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   "source": [
    "# Peter and the Wolf: Reinforcement Learning Primer\n",
    "\n",
    "In this tutorial, we will learn how to apply Reinforcement learning to a problem of path finding. The setting is inspired by [Peter and the Wolf](https://en.wikipedia.org/wiki/Peter_and_the_Wolf) musical fairy tale by Russian composer [Sergei Prokofiev](https://en.wikipedia.org/wiki/Sergei_Prokofiev). It is a story about young pioneer Peter, who bravely goes out of his house to the forest clearing to chase the wolf. We will train machine learning algorithms that will help Peter to explore the surroinding area and build an optimal navigation map.\n",
    "\n",
    "First, let's import a bunch of userful libraries:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random\n",
    "import math"
   ]
  },
  {
   "source": [
    "## Overview of Reinforcement Learning\n",
    "\n",
    "**Reinforcement Learning** (RL) is a learning technique that allows us to learn an optimal behaviour of an **agent** in some **environment** by running many experiments. An agent in this environment should have some **goal**, defined by a **reward function**.\n",
    "\n",
    "## The Environment\n",
    "\n",
    "For simplicity, let's consider Peter's world to be a square board of size `width` x `height`. Each cell in this board can either be:\n",
    "* **ground**, on which Peter and other creatures can walk\n",
    "* **water**, on which you obviously cannot walk\n",
    "* **a tree** or **grass** - a place where you cat take some rest\n",
    "* **an apple**, which represents something Peter would be glad to find in order to feed himself\n",
    "* **a wolf**, which is dangerous and should be avoided\n",
    "\n",
    "To work with the environment, we will define a class called `Board`. In order not to clutter this notebook too much, we have moved all code to work with the board into separate `rlboard` module, which we will now import. You may look inside this module to get more details about the internals of the implementation."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from rlboard import *"
   ]
  },
  {
   "source": [
    "Let's now create a random board and see how it looks:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "width, height = 8,8\n",
    "m = Board(width,height)\n",
    "m.randomize(seed=13)\n",
    "m.plot()"
   ]
  },
  {
   "source": [
    "## Actions and Policy\n",
    "\n",
    "In our example, Peter's goal would be to find an apple, while avoiding the wolf and other obstacles. To do this, he can essentially walk around until he finds and apple. Therefore, at any position he can chose between one of the following actions: up, down, left and right. We will define those actions as a dictionary, and map them to pairs of corresponding coordinate changes. For example, moving right (`R`) would correspond to a pair `(1,0)`."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "actions = { \"U\" : (0,-1), \"D\" : (0,1), \"L\" : (-1,0), \"R\" : (1,0) }\n",
    "action_idx = { a : i for i,a in enumerate(actions.keys()) }"
   ]
  },
  {
   "source": [
    "The strategy of our agent (Peter) is defined by a so-called **policy**. Let's consider the simplest policy called **random walk**.\n",
    "\n",
    "## Random walk\n",
    "\n",
    "Let's first solve our problem by implementing a random walk strategy."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "18"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "def random_policy(m):\n",
    "    return random.choice(list(actions))\n",
    "\n",
    "def walk(m,policy,start_position=None):\n",
    "    n = 0 # number of steps\n",
    "    # set initial position\n",
    "    if start_position:\n",
    "        m.human = start_position \n",
    "    else:\n",
    "        m.random_start()\n",
    "    while True:\n",
    "        if m.at() == Board.Cell.apple:\n",
    "            return n # success!\n",
    "        if m.at() in [Board.Cell.wolf, Board.Cell.water]:\n",
    "            return -1 # eaten by wolf or drowned\n",
    "        while True:\n",
    "            a = actions[policy(m)]\n",
    "            new_pos = m.move_pos(m.human,a)\n",
    "            if m.is_valid(new_pos) and m.at(new_pos)!=Board.Cell.water:\n",
    "                m.move(a) # do the actual move\n",
    "                break\n",
    "        n+=1\n",
    "\n",
    "walk(m,random_policy)"
   ]
  },
  {
   "source": [
    "Let's run random walk experiment several times and see the average number of steps taken:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Average path length = 32.87096774193548, eaten by wolf: 7 times\n"
     ]
    }
   ],
   "source": [
    "def print_statistics(policy):\n",
    "    s,w,n = 0,0,0\n",
    "    for _ in range(100):\n",
    "        z = walk(m,policy)\n",
    "        if z<0:\n",
    "            w+=1\n",
    "        else:\n",
    "            s += z\n",
    "            n += 1\n",
    "    print(f\"Average path length = {s/n}, eaten by wolf: {w} times\")\n",
    "\n",
    "print_statistics(random_policy)"
   ]
  },
  {
   "source": [
    "## Reward Function\n",
    "\n",
    "To make our policy more intelligent, we need to understand which moves are \"better\" than others.\n",
    "\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "move_reward = -0.1\n",
    "goal_reward = 10\n",
    "end_reward = -10\n",
    "\n",
    "def reward(m,pos=None):\n",
    "    pos = pos or m.human\n",
    "    if not m.is_valid(pos):\n",
    "        return end_reward\n",
    "    x = m.at(pos)\n",
    "    if x==Board.Cell.water or x == Board.Cell.wolf:\n",
    "        return end_reward\n",
    "    if x==Board.Cell.apple:\n",
    "        return goal_reward\n",
    "    return move_reward"
   ]
  },
  {
   "source": [
    "## Q-Learning\n",
    "\n",
    "Build a Q-Table, or multi-dimensional array. Since our board has dimensions `width` x `height`, we can represent Q-Table by a numpy array with shape `width` x `height` x `len(actions)`:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = np.ones((width,height,len(actions)),dtype=np.float)*1.0/len(actions)"
   ]
  },
  {
   "source": [
    "Pass the Q-Table to the plot function in order to visualize the table on the board:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "m.plot(Q)"
   ]
  },
  {
   "source": [
    "## Essence of Q-Learning: Bellman Equation and  Learning Algorithm\n",
