{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Policy Iteration\n",
    "\n",
    "由策略评估价值，根据价值改进策略...反反复复，这叫“策略迭代”。\n",
    "\n",
    "算法如下。\n",
    "\n",
    "![03-02-policy-iteration](images/03-02-policy-iteration.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 4.2 Jack’s Car Rental\n",
    "\n",
    "Jack manages two locations for a nationwide car rental company. Each day, some number of customers arrive at each location to rent cars. If Jack has a car available, he rents it out and is credited 10 dollars by the national company. If he is out of cars at that location, then the business is lost. Cars become available for renting the day after they are returned. To help ensure that cars are available where they are needed, Jack can move them between the two locations overnight, at a cost of 2 dollars per car moved. We assume that the number of cars requested and returned at each\n",
    "location are Poisson random variables, meaning that the probability that the number is $n$ is $\\frac{\\lambda^n}{n!}e^{-\\lambda}$, where $\\lambda$ is the expected number. Suppose $\\lambda$ is 3 and 4 for rental requests at the first and second locations and 3 and 2 for returns. To simplify the problem slightly, we assume that there can be no more than 20 cars at each location (any additional cars are returned to the nationwide company, and thus disappear from the problem) and a maximum of five cars can be moved from one location to the other in one night. We take the discount rate to be # = 0.9 and formulate this as a continuing finite MDP, where the time steps are days, the state is the number of cars at each location at the end of the day, and the actions are the net numbers of cars moved between the two locations overnight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-16T13:04:57.490129Z",
     "start_time": "2020-01-16T13:04:52.199283Z"
    }
   },
   "outputs": [],
   "source": [
    "#######################################################################\n",
    "# Copyright (C)                                                       #\n",
    "# 2016 Shangtong Zhang(zhangshangtong.cpp@gmail.com)                  #\n",
    "# 2016 Kenta Shimada(hyperkentakun@gmail.com)                         #\n",
    "# 2017 Aja Rangaswamy (aja004@gmail.com)                              #\n",
    "# Permission given to modify the code as long as you keep this        #\n",
    "# declaration at the top                                              #\n",
    "#######################################################################\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from scipy.stats import poisson\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-16T13:07:49.225095Z",
     "start_time": "2020-01-16T13:07:49.220114Z"
    }
   },
   "outputs": [],
   "source": [
    "# maximum # of cars in each location\n",
    "MAX_CARS = 20\n",
    "\n",
    "# maximum # of cars to move during night\n",
    "MAX_MOVE_OF_CARS = 5\n",
    "\n",
    "# expectation for rental requests in first location\n",
    "RENTAL_REQUEST_FIRST_LOC = 3\n",
    "\n",
    "# expectation for rental requests in second location\n",
    "RENTAL_REQUEST_SECOND_LOC = 4\n",
    "\n",
    "# expectation for # of cars returned in first location\n",
    "RETURNS_FIRST_LOC = 3\n",
    "\n",
    "# expectation for # of cars returned in second location\n",
    "RETURNS_SECOND_LOC = 2\n",
    "\n",
    "DISCOUNT = 0.9\n",
    "\n",
    "# credit earned by a car\n",
    "RENTAL_CREDIT = 10\n",
    "\n",
    "# cost of moving a car\n",
    "MOVE_CAR_COST = 2\n",
    "\n",
    "# all possible actions\n",
    "actions = np.arange(-MAX_MOVE_OF_CARS, MAX_MOVE_OF_CARS + 1)\n",
    "\n",
    "# An up bound for poisson distribution\n",
    "# If n is greater than this value, then the probability of getting n is truncated to 0\n",
    "POISSON_UPPER_BOUND = 11\n",
    "\n",
    "# Probability for poisson distribution\n",
    "# @lam: lambda should be less than 10 for this function\n",
    "poisson_cache = dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-16T13:08:00.174475Z",
     "start_time": "2020-01-16T13:08:00.170485Z"
    }
   },
   "outputs": [],
   "source": [
    "def poisson_probability(n, lam):\n",
    "    global poisson_cache\n",
    "    key = n * 10 + lam\n",
    "    if key not in poisson_cache:\n",
    "        # 设置字典，防止重复求泊松分布\n",
    "        # key 相当于一种哈希编码 Hash(n)\n",
    "        poisson_cache[key] = poisson.pmf(n, lam)\n",
    "    return poisson_cache[key]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-16T13:08:11.358555Z",
     "start_time": "2020-01-16T13:08:11.349579Z"
    }
   },
   "outputs": [],
   "source": [
    "def expected_return(state, action, state_value, constant_returned_cars):\n",
    "    \"\"\"\n",
    "    @state: [# of cars in first location, # of cars in second location]\n",
    "    @action: positive if moving cars from first location to second location,\n",
    "            negative if moving cars from second location to first location\n",
    "    @stateValue: state value matrix\n",
    "    @constant_returned_cars:  if set True, model is simplified such that\n",
    "    the # of cars returned in daytime becomes constant\n",
    "    rather than a random value from poisson distribution, which will reduce calculation time\n",
    "    and leave the optimal policy/value state matrix almost the same\n",
    "    \"\"\"\n",
    "    # initailize total return\n",
    "    returns = 0.0\n",
    "\n",
    "    # cost for moving cars\n",
    "    returns -= MOVE_CAR_COST * abs(action)\n",
    "\n",
    "    # moving cars\n",
    "    NUM_OF_CARS_FIRST_LOC = min(state[0] - action, MAX_CARS)\n",
    "    NUM_OF_CARS_SECOND_LOC = min(state[1] + action, MAX_CARS)\n",
    "\n",
    "    # go through all possible rental requests\n",
    "    for rental_request_first_loc in range(POISSON_UPPER_BOUND):\n",
    "        for rental_request_second_loc in range(POISSON_UPPER_BOUND):\n",
    "            # probability for current combination of rental requests\n",
    "            prob = poisson_probability(rental_request_first_loc, RENTAL_REQUEST_FIRST_LOC) * \\\n",
    "                poisson_probability(rental_request_second_loc, RENTAL_REQUEST_SECOND_LOC)\n",
    "\n",
    "            num_of_cars_first_loc = NUM_OF_CARS_FIRST_LOC\n",
    "            num_of_cars_second_loc = NUM_OF_CARS_SECOND_LOC\n",
    "            '''\n",
    "            注意作者的编程习惯，全部大写表示当前客观变量\n",
    "            （当前2个 LOC 各客观存在这么多车）\n",
    "            小写表示临时变量，用于计算\n",
    "            '''\n",
    "\n",
    "            # valid rental requests should be less than actual # of cars\n",
    "            valid_rental_first_loc = min(num_of_cars_first_loc, rental_request_first_loc)\n",
    "            valid_rental_second_loc = min(num_of_cars_second_loc, rental_request_second_loc)\n",
    "\n",
    "            # get credits for renting\n",
    "            reward = (valid_rental_first_loc + valid_rental_second_loc) * RENTAL_CREDIT\n",
    "            num_of_cars_first_loc -= valid_rental_first_loc\n",
    "            num_of_cars_second_loc -= valid_rental_second_loc\n",
    "            \n",
    "            '''\n",
    "            这里之所以要用2层 for\n",
    "            是为了遍历状态，求期望\n",
    "            '''\n",
    "\n",
    "            if constant_returned_cars:\n",
    "                # get returned cars, those cars can be used for renting tomorrow\n",
    "                returned_cars_first_loc = RETURNS_FIRST_LOC\n",
    "                returned_cars_second_loc = RETURNS_SECOND_LOC\n",
    "                num_of_cars_first_loc = min(num_of_cars_first_loc + returned_cars_first_loc, MAX_CARS)\n",
    "                num_of_cars_second_loc = min(num_of_cars_second_loc + returned_cars_second_loc, MAX_CARS)\n",
    "                returns += prob * (reward + DISCOUNT * state_value[num_of_cars_first_loc, num_of_cars_second_loc])\n",
    "                '''\n",
    "                这里很重要\n",
    "                作者在这个函数开头便说明了：\n",
    "                还车数当成常数，对结果没有影响\n",
    "                但若是还使用泊松分布生成返回值，则 O(n^4)\n",
    "                极大地影响了运行时间\n",
    "                '''\n",
    "            else:\n",
    "                for returned_cars_first_loc in range(POISSON_UPPER_BOUND):\n",
    "                    for returned_cars_second_loc in range(POISSON_UPPER_BOUND):\n",
    "                        prob_return = poisson_probability(\n",
    "                            returned_cars_first_loc, RETURNS_FIRST_LOC) * poisson_probability(returned_cars_second_loc, RETURNS_SECOND_LOC)\n",
    "                        num_of_cars_first_loc_ = min(num_of_cars_first_loc + returned_cars_first_loc, MAX_CARS)\n",
