Temporal_Difference.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mini Project: Temporal-Difference Methods\n",
    "\n",
    "In this notebook, you will write your own implementations of many Temporal-Difference (TD) methods.\n",
    "\n",
    "While we have provided some starter code, you are welcome to erase these hints and write your code from scratch."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 0: Explore CliffWalkingEnv\n",
    "\n",
    "Use the code cell below to create an instance of the [CliffWalking](https://github.com/openai/gym/blob/master/gym/envs/toy_text/cliffwalking.py) environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym\n",
    "env = gym.make('CliffWalking-v0')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The agent moves through a $4\\times 12$ gridworld, with states numbered as follows:\n",
    "```\n",
    "[[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11],\n",
    " [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23],\n",
    " [24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35],\n",
    " [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47]]\n",
    "```\n",
    "At the start of any episode, state `36` is the initial state.  State `47` is the only terminal state, and the cliff corresponds to states `37` through `46`.\n",
    "\n",
    "The agent has 4 potential actions:\n",
    "```\n",
    "UP = 0\n",
    "RIGHT = 1\n",
    "DOWN = 2\n",
    "LEFT = 3\n",
    "```\n",
    "\n",
    "Thus, $\\mathcal{S}^+=\\{0, 1, \\ldots, 47\\}$, and $\\mathcal{A} =\\{0, 1, 2, 3\\}$.  Verify this by running the code cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discrete(4)\n",
      "Discrete(48)\n"
     ]
    }
   ],
   "source": [
    "print(env.action_space)\n",
    "print(env.observation_space)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this mini-project, we will build towards finding the optimal policy for the CliffWalking environment.  The optimal state-value function is visualized below.  Please take the time now to make sure that you understand _why_ this is the optimal state-value function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f316c953550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from plot_utils import plot_values\n",
    "\n",
    "# define the optimal state-value function\n",
    "V_opt = np.zeros((4,12))\n",
    "V_opt[0] = -np.arange(3, 15)[::-1]\n",
    "V_opt[1] = -np.arange(3, 15)[::-1] + 1\n",
    "V_opt[2] = -np.arange(3, 15)[::-1] + 2\n",
    "V_opt[3][0] = -13\n",
    "\n",
    "plot_values(V_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1: TD Prediction: State Values\n",
    "\n",
    "In this section, you will write your own implementation of TD prediction (for estimating the state-value function).\n",
    "\n",
    "We will begin by investigating a policy where the agent moves:\n",
    "- `RIGHT` in states `0` through `10`, inclusive,  \n",
    "- `DOWN` in states `11`, `23`, and `35`, and\n",
    "- `UP` in states `12` through `22`, inclusive, states `24` through `34`, inclusive, and state `36`.\n",
    "\n",
    "The policy is specified and printed below.  Note that states where the agent does not choose an action have been marked with `-1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  2.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  2.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  2.]\n",
      " [ 0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n"
     ]
    }
   ],
   "source": [
    "policy = np.hstack([1*np.ones(11), 2, 0, np.zeros(10), 2, 0, np.zeros(10), 2, 0, -1*np.ones(11)])\n",
    "print(\"\\nPolicy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\")\n",
    "print(policy.reshape(4,12))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the next cell to visualize the state-value function that corresponds to this policy.  Make sure that you take the time to understand why this is the corresponding value function!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3160c1c278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "V_true = np.zeros((4,12))\n",
    "for i in range(3):\n",
    "    V_true[0:12][i] = -np.arange(3, 15)[::-1] - i\n",
    "V_true[1][11] = -2\n",
    "V_true[2][11] = -1\n",
    "V_true[3][0] = -17\n",
    "\n",
    "plot_values(V_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above figure is what you will try to approximate through the TD prediction algorithm.\n",
    "\n",
    "Your algorithm for TD prediction has five arguments:\n",
    "- `env`: This is an instance of an OpenAI Gym environment.\n",
    "- `num_episodes`: This is the number of episodes that are generated through agent-environment interaction.\n",
    "- `policy`: This is a 1D numpy array with `policy.shape` equal to the number of states (`env.nS`).  `policy[s]` returns the action that the agent chooses when in state `s`.\n",
    "- `alpha`: This is the step-size parameter for the update step.\n",
    "- `gamma`: This is the discount rate.  It must be a value between 0 and 1, inclusive (default value: `1`).\n",
    "\n",
    "The algorithm returns as output:\n",
    "- `V`: This is a dictionary where `V[s]` is the estimated value of state `s`.\n",
    "\n",
    "Please complete the function in the code cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict, deque\n",
    "import sys\n",
    "\n",
    "def td_prediction(env, num_episodes, policy, alpha, gamma=1.0):\n",
    "    # initialize empty dictionaries of floats\n",
    "    V = defaultdict(float)\n",
    "    # loop over episodes\n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # monitor progress\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        \n",
    "        ## TODO: complete the function\n",
    "        \n",
    "        # begin an episode, observe S\n",
    "        state = env.reset()\n",
    "        while True:\n",
    "            # choose action A\n",
    "            action = policy[state]\n",
    "            # take action A, observe R, S'\n",
    "            next_state, reward, done, info = env.step(action)\n",
    "            # perform updates\n",
    "            V[state] = V[state] + (alpha * (reward + (gamma * V[next_state]) - V[state]))            \n",
    "            # S <- S'\n",
    "            state = next_state\n",
    "            # end episode if reached terminal state\n",
    "            if done:\n",
    "                break\n",
    "        \n",
    "    return V "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the code cell below to test your implementation and visualize the estimated state-value function.  If the code cell returns **PASSED**, then you have implemented the function correctly!  Feel free to change the `num_episodes` and `alpha` parameters that are supplied to the function.  However, if you'd like to ensure the accuracy of the unit test, please do not change the value of `gamma` from the default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 5000/5000"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "**<span style=\"color: green;\">PASSED</span>**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3160979860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import check_test\n",
    "\n",
    "# evaluate the policy and reshape the state-value function\n",
    "V_pred = td_prediction(env, 5000, policy, .01)\n",
    "\n",
    "# please do not change the code below this line\n",
    "V_pred_plot = np.reshape([V_pred[key] if key in V_pred else 0 for key in np.arange(48)], (4,12)) \n",
    "check_test.run_check('td_prediction_check', V_pred_plot)\n",
