215_cartpole_q_learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q-learning\n",
    "\n",
    "- Init `Q`\n",
    "- Repeat an episode\n",
    "  - For each step:\n",
    "    - get an action from the policy(`Q`, `epsilon`)\n",
    "    - go one step and get a next state and the reward\n",
    "    - udpate `Q` with Q learning algorithm\n",
    "  - The current episode ends when the environment said it's done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "from IPython.display import display, HTML\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.lines as lines\n",
    "from matplotlib import animation\n",
    "from scipy.special import softmax\n",
    "import gym"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N=1296\n"
     ]
    }
   ],
   "source": [
    "# force = -1 or 1\n",
    "\n",
    "# x, x_dot, theta, theta_dot = observation\n",
    "# -2.4 <= x <= 2.4\n",
    "# -inf < x_dot < inf\n",
    "# -12º <= theta <= 12º\n",
    "# -inf < theta_dot < inf\n",
    "\n",
    "N_FEATURES = 4\n",
    "N_INTERVALS_PER_FEATURE = 6\n",
    "N_PIVOTS = N_INTERVALS_PER_FEATURE - 1\n",
    "N = N_INTERVALS_PER_FEATURE ** N_FEATURES\n",
    "\n",
    "def digitize(_min, _max, n_intervals=N_INTERVALS_PER_FEATURE):\n",
    "    return np.linspace(_min, _max, n_intervals+1)[1:-1]\n",
    "\n",
    "PIVOTS = [\n",
    "    digitize(-2.4, 2.4),\n",
    "    digitize(-3, 3),\n",
    "    digitize(-0.5, 0.5),\n",
    "    digitize(-2, 2),\n",
    "]\n",
    "\n",
    "def observations2state(observation):\n",
    "    \"\"\"digitize observation to a state\"\"\"\n",
    "    feature_indices = [np.sum(PIVOTS[idx] < val) for idx, val in enumerate(observation)]\n",
    "    \n",
    "    return np.sum(\n",
    "        [\n",
    "            feature_indices[i] * N_INTERVALS_PER_FEATURE**(i)\n",
    "            for i\n",
    "            in range(N_FEATURES)\n",
    "        ]\n",
    "    )\n",
    "\n",
    "N_ACTIONS = 2\n",
    "print(f\"N={N}\")\n",
    "\n",
    "def action2force(action):\n",
    "    return action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "uniform_q = np.ones((N,N_ACTIONS))\n",
    "initial_q = np.random.rand(N, N_ACTIONS) * uniform_q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_rewards(scores, epsilons):\n",
    "    plt.plot(\n",
    "        tuple(range(len(scores))),\n",
    "        tuple(h for h in scores)\n",
    "    )\n",
    "    plt.draw()\n",
    "    plt.show()\n",
    "\n",
    "    plt.plot(\n",
    "        tuple(range(len(epsilons))),\n",
    "        tuple(h for h in epsilons)\n",
    "    )\n",
    "    plt.draw()\n",
    "    plt.show()\n",
    "\n",
    "def get_action(q, state, epsilon):\n",
    "    if np.random.rand() < epsilon:\n",
    "        ret = np.random.choice(N_ACTIONS)\n",
    "    else:\n",
    "        ret = np.argmax(q[state,:])\n",
    "    return ret\n",
    "\n",
    "def run(q, epsilon, env):\n",
    "    observation = env.reset()\n",
    "    state = observations2state(observation)\n",
    "\n",
    "    for i in range(1000):\n",
    "        action = get_action(q, state, epsilon)\n",
    "\n",
    "        next_observation, reward, done, info = env.step(action2force(action))\n",
    "        next_state = observations2state(next_observation)\n",
    "\n",
    "        q = get_updated_q(state, action, reward, next_state, done, q)\n",
    "            \n",
    "        if done:\n",
    "            return q, i\n",
    "        else:\n",
    "            state = next_state\n",
    "    \n",
    "    raise Exception(\"Infinite loop encountered!\")\n",
    "\n",
    "def get_updated_q(state, action, reward, next_state, done, q, eta=0.1, gamma=0.9):\n",
    "    q_updated = q.copy()\n",
    "    \n",
    "    if done:\n",
    "        q[state, action] = q[state, action] + eta * (reward - q[state, action])\n",
    "    else:\n",
    "        q[state, action] = q[state, action] + eta * (reward + gamma*np.max(q[next_state, :]) - q[state, action])\n",
    "\n",
    "    return q\n",
    "\n",
    "def train(q, init_epsilon = 0.5, target_epsilon = 0.001, n_iterations = 20000):\n",
    "    assert target_epsilon <= init_epsilon\n",
    "    epsilon = init_epsilon\n",
    "\n",
    "    env = gym.make('CartPole-v1')\n",
    "    \n",
    "    all_rewards = []\n",
    "    all_epsilons = []\n",
    "    \n",
    "    avg_window = 50\n",
    "    avg_rewards = []\n",
    "    avg_epsilons = []\n",
    "    \n",
    "    decay = math.e ** (math.log(target_epsilon/epsilon) / (n_iterations - 1))\n",
    "\n",
    "    for i in range(n_iterations):\n",
    "        q, reward = run(q, epsilon, env)\n",
    "        all_rewards.append(reward)\n",
    "        all_epsilons.append(epsilon)\n",
    "        \n",
    "        epsilon *= decay\n",
    "\n",
    "        if len(all_rewards) >= avg_window:\n",
    "            avg_reward = np.average(all_rewards[i-avg_window+1:i+1])\n",
    "            avg_epsilon = np.average(all_epsilons[i-avg_window+1:i+1])\n",
    "            \n",
    "            if avg_reward > 490 and epsilon < 0.05:\n",
    "                break\n",
    "            \n",
    "            avg_rewards.append(avg_reward)\n",
    "            avg_epsilons.append(avg_epsilon)\n",
    "            \n",
    "            if i % 1000 == 0:\n",
    "                print(i, avg_reward, avg_epsilon)\n",
    "    \n",
    "    print(i, avg_reward, avg_epsilon)\n",
    "    print(f\"epsilon={epsilon}\")\n",
    "    print(f\"q={q}\")\n",
    "    \n",
    "    env.close()\n",
    "\n",
