{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Notebook for examples of intergation of systems of ODEs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Python initialization" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np #initialization\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "import time # note the new module\n", " \n", "%matplotlib inline " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining the Predator-Prey growth function" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def PredatorPrey(Population, t, r, a, b, d):\n", " \"\"\"\n", " this function returns the growth rate of two populations in the Predator-Prey model as a numpy array\n", " \n", " PredatorPrey(Population, t, args):\n", "\n", " Population -- an array of 2 numbers -- predator and prey current population sizes\n", " t -- time, unused\n", " (r, a, b, d) - the parameters of the population dynamics as described in the lecture\n", " \"\"\"\n", " \n", " dx = Population[0]*(r-a*Population[1])\n", " dy = Population[1]*(b*Population[0]-d)\n", " \n", " return np.array((dx,dy))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integrator functions" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def EulerSystem(xPrime, x0, t, args=()):\n", " \"\"\"\n", " Solves a system of ODEs using the Euler method.\n", " \n", " EulerSystem(xPrime,t0=0.0,x0=0.0,T=1.0,dt=0.1)\n", " xPrime -- the system to be integrated, returns the array of derivatives\n", " t -- the array of time points where the solution is needed; the zeroth entry corresponds to x0\n", " x0 -- initial condition\n", " \n", " Note that we do not ask for dt in this implementation of the algorithm\n", " \"\"\"\n", " \n", " x = np.zeros((t.size, x0.size))\n", " x[0,:] = x0\n", " for i in range(1, t.size):\n", " dt = t[i] - t[i-1]\n", " x[i,:] = x[i-1,:] + dt * xPrime(x[i-1,:],t[i-i],*args)\n", "\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constant intialization" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "dt = 1e-4 # time step\n", "SimulationTime = 10.0 # time to solve for\n", "P0 = np.array((1,1)) # initial population size\n", "r = 7.0 # intitalization of the 4 parameters\n", "a = 2.0\n", "b = 1.5\n", "d = 3.0 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Running various integrators and comparing them" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Euler took 0.6445209980010986s to run.\n", "Odeint took 0.011046171188354492s to run.\n" ] }, { "data": { "image/png": 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XXsrBgwd5/etfD8ChQ4e47LLLAPjWt77F7bffztOf/nQuvvhiPvKRj/Dggw8iIrz61a/mYx/7GGtra3zzm9/kxS9+8Th6NhCmCr8by/fCzkfA/sfB967TroTYhM2LKw8AAhe8GG79lJ7EznnyuFs1GFbM4VkXvAS+c7V2s/GysTZpYJRWoZLXK5PdF5iV1wQifxy2na37UPyoztiZ2RnY5Tcp8bDQrAMCqTn9e73c8uF3Y3Z2tvVcKcXzn/98Pv7xj/e874orruDlL385mUyGV7ziFSQS0afTCWOyEWD9FCycBXsugNoG5B8ed4sGR+4ozO3Vigxg7chYm+MLBZMltfvRMLNbu3cmDeun9ePcPthxCNaOjrc9frGxCLN7YPtB/XtuAvvRrEEsAfEkINCoefrYZZddxje+8Q3uvfdeAIrFInfffTcABw4c4MCBA7zvfe/jda97XUgNDxZTwu/G+mmY3QvbD+nfJ9G4N5bMADV9WPVcLjs6sDKkZndrspzEPhSX9OPsbk2WheM6F3yS0Gzqfszuge3n6tcmcfJt1DXhi2jS93gf9uzZw7XXXssrX/lKnvCEJ3DZZZdx5513tv7+C7/wC5x77rk85jGPCavlgSL6a5BRY2NRq2NLzawdhUPjbdLAKC5pn3F6Tj+uTShZpuYhkdb34sQt427R4NgwhD9jCF819YpxkoLPVoCzU0BM4kqlWYe4obt4ChpV1td7Y1uHDx/m1ltv3fTa8573PL77XfsMqxtuuIE3vvGNgTc3LEwVficq61ArauPedo5+LTeBamZjSatK0EQziYpsYwlmd+nn2w/pldakpWZuLOrHTnfIpN0La9Ka3QPZHZCcnbw+gCb8mKkyaQh/WDz5yU/mlltu4VWvmpxMvqnC78SG5XPdC8msNvJJNO7ism47aKKZxAwXy40A2pXQqLbjK5MCs6OTmZ2wzbhDJs1F2Jq0dmt3yPZzJ68PSmmffaxD4TdresUl/jXvTTfdFFADR4epwu/EumXce/Xj9oOTt3ytV3RmyIxR+PMHoHByvG3yg43ljj4Ykl+fsH5sLEFmu/YZz+/Xr03aveiMQ4Dux6T1QSlAQSyuf48bpd+Ri79VMCX8TpRW9ePMDv24cAAKE1YwylKVljtkfj9U19vbyicFxQ6XzpxFlqfG1x4/KC7rGAroFWNmm16lTBKs2jmZ7fpxbv/k9UE19KNF+JZrx2OmzpmEKeF3omJ2+6XN5oy5fZOnZoor+jFr8qTnJ5Qsy7k2ybT6MGGTb6XQ3ugDmiwnsQ8A6Xn9OL9PE35XaYJIo2kIXyyFb1w7U4W/xWGpGcu45/brLIVJKnplDdDMgn60yHKS3CGNug6eW2Q5txeQyZt8K4W2LYEmy0mbeLsJf26/jqdYq+FJwFThtzAl/E5YCr9Flvv0oxXMnQS0BqjVB+P/niSyrHaRTDypfciTNGmBDeGfNVn3AXRlydRcmyytMTFJ/bDq33cp/PjCvsDKI3/1q1/lZS9z3wl+88038x//Md5ihlPC70SloGf/REb/Pom+426ynLMG6AS5ErpVJRh3yASRDBjCX2j/PrdPT1qT5A6p5HvvA0zW5Gu5dKwSKRIDiZPNZkZaHtkP4dfrwbqdpoTfiXJeq3vrKDFLzUyScVtkadUMyWyDRHayyLK7D2CyQyZo0oJespyfQHdIzyplAkWQ6vLhQztTx2DQ8sgA//mf/8mFF17IM57xDP7pn9rnTnznO9/haU97Gk960pN42tOexl133UW1WuXd7343n/jEJ7j44ov5xCc+wcrKCj/5kz/Z2sF7yy16c+FVV13Fm970Jl7wghfwmte8JtCvYpqH34lKvleRwWSSpTVIRSYvlc5O4c/v0yWGJwXWgRu2ZHky0OJjoaJnTJiU5SBF0OfeFvy93f94ePH79fPuoC3olbxZaPkpj3zllVfyxje+keuvv55HPvKR/OzP/mzr0hdeeCFf//rXSSQSfOlLX+Id73gHn/70p3nve9/LjTfeyAc/+EEA3vzmN/OkJz2Jz3zmM1x//fW85jWvaRVzu+mmm7jhhhvIZrOBfi1Twu+EpfAtzO7Ry79JSkNzUseT2IdNRLNfx1KajbY/OcqoFbWydHKH7JuM2is9k1Z6Xu+2XZ+guJblw++sehtPUiqXufjiiwGt8F//+tdz/Phxx/LIANVqlcsvv5w777yT8847j0c96lEAvOpVr+Lqq68GIJfL8drXvpZ77rkHEaFWsw8O33DDDXz6058GdPmG5eVlcjmdOPLjP/7jgZM9hEz4IvK/gTeg59IfAlcopaKb8tKtZmJxTfqTpo5T85uNe3YPLN09vjYNClsf/l49cEur7U1AUYZTH6BdrmASUCm0A/8W5gNOV7aUeFhoNozfvpPwE2QzaW7+/vfbLlwDL+WRb775ZqTrcxbe9a538dznPpd//ud/5siRIzznOc+xfZ+yieVY1+xsQ5AIzYcvImcDbwEuVUo9DogDPxfW/wsE5fzmvGkwgbZJUsddfmPQhG9tkZ8E2JGlRfKT0g+7VYq1CWtS+gB6THT2AbQ9FSdo0lKN3hIKVmqm5d93gFN55AsvvJAHHniA++67D2DThJDL5Tj77LMBuPbaa1uvz8/PUyi0N0A+61nP4u/+7u8AneWze/duFha6vuuAEXbQNgFkRSQBzADHQ/5/w6F7+QpalU3S8rWybk/4xRWd3z4