2_ValueIteration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "\n",
    "#Markov decision process\n",
    "\n",
    "This week's methods are all built to solve Markov Decision Processes. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.\n",
    "\n",
    "State transition is defined by $P(s' |s,a)$ - how likely are you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience.\n",
    "\n",
    "This notebook is inspired by the awesome CS294 by Berkeley\n",
    "\n",
    "For starters, let's define a simple MDP from this picture: \n",
    "<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Markov_Decision_Process.svg/800px-Markov_Decision_Process.svg.png' width=300px> \n",
    "img by MistWiz (Own work) [Public domain], via Wikimedia Commons\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "transition_probs = {\n",
    "    's0': {\n",
    "        'a0': {'s0': 0.5, 's2': 0.5},\n",
    "        'a1': {'s2': 1}\n",
    "    },\n",
    "    's1': {\n",
    "        'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2},\n",
    "        'a1': {'s1': 0.95, 's2': 0.05}\n",
    "    },\n",
    "    's2': {\n",
    "        'a0': {'s0': 0.4, 's1': 0.6},\n",
    "        'a1': {'s0': 0.3, 's1': 0.3, 's2': 0.4}\n",
    "    }\n",
    "}\n",
    "rewards = {\n",
    "    's1': {'a0': {'s0': +5}},\n",
    "    's2': {'a1': {'s0': -1}}\n",
    "}\n",
    "\n",
    "from mdp import MDP\n",
    "mdp = MDP(transition_probs, rewards, initial_state='s0')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__class__',\n '__delattr__',\n '__dict__',\n '__dir__',\n '__doc__',\n '__eq__',\n '__format__',\n '__ge__',\n '__getattribute__',\n '__gt__',\n '__hash__',\n '__init__',\n '__init_subclass__',\n '__le__',\n '__lt__',\n '__module__',\n '__ne__',\n '__new__',\n '__reduce__',\n '__reduce_ex__',\n '__repr__',\n '__setattr__',\n '__sizeof__',\n '__str__',\n '__subclasshook__',\n '__weakref__',\n '_check_param_consistency',\n '_current_state',\n '_initial_state',\n '_rewards',\n '_transition_probs',\n 'get_all_states',\n 'get_next_states',\n 'get_possible_actions',\n 'get_reward',\n 'get_transition_prob',\n 'is_terminal',\n 'n_states',\n 'render',\n 'reset',\n 'step']"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(mdp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial state = s0\nnext_state = s2, reward = 0.0, done = False\n"
     ]
    }
   ],
   "source": [
    "print('initial state =', mdp.reset())\n",
    "next_state, reward, done, info = mdp.step('a1')\n",
    "print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "but it also has other methods that you'll need for Value Iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mdp.get_all_states = ('s0', 's1', 's2')\nmdp.get_possible_actions('s1') =  ('a0', 'a1')\nmdp.get_next_states('s1', 'a0') =  {'s0': 0.7, 's1': 0.1, 's2': 0.2}\nmdp.get_reward('s1', 'a0', 's0') =  5\nmdp.get_transition_prob('s1', 'a0', 's0') =  0.7\n"
     ]
    }
   ],
   "source": [
    "print(\"mdp.get_all_states =\", mdp.get_all_states())\n",
    "print(\"mdp.get_possible_actions('s1') = \", mdp.get_possible_actions('s1'))\n",
    "print(\"mdp.get_next_states('s1', 'a0') = \", mdp.get_next_states('s1', 'a0'))\n",
    "print(\"mdp.get_reward('s1', 'a0', 's0') = \", mdp.get_reward('s1', 'a0', 's0'))\n",
    "print(\"mdp.get_transition_prob('s1', 'a0', 's0') = \",\n",
    "      mdp.get_transition_prob('s1', 'a0', 's0'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#Optional: Visualizing MDPs\n",
    "\n",
    "You can also visualize any MDP with the drawing fuction donated by neer201.\n",
    "\n",
    "You have to install graphviz for system and for python. For ubuntu just run:\n",
    "\n",
    "*    sudo apt-get install graphviz\n",
    "*    pip install graphviz\n",
    "*    restart the notebook\n",
    "\n",
    "Note: Installing graphviz on some OS (esp. Windows) may be tricky. However, you can ignore this part alltogether and use the standart vizualization.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graphviz available: True\n"
     ]
    }
   ],
   "source": [
    "from mdp import has_graphviz\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "from IPython.display import Image \n",
    "print(\"Graphviz available:\", has_graphviz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1fc1c85a550>"
      ]
     },
     "execution_count": 0,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if has_graphviz:\n",
    "    from mdp import plot_graph, plot_graph_with_state_values, \\\n",
    "        plot_graph_optimal_strategy_and_state_values\n",
    "    display(plot_graph(mdp))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#Value Iteration\n",
    "\n",
    "Now let's build something to solve this MDP. The simplest algorithm so far is Value Iteration\n",
    "\n",
    "Here's the pseudo-code for VI:\n",
    "\n",
    "1. Initialize $ V^{(0)}(s)=0 $, for all $s$\n",
    "\n",
    "2. For $i=0, 1, 2, \\dots$\n",
    "\n",
    "3. $ \\quad V_{(i+1)}(s) = \\max_a \\sum_{s'} P(s' | s,a) \\cdot [ r(s,a,s') + \\gamma V_{i}(s')]$, for all $s$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "First, let's write a function to compute the state-action value function $Q^{\\pi}$, defined as follows\n",
    "$$Q_i(s, a) = \\sum_{s'} P(s' | s,a) \\cdot [ r(s,a,s') + \\gamma V_{i}(s')]$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting mdp_get_action_value.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile mdp_get_action_value.py\n",
    "\n",
    "def get_action_value(mdp, state_values, state, action, gamma):\n",
    "    \"\"\" Computes Q(s,a) as in formula above \"\"\"\n",
    "    q_Value = 0;\n",
    "    # YOUR CODE HERE\n",
    "    for next_state in mdp.get_next_states(state, action):\n",
    "        transition_prob = mdp.get_transition_prob(\n",
    "            state, action, next_state\n",
    "        )\n",
    "        reward = mdp.get_reward(\n",
    "            state, action, next_state\n",
    "        )\n",
    "        q_Value += transition_prob * (reward + gamma * state_values[next_state])\n",
    "    \n",
    "    return q_Value\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mdp_get_action_value import get_action_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "test_Vs = {s: i for i, s in enumerate(sorted(mdp.get_all_states()))}\n",
    "assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69)\n",
    "assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using $Q(s,a)$ we can now define the \"next\" V(s) for value iteration. $$V_{(i+1)}(s) = \\max_a \\sum_{s'} P(s' | s,a) \\cdot [ r(s,a,s') + \\gamma V_{i}(s')] = \\max_a Q_i(s,a)$$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "-------------------------\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def get_new_state_value(mdp, state_values, state, gamma):\n",
    "    \"\"\" Computes next V(s) as in formula above. Please do not change state_values in process. \"\"\"\n",
    "    if mdp.is_terminal(state): return 0\n",
    "    \n",
    "    return max(\n",
    "        get_action_value(\n",
    "            mdp, state_values, state, next_action, gamma\n",
    "        ) for next_action in mdp.get_possible_actions(state)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_Vs_copy = dict(test_Vs)\n",
    "assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8)\n",
    "assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69)\n",