    "\n",
    "Write a pseudo-code for our leaning algorithm:\n",
    "\n",
    "* Initialize Q-Table Q with equal numbers for all states and actions\n",
    "* Set learning rate $\\alpha\\leftarrow 1$\n",
    "* Repeat simulation many times\n",
    "   1. Start at random position\n",
    "   1. Repeat\n",
    "        1. Select an action $a$ at state $s$\n",
    "        2. Exectute action by moving to a new state $s'$\n",
    "        3. If we encounter end-of-game condition, or total reward is too small - exit simulation  \n",
    "        4. Compute reward $r$ at the new state\n",
    "        5. Update Q-Function according to Bellman equation: $Q(s,a)\\leftarrow (1-\\alpha)Q(s,a)+\\alpha(r+\\gamma\\max_{a'}Q(s',a'))$\n",
    "        6. $s\\leftarrow s'$\n",
    "        7. Update total reward and decrease $\\alpha$.\n",
    "\n",
    "## Exploit vs. Explore\n",
    "\n",
    "The best approach is to balance between exploration and exploitation. As we learn more about our environment, we would be more likely to follow the optimal route, however, choosing the unexplored path once in a while.\n",
    "\n",
    "## Python Implementation\n",
    "\n",
    "Now we are ready to implement the learning algorithm. Before that, we also need some function that will convert arbitrary numbers in the Q-Table into a vector of probabilities for corresponding actions:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def probs(v,eps=1e-4):\n",
    "    v = v-v.min()+eps\n",
    "    v = v/v.sum()\n",
    "    return v"
   ]
  },
  {
   "source": [
    "We add a small amount of `eps` to the original vector in order to avoid division by 0 in the initial case, when all components of the vector are identical.\n",
    "\n",
    "The actual learning algorithm we will run for 5000 experiments, also called **epochs**: "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      ""
     ]
    }
   ],
   "source": [
    "\n",
    "from IPython.display import clear_output\n",
    "\n",
    "lpath = []\n",
    "\n",
    "for epoch in range(10000):\n",
    "    clear_output(wait=True)\n",
    "    print(f\"Epoch = {epoch}\",end='')\n",
    "\n",
    "    # Pick initial point\n",
    "    m.random_start()\n",
    "    \n",
    "    # Start travelling\n",
    "    n=0\n",
    "    cum_reward = 0\n",
    "    while True:\n",
    "        x,y = m.human\n",
    "        v = probs(Q[x,y])\n",
    "        a = random.choices(list(actions),weights=v)[0]\n",
    "        dpos = actions[a]\n",
    "        m.move(dpos,check_correctness=False) # we allow player to move outside the board, which terminates episode\n",
    "        r = reward(m)\n",
    "        cum_reward += r\n",
    "        if r==end_reward or cum_reward < -1000:\n",
    "            print(f\" {n} steps\",end='\\r')\n",
    "            lpath.append(n)\n",
    "            break\n",
    "        alpha = np.exp(-n / 3000)\n",
    "        gamma = 0.5\n",
    "        ai = action_idx[a]\n",
    "        Q[x,y,ai] = (1 - alpha) * Q[x,y,ai] + alpha * (r + gamma * Q[x+dpos[0], y+dpos[1]].max())\n",
    "        n+=1"
   ]
  },
  {
   "source": [
    "After executing this algorithm, the Q-Table should be updated with values that define the attractiveness of different actions at each step. Visualize the table here:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 792x432 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "m.plot(Q)"
   ]
  },
  {
   "source": [
    "## Checking the Policy\n",
    "\n",
    "Since Q-Table lists the \"attractiveness\" of each action at each state, it is quite easy to use it to define the efficient navigation in our world. In the simplest case, we can just select the action corresponding to the highest Q-Table value:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "def qpolicy_strict(m):\n",
    "        x,y = m.human\n",
    "        v = probs(Q[x,y])\n",
    "        a = list(actions)[np.argmax(v)]\n",
    "        return a\n",
    "\n",
    "walk(m,qpolicy_strict)"
   ]
  },
  {
   "source": [
    "If you try the code above several times, you may notice that sometimes it just \"hangs\", and you need to press the STOP button in the notebook to interrupt it. \n",
    "\n",
    "> **Task 1:** Modify the `walk` function to limit the maximum length of path by a certain number of steps (say, 100), and watch the code above return this value from time to time.\n",
    "\n",
    "> **Task 2:** Modify the `walk` function so that it does not go back to the places where is has already been previously. This will prevent `walk` from looping, however, the agent can still end up being \"trapped\" in a location from which it is unable to escape. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Average path length = 3.45, eaten by wolf: 0 times\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def qpolicy(m):\n",
    "        x,y = m.human\n",
    "        v = probs(Q[x,y])\n",
    "        a = random.choices(list(actions),weights=v)[0]\n",
    "        return a\n",
    "\n",
    "print_statistics(qpolicy)"
   ]
  },
  {
   "source": [
    "## Investigating the Learning Process"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbab852fd68>]"
      ]
     },
     "metadata": {},
     "execution_count": 15
    },
    {
     "output_type": "display_data",
     "data": {
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133.949763 214.756364 \nL 133.980202 214.756364 \nL 134.132399 206.226264 \nL 134.254157 214.756364 \nL 134.284596 214.685867 \nL 134.315036 198.00165 \nL 134.345475 214.756364 \nL 134.375914 199.106098 \nL 134.436793 214.756364 \nL 134.528111 214.497876 \nL 134.558551 214.309885 \nL 134.58899 214.756364 \nL 134.649869 214.685867 \nL 134.680308 213.252434 \nL 134.710748 214.756364 \nL 134.741187 214.756364 \nL 134.802066 212.946949 \nL 134.832506 214.756364 \nL 134.954263 193.184376 \nL 135.076021 214.756364 \nL 135.10646 212.594465 \nL 135.167339 214.756364 \nL 135.289097 214.756364 \nL 135.502172 214.756364 \nL 135.532612 206.766738 \nL 135.593491 214.756364 \nL 135.62393 214.662368 \nL 135.65437 214.756364 \nL 135.745688 195.722257 \nL 135.806567 214.756364 \nL 135.867445 203.923372 \nL 135.989203 214.756364 \nL 136.050082 213.111441 \nL 136.080521 214.756364 \nL 136.110961 214.756364 \nL 136.202279 206.837235 \nL 136.293597 214.756364 \nL 136.324036 213.510922 \nL 136.384915 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138.150401 