JsCV8U1dnUsiytYmvow+Z7bqey6Qp/EwXCc3snqw+NBub/ffQrqvTZ/OVU3nkTCbD1VdfzUtf+lKe8YxncOhQu6TulVdeydvf/nae/vSn02i0J5TnPve53H777a2g7VVXXcWNN97IE57wBN72trfxkY98JLAuOyE0l45S6mER+X3gIaAEfEEp9YXu94nIm4A3ARw8eDCs5nhDJWevZhbvGk97/KBS0GWROzG7G1BQWmm7FaIMuzhEi/AnhGjsJq1YzJDlhExazaZO8+0RELsn60B21eyN+8QSrN/zDS2COlhwkPLIL3rRizbVxrdw+eWXtw5JAfid3/kdAHbu3Nlznc9+9rM9n7/qqqv69cg3wnTp7AB+AjgPOADMikhPHVGl1NVKqUuVUpfu2bMnrOZ4Q3UDUl2+s1kzQCcld9pulTJx6tghDgGTTfhg3GsT0ofahn5MdQsI49KZlHLVdlUxPSr8Mw1hunR+DHhAKbWolKoB/wQ8LcT/NxwaNX3zkzObX5/ZDfWyLkA2CTgjCN8mDpHdAcgE9cEifJvV1qT0oVbSj8mubJHZ3e0A+iRANXsCs1PCDx4PAZeJyIzo0POPAtE98t7RuCdQWaacCH9C+lBd711pxeI66DkxZGm26Se7V4wTFPBs9cFhTAzZD7sslVBwhij8IL6v0AhfKfVt4FPA99ApmTHg6rD+39BoEX5m8+uTRpY1B7cUTBBZliA10/v6JGUbWQX3euxpggKerT50EX4A2UaZTIbl5eXRkL4t4Zs0zQkhfKUUy8vLZDKZ/m92Qah5+Eqp3wZ+O8z/ERjqFuF3Ec3EkWW5l2Ra2SGT0oeSLgfRjYkiS2NP3f2Y3a1XMNWi/aQWJdSd+jC8CDrnnHM4duwYi4sjsMn8SV0fa6bU9foyJAowMxlnRWQyGc4555yhrjHdaWuhNUBtFBlMxjJcKT1IuyetScsOcVP4J34w+vb4Qb2kUwG7arZscoekxpyV1g993Zz+7SmZTHLeeSM6zP39L4Qn/By85Pc2v/7hN+vV8Gt6M2XOVEyLp1moOSj8mQlS+HWzBO+etGCyskPsJi2YrD7Uypoou4OFk+QidCJ8qw5QhPtQb3RkENmtesHY0/LoGhUBTAnfgpMPPzWj09ImwTCcBihEOjuk2VTcv9iRBVUrO09alZw+tzdiaDYV133zCA8um1TGWtHhPkSb8D/wn3fyJ1+6R//itOqNJ3XWVERXvR+8/h6e9N4vcmy1qFNHGxV7ATFJSQABYUsT/nXfepDrvnlE/+Lkw4dIG8afffkefuLPv8F6pd6H8KMb8PzbbzzA8/7ga3z+NlOfpVZynrSgfW5vhHD9nad512dv47c+rUvcUi/bxyEiXF7hZK7MX3z1Pv7oS3eTL9faK0bbMRFdAfHBr9xLoVLny3ec7ohD2AmI3XrSmpQ9NgFgyxJ+rlTjXZ+5lXd99jZt3E5qBiJLlkop/uCLd/ODo2vccM9Sh0vHifCjqci+cLuuVXT9HaaERd2J8KO7n+A7R/RZwrcdNyUVakVnNwJEsg+3HFtrPb/t4bzzqhci6w7Jl2uUa9qdc8/pQkemkYOLsFnXx5huEWxZwr/RDFCAO47n+xtGBJevJ3LtwqN3nsw7503D5uyQCEEpxd2ndJbEvZZbx82lA5Eky3tMHwrlOrlSre3D70ZqVk/IEbSnO060s1WOrhadM40gsi7Ch5bb9v3A0kbHyt3GnlrxuehNXGFhyxL+/Ysbref3Lq53kKXD0i+C6tgiSjCG7pQ3DYFtlgkai4UKa0VdL/zoSlEvrx3939YAjVYfAO45vU4qoYfTQ8tFTTR2RCkS2dXWiVyJbdkkInB8rdRBlg73ImK2BHDExFAO75phsVDpP2lBJCeusLBlCf/YapFsMo4InMpX3P2VFuFHzNf3oFEz5++Z5dhqqT1pTZA6Pm5WKU88ZxunCxWqlTKgJsql02wqTuTK/Mhhnb1yulA2cQiHTTIRVcfHc2UO7Zphz1xaE34/ARHBCqwPregxcMmhHZzuJHzXmFD0Jq6wsGUJ/+hqicO7Z9kzl+ZUrtyfLJs1KOdG28g+OJUvk4gJF+yfZ2mj36RlyHI9WkRzKq/b/JgDukrpWt58x3aKLD0P8XTkylWvFKs0mooL9+uSFssbVePScdhYFdGY0Mlcif0LGXbNpVnZqOkxEU/ZnzA201GBNUJYLFSYSyc4vGuWtWKNasWs5CcsnhIWtizhH1stcu6OLPu3ZTiZL7fVjKs6jpYSOF2osGc+ze65NMvr1T5BtmiqmdOG8C86yxB+zgQ97RSZ5Q6JWJbO6bxOE73Q9GF5vWpcOm4KP1r3AXRM6KxtGXbMJFkrVp0zjSCy7rXl9Sq75lLsnksDkM8bt6drxlS07ClMbFnCP12osH9bhp2zKVaLVa1mEpnNJXktRDSV7lS+zN75NDtnU+RKNeqVPkFbiGAfKsRjwqP2anWcK7gQPkTSHbK4rgn/8K4Zssk4y+sV59RSiKSLcKNSp1Cus39blh0zKVasMeHoloqmOl5ar7B7Ls32Gb3DuVQyiQB29yKRhvS2yPUhTGxJwm82FflSjW3ZJNuzSR00rDtkVUCkA557zRIcoFg0xm2nZlKzunJjxBTZqXyZPXNp9synANpHwDmq4+i5Q6xVyt55LSBWNqp9CH+P3gxUiU4Nl5WNKgC751JsnzFjwinTCCK7Ylxer7JrNsVCRhN+pehC+ACzuyLXhzCxJQl/vVqnqWAhk2T7TMqk0RVdlq/RVDOnCxX2zqfZNavJsrRhCGSCgoWnChX2LaTZOasnrY1WH9z839EaoKcLWuHvmU+zkE22Ny25TVoQqXuRK+lMqYVskp2zKdaKVZRTETuIbExoeaPCrrk027KG8EvGhz9BAiJMbEnCzxvj3pZNtgZo003NtFw60SGaar3JykaVvfMZ5jO6Bl6t5dJxIsvoEf7KRoWds6lWH6oll/RYiOQJZIuFCvPpBNlUnPlMQttXreh+HyBS9mSNiYVMkm3ZJE2FdhE63YfsDl1eOELquNFUrGxU2TOXYiFr7KncZ0zM7J768M90dKqZ7dkkSkGjvOFsFIkUZKLl61sr6iX4zrkU82b5WisXAdGZFXaIoJrJGddaMh4jk4xRs7Iq3JRlvayPo4wIVotVdphV1kImQbnsEjyHSCr8fLktgqzJt1l1mbQieCDNarFKU8GuuXTLpVMru2TpgBEQ0cr6ChNbmvC3ZZOtpV+96qJmIHKuBLsB2qiYSau7QqOFCGaH5Ev11j2YSyepV1zypiGaZGkmLYD5TJJa2SWWAhHtg86nX8gmmEvrvjRrLplGELkxsbyuRdCuufaKsZXI4HYvisuTcz7vkNiShN9avmYTrYHaqDjs7rQQMXWcswZoJsF82hB+1WWzD7TKsaSbAAAgAElEQVT7EBF3SLOpKJRrLJh7sJBJ0Ki6ZBpBJN0huU2En9C2BC4uwmj2AfSqdzZt8u6rLoFniJyLcNVa9c6kSMRjzKbiNKsO5xJYmN0zWefzDoktSviaLLdlk8wZJeB4ypKFiBF+vmOAWi4dVfXQhwgVi9roCJ4DzGUSNPuRZQTTS/PlestnPJ9J9F+lRNBFmC/XiAnMpRLMGQHhWMTOQoTHBOjVlnZL2ZxLYCGC9hQmtiThd7p0WsbtlkYH0TPuDpdOJhkjERNvfYDIKMtcx0oLNFkqt6qlEFF3SK09aaWTpJSp19/PHRKhgGe+VGM+kyQWk5YIErfNYxC5ipn5clvIAcyk44hbthRENuU6LGxZwo8JzKYSzBrCj3lRMxGqHdKZVSEi2mdZ7+fSiZaa6VxpAcylE6h+Lp0InkCW73BLzWcSZNCuBceAJ0SunnyuVGtNvLMpa0w4HBxiYXZ3pA6kscaE5b+fTSU04bv2IXoCIkxsScK3BmgsJsymtL9SGi5pmWDIMjq1Qyw1Yxn3XCZBbMKM21qlWOp4PpPUAxScVVkyA+mFyKxSKvUG5VqThUx7lZIRi/D7TL4R6QNoe+qMQwDEmg5HA1qI2IrRsidr1T6TihNveIhrQWT6EDa2JOF3BtkshR9vuNQNgciRZa5UI52IkUnqCWs+nSTW8Lh8jUgfun2uc+kEWPfByecKkQoWFspWdouxp1SCDEbx9pt8I9IH2OyWmk0niNEk0axO1JjIl+rMpRMk4prWNOFX3IXczE5AItOHsLHlCT+bjAOKRD/DiJxxt/sAMJuOk+i3SonYBrJcabPCt/qg3BQZRIos8119mEnFyaBf6+/DX4ZmI+wmekKug/CT8RgLCeO6nKCYUL5ca620AGbSCRLNPkIugvsJwsSWJXzLuGMxYXsKYjQmaunX6TcGyKYSJFSfScs6fDoixt0TZEslSKs+qhIilf+dL7fz1wGyqXiHD78PWUYoHTBf3iwgdqVMXronAREReyptHhMzyTjJZsV9XEOkBETY2JKE362Ot6eMynJbgs9ZtUOisSsvX6pvUjPZZEwbtyeyjIZxW+rYygrJJuNkpErTTRlDpFw6nRlfoCetrFgunX4xISLTj3ypnVoKsMMaE5PkIiy3hRxo15QWQS7jGiIXTwkTW5Lwc6X6JiWwy4txZ7ZDLBEt4+5UM6kE6X4KHyKljnOlGvPpBPGY9tfPpOJkqdD0MmkVlyKxO9LepWMU/oSQZbXepFRrbCLLbS2XjgtZWgfSRKAP0DtpzaTiekz0FRDREUFhY8sRvlLKLP3ahrE96UHht84ijYZh5LpWKdlUnBRVD4QfHXXc65bSZNmIpd0/GCF3SCvTyIoJpeJkvbp0IBL3orWnY6Z9L+aTFuG7kGXEzuftVvgzqThpqjTiU8K3sOUIv1xrUm00N7t0vBg3RGrp15lVATCTiJGZMDWT71ppWS6deszDfYBI9KNVg6ZD4adlEIU/fnvqXqUALMRN4HmSBES3Dz+l90TU4/0ExG59fGm9GnILx48tR/idO1QteFq+QmTIUim1aTs/wHyySUwUyotLp7QKjVrIreyPnqyK1gD1MGlBJO5FvlwjGRcyST2UMgm9SqnF0u6ppVZ54Qj0oXvHM8BczMo0moyYULOpKFTqXfakV1s18UD4sCV22245wu8OsgHMJzyk0UFkjLtYbdBoqk2KbC6u3VK1vu4Qy7jHvyW+W5FZLp2qOJR3thAlwjcrLTHkHosJ87Faf5KJxSKz27Y7WwpgPu511RsNl856tY5SdCl8y548uAghEvcibGxZwt9ElrHJUvi2k1ZcL0cnybi73VLZpFdFFiF3SHmzWwpgNl6j2s8tBZFxEdq5dGYthe8pw2X8FVjt+jCX0KveygSNibCx9Qi/2EuWszEPW+FBG0atOPbDN7oDhdAeoBUmSB13bOcHo8ik2n+ARsgd0r1KAX0v+q5SIDqEb2dP8QFWvY0KVNfDap4ndNbzt2CN67LnMTH+exE2thzh2/nwZzyrmWiQZXegEDoIf0LUcb3RZL1ik0ZHtf+kZe2OjIDPtTsOATAjVSr0uQ8Q6RXjjHjINILojIlyr8K3xnW1L+FHJwkgbGw5ws+VbNSMMW6VmAyyzNsE2VpqRk2Gcbdq0GQ2+/CzVCl7IcuI+L9zNgo/K7X+kxZExv+dL9VJxWOkE206yLbGhNcAelTGRIc9mZpGfe0pvaCPBY2APYWNrUv4HarMqm5YkclIB7RTZFmjZkr9CD8iG8js3AjZuCIpDco4nE7Uiai4Q0r1TZMWQFYq/d0IEJnywno/RKIVeAY9aYGXFWM0xoSdgLBqGpWljz1FbD9BmOhL+CLyaBH5sojcan5/goi8M/ymhYNcqbapoh7Q2ihT6auOo7t8tfpQ6kc0ETHu7lr4AImmJr6+kxZExh1ikWUnMtQoeu0DjP1e2K1SMlSoqxileh+KiNqYyHYKOaPwlRf3WjRWjGHDi8L/a+DtoKdLpdQtwM95ubiIbBeRT4nInSJyh4hc7r+pwaDz0GwLaYssVR8lEBE1Y5HlfGctHbNK2WhOhjpuT1odZGlOuyo2J4Pwy7UG1XqzR+Gnqfa3JYgOWXZlSwFkqFImRbHep3xFxMZE6wQ7IN20xsRk2NMo4IXwZ5RS3+l6zeuxT38C/KdS6kLgicAdgzQuDORKtU1ECVrNlFSKUj/jTmYhNQ/r41czs6n4plVK2hyr543wx2/cdrEUi/A992HMuyPt3FKg70XRax8gApNvb2ppSmm3VKnap3xzIg3pbRHoQ+/KPY21YvQ6JqYuHYAlETkfUAAi8j+AE/0+JCILwLOAvwFQSlWVUmM/Pbu7UiZo4y55MW7QVTMjQJY9fTCrFM+uhLErMmfCX1cJu49sRgR2R7azpTa3N6UqbHi6D1FRx732lFZa4ZdrHsZEBNwhepWy+T4kLRHk9V5sLI19P0HY8EL4vwr8FXChiDwM/Drwyx4+9whgEbhGRL4vIh8WkdnuN4nIm0TkRhG5cXExfKOxJcumVjPluhfjjgZZ9iiypqXwvZDl+NWMXXosdaPwG4P4v8d3L2z7ACSbFe+rFIiGPdmQZVmlKHki/AiMiXLvmJCaPi6z6HVM1Etj32MTNvoSvlLqfqXUjwF7gAuVUs9QSh3xcO0EcAnwF0qpJwEbwNtsrn+1UupSpdSle/bsGaz1PmBnGClVoaTSlL0o/IiQZbfPNdHUxl2oe1QztY2xGnf7IPl4+0UzQNe9DlAYL+HbrVLQhL/eSKL6qcXUnN7YNMY+6LpMvWMi2fTo0oFoxIRK9R5XrSUg1huTM/mGDS9ZOg0ReT9QVEoVzGvf83DtY8AxpdS3ze+fQk8AY4Wdwk80K1TwqmaisHyt92SGxBsDKnwY6yC1KmV2pgJSKwKw7knhW+6Q8fXBrkwHjRoxGpRUilqjD+GLmP0E4+tDqdag1lA2Y6JMiRRFzyIoAgq/SwRZLsLCQIR/Zvvxvbh0bjPv+4KI7DSvuZQB1FBKnQSOisgF5qUfBW731cqAUGs0KVYbjsbtefk65sM37NLoqBUpqyTlfoFniIRx2w7QulmlNCZE4Zd7t/NbJOPdRbg7InGIXhFUVgP48Md8Pq/dKqUVE/JE+NGIp4QNL4RfV0pdiU7P/C8ReTImgOsBbwb+TkRuAS4G/q+/ZgaDvM2GJYBEo2yM2yNZqiaUVsJooifYq5kyZUl77MP4jdsuUNhSZHUPhB+B05bsCnZtIvwJ8H/b5a8DxBtlyqS9K/wxH0jTfeQn0BYQ9bjNJ7oQAQExCngYWVrNK6U+KSK3AR8HDnq5uFLqZuBS/80LFnZ1vwFijUEUfgdZWs9HiGZTmRo03eq4RJU0Fa8kA2M17lypd8PSQEvwCGwgy5drpBIxMskOQqm3Cb/iVUAs3hlSC/vDbtc2QKxepsy8d4UP+l6MaUwUbBV+kQrp/unWoF1rcMYTvheF/wbriVLqNuAZwFtCa1GIcDTuRlkrMk9qZq9+HJNhFCqm7ne3mqmVqEramxshAsadL/eWJLAUWc6Lwoexx1Psyiq0FP4g7pD102NLB7RdpWDGhPLqljJjYv1U0M3zhI1qnabq7QO1MlXxOPEmM7qmzvrpcBoZETiOLBF5nlLqeuCQiBzq+vN4a6H6hLOaKVEm7d2HD2MzDCe3FLUy1ZhHt1RqRmeIjNG47XZ3WkHbvGfC3zM2kgH7sgoW4ZfweC/m9unywuUcZLeH0Ep3OG0eo1aihMfMtbl9+nFM98I2lgJQL1GLeRRBoPsxRnsaBdxG1rOB64GX2/xNAf8USotCRN6mwBLofN2qV5fO/H79WDgZdPM8wXaHKkCtSC2W8aYqwRj3ePoAmmg6D80GWmmZOS8+V4D5fXDyhwG3zDts4xBmleI5aNtpT2MgfLvzIQCkXqYeS3tLApg3hD+mMeG0SqFWGmxMzO/fuoSvlPpt83jF6JoTLpwUPrUStbhHw8hs07nTYyJLu8JpAFgDdBDjLozHuCv1BuVa0ybIVqIuSSoNodFUxGN9ksHmz4KN0zo7JOZxkggQ+XKd7TYTLwzg0mmp45Ow98KAW9gflgjalMOuFNSKNGJpb3n46QV99u24FL6jCLLGhMeMurl98PBNAbcuWvCSh/9WEVkQjQ+LyPdE5AWjaFzQsDUMpTTReCVLEW0YYyJLu5N9AKiVaAxi3PP7xzdptfrQO/E2zAHmnslSNccWuLXb8WytUsp4vBcthT8+spxJxUl21KCxyjXX4xlvq14RrfLHpfAdVu7U9Zjw1AdoK/wzuLyCl6DtLyql8sALgL3AFcD7Q21VSMiVaqS7syoaVVBNGvGMNzUDRh33LScUCpx9+CXq8ewA/srxKXzHVcqghG+R5dgmrt6SBG2XTnJwhT8G2G1EtDKNml5XvaDtacwKv2enrbGngdyctSJUCgG3MDrwQvjWuvolwDVKqR/gYeNVFGGvyNrG7VkJjDG44xhkq5doxNPeMhJAK7LaxliM23HSqpdpxnXtck++47nxqWOnkgSWS6ekPK4Y0/P6aM0xTr5OmUaNRHYAF+H4FH7BoaYRtRKNRGaAMWEJiDPXj++F8G8SkS+gCf/zIjIPjG+b6RCwVTMtws9S8mwYZ411CS4Cc6leNdMcZIDOjS/47LQfglqRZkKfoepN4VvBwtGvtsq1JrWGsk0FBCto68GeLBfhGN1rTplGJAYRQWNU+HZxCIBaCRXPUG00aTQ9uGnmxht8HgW8EP7r0UXPnqKUKgIptFtn4uC2fFWJQaL5+/TRdNbAGCHy5Trz6QSx7oBmrYwaZPk6xswKR59rrUxzUB8+jIVonHaobt545fVejE9A5OzSY41bSo+JAVaMlTxUiwG3sD+sOERnLXwA6qUBBcRU4aOUaiqlvmfVsldKLZtTryYOrgo/mfU+QMesjnvSGQHqJT1AvahK0CQD4yFLx6yKks6AAm9Ek0hDdud4Ji2XVEAYoLQCaLIcY9aX05ggmfUe15obXzzF1i0FerWV9CEgtrjCP2OgDaN72afVjCSyA0Tzx6iO7RRZowbNOpLM0mgqag2PG35gTArfyYdf0qeKwQDqeDyuBMc+1EqoeAokNkA64BgD6C5xLZUcIAmgNSbGISBs3FKg+2HsyZMQGnPK9SiwpQg/V7RTM2YJmswONkAhOmqmQ5GBRzVjGfcY/N+5Uo1UPEY60WV+tXLHAB0ggD6Widc5tVQSWTLJ+GAKv1oY+fkEzaaiULEpOmbsKZbMettpC2MdE4WKg8Kvl5BBxsSYU65HAU+ELyJxETkgIgetn7AbFjQs43baGRlLDaLwjTskKmrGDFBJzgAe3SGtYOH4+rCpFj5ArYikBugDmBTZMQae7Q7dSBrCHyRFFkbej1ZdJoe4Viw1M1gOO4xxTDiseo0Pf6CU662s8EXkzcAp4IvAv5uffwu5XYGjUHYwbqPwJTnjXZHN7IRYciyG4RZ4ltQAagbGRpaOPtd6mdggigzak9aIN8tYLp15u9VWMksmMYBLZ0wuQrcdqqBFkOc+ZHdCLDG2Va9dhg5ALK0FRGWgFeOZq/C9VKl6K3CBUmo57MaECbciUQCxzAzlWs3bxVpLv4iQZa2tyGAA457fD6fvCLJ5nmDrNwaoFVt9GEjhN2tQXIHZXQG20h1uG+BaCn/QJIARk6XzBjgtghKpGUq1PEqp3tVYN2KxsZGlbVzLWrm3BMQA9vTA14JsXqTgxaVzFMiF3ZCw4VZHByCenKHWUNS9BDxhLBtNrBO7nFYp8dSAxj2mYKEz4ZeIpy3CH0CRwcjJMleqkU3GSfXEITThp5PxwUgGRn4vHMeEIct4ZhaAitfMrzHsJ9Ab4OzcnGZMpHUfvNvTXl25dAwp16OAF4V/P/BVEfl3oGK9qJT6w9BaFQL6EX4iMwOsUa43mevO57XD3H5YfSDgVrrDrTQy+DBuaz9BtahLJo8I+XKdc3d2/b9mAxrVNuF7XqVY8ZSTsO+xAbbSHY6ZIfUyJLJkkjHvK63sDoinRq/wHesytRU+aHvaVI7ECfP7YfXBQNvYD8Vqg0bTeQOcHtcMtoEMtJtwx+GAWhkdeFH4D6H99ylgvuNnouCcN22MOzMoWY7e/+1Y99uatFqEH+1sI7f9EAP3wfJ/jzj47Jz7XTQ+/AFcOmPKDnGraQRCKmMCnhEuuV0oO2VL6XGdHNiexlvMLmz0VfhKqfcAmJIKSik12YefdG9aqpdBYqRSeoPGQNH80oquLJhIB9lURzgvwa1VShao+Nhtewp2PiKgVrpDKWXv0jFuBElmSSdiPjbBjTa91HbSglZqaSYZY2m97v2CYyDLvNOYsOIQKa3qByLL4jLUq5BIBdlUR7SD5w4iKDMD1CLvIhwVvGTpPE5Evg/cCtwmIjeJyOjWzgHB1aWTyJIxtWkGiubDSJVlrs/uzmRmDvDjDhkdWRarDepN5bofYqCAZ2pG12Mfgzp2CjwP3AcYz4rRpS4TySxZ48YZSATBSMnSceVuRFBq0JX7wgFz4fFUww0bXlw6VwO/oZQ6pJQ6BPwm8NfhNit45Eo14jFhNtXlizQDtG3cHtVMyzCOB9hKd7hmhgCp9KAZLqMnfOeJVyt8EhkyyQFSGkH3I/9wQC30BkeFXy8PnocPsHD2SG0J2nV0eusylSA50/Lbe3bpLJyjH0c5Jvpk36UsEeQ55XoXxNMjt6dRwQvhzyqlvmL9opT6KjAbWotCglVWoXezj2Xc+qvwPEgXzjYXHp1hOB9vaIw7O6Caye7QJxWNY4A6xFIsohmILLeNniz1AeYO2/kT2i010KS17WxdfKycD66RfeA8aZXMxKsJ37N7zRJBuWMBtbA/WoFnF5dOTAYQQSK6H1uY8O8XkXeJyGHz805gtOkpASBXstllCzYK36NxbzOEnxudYbjWoMEH4YvofoxwgDqdoWr58ElmBgt4glHHo7sPzaai4OjS8ZGHDx0CYnQTV65kcwg79Lp0vPZj2+j7UOij8MX0w3MfYCyrrVHB04lXwB70oeX/bJ5PXHnknEvutzVAYQCyzGyD1PzIFX6q+8QuaBl3JmttvBpAWY6YLJ1dOp0Kf1B1fA6sn9bBwhFgvVqnqWz60KjrTWDJLOlkzPvBG9BB+COcfB0Dz4bwBw3ajmFMuNXCB9orxkEIf9vZIxVyo4SXLJ1V4C0jaEuocDduH/5KGLk61m4Ehz4kMqQSCUQGmLRAk+V9X+n/voDgnFra9uGnEyUf6lhB4fhIcqf7BQqttEzr4I2+h7HDWFaMuVKN/dsyvX+olSA1QybhY0yM2B2SN8eWphM2sTnoWG0NMvke0LbUbEDMw/6DCYIj4YvIHyulfl1E/hXoKVSilPrxUFsWMPKlGufuyPb+oVaCzEJLzQymykZv3NtcluAiQiYR9+6WAk2W6ye1Oo172Yc3HLwo/HSy0poYPKGTLEdA+P1iKZv83/UGM91ZMHaYPwuQkatjRxE0u5tMSjsABhdBo3Vz2q7c691JAAOOiWYdNhbbmUdnCNws8Trz+PujaEjYWCtWnY17fj+ZhA/jXjgbTt4aUAv7w9EtVdeBQkAb96ABT9XUmTrbzw2opc6wyNK26BgYRZZnsVDBM0YcQO+3Q3VTEkCtyYyXlPR4Uqf6jti95mxPPoK2oO/FqdsCamF/OAfPi3pMiPhw6Zhso9zDZxzhO/rwlVI3macXK6W+1vkDXDya5gUDq97GdruToqygbWpAHz5ow9gYne/Y9nQi2HTQw+DL11GTZY35dKLXzdEK2g4R8ByRe80502hzH2BQexqdOi7XGlTrTVc358CJDGBWjKMdE/axufLmMTFQiqyVcj06d+2o4CVo+1qb114XcDtCxXqlTsNusw90lLP14680RFMYTUTf9vxR6DVuX9khoyN8xw1LMHhpYYD0nA4Yjiizor9bqp3hEtVsI8dNfNAaE8l4jERMBnfpoEa2tyNfdolrJdur3sEmrdHvJxgVHAlfRF5p/Pfnici/dPx8BZioUslrJhVwe9ZmbV3XaiYWE1J+cqdhZKos7xh4LraM21f+N4yuD46rFMvn6mPTEuhBOsJJC+wODrFT+AOutnIPj6S2v+OkBYYsdTDX/4pxNGRZKNnUwodNYyI7aB9mdurT4Ea0YqzUGzSboznPwc2H/9/ACWA38AcdrxeAiTrE3DHIBpuVQGLQ4I6lBMInGsst5ThAE+0B6rk8BIw8lc4597uodzjGYoMH2WCkGVNWSYL5tIMP31TLBB8Bz9qGLs+b3R5Qa+3hSPhKtUQQaHvyteod1eTrFrS1RNCgAmLEm6/e92938O8/PMH33vX80P+XI+ErpR4EHgQuD70VIcOxJEGjDo1qK+CZTfnI14WREM2GVQbWtiRvSRM3RJ4sc6Ua5+222ahdL/eoSk8Hb1hYOBsevqn/+wJAvlxnPp2wKUnQVvjZuk+XDmiiCZnwHcdER3YLaHsaKGg7wjGhC/E5uXSK7USGRNz72bwWRrj5Srtqw8+QA2/F0y4Tke+KyLqIVEWkISKj2/8dANaMcfcEbTvypsGHmknNQmb7SJRA/yV4e/k6UB9gpL7jvOuO57aqhAE3kG07W1dqHMHBFW4HuACbkgAGDnjCSIim3/kQ1r0Y2J7S87qY3Qj6UKo1qDaaDskYHWMiFaM8iC1B2702AqyVamzzlMo1PLwEbT8IvBK4B8gCbwD+LMxGBY3+xt3p64umErBKEvQL2upVyoDGPcLsENfAs1GVaZMiO9ieiNEF2lxr0MDmoO2gKbIwEnXsvJegHXgGbU9RFRDt2Fw/V62Pcb3tbB14bg74OR9wtKcQ4IXwUUrdC8SVUg2l1DXAc8NtVrDIOSn8jrxp0L6+ki+yDH+AOtbRgU0BqkxywI1XoMly47Su7R8iqvUmpVrDs8L3lUo3onvhmBkCm3duD3Iv5vaDxEa6YuwtOtZ2S8EQZJk7OmwT+6JF+HbquCtVuVRroAYJhi+cDaoxkmyjXLFqP2mFAC+EXxSRFHCziPyeiPxvBqiWKSJxEfm+iPyb71YOibVijWRcWqqrhS7jzvryf587EuN2DTybY/VAr1IGCtpCe6NJyETTmrTsluBdPnwY0P9tbRob0b1wdK3Bpk1LA/UhntBEs/ZQAK10R65UYy6dINF9nGeXws+kfIig7QdH0oe1os71d3bpGLdUKo5SUPV6XjXA9kPmn4ygHxFT+K8G4sCvARvAucDPDPA/3grcMXjTgoM1QHtLI3cZtx+Xzo5DUFrVmRUhwjHIplRPCtrACn+HMe6QzyPtn/ttKfz2LlXP2HauVscjOFM1X6o7pAK2CX/gwmMWdhweSR9c6/lDh4CIDR7w3G6NiXBDfY6xOWjtFoa2i3Cge7FjNITfbOoT4Gz7EAL6Er5S6kGlVEkplVdKvUcp9RvGxdMXInIO8FLgw8M2dBjkSi5lFWA4H/72EZNlT6ZRTZdGMOrY8rkOtHxt9eFIAC11huOkBSarwij8hB91nDTqOHyyXCtV2THrsKcjkdGppX5KdYC+FyPogz6E3X0DHPjYpQodZBluP1z313S5dGDQXc9mxRjyuC5UHCqvhgS34mk/xKZomgWl1BM8XP+PgSsZ86HnfZfgfnOOYbNxn+XlK/GHXKlGrE/uN+g+NM3ytaeCoBMWDkAsGfoAbU9aduq4vGnSggEHKGiyDHmAlmsNyrX+mSGJeIxkfMBdqqDtqXBi07XCgGshPhhuxdgpgvY/fohWumOt5ODSaa1625lGMKA9JTO6oF3IY8JVBIUAt+TPlw1zYRF5GXBaKXWTiDzH5X1vAt4EcPDgwWH+pSNypRp75mwOGrd16fhYgkPoRLNqir/15n6bPqR0WKWlZqoDEH4srn3gIffBPci2ASl9HF0rpdEPWd53/VBt7IdV4zfeYduHdu43+HQRtnzHR2HPo/02sy9ypRqHds30/qHWm6o8uJvzsH4MW0AUa2SSNudDWMkHPTGhQWMR4QsI1zERAtyKpz3o9uPh2k8HflxEjgD/ADxPRD5m83+uVkpdqpS6dM+ePb474oa1Ys05kg+bfMcD+yuzOyC9LXR3yOpGzd6NUN3QjxZZ+qnrD8a4jwzRwv6wyHKn3b2obrQmLV9Fu0ATTeFEOxgfAlY39ADdYafwq8VWH8Cni3BE7hAvgWfwKYKyO/Tu7RGIIHt3zubsO1+7nkHfi7DdUmaVEpmgrYgURCRvfspeN14ppd6ulDpHKXUY+DngeqXUqwJo88DomzdtjDvrx18JsONg6IaxWqzaq8oW4VsZCdE17tWNqt61bncvqr1LcF+TFoSaqdPODHGftMBniuwI4ilKKW1PbgIirb2w2WT7IBfPEBkNWRYdgp02binw6SLMP6zjZCHBMWU8JHgJ2s4rpRbMTwadofPB8JsWDBpNRcGpBk2LLNvukFpDUR8kfTMWHwEAACAASURBVAtGklmxWqw5qMrNfRhKHReXobI+RCvdsVrUE29PaeRmQ0++Qbh0IFSyXC1aCt+J8Odavw5ctAt0Tfx4OlSyLNUaVOpNB7dU95iwMlyiF09xTGfsWvWm/RL+jkM6ISJEAbHqdMZzSPC08aoTSqnPAM8b8DNfVUoNFRPwC9egiANZDrwN28qsCLHK4Vqx6qwqoWXcvo5qhA7fcXiDdLVYdXbnQPs++ClLACNRx20fvp09rW9W+H52qcZiOo89RLK0SGbnrMOYkFh71TvM5BvymMgVaw4TrxEtQUxaEOq9WNtwiQmFgL4Ve0Tkpzt+jQGX4pK9EzWsum3OqK5rNRXXf2v5+qoN5rqzYdyw47DOX14/FdoJOSsbVXbaLsE3G7fv5WunOt73WJ+tdMdqsepwH7rcUn5XKSNQx/1dOu1AaCYRG5woIXR3yOpGnz4kZ7VbBp8psqAnrVoRNpZgLqTYXKnK9hmbInNOQm7ghIzwRdBKscp8OkEqMbD29gUvrPbyjud14AjwE6G0JgS0AoVO/sounysMqQRCIPxSVS/BHU/sgk27Cq3PDITth/VjmMpyo8aB7XaHZluZRnqV4uvgDRiZOp5Nxe0HaK0raJuKt8h1IOw4DMdu9N/IPljZcBsTvasUGGJMrD0YHuEXa/a7tm1cteCjDwtnQywR8phwiKWEhL6Er5S6YhQNCQsrJqti16xNWmZ1Q5+WZODbMDrT0A4+1U8zXeGaChhUls7MTp1ZEbI6fsyBhd4/dK1SwGfVTwhfHTu51sCQ5WYf/nE/fdh+CMpreve2KXsdJPraU9d9AChVfarj1SNwzqV+mumKlgiyy9Jp2dOQbs5YXJcdCVXhO2TfhQQvWTqPEJF/FZFFETktIp8VkUeMonFBYGVD5+TusPVX9g5Q8JOva/YPhOQ7XnHz8/X4K31OWlZmRYj+75Vi1VPgGbSyHLgPYALoR3y1zwvWijV7W1LKlix9T1oQWj9WXRV+96rX+L8HzV5rrXof8NXGfnDcdAXBuXQgdHta3aiyc0QZOuAtaPv3wCeBs4ADwD8CHw+zUUHCUvi2xl1Zt3XpDDxIkxm9/Fu+z3c73bBWdMv93gCJQ0KvYHzvUgXYeR6s3O+7nW6wdqjapwJabqn2vZhJ+UhpBNj5CK2Miys+W+oOx/TYRhWa9ZZrDUz11UGVMcDO8/XjsqcKJgNjpahP7HJMZLARQQPfi/Sc3qm6HI499R0T0Brb7Vo6fuzpfH0fQgo+r2w42FNI8EL4opS6TilVNz8fY4KCtisbFTLJGDMpG+9VtyJLDWEYux4Z2gBtLcGdyDLVDrL5dumA7sPKA/oksIDh7kawd+kU/RD+rkfqx6V7Bv+sB6xueMuWAlO51Nd9sAg/HAGxulG1T48Fx7iWb3sKeUzY7+