    "assert test_Vs == test_Vs_copy, \"please do not change state_values in get_new_state_value\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's combine everything we wrote into a working value iteration algo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1fc1c8982e8>"
      ]
     },
     "execution_count": 0,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter    0   |   diff: 3.50000   |   V(s0) = 0.000   V(s1) = 0.000   V(s2) = 0.000\n\niter    1   |   diff: 1.89000   |   V(s0) = 0.000   V(s1) = 3.500   V(s2) = 0.000\n\niter    2   |   diff: 1.70100   |   V(s0) = 0.000   V(s1) = 3.815   V(s2) = 1.890\n\niter    3   |   diff: 1.13542   |   V(s0) = 1.701   V(s1) = 4.184   V(s2) = 2.060\n\niter    4   |   diff: 0.73024   |   V(s0) = 1.854   V(s1) = 5.319   V(s2) = 2.871\n\niter    5   |   diff: 0.61135   |   V(s0) = 2.584   V(s1) = 5.664   V(s2) = 3.540\n\niter    6   |   diff: 0.54664   |   V(s0) = 3.186   V(s1) = 6.275   V(s2) = 3.989\n\niter    7   |   diff: 0.49198   |   V(s0) = 3.590   V(s1) = 6.790   V(s2) = 4.535\n\niter    8   |   diff: 0.42210   |   V(s0) = 4.082   V(s1) = 7.189   V(s2) = 4.959\n\niter    9   |   diff: 0.36513   |   V(s0) = 4.463   V(s1) = 7.611   V(s2) = 5.352\n\niter   10   |   diff: 0.32862   |   V(s0) = 4.816   V(s1) = 7.960   V(s2) = 5.717\n\niter   11   |   diff: 0.29262   |   V(s0) = 5.145   V(s1) = 8.280   V(s2) = 6.032\n\niter   12   |   diff: 0.26189   |   V(s0) = 5.429   V(s1) = 8.572   V(s2) = 6.323\n\niter   13   |   diff: 0.23503   |   V(s0) = 5.691   V(s1) = 8.830   V(s2) = 6.584\n\niter   14   |   diff: 0.21124   |   V(s0) = 5.925   V(s1) = 9.065   V(s2) = 6.817\n\niter   15   |   diff: 0.19012   |   V(s0) = 6.135   V(s1) = 9.276   V(s2) = 7.028\n\niter   16   |   diff: 0.17091   |   V(s0) = 6.325   V(s1) = 9.465   V(s2) = 7.218\n\niter   17   |   diff: 0.15366   |   V(s0) = 6.496   V(s1) = 9.636   V(s2) = 7.388\n\niter   18   |   diff: 0.13830   |   V(s0) = 6.649   V(s1) = 9.790   V(s2) = 7.542\n\niter   19   |   diff: 0.12445   |   V(s0) = 6.788   V(s1) = 9.928   V(s2) = 7.680\n\niter   20   |   diff: 0.11200   |   V(s0) = 6.912   V(s1) = 10.052   V(s2) = 7.805\n\niter   21   |   diff: 0.10079   |   V(s0) = 7.024   V(s1) = 10.164   V(s2) = 7.917\n\niter   22   |   diff: 0.09071   |   V(s0) = 7.125   V(s1) = 10.265   V(s2) = 8.017\n\niter   23   |   diff: 0.08164   |   V(s0) = 7.216   V(s1) = 10.356   V(s2) = 8.108\n\niter   24   |   diff: 0.07347   |   V(s0) = 7.297   V(s1) = 10.437   V(s2) = 8.190\n\niter   25   |   diff: 0.06612   |   V(s0) = 7.371   V(s1) = 10.511   V(s2) = 8.263\n\niter   26   |   diff: 0.05951   |   V(s0) = 7.437   V(s1) = 10.577   V(s2) = 8.329\n\niter   27   |   diff: 0.05356   |   V(s0) = 7.496   V(s1) = 10.636   V(s2) = 8.389\n\niter   28   |   diff: 0.04820   |   V(s0) = 7.550   V(s1) = 10.690   V(s2) = 8.442\n\niter   29   |   diff: 0.04338   |   V(s0) = 7.598   V(s1) = 10.738   V(s2) = 8.491\n\niter   30   |   diff: 0.03904   |   V(s0) = 7.641   V(s1) = 10.782   V(s2) = 8.534\n\niter   31   |   diff: 0.03514   |   V(s0) = 7.681   V(s1) = 10.821   V(s2) = 8.573\n\niter   32   |   diff: 0.03163   |   V(s0) = 7.716   V(s1) = 10.856   V(s2) = 8.608\n\niter   33   |   diff: 0.02846   |   V(s0) = 7.747   V(s1) = 10.887   V(s2) = 8.640\n\niter   34   |   diff: 0.02562   |   V(s0) = 7.776   V(s1) = 10.916   V(s2) = 8.668\n\niter   35   |   diff: 0.02306   |   V(s0) = 7.801   V(s1) = 10.941   V(s2) = 8.694\n\niter   36   |   diff: 0.02075   |   V(s0) = 7.824   V(s1) = 10.964   V(s2) = 8.717\n\niter   37   |   diff: 0.01867   |   V(s0) = 7.845   V(s1) = 10.985   V(s2) = 8.738\n\niter   38   |   diff: 0.01681   |   V(s0) = 7.864   V(s1) = 11.004   V(s2) = 8.756\n\niter   39   |   diff: 0.01513   |   V(s0) = 7.881   V(s1) = 11.021   V(s2) = 8.773\n\niter   40   |   diff: 0.01361   |   V(s0) = 7.896   V(s1) = 11.036   V(s2) = 8.788\n\niter   41   |   diff: 0.01225   |   V(s0) = 7.909   V(s1) = 11.049   V(s2) = 8.802\n\niter   42   |   diff: 0.01103   |   V(s0) = 7.922   V(s1) = 11.062   V(s2) = 8.814\n\niter   43   |   diff: 0.00992   |   V(s0) = 7.933   V(s1) = 11.073   V(s2) = 8.825\n\niter   44   |   diff: 0.00893   |   V(s0) = 7.943   V(s1) = 11.083   V(s2) = 8.835\n\niter   45   |   diff: 0.00804   |   V(s0) = 7.952   V(s1) = 11.092   V(s2) = 8.844\n\niter   46   |   diff: 0.00724   |   V(s0) = 7.960   V(s1) = 11.100   V(s2) = 8.852\n\niter   47   |   diff: 0.00651   |   V(s0) = 7.967   V(s1) = 11.107   V(s2) = 8.859\n\niter   48   |   diff: 0.00586   |   V(s0) = 7.973   V(s1) = 11.113   V(s2) = 8.866\n\niter   49   |   diff: 0.00527   |   V(s0) = 7.979   V(s1) = 11.119   V(s2) = 8.872\n\niter   50   |   diff: 0.00475   |   V(s0) = 7.984   V(s1) = 11.125   V(s2) = 8.877\n\niter   51   |   diff: 0.00427   |   V(s0) = 7.989   V(s1) = 11.129   V(s2) = 8.882\n\niter   52   |   diff: 0.00384   |   V(s0) = 7.993   V(s1) = 11.134   V(s2) = 8.886\n\niter   53   |   diff: 0.00346   |   V(s0) = 7.997   V(s1) = 11.137   V(s2) = 8.890\n\niter   54   |   diff: 0.00311   |   V(s0) = 8.001   V(s1) = 11.141   V(s2) = 8.893\n\niter   55   |   diff: 0.00280   |   V(s0) = 8.004   V(s1) = 11.144   V(s2) = 8.896\n\niter   56   |   diff: 0.00252   |   V(s0) = 8.007   V(s1) = 11.147   V(s2) = 8.899\n\niter   57   |   diff: 0.00227   |   V(s0) = 8.009   V(s1) = 11.149   V(s2) = 8.902\n\niter   58   |   diff: 0.00204   |   V(s0) = 8.011   V(s1) = 11.152   V(s2) = 8.904\n\niter   59   |   diff: 0.00184   |   V(s0) = 8.014   V(s1) = 11.154   V(s2) = 8.906\n\niter   60   |   diff: 0.00166   |   V(s0) = 8.015   V(s1) = 11.155   V(s2) = 8.908\n\niter   61   |   diff: 0.00149   |   V(s0) = 8.017   V(s1) = 11.157   V(s2) = 8.909\n\niter   62   |   diff: 0.00134   |   V(s0) = 8.019   V(s1) = 11.159   V(s2) = 8.911\n\niter   63   |   diff: 0.00121   |   V(s0) = 8.020   V(s1) = 11.160   V(s2) = 8.912\n\niter   64   |   diff: 0.00109   |   V(s0) = 8.021   V(s1) = 11.161   V(s2) = 8.913\n\niter   65   |   diff: 0.00098   |   V(s0) = 8.022   V(s1) = 11.162   V(s2) = 8.915\n\nTerminated\n"
     ]
    }
   ],
   "source": [
    "# parameters\n",
    "gamma = 0.9            # discount for MDP\n",
    "num_iter = 100         # maximum iterations, excluding initialization\n",
    "# stop VI if new values are this close to old values (or closer)\n",
    "min_difference = 0.001\n",
    "\n",
    "# initialize V(s)\n",
    "state_values = {s: 0 for s in mdp.get_all_states()}\n",
    "\n",
    "if has_graphviz:\n",
    "    display(plot_graph_with_state_values(mdp, state_values))\n",
    "\n",
    "for i in range(num_iter):\n",
    "\n",
    "    # Compute new state values using the functions you defined above.\n",
    "    # It must be a dict {state : float V_new(state)}\n",
    "    new_state_values = {\n",
    "        state : get_new_state_value(mdp, \n",
    "                                    state_values,\n",
    "                                    state, \n",
    "                                    gamma)\n",
    "        for state in state_values\n",
    "    }\n",
    "\n",
    "    assert isinstance(new_state_values, dict)\n",
    "\n",
    "    # Compute difference\n",
    "    diff = max(abs(new_state_values[s] - state_values[s])\n",
    "               for s in mdp.get_all_states())\n",
    "    print(\"iter %4i   |   diff: %6.5f   |   \" % (i, diff), end=\"\")\n",
    "    print('   '.join(\"V(%s) = %.3f\" % (s, v)\n",
    "                     for s, v in state_values.items()), end='\\n\\n')\n",
    "    state_values = new_state_values\n",
    "\n",
    "    if diff < min_difference:\n",
    "        print(\"Terminated\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1fc14a58be0>"
      ]
     },
     "execution_count": 0,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if has_graphviz:\n",
    "    display(plot_graph_with_state_values(mdp, state_values))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final state values: {'s0': 8.023123818663871, 's1': 11.163174814980803, 's2': 8.915559364985523}\n"
     ]
    }
   ],
   "source": [
    "print(\"Final state values:\", state_values)\n",
    "\n",
    "assert abs(state_values['s0'] - 8.032) < 0.01\n",
    "assert abs(state_values['s1'] - 11.169) < 0.01\n",
    "assert abs(state_values['s2'] - 8.921) < 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Now let's use those $V^{*}(s)$ to find optimal actions in each state\n",
    "\n",
    "$$\\pi^*(s) = argmax_a \\sum_{s'} P(s' | s,a) \\cdot [ r(s,a,s') + \\gamma V_{i}(s')] = argmax_a Q_i(s,a)$$\n",
    "\n",
    "The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_optimal_action(mdp, state_values, state, gamma=0.9):\n",
    "    \"\"\" Finds optimal action using formula above. \"\"\"\n",
    "    if mdp.is_terminal(state):\n",
    "        return None\n",
    "    next_actions = mdp.get_possible_actions(state)\n",
    "    q_values = [\n",
    "        get_action_value(\n",
    "            mdp, state_values, state, action, gamma\n",
    "        ) for action in next_actions\n",
    "    ]\n",
    "        \n",
    "    return next_actions[np.argmax(q_values)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1'\n",
    "assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0'\n",
    "assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0'\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1fc1c891160>"
      ]
     },
     "execution_count": 0,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if has_graphviz:\n",
    "    try:\n",
    "        display(plot_graph_optimal_strategy_and_state_values(mdp, state_values))\n",
    "    except ImportError:\n",
    "        raise ImportError(\"Run the cell that starts with \\\"%%writefile mdp_get_action_value.py\\\"\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average reward:  0.9035\n"
     ]
    }
   ],
   "source": [
    "# Measure agent's average reward\n",
    "\n",
    "s = mdp.reset()\n",
    "rewards = []\n",
    "for _ in range(10000):\n",
    "    s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma))\n",
    "    rewards.append(r)\n",
    "\n",
    "print(\"average reward: \", np.mean(rewards))\n",
    "\n",
    "assert(0.85 < np.mean(rewards) < 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frozen Lake"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*FFF\nFHFH\nFFFH\nHFFG\n\n"
     ]
    }
   ],
   "source": [
    "from mdp import FrozenLakeEnv\n",
    "mdp = FrozenLakeEnv(slip_chance=0)\n",
    "mdp.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def value_iteration(mdp, state_values=None, gamma=0.9, num_iter=1000, min_difference=1e-5):\n",
    "    \"\"\" performs num_iter value iteration steps starting from state_values. Same as before but in a function \"\"\"\n",
    "    state_values = state_values or {s: 0 for s in mdp.get_all_states()}\n",
    "    for i in range(num_iter):\n",
    "\n",
    "        # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)}\n",
    "        new_state_values = {\n",
    "            state: get_new_state_value(\n",
    "                mdp, state_values, state, gamma\n",
    "            ) for state in mdp.get_all_states()\n",
    "        }\n",
    "\n",
    "        assert isinstance(new_state_values, dict)\n",
    "\n",
    "        # Compute difference\n",
    "        diff = max(abs(new_state_values[s] - state_values[s])\n",
    "                   for s in mdp.get_all_states())\n",
    "\n",
    "        print(\"iter %4i   |   diff: %6.5f   |   V(start): %.3f \" %\n",
    "              (i, diff, new_state_values[mdp._initial_state]))\n",
    "\n",
    "        state_values = new_state_values\n",
    "        if diff < min_difference:\n",
    "            break\n",
    "\n",
    "    return state_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter    0   |   diff: 1.00000   |   V(start): 0.000 \niter    1   |   diff: 0.90000   |   V(start): 0.000 \niter    2   |   diff: 0.81000   |   V(start): 0.000 \niter    3   |   diff: 0.72900   |   V(start): 0.000 \niter    4   |   diff: 0.65610   |   V(start): 0.000 \niter    5   |   diff: 0.59049   |   V(start): 0.590 \niter    6   |   diff: 0.00000   |   V(start): 0.590 \n"
     ]
    }
   ],
   "source": [
    "state_values = value_iteration(mdp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*FFF\nFHFH\nFFFH\nHFFG\n\ndown\n\nSFFF\n*HFH\nFFFH\nHFFG\n\ndown\n\nSFFF\nFHFH\n*FFH\nHFFG\n\nright\n\nSFFF\nFHFH\nF*FH\nHFFG\n\ndown\n\nSFFF\nFHFH\nFFFH\nH*FG\n\nright\n\nSFFF\nFHFH\nFFFH\nHF*G\n\nright\n\nSFFF\nFHFH\nFFFH\nHFF*\n\n"
     ]
    }
   ],
   "source": [
    "s = mdp.reset()\n",
    "mdp.render()\n",
    "for t in range(100):\n",
    "    a = get_optimal_action(mdp, state_values, s, gamma)\n",
    "    print(a, end='\\n\\n')\n",
    "    s, r, done, _ = mdp.step(a)\n",
    "    mdp.render()\n",
    "    if done:\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#Let's visualize!\n",
    "\n",
    "It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "def draw_policy(mdp, state_values):\n",
    "    plt.figure(figsize=(3, 3))\n",
    "    h, w = mdp.desc.shape\n",
    "    states = sorted(mdp.get_all_states())\n",
    "    V = np.array([state_values[s] for s in states])\n",
    "    Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states}\n",
    "    plt.imshow(V.reshape(w, h), cmap='gray', interpolation='none', clim=(0, 1))\n",
    "    ax = plt.gca()\n",
    "    ax.set_xticks(np.arange(h)-.5)\n",
    "    ax.set_yticks(np.arange(w)-.5)\n",
    "    ax.set_xticklabels([])\n",
    "    ax.set_yticklabels([])\n",
    "    Y, X = np.mgrid[0:4, 0:4]\n",
    "    a2uv = {'left': (-1, 0), 'down': (0, -1), 'right': (1, 0), 'up': (-1, 0)}\n",
    "    for y in range(h):\n",
    "        for x in range(w):\n",
    "            plt.text(x, y, str(mdp.desc[y, x].item()),\n",
    "                     color='g', size=12,  verticalalignment='center',\n",
    "                     horizontalalignment='center', fontweight='bold')\n",
    "            a = Pi[y, x]\n",
    "            if a is None:\n",
    "                continue\n",
    "            u, v = a2uv[a]\n",
    "            plt.arrow(x, y, u*.3, -v*.3, color='m',\n",
    "                      head_width=0.1, head_length=0.1)\n",
    "    plt.grid(color='b', lw=2, ls='-')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 0\niter    0   |   diff: 1.00000   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 1\niter    0   |   diff: 0.90000   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 2\niter    0   |   diff: 0.81000   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 3\niter    0   |   diff: 0.72900   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 4\niter    0   |   diff: 0.65610   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 5\niter    0   |   diff: 0.59049   |   V(start): 0.590 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 6\niter    0   |   diff: 0.00000   |   V(start): 0.590 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 7\niter    0   |   diff: 0.00000   |   V(start): 0.590 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 8\niter    0   |   diff: 0.00000   |   V(start): 0.590 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 9\niter    0   |   diff: 0.00000   |   V(start): 0.590 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state_values = {s: 0 for s in mdp.get_all_states()}\n",
    "\n",
    "for i in range(10):\n",
    "    print(\"after iteration %i\" % i)\n",
    "    state_values = value_iteration(mdp, state_values, num_iter=1)\n",
    "    draw_policy(mdp, state_values)\n",
    "# please ignore iter 0 at each step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 0\niter    0   |   diff: 0.90000   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 1\niter    0   |   diff: 0.72900   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 2\niter    0   |   diff: 0.59049   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 3\niter    0   |   diff: 0.47830   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 4\niter    0   |   diff: 0.40894   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 5\niter    0   |   diff: 0.34868   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 6\niter    0   |   diff: 0.29655   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 7\niter    0   |   diff: 0.25292   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 8\niter    0   |   diff: 0.21619   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 9\niter    0   |   diff: 0.18482   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 10\niter    0   |   diff: 0.15757   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 11\niter    0   |   diff: 0.13430   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 12\niter    0   |   diff: 0.11445   |   V(start): 0.000 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 13\niter    0   |   diff: 0.09751   |   V(start): 0.098 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 14\niter    0   |   diff: 0.04772   |   V(start): 0.139 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 15\niter    0   |   diff: 0.03479   |   V(start): 0.173 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 16\niter    0   |   diff: 0.01283   |   V(start): 0.186 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 17\niter    0   |   diff: 0.00734   |   V(start): 0.194 \n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALgAAAC4CAYAAABQMybHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJztnXl4E9fZt29tluR938Bgm9WAwWAIm4NDgJCV7HvSL3tKl6xf2jd536Yp9GrapmmbNm+aNGtp09Cm+dLsJQkQCGEzu42xjY0Bg/dN3iTbWr4/JpYQkm2NdJQYee7r4kJnZvTTyPPM0Zlzzu88KofDgYJCqKL+tk9AQSGYKAGuENIoAa4Q0igBrhDSKAGuENIoAa4Q0igBrhDSKAGuENIoAa4Q0miHO0ClUt0H3CeVIvJhapBPSUFheAyGw5jNZtVwx6nkDNWrVHMdeXm2gE5sgAMH9gOwYMFCIXo7d+4AoLDwAiF6AFu2fAHAypUXC9HbsOE/AFx11dVC9AD+/e93Abj55luE6L311t8BuOeee4XovfLKywA8+OBDQvQGeOutt2hoaBg2wJUmikJIowS4QkijBLhCSDPsQ6av9Ib3Ujujlu6EbmxaG9o+LYYOA2MPjkXfo5ett69wH33GPo/tuV/lEtEZ4dc57lywk15jr8f2/KJ8IrsiZettmb0Fi8HisX3hwYVE90TL1tswbQPmMLPH9gvKLyDWHCtbD+D97Pfp1nV7bL/4+MXE9cbJ1lufup4ubZfH9qsbriahP8Gvc3wt+jU6NZ0e22/puIUkW5JfmgMIC/Dq+dVYYixENkWi79LTb+ynK6GLfkO/XwE+QGxjLIYeg7Os69MFfK7xzfEYzUZhmkmtSRh7XXph1rCA9FJMKUT0uW5ivdX/v98A6V3pRPa5bmK9LTDNDHMG0VbXTWywGYY42jey+rKIscc4y0a7cYijfUNIgFt1ViwxFjR9GiZ8NQEV0sOtXW2HYZ9zhyb5VDLxjfECztJFWl0aic2JwvTGNI4hpS1FmN741vGkm9KF6QFMME1gbNdYYXpTuqeQackUpgcwvW86E/onCNUUEuAaqwZ1vxpbmI3ypeVENUUR0RJBVGMUGpvGeZzKocKhkucgahzbSEd8h7OcWZYZkB5AXVod7bHtzvLEyonSiwEpmTfl6eTTtMa0Oss5x3NcOx3y9U7En6A5stlZnnl6ZkB6AFUxVTQYG5zl/Kb8gDTLI8qp09c5ywtNgXf3Hg47zCntKWe50FwYsKaQAFc5VGTsz6Bmdg2WGAuWGAtNE5sIM4eRvzWf2NZYZrXPoqC5gA2pG9iRsMNn7fbkdrfy/H3zATBYDdxZdidH4o7wacanss63NbHVrbzowCIAVlatJLY3lk+zP6U8odxnvab4JrfykuIlAKSZ0lhetpw94/awK2uXz3oNMQ1u5aWlS52vr95+NS1RLWybsY2m2Kaz3zootZG1buXlR5cDkFOZQ/bJbIpmFVGRVeGzXo2xxq0sIsCrw6rdyiMmwAHiauOIqY8hXZ9OojGRj+Z8RFtkG6pMFT/a8SPncdecvoZaQy17fNSdXjSd5z96ftD9M1tmonFo+ETGud7z8T3cuvtWr/scOLjx8I38ouAXPust3buUJz94ctD9i6oX0aXv4n0f9c47dh6/WverQfcbe41ctPci3lz2ps/neNuu27j7k7sH3V+4u9DjRh2KW4pv4fqN1/PRdR/5/J7hWLt+LV2Lu7BEej64+4uQAHeoHHTHdRPZGkm9uZ56cz3GaiNtuW0cij/Ew3kPk9ORw/L65Xyc/jFVkVU+a/dr+nl8weMe28NsYdx15C5K4kvYmboTdv/QZ80dGTs4ajzqsf3CYxeSYE5gY9ZGrBqrz3ptEW38cuUvPbYndyRz8eGL2Zm9k4rkCijzUVAFz131nNddV26/kqaYJvZO2uvz+QGcGHuCP9/8Z4/tE6snMuXYFHbn7aY1rtXLO70T0x5DbLt/PTtDEWYJG3kBblfbqVxSib5DT7gpHJVNhSnNBEBUUxQAR6KPcCT6iIiPA6BP08eLM14UpgewKXuTUL3G6EbWLVwnVPO9Re8J1avMqqQyq1Ko5khCSICr7WqSKpPoSuyiI6UDu8aOzqwjsTqR5KPJIj5CQcEvhD1kjikZI0LKyZwtc4TqASzYuUCoXuH+wB+CzmRl6UqhegCrjq0SqndT/U0AzD49W5jmXR13AVBQVsCmfLG/ospQvUJIowS4gmyM3UYmlU0CIHdvrhDNhe9K3YyL/99i13iEAJQAV5BNr6EXi8GCTW2jJalFiGZ7cjsOlYP2pPaAR7/PRAlwBdnYNXb2LthLQ1oDtRm1w7/BByrzKzElmjhccFiI3gCyHzI1Gs3wB8lArRZ7j4nWA9BqhY2HAWAwBD4x6WzCw8OF6kVGDj27sjmvmea8ZiLxbRZmdPQwsyujYd939339cviZmL7GoWzLGj6PQSooBI+0tHRqa2sDt6ypVKr7VCrVHpVKtQd8H8pVUBgJyK7B8/OHP84X9u6VfgkWLVosRG/79q8AWLr0QiF6AJs3S32yl112uRC9jz76EICbbrpZiB7A+vVvAXD33fcI0Xv11VcAeOihh4Xo/f73vwPgJz8ZfK6OP7zyyitianAFhXMZJcAVQholwBVCGmH9X8XLiukL9zQJ52zJIbxDfhfW3vP3ejUIz9oxy2/T8Y75O7yahOfumUtUd5RsvU0zN2HWe5qEC0oKiDHHeHnH0Lw/4X16dD0e21dWr/TLIAzwj7R/eDUJX1V/lV8m4VejX6VT7cUg3HkLyTb/Jtb9Qf0HTCqTx/Z7bfeSSqpfmgOI7eAFYupj3EzG2r7APiKuKc7NdByoHkBCS4Kb6TisPzCTcHJ7MuEW100cqElYtEEYvJiE7YH1xWf1uxuEw+2B98NPckwizuG6kcMJXFN4gCfWJBJbL24ifPKpZBKa/FuOYDDS6tJIaglsOYIzyWjKILU9sJrmTLLbs4UahAEmd08m05wpTG9633Qm9k8UpgeQZ89jquC1L4UHeHNGM50Jrp+wjMMZAKT3pJPXmseWlC1e1+kYjLNNx1nlWQBo7BqWn1zOkfgjnIw+KesczzYdT6qSJg5Nr59OuDWcfWn7sGl8X4OxJqmGlijXnIzpNdMBiDJHkV+dz/7M/ZjCPX+CB+NY7DEawxud5TmNrqnDc0rm0BLXwon0E7LmbFREVFCvr3eWF7RLU4eT6pJIq03jyIwj9Ov7fdY72yB8gfkC309mEA6oD3DCccJZXukIfPqw8AA3pbpfyH+s+4dbeUnjEv449Y/4arhqS2pzK//99b+7lRfXLmZ36m62yzjHlgT3CUJ/feWvztcOHBQeL+R3i37ns15jbKNb+fUXX3crz6mew0ezP8JX9+LZBuGX/vCSW9mmslGXVMdHF/ruhzzbJPz8s+4+12nF0/jwmg991qvWuRuERQT4UdVRt5t2pW0EBvj0HdO5ed/NqB1SB82ORMlBn9ueS6Q1ksMxhzHpfK/NpuyfwhUHryDJLDUpdqfsBiRX/cyWmZj0Jo7EH4H6oVTcWVK0hFX7XUaAvenS7ZZfm49NZWN/6n7sKrvPeueVn8d1u65zLvhzcNxBAFLbU0npSOF0/GkaoxuHknCj4FQBhYcLSW+U1kYpnVDq3Detahp9uj5ZDniAy2ouY9VXq1A5pAg6OkXypGZVZqG1aTmRdYJeg+dD/WD8cPsPuebTa3jvIXEWurXr16JboqM7xfdf+OEQHuAWrYV3x73rsf3dce8S3R9Ne1i7l3cNzfZ07/XzBssGTHqT7LVRWo2tfDTFs/b7fMLnqB1qzDrPnpGhsKltbMnZ4rnDATHmGFnNkwGqxldRNd7TnL13+l4segt2je83IIDFaGH34t0e24sWFqG36DFHyPvO5wrCA3ww7Cq7X8E9FO0GsXq9Wt9rMJ9Q4VdwD0VPuGc3YiDYNfaQDW5QBnoUQhxhNXjuRjHWpQHyvxQ0q+sMFu4Sk01igAsPiZvYBbCqSqxBGODGuhuF6t3dIS0eNKt2ljDNB+wPAJLpeNcS31cA8wWlBleQjdqqJqNU6v5NqBEzRpG2Pw2AsXvE9v8rAa4gmzBLGBq75KhJOC0mwFNKpNV5E8sTFdOxwreLJdLCiWknsGqtHJt9TIhm1TKpx6jqwiqhpuNvrBdFIbQoKSyhfH45Vr3vazgORWd6Jzu/uxNzgtgeHcWTqXBOMnZsBjU1NYonU2F0860ngp07d54QvT17igBxHk9w+TzFNQqlv/V3vvN/BOnBunV/AWD16u8J0fvTn14A4MknfypEb82anwHw7LO/FaI3wO9+9zsxNbiCwrmMEuAKIY0S4AohjbBuwsMXHaY/3HPC/OTNkwk3ybceHbrwkFeP57St0/zyeIJgn+dDQCywHldqkkzgDsACeGY0GZZ3Mt7xaga5/NTlxPf5l0rxb4l/85pk9fqW60m0yk+l+JzqOa/+yfvs9/ntn/x5189pc7R5bH8k/BHGaAJbd154P3h0fTRh3S6Po7Y3sI+IaYhB3y3O4wnB8XmKZGz3WKKsLhO0iCSr43vHC/VkTnJMIh7XTSfCPzlNM40EtWtkNFIlP/v02Qi/svEn4omtE+fJTDyZSFyDf47ywQiGz1MkEzsnMq5nnFDNHHMOWb1ZwvRmO2YL90+epzuPXJ3YSXvCA7x1fCtdia5lCsYWS5Nn1A41cX1xtOjlrSfdPM7d4zmuNPALP5jP0y9mIzVNAB8WRfWJyqhKt6St81pcXakRXRFYjBZZnlGAI8YjnNaddpYLugoAaeKUwWygJ0rePPP9qv2cQKx/cnf/bqpsLpPHVYarAtYUHuAdqR1u5R9/+GMAZphmYLAbKI4u5u2Mt33WM6W4t/dEBPjZPs+AAnxKgCfjhVMRp9zKj7z3iPP1xGMT6Q3rpWhOEUcne6ZCHIwT+hNwxuoTA5qZFZnS/okn2Ldkn896R1Xuny0iwEttpXDGfTsiA/z8zeezZsuaQfdP7ZxKVL/vi+xctOkiHt/6OI/NfUzE6QGS969CXUFVrO/5OgfF20NmgFxQdwGr31lNcrP3hXS0Vi1ZJ7JkBfhtpbdx9z8HTwQ75vgYSuaX+Kz3/ZLvc92/rmPzk5t9fs9wrF2/lrir4uhNEuesEh7gNeE1PJznuTJpmjmNme0z+TLpS3q0vv8cinjA+iZ1haCCjy717pifUTyDtvg2Tqef9rp/MJrTm/nn6n96bE+oSyC5NpmjuUexhvk+cUrXo5P1+b6isgqcSsg3OJuwzlhHnbHum/q4kKUk1/da1hda0lpoSROTZ2ckogz0KIQ0wmrw6Z9OFyUFwMxNMwGYWC9uebABn2dBWQF/n/L3YY4eht972XYceMp/yWtrrvX/zYNwW/NtQvUedDwIDphcP1mY5v9E/g8Ac8rmUHp56TBHy2PE1+CxfVKferhVTJKliD5pxDKmV/7qrwouDCbpGUZjEZOUTGeS2vRhbYEthHo2IzrAjVYj5zeeD8Cqk2Ic59dWSrXkZccvQ2sfWSOY5wqGNgMJVdJAWebWTCGa2a9nA5D11yyQt6bRkIzoADdrzVRGVWLHTlFikRDNPSl7cOCgJL4Eq1qM3Wq0YYm10JXUhUPloH6mjDXzhqB5QTMOHLTmtwqNyhFfhb2X8R6z2mZRFSWgzxo4En+EbenbnGscKviBCsqvKCf2eCzdqWLWEWyZ14Kh3kDDhQ3DHywDxZOpcE6SmZlFdXW14slUGN3IrsHnzhUz0jTgoSwoOF+I3rZtXwKwfPkKIXoAn3/+GQCrVl0pRO/996Wlhu+88y4hegCvv/7a16/E+kZ/+1vf10cfikcekUa133jjL0L0BnjqqafE1OAKCucySoArhDRKgCuENEqAK4Q0wvrBRZuEixYXeTUI5+3MI7LLP6/etrnbvCaCnb9/vl+JYD+b/pnXRLCFRwr9SgT79pi3vSZtXVW7yq+krcEwRq/tXOvVIPxoxKN+G4QfrXmUFpvnjMafpf2M8frxfmkOID4RrGCTcFxTnFvSVl1/4POQE1sThWqmmFKI6HW58geSUflLRk+Gu+k4QINwMJimdTcIR6j8yz59JrOMs0jWukwe0ZrAPYDiE8EKNgmn1qYKNwin16eT3Opf2mlvjGseR5opTZjepK5JjDcHVnMFm/m6+cINwksil5AfITazh/hEsIOYhHPac1hRu4JPxn7C0SjfrVb16fWY4ly+zOwKaVKO3qrnjpI7KE0oZWf6TlnnWJtaS1uM62d2SrVkrFx6dCkJPQlsnriZlgjfTQAnE0+6JYKdcWoGAEmmJC7afxFFk4o4mu77dz4aeZR6g2uOx/y2+T6/1ytBMEbv6t9Fpa3SWb7acDUA2g4tE16eQMu8FloWyjNSbO3aSpmlzFm+NeHWgM9TfCLYlKETwd5XcR8vTn7R5wH/tqQ22nAF45uvvem2P70rnTFdY5DjDGyOb3Yrr3t5nfO1AweTmybz66W/9lmvIcZ9/sSrL7zqVr5s72Vs7t2Mrxkla8Ldk7YGHOBBMEaXWt3nba95wt2HazxtxNhgRA4HzQfdyiMywCftnkT2yWxn+ZczpCeZ3LZcChsK2ZC+geORx33WyzmYQ+apTOfU1t/mS6uUGmwG7ii5g7L4MjaN2wQt3/dZc07JHLJrXef4v4v+F4AVFSuIM8excdJGWTMN51XOY2qda42Q15ZJo4sp7SksO7iMfRP2UZpRCj66zS49cSmPvf4Y6+5cN/zBvhAEY/SdxjuZ0zUHlU0aTDz8xGFAmted/Vo2bXPaqF9RDzt811y7fi3Zt2bTn+F7SvHhEB7gdpWdFoPnT9MXaV/wReoXfo0od+o9lx4DeHr+037pWdVW2sM9c2y+Pevr5SzkaqrAFOG5nJkpwkRFeoXQlBwjif44z0DsS+yj+OfFI+Y7f7PTZUV/6ZGuFyzNkc4I+s7KQI9CSCOsBh8wCYti3ldiMj+cScGeAqF6Kw6Lm7kIcP3p6wGI7Ah80UkgKMbon0T9xP83D8KzGc8CML5sPLXUCtVWavCRhgPO3ypNIV705aJv+WS+OeJfl1aqTXw5cfR4MkclKsAhdVeqHCOoMRts7NJ3duAQ2oZXAnwEsnfeXqxaKwdmH/i2T+Ubw3SVCYfBQftN7Uoi2FCnMbWRt25/69s+jW8UW4KNmhdrhj9QJorpWOGcZOLESRw9elQxHSuMbmTX4LNmiVks5+BBqX05GhPBPvro/xWkB88++xsA1qxZK0TvySelbsAXX3xJiN53v3s/AB988KEQvQEefvhhMTW4gsK5jBLgCiGNEuAKIY2wbsLSi0rpj/CSCHbTZIwmefOCYXQmgn054mU61B0e22/vvp1ku38OpN/af0s7njMnV6tWk6aS70J6ovEJWu2tHtv/O+G/ydBl+HWOdxffTWNfo8f253KeIzs828s7fEd8Itg6JRFsoGRbs4m1u3KNGh3yK4izmcxkt8StEQTmoczV55KkSXKWI9WBz5+ZFzOPNL3rpovRBr6Ge1ASwcbUiVtcfjQmgp3RP4NJ1klCNfNV+eSocoTpLTYuJs+QJ0wPYEXiChbGLhSqGfREsGOKpaUEYvpimNg1kf1x+7GrzppN44AcUw7tunbqItwTVfmbCDbOEkdGRwaHkg559PKN9ESwJboSTmlcuTKX9i51vk6tSKUroYuuBM/lJYZir2Mv1Y5qZ/lS9aUAGFoMRNZF0jytWdYT2Vfmr6joq3CWb4i+QXphhejd0XTP6MYWLS9Z7WfNn1HS6bI93Ztxr6z3e0N8Itg09zbk239zT/p6Zd2VPD/heWdZb9PzQOkDJPe6tzFvKriJhvAGvxLBrjixgsW1i9E5dNxYeaNL87ybaDA2jPhEsMe0x9zKz/7iWbeyTWPjdM5pDq085LNmBRVu5aeffNqtbImxcPAed0/kUBT3FruVf/Ij92m0dp2dxus929VDUWRyT3IwIgM8b2sej3/1OHqb1G42aaUAjbFKzZZuTTdWlWuwyIGDjrAOZ4B36Dqc2wH+6+3/4mTfSSpi3C/QUHTrunGoHOCAHm0PNpXNTfM7n3yHKnWVdEygBMHvuKpnFZdvuZyMEumhzRLhWqzI0C09O/RGyEuWemfrndyw7gbUVqma7ouUHuDDuqTnpf6Ifhwa3/8eqyNXc+m6SzEcl87HGi1dU22HFFIOrQNbhLwafO36tcz5/hzsmeLmywoP8Pawdn4x9Rce2402I2PMY6iMqHRrMvRp+nhpykuM7R5Ll7aLdn27Uwfg7cy3ZbfBt6dvZ1/yPtK606iOcf0sm/TSzbYrddeIboOjgvKCcsoLyj12xZ2Ooye2R3aAWxIsFD3imQZG16XD2GKkY7xn781QOLQOTn/PSzJaO4QfCcc8yYwjzAEvy5IVzjfWfWDWmKmMrBx0/9n52QPForW4BXeo0DbGc9m0QOiP7Kc/UpyLHTX0TPc9k3WwUQZ6FEIaYTX4tE+niZICxHs8wZUIVghB8Dve2x34Q9XZPKJ+RKjeL5I9m5+B8mqutFBS5FOR9CC29ldqcIURgaZYSiir2ScmsewASoArjAjC3pB6c8L+EaaYjhVCj75bpW7Lvhv6RlciWIXRgW22DfMTZmyz5fWdD4fiyVQ4J8nJmUZpaaniyVQY3ciuwadMkTfJZzDKywfGt8X6HcWu/Chp3n//d4WovfTSiwA8/vgTQvQAnn5a6rZ77rk/CNF78MEHvn4l9rrs2bNXkJ7E7bffLqYGV1A4l1ECXCGkUQJcIaQR1k1YdUUV1kjPNVPGfzIeQ7vMNHhB8DsGQ/PNpDe95rW8tulaEq2JsvVeCHsBk8ozU8RdfXeR4kiRf4LAz0w/8+qhfCzqMcZqx8oTC8Z1Aa7YeAV15jqP7W+e/yZTYgKbcC+8HzzidIRzjjGAplfs0OtIZJxlHNE2l53HaA/MQznRNpFYh8uTGe7wz2R9JtN100lUu246ER5K0ZyffD5jI1w3XVxY4FZF8Ylgq2KIOi0/a/C5zNSeqWT1BuAKOotZ9llMtk8WpgewIGwBM8PET2ATyZXjruSC1AuEavod4Fq71msmMtMEE+YUV3rr5H0BJFwNgt8xGJpl4WXU6l2ZCRZ3uJaPU1vV2LXyJlccVB/khOqEs7zC5sokobaqsWvssnvxdvbtpNLqmo9/Tfg18gTOJBjXBXjv5HvsbXF1Jz46/dGANWUHeFx/HFc2XcmCzgW8n/A+dXqp7VTjqMGKle4x3XTT7Tw+oAAPgt8xGJonDSfdyjcekHygCY0J5BzMoWpqFcXzir291SuVGndjyK2HXfkiZ743k67ELsqXl9M23nfzw+H+w27lgAI8GNcF+LLxS7fytxLgczvmMr9TSky6qmWVc/tm22Z66GHt+rV8bvmcen39YBK+EwS/YzA0r62+lh/85QeD7p9QNoGWJN+z/l7bdy2rf70ajdX780tUUxRTNk5h512+Z3j+6fs/ZVLmJFoK5WUf9kowrguSJ3PlMytRp4nr3JMd4J/Ff8Zpw2mWti1lfcp6WnTSH6xFK/3/p/Q/jbo2eGdMJ+vvX++xPaotitk7Z1M2q4zG9Eb40subvaGCjY9t9Lprxvsz6EzppGaOvMXitT1awk+G04KAAA8ijm4BRvAzkN8GV0FpRCmlEaXDHzvK6YzrZOslW4VqlqzyMV2yAqAM9CiEOMK6CSd8MEGUVFD8jsHQvLXp1uEPksH3+r4nVA/gpzE/BWBm2Uza5gboyA/GdQE+WPYBAJ1PeU/ZHghKDT4a+LqXUmUduWkJHf1ft709FxQOCCXARwHJ/5G6amMPxBLWHDbM0d8OPat7nP877OIeNJUAHwV0T+7GrrHTH9VPX5zgKlIQ2oVaUINmngaVWtwvjeLJHAV0T+ymfU47HTM6YIRODQq7KQzbXhuGH8icmDcMSoCPEk7dJnZpPNGoIlSEvxD4pDIPXcV0rHAukpc3m/379yumY4XRTciZji+55FJBevDJJx8DcMMNNw5zpG/885//+PqVeGP0v/71jhC166679utXYq+LySRveebhKCwsFFODKyicyygBrhDSKAGuENKMHtMx8EXeF5j1Zo/ti4sXE90j35ry4cQP6QnzXM96RdUK4nr98BMG4XuvLl9NU79n58AzE54hyyjTZhek65L7ai4nO056bP/y1i+ZmRyYzW5Umo6T2pIIt7j6XMP6Axu+TutMI7LPZeIdSMA1ksiPyic1LNVZjtYK9JoJ4uKsi8mKdd10ieHyVyY4m1FpOs5oyiClzb9lGLyR3Z7NmM4xwvSCwbK4ZZwXfd63fRpDcvuM27l84uVCNYUH+Ig3HQM1STW0RLmcLdNOSulX8k7kEdkbSVFWEb069yxmsR2xzDkyh4OTD9IS5+6KORZ7jMZwV07I2Q2zAzvBIHzvjW0bOdzt8mXemXan/2JBui5/Lfkr205tc5Z/eYGfbZ4zEB7gI950DDTFubdJ33jpDedrBw7mHp/LH5f90bltbP1YLt96OSpUTDnhOqktD22hJ6yHuij3RWsCDvAgfO+9ne6LXwYU4EG6Lv+p/o9beUQG+Nr1a0k/ns6vx/86cLEgmVuXHFxC4ZFCZ3nT1E0ALKpcBMD2CduxqV0LsbfEtlCWWUbO8RxqUmo4mSo9EA3U8jfvuhmVUYVV6/mQ7RdB+N5r169lXvI8uh4QMFAXRNPxva/di3F6YAsnnUlQJluphI7UiafL2MWeLM85NfvH7UeFCqvGPVDNBjNfnPcF2/O206frcw7y9emkqacn00+O+Db4aEWZTXgGNs3Q6TP6wkbmXGqFwVEGehRCGuGm44LyAqoNAabQDpK59YIDFwQmcBaXV4rt0grG9/7TlD8BkFCWQG+yvPz2HgTpuhTfLa36te+pfYEJeUFoDZ7dkw1AliWLKOvI7gsfTej26gDQb9WD50DuiKD+99JKaHW/rEPODNfhEBrgZ66JHW4X785Q8A9NnTSa7FA5UJlHZgdA13apd6dnf48r3ZIAhAZ4UVQRbdo29kfupyGsQaS0QgBYVliwR9jpXd6LI17s0miiGPPUGFDBmDVjRq7p2KFysCZzDVaVoP5gBTHoof35dhz6kRlrBvLFAAAFLUlEQVTcAMZpRnLLc9Emie3YUzyZCucoKhwOh+LJVBjdyK7BZ87sF/LBhw4dBGDu3HlC9PbsKQKgoOB8IXoA27YNrHcs1p/4wQcfCtKDK66QuiqLi8WsOpubOwMQ56GMiRmYjSX+4VZIDa6gcC6jBLhCSKMEuEJII6xP5sjKI/RHeLbPJ22chNEkf/rjoQsP0RfuOblp2tZphHf4N4hUtLiIXqPncHXezjwiu2TmjQyCP/Hu4rtp7Gv02P5cznNkh2fLFwRWfrKS2p5aj+1vL3ubqbFTZesFxT85BigAMgAj0AM0InXYHfFPcgDhswmj6qLQd7s8idrewD4ipiHGXa8v8FOOa4rDaHbddLp+XcCaIpkXM480fZqzHKONCVizMLWQjMgMZzlOH1iSVWH+yWnAdUhtiSagAtAjBX0uIy/A44/HE1MX+AUZIPFkInENgWe8PZPU2lQSmhKEaopkReIKFsYuFKp5debVLBuzTJieEP+kDrgcKbiLgXdxLtaPCgjccyw+wFszW+lOclnW0g+lA6Cz60ixpHAqXN4qp83jmulMcKW2GFc6zvl6bPdY6o31XhPS6mw6Es2J1EV65kCvT6/HFOfKCZ9d4d/PPxAUf+JnzZ9R0unq9rs3417na/VxNfZEO8hsUb17/F32NLsG6X4868cA2Dvt2GvtaKfIC4XB/JMOh4OePT2E54Wj0g3Ti5cBDLQ2t+AKbpB6VAUMuwgP8M60TjpxBeQz7zwDQKY5E4Dq8GreGPeGz3qmFJNbeUDPYDOQbEmmR9PDO+PfcRtfnVM/h0uqL8FgM1AXUeecOlA2r4xeYy9tSW204cpXE1CAB8GfWGQqcis/8PsHnK81FRocegd9N/fRf63vYxJb6re4le//1f0AWIulv41ugY6oX/s+A/Rs/+Qda+4AoL+un/7afrRJWsa9MI4h7/qIM163f/3/cqT2+ABP+XxKXhEe4As2L+DpLU8Puj/VkorB7vtCQFN2TWHNpjUk93o3L4fZw0jrSXPbltqditYufbW0btc+jUOaVffQvx/iQPgBrzW/bILgT3wi6wmWPr8UbdEgl8cG6qPyOsB+E/4b8n+U7yxbcf/u1jIrDrPvg37rlq4j6/osrI2STg/uCyDZ2m30Vgwz/7z7jNfRQCtwEjgEBLbejxPhAV5nqOPBmQ96bE/oTSCnM4dd8bvoV/te81jVVp7JfcZju9quZmHTQspjymk2NEP9z537Pp7wMXtS95BpyqQorQiHSrpw7XqpmtiQtWFEt8FRg+VJi9dd2s+02MfbsU+2e90/GNqZWhKLPRu1/RX9WA9ZMVxpGL5JcQaaSA0zj3pGod1sp+m1JmKviEU/Tg//PYRIDVKPSThwPvAe0kNmByM3wAejRd/CNv224Q/0EbvazlcpXw26vzGikcYIzy63cx3rCrEzNXWTdegmi+tFUhvVpHzfx0WV+oGPgWuQnmXSgFOAuD4KxXSs8C1TglRjL0Z66JyN1HSpBAQk0xYW4DkbckRJATBzk6DfqDOY95WYiV1AUPyJr+a+6v+bB2HDJRuE6g34J4Vy8ut/QUAZqlcIaZQAVwhplABXCGmUAFcIaZQAVwhpZFrWVJ1AucDPTwSaR7BeMDRH4zkG4zuPdzgcScMdJLebsNzhcMz184Q8UKlUe0ayXjA0R+M5BuM7+4rSRFEIaZQAVwhp5Ab4nwV//kjXC4bmaDzHYHxnn5D1kKmgcK6hNFEUQholwBVCGiXAFUIaJcAVQholwBVCmv8PlOeMEqQo1HIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 18\niter    0   |   diff: 0.00255   |   V(start): 0.196 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 19\niter    0   |   diff: 0.00125   |   V(start): 0.197 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 20\niter    0   |   diff: 0.00042   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 21\niter    0   |   diff: 0.00019   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 22\niter    0   |   diff: 0.00006   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 23\niter    0   |   diff: 0.00003   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 24\niter    0   |   diff: 0.00001   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 25\niter    0   |   diff: 0.00000   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALgAAAC4CAYAAABQMybHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJztnXl8VNXd/9+zZWay7xsEkhCWsBN2iAQExAVw37U/d0sXtfrz6aPPU2uhL221au3jY7WupbVirT/rghYtKIgIhD0BkpCwJJB93yaZzPL745oZhpkkc2fO6DC579fLl/fce+eTO9zvPXPuOedzviq73Y6CQqii/r4vQEEhkCgBrhDSKAGuENIoAa4Q0igBrhDSKAGuENIoAa4Q0igBrhDSKAGuENJohzpBpVLdA9wjlSJmwoQAX5KCwtAYDIcxmUyqoc5TyRmqV6lm2fPyxAzt79u3F4B58+YL0du58xsACgoWC9ED2Lr1SwBWrLhYiN6mTf8C4IorrhSiB/DPf74PwI033iRE7+23/wbAXXfdLUTv1VdfAeD++x8QotfP22+/TV1d3ZABrjRRFEIaJcAVQholwBVCmiFfMr2lN7yX05NO0xXfhVVrRWvWYuwwknEoA323XrbevoJ9mI1mt/1Tvp5CREeET9e4c95Oeo29bvtnFs4ksjNStt7WGVvpMfS47Z9/cD7R3dGy9TZN3IQpzOS2f3HpYmJNsbL1AD7M/pAuXZfb/otPXkxcb5xsvQ2pG+jUdrrtv7LuShL6Eny6xtejX6dD0+G2/6b2m0iyJvmk2Y+wAD8++zimGBNRDVHou/SYDWY6EzrpM/T5FOD9xNbHYug2OMo6s87va41vjMdoMgrTTGpOwtjr1AuzhPmll9KWQoTZ+RDrLb7/+/WT3plOpNn5EOut/mlmmDKItjgfYoPVMMjZ3pFlziLGFuMoG23GQc72DiEBbtFZMMWY0Jg15HyTgwrp5damtsGQ77mDk3w6mfj6eAFX6SStJo3ExkRheiPqR5DSkiJMb3TzaNLb0oXpAYxpG8PIzpHC9MZ3jSezJ1OYHsAk8yTG9I0RqikkwDUWDWqLGmuYlZKCEqIao4hsiiSqIQqNVeM4T2VXYVfJ62asH1lPe3y7o5xZkumXHkBNWg2tsa2Ock55jrTRLyXzoTyTfIbmmGZHOfdkrvOgXb7eqfhTNEY2OspTz0z1Sw+gIqaCOmOdozyzYaZfmqURpdToaxzl+W3+d/ceDjvMae1pR7nAVOC3ppAAV9lVjD4wmspplZhiTJhiTNSPqSfMFMas7bOIbY5lWss0FjYs5LO0z9iZuNNr7dbkVpfy3H1zATBYDNxecjtH447yWcZnsq63ObHZpbzgwAIAVlSsILY3ls+yP6M0odRrvYb4BpfyoqJFAKS1pbGsZBl7Ru1hV9Yur/XqYupcykuOLHFsX7njSpqimtg+eTsNsQ3nfnRAqiOrXcrLji0DILc8l+zKbAqnFVKWVea1XpWxyqUsIsBPhJ1wKQdNgAPEVccRUxtDqi6VRGMiG/M20hLZAqPg4a8fdpx35ekrqTHWsNtL3UmFk3hh4wsDHp/aNBWNXcOnMq71rk/u4ubdN3s8ZsfO9Yev54n8J7zWW7J3CY999NiAxxecWECnvpMPvdSbc3wOv13/2wGPG3uNXLT3It5a+pbX13jLrlu489M7BzxesLvA7UEdjJuKbuLazdey8ZqNXn9mKNZtWEfnwk56It1f3H1FSIDbVXa64rqIbI6kvree+t56Ik5G0DK5hUMJh3go7yEmtE1gWe0yPkn/hONRx73W7tP08ci8R9z2h1nDuOPoHRTHF7MzdSfs/qnXmt9kfMMx4zG3/Rcev5AEUwKbszZj0Vi81muJaOE3K37jtj+5PZmLD1/MzuydlCWXQYmXgip4/ornPR66fMflNMQ0sHfsXq+vD+DUyFP86cY/ue3POZHD+OPj2T19N81xzR4+6ZmY1hhiW33r2RmMsJ6w4Atwm9pGWX4Zhg4DxjYjaqua1lSpaRHdIL1pl8SUUBLj7R0eGrPGzEuTXxKmB7Ale4tQvfroetbPXy9U84MFHwjVK88qpzyrXKhmMCEkwNU2NckVyXQkdtCe3I5NYyOsJ4ykk0mklIvrXVBQkIuwl8yRh8V1QQHkbc0Tqgcwb+c8oXoF+/1/CTqbFUdWCNUDWH18tVC9G2pvAGDGmRnCNO9ovwOA/JJ8tswU+yuqDNUrhDRKgCvIxthlZGzJWACm7J0iRHP++1I348L/t9A5HiEAJcAVZNNr6KXH0INVbaUpqUmIZmtyK3aVndakVr9Hv89GCXAF2dg0NvbO20tdWh3VGdVDf8ALymeW05bYxuH8w0L0+pH9kqlWi30mgl0PQKsVNh4GgMHg/8SkcwkPDxeqFxk5+OzKxumNNE5vJBLvZmFGRw8xuzIa9v1w37ebQ8/E1Gg0Q54DPljWYI/X5ysoBIq0tHSqq6v9t6ypVKp7VCrVHpVKtQe8H8pVUAgGZNfgs2aJeQPYs6cQgAULFgrR27HjawCWLLlQiB7AF19IfbKXXbZSiN7GjR8DcMMNNwrRA9iw4W0A7rzzLiF6r732KgAPPPAzIXq///1zAPziFwPP1fGFV199VUwNrqBwPqMEuEJIowS4QkgjrP/r0IWHMIe7m4QnbptIeLv8Lqy9F+z1aBCe9s00n03H38z9xqNJeNaeWUR1RcnW2zJ1Cya9u0k4vzifGFOMh08MzodjPqRb1+22f8WJFT4ZhAHeSXvHo0n4itorfDIJvxb9Gh1qDwbhjptItib7dI1/UP+BNlWb2/67rXeTSqpPmv2I7eAFYupi0Hc5Da1as39/Iq4hzsV07K8eQEJTgovpOKzPP5Nwcmsy4T3Oh9hfk7BogzB4MAnb/OuLz+pzNQiH2/zvhx9rH0uc3fkgh+O/pvAAT6xMJK7Ot9rGE8mnk0lo8G05goFIq0kjqcm/5QjOJqMhg9RW/2qas8luzRZqEAYY1zWOTFOmML1J5knk9OUI0wOYbpvOBMFrXwoP8MZRjXQkOH/CRh0ZBUB6dzrTmqexLWWbx3U6BuJc03FWaRYAGpuGZZXLOBp/lMroSlnXeK7peGyFNHFoUu0kwi3h7Evbh1Vj9VqvKqmKpijnnIxJVZMAiDJFMfPETPZn7qct3P0neCCOxx6nPrzeUc6rd04dzivOoymuiVPpp2TN2SiLKKNWX+soz2uVpg4n1SSRVp3G0clH6dP3ea13rkF4sWmx9xczAAfUBzhlP+Uor7D7P31YeIC3pbjeyHfWv+NSXlS3iBcmvOD1eGhLUotL+W9v/M2lvLB6IbtTd7NDxjU2JbhOEPrLq39xbNuxU3CygOcWPOe1Xn1svUv5jZfecCnnnchj44yNeOtePNcg/PIfXnYpW1VWapJq2Hih937Ic03CLzzj6nOdWDSRj6/62Gu9EzpXg7CIAD+mOuby0K6wBmGAT9o5iZv23oTaLnXQ9DvoJ7dOJtISyeHYw7SGtQ4m4cL4/eNZdXAVSSapSbE7RbIrGywGpjZNpU3fxtH4o1A7mIoriwoXsXq/0wiwN13yN86snolVZWV/6n5sKpvXenNK53DNrmscC/4cHHUQgNTWVFLaUzgTf4b66PrBJFzIP51PweEC0uultVGOjDniODaxYiJmnVmWAx7gsqrLWP31alR2KYKOjZc8qVnlWWitWk5lnaLX4P5SPxA/3fFTrvrsKj54QJyFbt2GdegW6ehK8f4XfiiEB3iPpof3R7/vtv99+/tEm6Np1Xsf3P3sSPdcP2/q2USbvk322ijNxmY2jnev/f495t+o7WpMOveekcGwqq1szd3qfsAOMaYYWc2TfipGV1AxusJt/95Je+nR92DTeP8AAvQYe9i90H0tg8L5heh79Jgi5H3n8wXhAT4QNpXNp+AejFaDWL1erfc1mFeo8Cm4B6M73L0b0R9sGlvIBjcoAz0KIY6wGnzqlqlDnySDmV/NHPokmczfJSabRD8XHhI3sQtgdYVYgzDA9TXXC9W7s11aPGha9TRhmvfZ7gMk0/GuRd6vAOYNSg2uIBu1RU3GkQwAEqrEjFGk7U8DYOQesf3/SoAryCasJwyNTXLUJJwRE+ApxdL6OYmliYrpWOH7pSeyh1MTT2HRWjg+w/tl+AajYqnUY1RxYYVQ0/F31ouiEFoUFxRTOrcUi977NRwHoyO9g50/3IkpQWyPjuLJVDgvGTkyg6qqKsWTqTC8kV2DT5/u/SSkwThwYD8As2bNFqIn2uMJTp+nuEah9G/9gx/8H0F6sH79nwFYs+ZHQvT++McXAXjssV8K0Vu79lcAPPPMs0L0+nnuuefE1OAKCuczSoArhDRKgCuENMK6CQ9fdJi+cPcJ8+O+GEd4m3zrkWiPJwj2eT4AxAIbcKYmyQRuA3oA94wmQ/JexnsezSArT68k3uxbKsW/Jv7VY5LVa5uuJdEiP5Xi86rnPfon77Hd47N/8tedv6bF3uK2/8HwBxmhGeGTZj/C+8Gja6MJ63J6HLW9/v0J0R5PCIzPUyQju0YSZXGaoEUkWR3dO1qoJ3OsfSzxOB86Ef7JiZqJJKidI6ORKvnZp89F+J2NPxVPbI245ESiPZ4QGJ+nSHI6chjVPUqoZq4pl6zeLGF6M+wzhPsn5+jmMEUnZr3xfoQHePPoZjoTncsUjCySJs+o7WrizHE06eWtJz2Qx9MfBvJ5+sQMpKYJ4MWiqF5RHlXukrR1dpOzKzWiM4IeY48szyjAUeNRzujOOMr5nfmANHHKYDLQHSVvnvl+1X5OIdY/ubtvNxVWp8njCsMVfmsKD/D21HaX8s8//jkAk9smY7AZKIou4t2Md73WO9fjKSLAz/V5+hXg4/28GA+cjjjtUn7wgwcd2znHc+gN66Uwr5Bj49xTIQ7EKf0pOGv1iX7NzLJM6XjOKfYt2ue13jGV698WEeBHrEfgrOc2KAP8gi8uYO3WtQMen9Axgag+7xfZuWjLRTyy7REenvXw0Cd7yboN6yhTl1ER624Jk42nl0w/WVyzmDXvrSG50fNCOlqLlqxTWbIC/JYjt3Dn3wdOBDvi5AiK5xZ7rffj4h9zzT+u4YvHvvD6M0OxbsM64q6IozdJnLNKeIBXhVfxs+nuK5OmmdKY2jqVr5K+olvr/c+hiBes71JXCCrYeKlnx/zkosm0xLdwJv2Mx+MD0ZjeyN/X/N1tf0JNAsnVyRybcgxLmPcTp3TdOll/31tUFoFTCfkOZxPWGGuoMdZ8V38uZCme4n0t6w1NaU00pYnJsxOMKAM9CiGNsBp80meTREkBTo9nTq245cH6fZ75Jfn8bfzfhjh7CH7vYd9J4HHfJa+uutr3Dw/ALY23CNW7334/2GFc7Thhmv8d+d8A5JXkcWTlkSHOlkfQ1+CxZqlPPdwiJslShFkasYzplb/6q4ITQ5v0DqPp8S4Z1FDo2qQ2fViLfwuhnktQB7jRYuSC+gsAWF0pxnF+dblUS1528jK0tuAawTxfMLQYSKiQBsoyt2UK0cx+IxuArL9kgbw1jQYlqAPcpDVRHlWODRuFiYVCNPek7MGOneL4YixqMXar4UZPbA+dSZ3YVXZqp8pYM28QGuc1YsdO88xmoVEZ9FXYBxkfMK1lGhVRAvqsgaPxR9mevt2xxqGCD6igdFUpsSdj6UoVs45g0+wmDLUG6i6sG/pkGSieTIXzkszMLE6cOKF4MhWGN997nsz8/AuE6G3f/hUAy5YtF6IH8O9/fw7A6tWXC9H78ENpqeHbb79DiB7AG2+8/u2WWN/os896vz76YDz4oDSq/eabfxai18/jjz8upgZXUDifUQJcIaRRAlwhpFECXCGkCdpEsIULCz0ahKfvnE5kp29eve2ztntMBDt3/1yfEsF+Pulzj4lgC44W+JQI9t0R73pM2rq6erVPSVsDYYxe17HOo0H4oYiHfDYIP1T1EE1W9xmNv0r7FaP1o33S7Oe8SAR7dtJWXZ//85ATmxOFaqa0pRDR63Tl9yej8pWM7gxX07GfBuFAMFHrahCOUPmWffpsphmnkax1mjyiNf57AIM+EWxqdapwg3B6bTrJzb6lnfbEqMZRpLWlCdMb2zmW0Sb/aq5AM1c3V7hBeFHkImZGiM3s8Z0lgs1tzWV59XI+Hfkpx6K8t1rVptfSFuf0ZWaXSZNy9BY9txXfxpGEI+xM3ynrGqtTq2mJcf7Mjj8hGSuXHFtCQncCX+R8QVOE9yaAysRKl0Swk09PBiCpLYmL9l9E4dhCjqV7/52PRR6j1uCc4zG3Za7Xn/VIAIzRu/p2UW4td5SvNFwJgLZdy5hXxtA0u4mm+fKMFNs6t1HSU+Io35xws9/X+Z0ngr2n7B5eGveSrESwLTiD8a3X33I5nt6ZzojOEchxBjbGN7qU17+y3rFtx864hnE8teQpr/XqYlznT7z24msu5cv2XsYXvV/gbUbJqnDXpK1+B3gAjNFHLK7zttc+6urDNZ4xYqwzIoeDpoMu5aAM8LG7x5Jdme0o/2ay9CYzpWUKBXUFbErfxMnIk17r5R7MJfN0pmNq67MzpVVKDVYDtxXfRkl8CVtGbYGmH3utmVecR3a18xr/d8H/ArC8bDlxpjg2j90sa6bh7PLZTKhxrhHy+lJpdDGlNYWlB5eyb8w+jmQcAS/dZpeeupSH33iY9bevH/pkbwiAMfp24+3kdeahskqDiYcfPQxI87qzX8+mJa+F2uW18I33mus2rCP75mz6MrxPKT4UwgPcprLRZHD/afoy7Uu+TP3SpxHlDr370mMAT8590ic9i9pCa7h7js13p327nIVcTRW0RbgvZ9YW0UZZepnQlBzBRF+ceyCaE80U/booaL7zdztdVvSXDna9QGkGO0H0nZWBHoWQJmgTwc7+Wkzmh7PJ35MvVG/5YXEzFwGuPXMtAJHt/i86CQTEGP2LqF/4/uEBeCbjGQBGl4ymmmqh2koNHmzY4YJt0hTiBV8t+J4v5rsj/g1ppdrEVxKHjydzWKIC7FJ3pcoeRI3ZQGOTvrMdu9A2vBLgQcje2XuxaC0cmHHg+76U74y2K9qwG+y03tCqJIINdepT63n71re/78v4TrEmWKl6qWroE2WimI4VzktycsZy7NgxxXSsMLyRXYNPmyZmsZyDB6X25XBMBPvQQ/9XkB4888zvAFi7dp0Qvccek7oBX3rpZSF6P/zhvQB89NHHQvT6+dnPfiamBldQOJ9RAlwhpFECXCGkEdZNeOSiI/RFeEgEu2UcxjZ584JheCaCfSXiFdrV7W77b+26lWSbbw6kZ23P0or7zMk1qjWkqeS7kB6tf5RmW7Pb/v9K+C8ydBk+XeOdRXdSb6532/987vNkh2d7+IT3iE8EW6MkgvWXbEs2sTZnrlGjXX4FcS7jGOeSuDUC/zyUU/RTSNIkOcqRav/nz8yOmU2a3vnQxWj9X8M9IIlgY2rELS4/HBPBTu6bzFjLWKGaM1UzyVXlCtNbaFzIdMN0YXoAyxOXMz92vlDNgCeCHVEkLSUQY44hpzOH/XH7sanOmU1jh9y2XFp1rdREuCaq8jURbFxPHBntGRxKOuTWyxfsiWCLdcWc1jhzZS7pXeLYTi1LpTOhk84E9+UlBmOvfS8n7Ccc5UvVlwJgaDIQWRNJ48RGWW9kX5u+psxc5ihfF32dtGGB6N3RdE3uwhotL1nt542fU9zhtD3dnXG3rM97Qnwi2DTXNuS7f3VN+np5zeW8MOYFR1lv1XPfkftI7nVtY96QfwN14XU+JYJdfmo5C6sXorPruL78eqfmnBuoM9YFfSLY49rjLuVnnnjGpWzVWDmTe4ZDKw55rVlGmUv5yceedCn3xPRw8C5XT+RgFPUWuZR/8R+u02htOhv117q3qwejsM01yUFQBvj0bdN55OtH0FuldnObVgrQGIvUbOnSdGFROQeL7NhpD2t3BHi7rt2xH+A/3/1PKs2VlMW43qDB6NJ1YVfZwQ7d2m6sKquL5g8+/QEV6grpHH8JgN9xdfdqVm5dSUax9NLWE+FcrMjQJb079EbIS5Z6e/PtXLf+OtQWqZo2R0ov8GGd0vtSX0Qfdo33/x5rItdw6fpLMZyUrscSLd1TbbsUUnatHWuEvBp83YZ15P04D1umuPmywgO8NayVJyY84bbfaDUywjSC8ohylyaDWWPm5fEvM7JrJJ3aTlr1rQ4dgHcz35XdBt+RvoN9yftI60rjRIzzZ7lNLz1su1J3BXUbHBWU5pdSml/qdijuTBzdsd2yA7wnoYfCB93TwOg6dRibjLSPdu+9GQy71s6ZH3lIRmuD8KPhmMaasIfZ4RVZssL5zroPTBoT5ZHlAx4/Nz+7v/Roe1yCO1RoGeG+bJo/9EX20RcpzsWOGroneZ/JOtAoAz0KIY2wGnziZxNFSQHiPZ7gTAQrhAD4He/u8v+l6lweVD8oVO+JZPfmp7+8NkVaKCny8Ui6EVv7KzW4QlCgKZISymr2iUks248S4ApBQdibUm9O2DthiulYIfQw3yx1W5qvMw+vRLAKwwPrDCumR01YZ8jrOx8KxZOpcF6SmzuRI0eOKJ5MheGN7Bp8wgQxuclLSo72qwrR6/c7il35UdK8994fClF7+eWXAHjkkUeF6AE8+aTUbff8838Qonf//fd9uyX2vuzZs1eQnsStt94qpgZXUDifUQJcIaRRAlwhpBHWTVi+qhxLhPuaKZn/ysTQKjMNXgD8joHQfCvpLY95La9uuJpES6JsvRfDXqRN5Z4p4g7zHaTYU+RfIPCrtl959FA+HPUwI7Uj5YkF4r4AqzavosZU47b/rQveYnyMfxPuhfeDR5yJcMwxBtD0ih16DUZG9Ywi2uq08xht/nkoc6w5xNqdnsxwu28m67OZpJtEotr50InwUIrmguQLGBnhfOjiwvy3KgoP8NjjsUSdkZ81+HxmQvcEsnr9cAWdwzTbNMbZxgnTA5gXNo+pYeInsInk8lGXszh1sVBNnwNca9N6zETWmt1Kd7JzRljKft9+WoGA+B0DoVkSXkK13pmZYGG7c/k4tUWNTStvcsVB9UFOqU45ysutzkwSaosam8Ymuxdvp3kn5RbnfPyrwq+SJ3A2gbgvwAeVH7C3ydmd+NCkh/zWlB3gcX1xXN5wOXPb5/JR4kfUhEltpypbFRYsdI3oogtnX7lfAR4Av2MgNCsNlS7l6w9IPtCE+gRyD+ZSMaGCotlFnj7qkXKNqzHk5sPOfJFTP5hKZ2InpctKaRntvfnhcN9hl7JfAR6I+wJ8Vf+VS/l7CfBZ7bOY0z4HgFWNqxz7t1i30EUX6zasY3PvZmr1tQNJeE8A/I6B0Lz6xNX85M8/GfD4mJIxNCV5n/X3avPVrHlqDRqL5/eXqIYoxm8ez847vM/w/MsPf8nYzLE0FcjLPuyRQNwXJE/miqdXoE4T17knO8A/j/+c0/rTLGlZwoaUDTSHSW/oTTrpH+6lES8NuzZ4R0wHG+7d4LY/qiWKGTtnUDKthPr0evjKw4c9oYLND2/2eGjyh5PpSOmgKk/eYvHabi3hleE0ISDAA4i9S4AR/Czkt8FVcDTyKEcjjw597jCnI66DbZdsE6pZvNrLdMkKgDLQoxDiCOsmzPkoR5RUQPyOgdC8ueHmoU+SwY/MPxKqB/DLmF8CMLVkKi2z/HTkB+K+AB8t/QiAjsc9p2z3B6UGHw5820upsgRvWkJ737dtb/cFhf1CCfBhQPK/pFXDYg/EEtYYNsTZ3w/da7od/7fbxL1oKgE+DOga14VNY6Mvqg9znOAqUhDa+VpQg2a2BpVa3C+N4skcBnTldNGa10r75HYI0qlBYTeEYd1rxfATmRPzhkAJ8GHC6VvELo0nGlWEivAX/Z9U5qarmI4VzkemT5/B/v37FdOxwvBGdg0+fry8zAIDUVraP5lBrLn1kksuFaQHn376CQDXXXf9EGd6x9///s63W+KN0f/4x3tC1K655upvt8Tel7Y2ecszD0VBQYGYGlxB4XxGCXCFkEYJcIWQRlg3YcWqCiyR7g6f0Z+ODg7TMfDl9C8x6U1u+xcWLSS6W7415eOcj+kOc1/PennFcuJ6ffATBuB7ryldQ0Ofe+fA02OeJsso02YXoPsy5bUpVLZXuu3/6uavmJrsn81uWJqOk1qSCO9x9rmG9fk3fJ3WkUak2Wni7U/AFUzMjJpJaliqoxytFeg1E8TFWReTFet86BLD5a9McC7CAzymIiboDQ8ZDRmktPhhpTuH7NZsRnSMEKYXCJbGLWVO9Jzv+zIG5dbJt7IyZ6VQTeEB3jamDVOKsxmQvM+3HOtAwMytVUlVNEU5nS0TK6X0K9NPTSeyN5LCrEJ6da5ZzGLbY8k7msfBcQdpinN1xRyPPU59uDMn5Iy6Gf5dYAC+9+aWzRzucvoyb0+73XexAN2XvxT/he2ntzvKv1nsY5vnLIQH+LmmY78CPEDm1oY41zbpmy+/6di2Y2fWyVn8z9L/cewbWTuSldtWokLF+FPOi9r6wFa6w7qpiXJdtMbvAA/A997b4br4pV8BHqD78q8T/3IpB2WAr9uwjvST6Tw1+in/xQJkbl10cBEFRwsc5S0TtgCwoHwBADvG7MCqdi7E3hTbRElmCbknc6lKqaIyVXoh6q/lb9x1IyqjCovW/SXbJwLwvddtWMfs5Nl03idgoC6ApuO7X78b4yT/Fk46m4BMtlIJHakTT6exkz1Z7nNq9o/ajwoVFo1roJoMJr6c8yU7pu/ArDM7BvnMOmnqaWV6ZdC3wYcrymzCs7BqBk+fYQ4LzrnUCgOjDPQohDTCavAxH40BIL80nxMGP1NoB8jcuvjAYv8EzmFludgurUB87z+O/yMACSUJ9CbLy2/vRoDuS9Gd0qpf+x7f55+QB4TW4Nnd2QBk9WQRZQnuvvDhhG6vDgD9Nj24D+QGBbW/l1ZCq/lNDXJmuA6F0AA/e03scJt4d4aCb2hqpNFku8qOyhScHQCdO6Tene793c50SwIQGuCFUYW0aFvYH7mfurA6kdIKftCzvAdbhI3eZb3Y48UujSaKEY+PABWMWDsieE3HdpWdtZlrsagE9QcriEGAGfszAAAFNUlEQVQPrS+0YtcHZ3ADGCcamVI6BW2S2I49xZOpcJ6iwm63K55MheGN7Bp86tQ+IX/40KGDAMyaNVuI3p49hQDk518gRA9g+/b+9Y7F+hM/+uhjQXqwapXUVVlUJGbV2SlTJgPiPJQxMf2zscS/3AqpwRUUzmeUAFcIaZQAVwhphPXJHF1xlL4I9/b52M1jMbbJn/546MJDmMPdJzdN3DaR8HbfBpEKFxbSa3Qfrp6+czqRnTLzRgbAn3hn0Z3Um+vd9j+f+zzZ4dnyBYEVn66gurvabf+7S99lQuwE2XoB8U+OAPKBDMAIdAP1SB12fiYSET6bMKomCn2X05Oo7fXvT8TUxbjqmf2/5LiGOIwm50On69P5rSmS2TGzSdOnOcox2hi/NQtSC8iIzHCU4/T+JVkV5p+cCFyD1JZoAMoAPVLQTyH4Ajz+ZDwxNf7fkH4SKxOJq/M/4+3ZpFanktCQIFRTJMsTlzM/dr5QzSszr2TpiKXC9IT4J3XASqTgLgLex7FYPyrAf8+x+ABvzmymK8lpWUs/lA6AzqYjpSeF0+HyVjltHNVIR4IztcWoI6Mc2yO7RlJrrPWYkFZn1ZFoSqQm0j0Hem16LW1xzpzw2WW+/fwDAfEnft74OcUdzm6/uzPudmyrT6qxJdpAZovq/ZPvs6fROUj382k/B8DWYcNWbUM7Xl4oDOSftNvtdO/pJnx6OCrdEL14GUB/a3MrzuAGqUdVwLCL8ADvSOugA2dAPv3e0wBkmjIBOBF+gjdHvem1XltKm0u5X89gNZDck0y3ppv3Rr/nMr6aV5vHJScuwWA1UBNR45g6UDK7hF5jLy1JLbTgzFfjV4AHwJ9Y2FboUr7v9/c5tjVlGux6O+YbzfRd7f2YxNbarS7le397LwCWIunfRjdPR9RT3s8APdc/edva2wDoq+mjr7oPbZKWUS+OYtCnPuKs7dZv/78MqT3ez+NeX5JHhAf4vC/m8eTWJwc8ntqTisHm/UJA43eNZ+2WtST3ejYvh9nCSOtOc9mX2pWK1iZ9tbQu5zGNXZpV98A/H+BA+AGPNb9sAuBPfDTrUZa8sARt4QC3xwrqY/I6wH4X/jtm/sdMR9mC63e3lFiwm7wf9Fu/ZD1Z12ZhqZd0unFdAMnaaqW3bIj5511nbUcDzUAlcAjwb70fB8IDvMZQw/1T73fbn9CbQG5HLrvid9Gn9r7msagtPD3labf9apua+Q3zKY0ppdHQCLW/dhz7ZMwn7EndQ2ZbJoVphdhV0o1r1UvVxKasTUHdBkcNPY/1eDyk/VyLbbQN2zibx+MDoZ2qJbHIvVHbV9aH5ZAFw+WGoZsUZ6GJ1DD1mHsU2kw2Gl5vIHZVLPpRevivQUSqkHpMwoELgA+QXjLbCd4AH4gmfRPb9duHPtFLbGobX6d8PeDx+oh66iPcu9zOdyzLxc7U1I3ToRsnrhdJbVST8mMvF1XqAz4BrkJ6l0kDTgPi+igU07HC90wxUo29EOmlcwZS06UcOOK/vLAAz92UK0oKgKlbBP1GncXsr8VM7AIC4k98bcprvn94ADZdskmoXr9/UiiV3/4XAJSheoWQRglwhZBGCXCFkEYJcIWQRglwhZBGpmVN1QGUCvz7iUBjEOsFQnM4XmMgvvNou92eNNRJcrsJS+12+ywfL8gNlUq1J5j1AqE5HK8xEN/ZW5QmikJIowS4QkgjN8D/JPjvB7teIDSH4zUG4jt7hayXTAWF8w2liaIQ0igBrhDSKAGuENIoAa4Q0igBrhDS/H9AqY0TJVHWJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 26\niter    0   |   diff: 0.00000   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 27\niter    0   |   diff: 0.00000   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 28\niter    0   |   diff: 0.00000   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after iteration 29\niter    0   |   diff: 0.00000   |   V(start): 0.198 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import clear_output\n",
    "from time import sleep\n",
    "mdp = FrozenLakeEnv(map_name='8x8', slip_chance=0.1)\n",
    "state_values = {s: 0 for s in mdp.get_all_states()}\n",
    "\n",
    "for i in range(30):\n",
    "    clear_output(True)\n",
    "    print(\"after iteration %i\" % i)\n",
    "    state_values = value_iteration(mdp, state_values, num_iter=1)\n",
    "    draw_policy(mdp, state_values)\n",
    "    sleep(0.5)\n",
    "# please ignore iter 0 at each step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "##Massive tests\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter    0   |   diff: 1.00000   |   V(start): 0.000 \niter    1   |   diff: 0.90000   |   V(start): 0.000 \niter    2   |   diff: 0.81000   |   V(start): 0.000 \niter    3   |   diff: 0.72900   |   V(start): 0.000 \niter    4   |   diff: 0.65610   |   V(start): 0.000 \niter    5   |   diff: 0.59049   |   V(start): 0.590 \niter    6   |   diff: 0.00000   |   V(start): 0.590 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average reward:  1.0\nWell done!\n"
     ]
    }
   ],
   "source": [
    "mdp = FrozenLakeEnv(slip_chance=0)\n",
    "state_values = value_iteration(mdp)\n",
    "\n",
    "total_rewards = []\n",
    "for game_i in range(1000):\n",
    "    s = mdp.reset()\n",
    "    rewards = []\n",
    "    for t in range(100):\n",
    "        s, r, done, _ = mdp.step(\n",
    "            get_optimal_action(mdp, state_values, s, gamma))\n",
    "        rewards.append(r)\n",
    "        if done:\n",
    "            break\n",
    "    total_rewards.append(np.sum(rewards))\n",
    "\n",
    "print(\"average reward: \", np.mean(total_rewards))\n",
    "assert(1.0 <= np.mean(total_rewards) <= 1.0)\n",
    "print(\"Well done!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter    0   |   diff: 0.90000   |   V(start): 0.000 \niter    1   |   diff: 0.72900   |   V(start): 0.000 \niter    2   |   diff: 0.62330   |   V(start): 0.000 \niter    3   |   diff: 0.50487   |   V(start): 0.000 \niter    4   |   diff: 0.40894   |   V(start): 0.000 \niter    5   |   diff: 0.34868   |   V(start): 0.349 \niter    6   |   diff: 0.06529   |   V(start): 0.410 \niter    7   |   diff: 0.05832   |   V(start): 0.468 \niter    8   |   diff: 0.01139   |   V(start): 0.480 \niter    9   |   diff: 0.00764   |   V(start): 0.487 \niter   10   |   diff: 0.00164   |   V(start): 0.489 \niter   11   |   diff: 0.00094   |   V(start): 0.490 \niter   12   |   diff: 0.00022   |   V(start): 0.490 \niter   13   |   diff: 0.00011   |   V(start): 0.490 \niter   14   |   diff: 0.00003   |   V(start): 0.490 \niter   15   |   diff: 0.00001   |   V(start): 0.490 \niter   16   |   diff: 0.00000   |   V(start): 0.490 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average reward:  0.887\nWell done!\n"
     ]
    }
   ],
   "source": [
    "# Measure agent's average reward\n",
    "mdp = FrozenLakeEnv(slip_chance=0.1)\n",
    "state_values = value_iteration(mdp)\n",
    "\n",
    "total_rewards = []\n",
    "for game_i in range(1000):\n",
    "    s = mdp.reset()\n",
    "    rewards = []\n",
    "    for t in range(100):\n",
    "        s, r, done, _ = mdp.step(\n",
    "            get_optimal_action(mdp, state_values, s, gamma))\n",
    "        rewards.append(r)\n",
    "        if done:\n",
    "            break\n",
    "    total_rewards.append(np.sum(rewards))\n",
    "\n",
    "print(\"average reward: \", np.mean(total_rewards))\n",
    "assert(0.8 <= np.mean(total_rewards) <= 0.95)\n",
    "print(\"Well done!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter    0   |   diff: 0.75000   |   V(start): 0.000 \niter    1   |   diff: 0.50625   |   V(start): 0.000 \niter    2   |   diff: 0.39867   |   V(start): 0.000 \niter    3   |   diff: 0.26910   |   V(start): 0.000 \niter    4   |   diff: 0.18164   |   V(start): 0.000 \niter    5   |   diff: 0.14013   |   V(start): 0.140 \niter    6   |   diff: 0.07028   |   V(start): 0.199 \niter    7   |   diff: 0.06030   |   V(start): 0.260 \niter    8   |   diff: 0.02594   |   V(start): 0.285 \niter    9   |   diff: 0.01918   |   V(start): 0.305 \niter   10   |   diff: 0.00858   |   V(start): 0.313 \niter   11   |   diff: 0.00560   |   V(start): 0.319 \niter   12   |   diff: 0.00260   |   V(start): 0.321 \niter   13   |   diff: 0.00159   |   V(start): 0.323 \niter   14   |   diff: 0.00076   |   V(start): 0.324 \niter   15   |   diff: 0.00045   |   V(start): 0.324 \niter   16   |   diff: 0.00022   |   V(start): 0.324 \niter   17   |   diff: 0.00012   |   V(start): 0.325 \niter   18   |   diff: 0.00006   |   V(start): 0.325 \niter   19   |   diff: 0.00003   |   V(start): 0.325 \niter   20   |   diff: 0.00002   |   V(start): 0.325 \niter   21   |   diff: 0.00001   |   V(start): 0.325 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average reward:  0.673\nWell done!\n"
     ]
    }
   ],
   "source": [
    "# Measure agent's average reward\n",
    "mdp = FrozenLakeEnv(slip_chance=0.25)\n",
    "state_values = value_iteration(mdp)\n",
    "\n",
    "total_rewards = []\n",
    "for game_i in range(1000):\n",
    "    s = mdp.reset()\n",
    "    rewards = []\n",
    "    for t in range(100):\n",
    "        s, r, done, _ = mdp.step(\n",
    "            get_optimal_action(mdp, state_values, s, gamma))\n",
    "        rewards.append(r)\n",
    "        if done:\n",
    "            break\n",
    "    total_rewards.append(np.sum(rewards))\n",
    "\n",
    "print(\"average reward: \", np.mean(total_rewards))\n",
    "assert(0.6 <= np.mean(total_rewards) <= 0.7)\n",
    "print(\"Well done!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter    0   |   diff: 0.80000   |   V(start): 0.000 \niter    1   |   diff: 0.57600   |   V(start): 0.000 \niter    2   |   diff: 0.41472   |   V(start): 0.000 \niter    3   |   diff: 0.29860   |   V(start): 0.000 \niter    4   |   diff: 0.24186   |   V(start): 0.000 \niter    5   |   diff: 0.19349   |   V(start): 0.000 \niter    6   |   diff: 0.15325   |   V(start): 0.000 \niter    7   |   diff: 0.12288   |   V(start): 0.000 \niter    8   |   diff: 0.09930   |   V(start): 0.000 \niter    9   |   diff: 0.08037   |   V(start): 0.000 \niter   10   |   diff: 0.06426   |   V(start): 0.000 \niter   11   |   diff: 0.05129   |   V(start): 0.000 \niter   12   |   diff: 0.04330   |   V(start): 0.000 \niter   13   |   diff: 0.03802   |   V(start): 0.033 \niter   14   |   diff: 0.03332   |   V(start): 0.058 \niter   15   |   diff: 0.02910   |   V(start): 0.087 \niter   16   |   diff: 0.01855   |   V(start): 0.106 \niter   17   |   diff: 0.01403   |   V(start): 0.120 \niter   18   |   diff: 0.00810   |   V(start): 0.128 \niter   19   |   diff: 0.00555   |   V(start): 0.133 \niter   20   |   diff: 0.00321   |   V(start): 0.137 \niter   21   |   diff: 0.00247   |   V(start): 0.138 \niter   22   |   diff: 0.00147   |   V(start): 0.139 \niter   23   |   diff: 0.00104   |   V(start): 0.140 \niter   24   |   diff: 0.00058   |   V(start): 0.140 \niter   25   |   diff: 0.00036   |   V(start): 0.141 \niter   26   |   diff: 0.00024   |   V(start): 0.141 \niter   27   |   diff: 0.00018   |   V(start): 0.141 \niter   28   |   diff: 0.00012   |   V(start): 0.141 \niter   29   |   diff: 0.00007   |   V(start): 0.141 \niter   30   |   diff: 0.00004   |   V(start): 0.141 \niter   31   |   diff: 0.00003   |   V(start): 0.141 \niter   32   |   diff: 0.00001   |   V(start): 0.141 \niter   33   |   diff: 0.00001   |   V(start): 0.141 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average reward:  0.737\nWell done!\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Measure agent's average reward\n",
    "mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8')\n",
    "state_values = value_iteration(mdp)\n",
    "\n",
    "total_rewards = []\n",
    "for game_i in range(1000):\n",
    "    s = mdp.reset()\n",
    "    rewards = []\n",
    "    for t in range(100):\n",
    "        s, r, done, _ = mdp.step(\n",
    "            get_optimal_action(mdp, state_values, s, gamma))\n",
    "        rewards.append(r)\n",
    "        if done:\n",
    "            break\n",
    "    total_rewards.append(np.sum(rewards))\n",
    "\n",
    "print(\"average reward: \", np.mean(total_rewards))\n",
    "assert(0.6 <= np.mean(total_rewards) <= 0.8)\n",
    "print(\"Well done!\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}