    "                        num_of_cars_second_loc_ = min(num_of_cars_second_loc + returned_cars_second_loc, MAX_CARS)\n",
    "                        prob_ = prob_return * prob\n",
    "                        returns += prob_ * (reward + DISCOUNT *\n",
    "                                            state_value[num_of_cars_first_loc_, num_of_cars_second_loc_])\n",
    "    return returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-16T14:12:29.413904Z",
     "start_time": "2020-01-16T14:12:29.404927Z"
    }
   },
   "outputs": [],
   "source": [
    "def figure_4_2(constant_returned_cars=True):\n",
    "    value = np.zeros((MAX_CARS + 1, MAX_CARS + 1))\n",
    "    policy = np.zeros(value.shape, dtype=np.int)\n",
    "\n",
    "    iterations = 0\n",
    "    _, axes = plt.subplots(2, 3, figsize=(40, 20)) # 注意这里\n",
    "    plt.subplots_adjust(wspace=0.1, hspace=0.2) # 这里的 subplot 技巧\n",
    "    axes = axes.flatten()\n",
    "    while True:\n",
    "        fig = sns.heatmap(np.flipud(policy), cmap=\"YlGnBu\", ax=axes[iterations])\n",
    "        fig.set_ylabel('# cars at first location', fontsize=30)\n",
    "        fig.set_yticks(list(reversed(range(MAX_CARS + 1))))\n",
    "        fig.set_xlabel('# cars at second location', fontsize=30)\n",
    "        fig.set_title('policy {}'.format(iterations), fontsize=30)\n",
    "\n",
    "        # policy evaluation (in-place)\n",
    "        while True:\n",
    "            old_value = value.copy()\n",
    "            for i in range(MAX_CARS + 1):\n",
    "                for j in range(MAX_CARS + 1):\n",
    "                    new_state_value = expected_return([i, j], policy[i, j], value, constant_returned_cars)\n",
    "                    value[i, j] = new_state_value\n",
    "                    '''\n",
    "                    注意这里的编程习惯\n",
    "                    使用 new_state_value 过渡\n",
    "                    增强易读性\n",
    "                    '''\n",
    "            max_value_change = abs(old_value - value).max()\n",
    "            print('max value change {}'.format(max_value_change))\n",
    "            '''\n",
    "            直到评估出当前策略对应的 最优价值 才结束\n",
    "            '''\n",
    "            if max_value_change < 1e-4:\n",
    "                break\n",
    "\n",
    "        # policy improvement\n",
    "        policy_stable = True\n",
    "        for i in range(MAX_CARS + 1):\n",
    "            for j in range(MAX_CARS + 1):\n",
    "                old_action = policy[i, j]\n",
    "                action_returns = []\n",
    "                for action in actions:\n",
    "                    if (0 <= action <= i) or (-j <= action <= 0):\n",
    "                        action_returns.append(expected_return([i, j], action, value, constant_returned_cars))\n",
    "                    else:\n",
    "                        action_returns.append(-np.inf)\n",
    "                new_action = actions[np.argmax(action_returns)] # 注意这句\n",
    "                policy[i, j] = new_action\n",
    "                if policy_stable and old_action != new_action: \n",
    "                    # 确认 policy_stable == True \n",
    "                    # 以保证程序安全性，如果为 False 就没必要考虑置为 False 了\n",
    "                    policy_stable = False\n",
    "        print('policy stable {}'.format(policy_stable))\n",
    "\n",
    "        if policy_stable:\n",
    "            fig = sns.heatmap(np.flipud(value), cmap=\"YlGnBu\", ax=axes[-1])\n",
    "            fig.set_ylabel('# cars at first location', fontsize=30)\n",
    "            fig.set_yticks(list(reversed(range(MAX_CARS + 1))))\n",
    "            fig.set_xlabel('# cars at second location', fontsize=30)\n",
    "            fig.set_title('optimal value', fontsize=30)\n",
    "            break\n",
    "\n",
    "        iterations += 1\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-16T14:13:36.797660Z",
     "start_time": "2020-01-16T14:12:30.598734Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "max value change 0.020714866829109724\n",
      "max value change 0.01752498189301832\n",
      "max value change 0.014826276628639334\n",
      "max value change 0.01254313570910881\n",
      "max value change 0.010611575530163009\n",
      "max value change 0.008977459770164842\n",
      "max value change 0.00759498609147613\n",
      "max value change 0.006425404193464601\n",
      "max value change 0.005435930515432119\n",
      "max value change 0.004598829696703888\n",
      "max value change 0.00389063733302919\n",
      "max value change 0.003291502340118768\n",
      "max value change 0.0027846305547996053\n",
      "max value change 0.0023558140037494013\n",
      "max value change 0.0019930326484427496\n",
      "max value change 0.0016861174636346732\n",
      "max value change 0.0014264653930240456\n",
      "max value change 0.001206798198722936\n",
      "max value change 0.0010209584465883381\n",
      "max value change 0.0008637369118673632\n",
      "max value change 0.0007307265586291578\n",
      "max value change 0.0006181990110007973\n",
      "max value change 0.0005230000359119913\n",
      "max value change 0.00044246113805002096\n",
      "max value change 0.00037432475153309497\n",
      "max value change 0.00031668096374914967\n",
      "max value change 0.0002679139766428307\n",
      "max value change 0.00022665681694888917\n",
      "max value change 0.00019175301355289776\n",
      "max value change 0.00016222418821598694\n",
      "max value change 0.00013724262737468962\n",
      "max value change 0.00011610807808892787\n",
      "max value change 9.822812404536307e-05\n",
      "policy stable False\n",
      "max value change 0.5643315459673204\n",
      "max value change 0.19760617142037518\n",
      "max value change 0.10013580858492332\n",
      "max value change 0.06076229858263105\n",
      "max value change 0.04080851176706801\n",
      "max value change 0.02724975517776329\n",
      "max value change 0.01637959485265128\n",
      "max value change 0.00917172069227945\n",
      "max value change 0.0049277609952014245\n",
      "max value change 0.0025834353657501197\n",
      "max value change 0.0013420404746966597\n",
      "max value change 0.0007016294298409775\n",
      "max value change 0.00037558255417025066\n",
      "max value change 0.00020989058543818828\n",
      "max value change 0.00013043237390775175\n",
      "max value change 0.00011051700198549952\n",
      "max value change 9.361574132071837e-05\n",
      "policy stable False\n",
      "max value change 0.04079438312567163\n",
      "max value change 0.010408227162770345\n",
      "max value change 0.005110707129347247\n",
      "max value change 0.0032318390198042835\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max value change 0.0021719229242762594\n",
      "max value change 0.0013911772695109903\n",
      "max value change 0.0008154469392138708\n",
      "max value change 0.0004459807777266178\n",
      "max value change 0.0002340408432246477\n",
      "max value change 0.00012037610895276885\n",
      "max value change 6.173777182993945e-05\n",
      "policy stable True\n"
     ]
    },
    {
     "data": {
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8Isntknxhh2sBAGCJjLV7nBuR/QEARkD2ZyD/AwCMwFjz/9oMY9477E/bwToAAIDlI/sDAMB4yP8AAKysWZpjXpCkklyww7UAALBE1mr3N5ae7A8AMAKyPwP5HwBgBMaa/Wdpjnl+kkuTfE9V/coO1wMAACwP2R8AAMZD/gcAYGXtm3ZAd99QVT+c5PeT/Ieq+r4kv5nkTUk+1t1f3eEaAQBYgGOqF10CCyb7AwCMg+xPIv8DAIzFWPP/1M0xVXX9+q9J9id5zrrzR7pFd/fU8wIAAPMl+wMAwHjI/wAArLJZXqtU67aN37e7AQCw5NbmsB2Nqjqhql5bVR8c9sdvcd1jh2s+WFWP3eT8RVV1+VGWs6pkfwCAEVj27M/cyP8AACMw1uw/Sxf3G5OMc50dAACWyc8m+bPufnpV/ezw/WfWX1BVJyT5+Ux+8dhJ3lFVF3X354bzD0/ypfmWvafI/gAAMB7yPwAAK2vq5pjuPncX6gAAYMmsLf9v/s5Pcu7w+XlJLsmG5pgkD0zy2u7+bJJU1WuTPCjJH1bVsUn+Y5IDSV40h3r3HNkfAGAc9kD2Zw7kfwCAcRhr/l/mVW0AAOBwTuruf0iSYX/iJtfcPslH132/cjiWJL+Q5L8nuXo3iwQAAAAAABZrltcqAQAwAvPoHq+qA5ms3HLIwe4+uO7865KcvMnQJ293ik2OdVXdNckdu/s/VNVp27wXAACspLH+chQAAMZorPlfcwwAAAszNMIcPMz5+291rqo+UVW36+5/qKrbJfnkJpddma+/eilJTs3k9Uv3SHJWVX0kk0x8YlVdYhlxAAAAAABYPZpjAADY1DHViy7hSC5K8tgkTx/2L9/kmlcn+eWqOn74/v1Jfq67P5vkfyTJsHLMn2iMAQBgrPZA9gcAAHbIWPP/UTXHVNUtkpyf5O6Z/Ar3lkmOOcKw7u77Hc28AACQSVPMi6rq8Un+Pskjk6Sq9if5ye7+ie7+bFX9QpK3D2OeNjTGMCXZHwAAxkP+BwBg1czcHFNVT0zytCTHTTMsyTjbkAAA9phlf+9od38myTc8eO3uy5L8xLrvz0nynMPc5yNJztyFEleG7A8AsNqWPfszX/I/AMBqG2v+n6k5pqp+McnPZRJ4j+RQIN6Rf+KquneSs5Nc3t2v2Yl7AgDwjcYakLkx2R8AYPXJ/hwi/wMArL6x5v+pm2Oq6ruS/JdMgu/7k/ybJH+R5Jrh2MOSvC7JtyZ5UJJ/n8myi8/LZHn7r045319299nD53+V5N8leWmSn6+qu3X306f9GwAAgCPbi9n/2rNOnmZKFuT0M47qDb/M0TknX7PoEgCAOdmL+X9eTjjj5osuYc868/Y3LLoEAIAkydoMY35y2F+b5IHd/YaNobe7r+7u93X3rya5S5LXJvmxJC+YYb6brPt8IMkDuvupSb4/yY9uNaiqDlTVZVV12VWvevkM0wIAjNta7f7G0ttz2f9Lb3nFDNMCAIyb7M9gz+X/L1528QzTAgCM2zJn/6p6ZFW9p6puqKr9h7nuI1X1v6vqXVV12bb+7hnqOSeTLvEXdfdHj3Rxd38pyY8k+XiSh1bVj0w531pVHV9Vt05S3f2p4b5fTnLdYeY92N37u3v/KQ8+f8opAQCA7MHsf+w9f2jKKQEAgMGey//H7X/IlFMCALDkLk/y8CRv3Ma153X3Xbt7yyaa9WZpjjl12P/VFudvuvHAEGZ/N5N3j/7YlPPdKsk7klyW5ISqOjlJqurY7NC7TAEA+EbH1O5vLD3ZHwBgBGR/BvI/AMAILHP2H1Yp/MDO/KU3NsuL3g+9XPNjG45fneRmmQTazVw+7O86zWTdfdoWp27I5B2nAADA7pD9AQBgPOR/AAD2ik7ymqrqJP+zuw8eacAszTFfSHJ8bvw+0CT5XCYB+fQtxh037E+cYc5v0N1XJ/nwTtwLAIBvtFa96BJYPNkfAGAEZH8G8j8AwAjsdv6vqgNJDqw7dHB980pVvS7JyZsMfXJ3v3yb09yru6+qqhOTvLaq3t/dh30V0yyvVbpi2N9+w/H3ZrLU4f23GHfvYX/1DHMCAADzJ/sDAMB4yP8AABy17j7Y3fvXbQc3nL9/d5+5ybbdxph091XD/pNJXprk7CONmaU55rJMgvD3bDj+mmF/t6p63PoTVXV+kh/NZGmbd84wJwAAc7Y2h42lJ/sDAIyA7M9A/gcAGIG9nv2r6hZVddyhz0m+P19/1eeWZqntdcP+AVW1fvzzk3x++PzsqnpbVb2gqt6W5CXr5nr2DHMCAADzJ/sDAMB4yP8AACxUVT2sqq5Mco8kr6yqVw/HT6mqi4fLTkry5qp6d5K/TPLK7v7TI9173wz1/GmSv0vyzZkso/iaJOnuT1XVTyb5g0zC8P5hSybd5knyB939RzPMCQDAnK3Vka9h5cn+AAAjIPszkP8BAEZgmfN/d780k9ckbTx+VZKHDJ8/lOS7p7331M0x3f2VJN+2xbk/qqp/SHJhJu8ZPXT/Dyb59e5+1rTzAQAAiyH7AwDAeMj/AACssllWjjms7n5jkvtW1U2S3DrJ1d39hZ2eBwCA3XXMEnePsxxkfwCA1SD7sx3yPwDAahhr/t/x5phDuvvaJB/frfsDAADLQfYHAIDxkP8BANiLdq05BgCAvW2tetElAAAAcyD7AwDAeIw1/8/UHFNV35ekkny4uz+6jev/SZLTktzQ3W+eZU4AAGD+ZH8AABgP+R8AgFU1dXNMVd03yeuSdJL9SY4YkJMcn+SSJF1V53T3pdPOCwDAfK2N9L2jfJ3sDwAwDrI/ifwPADAWY83/azOMefiwf1d3v3M7A7r73UneMXx95AxzAgAA8yf7AwDAeMj/AACsrFleq3SPTDrHXz3luFcnOSvJPWeYEwCAORtr9zg3IvsDAIyA7M9A/gcAGIGx5v9ZVo45fdi/b8pxH9gwHgAAWG6yPwAAjIf8DwDAyppl5ZibD/urpxx3zbA/boY5AQCYhp1+qAAAIABJREFUs1m6qFk5sj8AwAjI/gzkfwCAERhr/p/l7/4/w/7EKccduv6LM8wJAADMn+wPAADjIf8DALCyZmmO+ciwP2/KcecO+4/OMCcAAHNWtfsbS+8jw172BwBYYbI/g48Me/kfAGCFjTX7z9Ic8+dJKslDq+rO2xlQVWcmeViSTvL6GebceL/nH+09AACAI5L9AQBgPBaa/2V/AAB2074Zxvx2kv+Y5Jgkr6yqH+ju9251cVXdJclFw/XXD+O3raou2ngoyXlV9S1J0t0/PM39AADYniVu8GZ+ZH8AgBGQ/RnMLf/L/gAAizPW/D91c0x3f7CqnpXkp5L8kyTvqKo/SPKKJO9L8qUkxyb5ziQ/nOQxSb4pk87x3zpcmN7CqUnem0mw7kz+W+1P8t8PN6iqDiQ5kCR3esKTcsqDz59yWgAAGDfZn1VwzsnXLLoEAIA9Yc75f6bsn9w4/9/h8f85t7nv6vTRnHn7GxZdAgDAyqrunn5Q1TFJXpLkh4ZDh7vJocaji5L8SHdfP+Vca5mE8YckeVJ3v6uqPtTd377de5x38aXT/5EAAAvw5w+519I0bV/26Vfueobaf5sfWJq/l83J/ux1mmMAWFZPvdv9lyYLy/4cMq/8vxPZP0nu9oI3rVT+1xwDAKvr+fe5z9Lk4d3O/8ua/Wd5rVKGkHt+Vf10kp9OcsJhLv9skqd396/MONcNSX61qv542H8iM9YNAMD2rS26AJaC7A8AsPpkfw6ZV/6X/QEAFmes+f+owmZ3/7eq+o0kD05y70yWQrxlki8kuTLJm5K8qruvPtpCu/vKJI+sqh8Y7g8AAMyJ7A8AAOMxr/wv+wMAMC9H3Ynd3V9O8uJh23Xd/cokr5zHXAAAY1a1UqtTswNkfwCA1ST7s5l55n/ZHwBgfsaa/8e6Yg4AAAAAAAAAACPgHZ4AAGyqFl0AAAAwF7I/AACMx1jzv5VjAAAAAAAAAABYWVaOAQBgUzXW9nEAABgZ2R8AAMZjrPnfyjEAAAAAAAAAAKwsK8cAALCpkTaPAwDA6Mj+AAAwHmPN/1aOAQAAAAAAAABgZVk5BgCATa2NtX0cAABGRvYHAIDxGGv+t3IMAAAAAAAAAAAry8oxAABsaqTN4wAAMDqyPwAAjMdY87+VYwAAAAAAAAAAWFlWjgEAYFM11vZxAAAYGdkfAADGY6z5f6aVY6rqQ1X1t1X1fTtdEAAAsDxkfwAAGA/5HwCAVTXryjGnJekkN9t4oqpOSHJmknT3G2euDACAhRpp8zjf6LTI/gAAK032Z53TIv8DAKy0seb/3Xit0vcleWmSG3bp/gAAwHKQ/QEAYDzkfwAA9qzDBtiqel2S1ye5JMnbuvv6Ke491oYjAICVIMyNi+wPADBewtz4yP8AAOM11jB3pO7u+yY5b/h8dVW9KZOwDAAArBbZHwAAxkP+BwBgVI7UHPPcJOdm8p7RWyR5UJIHrjv/1Kq6Z5K3JvmL7v78zpeYVNXZSbq7315Vdx7qeH93X7wb8wEAkKyNtX18vJ4b2R8AYJSWPftX1SOTXJjkO5Oc3d2XbXHdR5J8Mcn1Sa7r7v3zqnEPem4WnP9lfwCAxVj2/L9bDtsc092PS5KqOi3J/TLpJj83ye2GS+6e5OxDl1fVB5J8eicLrKqfT/LgJPuq6rXDnJck+dmq+p7u/qWdnA8AAMZoVbL/OSdfs5MlAQCH8aBTv7roEhiPy5M8PMn/3Ma153X3jubUVbTo/L9Tz/3PvP0NO1USAOyYe54oJ8MyWtvORd39ke7+ne7+0e6+/bpTb07y4UxeS7WWSef+vQ+drKorqurZVfWYqrpdZvOIJPdKck6Sf5fkod39tEy62B+11aCqOlBVl1XVZVe96uUzTg0AMF41h43ls9ez/zte8soZpwYAGK9lz/7d/b7u/sBR3oZNLDD/z5T9h7m/lv//5hWvmGFqAIBxW+bsv5u21RxzGL/Y3XdMclKShyZ5RpJ3rTv/7Ukel+T3klxZVe+rqt+Yco7ruvv67r46yd929xeSpLuvSbJlW3h3H+zu/d29/5QHnz/llAAAwAZ7Ivuf9fAfmHJKAADmYX1Dw7Ad2IVpOslrquodu3T/Mdnt/D9T9h+u+Vr+v9MP/dAUUwIAMGaHfa1SVZ3Q3Z890k26+1NJLkpyUVX9RZKXDqeeluS8TJZfvGmS/yvJnTLpBN+uf6yqmw8h+ax1td0qRwjJAADMrqoXXQJzJPsDAIzXPLJ/dx9McnDrGup1SU7e5NSTu3u7S4Pfq7uvqqoTk7y2qt7f3W+codyVtwT5X/YHAFiQsT77P2xzTJJPVtVfZ/Kuz9cneeOhDu7t6O4Lk1xYVd+c5J6ZhOVzp6zxnO7+6nC/9aH4JkkeO+W9AACAzcn+AAAsTHfffwfucdWw/2RVvTSTxg3NMZtbdP6X/QEAmKsjNcesJblrku9O8lNJbqiqd647f9PtTNLdX8kkYL9+2gIPBeRNjn86yaenvR8AANuzzO8GZVfI/gAAI7UK2b+qbpFkrbu/OHz+/kxWN2FzC83/sj8AwOKsQv6fxZGaYx6eSbf3uUn+aZJjkuzP5N2tleRlVfWBJG9JcumwH+u/JQDASimpbmxkfwCAkVr27F9VD0vy60lum+SVVfWu7n5gVZ2S5Le7+yFJTkry0pr8MfuSvKC7/3RhRS8/+R8AYKSWPf/vlsM2x3T3y5K8LEmq6vgk98kkLD8xXw/J35HJ+0R/fBj2j4fGV9WZ3X35jlcNAADsKNkfAPj/2bvzcNeq+v7j7y8zAgqIKJNctYJaB0QERYsXUMQJQRzqBNSB6k+LOFUUhavWljpbtbUgiHUeUaEWAeXizCAIgqAgXmRSFBBkkPH7+2Ovw9k3JDk5J9lJTvJ+Pc96srOzstfayU7ySc46a0vjKjOPAY5ps/4K4Oll+WKqWVDUA/O/JEmSps1cM8fcJTOvpQrL34iIA8rqfy/b2BHYlmqqxTWZDc9nR8TVwClU5y49OTN/ObDeS5IkqTGrjLoDGhmzvyRJ0nQx+083878kSdJ0mdb83/PgmA5OzswTACJiDappF/cFXslsSN4I2JtqmkYi4o+Zeb8+25UkSZI0XGZ/SZIkaXqY/yVJkjRRBjYoKDNvzcwfA9+urX4k8Drgm8CfqQLzfQbVpiRJkpoT0XzR4mT2lyRJmixmf3Vj/pckSZos05r9+505pqtyztFzgY9GRADbADs32aYkSZKk4TP7S5IkSdPD/C9JkqTFpp/BMfMa85OZCZxViiRJksbcGA/w1vCZ/SVJkiaY2V8tzP+SJEkTbFrz/4IGx2TmwE7HJEmSJGl8mf0lSZKk6WH+lyRJ0qRq4rRKvwM+3cB2JUmSNETjfG5QjQ2zvyRJ0gQw+6tH5n9JkqQJMK35f+CDYzLzLOAfBr1dSZIkSePF7C9JkiRND/O/JEmSFrMmZo6RJEnSBJjSweOSJEnS1DH7S5IkSdNjWvO/5w+VJEmSJEmSJEmSJEnSxHLmGEmSJLW1yrQOH5ckSZKmjNlfkiRJmh7Tmv+dOUaSJEmSJEmSJEmSJEkTy5ljJEmS1NaUDh6XJEmSpo7ZX5IkSZoe05r/nTlGkiRJkiRJkiRJkiRJE2tRDI6JiIdExK4RsW7L+t1H1SdJkqRJF5GNF6mV2V+SJGn4zP4aBbO/JEnSaExr9h/7wTERcQDwTeCfgHMj4tm1m/91NL2SJEmSNGhmf0mSJGk6mP0lSZI0bKuNugM9eCXwmMy8ISKWAF+NiCWZ+RG6nA4rIvYH9gfY6rVvZtOnPbtTVUmSJLUxrecd1Uj1nf2fcfCBPOY5zxhGXyVp6uy++S2j7oKm2Nb3umPUXZhoZn+NwIKyP6yc/3d44xvZ6lnParqvkjQ2dtzYTK6VPf6+t466C1qEpjX/L4bBMatm5g0AmbkiIpZSBeUt6fK8ZebhwOEAO3/7R+M7d48kSZKkGX1n/0PPPMnsL0mSJI2/BWX/Uv+u/L/PKaeY/yVJktSTsT+tEvD7iNhm5koJzM8ENgIeMbJeSZIkTbiI5ovUwuwvSZI0AmZ/jYDZX5IkaUSmNfsvhsEx+wC/r6/IzNszcx9gp9F0SZIkSVIDzP6SJEnSdDD7S5IkaajG/rRKmXlZl9t+NMy+SJIkTZMxHuCtCWX2lyRJGg2zv4bN7C9JkjQ605r/F8PMMZIkSZIkSZIkSZIkSdKCjP3MMZIkSRoNR1FLkiRJ08HsL0mSJE2Pac3/07rfkiRJkiRJkiRJkiRJmgLOHCNJkqS2YlpPPCpJkiRNGbO/JEmSND2mNf87c4wkSZIkSZIkSZIkSZImljPHSJIkqYMpHT4uSZIkTR2zvyRJkjQ9pjP/OzhGkiRJbcWUBmRJkiRp2pj9JUmSpOkxrfnf0ypJkiRJkiRJkiRJkiRppCLi3RFxTkT8PCJOiIhNO9TbNyIuLGXfXrbtzDGSJElqK8Jx1JIkSdI0MPtLkiRJ02PM8//7MvMdABFxAHAI8Kp6hYjYEDgU2A5I4GcR8a3MvLbbhsd6ryVJkiRJkiRJkiRJkjT5MvP62tV1qAa/tHoqcGJmXlMGxJwI7D7Xtp05RpIkSR1M53lHJUmSpOlj9pckSZKmx3jn/4h4D7APcB2wc5sqmwGX1q5fVtZ15cwxkiRJkiRJkiRJkiRJ6ltE7B8RZ9TK/i23nxQR57YpzwbIzIMzcwvgc8Br2zXRZl27GWZW4swxkiRJaivGfPS4JEmSpMEw+0uSJEnTo+n8n5mHA4d3uf3JPW7q88D/Aoe2rL8MWFq7vjmwfK6NOXOMJEmSFqWI2DAiToyIC8vlBh3q7VvqXBgR+9bWvzAifhER50TE8RGx0fB6L0mSJEmSJEmS6iLiwbWrewAXtKn2HWC3iNig/F1gt7KuKwfHSJIkqYMYQunLQcB3M/PBwHfL9ZX3IGJDqlHlOwDbA4eWwLwa8BFg58x8JHAO7adnlCRJkqbA2Gd/SZIkSQMz1tn/sHKKpXOoBr28DiAitouITwJk5jXAu4HTS3lXWdeVp1WSJEnSYvVsZqdO/DTVtIlvaanzVODEmWAcEScCuwNfpUrp60TE1cA9gYua77IkSZIkSZIkSWonM/fusP4M4BW160cBR81n2w6OkSRJUlsRzU8yGBH7A/vXVh1ezkfai/tm5pUAmXllRGzcps5mwKW165cBm2XmbRHxauAXwI3AhcBr5r0DkiRJ0gQYRvaXJEmSNB6mNf87OEaSJEkjUwbCdBwMExEnAfdrc9PBPTbRbg7HjIjVgVcDjwYuBj4KvBX4lx63K0mSJEmSJEmSFolFPTgmIv4hMz816n5IkiRNpr7PDdq3zHxyp9si4g8RsUmZNWYT4Ko21S5j9tRLAJtTnX5pm7L935RtfRk4aEDdVkPM/5IGYffNbxl1F9SDre91x6i7oCm14ZoPGXUXRmT02V+qM/tLk2vHjc3ji8Xj73vrqLugMbLluquOugsaqOnM/4t9vpx3drohIvaPiDMi4owr/u+bw+yTJEmShuNbwL5leV+gXej7DrBbRGwQERsAu5V1lwMPi4j7lHpPAc5vuL/qX9v8X8/+P/v6/w67T5IkSZIGr6ff/n997LHD7JMkSZIWsbGfOSYizul0E3DfTverT9G/87d/lA10TZIkaaLF+I8ePwz4ckS8HPgd8DyAiNgOeFVmviIzr4mIdwOnl/u8KzOvKfXeCXw/Im4DLgH2G/YO6O4Wkv/r2f/QM08y+0uSJM3TIsj+mkCD+O1/n1NOMf9LkiTN07Tm/7EfHEMVgp8KXNuyPoAfD787kiRJGgeZeTWwa5v1ZwCvqF0/CjiqTb1PAJ9oso9aEPO/JEmSNB3M/pIkSRqaxTA45jhg3cz8eesNEbF8+N2RJEmaDtM6elwjZ/6XJEkaMrO/RsTsL0mSNALTmv/HfnBMZr68y20vGmZfJEmSJDXL/C9JkiRNB7O/JEmShmnsB8dIkiRpVFYZdQckSZIkDYXZX5IkSZoe05n/p3OvJUmSJEmSJEmSJEmSNBWcOUaSJEltRUzneUclSZKkaWP2lyRJkqbHtOZ/Z46RJEmSJEmSJEmSJEnSxHLmGEmSJHUwnaPHJUmSpOlj9pckSZKmx3Tmf2eOkSRJkiRJkiRJkiRJ0sRy5hhJkiS1FVM6elySJEmaNmZ/SZIkaXpMa/535hhJkiRJkiRJkiRJkiRNLGeOkSRJUgeOo5YkSZKmg9lfkiRJmh7Tmf8dHCNJkqS2pnVqRUmSJGnamP0lSZKk6TGt+X86hwRJkiRJkiRJkiRJkiRpKjhzjCRJktqKmM7R45IkSdK0MftLkiRJ02Na878zx0iSJEmSJEmSJEmSJGliOXOMJEmSOpjO0eOSJEnS9DH7S5IkSdNjOvO/M8dIkiRJkiRJkiRJkiRpYjlzjCRJktoKx1FLkiRJU8HsL0mSJE2Pac3/i2JwTEQ8BHg2sBmQwBXAtzLz/JF2TJIkSdJAmf0lSZKk6WD2lyRJ0jCN/ZCgiHgL8EWqE1+dBpxelr8QEQeNsm+SJEmTLYZQpFlmf0mSpFEx+2u4zP6SJEmjNJ3ZfzHMHPNy4G8z87b6yoj4IHAecFi7O0XE/sD+AFu99s1s+rRnN91PSZIkSf3pO/s/4+ADecxzntF0P6Wpsfvmt4y6C4vW1ve6Y9RdUI82XPMho+6CJE2jBWX/Uueu/L/DG9/IVs96VpP9lKbGjhtPXvZ//H1vHXUX1IMt11111F3QmFl/jQeNuguaUIthcMydwKbAJS3rNym3tZWZhwOHA+z87R9lY72TJEmaUBHjO8JbE6vv7H/omSeZ/SVJkubJ7K8RWFD2h5Xz/z6nnGL+lyRJmqdpzf+LYXDMgcB3I+JC4NKy7v7A3wCvHVmvJEmSJA2a2V+SJEmaDmZ/SZIkDdXYD47JzOMjYitge2AzqpNUXQacnpnOUSxJktSY6Rw9rtEx+0uSJI2K2V/DZfaXJEkapenM/2M/OAYgM+8EfjrqfkiSJElqltlfkiRJmg5mf0mSJA3TohgcI0mSpOELVhl1FyRJkiQNgdlfkiRJmh7Tmv+nc68lSZIkSZIkSZIkSZI0FZw5RpIkSR1M53lHJUmSpOlj9pckSZKmx3Tmf2eOkSRJkiRJkiRJkiRJ0sRy5hhJkiS1FVM6elySJEmaNmZ/SZIkaXpMa/535hhJkiRJkiRJkiRJkiRNLGeOkSRJUlsR0zl6XJIkSZo2Zn9JkiRpekxr/nfmGEmSJEmSJEmSJEmSJE0sZ46RJElSB46jliRJkqaD2V+SJEmaHtOZ/6dzryVJkiRJkiRJkiRJkjQVnDlGkiRJbQXTed5RSZIkadqY/SVJkqTpMa3535ljJEmSJEmSJEmSJEmSNLGcOUaSJEkdTOfocUmSJGn6mP0lSZKk6TGd+d/BMZIkSWorYjoDsiRJkjRtzP6SJEnS9JjW/O9plSRJkiRJkiRJkiRJkjSxHBwjSZKkDlYZQpEkSZI0euOd/SPi3RFxTkT8PCJOiIhNO9TbNyIuLGXfvhqVJEmSJtb4Zv8mjW/PJEmSJEmSJEmC92XmIzNzG+A44JDWChGxIXAosAOwPXBoRGww3G5KkiRJGlerjboDkiRJGk/BdJ53VJIkSZo24579M/P62tV1gGxT7anAiZl5DUBEnAjsDnyh+R5KkiRJi8e45/+mODhGkiRJkiRJkjTWIuI9wD7AdcDObapsBlxau35ZWSdJkiRJkJmWNgXY37bGvx33aXG0M6ltuU+Lo61J3Ccfv8XRzrDbslgs/RXfg8a/nUlty31aHG1N4j75+C2OdtynxdOW2b+3xwg4o1b2b7n9JODcNuXZLfXeCryzzfbfDLy9dv0dwBtHvd+W8Su+By2Ottwn23KfFmdbk7hPPn6Lo51J3SfLYMsqqJP9bWtRtDPMttwn2xpVO8Nsy32yrVG1M8y2JnGfJPXP96Dxb2dS23KfFkdbk7hPw2zLfVocbU3iPg2zLbP/HDLz8MzcrlYOb7n9yZn58Dblmy2b+jywd5smLgO2qF3fHLhisHuhCeF70OJoy32yrVG1M8y23CfbGlU7w2zLfdLYcHCMJEmSJEmSJGlsRcSDa1f3AC5oU+07wG4RsUFEbADsVtZJkiRJEquNugOSJEmSJEmSJHVxWERsDdwJXAK8CiAitgNelZmvyMxrIuLdwOnlPu/KzGtG011JkiRJ48bBMZ0dPncV2xqDdobZlvtkW6NqZ5htuU+2Nap2htnWJO6TpP75HjT+7UxqW+7T4mhrEvdpmG25T4ujrUncp2G2ZfZvUGa2O40SmXkG8Ira9aOAo4bVLy1avgctjrbcJ9saVTvDbMt9sq1RtTPMttwnjY3IzFH3QZIkSZIkSZIkSZIkSWrEKqPugCRJkiRJkiRJkiRJktQUB8e0ERG7R8SvIuKiiDiowXaOioirIuLcptoo7WwRESdHxPkRcV5EvK7BttaKiNMi4uzS1jubaqu0t2pEnBURxzXczoqI+EVE/DwizmiwnfUj4qsRcUF5vh7fUDtbl32ZKddHxIFNtFXae305Hs6NiC9ExFoNtfO60sZ5g96fdq/XiNgwIk6MiAvL5QYNtvW8sl93lvNpN9XO+8rxd05EHBMR6zfY1rtLOz+PiBMiYtMm2qnd9qaIyIjYqN92OrUVEcsi4vLaa+vpTbRT1v9T+aw6LyLe2287ndqKiC/V9mdFRPy8wba2iYifzrzXRsT2DbXzqIj4SXlfPzYi7jmAdtp+1jb1PiFpcMLs309bZv/+22o8/4fZfyHbNvsPvq2BZ/9ObdVuG1j+77BPA8/+ndoq6wea/zvsk9m/97bM/9IiFBOW/UtbQ8n/MeTsX9psPP/HhGX/0s7Q8n8MKfuXthZ9/u/QzsCzf5e2Bp7/O7Rj9u+jrbLe7L/wtvztX91lpqVWgFWB3wAPBNYAzgYe1lBbOwHbAuc2vE+bANuW5fWAXze4TwGsW5ZXB04FHtfgvr0B+DxwXMOP4QpgoybbKO18GnhFWV4DWH8Iba4K/B7YsqHtbwb8Fli7XP8ysF8D7TwcOBe4B7AacBLw4AFu/26vV+C9wEFl+SDg3xts66HA1sByYLsG29kNWK0s/3vD+3TP2vIBwCeaaKes3wL4DnDJoF7LHfZpGfCmQR13XdrZuRzja5brGzfVVsvtHwAOaXC/TgCeVpafDixvqJ3TgSeV5ZcB7x5AO20/a5t6n7BYLIMpmP37bcvs339bQ83/mP173b7Zf/BtDTz7d2qrrB9o/u+wT8sYcPbv0tbA8/9cn0uY/edqy/xvsSyywgRm/9LWUPI/Q87+pZ3G8z8TnP1LO43lf4aU/cu2JyL/d2hn4Nm/S1sDz/8d2jH799eW2b+/tvzt39K1OHPM3W0PXJSZF2fmrcAXgWc30VBmfh+4poltt7RzZWaeWZb/ApxPFVyaaCsz84ZydfVSsom2ImJz4BnAJ5vY/rCV0Ys7AUcCZOatmfnnITS9K/CbzLykwTZWA9aOiNWoAuwVDbTxUOCnmXlTZt4OnALsNaiNd3i9PpvqSw3lcs+m2srM8zPzV4PY/hztnFAeP4CfAps32Nb1tavrMID3ii7vqx8C/nkQbfTQ1kB1aOfVwGGZeUupc1WDbQEQEQE8H/hCg20lMDOS+14M4L2iQztbA98vyycCew+gnU6ftY28T0gaGLN/f22Z/fswovxv9u+B2b+Rtgae/Tu1VQw0/w/rPbxLWwPP/2b/vtsy/0uLz8Rl/9LWUPL/MLM/TF7+n+Df/oeR/WFC8v+wsn+Xtgae/83+jbRl9u+vLX/7V1cOjrm7zYBLa9cvo6Efk0chIpYAj6Ya2d1UG6uW6beuAk7MzKba+jDVB96dDW2/LoETIuJnEbF/Q208EPgj8Kmopov8ZESs01BbdX/PgD702snMy4H3A78DrgSuy8wTGmjqXGCniLh3RNyDavTpFg20U3ffzLwSqg9HYOOG2xu2lwH/12QDEfGeiLgUeDFwSENt7AFcnplnN7H9Nl5bpo08qsFp9LYC/i4iTo2IUyLisQ21U/d3wB8y88IG2zgQeF85Jt4PvLWhds4F9ijLz2PA7xUtn7WT/j4hLXZm//7bMPsv3Cjyv9l/4Sb9M30isn9pZ5j5fxjZH4af/83+82D+lxaNic7+0Hz+H2L2h+Hl/0nO/tBg/h9i9gfzfxMazf9m/76Y/fvjb//qysExdxdt1jU2AnqYImJd4GvAgS0jNwcqM+/IzG2oRp1uHxEPH3QbEfFM4KrM/Nmgt93BEzJzW+BpwGsiYqcG2liNavqv/8rMRwM3Uk3D1ZiIWIPqQ+IrDbaxAdXoyQcAmwLrRMRLBt1OZp5PNRXgicDxVFOj3t71TuooIg6mevw+12Q7mXlwZm5R2nntoLdfviwdTIMBvMV/AQ8CtqH6UviBhtpZDdgAeBzwZuDLZYR3k15Ig39MK14NvL4cE6+n/DdNA15G9V7+M6ppEG8d1IaH9VkraWDM/n0y+/dlqPnf7K9OJiX7w9Dz/7CyPww//5v9e2T+lxaVic3+MJz3o2Fkfxh6/p/I7A/N5/9hZX8w/w/aMPK/2b8vZv/++Nu/unJwzN1dxsqjyDanuanghiYiVqd6wX4uM78+jDbLtIDLgd0b2PwTgD0iYgXVFJi7RMRnG2gHgMy8olxeBRxDNQ3noF0GXFYbcf9VqsDcpKcBZ2bmHxps48nAbzPzj5l5G/B1YMcmGsrMIzNz28zciWoqtSZHugL8ISI2ASiXAzm1zahFxL7AM4EXZ+awfiT4PAOa3rrFg6i+oJ1d3i82B86MiPs10BaZ+YfyQ8GdwBE0814B1fvF18uUtqdR/RfNRg21RZka9TnAl5pqo9iX6j0Cqi/ujTx+mXlBZu6WmY+hCv6/GcR2O3zWTuT7hDRBzP4DYvZfkGHnf7N/fybyM33Csj+0Qf/8AAAgAElEQVQMMf8PMfvDEPO/2b935n9p0ZnI7A/Dz/8NZ38YYv6f4OwPzef/oWV/MP8Pygjyv9l//sz+ffC3f83FwTF3dzrw4Ih4QBlZ+/fAt0bcp76UEYVHAudn5gcbbus+EbF+WV6bKiBdMOh2MvOtmbl5Zi6heo6+l5mNjEqOiHUiYr2ZZWA3qmm5Biozfw9cGhFbl1W7Ar8cdDsthjEi9HfA4yLiHuVY3JXqfHwDFxEbl8v7U32gN71v36L6UKdcfrPh9hoXEbsDbwH2yMybGm7rwbWre9DMe8UvMnPjzFxS3i8uA7Ytr7eBmwlCxV408F5RfAPYpbS5FbAG8KeG2oLyXp6ZlzXYBlQ/Sj2pLO9CQ19ya+8VqwBvBz4xgG12+qyduPcJacKY/ftry+zfhxHkf7N/fybuM33Ssj8MN/8PMfvDcPO/2b+37Zr/pcVn4rI/DC//Dyv7w/Dy/4Rnf2g+/w8t+4P5fxCGlf/N/n0z+/fB3/41p8y0tBSq8xX+mmo02cENtvMFqum3bqN60355Q+08kWqKyHOAn5fy9IbaeiRwVmnrXOCQITxfS4HjGtz+A6mm6TsbOK/hY2Ib4Izy+H0D2KDBtu4BXA3cawjP0TupAtC5wGeANRtq5wdUXyrOBnYd8Lbv9noF7g18l+qD/LvAhg22tVdZvgX4A/Cdhtq5iOr8yzPvFZ9ocJ++Vo6Jc4Bjgc2aaKfl9hXARg3u02eAX5R9+hawSUPtrAF8tjx+ZwK7NLVPZf3RwKsG0cYc+/VE4GflNXwq8JiG2nkd1ef8r4HDgBhAO20/a5t6n7BYLIMrmP37acvs3397Q8n/mP3nu22z/+DbGnj279RWy+0rGED+77BPA8/+XdoaeP7v9Nhh9u+1LfO/xbIICxOW/UtbQ8n/jCD7l3aX0lD+Z0Kzf2lrKPmfIWX/0taiz/8d2hl49u/S1sDzf4d2zP79tWX2768tf/u3dC1RnlRJkiRJkiRJkiRJkiRp4nhaJUmSJEmSJEmSJEmSJE0sB8dIkiRJkiRJkiRJkiRpYjk4RpIkSZIkSZIkSZIkSRPLwTGSJEmSJEmSJEmSJEmaWA6OkSRJkiRJkiRJkiRJ0sRycIwkqaOIODoispQlfWxn+cx2Bte7yRIRS2uP9bJR90eSJEnTxew/PGZ/SZIkjZLZf3jM/tJ4cXCMhiYi9ipv/ndGxEYttx1VbvveqPqnhYmI/SJimR/q0soiYv2Z10ZE7Dnq/kiSNExm/8lk9pfaM/tLkqaZ2X8ymf2l9sz+0uK22qg7oKmytFz+IjP/1HLbzuXy5OF1RwOyH/CksrxsdN2Qxs76wKFl+dPAN0bYF0mShm1puTT7T5b9MPtL7Zj9JUnTbGm5NPtPlv0w+0vtmP2lRczBMRqmpeVypSAcEQ8AlrS7TZKmRWYuB2LU/ZAkaUCWlkuzvyS1MPtLkibM0nJp9pekFmZ/abx4WiUNRURsCDyiXG2dQnHXcnkTcOrQOiVJkiRp4Mz+kiRJ0nQw+0uSpMXEwTEalidRjYy8E/h+y227lMsfZuZtQ+2VJEmSpEEz+0uSJEnTwewvSZIWDQfHaFhmzk15Vmb+ueW2peWykakVI2KriHhvRJweEX+MiNsi4rqIODMiPh4Ru0bE3aY0i4i1I2KvUufUiLi6dt/zIuK/IuJRPbS/PCIyIrJcXzUi9ouIEyPi8oi4PSJWtNxn1Yh4aUQcGxGXRsRfI+LmsnxmRBweEc+JiHv08bj0tX8z+8Xsc8vMfraUZQvs3/oR8ZaIOCUiroqIWyPi+oi4OCJ+HBGHRcTSds9dy3Z2j4ijI+LCiPhLRNwUEb8p6544j/5sEBH/HBEnRcQVEXFLRNwYEb+KiM9HxIsjYq0u979HRLw+Ik6OiN+X+18VET+MiLdGxL3maH9Z7TFdWtY9LiI+FxGX1LZ3XETs3uM+rRYRry2P57URcUNEXBARH4iILXt9bAYtInYox/ivynN2Y3nOPh0Ru8y9hbu2ExGxZ0R8pjz/15fj6MryPL4tIpZ0uO/9y2PzldKPG8p9ryrH/ls6PWcRsaS8Nn5bW71vh9fHktr9lvb6uhnH40mSpBqzv9l/vv0z+698f7O/2b/extgdT5Ik1Zj9zf7z7Z/Zf+X7m/3N/vU2xu54kiZOZlosAy1ADqis6LMfqwEfAm7voa0ntbn/b3vs57/O0Y/ltbobAj/otq/ARsBpPba9Zx+PT1/717Jf3cqyBfTtscAfetz++h22cR/guz3c/5PA6nP0Z1/guh62dWiH+z8OuHyO+/4J2K1LH5bV6i4F3gbc0WV775xjnzYGzuxy/2uBJwNH19Yt6eN4u+t4meM1e3gPj/OXgbXnaO9BwM962NZv29x3KdV/u8x136uAJ7a5/5Iej92VHtPS7pyvm3E8niwWi8UyvWUen3lzlRV99sPs371ffe0fZv925dAO9x+7rIbZf6b8ts19l2L2n9fxZLFYLJbpLfP4zJurrOizH2b/7v3qa/8w+7crh3a4/9hlNcz+M+W3be67FLP/vI4ni2USy2pIE6iMKv4asEdZdQfwDapR6lcB9wAeCjwV2IZq6sdWawPXACcCZ1F9KN0GbAZsCzwfWB14a0RclZkf7qFrnwWeCJwNfAFYAdwTeGStzhFUIRHgolLv18DNpe7WwE7ADj20102/+/d2qkD/L8DflnV7tWnngvl0KqpR8cdQhTiopuM8DvgdVXDZCHg41Tlrt+6wjQ2Bn1AFJYBfAl+hehzvLP3dD9gceDlVONuvw7beCLy/tupHwLHAJcCqVIHoScDOtDmOImIbqvPtrl1WnQV8vuzP/age5ycA9waOi4jdMnN5u77U7A+8kOo5Oxo4D1gD2B14QenHIRFxSma2nuuXiFgDOB54dFl1FdWXhXOBdcp29qZ6zH4+R18G6X+o9gvgr8CngR9TvX63o3qu1gOeB9wrInbPzGzdSERsRfX8b1hWXQl8iep1dyPVsbUd8Ezav/bXKuvPo3rPOB+4uqzfAtgTeAzVF7HjImKbzFxRu/9VVK+FjYH/LutOBv6jTVtXdXow2hnH40mSpFEz+/fE7G/2N/ub/cHsL0la5Mz+PTH7m/3N/mZ/MPtL7Y16dI5l8grVG2u9HEZtxHPLbTOjqU9tc78n9dGHf661eQnwiC51HwNs2WE/Vutyvy2pPjwTuB5Yr0O95aw8EvNDwCod6m7M7CjO04F15mj/bv2e5/M00P0b0PHz3Npj9Z9z1N0BWLPN+mNq23h7u8cbWBf4Tq3e7m3qPJ7Z/0C4GXhBl75sBuzQsm4VquA508aHO/TlHbU6vwPWalNnWctxdEK74wN4fa3Otzv09e21OmcB925TZ2/u/t8XS/p4XrseJ1RhbKad3wMP63BMXlyr95o2dVYFzqnV+Sxwjw5trg48q0M7Hd8zSp0X1l6rn+pQZ0mtH0f38BgtrdVf1ub2sTyeLBaLxTLdBbN/a73lrPwZa/bv3i+zv9nf7G/2t1gsFssiKZj9W+stZ+XPWLN/936Z/c3+Zn+zv8Uy8jLyDlgmv1CNvk3ggja3/abc9q4Btrcu1WjPBG6Z68Ouz7Z2rn2AvKRDneW1Ome0+1Cr1X1cre7rx+C5m9f+DajNg2ptPnoB99+2dv8j56i7AfDnmZDQ5vYTatvafwF92aN2/58A0aXucbW6r2hzez3U/AnYoMN2VqH6YphUo7BXa7l9DWanrrwFeHCXPr2vJUgt6eN57XqcsPJUj0/rsp3tmZ36cAWwasvtL6pt5wfdXm8DOFY/Xdq5iTZTdDL4kDx2x5PFYrFYLK0Fs//yWh2z/9xtmv3N/mZ/s7/FYrFYFmnB7L+8VsfsP3ebZn+zv9nf7G+xjLysgtS8Hcvlj+srI2Jj4IHl6k8G2N7TmJ1W7fOZ+YsBbrtVfZ96me7w45l5Z5fbb6ot/23HWsMz3/0bhH4fg5fWlt/fsRaQmdcC3y5Xd4qINWdui4j7AE8pVy+mmn5wvp5TW35fZmaXuod1uF87/1P6fjfl+DqlXF2T2SkmZzyB2akrj83MC7u080GqQNqoiFjC7FSPv8jM/+tUNzNPo5peEKqR3o9pqfLi2vLb53i99Wvm9bE2K0+R2pRxPJ4kSWpl9p9l9p+b2d/sb/ZvbxyPJ0mSWpn9Z5n952b2N/ub/dsbx+NJmlirjboDmmwldGxbrv6o5ebHl8sEfjrAZp9YW/5WPxsqQX4fYDfgYVQjju/RofrmPWzyB3Pcfh5wBbAp8PJyDtUjgNOa+LBvYP8G4SSqYyKAT0TEg6i+7HQLc3V/Vy5vBbaOiLbnJ61Zs3b5QKopJWHl4+i4BT7+25fLpDrHazc/Bm6g+g+Iub6QzPV6uby2vEHLbY+tLX+320Yy88qI+CXVuV6btH1t+YQe6p9Ade5ZqB6r02q3zTxv11Gdt3bBImIH4CVU/9nxQKrznq7eofrmwM/6aa8H43g8SZJ0F7P/3Zj952b2N/vPxew/PseTJEl3Mfvfjdl/bmZ/s/9czP7jczxJE8vBMWradsyGkB+33DYTkn/VafTiAtXD3Pkda80hIl4A/Ddwrx7vcs8e6lze7cbMvCMi/hH4GtU0eC8r5c8R8RPgh8B3MrPvD+OG9q9vmfnLiDgMeCuwDtU0cMsi4lKqY+j7wP9m5iUdNrGkXK5BdQ7S+agHgEEcR5uUy99n5l+6VczMOyPiN8CjgA0jYo3MvLVD9T/N0e4tteW1Wm7btLZ80RzbmanTdEjepLb86x7q1+vcdd+IWI/Z4/SCOUZYdxQRa1D9x8BL56pbM4zXxzgeT5Ik1Zn9V2b2n4PZ3+zfQ32z//gcT5Ik1Zn9V2b2n4PZ3+zfQ32z//gcT9LEcnCMBiYitgXu37