ECAI_Exp1.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "6eXzKXL9J76b"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from tqdm.notebook import trange, tqdm\n",
        "\n",
        "ETA_Q = 5\n",
        "ETA_R = 5\n",
        "EPS = 1e-8\n",
        "STEP = 0.2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g4GAQ9f1J76e"
      },
      "source": [
        "# The power of contrastive examples\n",
        "\n",
        "We compare RL, contrastive examples and demonstrations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RgcJDZxsJ76g"
      },
      "source": [
        "## Environment 1 definition\n",
        "\n",
        "The environment looks like this:\n",
        "\n",
        "```\n",
        " ---- ---- ---- ---- ----\n",
        "|  1 |  2 |  3 |  4 |  5 |\n",
        " ---- ---- ---- ---- ----\n",
        "|  6 |    |  7 |    |  8 |\n",
        " ----      ----      ----\n",
        "|  9 |    | 10 |    | 11 |\n",
        " ----      ----      ----\n",
        "| 12 |    | 13 |    | 14 |\n",
        " ---- ---- ---- ---- ----\n",
        "| 15 | 16 | 17 | 18 | 19 |\n",
        " ---- ---- ---- ---- ----\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MhM-GZkGJ76g",
        "outputId": "dd20a059-133c-4749-c060-a8dbf5f0ea1e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "States: ['1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19']\n"
          ]
        }
      ],
      "source": [
        "S = list(map(lambda x : str(x), range(1, 20)))\n",
        "\n",
        "print('States:', S)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UlZgXAGoJ76h",
        "outputId": "0d3b025a-e326-4847-8bac-b8dce6246459"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Actions: ('Up', 'Down', 'Left', 'Right', 'No-Op')\n"
          ]
        }
      ],
      "source": [
        "A = ('Up', 'Down', 'Left', 'Right', 'No-Op')\n",
        "\n",
        "print('Actions:', A)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7zPS3eBhJ76i",
        "outputId": "1bdbd742-f33f-4650-c4c3-ae9f36a5533a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Transition probabilities ok?\n",
            "\t- Action Up: True\n",
            "\t- Action Down: True\n",
            "\t- Action Left: True\n",
            "\t- Action Right: True\n",
            "\t- Action No-Op: True\n"
          ]
        }
      ],
      "source": [
        "#               1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19\n",
        "Pu = np.array([[1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 1\n",
        "               [0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 2\n",
        "               [0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 3\n",
        "               [0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 4\n",
        "               [0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 5\n",
        "               [.8, 0., 0., 0., 0., .2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 6\n",
        "               [0., 0., .8, 0., 0., 0., .2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 7\n",
        "               [0., 0., 0., 0., .8, 0., 0., .2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 8\n",
        "               [0., 0., 0., 0., 0., .8, 0., 0., .2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 9\n",
        "               [0., 0., 0., 0., 0., 0., .8, 0., 0., .2, 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 10\n",
        "               [0., 0., 0., 0., 0., 0., 0., .8, 0., 0., .2, 0., 0., 0., 0., 0., 0., 0., 0.],  # 11\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., .8, 0., 0., .2, 0., 0., 0., 0., 0., 0., 0.],  # 12\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., .8, 0., 0., .2, 0., 0., 0., 0., 0., 0.],  # 13\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .8, 0., 0., .2, 0., 0., 0., 0., 0.],  # 14\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .8, 0., 0., .2, 0., 0., 0., 0.],  # 15\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],  # 16\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .8, 0., 0., 0., .2, 0., 0.],  # 17\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.],  # 18\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .8, 0., 0., 0., 0., .2]]) # 19\n",
        "\n",
        "#               1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19\n",
        "Pd = np.array([[.2, 0., 0., 0., 0., .8, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 1\n",
        "               [0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 2\n",
        "               [0., 0., .2, 0., 0., 0., .8, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 3\n",
        "               [0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 4\n",
        "               [0., 0., 0., 0., .2, 0., 0., .8, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 5\n",
        "               [0., 0., 0., 0., 0., .2, 0., 0., .8, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 6\n",
        "               [0., 0., 0., 0., 0., 0., .2, 0., 0., .8, 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 7\n",
        "               [0., 0., 0., 0., 0., 0., 0., .2, 0., 0., .8, 0., 0., 0., 0., 0., 0., 0., 0.],  # 8\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., .2, 0., 0., .8, 0., 0., 0., 0., 0., 0., 0.],  # 9\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., .2, 0., 0., .8, 0., 0., 0., 0., 0., 0.],  # 10\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .2, 0., 0., .8, 0., 0., 0., 0., 0.],  # 11\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .2, 0., 0., .8, 0., 0., 0., 0.],  # 12\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .2, 0., 0., 0., .8, 0., 0.],  # 13\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .2, 0., 0., 0., 0., .8],  # 14\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.],  # 15\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],  # 16\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],  # 17\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.],  # 18\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.]]) # 19\n",
        "\n",
        "#               1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19\n",
        "Pl = np.array([[1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 1\n",
        "               [.8, .2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 2\n",
        "               [0., .8, .2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 3\n",
        "               [0., 0., .8, .2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 4\n",
        "               [0., 0., 0., .8, .2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 5\n",
        "               [0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 6\n",
        "               [0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 7\n",
        "               [0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 8\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 9\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 10\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],  # 11\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],  # 12\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.],  # 13\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],  # 14\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.],  # 15\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .8, .2, 0., 0., 0.],  # 16\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .8, .2, 0., 0.],  # 17\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .8, .2, 0.],  # 18\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .8, .2]]) # 19\n",
        "\n",
        "#               1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19\n",
        "Pr = np.array([[.2, .8, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 1\n",
        "               [0., .2, .8, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 2\n",
        "               [0., 0., .2, .8, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 3\n",
        "               [0., 0., 0., .2, .8, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 4\n",
        "               [0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 5\n",
        "               [0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 6\n",
        "               [0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 7\n",
        "               [0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 8\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 9\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],  # 10\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],  # 11\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],  # 12\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.],  # 13\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],  # 14\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .2, .8, 0., 0., 0.],  # 15\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .2, .8, 0., 0.],  # 16\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .2, .8, 0.],  # 17\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .2, .8],  # 18\n",