    "    return q, all_rewards, avg_rewards, avg_epsilons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 85.68 0.3692542703947553\n",
      "2000 141.16 0.27062647367074655\n",
      "3000 155.9 0.19834215640395025\n",
      "4000 179.0 0.14536497657960504\n",
      "5000 183.16 0.10653799877497093\n",
      "6000 192.94 0.07808170475479007\n",
      "7000 196.52 0.05722608541100659\n",
      "8000 191.18 0.04194100092655724\n",
      "9000 169.74 0.03073856172561394\n",
      "10000 197.34 0.022528293461901803\n",
      "11000 202.72 0.01651098743122567\n",
      "12000 191.06 0.012100903533377476\n",
      "13000 225.54 0.008868752818936477\n",
      "14000 191.38 0.006499909394901198\n",
      "15000 168.24 0.0047637839281884\n",
      "16000 306.46 0.0034913774847796925\n",
      "17000 255.62 0.002558830737283703\n",
      "18000 219.76 0.0018753671783161595\n",
      "19000 247.54 0.0013744567009691894\n",
      "19999 154.76 0.0010076524617527016\n",
      "epsilon=0.0009996893023352328\n",
      "q=[[0.5488135  0.71518937]\n",
      " [0.60276338 0.54488318]\n",
      " [0.4236548  0.64589411]\n",
      " ...\n",
      " [0.32290711 0.34574585]\n",
      " [0.40051046 0.41091573]\n",
      " [0.10325322 0.51909894]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "q, all_rewards, avg_rewards, avg_epsilons = train(initial_q)\n",
    "plot_rewards(avg_rewards, avg_epsilons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "214\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<video width=\"600\" height=\"400\" controls autoplay>\n",
       "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAABNVW1kYXQAAAKvBgX//6vcRem9\n",
       "5tlIt5Ys2CDZI+7veDI2NCAtIGNvcmUgMTU1IHIyOTE3IDBhODRkOTggLSBILjI2NC9NUEVHLTQg\n",
       "QVZDIGNvZGVjIC0gQ29weWxlZnQgMjAwMy0yMDE4IC0gaHR0cDovL3d3dy52aWRlb2xhbi5vcmcv\n",
       "eDI2NC5odG1sIC0gb3B0aW9uczogY2FiYWM9MSByZWY9MyBkZWJsb2NrPTE6MDowIGFuYWx5c2U9\n",
       "MHgzOjB4MTEzIG1lPWhleCBzdWJtZT03IHBzeT0xIHBzeV9yZD0xLjAwOjAuMDAgbWl4ZWRfcmVm\n",
       "PTEgbWVfcmFuZ2U9MTYgY2hyb21hX21lPTEgdHJlbGxpcz0xIDh4OGRjdD0xIGNxbT0wIGRlYWR6\n",
       "b25lPTIxLDExIGZhc3RfcHNraXA9MSBjaHJvbWFfcXBfb2Zmc2V0PS0yIHRocmVhZHM9MTIgbG9v\n",
       "a2FoZWFkX3RocmVhZHM9MiBzbGljZWRfdGhyZWFkcz0wIG5yPTAgZGVjaW1hdGU9MSBpbnRlcmxh\n",
       "Y2VkPTAgYmx1cmF5X2NvbXBhdD0wIGNvbnN0cmFpbmVkX2ludHJhPTAgYmZyYW1lcz0zIGJfcHly\n",
       "YW1pZD0yIGJfYWRhcHQ9MSBiX2JpYXM9MCBkaXJlY3Q9MSB3ZWlnaHRiPTEgb3Blbl9nb3A9MCB3\n",
       "ZWlnaHRwPTIga2V5aW50PTI1MCBrZXlpbnRfbWluPTI1IHNjZW5lY3V0PTQwIGludHJhX3JlZnJl\n",
       "c2g9MCByY19sb29rYWhlYWQ9NDAgcmM9Y3JmIG1idHJlZT0xIGNyZj0yMy4wIHFjb21wPTAuNjAg\n",
       "cXBtaW49MCBxcG1heD02OSBxcHN0ZXA9NCBpcF9yYXRpbz0xLjQwIGFxPTE6MS4wMACAAAABlGWI\n",
       "hAA7//73Tr8Cm0WXagOSVwr2yqQmWblSawHypgAAAwAAAwAAAwLa9HiTO+TU8TYAAAMBBwAoYVMR\n",
       "ISAUsbwqBIiXQ4aUsP68ACYwaD/YxCW7HBmtAdl/0stOqJeBa8PgRl6eeF73bAp9J719ziXya0sb\n",
       "JL1g6R5XaNezCYY4buXxoOsfz9GgsxN6hvBG1XCX7p8RjOUdiAa4gCf+FakA/BhLNcBQy1p3gZH3\n",
       "wU6re5NHF2sJlUOTS+Od+Z2+B7oA9BXMB7u4Vph84lD++Rgda7nBJ3vBPMU2DZUXucW0yadKic4R\n",
       "MZHdXtyf9oig0XAMKmWPT64FHujhZgK0YI8mg/foT8aPnQqEIi7HDfwN5B3wD9qRAnV1/2h979jJ\n",
       "rZgBXFD6ajVYLz9viFKHlpqzmxqHADxQRxB5QR4b2ebzN5uSaVlob7Os/7qXCgW3TnLfogYNMTfj\n",
       "Xa4g//vRV5lcUoUl5gxCkYTyiOzGd2k8vSSYfPgFuO2uHatUtDACmBIaMDtOAT44AAADAAADAAAD\n",
       "AAGzAAAAbEGaJGxDf/6nhAAAAwJ8AAISL/fHUHajj+VrVTdS02qljo978y+Ga76br63rK8A2DqJc\n",
       "yFSKTjK2pwdr2OBk9Rr4eIs0XRu0AKRUSkqC4z21TmSkOILfwmKn5U77yRkceq2ccI2eXUIuSfR4\n",
       "ugAAABlBnkJ4hf8AAAMAFHsoKfDAnTjvowpQWU9TAAAAEAGeYXRCvwAAAwABdEwj1bAAAAAYAZ5j\n",
       "akK/AAADABunQy/7YC4GNUCcyfSdAAAAlkGaaEmoQWiZTAhv//6nhAAABpwbwWwDSYTNOo4tspL4\n",
       "9JYxnAtbVG/8dJce1hOHIKNr0rysrxohjNpX7SuxNPYziHgROmygwVe5Ji2CfyVD0sT1JkeGoBpY\n",
       "TYFI7T6aGSMAG4qKBbEZW4QQkafIKptEbtMLXtn9al0NE+e2xnCN474GOsMR4JNurfNgBxFZCCla\n",
       "LQsSIQAAACJBnoZFESwv/wAAAwP4mI7TzA3tVzXlwaeV72lEfCOf4hGhAAAAGAGepXRCvwAABWck\n",
       "Tix/Ms45GFc1rYtv/wAAAB0BnqdqQr8AAAWKvG+iwL43xR2UZXHyFYuXbnw//AAAAFdBmqxJqEFs\n",
       "mUwIX//+jLAAABng2F7cksAz85xfZ0ZKzCAGc4Tgu9jhrYRQD8HQefGTU1FuaYxc6j/5/pqxOyKZ\n",
       "flf7o2awTzelp+fDzK75BKaWQzKZY0AAAAAuQZ7KRRUsL/8AAAMD+REkfTPDTxS1PmgC5JMinW+A\n",
       "85w9sZuV3ols3qs4a1C0vQAAAB0Bnul0Qr8AAAWJLtXWD+AQiZm9Lf8x8JoxGu1HwAAAAB0Bnutq\n",
       "Qr8AAAWKv42iP0aHGAMxUXNaKDfzP01HwAAAAINBmvBJqEFsmUwIX//+jLAAABqvW8AjWun5sQD6\n",
       "ADZ9w9rQTN9Wrxe6D9HaUks5PgO3/sIjvZF7zlI5dJbP8tNTJAC97LhVEvo7XjjLHmNhc2aeqD9j\n",
       "RcdhXpH/+8wsaq/tZQTS/1G63BejmQCmF0L1MqqNrgck+og7rghd52gi/QSBXwAAAEZBnw5FFSwv\n",
       "/wAAAwP38YrrFzoizrUY/yQAE7eNflIuFVX/cGIh3LQQfrnVf/HW/u98AyQ0kxDEE66GuFJJOQKb\n",
       "mV5BpXjRAAAAIAGfLXRCvwAABYkwcRfeMsIOr5WcjRj57FEP0608eUPhAAAAIAGfL2pCvwAAAwIL\n",
       "rvrRm3dCF+1NBxJKTJc420H5r3+AAAAAbkGbNEmoQWyZTAhv//6nhAAAAwJ/knyhfGl/w/OzTImD\n",
       "bu30px8IyGm9n3ESuJs0hu4egS4iC7LWZMYFKyAnl8NBnfxIGxHsK63eJ+KOgy9EOjltAYhka+ll\n",
       "8BtbgADv1RJZPtfl8Hj1BVewiiVAAAAALEGfUkUVLC//AAADAYiIkkG9Ap/6oAIfVdDKxJvyMwLh\n",
       "qIHCcQ5AHumGJ7m1AAAAIAGfcXRCvwAAAwIK5sbECNrmN5VfLzkkzjjyAU2wABgQAAAAIwGfc2pC\n",
       "vwAAAwILr9xGq/RUWqE6qBbG4yHPdFT8Mll44G1JAAAAjkGbeEmoQWyZTAhf//6MsAAAGfLLyFRw\n",
       "EDy2QYKXi3IirDZ9RamMOCRfwZ49UQHT4Ew8UoavADzd02k/t0XSa+5uqSNqC6ZVRrDQoDpL7CS6\n",
       "dPFQXYeYRk2zg7aibZP6JpZ9mlkf9adauKKBxKpcfp8MFoP/53PR2+FwBVqbRGeldrXHMT4OinBj\n",
       "d6N0PWEAAAAkQZ+WRRUsL/8AAAMD4fHUT5E6KPJoNl5TvT+/RUKLb9quWf6kAAAAGgGftXRCvwAA\n",
       "BWckqiE3N9TWvrpDEwCNFgKrAAAAHwGft2pCvwAABWeTNPFPIGRC+Rml5PbjXBJHhHFWEpMAAACd\n",