    "plot_values(V_pred_plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How close is your estimated state-value function to the true state-value function corresponding to the policy?  \n",
    "\n",
    "You might notice that some of the state values are not estimated by the agent.  This is because under this policy, the agent will not visit all of the states.  In the TD prediction algorithm, the agent can only estimate the values corresponding to states that are visited."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2: TD Control: Sarsa\n",
    "\n",
    "In this section, you will write your own implementation of the Sarsa control algorithm.\n",
    "\n",
    "Your algorithm has four arguments:\n",
    "- `env`: This is an instance of an OpenAI Gym environment.\n",
    "- `num_episodes`: This is the number of episodes that are generated through agent-environment interaction.\n",
    "- `alpha`: This is the step-size parameter for the update step.\n",
    "- `gamma`: This is the discount rate.  It must be a value between 0 and 1, inclusive (default value: `1`).\n",
    "\n",
    "The algorithm returns as output:\n",
    "- `Q`: This is a dictionary (of one-dimensional arrays) where `Q[s][a]` is the estimated action value corresponding to state `s` and action `a`.\n",
    "\n",
    "Please complete the function in the code cell below.\n",
    "\n",
    "(_Feel free to define additional functions to help you to organize your code._)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def update_Q(Qsa, Qsa_next, reward, alpha, gamma):\n",
    "    \"\"\" updates the action-value function estimate using the most recent time step \"\"\"\n",
    "    return Qsa + (alpha * (reward + (gamma * Qsa_next) - Qsa))\n",
    "\n",
    "def epsilon_greedy_probs(env, Q_s, i_episode, eps=None):\n",
    "    \"\"\" obtains the action probabilities corresponding to epsilon-greedy policy \"\"\"\n",
    "    epsilon = 1.0 / i_episode\n",
    "    if eps is not None:\n",
    "        epsilon = eps\n",
    "    policy_s = np.ones(env.nA) * epsilon / env.nA\n",
    "    policy_s[np.argmax(Q_s)] = 1 - epsilon + (epsilon / env.nA)\n",
    "    return policy_s\n",
    "\n",
    "def sarsa(env, num_episodes, alpha, gamma=1.0):\n",
    "    # initialize action-value function (empty dictionary of arrays)\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "    # initialize performance monitor\n",
    "    plot_every = 100\n",
    "    tmp_scores = deque(maxlen=plot_every)\n",
    "    scores = deque(maxlen=num_episodes)\n",
    "    # loop over episodes\n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # monitor progress\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()   \n",
    "        \n",
    "        ## TODO: complete the function\n",
    "        \n",
    "        # initialize score\n",
    "        score = 0\n",
    "        # begin an episode, observe S\n",
    "        state = env.reset()   \n",
    "        # get epsilon-greedy action probabilities\n",
    "        policy_s = epsilon_greedy_probs(env, Q[state], i_episode)\n",
    "        # pick action A\n",
    "        action = np.random.choice(np.arange(env.nA), p=policy_s)\n",
    "        # limit number of time steps per episode\n",
    "        for t_step in np.arange(300):\n",
    "            # take action A, observe R, S'\n",
    "            next_state, reward, done, info = env.step(action)\n",
    "            # add reward to score\n",
    "            score += reward\n",
    "            if not done:\n",
    "                # get epsilon-greedy action probabilities\n",
    "                policy_s = epsilon_greedy_probs(env, Q[next_state], i_episode)\n",
    "                # pick next action A'\n",
    "                next_action = np.random.choice(np.arange(env.nA), p=policy_s)\n",
    "                # update TD estimate of Q\n",
    "                Q[state][action] = update_Q(Q[state][action], Q[next_state][next_action], \n",
    "                                            reward, alpha, gamma)\n",
    "                # S <- S'\n",
    "                state = next_state\n",
    "                # A <- A'\n",
    "                action = next_action\n",
    "            if done:\n",
    "                # update TD estimate of Q\n",
    "                Q[state][action] = update_Q(Q[state][action], 0, reward, alpha, gamma)\n",
    "                # append score\n",
    "                tmp_scores.append(score)\n",
    "                break\n",
    "        if (i_episode % plot_every == 0):\n",
    "            scores.append(np.mean(tmp_scores))\n",
    "    # plot performance\n",
    "    plt.plot(np.linspace(0,num_episodes,len(scores),endpoint=False),np.asarray(scores))\n",
    "    plt.xlabel('Episode Number')\n",
    "    plt.ylabel('Average Reward (Over Next %d Episodes)' % plot_every)\n",
    "    plt.show()\n",
    "    # print best 100-episode performance\n",
    "    print(('Best Average Reward over %d Episodes: ' % plot_every), np.max(scores))\n",
    "        \n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the next code cell to visualize the **_estimated_** optimal policy and the corresponding state-value function.  \n",
    "\n",
    "If the code cell returns **PASSED**, then you have implemented the function correctly!  Feel free to change the `num_episodes` and `alpha` parameters that are supplied to the function.  However, if you'd like to ensure the accuracy of the unit test, please do not change the value of `gamma` from the default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 5000/5000"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f31607717f0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.0\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "**<span style=\"color: green;\">PASSED</span>**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 2  1  1  1  1  1  1  0  1  1  1  1]\n",
      " [ 3  0  1  1  1  2  1  1  1  2  2  2]\n",
      " [ 1  1  1  1  1  1  1  1  1  1  1  2]\n",
      " [ 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f316075bb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_sarsa = sarsa(env, 5000, .01)\n",
    "\n",
    "# print the estimated optimal policy\n",
    "policy_sarsa = np.array([np.argmax(Q_sarsa[key]) if key in Q_sarsa else -1 for key in np.arange(48)]).reshape(4,12)\n",
    "check_test.run_check('td_control_check', policy_sarsa)\n",
    "print(\"\\nEstimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\")\n",
    "print(policy_sarsa)\n",
    "\n",
    "# plot the estimated optimal state-value function\n",
    "V_sarsa = ([np.max(Q_sarsa[key]) if key in Q_sarsa else 0 for key in np.arange(48)])\n",
    "plot_values(V_sarsa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3: TD Control: Q-learning\n",
    "\n",
    "In this section, you will write your own implementation of the Q-learning control algorithm.\n",
    "\n",
    "Your algorithm has four arguments:\n",
    "- `env`: This is an instance of an OpenAI Gym environment.\n",
    "- `num_episodes`: This is the number of episodes that are generated through agent-environment interaction.\n",
    "- `alpha`: This is the step-size parameter for the update step.\n",
    "- `gamma`: This is the discount rate.  It must be a value between 0 and 1, inclusive (default value: `1`).\n",
    "\n",
    "The algorithm returns as output:\n",
    "- `Q`: This is a dictionary (of one-dimensional arrays) where `Q[s][a]` is the estimated action value corresponding to state `s` and action `a`.\n",
    "\n",
    "Please complete the function in the code cell below.\n",
    "\n",
    "(_Feel free to define additional functions to help you to organize your code._)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_learning(env, num_episodes, alpha, gamma=1.0):\n",