        "               [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.]]) # 19\n",
        "\n",
        "Pn = np.eye(len(S))\n",
        "\n",
        "P = [Pu, Pd, Pl, Pr, Pn]\n",
        "\n",
        "print('Transition probabilities ok?')\n",
        "\n",
        "for aidx in range(len(A)):\n",
        "    print('\\t- Action %s:' % A[aidx], np.all(np.isclose(P[aidx].sum(axis=1), 1.)))\n",
        "\n",
        "gamma = 0.99"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "utyA_tD3J76k"
      },
      "outputs": [],
      "source": [
        "# Rewards are a convex combination of 7 features/rewards\n",
        "CELL_GOAL = np.zeros((len(S), len(A)))\n",
        "CELL_GOAL[2, :] = 1\n",
        "\n",
        "CELL_9  = np.zeros((len(S), len(A)))\n",
        "CELL_9[8, :] = 1\n",
        "\n",
        "CELL_10 = np.zeros((len(S), len(A)))\n",
        "CELL_10[9, :] = 1\n",
        "\n",
        "CELL_11 = np.zeros((len(S), len(A)))\n",
        "CELL_11[10, :] = 1\n",
        "\n",
        "RFEAT = (CELL_GOAL, CELL_9, CELL_10, CELL_11)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zcthHE-sJ76k"
      },
      "source": [
        "## MDP solver\n",
        "\n",
        "The next function is used to compute the optimal $Q$-function for MDPs. For computational efficiency, we pre-compute the optimal $Q$-function for all MDPs."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "KOVzIT71J76l"
      },
      "outputs": [],
      "source": [
        "def vi(M):\n",
        "    '''\n",
        "    Compute optimal Q-function for MDP M.\n",
        "\n",
        "    :param M: 5-tuple corresponding to MDP description: (S, A, P, R, gamma)\n",
        "    :return: np.array with shape (|S|, |A|), corresponding to Q* for M.\n",
        "    '''\n",
        "\n",
        "    S = M[0]\n",
        "    A = M[1]\n",
        "    P = M[2]\n",
        "    R = M[3]\n",
        "    gamma = M[4]\n",
        "\n",
        "    Q = np.zeros((len(S), len(A)))\n",
        "    quit = False\n",
        "    niter = 0\n",
        "\n",
        "    while not quit:\n",
        "        Qnew = np.zeros((len(S), len(A)))\n",
        "        V = np.max(Q, axis=1, keepdims=True)\n",
        "        for a in range(len(A)):\n",
        "            Qnew[:, a, None] = R[:, a, None] + gamma * P[a].dot(V)\n",
        "\n",
        "        if np.linalg.norm(Q - Qnew) < EPS:\n",
        "            quit = True\n",
        "\n",
        "        Q = Qnew\n",
        "        niter += 1\n",
        "\n",
        "    # print('Finished after %i iterations.' % niter)\n",
        "    return Q\n",
        "\n",
        "# --\n",
        "\n",
        "def greedy(Q):\n",
        "    '''\n",
        "    Compute greedy policy with respect to Q.\n",
        "\n",
        "    :param Q: np.array with shape (|S|, |A|).\n",
        "    :return: np.array with shape (|S|, |A|), corresponding to pi_g(Q).\n",
        "    '''\n",
        "\n",
        "    pol = (Q == np.max(Q, axis=1, keepdims=True)).astype(int)\n",
        "    pol = pol / np.sum(pol, axis=1, keepdims=True)\n",
        "\n",
        "    return pol\n",
        "\n",
        "# --\n",
        "\n",
        "def boltzmann(Q):\n",
        "    '''\n",
        "    Computes the Boltzmann policy with respect to Q.\n",
        "\n",
        "    :param Q: np.array with shape (|S|, |A|).\n",
        "    :return: np.array with shape (|S|, |A|) corresponding to pi_B(Q).\n",
        "    '''\n",
        "\n",
        "    Q = ETA_Q * (Q - np.max(Q, axis=1, keepdims=True))\n",
        "\n",
        "    pol = np.round(np.exp(Q), 3)\n",
        "    pol = pol / np.sum(pol, axis=1, keepdims=True)\n",
        "\n",
        "    return pol\n",
        "\n",
        "# --"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "M462WAssJ76m"
      },
      "outputs": [],
      "source": [
        "w = np.random.randn(4)\n",
        "r = np.sum([RFEAT[m] * w[m] for m in range(len(RFEAT))], axis=0)\n",
        "M = (S, A, P, r, gamma)\n",
        "Q = vi(M)\n",
        "pol = boltzmann(Q)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "r"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a5N1L7v66D7h",
        "outputId": "ebae402c-c32f-475f-836d-f29e67870432"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [-0.45738995, -0.45738995, -0.45738995, -0.45738995, -0.45738995],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [-0.13418367, -0.13418367, -0.13418367, -0.13418367, -0.13418367],\n",
              "       [-0.68468301, -0.68468301, -0.68468301, -0.68468301, -0.68468301],\n",
