kbrl_second_agent.ipynb

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    "colab": {
      "name": "Copy of kbrl_finalproj.ipynb",
      "version": "0.3.2",
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      "default_view": {},
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
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  "cells": [
    {
      "metadata": {
        "id": "XW3hgbfeT2p4",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Cloning github repo and imports"
      ]
    },
    {
      "metadata": {
        "id": "JQEeD6gCFEE-",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 122
        },
        "outputId": "d99c0d70-8023-47c5-f976-95b4fd5c31f8",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524972936520,
          "user_tz": 240,
          "elapsed": 2039,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "!rm -rf comp-767-Final-Project/; git clone https://github.com/navin-mordani/comp-767-Final-Project.git; cp comp-767-Final-Project/environments.py .;\n",
        "import environments\n",
        "import numpy as np \n",
        "import sklearn.metrics.pairwise as kernels\n",
        "import matplotlib.pyplot as plt\n",
        "import time"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'comp-767-Final-Project'...\n",
            "remote: Counting objects: 110, done.\u001b[K\n",
            "remote: Compressing objects: 100% (66/66), done.\u001b[K\n",
            "remote: Total 110 (delta 35), reused 83 (delta 25), pack-reused 17\u001b[K\n",
            "Receiving objects: 100% (110/110), 972.14 KiB | 24.93 MiB/s, done.\n",
            "Resolving deltas: 100% (37/37), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "pWbkHwRPJAfo",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Defining kernel"
      ]
    },
    {
      "metadata": {
        "id": "mKYt_ASgFFj6",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "def kernel(x,y, metric):\n",
        "  \n",
        "  # Kernels that worked: rbf, additive_chi2, chi2\n",
        "  \n",
        "  x,y = np.array(x), np.array(y)\n",
        "\n",
        "  if metric=='rbf': \n",
        "    return kernels.rbf_kernel(x.reshape(1,-1),y.reshape(1,-1))[0][0]\n",
        "  \n",
        "  if metric=='additive_chi2':\n",
        "    return kernels.additive_chi2_kernel(x.reshape(1,-1),y.reshape(1,-1))[0][0]\n",
        "\n",
        "  if metric=='chi2':\n",
        "    return kernels.chi2_kernel(x.reshape(1,-1),y.reshape(1,-1))[0][0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "argJGjXqJD6A",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Gathering data"
      ]
    },
    {
      "metadata": {
        "id": "3zl9aO-4FL_8",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "def gather_transitions(n_samples, max_episodes):\n",
        "\n",
        "  # Number of sampled transitions for each action\n",
        "  c0,c1,c2,c3 = 0,0,0,0\n",
        "\n",
        "  # Collection of historical transitions for each action\n",
        "  t0, r0 = [],[]\n",
        "  t1, r1 = [],[]\n",
        "  t2, r2 = [],[]\n",
        "  t3, r3 = [],[]\n",
        "\n",
        "  for i in range(max_episodes):\n",
        "    # Choose a random target to diversify states presented to agent.\n",
        "    target = np.random.randint(0,30)\n",
        "\n",
        "    # Initialize envt.\n",
        "    env = environments.EnvChaseTarget(6,2,target)\n",
        "    obs = env.reset(target)\n",
        "\n",
        "    # If all transition lists are full, no need to continue. \n",
        "    if c0==n_samples and c1==n_samples and c2==n_samples and c3==n_samples:\n",
        "      break\n",
        "    \n",
        "    # Gather data while episode is not complete and data lists are not full.\n",
        "    while True:\n",
        "      s = obs\n",
        "      action = np.random.randint(4)\n",
        "      obs, reward, done, info = env.step(action)\n",
        "      s_ = obs\n",
        "\n",
        "      if action == 0 and c0 < n_samples:\n",
        "        c0 +=1\n",
        "        t0.append((s,s_))\n",
        "        r0.append(reward)\n",
        "\n",
        "      if action == 1 and c1 < n_samples:\n",
        "        c1 +=1\n",
        "        t1.append((s,s_))\n",
        "        r1.append(reward)\n",
        "\n",
        "      if action == 2 and c2 < n_samples:\n",
        "        c2+=1\n",
        "        t2.append((s,s_))\n",
        "        r2.append(reward)\n",
        "\n",
        "      if action == 3 and c3 < n_samples:\n",
        "        c3+=1\n",
        "        t3.append((s,s_))\n",
        "        r3.append(reward)\n",
        "\n",
        "      # Episode is complete\n",
        "      if done:\n",
        "        break\n",
        "\n",
        "  return t0,t1,t2,t3,r0,r1,r2,r3"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "avPyRyTwJgsG",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Define $\\Theta$ tensor and $R$ matrix"
      ]
    },
    {
      "metadata": {
        "id": "LpqQPFmwILcE",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "def convert_gathered_to_matrices(metric, t0,t1,t2,t3,r0,r1,r2,r3):\n",
        "  # How many sampled transitions\n",
        "  m = len(t0)\n",
        "  \n",
        "  #Init Theta, R\n",
        "  Theta = []\n",
        "  R = []\n",
        "\n",
        "  # For each action-transition list and corresponding reward vector\n",
        "  for t, r in zip([t0,t1,t2,t3], [r0,r1,r2,r3]):\n",
        "    \n",
        "    # Append reward vector (m) to R matrix (m*M)\n",
        "    R.append(r)\n",
        "    \n",
        "    # Build two lists\n",
        "    X_states = []\n",
        "    Y_states = []\n",
        "    for s,s_ in t:\n",
        "      X_states.append(s) # start states\n",
        "      Y_states.append(s) # end states\n",
        "\n",
        "    # From both lists create a sheet (m*m)\n",
        "    theta = np.zeros((m,m))\n",
        "    for i,x in enumerate(X_states): \n",
        "      for j,y in enumerate(Y_states): \n",
        "        theta[i,j] = kernel(x,y, metric)\n",
        "    \n",
        "    # Stack this sheet\n",
        "    Theta.append(theta)\n",
        "\n",
        "  # Sheets to 3D matrix (m*m*M) then swap axes (m*M*m) \n",
        "  Theta = np.swapaxes(np.array(Theta), 0, 1)\n",
        "  \n",
        "  # Convert R list to vector then transpose\n",
        "  R = np.array(R).T\n",
        "\n",
        "  return Theta, R"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "e3V1Gv0-TuDG",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Do value iteration in matrix form"
      ]
    },
    {
      "metadata": {
        "id": "aJD5p5U2Tmg8",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "def do_value_iteration(Theta, R, gamma, n_iter):\n",
        "  J = np.zeros(R.shape)\n",
        "  for i in range(n_iter):\n",
        "    J_ = np.dot(Theta, R+gamma*J)\n",
        "    J_ = np.max(J_, axis=1)\n",
        "  return J_"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "13fr5uPFtICi",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Estimate action values given a new state $x$"
      ]
    },
    {
      "metadata": {
        "id": "RM7g7W-vUovo",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "def estimate_action_values(x, J, metric, gamma):\n",
        "  action_values = []\n",
        "  for a, (t, r) in enumerate(zip([t0,t1,t2,t3], [r0,r1,r2,r3])):\n",
        "    action_value = 0\n",
        "    for i,((s,s_),reward) in enumerate(zip(t,r)):\n",
        "      action_value += kernel(x, s, metric) * (reward + gamma * J[i,a])\n",
        "    action_values.append(action_value)\n",
        "  return np.array(action_values)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "LQjqOUU7zeKs",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Play game"
      ]
    },
    {
      "metadata": {
        "id": "j3a2a0xjVP_S",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "def play_game(env, vf, metric, gamma, n_episodes=100, random_policy=False):\n",
        "  \n",
