MDP_VI_PI_Q-learning_AIMA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markov Chain basics\n",
    "Andrey Markov was a Russian mathematician who studied stochastic processes. Markov was particularly interested in systems that follow a chain of linked events. In 1906, Markov produced interesting results about discrete processes that he called chain. A **Markov Chain** has a set of states S={s0,s1,...,sm} and a process that can move successively from one state to another. Each move is a single step and is based on a transition model T\n",
    "\n",
    "To summarise a Markov chain is defined by:\n",
    "\n",
    "$\\bf{Set\\ of\\ possible\\ States:}S=\\{{s_0,s_1,...,s_m}\\}$\n",
    "\n",
    "$\\bf{Initial\\ State}: s_0$\n",
    "\n",
    "$\\bf{Transition\\ Model}: T(s,s^′)$\n",
    "\n",
    "A Markov chain is based on the Markov Property. The Markov property states that **given the present, the future is conditionally independent of the past.**\n",
    "\n",
    "Let’s suppose we have a chain with only two states $s_0$ and $s_1$, where $s_0$ is the initial state. The process is in $s_0$ 90% of the time and it can move to $s_1$ the remaining 10% of the time. When the process is in state $s_1$ it will remain there 50% of the time.\n",
    "\n",
    "So, the transition matrix can be written as,\n",
    "\n",
    "$$T=\\quad\n",
    "\\begin{bmatrix}\n",
    "0.9 & 0.1 \\\\\n",
    "0.5 & 0.5\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "The transition matrix is always a square matrix, and since we are dealing with probability distributions all the entries are within 0 and 1 and a single row sums to 1.\n",
    "\n",
    "Here is the state diagram,\n",
    "\n",
    "![MDP-1](https://mpatacchiola.github.io/blog/images/simple_markov_chain.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
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   "source": [
    "%%html\n",
    "<style>\n",
    "body {\n",
    "    font-family: \"Comic Sans MS\", cursive, sans-serif;\n",
    "}\n",
    "</style> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random, time\n",
    "import numpy as np\n",
    "from collections import defaultdict\n",
    "import operator\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from seaborn import heatmap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Misc functions and utilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "orientations = EAST, NORTH, WEST, SOUTH = [(1, 0), (0, 1), (-1, 0), (0, -1)]\n",
    "turns = LEFT, RIGHT = (+1, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vector_add(a, b):\n",
    "    \"\"\"Component-wise addition of two vectors.\"\"\"\n",
    "    return tuple(map(operator.add, a, b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def turn_heading(heading, inc, headings=orientations):\n",
    "    return headings[(headings.index(heading) + inc) % len(headings)]\n",
    "\n",
    "\n",
    "def turn_right(heading):\n",
    "    return turn_heading(heading, RIGHT)\n",
    "\n",
    "def turn_left(heading):\n",
    "    return turn_heading(heading, LEFT)\n",
    "\n",
    "def distance(a, b):\n",
    "    \"\"\"The distance between two (x, y) points.\"\"\"\n",
    "    xA, yA = a\n",
    "    xB, yB = b\n",
    "    return math.hypot((xA - xB), (yA - yB))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def isnumber(x):\n",
    "    \"\"\"Is x a number?\"\"\"\n",
    "    return hasattr(x, '__int__')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function to generate grid data (list of lists) with arbitrary size and complexity for the grid world"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_mdp(nrows=3,ncols=4,terminals = [(3,2),(3,1)],main_reward = -0.04,\n",
    "            terminal_rewards = [1,-1],block_coords = [(1,1)]):\n",
    "    \"\"\"\n",
    "    Generates a list of list to feed to the main GridMDP class from simple user API\n",
    "    nrows: Number of rows\n",
    "    ncols: Number of columns\n",
    "    terminals: Coordinates of terminal points, list of tuples\n",
    "    main_reward: The default reward for traversing the grid world\n",
    "    block_coords: Coordinates of solid blocks, list of tules\n",
    "    \"\"\"\n",
    "    \n",
    "    x = [[main_reward] * ncols for i in range(nrows)]\n",
    "    for i,t in enumerate(terminals):\n",
    "        x[t[1]][t[0]]=terminal_rewards[i]\n",
    "    for b in block_coords:\n",
    "        x[b[1]][b[0]]=None\n",
    "    x.reverse()\n",
    "       \n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Class definitions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Base MDP class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MDP:\n",
    "    \"\"\"A Markov Decision Process, defined by an initial state, transition model,\n",
    "    and reward function. We also keep track of a gamma value, for use by\n",
    "    algorithms. The transition model is represented somewhat differently from\n",
    "    the text. Instead of P(s' | s, a) being a probability number for each\n",
    "    state/state/action triplet, we instead have T(s, a) return a\n",
    "    list of (p, s') pairs. We also keep track of the possible states,\n",
    "    terminal states, and actions for each state.\"\"\"\n",
    "\n",
    "    def __init__(self, init, actlist, terminals, transitions = {}, reward = None, states=None, gamma=.9):\n",
    "        if not (0 < gamma <= 1):\n",
    "            raise ValueError(\"An MDP must have 0 < gamma <= 1\")\n",
    "\n",
    "        if states:\n",
    "            self.states = states\n",
    "        else:\n",
    "            ## collect states from transitions table\n",
    "            self.states = self.get_states_from_transitions(transitions)\n",
    "            \n",
    "        \n",
    "        self.init = init\n",
    "        \n",
    "        if isinstance(actlist, list):\n",
    "            ## if actlist is a list, all states have the same actions\n",
    "            self.actlist = actlist\n",
    "        elif isinstance(actlist, dict):\n",
    "            ## if actlist is a dict, different actions for each state\n",
    "            self.actlist = actlist\n",
    "        \n",
    "        self.terminals = terminals\n",
    "        self.transitions = transitions\n",
    "        if self.transitions == {}:\n",
    "            print(\"Warning: Transition table is empty.\")\n",
    "        self.gamma = gamma\n",
    "        if reward:\n",
    "            self.reward = reward\n",
    "        else:\n",
    "            self.reward = {s : 0 for s in self.states}\n",
    "        #self.check_consistency()\n",
    "\n",
    "    def R(self, state):\n",
    "        \"\"\"Return a numeric reward for this state.\"\"\"\n",
    "        return self.reward[state]\n",
    "\n",
    "    def T(self, state, action):\n",
    "        \"\"\"Transition model. From a state and an action, return a list\n",
    "        of (probability, result-state) pairs.\"\"\"\n",
    "        if(self.transitions == {}):\n",
    "            raise ValueError(\"Transition model is missing\")\n",
    "        else:\n",
    "            return self.transitions[state][action]\n",
    "\n",
    "    def actions(self, state):\n",
    "        \"\"\"Set of actions that can be performed in this state. By default, a\n",
    "        fixed list of actions, except for terminal states. Override this\n",
    "        method if you need to specialize by state.\"\"\"\n",
    "        if state in self.terminals:\n",
    "            return [None]\n",
    "        else:\n",
    "            return self.actlist\n",
    "\n",
    "    def get_states_from_transitions(self, transitions):\n",
    "        if isinstance(transitions, dict):\n",
    "            s1 = set(transitions.keys())\n",
    "            s2 = set([tr[1] for actions in transitions.values() \n",
    "                              for effects in actions.values() for tr in effects])\n",
    "            return s1.union(s2)\n",
    "        else:\n",
    "            print('Could not retrieve states from transitions')\n",
    "            return None\n",
    "\n",
    "    def check_consistency(self):\n",
    "        # check that all states in transitions are valid\n",
    "        assert set(self.states) == self.get_states_from_transitions(self.transitions)\n",
    "        # check that init is a valid state\n",
    "        assert self.init in self.states\n",
    "        # check reward for each state\n",
    "        #assert set(self.reward.keys()) == set(self.states)\n",
    "        assert set(self.reward.keys()) == set(self.states)\n",
    "        # check that all terminals are valid states\n",
    "        assert all([t in self.states for t in self.terminals])\n",
    "        # check that probability distributions for all actions sum to 1\n",
    "        for s1, actions in self.transitions.items():\n",
    "            for a in actions.keys():\n",
    "                s = 0\n",
    "                for o in actions[a]:\n",
    "                    s += o[0]\n",
    "                assert abs(s - 1) < 0.001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transition matrix, init, termianls, rewards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Transition Matrix as nested dict. State -> Actions in state -> List of (Probability, State) tuples\n",
    "t = {\n",
    "    \"A\": {\n",
    "            \"X\": [(0.3, \"A\"), (0.7, \"B\")],\n",
    "            \"Y\": [(1.0, \"A\")]\n",
    "         },\n",
    "    \"B\": {\n",
    "            \"X\": {(0.8, \"End\"), (0.2, \"B\")},\n",
    "            \"Y\": {(1.0, \"A\")}\n",
    "         },\n",
    "    \"End\": {}\n",
    "}\n",
    "\n",
    "init = \"A\"\n",
    "\n",
    "terminals = [\"End\"]\n",
    "\n",
    "rewards = {\n",
    "    \"A\": 5,\n",
    "    \"B\": -10,\n",
    "    \"End\": 100\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Custom MDP subclass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CustomMDP(MDP):\n",
    "    def __init__(self, init, terminals, transition_matrix, reward = None, gamma=.9):\n",
    "        # All possible actions.\n",
    "        actlist = []\n",
    "        for state in transition_matrix.keys():\n",
    "            actlist.extend(transition_matrix[state])\n",
    "        actlist = list(set(actlist))\n",
    "        MDP.__init__(self, init, actlist, terminals, transition_matrix, reward, gamma=gamma)\n",
    "\n",
    "    def T(self, state, action):\n",
    "        if action is None:\n",
    "            return [(0.0, state)]\n",
    "        else: \n",
    "            return self.t[state][action]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "our_mdp = CustomMDP(init, terminals, t, rewards, gamma=.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['X', 'Y']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "our_mdp.actions('A')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grid MDP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GridMDP(MDP):\n",
    "\n",
    "    \"\"\"A two-dimensional grid MDP, as in [Figure 17.1]. All you have to do is\n",
    "    specify the grid as a list of lists of rewards; use None for an obstacle\n",
    "    (unreachable state). Also, you should specify the terminal states.\n",
    "    An action is an (x, y) unit vector; e.g. (1, 0) means move east.\"\"\"\n",
    "\n",
    "    def __init__(self, grid, terminals, init=(0, 0), gamma=.9):\n",
    "        grid.reverse()  # because we want row 0 on bottom, not on top\n",
    "        reward = {}\n",
    "        states = set()\n",
    "        self.rows = len(grid)\n",
    "        self.cols = len(grid[0])\n",
    "        self.grid = grid\n",
    "        for x in range(self.cols):\n",
    "            for y in range(self.rows):\n",
    "                if grid[y][x] is not None:\n",
    "                    states.add((x, y))\n",
    "                    reward[(x, y)] = grid[y][x]\n",
    "        self.states = states\n",
    "        actlist = orientations\n",
    "        transitions = {}\n",
    "        for s in states:\n",
    "            transitions[s] = {}\n",
    "            for a in actlist:\n",
    "                transitions[s][a] = self.calculate_T(s, a)\n",
    "        MDP.__init__(self, init, actlist=actlist,\n",
    "                     terminals=terminals, transitions = transitions, \n",
    "                     reward = reward, states = states, gamma=gamma)\n",
    "\n",
    "    def calculate_T(self, state, action):\n",
    "        if action is None:\n",
    "            return [(0.0, state)]\n",
    "        else:\n",
    "            return [(0.8, self.go(state, action)),\n",
    "                    (0.1, self.go(state, turn_right(action))),\n",
    "                    (0.1, self.go(state, turn_left(action)))]\n",
    "    \n",
    "    def T(self, state, action):\n",
    "        if action is None:\n",
    "            return [(0.0, state)]\n",
    "        else:\n",
    "            return self.transitions[state][action]\n",
    " \n",
    "    def go(self, state, direction):\n",
    "        \"\"\"Return the state that results from going in this direction.\"\"\"\n",
    "        state1 = vector_add(state, direction)\n",
    "        return state1 if state1 in self.states else state\n",
    "\n",
    "    def to_grid(self, mapping):\n",
    "        \"\"\"Convert a mapping from (x, y) to v into a [[..., v, ...]] grid.\"\"\"\n",
    "        return list(reversed([[mapping.get((x, y), None)\n",
    "                               for x in range(self.cols)]\n",
    "                              for y in range(self.rows)]))\n",
    "\n",
    "    def to_arrows(self, policy):\n",
    "        chars = {\n",
    "            (1, 0): '→', (0, 1): '↑', (-1, 0): '←', (0, -1): '↓', None: 'TERMINAL'}\n",
    "        return self.to_grid({s: chars[a] for (s, a) in policy.items()})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grid example\n",
    "\n",
    "![grid-mdp](https://raw.githubusercontent.com/aimacode/aima-python/c16bb8bdc28e8f9fcc6e7f76a92b9492bf019d87/images/grid_mdp.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_rewards = [[-0.04, -0.04, -0.04, +1],\n",
    "        [-0.04, None,  -0.04, -1],\n",
    "        [-0.04, -0.04, -0.04, -0.04]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_terminals = [(3, 2), (3, 1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_1= GridMDP(grid_rewards,grid_terminals,gamma=0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0, 0),\n",
       " (0, 1),\n",
       " (0, 2),\n",
       " (1, 0),\n",
       " (1, 2),\n",
       " (2, 0),\n",
       " (2, 1),\n",
       " (2, 2),\n",
       " (3, 0),\n",
       " (3, 1),\n",
       " (3, 2)}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_1.states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 0), (0, 1), (-1, 0), (0, -1)]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_1.actions((1,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[None]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_1.actions((3,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[-0.04, -0.04, -0.04, -0.04],\n",
       " [-0.04, None, -0.04, -1],\n",
       " [-0.04, -0.04, -0.04, 1]]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_1.grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.8, (1, 2)), (0.1, (2, 2)), (0.1, (0, 2))]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_1.T((1,2),(0,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.8, (3, 2)), (0.1, (3, 2)), (0.1, (2, 2))]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_1.T((3,2),(0,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Value iteration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value iteration function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def value_iteration(mdp, epsilon=0.001):\n",
    "    \"\"\"Solving an MDP by value iteration.\n",
    "    mdp: The MDP object\n",
    "    epsilon: Stopping criteria\n",
    "    \"\"\"\n",
    "    U1 = {s: 0 for s in mdp.states}\n",
    "    R, T, gamma = mdp.R, mdp.T, mdp.gamma\n",
    "    iter_count=0\n",
    "    while True:\n",
    "        iter_count+=1\n",
    "        U = U1.copy()\n",
    "        delta = 0\n",
    "        for s in mdp.states:\n",
    "            U1[s] = R(s) + gamma * max([sum([p * U[s1] for (p, s1) in T(s, a)])\n",
    "                                        for a in mdp.actions(s)])\n",
    "            delta = max(delta, abs(U1[s] - U[s]))\n",
    "        if delta < epsilon * (1 - gamma) / gamma:\n",
    "            return (U,iter_count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def value_iteration_over_time(mdp, iterations=20):\n",
    "    U_over_time = []\n",
    "    U1 = {s: 0 for s in mdp.states}\n",
    "    R, T, gamma = mdp.R, mdp.T, mdp.gamma\n",
    "    for _ in range(iterations):\n",
    "        U = U1.copy()\n",
    "        for s in mdp.states:\n",
    "            U1[s] = R(s) + gamma * max([sum([p * U[s1] for (p, s1) in T(s, a)])\n",
    "                                        for a in mdp.actions(s)])\n",
    "        U_over_time.append(U)\n",
    "    return U_over_time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting value updates over time/iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_value_update(mdp,iterations=10):\n",
    "    \"\"\"\n",
    "    Plot value updates over iterations for a given MDP.\n",
    "    \"\"\"\n",
    "    x = value_iteration_over_time(mdp,iterations=iterations)\n",
    "    value_states = {k:[] for k in mdp.states}\n",
    "    for i in x:\n",
    "        for k,v in i.items():\n",
    "            value_states[k].append(v)\n",
    "    plt.figure(figsize=(8,5))\n",
    "    for v in value_states:\n",
    "        plt.plot(value_states[v])\n",
    "        plt.legend(list(value_states.keys()),fontsize=14)\n",
    "    plt.grid(True)\n",
    "    plt.xlabel(\"Iterations\",fontsize=14)\n",
    "    plt.ylabel(\"Utilities of states\",fontsize=14)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PNFJHBod9CJowAgakMIYPQ9RhjKRgwC4lLlcNMirmghTQGbk+Nr/7OeH7cIY6hm71o+/ReR2d0nVf0S0/6jq2v2i6l+sEjCHMva5m793oln3a4n0VDN54DwkzfkPYgDnHh4GhiMo4GggKM75u8RXOhtfrHfRvVyIZB719y32ZpF8A/ig7l6zrFEgpa4UQRcDfhRB7pJRHenQo5c+AnwEsWrRIDmWAkqEOeLKnYQ+B4wE+s+AzrJw8dP0OljONMxBop7llO02NpTQ1/yOyxTA15XwyM/+ZzKyVpKbMDQffSWxGQwCbXpESPC3QURc+TkWlp6C9Vk+dp/Wn6n4hwOwAsz2c2sBqB3MymLOjyuzd6tnBZOuZZ7SAwQQGY2wqjOHz6GtTH3kGBvK/aNR+nwNkNIyztbISS860QfURj8BL8cB3DuO02Ww9HCoNlEQyDmqA6MDaE4HaPup+AVgXnSGlrA2nR4UQpejrEXoYB6OJ0RBsSUqJy3UwsnagrW0XUoYwmVLJyLiYrMyVZGQuV74GhgpfR6yC76H8w2nI17OtfRyk5ENKHuTM1NOUfPYfq2PWvEW9K/bOc5P1nJ/wFArF6CORjIP3gWIhxBTgJLoB0MNfsBDiPGAcsDMqbxzgllL6hBBZwDLgxyMi9TBSfrqcickTyXHkxFuUGKT00tDwBk1NpTQ2leLz1QGQnDyTgoK7ycpcSWrqfOVvYKB4WqD+QNQTf9TTfue539mznSUlrOjzYNKFEaUfm+bpir4X6t2lzJqxcnjHplCMEVpaWpgxYwZvv/02U6dOHdF7P/XUU2zZsoWXX3552O+VML/eUsqgEOKrwOvoWxmfl1LuE0J8F/hAStn5adwEvCRj/UzOBJ4VQmjoL/5+GL3LYTQipaSivoKLJ14cb1FiOFHzazT5KB/tCWI0JpGRsUx/XZCxHJstP97ijS6khIaP4eD/wsHX4cQ74cVsYYxWSM3XFXzeXCi+spvCHw8puWAd+1OrCkWisHHjRq666qoYw+D+++9nx44d7N27l7y8PKqqqgbcb2lpKU888QTvvfcebW1tTJs2jfXr13PDDTdE6tx1111s3LgxEnxpOEkY4wBASrkZ2Nwt79+6XX+7l3ZvA8Mbv3KEqWqvosXXwoKcxImnIKWkuvoZYBIl879LevoiFaNgoAS8UL1dNwYOvg6t4YAqeefDxQ9CwYWQOkFX/rZ0NZWvUCQQbreb5557jldeeSUmX9M0br/9dvbs2cOWLVvOqe+3336buXPn8o1vfIP8/Hxef/117r77bqSU3HHHHQBYrVZuvvlmnnzyyU+WcaDooqJeD7ZUkps46w06Ovbi851CiC+TkXFRvMUZPXScgkNbdGPgyFsQcIHJDkUr4VNf02cE0ibEW0qFQnEWNm/ejMFgYNmyZTH5P/3pTwF47LHHztk4ePjhh2Ouv/KVr/DWW2/x8ssvR4wDgDVr1nDFFVfgdruHNWyzMg4SlPLT5aRb05mSOiXeokRoaNwKGBCcH29REhtNg7rd4dmB/9XPAVInwvybYPpqmPypPtcAKBSfSP72TTi15+z1wthDQTAOUoXlzYVP//Ds9cKUlZWxcOHCEdtC2d7eTm5ubDj5RYsWEQwG2blzJ5dddtmw3VsZBwlKRX0FJTklCbWPt6FhK+npF9DRrt5x98DnhKOlujFwaIu+TRABkxbDZf+mGwQ5s9RrAoViFFNdXU1+/sisrXr11Vd58803e8xEOBwO0tLSzmldw0BQxkEC0uhp5HjHcW6YfsPZK48Qbnc1LtdBiov/hY72eEuTILRUdc0OVG3Xvf5Z02DaZTB9FUy7ApIy4y2lQjE6GMATPIAnDn4OPB5Pjyf54WDHjh2RtQWLFi3qUW632/F4PMMqgzIOEpBEXG/Q2PgGANlZl3P0yKh2H3HuhIJQ817X7oKGA3p+ZjEsvlufHShYAsZPZmhthWKsk5WVRUtLy7DeY/v27Vx11VV897vf5Stf+QodvXhHbG5uJjs7e1jlUMZBAlJ+uhyr0cqsjFnxFiVCQ8NWkpNnYrdPYpT7lhoY7mY4/KZuEBx+A7ytune+wmWw4HZ9hiBzZPc6KxSK+FBSUsKmTZuGrf9t27Zx9dVX8+1vf5v169f3WufIkSN4vV4WLBjenWzKOEhAKuormJs1F3OCPIH6/Y20tu1iyuSvxluUkUFK2PMH5lc8Af84oPsecGTBjKt1Y6DoErClxltKxRhCSklIkwQ7j5BGICQJahrBUGxeSJMEOvNDWrhNuH5IsqcuSNvuk2hS6rGnpERKPdUiqUTTuq67l+vydJ1rUeWys31nniaRhGNOIcNpZzym8HW3ss9NgRPN7tjPoJeTPsM/SQgGNZp8rnP7vAdSN8qlzuwLLqZywwZ2fVzNuIyuV4ZVR4/gdrmoPFyFx+vj1b+/DcC082ZgsfRvu/c7O8q484vX88W1d7Js1Wd5Z6/+EGY1QsnMrtcnZWVlFBUVUVxcPIBRDBxlHCQY7oCbA80H+PKcL8dblAiNjW8BGtnZl8dblOGn4zS8cj8c/BtmxyS4+AH9dcH4BWBI/HgQisEhpcQb0PAEQrj9QTz+UPhcTz1+/XAHQnj90fnB2DrhNv6gFlHwAU0jFJIEwoo+ovTDin1I+XD3kHUlBBiEwCBAhFP9WsSU6XWFHm4qHDiqM6aUnnZdXz0pA5cvKjBX95hTvYTa6R6bSpOghbTe6/VrYH216buH4pmzOb9kIa/8+U/c8uW7I/nf+vpXee/t7ZHrz1ymb3UsfX8vEwsKAZiWm8I/P/gt7n8odstiJ3966Td43G6e+68nee6/nozkT5w0iRPHj0euX3zxRe66665+DHBwKOMgwfio8SNCMsSC3MRxftTQuBWbdTzJyYnzmmNY2PsneO0BPaTwqo28753JyksujbdUigEQCGk0Of00dPhodPpocPoi5weP+fjvk7t0JR6lyN3+EN4oA2CgWEwGHBYjdrMRu8UYOU+1m7EYDZiNApPRgNkgMBrC50aByWDAZBSYwnl6KjD3km82GjAaRKSdMaqe2SgwGrrq7frgfZZcuDhWgRu6lHqnQjd2lhu6FHyswu8yCIaayspKZuQPbvYtXoGXfvDod7n//vv514fux2g0AvDujrIztjl27BhCCP7PZ69mak5yr3X+9NJv4aXf9siPXnOwd+9edu/ezX//938PYgT9QxkHCUbF6QoEgnnZ8+ItCgDBoIvm5jLGj78pobZVDimuJnjt67D/LzBhIXz2GcieDmM5XPMoIhDSaHbpCr/B6aMxkvp1AyCs/BudPlrcgV77SLaasIoQ44LOiPLOSLLgGGfEZjZGKXdTjKK3x5QZcVhMXWXhfKMhsf4u6pINFGX3roAUg2f16tWsW7eOmpoaCgsL+9Vm8+bN3HbbbT2cJw2U2tpafvWrX5GWljaofvqDMg4SjPL6cqaPm06KJTF8CTQ3b0fT/GRnXxFvUYaHylfh1fXgadX9EVx0/+AdqyjOSrBT4UeUe6yi71L4fppd/l77SLIYyUqxkp1sZWp2MkuKMslKtpKVYiE72Ropy0q2YrcYw6GMV4zwSBVjkfvuu29A9detW3f2Sv3gyiuvHJJ++oP6FUwgglqQDxs+5Nqp18ZblAgNjVsxmdJIT7sg3qIMLZ4W3SPbRy/pXtJu/QvkzYm3VGMOKSW1bV7217azr7YtnLZT2+ZB9vKa3WExkpVsJTvFypSsJBZPydAVfjgvKzms8FMsOCzq50uhGC7UX1cC8XHzx3iCnoRZb6BpQRob/05W1qVjK/zyoTfg5a+Csx5WbNADHplUAKnBEgxpHG10dRkCdboh0Bqe6hcCpmQlsaBwHJ/Pmkh2+Mk+O8USMQCSrGPo/5lCMYpRf4kJRHl9OQAlOYnh/Ki17X2CwTays8bIKwVfB7z+f6H8l5A9A77wO5iQGIbYaMPjD1F5qj0yE7C/rp0Dde34gvrqcYvJwIy8FD49J49Z+anMGp/GjLwUpfwVilGC+ktNICrqK5iQPIG8pLx4iwLojo8MBiuZmcMbGnREOLYN/roOWk/Asvth5cNgtsVbqlFBs8sf80pgf107RxucaOHXAml2M7PyU7l1SSGzxqcye3waU7OTMBnV1k+FYrSijIMEQUpJ+elylo5fGm9RAF2exoatZGR8CqNx+MKCDjt+F7zxHXjvWcgogi+/DgUXxluqhERKSU2Lp4chUNfmjdSZkG5nZn4qV8/NZ/b4VGaNT2VCuj2hd7LITs87GsiQ1uUBJ9rZTkyejC3v8ugT7q/bSfTaic72shdHO7KPix7t+xxIH/mxp2YXBBrP4ne/r77OhXPoSoY0tHPYNhqNCDHoPkYFPV05jAjKOEgQTnScoMnblDCvFJzO/Xh9tUyZMrBVuQnF8XfhL/dA81G48B647BGwjGJDZ4gJaZLSj+v5/X4fT1e+zf5THXSEHdMYBEzNcHBBbiozZ+Uxc1wS56XZSTeZkCENGZLg1pAft+IMtkBIQwZlV1lQT2VQg3DadR2uE1a6ssu9HmEXfHqe1q1OzHXUuRbbvqu/zjr6eKdh5OSWHSP8KY88hRg5XfZBvMU4I6E1yQRPu89e8QxYgKBzcH2MBkwmYPh3Lva878jfUtEbnesNFuQkxjvwhoY3AANZWaPQCVDAC299H97+KaRPgttfhSlj4NVIH0hNIr1BNE8QzRtC8wT0c08Q6QmFzwOR8ianj5dbnfzZ46ZOaliBabRzGQaKsTEdI0XSgLVJQJMX8ALNhICmswkjAKMBYRQIk55i6rqmM1/3uANhJzuiy40eGKKuo+pEudrT2/e47qV9OBUCjlVVMWXKlHBeWNhoL3m95PWoJ6Kze+b3XrdPV3x95IszlPWRHzVzU1lZyayZM/to1I9++0CTENLC7ppD0e6etV7cMHeex7pgluFzs82DP1l3Dx81JxMzodHbJA50uTMOBIOYTaazzND0PbEh+5q9OUu73mQaLH07igbQsA/hvfqLMg4ShIr6ClItqRSlF8VbFEDfwpiethCLZZSFHD5ZDn/5ih4xceFauPJRsCaGz4izIQMhgq2+sFIPonUq/M7DHewyAiJHCOkLnvmXygDCZqTSDH8KeHnD4yEg4YJUOw9MzGSKv4Xp06dFKXIDwiR0JW8S3a57Kvzoa10xJ+YrhpbSY8xbWRBvMQZFIKTh9AZx+vTD5QvSEU478/d7fExsbCUQ0ggENfwhjUBIwx+Uel748AU7z2W4vKtuIFy3q60WWWMyFPx8TT4Gp/fsFc9GoKcPjBj3y7FJtzqxBT3cNove27W1tnD18gv43ctbKJhc1PsN+urzDPQmE4BFdH3wTz31FFu2bOHll1/uV5+DQRkHCUL56XJKckowiPgv4vJ4TuB0VjJt2rfiLUr/Cfph20+g7HFIzoUv/gmKEzcWhAxpBE658dd0EKhx6ulpV9/vF00GDHZT5DCmWjHnJmGwmxB2EwabKaZchFOfUfBK5Sl+8241e0+2k2w1cdOSQm5dUkhxrm40lZaWkrJ84sgN/hNGMKTh8oXo8AW6FLo3iMsXwukL4PSFcHqDuPyd+WHl34sR4A/28wX0oUMR181mkwGz0YDFaMBiCucZu/LsZiOpNpOeZzJE2lmi2kXqm2LLzMau/jrdLxsNAoOhyz2zwQDGcL7oTFtPUpyTrM/qhEWOnaQRkcmQSHlnvIZwprOb++SRMkof+n/f4zPXXM2VS+cD0NDQwC233MKePXtoamoiJyeHNWvWsHHjxgF5MiwtLeWJJ57gvffeo62tjWnTprF+/XpuuOGGSJ277rqLjRs3UlZWxsUXD+9sqDIOEoBmbzNV7VV8dtpn4y0KAA2NbwCQnZW4yjWGU3v1tQWn9sC8m2D1D8GeHm+pIkhNEmz0xBgC/loXhH/oDQ4T5okppMzMwJTtiFHyhrDiF+aBGY3HGl38dvsR/rCrhjZPgOm5yXzvs3O4rmQCyWo74ZCgaZIml5+6Ng+1rV7q2jzUtXmpbdXTulYPzW4/3kD/FLrNbCDZaibZaiTZZiLJYmJ8uo0kq4nk6MNmIslqIsWqp8m2rrIkq4n3d27nsktWJuwMDkClsw77IJ1Y6a+jRnaMbreb5557jldeeSUhENBtAAAgAElEQVSSZzAYuO6669i4cSNZWVkcPnyYdevWcddddw0oBsLbb7/N3Llz+cY3vkF+fj6vv/46d999N1JK7rjjDgCsVis333wzTz75pDIOPglU1FcAJIzzo4aGrSQlTcfhmBxvUc5MKAg7/h1Kw8bAF36nh1WOI1JKQi0+3QCocRKo6cB/0on06auqhcWAeUIyyUvzsUxMwTIxGWOGbUh+5EKa5O8H6vn1O9VsO9iAySBYNSeP25YUsnhKRkIri0RDSkm7J0htm4faVg+1YWUfrfxPtXnxd4sKaDEZGJ9mIz/NzpKpujvnTqUdq8yNuiFgM5FsMZFkNQ7Z1k9TAr/aGe1s3rwZg8EQEyMhMzOTe+65J3JdWFjIvffeyw9+8IMB9f3ww7HRGr/yla/w1ltv8fLLL0eMA4A1a9ZwxRVX4Ha7cTiGb4F1QhkHQojVwH8ARuA5KeUPu5WvBX4CnAxnPSWlfC5cdjvwL+H8R6WUvxwRoYeAitMVWAwWZmfOjrco+P3NtLa+z+TJX4m3KGem4WN9bcHJXTD7OrjqcUga+fURoQ5/rCFQ40RzhYP/GAXm/CQcJTm6ITApGVO2Q188N4Q0OX289P4JfvfucU62eshNtfK1y6dz0+JJ5KQqXw694fIFY574e3vyd/tjt8kZDYK8VBv5aTbmTUrn03P08/x0OxPS7eSn2chIsijFfI786L0fcaD5QL/rh0KhSFTEc2VGxgw2LN7Q7/plZWUsXLjwjN9xbW0t//M//8OKFYOP49He3k5ubm5M3qJFiwgGg+zcuZPLLrts0Pfoi4QxDoQQRuA/gSuAGuB9IcTLUsr93ar+Xkr51W5tM4BHgEXoS7N2hdu2jIDog6aivoI5WXOwGOPvwrep6S1AS1yviFoI3vkvePN7+rbE65+HOZ8fmVt7g12GwAk9DbX59EIBphwHthkZWCYlY5mYgjkvSV+hPwxIKSk/3sqvd1axec8p/CGNpUWZ/MvVM7l8Vi5m5YAI0A2nD6pb2FXdwjuVXn64exu1rR7avcGYekJAdrKV/HQ703NTWDE9h/Hp+gxAfrqN8Wl2slOsCReBUTGyVFdXk5+f32vZTTfdxF//+lc8Hg/XXHMNL7zwwqDu9eqrr/Lmm2+yZcuWmHyHw0FaWhpVVVWD6v9sJIxxACwGDkspjwIIIV4CrgW6Gwe9sQrYKqVsDrfdCqwGXhwmWYcMT9DD/qb93D779niLAuivFKzWPFJSEjAIUfNR+Mu9cHwnnHcVXPPvkJJ79nbngAxq2FqgY/vJyIxAMMqxjDHThmVyKpaJYUNgfDIG6+CeYvqDxx/ir7tP8ut3qtlXG15guHgSty4tZFrO6NiVMVxIKTna6OKDqmY+qNINgqONLkCf7s+zw/SJDhZPySA/zd6l/NNs5KbasAyTIafoHwN5ggfo6LYgcSTweDw9nuQ7eeKJJ3jkkUf4+OOPefjhh1m/fj3PPvvsOd1nx44dkbUFixYt6lFut9vxeM7i6GqQJJJxMAE4EXVdA/Tmyu7zQojlwEHga1LKE320ndDbTYQQdwN3A+Tm5lJaWjp4ycM4nc4B93fIe4igDGI6bRpSWc4FKX1o8h8IPsU//vGPPuudyzgHJ5jG+Nr/ZeqRTUhh4tCM+zmdewnsqgQqh/RWJjeknRCk1ggmBoy0cZSgVeJNA1+xxJsm8aWCZnEBLggB1eFjGDnl0vj78QDbTwZxB2FisuC2WRYuGm/CZmqkZn8jNf0xo3thxL/PISKgSaraNA61hjjUonG4JURH+I1OshmKxxm58TwzxelGJqcZ8LldJCc7AadeqRXcrXAE/RgrjIbvMy0tjY6OjkH1EQqFBt3HQElLS6OhoaHX+yYlJZGUlMSECRN44oknWLVqFevXr2fixIHtBNq5cyfXX389Dz/8MLfcckuv42xubiY5ObnP8Xu93kH/H0gk46C3+bruO2tfAV6UUvqEEPcAvwQu7WdbPVPKnwE/A1i0aJFcuXLlOQvcHT1e/MD6+/jDj+E03HrZraRZ4+AGK4qGhq18tMfP/PlrychY1me9cxnnoPjbN+HQszD1UljzFDPTJtAPFy/9RmoS74FmXO/W4T3YAgLsMzM5aqlnwaeXYky1DuHd+k9Ik7xZeZpfv1NN2aFGTAbB6jn53LZ0MhdMHjdk77ZH/Ps8R1rdfnZVt/B+VQu7qpv5sKYtsrVvSlYSq84fxwWTx7GwMIOp2Uk9Pp/RMs7BMhrGWVlZOein/njMHCxevJhNmzad9b42m77Wx2w2D0jGbdu28fnPf55vf/vbPPDAA0DPcR45cgSv18uyZcv67Ntms1FSMjhvu4lkHNQAk6KuJwK10RWklNEO2n4O/Ciq7cpubUuHXMJhoKK+gmnp0+JuGIBuHJhMKaSnL463KF24m2HXC/oWxc8+HeMJbrCEnH5c75/G9W4doVYfhhQLKZcWkLw4D2OalT2l9XExDBqdPn4ftcAwL9XG16+Yzhcu+OQsMJRSUt3kDq8XaOb9qhYO1+tP/GajYPb4NG5fWsjCwgwWFo4jOyU+Bpzik8WqVavYsGEDTU1NZGbqC6BfffVVmpqaWLhwIcnJyezbt4+HHnqIJUuWMG3atH73XVpaytVXX829997LF7/4RU6dOgXorzKijYCysjKKioooLi4e2sF1I5GMg/eBYiHEFPTdCF8Abo6uIITIl1LWhS/X0DWn/DqwUQgxLnx9JZDwHnxCWojdDbu5ekp8t98BaFqQxqa/k5V5KQaDOd7idFHxGwh64aJ/HhLDQEqJv7od5846PHsbISSxTk0j7eoi7LMyEHFcyLe/tp1ntx1h8546AiHJRVMz+ddrZnL5zNwxH+EwENLYV9seWS/wQXULjU59sWeqzcTCwnFcVzKBRYXjmDcpHZt5+Nd3KBTdmTt3LosXL+all15i3bp1gP6U/swzz1BZWYnP52PSpElcd911fPOb34xpK4TgkUce4dvf/navfW/atAm3281jjz3GY489FskvKCigurrrveWLL77IXXfdNfSD60bCGAdSyqAQ4qvoit4IPC+l3CeE+C7wgZTyZeA+IcQaIAg0A2vDbZuFEN9DNzAAvtu5ODGROdhyEFfAlRD+DdraygkEWsjKTqBdCpoGH/wCCi6C3MFt89R8QdwVDbjeqSVwyo2wGUm+MJ+kJfmYc+IbjMkf1HjqrcP851uHcZiNfPHCQm5ZUjCmFxi2eQKUH29hV1ULH1Q3s/tEa8RZ0KQMOxcXZ7Fo8jgWFWZQnJOMQe0SGDNITdNjLIRCXUG0NC0qWFZnYK2o627lSInB6yXg8aKHwOwMeNAzlVGRMvuqK6PzzlBfAt+6804efPRR1l56KUajkU9NmsRbmzaF60T+gVOn8Yaf/qtqahBCsHzaNDz79/cSOELy9IMP8vSDD/b8vOxdkRX27t3L7t27B+Rc6Vzpl3EghLgRaJVSbglf/xv6or59wNqop/lBIaXcDGzulvdvUeffoo8ZASnl88DzQyHHSJFIwZYaGrcihIXMjAQKUHTkTWipgkv/9Zy7CJxy4XynDndFPdIXwjw+iXGfK8Y+PxuDJf5Pn/tr23ngDx9SWdfO50om8G+fmUW6I/5bWocDTZOUHqznZ9uO8u6xZqTUfQfMyk/lpsUFLCrMYNHkceR+Ql6djCSdAY/6c2g+H0G3G83pJORyEepM3W49dbkIuT1objea203Q40b6/GiBADIYQAZD4TSIFgwiA0FkKIQMBNBCIQiFSPned3Eaep8Nk30FROgFj8vVdRGZWRTdfS73ntc9BYjIFB1YIfZ85apV3HnyJMfa2ijoXGzYY1YzNjDDa3/+Mzddfz0LL70Uf58zoL0Ec0D3qN75+FJbW8uvfvWrAbllPlf6O3PwbWA9gBBiAfAw8G/o2wUfp9v0v6J/VNRXkJeUR35y7/tmRwopJQ0NW8nIuAiTKTmussTw/nOQlAMz1wyomQxqePY14nynDv+xdjAJHOdnk7QkH8uklIRwUhMIaTxdeoQn3zxEusPCz25dyJWz8+It1rDgD2q88mEtz247wsHTTsan2fjnS4u5cEoG8yelkzQK3DlrmkYwGOz1CAQCfeaHQiE0TUPTtJjz7tfnWtZb3VAwSNm2bV0Kfzg/GJtVPwbIKpuNjtTUYRBoZLjlzjuByL6Xs3LT2rXcBLigayaiB5LeviyTqevv48orrxyAlIOjv3+VhcDH4fPrgL9IKX8shNiC/hpAMUCklFScrmBh3sJ4i4LT9TFe7wkmF95z9sojRUs1HHwdlj8Ipv49SQdbvbjePYXr/VNozgDGDBtpn56CY1EuxqTEWUfx8akOHvjDbvaebGfNvPF8Z81sxiWNvdkCpy/IS+8d5xfbj1HX5uW83BT+343z+My88cPmpEnTNLxeL263u8dx9OhRfD7fWRV7b3mhUOjsN+8HBoMBg8GA0WiMnHe/7q3MZDJhEAIRCCL8PggGweMFrwfcbnC6wOUEnx+D1BDh6XGBjD0XAoPFgsFsQVgsGK0WDBYrBqsFg9Wql9lsGKw2DDYrRqtVvw4fRrsdo92OMJsxGAwRQzs6zkF/UpfLFVnQdzb6Mub7ch88UOP/XB4WzvUB41zaOZ39NUGGlv4aB16g8wXoZXRN37dF5SsGwEnnSeo99YnxSqFhKyDIyho+V5wD5oPn9am6hWvPWE1qEt/hVpw7a/Ee0JeZ2GZkkLwkH2vxuCF3VTwYgiGNZ7cd5d/fOEiqzcwztyxg9Zz4zhoNB/UdXjbtqOLX71TT4Q2ypCiDjZ+by8rp2QP6cZRS4vf7e1X0Zzpkn09mUFdXh9lsxmQy9TisVitJSUk98vuqf6ayzvxORW80Gs8YKEhKidbWRqCuTj9q6wjU1RKMnNcRrK/v8dRpTE/HND4fc/54zMXTMefnc6ihntkXXIAhKRlDcjLG5CQMKSkYkpMRlsRw71xZWYnVOrgdJj6fD4tl7BnV3YnX99Vf46AMeFwIsR3dRfH14fzpxDofUvSTzmBLJTmD24s6FDQ2bCUtrQSrNTveougEvFDxa90LYlrvDkRCrgDuXadxvltHqMmLIdlMyspJJC3OwzQu8d5ZHzrdwYN/+JAPa9q4em4+3712NpnJY2v73dEGJz8vO8afymsIhDRWz87jn1ZMZf6krgiZPp+PtrY2nE7nGRW8y+XC7Xb3+cQuhMDhcESOrKwsHA4HSUlJMfnRx44dO7jkkktG6uOIQfP7CZw6FVH0MYr/1CkCdXVItzt2jGZzRPEnXXQR5vx8TPl5uiEwPh9zXh6GXp6c95SWkpLgfg4UiU9/jYOvAk+jGwX3SCk7/Q98GvVa4Zwory8nxZzCtPT+74MdDrzeWjqc+5g2dWCuS4eV/X8FdxNccGdMtpSSQI0T585a3B81QFBimZxK2pWF2GdnDVscg8EQ0iTPlR3l8a0HSbIYeermEq45f3y8xRpSKo638Ow/jvL6/jpSjSFumJHG5VNTsGheave8TeX2Ntra9KMvl682my2ixNPS0sjPz+9TyTscDqxWK4Y+FrT1xUg8gUkp8R87hnvXLjy7yvEdPUqgrpZQQ2OPusbMTMz5+ViLikj+1DJM+fldij8/H2NGBmKAY1Qohop+GQdSyhrgM73krx9yiT4hVJyuYF7OPIyG+K6Y118pQHYibWF8/+eQOQ2m6FHNZCCEe3cDznfqCJx0IixGkhblkbwkH3NeUpyF7ZsjDU4e/MOHVBxvZdXsXB797NxR7azH7/fT3t5Oa2srbW1tfHi0jo+O1uJxdpBi9HO7LQBSg8Pwj8N6G6vVSlpaGmlpaUyaNClynpKSElH0drt90NH14oX0+/Hs24envBz3rnI85eWEWlsBMI4bh23mDKwrVmDOz8eclx9R/Ka8PAy2xJvhUig66fcyYSGEDbgGmAo8K6VsFUJMBVpGg0+BRKLV28qRtiNcXRR/50cNjVtxOKbhcEyJtyg6tbuh5n1Y/cPItqKm3x3AW9mMKddB+men4ijJwZDAK9xDmuSFHcf4yesfYzMb+Y8vzGfNvPEJ8a63L6SUuFyuyBN+pwEQfbi7TXtrEqzCSk5GKkUTCsjKGBdR/p2HbYwpwFB7O57du3VDYNcuPHv2IH26syZzYQHJl1yCY+EC7AsWYpkyOaG/c4XiTPTXz8E04A0gGUgH/gC0Al8JX9/Zd2tFd3Y37Abiv94gEGiltfU9CgrujqscMbz/HJgdurtkwH+iA29lMymXFZB6eUHC/9gea3Tx0B8+5IPqFi6fmcPG6+YmpMvjQCDA4cOH2bdvH0eOHKGsrKzH+32z2Ux6ejppaWnk5OVzrF2yvdpNjUuQmzWOtStmsqZk4pgODx2ordUNgQp9ZsB38KC+KNBoxDZrFuO+8AXsCxfgWLAAU1ZWvMVVjEKit5tKonwuoeeHhnUvat/09/Hr34Et6MZAa1T+y8DgglZ/AimvL8dkMDEnK75hkRsb30LKUOK8UvC0wJ4/wvk3gl1fxNb+9+MYHCZSlk9IaMNA0yS/3FnFj/73ABajgf934zyuK0ksmYPBIEeOHGHfvn0cOHAAv9+Pw+EgOTmZ4uLiyNN+p0Fgs9lodPrZ9PYxfr2zmnZvkAunTOZH109l5XkD23kwGpChEL7DhyPrBdzl5QTrdP9uBocD+/z5pHx1HY6FC7Gff36viwEVI4MMez4MhdNORdqpXPVzvUyL5HevI/WySP2uNjKqjdat37aWZq4omc/v//4WhVOKInWJag90yyeyiyYmvx+K34GBziW9119/PRdddBFf//rXz+VjGxD9NQ4uApZIKUPdfhCOA2NrddUIUHG6gtmZs7GZ4vtE2dC4Fasll9SUuXGVI8LuFyHoiSxE9J904q1sJvWKwoR+jXC8yc2Df/yQ9441c8l52fzgc+eTl5YYswXBYJBjx46xd+9eDhw4gM/nw2azMXv2bObMmcPkyZMpKyvrEcXvaIOTn/9tb8zOg7uXF1FSMK73G41CNK8Xz0cf4SmvwF2+C0/FbrRwCFxTdjb2RQtxfPnLOBYuwDp9OsKUuP8HhwIpJYHOQ+uWRp0HNYlfSoJS4te60kBMqkWuY8s0/JpkTSDIcY8vonR1BSx7VdR9KXcwQkfvC1zPmbCTQgMgEIjwtYDwueA/f/JjVqxaReGUokh53YnjPPK1r7HzH6XY7HauvfH/8H9/8EMsFku4rejsPpKKyP1EJH/ntm08suEhPt6/n7z88Xz1gQe49bbbIuI98sgjrFixgjvuuGPYvSQO5H97b15kCtB9HSj6iTfoZW/TXm6deWtc5QiFvDQ3l5GXdx1CJMC0sKbprxQmLob88wF91kDYjCQvS0z7U9Mkv3m3mh/+7QBGIfjx9edzw8KJcX+iDoVCVFVVsXfvXiorK/F6vVitVmbOnMns2bMpKirqcwHg7hOtPFN6hNf3n8JsNPD5BRO5e3kRU7ISd+FnfxFOJx1vvtm1XmD/fggEALBMm0rqpz+trxdYuBDzhPjM+mhS4glpuDUNd0g/elyf5bxWJvHM7iO9KvCglPilRlBDT6OV/jBOXxsAq0FgNgjMwsCqZIkrpMUo3c7zTsVsEKJLMRN2tESXog74/Nis1igF3qXMDX206e0+sQbAmb9zt9vNn365iVdeeYVpSfoDQCgU4rPXf57MzEy2l5XR1NTE7bffTrLRwE9/+tN+f0bHjh3ji59dw5e//GVe+u1v2b59O/feey956WnccsstgB74qaioiN/85jeRwE/DRX+Ngy3A14E7wtdSCJEKfAd4bTgEG6vsa9pHUAvGfb1BS8vbhEJusrMuj6scEY6VQvMRWKlHMvPXufDuayLlsgIMtsR7YjvR7OYbf/yInUebuLg4ix99/nzGp9vP3nCY0DSNqqoq9u3bR2VlJW63G4vFwowZM5g9ezZTp06NccMajZSStw7U88w/jvDusWZSbSbuXTmV2y+aTE5KYsyAnCsyGKTjjTdofmETOR9+SA26/wDb3Llkrr0d+4IFOEpKMKann7WvMxGSkuZAkEZ/kAZ/kAZ/gAZ/kLZgqFcF3qnwPd3yvdrANbTdYMBuFDiMBhwGI34EIhTCIgQWIUgyGzCLTsUclfZ1bjBgFoTTM9XTU5MQUYpfYAkbAJaoa2M3pVtZWcnM5MH9vXT4faRYR9bz6ebNmzEYDCxbtiySt2XLFvbt20d1dTWTJk0C4Mc//jF33nkn3//+90ntp5voZ555hvHjx0cMipkzZ/Luu+/y5JNPRowDgDVr1vDiiy8mjHHwdeAtIcTHgA34PTANOA3cOEyyjUkSxflRQ8NWjMZkxo1bElc5Irz3HDiyYNa1AHT8/TjCaiQlwWYNpJT87r3jbHytEiEEP/jcXL5wwaT4PGVqGsePH2ffvn3s378fl8uF2WzmvPPOY/bs2UybNg2z+cw/nm/sP823d3iocb5PfpqNf7l6Jl9YXEByAr/G6Q+ay0Xr//yZ5l/+kkBNDeaCAjquXcOcG2/ENmcOhn545/NrGo3+II2BWIXflRcI5wdpDgTR+uinu/LuPM82m7HbwvlGI3ZDP86NAoeh69xuMGDo9n+vtLSUlQsXDcGnOLKc2rgRX+WBftcPhkI0D3ILrHXmDPIefrjf9cvKyli4cGHM3/vOnTuZOXNmxDAAWLVqFT6fj127dvXb8dbOnTt7xE5YtWoVv/zlLwkEApG/5cWLF/Poo4/i8Xiw24fvgaS/fg5qhRDzgZuABegzMj8DfiulHOKXPmOb8tPlTE2bSrptcE8qg0HKEA2Nb5CVuRKDIQHcj7aegIN/g2XrwWQlcNqFZ28jKSsnYXAkTkyEk60evvmnjyg71MiyaZn86PPnM3HcyC5K0zSNmpoa9u3bx759+3A6nZhMJqZPn87s2bMpLi7ul0vZQEjjh387wC+2H2N8kuDxG/SYB5YEdCQ1EAL19bT85re0/P73aG1t2EtKyNnwDVIuvZSasjKYX8IJf4DGNlcPpd/gD9IYCESe/luDvXtntBsEWRYz2RYTBXYLC1OTyLaYyLSYyLaYyDbrZdkWE6kmYw/lrRi9VFdXk58f6/L81KlT5ObmxuRlZWVhNBo5FQ7Z3B9OnTrF5ZfHzuTm5uYSDAZpbGyM3Hf8+PEEAgFqa2uZOnXqOY7k7PR3K+Ny4O3uYZGFECYhxHIp5bbhEnAsEdJC7K7fzaopq+IqR1tbBYFAc+LsUti1SV9htOhLALS/dQJhNpD8qQnxlSuMlJL//uAE33u1Ek1KHv3sHL544chtq5RScvLkyYhB0N7ejtFopLi4mDlz5lBcXDwgP/V1bR6++rsKdlW3sPaiyXwquZ7LF/bupnq04Dt0iKYXNtH+yit0mC00XXMtjVddw/HsXA67fRz+4BDHZRrebR/12j7VpD/JZ1lMTE+ysWycmWyzruCzLCayw8ZAttlEkml0OmxKdAbyBA/Q0dFBSsrIhvbxeDw9DAHoe63CYINAde5wiM7vnC3oy9voUNHfucO3gHygvlt+WrhM/bX0g8Oth+kIdMQ92FJDwxaEMJOZuSKucgAQ9EH5L2H6akgvINDgxvNhA8nLJyZEJMW6Ng/f/NMe/nGwgSVFGfzk+nlMyhj+2QIpJXV1dRGDoLW1FaPRyNSpU7n88suZPn36OTkYKjvUwP0v7cYXCPHTm0r4zLzxlJY2DMMIhpeQlJzw+Nhb/iF7332fwy4vJ6bMpeaxz9BkCX8uHjCdqGey3cpUh5Wp7jZKiibryt5sijz9Z5lN2MawrwbF0JGVlUVLS0tMXl5eHjt27IjJa2xsJBQK9WpI9EVeXl6PmYb6+npMJlNMBMvmZt3nYHb28MbC6a9xIOg10jSZhENUK85OIqw3kFLS0LiVjHFLMZkSIKBm5SvgaoDF+vbFjrdOIEwGUi6O76yBlJLtJwP8c+k2giHJd9bM5tYlhRiGMcqjlJLTp0+zd+9e9u3bR0tLCwaDgalTp7Jy5UrOO++8c37HGNIkP/37If7jzUMU5yTzX19cyLSc5CEewdDTEQzpT/5uL0fcPg65vRxxeTnq8uIXArDCgk+RFgpQnJrMFSlJTHNYKU6yMdVhpdBmxRz+zkpLj7OysP8/1gpFd0pKSti0aVNM3tKlS3n00Uepqalh4kR9Bm7r1q1YrVYWLlzY776XLl3KX/7yl5i8rVu3UlJSErN2aO/evYwfP35Ahse5cEbjQAjxcvhUAr8RQviiio3AHODtYZJtzFFeX06OPYcJyfFTfC7XITye4xQU3BU3GWJ4/znIKIKiSwk2enDvrif5ogkYk+O7FuK7r+7nhT1+Lpg8jp9cP4/Jw7SVz+/3U1VVxaFDhzh8+DAtLS0IISgqKuLiiy9mxowZvcasHwhNTh/rf7+bskONfK5kAo9eNweHJXEWHGpSUuP1c9jt6zIAwgbBaX8wUs8ITAx4mXj0MPOOH2NKKMjcpRdw/uWXkJ08+rdaKhKfVatWsWHDBpqamiJP81deeSWzZ8/mtttu4/HHH6epqYmHHnqIu+66q987FQDuuecennrqKdavX88//dM/sWPHDjZt2sTzzz8fU6+srIzVq1cP6bh642y/EE3hVAAtQPRLDj+wHfj5MMg1Jqmor6AktySu++AbGsOBlrIui5sMEU7theM74crvg8FAe+kJMBhIWR7f99+Vde1seruKFRNNPH/3UoxDOFsgpaSpqYnDhw9z6NAhqqqqCIVCmM1mpkyZwrJly5g5cyZJSUOj7HZVt/DV35XT5PSz8bq53LQ4PjsrOvFrGttanOxqc4WNAS9HPb6YLXxpJiPTHFZWZqQyzWFlss9N1t82k/LbX2Fsb8dx4YVkfGktycuXq6iFihFl7ty5LF68mJdeeimyldBoNPLaa69x7733smzZMux2OzfffDOPPfZYpF1VVRVTpkzhhRdeYO3atb32PWXKFDZv3szXvvY1nm/kBrIAACAASURBVH76acaPH8+TTz7JtddeG6nj9Xr585//zOuvD38w5DMaB1LKLwEIIaqAx6SU6hXCOVLnrOOU6xRrZ6+NqxwNDVtJTZ2P1ZoA06vvPwcmG8y/mWCzF3d5PclL8jGmxnfWYOPmSlJtZm48zzwkhkHn7ECnQdD5zjIrK4sLLriA4uJiCgoKzrrtcCBIKXlhRxUbN1eSn27jf+69iDkThtejWl8ENMn2lg7+Wt/K3xrbaAuGMACFdgtTHTaWZ6QwzWFjmkNfG5BlNiGEwLt/P01PPUX73/4GUpK6ejUZX/oS9jmz4zIOhQJ0L4X3338/99xzT8SZWEFBAa+++mqfbY4dO4bNZmP58uVn7HvFihWUl5fH5HWEvXYC/OIXv+DCCy9kyZLh34Le362M3xluQcY65fX6Fx7PxYheby0dHXuYWvRQ3GToEqYNPvpvmHM9ODLo+N9DICBlRXxnDf5xsIGyQ4386zWzSApWn3M/TU1NHDp0iEOHDlFdXU0wGIzMDixdupTi4mLGjRseV8Qd3gAb/vQRm/ec4vKZuTx+wzzSRnhLaEhK3m5x8nJDK681tNIcCJFsNLA6K401OeksH5fS6yJAKSWusjKann8B9zvvYHA4yPjiF8m47VbMExJj94rik83q1atZt24dNTU1FBYW9qvN5s2b2bBhA0VFRYO6t9lsHpDXxcEwkJDNX0L3c1AAxDzaSSkHN+JPABX1FSSZkygeVxw3GRoa3wRIjC2MH74EARcsvpNgqxfXrtMkXZCHMa3/W/KGmpAm2fhaJYWZDm5dUsjb2/tvHPQ1O5CZmcmiRYuYNm0ahYWFQzo70BuVde3c+9tyjje7+danZ3D38qIRe42gScm7bS7+Wt/Kq/WtNAaCOIwGVmWmsiYnnUsyUvvcFaD5/bS/8irNm17Ad+gwptxcch56kPQbbsA4gPe2CsVIcN999w2o/k9+8pMhue/dd49cBN3++jl4CPgW8CywHPgvdA+Jy4HHztB0QAghVgP/gb726Dkp5f9n78zjo6rOBvycWZLJvu8kgbCFsCgEQVSQVRAU6lqhaqkaq4ZPbdWCVAtWRVptbSmtGwpqVVChBTQugKJRsCwhQBa2ACELIfs6mcks5/tjkpCEJEzITIbAfX6/Ifeee+4570lC7nvf8y7L21z/Lbby0GagBLhPSpnbeM0CHGzsekpKOdtRcjmCtOI0rgi5Ao3KdY5gpSVb8fSMw8vLeYkz7EJK25ZCVCJEjqTmv8cA8JnoWqvBJ3vyOHymhn/9YpRdyYCarAPHjh3j5MmTmM1mNBpNs3VgwIABBAYG9oDkNj7Zk8cz/83Az0PLhw+MZWxc0Plv6iZWKdlbrWdjcQWbiys502DGQyWYEuTLnNAApgT54tlJmKClspKKteso/+DfWEpKcR88mMg/Lcf3xhsRdiRzUlBQcA72PqmSgAellJ8KIRYAK6WUx4UQzwL22VXOgxBCDfwTmAbkA7uFEJuklFktuu0DRksp9UKIh4E/Az9vvFYvpbzSEbI4mipjFccqjnFD7A3n7+wkTKZqKip/Iib6PpfJ0MyJ76H0CPzsNSxVRup2F+GVGIbG33V5/OuMZv6y5QiJsQHcOCy83T4mk6lVZEFTvHFQUBCJiYkMHDiwR6wDbTGYLCzZmMm6PXmMiwtixdyRhPg4zwIjpSS9pr5ZISgwmnBXCSYH+jIn1J9pQb7nTRTUkJdH+Zp3qdywAVlfj9d11xH0p1/hOW6cywtXKSgo2K8c9AF2NR7XA012vo8a2x0RFzcGOCalPA4ghFgLzAGalQMp5bct+v8E3E0vYH/JfiTSpf4GZWXbkdJ8cWwp7F4FHgEw9FZqvsgHKfGZGH3++5zIm98fp6TGyBv3tM6b3jayoKV1YOzYsQwcOLBHrQNtOVlax8MfpJF9upoFkwbwm2mDHBpd0YSUkozaejYWV7KpuJJThga0QjAx0Ien4yKYHuyHjx2ZAy21dZxZ/hJVG/4DajV+s2YR+Kv56AYPdrjMCgoKF45oSs/YaSchjgO3SynThBC7gXeklK81bgN8IKXstv1SCHE7MENK+UDj+T3AWCnlgg76rwSKpJQvNJ6bgXRsWw7LpZT/7eC+B4EHAcLCwhLXrl3bXdGbqa2txdv73MQymyo2sa16G3+O/jPuKtfsqVutryE5gkr8pdslmjtapz24GcsYt/MB8qLnkNtnPrHfqaiNkBQPd2K92PNQYbCyMLWeK0PUPHKlzXpRVFTEiRMnMBptqT08PDwIDAwkKCgIPz+/Dkse9yR7isy8nWFEJSBpuDtXhl7YllVHP08pIQ8VO3FjJ1qKUKNGMgwz4zAxGhPewv6fmyY3F7+330FdUoJ+ymT0U6di7WY1xK7Qnd/b3kRvWKefnx8DBgzo1hgWi+Wi+H/obC5knceOHaOqqqrda5MmTdorpTxvZS57/5p8A8wG0oC3gVeFEHdiK8L0sZ1jnI/2Xnfa/csjhLgbGA20zP8b01ggKg74RghxUEqZc86AUr6JrWgUo0ePlhMnTuy24E1s376d9sZb/cVqhroNZfpk19RUsFiMpP7wKGFhNzMkfnK3x+tonXbx7TJAEnPLEnx3SmplAYPmXkVCsOvKHf/u0/1AIa/cM4GYIE+Ki4tJTU3Fw8ODyZMnu9w60BaTxcqfvjjEqvQTXNHHj3/+YlS3CkC1/XkeqTOwqbiSjcUVHNUbUQHXBXjzZGgAM0P8CNR2TQmRVivl775H8V//iiYoiMh31+A1ZswFy3uhdOv3thfRG9aZnZ3d7boIrqitYA/2vHC3fbJ1dkdtbdfXqdPpGDmye5l47f1f/iC2SoxIKV8XQlQA1wLrsTkpOoJ8oKVtuQ9Q2LaTEGIq8Hvgeillc8ZGKWVh49fjQojtwEjgHOWgp2mwNJBRmsFd8Xe5TIaKih1YLHWu31KwmGxFlgZOw+IWRd1Pu/G8MhSNCxWD7NPVfLI3nweu60dMkCdWq5WNGzfi5ubGiBEjGDt2rMtka4+iKgMLPkxjT24F946L5fezhuDugEJAJ/RGNhZXsLG4kuw6AwK42t+L+/uEMCvEjxC3C/OjMJeVUfj009R9n4r3lClEvPA8GieFcF5uSCmxmK2YG6xYzFYsJitmkxVDhaQ4txqrVSItEqtFYrXKs+fWpjZr6/PGY9nRuVVitbS4p3E8i0XaHojSJpOUIK22rzSdt2mPvkZFRVFdm/W0XaDtH9nq/CxWq8RYVdved6bd004f2R1clC2PXGTcVGk5u5Hfg3TF5yCv6URKuQ5YJ2ybs9HAKQfIshsYKIToBxQAdwHzWnYQQozEpozMkFIWt2gPAPRSSqMQIhib4vJnB8jUbbLKsmiwNjAqzHX+BiWlW1GrvQgMGOcyGQBbHYXaM3DVA9SmFiDNVnwmu9bXoCnh0YJJthDTnTt3UlBQwK233trscHix8MPRUh5bu496k4UVc0cy+4rIbo1Xbbaw9nQZq6U3J/6XDcAYPy9eGBjFTSH+hLt3z7GybscOChYuxFpVTdgfniVg7txL3tnQYrFirDNj1Jsw1JkxGcyYTa0f3pbG8+ZjkxWzyWL7am7Z1k6/FtctZmuHcuR8tcdhaxIChFqgUjV+1KpW503HQtg6C2GrIihUjV/baW9817S1t5jHdtDyi2g8OPt709TPZLKi1bajGIv2Tttt7HjNdvQ5e12033weueydv8Fk7Kyr07BXOThB+1UZAxuvdfvVRUppboyE+KpxvHeklJlCiD8Ce6SUm4CXAW/gk8Y/Mk0hi0OAN4QQVmy/dcvbRDm4jKbkR64qtiSlldLSrQQFXY/KRf4Ozex+G/xjsURcT+2/9+IxIgRtiPMrHHbE9sPFzQmP/Dy1lJaW8u233zJ48GCGDx/Od9995zLZWmK1Sv7xzTH+tu0IA0K8ee3uUQwIvXBz6jG9gbfzS1lXVI7eYqU/8NyASG4K8SdK1/3wQWkyUbJiBWWr3satfxwxq95GN3hQt8ftSSxmK4Y6E8Y6Mwa9CWOd7WFv1Jsw1Jow6M2NbSaMejOGxmOTwdKleVQagUajQq21fTRaNWpN07EKNw8Nnr6N5636qVr0U9vaNbb27ENZDL9ieOuHd9PDXC0QqrPHZ89VzectH/gqle26o8nOziYgvHspwmtqzPj49LzVsaKigvj4eHbs2EH//s4PC7fUNDQfP/nkkzQ0NLBixQqnz9vdqozegMFRwkgpU4CUNm1/aHE8tYP7dgDDHSWHI0k7k0Zf374E6lyzZ11dnU5DQykhwS7eUijOhtwfYOpz1O4oQpqs+LrQamC2WFmWcjbhUdN2gkaj4aabbrpo3nDL6xp4fF063x8p4WdXRrLs1uEXVDTJKiXfltewKr+Eb8trcBOCn4X5c3+fECr27mJidKhD5G3Iy6PgiScxHDiA/513Evb0IlQXWEnSUZgbLNRWGKkrlhxPL2n10Lcdt3jwN14zGTt+yAuVQOelwd1Ti85Lg6efG4ERXrh7adB5aW3t3hp0nlq07mo0bi0e+G5nH+JqjcopD96Cumz6jQh2+LgKNpYtW8bMmTObFYOSkhLuvvtuDh48SFlZGaGhocyePZtly5bh59e1lOUHDx5kwYIF7Nq1i8DAQH7961/z+OOPN19fuHAh/fv35/HHH+92tsXzcb6qjE3qiQReEkLoW1xWYws/THeSbL0eq7Syr3gfU2Pb1Wl6hJKSLQihIShoostkAGzhi2p3rPHzqP3HMTyGBaMNc10lvU/35nPkTC2vNSY8+umnn8jLy+NnP/vZRePklHaqguQPbEWTXrxlGPPGxHRZaak1W1hXVM47+aXk1BsJc9Pwu37h3BMZ1OxHsN1B8lZ99jlFS5aAWk3U3/6G7wznO+BKq0Rf00BNuYHacmPjV4Pta4Xt3FBrau5/8puDzccqlcDdW4vO0/ZQ9w7QERzljbuX7aGv89Lajj21Zx/8Xlrc3NVOeagrXPzo9XpWrVrF5s2bm9tUKhW33HILy5YtIzg4mGPHjpGcnExSUhIff2y/v351dTXTpk1jwoQJ7N69m8OHDzN//nw0Gg2LFy8GICQkhBtuuIHXXnvNYVkXO+J8ryBNb+MCm+m+ocW1BmzRCw7LkHipcbzyONUN1S7cUpAUl3xNgP/VaLUuTEFrrLGlSx52KzX76pFGCz6TY1wmTsuERzOGhVNeXs62bdsYMGAAV1xxhcvkakJKyZodJ3nx82zC/XSsf/gahvfp2hvIyXoj7+SX8tHpMmosVkb5evJav1hmhfjh5uBKhta6OopeXEbVhg14jBpF1Mt/dlgdhAaD2fbQr7A99Jse+C0VAKultVFT667GJ0iHd4CO0FgfvAN1+ATqOHoim7HXjG5+0Gvd1ReNhUihd5CSkoJKpeLaa69tbgsKCuKhhx5qPo+NjeWRRx7hpZde6tLYH3zwAXq9nnfffRcPDw+GDRtGdnY2K1eu5Omnn27+XZ09ezaLFy92rXIgpZwEIIRYDTwmpax2qjSXGK4utqTX51Bff5KY6F+5ZP5mDqyDhlqsI+6n9v0CdEODcItwndXgjRYJj6SUbNq0CZVKxc033+zyh0WNwcSi9Qf5/OBppg4J5S93XGl30SQpJakVtbyVX8LWsmo0QjA71J/7o4IZ5eec77chK4uC3z5BQ24uwY88TPAjjyA09m17WK0SfZWRmnLj2Yd9uYGaFgqAUW9udY9QCbz83fAJ1BHWz48BiTq8A9zxCdQ1KgHuuHlo2v05nq4/REjMxWEVUjiX1I+PUJrXXvRB+zgiz0FwtDfj77TfHyY1NZXExMRO/04UFhayYcMGrr/++g77tMfOnTsZP348Hi224aZPn86zzz7bXPIZYMyYMRQUFJCTk+NUnwd7qzK2eroIITywRQQcbaptoHAu+4r3EaQLItrHNXvrJSVbAQgOnuKS+QFbfNKuVRBxJbUnQ5GGU/i60GpQVGXgze9zmDUiglExAezevZuTJ09y8803d3l/0NEcOVPDQ+/vJbdcz6Ib43lwfBwqO8zXdRYLnxZV8HZ+KUf0BoK1Gn7TN4xfRgYT1s2Ig46QUlLx3nsUv/IX1AEBxKxZg9fYznMXVJfWk5tRxqmscsrya6mtNCKtrd/63T01eAfYHvIR/f0aH/ru+ATYHv5efm6oOqnVoKDgTHJzc4mIiGj32ty5c9m4cSP19fXcdNNNrF69uktjFxUV0adP6/oyYWFhzdealIPISFuU0smTJ12vHAgh1gC7pJT/EkK4YUuZPBRoEELcIqX8wmkS9mL2Fe9jVNgol72NlpRuwcdnODpd+7/MPULuDijJxnrjP6n5shDdkEDcolyXve2vWw5jtcKiGfFUVlayZcsW4uLiGDXKdaGmYHM8vPftXZitkg8eGMvVdhRNOlVvZHVBKR+eLqfKbGGEtwcrhsQwJ9QfdwdvHbTEXF7O6acXU/vdd3hPmkTEshfbzV1gNlkoPFrJqYxycjPLqDxjc1nyDdYRMcCvxdv+WQXAzcN1hckUXEtX3uDBNUmQ6uvrmx/YbXn11VdZsmQJhw8fZvHixTz++OO88UbX0gC1fVY0JVRq2d5kWaivr+/S2F3F3v+J04Em58TZgA8QDtwHLAUU5aANRXVFFNQW8Ishv3DJ/EbjGaqr04mL+61L5m9m91ug86e25hpkfYFLrQYtEx71CfDg/fc/RUrp8u0Eq1Xy24/TKa9rYMMj1zAsqmMLhpSSHZW1vJ1fypelVQgBs0L8eSAqmKv8vJy+jrqffqLwqd9hqaoi7JlnCPjFvFZzVpXoyc0o51RmGQWHKzCbrKg1KqIG+TNsQhQxQwPxD/N0+faNgsKFEBwc3FyOvS3h4eGEh4cTHx9PUFAQ48eP55lnniE62j7LcXh4OEVFRa3aiott2QNaKiRN+VdCQkIuZAl2Y69yEMDZHAczgPVSyuLG4ki/d4pkvZz0YlsQh6v8DUpKtwG4NoSxpgiyN2NNTKZ25xncBwXgFu2aPV8pZauER2lpaRw/fpyZM2cS4OKMfW+mHmf74RKenzO0Q8Wg3mLlP2cqWJVfQladgUCtmgUxocyPCibSAbkJzoc0mSj5x0rK3noLt379iH7rTXTx8ZgbLBQcreRURhm5mWVUFdveZnxDPBhybSQxQwOJGhyA1u3Sz4GvcOkzcuRI1qxZc95+VqstQVVTbRZ7GDduHAsXLsRgMKDT2Wq8bNmyhYiICPr27dvcLyMjA61Wy/Dhzo3et1c5KAKGCSFOY7MiPNjY7g2YOrzrMiatOA0PjQeDA11Tba6k5Gs8PGLx8hrokvkBSHsPrGbqVLdhravGd4rrrAbfHSlpTniESc/XX39N3759GT36vPVHnMre3HJe/uowM4eHc/fV51Y/LzA0sKaglH8XllFhtpDgpeOv8dHcEhqARw/tvTfk51P4xJPU79+P/x234/7A4xw5rid3y34KjlRgMVlRa1VEDQpg+MQ+xA4Nwj/MdcmtFBScxfTp01m4cCFlZWUEBdm2/j777DPKyspITEzE29ubzMxMnnrqKa6++uouFZeaN28ezz33HPPnz+eZZ57hyJEjLF++nEWLFrWytKWmpjJ+/Hg8PZ37f8xe5eAdYB22WgcWYFtj+1jgkBPk6vXsK97HiJARaFQ9v4dqNtdQUfET0dG/dJ351mKGPaux9ptOzd563Af44x7rmnDKlgmP7h4bw6cfr8VqtTJ79mxUTtybPx8VdQ3834f7iPL3YPltI5p/VlJKdlXVsSq/lJTSSqSEG0P8uD8qhHH+zt86aEl1Sgr5S1+gwqc/9b9awZ5ab6pf2g+AX6gHQ6+LJGZYEFED/dEo1gGFS5zhw4czZswY1q5dS3JyMmArcvT666+TnZ2N0WgkOjqaW265hUWLFrW6VwjBkiVLWLp0abtj+/n5sWXLFpKTkxk9ejQBAQE88cQTLFjQujDxRx99xHPPPeeU9bXE3miFPwohMoEY4BMpZVO+AzPwJ2cJ11upaajhSMURfj3i1y6Zv6zsO6Q0uXZL4XAK1BRS128F1lqTS60GLRMeZWce5OjRo8yYMcOllRallDz16X5Kao2sf/gafHVajFYr/z1Tydv5JRyorcdPo+bXfUKZHxVEjEfPpb6WUlKRW07GPz6hIM9M5cilWIUGTb6KqMGeXDE5mthhgfi5MPW1goKrWLJkCY899hgPPfQQarWaqVOnMnVq54nuTpw4gRCCadM6/5s8fPhwvv/++1ZtNTU1zceff/45arWa22+//cIXYCd2v9ZKKde30/auY8W5NDhQcgCrtLos+VFJyRa02kD8/FwzPwC7VyF9+1GT7YN7nCfu/VwTJtgy4dG1sV78619fEh0dzRgXlAxuyds/nGBrdjFLbk5gRB9/6iwW7kjPIa1azyBPHX8e1IfbwgPw6qF69SajhYLDFZzKLONkehE1VRZgED7hBoZdE0PsiBAiB/qjaa/QjYLCZcSMGTNITk4mPz+f2NhztwLbIyUlhXvvvbdV8qQLoa6ujtWrV6OxM5dId1DihpxAWnEaaqHmipCez7ZntRopLdtOWOhMhHDRH/KSI3DiO+r6r8SaacLnLtdZDZoTHt09is8//xyz2cycOXNcup2w71QFy784xPShYcy/pi9mq+TXmbmkV+v5V0Ist4T698jWQeUZPbkZZZz83sqhT1OxmK2oVVYCSrOIMuQy9P9uI3zaZKfLoaDQ23j00Ue71L9pC6K73HnnnQ4Zxx4U5cAJ7CveR3xgPJ7anje7VlT8D4ullpAQF24p7HkbqfKk5tQA3Pp64h7nGqtBU8Kjm0ZEoK0u4PDhw0ybNo3gYNcVpanSm1jw4T7C/XT8+Tab8rjwSB5by6r586A+3BrmvMgJi8lKwdEKcjPKyD1YRlWJLbLAzRcSxgbh9eN63Levx2/CdUS8tKzd3AUKCgqXB4py4GBMFhMHSw5y+yDn7wm1R0npFtRqTwICrnHJ/BhrIf1D6kJ+gyXXTMCdXS8W5CiaEh4tGB/Nxg/fISoqinHjxrlEFjjrZ3Cm2sAnD43Dz1PLKyeK+OB0Ob+JDePeKMcrLbUVBpt14GAZ+YcrMBstzZEFV0yJJnZYEAfXv0foW89hqaggdNHvCLjnbiUPgYLCZU6HyoEQ4l5gnZTS/kBNBbLLszFYDIwK6/n8BlJaKSnZSmDgBNRqXY/PD8DBT5AGPTVl43CL8cF9gL9LxMgqPJvw6MDOb2loaHD5dsLqH0/yddYZnpk1hJExAXxYWMYrJ4v4eXggv+sX7pA5rBYrZ05Uc7LROlBWYMtV7xOoI/7qcGKHBbXKO1C2ahUBf/s7qthYol9/DV1CgkPkUFBQ6N10ZjlYjS3zYYkQwgJESCmLO+mvAKSdsRVbcoUzYnXNQRoail23pSAl7F6F3useLOXgf4drrAZNCY/8PLRMiTDz5aYsJk+eTGhoaI/L0sT+vEpe+iKbqUNCuf+6fmwpreKpI3lMCvThlcHR3fo+1dc2cCqz3Fa3ILMMo96MUAki+vsx7tb+xA4LIjDi3BDIirXrKH7lLxgTE4l/8w1UXq4rhqWgoHBx0ZlyUAKMAzZhK9ksO+mr0EhacRoxPjEEe/T8vnZJyRaEUBMcNLHH5wYg73/IomyqNc+j7eONbpBr9qy/O1LCD8dKWXTDAFK3bSIiIqLbXsLdoarexIKP0gjxdueVO64gvaaeBzNzGertwaqhfdHaUVypJVJKSvNqyc0o5eTBMs6crAYJHj5a+o0IJnZ4MNFDAnDvpJpjzdatFP3xj3hffz1n7rxDUQwUFBRa0Zly8DrwXyGExKYYFHX0diOlVOKbsP3R3le8j+v7dK1Up6MoKdmCv/8YtFrXmPLZvQq96kYsdVr8b3ON1aBlwqOAsgyK6+u55557ul3a9UKRUrJo/QEKKw18/OurqUBy94HjhLhp+GBEHF4a++RqMJjJz67gZEYpuRll6KtsqUZCY324alY/YocFERrjg7BD0dDv3UvBb59AN3wYUa/+lZxdu7q1RgUFhUuPDpUDKeVSIcQnwEBgA5AEVPaUYL2RM+YzVBorXeJvUFd3HL3+GH2i5vX43ADUliAzNlHDu2gjvNANcU2CoU8aEx49MzGM7J++Y+LEiYSHO2Y//0J4/6dcvsgoYtGN8cRE+HBz2lEkkrVX9CfEreM3eyllc6hhbkYZhUcrsVokbh4aoocE0nd4EDFDg/D07VpdBePRo+Q9/AjayEiiX38dlZNTsCooKPROOo1WkFJmAplCiOeAj6SU+p4Rq3dy3HAccI2/QWnpFgDX+RukvUu9eRxmkzdBLrIa1BnN/OXrI4yK9qPi4HbCwsK47rrrelyOJjIKqnjhs2wmDQ7hF9fEcvv+HM4YTay/cgBxnudmPLSYrBQcqbA5E2aUUd0YahgY6dUcWRDe3w/1BdZUMJ0+zamkB1G5uxO9apUSqqigcAFUVFQQHx/Pjh076N+/f4/OvXLlSr7++ms2bdrk9Lns+isjpXxOSqkXQsQJIW4SQswSQsQ5W7jeRo4xhwD3APr69u3xuUtKtuDjMxSdLrLH58ZqQe5eQ7X4FZowT3QJQT0vA7aER6W1Rib4lqLX1zFnzpweySTWHjUGE8kfphHo5caf7riCh7JOcbCmnjeG9mWU37n7++Wn61j34i42/2M/2T8UEhDuyfVzB3HPC+OY+4exXHPrAKIGBVywYmCprORUUhLW2lqi33oTtz5R3V2igsJlybJly5g5c2azYlBSUsL06dOJjIzE3d2d6OhokpOTqaqq6tK4BoOB+fPnM2LECLRaLRMnTjynT1JSEnv27CE1NdURS+kUu/5yCiF8sBVfug2wnm0W64H7pZQ1Hd58GXHceJyRESN7/K3ZaCyhqjqduH6P9ei8zRz5kvrKWMymIAKnxNi17+1omhIeTeznQ2XON4wfP57ISBcoSti2BJ7ecJD8MTu6vgAAIABJREFUino+ShrL8vwzbCuv5uXBfbgh+NyEUMf2FvPNe9lo3FTMeHAYscOCHFrEyGowkPdIMqbcU0S/9Ra6+HiHja2gcDmh1+tZtWoVmzdvbm5TqVTccsstLFu2jODgYI4dO0ZycjJJSUl8/PHHdo9tsVjQ6XQsWLCAlJQUKivP3cV3d3dn3rx5rFixgvHjxztkTR1h72vVCmAEMAnY0dh2LTanxb8B9ztCGCHEDODvgBpYJaVc3ua6O/AekAiUAT+XUp5svPZ0oxwW4FEp5VeOkMleSvQllJpLXeJvUFq6DZAEu2hLQe5aRbX1HjQhHngMc032wb98fRiLVRJbvZ+QkBCuv941TqEAH+46xWcHTvPU9MF8RwMfNiY5uiey9ffGarGy8z85pG/NIzzOl+lJw/EOcGyBJWk2U/DEk9Tv20fUX/+C19VjHTq+gsLlREpKCiqVqlX0U1BQEA899FDzeWxsLI888ggvvfRSl8b28vLi9ddfB+DAgQPtKgcAs2fPZtq0aej1eqeWbbZXOZgN/ExK2dKWsV0I8SDwHxygHAhbIYB/AtOAfGC3EGKTlDKrRbf7gQop5QAhxF3YKkL+XAiRANwFDAUiga1CiEFSSkt35bKXfcX7ANf4G5SUbkGni8bba3CPz01ZDoaj9ZgtUS6zGmQVVvNpWj6TIqyoKsqZM/d+l20nZBVW89zmLCYMCsF3kD/PH8nnrnaSHNVVGfl6VSaFRysZPrEP194+ALXGsQmapJQU/fF5ardtI+z3v8f3xhsdOr6CgiP5ds2bFOcet7u/xWxBbWe0T0eExsYxaf6DdvdPTU0lMTGxU+twYWEhGzZscNoLyujRozGbzezcuZMpU6Y4ZQ6wXznwwPam3pZywFGp+MYAx6SUxwGEEGuBOUBL5WAOsLTx+FNgpbD9lOYAaxuzOZ4QQhxrHG+ng2Q7L0s3llJf+xK/fP8IYZp04kQ914WHcOtNN6Lz8HDavGZzLeXlO+jTxzUpb+Wut6k2z0MTqMVjREjPz9+Y8MjbTUVYWRrjrh1Hnz59elwOgFqjmQUfpuHvoWX2DXE8djSfyYE+vNwmydHpY5V8+VYGDXozU3+VwOCxzommKP3nv6j8+GOCkpIIvOdup8yhoHA5kZubS0RERLvX5s6dy8aNG6mvr+emm25i9erVTpHB09MTPz8/Tp486ZTxm7BXOfgReF4IcU9TxIIQwgt4jrPbDN0lCshrcZ4PtLWBNveRUpqFEFVAUGP7T23ubdfjqtHa8SBAWFgY27dvd4TsBKGnQuNFRZUHFUYPDgEpBbB4/ze4eVnx1RkIU9fRz6JnmJcb/WNj0Lp3LQytPaTcjZQNFOQHU1iwvdvj2UNtbS3bt29HZTEy8n8HMckbORNl5ND33/XI/C05UGLmh2NGrtEV4O/hhlqtdtjPtGmd9iCl5M0DRk6UWvjFOG9+ezSPWCzcW57Hj9/nNfcpPwJF6RI3L4idIjhdf4jT2w85RN6WeKSm4vvBh9RffTVZo0aS1ck6urLO3oyyzosHPz8/ampau6qNvm1ul8awWCwOyV/SVo7z9Q0MDGz3nueff54nn3ySo0eP8txzz5GcnMzf//73C5KpoaEBi8VCTU1N89eW6HQ6KioqOpTdYDB0+3fAXuXgN8CXQIEQ4gC2pEhXAHXA9G5JcJb2XnvbZmXsqI8999oapXwTeBNg9OjRsj2P0Ash1t+HDS8t4fZnXiCvso7NBzI5bNFw2uJFpdGD0nIvSk2eZAKfAeSZcfcy4KerJ1KlZ5C6gVnD4rtsisrI3Eh5eSDXXXs/KlXPmNK3b9/OxIkTkXvfp9h4C2pfGHXXBIS6Zy0XZouVZStSCdYZ6S9PM3fur4iJcVx56KZ12sO63afYefog86cN4GP3BiLUajYmDmzOZdBgMLP934co2ldMvyuCmTI/AXcP5/y8arZtI/+jtXhNGE/8P/+J0HacTwG6ts7ejLLOi4fs7Gx8fHy6NUZNTU23x+gq4eHh1NbWtjtvU1tiYiJ9+vRh/PjxPPfcc0RHR3d5Hjc324uOj49Pu+usqKggOjq6w/XrdDpGjuzeFrddf52klBlCiIHA3UA8tofxv4EPpJT13ZLgLPlAy+9iH6Cwgz75QggN4Idta8Oee51K5CCbB3jBoSyuu2Me141vna7XUF/Ptm+/Y+vxXI5a3SmyeFFt0FFc6k2x2Zt04OO8WvgmBZ2niQD3eqJUdQzRWLllTCKjRp/r6Gi1migr+5aQkOk9phg0IyWG77/DJH9JwLQBPa4YwNmERxO1x7j22rEOVQy6wuGiGpZsymT04CC+8LSABT5qkeSo8oyeL944SMXpOq7+WRyjboh1mm+GPi3Nlv1w6FD6/O1v51UMFBQU7GfkyJGsWbPmvP2sVltQn9Ho+LqFOTk5GAwGRo1yrvO73U+URiXgLSfKshsYKIToBxRgczBsm+5vE/BLbL4EtwPfSCmlEGIT8KEQ4q/YHBIHAj2aE9bd0wuPoBAKDme1e13n4cGsmTOY1abdUF/Pxi++JLWghGPSnWKzF9X17hRW+XDa6sMe4P1TpxGffY6Hp4lA93r6iDpGuMPMq30xm2sICZ7q9PW1RebvoaZ4LGpPE56jwnp8flvCo8NEauu5MggmT57c4zIA6BvMJH+YhqeHlooEf4oNxlZJjo7vK2Hru1moNSpufuxKouOdlznSeOyYLftheDjRbyjZDxUUHM306dNZuHAhZWVlBAXZ8rl89tlnlJWVkZiYiLe3N5mZmTz11FNcffXVDBgwoEvjZ2Vl0dDQQGlpKbW1taSnp1NXV9cqOiI1NZW4uDgGDhzo0LW1xTUu3e3Q6EOwAPgKWyjjO1LKTCHEH4E9UspNwNvA+40Oh+XYFAga+32MzXnRDCT3ZKRCE94RUZw+cgirxYLKzr0wnYcHP7/1Fn7epr2uppZ1mzbzU3k1J6QnJSZPaurdyavwJV/68hPwxglQe67A/X8mAlSbiZINDPOEn103lCtGOTeW3bj1cxrkFPyn9EFcYGKe7mBLeNTALLcTzJlzO25u3fffuBCe/W8mx0prGXJzf/brDawZ3o9Rfl5YLVb+t+k4aV+dIrSvLzMeHIZPoPPKaJuKijj1QBLCTUv026vQBLomfbWCwqXM8OHDGTNmDGvXriU5ORmwmfBff/11srOzMRqNREdHc8stt7Bo0aJW9wohWLJkCUuXLu1w/JkzZ5Kbm9t83rQ1IOXZXfKPPvqIpKQkB66qfS4a5QBASpkCpLRp+0OLYwNwRwf3vgi86FQBz4N3eB9KMtIpyT1BWFzXNMa2ePl4c98v5nJfm/bS0hI++uxL9lbXkys9KTX6UmfQUlCvolDq2F0Jqz/OgY0ncHcHP7WFSNnAYDcLM0f15fqJV3VLLgCtsZrqo1Go3fV4jY3t9nhdpajKwBvfHaOvqoyZYxPo169fj8sA8MmePD5Ny2fQtBj2GQy8MjiaG4L90Fc38PXbGRQcrmTohCjG3zEQtdZ5CpSlqoq8pCSsNTXE/vt93FwUraGgcDmwZMkSHnvsMR566CHUajVTp05l6tTOrbcnTpxACMG0aZ3nomkvAqGl02FGRgbp6eldSq50oVxUykFvxzvCFiBRcCiz28pBRwQHh/B/8+85p728rJJ1G39gd0k9J6UbpWipMwnO1AqKre6kA+u+LIZtKWh1Al+1lTAaGKg2M2lgKDfOGIu7zr4324jj+2mwTsT/Wm+Eg2Pz7eHlr7Ixm61MDK5i6tS2Npee4eiZGv6wMZPw0aEcVFl4om8Yd0cGUXS8ii/fzMBQZ2LKL4cQP679sCdHYTUYyEtOxngyl5i33kQ3ZIhT51NQuNyZMWMGycnJ5OfnExtr38tRSkoK9957b7dLxxcWFvLee+/h53duplVHoygHDsTN2wffkDAKDmUxauacHp07MMifh++7iYfbtOtr9WzY9AM/5ldxXGopllpqzILSWkGZ2Y0s3NhYVstju79B6yHw1lgJxUycqoFrony5fc54PL1b7F1bLXjmh2PV1OA1qXu/6BdCVmE1G9IKSVAXcc8tM3F3d2xGQXuob7CQ/GEaMtqL3CAt8yICeSI2jIPb8/nhk6N4B7hz2+8SCYl2rie1tFgofOop6vfsbcx+eLVT51NQULDx6KOPdql/0xZEd7nhhhscMo492FtbQQUgpbQ2nocDNwHZUsofnSde7yMqPoFTB9ORUrokKVFbPL09uXveDbRNgWM0GNi6dTdbDp3mmFlLkXCj2iyorBNUmjQcQcOX5WaezfwWtYcKL60kGDNxGBjnHsu0fgaEE03l7SGl5A//2YcbZu5JDO3ximhNLNmUwSFpxjQwiCmBvrzQN5Jt72Zz5H9niB0exNT5Cei8nBslIKWk6PnnqdmylbDFT+M7c6ZT51NQULi8sNdy8Dm2PAd/F0J4A3sAL8BbCHG/lPI9ZwnY24ganEB26rdUnSnCP9y5JuXu4K7TMeum8cy66dxrqd/vJWXvcQ4Z1RQKNyotUFMvqDGqOYEX2zDxfJYa1dIvcHOT+KgshKksDPTRcuOIvky6aqBTHAS/yS5iT14tE7zL+NnMtoEsPcN/9uWz9ugZrGNDucLHk5fDQtn0chplhbWMnd2PxBl9eySFdOlrr1G5dh1BD9xP4L33On0+BQWFywt7lYNE4HeNx7cC1UA/4BfAk9iKISlgsxwAFBzOuqiVg84YPyGR8RMSz2nP2H+EDd8fZG+thTNCR7UU1JsEJQYVpVYVmeXw39yTyC9y0egEnmorAcJMHzfJmEh/7ppyJeEh/hckk9li5dn1+/ARBhbdfh06O/0jHMmx4loWfZmNHB1ClIcbL6p9+fxPaQgV3LzgCmKG9kyp6opPPqF0xT/wmzOHkCee6JE5FRQULi/sVQ58gKYSUTcA/5FSmoQQ32ArlqTQSFBUNDovbwoOZTL0eucVxXAFw64YxLArBp2Tga26tp713+7nx+PFnDBYKZUa9Ba1zdrQoOEUsKO4jlf3/4jKXXVB1oa3tmVQWCf51SANCfGDnL/YNhhMFn798T5qrwzEV6dhUYmWn1KyCInxYcaDw/ANdl79jJbUfPMNRUuW4nXddUS88PxFsXWloKBw6WGvcnAKuFYIsRlbuuSmcMJAQO8MwXorQqUicvAQCg61nwzpUsTX24Nf3Xw1v2rnWlpWLv/ZeYiMcj2nLWqqJBhMKrusDVdF+DF36kg8PHWs3H6SCI2Rp+5qm0aqZ3hmcyZZfdxx06l5KNtMYVoeCddGMP6uQWi03c/vbg/6tH0U/Oa36BIS6PN3JfuhgoKC87BXOfgr8D5QC+QC3ze2TwAOOkGuXk1U/FCOp+1GX12Fp6/zQ04uZkYlxDIq4dxwn5bWhuMGK2XtWhv0/O3AjwiNAKuaiHBPFq7eTpyvB4kDI7h6ZH/c3J3/gNyQXsCHZj0E65ibZsD9hIEJ98STcG2k0+duwpiTQ97DD6MJD7NlP/Ty6rG5FRQULj/sra3whhBiL7b6BVuaohaAHOBZZwnXW4kafNbvYOBV41wszcVJ16wNaiw+7hwaHESGptGMXm9A830GQTVGgqoNhOgNRGGlv78XVw+N5oqhMWg03Y/UPV5Sy2+ycrFGeHLz3joSKgQznhpFaKxvt8e2F9OZM7bsh1otMatWoQnqGd8GBQWFy5eu1FbYgy1KoWXb5w6X6BIgrP9A1FotBYcU5eBC6Mja0GA0sefACfYcLiSnWk+hUFHqqaPYz4NDffywNhV/Kq/G7ZsDBFcZCaqpJ9TQQJRKMijYl+uu6Ev8wHareZ87n0Vy29ZMjBGeTMjQM9vdi2lPD0Xn3XPmfEt1NXkPJGGtrib2/fdwu4AKbwoKCo6joqKC+Ph4duzY0ePh1CtXruTrr79m06ZNTp/LbuVACPEIkIwtSmGYlPK4EGIhcEJK6fxcjr0IjVZLeP+BFF5Gfgc9gZu7lmuuGsQ1V53rkFhXZ2Dn3hzSTxRxvNZIkVpDiZeO/GAfMrw0yKbwwvwSPHKKCK4yElxTT5ixgT4aQXy4PxMSBxDTJ7h5zL8UqDkd7c7IHANP9A3jqllxqHogTLEJq9FI/iPJGE+eJOaN19ElJPTY3AoKCu2zbNkyZs6c2awY7N+/n+XLl/PDDz9QWlpKTEwMDzzwAE888QQqlf25YAwGAw899BBpaWlkZ2dz7bXXsn379lZ9kpKSWLZsGampqYwfP96RyzoHe5MgPY4tlPFPwPIWlwqBBYCiHLQhanACez77DyajAa17z4fdXW54eemYOmEoUycMPedaZVUdqbuOcuBUCbn1Js5otZR468gJ92OfV4v/Akfz8d5/kuBqA356Iwf6BjLgtJG/RrozaEJ4jyoG0mKh8Mmn0O/ZQ+Qrr+B1zTU9NreCgkL76PV6Vq1axebNm5vb9u7dS0hICO+//z4xMTHs2rWLpKQkTCYTixcvtntsi8WCTqdjwYIFpKSkUFlZeU4fd3d35s2bx4oVKy4O5QB4CEiSUn4uhHihRXsacO5fYwWi4oeya+OnFB07QvTQEa4W57LG38+Lm6ddyc3tXCs6U8H3e46RWVhOXoOFM25ulHp7cCzCn4EF1Sxf+RxUn+YIoA4Kwi0mBreYaLQxMY3HMWhjYlD7+zssrFBKyZkXX6RmyxZCFy3E7ybXRGgoKCi0JiUlBZVK1apGwn33tS6PFxcXR1paGuvXr++ScuDl5cXrr78OwIEDB9pVDgBmz57NtGnT0Ov1eDqxLLu9ykEskNFOuwnomQDvXkbkIFsBnIJDWYpycBETHhbAnbPar1T53RdfMGrNShpO5dFw6hSmvFM05J6ibtduzBtb7/mpfHwaFYVo3GJicYuJblYcNCEhiC6YF8veeIOKDz8i8P77CJo/vzvLU1DoNVRuzqGhsM7u/haLmXp195yO3SK98L/Zfr+B1NRUEhMTz/siUF1dTUBAQLdk64jRo0djNpvZuXMnU6Y4L5eOvd/Z48AobGGMLZkJKBvr7aDz9iY4OpaCw8q3p7ciPTzQJSS0u9dvNRox5efTkHtWaWjIy8OQlUXNlq1gNjf3FTodbtF90MbE4hYdjVtsTLPlQRsRgWgRVVG5fj0lf/s7vrNvJlTJfqigcFGRm5tLRETnmW/T0tJYs2YNH3zwgVNk8PT0xM/Pr93yzo7EXuXgFWClEMITEMA4IcQ92PwQ7uv0zsuYqPgEsn/YjtVqQaXqmUQ5Cj2Dyt0d9/79cW/HW1mazZhOnz5HcTCdyqXuxx+RBsPZzhoN2qhI3GJi0YSGUPXfjXhdey2RL7zQJWuDgkJvpytv8AA1NTX4+Di38mlb6uvrCQsL6/D64cOHmTVrFo8//ji33Xab0+Tw8PCgvr7eaeOD/XkOVgshNMAywBNbQqQC4FEp5TonyteriRqcwP4tX1B6KpfQvnGuFkehhxAajc1CEB0NtC5rLa1WzCUlmE6douHUqcYti1xMp/KoT0/HMzGRqL//HeGEwlUKCgrdIzg4mIqKinavHTp0iEmTJnHXXXexfPnydvs4ivLyckJCQpw6R1fyHLwFvCWECAZUUspi54l1aRA1xOarWXAoU1EOFABbem1tWBjasDA8r2rf10FBQeHiZOTIkaxZs+ac9qysLCZPnsydd97Jq6++6lQZcnJyMBgMjBo1yqnzdNluKaUsVRQD+/ANDsUnKOSyqrOgoKCgcKkyffp0srOzKSsra27LzMxk0qRJTJw4kcWLF1NUVNT86SpZWVmkp6dTWlpKbW0t6enpHDhwoFWf1NRU4uLiGDhwYLfX0xkdWg6EEAeA66WUFUKIg4DsqK+UUnHH74Co+ATysw4ipVQq6CkoKCj0YoYPH86YMWNYu3YtycnJAHzyyScUFxezbt061q1rvcsu5dnHphCCJUuWsHTp0g7HnzlzJrm5Z/3+R44cec44H330EUlJSY5YTqd0ZjlYDxhbHHf2UeiAqMEJ1FaUU12iGFsUFBQUejtLlixhxYoVWCwWAJYuXYqUst1PEydOnEAIwbRp0zod++TJk+eMUV1d3Xw9IyOD9PR0Hn74YecsrgUdWg6klM+1OF7qTCGEEIHAOqAvcBK4U0pZ0abPlcBrgC9gAV5scoYUQqwBrgeqGrvPl1KmO1Nme4mKP1uEyS+0Yy9XBQUFBYWLnxkzZpCcnEx+fj6xsefWgGmPlJQU7r333lbJky6EwsJC3nvvPfz8nF/t1970yd8At0opK9u0+wL/lVJO7qYci4BtUsrlQohFjecL2/TRA/dKKY8KISKBvUKIr1rI9JSU8tNuyuFwgqJjcPf0oiA7k4Txk1wtjoKCgoJCN3n00Ue71L9pC6K73HDDDQ4Zxx7sdUicCLQXW6UDHJHgeQ7wbuPxu8DP2naQUh6RUh5tPC4EigHnxnI4AJVKTeSgeCUZkoKCgoJCr6FT5UAIMUoI0RQvMaLpvPFzFfAgtnwH3SVMSnkaoPFr6HnkGoNNWclp0fyiEOKAEOJVIYS7A2RyGFHxQynLP0V9TfX5OysoKCgoKLgY0dJp4pyLQlg5G6XQnqt9PfB/Usp3zjuREFuB8HYu/R54V0rp36JvhZSy3cTUQogIYDvwSynlTy3airApDG8COVLKP3Zw/4PYlBrCwsIS165dez7R7aa2thZvb+9z2msK8ziycR39b7wF/749W//bGXS0zksNZZ2XFso6Lx78/PwYMGBAt8awWCyo1Zd+5tkLWeexY8eoqqpq99qkSZP2SilHn2+M8/kc9MOmFBwHxgAlLa41AMVSSos9wkopp3Z0TQhxRggRIaU83figb9e1v9HH4XPgmSbFoHHs042HRiHEauDJTuR4E5sCwejRo+XEiRPtEd8utm/fTnvjmRqMHPtsPYFaFRMcOJ+r6GidlxrKOi8tlHVePGRnZ3c79bEr0ie7ggtZp06naw6DvFA6VQ6klE0Bl85O8r4J+CWwvPHrxrYdhBBuwH+A96SUn7S51qRYCGz+Cu1VkHQZWjd3wvoPUJIhKSgoKCj0CjpLgnQrsFlKaWo87hAp5YZuyrEc+FgIcT9wCrijUYbRwENSygeAO4EJQJAQYn7jfU0hix8IIUKwWTnSgYe6KY/DiRqcQFrKJkwNRrRuF5VLhIKCgoKCQis6sxx8is1HoLjxuCMk0K2NHyllGXBOYWop5R7ggcbjfwP/7uD+7oZSOp2o+KHs2byBMzlH6TNkmKvFUVBQUFBQ6JAOtwuklM3FlRqPO/pc+h4hDiByUDyAsrWgoKCg0IupqKggLCyMnJyc83d2ME8++WSXcyxcKErB+B7C09ePwKhoJd+BgoKCQi9m2bJlzJw5k/79bZFn+/fvZ+7cuURHR+Ph4cHgwYN5+eWXsVqtXR774MGDXH/99Xh4eBAVFcUf//jHVmmYFy5cyJo1azh+/LjD1tMR5/M5sAsH+BxcFkTFJ3Bk5w9IqxWhUvQyBQUFhd6EXq9n1apVbN68ublt7969hISE8P777xMTE8OuXbtISkrCZDKxePFiu8eurq5m2rRpTJgwgd27d3P48GHmz5+PRqNpHickJIQbbriB1157jZdfftnh62vJ+XwO7KHbPgeXC1GDEzi47StK808REtPX1eIoKCgoKHSBlJQUVCpVqxoJ9913X6s+cXFxpKWlsX79+i4pBx988AF6vZ53330XDw8Phg0bRnZ2NitXruTpp59uruo7e/ZsFi9e7DrlQEqpvNo6mD5DhgI2vwNFOVBQUFA4yxdffEFRUZHd/R2RBCk8PJwbb7zR7v6pqakkJiY2P6g7orq6moCAdvP4dcjOnTsZP348Hh4ezW3Tp0/n2Wef5eTJk/Tr1w+AMWPGUFBQQE5OTvPWhjNQFIAexDckDO+AQAoOZbpaFAUFBQWFLpKbm0tERESnfdLS0lizZk2XyyoXFRURFta6cm/TeUulKTIyErCVd3YmF0ueg8sCIQSR8UMVp0QFBQWFNnTlDR5ckyGxvr7+nAd4Sw4fPsysWbN4/PHHue2227o8fluLRJMzYsv2JstCfX19l8fvChdFnoPLiajBCRzZmUp1aTG+wZ3Wl1JQUFBQuIgIDg6moqKi3WuHDh1i0qRJ3HXXXSxfvrzLY4eHh5+zrVJcbKsk0FIhKS8vB2zOic5EyXPQw0TFJwBKvgMFBQWF3sbIkSPJyjr3b3dWVhYTJ07kjjvu4NVXX72gsceNG0dqaioGg6G5bcuWLURERNC3b9/mtoyMDLRaLcOHD7+geezFLp8DIcQEIcQ5VgYhhFoIMcHxYl26hMT0xc3DQ1EOFBQUFHoZ06dPJzs7m7Kysua2zMxMJk2axMSJE1m8eDFFRUXNn64wb948PD09mT9/PhkZGWzYsIHly5ezYMGCVtsKqampjB8/Hk9PT4etqz3sdUj8Fghsp92/8ZqCnajUaiIGxit+BwoKCgq9jOHDhzNmzBjWrl3b3PbJJ59QXFzMunXriIiIaPVpiRCCpUuXdji2n58fW7ZsobCwkNGjR5OcnMwTTzzBggULWvX76KOPSEpKcui62sNe5UBg8y1oSxBQ5zhxLg+i4hMozcvFUFvralEUFBQUFLrAkiVLWLFiBRaLBYClS5cipWz308SJEycQQjBt2rROxx4+fDjff/89BoOB06dPs2TJklZWg88//xy1Ws3tt9/unMW1oNOSzUKITY2HEvi3EMLY4rIaGAbscJJslyxRg4eClBQezSZu5FWuFkdBQUFBwU5mzJhBcnIy+fn5xMbG2nVPSkoK9957b6vkSRdCXV0dq1evRqPp9NHtEM43Q9PGigAqgJaxEw3AD8BbTpDrkiZiwCBUajUFh7IU5UBBQUGhl9HV4kfJyckOmffOO+90yDj20KlyIKX8FYAQ4iTwipRS2UJwAFqdjtB+/RWnRAUFBQWFixK7fA6klM8pioFjiRqcQFHOEcwmk6tFUVBQUFBQaEW+twV+AAAdmklEQVSnyoEQokYIUd3OJ08IsVUIMb2nBL3UiIpPwGIyceb4MVeLoqCgoKCg0Irz+Rws6KDdH0gENgkhbpdSbu6gn0IHRA1uSoaUSdTgIS6WRkFBQUFB4Szn8zl4t7PrQoh9wGJAUQ66iKefPwERUUq+AwUFBQWFi47uVmX8HIh3hCCXI1HxCRQezkZara4WRUFBQUFBoZnuKgc6wHDeXgrtEjU4AUNtDeWF+a4WRUFBQUFBoZnuKgcPAOmOEORyJGrIUEApwqSgoKDQW6ioqCAsLIycnJwen3vlypXMnj27R+Y6X7TCig4+7wohDgL3A890VwghRKAQYosQ4mjj14AO+lmEEOmNn00t2vsJIf7XeP86IYRbd2XqCfzDIvD08yf/UKarRVFQUFBQsINly5Yxc+ZM+vfvD8D+/fuZO3cu0dHReHh4MHjwYF5++WWsXdwu3r59O3PmzCEiIgJPT09GjBjBO++806pPUlISe/bsITU11WHr6YjzRSt0VBOyGvgCeE1KecIBciwCtkkplwshFjWeL2ynX72U8sp22v8EvCqlXCuEeB2b0vKaA+RyKkIIouITFMuBgoKCQi9Ar9ezatUqNm8+64O/d+9eQkJCeP/994mJiWHXrl0kJSVhMplYvHix3WPv2LGD4cOH87vf/Y6IiAi++uorHnzwQaSU3H///QC4u7szb948VqxYwfjx4x2+vpacL1phklNnP8scYGLj8bvAdtpXDs5B2KpSTAbmtbh/Kb1AOQBbnYWj/9tBTVkpPkHBrhZHQUFBQaEDUlJSUKlUrWok3Hfffa36xMXFkZaWxvr167ukHLTt+/DDD/Ptt9+yadOmZuUAYPbs2UybNg29Xu/Uss3Or95gH2FSytMAUsrTQojQDvrphBB7ADOwXEr5X2yVISullObGPvlAlNMldhBR8Y35Dg5nEX/NBBdLo6CgoOAajhx5nprabLv7Wyxm1OruPcJ8vIcwaNCzdvdPTU0lMTGxVaXE9qiuriYgoN3d8S5RXV1NWFhYq7bRo0djNpvZuXMnU6ZM6fYcHdFjyoEQYisQ3s6l33dhmBgpZaEQIg74ptHvobqdfu2Vl26S40HgQYCwsDC2b9/ehek7p7a2tsvjSasVlUbLrm1bKGroHSGNF7LO3oiyzksLZZ0XD35+ftTU1LRqazA1YLGYO7jjXKSkS/3bo8HUcI4cnZGTk0NwcHCn96Snp7NmzRpWrVrVpbHb8sUXX7Bt2za+/PLLc8bx9fXl0KFDjBkzpt17DQZDt38Hekw5kFJO7eiaEOKMECKi0WoQARR3MEZh49fjQojtwEhgPeAvhNA0Wg/6AIWdyPEm8CbA6NGj5cSJEy9wReeyfft2LmS80h+3UV9bdUH3uoILXWdvQ1nnpYWyzouH7OxsfHx8WrUNG/p8l8aoqak5ZwxnYzKZ8PHx6XDew4cPc+edd/L4449z9913X/A8P/74Iw888AArVqxgzJgx58zn6emJlLJDOXQ6HSNHjrzg+aH7oYyOYhPwy8bjXwIb23YQQgQIIdwbj4OBa4EsKaUEvgVu7+z+i5mo+ARKc09i1Cu1rRQUFBQuVoKDg/+/vXsPr7q68z3+/hLCJXLxkhDCBkUuAtF0DOTEchwUaMPNFsc79YLOUTq2seKpeuK0j4XxnPHhVJ/D1Oqjj6VjtMcm3kdbMlOxY2o8OjPeUANBSbiZhEiFCIGEW1jnj98vmeywA0nYe/92dj6v58mTvddeWb/v4rLz3Wut31o0NjZGfG3Tpk3Mnj2bJUuWsGrVql5f4+2332bhwoU88MAD/OAHP4hYZ8+ePWRkZPT6Gt2RKMnBKqDAzDYDBf5zzCzPzNb4daYB75vZx3jJwCrnXNsy/yLgx2ZWjbcG4ddxjf4Uhaacj3PH2Pn5pqBDERGRLuTm5rJx4/F3l23cuJHZs2dzzTXXsHr16l63/9Zbb7Fw4UJWrFjBXXfdFbFOTU0NBw8eZPr06b2+TnckxIJE59xu4LiVFc659/E2WsI59w5d3FrpnNsCRJ586QOyJp+HDRhA3WcbGX/hjKDDERGRCObPn09RURG7d+/mrLPOAmDDhg3MnTuXOXPm8JOf/ISGhob2+qNHR1pmF1l5eTmXXXYZP/zhD7nhhhva22lpaQmbPqioqGDChAlMnjw5Sr2KLFFGDvq1QUPTGDV+gvY7EBFJYDk5OeTn51NaWtpe9sILL7Br1y6ee+45srKywr46MjNWrlzZZdvFxcU0Nzfz8MMPh7XRef1ISUkJy5Yti2a3IlJykCBCU7LZWf05rUePBB2KiIh0YcWKFTzyyCO0trYCsHLlSpxzEb/abN26FTOjoKCgy3aLi4sjtlFZWdlep7KykvXr13e5FiGalBwkiNDUbI4ePsSurVuCDkVERLqwYMECCgsLqa3t/oF5ZWVlLF26NGzzpN6or6/nmWeeYeTIkafUTnckxJoDgTFT/M2QNm0ga/KUgKMREZGu3HnnnT2qX1hYGJXrzps3LyrtdIdGDhLEsDPO5PTMLOo+07oDEREJlpKDBNJ2CFPHuSoREZF4U3KQQMZMyaalaR976rs/lyUiIhJtSg4SyNhp5wPolkYREQmUkoMEckZWiKHDR1CvdQciIhIgJQcJxMza1x2IiIgERclBgglNyebrL3eyv3FP0KGIiEg/peQgwYSmeusONLUgIpJ4GhsbyczMpKamJu7Xvueee3q8x0JvKTlIMKPOncDAQYM1tSAikoAefPBBFi1axMSJE9vLli9fTl5eHkOGDGH8+PG9bvvTTz/l0ksvZejQoYRCIR544IGwW9uLioooLi5my5bY76Sr5CDBpAxMJWvSedoMSUQkwTQ3N7NmzRpuvfXWsPJjx45x8803s3Tp0l63vW/fPgoKCsjMzOS9997jkUce4aGHHuLRRx9tr5ORkcG8efN4/PHHe32d7lJykIBCU7PZtXULh1uagw5FRER8ZWVlDBgw4LgzEn75y1/yox/9iPPOO6/XbT/77LM0Nzfz9NNPc8EFF3DVVVdRVFTEo48+GjZ6sHjxYkpKSnp9ne7S2QoJKDQlG+eOsXPz55zzjQuDDkdEJObu31xL5f6WbtdvPdpKysCUU7rmBcOG8j8nj+12/YqKCmbMmIGZndJ1I3n33XeZNWsWQ4cObS+bP38+999/P9u2bePcc88FID8/n7q6OmpqasKmNqJNIwcJKOu8aZgNoO6zDUGHIiIivu3bt5OVlRWTthsaGsjMzAwra3ve0NDQXjZmzBgAtm3bFpM42mjkIAENTksj/ZzxWpQoIv1GTz7BAzQ1NTF8+PAYRRNZS0vLcb/Ao6nziETbdELH8raRhZaW7o+y9IZGDhJUaEo2Ozd/RuvRo0GHIiIiQHp6Oo2NjTFpe/To0WEjBAC7du0CCEtI9uzx9sDJyMiISRxtlBwkqNDUbI4cOsift28NOhQREQFyc3PZuDE2I7ozZ86koqKCgwcPtpetW7eOrKyssNsjKysrSU1NJScnJyZxtFFykKBCU7IBHcIkIpIo5s+fT1VVFbt37w4rr66uZv369dTX13P48GHWr1/P+vXrOXz4cLfbvv7660lLS+OWW26hsrKSl19+mVWrVnHHHXeETStUVFQwa9Ys0tLSotavSJQcJKjhZ6UzIiOTuk1alCgikghycnLIz8+ntLQ0rPy2224jNzeX1atXs3PnTnJzc8nNzaW+vr69jpmxcuXKLtseOXIk69ato76+nry8PAoLC7n77ru54447wuqVlJSwbNmyqPYrkoRYkGhmZwLPAeOBbcC1zrnGTnXmAKs7FE0Fljjn/snMioFLgb3+a7c459bHOOyYC03NZvsnH+Gci8mtMyIi0jMrVqxg+fLl3H777aSkeLdSlpeXn/Bntm7diplRUFBwwno5OTm89dZbYWVNTU3tj9euXUtKSgpXX31174LvgUQZObgP+KNzbjLwR/95GOfcm865C51zFwJzgWbg9Q5V7m17PRkSA/CmFpr3fs3XDfUnrywiIjG3YMECCgsLqa2t7fbPlJWVsXTp0uM2T+qpAwcO8NRTTzFwYOw/1yfEyAFwOTDbf/w0UA4UnaD+1cA/O+eSegvBsdO8Q5jqNm3kjKxQwNGIiAjQ48OPCgsLo3Lda6+9NirtdEeijBxkOud2AvjfR52k/hKg8/6Rf29mn5jZajMbHIsg4+3MMWMZMmy4zlkQEZG4so57Nsf0QmZvAKMjvPRT4Gnn3Okd6jY6587oop0s4BNgjHPuSIeyBmAQ8CRQ45x7oIuf/z7wfYDMzMwZnReWnIr9+/czbNiwqLUHUF32Cge/3sMF19968spxEot+JiL1M7mon4lj5MiRTJo06ZTaaG1tbZ/zT2a96Wd1dTV79+6N+NqcOXM+cM7lnayNuE0rOOe+3dVrZvalmWU553b6v+h3naCpa4FX2hIDv+2d/sNDZvYUcM8J4ngSL4EgLy/PzZ49uwe9OLHy8nKi2R5A2t6vqPhtMfm5F5I28vST/0AcxKKfiUj9TC7qZ+Koqqo65d0Ng9ghMQi96eeQIUPIzc09pesmyrTCa8DN/uObgVdPUPd7dJpS8BMKzFvS/1dAZQxiDERoqr/uQFMLIiISJ4mSHKwCCsxsM1DgP8fM8sxsTVslMxsPjAP+1OnnnzWzT4FPgXTgf8Uh5rjInDCJlNRUbYYkIiJxkxB3KzjndgPfilD+PnBbh+fbgOOW7Tvn5sYyviANTE1l9MTzNHIgIiJxkygjB3ICoanZ7Npaw5EOe26LiIjEipKDPiA0NZtjra3srP486FBERPq1xsZGMjMzqampifu177nnnh7vsdBbSg76gDGTp4EZdZ/pnAURkSA9+OCDLFq0iIkTJ7aX7dixg+9+97ucdtpppKenc+edd/bo0CWAl19+mXnz5pGRkcHw4cO56KKLeO2118LqFBUVUVxczJYtW6LSlxNRctAHDBk2jPRx52hRoohIgJqbm1mzZg233vqf+860trZy2WWX0dTUREVFBSUlJbz44ovcfffdPWr7T3/6E3PnzmXt2rV89NFHLFq0iCuuuIJ33nmnvU5GRgbz5s3j8ccfj1qfuqLkoI8ITcmm/vNNHGttDToUEZF+qaysjAEDBoSdkfD666+zYcMGfvOb3zB9+nQKCgr4+c9/zq9+9Sv27dvX7bZ/8YtfcN9995Gfn8+kSZNYsWIFM2bM4Pe//31YvcWLF1NS0nmD4OhLiLsV5ORCU7P5eF0Zf96+lcwJp7azmIhIovm7321gY333f5lGY4fE7DEjWPHd87tdv6KighkzZoSdkvvuu+8ybdo0xo0b1142f/58Dh06xAcffMCcOXN6HV9TUxOnnx6++V1+fj51dXXU1NSETW1Em0YO+ojQ1GxAmyGJiARl+/btZGVlhZU1NDSQmZkZVpaenk5KSgoNDQ29vtZjjz1GbW0tS5YsCSsfM2YMANu2bet1292hkYM+YkT6KIaflUHdpo1MX7g46HBERKKqJ5/gIZjtk1taWo5LBICwkYTulJ/MSy+9xL333ktpaSlnn3122GtDhw5tjyWWNHLQh4SmZlP32UbidViWiIj8p/T0dBobG8PKRo8efdwIwVdffUVra2vEROJkXnrpJW666SaeeeYZFi8+/oPgnj17AG9xYiwpOehDQlOyOdC4h727vgw6FBGRfic3N5eNG8OndmfOnElVVRW1tbXtZevWrWPw4MHMmDGjR+0///zz3HjjjRQXF3P11VdHrFNZWUlqaio5OTk970APKDnoQ0LT/EOYNmm/AxGReJs/fz5VVVXs3r27vWzevHmcf/75LF26lI8++og33niDe++9l2XLljFixIhut11aWsoNN9zAqlWruOSSS2hoaKChoaF9pKBNRUUFs2bNIi0tLWr9ikTJQR+SPvZsBqedpkWJIiIByMnJIT8/n9LS0vaylJQU1q5dS1paGhdffDHXXXcdV155JQ8//HB7nW3btmFmFBcXd9n2E088wdGjR7nrrrvIyspq/7rxxhvD6pWUlLBs2bKo960zLUjsQ2zAAMZMmabNkEREArJixQqWL1/O7bff3n4r5dlnn33cfgQdbd26lSFDhnDJJZd0Wae8vDxieVNTU/vjtWvXkpKS0uWUQzRp5KCPCU3JZk/dFzTv2xt0KCIi/c6CBQsoLCwMW2NwMmVlZRQVFTFhwoRTuvaBAwd46qmnGDgw9p/rNXLQx7Ttd1D/+SYm5V0UcDQiIv1PTw8/euihh6Jy3WuvvTYq7XSHRg76mNETzyNl4EAtShQRkZhRctDHDBw0iMwJk7UoUUREYkbJQR8UmprNlzXVHDl8KOhQRER6RZu5xUa0/lyVHPRBoanZHGs9ypfVm4MORUSkx1JTU2O+/W9/1dLSQmpq6im3o+SgDxpz3jRAhzCJSN80atQo6urqaG5u1ghClDjnaG5upq6ujlGjRp1ye7pboQ8aOnwEZ409m9pNG9D9CiLS17TtHFhfX8+RI0d61cbBgwcZMmRINMNKSD3pZ2pqKpmZmT3ambErSg76qNCUbDa98xbHjrUyYMCpnWkuIhJvI0aMOKVfYuXl5eTm5kYxosQUVD8TYlrBzK4xsw1mdszM8k5Qb4GZfWZm1WZ2X4fyc83s381ss5k9Z2aD4hN5cEJTsznc0sxXO7YHHYqIiCSZhEgOgErgSuCtriqYWQrwGLAQyAa+Z2bZ/sv/G1jtnJsMNAK3xjbc4LVthqR1ByIiEm0JMa3gnKsCMLMTVcsHqp1zW/y6pcDlZlYFzAWu9+s9DawEHo9VvIlgREYmw844k+r/eJfhZ8X2XO/Ovt5aTfWwoXG9ZhDUz+SifiaX/tLPA1/uDOS6CZEcdFMI+KLD81rgIuAs4Gvn3NEO5aGuGjGz7wPfB8jMzOzysIve2L9/f1TbO5lBGaPZUfkxOyo/jts129T8yz/F/ZpBUD+Ti/qZXPpDP4eNG095Zlbcrxu35MDM3gBGR3jpp865V7vTRIQyd4LyiJxzTwJPAuTl5bnZs2d349LdU15eTjTbO5mLZ36TPXXdP/wjWj744ANmzJgR9+vGm/qZXNTP5NJf+rn+08q4/l5pE7fkwDn37VNsohYY1+H5WKAe+Ao43cwG+qMHbeVJL3XwEDInTIr7ddN21AZy3XhTP5OL+plc+ks/B++I/wdASJwFid3xHjDZvzNhELAEeM15O2i8CbQdcH0z0J2RCBEREYkgIZIDM7vCzGqBmcBaM/uDXz7GzMoA/FGBO4A/AFXA8865tqMJi4Afm1k13hqEX8e7DyIiIskiIRYkOudeAV6JUF4PLOrwvAwoi1BvC97dDCIiInKKEmLkQERERBKHkgMREREJo+RAREREwig5EBERkTBKDkRERCSMkgMREREJo+RAREREwpi3wWD/ZGZ/BrZHscl0vO2ck536mVzUz+SifiaXaPfzHOfcSY/y7dfJQbSZ2fvOubyg44g19TO5qJ/JRf1MLkH1U9MKIiIiEkbJgYiIiIRRchBdTwYdQJyon8lF/Uwu6mdyCaSfWnMgIiIiYTRyICIiImGUHIiIiEgYJQdRYmYLzOwzM6s2s/uCjicWzGycmb1pZlVmtsHMlgcdU6yYWYqZfWRmvw86llgys9PN7EUz2+T/vc4MOqZYMLP/7v+brTSzEjMbEnRM0WBm/2hmu8ysskPZmWa2zsw2+9/PCDLGaOiinw/5/24/MbNXzOz0IGOMhkj97PDaPWbmzCw9HrEoOYgCM0sBHgMWAtnA98wsO9ioYuIocLdzbhrwTaAwSfsJsByoCjqIOPgF8C/OuanAX5CEfTazEHAnkOecuwBIAZYEG1XUFAMLOpXdB/zROTcZ+KP/vK8r5vh+rgMucM59A/gc+Nt4BxUDxRzfT8xsHFAA7IhXIEoOoiMfqHbObXHOHQZKgcsDjinqnHM7nXMf+o+b8H6RhIKNKvrMbCxwGbAm6FhiycxGAJcAvwZwzh12zn0dbFQxMxAYamYDgTSgPuB4osI59xawp1Px5cDT/uOngb+Ka1AxEKmfzrnXnXNH/af/BoyNe2BR1sXfJ8Bq4H8AcbuDQMlBdISALzo8ryUJf2l2ZGbjgVzg34ONJCb+Ae8/4rGgA4mxCcCfgaf8KZQ1ZnZa0EFFm3OuDngY71PXTmCvc+71YKOKqUzn3E7wEnpgVMDxxMN/A/456CBiwcwWA3XOuY/jeV0lB9FhEcqS9h5RMxsGvATc5ZzbF3Q80WRm3wF2Oec+CDqWOBgITAced87lAgdIjiHoMP6c++XAucAY4DQzuzHYqCRazOyneFOezwYdS7SZWRrwU+Bn8b62koPoqAXGdXg+liQZtuzMzFLxEoNnnXMvBx1PDFwMLDazbXjTQ3PN7P8GG1LM1AK1zrm20Z8X8ZKFZPNtYKtz7s/OuSPAy8B/DTimWPrSzLIA/O+7Ao4nZszsZuA7wA0uOTftmYiX1H7svyeNBT40s9GxvrCSg+h4D5hsZuea2SC8xU6vBRxT1JmZ4c1PVznn/k/Q8cSCc+5vnXNjnXPj8f4e/9U5l5SfMp1zDcAXZjbFL/oWsDHAkGJlB/BNM0vz/w1/iyRceNnBa8DN/uObgVcDjCVmzGwBUAQsds41Bx1PLDjnPnXOjXLOjfffk2qB6f7/3ZhSchAF/qKYO4A/4L3pPO+c2xBsVDFxMXAT3qfp9f7XoqCDklPyI+BZM/sEuBB4MOB4os4fGXkR+BD4FO99Lym23jWzEuBdYIqZ1ZrZrcAqoMDMNuOtcF8VZIzR0EU/HwWGA+v896InAg0yCrroZzCxJOdIjIiIiPSWRg5EREQkjJIDERERCaPkQERERMIoORAREZEwSg5EJCGY2cpIB86ISPzpbgWRfsjMioF059x3Oj6O07XHA1uB/+Kce79D+TBgsHNudzziEJGuDQw6ABFJDv6hRq293anOObcf2B/dqESkNzStINKPmdlKvF30LvPPindmNtt/LWRmpWbW6H+tNbPJHX/WzCrN7BYzqwEO4Z1bsMDMKvyf2WNmfzCzaR0uu9X//p5/vfKO7XVof4CZ3W9mX5jZITP71Mwu7/D6eP/nrzKzdWbWbGYbzaygQ51UM3vEzOr9Nr4wsz6/KZBIrCk5EOnfHgaeB94Asvyvd/wDX94EDgKXAjPxTjR8w3+tzbnA9cA1wF/49U/DO9kyH5gN7AV+528tjl8O3rn1WcCVXcS2HLgXb4vcHOAV4GUzu7BTvb8HHvGv/x5Q6k9RANwJXIG3FfZk4Drgs5P/sYj0b5pWEOnHnHP7zawFONRxv3b/1EID/rptmsDM/gbvEJ/v4CUUAIOAm5xzX3Zo9qWO1zCzvwb24SUFb+MdEw2w+yR7xN8DPOyc+63//Gdmdolf3vG8i9XOud/51/oJsBRvK+i3gXOAz4EKvx87gHdO/KciIho5EJFIZuCNCjSZ2X4z2483AnAG3klxbWo7JQaY2UQz+62Z1ZjZPuBLvPeas7t7cTMbgXe88v/r9NLbQHansk86PG47DXWU/70YL1H43MweM7PLzEzveyInoZEDEYlkALAebzi+sz0dHh+I8PrvgDrgb/zvR/FOexwUoe7JRFrc2LnsSPsLzjnv4EXvg49z7kP/7ogFwFzgabzjbwucc8d6EY9Iv6DkQEQOAymdyj4Evgd85Zz7ursNmdlZwDSg0Dn3pl82nfD3msP+987XbOec22dm9cBfAv/a4aW/pIfHSjvnmoAXgBf82zb/DZiEN90gIhEoORCRbcBCM5sC7MabPngWb27/VTP7Gd5c/TjgcuAJ59zmLtpqBL4ClpnZF0AIeAhv9KDNLqAFmG9m24CDzrm9Edp6CHjAP3r4A7x1BrPwpjy6xcx+jLeQcj3eCMP1eOsfarvbhkh/pLk3EfkVUAW8j7dY8GLnXDNwCbAF71P3Jrwh+TPwEoCI/KH664BvAJXAY8D9eLc5ttU5incXwW14awRe7aK5R/AShJ/7bV0BXOWcW9+DvjXh3fHwH3ijIRcCC/3+iUgXtEOiiIiIhNHIgYiIiIRRciAiIiJhlByIiIhIGCUHIiIiEkbJgYiIiIRRciAiIiJhlByIiIhIGCUHIiIiEkbJgYiIiIT5/3iDPbGhusVTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_value_update(grid_1,15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Determining best policy by enumerating utilities from the value iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def best_policy(mdp, U):\n",
    "    \"\"\"Given an MDP and a utility function U, determine the best policy,\n",
    "    as a mapping from state to action.\"\"\"\n",
    "\n",
    "    pi = {}\n",
    "    for s in mdp.states:\n",
    "        pi[s] = max(mdp.actions(s), key=lambda a: expected_utility(a, s, U, mdp))\n",
    "    return pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value iteration visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def value_iteration_instru(mdp, iterations=20):\n",
    "    U_over_time = []\n",
    "    U1 = {s: 0 for s in mdp.states}\n",
    "    R, T, gamma = mdp.R, mdp.T, mdp.gamma\n",
    "    for _ in range(iterations):\n",
    "        U = U1.copy()\n",
    "        for s in mdp.states:\n",
    "            U1[s] = R(s) + gamma * max([sum([p * U[s1] for (p, s1) in T(s, a)])\n",
    "                                        for a in mdp.actions(s)])\n",
    "        U_over_time.append(U)\n",
    "    return U_over_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "columns = 4\n",
    "rows = 3\n",
    "U_over_time = value_iteration_instru(grid_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_plot_grid_step_function(columns, rows, U_over_time):\n",
    "    \"\"\"ipywidgets interactive function supports single parameter as input.\n",
    "    This function creates and return such a function by taking as input\n",
    "    other parameters.\"\"\"\n",
    "\n",
    "    def plot_grid_step(iteration):\n",
    "        data = U_over_time[iteration]\n",
    "        data = defaultdict(lambda: 0, data)\n",
    "        grid = []\n",
    "        for row in range(rows):\n",
    "            current_row = []\n",
    "            for column in range(columns):\n",
    "                current_row.append(data[(column, row)])\n",
    "            grid.append(current_row)\n",
    "        grid.reverse() # output like book\n",
    "        fig = plt.figure(figsize=(rows,columns))\n",
    "        fig = plt.imshow(grid, cmap=plt.cm.bwr, interpolation='nearest')\n",
    "\n",
    "        plt.axis('off')\n",
    "        fig.axes.get_xaxis().set_visible(False)\n",
    "        fig.axes.get_yaxis().set_visible(False)\n",
    "\n",
    "        for col in range(len(grid)):\n",
    "            for row in range(len(grid[0])):\n",
    "                magic = grid[col][row]\n",
    "                fig.axes.text(row, col, \"{0:.2f}\".format(magic), va='center', ha='center')\n",
    "\n",
    "        plt.show()\n",
    "\n",
    "    return plot_grid_step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_visualize(slider):\n",
    "    \"\"\"Takes an input a sliderand returns callback function\n",
    "    for timer and animation.\"\"\"\n",
    "\n",
    "    def visualize_callback(Visualize, time_step):\n",
    "        if Visualize is True:\n",
    "            for i in range(slider.min, slider.max + 1):\n",
    "                slider.value = i\n",
    "                time.sleep(float(time_step))\n",
    "\n",
    "    return visualize_callback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_grid_step = make_plot_grid_step_function(columns, rows, U_over_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a190e05d74c0414db3f979bb128b2694",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='iteration', max=15, min=1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "74cf8411f2a74b8ab42386a65bec697f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(ToggleButton(value=False, description='Visualize'), ToggleButtons(description='Extra Delay:', options=('0', '0.1', '0.2', '0.5', '0.7', '1.0'), value='0'), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import ipywidgets as widgets\n",
    "from IPython.display import display\n",
    "\n",
    "iteration_slider = widgets.IntSlider(min=1, max=15, step=1, value=0)\n",
    "w=widgets.interactive(plot_grid_step,iteration=iteration_slider)\n",
    "display(w)\n",
    "\n",
    "visualize_callback = make_visualize(iteration_slider)\n",
    "\n",
    "visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n",
    "time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n",
    "a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n",
    "display(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value iteration for a larger Grid World\n",
    "Let us use the `gen_mdp` function to generate a large (10x10) and more complex grid world and run value iteration on it and visualize!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "large_grid = gen_mdp(nrows=10,ncols=10,terminals=[(6, 3), (5, 2),(4,4)],main_reward=-0.04,\n",
    "                     terminal_rewards=[1,-1,-1],block_coords=[(1,1),(2,3),(7,5),(8,2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "large_gridworld = GridMDP(large_grid,terminals=[(6, 3), (5, 2),(4,4)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04],\n",
       " [-0.04, None, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04],\n",
       " [-0.04, -0.04, -0.04, -0.04, -0.04, -1, -0.04, -0.04, None, -0.04],\n",
       " [-0.04, -0.04, None, -0.04, -0.04, -0.04, 1, -0.04, -0.04, -0.04],\n",
       " [-0.04, -0.04, -0.04, -0.04, -1, -0.04, -0.04, -0.04, -0.04, -0.04],\n",
       " [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, None, -0.04, -0.04],\n",
       " [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04],\n",
       " [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04],\n",
       " [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04],\n",
       " [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04]]"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "large_gridworld.grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(large_gridworld.grid).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "columns = 10\n",
    "rows = 10\n",
    "U_over_time = value_iteration_instru(large_gridworld,iterations=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_grid_step = make_plot_grid_step_function(columns, rows, U_over_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "69a5672f8a134ee9abb5c37896be5e50",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='iteration', max=30, min=1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0e304e36a9b64142a986e369e6cf1601",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(ToggleButton(value=False, description='Visualize'), ToggleButtons(description='Extra Delay:', options=('0', '0.1', '0.2', '0.5', '0.7', '1.0'), value='0'), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iteration_slider = widgets.IntSlider(min=1, max=30, step=1, value=0)\n",
    "w=widgets.interactive(plot_grid_step,iteration=iteration_slider)\n",
    "display(w)\n",
    "\n",
    "visualize_callback = make_visualize(iteration_slider)\n",
    "\n",
    "visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n",
    "time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n",
    "a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n",
    "display(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7, 3):0.8,(6, 9):0.17,(0, 7):-0.04,(1, 6):0.05,(3, 7):0.14,(2, 5):0.1,(8, 5):0.41,(5, 8):0.21,(4, 0):0.19,(9, 0):0.22,(6, 7):0.36,(5, 5):0.51,(7, 6):0.37,(0, 4):-0.06,(3, 2):0.14,(2, 6):0.12,(4, 5):0.27,(9, 3):0.49,(6, 0):0.38,(0, 1):-0.09,(3, 1):0.11,(9, 9):0.05,(7, 8):0.2,(2, 1):0.05,(8, 9):0.08,(9, 4):0.42,(5, 1):0.25,(7, 2):0.65,(1, 5):0.03,(3, 6):0.2,(2, 2):0.07,(8, 6):0.31,(4, 1):0.17,(9, 7):0.17,(6, 4):0.8,(5, 4):0.64,(7, 1):0.51,(0, 5):-0.02,(1, 0):0.0,(0, 8):-0.08,(3, 5):0.17,(2, 7):0.07,(8, 3):0.64,(4, 6):0.29,(9, 2):0.38,(6, 1):0.5,(5, 7):0.3,(7, 4):0.67,(0, 2):-0.05,(1, 3):-0.04,(4, 8):0.14,(3, 0):0.12,(2, 8):0.02,(9, 8):0.11,(8, 0):0.3,(6, 2):0.65,(5, 0):0.28,(1, 4):-0.02,(3, 9):0.02,(1, 9):-0.07,(8, 7):0.22,(4, 2):0.13,(9, 6):0.25,(6, 5):0.64,(5, 3):0.65,(7, 0):0.39,(6, 8):0.26,(0, 6):-0.01,(1, 7):0.01,(0, 9):-0.1,(3, 4):0.04,(2, 4):0.03,(8, 4):0.53,(5, 9):0.13,(4, 7):0.21,(9, 1):0.3,(6, 6):0.49,(5, 6):0.4,(7, 7):0.28,(0, 3):-0.08,(1, 2):0.01,(4, 9):0.08,(3, 3):0.23,(2, 9):-0.02,(8, 1):0.39,(4, 4):-1.0,(6, 3):1.0,(0, 0):-0.05,(7, 9):0.13,(3, 8):0.08,(2, 0):0.06,(1, 8):-0.03,(8, 8):0.15,(4, 3):0.35,(9, 5):0.33,(5, 2):-1.0,"
     ]
    }
   ],
   "source": [
    "d,_=value_iteration(large_gridworld,0.001)\n",
    "for k,v in d.items():\n",
    "    print(\"{}:{}\".format(k,round(v,2)),end=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Policy Iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_utility(a, s, U, mdp):\n",
    "    \"\"\"The expected utility of doing a in state s, according to the MDP and U.\"\"\"\n",
    "    return sum([p * U[s1] for (p, s1) in mdp.T(s, a)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "def policy_evaluation(pi, U, mdp, k=20):\n",
    "    \"\"\"Returns an updated utility mapping U from each state in the MDP to its\n",
    "    utility, using an approximation (modified policy iteration).\"\"\"\n",
    "    \n",
    "    R, T, gamma = mdp.R, mdp.T, mdp.gamma\n",
    "    for i in range(k):\n",
    "        for s in mdp.states:\n",
    "            U[s] = R(s) + gamma * sum([p * U[s1] for (p, s1) in T(s, pi[s])])\n",
    "    return U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "def policy_iteration(mdp,verbose=0):\n",
    "    \"\"\"Solves an MDP by policy iteration\"\"\"\n",
    "    \n",
    "    U = {s: 0 for s in mdp.states}\n",
    "    pi = {s: random.choice(mdp.actions(s)) for s in mdp.states}\n",
    "    #if verbose:\n",
    "        #print(\"Initial random choice:\",pi)\n",
    "    iter_count=0\n",
    "    while True:\n",
    "        iter_count+=1\n",
    "        U = policy_evaluation(pi, U, mdp)\n",
    "        unchanged = True\n",
    "        for s in mdp.states:\n",
    "            a = max(mdp.actions(s), key=lambda a: expected_utility(a, s, U, mdp))\n",
    "            if a != pi[s]:\n",
    "                pi[s] = a\n",
    "                unchanged = False\n",
    "        if unchanged:\n",
    "            return (pi,iter_count)\n",
    "        if verbose:\n",
    "            print(\"Policy after iteration {}: {}\".format(iter_count,pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "def policy_iteration_gridworld(mdp,verbose=0):\n",
    "    \"\"\"Solves an MDP by policy iteration.\n",
    "    Expects a GridMDP for this function (for the purpose of visualizing grid)\n",
    "    \"\"\"\n",
    "    \n",
    "    U = {s: 0 for s in mdp.states}\n",
    "    pi = {s: random.choice(mdp.actions(s)) for s in mdp.states}\n",
    "    if verbose:\n",
    "        print(\"Initial random choice\\n\")\n",
    "        print_table(mdp.to_arrows(pi))\n",
    "        print(\"=\"*80)\n",
    "    iter_count=0\n",
    "    while True:\n",
    "        iter_count+=1\n",
    "        U = policy_evaluation(pi, U, mdp)\n",
    "        unchanged = True\n",
    "        for s in mdp.states:\n",
    "            a = max(mdp.actions(s), key=lambda a: expected_utility(a, s, U, mdp))\n",
    "            if a != pi[s]:\n",
    "                pi[s] = a\n",
    "                unchanged = False\n",
    "        if unchanged:\n",
    "            if verbose:\n",
    "                print(\"Final policy\\n\")\n",
    "                print_table(mdp.to_arrows(pi))\n",
    "                print(\"=\"*80)\n",
    "            return (pi,iter_count)\n",
    "        if verbose:\n",
    "            print(\"Policy after iteration {}\\n\".format(iter_count))\n",
    "            print_table(mdp.to_arrows(pi))\n",
    "            print(\"=\"*80)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_table(table, header=None, sep='   ', numfmt='{}'):\n",
    "    \"\"\"Print a list of lists as a table, so that columns line up nicely.\n",
    "    header, if specified, will be printed as the first row.\n",
    "    numfmt is the format for all numbers; you might want e.g. '{:.2f}'.\n",
    "    (If you want different formats in different columns,\n",
    "    don't use print_table.) sep is the separator between columns.\"\"\"\n",
    "    justs = ['rjust' if isnumber(x) else 'ljust' for x in table[0]]\n",
    "\n",
    "    if header:\n",
    "        table.insert(0, header)\n",
    "\n",
    "    table = [[numfmt.format(x) if isnumber(x) else x for x in row]\n",
    "             for row in table]\n",
    "\n",
    "    sizes = list(\n",
    "        map(lambda seq: max(map(len, seq)),\n",
    "            list(zip(*[map(str, row) for row in table]))))\n",
    "\n",
    "    for row in table:\n",
    "        print(sep.join(getattr(str(x), j)(size) for (j, size, x) in zip(justs, sizes, row)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({(0, 0): (0, 1),\n",
       "  (0, 1): (0, 1),\n",
       "  (0, 2): (1, 0),\n",
       "  (1, 0): (-1, 0),\n",
       "  (1, 2): (1, 0),\n",
       "  (2, 0): (0, 1),\n",
       "  (2, 1): (0, 1),\n",
       "  (2, 2): (1, 0),\n",
       "  (3, 0): (-1, 0),\n",
       "  (3, 1): None,\n",
       "  (3, 2): None},\n",
       " 3)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "policy_iteration(grid_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How the policy evolves over iterations: Small grid world"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial random choice\n",
      "\n",
      "↓   ↑      ←   TERMINAL\n",
      "←   None   →   TERMINAL\n",
      "↑   ↓      ↑   →       \n",
      "================================================================================\n",
      "Policy after iteration 1\n",
      "\n",
      "↓   ←      →   TERMINAL\n",
      "→   None   ↑   TERMINAL\n",
      "↑   ←      ←   ↓       \n",
      "================================================================================\n",
      "Policy after iteration 2\n",
      "\n",
      "↓   →      →   TERMINAL\n",
      "→   None   ↑   TERMINAL\n",
      "↑   →      ↑   ←       \n",
      "================================================================================\n",
      "Policy after iteration 3\n",
      "\n",
      "→   →      →   TERMINAL\n",
      "↑   None   ↑   TERMINAL\n",
      "→   →      ↑   ←       \n",
      "================================================================================\n",
      "Policy after iteration 4\n",
      "\n",
      "→   →      →   TERMINAL\n",
      "↑   None   ↑   TERMINAL\n",
      "↑   →      ↑   ←       \n",
      "================================================================================\n",
      "Policy after iteration 5\n",
      "\n",
      "→   →      →   TERMINAL\n",
      "↑   None   ↑   TERMINAL\n",
      "↑   ←      ↑   ←       \n",
      "================================================================================\n",
      "Final policy\n",
      "\n",
      "→   →      →   TERMINAL\n",
      "↑   None   ↑   TERMINAL\n",
      "↑   ←      ↑   ←       \n",
      "================================================================================\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "({(0, 0): (0, 1),\n",
       "  (0, 1): (0, 1),\n",
       "  (0, 2): (1, 0),\n",
       "  (1, 0): (-1, 0),\n",
       "  (1, 2): (1, 0),\n",
       "  (2, 0): (0, 1),\n",
       "  (2, 1): (0, 1),\n",
       "  (2, 2): (1, 0),\n",
       "  (3, 0): (-1, 0),\n",
       "  (3, 1): None,\n",
       "  (3, 2): None},\n",
       " 6)"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "policy_iteration_gridworld(grid_1,verbose=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How the policy evolves over iterations: Large grid world"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial random choice\n",
      "\n",
      "↓   ↓      →      ←   ←          →          ←          ↓      ←      ←\n",
      "←   ←      ↑      ←   →          →          ←          ←      ←      ↑\n",
      "→   →      ↓      ↑   ↓          →          →          ↓      →      ←\n",
      "←   →      ↓      ←   ↑          →          ↑          ←      →      →\n",
      "↓   ↑      ↑      ↑   ↓          ←          ←          None   ←      ←\n",
      "↑   ←      →      ←   TERMINAL   →          ↓          →      ←      ↓\n",
      "←   ←      None   ↓   →          ↓          TERMINAL   →      ←      ←\n",
      "←   ↓      ↓      ←   ←          TERMINAL   →          →      None   ↑\n",
      "↓   None   →      →   ←          →          ↓          ←      ↓      ↓\n",
      "→   ↓      →      ↓   ←          ↑          ←          ←      ←      ↑\n",
      "================================================================================\n",
      "Policy after iteration 1\n",
      "\n",
      "↓   ←      ←      ↑   ←          ←          ↑          ←      →      →\n",
      "↑   ↑      ↑      ←   ↑          ↑          ↑          →      ↓      ↓\n",
      "↑   ↑      ↑      ↑   ←          ↑          ↑          →      ↓      ↓\n",
      "←   ←      ↑      ↑   ↑          ↑          ↑          →      ↓      ←\n",
      "↑   ↓      ←      ←   ↑          ↓          ↓          None   ←      ←\n",
      "↓   ↓      ←      ←   TERMINAL   →          ↓          ←      ↑      ↑\n",
      "↓   ↓      None   ←   ↓          →          TERMINAL   ←      ↑      →\n",
      "↓   ←      ←      ↓   ←          TERMINAL   ↑          ←      None   ↑\n",
      "→   None   ↓      ↓   ↓          ←          ↑          ↑      →      ↑\n",
      "→   ↑      ←      ↓   ←          ←          →          →      →      →\n",
      "================================================================================\n",
      "Policy after iteration 2\n",
      "\n",
      "↓   ↑      →      ↑   →          →          →          ↓      ↓      ↓\n",
      "↓   ↑      ↓      ↑   →          →          →          ↓      ↓      ↓\n",
      "↓   ↓      ↓      →   →          →          →          →      ↓      ↓\n",
      "↓   ↓      ↓      ↓   ↓          ↓          ↓          →      ↓      ↓\n",
      "↓   ↓      ↓      →   →          ↓          ↓          None   ↓      ←\n",
      "↓   ↓      ←      ←   TERMINAL   →          ↓          ←      ←      ←\n",
      "↓   →      None   →   →          →          TERMINAL   ←      ←      ←\n",
      "↓   ←      →      →   ↑          TERMINAL   ↑          ↑      None   ↑\n",
      "→   None   ←      ←   ↑          →          ↑          ↑      ←      ↑\n",
      "→   ↑      ←      ←   ←          →          ↑          ↑      ←      ↑\n",
      "================================================================================\n",
      "Policy after iteration 3\n",
      "\n",
      "→   →      →      →   →          →          →          ↓      ↓      ↓\n",
      "→   →      →      ↓   ↓          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      ↓   ↓          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ←      ↓      ↓\n",
      "→   →      →      →   →          →          ↓          None   ↓      ↓\n",
      "↑   →      →      ↓   TERMINAL   →          ↓          ←      ←      ←\n",
      "↓   ←      None   →   →          →          TERMINAL   ←      ←      ←\n",
      "↓   →      →      ↑   ↑          TERMINAL   ↑          ↑      None   ↑\n",
      "↓   None   ↑      ↑   →          →          ↑          ↑      ←      ↑\n",
      "→   →      ↑      ↑   →          →          ↑          ↑      ←      ←\n",
      "================================================================================\n",
      "Policy after iteration 4\n",
      "\n",
      "↓   ↓      ↓      ↓   ↓          ↓          ↓          ↓      ↓      ↓\n",
      "↓   ↓      ↓      →   ↓          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ←      ↓      ↓\n",
      "→   →      →      →   →          →          ↓          None   ↓      ↓\n",
      "↑   ↑      ↑      ↓   TERMINAL   →          ↓          ←      ←      ←\n",
      "↑   ↓      None   →   →          →          TERMINAL   ←      ←      ←\n",
      "→   →      →      ↑   ↑          TERMINAL   ↑          ↑      None   ↑\n",
      "↓   None   →      →   →          →          ↑          ↑      ←      ↑\n",
      "→   →      →      →   →          →          ↑          ↑      ←      ←\n",
      "================================================================================\n",
      "Policy after iteration 5\n",
      "\n",
      "↓   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "↓   →      →      →   ↓          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ←      ↓      ↓\n",
      "→   →      →      →   →          →          ↓          None   ↓      ↓\n",
      "↑   →      ↑      ↓   TERMINAL   →          ↓          ←      ←      ←\n",
      "→   ↓      None   →   →          →          TERMINAL   ←      ←      ←\n",
      "→   →      →      ↑   ↑          TERMINAL   ↑          ↑      None   ↑\n",
      "↑   None   →      →   →          →          ↑          ↑      ←      ↑\n",
      "→   →      →      →   →          →          ↑          ↑      ←      ←\n",
      "================================================================================\n",
      "Policy after iteration 6\n",
      "\n",
      "→   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   ↓          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ←      ↓      ↓\n",
      "→   →      →      →   →          →          ↓          None   ↓      ↓\n",
      "→   →      ↑      ↓   TERMINAL   →          ↓          ←      ←      ←\n",
      "→   ↓      None   →   →          →          TERMINAL   ←      ←      ←\n",
      "→   →      →      ↑   ↑          TERMINAL   ↑          ↑      None   ↑\n",
      "↑   None   →      →   →          →          ↑          ↑      ←      ↑\n",
      "→   →      →      →   →          →          ↑          ↑      ←      ←\n",
      "================================================================================\n",
      "Final policy\n",
      "\n",
      "→   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   ↓          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ←      ↓      ↓\n",
      "→   →      →      →   →          →          ↓          None   ↓      ↓\n",
      "→   →      ↑      ↓   TERMINAL   →          ↓          ←      ←      ←\n",
      "→   ↓      None   →   →          →          TERMINAL   ←      ←      ←\n",
      "→   →      →      ↑   ↑          TERMINAL   ↑          ↑      None   ↑\n",
      "↑   None   →      →   →          →          ↑          ↑      ←      ↑\n",
      "→   →      →      →   →          →          ↑          ↑      ←      ←\n",
      "================================================================================\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "({(0, 0): (1, 0),\n",
       "  (0, 1): (0, 1),\n",
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       "  (0, 3): (1, 0),\n",
       "  (0, 4): (1, 0),\n",
       "  (0, 5): (1, 0),\n",
       "  (0, 6): (1, 0),\n",
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       "  (0, 9): (1, 0),\n",
       "  (1, 0): (1, 0),\n",
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       "  (1, 3): (0, -1),\n",
       "  (1, 4): (1, 0),\n",
       "  (1, 5): (1, 0),\n",
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       "  (1, 8): (1, 0),\n",
       "  (1, 9): (1, 0),\n",
       "  (2, 0): (1, 0),\n",
       "  (2, 1): (1, 0),\n",
       "  (2, 2): (1, 0),\n",
       "  (2, 4): (0, 1),\n",
       "  (2, 5): (1, 0),\n",
       "  (2, 6): (1, 0),\n",
       "  (2, 7): (1, 0),\n",
       "  (2, 8): (1, 0),\n",
       "  (2, 9): (1, 0),\n",
       "  (3, 0): (1, 0),\n",
       "  (3, 1): (1, 0),\n",
       "  (3, 2): (0, 1),\n",
       "  (3, 3): (1, 0),\n",
       "  (3, 4): (0, -1),\n",
       "  (3, 5): (1, 0),\n",
       "  (3, 6): (1, 0),\n",
       "  (3, 7): (1, 0),\n",
       "  (3, 8): (1, 0),\n",
       "  (3, 9): (1, 0),\n",
       "  (4, 0): (1, 0),\n",
       "  (4, 1): (1, 0),\n",
       "  (4, 2): (0, 1),\n",
       "  (4, 3): (1, 0),\n",
       "  (4, 4): None,\n",
       "  (4, 5): (1, 0),\n",
       "  (4, 6): (1, 0),\n",
       "  (4, 7): (1, 0),\n",
       "  (4, 8): (0, -1),\n",
       "  (4, 9): (1, 0),\n",
       "  (5, 0): (1, 0),\n",
       "  (5, 1): (1, 0),\n",
       "  (5, 2): None,\n",
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       "  (5, 4): (1, 0),\n",
       "  (5, 5): (1, 0),\n",
       "  (5, 6): (0, -1),\n",
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       "  (6, 0): (0, 1),\n",
       "  (6, 1): (0, 1),\n",
       "  (6, 2): (0, 1),\n",
       "  (6, 3): None,\n",
       "  (6, 4): (0, -1),\n",
       "  (6, 5): (0, -1),\n",
       "  (6, 6): (0, -1),\n",
       "  (6, 7): (0, -1),\n",
       "  (6, 8): (0, -1),\n",
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       "  (7, 7): (0, -1),\n",
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       "  (7, 9): (0, -1),\n",
       "  (8, 0): (-1, 0),\n",
       "  (8, 1): (-1, 0),\n",
       "  (8, 3): (-1, 0),\n",
       "  (8, 4): (-1, 0),\n",
       "  (8, 5): (0, -1),\n",
       "  (8, 6): (0, -1),\n",
       "  (8, 7): (0, -1),\n",
       "  (8, 8): (0, -1),\n",
       "  (8, 9): (0, -1),\n",
       "  (9, 0): (-1, 0),\n",
       "  (9, 1): (0, 1),\n",
       "  (9, 2): (0, 1),\n",
       "  (9, 3): (-1, 0),\n",
       "  (9, 4): (-1, 0),\n",
       "  (9, 5): (0, -1),\n",
       "  (9, 6): (0, -1),\n",
       "  (9, 7): (0, -1),\n",
       "  (9, 8): (0, -1),\n",
       "  (9, 9): (0, -1)},\n",
       " 7)"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "policy_iteration_gridworld(large_gridworld,verbose=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "pi1 = best_policy(grid_1, value_iteration(grid_1, .001)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0, 0): (0, 1),\n",
       " (0, 1): (0, 1),\n",
       " (0, 2): (1, 0),\n",
       " (1, 0): (-1, 0),\n",
       " (1, 2): (1, 0),\n",
       " (2, 0): (0, 1),\n",
       " (2, 1): (0, 1),\n",
       " (2, 2): (1, 0),\n",
       " (3, 0): (-1, 0),\n",
       " (3, 1): None,\n",
       " (3, 2): None}"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "→   →      →   TERMINAL\n",
      "↑   None   ↑   TERMINAL\n",
      "↑   ←      ↑   ←       \n"
     ]
    }
   ],
   "source": [
    "print_table(grid_1.to_arrows(pi1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "pi2 = best_policy(large_gridworld, value_iteration(large_gridworld, .001)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "→   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   ↓          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ↓      ↓      ↓\n",
      "→   →      →      →   →          ↓          ↓          ←      ↓      ↓\n",
      "→   →      →      →   →          →          ↓          None   ↓      ↓\n",
      "→   →      ↑      ↓   TERMINAL   →          ↓          ←      ←      ←\n",
      "→   ↓      None   →   →          →          TERMINAL   ←      ←      ←\n",
      "→   →      →      ↑   ↑          TERMINAL   ↑          ↑      None   ↑\n",
      "↑   None   →      →   →          →          ↑          ↑      ←      ↑\n",
      "→   →      →      →   →          →          ↑          ↑      ←      ←\n"
     ]
    }
   ],
   "source": [
    "print_table(large_gridworld.to_arrows(pi2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing computation efficiency (time) of value and policy iterations\n",
    "Clearly values iteration method takes more iterations to reach the same steady-state compared to policy iteration technique. But how does their computation time compare? Let's find out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_time(mdp,iteration_technique='value',n_run=1000,epsilon=0.01):\n",
    "    \"\"\"\n",
    "    Computes the average time for value or policy iteration for a given MDP\n",
    "    Returns average compute time in milliseconds\n",
    "    n_run: Number of runs to average over, default 1000\n",
    "    epsilon: Error margin for the value iteration\n",
    "    \"\"\"\n",
    "    if iteration_technique=='value':\n",
    "        t1 = time.time()\n",
    "        for _ in range(n_run):\n",
    "            value_iteration(mdp,epsilon=epsilon)\n",
    "        t2 = time.time()\n",
    "        print(\"Average value iteration took {} milliseconds\".format((t2-t1)*1000/n_run))\n",
    "        return (t2-t1)*1000/n_run\n",
    "    else:\n",
    "        t1 = time.time()\n",
    "        for _ in range(n_run):\n",
    "            policy_iteration(mdp)\n",
    "        t2 = time.time()\n",
    "\n",
    "        print(\"Average policy iteration took {} milliseconds\".format((t2-t1)*1000/n_run))\n",
    "        return (t2-t1)*1000/n_run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average value iteration took 19.995357990264893 milliseconds\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "19.995357990264893"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_time(large_gridworld,'value',n_run=100,epsilon=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average policy iteration took 28.557772636413574 milliseconds\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "28.557772636413574"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_time(large_gridworld,'policy',n_run=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average value iteration took 1.5953254699707031 milliseconds\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.5953254699707031"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_time(grid_1,'value',n_run=1000,epsilon=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average policy iteration took 1.9770958423614502 milliseconds\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.9770958423614502"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_time(grid_1,'policy',n_run=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How the computing efficiency (time) changes with number of states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 4x4 grid\n",
      "Average value iteration took 1.7866945266723633 milliseconds\n",
      "Average policy iteration took 2.558012008666992 milliseconds\n",
      "Ratio of policy/value iteration 1.4317008142579204\n",
      "--------------------------------------------------------------------------------\n",
      "For 5x5 grid\n",
      "Average value iteration took 2.704617977142334 milliseconds\n",
      "Average policy iteration took 5.174593925476074 milliseconds\n",
      "Ratio of policy/value iteration 1.9132439291642536\n",
      "--------------------------------------------------------------------------------\n",
      "For 6x6 grid\n",
      "Average value iteration took 4.286103248596191 milliseconds\n",
      "Average policy iteration took 7.908139228820801 milliseconds\n",
      "Ratio of policy/value iteration 1.845065032301991\n",
      "--------------------------------------------------------------------------------\n",
      "For 7x7 grid\n",
      "Average value iteration took 6.082546710968018 milliseconds\n",
      "Average policy iteration took 10.436816215515137 milliseconds\n",
      "Ratio of policy/value iteration 1.7158628961608338\n",
      "--------------------------------------------------------------------------------\n",
      "For 8x8 grid\n",
      "Average value iteration took 9.66587781906128 milliseconds\n",
      "Average policy iteration took 17.593543529510498 milliseconds\n",
      "Ratio of policy/value iteration 1.8201702792906946\n",
      "--------------------------------------------------------------------------------\n",
      "For 9x9 grid\n",
      "Average value iteration took 14.293503761291504 milliseconds\n",
      "Average policy iteration took 22.045588493347168 milliseconds\n",
      "Ratio of policy/value iteration 1.5423502075851567\n",
      "--------------------------------------------------------------------------------\n",
      "For 10x10 grid\n",
      "Average value iteration took 18.608932495117188 milliseconds\n",
      "Average policy iteration took 36.163437366485596 milliseconds\n",
      "Ratio of policy/value iteration 1.9433375544768379\n",
      "--------------------------------------------------------------------------------\n",
      "For 11x11 grid\n",
      "Average value iteration took 36.96401119232178 milliseconds\n",
      "Average policy iteration took 40.98654270172119 milliseconds\n",
      "Ratio of policy/value iteration 1.108822916659948\n",
      "--------------------------------------------------------------------------------\n",
      "For 12x12 grid\n",
      "Average value iteration took 35.46065330505371 milliseconds\n",
      "Average policy iteration took 51.189143657684326 milliseconds\n",
      "Ratio of policy/value iteration 1.4435476757104486\n",
      "--------------------------------------------------------------------------------\n",
      "For 13x13 grid\n",
      "Average value iteration took 41.8849515914917 milliseconds\n",
      "Average policy iteration took 71.86801195144653 milliseconds\n",
      "Ratio of policy/value iteration 1.7158432616177464\n",
      "--------------------------------------------------------------------------------\n",
      "For 14x14 grid\n",
      "Average value iteration took 58.59959840774536 milliseconds\n",
      "Average policy iteration took 85.99557876586914 milliseconds\n",
      "Ratio of policy/value iteration 1.4675114011447343\n",
      "--------------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "for i in range(4,15,1):\n",
    "    gridw=gen_mdp(nrows=i,ncols=i)\n",
    "    grid_mdp=GridMDP(gridw,terminals=[(3, 2), (3, 1)])\n",
    "    print(\"For {}x{} grid\".format(i,i))\n",
    "    vt=compute_time(grid_mdp,'value',n_run=100)\n",
    "    pt=compute_time(grid_mdp,'policy',n_run=100)\n",
    "    print(\"Ratio of policy/value iteration {}\".format(pt/vt))\n",
    "    print(\"-\"*80)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 5x5 grid\n",
      "Average value iteration took 5.028097629547119 milliseconds\n",
      "Average policy iteration took 7.09796667098999 milliseconds\n",
      "For 10x10 grid\n",
      "Average value iteration took 37.49123811721802 milliseconds\n",
      "Average policy iteration took 39.95161056518555 milliseconds\n",
      "For 15x15 grid\n",
      "Average value iteration took 75.91020822525024 milliseconds\n",
      "Average policy iteration took 104.14720296859741 milliseconds\n",
      "For 20x20 grid\n",
      "Average value iteration took 175.50591945648193 milliseconds\n",
      "Average policy iteration took 322.1123218536377 milliseconds\n",
      "For 25x25 grid\n",
      "Average value iteration took 280.520498752594 milliseconds\n",
      "Average policy iteration took 442.40652561187744 milliseconds\n"
     ]
    }
   ],
   "source": [
    "vi_time=[]\n",
    "pi_time=[]\n",
    "\n",
    "for i in range(5,26,5):\n",
    "    gridw=gen_mdp(nrows=i,ncols=i)\n",
    "    grid_mdp=GridMDP(gridw,terminals=[(3, 2), (3, 1)])\n",
    "    print(\"For {}x{} grid\".format(i,i))\n",
    "    vt=compute_time(grid_mdp,'value',n_run=100)\n",
    "    pt=compute_time(grid_mdp,'policy',n_run=100)\n",
    "    vi_time.append(vt)\n",
    "    pi_time.append(pt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure (figsize=(10,5))\n",
    "plt.plot([str(i)+'x'+str(i)+'\\ngrid' for i in range(5,26,5)],vi_time,color='red',lw=3)\n",
    "plt.plot([str(i)+'x'+str(i)+'\\ngrid' for i in range(5,26,5)],pi_time,color='blue',lw=3)\n",
    "plt.legend([\"Value iteration\",\"Policy iteration\"],fontsize=16)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.xlabel(\"\\nSize of the grid world\",fontsize=20)\n",
    "plt.ylabel(\"Average convergence time\\n(milliseconds)\",fontsize=16)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demonstrating the variability of policy iteration as compared to value iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "vi_iter=[]\n",
    "pi_iter=[]\n",
    "for i in range(100):\n",
    "    _,vi = value_iteration(large_gridworld,0.01)\n",
    "    _,pi = policy_iteration(large_gridworld)\n",
    "    vi_iter.append(vi)\n",
    "    pi_iter.append(pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure (figsize=(7,4))\n",
    "plt.plot(vi_iter,color='red',lw=3)\n",
    "plt.plot(pi_iter,color='blue',lw=3)\n",
    "plt.legend([\"Value iteration\",\"Policy iteration\"],fontsize=16)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.xlabel(\"Number of runs\",fontsize=20)\n",
    "plt.ylabel(\"Iteration counts\",fontsize=16)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "vi_iter=[]\n",
    "pi_iter=[]\n",
    "for i in range(100):\n",
    "    terminal_rewards = [random.uniform(2,4),-random.uniform(2,4),-random.uniform(4,6)]\n",
    "    large_grid = gen_mdp(nrows=10,ncols=10,terminals=[(6, 3), (5, 2),(4,4)],\n",
    "                         main_reward=-random.uniform(0,1),terminal_rewards=terminal_rewards,\n",
    "                         block_coords=[(1,1),(2,3),(7,5),(8,2)])\n",
    "    large_gridworld = GridMDP(large_grid,terminals=[(6, 3), (5, 2),(4,4)])\n",
    "    \n",
    "    _,vi = value_iteration(large_gridworld,0.01)\n",
    "    _,pi = policy_iteration(large_gridworld)\n",
    "    \n",
    "    vi_iter.append(vi)\n",
    "    pi_iter.append(pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure (figsize=(7,4))\n",
    "plt.plot(vi_iter,color='red',lw=3)\n",
    "plt.plot(pi_iter,color='blue',lw=3)\n",
    "plt.legend([\"Value iteration\",\"Policy iteration\"],fontsize=16)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.xlabel(\"Number of runs\",fontsize=20)\n",
    "plt.ylabel(\"Iteration counts\",fontsize=16)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q-learning class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "class QLearningAgent:\n",
    "    \"\"\" An exploratory Q-learning agent. It avoids having to learn the transition\n",
    "        model because the Q-value of a state can be related directly to those of\n",
    "        its neighbors.\n",
    "    \"\"\"\n",
    "    def __init__(self, mdp, Ne, Rplus, alpha=None):\n",
    "\n",
    "        self.gamma = mdp.gamma\n",
    "        self.terminals = mdp.terminals\n",
    "        self.all_act = mdp.actlist\n",
    "        self.Ne = Ne  # iteration limit in exploration function\n",
    "        self.Rplus = Rplus  # large value to assign before iteration limit\n",
    "        self.Q = defaultdict(float)\n",
    "        self.Nsa = defaultdict(float)\n",
    "        self.s = None\n",
    "        self.a = None\n",
    "        self.r = None\n",
    "\n",
    "        if alpha:\n",
    "            self.alpha = alpha\n",
    "        else:\n",
    "            self.alpha = lambda n: 1./(1+n)\n",
    "\n",
    "    def f(self, u, n):\n",
    "        \"\"\" Exploration function. Returns fixed Rplus until\n",
    "        agent has visited state, action a Ne number of times.\"\"\"\n",
    "        if n < self.Ne:\n",
    "            return self.Rplus\n",
    "        else:\n",
    "            return u\n",
    "\n",
    "    def actions_in_state(self, state):\n",
    "        \"\"\" Return actions possible in given state.\n",
    "            Useful for max and argmax. \"\"\"\n",
    "        if state in self.terminals:\n",
    "            return [None]\n",
    "        else:\n",
    "            return self.all_act\n",
    "\n",
    "    def __call__(self, percept):\n",
    "        s1, r1 = self.update_state(percept)\n",
    "        Q, Nsa, s, a, r = self.Q, self.Nsa, self.s, self.a, self.r\n",
    "        alpha, gamma, terminals = self.alpha, self.gamma, self.terminals,\n",
    "        actions_in_state = self.actions_in_state\n",
    "\n",
    "        if s in terminals:\n",
    "            Q[s, None] = r1\n",
    "        if s is not None:\n",
    "            Nsa[s, a] += 1\n",
    "            Q[s, a] += alpha(Nsa[s, a]) * (r + gamma * max(Q[s1, a1]\n",
    "                                           for a1 in actions_in_state(s1)) - Q[s, a])\n",
    "        if s in terminals:\n",
    "            self.s = self.a = self.r = None\n",
    "        else:\n",
    "            self.s, self.r = s1, r1\n",
    "            self.a = max(actions_in_state(s1), key=lambda a1: self.f(Q[s1, a1], Nsa[s1, a1]))\n",
    "        return self.a\n",
    "\n",
    "    def update_state(self, percept):\n",
    "        \"\"\"To be overridden in most cases. The default case\n",
    "        assumes the percept to be of type (state, reward).\"\"\"\n",
    "        return percept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Trial run function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_single_trial(agent_program, mdp):\n",
    "    \"\"\"Execute trial for given agent_program\n",
    "    and mdp.\"\"\"\n",
    "\n",
    "    def take_single_action(mdp, s, a):\n",
    "        \"\"\"\n",
    "        Select outcome of taking action a\n",
    "        in state s. Weighted Sampling.\n",
    "        \"\"\"\n",
    "        x = random.uniform(0, 1)\n",
    "        cumulative_probability = 0.0\n",
    "        for probability_state in mdp.T(s, a):\n",
    "            probability, state = probability_state\n",
    "            cumulative_probability += probability\n",
    "            if x < cumulative_probability:\n",
    "                break\n",
    "        return state\n",
    "\n",
    "    current_state = mdp.init\n",
    "    while True:\n",
    "        current_reward = mdp.R(current_state)\n",
    "        percept = (current_state, current_reward)\n",
    "        next_action = agent_program(percept)\n",
    "        if next_action is None:\n",
    "            break\n",
    "        current_state = take_single_action(mdp, current_state, next_action)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing Q-learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define an agent\n",
    "q_agent = QLearningAgent(grid_1, Ne=10, Rplus=2,alpha=lambda n: 60./(59+n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A single trial run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "run_single_trial(q_agent,grid_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The utility values are close to default rewards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(float,\n",
       "            {((0, 0), (-1, 0)): 0.0,\n",
       "             ((0, 0), (0, -1)): 0.0,\n",
       "             ((0, 0), (0, 1)): 0.0,\n",
       "             ((0, 0), (1, 0)): -0.04,\n",
       "             ((1, 0), (-1, 0)): 0.0,\n",
       "             ((1, 0), (0, -1)): 0.0,\n",
       "             ((1, 0), (0, 1)): 0.0,\n",
       "             ((1, 0), (1, 0)): -0.04,\n",
       "             ((2, 0), (-1, 0)): 0.0,\n",
       "             ((2, 0), (0, -1)): 0.0,\n",
       "             ((2, 0), (0, 1)): 0.0,\n",
       "             ((2, 0), (1, 0)): -0.04,\n",
       "             ((3, 0), (-1, 0)): 0.0,\n",
       "             ((3, 0), (0, -1)): 0.0,\n",
       "             ((3, 0), (0, 1)): 0.0,\n",
       "             ((3, 0), (1, 0)): -0.04,\n",
       "             ((3, 1), None): 0.0})"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_agent.Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Run for 200 iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(200):\n",
    "    run_single_trial(q_agent,grid_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Q-values looking somewhat improved"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(float,\n",
       "            {((0, 0), (-1, 0)): -0.1508648941545866,\n",
       "             ((0, 0), (0, -1)): -0.15942619614228645,\n",
       "             ((0, 0), (0, 1)): 0.18881994028315593,\n",
       "             ((0, 0), (1, 0)): -0.16681733227192963,\n",
       "             ((0, 1), (-1, 0)): -0.10230371985980848,\n",
       "             ((0, 1), (0, -1)): -0.09903276526347243,\n",
       "             ((0, 1), (0, 1)): 0.2323460339773079,\n",
       "             ((0, 1), (1, 0)): -0.10330784708249496,\n",
       "             ((0, 2), (-1, 0)): -0.09812219051602036,\n",
       "             ((0, 2), (0, -1)): -0.08731898850702297,\n",
       "             ((0, 2), (0, 1)): -0.08800729785095428,\n",
       "             ((0, 2), (1, 0)): 0.2795420480914207,\n",
       "             ((1, 0), (-1, 0)): 0.1106604144525899,\n",
       "             ((1, 0), (0, -1)): -0.18399600276552172,\n",
       "             ((1, 0), (0, 1)): -0.18572997655189435,\n",
       "             ((1, 0), (1, 0)): -0.17978408224669973,\n",
       "             ((1, 2), (-1, 0)): -0.042084991887391045,\n",
       "             ((1, 2), (0, -1)): -0.026684448203540993,\n",
       "             ((1, 2), (0, 1)): -0.044970243885790274,\n",
       "             ((1, 2), (1, 0)): 0.37027690837365956,\n",
       "             ((2, 0), (-1, 0)): -0.19076648145257852,\n",
       "             ((2, 0), (0, -1)): -0.19551976602101653,\n",
       "             ((2, 0), (0, 1)): -0.190408535849405,\n",
       "             ((2, 0), (1, 0)): -0.1677505024785688,\n",
       "             ((2, 1), (-1, 0)): -0.03521421637370417,\n",
       "             ((2, 1), (0, -1)): -0.46878992282614895,\n",
       "             ((2, 1), (0, 1)): -0.392489239377663,\n",
       "             ((2, 1), (1, 0)): -0.5382427258720168,\n",
       "             ((2, 2), (-1, 0)): -0.007158562280249654,\n",
       "             ((2, 2), (0, -1)): 0.007098710435666712,\n",
       "             ((2, 2), (0, 1)): 0.00561155553169799,\n",
       "             ((2, 2), (1, 0)): 0.4308045696856374,\n",
       "             ((3, 0), (-1, 0)): -0.17723336737124665,\n",
       "             ((3, 0), (0, -1)): -0.1919457075355029,\n",
       "             ((3, 0), (0, 1)): -0.18102346160877453,\n",
       "             ((3, 0), (1, 0)): -0.6178584778127101,\n",
       "             ((3, 1), None): -0.8216921388709806,\n",
       "             ((3, 2), None): 0.4944817795376873})"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_agent.Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Checking how a particular state's utility evolves over iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1=[]\n",
    "x2=[]\n",
    "x3=[]\n",
    "x4=[]\n",
    "\n",
    "q_agent = QLearningAgent(grid_1, Ne=40, Rplus=1.5,alpha=lambda n: 5000./(4999+n))\n",
    "for i in range(8000):\n",
    "    run_single_trial(q_agent,grid_1)\n",
    "    x1.append(q_agent.Q[((2,2),(-1,0))])\n",
    "    x2.append(q_agent.Q[((2,2),(0,-1))])\n",
    "    x3.append(q_agent.Q[((2,2),(0,1))])\n",
    "    x4.append(q_agent.Q[((2,2),(1,0))])\n",
    "\n",
    "plt.plot(x1)\n",
    "plt.plot(x2)\n",
    "plt.plot(x3)\n",
    "plt.plot(x4)\n",
    "plt.legend(['-1,0','0,-1','0,1','1,0'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function to convert the Q Values above into U estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_U_from_Q(q_agent):\n",
    "    U = defaultdict(lambda: -100.) # Large negative value for comparison\n",
    "    for state_action, value in q_agent.Q.items():\n",
    "        state, action = state_action\n",
    "        if U[state] < value:\n",
    "                    U[state] = value\n",
    "    return U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(<function __main__.get_U_from_Q.<locals>.<lambda>>,\n",
       "            {(0, 0): 0.3003134549950739,\n",
       "             (0, 1): 0.3606866544043642,\n",
       "             (0, 2): 0.44507052375099254,\n",
       "             (1, 0): 0.12240837870425501,\n",
       "             (1, 2): 0.539086434725801,\n",
       "             (2, 0): 0.054135841612979504,\n",
       "             (2, 1): 0.038400449149821256,\n",
       "             (2, 2): 0.6276427113103858,\n",
       "             (3, 0): -0.42464103886879784,\n",
       "             (3, 1): -0.5427216571679544,\n",
       "             (3, 2): 0.705470684129441})"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_U_from_Q(q_agent)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Running Q-learning over a long period and comparing to value iteration method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "defaultdict(<function get_U_from_Q.<locals>.<lambda> at 0x000002A6D6CF8E18>, {(0, 0): 0.3949253391464377, (1, 0): 0.3444579424029225, (2, 0): 0.21599987965126283, (3, 0): -0.32043700529600583, (3, 1): 0.9118318007579025, (0, 1): 0.3791678551264691, (0, 2): 0.5624728315423392, (1, 2): 0.7464843097346127, (2, 2): 0.8392698405259547, (3, 2): 0.9067980679662245, (2, 1): 0.06875679152878217})\n"
     ]
    }
   ],
   "source": [
    "q_agent = QLearningAgent(grid_1, Ne=25, Rplus=1.5,alpha=lambda n: 10000./(9999+n))\n",
    "qhistory=[]\n",
    "for i in range(10000):\n",
    "    run_single_trial(q_agent,grid_1)\n",
    "    U=get_U_from_Q(q_agent)\n",
    "    qhistory.append(U)\n",
    "print(get_U_from_Q(q_agent))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "({(0, 1): 0.5574828451603404, (1, 2): 0.7531405483223766, (3, 2): 1.0, (0, 0): 0.464516644753505, (3, 0): 0.22957996193922584, (3, 1): -1.0, (2, 1): 0.5691092225518013, (2, 0): 0.45103488646335127, (2, 2): 0.8553208559957037, (1, 0): 0.38642617706646115, (0, 2): 0.6467925974571826}, 21)\n"
     ]
    }
   ],
   "source": [
    "print(value_iteration(grid_1,epsilon=0.001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function for utility estimate by Q-learning by many iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "def qlearning_iter(agent_program,mdp,iterations=1000,print_final_utility=True):\n",
    "    \"\"\"\n",
    "    Function for utility estimate by Q-learning by many iterations\n",
    "    Returns a history object i.e. a list of dictionaries, where utility estimate for each iteration is stored\n",
    "    \n",
    "    q_agent = QLearningAgent(grid_1, Ne=25, Rplus=1.5,\n",
    "                            alpha=lambda n: 10000./(9999+n))\n",
    "    hist=qlearning_iter(q_agent,grid_1,iterations=10000)\n",
    "    \n",
    "    \"\"\"\n",
    "    qhistory=[]\n",
    "    \n",
    "    for i in range(iterations):\n",
    "        run_single_trial(agent_program,mdp)\n",
    "        U=get_U_from_Q(agent_program)\n",
    "        if len(U)==len(mdp.states):\n",
    "            qhistory.append(U)\n",
    "    \n",
    "    if print_final_utility:\n",
    "        print(U)\n",
    "    return qhistory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "defaultdict(<function get_U_from_Q.<locals>.<lambda> at 0x000002A6D6C696A8>, {(0, 0): 0.4900711154747255, (1, 0): 0.2405441517390302, (2, 0): 0.2176153447177856, (3, 0): -0.48331539625394726, (3, 1): -0.381204513862658, (0, 1): 0.6002481824070857, (2, 1): 0.37485218513982377, (0, 2): 0.7022048577156954, (1, 2): 0.7927537919153599, (2, 2): 0.858541903689368, (3, 2): 0.9674055267320101})\n"
     ]
    }
   ],
   "source": [
    "# Define a Q-learning agent\n",
    "q_agent = QLearningAgent(grid_1, Ne=25, Rplus=1.5,alpha=lambda n: 10000./(9999+n))\n",
    "# Run 10000 iterations to get a history\n",
    "hist=qlearning_iter(q_agent,grid_1,iterations=10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How do the long-term utility estimates with Q-learning compare with value iteration?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_qlearning_vi(hist, vi,plot_n_states=None):\n",
    "    \"\"\"\n",
    "    Compares and plots a Q-learning and value iteration results for the utility estimate of an MDP's states\n",
    "    hist: A history object from a Q-learning run\n",
    "    vi: A value iteration estimate for the same MDP\n",
    "    plot_n_states: Restrict the plotting for n states (randomly chosen)\n",
    "    \"\"\"\n",
    "    utilities={k:[] for k in list(vi[0].keys())}\n",
    "    for h in hist:\n",
    "        for state in h.keys():\n",
    "            utilities[state].append(h[state])\n",
    "    \n",
    "    if plot_n_states==None:\n",
    "        for state in list(vi[0].keys()):\n",
    "            plt.figure(figsize=(7,4))\n",
    "            plt.title(\"Plot of State: {} over Q-learning iterations\".format(str(state)),fontsize=16)\n",
    "            plt.plot(utilities[state])\n",
    "            plt.hlines(y=vi[0][state],xmin=0,xmax=1.1*len(hist))\n",
    "            plt.legend(['Q-learning estimates','Value iteration estimate'],fontsize=14)\n",
    "            plt.xlabel(\"Iterations\",fontsize=14)\n",
    "            plt.ylabel(\"Utility of the state\",fontsize=14)\n",
    "            plt.grid(True)\n",
    "            plt.show()\n",
    "    else:\n",
    "        for state in list(vi[0].keys())[:plot_n_states]:\n",
    "            plt.figure(figsize=(7,4))\n",
    "            plt.title(\"Plot of State: {} over Q-learning iterations\".format(str(state)),fontsize=16)\n",
    "            plt.plot(utilities[state])\n",
    "            plt.hlines(y=vi[0][state],xmin=0,xmax=1.1*len(hist))\n",
    "            plt.legend(['Q-learning estimates','Value iteration estimate'],fontsize=14)\n",
    "            plt.xlabel(\"Iterations\",fontsize=14)\n",
    "            plt.ylabel(\"Utility of the state\",fontsize=14)\n",
    "            plt.grid(True)\n",
    "            plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing the long-term utility learning for the small (default) grid world"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the Q-learning agent\n",
    "q_agent = QLearningAgent(grid_1, Ne=20, Rplus=2,alpha=lambda n: 10000/(9999+n))\n",
    "# Obtain the history by running the Q-learning for many iterations\n",
    "hist=qlearning_iter(q_agent,grid_1,iterations=10000,print_final_utility=False)\n",
    "# Get a value iteration estimate using the same MDP\n",
    "vi = value_iteration(grid_1,epsilon=0.001)\n",
    "# Compare the utility estimates from two methods\n",
    "plot_qlearning_vi(hist,vi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing the long-term utility learning for the large grid world"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the Q-learning agent\n",
    "q_agent = QLearningAgent(large_gridworld, Ne=20, Rplus=2,alpha=lambda n: 1000/(999+n))\n",
    "# Obtain the history by running the Q-learning for many iterations\n",
    "hist=qlearning_iter(q_agent,large_gridworld,iterations=30000,print_final_utility=False)\n",
    "# Get a value iteration estimate using the same MDP\n",
    "vi = value_iteration(large_gridworld,epsilon=0.001)\n",
    "# Compare the utility estimates from two methods (plot only 5 states)\n",
    "plot_qlearning_vi(hist,vi,plot_n_states=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using `pymdptoolbox` Q-learning: A more robust Q-learning algorithm\n",
    "\n",
    "The [MDP toolbox](https://pymdptoolbox.readthedocs.io/en/latest/index.html) provides classes and functions for the resolution of descrete-time Markov Decision Processes. The list of algorithms that have been implemented includes backwards induction, linear programming, policy iteration, q-learning and value iteration along with several variations.\n",
    "\n",
    "You can simply install it using,\n",
    "\n",
    "`pip install pymdptoolbox`\n",
    "\n",
    "Their Q-learning algorithm uses,\n",
    "* max 100 visits to each state, \n",
    "* a greedy approach of increasing probability for action choice, and \n",
    "* decaying learning rate (inverse square root). \n",
    "\n",
    "[Read here to know more details](https://pymdptoolbox.readthedocs.io/en/latest/_modules/mdptoolbox/mdp.html#QLearning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mdptoolbox\n",
    "import mdptoolbox.example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate a random MDP with a specific number of states and actions (here 20 and 4 for example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [],
   "source": [
    "P, R = mdptoolbox.example.rand(20, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value iteration using the generated MDP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "vi = mdptoolbox.mdp.ValueIteration(P, R, 0.96,epsilon=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "vi.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.8529969208974837,\n",
       " 3.624442947893675,\n",
       " 3.6547417765581227,\n",
       " 4.0246093074436935,\n",
       " 3.813761844823124,\n",
       " 3.7921651698355014,\n",
       " 3.979435874221074,\n",
       " 3.9266427021245596,\n",
       " 3.9732426836938033,\n",
       " 3.9808749764940545,\n",
       " 3.7052976577936563,\n",
       " 3.8497919779520147,\n",
       " 4.071472368796166,\n",
       " 4.029670437403848,\n",
       " 4.092324734926494,\n",
       " 3.7468884219170158,\n",
       " 3.7723812889006254,\n",
       " 4.333175893562366,\n",
       " 3.8692516570799422,\n",
       " 4.152081197501264)"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vi.V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q-learning with the same MDP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "ql = mdptoolbox.mdp.QLearning(P,R,0.96,n_iter=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "ql.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.26790319, 1.20111456, 1.35314556, 4.30174583],\n",
       "       [1.20172124, 1.20220774, 4.21206826, 1.40873712],\n",
       "       [2.05338455, 2.04121782, 1.88530214, 4.26199016],\n",
       "       [4.49688472, 2.17487507, 2.58013881, 2.54027993],\n",
       "       [4.48330274, 1.56274212, 2.01772658, 1.59944445],\n",
       "       [0.67295533, 4.03086782, 0.77909241, 0.78218475],\n",
       "       [2.025956  , 1.67834359, 4.42349985, 1.59679818],\n",
       "       [2.01863292, 4.48742921, 2.20328876, 2.12457993],\n",
       "       [1.76575621, 1.7346687 , 2.09397596, 4.10540127],\n",
       "       [4.315829  , 1.71150305, 1.76510607, 1.43910612],\n",
       "       [0.54861353, 0.59928687, 0.0363933 , 3.36432603],\n",
       "       [4.11615966, 0.7627823 , 0.57581723, 0.44108385],\n",
       "       [4.2439175 , 0.5760567 , 0.83643369, 0.8727218 ],\n",
       "       [0.16422905, 3.48734888, 0.1749688 , 0.23227082],\n",
       "       [0.79868696, 0.77326146, 0.76877622, 4.61281589],\n",
       "       [0.8373481 , 4.08986506, 1.16645089, 1.00864003],\n",
       "       [3.54461758, 1.21658831, 0.82005426, 0.84809806],\n",
       "       [4.79665135, 1.80648363, 1.20163289, 1.41884673],\n",
       "       [0.51214286, 0.62878474, 0.47870825, 4.00197222],\n",
       "       [4.39794974, 1.03131538, 0.93409556, 0.67139869]])"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ql.Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.3017458280342895,\n",
       " 4.212068255673687,\n",
       " 4.261990155217807,\n",
       " 4.496884723082577,\n",
       " 4.483302741098784,\n",
       " 4.030867824741414,\n",
       " 4.423499851338593,\n",
       " 4.487429209567494,\n",
       " 4.1054012707603285,\n",
       " 4.315829000571206,\n",
       " 3.364326028278491,\n",
       " 4.116159662563403,\n",
       " 4.243917495915591,\n",
       " 3.487348884896478,\n",
       " 4.612815893899296,\n",
       " 4.089865063060668,\n",
       " 3.5446175847696124,\n",
       " 4.7966513476870825,\n",
       " 4.001972219370916,\n",
       " 4.397949735404336)"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ql.V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How to asses the impact of number of states and actions on a Q-learning algorithm?\n",
    "\n",
    "To further understand the impact of number of states and actions on Q-learning, we create random instances of MDP with various number of states and actions (per state). <br>Then, we run value iteration (with error margin 0.001) and Q-learning (10,000 iterations) on them, and compute the **root-mean-square error (RMSE) of their respective prediction of utilities** i.e. we sum over the differences between utility predictions, square them, and take the mean.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20, 5, 0.3413233616483361\n",
      "20, 10, 2.2598902021109306\n",
      "20, 15, 4.520675542970938\n",
      "20, 20, 6.0075845843586295\n",
      "20, 25, 4.461530118713196\n",
      "================================================================================\n",
      "40, 5, 1.0074814928651283\n",
      "40, 10, 2.7419743345419993\n",
      "40, 15, 2.1178903886755593\n",
      "40, 20, 3.601293797441485\n",
      "40, 25, 4.187977689161319\n",
      "================================================================================\n",
      "60, 5, 0.9271964335536792\n",
      "60, 10, 1.8589253862698378\n",
      "60, 15, 2.066420005671096\n",
      "60, 20, 4.028988604485868\n",
      "60, 25, 3.5087269217355868\n",
      "================================================================================\n",
      "80, 5, 0.9078118885897555\n",
      "80, 10, 1.406263385570601\n",
      "80, 15, 2.6431847504244335\n",
      "80, 20, 2.2656847893695513\n",
      "80, 25, 4.115382711067253\n",
      "================================================================================\n",
      "100, 5, 0.8838367456841726\n",
      "100, 10, 1.3480455835278036\n",
      "100, 15, 2.3457299143588615\n",
      "100, 20, 2.744560058904662\n",
      "100, 25, 2.5167979918418517\n",
      "================================================================================\n"
     ]
    }
   ],
   "source": [
    "rmse_dict = defaultdict(list)\n",
    "mat = np.zeros((5,5))\n",
    "for i in range(5):\n",
    "    for j in range(5):\n",
    "        # Create a random MDP\n",
    "        P, R = mdptoolbox.example.rand((i+1)*20, (j+1)*5)\n",
    "        # Value iteration\n",
    "        vi = mdptoolbox.mdp.ValueIteration(P, R, 0.9,epsilon=0.001)\n",
    "        vi.run()\n",
    "        # Q-learning\n",
    "        ql = mdptoolbox.mdp.QLearning(P,R,0.96,n_iter=10000)\n",
    "        ql.run()\n",
    "        viv = np.array(vi.V)\n",
    "        qlv = np.array(ql.V)\n",
    "        diff = qlv - viv\n",
    "        diffsq = diff**2\n",
    "        rmse = np.sqrt(np.mean(diffsq))\n",
    "        rmse_dict[i].append(rmse)\n",
    "        mat[i][j]=rmse\n",
    "        print(\"{}, {}, {}\".format((i+1)*20, (j+1)*5,rmse))\n",
    "    print(\"=\"*80)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.34132336, 2.2598902 , 4.52067554, 6.00758458, 4.46153012],\n",
       "       [1.00748149, 2.74197433, 2.11789039, 3.6012938 , 4.18797769],\n",
       "       [0.92719643, 1.85892539, 2.06642001, 4.0289886 , 3.50872692],\n",
       "       [0.90781189, 1.40626339, 2.64318475, 2.26568479, 4.11538271],\n",
       "       [0.88383675, 1.34804558, 2.34572991, 2.74456006, 2.51679799]])"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame(mat,index=[(i+1)*20 for i in range(5)],columns=[(j+1)*5 for j in range(5)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>5</th>\n",
       "      <th>10</th>\n",
       "      <th>15</th>\n",
       "      <th>20</th>\n",
       "      <th>25</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.341323</td>\n",
       "      <td>2.259890</td>\n",
       "      <td>4.520676</td>\n",
       "      <td>6.007585</td>\n",
       "      <td>4.461530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1.007481</td>\n",
       "      <td>2.741974</td>\n",
       "      <td>2.117890</td>\n",
       "      <td>3.601294</td>\n",
       "      <td>4.187978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>0.927196</td>\n",
       "      <td>1.858925</td>\n",
       "      <td>2.066420</td>\n",
       "      <td>4.028989</td>\n",
       "      <td>3.508727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.907812</td>\n",
       "      <td>1.406263</td>\n",
       "      <td>2.643185</td>\n",
       "      <td>2.265685</td>\n",
       "      <td>4.115383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.883837</td>\n",
       "      <td>1.348046</td>\n",
       "      <td>2.345730</td>\n",
       "      <td>2.744560</td>\n",
       "      <td>2.516798</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           5         10        15        20        25\n",
       "20   0.341323  2.259890  4.520676  6.007585  4.461530\n",
       "40   1.007481  2.741974  2.117890  3.601294  4.187978\n",
       "60   0.927196  1.858925  2.066420  4.028989  3.508727\n",
       "80   0.907812  1.406263  2.643185  2.265685  4.115383\n",
       "100  0.883837  1.348046  2.345730  2.744560  2.516798"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,7))\n",
    "plt.title(\"RMSE error of Q-learning over \\na range of states and actions\",fontsize=20)\n",
    "heatmap(data,linewidths=1,linecolor='k',annot=True,annot_kws={'fontsize':15})\n",
    "plt.ylabel(\"Number of states\",fontsize=15)\n",
    "plt.xlabel(\"Number of actions/states\",fontsize=15)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this plot, we conclude that for this grid problem, with proper implementation of Q-learning, large number of states is not necessarily an issue. But the problematic situation is large number of possible actions. In particular, the **performance of Q-learning is worst for MDPs with small number of states but large number of actions/states**. This is due to the random nature of Q-learning initiation for every state visit and the policy of probabilistic walk over all the actions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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    "description": "Homework/Assignment 4 MDP/Untitled.ipynb",
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