       "QZu8SahBbJlMCG///qeEAAAGlUxMuZexAEwZnrfNQO2RJZnp5W7OMsBwXLlwfmkwLuyHGsl5eg5p\n",
       "0jUD/WFi7h0UbiZv97kcJ5GZ0CBwUArPzWWvocECt/iY+/lydWUqdZ70WENoZP1MbAsuqsGWBc9g\n",
       "qoW+UNyN/wXVLnchXJHXL9Ld1nMEQ0adzQTuTKGCuNgbIy3JVy5+Y07UkAAAADRBn9pFFSwv/wAA\n",
       "AwP4l8lRAA2gnWd7mbW8Sp5C/WvpslaT2JXYjZl+4jARXYEJLtdxGYDxAAAAKgGf+XRCvwAABWck\n",
       "qiBsJbABM4gWp1weN3Lr9S7d0vsuJ99XZGeGXACbgAAAACABn/tqQr8AAAWKu90ys9yLn1hGQ2YW\n",
       "YP6TOxBI8Ixd6QAAALBBm+BJqEFsmUwIb//+p4QAAAabwAZcAk6jV1btVVdjHZAcsGcQUA2Ccn7G\n",
       "URn4NZNhvLbQFQNrcGQvL98VzW/zO+DS1351U+3pX/svugKuokRu6IjkgrMyOq4nysAgnk7G8FNi\n",
       "TcYQqHAu0qKUsTpqM0i058Zn+sFe+Ebsg8T7uTo3zSz7a6hW0X1WxPhGyFm2QoKaQVtIULKA4OXc\n",
       "K4PBT8JujZ4N7ZpN7lz2d7B+oQAAADZBnh5FFSwv/wAACmUnYooL3nRFTZLg75xgAwzhaZCc2Mhq\n",
       "DQqboQkEf/oYiklEanNKNelj80IAAAAfAZ49dEK/AAAFiS2NjTFoZTYyYbP33iKy71uhL9ycfAAA\n",
       "AC8Bnj9qQr8AAA4rKaePcVdsNyrw7ONfYwZ8OAAdj3RtNHgif469HdcEfZRhPY5sfQAAAJZBmiRJ\n",
       "qEFsmUwIX//+jLAAAAnBDBACOt2H2NFBKY4dZT6skgCzWwuZdr3KVcej87MkWzojC6GHsY/JOL+o\n",
       "Hw226jWJJRbbzaP4lcUG9Vumrs20tMFeVpOwbsXvHDkbhDteuxdFa0fWq/oVQe3k89rwNdY7L2sx\n",
       "ifxqzV1CA2Isekeu5Ta0RfQPaCdu2chgdtfPd6uOIBAAAAA6QZ5CRRUsL/8AAAqGRf5mjN5FYHnV\n",
       "Svo6BdqulA5IAQkhHuYAIRai6qP7MUTo0rVdjuGyoLRepuipjQAAACMBnmF0Qr8AAA4nAaaXqG8W\n",
       "GfjhviSIQUYs2iu8LI7jqvWPgAAAACIBnmNqQr8AAA4rKaePeQDWNG+BANlkX3vtaPeIHak3U52p\n",
       "AAAAKEGaaEmoQWyZTAhf//6MsAAACcG7UH9e5onF7ygYG6kBlp3Ixpuhzm8AAAA4QZ6GRRUsL/8A\n",
       "AAqGRf5mdXc1gBZLzo0fVMa0LyvNhif0yjA6HROxxGwuDrZaY3WgGIzBcXaSqSEAAAAiAZ6ldEK/\n",
       "AAAOAo5lbO0gfZ226HUK+NayDYZk8btrfnXxtQAAACMBnqdqQr8AAA4CjmUDdhFM+uwEndRDG8AO\n",
       "7UzVFuh59+qJjQAAAIhBmqxJqEFsmUwIX//+jLAAABn9yU0n52ASaUwaczFWaA7y06txSOIcXyJA\n",
       "LOUIlS+zNRZyM15nvKMft+4XGx+9CI39nngDNbrAD/ofK8Jtn8EYVHtbxXekGuSbi+hCboN3UtRf\n",
       "wSxowi5v3+u0ivznyj+MIAGXdMHyzFo5uOmaXk/sXysmwZLwAAAASEGeykUVLC//AAADA+7XbtHm\n",
       "KUrtxnYuzHNzF71hNMwQu6nQAb72PfPCp6qZPPLxkKPHs1d0GkOFAZ7w79Ay1A3nxmc3RnfIDwAA\n",
       "ADABnul0Qr8AAAWJLtXXiSojPIoATSpil09raZknok6nocU2CcERCVGEhhzghp2qdA8AAAAlAZ7r\n",
       "akK/AAAFir0qjsr4Lw6uHap8QjJoPyopfnYzPqzlWf+Y0AAAALJBmvBJqEFsmUwIX//+jLAAABoA\n",
       "fDn0AmDaHRv0UMJ7adC7M7l4OPtLjfVARO4pcFUO9lcNUq9jfMngAhrI7KZtJd02klhr4eoYsWdl\n",
       "qOv/W0uP98Sil7oxtj7rRYeJGQF7ONOe4pgpwcPZzJPnesB3NPOn2pQ/otg0ffYSBdPapzNsGNgg\n",
       "j2OtrXBqiARQuRn2dAh89TQj1hmFMvOoXbxUarwXJGndHkaO8xra+ynxdrGxAAAANUGfDkUVLC//\n",
       "AAADA/kRByGRngXSCLVAxEhxfGqgGPHinwP7gA/A5nvQN2IfqAFhQqCXzlSRAAAAJAGfLXRCvwAA\n",
       "BYkwcRLEYfkyhS2JSgIwRcFLZjIDW6Q+7NI/wQAAACABny9qQr8AAAWKu2zPP/v+PL0woi411UqC\n",
       "QA0iaU52oAAAAERBmzRJqEFsmUwIX//+jLAAABoB8RmAAHTbfy6CRnjrQv3oKLriD2jfhT2MlBwW\n",
       "44cu51mGpZ4JOt/6/0JiZ4IyVgI/wAAAAEBBn1JFFSwv/wAAAwP5EQcoqig6ZTbzvrFsfs/W7oIe\n",
       "ermGAEHl9IMV5QayvoSz/d8d9oK+J8r4L0pCcXj/nRSdAAAAIQGfcXRCvwAABYktCVm+b0N/XIzq\n",
       "Xym72uMIYtrJmE5jQAAAACMBn3NqQr8AAAWKvC6QxSPbf9ekVIB+V1vB+12W5UrfpPlDGgAAAIhB\n",
       "m3hJqEFsmUwIX//+jLAAABngcDOxvUcAW05BjmtvUZvXWzCDvUf4EMFDk96d2K/69cyo0GLBm18S\n",
       "q+XVljSObbkBjv3wnxrWEKD9iQr+vEw1xogBS9mE6FV5CmD2WOln0y2sJYNLTSdca4XIu9sNLt6S\n",
       "G65nhwWff4P/x20d8PlceolIP2ahAAAALEGflkUVLC//AAADA/kRdfAo6CxAv07SCBjj0XJ4GM6W\n",
       "v2E9072qtQtl5vGgAAAAIAGftXRCvwAABYksfABkdulsfUdq1KHIAFZIO4X5KGNBAAAAIAGft2pC\n",
       "vwAABYq/4cekV52TZhPA4j2wPrirh+BxwNvTAAAAe0GbvEmoQWyZTAhf//6MsAAAGq4TnljeD7w6\n",
       "jXwAGl37vOSlxKzJGSvDRmPhLZ2ModlISTrhz7HKR4ZKAQQG2oap36VqFeRmQWJ8NGnTSkx2dMIY\n",
       "GvuVmexYhvxGBfwS629HDX+wwWuvVvCCuxGU03ElyweOoVu8OhzUIAAAAENBn9pFFSwv/wAACmUn\n",
       "YooJ//GQAPhQyoAQ6w2AG1g5HEbm3nV8gAO9vfz09zNRDv5XvhaNnGfAygOhiI5YLnCKbDGhAAAA\n",
       "JgGf+XRCvwAADgKOdNvOEYab4u0s3ktEa3EP/slGmIxlxNt7cRvQAAAAIwGf+2pCvwAADgKOY6LY\n",
       "E7nq4k9S1luAyrb7ycRz+zwjvfSBAAAAuUGb4EmoQWyZTAhf//6MsAAAGqCCCXPoSWNZPlhrd34Z\n",
       "JQzWGdL0ytzmAZUlfuVx9CpfLtxGOrsLgsvpSryn33ma2jVQ7JSGgNsG2+mhcFiC4ZPNbMu7AbTM\n",
       "PafVYBuansfYBmRZSEb/69uWq+a4v+KMSp/Hz4Ifr9x7CfigzitlQE35eNcoLDT7sIkYWyuALV1k\n",
       "87u20uqGZ8IsJRgny4B3llJpd/5nx8+0hZp23DuQ3rcvSRVoJNy5AAAAQkGeHkUVLC//AAAKZSdi\n",
       "ieWYmIX8iIZ4E3YBHlG0YHDRP67QXvNc9l0MtCSvB2alefgp5XGBqx0jsGdM7p6IVx9BZQAAACgB\n",
       "nj10Qr8AAA4nATSbNvJ4j20o0v4D8sdOtMND0LRdjZ4zGqmNaYDwAAAAKAGeP2pCvwAADisppV8F\n",
       "YXMj9vY7HZsIrnI1f2oW8PT9C9iVl7TAVMEAAACuQZokSahBbJlMCF///oywAAAai6iTBgBwAMAL\n",
       "S6nSF0G+DCBv1vRx1LTKRXO78OyFT8GsurXQ36BFtoB6JWr3eE+u92yyKxfs4AJyoh6U9TFgk2hS\n",
       "RdImt2Ov9UeLf7zKrsG40jcnNmvqNbCvYPb3Ut5Uh8o0zSFGfJIKKTOlVXIBQw3V7bAwJgAIgMCz\n",
       "UrYRJSWhJkB8H6VrgIg5Z5SuxKjok2V83QXDk5SougBAAAAAPUGeQkUVLC//AAAKhkX+W9T6oArX\n",
       "KxSZKbyx32lgB4y6x4R94/zev5jXEgbleuK6hvs0aRHJ2QLs5eNcaB8AAAA4AZ5hdEK/AAAOAo51\n",
       "TkgwBGQrEUwI4TR3zpc87G1lDZe2pEfJ+/+BNjuIak25DWiOpzohF11QqSAAAAAqAZ5jakK/AAAO\n",
       "Ao51MiMq1oCJ6ABUoTesqxWm1vxdvUWmo9T3spQrSBHxAAAAr0GaaEmoQWyZTAhf//6MsAAAGqdA\n",
       "XOWuf1RKBvgNJwzeAE3AJmkhr/tOoqP2jplrVhhD6B+BaOErWUhNnHiq2G58BNvmfspGAAyccmS/\n",
       "JEG2kXpfFwQA71unt1Ur7vRit19i4+/ZGxk7P0vW0WhoANZUPLGzvqrherunOCKpqOrdeFNWABwj\n",
       "9w1p8htDJEI1SYF8wCg4QA8sdSa3jc0Dvrx7/hoqumZ8kBd50OkLpOEAAABDQZ6GRRUsL/8AAApl\n",
       "J2J7S80DYrWzIUdeXpY3hp3Dk2SVzbEpeXiQ1IFvEALOl3iduVvK7wQWbunKe3jPGkh2n3evpQAA\n",
       "ACwBnqV0Qr8AAA4nATXQKAS3wtm/88bzS1KX0nmLjZ6q4r4q3HxYRVzJLtdfSQAAACQBnqdqQr8A\n",
       "AA4rKTYD2a35/4XpWyd+YiqEpVqbTW8Lbe/tAj4AAACEQZqsSahBbJlMCF///oywAAAao+8z5RC2\n",
       "+BcEAam5VUvUaW2/4kxO/UHNVVIEcj/P6TQx88Jy7vB1s7wxRDS4XpvUMxho5K/OAm+zOjy0WMrS\n",
