WjW+vlj8/mwQSHLx7ECNbjayG6IhIXxYvXowhQ4agXbt2sLKywrFjx8R1+/btQ5cuXSrUnru7u1obJYmMjFRbdnNzw/79+yu0HyIiIiKqnAo9Xt22bVvcvHlT7aLwt99+w/379/HDDz9gx44dCAkJQffu3TFmzBiMGjVKfDMgERHVHoIgIDk3GTHpMYhJi0F0WjRi0ov+jc2MhVJQat8WBCTlaP9YJRHVTD179sT9+/fxzz//wNXVVZyLEQDGjx+PFi1a6C84IiIiItK5Cicdo6KiNO5EN2vWDDNmzMCMGTNw/fp17Ny5E8uXL8fUqVPh6emJyZMnw8vLS6eBExFR1StQFuB+xv2ixGJ6tJhcjEmLQXp+uk72IYEEtua2OmmLiAyblZUVOnXqpFHu7e2th2iIiIiIqCpVKOnYrl07REVFlVmnTZs2WLhwIT7++GPMmTMHy5Ytg7m5OZOOREQG6ulRi9Fp0YhJi6n0qMVi1ibWcK7vDAkkuJxwuez9Q8CQ5kMqGz4R1SA3b97ETz/9hIcPHyI3N1dtHV84SERERFS7VDjpeODAgVLXK5VKhIeH44cffsCBAwdgZGSE8ePHw9/f/5kDJSKqS7ILsnEo+hAO3jmI5NxkNDBrgCGuQ/Cyy8uwMLaoVJuljVqMTotGRn5GhduTSWRoYtUEztbOcKnvAmdrZzjXL/q/3FQOiUSC7IJsDNs/DAnZCVBBpdGGFFIoLBTwduEoJ6Labtu2bXjnnXdgZmYGJycnmJiYqK3nCweJiIiIapcKJR3btGmDu3fvapSfOnUKO3fuxO7du5GXl4fhw4dj+/btGDx4MIyMKrQLIqI6LzotGgHhAXiS/QQSSCBAwL30e7gYfxHrL6/HhkEb4FLfpcRti0ctPv0YdHR60ejFh5kPoRI0E3/lsTax1kgquli7oKlVUxjLjMvc1sLYAhsGbdA4nuJ/FRYKbBi0odKJVCKqORYuXIiRI0fiu+++g4UFP/NEREREtV2FMoLGxsaQSqUQBEG8G920aVMkJibCy8sLa9euxdChQ2FmZlYlwRIR1XbZBdkICA9AQnYCgKJHj5/+NyE7AQHhAfhp2E9IzElUG61YnGCsqlGLleVS3wU/+/yMw9GHcfDOQcRnxcPe0h5DXIfA28WbCUeiOuLRo0dYu3YtE45EREREdUSFhyG2bt0a0dHRaN68OQAgNjYWxsbGOHr0KI4dO1bmthKJBGlpaZWLlIioDjgUfQhPsp+Uul4FFZ5kP0HvH3qLiciKeHrUokt9l6LEopajFp+FhbEFRrYaiRGuI5CQkACFQgGZTFZl+yMiw9OnTx/8/fff8PT01HcoRERERFQNKpx0bNeuHW7evCkmHefOnavzoIiI6qqDdw6Kjx6Xpaz1xaMWXayLkopPJxifddQiEVFlLV68GGPHjoWZmRkGDhwIGxsbjToNGjSo/sCIiIiIqEpUOulY/DZqJh2JiHQnOTdZ6xGMJY5arO+CpvWqdtQiEVFldOzYEQDw3nvvlXrzQ6lUVmdIRERERFSFKpV0LOsN1kREVHkNzBrgXvq9MhOPEkjQTtEO27y2cdQiEdUY3333HX9mEREREdUhFU46Nm7cGAkJCeKyn5+f1ttKJBJs3LixorskIqoz+jfrj4vxF8usI0CATwsf/vFORDWKr6+vvkMgIiIiompU4aQjAJiYmIj/37x5M6ysrODq6gpBKPuRQP6BTERUugJlASLuR5RZRwopFBYKeLt4V1NURES6lZKSgr///hsPHjyAl5cX5HI5cnNzYWJiAqlUqu/wiIhqta+O/qNVvQ8GtqriSIioLqhU0rFhw4bIyMiAlZUVunfvjrNnz0KpVGLMmDF444034OTkpOs4iYhqNUEQEPpHKP6K/0utvPilMsX/KiwU2DBoAyyMLfQTKBFRJalUKsyePRsrVqxAdnY2JBIJzp8/D7lcjldeeQVdu3blXOFEREREtUilbie3bdsWUVFRAIDffvsN0dHRePPNN7Fz5040b94cvXr1wpo1a5CYmKjTYImIaqsdUTvw062fxOWxbcZibve56NiwI5ytndGxYUfM7T4XP/v8DJf6LnqMlIiocubMmYNVq1bhyy+/xD///KP2hMywYcPwv//9T4/REREREZGuVWqkY/EbrDt37gwAaNasGWbMmIEZM2bg+vXr2LlzJ5YvX46pU6fC09MTkydPFt92TURE6n6L/Q2fnf9MXO7bpC8+7PQhZFIZRrYaqcfIiIh0Z/PmzVi8eDEmTJig8ZZqV1dX3LlzR0+REREREVFVqNRIx+effx63bt0qcV2bNm2wcOFCXLlyBVOnTsXRo0exYcOGZwqSiKi2upt2F9NPTodKUAEAWti0wNLeSyGTyvQcGRGRbiUlJcHd3b3EdUqlEgUFBdUcERERERFVpUqNdDQ3Ny/xwlCpVCI8PBw//PADDhw4ACMjI4wfPx7+/v7PHCgRUW2TlpeGoIggZBRkAABsTG2w0mMl6pnU03NkRES616pVKxw9ehSenp4a6yIjI/H888/rISoiIiIiqiqVSjoCQKdOncT/nzp1Cjt37sTu3buRl5eH4cOHY/v27Rg8eDCMjCq9CyKiWqtAVYBpJ6fhfsZ9AICRxAhf9fsKTaya6DkyIqKq8cEHHyAgIADGxsYYObJo6oiHDx/i999/x4oVK7B582b9BkhEVApt3/hMRETqKp0RfPXVVwEATZs2RWJiIry8vLB27VoMHToUZmZmOguQiKg2+uzcZ/gj7g9xeXa32Xix0Yt6jIiIqGr5+voiOTkZ8+bNw+LFiwEAPj4+sLCwwKJFizBq1Cg9R0hEREREuvTMwxBjY2NhbGyMo0eP4tixY2XWlUgkSEtLe9ZdEhHVaLuiduGHmz+Iy2Pdx+LVVq/qMSIiouoRHByMd999F2fOnEFiYiIaNGiA7t27o379+voOjYiIiIh07JmTjnPnztVFHEREdcIfcX9gybkl4nJPx56Y9uI0PUZERFR1tm7dWub6+Ph4HDhwQFx+++23qzokIiIiIqomTDoSEVWT++n3ERwZDKWgBAA4Wzvjs76fwUjKuW+JqHby9fVVW5ZIJAAAQRA0ygAmHYmIiIhqE6m+AyAiqgsy8jMQdDwI6fnpAABrE2us8lwFaxNrPUdGRFR1UlJSxK/z58/DyckJs2fPxuXLl/H48WNcvnwZH3/8MZycnPDHH3+U3yARERER1Rg1IukYFRWFgQMHwtLSEo0aNcKMGTOQn59f7nZjx45Fy5YtYWlpCblcjj59+iA8PLwaIiYi+pdSpcSMUzNwN+0uAEAmkeGLvl/AydpJz5EREVWt+vXri1+zZs3Cu+++i/nz56Nt27awt7dH27ZtsWDBAgQEBGDmzJn6DpeIiIiIdMjgk44pKSnw8PBAfn4+9u7di8WLF+Obb75BcHBwudvm5+cjODgYBw4cwLZt22Brawtvb2/8+uuv1RA5EVGRZReW4XTsaXF5ZpeZ6O7YXY8RERFVvzNnzqBTp04lruvUqRPOnj1bzRERERERUVUy+InE1q1bh/T0dOzbtw8NGjQAABQWFmLixIkICQmBo6Njqdv++OOPasteXl5wcXHBtm3b0Lt37yqNm4gIAPbd2oet1/99kcKoVqPwRus39BgREZF+2NvbY9euXRg4cKDGuh9++AEKhUIPURERERFRVTH4pGNYWBgGDBggJhwBYNSoUQgMDER4eLjGBOVlkclksLGx0erRbCKiZ3XxyUUsOLtAXO7SqAtmdZ2l9tIEIqK6IiQkBBMmTMCdO3fg4+MDe3t7xMfHY9++fTh16hTWr1+v7xCJiIiQsHKVTtpRBE3SSTtENZnBJx2joqLg5+enVmZjYwMHBwdERUWVu70gCFAqlUhLS8OmTZtw69YtXtQSUZWLzYzFB5EfoFBVCABoatUUX/b9EsZSYz1HRkSkHwEBAXBwcEBoaCimT5+OwsJCGBkZoWPHjjhw4ACGDh2q7xCJiIiISIcMPumYkpICGxsbjXK5XI7k5ORyt9+4cSMCAgIAAPXq1cOuXbvQvXvZc6mlp6cjPT1dXI6LiwMAKJVKKJXKCkRfMUqlEiqVqkr3Qc+GfWTYDKV/sgqyEBQRhOTcop9R9Yzr4et+X8PK2ErvsembofQRlY59ZNiqs3+qYh9DhgzBkCFDoFKpkJCQAIVCAanU4KcYJyIiIqJKMPik47Py8fFBhw4dkJiYiN27d2PUqFHYt28fvLy8St1m2bJlmD9/vkZ5UlISTE1NqyxWlUqFtLQ0AOAFuIFiHxk2Q+gflaDCvEvzcCv1VlEckOKjth/BKt8KCQkJeonJkBhCH1HZ2EeGrTr7JykpqcralkqlaNiwYZW1T0RERET6Z/BJR7lcLl5cPy0lJUVtnsfS2NnZwc7ODgDw0ksvITk5GdOnTy8z6RgcHAx/f39xOS4uDl26dIGtrW2VTnJePKLAzs4OMpmsyvZDlcc+MmyG0D8rLq3A7wm/i8sfdPwAL7d5WS+xGCJD6CMqG/vIsFVn/+Tl5VVp+0RERERUuxl80tHNzU1j7sa0tDTExcXBzc2twu116tQJYWFhZdaxtraGtbW1RrlMJqvyC3ypVFot+6HKYx8ZNn32z8G7B/Hdte/EZZ8WPhj3/Di+OOY/+BkyfOwjw1Zd/cP+JyKqu746+o/WdT8Y2KoKIyGimszgn5vy8vLCsWPHkJqaKpbt3r0bUqkUgwYNqnB7p0+fRvPmzXUYIRERcCXhCub+Nldc7mjfEZ90+4QJRyIiIiIiIqqTDH6kY2BgIFauXAkfHx+EhIQgNjYW06dPR2BgIBwdHcV6np6euHfvHm7fvg0AOHToELZu3YohQ4agadOmSE5Oxo4dO3DkyBHs3LlTX4dDRLXQ46zHmHx8MvJV+QAAR0tHLOu3DCYyEz1HRkRERERERKQfBp90lMvliIiIQFBQEHx8fGBlZQV/f3+Ehoaq1VMqlSgsLBSXXV1dkZeXh1mzZiExMRF2dnZo164dIiMj0bdv3+o+DCKqpbILsjH5+GQk5Ra9cMHcyBwrPFbA1txWz5ERERERERER6Y/BJx0BwN3dHceOHSuzTmRkpNqym5sb9u/fX3VBEVGdpxJUmP3bbNxIvgEAkECCpb2XonWD1nqOjIiIiIiIiEi/DH5ORyIiQ7X+8nocvXdUXJ7ccTI8mnnoMSIiIiIiIiIiw8CkIxFRJRyJOYI1l9eIyy83fxnjnx+vx4iIiIiIiIiIDAeTjkREFXQt6Rpmn54tLre1a4v5PebzTdVERERERERE/49JRyKiCkjITsDk45ORq8wFANhb2OPr/l/DVGaq58iIiIiIiIiIDAeTjkREWsotzMWUE1MQnx0PADCTmWGFxwooLBR6joyIiIiIiIjIsDDpSESkBUEQMO/3ebiaeFUsW9RrEZ6zfU6PUREREREREREZJiN9B0BEVBNs/HsjDt09JC5PbD8Rg50H6zEiIiIiIk0JK1eVuV4FIM3cDJKc3FJHoCiCJuk8LqK6przPojb4WaSajiMdiYjKcfz+cXx98WtxeZDTIExoP0GPEREREREREREZNiYdiYjKcDP5Jmb9Oktcdm/gjkW9FkEq4Y9PIiJ9ioqKwsCBA2FpaYlGjRphxowZyM/PL3ObuLg4zJgxAx06dICVlRWaNGmCMWPG4N69e9UUNREREVHdwceriYhKkZSThMnHJyOnMAcAYGduhxUeK2BuZK7nyIiI6raUlBR4eHigZcuW2Lt3L2JjYxEcHIzs7GysWlX642wXLlzA3r174efnh27duiExMRELFy5Ely5d8Pfff0Oh4IvBiIiIiHSFSUciohLkK/MRHBmMR1mPAAAmUhN83f9rNLJspOfIiIho3bp1SE9Px759+9CgQQMAQGFhISZOnIiQkBA4OjqWuF2vXr0QFRUFI6N/L4F79OiBZs2aYevWrZg2bVq1xE9ERERUF/D5QCKi/xAEAQvPLsTF+Iti2fye89FO0U6PURERUbGwsDAMGDBATDgCwKhRo6BSqRAeHl7qdjY2NmoJRwBo0qQJFAoFHj16VGXxEhEREdVFTDoSEf3H1utbsf/2fnHZv60/hjQfor+AiIhITVRUFNzc3NTKbGxs4ODggKioqAq19c8//yA+Ph7u7u66DJGIiIiozuPj1URETzn18BSWXVgmLvdv2h9BLwTpMSIiIvqvlJQU2NjYaJTL5XIkJydr3Y4gCJg8eTIcHR0xevToMuump6cjPT1dXI6LiwMAKJVKKJVKrfdJRedMpVLxvFURlRbrVeXUq8l9IxHKOwP6JxFUgCDUiFi1UdO+X8r7GWRIvVLTzq22+HtAv57l/Fd0GyYdiYj+353UO5h5aiZU/38B2FLeEkt6L+GbqomIaql58+YhIiICv/zyCywtLcusu2zZMsyfP1+jPCkpCaamplUVYq2kUqmQlpYGAJBK+TtW19LMzcpcLwDIMjGBBICktDoJCboOq9qYK7P0HYIWBJgKuf+f3SqtF2qOhBr2/VLez6DyPkPVqSZ/FsvC3wP69SznPykpqUL1mXQkIgKQmpuKoONByCzIBADITeVY6bESlsZl/xFKRETVTy6XixfLT0tJSVGb57EsGzZswIIFC7Bx40Z4enqWWz84OBj+/v7iclxcHLp06QJbW1u+9bqCikdJ2NnZQSaT6Tma2keSk1vmehWKEo/1c3JLnWvLrgZ/T+fIUvUdQrmKRjoCuVILCLXg5nZN+xlY3s+g8j5D1akmfxbLwt8D+vUs5z8vL69C9Zl0JKI6r0BVgOCTwXiQ8QAAYCQ1wvL+y9G4XmM9R0ZERCVxc3PTmLsxLS0NcXFxGnM9lmTfvn147733sGDBAvj5+Wm1T2tra1hbW2uUy2Qy/sFUCVKplOeuimiTwpI+9VWSmtwvNSaJJ5FAkEhrTrxlqInfL2X9DDKkHqmJ51Zb/D2gX5U9/xWtb0ifJyKiaicIApb8sQTnH58Xy+Z0m4OODTvqMSoiIiqLl5cXjh07htTUVLFs9+7dkEqlGDRoUJnbRkZGYvTo0QgICMAnn3xSxZESERER1V1MOhJRnfbDzR+w+5/d4vLbbd7GiJYj9BgRERGVJzAwEFZWVvDx8UF4eDg2bdqE6dOnIzAwEI6OjmI9T09PtGjRQly+ceMGfHx80LJlS7z11ls4e/as+HXnzh19HAoRERFRrcXHq4mozvr90e/49Nyn4nLPxj0R3ClYjxEREZE25HI5IiIiEBQUBB8fH1hZWcHf3x+hoaFq9ZRKJQoLC8XlP/74A2lpaUhLS0PPnj3V6o4bNw6bN2+ujvCJiIiI6gQmHYmoTopJi8G0k9OgFIom0XWp74LP+3wOmZRzihAR1QTu7u44duxYmXUiIyPVln19feHr61t1QRERERGRiI9XE1Gdk5aXhqDjQcjIzwAA1Detj1Ueq2BlYqXnyIiIiIiIiIhqByYdiahOKVQVYsapGYhJjwEAGEmMsKzvMjSzbqbfwIiIiIiIiIhqESYdiahO+fLPL3Hm0Rlx+aOuH6GLQxc9RkRERERERERU+zDpSER1xp5/9uD7G9+Ly2+0fgOjWo/SY0REREREREREtROTjkRUJ5x/fB6hZ/99q2lXh66Y0WWGHiMiIiIiIiIiqr349moiqvUeZDxAcGQwCoVCAEAzq2b4su+XMJYa6zkyIiIion8lrFyl7xCIiIh0hiMdiahWy8zPxOTjk5GalwoAsDK2wkrPlahvWl+/gRERERERERHVYhzpSES1llKlxKxfZ+F26m0AgFQixed9P0fz+s31HBkRERERfXX0H63rfjCwVRVGQkREVYEjHYmo1vr60tc4+fCkuDz9xeno2binHiMiIiIiIiIiqhs40pGIaqUDtw9g09+bxOVXW76KN93f1GNERERERERENZOu5pxVBE3SSTtUMzDpSEQ1XnZBNg5FH8LBOweRkJUAc2Nz3Em7I67v1LATPu76MSQSiR6jJCIiIiIiIqo7mHQkohotOi0aAeEBeJL9BBJIIEBQW29vYY+v+n0FYxnfVE1ERERERERUXWrEnI5RUVEYOHAgLC0t0ahRI8yYMQP5+fllbhMXF4cZM2agQ4cOsLKyQpMmTTBmzBjcu3evmqImoqqWXZCNgPAAJGQnAIBGwhEoepmMqcy0ukMjIiIiIiIiqtMMfqRjSkoKPDw80LJlS+zduxexsbEIDg5GdnY2Vq0qfU6BCxcuYO/evfDz80O3bt2QmJiIhQsXokuXLvj777+hUCiq8SiISNcKVYXYcn0LnmQ/KbNeUm4SDkcfxshWI6spMiIiIiIi0gdt5h1UAUgzN4MkJ7dmjMIiqsEMPum4bt06pKenY9++fWjQoAEAoLCwEBMnTkRISAgcHR1L3K5Xr16IioqCkdG/h9ijRw80a9YMW7duxbRp06olfiJ6NipBhdjMWNxJvYPbqbeLvlJuIzotGvmqskc8A4AEEhy8e5BJRyIiIiIiIqJqZPBJx7CwMAwYMEBMOALAqFGjEBgYiPDwcPj6+pa4nY2NjUZZkyZNoFAo8OjRoyqKlogqSxAEPMl+glspt3An9Q5upRb9ezftLnIKcyrfLgQk5STpMFIiIiIiIiIiKo/BJx2joqLg5+enVmZjYwMHBwdERUVVqK1//vkH8fHxcHd312WIRFQBgiAgMSdRHLVYnGC8m3oXmQWZFWpLCilUUJVZRwIJbM1tnyVkIiIiIiIiIqogg086pqSklDhqUS6XIzk5Wet2BEHA5MmT4ejoiNGjR5dZNz09Henp6eJyXFwcAECpVEKpVGq9z4pSKpVQqVRVug96NuyjiknJTSlKLKbdwZ3UO+K/aflpFWrHTGYGl/oucLVxhWt9V7SwaQHX+q448+gMFp1bVOa2AgR4O3uzzwwEP0OGj31k2Kqzf/g9QFR3aTMvnjYUQZN00g4REdVMBp901JV58+YhIiICv/zyCywtLcusu2zZMsyfP1+jPCkpCaamVfcWXJVKhbS0omSMVMopbQ1RbemjnMIcHI87johHEUgtSIWNsQ08HT3h4eABcyPzCreXWZCJmMwYxGTG4F7mPfH/qfmpFWrHWGKMppZN4VTPCc5WznCu5wwnSyc0smgEmUT2n4MAulh1gcJUgcS8xBLfXC2BBHamduhcrzMSEhIqfFyke7XlM1SbsY8MW3X2T1ISp6YgIiIiosoz+KSjXC4XL66flpKSojbPY1k2bNiABQsWYOPGjfD09Cy3fnBwMPz9/cXluLg4dOnSBba2tlX61uviEQV2dnaQyWTl1CZ9qA19FJMWgwm/TsCT7CeQQAIBAh7iIa6mXsXOmJ1Y77kezvWdS9w2qyALd9PuiqMWi0cxxmfHVygGmUQGJ2snuNZ3VRu92NSqKYykFfuxtGHQBkyIUD+e4n/tLeyx3nM9mtVvVqE2qerUhs9Qbcc+MmzV2T95eXlV2j4RERER1W4Gn3R0c3PTmLsxLS0NcXFxcHNzK3f7ffv24b333sOCBQs05oYsjbW1NaytrTXKZTJZlV/gS6XSatkPVV5N7qPsgmxMiJiAhOyiUX/FowOL/03ITsCEiAnYPXQ34rLi1F7ocjvlNh5lVewlTBJI0NSqadHj0DauaClvCVcbVzhbO8NEZqKTY3Jt4IqffX7G4ejDOHjnIOKz4mFvaY8hrkPg7eINC2MLneyHdKcmf4bqCvaRYauu/mH/ExEREdGzMPiko5eXFxYvXozU1FRxbsfdu3dDKpVi0KBBZW4bGRmJ0aNHIyAgAJ988kk1REtk2A5FH8KT7CelrldBhSfZT9BnV58Kt924XmO42hSNWCz+cqnvAjMjs2cJWSsWxhYY2WokRriOQEJCAhQKBf9YJiIiomqjqzkQiYiIahODTzoGBgZi5cqV8PHxQUhICGJjYzF9+nQEBgbC0dFRrOfp6Yl79+7h9u3bAIAbN27Ax8cHLVu2xFtvvYWzZ8+KdRUKBVxdXav9WIj07eCdg+Kjx5Vlb2GPljYt1RKMrjauHFFIRERERERERCKDTzrK5XJEREQgKCgIPj4+sLKygr+/P0JDQ9XqKZVKFBYWist//PEH0tLSkJaWhp49e6rVHTduHDZv3lwd4RMZlOTcZK0TjrZmtmJCsYX83+SitYnm1ANERERERERERE8z+KQjALi7u+PYsWNl1omMjFRb9vX1ha+vb9UFRVQD1TetX24dCSRop2iH772/r4aIiIiIiIiIiKg2qhFJRyJ6dv+k/IMH6Q/KrSdAgE8Ln6oPiIiIiOqstIMHIcnJhfQZ2lAETdJJLJyPkUj/+Dkkqp2e5fc8EdUQh+8extjDY5Gcl1xmPSmkaGjREN4u3tUUGRERERERERHVRhzpSFSLFagKsOzPZfj+xr+PSsskMlgaWyI9P118qUzxvwoLBTYM2sCXwhARERERERHRM2HSkaiWSshOwIcnP8TF+Itimb2FPb7q9xVa2LTA4ejDOHj3IJJykmBrboshzYfA28WbCUciIiIieiZn7yYBAG4f/UfPkVB1+EoH/dzi/79nAKBbc9tnbo+IDAOTjkS10MUnFzHt5DQk5iSKZV0adcFnfT6DrXnRL/GRrUZiZKuR+gqRiIiIiIiIiGoxJh2JahFBELAjage+OP8FCoVCsfyd59/B5Bcmw0jKjzwRERERERERVT1mIIhqieyCbMz/fT4ORx8WyyyMLLCo1yIMdBqox8iIiIiIiIiIqK5h0pGoFriXfg9TT0zF7dTbYplLfRcs77cczW2a6zEyIiIiIiIiIqqLmHQkquFO3D+BkNMhyCzIFMsGOg3Ewp4LYWlsqcfIiIiIiIiIiKiuYtKRqIZSqpRY/ddqbLi6QSyTSqT4oOMHGPfcOEgkEj1GR0REREREVHFnn3qTdXn4pmsiw8akI1ENlJqbipm/zsSZ/2vvzsOjqNK+j/+6Q3bIRoIEBcIeFBBkEXBhNUqMGjWC+jqKCpoHJwwEcZDLR9ARCCqgA/KgjjPiOCgGQRkEBRdmBjHIYhCQoOxbhJA0iSEkId31/oH00IYlCd1dneT74eor9Kk6de6u06eXu6tOHV7rLIsKitJLN76kXrG9TIwMAAAAAACApCNQ62zL36b0r9J1+MRhZ1mX6C6a0X+GmoY2NTEyAAAAAACA00g6ArXIkp+W6IWsF1TuKHeWDeswTE/