kw98IIiPZ51T76sPtRRkCEc4y3436IkOCF8L8iIm8TkcMickhErgT+XUR2isjOsBs4LFY2avapgNCjZqxSBP6N+55QlIBrGdjuIJtfnyvArkdBsxaKz9LdLWXj0vHrDrEIPzSi8bYfArSA8NWHZFYX7wqRLN3HRACJDKAnrrBWKcaedtuVTKmuQzwFiXYffe16hlDtqVxrUKw27L0PIcFLls7Pmsdf6nr9F9FKP9L+/JWNCjvnPAbZhnGHdCqB2d1+muqIlY1+m33aAzQeE1Jxn0TTadyWygwI3pbg3ZuWfAY8Y0k9+QaMRlORLzuU6bCbtBJx6k1FrdEk2V13vh9CJEvH9FjodekMMyZ2PRJKK9q9NhOsNnTPNNo8JsA669mPCOpwrx28bPDPu8B11RsSvOy0Pc/lJ9JkDyYKPhI1E54SWDW5urak4WjcPictCKUPLYVvN0Bbuzvb/m9fR+uBPkRk53mh9CFXqqGUN78xBECWS+H4jlc2as6qsnvF6KeWvIUQx8TSui7T4WXHMwyxYtx20AiIEMb1hssGuJDgJUsnKSJvEZFPmZ9fE5HRtXBIrDptWIIe4x4qmm8pgRB8x2vFKtudjMLaKNOBrN+A58xOXfgqpD6AywDt2N0Jug++fPhg3GvB+78HjUMM5/9+FFRyeuNSwFhzCjyDTVxryD5ASAKiwo6ZlEMcYr1HBPleMYYoICKp8IG/AJ4MfMj8PNm8NhFw3KHaqOvdsanOPHyfhcegw5UQgnG7rVJqvQrfdzoghBZoWy26FImyFFnHiWTZZHzwyqUWdp2vCT/gA6itVcouOxehncLvKFU9MEJSx0opnRlie4BLVcdwNu0W9pmlAzq9VOKh2NPyepVdjkKud0ykk/HBS6ZYCElAuLqlQoIXwn+KUuq1Sqnrzc8VwFPCblgQqNQbrFfq9gEqy43QufHK7zZy0Js0dj4iJOOuDGTcvpevoFVZSC6d+YyTW2p9UzojDDtpPQoalcAPNF8q6D0djpv4oEtA+DiM3cKucFIzvRVOa/ehleHipw/xpM5jD2NMuK7cbcZEwkfpcwstAeFzwnDAqluZjpDghfAbItKK4JlNV8FKp5DQ8pF5VGSWcfsmmt3hkOXSesU+GwFs/ZVZv5uWQBt34UTgVTMX1yv2h9BATx15GMKHDx3qOFjX1JKVGTLvQpbJzjhEuzbTwNh+UGeaBNyHdraUtzgEDLvaCkcdL/sZE34mLdB9aFQgH6yAWNlwyb4LCV4I//+gUzO/KiJfA64HfjPcZgWD1pLJY940WLnTfpd+5+uNSwG6EppNxfJ6ld3zTsa9vmkJDj6PpbMQUuB2qeA2QO37UK41aQ5Sh91Ci/CDJZqlQgWRfvbU4Q4ZxoffWjEG24fldbd0RmfCH85FGLw6dnTVgq2bM5MYRgSF415bdVv1hgQvWTpfBh4FvMX8XKCU+krYDQsCrpkhlYJ+tMlw8U2Wux6ld1wGmMeeK9WoN5X9AFVK9yO9uT7N0AMUgif89Yq9MgYo5/WpYR1oZbj4UWVze/V3snT34J91wdK6DhQm7AZoy57axzcPlfUFJlMn2D4sGreUrYCwAs/JgFIaAXY/Up91kHvI3+dtUG80WS3W7GMpYBIZNguITHKIlbsVfF68y9/nHbC0UXVe9YYEL1k6GeBXgauAdwO/bF6LPJY3LJ+rN5cODHHqFcDei/Tj6Tv8fd4GS+tmgNq6pdb1AQ2ZzYTvuw4NaJKReKB9AJ1G56jwK/mePvje0g86+LvnQjh95+CfdcHyetX+PoCetJKzOqvDwHepagt7L9Lq2DqjNQBY9rTHjvDL5iC7bnsaRkDsfYx+DPBeWAkAjnGtSqF1YpcF7eb0OWnN7YXszsDHxGKh4rxyDwle1hIfBR4L/Bn6pKvHANeF2aigYKmZvfM281PFGHfaxrj9Kvw9F+jH07f7+7wNlswS3FYJlO374OukJQuJtCb9AI27Wm+SK9WcCb+ct+0D+HSHgCbL07cFmse+tF6xD9iCqWwZQh9UI1CVbxG+LVm6jImhJi0IdEy0hJydPTVqukx1V5XRzDBxCBE9cQUtggouca2Q4IXwL1BKvV4p9RXz8ybg0WE3LAgsrldIxWMsZG02FJdz+tHOMPymb6XndXrmqSAJ32UJXrFXZEO5dAD2PUaTZUCwBqizwu8lS9912C3seyyUVvWhNAFhecMlllLpLWXcPpvApz3tNQfRBEg0i4UK85lEy920CQ5jwncOu3WthXMC7YMVh7D14TuIoNlUgo1qHeVXAOwzhB+ggFhcr9ivtEKEF8L/voi09hSLyFOBb4TXpOCwWNBfqIjN5ozW8tXGuP0qAQhcCbRdOm4Kv3vSGiIOAboPq0cCy9RZKliBQpsB6hCHmBmmJhC0leWp4CaupYJLeqzdKsUQfrHqsxjdrvP13o4g+7BedSYZB5fOUBlTYFZbARL+hos9VaxJq8ue0nGaCip+xdzei6BaCOx823KtQaFcjyThPxX4bxE5IiJHgG8CzxaRH4rILaG2bki4+sgsNdOzfPWZc2xh32N0Kl3dx0lHNlharxCPCdvtqgI6KfxUglKt4S/DBdp+14CCVK6rFIc4xNBk2fIdB0M05VqDQsVlgNrEIWZNhdaNik97iidh96ODVfhu6YyVPCCbAs8wZNAWNFku3RVYFdZlY0877dxrDkLOOrJ0vRINe3KNzYUIL4T/IuA84Nnm5zzgJcDL2Hz8YeSwWKiw143wU3ObgmwAM6kEG36NArRhNOuB5U8vFfSOwpjdFnKHJfisRZa+3SGWcQejLBetQOEAcYihUhpBF7Cb3RuY79hVVYKtwo/HhEwyxobfSQsCV8dLBRc3Qjmv3ZKxzbQwVFwLtHutUQ3srIXFQoWEkwhyEHJWefSi38l3z4X6MSB7suKLkVP4SqkH3X5G0Ui/WHQz7kquxygAZtNx/4oM2kogID++66YrhyDbbNpSlj6JZvthndYWuJoZLA4BPrN0LOx7TGAD1HWXLdgqfNDK0reqBN2H3EPtiXFIuG6AczhScaigLQQeuD2V10LOVgQ52JMlgnzfi+x2fchRQGOiRfhzo014HF3G/4hRazRZKbrkuToY92x6SIW/65H64OOgiGa94pxv7OBzHXr5GotpRROQ73ipUGU2FW+5aTbBIQ4xm9bv3Rg6nnJnIBvhXN1SYKvwQdtTcdgVI8Di8GmNlt/YcZVSse/DUEFb0G4piQU2Jk4XyuxdcCBKB5eOJYJ8uwhBT1yBCTmXXdsh4owl/JWNKkq5LJls0uhAk+VQ0fxEyvhdgzMMx0mrktc5812bTIZW+GDIMsBVipvvGxwnraH7UC8FciZpa8OSHVnWK3rrvY09zaQSrA+1YrSCz7f6v4aBaw4+OI4JK+vL95hIZvVRgQEJiNP5Pq5asFn1DqnwQdvT0l2BxOcW+60YQ8IZS/in8/2MO++o8JtqCN8xwP7Hw4kf+P+8QbOp+quZzMKmKpMQkHGf9QTYWIT8Cf/XMFh0yzd2HKBDrlJA3weAEzf7v4bByXwZcNjT4bBKAZhLx4ebtLYf0nYagD0tuZVVAH0vbBR+JhmjqaDWGCIl8awnwvHh7wPAqUKZfU5joo+b03fJbdB9aFRhcXi3zuJ6mR0zSVKJ0VLwGUv4i+vWAB3MuAMhmgNP0gXICif9XwNYKVapNRT7F1zUsU0f2up4GOO+WD8e/77/axiczJfZt63PAO1SlulEjGRchldk8VQgRHMqX2b3XNp+gDr0AUwSwDBuBBF9LwLow2kzaQ2SaQQBBNABDlysi48NWd+/XGuwVqy5jOu8bTJGO2NqyHENgdyLpYLLzvMQceYSfr8ouIMPf87yHQ9DlgEZxsmcHqD7t2Xt31C2H6CBuHT2P177XYckfKUUJ3Nlzurnc+2auERk+HhKIgX7HhfMpJUrs3/bYKsUMC7CYfoA2p5O3TZ0iYVTecue3FaMvWNiqJO7LLQExHBjwhrXjgrfQcjNpKxxPcS92HGeXsUFsGI8XSiPPEMHzmDCt1w6zkXHHMjSKIH18vjJsk34DsZdWtEnVHVh6KAt6KqPey4aug/5Up1SreHSh1W9uairphHoezHUfQCtLE/8YOhqjSfzFfY7ksyafsxu7/nT0FlfoPvQrA0dUzmRK5OICbvt/MbWmHAI2kIA7hCAE8PZ0+mCWbk7rnqdkzFgyCSAWEy7OgNQ+FpAjL4k2RlL+MdzZXbNpuy3kFc3dK68ncLPBEGWs7D7guEJ3yiys5wMo7gCM7t6Xg5E4YNWlse/P9R28pP9VGVxWR+taLMbej4zZEoj6D5U8rD6wFCXOZV38RsXV/Sjzb0Yel8HdKwYhxcQ+xYyDumMBT0mbA4bDySAnlnQGWxDkuWpvEt9LIDSmu24TidixGMSwL24WAfQhwjcNpqKU4UKB5xW7iHijCX8E7kSZ213IRmAmd09fwrEuCEQsjyVLxOPibOvr7isq/h1wSpLEIhxF5cg/7DvS5zIlQCc1XFp1ZYoQU9cgRA+DEWWlXqDlY2qcx8swre5F0NnfYEJ3G4fmvBP5Mou4sEaE733whJB+XJtqP8fRCzCikPsc1L4xRW96a4LIsLsMOckWzjwpKEDt4uFCo2mmir8IHFircxZTjOoi3G3l34BkOXGaR289YkTuTJ75tL2BzU3G9qVYNOHWEwb91DpgAAHLtGPQxBNX7eUw6QFAfm/91yoD0cfog+We9Ax8FyyCL/XvWZlfQ1VmkBE29OwMaG8ixvBZdJayOgdrYG414YM3J4qVEjGxfmMZ2vFaIOhY0IQSCziuBFBB5wEaYg4Ywn/+FqJA37UTBD+b2gry4dv8n2JU24DtJzTNWjCNO59j9WbyIbog2s6Ixi3lDPhD30f4kkdU3n4e74v0XJLOSr8Za3AuzJDIKAUWdD2dPp2fRykDyil9Kq336TlMiYKQxO+ERDHbvR9iZO5MnvnHdxSShnCt18xzqTiwwu5nY/QLqNhxkTOctVOXTqBoFCuUajUOWt7H4Vvs/RrpWUOa9xnPRHiaXjoW74vcTJX7u9GcDDuuXSC9WGNO5nR/Tj6Hd+XOJlzSWcEV0UWCOEDnPMjcPx7vrNc+q9SnCetQNIBAc69TPvYj/ubuHKlGuVa0znjqyWCevsxH0RcC/SkFUvCUf9j4uHVEmc7jetKQQe3XcbE0AF0ETj3qXD0274vcXxNK3zHyTdEnJGEf8IM0AP9CN/GuAPzfyfScPYlwxN+XzdCiAof4ODlWpH5Jcu8Szpjs9nXhz/0AAU4eBnUy743L51q+Y3dAs/OfYAAXITn/oh+fOibvj5+ItcvAaC/D78wrA8/NaMFxBBj4uG1EmfvGNxVCwEF0EHb0+KdbdE1IE7mymSTcbbZFX8LGWck4VszqKNLZ2NJlySw2RkZmP8btGGcuNnXMtxapbj6vsHFpTPkDk8LBy/TZQN8+ixdVymVnD7RycmHb7J0fJd5tnDwcv3okyyPrZaYSydYyNgcpAOucYjZIPZ1gL7Pey7yTZaeYikSd8hwiZNKxCgEZU8P+1tt1RtNTubLzgq/z6p3Np0YLi3TgmVPPlW+FTy3PacjZJyRhN9SM24Kf2ZXTxlYC8Gp46fpZbgPf9/RFT1pnbtjxv4NLeN2c4cEaNw+yFIp9f+3d97hcVVnHn7PjGbUe7fV3AtuwrJxIY4BO4AdTBJCCS0hhScbspBNNtlk00kj2Q0bsmRDCARCCSSUBOPQTce9ybYs25Jt9V5H0qiMZs7+cWbGwtadIt0r2dJ9n8fPlTV37r1H95zf+c53zvk+qtuc5AQtg9YQfJRhnv0XSldLAkcoljXtTnKSo7UbaJBRCugwYgQlltW7RhQMri7YainfEl+NMiZERYzehw+qPo3QgGhw9OH2yBFb+HGR1tGPUuC0a2qE9SngCkKDMUzwhRC5Qoi3hBClQogSIcRdRt3rTOo6erEIyNTayRZgCA46+b8BcpcBYkQVo7pdjQpyU7Qqt3elQ0B3iA5liE2D1FkjKkO700XPgJsczQYauNPSXSyrdoxoA1Z1W692pwUB5yHiI3Va0ghKLPsdI9qAVdPei80qgrilhi8DqDahi+DnXqSOIzAgattVp6Vp4fcGrk+J0TYcvTq8B1u0Ev0RCn5dRx9ZCWM/YQvGWviDwDeklPOAFcAdQoj5Bt7PT21HL5kJUURYA00UBhB8vayZ6GQVz6VqW9hfrW7zCr6W0HQ3gS1WxQ0ZhvioCH2sGfCK5fawxdJXhrwUrTJ4883GZQ77sW6rQ0CJZW9b2AnBpZRUtzu1O97+LpU0OzZ92I99flpdhCbPm2m0MnyxrPKOtIZd4gvKzTnMvhQf8VE2uvWoT/7R1ggE3+uq1bTwfcs9NdxridE2uvRwEYJ6F3X7wNUX1tf6XG4au/q024TBGCb4Usp6KeU+789dQCkw1aj7DaWq1Rn4D9rVAPHDiwzoaAkA5K+Cqp1h+yx9fuOkGI2Jna56VQaNIXhStJ3OXpc+lTt/tVrzH2aI3tOjFI134dujEJ897Me6rQ4B9R4AKt4L62vtThfOAbe2hd/l7bQ0ypDgFfxOPepTUp5KCB5mGUB1vprvAbz1KUvzY90sfFD1qXJb2CkPg1r43Q0QET3sPASodyEl+sxF5K9WG7DC9OPXtPciJeSlTjwL348QogAoBM766wghbhdC7BFC7GlubtblfpVtTvJTNSq3lN7KPXwDBSX4ujRQgBmXgKsn7KWNyvcdwG/c1RC0DB6JPq6p6WvV8eRbYX3NPw+hKfgNKubQMMtj4bR1rMu7SJ6mdqyeeDOsr50eaWk0UH+nNbxYRtmsRNks+pRBCFWfTr0TtlhWtTnJ0xqlSOmtT9qCr0uYCx8zLlWuqTDntmo7ekmL0wiXAiqUd3yW9jyEnqOtgouVH3+E9WnCWfg+hBBxwHPA16SUZ+Vpk1I+KKUsklIWpacPPywOB+fAIM1d/eSnnh2MC1CW6mBfQLFMirHR4dQnCTkFH1Gbl05sDetr1e0BJjtBNVANVwhAondk0OnUoXInZCvXVHl4Zahqc5ISa/e7Zs6i21sGy/ANODFa7abU5V0IoYTm1LvgDv1vEnyU4g2BPWYGxKVq010YO4c7e110OF3aItPXqRLFBChDfJRNPwt/2hpAhC+W7U5t6x5CMoJAJwMiMk7NR4RZhiq/4Gvok8EYKvhCCBtK7J+UUj5v5L18VLYG6UF9CT0SAgi+nu6QqAS18SeMiqFWt/Rq+41hbCs3KKGp2q4Cz4VITbtT2zKGoFalz52lWxlmXgYD3VCzO+Sv1HjdCJoTz34LP7CLULcyTF9LuGIZ1Kr0d1qBLXzd5oRiUtQelTDFsqLFybS0AEIZxC2l63wKqNFWw8GwQkVUtTmJtlm100wajJGrdATwMFAqpbzXqPuciU/wNV06XXXqGD9F8xq6ukMAZl6qNv2EWDFaewbodbm1J2z7u5SbKJBYGiH47gHlew2R6jYnOQH9xo0hdVodeoxSQI22hDWskUpVm5OkGBvxUVpzKQ0qxeQwYYV96Cr4MSlqhUgYI0a/W2qEcymglmXqsifCx4xLlUuntyOk0/tcbuo6eynQEny/WypQGfRuE5eo48m3Q/5KpXd+cTzW4IOxFv5q4BbgUiHEAe+/DQbeD4CqNmWB5msNmUKw8HV1h4Cq3BCyRXOqRZWhIG3kFpmvDLqJZf4qFYSs/I2QTne5PdR29AaZPK8P6JayWS3ERUboV4boJMgpCkssTzZ3B7YquxsC+o3BJ/g6GQ+g6lPNHrX+PwSqQhb8QKMtOx6p0/JSUGWQbjUfEQKVrU6kRPtd+IygUNq1XoKfvUStxAuxTUAIk+cGY+QqnfellEJKuUhKucT77yWj7uejstVJYrTN/3LPIgRrRnfrOLtQCdvRLSGdfrK5G4CZ6fHDn9BRpY4J2ouekrz+b93KYIuGaR+Foy+FFPK5qs2Jyy2ZmT78slEGnGovQWLghVuJ0TY6enWaTwGYfbnyf3eGFvL5RHMPM7TKANBZE3C0CGqyUDc3AsCcK5VYHn8tpNNPtfSQEmv3W7hn4fCNerUFPzlWfbddr843Z7kSy6P/DOl0nxGkKfi+dh0XgktHr07LYoVZl8PxV0KaRJdSeifPJ6DgjxcVrT0UaLlzANorVaWI0E4vprsrwWKBuRuh7HVw9QY9/URzD/YIi/Z64/YKdUyZpnkNfxn0FMt5V0FnVUgxaU40qU5rRoaGWPo6rWTtMoDy4+s20gKYt0kdQ+h8HX0umrv6Awt+eyUkFwS8jq4uHVBRJ+OnQOnmkE4vb+rW7nhB1afY9GGzjvnwhSNu69GpPlkjYM4GOPZKSMlEKlp9o16NZ2yvVMekPM1rxNqtWC1C33cx7+NqpFX5QdBT6zr76HW5mZExPhO2MAEFv6yxm5kZGpYxqMxHAYQS1PAV9BbLTWqDTgj+4xNN3UxPi9XeJNNeoSJxBrBmomwW7BE6LQf0MWeD8oGXvhj01BPNqoFOT9dqoBXqGEQsk2JsdOhZhrRZKkZ+CGU4GawMA07l0kkpCHidxGgb3f2DDLpHl2bRj8WihKZ8a9BJdCkl5c3d2h0vqHcRpONNiVVtol0vwQdlQPR3QsW7QU891dxDWlyAUYovo1mAti2EICEqQt82MeMytfY/hPpU1tgFwKxA+mQwE0rwO50umrr6mZ0ZoHK3nQrJqgQd3SGg1u1GJYUolt2BrcqOSmXJaMQCAlW5E6N1to5jU6FgdUiW5YnmbjITIgM00Ap1DCb40Xb9lsj6mLdJWWRBJtF9rjXNd9HhtSqD1KfTrgQd/fjzrlJLKYMYEK09A3Q4XcwMKPjBRyl+C1/PdzH9ErVbvDT4aOtUSw8FWkutQbVrW6zmjmcfus+n2GPU6q+jW4LuRC/3jnoDvguDmVCCX9bk7UG1BN/Vq1bpBLHwdXfpgErEMXcjHHs5oFunf9BNVZuTGVpWJXgtsoKgt0yKtulbBlBi2XIcGksCnlbeFKTTaq9QYSEChLgANdGmfxmuUsljjrwQ8LQTzd1YLULb5xpip+UTy3Y9xTJvlfrblfw94GlBRWZwQGWhClaGWB33RPiwRcHsjykjKMDeCCklx5u6tNs1KAs/uSDg5DmokUpbz8hCfWsyb5OaQwiy67assZvUWLt/tDQeTCjBP96oKrfmkMnv+54e8Dq+3ZG6Dl8BFl2nhrABJqoqW514ZADft5TeUUpB0Nslx9r1tcgALvik2kh24C+ap0gpg49S2k6G1ECTopVLZ1Q5Yc8ka6EKNRygDAAnmnrIS4nRTt7S5nUjJOUHvE6qd811S5eOQmONgAXXqLoUYLVOUMHvrFadXxAjKNZuxW610Najc+e76AY1eV+mPQHd1NVPh9PF3Cztpa+0BXfVAqTFRdLSpXObmLtRjS4OPBnwtPLm7nG17mHCCX4X0Tar9m685mPqmDoj6LXS4yNp6dbZEihYA4l5sP8JzVNK69VmZM1Oq7NGbUvPmBf0dunxkfqKDKgwzbH54wAAHr9JREFUCHOuhIN/1bTKGhx9dPUNBrbImkqVLz0IKbF23B6JQ89huBBQeBPU7jldJ4ahtMHBvOwA/tbmUhWoSyM0hI90b9TWlm6dhWbJTSrU8OHnNE8pb+omxm7Vzg3RfFQdU2cFvJUQguRYm/5G0Mx1EJsRsPP1tYk5WRrvwu3yzs0FNuQAUuMMaNeRcXDBJ6DkH5pzKlJKyhqDjFLGgAkl+OVN3czKjBs+3yWo4F/Cqqy7IKTHRdKsd8WwWGDJjWqjRkf1sKccqXdgt1q0K4YvNG7mBUFvlx4XSbPegg+w5Gboada0ykpqVQOdn61hkfU51GqfEDstgKau8KISBmXR9aouaHS+XX0uKlud2mUAaDyi3kOQUUpanE/wdX4X2YshcwHs17YsS+sdzM6M197o43PNhfAukmPs+rqlQI1UFl+vljZqzKkca1Cu2rlagt9arjYFZi0Merv0ODXq1W0C3ceSG2GgS3OOrtHRj6NvcFwnbGECCb6UkpK6Tu1KAapyp81SvsMgZMRH0eQwQixvVMd9jw378ZE6B7Oz4rBphXb2NdAQrOP0+Ei6+gfp1SPLz1BmrlP7CvY8MuzHJXUOhIB5WmLpsypD6LR8yc9177jiMmD2FVD81LAhbo96RWb+FI0yeDxqlJIRPOJ3cowdq0XoXwYhlJVftw/qDw7ziJIjdQ4WTh0+eiSgjKDkAmWlBiE5xq7fssyhLLlJJQrS6HyPNXSRlRDlXz13Fr42EUJ9SouPREod9xP4yFul/o57Hx3240O1nQAsmBrAgBgDJozg17T30u50sSgnSfukhsPKIgqB9HgDLHyA5HzlEtnz8FmpD1Wn5QhiVR5WIXKjA5TTy2lXgs7lsEZA0Reg/PVhXSIldZ1MS431JzA5i4ZD6hiWhW/Au1j+JTVSOfTMWR8dqfONUjTEsqNC7ezMDC74VosgJdau/3sAZUDY42D77876qKrNSVf/IBdodVrgHaWMc5vImKcCqu16cFg3YWlDl7Y7B1SbsNiCuqXAwNGWxQLLb1fxpoaJAnq4thNLICNojJgwgu/rQTWtma5G5UbIXhzS9dLjI+lwuugf1Nk6Blj5VZWEpfipD/260dFPW88AF0wJYJFV74acpSHdxieWhjTSZV9QoRa233/WRyV1Dm3LGFTwspi0oJOdABkJBrl0QAUiy1ygxPKMSeEjdQ5SYu1kJmhs0KvZo45TQ3sXaUb4jkF1/IW3wOFnT++Y9XK4zmdVatSn3nZoLQu5TWQlRtHQ2afvBLqPlV8FR+1Zq476XG7KGrsCd1q1+yBjLkQEX/2S6l0hY8i7KLxFxVTa/n9nfXS4tpMZ6XHE2DWMoDFiQgm+zSqYqzXJ5ss6VbA6pOv5xLJV74k2UHFpplyoxHKIRXPY22lpimVnreq0fHlmg5DutWYM8ePHpinrsvjp0/GJUHshajt6Awt+1XaVMSiEAFLxkRFE2SzGlEEIJTTNpWfNRxyq7WR+doK277tqu2rcIbh0wGcdG1CXAFZ8Wa202fFhoTlc68BmFdrzQVXeZYQh1qfMhCj6Bz36L5MFmLke0mbDB7/90Hr2w7WdDHokhXnJw3/P7VIGRN6qkG6TZmS7jkqAC29VnZZvRaCXw3Wd2h3vGDJxBL+mkzlZ8URGaCRHqNymlk5lhWjhGymWQsBHv6WWJg7x5e+taifCIligZeH70sL58oIGISPewDIArLpTWcZv/8L/q33VaongEi3XmqNeNQZfur4gCCHUfIpRZVhwjdo4tfVuf3Lw7v5BjjY4uDBfQ2RA5TPNXa4Zy/9M0uLs+q+Y8pFcAAuvg11//FCMoIM1HczODNAmqrYrV0iIoxRfAvQGhwGjLYsFPvINaDwEJacjqe+vUtE0l+Rq1Kf6YrWDPT9EI8ioRQA+Vt6h9ty89XP/r5q6+mh09JuCrxduj6S4ukPbfy8lHH9VWffW0IZUvorRaETlBjVhmLcS3r4H+tVa6b0V7VwwNZFou0YDPf6K2mwT4hA8JdaORRhYhpRpyrWz/3G/L39PRRtWi2BJnsa7KHtVHaevDfk2GfGRxkygg3IDXPZ95Qf2+vKLqzvwSFiqJfgd1Wq11LQ1Id8mOzGKRkcfbr3CC5/JJf+prHxv5+tye9hf1UFRoE6r/A3IWaZ2i4ZAVqJqE4YIPsDCayHjAnjzp/74OgeqO5iaFO1vj2fhi0CbH9rIPT4ygrjICOo6DCpDwhS46Mtw8G/+uaq9FcoIKtRqE2PIhBD8I3UOuvoHuWja8MmLaTiotsHPuyrka/oCl/kSJ+uOELD+J9DTBG//goFBD8U1ARqo26XcDrOvDNmqjLBayE6M9ifxMIQ131SThv/8BkjJ7op2FkxJ0PZVHn1JhYUIcaIQlCvBMJEBmP9JFWP+9R9Cbzt7K9vVAhgtq9K3cW7ux0O+RU5yDIMeaVznm5wPy76kNv/U7OFInYNel5tlWm2i7ZTq5OZuDPkWmV4Lv7HToDJYrLDuR2pN/fb/BZTgaxoPoMJ85F6kVl2FgBCCnGSD28TFX1N5dV/6Fng87DzVRpTNoj1yP/AXePk/QgoiN1omhODvPNUKwEXTNLbpFz+tdofOCT0cf2qsnWib1R9L3BByl0HR52H77zi1/036Bz3agn90i0pFN//qsG6RkxztT4BhCLFpsP5uqHiPwV1/ori6g6X5GiLT1aBi0c/bFJL/3kduSgy17b3GWccWC3z8N2rFzqvfZW9lO7Mz4v0hNs7i4NPKdx/CBj4fvoxZhgrN2m+rKJr/+Ap7T6qcCcsKNN7FoWfVcV7onZZviayhne/sj6n68fYvqS8vprajl2VabaL5mLKiwzDkQCVBr2k3sE1EJ8PHfqrmDfc8zO6KNi7MSx5+x7aUsPMBqHg/pEnn0TIhBL/8WAnTUyLJGm43YW8H7HtchQQIsiNyKEKoGCq+RNyGsf5uSMxlyht3kEonSwuGqdxSwo4HlGU887KwLp+bEmOsyAAs/RxMX4t4/bvMdJ9k2XBlANjzJ7XeuujzYV0+LyWGAbfHOOsYYMoSZZkdeJKsihdYNk2jDNW7VTz9MMvg2/1tqNBEJcBVv4GWY8zcczd5ydF+q/xDDA6odzHj0pBCdPiwR1jIiI+k1uj6tOG/wR5D1AtfIpo+Vs/UaLe7HgSrXYVnCIOc5GjjRu4+Cm+G6ZcgX/8BsuGQdsdbvUvNQxTdZuzzeDnvBd/T3cq3ar7C/0TcP/xW/7d/ofKYrroz7GvnphhsCQBExsP1j2EfaOeJ2N+QYRvGV136IlTvUGUI0Z3jIyc5msauPmOWl/oQAj75ID2WBP5o/29Wpw6zvdxRD9vuV26QMCxjOJ2L1Ze+0jDWfofOzBXcLf7A1Yknz/7c44HXf6CWlC4OT2SmJI2BhQ8waz3uVXexpuuffCtRIxPTrj+oIIIr7wj78gVpsf7Y9IYRnwmf+iOJXcf5v+g/MDN1GP996wm14GHRdRAXOELmmUxNjqarb1DfaLhnIgR88gH6I+J50PZrPpI1jLtGSnjzJ2pEsPgzxj3LEM57wR+MSqZy7u0sdrwFT1yjYs342Pe4Gi4t+yJkLwr72jnJMVS1OY1ZdzyE7tSF3DVwB7M9J+CRDWoHp4+GQ7D5X9W28aXhWwG5yTFIifFWWXwm34v5HvGWARL+sgEqhiSE6OuEZz4LSPjYT8K+tE/wDXVNAVhtPJpzN9VkUPT+l6D4r6fX50sJb/1MDdPX/VB11GEQZbOSER9pvAEB7J7+VV5yL+fjDb+DN378YUOoepeaFJ31MbVjOkympcb6s08ZiWfGOn4tPsclcifirzeDs+30h/3d8PyXVE6IS78f9rWnJqn6ZPi7iM/ioak/I5lulr7xGbXJbSjb74eK9+DS7wVMPqMn47sLQAfsERYKb/g+7J8GL30T7luilmj1OaD+gErLd/nPRnTtvJQYnANuWroHtFcJ6MAH5S284i7i2KUPM3/bv8HvV8O0j6jk2GWvqxjf1z0e8gqjoeSlnraOpweKXjlKWrr72dyQykWrHuamU/8Bj25QScOTC1TM9p4muObhkAJcnUl2UhRWi6CyzXihee3UAMVZ/8Of7PfC329X1nDeSqg7AJXvq6F64S0junZ+aow/qYqRvFXWyp89d7Ku8GXs79+rJjbnbVIbrYqfUqkMP/H7EV27IC2Wlu4BHH0u7VwHOnCgpoPf9a5n3fJcCg//HO5fBks+o4LVHfgLtJ2A6x4LmJZRC1+axJPNPYE3OY4SKSVPVKXQlXMv32n/ATz4URVGYsoStUz84F/Ve1kanntwNJz3Fr6fwpvhKzvU9uaBHiWWV9wDNz8XMJ1hIGZnKivOl6nGKF4raSQ+MoKZKzfBV3fD6juhp1UFhVr6Wbj97ZBCvw7HbG+wpmMGl+HN0iYAFi9dCf+yTVktzja1lDRjLnzuJRVRcATYrBbyUmI40WSsWFa1Oimpc7B8/ky47SXY+GsVlGv3Qyre+ZW/gqv+N6wJ56HMzozneGOX4SPGN0ubKMxPx/6p/4MbnlIi+cF9SmDmXw1f3BrWfNZQpqUpA6LCYCv/1cMN2KyC6VfeCV96C6ZeqHZEb/2x8tvf/HzYk7U+pqfHYhHGt+sj9Q4aHH3MKFyjtGnR9arDffEuOLIZVt+ljKAAiYz05ry38D9Ecj5c8fPg54WIb9duaUMXq7QmjkZJn8vNayUNXL4gS83iR6SppWnrfqTL9RNjbGQnRvkjDhrF5uI68lNj1BZ4IdRyzTXf1O36c7PiOeINk2sUWw6p0AQbF2aruZJlX1T/dGJuVjxP7hyk0dE//AIDHSitd1DW1M0tK71hK+ZuUP/cgyAsoxYX3yjxRHN34LhVo0BKySslDayakaZWSkUvgpueUZPNg31qcnoURNmsFKTG+vNnGMWWg/VYLYJL52ZAXCRcfb8yIrobVfDBERqio2HiWPgGkBYXSVpcJEcNFJp3jjfT1T/IVYunGHaPOVnx/pjiRtDU1ce2Ey1ctWiKdiiCUTIvO4HKVifd/TrGxT+DLcX1FOYlkauV4WqU+EaMRxuMexcvHKjDahGq0xqKNUIXS3J6WiyRERYO1xpXhkO1nVS2OrliwRnumgj7qMXex6zMOI43GWcEeTySF/bX8pFZaf6AbYAS+aS8cRF7MAU/KPOy4/2hco3g2b01pMbaWTUjcKq/0TA3K4ETzd0MDOocA9zL5gN1eCRsWmJcp+WLIHrMILEsqevkSL2DTQZ3vACl9cbUJ7dHsvlALWtmpZEaZ4ygRFgtzJ+SwKGaTkOuD/DUrmqibVY2LsoOfvIImZMZT0VLD84BYwyIXRVt1HX28cnCqYZcf6SYgh+EhVMTKa13GFIxatqdbC1t5Ppludrx73VgcU4iLrf0R0/UE7dH8tj2Soryk/0WrBFc4I0jXlxtjNA8saOSKJuFTxXmGHJ9gKQYO9PSYtlbqZ2ScDS8fqSRus4+rl+Wa8j1fSycmkhJXSceAzbC9fQPsvlALRsXZRs6KVyYn4xHwgFvrB69eXx7JfFREayfn2nI9UeKKfhBWD4thUGPZF+l/hXj8R2VANy8IniY4NHg216/61RbkDPD5+1jTVS1Ofnc6gLdrz2U7MRoclOi2XGyVfdrdzgH+Mf+Oj6xZCqJMcaJDEBRfjJ7KtsMEctHPjjF1KRo1s8Pf+VKOCzOSaJnwG3IyPfp3dX0DLi58aI83a89lAvzkhECdlfo3/nWtDt5+XA9Ny7PG/dwyGdiCn4QigpSsFqE7kLT0t3P49sr2bAw278pxyjS4iKZkR7LTp3LIKXkt1vLmJoUzeUXGCsyACunp7LzlP5i+Yd3T9I36ObzF49sJVQ4LJuWQofTRVmTvhOGeyra2Hmqjc+tKsCqleJTJ1bNVO7H98qadb1u/6CbB989wYrpKVyoFQ5ZJxKjbczJjGd3hf5G0EPvnUIIwa2rCnS/9mgxBT8IcZERLMlN4s2jTbpe9/dvn6DP5eZr62brel0tLp6ZxvaTrbq6pl4taaS4ppO71s0y1CXlY9WMNDp7XRTX6Dfaaurq49EPKrhq0RRDXVI+Lvau9tp6tFG3a0opueflo6THR3LTCmMtY1CjrdmZcbxXNnwO2pHy+PZKGh39/OulwTNX6cGa2ensPNWKo0+/HbcVLT08saOS64py/eE0ziVMwQ+BKxdkcaTewclmfayy0noHf95WwbVLc5mZMTZZ7K9cmE2fy6Nbx9XTP8hPthxhZkYcnxqjialL5mZgt1