    "    # initialize empty dictionary of arrays\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "    # initialize performance monitor\n",
    "    plot_every = 100\n",
    "    tmp_scores = deque(maxlen=plot_every)\n",
    "    scores = deque(maxlen=num_episodes)\n",
    "    # loop over episodes\n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # monitor progress\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        \n",
    "        ## TODO: complete the function\n",
    "        \n",
    "        # initialize score\n",
    "        score = 0\n",
    "        # begin an episode, observe S\n",
    "        state = env.reset()\n",
    "        while True:\n",
    "            # get epsilon-greedy action probabilities\n",
    "            policy_s = epsilon_greedy_probs(env, Q[state], i_episode)\n",
    "            # pick next action A\n",
    "            action = np.random.choice(np.arange(env.nA), p=policy_s)\n",
    "            # take action A, observe R, S'\n",
    "            next_state, reward, done, info = env.step(action)\n",
    "            # add reward to score\n",
    "            score += reward\n",
    "            # update Q\n",
    "            Q[state][action] = update_Q(Q[state][action], np.max(Q[next_state]), \\\n",
    "                                                  reward, alpha, gamma)        \n",
    "            # S <- S'\n",
    "            state = next_state\n",
    "            # until S is terminal\n",
    "            if done:\n",
    "                # append score\n",
    "                tmp_scores.append(score)\n",
    "                break\n",
    "        if (i_episode % plot_every == 0):\n",
    "            scores.append(np.mean(tmp_scores))\n",
    "    # plot performance\n",
    "    plt.plot(np.linspace(0,num_episodes,len(scores),endpoint=False),np.asarray(scores))\n",
    "    plt.xlabel('Episode Number')\n",
    "    plt.ylabel('Average Reward (Over Next %d Episodes)' % plot_every)\n",
    "    plt.show()\n",
    "    # print best 100-episode performance\n",
    "    print(('Best Average Reward over %d Episodes: ' % plot_every), np.max(scores))\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the next code cell to visualize the **_estimated_** optimal policy and the corresponding state-value function. \n",
    "\n",
    "If the code cell returns **PASSED**, then you have implemented the function correctly!  Feel free to change the `num_episodes` and `alpha` parameters that are supplied to the function.  However, if you'd like to ensure the accuracy of the unit test, please do not change the value of `gamma` from the default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 5000/5000"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3160685e48>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.0\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "**<span style=\"color: green;\">PASSED</span>**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 2  1  3  1  1  1  0  1  0  2  2  0]\n",
      " [ 0  0  1  3  3  3  1  2  1  2  2  2]\n",
      " [ 1  1  1  1  1  1  1  1  1  1  1  2]\n",
      " [ 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  0]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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MwfvuKs4m+707iRxwNcmj/w9H1nqOfPUs+tAYIs6+GABfdRXmxM5E9B3F4c8b7oc+lxNn7g7ajByLObkLPmcF+d9OJPvdMbR7aH7tHxZOtwM/TKQ8cxUdrpiEJSqV8oPryFwwHoM1irizg1+Alx9YQ2TGINKGP4DBGknhtm/Y/cV9dP3bx0S09W9nn9fNrk9vx2CJoNNVUzFFJOIqP4JiMDVYnz1nEwUbZxMSHzzBaEnn3b4iYLo8fxsbv72bhE5/Pm5dn9fFlkUPEZ3cn5JDawOWZW/9lD2rJtNtxPNEJvSkLG8LO5aNx2CJIL7diGbtw+9RYc9m2aLRpLcfxfALP8RoisBevh+DIfixAtCr/5P06BN4rli2aDRxCXXnigp7Nr8svZN2Ha9m4ND/oyB/PRtWP4vFHENquv+Y8niqiIjqTHr7UaxZGfzc3hJSYs9heJ+6c75OF/ycf9SOzE9Zs2Myw3o+T3x0TwpKt/DLpvGYjRGkJ/q3dV7xRpauf5C+tn+QkXQRWYcXs3Td/Vw+9DPio3sCUF6ZzTcrRtMpdRSXnvMhJmMEpRX7MTaxLVpCetQ5XNKlLj56pen4eDUXVmM0A9PuZPOR4MmR2+cgwpJCp9gLWZE1tVnb+0fYVrqI3KqthBvij1vWpAthcOzfSLB2xqhYOFi1gXk5T2PUWRgYeyMAmRWr6RF1CW1D+mDUWVhVOIMPM8dwb+e5xJozAHD5qoi3dKZX9Ci+PHhmHC/xhnZcF/M0bQypuDUny+wz+E/+GP6dspgIfWyTdZ9MWkCoPrJ2OkwXE7DcpFh5JuWHgHlHEx6APc41DAu/gXRTDzQ0FpS+zrS82xifvIBQfVQz9O7kuDQnBzw7uNwylraGLlRpFXxeNZHJ9jG8EDkfvRL8GmC3ez1vVz7K9SGP0dc4kjKtiI8qn+Xtiod5LOLDgLL53mxmVU2is6Hh9db7lePJ9qj8PXQiMbpEVlXPZ5L9Nl6MXEiMLqHZ+tnsVzK64f4LEa28OOhyrdKOtvRLdPe9iK7XEAD0D0zCe+f5aFtWofQeFrzero0o/c5H199/ElbiU9H6j0DbvaXeZ18R2JbbnsC7ZA5a5k6U3sNQ0jujf/yNugJJ6ehueRTfhLvQqipQQsJOsdeNMw3zx8NnbyQeVXbcy7/EeteLGHr442EdO4mK+8/Hu20VhrODx8PY74KAaf11D+Ja8hnePZsCkh7FYEIX1TDbrs+7fyuuRR8R+sJXVNxzzgn37Y/gzc/CnbmJuPHzMKb5+xF5wzPkPToEx9oFhA69Nmg9nTUcrOG109V71+MtzCb09rovt8i/jg+oE37ZfTi3Lce5ackZkfS4C7NwHtxExoPzsCT7+55w1TPYnxtC+cYFRA0M3vfSXz/HEBlP4qinADAndMBxcDPFP71fm/SEdT2PsK7nAXB4VsO/QOmt4bS984OAeYlXP0fm5Eupzt+HJallLvgrcjYS2+MKIjMGARAXlUrBpjlUHtrSaNKTcXHgdk499z5K9y6nRF1Sm/QUbv4KT2UR3W7+BJ3en+iYo1IbrMvjtLNv7sO0+8sEcn/5T3N2rVmYQwOP7fz9SwmJyiAmZcBx6+5eNZnwWBvRKQ2TnkO75pNy1rUkdf4LACGRaZTnbSVr/fQzKunZtmkqCUlD6NXv8dp5YeFpTdYxmcKBunNFYf56KiuyGTik7lyxb8/nWEPi6TPAf0xFRHaguHAz6o73a5OepJTzSErxH1NrVzU8plqKTm8ixNL0Ob++PTnz6ZJ+LR1T/ds6IjSNgpKtbN47vTbp2bb/Q5LbDKR357EARIeP5VDharbt/5ARfacAsG7XVFLihjCoe922iAhtelu0BL3ORJjpxOMTaUllZEf/OUUt/D5omaTws0kK9/9FevXBt4OWOVOUuHJZkDuB2zrM4KP9fz9u+ZSQ7qSEdK+djjGnsaPsB7Iq19cmPdelvxJQ5/KUZ9lZtpQ95b8QW/OUgi3iPGwR/uPlq+wz43gZEBZ4zXhV9BP8WjGHHNdOulmDX3sdFa6PIUwf00QJhQh94/vZfQnvBUzfEjuJh7P7sb96Az1CTv85NkQXzqMRgdcAt4Y+x7/KLuWQdx9phuDXAHs9m4jRJfIny60AxJHGBZab+KTyhYByHs3Nfyse4pqQB9npXo1dK6ld5tKcrHMt5h9hr9PV6H8S6sqQf7DR/SPLnJ9yTciDzdbP0/5Oj7ZvG3jcKL2G1s5TYpMgtQParo2N1lO69kXbthotZ59/Pdl70bb+htL33OCf43ahLZ4FIWEo7bo23qCqCjCawGw5tQ79Tt7MbeB1o+9RFw9dmyR0yR3w7G48HvVpPi/uXxeAswp9p94Byzy712MfO5iKcRfjmD4eX1lRYF1HBY43xmG54zl0kW1+f4d+J83jAkAx1v3FXdHpwGDCtXf9Ca+nasUXGJI7YerQ+G1qAM1ZiS4k4tQa28x8R/tuCOy7YjBRldl43x0HNhHaaUjAvNDOQ3HmbEPzuk+9Pc4KAPTWyOOU/OOEp/WhZM+PVJcdBsCevYGqvJ1Edmj6C+lY3upKDJa67VysLiEstQ8HFr3AhleHsPmtS8j5aRq+Y+KVufApYrpeTGS7wb+/M38wj6uSI3sWkHrWdcctW5C5nMLM5XQ598mgy31eF3q9OWCezmCmLG9rgxi1FE3zcShnGRFRHfl56R3Mmz2IHxZezcGshSe1nv17viAishOx8XXniqKCTSQkBR5TiclDKS7ahs93ZvS/MXlF6/l40WBmLb2YnzeNx1Fd1GR5n8+FXhe4rfV6MwUlW2v7mleyiZT4wHikxg8lr9j/HaVpPg4eWUZ0eEe++/UOPl40iK9/vpp9uSe3LU6H3LL1vPnrYN5dezHf7x5Ppavp+LQmXs3D7APjGJ4wlnjLqT1yeKhqBwcrN9IutH+jZbyaG4+vGqvhzPhuPREezcVK+ywsShippiauGWtMOnwN/8oZyut5t7Db+VuD5W7NyVM55zM+51z+m38X2a4dTa7P6atEw0eI7syJmUPzXwOE6hq/Buhs6EOpr4CNrmVomobdV8zq6oWcbQq8Nv/S8Sqx+hSGmq9ssA4vHnx4MRJ4HjIpZvZ4NjRDT+qc/mdWSgtBp4dj3qFRItv4lzVCuervKI5KvP+81F/f60G55m50f74xoJxv7Y/4pjwE1Q6IjkP/9Af+R9uC0CrL8X32GsqF17XY4ztaTTyU8Ibx0MoajweA96BK5TPXg7saLCFYH3wDfdu6bNzQcxiG/heii0vFV5hL9RdTqXrxFkJf+Ko2qXC8/zT6nsMw9jqv+Tt3CgyJ7dG3SaF87qtE/e15FHMIFUtm4Cs5gq+s4ITW4XPYca5fRPiopv86UPnjTLwlR7AOuqLJcqeLOb49hugUCr57laRrn0dnCqH4lxl4yo7gtTfed4+9kNBOgRflhvBY8HnwVpZgiDj+IwzH0jwu8r+ZSFi38zFGNf5u2R8t/eLxZC18mk3ThqPoDLXzojudf8LrOLJuJi77EWJ71G3n6tJsyrN+I7b7X7Bd/zbVpblkLXoOr7uK9Av8j17kb5iNs/ggHa6Y1NiqzyhHdn+Lz+smuWvDL5X6qivz2fHjeHpe8gYGU/C727Fth5K7Yw7xHS4kIr4H5fnbyN0xB83nxu0swRx68vtUc3M6i/B4qti59W2697qfHr0fJv/Ib6xe8TAGg5Xk1OPvIy6XnewDi+jRO/Bc4XQUkpAUeExZLLFomodqZwnWkJbvfzBp8cNol3Qh4SGp2KtyWbdrKgtW3cKV536FXt/w0U3wJy/qgTm0S7qQ2KgeFJZtQz04B5/mxukqIcQSj8NZiNUc+D1qNcdSVe0/Lzmqi3B7q9i05236drmfAd0eJrfwN37c8DAGvZX0xBM/Xv9I7aKH0Tn2QiItqZQ5c1mRNZXZW27hb32+wqALHp/WZNmRaYQYohgYe8NJ152041wqPcX4NC/nJ9zLgNjRjZZdcuRVTPoQukScOe/LNmZr1Y98UPgQbs1BhD6O+xI+aPLRtkh9HH+NeYZ0Uw88uFlbMY9pebdyf8LHdLT4E8F4YztubPMiqaYuOH2VLLd/xJQjo3kiaR7xxoyg651TMoFUY1famXsHXX66eTQXn1VNpJfxfGJ0jV8DdDT2ZmzYK7xV8TBuqvHi4SzDEO4Mfbm2zFb3Cla7vuP5iLlB12FVwuho6M18539JMXQmSonlV9e37PVsIkHXtln79buu9H0/zcf3Vt3LsvqnpqN0O9XHhLSml65YiLZ8LroHX0Fp2xEtcye+917El5CK7oK6x36UHgPRT5kL5SX4fpiNd/ID6Cd+jhIT+CWlOavwTrgbYhLQ3fzIKbY5kHvlfBzv1cUj5NHpGLqcYjy0puMBoEtuR9iLc9GqynGvWYzzrcfQjf8YfZr/RTjj4Etry+rb2tC3O4uK+0fg2bQcY/+LcP0yF99BldDnvzy1NjaDqtXzKZtZF7OYf0wn+q7XKf3oSY48NBB0esxdBmPuHvyOXjCO3+aj+byENJHMODZ8T/mXk4j++xQMbVJ+Vx9OVdmG+Rz5sq7vaXdMJ/Xm1zk8+0n2PO3ve2jHwYR2OZG+K4GTtfuP0qDk8WheD4c+ewSv007qbf896fqnqnDrfDIX1sXDNno6lYe2YM/eQOfr/os5Mpnyg+s4uGQS5qgUojocPy7FO78ne8kkOl41BXNUve2saRhD29Du0hdQdHpCk7rjcZRy4IeXaDvyUZzFmWQvn0K3m2fWPv7W0g6r89nxY118+lw2neiUuvNLzvbZxLcficna1CMXsHXxI6R2H01UYq9Gy7QfcA/VVQWsmTMaNA1TSBuSu4wia8O7oLTMu38H9s9n/eq6/g8d4X+MKCVtJLZutwEQHdOVkqJt7FVnnlDScyBzPprmJb19sHNF4LGjHf2OUk7+mPoj7M2Zzy+b6+Lxp0HT6ZBSd86PibARG3UWn/0wgoN5y2mXfFHQ9fTufA9VzgLmrRgNaFjNbeiUNoote99FqbetG/Ra01Bq5mr4AEhPHMnZHfzbok1kVwpLt7Eja2aLJD078uazeE9dfK7pMZ2u8XXxiQu1kRh2Fm+vGcH+4uV0jg0en/9Vm0rmMz+nrv9/a/c2G4q/4j7bvFNa35gOM3H5qsiu2sziw5OJNqXSO6bhI8arCj5kbdEsbuswA4u++V8ZOFVrK+bzWXFdPO6Jn05HSz86WwbyRNJcKnwlrLLP5v2CBxiX+DmRjbzvlGBsT4Kxfe10e3Nvijy5LCl/rzbpaW/uTft6yUt7c29eOjyKn+yfcG3M+Abr/LL4JfZVr+ehhM/Qnabz66rq+cyorIvHuPDp2Iz+7xOv5uGtykeo0uw8GNb0NUCudy+fVL7AFdZ76G4cSpmvgM8dk/ig8t/cFTYJu6+Ydyse5+6wV5q8Y3Rn6CTeq/wXD5aeiw496fpuDDJdygFP03fITtbvSnqUASPQd+5ZNyPmBF42iooFnxfKSyCy7stZKytG6db47VLfh5PQXXE7umH+k5aSboOCQ/i+fCcw6bGEQFI6JKWjt/XCc89FaEu+qB3sAEBzVOJ94U4A9E++hWIKvKV2qgx9RhDWoS4eygnEQ6mJh2YvQYmoF4/yYpQujccD/I9BKYnpAOjb9/C/m/PdDKx3vhi0vC46ASUmAd+RLAC823/Dl7sX+x2Bf1lwTHsQ16IPCX36s+O2//ey9ByBqV1dzPRRCSgmC/FPzcPnsKN53OjDYyh46VqM6d2bWFOdyhWzsfa5CF1o8JcBHRu+p/T9R4m67eUWHbktrNsI2rWt67shMgGd0UK7h+bhddjRvG4MYTFkvX4tltTG+24Ij8VjD7wr6KkoAp0BfSMxaIzm9XDo04eoPrybtnd/jD70jxnVMJjoziMIS6mLhyk8gV2f3ErHq6cS3dn/jHNIQheq8nZy+Nf3j5v0FO/8nn3zHqX9FS83GLnNGBaHojMEDN5hie2Az+3AU1VCRc4mPFUlbHn7srpKmhf7wbXkrf+c/o9tQhdk0IM/Uly7EQxOqIuPOazu/FJesJPy/G10GvzQcddTnPMbJblr2b/mTaDmYl7z8cMb3eg6/GlSu/8VvcFC9wteotv5z+FyFGEOiSOg/dPxAAAgAElEQVRn+yz0xlBM1tO3T9SXnDaCmNh6/bfEoCiGBqO0hUe2J/sEH3HL3DOb1LYXYTYHHicWayxOR+AxVe0sQlEMDcq2lLaJI7gqqi4eodaG3zehlgRCrQmUVWY1uh6D3sJ5vV9iWM/nqKouIsQSx66sWRgNoVhM/m1ttcRSVR0YD4erqPbuj8UUjaIYiDpmlLaosPbsO9Qyj7h1bDOCpIi6+ISZGsYnzJxAuCmBEkfWaWzZ6dE1YgRp9a7P1hXNpsJTwMvb6x6l9+Hl+8OTWVX4IY92+7nJ9cWY/e9nJVptVHgKWZb3RoOkZ1XBhyw5MpWb200nNaR5R936vXqEjCDDXBePSL1/fzDrQojTpRNHOu3MvXg29yJWVXzBn6PubWxVDWSYe7K+ckGjy3WKnram7hS4sxos+7L4RdZXLeSfCR8Sazx978D1No2gg6EuHtE1gwV4NQ//rXiIHO9uHo/4mDBd0+f7bx1v095wNpdYx9TM6YJZsTLBfiPXeB8k33eQUq2ASfbbausc/SPJbcXdeDHyW5L07UnQt+VfEZ9QrVXh0CqI0sXzZsUDxOkbvmv7e/y+pMcaBtaTy+SVDt3BYETbvBLlXP8FhVZ4BHL2oXRp4rZetROOHdlNpwfN1/QH+nxoblftpOaowPvc3wEN/b/fRbGGnlT7m6JYw/wxOQn6dt1Bb8S7dSW6If54+IqO4Du0D0Pnk7zNqfnA42p0sc9ejFacjxLl/wuG+boHMV16e0CZyscvw3zjYxj7np5kQGcJQ2cJHjNdzcAEnrws3Ae2EX7F/cddnytzC56cXURe96+gyx3rFlIy43Gib52ItW/LDcsNoLeEoW+k7/qavrsKsnDmbCPu4sb7bk3vRcX2JQHzKveswpLaHUXf9MhE9WleN7mfPIQrz5/wGCJO/GXf5qA3h6E318XDU12B5nM3GFVQUY5/3BftWMi++Y/T4fKJtOnacDuHp/ahcPu3aJoPRfG/2ugsykRntGIIiSbadgE9kgITzf3fPIElJoPkIXedVFybi8EU1ujjaDnbZ2GJSCEm7fgDkQy+4ZuA6YL9S9m/7i0GXvcFltDAC0Od3oglzP9ow5HdC4lrd35tvE43ozEMozGw/zGxPbCXZwbMqyjPIiT0+MOsFxVuobRkF736NTxXtInrxaHswGMq79AqYtp0P+5oaKeLyRCGKazp7xtndTFVjnxCLMd/HE+nMxJm9W/rfYcW0jahblsnRPcit2AVPTuOqS2fW7CKhBj/d5ReZyIuqgdlFYHboqwyi3Brywx5bzKEYTI0HZ8qdzF2Vz6hpjPzccXfw6wPw1zvTsuQuNvpFR14R3PG/js4O/ov9IsJPkhOYzTNh1cLvNZYWfABS4+8zt/avRMwVPWZwqILw6I7/vWZhg+P1vh1VDA5rp1ENjFogaZpHHKrpBgDBwOYU/wC6ysXcn/ix7XDXZ8uViUM6zF34o4ONpDj3c0TER8HHXL6WC7NiY7A7+i6aY32hh5MiAj8zvnSMZVKrZybQ/5NnC4wqTErIZiVECp9ZWxzr+A6a/M8iXVUs7/IotlLofAwWmW5f8bhg2ihERAVixIdhxIajjLyanwfToLINijhUfg+eAnSbShn131he+77E7pLbkJ3yU0AKP3Px/fVOxCf6n+8bf9OfPM/QDk6WlxVBb6vp/tHd4uOg/JifAtnQtERdEP8w7dqjgq8z9wBjgr0j78JTgea0+H/wLDIgJfnmy0eFaX4Cg+jVfnj4cs7iDckAiUqFl1UHEpIOMbhV+P8bBJKZBv/kNWfvIQuzYa+e108Kh7+E6aLbsJ0kT8ezs8nY+g1HF2bRDRHJe5V3+LduQbTw/5HPjRnJdVfvoFhwEXoouLwFeRSPWsKSkRM7chvupiEoHfndDGJ6OJbbtQdx/rv0IVFo49JwZ2rUj77RSy9LsDSre4vVCUfPApA9G2B71tU/TILfXwGps4NR69yrF1AyfuPEnHNo5g69cdb846QYjA2elfodCvf/B360GiM0SlUH1bJm/8iYWddQKitru+HPvP3PXm0v+9Rg6+nZOVM8uZNIGrQ9TiyNlC27muSb6gbUcdXXYmr8KB/QvPhKT2EM3cn+pBIjNHJaF4PuR/fjzN7K6m3vQUoeMr98dFZw9EZT/9AHwZzGOFtB5C97BX0xhBMkcnYD66lYOtc2o6sOxHum+ePx9F3b4q2L2DfvEdpe8GjhLftj6uiph96IwarfzvH9x3NkXWfcOD7CST0v5Hq0lxyfp5GQt/RKIqCwRIRMPABgM4YgsEaSUh8y/yOQmO8bgdH1G/I6DMGJcijV3tWvUJZ3hb6XekfPjS8TWD7y/O3oSi6gPmVJZmU5W0mMrEXHmc5BzZ9QEXxHrpfGPj7JC2tS7cx/PrLA8TG9yM+cRD5eas5mLWQIcPfrC2zeqV//6g/OhvA/j2zCAvPIC6h4bmiQ6fr2btrJhvXTqBD5+spzN9A1v6vGTS07phyuyupsPuPKU3zUVV5iJLinZjMkYSeQNLV3NyeStarb9Au6SJCLHHYq3JZu3MKVnMMGUl1o33+uMEfj/NrhrUurcikoGQz8dG9qHaXs3XfB5SU72F477pt3b39zXyz8iY27XmbjMQLyDqyhEOFq7l86Ke1ZXp2HMPSdQ+QGNOP5NhBHC5azb7chVw0oG5btCSXt5KVB96gc+xFhJniKHPm8nPmFEKMMXRuUxefBbv88bm03rDWeRU7/evwVKCgkFexE71iJDa0IwBen4vCKv8gSx5fNZXuAvIqdmLShxBtTT9dXWxSmLENYcbAwYr0ipFwQyxxlrrHteYc9Pf/mrb+/v9a8DHR5lRize0AyKpYy8qC9xnQpu69oF/y32XJkalc03YSseYM7G7/Odeos2DR+/+AV+2tpNhVd7yUug5x2LETqz6SKNPpP14cvgqWlE2nR8gIIvRxVHiL+dk+k1LPEfqE1g35/1GhPx43x/rj8WP5DGIMqSQZO+LV3KypnM8WxxLGxE2rrbOw9A0yzD2JN2Tg1CpYXv4RuS6Vv8Y8U1tmVtGzrK2cx9/j3iREF0G51x8zsxKCWdd8f4w/UV7Nw5sV97Pfs5UHw/3XAKU+f5tClHBMiv8a4O0KfzzuCvPHo5fpfD6ofIqlzk/pYRxGqS+fT6teJF1/Vu3v+6QaAr9zQpQIvHgD5m91/YIPH8n69uT5DjKrahKJunYMMzfvbzk1f9Kzdhm+aXXDEfr+439+Ufnrfeiv9/9Yl+72f+HTG/BNfhBcTpSzB6O/f1Lgb/TkZqKV1w1pp/v7eHyfvobvnWehrMj/46QXXofu6GNrej1k78W79Euwl0J4FErHHugnzETJ8A//q+3bDrv9Pz7nvffigHbrnv8I5ZgfUW0O7vXLcL5TFw/nu/54mK66D8vV/nhYbvoXTr0Bx7QH0VxODGcNxjp2UsBfuH2HM/HZ6+KhlRbi+M8jaGUFKCHh6NJs/neIjg5xrdPjzd6Ne8VctEo7SlQchm4Dsf5z6knfjTrdvGUFlH0xEV95EfrIOKyDriD80nsCyxQfblDP56zAsW4hYZfeE/Tir/Lnz8HnoXz2i5TPrnsE0NR5ALHjPm7+jpwCj72A/G8m4qkowhAeR2TfK4i9ILDv7tLAvpti0ki74x3yvnmJ0l8/wxART8IVT9YOVw3gyNlG9lt1P6hWuHgahYunEdH3SpKvn4i77AgV25cCkPVa4Enm2B8yPZ06XjWF7GVT2DvvYTyOMsyRyaSddz8J/W6qLXN0ZLej8tZ/jubzcGDxixxYXLedw9sOoNvN/u1sjkyiyw3vc3DJRLZOH4UpNJb4nleTPGzs6elYMzqyZyFet4PkrsG3UXVlAVVl2Se1Tk3zcWDjDCpLM9HpDESnDGTANZ9hjWjeRw1+r5S2F9B30HPs3Po2m9ZNICw8nYFDXiY5dXhtmarKhucKt7uC7KyFdDs7+LkiLDyNYSPfYdO6l9i3+zOs1nh69X+ydrhqgJKibSz/oe6Y2r55Gts3TyOj/ZUMGHL6k0NF0VNcvps92XNxue2EWOJIih3IyH5TA+54VDoC46FpPrbum0FpZSY6xUBy7EAuH/YZ4SF12zohpg8j+k5h3a6prN81jYjQNEb2fbX2N3oAMpIuYFjP59i4521+3TaByNB0hvd+mbYJw//wvp8IBT2FlbvZkTcXp8dOmCmOtKiBXN41MD726ob7y0cbAh/j2lf8IxHmFO4auAyACld+QJnSwwfZfHgWaZEDuL7nmfHdcqJKXcfsH3hZfGgyJe5cdOiJMbfloqRx9G9TN5DB6sJP8WpuZh0IHBCkd/SVXN3WfyzkOrbx/r6642VZ3jSW5U0LKHM66dFz2L2XXwu+pMpbSog+inRTDx5InEmKqe5nP4o9gfHwaG6+LnmZMm8eRsVCkrEjY+Pf4Sxr3WBQDl85nxX9G7u3AIsunFRTNx5I/IQMc90jf79U+P9gMC3/1oD1/znyPi6NOv0/bFvsO8IGt/8a4OnywO+SMaEv1SYfxb7AeAwzX4VTq2RJ9Uw+r3oZqxJOV+NA/hpycndoqjQ7XzimUOI7QqgSRT/TRVxjfRDDcX5H62QpWiMvzNtstgwgU//2Uv+PfQpCqlq6BWeWsIqWbsGZJaK8pVtwZoksa+kWnFkkHoGiSlu6BWcW2T8Cyf4RSPaPQLJ/BAq3t3QLzhwF3hweLhsJ0E5V1az6y1rm4WwhhBBCCCGEOE0k6RFCCCGEEEK0apL0CCGEEEIIIVo1SXqEEEIIIYQQrZokPUIIIYQQQohWTZIeIYQQQgghRKsmSY8QQgghhBCiVZOkRwghhBBCCNGqSdIjhBBCCCGEaNUk6RFCCCGEEEK0apL0CCGEEEIIIVo1SXqEEEIIIYQQrZokPUIIIYQQQohWTZIeIYQQQgghRKsmSY8QQgghhBCiVZOkRwghhBBCCNGqSdIjhBBCCCGEaNUk6RFCCCGEEEK0apL0CCGEEEIIIVo1SXqEEEIIIYQQrZokPUIIIYQQQohWTZIeIYQQQgghRKsmSY8QQgghhBCiVZOkRwghhBBCCNGqSdIjhBBCCCGEaNUk6RFCCCGEEEK0apL0CCGEEEIIIVo1SXqEEEIIIYQQrZokPUIIIYQQQohWzXC8AtVmwHIaWvI/wOhu6RacWXySMgfQlJZuwZlF0Vq6BWcWna+lW3Bm0XtbugVnFpOrpVtwZjFXt3QLzizWqpZuwZklzN7SLTizRJe0dAvOHK4mrj3kslUIIYQQQgjRqknSI4QQQgghhGjVJOkRQgghhBBCtGqS9AghhBBCCCFaNUl6hBBCCCGEEK2aJD1CCCGEEEKIVk2SHiGEEEIIIUSrJkmPEEIIIYQQolWTpEcIIYQQQgjRqknSI4QQQgghhGjVJOkRQgghhBBCtGqS9AghhBBCCCFaNUl6hBBCCCGEEK2aJD1CCCGEEEKIVk2SHiGEEEIIIUSrJkmPEEIIIYQQolWTpEcIIYQQQgjRqknSI4QQQgghhGjVJOkRQgghhBBCtGqS9AghhBBCCCFaNUl6hBBCCCGEEK2aJD1CCCGEEEKIVk2SHiGEEEIIIUSrJkmPEEIIIYQQolWTpEcIIYQQQgjRqknSI4QQQgghhGjVJOkRQgghhBBCtGqG5l6hsnIxysJZKHu3o5SX4H35I7SzBwaWWTgL5advUfbtRKm045mxFBJSm17vd7PRLZ0LB/aC5kPr0BXf3+6H7v1qy+hvGYGSn9ugrq//efiee8c/sXUtui/f87evKB/vQy+hXXjV7+94I7yrF+NZMgvf/u1gL8H09EfozwqMh+Z24f74ZbwrvwVXNbrugzCNeQalTWKT69ZK8nHPfAXvxp/AWYkSn4bx78+g7zbAv1zT8HzxBp6ls6CiHF2nnhjv+De6tE6Bbdz0C+4v3kA7sAsMRnTtz8L87w+bNQ6N8ZYXYp8zGdeOFfgcdkyd+hEx+ikMCRlN1nOs/obKRe/iyc9CZwnD1HUw4dc+hj4yLkjZbyl7dxzmHsOJ/ufbtfPzHx+Br6jh/mLucR7R/3znd/ftVHjshRQsmEzlbn88rO37kTDqKUxxGU3Wq9q3hvz5E3Hl7cEQEU/M8DFEnTM6aNmipW9R+N2rRJ1zIwlX/TtomSNfPEXZ6tnE/eVRYobf8Xu7dcq8rkoO/jiFEvUH3I5SzBFJJPQZTdLAWxutU7xrMXkbPqcybwc+TzXW2I6kDLmbmM4ja8tUFewh5+dpVB7ZTnVpDinD7iPt3H80us7clW+RvfxVEvreSLs/BY/Z6bDoTVvQ+W2730C3854OuqyieC87fn6WiuJ9eFx2zKHxJHW8lI4D7kOnN9WW83ld7Fv3Xw6p83BW5mMOiSWj1+1k9Ly5tkzW5g/J3vYZDvshjJYoEtqNpPPghzGYQpu3oyehvDyTzZteIS/vN3w+NxER7Rl8zmQiIzsELZ+Xt5plS29uMP/SSxcSUa9O9sHv2bLlNSoqDhIW1pazez5IWtqFtcs/+zT4tujU6Qb69Q++Lf5oS7c8zq5DXwfMS4jsyTWDZzdZz+tzsW7ff1EPzaPSmU+IOZZeGbfTM8Mfp71HvmPD/umUVR3Ep3mIDEmnV8atdEm5snYdHy0fgd3Z8HyaHncef+nbMufT+hbsf4qNBbMZ2fZRBic1fk6bv+9xthR+3WC+UWflsf6bAMgqX80nOxvuQ3efvZBYa8P9blvht8zdN46OUcO53vZ2g+Wny3dFU9lsX0SZ5wh6xUiKuRt/anM/7ax9mqy3ofwbfix5lwJ3FhZdGJ1CBnNZ7GNEGPzft2vKv2JW3hMN6k3ssAWjzgzA90XTWFz8RsDycH0sz7Rf2Uy9Ozkezc1Xjqlscf9MvjcbqxJGV+NArrWOo40+ucm6S5wzWer8hEJfLm10SVxmHcsQ86ja5Wtc37HQMZ0830G8mocEfToXW25lqLnueHFoFXxV9Rob3Eso9xWRbujGDSH/or3h7D+sz8ezSlvM98xiH9spp4QJfEQPZeBx6y3QZrKAT8gnlziSuJaxjFDq4uHR3MzhbZYxlyLySKEdt/AwfZVza8t4NS+fMY3lzKeEAqKJYziXMZp/oFeaL1Vp9qQHZxVat95oIy5DP/mx4GWqHWh9hqINGon+nZdOaLXKltX4zr0ErVsfsFjQfT0D/fgxeN+cCykZAHhfmwM+b12l4gL0/7wKbdif69bjqIKMzvhGjkL3SiPta0ZadRW6zr3RD7sM9xvBP889YwLedUsx3T8FJSwK90cTqZ54F+aXv0LR6YOvt7Kc6qdGo+vSF/MT70BENFpeDkpEm9oynnnT8Xz7PqZ7JqIkt8Mz502qX7gNy9RFKNYwALxrluD67xMYr38AXY+XwKfhy9ze/IEI1gdNo/TNe0FRiLr3P+isYVT+MIPiKbcR+9wCdOaQoPVce9dT9t6jhF/7GOZeI/GVF1H+6bOUvfswMeMCkzVPQTb2OZMwdurXYD2xT85Bq7e/+MoKKHrhKiz9/tyg7OmgaRq5M/zxSLn1P+gtYRT/PIPst2+j3SNNxKMom5x37yRywNUk3fB/ODLXk/fVs+jDYgg/++KAso4Dmyj7bTbmpOAXbAD2zYtwZm/FEBHfrP07FQd+mEhZ1io6XD4Jc1Qq9oPr2L9wPIaQKOJ6jApap/zgGiIyBpF23gMYrJEUbvuG3XPuo9tNHxPR1r8f+NwOzJEpxNguJPunqU22wZ67ifyNswmJbzxmp8v5t64ImC4r2MaGBXeT2LHxfVbRGUm2XUlEXDeMpnDsRbvY9uNTaJoH2zmP1pbbvHgczorDnHX+84REpuOqKsLrddYuP7T7G9RV/0f3ES8QndQPR3k225Y9iddbTY8RLzZ/Z09ARUU2S34YTUa7UYzo/iEmUwTlZfsxGIIfK/VdcukCTKbI2mmzOab234UFG1m58kF69PgHqWkXkZO9mJUr7ueCCz8jNrYnAKOuDNwWxcXb+Pmnu2nbtmXOH0eltjmHC86eVDutV4zHrbN48zgqnIc5/6zniQxJp8oVuO0txij6dbiH6NB26HRGsvJ/ZNm2J7GYYsiIOw+Aa8+Zg0+rO59WVRcwe9VVdExs2XgA7CxaxKHKrYQbj39Ouyj9SUakjQuYN2PHaNqG929Q9q4eC7Aa6vahEGNMgzIlzmyWHpxEWnjD76DTLd7Yjqvin6aNMRW3z8lPpTOYfmgMT6QvJtwQG7ROpmM9n+Y9ymWxj9E9bCQVniK+LHiWmUceZmxq3fetSbHyRMYPAXWPJjxHxRnbcU/qx7XTOoJf35wOLs3JAc8OLrOMpa2hCw6tgs+rJvKKfQzPR85v9EJ7mfNTvqiazG2hz9Pe0JP9ni3MqBxPiBJBb9MIAMKUKC6z3kOSvh0GjGxy/8j7lU8SrsTQ0+Q/Xj6oHE+2R2VM6ERidImsqp7P/9lv48XIhUTrEk5bHOqrpoou9GY4l/EqJ3Z9vFD7lA+ZzL08j42e7GYLbzKeMC2CAYo/Hp8wleXM415eII0ObOAXXuI+XtY+p4PSDYAvmc5CPuUBJpJOZ7JQmcrjGDBxPfc2Wx+bPenRRtZciJQVN17mylv9/9i99YTX63vslcDp+55F/+tSlHW/oNUkPUQFnnCU7+dASBjasD/VffaA89AG+Hc6pjT8y0RzM5zrj4dWXow7yHKtyo532ZcY73kR/dlDADDeN4nqe8/Ht2UV+l7Dgq7XM+9dlOg4TPfVfbkRn1a3Xk3Ds/AjDKPuRD/o4pr1vox3zGC8K77FcOH1aD4v7g9ewHjjIxguuK62ri41+F9Im5s3Lwv3/k20+fc8jGldAIi48RkKHh6Cc80CQoZdG7See98mdNGJhF54q39GXBohI27C/tkLAeU0j5uy6Q8RfuWDVO9ajVZRErBcFx64vzhWzEGxhGHp+ydagrswC+eBTaQ/NA9Lsj8eCVc9w75nh1C+aQFRA4PHo+zXzzFExpNw5VMAmBM64Dy4meKf3g9IerwOO4c/fZiE6yZQ9MN/grehOJf8eRNIvWsGOe/+vZl7ePLsuRuJ7X4FkRmDALBEpZK/eQ4VuVsaTXoyLhofMJ167n2U7F1Oye4ltUlPWPLZhCX7/6KWu6rxv7x6nHb2zn2Y9n+ZQM4vwWN2OplDA+9k5q9ZSkhUBjEpAxqtExqVTmhUeu20NSKFpNw1FB9aXzuv8OAKinJWce5NP2Cy+o+LkIjAu++lRzYSldiLFNuo2uXJtlHk7V/8u/t1qrZsnkpi4hD69Hm8dl5YWFoTNepYzDGYLQ0vUgFU9UPiEwZyVvexAERGjiUvbzWq+iGxsVMAsFoDt0VuzlLCwzOIT2h8W5wOep2JUHPDO96NOVi4gpyiVdx07g9YTf54RIQEbvvUNoMDpntm3MKuQ3M5XLyuNuk5WveonTlzMBnC6JDYMufTo0qrc1l8YAI3dp3BZ7uOf06zGMKB8NrpbPt6SquzuaLDpAZlQ40xQROdo7w+N1/vfYjhaQ9yoHw1VZ6SRsueDn0jrgiYviL2CdaUzyG3eiddDMGvNbKcm4gyJHJe9K0AtDGmMTTyJr4ueOGYkkrtnZ/G6BXDccucLiG6cB6J+CBg3i2hz/Fk2aUc8u4jzRD8j1yrXPM5z3wtg8x/ASBen0amdysLndNrk55uxsDj5SL9Laysnstuzzp6ms7DpTlZ51rMfWGv09Xov5NyZcg/2OT+kWXOT7k65MHm7u4JOb/m7ky51vj1+7GWM5+LuJbzFH88Ekljj7aVL5nOAEbUlJnHVfyd/spwAC7hBjZrvzKX9xnHZAB2sZH+nF+bKCWQygBtBLvZ0lzdA/6X3+lxu8FVDeERwZdrGrrFc9BGXA4W6+lt20nw7d8GXjf6nkNr5+lik1BSOuDbvbHRet61S1A69sT16gM4xgzG+cgVeBZ9gqZpAGj5OVBaUJtIASgmC7qu/fGp/vVq+7ejFR0GownnY1fi+PsQql+4HV/mjj+ot4E0j8vfLmPdIzaKTgcGE6496xurhrFjH3xlBTg3L0PTNHz2YpxrFmLufm5AuYq5r6Jvk4L1nCsbWVO9tmgajhVzsA66HMXcMvvL0XjoDIHxUAwmHJmNx8NxYBOhnYcEzAu1DcWZvQ3NW5dq5815ivAeFxPaafCxq/B/vtfDoZnjiLlgLOaE05P4Hk94ah9K9vxIdflhAOw5G6jK20lUh+Bf0I3xuirRWxo5VzRh/8KniOl6MZEZwWPWkjyuSg7vWUBat+uOX7ieytIDFB78hZiUur9c52UuITK+B1mbZvDjjHP5+ZOL2PHzC3hclbVlopP6Yi/cSekR/yM+Dvsh8rOWEZd+boPPOB00zUdu7jIiIzvy44938NWXg/h+0dUcOLDwhOp///01fP3VUJYtvYW8vN8ClhUWbiIpMfCYSkoaSmFB8HOy213JgQML6NDx5LbFH+FwyXreXzaYT36+mB+3jaequqjJ8pl5S4iP7MGmrBnM+PFcPvn5In7e8QIuT2XQ8pqmkV30K6WVmSTHBL97oWkaO3PmYEu+HKO+5b5/fZqHuXvHMTRlbNDHzk7ExvwviLN2Ii284SNg7227hqkbhvLJzlvIKvutwfLlOa8SZU75f+3deXwV9b3/8decPcnJfpIACRAghH2JoojihrhUW7W2tVRttYraVvtzafW21VavdaUuWHtdoO5SFq0sWlyquCMgKjuyBAJhyUr27Wzz++NgDgMJoCUhOX0/H4884Mz5zmTmnTkz85nlexiVceh9UGcLmn4+rZ2Nx+Yl2z2k3Xb9PMdQGyxnbX1kf1sf2sOX9QsZkmD93AfMZu7eejp3bT2Fv++8lh3NBx5HVAaK+d8tJ3PP1gm8uPsmKgPFR3y5/hNNZj0ACbbkdtsETD9Ow3oFy4WbLcHVBM0DT22bpsm6wKfsDm1lkCPyeQkRJEwIJ/tNx3CzMfjFfwdFvF0AACAASURBVLoYnSqA/4DlcONmE9E8AgRw7b+suFlPdFmHciyrWcoOsxCA7eZmVrOEMRzZ/cuRv72tk9heeAQ88Zhjz2jzfeOLTzBKdhA6u+2z412FWV0BNjskplqGG8npkffaG6+smNDb/8Bx3hW4L7yGcNF6As9Ezrw4zrkMs7o80jDFesnaSE7HrCoDIFwa2eAEZz+K82f/g5GZQ/DNGbTceRmeR97ASOvYS6yOHv2xpWdTN/cRkn/2Zwx3PA3/fo5wVQnhmvJ2x3MNKCDl6oeo+ftvMQMtEAriGnoSyVc+0NqmZe3HNH32Br4/zTusefGv+4RQxQ7ixh+99cWV2R9HajblbzxCjx/9GZsrnj0fPkewpoRgbft5BOsqiN+vkLF7fRAOEmqowpGUSfWSOfgrttPzJweerfxaxduPYY9PIfXES47YMv2ncs++na0L7+DLx07DsEU2V7ln3U7qwNMPexoly2fgryshY8QFh268j9Iv59BStZ28C9rP7Gjavel1wqEA2YMP74BqyT8nUVu+lnDIT87Qi8k/4ebW95pqi6na/Tk2u4uCcx4j4K9l/Yd309JYRsE5fwWg58Dz8DdXs3TuZYCJGQ7Sa9AF5I+7pSMW75CamysJBhtZu/YpRo68gdGjf0tpyRI+XfxbHI44srPbXkfi4jIYc9ydpKePIBwKsLVoPovevYIzJr5IZuZxe6ddgcdj3XZ6PD6am9v+HG7b9jrhcIB+/Y7uwW2fjJPp3+NMkuJyqG3aydJNU5n/2eVcfOKr2G2uNsepbSpmd9Xn2G0uzil4DH+glg/X301jSxnnFPy1tV1LoI7n3j+FcNiPYdg4Zeif6Lv3Ks/+iis/obZpB0Nyju7+94MdjxHnSOHYrG+3TWsO1rF+z5uc3tt65j3RmcF3cu+kl3cEoXCA1RXzeemrK/jpkBfpmxRZhwqrP2Zt5RtcPeLw9kGdZV39e7xYcjMBs4lEewbXZj/b7q1tALlxBVzW4yFmlP6WQLiFMEHy40/iJ1nR/W2msx8/zrqXXu7BtIQb+Kj6Bf624yf8ps98Mly5APTxjGRS1n1kuvpTH9rDO3ue4LHiSdzS93US7Knt/PbOEzT9zGq8n9HO00mztf889QjneD5seYVjXWfSzz6CotAaPmh5hRAB6s0qUozILZSN4Tpuqj6FIH4MbPw04U+M3HtrW5zhJc9RwGvNT5DjyCfZ8LHE/zqbgyvIsvXplOU9UgoYz795hRPNM8ljBJtZw9u8QpAAtVSRRiYFjGcBzzPcPJ5e5LKST/mUfxMmejvsD7iaJhq4jvOwmXZCBLmYX3CucekRnd//qOgxFi3A9lj0gc3Qn6dbOhboKMa85zEWziZ033OQ4G27zZtzMPNHwID2z2AcacGPFhCYFs3D9Yfp2Id82zzMg78dNrENGI7zksi9x7Z+QzF3byP41gwc51y2T0PjIL8iDIDjol9gPyFyC4Lz2j8TXv0pwQ/n47zwmm85721rWrKA2pei+aT+v+mk/vKv1Dx3G2U3jgWbHdeQcbiGH7yyD+7aTO2su/F+91e4ho0nXF1O3StTqHnxT6RcNYVw3R5qnv0dyVc/hC2h/TM2+2r8aA7O3BE4+3Te+lL7xQJKXonmkTN5OtmX/5WSObex+U+RPOIHjiNh8GGc6TD2/zt/vf4Y+Mu2UPHGw/S+bgaGo+0Dn8bCZdR+9ip9b57/7RbmCKhYs4AtC6N5DJ40nfpdq6jb8QWDfvQEruRe1G1fzrZ3p+BOySZlwKFzqfzqLba/O4W87z+MOzn7sOelqXILxe8/zLCfzrA87N+Zdm1YwNr3o3kc+73ppPWKbk+K180hq98ZrbejHcqosx4hFGigtuIrNiyewpYvpjPg2GsB9l4hNhh55kM43ZFbe4xT/sjy166ipbECd7yPPTuXUfjZ4ww99Q5SskbSWLOd9R/dw+Zlf2Xg2BuO3IK3o2jrAj77LJrHqadGbkvMyTmDwUN+DkBq6hD27FnDpo0z2i16kpL6k5TUv/W1L6OAhvqdfLX+6daiBzhg02liHjhwr8LNc8jOOQNPO7fLdYQNuxbw/tpoHt87djoDe57X+jo9cRCZScN44YMJFJW9z4AeZ7U5na//9meOfAi3M/K3P8X4I68tv4rGlgri3ZEDYpcjgR+fOI9AqJEdlZ/yyVf3kxiXQ+/0A6+CriueQ2byCDKSOm97urpiAQu3RvOYNOgpVpW/yuQR336btqZiAWEzxAif9YRJelx/0uOi61BOYgHVLTtZsvtp+iYdR2NgD69t+R0X5j1keeanM31eu4BXyqJ5XJ09nf5xYxgQP5bf9JlHQ6iKJbVzeGH3jfy/3rNIcrT9vFNJy2bmlt/NmWm/YlD8eGqD5bxeMYWXy/7EJT0iJ4Ry4wrIjStoHSfXU8BD2y/k4+qX+H5m5HbjIQnWArmvZxT3Fk1kee08Tk39+ZFe/AMsblnA8w3RPG5OnM4g594rL2aQpxpuodGs40bvEwedzvlxv6ImXM49tT/BxCTJSGe8+0IWNv/d8oySx0jgruR5NJuNrAt8yqzG+8mw5bTe+nZNwhSebvgDN1Wfgg07fe1DOcF1HtuCnXOnzfvmAh4nmscdTGeY8c2PV3/Mr6iinFuJ5JFCOhO4kFeJ5nE1t/E3bud6zgMMetKbiVzEO7zaOp2PWMh7zOM3PEQf8tjKeqZzL5lmDmcZR+7kyX9U9JgnTCA0eFR0QHrHP3xlzHse2wtTCd01HQa108tFdSXGkkWEf9W5vSzZx0zANjCax+FcKTFSfJHOF+qqICm6wzRr9mAbcuCDk63jpWZg7PfsjZHTH/ON3Xunu/e+2epy8PXcZ7qVGMk+S5t9p2PYHRg9+2JW7D7kvH9T7tETSO8fzceekoXh8uC7Yz7hxjoIBbAlplF5749w9h3e7nTq33gKZ+5IEs6eHBmQMxjDHceeKZcS+v5NBMu3E64pp+rhfTakewu8kmuH4vvf13H0iO6wQrWVtKxYRNIlnbu+eIdOIPfmaB6O5CxsTg+5N88n1FSHGQrg8Kax7dEf4endfh6ORB+hOutVwVB9Jdgc2BNSaNjwEaGGKooe/F60QThE09bPqF4yi4H3rqBx81KCdeUU3jXe0qb8Xw9S9dHzDPjjh0dsuduTOnACIydH83AlZrF+xhUMvGgqqfmR+3wTsgbTULqeXUueOWTRU/nVWxTOv5UB5z9g6bntcNTtWEGwsYqV0/bJzAxRt/0zSr+YxfG3rrDchtgRMvtNIDkrmofHG92e1Javp7ZsjeVqzaHEJUa2A960PDBDrHnvdvoVXIXN5sAdn4EnIau14AFISI1sF5rrduGO97Fp6VR65p9H76GRHVBi+iBCgUbWvHc7A467DputY28cyM6ZQLovmofbnYZhOCw9rkGkqNm2/fBucftaum8U27f9q/W1x+Ojucn6mWpprjzg6g9AVdV69uxZw8hRh/+3OBL6ZU4gKzmah9dz4P4mwZNFgieLmsaidqcT784gwZPVWvAApCZEMq1r3tVa9BiGjZSEyLNhGUlDqGoo5PPCJw8oehpbKtlatohThnbu9jQ/dQLZ3mgeX5bNoS5QztQvots0kxCLtj/Ist3Pc8Mxh96mfVk+h8FpZxHnSDlk22zvKNZWRtahsqZN1AfKmbE+ug8yieyD7lk6lF+MfN1SNHWEYd4J9PVE80h2RNYPty0et6svPvrSN2409xWdxdKalzkzve2HxRdVPUUfz0hOT43sb3u5B+OyxfF/Oy7lO+k3kersecA4NsNOb/dwKgJF7c6f25ZAliuP8oO0OZIKXBMY4Ijm8XVnASEzyBP1N7MjtJHfJb2I13bwq04uw8NV3vu43LyLWrOSFCOD91tm4yEBrxEd12bYyLJHPi99HUPYHS7ktaYnW4ueTHsffp/0Ei1mI01mPSm2TB6vvxGf/eA9GR8pxzOBfKJ5pPPtjt/dhocbuI/rzLuoppJUMniL2cSRQBKRPJKNNG7jcfxmC3VUk0Ymz/MgWUSX9TmmcCFXcooROXGTyyDKzF28wjTOoosUPcR7Iz+dxHj1WWwv/pXQXdMOekXJ+Per4HRinnpup80bgBHnbe0V7XDZ+g8Hu5PQqk9wjI8cYJmVJZg7C7HlF7Q/3qBjMHdttQwzdxVh+CJdLRqZOZCSQWjVYmx5keLQ9LcQ/mo5zstujf5upysyncGRPM1wGLO0GNs+zxgdKTaPF5un7Xxs8ZEdbrC0iEDRGrwXtH/m2PQ3R24JtExg72vTxJk7gvQ7X7O8XT9vKuHGWpIu+RN2n3Wj0rT4VQyHE8/xnbu+2DxeXO3kYY+L5OEvL6J5xxp857SfR1zf0dStfccyrGHjYjy9h2PYnXiHTyQ3x1o0lcz+Pc6MXNInXIthd5Jy4iUH9PS2Y/pVJBZ8t90OFI40u9uL3R3NI9hSjxkOHNCDoWGztxax7alct5DNr/2OvO/dT/qQb/4gddqgiXh7WjMrfP33eNJyyT4xkllHc7i8OFxtrx/F62YTl5hNes6J32rapmlGei7cm2Nqz2MoKXyToL+htfvpxuoiADyJkStkoWAzhrHf586wtz5H2NGcTi9OpzWP9PQR1NVat4N1dUUkxB+8y9n9VVetx7NPxwQ+32hKShYzZOjk1mElJYvxZRy4Td68eTYJCdn06PHt/hbflsvhxeU4+P6myb9nbxfU7fda1jP1GApL3sQfbMDliPztq/cWSYme9q+OmmaYcNh/wPCvdr6K3eZkYM/O3Z667V7c9mgeJ/S88oArNDO/uoph6d+lIPPQ27Sd9asobfyKM/v+4bB+f2njeryuyDrUK2EE14yw7oPe3zGV5mAt5+T+iRR3xx/YemxePO1sP/ZlEiZoHvh3/Jo/3Ixtv8999IpG25990zTZ7d9AT3f7PV4Gwi2U+beSF3foLpGPhDjDS5zdmkfQDPBE/c3s3FvwpNgOv5MFh+EkzYjcBrfUv5DRrtOxGe0/Jm+aYYIcmLPbiMdtxNMQrmF14GN+HNc5twvHG17iOXLH7w7DiY9IHh+ZCzmOA/NwGW7SySJoBljM24wn2rNjC80H9OZnw956suCIzecRnRpAXTWU7cZoqI283rUdEpIg1Qdpe1eoPeVQVYGxswgAY1shZn0dZPaExMgZFdvvLodBIwn/PHL7lvHK37E9P5XwLVMiXVTv2XtvtdsDCdEzVJgmtrdewTz1vLYLsqaGyDxBZIdftgsK10NiMmR+sx3l4TDrqzErdmPuzcMs2U44IQkjxYeRkoERn4h9wg8IvDgFIykdIzGFwAv3YfQZhG1kdCfafOM5OM65rPXWNcd5l9Pyx58QePUJ7Ceei7l1HcE3XsT5k8jZRsMwcJz7M4Jzn8SW3R+jZy7BV58ATzz28ZFeNox4L/YzJxGY8xhGWg+MzGyCb87ArK/BcfL5RzyLtjQvfwPDm4o9PZvgzg3UzroXd8FE3MOiRVf105EiLeWqyKV098jTqX3xjzS+/w9cw04mXFNG7ax7cfQZhj098je0Zedbfo8Rl4QtFMK533DTNGn66BU8x5/XbkHWmepWvoE9IRVHajYtuzdQNv9evMMnkjAomsfumZE8vn4+J3ncJKo+mUHZ/HtIPmESTUVfULN8Lr0ujfR4aI9Lwh5nfYjfcMVjj0vG3TOShyMxHUdiuqUNdieORB+uzI49I9keh9tLYp/j2f7eQ9hc8biTe1G77TPKV8+j74TojmHzgkgeeedH8qhY+y8KF9xKnzNuJbHPcfjrI9sKm92JIy6yfQmH/DSVRx6YDAdbCNSX01CyHrsrHk9aXxyeJBz7dXxgc8bj8CQTn2ldhzpbKNDE7o2v0a9gMsYBtzXChk8foqZ0FcdfGOlOdueGedjtbrzp+dhsLmrKVrNxyUNkDTi79da9ngO/S+Hyx1m96PfkHfdrgv5a1n98D1kDzsYdH1kvMnJPp2jFsyRnDid57+1tm5c+Smbu6R1+lac9Q4ZM5pNPbiQjcwxZWSdQWrqUbdsWcvIp/9fa5tPFkfVj3ImR9eOrr57Dm5BDcnIe4XCArUUL2LHjHcaf/FjrOPmDfsa771zG2rVP0TtnIsU73qG0dCkTz/yH5fcHg01sK3qNIUPa/lt0Jn+wgc82/40BWWcR786grmknn258mDhXGv2zJra2e2dVJI+vu7Ue2PO7LC98nEWrf89xeb/GH6zl4/X3MCDrbOLdkb/98sInyEoeRVJ8b0JhP9vKP2DjrgWcPMTaU6Jpmqzb8QoDe553yIKsoyU400lwWrdpNsNJgstnucoyvzCSx/69s31ZNps0Ty59Ew/sjW/p7udIceeQEZ+395meBWyoeocfDoysQy57PJnx1u2Ex55E2AwdMLyzNIfqea9qOkO9E0iyZ1Af2sMnNTOoDpYwKjF68PmPkkgeX9+6NtR7Oi+X/pHF1f9gUMLJ1AbLmF9+LznuYaQ6I/vbtyr/Rl/PKDJcuTSH6/mo+gV2tWzgB5l3tk53QfkDDEs4nRRnT+pDe/h35eP4zUbGJB2d5+BCZpD/q7+BrcHV3Jj4JGBQHY7sK+KNRFyGB4Bp9ZE8rvFG8igJbaUwuJIBjtE0mrW82fwsO0KbmJxwf+u0FzQ9wQDHKDJsvQniZ6X/Axb7F3BpfPTzstr/ESZhetr7UxrezuzGKfS09WO8u+O+N/JQ6sxqytlNA5Hj1d1sJ8FMIhUfqUbk+P0RM5LHTUYkj53mVjaykkGMpp5a5vMs29nEjUTz2GCupJJS+jOESkqZyWOYhLmI6Eml4zidfzKNLDOHPuSxhfXM51lOp+1eWr+tI//lpEsWYd+nK2j7o5E/cvjS6wlfFvnyP9vCWdhmRL+kyn5H5NmRfb8o1NhdjJkRvWxqe+0fGMEA9vusDxSGJ36f8G+i4RqrlmLsLCJ0y1/anr9Na7D/T/RLxewvPQYvPXbAdI6U0PJFBB6P5hF4KpKH44fX47w4kofz8j+A3YF/6k3gb8Y2fByu66ZYznCbu7Zi1ka7u7TljcR1y/8RmPkwwX8+juHrhfPHN2A/O/rApuOCq8Hfgv/pu6ChBlveKNy3PWO5GuW87FYMhxP///0O/E3Y+g3DfccLHd6JwddCNeU0zLmfcG0ltuQM4sZdgPe7v7K22WO91S7+pIswmxtoXDSD2pcfwBaXiGvQWBJ/8M3PkPg3LCVUVkTc5LbXl84WrC2nbMH9BOsrcSRmkDzmAtInWvMIVFnzcKX3JmfyNMoW3Ef14pk4kjLJuuC2A67cdEcDv/8wxe89zOZ5vyXYXIM7uRe9T72BrDHR59Zaaqx5lH4xCzMcZNu/72Xbv6PfH5PY53iG/TTyHRH+ujJWPx3dmJZVbafsy9mWNl3V7s0LCQWayB7S9s6xpbGcxtpor0iG4WDL59NoqCkCE+ISe9Fn+KXkjr6itY3DlcCY859l/Ud38+krP8TpTiKr30Tyx0W/r2TAmF9iYLBp6aM015fgikslI/d08scene5VAXJ6T+S44+9i3dqn+OLze/Am9uWEcQ+QnX1aa5vGRuv6EQ4H+PLLB2hqKsVu95CcnMepp06jV3b0mYOMjGM48aSHWbVqKmtWP4bX25uTxj/S+h09X9u+bSHBYBP9+h+9A5Wv2Qw7lXUb2bBrHi2BOuLdGeSkjeXs0VMtBUhd037bD0cC5495lo/W380rn/4QtzOJflkTGZcf/dsHgo18sO5O6ptLcNg9pCb054wRD5Df67uWae3cs5SaxiLOHNk1tqeHo6blwFu5W0L1rK1cyMnZv2qzmA2ZAd7Z/gB1/lIcNg8Z8XlMGjSNvJS2O3boCmyGnRL/Zpbt+icN4WoSbCn09ozgupwZ9HIPbm1XHbTmcXzSRbSEG/i4ZgYLKh7AY0skL24s3/VF97fN4VpeKfsTtaFy4myJ9HIP5bqcl+jjiT6CUBMs4aWSm2kIVZNgT6WvZzT/L2cOac7Df9bySNoTLuHLwLsA3Flr/fxelXAfJ+8tPirD+20/CPNW83OUhLZiNxwMdozl9qSZZOxzW1qL2cgLDXeyJ1yCy/DQ096fqxMeaO3mGqDJrOPlpoepCpeQYKQwxnUWP4i7CcdhfK9WR1nGIh4lerz6NyLHq5O4nkuIHK+Wc2Ae83iOnWzFgYMRjOUBZpJlRPMI0MIMplJCMR7iGcOp3MQUvEb0xOI13M4MHuVJ/peavbfJncXFR/Q7egCM9m5NGDRoUC6wNfjcu5DVOfcYdnWJdUd7DrqW5JqjPQddi/KwSj26X0nR5aRUH+056Fq0flilHf5XY/xX0Pphlar1wyL94D2x/9dJ0+elVam5g6s5A6Dfhg0bivZ9r/t+T4+IiIiIiMhhUNEjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMU1Fj4iIiIiIxDQVPSIiIiIiEtNU9IiIiIiISExT0SMiIiIiIjFNRY+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMU1Fj4iIiIiIxDQVPSIiIiIiEtNU9IiIiIiISExT0SMiIiIiIjFNRY+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITHMcqkFdIoSTO2NWuj5n4GjPQdfirTvac9C1GObRnoOuxR482nPQtXiaj/YcdC3xjUd7DroWbU+tkmuO9hx0LSnVR3sOupa0qqM9B12Lr/xoz0HXEbABaW2/pys9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMU1Fj4iIiIiIxDQVPSIiIiIiEtNU9IiIiIiISExT0SMiIiIiIjFNRY+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMU1Fj4iIiIiIxDQVPSIiIiIiEtNU9IiIiIiISExT0SMiIiIiIjFNRY+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMc1xNH6p6/23cc+bjWPjWmzVVdT87QWCx4xtfd+orSbu74/hWvYJtpJdhFNSCZx0Go3X3IiZnHrwab/3FnHTH8W+czuh7D40XXsT/lPP7OAl+s+Yi9+Gt2ZD4VqorYJ7XsAYMdba5s3Z8NHrsGU9NNTB9HcxsnIOY9pvwYxHYfd26NkHLrsJY1zXzqPl87dp+mA2wW1rMeurSL7lBVyD98sj4Kd+zgO0LHsd09+Ca8gJeC+7E3taj4NOu2nRDBrfeppwdTmO7IEkTPoDrvwxHbk4R1ywroKyfz1I46aPCTXVEd9vDFkX/hFXRu5Bx2ssXEbpa/fjL92EIymTtNMmkzruJ50z0x0o5G9g2wcPU7nx3wSbq3El9aTH6J+QfdwVBx2vZvsyti66n8aKTbi8mWSPnUzPgu6fx7ynB7U5vN+QSxh14h3tjlezZwOrPv0zVeWrcLmTyR38YwaNvg7DMDpqVjtNTf1WPlv7ELvLlxAyA6R4+3PamAdJSRzQ7ji7K5axdPX9VNdtIt6TyYiBkxnSr/uvH//a9DvWlM21DOvpHcXPRs056Hjba5axaOv9VDRuwuvKZGz2ZAp6dv889vXK7j+ytGYO52XcymnpVx20bWHjMl4rvZ9S/yaSHJmcljaZcandP4+5DVNZ3vIme0IlOAwnfRxD+X7CDeQ5jznoeBv8y5jdcD87g5tIsWXynfjJnBbXvfMImgFeYiqf8yElFBOPlxGM5XJ+Q4bR66DjrjGX8TT3s51NpJHJRUzmO0b3zgPgfdfbzPPMZqNjLdW2Kv5W8wLHBMYecrwvHcv4q/d+tto34QtncmnTZL7f3Pl5HJ0rPU2NBEcU0PDr37X5tq28DFt5KQ3X3UL1S69Rf8dfcKxYjvdPvznoZB2rv8T7p5vwn/U9ap6fj/+s7+G9/QYca1d2xFIcOS2NMLgArmo7j0ibJhg9HiZdf9iTNb/6EqbcBKd+Dx6dH/n3gRswN3TtPMyWRpwDCvD+uP086mfdg//zt0i65mFSfjcDs7mBmr9eixkOtTtO87KF1M+6l/hzf0HqHfNwDCigZurVhCp3dcRidAjTNNnx3HUEKorIvvxxcm+cizM1m+3Tfk7Y39jueP49xRQ/fQ1xuQXk3jiP9AnXUjrvbmpXvdWJc98xti66nz2F7zPwu1MomLyQ3uN+ybYPHqRszbx2x2muLmbdK9eQlF3A6CvmkXPCtWx9524qNnT/PM75yceWnxPOfBKA7H7faXecgL+exW9eiTsundPOf4URJ9zO5tVPs3nNs5012x2mrqGY1z