       "rP85l4xJ6ZBalnjQQFBu9OyzlqccsAHXKTq+sNPLgsh4/ABEM/Qkat9niS5sG/ACvLWwAAAAR0Ge\n",
       "ykUVLC//AAAKhkX+BrlqyO8g98ihn9z1Ako/8NP0xk+gF9gCnWhJkzUrgvK+/s8Khd9RFHLpKsCa\n",
       "IYLeC2ByOF9isX5fAAAAKgGe6XRCvwAADicBNhf1xKMOLYZ+GqcQsIW79dRu9yvlZZfFA8vKvARm\n",
       "hAAAADABnutqQr8AAA4rKaTihMd2+XSjbOUbToZhsgVfVC7WZcAyAvd9h9fR/tPuUviypIAAAACZ\n",
       "QZrwSahBbJlMCF///oywAAAahbQ7ABA+yUsxx3IKllX3XxynnfXMiWnHhwpv9RaklKrbNgdf9OIP\n",
       "EuvCrJnt5wkxXeAc8GKc0EeIXjH6ZCaHpJTZ/ZXqXR/l8LP0jWpuQD0q4xkmoP4EPGKlN7FXLuCb\n",
       "SN92UxP5H4aE5IUCsniGyPTKeQw4JQ4wgKuttNVFHxSvjSEfYAVRAAAASkGfDkUVLC//AAAKzPCy\n",
       "jL/Rik1jOgBuI5KO1nv/WQIDVlMVIhzNDyBVDQpXi2eufyYbXGXLeX9BtC/AXsIIgwZ/UMpo6yru\n",
       "dqSBAAAALgGfLXRCvwAADicBpze6x+YRK8Gzuic+cQYwrKvnumHXGqUXWsALPRO7GiQ+0IEAAAAy\n",
       "AZ8vakK/AAAOgySriHb9rV6ADieBmurON+/4n6otnYIrcuRwYw8VZ3dnwak1fz4RH0gAAACPQZs0\n",
       "SahBbJlMCF///oywAAAahVKuQAW9giNPgpNV/noabA3odiZPVWLgU7d8wUpGUHVdC5ULK/q4w4mW\n",
       "qczLraEAXjRhOjTn8L11fkxB7rTOw+UZrP0aJXXup+AOHBd4olqiFUq23+xjH3sMlmPynR+bNBwd\n",
       "AHdYDOMxZN3K99ohYvQtvxtQ2VoZ/jlM9QoAAABcQZ9SRRUsL/8AAArORPvJv4OWuCR/uIAbI/7D\n",
       "lbR5s6PzpkW5ZgQIb81QPFVbTBn99u/OT7UuvVLFymsAnawxNKNkcRSfVww/8GIE16Z3u6hTAeEg\n",
       "bo45sBu3DpkAAAA3AZ9xdEK/AAAOfvq5tPjxjdjzUzcdH+KB9Kf/uDZG5HpUikU/X6W4LDAqbM+V\n",
       "4vsP7e/BRsjqSAAAADwBn3NqQr8AAA6DJKtV4RUiNyixQAlsM2/Ov5FqjcH+F0oOgviasSLgJoW6\n",
       "AMZhJa/tlr17p5GM2FQycpIAAACaQZt4SahBbJlMCF///oywAAAagT1fXQ13khWAFSahitY5B/8p\n",
       "pZ5RwjCidpKG3K+T9Y1CidVLuf04iqo/54ODZ6QQgKKYHoDXdDpK+bhLcr2ZcWBKJqYfU41ge7Sd\n",
       "OQjURlApryabUp5/GeOcVXPMDNTl4S/iszs5Y7ISMzeZ01DCBboOiJSQohBqpcOyJ4x4eNjyZrM4\n",
       "GyfZUQAAAFNBn5ZFFSwv/wAACs5E+9kIg+zRrAC3fboW8+Oscl5ozh2DexZE7HBdOhIWdJ5/eLXd\n",
       "ofeROI19irtgILLTmen8hLbRGWL3mdvbsyLpOe+Tfcn0wAAAADUBn7V0Qr8AAA5++rp4rMjMv2+x\n",
       "wAmLv1X4vxdYB6mFuLCZ0ZoDNvgZw10YHMgbfT3HMy7KTwAAADkBn7dqQr8AAA6DJKtnCT2hbqqw\n",
       "Bc52xweqItezJ+B9YBjzqXW1Sz5WpHqup1tAX6inMsby6El/ufEAAABvQZu8SahBbJlMCF///oyw\n",
       "AAAanFQf63jQBStTpO9jBElFjYQP2SwHaiJSI49Cm60ErdtlYXeFgtEzeVBPIX6SHS6h2GQF5PPI\n",
       "5ufhNF6WUmJOkiQViYvXWPkUaI2nqUz5CjkxAaVCg4NReKQdC4GAAAAAVUGf2kUVLC//AAAKzkT7\n",
       "2SvpwORcAFqnSO9ViEmS2jdGbxWhSMM5MY7OiQ56e44JDM0Swt2wAxneXz9e4YDUrGlmJYflmn7A\n",
       "1MEM6nyIWoPmU5bdVBEAAAAqAZ/5dEK/AAAOWo3pAkjwnKwWnWh+knPx/cjOIfioETeDYrAIjt6I\n",
       "Qe6CAAAANwGf+2pCvwAADlQx176fy5KHuvKuYMhWVqWTpYdgb9C7hLeUdcAApzxpzLJkZbO35rub\n",
       "DDCNy4EAAACFQZvgSahBbJlMCF///oywAAAbQ+mMMtO7Q+gH8UI2YjNbOnC1oGJQv0TLnjSWIOmh\n",
       "ZwEKyF2z8vH+TupV0xXvl4Jnv/7kjC1rU7BB8L9OcXk6g9sOEhbuvw+uaWlcZNu3R+0F52chvOhn\n",
       "VEbaTKmGMOqNRv6+hmd4enGtDe4B60mq+MzNawAAAFBBnh5FFSwv/wAACoZGASWvFmAqN8e9K6gJ\n",
       "kiUj/2KwcA/kid4CA+8jptjhMXNNJz4yGnMbWXFEWOUuul12ez1eqo0pJxHv2PSJQNZc4TfScAAA\n",
       "ADkBnj10Qr8AAA4nAbfTGJQlWAATfpILAf9zfLickJpd7N/heE9mbATFCxrGYMCg7LxrC3SUoqH3\n",
       "m90AAAA0AZ4/akK/AAAOKym3dX3lqMxPJeS+QABMz8wC056UBAgvS92rv5xzHtQtlV8bTDG88X5Q\n",
       "uQAAAJ9BmiRJqEFsmUwIV//+OEAAAGlOpi2AJ/c+8VsOfXUeoWl/4VKXNg31GTXqB9QDHRJbA7gj\n",
       "owEOc9cNg9mF0bJb+ZsZz6uJ/bXtWvg/2g29rcH5TlOC2wfnf1jOd6YAJwb2SvzzVS6+z+ILH1KN\n",
       "kOVxzP7Dxh/+m9ZVSvIZQgFEbeAioZXHCBIlEHWlKcf9qNUIYAAA8YfiqNZzeq7GH0wAAABoQZ5C\n",
       "RRUsL/8AAAsU9wfNnTa/AAcHGPl8i5CWkRajUgzY/12eFL2tToGdITOIFeWGP+J3utgU6s8VarVn\n",
       "MTnh9RBtLWIuH7nm4O9RqJadG9YGlCYfnL+eajLCaCYntGFbONtv8iEOScEAAAA2AZ5hdEK/AAAO\n",
       "3EqkK2daN11Xby9xcsikmlCHS787XxWGJaKLuSwZhZrpmOmKNzRx78nywXugAAAAPwGeY2pCvwAA\n",
       "Dt18YiBSCAsssCFZkfseMAVPG8D5zs7lj8TbDoypaLjvTIAOTjD4QR3KRmtiv3TyWGvunOIUfQAA\n",
       "AJRBmmhJqEFsmUwIX//+jLAAABtAEWQjKgCO8rFI/nUSMqr3ndGmCVEIawPZn4C9PBUwzX86ghus\n",
       "2NHSUTj2oqd9AF/foAvM4eXdA9R2AmWg/82B5HxlgPOvbHXyEJzPkgulfgcGU8gK3PS/daStpfIJ\n",
       "9IrBtHHYu82ztfkvqif1xdfVH3aTjcrn6HGUG12ehvMIDFxBAAAAOkGehkUVLCv/AAAFr4MHKUe0\n",
       "ndWYDDAFMY+XA8aPcN8+fr7YZafp/3+dqoojNFWM+mRdQLHVly/a+YEAAAAwAZ6ldEK/AAAFq7Sm\n",
       "XkfL08Rrjlp5hBqx1PWUqsNE8LmKyXSN6hsDOklktvIn13ehAAAAMgGep2pCvwAABaxmlUTCAgBL\n",
       "XAkGc3XOyyX9vjFwaaxgmBPy+Hgq7A4XEYtqeppzHYeAAAAAf0GarEmoQWyZTAhf//6MsAAAGyLk\n",
       "nX6MgYFFOAKcnwD1MBoCM2ZX9vRtk4jiAGru+/3C9mdF2S51dOxMLKiLlWCBvhcNIC2xQkSPTsUi\n",
       "uP5KQF/mZEK4W/hPKyXBSZNHver1F9LyXIN2jabvzQ6nZltOMdq+LAlIGV160kG7NzwAAABOQZ7K\n",
       "RRUsL/8AAAQXgsZ1qG5XUzwvJ/MqreJxAATt4Rk4SE2yLnIT6IuytVX5SKdKlzubflHII0uBCcCm\n",
       "+CwfFh8Mbbhsbp8Mk9T+L14PAAAAPAGe6XRCvwAABatcVJAQAHx/4PJaOs0m8lWjLtpqlbvnwFJ4\n",
       "Y9h6w3K1vvxLeZeBLM9IqKGMzHGwCTRpOAAAAEABnutqQr8AAAWunAG+AD87uJ4+qEZM3asY4YG7\n",
       "/nqQp7ASbs1sky4+C6pnnthOiC9vbBvnpQG2vyXImbGraFPHAAAAm0Ga8EmoQWyZTAhf//6MsAAA\n",
       "G8WDr7YBMGvhtEzQ3aAJcMbPmut01tjEyFRNWa7bClX4R5zD6ir144VnbS7V75y7i6Gmm0OeGnT/\n",
       "T1mH0mEUXV4NuVPcEX0amWb3XKPJLv/+p7zAkW0dxEgluomuuEmt+AEDG+Jb4fyVB/jRiLH8zeKK\n",
       "+5ugUWKgs2/anWO28F4A9o9upvfXb0dNAAAAQEGfDkUVLC//AAAK9Sdih+Wjxtq98JMANur9B5hA\n",
       "6JiSyQN+wqWxXHyyz6rRRVm6DICwFvIwwTQZZq+F+TR37oEAAAAwAZ8tdEK/AAAO1wCFoXsf653B\n",
       "ituW01Mp+Jr+tdbQ3DqXfdE1rnPJcRtdmS4SDPLhAAAARgGfL2pCvwAADtspp3XVoAFh9ilAUXwn\n",
       "AOlvj2Op9hmI/Yj0T0cYAPOn5uZXocN7dkiZJdjd9u3q305gKj5KCAWPtrwyAuAAAAClQZs0SahB\n",
       "bJlMCF///oywAAAb5dCQ4bgCBwcQC4SgKTVrxLP+nqP1JpS5JtZtKSghLjcQSHzwQ0KTIG+Nksm9\n",
       "k/Ufyo3+U5Zv72kz+626DVdkkQOSySvYvV4IUqQXAmEcMjrxjF2+8lh0/+2/hhK3D6z4nFvwtm30\n",
       "jIAKA70SzCXpxtEnQXh/CB1DHnez59pqtwxwLCkNyk9P0Q4lqpw6/rG6yLo8AAAAXUGfUkUVLC//\n",
       "AAALFkX+H2twlUM4i7LKQA2SHzgqKf24eFqfx/2R8AFoC1/d4cykSdEcmc//+CJDBMj/78BQyVq2\n",