1fEoBfgEmRgYAAAAAAPBfJB2BWqDcXq5p307Toh8XOcsC/QL1v73/V3e0vcPEyAAAAAAAACoj6Qj4uNziXKWvTtfW/K3OsssbXq5Z/WepY+OOJkYGAAAAAABwbiQdAR+WlZulp/71lGxlNmfZdZdfp+k3TFd4YLiJkQEAAAAAAJwfSUfABxmGobe2vqXZ382Ww3A4y1OvTlVql1T5Wf1MjA4AAADwrlmrfjQ7BABANZF0BHxMcXmxnvn6GX2x/wtnWaOARpp2/TT1a97PxMgAAAAAAACqhqQj4EN2Hd+lMV+N0d6ivc6y9pHt9Ur/V9Q8rLl5gQEAAAAAAFSD1ewAAJz26d5Pdd8n97kkHJNaJ+ndxHdJOAIAAAAAgFqFIx0Bk1U4KjRr4yy988M7zrIGlgZ6qtdTurfDvbJYLCZGBwCAb8rJyVFaWprWrl2rRo0a6cEHH9QLL7yggICAC9abO3euli9frnXr1unYsWPKzMxUSkqKl6IGAKDq8mbPcct2YtJ+75btANVF0hEw0bGTxzT+X+O14cgGZ1mT4Caa0X+Gujbpal5gAAD4MJvNpoEDB6pdu3ZavHixDh06pPT0dJWUlGjOnAt/QXvnndM/8iUmJjr/DwAAAPcj6QiYJPtotsatHqejJ486y7pf1l0v93tZ0cHRJkYGAIBvmzdvnoqKirRkyRJFRUVJkioqKjRq1ChNnDhRzZo1O2/dtWvXymq1au/evSQdAQAAPIikI+BlhmHo/R3v68X1L6rCUeEsf/DKBzWm+xj5W/1NjA4AAN+3YsUKDR482JlwlKShQ4cqNTVVK1eu1PDhw89b12plSnPgbFm786u8bu/WjT0YCQCgriHpCHjRyYqTev6b57Vs9zJnWXCDYD3f93nd0uoWEyMDAKD2yMnJ0SOPPOJSFhERodjYWOXk5JgUFQAAAM5G0hHwkgNFBzRm9Rj9aPvRWRYXFqdZ/WepbWRbEyMDAKB2sdlsioiIqFQeGRmpgoICj7RZVFSkoqIi5/3c3FxJkt1ul91u90ibdZXdbpdDksMN23GHS42jtnGcdZMkw1r1ixZWdV+d2abFqG97t2oshkMyDPbPWarzPDxbTfbgb8dAfeCO10t37a8z75sOh4P3T5Ncyv6vbh2SjoAX/PvgvzXhPxP0S/kvzrKBzQfqhetfUKOARiZGBgAAqmLmzJl67rnnKpXn5+crMDDQhIhqL4fDoRMBAbJIqlma4TQjL88t8RQGB7llO7WFIbnu/8iqfxY9XtV99es2g+0nqhtePWEo0Cj9NYtzKaOgDqnG8/BsVX5OnqXSGKgH3PF66a7XSiMvTw6HQ4WFhZKY9sQMl7L/8/OrPiWHRNIR8CiH4dC8zfP0f5v/z1lmtVg1uttoPdLpEVks9eVtDgAA94mMjHR+WD6bzWZzmefRndLT0zVixAjn/dzcXPXq1UuNGzdWTEyMR9qsq+x2uwrLyxV+slSX8lUz2k373XKy1C3bqS0cOp10ce5/2y8XrnCWiPAqzj3+6zZP+oVWN7x64fSRjlKpNUSGhYSLpGo9D89W5efkWSqNgXrAHa+X7nqtjI6JcR4tFx0dLT8/P7dsF1V3Kfu/rKysWuuTdAQ8pLCsUBP+M0FrDq1xlkUGRmr6jdPVp1kfEyMDAKB2i4+PrzR3Y2FhoXJzcxUfH++RNsPCwhQWFlap3M/Pjy9MNWA961ZT7trv9SXpcLaz97/FYVSrXlWc2SYJtQuwWGRYrOyjX1XneXi2mu49d7wG1SbueL101746E4vVauU91EQ13f/VXZ+kI+AB2/O3a+zqsTpUfMhZ1qlxJ83sP1OxDWNNjAwAgNpvyJAhmjp1qo4fP+6c2zEzM1NWq1UJCQnmBgfUYdW50jUAACQdATf7eOfH+lPWn1Rm/+9hxyntUzSh1wQF+jHnEwAAlyo1NVWzZ89WcnKyJk6cqEOHDmn8+PFKTU1Vs2bNnOsNGjRI+/bt086dO51lGzZs0N69e5X36/xWWVlZkqSYmBj169fPuw8EAACgDiPpCLhJub1cL65/UQt3LHSWBVgD9EzvZ3RnuztNjAwAgLolMjJSX3zxhdLS0pScnKxGjRppxIgRmjJlist6drtdFRUVLmVz5szR/PnznfdnzJghSerXr59Wr17t8dgBAADqC5KOgBv8fOJnjVs9Tt8f+95Z1iy0mWYOmKmrGl9lYmQAANRNHTt21Oeff37Bdc6VRHz77bf19ttveyYoeFXe7Dlmh4CLaLv8vUvexs7E+9wQCVC/8XoJs9SKeVNzcnJ00003KTQ0VE2bNtVTTz2l8vLyi9abO3eukpKSFBMTI4vFokWLFnkhWtQ33+Z+q2HLhrkkHPvE9tHCpIUkHAEAAAAAQL3k80c62mw2DRw4UO3atdPixYt16NAhpaenq6SkRHPmXDhb/84770iSEhMTnf8HaqLkVIk+2fOJlu1aprwTeYoJjVFS6yQdLz2u1za/Jrthd647svNIPdH1CflZuQoXAAAAAACon3w+6Thv3jwVFRVpyZIlioqKkiRVVFRo1KhRmjhxostk4b+1du1aWa1W7d27l6QjamxP4R6NXDlSR0qOyCKLDBk6eOKgNh3d5LJeQ/+Gmnr9VA1oMcCkSAEAAAAAAHyDzycdV6xYocGDBzsTjpI0dOhQpaamauXKlRo+fPh561qtteLscfiwklMlGrlypPJKTl/h0pDh8veM1uGt9eeBf1bLsJZejxEAAAAAzOKOuTsB1E0+n5XLyclRfHy8S1lERIRiY2OVk5NjUlSoLz7Z84mOlByRQ44LrjeswzASjgAAAAAAAL/y+SMdbTabIiIiKpVHRkaqoKDAI20WFRWpqKjIeT83N1eSZLfbZbfbz1ftktntdjkcDo+2gepZtmuZ85Tq87HIopV7V2pY+2FejAznwhjyffSR76OPfJs3+4fnAAAAAC6FzycdzTBz5kw999xzlcrz8/MVGBjosXYdDocKCwslcWq4rzhSfOSCCUfp9KnWR08cVV5enpeiwvkwhnwffeT76CPf5s3+yc/P9+j2AQAAULf5fNIxMjLS+eH6bDabzWWeR3dKT0/XiBEjnPdzc3PVq1cvNW7cWDExMR5pU/rvEQXR0dHy8+PKx2Y6ZT+lD376QD+f/Pmi61pkUZPQJh59bqBqGEO+jz7yffSRb/Nm/5SVlXl0+wAAAKjbfD7pGB8fX2nuxsLCQuXm5laa69FdwsLCFBYWVqncz8/P4x/wrVarV9rBuRmGoc/2fqZXN72qg8UHq1ZHhpLaJNFnPoIx5PvoI99HH/k2b/UP/Q8AAIBL4fNJxyFDhmjq1Kk6fvy4c27HzMxMWa1WJSQkmBucm5ScKtEnez7Rsl3LlHciTzGhMUpqk6RbW92qEP8Qs8OrN9b/vF4zN8zU1vytLuVWWWX8+u+3rLIqJiRGia0SvRUmAAAAAACAz/P5pGNqaqpmz56t5ORkTZw4UYcOHdL48eOVmpqqZs2aOdcbNGiQ9u3bp507dzrLNmzYoL179zrn2svKypIkxcTEqF+/ft59IOexp3CPRq4cqSMlR5wXLDl44qA2Hd2k1ze/rjcT3lSr8FZmh1mn7Tq+S69sfEWrD652KQ9uEKzhVw1X/+b9NfrL0S59dOZvTEiM3kx4k+QwAAAAAHhZ1u6qzT/cu3VjD0cC4Fx8PukYGRmpL774QmlpaUpOTlajRo00YsQITZkyxWU9u92uiooKl7I5c+Zo/vz5zvszZsyQJPXr10+rV6/2eOwXU3KqRCNXjlReyemk6Jkj6c78zSvJ08iVI7U0eSlJLQ/IK8nTa9mvacnOJXIYDme51WLVXe3u0qirRykm5PQ8jUuTl2r5nuVatmuZjp44qiahTZTUJkmJrRLpGwAAAAAAgN/w+aSjJHXs2FGff/75Bdc5VxLx7bff1ttvv+2ZoNzgkz2f6EjJkfMud8ihIyVHtHzPcqW0T/FiZHXbiVMn9Pa2tzV/23ydrDjpsqx/8/4ae81YtY5o7VIe4h+ilPYpurPNncrLy1NMTAxzXQEAAAAAAJxHrUg61lXLdi1znqZ7PhZZtGzXMpKObnDKcUqLf1ysuZvnqqC0wGVZ5+jOSu+erh5Ne5gUHQAAAAAAQN1B0tFEBaUFF0w4SqdPtd6ct1l/2/o3JbdNVmRQpJeiqzsMw9CXB77UKxtf0d6ivS7Lrmh4hf7Q/Q+6ueXNslgs5gQIAAAAAABQx5B0NFFUUJT2Fe27aOKxwqjQzI0zNee7Obo57mYNix+mLtFdSJJVwea8zZq5YaY2Hd3kUh4RGKHUq1M1tP1Q+fv5mxQdAAAAAABA3UTS0URJbZIqJcMupNxRrn/u/qf+ufufio+K17AOw7iQyXnsK9qnVze9qlX7VrmUB/oF6oGOD+iRzo8oLCDMpOgAAAAAAADqNpKOJrq11a16ffPryivJk0OOSsutsio6OFr3d7xfH+38yOXU4JyCHD33zXOasWGGbm9zu4Z1GFbp4if1UUFpgeZtnqfMHZmqMP57NXOLLLqtzW1K65ampqFNTYwQAAAAAOBNWbvznf83rBYpspFk+0UWh+tZh71bN/Z2aECdRtLRRCH+IXoz4U2NXDlSR0qOOC8qc+ZvTEiM3kx4U63CW+mRTo9o3c/rtDBnob468JXshl2SVHyqWAtyFmhBzgL1bNpTwzoM08AWA+VvrV+nDJ+sOKl3f3hXb219SydOnXBZdl2z6zS2+1h1iOpgUnQAAAAAACBv9hw5JBUGB8lyslTWGmwjJu337g4LHkLS0WStwltpafJSLd+zXMt2LdPRE0fVJLSJktokuZw6bbFY1Du2t3rH9taRE0f04U8f6sMfP9TRk0ed21r/83qt/3m9ooOjdXe7u5XSPqXOH9Vnd9i1dNdSzflujsu+kKT4qHiN7T5WfZv1NSk6AAAAAACA+omkow8I8Q9RSvsU3dnmTuXl5SkmJkZ+fn7nXf+y0Ms0qusojewyUqsPrNbCnIVa9/M65/JjJ4/p9e9f11+2/EX9ruinYfHD1Du2t6yWmvyG4JsMw9CaQ2s0c+NM7Ty+02VZ09CmGt1ttG5tfWudeswAAAAAAAC1BUnHWszf6q+bWt6km1repN2Fu5W5I1Mf7/xYv5z6RZJkN+z68sCX+vLAl2rRqIWGdhiq5LbJCg8MNznyS7Mtf5tmbZjlkmiVpEb+jTSiywj9v47/T4F+gSZFBwAAAAAAAJKOdUTr8Nb6Y68/Kq1bmj7d+6nez3lf2wu2O5fv/2W/Xt7wsmZ/N1u3xN2ie+PvVafoTiZGXH2Hig/pz5v+rOV7lruUN7A20H3x9+mxzo8pIijCnOAAAAAAuF3b5e+5ZTs7E+9zy3YAAFVH0rGOCfEP0V3t7tKdbe/UlmNbtHDHQn2651OVO8olSWX2Mn2862N9vOtjXdn4St3b4V7d0uoWBTcINjny8yssK9Sb37+pBTkLdMpxymXZkLghSrsmTc0bNTcpOgAAAAAAAPwWScc6ymKxqEtMF3WJ6aLxPcbr410fa+GOhTrwywHnOj/k/6Bn1z6rlza8pDva3KGhHYaqVXgrE6N2VWYv0/s57+