/8CYnxOXxn/PNcNOF1jh1yIw57/EHHefvTa8hKK+DC0+cxMv9aPl11N1t3dv/1A6Bv8olcd9zHrT8/GjrtoO2rm4t5Zd01ZCcVcMXoeZyQcy3vbL2bDRWxkQfAqto3KW5eTZIj85Bt9/iLebr4GnLjCrgxdx4T0q9lXundrKrt/nn0sPfjUu8d3JX2Gr9L+QcZ9hweqZlMTbii3XHKQ8VMrbmGAY4C7kidx7nx1/KP+rtZ3tK982ihmULWcTG/5BFe5TYep4Ld3MlkQmaw3fFKzGL+l2sYTAFTmccPuZZp3M1is3vnAdBkNDIiUMCvGw5yvLqfXbZifpN8DSMCBTxXPY+fNl7Lwwl3856r8/M4Kld6/N+5EACjek+b74cG5FN/399aX4dz+tJ43a0k3nItRkM9ZoK3zfE8c54ncMxYmq74JQBNV/wSxxdL8cx+nvq7Hj7CS3HkGKdH8jBr284DwLjgikibTasPf8ILnocRYzEuR5BE1AAAGl9JREFUjuRB719irl4aGX5L183Dc2Ikj3Bd23mEG+to/uifJF55L65hJwGQOHkKe249ncC6xbiGn9zmeE1vP4vnxO8Td+rFkXEu/SOBNR/R9P5MvD84eEHdVQQqimjevoLcm+bj6TUYgKyL7qTurpOo/fJfpIz9UZvjVX86C0dyJj0u/CMA7qwBNG1fyZ4PniFp5NmdNv8doW7nl2QOu4CUvicA4EnOoXTVK9TtXkXm8AvbHKdkxSxc3kz6nxnJI943gLrdK9m17Bl8g7p3Hp74DMvr3dvexZuci6/n8e2Os6NwAaFgE8ee8gB2h4ektHzqqwspXPMsecN/3q2v9ixfP5XszJMYOyK6k05K6H3QcdYXzSLek8m4UZH1IyVxAOVVK1m9+Rn6ZXfv9QPAYXPhdWUcuuFeK0pm4XVlcmb/SB6++AHsrlvJsl3PMMjX/fOoCuxkftk9XNP7OZ4uvvqQ7T+tnkWyI5MLe0TyyHIPYHvTSj7Y8wwjk7p3HuM8F1he/zjh93zU/ArFwfUku9ret77fNIsUeyaXJkby6OUYwNbgSt5qfIYx7u6bR4KRyJ+xnvj5lXkX13MexRSSS9tX1d9kFmlkcq0RyaM3A9hormQuz3Ai3TcPgO+0RPap1Ub7x6v7m+uZhS+cyc0NkTxyQwNY51zJP+Ke4XR/5+bRbZ7pMRrqwenCdHvabeNYs4LA8SdZhgXGjsex+suOnr2u6asVUGDNg4Lx8FX3ziO4bQ2EAriGjW8dZk/rib3nAAKb2142M+gnuG1ta5H0Neewkwi2M05XFA76ATAcrtZhhs2G4XDRuPXzdsdr2raChIHWZU/IH0/zjjWYoUDHzGwnScw5hj2F79FSuxuA2h1f0FC6ntR+be+gAep2riAl15pHar/x1JesIdzN89hXMNDAzq3/ou+giw/abk/ZCtKzxmB3RLevmTnjaW4so7F+R0fPZocxzTDFJYtISczjzcVXMWPhCcx//wds2bHwoOOV7VlBdqZ1/cjJHE9F9RrC4e6/fuyo/ZzHlo1j2udn88bm22nwVx60/c66FeSmWPPolzqekvo1hLp5HiEzyIxdv+GM9F+S5W7/dsd9bWtawcAEax75CePZ0byGkNm989hX0PTzQfNs4gwvvR1D2m1XGFzBMKc1j2Gu8WwLriEYQ3kANFIPgJfkdtt8xQoKsOZRwHg2E3t5HI41zhUc77fmMdY/nq8cawjSuXl0i6LHqKslfvqjNJ9/MTjavzhlq6wgnOazDAun+bDtKe/oWeyaqisgxZoHKT6o6t55hGsqwGbH8Fqf77IlpROubfsSfLiuCsIhjCTfgePUdJ883Jn9caRmU/7GI4QaqzGDfirfm0awpoRQXfvLEayrwJGYbhnmSPRBOEiooaqjZ7tD9Z94OwmZg1n+xGks/ssw1sz8KX1P+y1peae3O46/oQJngjUPZ4IPMxwk2NS989jXjsLXCYUC9Mn7/kHbNTdW4I6z5uGOi3xWWhrbv62lq2tqqSQQbGTlxqfIzhzPOSc+S/+c7/L+579le8l77Y/XXEGc25qHx+3DNIM0+7v3+tEv5WTOG/gAk4Y9x4R+/8PuulXMWns5wbC/3XEa/BUkOK15JDh9hM0gTcHuncfbFY8Rb0vhxNRLDnucumAFiQ5rHokOH2GCNIS6dx4AK1ve41flBfyiYiT/bnqOm5OfJdnma7d9bbiCJJs1jyTDR4gg9eHun8fXAqafZ7if4zkdn9H+88PVVJCCNY8UInnUEjt5HK49tgrSwtY8UsM+QkaQaqNz8+jw29tcby3AOyX68GztQ9MJjv4GD443NZJ46y8IZ2TReN0t3/j3G6YJXejWDPP9BfD4Pg8T3zEdY1gHPki//6J3sTyalyyg7oVoHsk3Tv/2HQuY5qHb7L/sZhvDupCaLxZQ8s9oPr2vmk7Oz/7K7jm3semOsWCzk5A3joTBpxzG1PZfdrPt4V1Y2doFFL4VzWPoj6ZTv3sVtTu/YMgPnsCd1Iva4uUUvTcFT3I2qf3bz8WIgTyKNy9gxSfRPMadPR1fj+jnp2jDHHr2PQN3XNqhJ3bAZ8Nse3gXtrl4AZ+siOZx1rinAOjT8wxG5P0cgPSUIVRUr2H9lhn06dF+YdzGxrOd4V3X2rIFvFUYzeNHQ6czNOO81tcZCYPIShjGk59PoLDqfQaln9X+xPZbD8xumMcXNQv4Z0k0jyt7P8Xymle5KXf+t5ha989jSfMCXqiL5nFj8nTyXWMY7BrLHWnzqA9X8WHzHJ6svZE/pERuYWvPAdvTvXl0p1tj3zcX8DjRPO5gOsOMyPY0ZAZ5mFtooI7beeIwptZOHt1o/XjLvYAp3mgeD9VMZ3Tw2x2ftbt+dHIeHV70+MdPoHrYqNbX4Yyswx+5sYGk31wDQO1fngS3+6DNw+k+bHusZyWNqkrCqe2foeh0x0+A/GgepH+DPL6pFB9U7XeWtqbywKs/R5Fr1ATS7ojmYUs9dB62ZB+EQ5j1VRiJ0YO5cN0enPnHtT1OYirY7Jj7XdUJ11ViS+o6eezPO3QC/fpE83EkZ2Fzeuh383xCTXWYoQAObxpFf/0Rnpzh7U7HkegjWGddF4L1lWBzYE9I6bD5P9LS8iaQ2Cuah8ubxdpZVzDowqmk5U0AICFzMPVl69m57Jl2ix5Xgg9/gzWPQGMlhs2BI6775NGjzwROz4zmERcf/fxUV66numINQ8fcfMjpeOJ9B1zRaWmO3PK0/xWgrqxPjwlknh7Nw+NOwzAcB/TSluLtz5ad7d/iFufx0dRizaO5pRLDcOBxdZ/1Iy9tAr0So3l4XQduXxPdWSS6sqhqKmp3OgkuHw1+ax6NgUpshoM4R/fJY6h3An36RfNYWj2HumA5f94cvVU6TIiF5Q/ycdXz3J73YZvTSXT4qAta86gPVmLDQYK9++QxyjWBO9KieaTaIuuH24gny96XLHtfBjhH8/s9Z/FR88t8L+G6NqeTZPMd0NFBrVmJHQcJRvfJ43gmkE80j3QieYTMIH/hZraxkXt5kSTj4L0Ip+CjGmse1UTySKT75DHeP4FhVdE8MsLf7ng1Leyj0mbNo8pWid10kGx2bh4d35FBgpdwOx0PHFRDPUm/uRpMk9qH/w7xCYccJTh8NM5li2m+dHLrMOeyxQRHFHzz399BjHgvxH+LPL6NwaNhxWK4KJoHKxZHeorrImxxXoj7Znk4+g4HuxP/2k/wnPA9AEJ7SgjtLsSZ1/ayGQ4Xjr7D8K9bjPu4aC9WgXWLcR17kLObR5nd48XuaTsfe1wiAP7yIpp3rCHj7BvanU5c39HUr33HMqxh02I8OcMx7M4jN8MdzOH24nBH8wi21GOGAxiG3dLOMOxghtudTmL2aCo3WfOoLlqMt8dwbN0oD6fLi9PV9vqx7avZxHuzyeh14iGnk5Y5mrWfPUgo2ILdETm5VLZzMZ74TOK9h+4av6twOb24nNY8MlJHUFO31TKspr4Ib3z7Xc5mpo1m+27r+rGzbDG+lOHYbN1n/XA7vLgdB9++Ngb2UOcvw+tq/yx+duJoNlVa8yiqXkwP73Ds3SgPj92Lxx7N49S0Kzk22frg/vTiqxid9F3GJrfdKQxA37jRrK235rGpYTE5nuHYje6TR5zNSxyH3v+aZpgA7d/+OMAxmi/91jzW+RfT1zEcRzfKI97wEr9fHkEzwF+4me1s5B5eJNU4dAcggxnNUqx5rGAxeXSvPBJMLwnmf368Ojwwmo9c1jyWuRYzODgcB52bx1F5pseorca+cT32LZsAsO/Yjn3jeozKvWfhG+pJuvEqjLpa6m+/H6O5CaOyPPJ+IPrBS/r15cQ/8VDr6+aLf4bziyV4XngKW1EhnheewvnFUpp/fHmnLt83ZdZVY25ZD9siebB7O+aW9Zj7PHtjVpVH2uwqigwoLoy0qauOtrn9cszno3nwvZ/BqiWYLz+FuaMQ8+WnYPVSOL9r5xGurya4fT3BnZE8QmXbCW5f3/rsjS0+Ec/JP6Dh5Sn41y0msG0ddX+/BXvOIJxDowd4e247h6Z3X2p9HXfWz2n+ZC5NH75McFch9f+4m1B1GXGnTurcBfwP1a58g4bNS/BXFlO35h22T78S77CJJAyKnq3cNfNWds28tfV1yrhJBKpLKZ1/Dy2lhVQvfZma5XNJO/XKo7EIR4zD7SWp9/Fs++AharYvpbm6mNLVr1K+dh5p+dHvo9r4+q1sfD2aR4/Rk/DXlbLlnXtorCikZOXLlK2eS6/ju3ceXwsGmygufI2+g37U5u0laz97iI8XRrcDOQO+h90Rxxcf/o7aPRvZVfQ2m1ZNY0A377kNYETeZLbufIOvimZTW7+Nr4rmsGXnQob0u7S1zQef38oHn0fXjyG5k2hoKmXJqnuoritkQ9HLbNo+lxF53Xv98IcaWLT1AXbWfklN8w621yzln+t/SbwzjYFpE1vbvb7xVl7fGM1jdI9J1PlLeWfLPVQ0FrKy5GVWl83l+F7dOw+vI50e7nzLjx0niXYfme7+re1m7rqVmbuieYxLmUR1oJT5pfdQ2lLI0uqXWV4zl1PTunceTeF6Xm14hC2BlVSGdlEUWMMzdb+nKlzCce7oycK/197K32ujeZwWN4mqUCkz6+9hV7CQD5te5pPmuZwd373zCJlBHuAGNrCC3/IwBgZVZjlVZjktZnNru0fMW3nEjOZxDpOooJTp5j0Um4W8bb7MIubyfbp3HgC1RjUb7evZ4ogcn+2wbWejfT2VRvR49S7vrdzljebx/eZJlNlLmZpwD0X2Qha4X2ahey6XNHV+Hkfny0k/WoT3nt+3vvbefzsAjVdeT9PkX+PYsBbn2hUApP7Y2p3dvl9kattZjJHVs/W94IhjqP/fh4mfNpX4vz9GKLs39X9+hOA+t9d1ScsWwaPRPPhbJA8mXQ+X/Dry/zdmwaxoN97cFbntjxvugzMuivy/pBh80TyMIcdg3vIwvDQVZj4GPXrDLY9gDOraefhXLKLu2Wge9c9H8og//3oSLojk4Z30B+ptDmqfvAkz0IxryDiSJ0/BsEXP+IdKthKujz4k5zn+XMz6Khpff4JwTRmO7HySb5iG3ZfdSUt2ZATryil77X6C9ZU4EjNIPvYCfBN/ZWkTqN5tee1K603vq6ZR+tp9VH86E0dSJlkX3Nbtu6sGGHT+w2z74GE2vvZbgs01uJN60Wf8DfQ85rLWNl/37PY1T0pvhv5wGlsX3UfJipm4vJn0m3hbt++u+ms7tywkFGyiz8CL2ny/uamchrri1tdOVyInnvMMqxbfxfsLfoDTlUze8CvJG/7zzprlDpPbayInjb6LlRufYsmqe0jy9uXUYx+gT4/TWtvUN1rXj8SE3pw1bhpLV9/H+qKZxHsyOWHkbd2+u2oDO+WNG1lbPo/mYB1eVwZ9ksdywaCplitCtS3WPFI8vfnh0Gks2nofK0pm4nVlMrHfbTHRXfXhqA5Y80hz9eaq3tN4rfQ+Pq2eSZIjkwuybuv23VXbDDu7gpv5uPmfNISrSbCl0M8xgv9JmUFvx+DWdnvC1jwy7L25MXkasxru4/2mmaTYMrnEe1u37q4aoIISlvIuADdh3ZbewH2csXdYOdY8ehi9ucOcxt+5jzeYSRqZXM1tnGh07zwAPnIt4p7E6PHZ/YmR47MrG69ncmPk+KzUbs2jV7g3D9VM41Hvfcz1zMQXzuSmhts6vbtqAMNs5+HvQYMG5QJbq/75LuGe3ef2ho7k676dGHUIX/fp9KxTpB9+t/X/FdL1ebHIUB4W6QfvJfm/jranVj6tHxZpysNC21MrbT+idtt28IO0MwD6bdiwoWjf97pFl9UiIiIiIiLflooeERERERGJaSp6REREREQkpqnoERERERGRmKaiR0REREREYpqKHhERERERiWkqekREREREJKap6BERERERkZimokdERERERGKaih4REREREYlpKnpERERERCSmqegREREREZGYpqJHRERERERimooeERERERGJaSp6REREREQkpqnoERERERGRmKaiR0REREREYpqKHhERERERiWkqekREREREJKap6BERERERkZimokdERERERGKaih4REREREYlpKnpERERERCSmqegREREREZGYpqJHRERERERimooeERERERGJaSp6REREREQkpqnoERERERGRmKaiR0REREREYprjUA2qUiCY3hmz0vVV+I72HIiIiIiISFuaHEBa2+/pSo+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMU1Fj4iIiIiIxDQVPSIiIiIiEtNU9IiIiIiISExT0SMiIiIiIjFNRY+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMU1Fj4iIiIiIxDQVPSIiIiIiEtNU9IiIiIiISExT0SMiIiIiIjFNRY+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMOypFj/ftt8m+6ir6n3AC+YMGEbd06QFtsm6/ndyJE8kbOZL+J5xAr1/+Eldh4aGn/dZb9D33XPKGD6fvuefi/fe/O2IROtSM5BlM6DeBEXkjuKjPRSyPW37Q9svilnFRn4sYkTeCM3LPYGbyzE6a086hPKyUh5XysFIeVsrDSnlYKQ8r5WGlPKJiIgvTNNv8yc/Pz83PzzcdxcVtN/gPfhLnzjXTHnvMTJw718zPzzfjliw5oE3yzJlm3GefmY7iYtO9Zo3Z69przf7jx5v4/e1O1/PFF+bAIUPMtMcfN12bN5tpjz9uDhwyxPSsWHFE5vuIB9HGz7+8/zKHDhxqzk6ebW52bTbvyrjLHJ032tzp2Nlm++2O7eaovFHmXRl3mZtdm83ZybPNoQOHmm963+yU+VUeykN5dJ0f5aE8lIfyUB7K4785i2JHsZmfn2/m5+fn7v9uu6N1ZNHz9Y+tsrLdomf/H9f69WZ+fr7pLCxst03PG24ws6+4wjIs+/LLzR433XRE5rczVqwf9v6heVvWbZZhZ+aeaT7oe7DN9lN8U8wzc8+0DPtD1h/Mi3tf3CnzqzyUh/LoOj/KQ3koD+WhPJTHf3MWByt6usUzPUZjI8mvvkqgVy+COTnttvOsWEHjSSdZhjWOH0/cl1929CweEX78rPWs5aQG6zKc1HgSX3raXoYVnhWc1GhtP75hPGs8awgQ6LB57QzKw0p5WCkPK+VhpTyslIeV8rBSHlbKIyqWsujSRU/yjBnkFRQwsKCAhA8/ZMdzz2G6XO22d1RUEPT5LMOCPh/28vKOntUjospeRcgI4QtZlyE9mE65o+1lqHBUkB5MtwzzhXwEjSBV9qoOm9fOoDyslIeV8rBSHlbKw0p5WCkPK+VhpTyiYimLDi96EhcsIK+goPUnbvnBH3zaV93557Nt7lyKX3oJf24uPW+4AaOp6Rv9fsM0wTC+6WwfVQYHzm9bw9p7z8Q85DjdifKwUh5WysNKeVgpDyvlYaU8rJSHlfKIioUsHB39C+onTKB51KjW18GsrMMeN5yYSDgxkUBuLk2jRpF3/PF433qLugsvbLN90OfDUVFhGWavrCS039Wfrio1lIrdtFNut1bOlY5KfMG2l8EX9FHhsC5zpb0Sh+kgJZTSYfPaGZSHlfKwUh5WysNKeVgpDyvlYaU8rJRHVCxl0eFXekyvl0Dfvq0/psfzraZjAJgmRqD9ewGbR48mfvFiy7D4xYtpKij4Vr+zs7lwMax5GIvjrcuwOH4xBc1tL8Po5tFtth/ePBwnzg6b186gPKyUh5XysFIeVsrDSnlYKQ8r5WGlPKJiKov2+j/oyN7bbFVVpnvdOjNuyRIzPz/fTJozx3SvW2fay8pMTNN0FhWZqU89ZbpXrzYdO3eans8/N3tde605YMyY1jaYppnzs5+ZvgcfbH3t+fxzc+CQIWbqk0+azs2bzdQnnzQHDh3a7bqsHjZwmDknaY652bXZ/HPGn83ReaPNHY4dpolp3tLjFvOWHre0tv+6W8C7M+42N7s2m3OS5pjDBg6LiS4SlYfyUB7KQ3koD+WhPJSHsjjcn4P13tbht7e1xbtoET1+//vW1z1uvx2Ayuuvp/LXv8Z0uYhftozUZ5/FXldHMD2dpjFj2D5rFqGMjNbxnMXFBHr2bH3dfMwx7H74YXxTp+J77DH8vXuz+5FHLLfXdXXn1p9LVVkVT6Q/QZm9jHx/PtN2TiM7mA3AbsduS/vewd5M2zmN+zLuY2byTDJDmdxWdhtn1599NGb/iFMeVsrDSnlYKQ8r5WGlPKyUh5XysFIeUbGShWGaZptvDBo0KBfYuuXddw/aTfR/E7P7P4cmIiIiIhKTdjh2cEb/MwD6bdiwoWjf97p0l9UiIiIiIiL/KRU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMU1Fj4iIiIiIxDQVPSIiIiIiEtNU9IiIiIiISExT0SMiIiIiIjFNRY+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMU1Fj4iIiIiIxDQVPSIiIiIiEtNU9IiIiIiISExT0SMiIiIiIjFNRY+IiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIxTUWPiIiIiIjENBU9IiIiIiIS01T0iIiIiIhITFPRIyIiIiIiMc1xkPfsAI6Skk6ala5vx8HSEhERERGRo6bE0Vq32Pd/72CH8T0B+lx6aQfMUvd0Rv+jPQciIiIiInIIPYHCfQccrOj5DDgZ2A2EOnCmRERERERE/lN2IgXPZ/u/YZim2fmzIyIiIiIi0knUkYGIiIiIiMQ0FT0iIiIiIhLTVPSIiIiIiEhMU9EjIiIiIiIx7f8DKfgbRdcNsVYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3160a8f240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_sarsamax = q_learning(env, 5000, .01)\n",
    "\n",
    "# print the estimated optimal policy\n",
    "policy_sarsamax = np.array([np.argmax(Q_sarsamax[key]) if key in Q_sarsamax else -1 for key in np.arange(48)]).reshape((4,12))\n",
    "check_test.run_check('td_control_check', policy_sarsamax)\n",
    "print(\"\\nEstimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\")\n",
    "print(policy_sarsamax)\n",
    "\n",
    "# plot the estimated optimal state-value function\n",
    "plot_values([np.max(Q_sarsamax[key]) if key in Q_sarsamax else 0 for key in np.arange(48)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 4: TD Control: Expected Sarsa\n",
    "\n",
    "In this section, you will write your own implementation of the Expected Sarsa control algorithm.\n",
    "\n",
    "Your algorithm has four arguments:\n",
    "- `env`: This is an instance of an OpenAI Gym environment.\n",
    "- `num_episodes`: This is the number of episodes that are generated through agent-environment interaction.\n",
    "- `alpha`: This is the step-size parameter for the update step.\n",
    "- `gamma`: This is the discount rate.  It must be a value between 0 and 1, inclusive (default value: `1`).\n",
    "\n",
    "The algorithm returns as output:\n",
    "- `Q`: This is a dictionary (of one-dimensional arrays) where `Q[s][a]` is the estimated action value corresponding to state `s` and action `a`.\n",
    "\n",
    "Please complete the function in the code cell below.\n",
    "\n",
    "(_Feel free to define additional functions to help you to organize your code._)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_sarsa(env, num_episodes, alpha, gamma=1.0):\n",
    "    # initialize empty dictionary of arrays\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "    # initialize performance monitor\n",
    "    plot_every = 100\n",
    "    tmp_scores = deque(maxlen=plot_every)\n",
    "    scores = deque(maxlen=num_episodes)\n",
    "    # loop over episodes\n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # monitor progress\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        \n",
    "        ## TODO: complete the function\n",
    "        \n",
    "        # initialize score\n",
    "        score = 0\n",
    "        # begin an episode\n",
    "        state = env.reset()\n",
    "        # get epsilon-greedy action probabilities\n",
    "        policy_s = epsilon_greedy_probs(env, Q[state], i_episode, 0.005)\n",
    "        while True:\n",
    "            # pick next action\n",
    "            action = np.random.choice(np.arange(env.nA), p=policy_s)\n",
    "            # take action A, observe R, S'\n",
    "            next_state, reward, done, info = env.step(action)\n",
    "            # add reward to score\n",
    "            score += reward\n",
    "            # get epsilon-greedy action probabilities (for S')\n",
    "            policy_s = epsilon_greedy_probs(env, Q[next_state], i_episode, 0.005)\n",
    "            # update Q\n",
    "            Q[state][action] = update_Q(Q[state][action], np.dot(Q[next_state], policy_s), \\\n",
    "                                                  reward, alpha, gamma)        \n",
    "            # S <- S'\n",
    "            state = next_state\n",
    "            # until S is terminal\n",
    "            if done:\n",
    "                # append score\n",
    "                tmp_scores.append(score)\n",
    "                break\n",
    "        if (i_episode % plot_every == 0):\n",
    "            scores.append(np.mean(tmp_scores))\n",
    "    # plot performance\n",
    "    plt.plot(np.linspace(0,num_episodes,len(scores),endpoint=False),np.asarray(scores))\n",
    "    plt.xlabel('Episode Number')\n",
    "    plt.ylabel('Average Reward (Over Next %d Episodes)' % plot_every)\n",
    "    plt.show()\n",
    "    # print best 100-episode performance\n",
    "    print(('Best Average Reward over %d Episodes: ' % plot_every), np.max(scores))\n",
    "        \n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the next code cell to visualize the **_estimated_** optimal policy and the corresponding state-value function.  \n",
    "\n",
    "If the code cell returns **PASSED**, then you have implemented the function correctly!  Feel free to change the `num_episodes` and `alpha` parameters that are supplied to the function.  However, if you'd like to ensure the accuracy of the unit test, please do not change the value of `gamma` from the default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 10000/10000"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3160a8bf98>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.02\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "**<span style=\"color: green;\">PASSED</span>**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 1  0  1  1  2  2  1  1  1  2  2  2]\n",
      " [ 1  1  1  1  1  1  1  1  1  1  1  2]\n",
      " [ 1  1  1  1  1  1  1  1  1  1  1  2]\n",
      " [ 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  0]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f31609780b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_expsarsa = expected_sarsa(env, 10000, 1)\n",
    "\n",
    "# print the estimated optimal policy\n",
    "policy_expsarsa = np.array([np.argmax(Q_expsarsa[key]) if key in Q_expsarsa else -1 for key in np.arange(48)]).reshape(4,12)\n",
    "check_test.run_check('td_control_check', policy_expsarsa)\n",
    "print(\"\\nEstimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\")\n",
    "print(policy_expsarsa)\n",
    "\n",
    "# plot the estimated optimal state-value function\n",
    "plot_values([np.max(Q_expsarsa[key]) if key in Q_expsarsa else 0 for key in np.arange(48)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}