       "j7w/oi+GO3Y7StnYAqIhvtad0VwdJOnGEvMhcQAAAEcBn3F0Qr8AAA6yjnVBYu7142N1TUd8iXSO\n",
       "qp6TVrCGUoYATuov+S0s3UMSaz7QMhvXCe0a9syrUidN9KuWXOH9ewcHmcSAuAAAAEYBn3NqQr8A\n",
       "AA6yjnVGtMfmFUjoreWj8zQ4a39oK6YsOcr3B4nQbmgsvRzppF5XK8PiliS3wSAxEP9AB1GwEx/N\n",
       "UjkNlO9AAAAApUGbeEmoQWyZTAhf//6MsAAAG8L2vGzuWSEAOL2dEgwQvSESCU/iVBIR5mT6Viuk\n",
       "kF4GW8hUZmPkO5U20CwVQrKMIrHRLc3ZToq8mftUizFhNQrm37SXXAGRQ/OUQ+Ks8MdLPJzp6LvM\n",
       "cg+GOb+RKgDUXiY3ngyzQIanwbNT7nWsY8sCGC3QjyV51Bkl9WXe4SKNctBxXrUr079wJrABt7Y1\n",
       "cIZpJwAAAEtBn5ZFFSwv/wAAC1zl24o0GSp17fbcANukSC3TqDgABdXPwGZWgdYyvARqNJB0P8pd\n",
       "kFBiBmVQCufuOe78WYBAbkBqZSYLYhPfK90AAABLAZ+1dEK/AAAO1wGfJNKXY5mhzQAfeVfyncnQ\n",
       "1ZcoEdQ1Np9AI5iVLcyHS424TTLrXMn2JProXfBMvMXsyv+F9yzmywBoUn2BEnehAAAAUAGft2pC\n",
       "vwAADzMkq1jVx9woATLxWdEvp9oINwdxJBKXHAz7N3C5GkpneS/WmJudfwETnaDNFDWDUQlyVTiz\n",
       "5WqSJw/BcdosU3J12YSvnNVRAAAAk0GbvEmoQWyZTAhf//6MsAAAHJT0Y+rL09LAFW7BlZnZxymb\n",
       "8h1Ag2pZ8f5gCL0iGreOWgls/7TqiN4qPHMtKZXfYEjT8uuKkAW7pSgGspwZOxNqcW8py/kQ1Uyt\n",
       "iYb+5ec49RDRYYdCqBYQwrH0AW+zQPn3ruAvuXrmGeyQl8a3o9A5198zCmligHL6FlVMNh/5gAAA\n",
       "AExBn9pFFSwr/wAADzV4s/9poWGcQNaAG5a8SDAliJlyG5fAaHECUPI8sFjz1sxjLT8E7pjE8eKi\n",
       "/nmulPOCOcdhphA74SbRFyWmeeqDAAAARQGf+XRCvwAADwqN6PZd1QePhvpzrRACaMF5JuvbZE6r\n",
       "U+FjCG8+ImbpDcJCPHwYHuZlOqlxlx5KFy4xZ7407xoR9R28YAAAAEkBn/tqQr8AAA8KjhCAIm9N\n",
       "UAb0HFDEzGeJmCqh9Pjy7LM5t1yD1PBtNbSL+n7wRnXdQHLVBmnqUe/QEJJXktH3+MH61pM7z+l3\n",
       "AAAAg0Gb4EmoQWyZTAhf//6MsAAAHGlo5N74egABWnysCBDdgpeYyDT3DruhsR/PyRX5udmhJTzh\n",
       "TDONQ9h9nqoxYulXVuPK2rLV1KRg2IdhctwdTbK9WLoeXDUWZTLFJyHpIu5Gz2/Fdaw5eSlwnTUO\n",
       "Tc0SNs53H1VqLTTSrSpP+/f5iGu5AAAAP0GeHkUVLCv/AAAO3XpZWQ66QOt6FLgJplLB95JHBFf5\n",
       "MqTL1J9eHqABOaYPX+uvACvKFWn9bBLS/+G8E7QonAAAAE0Bnj10Qr8AAA7XAbZ1rJk2DuZuzI5n\n",
       "PRAHEQEOP/mcAATfo59U418wCj0StSvLm0w5MZVUP4/SCIkFOZIHaYiMr2rFmiXaYkBYPkFxYAAA\n",
       "AEEBnj9qQr8AAA7bKbafTCbBExnVziZ7eQrAgEMvUW4ZRjC4p1VP0eE9EH1GYALtYMCeUpNaL0Wb\n",
       "I1cER3n75Q9uIQAAAHdBmiRJqEFsmUwIV//+OEAAAG45I+0IVFxBgA4lU3pl28gNxi91j4Mqybim\n",
       "JfwmZlyS3LG20HfvCAX+CNEiUDuWDHfJAVnX553QJTheSPK5ZpDkuR1PRDhQOWy2L0phlccIF1xS\n",
       "cD4EPId6QFDgm5Iqw+U64J6toAAAAEBBnkJFFSwr/wAADt16WfL+CUUdmaUka2H8fN+7jajoECIA\n",
       "bttmXZIrfGMLrI7Ol+tZJS60wkrnGR4v+f+pQonBAAAASQGeYXRCvwAADtcBtnOLFHFEkOR6AD+k\n",
       "LL1SpqoiwUATY4lYb4edqXmRy11Lx/FgbFtpobK1WXlJm4sku/z+ErfbRVJQ8bs2ZQwAAABJAZ5j\n",
       "akK/AAAO2ym2nKhcABOqzbRD0njYb5ZlvBzpRSG2tSwDFjwb4fRpA92IzQ0dUkw1w+4biiYgpyIA\n",
       "h4DEnVlqLcxLadkDgQAAAIZBmmhJqEFsmUwIV//+OEAAAHDxvJxXeEQ0CMQhss5i0pJLQSkZ3HNN\n",
       "mhdjDCkApV0MTdKkfnjzCIP7Ty8bKX+jDshuJDpBKyJa0jB6/+scep2ybmAWJwHTFMlr6u+KOG/X\n",
       "uEM/65b9XD0YkzxS067R+dIOi/jm1UQ96OXqf5XpYDxE9efIuQAAAFlBnoZFFSwv/wAACxZGA86k\n",
       "oYAHB7kKeChf/cnCOb85iMTRM3pyCbDgRZxXOVj79fIcpY5J+gPdy5HxFDmO6aIeRes40N5edL4M\n",
       "aDM+LvN5t4plpP1KP/244QAAAEcBnqV0Qr8AAA9ijvgkAgntd0hhAoCEIT2lcHmq03HvD4CPiEAH\n",
       "7QSTaKYzfcS9GSFRNIRj1UI4EL0MQ1+0fthzvjFgoJOe8wAAAD4BnqdqQr8AAA9ijvji9I1D/tcQ\n",
       "ZRL/KY2KmvHeDPPmdMAJvy+4XwwEjQw9wugfOsz5YP45L4b7uFOrCqO+kAAAALpBmqxJqEFsmUwI\n",
       "X//+jLAAAB0j7itCABxdg8hrRr001qg/oH4dtLtA6fgEcjQbFRXTjqyYT+dxf9AXlSMpWY9fZDtt\n",
       "gN+m+jq9AygV+qMI0DxG2ac2ewmBEKKmm7jI21AGkDlY5Wcq3qEvAdxyUBZgHDANwxVUJw8NnxY9\n",
       "I7D8iaPXXTUq88ZdbwwzyYrfR3yIPezUZAIO9b4PykuBw59jAZ0zxT+qF1/2T+4UWrT6MiDqTdxT\n",
       "9fqYuswAAABaQZ7KRRUsL/8AAAvyoM5o3/oaj2AN/6GAAjNeINFAkDbALPQpgQONPdpGUorbduBu\n",
       "QHK5Skw6y5BkRIdKgrrE463ZYa8e6zkVe8xdeuHjxvTbtruCY3CBgBDxAAAAPwGe6XRCvwAAD+RJ\n",
       "mD0bjMbGCVif3AUjYh32i6qpkIzRH4BPONYaIFu0GHFIADrL7RM/plsB+tcTF45aL05ScAAAAEoB\n",
       "nutqQr8AAA/lfC8gk1sBMLdj8eq40aIk4IABN73QFREsjyV1GhOdfJaLgcDs8jHQbguMpfBgBBeQ\n",
       "qKYZ/2JslWl5Y4A4lmL3PgAAALpBmvBJqEFsmUwIV//+OEAAAHPT0di4gEv8+51P3M6sADebKTUx\n",
       "T2hhXigvAxnXpeBJBYvZWScoboID9RYLs25+Ju1MZmet4NTANhAAPDs6kMX7ZajW4N/EkFIyBQf3\n",
       "+4mNbETLCxhk7n+nLq6NMqmwkpIh+ZA35kQRT0Dc/lY0vWVKJDukWfvGwIu33uHTnReqg//GbcxJ\n",
       "ksdCOqt59R/FAhPhl2uurK40M2nYEWZIM7yvr0cyQuOkCNUAAABEQZ8ORRUsL/8AAAvzjPOWvjGM\n",
       "y0+XKAMmXTbzKJXpIIv1UEd8V4VgBoWaAMEVC59tSCiqBy1DSSRlLoLm8uu9I5TlltEAAABKAZ8t\n",
       "dEK/AAAP3we4CbUazIATOfaduez3hfQL4qt9PQ6SF2Mnrm5780iCfrcmVZCY7nm987KsDT07DApM\n",
       "pZzaCp+tBA8HD66qP3UAAABRAZ8vakK/AAAP4y/EtsYBQaAA4xAJhubTr3mFSy2s1ZBa4mUkEht6\n",
       "nxM7b8sR32PZ2ZO//agT4F4OPzSs5skZfd/fiDWq8hCYAn3bWU4iXLiAAAAAi0GbMkmoQWyZTBRM\n",
       "L//+jLAAAB3t6qQbUcwArsXCQZk4C1xulFl9zpkc6tZIUmMGePwX12YAJmHLh4ktsi6XRn1R4AKa\n",
       "/9ygJGC1RGYgEfmmUkqOVUCHewcsd7H6mupoDAEvRaQPUF9teB6AYbvYNxb99yAaD9P3m+V5viW+\n",
       "H+FputyeOqYbhhYC2j4AAABQAZ9RakK/AAAP5XwxkKIaYvJwkaXdkQubh4tg6m0xS5p2azewEMoA\n",
       "ceV1pIVXN6Pa93X/tTkWRt8/nZk962vsMhRFG+T4GuOGU9QnRpHACpkAAACXQZtWSeEKUmUwIV/+\n",
       "OEAAAS7om0FE6s68hCfcAHCioTFNfCSa3P7t788i4SwZfSpln22i+xe/H/1J/btfcHBV3135otDO\n",
       "w8ndbQAGR1ttUrSiet0dpHaGTOYcJCDcoLDeJEMqHvPdbpoqscMRFaKvTlN4dO8k749rA0D0OMh5\n",
       "qI33TEjO71kqOscQMoXvyxzdMbLR18GPtQAAAFxBn3RFNEwv/wAAC/Bxmi/9p+2olI4IbX5ATqk4\n",
       "67D7YOGcMestpmZdBGaFniAEjMMhqriLe5m19snoCaCAVMQxD0ECCMfa7DnAS5aw0Ft9qpC7XIaA\n",
       "HA/yYChNuAAAAEgBn5N0Qr8AAA/fB7gNDE4PiCI4ATTy7U9knqwkrc/J1tRYy373a6u11TJ21da5\n",
       "6uuUONB2EPOJ6vWlcvJ0pvqy+JvSkIUmbxcAAAAxAZ+VakK/AAAO2ynnif1WP+wGc0pY+Jkqwdaq\n",
       "SSKaKkFJu7Y1Nxp1MjHIAeVTIc5eQAAAAHlBm5dJqEFomUwIX//+jLAAAB3rJ3Q88RYAU8wCXSrb\n",
       "ZAwd05KCe5hk9I9JeC7wp1amHq8Gq5tO49HPGW+BlDGDsfRy2xmLHsZJTckQ0pSpZLKwuJgONrEd\n",
       "d9CWj3ESSDiaTxNnoqDTmIGa63csGwTXTnI/0N3A0hZRAAAAxUGbu0nhClJlMCF//oywAAAejTC0\n",
       "c0AIXlqzly6/DUAA5cD6HLRV6rngIUqwx52FnbEv9bTf0IMoAi452e7hjrVi+MvGZ+MeIyVT6lDc\n",
       "OGLCAhPZwm+JIt9Eijog7t2+2zKHOg4VitZVvYkR0AQlHAIA0AKc1C9ywi+505HsYbx/fQrt//EA\n",
       "1lWKmNBp5IdZkocfo7oHRa/5x3J1I6wMbw+OKrNkNfqbWO2cGwHtfJYUZS3eP+puUV0LuoDLtv/2\n",
       "hwSHmPmBAAAAYUGf2UU0TCv/AAAQ3Xjql/bQ5hU2GaAFluCaWZZiFd/4qYD3jSY9QtbddCaf21V6\n",
       "oanvArNNDGCSBVYUbF1BogcGGYjGoGNTV0Ho9Eplp2Q++/uA+dXGzLWLDTKZGi+gAScAAAAtAZ/4\n",
       "dEK/AAAO1wHnNUA6+kyXRmrMP/Jct+465Phl6U2rYkejurGifK93spm9AAAARgGf+mpCvwAAEN1c\n",
       "U16IXZN8zP9Os6Dv9gQRRmCEb31AAH5Q6VYzrJ+QWJmeCfnVThq8kaxlr0BX2shFSdqgIQE1WIPj\n",
       "dv8AAACzQZv/SahBaJlMCF///oywAAAeepv9EIPnojABtyu/fFLLnGWmL3P8icrbUeJDARCeMbZP\n",
       "P9Ueh4uYTDsIXdhn8LV3IeYBaj0EzHrh+qUTWh8bDUhTb6+CjThYRsHKRM4zhR28kmNC/M5RoOBI\n",
       "34F9gaZNFgF46VNC5iDSrRTBMrBF5GShvHDyyGHLZZd0ae3ohKoZ7JCXydklcxjx/58FDOMKvNcc\n",
       "z+KxemGrzPeS++GwLxcAAABDQZ4dRREsL/8AAAyUQUJ1/Js+HSLN44aWPYMFPXwtRKx3rE4RRdee\n",
       "0oaq6xVoG4ujriYW9tGpKNd5DtfTpkrzT9of4QAAACcBnjx0Qr8AABDXNj8z+ZY1b/tyjwe3q85b\n",
       "ghO5/3j00Jl9mQjWih4AAAA3AZ4+akK/AAAQ3Xc1LJdTif+7Nrnn8Nu3y2G30q3+5GC60571H8sK\n",
       "sf6huirX2kM/TIfthI9DwAAAAK9BmiNJqEFsmUwIX//+jLAAAB8z7q4/gAo9vcJiI/vETakR32HT\n",
       "3G1HjDgQBTB+Lh55t2I+ARMhIaG78gMStWO2obZrI6hBQ2ok7J7gEpC/BfgO6W6Ck+IqzqgnQE5O\n",
       "s3fdr1O3HiG+hGlzRdX6n9A3ytdjA+m7hfyAhmm1JNB+b1Q2AFMohFz+IM+B5j0l6y/rUJpO70Qm\n",
       "wUkH6iZQussZbcADdzfQjMpdpk1/hDYVAAAAS0GeQUUVLCv/AAAQ4Mp+TGS2lkYfDOjGgAbf+gRT\n",
       "UI9Op9ObCDfS0bk2+Fx03DPXLjiL1+LaH3Ue/KM3u479pZ/y7ErafFZbo+/xNwAAAEcBnmB0Qr8A\n",
       "ABDXNj80Ay8xAz3BUm25GBbprwwXXtnF/N5VGbTKt1LVsD2Id+kADq9K+j0TT1UrlUgd4LoC09Wl\n",
       "7Cdf9KAlDwAAAFQBnmJqQr8AABDddzUsm2JcT9NbkNZ2A72PChMO9h/l/SzRmUAKgU5bsyMu194t\n",
       "YnSzqig38mopFRmW8ql6oY79scf9dWFSNu8XhAMtREhJF/P8riAAAACUQZpnSahBbJlMCF///oyw\n",
       "AABS+ZcxgRqGlcG+M+nhsRFUN2DOrTw8oAchgGdClFnvewLeorboVeYB6qJ9qJn9+8F19SDAjCcY\n",
       "GobdN/sVW+13qMYmYcD+WR21Apa31caSKS9C7QGFysdpD4j0E8coFkoGW6FPrslQurjw8YGuRzGn\n",
       "P9BJuQvtwRL0CeW/VflXJsEutwAAAEtBnoVFFSwv/wAADJBjiNxJODWJiGmVN5DJQ0bsE1FlY6++\n",
       "aMPyRGQBtQslR5WRViADdJBoR4lwpnZ352ZrCIkV/tzimBoX7wVAlYEAAAA7AZ6kdEK/AAAQ1zY/\n",
       "NAMs8YHzNoAP6iCOWJo9E/jedIuP1iUoWOKBGMH5S2Gy7fZTxh8NOzPRBGmIFz8AAAA7AZ6makK/\n",
       "AAAQXYjo1WJWcW/o6NTYJ9FeJjIhg3WrcLxcFpm+zc6iVaSC6UF6IgJuHWkkdGpLJMuqyWUAAADB\n",
       "QZqrSahBbJlMCF///oywAAAgLy+NricxAEL3u9iYYpRLqnLLIJ9x4MribY7NxhV+eJJtCf2DBalz\n",
       "xSS3GnSfLcIt7h+lgIgK13i6D0/c68eEnuqDaJV60Sl1WU1eyRmqqv++sD8ieG01WYTGTUx+Uwba\n",
       "uI5+sDYTyULNZHUJLq4Ptl4R9Sp1q7/9nFmCV1vqHrqLR31QQpeUzaDXgTcM9khL5ZVQIrGawGPn\n",
       "FkqsT16wTkrxqNFvL8YQAGO+9fwnpgAAAFNBnslFFSwr/wAAEd2J9jUmkeB2cSAK3f8fJ0a/VYB6\n",
       "nudXAYrTciApbQIXUZTTiSOvChF+cLXOwHbs7aR+mOzbp8SL3IaFOc2VsGEtSnWJKhAHdAAAAEIB\n",
       "nuh0Qr8AABBXTJlMHkdGfs25tf+oAPnien2OZyaUvUACnO/7aXpVbEVg+npebeKLIkjaVHrJgEpX\n",
       "rheOnP4OlqUAAABaAZ7qakK/AAAR3YnsdCqP17AyBvLAAW2AAUkmUd053wYGezqzOblkl61/PFqb\n",
       "4rmiymBEqmQpl9MBBImZrkQVYTscKBsPKfUy06OztVy0/mk/Lhzzbarp4LOAAAAAkkGa70moQWyZ\n",
       "TAhf//6MsAAAH/sgquTw7p2QAF0AHhIPmlveItk1+9/ZnnJppVMR+NtzrzJMPEHgCQ67Qoslm4mP\n",
       "w0IQ5hm/9+ltn8ZctWrS1IG4rHq+/QQE3z5ZiJVJLq20JPOqzBuOB7wos+ngUKbrSFLPghrTkeFl\n",
       "qWOPaR2Uw3rEtFKI0OJ713/+vlprnsr/AAAAW0GfDUUVLCv/AAAR4M/ltL/IjiS9p/6MaAIlPK8F\n",
       "vFNzsdTFZFyDlskBL+RLO8c8ebIlVNZanhTFlZkPYmMOnjvjvQOo4VnVPkn6zXlWJn17kAzM0tFX\n",
       "vNMAAR8AAABQAZ8sdEK/AAARpVLIpVt9wc0Y7ACdkaKhvZF56sL4ETtgMH9+z33j4kArEcYKgmvX\n",
       "Qnf4Y47WppLd1qp0hJe8MGS4ftuUrJIedGdNwQAqd0EAAABFAZ8uakK/AAARpVLJY8WJ0OfIgAb6\n",
       "1XLss9gBOmC80YMYHKBWYxrlFLLmaeAe0osByhYwE3MZKCPHhT0UXTXKZH0dQJP9AAAAjUGbM0mo\n",
       "QWyZTAhf//6MsAAAV33NDWdIo4UAnP6ecgwfLOYSTYRuHuCLKdSwAs13WMuyShp8SUZoJ+XCaMhD\n",
       "jlDFUFYEQAhloLQE5PJS/wulUd+6ek/U6gQL8uI6pl5FqyvBdUSxd5IgY7q2JPUQcILl5P9B0kAG\n",
       "ewBlVmK9HOvIItdSjBdyG8c3azL8sgAAAFxBn1FFFSwv/wAADYKX/YuvJtddDUavPrREKKjjmKa+\n",
       "OxTBGuG+sWUQQFvteQTBxhs05fPUP0VfyflF+SCq+3YUP2ZaV+LjMyYFTmLwZCLg5MLnMpCTXflr\n",
       "LAB0wAAAAGQBn3B0Qr8AABHXTZizp4tEdWu1iAE0NbW3KQFjHdfsslnNynRilOZshUXljJhoV7aI\n",
       "LnLw2pNdaB2yDrhhCOgV37gsj7LMjjeeTfdMoUrAHmc3UzUssX+zdnz59jVjGgcGvbVVAAAAZQGf\n",
       "cmpCvwAAEl2I6PQqiZbnkMNCcWzGr6zlKADc1ieixluG1ozdany+N+5EbSqZutYABPZt4yYnyscj\n",
       "R09cBF5S14T4UWYXPIjHkX2dzrqIfQKoIon4kgYQyAFSKL526jaYvBLwAAAAqkGbd0moQWyZTAhf\n",
       "//6MsAAAIQzDsbWAKXzhihHLZgpPTfJcssu+4gScQIWtiS2fgCyFKtiTE/l2MHwQ5YY/SIQkEZPy\n",
       "Dg71xzTLByFi8oht43VMFy0K07oZeQYmIwHmnHR5z8Ysf5QIAgWOTyYiAC6hezSDbCv/U1ImbmvN\n",
       "aUI2UB29ZJflc3hAAgknpfQn7OWaUGpxRCJFRLWEMy9svORTrCQwcxIhPTyAAAAAWEGflUUVLCv/\n",
       "AAASYM+XdItYH4E1hIASxiqNAPBKpPOJ31hUXy23bUGsxRXaxWwdPwR+OQ2GsdhuSUDpu6KxpzOq\n",
       "xcigXK0sfsPx0SdQyPng2gBs0p52VMEAAABEAZ+0dEK/AAASJVK6lON9z5YdwAtwWWAMRwDohoMa\n",
       "In7ZjmxRWHHfbCC5UNTfeF0T/6TOhLQTlutOn84FIaiB1vC2ZqQAAAA6AZ+2akK/AAASJVK7Mm81\n",
       "1SXrpgBNR/eGM7CwprrL9bjZc/VUIIUnLkQL54UnTzICVCOpAwSxO07UgQAAAMRBm7tJqEFsmUwI\n",
       "X//+jLAAACIAya05YChI+CfiJEOmmr5zKQfZmYuMMnR9VoJEJDLWoGy1+rXykw6vyjJJuJPljYzA\n",
       "dJk8i4xUmNxAcbwJu473AxqjYFQwi1WQRuack0qXclqkO/sF877JWbGDzYoSIR1L7EMeOJzk8mh/\n",
       "hjridAQlBgk9vcphvp7AcGo08jhTgkyZ1cQQRBYAleC+sP4gxaGfpgUe0qkMbDjaA3I4pBmgVvTc\n",
       "rqfjqAG6BBJAGhdp2WnzAAAAR0Gf2UUVLC//AAAN0o1/1/NhJzUZFhmgtKg70FsAOsNNeq7fn4bT\n",
       "5h4lOU4l4cWKODC66H8OiH+3ss95kOi2D0Af/dw/eAm4AAAAMwGf+HRCvwAAEldMmXU98Go45b1x\n",