        "  elapsed_episodes, num_wins, num_losses = 0,0,0\n",
        "  \n",
        "  while True:\n",
        "    if elapsed_episodes > n_episodes:\n",
        "      break\n",
        "    \n",
        "    # At each episode, reset environment.   \n",
        "    obs = env.reset(env.init_target)\n",
        "    \n",
        "    while True:\n",
        "      s = tuple(obs)\n",
        "\n",
        "      # Pick an action\n",
        "      if random_policy:\n",
        "        # Random policy\n",
        "        action = np.random.randint(4)\n",
        "      else:\n",
        "        # KBRL policy\n",
        "        action_values = estimate_action_values(s, vf, metric, gamma)\n",
        "        action = np.argmax(action_values)\n",
        "      \n",
        "      # Take action from state s\n",
        "      obs, reward, done, info = env.step(action)\n",
        "      \n",
        "      # End up in s_\n",
        "      s_ = tuple(obs)\n",
        "\n",
        "      if done:\n",
        "        # Episode is over\n",
        "        elapsed_episodes+=1\n",
        "        \n",
        "        # Get distance remaining from target\n",
        "        distance_from_target = s_[2]\n",
        "        \n",
        "        if distance_from_target <= 0:\n",
        "          # Player 2 won\n",
        "          num_wins+=1\n",
        "\n",
        "        else:\n",
        "          # Player 2 lost\n",
        "          num_losses+=1\n",
        "        \n",
        "        break\n",
        "        \n",
        "  return num_wins/(num_wins+num_losses)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "_ok7d5efa2rt",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Experiment: Studying the effect of $\\gamma$ on performance\n",
        "\n",
        "*   Number of gammas tested = 11\n",
        "*   Number transitions collected at data gathering step = 100\n",
        "*   Number of games played by agent using random/KBRL policies\n",
        "*   Performance measure = number wins / (number wins + number losses)\n",
        "\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "MO6rmeDYNlQ8",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 210
        },
        "outputId": "ff36eb78-b78e-47d3-fda3-45d327581412",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524950662890,
          "user_tz": 240,
          "elapsed": 1495594,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# Define envt conditions\n",
        "max_shots=6\n",
        "num_lives=2\n",
        "target_score=20\n",
        "\n",
        "# Initialize envt\n",
        "env = environments.EnvChaseTarget(max_shots, num_lives, target_score)\n",
        "\n",
        "# Define kernel metric\n",
        "metric='additive_chi2'\n",
        "\n",
        "# Gather transitions\n",
        "t0,t1,t2,t3,r0,r1,r2,r3 = gather_transitions(n_samples=100,max_episodes=10000)\n",
        "\n",
        "# Create Theta and R matrices\n",
        "Theta, R = convert_gathered_to_matrices(metric,t0,t1,t2,t3,r0,r1,r2,r3)\n",
        "\n",
        "# List of gamma values to plot\n",
        "gammas = [0.1, 0.3, 0.5, 0.6, 0.7, 0.8, 0.85, 0.9, 0.95, 0.99, 1.0]\n",
        "\n",
        "# Percentage wins lists for random/kbrl policies\n",
        "rand_list = []\n",
        "kbrl_list = []\n",
        "\n",
        "for gamma in gammas:\n",
        "  print(gamma)\n",
        "  # Compute value function by iterating over update rule\n",
        "  vf = do_value_iteration(Theta, R, gamma, n_iter=1000)\n",
        "  \n",
        "  # Play game according to random policy\n",
        "  random = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=True)\n",
        "  rand_list.append(random)\n",
        "  \n",
        "  # Play game according to KBRL policy\n",
        "  kbrl = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=False)\n",
        "  kbrl_list.append(kbrl)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.1\n",
            "0.3\n",
            "0.5\n",
            "0.6\n",
            "0.7\n",
            "0.8\n",
            "0.85\n",
            "0.9\n",
            "0.95\n",
            "0.99\n",
            "1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "faFXWlLaOF4k",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 416
        },
        "outputId": "f8928224-4fa5-4108-95cb-4c9677467c0f",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524950663838,
          "user_tz": 240,
          "elapsed": 911,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(gammas, kbrl_list, label='kbrl')\n",
        "plt.plot(gammas, rand_list, label='random')\n",
        "\n",
        "plt.scatter(gammas, kbrl_list, color='red')\n",
        "plt.scatter(gammas, rand_list, color='red')\n",
        "\n",
        "plt.xlabel('Discount factor')\n",
        "plt.ylabel('Percent win')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "print(kbrl_list)\n",
        "print(rand_list)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ufP6ywzvoEHrVqlUIDw9HTEwMPvzwQ1x99dXIyMi4rB9KREQUaqNHj4FOFwaH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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fbcb85eb5f8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "[0.6453546453546454, 0.6563436563436563, 0.6523476523476524, 0.6333666333666333, 0.6513486513486514, 0.6613386613386614, 0.6543456543456544, 0.6703296703296703, 0.6583416583416584, 0.6573426573426573, 0.6733266733266733]\n",
            "[0.13586413586413587, 0.13586413586413587, 0.14085914085914086, 0.14985014985014986, 0.15184815184815184, 0.16383616383616384, 0.15284715284715283, 0.14985014985014986, 0.14185814185814186, 0.15184815184815184, 0.13186813186813187]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "eA-0ZsMNcCDe",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Experiment: Studying effect of sample size on performance"
      ]
    },
    {
      "metadata": {
        "id": "MgOenreRhZsA",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "outputId": "3fbdbc97-653f-4a1d-a975-e4b5becc5102",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524954741240,
          "user_tz": 240,
          "elapsed": 3124482,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# Define envt conditions\n",
        "max_shots=6\n",
        "num_lives=2\n",
        "target_score=20\n",
        "\n",
        "# Initialize envt\n",
        "env = environments.EnvChaseTarget(max_shots, num_lives, target_score)\n",
        "\n",
        "# Define kernel metric\n",
        "metric='additive_chi2'\n",
        "\n",
        "# Try diff sample sizes\n",
        "sample_sizes = [10,30,50,70,80,100,200,500,1000]\n",
        "\n",
        "# Percentage wins lists for random/kbrl policies\n",
        "rand_list = []\n",
        "kbrl_list = []\n",
        "times = []\n",
        "\n",
        "for n in sample_sizes:\n",
        "  print(n)\n",
        "  \n",
        "  # Take first n samples\n",
        "  #s0,s1,s2,s3 = t0[:n],t1[:n],t2[:n],t3[:n]\n",
        "  #g0,g1,g2,g3 = r0[:n],r1[:n],r2[:n],r3[:n]\n",
        "  \n",
        "  # Gather n samples\n",
        "  t0,t1,t2,t3,r0,r1,r2,r3 = gather_transitions(n_samples=n, max_episodes=10000)\n",
        "  \n",
        "  # Time it\n",
        "  start_time = time.time()\n",
        "\n",
        "  # Create Theta and R matrices\n",
        "  Theta, R = convert_gathered_to_matrices(metric,t0,t1,t2,t3,r0,r1,r2,r3)\n",
        "\n",
        "  # List of gamma values to plot\n",
        "  gamma = 0.95\n",
        "\n",
        "  # Compute value function by iterating over update rule\n",
        "  vf = do_value_iteration(Theta, R, gamma, n_iter=1000)\n",
        "\n",
        "  # Play game according to random policy\n",
        "  random = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=True)\n",
        "  rand_list.append(random)\n",
        "\n",
        "  # Play game according to KBRL policy\n",
        "  kbrl = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=False)\n",
        "  kbrl_list.append(kbrl)\n",
        "  \n",