              "       [ 0.36912426,  0.36912426,  0.36912426,  0.36912426,  0.36912426],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],\n",
              "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zHt6k7pbJ76m"
      },
      "source": [
        "## RL updater\n",
        "\n",
        "We perform maximum likelihood estimation using SGD, where\n",
        "\n",
        "$$r_t\\sim\\mathrm{Normal}(w^\\top\\phi(s_t,a_t);\\eta)$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "gGr9dYM7J76m"
      },
      "outputs": [],
      "source": [
        "# Weight update\n",
        "def rl_update(wold, s, a, r):\n",
        "    '''\n",
        "    Updates the weights wold given the triplet (s, a, r) and the weight w.\n",
        "    The update is a Stochastic Gradient Descent (SGD) update on the negative log likelihood, assuming the\n",
        "    reward is disturbed by 0-mean Gaussian noise.\n",
        "\n",
        "    :param wold: np.array with shape (nfeat,)\n",
        "    :param s: int (state index)\n",
        "    :param a: int (action index)\n",
        "    :param r: float (reward)\n",
        "    :return: np.array with shape (nfeat,)\n",
        "    '''\n",
        "\n",
        "    feat = np.array([RFEAT[m][s, a] for m in range(len(RFEAT))])\n",
        "\n",
        "    grad = feat * (feat.dot(wold) - r)\n",
        "    wnew = wold - STEP * grad\n",
        "\n",
        "    return wnew"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-bLtdUSwJ76n"
      },
      "source": [
        "## Demonstration updater\n",
        "\n",
        "We perform maximum likelihood estimation using SGD, where\n",
        "\n",
        "$$\\mathbb{P}[a_t\\mid s_t]=\\frac{\\exp\\{\\eta Q^*_w(s,a)\\}}{\\sum_{a'}\\exp\\{\\eta_Q Q^*_w(s,a')\\}},$$\n",
        "\n",
        "where $Q^*_w$ is the optimal $Q$-function for the MDP with reward $w^\\top\\phi$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "O-ltVWL7J76n"
      },
      "outputs": [],
      "source": [
        "def policy_feat(pol, feat):\n",
        "    '''\n",
        "    Compute the policy-weighted feature matrix.\n",
        "    \"pol\" can be a single action index or a full\n",
        "    |S| x |A| policy matrix.\n",
        "\n",
        "    :param pol: int (action index) or np.array with shape (|S|, |A|) (policy)\n",
        "    :param feat: tuple (each element is a (|S|, |A|)-shaped np.array)\n",
        "    :return: np.array with shape (|S|, |nfeat|)\n",
        "    '''\n",
        "\n",
        "    if isinstance(pol, int):\n",
        "        return np.hstack([feat[m][:, pol, None] for m in range(len(feat))])\n",
        "\n",
        "    else:\n",
        "        return np.hstack([np.sum(feat[m] * pol, axis=1, keepdims=True) for m in range(len(feat))])\n",
        "\n",
        "# --\n",
        "\n",
        "def policy_trans(pol, P):\n",
        "    '''\n",
        "    Compute the policy-weighted transition probabilities.\n",
        "\n",
        "    :param pol: np.array with shape (|S|, |A|) (policy)\n",
        "    :param P: tuple (each element is a (|S|, |S|)-shaped np.array)\n",
        "    :return: np.array with shape (|S|, |S|)\n",
        "    '''\n",
        "\n",
        "    return np.sum([np.diag(pol[:, a]).dot(P[a]) for a in range(len(A))], axis=0)\n",
        "\n",
        "# --\n",
        "\n",
        "def policy_rew(pol, r):\n",
        "    '''\n",
        "    Compute the policy-weighted reward.\n",
        "\n",
        "    :param pol: np.array with shape (|S|, |A|) (policy)\n",
        "    :param r: np.array with shape (|S|, |A|) (reward)\n",
        "    :return: np.array with shape (|S|,)\n",
        "    '''\n",
        "\n",
        "    return np.sum(pol * r, axis=1)\n",
        "\n",
        "# --\n",
        "\n",
        "def discounted_freq(pol, P):\n",
        "    '''\n",
        "    Compute the discounted visitation frequencies given a policy pol.\n",
        "\n",
        "    :param pol: np.array with shape (|S|, |A|) (policy)\n",
        "    :param P: tuple (each element is a (|S|, |S|)-shaped np.array)\n",
        "    :return: np.array with shape (|S|, |S|)\n",
        "    '''\n",
        "\n",
        "    Ppol = policy_trans(pol, P)\n",
        "    return (1 - gamma) * np.linalg.inv(np.eye(len(S)) - gamma * Ppol)\n",
        "\n",
        "# --\n",
        "\n",
        "# Weight update\n",
        "def demo_update(wold, s, a, pol=None):\n",
        "    '''\n",
        "    Updates the weights wold given the pair (s, a) and the weight wold.\n",
        "    The update is a SGD update on the negative log likelihood, assuming the\n",
        "    actions are selected from a Boltzmann distribution (pol, which can be\n",
        "    precomputed).\n",
        "\n",
        "    :param wold: np.array with shape (|nfeat|,)\n",
        "    :param s: int (state index)\n",
        "    :param a: int (action index)\n",
        "    :param pol: np.array with shape (|S|, |A|) (policy)\n",
        "    :return: np.array with shape (nfeat,)\n",
        "    '''\n",
        "\n",
        "    if pol is None:\n",
        "        rhat = np.sum([RFEAT[m] * w[m] for m in range(len(RFEAT))], axis=0)\n",
        "        M = (S, A, P, rhat, gamma)\n",
        "        Q = vi(M)\n",
        "        pol = boltzmann(Q)\n",
        "\n",
        "    feat = policy_feat(greedy(Q), RFEAT) # (nS, nF)\n",
        "    disc = discounted_freq(greedy(Q), P) # (nS, nS)\n",
        "\n",
        "    grad = np.zeros(wold.shape)\n",
        "\n",
        "    for a_idx in range(len(A)):\n",
        "              #              (nS, nF)                     (nS, nS) (nS, nS) (nS, nF)\n",
        "        grad += ETA_Q * (policy_feat(a_idx, RFEAT) + gamma * P[a_idx].dot(disc).dot(feat))[s, :] * (pol[s, a_idx] - int(a == a_idx))\n",
        "\n",
        "    # Gradients are too small, so we push the step-size up\n",
        "\n",
        "    wnew = wold - 2 * STEP * grad\n",
        "\n",
        "    return wnew"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vQFCuICrJ76n",
        "outputId": "8267a7cf-5bee-44af-f10c-70cf04589439"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "policy_feat(.): (19, 4)\n",
            "policy_feat(.): (19, 4)\n",
            "policy_trans(.): (19, 19)\n",
            "policy_rew(.): (19,)\n",
            "discounted_freq(.): (19, 19)\n"
          ]
        }
      ],
      "source": [
        "print('policy_feat(.):', policy_feat(pol, RFEAT).shape)\n",
        "print('policy_feat(.):', policy_feat(0, RFEAT).shape)\n",
        "print('policy_trans(.):', policy_trans(pol, P).shape)\n",
        "print('policy_rew(.):', policy_rew(pol, r).shape)\n",
        "print('discounted_freq(.):', discounted_freq(pol, P).shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r7k45CqBJ76o"
      },
      "source": [
        "## Contrastive examples updater\n",
        "\n",
        "We consider the following contrastive examples:\n",
        "\n",
        "- In state $s$ action $a$ is better than action $a'$ because it will eventually lead you through state $s'$ and that is good.\n",
        "- In state $s$ action $a$ is worse than action $a'$ because it will eventually lead you through state $s'$ and that is bad.\n",
        "\n",
        "We consider that, given the target reward $r$,\n",
        "\n",
        "- A state $s$ is good if $r^*(s)>0$ for the optimal policy $\\pi^*_r$ given that reward.\n",
        "- A state $s$ is bad if $r^*(s)<0$ for the optimal policy $\\pi^*_r$ given that reward.\n",
        "- An action $a$ is _better_ than an action $a'$ in state $s$ and leading to state $s'$ if the following two conditions are cumulatively met:\n",
        "\n",
        " - $Q^*(s,a)>Q^*(s,a')$ ($a$ is better than $a'$)\n",
        "    * The transition probabilities by first taking action $a$ and then following $\\pi^*$ lead to larger transition probability from $s$ to $s'$ than those same probabilities taking action $a'$.\n",
        "    \n",
        "- An action $a$ is _worse_ than an action $a'$ in state $s$ and leading to state $s'$ if the following two conditions are cumulatively met:\n",
        "\n",
        " - $Q^*(s,a)<Q^*(s,a')$ ($a$ is worse than $a'$)\n",
        "    * The transition probabilities by taking action $a$ in $s$ and following $\\pi^*$ elsewhere lead to larger transition probability from $s$ to $s'$ than those same probabilities taking action $a'$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "MTFJKY7ZJ76o"
      },
      "outputs": [],
      "source": [
        "def sigmoid(z, eta):\n",
        "    '''\n",
        "    Compute sigmoid function.\n",
        "\n",
        "    :param z: float\n",
        "    :param eta: float\n",
        "    :return: float\n",
        "    '''\n",
        "\n",
        "    return 1 / (1 + np.exp(-eta * z))\n",
        "\n",
        "# --"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mQ4Px7V8J76o"
      },
      "source": [
        "We perform maximum likelihood estimation using SGD, where\n",
        "\n",
        "$$\\mathbb{P}[(s,a,a',s',k)\\mid w]=\\sigma(kr_w(s'))\\sigma(k(Q(s,a)-Q(s,a')))\\mathbf{P}_{a}^\\infty(s'\\mid s)$$\n",
        "\n",
        "(see precise definition in the paper)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "Uq4h5tnFJ76p"
      },
      "outputs": [],
      "source": [
        "# Weight update\n",
        "def explain_update(wold, s0, s1, a0, a1, k, Q=None):\n",
        "    '''\n",
        "    Updates the weights wold given the tuple (s0, s1, a0, a1, k)\n",
        "    and the weight wold. The update is a SGD update on the negative\n",
        "    log likelihood, assuming the distribution above.\n",
        "    '''\n",
        "\n",
        "    # Compute policy\n",
        "    r = np.sum([RFEAT[m] * wold[m] for m in range(len(RFEAT))], axis=0)\n",
        "\n",
        "    if Q is None:\n",
        "        M = (S, A, P, r, gamma)\n",
        "        Q = vi(M)\n",
        "\n",
        "    pol = boltzmann(Q)\n",
        "\n",
        "    paux = pol.copy()\n",
        "    paux[s0] = np.zeros(len(A))\n",
        "    paux[s0, a0] = 1.0\n",
        "\n",
        "    # Component 1 - reward\n",
        "    fpol = policy_feat(greedy(Q), RFEAT)      # (nS, nF)\n",
        "    rpol = policy_rew(greedy(Q), r) # (nS,)\n",
        "\n",
        "    grad_R = ETA_R * k * fpol[s1, :] * (sigmoid(k * rpol[s1], ETA_R) - 1) # (nF,)\n",
        "    #print('grad_R:')\n",
        "    #print(grad_R)\n",
        "\n",
        "    # Component 2 - Q-values\n",
        "    fa0 = policy_feat(a0, RFEAT)   # (nS, nF)\n",
        "    fa1 = policy_feat(a1, RFEAT)   # (nS, nF)\n",
        "    freq = discounted_freq(greedy(Q), P) # (nS, nS)\n",
        "\n",
        "    diff_Q = Q[s0, a0] - Q[s0, a1]       # scalar\n",
        "    diff_P = P[a0][s0, :] - P[a1][s0, :] # (nS,)\n",
        "    diff_F = fa0[s0] - fa1[s0]           # (nF,)\n",
        "\n",
        "    grad_Q = ETA_Q * k * (diff_F + gamma * diff_P.dot(freq).dot(fpol)) * (sigmoid(k * diff_Q, ETA_Q) - 1) # (nF,)\n",
        "    #print('grad_Q:')\n",
        "    #print(grad_Q)\n",
        "\n",
        "    # Component 3 - Pam\n",
        "    Pam = discounted_freq(paux, P) # (nS, nS)\n",
        "    pf = Pam.dot(fpol)             # (nS, nF)\n",
        "\n",
        "    grad_P = np.zeros(len(RFEAT))\n",
        "\n",
        "    for k in range(len(RFEAT)):\n",
        "        # for a single k\n",
        "        grad_aux = np.zeros((len(S), len(S)))\n",
        "\n",
        "        for a in range(len(A)):\n",
        "            for ap in range(len(A)):\n",
        "                fa  = policy_feat(a, RFEAT)  # (nS, nF)\n",
        "                fap = policy_feat(ap, RFEAT) # (nS, nF)\n",
        "                    #  (nS,)            (nS, nS) (nS, nS) (nS,)\n",
        "                dT  = fap[:, k] + gamma * P[ap].dot(freq).dot(fpol[:, k]) # (nS,)\n",
        "                tmp = ETA_Q * np.diag(paux[:, a] * dT * (pol[:, ap] - int(a == ap))).dot(P[a]) # (nS, nS)\n",
        "\n",
        "                grad_aux += tmp\n",
        "\n",
        "        dPk = Pam.dot(grad_aux).dot(Pam)      # (nS, nS)\n",
        "        if np.isclose(Pam[s0, s1], 0) and not np.isclose(dPk[s0, s1], 0):\n",
        "            print('Whoa! Zero!')\n",
        "            print('dPk:', dPk[s0, s1])\n",
        "\n",
        "        elif np.isclose(Pam[s0, s1], 0):\n",
        "            grad_P[k] = 0.                        # scalar\n",
        "\n",
        "        else:\n",
        "            grad_P[k] = dPk[s0, s1] / Pam[s0, s1] # scalar\n",
        "\n",
        "    #print('grad_P:')\n",
        "    #print(grad_P)\n",
        "\n",
        "    grad = grad_R + grad_Q + grad_P\n",
        "\n",
        "    wnew = wold - STEP * grad\n",
        "\n",
        "    return wnew"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EHi5ZyhkJ76p",
        "outputId": "5af6c7db-9b08-4a18-b643-e4fb125b579a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "P[a][s, :]: (19,)\n",
            "freq: (19, 19)\n",
            "fpol: (19, 4)\n",
            "P[a][s, :].dot(freq): (19,)\n",
            "P[a][s, :].dot(freq).dot(fpol): (4,)\n"
          ]
        }
      ],
      "source": [
        "freq = discounted_freq(pol, P)\n",
        "fpol = policy_feat(pol, RFEAT)\n",
        "print('P[a][s, :]:', P[0][0, :].shape)\n",
        "print('freq:', freq.shape)\n",
        "print('fpol:', fpol.shape)\n",
        "print('P[a][s, :].dot(freq):', P[0][0, :].dot(freq).shape)\n",
        "print('P[a][s, :].dot(freq).dot(fpol):', P[0][0, :].dot(freq).dot(fpol).shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2b_HimgRJ76p"
      },
      "source": [
        "## Experiments\n",
        "\n",
        "We now generate a random reward, and compare the performance of an RL updater, a demo updater and an contrastive examples updater in randomly selected sample rewards, demos and contrastive examples.\n",
        "\n",
        "We start by defining the samplers."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "EaY9kXR1J76p"
      },
      "outputs": [],
      "source": [
        "def sample_reward(M):\n",
        "    ''' Samples a reward for MDP M. '''\n",
        "\n",
        "    S = M[0]\n",
        "    A = M[1]\n",
        "    R = M[3]\n",
        "\n",
        "    # Sample a random state\n",
        "    sample_s = np.random.choice(len(S))\n",
        "    print(sample_s)\n",
        "\n",
        "    # Sample a random action\n",
        "    sample_a = np.random.choice(len(A))\n",
        "    print(sample_a)\n",
        "\n",
        "    # Sample a noisy reward\n",
        "    sample_r = R[sample_s, sample_a] + np.random.randn() / ETA_R\n",
        "    print(sample_r)\n",
        "\n",
        "    return (sample_s, sample_a, sample_r)\n",
        "\n",
        "# --\n",
        "\n",
        "def voice_reward(M, s, a, r):\n",
        "    ''' Converts a reward sample into a natural language string. '''\n",
        "\n",
        "    return 'The reward in state %s when performing action %s is %.2f.' % (M[0][s], M[1][a], r)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "example = sample_reward(M)"
      ],
      "metadata": {
        "id": "SjABUVGDED3d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8b61596d-9ef6-4698-9ca2-377128da09bd"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "9\n",
            "3\n",
            "-0.6333231825400135\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "NlSSm3f0J76q",
        "outputId": "85e4b39e-6e2e-4b19-9d78-273252ad5d85"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'The reward in state 10 when performing action Right is -0.63.'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "voice_reward(M, *example)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "YJNptXPOJ76q"
      },
      "outputs": [],
      "source": [
        "def sample_demo(M):\n",
        "    ''' Samples a demonstration for MDP M. '''\n",
        "\n",
        "    S = M[0]\n",
        "    A = M[1]\n",
        "\n",
        "    # Sample a random state\n",
        "    sample_s = np.random.choice(len(S))\n",
        "    print(sample_s)\n",
        "\n",
        "    # Sample a noisy action\n",
        "    Q = vi(M)\n",
        "    pol = boltzmann(Q)[sample_s, :]\n",
        "    sample_a = np.random.choice(len(A), p=pol)\n",
        "    print(sample_a)\n",
        "\n",
        "    return (sample_s, sample_a)\n",
        "\n",
        "# --\n",
        "\n",
        "def voice_demo(M, s, a):\n",
        "    ''' Converts a demonstration sample into a natural language string. '''\n",
        "\n",
        "    return 'In state %s you should perform action %s.' % (M[0][s], M[1][a])"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "example = sample_demo(M)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RpiBjKR1LU5l",
        "outputId": "81bc08dd-e6bc-4538-876f-5d422453b9fa"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "12\n",
            "4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "voice_demo(M, *example)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "OWhuHNPMLlNm",
        "outputId": "6fd165fa-c4b4-4f3a-f310-10bcf9aad243"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'In state 13 you should perform action No-Op.'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "id": "6G6YXh88J76q",
        "outputId": "93110ddd-cd61-4b22-b59d-6d353bbb2344"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
            "18\n",
            "0\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'In state 19 you should perform action Up.'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "Q = vi(M)\n",
        "pol = boltzmann(Q)\n",
        "print(pol.sum(axis=1))\n",
        "voice_demo(M, *sample_demo(M))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "s_RXa80KJ76q"
      },
      "outputs": [],
      "source": [
        "def sample_explain(M, echo=False):\n",
        "    ''' Samples an contrastive examples for MDP M. '''\n",
        "\n",
        "    S = M[0]\n",
        "    A = M[1]\n",
        "    P = M[2]\n",
        "    R = M[3]\n",
        "    gamma = M[4]\n",
        "\n",
        "    Q = vi(M)\n",
        "    pol = boltzmann(Q)\n",
        "    rpol = policy_rew(pol, R)\n",