       "lfwAE5q+V5ch08doJypFkcXCACMgYP9HafkZ2v/6hwAAADEBn/pqQr8AABLddzUsugGV+CvJYZCS\n",
       "cD5dmeUEzYuCCKPLkpX0Ztxd1Q8OKpBcr2UMAAAAsUGb/0moQWyZTAhf//6MsAAAWb3NDXRdXPkx\n",
       "BAEe9slm/YXpizMAT48+uHisJdcpb9+OE1dXX2gpL68OByVoB58Z5tbIsHz9PQV7yqu+mWN/1tB7\n",
       "UmRhjbqVZYZwZls+QB7MDh+Rz0S1XaZy9P0XV1bcOolB0CF7C+J4VXfwYve8iQ0PJRHHXysXrqzF\n",
       "dvneKhwzspcdCP1WHZt9vSRuepYOeV9WUjVtF//hTyKW+70B4wAAAFZBnh1FFSwr/wAAEuDJnTG0\n",
       "cVmn1uIAJIRtJTBF0R4IJD0nwje8v1I1egUF/riaGlp27O3+AMRiXQAEeP0YZuAKOJLSr9vo7gc5\n",
       "r1+eSIqA0n8H6iAFbQAAAF8Bnjx0Qr8AABJbP5AVTgnozEecAbaIASxaTpxW8x3/eMwNdphCurpg\n",
       "LN/mHhXKTEo8jmhXMZOeqkRUu1QLcxuy3zRQZCHNgWkn3pTrTumych5XTXCrdNs3kFQv7teyoAAA\n",
       "AFIBnj5qQr8AABKlUa4B7SGWCVufpKEk8UAGdoZEhGRHVFeNE+zo0tdpbQZln2ouUA22swkklj4j\n",
       "uE+l1jCXfvgF8h5pZxpyaotUGgiOpiVGALZUAAAA6UGaI0moQWyZTAhX//44QAAAh3EumDOhWCS1\n",
       "R2NMZiFWnl8Z66ulBAVznikBzxOIdfm2BenU1QIZCsnjBvD46pvyl0N3wk4AyZP8I9lJHcnMnH62\n",
       "xKFuJaAsAF8RbWdgOt9my5gwK836bZ2p6x1pnYwh5RtHi4h0PZaMIXBJztclsMs6Y2wE312v2waf\n",
       "nkGBtaQDElCFEmi0msVDQ6RdmPYj+RfbCKr4ph4St86OQAEGM2o/Iv55k34oXnjEiKL+mgqYrQ3J\n",
       "xTj94c2Kg7LWM1x4vjA6H6HEqEi85GqrstA7XsjvRsHOL5zxAAAAWEGeQUUVLC//AAAOKlN/1QfH\n",
       "CofxdLHRKB4HS+1AJdiAFjw42PQgnvfai8+Wi16gHpHjLaCN0FheVkfj40L90cFkd/mdptFSGrO2\n",
       "XwuDUWYv7EWjTUwAwIAAAABNAZ5gdEK/AAAS10u5dh3tfdiWjIU4+yGzFVyl8haxw0jk5tMkAONh\n",
       "KsZLj4/dOyWclY8gQ82J44FGARwFksZPDVOraJvhkdsIF5Hb7UEAAAA9AZ5iakK/AAATXXc0rvrB\n",
       "CBhAxcM518FGbsU0JimMxqEQMHuybZy4T4yIxdOk6e8eXa45cs5hlDfItV2yoAAAAM5BmmVJqEFs\n",
       "mUwUTC///oywAABb+Zcxgg6/iy9sM88AC/GO1EY6deUy7N5I2L2eHZ8wx6lXH8nUIQ5JuB9DdNgb\n",
       "9YLrWFRepPkCZ6pfYmF6nBJ9FYKAHbUrBcANV7/k6HmGfcP3xf6XQP++L58gxeMr21u4xJo8OYw4\n",
       "/gFquJPdaItK+R9cFl4YHb/86hBIYq3HNOGApl4ySBGwDG/Cs4/4MRjWIeJ6SeCnXWoSFS97+iVL\n",
       "SwX/lem0xLVHackZQPz8zUYnqf1kJD7OS6jCgQAAAEgBnoRqQr8AABLgz1d0oVlUw3QpaXodkAVa\n",
       "ttkKH/ghU0I81DKFdjgEb0M/utW85yRYncAHiF3UJZNNsoTVhP0hB8pgTAgABQUAAAC3QZqJSeEK\n",
       "UmUwIX/+jLAAACMk7nIvZsAG8IZlWy7uOJX/Ro5Tl4p9A6fehG4fajMemDH3Wn7WY5y5SBtXsjjT\n",
       "lbi68sOJPFeMN4ydFoTEnx1ddPqXT0HVHybYukRhqmTutzb8dv/KFG6nipoiB1zUg1GsovsO7Sv7\n",
       "twUpv1uaQfQ2w9qFGBM/awwGSD5M4Ewt1H16xAvNiYiiVMYW1ezqfK2Mgwm4Tav5a0CsLlv7dgX+\n",
       "QK/9K2q/AAAAXkGep0U0TC//AAAOJ8Bs3h4n5/Rja8Zf3HjVb4S04BJvNQKUeiFHFSf1Gx4F+MI0\n",
       "9S+BxQrBXrjyCykV52bCBVQsTCGbqww7L1h/ZQ8FrwBgX65gScaahdlKr2wABL0AAABEAZ7GdEK/\n",
       "AAATV0rrrJOq2rysfvwvDQ556jIkwvBAHh2XQ9HKaXHhbz35IgAN9n5HcK+CsXFvJM6QyvFjwrJB\n",
       "ob3NglYAAABDAZ7IakK/AAAQXYjo1kcku9eGTWIiCS/xqIMUCudbq85EWIV1/ybEOK8+XqSABnK/\n",
       "yzhUl69n4IX1BmhNwJN9f6hbuAAAAKxBms1JqEFomUwIX//+jLAAACQpW6UyEG7WAFYUI+gW9fno\n",
       "KX5ozHU2q6Ly0m8DNKVCyA/LDByGSOwmpPRe1qcLk/HuvdY59/lKrVbTqB7uNfY50EDwv5VnAeBz\n",
       "22J4LHpZiHX75uyhhLQ6trrw5d3Dc/Wz/gfZDBZWfqyQxfERQZDOKf+s5t9X1vve1IT3In+5vyPS\n",
       "vwy1bKGWqmVKefuo+Oo7CopQCy2JiwINAAAAY0Ge60URLC//AAAOgmdFV1qrQKUbOnBqygVPeDei\n",
       "c+oU6wrZVnkk/bq18DHL357km8PZk83G9HqFK7J09vfih4jBDYx7xlcw7FwdFsLR2A9GBTCFUFId\n",
       "fZhuZ/QhA/1lkYCXgAAAADoBnwp0Qr8AABBXTJlNjeybEmQ8j/T483MxhJjJoGezbtrV0QUKnoKr\n",
       "yeseUsUMZ5ZN8tHee0QHgExYAAAAQgGfDGpCvwAAE+sGjNCbSugSSO6LB60O5oAP7RwCPVU+F4zM\n",
       "4VzygIrxRAWm6YC+2MrIIawM65WL8zOE67SPhDGd0QAAAHxBmxFJqEFsmUwIX//+jLAAACUA1T9n\n",
       "0DJ4hy9WvDIxo3812/o0iHUS9UC+NlfSEMWk+8ZXwh37JHsmzvGVaig411l4D4SA1P1asFst+trE\n",
       "v04LsvowErqW91wM56Ta1bDxPnMIsS8nadwXKWPuaMLxQyfWIcMXPA9IVfirAAAATUGfL0UVLC//\n",
       "AAAOhEdYaFld1FRRiRPERxjw5ZxTZ0YABdSCQTWggeKWNCbbYOyVFZMioylCRJSuFVndOi2HbY0z\n",
       "tmB5QRRkWo9N4CLhAAAASwGfTnRCvwAAE+TKQCyTt1c0dlQDUqiEaCZnEGromZIgVCeUDYM8DE1x\n",
       "x7aRLVyhTKp7tINMKukZZp52ubVYhRja0rsK7U+DNKU2YAAAAD0Bn1BqQr8AABPrBozQm1centG9\n",
       "1IKYBhtfW2Z8ENUqAAE7beroySW+OOPbtB+wTmdxOSa8fKFonAQWf2BAAAAAWEGbVUmoQWyZTAhX\n",
       "//44QAAAjnqIGFB2RCXKtEyuy2FWxs75VQVPXkKljEdUekFdTmHBWzc3xE5QYZuqqtFxvk+KzO78\n",
       "WzmGNiDIDn6PPuA1WwYDUAl9LrkAAAB6QZ9zRRUsL/8AAA6ER1hoWV3UVE0V9aipgn4AC6DSsKss\n",
       "QInK4zXkPc6Zju7ePeu1L03mqxj/fleb5JdnuiuT068UIDL28DmY1erC6H9rbFV4IFabHi5voBf2\n",
       "I9iNE/U2z/Kh4pjRjWx0iA2rCW/aGva/+zIISye8BDwAAABDAZ+SdEK/AAAUfH2Za4Niq20kDPWV\n",
       "hv5BUas3cKwACd8LhzE0NRF6udSCToB0JYQht6prv9XLfQ/3NHsRX+sK2pdjlgAAADUBn5RqQr8A\n",
       "ABR2jrEJktMOnehhmpcf+9FqvM10hNzUgiFFq5WCJguBdI7lVuSWqucjre/HrQAAAD1Bm5ZJqEFs\n",
       "mUwIV//+OEAAAI54yw3QATqknOpCSvrK+wkY98kfhZn9fAlna4yi+F52lr9hMrDyrLE+MYoIAAAN\n",
       "Q21vb3YAAABsbXZoZAAAAAAAAAAAAAAAAAAAA+gAACGYAAEAAAEAAAAAAAAAAAAAAAABAAAAAAAA\n",
       "AAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIA\n",
       "AAxtdHJhawAAAFx0a2hkAAAAAwAAAAAAAAAAAAAAAQAAAAAAACGYAAAAAAAAAAAAAAAAAAAAAAAB\n",
       "AAAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAQAAAAAJYAAABkAAAAAAAJGVkdHMAAAAcZWxz\n",
       "dAAAAAAAAAABAAAhmAAABAAAAQAAAAAL5W1kaWEAAAAgbWRoZAAAAAAAAAAAAAAAAAAAMgAAAa4A\n",
       "VcQAAAAAAC1oZGxyAAAAAAAAAAB2aWRlAAAAAAAAAAAAAAAAVmlkZW9IYW5kbGVyAAAAC5BtaW5m\n",
       "AAAAFHZtaGQAAAABAAAAAAAAAAAAAAAkZGluZgAAABxkcmVmAAAAAAAAAAEAAAAMdXJsIAAAAAEA\n",
       "AAtQc3RibAAAALRzdHNkAAAAAAAAAAEAAACkYXZjMQAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAJY\n",
       "AZAASAAAAEgAAAAAAAAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABj//wAAADJh\n",
       "dmNDAWQAHv/hABlnZAAerNlAmDPl4QAAAwABAAADADIPFi2WAQAGaOvjyyLAAAAAHHV1aWRraEDy\n",
       "XyRPxbo5pRvPAyPzAAAAAAAAABhzdHRzAAAAAAAAAAEAAADXAAACAAAAABRzdHNzAAAAAAAAAAEA\n",
       "AAABAAAGyGN0dHMAAAAAAAAA1wAAAAEAAAQAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAA\n",
       "AgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAA\n",
       "AAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQA\n",
       "AAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAA\n",
       "AAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAA\n",
       "AAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAA\n",
       "AQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAAB\n",
       "AAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEA\n",
       "AAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAA\n",
       "CgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAAC\n",
       "AAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAA\n",
       "AAAAAQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAA\n",
       "AAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAA\n",
       "AAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAA\n",
       "AQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAAB\n",
       "AAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEA\n",
       "AAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAA\n",
       "BAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAK\n",
       "AAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIA\n",
       "AAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAA\n",
       "AAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAABgAAAAABAAACAAAA\n",
       "AAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAABAAAAAABAAAKAAAAAAEAAAQAAAAA\n",
       "AQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAAB\n",
       "AAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEA\n",
       "AAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAA\n",
       "AgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAA\n",
       "AAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQA\n",
       "AAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAABgAA\n",
       "AAABAAACAAAAAAEAAAoAAAAAAQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAA\n",
       "AAEAAAAAAAAAAQAAAgAAAAABAAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAoAAAAA\n",
       "AQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAABAAAAAAcc3RzYwAAAAAAAAABAAAAAQAAANcAAAAB\n",
       "AAADcHN0c3oAAAAAAAAAAAAAANcAAARLAAAAcAAAAB0AAAAUAAAAHAAAAJoAAAAmAAAAHAAAACEA\n",
       "AABbAAAAMgAAACEAAAAhAAAAhwAAAEoAAAAkAAAAJAAAAHIAAAAwAAAAJAAAACcAAACSAAAAKAAA\n",
       "AB4AAAAjAAAAoQAAADgAAAAuAAAAJAAAALQAAAA6AAAAIwAAADMAAACaAAAAPgAAACcAAAAmAAAA\n",
       "LAAAADwAAAAmAAAAJwAAAIwAAABMAAAANAAAACkAAAC2AAAAOQAAACgAAAAkAAAASAAAAEQAAAAl\n",
       "AAAAJwAAAIwAAAAwAAAAJAAAACQAAAB/AAAARwAAACoAAAAnAAAAvQAAAEYAAAAsAAAALAAAALIA\n",
       "AABBAAAAPAAAAC4AAACzAAAARwAAADAAAAAoAAAAiAAAAEsAAAAuAAAANAAAAJ0AAABOAAAAMgAA\n",
       "ADYAAACTAAAAYAAAADsAAABAAAAAngAAAFcAAAA5AAAAPQAAAHMAAABZAAAALgAAADsAAACJAAAA\n",
       "VAAAAD0AAAA4AAAAowAAAGwAAAA6AAAAQwAAAJgAAAA+AAAANAAAADYAAACDAAAAUgAAAEAAAABE\n",
       "AAAAnwAAAEQAAAA0AAAASgAAAKkAAABhAAAASwAAAEoAAACpAAAATwAAAE8AAABUAAAAlwAAAFAA\n",
       "AABJAAAATQAAAIcAAABDAAAAUQAAAEUAAAB7AAAARAAAAE0AAABNAAAAigAAAF0AAABLAAAAQgAA\n",
       "AL4AAABeAAAAQwAAAE4AAAC+AAAASAAAAE4AAABVAAAAjwAAAFQAAACbAAAAYAAAAEwAAAA1AAAA\n",
       "fQAAAMkAAABlAAAAMQAAAEoAAAC3AAAARwAAACsAAAA7AAAAswAAAE8AAABLAAAAWAAAAJgAAABP\n",
       "AAAAPwAAAD8AAADFAAAAVwAAAEYAAABeAAAAlgAAAF8AAABUAAAASQAAAJEAAABgAAAAaAAAAGkA\n",
       "AACuAAAAXAAAAEgAAAA+AAAAyAAAAEsAAAA3AAAANQAAALUAAABaAAAAYwAAAFYAAADtAAAAXAAA\n",
       "AFEAAABBAAAA0gAAAEwAAAC7AAAAYgAAAEgAAABHAAAAsAAAAGcAAAA+AAAARgAAAIAAAABRAAAA\n",
       "TwAAAEEAAABcAAAAfgAAAEcAAAA5AAAAQQAAABRzdGNvAAAAAAAAAAEAAAAsAAAAYnVkdGEAAABa\n",
       "bWV0YQAAAAAAAAAhaGRscgAAAAAAAAAAbWRpcmFwcGwAAAAAAAAAAAAAAAAtaWxzdAAAACWpdG9v\n",
       "AAAAHWRhdGEAAAABAAAAAExhdmY1OC4yOS4xMDA=\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def display_frames_as_video(frames):\n",
    "    fig = plt.figure(figsize=(frames[0].shape[1]/72.0, frames[0].shape[0]/72.0), dpi=72)\n",
    "    plt.axis('off')\n",
    "    \n",
    "    ims = []\n",
    "    for i, frame in enumerate(frames):\n",
    "        im = plt.imshow(frame, animated=True)\n",
    "        ims.append([im])\n",
    "        \n",
    "    anim = animation.ArtistAnimation(fig, ims, interval=40, blit=True, repeat=False)\n",
    "    display(HTML(anim.to_html5_video()))\n",
    "    plt.close()\n",
    "\n",
    "def test(q):\n",
    "    env = gym.make('CartPole-v1')\n",
    "    env._max_episode_steps = 1000\n",
    "    observation = env.reset()\n",
    "    state = observations2state(observation)\n",
    "    \n",
    "    frames = []\n",
    "\n",
    "    for i in range(1000):\n",
    "        frame = env.render(mode=\"rgb_array\")\n",
    "        frames.append(frame)\n",
    "        action = get_action(q, state, 0)\n",
    "        observation, reward, done, info = env.step(action2force(action)) # take a random action\n",
    "        if done:\n",
    "            print(i)\n",
    "            break\n",
    "        else:\n",
    "            state = observations2state(observation)\n",
    "    env.close()\n",
    "    display_frames_as_video(frames)\n",
    "    \n",
    "test(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# q, all_rewards, avg_rewards, avg_epsilons = train(q, init_epsilon=0.001, target_epsilon=0.001, n_iterations=5000)\n",
    "# plot_rewards(avg_rewards, avg_epsilons)\n",
    "# test(q)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}