{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# DCEGM Upper Envelope\n", "## [\"The endogenous grid method for discrete-continuous dynamic choice models with (or without) taste shocks\"](https://onlinelibrary.wiley.com/doi/abs/10.3982/QE643)\n", "\n", "
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\n", "\n", "[![badge](https://img.shields.io/badge/Launch%20using%20-Econ--ARK-blue)](https://econ-ark.org/materials/dcegm-upper-envelope#launch)\n", "\n", "\n", "\n", "This notebook provides a simple introduction to the \"DCEGM\" algorithm . DCEGM extends the EGM method proposed in to problems with both continuous (e.g. consumption) and discrete (e.g. retirement) decisions.\n", "\n", "The main challenge for the EGM algorithm in discrete-continuous problems is that the discrete decisions generate \"kinks\" in the value function, making it non-concave and rendering the first order condition used by EGM a necessary but not sufficient for optimality. In practice, this causes the EGM inversion step to produce (resource, consumption) points that are not optimal. DCEGM incorporates a method to filter the points produced by EGM so that only the truly optimal ones are used in producing an approximation to the solution.\n", "\n", "This filtering process consists mainly of computing \"upper-envelopes\" of the candidate points: lines that are made up only of the points with the higher values.\n", "\n", "This notebook presents HARK's tool for calculating upper-envelopes and then uses it to solve a simple three-period discrete-continuous problem using DCEGM." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Upper envelopes\n", "\n", "Start by importing the tools." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# imports\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\")\n", "from HARK.rewards import CRRAutility, CRRAutilityP, CRRAutilityP_inv\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# here for now, should be\n", "# from HARK import discontools or whatever name is chosen\n", "from HARK.interpolation import LinearInterp\n", "from HARK.dcegm import calc_nondecreasing_segments, upper_envelope" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Applying EGM to value functions with kinks, as the ones that result from discrete-continuous problems, will often result in grids for market resources that are not monotonic and candidate choices at those points that are sub-optimal.\n", "Consider the following example output." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Value')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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tu4uTA9e1KRzp1Ld1fdycNdJJFG5ERKSSysgtYPWBJFZExLHpWArnBjrhYIJeLfy4OSSQQR0a4O3mbN9CpdJRuBERkUojz2xh7R+nWBkRz8+HksgzW23vdQ6qzdDOgQzpFEB9Lzc7VimVncKNiIjYlcVqsDXyNCsi4lm1P4GMXLPtveb1PBnWuSE3hQTS1M/TjlVKVaJwIyIiFc4wDPbFpbEiIp5v98STnJFney/Ax42bQwoXqWwX4K2RTlJqCjciIlJhIk9lsiIinpV74olKybJt93F35oaOhYtUhjf1xUEjneQKKNyIiEi5SkrP5ds9hYFmb2yabbubswMD2jVgaEgg17Sqh4uTFqmUsqFwIyIiZS4tu4AfDySwIiKeLZGnMc6NdHJ0MHFNSz+Gdm7IgHb+eLrqa0jKnv5ViYhImcgtsPDLoWRWRMSx9o9T5Fv+GunUrWkdbu7ckBs6NKBuLVc7Vik1gcKNiIhcNovVYOOxFFZExPHTgSQy8/4a6dSmgRdDOzfkppAAGtXxsGOVUtMo3IiIyGWxWg3u/2wHPx9Ktm1rWNudoZ0DGdq5Ia0beNmxOqnJFG5EROSyLNp6kp8PJePq5MCIbkEM7RxI18Z1NHRb7E7hRkRESu3k6SxeXXUYgKmD2zCmV7CdKxL5i8bdiYhIqVisBk8u3UtOgYUezeoyqkdTe5ckUoTCjYiIlMq8TVFsO5GKp4sjb9zeSRPuSaWjcCMiIiV2LDmTN1b/AcCzN7YjyFejoKTyUbgREZESMVusPL50D/lmK31a1ePObkH2LkmkWAo3IiJSIjPXR7In5ixebk68dltHjYqSSkvhRkRELulwYjrv/nwEgBdvbk+Aj7udKxK5MIUbERG5qHyzlclL9lBgMRjQzp9bujS0d0kiF6VwIyIiF/Xhb8c4mJBOHQ9nXr1Fj6Ok8lO4ERGRC9oXm8ZHvx0D4OVhHajnpUUvpfJTuBERkWLlmS08vjQCi9VgSKcAbuwUaO+SREpE4UZERIr1zpqjHEnKxK+WKy8P7WDvckRKTOFGRETOs/PkGT5ZfxyAabd2xNfTxc4ViZScwo2IiBSRk2/hiaV7sBpwa9eGDGjnb++SREpF4UZERIp4Y/VholKyaODtxvM3tbd3OSKlpnAjIiI2W46fZt6mEwC8fnsnfNyd7VuQyGVQuBEREQAy88w8uWwPAHeFN6ZPq3p2rkjk8ijciIgIAK+uOkTsmRwa1XHnmSFt7V2OyGVTuBEREdYfOcXnW6MBeOP2TtRydbJzRSKXT+FGRKSGS8sp4N9f7QVgTM+m9GzuZ+eKRK6Mwo2ISA338ncHSUjLJdjPk39f38be5YhcMYUbEZEabM3BJJbtjMXBBG/e0Ql3F0d7lyRyxRRuRERqqDNZ+Uxdvg+A+3o3I7SJr50rEikbdg8306dPJzg4GDc3N0JDQ9mwYcNF91+0aBEhISF4eHgQEBDA2LFjOX36dAVVKyJSfTy38gApmXm0rF+Lxwa0snc5ImXGruFmyZIlPProozzzzDPs3r2b3r17M3jwYKKjo4vdf+PGjYwaNYrx48dz4MABli5dyvbt25kwYUIFVy4iUrV9vzeBb/fE4+hg4q3hIbg563GUVB92DTdvv/0248ePZ8KECbRt25Z3332XoKAgZsyYUez+v//+O02bNmXSpEkEBwdz9dVXc//997Njx44KrlxEpOo6lZHHs98UPo56qG9zOjWqbd+CRMqY3cJNfn4+O3fuZODAgUW2Dxw4kM2bNxd7TM+ePYmNjWXVqlUYhkFSUhLLli1jyJAhF7xOXl4e6enpRX5ERGoqwzB45ut9nMkuoF2ANw9f29LeJYmUObuFm5SUFCwWC/7+RVeb9ff3JzExsdhjevbsyaJFixgxYgQuLi40aNCA2rVr88EHH1zwOtOmTcPHx8f2ExQUVKafQ0SkKvkmIo6fDibh7Fj4OMrFye5dL0XKnN3/VZtMpiKvDcM4b9ufDh48yKRJk3juuefYuXMnP/74I1FRUUycOPGC5586dSppaWm2n5iYmDKtX0SkqkhMy+X5FQcAeOS6lrQN8LZzRSLlw27za/v5+eHo6HheK01ycvJ5rTl/mjZtGr169eLJJ58EoFOnTnh6etK7d29eeeUVAgICzjvG1dUVV1fXsv8AIiJViGEYTFm+l/RcMyGNfJjYp7m9SxIpN3ZruXFxcSE0NJQ1a9YU2b5mzRp69uxZ7DHZ2dk4OBQt2dGxsIe/YRjlU6iISDWwZHsMa/84hYuTA28ND8HJ0e4N9yLlxq7/uidPnszs2bOZO3cuhw4d4rHHHiM6Otr2mGnq1KmMGjXKtv9NN93E8uXLmTFjBpGRkWzatIlJkyYRHh5OYGCgvT6GiEilFnsmm1e+PwTAkwNb06K+l50rEilfdl32dcSIEZw+fZqXXnqJhIQEOnTowKpVq2jSpAkACQkJRea8GTNmDBkZGXz44Yc8/vjj1K5dm2uvvZbXX3/dXh9BRKRSs1oNnlq2l8w8M2FN6jDu6mB7lyRS7kxGDXuek56ejo+PD2lpaXh7qzOdiFRvC7ac4LkVB3B3duSHR3rT1M/T3iWJXJbSfH/roauISDV1IiWLaasOAzD1hjYKNlJjKNyIiFRDFqvBE0v3kFNgoWfzuozs3sTeJYlUGIUbEZFqaO7GKHacPEMtVyfeuL0TDg7Fzx8mUh0p3IiIVDPHkjP4309/APDskLY0quNh54pEKpbCjYhINWK2WHn8yz3km630bV2PEd205IzUPAo3IiLVyMfrjrMnNg1vNydev63TBZezEanOFG5ERKqJg/HpvPfLUQBeHNoef283O1ckYh8KNyIi1UC+2crjS/dQYDEY2M6fYZ0b2rskEbtRuBERqQY+/PUohxLSqePhzH9v6ajHUVKjKdyIiFRxe2LO8tHa4wD895aO1PNytXNFIvalcCMiUoXlFlh4fOkeLFaDm0ICuaFjgL1LErE7hRsRkSrsnTVHOJacST0vV166ub29yxGpFBRuRESqqJ0nU/lkQyQA027pSB1PFztXJFI5KNyIiFRB2flmHv9yD4YBt3VtRP92/vYuSaTSULgREamC3vjxD06czibAx43nbmpn73JEKhWFGxGRKmbz8RTmbz4BwOu3dcLH3dm+BYlUMgo3IiJVSGaemaeW7QXg7u6NuaZVPTtXJFL5KNyIiFQh//3+ELFncmhUx52nb2hr73JEKiWFGxGRKmLdkVMs3hYNwJt3hFDL1cnOFYlUTgo3IiJVQFpOAf8+9zhqbK+mXNWsrp0rKmQYBrkFFnuXIVKEwo2ISBXw4rcHSEzPJdjPk6cGtbF3OQCczszjjo+30OWlNcSdzbF3OSI2atMUEank1hxMYvmuOBxMhY+j3F0c7V0SUSlZjJm3jZOns/Fyc8Ld2f41ifxJ4UZEpBJLzcpn6vJ9ANx3TTNCm9Sxc0WwK/oMEz7dQWpWPh4ujswfG46vZkeWSkThRkSkEvvPiv2kZObRyr8Wj/VvZe9yWH0gkUmLd5NntuLi5MDsUWGVInCJ/J3CjYhIJfXd3ni+35uAo4OJt+7ojJudH/18uvkEL3x7AMMAJwcT0+/uSs8WfnatSaQ4CjciIpXQqYw8/vPNfgAe6teCjo187FaL1Wrw2o+H+WR94SKdJhO8PaKz1rOSSkvhRkSkkjEMg6e/3seZ7ALaBXjzcL8Wdqslt8DCE0v38N3eBNu2127tyM0hgXarSeRSFG5ERCqZr3fHseZgEs6OJt4eEYKLk31m7Tibnc+/PtvJtqhU27b/3NiOEd0a26UekZJSuBERqUQS0nJ4fuUBAB7t34o2DbztUkfsmWzGzNvOseRM27bJA1ox/upgu9QjUhoKNyIilYRhGPz7q31k5JoJCarN/dc0s0sd++PSGDt/O6cy8mzb/nVNM/7vWvs9HhMpDYUbEZFK4ovtMaw/cgpXJwfeuiMEJ8eKfxy19o9kHly0i+z8v5ZUuKd7Y6YOboPJZKrwekQuh8KNiEglEJOazSvfHQTgyUGtaVG/VoXXsGR7NE9/vR+L1bBtG9Y5kJeHdlCwkSpF4UZExM6sVoMnl+0hK99CeFNfxvaq2H4thmHwzs9Hef+Xo0W2D2znz5t3hODgoGAjVctltXmazWZ+/vlnZs6cSUZGBgDx8fFkZmZe4kgREfmnBVtO8HtkKu7Ojvzvjk44VmCYKLBYeXLZ3vOCTe+Wfnxwdxe7PBoTuVKlbrk5efIk119/PdHR0eTl5TFgwAC8vLx44403yM3N5eOPPy6POkVEqqWolCxe+/EwAE/f0IYmdT0r7NoZuQU8uGgXG46mFNke1qQOM+8NxdVJi2FK1VTqSP7II48QFhbGmTNncHd3t22/5ZZb+OWXX8q0OBGR6sxiNXhi6R5yC6z0alGXe7o3qbBrJ6blMnzm7+cFmw4NvZk7thseLuq1IFVXqf/1bty4kU2bNuHiUnQF2CZNmhAXF1dmhYmIVHdzNkay8+QZark68cbtFde35UhSBmPmbiM+LbfI9pb1a7FgXHe83ZwrpA6R8lLqcGO1WrFYLOdtj42NxcvLq0yKEhGp7o4mZfDmT0cAeO7GdjSs7X6JI8rG5uMp3P/ZTjJyzfh6upCTbyGnwEJjXw8WTuiOr6fLpU8iUsmV+rHUgAEDePfdd22vTSYTmZmZPP/889xwww1lWZuISLVktlh5fOke8s1W+rWuxx1hjSrkuisi4hg9dxsZuWbaNPDC09WRnAILDbzdWDShO/7ebhVSh0h5K3XLzTvvvEO/fv1o164dubm53H333Rw9ehQ/Pz8WL15cHjWKiFQrM9YeZ29sGj7uzrx2W6dyn0PGMAxmrDvOGz/+AcC1beqTkpnH4cQc6nq6sHBCd4J8Pcq1BpGKVOpwExgYSEREBIsXL2bXrl1YrVbGjx/PPffcU6SDsYiInO9AfBrv/1o47PrFm9uXe2uJ2WLlhW8PsPD3aABG9WhC5Kks9sam4eXmxILx4XaZMFCkPJkMwzAuvVv1kZ6ejo+PD2lpaXh722dBOhGpmfLNVm7+cCOHEzO4vn0DZozsWq6tNtn5ZiYt3s3Ph5IxmeCZG9qy/UQqqw8k4eHiyGfjuxPapE65XV+kLJXm+7vULTcLFiy46PujRo0q7SlFRGqE9385yuHEDHw9XXjllvJd0iAlM4/x87ezJzYNVycH3hnRmTUHk1h9IAkXJwdmjQpTsJFqq9Th5pFHHinyuqCggOzsbFxcXPDw8FC4EREpxp6Ys8xYdxyA/w7rgF8t13K7VuSpTMbM2050ajZ1PJyZPTqM5bvi+Hp3HE4OJqbf3ZVeLfzK7foi9lbq0VJnzpwp8pOZmckff/zB1VdfrQ7FIiLFyC2w8PjSPVisBjeHBDK4Y0C5XWvnyVRum7GZ6NRsGvt68NUDPfnpQBKLtkZjMsHbIzrTv51/uV1fpDIok0VDWrZsyWuvvXZeq05JTJ8+neDgYNzc3AgNDWXDhg0X3T8vL49nnnmGJk2a4OrqSvPmzZk7d+7lli4iUu7eXnOEY8mZ1PNy5aWh7cvtOj/uT+TuWVs5k11ASCMflj/Yk+/3JjBzfSQA027pyM0hgeV2fZHKoszm13Z0dCQ+Pr5UxyxZsoRHH32U6dOn06tXL2bOnMngwYM5ePAgjRs3LvaY4cOHk5SUxJw5c2jRogXJycmYzeay+AgiImVu+4lUZm0oDBev3dqR2h7lM0nevE1RvPTdQQwD+retz/t3deGLbTG8taZwosD/3NiOO8OL/7sqUt2UerTUypUri7w2DIOEhAQ+/PBDgoKC+OGHH0p8ru7du9O1a1dmzJhh29a2bVuGDRvGtGnTztv/xx9/5M477yQyMhJfX9/SlG2j0VIiUlGy880Mfm8DJ09nc0doI/53R0iZX8NqNXh11SFmb4wCYORVjXnhpvYs3xXHU1/tBeCx/q14pH/LMr+2SEUq19FSw4YNK/LaZDJRr149rr32Wt56660Snyc/P5+dO3cyZcqUItsHDhzI5s2biz1m5cqVhIWF8cYbb/DZZ5/h6enJzTffzMsvv3zBOXby8vLIy8uzvU5PTy9xjSIiV+L1Hw5z8nQ2gT5u/OemdmV+/twCC49/uYfv9yUA8NT1rXmgT3O+25vAv5cXBpt/XdOMSde1KPNri1Rml7W2VFlISUnBYrHg71+0Y5u/vz+JiYnFHhMZGcnGjRtxc3Pj66+/JiUlhQcffJDU1NQL9ruZNm0aL774YpnULCJSUpuPpfDplpMAvH57pzJfjPJsdj73LdjB9hNncHY08eYdIQzt3JBfDiXx2JIIDAPu7t6YqYPblPsMyCKVTZl0KL4S//ylMwzjgr+IVqsVk8nEokWLCA8P54YbbuDtt99m/vz55OTkFHvM1KlTSUtLs/3ExMSU+WcQEfm7jNwCnlxW2HIy8qrG9G5Zr0zPH5OazW0zNrP9xBm83Jz4dFw4Qzs3ZPPxFB5YtAuz1WBY50BeGVq+c+mIVFYlarmZPHlyiU/49ttvl2g/Pz8/HB0dz2ulSU5OPq81508BAQE0bNgQHx8f27a2bdtiGAaxsbG0bHn+M2VXV1dcXctvPgkRkX/67/eHiDubQ2NfD6YOblum594Xm8bY+dtJycwj0MeNeWPDad3Ai13RZ5jw6Q7yzVYGtPPnf3eE4OCgYCM1U4nCze7du0t0stL8F4KLiwuhoaGsWbOGW265xbZ9zZo1DB06tNhjevXqxdKlS8nMzKRWrcK1UI4cOYKDgwONGlXMqroiIhfz2x/JfLE9BpMJ/nd7Jzxdy2xQKr8dTuahz3eRnW+hTQMv5o8Np4GPGwfj0xkzdxvZ+RZ6t/Tjw7u74Oxo94Z5Ebsp0W/db7/9Vi4Xnzx5Mvfeey9hYWH06NGDTz75hOjoaCZOnAgUPlKKi4uzLflw99138/LLLzN27FhefPFFUlJSePLJJxk3bpwW7RQRu0vLLmDKuRFKY3sG071Z3TI79+Jt0Tz7zX4sVoPeLf2Yfk9XvNycOX4qk3vnbCU910xYkzrMvDcUVyfHMruuSFVUdv9JcRlGjBjB6dOneemll0hISKBDhw6sWrWKJk2aAJCQkEB0dLRt/1q1arFmzRr+7//+j7CwMOrWrcvw4cN55ZVX7PURRERsXvz2AEnpeTTz8+Sp61uXyTkNw+DtNUf44NdjANzWtRGv3dYRZ0cHYlKzGTl7K6ez8unQ0Ju5Y7vh4WLXP+silcJlrQq+fft2li5dSnR0NPn5+UXeW758eZkVVx40z42IlIfVBxK5/7OdOJhg2QM96dr4yhelzDdbmbJ8L8t3xQEw6bqWPNa/JSaTieT0XO6YuYWTp7NpUb8WS/51FXXLcb0qEXsrzfd3qR/KfvHFF/Tq1YuDBw/y9ddfU1BQwMGDB/n111+LdPQVEakpUrPyeebrfQDc36d5mQSb9NwCxs3fzvJdcTg6mHj9to5MHtAKk8lEalY+98zeysnThetHLZrQXcFG5G9KHW5effVV3nnnHb777jtcXFx47733OHToEMOHD7/gkgkiItXZf77ZT0pmPq39vXi0DGYCTkzLZfjHW9h4LAUPF0dmjw5jRLfCv6/puQWMnruNo8mZNPB2Y9GE7vh7u13xNUWqk1KHm+PHjzNkyBCgcJh1VlYWJpOJxx57jE8++aTMCxQRqcy+3RPP9/sScHIw8dbwkCvuzHs4MZ1bpm/icGIG9bxc+fL+HvRrXR+AnHwL4+dvZ19cGr6eLiyc0J0gX4+y+Bgi1Uqpw42vry8ZGRkANGzYkP379wNw9uxZsrOzy7Y6EZFKLDkjl/+sKPwb+FC/FnRoeGWP5jcfS+GOGVtISMulRf1aLH+gp+2ceWYL//psh23ivgXjwmlRv9YVfwaR6qjE4SYiIgKA3r17s2bNGqBwhe5HHnmE++67j7vuuovrrruuXIoUEalsDMPg6eX7OJtdQPtAbx6+9srWb/p6dyyj520jI89MeLAvX03saWuVMVusTFq8mw1HCx9TzR8bfsVBSqQ6K/GYwa5du9KlSxeGDRvGXXfdBRTOQ+Ps7MzGjRu59dZb+c9//lNuhYqIVCZf7Yrj50PJuDg68Pbwzpc9aZ5hGExfe5z/rf4DgCGdAnjrjhDcnAsfb1mtBk8t28vqA0m4ODkwa1QYoU2uvMOySHVW4qHgW7ZsYe7cuXz55ZcUFBRw6623Mn78ePr161feNZYpDQUXkSuVkJbDwHfWk5Fr5qnrW/Ng38trtTFbrDy38gCfby2cz+tf1zRjyvVtbMsmGIbBf1bsZ+Hv0Tg6mJg5MpT+7YpfnkakuiuXoeA9evRg1qxZJCYmMmPGDGJjY+nfvz/Nmzfnv//9L7GxsVdcuIhIZWcYhS0pGblmOgfV5l+9m13WebLzzdz/2U4+3xqNyQQv3tyep29oWyTYvPbjYRb+Xvj+28NDFGxESqjU7aju7u6MHj2atWvXcuTIEe666y5mzpxJcHAwN9xwQ3nUKCJSaXy+LZoNR1NwdXLgreEhOF3G46hTGXnc+cnv/HI4GVcnB2bcE8ronk2L7PPRb8eYuS4SgGm3dGRo54ZlUb5IjXBF83Q3b96cKVOmEBQUxNNPP83q1avLqi4RkUonJjWb/35/CICnrm9D83qlH610/FQmY+ZtIyY1hzoezswe3e28PjRzN0bx5k9HAHh2SFvuDNccYiKlcdnhZt26dcydO5evvvoKR0dHhg8fzvjx48uyNhGRSsNqNXhi6R6y8y2EB/sy9h8tLSWx40QqExbs4Gx2AU3qejB/bDjBfp5F9vlyewwvfXcQgMf6t2LCZT72EqnJShVuYmJimD9/PvPnzycqKoqePXvywQcfMHz4cDw9PS99AhGRKurTLSfYGpWKh4sjb94eYusbU1I/7EvgkSUR5JuthATVZs7oMPz+sWTCd3vjmbK8cFXx+3oHM+m6KxteLlJTlTjcDBgwgN9++4169eoxatQoxo0bR+vWZbPqrYhIZRZ5KpPXfzwMwNQb2tK4bulmBZ6zMYpXvj+IYUD/tv58cFcX3F2KzmT86+EkHv0iAqsBd4U35ukb2mIylS5AiUihEocbd3d3vvrqK2688UYcHa9senERkarCcu5xVG6Bld4t/RjZveT9X6xWg1e+P8TcTVEA3HtVE164uT2O/2j12Xw8hYkLd2G2GgztHMgrwzoo2IhcgRKHm5UrV5ZnHSIildKsDZHsij6Ll6sTr9/WqcShI7fAwuQvI1i1LxGAKYPbcP81zc47flf0GSZ8uoN8s5UB7fx5846Q88KPiJTOFY2WEhGpzo4kZfD2uVFL/7mpHYG13Ut03JmsfO5bsIMdJ8/g4ujA/+7oVOxQ7oPx6YyZu43sfAtXt/Djg7u6XPZMxyLyF4UbEZFiFFisPP7lHvItVq5rU587QhuV6LiY1GxGz9tG5KksvN2c+GRUGFc1q3vefsdPZTJq7lbSc82ENqnDJ6NCbUsuiMiVUbgRESnG9N+Osy8uDR93Z6bd2rFEj6P2xp5l3PztpGTmE+jjxvxx4bTy9zpvv5jUbEbO3kpKZj7tA72ZO6YbHi76cyxSVvTbJCLyD/vj0vjg16MAvDS0PfW93S55zK+Hk3ho0W5yCiy0C/Bm3thu+BdzXHJ6LiPnbCUhLZcW9WuxYFw4Pu7OZf4ZRGoyhRsRkb/JM1t4YukezFaDwR0acHNI4CWP+XxrNM9+sw+rAb1b+jFjZCi1XM//85qalc/IOVs5eTqbIF93Fo7vTt1/zHUjIldO4UZE5G/e/+UohxMzqOvpcskh2YZh8OZPf/DRb8cBuCO0Ea/e2rHYTsHpuQWMnruNI0mZ+Hu78vmEq2jgc+kWIREpPYUbEZFzdkefYcbawqDy31s6XLRVJd9s5d9f7eXr3XEAPNq/JY9c17LYMJSTb2H8/O3si0vD19OFRRO6E+RbuokARaTkFG5ERCicl+bxpXuwGjCscyDXdwi44L7puQU8sHAnm46dxtHBxLRbOjK8W1Cx++aZLfzrsx1sP3EGLzcnFowLp0X98zsZi0jZUbgREQHeXP0HkaeyqO/lyos3d7jgfglpOYydt53DiRl4ujgyfWQofVrVK3Zfs8XKpMW72XA0BQ8XR+aP7UaHhj7l9RFE5ByFGxGp8bZFpTLn3BIJr9/WCR+P4kcvHUpIZ+y87SSm51Lfy5W5Yy4cVqxWg6eW7WX1gSRcHB2YNSqM0Ca+5fYZROQvCjciUqNl5Zl5YukeDAOGhzWiX5v6xe636VgKEz/bSUaemRb1azF/bDca1Sm+34xhGDy3cj/Ld8fh6GDio3u60quFX3l+DBH5G4UbEanRXvvhMNGp2QT6uPHsje2K3Wf5rlieWrYXs9Wge7Avn9wbdsHWHcMweO3Hwyz8PRqTCd4eHsKAdv7l+RFE5B8UbkSkxtp0LIXPfj8JwBu3h+DtVjSwGIbBR78d481z60vdFBLIm3d0wtXpwsskfPTbMWauiwTg1Vs6FrumlIiUL4UbEamRMnILeGrZXgDuvaoJV7cs+tjIbLHynxX7WbwtBoD7+zTj34Pa4HCRFbvnboyyBaFnh7TlrvDG5VS9iFyMwo2I1EivfHeIuLM5NPb1YMrgNkXey8oz8/Dnu/jtj1M4mOCFm9szqkfTi57vy+0xvPTdQaBwzpsJvZuVV+kicgkKNyJS4/x2OJklO2IwmeDNO0Lw/NtSCckZuYyfv4N9cWm4OTvw/p1dGNi+wUXP993eeKYsL2wFuq93MI9c17Jc6xeRi1O4EZEa5Wx2Pv/+qjCIjO8VTHjwX8OzjyVnMmbeNmLP5ODr6cKc0WF0aVznouf79XASj34RgdWAu8Ib8/QNbUu0griIlB+FGxGpUV5YeYDkjDya1/PkiUGtbdu3n0hlwqc7SMspoGldD+aPDaepn+dFz7X5eAoTF+7CbDUY2jnwkmtRiUjFULgRkRrjx/2JfBMRj8O5x1FuzoWjnr7fm8BjX0aQb7bSpXFtZo8Ku+Rq3buizzDh0x3km60MaOfPm3eE4HiRzsYiUnEUbkSkRjidmcczX+8DYGKf5rbHTbM3RPLfVYcwDBjQzp/37+yCu8uFh3oDHIxPZ8zcbWTnW7i6hR8f3NWl2JXARcQ+FG5EpNozDINnv9nP6ax82jTw4pH+LbFYDV75/iDzNp0AYHSPJjx3U/tLtr4cP5XJqLlbSc81E9qkDp+MCrW1AIlI5aBwIyLV3so98fywPxEnBxNv3hGCYcBDi3bx44FEAJ6+oQ339W52yf4yManZjJy9lZTMfNoHejN3TDc8XPRnVKSy0W+liFRryem5PLfiAAD/d21LAmu7c8/srew8eQYXRwfeGh7CTSGBJTrPyDlbSUjLpUX9WiwYF46Pe/FLMIiIfSnciEi1ZRgGU5fvIy2ngI4NfbgxJIDbZmwmKiULbzcnZo0Ko3uzupc8T2pWPiPnbOXk6WyCfN1ZOL77JTsci4j9KNyISLW1bGcsvxxOxsXRgVE9mjBi5hZSMvNpWNud+WO70dLf65LnyMgtYPTcbRxJysTf25XPJ1xFAx+3CqheRC6Xwo2IVEvxZ3N46dvC5RA6B9XmuRUHyCmw0D7Qm3ljulHf+9IBJSffYput2NfThUUTuhPk61HepYvIFVK4EZFqxzAM/v3VXjLyzABsO5EKQJ9W9fjonq7Ucr30n748s4V/fbaDbSdS8XJzYsG4cFrUv3RLj4jYn8KNiFQ7i7ZGs+FoSpFtI8KCeOWWDiWaj8ZssTJp8W42HE3B3dmR+WO70aGhT3mVKyJlTOFGRKqV6NPZvPjtgSLbHuvfiknXtSjR0ghWq8FTy/ay+kASLo4OzBoVRmgT30seJyKVh8KNiFQbVqvB/Qt3UmAxAHAwweu3deKOsKASHW8YBs+t3M/y3XE4Opj46J6uXN3SrzxLFpFyYPf5wqdPn05wcDBubm6EhoayYcOGEh23adMmnJyc6Ny5c/kWKCJVxqurDnEoId32ev7Y8FIFm9d+PMzC36MxmeDt4SEMaOdfXqWKSDmya7hZsmQJjz76KM888wy7d++md+/eDB48mOjo6Isel5aWxqhRo7juuusqqFIRqey+35vA7I1Rf72edDXXtKpX4uM/+u0YM9dFAvDqLR0Z2rlhmdcoIhXDZBiGYa+Ld+/ena5duzJjxgzbtrZt2zJs2DCmTZt2wePuvPNOWrZsiaOjI9988w0RERElvmZ6ejo+Pj6kpaXh7e19JeWLSCWx9o9kxszbbnu98d/9aFSn5EO2522K4sVzw8afHdKWCb2blXmNInJlSvP9bbeWm/z8fHbu3MnAgQOLbB84cCCbN2++4HHz5s3j+PHjPP/88yW6Tl5eHunp6UV+RKT6WLYztkiwWf3oNaUKNl9uj7EFm0f7t1SwEakG7BZuUlJSsFgs+PsXfabt7+9PYmJiscccPXqUKVOmsGjRIpycStYXetq0afj4+Nh+goJK9vxdRCo3wzB4/5ejPLF0j23bq7d0pHWDks9F893eeKYs3wvAhKuDeeS6lmVep4hUPLt3KP7n0EzDMIodrmmxWLj77rt58cUXadWqVYnPP3XqVNLS0mw/MTExV1yziNhXgcXK1OX7eHvNEdu269rU567wkv/Hy6+Hk3j0iwisBtwVHsQzQ9qWaKi4iFR+dhsK7ufnh6Oj43mtNMnJyee15gBkZGSwY8cOdu/ezcMPPwyA1WrFMAycnJz46aefuPbaa887ztXVFVdXLXAnUl1k5Zl5cNEu1h05ZdtW28OZabd1LHE42Xw8hYkLd2G2GgztHMgrw0p+rIhUfnYLNy4uLoSGhrJmzRpuueUW2/Y1a9YwdOjQ8/b39vZm3759RbZNnz6dX3/9lWXLlhEcHFzuNYuIfSVn5DJu/nb2xxXtO/fS0A7U9yrZYpa7o89w36c7yDdb6d/WnzfvCMHRQcFGpDqx6yR+kydP5t577yUsLIwePXrwySefEB0dzcSJE4HCR0pxcXEsWLAABwcHOnToUOT4+vXr4+bmdt52Eal+jiVnMHruduLO5uDl6mRbN+qGjg24qVNAic5xKCGd0XO3kZVvoVeLunx4d5cSLccgIlWLXcPNiBEjOH36NC+99BIJCQl06NCBVatW0aRJEwASEhIuOeeNiFR/26JSuW/BDtJyCgj286RdoDff703Ar5YLLw/tUKJHSsdPZXLvnK2k55oJbVKHWaPCcHN2rIDqRaSi2XWeG3vQPDciVcu3e+J5/Ms95FusdG1cm4evbcGET3dgNWDmvaEMat/gkueIPZPNHR9vISEtl/aB3nx+31X4uDtXQPUiUlZK8/2ttaVEpFIyDINZGyJ5ddVhAAa19+f12zpx64zNWA24pUvDEgWb5PRc7pm9lYS0XFrUr8WCceEKNiLVnMKNiFQ6FqvBS98e4NMtJwEY07Mp/7mxHa+uOkTkqSz8vV154ab2lzzPmax8Rs7ZysnT2QT5urNwfHfq1tLoSZHqTuFGRCqVnHwLj3yxm58OJgGFyyGMvzqYbVGpzN1UuHbUa7d1wsfj4q0vGbkFjJ63jSNJmfh7u/L5hKto4FOyEVUiUrUp3IhIpXE6M48JC3awO/osLo4OvD0ihBs7BZKVZ+aJZXswDLizWxD9Wte/6Hly8i2Mn7+DvbFp+Hq6sGhCd4J8S74kg4hUbQo3IlIpnEjJYsy8bZw4nY2PuzOzRoURHuwLwLQfDhGTmkPD2u48M6TtRc+TZ7Zw/8KdbDuRipebEwvGhdOifsmXZBCRqk/hRkTsbnf0GcZ/uoPUrHwa1XFn/thutkCy8WgKC38vnBLif7d3wsvtwo+jzBYrjyyOYP2RU7g7OzJ/bDc6NPSpkM8gIpWHwo2I2NVPBxKZ9MVucgusdGzow5wxYbbZhtNzC3hqWeHCmKN6NKFnC78LnsdqNXhq2V5+PJCIi6MDs0aFEdrEt0I+g4hULgo3ImI3C7ac4IWVB7Aa0K91PT68uyuern/9WXr524PEp+XSpK4HUwa3ueB5DMPg+ZUHWL47DkcHEx/d05WrW144CIlI9aZwIyIVzmo1eH31YWauiwQKV+V+eWgHnP62FMIvh5JYujMWkwneuiMED5fi/1wZhsHrP/7BZ7+fxGSCt4eHMKDd+YvvikjNoXAjIhUqz2zhiaV7+XZPPABPDGzFQ/1aFFlC4Wx2PlOWFy6UO+HqYMKaXvjx0vS1x/l43XEAXr2lI0M7NyzH6kWkKlC4EZEKk5ZdwL8+28HWqFScHEy8cXsnbu3a6Lz9nl95gFMZeTSv58njA1tf8HzzNkXxv9V/AIXz4dwV3rjcaheRqkPhRkQqROyZbMbO287R5ExquTrx8cjQYvvF/LAvgRUR8TiY4K3hnS+4uOWXO2J48duDADzavyUTejcr1/pFpOpQuBGRcncgPo2x87aTnJFHA2835o3tRtuA8xe+S8nM45lv9gPwYN8WdA6qXez5vt+bwJSv9gKFj60eua5ludUuIlWPwo2IlKt1R07x4MKdZOVbaO3vxfxx3QjwcT9vP8MwePbr/aRm5dOmgReTLhBYfjuczCNf7MZqFHZEfmZI2yL9dUREFG5EpNx8uSOGqcv3YbEa9Gxel4/vDcX7ApPwrdwTz48HEnFyMPHW8BBcnBzO22fL8dNMXLgTs9VgaOdAXhnWUcFGRM6jcCMiZc4wDN79+Sjv/XIUgFu6NOT12zoVG1gAktJzeW7FAQAmXdeS9oHnzyq8O/oMEz7dTp7ZSv+2/rx5RwiODgo2InI+hRsRKVMFFitPL9/H0p2xADzUrzlPDGx9wRYWwzCY8tVe0nIK6NjQhwf6Nj9vn0MJ6YyZt52sfAu9WtTlw7u74OxYfFASEVG4EZEyk5ln5sFFu1h/5BQOJnhlWEfu7n7x4dlLd8Ty2x+ncHFy4K3hIeeFlshTmdw7ZytpOQWENqnDrFFhFxxBJSICCjciUkaS0nMZO287BxPScXd25KN7unBtm4vPFBx3NoeXvisczv34gFa08i+6enfsmWxGzt5KSmY+7QO9mTum2wVnKhYR+ZP+SojIFTuSlMHYeduJO5uDXy0X5o7pRqdGtS96jGEY/HvZXjLzzIQ2qXPePDXJ6bncM3sr8Wm5NK/nyYJx4fi4X3hFcBGRPynciMgV2XL8NP/6bAcZuWaa+Xkyf2w4jet6XPK4hVuj2XgsBTdnh/M6B5/JymfknK2cPJ1NkK87iyZcRd1aruX5MUSkGlG4EZHLtnJPPE98uYd8i5Wwc/1h6ni6XPK4k6ezePX7QwBMub4NwX6etvcycgsYPW8bR5Iy8fd2ZdH4q2jg41Zun0FEqh+FGxEpNcMwmLk+ktd+OAzA4A4NeGfEhZdK+Dur1eDJpXvJKbDQo1ldRvVoansvJ9/C+Pk72Bubhq+nC4smdC9RK5CIyN8p3IhIqVisBi+sPMBnv58EYPzVwTxzQ1scSjjnzNxNUWw7kYqniyNv3N7Jdlye2cL9C3ey7UQqXm5OLBgXTov6Xpc4m4jI+RRuRKTEcvItTPpiN2sOJmEywbND2jH+6uASH38sOdO2ivczQ9oR5FvYKmO2WHlkcQTrj5zC3dmR+WO70aHh+RP5iYiUhMKNiJTI6cw8xn+6g4iYs7g4OfDeiM4M7hhQ4uPNFiuPL91DntnKNa3qcVd4EFD4mOqpZXv58UAiLo4OzBoVRmgT3/L6GCJSAyjciMglRaVkMWbeNk6ezqa2hzOzR4UR1rR0AWTm+kj2xJzFy82J128rXBPKMAyeX3mA5bvjcHQw8eHdXbi6pV85fQoRqSkUbkTkonZFn2HCpztIzconyNed+WPDaV6vVqnOcTgxnXd/PgLACze1J8DHHcMweP3HP/js95OYTPD28BAGtm9QHh9BRGoYhRsRuaDVBxKZtHg3eWYrnRr5MGd0N+p5lW6+mQKLlce/3EOBxaB/W39u7doQgOlrj/PxuuMA/HdYR4Z2bljm9YtIzaRwIyLF+nTzCV749gCGAde2qc+Hd3e5rKUPPvz1GAfi06nt4cyrt3bAZDIxb1OUrWPxs0PaXnL9KRGR0lC4EZEirFaD1348zCfrIwG4u3tjXrq5PU6XsQr3vtg0PvztGAAvD+1AfS83vtwRw4vfFq4n9ch1Lc9bdkFE5Eop3IiITW6BhSeW7uG7vQkAPDmoNQ/2bY7JVLI5bP4uz2zh8aURWKwGQzoFcFNIIN/vTWDKV3sBmHB1MI/2b1mm9YuIgMKNiJxzNjuff322k21RqTg7mnjj9k7c0qXRZZ/vnTVHOZKUiV8tF14e2oHfDifzyBe7sRpwV3gQzwxpe1mhSUTkUhRuRITYM9mMmbedY8mZeLk6MfPeUHq2uPwh2TtPnuGT9YWdhV+9pSN/JGYwceFOzFaDm0MCeWVYRwUbESk3CjciNdz+uDTGzt/OqYw8AnzcmDe2G20aeF/2+XLyCx9tWQ24tUtD6nm5MnL2VvLMVvq39eet4UVXABcRKWsKNyI12No/knlw0S6y8y20aeDFvLHdCPBxv6JzvrH6MFEpWTTwdmNEtyDGzNtOVr6FXi3q8uHdXXC+jI7JIiKloXAjUkMt2R7N01/vx2I16NWiLjNGhuLt5nxF5/w98jTzNp0AYGKfZjz0+S7ScgoIbVKHT+4NK9Gq4SIiV0rhRqSGMQyDd34+yvu/HAXg1q4Nee3WTrg4XVmLSlaemSeX7QGgd0s/PlkfSUpmPu0CvJk7phuervpzIyIVQ39tRGqQAouVqcv3sWxnLAD/d20LJg9oVSade19ddYiY1BxcnBw4lJBOSmY+zet58tn4cHzcr6xFSESkNBRuRGqIjNwCHly0iw1HU3B0MPHKsA7cFV42MwOvP3KKRVujAcg3W0nJLFyHatGEq6hbq3TLNYiIXCmFG5EaIDEtl7Hzt3MoIR0PF0c+ursr/drUL5Nzp+UU8O9zE/P9yd/blUXjr6KBj1uZXENEpDQUbkSquSNJGYyZu434tFz8arkyb0w3OjbyKbPzv/zdQRLScm2vfT1dWDShO43repTZNURESkPhRqQa23w8hfs/20lGrplm9Tz5dGw4Qb5lFzp+Pphk678D4OXmxIJx4bSo71Vm1xARKS2FG5FqakVEHE8s3UOBxaBb0zrMGhVGbQ+XMjv/max8pizfZ3vt7uzI/LHd6NCw7FqFREQuh8KNSDVjGAYz1h3njR//AGBIxwDeGh5S5nPMPLfyACmZeQC4ODowa1QYoU18y/QaIiKXw+5ThU6fPp3g4GDc3NwIDQ1lw4YNF9x3+fLlDBgwgHr16uHt7U2PHj1YvXp1BVYrUrmZLVb+s2K/LdhMuDqYD+7qUubBZtW+BL7dEw+Ao4OJD+/uwtUtL38tKhGRsmTXcLNkyRIeffRRnnnmGXbv3k3v3r0ZPHgw0dHRxe6/fv16BgwYwKpVq9i5cyf9+vXjpptuYvfu3RVcuUjlk51vZuLCnSz8PRqTCZ6/qR3P3tgOhzJexyklM49nv9kPgMkEbw8PYWD7BmV6DRGRK2EyDMOw18W7d+9O165dmTFjhm1b27ZtGTZsGNOmTSvROdq3b8+IESN47rnnSrR/eno6Pj4+pKWl4e19+YsDilQmKZl5jJ+/nT2xabg6OfDenZ25vkNAmV/HMAzu/2wnPx1MAgpX/L67e9nMlSMicjGl+f62W5+b/Px8du7cyZQpU4psHzhwIJs3by7ROaxWKxkZGfj6Xvg5f15eHnl5ebbX6enpl1ewSCWUllPAwt9PMmdjFKlZ+dTxcGb26PLr+7L5+GlbsHl2SFsFGxGplOwWblJSUrBYLPj7+xfZ7u/vT2JiYonO8dZbb5GVlcXw4cMvuM+0adN48cUXr6hWkcrmVEYeczdFsXDLSTLyzAA0q+fJ7FFhNKtXq9yu6+vpQmNfD+7u3pgJvZuV23VERK6E3UdL/XNNG8MwSrTOzeLFi3nhhRdYsWIF9etfeKbVqVOnMnnyZNvr9PR0goKCLr9gETuKPZPNJ+sjWbI9hjyzFYBW/rV4sG8LbuwUgJNj+Xajaxvgzfqn+pXrNURErpTdwo2fnx+Ojo7ntdIkJyef15rzT0uWLGH8+PEsXbqU/v37X3RfV1dXXF21to1UbceSM5i+9jgrI+IxWwu7yXUOqs1D/VpwXZv6Zd5pWESkKrNbuHFxcSE0NJQ1a9Zwyy232LavWbOGoUOHXvC4xYsXM27cOBYvXsyQIUMqolQRu9kTc5bpa4/x08Ek/uz6f3ULPx7s15wezeqWyWreIiLVjV0fS02ePJl7772XsLAwevTowSeffEJ0dDQTJ04ECh8pxcXFsWDBAqAw2IwaNYr33nuPq666ytbq4+7ujo+PZkWV6sEwDLZEnmbG2uNsOJpi2z6ovT8P9m1BSFBt+xUnIlIF2DXcjBgxgtOnT/PSSy+RkJBAhw4dWLVqFU2aNAEgISGhyJw3M2fOxGw289BDD/HQQw/Zto8ePZr58+dXdPkiZcpqNfj1cDIfrT3G7uizQOEEeUM7B/JAn+a09Nd6TSIiJWHXeW7sQfPcSGVjtlj5fl8C0387zh9JGQC4ODlwZ7cg7uvdrEwXuhQRqaqqxDw3IjVdboGFr3bFMnNdJNGp2QDUcnVi5FVNGHd1U+p7udm5QhGRqknhRqSCZeaZ+XzrSWZviCI5o3CCSV9PF8b1asq9PZri4+5s5wpFRKo2hRuRCnImK5/5m08wf/MJ0nIKAAjwceNf1zRjRLcgPFz06ygiUhb011SknCWm5TJ7QySfb4smO98CQDM/Tyb2ac6wLg1xcbLr+rUiItWOwo1IOTmRksXM9cf5amcc+ZbC2YTbB3rzYN8WXN+hAY6aeE9EpFwo3IiUsUMJ6Uxfe5zv98ZzbjJhwoN9ebBvc/q0qqeJ90REypnCjUgZ2XkylY9+O86vh5Nt2/q1rseD/VrQrWn5rNItIiLnU7gRuQKGYbD+aArTfzvG1qhUABxMcEPHAB7o25z2gZo5W0SkoinciFwGq9Vg9YFEPlp7jP1x6QA4O5q4rWsj7u/TnGA/TztXKCJScynciJRCgcXKN7vjmLHuOJGnsgBwd3bk7u6NmdA7mAAfdztXKCIiCjciJZCTb2HJ9mg+WR9JfFouAN5uTozpFcyYnk3x9XSxc4UiIvInhRuRi0jLKWDh7yeZuzGK01n5APjVcuW+3sHc3b0xXm6aTVhEpLJRuBEpxqmMPOZuimLhlpNk5JkBaFTHnYl9mnN7aCPcnB3tXKGIiFyIwo3I38SeyWbW+ki+2B5Dnrlw4r1W/rV4sG8LbuwUgJOjZhMWEansFG5EgGPJGcxYG8mKiDjM52beCwmqzUN9m9O/rT8Omk1YRKTKULiRGm1v7Fmm/3ac1QcTMc7NJnx1Cz8e7NucHs3rajZhEZEqSOFGahzDMPg9MpXpa4+x4WiKbfug9v482LcFIUG17VeciIhcMYUbqTEMw+CXQ8lMX3uMXdFnAXB0MDE0JJCJfZvTyt/LvgWKiEiZULiRas9ssfL9vgRmrD3O4cQMAFycHBgRFsS/rmlGkK+HnSsUEZGypHAj1Vae2cJXO+P4eN1xolOzAajl6sTIq5ow7uqm1PdyK9frmy1WsvIt+LhrLhwRkYqkcCPVTlaemc+3RjNrQyTJGXkA+Hq6MK5XU+7t0bTMwobFapCUnkvsmRxiUrOJPZND7Jlz//dsNglnczFbDV4e1oF7r2pSJtcUEZFLU7iRauNMVj7zN59g/uYTpOUUABDg48Z9vZtxZ3gQHi6l++dusRokZ+T+FVpSc4j5M7ycySH+bI5t2PiFODuaqO/letmfSURESk/hRqq8xLRcZm+I5PNt0WTnWwAI9vPkgT7NGdalIS5OxU+8Z7UanMrMO7/V5UxhiIk/m0OB5eLhpTgeLo70bV2PQe0b0K9Nfby1RIOISIVSuJEq6+TpLD5eF8lXO2PJtxTOJtwuwJuH+rXg+g4NMAEpmXnEFAkufwWYuDM5tuMuxMnBRGBtdxrVccfH3ZkjSRlEpmTZ5sT5Ux0PZ/q39WdQ+wZc3dJPyzOIiNiRwo1UOYcS0pmx9jjf7o0vEjK6B/vSrF4tvtgezVs//UHs2RzyzRcPL44OJgJ83GhUx52gOh40quNBozqFYaaRrweOJhO/HE5i9YEkfj6UVKQlJ9DHjYHtGzCofQO6Na2jpRlERCoJhRuptAzD4HRWvu2x0co98aw5mHTB/bdGpbI1KrXINgcTBPicCyvngkuQ718BpoG323mh5OTpLFYfSOSN1X+wK/pMkQDVon4tBrUvbKHp2NBHMxiLiFRCCjdiN4ZhkJqVb3tMFHsmu0iH3dgz2eQWXLzlxcEEDbzdaGQLLH8Fl6A6HjTwccP5Ei0qhmFwKCGD1QcSWX0g0TYXzp9CgmrbAk3zerWu+HOLiEj5UriRcmMYBmeyC4rt7/Jna0xOgaXU532gb3N6t/Cj0bnwcqEOwxdjsRrsij7D6v2JrD6YSExqju09RwcTVzXzZVD7Bgxo50+Aj3upzy8iIvajcCOXzTAM0nIKip/n5dz/zsq/eHgxmcDfy83W2uLv48auk2fYfuKMbR93Z0fuCm/MfdcEX1HQyDNb2Hz8ND8dSGTNwSRSMvNt77k6OdCnVeEIp+va1qe2h8tlX0dEROxL4UYuyDAM0nPMf3tUdH6AycwzX/I89b1ci/Rz+evRkQeBtd1wdXIkJ9/Cku3RzNoQRdzZwlYUbzcnxvRsyphewfh6Xl7YyMwzs/aPZFYfSGLt4WQy/lavt5sT17X1Z1B7f65pVa/U8+CIiEjlpL/mNVx6bsHfWl3+0fKSml0kDFxIPS9XW1gJ+ke/l8Da7hcdFp2eW8DsDVHM3RjF6azClhS/Wq7c1zuYu7s3xusy5og5nZnHz4cKRzhtPJZSZMRUfS9XBp7rP3NVs7qX7I8jIiJVj8JNNZeRW3BeP5e/t8Ck5146vPjVcj2v1eXPlpiGlwgvF5KSmcfcjVF8tuWkLUA1quPO/X2ac0doo1KfM/ZMNj8dSGL1gUS2n0jl7xMHB/t52gJN50a1cXDQCCcRkepM4aaKy8wz25YG+DO0/H3E0Z/LEFxMXU8X27wuRQJMHXca1vbA3aXsJqSLPZPNrPWRfLE9hrxzLSqt/GvxQN/m3NQpsMRzxRiGwdHkTFuH4P1x6UXebx/ozfXtGzCoQwNa1q+lIdsiIjWIwk0lZ7ZYiUzJumCH3TPZlw4vvn+Gl2IeHTWs414hfU2OJWfy8brjfLM7zrYeU0hQbR7q25z+bf1L1JpitRpExJ5l9YFEfjqQRFRKlu09BxOENS0c4TSwnT9Bvh7l9llERKRyU7ipxLafSOXfy/YS+bcv8eLU8XAuOrPu3x4dNaztjqer/W7zvtg0pq89xo8HEm2T4fVqUZeH+ragR/O6l2xRKbBY2RqZyo8HElhzMImk9Dzbey6ODlzd0o9B7f3p39afurW0QKWIiCjcVErZ+Wbe+PEPPt1yAsMATxdHmvp5nlse4G8Bxrewz8vldLotT4ZhsDUqlY9+O8aGoym27QPb+fNgvxZ0Dqp90eNz8i2sO3KKnw4k8svh5CKP1mq5OtGvTX0Gtfenb+v61LJjcBMRkcpJ3wyVzObjKfz7q722SeVGhAXx9JC2+LhXrgBTHMMw+PVwMh/9doxd0WeBwgnxhoYEMrFvc1r5e13wuNgzOWyNSuWnA4msP3qqyMzEdT1dGNDOn0EdGtCzeV1cnbQopYiIXJjCTSWRmWdm2qpDLNoaDUDD2u5Mu7Uj17SqZ+fKLs1ssfL9vgRmrD1uW7rAxcmBEWFB/OuaZuf1f0nNymdP7Fn2xJz7iU0jNSu/yD6N6rgz6NyilKFN6uCoEU4iIlJCCjeVwPojp5i6fJ9t8rp7ujdmyuA2le5x0z/lmS18tTOOmeuPc/J0NlD42GjkVU0Yd3VT6nu5kZNvYceJVCLOhZg9MWeJTs0+71zOjibaBXjTp3XhI6d2Ad4a4SQiIpdF4caO0nIK+O/3B/lyRywAQb7uvH5rJ3q28LNzZReXlWdm8bZoZm2ItHXwrePhzOieTenZ3I8TKVm8+/NR9sSc5XBiBpa/TzpzTrN6nnRuVJuQoMKftgFeetwkIiJlQuHGTn49nMTTy/eTmJ4LwJieTXlyUGu7jmy6lLPZ+czffIL5m09w9m9D0D1cHAny9eCT9ZG8+/PR846r5+VK56DadA6qTUij2nRs5FMl+hCJiEjVVHm/Saups9n5vPTtQZbvjgOgaV0P3rg9hPBgXztXdmFJ6bnM3hDJoq3RZBezEGZ2voW9sWlA4ciujo186BxUh85BPoQE1aaBt5seMYmISIVRuKlAqw8k8uw3+zmVkYfJBBOuDmbygNZlOgNwWXv7pz/4eF0k+Rbree85OZhoE+BFyLnHS52DatO8Xi11/hUREbtSuKkAqVn5PL/yAN/uiQegeT1P/ndHCF0b17FzZZc2b/MJW7BpWtejsI/MuTDTPtD7staVEhERKU8KN+XIMAy+35fA8ysOcDorHwcT3N+nOY9c17LKhIKvH+xJ/NlcOjb0oY6ni73LERERuaSSrVJYjqZPn05wcDBubm6EhoayYcOGi+6/bt06QkNDcXNzo1mzZnz88ccVVGnpnMrI44GFu3j4892czsqntb8X3zzUi39f36bKBBuAFvW9uKZVPQUbERGpMuwabpYsWcKjjz7KM888w+7du+nduzeDBw8mOjq62P2joqK44YYb6N27N7t37+bpp59m0qRJfPXVVxVc+YUZhsE3u+MY8M46fjyQiJODiUnXtmDl//WiU6Pa9i5PRESk2jMZhnH+JCQVpHv37nTt2pUZM2bYtrVt25Zhw4Yxbdq08/b/97//zcqVKzl06JBt28SJE9mzZw9btmwp0TXT09Px8fEhLS0Nb2/vK/8Qf5OUnsszX+/j50PJALQL8OZ/d3SifaBPmV5HRESkpinN97fd+tzk5+ezc+dOpkyZUmT7wIED2bx5c7HHbNmyhYEDBxbZNmjQIObMmUNBQQHOzufPnZKXl0de3l8rSaenp5dB9efbefIMY+dtIz3XjLOjif+7tiUP9G2Os6Pdn/yJiIjUKHb75k1JScFiseDv719ku7+/P4mJicUek5iYWOz+ZrOZlJSUYo+ZNm0aPj4+tp+goKCy+QD/0KaBF15uznRq5MO3/3c1k65rqWAjIiJiB3YfLfXPyd0Mw7johG/F7V/c9j9NnTqVyZMn216np6eXS8DxdHVi8X1XEVjbDSeFGhEREbuxW7jx8/PD0dHxvFaa5OTk81pn/tSgQYNi93dycqJu3brFHuPq6oqrq2vZFH0Jjet6XHonERERKVd2a2JwcXEhNDSUNWvWFNm+Zs0aevbsWewxPXr0OG//n376ibCwsGL724iIiEjNY9fnJ5MnT2b27NnMnTuXQ4cO8dhjjxEdHc3EiROBwkdKo0aNsu0/ceJETp48yeTJkzl06BBz585lzpw5PPHEE/b6CCIiIlLJ2LXPzYgRIzh9+jQvvfQSCQkJdOjQgVWrVtGkSRMAEhISisx5ExwczKpVq3jsscf46KOPCAwM5P333+e2226z10cQERGRSsau89zYQ3nOcyMiIiLlozTf3xrWIyIiItWKwo2IiIhUKwo3IiIiUq0o3IiIiEi1onAjIiIi1YrCjYiIiFQrCjciIiJSrSjciIiISLWicCMiIiLVil2XX7CHPydkTk9Pt3MlIiIiUlJ/fm+XZGGFGhduMjIyAAgKCrJzJSIiIlJaGRkZ+Pj4XHSfGre2lNVqJT4+Hi8vL0wmU5meOz09naCgIGJiYrRuVSWm+1Q16D5VDbpPVUN1uE+GYZCRkUFgYCAODhfvVVPjWm4cHBxo1KhRuV7D29u7yv7jqUl0n6oG3aeqQfepaqjq9+lSLTZ/UodiERERqVYUbkRERKRaUbgpQ66urjz//PO4urrauxS5CN2nqkH3qWrQfaoaatp9qnEdikVERKR6U8uNiIiIVCsKNyIiIlKtKNyIiIhItaJwIyIiItWKwk0pTZ8+neDgYNzc3AgNDWXDhg0X3X/dunWEhobi5uZGs2bN+Pjjjyuo0pqtNPdp+fLlDBgwgHr16uHt7U2PHj1YvXp1BVZbc5X29+lPmzZtwsnJic6dO5dvgQKU/j7l5eXxzDPP0KRJE1xdXWnevDlz586toGprrtLep0WLFhESEoKHhwcBAQGMHTuW06dPV1C15cyQEvviiy8MZ2dnY9asWcbBgweNRx55xPD09DROnjxZ7P6RkZGGh4eH8cgjjxgHDx40Zs2aZTg7OxvLli2r4MprltLep0ceecR4/fXXjW3bthlHjhwxpk6dajg7Oxu7du2q4MprltLepz+dPXvWaNasmTFw4EAjJCSkYoqtwS7nPt18881G9+7djTVr1hhRUVHG1q1bjU2bNlVg1TVPae/Thg0bDAcHB+O9994zIiMjjQ0bNhjt27c3hg0bVsGVlw+Fm1IIDw83Jk6cWGRbmzZtjClTphS7/1NPPWW0adOmyLb777/fuOqqq8qtRin9fSpOu3btjBdffLGsS5O/udz7NGLECOPZZ581nn/+eYWbClDa+/TDDz8YPj4+xunTpyuiPDmntPfpf//7n9GsWbMi295//32jUaNG5VZjRdJjqRLKz89n586dDBw4sMj2gQMHsnnz5mKP2bJly3n7Dxo0iB07dlBQUFButdZkl3Of/slqtZKRkYGvr295lChc/n2aN28ex48f5/nnny/vEoXLu08rV64kLCyMN954g4YNG9KqVSueeOIJcnJyKqLkGuly7lPPnj2JjY1l1apVGIZBUlISy5YtY8iQIRVRcrmrcQtnXq6UlBQsFgv+/v5Ftvv7+5OYmFjsMYmJicXubzabSUlJISAgoNzqraku5z7901tvvUVWVhbDhw8vjxKFy7tPR48eZcqUKWzYsAEnJ/3pqgiXc58iIyPZuHEjbm5ufP3116SkpPDggw+Smpqqfjfl5HLuU8+ePVm0aBEjRowgNzcXs9nMzTffzAcffFARJZc7tdyUkslkKvLaMIzztl1q/+K2S9kq7X360+LFi3nhhRdYsmQJ9evXL6/y5JyS3ieLxcLdd9/Niy++SKtWrSqqPDmnNL9PVqsVk8nEokWLCA8P54YbbuDtt99m/vz5ar0pZ6W5TwcPHmTSpEk899xz7Ny5kx9//JGoqCgmTpxYEaWWO/3nTwn5+fnh6Oh4XgpOTk4+Ly3/qUGDBsXu7+TkRN26dcut1prscu7Tn5YsWcL48eNZunQp/fv3L88ya7zS3qeMjAx27NjB7t27efjhh4HCL1HDMHBycuKnn37i2muvrZDaa5LL+X0KCAigYcOG+Pj42La1bdsWwzCIjY2lZcuW5VpzTXQ592natGn06tWLJ598EoBOnTrh6elJ7969eeWVV6r8kwW13JSQi4sLoaGhrFmzpsj2NWvW0LNnz2KP6dGjx3n7//TTT4SFheHs7FxutdZkl3OfoLDFZsyYMXz++efV5plzZVba++Tt7c2+ffuIiIiw/UycOJHWrVsTERFB9+7dK6r0GuVyfp969epFfHw8mZmZtm1HjhzBwcGBRo0alWu9NdXl3Kfs7GwcHIpGAEdHR+CvJwxVmr16MldFfw61mzNnjnHw4EHj0UcfNTw9PY0TJ04YhmEYU6ZMMe69917b/n8OBX/ssceMgwcPGnPmzNFQ8ApQ2vv0+eefG05OTsZHH31kJCQk2H7Onj1rr49QI5T2Pv2TRktVjNLep4yMDKNRo0bG7bffbhw4cMBYt26d0bJlS2PChAn2+gg1Qmnv07x58wwnJydj+vTpxvHjx42NGzcaYWFhRnh4uL0+QplSuCmljz76yGjSpInh4uJidO3a1Vi3bp3tvdGjRxt9+vQpsv/atWuNLl26GC4uLkbTpk2NGTNmVHDFNVNp7lOfPn0M4Lyf0aNHV3zhNUxpf5/+TuGm4pT2Ph06dMjo37+/4e7ubjRq1MiYPHmykZ2dXcFV1zylvU/vv/++0a5dO8Pd3d0ICAgw7rnnHiM2NraCqy4fJsOoDu1PIiIiIoXU50ZERESqFYUbERERqVYUbkRERKRaUbgRERGRakXhRkRERKoVhRsRERGpVhRuREREpFpRuBEREZFqReFGREREqhWFGxEpE2PGjMFkMmEymXBycqJx48Y88MADnDlzxt6liUgNo3AjImXm+uuvJyEhgRMnTjB79my+/fZbHnzwQXuXdUH5+fn2LkFEyoHCjYiUGVdXVxo0aECjRo0YOHAgI0aM4KeffrK9P2/ePNq2bYubmxtt2rRh+vTptvfy8/N5+OGHCQgIwM3NjaZNmzJt2jTb+9HR0QwdOpRatWrh7e3N8OHDSUpKsr0/ZswYhg0bVqSeRx99lL59+9pe9+3bl4cffpjJkyfj5+fHgAEDADhw4ABDhgzB29sbLy8vevfuzfHjx8ukbhGpeE72LkBEqqfIyEh+/PFHnJ2dAZg1axbPP/88H374IV26dGH37t3cd999eHp6Mnr0aN5//31WrlzJl19+SePGjYmJiSEmJgYAwzAYNmwYnp6erFu3DrPZzIMPPsiIESNYu3Ztqer69NNPeeCBB9i0aROGYRAXF8c111xD3759+fXXX/H29mbTpk2YzeYrrltE7EPhRkTKzHfffUetWrWwWCzk5uYC8PbbbwPw8ssv89Zbb3HrrbcCEBwczMGDB5k5cyajR48mOjqali1bcvXVV2MymWjSpIntvD///DN79+4lKiqKoKAgAD777DPat2/P9u3b6datW4lrbNGiBW+88Ybt9dNPP42Pjw9ffPGFLYi1atXK9v6V1C0i9qFwIyJlpl+/fsyYMYPs7Gxmz57NkSNH+L//+z9OnTpFTEwM48eP57777rPtbzab8fHxAQofKw0YMIDWrVtz/fXXc+ONNzJw4EAADh06RFBQkC3YALRr147atWtz6NChUoWbsLCwIq8jIiLo3bu3Ldj83ZXWLSL2oXAjImXG09OTFi1aAPD+++/Tr18/XnzxRR5++GGg8BFP9+7dixzj6OgIQNeuXYmKiuKHH37g559/Zvjw4fTv359ly5ZhGAYmk+m86/19u4ODA4ZhFHm/oKCg2Br/zt3d/YKfx2q1XlHdImIfCjciUm6ef/55Bg8ezAMPPEDDhg2JjIzknnvuueD+3t7ejBgxghEjRnD77bdz/fXXk5qaSrt27YiOjiYmJsbWenPw4EHS0tJo27YtAPXq1WP//v1FzhcREVFsi8zfderUiU8//ZSCgoLz9vX397+iun19fS96bREpHwo3IlJu+vbtS/v27Xn11Vd54YUXmDRpEt7e3gwePJi8vDx27NjBmTNnmDx5Mu+88w4BAQF07twZBwcHli5dSoMGDahduzb9+/enU6dO3HPPPbz77ru2DsV9+vSxPWa69tpr+d///seCBQvo0aMHCxcuZP/+/XTp0uWiNT788MN88MEH3HnnnUydOhUfHx9+//13wsPDad269RXVLSL2oaHgIlKuJk+ezKxZsxg0aBCzZ89m/vz5dOzYkT59+jB//nyCg4MBqFWrFq+//jphYWF069aNEydOsGrVKhwcHDCZTHzzzTfUqVOHa665hv79+9OsWTOWLFliu86gQYP4z3/+w1NPPUW3bt3IyMhg1KhRl6yvbt26/Prrr2RmZtKnTx9CQ0OZNWuWrRVnwoQJl123iNiHyfjnQ2oRERGRKkz/aSEiIiLVisKNiIiIVCsKNyIiIlKtKNyIiIhItaJwIyIiItWKwo2IiIhUKwo3IiIiUq0o3IiIiEi1onAjIiIi1YrCjYiIiFQrCjciIiJSrfw/PbGMWE+ZWjsAAAAASUVORK5CYII=", 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