        "  # Done. Store time elapsed.\n",
        "  times.append(time.time() - start_time)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "10\n",
            "30\n",
            "50\n",
            "70\n",
            "80\n",
            "100\n",
            "200\n",
            "500\n",
            "1000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "v6kOo8X0DRjY",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 416
        },
        "outputId": "29695235-55a8-44aa-b5e1-d53512d3c16b",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524954741893,
          "user_tz": 240,
          "elapsed": 610,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(sample_sizes, kbrl_list, label='kbrl')\n",
        "plt.plot(sample_sizes, rand_list, label='random')\n",
        "\n",
        "plt.scatter(sample_sizes, kbrl_list, color='red')\n",
        "plt.scatter(sample_sizes, rand_list, color='red')\n",
        "\n",
        "plt.xlabel('Sample size')\n",
        "plt.ylabel('Percent win')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "print(kbrl_list)\n",
        "print(rand_list)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EQcCxY8ewceNGAMCOHTtQXR3nvtcSYRkGhiJl3MPmwTXeUUqjhl3bP2weV887ZM6bZRhU\nGjTot9ghJLD+nJCpTl0cRu/QBJoWm4L5HYSQ3CVZ8B4aGkJpaWnw2GAwwGz2bb1psVig1Wrx1FNP\n4bOf/Sx+9KMfSdWMhJQVqTA24Q6rcBbNjGu8pwjOeccRgEN73gBQVaaBxyvAEueXCkIiCZRC3dxE\npVAJyQdpm/gKrVwmiiIGBgZw3333oaamBg899BAOHDiADRs2RH19aakGMllq1zobjfqw42qTHqc7\nRwE5B2O5bsbXunjf7zOvrnTadabS6XwBXq9Xx3xu74gvSJcU+55bP6cU7388ADsvxnxtJmRjm3JJ\nOu7fua4RnO4cxTVXGrHyqsyOcEmB/gaTQ/cveZm4h5IFb5PJhKGhoeDx4OAgjEYjAKC0tBTV1dWY\nM8fXC1izZg3OnTs3Y/AeGUntvK/RqIfZbA17TKf0fTk4d2kY8hi95J7+cQAAKwjTrjOV0+nb1nPY\nYoNZN3MBGPOwb2rB7fLAbLaiyJ9YdPriMOaUpb9+7kwi3UMSv3Tdv9/uPQ0A2LiiJu/+vehvMDl0\n/5In9T2M9sVAsmHztWvXYt++fQCA9vZ2mEwm6HS+3qxMJkNdXR0uX74cPD9v3jypmhK3RNZ6B+e8\ndbE3dZfNZqmYfw1uYK13Py0XI7NgHnXg6JlBzDHpsGRuaewXEEJygmQ97xUrVqCxsREtLS1gGAY7\nduzAnj17oNfrsWnTJmzfvh2PP/44RFHElVdeGUxey6RE1npbrC7oNXLI4xjKDyasxTPnzYfPeVcY\n1GBAhVrI7Ow/0gVRBDZfS6VQCcknks55b9u2Ley4oaEh+PPcuXPx29/+Vsq3T1i8JVJ9BVqcqDTE\nN4w92yItvv/nUF6iokItJGE2hwcHT/bCUKTE6gZTpptDCEkhqrAWwuBf9hVr2Nzu8sLtEeJa4w0k\nuFQsGLwne/RVZVqM2z2wOTxxvR8hAPD28W64PQJuoVKohOQd+i86hFzGoUiriDlsPjIe/zIxYDJ4\nz2bOG0Cwh0+V1ki8PF4ebx7rhlopw/rl+ZdhTkiho+A9RVmREharc8Y12ZYE1ngDk8PmCRVpkU3+\n0wTKpNLQOYnXex/1Y9zuwYZrqqFWUilUQvINBe8pyopU8PIixifcUZ8T3Mc7jupqwGyHzUODt2+D\nkn5KWiNxEEJKoTavpFKohOQjCt5TxJNxPlldLb4570QS1rwRgzdtDUrid+LcEPotdqxprIx7dIgQ\nklsoeE8Rz1rvQDa6QYph8whz3nqNAjq1HH00503isLctUAqVet2E5CsK3lOUxxG8A8PmJVIkrPG+\nLUFDe94AUFmmgXnEAS8fu+46KVwXesZwrnsMy+rLUGOcucQvISR3UfCeIp5hc4vVBa1KBqU8vlrr\nXEL7eU8fNgd8ldYEUcTgiCOu9ySFKbAByRbagISQvEbBewpDHIVaRqyuuOe7Ad92o0BiS8VkU4O3\nP2mN5r1JNAMWO46fNeOKSj0WzSnJdHMIIRKi4D2FViWDUsFhKErP2+Hywunm4840B5Kf8wZ8w+YA\n0G+h5WIksv1HuiAC2EKlUAnJexS8p2AYBuVFKliizHkH1njHm6wGhC4Viz1fHWmdN0AZ52Rm43Y3\n/nKqD+XFKqxcZMx0cwghEqPgHYGhSAW7ywuHyzvtXCBZLZElOByX2LA5w0z21gPKi1WQcQwFbxLR\nW8e64fEKuGV1XTDHghCSv+i/8ghmSlqzjCe2xhsAOCaxYXO5jJ027MmxLCpKNei3TECMY3cyUjhc\nHh5vHe+BViXD+mVUCpWQQkDBO4KyGTYoCRZoSWDOO7hULM4tQafOdwdUlmngcPEYm6H6Gyk8753q\ng83hwU0raqBUxLcCghCS2yh4R1A2w1rvYGnURIbNE0xYmzrfHUDz3mQqQfCVQpVxLG6mUqiEFAwK\n3hHMOGzu73mX6GbR8042eBsCNc4p45z4HD9rxuCoA9dfVYlirSLTzSGEpAkF7whm7nm7oFbKEtqp\nKdjz5uMN3pGHPgPLxXqp500AiKJIpVAJKVAUvCMo0SnBsUzk4D3uSmiNNxCyVCzZOe/Avt7U8yYA\nznWP4WLvOK5eUB4s4kMIKQwUvCNgWQaleuW0YXOn2wu7y5vwTk2J7ioWbdhcrZShVK+kDUoIgJBS\nqNdSKVRCCg0F7ygMRSqM2dxhG4GMzKJACxB/whovCOAFMWrwBny9b8u4C0739DXopHD0DU/gw/ND\nqK8uwsLa4kw3hxCSZhS8oygrUkHEZIIaQn5OZI03EH/CmtfrOz9T8K72D48OWGiDkkK2r22y102l\nUAkpPBS8owhknFtChs5HggVaEu15+25zrOAdLI0aZc4bmExa66N574I1ZnPhvY/6YSpV45qFVAqV\nkEJEwTuKSIVaZrPGGwitbR4jeEfZDjQUrfUmbx7vhpcXsXl1XfBvixBSWCh4RxFprXewuppEc94e\nLw9g+nagoYJbg1LSWkFyur14+3gPdGo51i6tynRzCCEZQsE7ikhrvYM7ihUlOOcd537e8fS8S3QK\nKBUcLRcrUAdP9mHC6cXNK2uhkFMpVEIKFQXvKAwRgveI1QWVgkuoQAswuatYzJ53HHPeDMOgyqBB\nv8UR19Izkj94QcDrR7ogl7HYuKIm080hhGQQBe8olHIOeo08bNjcMu5MeMgcCF3nPfN+3vH0vAHf\nvLeXFzAUZc9xkp+OnTFjaMyJdUuroNdQKVRCChkF7xkYilQYHndBFEW4PDwmnN6Ek9WA1CasAUBl\nGdU4LzSiKOK1w51gANxCpVAJKXgUvGdQXqSClxcwbvdgdJZrvAHfnDeD1Mx5A0CVgTLOC83pzlF0\n9FuxYpERFaWaTDeHEJJhiU3eFpjQjHOXx5cJPpthc8DX+45V2zwYvGeY8wZouVgholKohJBQFLxn\nEEhas4w74fYv4ypNcFOSAI5lYu4qFkxYi9HzNpVqwDA0bF4ous02nLo4jIW1xaivplKohBCJg/eu\nXbtw4sQJMAyD7du3Y9myZcFzGzduRGVlJTjOt9zlhz/8ISoqKqRsTsICy8WGxpzg/clmhlkMmwO+\nnneqhs3lMhbGEjWt9S4QoaVQCSEEkDB4t7W1oaOjA7t378aFCxewfft27N69O+w5//Iv/wKtNnu3\nMiwvnux5B4a8Z5OwBvh73vEOm0fZzztUlUGDExeGYXN4oFPLZ9Umkv1GrC683z6AqjINli8oz3Rz\nCCFZQrKEtUOHDqG5uRkAUF9fj7GxMdhsNqneThKGkBKpwbrmSQybx93zjjHnDYRUWqOh87z2xtEu\n8IKIzU1zgsV+CCFEsuA9NDSE0tLS4LHBYIDZbA57zo4dO/DZz34WP/zhDyHG6JVmgk4th0LOYnjM\nCYvVCYWchSbBAi0BLMvEXR411rA5ELpBCQ2d5yuHy4sDH/agSKvAmsbsmlIihGRW2hLWpgbnRx55\nBOvXr0dxcTEefvhh7Nu3D1u2bIn6+tJSDWRxDCcnwmjUx3xOhUGDEasLLMvAWKKGyVQ0q/eSyzmA\nYWZ8T7nSN/xtLNfFbNviet8Q6pjDG9fvIZVMvnc+mOn+/fGd83C4ePzNxoWoripJY6tyC/0NJofu\nX/IycQ8lC94mkwlDQ0PB48HBQRiNk9sXfvrTnw7+fMMNN+Ds2bMzBu+RkdT2MI1GPcxma8znFWsU\n6BrwDfdXl2njek1EogiPV5jx9WPjvj26J2zOmO+j9pdcvdg1Mvs2JSnee0gim+n+eXkBfzhwHko5\nh6YrjXSfo6C/weTQ/Uue1Pcw2hcDyYbN165di3379gEA2tvbYTKZoNPpAABWqxVf+MIX4Ha7AQBH\njhzBwoULpWpKUgJrvYHZr/EGAJZl46+wFsect04th14jp4zzPHXkk0FYxl1Yv6yKEhIJIdNI1vNe\nsWIFGhsb0dLSAoZhsGPHDuzZswd6vR6bNm3CDTfcgK1bt0KpVGLJkiUz9rozqSxkBzHDLJPVgAQT\n1uKY8wZ8Gefnesbg8Qpxv4Zkv2ApVAbYtJpKoRJCppN0znvbtm1hxw0NDcGf77//ftx///1Svn1K\nhAbv2ZRGDWCZOBLW4izSElBZpsXZ7jEMjthRY9TNum0ku3x8eQTdZhuaFptgLFFnujmEkCxE3bUY\nwobNk9jIiePi73nL4u15U8Z5Xtp7uAMAFWUhhERHwXsmXi9qn/s/wcMrvvIgtE8+Bni9CV+Ki2up\nWPxz3kBI8KZ577zROWBF++URNMwpwRWVs1vZQAjJfxS8Z6Dd+QRqn/sxWMG3/tp0/iNonvs5tDuf\nSPhaqSyPGkBbg+afvcFSqHMz3BJCSDaj4B2N3Q7la6+AEwWU2YYh97pR5PQtB1C+9ipgT6y3yzEM\nBFGcsRiNhxfAML5eejzKi1SQcSwNm+cJy7gTbR8PoqZci6XzDZluDiEki9GuYlGwA/1ge7oBAJ97\n7wXYlRoEQirb2w12oB/CvPnxX88fkHlBhIyLHJwDWeNMnGUwWZZBpcG3QYkoinG/jmSn/Ue6IIi+\nUqj0b0kImQkF7yiEikoINbXgujrR/PFb4eeqayFUVCZ0vUBvWhBEIEqhOK9XiHu+O6CyTItu8wRG\nbe6k1qGTzLI7PXjnRC9KdApcR6VQCSEx0LB5NBoNXLfeHvGU69bbAI0mocuF9ryjmc167SpDIOOc\n5r1z2YEPe+Fy89i0qg6yBL/AEUIKD/W8ZzCxsxWAb46b7e2GUF0L1623BR9PRLDnHWPOO+HgHbJc\nbMkVNE+ai7y8gNePdkGp4HDj1dWZbg4hJAdQ8J6JTIaJ730fE9t3+Oa4KyoT7nEHcHH2vDXKxBaT\nVwUzzilpLVe93z6AMZsbt6yug0ZFpVAJIbFR8I6HRpNQclokbOicdxQerxB3gZaACoOvAlcvDZvn\nJFEUsa+tExzL4BYqhUoIiRNNrqUJF2fwTnTYXKWQwVCkRD8VaslJpy4Oo2doAk2LTTAUzb78LiGk\nsFDwTpNAz9sbJXjzggBBFBPONgd8SWsjVhccrsQrv5HM2nvYV5RlcxOVQiWExI+Cd5rE6nknWl0t\nVLDSGvW+c8r5rlGc7hxF4xWlmFMRec9eQgiJhIJ3mrCs71ZHS1hLJngHMs4paS237DlwHgCVQiWE\nJI6Cd5pI2fMOZJz3WShpLVeYRx1490QP6kw6LLmiNNPNIYTkGAreaRIzePOJ7SgWirYGzT2vH+mC\nIAJbqBQqIWQWKHinSawKa8n0vIu1CqiVHA2b5wibw4M/n+xFeYkaqxebMt0cQkgOouCdJlIOmzMM\ng0qDFgMjdvCCMPtGkrR4+4MeuD0C/uqG+VQKlRAyK/TJkSYsE+h5Rw6uyQRvwDd07uVFDI05Z9dA\nkhYeL483j3VDrZThFkpUI4TMEgXvNIlVHjWZOW+A5r1zxXsf9WN8wo0NV1dTKVRCyKxR8E6TWOVR\nJ3veUfYLjaHSQDXOs50gitjX1gWOZdC8ikqhEkJmj4J3msTqeXtTMGwO0Nag2ezE+SH0W+y4rrGC\n9l4nhCSFgneaSJmwBgCmUjVYhkEfVVnLWoFSqFuoFCohJEkUvNMk5lKxJOe8ZRwLY6mahs2z1IWe\nMZzrHsPS+WWoMeoy3RxCSI6j4J0mwZ63KE3PG/BtUGJzeGC1u2d9DSKNvW3+Xve11OsmhCSPgnea\nBHve/MzBO9H9vENRxnl2Ghix4/gZM+ZW6tEwpyTTzSGE5AEK3mkSu8IaDyC5nnclJa1lpf1tXRAB\n3HotlUIlhKQGBe80iTlsnuScNxCyQQn1vLPGuN2Nv5zqQ3mxCisXGTPdHEJInqDgnSZS1jYPqDT4\ntwaljPOs8fbxHni8AjatrgPH0n9uhJDUoE+TNJH5P7ilWioGADq1HEUaOQ2bZwmXx1cKVauSYf2y\nqkw3hxCSRyh4p0k6et4AUFmmxdCoMziHTjLnvVN9sDk8uGlFDVQKWaabQwjJI5IG7127dmHr1q1o\naWnByZMnIz7nRz/6Ee69914pm5EVYpZHTcGcNwBUl2kgAhiwOJK6DkmOIPhKoco4BjevpFKohJDU\nkix4t7W1oaOjA7t370ZraytaW1unPef8+fM4cuSIVE3IKpPlUaXZVSygMpC0RvPeGfXBOTMGRx24\n/qpKFGsVmW4OISTPxB0pRFGEIAjB/8Vy6NAhNDc3AwDq6+sxNjYGm80W9pynn34aX/va1xJscm5K\n17A51TjPPFEUg6VQN1MpVEIWVc21AAAgAElEQVSIBGJOxP3rv/4rfvGLX2BiwhcMRFEEwzD45JNP\nZnzd0NAQGhsbg8cGgwFmsxk6na805J49e9DU1ISampq4GlpaqoFsljtuRWM06lN6vZmUjbkAACqV\nIuL7Mv7gXl1ZDC6JofNGznePRmyetPx+6byHuaL94jAu9I7j2sZKLGuonPG5dP+SR/cwOXT/kpeJ\nexgzeP/Xf/0XXnrpJVRXVyf1RmLI+ubR0VHs2bMH//Zv/4aBgYG4Xj8yktphYKNRD7PZmtJrzmR8\n3DcHbbU5I77vhMMDlmFgsSTZYxZFyGUsLveOSf77pfse5ooX9p0GANx0dfWM94fuX/LoHiaH7l/y\npL6H0b4YxOzizZ07d1aB22QyYWhoKHg8ODgIo9FXpOL999+HxWLBPffcg3/4h39Ae3s7du3alfB7\n5BKOi72rWLJD5gDAMgwqDRr0WSaiFoQh0ukbnsCH54cwv7oIC2uLM90cQkieitnzXrRoER599FE0\nNTWB4yaHrT/zmc/M+Lq1