209.375116 \nL 138.21128 214.756364 \nL 138.363477 206.672743 \nL 138.454795 214.756364 \nL 138.485234 205.967776 \nL 138.546113 210.338571 \nL 138.576553 214.732865 \nL 138.637431 211.41952 \nL 138.667871 207.659697 \nL 138.69831 213.604918 \nL 138.789629 213.299432 \nL 138.820068 214.756364 \nL 138.911386 201.737974 \nL 139.002704 214.756364 \nL 139.033144 213.322931 \nL 139.094023 214.756364 \nL 139.124462 210.033085 \nL 139.21578 210.503063 \nL 139.276659 209.7276 \nL 139.337538 214.756364 \nL 139.398417 212.92345 \nL 139.428856 214.756364 \nL 139.459295 214.756364 \nL 139.520174 204.863328 \nL 139.611493 211.114034 \nL 139.641932 211.255028 \nL 139.672371 210.738052 \nL 139.702811 214.756364 \nL 139.794129 213.957401 \nL 139.824568 214.756364 \nL 139.855008 213.581419 \nL 139.885447 207.119222 \nL 139.915887 214.756364 \nL 139.946326 214.004399 \nL 140.037644 211.325525 \nL 140.128962 214.756364 \nL 140.159402 207.260215 \nL 140.220281 214.380381 \nL 140.25072 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147.221344 214.591871 \nL 147.312663 210.57356 \nL 147.373541 211.231529 \nL 147.403981 214.756364 \nL 147.495299 214.19239 \nL 147.525738 214.732865 \nL 147.556178 208.317666 \nL 147.617057 214.262887 \nL 147.677936 213.816408 \nL 147.799693 214.756364 \nL 147.95189 201.502985 \nL 148.043208 214.756364 \nL 148.073648 211.513516 \nL 148.104087 210.78505 \nL 148.134527 197.79016 \nL 148.164966 214.756364 \nL 148.195405 214.568372 \nL 148.225845 214.756364 \nL 148.347602 211.8425 \nL 148.438921 214.756364 \nL 148.46936 209.093129 \nL 148.530239 212.617964 \nL 148.651997 214.756364 \nL 148.682436 201.549983 \nL 148.743315 214.756364 \nL 148.773754 213.698913 \nL 148.804194 214.756364 \nL 148.834633 202.724928 \nL 148.895512 212.335977 \nL 149.017269 214.756364 \nL 149.047709 214.662368 \nL 149.078148 213.698913 \nL 149.108588 207.213217 \nL 149.169466 214.027898 \nL 149.199906 211.137533 \nL 149.291224 208.787644 \nL 149.321664 214.756364 \nL 149.352103 214.756364 \nL 149.382542 188.484596 \nL 149.443421 206.860734 \nL 149.534739 214.756364 \nL 149.565179 207.401209 \nL 149.626058 214.756364 \nL 149.656497 212.547467 \nL 149.717376 214.756364 \nL 149.778255 214.756364 \nL 149.869573 212.312478 \nL 149.900012 214.262887 \nL 149.930452 207.518703 \nL 149.99133 214.685867 \nL 150.02177 208.740646 \nL 150.052209 206.226264 \nL 150.082649 209.7276 \nL 150.234846 214.756364 \nL 150.265285 201.573482 \nL 150.326164 213.9809 \nL 150.356603 213.792909 \nL 150.387043 214.756364 \nL 150.417482 209.539608 \nL 150.478361 213.651915 \nL 150.5088 213.487423 \nL 150.53924 214.756364 \nL 150.569679 208.811143 \nL 150.630558 214.051397 \nL 150.660997 214.756364 \nL 150.691437 207.659697 \nL 150.752316 214.756364 \nL 150.843634 212.852953 \nL 150.904513 213.628417 \nL 150.934952 214.756364 \nL 151.02627 208.388162 \nL 151.05671 209.116628 \nL 151.117589 214.756364 \nL 151.148028 213.463924 \nL 151.178467 204.275855 \nL 151.239346 214.732865 \nL 151.269786 208.01218 \nL 151.300225 211.889498 \nL 151.330664 190.435005 \nL 151.361104 214.756364 \nL 151.391543 211.748505 \nL 151.421983 212.429973 \nL 151.452422 204.322853 \nL 151.482861 214.756364 \nL 151.513301 207.80069 \nL 151.665498 214.756364 \nL 151.726377 208.975635 \nL 151.756816 210.15058 \nL 151.787256 214.756364 \nL 151.817695 211.748505 \nL 151.848134 206.155767 \nL 151.909013 214.521375 \nL 151.969892 214.756364 \nL 152.000331 214.145392 \nL 152.06121 214.756364 \nL 152.182968 197.625667 \nL 152.243847 214.756364 \nL 152.304725 213.181937 \nL 152.335165 212.71196 \nL 152.365604 214.756364 \nL 152.426483 205.897279 \nL 152.456923 214.756364 \nL 152.548241 208.458659 \nL 152.57868 213.111441 \nL 152.60912 214.756364 \nL 152.700438 214.19239 \nL 152.730877 214.215889 \nL 152.822195 214.756364 \nL 152.852635 208.364663 \nL 152.913514 214.121893 \nL 152.943953 184.654276 \nL 153.065711 214.756364 \nL 153.09615 210.926043 \nL 153.157029 214.756364 \nL 153.187468 214.756364 \nL 153.248347 206.320259 \nL 153.309226 207.706694 \nL 153.370105 214.756364 \nL 153.430984 213.158439 \nL 153.461423 213.816408 \nL 153.491862 207.518703 \nL 153.522302 214.756364 \nL 153.552741 212.617964 \nL 153.644059 214.756364 \nL 153.674499 214.356882 \nL 153.704938 214.756364 \nL 153.735378 213.839907 \nL 153.765817 207.542202 \nL 153.796256 214.756364 \nL 153.826696 214.239388 \nL 153.887575 214.756364 \nL 153.918014 204.839829 \nL 153.978893 213.792909 \nL 154.039772 214.756364 \nL 154.070211 213.322931 \nL 154.100651 188.790082 \nL 154.161529 214.215889 \nL 154.191969 214.756364 \nL 154.222408 200.11655 \nL 154.283287 202.630932 \nL 154.405045 214.756364 \nL 154.435484 214.756364 \nL 154.465923 214.591871 \nL 154.496363 208.975635 \nL 154.526802 214.756364 \nL 154.557242 214.756364 \nL 154.587681 214.756364 \nL 154.678999 213.698913 \nL 154.739878 214.756364 \nL 154.770317 214.145392 \nL 154.800757 213.13494 \nL 154.831196 214.756364 \nL 154.861636 214.756364 \nL 154.892075 205.02782 \nL 154.952954 214.756364 \nL 155.013833 213.534421 \nL 155.044272 206.461253 \nL 155.105151 214.756364 \nL 155.16603 214.756364 \nL 155.196469 204.487345 \nL 155.257348 214.756364 \nL 155.379106 213.228935 \nL 155.439984 211.959995 \nL 155.561742 214.756364 \nL 155.622621 214.756364 \nL 155.713939 205.215811 \nL 155.805257 214.756364 \nL 155.835697 202.865921 \nL 155.896576 212.641463 \nL 156.018333 214.756364 \nL 156.048773 213.322931 \nL 156.109651 214.756364 \nL 156.140091 196.356727 \nL 156.261848 214.756364 \nL 156.322727 207.777191 \nL 156.353167 213.040944 \nL 156.414045 214.756364 \nL 156.566243 204.017367 \nL 156.657561 214.756364 \nL 156.688 214.239388 \nL 156.748879 214.756364 \nL 156.779318 208.035679 \nL 156.840197 207.80069 \nL 156.870637 214.756364 \nL 156.961955 202.912919 \nL 157.022834 214.756364 \nL 157.083712 214.356882 \nL 157.175031 200.539531 \nL 157.23591 214.756364 \nL 157.296788 207.847688 \nL 157.357667 214.756364 \nL 157.388107 204.463846 \nL 157.418546 211.278527 \nL 157.448985 210.103582 \nL 157.479425 213.816408 \nL 157.570743 213.534421 \nL 157.631622 214.756364 \nL 157.692501 207.988681 \nL 157.753379 214.756364 \nL 157.814258 214.521375 \nL 157.844698 214.756364 \nL 157.996895 205.403802 \nL 158.027334 205.521297 \nL 158.149092 214.732865 \nL 158.179531 214.756364 \nL 158.209971 204.510844 \nL 158.270849 211.983494 \nL 158.392607 214.756364 \nL 158.453486 214.756364 \nL 158.483925 212.970447 \nL 158.544804 213.416926 \nL 158.605683 214.756364 \nL 158.666562 210.503063 \nL 158.697001 214.756364 \nL 158.72744 213.816408 \nL 158.788319 214.756364 \nL 158.818759 214.756364 \nL 158.940516 210.832048 \nL 158.970956 211.372522 \nL 159.092713 192.620402 \nL 159.031835 213.76941 \nL 159.123153 200.32804 \nL 159.24491 214.756364 \nL 159.366668 212.194984 \nL 159.397107 212.805955 \nL 159.427547 212.335977 \nL 159.457986 214.756364 \nL 159.518865 212.852953 \nL 159.549304 212.429973 \nL 159.640623 214.756364 \nL 159.671062 214.709366 \nL 159.701502 213.675414 \nL 159.731941 214.756364 \nL 159.76238 214.685867 \nL 159.79282 202.25495 \nL 159.853699 210.855547 \nL 159.975456 214.756364 \nL 160.066774 211.865999 \nL 160.158093 214.756364 \nL 160.27985 211.325525 \nL 160.340729 207.565701 \nL 160.371168 214.756364 \nL 160.492926 200.657025 \nL 160.584244 214.168891 \nL 160.614684 209.28112 \nL 160.736441 214.732865 \nL 160.675563 208.670149 \nL 160.766881 214.568372 \nL 160.858199 214.756364 \nL 160.888638 197.155689 \nL 161.010396 214.756364 \nL 161.071275 214.756364 \nL 161.101714 208.905138 \nL 161.162593 214.756364 \nL 161.284351 211.678008 \nL 161.375669 211.231529 \nL 161.406108 214.756364 \nL 161.527866 209.892092 \nL 161.588745 208.411661 \nL 161.649624 214.756364 \nL 161.740942 213.416926 \nL 161.771381 214.756364 \nL 161.801821 213.440425 \nL 161.83226 207.142721 \nL 161.893139 214.756364 \nL 162.045336 214.756364 \nL 162.167094 208.153173 \nL 162.319291 214.662368 \nL 162.410609 214.756364 \nL 162.441048 205.192312 \nL 162.593245 214.756364 \nL 162.745442 205.591794 \nL 162.775882 214.756364 \nL 162.8672 212.899951 \nL 162.958518 214.756364 \nL 162.928079 212.171485 \nL 162.988958 213.675414 \nL 163.049836 214.756364 \nL 163.080276 213.55792 \nL 163.110715 210.949542 \nL 163.171594 214.756364 \nL 163.202033 214.662368 \nL 163.232473 213.040944 \nL 163.262912 197.696164 \nL 163.323791 214.756364 \nL 163.35423 208.693648 \nL 163.415109 213.910403 \nL 163.445549 214.756364 \nL 163.567306 207.119222 \nL 163.719503 214.756364 \nL 163.749943 214.638869 \nL 163.780382 208.059178 \nL 163.841261 214.756364 \nL 163.8717 212.852953 \nL 163.90214 214.756364 \nL 163.932579 199.670071 \nL 163.993458 209.234123 \nL 164.023897 213.76941 \nL 164.115216 212.476971 \nL 164.145655 214.61537 \nL 164.176094 211.63101 \nL 164.206534 212.735458 \nL 164.236973 212.641463 \nL 164.328291 214.756364 \nL 164.358731 213.510922 \nL 164.38917 214.40388 \nL 164.480489 209.915591 \nL 164.510928 211.725006 \nL 164.541367 214.40388 \nL 164.571807 207.424708 \nL 164.602246 212.735458 \nL 164.663125 209.915591 \nL 164.693564 212.71196 \nL 164.724004 212.970447 \nL 164.784883 211.255028 \nL 164.845761 214.756364 \nL 164.876201 214.756364 \nL 165.028398 193.983338 \nL 165.119716 214.756364 \nL 165.150155 213.393428 \nL 165.180595 211.889498 \nL 165.211034 213.487423 \nL 165.241474 214.756364 \nL 165.271913 207.683195 \nL 165.363231 212.147986 \nL 165.393671 214.756364 \nL 165.42411 200.915513 \nL 165.484989 214.756364 \nL 165.515428 214.756364 \nL 165.576307 210.291573 \nL 165.637186 212.382975 \nL 165.758944 214.756364 \nL 165.819822 212.241982 \nL 165.850262 214.756364 \nL 165.880701 214.756364 \nL 165.911141 213.581419 \nL 165.972019 214.662368 \nL 166.032898 214.756364 \nL 166.063338 214.309885 \nL 166.124217 214.756364 \nL 166.154656 214.61537 \nL 166.185095 214.756364 \nL 166.215535 212.006993 \nL 166.276414 213.487423 \nL 166.306853 214.756364 \nL 166.337292 211.912997 \nL 166.367732 214.239388 \nL 166.428611 214.709366 \nL 166.45905 206.273262 \nL 166.580808 214.756364 \nL 166.611247 212.288979 \nL 166.672126 213.55792 \nL 166.733005 214.756364 \nL 166.885202 209.445613 \nL 167.037399 214.756364 \nL 167.159156 212.500469 \nL 167.220035 214.756364 \nL 167.250475 204.957323 \nL 167.311353 214.756364 \nL 167.433111 212.547467 \nL 167.46355 214.40388 \nL 167.49399 207.80069 \nL 167.585308 207.965182 \nL 167.615747 214.756364 \nL 167.646187 195.22878 \nL 167.707066 214.756364 \nL 167.767945 214.756364 \nL 167.798384 211.865999 \nL 167.859263 214.098395 \nL 167.920142 214.756364 \nL 167.950581 213.299432 \nL 168.01146 214.756364 \nL 168.041899 214.732865 \nL 168.072339 214.333383 \nL 168.163657 193.818846 \nL 168.285414 214.756364 \nL 168.315854 208.787644 \nL 168.376733 211.184531 \nL 168.407172 214.756364 \nL 168.437611 214.450878 \nL 168.468051 203.429895 \nL 168.52893 214.756364 \nL 168.589809 212.100988 \nL 168.620248 212.147986 \nL 168.650687 214.756364 \nL 168.681127 211.513516 \nL 168.742006 213.463924 \nL 168.772445 210.526562 \nL 168.802884 184.325291 \nL 168.863763 214.685867 \nL 168.924642 214.756364 \nL 168.955081 214.027898 \nL 168.985521 209.351617 \nL 169.0464 214.756364 \nL 169.076839 214.756364 \nL 169.107278 207.612699 \nL 169.168157 214.591871 \nL 169.198597 213.628417 \nL 169.229036 214.756364 \nL 169.259475 214.756364 \nL 169.320354 214.027898 \nL 169.442112 200.398537 \nL 169.381233 214.756364 \nL 169.472551 206.132268 \nL 169.56387 214.756364 \nL 169.685627 200.586528 \nL 169.807385 214.756364 \nL 169.868264 214.756364 \nL 169.898703 214.568372 \nL 169.929142 207.824189 \nL 169.959582 214.756364 \nL 169.990021 214.756364 \nL 170.0509 211.396021 \nL 170.081339 214.756364 \nL 170.233537 195.886749 \nL 170.263976 214.756364 \nL 170.355294 213.228935 \nL 170.416173 212.26548 \nL 170.446612 213.76941 \nL 170.477052 213.510922 \nL 170.56837 200.563029 \nL 170.629249 203.782378 \nL 170.751006 214.756364 \nL 170.842325 206.907732 \nL 170.872764 207.824189 \nL 170.994522 214.756364 \nL 171.024961 207.753692 \nL 171.08584 214.662368 \nL 171.116279 214.756364 \nL 171.268476 212.71196 \nL 171.298916 214.638869 \nL 171.329355 210.738052 \nL 171.359795 209.351617 \nL 171.481552 214.709366 \nL 171.511992 214.756364 \nL 171.542431 214.286386 \nL 171.57287 206.884233 \nL 171.60331 214.756364 \nL 171.664189 209.116628 \nL 171.755507 214.756364 \nL 171.785946 214.286386 \nL 171.877265 214.756364 \nL 171.907704 212.124487 \nL 171.938143 214.756364 \nL 171.968583 206.437754 \nL 172.059901 211.396021 \nL 172.09034 213.651915 \nL 172.12078 213.534421 \nL 172.151219 205.756286 \nL 172.181659 214.756364 \nL 172.212098 214.756364 \nL 172.272977 214.756364 \nL 172.303416 213.252434 \nL 172.364295 214.333383 \nL 172.394734 214.756364 \nL 172.486053 208.43516 \nL 172.577371 206.343758 \nL 172.60781 214.756364 \nL 172.63825 191.680446 \nL 172.699129 214.756364 \nL 172.729568 214.333383 \nL 172.760007 214.756364 \nL 172.790447 211.466518 \nL 172.851326 214.756364 \nL 172.912204 214.756364 \nL 172.942644 208.623151 \nL 173.033962 211.772004 \nL 173.12528 214.756364 \nL 173.15572 212.030492 \nL 173.216598 214.756364 \nL 173.338356 214.709366 \nL 173.368796 202.724928 \nL 173.429674 214.756364 \nL 173.460114 214.756364 \nL 173.581871 205.709288 \nL 173.703629 214.756364 \nL 173.734068 214.756364 \nL 173.764508 214.544874 \nL 173.855826 214.662368 \nL 173.977584 214.756364 \nL 174.129781 210.855547 \nL 174.16022 204.134862 \nL 174.19066 214.638869 \nL 174.221099 214.215889 \nL 174.251538 210.620558 \nL 174.281978 214.756364 \nL 174.312417 214.756364 \nL 174.342857 214.756364 \nL 174.464614 204.745833 \nL 174.495054 207.871187 \nL 174.616811 214.756364 \nL 174.647251 214.709366 \nL 174.67769 214.145392 \nL 174.708129 214.709366 \nL 174.769008 203.429895 \nL 174.799448 214.756364 \nL 174.890766 214.756364 \nL 174.982084 213.416926 \nL 175.012524 214.756364 \nL 175.042963 211.560514 \nL 175.073402 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177.112843 214.756364 \nL 177.143282 214.027898 \nL 177.173721 208.270668 \nL 177.2346 208.811143 \nL 177.295479 214.756364 \nL 177.356358 212.241982 \nL 177.417237 214.756364 \nL 177.447676 214.568372 \nL 177.508555 208.106176 \nL 177.538994 214.756364 \nL 177.569434 212.359476 \nL 177.599873 212.335977 \nL 177.660752 214.756364 \nL 177.691191 200.022555 \nL 177.78251 214.756364 \nL 177.812949 213.087942 \nL 177.843388 214.756364 \nL 177.873828 214.638869 \nL 177.904267 196.427223 \nL 177.965146 214.756364 \nL 177.995585 208.599652 \nL 178.056464 209.892092 \nL 178.178222 214.756364 \nL 178.208661 214.756364 \nL 178.29998 208.482158 \nL 178.421737 214.756364 \nL 178.482616 211.443019 \nL 178.513055 214.756364 \nL 178.573934 212.030492 \nL 178.634813 213.158439 \nL 178.665252 214.756364 \nL 178.756571 205.380303 \nL 178.847889 214.756364 \nL 178.878328 207.683195 \nL 178.939207 214.756364 \nL 178.969647 214.756364 \nL 179.030525 210.879046 \nL 179.060965 214.19239 \nL 179.121844 212.993946 \nL 179.182722 210.78505 \nL 179.213162 214.756364 \nL 179.243601 210.432566 \nL 179.274041 202.395943 \nL 179.30448 214.756364 \nL 179.334919 214.756364 \nL 179.365359 214.756364 \nL 179.395798 208.129674 \nL 179.456677 214.215889 \nL 179.487116 214.756364 \nL 179.517556 211.114034 \nL 179.578435 214.756364 \nL 179.608874 214.756364 \nL 179.669753 196.544718 \nL 179.730632 212.05399 \nL 179.791511 214.732865 \nL 179.82195 214.168891 \nL 179.852389 200.821517 \nL 179.913268 214.756364 \nL 180.035026 208.576154 \nL 180.126344 214.756364 \nL 180.156783 214.732865 \nL 180.187223 214.427379 \nL 180.217662 214.756364 \nL 180.278541 203.735381 \nL 180.30898 213.158439 \nL 180.369859 214.756364 \nL 180.400299 214.239388 \nL 180.430738 204.769332 \nL 180.491617 213.933902 \nL 180.552496 214.756364 \nL 180.674253 205.920778 \nL 180.735132 214.756364 \nL 180.765572 211.748505 \nL 180.796011 204.275855 \nL 180.82645 214.756364 \nL 180.85689 211.278527 \nL 180.887329 213.910403 \nL 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204.299354 \nL 187.066529 210.879046 \nL 187.218726 214.756364 \nL 187.340484 211.748505 \nL 187.370923 214.380381 \nL 187.431802 201.808471 \nL 187.462241 214.756364 \nL 187.492681 211.137533 \nL 187.52312 214.756364 \nL 187.553559 209.06963 \nL 187.614438 214.709366 \nL 187.644878 195.369773 \nL 187.736196 196.403725 \nL 187.827514 214.756364 \nL 187.857954 213.675414 \nL 187.888393 214.756364 \nL 188.010151 209.892092 \nL 188.04059 214.544874 \nL 188.101469 187.732631 \nL 188.131908 214.756364 \nL 188.162348 213.017445 \nL 188.192787 202.88942 \nL 188.223226 214.427379 \nL 188.253666 213.158439 \nL 188.344984 214.756364 \nL 188.405863 200.069553 \nL 188.466742 212.359476 \nL 188.52762 214.756364 \nL 188.588499 187.591638 \nL 188.679818 214.756364 \nL 188.710257 214.380381 \nL 188.771136 211.63101 \nL 188.801575 214.286386 \nL 188.832015 214.756364 \nL 188.862454 214.732865 \nL 188.923333 214.756364 \nL 188.984212 202.771926 \nL 189.07553 214.756364 \nL 189.105969 211.278527 \nL 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214.756364 \nL 191.023652 214.356882 \nL 191.054091 201.385491 \nL 191.084531 214.568372 \nL 191.14541 208.64665 \nL 191.267167 214.732865 \nL 191.328046 211.959995 \nL 191.358485 214.756364 \nL 191.388925 214.427379 \nL 191.449804 214.638869 \nL 191.541122 203.594387 \nL 191.571561 213.675414 \nL 191.63244 202.701429 \nL 191.662879 198.283636 \nL 191.784637 214.732865 \nL 191.815077 208.200171 \nL 191.845516 214.756364 \nL 191.906395 210.291573 \nL 191.936834 214.756364 \nL 191.967274 210.174079 \nL 191.997713 199.294089 \nL 192.058592 214.756364 \nL 192.119471 213.205436 \nL 192.14991 214.756364 \nL 192.210789 214.309885 \nL 192.241228 214.756364 \nL 192.271668 203.805877 \nL 192.332546 210.197577 \nL 192.454304 214.756364 \nL 192.606501 208.928637 \nL 192.728259 214.756364 \nL 192.789138 214.286386 \nL 192.819577 201.1975 \nL 192.850016 214.756364 \nL 192.880456 213.651915 \nL 192.941335 211.231529 \nL 192.971774 212.26548 \nL 193.032653 214.756364 \nL 193.15441 190.622996 \nL 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209.774597 \nL 195.467805 208.881639 \nL 195.498245 214.756364 \nL 195.528684 205.944277 \nL 195.589563 214.638869 \nL 195.680881 206.508251 \nL 195.711321 214.756364 \nL 195.802639 211.490017 \nL 195.833078 214.756364 \nL 195.863518 188.837079 \nL 195.924397 214.544874 \nL 196.046154 181.411428 \nL 196.167912 214.756364 \nL 196.289669 200.281043 \nL 196.380988 214.756364 \nL 196.350548 179.696008 \nL 196.411427 213.181937 \nL 196.441866 211.114034 \nL 196.472306 214.756364 \nL 196.502745 212.641463 \nL 196.533185 212.547467 \nL 196.563624 213.76941 \nL 196.594063 211.983494 \nL 196.624503 210.385569 \nL 196.685382 214.756364 \nL 196.746261 213.393428 \nL 196.807139 214.756364 \nL 196.837579 214.568372 \nL 196.898458 214.756364 \nL 196.928897 209.304619 \nL 197.020215 214.756364 \nL 197.050655 212.171485 \nL 197.141973 214.756364 \nL 197.172412 183.526329 \nL 197.29417 214.756364 \nL 197.415928 213.675414 \nL 197.476806 214.756364 \nL 197.507246 214.333383 \nL 197.568125 205.051319 \nL 197.598564 206.555248 \nL 197.629003 214.756364 \nL 197.689882 207.260215 \nL 197.720322 196.803206 \nL 197.750761 214.756364 \nL 197.7812 214.756364 \nL 197.81164 211.302026 \nL 197.872519 214.756364 \nL 197.902958 214.756364 \nL 197.933397 175.842189 \nL 197.994276 213.487423 \nL 198.055155 212.382975 \nL 198.116034 214.756364 \nL 198.176913 187.168658 \nL 198.237792 204.910326 \nL 198.268231 214.756364 \nL 198.32911 206.061771 \nL 198.359549 203.594387 \nL 198.389989 186.111207 \nL 198.450867 214.756364 \nL 198.542186 202.654431 \nL 198.572625 213.55792 \nL 198.603064 213.463924 \nL 198.633504 214.756364 \nL 198.663943 207.542202 \nL 198.724822 214.568372 \nL 198.81614 214.756364 \nL 198.877019 206.320259 \nL 198.907458 214.521375 \nL 198.998777 213.886904 \nL 199.029216 200.516032 \nL 199.090095 201.291495 \nL 199.181413 214.756364 \nL 199.211853 213.087942 \nL 199.242292 214.756364 \nL 199.272731 213.863406 \nL 199.303171 189.753537 \nL 199.394489 205.004321 \nL 199.485807 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205.02782 \nL 204.325673 202.536937 \nL 204.447431 214.756364 \nL 204.47787 214.756364 \nL 204.508309 211.114034 \nL 204.569188 212.664962 \nL 204.660507 214.756364 \nL 204.751825 206.484752 \nL 204.843143 214.756364 \nL 204.873582 213.322931 \nL 204.904022 211.20803 \nL 204.934461 214.756364 \nL 204.964901 183.338337 \nL 205.025779 214.756364 \nL 205.056219 214.521375 \nL 205.117098 214.756364 \nL 205.147537 201.455988 \nL 205.208416 214.756364 \nL 205.360613 214.756364 \nL 205.391052 199.0591 \nL 205.451931 214.756364 \nL 205.482371 213.722412 \nL 205.543249 214.709366 \nL 205.573689 214.756364 \nL 205.665007 207.448206 \nL 205.695446 189.988525 \nL 205.756325 212.617964 \nL 205.786765 214.756364 \nL 205.817204 203.852875 \nL 205.878083 211.443019 \nL 205.938962 214.756364 \nL 205.99984 214.662368 \nL 206.03028 214.756364 \nL 206.152037 191.492455 \nL 206.273795 214.756364 \nL 206.304235 197.625667 \nL 206.365113 214.685867 \nL 206.395553 214.544874 \nL 206.425992 208.411661 \nL 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209.657103 \nL 208.404554 214.756364 \nL 208.434993 210.268074 \nL 208.465432 207.941683 \nL 208.495872 213.416926 \nL 208.556751 214.756364 \nL 208.58719 203.500392 \nL 208.678508 207.354211 \nL 208.708948 206.29676 \nL 208.800266 213.463924 \nL 208.830705 212.429973 \nL 208.861145 203.946871 \nL 208.891584 214.732865 \nL 208.952463 208.317666 \nL 208.982902 213.792909 \nL 209.013342 207.777191 \nL 209.043781 212.899951 \nL 209.135099 214.756364 \nL 209.165539 194.688305 \nL 209.226418 214.756364 \nL 209.287296 212.899951 \nL 209.317736 214.756364 \nL 209.348175 209.586606 \nL 209.409054 213.463924 \nL 209.439493 214.756364 \nL 209.469933 201.573482 \nL 209.530812 213.534421 \nL 209.561251 214.286386 \nL 209.591691 204.064365 \nL 209.652569 209.774597 \nL 209.713448 207.424708 \nL 209.774327 214.756364 \nL 209.804766 206.578747 \nL 209.865645 214.450878 \nL 209.896085 214.756364 \nL 209.987403 208.670149 \nL 210.017842 214.756364 \nL 210.10916 214.215889 \nL 210.1396 208.082677 \nL 210.200479 212.312478 \nL 210.261357 214.756364 \nL 210.291797 213.628417 \nL 210.322236 197.625667 \nL 210.352676 214.756364 \nL 210.383115 214.756364 \nL 210.413555 208.22367 \nL 210.474433 214.544874 \nL 210.504873 214.756364 \nL 210.535312 214.121893 \nL 210.596191 208.85814 \nL 210.62663 210.244575 \nL 210.717949 214.756364 \nL 210.748388 193.066881 \nL 210.809267 214.756364 \nL 210.931024 206.108769 \nL 211.052782 214.756364 \nL 211.113661 214.756364 \nL 211.204979 209.328118 \nL 211.296297 214.756364 \nL 211.326737 209.022633 \nL 211.418055 210.244575 \nL 211.448494 211.701507 \nL 211.509373 213.275933 \nL 211.539813 189.965027 \nL 211.570252 214.756364 \nL 211.66157 201.573482 \nL 211.69201 214.732865 \nL 211.722449 191.915435 \nL 211.752888 211.396021 \nL 211.813767 195.722257 \nL 211.844207 214.756364 \nL 211.874646 214.40388 \nL 211.905086 206.014774 \nL 211.935525 214.756364 \nL 211.965964 214.027898 \nL 211.996404 213.252434 \nL 212.026843 214.756364 \nL 212.057283 198.84761 \nL 212.118161 212.899951 \nL 212.148601 211.701507 \nL 212.17904 199.411583 \nL 212.20948 214.756364 \nL 212.239919 214.333383 \nL 212.300798 214.756364 \nL 212.331237 199.952058 \nL 212.392116 208.85814 \nL 212.422555 211.983494 \nL 212.452995 182.468878 \nL 212.483434 213.158439 \nL 212.513874 203.194906 \nL 212.544313 214.756364 \nL 212.635631 212.735458 \nL 212.666071 206.437754 \nL 212.72695 210.409068 \nL 212.757389 214.756364 \nL 212.818268 213.322931 \nL 212.848707 211.725006 \nL 212.879147 198.236639 \nL 212.909586 214.756364 \nL 212.940025 199.223592 \nL 213.000904 214.756364 \nL 213.061783 212.171485 \nL 213.092222 207.307213 \nL 213.122662 214.756364 \nL 213.153101 210.009586 \nL 213.183541 214.756364 \nL 213.244419 208.341165 \nL 213.274859 214.568372 \nL 213.335738 214.756364 \nL 213.396616 213.510922 \nL 213.427056 214.756364 \nL 213.457495 212.735458 \nL 213.487935 213.9809 \nL 213.518374 209.234123 \nL 213.579253 214.756364 \nL 213.609692 214.756364 \nL 213.761889 197.155689 \nL 213.883647 214.756364 \nL 213.914086 214.756364 \nL 213.944526 214.497876 \nL 214.005405 214.756364 \nL 214.035844 214.756364 \nL 214.066283 214.61537 \nL 214.127162 214.756364 \nL 214.188041 209.422114 \nL 214.309799 214.756364 \nL 214.370678 209.539608 \nL 214.401117 214.662368 \nL 214.431556 214.756364 \nL 214.522875 194.218327 \nL 214.553314 210.244575 \nL 214.614193 209.539608 \nL 214.675072 214.756364 \nL 214.76639 213.275933 \nL 214.857708 214.756364 \nL 214.827269 212.92345 \nL 214.888147 214.450878 \nL 214.918587 204.087864 \nL 215.009905 210.197577 \nL 215.101223 214.756364 \nL 215.131663 214.732865 \nL 215.192542 214.756364 \nL 215.25342 206.484752 \nL 215.28386 212.05399 \nL 215.314299 195.745755 \nL 215.375178 203.006915 \nL 215.496936 214.756364 \nL 215.527375 206.531749 \nL 215.588254 214.756364 \nL 215.618693 214.756364 \nL 215.649133 206.790237 \nL 215.710011 214.732865 \nL 215.77089 214.756364 \nL 215.831769 213.534421 \nL 215.862208 199.90506 \nL 215.923087 208.717147 \nL 216.014406 214.756364 \nL 216.044845 212.92345 \nL 216.105724 202.842423 \nL 216.136163 214.756364 \nL 216.227481 206.978229 \nL 216.257921 214.756364 \nL 216.349239 214.709366 \nL 216.440557 202.372445 \nL 216.410118 214.756364 \nL 216.470997 211.889498 \nL 216.531875 209.868593 \nL 216.592754 214.215889 \nL 216.684072 205.544796 \nL 216.775391 214.756364 \nL 216.80583 206.790237 \nL 216.866709 214.756364 \nL 216.927588 211.396021 \nL 216.958027 186.628183 \nL 216.988467 214.591871 \nL 217.018906 212.758957 \nL 217.049345 209.398615 \nL 217.110224 213.863406 \nL 217.262421 214.756364 \nL 217.292861 201.549983 \nL 217.353739 213.463924 \nL 217.384179 213.675414 \nL 217.414618 200.398537 \nL 217.445058 214.521375 \nL 217.475497 211.560514 \nL 217.505937 214.756364 \nL 217.597255 212.735458 \nL 217.658134 214.756364 \nL 217.719012 202.489939 \nL 217.779891 212.077489 \nL 217.84077 210.832048 \nL 217.932088 214.756364 \nL 217.962528 211.349023 \nL 218.023406 212.876452 \nL 218.114725 214.756364 \nL 218.145164 214.732865 \nL 218.206043 214.756364 \nL 218.297361 200.610027 \nL 218.388679 214.756364 \nL 218.419119 207.095723 \nL 218.540876 214.756364 \nL 218.571316 214.591871 \nL 218.632195 203.077411 \nL 218.662634 211.678008 \nL 218.693073 214.756364 \nL 218.723513 201.385491 \nL 218.784392 211.043538 \nL 218.87571 214.756364 \nL 218.936589 201.878968 \nL 218.967028 214.756364 \nL 218.997467 214.756364 \nL 219.027907 201.737974 \nL 219.088786 214.756364 \nL 219.149665 214.756364 \nL 219.180104 197.696164 \nL 219.240983 214.756364 \nL 219.271422 213.087942 \nL 219.301862 214.450878 \nL 219.332301 195.581263 \nL 219.39318 210.503063 \nL 219.423619 210.080083 \nL 219.454059 212.030492 \nL 219.514937 202.771926 \nL 219.545377 214.756364 \nL 219.575816 212.547467 \nL 219.636695 214.756364 \nL 219.697574 214.756364 \nL 219.819331 213.487423 \nL 219.91065 214.756364 \nL 219.971529 195.722257 \nL 220.001968 214.732865 \nL 220.032407 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222.102287 214.756364 \nL 222.132726 213.228935 \nL 222.193605 214.756364 \nL 222.224045 197.437676 \nL 222.284923 211.889498 \nL 222.345802 210.78505 \nL 222.406681 214.756364 \nL 222.437121 214.497876 \nL 222.46756 212.406474 \nL 222.497999 214.756364 \nL 222.528439 213.722412 \nL 222.650196 214.756364 \nL 222.680636 214.004399 \nL 222.802393 203.147908 \nL 222.832833 206.08527 \nL 222.863272 214.685867 \nL 222.924151 208.64665 \nL 222.95459 206.437754 \nL 223.076348 214.756364 \nL 223.106787 214.732865 \nL 223.137227 213.205436 \nL 223.167666 194.241826 \nL 223.228545 211.278527 \nL 223.289424 210.597059 \nL 223.350303 214.756364 \nL 223.380742 189.236561 \nL 223.47206 204.722334 \nL 223.532939 211.114034 \nL 223.563379 189.941528 \nL 223.593818 214.732865 \nL 223.624257 211.63101 \nL 223.715576 214.756364 \nL 223.746015 203.735381 \nL 223.806894 211.584012 \nL 223.837333 214.756364 \nL 223.867773 206.08527 \nL 223.928652 209.798096 \nL 223.98953 214.756364 \nL 224.01997 197.672665 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228.068411 214.756364 \nL 228.09885 210.291573 \nL 228.159729 214.756364 \nL 228.190169 214.756364 \nL 228.220608 214.380381 \nL 228.251047 199.505579 \nL 228.281487 214.756364 \nL 228.311926 211.560514 \nL 228.342366 212.852953 \nL 228.372805 190.998978 \nL 228.433684 214.521375 \nL 228.464123 214.61537 \nL 228.494563 214.239388 \nL 228.555441 214.756364 \nL 228.61632 203.335899 \nL 228.677199 192.808393 \nL 228.738078 214.756364 \nL 228.890275 207.330712 \nL 228.920714 213.087942 \nL 228.951154 197.437676 \nL 228.981593 214.756364 \nL 229.012033 208.458659 \nL 229.042472 214.756364 \nL 229.13379 213.322931 \nL 229.225108 214.756364 \nL 229.255548 213.440425 \nL 229.285987 214.756364 \nL 229.346866 203.335899 \nL 229.377305 208.43516 \nL 229.468624 214.756364 \nL 229.529502 191.844938 \nL 229.559942 196.192234 \nL 229.6817 214.756364 \nL 229.712139 213.181937 \nL 229.773018 214.732865 \nL 229.864336 213.228935 \nL 229.894775 214.40388 \nL 229.925215 214.732865 \nL 229.955654 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231.72114 210.221076 \nL 231.782019 214.756364 \nL 231.812458 213.76941 \nL 231.903776 200.892014 \nL 231.934216 212.382975 \nL 231.964655 214.756364 \nL 232.055973 213.910403 \nL 232.086413 214.168891 \nL 232.177731 214.239388 \nL 232.20817 196.450722 \nL 232.23861 214.756364 \nL 232.329928 214.286386 \nL 232.360367 214.732865 \nL 232.451686 200.633526 \nL 232.421246 214.756364 \nL 232.482125 208.43516 \nL 232.543004 214.756364 \nL 232.603883 213.745911 \nL 232.664761 213.275933 \nL 232.72564 197.155689 \nL 232.786519 206.132268 \nL 232.877837 214.756364 \nL 232.847398 198.518625 \nL 232.908277 213.252434 \nL 232.999595 214.756364 \nL 233.030034 211.278527 \nL 233.121353 213.275933 \nL 233.24311 200.563029 \nL 233.27355 210.479564 \nL 233.303989 214.756364 \nL 233.395307 212.570966 \nL 233.425747 208.200171 \nL 233.456186 186.581185 \nL 233.517065 211.20803 \nL 233.547504 214.756364 \nL 233.608383 209.140127 \nL 233.638823 207.871187 \nL 233.669262 188.249607 \nL 233.730141 214.756364 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237.839461 199.881561 \nL 237.8699 214.756364 \nL 237.90034 214.685867 \nL 238.052537 203.382897 \nL 238.143855 214.756364 \nL 238.174294 205.615292 \nL 238.235173 211.137533 \nL 238.296052 214.756364 \nL 238.326491 212.547467 \nL 238.356931 198.84761 \nL 238.38737 214.756364 \nL 238.41781 205.967776 \nL 238.539567 214.756364 \nL 238.661325 198.072146 \nL 238.691764 214.756364 \nL 238.783082 212.241982 \nL 238.813522 200.093051 \nL 238.874401 214.756364 \nL 238.90484 203.547389 \nL 239.057037 214.756364 \nL 239.087476 207.213217 \nL 239.148355 211.090536 \nL 239.270113 214.756364 \nL 239.361431 191.539453 \nL 239.42231 214.756364 \nL 239.483189 205.87378 \nL 239.544068 214.756364 \nL 239.604946 210.009586 \nL 239.635386 214.427379 \nL 239.665825 201.385491 \nL 239.696265 214.756364 \nL 239.726704 211.41952 \nL 239.787583 214.450878 \nL 239.818022 209.445613 \nL 239.878901 214.756364 \nL 240.000659 209.375116 \nL 240.031098 191.492455 \nL 240.091977 214.662368 \nL 240.122416 214.61537 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254.733332 214.756364 \nL 254.763771 214.756364 \nL 254.794211 198.730115 \nL 254.885529 206.813736 \nL 254.946408 214.756364 \nL 254.976847 213.487423 \nL 255.007287 141.345807 \nL 255.068165 214.756364 \nL 255.098605 213.886904 \nL 255.159484 196.239232 \nL 255.189923 212.664962 \nL 255.220362 210.808549 \nL 255.250802 212.735458 \nL 255.281241 212.030492 \nL 255.311681 214.662368 \nL 255.34212 201.925966 \nL 255.402999 214.756364 \nL 255.463878 211.513516 \nL 255.494317 199.599575 \nL 255.555196 214.756364 \nL 255.616075 214.756364 \nL 255.646514 213.275933 \nL 255.676954 213.698913 \nL 255.707393 201.033007 \nL 255.737832 214.732865 \nL 255.768272 211.067037 \nL 255.798711 214.145392 \nL 255.829151 194.194828 \nL 255.85959 214.756364 \nL 255.890029 214.756364 \nL 255.920469 214.756364 \nL 255.950908 191.210468 \nL 256.011787 212.71196 \nL 256.042226 208.811143 \nL 256.103105 212.946949 \nL 256.133545 214.756364 \nL 256.163984 214.638869 \nL 256.224863 167.923061 \nL 256.255302 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288.947226 213.064443 \nL 288.977665 214.756364 \nL 289.038544 214.215889 \nL 289.099423 204.111363 \nL 289.129863 208.811143 \nL 289.190741 214.756364 \nL 289.25162 212.876452 \nL 289.28206 214.756364 \nL 289.434257 196.521219 \nL 289.556014 214.756364 \nL 289.586454 212.218483 \nL 289.677772 212.735458 \nL 289.708211 189.04857 \nL 289.76909 212.852953 \nL 289.829969 214.756364 \nL 289.860408 205.051319 \nL 289.951727 211.231529 \nL 289.982166 210.526562 \nL 290.012605 211.043538 \nL 290.043045 212.735458 \nL 290.073484 208.059178 \nL 290.103924 214.732865 \nL 290.134363 212.030492 \nL 290.195242 214.286386 \nL 290.225681 207.213217 \nL 290.28656 214.756364 \nL 290.408318 199.552577 \nL 290.469196 198.283636 \nL 290.530075 214.756364 \nL 290.621394 214.685867 \nL 290.651833 203.523891 \nL 290.712712 214.756364 \nL 290.743151 214.756364 \nL 290.864909 204.557842 \nL 290.925788 214.756364 \nL 291.017106 214.427379 \nL 291.047545 214.356882 \nL 291.077985 190.834486 \nL 291.108424 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297.561578 209.351617 \nL 297.592018 214.756364 \nL 297.622457 201.174001 \nL 297.652897 213.322931 \nL 297.805094 203.899873 \nL 297.896412 214.756364 \nL 297.926851 203.194906 \nL 298.01817 209.962589 \nL 298.139927 214.756364 \nL 298.170367 205.192312 \nL 298.231245 214.756364 \nL 298.261685 214.756364 \nL 298.292124 205.779785 \nL 298.353003 206.696242 \nL 298.383442 214.121893 \nL 298.474761 213.181937 \nL 298.535639 214.756364 \nL 298.566079 211.325525 \nL 298.626958 214.544874 \nL 298.687837 214.756364 \nL 298.748715 213.205436 \nL 298.809594 214.756364 \nL 298.840034 213.886904 \nL 298.870473 203.194906 \nL 298.931352 208.176672 \nL 299.02267 214.756364 \nL 299.053109 208.035679 \nL 299.113988 214.756364 \nL 299.144428 214.662368 \nL 299.235746 207.424708 \nL 299.327064 214.756364 \nL 299.357503 211.772004 \nL 299.387943 211.41952 \nL 299.418382 206.531749 \nL 299.448822 207.612699 \nL 299.479261 214.756364 \nL 299.509701 202.019961 \nL 299.54014 212.641463 \nL 299.601019 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301.366504 207.777191 \nL 301.396944 214.756364 \nL 301.427383 211.090536 \nL 301.457823 202.583935 \nL 301.488262 212.218483 \nL 301.518701 203.923372 \nL 301.640459 214.756364 \nL 301.670898 214.098395 \nL 301.701338 214.756364 \nL 301.731777 196.779707 \nL 301.823095 204.534343 \nL 301.883974 214.756364 \nL 301.914414 211.161032 \nL 301.944853 199.247091 \nL 302.005732 214.732865 \nL 302.036171 209.892092 \nL 302.066611 214.756364 \nL 302.12749 211.137533 \nL 302.157929 210.926043 \nL 302.188368 197.061694 \nL 302.249247 211.748505 \nL 302.279687 208.975635 \nL 302.310126 214.756364 \nL 302.340565 213.910403 \nL 302.401444 214.756364 \nL 302.431884 202.25495 \nL 302.492762 207.918184 \nL 302.553641 214.756364 \nL 302.584081 208.811143 \nL 302.61452 196.004243 \nL 302.644959 214.756364 \nL 302.705838 202.513438 \nL 302.736278 202.536937 \nL 302.888475 214.756364 \nL 303.010232 203.453394 \nL 303.13199 214.756364 \nL 303.192869 206.061771 \nL 303.223308 211.278527 \nL 303.314626 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(lpath)"
   ]
  },
  {
   "source": [
    "What we see here is that at first the average path length increased. This is probably due to the fact that when we know nothing about the environment - we are likely to get trapped into bad states, water or wolf. As we learn more and start using this knowledge, we can explore the environment for longer, but we still do not know well where apples are.\n",
    "\n",
    "Once we learn enough, it becomes easier for the agent to achieve the goal, and the path length starts to decrease. However, we are still open to exploration, so we often diverge away from the best path, and explore new options, making the path longer than optimal.\n",
    "\n",
    "What we also observe on this graph, is that at some point the length increased abruptly. This indicates stochastic nature of the process, and that we can at some point \"sploil\" the Q-Table coefficients, by overwriting them with new values. This ideally should be minimized by decreasing learning rate (i.e. towards the end of training we only adjust Q-Table values by a small value).\n",
    "\n",
    "Overall, it is important to remember that the success and quality of the learning process significantly depends on parameters, such as leaning rate, learning rate decay and discount factor. Those are often called **hyperparameters**, to distinguish them from **parameters** which we optimize during training (eg. Q-Table coefficients). The process of finding best hyperparameter values is called **hyperparameter optimization**, and it deserves a separate topic."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "## Exercise\n",
    "#### A More Realistic Peter and the Wolf World\n",
    "\n",
    "In our situation, Peter was able to move around almost without getting tired or hungry. In a more realistic world, he has to sit down and rest from time to time, and also to feed himself. Let's make our world more realistic by implementing the following rules:\n",
    "\n",
    "1. By moving from one place to another, Peter loses **energy** and gains some **fatigue**.\n",
    "2. Peter can gain more energy by eating apples.\n",
    "3. Peter can get rid of fatigue by resting under the tree or on the grass (i.e. walking into a board location with a tree or grass - green field)\n",
    "4. Peter needs to find and kill the wolf\n",
    "5. In order to kill the wolf, Peter needs to have certain levels of energy and fatigue, otherwise he loses the battle.\n",
    "\n",
    "Modify the reward function above according to the rules of the game, run the reinforcement learning algorithm to learn the best strategy for winning the game, and compare the results of random walk with your algorithm in terms of number of games won and lost.\n",
    "\n",
    "\n",
    "> **Note**: You may need to adjust hyperparameters to make it work, especially the number of epochs. Because the success of the game (fighting the wolf) is a rare event, you can expect much longer training time.\n",
    "\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}