uN799QUXmRy7Iel/XQuB7jat3RmgAAAAAAAPUBScd6ICIoQg9d9ZB+d+XvlHU4S+/veF//OvgvOQyHJOmX8l/07vZ39e72d3Vt7LW6t8O96t+8vxpYzXl6OAyHlu9ZrtmbZuvwicMuy9qEt1F6j3TdcPkNslgspsQHAAAAAACACyPpWI9YLVb1vbyv+l7eV7nFuVr00yJ9+OOHyi/Nd66zLned1uWuU5OQJkppl6K729+tJiFNvBbjutx1mrFhhst8lJIUExyjJ7o+oTva3mFaMhQAAKC+y5s955K34ZCk4KBL3g6AS+euOTMB4FzI3tRTsQ1jldYtTaldUvXFgS+0MGehNhzZ4Fx+tOSo5m6eq9e/f10DWwzUsA7D1KtpL48dXfij7UfN2jhLaw6tcSkPaRCihzs9rAevfFAh/iEeaRsAAAAAAADuRdKxnvP389ctcbfolrhbtNO2Ux/8+IGW7lqqE6dOSJLshl2r9q3Sqn2r1Cq8lYa2H6rb296usIAwt7R/5MQRvZb9mj7e9bHzdG9J8rP4KaV9ilKvTlV0cLRb2gIAAAAAAIB3kHSEU9vItpp47USNuWaMPtnzid7PeV8/2n50Lt9TuEfT10/Xq5teVWLrRA3rMExXNr6yRm0Vlxfrr1v/qr//8HeV2ktdlg1qMUh/uOYPPnVRGwAAAAAAAFQdSUdUEuIfonva36OUdinanLdZC3cs1Gd7P9MpxylJUqm9VIt/WqzFPy1Wl+guGtphqG6Ou1lBDU7PzVNyqkSf7PlEy3YtU0FpgaKCopTUJkm3trpV/lZ/Zf6YqXmb58lWZnNp9+qYqzWuxzh1a9LN648ZAACgrnPHfIwwX9bu/IuvJKl368YejqR2ccfchTsT73NDJABQf5B0xHlZLBZ1bdJVXZt01fie4/XRzo/0wY4PdKj4kHOd7499r++Pfa+XNryk5DbJ6tusr55d+6yOlByRRRYZMrSvaJ82Hd2kVze9qpAGIco9kevSTsuwlhpzzRgNajGIK1IDAAAAAADUASQdUSVRQVF6pNMjeujKh/T14a/1wY4P9O+D/5YhQ5JUWFao+T/M1/wf5jvrnFl29jqFZYUu20y9OlUp7VPkb/X34qMBAAAAAACAJ5F0RLX4Wf104xU36sYrbtSh4kPK3JGpJTuXqKC0oMrbaGBpoIc7PaxHOj2ihgENPRgtAAAAAAAAzGA1OwDUXpc3vFxjuo/RqpRVyrghQw39q5ZAvLLxlRp9zWgSjgAAAAAAAHUUSUdcsgC/AN3a+lZFB0dXaf2i8iIPRwQAAAAAAAAzkXSE20QFRcmiC18IxiKLGgdzJT0AAAAAAIC6jDkd4TZJbZK06eimC65jyFBS6yQvRQQAAACYJ2t3fpXW692aH+WBuorXAdRnJB3hNre2ulWvb35deSV5cshRablVVsWExCixVaIJ0QEAANROebPnmB0CAEltl7/nlu3sGjLskrfhrlgAwJM4vRpuE+IfojcT3lRMSIwkOU+1PvM3JiRGbya8qRD/ENNiBAAAAAAAgOdxpCPcqlV4Ky1NXqrle5Zr2e5lyj+Zr8bBjZXUOkmJrRJJOAIAAAAAANQDJB3hdiH+IUppn6KU9ilmhwIAAAAAAAATkHQEAAAAAABAreBLcx3HpP3e7BB8GklHAAAAADBRVa9u645tGlaLFNlIsv0ii8Nwe7tAbVadsejuq03X17ZRt3EhGQAAANQ6OTk5uummmxQaGqqmTZvqqaeeUnl5+UXrGYahjIwMtWjRQsHBwerTp4+ysrK8EDEAAED9QtIRAAAAtYrNZtPAgQNVXl6uxYsXa+rUqXrjjTeUnp5+0brTp0/XpEmTNHbsWC1btkyxsbFKSEjQ7t27vRA5AABA/cHp1QAAAKhV5s2bp6KiIi1ZskRRUVGSpIqKCo0aNUoTJ05Us2bNzlmvtLRU06ZN07hx4zR27FhJ0g033KD27dvr5Zdf1ty5c732GADUX60/+4BT3IE6gvklL4wjHQEAAFCrrFixQoMHD3YmHCVp6NChcjgcWrly5XnrrV27VkVFRRo6dKizLCAgQHfddZeWL1/u0ZgBAADqG5KOAAAAqFVycnIUHx/vUhYREaHY2Fjl5ORcsJ6kSnU7duyo/fv36+TJk+4PFgAAoJ7i9OoqqKiokCTl5uZ6tB273a78/HyVlZXJz8/Po22hZugj30b/+D76yPfRR77Nm/1z5nPPmc9BvsRmsykiIqJSeWRkpAoKCi5YLzAwUEFBQZXqGYYhm82m4ODgc9YtKipSUVGR8/6BAwckSQcPHpTdbq/Bo6i6ApvNo9v3NoekopOBKi4tq/NHQOSdKLr4Sl5mWCySn0MqLpbF4NReM9AH5nLX/j9oq9ormCdeB6radlVVJ0Z3tF2f3ge8qWTfviqtZ7fbVVBQoJKSkmp/nqzu50OSjlWQl5cnSerVq5fJkQAAAHhXXl6e4uLizA7DdDNnztRzzz1XqbxPnz4mRAMAAPAbk571WlNV/XxI0rEKOnfurG+//VYxMTFq0MBzuyw3N1e9evXSt99+q9jYWI+1g5qjj3wb/eP76CPfRx/5Nm/2T0VFhfLy8tS5c2ePtlMTkZGRKiwsrFRus9lc5nk8V72ysjKVlpa6HO1os9lksVgUGRl53rrp6ekaMWKE835paakOHDigVq1aefTzYV3E64y52P/mow/Mxf43H31grkvZ/9X9fMgnpCoICgpSz549vdZebGysrrjiCq+1h+qjj3wb/eP76CPfRx/5Nm/1j68e4RgfH19p7sbCwkLl5