rYXFwX/OQQ+cmWUtweydfWjY3ITEmKZnFuEi8fatDtmpuL69hT2c5dl80aMxfCJXMz2HGylVadMkc1Ofr4zRtlrJ2TbugChqFcfkEWLrfkLZ3ahJSSn/7zCDarhX8bo/oULqbgh8DGRdkIAc/vqw1+chD6B91869mDJMXY+M6G4InI9WJZQQoZ8ZE8u7cm+Mkh8MtXjlLX2csvPrWQiDGw7kENwz86J50Xi+t1WXH0akkDLxbXccclMw3dhXwmGxdmcai2U5e9EU1dffxwcwmFeUl8Zrnx1r2Pay7MYdAj+fv+0bcJj0fy7ecPMTDo4UdXXWDY0t4zKcxNIjsxSrc28fy+Wt4obeLr62eTMVzQunMAU/BDIDsxmvXzMnl8RyU9o1gHLqXkhy+UcKi2k599ciFJMcaHQ/VhtQhuXpHP28eaRy00z+2t4bHtlXx+9TTtKIAGcfOKfFq6+/nHKIXmRHM3//63YhZOTeTLa8MP9zAarl2aS5TNwh/fGyZAWxj0udz8yxP76HO5+a9PLzbcdz+U2ZnxLMlN4rHtlbjco+t8f//OCd482sR3N86jIG1sYsoAWLxt4r2yllG3iSN1Dr7/wmGWFSSPyVzQSDEFP0T+Ze0MOntd3P9W+Yi+L6XkV68e4+nd1dxxyYwxmeQ8k1tW5BNrt/Lzl0pHvL3/tZIGvvP8IVZMT+HbV47dCMXHmllpLJyayH1by0a8Cauq1cmtD+/CFmHhgVuWaqcANIjkWDs3LMvj7/trOVI3sn0F/YNu7np6P3sr27n3uiVj5hocyl2XzaKqzclfdlaN+BpP76riv149xscXZXPrSmNXqw3HjcvziIuMGFWbONnczRf+vJuEKBv333jhmHa84WIKfogU5iVzXVEOD757km3l4U1W9Q64+eazB/n92ye48aI8vrF+jkFPGZjkWDvfvHwO7xxv5rHtlWF9V0rJox+c4itP7mPelAT+cHPRmEzUnokQgh9tmk9dZy8/eOFw2I10d0Ubn35gGz0Dgzz2+eXjNrH2tXWzSIq28fW/HQi742ru6ue2R3bzakkjP7xqPhvO3FU7Rqydk87FM9O45+WjYcel8Xgk//P6cb79/CHWzE7n19ctHjNXzlCSY+18ff1s3jnezF92hd9x7TzZyrUPbGdg0MMjty0bPv/AOYQp+GHw3Y3zmZEey+2P7+WNI8FXWUgpea2kgQ2/fY/n9tVw52Wz+NknFmAZRwvglpUFrJuXwY9fLOGRD06FJJhHGxzc+qdd/OjFI3x0djpPfGG54evVA7E0P4W7LpvF8/tq+c+/Hw4p1n+Hc4Afv1jCDQ/uIMZu5enbV4xrUumkGDv3Xr+EsqZubntkFy0hTH4Ouj38dXcVV973Lnsr2/n1tYu5bfX4uQ+EEPz6usXERkZw40M7Q959e6imk2se2MZ9W8v49NIc/njr2I+yhvLZVQWsnZPOD14o4a+7q0JqE+09A9z94hFu+OMO4qMieObLK5mXrU/YByMRRkfuC4eioiK5Z8+e8X6MgNR39vLFP++hpM7BZXMzuLYol6X5yaTFKX+8o2+Q8qYutpW38vf9tZxs6WFGeix3X71AO3PPGOMcGOTOpw7wRmkjhXlJ3Loyn1Uz0siIj0QIQf+gm+o2JztPtbGluJ7tJ1tJiIrg6+tn89lVBeNiiZ2JlJJfvnKMB945QUFqDF+4eBpr52QwNSkai0UgpaS5q599Ve28UdrEloN1DAx6uH5ZHt/ZMNfQXZzh8GJxHf/+TDGRERY+f/E0Ni7MZnp6nN8t0Odyc7i2k3ePN/PcvlpqO3pZkpvEL69Z5A/VMN6UNXZxy8Oq07q2KJdPL81hcU6ifzLf45FUtzt5v7yFF4vr2HGyjZRYO9/dMI9PXTj1nKhPXX0uvvLkPt4ra+Ejs9K4bXUBK6anfmjVU2evi/1V7bx8qIEtB+vodbm5flke39s4j9jI8dtgJYTYK6UsCulcU/DDp8/l5uH3T/HQeydpd6o1vBEWgUUIBoZMYC3NT+bG5XlsWjJlXNwfgfB4JM/srea3W8v96d7sERbsVsuHXAy5KdFcX5TLTRflkxw7dpPMofLO8WZ+9cpRSry+8MgIC9F2K30uN30u9S5i7VY2LZnK51YVnDMiOZTjjV384qVS3jqmNjLZIywkREXg9kh//RJCreG/eUU+H5ufeU6I5FA6nS5+9epRntlbw8CgB6tFkB4XiUTS4XTR711VlZcSw00X5fGZi/LOmU7Xx6Dbw6PbKvjdW+W0O10IAZnxUUTZLHT2uvzvItZu5cqF2dy+ZvqY7N0Ihin4Y4TL7WFPRTul9Q6au/vxSElabCR5qTEsK0gh5RwUyDPxeCTFNR0crOmkrqOXAbeHxGgbOckxLM1PpiA15pwTlzORUlLW1M2uU21UtvYwMOjBZrWQkxzNBVMTWZKbdM51uMNR29HLB+UtlDd1090/iEWoxOFzsuIpyk82LCCannQ4B/igvJWSuk6au/qxCEFCdAQzM+IozEtmVkbcOV+fBgY9fHCihQNVHdR19NI/6CEhOoLsxGgKc5MozEsm2j5+LqgzOWcEXwhxBXAfYAUeklLeE+j8803wTUxMTMabcATfMLNHCGEFfgdcCcwHPiOEmG/U/UxMTExMAmPkOHc5UC6lPCmlHACeBq428H4mJiYmJgEwUvCnAtVD/l/j/d2HEELcLoTYI4TY09ysb/Q9ExMTE5PTGCn4w83MnDVhIKV8UEpZJKUsSk9PN/BxTExMTCY3Rgp+DTA09U4OoF+YQxMTExOTsDBS8HcDs4QQ04QQduAGYLOB9zMxMTExCYBh28OklINCiK8Cr6KWZf5JSlli1P1MTExMTAJj6H5gKeVLwEtG3sPExMTEJDTOqZ22QohmILwwjqdJA/TNuXbuY5Z54jPZygtmmcMlX0oZ0oqXc0rwR4MQYk+ou80mCmaZJz6TrbxgltlIzv0AIyYmJiYmumAKvomJickkYSIJ/oPj/QDjgFnmic9kKy+YZTaMCePDNzExMTEJzESy8E1MTExMAmAKvomJickk4bwXfCHEFUKIY0KIciHEt8f7eYxGCJErhHhLCFEqhCgRQtw13s80VgghrEKI/UKILeP9LGOBECJJCPGsEOKo932vHO9nMhohxL956/VhIcRTQoio8X4mvRFC/EkI0SSEODzkdylCiNeFEGXeY7IR9z6vBX+SJlkZBL4hpZwHrADumARl9nEXUDreDzGG3Ae8IqWcCyxmgpddCDEVuBMoklIuQIVkuWF8n8oQHgWuOON33wa2SilnAVu9/9ed81rwmYRJVqSU9VLKfd6fu1AicFaegYmGECIH2Ag8NN7PMhYIIRKANcDDAFLKASllx/g+1ZgQAUQLISKAGCZghF0p5btA2xm/vhr4s/fnPwOfMOLe57vgh5RkZaIihCgACoGd4/skY8JvgG8BnvF+kDFiOtAMPOJ1Yz0khIgd74cyEillLfDfQBVQD3RKKV8b36caMzKllPWgjDogw4ibnO+CH1KSlYmIECIOeA74mpTSMd7PYyRCiI8DTVLKveP9LGNIBHAh8HspZSHQg0HD/HMFr9/6amAaMAWIFULcPL5PNbE43wV/UiZZEULYUGL/pJTy+fF+njFgNbBJCFGBcttdKoR4YnwfyXBqgBoppW/09iyqA5jIrANOSSmbpZQu4Hlg1Tg/01jRKITIBvAem4y4yfku+JMuyYoQQqD8uqVSynvH+3nGAinld6SUOVLKAtQ7flNKOaEtPyllA1AthJjj/dVlwJFxfKSxoApYIYSI8dbzy5jgE9VD2Ax81vvzZ4EXjLiJofHwjWaSJllZDdwCHBJCHPD+7j+9uQdMJhb/CjzpNWZOAreN8/MYipRypxDiWWAfajXafiZgmAUhxFPAWiBNCFED/BC4B/ibEOILqI7vWkPubYZWMDExMZkcnO8uHRMTExOTEDEF38TExGSSYAq+iYmJySTBFHwTExOTSYIp+CYmJiaTBFPwTUwC4I1Y+ZXxfg4TEz0wBd/EJDBJgCn4JhMCU/BNTAJzDzBDCHFACPFf4/0wJiajwdx4ZWISAG9E0i3e+OwmJuc1poVvYmJiMkkwBd/ExMRkkmAKvolJYLqA+PF+CBMTPTAF38QkAFLKVuADb1Jtc9LW5LzGnLQ1MTExmSSYFr6JiYnJJMEUfBMTE5NJgin4JiYmJpMEU/BNTExMJgmm4JuYmJhMEkzBNzExMZkkmIJvYmJiMkn4fym6xLorSSCLAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t=np.arange(0,SimulationTime,dt)\n", "\n", "tt1 = time.time() # initial time\n", "PEuler = EulerSystem(PredatorPrey, P0, t, args=(r,a,b,d))\n", "tt2 = time.time() # time after euler\n", "POdeInt = odeint(PredatorPrey, P0, t, args=(r,a,b,d))\n", "tt3 = time.time() # time after odeint\n", "\n", "\n", "print('Euler took ', tt2-tt1, 's to run.', sep='' )\n", "print('Odeint took ', tt3-tt2, 's to run.', sep='' )\n", "\n", "\n", "plt.plot(t, PEuler[:,0],label='Prey')\n", "plt.plot(t, PEuler[:,1],label='Predator')\n", "plt.legend()\n", "plt.title('Predator-Prey dynamics: EulerSystem solver')\n", "plt.xlabel('t')\n", "plt.ylabel('population size')\n", "plt.show()\n", "\n", "plt.plot(t, POdeInt[:,0],label='Prey')\n", "plt.plot(t, POdeInt[:,1],label='Predator')\n", "plt.legend()\n", "plt.title('Predator-Prey dynamics: odeint solver')\n", "plt.xlabel('t')\n", "plt.ylabel('population size')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }