week_08_qlearning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pwUEmpTvyXZV"
   },
   "source": [
    "# Practice: Q-learning\n",
    "\n",
    "_Reference:_ This notebook is based on Practical RL [week03](https://github.com/yandexdataschool/Practical_RL/tree/master/week03_model_free)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "S4_8lIHAyXZY"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "??? ????????????? ????????????? ?????????? Windows ??? Linux.\n",
      "\n",
      "???????????? ????? ?????????? ?? Microsoft Store:\n",
      "\n",
      "https://aka.ms/wslstore\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "\n",
    "if \"google.colab\" in sys.modules and not os.path.exists(\".setup_complete\"):\n",
    "    !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/master/setup_colab.sh -O- | bash\n",
    "    !touch .setup_complete\n",
    "\n",
    "# This code creates a virtual display to draw game images on.\n",
    "# It will have no effect if your machine has a monitor.\n",
    "if type(os.environ.get(\"DISPLAY\")) is not str or len(os.environ.get(\"DISPLAY\")) == 0:\n",
    "    !bash ../xvfb start\n",
    "    os.environ[\"DISPLAY\"] = \":1\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QeYgwaKKZGgd"
   },
   "source": [
    "## Q-Learning Agent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YRmBDXR2y37a"
   },
   "source": [
    "This notebook will guide you through implementation of vanilla Q-learning algorithm. This part is based on the [Berkeley's RL course](https://inst.eecs.berkeley.edu/~cs188/sp19/projects.html).\n",
    "\n",
    "You need to implement the main methods of the agent, namely, action sampling and q-values update procedure.\n",
    "\n",
    "In order to simplify the implementation, agent also has separate function to estimate the value function of the state given the q-function estimates. The value-function in this case can be estimated as the maximum of q-function values in current state:\n",
    "\n",
    "$$\n",
    "V(s) = \\max_a Q(s, a)\n",
    "$$\n",
    "\n",
    "Once we can evaluate states, we can try to update our q-values accordingly, i.e. suppose we were in a state $s$ and took action $a$, which changed the state to $s'$ and yielded the reward $r$. In this case we can deduce that our q-function should be equal to:\n",
    "\n",
    "$$\n",
    "Q(s, a) = r + \\gamma V(s')\n",
    "$$\n",
    "\n",
    "Here $\\gamma$ is the discounting factor.\n",
    "\n",
    "However, we don't want to change our q-value so radically on each step, because this would mean that we will be discarding all our previous updates to this value. Instead we will call this new value $Q'(s, a)$ and will update our q-function in a following maner:\n",
    "\n",
    "$$\n",
    "Q_{n+1}(s, a) = (1 - \\alpha) \\cdot Q_n(s, a) + \\alpha \\cdot Q_n'(s, a)\n",
    "$$\n",
    "\n",
    "Action sampling is done using the simple $\\varepsilon$-greedy strategy, which means that we take random action with probability $\\varepsilon$ or the best action (wrt the q-function values) otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "P95haD6wyXZZ"
   },
   "outputs": [],
   "source": [
    "import random\n",
    "from collections import defaultdict\n",
    "\n",
    "\n",
    "class QLearningAgent:\n",
    "    def __init__(self, alpha, epsilon, gamma, n_actions):\n",
    "        self.alpha = alpha\n",
    "        self.epsilon = epsilon\n",
    "        self.gamma = gamma\n",
    "        self.possible_actions = range(n_actions)\n",
    "        self._qvalues = defaultdict(lambda: defaultdict(lambda: 0))\n",
    "\n",
    "    def get_qvalue(self, state, action):\n",
    "        return self._qvalues[state][action]\n",
    "\n",
    "    def set_qvalue(self, state, action, value):\n",
    "        self._qvalues[state][action] = value\n",
    "\n",
    "    # -------------------------START OF YOUR CODE-------------------------#\n",
    "    #                          !!!Important!!!                           #\n",
    "    #              Please avoid using self._qvalues directly.            #\n",
    "    #  There's a special self.get_qvalue/set_qvalue functions for that.  #\n",
    "    # -------------------------START OF YOUR CODE-------------------------#\n",
    "         \n",
    "\n",
    "    def get_value(self, state):\n",
    "        # Agent parameters.\n",
    "        possible_actions = self.possible_actions\n",
    "\n",
    "        # YOUR CODE HERE\n",
    "        # Calculate the approximation of value function V(s).\n",
    "        value = max(self.get_qvalue(state, action) for action in possible_actions)\n",
    "\n",
    "        return value\n",
    "\n",
    "    def update(self, state, action, reward, next_state):\n",
    "        # Agent parameters.\n",
    "        alpha = self.alpha\n",
    "        gamma = self.gamma\n",
    "\n",
    "        # YOUR CODE HERE\n",
    "        # Calculate the updated value of Q(s, a).\n",
    "        # qvalue = ...\n",
    "        \n",
    "        qvalue = (1 - alpha) * self.get_qvalue(state, action) + alpha * (reward + gamma * self.get_value(next_state))\n",
    "\n",
    "        self.set_qvalue(state, action, qvalue)\n",
    "\n",
    "    def get_best_action(self, state):\n",
    "        # Agent parameters.\n",
    "        possible_actions = self.possible_actions\n",
    "\n",
    "        # YOUR CODE HERE\n",
    "        # Choose the best action wrt the qvalues.\n",
    "        best_action = max(possible_actions, key=lambda action: self.get_qvalue(state, action))\n",
    "\n",
    "        return best_action\n",
    "\n",
    "    def get_action(self, state):\n",
    "        # Agent parameters.\n",
    "        possible_actions = self.possible_actions\n",
    "        epsilon = self.epsilon\n",
    "\n",
    "        # YOUR CODE HERE\n",
    "        # Choose action in an epsilon-greedy maner.\n",
    "        # action = ...\n",
    "        \n",
    "        action = random.choice(possible_actions) if (random.random() < epsilon) else self.get_best_action(state)\n",
    "\n",
    "        return action"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "t6lkqpS-yXZb"
   },
   "source": [
    "## Try it on taxi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "chnLpPKAZENJ"
   },
   "source": [
    "Here we use the qlearning agent on taxi env from openai gym.\n",
    "You will need to insert a few agent functions here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "id": "6REbLYeDyXZb"
   },
   "outputs": [],
   "source": [
    "import gym\n",
    "\n",
    "\n",
    "env = gym.make(\"Taxi-v3\")\n",
    "n_actions = env.action_space.n\n",
    "agent = QLearningAgent(alpha=0.5, epsilon=0.25, gamma=0.99, n_actions=n_actions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "id": "Ud0VvArnyXZb"
   },
   "outputs": [],
   "source": [
    "def play_and_train(env, agent, time_limit=10 ** 4, render=False):\n",
    "    total_reward = 0.0\n",
    "    state = env.reset()\n",
    "    for _ in range(time_limit):\n",
    "        if render:\n",
    "            env.render()\n",
    "        # YOUR CODE HERE\n",
    "        # Pick action given current state, take the selected action and update agent.\n",
    "        action = agent.get_action(state)\n",
    "        next_state, reward, done, _ = env.step(action)\n",
    "        agent.update(state, action, reward, next_state)\n",
    "        \n",
    "        total_reward += reward\n",
    "        if done:\n",
    "            break\n",
    "\n",
    "        state = next_state\n",
    "    \n",
    "    env.close()\n",
    "\n",
    "    return total_reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "id": "TX5UO6B5HnZY"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "# Helper functions to plot rewards during training.\n",
    "\n",
    "\n",
    "def moving_average(data, span=100):\n",
    "    return pd.Series(data).ewm(span=span).mean().values\n",
    "\n",
    "\n",
    "def plot_rewards(rewards, epsilon):\n",
    "    rewards_ewma = moving_average(rewards)\n",
    "    plt.plot(rewards, label='rewards')\n",
    "    plt.plot(rewards_ewma, label='rewards ewma@100')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    plt.title(f\"eps = {epsilon:e}, rewards ewma@100 = {rewards_ewma[-1]:.1f}\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "id": "bIXSPSsnyXZc"
   },
   "outputs": [
    {
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mn1+sD4rfnV/IjW98x+/e+ZE/fGAtZnWosIQnPl/Lqp2HWP3TIe7+8ggLN+3j1Mdz2JR3mMISD2t+ymdZ7kH+s2Azv3v3R974divd7v2EIQ/PKneN5hUUkbv/CD/719cMePBzPvpxB+99b/1PAaYv3kb2o3PYf7jYn3epx8uTs9ayZMt+npi5hrcWbeW/3+UyYsoXfL0+z98meQVF7DgQvE799a8tYcCDn/OrVxcz8E+f+8P/+10uT3y+1n8/GGNYseMgW/YeZvuBoxSXeulyzyec9OfZrNtVtoLiki376HTXx5z059lsPOjhu637mb5oGwMe/JyfP/8tHyzdwfTF29i69wi/eOFbnv9yY1D7f70hjxFTvuCr9XkYYz1cNucd5odtB3jj261MfuN7bnrze7butR4AB4+UsDnvMF6v4ZpXFnH3f5cx9om5LNq8jxKPl2dy1rMpL3A1z5rjuJnYLSsryxwvX/he9OzXLN6yn1m3j6Zbeiqd7voYgM1Tzgybfuq8DfRrl8bwri38YZ3u+hiHwAtXDmFE15YkuBwYYyjxGBJcDn+eADNuHcULX27i7SW5/OWCflw6tEO4Yvzk5OSwNbET979ftprdVSM6c8e4HizavI/9R4q57a2ldG2VgtdQ6cU3oH0aP2w7gMsh3Hxad5743FqRbmjn5jhFWLBxL78c0YkxJ6TzybKdTFtkLVf71wv7Mb5Pa75av5cb3/iuwjJ8ZDRJZNch64b+4o5TaJuWzPrdBZz1j/lB6W4d250nZ63z7//+zF7sKSjiX3M3Rsy7eUpCOTG7YnhH7j2zNz1+/2lQ+N0Te/LToULapSVzydAO3Pzm93yxejftmyfz3q9H8OL8TbyzJJd2zZL55YjO/Gb6UortB+CNY7ry9JwNACy9fxzr9+SXMw5EIPTWHNKpGXkFxWzKO8xLvxzCiu0H2X+khASXg2dzNtAuLZk+bZswc2XZ8roT+7Ymye3kve+3AwY3HhIowYWH/1w1hM9W7uHlb7ZRihMvDgRDEsU48NKjVSM27ilA8NqxBocYHHjtn0EwODBcNqQdVw7vwAXPzKek1GOlxUor9gqV/ze0M68uzPUffUb/trz/4y66ZjRh9a4jeBEcGNyUkkApLjy4CX4Lc+ClcaKLi7MyefmrTQggYuXvK6dtk0R22g/ukzo35/rRXbn6lUV47JUkBUOXFsls3VuAm1ISKWFQx+aM79eOBz9ahctuIy8OPDgQwIkHJ16cYtXeiddfp7P7t2Hmyt0UlZZZ7CbMqqEG4aBJIYES3HgQMRSaBLyIlTdeEqWEZKzre2CHNL7feoCURBe/vfdRcMY2IYOILDHGZJULry/xF5EJWMv3OYHnjTFTKkp/PIn/2Cfmsn53AZ/fNpruGZWLf2j89gNHGTHlC3/8Gf1a889LB/FMznoem7mWH/84jv5/nBmUx69GdebfX24C4IUrsjitV0ZQfF5BEY0SnDRKcJGTk8OXBem8MH9TzZxwFbh0aAfeXLi1zsutKRx4acFBUuUoXgQ3HnabNBIpoZEUkkIRyRTiFo8/vYBfJEtwUmqcJEoJCZSQaP8SpJREigP2A+IoIdHeNwhFJOA1gks8dh6lJFBCAqUkipVHEsUkSbE/PtHOQzk+2X3LFtKbpcV0bCTxr5e5fewFm58GTsdav3ORiHxgrAWkj3t87oy5a/ewsRKrOfTh+93W/VwQ4M4B+GTZT7zYwbLsAfYWlHcHBVrnV7+ymHdvOJnBHZsB8Ma3W7nnvWV0atGInN+OASyXSH2w8+DRyhPVIIkuByd1acG8tXsAQxOO0Fb20kb2kiH7SaOANCkgjQIaSREHTQqntHdx9OAeSgvySOUITrGssmSnoYnJR0zt+2S9RiiSBIpxU2hcFBk3xbhx4CVBSnHgpdQ4rTB3Iq3SmrBhH+R7ktlrmlBIAoVe63hXYhId05uTmtKIbm1bcKBIeHa+9fblpMySdeJFBLL7duTDZbttm936eWwr2CB4jdA0JYm9h0txOB0Ue/C/B3jtX6+2aRw4WkrX9Cb0zUzD4zU8N2ctLtuCFkxZmfbfbi0bsT7vCCW4KMFFaqNkdh2xLGwBEt0uRvVoxYwV1puNr26+bQBjBHEIHi+M7tGSeWvz7OOt6/3Unq1wOp18tmIXXhw8O+kkHp29meXbD/qteQ8OinEhGK44KZMPl+1i75FS+mQ2Z3CnFkz9cou/LQK5/KT2fLr8JxonOHGI8OQlA1i5M59731sGgFs8pHKEQhIowQlgv2UZTmiTxu6CUu4/fxD3fbyBDXmWW6hxkouPJ48kPa1pjV9j9TWx21CsBa83AojINOBcoGGIvy3oD31c+YJRhSVlr4+975/BkeLwwrJs+0Ec4rvAywt3i5TEoP0Ln/2a/1w9lCGdmnOPffFttv2MxR7Dy19vrvxEIuAQiPXZEeqzjZYrhnfkfz/s4OBRy3q97pQuYV04c28aSEHuSv71/hwSpZgrezno48ylpO06SvZvpZEpX36RcXGAxhiEREpIK8rAk9aMnPzmrCUTj3HiMQ6aN0rm9Kw+7KI5f56diwODQWgu+Vx5Sk86tE7n2mkrOUISz006ifnr9/HCV5sxWOII4MbDie0ac8cZ/Xjos438YuQJHCpxMHn6SopwU0QC/Tq0wu1O4NlfDKZpkpvf/Wcx89bm0SOjMUtzrf6A5ydl0SYtieYpCaQkukhNcpNZUITb6eDG179j/vo8//l1bNqIudeN8e9nAH+cCM/N3cCUT1f7w9c+NJGv588jKzubPhd4+H7rfnblF9Ikyc2bC7cya1VZH8XGu8/A4bCuR4/XsHXfEfYdLuKng0X0bJNK11aNy7XzOweW+l2Bd7y9NChu7UMTcTuFVxds4dwBbdl/pITMZsnsOlRIemoSCa6y7sm+W/ezJ7+IGct/YkLf1vTLbErTZDeNElzk7j9CZrNGrN9dQNdWKdxk3zN5BUW4HQ6aNnIDcKXHy5a9R8hIb8xjvU4Oqsu2fUdolZrIN199SXZ2NhdOLOX1b7cwaXgnktxORg0toEvLFC589mu+23qAG8d05VejupDWKIFbzg8+57YdYFtpU9qlJXPtf5YA8NVdp9K8UQK97p/B4I7NePWqoaQklknxG91OIK+giASXg0Sn01/nmqZe3D4ichEwwRhzjb3/C+AkY8zkkHTXAtcCZGRkDJ42bVpM5RUUFNC4cfmLsbb47dwj7Dlavl1fnhA8Pez+Qi+lXvjtvMoFcXxHF0vzPPx02PDnkcncMz/4mDM6u/lkU/Br/U0DE2mWKDz4TVnH5csTUpizsYBX1pb3SUZLkhMKYzR+KzpWgJPbuli518P+ouD2G9vBxbc/lZJfDJeckMCotL28vWgDTThMV8cOuspOesg2ujt2+K08sES3MLkNRxplUpjUisKkVvxtVSo7TAt+O7otO484uGNRkl26xcsTUvB4DVfPDB6V8fCIZNqlWiJ05YzgN7pnxzYi2SX+//3LE1L4fEsJr68q/5bWt6WT32Ql+fc3HvDw4DeFpLphyuhGNHKBSPn/z7tri/lwYwnndXNzXreE8I0IHC4xbDjgoVmSg/u+OkrrRsKU0Y3KpTPG8MvPjjC8rZMx7d30aOas8F4p8hi253tJcgltG8c+VuTL3BJeWG61y4i2Ln7RO4EkV+zXY21RmW4cKjZsPeSlb0tnVPn5rhmfDhSVGlwOcDpq99zHjBlz7Lh9IExvCJRTS2PMVKxFnsnKyjKx+u3r2uef+O0XcLS8oGdnZ9PvD59x6+k9uHpk56BO28ro37Mr67/LhcOHGTJkCMyfFxTfvn172BRsCY8+aZDl3vnmm6A65Gz7HIh9GJ7L5QJP+eGQFw7K5N3vcis8NpLw33tGL64Z1RkR4T8LNnPf+ytozBGSKaYEJw/2K2bR7rdJdR/i5L37SNqylTNt/fPgYJu3FRtMW3qMuZKDab342bTteBHuvHQ8p/fvRKD09Z+7gR0rfuLkiSPIycnhLxd04fGZa8krsDra/NfKzLL/z10Te3L5KV39+62+mhU0smriWMuynjmkmL2Hi+mW3pgeB47y+qqyvhv/sS2ak5091L/ffk8BfDOX5KREzjx9TLn0Pja4NvHhxpUM6tOD7OGdIqbzsSe/iPu+msV5Q7qQnd0zbJrNIcXVxb2SumUfLyy3OrjbtmnNhLEn1mp5sVLjbTHDup6OlWmi60v8c4H2AfuZwI56qku1KCr1cMf0pdw5oSftm1sSE/gy1So1MUgk8otK+dNHK7l6ZOegfBJdDopKvVSEz+2zYsehcnGRfPjekDe7tbvyWbyrej7rgqLw4+AbJ0ZnAflolOCkd5smLN6ynwSXAzFe2PwVv9jzDhObf0nLIwEPs9lwiklhpzSnqGVfkkb+mp+9f4SDpDDzT7/kkkfm4zWGhaeMJdVrWPvmJwA4E5LLlXvdKV25LkDILx3agfMHtqPnfTPC1vO2sT24cFBmUNic32Rz4EgxI/86Jyi8WUoCzVKsp1LbtGQ2TzmT3P2WG2FZ7kEuem4BZ5/YNuiYRNul0Tix4ttx0vCOJDil0tFcPlqlJrLg7lNJT02qPHEdMrhjc164IourX1nMuD6t67s6dcYnN49ifx18+xAt9SX+i4DuItIZ2A5cAlxWT3WpFl+tz+OjH3dSUFTKy7+0rLlAIU4PEf9IJLmdFYr/2oCxyLe+9UO5+OfDjNwxhnLvU+P+FvzG0CIlgb1V/DimSZKLf1w2iCteXBgUnhJGvJ6flMU1r4YfpeUQoW+jA7RwLGLEqndh/lw4kgcJqSRlDOatQx1oL7vxtB/OqDMu56Rnd1LkEeaenU3TFiks+p9tmbsSmX9nmQnrcAjZJ7QiZ0357xcikeiK7Ma4ZWz3cmGNE100clsPu6GdmleYd2YzyyjI6tScNQ9NINEV/JBs2zSZX43qzP8NqVjU3U4Hv4jC4g+kTdPyD79jgdN6ZYRti4ZM77ZN6rsKQdSL+BtjSkVkMvAZ1lDPF40xKyo57JjCGIOIIP5RBmVxgdZ2YHhF/SuuSvx+7/8Q/sWoojcGY4y/YzbcGHaAe87oVa7zrTLeueFkwlU3nPgnhIiqEw8XOudxruNr0jhKn00bIQFKdjSCXhOh1znQ/XQaJ6Swa/Y67vx8Lde178KozF4UeSyxD7SQW9hWtssZXryj7dIK52OvDIdDmHX7KbRNi96yDid2Dodw75m9q1z+8U48Cf+xSL0t42iM+QT4pL7Kr4iiUg8f/LCDiwZnhhWFdbvyOf1v8/j3pCzcTt9QszK8ER4EFY2QibXbPcFZgfgDu/Otzt5BHdKCRmsAPHHxiX5Xko8eGY05eLTE/yFVKFee3IkeGalsDPOVa5K7/M3s9hZypuMbhjpWcXHqMpxH9pBgj4FfaTrzfstr+XBHKuddcAlnZfUIOjZSR1jjJOuyXf7A+LAPISiz5EPPr6bpll53AwkUpSY5btbwrUv+Pmsdz+RsICXRxRn92pSL/37bAQBmLP+JcwZY/lsTZO2Hl/KKLP9YR10luBwQwas0Z/Vu/jXP8pu7HMGW8cAOaVwwKJMPlwa/UThEaJGSGFH8fZZ8OGFOlhJOdixngmMRDrxkyAGy3tvE8IR9FBkXRzJO5431br73dmeWdxCpiW5Oad6KWbk7OdtVfqHsUN3+/Zm9mPLpar/FWJGP/E/n9SWzWSNGdW8ZMU1l/P2SAWEfaIrSEFDxD4Nv1Ed+YdnQyd2HCsk9cJRBHZr5hyoZjN/yjMbtU5HlH+u4eXcEdwfA0twD/m2XM1hJmyZbY4erOszMlz74OMNZjm84b94tXJYQ7Gc/0OpUbt04mO+8PXh7wkQefTKgz0EqfuORkEFh14zqwjWjukRVz/TUJO47q2qulOcnZdEytex7iXMHtKvS8YpyPKHiHyXnPf0VOw4WsnnKmUGuIJ9ABQp+YIdv0IMgQOo+WVY22RgQ80x+7grGRwc+GEIfEoM7WF//hhP/ijwlvr4Jp0A3yeUs5zdc6/yYRlLEvsTe/LngLPaYpuSZpmwybXh+3ARy7C+WQx9AAn71j8XnXtOM7Z1ReSJFaSCo+FfC/sPF7D9SzI6Dlu88GpEOtOIDLdvAt4Bfvx48kVllwzwjUZHlH9iJ7A4R3l+P6QaAM4zoVqTDTodAUT7NPvk1sxI/AGB/h3EsajSMXZ3P57X3gr9qDsy/XVoyCS4HvxrV2T+xmaIo9YOKfyWc/rd5/k+ti0u9fpcQAIZK3T6RXEA1RUIF4j8nYKhj6GgYv/vGWTWLu/XRDfDvy0ncu54Fnt78w3Meb1x1J6cA0+3ZOsOVA1aH8NqHJrLmp/xy4l//dr+ixBcq/pXgE/sWKQnsPFhIXkFxgM8fv2pFEnwiPBRqitChlJFwR/Dth1r+4d0vhhNlA+c5v+Li72ZBo+YcvvhdLn0l5CvmMIc6HcIjF/YPqmfgcyg5wVml81AUpWZQ8Y8S38iSQ0dLgtwi/nH+AWm9AR6cILdPLdSrIrdPIJHGwVf2fUELDjI14QkGO6y58Tekj6frFc/hdaQCMys8Fizxv3hI+5Awqy4iwn1n9qZtWjJje6m/XVHqEhX/KPEJfrAPP3C0T/iO3YhvBDVERW6fQEI7W304wnX4IiRRxGTX/5jsep+jJoGnS8/hTc+pXN0/m66NmuMMM8VDempiubBwHcqBD5ymjdzcfnqPcmkURaldVPwrIJxWW1/22tuUuUkC01pvA6ZcuImtT7dC3FG6S6L92MlpSrk9/0nGJOUAMMszkCdLL2S5sYZYusIO9bTIPiGdf142kMlvfF+WX5hywz1wFEWpW1T8wxA6vjwQExIf7o0gUO8C3wJMDTp+TshIZc2ufBKi7LCN5qUjiSIeKpjCgNIf2W5acG/J1eR4BwSl8blsIn0fEOq+qcjyPwZGdypK3KK9bFHiF88QEfV3/gaoa6CVHej/3x3l4urR0CzF+kgrWp9/ZQ+ezrKT6QkP0q90OU82vo0RRf/gksuuKpfO5z4KZ9FDeUEPJ/6+sMq031/n42OZaUU5rlDxryKhQzcrs/wDCZ1RszqkJlniH6kjtxwVCOhYxxI+TLiXPo6tHBz3JHOSxgLQ3F4dbGLf1jxwTh8AurS0pmGI5LoJfSiE61BWg19R6h91+1SR8oLv+8K3bK3cQL3bHuOyhZXh6+iNdph+JO1vt/Qpnk94kp+cbWh83Xs0T+8F3823ynA5mPfbMaQ3SSTR5WBEtxZ0S0+tsJzQvgX17yvKsYla/lUkUES37w9Y5s8Ynp27Hoh9np6q4JtCwumoxr9w3ee0X/oky7yduK/5E5DeKyjaGEOHFo1IcjsRkUqFH8K4fcK8BiXak6UNsqeYqDzT6JIpihI9avlHic/d45vHH+C7rQd47ZstVjjlZ86sTTx2fSobp+/DG/pE2rcJ3r2aw816cdHOOznRGaUQV0LoR2LhviBunOjig8kjwi7yHZSXqr6i1Bpq+UeJz9UfqqHfbtzrj6/thZgD8Yl5tG6VwGonUQRv/QKAtdnPUkTIYuA1OAwnUsdw/8y0sIu/KIpSN6j4R4k3wnCfslATtRVeXR772Yl+yz/a/t6OLaylBB14edz9LOxaDhc8T/uu1rTHlw8rv4RgTXivansxFUVRYkNNryjx+N0+wS7onfZsn3Vp+V80OJP3f9gORO9qGtumiO7uhxjuXGkFjP8z9BhHS2DzlDOD0pYNX604z95tmnDWieUXuwkk0pfFiqLULyr+UeIbr2991Rsm3hD1B1c1gU+Yo3nguCml1YeTaOtcDcBDJZfz++E3VrsOn9wyqsL4hfeeFvV3CIqi1C16Z0aJz+0TaX4eY0z0Y+6j5Nax3SPG+Ub7RHI1uSmbe2ey63+4967mmuI76FP4As97zgx7jI+a8tSkp0a/sHk4kt0O+68upagoNU211EpEfiYiK0TEKyJZIXF3i8h6EVkjIuMDwgeLyDI77ik5FpZwigKf2Fpun/JVrg23T0XTHPvcUOE6fM9wfMO6pEl8n3gtm5Mu4xbXfznS8yJmeQdzmORKy/3t+BNIT02kZ+vKh3bWJped1JE7Tu/B9ad0rdd6KEpDpLqm6nLgAiDo01UR6Q1cAvQBJgDPiIjPfHsWuBbobv8mVLMOdYJ/qCeRLeOa7vCtqLPUtzJX8Dz9hrtcb/JMwlMANJMCAHabNArG/Cnqck/u2pKF946t99E4CS4HN53WXRdRV5RaoFp3tzFmFYRdAORcYJoxpgjYJCLrgaEishloYoxZYB/3KnAe8Gl16lEXlFn+1tRuoRhMkOU/sW9rWjdN4qWvNsdcZkWPksd+diIvf72Zk9I9XOf8kOc9Z/Af91842e7Qva74Nr729qEINwbhq+Tm/mN/P6x67hhFUY5/asu0awd8E7Cfa4eV2Nuh4WERkWux3hLIyMggJycnpsoUFBSEPfabHaU892MR/zy1EY0TyqR250/WBGxr1qzxhxWXlACwYuUq3GHelwoKDpPkLZvKYc+ePXjyq/cmsHHjxrDhvnMZngy9Pv01I9zbGexYy8nOlaz3tuVnxfeznyZBxyxYsMC/neQ5GnNbVoW6KKO6RLo24hVtjzIaeltUKv4iMgtoHSbqXmPM+5EOCxMW3mSuYDi5MWYqMBUgKyvLZGdnV1zZCOTk5BDu2L89/RVQRNueA4KmGvg070fI3cYJJ5wAK5YB4HC4gFJ69epJkssJPwQvwJ7cqBHpLRvDnl0AZKSn07ppEmzZFFOdAbp36wprVpUL95/Lzh8hxxryOc65hGXeTpxb/BDeMN68ESNOhjmzAGic0ihse9QYMz4OrucxTKRrI17R9iijobdFpeJvjBkbQ765QODafZnADjs8M0x4vRBu8fVIBI3zD/MIM6bMDw9Wmup2AVTaFz7vEUrdjfm6sDPrTCaPlP5fWOGH4P6D46SPXVGUWqS23D4fAG+IyBNAW6yO3YXGGI+I5IvIMOBbYBLwj1qqQ6WEm4s/Et4A8Q+HIXi0j4hUW2QrfHgs/Des+pAd/W5i0qLhleYVmJVqv6Io1R3qeb6I5ALDgY9F5DMAY8wKYDqwEpgB3GiM8diH3QA8D6wHNlCPnb3+JRijSOv7yMtrTNhZO40Jnt5BiCyyl5/Ugb7tmoSPDCDiaJ/De+Hz+6HtILb3ub7SfELz0o87FEWp7mif94D3IsQ9DDwcJnwx0Lc65dYU0U5jAAFunwjpLcu/TFYdEnlWylHdW7HrUBHLtx+quH6RLPR5j0LJUTjvWcyhKEfuBOSllr+iKHFtBPoXZYlC/X1DPTHhl0Q0Jnicv+X2CZ+XQ6L7JiCc2+iLc4pg4b8g6ypI7xn1XPeBxan2K4oS3+JP9G4fHwYT1vL3GhM0d70Q2WcvIlFNeBaaopvk0iXnJsjoC6c/WC79y78cEjmvoA7fSotWFKWBE9fij9/yDx+9NPdguTCvCT+/T1jLP4KN7ZDoFl4P9NOncoR/uf8G4oDLpkNiY/sUytJkn5BeQV4B25WWrChKQyeuZ/X0D/WMYPt/YE+bHEhFHqLg0T6RLWyR6OYB8iVpRCFzE2+luRTAhKehSdk0ytFa8YEPidq2/N+5fjhNkt21W4iiKNUiro1Av9unCn6fSG6f8KN9wqusiAR9ExCxfnaSe12v01wKmFp6Jgz8efSVDZNX6HZtkNWpOT0y6ndSOEVRKia+xb8St0848TaROnwJHu0jErlj1SESleUvInSQXVzq/II3S8fw59LLy6epNJey+lT1GEVRGi4q/kR2+4Sdi8IY/5j/QLzGBAmsQyTiOH0BUhIq97i5vMV8knA3DjH8rfSi8HlFacYHjfNX9VeUuCeuxT8WDOFHBxkT/AZRkc/fIcLNp0VeqMVH+x2f0VgK+dAzjN00C5smep9/+G1FUeKTuBb/WHz+97+/Iux3AdZDITA80lgfS7Armys/jXz6rnqC1d723FwymetGd+H203tEX9EQdG4fRVECievRPj4N9BjD5rzDdGqZEtVx4S1/ExThkPCrbAWWWxHXuz4ksXg/t5c8iMHB3Wf0Cp9XFPWNtkxFUeKH+Lb8bUX85xfryX4sh/W780MShD8urOUfrP0Vim3kdwKL4Y4VXO/6iN3pI1lpOlWYNmq3j6q/oigBxLf423+XbNkPwPYDhWHjQ4k0t0/wsRVP7xCOLFnNJwl382aCNSXS9g5nR6hBZGbeNppnLh9U5eMURYkv1O0TQLgvd8MRaVbPwDcCh0SelTOcFZ5MIc8mPEkrsSZ7u6l4MuMzJwI/VFKb4Lx6ZKRai8iEwSHh664oSvyhln8gtjCWDQENT2mYsZ6hs31a0zuEJ9TyP9vxNauSrvIL/9ulo/nQOxyH/d1Ai5SESKcQ9u0iUrkzbzuFRy/qHzEvRVHihzi3/INlMlrLv7i0vPh7veW/Fog8vUNZRAIl/CPhn/79oYVP+4d1JjgdLH9gfIUzgIaLieTf75bemG7pjcnJ2RAxP0VR4gO1/AMIdYlEktzSML6TUMs/4kIsBD8ULnLOA2CHac6QwmeCxvO3bppE40QXSW5nxLzC5l+l1IqixCNxbvkH70dr+Zd6wrh9QqZ9EIn8/YDvwZBIMX92vwDAmKInKCLYvdMmgu8+kHBWvg7sURSlMuLb8g9RydAhnJHcJyWe8Koe5PMncp+BL9dpCQ8B8FDJ5eWEH6B5Bb7+0LwCqeitQ1EUBeLd8g/ZD7XUI2loSVjLP/TBUYnlv3cDAx3rAXjRM7Fcms1Tzgx/sKIoSg0Q55Z/8N9oh0GGE3+vCX4AFJZ4I7qRRIDZD1JinJxR9Ge81fg3hB3to4a/oiiVEN/iH2L7R5rdM5R/f7mpXJgJObqwxMPRYk/Y411F+2D1x7zsGV/pF7yVEW5AaWVfECuKolRL/EXkURFZLSI/ish7IpIWEHe3iKwXkTUiMj4gfLCILLPjnpJ6nHfAb/nb+9X5AMobMqunxxiORBD/tHX/A28Jb3tOib1AG7X8FUWJhepa/p8DfY0x/YG1wN0AItIbuAToA0wAnhER33jFZ4Frge72b0I16xAzZW4f3+ye1VD/kNE+xsDRknDib0hbMw3aDmKtaR97eRWgHb6KolRGtcTfGDPTGFNq734DZNrb5wLTjDFFxphNwHpgqIi0AZoYYxYYS2lfBc6rTh2qg889Umb5B4t/dZZ39BrD0eLScunGOr4jad9qGPqrqlY3agKl/+qRnWmUULXvBBRFafjU5Gifq4C37O12WA8DH7l2WIm9HRoeFhG5FustgYyMDHJycmKqWEFBQdhj9+yxJnLzWfwrV66i2cH17NhZBEBpaUnUZXi9hu07dvj3f/ppFyVhVvy6yvkpR9zNWLQvA7DKb9tY2FEQ/KSJ9ly3HCp7u/AdE/gGM6rxbkadmhSUX6T2iEe0LYLR9iijobdFpeIvIrOA1mGi7jXGvG+nuRcoBV73HRYmvakgPCzGmKnAVICsrCyTnZ1dWXXDkpOTQ7hj3935Pfy0w3L7GMMJPXuRPTiTGXt/hNxtOJ0uKClvvYdFhDZt2sK2rQC0TE/n0NES2J0HWDN2vpP4IAD7Bt/FKaeeBjM/BuCS4d154vO1QdlFe64rdhyEr+eXP+azjyPmE6k94hFti2C0Pcpo6G1RqfgbY8ZWFC8iVwBnAaeZMpMzFwh0aGcCO+zwzDDh9YLvSVQ21DPE7VOFvDxew5sLt5YdawwD26fx5bo8rmyzlT/uf9AfV9hlXIw1Lo+O7FEUJRaqO9pnAnAncI4x5khA1AfAJSKSKCKdsTp2FxpjdgL5IjLMHuUzCXi/OnWoDj7R983VU67Dtxr9vx6v4ZaxPZjzm2xuNtYL0Tue0Uws+gueluFX5YoF7dtVFCUWquvz/yeQCHxuj5j5xhhzvTFmhYhMB1ZiuYNuNMb4nNM3AC8DycCn9q9e8OmmT/OrM9gnFK8Bp0PovHk6HFjGu56R/K7kWrw4yi3vWB39VvFXFCUWqiX+xphuFcQ9DDwcJnwx0Lc65dYWNbnQiTEG8tbDrD+Sn9KJP+39hf9LXmfonEI1V6yiKEpUxPcXvpXM518dUfYa4IOboPAAywY/yAFS/XEVTM9fZdTnryhKLMS5+Afvh/r8q/XRl6cEdnwHQ6+lqO3woCh1+yiKUt/Et/iXm9uHCverQrviDVBaCB2GkRzykZV+gasoSn0T3+IfuphLDTr9uxattjbaZZGSENy1Eurzrw76GFEUJRbiW/xD9muyw7dL0SpISYe0DjRKDLH8a7DV9SVCUZRYiO/FXEJ9/iHx1XH5dyteDd2GgEi5uXV8bp+PbhrJ5r2H2bTncOwFKYqixECcW/4VL+MYK2nk09azHTIHA9DIHeL2sTt8+7Zryln921aztMim/88GZ0aMUxQlvolry98TIvblh3rG9jAY4NhgbWQOASjn9qlJV02kvHQZSEVRKiLOLf9gys3uEOOLwEDHerwItB0IgNvp4MvfjfHHh3b4+navHd2lymWpy19RlFiIa/FvlpIQtB/a4RurE2iArGersyMkln3Y1b55I/926FBP30NGO28VRakr4lr8Q338kRZcrwpt2Mspzh9Z4zohYprQj7x8xPK1bj2ugqkoynFMnIt/6H51xd/wiPtfACxKyIr6KJ9+xzLtg0q/oiixEN/iH7L/2My1FSeohB6Syyjnch4uuYyvXcMrPyAENeIVRakr4lv8KxH3wNE+H900MmK6h87swpXOGcxMvBOAjz3DYnIhxfLioQ8MRVFiIa6HeoYbyhno+gkU477tmkbM5+cbfgvuL/37O2jJVXU0xl5n9VQUJRbiWvzDcaiwbM3eigzxlAQnh4s9tGI/bP6SN0vH8I23F4dIYf3DE/0fclWFWKx4tfwVRYkFdfuEMOnFhUxbtM2OD07w+zPLll+cf+epAPR2WOv29hz/K973jmSOdyAupyOmUTg1uZKYoihKRcS1+Idj6bYDEePOPrFsKgbfNwKXOWcD0KR97IuT6XBNRVHqmrgW/8qGdobGhmp0Ewo41fE99L0IUlrUWj0qQp8biqLEQnyLf2XxIQlCO1cvdH6JWzww8lZcNbk2o6IoSi0Td+L/1xmreTbHmnitqgZ3kL4bw22ud9nszYDW/aq1Old13D7qMlIUJRaqJf4i8icR+VFEfhCRmSLSNiDubhFZLyJrRGR8QPhgEVlmxz0ldaxez+Zs4K8zrFW2qjprZ5DAb19CEznCZtMaAJezfkRYpV9RlFioruX/qDGmvzFmAPARcD+AiPQGLgH6ABOAZ0TEN6/xs8C1QHf7N6Gadagzgh5T278D4L7SK4GaWZoxFs+/Gv6KosRCtcTfGHMoYDeFMv06F5hmjCkyxmwC1gNDRaQN0MQYs8BYvZyvAudVpw7Voapun7KXFAOLnmeDtw3bTDpATOP6FUVR6otqf+QlIg8Dk4CDgG/S+nbANwHJcu2wEns7NDxS3tdivSWQkZFBTk5OTHUsKCggJycnaMqFE+79uEouk5ycHI6WWsd3lR2Qt4b9XW7gqbYp5OTkcLjEBKWtLK9ANm4sBmDb1q1R5+Fjf6G3ysf42kPRtghF26OMht4WlYq/iMwCWoeJutcY874x5l7gXhG5G5gM/IHwrmhTQXhYjDFTgakAWVlZJjs7u7LqhiUnJ4fs7GwOHCmGzz4HoMhTtTyys7M5XFQKsz6ju2wHIGv8pdDmRADyC0tg9kx/2rDM+Dhs/AqzHtatoX2HDrBxQ8V5hLDrUCHkzK7SMb72ULQtQtH2KKOht0Wl4m+MGRtlXm8AH2OJfy7QPiAuE9hhh2eGCa8TDhdXUfFD8Hl9ejm2WBvNy1becjkq96CdO6Aty3IPVqsOkVDfv6IoVaFabh8R6W6MWWfvngOstrc/AN4QkSeAtlgduwuNMR4RyReRYcC3WO6if1SnDlXBG7pUV5Qku62+agfwC+dMbnS+D11PDVqpKwrt5++XDIyp/IpQzVcUJRaq6/OfIiInAF5gC3A9gDFmhYhMB1YCpcCNxhif2X0D8DKQDHxq/45pPr99NADOVf/lT+6XrcCznwpKE43lHwm3PUw0pg/FVP0VRYmBaom/MebCCuIeBh4OE74YiH0inGoQyxz7iS4Hmc2s9Xcd6yyf/sMll3FvWvugdNUZ7DNpeCd2HSri+lO68o8v1lfpWJ3SWVGUWIirL3xj8fr4felF+Tg2zuETz1D+7TkrTLrYRTjJ7eS+s3qTkhj7s1gfAYqiVIU4E/+qq7//q96t3yBH8njXM6qGa1U9tKNXUZRYiCvxj2mZRN/G/s0ALPN2iZS0XlDtVxQlFuJM/Kuu/v7hoQe2gDORPURezrE+0QneFEWpCnG1jGOMIz0tDmyFtPaYw7X7vPxw8kiapbijTq+iryhKLMSV+Fd1Fs8g9m+BtI6wvebqE45+mVV7s1DpVxQlFuLK7eP1Vp4mLKVFsHd90Be9xwpq+CuKEgvxJf6xLpe4aR4UF0D302u2QoqiKPVEXIl/zKyfBa4k6Dy6vmtSDv3IS1GUWIgr8Y/N8jeW+HccAe7kGq9TtVHtVxQlBuJM/Kt+TB/ZYvn7e5X/qvdYQp8BiqJUhbgS/1jG+Q9w2HPtdIt2Zuu6RTt8FUWJhbgS/1gs/+6SCwmp0LR95YnrAdV+RVFiIa7EPxbLv53kQVqHY97EPsarpyjKMUZciX8sln9r2QdN2tR8ZWoI/cJXUZRYiK8vfKto+TvxkCl5kBrdTJ6PXtSf5ARnLFWLGZV+RVFiIa7Ev6qW/8mOFTSTAmvJxij4WVbd9wuo4a8oSizElfhHb/kb/uB6lTayz9rtOKLW6lRT6MdeiqJUhfgS/yjT9ZNN/NL1GQBedyMcjdNrr1LVREVfUZRYiLMO3+jkv5uUTd1Z0OvSY9q3cgxXTVGUY5gaEX8R+Y2IGBFpGRB2t4isF5E1IjI+IHywiCyz456SOhyuEq3Pv4UcAuAjzzD2j36wXPzYXsfgm4A+BBRFqQLVdvuISHvgdGBrQFhv4BKgD9AWmCUiPYwxHuBZ4FrgG+ATYALwaXXrEQ3R+vxbyiGKjIvJJTcxT4Kfj5unnFkbVVMURalTasLy/xvwO4Jd6ucC04wxRcaYTcB6YKiItAGaGGMWGEuJXwXOq4E6REW0/b3psp+9NAFE3SqKojRIqiX+InIOsN0YszQkqh2wLWA/1w5rZ2+HhtcJ0fj8M9jHBc75LPV2rYMaKYqi1A+Vun1EZBbQOkzUvcA9wLhwh4UJMxWERyr7WiwXERkZGeTk5FRW3bAUFBSQk5PDj7tLK037eeLvAJjpyQJg4bffsCH52O0XL/ZYzWe83qjbx9ceirZFKNoeZTT0tqhU/I0xYaezFJF+QGdgqd1nmwl8JyJDsSz6wC+eMoEddnhmmPBIZU8FpgJkZWWZ7OzsyqoblpycHLKzsyle8RN8tyRSabRmH03kCAAzvEMAGD58OG3TjsF5/G2KS73w+af0bpdGdnZ03yP42kPRtghF26OMht4WMXf4GmOWAf5hLyKyGcgyxuSJyAfAGyLyBFaHb3dgoTHGIyL5IjIM+BaYBPyjOidQFSoa7XOB40ueSHgOgJuLJ3OUJODYH0qZ4HIw7dph9GydWt9VURTlOKJWPvIyxqwQkenASqAUuNEe6QNwA/AykIw1yqdORvrY9YoYN8SxBoBS42C+t68//Hj4iGpYlxb1XQVFUY4zakz8jTGdQvYfBh4Ok24x0Dc0vC6oqLs3Q/ZTZFyMKvo7+2jiDz/WLX9FUZRYOHZ7MmuBikb79HRs5RPvSeymWVC4ar+iKA2ROBP/8OFNKKCt7GONt/ysnDpfvqIoDZG4Ev9IPv8TxPr0YLXpUC5OtV9RlIZInIl/2FAedr8AwHrTtlysar+iKA2RuJrSOZzPf27CbXR07AZgj0krF69uH0VRGiJxb/n7hB+giIRy8Sr9iqI0ROJK/KOdzz8QNfwVRWmIxJXbJ1T7XVhz/RQaNy97xoc54vj4yEtRFKWqxJXlb0I+85p2aWcA/lh6BVNKLwt7jMRVCymKEi/ElbSFjvNPKtwDwC7TLExqC7X7FUVpiMSZ+Aerf+JRq7N3d4j4j+zmX41SR/soitIgiTPxD953F+YBsMc0DQp/7ZqT/Nsq/YqiNETiSvxDe3xdJfkAHKJRxEPU8FcUpSESV+Ifavk7S/Lx4KAwzPh+HzraR1GUhkiciX+w+juLCzgqjajIuaOWv6IoDZG4Ev/Qcf7OkgKOOFIqPEbFX1GUhkhciX85y7/kkG35R0bdPoqiNETiSvwDtd9NKY13f0eeM6PCY9TyVxSlIRJX4l8a0OPbUX7CVbiPb5JHVXiMar+iKA2RuBL/olKPf7uT7AJgpyszKI0jRO31Iy9FURoiDV78dx8q5MoZh/ly3R6KSr1Yy7gbBjrWYcRZTvw7tQzuAA59GCiKojQEqjWrp4j8EfgVsMcOuscY84kddzdwNeABbjbGfGaHDwZeBpKBT4BbTKT1FWuA77cdAOCVr7fQoXkj5ifewhGTyEFSOJI+kMOOFKAIgH/9YjAD26eFnmNtVU1RFKXeqIkpnf9mjHksMEBEegOXAH2AtsAsEelhjPEAzwLXAt9gif8E4NMaqEdYHLZ4G2NYmnuATMkDgU3eDEoa94SjZWnH92ldW9VQFEU5pqgtt8+5wDRjTJExZhOwHhgqIm2AJsaYBba1/ypwXi3VAShz22zYU8CSLfv94S3kEJ7klhHW9VUURWnY1ITlP1lEJgGLgTuMMfuBdliWvY9cO6zE3g4ND4uIXIv1lkBGRgY5OTlVrtzyPdaCLXsPHQkKbyJH+X5fIQcOHPCHhcs/ljKPdQoKChrkecWCtkUw2h5lNPS2qFT8RWQWEM4fci+WC+dPWL2ofwIeB64i/AhJU0F4WIwxU4GpAFlZWSY7O7uy6pZjz1+u4kpnCp+nnE/BgcNBca27DyBtbRrs3wdAUP4zPi4f1kDIyclpkOcVC9oWwWh7lNHQ26JS8TfGjI0mIxH5N/CRvZsLtA+IzgR22OGZYcJrjX5HF9LY0ZoZ3vNIoTAozpPcMsJRiqIoDZtq+fxtH76P84Hl9vYHwCUikiginYHuwEJjzE4gX0SGiTWMZhLwfnXqUBklOHFTSqnXS2pg7y7gTW5Rm0UriqIcs1TX5/+IiAzAct1sBq4DMMasEJHpwEqgFLjRHukDcANlQz0/pRZH+gCU4CKBUvIKiukhwX5/b3Jz4HD4AxVFURow1RJ/Y8wvKoh7GHg4TPhioG91yq0KJbhwYz13GtuW/5SSS+jp2ErfJu0xrK6rqiiKohwzNPgvfEuME7dYI36a2Jb/t95e3FoyGRzuCrqbFUVRGi4NX/xx4cIS/1Qs8fct26gf7yqKEq/Ehfgn+Nw+Yrl9CkwyoDN2KooSvzR48ffioLdjCyfJKrqKNar0INbkbTpvj6Io8UpNfOF7TNNTtgLwVuKfANjuaEMhiYBa/oqixC8N3vL3hJziKnfZQCMRMNrjqyhKHNLgxT9RSoL2v04c6d8WhOYpCXVdJUVRlHqnwYt/gj3SZ5PXWqt3c2IPf5wIPHLhifVSL0VRlPqkwfv83bb431hyi/WRl6sZsM8f37SRu55qpiiKUn80ePFPwHL77DTN2U8TTg5Yl1EH+yiKEq80eLePscf0HCEJAGeQ+Kv6K4oSnzR4y///iu9nvHMhRVjuHUeA4Kv0K8cDJSUl5ObmUlhYWHniatK0aVNWrVpV6+UcDxxvbZGUlERmZiZud3Su7AYv/itMJ1aUdvLvO9Xtoxxn5ObmkpqaSqdOnWr9bTU/P5/U1NRaLeN44XhqC2MMe/fuJTc3l86dO0d1TIN3+4QSJP5q+yvHAYWFhbRo0ULdlEpERIQWLVpU6e0w/sRf1PJXjj9U+JXKqOo1En/i71Cfv6IoStyJv9fodA6KcjyRk5PDWWedVd/VaHDEtfh79EGgKFXGGIPX6621/D0eT+WJlGrT4Ef7hOIN0PtSj4q/cnzxwIcrWLnjUI3m2bttE/5wdp8K02zevJmJEycyZswYFixYwHnnncdHH31EUVER559/Pg888ACPPPIISUlJ3Hzzzdx2220sXbqUL774gtmzZ/PSSy/x2muvccMNN7Bo0SKOHj3KRRddxAMPPABAp06duOqqq5g5cyaTJ08mLS2NW2+9lZYtWzJo0CB/PebOncstt9wCWD7uefPmHTcjco414k78TYC1X+pV8VeUaFmzZg0vvfQS5513Hu+88w4LFy7EGMM555zDvHnzGD16NI8//jg333wzixcvpqioiJKSEubPn8+oUaMAePjhh2nevDkej4fTTjuNH3/8kf79+wPWOPX58+dTWFhI9+7d+eKLL+jWrRv/93//56/DY489xtNPP82IESMoKCggKSmpXtqiIRCH4l+23aZp5AvnhuyufLtxbx3USFGipzILvTbp2LEjw4YN4ze/+Q0zZ85k4MCBABQUFLBu3TomTZrEkiVLyM/PJzExkUGDBrF48WK+/PJLnnrqKQCmT5/O1KlTKS0tZefOnaxcudIv/j6RX716NZ07d6Z79+4A/PznP2fq1KkAjBgxgttvv53LL7+cCy64gMzMzLpuhgZDtcVfRG4CJgOlwMfGmN/Z4XcDVwMe4GZjzGd2+GDgZSAZ+AS4xZi6c777fP5TLuhHktsZMd2dE3rWVZUU5bggJcVaAc8Yw9133811111XLk2nTp146aWXOPnkk+nfvz9z5sxhw4YN9OrVi02bNvHYY4+xaNEimjVrxpVXXhk0Lt2XP0QetnjXXXdx5pln8sknnzBs2DBmzZpFz556r8ZCtTp8RWQMcC7Q3xjTB3jMDu8NXAL0ASYAz4iIT2mfBa4Futu/CdWpQ/R1tf763PwuZ9z1dStKjTB+/HhefPFFCgoKANi+fTu7d+8GYPTo0Tz22GOMHj2aUaNG8dxzzzFgwABEhEOHDpGSkkLTpk3ZtWsXn376adj8e/bsyaZNm9iwYQMAb775pj9uw4YN9OvXjzvvvJOsrCxWr15dy2fbcKmuAt4ATDHGFAEYY3bb4ecC04wxRcaYTcB6YKiItAGaGGMW2Nb+q8B51axDhfhE3/dxl+8lw+3UUf6KEgvjxo3jsssuY/jw4fTr14+LLrqI/Px8AEaNGsXOnTsZPnw4GRkZJCUl+f39J554IgMHDqRPnz5cddVVjBgxImz+SUlJTJ06lTPPPJORI0fSsWNHf9yTTz5J3759OfHEE0lOTmbixIm1f8INFKmOx0VEfgDex7LeC4HfGGMWicg/gW+MMa/Z6V4APgU2Yz0sxtrho4A7jTFhB/GKyLVYbwlkZGQMnjZtWpXr+MsZhzGA2wElXujdwsHKvV5+fWIiQ9tYXq8rZxwG4OUJKRXk1HAoKCigcePG9V2NY4LjoS2aNm1Kt27d6qQsj8eD0xnZHRpPHI9tsX79eg4ePBgUNmbMmCXGmKzQtJX6/EVkFtA6TNS99vHNgGHAEGC6iHQh/MezpoLwsBhjpgJTAbKyskx2dnZl1S3HqZsXMXv1btwuJyXFHpo2bQZ799K/Xx+y+7axEs34GIBY8j8eycnJiZtzrYzjoS1WrVpVZ8MZj6fJzGqb47EtkpKS/B3xlVGp+Pus9HCIyA3Af20XzkIR8QItgVygfUDSTGCHHZ4ZJrzWePryQXzw+Vz+9K21qIvHHt7pcqjPX1GU+KW6Cvg/4FQAEekBJAB5wAfAJSKSKCKdsTp2FxpjdgL5IjJMrO78SVhuo1ojye0kvZHD/85R7LG+THSqz19RlDimuuL/ItBFRJYD04ArjMUKYDqwEpgB3GiM8X2zfQPwPFYn8AasvoBa576zepPgdJDosk7ZrZa/oihxTLXG+RtjioGfR4h7GHg4TPhioG91yo2Fi7PaW79/LQDApZa/oihxTNyZvz6fvw71VBQlnok78S/1+fzV7aMoShwTdwpY6h/to5a/ohwPHE/z+e/atYtbbrmF/v37M2jQIK655hq2bdsWlOaqq64iPT2dvn2Dvd/79u3j9NNPp3v37px++uns37/fH/eXv/yFbt26ccIJJ/DZZ5/VSF3jbmI33zTO6vNXjks+vQt+WlazebbuBxOnRJXUGIMxBkctvjkfjx9XgTX1xEUXXcTdd9/No48+SkJCArNnz+b888/nrbfeomvXrgBceeWVTJ48mUmTJgUdP2XKFE477TTuuusupkyZwpQpU/jrX//KypUrmTZtGitWrGDHjh2MHTuWtWvXVruN4s7yL7EXodBx/ooSHZs3b6ZXr178+te/ZtCgQWzbto1HH32UIUOG0L9/f/7whz8A8Mgjj/hn77zttts49dRTAZg9ezY//7k1LuSGG24gKyuLPn36+I8Da0K4Bx98kJEjR/L2228zY8YMevbsyciRI/nvf//rTzd37lwGDBjAgAEDGDhwoH9aiUBee+01hg4dyoABA7juuuvweDxMnz6d22+/HYC///3vdOnSBbAEe+TIkf463HPPPQwfPpysrCx++OEHxo8fT9euXXnuuecA64vw0047jUGDBtGvXz/ef79spPoNN9zAK6+8wsUXX0xCQgIAp512Gq+99hp33HGHP93o0aNp3rx5uXq///77XHHFFQBcccUV/O9///OHX3LJJSQmJtK5c2e6devGwoULo/vnVUDcWf7a4asc10Rpodc0vrn8n3nmGWbOnMm6deuOyfn8V61axVtvvcVXX32F2+3m17/+Na+//jrjxo3j0UcfBeDLL7+kRYsWbN++PahuAO3bt2fBggXcdttt3HDDDSxYsIDCwkL69OnD9ddfT1JSEu+99x5NmjQhLy+PYcOGcc4557Bu3TpatWpF//79+eijj7j//vvp0qULxhjeffddHA4HeXl5tGzZMmIb79q1izZtrFkH2rRp458sb/v27QwbNsyfLjMzk+3bt1fn3wnEoeV/86nWHOEZTXQRCEWJFt9c/gAzZ870z+c/aNAgVq9ezbp16xg8eHDQfP7Dhw/3z+fvE9jp06czaNAgBg4cyIoVK1i5cqW/jHDz+YuI/60Byubzf+qppzhw4AAuV7D9Onv2bJYsWcKQIUMYMGAAs2fPZuPGjbRu3ZqCggLy8/PZtm0bl112GfPmzQuqG8A555wDQL9+/cjKyiI1NZVWrVqRlJTEgQMHMMZwzz330L9/f8aOHcv27dvZtWsXS5cuZdiwYXg8Hh544AG++OILHn/8cWbOnAlA9+7d2bRpU0xtH27+tUhTXleFuLP8LxycyYWDdQEIRakKgXPtH8vz+RtjuOKKK/jLX/5S7tjhw4fz0ksvccIJJzBq1ChefPFFFixYwOOPP+5Pk5iYCIDD4fC7bnz7paWlvP766+zZs4clS5bgdrvp1KkThYWFGGNwOp3k5eXRtWtX0tLSSEtLo3fv3gDs3r2b9PT0Cts4IyODnTt30qZNG3bu3OlPn5mZGdRpnJubS9u2bSvMKxrizvJXFKV6HMvz+Z922mm88847/vrs27ePLVu2lKvbwIEDmTNnDomJiTRt2jTqcz948CDp6em43W7mzJnjz7tfv34sWLCAli1bsmHDBg4ePMjWrVtZtWoVy5YtY/fu3UFTU4fjnHPO4ZVXXgHglVde4dxzz/WHT5s2jaKiIjZt2sS6desYOnRo1HWORNxZ/uF45aqhFBSW1nc1FOW4YNy4caxatYrhw4cD0LhxY1577TXS09MZNWoUDz/8MMOHDyclJSXifP5dunSJaj7/li1bMnLkSJYvXw5Y8/nPmTMHp9NJ7969y83n37t3bx566CHGjRuH1+vF7Xbz9NNP07FjR0aNGsW2bdsYPXo0TqeT9u3bV3kVsMsvv5yzzz6brKwsBgwY4D++V69ebN68maVLl/L73/+eMWPG0KVLF8455xwee+wxXnzxRX8el156KTk5OeTl5ZGZmckDDzzA1VdfzV133cXFF1/MCy+8QIcOHXj77bcB6NOnDxdffDG9e/fG5XLx9NNP18xoKN/QrWP9N3jwYBMrc+bMifnYhoi2RxnHQ1usXLmyzso6dOhQnZV1rFPVtli5cqUZOHCgmTlzpvF6vcbr9ZrFixebDz/8sJZqGL4OoQCLTRhNVbePoihKDdCrVy8++OAD3n33XQYNGsSwYcN48cUXGTJkSH1XLSzq9lGU4wBjTI2M8FBql8zMTP83AXWNqeKqjGr5K8oxTlJSEnv37q3yza3ED8YY9u7dW+67h4pQy19RjnEyMzPJzc1lz549tV5WYWFhlQSkIXO8tUVSUhKZmdEPY1fxV5RjHLfbTefOneukrJycnKjXgG3oNPS2ULePoihKHKLiryiKEoeo+CuKosQhcryMIBCRPcCWGA9vCeTVYHWOd7Q9ytC2CEbbo4yG0hYdjTGtQgOPG/GvDiKy2BiTVd/1OFbQ9ihD2yIYbY8yGnpbqNtHURQlDlHxVxRFiUPiRfyn1ncFjjG0PcrQtghG26OMBt0WceHzVxRFUYKJF8tfURRFCUDFX1EUJQ5p0OIvIhNEZI2IrBeRu+q7PnWBiLQXkTkiskpEVojILXZ4cxH5XETW2X+bBRxzt91Ga0RkfP3VvnYQEaeIfC8iH9n78dwWaSLyjoistq+R4XHeHrfZ98lyEXlTRJLipj3CrfDSEH6AE9gAdAESgKVA7/quVx2cdxtgkL2dCqwFegOPAHfZ4XcBf7W3e9ttkwh0ttvMWd/nUcNtcjvwBvCRvR/PbfEKcI29nQCkxWt7AO2ATUCyvT8duDJe2qMhW/5DgfXGmI3GmGJgGnBuPdep1jHG7DTGfGdv5wOrsC7yc7FufOy/59nb5wLTjDFFxphNwHqstmsQiEgmcCbwfEBwvLZFE2A08AKAMabYGHOAOG0PGxeQLCIuoBGwgzhpj4Ys/u2AbQH7uXZY3CAinYCBwLdAhjFmJ1gPCCDdTtbQ2+lJ4HeANyAsXtuiC7AHeMl2gz0vIinEaXsYY7YDjwFbgZ3AQWPMTOKkPRqy+Idb8y5uxrWKSGPgXeBWY8yhipKGCWsQ7SQiZwG7jTFLoj0kTFiDaAsbFzAIeNYYMxA4jOXWiESDbg/bl38ulgunLZAiIj+v6JAwYcdtezRk8c8F2gfsZ2K90jV4RMSNJfyvG2P+awfvEpE2dnwbYLcd3pDbaQRwjohsxnL7nSoirxGfbQHW+eUaY76199/BehjEa3uMBTYZY/YYY0qA/wInEyft0ZDFfxHQXUQ6i0gCcAnwQT3XqdYRa5XvF4BVxpgnAqI+AK6wt68A3g8Iv0REEkWkM9AdWFhX9a1NjDF3G2MyjTGdsP7/Xxhjfk4ctgWAMeYnYJuInGAHnQasJE7bA8vdM0xEGtn3zWlYfWRx0R4NdhlHY0ypiEwGPsMa+fOiMWZFPVerLhgB/AJYJiI/2GH3AFOA6SJyNdZF/zMAY8wKEZmOJQKlwI3GGE+d17puiee2uAl43TaINgK/xDIC4649jDHfisg7wHdY5/c91pQOjYmD9tDpHRRFUeKQhuz2URRFUSKg4q8oihKHqPgriqLEISr+iqIocYiKv6IoShyi4q8oihKHqPgriqLEIf8PgNiRiJLfoiQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import clear_output\n",
    "\n",
    "\n",
    "rewards = []\n",
    "for i in range(1000):\n",
    "    rewards.append(play_and_train(env, agent))\n",
    "    agent.epsilon *= 0.99\n",
    "\n",
    "    if i % 100 == 0:\n",
    "        clear_output(True)\n",
    "        plot_rewards(rewards, agent.epsilon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sj0kO9NyyXZd"
   },
   "source": [
    "## Binarized state spaces"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MZUgRkNegoc5"
   },
   "source": [
    "Now that we know how to use our agent in case of discrete observation space, let's try to use agent to train efficiently on `CartPole-v0`. This environment has a continuous set of possible states, so you will have to group them into bins somehow.\n",
    "\n",
    "The simplest way is to use `round(x, ndigits)` to round real number to a given amount of digits.\n",
    "\n",
    "The tricky part is to get the `ndigits` right for each state to train effectively.\n",
    "\n",
    "Note that you don't need to convert state to integers, but to __tuples__ of any kind of values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "id": "eBp_wHDXyXZd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first state:[-0.00619862  0.02346971 -0.01883222  0.04197386]\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"
    }
   ],
   "source": [
    "def make_env():\n",
    "    return gym.make(\"CartPole-v0\").env  # .env unwraps the TimeLimit wrapper\n",
    "\n",
    "\n",
    "env = make_env()\n",
    "n_actions = env.action_space.n\n",
    "\n",
    "print(f\"first state:{env.reset()}\")\n",
    "plt.imshow(env.render(\"rgb_array\"));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "env.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JU1sIGMSyXZd"
   },
   "source": [
    "### Play a few games"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XG-wxq7QhEfS"
   },
   "source": [
    "We need to estimate observation distributions. To do so, we'll play a few games and record all states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "id": "-7tC9VbOEhmI"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "\n",
    "def visualize_cartpole_observation_distribution(states):\n",
    "    states = np.array(states)\n",
    "    fig, axes = plt.subplots(2, 2, figsize=(16, 9), sharey=True)\n",
    "    axes = axes.flatten()\n",
    "    for i, title in enumerate(\n",
    "        ['Cart Position', 'Cart Velocity', 'Pole Angle', 'Pole Velocity At Tip']\n",
    "    ):\n",
    "        ax = axes[i]\n",
    "        ax.hist(states[:, i], bins=20)\n",
    "        ax.set_title(title)\n",
    "        xmin, xmax = ax.get_xlim()\n",
    "        ax.set_xlim(min(xmin, -xmax), max(-xmin, xmax))\n",
    "        \n",
    "        ax.grid()\n",
    "\n",
    "    fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "id": "kiTRSS6byXZe"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "states = []\n",
    "for _ in range(1000):\n",
    "    states.append(env.reset())\n",
    "    done = False\n",
    "    while not done:\n",
    "        state, _, done, _ = env.step(env.action_space.sample())\n",
    "        states.append(state)\n",
    "\n",
    "visualize_cartpole_observation_distribution(states)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "F5yL-LJHyXZe"
   },
   "source": [
    "### Binarize environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "id": "nFHn7eOoyXZe"
   },
   "outputs": [],
   "source": [
    "from gym.core import ObservationWrapper\n",
    "\n",
    "\n",
    "class Binarizer(ObservationWrapper):\n",
    "    def observation(self, state):\n",
    "        # YOUR CODE HERE\n",
    "        # Binarize state, e.g. round it to some amount digits (hint: you can do that with round(x, ndigits))\n",
    "        # You might need to pick a different n_digits for each dimension based on histograms.\n",
    "        features_ndigits = [1, 1, 2, 1]\n",
    "        for feature_index in range(len(state)):\n",
    "            state[feature_index] = round(state[feature_index], features_ndigits[feature_index])\n",
    "\n",
    "        return tuple(state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "id": "l26s0px8yXZe"
   },
   "outputs": [],
   "source": [
    "env = Binarizer(make_env())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "id": "vb9JspcfyXZf"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "states = []\n",
    "for _ in range(1000):\n",
    "    states.append(env.reset())\n",
    "    done = False\n",
    "    while not done:\n",
    "        state, _, done, _ = env.step(env.action_space.sample())\n",
    "        states.append(state)\n",
    "\n",
    "visualize_cartpole_observation_distribution(states)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CnGfei25yXZf"
   },
   "source": [
    "### Learn binarized policy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hQGhbh2hkjUn"
   },
   "source": [
    "Now let's train a policy that uses binarized state space.\n",
    "\n",
    "__Tips:__ \n",
    "* Note that increasing the number of digits for one dimension of the observations increases your state space by a factor of $10$.\n",
    "* If your binarization is too fine-grained, your agent will take much longer than 10000 steps to converge. You can either increase the number of iterations and reduce epsilon decay or change binarization. In practice we found that this kind of mistake is rather frequent.\n",
    "* If your binarization is too coarse, your agent may fail to find the optimal policy. In practice we found that on this particular environment this kind of mistake is rare.\n",
    "* **Start with a coarse binarization** and make it more fine-grained if that seems necessary.\n",
    "* Having $10^3$–$10^4$ distinct states is recommended (len(agent._qvalues)), but not required.\n",
    "* If things don't work without annealing $\\varepsilon$, consider adding that, but make sure that it doesn't go to zero too quickly.\n",
    "\n",
    "A reasonable agent should attain an average reward of at least 50."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "id": "0KWSvLWayXZf"
   },
   "outputs": [],
   "source": [
    "agent = QLearningAgent(alpha=0.5, epsilon=0.1, gamma=0.99, n_actions=n_actions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000.0"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "play_and_train(env, agent, render=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "agent.epsilon = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "rewards = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "id": "DrUyIy5dyXZf"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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m8eLF/Otf/+K9995r7qzEVKy/r7Kysiq/neZQVFQUF/mIteOhXFPmh+7sX1i0i7OSDkac5vfo21/z2qaKmOTlmn9+xf+MTo7JuoLF+qRypPp4dY+X89cAok0LTTRmBjADYPTo0Sb8qsH09PRanXxsqpOv/odOOByN07vX6/XidFYeJTgcDlwuV6s7sRzr7ys5OZmRI0fGbH311VqufA13XJRr/mdVpkebBnBC34GwaWtM8lLuaENq6g9jsq5g9d1T5YhIbwD7PddOzyLo2bBUPqM4yx4OTw9ZRkRcQCesJ1+1SBkZGQwZMoQ77riDUaNG8eijj3LWWWcxfPhw/va3vwHw9NNPM336dADuueceLrjgAgAWLFjAz39uPa/n9ttvZ/To0QwbNiywHFi37HjkkUc477zzeO+995g/fz6DBw/mvPPOY+7cuYH5Fi9ezIgRIxgxYgQjR45slTUipY5XjkY6F1bfGsJcrEf+PWm/fxyU/raIPIv1aL1BwEpjjFdECkVkDPAdcDPwfNi6lgPXAgtjcf7g4U82s+VAQcRp4UfWtTX0xI787UfDapxv27ZtvPbaa1x99dXMmTOHlStXYozhyiuvZMmSJUyYMIFnnnmGu+66i9WrV1NeXo7b7WbZsmWMHz8egKlTp9K1a1e8Xi8TJ05kw4YNDB8+HLCOcJctW0ZZWRmDBg1i4cKFnHzyyVxzzTWBPEybNo0XXniBcePGUVRURHJy7KuXSqnm0Vh9I2rT7fQdrJ31qSKSJSK3YgWCi0RkB3CRPY4xZjPWA8a3APOBO40xXntVtwP/BnZiPed2np3+H6CbfQL6XuweSy1Zv379GDNmDF9++SVffvklI0eOZNSoUWzdupUdO3Zw5plnsmbNGgoLC0lKSmLs2LGsXr2apUuXBgLC7NmzGTVqFCNHjmTz5s1s2bIlsP6f/exnAGzdupUBAwYwaNAgRCSQDjBu3Djuvfdepk+fTl5eHi5Xq7rkRCnVCGrTy+iGaiZNrGb+qcDUCOmrsR5IHp5eBlxXUz7qKtqRfGOfQ/DfItcYwwMPPMBvfvObKvP079+f1157jXPPPZfhw4ezaNEidu3axZAhQ9izZw/Tpk1j1apVdOnShSlTpoT0nQ++BW913Sjvv/9+Lr/8cj7//HPGjBnD119/zeDBg2NcUqVUc2is7tN6L6NGdMkll/Dqq69SVFQEwP79+8nNtU63TJgwgWnTpjFhwgTGjx/Pyy+/zIgRIxARCgoKaNeuHZ06dSInJ4d58+ZFXP/gwYPZs2cPu3btAgjpXbRr1y5OP/10/vSnPzF69Gi2bo3NySylVOul7QiN6OKLLyY9PZ2xY63nvLdv356ZM2fSs2dPxo8fz9SpUxk7dizt2rUjOTk50Fx0xhlnMHLkSIYNG8bAgQMZN25cxPUnJyczY8YMLr/8crp3787ZZ5/N9u3bAfjnP//JokWLcDqdDB06lEsvvbRpCq2UarE0IMRY//792bQpcJcP7r77bu6+++4q802cOBG32x0Y9+/I/V5//fWI68/IyAgZnzRpUuDoP7gp7Pnnnw9fVCnVSjTWdbvaZKSUUgrQgKCUUsqmAUEppVoY7WWklFKqUWlAUEopBWhAUEopZdOAoJRSTaAlPOBFA0IrsnTpUq644ormzkat5OTkcPfddzN8+HBGjRrFr371KzIzM0PmueWWW+jZsyfnnHNOSPrRo0e56KKLGDRoEBdddBHHjh0LTHviiSc4+eSTOfXUU/niiy+apCxKtRYaEBqJMQafz9eo2/B6vTXPFId27drFpEmTGDduHKtXr2bt2rXccMMN/PjHPw7chgNgypQpzJ8/v8ryTz75JBMnTmTHjh1MnDiRJ598EoAtW7Ywa9YsNm/ezPz587njjjta7GekVDSNdWFa671Sed79cHBjxEltvB5w1qPoJ5wOlz5Z7eSMjAwuvfRSzj//fJYvX85HH33E7NmzmT17NuXl5fz4xz/m4Ycf5umnnyY5OZm77rqLe+65h/Xr17Nw4UIWLFjAa6+9xsyZM7n99ttZtWoVpaWlXHvttTz88MOAdSX0Lbfcwpdffsnvfvc7OnfuzO9//3u6d+/OaadV3jtw8eLFgSukRYQlS5ZUuaHfzJkzmT59OhUVFZxzzjm8+OKLvP/++6xYsYJnn32W5557jueee47du3eza9cuJk+ezLJly+jfvz833ngjixYtwu12M2PGDB544AF27tzJH/7wB377299SVFTEVVddxbFjx3C73Tz22GNcddVVgPWshzfeeCNwO2+wrtyeOXMm9913Hx999BFg3e8p/MpsgI8//jjw5KrJkyeTmprKU089xccff8z1119PUlISAwYM4OSTT2blypWBW4copaLTGkKMbdu2jZtvvpnvv/+ebdu2sWPHDlauXMm6detYs2ZN4HkIS5cuBWD16tUUFRVFfB7C6tWr2bBhA4sXL2bDhg2Bbfifh3D11Vfz61//mk8++YSlS5cGbpwHlc9DWLduHUuXLqVNmzYh+UxPT+fdd9/lm2++Yd26dTidTt56662QvC1dupRu3bqxf//+kLwB9O3bl+XLlzN+/HimTJnCnDlzWLFiBX/9618Defzwww9Zu3YtixYt4r777sMYw/bt2+nRowfDhw/n008/ZdSoUVx77bVcc801DB48GIfDweHDVZ6eGiInJ4fevXsD0Lt370C59+/fT9++lc9nSklJYf/+/XX7ApU6jrXeGkKUI/nSRrz9tf9ZCEDI8xDAeibrjh07uPnmm0OehzBq1KjA8xD8T1KbPXs2M2bMwOPxkJ2dzZYtWwJH1JGeh+BPf/PNN4HK5yHcdNNN/OQnPyElJSUknwsWLGDNmjWcddZZ1mdSWkrPnj054YQTKCoqorCwkMzMTG688UaWLFnC0qVL+clPfhJY/sorrwTg9NNPp6ioiA4dOtChQweSk5PJy8ujXbt2PPjggyxZsgSHw8H+/fvJyclh/fr1jBkzBq/Xy8MPP8zChQvJz88P1G4GDRrEnj176N69e50/+0jV6Ma6gEep5tRYv+vWGxCaSfCzCuL5eQjGGCZPnswTTzxRZdmxY8fy2muvceqppzJ+/HheffVVli9fzjPPPBOYJykpCbCe4+wf9o97PB7eeustDh06xJo1a0hISKB///6UlZVhjMHpdHL48GF+8IMf0LlzZzp37szQoUMByM3NpWfPnlE/4169epGdnU3v3r3Jzs4OzJ+SkhJyYjorK4sTTzwx6rqUUpW0yagRxfPzECZOnMicOXMC+Tl69Ch79+6tkreRI0eyaNEikpKS6NSpU63Lnp+fT8+ePUlISGDRokWBdZ9++uksX76c7t27s2vXLvLz89m3bx/p6els3LiR3Nxc+vXrF3XdV155JW+88QYAb7zxRuDcxJVXXsmsWbMoLy9nz5497Nixg7PPPrvWeVbqeKc1hEYUz89DGDp0KI899hgXX3wxPp+PhIQEXnjhBfr168f48ePJzMxkwoQJOJ1O+vbtW+enrd1000386Ec/YvTo0YwYMSKw/JAhQ8jIyGD9+vX8+c9/5vzzz2fgwIFceeWVTJs2jVdffTWwjhtuuIG0tDQOHz5MSkoKDz/8MLfeeiv3338/P/3pT/nPf/7DSSedFAiEw4YN46c//SlDhw7F5XLxwgsv1OvZ2Uodr6Sxui81ttGjR5vVq1eHpKWnpzNkyJAal23sR2g2l5ZSrvT0dG666SaeeuopLrzwQgDWrl1LdnZ2xOsoYl2u2v5OGltaWhqpqanNnY2YOx7K1f/+z6pMz3jy8mqnAdx/6WCenBebJxcO6d2ReXePr3nGCERkjTFmdKRp2mSkmtyQIUOYO3cu77//PqNGjWLMmDG8+uqrgRPcSrVGO3KKYrYuvQ6hlowx2rOkBUhJSeHll19u8u221BqxavneX5vV3FmoUauqISQnJ3PkyBH906uIjDEcOXKE5OTk5s6KUnGpVdUQUlJSyMrK4tChQ1HnKysra5U7BS1XzZKTk6tck6GUsrSqgJCQkMCAAQNqnC8tLS1wsVhrouVS6vigT0xTSinVqDQgKKVUHbTmc5QaEJRSqg5eWbK7ubPQaDQgKKVUHby3OrPmmRpZY9VSNCAopZQCNCAopZSyaUBQSikFNDAgiMg9IrJZRDaJyDsikiwiXUXkKxHZYb93CZr/ARHZKSLbROSSoPQzRWSjPW266L0nlFKqydU7IIhIH+AuYLQx5jTACVwP3A8sMMYMAhbY44jIUHv6MGAS8KKI+O9N/BJwGzDIfk2qb76UUkrVT0ObjFxAGxFxAW2BA8BVwBv29DeAq+3hq4BZxphyY8weYCdwtoj0BjoaY5Yb69T5f4OWUUop1UTqfesKY8x+EZkG7ANKgS+NMV+KSC9jTLY9T7aI+J+H2AdYEbSKLDvNbQ+Hp1chIrdh1STo1asXaWlp9cp7UVFRvZeNZ1qulkXL1bL4y1VSUhJxelOWubi4uFG2V++AYJ8buAoYAOQB74nIz6MtEiHNREmvmmjMDGAGWA/Iqe9DOI6HB3i0JlqulqW1l6vtmjQoLq4yPVDm+ZEfkBNL7du3JzW1fg/IiaYhTUYXAnuMMYeMMW7gA+BcIMduBsJ+z7XnzwL6Bi2fgtXElGUPh6crpZSKIB4vTNsHjBGRtnavoIlAOjAXmGzPMxn42B6eC1wvIkkiMgDr5PFKu3mpUETG2Ou5OWgZpZRSTaQh5xC+E5E5wFrAA3yP1ZzTHpgtIrdiBY3r7Pk3i8hsYIs9/53GGK+9utuB14E2wDz7pZRSLcrsOLitRUM06HkIxpi/AX8LSy7Hqi1Emn8qMDVC+mrgtIbkRSmlmtsf52xo7iw0iF6prJRSCtCAoJRSyqYBQSmlFKABQSml6qT1Pi9NA4JSSimbBgSllKqD1nwrZg0ISimlAA0ISimlbBoQlFKqhWmsZ4hpQFBKqTrQXkZKKaVaPQ0ISilVB9rLSCmlVKunAUEppVqYeHxAjlJKqVZEA4JSStWB9jJSSinV6mlAUEopBWhAUEqpOtFup0oppVo9DQhKKaUADQhKKVUn2stIKaVUq6cBQSmlFKABQSml6kR7GSmllGr1NCAopZQCNCAopVSdaC8jpZRSrZ4GBKWUUkADA4KIdBaROSKyVUTSRWSsiHQVka9EZIf93iVo/gdEZKeIbBORS4LSzxSRjfa06SLSmk/kK6VasNa8c2poDeE5YL4xZjBwBpAO3A8sMMYMAhbY44jIUOB6YBgwCXhRRJz2el4CbgMG2a9JDcyXUkqpOqp3QBCRjsAE4D8AxpgKY0wecBXwhj3bG8DV9vBVwCxjTLkxZg+wEzhbRHoDHY0xy431XLj/Bi2jlFJxpTWfVHY1YNmBwCHgNRE5A1gD3A30MsZkAxhjskWkpz1/H2BF0PJZdprbHg5Pr0JEbsOqSdCrVy/S0tLqlfGioqJ6LxvPtFwti5arZfGXq6SkJOL0pixzcXFxo2yvIQHBBYwC/p8x5jsReQ67eagakZreTJT0qonGzABmAIwePdqkpqbWKcN+aWlp1HfZeKblalm0XC2Lv1xt16RBcXGV6ampqTD/s0bZtgsPf3W9yYueKzlIN9q3b09q6viYb6ch5xCygCxjzHf2+BysAJFjNwNhv+cGzd83aPkU4ICdnhIhXSmlFDDOsZmbXV/xeMJ/GnU79Q4IxpiDQKaInGonTQS2AHOByXbaZOBje3gucL2IJInIAKyTxyvt5qVCERlj9y66OWgZpZSKK83Ry0jwAeBo5DMYDWkyAvh/wFsikgjsBn6JFWRmi8itwD7gOgBjzGYRmY0VNDzAncYYr72e24HXgTbAPPullFIK8IchieeAYIxZB4yOMGliNfNPBaZGSF8NnNaQvCilVFNojl5GXrsxx2HXFKwOmbGnVyorpVSc82BdsuWyA0Jj0YCglFJxzmesXbVTvNzjmkMX37FG2U5DzyEopZRqZCJWE9HZjm2c7djGuJIMrGt9Y0trCEopVQfN0cvoz66ZIeMDvBmNsh0NCEopFedOc2SEjHcy+Y2yHQ0ISilVB/FwL6PNrqGNsl4NCEopFcdS5FCVtDeTb2yUbWlAUEqpOHadc3GVtHKSGmVbGhCUUiqO9ZeDVdLcktAo29KAoJRSddDUvYyucn5bJc3TSFcMaEBQSqkWxo3WEJRSqtk1ZS+jCY71EdO1yUgppY4z/018KmK6t5F23RoQlFKqBfjAe15gOJGKRtmGBgSllGoBFnhHBYaPSLdG2YYGBKWUqoOm6mWUFFYLyKddYNgnzkbZpgYEpZSqg6Y6qZzqWBcy7jaNf3NqDQhKKRWH2lMWMt4UgUgDglJKxaEyEkPGm6KpSgOCUkrFodtdcwPD/+u+pUm2qQFBKaXiUKFpGxiuwMVhOjb6NjUgKKVUHTRVL6NZ3tTA8Ife89hl+jT6NjUgKKVUHTRVLyMnvsCw/2Z2m339KDeNc9sKoJFumaeUUseZnblFMV3fWY5tVdIur3gcgMEx3VIlrSEopVQMfLxuf4OWT8DDJY5VgfEbXIsAKDBtguYSGrPRSgOCUkrFgf9xvcsrif/gXMemkPSrKh5rsjxoQFBKqTjQRw4D0IXQpqfg3kaNTQOCUkrVQXUNNqaBZ5uHyD4AXkicTjtKA+lN0d3UTwOCUkrVQWP1MvqBIzsw/GjCa0FTmu6hnRoQlFIqzox3bGiW7WpAUEqpONOU5w2CNTggiIhTRL4XkU/t8a4i8pWI7LDfuwTN+4CI7BSRbSJySVD6mSKy0Z42XUSaro6klFIxYGLYmDTQcTBm66qLWNQQ7gbSg8bvBxYYYwYBC+xxRGQocD0wDJgEvCgSeMrDS8BtwCD7NSkG+VJKKVUHDQoIIpICXA78Oyj5KuANe/gN4Oqg9FnGmHJjzB5gJ3C2iPQGOhpjlhtjDPDfoGWUUiqutObmi4beuuKfwB+BDkFpvYwx2QDGmGwR6Wmn9wFWBM2XZae57eHw9CpE5DasmgS9evUiLS2tXpkuKiqq97LxTMvVsmi5WhZ/uYpLSiJO37t3Xz3XbPhhNSeRP/WeEzUvsVbvgCAiVwC5xpg1IpJam0UipJko6VUTjZkBzAAYPXq0SU2tzWarSktLo77LxjMtV8ui5WpZ/OVquyYNiourTD/ppJNg9646r3esYwtvJD4VcdoK39CI6e3btyc1dUKdt1WThjQZjQOuFJEMYBZwgYjMBHLsZiDs91x7/iygb9DyKcABOz0lQrpSSrV6PcivdtoU5xdNmJMGBARjzAPGmBRjTH+sk8ULjTE/B+YCk+3ZJgMf28NzgetFJElEBmCdPF5pNy8VisgYu3fRzUHLKKVUi1DfvpGeoN3w596zQ6Ytr6aG0Fga4zqEJ4GLRGQHcJE9jjFmMzAb2ALMB+40xnjtZW7HOjG9E9gFzGuEfCmlVKOp760rvEG7YR8O0n2VDSmLfWc0NFt1EpPnIRhj0oA0e/gIMLGa+aYCUyOkrwZOi0VelFKqJfHiDAwLPjxB49mma5PmRa9UVkqpZhRcQzhNMtjqOykwvtkMaNK8aEBQSqk62H2oag+jhnAEPSqznyOXpzw31LhMQ++sWn1elFJKNVh999GXOVeGjJeQVOMyjXVzH32mslJKNaOrHctCxktIJt3Xl3W+k5s8LxoQlFKqGT3luZ4HE94B4Am31Vx0aUXkC9UamwYEpZRqRJc7VpCImw994yNOv865BIAzy17iCJ2aMmtVaEBQSqkYeO2bPRHTX0icDsCHZZEDwiDHfgDccbA71pPKSikVA2VuX80zRVGhAUEppY4X0fshaQ1BKaVasS4UBIZ/5Fgedd7gK5abiwYEpZRqJIMdmYHhPnI44jyZvh6UmYSmylJUzV9HUUqpVsprKo+5HdU0GR2iE3t8JzRVlqLSGoJSSjWS4BvVufBGnMcZdkO75qQBQSmlGokE1QoSxR1xngS8cXH+ADQgKKVUo/mJs/K2FElEDghOvLg1ICilVOu2xjcoMJxrOkecx4U35BbYzSk+cqGUUq1QNt0Cw9VdZ+DCGxfXIIAGBKWUajTOoGcdVNdk1M+RS2eKmipLUWlAUEqpRuLCExhOjBAQxA4YFzjXNVWWotKAoJRStbRwa06d5p+R8GxgOFE8VaYH1yDigQYEpZSqpez8sjrNnyiV1x5EqiGc7dja4DzFkgYEpZRqAolUrSH0l7rVOBqbBgSllKqljMPF9V42iYoqadt9fQDY6utb7/XGkgYEpZSqhWNlPv5vaeSH4NTGja5FVdLKSATgGc919V5vLGlAUEqpWiisiP48g/rwn1TWexkppdRxJMPXq0qaPyD44mRXHB+XxymlVCu21ncyEiHdf/O7ut66YuvBwhjkqioNCEopVQsikXbp0W3x9WO/6Y4P4aQIPYoqawh1X3djiI96ilJKtUIOfHhwUEISbexeRt3JZ0bCM3SgBKfEV5NRfORCKaVaIf+dTEtNIm2lHIA7XR9xsXMN1zkX47BrCMFPVmtO9c6FiPQVkUUiki4im0Xkbju9q4h8JSI77PcuQcs8ICI7RWSbiFwSlH6miGy0p02X+tTNlFIqzjjw4cVJGUkkYwUEf48iF55Ak1FruP21B7jPGDMEGAPcKSJDgfuBBcaYQcACexx72vXAMGAS8KKI+PtavQTcBgyyX5MakC+llIoLgRoCiYEmI39AaEMFP3WmAa2gycgYk22MWWsPFwLpQB/gKuANe7Y3gKvt4auAWcaYcmPMHmAncLaI9AY6GmOWG2MM8N+gZZRSqsVyiMFrHJSYZBLESwKeQEC4w/UxVzi/A1pHDSFARPoDI4HvgF7GmGywggbQ056tD5AZtFiWndbHHg5PV0qpFs1fQ/BfkdyGcjzGCghJQXc/jZcaQoO7nYpIe+B94PfGmIIozf+RJpgo6ZG2dRtW0xK9evUiLS2tzvkFKCoqqvey8UzL1bJouVqWkpISIu+uque0zyGUkgRAMhURn59cn26njfEZNyggiEgCVjB4yxjzgZ2cIyK9jTHZdnNQrp2eBQTfwSkFOGCnp0RIr8IYMwOYATB69GiTmppar3ynpaVR32XjmZarZdFytSyZnywESkPSbnHO468Jb3Jq2euU27WAYD0kHwOUGCsgtJUyvBECQn2ajBrjM25ILyMB/gOkG2OeDZo0F5hsD08GPg5Kv15EkkRkANbJ45V2s1KhiIyx13lz0DJKKRW3bnN9CkAXql45/DOndTO7n7sWUGLXEDpSwgMJ71SZN17OITSkhjAO+AWwUUTW2WkPAk8Cs0XkVmAfcB2AMWaziMwGtmD1ULrTGON/esTtwOtAG2Ce/VJKqbhWbJJBsK4xCGvofirh/yrnIxmAK5wrIq6nxZ9DMMYso/oGtYnVLDMVmBohfTVwWn3zopRSzcF/bqB9WFNSuBJjBYQJjg0Rp3elgD30jm3m6iE+wpJSSrVA/iP/DlISdb4i2gAw2JEZcXoe7WObsXrSgKCUUvVUairPDVTnD+7bAieVc03niPPsMvHR014DglJK1VOx3WR0n+u9KtP8j8d8z5saqEmUmqo9keKJBgSllKqnUntHf7LjAE68IdNOcewPDBfbTUb9HLnEMw0ISilVC5F60JSbhMBw8InlLhSEzOeO0n8np5pmpOagAUEpperJf/tqgI5SHBj+Pvm3UZd73H0DAMPLZjCufHrjZK4eNCAopVQ9uYKaiX7v+iDKnKFe9V5K/7K3KaA9njh6cKUGBKWUqieXVAYEf20huNbwsueKwPBC74jAcLxcmRwuPnOllFItwI+d3wSGd9i9ikbIzkDaOMemwPAa3ymBYROnu974zJVSSjWRXYeK6H//ZyzaVrceQME1AYBecgywbmjnd7ojIzCcT7v6Z7KJaEBQSh3X1uy1duSfbcgOSfd4fUz65xIWbs2JuNzVjmWB4W2+FHpJHlD9xWf5Jv4DQvyczVAqjvl8hk82HOCK4SfidOgjv5vL7NWZjB/Und6d2sR83Sbs5nRHiyvYerCQP72/EYdspC3ukOmnBR3955gugRpCcM1hnveswHC83J4iGq0hKFULs1Zlcvesdcxcsbe5s3LcKihz88c5G7jp3981+bZzCsrZU1C5o+8rOdzimg9Auq8vuXShlxwFwBUUEDJNz8BwntGAoFSrcLioHIBDheXNnJPjl9drHcIfLa5oku1FfGyjrWPQRWj/476dg6YLPcnDgY+2UgbAx95zme75cWC+vBieQ3j/9rExW1cwDQhK1YK/kchE3U2oWDqQF3pLaZ/dphPrBrv6fLfBj8EsIhkfgkt8DJBsHnC9DcA3vmEU0TYwXyzPIYzs2yVm6wqmAUGpWqj+UeHKb0NWHj/8+yJKPQ0Pmh+v28+5Ty5k+a4jgTT/Wh31/DJKK7x4vD6MMbyUtosjRfWv7SUEXZDmMU5yjbWDHiG7+Np3JgCLgq47ACi0g8Ma36B6b7exaUBQqhbE3gmFn3hUlZ75cjt7j5Sw41jlzjLjcDFeX90/tLV2z5+tByvvCRSoIdQQD4wxbD6QXyV9yF/nc+fba1m7L4+n5m/lD3MiP6wmXKTNBd+mogIXC7yjAEgUN3e45gJwhE6h+cLB5eVT+WXFH2q13eagAUGpOoineFDh8fHc1zsoc3trnrkJhH82uw8VkTotjecW7Khx2fwSN7mFZbXcgFDm9vLkvK2UVHiqzDbggc+5fPoy7pu9ngc+2Bgy7YvNOSzdcQiAwjKr15DUo8bx94RXAsMVJJBDFyqMk75yKJAe6bGYm80ACuK4t5EGBKVaqLe+28s/vt7OK4t312v5i/+xmNGPfRXjXFkKy9ys3ZcHwMo9R6LPDIye+hVnT10QdZ7KJiOYuWIvLy/exUtpu6qd//21Wbyzch9gXXzm98+vqwlQdYj2KXIYgExfD/Jphw8H+013BkkWAGVBd0FtSTQgKFUL/oPIpmwySs8uwETZYJnb6t5YWk0NYfbqTJ75cltIWk5BGVnHrKd7bc8p4nBRw3rs3DBjBfM3ZVdJv/qFb/if99bXej1ub2g5Ix21f28HGJHK+Su8virzhXto7mYmPrO4Snr4R+sOa9qK9l2/6bkQgB9VPIa/USnT9OQi51oAksVd3aJxTQOCUrUg9p++qXoZfbUlh0ufW8qH3++vdp6aWjr+OGcDzy+07qtz0bOL+ffS3Zzz+ALOe2pRyHxfbD5YrzwaY1i++wi/nbm2yrRdh4ojLBFq5oq9THh6Ucg5hr1HQpcL3in/duYaIOykci2+jte/zYiY7l/UH7g+WX+g5pUBHSnmF66vAcijQyA9+JqDlkoDgmq13F4fx2LdZ72Jagi77SaOrQcLY7K+HblFPPZZesRpv3lzTZW0t7/bx74j0R8cv3x3ZVNQ5tES3J7IR+sSdlr2hUU7WbP3GH//Yhv7jpaEnAf44d/TKPd4q92JA2Tnl8Wk15cxBl89Tnh/mvhgxPRjQecGflVxX73z1Zw0IKhW60/vb2Dko1/V608fLtBk1OA11W17sch7Xbm9Ph78cCPXvPxt1Pme/XJ7YPi3M9cEAkT4vnpdZl7I+N+/2MY1L31LfqnVrBJewpz8yu6gj3y6hf73f1an/NfW2n15fJ95LCQt82gJs1dn8tinWwJpuWEXI37hO4tItvj6BYYPm04R54l3ei8j1Wp9sNZqbimu8NAhufqTfBUeHwlOCbRbj3r0K84/tSfP/PSMwDxNfRnC459vBWoXgOrTjBV+xXVeSQWd24Y+AL6mK4I9QcFq84GCauer7hyHnwmrWEQ6+q+ppvftzsO4fYYJg7pHnS/cNS8tDxkf/3Rlc9p/vtkTcZl9dtPQbRX3hKQv8I0KDO80J9YpH3XVWNfFaA1BtXr+k6/hNmTl0f/+zzjlz/N4Juho92hxBe+vzYq4TLSTvA21aFtu4KjZr9zj5c8fbQxcROXzmardM+uRpX8tDO1pM+KRr1i0LZeMw5Vt+L4IZc04XExphbWDDz/y99t+rPoTvUXlVbuJhge04J2y39GS0IAwd11oe/+N//6Oya+uJJYVquq+6h72XU2X+4aFpJdTGVCDr1BuSTQgKAC8PsMb32ZQ7mncPu0ffb+fg/k19DevhdzCsmpvSxwufMd2ML+MMY8v4JUlld01Z63KjLqOHblWm75/VYcKywO3TQYriHxknwBelXE05CrY0gpvjUe4a/Ye45evreLOt0JP0H6yPpuZK/bxxLyt+HyGFxbt5OypCwI9hQDeW5PFK4ur734ZSaR93S9fW0XqtLRAGcN3iBmHi0mdlsb1/7ci6rUPn+yu2sPm+QU7OFxUzoNh1wUAtdqJh/cS2pJt1UjW7gtt8tm4v+oFabHmv0q5kKp3XL2v4rc877m60fPQWLTJSAHw4ff7+dvczRwuKue+i0+t8/Ifr9vPhEE96NIusdp5Sio8/P7ddQzs0Y6F96XWaf1en6Go3EOnNlbTzzUvfUvm0VJ2Tr0UlzP6cY0nbI/zyfoDHCwoC7v/ffS90pw1Vo3hw+/307ltAtPsGkXGk5cDVhv6yj1HOWtAV657eTlOh/DxneM4kFfKnW+vxe017Hr8smpvnX3NS1Z7/facQn7939WBdH+NYc6aLJZsP0TfrtaRZ3BQPVpcwRPztvKr8QPZerCAH/RoT3JC5b12vt15uMr2Fm8/VCWt8pMwIfP169qW/t3bkTotDYD1mXl17n77zFfbeear7RGnRaqJ1NaqjGOszjgaGL/6hW+izB0bt7s+sYeqfpfv+yZAzT1h45bWEBRA4Gg7ryT06G7XoaJAM8KBvNKQJgW/rGMl3D1rHXe+XbX7YTD//353LbokAszfdJDcAmvH94MHP+eMh78M9EjJPGrd+OxN+3bUmUdLuH7GcjZFOEKs8PhC8r0pwm0Nou2TtgS1jx8prggEg2DZ+VZ+xj25ELAC2BXPL+O2N9cE+sz7LwI7VlxB//s/Y8r8Yg7klXL6Q18E1pNbWM5XWyLXfHLDaiXhu6PnF+7g8unLGPyX+fz4xcod440Rbhe9t4YeRH6TX11J6rS0wPfgN+Sv82u1fG3c/37VWkNdXPvy8ppnihFpyXv7WtAaggLg841WX/Q9YTt8f1X9/dvPDRzFZjx5OXklFazYfZTUU3sE+rV/u+sId769lhduHEUk/maXSArK3Dz08Wb+9qNhdGqbQIXHF+h3/rNTK2sdJRVe2iZW/mw/35jNB2v3B5oKrnh+Ga9OGc0Fg3sF5nn883S+2pLDg5cN5liJm4/XVe1vHu0YNdpJUf/JWH+AiuZYibtKj5lz7QBSV3/5eDM/Hhl64jL4Clz/RVz1ESk4nv149KuIG+Lr9No1/TWUAx9tKat3+34ibrYnTwag1FRfE27JNCA0oTK3l3KPL9DsEWx7TiEX/2MJs24bw5iB3Rq0HbfXR0GpG6dDeOLzrWTllTCybxfuvegUHA7BGFPt/VuWBTUvBFfF/cEArCtoL31uKQCXDKvc8YL1GEKHfM8n6w/w5q1nM35QDwA27c9nQYQ//q5DRXRvn8Tr32Twwff76dOlDfddfCo5QUek726rbH+ft+kgVw6v3BGuyghtQwa45fXVIeP+I25/z51IKjw+iss9tEuq/Es8/nk6C9Jzol5k9c7KTJ6aX/16G0t6dgHp2dX37GmIwX+p+9F/EhWkOtbzl4Q3ubPiLtabkwEYInvJMj0Cd/qsq/aUcLXzG+Z4J1BGEs8kvMgq32BmeS+ocbki2uDCS1cKmZrwKhc5K6+3mFLxR9J8Z+CvZ32e+ABDHVZtc2zZ82QT+h88R9J5N+nRwPid7rvqVZ54J43Za6IxjR492qxevbrmGSNIS0sjNTU1thmK4t1V+8gvdfP2d/vIOFISaHcGq2fJL19bFRi/eWw/HrnqNIrKPfz5w418tO4AX94zgVN6daCgzM0F0xZzuKicPU9cFrJT93h9fPBFGj+97AKueH4pm/ZX3VlcPeJErh7ZhylB2wMYO7BbyEVGe564jIIyD2c8/GWNZXM5pEobfbC/XDGUR4P6dPs9+ZPTyTxWwguLrJOhg0/owNaDhZzSqz2DT+jI3FpeNRprItU3HznwRbxhWawkUUEFLoy9jVGyna3mJEpIrtN6ulLAUToQ3qh0l/MD7k2YA8Dl5VNx4+Im59fkmC686b24ljttQzcKKCeBYpL5iWMZzyS+XGWudF9fhjisE/U+I2wzKXzoPY+NZiADJZu+coh9pidtKWOhbySlJonZiY/Q12Gd23jGfS332XmNZLXvFHb6TsSNiwOmO5/5zqEbBWwx/fi96/2gdv7oPMaBSyI3A73jOZ/Rju0McoReLf4X9xRmei8MfE/NIfz/XxcissYYMzritHgJCCIyCXgOcAL/NsY8GW3+eAgIG7LyuPnVlcz57VhO7tkhZFpphReD4UBeGRc+G9pD4sHLBrNxfwFFZW4WbQs9uXdCx2T+OOlU7p1d831g7rrgZKbbtybwe+UXZ0a88rQ2GrrDc+DDiQ93lIqnEy9JuGu1k+tEET+QA7hxkWO6kCKHyKcdB0w3kqngJ86l7DAplJgkPLhIwk1fRy5Q+YzbEbKTvaYXDgxbzUl4cCDA2Y502lHOJl9/2ksp+aYdO0wK20xfenOEsxzb2Gd6kmFOwIFhims+v3N9zCHTkcOmEwJkmBP42jeKFb4huI2L8xybOM2xh1+6vmCl71QS8FJOApm+Hgx0ZHOqZPKtbxgpchg3TgTDdtOXfb6enObYw8XONRwynThm2nOyHMAh1n+zyCSTgAc3LtpLGcu8w9hjelNAWyY6vqezFOHFwT5fL8Y6K4NvgWmDEx9FtAk8AD6aMpPAFtOPbb6+nO3YyiLfCDpRzBmOXSTgYYdJ4ULH2kC+IvnaO5Lxjo0kSWX30hzTuVbbj8ZnJOp2a2OZdxhPem6gixTxZmLV3ctU941Mdn0ZuHFduPe95/GQe0q9azux1KoDgog4ge3ARUAWsAq4wRhT9dDSFuuA4PMZcgrL6N4+iVK3l/wSN93aJ5KeXcDKPcd4av5WvrpnAqsyjnFi52QyDhfz0CebScCLCw9OfFxxei++3LgfJ15c+HCKFyc+EvDQlnK8OGlHacgP2xihrZTRQ/JIxEM5CZSbRBLFTSIenHhx2C3cVhtoOe2kjGQqyDPt7Sc1eTFGcOPChReXeGhPGR2lBMHQjjLaUUouXcg2XakwCTjER4VJwIUXH8IARzbXOJeRazqT7juJChIooA2dKGaoYy9OfBw1HSgnASc+knDThgqKScZjl6uH5NNeyigw1h/mkOnEQdMVLw5ceOkoJfxADpCIm63mJAppSxvKcdqBxBH07sJLihxu8E6grqIdMQJ4jbDRDKSXHKO3HK0y3W2cJIh1zmG37wROkGN47J1/Bykly3QP2eEcMp3oIZUnudf4BjFcdlNCEoJhk28A2XTlHMdWepAXsqP1KzWJtJEKKowTB4YMcwJOvAxwWE1l23196C8H8eDih+XPkiQebnHO4xbXfD7wnsdc77n8PeEVdpvenCS5IeUqMG3ZZlJoSzmnSBYJ4uVD7zgOmq6MdWyhlxzj6vJHyKFrSJ6GyR7aUs4m059SknDh5SrHt1zuXEGW6cEecwKTnKv42juK9lLKWMcWPveew2feMRyhIz8Qq4a4w6QErdXgr/WcJDkMkww2+AZyg2shZzm2cZZs423vBXSRQv7puTZo2crlwrWljG6ST6YJbfoUfJzAMdpLKXvMCRgEb9BT0ppbaw8IY4GHjDGX2OMPABhjnqhumfoGhBWzn6b/5pcCfQUEEAwODILPfjcI1g7YP71ynspXpD9nU6gwTspJpINEPpHpM0I5CeTRHi8OvMbBMTrQU47Rk7yIO7xSk4gDH2m+EfSWIyRgBRUvDrabFPJNO3pKHj7EDlFCRymhwLRD8FFOAvmmHYfoTE/y6CAlJOGhsxTiwODFQYVxscf0poQkTpUsOkgJ+aYdXhx2GJDAsBcHuaYza32DcGDoKXnkm3Y48NFHDtNBSukjh3jNM4lkcZNMBR0p5jCdOGI60o4yOksRK3xD6C4FdKAEJz5OkKO0kzI2+gay1/SktxylrxyizCRyumM33aSA7uSz3DeUUpLoJzm4cbHeN5A15pSQZgLBxyjZwWBHJh0p4RjtmeOdgKeOp+Y6UkwBbant9dD+32kniikmOXBBlNMO7pV5NIEl6sKFhxQ5xCHTmVKSArXGJCowCBW0zFs7x7Mvfj+Bxdtzq5zn+vPlQ3jss/SQZt1HrxrGL8b2r/e2WkJAuBaYZIz5lT3+C+AcY8zvwua7DbgNoFevXmfOmjWrztsq2LOKxMylFFRg7/ax/0Rih4TQd2u6I2ge7NAA5STgNq7AcbwXhz0cNG6sY94SknDgo5jkQNgR+w9bapI4TEfKTQJJ4gm0JVeYBNy48CE4MPgQSkgO/CET8GAAr90M4m9WiN7s48+9Nb8H66gyWjNPPOucJOSVV/8bPusEJ6sOVvYScjmgU6JwpCx0mYGdHOzO95HggEgXNic7ocxezSldHNVejTupfwK5JT76d3JwtMyQlukJLN82QThqb3dQZwc9kryc2zeZNzZXcKjUSm+fAEV2z9+JJ7n4LtvDoC5OzjrBxYntBIfAX78t48xeTtbkeOmWLFw2MIET2jr4++oyuiYLd5yRxNEyw4vry/lBJwe78n0M6epgaDcn7RKEfYU+DpX42HzEx6T+Ltw+yC0xdGsjZBX6OFjso8gNvdoKp3Z10rONsDjLQ9dkYUAnBy6H0ClReGtrBef3dXH5wARe+N66EO+Mnk52Ha1gaI8k2ifA0G5ODhT5SHQKaZluhnZzUuyG3fleBnRy8u0BD307OPj2gCfw2V/Q18Wy/R4qfJDa18W5J7p4eX05R8sMJ3d2cHJnJ4UVhr4dHBRUGNw+w1d7qx6cTUhxkdrXxZFSw4ZDXvp1dLA4y0OPNkKvdg4qvIYF+zy4BH43MolTuzr5PtfL2hwPu/Otg8FLByQgAoUVhnHdK9hRkowAI3o6OVxq5aHcY9hX6KNdglDmNRRVGNq4hKnflXFeH6ssU89rw9FSH19kePj50ESyi310ShR6tHWQ5IREZ2XQ3pnnxSWQV24Y0bPyf5ld5MNjoG+Hhp27OP/886sNCBhjmv0FXId13sA//gvg+WjLnHnmmaa+Fi1aVO9l45mWq2XRcrUsraVcwGpTzX41Xi5MywL6Bo2nAM3TzUQppY5T8RIQVgGDRGSAiCQC1wNzmzlPSil1XImLhmNjjEdEfgd8gdXt9FVjzOZmzpZSSh1X4iIgABhjPgc+b+58KKXU8SpemoyUUko1Mw0ISimlAA0ISimlbBoQlFJKAXFypXJ9iMghYG89F+8ORL6DVcum5WpZtFwtS2spVz9jTI9IE1psQGgIEVltqrt0uwXTcrUsWq6WpbWWK5g2GSmllAI0ICillLIdrwFhRnNnoJFouVoWLVfL0lrLFXBcnkNQSilV1fFaQ1BKKRVGA4JSSingOAwIIjJJRLaJyE4Rub+58xONiPQVkUUiki4im0Xkbju9q4h8JSI77PcuQcs8YJdtm4hcEpR+pohstKdNl/o+kDWGRMQpIt+LyKf2eIsvl4h0FpE5IrLV/t7GtpJy3WP/BjeJyDsiktwSyyUir4pIrohsCkqLWTlEJElE3rXTvxOR/k1Zvgar7sk5rfGFdWvtXcBAIBFYDwxt7nxFyW9vYJQ93AHYDgwFngbut9PvB56yh4faZUoCBthlddrTVgJjsR6wOw+4NA7Kdy/wNvCpPd7iywW8AfzKHk4EOrf0cgF9gD1AG3t8NjClJZYLmACMAjYFpcWsHMAdwMv28PXAu835e6zz59PcGWjiH8NY4Iug8QeAB5o7X3XI/8fARcA2oLed1hvYFqk8WM+XGGvPszUo/QbglWYuSwqwALiAyoDQossFdLR3nBKW3tLL1QfIBLpi3TL/U+DillouoH9YQIhZOfzz2MMurCubpbHKEuvX8dZk5P9h+2XZaXHPrnqOBL4DehljsgHs9572bNWVr489HJ7enP4J/BEIflp9Sy/XQOAQ8JrdFPZvEWlHCy+XMWY/MA3YB2QD+caYL2nh5QoSy3IEljHGeIB8oFuj5TzGjreAEKm9Mu773YpIe+B94PfGmIJos0ZIM1HSm4WIXAHkGmPW1HaRCGlxVy6sI8JRwEvGmJFAMVYTRHVaRLnsNvWrsJpNTgTaicjPoy0SIS3uylUL9SlHSytjiOMtIGQBfYPGU4ADzZSXWhGRBKxg8JYx5gM7OUdEetvTewO5dnp15cuyh8PTm8s44EoRyQBmAReIyExafrmygCxjzHf2+BysANHSy3UhsMcYc8gY4wY+AM6l5ZfLL5blCCwjIi6gE3C00XIeY8dbQFgFDBKRASKSiHXSZ24z56lads+F/wDpxphngybNBSbbw5Oxzi3406+3ezoMAAYBK+1qcKGIjLHXeXPQMk3OGPOAMSbFGNMf6ztYaIz5OS2/XAeBTBE51U6aCGyhhZcLq6lojIi0tfMzEUin5ZfLL5blCF7XtVi/7RZTQ2j2kxhN/QIuw+qtswv43+bOTw15PQ+rurkBWGe/LsNqk1wA7LDfuwYt87922bYR1IMDGA1ssqf9izg50QWkUnlSucWXCxgBrLa/s4+ALq2kXA8DW+08vYnV86bFlQt4B+s8iBvraP7WWJYDSAbeA3Zi9UQa2JzfW11feusKpZRSwPHXZKSUUqoaGhCUUkoBGhCUUkrZNCAopZQCNCAopZSyaUBQSikFaEBQSill+//XAtXH2a6XlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Input \u001b[1;32mIn [114]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m10000\u001b[39m):\n\u001b[1;32m----> 2\u001b[0m     rewards\u001b[38;5;241m.\u001b[39mappend(\u001b[43mplay_and_train\u001b[49m\u001b[43m(\u001b[49m\u001b[43menv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43magent\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[0;32m      3\u001b[0m     \u001b[38;5;66;03m# YOUR CODE HERE (optional)\u001b[39;00m\n\u001b[0;32m      4\u001b[0m     \u001b[38;5;66;03m# Adjust epsilon.\u001b[39;00m\n\u001b[0;32m      6\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m np\u001b[38;5;241m.\u001b[39mmean(rewards[:\u001b[38;5;241m10\u001b[39m]) \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m150\u001b[39m:\n",
      "Input \u001b[1;32mIn [63]\u001b[0m, in \u001b[0;36mplay_and_train\u001b[1;34m(env, agent, time_limit, render)\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[38;5;66;03m# YOUR CODE HERE\u001b[39;00m\n\u001b[0;32m      8\u001b[0m \u001b[38;5;66;03m# Pick action given current state, take the selected action and update agent.\u001b[39;00m\n\u001b[0;32m      9\u001b[0m action \u001b[38;5;241m=\u001b[39m agent\u001b[38;5;241m.\u001b[39mget_action(state)\n\u001b[1;32m---> 10\u001b[0m next_state, reward, done, _ \u001b[38;5;241m=\u001b[39m env\u001b[38;5;241m.\u001b[39mstep(action)\n\u001b[0;32m     11\u001b[0m agent\u001b[38;5;241m.\u001b[39mupdate(state, action, reward, next_state)\n\u001b[0;32m     13\u001b[0m total_reward \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m reward\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "for i in range(10000):\n",
    "    rewards.append(play_and_train(env, agent))\n",
    "    # YOUR CODE HERE (optional)\n",
    "    # Adjust epsilon.\n",
    "    \n",
    "    if np.mean(rewards[:10]) > 150:\n",
    "        agent.epsilon *= 0.6\n",
    "    if np.mean(rewards[:10]) > 190:\n",
    "        agent.epsilon *= 0.2\n",
    "\n",
    "    if i % 100 == 0:\n",
    "        clear_output(True)\n",
    "        plot_rewards(rewards, agent.epsilon)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "id": "Y5KKOknoBn1E"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your agent has learned 12660 Q-values.\n"
     ]
    }
   ],
   "source": [
    "print('Your agent has learned {} Q-values.'.format(len(agent._qvalues)))"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "practice_qlearning.ipynb",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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