uZWmq/xt/UkaceOHbr66qud5Tk5OWrRosV5T62WpLCwMIWFhbmUtW3btibh41e8zpiL/W8++sBc7H/z0Qfmqun+r87nQ06fBwAAQK0yZMgQff755zp+/LizLDMzU1arVQkJCeet17dvX4WFhSkzM9NZdurUKS1evFiJiYmeDBkAAKDeIekIAACAWiU1NVWNGjVScnKyVq5cqb/97W8aP368UlNT1axZM+d6gwYNcjkaMSgoSE8//bRefvllvfrqq/ryyy913333KT8/X08++aQZDwUAAKDO4vRqHxIWFqZJkyZVOnUHvoM+8m30j++jj3wffeTb6J/TIiMj9cUXXygtLU3Jyclq1KiRRowYoSlTprisZ7fbK11d8Y9//KMMw9DLL7+svLw8de3aVZ999plat27tzYdQr/E8Nhf733z0gbnY/+ajD8zlzf1vMYxLuEY8AAAAAAAAAPwGp1cDAAAAAAAAcCuSjgAAAAAAAADciqQjAAAAAAAAALci6QgAAAAAAADArUg6eklOTo5uuukmhYaGqmnTpnrqqadUXl5+0XqGYSgjI0MtWrRQcHCw+vTpo6ysLC9EXP/UtI/i4uJksVgq3UpLS70Qdf2xc+dOpaamqmvXrmrQoIE6depUpXqMIe+paR8xhrwjMzNTd9xxh6644gqFhoaqa9eu+utf/6qLXU+OMeQ9Ne0jxhDqio0bN8rPz08NGzY0O5R6w26368UXX9SNN96o6Oh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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.default_rng(11)\n", "n = 400\n", "P = rng.standard_normal(n).tolist()\n", "mus = np.linspace(0.0, 2.5, 11)\n", "\n", "mmd_vals = []\n", "for mu in mus:\n", " half = n // 2\n", " Q = np.concatenate([\n", " rng.standard_normal(half) - mu,\n", " rng.standard_normal(n - half) + mu,\n", " ]).tolist()\n", " mmd_vals.append(float(opt.mmd_gaussian(P, Q, sigma=1.0)))\n", "\n", "for mu, m in zip(mus, mmd_vals):\n", " print(f\"μ = {mu:.2f} -> MMD² = {m:.3e}\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "axes[0].plot(mus, mmd_vals, 'o-', lw=2, color='C2')\n", "axes[0].set_xlabel(r'séparation $\\mu$')\n", "axes[0].set_ylabel(r'$\\widehat{\\text{MMD}}^2$')\n", "axes[0].set_title(\"MMD croissante avec la séparation\")\n", "\n", "mu_show = mus[-1]\n", "half = n // 2\n", "Q_show = np.concatenate([\n", " rng.standard_normal(half) - mu_show,\n", " rng.standard_normal(n - half) + mu_show,\n", "])\n", "axes[1].hist(P, bins=30, density=True, alpha=0.5,\n", " label=r'P = $\\mathcal{N}(0,1)$', color='C0')\n", "axes[1].hist(Q_show, bins=30, density=True, alpha=0.5,\n", " label=fr'Q (μ = {mu_show:.1f})', color='C3')\n", "axes[1].set_xlabel('x'); axes[1].set_ylabel('densité')\n", "axes[1].set_title(\"P vs Q (mélange séparé)\")\n", "axes[1].legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "d3d9b723", "metadata": {}, "source": [ "**Résultat attendu.** MMD croît monotone en $\\mu$.\n", "\n", "**Lecture du graphique.** Gauche : courbe croissante. Droite : la\n", "gaussienne unique vs le mélange bimodal sont visuellement\n", "distincts à $\\mu = 2.5$.\n", "\n", "**Conclusion.** MMD avec noyau gaussien est un détecteur efficace de\n", "différence distributionnelle, applicable à la calibration de modèles\n", "génératifs (GAN, normalizing flows) en boucle d'apprentissage.\n" ] } ], "metadata": { "kernelspec": { "display_name": "rhftlab", "language": "python", "name": "rhftlab" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }