{ "cells": [ { "cell_type": "markdown", "id": "international-flavor", "metadata": {}, "source": [ "# Loss landcape of a linear regression model\n", "\n", "We'll assume $\\beta = 0$ to be able visualize the loss as a function of the slope $\\alpha$ and error term $\\sigma$.\n", "\n", "$y \\sim \\mathcal{N}(\\alpha x, \\sigma)$\n", "\n", "## Setting up the environment" ] }, { "cell_type": "code", "execution_count": 2, "id": "ultimate-pierce", "metadata": {}, "outputs": [], "source": [ "import os\n", "\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import seaborn as sns\n", "import torch\n", "import torch.nn.functional as F\n", "from sklearn.model_selection import train_test_split\n", "\n", "cwd = os.getcwd()\n", "if cwd.endswith('notebook'):\n", " os.chdir('..')\n", " cwd = os.getcwd()" ] }, { "cell_type": "code", "execution_count": 3, "id": "treated-humanity", "metadata": {}, "outputs": [], "source": [ "sns.set(palette='colorblind', font_scale=1.3)\n", "palette = sns.color_palette()" ] }, { "cell_type": "code", "execution_count": 4, "id": "acquired-panama", "metadata": {}, "outputs": [], "source": [ "seed = 444\n", "np.random.seed(seed);\n", "torch.manual_seed(seed);" ] }, { "cell_type": "markdown", "id": "dominican-traffic", "metadata": {}, "source": [ "## Normal distribution\n", "\n", "If $z$ is drawn from a normal distribution with mean $\\mu$ and standard deviation $\\sigma$, then the probability of $z$ follows the relationship:\n", "\n", "$z \\sim \\mathcal{N}(\\mu, \\sigma) \\iff P(z \\mid \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}(\\frac{z - \\mu}{\\sigma})^2}$\n", "\n", "$P(z \\mid \\mu, \\sigma)$ is the probability density function (PDF) of the normal distribution." ] }, { "cell_type": "code", "execution_count": 35, "id": "funky-census", "metadata": {}, "outputs": [], "source": [ "def plot_normal_distributions():\n", " f, ax = plt.subplots(1, 1, figsize=(12, 6))\n", " \n", " normal_fn = lambda z, m, s: (1/(s * np.sqrt(2*np.pi))) * np.exp(-0.5*((z - m) / s)**2)\n", " \n", " x = np.linspace(-7.5, 10, 300)\n", " \n", " ax.plot(x, normal_fn(x, 0, 1), label=r'$\\mu = 0$, $\\sigma = 1$', color=palette[0])\n", " ax.plot(x, normal_fn(x, 0, 2), label=r'$\\mu = 0$, $\\sigma = 2$', color=palette[1])\n", " ax.plot(x, normal_fn(x, 5, 0.9), label=r'$\\mu = 5$, $\\sigma = .9$', color=palette[2])\n", " \n", " ax.set_xlabel('$z$');\n", " ax.set_ylabel(r'$P(z \\mid \\mu, \\sigma)$');\n", " ax.set_title('Probability density function (PDF) of the normal distribution');\n", " ax.legend(loc='upper left');\n", " \n", " return f, ax" ] }, { "cell_type": "code", "execution_count": 36, "id": "centered-series", "metadata": {}, "outputs": [ { "data": { "image/png": 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4+HjTa9pY195YmUtdzb3OW/s+cvv7T2Nt+/j4wNvbG0FBQaZtnp6eph7bIUOG4JtvvoFGo0F6ejq2bt1q6uG//f2mMdeuXUN5eXm9v3+JRIJBgwY1eUxSUhI2bdqEWbNm4ddff4Ver8d//vOfencXGxMREdHs4829r5pDa38vERER9d4rAwIC6pXCENIc6gEnTm3gwIGmxILH40EmkyE0NLRBT9/tvXFyubzR2/He3t71blEaewONjKPsjR/su3fvxvvvv4+8vDz4+vqiR48eEIvFDeanvf1cXl5eKCgoaMMzbVxiYiJCQ0Pxzz//IDQ0FPv378dHH33U5P5yubzBTAF1B8wZ68Gff/75Ro8vKSkxJRK39/jyeDzT8x43bhy0Wi1+/PFHfPzxx/j444/Rs2dPLFmyBOHh4S0+r+DgYPTu3Rvbtm3DiBEjsG3btmbr2u9E3edh7Fk0GAwAgMrKygavgdYy1lvfPiDR+Fqo+zpr7lo2pqqqqtG7CUBtKYZQKATDMBCLxQgJCYGLi0ur4y4uLgYA+Pn5mbZJpdJ6X2ibYozJ+PdRV1uuR3vcnuDWvYYVFRWoqKhotBe/pefV3O+mte8jTZX+uLq61vu5qd8pUNuzvHjxYmzatAkGgwERERGIjY0F0Lr5sI3X//a/fx8fH1y/fr3RY9566y34+vrizz//xJ49eyAQCHD33Xdj0aJFzcbaUqlTS++rd6q1v5fmXjOEtIQScOLUZDJZqxKDxo5rrAa7tLS0Xs/M7R8IxmO8vb1x/fp1zJkzB48//jieeeYZU8LyyCOPNGhXLpfDw8OjXjvtTezqYhgG9913H3bs2IHY2FgIhcJmbyl7eHg0eN51e7WNvUEffPABoqKiGhwfGhqKkpKSVsX28MMP4+GHH0ZhYSH27NmDL774AosWLcI333zTquPHjRuHJUuWIC0tDYWFhbjnnntadVxdxkTaqLle5ca4ubk1GKRaXl6OzMxMJCYmNnus8fd9+/Uy/lz39dBWHh4eTSasXbt2bZA0tkVKSgoCAgKanAKwOcZa5Mamg7Pk9WiJTCZDSEgIli1b1uCx5hLJ1rTbmvcRc1i9ejX+/PNPfPHFF+jfvz8kEgmuXLliqhFvifH6lpWV1dve3MBciUSCOXPmYM6cObh48SK2bt2KtWvXIioqqk3lc7dr7n3V6E7+dq35eyHOi0pQCGmHXr164dChQ/WSmOzsbJw/f75ePeO5c+fqDXDauXOnqeYxPT0dWq0WM2fONCXfJSUluHjxYoMPjyNHjpj+X1JSglOnTiEpKanNcRt7aOsaN24crl69ih9++AEjR45sUBZQV+/evbFnz556vTx1Zxvp1KkTPD09UVJSgoSEBNO/rKwsrF27ttHzN+bdd9/F//3f/wGova37+OOPY/To0U32+jfW7pgxY6DVarF06VL07t27VbWhdbm4uNQ7X1lZWZM9fU3p0aMHjh49Wm82ja1bt2LWrFlNxm1kvJbbt2+vt33btm3g8/mtHkDZmMDAQIvM1nDjxg1s3769wfiJ1jLG1Fh5jDmvR2tfh0Y9e/ZEUVERfHx8TK/p+Ph4fPfddzh8+HCb2qqrte8j5nD69Gn06tULw4cPN/XcGmNvTa9tp06d4Ofnh507d5q26XQ6HDt2rNH9WZbFAw88YKqnjo6OxksvvYTw8HDT31Vbfw9Gzb2vAq37223u3Nb8vRDnRT3ghLTD1KlT8fvvv+Ppp5/GjBkzoNFosGzZMgQEBODhhx827ceyLGbNmoWZM2fi+vXr+Oyzz/D444/Dx8cHsbGx4PP5WLJkCR5++GEUFRVh9erVUKvVDeoIly9fDj6fD29vb6xYsQI+Pj7tSnJkMhnOnDmD06dPmz5IOnXqhISEBKSmpmL27NnNHv/ss89i/PjxmDNnDsaPH48TJ07Um8ZMIBBg5syZ+Pzzz6HVapGYmIjMzEx89tlnGDduXLPJfV29e/fGyy+/jM8//xz9+vXDzZs3sXXrVjzxxBNNPq+srCwcP34cffr0AcMwcHd3x7Bhw7B9+/ZGF4FpyaBBg7Bp0ybExMTA1dUVX375ZYNb/i2ZMmUKfv/9d8yaNQuTJ09GUVERvvjiC0yaNAkikch0x2Dbtm3o379/vWP5fD5mzZqFDz74AK6urhg8eDBOnz6NVatWYfLkyfD09GzzczLq27cvli1bBpZlWzWwsjE5OTk4ffo0gNqFeDIzM/HNN98gPDwc06dPb1ebZ86cMQ2kvJ05r4dMJsOJEyfQs2dPUxlGc4YNG4aoqChMnz4ds2bNgre3NzZt2oRdu3aZBuC2R2vfR8whPj4e3377LTZu3Ijw8HCkpKRg7dq1AFrXO8wwDJ5//nksXLgQXl5e6NmzJ37++WeUlJQ0Om87wzDo1q0bvvzyS7i4uKBjx444evQorl27ZpqxRCaTobKyEvv27WtQg9+c5t5Xgdb97Tb3GrDm74U4L0rACWmHkJAQ/Pjjj/joo4/w6quvQiwWm2aiqDtwZ8CAAejcuTPmzJkDoVCIyZMnm2rOO3XqhMWLF2PlypXYsWMHAgICMGbMGIwaNQobN26sN7/u/PnzsXTpUuTl5aFPnz74/PPP652ntaZPn453330XzzzzDI4ePQqBoPYtYODAgSgsLERycnKzx8fGxuKrr77Cxx9/jOeffx5xcXGYO3duvQWLnn76aUgkEnz//fdYtWoV/P398dRTTzVZF96Ye+65B2VlZfjhhx/wzTffwMvLC48//niTXxCmTJmCOXPmYMaMGdixY4epB3XgwIH4999/m5zVpTlvvvkm3nnnHbz55pvw8PDAtGnTcO7cuTa10bFjR3z//fem6eK8vb3x5JNPmmbF6NevH/r27Yu33noLL774YoNe3ClTpkAsFuO7777Djz/+iKCgILz00kt4+umn2/x86ho+fDjee+89XLhwAfHx8e1q4+uvv8bXX38NoLYWOTg4GOPGjcOzzz7bpprxug4fPtzoXO1G5roezz33HJYtW4bLly/j77//bnF/oVCIb775Bh9//DEWLVoEtVqN6OhorFq16o4Wbmrt+4g5zJgxA4WFhfj000+h1+vRqVMnLFu2DIsXL8aZM2daNSf8Y489Br1ej2+//RbffvstRo4ciQkTJuDs2bON7v/GG29AKBRixYoVKCsrQ8eOHbFkyRLTl82xY8fit99+wwsvvIAPP/yw1c+lufdVoHV/u829Bqz5eyHOi2FpxAAhTm/ChAno3bs35s6dy3UoZvXSSy+BZVl8/vnnXIdic15++WV4e3vjrbfe4joUAMDFixfxyCOPYO/evWYZ30AIIbaMasAJcWJff/015syZg/T0dEycOJHrcMxm48aNmD9/PrZt24ZJkyZxHY5NmjVrFrZu3VpvEC2Xvv/+ezzxxBOUfBNCnAIl4IQ4sYMHD+LIkSN45513TIumOILTp0/j77//xuzZs9s1WNUZREZG4vHHH8eaNWu4DgVXr17FyZMnWxyDQAghjoJKUAghhBBCCLEi6gEnhBBCCCHEiigBJ4QQQgghxIooASeEEEIIIcSKnHIe8PLyahgM1i999/FxQ2lp48s/kztD19Yy6LpaDl1by6Frazl0bS2Hrq3lcHVteTwGXl6NL+DmlAm4wcBykoAbz00sg66tZdB1tRy6tpZD19Zy6NpaDl1by7G1a0slKIQQQgghhFgRJeCEEEIIIYRYESXghBBCCCGEWBEl4IQQQgghhFiRUw7CbI5SWY2qqgro9Tqzt11UxIPBYDB7u8R615bPF8DNzRNSaeOjmgkhhBBCWkIJeB1KZTUUinJ4evpBKBSBYRizti8Q8KDTUQJuCda4tizLQqvVoKKiGAAoCSeEEEJIu1AJSh1VVRXw9PSDSCQ2e/JN7B/DMBCJxPD09ENVVQXX4RBCCCHETlECXoder4NQKOI6DGLjhEKRRUqUCCGEEOIcKAG/DfV8k5bQa4QQQgghd4IScEIIIYQQQqyIEnBCCCGEEEKsiGZBIYQQQkiTWJbFhuxT2JKfAS1PD3dGjFeih6CrLJDr0AixW9QDTtrl0KH9ePLJRzFsWD9MnPggtmz5k+uQmnT6dBpee+0l3H//GAwcmITdu3dwHRIhhNiFXGUlJhxfj5fP/o0bNeXgMzwcLb2BkQfW4o1z/0DP0tS6hLQH9YCTNrtw4TzefPM1PPnk07jrrtE4efI4Pv54MWQyDwwePJTr8BpQKpWIjIzCPfeMw5tvzuU6HEIIsQsKrRqPHluPfJUCHyXcg0kdEhHgL8Ol3CJ8mLUX391IgYjHx4Kuo7kOlRC7Qwm4A7l0KQtPPfUE/vprB7y9fQDU3jq8++5hmDt3HkaMGGWW82za9CO6deuBadNmAgA6dgxHevp5bNiwrk0J+KVLWVi79ktkZWWirKy03mMffvgZBgwYZJZ4+/UbgH79BpilLUIIcQYGlsX/nf4D12rK8EvfJ9HfJ9z0mKdIig8SxoLPMFhz7Rg6u/ngyY5J3AVLiB2iBNyBXLyYBV9fP1PyDQC5uTmoqqpCdHRsg/3XrfsW69d/12ybc+fOw6hRd9fbdu7cWTz44Ph625KT+2Px4gXQ6XQQCFp+Wd28eQOzZj2DYcNG4NNPV0ClUmHx4neh1eowffpMdO/e0yyxEkIIabs1V49iW2EmFsaNrpd817Wg62hcrynHvPPb0Ne7I6Ld/awbJCF2jBLwFmw6X4ANZ/PN0hbDMGBZtlX7PtYtCBPi2zbA5dKlrAaJdlZWJlxcXBEaGtZg/wceeBjDh49stk1vb+8G28rKSuHl5X3bfj7Q6XSoqKiAr69vi7EuW7YU8fEJmDfvHdO2CRMew7JlSzFixKgGSXxLsfL5DDw8vFo8LyGEkOaVqKvxycX9GBUQjWcikpvcj8/w8Hn3+9Fv73IszNiFH/o8bsUoCbFvlIA7kIsXs9CrV9Jt2zIRFRXd6OIxMpkHZDIPa4VnIpfLkZp6Au+991G97RKJFHq9vtEe9JZiFQh40OloMBAhhNypzy8dgMqgxfwuI1tceMxX7Io5UYOwKGM39hdfwRC/zlaKkhD7Rgl4CybEB7a5J7oplkwSWZbFlSuXMHHipHrbMzPTERUV0+gx7S3r8Pb2QXl5Wb1tZWVl4PP58PT0bDHWixczodPpEB1dP67MzAzExsaZNVZCCCGtd6O6HN/fOInHw3oi0q3lu5kAMD08Gd/fOIl303di9+CZ4DM0wRohLaEE3EHk5uaguroaAQH/+7JQWlqCs2dPY8yYexo9pr0lKAkJ3ZCSchyTJz9l2nb8+BHExXVtVf23wVD7JUSlUpq2lZeXY9eubZg+/bl2xUolKIQQcueWXtoPAcPDK9FDW32MmC/AGzHD8dypzdhTdAmjAhrv9CGE/A8l4A7i4sUsAMBvv23EpElTUVpaglWrlkOr1cJgMECr1UIoFNY7pr0