{ "cells": [ { "cell_type": "markdown", "id": "ad83f20b-d955-48dd-b0a8-7c871050a57c", "metadata": {}, "source": [ "# MMMC the 2023 update\n", "\n", "See the [original blog post](http://www.mglerner.com/blog/?p=16) for details and history. Here's the short story: in my Statistical and Thermal Physics class, we want to use Monte Carlo simulations to generate brackets for March Madness. There are at least two obvious ways to go about this:\n", "\n", " 1. Make some function that tells us the chance that team A beats team B, then flip coins for each matchup. That gets you one bracket. Repeat 100,000 times, collect statistics. This is the way Nate Silver's 538.com handles simulations for [basketball](http://fivethirtyeight.com/interactives/march-madness-predictions-2015/#mens), [elections](http://fivethirtyeight.com/interactives/senate-forecast/), etc, and I should probably implement it (note to self/motivated students: it's as easy as just generating 100,000 new brackets at a given temperature).\n", " \n", " 2. Generate one bracket, then do a Monte-Carlo walk through bracket space. This is tougher. We have to figure out how to make a move in bracket space, which is part of the fun of Monte Carlo simulations in general. To see how this is done, check out the code in `Bracket.swap` and `Brackets.simulate`.\n", " \n", " \n", "Please also see the [2015 Version](MMMC2015.ipynb) for more information, including what we did in 2015 to calibrate \"temperature.\"\n", "\n", "As you can tell, we take option 2 above. I've made things a bit nicer from a user standpoint this year; here's a walkthrough. First, load up our standard IPython setup" ] }, { "cell_type": "code", "execution_count": 1, "id": "cc96ebc7-dc61-464e-88b9-5af9fc76a81b", "metadata": {}, "outputs": [], "source": [ "import seaborn as sns\n", "sns.set_style('darkgrid')\n", "import numpy as np\n", "#from bqplot import pyplot as plt\n", "from matplotlib import pyplot as plt\n", "from IPython.display import HTML" ] }, { "cell_type": "code", "execution_count": 2, "id": "f4b00692-207f-418b-b129-17b31e59be9b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N. Carolina (1) \n", "Texas So. (16) N. (1) \n", "Arkansas (8) \n", "Seton Hall (9) Set (9) Set (9) \n", "Minnesota (5) \n", "Middle Tenn. (12) Mid (12) \n", "Butler (4) \n", "Winthrop (13) But (4) Mid (12) Mid (12) \n", "Cincinnati (6) Kan (11) Kan (11) Kan (11) Mid (12)\n", "Kansas St. (11) \n", "UCLA (3) Ken (14) \n", "Kent St. (14) \n", "Dayton (7) Day (7) Day (7) \n", "Wichita St. (10) \n", "Kentucky (2) Ken (2) \n", "N. Kentucky (15) \n", "Total bracket energy: -0.0857\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/4w/ssz2zjl56pxgf3w8b2b78c2c0000gr/T/ipykernel_68822/2338544252.py:1: DeprecationWarning: the imp module is deprecated in favour of importlib and slated for removal in Python 3.12; see the module's documentation for alternative uses\n", " import imp\n" ] } ], "source": [ "import imp\n", "from MarchMadnessMonteCarlo import KenPomeroy\n", "imp.reload(KenPomeroy)\n", "import MarchMadnessMonteCarlo as MMMC\n", "imp.reload(MMMC)\n", "teams = MMMC.Teams['south']\n", "b = MMMC.Bracket(teams=teams,T=0.5)\n", "print (b)" ] }, { "cell_type": "code", "execution_count": null, "id": "16ffe3ca-d9cd-41e7-9750-3fcbafb6b008", "metadata": {}, "outputs": [], "source": [ "sr = MMMC.simulate(1000,['Kentucky','Wisconsin','Villanova','Duke'],0.5)\n", "MMMC.showstats(sr,newfig=True)" ] }, { "cell_type": "code", "execution_count": 12, "id": "94dae5cd-cb1c-4fed-ab35-a13cb9872350", "metadata": {}, "outputs": [], "source": [ "def adjEM_energy_gain(winner, loser):\n", " strength = MMMC.RAS.kenpom['AdjEM']\n", " A,B = strength[winner], strength[loser]\n", " result = -(strength[winner] - strength[loser])\n", " return result\n", "\n", "def def_energy_gain(winner,loser):\n", " strength = MMMC.RAS.kenpom['AdjD']\n", " # Lower numbers are better\n", " A,B = strength[winner], strength[loser]\n", " result = A/B\n", " #result = A-B\n", " return result\n", "\n", "MMMC.set_energy_function(def_energy_gain)" ] }, { "cell_type": "markdown", "id": "1c368fed-257b-43ca-beb5-e424be58270b", "metadata": {}, "source": [ "# What should our temperature be?\n", "\n", "If we had chosen option 1 at the top, we'd just flip coins with a given probability of winning. Here (and this may be a questionable decision), we need to set an overall temperature for our simulation. Intuitively, the higher the temperature, the closer we come to a random outcome. The lower the temperature, the closer we come to a \"best seed always wins\" bracket. If we're going to make sense of temperature, we should pick a reasonable energy function.