a9fimWeeQUtLC9rb22EymYJD5lu2bMGWLVsAAN3d3fjmN7+J7du3J/N7\nZL149vNORfAGfPPeXYM2jFpdMBSpUnJNEp99bV0AfNt+UilUQohUYgbvwcFBKBQKfPjhh2GPxwre\nK1asQGNjI1paWsAwDHbs2IE9e/ZAr9dj06ZNybU6B7FMenrewGSltb5hOwXvNBqbcOO9j/phKlVj\nxZVUCpUQIp2Ywfupp56a9cW3bdsWdtzQ0DDtObW1tXj++edn/R65ItjznqG2ebJrvAMma5xPoHGe\nISXXJLG9eawLXl7A5tV1wdUFhBAihajB+6tf/Sr++Z//GTfeeGPE4b8DBw5I2a68E8+WoBplaqpw\nBZeL0VrvtHG6vXj7eA90ajmuX0qlUAkh0ooaLZ588kkAwPPPPx82101mh4tVYc0rJLWXd6iKwAYl\ntLtY2vzlZB8mnF58au0VUMrpvxdCiLSiBu/y8nIAwL333ovly5dj3bp1WLduXdJLxgpVPEVaUjXn\nrZRzKCtSUaGWNOEFAfuPdEEuY7FxZW2mm0MIKQAxo8Vbb72FBx98ECMjI/jWt76Fu+66K2KpUzKz\nwHaQkZZv8YIAQRRTNucN+IbOR21u2J3elF2TRHbsjBlDY06sW1qFIg2VQiWESC/mJCvHcWhsbITX\n64UgCGhra8Px48fT0ba8MtNSsVSVRg1VWabBR5cs6LfYMb+6KGXXJeFEUcRrhzvBALhlNW1AQghJ\nj5jB+4EHHgDLsmhsbMSqVavw+c9/Hno9ldNL1Ey7ikkRvEMzzil4S+dM5yg6+q1YeaUxmGtACCFS\nixktFi9eDI/Hg9OnT+PMmTO4cOECeJ72ik7UTAlrkgTvQNIaZZxLam+bbwOSLdfSBiSEkPSJ2fN+\n7LHHAABWqxVtbW34xS9+QUPnsxDoeXsj7MiWqr28Q1WVB3reFLyl0mO24eSFYSysLUZ9DZVCJYSk\nT8zgffbsWRw5cgRHjx7F2bNnUV9fHwzoJH7p7nkXaeTQKGWUcS6hYK+btv0khKRZzOD93e9+F2vX\nrsXf/d3fYenSpVSveZbSPefNMAyqyjS43G+FlxcgS2GvngAjVhfebx9ApUGD5QvLM90cQkiBiRm8\nC6F0aTqwDAMG6cs2B3wZ5xd6xzE05gzWOyep8caxLvCCiM1NdcG69YQQki7UHUsjjmMi97wlmPMG\nwjPOSeo4XF4c+KAXRVoFrr+qMtPNIYQUoFlFC6fTmep2FASWZWL0vFNbVrOKyqRK4s8neuFweXHz\nytqU/5sRQkg8YgbvL3zhC9Meu+eeeyRpTL7j2Mg9b6+Ew+YAZZynkpcX8PrRLijkLG66pibTzSGE\nFKioc94vvfQSnn32WfT29mLDhg3Bxz0eT7DuOUkMy8Tqeac2eBtL1OBYBn0WGjZPlSOnB2EZd+Hm\nlbXQqeWZbg4hpEBFDd6f+tSncPvtt+OJJ57AV77yleDjLMvCZDKlpXH5hos2bC7RnLeMY2EqVaN/\n2A5RFGmlQJJEUcTew51gGCqFSgjJrBmjBcdxePrpp2G1WtHV1YXOzk5cvnwZbW1t6WpfXmGjDJtL\n1fMGgEqDBhNOL6x2T8qvXWg+vjyCrkEbVjeYYCxRZ7o5hJACFnOp2COPPIJPPvkElZWTWbUMw2DN\nmjWSNiwfRe15+4N3qvbzDlVVpsUH54bQNzyBIi3teJWMQFGWzVSUhRCSYTGDd3d3N15//fV0tCXv\ncSwbHCIP5fH6asVL0fOuCiStWexYNKc05dcvFJ0DVrRfsqBhTgnmVdFGL4SQzIoZLebNmwe3252O\ntuS9qEvFJJrzBkIyzoco4zwZ+2gDEkJIFonZ82ZZFrfffjuWLVsGjptc0/qDH/xA0oblo2hLxaSc\n8w6s9aaM89mzjDvR9skgqsu1WDq/LNPNIYSQ2MH7+uuvx/XXX5+OtuQ9X8870rC5dMFbo5KjWKug\nQi1J2H9kshQqZewTQrJBzOD913/91zh79iw6OzvR3NyM8fFxFBXRnN9sxK6wJk212qoyDc50jsLl\n4aGUU0WwRNidHrxzohfFOgWuW0KlUAkh2SFm8P7Vr36FP/3pT3C73WhubsbPfvYzFBUV4ctf/nI6\n2pdXog6bSzjnDQCVZVqc7hzFgMWOORV6Sd4jX73zYS9cbh53Xn+FZF+uCCEkUTE/jf70pz/hxRdf\nRHFxMQDgG9/4Bg4cOCB1u/JSJnveANBvoaHzRARKoSoVHDZcXZ3p5hBCSFDMaKHVasGyk09jWTbs\nmMRPxjIQRUAQwwN4uoI31ThPzPvtAxi1uXHj8mpoVFQKlRCSPWIOm8+ZMwc//elPMT4+jv379+PV\nV19FfX19OtqWd1jWl+wkCCJYbjLxSfLgbaCtQRMliiL2tXWCZRhsWkWlUAkh2SVmtPj2t78NtVqN\niooKvPTSS7j66quxY8eOdLQt74QG71AeXgDLMOAkGtEoLVJCIWcp4zwBpy5a0DM0gaYlJpQVqzLd\nHEIICROz581xHJYvXx7cGvStt96CTBbzZSQCzr/MaOq8t8crSJoMxTIMKg0a9A/bIYgiWFruFNPe\nwx0AgC1UCpUQkoXi6nm/8847weO2tjY88cQTkjYqXwV63lODt1fi4A34apy7vQIs405J3ycfXO4f\nx+nOUSy5opSy8wkhWSlmxLh8+TIeffTR4PHjjz+O7u7uuC6+a9cubN26FS0tLTh58mTYuRdffBF3\n3303WlpasHPnToji9CzsfMNFGzZPR/D2V1qjofPY9h6mUqiEkOwWM2I4nU6Mjo4GjwcGBuByuWJe\nuK2tDR0dHdi9ezdaW1vR2toaPOdwOPDKK6/gN7/5DV544QVcvHgRH3zwwSx/hdwRreft4QXJ1ngH\nVFLGeVyGRh04etqMOpMOjVcYMt0cQgiJKObk9cMPP4w77rgDVVVV4Hkeg4ODYYE4mkOHDqG5uRkA\nUF9fj7GxMdhsNuh0OqjVavz7v/87AF8gt9lsMBqNSf4q2S+QkBap561RSptHUFXmzzintd4z2n+k\nC4IoYkvTHCqFSgjJWjEjxoYNG/DGG2/g/PnzYBgG8+fPh1qtjnnhoaEhNDY2Bo8NBgPMZjN0Ol3w\nseeeew6//vWvcd9996GuLv+X4wSGzfkI67yl2Ms7VEWpGgyAflouFpXN4cGfT/aiVK/E6sWmTDeH\nEEKiihm877vvPjz//PO46qqrknqjSHPaDz30EO677z588YtfxMqVK7Fy5cqory8t1UAmS21dbqMx\nvclIWq0CAFBSooHROPklxsML0KjkkrfHZNBgYMSR0vdJ9z2U0ttvnIXbI+DzWxagqrI4Le+ZT/cv\nU+geJofuX/IycQ9jBu/Fixfjxz/+Ma655hrI5ZNVptasWTPj60wmE4aGhoLHg4ODwaHx0dFRnDt3\nDqtXr4ZKpcINN9yA48ePzxi8R0ZSO9xrNOphNltTes1Y3C4vAMBstkIB35cZXhB8w+iiKHl7TCVq\nnLo4jI4uS0oqhmXiHkrF4+Xx33++ALWSw8oFZWn5vfLp/mUK3cPk0P1LntT3MNoXg5jB+5NPPgEA\nHD16NPgYwzAxg/fatWvxzDPPoKWlBe3t7TCZTMEhc6/Xi8cffxwvvfQStFotTp06hU996lNx/zK5\nKlLCmtTV1UJVlWlw6uIw+obtqK9JT88yVxxqH8D4hBu3XjsHaonzDwghJFkxP6Wef/55AL5h70QS\neFasWIHGxka0tLSAYRjs2LEDe/bsgV6vx6ZNm/Dwww/jvvvug0wmw6JFi3DzzTfP/rfIEcGlYmJm\ngndoxjkF70mCKGLv4U5wLINmKoVKCMkBMYP36dOnsX37dtjtduzduxfPPvss1q1bh+XLl8e8+LZt\n28KOGxoagj/fdddduOuuu2bR5NyV8Z63f613n4WS1kKdPD+Mfosda6+qRKlemenmEEJITDEjxne+\n8x3s2rUrOF9922234amnnpK8YfkoUpEWqffyDhVYLkaFWsIFSqFupqIshJAcETNiyGSysB7zvHnz\nqLb5LEUM3mnsees1cmhVMirUEuJC7xjOdo9h6fwy1IasACCEkGwWV/Du6uoKzne/8847BVHKVAqZ\nHjZnGAZVZVqYRx3w+nv8hY5KoRJCclHMLvQ3vvENfPnLX8alS5ewcuVK1NTU4Ac/+EE62pZ3uAwH\nb8CXtHa+ZwzmUUdwGL1QDYzYcfyMGXMr9GiYU5Lp5hBCSNxiBu+Ghga8/PLLsFgsUCgUYRXSSGIi\n9rzTOOcN+JaLAb6M80IP3vuPdEGEr9dNpVAJIbkkavC22Wz42c9+hosXL2L16tW4//77aa47SYH9\nvCPPeae2elw0VQZ/jfPhCQD5X08+GqvdjXdP9qG8WIVVDYV7HwghuSlqd2/nzp0AgK1bt+L8+fP4\n6U9/mq425S02QsKaN83D5oGed6FnnL91vAdur4BNq+uCG8YQQkiuiNqV7unpwQ9/+EMAwA033IAH\nHnggXW3KW9kw511eogLHMgW9u5jLw+PNY93QqmRYv6wq080hhJCERY0YoUPkHJeeId18x3HTtwQN\nznmnKXhzLIsKgwZ9w/aCXTXw3kf9sDk82HBNDVQKmgoihOSeqBFjagIPJfQkj2Vm6HmnKWEN8FVa\nc7i8GJ9wp+09s4UgiNjX1gkZx6B5ZW2mm0MIIbMStdvxwQcfYMOGDcHj4eFhbNiwIVjj/MCBA2lo\nXn6ZHDafXGOd7mFzILzGebGusMqBfnDOjMERB25YXlVwvzshJH9EDd579+5NZzsKQqSENbeXB5De\n4B1cLmaxo2FuadreN9NE/wYkAHDLairKQgjJXVGDd01NTTrbURCyIWENmKxx7lsuVjjO94zhQu84\nrl5Qjurywl7jTgjJbbRGJo0i9bwzMmxuKMzlYlQKlRCSLyh4p1GwwpqYuQprAKBWylCiUxRUz7tv\neAIfnhvC/OoiLKylvcwJIbmNgncaybKk5w34hs6Hx11wufm0vm+m7Gvzl0JtolKohJDcR8E7jSLV\nNvemuTxqQCDjvL8AirWMTbjx3kf9MJWoseJKKoVKCMl9FLzTKJiwxmdBz9sQyDjP/6HzN491w8sL\nuKWpLvgFihBCchkF7zQKJqxleM4bmMw4z/ekNZebx9vHu6FTy7F2KZVCJYTkBwreaRRxS1B/z1sm\nS2+PMHRr0Hx28GQvJpxebFxRA6WcyvwSQvIDBe804qIkrHEsk/adrUr1SijlXF4Hb14QsP9IF+Qy\nFhupFCohJI9Q8E6jaLXNZWme7wZ8teoryzQYGLGHfZnIJ8fOmDE05sTapVUo0igy3RxCCEkZCt5p\nFG1XsXTPdwdUlWng8QoYHndm5P2lFCiFygDYvLou080hhJCUouCdRpHLo/JpzzQPCGac5+HQ+ZnO\nUVzut2LFlUZU+H9PQgjJFxS804iNsqtYxoJ3MOM8/5aL7W3zlULdTKVQCSF5iIJ3GnFM5IS1TAXv\nypDdxfJJj9mGkxeGsaC2GAtqqBQqIST/UPBOo4hLxTI4511RqgbD5N+w+b62LgDArU3U6yaE5CcK\n3mk0damYKIoZ7XnLZRyMxeq8GjYfsbpwqL0fFQYNli8sz3RzCCFEEhS802hqz5sXRIhi+kujhqos\n02Dc7oHN4clYG1LpjWNd4AURm5vqgkvzCCEk31DwTqOpPe9gXfMMDZsDk5XW8mGDEofLiwMf9KJI\nI8faqyoz3RxCCJEMBe804qbs5x2sa57Bnncg4zwf9vY+eKIXDpcXN6+sTfsubYQQkk4yKS++a9cu\nnDhxAgzDYPv27Vi2bFnw3Pvvv49/+qd/AsuymDdvHlpbW8GmuURourFTet7eDO0oFqoyT9Z6e3kB\n+492QSFncdMKKoVKCMlvkkWNtrY2dHR0YPfu3WhtbUVra2vY+W9/+9v4yU9+ghdeeAETExM4ePCg\nVE3JGuyULUEztR1oqOCweY4H7yOnB2EZd2H90mro1PJMN4cQQiQlWdQ4dOgQmpubAQD19fUYGxuD\nzWYLnt+zZw8qK33zkgaDASMjI1I1JWuwDAOGCRk2D855Z26IV69RQKeW5/SwuSiK2He4EwwD3NJE\npVAJIflPsuA9NDSE0tLS4LHBYIDZbA4e63Q6AMDg4CDeffdd3HjjjVI1JatwLDOZsJYFc96AL+Pc\nPOoMfpnINR93jKBz0IZVi0wwlqgz3RxCCJGcpHPeoURx+s5Vw8PD+Pu//3vs2LEjLNBHUlqqgSzF\nSUhGoz6l14sHx7FgWQZGox6DVjcAoLhIlZG2BMyrLsb57jF4GQbVCbYjk+0OeGvPKQDAZ7c0ZEV7\nEpFr7c1GdA+TQ/cveZm4h5IFb5PJhKGhoeDx4OAgjEZj8Nhms+GLX/wivvrVr2LdunUxrzcykto5\nWaNRD7PZmtJrxoNlAJebh9lshXnIN43gdnsz0paAUq1vu8yPz5uh5uJfG52pexiqc8CKD86asaiu\nBCUqWcbbk4hsuH+5ju5hcuj+JU/qexjti4Fk47Vr167Fvn37AADt7e0wmUzBoXIAePrpp3H//ffj\nhhtukKoJWYlj2axa5w1MJq3lYsZ5oBTqFtqAhBBSQCTrea9YsQKNjY1oaWkBwzDYsWMH9uzZA71e\nj3Xr1uGPf/wjOjo68Pvf/x4AcMcdd2Dr1q1SNSdrsCwTrLCWLXPeuRq8LeNOtH0ygOpyLZbWl2W6\nOYQQkjaSznlv27Yt7LihoSH480cffSTlW2ctjmWCW4J6vDyAzAfv8mI1ZByDfktuZZy/fpRKoRJC\nClN+V0XJQizDTB82z3DwZlkGFQYN+obtERMLs5Hd6cU7H/aiWKfAdUuoFCohpLBQ8E4zLnTYPEvm\nvAGgyqCB081j1ObOdFPi8s6JHjjdPJpX1mb8yw8hhKQbfeqlGZuF67wBoNJf4zwXtgf18gLeONoN\npYLDTdfUZLo5hBCSdpmPGgUmYs87C4J3MGktB3YXO/zxAEasLty4vBoaFZVCJYQUnsxHjQLDsQyE\nqeVRsyl4Z3nGuSiK2NvWCZZhsGkVlUIlhBSmzEeNAsNmac87sLtYtg+bn7poQY95Ak2LTSgrVmW6\nOYQQkhGZjxoFhmOZyV3F+OxJWFMpZCjVK7N+2HxfWycAKspCCClsmY8ahcBuB3vpou//2exbKhZQ\nVaaBZdwFp9ub6aZE1NFvxScdI1hyRSnmVFA9ZkJI4cqOqJGvvF5on3wMhvVNMKxZAcP6JsgvX4II\nQBBFeIPBO3NbgoaqMvgzzrO09/3a4Q4A1OsmhBAK3hLS7nwCmud+Dq6rE4wggOvqhKLHN+wrCGLW\n9bwrszhpbWjUgaOnzag16tB4hSHTzSGEkIzKjqiRaSHD2qm8pvK1V+BSyLB3cyNeumM5RACs4CuJ\nytsmsmrOG8jujPP9R7sgiCK2XFsHhkqhEkIKXNr2885KXi+0O5+A8rVXwPZ0Q6iphevW2zGxsxWQ\nJXBr7HawA/0QKioBjS8Aevq68MrVBrx8+waMlfgeu+qjHsj8wRsDA8Get0yWHcGoKksLtUw4PTh4\nog+leiWaFldkujmEEJJxBR28A8PaAVxXZ/B44nvfj32BCMF/9I7bsPf+zXiz5yBs91wHtd2NpsMX\n0XbtfPz5hivBjfiCt6fcBI93DBzLgGOzo+ddolNApeCyLuP87eM9cHl4/NW6eZBlySgFIYTAbgcu\nDAIyXbDjli6F+0noH9YGgF/ddz2eeXgjXArfdxnla6/GNYQeOqftUMrwx1Xl+McVTvz35X3gIeCv\nLgHPfuU/8NWfvAH9uAPvXr8AjOgfNleq4PEKkEWa75ZiGD8ODMOgqkyDAYs9mBGfaR4vjzeOdUOt\n5HDj1dWZbg4hhIQlI+PKK2FY3wTtk48B3vSt1CncnndfH9iebgDAhFaJg+uvxFC5Do/9YC/Uvd2+\nYfB586O/3h/8RQCv3LYMv/+blbBrldBZnbj7tbNo+tYvob6+COwlBsxrr2LN4YvYv6kR49cYgQl/\nwhovhM93p2oYPwmVBi0u9VkxNOaAqTS93yQjOdQ+gPEJN7ZcOwdqZeH+uaZdhKkgQohP0qO2KVC4\nn4ZVVRBqasF1deJ/PvcOPHIO712/AP/723fisX8/6fvQmgE70A/X8AB+/rVNOHxtPfTjDnzuP9/H\n5v3tUHkEWL48CqHIgInvfR8T23dgeccJ7O/7A4YXATgO8IIAj5cPyzQP/EGIAKx6FbQ9XWn/gwhN\nWst08BZEEfvaOsGxVAo1bbLgCyTJHEEUIIoiBFGAANF/LEAQRQgQfI8HjgPn/M8TRNF/POV88LX+\n85Gu7X9MDL0+QtoSaBeEKe8V6fzktfnAc6e9LvR5gfcPbePke007L/DANXYIP7sXAPA3e47hljc+\nBuAbtZ3YviMtX3gL979GjQauW2+H5rmfQ8YLeOSZN6Gxu/FG8xLs/Meb8TDrggHR/wF6izj8v6f+\nFr0VOiz5uBdf/fHrKBlzAAD4urnhwV+jwdyG62AaPQizvRNg64NLxRRy/xpvf0++r7IYz375Jpy9\nshKMIEJnc6LIPg7t0Z9BryqGXqGDXqFHkULn/1kHvVwPvUIHBZf8Jh2hwXv5ghmemIa5npPnh9E3\nbMfaqypRqldK8h4kXDb0KOIliiJ4gYdH8M74oR/+eGiwCH2e/4M85EPddzzlfDzBaur5sGAVKVCE\nt3HGABo1yM1wPuz3CA+CIkQIwuT7FDoGDFiGBcswYBgWLHw/swwLhmF8x7wAmccDmSCC4wWoXJ7g\n69l4Rm1TpHCDN+DrTcD3bYnt7caD+zqgWLgEr84F/unYz/GVa76ICo1x2us+HDyFX3+yG64KHe74\n0wnc85/vgwuZI3bdetu0gMYwDFZXXoNXLr0OztAP3h+8tWpfwGX6+/D64iL85nOb4FLJsfjjXjAA\nxorVGCtSo2f8MjA+8++j4pSTAV2h9wd2HYoUOugUOhSFPKaWqSIuuQpuDWqJknEe0jNDTzcMEvbM\n9vqLsmxuKsyiLKHBhxcF8CI/eSwEHueD54UpP/OhrxemHE+9nshDcLmgcJ+G+JlVEFgGPMdCYBnf\nz/JLsLf/DoKM83/YTwmQEGcIjKG9n3iDXKwemwgR2ZGXkSkMGF9AYViwCAQYf7BBSABiWHBgwbLy\nyfP+1yjkcvC86HtuSKAKC1ZhwWzyfMwgN9P5kMfC2xxy3v9+4W2ecj5Su0MCcGhbw58XeF1Iu/z3\nMya7HYb1TeC6OqedEqprY47apkpBB2/IZMFh7cD83u0aDeSX38Z/X3wN/3TsZ/iHq/8H6rhSsAP9\n8JiMeLnvIF7vPAAFp8CDDS244S0GqOmF2NsNoboWrltvC34pmKqpcoUveJf1Al1d8Hh9c96jrjH8\nx8gb+OTBddBZnfjSLw7g+vcvBF/H183F4DvvwiYXYXXbMO62weq2wuq2BY9tHhvG/Y8Nj3fF/BYt\nY2XQy3XQK7RhgV4r00JW1odLVgd6bCUoUuihlWvAMr7h/XT1zC70juFs9xiumm9ArUmX/kAWvG7o\ndaa+x+Rjk8f+n4Wp15z+eoYR4eF58ELkdmckOG1ZFP3cwJGkLh3PhzEDBhzDgWVlk8Foht6QUiGH\n1yOEnw8LZqGBIDSARAkYU4NgWJsnXzPj+bAAEiVQRA1w0QJoSLtCfrdkGY16mM3WpK9TUEJGbaeK\n1HGTCiOKYk58fU31H1isP9qDPYew+8wfofKK+MZzh1B74ix+vO12fLSwHCZ1Gb649H5U6/zfsOJN\n7vF68c2Xv4uxIge+ueMd/O/bv4ea0ouYWNIDh9eJZUPAl7/1axhGwrPM7Q99KaHAKIgC7B4Hxt1W\nf1C3BQO91W31HXsmjz3CzBmSDBjo5Fro5RoYTnyMkoER6K1OAADPMhA4Ft4iPRy33QGeY2YVyEID\nqyAKcHg84AUBHAeIyFAgSwFfMAp8KHO+n1kWHMNBznEQRd95juGCH9hc8P/9j7GBx7jp5/w/T76H\n/7ns1Me4kGtPORd4rsuD4kf/F+T9/ZDxAlhB9P9PgGiqhPXffgNWrQkGq8A1IvekpgdQKVDwSQ7d\nv1kKjkC+Cq63G3xoxy3FI5BGY+R9HAq75z2D9TVrULLnD/iXRTye+sIq6G1LMVymw6qjl/DgBCCu\nCZ/TjmeOQ7vzCdSyboxvkOMvN14BbsEpDJX1Q+kEPtt4F9auXwnVSQa8fxg/Vk8+GpZhoVNooVNo\nYz5XFEW4eNdkgPfY8NL7p9E9YsH6lWVwCnZfL99jw4hzFL0Ly4GF5ZEvNnRixveaFsjY8MAiY2VQ\nckqIAmAdc0Ahk6G2VB8e3FIUyKYFVH8QCw2e04Pe5PMDbfC9Ltpz2RmDVjZ+cGoXXAvNW9N7FPZN\nf4ui8nkZaBEhWShk1NbotcGSgXXe1POOxj+vcaIc+NHXboFXxmHri0fw6f8+DrF2LiwHDyf2j+W/\n3i8XbcD+B7VgWN9t15Y3VxEAABstSURBVJhl2PX/3oT8j29PXi/Dy3RefPs89h7uxDc/vwILa0vC\nfgfdTddhYtwMq14FRgQ4XgDHC0BFNcZ3/wGcRhuxFxkrkIV6fv8ZvH28Bw99agmuW5Ke+aNMyMbg\nHdqjmPYFMguzzbPyHuYQun/Jk/oeUs87QexAP9iebqzoEvD9b/4XXEoZ6i+aAQDiLDIKA9dTzuHB\nD1dDUdoFV18DFv25F1WnzsISer04e/JSqTJMZpyHBW+NBuKmW1H+3M9RPqWEqv3Oz0FemnwRFavd\njXdP9qGsSIXVDaakr0cSFCEPhNZ5E5J9CrfCWgxCRSWEmloAQG3PSDBwA7PLKAxcjxN4eC434oH/\n7zy8ffOh8HjTmqEYj8ka59MrvE3sbIX9oS+Br5sLcBz4urm+OfkEh/ajeft4D9xeAbesrsuasrEF\nKfAFkgI3IVmJPh2j8WcURjKrjEL/9ThBAEQWgqgAACh4d1ozFOMR2Bq0N9IGJf6emeXgYeDMGVgO\nHvYl06VgSNXt4fHm8W5oVTKsX16V9PUIISRf0bD5DKauA59tAlno9fjWfwUAOJS+AMksWoSJ7fem\npsEpolPLodfII/a8gzQawFgBpHCu592P+mG1e3D7mrlQKehPkxBCoqFPyJmkev5PJoOw5Tbg7fMY\n+fuvAO1jYNatz8pEoCqDBud6xvwlXDnJ308QfKVQZRyDm1fWSv5+hBCSy2jYPB4pnP9jWV9hBYem\nCAAi7yqWBSrLtBBFYGDEkZb3++DcEAZHHFjTWIkSHZVCJYSQmWRn5MhjnD94O92+rUHlWRq8AzXO\nZxw6T6G9bYVdCpUQQhKRnZEjjwV63i6PP3hz2flPMLlBSZQa5yl0rnsUF3rGcfWCclSXxy4sQwgh\nhS47I0ceC/S8XVnf8/YF0T6L9D3vvYd9Bf43N9G2n4QQEg9JI8euXbuwdetWtLS04OTJk2HnXC4X\nHnvsMdx1111SNiHrsExg2NxXTzxbg3dZkQpyGYs+iYfN+4Yn8OG5IcyrKsKVdSWxX0AIIUS64N3W\n1oaOjg7s3r0bra2taG0NX171gx/8AIsXL5bq7bMWN3XYPEuDN8syqCjVoH/YDikr6O4/0gURwK3X\nzknJLkmEEFIIJIschw4dQnNzMwCgvr4eY2NjsNlswfNf+9rXgucLCcdNSVjL0jlvwDfv7fLwGLG6\nJLn+2IQb757qh7FEhRVXTt83nRBCSGSSLTAeGhpCY2Nj8NhgMMBsNkOn0wEAdDodRkdH475eaakG\nshSvN45W8F1KJX2+oiYer2+/7fIybUbaEY/6ulIcOT0IBy9GbWMybd939BN4eQF/c9NCVFQUzfo6\nuSxb/+1zCd3D5ND9S14m7mHaqoMkO/Q6MpLauddM7aYz4d8H2+70zXnbJ1xZu6tPkdr3Zen0xWHU\nlKqnnU/mHrrcPP70l4vQqeVYPt+QtfdASrSjU/LoHiaH7l/yMrWrmGRjtiaTCUNDQ8HjwcFBGI00\nNDptqViWznkDQJXBn3EuwXKxv5zqw4TTi40raqCUS1/BjRBC8olkkWPt2rXYt28fAKC9vR0mkyk4\nZF7IAglrvOAbicjm4F0ZsjVoKvGCgH1tnZDLWGxcQaVQCSEkUZINm69YsQKNjY1oaWkBwzDYsWMH\n9uzZA71ej02bNuGRRx5Bf38/Ll26hHvvvRd333037rzzTqmakzUCPe+AbE5YUyo4lBUp0Z/itd7H\nzpgxNObEhqurUaRVpPTahBBSCCSd8962bVvYcUNDQ/Dnn/zkJ1K+ddbipgbvLO55A74a5+2XLHC4\nvFArk/9zEUXfBiQMqBQqIYTMVnZHjjzEseG3PB07diWjyj90nqre99muUVzqs+KaK42oMGTPHuaE\nEJJLKHin2bRh8yzveae6xvlr/lKoW66lXjchhMxWdkeOPDRt2DyL57wB37A5kJqktZ6hCZy8MIwF\nNcVYUFOc9PUIIaRQZXfkyEO52vNOxdag+9qo100IIamQ3ZEjD4UGb45lpgXzbFOsVUCt5JLeXWzU\n5sL77f2oMGhw9cLyFLWOEEIKEwXvNAsdNs/2XjcAMAyDSoMWAxY7eEGY9XXeONoNLy9ic1NdcGc1\nQgghs5P90SPPsDkWvAHf0DkviBgadc7q9Q6XF29/0AO9Ro7rGytT3DpCCCk8uRE98ogsR4M3MPuk\ntYMneuFweXHzylooqBQqIYQkLTeiRx4J63lneaZ5QFUg49yS+HIxLy/g9aNdUMipFCohhKRKbkSP\nPJKrw+bA7HreR08PYnjchfVLq6FTy1PdNEIIKUi5ET3ySK4lrAGAsUQNjmUSXi4miiL2Hu4EwwCb\nmuokah0hhBSe3IgeeSQ00zpXhs1lHAtjiRp9wxMJ7cv+cccIOgdtWLnIBFPJ9P3ACSGEzE5uRI88\nkos9b8A3dD7h9MLq8MT9mn3+Uqi3UlEWQghJqdyJHnkifM47dzKvKxOstNY1aMNHlyxYVFeCeVVF\nUjaNEEIKDgXvNAvtectyqedtCNQ4jy/jfC9tQEIIIZLJneiRJxiGCc5758qcN5BYxrll3Im2TwZQ\nVabB0voyqZtGCCEFJ3eiRx4JDJ3n0px3cNg8jhrnbxztBi+I2NI0h0qhEkKIBHIneuQRLgeDt1Yl\nR5FWEXPY3O704sCHPSjWKXAdlUIlhGSpV199GT/96T9HPY6ktXUn3n33oNRNi0vuRI88kos9bwCo\nMmgwNOqE28NHfc47J3rgdPNoXlmbc78fIYTkClmmG1CIgj3vHJrzBnzz3me6RjEw4kCdSTftvJcX\n8MbRbijlHDZcU5OBFhJCSOJ+8YufQqVSoa+vB9u2PYLBwQHcfffncMcdf4WWlr/GddetRWlpaaab\nGYaCdwbkas+7smwy4zxS8D788QBGrC5sWlUHrYpKoRJCYnvxrfM4cnowpddc3WDC3RsXxPXct956\nA4ODA1i1qglvvfU6fvnL32BiwoYHHvgcbr/9U/B6vbjuuutx3XXXo7V1Z0rbmQwK3hmQi3PewGTG\neaS13qIoYl9bJ1iGwabVtAEJIST7Xbp0Ee+88zb+4z9exJtv7seyZVdDJpOhuLgEWq0WY2NjAIAl\nSxoz3NLpKHhnQM4Gb4N/uViEjPOPLlnQbZ7AdUsqUF5MpVAJIfG5e+OCuHvJqdbf34t58+bjwIE3\n/Y+Er44JLJaRybJvJDG3okeeYHN0zttQrIJCxkbMOA8UZdncREVZCCG5Yc2adfjmN7+NX/3qX2Gx\nDKO9/SR4nsfIyAgcDgeKiooz3cSoqOedAbna82YZBpUGDfotdgghG5R09FvxSccIFs8txdxKfQZb\nSAghiSktLcUXvvA/8aMffR9NTdfhW996HD09XXjooS+DyeI6FRS8MyBXE9YAX7GWzkEbRsZdqDD5\nHtvbRhuQEEJyy2233Rn8ubl5M5qbN0d83u9//3Lw5yee2Cl1s+KWe9EjD3BM7gbvqkDGucU3dD40\n5sCRTwZRa9SicZ4hk00jhJCCkXvRIw/k6pw3ML3G+f4jXRBEEZub5mT1EBMhhOST3IseeWByzjt3\ntgQNqDRMLhez2d04eKIPpXolrl1SkeGWEUJI4aDgnQG5mrAGABUGDRj4CrW8dugyXB4em1bVQZaD\nowiEEJKrJP3E3bVrF7Zu3YqWlhacPHky7Nx7772Hz3zmM9i6dSueffZZKZuRdVj4MrVlHleGW5I4\npZxDWbEKPWYbXj5wDmoFhxuvrs50swghpKBIFrzb2trQ0dGB3bt3o7W1Fa2trWHnv/e97+GZZ57B\nb3/7W7z77rs4f/68VE3JHl4vtE8+BuXRNgCA8Z6/gfbJxwCvN8MNS4DXi9rhLlgdXozYvdh8ch/K\nv/tEbv0OhBCS4yQL3ocOHUJzczMAoL6+HmNjY/j/27v3sKjKfYHj34FxRAQVcEYFxFA7kmZejj5q\nSnYRsODxmAGlonnSx2vlJQVEjtIWLyiWhT2lYj08xClTycs5qVl520XsDMLLTk23JJdkBkWRkdvA\nOn/gHuVobQlwZsnv84+z1rvmnd/7c+HPd83LWmVlZQDk5eXRvn17unTpgoODAyNHjiQjI6O5QrEb\nbeOW4LzpfbTldSu1nfJycd70Pm3jltg4snvXNm4JPjl1f1eONRb+48gnqhuDEEI0halTJ5Gfn2+T\nz2624l1cXFzvKSzu7u6YTCYATCYT7u7ud217YN24Qeu9/wuAtqZultraUlX3594v4Madtxy1OzfH\n4H2l7mQdefoIHcsuAyoagxBCPADu201alNvuyPVnuLk5o23i1dl6/X28G9h5IxTUFb0x2XvoYfwH\nLpV1M3DHwnz0ljLQ2/mK7Ztj8Dde5mLHboT+sMPapJox2Jn7eg4+oCSHjdNS85eens6RI0cwGo10\n69aN3NxcKisrGT9+PGFhYURHR2MwGDh16hSFhYUkJibSp08f4uPjyc7OxtfXF0WpAaCmxkxMTAzV\n1dVoNBpWrFiBRqMhMjISHx8fsrOzGT9+PGfOnCEnJ4eJEycyceLERsXfbMXbYDBQXFxs3TYajej1\n+ru2FRUVYTAY/rC/kpKmndXp9a6YTNebtM8/pHXB3csbx7yLPJZ3ksfyTlqbajy9uaJ1gfsZz59x\ncwwueReZcXBzvSbVjMGO3Pdz8AEkOWwce8hf+rn/Idt4okn7HGDoy7ieIX94zPXrFVy8mM+7777P\n7t07WbAghsrKCsLDx/Lkk6OpqKjm6tUyVq9ez86d2/nkk22MGWPhb387xubNKZhMRl566XkAEhIS\nCQwM5plnAjl48CsSE99m6tQZ/P3vP/OXvyRQWlrKpEnhbNu2mxdfrGLJkkgCA8fc01h+7z9XzXbZ\nfPjw4ezfvx+AU6dOYTAYcHGpewa0t7c3ZWVl5OfnY7FYOHjwIMOHD2+uUOyDszOVzwbftany2efA\n2fk+B/QnPAhjEEKImx55pDetWztRWnqNmTNf4Y03Xufq1RJre79+AwDQ6zthNpeRm/sPevd+FAcH\nBzp16oynpxcAZ878zIAB/w7AwIGD+OWXMwB4eXnTvn0HPDw64ubmjl5vwM3NHbO5rNGxN9vMe+DA\ngfTp04eXXnoJjUbDsmXLSE9Px9XVlYCAAOLi4njjjTcAeO655/D19W2uUOyGOa5uxX3rvV/gUJhP\nrac3lc8+Z92vBrePwbEwnxoVjkEIYT/G9Qz5l7Pk5qLVtiI7+0eyso6xYcMmtFotAQH+1nZHx1tf\n1SqKgqLcukMmQG1t7c1XGutXw9XVFjQahzve///7anTsje7hDyxcuLDetp+fn/X14MGD2bp1a3N+\nvP3RajHHJ2COWYZD0SVqO3VW32z1tjHoLWV1l8rVNgYhhLjp2rWrGAyd0Gq1/PWvh6mpqaW6uvqu\nx/r4dOOzz/4bRVEoKrrEb78VAnUz+KysYwQEjOann37Ez++RZo9bnipmC87O1Pp2t3UUjePsXLc4\nTb5vFEKo2KBBQ0hLS+HVV6fj7z+Sxx8fQWLiqrse27Pnw3Tv3oMZM/6Trl19ePjhfwNg2rSZrFq1\nnD17dqLVtmLx4v/C0sz3vtAoTTF/vw+aelGFPSzUUDvJYeNI/hpPctg4kr/Ga+4c3vcFa0IIIYRo\nHlK8hRBCCJWR4i2EEEKojBRvIYQQQmWkeAshhBAqI8VbCCGEUBkp3kIIIYTKSPEWQgghVEaKtxBC\nCKEyUryFEEIIlVHN7VGFEEIIUUdm3kIIIYTKSPEWQgghVEaKtxBCCKEyUryFEEIIlZHiLYQQQqiM\nFG8hhBBCZbS2DsAWVq5cSU5ODhqNhpiYGB577DFbh2S31qxZw48//ojFYmHGjBn07duXyMhIampq\n0Ov1rF27Fp1Ox+7du0lJScHBwYHw8HDCwsJsHbrdqKioICQkhNmzZzNs2DDJXwPt3r2b5ORktFot\nr7/+Or169ZIc3iOz2UxUVBTXrl2jurqaOXPmoNfriYuLA6BXr168+eabACQnJ7Nv3z40Gg2vvvoq\nI0eOtGHktnf27Flmz57NlClTiIiI4Lfffrvn8666upro6GgKCwtxdHRk1apVdO3atWkDVFqYzMxM\nZfr06YqiKMq5c+eU8PBwG0dkvzIyMpRp06YpiqIoV65cUUaOHKlER0crX3zxhaIoirJu3TolLS1N\nMZvNSmBgoFJaWqqUl5crwcHBSklJiS1DtytvvfWWMm7cOGXHjh2Svwa6cuWKEhgYqFy/fl0pKipS\nYmNjJYcNkJqaqiQmJiqKoiiXLl1SgoKClIiICCUnJ0dRFEVZsGCBcujQIeXixYvK888/r1RWViqX\nL19WgoKCFIvFYsvQbcpsNisRERFKbGyskpqaqiiK0qDzLj09XYmLi1MURVGOHj2qzJ07t8ljbHGX\nzTMyMhg1ahQAPXr04Nq1a5SVldk4Kvs0ePBg3nnnHQDatWtHeXk5mZmZPPPMMwA89dRTZGRkkJOT\nQ9++fXF1dcXJyYmBAweSlZVly9Dtxvnz5zl37hxPPvkkgOSvgTIyMhg2bBguLi4YDAaWL18uOWwA\nNzc3rl69CkBpaSkdOnSgoKDAerXxn/nLzMzE398fnU6Hu7s7Xl5enDt3zpah25ROp2Pz5s0YDAbr\nvoacdxkZGQQEBADw+OOPN8u52OKKd3FxMW5ubtZtd3d3TCaTDSOyX46Ojjg7OwOwfft2nnjiCcrL\ny9HpdAB4eHhgMpkoLi7G3d3d+j7J6S0JCQlER0dbtyV/DZOfn09FRQUzZ85kwoQJZGRkSA4bIDg4\nmMLCQgICAoiIiCAyMpJ27dpZ2yV/d6fVanFycqq3ryHn3e37HRwc0Gg0VFVVNW2MTdqbCilyd9h/\n6auvvmL79u18+OGHBAYGWvf/Xu4kp3V27txJ//79f/e7Lsnfvbl69SobNmygsLCQyZMn18uP5PCP\n7dq1C09PT7Zs2cLp06eZM2cOrq6u1nbJ35/T0Lw1Rz5bXPE2GAwUFxdbt41GI3q93oYR2bejR4/y\nwQcfkJycjKurK87OzlRUVODk5ERRUREGg+GuOe3fv78No7YPhw4dIi8vj0OHDnHp0iV0Op3kr4E8\nPDwYMGAAWq0WHx8f2rZti6Ojo+TwHmVlZTFixAgA/Pz8qKysxGKxWNtvz9+FCxfu2C9uacjPrsFg\nwGQy4efnR3V1NYqiWGftTaXFXTYfPnw4+/fvB+DUqVMYDAZcXFxsHJV9un79OmvWrGHjxo106NAB\nqPv+5p/5+/LLL/H396dfv36cOHGC0tJSzGYzWVlZDBo0yJah24X169ezY8cOPvvsM8LCwpg9e7bk\nr4FGjBjB999/T21tLSUlJdy4cUNy2ADdunUjJycHgIKCAtq2bUuPHj04duwYcCt/Q4cO5dChQ1RV\nVVFUVITRaKRnz562DN3uNOS8Gz58OPv27QPg4MGDDBkypMnjaZFPFUtMTOTYsWNoNBqWLVuGn5+f\nrUOyS1u3biUpKQlfX1/rvtWrVxMbG0tlZSWenp6sWrWKVq1asW/fPrZs2YJGoyEiIoIxY8bYMHL7\nk5SUhJeXFyNGjCAqKkry1wCffvop27dvB2DWrFn07dtXcniPzGYzMTExXL58GYvFwty5c9Hr9Sxd\nupTa2lr69evH4sWLAUhNTWXPnj1oNBrmzZvHsGHDbBy97Zw8eZKEhAQKCgrQarV06tSJxMREoqOj\n7+m8q6mpITY2ltzcXHQ6HatXr6ZLly5NGmOLLN5CCCGEmrW4y+ZCCCGE2knxFkIIIVRGircQQgih\nMlK8hRBCCJWR4i2EEEKojBRvIVTk8OHDTJw4kUmTJhEaGsq8efMoLS1tts9LT09n4cKFjerj559/\nZvny5U0UkRAC5FfFhFCNqqoq/P392bNnj/XuV2vXrsXDw4NXXnmlWT4zPT2d7777jsTExGbpXwjx\n57S426MKoVaVlZXcuHGD8vJy675FixZZXx84cIDk5GR0Oh01NTWsWbMGb29vJk2axKBBgzh+/Di5\nubnExMSwc+dOzp49y9ixY5k1axZJSUnk5eVRUlKCyWRi6NCh9R6oAnD69GkSEhKwWCxUV1ezdOlS\nevfuXe+YlJQUdu/eTZs2bXBycmLt2rWcPXuW9evXk5KSwtSpU63Hnjx5kvj4eIKDg0lNTWXv3r3U\n1NTQvXt3li1bdseDIYQQt0jxFkIlXF1dee211xg7diz9+vVjyJAhBAUF0b17d6DukY9vv/02np6e\nbNy4kbS0NKKiooC6ByNs2bKFpKQkEhMT2bVrF0aj0Vq8AX755Re2bdtGbW0twcHBjB07tt7nL1q0\niPfeew8fHx9Onz5NTEwM6enp9Y5599132b9/Px07duTo0aMYjUZrm06nIzU1FYBvvvmGjz76iKCg\nII4fP86BAwdIS0tDo9GwcuVKtm3bxqRJk5otl0KonRRvIVRk+vTphIWF8e2335KZmUl4eDgLFixg\nwoQJdOzYkaioKBRFwWQyMWDAAOv7Bg4cCEDnzp3p06cPOp2Ozp07c/36desxQ4cORaut+yfh0Ucf\n5fz589a2y5cvc+HCBZYsWWLdV1ZWRm1tLQ4Ot5bOhIaGMm3aNIKCghg9ejS+vr5kZmbWG8Ovv/7K\nunXrSElJQavVkpmZycWLF5k8eTIAN27csMYhhLg7+QkRQkXKy8txc3MjJCSEkJAQRo8ezerVqwkL\nC2PevHl8/vnnPPTQQ3z88cecPHnS+r7bi+HvFcba2lrra0VR0Gg01m2dTkerVq2sM+ffs3jxYgoK\nCjh8+DBz5swhKiqq3uXv8vJy5s+fT3x8PB07drT2/fTTT7N06dKGJUOIFkxWmwuhEkePHuXFF1+k\nrKzMui8vL49u3bphNptxcHDAy8uLyspKvv76a6qqqhrU/w8//EBNTQ1VVVWcOHGCXr16WdtcXV3x\n9vbm8OHDAFy4cIENGzbUe/+1a9dISkqiS5cuTJgwgYkTJ3LixIl6x8TGxvLCCy/ccVXgyJEjmM1m\nANLS0sjOzm5Q7EK0NDLzFkIl/P39yc3NZcqUKbRp0wZFUfDw8GDp0qV06NCBkJAQQkND8fT0ZOrU\nqURGRrJ379577r9r167MnTuX/Px8goOD6dGjh/VxkgAJCQnEx8ezadMmLBbLHQva2rdvj9lsJjQ0\nlHbt2qHValmxYgW5ubkA/PTTT+zbtw+j0Wh9XOKoUaN4+eWXrb/+1rp1awwGA+PGjWt8woR4gMmv\nigkhSEpKwmKxMH/+fFuHIoS4B3LZXAghhFAZmXkLIYQQKiMzbyGEEEJlpHgLIYQQKiPFWwghhFAZ\nKd5CCCGEykjxFkIIIVRGircQQgihMv8HW5oEjK3XcTcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fbcb84a8c18>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "[0.6463536463536463, 0.47652347652347654, 0.6613386613386614, 0.6283716283716284, 0.0, 0.6493506493506493, 0.0, 0.6683316683316683, 0.6393606393606394]\n",
            "[0.15084915084915085, 0.13186813186813187, 0.14785214785214784, 0.15784215784215785, 0.12987012987012986, 0.14385614385614387, 0.13486513486513488, 0.13986013986013987, 0.14585414585414586]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "MrqLkoLPCir-",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "outputId": "e506c6c0-fb59-427b-8b32-04c89cc18b1d",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524955288796,
          "user_tz": 240,
          "elapsed": 582,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(sample_sizes, times, label='time to execute')\n",
        "\n",
        "plt.scatter(sample_sizes, times, color='red')\n",
        "\n",
        "plt.xlabel('Sample size')\n",
        "plt.ylabel('Time to execute')\n",
        "plt.show()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Gr0+y/PPDOEsMBvdowrjrorDoXLvP8auoJ3Y4HMycOZOYmJiyba+88grjx49n8eLFxMbG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\nIiakgBcRETEhBbyIiIgJKeBFRERM6F+haNZXibjXmgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fbcb84479b0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "muUFq21jdef2",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Experiment: Studying effect of varying the target score, 100 samples. "
      ]
    },
    {
      "metadata": {
        "id": "xXfn6YZEbDN-",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 158
        },
        "outputId": "195468f1-1451-40ff-b431-cdc219daf546",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524956884510,
          "user_tz": 240,
          "elapsed": 284,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# Define envt conditions\n",
        "max_shots=6\n",
        "num_lives=2\n",
        "target_scores = [5,10,15,20,25,30,40,50]\n",
        "\n",
        "# Percentage wins lists for random/kbrl policies\n",
        "rand_list = []\n",
        "kbrl_list = []\n",
        "\n",
        "for target_score in target_scores:\n",
        "  print(target_score)\n",
        "  \n",
        "  # Initialize envt\n",
        "  env = environments.EnvChaseTarget(max_shots, num_lives, target_score)\n",
        "\n",
        "  # Define kernel metric\n",
        "  metric='additive_chi2'\n",
        "\n",
        "  t0,t1,t2,t3,r0,r1,r2,r3 = gather_transitions(n_samples=100, max_episodes=10000)\n",
        "\n",
        "  # Time it\n",
        "  start_time = time.time()\n",
        "\n",
        "  # Create Theta and R matrices\n",
        "  Theta, R = convert_gathered_to_matrices(metric,t0,t1,t2,t3,r0,r1,r2,r3)\n",
        "\n",
        "  # List of gamma values to plot\n",
        "  gamma = 0.95\n",
        "\n",
        "  # Compute value function by iterating over update rule\n",
        "  vf = do_value_iteration(Theta, R, gamma, n_iter=1000)\n",
        "\n",
        "  # Play game according to random policy\n",
        "  random = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=True)\n",
        "  rand_list.append(random)\n",
        "\n",
        "  # Play game according to KBRL policy\n",
        "  kbrl = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=False)\n",
        "  kbrl_list.append(kbrl)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5\n",
            "10\n",
            "15\n",
            "20\n",
            "25\n",
            "30\n",
            "40\n",
            "50\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "yHXxcjs7e-Qt",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 396
        },
        "outputId": "7c13287c-9821-4f72-c98b-759f3549a5ab",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524956525071,
          "user_tz": 240,
          "elapsed": 824,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(target_scores, kbrl_list, label='kbrl')\n",
        "plt.plot(target_scores, rand_list, label='random')\n",
        "\n",
