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@Gilles86
Created August 30, 2023 10:40
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{
"cells": [
{
"cell_type": "code",
"execution_count": 145,
"metadata": {},
"outputs": [],
"source": [
"import scipy.stats as ss\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns"
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {},
"outputs": [],
"source": [
"def logodds(p):\n",
" # return ss.norm.ppf(p)\n",
" return np.log(p / (1 - p))\n",
"\n",
"\n",
"def inv_logodds(x):\n",
" return (np.tanh(x / 2) + 1) / 2\n",
"\n",
"def inv_logodds_deriv(x):\n",
" return inv_logodds(x) * (1 - inv_logodds(x))\n",
"\n",
"\n",
"def plot_identity_line(xmin=0, xmax=1):\n",
" plt.plot([xmin, xmax], [xmin, xmax], 'k--')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def logodds_deriv(p):\n",
" return 1 / (p * (1 - p))"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [],
"source": [
"def get_posterior(p, sd_likelihood, mu_prior, sd_prior):\n",
"\n",
" mu_likelihood = logodds(p)\n",
" mu_prior = logodds(mu_prior)\n",
"\n",
" mu_posterior = (mu_likelihood / sd_likelihood**2 + mu_prior / sd_prior**2) / (1 / sd_likelihood**2 + 1 / sd_prior**2)\n",
" sd_posterior = 1 / np.sqrt(1 / sd_prior**2 + 1 / sd_likelihood**2)\n",
"\n",
" return inv_logodds(mu_posterior), sd_posterior"
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x141f53d30>]"
]
},
"execution_count": 110,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p = np.linspace(1e-3, 1-1e-3, 100)\n",
"plt.plot(p, get_posterior(p, 1., .4, 1)[0])\n",
"plt.plot([0, 1], [0, 1], c='k', ls='--')"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {},
"outputs": [],
"source": [
"def get_p_distribution(grid=None, mu_p=0.5, sensory_noise=0.1):\n",
"\n",
" if grid is None:\n",
" grid = np.linspace(1e-3, 1-1e-3, 100)\n",
"\n",
" sensory_grid = logodds(grid)\n",
"\n",
" p_sensory = ss.norm.pdf(sensory_grid, loc=logodds(mu_p), scale=sensory_noise)\n",
"\n",
" return grid, p_sensory / inv_logodds_deriv(sensory_grid)"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0000000000000002"
]
},
"execution_count": 86,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x, p = get_p_distribution(mu_p=.5, sensory_noise=.5)\n",
"np.trapz(p, x)"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x141d2bdf0>]"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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S3vtbL7QN8MKJ0moeqEdE1AosIy6mcW+R3rEB8NGqBKchAAjw1mDG6CSoFBJ+3FeIhdtOio5ERORSWEZczLashoPa+sUHC05Cf5QUE4gXhzXMH3nrh0zsy+P8ESKilmIZcSGyLDeNjLCMOJ9x18bh5q5hqDNbMGHxbhg4f4SIqEVYRlxIVkkVTlcYoVEpkBgdIDoO/YkkSXjvnl6ICvRCzplq/PPbvZw/QkTUAiwjLiT1eMOoSHJMIHRqpeA01By9txozRveGWinhp/1FnD9CRNQCLCMuhLdoXENidAD+ecv5+SMHCjh/hIjoclhGXETDfJHGyatBgtPQlYy7Ng6DO4eizmzBU4vTUWk0iY5EROS0WEZcxPHTVSipNEKrUqAX54s4PUlq2H8kQq9DdkkVXv6O+48QEV0Ky4iLaNpfhPNFXEagjwbTRyVBqZDwfUYBlqXliY5EROSUWEZcBOeLuKZr2gVh0s2dAACvrtqPo6cqBCciInI+LCMu4I/zRfq3ZxlxNX+/vj0GdQxBbX3D/JHaerPoSEREToVlxAUcP135h/kietFxyEoKhYT37+2FEF8NDp+qwFs/HBQdiYjIqbCMuIDUc6MiybGB0Ko4X8QVhfrp8MG9iQCARdtz8NO+QrGBiIicCMuIC+B8EfdwXac2GH99ewDAC8v3IvdMteBERETOgWXEycmyjO0sI27jH0M6ITE6ABW1Jjz7dTrqzRbRkYiIhGMZcXLHiitRUlnH+SJuQq1U4ONRSfDTqbA7pwwfrj0iOhIRkXAsI06u8RZNSjvOF3EX0UHeeHdETwDA7A3HsfVYieBERERisYw4ue3ZDZNX+8bxFo07ubVHBEb1iYEsA88tzUBppVF0JCIiYVhGnNyevDIADStpyL28entXdAj1RXGFEc9/u5fbxRORx2IZcWKllUbknqkBAHRvy/ki7sZLo8SM0UnQqBT4/VAx5m85IToSEZEQLCNObG9+w9Hz8W18oPdSC05D9tA53B+v3NYFAPDOT4ew/9z/5kREnoRlxIntyS0DAPSKChCag+zrgX6xuLlrGOrMFjy9JB1VRpPoSEREDsUy4sT25jX8K7lXFG/RuDNJkvDfET0R7q9DdkkVXl91QHQkIiKHYhlxUrIsY++5yas9owOEZiH7C/TRYNp9iZAkYNmuPKzaUyA6EhGRw7CMOKn8shqUVNZBpZDQNcJfdBxygH7xwXjqhg4AgJdX7ON28UTkMVhGnFTjLZrOEX7QqbnZmad4dnBH9I4JQIWxYbt4E7eLJyIPwDLipBonr/bk5FWPolIq8NF9SfDTNmwX/9FvR0VHIiKyO5YRJ9W42Vkiy4jHiQ7yxtt39wAAzFh3rOlIACIid8Uy4oTMFhn78w0AgJ48HM8jDe8ViXtTohq2i/86A2XVdaIjERHZDcuIE8o6XYlKowneGiU6hvqJjkOCvH5HN8SH+KDIUIt/Lud28UTkvlhGnNCec5NXu0fqoVRIgtOQKN4aFaaPSoJaKeGXA6eweEeO6EhERHbBMuKEmnZe5S0aj9e9rR4vDO0MAHjrh4M4eqpCcCIiIttjGXFCTZudcfIqARh3bRwGdQxBbX3DdvG19WbRkYiIbIplxMkYTWZkFjb86zeRO68SAIVCwvv39kKIrwaHiirwzk+HREciIrIplhEnc6iwAnVmCwK91YgK9BIdh5xEqJ8O/3dPLwDAF1tP4PdDpwQnIiKyHZYRJ9N4i6ZXdAAkiZNX6bwbOofi4YHtAADPL9uLYkOt2EBERDbCMuJkMnIbVtJwvgg158VhndElwh+lVXX4x7I9sFi43JeIXB/LiJNpGhmJ4koauphWpcTHoxKhUyuw6WgJ5m7OFh2JiOiqsYw4kUqjCcdOVwLgyAhdWodQP7x6ezcAwH9/OYT9+eWCExERXR2WESdysMAAWQYi9Tq08dOKjkNObFSfaNzSLRz1ZhnPLElHldEkOhIRUauxjDiRQ0UN59F0ifAXnIScnSRJeGdED4T765BVUoU3/ndAdCQiolZjGXEih4oa9hfpHMHzaOjKArw1+HBkIiQJ+CYtDz/uLRQdiYioVawuIxs3bsTw4cMRGRkJSZKwcuXKy75+/fr1kCTposehQ9y46c8OFTaMjCSEc2SEWqZ/+2BM+EsHAMCLK/Yi72y14ERERNazuoxUVVWhV69emDFjhlXvO3z4MAoLC5seHTt2tPaj3ZosyzhyqmHyaudwjoxQyz17U0ckRgegotaEiUszYDJbREciIrKKyto3DBs2DMOGDbP6g0JDQxEQEGD1+zxF3tkaVBpNUCslxIX4iI5DLkStVGD6fUm4dfom7DxxFjPWHcNzN3USHYuIqMUcNmckKSkJERERGDx4MNatW3fZ1xqNRhgMhgse7u7wufki7dv4Qq3kVB6yTkywN/59Z3cAwPTfjiLtxBnBiYiIWs7u33oRERH49NNPsXz5cqxYsQIJCQkYPHgwNm7ceMn3TJ06FXq9vukRHR1t75jCHT53NDxv0VBr3ZnUFncntYVFBp79OgPlNfWiIxERtYjVt2mslZCQgISEhKZf9+/fH7m5uXjvvfdw3XXXNfueKVOmYNKkSU2/NhgMbl9IMjl5lWzgjb92Q9rJs8g5U42XvtuHGaOSeMYRETk9IfcD+vXrh6NHj17yv2u1Wvj7+1/wcHeHuayXbMBPp8b0UUlQKST8uLcQy9LyREciIroiIWUkPT0dERERIj7aKRlNZmSVVAHgbRq6eonRAZh4c8ME1tdWHcDxc0cMEBE5K6tv01RWVuLYsWNNv87OzkZGRgaCgoIQExODKVOmID8/HwsWLAAATJs2De3atUO3bt1QV1eHhQsXYvny5Vi+fLntfgoXd7y4CmaLDH+dCuH+OtFxyA2Mv749Nh8tQWpWKZ5Zko4VTw6AVqUUHYuIqFlWj4ykpaUhKSkJSUlJAIBJkyYhKSkJr776KgCgsLAQOTk5Ta+vq6vD5MmT0bNnTwwaNAibN2/Gjz/+iLvvvttGP4LrO3yqYb5I53B/3t8nm1AqJHw4MhGB3mocKDDgvV8Oi45ERHRJkizLsugQV2IwGKDX61FeXu6W80emrs7EJxuzMKZfLN46tzyTyBbWHCjC41/tAgB8+UgfXN+pjeBERORJWvr9zQ0tnEDjmTQJnC9CNjakWzjG9IsFAPzjmz04XWEUnIiI6GIsI06gaSUNywjZwcu3dUFCmB9KKo2YvGwPLBanHwwlIg/DMiJYeXU9igy1AIBOLCNkBzq1EtNHJUGrUmDDkdOYtyVbdCQioguwjAh2qKhh8mrbAC/469SC05C7Sgj3w79u7woAePfnQ9ifXy44ERHReSwjgh3iLRpykAf6xmBI1zDUm2U8syQdVUaT6EhERABYRoTj5FVyFEmS8O6Ingj31yGrpAqvrzogOhIREQCWEeEOFzWeScMyQvYX6KPBhyMTIUnAsl15WLWnQHQkIiKWEZFkWcaRUw1bdXfmAXnkIP3bB+OpGzoAAF5esQ+5Z6oFJyIiT8cyIlDe2RpUGk1QKyXEt/ERHYc8yLODO6J3TAAqjCY883U66s0W0ZGIyIOxjAjUOF+kfRtfqJX8n4IcR6VU4KP7kuCnUyE9pwzTfj0iOhIReTB+AwrUOF+EK2lIhOggb7xzd08AwKz1x7H1WIngRETkqVhGBDq/kobzRUiM23pGYFSfaMgy8NzSDJRWcrt4InI8lhGBjhU3TF5NCPcVnIQ82au3d0OHUF8UVxjx/Ld74QJnZxKRm2EZEcRikZFdUgUAiA9hGSFxvDRKzBidBI1Kgd8PFWP+lhOiIxGRh2EZESS/rAZGkwVqpYSoQC/RccjDdQ73xyu3dQEAvPMTt4snIsdiGREk69yoSGywD1RcSUNO4IF+sRjaLQx1ZgueXpKOSm4XT0QOwm9BQbJON8wXiQ/h/iLkHBq3i4/U65BdUoVXv98vOhIReQiWEUGa5ou04XwRch4B3hpMuy8JCglYsTsfK3bniY5ERB6AZUSQrNONk1c5MkLOpU9cEJ67qRMA4F8r9zeN4hER2QvLiCBNt2m4DTw5oQk3dEC/+CBU15nx9JJ0GE1m0ZGIyI2xjAhQXWdCQXktAN6mIeekVEiYNjIJgd5qHCgwYOrqQ6IjEZEbYxkRoHG+SIC3GkE+GsFpiJoXrtfh/Xt7AQC+2HoCaw+eEpyIiNwVy4gA5zc74y0acm43dg7Do9fGAQCe/3YPCspqBCciInfEMiJA4+TVOO68Si7ghVs6o2eUHmXV9Xj263SYzBbRkYjIzbCMCMDJq+RKNCoFPh6VBF+tCjtPnMVHvx0VHYmI3AzLiACNu6+2ZxkhFxEb7IOpd/cAAMxYdwxbjpUITkRE7oRlxMFkWUb2aW54Rq5neK9IjOoTDVkGnluagdMVRtGRiMhNsIw42OlKIyqMJkgSEBvsLToOkVVevb0bOoX54nSFEZO+yYDFIouORERugGXEwRonr0YFekGrUgpOQ2QdL40SM0f3hk6twKajJZi94bjoSETkBlhGHOz8NvC8RUOuqWOYH978a3cAwAdrj2DniTOCExGRq2MZcTCupCF38LfkKNyV1BZmi4xnlqTjbFWd6EhE5MJYRhyMp/WSO5AkCW/d2R3xIT4oLK/F5GV7IMucP0JErcMy4mBNy3q5+yq5OF+tCh+PToJGpcBvh4rx+aZs0ZGIyEWxjDhQncmCnDPVADgyQu6hW6Qer9zeFQDw7s+HsDvnrOBEROSKWEYcKOdMNcwWGd4aJcL8taLjENnEA31jcFvPCJgsMp5enI6yas4fISLrsIw4UOPk1bgQH0iSJDgNkW1IkoR37u6B2GBv5JfVYPKyvZw/QkRWYRlxIE5eJXflp1Nj5uje0CgV+DXzFOZtOSE6EhG5EJYRBzq/xwgnr5L76d5Wj1du7wIAeOenTGTklokNREQug2XEgbJKuMcIubcH+sXith4RqDfLmLBoN+ePEFGLsIw4EHdfJXcnSRKmjuD8ESKyDsuIg5RX16P03C6VcRwZITfm3zh/RNUwf4T7jxDRlbCMOEjjLZowfy18tSrBaYjsq3tbPV79w/4ju07y/BoiujSWEQc5UdpwiyaOk1fJQ9zfNwbDe0XCZJHx1OJ0nOH5NUR0CSwjDpJTWgMAiA1iGSHPIEkSpt7do+n8mknfZMBi4fwRIroYy4iDNG4DHxPsLTgJkeP4alWYeX9vaFUKrD98GrM3HBcdiYicEMuIg+SeKyPRQSwj5Fm6RPjjzb92AwC8v+Ywth4vEZyIiJwNy4iDNI2MsIyQB7o3JRojekfBIgPPLMlAsaFWdCQiciIsIw5QW29G0bm/fFlGyBNJkoR/39kdCWF+KKk04ukl6TCZLaJjEZGTYBlxgLyzDZNXfbUqBHqrBachEsNLo8SsB3rDR6PE9uwz+GDtEdGRiMhJsIw4wB/ni/C0XvJk7dv44p0RPQEAs9Yfx2+ZpwQnIiJnwDLiAOfni3gJTkIk3vBekRjbPxYAMHFpRlNZJyLPxTLiAJy8SnShl2/rgl7RATDUmvD3RbtQW28WHYmIBGIZcQCWEaILaVVKzLq/NwK91difb8CbPxwUHYmIBGIZcQDuMUJ0sbYBXph2XxIkCVi8PQcrdueJjkREgrCM2JksyxwZIbqE6zu1wTM3dgQAvPTdPhwqMghOREQisIzYWWlVHarrzJAkoG0gJ7AS/dkzgztiUMcQ1NZb8PeFu2GorRcdiYgcjGXEzhpHRSL8ddCqlILTEDkfpULCR/clIVKvQ3ZJFV5YtheyzAP1iDwJy4idcb4I0ZUF+Wgw8/7eUCsl/HygCJ9uzBIdiYgciGXEznJKOV+EqCWSYgLx2vCGA/Xe/fkQD9Qj8iAsI3bGyatELXd/3xjc3bvtuQP10lFUzgP1iDwBy4idNZWRYJYRoiuRJAn/ubMHOof7oaSyDk8u2oU6Ew/UI3J3LCN2xjkjRNbx0ijxyZhk+OlU2J1ThrdXZ4qORER2xjJiR0aTGYWGhmFm3qYharnYYB98eG8iAOCLrSfwXTo3RCNyZywjdpR/tgayDHhrlAj20YiOQ+RSbuoahqdv7AAAmLJiHw4WcEM0InfFMmJHf5y8KkmS4DRErue5mzrhuk5tUFtvwfiFu1BezQ3RiNwRy4gdcb4I0dVRKiRMvy8R0UFeyDlTjeeWpsNi4YZoRO6GZcSOuKyX6OoFeGsw+/5kaFUKrDt8Gh/9dlR0JCKyMavLyMaNGzF8+HBERkZCkiSsXLnyiu/ZsGEDkpOTodPpEB8fjzlz5rQmq8thGSGyje5t9Xj7rh4AgI9+O4pfD54SnIiIbMnqMlJVVYVevXphxowZLXp9dnY2br31VgwaNAjp6el46aWX8Mwzz2D58uVWh3U1OWdqALCMENnCiOQojO0fCwCYuDQDWacrBSciIltRWfuGYcOGYdiwYS1+/Zw5cxATE4Np06YBALp06YK0tDS89957GDFihLUf7zJkWeacESIb+9dtXZFZaMDOE2fxxFe78N2EgfDVWv3XGBE5GbvPGUlNTcWQIUMueG7o0KFIS0tDfX3zM+ONRiMMBsMFD1dztroelUYTACAq0EtwGiL3oFEpMPP+3gjz1+JocSUmf7OHJ/wSuQG7l5GioiKEhYVd8FxYWBhMJhNKSpo/CGvq1KnQ6/VNj+joaHvHtLnG+SLh/jro1ErBaYjcR6ifDrMfSG464XfW+uOiIxHRVXLIapo/77HR+C+ZS+29MWXKFJSXlzc9cnNz7Z7R1jh5lch+escE4s2/dgcAvLfmMNYfLhaciIiuht3LSHh4OIqKii54rri4GCqVCsHBwc2+R6vVwt/f/4KHq+F8ESL7GtUnBqP6xEA+d8LviZIq0ZGIqJXsXkb69++PtWvXXvDcmjVrkJKSArVabe+PFyanlCMjRPb2+h1d0TsmAIZaEx7/Kq1pnhYRuRary0hlZSUyMjKQkZEBoGHpbkZGBnJycgA03GIZO3Zs0+vHjx+PkydPYtKkScjMzMS8efMwd+5cTJ482TY/gZNquk0TzMmrRPaiVSkx54FkhPppceRUJf7xTQZ3aCVyQVaXkbS0NCQlJSEpKQkAMGnSJCQlJeHVV18FABQWFjYVEwCIi4vD6tWrsX79eiQmJuKtt97C9OnT3XpZL3C+jEQHcmSEyJ5C/XWYMyYZGqUCvxw4hZnrjomORERWkmQXWBdnMBig1+tRXl7uEvNHTGYLEl75GWaLjG1TBiNcrxMdicjtfbMzFy8s3wsA+HxsCm7qGnaFdxCRvbX0+5tn09hBcYURZosMtVJCqJ9WdBwij3DvNdFNO7Q+tzQDx4orBCciopZiGbGD/LKGbeDD9TooFM0vXyYi23vl9q7oExeESqMJjy3YhfLq5jdWJCLnwjJiB/lnG8pI2wBOXiVyJLVSgVn390bbAC9kl1Th6a/TYeaEViKnxzJiB40jI20DOHmVyNFCfLX4dGwyvNRKbDxyGu/8lCk6EhFdAcuIHTSVEZ5JQyREt0g93vtbLwDAZ5uysWJ3nuBERHQ5LCN2cP42DVfREIlyW88IPH1jBwDAiyv2ISO3TGwgIroklhE74G0aIucw8aZOuKlLGOpMFjy+IA1F5bWiIxFRM1hGbEyW5fMjI7xNQySUQiFh2n2J6BTmi+IKIx7/Kg219WbRsYjoT1hGbKysuh415/6yi+BmZ0TC+WpV+HzsNQj0VmNvXjle+HYvXGCvRyKPwjJiY423aEJ8tdCplYLTEBEAxAR7Y9b9yVApJKzaU4BZ64+LjkREf8AyYmN5vEVD5JT6tw/GG3/tBgD4v18O45cDRYITEVEjlhEbKzg3MhLFDc+InM79fWPx4Lkt4ycuzcDBAoPgREQEsIzYHPcYIXJur9zeFdd2CEF1nRmPLUjD6Qqj6EhEHo9lxMYaV9JEcvIqkVNSKRWYObo34kN8kF9Wgye4woZIOJYRGzs/MsI9Roicld5bjc8fTIG/ToXdOWV4cTlX2BCJxDJiYwVlPCSPyBXEt/HF7AeSoVRIWJlRgJnrjomOROSxWEZsqKbOjNKqOgCcM0LkCgZ2CMGb51bYvLfmCH7aVyg4EZFnYhmxocZbNL5aFfx1KsFpiKgl7u8bi4cGtAMATPwmA3vzyoTmIfJELCM2lP+HWzSSJAlOQ0Qt9a/buuD6Tm1QW2/Bo1+mobC8RnQkIo/CMmJDBVzWS+SSVEoFZoxOQkKYH4orjHjkizRUGU2iYxF5DJYRG2o6II+TV4lcjp9OjbkPpSDEV4PMQgOeWZIOs4UrbIgcgWXEhhpv00SyjBC5pKhAb3w6NgValQK/HSrG26szRUci8ggsIzaUz3NpiFxe75hAvH9vLwDA3M3ZWLjtpOBERO6PZcSG8rnHCJFbuL1nJCYP6QQAePX7/Vh3uFhwIiL3xjJiIyazBUWGWgBAFEdGiFzehBs64J7kKFhk4KlFu3moHpEdsYzYyKkKI8wWGWqlhDa+WtFxiOgqSZKEt+/qgf7xwaiqM+ORL3aiqLxWdCwit8QyYiON80Ui9F5QKLjHCJE70KgUmPNAMtq38UGRoRaPfLETlVzyS2RzLCM2wjNpiNyT3luNLx7ugxBfDQ4WGvD04t0wmS2iYxG5FZYRG8nnhmdEbis6yBufnVvyu+7wabz+vwM85ZfIhlhGbCTvLPcYIXJnSTGB+Oi+REgSsHBbDj7ZmCU6EpHbYBmxkcbbNFEsI0Ru65buEXjltq4AgHd+OoRVewoEJyJyDywjNsLbNESe4ZFr4/DIwDgAwORv9mB7VqngRESuj2XEBmRZ5rk0RB7kX7d1wbDu4agzW/DYgjQcK64QHYnIpbGM2MDZ6nrU1JsBAOF6neA0RGRvCoWED0cmondMAAy1Jjw4byeKDdyDhKi1WEZsoHG+SBs/LXRqpeA0ROQIOrUSnz94DeJCfJBfVoOH5u9ERW296FhELollxAbyeIuGyCMF+Wjw5R/2IHly0W7UmbgHCZG1WEZsgBueEXmumGBvzH+oD7w1Smw6WoIXV+zlHiREVmIZsYHGMhIZwPkiRJ6oR5QeM+/vDaVCword+XhvzWHRkYhcCsuIDRSeOzyLG54Rea4bEkIx9e4eAICZ645jQeoJsYGIXAjLiA007jESoWcZIfJk96ZE4x83dwIAvLbqAH7cWyg4EZFrYBmxgcJy3qYhogZP3dgBY/rFQpaBiUszsPV4iehIRE6PZeQq1ZstKK4wAuDICBEBkiTh9Tu6NW2K9sSCXThYYBAdi8ipsYxcpaLyWsgyoFEpEOyjER2HiJyA8tymaH3jglBhNOHB+TuQe6ZadCwip8UycpUaJ69G6HVQKCTBaYjIWejUSnw6NgWdw/1wusKIMXO3o6TSKDoWkVNiGblKjfNFIrgNPBH9id5LjS8f6YO2AV44UVqNB+ft4C6tRM1gGblKBWVc1ktElxbmr8PCR/si2EeDAwUGPLYgDbXnzrIiogYsI1epacMzTl4lokuIC/HBl4/0ga9WhW1ZZ/Ds1+kwW7hLK1EjlpGr1HSbhst6iegyurfV49OxydAoFfjlwCm8/N0+bhtPdA7LyFXibRoiaqkB7UMwfVQSFBLw9c5cvPszt40nAlhGrlpBOW/TEFHL3dI9vGnb+DkbjmP2+uOCExGJxzJyFWrqzCirbpgZz9s0RNRSI6+JwUu3dgYAvPvzISzaflJwIiKxWEauQuOoiK9WBX+dWnAaInIlj1/XHhNuaA8A+NfK/Vi1p0BwIiJxWEauQtNKGo6KEFErTB6S0HSOzaSlGVh3qFh0JCIhWEauQmFZ4+6rnC9CRNaTJAlv3NENf02MhMkiY/zCXdiWVSo6FpHDsYxchQKe1ktEV0mhkPDe33phcOdQGE0WjPtiJzJyy0THInIolpGr0DgywpU0RHQ11EoFZt7fGwPaB6OqzowH5+1AZiFP+iXPwTJyFQqaNjxjGSGiq6NTK/HZ2BT0jglAeU09xszdjqzTlaJjETkEy8hVOL8VPG/TENHV89GqMP/hPuga4Y+Syjo88Pl25J2tFh2LyO5YRlpJlmUUlp+bwMqRESKyEb2XGl+N64P2bXxQUF6L0Z9tR9G5v2uI3BXLSCuV19Sjuq7h5M0IjowQkQ0F+2qx6NF+iAnyRs6Zaoz+fBtOVxhFxyKyG5aRVmo8kybYRwOdWik4DRG5m3C9Dosf64u2AV7IOl2FBz7fjjNVdaJjEdkFy0gr8bReIrK3qEBvLHq0L8L8tTh8qgJj5m5H+bkjKIjcCctIK52fvMr5IkRkP+1CfLDo0X4I8dXgQIEBY+fvgKGWhYTcC8tIKxWcm1AWycmrRGRnHUJ9sejRfgj0VmNPbhkemrcDlUaT6FhENsMy0kqF50ZGOHmViBwhIdwPX43rC72XGrtzyvDw/B2oYiEhN8Ey0kocGSEiR+veVo+F4/rCT6fCzhNn8fAXO1Fdx0JCro9lpJV4Yi8RidAjSo+vxvWFn1aFHdlnMO6LNNSc22aAyFW1qozMmjULcXFx0Ol0SE5OxqZNmy752vXr10OSpIsehw4danVo0SwWGacMPLGXiMRIjA7Al+P6wFerQmpWKcZ9uZOFhFya1WVk6dKleO655/Dyyy8jPT0dgwYNwrBhw5CTk3PZ9x0+fBiFhYVNj44dO7Y6tGgllUbUm2UoJCDUTys6DhF5oN4xgfji4Wvgo1Fi63EWEnJtVpeRDz74AOPGjcOjjz6KLl26YNq0aYiOjsbs2bMv+77Q0FCEh4c3PZRK190oLP/cLZpwfx1USt7pIiIxUtoF4ctH+jQVkkc4h4RclFXfpHV1ddi1axeGDBlywfNDhgzB1q1bL/vepKQkREREYPDgwVi3bt1lX2s0GmEwGC54OBOeSUNEziKlXRAW/OGWDQsJuSKrykhJSQnMZjPCwsIueD4sLAxFRUXNviciIgKffvopli9fjhUrViAhIQGDBw/Gxo0bL/k5U6dOhV6vb3pER0dbE9PuCrisl4icSHJswwiJr1aFbVln8PD8nVz2Sy6lVfcYJEm64NeyLF/0XKOEhAQ89thj6N27N/r3749Zs2bhtttuw3vvvXfJ33/KlCkoLy9veuTm5rYmpt00nkvTliMjROQkkmMDmwrJ9uwzeGj+DlRwp1ZyEVaVkZCQECiVyotGQYqLiy8aLbmcfv364ejRo5f871qtFv7+/hc8nEnTuTQcGSEiJ5IcG4ivxvVp2odk7LwdKK9hISHnZ1UZ0Wg0SE5Oxtq1ay94fu3atRgwYECLf5/09HRERERY89FOpYBzRojISSXFBGLxo/2g91IjPacMY+ZuR1k1T/sl56ay9g2TJk3CmDFjkJKSgv79++PTTz9FTk4Oxo8fD6DhFkt+fj4WLFgAAJg2bRratWuHbt26oa6uDgsXLsTy5cuxfPly2/4kDtS4FTxv0xCRM+oRpceSx/rhgbnbsTevHKM/246Fj/ZFkI9GdDSiZlldRkaOHInS0lK8+eabKCwsRPfu3bF69WrExsYCAAoLCy/Yc6Surg6TJ09Gfn4+vLy80K1bN/z444+49dZbbfdTOFCdyYLTlUYAvE1DRM6ra6Q/vn68H0Z/th0HCw2479NULBzXF6H+/HuLnI8ky7IsOsSVGAwG6PV6lJeXC58/crK0Ctf/33ro1ApkvnnLJSfuEhE5g2PFlbj/8204ZTCiXbA3Fj3Wj6O65DAt/f7mjl1Wyjt7/hYNiwgRObsOob5Y9sQARAV64URpNe6dk4oTJVWiYxFdgGXESvmNZSTQW3ASIqKWiQn2xrLx/REf4oP8shr87ZNUHDlVIToWUROWESvlcfIqEbmgCL0Xlj7RH53D/XC6woiRn6Rib16Z6FhEAFhGrNY4MhIVyDJCRK6ljZ8WSx7rh55Repytrsfoz7ZjW1ap6FhELCPWyi+rBsCRESJyTYE+Gix6tC/6xgWh0mjCg/N24PdDp0THIg/HMmKlxhN723JkhIhclJ9OjS8f6YPBnUNhNFnw+IJd+D4jX3Qs8mAsI1YwW2QU8lwaInIDOrUSc8Yk46+JkTBZZDy3NANfbTspOhZ5KJYRKxRX1MJkkaFSSAjjxkFE5OLUSgU+vDcRY/rFQpaBV1bux0e/HoULbD9FboZlxAqNk1fD9TooFdxjhIhcn0Ih4c2/dsMzN3YAAHz46xG8tuoALBYWEnIclhEr5HNZLxG5IUmSMGlIAt64oxskCViQehLPfJ0Oo8ksOhp5CJYRKzTtvsrJq0Tkhh4c0A4f3ZcEtVLCD3sLMe6LNFQaTaJjkQdgGbFC48hIFEdGiMhN3dErEvMeugbeGiU2HyvBfZ+moriiVnQscnMsI1bI58gIEXmAQR3bYMlj/RDso8H+fANGzN6KrNOVomORG2MZscL5OSM8l4aI3Fuv6AAs//sAxAZ7I/dMDUbM3ordOWdFxyI3xTLSQrIsc2SEiDxKuxAfLP/7gD9sH78Nvx7kbq1keywjLXS2uh419Q0zyyP03GOEiDxDiG/DeTZ/SWiD2noLHv8qDV+lnhAdi9wMy0gLNY6KtPHTQqdWCk5DROQ4PloVPhubgpEp0bDIwCvfH8B/fjzIvUjIZlhGWogH5BGRJ1MrFXhnRA88PzQBAPDZpmxMWLwbtfXci4SuHstIC3GPESLydJIkYcINHfDRfYnQKBX4aX8RRn22DSWVRtHRyMWxjLRQYxnhHiNE5On+mtgWX43rA72XGuk5Zbhz5hYcPVUhOha5MJaRFmpa1suRESIi9I0PxoonG5b+5p2twd2ztmLDkdOiY5GLYhlpoaZlvRwZISICALRv44vvnhyIPu2CUGE04ZEvdnKlDbUKy0gLcWSEiOhiQT4afPVoH4zoHQWzRcYr3x/Aa9/vh8lsER2NXAjLSAtUGk0or6kHwJERIqI/06qUeO9vPfHCLQ0rbb5MPYmH5u9EWXWd4GTkKlhGWqDxFo2/TgU/nVpwGiIi5yNJEp78SwfMeSC56ZC9O2duwbFiTmylK2MZaYGmPUYCeSYNEdHl3NI9HMv/PgBtA7xworQad87cit8PcQt5ujyWkRbg5FUiopbrEuGPVU8NRJ+4IFQaTRj3ZRpmrT8GWeaOrdQ8lpEWyDs3eTWKk1eJiFok2FeLheP6YnTfGMgy8N+fD2PC4t2oMppERyMnxDLSAhwZISKynkalwNt39cDbd/WAWilh9b4i3DVrC7JLqkRHIyfDMtICXNZLRNR6o/vG4OvH+yPUT4sjpypxx4zNnEdCF2AZaQGOjBARXZ3k2ED88PS1SI4NREVtwzySD9Ychpkn/xJYRq7IaDKjuKLhECiOjBARtV6ovw5LHuuHMf1iIcvA9N+P4aH5O1DKg/Y8HsvIFRSW1QIAdGoFgn00gtMQEbk2jUqBt+7sjmkjE+GlVmLT0RLc/vFm7M45KzoaCcQycgWN80UiA7wgSZLgNERE7uHOpLZYOWEg4tv4oLC8FiM/ScW8zdlc/uuhWEaugPNFiIjsIyHcD6ueuha39YhAvVnGmz8cxBNf7UJ5db3oaORgLCNXkHe2YfdV7jFCRGR7vloVZoxOwht3dINGqcCag6dw6/RNvG3jYVhGruD4ufXw7YJ9BCchInJPkiThwQHtsPzvAxAb7I38shrcOycVn248DgtX23gElpErOHqq4ZCnTmF+gpMQEbm3HlF6/PD0tbitZwRMFhlvrz6EB+fvQLGhVnQ0sjOWkcuoN1uadgrsGOYrOA0Rkfvz06kxY1QS/nNXd+jUCmw6WoJbPtqE3zK5SZo7Yxm5jBMlVag3y/DWKBGp55wRIiJHkCQJ9/eNxQ9PX4suEf44U1WHcV+m4ZWV+1FbbxYdj+yAZeQyjpyqBAB0DPWFQsFlvUREjtQh1A8rJwzAuGvjAABfbTuJ2z/ejH155YKTka2xjFzGkXPzRTpyvggRkRBalRKv3N4VCx7pgzZ+WhwrrsRds7bgo1+Pot5sER2PbIRl5DKOFjdOXuV8ESIika7r1AZrnrsOt/VomNz64a9HcM/srThWXCk6GtkAy8hlNN2m4cgIEZFwgT4azBidhI/uS4S/ToU9eeW4bfomfLYxiwfuuTiWkUuoM1lw4txKGi7rJSJyDpIk4a+JbbFm4vUY1DEERpMF/1mdibtnb226tU6uh2XkEk6UVsFkkeGrVSFSrxMdh4iI/iBcr8OCR/rg3RE94KdVYU9uGW6fvhkzfudcElfEMnIJjQ27Q6gvD8gjInJCkiRh5DUxWDvpegzuHIo6swXvrTmCO2ZsQTq3k3cpLCOX0DhfhJNXiYicW7heh88fTMG0kYkI8FYjs9CAu2dvxavf74ehlofuuQKWkUto3Aa+YyjnixAROTtJknBnUlv8Nul63N27LWQZWJB6Ejd/sAGr9xVCljnB1ZmxjFzC+T1GODJCROQqgn21+ODeRCx+tC/iQnxwymDEk4t248H5O3H8NJcBOyuWkWYYTWacKK0GwJU0RESuaECHEPz07CA8c2MHaJQKbDxyGrdM24ipP2Wi0mgSHY/+hGWkGSdKqmG2yPDTqhDBlTRERC5Jp1Zi0pAErJl4HW7sHIp6s4xPNmThxvfW47v0PFi4N4nTYBlpRtNKmjCupCEicnXtQnww76FrMPfBFMQGe6O4woiJS/fgrllbsD2rVHQ8AstIsxonr3bi5FUiIrcxuEsYfnnuOjw/NAE+GiX25JVj5Kfb8PiCNGRxPolQLCPNOL8NPCevEhG5E51aiQk3dMD652/A6L4xUEjAmoOnMOTDjfjXyn04ZagVHdEjsYw040jTAXkcGSEickdt/LR4+64e+OW563BDQhuYLDIWbsvBdf9dh//8eBBnqupER/QoLCN/YjSZcZIraYiIPELHMD/Mf7gPvn68H1JiA2E0WfDZpmwMevd3vL/mMM6ylDgEy8ifZJ2ualpJE+avFR2HiIgcoF98MJaN74/5D1+DbpH+qKoz4+Pfj2Hgu79j6upMFFfw9o09sYz8yR83O+NKGiIizyFJEm5ICMX/nroWs+/vjS4R/qiuM+OTjVkY9O46vPr9fuSeqRYd0y2pRAdwNseKG8+k4S0aIiJPpFBIGNYjArd0D8e6w8X4+PdjSM8pw4LUk1i47SRu6R6ORwbGITk2kP9otRGWkT85PzLCMkJE5MkkScKNncNwQ0IoUo+XYtb649h8rASr9xVh9b4i9IrS45Fr43BL93BoVUrRcV0ay8ifHOVpvURE9AeSJGFAhxAM6BCCQ0UGzNucjZUZBdiTV45nv85AkI8G9yRHYVSfGMSF+IiO65Ik2QWOMjQYDNDr9SgvL4e/v7/dPqfSaELP13+BRQa2vzQYYf7cCp6IiC5WUmnEwm0nsWRHDk4ZjE3P948Pxt9SojC0Wzh8tPz3fku/v3ml/uDj347CIgOxwd4I9eNKGiIial6IrxbP3dQJT93QAesOn8aSHTlYd7gYqVmlSM0qhU69Dzd3DcediZG4rlMbqJVcL3I5HBk551CRAbdP3wyTRcbcB1MwuEuYXT6HiIjcU35ZDZal5eL7jAJkl1Q1PR/grcaNnUMxpGs4rusUAm+N54wDtPT7m2UEgMUi495PUpF28iyGdgvDJ2NSbP4ZRETkGWRZxt68cqzMyMf/9hSipPL8bRytSoFrO4TgL51DMbB9MOJCfNx6RU5Lv79bNW40a9YsxMXFQafTITk5GZs2bbrs6zds2IDk5GTodDrEx8djzpw5rflYu/l2Vx7STp6Ft0aJ14Z3Ex2HiIhcmCRJ6BUdgNeGd8O2KTfi68f7Ydy1cYgO8oLRZMFvh4rxysr9uPH9DRjwzu/4xzd7sHxXHrJLquAC4wN2YfXIyNKlSzFmzBjMmjULAwcOxCeffILPP/8cBw8eRExMzEWvz87ORvfu3fHYY4/hiSeewJYtW/Dkk09iyZIlGDFiRIs+054jI2eq6nDj++tRVl2Pl2/tgseui7fp709ERAQ0jJgcPlWBXw+ewuZjJdh9sgx1ZssFr9F7qdErOgCJUXp0a6tHx1BfxAR5Q+Wic07sdpumb9++6N27N2bPnt30XJcuXXDnnXdi6tSpF73+n//8J1atWoXMzMym58aPH489e/YgNTW1RZ9pzzLy/LI9WLYrD53D/fC/p6/lJCMiInKImjoz0k6ewZZjpdiRXYr9BQbUmSwXvU6jVCC+jQ/ah/oiOtAbbQN0iNB7ITLAC2H+Wui91E5bVuyymqaurg67du3Ciy++eMHzQ4YMwdatW5t9T2pqKoYMGXLBc0OHDsXcuXNRX18PtVp90XuMRiOMxvP32AwGgzUxW2xH9hks25UHAPjPXd1ZRIiIyGG8NEoM6tgGgzq2AQDUmSw4XFSBjLwyZOSU4fApA44VV6K23oJDRRU4VFRxyd/LT6dCgLcaAV4aeGmU0KmV0KkU8NIooVEqoFRIUCgkKCRAKUnNzlO5JzkK3dvq7fbzXo5VZaSkpARmsxlhYReuNAkLC0NRUVGz7ykqKmr29SaTCSUlJYiIiLjoPVOnTsUbb7xhTTSrybKM11cdAACM6hON5Nggu34eERHR5WhUCvSI0qNHlB5j+sUCaFhgkV9Wg6PFFTheXIX8shoUlNWgsLwW+WU1OHPuVOGKWhMqak3IRU2rP793bKBrlJFGf25UsixfdjZwc69v7vlGU6ZMwaRJk5p+bTAYEB0d3Zqol8304chEvLfmMP55S2eb/t5ERES2oFBIiA7yRnSQN25s5qvKZLagvKYeZTX1KKuuQ1l1PWrqzaitt6Cm3gxjvRlGkwWyLMNsAcyyDIul+dkZHUPF7TxuVRkJCQmBUqm8aBSkuLj4otGPRuHh4c2+XqVSITg4uNn3aLVaaLX233QsIdwPn43lMl4iInJNKqUCwb5aBPu69kadVk2S0Gg0SE5Oxtq1ay94fu3atRgwYECz7+nfv/9Fr1+zZg1SUlKanS9CREREnsXqGZuTJk3C559/jnnz5iEzMxMTJ05ETk4Oxo8fD6DhFsvYsWObXj9+/HicPHkSkyZNQmZmJubNm4e5c+di8uTJtvspiIiIyGVZPWdk5MiRKC0txZtvvonCwkJ0794dq1evRmxsw2SbwsJC5OTkNL0+Li4Oq1evxsSJEzFz5kxERkZi+vTpLd5jhIiIiNwbt4MnIiIiu7DrdvBEREREtsIyQkREREKxjBAREZFQLCNEREQkFMsIERERCcUyQkREREKxjBAREZFQLCNEREQkFMsIERERCWX1dvAiNG4SazAYBCchIiKilmr83r7SZu8uUUYqKioAANHR0YKTEBERkbUqKiqg1+sv+d9d4mwai8WCgoIC+Pn5QZIkm/2+BoMB0dHRyM3N5Zk3dsTr7Di81o7B6+wYvM6OY69rLcsyKioqEBkZCYXi0jNDXGJkRKFQICoqym6/v7+/P/+gOwCvs+PwWjsGr7Nj8Do7jj2u9eVGRBpxAisREREJxTJCREREQnl0GdFqtXjttdeg1WpFR3FrvM6Ow2vtGLzOjsHr7Diir7VLTGAlIiIi9+XRIyNEREQkHssIERERCcUyQkREREKxjBAREZFQbl9GZs2ahbi4OOh0OiQnJ2PTpk2Xff2GDRuQnJwMnU6H+Ph4zJkzx0FJXZs113nFihW4+eab0aZNG/j7+6N///745ZdfHJjWdVn757nRli1boFKpkJiYaN+AbsTaa200GvHyyy8jNjYWWq0W7du3x7x58xyU1nVZe50XLVqEXr16wdvbGxEREXj44YdRWlrqoLSuaePGjRg+fDgiIyMhSRJWrlx5xfc4/LtQdmNff/21rFar5c8++0w+ePCg/Oyzz8o+Pj7yyZMnm319VlaW7O3tLT/77LPywYMH5c8++0xWq9Xyt99+6+DkrsXa6/zss8/K7777rrxjxw75yJEj8pQpU2S1Wi3v3r3bwcldi7XXuVFZWZkcHx8vDxkyRO7Vq5djwrq41lzrO+64Q+7bt6+8du1aOTs7W96+fbu8ZcsWB6Z2PdZe502bNskKhUL+6KOP5KysLHnTpk1yt27d5DvvvNPByV3L6tWr5Zdffllevny5DED+7rvvLvt6Ed+Fbl1G+vTpI48fP/6C5zp37iy/+OKLzb7+hRdekDt37nzBc0888YTcr18/u2V0B9Ze5+Z07dpVfuONN2wdza209jqPHDlS/te//iW/9tprLCMtZO21/umnn2S9Xi+XlpY6Ip7bsPY6/9///Z8cHx9/wXPTp0+Xo6Ki7JbR3bSkjIj4LnTb2zR1dXXYtWsXhgwZcsHzQ4YMwdatW5t9T2pq6kWvHzp0KNLS0lBfX2+3rK6sNdf5zywWCyoqKhAUFGSPiG6htdd5/vz5OH78OF577TV7R3QbrbnWq1atQkpKCv773/+ibdu26NSpEyZPnoyamhpHRHZJrbnOAwYMQF5eHlavXg1ZlnHq1Cl8++23uO222xwR2WOI+C50iYPyWqOkpARmsxlhYWEXPB8WFoaioqJm31NUVNTs600mE0pKShAREWG3vK6qNdf5z95//31UVVXh3nvvtUdEt9Ca63z06FG8+OKL2LRpE1Qqt/2/us215lpnZWVh8+bN0Ol0+O6771BSUoInn3wSZ86c4byRS2jNdR4wYAAWLVqEkSNHora2FiaTCXfccQc+/vhjR0T2GCK+C912ZKSRJEkX/FqW5Yueu9Lrm3ueLmTtdW60ZMkSvP7661i6dClCQ0PtFc9ttPQ6m81mjB49Gm+88QY6derkqHhuxZo/0xaLBZIkYdGiRejTpw9uvfVWfPDBB/jiiy84OnIF1lzngwcP4plnnsGrr76KXbt24eeff0Z2djbGjx/viKgexdHfhW77z6WQkBAolcqLGnZxcfFFja9ReHh4s69XqVQIDg62W1ZX1prr3Gjp0qUYN24cli1bhptuusmeMV2etde5oqICaWlpSE9Px1NPPQWg4QtTlmWoVCqsWbMGN954o0Oyu5rW/JmOiIhA27ZtLzgqvUuXLpBlGXl5eejYsaNdM7ui1lznqVOnYuDAgXj++ecBAD179oSPjw8GDRqEf//73xy9thER34VuOzKi0WiQnJyMtWvXXvD82rVrMWDAgGbf079//4tev2bNGqSkpECtVtstqytrzXUGGkZEHnroISxevJj3e1vA2uvs7++Pffv2ISMjo+kxfvx4JCQkICMjA3379nVUdJfTmj/TAwcOREFBASorK5ueO3LkCBQKBaKiouya11W15jpXV1dDobjwa0upVAI4/y93unpCvgvtNjXWCTQuG5s7d6588OBB+bnnnpN9fHzkEydOyLIsyy+++KI8ZsyYptc3LmeaOHGifPDgQXnu3Llc2tsC1l7nxYsXyyqVSp45c6ZcWFjY9CgrKxP1I7gEa6/zn3E1TctZe60rKirkqKgo+Z577pEPHDggb9iwQe7YsaP86KOPivoRXIK113n+/PmySqWSZ82aJR8/flzevHmznJKSIvfp00fUj+ASKioq5PT0dDk9PV0GIH/wwQdyenp60xJqZ/gudOsyIsuyPHPmTDk2NlbWaDRy79695Q0bNjT9twcffFC+/vrrL3j9+vXr5aSkJFmj0cjt2rWTZ8+e7eDErsma63z99dfLAC56PPjgg44P7mKs/fP8Rywj1rH2WmdmZso33XST7OXlJUdFRcmTJk2Sq6urHZza9Vh7nadPny537dpV9vLykiMiIuT7779fzsvLc3Bq17Ju3brL/p3rDN+FkixzbIuIiIjEcds5I0REROQaWEaIiIhIKJYRIiIiEoplhIiIiIRiGSEiIiKhWEaIiIhIKJYRIiIiEoplhIiIiIRiGSEiIiKhWEaIiIhIKJYRIiIiEoplhIiIiIT6f/oRJq5IM9vXAAAAAElFTkSuQmCC",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(*get_p_distribution(mu_p=.3, sensory_noise=1.))"
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p = np.linspace(1e-3, 1-1e-3, 100)\n",
"mu_p, posterior_noise = get_posterior(p, .5, .4, 1)\n",
"plt.plot(p, mu_p)\n",
"plot_identity_line()"
]
},
{
"cell_type": "code",
"execution_count": 177,
"metadata": {},
"outputs": [],
"source": [
"p = np.linspace(.05, 0.95, 12)\n",
"mu_p, posterior_noise = get_posterior(p, .5, .4, .75)\n",
"\n",
"grid, p_density = get_p_distribution(grid=np.linspace(1e-3, 1-1e-3, 100)[:, np.newaxis], \n",
" mu_p=mu_p[np.newaxis, :], sensory_noise=posterior_noise)"
]
},
{
"cell_type": "code",
"execution_count": 183,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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fvt3/mtvt5r333mPp0qXBnOqypmkUbpfYKAW7VULXobZRWD8EAoFAcPkyYstHe3s7J0+e9P985swZDh8+TEJCAlOmTOGf//mfWb9+PdnZ2WRnZ7N+/XoiIiJYuXJlUBd+OdM4ioBTSZJISTJzptJNzUUPk5MtoVqeQCAQCAQhZcTi46OPPmLZsmX+n33xGt/85jfZvHkz//Iv/4LD4eDuu++mqamJa6+9lm3bthEdHR28VV/m+Eqrx4/A7QKG6+VMpVtkvAgEAoHgsmbE4qOgoGDQ9sOSJPGzn/2Mn/3sZ4Gs64pFVXVa2nyWj+G7XaA76FT0eBEIBALB5YxoEhJmmttUdB1kGWKGWd3UR8oEw9UixIdAIBAILmeE+Agz/hofMSZkeWQZK8LyIRAIBIIrASE+wsxIutleii/dtq7Bg1cddVV8gUAgEFyGlJaWkp+fj91uJy0tjXXr1g0aBlFRUcG3v/1tMjMzsdvtTJ8+nZ/+9Ke43e5e4+6//34WLVqE1WplwYIFIX4XBiEpMiYYGF+Nj+F0s72U+BgFi1nC7dGpb/T6xYhAIBAIrmxaW1tZvnw5y5Yto6SkhPLyclavXk1kZCQPPPBAv8d8+umnaJrGr371K7Kysjh69Chr1qyho6ODJ5980j9O13W+9a1vsW/fPj7++OOwvB8hPsKMv7rpCDNdAGRZIjnJzPlqN9X1biE+BAKBYAwoKCggJycHgJdeeglFUbjrrrt49NFHB6zmHShbt27F6XSyefNmrFYrOTk5lJeXs3HjRgoLC/ud9+abb+bmm2/2/zxt2jTKysp49tlne4mPp59+GoCLFy+GTXwIt0uY6a7xMXK3C/SI+xDptgKB4ApD13Xc3vBvo2nuvmXLFkwmE/v27ePpp5+muLiY5557bsDxu3fvJioqatBt/fr1Ax6/Z88e8vPze1UEX7FiBVVVVVRUVAx73S0tLSQkJAx7fKgQlo8w0zTKGh8+fNYO0eNFIBBcaXhU2PAHLezzPvAVGcsIL8np6ekUFxcjSRIzZ86ktLSU4uJi1qxZ0+/43NxcDh8+POg5BxMFNTU1ZGRk9HrN17akpqaGzMzMIdd86tQpNm3axIYNG4YcG2qE+Agzo+lo2xOR8SIQCARjz5IlS3q5OvLy8tiwYQOqqqIofa/vdrudrKysgObsr2lrf6/3R1VVFTfffDNf+9rX+M53vhPQOoKBEB9hZjSl1Xvis3wIt4tAILjSMCuGFWIs5g01u3fv5pZbbhl0TFFREUVFRf3uS0lJoaamptdrdXV1AAM2bvVRVVXFsmXLyMvL49e//vUIVh06hPgIIx6vTmt7YOKjp+VD1XSUEdYKEQgEgvGKJEkjdn+MFXv37u3zc3Z2dr9WDwjc7ZKXl0dRURFutxuLxSg4uW3bNlJTU/u4Y3pSWVnJsmXLWLRoES+88AKyPD5CPS+TX/OVQUub4XIxKRAdObovQGK8CZMCXhUam71MSBAZLwKBQBBuzp8/T2FhId/97nc5ePDgkLEUgbpdVq5cySOPPMLq1aspKirixIkTrF+/nocfftjvdtm/fz+rVq3inXfeIS0tjaqqKgoKCpgyZQpPPvkkFy9e9J8vJSXF/++TJ0/S3t5OTU0NDofDL5LmzJnjFzrBRoiPMOJzucTHmkadjqXIEknxZmrqPdQ3CfEhEAgEY8GqVatwOBwsXrwYRVG47777WLt2bcjmi42NZfv27dxzzz3k5uYSHx9PYWGhv7krQGdnJ2VlZXg8hlt+27ZtnDx5kpMnTzJ58uRe5+uZ4fOd73yH9957z//zwoULAaNr/WBWlUAQ4iOMBFLjoyeJcQo19R4amr3BWJZAIBAIRojZbOapp57i2WefDduc8+bNY9euXQPuv7Tx6+rVq1m9evWQ5925c2cQVjcyxofz5zNCU4CZLj4S4wzxUi/Eh0AgEAguQ4T4CCONAZRW74lPfAjLh0AgEAguR4TbJYx0u10Cs3wkCfEhEAgEY8ZYuCmuNITlI4x0d7QNjuWjvkmID4FAIBBcfgjxEUZ6ZrsEgnC7CAQCgeByRoiPMOLr6zLapnI+fOKjuU3Fq468IZJAIBAIBGOJEB9hwuPRaeswGiYF6naJiVIwKaDr3a4cgUAgEAguF4T4CBM+q4fZJBFpD+xjl2VJpNsKBAKB4LJFiI8w0d5pWD2iI+VRVzftiYj7EAgEAsHlihAfYaLDYQSbRtqD0z5RiA+BQCAQXK4I8REmOhyG5SMiQJeLDyE+BAKBIHzoXi/u2hq8rS1jtobS0lLy8/Ox2+2kpaWxbt26XuXU++P2229nypQp2Gw2Jk2axJ133klVVVWvMefOneO2224jMjKSpKQkvv/97+N2u0P5VoT4CBedTkN8BBrv4UPU+hAIBILwoDqdOM+dxdvSjLu2Fl1Tw76G1tZWli9fTmpqKiUlJWzatIknn3ySjRs3DnrcsmXL+P3vf09ZWRmvvvoqp06d4qtf/ap/v6qq3HrrrXR0dPD+++/z29/+lldffZUHHnggpO9HVDgNEx2doREfwvIhEAgEocPb2oq7ttpILwTQNQo+n8+8BQsAeOmll1AUhbvuuotHH300KDF9/bF161acTiebN2/GarWSk5NDeXk5GzdupLCwcMB5f/CDH/j/PXXqVH784x/z5S9/GY/Hg9lsZtu2bRw/fpzz58+TmpoKwIYNG1i9ejWPPfYYMTExIXk/wvIRJnwxHxG24HzkSfFCfAgEgisLXQePGv6tP8+Fruu462px11SBriNHRmKKTzD2qSpbtmzBZDKxb98+nn76aYqLi3nuuecGfG+7d+8mKipq0G39+vUDHr9nzx7y8/OxWq3+11asWEFVVRUVFRXD+nwbGxvZunUrS5cuxWw2+8+bk5PjFx6+87pcLg4cODCs844GYfkIE6FyuzS3qqiqjqKERm0LBAJBuPBq8Mr74Z/369eD+ZJcAE9dLd6WZgBMCYmYE5PQvV68TY2gqaRPnkxxcTGSJDFz5kxKS0spLi5mzZo1/c6Rm5vL4cOHB11HQkLCgPtqamrIyMjo9VpycrJ/X2Zm5oDH/uhHP+KZZ56hs7OTJUuW8MYbb/Q6r+88PuLj47FYLNTU1Ay63kAQlo8w0R1wGpxsl9goBUUGTe+uISIQCASCwNE1DW9bKwCWlElYkiYgSRKy2YwcEQHA4qsX9nJ15OXlceLECVS1/3gQu91OVlbWoNtg4gPo41rxBZsO5er54Q9/yKFDh9i2bRuKorBq1apegar9Ha/reshcSCAsH2HDJz6CZfmQZYmEOBMXG700NHtJijcH5bwCgUAwVphkwwoxFvP2RHM6QNOQFAUlunfMgykm1hjj9ozoBr17925uueWWQccUFRVRVFTU776UlJQ+loi6ujqAPpaLS0lKSiIpKYkZM2Ywe/Zs0tPT2bt3L3l5eaSkpLBv375e45uamvB4PEOeNxCE+AgTnUEWHwBJfvER/shrgUAgCDaS1Nf9MRaoHR0AyJFRfcSFEhUFSJQcOoTmdKDYDUvI3r17yc7ORlH6fwOBul3y8vIoKirC7XZjsVgA2LZtG6mpqX3cMYPhs3i4XC7/eR977DGqq6uZNGmS/7xWq5VFixYN+7wjRbhdwkSw63xAz3RbT9DOKRAIBJ911I52AJTIyD77JFkBReFCdTWFP/gBZWVlvPLKK2zatIn7779/wHMG6nZZuXIlVquV1atXc/ToUV577TXWr1/fK9Nl//79zJo1i8rKSv/PzzzzDIcPH+bs2bO8++67rFy5kunTp5OXlwfATTfdxJw5c7jzzjs5dOgQ77zzDv/3//5f1qxZE7JMFxCWj7DR6a9wGnzxITJeBAKBIDhoHg96V4EtJaKv+ACQTAorv3wHna2tLF68GEVRuO+++1i7dm3I1hUbG8v27du55557yM3NJT4+nsLCQgoLC/1jOjs7KSsrw+MxHkjtdjt/+MMf+OlPf0pHRweTJk3i5ptv5re//a0/a0ZRFP7yl79w9913c91112G321m5ciVPPvlkyN4LCPERNrpjPoJnU+xOtxVuF4FAIAgGPquHbLcjDeBCkWQFs8XKfzz4I5795a8whdBC0JN58+axa9euAfcXFBT0CiSdN28eO3bsGPK8U6ZM6ZUBEw6E2yUM6Lruj/kIhdtFWD4EAoEgOGhd8R4DWT18SF1xF2NZbv1yRoiPMOB06WhdYjQUbpd6IT4EAoEgYHRNQ+3sBIxg08GQu8SH1tmB5hVxdyNFuF3CgM/lYlLAYg5e3rRPfDS1ekWhMYFAIAgQzeEAXUNSTMg9Koleys6dOwFwnjuL5nSgtrcjx8WHaZVXBsLyEQb8pdXtSlCLtsRGdxUa06C5TcR9CAQCQSD44z0iI4d1rZbtdgB/gKpg+AjxEQaCXVrdhyJLxMeK7rYCgUAQDNTOrniPIVwuPvyuFyE+RowQH2EgFDU+fIigU4FAIAgcze3usmBIKF0l1IfCF3QqLB8jR4iPMNDRGRrLBwjxIRAIBMHAZ/UYLMX2UmRzl/jwetA1LWRruxIR4iMM+NwuEbbgf9z+Wh8tQnwIBALBaNEGqWo6IIoCsiFUdI+wfowEIT7CQIe/umnwmxYkipgPgUAgCIieKbYjER+SJIm4j1EixEcYCEWBMR/C7SIQCASBYaTY6kgmE5Jl4BTb/hBxH6NDiI8w0BGCjrY+ukusC/EhEAgEo0FzOgCQ7REjLocgm83GOcLgdiktLSU/Px+73U5aWhrr1q3rVU69P26//XamTJmCzWZj0qRJ3HnnnVRVVfUaU1JSwo033khcXBzx8fHcdNNNQ3bgDRQhPsJAKMWHv9BYixdVG/xLKBAIBIK+aF3t5QcrLDYQPktJqC0fra2tLF++nNTUVEpKSti0aRNPPvkkGzduHPS4ZcuW8fvf/56ysjJeffVVTp06xVe/+lX//ra2NlasWMGUKVPYt28f77//PjExMaxYscLfoC4UiAqnYaDTX2Qs+OIjLkZBlkHVoKVNJSFW/EoFAoFgJGguJwCyzTas8QUFBeTk5ADw0ksvoUjwna9/ncef+U9kOTTP9Fu3bsXpdLJ582asVis5OTmUl5ezceNGCgsLB7TY/OAHP/D/e+rUqfz4xz/my1/+Mh6PB7PZTFlZGU1NTaxbt4709HQAfvrTnzJ//nzOnTvH9OnTQ/J+hOUjDISio60PRZaIjxGuF4FAcPmj6zqqFt7N6/GiuY0n/JFYPrZs2YLJZGLvnj088ZOf8MzmLfzm178ecPzu3buJiooadFu/fv2Ax+/Zs4f8/HysPda4YsUKqqqqqKioGNaaGxsb2bp1K0uXLsXc5S6aOXMmSUlJPP/887jdbhwOB88//zxz585l6tSpw/swRoF4TA4DnSF0uwAkxZloaPbS0OwlO3TfFYFAIAgpmg7vHg1/4Oa1VgmTSUFShn9LTE9Pp7i4GEmSmGqzcKy8nF/84hd893vf63d8bm7ukHEUCQkJA+6rqakhIyOj12vJycn+fZmZmQMe+6Mf/YhnnnmGzs5OlixZwhtvvOHfFx0dzc6dO7njjjt49NFHAZgxYwZvv/02JlPoJIKwfISBUFY4hR7dbUW6rUAgEIwK2To8l4uPJUuW+F0dktnCtQsWcOLkSVS1/z5bdrudrKysQbfBxAfQx7XiCzYdKkj2hz/8IYcOHWLbtm0oisKqVav8xzocDr71rW9x3XXXsXfvXj744APmzp3LF7/4RRwOx7A+i9EQdFnj9Xr52c9+xtatW6mpqWHSpEmsXr2ahx56KGS+sPFOqHq7+EiMM9w5wu0iEAguZ2QJluVYwjqnq7YGvVVHGqH46Imv1sdg7N69m1tuuWXQMUVFRRQVFfW7LyUlhZqaml6v1dXVAd0WkIFISkoiKSmJGTNmMHv2bNLT09m7dy95eXm8/PLLVFRUsGfPHv89+uWXXyY+Pp4//elP/H//3/835HsbDUEXHz//+c/55S9/yZYtW5g7dy4fffQR//RP/0RsbCz3339/sKcb97g9Gm6PoTBDJz66LB9CfAgEgssYSZJQgtf4e3hzup0ggWwbWabL3r17u89hsbD/yBGyMjNRBijNHqjbJS8vj6KiItxuN5YusbNt2zZSU1P7uGMGw2fxcHVl+HR2diLLci/rie9nLYQl44N+N9yzZw933HEHt956KxkZGXz1q1/lpptu4qOPPgr2VJcFvngPSQK7NbTio1GID4FAIBg2uqahu4wYk5G6Xc6fP09hYSFlZWX8/o9/5JcvbeXu1asGHB+o22XlypVYrVZWr17N0aNHee2111i/fn2vTJf9+/cza9YsKisr/T8/88wzHD58mLNnz/Luu++ycuVKpk+fTl5eHgDLly+nqamJe+65h08++YRjx47xT//0T5hMJpYtWzaiz2QkBP1ueP311/POO+9QXl4OwJEjR3j//ff54he/2O94l8tFa2trr+1KwudysdtkZDk0kj7BJz5EfxeBQCAYNkZJdB1kBWmEwZWrVq3C4XCwePFi7it8gO/94zf41t9/dciiX6MlNjaW7du3c+HCBXJzc7n77rspLCyksLDQP6azs5OysjJ/fQ673c4f/vAHbrzxRmbOnMm3vvUtcnJyeO+99/xZM7NmzeLPf/4zH3/8MXl5eXzuc5+jqqqKt956i0mTJoXkvUAI3C4/+tGPaGlpYdasWSiKgqqqPPbYY3z961/vd/zjjz/OI488EuxljBtCWWDMh6+/S2OLiq7rI67QJxAIBJ9FdH99D+uIr5tms5mnnnqKZ599Fl3XcZw8AbqG7nGPuET7cJk3bx67du0acH9BQUEv8TNv3jx27Ngx5HmXL1/O8uXLg7LG4RL0O+Lvfvc7XnrpJV5++WUOHjzIli1bePLJJ9myZUu/4x988EFaWlr82/nz54O9pDGlozN0HW19xHeJD49Xp61DtHUWCASC4dBd2XT0waYgGsyNhqBbPn74wx/y4x//2B8hO2/ePM6ePcvjjz/ON7/5zT7jrVZrr6IpVxqhznQBMJskYqIUWttVGlq8xEQFv5iZQCAQXGlozi7LRxDuQZLFAi6naDA3TIIuPnyRsz1RFCWkUbPjmY4QllbvSWKsIT4am71kpl25Yk4gEAiCga7ro7Z87Ny5s89rkllYPkZC0MXHbbfdxmOPPcaUKVOYO3cuhw4dYuPGjXzrW98K9lSXBaEsrd6TxDgTZyrdIuhUIBAIhoHucYOugSQZVosA8bld9BA2Y7uSCLr42LRpE//6r//K3XffTV1dHampqXz3u9/l4YcfDvZUlwWhLq3uw5fxIgqNCQQCwdD0tHoEI0jfJ2B0tyvgc30WCLr4iI6O5qmnnuKpp54K9qkvS0JdWt2Hr5ttQ3P/pX0FAoFA0E0w4z0A5K5Gbbqqoqsq0gDFxgQGn81652HEF/MRastHd7qtsHwIBALBUPgsH4GUVe+JpHTXChFxH0MjxEeI6QxTzEdCV38XIT4EAoFgcHRd767xEcRsS1/Qqe4R4mMohPgIMX63SwjrfEBPt4sQHwKBQDAYuteLrqqAFFTxIWp9DB8hPkKMP9slIsRul66A0/ZODZf7s5nWLBAIBMPB73KxWJCC2G29O+hUiI+hEOIjxISjyJjv/BazEbHd1CKCTgUCgWAgQuFygR6WjxC5XUpLS8nPz8dut5OWlsa6deuG3UvG5XKxYMECJEnqt7vu5s2bmT9/PjabjZSUFO69994gr743Qc92EfSmo7OryFiI3S6SJJEYZ6L6ooeGFi8pE8whnU8gEAguV4JVVv1S/DEfbnfQ+2y1trayfPlyli1bRklJCeXl5axevZrIyEgeeOCBIY//l3/5F1JTUzly5EiffRs3bmTDhg088cQTXHvttTidTk6fPh20tfeHEB8hRNV0HC5DlYY64BQgIVah+qJHBJ0KBALBIGg9GsqNhoKCAnJycgB46aWXUBSFu+66i3W+Jqm6DpoGQUy33bp1K06nk82bN2O1WsnJyaG8vJyNGzdSWFg4qNB588032bZtG6+++ipvvvlmr31NTU089NBD/PnPf+bGG2/0vz537tygrb0/hNslhDic3bEXoa7zASLoVCAQXN7ouo6maSHdVK+K6vGgAZgsaJo2bNdFT7Zs2YLJZGLfvn08/fTTFBcX8/x//zfIhuDQvb2vw7t37yYqKmrQbf369QPOt2fPHvLz83v1QluxYgVVVVVUVFQMeFxtbS1r1qzh//2//0dERESf/du3b0fTNCorK5k9ezaTJ0/mH/7hH0Le5FVYPkKIL9jUYpYwm0Lf5t4XdCosHwKB4HJE13WOn64L/URynPH/cw0AzJk2ccQukvT0dIqLi5EkiZkzZ1JaWkpxcTH/uPwL6G7VEB89hEJubm6/sRY9SUhIGHBfTU0NGRkZvV5LTk7278vMzOxzjK7rrF69mu9973vk5ub2K1JOnz6NpmmsX7+eX/ziF8TGxvLQQw+xfPlyPv74YyxBKD3fH0J8hJCOzvAEm/rwWT4aRZVTgUAgCClLlizpJVjy8vLYsGEDmiQhAbra+yHQbreTlZUV0JyXCiSfxWYg4bRp0yZaW1t58MEHBzynpml4PB6efvppbrrpJgBeeeUVUlJSePfdd1mxYkVAax4IIT5CSKczPNVNffjdLsLyIRAILkMkSWLOtIkhncPdUI+3qRFTTByWiRP98wYLyWQCV/9ul1tuuWXQY4uKiigqKup3X0pKCjU1Nb1eq6szrEQ+C8il7Nixg7179/Zy1YBhhfnGN77Bli1bmDRpEgBz5szx758wYQJJSUmcO3du0PUGghAfISRcfV18JIrmcgKB4DJGkqSgCoF+5/B4kAHFakEOoMbH3r17+/ycnZ2NyWLB29FXfATqdsnLy6OoqAi32+13hWzbto3U1NQ+7hgfTz/9NP/2b//m/7mqqooVK1bwu9/9jmuvvRaA6667DoCysjImT54MQGNjI/X19UydOnXQ9QaCEB8hpCNMpdV9JHaVWG9q8aJpOrIc+jgTgUAguJzQurrOypbAanycP3+ewsJCvvvd73Lw4EE2bdrEhg0b/P1dLhUfgbpdVq5cySOPPMLq1aspKirixIkTrF+/nocfftgv2Pbv38+qVat45513SEtLY8qUKb3OERUVBcD06dP9QmPGjBnccccd3H///fz6178mJiaGBx98kFmzZrFs2bJRr3cohPgIIZ1htnzExZiQJFA1aG1XiYsRv16BQCDwoWsautsDdFcjHS2rVq3C4XCwePFiFEXhvvvuY+3atajtbcZcanAt0LGxsWzfvp177rmH3Nxc4uPjKSwspLCw0D+ms7OTsrIyPB7PiM794osv8oMf/IBbb70VWZbJz8/nrbfewmwOXb0ocXcKId2Wj/CID5MiERut0Nyq0tDiFeJDIBAIeqB7PIAOsuy3UIwWs9nMU089xbPPPtvr9YEsH8Fg3rx57Nq1a8D9BQUFg6YNZ2Rk9Ls/JiaG559/nueffz4o6xwOos5HCOlwhDfgFCBRZLwIBAJBv/gavskWS8hiSySlW3yMpn7IZwUhPkJIZ5g62vbEn24rMl4EAoGgF7rb11AuuD1deuK3qPiqnAr6RdjlQ0i4A04BErqCTkW6rUAgEPSmp+UjEHbu3DngPkmWQZZB09C9XqQglli/khCWjxDiFx8RY+F2EeJDIBAIeqKFwfIBPeI+ghx0eiUhxEcIGRO3iyixLhAIBH3QdR09SJaPoegZ9yHoHyE+QshYBJx2VzkVAacCgUDgQ/d4jDgMSUIKYQophDbj5UpBiI8QMhYxH8LtIhAIBH3xxXtIIcx08dHtdhEPgQMhxEeI0HWdTmd4i4xBd8Bph0PD5RaR1gKBQADdmS6BVjYdDsLtMjRCfIQIp1v3Z1mF0+0SYZOxWQxVL3q8CAQCgUGwMl2Gg3C7DI0QHyGio9NQHooMVkv4eqxIkiQazAkEAsEldNf4CKP4ENkuAyLER4jodBq+vgi7HHL/4qV0Z7wIf6NAIBDout7D8hEGt4vJcH8H2/JRWlpKfn4+drudtLQ01q1bN2QV1YyMDH+3YN/24x//uN+xDQ0NTJ48GUmSaG5uDuraL0UUGQsRYxFs6sOf8SIsHwKBQGCIAE0DQp/pAt0xH2gauqYiyYHfB1pbW1m+fDnLli2jpKSE8vJyVq9eTWRkJA888MCgx65bt441a9b4f/Z1t72Ub3/728yfP5/KysqA1zsUQnyEiI4xqPHhIzHW+KKLWh8CgUCAv76HZDEbFUgDpKCggJycHABeeuklFEXhrrvu4tFHHzWsC4rSo8qpimQJXHxs3boVp9PJ5s2bsVqt5OTkUF5ezsaNGyksLBzUwh4dHU1KSsqg53/22Wdpbm7m4Ycf5s033wx4vUMh3C4honMMqpv6EIXGBALB5Yiu62iaGvRNdTnQdR3JbOl3/2gawG3ZsgWTycS+fft4+umnKS4u5rnnnvPvvzTjZffu3URFRQ26rV+/fsD59uzZQ35+PlZrt9toxYoVVFVVUVFRMehaf/7zn5OYmMiCBQt47LHHcHeJMR/Hjx9n3bp1vPjii8hBEGfDQVg+QkS322UMxIdwuwgEgssQXdeoLS8N3QRtLmir7/Ny8ox5SNLIrBPp6ekUFxcjSRIzZ86ktLSU4uJiv3tDMpnQPW6/+MjNzeXw4cODnjMhIWHAfTU1NWRkZPRed3Kyf19mZma/x91///1cffXVxMfHs3//fh588EHOnDnjF0oul4uvf/3rPPHEE0yZMoXTp08P5+0HjBAfIcJX3XRM3C4i4FQgEAhCypIlS3q5OvLy8tiwYQOqqqIoSp+MF7vdTlZWVkBzXupa8VlsBnO5/OAHP/D/e/78+cTHx/PVr37Vbw158MEHmT17Nv/4j/8Y0NpGihAfIaJzHFg+mlq9qJqOIoc320YgEAhGgyTJJM+YF/TzOk6fAlXFmj4V2dY320WSgn+d9nWz7el2ueWWWwY9pqioiKKion73paSkUFNT0+u1uro6oNsCMhyWLFkCwMmTJ0lMTGTHjh2Ulpbyv//7v8Z6uwRNUlISP/nJT3jkkUeGfe6RIMRHiBjLbJe4aAVZMoK7W9pUvxgRCASC8YyRChrca6bu9SJpGkgSis0WlIBTgL179/b5OTs7G6VLdFxaaCxQt0teXh5FRUW43W4sXbVKtm3bRmpqah93zGAcOnQIgEmTJgHw6quv4nA4/PtLSkr41re+xe7du5k+ffqwzztSxF0pRPizXcbA8qEoEnExCo0tKo0tXiE+BALBZxZ/TxdTcDJdfJw/f57CwkK++93vcvDgQTZt2sSGDRv8+4Ptdlm5ciWPPPIIq1evpqioiBMnTrB+/Xoefvhhv9tl//79rFq1infeeYe0tDT27NnD3r17WbZsGbGxsZSUlPCDH/yA22+/nSlTpgD0ERj19UZMzOzZs4mLixv1eodC3JVChGMM+rr0JDHORGOLSkOzl6wpY7IEgUAgGHM0X2VTa3Arm65atQqHw8HixYtRFIX77ruPtWvX+vcHu8R6bGws27dv55577iE3N5f4+HgKCwspLCz0j+ns7KSsrAyPxwOA1Wrld7/7HY888ggul4upU6eyZs0a/uVf/iUoawoEIT5ChL+p3BgEnIIhPk6cdVHfJDJeBALBZxc9RJVNzWYzTz31FM8++2y/+0PRXG7evHns2rVrwP0FBQW90oavvvrqPu6hobj0HKFC1PkIEU6XIT5s1rETHyDSbQUCwWebcDaU64nP8mFUORUdxi9FiI8QMdaWj6R4IT4EAoHAX93UHF7xgSxDVyyG6G7bF+F2CRG+mA/7GFk+krosH8LtIhAIPqvomobuNeIfgmn52Llz55BjJEnqKjTm6Qo6DbP4GecIy0cI0HW9W3yMseWjXlg+BALBZxSf1QNZASX8ZQ+CHXR6JSHERwjweHXULhef3TY2Bb4S44zOjY3NRqExgUAg+KyhebrjPQarAhoqQhF0eqUgxEcI8MV7wNgFnMbHGIXG1K5CYwKBQPBZo7ub7di4PITlY2CE+AgBTqdhabBZpDErba4oEvFBaDDn9ugcO+PhbI2Xtk4tLClYAoFAEAzGKtPFR3ehMfEAeCki4DQE+CwftjGK9/CRFGeiodlLfZOX7KkjP97t0fmv1zo4eaH7D8dsgoRombnTTNzxOZvoGyMQCMYtY275EG6XARGWjxDgcI1tmq2PxPjRZ7x4VZ3n3+jk5AUViwliIyUkwOOF2iaNHQfc/O+7TmEJEQgE4xJd18eP5UOIjz4Iy0cI8ImPsUqz9THajBdN03nxLQfHzngxm+Dur0SSNdmEx6vT3K5Rdk7ld39zsPuIm8QYmS9cE9zKgQKBQBAoutcLutFQLuw1Prq4tL+LoBth+QgBY51m6yPRF/MxAsuHruv89m8ODpZ5UGRYc1sEWZON85hNEhPiFK6fb+ErBTYA/rjbyYEyd/AXLxAIBAHQXVzMPCaZLgCSqSu9V1WDUuW0tLSU/Px87HY7aWlprFu3bljW57/85S9ce+212O12kpKS+MpXvuLfd+TIEb7+9a+Tnp6O3W5n9uzZ/OIXvwh4rUMhLB8hYKwLjPkYTZXTP+5y8uFRD5IEq78YwZxMc7/jll1tpaFFY+chN//vLQexkbJfpAgEAsFY42soF+yeLiNCVowqp7qOrqoBddVtbW1l+fLlLFu2jJKSEsrLy1m9ejWRkZE88MADAx736quvsmbNGtavX88NN9yAruuUlpb69x84cIAJEybw0ksvkZ6ezocffsjatWtRFIV777131OsdCnG3CAFjXVrdx0jdLmeqvLxzwHhaWLnczsIZ/QsPH1/Jt9HYqvHxKS+//lMnD6yMJDk+/IV8BAKB4FJ6Wj6CTUFBATk5OQC89NJLKIrCXXfdxaOPPtrLyiJJEpJiQvd6DDdQAGvZunUrTqeTzZs3Y7VaycnJoby8nI0bN1JYWNivdcfr9XL//ffzxBNP8O1vf9v/+syZM/3//ta3vtXrmGnTprFnzx7+8Ic/hFR8CLdLCPA3lRujAmM+fM3lmlq8qOrQprmdh4w/1sVzzOTlDO0jlWWJ1V+MICNFodOl8/t3nIEtWCAQfKbRdR1d9QZlU10OdF0zSpwPNX4UgfNbtmzBZDKxb98+nn76aYqLi3nuuef6jPPFfezetYuoqKhBt/Xr1w843549e8jPz8dq7bbkrFixgqqqKioqKvo95uDBg1RWViLLMgsXLmTSpEnccsstHDt2bND31tLSQkJCwjA+hdETEstHZWUlP/rRj3jzzTdxOBzMmDGD559/nkWLFoViunHHeLF8xEUrKLJRaKyp1UtS/MCqu7ld49AJowfCsoXDN1NazBL/dGsEj7zQRtk5LycveIX7RSAQjA5NpaPkr0E9pavpJK4hxkRe80VQRnbdSk9Pp7i4GEmSmDlzJqWlpRQXF7NmzZpe43zi4+r58zh8+PCg5xzshl9TU0NGRkav15KTk/37MjMz+xxz+vRpAH72s5+xceNGMjIy2LBhA/n5+ZSXl/c73549e/j973/PX/7yl0HXGihBv0s0NTVx3XXXsWzZMt58800mTpzIqVOniIuLC/ZU4xZHV5GxsY75kGWJhDgTFxuNWh+DiY/3j7jRNJieppCePDLXSWKsTN5cCx+UuvnrHiff/1pUoEsXCASCcc2SJUt6uTry8vLYsGEDqqqi9OgjI3X922Y2k5WVFdCcl7pWfBabgQJqta4g15/85Cf8/d//PQAvvPACkydP5n/+53/47ne/22v8sWPHuOOOO3j44YdZvnx5QGsdiqCLj5///Oekp6fzwgsv+F+7VK1d6YyXbBcwCo1dbPQOGnTq8ep8UGq4XPJHYPXoyYprrew95qb8vEr5eS8z0oX1QyAQjBBZMawQAaI6nbgunENSTNgzpw1r3lDhs3y8/8EH3P6Nfxx0bFFREUVFRf3uS0lJoaamptdrdXV1QLcF5FImTZoEwJw5c/yvWa1Wpk2bxrlz53qNPX78ODfccANr1qzhoYceGnSdwSDod4jXX3+dFStW8LWvfY333nuPtLQ07r777j6mqCsZf52P8SA+hhF0eqjcQ1unTlyUxFXTR/eVSIiRWTrPwu4jbv76oZPsf4gcs/Q2gUBweSJJ0ojdH/2iqkiSjGy1+auMBpu9e/f2+Tk7O7uX1QPwd9O9OicnILdLXl4eRUVFuN1uLF1F07Zt20ZqauqAD/iLFi3CarVSVlbG9ddfD4DH46GiooKpU7vLXh87dowbbriBb37zmzz22GODrjFYBP3uePr0aZ599lmys7N5++23+d73vsf3v/99XnzxxX7Hu1wuWltbe22XO53jJNUWuoNOB6pyqus673YFmn7uKguKMnrBcNNiKyYFTlaqlJ8XvQwEAsHYEI7KpufPn6ewsJCysjJeeeUVNm3axP33399nnN/tYjHcLoNtg4mPlStXYrVaWb16NUePHuW1115j/fr1vTJd9u/fz6xZs6isrAQgJiaG733ve/z0pz9l27ZtlJWVcddddwHwta99DTCEx7Jly1i+fDmFhYXU1NRQU1PDxYsXg/p5XUrQJaGmaeTm5vqjdhcuXMixY8d49tlnWbVqVZ/xjz/+OI888kiwlzGmOMeh5WMgt8uZapXztSomBZbOC+wPNT5a5rp5Ft477OYvHzqZkS6sHwKBIPyEo6fLqlWrcDgcLF68GEVRuO+++1i7dm2fcf7+LgE2l4uNjWX79u3cc8895ObmEh8fT2FhIYWFhf4xnZ2dlJWV4fF4/K898cQTmEwm7rzzThwOB9deey07duwgPj4egP/5n//h4sWLbN26la1bt/qPmzp16oBZNMEg6HfHSZMm9fIvAcyePbuPf8nHgw8+SEtLi387f/58sJcUdsZLkTEY2vLxXpfVI3eWmeiIwNe7fLEVswKnq1Q+OStKCgsEgvATDsuH2Wzm2WefpaWlhcbGRh5//PF+H7Z8lg/dG7g1eN68eezatQun00l1dTU//elPe81ZUFCAruu93DBms5knn3yS2tpaWltb2b59O3PnzvXv/9nPfmakOF+yhVJ4QAjEx3XXXUdZWVmv18rLy3v5l3pitVqJiYnptV3ujJdUWzACTqF/y0fP9NrRBppeSlyUzPVXGX/wf/3QJRrPCQSCsKLrOrpnbLvZ9sIXA6Kp4nrYg6DfHX/wgx+wd+9e1q9fz8mTJ3n55Zf59a9/zT333BPsqcYluq73cLuMvcvB19m2uU3F4+39xe+VXjsxeNHey6+xYjZBRY3KqUoR+yEQCMKH7vGArhsN5UzBr246UqQeAaiBul6uJIIe83HNNdfw2muv8eCDD7Ju3ToyMzN56qmn+MY3vhHsqcYlHq+Oz7o2HmI+YqMUzCYJj1enqcXLxMTuP0af1eNzVwX36SAmUiZ3ppk9xzzsOeYWRccEAkHY0HrEe4Qq5mznzp3DHmtk8CigqsZmEtdDCFGF0y996Ut86UtfCsWpxz2+AmMAtnEQ8yFJEolxJmrqPdQ3d4uPxlaN2kYNWYI5GcF/OliSY2HPMQ+Hyjx8tUDHbh17K5BAILjy0cMQ7zFSJEVBV1Vh+ejB2N8drzB8waY2i4Qij48bblI/QafHK4x/Z0xSiAiBe2haqkJyvIzbCwfLPEMfIBAIBEFA8xjF1CXz+BIfALoqgvB9CPERZBz+pnLj56NN7Cfo9JMKQxDMzgiNCVCSJH9zuj1H3SGZQyAQCC6l2/IRnCD6YBCsdNsrifFzh7xCGE+ZLj4SL6lyqqo6ZeeMf8+eGjr/4+I5ZmTZCDytrhd/dAKBIPRoYajxMVL8QadCfPgZP3fIKwR/afVxEO/hw59u2+V2qahRcbohwiYxZYRN5EZCTKRMTqYx955jwvohEAhCi+71+m/w4ynmA7/bRYgPH+PnDnmFMJ4KjPnw93fpEh+fVHRbPeQQx6X4XC/7j3vwqiLHXSAQhA6/1cNkRpLHzzVYxHz0Zfz8dq4QxlNHWx+Xul18waahivfoyZxMEzGREu0OndJT4g9PIBCEjvHocgER89Ef4+cOeYXgGEcFxnz43C6t7SqNrV7O1xp/AKGM9/ChyBLXzjEuBHuF60UgEIQQ3W1kuowrlws9LR+BiY/S0lLy8/Ox2+2kpaWxbt26Qaum7ty5E0mS+t1KSkr8486dO8dtt91GZGQkSUlJfP/738ftDu31WlQ7CTLj0fIRFSFjMUu4PToHP/WgA2lJMrFR4VljXo6Z7SUujld4aW7TiIseP5+NQCC4cvD3dLGOn0wXoLvEegD9XVpbW1m+fDnLli2jpKSE8vJyVq9eTWRkJA888EC/xyxdupTq6uper/3rv/4rf/vb38jNzQVAVVVuvfVWJkyYwPvvv09DQwPf/OY30XWdTZs2jXq9QyHER5AZjzEfkiSRFG+iqs7D8RCn2PbHxHiFrDSFk5Uqe4+7uflaW9jmFggEnx18lo9Qu10KCgrIyckB4KWXXkJRFO666y4effTRwZvLqUZ/l9FUXt26dStOp5PNmzdjtVrJycmhvLycjRs3UlhY2O85LRYLKSkp/p89Hg+vv/469957r3/8tm3bOH78OOfPnyc1NRWADRs2sHr1ah577LGQ9VsT4iPIdHZVOB1PqbZguF6q6jycrTXWNzsEVU0HY0mOhZOVDj76xCPEh0DwGUHXdRyH99L25u/ROtpBVoxAUFlGS05Hv+6WPuMZZVCmrqnobicAkiyhe0dQ3FAxjVgQbNmyhW9/+9vs27ePjz76iLVr1zJ16lTWrFnTZ6ykKHzw0Uf83ZrvwiDzFBUVUVRU1O++PXv2kJ+fj7WHVWfFihU8+OCDVFRUkJmZOeSaX3/9derr61m9enWv8+bk5PiFh++8LpeLAwcOsGzZsiHPOxqE+Agy3TEf40t8JMabMFkUXB6wmIwKpOHkqiwzv/2bg5pGjep6lUlJ4Z1fIBCEF7W5keb/eR7n0Y/63e/1qqitLajtrehWq3HzV7243nh21HP6rrruT3eM6Djrl+6CETahS09Pp7i4GEmSmDlzJqWlpRQXF/cvPmSZq+fPZ88f/4A1LX3AmJSEhIQB56upqSEjI6PXa8nJyf59wxEfzz//PCtWrCA9Pb3XeX3n8REfH4/FYqGmpmbIc44WIT6CzHiM+QCjyqnNZnzhZ0wxYTaFNyDWbpWYNdXE0dNeDpZ7uFWID4HgikTXNDr37qDlTy+hOx2gKEQv/zvsV10LuoauaaB6adyzE9BRW5vx6iqmhIljvfQRsWTJkl7Wkry8PDZs2ICqqihK3+tbRGQk06dOxZo+BcUeMao5L7XO+IJNh2O1uXDhAm+//Ta///3vhzyv79yhaswHQnwEnfFYZAwMt4vVboiPcGS59MfVM8wcPe3l0AkPty4VrheB4EpD1zQaX9iI82Mjk8I8NYv4/++7mFOn9Bkbm5xOQ9mnIEnojk48NRdQEicaVohR4G6oR21qQImJwzIxeegDeqKE/pr4wYGDfPmbq0ftdklJSeljiairqwPoY7nojxdeeIHExERuv/32Pufdt29fr9eamprweDzDOu9oEeIjyIxXy0dstILFZpgV54Qx2LQn86abMSkOahqE60UguBJp/fPLhvAwmYm97etEfv6WAYt9SZKEbLVhSkxG6mhG93hQ62uRUyYjjabtvFcF2YRsj0AaoQtlNOzdu7fPz9nZ2f1aPQByFyxgzx//gDlpAqbo/oM4B3O75OXlUVRUhNvtxtLlttm2bRupqal93DGXous6L7zwAqtWrcJs7v3Z5OXl8dhjj1FdXc2kSZP857VarSxatGjQ8wbC+LpDXgGMx2wXAKdXQZIkVK/KhPixuen7XC8AB8tFp1uB4EqiY/97tO/4MwDx/3gPUQW3DqvKqGyxYEqejGSxgqaiNtUPWrtiIDRPeBvKnT9/nsLCQsrKynjllVfYtGkT999//4Dj7VFRTJ86lelTppKVldXvNpj4WLlyJVarldWrV3P06FFee+011q9f3yvTZf/+/cyaNYvKyspex+7YsYMzZ87w7W9/u895b7rpJubMmcOdd97JoUOHeOedd/i///f/smbNmpBluoAQH0Gn0zn+iowBtHQY/3c5PbR3jl2VvYUzDNV96IQQHwLBlYLrTDnNv/01ANEr/p6IhXkjOl6SZZSECSBJaI4OtM6OER2vaxq627imhKu66apVq3A4HCxevJh77rmH++67j7Vr1w44PtAS67GxsWzfvp0LFy6Qm5vL3XffTWFhIYWFhf4xnZ2dlJWV4fH0vr4+//zzLF26lNmzZ/c5r6Io/OUvf8Fms3HdddfxD//wD3z5y1/mySefHNU6h4twuwQZp2v8dbUFuHDRWJfb5aG2wUNUxNhYP+ZNM6PIXa6XBpVJicL1IhBcznib6ml8/klQvdjmX0P0zV8d1XlkixUlJg61pQm1qR7ZZvOXJR8K3eMBdJDl0blsRoHZbOapp57i2WeHl50TjCqn8+bNY9euXQPuLygo6Ndq9PLLLw963ilTpvDGG2+Mel2jYXzdIS9zPB7dX8BuPLlddF3nbI2xMI/LS13D2PVYibB1u14OCdeLQHBZo7ldND73JFpbC6bUKcT/470BNXSTY+J7uV9Gsg4wXDihzNAIBNHfpTfj5w55BeBzuQDYxpHlo75Zo8OpAzoet5e6xrG96ftdL0J8CASXNW1//T2eC2eQI6NJ/M4Pka2BZbFJktTtfunsQOtsH9Zxur+h3Dgrq94TXyCqEB+AcLsEFV+ardUioYS4Vf1IqOiyekR1XRfG0vIBMH+64XqpbtCoaVBJEa4XgeCyw1Nzgfb33gQg/hv3YEoMTp2Onu4Xb1M9Zqvd77IYCH9PlzDFe+zcuXPExwSrudyVwvh5PL8CGK9ptj6Xy8Q4QxDVNoytxUG4XgSCyxtd12n53xdAU7HNy8U2d2FQzy/HxCOZLaCqqG3NQ47X/D1dxq/lI9CA0yuN8XWXvMwZrwXGKqoN8TE1xfjy142x+IBu14tIuRUILj+ch/fiOnEUzGZi/+6bQT+/JEkocUbaqdbealRFHQBd1/1ul3BZPkaDZOqy3uj6oO/ns4JwuwQRX8zHeMp08ao6Fy4a4mP2VOOGX9foDXnp3KEYjuulrVNnz6c6Z2p1TIrRk8a3pSVJXD1dwqSMH/eWQPBZQHM5afnj/wMg+sY7guZuuRTJZhQL070etI42lOjYfsfpHg/oOkgSkjm8DTNHhCQb1U11HV31IsnjVyiFAyE+gohzHBYYq7yo4lUh0iaRNcWMJIHbo9PSphIXM3a//gibxMwpJo5XeDlyytNLfLQ7DNFx6JSOOsADwqcXdD46oVMwT2J2ujRuI9wFgiuNtm2voTY3oCROJPrGO0I2jyRJyNGxqE31aG0tyFEx/f6da/5g0/Gb6QLG+5EUBd3rNeI+xrFOCgdCfASRznEY8+ELNp2aomAxyyTGmahv8lLb4B1T8QEwP8sQH6UnvaxYDKqq895RnQMnu1OWJyfBtTNlTAq4veD26nQ44KOTOi0d8Ke9OvvLdW68SiZ9wvi98AgEVwKeuira3zWqmMb+3TdDXtBLjoxGbWlC93rQnZ1I9sg+Y/QeabbjHUkxoXu9IuMFIT6Cij/mYxxVNz17SbzHxARDfNQ1epiZObbN3XKmmQEnFTUqTW0q7x2V+OS8USAnLRE+lyOTMfHSjovGvxdl6+wv09lbplPdCC+9q/H5HInr5owf4ScQXGm0/GELqCrW2Quw5YSu74cPSZaRo6LRWptR21qQ+xEf3Zku4zfY1I8v6NQrxIe4UgeR8djXxWf5yJjUJT4Su+I+xkHQaVyU7BdFf9yj8cl5HVmGv8uTufMGmczkgd0pFpPE9XNlvneLzFWZxphdR3U+OC4CuQSCUOA69SmuTw6DohD3ldVhc3EoUTFG51unw5/V0hO9h9tlvCMyXroZP3fJK4Dxlmrb6dSpazLW1NPyAUbQ6Xhg/nQT0TEWapqNz+z2ayVmjSCGI8ou8cVrZArmCQEiEISStm2vAhBxbQGmiZPCNq9kMvstHlpbS699uq73qm463gm01kdpaSn5+fnY7XbS0tJYt27doE34du7cacSa9LOVlJT4x73zzjssXbqU6OhoJk2axI9+9CO83tDeI8bHXfIKweEyvgTjRXycrTG+PEmxMlF2Y03JXZaPsa714UOxmImJMS4aN14lMTt9dJ9d3mwhQASCUOGuKMf16ccgK0R/4cthn1/uynTROtt7WQ101QtdaauS+coWH62trSxfvpzU1FRKSkrYtGkTTz75JBs3bhzwmKVLl1JdXd1r+853vkNGRga5ubkAfPzxx3zxi1/k5ptv5tChQ/z2t7/l9ddf58c//vHo3uQwETEfQWS8pdqevcTlAj3dLmNv+Th6VqPkhPHvlhYXZslMIHo4b7aMjsZ7pTq7jupIksbS2ePjdyEQXM60vv0HACKu+XzIUmsHQ7bakKw2dJcTrb0VJdaoAeJ3uZgtAfWUGSkFBQXk5OQA8NJLL6EoCnfddRePPvrooFZbf9O7UYiPrVu34nQ62bx5M1arlZycHMrLy9m4cSOFhYX9zmuxWEhJSfH/7PF4eP3117n33nv943/7298yf/58Hn74YQCysrJ4/PHH+frXv85Pf/pToqOjR7zW4SCuzEHE19HWNk5iPnpmuvjwuV3qmzyo2sDmulDT5tB5+4Axf3yESnubh9JTgVtjls6Wye+ygLxXqnOyauzeo0BwJeA+dwrX8UMgy0Tf9OWQzqXrOrrH3e8mWe3oXg/e5gY0twvd40btaEf3epBkacDjhrUN4roYiC1btmAymdi3bx9PP/00xcXFPPfccwOO3717N3Fpk5m4cBGJM2YSFRXVZ1u/fv2Ax+/Zs4f8/Hys1u7A2hUrVlBVVUVFRcWw1vz6669TX1/P6tWr/a+5XC5stt7JB3a7HafTyYEDB4Z13tEgLB9BZDxZPnRd91c2zeghPhLiTJgU8KrQ1OIlKX5sks13HNFxeyE1EZbOkDlaDkfPeFE1PeC+OEtny3Q4NT46ofNGicZ3bpKJso+fDCSB4HKibZth9bAvuh5TUsoQowPE66H9lz8Zcpj7kp81IJBHl6jvPQYjdNukp6dTXFyMJEnMnDmT0tJSiouLWbNmTb/jc3NzObB3D+7qKiSTCVv61D5jEhISBpyvpqaGjIyMXq8lJyf792VmZg655ueff54VK1aQnp7uf23FihU89dRTvPLKK/zDP/wDNTU1/Nu//RsA1dXVQ55ztIz9XfIKYjxluzS26rQ7dBQZJk/sFh+KLPkFR+0YuV7O1ukcP6cjSbDiaplpaQqRNolOp86pyuCkoC2bL5EcBw4X/HmfNqonG4Hgs477QgXO0o9Akohe/ndjvZxxxZIlS3q5OvLy8jhx4gTqAC4Vu91O9owZTJ86lWnp6WRlZfXZBhMfcGnZAfzXteEE6F+4cIG3336bb3/7271ev+mmm3jiiSf43ve+h9VqZcaMGdx6660AKEM09AsEYfkIIuMp26WiK9g0bYKC2dT7izkx0URNvYe6Bg9zs+xhXZeq6rx90PicFk6XSIk31pYzzcS+44brZUZ64F9LkyJxxxKZF7ZrVNTB3k918mYL64dAMBL8Vo+FSzEnp4Z+QpPZsEIMgOZ04L1YDbKCOTUdx+lToGnY0qci2wKoW2QKvQV49+7d3HLLLUYpeDBKrV9CUVERRUVF/R6fkpJCTU1Nr9fq6uqAbgvIYLzwwgskJiZy++2399lXWFjID37wA6qrq4mPj6eiooIHH3xwWNaU0SLERxAZT0XG+nO5+JiYYAYcY5JuW3JCp6EVIqzw+Zzuz2n+dDP7jnv4+JSHr+TbglJDIDFGYvlCib9+ZASgTpmok5Y49r8bgeBywFN1DueRfYbV46bwWD0kSRrU/SGbzEitTaCq6G43kqyAbEKOjAprwCnA3r17+/ycnZ09oLUgNzeXQ4cO4aw4A+hY06cgXyJ6BrN85OXlUVRUhNvtxtKVVrxt2zZSU1P7uGMuRdd1XnjhBVatWoV5gP43kiSRmmoIzFdeeYX09HSuvvrqQc8bCGP/iH4F4RhHMR++TJepk/oRH4ldtT7CnG7b2qnz/nFD9S+bL2G3dAuBWRkmzAo0tOhU1QcvTXZ+ptH7RdPh9b0aTrdwvwgEw6Ftx+sA2K5ajHlS+hCjw4MkSf6aH2p7m/GaxRx24QFw/vx5CgsLKSsr45VXXmHTpk3cf//9A4632+1kZ2eTNW0a06dOJSsjc0Rul5UrV2K1Wlm9ejVHjx7ltddeY/369b0yXfbv38+sWbOorKzsdeyOHTs4c+ZMH5eLjyeeeILS0lKOHTvGo48+yr//+7/z9NNPC7fL5YDH092PZKxjPjRdp7Krk+2UiX2/PGNV62PHER2P1yidPi+jtwXCapaYOdXE0dNeSk95SJsQnC+9JEncvAiqGnWaO4w1fPEaYf0QCAZDbWnCcfBDgDGp6zEYckQUWnsrmsNh/Gwdm7Lqq1atwuFwsHjxYhRF4b777mPt2rVDH6gooHpHXOsjNjaW7du3c88995Cbm0t8fDyFhYUUFhb6x3R2dlJWVobH0/va/vzzz7N06VJmz57d77nffPNNHnvsMVwuF1dddRV/+tOfDBdRCBHiI0j4Ml1g7FNtG1o0XB4wKTAxoe9aDLdLeKucnqvT+eR8d5Bpf26V+dPNHD3t5eNTXm5eEry5bRaJ2xbLvPSuxpEzOgum6aQK94tAMCAdH2wHVcUybRaW9GljvZxeSFYbKCZ0j6+y6diID7PZzFNPPcWzzz47ouMkRUFndIXG5s2bx65duwbcX1BQ0G9w/csvvzzoeXfs2DHitQTK2PsHrhB88R5Wi4SijO2NreqisZZJiXK/aas+t0tjsxePNzxuiD2fGmtakCmRHN//55MzzVjXuVqV5vbgVihNnyCRM9WY9+2DIvtFcGWiqyreylO4P/4Qz6cH8J75BLW6ArWxdtj9RHSPm473twEQlf/FUC53VEiShBwRid5Vp0gaI8vHaBH9XQyE5SNI+INNx0Ga7YUul0vqAK6LuGgFi1nC7dFpaPKSMiG0kd4XW3RO1xjB3dfOGliYxUTKZKQoVNSoHDvt5br5wS2XvGy+xIkqnZomOHJaZ8F0Yf0QXP7ozk68Z8vwnjmO91wZuBz9jpPsUZivug5LTl6/rel9dB74AK2jDSVhArZ5uaFadkDI9kjQ641/XwY9XXoSaH+XKwUhPoLEeEqzrao3vtSTBxAfkiQxMcHEhVoPtY2ekIuPfWXGE8rMNIiPGvyGnzPdREWNSulpT9DFR5Rd4vq5Eu8c1tlZqjNzso7dKgSI4PJEV724D+7EXfIO9HiKlmwRyClTwetBdzmMzdGB7mjHvfdt3B/twDw7F8uCzyPHJfU+p67TvvOvAER+boX/RjnukLqvs7rXC2F2vezcuXP0ByujL7F+JSHER5AYTwXGKrvcLqlJA184JiaauVDrCXnGS5tD59g5Q3wsnjn0ZzNvmpk3PnBRdtaL26NjMQdXHORmSXx8RudiC7x3VOfmRd3n13Wob4NWB3Q4ocMF7U7j9cRomBgDE2LBNjZFYQUCP2p1Bc4d/4vWWAuAnJCMKXMOpsw5yMlT+mR/6KqK9+THuA+9h3axEk/pHjxH92LJuwXL1QX+GCxX+VG81eeQLFYil9wQ9vc1XHydbCVJQnd0QMTAlpzxhmQSlg8Q4iNojJc0W4dLp77FWEvahIHXEq6g0wMndDQNJicxrBobqUky8dESTW06Zee8zJse3Du9LEvcdLXM1nc1Dp3SuSpTJzle4txFKD0HTR39H1fTDMe6/h1jh4yJMHcymMVfkCCM6C4Hrj1v4indC+hI9kisn78DU/aCwRuaKQrmmQsxzViAWnkK98H3UM9+ivvDv6I11WFb9vdIiomO9wyrR8S1Bcjj+IauuQzxgSyhOTrQNW1M0m1Hg3C7GIhLZ5DwxXzYxrjAWHWD8YWOi5KIsg8iPsJQ68Pl0Tl0yrB6XDsMqwcYTzLzppnZdcRN6WlP0MUHwJQJEnOmSBw/p7PtkE5sNLQ6jN+bSYGkaIi0QZTV+L+uw8VWY2vpNCwjH5+F8iq4KgOyU+Ayue4JLmO01iY6//Rr9GYj1sE85xqs130JyRYx7HNIkoRpchamyVm4j3yAa/ef8H7yEY6WRkyLV+A8dhCAqM+HNs0yUPQu8SEpCmgautOBNI7FUk9EwKmBEB9BYrw0lfPV9xjM5QLhqfXx8RkdpwfioyB7BJWZ5003seuIm6OnvWi6jhyEaqeXcu0siYYOCckk0eoAiwlmp8GsNLD2o3eyJxn/d3mgqgkOV0CbA/adgE8uwNXTID2x34rJAkHAqI21OP74G/SOFqToOGxf+D+YJmcFdE7LVdchxyXieGsratVpOrZsAMA292pMEycFY9khw+d2ke0R4OpEc3SMa0tNT6SumI/PuuVDPK8FifES83Hhos/lMrj4mJjgs3yERn1rmk7JCZ/VQxpRufSsySasZmjt0DlfG/w/0IstsOu4hMkkoWo6HrfG312jc1VG/8KjJ1YzZE6EO3JhcZbxc6sDdh4zhIgW3AxhgQC17gKOV59F72hBjp9IxFfvDVh4+DBNnUXEV++ByBjc9Q0ARFzzuaCcO1TomobeVURLiYoGjJ4vl036vC+IV1UvnzWHACE+gsR4yXap6rJ8DBbvAUbAKUBzm4rLHfw7ZlmlTksH2K3462sMF7NJYnaGIY5KTwVXHJ2pg7ePgNMDcZE6rW0adU06n14Y2UVAlg0ryd8thrldlafLq+FvpYZ1RCAIBt4Lp+j8wy/RnR3IE9Ox//3dyFGxQZ1DSUyBKfNB15EtZtRP9qB7Lm1aP37Q/C4XE3JEhJH5onrH9Zp70iuD6DNs/RDiI0g4XMbNayzFh6brVNb7xMfglo+oCNnvIroYgqBTX3rtoiypT1fd4ZAzzRBHR08H506u63CkAnZ/ApoOkxPhloUSeTONte0+puNVR/4UYjHBommwbC6YZCMw9a+HoLUzKMsWfIbxXjiJ4/XnwONCmTydiL9b6+9rEkx0Xadz/3sAWJIS0RtqcP7td+P2qVz3ZbpYLUiS7O9mqzv7r28y3pAkCWQRdCrER5DoHAdul4ZmDbevrHr84OuQJMkfdBrsuI+6Zp3qRsM6sGiUhbzmZpqQMNxITW2BW2YOnoEjZ41/z5kMBXPBrMDVWRLRdiN+4+DJ0V9s05PgloUQaTXO9ddDUN0U8LIFn1G0pos4/voiqF5MmXOw3/ZtJEsALeMHwX3qE7y1lUgWK9H/8D2QFSMt96Pwl9weDj7Lh6+sui/gVnNcPop/tOm2paWl5OfnY7fbSUtLY926dUOKxPLycu644w6SkpKIiYnhuuuu49133/Xv37x5M5Ik9bvV1dWN/M0NEyE+goTTNfZul8qubrCTkpR+y6pfii/otKY+uOKjtML4Y8ieBBGjzP6JjpDJTDX+QAO1fpyqgWPnjX9fmw2508H38ZgUo/AYwIef6rg8oxcg8VHwxauNbBm3F3YchdrmgJYu+AyiOzvpfOO/weVATpmK7eZ/RDKFrriMr5S6Pfd6LJmzseZ/GQD33rfxnjkesnlHiz/YtKusutwlPnS3E/0yCboaTcZLa2sry5cvJzU1lZKSEjZt2sSTTz7Jxo0bBz3u1ltvxev1smPHDg4cOMCCBQv40pe+RE1NDQD/5//8H6qrq3ttK1asID8/n4kTJ47+TQ6BEB9BYjwEnPoyXdKShreG1InGBa2qLnjiQ9O6i4rNywjss5jX5XoJJO7jYgvsKe863xSY2U/WzfwMiYRocLigpDwwU7PdAisWwOQEUDVDgDS2B3RKwWcIXfXiePNF9OZ6pOh47LeuDqnwUFubcRzZD0DkdTcBYMlZgnleHqDjePtl1K5CZuMFf5ptl/iQzGbjM9L1sLleCgoKuPfee7n33nuJi4sjMTGRhx56aNiuqtFkvGzduhWn08nmzZvJycnhK1/5CkVFRWzcuHHAeevr6zl58iQ//vGPmT9/PtnZ2fz7v/87nZ2dHDtmVC6y2+2kpKT4N0VR2LFjB9/+9reHvbbREPI75eOPP44kSfzzP/9zqKcaU8ZDqq1ffAyzHX3qRKN8eWVd8AK1TtcY1UEjrDAtwGy9nOnGH2j5eS8u98hFQbsT3j1mxHhMSYIFGf2Pk2WJz+cY1o99ZTqdrsAEiCLD5+cYFVE9KrxTarhiBkLXdRxuncZ2jeomlYY2jU6XjjZOfe6C/tHdTrSGKrxnSvEc34P31GHUynK0+kq0jmZ0bfAbja7ruHa+hnrhFJit2G/7FnJEVEjX3Ll3B2gq5oxsLJMz/K9bP3c7Suo08Lhw/u33YbMo6LqO5nIOuHk72o3MFo8beoxFUdA9btTWpkGPH2gbTXzLli1bMJlM7Nu3j6effpri4mKee+65Acfv3r2bqKgooqKiSMyewcSFi4ifPNn/WlRUFOvXrx/w+D179pCfn4+1RyO9FStWUFVVRUVFRb/HJCYmMnv2bF588UU6Ojrwer386le/Ijk5mUWLFvV7zIsvvkhERARf/epXh/dBjJKQ1vkoKSnh17/+NfPnzw/lNOOCbrfL2BV68AebDlHjw0daCCwfPpfL3CnSsFw/g5GSIJMUK1PfovHpWS9XZQ//CdCjwrtHjayW+Ei4btbgNThmTZZIjtOpbYa9n+rccFVgazcpcMM8ePuwUTV1+8dGTIjdYlxgmzp0qhpVWjt1HB6d/q59EmCzQJRNJjVeJjFGDknNE8Ho0HUdrfYs6tmjaE214BygPK4PsxVl8kyUKbOR4ib2ST/3HNqF5/h+kCTsN3/DyEIJIbqm0fHhOwBEXbe81z5JMWFbsZKOl55Aqz1nlGKfvzSk6wEjmLT6X74Z8nkuZdJ/bEGyjiymJj09neLiYiRJYubMmZSWllJcXMyaNWv6HZ+bm8vhw4cBcDc2oLY0o8TEYkns7q+TkJAw4Hw1NTVkZGT0ei05Odm/LzMzs88xkiSxfft27rjjDqKjo5FlmeTkZN566y3i4uL6nee///u/WblyJXa7fZB3HzghEx/t7e184xvf4De/+Q3/9m//Fqppxg2dY5xq63DpNLQYd7Ch0mx9pCUblo/6Ji9Ol4YtQJeRw6Vzosrncgn8JilJEvOmm3j3oJuPT3uGLT50HT741Ljp28ywLMcILh1qrs/Pk/mf3RoHT+osmamPOl7Fh8UEN86Dtw4bVpi/fayTk65S06zRcYl1RZLAbpawmo14EYdbR9PB4QaHW+Niq4bFBKkJCqnxChGiId6YoXtcqGePo575GL2jpfdOexRydCJSRAy6x4nu7ABnh/F/jwv1zMeoZz5Gik5AmTIHJWMuktmKt+oMrg//AoD1+tswZcwO+ftwHj+E2lSPFBGFfWFen/1yVCzWvFtw7fojrj1vYpo2N+hpvpczS5Ys6SUg8/Ly2LBhA6qqovTTkM9ut5OVZdRn8TQl4LlYhxIdjXVS2rDnvFSw+iw2A9VR0nWdu+++m4kTJ7J7927sdjvPPfccX/rSlygpKWHSpN7m6T179nD8+HFefPHFYa9ptIRMfNxzzz3ceuutfOELXxhUfLhcLly+Ov0YQTWXI2Md8+HrZBsXJRE5SFn1nkRHKkRHyrR1aFRf9JA5ObDOkJ+c11E1mBgLyfHBuTnOm2bm3YNujp32omk68jCsKadr4Vy9EVRaMBeihvlAMz0FUuKhpgn2l+sUzA/8PURY4cZ5Ou8dU7GaVU51uc8VGVLiZJJjDSFhNfe+gOi6jstrCLqLrYY7xu2FijqVijqVlDiZ7EkmrEFuvCcYGF314i3/CPXkIVC7rIUmC8rUOShp2UjRCUjm/v+GdF1Du3gB9dwnaFUn0dsa8R57H+/pw5jmXIfznVdB1zHNXIj5quvD8n58gaaR1xYgmfvvIG2el4en7ABa7Xlcu1/HfsudIV2TZLEy6T+2DLjfXVuD2taKKT4Bcw+LAYD3Yg26y4Ecl4AyQpEkhaEr7u7du7nllh5l633mzh5/90VFRRQVFfV7fEpKij9I1IcvG8VnAbmUHTt28MYbb9DU1ERMTAwA//Vf/8X27dvZsmULP/7xj3uNf+6551iwYMGALplgEhLx8dvf/paDBw9SUlIy5NjHH3+cRx55JBTLCBsej463y507VjEfI4338JE60ULZGSeVte6AxcfHFcGzeviYnmbcnNsdOmeqVaanDf6Vdbih5JTx76syDCE0XCRJ4ro5Mq9+oHHgpM61M3XsAVoYOpwaZZVeIqzGZ+NRJRKiFBZNkzEpgzQCkyRsZrCZJeKjZLJSFC62alQ1qjS069Q0a9S3ucmeZCI1Xh5RBVnByNGaavEc3I7e1ghgWC6mXYWSPhPJ1P+NuyeSJKNMnIIycQq6pwC18gRq+UdoHS04t72M3tmJFB2PreArYfldeutrcX16BIDIpV8YeN2yjG3ZV+n83S/wnvwY75njmDLnhGxdkiQN6f6QzBaU6BjkS8YpMXGozSqoWp99oWDv3r19fs7Ozu7X6gG93S5qZyfu2mokswXb5HT/mMHcLnl5eRQVFeF2u7FYjO/ctm3bSE1N7eOO8dHZaaQfy5c0n5JlGe2SOJ729nZ+//vf8/jjjw+4hmAS9Dvl+fPnuf/++3nppZew2Yb+Ajz44IO0tLT4t/Pnzwd7SSHH11QOCNh1MVoqh1lW/VJ8cR+VAcZ9NLQatT0kCeaOsKLpYCiKxNxMX7XTode4/6ThtkiIMrrOjpTsVEOwuL3w0YnRB3zqus7Zi172nfDQ6tAxKZAYbeJiq5nyKoX61pF9RrIskRynsHCahcVZZqJsEl4VPrng5cBpDx3OyyPF8HJDV714jn2Ae9fvDeFhsWO+5hYsN3wDU+a8YQmPS5HMVkwZOVhu+AZS1AR03w0iNgrt4oVgv4V+6fjwHdB1rDPnD9nHRZmQinmhUXLd+d5r/iJf4cYIRjWC4+V+LBWSvSvl1uUIS4Ds+fPnKSwspKysjFdeeYVNmzZx//33Dzje53bJysoie8YMpk+dyvT0yf7XsrKyBhUfK1euxGq1snr1ao4ePcprr73G+vXrKSws9AvW/fv3M2vWLCorKwFDsMTHx/PNb36TI0eOUF5ezg9/+EPOnDnDrbfe2uv8v/vd7/B6vXzjG98IwqczNEG3fBw4cIC6urpeZhtVVdm1axfPPPMMLperlzK0Wq29oncvR3zxHhazhDLI02wo6a5sOjLx48t4qQow48UXaDo9BSKDHHQ7b7qJkk89lJ7y8uXPDzzuXD2cvWgEai6dObpOs5IksXSOzB/3aHx0QmfxTH3Erg2PV+fjsx6aOozPJDFaZs5kExaTRKcLTtXCrk/gS4sMt8xIiYmQWZxt5ny9yqkaleYOnX0nPMyZbCIlvn/x6fGqdDjcuD0qbo/X+L9XRULCZJIxKzImk4LZpBAdYcFqMV121hRd19FdDtT2RrSOFi6N4pVMFuToeJSoeH+q42Bo7U149v3Fb+2Q02Zgnp+PZA1OIJ7e0YrnlFFHQ5mQgiyBp+Sv6B15KNm5Ifv8da+Xzn1GkanISwJNB8K6+Ca8Jz5Gb2vCtX8btutvC8naBkP3eEDXQJKQLH1Fn2QyIykmdNWL7nL6xUioWLVqFQ6Hg8WLF6MoCvfddx9r164d3sH+ImMauq4P63cdGxvL9u3bueeee8jNzSU+Pp7CwkIKCwv9Yzo7OykrK8PT1fsmKSmJt956i5/85CfccMMNeDwe5s6dy5/+9CeuuuqqXud//vnn+cpXvkJ8fPwwP4HACLr4uPHGGyktLe312j/90z8xa9YsfvSjHw1okrqc8Vk+xsrloum6P+ZjuJkuPtKSuywftaO3fGiaTunZLpdLZvA/g9kZZhTZQW2TRm2jSnJC3/fo8hiN3QByphiWj9EyazIkxkBDKxw4obN0zvBvAi6PzsEzHjqcOooMMyaZSE3odotcm23U/WjqgF3H4aarRieSZEli6gQTE2MVPrngobFd5+h5L51uncyJCpIkoWkarR0umloddDgGFpcer0rPTODaBrCYFWIibcRG2bBZAxciuq6jayqSrAT1pqqrXrz1lXhb6tDaGtE9w3kql5AjY1GiEzAlpaFE9b3Yag1VuPe+AR4nWCMwX7UMJXV6ENet4nj7ZaN0emomttu/g1q2D/XkIbzH96C7HJhyPhcSAeIsLUFrb0WOiceWc/WwjpHMFmwFX8Hx5+fxHN6Nec61KAmhK0DVH5rTCRjFxfr7XCRJQrJHoLe3ojk7jY63IcRsNvPUU0/x7LPPjvhYSfZdw3TQVBiGGAaYN28eu3btGnB/QUFBn7Th3Nxc3n777SHP/eGHHw5rDcEi6OIjOjqanJycXq9FRkaSmJjY5/UrhbFuKlffVVbdrMCEIcqqX4ov46XqonvYCvxSKuqg3WGkhWaFoBO33SqRnW7i07NeSk95+xUfB04b8R4xdpg/NbD5JEli6WyJP+/T2V+uk5utYxmG9cPp1jl42kOnW8digqunmYm65DthUiB/DvzlINS1GmXfcwO4p9ktEgszzZysUTl7UeV0rUqH00uczUlbu6tXrRC71YzVYsJiVvwbgMer4fWqeFUNp9tLe6cLt0elvrmD+uYOrBYTyQlRREf2f9G/FE314mpvxeNy4nW7UN1OvG430BWZLyvIirGZrHZsUTFYIqKRR/BgormdeGrP4KmtAG8P4SxJyJFxKFFxIPe8vHVZRdoa0d0OtI5mtI5mPDWnUWKSMKdmocROQJIk1MqTeA68DZqKFJeMZclt/hLewcJ9YAda7Tmw2LDd9HVkswU553NItii8R3ejnjqM7nZiXnhjjxtVcOj48G8ARC4pGJYFyIcpYxamzDl4zxzHvW8b9lv+MajrGgrN5RMfA7vzZZsdrb113Pd5kWTZeOrQNHSvOqLfw5XCZ+8dh4BOR5flY5hZJsHGF+8x3LLqPUlONCPL4HTpNLaoJMaN/CtxvKui6ex0adAgykCYN71LfJz28IVrevsqqprgZFcQ+NKZRiZJoMxJl9h9TKe5HQ6d1rl25uDvq9OlceC0B5fHSO+9epplwHTYmAhjne8dh+MXIDUBUgOwdEqSRPYkE3YzXKhrB7eTlq77scWsEBdtJy7ahsU8vN+tqmm0d7ho6XDR1uHC5fZyrqaZCJuZlMRoIux9Td66ruPqaMPR0oizva/Lo9dYTUXVVFQPeJwOHC2GW8MSEYU1KoaI2ATkAS7GmrMDd2U53vpKwwQPSNYIzBOnoEQnIkfFDXmz1lydqG2NqM21eBuqUFvrUVvrke3RKIB+xrDcyimZmHNvDnqFUbWxFneJUV/DVvAV5OjuX74payGSxYbn0N/Qzn+Kx+3EfM0tQVuD92INrvKjIElELLlhxMdblqzAe+YTvCePoF5chjJh+GmigeIXH4PEEko2O0gSuseN7vWEtDpsoEiKCV1zf2aby4VFfOzcuTMc04wZHV3iY7gprsGmusH48k4aZln1nphNEsmJZqoveqiqc49YfKhad22P2emhixGYP93M/+xwcrpKpa1TIzrCeK+aDh+dNMbMTB1ZdstgyLLE0lkSf/1IZ1+ZztXT9QG787Y7NQ6e9uD2QoRV4upMMzbL4J/F1AnGesuq4MMyuD3XqAsyWto6XHR2tBJlMb4LbtWER7eTNcWOzTKy74Uiy8RG24mNtqOqmt8C0un0cLqykehIK5OSorGYTWiaSkdDHZ3NDWg9+lSYLDYsEVGYLFZMViuKxYaiGOM1VUVXVTTVg6uzHVd7G6rHhbuzHXdnO+31NUQmTCQyPskvQnRdx1NzBvf5TwwzNSBHxWNJnY4SP2lEFjvZGoFsjcCcNBktfQ6e6lOGBaX2LHqnkeovT52DecENSFJw/6Z1XcO5439AU1EyZmOasaDPGGXKbLDY8JS8iVZbgWf/XzAvud14Wg6Qjj1GszjrrKswJY7cbaIkpWKacRXe8sO49r5NxG3fCnhNw0HXdb/bZbBsGElWkCxWdJcTzelEiQqN+AjGPU1SFHTPZ7ezrejtEgQ6HMaXZ8zER1e8R+oI4z18+DNeRhH3cbYOnG4jcDI9aejxoyU+WmbyRBldh2Nnum9yp2qgudO4cQ9UPn205GRIxEYY5eJ9acSX4vLoHOoSHlE2idzpQwsPH1dPg2gbdLqg5OTo1qhpGudrmjlb3YTbo2JSZCYkxNCpRdHmNnHojBe3d/RZO4oik5wYzYypE4iPMQIt2zpcnDxXT0NdLRdPf0p7Qy2a6kVWFCLik0jKmEFS5kxiUyYTmTABa2QMJrMFSZZRTGbMVhuWiEhs0XHEJk9m4vTZTJg2m5iJaZgsNnRNo72+hrpTx2m7WI23vRnH8Q9wnz0KmoocnYh97vVE5HwOU0JqQHERstWONSMHa1Q8cpfwUKPjcXvceBuqR33egfCU7kGrPgtm66BptUpKJpalXwbFhFZ3Du/H7wXc4t4INN0JQGTejaM+j/Xam0CSUSs+Qa2uCGhNw0X3eEAzgk3lfoJNe+ITJ7prnLteRtFc7kpCiI8g0N7ps3yMTTBtVUOX2yVxdL/O1OTR93gpu2BcEGekScMqABYI3Y3mDJHkVeFwRde+KWAN8kOOIkt+d8u+Mh1N633xVzWdwxUeXF6ItEosmmbGMoB1pD/MilH2HYwMmHP1I1uf2+Pl9IVGWtqNJ8KkuAiypyaRnBDB1dOsWEzQ4TLEkScAAQJgNimkTYwla0oSESadKE8D7sZqNK8HxWwhLnUqE7PmEps8GbMtYsSCwGSxEpkwgaTMmcSlZhgiRFVxV57AcXQ3WlsjyArWzPnY5yxFiR44JXGkeE8cRD1xAABl1hKkiVNA8+I6eQBn+UdGH5EgoLU14/rwTQCsS29Bjo4bdLycmIo5dwUAakUp6qlDAc1vBJq2jCjQtN91xU3APDsXANfetwJa03DpjvewDmkBkruykXSXI2DBFlK6Ml4Qlg/BaPG5XaIiwv9xerw6F5uM+VMTA7N8jLTHi6bplFcaf9yzJoc+LXN+lrHOTyq8eLw6n1QaQaaRVpgVItfz/EyJCCu0dBgVXH3ous6x817aHDpmBa7KMA/olhmMibEwt6vG0N5yw4o0HDocbk6db8Dp9qIoMplpCaQkxaB0XZgjusSQWYE2p86hCg9eNcAnZ13H3VKH3VmLGQ86Ep1yFK3mCci26KC4KCRJwh4TR+KU6URrDqzOZiR0vCYbaupsTBOmBDUDxFtxFO+x9wEwzcnDPGsx9rmfwzJ5JiDhbayi8+guNGdgrYl1Xce58w/gcSFPmtrVNXZolEnTMeUYNTa8R99HrTo16jX4+riMNNC0PyyLvwCygnrhFN7zJwI613DoznQZunaUZLUZcR9eL3jHr1VhNJ1trySE+AgCnV1ul7EIOK1r0tB0sFshNmp0F+XR1vo4X2+4DGwWmBKGrLvJE2TioiTcXsP1cvSc8frCzOAEmfaH2SSRm218rns/1f1PUqdrVepaNCQJ5meYA+q1siAD4iKMJnh7Twwaq4mu6zS0dHKmshFV07FZTUyfnEhkP0GgkTaZq7sESGunYaVRtdEJENXrofH8KToajHLOtph4IidNx22KxulWOXWhYdB03pGguZ04P9kDbfUgSWiJU3BETqCzvZWLFWV4nJ1BmUe9UI73sBEDoWQvwjTjGsDIRLBMnok953NI1gh0VyeOo++jtjeNei7viSOoFZ+ArGC74WsjEmrK9AUomfMA8Bx422hiN9L5L9bgKi8ddaDppcjR8X4B5drzZsgtDFpXC47hNH+TZNlfLl0bx66XbreLEB+CUTKWbhdffY9JiaOvn+CzfNQ1enF7hl8Z8FOfyyU18A62w8FoNGes9eh5CY8K8VGQGWLhc3WWhMUEdS1wugZqmlTO1Bmf++w0E/GRgf0ZKXJ3191z9VBxceCxdY3tVF80YhNio2xMS0v0p8z2R7RdZmGmGUWG5g7DWjPSG4Xb0UF9RTnuznYkSSYudSrxqVOJjY0y3DA2M5qmU1HVSGuHc0TnvhS1owXH0V1oHc1gMmOfvZSY7AUkpE9HNplQ3S7qK8rpbG4IbJ66c3gOGL1NlMx5mOb07diqRMVhn3s9cmQsuteN4/iHeJvrRjyX7uzEteuPAFiuuRElof8+HAMhSRKmefnIE6eC6sW9989Go7oREGigaX9Ycm8Akxmt9jzqmeNBOWd/9Aw2HSzTpSfdrpfAvo+hRMR8CAJmLN0u1Q3dabajJTZaIcJuBHNWXxye60XXdcq7xMfMMLhcfMybbsJikVC70ikXZfbqyxQS7BaJBdOMSUpOqBy/YFwspk5QSO2n5shoSIyG+VOMf5ecNIqmXUpdYzsXm4ybTnJCFJOTY4cVZxMTIbMgw4wkQV2Lxuna4T9pdTTV03D2pBHbYbGSmJGNPaY7NdRsUshITSA60oquw7nqZppaR/e06W2qxXHsfXS3E8kWRUTO51BiEgGwRsUwIXMWtq6GYS0152m7WD2qJ26tvRlPyZuga8iTZ2KaXzCgcJctNuxzrkOJnQCairNsH56L50Y0n2vv2+iODuT4iVgWLRvxesF4mjdfczNSTCK4OvEc2Dbs994r0HSQPi4jRY6IxtLVBM9V8k7IrB9GsKk6rGBTH5LNEB+ac/zGfQi3iyBgxjLV1pdmmzrKYFMwnqxGmvFS2WC0ibeaIWNkD3IBMSPdxNR0G5IkEWfXSA1e3OGgLJ4hoSg6kXYVTYekaKPZWzDJmdLtfjlwuve+usZ26hqNuIOUxGgmJESNyNIVHyUzu6sp35k6lZqmwS94uq7TVl9Da+0FQMcWFUvS1BmY+yktLssSU1LiiIs29lXWtVDfNLInc29TLc7y/UYKamwSETnXI9t6l6mVFRNxaRlEJRpfuPaGWlpqzo/o5qJ7XHj2/hk8LqSEFKOI1xCfo6SYsM28FlNSGug6rlOH8dSeHdZ86sVKPEf3AGAt+LuAYi0ksxXzNbcYGTAXzw87ALVXoOnchaOevz/MCz/flZFzHrXq9NAHjAKfy0W2DB1s6kOyWI2nEtXbuwjdeMJXVM8rxIdglHSOYaptdX3glg8YedyHz+WSNSl0hcX6o80hER9nrNUdpBiD4RAdIXHVNB271cj4m5Me/N4nigxLZhj/PlkDNc3Gvy82dQuP5MQokuIjR3X+1ASFqV3fk+MXvLR09u9i03WdtovVtNcblduiklKIS8sYtAKpIWBjSIwzKoHWNLT51zwUhvAoMVrKJ6Rim7lkwIZtkiQRPWESMclG10BHSyNNF06jaUNfwHVdw/PR2+jtTWCPwrL41mGLAUmWsU6/GnPKNABcZ47gbawacj7ne68Z7yv7KkyTs4Y112DI0QndAajHPkQbhhuou6LpsqBX0pTtUf7MF/fB94J6bh++TBfJNvxGSEbch63X8eONnjEfwxXQpaWl5OfnY7fbSUtLY926dUMee/DgQZYvX05cXByJiYmsXbuW9vbef5uSJPXZfvnLX47ujQ0TIT6CgD/mIyK8MR8uj05DS2Bptj5G0t1W13V/iu2sEBYW64/SrqbHDY1ujp70hM2kWt+qoijGZ33igkzryB7sh83EWJjRVaJ+bznUNXZQ22BcKCYmRDEhPoCmNUDWJIWkaBlNhyMVHpzu3p+fruu01lbS0Wjc1KInphKdlDIsoSVJEimJ0SR3Ndapa2ynoXnwD8rbXNclPDSUhElYs64e1tNtZHwS8WmGz83V0UbjuVNoQ5ivvcf3oNVWgGLCcu2XkGwjE3GSJGGZOhfTRMM/5jxxEG/LwAE63k8PdtX0sGC9/ksjmmswlIwc5EnTwCemBnmy71XRNC/wQNP+sCz8PCAZdT8aRx4MOxQjyXTpiS8+ZLyWWpf8Yl43nmiGoLW1leXLl5OamkpJSQmbNm3iySefZOPGjQMeU1VVxRe+8AWysrLYt28fb731FseOHWP16tV9xr7wwgtUV1f7t29+85ujfGfDQ4iPANE03d/VNtyWj5oGFR3jqTw6wHiTkVg+qpugtRPMJsgMo8ul1WEUNQO4eNFFfYtGZX3oW2e7vbo/zsPllmjtlNnzaehEz9XTwG4BWXdS19gGGMJjYiDd8rqQJImcKSYibUbW0JGz3Rkwuq7TUnOezmaj4EhM8mSiRtg8TJIkJvRYa3V9G81t/V/8vS0XcZbtN4RHfAq2rEUjquJpi44lcUoWkqLgcXbSOIgFRD3/qb+Wh3nhF5DjRhd0KUkS1syrUBImga7hLNuP2t7cZ5zucuD64C8AWK75AnJU3KjmG2gN5oU3gi0Svb0J79HdA47t2GOk11pnXYUpYULQ1tATOW4CpulzAfAcCq71Q9f1YZVV7w9f92HN5Qz6Q0pBQQH33nsv9957r9+i8NBDD41oHn9/F4YXdLp161acTiebN28mJyeHr3zlKxQVFbFx48YB533jjTcwm83853/+JzNnzuSaa67hP//zP3n11Vc5ebJ3ZcO4uDhSUlL8m90enO7NAyHER4A4XJo/NTLc4qM6wOJiPfF3t60b2ppQ1sPlMpraFqPl6DmjNVlaAmQkG+/5yInQ+nN1Xef4eS9uL0TaJK7KMMzWx8/ptHaGRoBYTHB1hoep8S0AREVGMGGUrpb+MCkSCzK6aoA4dE5Ue/3Cw9dnJXbSFCLjR1+ydkJ8JAmxhgvmQm0LbZdkwahtjb2FR3buqMqHW+yRJKZPR5JlPI4Omi5UoF/yFKm1NuA5ZNyElRm5KJNnjPJdGUiShC3rapSYJNBUHJ/uRXP0NmO79m1Dd7Qjx03AsuBzAc3X7xosdsyLbgJArTjab/2PXoGm1wUv0LQ/LAvzAfB8ehCto3XU59F1HdXh6N7a29A6O9FcbnRN671viE3TNDS3G62zA7W9ddCxoxEnW7ZswWQysW/fPp5++mmKi4t57rnnBhy/e/duoqKiem0Tr1rIxIWLiElIJCoqivXr1w94/J49e8jPz8dq7XY/rVixgqqqKioqKvo9xuVyYbFYkHv8bflExfvvv99r7L333ktSUhLXXHMNv/zlL9GGYY0JBNFYLkA6ulwuZpOExRxm8dEjzTZQUpKMbIhOh0ZLm0pcTP9fDV3X/fEeMycHPO2w6XDC6S6L7rwpEKWY+fiUlyMnPdy6dGRPRCOhslGjvs2o55GTbiLaLjNlgsq5i1BSrnPjguCLL49XxeNsQpF1WpwWKtujmZoS3HnsFom56SYOV3i50KARq1VBhyE84lIzsMfEBXR+SZKYlBSNqmm0tDk5V9NMRmoCkXYLmrMdR1lXcGncRGzZI7N4XIrZFkHC5Ok0nj+Fu7ONpqqzxKdlIEkSuteDp+SvRln2iVMxzR5eca8h35+sYJu5GMfxD9A6WnB8upeInM8jmS2o9dV4Pjbak1vzvxyyjqXKhHS07EWoJw7gObIDOSnNH+cA4CgtQWtvRY6NxzZn9BVNh7WWSRkokzJQqyvwHHkf69Ivjuo8mtNJ6R03BXl1QzPvT9tQRvikn56eTnFxMZIkMXPmTEpLSykuLmbNmjX9js/NzeXw4cO9XnNVVaK5nJgnJGOKiiIhYeAI+pqaGjIyMnq9lpyc7N+XmZnZ55gbbriBwsJCnnjiCe6//346OjooKioCoLq6u33Ao48+yo033ojdbuedd97hgQceoL6+noceemg4H8WoEJaPAPFnulymabY+rBaZiQnGRXKwuI/6VmhuN4Ijpwf5hjgYxy4YTeSSY424iJxME7IMVfUadUNkbowWp9uwCgBkpShEd1m2lswy/n/4tI7DHVzrh6bpnKtuxqtqmE0K55vjqG2ROD3y8hJDkhSjkDFBIV5ugg4jdiE2JT1g4eFDkiQmT4wlOsJIwz1b3YSjowPHp/vA60aOjOuyeAT+/bVERBI/uSsGpL2F5upz6LqO9+Od6G1NYIvEvGh5UIOEJcWEfdYSfyEy58kDaJqGa9efQNcwTZ+HaUpgVpahMM1eghSdAC4H3mMf9NrX+YEv0PSGHvEFocN8tWH9cB/di+4en0GewWTJkiW9vk95eXmcOHECdYDYI7vdTlZWVu9t+nSmT53K9IwMsrKyBhUfQJ/vr89iM9D3eu7cuWzZsoUNGzYQERFBSkoK06ZNIzk5GaXHd+Khhx4iLy+PBQsW8MADD7Bu3TqeeOKJYX0Oo0VYPgJkLJvKVfkbygVn7tSJFmobvFTVuZmb1f9TgK+DbUYyWMzhER8ON5zoEunzumphRNplZqSb+PSslyMnvSy/JvgX17IqL6oGsRESU3oIvGkpMCEWLrbAoZM6S+cE53PQdZ3KuhYcLg+KLJGRGo9bljl0Bg6cgvTEwDrf9kdqZDsRLUZWS7M0gYkxwc1dliSJ9JQ4Kqoa6XS46Px0P1ZPB5LFjm3m4qBaBayR0cSnZdB04QzO1iY6GisxnfsEkLDkrkCyRgRtLh+S2YptxjU4jr2P2nIR1/63UStPgWLCev1tQZ+vz/yygnnBDbh3/y/q2WMo6bOQk9Lw1lXjOnE0aBVNh4Mpcw5S3AT05ot4jpeMyt0k22zM+9M2/8+u6gtoHZ2YJ0zEFBs34vPpLgfeizWgyJgmTUFigHouI4wnGQ27d+/mlltuuWSBXQ8vkvGfoqIiv2XiUlJSUqipqen1Wl2d8VTis4D0x8qVK1m5ciW1tbVERkYiSRIbN27s11LiY8mSJbS2tlJbWzvouQNBiI8AGasaHw6XTnO78cVNCVKhq9SJZg59Mrjl42SX+MhODZ/V45MLoGpGIa5J3fWtuCrLJz48LL9m+Gl4w6GuReViq4YEzJ7cO61WkiSWzJL48z6dkhM6i2fqQUk3rm/u8DeJS0+Jw2oxMWey0bm31QFHKuCawLM1/bg722mpPosENGtxVHoTocrL7MnB7dAny4YAaTq6F6unDU1SiJx5LbIl+Bd8W1QscalTaT3zCUrFQQBMs65FTgqdj1CJjMU6bQHO8hK8Rw13i+XqfOQexdhCiZyYipKRg1pxFM/hHViWfb070HT2AkwJIWw33QNJkrEs/Dyud1/FfXgX5nlLR2xxkSTJ7/7QdR1JN5rJmWLjRuwWAdBtVrS2ZtB1ZJMJ2Ty8ImXDYe/evX1+zs7O7mVR6El/bhd3QwNqazNKTCyWxKRBLR95eXkUFRXhdruxdBVb27ZtG6mpqX3cMf3hExH//d//jc1mY/ny5QOOPXToEDabjbi4uCHPO1qE2yVAfGm2UWFOs/UVF4uLkoiwBUcIpPkyXmr7z3jpcOpUdlW1zpoUHvHh9kJZVzmFeVN6VzOdP92MBFRUqzS3BS84yqvqlFV1VzGNsvX9M5mdLhETYfS2Ka0I3PXS6XD7U2pTJ8QQFWGIKUWGxV2C49NKaAqsv5kfr9tF44UzoOtG9dDJ6YBEZaNGTXPw3Vha9QkinA3oSNRFZ1EbnPYs/WKLjCam9gSSruGJiMM7eWboJuvCnJSG0ukElxPMFpSu2hfhwjRnKVgjjOyXT/eFpKLpcDDPWoRkj0Jva8Z7+mhA59K93q7qnxKydXQPF5Ik+/vBBDvl9vz58xQWFlJWVsYrr7zCpk2buP/++wcc35/bJTs723C7TJkypNtl5cqVWK1WVq9ezdGjR3nttddYv349hYWF/oej/fv3M2vWLCorK/3HPfPMMxw8eJDy8nL+8z//k3vvvZfHH3/cLyz+/Oc/85vf/IajR49y6tQpnnvuOX7yk5+wdu3aXsGtwUaIjwDpHCPLR1VXimlqEOI9fPTMeOmPU9VdlpZ4I703HHxaCR7VqPyZnth7X2yUTGaq8f6PnApe1svpWhWXx0h3zUzu//NVZInFM4zPYF+ZjjbKhm0AqqpxvrYZMPq1xMf0fsJLTYApSUamz/6TgzeeGw6aqtJ04Qy6pmK2RRCfmkFSjELmROO9fnrB26f+RyB4G6vxVJYDoKfNwWmJpbGlk8aW0CgQ79H3kTpb0M1WOlJn0Vx1Dq/bFZK5fGidbagnu262kzNwnTkyaP2NYCNZbJjnfR6Azg/eRutoQ45NwDYnuBVNh1yHyYw551oAPKV7AjqXv7iY1RJQQHJ3n5fgio9Vq1bhcDhYvHgx99xzD/fddx9r164d0Tkk0/Cby8XGxrJ9+3YuXLhAbm4ud999N4WFhRQWFvrHdHZ2UlZWhsfT/d3bv38/y5cvZ968efz617/mV7/6Fd///vf9+81mM//1X/9FXl4e8+fP5xe/+AXr1q1jw4YNI3ovI0W4XQKkY4w62tY0+DJdgjfv5BTD8lFb78Hl1rBaep/bF++RFSaXi6oZ4gOM0uP9xVRdlWXmdJXKkRMe8hcErtJbHRrnumJpZqaZB22Yd1WmxPvHdZraobwSZqWPfD5fnIfHq2ExK6ROjOk3eCx3OlQ2Qm0LnKmDaaN0wxoptefwup3Iion4tEz/hT0zWaGhTaPVoXPsvIerp5kDDtDUHO04u8qAm1OmYU2fzsSuUvFVF1uxWkz9duQdLWptBeqZjwGwLFqByen21wBJmpqNHKLME/eet8DjQp6Qhj5pKrqzA9fpI1izFwW9Eu5AyGnZyOc/wXmoFICIJcvCEmh6Kea5S3B/tAO18hRqQw1KYsqozjPa4mKXItls0NJd7yNYvw+z2cxTTz3Fs88+O/q1jbC53Lx589i1a9eA+wsKCvqkDb/44ouDnvPmm2/m5ptvHtb8wURYPgJkrNwu/m62QbR8xMeYiItW0HQ4W9Xb9eJVdc50pbqGK96jos7ocxJhgYwB6iNdlWVYa05eUGl3BOZ6MdKIjYtAcqxMUvTgfx4Ws8SiLOOz2FumjapWQGOrg9YOFxKQnhyHMsATXpStO9j2wGnDHTUaOhrrcLa1ABLxaZko5u74DrmrAJksQVOH7hdho0VXvUb1UtWLHJ2AZcocwKgBEhtl3FDO1TTjCVJvC93t6K7nMe0qlJQM4idnIpvMqG4XTVVnQ1IRV71Yied4CQDWz9+BfeY1IEl4G6vwXjwf9PkGQpIk9JRZeJuNOhv2KVPCNndP5Og4TJldRcdKPxz1eUbayXYguvu8qGG1Rg0Lnxj+DDaXE+IjQMYq4DSYBcZ6kpFmWA/OVPY2U5+tA48Xou2QHBfUKftF1+F4l9VjZpq/EGAfkuJkJk8wyoWXngqsNXVlo/HUr8gwI3V4T8iLsiRMClQ3wrmBK233i8PloabeuFEkJ0Vjtw0e6Dk3HaJtRvbPx8Pra9YLZ3srbReNtKGY5DQsEX0Ll0VYZf97P1mj0jZKQafrOq7Th9EcbUZGSI8iYkYfmFhsFpPhcqppDlgU6LqO5/C74OxAiorHNPc6ABSTmYTJmUiSjLujzd+vJljouo5r9+tAV/+W1EyUqHgsk2cB4KooRXMGKVBnGDgOGjd7c1IC2oVjY3azNc9fChhFx0aTdqvrOlpXjIZsC6zSpiR193nRx1mfl9H0d7lSEOIjQMYi1batU6OtU0cCUoJQYKwnmZMNE3jFhd7iw+9ymSSFxYxc22IEVypyd6+TgViQbdy0D5WP/kLrUXVO1RjiZXqKCesw04gjbRLzM4yxez4d/o1a0/Sumy5ER1hJjB06DVSRu7NdPqmEkYRMeN0umqsMxWKPTSAiLnHAsWkJhtVH1+Hoea+//PpI8NScxttQBZKEbUZun8wWXwaMLEl0Oj3DbkI3ENqFMrSqkyDJmBfd1CuF12yLIDbF8Im1N9Tiah99Bc5L8Z4+hlp52kitXXpr95ypWcjRiaCpOE8c7FN1NRRoLied+43y5vZp08HZgberpHy4USZnIcdNAI8Lz6cHR3y87nYZ/U5kedTBpj3x93kJkvjYuXMnTz31VMDn8bvF9OH1d7mSEOIjQLoDTsPndvFZPRJj5WHfJIdLZpfl43QP8aHruj/FNistPC6XTy4Y/5+eDNYhMj8XzjQGfHrWO2rXS0WtikeFCKvE5BFakxbPlJAkOFMDNU3Du1HXNrTh9qiYFJm05NhhC7rJiUZ5eV2Hj/pW1O4XXdNoqqzwB5jGJk8edD5JkpiTbsJiMjKcTtWMzCSstjbgPnscAMvUuSjR/Qsdq8VE2sQYAC42ddDWMbqgUL2zDc+RnQCYZi1Gju8bEGOPjfcLrubqs6iewDsi66q3u3/Lws/3Sq31lWBHMaN1NOOuLAt4vqFwHPgA3elASUrBXnA7AOqJA+idwRNbw0WSpG7rR+mHI36qVx3dVo9gPOz4M17Gm+WjV3+Xz5brRYiPAOnuaBu+j9JfVj1IxcV6kjnZEB9nq9z+J97aZmhzgFmBjNH14xoRbQ4435XSO3sY5RmS4xUmTzRcL4dPjNz10unSOdcVwDtjkoI8wotdfJTE7K7uvnuH0XCuw+GmoctskTYxFpMyst/jNdNBlowA1AsNQ49vvViF1+VAVhSj7PgwMgcsJonZkw3rwbl6lab24Yk63evGefIgoGNKTMOcPHAhI4DYaHuPHjDNuD0juwDruo7n4HbwupHiU1CyB05xjZmYhslqN7J9ghD/4Sndg95SjxQRhWXRsj77Zasd27SrjLGVJ1Bbh/HLGiW6rtPxvlGcK/L65Sip2UiJaaCpeI6NPu4iEMyzFoHJjNZYa1iHRoDmCI7LxYdksUFXuf3xFvcx0qDTKwUhPgJkLGI+qvzxHsG3tqRMMGO1SLg9OtUXjT/Skz2qmgajmNZQfNIV65GWAMPwRgCwaKbhLjpYNvInWqOxGiRGSyTFjO4zXTLL+Fw+vaDT1D7wTU3VNC7UGg3j4mPsREeO3KQcEwGz0ox/l5wysoIGwtnWQmeT0aU2dtIUlBEUWZoQo5CaYHyvj1/wDOl+0XUd56nD6G4Hki0S67SrhvXUmpIUjc1qQtV0zteOLP5DPfMxWv0FUEyGu2UQYSXJsl98eRwdtF2sGvY8l6I7O3Ht3w6AZcnNvXqq9MSUmIppguHycZ48GLIbn+fsCTyVFWA2E7m4wLA8dKXeapXlaA2jf6+jRbLaMc80esqMNPDUJz5GU1is37XIMpLZ+Fv7/9l77zA5qiv9/1Oh4+Sck2ZGOQtJKCBEEME2wWAMDmAc8C4GvP5h7LUNXuM1jtiLIzZeh68DBi/BgEkiCJRRRjmMJufcPZ27q+r+/qieURrN9PR0C69X7/PM80gz1fdWd1fVPfec97yv8Y+W/YiWCM9nPs5jQngvOB/JaLMdhiJLVBSbC1RjtPRSdw5VTcMaHI9yAmeUxP66hVPN0ktdq447xl06wIDXGFEyrS2Kvw2zIFNiSqFZDtl29OyLZ3efh4imY1FlCnPT4p5vbgXYLWaW6HD76MfokTCuzhYAUrLysKdmTHieqUUqNsuwxP3YO7NIdxP6YJfJ86hdFLN0uixJlBdmIssSgWBkRGxtPBg+N1p0V6/OWhGTbb1qtZFZZHaB+AZ6CXpcMc11OkI73oBQADmnEMuMxWMea6ucY/q/hAOEWg7FNd948EazHs4Fy5FTUgHT6l6pGO462fCeEBqHSy9a/QEMrzum1xiRE9mJRMqeSwnmfSQKI7yP88HHecQKTRcEQ+YNfa5abYUQSWmzPRnDpZfGthCegKBr0Pz9udD3ON4Jmm5mPE6WUh8PORkylUUKAthTF9vuUgjBsaiSaUmOPKqS6USwLGo4t69R4Aue+aD3+kMMDJk7upL8jLO21cYCqwoLp5j/3t9sBgcnQwiBq6M5yvNwkJY/Dmv3LFAViZlRufW2foOBswR2us9NuPmgeW7lM1FSMic0j9WiUpJvBkd9Lh9e/9j8DyEE2p43QI8g5ZSgVM2NeS57WiYpWWbvtquzdcL8D2Owl8g+08TNtvKacctYkqJimzIfAK2nGc09wbaocaB7hwjsMaW+U1ae6girzlgGqgXh6sFoPZLQeWOBkluMUlQFwiBycFtMrxnpcrHZE6pTIv+D8j4YLrto58su5xEj/CeRG52TXLhihcsrCITMmn9BVnLmHCadNrWHRkouxdlmZ0cyYYgTu/gZpaOLio2FRVHi6e6jsQUfHQMG3qBAVWBKweTFp8ryoDjHLIPsOHZq8KHrBu095s4vO8M5Ip8+GVQXmH43ER12N576N29fF+GAD0mWySyuRJLiv1Zy0mRKouWXw20RNP3U9yZ0jWDdLhAGSmYBlsIpcc1zsrprW48bbYx6kt64H6Ov3Sy3LLxswqTEtPwiVJsDYegjDrixIrTlJTAMlIrpMbvWqhm5WAoqzdc37E1ofd+/7W3QIljKpmCtONX8R7I7UactASByaMt7wnewzF1mzn9wG8IYf3c/wvdIUMllGCPttpHwPxS/4uR22/9LOB98TALDJRe7TUI5B1wIOCEulp8tY1GTM+dw5qOhLXyiy+UcZD3a+sEXApsKU+Igti6Yanq9NHToDAyNXXrRdEF9t/kAmpKvYE3AZylJ0kj2Y3e9IBQ5saB19XuIaAYWVaEwJ3XSc5nznfB9qe+CqGQIYb8Xb7+pCJdRWIZqnXygU1ukYo+WX453nfrgDjUfQAS9pp5H9fxJdScU5qZhtShomkFHj3vUoMAst5iZB3XmCuQJZlnA1H7IKq4ASSLs9+IbjC0bobXXozUcBEnGtvIDE5rTWj4TyepAhPyEE1R+EYaBb/MbwJlZj2EoU+YhOdMh6ENv2JuQeScCtXoOkt2J8A2hN4/f9ZNosukwJEVBinKe3ovsR1NTE5IknWEudz74OI8Jw/cetNkmw9PldJQXWZEl8PgMmnrOXfAxLKVeWwRqHG8vM1WmutR84e5xND9a+nTCmunfUppA4m5tsZmNCEVgT7352fkCYQaj5ZbSggzkSZRbTkde+gmp9e3HQdf0EZ6HIyMbR4KcVVVFGnG7Pbn8og10ovWY89lqFo2Q+uKFIsuURlXshnwhXJ5T/TjMcsub0XJLMcqU2Mstp0O12ckoMIlFnt5OIsGxhVOEMAht/DsAltlLUbInpnEvKSq26vlAlB8z1Dfxkz4NoSN70fu7kRwpOBYuP+u86nTTb0U7tjMu0a/JwJzf7EIKH3hnzGOFoWOEzJJbojMfYJJg4b0hnZaVldHZ2cns2bNPPSf1POH0PCaIE9Lq57DTJZr5KE5Cm+0wbFaZkgIraRl2NF0izQH5E+cqTghuP3S5QAKmFsc/Tiyll7AmaO41P8fqQhV5DP+WiUKSpJHOl+3HBGHtRLklK92RUB+TYSysAlWGPg90tLSjR8IoFivp+RNg7MaAM8ovwQDB6E7aUlyDmpEY63an3UJBNDvU2eshdJKWvN504ER3y4LLJ60B4cjIwZaaDiMcmbNnzLQjuzF628Fqx7pk9CzDeFAz8lDzKwDMzqBJpv+9618BwLl0NfIYGS65bBpSei5oYbRjOyc1ZzywzDKDH735CIbXddbjTEl1gaRakC3jCPzEgUSLjcWKcDiMoigUFhaiqqeWeCdCOA2HJ69P84+C88HHJPBeONqeCD6Sm22pLLGSmW3uEqrPgarp0WgnYEmO6WMSL+bXWpAlaOnW6R0c/WZu7NHRDUhzSBRkJP67m1Uuke4EXxAONXlHxMQKc+LvbhkLTpvp+5Jnc6OGBwCzrVZOgqlY7XD3S0jgOvIuaGFkZzrWBNvW52am4LRbMISgrdssvwi/B+3gJsC0kI+lu2U8SJJERmE5sqKihUMM9YzekioiYUJbXwXAesGlyM74S2e28plIVrtZfmmLnwQa6W4ndGQvSBKpF1055rGSJKPONDMjesNehN8T97zxQMnORymuAiFGfHBGQ7L4HsMYERsLhyaVaVi9ejV33303d999N5mZmeTk5PDAAw+MlAkrKyt56KGHuP3228nIyOCOO+4Yteyyfv16Lrx4NVmz51K5eAlf+cpX0E4ing7Pc++995Kbm8uaNWviPud/NJwPPiaBc+1oq+uC7oHkl13A9HjJzDZFNmqKkht4RHSTswAwfRJZD4A0p8zUcnNnMVrpJRAWtEVblWsK1aQEVYoisXSaRKpdQxZmKr8oLx1lgmJiE8H0ogiz0k0TM5+Sh20Si+NYGC6/5Gtt2IO9CEnGVrMQSU7s9ShJEqUF0fbbUITeAS+RvetAiyBlF02q3HI6FFUdab/1u/oIjiK/Ht6zHuFzI6VnYZ23clLzSaoFW1VUfKyzAd0XWwvq6fBtMIMh++xFqLnjl4DkgooR4THtSGydJ4nEcPYjcmj7WTNMmt9PIBgkBAQCgYT/BMMRghGdQDCI3z048vt42pD/8Ic/oKoq27Zt46c//SmPPPIIv/nNb0b+/vDDDzN79mx27drF17/+9TNe397ezvve9z4WL17MO88/x08e/Aa//e1veeihh0adZ/PmzTz22GMTPs9/VCTHX/r/CM61o22Py0DTwWqB7PTkBgR5eXZsAxaEIaiI0749VjR2mwFImmNi7bVnw6JpFo40a+w8EuHKpaemUeq7TEGx7FSJnHFcayeDuZUQDHiQJRBYSY9DTCxWCCHw9LRikTU8ETs7eoooLJtcBmksZKt+rJpJHOy0T6XanpyMjtWiUJyXTlu3G3/jIdK7m0GWsSy4bFLdO6PBlpqOMysX/2Af7q5WrFXTkKM6JYbXTXjXW+Zxy9+PpE6+HKBmFaBmF6MNdBBq2Itj9kUTCoQNv2/ExyX14qtjeo0kSVhmLSe84Sn0lsMoNQuQ08/u8ZNoqDVzYcPzCI8LvfUYRLt/hiGEwO92sey6DyJZLBNvd4sVuo4QRlTa3Hx2v/vuuzgmmG0pKyvjkUceQZIkpk2bxv79+3nkkUe44447ALj00ku57777Ro5vamo65fWPPvooZWVl/PznPydYX8e06in0GYKvfPWr/Md//McIN6ympoYf/OAHk3jD/5g4n/mYBM61uumwrHpxzsQlwCcKDZObMOQOoGvJEycSAo5EM93TihPzvJlXYzGdZvsN2npPpFY9AYMul/md1RQmN+72+oNkOjU0HXY2pJJMfaeAeyBqlibRJSrQhcyuGH1fJgphGASP70YWOkNKNi2U09iTPKJcRqqdDKsgr3MPAMrUJchp2UmZKz2vGMViw9AiDHWfUG4Lb1sLWgS5sMJcQBMEa+VsUFQMn4tIV+P4LzgJvnfWIcIh1KIyrDWzYn6dnF2EXFQNCLRDWyd4xpODpFpOKJ6OovlhhKJmchLJCzzA1CmASYuuXXjhhacEjMuWLaOurg49Ws654IKzS/0DHD58mGXLlpnl0WgwvfzCC/F6vbS1tY0cN944/1txPvMxCZxrddMTnS7Jn6/dpA7gGvDT1K4yozo5NdgeN7h8pmNrdYIyLE67xOwpKu/WaWw7GKZ0tXnux6MGaQUZMulJJAlHNJ2ufrOmfrwnhS6XwpE2wczyxD9Q9UiYoR5zoUzLK2SOzUHzLmjuMwm8hZmJnS/SUYfhc4FiwVI1Hzokmnt08jNk0pNwH0iSRH7XHoQeJmTPxJ89lfjk0mKYS5bJLC6nv7mOwNAg9rQMLEEfkUMmQdN+0TUJLdPJVju28pmEGvcRbj2Mml2EbBv/PhOGgW/jWsDMekz0nNSZywh3NmB0NWD0dyDnTLLWOQFYZi0lsm8zWuMhFP+pSrZGMIDdZmPb2tewl8Zg6hQnhBYh0tkKkoSluAJJlrEnUEl1GCkpKWOfhxAj352kKAjNwIjyPU7+Tscb538rzmc+JoFz7Wh7rsimwbCgNdoF6BoI0Ngen9toLBgmmlblj+9eOxEsnWVmbnYcjqDrgkGvQb/HlFGvLkzu59fV58EwBHabSmGUN7PlsEi4vLUQAldnK8IwsDicpGTnk5V6oltox3FTuC1R0L0uwu3HALBVzSEvN5X8DBkBHGrVMJKQ3tE76hEdxxGSRE/JYvqHguOqn04GVkcKKdmmyIy7s5Xgxr8DArV2PkphRcLnU/MrkFOzwNAJNe2P6TXB/TvRB3qRU9JwLrpownPKadkoFTMBiBzaek5l15XcIuTCcjAMtIYDp/zNCASQJInU7CwcDkfyflLTcKak4rDZsCsSDkd8zrnvvPPOGf+vra1FiZHoPXPmTLZsMR1/pai2wJatW0hLS6OkJLGdav+IOB98TALn2tH2XGh8ADR2C4QAi6QTDmk0tiWnvcsfMnfocMIoLVGYWaGS5pTwBgQHGyMjwljF2TJOW/K+L68/hNtrtvGV5GWwqFbGqkKvG+oS7O0VcA8Q9ntAksgsLB95gM6rNOXXB31Q15mYuYShE6rfA0KgZBeh5phf2LRiFYsC3uCJ9uVEQYRDRPaaXAu1ZiHOAjOqau9xo4/REjtZpOUWolrtSF3NGO31oKjYlsfGq5goJEnCNmUeSBL6YBfawPhfmHdDtL122WVI1vhat9VpS0CWEf3tGL2tcY0RL6zDxNPj+4ATgU+yO12GIUnSia6XYPwtt62trdx7770cPXqUJ554gp/97Gf827/9W8yv/9znPkdrayv33HMPxxobefGNN/nPb3+He++9N6FaQP+o+Od/h0nEuSy7hMKCPnfUzTbJZZfj0UWyMNOcb9hgLuHzdJmcj7x0yE5wc4aiSCyeYaZS9jVquP0CWUqMjPrZYAhBZ6/ZKZGd4cRht+CwSiyqMYOCLYeNhO0yTym35Bah2k6kje0WmF9p/ntPIwQToKgdbj2KEfAgWazYq+aOBDo2i8TUYvMzbezW8QUTFxRoBzdCyI+Umok6fSmFuWlYVIWIZtDVl7xWUUmWySgoxnZst/n/GYuR05PDMwFQnOlYikyp2lDT/jG1PyLtzYSPHwJZJmVl/G2XkjMNpdLkr2iHz232Q62dDxYbeF0jfiYnzOSkhJrJnQ2SfVhsLDDOkWfHbbfdRiAQYMmSJdx1113cc889fPazn4359SUlJbz88sts376dxVdcxecffJDbP/YxHnjggbjP6X8TznM+JoFzSTjtjLaHpjkl0pKYaTEMQX2X+SCaVanwLNDSGULTBWoCJeQNAcdOIpomA0tnWlm3K4zdYZ53aY6CzZI8Ilu/y0cooqMoMgUnRVOLp0rsqBN0DpidPVMKJzfPqeWWFFKy8844ZmqxmfUY9MHeJlhaG/98umeASOdxAGxV889QMS3MlOlySfR7BIfaNC6otkyaG6H3tqI3mxLklgWXIykqCqZCbGP7AINDAdJT7KQlq4vo6G7kgAfDaidQUIlDi6AkoMvlbLCWTkXrb49qfxzFVjE6iXRYVMwxbylq1uRE3dSpF6A3H0AMdmN0NaIUxefJM1FIFiuWaQsI1x+EqKmf4Tdb0mW7LeFt26Oew8l6H4YxrjngaLBYLPz4xz/ml7/85Rl/O72zBUztj9ODvIsvvpjt27cT7u1BGxxAzco+RYTs7bffnvB5/W/B+czHJOAbKbsk/2Y5VyWXzkEIhEz+xewqBaddRtOhvTuxpZe2fvCHzV16xZlrZ0JQkqcwp0YhM10GAZX5yfvswhGdngGTQFeYk3aKpkeKXWLBFHMx3nRw8tmPU8otRWWjLvSyBIujvi/HOmAgNpf6MyB0jWC92Wmi5pahZp8ZOUmSxPQSC4oMbr+grX9y2Q+hRUwJdUCpmnsKITLFYSUnw+TRtPe40ccwn4sXht9LaIc5vz5jCUKWGepqS2p2QJIVbJVzgKj2h/9MrRF9yIV/50YAUmJsrx1zTrsTZYqpN6IdfuecZj+GNT+EFkYYOrrfB4DsPDfkSkm1gKKCEIhw8jhEMZ/P/0Fn2/PBxyRwLjMf50JWHRgxkptSKGFRZSpLzJpyQ4JLL8NE0+pCs9MlGRBCUF1h7lY7e/WEmMedDZ19QwhhSoNnpp2ZNr5wuoSqQHs/NHTFP8+p3S1FqNazp6gLM6Eyz6yq7zhOXO2+4ZbDiKAPyWrHVjn7rMc5rNJI+/LxLo1gOP6FTDu8FeEfAkfqiCrnySjIiZrP6QYdfWcu0pNF+J1XIRxEzishdfGlAAS9boIeV8LnOhlqVgFKdhEgCDXuOyMY8K5/BXQNa+VUrJWxuemOO2ftIlCtiKE+jI66hIwZC+S8EqTMfBCm1Plw8KGcq+BDkpCHsx+TKL0kCiP+LueDj/MYD+GIQSSqf3Fug4/kZj7qO833VB3tZxx2uK1rSlzwMeQ3MywAU5PVNwmmpocE4Yhg96EI7QkmRA5jyBfE4zM/n+K89FEzEakOiYXV5u83xpn9EELg7jqp3JI1fspo0RQzuOt2Q1Nsxq0j0Ny9RLpN/QnblPnjimuV5shkOCV0Aw63a3G9R2OgC70+6hcz/9IRF9KTIcsSpQWm2ZDbE2TImzifDr23g8ih7QDYLroWqyOF1ByzB3youw09yZb0torZICsYngG0vhNEUCPox7f5NQBSL782YS2/ktWOWrMAAO3wtjG9bRIJSZJGNFMMn9f0NZHlpJNNTzmHaPARj8nc22+/zY9//OPEnUv03pqs18//JpwPPuLEcNZDlsCRxO6JYZwLjQ9PQNDtMv9dXWg+3GZMMR8GhxsStzs4FiX0l2SbqqbJgCEEDd3mjez1GkQ02HYo8V07hiHo7DXJj7mZKdjH6Be+cLqERYHOAaiPowslMDRIyDfc3TJ6ueV0pNhN3xeAXQ2mkmwsEFqEUP27gNkOqmbmj/saSZKYWaoiS9DvOSHoFiuEoRPZ8wYgkMumo5ymgHkynHYruZnmLrm9dwgtAeUXIQShjS+AEKg181BLTA5Eam4Bqs2OoeuniI8lA7LNgbXUzGqEmw8hNPOa9W15ExHwo+YXY5+1KKFzKtXzwWpHeAfRW+P3mpkoLFUzQAIjapamOJ1J95A6GcOkUxEKntOS06jnMpz5iMQXtP9vxPngI04M8z2cDjmhrqijYchn4A0IJKAogfbvp2O45FKcbQp1AcysNncHLZ1hPL7JZw403exygeQRTQE6BwwCYbPldFqJeWPvOBxBT6TwBdA76CWi6aiqTF722CnjFLvEwpr4sh/6SaqbabmFp3S3jIdZUal1fwgOtMT2mlDLIUQ4gGRznpX8OBpS7DJVBeY1eqxDIxSZwHs8thPhGQCrA8uc8fUr8nNSsVlVdN2go3fy5Ret/gD6cGvtiveP/F6S5BHvl6DHRWDINem5xoKlsBrZkYbQwoRajyA0De/bLwOQeuk1cZEjx4JksZnlF0A/uh1hnBtrd8nmQFIt6Jo537nie4zMr1pMeXUhEOFz63J75rlESabCMFVe/8GRiADpfPARJ85lm+1w1iM3U8aaxG6N4eCjpvjEHJnpKsX5FlMGvWHyN2hzL4Q1SLGZQU4yoBuChh4z61GZpzC7ykKqQ8LjFxxuSlxaMxzR6HOZteqi3HSUGBaFC6dJWFToGjzR0jwezHJLG8LQsdgdIyJYsUKR4YJq898HW8HtH/t4zdWD1tMMRMstysSa4iryFFLtEhEdjnbE9nkb7j60o6bbqWXuxUjW8VNisiRRmm+WX4a8Qdye+LNzQosQ2vwiANaFFyOnn2oyZLE7Tym/GEmszUuyjK3KJJ9q3U14t6zFcA8gp2fhXDxxUbFYoFTNBZsT4R8a6TJKNiwWCygWAhGzlKU4nOdk3mGcwvuYhN5HQs7lJJ+Z/w28D3+0O8liib8D7HyrbZzwnUN103NBNo1ogqYe89+1xacGODOmOOjoiXC4IcDiOZPbnQwTTacWjVgsJBztAzqhiNmxU5KjoMim5sdbu8Ns2R9m9pTEtEx29noQwuzAONk4zu/309vbi8vlwuPx4PV68Xg8+Hw+IpEIbU1h6jsivPumxtJpMqqqoqoqFosFi8WC0+kkLS2N1NRUUlNTsUoCNeIjLTWNjJPExCaCshyzzNU+ANuPw+VzRrfPEFqEUMO7AFgKq1AzJt7OKUsSs8pUttdF6HEbdLt0CjLPfp8IwzDLLcJALpqCXBJ7X7DDbiEvK4XeQR8dvUM4HVYs6sTvyfDutxFDA0gpGVgXXjLqMak5BQS9brRQEHdPO1nFiVc8HYaSnouaW0qktxXvm3835199dUJM7UaDpFpQpy5G278e7eh2lPIZEw46JwpFUXAEAvRFNKScbITfi3KOSw66rKBrOpLXgyUGaftkIixJCN1A+Hzn/HOIFUII/H4/PT09ZGZmxqzmOhrOBx9x4lyqm54LsmlTj1kSSXdCXsapf5tZY+fNd4Y4VD853ke/B/o8ZtBRkySiqW4ImqJGZ1X5Kko0wlkxx8pbu8Psb9AYGDLITo//e/N6vRw8fIxdew/T2d5G0DdAV2cH3d3d9Pb2juwKzgYhTD8bIWD7G2ZpaMz3FAkjhMBitZKXX0BeXh4FBQWUlpZSXFxMSUkJpaWlVFZW4nSOvnuUJFhSA8/vMMm+LX2jtziHmg8gwkEkewrWshmxfiRnIM0hU5mv0Nijc7RDIytVPmu3kV6/B+HqAYsNy7xLJhxc5WWn4vGFCIY1OnqHKC/MnJhD7NAA4Z3rALCt/ACSdXTtEEmWySgsp7/5GMGhQYJpmdjTMkY9NhGwls8ksH8HhmsQyWojZXn8omKxQKmchXZ8FwS86E0HUKvnJ3U+AGX7ZjSfn95lKxnwe5FT0pM+58kQmoY+NIgkSShub3IN7cZBZHAQEQ6hBIIo55B4Gw8yMzMpLJycYNH54CNOnNs22+RrfJxccjn9wT0zaipX3xIiGDKwx0mwHSaalueCIz5V6HHR2qcT1szxi7NOnGdhjsLUMoVjrTqb94e5ZkVsnInOzk7279/P4cOHOXLkCEeOHKGjo4NwlLmpyNIpmh7DcDgcZGVlkZaWNvKTkpKCxWJBVVXa+hU6BlVS7DC3QkPXdXRdJxKJ4PP58Hq9eL1eBvt7cQ0O4vX5EUj09PTQ09PDwYMHRz3fwsJCpkyZQlVVFbW1tUyfPp1p06aZ2RQHzC6Hfc1m621xNlhOuqS0wS60qNS2vXri5ZbTUZWv0OM28IUExzo0ZpefuWs3PINoh02PDHX2RUj2iWfWZMnsfqlv7cfjC+HyBMlKj/3hHdr4d9A1lJJq1Np5Yx5rjXro+AZ6cHe3YnWmICcpQyBb7UTqGwCw1NSO+H8kC5KimtmPvW+hHduJUjEraZmWYXh37UDu7CA31IWtpBD7NZ9CyZyceNpEIAyD3h8/gAgEyLr937CWVJ6zuU9Hx9uv4960nuzrPkTetR98z85jPFgslkllPIZxPviIE+eK82EYYkTdNFllFyEEx6MttjVFZ0b++dkqOZkq/S6NuuYgc6ZOvDYb1kx1TzhhfJZoaPoJf5GqfPUMIvBF82wca/WzZX+Yq5basJy2E9d1ncOHD7N79252797Nnj176Oo6U5RD1w0ys7IpKSll1sypVFZUUFpaSkFBAfn5+eTl5Y3rRBkIC375kkEoAtcslZhdceZ3G/S4GWw3W13Tiirx+AP09/fT29tLZ2cn7e3ttLe309HRQXNzMy6Xi66uLrq6utiyZcvIOJIkUV5ezvTp05k1ey4udS7ZJbPZ1+xkUVTUUkTChBqiLa5F1ShpOeN82uNDliVmlqnsOB6hy2VQmKmTm37ioSWEMMstho6cX45SHn+mxW6zkJedSs+Al86+IVKdsZVftJajpsGZJGO7+PqYMiZpuYUEvW70cIihno4RMmqiEWo8RqS1CWQZW20toZbD2JOcjVAqZqLX7TK5H437RoioyUCovY1wZweSqpIxdz5Gex3K8T3YV16TtDlHQ0peEcEDO5GajmGvnn5O5z4ZjpQUhnp7oLM9KS67/2g4H3zEiRFH2ySrm/a7zTZRVTEJp8lAtwu8AbCoUDEKl1GSJGZW29m4y8uh+viCj/pu0AzIcEJBkjLVLX06ER2cVonCrDM/q7nVKhkpEm6fYO/xCBdMt9LR0cGmTZvYvHkzW7ZsYWjo1K4JRVGYPn36yE91TQ2qM4+U1DTKCjLIiLNX2GGVWDZd4u39gg0HBNNLT5WvN3QNd7eZhUjJzic1I5PUjEyKis5er3K5XDQ2NtLQ0EBDQwNHjx7lyJEj9Pb20tzcTHNzM2vXrkXTIRCRyS+pZs1FC1ixbBGzcywUqBqyMw1rWeIewBlOmfJchZY+ncPtGstS5JH3qTfsQwx0gmrBMv+ySbdZ5mWl4PGFCIQitPe4qSjKGnNMoWuE1j8PgGXucpSc2NLIkiyTWVhOf0sdAfcA9rRM7KmJLxd41j4DgGP+hchOJ1pvC3p+OUpa8nxmJFlBmbYEbc8baHW7UCrnjKq1kggM7TL1VJwzZ2NbsJJAex3a4V2IZVcnnW9yMqw1Mwge2Eno+GHSLrv2nM17xnnkmnXQSF/Pe3YO5xIJ/4a/+93v8uyzz3LkyBEcDgfLly/n+9//PtOmTUv0VO8pRjgfSc58DJdcCnPkEf5ColEXLblUFXBW/5YZUxzR4GPivA9xmo9LMsqqEU3QEs16TClUkEeZRFEkVsyx8Kfn9vLQd9YT7ltPfX39KcekpaWxaNEiFixYwMKFC5kzZw6Ok+qvzR2DePwhk2SaOrndyQW1EjuPC9w+2FMvWDz1xDkP9XRgaBqK1UZabmyLYmZmJgsWLGDBggWn/H5gYIAjR45w8OBB9u/fz759+6hv7qS7rY4n/1rH88/8BREJkp+dyeIVF7N8VR/Lli2jrKxsUu9vGNWFCr1DBoGwWX6ZWWbB8LnRDm0GQJ21AsmZNul5JEmipCCD+tY+vP4wg0MBsjPOHihH9m7CcPUiOVKxLb1iQnNZnabIm2+wF3dXK9aq6cgJSEUPI9x0jNDhd0GWSX//zWjuLrTeFkKN+3DMuTipehhK2XT0up0Irwu9YS/qtMVJmcez0ww+0hctQamYhpSSjvANoTUcxDJO+SuRsNXMBCDccDhun5dEwDISfPS9J/OfayQ8+Fi/fj133XUXixcvRtM07r//fq644goOHTo0bir6fxPOVdml/RyQTYf5Hqd3uZyMmTXmQnu0MUhEE2eULMZCl8ts71QVmFIwqVM9K5r7dDTD1NIoyDj1OxFCsG/fPl588UVeXfsGB460AZCdLmOzKsydO5eVK1eyYsUK5s6de9Z65pAviMdvKpkWnUXJdCKwqBIXzZJ4Zadg8yHBnEqB3SoR8g4RcA8AmGJik3wYZmdns3z5cpYvPyFV3tjSy6+f3Ufr0W34j7/KoeON9A75eeX1N3nlddPXpKSkhOXLl7NixQpWrFhBenp8u3slWn7ZVR+hY9AgP10jbd8boGtIOSUoUU+TRMBuVSnITqOr30NXn4dUpxWr5czHnOF1E9r+BgC2Fe9DiqPTITUvWn6JhPH0dpBRmJhgDWDoVTPr4Vy8CjW3ECUjC22gE8M/RKS7CWthVcLmOh2SLKNOW0pk11q047tRquaelYQbL4xIBO9e0zU47YIlSLKCZeZiwjveJHLgnXMafFhKKpHsDkQwQKS9CWvZuTHYO+M8coaDjwlKEf8vRcKDj1dfffWU///+978nPz+fXbt2sWrVqkRP957hXLXatnSbwUdZkkzRPAFBV1TqvHoUvscwSguspDplvH6DhtYQ06pi3/UPt9dOKRi/syMehDVBazRIqy5QRoKCtrY2XnjhBZ5//vlTXCbTUh1klizjijVr+I8vXBHTonqGkmmC3sjcSontRwX9Hth2VHDRTANXl1lucWblYnWmjjNCfKgqz+NjH7wUW1sqRcpsApKNeiOdHTt3snXrVt59913a29t56qmneOqpp5BlmXnz5rFq1SpWrVrFzJkzkScQFGWlnCi/9B/YS2p/OygWLAsvT/guPifTyZAviD8Yoa3bTVVJ9hlzhDa+AJEQcmE56vT4eA2yrJBRWMZAaz1+Vz/2tExsKZPP4Jyc9Ui7wiQeShYbtrLphJr2E249jJpdhDyGr89kIZfWIh3bgfAMoNXvwTLjwoSO7z98ACMQQM3IxFFttlZbZi4hvGMdettxDHcfchxt3vFAkmWsU6YTOrSH8PHD713wkWcGH5rbhREOI1uTxMr/B0HSC2tutxswd1+jIRQKEQqd8A05veb+jwrfOWq1bU1y8FF/kqppiv3si4AsS8ysdrB9v4/DDYGYgw9fCFqjWcTpSSKaNvXo6AakOSQy7BovvvgKTz75JDt27Bg5xm63s2bNGq6++moKypfyq7/rGCpYbLEtFn0un6lkqoyvZDoRyLLE6rkyz2w22H5MMCurA0OLoFispOUl0fgGmGpvJax0YwiJ5rRlXDgrnQuXLeOee+7B7/ezc+dOtmzZwqZNm6irq2PPnj3s2bOHn/zkJ+Tn53PppZdy6aWXcuGFF2Kzjb8zri5U8PQNUNq3DQB19grklMQTgKRo98vxln78wQj9Lj+5WSe+M63pMNrxfSDJ2FffgCTFfw/bUtJwZubid/Xh7mwhNwHll9OzHsNQCyqJ9LZg+NyEWw5hr1k4qXnGgiTJqNMvJLLjZfT6PahT5iLZEicCNhQtuaQtXDyS2ZPTs1HKp6K3HCVycDu25e9L2HzjwVYzg9ChPYSOHyL1kveP/4IkQElLR7JYEZEwkf4+bEVJlID+B0BSgw8hBPfeey8rV65k9uzRHTG/+93v8s1vfjOZp5EUnItW2yGfgdtnyqonK/io6zxT1fRsmFFtZ/t+H4fqA1x/Wda4x4PJ9RCYJNPMJFTdgmFBW79Ob3cbW7Y/yxdefJaBAbNkIUkSy5Yt47rrrmPNmjUjZT8hBEU5Xjr7DbYdDLN64dgLZzii0TtoetIX5abFpGQ6EdQWQ0kO6EEvEW8/ABmFZchy8rJqRshPuOUAAIf06RzrS6dkEIqiX6vT6RzJcgB0dHSwceNGNmzYwJYtW+jp6eHJJ5/kySefxOFwsGrVKq644gpWr15Nauro2RpZEswYWI8sNFyOEpTsmYxvjRcfrBaVwtw0OnqH6B4wyy92mwURCRN8+28AWOavRMkrmfRcaflFhHxDCSm/hBpPznrccMrfJEnCVjWXwIGNaH1tJvk0PXnZAbm4GikjD+HuRavbjWX2yoSNPbTN7MZKu2DJKb+3zF5qBh+HdmBdesU5I57aakwLgVD9IYSuj1jcn0tIkoQlN5dwZ8f54GOyuPvuu9m3bx+bNm066zFf/epXuffee0f+PzQ0lDCiWzJxLjgfwyWX/GwZmzXxBLOIJmiKtr/GEnwM630caQhiGGJcTxvdgLqotse0yT/jz4AQgpfe3MEf/vA79u14C1v0as7Pz+fDH/4wN91006hCOJIkcdE8K/+zLsjGvWEuXmAdM/V/ipLpJEmmo0GSJC6ZIwh0mlwU2ZmdkPT92SCEIHh8D+gacmoWkrUaOuGdOrhmkcnNOR3FxcXcfPPN3HzzzYTDYbZt28abb77JunXr6O7uZu3ataxduxar1crKlSu54ooruOyyy04paen17yK7OjFkC3W5FyPadTJTlAnxhyaCrHQHQ74gXn+Yth431aU5hLe/jvAMIqVlYlsyMZLp2ZDI8ovn1acBcC6+GDX3TIKUkpqFWlCJ1t1EqHG/ST5NEkFSkiTUGcuIvPOCSTytno/kmHwZMNjSTLCxARSF9KXLT/mbWjkTyZmK8HvRGg9hiTrfJhuWsilIjhREwEektQFrZewquwk9j9w8M/jo/efveEnaynnPPffwwgsv8NZbb1FaWnrW42w2G+np6af8/KNDCDGS+UhNYqtta1SpszxJWY+TVU3zY8h+V5XasFslvH6D1q7xHWJb+iAYMQW/yicvGzECXddZu3YtN334Fr5w58fZ8846LAqsWLGCn//857z99tvcc889YyrwLZ5hxWaB7kGDQ41n91IYJplKQHECSKZnQ7rRRZotgjdsYXPr5JQDx0Oksx7D0w+ygr1mAQumyDit4AnA/hiM56xWKxdddBEPPvgg69ev59lnn+XOO++ksrKScDjMunXr+MpXvsLy5cu58847efHFF/F2t6Ed2gqAZc5KlNR0wlrs3i/xQJIkSvIzUGSJYEijt6Ge8LsbALBf/MGEkiiHyy8A7s4WDH3i5myhxmOEjuwFWRnheow6V9l0JNWKEfAQ6ao/63GJgFxQgZRdBIaOdmzH+C+IAa4Nppps2sLFqKc97yVFwTLDzIZEDm5LyHyxQJJlbLXR7Mex/eds3tMx0vHS/8/f8ZLw4EMIwd13382zzz7LunXrqKpKHiv7vUIwJEaMB5OZ+RjhexQkJ/gYUTUtOlPVdDSoisTUKNfj0PHxW26PRt3HpxZBIjZnuq7zt7/9jauvvprPf/7z7Nq9B1W1cOUHbmTtq6/wu9/9jjVr1sSkvuewSayYaxK6XtsRGvWYk0mmOZkp2JLBlgVCPg9+l/mw2dpewtF2hYau5Hg76P4hwlHbdFvFLGR7KlYVlkQ3egdaYdAX+3iSJDFr1iy+8IUv8Oqrr/Liiy9yzz33UFNTQyQSYd26dXzxi19k+YoV3PffT7G+1YUomcasMvOz7HKZ3i/JgkVVKM5LByGQt7wAhoFaPRu1ambC50rLL0KxWNG1CJ7eGF0DT4Ln1acAcC5ZNWrWYxiSasUadRoOtx3DCI3jFDgJDGc/APSmgxi+yXPyXOvfAiDz4tE9dCyzzOBDb6nDiHZ9nQvYppldV8Gj72HwkWMGsP8XOl4SvnLedddd/PnPf+Yvf/kLaWlpI4qLgcDkfEH+kTBcclEVkuoyO1x2KU9C8GEYYkTfo7Yk9vcwc4pZejk0jsPtoBd6hkxNj9pJ8iZ1XefZZ5/lqquu4itf+QrNzc2kpqZz9Y2f5Ye/fY3/+sG3mTJl4gz1SxfaUGSob9epbz9zB9476DVJpmpiSaYnwzB03MPdLZk5FBeaO8E39hjoRmIDEGHohI7vBmGgZBag5p8wRivPNc3nhIAtRyGeqSVJora2lrvvvpuXXnqJF198kc997nOU52YSDAR5bc9hPv+zP3HRRRfx44e/hb97H0IIDrdrBCPJM9LKSHOQ13MYm6sTQ7WirkyOkNRw+QXA7+on5PPE/NrQsQOEjuwzsx5rxpfWVnNLkdOywdAJNR2I+5xjgZJXipxXBsJAPzq5bESgqZFgc6Oparp8dIdeOSMHpawWEEQObZ/UfBOBfaoZfIQbj2KE3huXW2ueqfJ4PviIA7/85S9xu92sXr2aoqKikZ+//vWviZ7qPYPvJHXTZKXhPX4Dl9d8IJcmoezS3g++oOn8OprB2NkwrPdx6HgAMYbz4pHoxq88F5xxZrcNw+CFF17gqquu4qtf/SotLS1kZWXxpS99iV/8+Q1u+Pg91Fbmkx5nx1FmmszSmaZ3xeunZT+CYY2+aAqgODc94STTYXh6OtEjYRTVQlpeMStnSThtpgnfrrrELsjh1qMY/iFQrdimzDvj2l1aa7ZC93vgYOvk56utreWeWz/MC1/6GE98+ZN84uMfIzcvH5fLxV/+8he+dPfHeeCuD/DsXx5j/c7mMa+nycDwunEeMHfbrtoV9ASTl600yy9mjdEVY/lFGAbu5/8EQMrKNWNmPYYxTD5FktAHu9AGuyd34uNAnRnNfrQcwfDEn40YKbksWoKaenZejGW22dobObwDYSQvM3YylLxClOw80HXCDUfOyZyn43zmYxIQQoz6c/vttyd6qvcM56LTZYRsmiVjTwLZ9GjbCWEx5SyqpqOhtsKORZUYHNJp6Ryd9xGKnPBxmRYHYVsIwaZNm/jgBz/Il770JVpaWsjOzuZLX/oS69at46aPfgpvxAyCqieZFbpssQ0JONCgjbgHCyHo7B1CAGlOG2kpiRVYGsbJ5ZaMonJkRcFulbh4jvl9bDok8AUTsyDrQ/1EOo8DYJ8yb1SNCKcNFleb/97bZDrvTgZCCxPZ9RoSMGfFJdz/vf9iw4YN/Pa3v+W6667D4XAw2NPK3x7/OZ/5yBXcdMttPP/88wnNkgohCL71DISDkFeKp2I+g0MBhrzJ29mm5RejWKwYWoShnvZxjw/s2kykrQnJ7iDtyhtjnkdxpmMpNDN+oab9CD15/Bk5qxC5sAoQaEfiy34IIU4quVw65rFq1UyTAOobQms8HNd8E4UkSdimml2Zofeo9DLM+Qif53ycx2g4F9LqydT3EEJwtN1c1KaVTiywsVll5k0zSy/b94++OtV1mT4uWSkT93E5ePAgn/zkJ/n0pz/NkSNHSEtL44tf/CLr1q3jM5/5DE6nk/ou8yFblCWTYp/cd1CQpTC/1uQfDGc/3N4gvkAYSYKivLSkZLcM/dRyy8ndEXMrJQqzzCBu/f7JBx9CCxM8bqpJqnllqNlnr4NNKYCSbLPssjnO8sswtP0bET43OFKxzF0NmF45K1eu5Ac/+AFbtmzhBz/4PkuXmrvcbdu2cd+XvszKlSv5xje+wf79+yedDdGO7EJvOgyKivOKW8jNMj/n9h43ES05O2pZVkbM5gLuAYIe91mPFeEwQy8+AUDa5dejTNAjxlo6DcnqQIT8hNuOxX/SMWCY+2G012G4Jt6NEWxqINTajGSxkrFs7LZdSVFPEE/3bxnz2ERimPfxXpFOT0is9yKGiYX/pDgffMSBE222yet0SSbfo2sQhvymnXpVHHLnS+aa7Xbb950ZfBgCjkQ3ezNKY/dx6evr42tf+xo33HADW7duxWKxcPvtt/PGG2/w2c9+dsRfpd9jMOAVSBJMKUgMAXTNEjMLsOtIhN5Bjc4+s1afn5U6qjR3IjDU035KueVkyLLEmgXmrbm3UdA5EP8CLIQg1LAPEQ4g2ZzYKkbX2xmGJMGyqea10e+BQ3GWX/TOevTmgwBYFq4ZtbPE6XRy/fXX89STf+C3T77GBz92N5m5JXi9Xp588kk+9KEPce211/LHP/4xLvFBw+smuPEFAKxLr0DJLiA/JxW7TUU3BG3d7qSVeqzOVFKyzfq9u6sVXRs9K+Hd8Aq6qx8lM4fUiycuqiUpKrYqc8GMdNaj+84e6EwWckYucqnp0aUd3Dzh17vejpZcLliCEoPVhmXOhYCE3lqHMXhuWk9tteb9EWlvRh9ynZM5T4YlO8e8CXUdzX3u5z+XOB98xIETjrZJzHz0JK/TZbjkUl1EXBoLF8xyIklQ3xqibzByyt9aesEfArsFqkZxyD0dkUiE3/3ud1xxxRU884yp7HjNNdewdu1avvrVr5KZmTlyrBCC453mQ7w0W8GRoHJUeYHC9AoVQ8DhpiF03cBmUcjJSg7JNOhxj3i3ZBRXjKqIWZorMbPcfH+v7zHiXiS13ha0gQ6QJOy1i5BUy7ivcdpgSY3573ebJl5+EUEfkT2mP4xSsxAlb2zdHkmSuHhRBTd+9F/49qMv8e3/+h3XXHMNNpuNY8eO8e1vf5uVK1fy5S9/mV27dsX0WYyUW0IB5PwyrAtMsTRZkigryESSwBcI0+9OXqdIWm4hqtWOoWsMdbeecd66dwjP66bgWfr7b0aKU05bzSpEyS4CBKGGvUkLqADUGReCJGP0tqL3xNCXHYUQYoTvkbX6spheI6dno1TNACC8f+vETzYOKGkZWEpMInao7uA5mfNkSKqKmmUq/f2z8z7OBx9xINllF2/AYNBjPkASXXaZTMllGJnp6oi8+o7TSi+Hh9tri0EZ5+PZtGkT11xzDd///vfx+XzMnj2bv/71r/zwhz+kpORMVbJul4EnKFBkqEpwULZmsY38TIOsVJPHUpyfMaoz7mSha9pIuSUlKw/bGN4tl86VsKgmOXhv48QXFCPgGemEsJZOR0mNTZUWRim/xJgBFkIQ2fUahINI6bnmYhUDbBaJGaUqsiyTWXYBX/nGD9i0aRP/8R//wbRp0wiFQjz//PN89KMf5f3vf/+42RDt6G6z3CIr2C//MNJJarE2q0phrlne6O7zEAhGzjbMpCDJMpnFZvkl6HETPG0n7Vn7LCIYwFJSieOC0Ts/YoWtcg4oKobPRaS7aVJjjQU5JQOlyhT+0g5ujjnQCTQcJ9TehmS1niEsNhasc81jI4d3IsKjt8QnGrZp5vt773gf/zc6Xs4HH3Eg2eqmwyWXvEwZhy2xC2DfEAx4zMBgLCO58bBkjpkV2HZS8NE7ZP7I0thE076+Pu69914+/elP09jYSE5ODt/5znd46qmnmD9//qivMQzB8SjXozJfwZpgVcyaUpnLL4ggSeAJWEhxJN7USQiBu6sVQ9dQrfZxvVvSnBKrZpnvc91egTcQewAiDJ1g3W4wdJT0XCzFNRM619PLL/uaY3udfmwnRm8rKCqWC66ckDx2foZCaY55Tx1siWBzpPGxj32M559/nqeeeooPfehDOBwO6uvr+fa3v81FF13E1772Nfbt23fKImj4hghueB6IlltyzhRty053kJ5iQwCt3S70JNXXLXYnqVF/Fnd3G3rEDG613i58m14DIP26j01apVS22rGVRbMErYcxwsmTNlCnXQCqBeHuxWivi+k1rrfNTFj6kmUoztg9YpSyWqTMXAgHiRzdHdf5ThQnSKf7kppFOhv+r3S8nA8+4kCyHW1bk8j3GC65VBaYu814MRx8HKwL4POb5zuc9ajKN1VNT4dhGDzxxBNcddVVvPTSS8iyzG233cbatWu58cYbx3RJbe3XCUbApkJ5buI/l36Xn3SnQSAEL2xWGPIlfjEKDA0S8roBiczi8pgWnAtqT5BPX98T+zmFWw9j+N1mW23NwrhIs04bXDjV/Pf+Fuh2jX280d+BduQdANS5FyOnT1zWtrZIJdUuEdHhQGsEIQSSJDF37ly+/e1vs2nTJh588EGmTp1KMBjkmWee4aabbuKGG27gqaeewu/3EXzjf6LlllKsCy8edZ5h9VOLKhOO6HT0DCVtoUnNKcBidyIMHVdHM4Zh4Hr2D2Do2GbMxz4tMRLiakElcmoW6BqhxuTt2iWbE7XWdALWDm0ZtxXWLLnE1uVyxlySjHVONPuxf8s5CQasU6aDoqK7+tF7u5I+3xnzj5BO/7k7Xs4HH3HAl2TOR0sSlU2HSy7T4yy5DKM430pZoRXdgF2H/PhC0BwN1KeP4uNy/PhxPvrRj/Lggw/i8XiYNWsWTz/9NPfffz9paWP7YER0QVOUAzOlUEUZx1NmogiFNXoHTOO4Y202PH6JV95JbIpXi4QZ6ja9W9JyC7HYY9v9ybLE+y6QkSQ40gbH2sd/+GqD3UQ6GwCwV8+flPV6VT5UF5jmgJuOQPgs3ZwiHCS881VTSbR0Gkp5fAqiiiwxp1xFlmDQK2jqPXVhS01N5SMf+QgvvPACTz75JNdddx1Wq5VDhw7xwAMPsGrxBfzgN3+kxeXDfvnNp5RbzphLkSkryATMDieXJznZAkmSyCyuQJJlwgEf7i1vEDq0GxSFjOtvTeg8p2h/DHQmbOzToVQvAJsT4R9Cbxxb5CxQd5RwZweyzU76kmUTnssyw8y0GP1d6B0N8Z5yzJBtdqxVZtQdPLov6fOdjpF2275/bn+X88FHHBje6Ser7DJCNk0w32PQK+hxmSn1WIzkxsOSuWb2Y/s+H0fbTXXMggzIOSmW0HWdX/3qV1x//fXs2bMHp9PJ/fffz1NPPcWsWbNimqepRyeiQ4pNoigrsZ+5EIL2HjcCSHVaWTzD5GBs3h+mZzAxrZhCCNwdzQjDwOJwkpITAxP3JBRkSSydZn5fr+02CI2hBmqE/CNttZbCKtSsyfvELKmBVDv4Qqb53OmbTyEEkd2vQ8CLlJKJZd4lk2pPTrHLTC8xyzUNXTquUbJQkiSxYMECfvCDH7Bx40a+/OUvU1qYj7uvh8e3H+CDv32Rz375ft566y30MYS+nA4rBTnmd97RO0TwbNHVJKFabaQXlCIiYfwv/w8AqZdei6Xw7L5X8UBJycBSZIq1hBr3IbTxPZjigaRaUKcvBUA7ug0ROXuw3veSWQJLX74SJdq1NqG5bA4s0xYCENl3btpu7e9hy63lfObjPM4Gjy95pnLegMHAUHLIpsMll4o8cCaASzJcenn3qJ9jnebYM056lh49epSbbrqJRx55hEgkwsUXX8wrr7zCbbfdFpP/CkAwLGiNin/VFCkJJ4EODgXwByPIkkRxXgZTyy3MqlIxDHhxc2KyH97+bsIBn0lALKqIa2FeOVMiM9U0f3t73+jBhzAMgnW7QI8gp2RijTP7cDosKlw0AyRMM8LG0zZkesNejK5GkGUsi69CskyeL1OUJVOYKSOA/S0RwtrZA67MzEw+9YnbeO4z1/CzW9Zw8cJ5yHYnmzZt4l//9V9Zs2YNv/nNb3C5XKO+PjczhRSHFSGgtcuFkWBZ+2E40rNQ9u4AnwfSM0m9PDky79bSaUj2VEQklFTpdaViJlJqJoSDaHWj8zE0j4fBda8DkHvN+LLxZ4MlSjzV6g9geJPXTjyMEdJp3cFzrrdhyY1yPvrPcz7O4yQIIegdMNnxeVmJ14AYznrkZsg47YldaIeDj6mTLLkMo7rMRnaGQn5hKmFNItUOpTlmtuPRRx/lhhtu4ODBg6Snp/P973+fxx57bEyn2dFQ361hCMhMkchNS+zlGtF0uvqjmh45qVgtZkB07Uo7ErD7WITmrsnthMN+L94+s26cXlCKGqeTqkWVuHqR+f531wva+s5cIMMtBzG8g6BYsNdeMGbJYaLIS4d5lea/t9WZQRCA0d+JdmATAOqsi5AzJ5bVORskSWJ6iYrTKhGKwIGWCMYY9f7Qpr+Dq5eVc2fy62f/zhtvvMFnPvMZ0tPTaW9v5+GHH2bVqlXcf//9HDlyqnS2JEmUFWSgKjKhsEZHb3L0P7SOFrRd5mclrVyDZzA5O1tJVrBXzzfn7GtLmvS6JCuoM82gQD++G+E/08tmYO1LiFAI+5RqUmbNiXsuJbcYpbgKhEHkwDtxjxMrLGVTkBxORMBPpCW5zsFnzH2+2+U8RoPXbxAImQ+m3GQEH0kimw75BR1RS4ZpEzCSGwuyLLF4Tgq1U80Wzhkl0NLcxC233MJPfvITNE3jsssu4+WXX+b666+f8I7f7TfoHDR3HbVFakKVRoUQdPQOYRgCh81CTsYJDkZJnsLiGaYexvMbg3EvRIau4eow20Qc6Vk4M7Indc6VBRJzq8zP4MXtBuGTyi9afweRrkYA7DULkGPklEwEs8shPx0iOmw4BJrfR3jHyyAM5OIalCmJIU4OQ1Uk5laqKDIMeAUNXaOXT7TGQ0SiOhD2NTcjO1IpLS3lS1/6Ehs2bOA73/kOM2bMIBQK8fTTT3Pdddfx8Y9/nLVr146UZFRVoTQqx+vyBBkYSiz/QxgGrqd+A4aBddZCpIoaAu4BAkODCZ1nGEpaNpaiqPR6416Elpx2YrmoGimnBAydyGnCY8Iw6HvxOQByr7lh0vevZZh4evCdpErJg9kmPeJye/DcdNkMYzjzYfj96P7k6dC81zgffEwQvQPmRZ+ZpmCzJv7ja00S2fRwS9SkLhdSHYlbxKfWZpCSaiEU0tix7nGuu+469u3bR3p6Oj/84Q/5xS9+QV7eBJzrojD1SE7IqGckmNzr9gbx+MyySkl++hkPxvcvt6MqcKxV50jzxB90w221uhZBsVhJL0hMbf/SeRJpDtM1+M295ndqBLwEG94FwFJckxCex2iQJVg5w+w4GvDouDa+AkEfUlo2lgWXJ0WGPtUuM6PUDPKbenV63KcGIIbXZXa3AJb5F6GWTzvl7w6HgxtvvJG//e1v/OUvf+Hqq69GURR27NjB5z//eS677DJ+/etf43K5SHXaKIwSlrp6h/AHE8eX8G97m3DjMSSrjaybPk1qjikt7O5qRUuSfoW1dDqSPQURDhJqTo5gliRJWOaYAm5G+zGM/o6Rv3l27SDc0Y6ckkrWpWsmPZdaPQcpJQPh9xI5kvyAwDF7MQCB/TuSPtfJUBxOZKdZ0v5nzn6cDz4miJ7hkkt2cmS3W3qSk/nY32wuVLMrEpk9gCHNypCrl589eDvfePCbBINBli9fzt///neuueaauBekzkGDoYApKFZTmNjPOqLpdPSaAlX52anYbWeqfuZkyFw0z+QuPL8xOGbKfzSc7OmRWVw5qoppPHBYJa5Zat627zYI6lojBOt2gK4hp2VjLZuekHnOhlS7GYDMC2wiNdCBoVixLH1/QngeZ0NhpjLSXn2wVcMXNLNhQtcIvPwnRNCHnFuMbfnZ5cklSWLRokX8+Mc/Zt26ddx5551kZWXR2dnJj370I1atWsUDDzxAf0/biP5HS6cLLQH+L/qQC/cLjwOQdvVNqFm5pOYWYnWkIAyDwfbGpPAKJEXFPmU+EFW6jcOPJRbImXkoFSZ5PLJ/w0imsO+FZwHIvuLquIimp0NSFKzzTTG2yJ71CJFcLoZ95gKQZbTOVrS+5LoGnw5r3gmPl39WnA8+JojhzEde9vgy1ROFx2/Q70482bTbJeh1m8Ji08sSF3y09cPWTW/xyFevoenIFjTDwgMPPMBvf/vbCXM7ToamnxAUq8pXJqVHcjqGu1uGyy15Y0ioX7nUht0Kbb0GW/fHnraOhAK4h9tq84qxOhJbAqnIH+5+EQTr92D4PUgWm8nzkJJ/Sxf6jjA1tBeAd5xX4CZ25dR4UVOkkJkioRuwr1lD0wWhjS9gdLeAzYHjfbfFLGhWWFjIF77wBdavX893v/vdkZLMU089xbXXXsv9X/48u7ZvJhSO0DpJ/xchBINPPIbwe7GUVJJ68dXAcPttJbKiooWCMbnfxgMlPQdLYRWAKb2epPKLOnMZqFaEqwe95TChzg6GtpulsNxrrk/YPJbZS8FqxxjsQU+y262ckoq12hRuC+7fmdS5Tocl53zwcR6nYTjzkZ+EzEddm7nLKs5NLNn0QJP58KwpJmF+KIFAkK99/Vv84ZE7CfkGSM2sZvFVP+eWWz4+plhYLGjs0Qlr5rkmWlBscCiA12861pYUZIyZmUl1yFy9zNTIeH5jEI9//J2WoesMtjWBENhS0kjJnnjJKRasmi1xSf5xquxdGELCVnvBpPQ8YoXh6iHyrunR0Zq1hDZ1Cm8fOrv+R6IgSxJzyi3YVPCFBE1bdozwPBxXfAQ5Y+KCZjabjRtuuGGkJHPllVeiKArbt2/n2w9+jX/91Ed4/M9/4nhzx/iDnQX+rW9GNT1Usj5+1ykBkmKxkFls+oj4Xf34o34/iYa1bAaSzYkIBwg1Jke3QrI5UaeZLrTaoS1m1kMI0hYuxl5anrh5rHass02tkPDutxM27tngmPPelF7+L3S8nA8+JohkZj7qWs2xp5YlLrAxDMHBKN9jTkVivu66ujquvf5DvPHSnwG44zOf5KqP/AKsZWzd653U2P6QQUu0tXZqsYKcQEGxcESjK+pYW5Cdht06/ue8eoGV0jwZf0jw7PrgmMcKIXB3tqBHQiiqJe622pjg7mK23bRQf2tgNnu6kp99EAEv4Xf+bpZ4CiooW7aEFJvZ+bL5yJn6H4mGzSIxt8JCiq+T3H3PAWBdfDlq5YxJjTtckvnpT3/KG2+8wR133EFGRjp9PV389rGfcc3VV/LV+79OU1PThMbV+rpw/+2PAKR/4BYsxWcuwraUtBH+x1BXG5HQ2NdYPJAUFXvNIkBC628n0teW8DkAlOp5SCkZGD4PA6/+HYDca+Nvrz0bLPNWgKygdzahdzYlfPyTYZ9zAQDhhiPo3ok7K8eL4Y6XcO/54OM8ouhNYubjWDT4qC1N3NiN3eALgsMGUybJQxRC8NRTT3HjjTdy5Ggdqek5PPi93/CNr3+Vqy4yI/W1mybXg3+sQ0cIyElNbGutEKaFuiEETruFnMzYSiGKLPGRNQ4kYMfhyJjkU99AL0GvGySJzJIqZDU5vCDdPzQiJDZor+SQr5y39gm6B5O3+gstbAYeQR9SWhaWRVdht8pcPNMkorb2mw64yUa6EmTmkSdQjAiurFr6aiYm1z0eiouLue+++9iwYQPf/vZD1NTUEAoFefKJJ7jiiiu444472LRp07ilGGEYDP75F4hwCGvNTFJXv/+sx6bmFmJ1piKEgau9CWMcufJ4oKRlYS01VTtDjfswQonvopBkBXX2RQwdb0X3+bHk5k3IRC5WyKkZWKab8u7Jzn6o2XlYSipBiHPa9XIi8/HPKzR2PviYIHpGMh+JXVjcXoPuAQMJqClNXKnhQJRoOrNMQlHi34V7vV7uu+8+HnjgAfyBEFNmreT/+84LfOwGkwB2+bJ0FBkONwRp7oiPvd87pNPnMT+DqcWJba3td/lHxMRKxym3nI6KQpVV801C5V/fDJzS4jqMkN+Lp9dMz6fnlySc5zEMoYUJHtsRNYzLoWTOLGqKQDfgmS0G/lDiAxAhDCI71yLcvWB1YLnwWqSoXkluumlAB6b/S30SeXnC0AmsfRzZO4DuzOL4jJs40mEw4E088dDhcPDhD3+Yta++zH/99FGWXLgCTResX7+BT3/607zvfe/jiSeewH+WVkjvm8+b3S12B1kf+9yYPj7D8uuyqqKFg7g6WpKiM2IpqR3xfgke35OUOaSCSlyHzPbyrLnTYJIl2LPBssDssNEaDqEPJFeGfDj7cS55H+c5H+dxCnwBfcTXJdFll7o2M6gpyZMTJtseiogRL5DZlfEv5AcPHuSGG27gxRdfRFEUrv/4l/jkff/NvKm5pEZpBtkZ6ojc+qtxZD80XXAk2lpbnquQYk/cpekPhkfExApz07BaJh44fmCFnYwUiV6XwWvbTw2udC2Cq70JiOp5ZE6cfxALhKETOLoDEfQhWR3Yay9AVhQ+sFQmMwXcPnjhHSPhCp3agU1RBVMF64UfQE7JOOXv1YUwu8z899aj0J0EAUohBKH1z6G3HAPVQuoHbiU3NxUB7GuO4Aslp/NBlmWue98avvP9H/Gr3/2FD1x3IykpKTQ0NPDggw+yatUqvv/979PefoIwGm5rZOjlpwDIuPGTqDHwfhTVQlZJFUgSIa8bb3/iozhJkrHXLARZwfD0E+k4nvA5hrZsJNjVg2RRSa/Ixmg7mvA5AJTsAtSqmYAgsmd9UuYYhj3K+wgd2YuRpLbo02E53+1yHidjmO+RliLjsCX2oxspuSSQ73G0TaDpptdKURyUACEEjz/+ODfffDPNzc0UFxfzi18/ztzVn0GWZWafVsK+aqW5KK3f4SEQnNhiUN+lE4qYbrhTChOX+dF1g9YuczVMT7GRlR5fy5/DJnHTpeZrX98RoqvfTI0Pt0oauoZqs5NRWJYUnocQglD9HgxPPygq9ulLkSxm9sFhlbhxhYxFMctsGw4kLvjQGveh178LgGXhGuTsolGPW1AF5blgCHj7wAkF1EQhsmdDVNlSwn7lR1ELyphZppLhlNB0eLdRG1OCfTKQZYnyoizKyyv41L98nj89+Rxf+9rXqKiowOPx8Lvf/Y7LL7+cu+66i63r36b/d/8Fho597hKci1fFPI/VkUJGVA/G29dFwONK/Huxp2CrNMWzwm1H0L2Jm0PoOp3/778ByL30ElSHjcj+jYhw4nksAJaFqwGIHNmF4UseH8NSUoGSnYeIhAkdPTdeL8OZD801iNCSzOZ+j3A++JgAhksu+Ukhm0ZJlgkMPvY3ndD2mOiC6PP5uPfee/nP//xPIpEIl19+Oc899xxa2gIApuRDxmmVhdm1DkryLQRDgvU7zpRaPhvcfoPW6GI+vcSSMNdaIQTtvUNENB2LqlCSP7Fyy+mYV6Mye4qKbsDjrwXQdANXVyuRgB9JVsgqqRozvT4ZhFsOo/V3gCRhn7oYxZl+yt/zMyXet9h8b1uPiBEp/clA7ziOttfcVaozlqFEOQOjQZJg5XQz0A1psO5A4jpgIsf3E9r8EgC2i67BMmU2YPJx5lZYsFsgEBbsaYig6ckJQCyqQkVRFpIkIWQrl111Pa+88gqPPfYYK1aswDAM3njjDW69+SZu+/0zvNzpxnbdrRO+3pyZOTizzHq/u6OFSDDxTrtqXhlKdpHJY6jbmTDzuYE31xJqaUZJS6fgs/+GlJYN4cCI/H6ioRZXIRdWgKET3rMhKXOAWRazzz63pRc1IwNJVUEIIgP952TOc43zwccE0JskgbFBj0GvyzDdZhNENnX7BC3RjN2sCQqLHT16lBtuuIGXX34ZRVH42te+xs9//nN8RgadLpNgOOzzcTIkSeLKaPZj7ebY9BEMITgcLTkVZsrkJJBkOjgUYMhr7rrKCjNQlMmNLUkSH77Ugd0KjZ067+7tIBiVx84qqYzbt2U8hLsaiXSaKXLblPmoGaOn8WeWyyyZekJ+vc8d/0Ks97QQ2fkqIFAqZqJMvWDc16gKXDILnDZw++GtAzBZjS69q4Xg608AAsuc5VjmrTzl7zaLxIIpFiwKeIKCd5si6MkyhrNbKCsclmAP0DvoZ/Xq1fzud7/jpZde4oYL5mLTNRrcXh7edYxLrn4/Dz/88CklmViQnl8yQkAdbG/ESPDOV5Ik7FPmm+23IX9C+B9GOEzXH38HQMHNH0NNy8Ay3yQD6y2HMJLUYWO74DIAIvs2J9VwzjHM+zi465wYzUmyjCXf7IIKtbcmfb73AueDjwmgJ0lttsMttmX5Co4EuM0CHIwSTSvyISMl9jGfeeYZbrrpJpqamigsLOTxxx/nE5/4BCCxp8E8ZmoxpJ2lenHJkjSsFonmjjBHGsdPtzb36niDAotikkwThWAoQmefmYotyEnDaU+MAmd2usxH1jiYXuijxGky0dMLSrGlpCVk/NOhDXQRbjJTvday6VjyysY8/pK5EuV5ZtbhqU0GvuDEFxVjoJPItpfAMD1b1PmXxryDd9rg0tlgUUzux/pDJhk2HhiuXgIv/R60CErFdGyrrh31PFJsMguqLCgyuHyCAy3ahBVpY0V6ip3ifDPr1Ofy0efyAVASdHN3rswzN17CfZ+7k7LKKoaGhvjNb37D5Zdfzuc+9zm2bt0a0yIvSRJZJZUoFit6JJwUBVRJtWCfuhgkGd3VPWn+R//LLxDp6UbNziH32hsAkHOKUSrNLFXk3beS4seiVE5HLqoAXSO8882Ejz8Ma/V0JEcKhneIcOOxpM1zMhxTagAI1Ceem/OPgPPBxwSQrDbbupEW28RwHQxDsPekkkssCAQCfO1rX+NrX/saoVCIVatW8dxzz7FggVlmae6Ffq+5qMwdQzMoxalw0SJzIX5149g7EV/IoLF7WNNDxaomJvDSDYPWLhdCQKrTSm6MbbWxYk65xvXzzbTSu23pGLbJGcadDZq7j2CdmeZV8yuwFNeO+xpZlrh+mUlAdfngfzYao3bnnA2Gu4/w1hdAjyDnl2NZdMWEVVOzU80ARJGhfcDUAJloMsIYGsT/t18j/F7k3GIcV31sTJfedKfMvEoLsgS9QwaH27SkdHMAZKc7KchOBaCrz8NAYyODf/45AIWXf4A7H/o+r732Gr/85S9Zvnw5hmHw5ptvcvvtt/P+97+fv/zlL/h8vjHnkBWVrFKzjBcO+HB1Nif8/SgpGdiqovyP1sNo7vjaOvWAn+6/mHomhR+/Hdl+QuxOnbkcbE6EdxDtWOJLFpIkYVtmqsZGDm7DcCenRCEpKvZZCwEIHjg3pRdHtXm/B46fm2DnXON88DEBJEtg7FhbYsXFjneCywt2a2xy6s3Nzdx8880888wzyLLMF77wBR577DGyskyWqmHAnibz2Jml5rhj4aqV5s5w67teBtyj73ZEtNxiCMhOlSjMTMylOKznEYroqIpM6SR5HqfD3Ik2oMiCVpeTl/dl86dXAwnfaeueAYJHt4EwULIKsFXNifl9pNglbl4l47BB1yA8u9WIqRRh+FyEtzwHkRBSdhGWJe+PWbL8dBRkwupZZomuqRe21cUuQmZ43fifewzhdSFn5uG47g6kGNRbs1NlZpeb59s5aEQ1Y5ITgORmpZhOyOEg3j/9BBHwY62aRsb1twGgKAqXXnopv//973n55Zf56Ec/isPhoL6+nm9+85tcdNFFPPTQQzQ0NJx1DovNMdIBE/S4GeppT/j7UfPKUaPZtNDxnRjhiXNMev/2NJprEGtxCTlXfeCUv0lW+4jxnH5sJ8Zg4rt41JJqlPKpYBiEtr2W8PGHMVx6Cbz7zjkpvThqosFHfV3S53ovcD74mACSkfkYGDL9XGQJqhPE99hxzLwx5k+Rxs0mvPbaa9xwww0cPXqUnJwcfv/733PnnXeeIpFe12V2L9gtMHPsrD8A1eV2Zkyxo+nwxEujS0Y39eq4fKZx3PQSS8IChJ4BLx5fCAkoL8pEVRPYOaNp9LfWY2gaqtVO6ZRKVEXiUJPGW7sS54Cqe10Ejrxjanlk5MXl2ZKdJvHhldEOmC54eYcYc+EyPIOENz4DIT9Sei7WC69BUicXZJdkmyZ0ElDXCbsaxg9AjICXwHO/Rrj7kdKzcXzwX5CdqTHPmZ+hMDN6H7X26xztSE4GRJIkCjLtZL76O5T+TgxnOrZb7jJJgqehurqab3zjG2zcuJEHHniAyspKfD4ff/rTn7j66qu5/fbbef3119H1MwkytpQ0MovMVKN/sA/fQGJbLyVJwlY5B9mZjoiECR7biZiAyJk2NETPU08AUHTbp0d9/3JJLXJJLQiDyK61SfGXGc5+aEf3oPd3JXx8ANvMBUh2B/pAL6G65LgEnwxnjUnwDra2YAST0zH0XuJ88BEjAiGDId+wxkfigo/hFtvyAgV7AnxXugZNoqkswaKas4+naRrf+973uOeee/B6vSxatIjnnnuOCy+88JTjIjrsMzWDmFthll1iwW3XmVoXb20bOkN0zO03aOgyH3DTilWcCeK5uL1BegfNdHZxfkbCeB5gerYMtNajh03p9OyyKRTnW7nxEnNH/sKmIPXtk69p6/4hAke2Rl1qc7BPXTxmuWEsFOdIXL9cRpJMsbm394++CBtD/YQ3PRNVL83Guvz6mDINsaAyDy6MNskcahs7ABFBP4Hn/htjsAcpNQPn9f+CnJox+sFjoDj7RADS1m9wuD3xAYipYPpzpOajCKsN7zWfpdUn8PjPrgORlpbGrbfeyiuvvMJvf/tbLr30UmRZZuvWrdx9991ceumlPProo/T1nVr+cKRnkZZfDICnt4OAezCh70VSVOy1F4CiYngHTQO6GD+vzt/+CsPnxV41hczVl40+viRhmXcJ2FMQXldSul+U/FLU6jmAIPzOqwkfH0C22nAuMgnP/nfWJWWOk6Fm56BmZoFhEGisT/p85xrng48YMZz1SHHIpDgSt5uuS7C+x/Zj5kNjeplEunP0Rb27u5uPf/zj/P73vwfg05/+NH/84x/Jz88/49hDrRAIm1bqtaNLPIyKaVUOls1PwRDwx+dP1GE1XXCgJYIACjJkirIScwkGQxHao+pWORnOuPU8RsOwlocWCiArKtll1ShRC/kVc6wsmGpBN+DXz/vpHYy/vcMIeAge3gJaBDk1C8f0pXGXPYZRUyTxvgvM6+CdI4LNh05NFxuuXjPwCPmRMnKxrrwRyZ5YjkxtESwxuXMcahu9BGMEvPif+zVGXweSIxXn9Z9FzoifS1OcrTArek91DBgcSiAHRAiB++nfEXx3GygqOZ+5D2dlDUJAS+cgHt/YQlSyLLNy5Up++ctf8uabb/LZz36WrKwsurq6+MlPfsKqVav4/Oc/zzvvvDNyzqnZ+aRkmV1Ors4WU8Y/gZAdqWYAgoTW10akfXyewdDObfS/Ynq4lN71hbFVXK12LIuuAEBv2o/e1ZiQ8z4Z1guvBElCaziI3tWS8PEBnMvMDp7A3u1J93qRJOmk0ss/H+n0fPARI3pHND4Sl/UQQoxkPqaWTT6g8QQEh6MmcsMtl6djy5YtXH/99ezZs4fU1FR+/vOf8+Uvfxl1lHTpkN+UzAZYWGUSCCeCj1+Tg6rAnsN+9h41ZaiPdmgEwmCzwPSSxEioa7pBc6cLQwhSHFYKcxPXeSKEYLCjibDfiyTLZJdNQbWdyApIksTHr3RQXqDgCwoe/Zsfb2Di9WDd58J/cDMiEkZ2ZuCYfuGkA49hzK2SWT3H/Jw3HBBsOGAghMAY7Ca8+VkIB5EyC7CuuAHJlrig7WRMLzkhw36sEzYfPUFCNTyDBJ5+FKO3HcmeguP6zyJnnRkITxRFWQqzy1QkTA7IwdbEdMF41j6Db/PrIElk33o3jmlzKSvKJC3FZgYgXeMHIMMoLi7mi1/8Ihs2bODhhx9mwYIF6LrO2rVr+cQnPsFVV13F73//e1wuF2n5xdjTMwHBYHsTwQQvfmpm/gkCatvRMQ3oNK+H1v/6PgC513+I1LkLxh1fyStDqTaPi+x+AxFMrL+Mkl2AGvV8CW19JaFjD8NaNgVLaRXoGoGdG5Myx8kYIZ3+E/I+zgcfMSIZbbb9bsGgRyDLMCUBbaa7jwsMAaW5UJR96qJuGAaPPvoon/rUpxgYGGDGjBn87W9/Y82aNaOOJQS8U2cuEMVZUBGHM3xRnnVE9+MPz/XROajROWguzLPLLFgS0N1iGAYtnYNENB2rRaGsMDNh/JFhl9qQdwgkiaySKiyjZAVsFol/vd5Jdropv/7r5/1EJqC2qQ/1Ezi0BbQwckomjhnLJs23OB3LZshcMtf8XDYfEry7rdkMPKLkUuuKxJVazobaIrhohilI1tANGw5BpL8H/9OPYrh6kVIzcX7ocyi5E0ixjYPCLIXZ5WYA0uUy2Ns4OSEy78a1eF45IZ3uWGDau8uSRFnhqQHIkC/2Or3VauXaa6/lySef5IUXXuAjH/kITqeTpqYmvve977Fy5Uq+9KUvUdfWgy01HYRgsL3RvDYTCEtBJZaiagBC9e+ie0bvHul47OdE+nqxFpdS9MnPxjy+OnMZUnoOhANE9ryR8HKYbcka0/G27TiR+gMJHXsYw9kP39Z1SSM0D+OfuePlfPARI5IhMDac9agsVLBNku8R0QS764ezHqd+rQMDA9xxxx385Cc/QQjBTTfdxJNPPkl5+dl7Zuu7octlZjuW1poLRjz48FXZOB0yfW6dgy3R95uvkJU6+UtPCEFLl8s0jItKYKuTFBI7eWxXRzOBYRGx4soxtTzSU2Q+98EUHDZo6NBj7oDRBrsJHD7B8XDMWIZkSRxX5WRcOF3msvkSs+RDTO18EbQIUm4p1uXXjUi1JxtV+bA66oTrbmnD89SjZldLVj7OD92VkIzH6SjIVJhbqSJL0O8V7KyPEJpA+/EwPG++gPtpU0gr7cobSb3oylP+PhyApA8HIJ0uBtwT391PmzaNBx98kE2bNvHNb36TmTNnEolE+Pvf/86tt97Kx+64i6dfXMvgoIuB9kZCCZYWt5bPRMkqBGEQOLoDI+g95e9D27cysPZlkCTK7/sqiiP2bJmkqFgWXWn6y3Q3oR/fk9Bzl9OzsS68GIDQ+ueSIu3uXLQSyWJF62oj3JTcjMRI2aWxPik6Ke8lzgcfMSIZ0uoHGsyAJhEttvubBMEwZKZAbfGJ3+/cuZPrrruOTZs2Ybfb+e53v8tDDz2E3X72XW4wDDuj/KZ5FWcXFIsFaSkKN16RxfvW5IIkkWaXmFIw+RLTcEut1x9GkqCyKAu7NTGBocnxaCLocQESmSWV2NPGJz4W5ijccU0Kigy7j0V4bkNwzJ1RpK+d4LHtZjttZgGOGRcmPONxMoQQLNDe4Qr1LRTJ4LA+lbft1yDk5M05GspyYU32YS5q+BWWiI+hlFL0992JnJaZtDnz0hUWVVuwquANCrYfD+ON0X9ICMHQS39l6IXHAUhd80HSrr5p1GOHA5DM6E3T0TtEd78nrh1ySkoKt9xyC88+++yI+J/D4aChoYGf//fvuOETd/DAQ9/jleefJeBJHAdEkiTsNQtNA0EtTODQVoyQGURpHg+tj/wAgLwbPkzq7LkTHl/OyEWdbbphawc3o/c0J+zcAayLL0dKz0b43ITeWZvQsQFkh3Mk4+Xfmlziqa24FNnhQITDBFv/uZROzwcfMSLRmQ+P3+BAoxnQLJw2uYe/EIIddebD7YJaCVmWMAyD//7v/+a2226jp6eHKVOm8PTTT3PDDTeMO97OBlMhMyvF1PWY7LlVTkkhN8eK36/T2uRDnmRZRAhBV58Hd1Q6vbwwC6cjMdmCYXJpyOs2Sy2llTgmsChOLVf52BXmwrNuV5hn158ZgAghCLcfI3R8FwiBmlMyqa6WWCB0jcjOtehRoae+/MW8ql/O7gaZpzYZcWUC4joPIQjtegvnW7/HYoQYSKtmfeW/8PLhVLpcyZ07wymzuMaK0yYRisDO4xH6PWMHIMIwcD/7BzyvPQtA+jUfJeMDt4xZ2pMkiZL8dPKyTJfn3kEf7T1DcafoJUli9uzZPPTQQ2zatIn//M//ZM6cOQgk1m/Zxhfvf5DLLruMH37/u7QmaIGSFBX7tKVI9hREOEDg0Bb0kJ/2R39MpL8PW2kZRbffEff4StUclIqoK+2OVzESaHAnqRbsl5jPuci+zeg9iZd2HyGe7tmCkWDuysmQZPmE0uk/WenlfPARI3oTnPnYdSSCYUBZgUJx7uQWnboOGPCYJM65VRIDAwP867/+Kz/84Q/RdZ1rrrmGZ555htra8RUyOwbNejyYBMHJ+qQ1dOv0ewQIwStv9PHXl/s52jg5s6zeQR/90XR2aUEGaSmJKRkYhs5AWwMhn8ckE5ZOwR5Hq+eSmVZuutTMLL21O8yTbwZHSjDC0AnV7ybcegQAS2EVtpqFSTOkAxB+D+FNz2C0HwNJxrJwDaXLl/HB5QqqAg1d8Mc3DVy+5AYgQosQfO0JwlteBgSWWUvJu/kzZGbaCWvwxj5TDySZcFglLqi2mG64BuxpjNDUM3onjNB1XE8+hm+DSV7M+NCnSLv8upjmkSSJgpw0ivNMwT2XJ0Bz5yB6vFrzUaSmpnLzzTfz9NNP8/zzz/OJ2z9JRkY63b19/PJXj3HZJZdw66238re//Q2/f3KLomy145ixfMQDpvOXP2TwzddAlim/72vItvjvO0mSUOeuRsouhEiIyLYXEZHEaeWo5dNQp843zfPWPT0h7ZJYYK2ahlpQggiHCOzektCxT8c/q9jY+eAjBoTCBi6PefEmKvOx7ZB5oy2dOblgRtcF6/aaD7SF1RJ7dm3j2muvZf369VitVr71rW/x8MMP43SO3z4Z0c02SIBpxZCbPvbx46HLpdPYY35uM8tUakqt6Ab86P914/FN/GEghKBnwEvPgFmDLspNG0lvTxZ6JEx/8/GTulqqJ+XXcvF8Gx+7woEEbN4X5s+vBtCC5g5S62sHJGxVc7FVxq5cGg/07iZCbz2BGOwGiw3L8utQymcAML1U4uOXyKTYoW8I/vCGQVtfcgIQw+vC/8yjaMf2gCRju/h6bJfciNOhcsU8Uw/EELD1mPkzWUO6sWBVJRZOsYy0eR/v0tnXrJ1CRNW9Q/T98tv4t70NskzWx+86g+MRC7IznJQXZSJJ4PWHqW/rJxhKjMjW9OnT+frXv86Wd7bzvYf+kyUL52MYOu9s3cJXvvIVli9fzr//+7+zdetWjDgVOWWbA8eM5XiPNNL38usAFH/qs6TMnD3p85cUFeuS95v6H54BIrteSyiB07byGrA5MHrbiexLbIAgSdIJ4umW5HnKADimnA8+/s+ib9DMejhsEqnOyX9k7b06rT0GigwXTJ9c8LHruGDQCw6Lzs7Xf8Ltt99Ob28v1dXVPP3003z4wx+OaXETAt45ZiqZOq2woGpSp8WQ3+BQlFBbkadQnK1y5835FOVZ6BvU+Nmfuyf0oBFC0N1/IvDIz04lJzNlcicZRSTop6/52Ck6HrYJqGqeDctmW/nE+xzIErS3DDCwawOGdxAUC/YZF2IpqJz8yZ8FQhhEDm0lsvUFiASRMvOxrv4IymnGdEXZErdfLlOQCf4Q/OVtgz31RkIXgUj9AfxPPILR04Zkd+K4/rNY564YuS5VxeyCmVdhHl/XCS/vNr1pkgVFlphZqjKjREWK+sFsq4vgDRiE2xrp/dHXCNcdRLLZyf7UF3EuXhX3XOkpdqaU5GBRZcIRnfq2AVyeyWX/TobdbudDH72V//71Yzz1/x7jUx+9mZLCAgKBAM899xy33347l156KT/60Y+oq5v4AhZoaKD7qecByFi6kJRpxRgJInJK9hSsS99vElC7GtAOv5OQcQHklHRsy98HQOidtRgeV8LGBsxrQlGItDYQbku8bskwTs58JLu75lxCEv9g72ZoaIiMjAzcbjfp6ZPceicIew77+NYvO6kotvLIV8ZwVYsRz64PsG5XmHk1KndcG/8C6g8KfvWKQU93O3tf+jINx0zm+E033cT999+PYwIs9CPtsP24KYV9xTzTmyNe+IIGuxoihDXITZOZV3lCz6OhNcRXH2kjogk+cX0O112aNe54Qgg6e4cYGDIf2IU5aeRmJSbwCHhcuDqaTe6FzU5WSRWqNXGdH0IImvfXkek9iioLXBEn6bOWkJ6dvGtbBLxEdr+O0WvW/5WqOaizLxpTNyQcEbywzaCuw/z/tFK4+gIZxyS6sEQkTGjjC0QObgNAzivBcfVtY4qHdQ7CpiOmsJ0iw+IaqC2Mv9sqFgz5DfY1RwhGIKNhK0Ubf4ukhVFyC8n5zH1YimLwFIgBmm4aHvoCZtYzJ8NJYW5aQjNfflc/7q5WhBAcaWjm7Xd28cqrrzI0dKIjZtq0aVx77bW8//3vp6ho7LbmUEc7x/7tX9DdbtIWL6Xg+ktB15BsThzTL0R2TD5IB9BbDhPZbWZW1FkrUWsXJmRcIQz8zzyK0dmMUlpj+gQlsMQ58P9+TGDPVuxzF5Pz6fsSNu7JMMJh9l13Beg6M//0FNaCwqTMc65xPvMRA0Y0PrImX3LRdcGOw2bademsyZEk1+832L35OZ740fU0HDNFwx555BEeeuihCQUefUMnulsWTplc4OEPnQg8Uu2SqbFw0sN1SpmNT92QC8CfXxif/yGEoK3HPRJ4FOelJyTwEELg7e/G1d4EQmBLSSOnvDahgYcRCRE8uo1c/xFUWXBoMJcf717A956Cho7Et80JIdCaDxF6889m4KFYsCy6Esu8S8YVLLNaJG5cYWqByBIcbYPfvWbQ2hvf3kTvbsX35I+jgYeEdeFqnDfdPa5qaVEWfGCRqS2jG2Y2bv0hMxhJFtKdMosroWL34xS/9UskLUyoYi5p9zyUsMADQFVkKouzRq7ffrefhrYBQuHEXQvOzByyS6cgKyozqiu567abeXPtK/z0pz/l8ssvR1VVjh49ysMPP8zq1av56Ec/yuOPP36GpDuANuSm4YEvobvdOGqnUfnAt3DOXjXCAfEf3ITuGd27aaJQymegzjA7SLSDm9Aa9iZkXEmSsV96E6gW9LbjhBPc/ZJ21YdM4799Owg1HEno2MOQrVbsFWYq2v9PRDo9n/mIAX/+ez/Pvj7I1asyuONDcahtnYT9DREee85PqkPi259NQ1Hi2/XUNQ/yiX/9D+r2vka6ExZfsICHH36YsrKJPSyDEXhpF/hCUJ4LF8+Mf5fpDwl2NYQJRczAY+EUy6jGdkII/usP3Wze7SU3S+V795aSnXHm4qjrBq3dLrx+c+UpLchICMdD1yKmeJjPA4AzM5f0gpKE7kA1dy+h47sRkZDJcaiczYCllP9+IUDXgFlyu+lSByvnJqhLJ+Al8u46jO4mAKSsAiwL1yCnTVyivGNA8Pw7Bi6veS0snyGxfIaEGsO1KiJhwjveJLznbTAMpJQM7GtuQS2rmdj7EXCwDfY0mv+2qrBoCtQkIQsSbj7O4OO/QOs20z79866hZ+GNKKrM1GKV4iw54bwctzdIe48bwxBIkpnNy85wJmweLRxisL0JLWQG7Wl5RaRk5+PxeHj11Vf5+9//zvbt20eOl2WZpUuX8r73vY/LL7+cVC1Cw/33EWxuwpJfwNSf/ApLjrlpMMJBgke3Y/hcICvYaxehZiVmNx45tGWkI0tdcBlqxazEjHvsXYJrzVZp+/s+gaV68pyVYQw++Wv8W9/EWjmV3C/8Z1I4XC0//A4Dr71Cwcdvp+i2Tyd8/PcC54OPGPDIH7rYuMvLbdflcP1l45cJxsJv/+5jT53GJQut3Lg6voV0w4YN3HHXVxno78NuU7j/3z/PHXfcgaJMrGvGELBuv9nhkuaA9y80H/LxIBAW7Kw3A48UmxTVVDj7TegPGHzph6109kYoyrPwzbuLyc06wX8JhiK0dLkIR3Qkiah40+QVOEM+D66OZgxdA0kio6AUZ2bOpMcdhtDChFoOofWYuvSyIw1b7SIUp3ktB8OCP73qZ+9xc7e7dJaFD6124IjTXE8IA735kGnWpYVBVlBnXIhSvWBS6eVQRPDabsGBZvPxkJ0GVy6UqSwYw6yw8RDB9c8hPKYwm1ozF/slk/OKGfDC1qPQH9W5KsgwjeoyEmA/IzQNz9qn8bzxPBgGcnomWbf8C0bNAg62RnD7o+89VWJasUqKPbGJ4oim09btHinDpDislORnYI3VvXEcCMPA3dU6IpRnS00no7AMJaol09XVxauvvspLL73Evn37Rl4n6RpT9QjLUh2srK1h8SM/H9l5j4ytawTrdqK7egCwVszCUjhl0guvEALtwEb0+ncBsCy6EqVs2qTGHEZw4wtE3t0IVjspH/48ctbkNpLD0N2DdD/0b4hwiOxP3otj/tKEjHsyev/2NO2//AnpF65gyn9+L+Hjvxc4H3zEgK8+0sbRxiD3fbKQ5Qvir3H6Agb3/9qDpsNXbk2lNG9iDxm32813v/td/vrU3/AGILugiv/36x+ybHF8UfzuBjjQatbW37cAsuJ8a/6QYHdDmGAEnDaJRVMs2CzjP4S6+yN842ft9Axo5GerfPOeEgpyLOausNuNIQQWVaa8MAuHffJaKJ6+Tnz95sNStdrJLKnAkiAvEyEEWn8H4eYDZrYDUAsqsZXPPKPkIYTg9R0h/r4phAAyUyVuudzB7CkTe49GXzuR/RsQbtNmXcoqwLLgcuT0xAVTh1sNXt8jGFYKn1Uucdl8iRT7ie/XGBoktOE5tMZD5nmkZWJbdR2WKYnZXRoCjrTBu02gGaY66oxSmFMef7AcajyK+6nfEmk3Ba4cC1eQ8aFPokQ7nIQQNPfq1HfrCGFyocpzFaoKlJgyQLFCCMGA209XvwchTJEyk0ydmCyIEAK/q5+hnnYQAklWyCgsxZ52qg1BW1sbr7zyCi8++QR7t20zj7VYsObls2DRIi6//HIuv/xyKisrT4xtGIQa96H1moG2klWIvXrBpIXyhBBo+95Gb9wPkoQ6/zLUipmTGhPM1unA3x5D72xEzi7A+eHPJ0xNeOjl/8Gz9hmU3EIKvvojpFG8siYD7753OX7fPVhy85n1l2cSOvZ7hfPBRwz4zNcbGXDr/OC+UmrK4999b3g3xP+sC1KSJ/PVWyfWxvnaa6/xzW9+k97ePob8EnNXfoz7vngvVyyOj/+wtwn2RoUFV0yD6jizpgNeg/3NESI6OK1mxiOWwGMYvQMRvvHzDrr6IuRlq3zpU5kEo0z6FIeVssLMSUumh/1e3F1taNFxnZk5pOeXJIx4ZgR9hJr2j+wCJUcq9qp5KOMEAXWtGo+/FqDPbbZBLp5u4cZL7KQ6xj4v4R8icnAzRnu0c0G1ok5fijJlXlL0QoJhwfoDgt3HzUeFzQIrZkgsKPZhvLuOyP6tYOggy1jnX4x1yeVJkYj3BMxW8I6oo7xVhbkVZlt4rJeINtDL0AuPE9izFQA5JY3MD38Gx/wLRz3eHxIc69Doi4qRWVWoKVIpykxsKSYU1mjrcRMImnwwm0WhKC+dVGdiOEiRYABXZ8tIGcaemkF6YelIFgRg4I21tP7X9+jy+tjtSGNPaiZ7D5zqj1JdXc1ll13G6tWrmT9/PrIsE+luJNx80AxYbE7stYtQUieXIRZCoO15E73FDGiV2kWoM5dP+jM3fEP4n/wxwu9BrZ2P/cqPJuR7NIIBuh/6NwyPm4wbP0nqqqsmPebJ0H0+9n/QHHP2U39HzchM6PjvBc4HH+MgEhHc/EWTjfn7b1eRkRZ/SvThx700d+vcuNrOJQtje6j09vbyrW99i7VrTaKUPbOKVTc8xKw5C/jUGhnrBBb6YZwceCyaArPi5NS19escbdcQQLpDYl7lxAKPYQy4NR75YwcrFiiUFpqfbyI6AQxdY6ing4DbJMXJikJ6QRmO9My4xzxl/EiISPsxIt1NJjFBkrGW1GIprolZrTQcEby0Jci63WGEgFSHxDUr7Fw424Iin/reRcCLVrcbvWm/udgjoVTOQp1xIZItAXWIcdAxIFi7y2CgP8AC/wbm+zdjEWbJQCmtwXbx9SjZBUk9ByGgfQB2NcCwbUqqHeZVQlXe2UXxjGAAz+vP4X37JdAiIEk4l64m/f23oMRwPfQN6Rzr0PGHzcdlis20CcjPSFwQIoRg0BOgu987IkaWnmKjIDcNm2XyO+lhkrW3rwsw74e0vGIssoWOX/7EFBADMi++lPIv3Y9stdLd3c26det444032Lp1K7p+QoAlIyODVatWsXr1apbNn4299zgi5AdJwlo+C0th1aQ+GyEE2pFt6EdNbopcNAXLoisnnVnROhoJ/O1XYBhYZl+IbfUHkaTJB+2+Ta/jeuo3yClpFHz9p8iOxN6Th26/hXBHO9Xfe4S0hRckdOz3AueDj3HQ2Rvmrm+1YLNK/OXh+GuaR5o1fv6MD1mGb382jbRx9EIikQh/+MMf+MUvfoHf70dRFFa97w5KFvwLToeNT1wmk5sx8XPZ12ymr8HsbJkdR+BhCHM32NZvPiALMmVmlqpnLJaxQAhBIJ1AZQAAJmJJREFU36CP7qh+RyAkeG1TiKVzs7nswviCDyEEAfcAnt5Ok9sBODKySc8vRk6ATb3QNSKd9YQ7jkeDAFAy8rBVzkZ2xCdM1tRpZkE6o59pfpbMB5bbmD/VghTwotXtQm8+ODKflFOCZe4q5IzE1K1jgeF1E963heC+rSgRcwfdrZayL/dKqhfWMqtSTmhJYsxzEVDfZV7Lw50wKTbTDqCmCIZpE7rPg2/Dq3g3vIrwm9eYtXYWGdffhrW0cmJzGoKWPp2mXn1EBC0ZQYiuG/QMeEdUfAEy0xzkZ6dgTUAQEgn6o1mQIKFDBxl68kkMlwtkmYKbP0bhJz4zagbN4/Gwfv163n77bdavX39K+64kScyZPYul0yq5cGopc2oqsWTkYquai5IycZXgk6G3HiGy500wdKSMPKwXXoM0yRbfyOEdBN94ChCoMxZjv/RDk84aCl2j53tfQuvpIHXNB8n4wC2TGu90NH7r67g3vk3xZ+4k/8MfTejY7wXOBx/jYO9RP9/8RQelBRZ+en9FXGMEw4Lv/NHDwJBg1TwrH75sbJ7Bpk2beOihh2hsNIVr5s2bxy2f/g+Ouk1lyg+tkKktmfiDbn+L2T0AsLAKZschWeIPCQ61RUakuKsLFSrzlLgevIFQhI4eN4GQGSDYbVb++pKfXYfM8siSuSnceXN+zNkmIQRBjxtvX9dIiUW12skoLMWaANEwEQkR6W4i0tWI0MwVT07JwFo+EzUBQYCmCzbuDbN2WwhvQFBi7WdNwVFmWeuRhBmUSDnFqNOWIOeVJVUZ9WToPW2E392IVrf3RPCTXUBbxZW81j8DX8g8D6cNFlRLLKyWSHWcm3OL6KZGzeE2s3MLzNLIzPR+io++RHjbG4iwycFR8orIuO5j2GdfMKnPLqILWvt0Wnp1tKhwqNMmUZajUJSVuAAsGIrQ1e8Z6fYCyEp3kJc1+SBE8wzR8vP/YugtU51Tyc8n99P/Qu7yi2LiQem6zrvvvstbb73F22+/fYp4mdAjpKgyi2bWsmT2dFZcuoYZK9cgTyJjYfR3Et72IoQDYHVgmbcapWR8u4ixEDm6m+DrT5oaP1MXYF9z86T9lQL7dzDwmx+CopB75/3YahPTrQPQ/cQf6fz9f5N58aVU3v/NhI37XuF88DEO/vvpXl7Z4GbJnBS+csfYgjxnw1/fDLBxb5icdImv3ZaG7SzCTceOHeORRx5h3TrTKTEnJ4f77ruPC1ZexxMbwDDgolkSK2dNLEKP6LC9Duqjni0Lqkyy3kRgCPOBW9+lYwizxj67TCUvY+I3azii0TPgxeUxAwRZlijKTSczzY4h4IV1Lp54qR9Nh8w0hbs+ms+iWWfntgghCPmG8PR2jdS0JVkhNSeflOy8SadUjYCXcFcDWm/ricXXnoK1bDpqdnFCgwCha4Ra6nAf2ktGpGfk982RQnyli5m5sAK7LfnyPCIUIHJ8P9rhneidJ9QblaIqLPNXok6ZjSTLRDSTC7KjTjAs2inLMKNUYn61RFku5yRI0nSo7zRo37GPzLq3yOvYgSzM70oUVJB15fU45y9FmmBH2FiI6IKWXp2WPp1hyxZFhuIshdIcOWHdMf5gmJ4B7ylBSFqKjZwMJykO64Q+X93no/dvT9HzzF8xfGYvdcaVV2O7/DIkq8nTsaWmk5pTgNURO5+su7ubTZs2sXHjRjZv3syQ242IhBCGubHIzcpkyYXLWHLRJSxZsoTq6mrkCWYaDN+Q6QEzZGqSyMU1WOatnlTJMXJ8n9mCaxio1bOxX/mxcTVxxoIQgsE//ITAnq1IjhTyvvCfWAon6c4ZhffgPo7/f3chqSrTf/NnbMUlCRn3vcL54GMMdPdHuOehZjQdvnl3MXOmTvwiP9qi8bOnTZ3oez6UwrTyMy/spqYmfvazn/HSSy8hhEBRFG699VbuvvtudDmVP75p4AuaqpMfXDax9O6gFzYcNuvjEmapZaIcD0/A4HCbxlDAvFSyUiRmlFpwTrA9VNMNege8DLj9DF906al2inLTsKinLgoNrSF+8qduWrvMB+7CmU5uvjqb2ooThF/D0AkODeIb7EMLmYGMJMukZOWRkp2PPImFRhg62mAXWm/rCJEUzEyHpajaDDoSRO4UQiAGOtHbjqK310E0ayMkmU61ihfbp3LMmw+A3QpLZ1pZNttKSV5iSY9C19Hb6ogc2YVWfwCiJStkGbVmHtb5F6EUjH7x6IbgWDvsrDNoO0mvKt1pdsjMqpDIi6NMGAu0vm7829fj3/Y2uqt/5PeDuTNpmnodAwXzcNgkphRARS7kpCVWK0TTBZ2DBq39Ov7QicdphlOiMFOhIFMes+08VvgDYXoGTw1CrBaFnAwnmWkOlDFYt3rAT9/zz9Lz1BPoHrNcYq+oovSee0mdOx8tHMTT20nQ4z4xtiOFlJx8bCnpEwtwdJ3Dhw+zdetWtqx/i53btxEcvj8lGVQrmdk5XHDBBSxcuJD58+cze/Zs7PbxyfxC19CO7kCv2xkVgLFjmbsauaQ27ntBazxE4OU/gqGjFFdhX3MLcvrE9XFGzjEcpu/RbxFuPIaSnUfe//dQTLyiWFD/tS/i2bmdjItWU/X1byVkzPcK54OPMfCzP3fz1nYPc6c5ePCuiUeZJ5dbLppn5ebTyi3Nzc089thjPPfccyNErquuuorPf/7zVFdX09gteH6rQSAMeRlw26WxE0yFMD0ydtSbSpEOK6yaMTH10kBY0Nyr0d5vIABVhto4RJdCYY1+tx/XUGDE3TXFYaUwJ23MFtpQ2ODxF/t5eYObYV+shTOd3HJlKvlOD353PyL6B0mScWblkpqdjxxnm5sQAsM7SKS3Fa2/A/QTBmBKZgGWomqU9JyEtUAKVzd6+3H09mMQ8J74oyMVtXIOSsUsJLuTYFiw7VCYDe+G6R44YRCWnyWzcKqFRdMtFOXEF2iJcBCt+Sha40G0piMQOqE4K2flo864AMu0hcgTcPftHBDsrhccbROc7KGWnwE1xRLVRRLF2WbGK65zFoJIezPB/TsI7t8x0i4LIDlTcF5wEc6ll+DPquR4l5nxO/k8nDYzCCnPNe+rOE9j1PMa8JoZwuHuGDCD/uw0mYIMmZw0OS5S9skIhjUGTrufJCDVaSMjzU5aig0lGhj76+sYWPsyg2++NhJ02ErLKbz1k2SuuuSMTJAWCuId6CHgHoToFkFRLTgysnFkZMelABwK+Nn15sts2/gWuw4eYd+xRoLhCKjWkSyDoijMmDFjJBCZM2cOVVVVZ9UuMlw9RHa/MZIFkXKKUacvRc4tjev+1JqPEnjljxAJg8WG7aJrscxcHPe9rnuH6H3k6+h9XVgqasi9+z+QE6CeHGhs4OidnwTDoOa/fkHq7LmTHvO9wvng4yxo7Qzz/32vBUPA979YesqOO1aMVm4RQrB582b++Mc/sn79+pFjL7nkEv7t3/6NGTNmIITgnSNme6MQUJgFN66QSXfGdiP0e0wiXntU+bgk22yntcfY/egPGTT26HQNGiMZirx0meklaswPTiEEHl+Ifrd/REQJwG5TKcxJm1ALYWdvmFfe7iXiczO/WqM878SDXVatpGbn4sjIjotMKgwd3d2LNtiNPtg1otEBIFkdqHmlWHLLEuJhIUJ+jJ4W9O5mjJ7mkQwHAKoVuagapbQWOa981KyKEIKjLTqb9oU42KAROcn5tTBbZkalyvRylZqys39PQtfQu1vR2xvQ246jdzSOlJIAJEcKau18LNMXIefH9yAfRkQTHO+Eg80G9V1wsrGqwwZTCiWqCqAsVyIjZezyjD7kInT8IKG6g4SO7EMf6D3xR1nGVjsb54WrccxZfEabr25AWz809UJ7PyM8DTD5IYWZ5k9xlim2l4isSCgi6HbpdLmMkYzhMNIdErnpZiCS7pDiX+AMA5cnyKDbT/BkifahQawHdqJtXke48fjIr63FJRR+/HayLrl83NKCHgnjG+zF7zoR4IOZDXFkZGNLTT+lTTcWCC1CpLsJf+sxDtcdZ/fh4+w/3szehlYGhrxwWnnU6XQya9YsZsyYMfJTU1ODxWLOKwwd/dhOtGM7TyJix8+JMtx9BF//K3pnEwBK5Qzsl34IOSW+dUjr6aTnkQcQfi/2uYvJ/uS9CcmWtv74YfpffgHntBnU/uRXSWmvPxc4H3ycBT/4bSfv7PWxdG4K//6ZiXM9DjVGePRvJlv9ng+lkJc6xKuvvsrjjz/O8eMnHgirV6/mzjvvZP78+YD50Hpxu8GxdvPv86okrlgYm7T1gNdso22NZp4lySSWziwd/4FqGIJ+r0HnoEGP+8TDJjtVojJfJTt1/AvcEAKfP8yQL8iQLzTSLggTr1ELYRAO+An7PIR8Q0SCJ3bkugGHWhQ27LdwvFNl4awULlqUxtxpDlIcY2cAhKFj+FzoQwPoQ/3onv5TFl9kBTW7CDWvDCU9N+6FQQiB8A8h+jswBjoxBjoRQ/2nHqRakQsqUEqmIhdUTKjWHAwL9tdH2HU0wuEmjZM+ahQZphQr1JSqTMn0USp3YnW1o3c1mw9W7VRLdzkrH7VqJkrVTJTCiqQ8zPwhQX2noL4TGrpOzYiAueiX5pockcJMg+xAG0ZHI5GWekLHD6F1t5/6AosF+/R52OcuwT5r4Yg42HjQdFMnpKXPDEhOt1VxWiEvHXLTITfNLNGok6SJ+IIGXS6DPo+B57RARJEhM0Ui0ymTmWJuMCbaNSY0jcF9e+nfugX/nh2IlpMcVlUVZf4S0i+7kqzFF+JMsU9IN0cYBkGvG797gHDUjmAYFrsTW2o69tR0VJsj5ntF6BqR7kYiXU2IcCBqHDnA/uYuDnf0cbC+hcPH6ggEzvR9UlWVqqoqamtrqa2tpbq6mpqyYoqDPUhtR04EIZkFKOUzUEpqkSYgJCgMg8i7GwhtfdUcy+bAOm8lljnLkeMgrYfqj9D3i2+BrmGbOpvMmz6Dmh8fd3AYkcEBDt9+C0YgQMVXv0HWJZdParz3CkkLPh599FEefvhhOjs7mTVrFj/+8Y+56KKLxn3dP0LwUdcc5N9/1IYkwSNfKaO8KPZdeigieHFzkLd3hwkFh0gJbWKo7dQeeafTyY033sitt95KRYXZQRMMC/Y1msS9Ib/5ULpigcT86rEfFLoBHQNmarklWmuXgKp8U4ApfQyaiiEELp+gy6XT4zZG2gfBdKOtylfISDn7/EIIQhEdfyCMLxDG4w9hGCcuJ0WWyEp3kp3hHFcy2tA1IsEAkaCfsN9L2O9DCOOUY6zONBzpmXg0Jxt3B9i40zvCCQEzfT6lzMbsWgezahxMq7TikAIYPjeG343udZuW9qeNK1kdqFkFKFmFZlllgox3oWsIrwsx1Ifh7kO4ezGG+k4pYYzMlZ5rBhwFlUjZhZNm14Ppbny03kvH8S68nV04g30USL0US11kSJ4zjtctTkRhNY7KaqwVUxMmMx0rdEPQ3gf1HQbdbf2EO9pJ87eT4e8gy99Ctq8Z1TjTSU4qrMAxdSb2aXOw1c5Ctk1Obt8QMOAxnXQ7XdDjNn93ypyYUu6ZKebP/9/evcfGUd17AP+eM6/1rned2I4dxzaBpAkBCqE4TZpEXKpemkqgUuitmgpuRF8SUVU1bdRWQSDScLmKKCpS4RLa0hSudEOJoFD1j7TFumrT8LilgaSiODTBARInfq1fu971zvN3/5jdtde7MV5jj7Pm95HGszs7O3P253n85szMmcXZfiQ0s9M1pk2IJz3EEx4GR72CpDE3v7AhEK3KdRIRQ0BX/ZohIoLd14v0P0/43cm3kT75NrxJO2pt5WrIDf8C59pNENWFiZmuKQiHNFSFdIR0FSFdnfJ6kRzXtjCWGEImOQI7ky74TEgJvSoCrSqS7YchP2DZJiK/1rH/LJzB7oL10lN0nElYePtcHCfPnMPbJ0/hxIkTBbf3TqQoClqWNWH5ogguCQOt9YvQUr/Y79ZcjaoVV0M2LIeY5qkPd6AHmfZn4PVnk15FhbamDdq115fdls3Y8f/D4P/8F2DbgKohuuU2RP/1lg/VXknuzhetoRFX7D8AaczeAzGDMifJx8GDB7Ft2zbs27cPmzdvxs9//nP88pe/REdHBy65ZOrbLC6G5OP+fedw/O0x3PDJKHZsm/6C9veTSTz61Gv454mj6Dv7Bkb730TEcPO1DldddRW+8IUv4Itf/CKiUX+DMDRKOHrKTzxyR2GxsH9h6bK60ls3y8kevfUDXYMoSBouXeInHYtKXKjuuISRNGE45WE47WEkRQUbW10FGhcpWLZYIjqplU0igmW7yFgOTMvBWMZGOmPBnbS1VhWJWMRArDpUspbDc124tgnHynZmBnYmDdcu3tlIRYUeroYRicKoroEy6VoOIsJ750z87dgATp8egealsTRqYWnUQmPUwrKYCV0tXrxJ0aHGaqHE6qHE6iDDU19QR+QBmTRobBQ0lvT7qWHQ6DC80WFgrHgHDwAQEmJRA2RdE2TtMsjaphk954SIQJk0KDUCSiXgjSZAyUF4Cb+jkUFQunQZPAj0UT26qAnnaBlOe8vRh3oAAooE6mok6mLS79dI1MUEaqolaiISsYiYUSN2+XJbFtzEENyRIXiJIbjDg3AG++AO9sMZ6IM70Je/DXYyS6nCYOQyxKMr0B9dhb7YGphaFEIANRFgURiIRQRqwkAs4p/KqA75SUFIn9kdNrbrn7KMJ4B4EuhPXPhpukL4jZtFQ36tTSTktzMS1v1rSsLGB7e6SkRIZvwDgOGUh+GU528DPBcyOQQ53Ac51Acl3gW1vwta/CxkXxcwliqalhKrQaxtPaKf3IBo23poi/0WRh3Xw2jaxGjaQjpjwZp4rm4CTZUwdBWGpkLXFOiaAk1ToatKyWtzXMeGOZpAZjQBK50sODWTL5OmQzVC0IwqqEYIqm5A0XQIWXxrPjkWnPg5OMO9cEfixQcIRhgyUoPelI3Oc33oPHsene+9j3feeQednZ2FtSREgGP5t8O7/vZ3SU0UTbUxLG1oxNKWS7DsspVoWnk56pua0dDQgCVLlhQ9CZw8F07nP2AdOwyv9+z472q6FErrKqiXrIZsbJ3WAYQT78Hws/thvu0/Q0dtbEbNrdtgrL56Rk2xe6aJE1+/HXZ/H5q+fhcav/LvZU9jvs1J8rFhwwZcd911ePzxx/PDrrjiCtx6663Yu3fvlN+d7+TjH6fSuO/R81AV4NF7l6Oxrjg7zWQy6O3txclT7+D4m51460QnTrzdiVMn3wJ5DqQEYmF/w71q1SrcfPPNuOmmm9Dccgn6R/wL8roH/RYj4xMS+foY8MlV/p0BihTI2EDaAtKmf9fKUMo/tTKaKSxP2ABa6wgrl/obP8shWA4hYxPSpt+lzOKqbgDQFMKSmEB9VKLaILgewXFd2I4H2xnvW5aDUguKAPlHUbpExFChKX7Vpec6fufYcG0brmPDc+x8o19FiKBoOjTDgKb7naJIwHVBrg2yLZBjZvsWyMr4VbaWCZQsmW/MljgzZODskIFzwzrODutIpCUiuouGGoGGmIvFYQ+LqhzEdBsRzUFYmjCQgeZloLoZSGcs387GBak6RE09ZKze79fUQ8TqAan41beODXJswLb8WxBty39tZUBWBjCzv8fMgDIp0FjKTzjGUn5i4ZXeaRT8L8LVkLWNkIsbIBc3Qi5ZBmVJMzKehjO9Ls72uugedNET99A96MIqsTwAgCAPKtlQyUa1ZiNm2KjRLFSrFiKKiYhiIeSNwaAxGN4YNHcMqp2CkhmFNEch0kk/IZt0dFySlFCXLIXa2Ay1sQXa0mZorSuRqW5Eb0Kid4gwkAAGkoTBZPFpklIU6ScDVbp/bUmVLhDS/feG5ifZhg4YmoCuAJrqN0qW66vZTgiBtOWve8MpvxtKAyOp4hqSIp4Lw8ugChmEKIOQNwbdTUOz0lCtUShmCoo5CjE6DIwOA8kReMlhuEMDcAfjhRfITEJSgdu0AvYll8Np9Ts0LYehq9BVQFNFvu//nmxfCkB4cGwbtu3Asm2YlgNncvVLUTwFVFWBqkhoqoSqSChSQlH8TgoAjgXPGoNjpuFk0vCcCyxc8GtJFE2HouqQqgpF1SAVFVJVIRUVQsBPtBMDcJNxUKY42QIASAUyFAGMMOKJNM70xPFedy/e7zqPs+d70NXdjXNnzyKVHPFPNZaKqRD+veFSQSQSQW1tLWpra7G4rj7fRaNRVHsWIv3vIzzcg4ihIaJrCOsawtXViF26GuHGFsjF9ZCLsut+JFp0iz8RYeyNVzDy/H/DG/XvKhK6AWPVVTDWrIVx+TVQ6xunfTv44P++iDMP/gdkOIyGf/sKqq+9DuE1V0JqH64F2KDMevJhWRbC4TCeffZZ3HbbbfnhO3bswPHjxwsusgQA0zRhmuNHP4lEAq2trbOefAx29+GBmz9d8jMCQPBrAYgIHhFsj2C5rt/3XCQsGyOmjRHTgjnFylpXZeCa+sW4un4R1tYvRkt0Zs9eYdNROh0q+JymGre8WREAkMguL7kpFs5PwE/IRP7TWVi9aHzqnpDwIEBQ4EGChPT7kCDhj1swb6LsN/3XAgRBBMDz3xMB5GWHexDkT222uELCFjpsYcCWBiwZgiWrYMoQbBmCJUMgIfNRnBgvAQCiMMoCAhD+PkMIka9VFCI7vCBuNCEG2fHIywdUkDdhHA+CAEFuNi7e+GvPyb8Xnt9JcqB4DiQ5kJ4L6doQng3pWJCuBTGNZHEqJBTY0TrYsQaYi5ph1bfCqW+Bu6QVtKQZ0tCgSoKqXLhJ+enPzIMqPCjShSJcqNLLdu6M7wQSlI0RuVDIhgoHClwo+IAkvmTxPEjXguLYUFwT0rOheDamUzQiwmBiFOf6B9HdP4D+3n709vejtz+O/qFhDCRSiCdGCy/YLfmD/D9E2eXJ8/LrVk5I9WuKqrI1RrqqQtMU6KoGTVWgqQqklFCEgDRNwLSggCCE8IcJ/8GCQkpIRfGbCpAyu5z7C7cUAuNLOSHdPQjXtPz1AgCEgBLSIFUlX+YLxUlRJB762z8u8Oncm91H7wGIx+NwXReNjYWnKxobG9HT01M0/t69e7Fnz9y31maaJp7/53uzNj1dCjRXhdBcFUJLtv+x6jCWhozxKsXEGFKJ4vP+jM22iZukUmhSP2hqtpudZwhXDoKAq4XgaVVwtSq4RsTv9Ag8IwInXAMnsghueBHccA3c6lrYsUY41bV+rVkpLoD0hDkIQBHkH8Bn+4rwh0tB/k5N+u8FcsMnXIQuJBxIOJ46Pv186cmftvAghZd/LQT5KW/uPQhCZJNv4SdPrlBQlIIRQYELSS4kXEh4kORBwM32CSKbTueTaClBMgRHC8FBND8d4TmQ2U54LqTnjieI5PoJoxCoq4miriaKaz42qYVq8gDHAWwLqdQoBgYGMZQYxUgiieHkKIaSKQynxpBMZ5AYy/j9dAapjImUaSGVMZExbT8JIULGdZFxXCQypU8lll5ACOQf9fr9svnfy3Xl0KTAQzOY42yZ9eQjp+icHlHJ87B33303du7cmX+fq/mYbYZh4I5rLtQcr8iumH6eqEgBTUroioQm/S6qa6gJ6ajRNdQYOiKaGljz1nMqlzBP6zhimhO7wNupx5s8cokviw/6XGQ/ERNGEYXTL/U/K5r/xEPo8eEEkdvOFNRr+O/H6zvy44mCTWi2XiRXgwJM6OWndcHhE8o1uS6ACj7L1r3kjpByw0Ru/tJ/LfzXJES2nH4tCoSAJxSQVPz3M1wu8r85G6t8zCa/z8Vk4u+eWGGFwtf5cUUuln5AaPL2BpN+f24+Ihcf+LHIxSr3vxIy2wlAKv4wqfrDpALKxsaTCjyp+Z9JFZ6iwZMaXEX3Xys6XMWAp+oT9/LTC9wIIBKZfO1OYU3PhBoeMaEmKDeHgllNWKtLrefZxERIZI+6c/PJbguzR+FiwnRFwbwnzRPZpTyXBAmCIuAnKtlkaGKCIkVubZkwXb/qLv9aySU88LIJ0PiaJrPjSkGAQhDKxP98dn7k+TUwyCYj8Kfl1/B5yK+5iwmRZkIEQEtuTSW/RkuSl639ciFcDwJetqbMg+e6yJgmLNOCaVnIWJZfmz82Btu24JgmLMuEbVpwXBeu68BxXLieB8dxQZ4H1yN45MF1PZDjwHUckOvCcxyQ5/m18V62fj6fYIyvFeMVewTPsuGkTf8anIIVpzgxKbeF2dk268lHfX09FEUpquXo6+srqg0B/KTACOBK3dqmBvznq3+f8/kwxhhjbGqznvrouo62tja0t7cXDG9vb8emTZtme3aMMcYYqzBzctpl586d2LZtG9atW4eNGzfiF7/4Bc6cOYPt27fPxewYY4wxVkHmJPnYunUrBgYGcP/996O7uxsf//jHcejQoXyDWowxxhj76OLm1RljjDEWqMp8Ig1jjDHGKhYnH4wxxhgLFCcfjDHGGAsUJx+MMcYYCxQnH4wxxhgLFCcfjDHGGAsUJx+MMcYYCxQnH4wxxhgLFCcfjDHGGAvUnDSv/mHkGlxNJBLzXBLGGGOMlSsajUIIMeU4F13ykUwmAQCtra3zXBLGGGOMlWs6j0e56J7t4nkezp8/P63MqVyJRAKtra04e/YsPzdmDnGcg8FxDg7HOhgc52DMdZwrsuZDSomWlpY5nUcsFuMFOwAc52BwnIPDsQ4GxzkY8xlnvuCUMcYYY4Hi5IMxxhhjgfpIJR+GYWD37t0wDGO+i7KgcZyDwXEODsc6GBznYFwMcb7oLjhljDHG2ML2kar5YIwxxtj84+SDMcYYY4Hi5IMxxhhjgeLkgzHGGGOBWlDJx759+3DZZZchFAqhra0NR44cmXL8w4cPo62tDaFQCCtWrMDPfvazgEpa+cqJ9fPPP4/PfvazWLJkCWKxGDZu3Ig//vGPAZa2cpW7TOe8/PLLUFUV11577dwWcIEoN86maeKee+7B8uXLYRgGVq5ciV/96lcBlbaylRvrAwcOYO3atQiHw2hqasLXvvY1DAwMBFTayvSXv/wFn//857Fs2TIIIfDb3/72A78T+P6QFohnnnmGNE2jJ554gjo6OmjHjh0UiUTo/fffLzn+6dOnKRwO044dO6ijo4OeeOIJ0jSNnnvuuYBLXnnKjfWOHTvowQcfpNdee41OnjxJd999N2maRm+88UbAJa8s5cY5Z3h4mFasWEFbtmyhtWvXBlPYCjaTON9yyy20YcMGam9vp3fffZf++te/0ssvvxxgqStTubE+cuQISSnppz/9KZ0+fZqOHDlCV111Fd16660Bl7yyHDp0iO655x76zW9+QwDohRdemHL8+dgfLpjkY/369bR9+/aCYWvWrKFdu3aVHP+HP/whrVmzpmDYXXfdRZ/61KfmrIwLRbmxLuXKK6+kPXv2zHbRFpSZxnnr1q1077330u7duzn5mIZy4/z73/+eampqaGBgIIjiLSjlxvqhhx6iFStWFAx75JFHqKWlZc7KuNBMJ/mYj/3hgjjtYlkWXn/9dWzZsqVg+JYtW/DKK6+U/M6rr75aNP7nPvc5HD16FLZtz1lZK91MYj2Z53lIJpOora2diyIuCDON85NPPonOzk7s3r17rou4IMwkzr/73e+wbt06/PjHP0ZzczNWr16N73//+xgbGwuiyBVrJrHetGkTurq6cOjQIRARent78dxzz+Hmm28OosgfGfOxP7zoHiw3E/F4HK7rorGxsWB4Y2Mjenp6Sn6np6en5PiO4yAej6OpqWnOylvJZhLryX7yk58glUrhy1/+8lwUcUGYSZxPnTqFXbt24ciRI1DVBbFqz7mZxPn06dN46aWXEAqF8MILLyAej+Nb3/oWBgcH+bqPKcwk1ps2bcKBAwewdetWZDIZOI6DW265BY8++mgQRf7ImI/94YKo+ciZ/AhfIprysb6lxi81nBUrN9Y5v/71r/GjH/0IBw8eRENDw1wVb8GYbpxd18Xtt9+OPXv2YPXq1UEVb8EoZ3n2PA9CCBw4cADr16/HTTfdhIcffhhPPfUU135MQzmx7ujowHe+8x3cd999eP311/GHP/wB7777LrZv3x5EUT9Sgt4fLojDo/r6eiiKUpQ99/X1FWVzOUuXLi05vqqqqKurm7OyVrqZxDrn4MGD+MY3voFnn30WN95441wWs+KVG+dkMomjR4/i2LFj+Pa3vw3A30kSEVRVxYsvvojPfOYzgZS9ksxkeW5qakJzczNqamryw6644goQEbq6urBq1ao5LXOlmkms9+7di82bN+MHP/gBAOCaa65BJBLB9ddfjwceeIBrqGfJfOwPF0TNh67raGtrQ3t7e8Hw9vZ2bNq0qeR3Nm7cWDT+iy++iHXr1kHTtDkra6WbSawBv8bjq1/9Kp5++mk+XzsN5cY5FovhzTffxPHjx/Pd9u3bcfnll+P48ePYsGFDUEWvKDNZnjdv3ozz589jdHQ0P+zkyZOQUqKlpWVOy1vJZhLrdDoNKQt3U4qiABg/Mmcf3rzsD+fsUtaA5W7h2r9/P3V0dNB3v/tdikQi9N577xER0a5du2jbtm358XO3Fn3ve9+jjo4O2r9/P99qO03lxvrpp58mVVXpscceo+7u7nw3PDw8Xz+hIpQb58n4bpfpKTfOyWSSWlpa6Etf+hK99dZbdPjwYVq1ahV985vfnK+fUDHKjfWTTz5JqqrSvn37qLOzk1566SVat24drV+/fr5+QkVIJpN07NgxOnbsGAGghx9+mI4dO5a/pfli2B8umOSDiOixxx6j5cuXk67rdN1119Hhw4fzn9155510ww03FIz/5z//mT7xiU+Qrut06aWX0uOPPx5wiStXObG+4YYbCEBRd+eddwZf8ApT7jI9EScf01dunE+cOEE33ngjVVVVUUtLC+3cuZPS6XTApa5M5cb6kUceoSuvvJKqqqqoqamJ7rjjDurq6gq41JXlT3/605Tb3IthfyiIuO6KMcYYY8FZENd8MMYYY6xycPLBGGOMsUBx8sEYY4yxQHHywRhjjLFAcfLBGGOMsUBx8sEYY4yxQHHywRhjjLFAcfLBGGOMsUBx8sEYY4yxQHHywRhjjLFAcfLBGGOMsUBx8sEYY4yxQP0/gg46XFmqmysAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"grid, p_density = get_p_distribution(grid=np.linspace(1e-3, 1-1e-3, 100)[:, np.newaxis], \n",
" mu_p=mu_p[np.newaxis, :], sensory_noise=posterior_noise)\n",
"\n",
"for i in range(12):\n",
" plt.plot(grid.flatten(), p_density[:, i], color=sns.color_palette('coolwarm', 12)[i], label='p = %.2f' % p[i])\n",
"\n",
"grid, p_prior_density = get_p_distribution(grid=np.linspace(1e-3, 1-1e-3, 100)[:, np.newaxis], \n",
" mu_p=0.4, sensory_noise=0.75)\n",
"\n",
"plt.plot(grid, p_prior_density, c='k', label='prior', alpha=.85)\n",
"\n",
"plt.legend()\n",
"\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 179,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x29f136710>]"
]
},
"execution_count": 179,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(p, np.trapz(p_density * grid, grid, axis=0))\n",
"plot_identity_line()\n",
"\n",
"plt.plot(p, get_posterior(p, .5, .4, .75)[0], c='k', ls='--')"
]
},
{
"cell_type": "code",
"execution_count": 180,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x29f010df0>]"
]
},
"execution_count": 180,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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KgbvS+omOQxegUNj2HpHaFrPuOFkjOhIROQmWEXJ572TZRkXmjYpCcB8vwWnoYoZG+eP2cbEAgOfX/wSThYtZiYhlhFxcaV0Lfsg7AwC4b2K84DTUFYvSk9DXR41jZxrx3o5TouMQkRNgGSGX9uHuYlhlIC0hCInc+t0lBPho8NSVtsWsr/5wDLVNRsGJiEg0lhFyWUazFR/usZ15csd4rhVxJTeNjsGQCB0aWs34V8Yx0XGISDCWEXJZG3MrUNVgQIifF9KTucmZK1EqJPy/q4cAAN7fdQpHKxoEJyIikVhGyGWtadv6/bdjYqBW8kfZ1aT1D8KVyeGwysBLX+dClmXRkYhIEP4NTi7pRGUDdhbUQiEBt46NFR2HuumZuYOhUSqw9UQ1NuVXio5DRIKwjJBLWrOzGAAwc3AYIgO8Baeh7ooN8sF9k2x3Qf3lmzyeW0PkoVhGyOU0G81Yt+80AC5cdQcLpvdHcB8NCqqb8N6OItFxiEgAlhFyOesPlKHBYEa/IB9MHhAsOg5dJj+tGovSkwAAr/14nLf6EnkglhFyKbIsY80u28LV28fFQsHTed3CTaNjMLjtVt/XNx0XHYeIHIxlhFzKwdP1+KlUD41KgZtSY0THoR6iVEh4Zq5tI7Q1O0/hVE2T4ERE5EgsI+RSPmrb5Gzu0HD09dUITkM9aXJiCCYnBsNkkfH374+KjkNEDsQyQi6j1WTB1wfLAAA3j+aoiDtaPGcwJAn45lA5corPio5DRA7CMkIu4/sjFWgwmBHd1xvjE4JEx6FeMCRShxtSogEASzbkcyM0Ig/BMkIu45O9ttt5542K5sJVN/a/6QPhpVJgd1EtMnLPiI5DRA7AMkIuobSuBdtOVgMAbkyNFpyGelNkgHfHRmh//S4fZgs3QiNydywj5BLW7TsNWQbSEoIQE+gjOg71soen9UdfHzUKqpo6TmYmIvfFMkJOT5ZlfNq24ypHRTyDTqvGYzMTAdg2Qms2mgUnIqLexDJCTm93YS2Ka5vRx0uFOcPCRcchB7l9XD9E9/VGVYMB724rEh2HiHoRywg5vU/aRkWuGhYBH41KcBpyFI1Kgf9NHwgAWJF5EnXN3CaeyF2xjJBTazKYseFwOQDgptGcovE0146IwqBwPzS0mrE886ToOETUS1hGyKl9c7gczUYLEoJ9kdqvr+g45GBKhYTfz7Ydord6WxEq6lsFJyKi3sAyQk6tfeHqvNRoSBL3FvFEMwaFYnS/vjCYrVjKQ/SI3BLLCDmt0roW7C6shSQBN4yKEh2HBJEkCU/NsR2i99GeEhRW8xA9InfDMkJO66u2c2jGxQciwt9bcBoSaUxcIGYMCoXFKuOfG3mIHpG7YRkhp/XlAVsZuW4kR0UI+P3sJEgS8PWhcvxUWi86DhH1IJYRckrHzjQgr1wPtVLCnKHcW4SAwRE6XDsiEgDwr4xjgtMQUU9iGSGntL5tVGTqwFAE+GgEpyFn8cSsgVAqJPyYX4n9xWdFxyGiHsIyQk5HlmV8ebAUAHDdyEjBaciZxAf74sZRtv1mXtnI0REid8EyQk4np6QOJbUt8NEoMWtwmOg45GR+N3MA1EoJW09UY8fJGtFxiKgHsIyQ02mfopmdHA5vjVJwGnI20X19cOvYWADAKxlHIcuy4EREdLlYRsipmC1WfH3IVkau5RQNXcCC6QPgpVJgT9FZZB2vFh2HiC4Tywg5le0na1DdaESgrwaTBgSLjkNOKkynxV1p/QAA/9zI0REiV8cyQk6lfW+Rq4ZFQK3kjydd2Pyp/eGjUeLQ6Xpk5J4RHYeILgP/tien0Wqy4PsjFQB4Fw1dWlAfL9w3MR4A8ErGMVitHB0hclUsI+Q0NuVXotFgRlSAN0bF8oReurQHJyfAz0uF/IoGfNdWZInI9bCMkNP45nA5AODqERFQKHhCL12av48a906yjY689sNxjo4QuSiWEXIKLUYLNudXArCtFyHqqvsnxcNPq8LRMw3Y8FO56DhE1A0sI+QUMo9VotloQVSAN4ZF+YuOQy7E31uN+38xOmLh6AiRy2EZIaew4bBtvn/usHBIEqdoyD73TYqHTqvC8crGjuk+InIdLCMkXKvJgh/zbLdmzuUUDXWDTqvGA5MTAACv/XCMoyNELoZlhITLOlaFJqMFkf5ajIwJEB2HXNS9E+Pg763Gyaqmjl18icg1sIyQcN/+ZJuiuXJoBKdoqNv8tGo8OLlt7ciPXDtC5EpYRkgog9mCH9p2z7xqeLjgNOTq7p4QhwAfNQqqmvDVQY6OELkKlhESauvxajQYzAjTeSElhhud0eWxjY7Y1o68vomjI0SugmWEhGq/i2bOUG50Rj3jrrR+HWtHeGcNkWtgGSFhjGYrMnLbywinaKhn+Gl/3nfk9R+5KyuRK2AZIWG2n6yGvtWMED8vjI4LFB2H3Mg9E+Pg17bvSPsCaSJyXiwjJMyGtiH0K5PDoeQUDfUgnVbdcaLv65s4OkLk7FhGSAizxYqNbXfRzBnGKRrqefdNjO840XdjLkdHiJwZywgJsbuoFnXNJgT6ajCWUzTUC/x91LhnYhwA4LUfT0CWOTpC5KzsLiNZWVm45pprEBkZCUmS8MUXX1z09Vu2bIEkSec98vPzu5uZ3EBG26jIzEGhUCnZial33DcxHr4aJfLK9R0/c0TkfOz+FGhqasKIESPwxhtv2PW+o0ePory8vOORmJho75cmNyHLMjYesX0wXDEkTHAacmd9fTW4e0IcAGDppuMcHSFyUip73zBnzhzMmTPH7i8UGhqKgIAAu99H7ie3XI/SuhZo1QpMTgwRHYfc3AOTE7B6exF+KtVjy9EqTB8UKjoSEf2Kw8bHU1JSEBERgZkzZ2Lz5s2O+rLkhNqHy6ckhsBboxSchtxdoK8Gd4zvB4CjI0TOqtfLSEREBN5++22sW7cOn332GZKSkjBz5kxkZWVd8D0GgwF6vf6cB7kPTtGQoz0wOR5eKgVyiuuw/WSN6DhE9Ct2T9PYKykpCUlJSR2/TktLQ0lJCV5++WVMmTKl0/csWbIEL7zwQm9HIwFKapuRW66HQgJmDmYZIccI9dPi1rGxWL29CEt/PI6JA4JFRyKiXxByG8P48eNx/PjxC/73xYsXo76+vuNRUlLiwHTUm37Is42KjI4LRKCvRnAa8iT/MyUBaqWEXYW12F1YKzoOEf2CkDKSk5ODiIiIC/53Ly8v6HS6cx7kHtqnaNI5RUMOFhngjRtTYwDYdmUlIudh9zRNY2MjTpw40fHrwsJCHDhwAIGBgYiNjcXixYtRWlqK9957DwDw6quvIi4uDsnJyTAajVizZg3WrVuHdevW9dx3QS6hrtmI3UW2f5GmD+Guq+R4j0zrj4/3liD7eDUOlNRhZEyA6EhEhG6MjOzduxcpKSlISUkBACxcuBApKSl47rnnAADl5eUoLi7ueL3RaMSiRYswfPhwTJ48GVu3bsU333yDG264oYe+BXIVm/IrYbHKGBTuh9ggH9FxyAPFBPrg+pFRAIA3ODpC5DQk2QXuc9Pr9fD390d9fT2nbFzY/P/uw3dHKvDYjAFYmJ506TcQ9YKCqkbMfCUTsgx889gkJEf6i45E5La6+vnNfbjJIVpNFmQdrwIApCdziobESQjpg6uHRwIAlm0+KTgNEQEsI+Qg205Uo9loQaS/FsmRHN0isR6dPgAAsOGncpyobBSchohYRsgh2m/pnTUkDJIkCU5Dni4p3A9XDAmDLAPLt3B0hEg0lhHqdbIs48e8SgDALG50Rk6ifXTkiwOlKKltFpyGyLOxjFCvO1KmR2WDAT4aJcYlBIqOQwQAGBETgMmJwbBYZbyVxdERIpFYRqjXtY+KTE4MhpeKB+OR81jQNjry8d7TqNS3Ck5D5LlYRqjXbcq3rReZwaPbycmMiw/E6H59YTRb8U52geg4RB6LZYR6VWVDKw6ergcATE9iGSHnIkkSFsywjY68v6sYZ5uMghMReSaWEepVW47a9hYZHu2PUJ1WcBqi800bGIKhUTo0Gy14d1uh6DhEHollhHrVprb1IpyiIWclSRIWTLONjry7vQgNrSbBiYg8D8sI9RqD2YLstl1XZw7iLb3kvGYnh6N/iC8aWs1Ys7P40m8goh7FMkK9ZndhLZqMFoT6eXHXVXJqCoWER9pGR1ZuLUCrySI4EZFnYRmhXvPjL6ZoFAruukrO7dqRkYgK8EZ1oxEf7y0RHYfIo7CMUK+QZRk/8pZeciFqpQLzpyYAAN7KLIDJYhWciMhzsIxQrzhZ1YiS2hZolApMHBAsOg5Rl9w0OgbBfbxQWteCLw+UiY5D5DFYRqhXtE/RjO8fBF8vleA0RF2jVSvxwOR4AMCyLSdgscqCExF5BpYR6hWb8m1lZCanaMjF3D4uFjqtCgVVTdh4pEJ0HCKPwDJCPa6+2YS9p84C4HoRcj1+WjXumRAHAHhzywnIMkdHiHobywj1uOwTVbBYZQwI7YOYQB/RcYjsds/EeHirlfipVI/MY1Wi4xC5PZYR6nHtW8BPGxgiOAlR9wT6anDbuFgAwLItJwWnIXJ/LCPUo6xWueNfktN4MB65sAcnJ0CtlLC7sBZ7i2pFxyFyaywj1KPyKvSoajDAR6PEmPi+ouMQdVu4vxbzRkUD4OgIUW9jGaEe1T5FM6F/ELxUSsFpiC7PQ1P7QyHZ7g7LLdOLjkPktlhGqEdltpWRqZyiITcQH+yLucMiAADLMzk6QtRbWEaox9S3mLCv2HZLLxevkrt4eFp/AMA3h8pQVN0kOA2Re2IZoR6z7UQ1LFYZ/UN8eUsvuY3kSH9MTwqBVQbeyuLoCFFvYBmhHrPlqG3XVd5FQ+7mkekDAADr9pXijL5VcBoi98MyQj1Cln95Sy+naMi9jIkLxNi4QBgtVvw7u0B0HCK3wzJCPSKvvAFn9AZ4q5UYExcoOg5Rj3t4um3tyPu7inG2ySg4DZF7YRmhHtE+KpLWPwhaNW/pJfczbWAIhkTo0Gy04D87ikTHIXIrLCPUI35eL8IpGnJPkiThkbbRkdXbi9BkMAtOROQ+WEbosjW0mrDvVPstvVy8Su5rztAIxAf7oq7ZhA92F4uOQ+Q2WEbosm07UQ2zVUZCsC9ig3hLL7kvpULCQ1MSAADvZBfAYLYITkTkHlhG6LJt6dh1lVM05P5+MyoKYTovnNEb8Pn+UtFxiNwCywhdFlmWkdW2eHUqd10lD+ClUuLBybbRkRWZJ2GxyoITEbk+lhG6LCerGlFW3wqNSoFx8UGi4xA5xK1jYxHgo0ZRTTM2HC4XHYfI5bGM0GXJOlYNABgXHwhvDW/pJc/g66XCPRPiAADLtpyELHN0hOhysIzQZck6bpuimZwYLDgJkWPdMyEOPhol8sr12NI2VUlE3cMyQt3WarJgZ0ENAGAK14uQhwnw0eD2cbEAgGWbTwhOQ+TaWEao2/YWnUWryYpQPy8khfmJjkPkcA9MToBGqcCeorPYU1QrOg6Ry2IZoW7L7piiCYEkSYLTEDlemE6LealRADg6QnQ5WEao29rPo5kykOtFyHM9NKU/FBKw+WgVjpTVi45D5JJYRqhbKvWtyK9ogCTZRkaIPFVcsC+uGh4JAFi+5aTgNESuiWWEuiXruO2W3qGR/gj01QhOQyTWI9NsB+htOFyOwuomwWmIXA/LCHVL+3oRTtEQAYMjdJgxKBRWGXgrk6MjRPZiGSG7Wa0ysttGRqZwioYIALBgum10ZN3+0yivbxGchsi1sIyQ3Y6U6VHbZISvRolR/fqKjkPkFFL7BWJsfCBMFhn/zi4UHYfIpbCMkN3ad11N6x8MtZI/QkTt2teOrN1VjNomo+A0RK6DnyRkt59P6eV6EaJfmjowBMmROrSYLFi9vUh0HCKXwTJCdmk0mLHv1FkA3AKe6NckScKC6QMAAKu3FaLRYBaciMg1sIyQXXaerIHZKiM20Af9gnxFxyFyOrOTw5EQ4gt9qxnv7zwlOg6RS2AZIbtk85ReootSKiQ8PNW2duSd7EK0miyCExE5P5YRskv2CdstvSwjRBd2fUoUogK8Ud1owCf7TouOQ+T0WEaoy8rqWlBQ1QSFZLuThog6p1Yq8D9TEgDYNkEzWayCExE5N5YR6rKtbRudjYgJgL+3WnAaIud2y5gYBPfR4PTZFnx1sEx0HCKnxjJCXdYxRTOAoyJEl6JVK3HfpHgAwLItJ2G1yoITETkvlhHqEqtVxra2MjKJW8ATdckd4/vBT6vCicpGbMw9IzoOkdNiGaEuyS3/eQv4lNgA0XGIXIJOq8bdaXEAgDc3n4Asc3SEqDMsI9Ql7QfjpfUP4hbwRHa4d2IcvNVKHC6tR1bbnyMiOhc/VahLtp6w7S8yietFiOwS1McLt46NBQC8uemE4DREzollhC6pxWjBnkLbFvBcL0Jkv/+ZkgCNUoHdRbXYXVgrOg6R02EZoUvaXVQLo8WKCH8t+odwC3gie4X7a3Hj6GgAwBubOTpC9GssI3RJW3+xBbwkSYLTELmmh6f2h1IhIetYFQ6drhMdh8ipsIzQJbUvXuUUDVH3xQT64LoRkQBsd9YQ0c/sLiNZWVm45pprEBkZCUmS8MUXX1zyPZmZmUhNTYVWq0VCQgJWrFjRnawkQGVDK/IrGgAAE/sHCU5D5Noemd4fkgR8f+QMjp1pEB2HyGnYXUaampowYsQIvPHGG116fWFhIebOnYvJkycjJycHzzzzDB577DGsW7fO7rDkeO0bnQ2N0iGoj5fgNESubUCoH65MDgcALOPoCFEHlb1vmDNnDubMmdPl169YsQKxsbF49dVXAQCDBw/G3r178fLLL2PevHn2fnlysI4pmgGcoiHqCQumD8C3P1Vg/cEyPDFrIOKCuSicqNfXjOzYsQPp6ennPDd79mzs3bsXJpOp0/cYDAbo9fpzHuR4six3HI43OZH7ixD1hKFR/piWFAKrDKzIPCk6DpFT6PUyUlFRgbCwsHOeCwsLg9lsRnV157sRLlmyBP7+/h2PmJiY3o5JnThR2YjKBgO8VAqk9usrOg6R2/jdjAEAgHX7T6O0rkVwGiLxHHI3za9vB20/n+FCt4kuXrwY9fX1HY+SkpJez0jna5+iGRsfCK1aKTgNkftI7ReICf2DYLLIeIujI0S9X0bCw8NRUVFxznOVlZVQqVQICur87gwvLy/odLpzHuR4Haf0cgt4oh73aNvoyId7SlCpbxWchkisXi8jaWlpyMjIOOe5jRs3YvTo0VCr1b395ambTBYrdhbUAAAmsowQ9bi0hCCk9usLo9mKt7MKRMchEsruMtLY2IgDBw7gwIEDAGy37h44cADFxcUAbFMsd911V8fr58+fj1OnTmHhwoXIy8vDqlWrsHLlSixatKhnvgPqFQdK6tBktCDQV4MhERyZIuppkiR1rB15f1cxahoNghMRiWN3Gdm7dy9SUlKQkpICAFi4cCFSUlLw3HPPAQDKy8s7igkAxMfHY8OGDdiyZQtGjhyJl156CUuXLuVtvU6ufb3IhP5BUCi4BTxRb5g6MATDovzRYrJg1bZC0XGIhJHk9tWkTkyv18Pf3x/19fVcP+Ig85Zvx75TZ/G3ecNwy5hY0XGI3Nb3Ryrw0H/3oY+XCtuemgF/H05fk/vo6uc3z6ah8+hbTThQUgeA60WIetsVg8MwKNwPjQYzVm8vEh2HSAiWETrProJaWKwy4oN9Ed3XR3QcIremUEhYMN22dmTVtkI0tHa+GSSRO2MZofNsPV4FAJg4gAfjETnC3GERSAjxRX2LCe/tOCU6DpHDsYzQebae4Hk0RI6kVPx8Z82/swvQZDALTkTkWCwjdI7y+hacrGqCQgLS+nNkhMhRrhkeifhgX5xtNmHNTo6OkGdhGaFztB+MNzw6AP7eXNVP5CgqpaJj7cjbWQVoNnJ0hDwHywido32Khqf0Ejne9SMjERvog5omI9buKr70G4jcBMsIdbBa5Y7zaHhLL5HjqZQKPNo2OrIiswCtJovgRESOwTJCHY6eaUB1oxHeaiVGxfYVHYfII/1mVBSiArxR3WjAB7s5OkKegWWEOrSvFxmXEAiNij8aRCKof7F2ZEXmSY6OkEfgJw51+PmWXk7REIl0Y2o0Iv21OKM34OO9JaLjEPU6lhECABjMFuwqrAEATOLiVSKhNCoFHm4bHVm2maMj5P5YRggAsO/UWbSarAju44WkMD/RcYg83s2jbaMjFfpWfLSHoyPk3lhGCAA67qKZNCAIkiQJTkNEXiolHmkfHdlygqMj5NZYRgjAz4tXJyVyC3giZ3HT6J/XjnzIO2vIjbGMEOqbTThUWg+Ai1eJnImXSokFM9pHR7h2hNwXywhh+8lqyDIwILQPwv21ouMQ0S/clBqDSH8tKhu47wi5L5YRQjZv6SVyWhqVgqMj5PZYRqhj8SrPoyFyTjelxiAqwBtVDQaeWUNuiWXEw5XUNuNUTTNUCgnjEoJExyGiTmhUP+/KujzzJFqMHB0h98Iy4uHad11NiQ1AHy+V4DREdCE3pkYjuq9tdGTNzlOi4xD1KJYRD9d+Sy9P6SVybhqVAo/NSARgGx1pMpgFJyLqOSwjHsxilbHtJNeLELmKG0ZFIS7IB7VNRqzeXiQ6DlGPYRnxYLlletQ1m9DHS4UR0QGi4xDRJaiUCjw+yzY68nZWAfStJsGJiHoGy4gHyz5RBQAYnxAElZI/CkSu4NoRURgQ2gf1LSas2looOg5Rj+AnkAdrXy/CKRoi16FUSHhy1kAAwMrsQtQ1GwUnIrp8LCMeqsVowd6iswC4eJXI1cwZGo5B4X5oMJjxdlaB6DhEl41lxEPtLqqF0WJFpL8W/UN8RcchIjsoFBIWXmEbHVm9vQg1jQbBiYguD8uIh8o+ZlsvMjkxBJIkCU5DRPa6YkgYhkf7o9lowfItJ0XHIbosLCMeKrttvcgkrhchckmSJOF/05MAAO/tPIXy+hbBiYi6j2XEA1XqW3H0TAMkietFiFzZlMRgjI0PhNFsxdIfT4iOQ9RtLCMeqH1UZFiUPwJ9NYLTEFF3SZKE38+2jY58vLcEhdVNghMRdQ/LiAdqP49mEkdFiFzemLhATE8KgcUq418Zx0THIeoWlhEPY7XKHSMjkxNDBKchop6wqG10ZP3BMuSW6QWnIbIfy4iHya9oQHWjAT4aJUb1CxAdh4h6QHKkP64eHgEA+OfGo4LTENmPZcTDbG3bAn5cfCC8VErBaYiopyy8YiCUCgk/5ldi36la0XGI7MIy4mE4RUPknhJC+uCm1GgAwN+/OwpZlgUnIuo6lhEP0mqyYFeh7V9MUwZy8SqRu3lsZiI0SgV2FdZiS9vGhkSugGXEg+wpqoXRbEW4Tov+IX1ExyGiHhYZ4I270voBAP72bT6sVo6OkGtgGfEg2b84pZdbwBO5pwXTB8BPq0J+RQO+PFgqOg5Rl7CMeBBuAU/k/vr6avDwtP4AgJe/PwaD2SI4EdGlsYx4iMqGVuSV2/Yf4GZnRO7t3gnxCNN5obSuBWt2FouOQ3RJLCMeYlvbrqtDo3QI6uMlOA0R9SZvjRJPzhoIAHhj03HoW02CExFdHMuIh8g61r4FPG/pJfIEN6ZGY0BoH5xtNuGtzJOi4xBdFMuIB7BaZWS13eY3LYllhMgTqJQK/KFtm/iVWwtxRt8qOBHRhbGMeIDccj1qmozw1SgxKrav6DhE5CBXDAlDar++aDVZeYgeOTWWEQ+Q2TYqMmFAMDQq/l9O5CkkScLiOYMAAB/vLcHRigbBiYg6x08mD5B51FZGpg7kFA2RpxkdF4g5Q8NhlYH/25AnOg5Rp1hG3Jy+1YT9xWcBsIwQeaqnrhwEtVJC5rGqjvVjRM6EZcTNbT9RA7NVRkKwL2ICfUTHISIB4oJ9cef4OAC20RELt4knJ8My4uba14tM4agIkUd7bOYA+HurkV/RgE/3lYiOQ3QOlhE3Jss/39LLKRoizxbgo8HvZgwAALy88RiaDGbBiYh+xjLixk5WNaG0rgUalQLjEgJFxyEiwe5M64fYQB9UNRjwdlaB6DhEHVhG3Fj7FM3YuED4aFSC0xCRaF4qJZ5uu9X37awCVNRzIzRyDiwjboxTNET0a3OGhmN0v75oMVnw9+/yRcchAsAy4rZaTRbsLKgBAEzlFvBE1EaSJDx3zRAAwGc5pR23/hOJxDLipnYV1sJgtiJcp0ViaB/RcYjIiQyPDsCNqdEAgBe/yoWVt/qSYCwjbuqXUzSSJAlOQ0TO5g+zk+CrUeJASR2+OFAqOg55OJYRN9W+eJVTNETUmVCdFo/OSAQA/PXbfN7qS0KxjLihktpmnKhshFIhYWL/YNFxiMhJ3TcpDv2CfFDZYMDyLSdFxyEPxjLihjYfrQQApMb2hb+PWnAaInJWXiolnpk7GADwdnYBSmqbBSciT8Uy4oZ+zLOVkemDQgUnISJnlz4kDBMHBMFotuIv3/BUXxKDZcTNNBvN2NF2S+/MwSwjRHRxkiThuauToVRI+O5IBU/1JSFYRtzM9hM1MJqtiArw5i29RNQlSeF+uDstDgDwp/VHYDBbxAYij9OtMrJs2TLEx8dDq9UiNTUV2dnZF3ztli1bIEnSeY/8fO781xs2ta0XmTEolLf0ElGXPXFFIkL8vFBQ3YR/ZxeKjkMexu4y8tFHH+GJJ57As88+i5ycHEyePBlz5sxBcXHxRd939OhRlJeXdzwSExO7HZo6J8syNuf/XEaIiLpKp1Xjmbm2c2te33QcpXUtghORJ7G7jLzyyiu4//778cADD2Dw4MF49dVXERMTg+XLl1/0faGhoQgPD+94KJXKboemzuWVN6C8vhVatQJp/YNExyEiF3P9yCiMjQtEq8mKl77KFR2HPIhdZcRoNGLfvn1IT08/5/n09HRs3779ou9NSUlBREQEZs6cic2bN1/0tQaDAXq9/pwHXVr7Lb0T+wdDq2bZIyL7SJKEF6//eTFrJhezkoPYVUaqq6thsVgQFhZ2zvNhYWGoqKjo9D0RERF4++23sW7dOnz22WdISkrCzJkzkZWVdcGvs2TJEvj7+3c8YmJi7InpsTbl85ZeIro8g8J1XMxKDqfqzpt+vTBSluULLpZMSkpCUlJSx6/T0tJQUlKCl19+GVOmTOn0PYsXL8bChQs7fq3X61lILqG2yYicttM3WUaI6HI8cUUivjpUhsLqJryVWYDHZnKNH/Uuu0ZGgoODoVQqzxsFqaysPG+05GLGjx+P48ePX/C/e3l5QafTnfOgi8s8VgmrDAwK90NUgLfoOETkwnRaNf54lW1n1jc2n0BBVaPgROTu7CojGo0GqampyMjIOOf5jIwMTJgwocu/T05ODiIiIuz50nQJm/Jtc7scFSGinnDtiEhMGRgCo9mKZz//CbIsi45EbszuaZqFCxfizjvvxOjRo5GWloa3334bxcXFmD9/PgDbFEtpaSnee+89AMCrr76KuLg4JCcnw2g0Ys2aNVi3bh3WrVvXs9+JBzNbrMhsW7w6k2WEiHqAJEn483VDkf5qJnYU1GDd/lLcmBotOha5KbvLyC233IKamhq8+OKLKC8vx9ChQ7Fhwwb069cPAFBeXn7OniNGoxGLFi1CaWkpvL29kZycjG+++QZz587tue/Cw+0vroO+1YwAHzVSYvuKjkNEbiI2yAePzxyIv32Xj798k4sZg0IR6KsRHYvckCS7wNibXq+Hv78/6uvruX6kE0s25OGtrAJcNzISr/02RXQcInIjJosV17y+FfkVDZg3Khr/vHmE6EjkQrr6+c2zaVycLMvYmHsGADBrcNcXERMRdYVaqcD/3TAMkgSs238a209Ui45EbohlxMWdqGxEYXUTNEoFpiWFiI5DRG5oVGxf3DHONhX/zOeH0WLk3iPUs1hGXNz3R2y3WU8YEAQ/rVpwGiJyV7+/MgnhOi2KaprxSsZR0XHIzbCMuLjvj9imaGYnhwtOQkTuTKdV4/9uGAoAWLm1EPvbNlkk6gksIy6srK4Fh0vrIUlcL0JEvW/GoDDckBIFqwz84dNDaDVxuoZ6BsuIC9vYNkWTGtsXIX5egtMQkSd47pohCO7jhROVjVj644V30iayB8uIC+MUDRE5WoCPBn++3jZd81ZWAQ6frheciNwBy4iLOttkxO6iWgBAejKnaIjIca4cGo6rh0fAYpXx+08Pwmi2io5ELo5lxEX9mF8Ji1XGoHA/9AvyFR2HiDzMC9cmI9BXg/yKBry+idM1dHlYRlxU+y296ZyiISIBgvp44aXrbNM1b24+wbtr6LKwjLigFqMF2cdtp/TO5hQNEQly1fAI/Kbt7pqFHx1Ak8EsOhK5KJYRF5R5rAqtJiuiArwxJIJn9RCROH+6NhmR/rbN0P6yIU90HHJRLCMuqP2W3tnJ4ZAkSXAaIvJk/t5qvNx2eN7aXcXYlH9GcCJyRSwjLsZkseLH/EoAnKIhIucwoX8wHpgUDwD4w6eHUdNoEJyIXA3LiIvZeqIa9S0mBPlqMDouUHQcIiIAwKLZSRgY1gfVjQYs/uwwZFkWHYlcCMuIi/nqQBkAYO6wCCgVnKIhIuegVSvxr1tGQq2UsDH3DNbsKhYdiVwIy4gLaTVZOm7pvXZkpOA0RETnSo70x1NXDgIAvPR1LnLL9IITkatgGXEhm/Mr0WS0INJfi9TYvqLjEBGd5/5J8ZgxKBRGsxWPfrAfzUbe7kuXxjLiQtYftE3RXDMiEgpO0RCRE5IkCS/fNAJhOi8UVDXhuS+PiI5ELoBlxEU0tJo67qK5ZgSnaIjIeQX6avDab1OgkIBP953G5zmnRUciJ8cy4iI2HjkDo9mKhBBfJEdyozMicm7jE4Lw2MxEAMCzn/+EgqpGwYnImbGMuIj2KZprR0RyozMicgm/m5GI8QmBaDZa8PAarh+hC2MZcQE1jQZsPVENwFZGiIhcgVIhYelvUxDi54WjZxrw1DruP0KdYxlxARt+qoDFKmNolA4JIX1ExyEi6rJQnRbLbh8FlULCVwfLsHJroehI5IRYRlxA+0ZnHBUhIlc0Ji4Qf7xqMABgybf52FlQIzgRORuWESdXVteC3UW1AICrh7OMEJFruntCHK4fGQmLVcaja/ejvL5FdCRyIiwjTu7rQ7ZRkbFxgYgM8BachoioeyRJwpIbhmNwhA7VjUY88v5+tJosomORk2AZcWKyLOPTfbb787n9OxG5Om+NEm/dkQqdVoWc4joeqEcdWEac2P7iOhw70witWsEyQkRuITbIB8tuT4VSIeHznFK8semE6EjkBFhGnNgHu22nXl41LBI6rVpwGiKinjEpMRgvXTcUAPDPjGMd09HkuVhGnJS+1dTxB/S2cTGC0xAR9azbxsXi/knxAID//fggcorPCk5EIrGMOKkvc0rRarIiMbQPRvGEXiJyQ8/MHYyZg0JhMFvx4Hv7cPpss+hIJAjLiBOSZRkf7C4BANw6NpbbvxORW1IqJLx2awoGhfuhutGAe97dg7NNRtGxSACWESd0uLQeueV6aFQK3DAqSnQcIqJe08dLhVX3jEG4TosTlY24d/UenmHjgVhGnFD7wtW5Q8MR4KMRnIaIqHdFBnjjv/ePhb+3GgdK6jB/zX4YzVbRsciBWEacTKPBjPVt27//dmys4DRERI6RGOaHd+8dA2+1ElnHqrDok4OwWrkHiadgGXEyXx0sQ5PRgoRgX4yLDxQdh4jIYUbF9sXyO2yH6q0/WIYXv87lpmgegmXEyXzYNkXz27ExXLhKRB5nWlIo/nnzCADA6u1F+Pv3R1lIPADLiBM5dLoOB0/XQ62UMG9UtOg4RERCXDcyCi9dlwwAWL7lJAuJB2AZcSLLt5wEYDudN6iPl+A0RETi3JkWhxeuZSHxFCwjTuJEZSO+O1IBAHh4Wn/BaYiIxLt7AguJp2AZcRJvZZ6ELAOzBodhYJif6DhERE7h7glx+NM1QwDYCsmSb/NZSNwQy4gTKKtrwec5pQCAR6ZzVISI6JfumRjfUUjezirAHz49BLOF+5C4E5YRJ/BOdgHMVhlpCUE8h4aIqBP3TIzH3+YNg0ICPtl3Gg/9dx9ajBbRsaiHsIwIVtNo6NhxlaMiREQXdsuYWLx152h4qRT4Mb8Sd67chbpmnmXjDlhGBFu9vQitJiuGRflj0oBg0XGIiJzaFUPC8N/7x0GnVWHvqbO4+a0dPO3XDbCMCNTQasJ/thcBAB6Z1p+bnBERdcHY+EB8PD8NYTovHDvTiOve2IbdhbWiY9FlYBkRaO2uYuhbzegf4ovZyeGi4xARuYxB4Tp89shEJEfqUNNkxG3v7MTaXcWiY1E3sYwIUttkxLK2Tc7mT+0PhYKjIkRE9ogK8Man8yfg6uERMFtlPPP5Yfy/L36CiXfauByWEUH+/l0+6ltMGByhw29SokTHISJySd4aJV6/NQW/n50ESQL+u/MUbn9nF8rqWkRHIzuwjAiwv/gsPtxTAgB46bpkqJT8v4GIqLskScKC6QPwzp2j0cdLhd1FtZjzWja++6lCdDTqIn4KOpjFKuO5L38CAMwbFY3RcYGCExERuYdZQ8Lw9e8mYXi0P+pbTJi/Zh/++MVhtJq4H4mzYxlxsLW7i/FTqR5+WhWenjNIdBwiIrcSF+yLT+dPwENTEwAAa3YW49o3tuKn0nrByehiWEYcqKbRgH98lw8AWJSehBA/nsxLRNTTNCoFFs8ZjPfuG4vgPm23/765Df+3IY+7tjoplhEH+tt3+dC3mjEkQofbx8WKjkNE5NamDAzBd09MxtXDI2Cxyng7qwDpr2Yi61iV6Gj0KywjDrL1eDU+3nsaAPDS9Vy0SkTkCMF9vPDGbaOw6p7RiPTXoqS2BXet2o3HP8xBKe+4cRr8RHSAwuomLFi7HwBw69hYpPbjolUiIkeaMSgMGQun4t6JcZAk4MsDZZj+8hYs+TYP9S0m0fE8niTLsiw6xKXo9Xr4+/ujvr4eOp1OdBy71LeY8Jtl21BQ1YSU2AB88OB4aNVK0bGIiDzW4dP1+L8NedhRUAMACPBR49HpA3DH+H78+7mHdfXzm2WkF5ktVty7eg+yj1cj0l+LLx+dxEWrREROQJZlbD5aiSUb8nG8shGAbUrnvklxuH1cP/h7qwUndA8sI07gT+uPYPX2Inirlfj04TQkR/qLjkRERL9gtlixbv9pvPbDcZTVtwIA+nipcNu4WNw3MR7h/lrBCV0by4hg/9lehOfXHwEArLgjFVcO5UF4RETOymSxYv2BMryVdRLHzthGSpQKCdOTQnHLmBhMSwqBmjce2I1lRJBWkwUvfZ2L99tOj/z97CQsmD5AcCoiIuoKq1XGlmOVWJFZgN2FtR3Ph/h54YZRUbh2RCSGROggSTzctCtYRgQormnGI2v34adSPSQJeGxGIp6YlcgfWiIiF3T8TAM+2Xcan+0/jepGY8fzUQHeSE8OwxVDwjA2LpBbNVxEVz+/u3UFly1bhvj4eGi1WqSmpiI7O/uir8/MzERqaiq0Wi0SEhKwYsWK7nxZp7bxSAWuej0bP5Xq0ddHjf/cOxZPXjGQRYSIyEUlhvnhmbmDsWPxTKy4IxXpQ8KgVStQWteCd7cV4bZ3diHlpQzcv3oP3so8iQMldTBZrKJjuyS7R0Y++ugj3HnnnVi2bBkmTpyIt956C//+97+Rm5uL2NjzdxUtLCzE0KFD8eCDD+Khhx7Ctm3b8Mgjj+CDDz7AvHnzuvQ1nXVkpNVkwYbD5fhwdwl2F9mG80bFBuCN20YhMsBbcDoiIuppLUYLso9XISP3DH7IO4OzzefuUeKjUWJopD8GR/hhcIQOgyJ0SArzg7fGM28Z7rVpmnHjxmHUqFFYvnx5x3ODBw/G9ddfjyVLlpz3+qeeegrr169HXl5ex3Pz58/HwYMHsWPHji59TWcpI1arjDMNrSisasL3RyrweU4p9K1mAIBCAu6bGI+n5gziIiciIg9gtliRW67H7sJa7CyoxZ6i2gtuoBam80JsoA9iAn0Q09cHEf5aBPfxQlAfTcf/equVbjea3tXPb5U9v6nRaMS+ffvw9NNPn/N8eno6tm/f3ul7duzYgfT09HOemz17NlauXAmTyQS1+vx7uQ0GAwwGwznfTG9Yt+80DndykqPFKsNkscJoscJkkdFiNKO4thmnapphMJ87BBfd1xu/HRODG1NjeAsYEZEHUSkVGB4dgOHRAXhgcgKsVhnHKxtxpKweeeV65JU3IK9cj5omI87oDTijN2BP0dkL/34KCb5eKvTxUsFPq4K3RgkvlQJeKiU0KgU0KgXUCgkKhQSVQoJSIUGSJCgkQIIESQIkoNNC05WOM29UNIZGidmCwq4yUl1dDYvFgrCwsHOeDwsLQ0VFRafvqaio6PT1ZrMZ1dXViIiIOO89S5YswQsvvGBPtG7JPFaF9QfL7HqPSiEhJtAHQ6P8cfPoaEzsHwyFwr2aLBER2U+hkJAU7oekcL+O52RZxtlmE0pqm1Hc9jh9thln9AbUNBpQ3WhEVaMBRrMVZquM+haTsO3pU2L7ukYZaffr1iXL8kWHljp7fWfPt1u8eDEWLlzY8Wu9Xo+YmJjuRL2o9OQwxAb6nPe8UiHZGqhSglppa6VRfb0RH+SLyAAtV04TEVGXSJKEQF8NAn01GBET0OlrZFlGk9GCxlYzGg0mNLSa0Wgwo8VogcFshdFshcFshcFsgcUq2x6yDIvF9r+yDMi23wjWThZeyOjaaozE0D7d/j4vl11lJDg4GEql8rxRkMrKyvNGP9qFh4d3+nqVSoWgoKBO3+Pl5QUvr97fNv3q4ZG4enivfxkiIqILkiQJfdqmZwDPnO6365/4Go0GqampyMjIOOf5jIwMTJgwodP3pKWlnff6jRs3YvTo0Z2uFyEiIiLPYvd8w8KFC/Hvf/8bq1atQl5eHp588kkUFxdj/vz5AGxTLHfddVfH6+fPn49Tp05h4cKFyMvLw6pVq7By5UosWrSo574LIiIicll2rxm55ZZbUFNTgxdffBHl5eUYOnQoNmzYgH79+gEAysvLUVxc3PH6+Ph4bNiwAU8++STefPNNREZGYunSpV3eY4SIiIjcG7eDJyIiol7Rq9vBExEREfUUlhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgolhEiIiISimWEiIiIhGIZISIiIqFYRoiIiEgou7eDF6F9k1i9Xi84CREREXVV++f2pTZ7d4ky0tDQAACIiYkRnISIiIjs1dDQAH9//wv+d5c4m8ZqtaKsrAx+fn6QJKnHfl+9Xo+YmBiUlJTwzJtexOvsOLzWjsHr7Bi8zo7TW9dalmU0NDQgMjISCsWFV4a4xMiIQqFAdHR0r/3+Op2OP+gOwOvsOLzWjsHr7Bi8zo7TG9f6YiMi7biAlYiIiIRiGSEiIiKhPLqMeHl54fnnn4eXl5foKG6N19lxeK0dg9fZMXidHUf0tXaJBaxERETkvjx6ZISIiIjEYxkhIiIioVhGiIiISCiWESIiIhLK7cvIsmXLEB8fD61Wi9TUVGRnZ1/09ZmZmUhNTYVWq0VCQgJWrFjhoKSuzZ7r/Nlnn+GKK65ASEgIdDod0tLS8P333zswreuy9+e53bZt26BSqTBy5MjeDehG7L3WBoMBzz77LPr16wcvLy/0798fq1atclBa12XvdX7//fcxYsQI+Pj4ICIiAvfeey9qamoclNY1ZWVl4ZprrkFkZCQkScIXX3xxyfc4/LNQdmMffvihrFar5XfeeUfOzc2VH3/8cdnX11c+depUp68vKCiQfXx85Mcff1zOzc2V33nnHVmtVsuffvqpg5O7Fnuv8+OPPy7/7W9/k3fv3i0fO3ZMXrx4saxWq+X9+/c7OLlrsfc6t6urq5MTEhLk9PR0ecSIEY4J6+K6c62vvfZaedy4cXJGRoZcWFgo79q1S962bZsDU7see69zdna2rFAo5Ndee00uKCiQs7Oz5eTkZPn66693cHLXsmHDBvnZZ5+V161bJwOQP//884u+XsRnoVuXkbFjx8rz588/57lBgwbJTz/9dKev/8Mf/iAPGjTonOceeughefz48b2W0R3Ye507M2TIEPmFF17o6WhupbvX+ZZbbpH/+Mc/ys8//zzLSBfZe62//fZb2d/fX66pqXFEPLdh73X+xz/+ISckJJzz3NKlS+Xo6Ohey+huulJGRHwWuu00jdFoxL59+5Cenn7O8+np6di+fXun79mxY8d5r589ezb27t0Lk8nUa1ldWXeu869ZrVY0NDQgMDCwNyK6he5e53fffRcnT57E888/39sR3UZ3rvX69esxevRo/P3vf0dUVBQGDhyIRYsWoaWlxRGRXVJ3rvOECRNw+vRpbNiwAbIs48yZM/j0009x1VVXOSKyxxDxWegSB+V1R3V1NSwWC8LCws55PiwsDBUVFZ2+p6KiotPXm81mVFdXIyIiotfyuqruXOdf++c//4mmpibcfPPNvRHRLXTnOh8/fhxPP/00srOzoVK57R/1Hteda11QUICtW7dCq9Xi888/R3V1NR555BHU1tZy3cgFdOc6T5gwAe+//z5uueUWtLa2wmw249prr8Xrr7/uiMgeQ8RnoduOjLSTJOmcX8uyfN5zl3p9Z8/Tuey9zu0++OAD/OlPf8JHH32E0NDQ3ornNrp6nS0WC2677Ta88MILGDhwoKPiuRV7fqatViskScL777+PsWPHYu7cuXjllVewevVqjo5cgj3XOTc3F4899hiee+457Nu3D9999x0KCwsxf/58R0T1KI7+LHTbfy4FBwdDqVSe17ArKyvPa3ztwsPDO329SqVCUFBQr2V1Zd25zu0++ugj3H///fjkk08wa9as3ozp8uy9zg0NDdi7dy9ycnLw6KOPArB9YMqyDJVKhY0bN2LGjBkOye5quvMzHRERgaioqHOOSh88eDBkWcbp06eRmJjYq5ldUXeu85IlSzBx4kT8/ve/BwAMHz4cvr6+mDx5Mv785z9z9LqHiPgsdNuREY1Gg9TUVGRkZJzzfEZGBiZMmNDpe9LS0s57/caNGzF69Gio1epey+rKunOdAduIyD333IO1a9dyvrcL7L3OOp0Ohw8fxoEDBzoe8+fPR1JSEg4cOIBx48Y5KrrL6c7P9MSJE1FWVobGxsaO544dOwaFQoHo6OhezeuqunOdm5uboVCc+7GlVCoB/Pwvd7p8Qj4Le21prBNov21s5cqVcm5urvzEE0/Ivr6+clFRkSzLsvz000/Ld955Z8fr229nevLJJ+Xc3Fx55cqVvLW3C+y9zmvXrpVVKpX85ptvyuXl5R2Puro6Ud+CS7D3Ov8a76bpOnuvdUNDgxwdHS3feOON8pEjR+TMzEw5MTFRfuCBB0R9Cy7B3uv87rvvyiqVSl62bJl88uRJeevWrfLo0aPlsWPHivoWXEJDQ4Ock5Mj5+TkyADkV155Rc7Jyem4hdoZPgvduozIsiy/+eabcr9+/WSNRiOPGjVKzszM7Phvd999tzx16tRzXr9lyxY5JSVF1mg0clxcnLx8+XIHJ3ZN9lznqVOnygDOe9x9992OD+5i7P15/iWWEfvYe63z8vLkWbNmyd7e3nJ0dLS8cOFCubm52cGpXY+913np0qXykCFDZG9vbzkiIkK+/fbb5dOnTzs4tWvZvHnzRf/OdYbPQkmWObZFRERE4rjtmhEiIiJyDSwjREREJBTLCBEREQnFMkJERERCsYwQERGRUCwjREREJBTLCBEREQnFMkJERERCsYwQERGRUCwjREREJBTLCBEREQnFMkJERERC/X8o0LpBoS66HAAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"grid, p_density = get_p_distribution(grid=np.linspace(1e-3, 1-1e-3, 100)[:, np.newaxis], \n",
" mu_p=0.4, sensory_noise=0.75)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"grid, p_density = get_p_distribution(grid=np.linspace(1e-3, 1-1e-3, 100)[:, np.newaxis], \n",
" mu_p=mu_p[np.newaxis, :], sensory_noise=posterior_noise)\n",
"\n",
"for i in range(12):\n",
" plt.plot(grid.flatten(), p_density[:, i], color=sns.color_palette('coolwarm', 12)[i], label='p = %.2f' % p[i])\n",
"\n",
"grid, p_prior_density = get_p_distribution(grid=np.linspace(1e-3, 1-1e-3, 100)[:, np.newaxis], \n",
" mu_p=0.4, sensory_noise=0.75)\n",
"\n",
"plt.plot(grid, p_prior_density, c='k', label='prior', alpha=.85)\n",
"\n",
"plt.legend()\n",
"\n",
"sns.despine()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "base",
"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": "3.10.9"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}
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