lKBMmPIFZs6bhu+++wogRI3HyZAp2796BRYs+NO0jl1eCx+PDzc2twfGxsXGQSl2watVyzJjxPMrLy7BixeeIjo7F/fc/1Og576QEpaamBrm52aafCwrycelSFqRSl0Zr4wkhxBmVqKvxR955PBHWC4ES9zYde29QHBZm7MI3105QAk5IK9B9Igdx6VIWunfvCaVSialTH8NHH72PiRMnwcfHFz///EOreqZbq2vXeLz33of4999dePLJifj55x8wd+4b9aYgnDdvLpYt+6TR42UyGRYv/gjZ2dl46qnH8d577yApqQ+WLFkKHs/8L8nMzHQ89dQTeOqpJwAAq1evwFNPPYElSxaZ/VyEEGKvfs4+DY1Bj6nhvdt8rJDHx5SOSdhfchUXFcUWiI4Qx0I94A7COAPKiy++Um/78OF3WeR8gwYNxaBBQ5t8/I035uOnn9Y1+Xjv3n3xww+bLBBZQ716JeHQoZNWORchhNgjPWvAupsn0d8nHDHtnE5wUodEfHbpAL69fgJLEhovfSSE1KIecAdx6VIWoqKiuQ7DZMOG9Rg6dATXYRBCCGmFvUVXcLOmAlPuYEEdX7Er7g+Ox6acM1Bo1WaMjhDHQwm4AygtLUFpaalNJeBz5sxF795Nzx9LCCHEdvxwMxV+YlfcHdhw0ba2mNwhETV6LbYXZpopMkIcEyXgDsDHxxeHDp1scrpBLpiz5pwQQojlVGpV+Lf4Mh4KSYCIx7+jtpK8QhEq9cDvuefNFB0hjokScEIIIcSJbS/IhMagx/1BXe+4LYZh8EBwPA6UXEWppsYM0RHimCgBJ4QQQpzYn3kXECr1QE/PELO090BwPHSsAVvy083SHiGOiBJwQgghxEmVa5Q4UHIV44K6trjsfGt1lQUgys0Xf1AZCiFNogScEEIIcVLbCjKgYw24P/jOy0+MjGUox8puoEClMFu7hDgSSsAJIYQQJ/V3fjo6unihm0eQWdsdG9gFLIDdhRfN2i4hjoIScEIIIcQJVes0OFx6HWMCY8xWfmIU6+6HUKkHdhVdMmu7hDgKSsAJIYQQJ3S49Bo0Bj3u8o8ye9sMw+Au/ygcKLkKlV5n9vYJsXeUgBNCCCFOaHfRJbjyRejj1cEi7Y8MiIZSr8WR0usWaZ8Qe0YJOCGEEOJkWJbFnqLLGOzbCWK+ZRZO6+8TDilPgF1UB05IA5wn4FqtFgsXLkRycjKSk5PxySefwGAwtHjc9OnT8dJLL1khQkIIIcSxZFUVI1dZiRH+kRY7h5QvxCC/TthddAksy1rsPITYI87XC//0009x+PBhrF27FtXV1Xjttdcgk8kwY8aMJo/5/fffcfDgQYwdO9aKkZK6Dh3aj7Vrv0R29k0EBARi0qSpuPfe+7kOq1E//vg99u37FzdvXgePx0d0dCyeeeZZxMd34zo0QgjhxJ5bgyOHW6D+u667/KOws/AiLlaVIMbdz6LnIsSecNoDrlarsWHDBsybNw/du3dH//798corr2DdunVNflsuLi7G0qVL0a0bJU9cuXDhPN588zUMGTIc//3vBjzyyER8/PFiHDiwj+vQGnXqVCruv/9BrFz5NVat+gYBAQF46aXnkZOTzXVohBDCiX+LLqOLuz+CpTKLnmeIX2cAwMGSqxY9DyH2htMEPCMjA0qlEklJSaZtSUlJKC4uRk5OTqPHLFiwABMnTkTnzp2tFabduHQpCwMHJqGsrNS0jWVZjBkzFHv27DTbeTZt+hHduvXAtGkz0bFjOB5++FHcddcobNiwrs3xzp37IsaNG42BA5Pq/Tt8+KDZ4v3kky9w770PIDIyCuHhEXj99bchEolw7Nhhs52DEELshVKvRUp5tik5tqSOLl4Ik3ricMl1i5+LEHvCaQlKYWEh3Nzc4Orqatrm5+dneiwsLKze/v/88w+uXbuGTz/9FPPnz7dqrPbg4sUs+Pr6wdvbx7QtNzcHVVVViI6ObbD/unXfYv3675ptc+7ceRg16u56286dO4sHHxxfb1tycn8sXrwAOp0OAkHLL6ubN29g1qxnMGzYCHz66QqoVCosXvwutFodpk+fie7de5ol1sZoNBpoNFq4u1u254cQQmxRankONAY9BviEW+V8g3wjsLUgA3rWAD7D+dAzQmwCpwm4UqmEWCyut00kEgGoTZLqKi8vx+LFi7FixQrTPtagvfoztFd+MktbDAO0dhyKsPPjEHaa2Kb2L13KapBoZ2VlwsXFFaGhYQ32f+CBhzF8+Mhm2/T29m6wraysFF5e3rft5wOdToeKigr4+vq2GOuyZUsRH5+AefPeMW2bMOExLFu2FCNGjGqQxLcUK5/PwMPDq8XzAsDKlcvg7u6OQYOGtGp/QsytuFqDAp0cnjBAIuBzHQ5xModLr4HPMOjr3dEq5xvoG4Gfsk/hXGUBengGW+WchNg6ThNwiUTSINE2/iyRSOptf++99zBmzBj06NHjjs/r4+PW6PaiIh4Egvrfzg18HnRmXCCstYuN8fkNY2nJpUtZSEzsXe+4y5ezEB0dDaGw4Ye8t7cXvL1bl7Q2jI+pdx4+v/aJCQRMi3HL5XKkpp7ABx98XG9fV1cX6PV6SCQNv2DdSax1ffvt19i9ezuWL18Fmcy93e3weDz4+bX/eHviLM/T0liWxfrUHKw4dA0ncyoBADwGSAr1xNJxXTEgouGXXdJ+9Lpt2vET2UjyDUOn4JY7SxrT1mt7v2s8Zp3ajNOqPIz0i2nXOZ0FvW4tx9auLacJeGBgIBQKBZRKJaRSKYDaQZYAEBAQUG/fLVu2QCKR4LfffgPwv0S9Z8+eOHXqVJvOW1paBYOhYVe0wWCATld/CkRexwmQdpzQpvabIhDwGrTfnLbsy7IsLl++hEcfnVTvuPT0C4iMjGm0rfaWdXh7+6CkpLRem8XFpeDz+XBz82gx7vT0dOh0OnTuHF1v3wsX0hEbG2fWWOv65ps1+OWXn/H55ysRGRnbput7O4PBgOJiRbuPtxd+fu5O8TwtTaHWYe6Oi/g9owjx/m74z6BwdOvgjbRrpdhwrgCDVh7Gkz2C8MHIKAh4dIv+TtHrtmnVOg1OFN/Ec536tesatefa8sEg2s0P229kYmpgUssHOCl63VoOV9eWx2Oa7PTlNAGPjY2FVCpFamoqBg4cCAA4efIk/P39ERISUm/fnTvrDyL85JNPoNFoMG/ePKvFa8tyc3NQXV2NgIBA07bS0hKcPXsaY8bc0+gx7S1BSUjohpSU45g8+SnTtuPHjyAurmur6r+N87yrVErTtvLycuzatQ3Tpz/XrlhbKkH58ssv8Pfff+Dzz79EbGyXFmMkxFyqNXo8/PNpnC+swhuDIzA7uQP4PAZ+fu64K1SG55PD8NGh61idkgOl1oAv7okFr7W3yghpo+NlN6FjDRjgG2HV8w7yjcBPN9OgMegh4lHZFSGcl6CMHz8eCxcuxJIlS6BWq7F06VJMnToVAFBRUQE+nw93d3d07Fi/Vs3V1RUCgaDBdmd18WIWAOC33zZi0qSpKC0twapVy6HVamEwGKDVaiEUCusdI5N5QCbzaPO5Jkx4ArNmTcN3332FESNG4uTJFOzevQOLFn1o2kcurwSPx4ebW8NvfrGxcZBKXbBq1XLMmPE8ysvLsGLF54iOjsX99z/U6DlbirW5uwufffYR/vnnbyxa9CH8/PxQWloCABCLJY3GR4i56A0snt+SgXOFVfjuwXiMiWp4y99VJMCC4ZHwlAix5OA1uIn4WDIqmoNoiTM4XHoNQoaH3l4NxwVZ0kDfCHxz/QROVeQi2buDVc9NiC3ifCGeuXPnQq1WY/r06RCLxRg/fjymTZsGAJg9ezZCQkKwZMkSjqO0fZcuZaF7955QKpWYOvUxBAQE4plnZmHZsk/w888/YOzY+8x2rq5d4/Heex9i7dov8f3338DfPwBz576BwYOHmvaZN28ugoKC8eab7zY4XiaTYfHij7Bs2ad46qnH4e3tg7vuGo1p02aAZ4Hb77/9tgkA8Oqr/1dv+91339tofISYy4eHrmHbpRK8NyKy0eS7rjn9OkCu1uHLE9noF+aJ+7v4WylK4kwOl1xHT88QuAqsN5kBAPS5lXSfKLtJCTghABjWCdeHbaoGvKDgBgIDLdej3tYa8LZ49dX/Q1hYR7z44isWab+tcnNz8NNP6zB3rnVKhCx5bRtj6deKraCaxPY7W6DA6HWpmBAfiM/vjgFzW1lJY9dWZzDg3h9O4UaFEvun9YG/q3WTJEdBr9vGVes0iN6xBM93HoB5sSPa1cadXNtB+1aio4sXfujzeLuOd3T0urUcW6wBp9E+DuLSpSxERdnObesNG9Zj6ND2vcETYu/0Bhav7siCj4sQC4Z3bpB8N0XA4+GLsbGo1ugxd0dWkysCE9IepypyoWdZq5efGPXxCkNKeTYM9LomhBJwR1BaWoLS0lKbSsDnzJmL3r2TuQ6DEE58m5aLMwVVWHSrtrston1d8dqgCGy/VIoD18stFCFxRinl2QCAJK4ScO8OqNSqkKUo5uT8hNgSSsAdgI+PLw4dOomoKNuZX7U1s6EQ4oiq1DosPXwdgzt64YF21nE/kxiKUJkY7x+4Sr3gxGxOlGUjxt0PXiIpJ+c31n6fKL/JyfkJsSWUgBNCiBl9k5aLcpUO84ZEtLr05HZiAQ9zB4bjTEEVtmRRbyG5cwaWRWp5Nvpw1PsNAB1dvOAvdkNKWTZnMRBiKygBJ4QQM6lS67A6JRt3dfJGzyDZHbX1SNdARPu4YMnBa9A3MmickLbIUhRBrlOjN4czkDAMgz7eHXC8jHrACaEEnBBCzOTbU7koU+rwyoDwO26Lz2Pw6oBwXC5TYsflkjsPjjg1Y9LLZQ84ACR7hSFbWYE8pZzTOAjhGiXghBBiBhq9AWtP5mB4hDd6Bd9Z77fRPTG+CJOJ8dXJHLO0R5xXSnk2/MSu6OjS9IrB1mDsgT9ZTmUoxLlRAk4IIWawJasYxdVaPJMUYrY2BTwenu4VgiPZlThXSPMDk/ZLKc9GH68O7R6XYC5xsgCIeXykVeRyGgchXKMEnBBCzOC/p/IQ7inB0Ahvs7b7ePcguAh51AtO2q1EXY2bNRXo5WW+L4ftJeLxkeARhFOUgBMnRwk4IYTcoQtFVTieU4mpPUPAM3MPo6dEiIkJgfg9owglNRqztk2cgzHZ7eUZynEktXp5huBMRR60Bj3XoRDCGUrACSHkDn2XlguJgIeJCYEWaX9KjxBo9Cw2pxdZpH3i2NIqcsEDg24eQVyHAqD2i4DKoEOGgl7PxHlRAk4IIXegRqvH5owiPBDrDy9p21a9bK1YP1f0CHTHxnMFFmmfOLbTFbmIdfeHq0DEdSgAgF5etT3xaeVUVkWcFyXghBByB3ZcKkG1Ro9H4gMsep5HEwJxvqgK52kwJmkDlmVxqiIXPT2DuQ7FJEzqAV+RKw3EJE6N1gsnbfbNN2vw3XdfNdi+b98xu1uCvqamBt9+uxb79u1BWVkpwsM74bnnZqN372SuQyN24tf0QgS7i9G/g6dFz/NAF3+88+9lbDxfiPgAd4ueiziOa9VlqNCqTL3OtoBhGPTyCqGBmMSp2Ve2RGxGaGgYVq6sn4TbW/INAB999D6ysjIwb9478PcPwI4d/+C11+Zg7drvERUVzXV4xMYVV2uw92oZnusTZvbBl7fzlgoxOtIXv10oxNtDO0HEpxuYpGXGXuaentzPgFJXL88Q7Cy8iEqtCh5CCdfhEGJ19A7uQC5dysLAgUkoKys1bWNZFmPGDMWePTvNei4ejwcfH996/9rq0qUszJ37IsaNG42BA5Pq/Tt8+KBZ422MWq3G3r27MXPm8+jVKwmhoWGYNm0mIiI64+eff7D4+Yn9+zOzCHq2dtl4a3gkPgClSi0OXi+3yvmI/TtVkQsXvhAx7n5ch1KPcUaW09QLTpyU/XVZkiZdvJgFX18/eHv7mLbl5uagqqoK0dGxDfZft+5brF//XbNtzp07D6NG3d1ge0FBAR58cCx4PB6io2MwbdqziIyManWsN2/ewKxZz2DYsBH49NMVUKlUWLz4XWi1OkyfPhPdu/c0W6xN0et10Ov1EInE9baLxWKcPXu61e0Q5/XrhULE+7sh1s/VKucbGu4NdxEff2UVY0Rnn5YPIE4vrSIX3TyCwWdsq7/NOCPL2cp8DPHrzHE0hFgfJeAt2JRzBhtunjJLWwzDgGXZVu37WIeemBDavU3tX7qU1SDRzsrKhIuLK0JDwxrs/8ADD2P48JHNtunt3XBRkbi4eMybNx/h4Z0gl1fi559/wHPPPY3vvvup0fM0ZtmypYiPT8C8ee+Ytk2Y8BiWLVuKESNGNShnaSlWPp+Bh0fbllh2cXFFfHw3rFv3LSIjo+Dj44vdu3fgwoVz4PP5bWqLOJ8cuQqn8hV4a0gnq51TLOBhTJQvtl8qgVZvgJDKUEgztAY9LsgL8HR4H65DacBTJEUHF0+cq6SZfYhzogTcgVy8mIVevZJu25aJqKjoRpcflsk8IJN5tPk8/foNqPdzt2498OSTj+LXXzdizpxXWzxeLpcjNfUE3nvvo3rbJRIp9Hp9o7XkLcUqEPCg0xla+Qz+5+23F+KDDxbioYfuAZ/PR3R0DO66azT27fu3zW0R57I1qxgAcG9M28uv7sR9sX745UIhDt4ox/BO1AtOmnapqgQag95m5v++XYIsCGcr87gOgxBOUALeggmh3dvcE92U9iaJrcGyLK5cuYSJEyfV256ZmY6oqJhGjzFXWYdAIECXLnHIzr7ZqlgvXsyETqdDdHT9uDIzMxAbG2fRWG8XEhKKFSvWQqlUorq6Gr6+vpg//w2EhNjWgCVie/65WII4P1dEeLlY9bymMpTMYkrASbPOVuYDABJsNAHv7hmErQUZNBCTOCVKwB1Ebm4OqqurERDwv8FgpaUlOHv2NMaMuafRY9pbgnI7g8GAS5cuNpk8N7Y/AKhUStO28vJy7Nq1DdOnP9euWNtTglKXVCqFVCqFXC7HiRNH8fDDj7a7LeL4iqo1OJ5TiVcHhFv93GIBD6OpDIW0wrnKfLjwhejk2vL7OBcSZLVfDM5XFmCAbzi3wRBiZZSAO4iLF7MAAL/9thGTJk1FaWkJVq1aDq1WC4PBAK1WC6Gw/ip97S1BWb78MwwYMAiBgUGQyyuxYcMPyM6+iXnz3jXtI5dXgsfjw83NrcHxsbFxkEpdsGrVcsyY8TzKy8uwYsXniI6Oxf33P9ToOe+kBOW33zbit9824aeffmvwWErKMeh0enTsGI7c3GysXPkFvLy88cQTT7ZwFYgz236pBCyAsVYuPzG6N8YPv14oxJHsCgwJt83kinDvXGU+4mWBNjcA0yj+Vs/8OXk+JeDE6VAC7iAuXcpC9+49oVQqMXXqYwgICMQzz8zCsmWf4Oeff8DYsfeZ7VwlJcVYtGg+KirKIZPJEB0di1WrvkFsbBfTPvPmzUVQUDDefPPdBsfLZDIsXvwRli37FE899Ti8vX1w112jMW3aDPB45v+gqKiowM2bNxp9rLq6GqtXr0BhYQFcXd0wYMAgPPvsC3Bxsc6sFsQ+bc0qRicvKbr4cvM6GRLuBYmAh52XSykBJ43SswaclxfgsbCeLe/MET+xK4IlMpytyOc6FEKsjhJwB2GcAeXFF1+pt3348LvMfq4FCxa3uM8bb8zHTz+ta/Lx3r374ocfNpkzrCZNmzYT06bNbPSxoUNHYOjQEVaJgzgGhVqHQzcrMDMptNHBzdbgIuRjYEdP7LxcivdGRHIWB7FdV6vLUKPX2mz9t1E3jyCck1MCTpyPbd6XIm126VKWTa3cuGHDekpsiUPaf70cOgOLkZHcDoAcHemLm5UqZJXUcBoHsU3nbg3AtNUZUIwSPIJwuaoE1ToN16EQYlWUgDuA0tISlJaW2lQCPmfOXPTuncx1GISY3a4rpfAQC9A7RMZpHCNvLcSz80oJp3EQ23S2Mh9iHh9RbtyMU2itBI8gsAAuyGk+cOJcKAF3AD4+vjh06GST0w1yobG5vAmxdwaWxZ6rpRga4QWBBcYrtEWQuxjdAtyw63Ipp3EQ23S+sgCx7gEQ8mx7UbG6K2IS4kwoASeEkFY6W6BAcbXW1PvMtVGRPjiZJ0dJDd2+J//DsizOyfPRzSOw5Z05Fihxh7/YjRJw4nQoASeEkFbafaUMDIBhnWxj