        "plt.scatter(target_scores, rand_list, color='red')\n",
        "plt.scatter(target_scores, kbrl_list, color='red')\n",
        "\n",
        "plt.xlabel('Target score')\n",
        "plt.ylabel('Percent win')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "print(kbrl_list)\n",
        "print(rand_list)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gd9h1TuM6bJEdi9bSpM+5EMIJaFa89+zZw/Tp0wGw2WxUV1dTV9dxnbHdbufQ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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fbcb860ce48>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "[0.8971028971028971, 0.8151848151848152, 0.7362637362637363, 0.6783216783216783, 0.0, 0.24575424575424576, 0.0, 0.0]\n",
            "[0.8521478521478522, 0.7042957042957043, 0.42657342657342656, 0.13486513486513488, 0.029970029970029972, 0.001998001998001998, 0.0, 0.0]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "6vaqvy7veJS-",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Experiment: Studying effect of varying the size of state space, 100 samples, target score = 20. "
      ]
    },
    {
      "metadata": {
        "id": "R9faGvUJfVa_",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 122
        },
        "outputId": "068a00b3-ebdb-4709-9bed-66b841899d95",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524958274081,
          "user_tz": 240,
          "elapsed": 1289557,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# Percentage wins lists for random/kbrl policies\n",
        "rand_list = []\n",
        "kbrl_list = []\n",
        "\n",
        "# Varying environment conditions\n",
        "max_shots_list = [6,9,12,15,18,21]\n",
        "num_lives_list = [2,3,4,5,6,7]\n",
        "\n",
        "for max_shots, num_lives in zip(max_shots_list, num_lives_list):\n",
        "  print(max_shots, num_lives)\n",
        "  \n",
        "  target_score = 20\n",
        "\n",
        "  # Initialize envt\n",
        "  env = environments.EnvChaseTarget(max_shots, num_lives, target_score)\n",
        "\n",
        "  # Define kernel metric\n",
        "  metric='additive_chi2'\n",
        "\n",
        "  t0,t1,t2,t3,r0,r1,r2,r3 = gather_transitions(n_samples=100, max_episodes=10000)\n",
        "\n",
        "  # Time it\n",
        "  start_time = time.time()\n",
        "\n",
        "  # Create Theta and R matrices\n",
        "  Theta, R = convert_gathered_to_matrices(metric,t0,t1,t2,t3,r0,r1,r2,r3)\n",
        "\n",
        "  # List of gamma values to plot\n",
        "  gamma = 0.95\n",
        "\n",
        "  # Compute value function by iterating over update rule\n",
        "  vf = do_value_iteration(Theta, R, gamma, n_iter=1000)\n",
        "\n",
        "  # Play game according to random policy\n",
        "  random = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=True)\n",
        "  rand_list.append(random)\n",
        "\n",
        "  # Play game according to KBRL policy\n",
        "  kbrl = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=False)\n",
        "  kbrl_list.append(kbrl)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6 2\n",
            "9 3\n",
            "12 4\n",
            "15 5\n",
            "18 6\n",
            "21 7\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "tf0rVqlGgs3G",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 414
        },
        "outputId": "a2c551f1-7730-4a4c-fa6b-afe7079fc2f1",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524958282570,
          "user_tz": 240,
          "elapsed": 462,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.plot(kbrl_list, label='kbrl')\n",
        "plt.plot(rand_list, label='random')\n",
        "\n",
        "plt.scatter([i for i in range(len(max_shots_list))], rand_list, color='red')\n",
        "plt.scatter([i for i in range(len(max_shots_list))], kbrl_list, color='red')\n",
        "\n",
        "\n",
        "plt.xlabel('index of max_shots, num_lives combination')\n",
        "plt.ylabel('Percent win')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "print('Combinations of max_shots, num_lives:', [(m,n) for m,n in zip(max_shots_list,num_lives_list)])\n",
        "print(kbrl_list)\n",
        "print(rand_list)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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YuGfuOEYOiA9qDV8e3MQ/8l8n0hrBvRPuICO6f1D3LyLSFQpvCQlHs4en39pJ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\nSUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fbcba825978>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Combinations of max_shots, num_lives: [(6, 2), (9, 3), (12, 4), (15, 5), (18, 6), (21, 7)]\n",
            "[0.0, 0.6933066933066933, 0.9410589410589411, 0.9820179820179821, 0.977022977022977, 0.981018981018981]\n",
            "[0.13586413586413587, 0.5604395604395604, 0.8631368631368631, 0.9560439560439561, 0.97002997002997, 0.993006993006993]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Ck5XvmMvobmB",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Studying effect of 4 arbitrary state spaces of varying sizes"
      ]
    },
    {
      "metadata": {
        "id": "2Yv7kUYSliw2",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 105
        },
        "outputId": "590516ca-4e2f-42b0-bb35-70cf741b36c9",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524959804755,
          "user_tz": 240,
          "elapsed": 1384175,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# This can be used to see if learning on smaller state spaces can generalize to larger\n",
        "# or if learning on smaller targets can generalize to larger targets\n",
        "\n",
        "# Percentage wins lists for random/kbrl policies\n",
        "rand_list = []\n",
        "kbrl_list = []\n",
        "\n",
        "# Varying environment conditions\n",
        "max_shots_list = [6,9,12,15,18]\n",
        "num_lives_list = [2,3,4,5,6]\n",
        "target_scores = [20,30,40,50,60]\n",
        "\n",
        "for max_shots, num_lives,target_score in zip(max_shots_list, num_lives_list, target_scores):\n",
        "  print(max_shots, num_lives, target_score)\n",
        "\n",
        "  # Initialize envt\n",
        "  env = environments.EnvChaseTarget(max_shots, num_lives, target_score)\n",
        "\n",
        "  # Define kernel metric\n",
        "  metric='additive_chi2'\n",
        "\n",
        "  # Gather transitions\n",
        "  t0,t1,t2,t3,r0,r1,r2,r3 = gather_transitions(n_samples=100, max_episodes=10000)\n",
        "\n",
        "  # Create Theta and R matrices\n",
        "  Theta, R = convert_gathered_to_matrices(metric,t0,t1,t2,t3,r0,r1,r2,r3)\n",
        "\n",
        "  # List of gamma values to plot\n",
        "  gamma = 0.95\n",
        "\n",
        "  # Compute value function by iterating over update rule\n",
        "  vf = do_value_iteration(Theta, R, gamma, n_iter=1000)\n",
        "\n",
        "  # Play game according to random policy\n",
        "  random = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=True)\n",
        "  rand_list.append(random)\n",
        "\n",
        "  # Play game according to KBRL policy\n",
        "  kbrl = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=False)\n",
        "  kbrl_list.append(kbrl)"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6 2 20\n",
            "9 3 30\n",
            "12 4 40\n",
            "15 5 50\n",
            "18 6 60\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "5xBu5BqGosLo",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 414
        },
        "outputId": "844781fe-39ef-4647-8664-4b4190272da1",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524960198514,
          "user_tz": 240,
          "elapsed": 796,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(kbrl_list, label='kbrl')\n",
        "plt.plot(rand_list, label='random')\n",
        "\n",
        "plt.scatter([i for i in range(len(max_shots_list))], kbrl_list, color='red')\n",
        "plt.scatter([i for i in range(len(max_shots_list))], rand_list, color='red')\n",
        "\n",