\n", "\n", "We can use [KenPom](http://www.kenpom.com)'s `AdjEm` (log5 is no longer used. See [here](http://kenpom.com/blog/ratings-methodology-update/) defined as\n", "\n", "```python\n", "def log5_energy_game(winner, loser):\n", " A,B = strength[winner],strength[loser]\n", " # see http://207.56.97.150/articles/playoff2002.htm\n", " win_pct = (A-A*B)/(A+B-2*A*B)\n", " return -win_pct\n", "```\n", "\n", "Conveniently, that's coded up for you in MarchMadnessMonteCarlo.examples.\n", "\n", "Later on, we could make a fancy energy function with, e.g., a weighted average of KenPom, Jeff Sagarin, and the NCAA rankings. " ] }, { "cell_type": "markdown", "id": "72eb97aa-f493-432a-8b24-a86b0a99f157", "metadata": {}, "source": [ "Now, what should our actual temperature be? Historically, we know that an 8 seed vs. a 9 seed should essentially be a tossup. So, as a proxy here, we could just look at the chance of an 8 seed winning over a range of temperatures, and pick the point where it's pretty close to 0.5." ] }, { "cell_type": "code", "execution_count": 18, "id": "5eae2125-de8d-44f2-8dd9-4b8454da6f45", "metadata": {}, "outputs": [], "source": [ "def winpct8(team8,team9,T,numtrials=1000):\n", " results = [MMMC.playgame(team8,team9,T)[0] == team8 for i in range(numtrials)]\n", " return np.average(results)\n", "def plotwins(team8,team9,numtrials=10000):\n", " Ts = np.linspace(0,1,100)\n", " pct = [winpct8(team8,team9,T,numtrials) for T in Ts]\n", " plt.plot(Ts,pct,label='{t1} vs. {t2}'.format(t1=team8,t2=team9))\n", " plt.xlabel('T')\n", " plt.ylabel('winpct')" ] }, { "cell_type": "code", "execution_count": 19, "id": "e92296d5-feff-49b4-8aba-8f8a5e7f1628", "metadata": {}, "outputs": [ { "data": { "image/png": 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K6v3b7XZef/0tpk//mJ9//p4mTWRSUpKx2WysW7cGSZLIzMxg1SpP1c3PP/+Ejh278MEHs3jiiad5663XKSwsYOPG9bz66hTeeut9XC43zZo1p2vX7jzwwHgsFnOZFTNPj8toNHLkyGEmTXqOjz6ay5o1q8jISC9pW2BgII0bN2HLlk3Y7XY2bdrAZZf1YuHCeTz88ERmzfqU6OgG5yzmNnz4CJYsWQjA4sULuOqq4Zw4kUrLlq15550PmT7941JDM5GRUbzzzodcd91N/Pbbz+Tn5/PDD98ya9ZnTJ78Dk6nA4B5834hICCQadM+YvLkt3nnnTcBKCoq4u677+XFFz3nOioqmvffn8mTTz7LW2+9XmaMd955Dx07dqqWMhL1oOfvWT5A48jDXVzo7fQ7fbuGdy/3pVWhkSSeGdgUm9PN+ysOEOlvYoAcVq3HEOoGW7Prz9tL95aAgEDGj5/Aa6+9ULIS1aFDB2nZsnVJTZ62bdtx4MA+ABo1KvtbakJCYwwGAwBared1Xbp0Z9OmDZw4kcrAgYNYv/5fNm/exOjRD/Ljj9+yceP6kpLKeXl5WCw+PProE7z55qsUFhYwcODgUscor2LmmXE1aBCDj48PLpebkJDQs6qBDhs2gkWL5pORkUHPnr3R6XRMmvQc33zzJTNnfkDLlq3Pec4uu6w3s2ZNw2az8scfS5g6dTo6nY5du3awceN6fHx8sNsdJc9v0uRUZdJt27Zw6NBB4uMTSs5X8+aeEjL79iWxdesmdu7cDoDL5SQnJ7u4fXEl+2vbtkPJOc/IqN6OaVku+Z6/ajxZ3O3UuH+Cf2MA9lXDzV5l0WokXhgk066BPy8uVtiRnOuV4wjCufTs2ZuGDWNZuHA+ALGxcezcuR2n04mqqmzevImGDT3JVaM5VYZSkjQlY99lVafs3ftyvvzyMxo3bkKXLt356afvadiwITqdjtjYOG688VY+/HA2L788mYEDB5Geno6i7OL119/izTenMmPG+zidTiRJQlXd5VbMPDuuc5fK7NSpC3v3KixY8BtDh14NwG+//cLEiU/x4Yez2btXYdu2LeW+XqfT0avX5Xz22Rzi4hIICAhk4cL5JYvHeFZDs552bkrHEx3dgIMH92OzWXG5XOzZo5Sc95PrF7z99vv07XsFfn7+Z+3j5FoA+/YlERERWWaMGo0Gt7t6ride8skfw6ma/if56f0JN0WwLzfJe4fVaZgyvCUhPgYe+2UHKbkXZ01v4dL28MMTMBqNADRunEi/flfwwAP3ct99dxEVFUXv3pef9Zq2bduV9MLL0rp1W44cOUSXLl1JTGxCSkoyvXv3AzzDEsuWLWXcuNFMmPAQCQmNCQkJITMzg5Ejb+XRRx/k5ptvR6fT0aJFK2bO/JCcnOwyK2ZWliRJXH55f5xOBzExDUvafN99dzJ+/BiCgoJo0aIVGzb8x6efflTmPoYNG8E333xRcqG3Y8fOrF27ijFj7uGtt14nJqZhuRepg4KCGDVqDGPG3MPEieMxm80AXH31tRw6dJBx40YzZsw9REZGlbmWcHLyMcaPH8Nbb73G449PKvMYDRrEsH9/Et9//3Wlz8+ZLvmqnkHZG9B9dTXZV3+HI+ayksefXv8ExwuP8mnvCz+J57I/o4B7vt7sKQdxQ2uCLQavHg8ungqXNeliabOo6uldos3lE1U9z1TS8y8o9XBj/0SO5B/G5rJ59fAJIT68MbwFR7KLGPWNWAhGEISLwyWf/E+N+ZcuvdzYLxE3bg7m7fd6DF1jg5h+QxtyrE5GfbtFlIEWBKHWXfLJv/yev6fMw7487437n65NtD8f3dwWrQT3f7eFnSnlL0AtCILgbfUn+Z/R84+2NMCkNVf7nb7nkhDiw5xb2hFg1vPQT9vYmya+AQiCUDvqQfI/uYh76USrkTQk+CXUWM//pEh/E9NvaI1Jp2Hcj9s4KBaCEQShFlz6yV/S4Nb7nDXsA54yD/tyk2q8Dk+DADPTbmgDwNgft3IkS1wEFgShZl36yR9Q9b5nDfsAJPgnUuDMJ9WaUsarvCsu2MK069tgd7oZ8/0WMQtIqBYbN66nZ89OJXfYnnTXXTfz6qsvAKcqRVbVe++9TUpK6b+ZOXNmcfPN1zJu3OiS/3bu3F5utcrq0rNnp7NKIUydOoXrrx9Wbqynx3yuSprVbc2aVTz88AM88shYxo8fw++/LwKo1kqdlXHpl3cAVEM5Pf+TF31zk4g0R9V0WCSG+TD9hjaM/WErY77fyswb2xATaK7xOIRLS2xsHH/8sYT+/QcCnjtGi4pOdS7OrBRZWQ8/PKHMx2+++VZGjChdzmLNmlUXdKzzCQgIYPPmjTidTnQ6HS6Xi927d5031nO50PNTnrfeep3PPvsGPz8/CgsLuOuuW+ncuSsHDuxn1arlDBw4yCvHLU/9SP7l9fz9EgDYn5vEZRG9ajosAJqG+zLt+jaM/XErD3y/lU9vbUeor7FWYhGq1+9HF7Ho6Pxq3efgmKEMjBl8zuckJjbhyJHD5OXl4efnx5IlCxk4cHBJjf/hw6/kt9+WsGnThpI7Xa1WK8888yJ6vZ7nnnuKiIgIkpOT6d9/IAcO7GPPHoUePXpy//0PMm7caB5/fBKxsXEX1JYLrcQJnnpD7dp15L//1tG9+2X8++9aOnXqwuLFCwBKYvX39+fVV18gPz8fVVV55pkXAVi5cgXLlv1JTk4Oo0aNoWfP3iXnZ+fO7bzzzptYLBaCgoIwGIw8/fQLzJz5Ibt376SwsJC4uHgmTXqeOXNmkZx8nKysLFJTk3noocfo2rV03bDg4GB++OEbLr+8P/HxCXz11Q8YDAZefPGZaqvUWRn1Y9jH4IOmjJ6/RedDtKWB12r8VJQc4cuH17cmu8jBpAW7cVZT7Q6h/urduy8rVixDVVV27dpBq1ZtznrOgQP7ee65l3n//Zn07NmbZcv+ADxlBp588jnefPNdPv54Jg899CizZ3/G/Pm/nvOY3377dcmQz7vvvnneGKujEifAgAGDSoa5/vhjcZk96LlzP6Fnz97MnPkJo0ePLamjExYWxnvvzWD8+MfOGgJ6663XmTTped5/fybR0TEAFBTk4+fnx9Sp05k58xN27NhGWtoJAPR6A2+//T4PPzyB7747u3LA5MnvYLVaefHFp7n66kF88cWnqKparZU6K6Pe9Pw1ecfK3Hbyom9tax7hx1MDmvD8IoWZqw4yrld8bYckXKCBMYPP20v3lgEDBvH225OJjm5A27bty3xOWFgYU6dOwWy2kJZ2oqT6Z1RUA3x9fdHr9QQHB+PvHwCcv7BaWcM+53OhlTgB2rRpyzvvTCYnJ5ucnBwiIs4ewj18+BBXXTUc8NTrAc+Yvyw3ByAkJBSrtXT9rfT0dBISPEUg27Ztz59//o7RaCIrK4vnn5+ExWKhqKio5MOpadOTVT4jsdtLVw7Izc0lJSWFsWPHM3bseNLSTvD0008gy82xWCyVOWXVpn70/MuZ7QOe2v7HC49R5Kz9KZdDWkRwTZtI5v57hJX7vF/SVbh0NWgQQ1FRET/++O1ZJZRPeuONV5g06XmefvoFQkNPlR0/X5KvThdaiRM88XbrdhlvvTWZXr0uL/M5cXFx7N69E/AsHzl9+vvFry1/v+HhERw44KkAsGPHNgDWrl3FiROpvPjia4we/eAZVT7L35fDYee5554sGXoLCQklJCQEg8FQrZU6K6N+9PzPWMf3dAn+iaio7M/bR8ug8/cyvG1C30R2puTzwmKFz29vT4MAcQFYqJr+/QewZMlCGjWK5fjxs7/5XnnlEEaPvhs/Pz+CgkK8tqTiF198xrx5niEji8XCBx/MKtl2shLn+vX/nlWJMzAwiLCwsJJKnFu3bmbUqPvLPMbAgYMZNeqOcqth3nHHPbz++kssWbIQSZJ48slnS64LlGfChP/j9ddfwmy2oNfrCAsLp3nzlnz22RxGj74bg8FAdHSDCp23kJBQHn30cZ5++gm0Wi1ut4sePXrRpUs30tJOlFTqbNy4CVu3bmbkyPvOu88LdclX9QwMtOBY8BTmbZ+RPmbfWdtTi1K4Zdm1PNxyAlfHXnehoVaLo9lF3PnlJiL9jXxySztMem2lXn+xVLisSRdLm0VVT++qyTb/9NP39Os3gKCgIGbPno5er6+RpHwmUdXzAqgGXySXDdxnXzgKN0UQZAhmV/bOWoisbDGBZl65qhlJaQW8vGSPWAxeEGpBcHAwjz32IGPHjiIpaQ/XXntDbYdUrbwy7CPLsgaYDrQFbMAoRVGSTtt+GzABcAGfKIoywxtxnKQWL+Uo2fNRTYGltkmSRIugVuzM2u7NECqtR3wwD/SMY/o/B2kW4csdnRvWdkiCUK/07XsFffteUdtheI23ev4jAJOiKN2BJ4G3z9j+FnAFcBkwQZblIC/FAXgu+MLZlT1PahHYkqOFR8ixZ3szjEq7u0tD+jcN5cOVB1i0K7W2wxEE4RLireTfE1gMoCjKWs4ec9oKBAAmQAK8Oq6h6suu7HlSiyDPeqG7snd4M4xKkySJ566UadsggOcWKsz45wBuMQQkCEI18NZsH38g57SfXbIs6xRFOTnovh3YABQAPyuKkn2unWm1EoGBVZsLq9VqsAQFe4IyOVHL2E8X3w5o12nZV6QwKHBAlY7jLYHAl/d25cX5O/lk3RGO5NqYcl0bfIzlv3VarabK56uuuljanJoqodXW3KW0mjzWxUK0uWySVLk86a3knwv4nfaz5mTil2W5DXAVEA/kA1/KsnyDoig/lLczl0ut8kyOwEAL+XY9QUB+ZgYOn7L3k+CXyMaUTWTH1v6MkbJM7BNPjL+RqX/v4+ppq3htaHOahvuW+dyLZeZLTbpY2qyqao3NRhGzfeqHirZZVc/Ok2FhfuU823vDPquAIQCyLHcDtp22LQcoAooURXEBJwDvjvmXs6DL6VoEtmR39i5cqsuboVSZJEnc0qEB029oQ4HdxcivN/HD5uNiJpBQri+//Iyrr74Sm+3sdaoXLpzHjBkf1EJU1e/o0SM8/vjDPPbYOB5++AGmT38ft7v8ZLlvXxKbN2+8oGOOGzeaQ4cOlvxss9lKKomWJTn5OKNH3w3A9dcPK/M9qWneSv7/A6yyLK8G3gUelWX5VlmWRyuKcgiYBfwjy/I/eEY2PvNSHMD5L/iCZ9y/yFXIwbwD3gzlgnVsGMjXd3agU6NA3vwziVs+38Bn6w6TnGs9/4uFemXp0sX07z/wrPLOl5pZs6Zx3XU38c47HzJ16nSOHDnMypXLy33+33//ycGD3l+7+2LnlWEfRVHcwJgzHt592vaZwExvHLssp3r+5a+b2yLw5EXf7TT2T6yRuKoqyGLg3WtaMX97Kr9uT2HaPweZ9s9B7u3WiDGXxdV2eEIx6+IFWBfMq9Z9mq4ahmnQVed93saN64mOjmHEiOt46aXnGDJkGOPGjSYwMIi8vDwGDPCUe87KymLSpAnce+8YmjdvweTJr5Cfn0dOTjbDhl3DNddcz7hxo2nSRGb//n0UFubz8stvEBQUzHPPPUlBQQE2m5UHHhhPhw6d+Omn71i+fBlOpxNfX19efXUKycnHee21F9HpdGi1Wp555kXCwsJLYr333jt45ZU3iIqK5q+//mDr1s3063cFH344FZ1Oh5+fH88//woWi0+ZbY2MjGLRonlYLBZatGjFyy9PRqv13Bg5c+aHbNmyEbdb5aabbqN16zYsWjQfnU5P06bNKCjIZ/bsGRiNRvz9A3jqqefYu1fhq68+R6/XkZx8nH79BnDXXfdW+D0qr1rqxaZ+lHco7vlr7OX3/KMtDQgwBLIjaztDG42oociqTiNJDG8dyfDWkRzLKWLGPweZs/YwzSN8ubpTo9oOT6hl8+f/yrBhI2jUKA69Xs+OHZ77WAYMGESfPn1ZuHAeWVmZPPnkY4wfP4GWLVuhKLu54oqB9OnTj/T0NMaNG80113gKtTVv3pKHH57ArFnTWLp0CZdd1ovMzAymTp1OVlYWR44cwu12k5OTw9Sp09FoNDz22Dh27drB3r17kOVmPPTQY2zZsom8vNxSyX/o0KtZvHgBI0fex6JF83jggYdYtGgBffr05ZZb7uCff1aQm5tXbvK/774H+OWXH5k1axr79iXRo0dPHn30CbZv30py8jFmzPgEm83G/feP5IMPZjF48FBCQkJo3rwlN954NdOnf0xYWDjff/8Nc+fOoUePnqSmJvPZZ9/gcDgYMWJQmcn/lVeew2g0AZQafj1ZLTU0NIzPP/+EZcv+KLe+Um2qF8kfrRFVoyu3vg8U3+wV2Iqd2RfXzV4V0SDAzHNXyhzOKuLFxXvo0DgUv5qrzSWUwzToqgr10qtbbm4ua9asIisrkx9//I6Cgnx+/vk7ABo1OnX7/7p1qwkJCUVVPePjISEhfP/91yxfvgyLxadUKeWTFSsjIiLIyMggIaEx1157Iy+88DROp5Prr78ZjUaDXq/nhReexmw2c+LECZxOJ0OHXs1XX81lwoSH8PHx5f77HywV78CBgxg7dhTDho2goKCAhIRE7rhjJJ9//gkPP/wAYWHhtGjRqtz2bty4nhtvvJUbb7yVwsJCpk2bymeffUxwcDCKsptx40YD4HQ6SUlJLnlddnY2FotPyQdRu3btmTVrOj169CQhIRGdTodOpytJ8Gd65pmXStY0sNls3Hab54OyvGqpF5v6MWdKkoore5af/MFz0fdIwWFy7bk1FFj1Meg0vD6sOSoq47/djN1Zv2ZECKf8/vtChg69mnffncY773zA7Nlz+fffdWRnZ6PRnPqTHzRoKM8++zKTJ79CUVER33zzBa1ateG5516mX78rSvVmz6z0uW9fEoWFBUyZ8h5PP/0iU6dOISlpLytW/M1LL73Oo48+UfKh8s8/y2nbtj3vvTeDvn3789VXc0vty8fHF1luzvvvv8OQIZ6LpkuXLmLIkKF88MEs4uMT+O23n8tt74wZ7/Pff2sBT+G4hg0bYTAYiI2No337Tnz44Wzef38m/fpdQYMGDUqqaAYGBlJYWEB6ejrgqfbZsGGj4vZW9eyXXy31YlM/ev6cXM2r/GEfKH2zV9fw7ud87sWoQYCZFwbJTPx1J88u3M1zg5riY6g3b7FQbN68X3n22ZdKfjaZTPTp04/5838567nx8QlceeVg3n//HQYMuJK33nqd339fREBAAFqtFrvdXuYxYmIa8umns1m8eAE6nZ57772fmJiGmM1m7r33DgwGPSEhoaSnp9GyZWteeulZtFotGo2Ghx567Kz9DRs2ggkTxvPUU88B0KxZS1555QUsFgs6nY4nnnia3Nwc3njjFV59tfQyiy+++DpTp05h5sxp6PV6oqMbMHHik5jNFjZt2sDYsaMoKiqkd+++WCw+yHJzpk9/j7i4eJ544mmefvpxNBoJPz9/Jk16gf37L2x9j5qqlnqh6kVVz+zsQoK+6Y8rMJ7cwR+X+9wiZyEj/hjMkJhhPNxqYlXDrXU/70jljSUKMYFmXruqOXJE2fcDXEoulnn+oqqnd4k2l09U9SyHqvc5b8/frLPQL2oAS44tJM9R94Z+Trrnsnhm3tgWq8PFyG82MXPVQY7lFJ3/hYIg1Bv1J/mfY0GX010ffxNWl5UFh3+rgai8p31MAF/d2ZGeCSHMWXuYER//x6hvNvPdxmMczRYfBIJQ39Wf5F+Bnj9AY/8mtA/pyP8O/YizjPr/dUmgWc+bw1sw774uPNgzjjybk7eW7eOaOf9xw6f/MXPVQfJtdbuNF6O6MJQqXFqq8jtXf5J/BXv+ANfH3Uya9QTLU/7yclQ1I9LfxN1dG/Hd3Z346Z7OTOjbmEg/E3PWHubaOf/x85bjOGthDdFLkU5noKAgV3wACDVGVVUKCnLR6QyVel29mQpyrkXcz9Q1vDsxPo348cB39IsaUKMLWntboyAzjYIacHOHBuxKzePdZft4/Y8kftqSzKtDmxMXXPuVMeuyoKAwsrLSyM/P9vqxJEmqdx8yos1l0+kMBAVVblppPUr+vp7Cbqp63km8GknDdXE38N6Ot9mRtY1WwW1qKMqa1TzCj1k3teWvvelM/iOJO7/cyKQBTRnUPPz8LxbKpNXqCA2NqpFjXSwznGqSaHP1qTfDPm6DL5LqAlfFCqANbDAEP70fPxz41suR1S5JkujfNIwv7+iAHO7Lswt389JiRRSKE4RLXL1J/iWVPStw0RfArDMztOEIVqWu4HjhMW+GdlGI8DMy48a23N2lIQt3pjLi4395at5OthzLEauHCcIlqP4k/5OVPSt40Rfgmrjr0Ugafj74vbfCuqjoNBIP9ornl1FduL1TDGsPZTHq2y0Mnb2OyX/s5d9DWfVuvFUQLlX1L/lXsOcPEGoKo2/0FSw8Mp98R/nloC81kf4mHuqdwILR3XhhkEyrKH8W7EjlwR+38fayfbjEzCBBqPPqUfL3B0Bjy67U626Ivxmrq4j5h3/1QlQXN4tBy1UtI3hzeAuWju3OLR0a8N2m40yavwubKBwnCHVavZnt4wpMAECbtRdHzGUVfl2if1Pah3Tk50M/cH38zeg09eaUlWLSa3msb2Mi/Y28+/d+Tny/hTbR/rhVkICWkX50jQsi0HzxLVohCMLZ6k0mc/tE4jYGoMvYff4nn+GG+FuYtH4ifyf/yRUNrvRCdHXHrR1jCPM1MuXPJPanF6LRgNOl8s3GY2gkaBHpR5tof5pF+NI8wo/YIPMldZ+EIFwq6k3yR5JwhjRHl7Gr0i/tEtaNWN94vt73Of2iB6CR6s1oWZkGyGEMkE/dUOJyq+xKzWPNgSzWHsripy3JJcNCDQNNDG4RweDm4cQEmmsrZEEQzlB/kj/gCmmGcfcPoLqhEglcI2m4I/FuXtn8PCtSlnF5VH8vRln3aDUSraL8aRXlz309YnG6VQ5kFLAtOY+lu0/w0epDzF59iNggc8k3gv5NQ4n0L3uFJEEQvK9edWGdIc3ROArQ5B2t9Gv7RPUj1jeOuXs/wa2Ki53notNINAnz5do2Ucy4sS2/3deFh3rFExdsYdPRHKYu38/tX2xk09Gc2g5VEOqtepb8mwGgS6/80I9W0nJH4kgO5R9gefKlUfCtpkT6m7izS0PeGtGSBfd34/u7OxFg1vPgj1tZuDO1tsMThHqpfiX/4OLkn1n5i75wsvcfz+dJn+JSXdUZWr0SH2Lhk1va0Tban+cXKdz11SZu+3wD133yH4/+bzsbjmSXuplMVVVxc5kgVLN6NeaPwQeXfyzaKvT8wdP7vzNxJC9vfo7lyX/RL3pANQdYfwSY9bx/XWtm/HOQ3SfyMen0GHUaNh7NYcz3W2kV5UeHmED2pOWzOzUfVVUZ1iqS69pGiQvHglAN6lfyxzP0U9WeP3h6/1/t+5x3t08hytKA5oEtqjG6+kWv1TC+T0Kpx6wOF/N3pPLF+qN8tf4ICaE+9G4cTL7NxTcbjvLV+qO0iwkgLthMtL+J+BALXWODaqkFglB31cPk3xzDwaXgLAJd5XuQGknDK53eYMLah3ji34d5o/O7tAhq5YVI6yeTXsv17aK5tm0ULreKXntqZPJEno3/bU1m1YFM/tqTTo7VswqZj0HLoFaR9IoNIthHj1mnRaeVSM+3k5pnI9fmZEDTMAIt4gY0QThJqgtjqQ6HS61qPesza2EbkuYTsGQMWTcsxBle9Tr9J4pSmbDuIbLsmTzT7iW6hHW7aOb/15ea5wV2J9uT81i86wTLktIpsJV/HSbQrOexvgkMahZ+ydx0Vl/e59OJNldOWJjfBqBTWdvqXfLXZu8n+Kve5PZ7B1vzGy8orjRrGhPWPcTRgsNEmCPpHz2QIQ2HEW1pcEH7vVD18Q/EaDGyWkkl3+bC6nBhd7kJ9TUQ6WfC6nQx5c8ktiXn0S0uiPt7xNIy0q/OfwjUx/dZtLlyzpX8692wj8s/FlVnQpexC9sF7ivMFMasyz7ln9Tl/Hn8d77d/xXzD//CR72+IMxUuSXVhAtjNmjp2DCw3O0f3dyOn7YcZ/o/Bxn59WYah1oY3iqSNtH+RPoZCfYxoKnjHwaCUBn1rucPEPjDVagGf3Ku/qY6witxMO8AY1ffS7PAFkzp8h5aSVut+68o0TsqX4Hdye+70/hlWwo7U06V6dZrPXcpX54YQt8moUTVgbuPxftcP4iefzVyBjfDeOjPat9vnF88D7V4jCnbXuO7fV9xa+Kd1X4M4cL4GHRc0yaKa9pEcSizkMNZRaTk2TiWbWXtoUze/Xs/7/69nwCTjgCzngCTnih/I/EhFhJCfZDDfYj2N5UMGaXkWlm06wR7TuTjVsGtqkQHmBjdIxYfQ7388xLqiHr52+kKbY5m93dIhWmoluodnhkUcxXr09fxyd6PaBfSQcwEuojFBluIDbac9kgCR7KKWLk/g6PZVrKLHGQXOdienMvvSlrJs0J9DLRr4E+ezcm/h7JRgUZBZrQaCQlYsS+Df/Zn8sawFiSGeZYPtTpcbD6Ww8ajOWw6mkNavp1JA5rQRUxTFWqJV5K/LMsaYDrQFrABoxRFSTpte2fgHTyl4FOA2xVFqbEVw0vu9E3bjiO2b7XuW5IkHm31BDuzdzBuzWiMGiMmnZkYn4ZMbP0Usb5x1Xo8oXo1DDJza8eYsx4vtLs4kFnIzpQ8thzLYevxXLQaiVHdGzGkRUSpG882HMnm6QW7ufvrTdzQLpqktAI2Hs3G7lLRStA80g+tRuKxX3Yw5eoWdI8LrskmCgLgpTF/WZavBYYrinK3LMvdgKcURbm6eJsEbAKuVxQlSZblUcBKRVGU8vZX3WP+OAoJ+bQ9tsZDye//dpX2ez7HCo7yx/ElFDmLKHIVsTJlGVaXjYmtn/T6ncFiXLT2ZRTYeWbhbtYfziY+2EL3+CC6xQXRNjoAi0FLdqGDB3/cyoHMQiYPa0FCiIUDGYUk51ppEuZL6yg/dNrypw473Sq7MouYt+koUf4mbu7QALPec40pLd/GrNWH8DPqGN87vs7PajrdxfY+14Q6NdVTluV3gH8VRfm2+OdjiqI0KP63jOdbwS6gNbBAUZQ3z7U/t9utulxVi1Or1eBynV2FUzv/IaSdv+B8ZBcUr+/rTScKU3ly1f+xOW0z1yZex8gW99DA1ztTQstr86XsYmyzqqrkWp0ElLO6WXahnXs+X8+2Y7lnbfMxaOkcF0zX+GA6xQbRMtqfjAI7Gw5l8e/BTH7fmUp6vh2LQUuh3UWYr5FxfRuTVehg1or9WJ0uVBUmDW7GyB5xXm5pzbkY32dvu5A26/XaGk/+HwM/KYqyqPjnw0CCoihOWZYvA/4AOgJ7gfnAm4qilHsFttp7/oAu+T+Cfr6mWub7V5TT7eRjZSY/HPDMMuoQ2omhDa+mZ2Sfap0ZJHpHdUee1ckv25LxN+mIC7YQ4WdkV2o+6w5l8e+hLI5ke0ZD9VoJR3EHyKzX0C0umOs6xtAuwpfdqXl8sOIAW457PkT6NgllfO943lu+n5X7Mnj/utalri3kFDnYejyXLcdzybU66N80jE4NA9FqLv5vCHX1fb4QdbHnv1ZRlO+Lfz6qKEpM8b+bAT8oitK6+OdHAf25ev/eSP6oKkFf98FtCSPnmp+qtO+qSi1KYcnRhSw8Mo8T1lQS/Bpzb9MxdAvvUS1f0cUfyKUjPd/GpmO5bE/OJdzXSPuYAJqG+6LTSKXarKoq649kY9RpaRPtD3imtY78ejOZBXYmD2vB9uRcliVllExx1WokjFoNhQ4X4b4GrpDDiA0yE+FvItzXgMWgxaLXYtZrMelLd05sTjdp+TYMWg1+Jh0mneas312rw8WetAIaBJgI8TFUy/m4VN/nc6lrUz1XAcOA74vH/Ledtm0/4CvLcmLxReBewBwvxVE+ScLa7EZ8105Gk3MQd0BcjR06whzJnU3u4bbEu1iRvIxP9szm6Q2PIwc0p5FvLBatBX9DAIMbDiXSHFVjcQkXn1Bf41nLZpZFkiQ6Nyo9c8jHoOOtq1ty11cbeeCHrYBnjeX7e8TSPiag5C7n5UnpLNiZynebjuNyl90ZNOk0BFn0+Bp1ZBTYySx0lNqu00iE+hgI9zMS6mPgeI6VvWn5uFQwaCVGtI7izi4NifAzXsDZKJvd6caguzhKq9Ql3ur5n5zt0wbPjJ6RQAfAV1GU2bIs9wMmF29brSjKw+fan1d6/oAmP5ngz7tS2PEhCrs+XqX9Vwen28nCI/NYcOQ38hy5FDoLyXfkodXouCH+Zm5JuAMfvU+F9yd6R/VDRdu8PTmXXan59EoIPufSmS63SnqBnZRcK+kFdgrtLoocbgrszpJpr7lWJyEWA5H+RsL9jDhdbvJsLnKtDtIL7JzIs3Ei306En5HWUX7I4b6sPpDF/J2pSMA9XRsxqnujUt8SVu3PRDmRT/f4IJqF+57z2+/pbT6RZ+O95fv5c08at3duyOjusSUfAk63yvrDWezPKORotpW0fBvXt42ma1zpD8gTeTb8TbqzvtlcTOrUsE9181byBwiYdzvazD1k3rEGNBfPL0Ba0Qk+3jOTpccWE2QIYmyLh+kXNaDUH8bh/ENEmCMxakv3pkQirB/qUpuTc61MW3mAJbvTuLFdNBP6NUYCvlx/lPdXHCh5XrivgT6JoVzVMoIWEWd/EAQGWkg6msWiXSf4eM1hnG43HRoGsvZgFomhPkzo25itx3P5actxTuTbAc/Fc6NOQ06Rg8f6JnJj+2icLjef/nuEOWsP0zDQxORhLWgcWvEOVmWpqsqqA5n8sSedK5uF0S02qMJDvCL5eyn5G/fOw//3B8gdOANbk2FVDdFrdmfv5P0d77A7Zyc9wnvySKvHOVpwhK+S5rIh4z+aB7Zkcue38dP7l7ymLiWF6iLafPFTVZX3lh/gqw1HGdoyAh+Dlu82HeeKpmE8cnkC/x3OYsW+TFYfyMTmdJMQYqFHfDAOl5sCu4uMAjt70wtIL07qvRKCeaxvY2ICzfyzP4NXft9LRoFnW5dGgdzQLpp2DQIIMOsodLh4dsFuVu7P5OpWkexJy2dXaj6XJ4aw9XguhXYXTw1oQv+mYexNy2dnSj6Hswo5nmMlJc9GhJ+R0T1iaR7hV9IeJTWflDwrnRoFnvNu7t2peby34gDrD2ej00g43SqdGgXyUK94WkT6lfu6k0Ty91Lyx2Uj8KcR6DL3kDP442q/6as6uFQXPx/4njl7ZuFW3ThVJ0GGYPpGX8G8w/+jkU8cb3Z5l0BDEOvSVvPdwS9xuVR6R/alT2RfwszhFT5WSlEyKYXJtA1uX6fmh9e1RFgd6mKbVVXl4zWHmb3mEAC3dmzAw30SShXVy7M6WaqcYN6OVHal5mPWa7DotQSa9bSKCSQ+0ETrKD9aRvmX2nd2kYM/96TRISaQ+BALZ3K5VT5ceYAv1x8lyKznySsS6dc0jPR8G5MW7GbT0Ry0EpycVe5j0BIdYCLCz8i247nkWJ1c2SyMllH+zN+ewp60AsBzTaNrbBCto/05kWfjeK7Vs46E1Umu1YnN6SbApOO+7rEMbx3Jb9tS+HjtYbKLHMjhvvRJDKFnQrDnRsKMQg5mFpJRYCeryEG+zcWkIc1pEVK11esuKPnLstxJUZT1p/3cR1GU5VWKpIq8mvwByZpFwK+3oMvcQ+6Qj7HH9qvSsbztaMERvtv/FY39mjC44VCMWiP/pa3juQ1PEm6OwE/vz87s7cT4xmCUzOzL2wuAHNCcTqFd6BTahWhLA7LtWWTbs3CpLgINQQQZg0kpTObngz+wKnUFbty0DmrLwy0nkuDfuJZbXTF1MRFeqLrc5nnbU1CB4a0iK/W66mjz5qM5xAVbSi3u43SrfLfxGNlFDlpE+tEi0o9wX0NJByjf5uSL/47w1YZj2JxumoX7MqxVJAkhFlbsy2DZ3nRS8mz4GXVE+RuJ9DcRaNYRYNIT5mdkWMsIfI2nvh3k25z8si2FZXvT2XY8l9OzsFmvIczXSJBZT7CPgQkDZSJMVRuSrlLyl2W5F9ACeBRPKQYALfCgoig1WrDG28kfij8AfrsVXYZCYfsx2JpcjStErtIxa9rWzM1MWj8Ri86HOxNHclOrGyjIdXAk/zDLU/5iXdoadmXvxH2eRef99f5c1fBqws3hfLrnY/Kd+VwXdyOj5DHoNRf3Klh1ORFWlWhzzcsstJNb5CTujG8WqqpS6HBVqZhfeoGd9YezCTSfutfj9G/dNT7sI8tyK+A64G7gUzwzc9zABkVRFlYpkiqqieQPng8Avz8fxXDoLyTVjTNYprDTw9iaDK/SsWtSrj0Xk9aEQWsos835jny2ZG4ky5ZJoCGIQEMQWo2WLFsWWfZMjBojvSIvL7l4nGPP4WNlBguO/Ebb4Pa82OF1/A3+ZR260k7+zlXnsFJtJ4XaINpcP9TamL8sy9FAuKIom2VZHoGnHIPjnC+qZjWV/E+SCtMw7luAaec36NN3UNT8JvJ7vQx6z6e9VJQJGh2qsXqSYXWrzj+QP44tYcq214gwR/F6p7do4HN20bPyuFV3qaUtXaqL348u4pM9s3G4HbQObkOroLZcHtWPCHPlvv6fSSSF+kG0uXIu9Cav9/GUY9gMNAVuBG6tUiR1hGoJw9r6bqwtb8fy7ztYNnyAPmUDjshO6JP/Q5e9DxUJV0hzHNGdsSUMwRFzWW2H7RVXNLiScHMEz214ivv+uYtIcyQ+el/89QG0CmpNx9AuJPo3QSNpcKkusm1Z/Ju2ln9SV7A+/V+CDEG0DWmPHNCMJUcXsTdXoUVgKxr5xrItcwurUlfy7f4vmdJlKon+Tc86vlt1s+bEPxwvPE6viD5EWs5905vdZWfBkd9YlbqCy6P6MyjmKnSaelm5XBDOqSI9/zWKonQ/7edliqLU6JSYmu75n0l/5B/8/nwEyVmEI7ITjuguSC47+uP/ok/ZgOQsxB7Ti4LuT13QovDVxRu9o2MFR/lu/1dk27MpcOaTacvgUP5BAHx0nvnRBc6CkueHmyLoHn4ZWfYstmVuJsueRbgpgvuaPVDqfoWDeQd48r/HKHQW8maXd2kW2ALw3Pj2V/JSvtn3JYfyT80Dbx3Uls5hXXGrbqwuKyoqIcZQ4kJiSMlO48ukuZywphJiDCXDlk6UOZpbGt9OkDEEm8uKS3XRObQrgcay6+inFCUz6b+JBBgCubvJKNqGtK/Uefo3bS17cnYzOGYoIabQUttcqotjBUdIyt1LobOQgQ0GY9BWvezBxdILTi48zns73mJIzDB6R11YanCpLlxuJwZt2XcCXyxtrkm1OeyzBrhLUZQ9siw3Bj5VFKV3lSKpotpO/gCoxVX1pDNuI3fZMG//Asv699BYs7A37I0jvC3O0Ja4fSLR2HKQ7LmoWgOOhr1RDeef13uhauoPJNOWwYb0/9iRtQ2dRo+vzhc/vR9tgtuR6N+0JMGrqkpy0XFCjaFl/lGnFCYzYd1D5DiyubrRdezJ2c2O7O1YXUUk+DXmlsZ30CygBcuT/2Lp8cUlHzp6jSdxOtz2kn3JAc24p+n9dArtwrq0NXy252P25O4udTyT1sSwRtdwY/wtpRL0sYKjTFj3EIXOQoxaIxm2dNqHdOSK6CuJMEcSbo5Ap9GRa88hx56NWeeDHNAMvUZPgaOA6bveY9HR+QAYNAaGNhpB36j+7Mzazn/p69ietRWr69SyFQMbDOb/2jxTcp5Si1L4dM9HBBmDaR3UllZBbdBptBQ4CrC6rDTwiSk1jFbV9zndmsa2zC1szdpCli2TlkGtaRfcngT/xEoXGNydvZOn1z9Olj0LvUbPG53fpV1Ih0rHdLTgCIuOzOf3Y4sAeKfrhzT0bXTW80Tyr5wLTf5dgVlAOHAcGHP61M+acFEk//OQbLmYN8/CeGAJ2qwkJLfzrOeoGgP2hj1xRnZCk3cUbdY+NNZMHJEdcTTsjT2mJ6r5whf2qIt/IGnWNB5fN54jBYdJ8I2nvVOihyGCtj3eRNKcSniqqmJ1WTFoDWglLaqqkufIw6rPJSMnl2YBzUtdSFZVlaTcPaioGLUmrM4ifj70A38eX4pO0tI5rCudQrsQn3Ocl1MX4UBlSpepNPKNY97hX/hm3+dk2bPKjdukNdMmuC0H8w6Qbk3jlsa3c0WDQXy3/yt+P7a4ZIZVrG8c7UM6IQc0I9G/CStS/uaLpE8ZLY/l5sa3c7TgCBPXjSfHno1LdeFUz/796RjamRc7vIal+JtWYKCF4+lpbMrYyPr0f9mUvh5J0tA6qA2tg9siIbEpYwObMjaQUpRcRuwmAg1BJdt8dX60CmpNq+A2NA9sia/OF6PWhI/Oh2BjSKnz6lbdrEpdyetbXiTIEMzT7V5gyrbXSLem8373mcT7JZBhTWdlynLkwOY0L/5GdzqX6mJN6j/8fOgHNmdsRCNp6RLWjd3ZO9Bp9LzbddpZ15iq8rt9MO8AK1KWkWXPwuayYnPZCDaG0Mg3lhifhqiqSpY9kxx7Nu1DOhLv56XpzaqKNnsfrsDGUHwuXaqLw/kH2ZebhFt1o9PoMGgMNA1oRrg5Aqjlm7xkWQ4DGgN7FEXJrFIUF6AuJP9SXDZ0mXs9y0Qa/VGNgUhFGRj3L8a4fxHavCO4TcG4ghrjNvijT/4Pjd1TjtflF4MzpDnO0BY4GvbGEdnJU3ZCVdGd2Iz+6CrsjfriCmtZ7uHLa7Nkz0ey5eD2jfJ8g1FVdOk7MCbNR1OYii3+SuyxfaGcr9ze5rblwLbPCNv8ERpbNgD5lz1HUbvRZz1XsuejS9uKZMvDHtefwGD/Sr3PxwqO8tPB71l7YlVJ8gtxqbzd4XUaNbi85HlOt5PUohROWFM5UZSKW3XjbwggQB9Apj3Tk1zT12PQGnmk5cRSy3YeKzjK7pydtApqc9YFbbfq5pXNz7M8+S9GN3uQ7/d/jRs3b3Z+l0a+cezO3smu7B1IkgYfnQ859mw+3fsxjf0Seb3zW/jofFmU8j8+2f4R+a4iTFoTbYM9Q1Tbs7ZR4MwHwE/vR9vgDsT7JeBZZBJ89Z4kn+jfFJ1GR1rRCbZkbmJL5ia2ZW7hcMGhs86Xj86XBL/GRFsacLzwGPvyPENXckBzXu00hWBjMClFyTy0+n60kpbG/k1Yl7YGt+pCJ+mY2OYpBjYYDIDD7WD+4V/54cA3pBQlE26KYHijaxgYM5hQUxj7cpOYsG4cJq2ZN7tMpcCZj5K9m2x7Fp1jOpJgkDFojWxK38DiowtYn/4vZp2ZAH0gAYYAgo0hhJrCMGvNrExdjpKzCw0afPV+mLQm9Bo9Gbb0Ut/CTjJpzbzccTIdQzuf8/fH7rKz9PhikguP0z96IPF+CWc9R1VV/kpeyuIjC4i2NKBl1mGa7l1EUuKV7ApNJCl3L3tzlTLjAGjs14Ru4T0Y3f5eXIVVu251oT3/scAjwHagJfCyoihfVimSKqpzyf9cVBXJkV96+MftRHdiC/pja9Bl7EKXsdvz7UF14TYF42jQDV3qFrT5xzy70Ogo7PAghZ3Gl07Uqhtj0nz8Nn2Ayw3WJldjazICyZ6LedtcTHt+RnIWoerMOIMSkex56HIOokpaVIMvGlsOboM/tsShFLUfgyvQ8wst2fOx/PcuJuUn3JZwnIEJuIKbYG15O26fiEo1X7LnY1n3Jrrs/ahaI6rWgKYoE23OfrT5niRsb3Q5BV2fwLLxQwz7F5Mz9HMcjS4Hlx3zts8w7fzGc36Kb41xBiXCFS+RFdarpEdV4bfDaSfvxwFskWx0KbITpUrkXPNDSdtPpylI8bxdPpWfmaRL2Yjh4B9IqhtV0niqyqLyQM5ydjmzCNP68G7cPTQKaIrkKEBjzUKy5eGI7oIr2HMhfN2JNby46RkC9X6ojgJSXQX0KSzizpxcWga2wt3sRuyx/XBYwjiYfwC36q7SUE62LYt9eUkUOQuxuWzkOfI4mL+f/Xn7OFZwlChLNE0CZJr6y/SNvgKT9lSxuKTcPTy69kFMWhODgrrQH18+LNjCxrw93Jl4Dwl+jflImcGxwqO0DmrLdfE3cVl4T7RnXJTfk6Mwcd148p15Z8WnkbT46/3Itmfjp/ejR3gvVFRy7Nlk27PJsKWTacvErbpo7NeEK2OG0D96AEHGU9+q3aqbNOsJjmbvRaPVEmSOQitpeWHjJI4WHuHZdi/RM7IPjtxDJK17hSzsaFrehY8phB3Z2/npwHdk2NKRkFBRaR3UlitjhtAisBUNfRuRZctk6vYprD7xD1HmaPJsGeS7bSXHt0h64gObIQc0o2lAM5r4yxg0BhxuB7bsvWwqOsLazA1sz9rGs12epU/IwEq9hyddaPLfBHRXFMUqy7IFWK4oyrk/FqvZJZX8K0iy5WI4vBzDgSXoj6/FGdYKW+OrcER1wWf9VEy7f8AZ1BRb4lWoBj9UraFkaqoa3gKnxow+ZUPJ/lStEWvTETjD26LN2ocuKwkkCVvCYGwJg1ENfuiP/oNp768Y980Hlx1b4jAc0V2x/Pce2sJUbAmDwO1Em70fbc4hVJ2Jwo4PUdR2FJqCVEzKjxj3LwK3G9Xoh9vgj6NhL6zy9ajmYHQntuL3+1i0uYdxhrZCcjvAZUc1+uMKbIwrMB57gx44o4p/vewFBP08Ak3+cfIvex7LpunospKwR3fFEdMTZ1gbcBbhU/xh4ojshL1hb5zhbXEGNUZbkII2+yCa3ENo84+jyU9GsuVQ1H4MtqbXAGDePBvfVS+Rc9VnuPwaEvjLDag6I3mXv4krtAVuSzi69B2YN83AmDQfULHH9sPa8g6cQYnoU9ajT/4PyZ7vGb6L7ooruCmS0wqOQvQntmDeNBND8rripK8F1Y1UPByUptXwcUAAd+TmEuMs+yY8R3g7rPJ1aIrS2XvsLx7RZxLpdPKIJoKWTW5HsmZj2v0DuizPHd2qzoQrIA5HZCeKWo88dbOi24X++Fr0yf+izTmENvcwOK04is+nI7orajmr2knWbIx7f8V44HdwFvdUJQlXYGOcEZ5rXJr8ZPSpmylK3YDfia0YHJ4JAA7g+dgWzNN4vo3E+cZzf7NxdAnr5hlKchXPHNeediOhqnL44HxWpSynUUQ3EqN64q8P4LBzL/8cWkNy4XF6RvamR3jPkutI2oxdGPctwh7TE1tkBwpdhaVqXpU+qUVYNs/EsnEauOy4AhNxhrYgIyiex/LWoViP01Ifwi77CRxldCg6hHTitsgraeLWsrBoH/NOLOdY4VHA8+1BQsKlOrm36f3c4N+O4J9HcCg4gV2X/R/ypjnEH/ibgoHTSt9D5CzCd9XLmLd/jtvgh7XVHeS2upuQhom1Nua/GBhavAqXBCxSFGVQlSKpovqY/M/HcOgvfFc8izb31Fd0l38sBV0mYO5yK9k5VjQ5hzAmzQOdCat8Haqp7BkuZ5IK07Bsno1521wkZyGO8Lbk934FZ8SpmS+anIP4rnoZ44EluE1BaKxZqEg4GnRHNQYg2fPRFJ5Al6mUXOswHFmJ2xJK3oAPcER3q1AsmtzDBP1wFRprFi7/WPJ7vYg97orST3I5CD7wI+q/s0t9IzhJ1ehwWyJw+0YhOfLRZeymsMODFLW+m6Cv++KI7kru0LkAaNN3EvjrTWisnnF+t8EPjT0Pt94Xa8vbULVGTLu+RVt4omT/boMfqt6CtiC1zDa4fBtQ1O4+rM1vLp1cVTe4XeB2oCnKQFOY5jmPBl/cpmBUrQHjgd8x7frWcx4lDc7wdhQ27IWz8VD8Ezue+t1WVXRpW9Gd2II2+wDa7P0Yjv6D5LJhb9gbV2A8hn2LSuJ2+Ubh8o8FSeOZseayFT8ejSswAZdfDBTf1a0pSvfc+Oiy4QxqitviuUguuR1oM/egseWUOtfOkOY4IzvgiOyEM6wNhgNLMG+czk8GJ1pTMENUX7R6PySXFU1+MprCNNAZcUR1xR7TA6D4wyzp1Dn0b4QzrBV6VwHuvFRw2XFEdsYRcxlu3yjMWz7GeGBJyfOdIS0oanUHzpDmqKYg3MYANPZcNIUn0GYlYVn/Adr8Y9gaX4UzKBFd+k506TvQ5h+nQJJ4LjSYI3o9HYyRtGp+Lw2cTqTVr5CvAd+YvrRK3ooua8+p+DR69oYksC28KTss/uTpTdwV3p/Yolx817wOziKyb1zo+dboLCLgt9vRp27EljAYR/H747viac/vZuuRaIrSMe5bABo9rhu+JCukZMJlpVxo8v8diAZWA+0BPbATQFGUGpnvL5L/ObhdSI58JHsBbp9w0Oiqrc1SUSa6rD04orqcPcupmP7ISszb5+IMa4tVvg63X3Sp7dqM3Zh2fo1p7zwcUZ3I6/tmhT+ETtKlbUOXsgFr85tBV3Y9+pNtluz5nj/i7AOeBBcQh9uvAZwcVnDZ8V3xLOadX+E2BiI5Csm85U/cgfGn2m3LQZe2HW2mgi4rCZd/I6wtbj11U5/LgeHQH2gK03FEdsQVLIOkQZN3FH3yOrQ5h1F1ZlSDD26fSOyN+pbu1VZW8YVCtzkU1RR4VpvLIxVlYtr5NeZtn6KxZmOP6481cbindpX+tPIEziL0yRvQp27wfKvL3o8m7xhS8Qw3VWvEFj8QW/ObcIadUdlFdaPNOYg2fSdu3yicoS3LfI8kex6mbXPRZexGchQgOfJBY8DlG+X5ULZmYzi2Gl2mAoAjqgvWZjfiCG+DPvlfDEdWos1KQuMbgkMfBKqKPnldyQeP2xhAUZt7sLa4BcOhZZi3zUWXsbPcc+MMaUF+rxdxNCidVCVbLtqsvegy9+AKjC/VSdHkHsZ/0X3oMhXPB1X8AJzBMtq8I2hzDqJL3YI+ed1Zkz3cel9yhn+FM7LjacfJwWf1KxgO/oW20NNpcJtDyO0/taS4pDZ7P8bdP2DocBPZhrhy23IuF5r8+5S3raYKvInkXzmizeehqpi2z8V35fPFC/lM9G5wXlLhNrtdoDpr7UJ+ZUiFaUhOG27/su8kL9Vmt8vzQZ+VhD3uitJ33Ksq2kwFTUEKmqJMJFuOZyjSEo7bEo4rqEnV1u9QVXBZQVd2lU3Jlov+yAp0mQqugHicwTKuoIRyn++Jcze6E1uxN+qL6nN2Bd7avMN3IzAYKPk4VxTl8ypFIggXA0nC2vpubE2uRjUG1nY03qfR4qnJePFTLWFUuMi8RoszvE3ZN1ZKEq6QZrhCmlVneJ4JBeUlckA1+mNPHIqdoRXanQrY8kwUpoWjj/WhJhejrEjy/xXP/P4jxT9f/AsACEIFVHb4SfAOd042qs2GNrxyM8eqQnU6sf78A9omTTG071ju82x//4VksWDocu5rU6qqVrpAoep0Yl/9D7bfF+HYvBE1xzN0pWvbnoC330cy1sw3tIokf42iKLd7PRJBEC5Z7vR0nPv2om3YCG10g5LHnfuSyJ0wHtVuJ/DjuaW2VTe1sJDc55/GsXYVAPou3fC5/0F0TU+VbldtNvLfexvbvF9AkvB5ZCLma28ovR9VxfHvWgo/moHz0EGMPXtjHDAIffEHhWq3gd0BLieq2w12O+6MdNxpaTj3J2FbtAB32gk0IaEYevRC37Ydqt1OwTtvkvfSs/i99DqS1vvf1CqS/LcW3+W7meJev6Io9nO+QhCEi5qqqhR9/QX2f5bjO/EpdI0TK/d6hwPXoQNogoKRgkPK7P2qRUXkv/cW9jWrUTMzPA/q9ZhvuwvL7Xfh3KuQ+/ijSCYTqCq5Tz1O4Mw5SObSwyqqqmJbugTHxvXoBvRDbd0JyeAp7aG6XKhFRWh8S09RdefnY/3hG6TAIPRt2yP5+5P7fxNw7duLz2NPgM1G4Refkn3vHehatUbfviO6Zi0o+vwTnMpuzLfdhevQAQrenYI7Ix3LqDG4007g3LGNop9/xLl5I5rIKIx9r8C+agW2P36v2ImTJM+HzqOPY+h+GZLutBTsclHw3tsUvPsm5htvxXnoIO7k4/gMHwKmgIq/ORVUkQu+W4DTJ8uqiqKcfQeMF4kLvpUj2lw/BPjoydiVhDYs/KyEeS6q203Bh1Ox/vAtGAwgSfhO+D9Mg4eiqiqu/ftwbN2M68hhXEeP4E5PQ+MfgCYsDMnXD+deBeeuXWD3TA+V/P3RxidgGjwU45VDkHQ63FmZ5P7fBJzKLoz9B6Jr1hxtQmNsC+dhW7oETYMY3BnpaELDCHjnA1yHD5H7xKMYLu+H3wuvlnyYOJVd5E99G+f2rZ5Y7XYkXz/07TvgSknBdegAOByY77oXy933Imm1uLMyyZnwMK69yqlGSxKYTPi/+BqG7p4KvO78fKw/fYd9zSqcu3eBy4Xk44PvMy9i7Nkb1ekk/+03sM3/FcnfHzXXcxe+FByM5c57MA0bgWQwoDocOP5di2PXDiS9HgxGz/+1WiStDvQ6NCGhaELD0IRHnPVBdbqCWdMp+vKzUo9FvvMuzs5Vqxos1vCtZ0lBtLlmOXbtxJ2ZgfGyXpV+rWq14lR2oZObe3rA5XBnZ3uS7t49uJL24tyXhOvwQXA60YRH4Pf8y+jbtDv/8RwO8t94BduSRZhuuBnLrXeS9/KzODZuQN++I67Dh3BnpHuebDajbRCDJjQcNS8Hd3o67twcdHEJ6Fq3Qd+8Be7sbFwH9uPYvg3X/iS0cfGYb76Nws8/xZ2Rjt/zr2DsVXrCoP2/deS/8yaSxYeAKe+iCQ4BoPCruRTOnIah/0BQVc+HT9IepMAgfO4fi3HgYAzKNjJ//gXHjm1oYxqiS2iMOyMd29Ilnh71mHHkPT8J14lU/F95A23DRji2bMa5PwnTwMGlhnhKnZfCQhw7t6NtFFvq2oOqqlh/+Banshtd8xboWrZGl9jEk9y9QFVVbH8sAacTbWw82thYghuE1/hKXh8qijJOluUNgO30bYqi9KhSJFUkkn/liDZXH9eJVJw7d+Dcn4RrXxKSnz+mQUPQtWmHmptLwcwPsS34DQDTtTfg89Cjpb/Kl0FVVZw7t2NdMA/7X0tRCwqQfH0xDhyMachQMJlRc7JxZ6Tj2LYVx4b1uPafuuFJEx6ONqEJPi2a4QgOo+ibL3EnH8dy9yjMd44sGS9W3W6ce3bjWLMax64duI8dxXX8GDidWO4bg/mOkUiShOp0UvjpR9iWLkbXvBWGLt3Qd+yEJiKywhczVVXFvnwZhbOn4zpyGCkgEP833kbfsnXZz3e7PaVOThvbVlWV/MmvYFuyEE1kFNqGjdA1b4H5xltLestlvc+qqmKb9yv5U6eAw4Hk64v/G++ib9O2QrFf7GpjGccIRVFSZVnOBJYAG4BFQL6iKGdXfvIikfwrR7T5wjgPH8L+95/YV/yNUykuB63RoG0Qgzs9HbWoEE1UNGpBPmpBAeYbbkFV3Vi/+xp9h474Pf8Kqt2OOzkZtagQbaNYNFHR4HRi++N3in76DtfePWAyYby8P4au3bGvXont77/AccYieUYj+jbtPGPSLVqiS2yCJiCwVJvdhQUUvPMmtiWLkMwWpMBANAEBuFJTUbMyQZLQxjf2XGyNiUHftn3J0Ed1U51O7MuXoWveosoXb1WXq9wLnud6nx27d1L05edY7roHXZOzFwaqq2q7qmdzYHjxfycURbmmSpFUkUj+lSPaXHmq04l91UqsP/+AY6OnYrmuZSsMvfqg79AZXXwCksmEWlSEbcXf2JYsBJ0OnwfGoYv3lAC2Ll5A/pTXwV7GfAiDEcmgR83PR5vQGPN1N2K4YiAai0/JU9w52djXrELS6ZACAtEEBKKNiy+5uHm+NtuWL8OxZRNqTg7unGw0/v7ou12GoUs3NIGBVT43FxPxu105F3STlyzLbYEBQL/ih3ZVKQpBqISKLPKuqqpn6EBT/q0xtmV/UPTt12gbJ2Ls0xd9h07gduM6fhTXoUOecXRlN87dO1FzctBERGIZPRbjoCFow86+21IymzFdORjTlYPP2mYadBW6+MbYV6/0XNyLjEIymXEdPojr4AHcebmeKYEdOpXZLk1AIKZBV1Xk9JTJ2Kcvxj41usieUIdVZKrnCmA/8LSiKAu9HI9QT6kuF9b//Yh93RrcKcm4UlPQ+PljvvEWz6wKiwXHrp1Yf/4ex4b1qIUFqFYruN1I/gHkhoWihoSh79QFQ4+eaHx9yX9nCvblf6GJaYjrj989c7eNRk/P/OQ3Xq0WbVw8hh69MPTqg6FHzwuaY62Tm6GTS99Vqm9d+0t7CsKZKjLVUwf0BK4EuuAZ9rmlBmIrIYZ9Kqe22lxy92RsHPqOnZF0uuKLmzuw/b4IQ7ceZY41Ow/sI//1V3Du2oE2oTHamIZoIiJxJe3FsWkDkp8/mqhoXHt2I5ktGHr2QgoM8syO0WhQs7PQ5uVg3X8A18Hi9X61WtBosNwzGvPNt4HLhWP9v9jX/4vG398z/t2wkWdYxVj+LJuLmfjdrh9qs7ZPINAAiAUsQI1e7BXqjoIP3sX68w8ASIFBGC7rhXP3Tlz7PDNVrL/+7Jn617c/4Jl2WPTV5xTOnYPk44vfC69i6HdFqSERx45tFH31Oa7UVHwemYhx0BA0PmfPkz75B+JKSca+ZhWuA/sxXXM9uvjiW1J0OgyX9cJQhemYgnApqkjyXwL8D3hVUZQdXo5HqKOKfvwO688/YLrxFvTtOmBbuhjb0iXo4uPxffwp9N0vI++5SeS9+Ay4nGgio8h/8zVcB/Zj6HcFvo88jibo7Fo7+pat0b82pcJxaCOjMF9zfXU2TRAuSedN/oqilF/9SBAA+9rVFHzwLoaevfEZOx5Jq8XYq89ZRa8C3n6fnCceJe/l50FV0YSF4T/5bdEbF4RaULVVgc9DlmUNMB1oi+cGsVGKoiSV8bzZQKaiKE96Iw7hwpy861EnN0fjd2rNYefBAzjWrsZ56CCuI4dx7tqJtnEifs++VOpi6ZkzWiSLhYApU8mf8hpSUDCWe0eXmuooCELN8UryB0YAJkVRusuy3A14G7j69CfIsnw/0BqokQVhhMpx7t9H3rNP4jp8CLRa9G3aoU1sguO/dSUXVaXAILQNG2G8cjCWkaOQLJbz7NUzVdLvuZe9Hb4gCOfhreTfE1gMoCjKWlmWS11tlmW5O9ANmAVU82oLwvmoDgeFc2bhTkvD96lnzypHYF28kPy3XvcUuXr6BVyHDmJf/Q+On75H16YdPo9ch6H35WXOgxcEoW7wVvL3B3JO+9kly7KueBH4KOAF4BrgxorsTKuVCAw8f6+y7NdqqvzauupcbXakJJMyYSK2rVsAMAUHEvb004DnpqmMd98h/9NPMXXqROSbU9CFhRW/ciKqw+G1glYXSrzP9YNoc/XxVvLPBfxO+1mjKMrJVY1vAEKBhUAkYJFlebeiKJ+VtzOXS63yPFcxL9gz/951cD+ObVspnDMb7Hb8XnwV565d5Hz7Ja6G8RiHDqfgnTex/vozphHX4fPwBPJ1Ojjr3J1Re+YiId7n+kG0uXLCwvzK3eat5L8KGAZ8Xzzmv+3kBkVR3gfeB5Bl+W6g2bkSv1A1nqXiVmKd/xuOTRvAagXwXJh96XV0jWIx9OmHc38S+e++iW3l3zjWrsZ8251Y7n+w0kvTCYJQt3gr+f8PGCDL8mpAAkbKsnwr4KsoymwvHVMolv3VV2TOnoWamYkmNAzTkGHoWrZG36IlmgYxJYld0mrxe+EVskePxLF2dakyv4IgXNrEYi6XGPvG9eQ+PBZ9h46Yb7oNfZdu560v7zqRiuvggfMuVn0xq2/vM4g21xe1Wd5BqCPUoiLy33gVfcOG+L/x7jlXhjqdNjyi1OpFgiBc+kTyr4NUmw3rgt+w/vY/dC1a4fPAQ2j8/Cj4aAbu48eI+uRTbBVM/IIg1E8i+dchJ8seF305F3dGOtrGidgWzsOx+h9M192I9cfvMF1zPebOnbHVs6/GgiBUjkj+dYQrNYW8l5/DuWUz+vYd8X3+ZfTtOuDas5u8ya9QOHu6ZyGSMQ/WdqiCINQBIvlf5FSXC/uyP8l/+w1wufB95sVSq0jp5OYEfjQX6/xf0bdsLWrlCIJQISL5X4RUVcWxaQP2v/7AtvJv1MxMdM1b4vf8y2gbxJz1fEmnwzziupoPVBCEOksk/4tQ4acfUfTpx2A2Y+jWA2Offhj69D3vlE1BEISKEtnkIlP45VyKPv0Y45Bh+D72eJ1dYlAQhIubSP4XkaLvv6Fw1jSMA67E94lJF7SQuCAIwrmI5H8RcKWmUDh7hmeR8z598Z30vEj8giB4lUj+tUi12Tzj+z98C0iYb78byz33ibF9QRC8TmSZWlQwezrW77/BOGgIllEPoI0QJRYEQagZIvnXEuf+fVh/+h7T8Gvwffyp2g5HEIR6RlPbAdRHqqpSMPUtJB8fLKMfqO1wBEGoh0TyrwX2P5fi2LQBy30PoAkIrO1wBEGoh0Tyr2FqYSEF095D27QZpmEjajscQRDqKZH8a5A7PZ2cJx7BnZ6G76MTxXROQRBqjbjgW0McmzaS+8Ik1MJC/J5/GX2rNrUdkiAI9ZhI/jWg6H8/UvDe22gbxOA3dRq6+Ma1HZIgCPWcSP5epKoqRV98RuFHMzBc1gvfZ19E4+Nb22EJgiCI5O8tqqpSOOMDir75EuPAwfg+9ay4c1cQhIuGyEZeUvTZHIq++RLTtTfg8/AEJI24ti4IwsVDJH8vcKenU/jVXAz9rsDnkYlIklTbIQmCIJQiuqNeUDh3Djid+Nz/oEj8giBclETyr2auo0ewzvsF0/Br0EY3qO1wBEEQyiSSfzUrnDML9Hosd95T26EIgiCUSyT/auTcuwfbH79jvuFmNKGhtR2OIAhCuUTyrybu/HzyJr+C5OeP+ZY7ajscQRCEcxKzfaqBWlRE7v89imvfXvxfm4LGz6+2QxIEQTgn0fO/QKrdTu7TT+Dcvg2/51/G0KNnbYckCIJwXiL5X6D8Ka/j+G8dvk88jbHvFbUdjiAIQoWI5H8BHNu3Ylu8APPtd2O6alhthyMIglBhXhnzl2VZA0wH2gI2YJSiKEmnbb8FeARwAVuBsYqiuL0Ri7eoqkrBh1ORgkOw3HF3bYcjCIJQKd7q+Y8ATIqidAeeBN4+uUGWZTPwCtBXUZQeQAAw1EtxeI192R84d2zH574xSBZLbYcjCIJQKd6a7dMTWAygKMpaWZY7nbbNBvRQFKXwtBis59qZVisRGFi1BKvVaqr82vKodjuHZs/A0LQpEbfceNGtyOWNNl/sRJvrB9Hm6uOt5O8P5Jz2s0uWZZ2iKM7i4Z1UAFmWHwJ8gaXn2pnLpZKdXXiup5QrMNBS5deWp/CbL3EeO4r/ux+Sk2er1n1XB2+0+WIn2lw/iDZXTlhY+dPOvZX8c4HTj6pRFMV58ofiawJvAk2B6xRFUb0UR7VTbTaKvvocfdfuGDp1qe1wBEEQqsRbY/6rgCEAsix3A7adsX0WYAJGnDb8UyfYlv2JmpON+ebbajsUQRCEKvNWz/9/wABZllcDEjBSluVb8QzxrAfuBVYCf8myDPCeoij/81Is1cr6vx/RNopF37FzbYciCIJQZV5J/sXj+mPOeHj3af+uk/cXOJVdOHdu96zMJer0C4JQh9XJJFxbin7+EcxmjIOuqu1QBEEQLohI/hXkzsnG9sfvmAYOQuPrW9vhCIIgXBCR/CvIunA+2G2YrrmhtkMRBEG4YCL5V4DqdmP95Sd0bduha5xY2+EIgiBcMJH8K8Dx3zrcx49hHnF9bYciCIJQLUTyrwDrrz8jBQZh6H15bYciCIJQLUTyPw/XiVTsq//BdNVwJIOhtsMRBEGoFiL5n4d1/q/gdmMaPqK2QxEEQag2Ivmfg+p0Ypv3K/ou3dBGN6jtcARBEKqNSP7nYF/9D+70NExXX1vboQiCIFQrkfzPwfrrz2jCwzF0v6y2QxEEQahWIvmXw5WaiuO/dRivGo6k81b9O0EQhNohkn85bEsXg6piEnV8BEG4BInkXwZVVbEtXoiudVtxoVcQhEuSSP5lcO3ZjevQAYxXDq7tUARBELxCJP8yWJcsAr0eY78rajsUQRAErxDJ/wyq04ntj98x9OiFxs+/tsMRBEHwCpH8z+D4dy1qVqYY8hEE4ZImkv8ZrEsWIQUEYOjWo7ZDEQRB8BqR/E/jzsvD/s8KjP0GIOn1tR2OIAiC14jkfxrbH0vAbsM4ZGhthyIIguBVIvmfxrbgN7SNE9HJzWs7FEEQBK8Syb+Yc+8enMpuTEOvRpKk2g5HEATBq0TyL2ad/ysYDBgHDqrtUARBELxOJH9AtdmwLV2CodflaPwDajscQRAErxPJH7Cv/Bs1LxfT0OG1HYogCEKNEMkfsM77FU1UFPoOnWo7FEEQhBpR75O/c4+CY+N6TEOGI2nq/ekQBKGeqNfZTnW7yX/7DaSgYEzX3VDb4QiCINSYep38bfN/xblzOz5jx4siboIg1Cv1Nvm7szIpmDkNXbsOooibIAj1jlcWp5VlWQNMB9oCNmCUoihJp20fBjwHOIFPFEX5yBtxnEvB9A9QCwvwfewJcVOXIAj1jrd6/iMAk6Io3YEngbdPbpBlWQ+8CwwE+gCjZVmO9FIcpahOJ7bly8h5eCy2xQsw33w7uviEmji0IAjCRcUrPX+gJ7AYQFGUtbIsnz6HsjmQpChKFoAsy/8AvYAfqjsIV0oyR8Y+gzMvHwB3Tg5qViaaiEgs9z+I+aZbq/uQgiAIdYK3kr8/kHPazy5ZlnWKojjL2JYHnPO2Wq1WIjDQUukgnK5AXI0boysoBEBjNOAzYCA+ffogabWV3l9dodVqqnS+6jLR5vpBtLn6eCv55wJ+p/2sKU78ZW3zA7LPtTOXSyU7u7DyUWjNhL/8SqnXOoGcPFvl91WHBAZaqna+6jDR5vpBtLlywsL8yt3mrTH/VcAQAFmWuwHbTtu2C2giy3KwLMsGoDewxktxCIIgCGXwVs//f8AAWZZXAxIwUpblWwFfRVFmy7L8GLAEz4fPJ4qiHPNSHIIgCEIZvJL8FUVxA2POeHj3advnAfO8cWxBEATh/OrtTV6CIAj1mUj+giAI9ZBI/oIgCPWQSP6CIAj1kEj+giAI9ZCkqmptx1ARacCh2g5CEAShjokFwsraUFeSvyAIglCNxLCPIAhCPSSSvyAIQj0kkr8gCEI9JJK/IAhCPSSSvyAIQj0kkr8gCEI95K2SzjWuLiwaX90q0OZbgEcAF7AVGFtccbXOOl+bT3vebCBTUZQnazjEalWB97gz8A6e0ukpwO2KolhrI9bqUoE23wZMwPN7/YmiKDNqJVAvkGW5K/CGoiiXn/F4teevS6nnP4KLcNF4LxtB+W02A68AfRVF6YFnqcyhtRFkNRtBOW0+SZbl+4HWNRyXt4yg/PdYAj4CRiqKcnLd7NjaCLKajeDc7/FbwBXAZcAEWZaDajY875Bl+QngY8B0xuNeyV+XUvIvtWg8UOai8Yqi2IGTi8bXdedqsw3ooSjKyfXfdECd7hEWO1ebkWW5O9ANmFXzoXnFudrbFMgAHpFleTkQrCiKUvMhVrtzvsd4vsUG4EmSEnCp3Km6D7i2jMe9kr8upeRf5qLx5Ww776LxdUS5bVYUxa0oSiqALMsPAb7A0poPsdqV22ZZlqOAF4AHayEubznX73Uo0APPEMkVQH9ZlvvXcHzecK42A2wHNgA7gPmKomTXYGxeoyjKT4CjjE1eyV+XUvKv1kXj64hztRlZljWyLL8FDACuUxTlUughnavNN+BJiAvxDBfcKsvy3TUbXrU7V3sz8PQIdyqK4sDTW+5Y0wF6QbltlmW5DXAVEA/EAeGyLN9Q4xHWLK/kr0sp+dfHRePP1WbwDH2YgBGnDf/UdeW2WVGU9xVF6Vh8sWwy8LWiKJ/VRpDV6Fzv8X7AV5blxOKfe+HpDdd152pzDlAEFCmK4gJOAJfEmP85eCV/XTKF3U6bIdCG4kXjgQ6cWjT+5NXyk4vGT6u1YKvJudoMrC/+byWnxkTfUxTlf7UQarU53/t82vPuBppdQrN9yvu97ofng04CViuK8nCtBVtNKtDmMcA9gB3POPl9xWPhdZ4sy3HAt4qidJNl+Va8mL8umeQvCIIgVNylNOwjCIIgVJBI/oIgCPWQSP6CIAj1kEj+giAI9ZBI/oIgCPXQJVPYTRBqkizLb+O5oSoSsOCZc5+mKMqlfsORcIkQUz0F4QJcKvcTCPWPGPYRBEGoh0TyFwRBqIdE8hcEQaiHRPIXBEGoh0TyFwRBqIfEbB9BEIR6SPT8BUEQ6iGR/AVBEOohkfwFQRDqIZH8BUEQ6iGR/AVBEOohkfwFQRDqIZH8BUEQ6qH/B7rF6AvaSRUDAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.clf()\n", "plotwins('Wisconsin','Va. Tech')\n", "plotwins('Northwestern','Vanderbilt')\n", "plotwins('Miami FL','Michigan St.')\n", "plotwins('Arkansas',\"Seton Hall\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "a5d2600e-2698-4a55-9426-9e7292c9339b", "metadata": {}, "outputs": [], "source": [ "MMMC.playgame('Wisconsin','Va. Tech',10)" ] }, { "cell_type": "code", "execution_count": 20, "id": "0b8bc74a-1326-4d4b-a10e-d0f905e5507b", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/mglerner/coding/MarchMadnessMonteCarlo/MarchMadnessMonteCarlo/Brackets.py:63: RuntimeWarning: overflow encountered in exp\n", " boltzmann_factor = exp(-ediff/T)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Lowest energy bracket\n", "Kentucky (2) \n", "Wisconsin (8) Wis (8) \n", "Villanova (1) Vil (1) Wis (8) \n", "Duke (2) \n", "Total bracket energy: 2.9451951068216125\n", "\n", "Most common bracket (142)\n", "Kentucky (2) \n", "Wisconsin (8) Wis (8) \n", "Villanova (1) Vil (1) Wis (8) \n", "Duke (2) \n", "Total bracket energy: 2.9451951068216125\n", "\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sr = MMMC.simulate(1000,['Kentucky','Wisconsin','Villanova','Duke'],0.5)\n", "MMMC.showstats(sr,newfig=True)" ] }, { "cell_type": "code", "execution_count": null, "id": "1a45407f-70fc-4e0f-a187-d390922d3dce", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.4" } }, "nbformat": 4, "nbformat_minor": 5 }