L66eXyVuAhLaN5dyuXf4qIPVvu98PMnOuNu5P6h9UNC9lAROwEfB7uOvXYmVQjm39DNTK1/qExE8RWnWu7mXlzD3WOi4jtqcLhM6hGrK5PNW3k04D3RMS5wJsz8/he9qdVU/s3KJn5tog4HXgLs6NftwBeUMrHIuJ44MDMbA1VvYb+dtaoLfd9HFGNOAa4scf69XbWozqHbjv9/DfBurXlmzrWmtVr3/uxXm25l/ZaH6cZg3jOAD7ObEC+hWoKztOpvuTeCNxRbtsF+KeyPIzXxzgeT5KkKWX2N/sPitn/rvua/dsz+/fG7C9JaozZ3+w/KGb/u+5r9m/P7N8bs7/UBwfHaJAOAPbtcNsawNc73PZEVp7KDmBnYPkC+3F9bXndjrW6W8ZsgNw/M49oVyki1lng9rvKzLOBvcqI2CdQnb91p3K5OtWI3m9HxEsz83MLaGIZI9y/XmTmMcAxEbEp1ZSJOwJLqc7xGFRfGHaMiMdnZn2E9w1UXypWZOYD+ujCII6jv5S+9Po41tvpOkK4D/Xg1GkqzbphHAP1fe2lvU6PU9/PWTkP6svL1cuAJ2XmxR3qbraQNvowjseTJGl6mf0HxOxv9sfs343Zvzdmf0lSk8z+A2L2N/tj9u/G7N8bs7/Uh1XmriItOpfVlh863zuXqdVmzl95RqcAWWw53+3PR2b+JTOPz8xDMnMp1fRqHyo3B/DBiJjXyNVx2r9eZOYVmfmlzHxdZj4K2IpqtDtUo8Xf3XKXmSkst4iIfqa86+s4Kq4sl/crX3g6KueZfVC5enWXqfD6dUVt+W96qN9LnX5dWVt+cA/163Xu2p8y5eB15erW5TGdr12oXlsAh3UKyMWwXx/jeDxJkjRqZv8uxmn/emH2Hzizf3dmf0mSFhezfxfjtH+9MPsPnNm/O7O/JMDBMRqgzNwvM2OmUI30nbFNy23vKut/W19fK8v76MoPast7LOD+92Z2VqXfzFH3qQvY/oJl5tWZ+QbgjLJqY3oLFXWD3r+7pmZbYCiZl8y8EHgus1Pctf73wSnlclXgWX009UNg5tyVz4yIhbxfnlYuA9h1jro7Mjvi97RuFftU3/Yu3SpGxCYs/AvCfNT79JQe6u9WW259rH5YLten+q+L+bpvbbnf10d92sJBvDbG8XiSJE0ps3/zzP5m/wEw+3dn9pckqQdm/+aZ/c3+A2D2787sLwlwcIyatXO5vBo4p+W2peXy5Aba/T/gmrL8ooh4xDzvXz8f44M6VSojOF8/z20Pyora8nxPjzbo/atP1zeU6Rgz8zrg2nK1df//p7Z8yEKniMzMPwInlKsPBF6xgM18rbb8pjm+RLylw/0G7UfAH8ryHhHR8RgADmQI59TMzBVU578FeFRE7NapbkRsx2y4vwT4WUuVz9aW/2UBX256fX08m5V/CGhn0K+NcTyeJEmaYfZvzorastl/ZWb/7sz+3Zn9JUlaGLN/c1bUls3+KzP7d2f2787sLwlwcIyaNfNBdkpmzozEJSLWBnYoVwcekjPzRuCwcnUN4NhuQTkitomIu6ZJKwHswnJ1u4jYq8191gW+AmwxsI5X231qRLwuIu7Vpc7fMDvK9gbmHuW6kgb277e15W3n05d2IuKAiNg7IlbvUud5wEbl6tn12zLzVGZDwVZUz399VHDrtlaLiD0j4v+1uXkZsyPVPxIRz++ynU0iYvuW1f8LnFeWnwC8r11oi4i3MTva/VJgIeeT7Ulm3gZ8tFxdA/hyRGzYpk97Am9oqh9t/Htt+eiIeEhrhYi4P/BFZj+73peZd7RU+wqzX8qfCPxPRLQ9x2p57p/Rsvr02vKbImKDNvfbATiq454UmXkNs9M9bjOA/7AYu+NJkqQas/88mf3N/pj9wezfydgdT5Ik1Zj958nsb/bH7A9m/07G7niSJtl8R55KPSlv3DNTmy1vuXlHYM2y3MQIcoD3U31A7kF1fsCzIuKY0pergLWBrammaduOarT7JbX7fxT4j7L81Yj4HNW0bX8BHg7sB2xKNVp5nwH2exPgw8B7I+Jk4FTgYqpRrRsBjwWez+xo1A9n5s0LaGeQ+/dd4ICyfGREfIjqsZwJLxdl5kXz6Nu2wEeAayPiBKoRwpdTTVV3P6rnbGZauwT+rc02XkYVkB9B9dxeHBFfBX4C/AlYi+qx3rZsb0PgyNaNZOZPI+ItVMfTWsCXIuIA4FvA76jC2pZU53J9MvCv1Kayy8w7I+KlVKO21wbeCOxcHu/LqKbyez6zU0TeBuyTmX/t/eFakPdRTVG5DdVj8MuIOIIqgK0D7A7sTRXwfs7sf3w0JjO/XIL5C6memzMj4miq5+wOqtfpy4GZ88meAPxnm+3cUb5E/YTqeX0xsEtEfJHqC9XMa2lbqiD5V6rwOeMnVMfcY4AlwAUR8QngV1TP4S7AC6imOPw88KI5du17wF5Uo9G/FBFfB/5cu/2UXl/DY3w8SZKmnNl/wcz+Zn+zv9m/rTE+niRJU87sv2Bmf7O/2d/s39YYH0/SZMpMi2XgheoDKEt5eMtt7y7rf9VwH1YHPk71AZtzlJ1a7htU07R1u883qD6oZq4v79CP5TN1eujzPj30NakC44eBVRb42Axy/1alOt9rp+0sm2ffjurxMbgBeGmX7axHNdq4l20l8K4u23oF1ReIubZxSIf7Px64Yo77Xg08tUsfltXqLp3jMZyzLtV5a8/s0p9rqYL/0bV1S/p4Pc75OqAasHlED4/zV4C152jvwVQjyefa1sVt7vs3VF+COt3nr1RfxParrduvQz+2oQrmnba1pFZ3aW19x9fNOB5PFovFYpnugtm/vq05M0+trtnf7N+pD8tqdZfO8RjOWRez/0wx+5v9LRaLxdJnwexf39acmadW1+xv9u/Uh2W1ukvneAznrIvZf6aY/c3+Fkvb4mmV1JSZ847+idnpwFpvO7nJDmTmbZn5GuBRVCOSf0E1cvOOcvkzqpHUO2Xm91vum5n5EqrRoSeX+rdSjdI8DnhBZu6ZCxu93c1nSn/fAHwTuAi4sfR5ZjTvx4DHZOaBmXnnQhoZ5P5lNb3dU4CDqEbfXsvs6PGFeBVVWHhX6dvlwC3A7VTH0w+BQ4GtMvMzXfr1l8z8e6ovbB8GzqIKDrdTBewLqb4IvAF4UGYe0mVbn6Q6/+g7qEbv/rFs50bgAqovHM9ndlrP1vv/hCq0vQE4pdz/ttKfnwAHlz58p9sDM0iZeRXVNKf/BPwUuJ4qzP0K+BCwTWaeNKz+lD7dnpmvpAqBRzJ7/N9MNY3nZ4FdM/N5cx2bmXkhVUD9e+CrVKH3Zqrj/ArgRKrzcz6xzX0vAh5N9d8J51OF4huoHpuPAdtm5pzTK5Zt/ZxqNPony/1v6n6PnrY5dseTJGnqmf0Xxuxv9h8Ks7/ZX5KkATL7L4zZ3+w/FGZ/s7+k7iIzR90HSZIkSZIkSZIkSZIkqRHOHCNJkiRJkiRJkiRJkqSJ5eAYSZIkSZIkSZIkSZIkTSwHx0iSJEmSJEmSJEmSJGliOThGkiRJkiRJkiRJkiRJE8vBMZIkSZIkSZIkSZIkSZpYDo6RJEmSJEmSJEmSJEnSxHJwjCRJkiRJkiRJkiRJkiaWg2MkSZIkSZIkSZIkSZI0sRwcI0mSJEmSJEmSJEmSpInl4BhJkiRJkiRJkiRJkiRNLAfHSJIkSZIkSZIkSZIkaWI5OEaSJEmSJEmSJEmSJEkTy8ExkiRJkiRJkiRJkiRJmlgOjpEkSZIkSZIkSZIkSdLEcnCMJEmSJEmSJEmSJEmSJpaDYyRJkiRJkiRJkiRJkjSxHBwjSZIkSZIkSZIkSZKkieXgGEmSJEmSJEmSJEmSJE0sB8dIkiRJkiRJkiRJkiRpYjk4RpIkSZIkSZIkSZIkSRPLwTGSJEmSJEmSJEmSJEmaWA6OkSRJkiRJkiRJkiRJ0sRycIwkSZIkSZIkSZIkSZImloNjJEmSJEmSJEmSJEmSNLEcHCNJkiRJkiRJkiRJkqSJ5eAYSVMnIo6OiCxlSZvbl9RuP3roHZQkSZI0EGZ/SZIkaTgiYkXJ1StG3ZcmRMTyme8Oo+7LIM31nUmSJslqo+6AJKl5EfFQYEfgscCjgPsCGwFrAX8GfgUsBz6VmRePqJuSJEmSGhQRBwP/Ulv16czcb0TdkSRJ0hiLiP2AJQCZuWyUfZEkaRAcHCNJ0+FTwA4dbrtPKU8E3hIR78nMdw6tZ5IkSZIaFxFbA+8YdT8kSZK0aOwHPKksLxtdNyRJGgwHx0hSi8xcAcSo+9GA64DTgHOAK4ArgQS2BJ4O7ASsDiyLiFUz85BRdVSSJEkahgnO/iuJiAA+CawJ3AisM9oeSZIkadJk5pJR90GSpG4cHCNJ0+EfgAsz8/YOt/97RLwY+AzVHwfeGhH/nZmXD62HkiRJkpryaqqZIm8E3gs4U6QkSZIkSZoqq4y6A5Kk5mXm+V0GxszU+RxwbLm6GvDUxjsmSZIkqVERsTnwb+XqIcDvRtgdSZIkSZKkkXBwjKTGRMTSiMhSlpV1j4iIwyPiNxFxc0T8MSJOiogXzmO7W0TEYRFxZkRcExG3RMTlEXFsROwXEav22e8ltX4f3UP97SLiPyLi7Ii4OiJuK/06NSI+EBE71OquGhGXlW3/MSLW6GH729b688V+9q0Hv6wt36/htiRJkjQhzP5jnf3/C7gncBbwkQFtU5IkSQ2IiIdGxEci4tyIuK7k6Esi4ssRsVcP919RsuSKcn2diPjniDij5NYby7bfExEbdtjG8ohI4Em1ddmmLOvWdpvtLqvdd2lZt2tEfC0iLo2Iv5bvDodHxJYt910rIv4xIn5csvVNEfGLiDgoItac4zG5Z0S8OCKOjIizIuLPtRx/ZsnxD5rrse1XRHywtv/P6vE+Z5b6t0bEvVtuWzsi9oqIj5fvIzPfT66LiPMi4r8i4lED6PfdnrcB1V03Ig6MiBMj4oryXe+aiDg9It4VEffpt++S1MrTKkkamoh4KXAE1XnuZ6wF7ArsGtVpfZ6bmX/tso1/BD4ErN1y06alPBN4Q0TskZkrBtj9dn1ZBzgceFGbmzcAti/lDRGxJDMvycw7IuJIqv/Y3AjYE/jyHE29srZ8RP8976r+JeD3DbclSZKkCWX2H4/sH9VApGcCdwCvLH3qd7OSJElqQES8EzgYaB0Afv9SnhcRpwB7Z+bVPWxvS+D/gIe23PS3pbw8Ip6ZmWf03fkFiIjDgLe0rH5gKc+NiF0z86yIuB/VjOfbtdR9ONUMiU+PiKdm5s1t2lgDuIqVv5fM2KCURwMHRMSBmfnxvnaqu88Ary/LL2F2Fve2IuKhpW8A327znP8SWNLmrvcEHlbKqyLi3zLzbQvtdBMi4mnA0cDGLTetQfU8bwccGBEvycxvDbl7kiaYg2MkDctjgZkAdhTwfaofaB8LvBxYB3gG8Fngue02UH4c/0Rt1bHA/wJ/BrYC/gF4APAI4IcR8ejM/OPA96Tqy1rAyaX/AH+l+qH7R8C1VAH04cDTS9/qv0AfweyXnFfS5QfyiLgHsz/AXwx8b2A7cfe2ngE8p1z9K/DtptqSJEnSRDP7zxpZ9i//WTozU8xHM/Nn/WxPkiRJzYmIfwMOKlfvAL5IlQdvpsq8LwPuSzWby/ci4nHtBoPUrA58hWpgzKnAF6j+GXJLYF+qgRP3BU6IiG0ys37qzbdTDe7+F6pBNADtZq25YJ67Wfcaqu8CvwU+BfwaWB94KfAEqkErX42Ih1N9D9iW6vfq44CrgYcABwD3Bv6OKnO/vU07q1ANjLkCOBE4B/gDcCewBbAj8Cyqv5d+LCKuyMxj+tivjspAn/OoHtM9IuKemXl9l7u8tLb8mTa3rw1cQ7VfZwGXA7cBm1E9Xs+nOg7eGhFXZeaHB7AbfYuIvYEvUX1HuoPqOf0u1fG5HrAz8IKyfExEPCUzG/u7iKTp4uAYScPydOAvwG6Z+dPa+s9GxMeA5VT//bl3ROydmV+r3zkillD91yhUgelFmfnlljrvpwr8z6AKgP8JPG/ge1L5ILM/jp8N7NOKiLEAACAASURBVNHyBWLG6yNiF6of8QHIzMsi4ttUoXvXiHhAZv62QzsvoPqxHeCTmZn9djwitgM2L1fXoHqsngI8ray7A3hNZjpzjCRJkhbC7F+MOPt/GLgPcCnwjj63JUmSpIZExOOZnUHlRuDpmfn9WpUvlPz7HaoZNR4JvAt4c5fNzsy2+F7goHq2jIgPUc3a8SKqQSgfp8qrAGTmD0u9A2vrvrHA3evkuVSDIp5Xn00yIo6gGgyzO9UMMj8AtgFenJmfr28gqtOQ/pxqkMhrIuLdmXlLSzu3Uf3u/Z1O+ToiHkn12N4PeH9EfDMz7xzAPrbzWarZbtYC9qYaGNSuT8HswPk/Uz1WrfYDTsrM2zts42DgeKqBRO+KiCMz8y999b5PEbEF1T9QrEo1SOlZmXl6S7WjIuI/qAb93Av4dEQ8MDNvG25vJU2iVUbdAUlT5c0tP44DkJkXUv0H6Yw3tbnvAcxOp/6B1h/Hy3ZupgqMV5ZVe0fEVv11+e4i4v7MTnd+NfC0Dj+Oz/Tre5n555bVM/8FG6y8761eUS5vp0NQXoA3AceU8iWqH/tnBsb8iOqPGEcNqC1JkiRNJ7P/rKFn/4h4KtVU7QCvzcwb+tmeJEmSGvVmZmcffHPLwBgAMvMaqgElN5VVr46I9efY7k9oGRhTtnUbVS5dUVY9MyK2XmDfF+oq4CWtp1ktg1LeVVv1GOC/WwfGlLq/phpsAtWsM9u3qXNHZh7fbeB5Zp7D7MyXD6SaTaYpnwNm+vKSLvX+jmqWH4CvtBn0Q9mvtgNjyu2XAP+vXF0PePb8uztwb2b2HwKe12ZgDABl/RvK1c1p7h8hJE0ZB8dIGpZr6fIDb2YeT3WOTIDHlfOI1s2c7ud24ANdtnM91X+NQvWFYs8F9ba7FzA789ZHM/PKbpU7OB64pCz/Q0S0nkeWiHgYs0H82CHM5PIH4ASqKSwlSZKkhTL7r2yo2T8i1gH+u1z9emZ+a6HbkiRJUrMiYk2qmRehGox9ZKe6ZbDDF8rVdYDd5tj8BzsNCimDUv6ztqrdaZOa9JnMvK7DbadTzfgy4+NdtvPD2vLD+ujPj2vLO/Sxna4y81KqmTQBlkbEZh2q1gfOtDulUq+Gsl+9KLPhvLhcPS0zfzDHXb5E9Z0Q5j7WJaknDo6RNCw/yMxb56hTP2/kzLTlRMTGzI6SPjszr5pjOyfUlpsIfE+sLS/oh+YyAv6IcnVTqungW72ytnxEm9sXJDP/PjMjM4PqS9TDgbdSnWLpncAvyn+aSpIkSQth9q8ZQfb/V6rH8HqqWXgkSZI0vh4FrFmWl/eQo+eTf783j9sf27FWM07tdEOZDeXqcvVGZgfWt/OH2vIGnSpFxJKIODQiTo6IKyPi5ojImQJcUKu+eQ/978fMbDerMHvqpHpf16CaJQiqQfY/bK1Tq7txRLwpIk6IiMsi4saW/arPzNP0fs3lb4ENy/I1EbFntwI8BZiZAfOhI+mxpImz2txVJGkgLppnnU1ry5vUlnuZ1aReZ5OOtRauHiLP72M7RwKHAqtTTaF+14/t5T8GXlquXkp1ztOBy8ybgPOA8yLiC1SnVdoMODYiHpuZZzfRriRJkiaa2f/uhpL9I+JxwGvL1bdl5uUL3ZYkSZKGoqn8e005FVM3nTL5MFw9x+0zpxG6ptspkWr1ANZqVyEiDgQOY3YQ0lzuOXeVvnwV+BjVqWRfAryv5fZnMjvQ57Od9j8iXkA1Y+S9emy36f2ay5La8u6l9KrjwCdJmg8Hx0galpvmrsKNteV1a8vrdajTyQ215fU61lq4mRB5R+s5UecjM38fEd8C9gaeHhGb1X683gu4d1k+svy3aaMy85KIOIhqmsbVqc6z+oKm25UkSdLEMfu3GEb2L/9heiTVf6D+f/buPMzSs6wT//eu7iSIYQlbyIQlQmBcIoI2qINKQDEMSHBGkWVUDGj/xH3EBdxGnNERR4fBBTAubCrCgAqExUEliKAQFIwoLqhsAgIalsiWrr5/f5zTdqWsqu5zquo9p877+VzXe51z3u153tOnq7711l3P89okT5m3vwAADGa/8u9uMvkQTjfz7uq+eFX9lyRP3LDqVUlemeStST6c5MRIPbfKyalJ/800qHupuz80/dngIUnuUlWf2d1/tmGXjVMq/Uq2UFVflOTXcnKGkD9J8jtJ/jbJB3P9oqHfnD7u63WdhtMt4tnKmXvWC2DUFMcAQ7nhaezzyRuebwz5H95mn+1sDPIf3nav+X1o+nioqm6wm5vkSZ6ayQ3yQ0kuS/I/putPDKt+PMkv7+L8s3rZhucXD9guAACrQ/bf2n5n/89P8unT53+b5Puqaqv97rbh+V2q6gemz/+qu//vLtoHAGB2+5V/d5PJV8mPTB+PJbm0u1+61U5V9RnDdSnJ5A9UT/xh6lcn+d5pP26a5P7T9Vd1919ucWyS/HBOFsYc7e4tp2atqtP5TO2ltR22bfyM/XB3P36/OwOwmeIYYCgXzrjPuzY8f/eG53c6jfNs3Odd2+41v3cm+ezp809L8oZdnOt3Mxm+8sIkj6yqH03yKUnuPd3+0u5+xy7OP6uNP1DddMB2AQBYHbL/1vY7+2+shHn4aR5zt5wslnlBEsUxAADD2q/8e7OqutkpplbaLpOvhKq6Q5I7TF/+1naFMVO3H6BLG/12kvcluWWSh1fV46YjSH5VTk7/tN2oMWcm+cLpy9dvVxgztRfXtXEUmlON4HKLHbZtnPJ16GIkgCQ7V/AB7KUvmIa2ndx7w/OrTjzp7vcmedv05V2r6panOM+Xbnj+utPv4ml71Ybnl+7mRNP5Qi+fvvyUJF+S5Otz8sb2TsF2P2z8gej9A7cNAMBqkP23sITZHwCAxfvTnCw+uLiqzjjF/rPk33vPsP2qLbb/65RGtc2QhEvu3A3P//YU+16ynx3ZrLuPJfn16cvbJLnX9PmJKZU2bt/s5jk5+MEQ1/WBDc//3Sn2/dwdtr0hJ0fm/NIFjGoDoDgGGMzNkjxiu41V9aU5WS38h939nk27PH/6eDjJd+xwnhsl+abpy87J+TT30nOSXDd9/q1Vdd4uz/e0nPwB6NFJvm76/N1JXrzLc8/q6Ibnrxm4bQAAVoPsv719y/7dfWV316mWTKZ0OuEZG7Z9+W7aBwBgdt398ZzMgbfIyXz4b1TVbZM8bPryX5L8v1Oc/r/ucK6zcjJLJ1tn6Y3T4BzEQoaPbHh+x+12qqrb5PoZeSjP2vD8q6vq9km+YPr6t6d/OLCV072uG2WHz8AM/mLD8/vs0N49c3LUzX+ju9eT/Or05U2SfN8e9A1gJopjgCH9ZFXdffPKqrpjkl/esOqntjj2Z5J8dPr8e6rqK7Y4zw0yGWrwRPXy87v7b3bX5X9rOtT5ib/qvHmSl1TV7bbbv6ruNZ0rdLvzvT8nfwHwn5KcuOH+tGkF+a5U1aVV9eCq2nYqvapaq6rvTPKtG1Y/ebdtAwAwWrL/1ufb1+wPAMCB9L9ycpSWn5oWGVxPVZ2T5Hk5WaTylO7+wOb9NrlnVf3Y5lFfpveJfzGT0QyT5Iru/qstjv/7Dc+3LXpYYm/OpIgoSR5UVffYvENVnZvJ9KI3GrJjSdLdVyU58b5/RZJH5eSokltOqTQ97oNJTvzsc6Sq/tPmfarq7EymTL3tHnT1j3Jy9JiHVtXnbNHeHbNDnzf4sQ3nelxVfVdVbfu76qq6ZVX9QFXdZdZOA2xl21+UAuyxlyS5b5JXV9UzMhmefD3J3TMJfWdP9/uN7n7+5oO7+61V9V+TPDWTr13Pq6oXTM/7gUzmWn1kTs4h+g9Jvnn/LiePmfb97knumuSvquo5mYy28s+ZhOnPSHL/JJ+WyQ8aO/2w8vNJHr7hdWfyA8peuEOSJyZ5f1X9dpI3JnlPJr9wuEmST0/y5bl+lflPdfcr9qh9AADGRfZfXPYHAOCA6e4/qqonJHlcJtnylVX17CS/l8k93IsymY7zxDRBVyf5oVOc9l2Z5OTHZTJd07OT/GOS22cyyuOJkRyvyfZZ+neTfNv0+S9V1RMzmQJ1fbruLd39ltO9zqF19yeq6ueTfGeSM5L8flX9ciZTSF2XScHPZUlumuSZSb52Ad38lST/PZP79N87XffhTAp2dvIzSX56+vx5VfWrSf5geuxFmYxA9O+yB9fV3R+vqp9J8oOZvI9XVtVTk7w+yVlJPn/aRiV5YXaYjra731lVD53ud2YmhWFHq+r5mRQzfSTJjTP5me/zknxhkkNJrtzNNQCcoDgGGMpVSZ6dyU3fr58um70kyX/Z7gTd/fPTKvcnJrlBkgdNl83elOSBOww7uGvd/bGquk8mw6J/5bQ/j8j2w8cf32b9ifP9flW9OZOb6UnyO9399zsdM4dbZPL+bvseZxKef7C7n7THbQMAMB6y/87nGyL7AwBwgHT391XVsUymmjmU5Kuny2avTPIV3f3RLbZtdF2SB2eSuz9/umz23iQP6O63b3OOF2dScPEFSS5M8nObtj8+yQ+foh+L9v1J7pbk3pkUcjx6umz080l+IosrjvmRTApLzpyue95p/Pv+bJLPzeRnqrUkXzNdNnpBkm/M3lzXj2ZSrHLfTP7Y4bs2bf/QtC9HskNxTJJ0929X1b0ymWLpDpkUwjx2h0OuTfLB+boNcH2mVQIG092/kslfW/5ikr9L8rFM/tLy95L8l+5+QHd/7BTneGqSOyd5QiYjoHwgySeSvDuToH9Zkrt291v36TI29uXa7n5wknsmuTyTIRA/nORYkn9K8oeZhOq77fADxka/s+H5L2y71+yenEmF9Q8meVkmc4T+07SfH0ryt5nMKftNSS5QGAMAwG7J/qe0X9kfAIADqrt/KMldMhkV5C8yyZsfT/LOTKbm/Iruvri7/+k0z/e2JPfIpPDgTzLJ0x/NZISO/5nk07r79Tscv55JMcRjM8m71+TkqDEHwvRnji/N5N73H+bke/q2JM9Nckl3f2NOUeC+j/17ayYFSBudcnqinvjqTEakfEVO/qz0ziRXJHlId3/5aRTZnG4/P57JSJmPzmQEzQ9l8jPeWzIZweau3X3FDOf7oyT/PpMCsOdmMoXXtZn8fPXPmYxK8wt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0MftLkiRJ02M6878zx0iSJEmSJEmSJEmSJGliOXOMJEmSuoopHT0uSZIkTRuzvyRJkjQ9pjX/O3OMJEmSJEmSJEmSJEmSJpYzx0iSJKkHx1FLkiRJ08HsL0mSJE2P6cz/Do6RJElSV9M6taIkSZI0bcz+kiRJ0vSY1vw/nUOCJEmSJEmSJEmSJEmSNBWcOUaSJEldRUzn6HFJkiRp2pj9JUmSpOkxrfnfmWMkSZIkSZIkSZIkSZI0sZw5RpIkST1M5+hxSZIkafqY/SVJkqTpMZ3535ljJEmSJEmSJEmSJEmSNLGcOUaSJEldheOoJUmSpKlg9pckSZKmx7Tm/0UxOCYifhd4JrA9kMD1wAmZefGCdkySJElSrcz+kiRJ0nQw+0uSJKlNYz8kKCLeBHyW4oevzgTOKpc/ExFvXsi+SZIkTbZooUmzzP6SJEkLxeyvdpn9JUmSFtJ0Zv/FMHPMy4Hfz8y7qjdGxPuBi4Cjum0UEUcARwDs9YY3sMszntF0P6WpsPc2dyx0F2r3xAfdudBdWNR22nTpQndBY2aLFTsvdBckLV5mf2nMmP9VZfZXJ7O/pBHMK/uX69yX/z/84XdxxBHPbbKfAGRm4zWAVv/FJuL2lird21IdWBLt/WPckpZKbbCkpXMPWNZSrbbqACxr6Xlq95jam/dgyZJ2ai1d1t7jt6SlrzRLW3w/v2Ppilbq5PIWvw8ub3F+j2VjP5eIarQYBsfcC2wHXN1x+7b0SVWZeQxwDMBLTjutvXdVSZKkCREt/lFJKpn9JUmSFoDZXwtgXtkf1s//8GPzvyRJ0hxNa/5fDINjXgt8MyIuA64pb3sI8HDgVQvWK0mSJEl1M/tLkiRJ08HsL0mSpFaN/eCYzPxaROwC7AlsT/EjVdcCZ2XmPQvaOUmSpIk2naPHtXDM/pIkSQvF7K92mf0lSZIW0nTm/7EfHAOQmfcC31/ofkiSJElqltlfkiRJmg5mf0mSJLVpUQyOkSRJUvuCJQvdBUmSJEktMPtLkiRJ02Na8/90HrUkSZIkSZIkSZIkSZKmgjPHSJIkqYfp/N1RSZIkafqY/SVJkqTpMZ3535ljJEmSJEmSJEmSJEmSNLGcOUaSJEldxZSOHpckSZKmjdlfkiRJmh7Tmv+dOUaSJEmSJEmSJEmSJEkTy5ljJEmS1FXEdI4elyRJkqaN2V+SJEmaHtOa/505RpIkSZIkSZIkSZIkSRPLmWMkSZLUg+OoJUmSpOlg9pckSZKmx3Tm/+k8akmSJEmSJEmSJEmSJE0FZ46RJElSV8F0/u6oJEmSNG3M/pIkSdL0mNb878wxkiRJkiRJkiRJkiRJmljOHCNJkqQepnP0uCRJkjR9zP6SJEnS9JjO/O/MMZIkSZIkSZIkSZIkSZpYzhwjSZKkriKmc/S4JEmSNG3M/pIkSdL0mNb87+AYSZIk9eAkg5IkSdJ0MPtLkiRJ02M68/90HrUkSZIkSZIkSZIkSZKmgjPHSJIkqatgOqdWlCRJkqaN2V+SJEmaHtOa/505RpIkSZIkSZIkSZIkSZMrM21dGnCEtca/jse0OOpMai2PaXHUmsRj8vFbHHXarmWz2UZrvgeNf51JreUxLY5ak3hMPn6Lo47HtHhqmf1ttsXTfA9aHLU8Jmt5TIuz1iQek4/f4qgzqcdkq7c5c0xvR1hrUdRps5bHZK2FqtNmLY/JWgtVp81ak3hMkkbne9D415nUWh7T4qg1icfUZi2PaXHUmsRjarOW2V9aPHwPWhy1PCZrLVSdNmt5TNZaqDpt1vKYNDYcHCNJkiRJkiRJkiRJkqSJ5eAYSZIkSZIkSZIkSZIkTSwHx/R2jLUWRZ02a3lM1lqoOm3W8pistVB12qw1icckaXS+B41/nUmt5TEtjlqTeExt1vKYFketSTymNmuZ/aXFw/egxVHLY7LWQtVps5bHZK2FqtNmLY9JYyMyc6H7IEmSJEmSJEmSJEmSJDXCmWMkSZIkSZIkSZIkSZI0sRwc00VEHBwRl0bE5RHx5gbrfCwi1kXEhU3VKOvsGBGnRsTFEXFRRLymwVobRsSZEXFBWeudTdUq6y2NiPMi4qSG66yNiB9GxPkRcXaDdbaIiC9GxCXl8/XEhursWh7LTLslIl7bRK2y3uvK8+HCiPhMRGzYUJ3XlDUuqvt4ur1eI2KriDglIi4rL7dssNazy+O6NyL2aLDOe8vz7wcR8ZWI2KLBWu8u65wfESdHxHZN1Knc98aIyIjYetQ6vWpFxOqIuK7y2npaE3XK2/+i/Ky6KCLeM2qdXrUi4nOV41kbEec3WGu3iPj+zHttROzZUJ3HRMTp5fv6iRHxgBrqdP2sbep9QlJ9wuw/Si2z/+i1Gs//Yfafz77N/vXXqj3796pVua+2/N/jmGrP/r1qlbfXmv97HJPZf/ha5n9pEYoJy/5lrVbyf7Sc/cuajef/mLDsX9ZpLf9HS9m/rLXo83+POrVn/z61as//PeqY/UeoVd5u9p9/Lf/2r/4y01ZpwFLgCuBhwArgAuD3Gqq1L7A7cGHDx7QtsHu5vBnw4waPKYBNy+XlwBnAExo8ttcDxwMnNfwYrgW2brJGWefjwCvK5RXAFi3UXAr8FNipof1vD1wFbFRe/zxweAN1HgVcCGwMLAO+ATyixv3f7/UKvAd4c7n8ZuDvG6z1SGBXYA2wR4N1DgKWlct/3/AxPaCy/GrgQ03UKW/fEfg6cHVdr+Uex7QaeGNd512fOvuX5/gG5fVtmqrVcf8/AEc2eFwnA08tl58GrGmozlnAfuXyy4B311Cn62dtU+8TNputnobZf9RaZv/Ra7Wa/zH7D7t/s3/9tWrP/r1qlbfXmv97HNNqas7+fWrVnv8HfS5h9h9Uy/xvsy2yxgRm/7JWK/mflrN/Wafx/M8EZ/+yTmP5n5ayf7nvicj/PerUnv371Ko9//eoY/YfrZbZf7Ra/u3f1rc5c8z97QlcnplXZuadwGeBZzZRKDO/DfyyiX131LkhM88tl38NXEwRXJqolZl5a3l1edmyiVoRsQPwx8BHm9h/28rRi/sCxwJk5p2Z+asWSh8IXJGZVzdYYxmwUUQsowiw1zdQ45HA9zPz9sy8GzgNOKyunfd4vT6T4ksN5eWhTdXKzIsz89I69j+gzsnl4wfwfWCHBmvdUrm6CTW8V/R5X/0A8Fd11BiiVq161Pkz4KjMvKNcZ12DtQCIiACeA3ymwVoJzIzk3pwa3it61NkV+Ha5fArwrBrq9PqsbeR9QlJtzP6j1TL7j2CB8r/Zfwhm/0Zq1Z79e9Uq1Zr/23oP71Or9vxv9h+5lvlfWnwmLvuXtVrJ/21mf5i8/D/Bf/tvI/vDhOT/trJ/n1q153+zfyO1zP6j1fJv/+rLwTH3tz1wTeX6tTT0x+SFEBErgcdSjOxuqsbScvqtdcApmdlUraMpPvDubWj/VQmcHBHnRMQRDdV4GPBz4N+jmC7yoxGxSUO1qp5HTR963WTmdcD7gJ8ANwA3Z+bJDZS6ENg3Ih4YERtTjD7dsYE6VQ/KzBug+HAEtmm4XtteBvx3kwUi4m8j4hrghcCRDdU4BLguMy9oYv9dvKqcNvJjDU6jtwvwhxFxRkScFhGPb6hO1R8Crax2rwAAG8pJREFUP8vMyxqs8VrgveU58T7gLQ3VuRA4pFx+NjW/V3R81k76+4S02Jn9R69h9p+/hcj/Zv/5m/TP9InI/mWdNvN/G9kf2s//Zv85MP9Li8ZEZ39oPv+3mP2hvfw/ydkfGsz/LWZ/MP83odH8b/Yfidl/NP7tX305OOb+osttjY2AblNEbAp8CXhtx8jNWmXmPZm5G8Wo0z0j4lF114iIpwPrMvOcuvfdw5Myc3fgqcCfR8S+DdRYRjH9179l5mOB2yim4WpMRKyg+JD4QoM1tqQYPflQYDtgk4h4Ud11MvNiiqkATwG+RjE16t19N1JPEfE2isfv003Wycy3ZeaOZZ1X1b3/8svS22gwgHf4N2BnYDeKL4X/0FCdZcCWwBOAvwQ+X47wbtLzafAf00p/BryuPCdeR/m/aRrwMor38nMopkG8s64dt/VZK6k2Zv8Rmf1H0mr+N/url0nJ/tB6/m8r+0P7+d/sPyTzv7SoTGz2h3bej9rI/tB6/p/I7A/N5/+2sj+Y/+vWRv43+4/E7D8a//avvhwcc3/Xsv4osh1obiq41kTEcooX7Kcz88tt1CynBVwDHNzA7p8EHBIRaymmwDwgIj7VQB0AMvP68nId8BWKaTjrdi1wbWXE/RcpAnOTngqcm5k/a7DGk4GrMvPnmXkX8GVg7yYKZeaxmbl7Zu5LMZVakyNdAX4WEdsClJe1/LTNQouIlwJPB16YmW39keB4apreusPOFF/QLijfL3YAzo2IBzdQi8z8WfmHgnuBj9DMewUU7xdfLqe0PZPif9Fs3VAtyqlR/wT4XFM1Si+leI+A4ot7I49fZl6SmQdl5uMogv8Vdey3x2ftRL5PSBPE7F8Ts/+8tJ3/zf6jmcjP9AnL/tBi/m8x+0OL+d/sPzzzv7ToTGT2h/bzf8PZH1rM/xOc/aH5/N9a9gfzf10WIP+b/efO7D8C//avQRwcc39nAY+IiIeWI2ufB5ywwH0aSTmi8Fjg4sx8f8O1ficitiiXN6IISJfUXScz35KZO2TmSorn6FuZ2cio5IjYJCI2m1kGDqKYlqtWmflT4JqI2LW86UDgR3XX6dDGiNCfAE+IiI3Lc/FAit/jq11EbFNePoTiA73pYzuB4kOd8vI/Gq7XuIg4GHgTcEhm3t5wrUdUrh5CM+8VP8zMbTJzZfl+cS2we/l6q91MECodRgPvFaWvAgeUNXcBVgA3NlQLyvfyzLy2wRpQ/FFqv3L5ABr6klt5r1gCvB34UA377PVZO3HvE9KEMfuPVsvsP4IFyP9m/9FM3Gf6pGV/aDf/t5j9od38b/Yfbr/mf2nxmbjsD+3l/7ayP7SX/yc8+0Pz+b+17A/m/zq0lf/N/iMz+4/Av/1roMy0dTSK3yv8McVosrc1WOczFNNv3UXxpv3yhursQzFF5A+A88v2tIZq/QFwXlnrQuDIFp6vVcBJDe7/YRTT9F0AXNTwObEbcHb5+H0V2LLBWhsDvwA2b+E5eidFALoQ+CSwQUN1vkPxpeIC4MCa932/1yvwQOCbFB/k3wS2arDWYeXyHcDPgK83VOdyit9fnnmv+FCDx/Sl8pz4AXAisH0TdTruXwts3eAxfRL4YXlMJwDbNlRnBfCp8vE7FzigqWMqbz8OeGUdNQYc1z7AOeVr+AzgcQ3VeQ3F5/yPgaOAqKFO18/apt4nbDZbfQ2z/yi1zP6j12sl/2P2n+u+zf7116o9+/eq1XH/WmrI/z2Oqfbs36dW7fm/12OH2X/YWuZ/m20RNiYs+5e1Wsn/LED2L+uuoqH8z4Rm/7JWK/mflrJ/WWvR5/8edWrP/n1q1Z7/e9Qx+49Wy+w/Wi3/9m/r26J8UiVJkiRJkiRJkiRJkqSJ488qSZIkSZIkSZIkSZIkaWI5OEaSJEmSJEmSJEmSJEkTy8ExkiRJkiRJkiRJkiRJmlgOjpEkSZIkSZIkSZIkSdLEcnCMJEmSJEmSJEmSJEmSJpaDYyRJPUXEcRGRZVs5wn7WzOynvt5NlohYVXmsVy90fyRJkjRdzP7tMftLkiRpIZn922P2l8aLg2PUmog4rHzzvzcitu6472Plfd9aqP5pfiLi8IhY7Ye6tL6I2GLmtRERhy50fyRJapPZfzKZ/aXuzP6SpGlm9p9MZn+pO7O/tLgtW+gOaKqsKi9/mJk3dty3f3l5anvdUU0OB/Yrl1cvXDeksbMF8I5y+ePAVxewL5IktW1VeWn2nyyHY/aXujH7S5Km2ary0uw/WQ7H7C91Y/aXFjEHx6hNq8rL9YJwRDwUWNntPkmaFpm5BoiF7ockSTVZVV6a/SWpg9lfkjRhVpWXZn9J6mD2l8aLP6ukVkTEVsCjy6udUygeWF7eDpzRWqckSZIk1c7sL0mSJE0Hs78kSVpMHByjtuxHMTLyXuDbHfcdUF5+NzPvarVXkiRJkupm9pckSZKmg9lfkiQtGg6OUVtmfpvyvMz8Vcd9q8rLRqZWjIhdIuI9EXFWRPw8Iu6KiJsj4tyI+GBEHBgR95vSLCI2iojDynXOiIhfVLa9KCL+LSIeM0T9NRGREZHl9aURcXhEnBIR10XE3RGxtmObpRHx4og4MSKuiYjfRsRvyuVzI+KYiPiTiNh4hMdlpOObOS5mn1tmjrOjrZ5n/7aIiDdFxGkRsS4i7oyIWyLiyoj4XkQcFRGruj13Hfs5OCKOi4jLIuLXEXF7RFxR3rbPHPqzZUT8VUR8IyKuj4g7IuK2iLg0Io6PiBdGxIZ9tt84Il4XEadGxE/L7ddFxHcj4i0RsfmA+qsrj+mq8rYnRMSnI+Lqyv5OioiDhzymZRHxqvLxvCkibo2ISyLiHyJip2Efm7pFxF7lOX5p+ZzdVj5nH4+IAwbv4b79REQcGhGfLJ//W8rz6IbyeXxrRKzsse1DysfmC2U/bi23XVee+2/q9ZxFxMrytXFV5eaX9nh9rKxst2rY1804nk+SJFWY/c3+c+2f2X/97c3+Zv9qjbE7nyRJqjD7m/3n2j+z//rbm/3N/tUaY3c+SRMnM222WhuQNbW1I/ZjGfAB4O4hau3XZfurhuzn3w3ox5rKulsB3+l3rMDWwJlD1j50hMdnpOPrOK5+bfU8+vZ44GdD7n+LHvv4HeCbQ2z/UWD5gP68FLh5iH29o8f2TwCuG7DtjcBBffqwurLuKuCtwD199vfOAce0DXBun+1vAp4MHFe5beUI59t958uA1+wxQzzOnwc2GlBvZ+CcIfZ1VZdtV1H8b5dB264D9umy/cohz931HtOy7sDXzTieTzabzWab3jaHz7xBbe2I/TD79+/XSMeH2b9be0eP7ccuq2H2n2lXddl2FWb/OZ1PNpvNZpveNofPvEFt7Yj9MPv379dIx4fZv1t7R4/txy6rYfafaVd12XYVZv85nU822yS2ZUgTqBxV/CXgkPKme4CvUoxSXwdsDDwSeAqwG8XUj502An4JnAKcR/GhdBewPbA78BxgOfCWiFiXmUcP0bVPAfsAFwCfAdYCDwD+oLLORyhCIsDl5Xo/Bn5TrrsrsC+w1xD1+hn1+N5OEej/Bvj98rbDutS5ZC6dimJU/FcoQhwU03GeBPyEIrhsDTyK4jdrd+2xj62A0ymCEsCPgC9QPI73lv09HNgBeDlFODu8x77eALyvctP/ACcCVwNLKQLRfsD+dDmPImI3it/b3ai86Tzg+PJ4HkzxOD8JeCBwUkQclJlruvWl4gjg+RTP2XHARcAK4GDguWU/joyI0zKz87d+iYgVwNeAx5Y3raP4snAhsEm5n2dRPGbnD+hLnT5BcVwAvwU+DnyP4vW7B8VztRnwbGDziDg4M7NzJxGxC8Xzv1V50w3A5yhed7dRnFt7AE+n+2t/w/L2iyjeMy4GflHeviNwKPA4ii9iJ0XEbpm5trL9OorXwjbAh8vbTgX+qUutdb0ejG7G8XySJGmhmf2HYvY3+5v9zf5g9pckLXJm/6GY/c3+Zn+zP5j9pe4WenSObfIaxRtrtR1FZcRzx30zo6nP6LLdfiP04a8qNa8GHt1n3ccBO/U4jmV9ttuJ4sMzgVuAzXqst4b1R2J+AFjSY91tmB3FeRawyYD69+v3HJ+nWo+vpvPnTyuP1b8OWHcvYIMut3+lso+3d3u8gU2Br1fWO7jLOk9k9n8g/AZ4bp++bA/s1XHbEorgOVPj6B59+evKOj8BNuyyzuqO8+jkbucH8LrKOv/Vo69vr6xzHvDALus8i/v/74uVIzyvfc8TijA2U+enwO/1OCevrKz3513WWQr8oLLOp4CNe9RcDjyjR52e7xnlOs+vvFb/vcc6Kyv9OG6Ix2hVZf3VXe4fy/PJZrPZbNPdMPt3rreG9T9jzf79+2X2N/ub/c3+NpvNZlskDbN/53prWP8z1uzfv19mf7O/2d/sb7MteFvwDtgmv1GMvk3gki73XVHe964a621KMdozgTsGfdiNWGv/ygfIi3qss6ayztndPtQq6z6hsu7rxuC5m9Px1VTzzZWaj53H9rtXtj92wLpbAr+aCQld7j+5sq8j5tGXQyrbnw5En3VPqqz7ii73V0PNjcCWPfazhOKLYVKMwl7Wcf8KZqeuvAN4RJ8+vbcjSK0c4Xnte56w/lSPT+2znz2ZnfpwLbC04/4XVPbznX6vtxrO1Y+XdW6nyxSd1B+Sx+58stlsNputs2H2X1NZx+w/uKbZ3+xv9jf722w2m22RNsz+ayrrmP0H1zT7m/3N/mZ/m23B2xKk5u1dXn6vemNEbAM8rLx6eo31nsrstGrHZ+YPa9x3p+oxDTPd4Qcz894+999eWf79nmu1Z67HV4dRH4MXV5bf13MtIDNvAv6rvLpvRGwwc19E/A7wR+XVKymmH5yrP6ksvzczs8+6R/XYrptPlH2/n/L8Oq28ugGzU0zOeBKzU1eemJmX9anzfopA2qiIWMnsVI8/zMz/7rVuZp5JMb0gFCO9H9exygsry28f8Hob1czrYyPWnyK1KeN4PkmS1MnsP8vsP5jZ3+xv9u9uHM8nSZI6mf1nmf0HM/ub/c3+3Y3j+SRNrGUL3QFNtjJ07F5e/Z+Ou59YXibw/RrL7lNZPmGUHZVB/iXAQcDvUYw43rjH6jsMscvvDLj/IuB6YDvg5eVvqH4EOLOJD/sGjq8O36A4JwL4UETsTPFlp1+Yq/rD8vJOYNeI6Pr7pBUbVC4fRjGlJKx/Hp00z8d/z/IyKX7jtZ/vAbdS/A+IQV9IBr1erqssb9lx3+Mry9/st5PMvCEifkTxW69N2rOyfPIQ659M8duzUDxWZ1bum3nebqb43dp5i4i9gBdR/M+Oh1H87unyHqvvAJwzSr0hjOP5JEnSfcz+92P2H8zsb/YfxOw/PueTJEn3Mfvfj9l/MLO/2X8Qs//4nE/SxHJwjJq2B7Mh5Hsd982E5Et7jV6cp2qYu7jnWgNExHOBDwObD7nJA4ZY57p+d2bmPRHxf4AvUUyD97Ky/SoiTge+C3w9M0f+MG7o+EaWmT+KiKOAtwCbUEwDtzoirqE4h74N/GdmXt1jFyvLyxUUv0E6F9UAUMd5tG15+dPM/HW/FTPz3oi4AngMsFVErMjMO3usfuOAundUljfsuG+7yvLlA/Yzs07TIXnbyvKPh1i/us5920bEZsyep5cMGGHdU0SsoPgfAy8etG5FG6+PcTyfJEmqMvuvz+w/gNnf7D/E+mb/8TmfJEmqMvuvz+w/gNnf7D/E+mb/8TmfpInl4BjVJiJ2Bx7ScfPTyss7gd/tGM17UHl5Y0Qc2rHddzNz0Bt3L9UPq1vns4OI2Bc4Hu776bFzKUY2X0ExMrX6oTETxJYO2m9m/maIdU6KiD0pwuEfU4xY3YJi2sinAn8bERcCf5mZXxvmeDo1dXx1ycy3RsRZwJuYHf26I/Dcsv1LRHwNeG1mdoaqYUN/NysqyyOfRxQjjgFuG3L9ap3NKH5Dt5tR/jfBppXl23uuNWvYvo9is8ryMPU6H6cZdTxnAB9kNiDfQTEF51kUX3JvA+4p7zsA+ItyuY3XxzieT5KkKWX2N/vXxex/37Zm/+7M/sMx+0uSGmP2N/vXxex/37Zm/+7M/sMx+0sjcHCM6vRq4KU97lsBfLnHffuw/lR2APsDa+bZj1sqy5v2XKu/1cwGyCMy8yPdVoqITea5/74y8wLgsHJE7JMofr913/JyOcWI3v+KiBdn5qfnUWI1C3h8w8jMrwBfiYjtKKZM3BtYRfEbj0HxhWHviHhiZlZHeN9K8aVibWY+dIQu1HEe/brsy7CPY7VO3xHCI6gGp15TaVa1cQ5Uj3WYer0ep5Gfs/J3UF9eXr0W2C8zr+yx7vbzqTGCcTyfJEnTy+xfE7O/2R+zfz9m/+GY/SVJTTL718Tsb/bH7N+P2X84Zn9pBEsGryItOtdWlh85143LqdVmfr/y7F4BsrTTXPc/F5n568z8WmYemZmrKKZX+0B5dwDvj4g5jVwdp+MbRmZen5mfy8zXZOZjgF0oRrtDMVr83R2bzExhuWNEjDLl3UjnUemG8vLB5Reensrfmd25vPqLPlPhjer6yvLDh1h/mHVGdUNl+RFDrF9d577jKaccvLm8umv5mM7VARSvLYCjegXkUtuvj3E8nyRJWmhm/z7G6fiGYfavndm/P7O/JEmLi9m/j3E6vmGY/Wtn9u/P7C8JcHCMapSZh2dmzDSKkb4zduu4713l7VdVb6+0NSN05TuV5UPmsf0DmZ1V6YoB6z5lHvuft8z8RWa+Hji7vGkbhgsVVXUf331Ts80zlMxJZl4G/CmzU9x1/u+D08rLpcAzRij1XWDmtyufHhHzeb88s7wM4MAB6+7N7IjfM/utOKLqvg/ot2JEbMv8vyDMRbVPfzTE+gdVljsfq++Wl1tQ/K+LuXpQZXnU10d12sI6XhvjeD5JkqaU2b95Zn+zfw3M/v2Z/SVJGoLZv3lmf7N/Dcz+/Zn9JQEOjlGz9i8vfwH8oOO+VeXlqQ3U/W/gl+XyCyLi0XPcvvp7jDv3Wqkcwfm6Oe67Lmsry3P9ebS6j686XV8r0zFm5s3ATeXVzuP/RGX5yPlOEZmZPwdOLq8+DHjFPHbzpcryGwd8iXhTj+3q9j/Az8rlQyKi5zkAvJYWflMzM9dS/P4twGMi4qBe60bEHsyG+6uBczpW+VRl+W/m8eVm2NfHM1n/DwHd1P3aGMfzSZKkGWb/5qytLJv912f278/s35/ZX5Kk+TH7N2dtZdnsvz6zf39m//7M/pIAB8eoWTMfZKdl5sxIXCJiI2Cv8mrtITkzbwOOKq+uAE7sF5QjYreIuG+atDKAXVZe3SMiDuuyzabAF4Ada+t4sd+nRMRrImLzPus8nNlRtrcyeJTreho4vqsqy7vPpS/dRMSrI+JZEbG8zzrPBrYur15QvS8zz2A2FOxC8fxXRwV37mtZRBwaEf+3y92rmR2p/o8R8Zw++9k2IvbsuPk/gYvK5ScB7+0W2iLircyOdr8GmM/vyQ4lM+8C/rm8ugL4fERs1aVPhwKvb6ofXfx9Zfm4iPjdzhUi4iHAZ5n97HpvZt7TsdoXmP1Svg/wiYjo+hur5XP/xx03n1VZfmNEbNllu72Aj/U8klJm/pLZ6R53q+F/WIzd+SRJUoXZf47M/mZ/zP5g9u9l7M4nSZIqzP5zZPY3+2P2B7N/L2N3PkmTbK4jT6WhlG/cM1Obrem4e29gg3K5iRHkAO+j+IA8hOL3Ac+LiK+UfVkHbATsSjFN2x4Uo92vrmz/z8A/lctfjIhPU0zb9mvgUcDhwHYUo5VfUmO/twWOBt4TEacCZwBXUoxq3Rp4PPAcZkejHp2Zv5lHnTqP75vAq8vlYyPiAxSP5Ux4uTwzL59D33YH/hG4KSJOphghfB3FVHUPpnjOZqa1S+D/ddnHyygC8qMpntsrI+KLwOnAjcCGFI/17uX+tgKO7dxJZn4/It5EcT5tCHwuIl4NnAD8hCKs7UTxW65PBv6OylR2mXlvRLyYYtT2RsAbgP3Lx/taiqn8nsPsFJF3AS/JzN8O/3DNy3sppqjcjeIx+FFEfIQigG0CHAw8iyLgnc/s//hoTGZ+vgzmz6d4bs6NiOMonrN7KF6nLwdmfk/2ZOBfu+znnvJL1OkUz+sLgQMi4rMUX6hmXku7UwTJ31KEzxmnU5xzjwNWApdExIeASymewwOA51JMcXg88IIBh/Yt4DCK0eifi4gvA7+q3H/asK/hMT6fJElTzuw/b2Z/s7/Z3+zf1RifT5KkKWf2nzezv9nf7G/272qMzydpMmWmzVZ7o/gAyrI9quO+d5e3X9pwH5YDH6T4gM0Bbd+ObYNimrZ+23yV4oNq5vqaHv1YM7POEH1+yRB9TYrAeDSwZJ6PTZ3Ht5Ti91577Wf1HPv2sSEfg1uBF/fZz2YUo42H2VcC7+qzr1dQfIEYtI8je2z/ROD6Adv+AnhKnz6srqy7asBjOHBdit+tPbdPf26iCP7HVW5bOcLrceDrgGLA5keGeJy/AGw0oN4jKEaSD9rXlV22fTjFl6Be2/yW4ovY4ZXbDu/Rj90ognmvfa2srLuqcnvP1804nk82m81mm+6G2b+6r4GZp7Ku2d/s36sPqyvrrhrwGA5cF7P/TDP7m/1tNpvNNmLD7F/d18DMU1nX7G/279WH1ZV1Vw14DAeui9l/ppn9zf42W9fmzyqpKTO/O3ojs9OBdd53apMdyMy7MvPPgcdQjEj+IcXIzXvKy3MoRlLvm5nf7tg2M/NFFKNDTy3Xv5NilOZJwHMz89Cc3+jtfj5Z9vf1wH8AlwO3lX2eGc37L8DjMvO1mXnvfIrUeXxZTG/3R8CbKUbf3sTs6PH5eCVFWHhX2bfrgDuAuynOp+8C7wB2ycxP9unXrzPzeRRf2I4GzqMIDndTBOzLKL4IvB7YOTOP7LOvj1L8/uhfU4ze/Xm5n9uASyi+cDyH2Wk9O7c/nSK0vR44rdz+rrI/pwNvK/vw9X4PTJ0ycx3FNKd/AXwfuIUizF0KfADYLTO/0VZ/yj7dnZn/myIEHsvs+f8bimk8PwUcmJnPHnRuZuZlFAH1ecAXKULvbyjO8+uBUyh+n3OfLtteDjyW4n8nXEwRim+leGz+Bdg9MwdOr1ju63yK0egfLbe/vf8WQ+1z7M4nSdLUM/vPj9nf7N8Ks7/ZX5KkGpn958fsb/Zvhdnf7C+pv8jMhe6DJEmSJEmSJEmSJEmS1AhnjpEkSZIkSZIkSZIkSdLEcnCMJEmSJEmSJEmSJEmSJpaDYyRJkiRJkiRJkiRJkjSxHBwjSZIkSZIkSZIkSZKkieXgGEmSJEmSJEmSJEmSJE0sB8dIkiRJkiRJkiRJkiRpYjk4RpIkSZIkSZIkSZIkSRPLwTGSJEmSJEmSJEmSJEmaWA6OkSRJkiRJkiRJkiRJ0sRycIwkSZIkSZIkSZIkSZImloNjJEmSJEmSJEmSJEmSNLEcHCNJkiRJkiRJkiRJkqSJ9f8BA2ewLW7j+8UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 2880x1440 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure_4_2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多线程解法 如下\n",
    "\n",
    "jupyter 上迟迟不执行，怀疑 jupyter 无法处理多线程。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2020-01-16T14:33:22.506Z"
    }
   },
   "outputs": [],
   "source": [
    "# This file is contributed by Tahsincan Kรถse which implements a synchronous policy evaluation, while the car_rental.py\n",
    "# implements an asynchronous policy evaluation. This file also utilizes multi-processing for acceleration and contains\n",
    "# an answer to Exercise 4.5\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import tqdm\n",
    "import multiprocessing as mp\n",
    "from functools import partial\n",
    "import time\n",
    "import itertools\n",
    "%matplotlib inline\n",
    "\n",
    "############# PROBLEM SPECIFIC CONSTANTS #######################\n",
    "MAX_CARS = 20\n",
    "MAX_MOVE = 5\n",
    "MOVE_COST = -2\n",
    "ADDITIONAL_PARK_COST = -4\n",
    "\n",
    "RENT_REWARD = 10\n",
    "# expectation for rental requests in first location\n",
    "RENTAL_REQUEST_FIRST_LOC = 3\n",
    "# expectation for rental requests in second location\n",
    "RENTAL_REQUEST_SECOND_LOC = 4\n",
    "# expectation for # of cars returned in first location\n",
    "RETURNS_FIRST_LOC = 3\n",
    "# expectation for # of cars returned in second location\n",
    "RETURNS_SECOND_LOC = 2\n",
    "################################################################\n",
    "\n",
    "poisson_cache = dict()\n",
    "\n",
    "\n",
    "def poisson(n, lam):\n",
    "    global poisson_cache\n",
    "    key = n * 10 + lam\n",
    "    if key not in poisson_cache.keys():\n",