5pG7OvvAwNbWpRNidFNZgUqtyuYHYBoleASZatYJcRaUgBNCSCvtulqKXsEy+LqIuA4FANAtwB3eUgH2XSvjOhRiQ87Z+AqYt+vmEYiLVcVQ6rVch0KI1VACTgghrVBao8GZfAVG2EjvNwDweQwGh3tj37VysCzLdTjERpyrzAefYdDFPYDrUFolQRYEPcsiQ17EdSiEWA0l4LehDzHSEnqNOKeDNyrAonYRHFsyLMILRdUapBdXcx0KsRFnKwsQ4+YPCd8+BsMnmAZi5nEcCSHWQwl4HXy+AFotDWYizdNqNeDbyQcbMZ9918rgIRagR5A716HUY1wJcy+VoRDcGoBZmW835ScAECr1gLdQSnXgxKlQAl6Hm5snKiqKodGoqZeTNMCyLDQaNSoqiuHm5sl1OMSKWJbFgevlGNjRk/PpB28X5C5GrK8r1YETAEChugolmmok2MEMKEYMw9QOxKS5wIkToW68OqRSVwBAZWUJ9Hqd2dvn8XgwGAxmb5dY79ry+QK4u3uZXivEOVwpUyJXocaL/TpwHUqjhkV44Zu0XFRr9HAV2fa8z8SyztrZAEyjBI8grLl6FBqDHiIbn7ucEHOgBPw2UqmrxZIrPz93FBcrLNK2s6NrSyxp//Xa3uUhEbYzALOuYRHeWJWSg2PZFRhhI3OUE26cq8wHA6CrzD4GYBoleARByxqQqSgyLc5DiCOzrXuphBBig/ZdL0dHTwnCPaVch9Ko3qEeEPEZHLpZwXUohGPnKvPR2dUHbgIx16G0iTHppjpw4iwoASeEkGboDAYcuVlhc7Of1OUi5CMpWIZDN2hBHmdnbwMwjTq6eMGVL0K6vJDrUAixCkrACSGkGWcLqlCl0WNgB9tNwAFgYEcvnCusQrmSFjNxVhUaJXJVcnSV2c8ATCMew6CLzJ8ScOI0KAEnhJBmHM2uAAD0C/PgNpAWDOzoCRb/i5c4nwxF7UI2XWT+HEfSPnHuAchQFNIsZMQpUAJOCCHNOHKzApHeUvi72XZNbc8gGaRCHg7eqOA6FMIRY++xvayAebs4WQAqtCrkqeRch0KIxVECTgghTdAbWBzPqUT/Dp5ch9IiEZ+HvqEeOEx14E4rU1EIT6EEQRLbWiyqteJuzdxCZSjEGVACTgghTThfVAWFRo9+YZ5ch9IqAzt6Iau0BkVVaq5DIRzIUBQh1j0ADMNwHUq7GHvuKQEnzoAScEIIacKRW9P69beXBPxWT/1hmo7Q6RhYFpmKInRxt8/6bwBwF4rRwcUT6QpKwInjowScEEKacCS7Ap28pAh0t+36b6P4ADe4ivg4nlPJdSjEyrKVFajSaUxlHPYqzj2AesCJU6AEnBBCGqE3sDieXWk35ScAIODx0DtYhqPZlIA7m0y5fc+AYhQnC8CVqlIo9TSdJnFslIATQkgj0ourUKnW2cUAzLqSwzyQWVJN84E7mYxbZRuxdlyCAtQm4AawyFIUcx0KIRZFCTghhDTif/Xftj3/9+36hnoCAE7kUi+4M8lQFCFM6ml3S9DfLo4GYhInQQk4IYQ04mh2JcI9JQiWSbgOpU16BrlDyGNwnMpQnEq6vNDu678BINzVG1K+0NSjT4ijogScEEJuY2BZHMuusKv6byOpkI+eQe44RgMxnYZar8PV6lK7ngHFiMcw6OLujwvUA04cHCXghBBym4ziapSr7K/+2yg5zBNnChSo1ui5DoVYwaWqEuhZFrF2PgDTqKssABlyWpKeODZKwAkh5DZHsysAwC57wAGgb6gHdAYWafm0pLczMJZr2OsS9LfrIgtAuVaJfJWC61AIsRhKwAkh5DZHblYgzEOCMA/7qv826hPqAQagOnAnkS4vhIjHR2dXH65DMYuuskAANBCTODZKwAkhpA6WZXEsuxID7LT3GwBkYgG6+rvhWE4F16EQK8hUFCHazQ8CnmN8pBtr2dMVBRxHQojlOMZfKyGEmMnlshqUKrVItrPpB2+XHOaBk3lyaPUGrkMhFpYhL7L7+b/rkgklCJV6IP3W4kKEOCLOE3CtVouFCxciOTkZycnJ+OSTT2AwNP6BkZGRgUmTJqFHjx4YPnw4vvrqKytHSwhxdCdyauum+4TYdwLeN9QDSq0BZwuruA6FWFCZpgYFaoVDTEFYV1dZIJWgEIfGeQL+6aef4vDhw1i7di0+++wz/PHHH/j6668b7FdVVYVp06YhOjoaf/31F9566y2sWrUKv//+OwdRE0IcVUpuJbylAnT2lnIdyh3pG1r7BeL4rQGlxDFlGJegd6AecACIk/njSnUJVHod16EQYhGcJuBqtRobNmzAvHnz0L17d/Tv3x+vvPIK1q1b12D6oby8PPTr1w9vvvkmOnTogOHDh6N///44ceIER9ETQhxRSm4lkkI8wDAM16HcEX83MTp5SWk+cAdnmgHFwXrA49wDoWdZXKyiJemJY+I0Ac/IyIBSqURSUpJpW1JSEoqLi5GTk1Nv3+joaCxduhR8Ph8sy+LkyZNISUlB//79rR02IcRBldZocLlMafflJ0bJoR44nlMJA82n7LAyFUXwEkoRIHbjOhSzMpbUXJDTQEzimDhNwAsLC+Hm5gZXV1fTNj8/P9NjTenduzeeeOIJ9OzZE2PHjrV4nIQQ55CaV1v/3TtExnEk5tE3zAMVKh2ySqq5DoVYSLq8EF1kAXZ/x+Z24a5ekPIEyKSBmMRBcZqAK5VKiMXiettEIhEAQKPRNHqMwWDAd999hxUrVuDcuXP44IMPLB4nIcQ5nMiVQ8hj0D3QnetQzKJvqCcA4ASVoTgkA8siU1HkcPXfAMBneIh290e6ggZiEsck4PLkEomkQaJt/FkiaXwBDB6Ph4SEBCQkJKC6uhpvvfUWXnvtNVPi3ho+PtzdqvPzc4wPdltE19YynOm6nimqQq9QD3QI9rTK+Sx9bX193eDvJsL5UqVT/R4B53jdXlWUokavRe/gDlZ9vtY6V0//EPyTneEUv0sjZ3qu1mZr15bTBDwwMBAKhQJKpRJSae2MA8XFtQMuAgLqDyjJycnBlStXMGTIENO2qKgoaLVaVFVVwdvbu9XnLS2tgsFg/ZpIPz93FBfT0rqWQNfWMpzpumr1Bpy4WYEpPYKt8pytdW17Bbnj0NVSp/k9As7zuj1ccBUAEMZ4WO35WvPadhJ6o0hVhfScfPg5WI17Y5zldcsFrq4tj8c02enLaQlKbGwspFIpUlNTTdtOnjwJf39/hISE1Nv3zJkzePHFF1Fd/b9axgsXLsDHx6dNyTchhDTmXGEVVDqDw9R/GyUFe+BquRKlNY2X9RH7ZZwn25EW4amri6z2eWVQHThxQJwm4BKJBOPHj8fChQuRlpaGo0ePYunSpZgyZQoAoKKiAgpF7TeWoUOHwtvbG/PmzcPVq1exe/dufPrpp5g1axaXT4EQ4iBScmvrpHs7yAwoRsYvFCdvDTAljiNDUYSOLl5wFbS+BNOexLrX3gnPoDpw4oA4LUEBgLlz50KtVmP69OkQi8UYP348pk2bBgCYPXs2QkJCsGTJEri6uuKbb77Be++9h4cffhju7u6YNm0aJk2axPEzIIQ4gpRcOcI8JAh0F7e8sx3pHugOAY/ByVw5Rkf6ch0OMSNHHYBp5Cd2ha/IFRkK6gEnjofzBFwsFmPRokVYtGhRg8fWr19f7+eIiAh888031gqNEOIkWJZFSm4lBnTw5DoUs5MK+Yj3d6MecAej0utwpaoU9wbFcR2KRcXJAqgEhTgkzpeiJ4QQruXI1Sio0jhc+YlRYogMp/Ll0BkMXIdCzORiVTEMYB26BxwAurj7I0tRBD1Lr13iWCgBJ4Q4vROm+m/HGoBplBQsg1JrQHoRLcjjKDLkjrkE/e1iZf5QGXS4Xl3OdSiEmBUl4IQQp3cytxKuIj66+DnmVGfGnn0qQ3EcGYoiiHl8RLg49ixgXWggJnFQlIATQpxeSq4ciUEy8HmOtZy3UahMjAA3EU7m0oqYjiJDXogYd38IeI79MR7t7gceGNOUi4Q4Csf+yyWEkBZUa3S4UFSFPqGOWX4CAAzDIClYRj3gDiRDUeSw83/X5cIXIsLVG5k0EwpxMJSAE0Kc2ql8BQwskBjsuAk4UFsHfqNChaJqWpDH3pVqalCkrnL4AZhGse7+NBMKcTiUgBNCnFrqrV7hXg6egJvqwKkMxe45ywBMozhZAK7XlKFaR18eieOgBJwQ4tTS8uXo7C2Fp0TIdSgWlRDoBiGPMX3hIPbLmIDHuTtHAt7F3R8sgCxFMdehEGI2lIATQpwWy7JIzZM7fPkJAEgEfCQEuOFkLiXg9i5DUQRvkQv8xK5ch2IVxp7+TJoJhTgQSsAJIU4rR65GcbUWvYIcPwEHgKQQD5wuUECrp0VN7FnGrSXoGcYxZ+25XUcXL0j5QlqSnjgUSsAJIU4r7VY5hjP0gAO1AzFVOgPOF1VxHQppJwPLIlNRhDgnqf8GAB7DINbdn6YiJA6FEnBCiNNKzZNDIuChi59z3Mo3rvRJZSj260ZNOZR6rdPMgGLUxd0fGYoisCzLdSiEmIWgLTuXlZXh6NGjOH36NIqKiqBWq+Hl5YWIiAgkJSWhV69eloqTEELMLi1fju6B7hDynaMvIlgmQZCbCGn5lIDbK+MAzFgnGYBp1MXdHz9ln0Kxuhr+EsdcsZY4l1Yl4CkpKfjvf/+L/fv3Q6fTITg4GJ6enhCLxcjOzsb27duhVCoRFBSE8ePHY8qUKXBzoz8QQojt0ugNOFugwNO9QrgOxaoSg2U0E4ody1AUgQEQ4+7HdShWZRyImaEopAScOIQWE/Dp06cjNTUVI0aMwPLly9GrVy94eHjU24dlWVy+fBl79+7F1q1bsX79enz44YcYMmSIxQInhJA7kV5UBbWedfj5v2+XGCzDloslKK7WwM9VxHU4pI0yFEUId/GGq8C5fnfGBDxdXoghfp05joaQO9diAt61a1d8/PHH8PLyanIfhmEQFRWFqKgozJgxA4cOHYJSqTRroIQQYk6pTjYA0yjxVh14Wr4coyN9OY6GtFWGvBBdZM5V/w0APiIX+IvdaCYU4jBaLHx86aWXTMn3+fPnoVarW2x04MCBGDly5J1HRwghFpKWr0CAmwjB7mKuQ7GqhAB3CGhBHruk1GtxrboMsU42ANOoi7s/MikBJw6iTSOPHnnkEaxZs8ZSsRBCiNWk3VqAx1nmUjZyEfLR1d+VEnA7dFFRDANYdHGyAZhGXWQByFIUQWegeeyJ/WvTLCgsy+L48eOYMWMGKisr4efnhxEjRmDkyJE06JIQYjfKlFpcLVfi8W5BXIfCicRgGTaeL4TewILPc64vIPbMWH7hTHOA19XF3R9qgx7XasoQ5UblU8S+tXnurbS0NNy4cQNeXl7Iy8vDvHnzcPfdd+P48eOWiI8QQszu1K3e317B7hxHwo3EYBmqNXpkllRzHQppgwx5IaQ8AcJdmx6T5chMM6HQgjzEAbQ5AX/sscewY8cOrF69Gps3b8a+ffvQt29fTJ8+HefOnbNEjIQQYlapeXLwGKBHoPMm4ACoDMXOZCiKEOXuBz7jHPPW3y7KzRc8MDQQkziENv0V8/n8BoMrAwIC8PHHH2P48OFYvny5WYMjhBBLSMuXI9bXFa6iNlXhOYxwTym8pQJKwO1MhqLQactPAEDKF6Kzmw/1gBOH0KYEPCAgAFeuXGn0sYceegipqalmCYoQQizFwLJIy1M43fSDdTEMg17BMqRRAm43itXVKFZXO90S9LeLvbUkPSH2rk0J+LBhw7BixQpkZGQ0eKy0tBQGGplMCLFxV8uUqFTrnG4BntslBstwsbQGlSot16GQVshU1Pb6OusMKEZd3P1xo6Yc1ToN16EQckfadP91zpw5uHDhAh555BGMHj0aAwcOhK+vL65du4aVK1ciKSnJUnESQohZOOsCPLczPv9T+QoMjfDmOBrSkgx5ba+vMy7CU5exBCdTUYREr1COoyGk/dqUgLu7u+Onn37Cd999hz///BNbt241PRYVFYX58+ebPUBCCDGntHw53EV8RPm4cB0Kp3oGycCg9gsJJeC2L0NRCF+RK/zEzj3lr/EOQIa8kBJwYtfaPAKJx+Nh2rRpmDZtGgoLC5Gbmwt3d3dERkY63YIWhBD7k5YnR48gd/Cc/P1KJhYg2teFBmLaiXR5kdP3fgNAmIsnXPhCqgMndu+O5jIKCAhAr169EBUVRck3IcTm1Wj1uFBU5fTlJ0aJwTKk5snBsizXoZBm6FkDLiqKnH4AJgDwGIYGYhKH4JyTiRJCnNK5QgX0LJx+AKZRYrAMFSodrpYruQ6FNONGdTmUBh1inXwAplGcLAAZ8kL64kjsGiXghBCnkZp7awXMIErAAVqQx144+xL0t4t190e5VolCdRXXoRDSbpSAE0KcRlq+Ah08JPBzFXEdik2I9nGFm4hPCbiNS5cXggEQ7e7HdSg2oe5ATELsldkS8BUrVmDTpk1Qq9XmapIQQswqNU9O5Sd18HkMega5UwJu4zIVRYhw9YYLX8h1KDbBOBg1XUEJOLFfZk3A58+fj2HDhmHt2rXmapYQQsyiQKFGnkJNAzBvkxgsQ3pRFao1eq5DIU3IUBQ6/QI8dXmLXBAodjfNjU6IPWrzNIRN2bNnD5RKJU6dOkVL0hNCbE5avrH+253jSGxLYrAMehY4W6hAvzBPrsMht6nRa3GtugwPhSRwHYpN6SLzRybNhELsmNkS8JCQEABAZGQkHnnkEXM1SwghZpGaJ4eIzyAhgBLwunrVGYhJCbjtyVIUgQUtQX+7WHd/HC49AZ3BAAGPhrMR+9OmV+3169ctFAYhhFhWWp4cXf3dIBbQh3Vdvi4ihHtKqA7cRpmWoKc5wOuJkwVAY9DjSnUp16EQ0i5t6gEfM2YMXFxcEB0djS5duqBLly6IjY1FTEwMjh49ikOHDuGtt96yVKyEENIuOoMBpwoUeKJbENeh2KTEYBkO3qgAy7K0qJqNyVQUQsoXoqOrF9eh2BTTTCiKQsTQ7DDEDrUpAf/++++RkZGBjIwMpKam4pdffoFerwePx4NQKATDMJSAE0JsTlZJDZRaA82A0oTEYBl+Sy9CrkKNUJmE63BIHenyIsS4+YHP0J2buqLcfMFnGGTKi4BgrqMhpO3alIAnJycjOTnZ9LNGo8Hp06fx448/Yu/evZg/f77ZAySEkDtlLK9IpAV4GmVakCdXTgm4jclQFGJUQDTXYdgcMV+ATq4+tCQ9sVt39JVaJBKhT58+WLZsGe666y5cunTJXHERQojZpObJ4SMVoqMnJZeNifN3g0TAozpwG1OsrkKppoYGYDYhThaAdFqMh9gps93TGj16NP744w9zNUcIIWaTlidHz2B3qm9ugojPQ7cAN0rAbYwxuaQl6BvXxd0f2coKVOloAUBif9qUgG/atAlnz56FRqNp8JhSqaQPN0KIzZGrdbhUWkML8LQgMViGc4UKqHUGrkMhtxgT8C6UgDfKeGeA5gMn9qhNNeALFy6EXq8Hn89HeHi4aRYUPp+PH374AXPmzLFQmIQQ0j6n8uVgQfXfLUkMlmFVSg4uFFXRYFUbcUFeiECxO3xELlyHYpOMX0zS5YVI8grjOBpC2qZNCfipU6dw+fJlpKenIyMjA+np6dizZw9qamoAAGvWrMHBgwcRFxeH+Ph4DBkyxCJBE0JIa6XmysEA6ElJZbMS6yzIQwm4bchQFFL5STPCpB5wE4hoSXpil9qUgAuFQtP833Vdv369XlL+448/ory8HBkZGWYNlhBC2io1T45oXxfIxGZb+NchBcskCHITITVPjme4DoZAY9DjoqIYw/wiuQ7FZjEMg1h3f5oJhdgls3wihYeHIzw8HGPHjjVtKyykkcmEEG6xLIvUPDnujvblOhS7kBgso4GYNuJKVQm0rAFdqQe8WV3c/fF3fjotIkXsjsVm9g8IoDcNQgi3rpYrUa7S0QDMVkoMluFmpQpF1Q0H2hProgGYrdNFFoAKrQr5KgXXoRDSJrS0FiHEYRl7c5OCPTiOxD4khtR+UUmjXnDOXZAXQsTjo7OrD9eh2LS6S9ITYk8oASeEOKzUPDncRXxE+9IsEq2REOAOAY+hMhQbkKEoRIybH4Q8Pteh2LQu7v4AQAMxid2hBJwQ4rBO5srRM0gGHtWGtoqLkI+u/q6UgNuAC/JCKj9pBU+RFMESGfWAE7tDCTghxCFVa/RIL66i+u82SgyW4VS+HHoDy3UoTqtYXY0idRUNwGylWHd/6gEndqfFWVBWrFjR7saDg4Px0EMPtft4QghprzMFChhYICmEEvC2SAyW4du0PGSWVKOrvxvX4TilDFqCvk26yPxxsOQqtAY9lewQu9FiAn769Ol2N25coIcQQqztZF4lANCiMm1Ud0EeSsC5kX6rnMI4wJA0r4t7ALSsAVeqSxF7qyacEFvXYgL+9ddfWyMOQggxq9Q8OTp5SeEtFXIdil0J95TCWypAap4cT/YI5jocp3RBXogAsRt8xa5ch2IXjHcKMuSFlIATu0E14IQQh2NcgIfKT9qOYRj0CpbRVIQcypAXIk4WyHUYdiPSzRcChkcrYhK7wnkCrtVqsXDhQiQnJyM5ORmffPIJDAZDo/tevnwZ06ZNQ1JSEoYMGYIPP/wQarXayhETQmzdzUoViqu1NACznRKDZbhYWoNKlZbrUJyO1qDHxapixMmoJ7e1RDw+Orv50EBMYlfMshT9nfj0009x+PBhrF27FtXV1Xjttdcgk8kwY8aMevtVV1fjmWeeQe/evbFx40YUFxfjzTffhF6vx7x58ziKnhBii4zT6FEC3j7G63YqX4GhEd4cR+NcLleVQmPQI47qv9uki3sAUsqzuQ6DkFbjtAdcrVZjw4YNmDdvHrp3747+/fvjlVdewbp168Cy9afAOnr0KBQKBd577z107twZffv2xYsvvoi//vqLo+gJIbYqNU8OqZCHLn5UQ9sePYNkYACaD5wDxvmsqQSlbeJk/shVVkKuVXEdCiGt0qYE/Ndff0VBQYHZTp6RkQGlUomkpCTTtqSkJBQXFyMnJ6fevgkJCVi5ciVEIpFpG8MwqKqqapCsE0Kc28k8OXoGukPA47zKzi7JxAJE+7pQAs6BC/ICiHh8RLrREvRtEXvrjkEm1YETO9GmT6e33noL48ePx9WrVxs8ZjAY2pwIFxYWws3NDa6u/+ul8vPzMz1WV0BAAJKTk00/6/V6rF+/HsnJyWBolTtCyC1KrR7nC6to+sE7lBgsQ2qenDo4rCxdXoRoWoK+zUxL0lMCTuxEm2vAAwMD8eSTT2LdunXo1KmTafu5c+cwZcqUNs0brlQqIRaL620z9nBrNJpmj120aBEyMzOxadOm1gdPCHF45wuroDOwSArx4DoUGJSFMFSkwyC/DLY6F6yqEKymEtArkc8HtHoG4EvBiL3BSPzAc+sIRtYZfO/uYITunMaeGCzDT2cLcLVcic7eLpzG4kzS5QUY7NeZ6zDsTqjUA+4CMdLltCQ9sQ9tTsDfeustbNiwodEkvK0zkkgkkgaJtvFniUTS6DF6vR4LFizAb7/9hmXLliE2NraNzwDw8eFucQk/P24/VB0ZXVvLsLfrmnGhtgdsVHwQ/GSNv49YirbiMpQ390KdfwSqvKPQVf7vbiHDF4PvEgi+xAuMQApAAAGjAasuh77yPHQ1hYDBOOsIA6FPF4gD+0AS3B8uEWPBd7HurBgjuwYB2y/iokKDvjH2NyDQ3l63AFCsqkKhugrJQR1sOn5bja27TzAu1hTbbHytYc+x2zpbu7ZtTsB5PB6WLFmC119/vdEkvC0CAwOhUCigVCohlUoBAMXFxQBqS05up9Vq8eqrr+Lff//FF198gREjRrTrvKWlVTAYrH9b1c/PHcXFCquf1xnQtbUMe7yuBy4VI8xDAr5ai+Jiy0+jZ6i6Ad2NP6C78QcM5WcBoLY3268PRJ2fqu3NlkWCkfjXK5e7/dqyBj1YZT4MFZkwlKZBX5qKqkt/ourCfwGGB55fPwg63AtB2L3guVh+gRxfHuAm4mNfVhHu7uhp8fOZkz2+bgHgYEntF7YOPE+bjd+Wr22s1A8/Zp9CQVEl+Iz9jf+w5Wtr77i6tjwe02Snb7umIWQYpkES3h6xsbGQSqVITU3FwIEDAQAnT56Ev78/QkJCGuw/f/587N+/H2vWrEH//v3bdU5CiGNLzZOjT6hly09Ygw767K3QZK6GoeQEAIDnkwhRr/cgCBkFxr1Tm8emMDw+GNdQ8FxDgZC7as/DsjBUXIAuewv0N/+C5uQb0KS+CX7IGAhjZoAfMNBiY2D4PAY9g9xpIKYVnausneQg3oNmQGmPeI8gKK+fwNXqMkS5+XIdDiHNavdXRGMSPmDAADz55JO4cuVKm9uQSCQYP348Fi5ciLS0NBw9ehRLly7FlClTAAAVFRVQKGq/sezfvx+bN2/G3LlzERUVheLiYtM/QggBgDy5CnkKNZIsNACT1cqhyViFmr+SoDr0NFhVMUQ95sPl/lNwGbMToi7PgSfrbLakmGEY8L3iIe72OlzuPQKXe49CGPci9MXHodrzAJRbB0F7eR1YvWUWJEsMliG9qArVGr1F2if1navMR4jUA94iqrlvj4RbX1zOV+ZzHAkhLWtTD/jXX3+NsLAw0891e8Lnz5/frgDmzp0LtVqN6dOnQywWY/z48Zg2bRoAYPbs2QgJCcGSJUuwbds2AMDChQuxcOHCem2cPXu2wWBOQojzsdQCPKxeBW3WV9Bc+AzQVILn3x/ixPfBDxkDxoqzVfA8oiHu8RZECa9Cd30ztFlroT7+EjTnP4Oo2+sQhI83azyJwTLoWeBsoQL9wjzN1i5p3Hl5ARJo/u92i3bzg4jHx9nKfDwYksB1OIQ0q00JuLFMpC5jEi6RSLBly5Y2ByAWi7Fo0SIsWrSowWPr1683/X/JkiVYsmRJm9snhDiP1Dw5xHwG8QHmGWjNGvTQXf8FmjMfgK3JAT/4Loi6vQ6+T0+ztN9eDF8CYefHIej0GPT5e6E5vQjqo7OgTV8OUY/aEhVz9MIbp3JMzZNTAm5h1ToNLleV4P7grlyHYreEPD5i3f1xXm6+9UoIsRSzjFJgGAYLFixAamqqOZojhJB2OZknR7dAd4j4d/7Wpi9Ng3L7CKiPPg9G4gvJiD8gHbaR8+S7LoZhIAgeDundeyAe+A1Ygwaq/ZOg2vsoDFU37rh9XxcRwj0lVAduBenyQrAAunkEcR2KXUuQBeJ8ZQHNX09sXoufUm+88QZu3rzZ6gYNBgM2b96MP/74407iIoSQNtHoDThboLjj8hNWVw116ltQ7hgNVlUM8YC1kI7ZBUHgIDNFan4Mw4Ow4wNwufcwRImLoS8+hpotA6C58AVYw53NBJMYLMPJXFqQx9LO3qpbjpdRAn4n4j2CUK5VIldFXxqJbWsxAWcYBmPHjsVTTz2FX3/9tdHBlpWVlTh8+DDef/99DB48GKtXr65XK04IIZZ2oagKaj17Rwm4Ln8varYMhDZzFQSRU2oHPYY/DMZOpjRjeEKIYmfC5d6j4AcNg+b0Aii3DYe+7Gy720wMlqGoWoNchWUGepJa5+X58BG5IEhiW3MV2xsaiEnsRYs14IsXL8bTTz+N77//Hh988AFqamogFAohk8kgEomgUChQVVUFlmURFxeHF198EQ888ACEQqE14ieEEABASm5tj1d7ZkBh9SpoTr0LbdZXYGRRkI7cCr5/X3OHaDU81xBIh6yHLnsr1CmvQbljFEQ93oYw9rk2f5kwfqFJzZUj1MoLGzmTc5UFSPAIsti0ks6ii3sAGNTeURgT2PaF+gixllYNwoyMjMSiRYvw1ltv4dSpUzh79iyKi4uhVqvh6emJiIgIJCYmokOHDpaOlxBCGpWSU4lQmRjBbUwSDZUXoTr8DAzl5yGMfRaiHm+D4TtGoikIuwd8/35QHXsRmrT50Of9C3H/leBJWz/TRpy/GyQCHlLz5Li/i3VX43QWar0OWYoiDPXrx3Uods9VIEKkmy8NxCQ2r1UJeFlZGU6fPg2VSoW4uDj07Wu/PUOEEMfDsiyO51ZiQAfPNh2ju/oT1CmvAwIpJEM3QBAyynJBcoQRe0MyeB10l9dBnfomarYOhqT/agiCh7fqeBGfh24BbjQQ04KyqoqhZQ1IoAGYZpEgC8KxsjsfhEyIJbWYgKekpGDWrFmmMhNjTfgHH3wAkUhkjRgJIaRZNypVKKzSILmVK2CyejXUKf+B7sp68AMGQdx/FXgujpv8MAwDYdSU2t7wQ9Oh2jsBoh5vQRj3YqtKHhKDZfg2LRdqnQFigX3Uw9sTY70yzQFuHvEegdicdw6lmhr40KJGxEa1+E66dOlSeHh44JNPPsGaNWvw9NNPY/fu3fjss8+sER8hhLQoJacSANA7pOUE3KAshHL3A9BdWQ9h15cgGf6bQyffdfE8oiEdvQ2Cjg9Ac3pR7Wqe2qoWj0sMlkGtZ3GhqOV9SdudrcyHm0CEcFdvrkNxCDQQk9iDFnvAs7Ky8OGHH2LUqNpbs0OGDEFYWBg++ugjvPrqq+DzrbcKHCGENOZ4TiVkYj5ifV2b3U9fmgbV/ifBaiohGfgtBB3vt1KEtoMRuEI84CvwvLtDc3ohlJUXIRnyA3juEU0ek1hnQZ5eZl5llNSugBkvCwSPBmCahXEqx3OVBRji15njaAhpXIs94EqlEoGB9W+LjRo1CjU1NcjOzrZYYIQQ0lonciuRFOwBPq/pBEZ3408od94L8IS3eoGdL/k2YhgGorjZkAzbBIOyAModY6AvOdnk/sEyCYLcREjJrbRilM5BzxpwQV5I9d9m5CWSIkTqgXNy6gEntqtdxXweHrW3eWtqaswaDCGEtFW5Uouskhr0aab+W5OxCqpD08Dz6QGXMbvB94q3YoS2SxA0DC6jdwBCt9qynOytTe7bO9QDJ3IqaUEeM7tSVQqlXot4qv82q26yIJyvpJlQiO1q1Swos2fPRmxsLKKiohATE4NOnTrRXKWEEJtg7JVtbAAmyxqgSXsb2szV4IfdC0n/1WAEUmuHaNN4skhIR2+Hat8TUB2YAlHi+xDFzmywX99QD/yVWYyblSp09KRraC7G6fKoB9y84j0Csb0wE9U6DVwFNGEEsT0tJuCvvfYaMjMzkZmZicOHD0On04FhGLAsi//85z/o1q0bunTpgtjYWMTGxsLNzc0acRNCCADgRK4cAh6DHkH1VxBk9Sqoj8yC7uafEMbMgKjXe2B4NGalMTyJH6R3/QHV4ZnQpM4DW5MPUc936nW09A3zBFBbb08JuPmcrcyHmMdHlJsv16E4lASPQLAALsgL0Meb1ightqfFBPzpp582/V+j0eDKlSvIzMxERkYGMjMzsXv3bvz2228AausKMzIyLBctIYTc5kROJboFuMFF+L/kmtVVQ7V/MvQF+yHqtRDC2Fl0164FjMAFkkH/hebk69BmLAerlUPc+2PTl5ZYX1d4iAU4ll2JCfFULmEu5ysLEOseACF9OTSrugMxKQEntqhVJShGIpEIXbp0QZcuXfDggw+atufn5yMjIwNZWVlmD5AQQpqi1hlwOl+Op3uFmLaxGjmU+ybCUJICcd/lEHZ+nMMI7QvD40PU+yNAJIP2wueAVgFx/y/B8ITg8xj0DpXheE4F12E6DJZlcU6ej3FBcVyH4nCCJO7wFrnQQExis9qUgDclKCgIQUFBGD68dSurEUKIOZwtUECtZ00DMFlVKZR7H4Gh/AIkA7526plO2othGIh7vA1GKIPm9EKwumpIBn4DRiBF31BP7L5ShuJqDfxcqa72TmUrK1GpVSGe6r/NjmEYdPcIwtkKSsCJbaIlzQghdut47v8W4KldYOc+GCoyIRmynpLvOyTq+iLEvT+GPncnVPsfB6urQd9bX3RO5NB0hOZwtjIPAK2AaSk9PEOQqShCtU7DdSiENEAJOCHEbp3IqURnbyl8eOVQ7r4fhuocSIb9DEHIKK5DcwjC6Kch7rcC+oKDUO1/At38+JAIeDhGCbhZnK7Ig5DhIY4ScIvo6RkMA1jTTDOE2BJKwAkhdollWaTkVmJokB7K3Q+Arc6FdOjPEAQO5jo0hyLsNBHifiuhLzgIw6HJ6BsopDpwMzlVkYs4WSAkfLNUg5Lb9PCoHRtyqiKX40gIaYgScEKIXbpcVgNGXYoXVHPAVudAOuxn8AP6cx2WQxJ2etSUhL8rXohLRaWoUuu4Dsuu6VkDzlTmoadnMNehOCx/iRtCpB6UgBObRAk4IcQunbp+DT/4vQN3bS4kwzaAHzCA65AcmjEJD1WnYJX3EqTmFHMdkl27XFWKKp0GPT1DWt6ZtFsPj2CcrsjjOgxCGqAEnBBid1hNJbpfnI4OgkJIh/4EQcBArkNyCsJOj4JJ+hwDJWfhdeZ5sAYt1yHZLWOvLCXgltXTMwQ3aspRqqnhOhRC6qEEnBBiV1hdDZT7HoO//hrWSd+HIGgI1yE5FbeYSfhaPwudlPuhPjobLGvgOiS7lFaRA3eBGJG0AqZFGb/gnKYyFGJjKAEnhNgNVq+B6sAU6ItT8FLZi/DpNJrrkJxSWcgULFM8Dt31X6BOeQ0sy3Idkt05XZGHHp7B4NEKrRbV3TMIDEBlKMTmUAJOCLELrEEH1ZGZ0Of/i1Mh72Kbsj/6d/DkOiyn1DfMA19UPoSSsBnQXfoOmtMLuQ7Jrij1WqTLC6n8xArcBGJEufnRQExicygBJ4TYPJY1QH38Jehv/gVRr/fws2IY/FyFiPR24To0p1S78iiDv4XPQhA1Fdr0L6A5/xnXYdmNC/IC6FgDJeBW0tMzBKcqculODbEplIATQmway7LQpL0N3dWfIEyYC2HsszhyswL9wzzB0O17Tvi6iBDl7YJjOZUQ9/4YgvDx0Jx5D5qsr7gOzS6cKqcBmNbUwzMYpZoa5ChpASliOygBJ4TYNO2FT6HNXA1hzAyIEv6D6xVK5FdpMIDKTzjVv4MnjuVUQs8C4n4rwA8dA83JN6C98QfXodm8UxV5CJK4I1DiznUoTsH4RYfKUIgtoQScEGKztNc2QXNmMQThj0CU+D4YhsHhmxUAQPXfHBvY0RNVGj3OFFSB4QkhGfA1eH59oD7yHHQFB7kOz6adqsil3m8ripMFQMTjUwJObAol4IQQm6QrOAD1sf8DP2AgxH2/AMPUvl0dvllB9d82wPgF6OCNcgAAI5BCOuRH8NwjoDowGfryCxxGZ7vKNUpcqymjBNyKRDw+4mWBNBMKsSmUgBNCbI6+IhOqA1PAc+8EyeB1YPgiALX14FT/bRt8XUSI83PFoVsJOAAwYi9Ihv0CRuAG1d5HYKjK5jBC23SaFuDhRA/PYJypzIOe5q0nNoIScEKITTEoC6Da+ygYvhSSoRvBiDxMj10rV6KgSoOBHb04jJAYDezohZRcOVQ6vWkbzzUEkuG/gtWroNw7Hqy6jMMIbc+pilwwALp7BHMdilPp6RmCGr0WFxUlXIdCCABKwAkhNoTVVkG173Gw6jJIhv4EnltYvcdN9d9hntYPjjQwsKMnVDoDUvPk9bbzPWMhHfIj2KpsKPc9BlZHy4AbnarIQ5SbH9yFYq5DcSqmFTErqQ6c2AZKwAkhNoE16KA69AwM5ecgGfg1+D49GuxzJLsC/q4idPaWWj9A0kD/ME/wGeDQjYoGj/H9+0EyYA0MJalQHXoGrEFn/QBtDMuySKvIofITDnRy9YG7QEwDMYnNoAScEMI5lmWhPvk69Hk7IU76CILQhkvMm+q/O1D9t61wFwvQPdC9Xh14XYIO90Hc+0Poc7dDkzrP6RdCyVZWolRTg56eVH5ibTyGQQ/PYNMc7IRwjRJwQgjntOnLobv0HYRxsyGMfqrRfYz13zT/t20Z2NELafkKVGsa7+EWRk+DsMsL0F78BtrM1VaOzracogGYnEryCkW6ohDVOg3XoRBCCTghhFva679Dc3oBBB0fhKjH/Cb3O0T13zZpYEdP6AwsjmU3vcqgqOc74IfdV7ui6c2/rRidbTlZng0pT4A4WQDXoTil3l4doGdZKkMhNoEScEIIZ/RFx6A+Ogs8v74Q91thmuu7MQevlyPQjeq/bU3vEA+I+IzpC1JjGIYHSf9V4PkmQnXkWehLTlovQBtyoiwbPTxDIOTxuQ7FKSV6hQIAUsppekzCPUrACSGcMMgvQbl/EhjXMEiHrAfDlzS5r97A4sCNcgwN96b6bxvjIuQjKVjWZB24kXGhHkYaCNW+J2BQXLdOgDaiWqfBeXk++niHtbwzsQgPoQQx7n5IKaMEnHCPEnBCiNUZVMVQ7p0IhuFDOmwjGLF3s/ufKVCgQqXDkAia/9sWDezohXOFVShXapvdj5H4QjpsI1hWD+W+R8Gqm0/aHcnpijzoWRZJXpSAc6mPVxhSK3JgcPIBwYR7lIATQqyK1dVAte8JsMpCSIbWLl3ekn3Xy8AAGBxOCbgtGtjREyyAo9kVLe7Lk0VCOmQ92KqbUB54EqxebfH4bEFK+U0AoAScY0leYajUqnCxqpjrUIiTowScEGI1rEEP1eGZMJSmQTJgDfi+Sa06bt+1cnQLdIOvi8jCEZL26Bkkg1TIw8FG5gNvDN+/H8T9VsBQdATqY//nFNMTppTnINrND14iGsPApd63vgCdpDIUwjFKwAkhVqNJexv6nH8gSnwfgrB7WnWMQq3DydxKDAlvvkyFcEfE56FvqAcOXG/9svPC8Ich6v4WdNd/hebsBxaMjnsGlsXJ8mz0vjUIkHAnwtUbPiIXnKCBmIRjlIATQqxCk7kG2qw1EMbMhCh2ZquPO3SzAnoWGEr13zZtaIQ3LpcpcbNS2epjhF3nQNB5MrTnl0J75UcLRseti1XFqNSq0Nu7A9ehOD2GYdDbKwwnym5yHQpxcpSAE0IsTpe9BZrUN8EPuweiXovadOy+a2VwEfLQO8TDQtERcxjRqfYOxb9XW98LzjAMxH0+Bj9oGNTHX4Yuf6+lwuOUcdaN3lT/bROSvTvgek05ClQKrkMhTowScEKIRelLUqA6PBM8n16Q9F8Npo1zIO+7VoYBHbwg4tPblS2L9HZBmIcEe9qQgAMAwxNCMvBb8DyioTr4FPTl6RaKkDvHym7AT+yKTq5URmUL+vp0BFD7eyGEK/SJRgixGIPiGpT7ngAjDYRk6I9gBC5tOv56uRLXK1QYRuUnNo9hGIzo5I1DN8qh1hnadqxIBsnQn8EIXKHaNxGGmnwLRWl9LMviaOkN9PXuSHPY24gEWRBc+EIcL6UyFMIdSsAJIRbBqsug3PsowBogHfYzeBK/Nrex79agvqER1HNoD4Z38kaN1oBjORVtPpbnGgLJ0A1gNRVQ7XscrLbK/AFy4KayAnkqOfrd6nUl3BPweOjj3YF6wAmnKAEnhJgdq1dBuX8S2OocSIf8AJ4sql3t7LtWjjCZGJ28aOo2ezCwgxdEfKZNdeB18b27QTLwGxgqzkN16BmwBp2ZI7S+o6W1SV4/73BuAyH19PXugAxFEco1rR80TIg5UQJOCDErljVAfeR5GIqPQ9xvJfj+fdvVjlZvwKEb5RgaQcvP2wtXER99Qz3bnYADgCBkJMRJH0GftxOak2/Y/RzhR0tvwEsoRYx72+8AEcvp5xMOADQbCuEMJeCEELPSnF4I3c0/IOrxDoThD7a7nVP5Cig0eio/sTMjOnvjYmkNsitV7W5DGP0UhF1mQ3vpW2gzV5kxOus7VlZb/82jL5E2pYdHMMQ8Po5SGQrhCCXghBCz0V78Ftr05RBETYUwbvYdtbX3Whl4TO0y58R+/G86wtI7akfUcz74HcZBkzYfupt/mSM0q8tTynGjppzqv22QmC9AL89QU4kQIdZGCTghxCx0OTugPvkf8INHQZz04R2Xjey+UorEYBk8JUIzRUisob3TEd6OYXiQ9PsSPN9EqI48B31JipkitJ6jpdcB/G/aO2Jb+vl0xLnKfFRq23+3hpD2ogScEHLH9KWnoTo0HTyvBEgGfgWGJ7ij9vIVapwtrMKoSB8zRUisxTgd4cF2TEfYoC2BFNIhP4KRBkK1bxIMiuvmCdJKDpdeh0wgRldZANehkEYM8u0EA1gco15wwgFKwAkhd8RQlQ3VvsfBiL0hGfoTGKHbHbe5+0pt+cKozr533BaxPuN0hMdzKu+4LUbiC+mwjWBZPZT7HgWrLjdDhNZxsOQaBvhEgM/QR60t6uUZAilPgIMlV7kOhTghzt8VtFotFi5ciOTkZCQnJ+OTTz6BwdB8r0l5eTn69++PK1euWClKQkhjWHUFVPseBatXQjJsI3jSQLO0u/NKKcI8JIjxbdvCPcQ2/G86wjurAzfiySIhHbIebNVNKA88CVavNku7lnSjuhzZygoM9I3gOhTSBDFfgD7eHXDoVqkQIdbEeQL+6aef4vDhw1i7di0+++wz/PHHH/j666+b3L+srAwzZsxAaal53tgJIe3D6lVQHpgMg+IqJIPXge8Za5Z2lVo9Dl4vx8jOPjT9oJ0yTkd4p3XgdfH9+0HcbwUMRUegPvZ/Nj89obFXdRAl4DZtoG8EMhVFKFY7xsJPxH5wmoCr1Wps2LAB8+bNQ/fu3dG/f3+88sorWLduXaNvrocPH8aDDz4IrVbLQbSEECPTXN9FRyDutxKCwEFma/vwzQoodQaM6kz13/ZsZKQPLpbW4GpZjdnaFIY/DFH3N6G7/is0Zz8wW7uWcKDkGgLEbohyozIqW2a8Q3G45Dq3gRCnw2kCnpGRAaVSiaSkJNO2pKQkFBcXIycnp8H++/btw6RJk/DFF19YM0xCyG00ae/UzvXd810Iwx82a9s7L5fCRchD/w6eZm2XWNeYqNovUNsvlZi1XWHXlyDoPAna80uhvfKjWds2FwPL4lDpNQzy7UR3cWxcN48gyARiqgMnVsdpAl5YWAg3Nze4urqatvn5+Zkeu92bb76JZ555Bjwe55UzhDgtTeZqaDO/hDDmGQi7vGDWtg0si+2XSzA8whtiAf2d27MOHlJ09XfF9svmLRdkGAbiPp+AHzgU6uMvQ5e/16ztm0OGohBlmhqq/7YDfIaH/j7hOFByzebLmohj4fQTTqlUQiwW19smEokAABqNhouQCCHN0N34E5rUt8APuxeiXu+bvXcvNU+OwioN7o6mZbsdwd1RvjiRU4niavO+nzM8ISSDvwPPMxaqA1OgLz1l1vbv1MGSawCo/tteDPbrhGxlBa5Vm2/MAiEtubPJeu+QRCJpkGgbf5ZIJBY7r4/PnU+T1l5+fu6cndvR0bW1DON1VeYcRMHRZyEO7ofA+38ETyA1+7n2Hc+GkM/gseSO8JQ6/gI8jv6afbxPR3xy+AaOFlZjWrK5a/rdoRu/Ffk/D4Z6/2MInrAPQq8o06NcXtvDadcR4+GHHh1COYvBkhztdTte3B3zzm/DSWUOkiPCOY3F0a6tLbG1a8tpAh4YGAiFQgGlUgmptPbDvLi4GAAQEGC5hQtKS6tgMFj/VpOfnzuKixVWP68zoGtrGcbraqjMRM3Oh8C4doCg//coLdcBMO/1ZlkWv53Jw8AOntBWqVBc5dir0znDazZYyCBMJsYvp3IwrpOXBc7gBtHQjajZORa5v42FdNQ28KQBnF7bGr0WBwquYErHJIf8/Tri61YGMcJdvPDXtQuY4Nedszgc8draCq6uLY/HNNnpy2kJSmxsLKRSKVJTU03bTp48CX9/f4SEhHAYGSHEyFCTD+W/j4LhSSAd9gsYsbdFzpNZUo1r5UqMpfITh8EwDEZH+WL/tTJUqXUWOQdPFgXp0A1glcVQ7Z0IViu3yHla62jpdagNegz3j2p5Z2IzhvlF4nDpdaj1lnmdEnI7ThNwiUSC8ePHY+HChUhLS8PRo0exdOlSTJkyBQBQUVEBhYK+DRLCFYO6Eqp9E8FqyiEZ9jN4bh0sdq5tF0vAABhDy887lPti/KDWs9h5xXJrN/B9kyAZ9B0MFelQHZgCVsfdQj3/Fl2GlCdAX++OnMVA2m6Yf2co9VqklGdzHQpxEpxPMzB37lwkJydj+vTpePnll/Hggw9i2rRpAIDZs2fj/fff5zhCQpwTq1Oi8K+HYKjIhGTQf8H37mbR8/2VVYzeITL4u4lb3pnYjT6hHghwE+HvrGKLnkcQchfEfZdBX3AAxTufBss2v6Kypewtvoz+vhGQ8Dmt8CRtNMAnAkKGh3+LLnMdCnESnL9DiMViLFq0CIsWLWrw2Pr16xs9JjQ0FFlZWZYOjRCnxRp0UB2eDn3uIYgHrIEgeLhFz3expBoZxdV4b0SkRc9DrI/HMLgn2g8/nc1HtUYHV5HlPnaEnSaCVRah+vQCCBlviBLNP1NPc65Xl+FqdRmeDu9jtXMS83AViNDHuwP2Fl/GfIzkOhziBDjvASeE2BaWNUB9/EXoc7bDZ9gysy+005i/MovBoLZcgTiecbF+UOkM2GnmOcEbI4ybDVnP/4M2aw206dZdtO3f4tre0xFU/22XhvtHIkNRhBxlJdehECdACTghxIRlWWjS5kN39WeIur0OWfdnrXLOPzOL0C/MA4HuVH7iiPqEeMDf1fJlKEDtwE/vwR9B0PFhaE4vtOpqmbsKLyHCxRsRrpYZqEwsa1RADABgV+FFjiMhzoAScEKIifbC59Bmrqpd5TL+VaucM7OkGhdLazAu1t8q5yPWx+cxuDfGF3uuWm42lLoYhgdxvxXgBw2D+vgc6G78afFzVunUOFx6DaMDYyx+LmIZka4+iHDxxs5CKnEllkcJOCEEAKC99D00Z96DIHw8RImLrVY7+2dGMXgMcA+Vnzi0B7sEQKUz4J9LJVY5H8MXQTL4e/B8+0B1eAZ0uTster69RVegMegxOoAScHvFMAxGBUbjcOl1VHE4kw5xDpSAE0Kgvb4Z6hOvgB88CuJ+K8Aw1nlrYFkWv2cUYkAHT/i7iqxyTsKN3iEyhHlI8NuFQqudkxG4Qjp0A3heXaE6MBW6goMWO9eOwix4CaXo7RVmsXMQyxvlHwONQY99xVe4DoU4OErACXFyupt/Q33kWfD8+0My6BswPOstAX8yV47rFSo80jXQauck3GAYBg/F+ePAjXIUVVmvd5ERySAd9gt47uFQ7X8C+pKTZj+HzmDAnqJLuCsgGgIefazasz7eYfAQSrCT6sCJhdE7BSFOTJezA6rDz4Dnkwjp0J/ACFysev5fLhRCKuDhnmhfq56XcOPhuAAYWOCPTMsPxqyLkfhAMmIzGIk/lHsnQF9+waztnyi/iXKtEqMDos3aLrE+IY+PEX5R2F10CToDN3PJE+dACTghTkqXvxeqg1PB8+wK6bCNYIRuVj2/WmfAn5lFuDvaF25izpckIFYQ4+uKeH83/JZuvTIUI540ENIRm8EIXKH692EY5JfM1vaOgiyIeHwM9etstjYJd+4OjEWZpgbHym5wHQpxYJSAE+KEdIWHoNo/CTyPGEiH/wpGJLN6DHuulqJCpcMjXQOsfm7CnUe6BuB0vgIXS6qtfm6eWwdIR2wGACh33w+D/M5XPTSwLLbkp2OIb2e4CWgaTUcw3D8SUp4AW/LTuQ6FODBKwAlxMvqi41Dtexw8t/Da5FvsxUkcv1wohJ+rEIPDuTk/4cZDXQMg4DH4+VwBJ+fnyaIgGfEHYNBDuXvcHfeEn6rIRa5KjnHBceYJkHDOVSDCcP8obC3IgJ6lMhRiGZSAE+JE9CUpUO6dAEYaeKsmlpva66JqDXZeLsUjXQNp0JqT8XcVYWRnH2y6UACtnpvkhu8ZC8ldfwKs4VZPePuT8L/yL0DE49P0gw7mvuA4FKurcaIsm+tQiIOiTz5CnIS+6CiUex4GI/WH9K4/wJNyV/rxy/kC6AwsnugWxFkMhDuPdQtEcbUWe66WcRYD3zO2tiecNUC5q31JOMuy2JJXW34iE0rMHyThzF3+UZBQGQqxIErACXECuoL9UP47AYxLMKR3/QWeSzBnsbAsix/P5qNvqAcifaw76wqxDSM6ecPfVYQN5/I5jYPvGQvpXX8AuJWEV7Zt6rk0Kj9xWG4CMYb5RWJrfgYMLMt1OMQBUQJOiIPT5e6Gau9j4LmHQzryb/BcuO11PpZTiStlSjzRnXq/nZWAx8OE+ADsulyKAgW3Kw7yPOok4bsfgKGy9cuQ/5VH5SeO7P7grihQK3Ck9DrXoRAHRAk4IQ5Ml/0PVAcmg+cZC+ldf4In4X659x/P5MNdxMe9tPS8U5vUPQh6FvjxLLe94EDdJJyFctc46MvOtniMzmDA73nnMcIvispPHNSowBi4CUT4Lbfl1wMhbUUJOCEOSnfjT6gOPgWeVwKkI34HI/bmOiSU1GjwV2YRxncNgIuQz3U4hEMRXi4YFuGFdafzOBuMWRfPIxbSkX8DfDGUu8dBX3S02f0PlFxFkboKj4R2s1KExNpc+ELcExiHLfkZUOq1XIdDHAwl4IQ4IO3VDVAdng6ebxKkI34FI/LgOiQAtb3faj2Lp3uFcB0KsQFTe4agoKp2RhxbwJNFQjpqGxhpAJT/jocud1eT+/6acxaeQglG+EdZMUJibeNDE6DQqWlpemJ2lIAT4kBYloXmwjKoj74AfsAgSIdvAiO0/iI7jdEZDPj+VB4GdfREtK8r1+EQGzCysw9C3MX476k8rkMx4bmGQDpyC3iyaKj2T4L2+uYG+yi0amwryMD9wfEQ82kVV0fW3yccgWJ3KkMhZkcJOCEOgmUN0KS+Cc3phRB0fBiSoT+DEdhOorvzcilyFWrq/SYmfB6DyT2CceBGObI4WBmzKTyJX+2YCb8+UB+eAe3F7+o9vqUgHUqDjspPnACf4eHBkHj8W3QZxeoqrsMhDoQScEIcAKtXQ314JrRZayCMfRbiAavB8EVch1XPV6m5CJWJMTqSm8V/iG2a3CMIEgEPq1Nsa8ETRiSDdNgm8INHQp3yKjTnl4K9NR3dxuzTiHDxRqJnKMdREmt4LKwndKwBG7PPcB0KcSCUgBNi51itHKp9E6G7sRminu9C1Os9MIxt/WmfzpfjyM0KTOsVAj6P4TocYkN8XUSYEB+A3y4Uoqhaw3U49TACKSRD1kEQPh6aM4uhPj4HmZV5OFZ2E0906AWGodeyM4h290Oydwf8lJ1m+hJGyJ2yrU9pQkibGJSFUO66H/rCwxD3WwlR3GybTApWnsiGu4iPyT24WwCI2K6ZSWFQ61n8Ny2X61AaYHhCiPuvgrDry9Bd+QHfH1kMIcPDo2E9uA6NWNGkDr1wtboMR0pvcB0KcRCUgBNip/Tl6VBuHwWD/DIkQ36CsNNErkNq1PVyJbZkFWNKz2C4i2nAGmko0scFoyJ98N9TeajR6rkOpwGG4UHc400Y+nyO33TuGM3mwkdbxnVYxIruDYqDh1CCH26mch0KcRCUgBNih3S5O6HcOQZgdZCO/BuCkLu4DqlJq1OyIeAxeCaR6mVJ015IDkOpUov1p21nRpTb7ZB2g5yR4FHVGSh3jIK+NI3rkIiVSPlCjA/phq0FGShR286AYWK/KAEnxI6wLAtNxiqo9j9RO2fxmF3g+/TgOqwmFSjU+OlsPsZ3DUCgu5jrcIgNSw71RP8wD6w8kQ2VzvZ6wVmWxXfXU9DZ1QfD7/oW4Eug3DUOuuwtXIdGrGRKxyRoDHqsp15wYgaUgBNiJ1i9GurjL0GT9hb4oXdDOvJv8Fxsu6b6i+M3oWeBF/t15DoUYgdeHhCOwioNNpwt4DqUBk6W5yCtIhfTI5LB9+wC6egd4Hl2gerAFGjOfgSW5X41T2JZ0e5+GOYXie+up0BjsL0vicS+UAJOiB0wVOdCuete6K6sh7DrS5AM+q9NzfHdmHyFGj+czsOE+ACEe0q5DofYgYEdPNE7RIblx25CYwPL09e1+upReAolmBDaHQDAk/pDetdfEEQ8Cs25D6E6MBmsVs5xlMTSZkQko0hdhT/zznMdCrFzlIATYuP0hYeh3DYchsosSAZ/D3GPt2xumsHGfHGstvd7DvV+k1ZiGAavDghHrkKNdTZUC36juhzbCjLxZMckuAr+N78+I5DWzj6UuBj63F2o2T4ShkpastyRDfXrjCg3X6y9eoymJCR3xPY/xQlxUsZ6b+WeBwGxJ1zG7IIg7F6uw2qVGxVK/HAmD4/GB6Ij9X6TNhgS7oX+HTzx6ZEbqFLruA4HAPDVtWPgMwyeDu/T4DGGYSCKnQnpiN8BdQVqto+E9vrvHERJrIFhGMyI6Itz8gIcLLnGdTjEjlECTogNYtXlUO2fVFvvHTIaLmN2gecRw3VYrbb4wDXwGQZzB4ZzHQqxMwzD4K0hnVBao8XqlByuw0Gxugo/3kzDgyEJCJS4N7kfP2AApHf/C55nF6gPT4fqxKtg9SorRkqs5ZHQ7ggUu+OzSwe4DoXYMUrACbEx+qLjqPlnCPT5eyBKXAzJ4HVghDKuw2q1U/ly/JFRhGd7hyGIZj4h7ZAYLMO90b74MiWb89UxV145ArVBjzmRg1rcl+caAunIvyHsMhu6S99BuWMMDIqrVoiSWJOEL8DznfvjaNkNHKOFeUg7UQJOiI1gDXpozn8K5e77AJ4Q0lHbIIqdaZMrWzaFZVks2HsFPi5CvJAcxnU4xI7NG9IJGp0B7+/nLoEtVlfj++speCgkAZ3cfFp1DMMTQtzrXUiG/ARDdQ5q/hkG7ZWfqF7YwTzRMRG+IlfqBSftRgk4ITbAoLgG5a57oTnzPgQdxsHl7r3g+/TkOqw225xRhKPZlXh9UATcaNVLcgc6e7tgRlIofj5XgNQ8bmYXWWXs/Y5quff7doLQ0XAZuw887+5QH5sN1cGpYFWlFoiScMGFL8Rznfthf8lVHC+7yXU4xA5RAk4Ih1iWhfbyOtT8MwSGykyI+6+GeMBXYET2U3JiJFfr8O6/V9Aj0B1PdAviOhziAF7u3xEBbiLM230JBiv3IOcqK/Ht9RN4KCQBkW6+7WqD5xoK6YjfIer5LvS5O1CzdRB0eXvMHCnhylPhfRAodseijF10h4O0GSXghHDEUJ0L1b7HoT7+Evi+iXC55xCEEY/YVclJXR8dvIbiag0+HBUFPs8+nwOxLW5iAeYP7YTT+Qp8f8q60xIuydoLFixejx1+R+0wPD5EcbMhHb0LjNgLqr0ToDr2f2DVFeYJlHDGhS/E3JihOFmeg38KMrkOh9gZSsAJsTKWNUB78RvUbOkPfeGh2oGWw38DzzWE69Da7WRuJb5Jy8WTPYLRI8j+eu+J7Xo4LgBDwr2waP9V5MitM6vI2cp8/JpzBjMi+iJU6mGWNvneCZDevQfCuBehu/ozarb0p2XsHcCjoT0Q7eaH9zN3Q0urY5I2oAScECsyVGZBueteqFNeA983CS73Hro10NJ+/xSVWj1e/CcTQW5ivD20E9fhEAfDMAw+GRMNlmXx2o6LFr/Vz7Is3rmwA14iF8yOHGjWthm+BOKe8yEdswuM1B+qA1OgOvg0DDX5Zj0PsR4Bj4e3utyFq9Vl+Oraca7DIXbEfj/1CbEjrLYK6lMLbtV6Z0HcbwUkw38Fz83+V4n86NB1XC5T4rO7Y+BOAy+JBXTwkGLe4E7Yc7UMP561bLK6KecMjpbdwBsxwyETSixyDr53d0jH7IKo+5vQ5WxHzd/J0GR8Cdagtcj5iGWN9I/CSP9ofHJxH3KVlVyHQ+wEJeCEWBDLstBe/x01f/eFNv0LCMLHw+XeoxB2esxua73r2n+9DKtOZOPJHkEYEuHNdTjEgU1LDMGgjp54a89lXCqttsg5SjU1WJC+E729wvBEh14WOYcRwxNCFP8yXO49DL5/f2jS3obyn6HQFx626HmJ+TEMg/fj7wbLsnj7wnauwyF2ghJwQixEX3oaqj0PQH14OhipP6SjtkPSbwV4Un+uQzOLoio1nt+SgWgfF7w7LJLrcIiD4zEMVtzTBVIBD8/+lQG1zmD2cyxM3wW5To2PEu4Fz0pfkHnuEZAM3QDJkB/A6qqh3D0OygNTaQEfO9PBxRMvRQ/GPwWZ2JqfwXU4xA5QAk6ImRmqbkB1aAaU20dAX5EBce9PIB29C3y/3lyHZjY6gwGztmSgSq3H2vu7wlXE5zok4gQC3cX4fGwszhdVYd7uS2Zte1tBJjbmnMbznfuji8y6X5IZhoEg9G643HsEom6vQ5//L2q29If65Dyw6jKrxkLa77lO/dHNIwhzz21BkaqK63CIjaMEnBAzMSiLoE59EzV/J0OX8w+EXV+G6/0nIYx+CgzPsRLUhXuv4uCNCiweGYVYP1euwyFOZHSkL/6vbwf8cCYf606bZ2rCQpUCr5z5C908gvBK9FCztNkejMAFooS5cBmXAkGnx6G9+BWq/0yE5twnYLXcLEZEWk/I42N5jwdRrVPjlbN/09zgpFmUgBNyhwyqYqjT5qPmz17QZq2FIGICXMadgLjHm2CEjjcl309n87HmZA6mJ4bgcVpwh3Dg9UERGNHJG/N2XcKRmxV31JaeNeDFM39CqddiZc+HILKBL8s8aQAkyZ9COvZgbX342Q9Q/UcvaC4sA6ulnlVbFuPuhzdj78Kuoov45voJrsMhNowScELayVCTD3XaO6j5oxe0masg6HAfXO49CknfL8BzCeY6PIvYe7UMr+24iCHhXlgwvDPX4RAnxecx+PK+LojwkmLK5nNIL25/UvpR1l7sK76CRV3HIKqdK15aCt8zFtKhP0I6Zhf4vonQnF6Imj8ToTn/GVgNzbZhq6ZHJGNUQDTeTd9Jy9STJlECTkgb6SsyoTr6Amr+7Alt5pcQhN0Dl3uPQNJ/FXgyxx2MmJJTiaf+OI9oXxd8dX8cBDx6+yDc8ZQIsWFCN7gI+Xhs01ncrFS2uY0t+elYdvkQJnXohUkdEy0QpXnwfXpBOmwjpKO3g+fdHZoz76H69wSo0+bDUJPLdXjkNjyGwYoeD6KDiyeeSf0F+UoqHyIN0ScoIa3Asgbo8v6Fcu9EKLcOgO7GHxBGToHLfSmQDFgNniyK6xAt6lS+HE/8eg6BbmL8PKE7PCRCrkMiBKEyCTZM6Aal1oCHfjrdpiT8ZHk2Zp/6HYmeoXi/690WjNJ8+L69IR2+CdKx+yEIvRvazNWo+TMRqsMzoS9JoZpjGyITSvBN4qOo1mnw+IkfUam1ziquxH5QAk5IM1h1BTQZX6Lm72So9j4CQ9lpiLq9DtcHzkDc+0Pw3MO5DtHijmVXYPzPZ+AhEeCXR7vD31XEdUiEmMT5ueHXid2h0Ojx4E+nca28psVjMhVFmHTiJwRKZPhv74kQ8+1rASm+VzwkA9bAZdxJCKOegi5nO5Q7xkC5fQS0V34Eq2v73QBifl1k/vg2aQIuV5VgasrPUOl1XIdEbAjDOuFX5tLSKhgM1n/afn7uKC5WWP28zsCc15ZlDdAXHIDu6gbosrcAehV4fskQRk+DIOxeMHyxWc5jD44UVuPxH1MR4i7GrxN7IMjdeZ67pdH7gXmdK1RgwsYzYBgGW6cnI0LaeFJ9qaoEjxxdBwNY/D3gaXR08bJypObHahXQXfsF2otfw1CZBQjdIejwAISdJoLnl2zWRb/oddt2m3PPYdapzRjm1xnfJj0KKb/xO4h0bS2Hq2vL4zHw8XFr9DFKwK2I/rgsxxzXVl+RCd2NzdBd/RlsTS4g8oCg44MQRj0Fvle8mSK1DyzLYnVKDhbsu4Iege5Y93AC9XybGb0fmN/l0ho89stZFNdosHxsLO6LrT+f9wV5ASYcWw8GDH7pOxldZAEcRWoZLMvCUHQE2qs/QXfzb0BXDca9E4QRj0IQ8Sh4bmF3fA563bbPTzdP4ZWzf2GATwS+7z0RroKG76d0bS2HEnAbQQm442nPtWVZFoaKDOhu/gndzb/Ayi8CDA/8oOEQdHoMgtAxYPgSC0VsuxRqHV7enoW/MosxvlsQPr4rEi5C7qdmczT0fmAZRdUaPPN3Bo7dKMdzvUPx1tBOEPB42Fd8BTNSf4GbQIxf+j6Jzm4+XIdqUay2Crrsv6G7+jP0hYcAADy/ZAjC7oUg7B7w3Dq2q1163bbfLzln8OLpP9FVFoB1vR9DkLT+NLV0bS2HEnAbQQm442nttWUNehjKTkGXswO6m3+CVVypTbr9+0PQYRz4YfeCJ3WsXrG2SMmtxOytmbhZocTrgyOw4J6uKC2leYctgd4PLEfm5YJZG0/ju1N56BnkhsG9lFhxfS9i3P2wrvdjCHPx5DpEqzJUZUN3bSN02X/DUH4eAMDziocg7F7wQ+8Bz7NLq8tU6HV7Z3YVXsSzab/BXSDGN0kTkOgVanqMrq3lUAJuIygBdzzNXVtDTT70+Xuhz/8Xuvx9gKa8NukOGAhBh/vBDx0LntS6S0/bmmqNDh8duo41KTkIkYmx8t4u6BvmSa9ZC6JraznGa/vj+Rv4z4Ut0LmWIFrUAX8OeQxeYue7q1WXQXEdupyt0GVvhaH4BAAWjGsH8IOGgh84BILAwWDE3k0eT6/bO5chL8STKT8jXyXHf2KG4fnOA8BjGLq2FmSLCbh9Df0mpBUMyiIYio9BX3wc+oKDMFRcAAAwkgAIQsfUlpgEDW32Q8ZZGFgWv10oxKL9V1FYpcHUnsF4e0gnuInprYHYL5Zl8UfeeXyYvwOMm/L/27v36KjK81/g37135pbrJJIbAQR+QOROIBCVX0SQ41oqCzwteKotx3IRVmtpqTdAWECpKOcg1CLUBR6WCqjFKl1VtItiuxCKFAmCXE1I5E4uk8skk8nc93v+mMmQYWZyg5lJ4PtZa7Nn3v3MzDsvb/Y8s9939kauazi+P52KqZdO4HeT/gsT+6Xd0h8mdidyUl9oBz8L7eBnodoq4bnyd7ivfQn3xb/CXboNDkiQ00ZAyXoQSlYhlB5jbssr+sbS4ORMfPnAfLxw4jOs/v6f+EdlCf7v8ClIT0+KddUoingEPIr47fbWE6oHwnIO8Y7TMJftg8f0HwjLD96Nih5Kj3wo2Q9B6fkQZOOQO/ZD90aqEPi82ITXD17E99VW5GUn4ZWHBiA/JyUgjn02cti2kXGyvhz/p2wfvrxWghEp2Vg/YiqGpWThH6XVWPbPUlw023Ff7xS8ML4vxvcxcp/gI1Q31Jpj8FTsg7v8K6jVRwDhBiBBNg6B3GMslPSxSB/0IOpcmWy3W0AIgY+vnsCK03vQ4HbgV0P+G8/kFOAubXysq3bb6YpHwJmARxE/cG+O8Dih1hdDrTsBtfY7eGpPeOczenznvNWlQUkvgJJ+L5SMeyGnjoCk8MwdLZntLnx8uhL/7+hVnK+zYWBaPJ4ffzemDc6AHOIDlX02cti2t9aJ+nJsLD2IT8tPI1VrwPMDJ2BW37FQpOuXu3B6VLz/XTnWf30RVVYnRmYlYs7oXpiS2wMJWo76tCRcFniqi6CajsBT/Q081UWAy9dftalQ0oZDTh0OOXWYd508AJLMC3R1Ro2zCa+e/RIfXjmOBEWLuf3GYXbfAqTrEmJdtdsGE/AQXC4XXnvtNXz++ecAgBkzZuC5556DHOIy1xaLBStXrsS+ffsQHx+P2bNnY9asWR1+TSbgXZtwNUK1lHmT7foS77qhBMJyHhAeb1BconeYNG0E5NQR6DFwPMzuHB6VCcHm8mBvWQ0+OVOJf5bVwqUK5PdMxrz8XpiSmw5FDt9m7LORw7a9eU0eF/5efhY7Ln2LQ7UXkRinxTP9CrBs7MNwNYS/6Ind7cFHpyqx+chllNbaYNDImDIoHTOGZeK/+6S2+jdxpxKqB2pDCeLtJ1B/4Wuodaegms8CqsMbIOsgp+RCThnkTcaTBkBOGQg5qT+kOB7RbQ+TxorFhz7HFxVnoZUVTOs5DE/1zkNBWh9+tt2krpiAx/wr//r163Hw4EFs2bIFVqsVL730EpKTkzFv3ryg2KVLl6Kqqgrvv/8+Lly4gCVLliAjIwOPPfZYDGpOnSU8dgjrZaiNlyEaL0K1XoRovAzVehFq4yXAUXM9WIqDlNQPcso9kHtPhWwcDCVtJKSkfpBaHNnSpiVBYjIDwDusWVLThH9frMOBi2YcuFiHRqcHmYlazBmTgx8PycSILM41pO7J5GjEP6tK8WXVOewzlaLR7USfeCNWDP4f+Gmf0UjW6GHUGWBC+P2BPk7B/x7VEzNHZuPI1QZ8dKoCf/u+Cn85XYk0Qxwe6JuGB/umYkLfVPRMvrN/tNlMkhUoxsFITh8HR9b/AuCbttJQ6k3G605BNZ+Gx/QN3Bc+AXD9IJcU3wtSYh/ICb0gJfSGnNAbUkIv//pOPN1rKEOMWdia/wTKGmuw+fwh7Lp6Eh9d+Q45+mRMzhyEhzMHYfxd/aDvZldupdBiegTc4XCgoKAAf/zjHzFhwgQAwF//+lesW7cOBw4cCPjGd/XqVTz00EPYvXs3BgwYAADYuHEj9u/fj48++qhDr8sj4LeWEAJwWyAc9RDOOu9iq4KwVULYfWtbJVRbJYS9EnDWBz6BrL2+U068G3JCb8jJ/wU5ZRCkxP7tmkZyu7ZtW4QQKLc4cLKqEacqG3GqqhFHrzWgstEJAOidoseEvqmYdk8GxvcxdvjI3p3artHAtm2bKgTKrDX4znwNx81XcaTuCr6rvwYAyNIlYXLmQPzPnsNx3113B0yh6kzb2lwe/KO0Bl/+UIN95+tQZfX+DfU16jEiKwkjs5IwPDMRQzMScZdBc8cekWxP2wq3DarlB4iGUqgN57xJuvUKhPUyhO0aINSAeEmfAcmQCUmfDsmQ4V3rM3zlvtu6VEha422drN/Ytla3E59XnMXfy7/Hvuoy2DwuxCsaFKT1wShjDvKMOcgz9kS6LvQRVrqOR8BvcPbsWdhsNuTn5/vL8vPzYTKZcOXKFfTuff2qXcePH4fRaPQn382xb731FlwuFzQazj3rCCEE4LED7iYIdxOE2wq4rb61t8x7vwlwN3rXrkYIpxnC6Uu0HXWAsx7Cafb9WCcERe/bsWZ6hyazCr0704TekBP7QErsA8mQHXA0m7xUIVBnc8FkdaG6yQmT1QlTkwvlFgcumG24UGfDxXo7rE7vtBwJQP80A+7vbcT4PkYU9k1FX6Mhtm+CqBWqEKh1NsHkaESVoxHX7A24aK3D+aZanLfW4gdrDRrd3kTYoGgwMiUbi3InYnLGQAxLzrqlSbBBo2Da4AxMG5wBIQTOVlvx1fk6FF2tx7FyCz793uSPTdYp6JdqQL/UePRO0SMzQYuMBC0yErVIj/euk7TKHZukS3EGKKlDgdShQduE6oJoKveOglovQ1iveJNz38Eatb4Ywm4CVGfoJ5d1kLRGQJsCSZviTcp9t6E1QopLBOLivdNeblwr3nVzGRRDl/4/SojT4oleI/FEr5Gwe9w4WHMeeytLcKTuMv547gBU3yhDui4B/RPuQr+ENPRPSEMfQyoy9InI1CUhQ5eIxDhtl36fd6qYJuCVlZVITExEQsL1Hxqkp6f7t7VMwCsrK5GREXiu5vT0dLjdblRXVyM7Ozs6le4EIVR8cfR9mF11cDgckCC8RwCEgAQVElTffRWAgCQ88A7fqZCEd3093tPi8b7HwgNZdQNwA8INWXVDghuSf+2BJFyQhG8ND2ThhkD7/yAFZKiyDm4lAR45Hh45HR6lLzyJ8fDI8XAr8fDICfD41m4lGc64ZKiSHmjxhy8AwOlb6gDgKoS4GvBK1/+9sR3D1U0gPl6HpibHDc8SFBhiW3BkqNcJWZ8wtfGoAh4h4FFx/bbwlrtVb9LhEQIujwq7W4XD3WLt8a4dHhVNTg9CDdRoFAk94rVIN2pxX44GGYk63J2iR69kHXRxzVesNONkkxknm1rWrGOjPgJAcqMeDQ32DjymgyNLHQ7v+MhVRx/RmUHBDr8GBJLqDbBYbBF5fqDj76Mz70EVAk7VA5fq8a6Fx3/fpXrgUN1wqR7YVTcsbgcaXA40uh1ocNvR6HKg3m2H54Z6KpKEPoZU9E1Iw9jU3hieko2RKT0xKKlHwA8qI0mSJAxJT8SQ9EQA3s+hWpsLJyssKK5pwvm6JvxQa8Ox8gZ89n0VPCEaT6tISNLGIUGrIEmnIEkbh0StggStAl2cDK3iXXSKBG2cDJ3SXCZBkSXIkgRZQsBa8d2WfGulZYwshd2jh8u9WvsECJewGaubUF8f3G879toJkDAYwGAgAd6lJSGgeBqgcVVD46yGxlUNxW1GnMcCxV2POHcDFHcDFFcD4mzXoLi/95Z5Gryfjx3gkfUQksa7yBqokgZC1kJIWghJA1XW+LersjYgVkAGJAVCkiGgAJIMISkAZAhJBuDb1rJMUiDgK/M9zrtdgiFeB5vN5fts9i3+9pOQDglPQcJTOg1sPbJR5nbje5cTFz0uXLVU4h/mq6hVPUHvUQMJCbKMBElGvCQjQVaQIMkwSDI0kgyNJEEDGXGS5L3tL/P2QwmAjOY1IEGCJDXXUPKVwRfrvd8aqZV7oUvafpa2FAwYgVGZozr0mEiLaQJus9mg0+kCyrRa73QDp9PZ6di2hBsOiJTTl0swt7wMos1voM3d9iYu+y21eHikrx4uAPgPfLsB1PsWajcJgMa3hNl8IzeACt8CF7xfZOoiUjuiTtEpcdDKim+Jg16JQ4pWjxStHj0S0pCi1XvnamsNyDIkISs+CVmGZGQbktAnMRUa+eZ3Xrf6nMrpAHL7BF87QFUFam1OVDQ4UGFxoLLRgYoGB0xWJxrsLjQ63GhwuNFgd6PO4cYli8P7Jbvl4lHhicG0yO7BAO+XoN5tBUKCCoPkgEFywiDZES85YJDtvjIH4iUH9JID8ZIdBtnhL4+DBxrJDa