        "plt.xlabel('index of max_shots, num_lives, target combination')\n",
        "plt.ylabel('Percent win')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "print('Combinations of max_shots, num_lives, target:', [(m,n,t) for m,n,t in zip(max_shots_list,num_lives_list, target_scores)])\n",
        "print(kbrl_list)\n",
        "print(rand_list)"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KdZnRmIH9ebXKFiiEmJDBaOKVD87xv/vP4+3pwhNfTZPGbUXSvIXicvJGZ93rs6Kv+HxG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\nA10AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fbcb85c65f8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Combinations of max_shots, num_lives, target: [(6, 2, 20), (9, 3, 30), (12, 4, 40), (15, 5, 50), (18, 6, 60)]\n",
            "[0.0, 0.4225774225774226, 0.0, 0.34665334665334663, 0.5024975024975025]\n",
            "[0.15684315684315683, 0.1088911088911089, 0.055944055944055944, 0.03696303696303696, 0.02197802197802198]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "erH8NkGwuJjU",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Studying the effect of 3 different kernels on performance\n",
        "*   RBF kernel\n",
        "*   Chi-square kernel\n",
        "*   Additive Chi-square kernel\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "rFELxUuTo9ML",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "18e47df6-7a6a-4d31-cb4c-9e74e9395406",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524973481016,
          "user_tz": 240,
          "elapsed": 473850,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# Percentage wins lists for random/kbrl policies\n",
        "rand_list = []\n",
        "kbrl_list = []\n",
        "\n",
        "max_shots = 6\n",
        "num_lives = 2\n",
        "target_score = 20\n",
        "\n",
        "# Initialize envt\n",
        "env = environments.EnvChaseTarget(max_shots, num_lives, target_score)\n",
        "\n",
        "# Gather transitions\n",
        "t0,t1,t2,t3,r0,r1,r2,r3 = gather_transitions(n_samples=100, max_episodes=10000)\n",
        "\n",
        "# Define kernel metric\n",
        "metrics =['rbf', 'chi2', 'additive_chi2'] \n",
        "\n",
        "for metric in metrics:\n",
        "  print(metric)\n",
        "  # Create Theta and R matrices\n",
        "  Theta, R = convert_gathered_to_matrices(metric,t0,t1,t2,t3,r0,r1,r2,r3)\n",
        "\n",
        "  # List of gamma values to plot\n",
        "  gamma = 0.95\n",
        "\n",
        "  # Compute value function by iterating over update rule\n",
        "  vf = do_value_iteration(Theta, R, gamma, n_iter=1000)\n",
        "\n",
        "  # Play game according to random policy\n",
        "  random = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=True)\n",
        "  rand_list.append(random)\n",
        "\n",
        "  # Play game according to KBRL policy\n",
        "  kbrl = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=False)\n",
        "  kbrl_list.append(kbrl)"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "rbf\n",
            "chi2\n",
            "additive_chi2\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "nx-fgpX9txSD",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 414
        },
        "outputId": "e6f5f56e-e991-4c5d-fe6d-80156f09112b",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524973727434,
          "user_tz": 240,
          "elapsed": 397,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(kbrl_list, label='kbrl')\n",
        "plt.plot(rand_list, label='random')\n",
        "plt.scatter([i for i in range(len(metrics))], kbrl_list, color='red')\n",
        "plt.scatter([i for i in range(len(metrics))], rand_list, color='red')\n",
        "plt.xlabel('index of kernel metric')\n",
        "plt.ylabel('Percent win')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "print('Kernel metrics:', metrics)\n",
        "print(kbrl_list)\n",
        "print(rand_list)"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lYTKZyMnJYenSpdhsNqZMmUJ2djYPPfQQhmFw/vnnM2nSJF+VIiIiTQzD4LNdxby1bi+H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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fbcb8175748>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Kernel metrics: ['rbf', 'chi2', 'additive_chi2']\n",
            "[0.4145854145854146, 0.4645354645354645, 0.6763236763236763]\n",
            "[0.12287712287712288, 0.16283716283716285, 0.15384615384615385]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "3lfGfwJFGLdx",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "outputId": "a7131a2a-6781-4c2b-e371-a9227c2b0891",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524978923264,
          "user_tz": 240,
          "elapsed": 1104538,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# Percentage wins lists for random/kbrl policies\n",
        "rand_list = []\n",
        "kbrl_list = []\n",
        "\n",
        "max_shots = 6\n",
        "num_lives = 2\n",
        "target_score = 20\n",
        "\n",
        "# Initialize envt\n",
        "env = environments.EnvChaseTarget(max_shots, num_lives, target_score)\n",
        "\n",
        "# Gather transitions\n",
        "t0,t1,t2,t3,r0,r1,r2,r3 = gather_transitions(n_samples=100, max_episodes=10000)\n",
        "\n",
        "# Define kernel metric\n",
        "metrics =['rbf', 'chi2', 'additive_chi2'] \n",
        "\n",
        "# Create Theta and R matrices\n",
        "Theta, R = convert_gathered_to_matrices(metric,t0,t1,t2,t3,r0,r1,r2,r3)\n",
        "\n",
        "# List of gamma values to plot\n",
        "gamma = 0.95\n",
        "\n",
        "n_iters = [100,500,1000,1500,1800,5000,10000]\n",
        "for n_iter in n_iters:\n",
        "  print(n_iter)\n",
        "  # Compute value function by iterating over update rule\n",
        "  vf = do_value_iteration(Theta, R, gamma, n_iter=n_iter)\n",
        "\n",
        "  # Play game according to random policy\n",
        "  random = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=True)\n",
        "  rand_list.append(random)\n",
        "\n",
        "  # Play game according to KBRL policy\n",
        "  kbrl = play_game(env, vf, metric, gamma, n_episodes=1000, random_policy=False)\n",
        "  kbrl_list.append(kbrl)"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100\n",
            "500\n",
            "1000\n",
            "1500\n",
            "1800\n",
            "5000\n",
            "10000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "q4nYRZOHHMVV",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 414
        },
        "outputId": "40fa8bcc-8bd8-4611-aca2-b7db1502be62",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1524979595017,
          "user_tz": 240,
          "elapsed": 483,
          "user": {
            "displayName": "Julyan KB",
            "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
            "userId": "115093888831353118479"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "plt.plot(n_iters, kbrl_list, label='kbrl')\n",
        "plt.plot(n_iters, rand_list, label='random')\n",
        "\n",
        "plt.scatter(n_iters, kbrl_list, color='red')\n",
        "plt.scatter(n_iters, rand_list, color='red')\n",
        "\n",
        "plt.xlabel('n iterations')\n",
        "plt.ylabel('Percent win')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "print('n_iters:', n_iters)\n",
        "print(kbrl_list)\n",
        "print(rand_list)"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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2R44cwYULF5CYmIjXXnsNeXl5GDRoEF599dXW6B8RERHZqdGwl8vlCAsLg8lk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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fbcba825e10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "n_iters: [100, 500, 1000, 1500, 1800, 5000, 10000]\n",
            "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n",
            "[0.12387612387612387, 0.15584415584415584, 0.14985014985014986, 0.13886113886113885, 0.15384615384615385, 0.16083916083916083, 0.14685314685314685]\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}