    "        poisson_cache[key] = math.exp(-lam) * math.pow(lam, n) / math.factorial(n)\n",
    "    return poisson_cache[key]\n",
    "\n",
    "\n",
    "class PolicyIteration:\n",
    "    def __init__(self, truncate, parallel_processes, delta=1e-2, gamma=0.9, solve_4_5=False):\n",
    "        self.TRUNCATE = truncate\n",
    "        self.NR_PARALLEL_PROCESSES = parallel_processes\n",
    "        self.actions = np.arange(-MAX_MOVE, MAX_MOVE + 1)\n",
    "        self.inverse_actions = {el: ind[0] for ind, el in np.ndenumerate(self.actions)}\n",
    "        self.values = np.zeros((MAX_CARS + 1, MAX_CARS + 1))\n",
    "        self.policy = np.zeros(self.values.shape, dtype=np.int)\n",
    "        self.delta = delta\n",
    "        self.gamma = gamma\n",
    "        self.solve_extension = solve_4_5\n",
    "\n",
    "    def solve(self):\n",
    "        iterations = 0\n",
    "        total_start_time = time.time()\n",
    "        while True:\n",
    "            start_time = time.time()\n",
    "            self.values = self.policy_evaluation(self.values, self.policy)\n",
    "            elapsed_time = time.time() - start_time\n",
    "            print(f'PE => Elapsed time {elapsed_time} seconds')\n",
    "            start_time = time.time()\n",
    "\n",
    "            policy_change, self.policy = self.policy_improvement(self.actions, self.values, self.policy)\n",
    "            elapsed_time = time.time() - start_time\n",
    "            print(f'PI => Elapsed time {elapsed_time} seconds')\n",
    "            if policy_change == 0:\n",
    "                break\n",
    "            iterations += 1\n",
    "        total_elapsed_time = time.time() - total_start_time\n",
    "        print(f'Optimal policy is reached after {iterations} iterations in {total_elapsed_time} seconds')\n",
    "\n",
    "    # out-place\n",
    "    def policy_evaluation(self, values, policy):\n",
    "\n",
    "        global MAX_CARS\n",
    "        while True:\n",
    "            new_values = np.copy(values)\n",
    "            k = np.arange(MAX_CARS + 1)\n",
    "            # cartesian product\n",
    "            all_states = ((i, j) for i, j in itertools.product(k, k))\n",
    "\n",
    "            results = []\n",
    "            with mp.Pool(processes=self.NR_PARALLEL_PROCESSES) as p:\n",
    "                '''\n",
    "                多线程，传入 all_states 参数\n",
    "                固定 func, policy, values\n",
    "                在临界区（不知理解的对不对）\n",
    "                '''\n",
    "                cook = partial(self.expected_return_pe, policy, values)\n",
    "                results = p.map(cook, all_states)\n",
    "\n",
    "            for v, i, j in results:\n",
    "                new_values[i, j] = v\n",
    "\n",
    "            difference = np.abs(new_values - values).sum()\n",
    "            print(f'Difference: {difference}')\n",
    "            values = new_values\n",
    "            if difference < self.delta:\n",
    "                print(f'Values are converged!')\n",
    "                return values\n",
    "\n",
    "    def policy_improvement(self, actions, values, policy):\n",
    "        new_policy = np.copy(policy)\n",
    "\n",
    "        expected_action_returns = np.zeros((MAX_CARS + 1, MAX_CARS + 1, np.size(actions)))\n",
    "        cooks = dict()\n",
    "        with mp.Pool(processes=8) as p:\n",
    "            for action in actions:\n",
    "                k = np.arange(MAX_CARS + 1)\n",
    "                all_states = ((i, j) for i, j in itertools.product(k, k))\n",
    "                cooks[action] = partial(self.expected_return_pi, values, action)\n",
    "                results = p.map(cooks[action], all_states)\n",
    "                for v, i, j, a in results:\n",
    "                    expected_action_returns[i, j, self.inverse_actions[a]] = v\n",
    "        for i in range(expected_action_returns.shape[0]):\n",
    "            for j in range(expected_action_returns.shape[1]):\n",
    "                new_policy[i, j] = actions[np.argmax(expected_action_returns[i, j])]\n",
    "\n",
    "        policy_change = (new_policy != policy).sum()\n",
    "        print(f'Policy changed in {policy_change} states')\n",
    "        return policy_change, new_policy\n",
    "\n",
    "    # O(n^4) computation for all possible requests and returns\n",
    "    def bellman(self, values, action, state):\n",
    "        expected_return = 0\n",
    "        if self.solve_extension:\n",
    "            if action > 0:\n",
    "                # Free shuttle to the second location\n",
    "                expected_return += MOVE_COST * (action - 1)\n",
    "            else:\n",
    "                expected_return += MOVE_COST * abs(action)\n",
    "        else:\n",
    "            expected_return += MOVE_COST * abs(action)\n",
    "\n",
    "        for req1 in range(0, self.TRUNCATE):\n",
    "            for req2 in range(0, self.TRUNCATE):\n",
    "                # moving cars\n",
    "                num_of_cars_first_loc = int(min(state[0] - action, MAX_CARS))\n",
    "                num_of_cars_second_loc = int(min(state[1] + action, MAX_CARS))\n",
    "\n",
    "                # valid rental requests should be less than actual # of cars\n",
    "                real_rental_first_loc = min(num_of_cars_first_loc, req1)\n",
    "                real_rental_second_loc = min(num_of_cars_second_loc, req2)\n",
    "\n",
    "                # get credits for renting\n",
    "                reward = (real_rental_first_loc + real_rental_second_loc) * RENT_REWARD\n",
    "\n",
    "                if self.solve_extension:\n",
    "                    if num_of_cars_first_loc >= 10:\n",
    "                        reward += ADDITIONAL_PARK_COST\n",
    "                    if num_of_cars_second_loc >= 10:\n",
    "                        reward += ADDITIONAL_PARK_COST\n",
    "\n",
    "                num_of_cars_first_loc -= real_rental_first_loc\n",
    "                num_of_cars_second_loc -= real_rental_second_loc\n",
    "\n",
    "                # probability for current combination of rental requests\n",
    "                prob = poisson(req1, RENTAL_REQUEST_FIRST_LOC) * \\\n",
    "                       poisson(req2, RENTAL_REQUEST_SECOND_LOC)\n",
    "                for ret1 in range(0, self.TRUNCATE):\n",
    "                    for ret2 in range(0, self.TRUNCATE):\n",
    "                        num_of_cars_first_loc_ = min(num_of_cars_first_loc + ret1, MAX_CARS)\n",
    "                        num_of_cars_second_loc_ = min(num_of_cars_second_loc + ret2, MAX_CARS)\n",
    "                        prob_ = poisson(ret1, RETURNS_FIRST_LOC) * \\\n",
    "                                poisson(ret2, RETURNS_SECOND_LOC) * prob\n",
    "                        # Classic Bellman equation for state-value\n",
    "                        # prob_ corresponds to p(s'|s,a) for each possible s' -> (num_of_cars_first_loc_,num_of_cars_second_loc_)\n",
    "                        expected_return += prob_ * (\n",
    "                                reward + self.gamma * values[num_of_cars_first_loc_, num_of_cars_second_loc_])\n",
    "        return expected_return\n",
    "\n",
    "    # Parallelization enforced different helper functions\n",
    "    # Expected return calculator for Policy Evaluation\n",
    "    def expected_return_pe(self, policy, values, state):\n",
    "\n",
    "        action = policy[state[0], state[1]]\n",
    "        expected_return = self.bellman(values, action, state)\n",
    "        return expected_return, state[0], state[1]\n",
    "\n",
    "    # Expected return calculator for Policy Improvement\n",
    "    def expected_return_pi(self, values, action, state):\n",
    "\n",
    "        if ((action >= 0 and state[0] >= action) or (action < 0 and state[1] >= abs(action))) == False:\n",
    "            return -float('inf'), state[0], state[1], action\n",
    "        expected_return = self.bellman(values, action, state)\n",
    "        return expected_return, state[0], state[1], action\n",
    "\n",
    "    def plot(self):\n",
    "        print(self.policy)\n",
    "        plt.figure()\n",
    "        plt.xlim(0, MAX_CARS + 1)\n",
    "        plt.ylim(0, MAX_CARS + 1)\n",
    "        plt.table(cellText=self.policy, loc=(0, 0), cellLoc='center')\n",
    "        plt.show()\n",
    "\n",
    "\n",
    "TRUNCATE = 9\n",
    "solver = PolicyIteration(TRUNCATE, parallel_processes=4, delta=1e-1, gamma=0.9, solve_4_5=True)\n",
    "solver.solve()\n",
    "solver.plot()\n"
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