3kggZuaCU3NJIbGrh95bYWt6+XK1AhS6p3DRWKpEL2Hq7y3fZuUyS1zbp3xlAAU28oa4QG5XISTFI8quQEmKQE1MoGWKCFRdLBInnXlZIWTZIGTihwSop3DQXqbToanX74NCrmFMa6GgFimoDr9fqg5Ln5vl6v73RsW6I9BzxDn42dI55EPZpgaXQCkuxdfN+eIUn+b8+QQh/FCJW7h4wL860w3HOGP2bSMq6t76vXny/k67bj8S3LWhsqC7fFmBKPhgZbu2JvrFJ72rEjw3dxsoQ4GYiTFcTJgCJLiJO8R7U6895a17FHdXQU8q60BNTWNrUd2PI1OvYSHR4a7Uw7taef3/RrdPB9eNvW2v7n70ytOviQjr6GIknQyt5kWyMr0EoKFKn1ft4qB2B2dKy/hRKL+Z6ZcRIyU/VAaufmKHtUAYdHhdOjQhXekTJVFf7bHt9aCMAjvKMP/jiBsAl8uE+61kZIwj8GSE2NR11dUzvjO1an7sDjW9o/LgjfsKpv1Fp4R60l4fHd98A72q0iJVmP+oYmX3zz4iUFlYkWcbh+5F8IyBDIBJDpi5dEi8e0iGsuk1qUe1QPnEKFS6hwCxXecXlvv1N9Y5DqDfcFvP/XzbE3jmq10jDtKAmxLcTzt/WK9w4cxjngLWVlZcFiscBms8Fg8M5VNZm88+wyMzODYpu3NauqqoJGo0Fqamp0KnwTHrg7lz+6iiC2bWSkG5NgcrFdIyE9OQnJDl3bgXRHUGQJ8bKCeE2khy5vTnp6EkwGnoUjEvg5FjldsW1jOtZwzz33wGAw4OjRo/6yoqIiZGRkICcnJyB21KhRqKmpwfnz5/1lR48exbBhw/xTUYiIiIiIurqYJuB6vR7Tp0/HqlWr8O233+LQoUNYt24dnn76aQCA2WyGxeL9xpKTk4OJEydi0aJFOHPmDPbs2YOtW7f6Y4mIiIiIuoOYjyO9+OKLcDgcmDt3LnQ6HaZPn445c+YAABYsWICcnBysWbMGALBmzRosX74cTz75JFJSUrBw4UI88sgjsaw+EREREVGHxPxS9LHAC/Hcfti2kcF2jRy2beSwbSOHbRs5bNvI6YoX4rk9zzdDRERERNRFMQEnIiIiIooiJuBERERERFHEBJyIiIiIKIqYgBMRERERRRETcCIiIiKiKGICTkREREQURTG/EE8syLJ0R7727Y5tGxls18hh20YO2zZy2LaRw7aNnFi0bWuveUdeiIeIiIiIKFY4BYWIiIiIKIqYgBMRERERRRETcCIiIiKiKGICTkREREQURUzAiYiIiIiiiAk4EREREVEUMQEnIiIiIooiJuBERERERFHEBJyIiIiIKIqYgEdAbm5uyGXJkiUh44uLi4Ni8/Lyolzr7qOgoCCovU6ePBk2fuPGjRg/fjxGjx6NZcuWwWazRbG23YcQAlu2bMHkyZORl5eHn/zkJzh27FjYePbb1rlcLqxatQoFBQUoKCjA66+/DlVVQ8ZaLBY8//zzGDNmDAoLC/HOO+9EubbdS0VFBX7961+joKAA48ePx8svv4yGhoaQsWvWrAnqp6tWrYpyjbuPf/3rX0HtNWXKlJCxFRUVmDdvHvLy8jB58mR8+umnUa5t97Fr166wucGRI0eC4tlv28fhcOCxxx7D/v37/WUd3Z/Gqh/HReVV7jD//ve/A+4fOHAAy5cvx09/+tOQ8aWlpejbty927NjhL5NlfjcKxWQywWw2Y/fu3TAajf7y1NTUkPE7duzAhx9+iLVr1yIhIQGLFy/Ga6+9xh1ZCNu3b8fWrVuxevVqDBgwAB999BHmzJmDL774AllZWUHx7LetW79+PQ4ePIgtW7bAarXipZdeQnJyMubNmxcUu3TpUlRVVeH999/HhQsXsGTJEmRkZOCxxx6LQc27NlVV8eyzz8JoNOK9996D0+nEypUrsWTJEmzatCko/ty5c/jlL3+Jp556yl9mMBiiWeVupbS0FPfddx/Wrl3rL4uLC50qPPvss8jOzsZf/vIXFBUV4eWXX0avXr0wevToaFW323j00UdRWFgYULZkyRJYLJaQBy7Yb9tms9nw29/+FqWlpQHlHd2fxqwfC4ooq9UqCgsLxVtvvRU25o033hC/+MUvolir7uvrr78WY8aMaXf8pEmTxI4dO/z3Dx8+LIYOHSosFkskqtetTZ06VWzevDmg7OGHHxbbt28PGc9+G57dbhcjR44U+/bt85ft2rVLjB8/XqiqGhB75coVkZubK86dO+cve/PNN8WMGTOiVt/u5MyZM2LQoEGiqqrKX1ZUVCRyc3ND/l1PmDBB7N27N5pV7NZefPFF8corr7QZ980334ihQ4eK+vp6f9nixYvFwoULI1m928bevXvFsGHDxKVLl0JuZ79t3cmTJ8Wjjz4qpk2bJgYNGiS++uorIUTH96ex7Mc8XBVh77zzDjQaDWbPnh02pqysDP369YtirbqvjrSVyWTClStXMG7cOH9ZXl4eVFXFqVOnIlXFbmvZsmWYOnVqUHm4oX322/DOnj0Lm82G/Px8f1l+fr6/T7Z0/PhxGI1GDBgwICD29OnTcLlcUatzd5GdnY23334b6enp/jJJkiCEQGNjY0Cs1WpFeXk5+2kHlJaWtqu9jh07htzcXCQnJ/vL8vPzcfz48QjW7vbgdruxdu1azJo1C7179w7azn7btkOHDmHChAn485//HFDe0f1pLPsxp6BEkN1ux3vvvYcXXngBWq02bFxpaSmcTicef/xx1NTUYOzYsVi8eDEyMjKiWNvuobS0FG63G7NmzUJJSQn69++PF154ASNHjgyKraysBICAdtRoNDAajaioqIhanbuLsWPHBtzft28fLly4gPvvvz9kPPtteJWVlUhMTERCQoK/rDlhrKysDPjQraysDGqz9PR0uN1uVFdXIzs7OzqV7iaMRiMeeOCBgLJ3330X/fr1C5oqVVZW5t9+4MABxMfH48c//jFmzZrF6VIhCCFw/vx5HDlyBNu3b4fdbkdhYSFefPFFJCUlBcSG6rc9evTw73cpvD179qCqqgpz584NuZ39tm3PPPNMyPKO7k9j2Y+ZgHeCw+EIm8ClpKT45ybv3r0bsixj2rRpYZ/L7Xbj0qVLyMjIwO9+9zs4HA6sX78ec+fOxSeffAKNRhOJt9BltdW2ZWVlMJvNWLhwIe666y7s3LkTTz/9ND777LOgIwl2ux0AoNPpAsq1Wu0deWSxvf0W8CbXixYtwpQpUzBq1KigePbb1tlstpD9DgCcTmenYynYli1bsHfvXmzZsiVoW1lZGWRZRk5ODjZv3oxTp07h1VdfhcfjCTkX/0537do1NDU1QZIkrFu3DtXV1VizZg2ee+45vP322wGx4fqtx+OB2+0OO2+cgA8++AA/+tGPAo66tsR+23kd3Z/Gsh/zL6QTTp48GfYHlb/61a+wYMECAMAXX3yBRx55JOg/t6W4uDj85z//gU6n8yctGzduRGFhIYqKinDffffd+jfQhbXVtlu3boXL5fIfWRw6dCiOHz+OXbt24Te/+U1AfHO7O51O6PV6f/mN9+8U7e23p06dwjPPPIOBAwdi9erVIePZb1un1+uDdvbN92/sex2JpUCbNm3Chg0bsHz58qAfuAHA448/jgcffND/I+3c3FyYzWZs376diUwIOTk5OHz4MFJSUiBJEgDvD9ynT5+Oy5cvBxzk0Ov1MJvNAY93Op3QaDRMvltRWVmJoqIiLFq0KGwM+23ndXR/Gst+zL+STsjPz0dxcXGrMU1NTfjmm2/CDpO0lJiYGHC/R48eMBqNqKqquql6dkftaduW03kkSUL//v1DtlXzcLTJZPIfaXC5XDCbzcjMzLyFte4e2tO2R44cwfz58zFy5Ej86U9/ajUBZL8NLysrCxaLBTabzX/mApPJBABBfS8rK8u/rVlVVRU0Gk3Ys/sQ8Oqrr2Lbtm1YuXIlnnzyyZAxkiQFteGAAQNgMpkghPAnmXRdy5EwAP65tDdOncrKygo6/avJZOIUtDbs378f2dnZGDFiRNgY9tvO6+j+NJb9mJOJIuTMmTMQQrR5Gpvi4mLk5eXhhx9+8JdVVFSgrq4O/fv3j3Q1uxUhBCZNmoSdO3f6y1RVRXFxcci2Sk9PR05ODoqKivxlx44dg6IoGDJkSFTq3J2UlJRg/vz5GDduHDZv3tzqKa/Yb1t3zz33wGAw4OjRo/6yoqIiZGRkICcnJyB21KhRqKmpwfnz5/1lR48exbBhw1r97cidbOPGjdixYwfWrFkTNvkGgD/84Q9Boz5nzpxBv379mMSE8NVXX2Hs2LEBP2Y9c+YMZFlG3759A2JHjRqF4uLigNijR4/yWgBtOH78eMCPs0Nhv+28ju5PY9mPmYBHyLlz59CrV6+Q00+sVitqa2sBeL/V9unTB8uWLcPZs2dx4sQJLFy4EPfffz+GDx8e7Wp3aZIk4cEHH8Sbb76JgwcPoqysDCtWrEB9fT1mzJgBILBtAWDmzJl44403sH//fnz33XdYsWIFpk+fHnT0loCXX34ZGRkZWL58Oerr62EymWAymWC1WgGw33aEXq/H9OnTsWrVKnz77bc4dOgQ1q1bh6effhoAYDabYbFYAHiH/SdOnIhFixbhzJkz2LNnD7Zu3eqPpUDFxcXYtGkT5syZg/Hjx/v7qclkgsfjQW1trb/PTpo0CceOHcOmTZtw6dIl/O1vf8Pbb7+N+fPnx/hddE2jR4+GwWDA4sWLUVZWhsOHD2Pp0qWYPn06evToEdC2+fn5/h/Bl5SUYOfOndi9ezdmzpwZ43fRtZ07dw4DBw4MKme/vTXasz/tMv044ic6vEO9+eab4oknngi5bcOGDWLixIn++9euXRMLFiwQ48aNE2PGjBEvvfSSMJvN0apqt2K328WaNWtEYWGhGD58uJg5c6YoLi72b7+xbVVVFevWrRPjxo0T+fn5YunSpcJut8ei6l3a5cuXxaBBg0Iua9euFUKw33aU3W4Xy5YtE3l5eeLee+8Vr7/+uv8c4D/72c/EokWL/LF1dXViwYIFYsSIEaKwsFC8++67sap2l7dhw4awfbW0tFRMnDhRbNiwwR//5ZdfimnTponhw4eLhx56SHzwwQcxrH3XV1JSImbPni1Gjx4tCgoKxO9//3vhcDiEECKobS9fvix+/vOfi+HDh4vJkyeLzz77LFbV7jYmTpwoPvzww5Dl7Led0/I84EK0vT/tKv1YEkKIyKf5REREREQEcAoKEREREVFUMQEnIiIiIooiJuBERERERFHEBJyIiIiIKIqYgBMRERERRRETcCIiIiKiKGICTkREREQURUzAiYiIiIiiiAk4EREREVEUxcW6AkRE1DUdOHAAc+fODbntlVdewYwZM6JcIyKi2wMvRU9ERCHV1tbi0qVL/vuqqmL16tUoLy/Hxx9/jJ49e8awdkRE3RePgBMRUUhpaWlIS0sD4E2+lyxZgvLycmzbto3JNxHRTeAccCIialVz8n3gwAFs27YNAwYMiHWViIi6NSbgREQUFpNvIqJbjwk4ERGFxOSbiCgymIATEVEQJt9ERJHDs6AQEVGQFStW4JNPPsHKlSuDku9hw4YhLo6/4Sci6iwm4EREFEAIgTFjxsBqtQZt0+l0OHbsGBRFiUHNiIhuD0zAiYiIiIiiiHPAiYiIiIiiiAk4EREREVEUMQEnIiIiIooiJuBERERERFHEBJyIiIiIKIqYgBMRERERRRETcCIiIiKiKGICTkREREQURUzAiYiIiIii6P8D58LygL3FodsAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, _ = plot_normal_distributions()" ] }, { "cell_type": "code", "execution_count": 37, "id": "casual-example", "metadata": {}, "outputs": [], "source": [ "#f.savefig(\n", "# '/Users/srom/workspace/romainstrock.com/assets/img/uncertainty/normal.png', \n", "# bbox_inches='tight', \n", "# dpi=120,\n", "#)" ] }, { "cell_type": "markdown", "id": "strong-record", "metadata": {}, "source": [ "## Softplus" ] }, { "cell_type": "code", "execution_count": 5, "id": "developing-insulin", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, ax = plt.subplots(1, 1, figsize=(10, 5))\n", "x_r = np.linspace(-10, 10)\n", "y_r = np.log(1 + np.exp(x_r))\n", "ax.plot(x_r, y_r);\n", "ax.set_xlabel('x');\n", "ax.set_ylabel('y')\n", "ax.set_title('softplus(x) = $ln(1 + e^x)$');" ] }, { "cell_type": "code", "execution_count": 6, "id": "regular-merchant", "metadata": {}, "outputs": [], "source": [ "f.savefig(\n", " '/Users/srom/workspace/romainstrock.com/assets/img/uncertainty/softplus.png', \n", " bbox_inches='tight', \n", " dpi=80,\n", ")" ] }, { "cell_type": "markdown", "id": "spanish-currency", "metadata": {}, "source": [ "## Generate dataset" ] }, { "cell_type": "code", "execution_count": 7, "id": "intermediate-indonesian", "metadata": {}, "outputs": [], "source": [ "def generate_samples(α, β, σ, min_x=-1, max_x=1, n_samples=500):\n", " x = np.linspace(min_x, max_x, n_samples)[:, np.newaxis]\n", " y = α * x + β\n", " dist = torch.distributions.Normal(torch.from_numpy(y), σ)\n", " y_sample = dist.sample().detach().numpy()\n", " return x, y, y_sample" ] }, { "cell_type": "code", "execution_count": 8, "id": "sustained-mobile", "metadata": {}, "outputs": [], "source": [ "def plot_line(x, y, y_sample):\n", " f, ax = plt.subplots(1, 1, figsize=(12, 6))\n", " ax.plot(x.flatten(), y.flatten(), '-', color=palette[0], linewidth=3)\n", " ax.scatter(x.flatten(), y_sample.flatten(), color=palette[0], alpha=0.8)\n", " ax.set_xlabel('input x')\n", " ax.set_ylabel('output y')\n", " return ax" ] }, { "cell_type": "code", "execution_count": 9, "id": "lightweight-merit", "metadata": {}, "outputs": [], "source": [ "α_actual = 2.6\n", "β_actual = 0.0\n", "σ_actual = 0.7\n", "\n", "x, y, y_sample = generate_samples(α_actual, β_actual, σ_actual)" ] }, { "cell_type": "code", "execution_count": 10, "id": "smart-gravity", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_line(x, y, y_sample);" ] }, { "cell_type": "markdown", "id": "endless-girlfriend", "metadata": {}, "source": [ "## Model" ] }, { "cell_type": "code", "execution_count": 11, "id": "painted-devon", "metadata": {}, "outputs": [], "source": [ "initial_α = 1.8\n", "initial_s = 1.5" ] }, { "cell_type": "code", "execution_count": 12, "id": "vulnerable-paste", "metadata": {}, "outputs": [], "source": [ "class LinearNormal(torch.nn.Module):\n", " \n", " def __init__(self):\n", " super().__init__()\n", " self.α = torch.nn.Parameter(torch.tensor(initial_α))\n", " self.s = torch.nn.Parameter(torch.tensor(initial_s))\n", " \n", " @property\n", " def sigma(self):\n", " return F.softplus(self.s) # ensure σ > 0\n", " \n", " def forward(self, x):\n", " m = self.α * x\n", " σ = self.sigma\n", " return torch.distributions.Normal(m, σ)" ] }, { "cell_type": "code", "execution_count": 13, "id": "sacred-harvard", "metadata": {}, "outputs": [], "source": [ "def compute_loss(model, x, y):\n", " out_dist = model(x)\n", " neg_log_likelihood = -out_dist.log_prob(y)\n", " return torch.mean(neg_log_likelihood)\n", "\n", "\n", "def predict(model, x):\n", " model.eval()\n", " out_dist = model(x)\n", " return out_dist.mean, out_dist.stddev, out_dist" ] }, { "cell_type": "code", "execution_count": 14, "id": "velvet-sword", "metadata": {}, "outputs": [], "source": [ "def plot_results(x, y, y_pred):\n", " f, ax = plt.subplots(1, 1, figsize=(12, 6))\n", " ax.plot(x.flatten(), y.flatten(), '-', color=palette[0], linewidth=2, label='Actual line')\n", " ax.plot(x.flatten(), y_pred.flatten(), '-', color=palette[1], linewidth=2, label='Predicted line')\n", " ax.set_xlabel('input x')\n", " ax.set_ylabel('output y')\n", " ax.legend()\n", " return ax" ] }, { "cell_type": "code", "execution_count": 15, "id": "damaged-uganda", "metadata": {}, "outputs": [], "source": [ "model = LinearNormal()" ] }, { "cell_type": "code", "execution_count": 16, "id": "advised-kingston", "metadata": {}, "outputs": [], "source": [ "y_pred, _, y_dist = predict(model, torch.from_numpy(x))\n", "y_pred_sample = y_dist.sample()" ] }, { "cell_type": "code", "execution_count": 17, "id": "enabling-waterproof", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plot_results(\n", " x.flatten(), \n", " α_actual * x.flatten(), \n", " y_pred.detach().numpy(), \n", ")\n", "ax.set_title('Prediction just after initialization');" ] }, { "cell_type": "code", "execution_count": 18, "id": "surprising-department", "metadata": {}, "outputs": [], "source": [ "def compute_train_test_split(x, y, test_size):\n", " x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=test_size)\n", " return (\n", " torch.from_numpy(x_train),\n", " torch.from_numpy(x_test),\n", " torch.from_numpy(y_train),\n", " torch.from_numpy(y_test),\n", " )" ] }, { "cell_type": "code", "execution_count": 19, "id": "liquid-maine", "metadata": {}, "outputs": [], "source": [ "x_train, x_test, y_train, y_test = compute_train_test_split(x, y_sample, test_size=0.2)" ] }, { "cell_type": "markdown", "id": "martial-ribbon", "metadata": {}, "source": [ "## Loss function\n", "\n", "The **probability density function** (PDF) of the normal distribution $\\mathcal{N}(\\mu, \\sigma)$, also called **likelihood function**, is defined as:\n", "\n", "$P(z \\mid \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}(\\frac{z - \\mu}{\\sigma})^2}$\n", "\n", "It is customary to consider the logarithm of the likelihood function for numerical stability reason. It is also typical in machine learning to minimize rather than maximize functions, so we'll consider **the negative log likelihood**:\n", "\n", "$-\\ln{P(z \\mid \\mu, \\sigma)} = \\ln{(\\sigma\\sqrt{2\\pi})} + \\frac{1}{2\\sigma^2}(z - \\mu)^2$\n", "\n", "In the context of linear regression, we have $\\mu = \\alpha x + \\beta$ and we want to minimize the sum of the negative log likelihood function evaluated for all points $(x, y)$ in our dataset of observations $\\mathcal{D} \\subset \\mathbb{R}^2$.\n", "\n", "$\\text{Loss}\\,(\\alpha, \\beta, \\sigma, \\mathcal{D}) = \\sum\\limits_{(x, y) \\in \\mathcal{D}} -\\ln{P(y \\mid \\alpha x + \\beta, \\sigma)} = \\sum\\limits_{(x, y) \\in \\mathcal{D}} \\ln{(\\sigma\\sqrt{2\\pi})} + \\frac{1}{2\\sigma^2}\\{y - (\\alpha x + \\beta)\\}^2$" ] }, { "cell_type": "code", "execution_count": 20, "id": "decimal-river", "metadata": {}, "outputs": [], "source": [ "def loss_fn(x, y, alpha, sigma):\n", " m = torch.from_numpy(alpha * x)\n", " σ = torch.from_numpy(sigma)\n", " observations = torch.from_numpy(y)\n", " \n", " dist = torch.distributions.Normal(m, σ)\n", " neg_log_likelihood = -dist.log_prob(observations)\n", " \n", " return float(torch.mean(neg_log_likelihood).detach().numpy())\n", "\n", "def fitness_fn(x, y, alpha, sigma):\n", " output = np.zeros((len(alpha),))\n", " for i in range(len(alpha)):\n", " output[i] = loss_fn(x, y, alpha[i], sigma[i])\n", " return output\n", "\n", "# Create a grid of 300 by 300 = 90,000 input points\n", "a = np.linspace(1.5, 3.5, 300)\n", "b = np.log(1 + np.exp(np.linspace(-1.0, 2.0, 300)))\n", "A, B = np.meshgrid(a, b)\n", "X_grid = np.array([[u, v] for u, v in zip(np.ravel(A), np.ravel(B))])\n", "\n", "# Sample outputs based on grid points\n", "alpha = X_grid[:,:1]\n", "s = X_grid[:,1:]\n", "zs = fitness_fn(x, y_sample, alpha, s)\n", "Z = zs.reshape(A.shape)" ] }, { "cell_type": "code", "execution_count": 21, "id": "straight-trustee", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16, 6))\n", "gs = mpl.gridspec.GridSpec(1, 2, figure=fig)\n", "ax1 = fig.add_subplot(gs[0,0], projection='3d')\n", "ax2 = fig.add_subplot(gs[0,1])\n", "\n", "# Plot surface\n", "ax1.plot_surface(A, B, Z, cmap='coolwarm', linewidth=0)\n", "\n", "# Plot filled contours\n", "cs = ax2.contourf(A, B, Z, cmap='coolwarm', levels=80)\n", "\n", "# Colour map\n", "cbar = plt.colorbar(cs, ax=ax2)\n", "cbar.ax.set_ylabel('Loss', rotation=360)\n", "cbar.ax.get_yaxis().labelpad = 25\n", "\n", "# Surface labels\n", "ax1.get_xaxis().labelpad = 10\n", "ax1.get_yaxis().labelpad = 10\n", "ax1.get_zaxis().labelpad = 10\n", "ax1.set_xlabel(r'$\\alpha$');\n", "ax1.set_ylabel(r'$\\sigma$');\n", "ax1.set_zlabel('Loss');\n", "ax1.grid(False);\n", "ax1.view_init(20, 25);\n", "ax1.set_facecolor('white');\n", "\n", "# Contour labels\n", "ax2.set_xlabel(r'$\\alpha$');\n", "ax2.set_ylabel(r'$\\sigma$');\n", "ax2.grid(False);" ] }, { "cell_type": "markdown", "id": "imperial-gabriel", "metadata": {}, "source": [ "## Visualizing gradient descent" ] }, { "cell_type": "code", "execution_count": 22, "id": "finnish-athens", "metadata": {}, "outputs": [], "source": [ "def train_one_step(model, optimizer, x_batch, y_batch):\n", " model.train()\n", " optimizer.zero_grad()\n", " loss = compute_loss(model, x_batch, y_batch)\n", " loss.backward()\n", " optimizer.step()\n", " return loss" ] }, { "cell_type": "code", "execution_count": 23, "id": "occupational-latino", "metadata": {}, "outputs": [], "source": [ "optimizer = torch.optim.SGD(model.parameters(), lr=1.0)" ] }, { "cell_type": "code", "execution_count": 24, "id": "central-grain", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8, 6))\n", "gs = mpl.gridspec.GridSpec(1, 1, figure=fig)\n", "ax2 = fig.add_subplot(gs[0,0])\n", "\n", "# Plot filled contours\n", "cs = ax2.contourf(A, B, Z, cmap='coolwarm', levels=80)\n", "\n", "# Colour map\n", "cbar = plt.colorbar(cs, ax=ax2)\n", "cbar.ax.set_ylabel('Loss', rotation=360)\n", "cbar.ax.get_yaxis().labelpad = 25\n", "\n", "# Contour labels\n", "ax2.set_xlabel(r'$\\alpha$');\n", "ax2.set_ylabel(r'$\\sigma$');\n", "ax2.grid(False);\n", "\n", "fn = lambda x: np.log(1 + np.exp(x))\n", "\n", "# Initial value\n", "xx = [initial_α]\n", "yy = [fn(initial_s)]\n", "\n", "# gradient steps\n", "for _ in range(5):\n", " loss = train_one_step(model, optimizer, x_train, y_train)\n", " \n", " xx.append(float(model.α.detach().numpy()))\n", " yy.append(fn(float(model.s.detach().numpy())))\n", "\n", "ax2.plot(xx, yy, 'o-', color='white', markersize=10);\n", "ax2.set_title('5 steps of gradient descent');" ] }, { "cell_type": "code", "execution_count": null, "id": "burning-inside", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 5 }