        "\n",
        "    sample_complete = False\n",
        "\n",
        "    while not sample_complete:\n",
        "\n",
        "        # This ensures that the search for next state doesn't go on forever\n",
        "        stop_sample = False\n",
        "\n",
        "        # Sample a random initial state\n",
        "        sample_s0 = np.random.choice(len(S))\n",
        "\n",
        "        if echo:\n",
        "            print('Sampled state %s' % S[sample_s0])\n",
        "\n",
        "        # Sample a random initial action\n",
        "        sample_a0 = np.random.choice(len(A))\n",
        "\n",
        "        if echo:\n",
        "            print('Sampled action %s' % A[sample_a0])\n",
        "\n",
        "        paux = pol.copy()\n",
        "        paux[sample_s0] = np.zeros(len(A))\n",
        "        paux[sample_s0, sample_a0] = 1.0\n",
        "\n",
        "        Pam = discounted_freq(paux, P)\n",
        "\n",
        "        # Sample a random second action (different from the first)\n",
        "        quit = False\n",
        "        while not quit:\n",
        "            sample_a1 = np.random.choice(len(A))\n",
        "            quit = sample_a1 != sample_a0\n",
        "\n",
        "        if echo:\n",
        "            print('Sampled another action: %s' % A[sample_a1])\n",
        "\n",
        "        # Sample a random via state with non-zero reward (to fit the \"good\" or \"bad\" description)\n",
        "\n",
        "        quit = False\n",
        "        while not quit:\n",
        "            paux = np.maximum(rpol * (Q[sample_s0, sample_a0] - Q[sample_s0, sample_a1]) * Pam[sample_s0, :], 0)\n",
        "\n",
        "            # Ensure that there is a next state to sample\n",
        "            if np.isclose(np.sum(paux), 0):\n",
        "                if echo:\n",
        "                    print('Zero support distribution. Restarting sampling.')\n",
        "                stop_sample = True\n",
        "                quit = True\n",
        "            else:\n",
        "                paux = paux / paux.sum()\n",
        "                if np.isclose(paux[sample_s0], 1.):\n",
        "                    if echo:\n",
        "                        print('Departing from sink. Restarting sampling.')\n",
        "                    stop_sample = True\n",
        "                    quit = True\n",
        "                else:\n",
        "                    if echo:\n",
        "                        print(np.round(paux, 3))\n",
        "                    sample_s1 = np.random.choice(len(S), p=paux)\n",
        "                    quit = (sample_s1 != sample_s0)\n",
        "\n",
        "        if not stop_sample:\n",
        "            if echo:\n",
        "                print('Sampled another state: %s' % S[sample_s1])\n",
        "\n",
        "            # Check which one is better\n",
        "            if Q[sample_s0, sample_a0] > Q[sample_s0, sample_a1]:\n",
        "                k = 1\n",
        "            else:\n",
        "                k = -1\n",
        "\n",
        "            sample_complete = True\n",
        "\n",
        "    if echo:\n",
        "        print('Q(%s, %s) =' % (S[sample_s0], A[sample_a0]), Q[sample_s0, sample_a0])\n",
        "        print('Q(%s, %s) =' % (S[sample_s0], A[sample_a1]), Q[sample_s0, sample_a1])\n",
        "        print('reward(%s) =' % S[sample_s1], np.sum(R * pol, axis=1)[sample_s1])\n",
        "        print('P_m[%s](%s, %s) =' % (A[sample_a0], S[sample_s0], S[sample_s1]), Pam[sample_s0, sample_s1])\n",
        "\n",
        "    return (sample_s0, sample_s1, sample_a0, sample_a1, k)\n",
        "\n",
        "# --\n",
        "\n",
        "def voice_explain(M, s0, s1, a0, a1, k):\n",
        "    ''' Converts an exmplanation sample into a natural language string. '''\n",
        "\n",
        "    REL1 = ('better', 'worse')\n",
        "    REL2 = ('good', 'bad')\n",
        "\n",
        "    k = 1 - (k + 1) // 2\n",
        "\n",
        "    return 'In state %s, action %s is %s than %s because it may eventually lead you through state %s and that is %s.' % (M[0][s0], M[1][a0], REL1[k], M[1][a1], M[0][s1], REL2[k])\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "example = sample_explain(M, echo=True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XmC88r5fNrTr",
        "outputId": "8a186961-f973-4659-91fc-890550eba097"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sampled state 13\n",
            "Sampled action Right\n",
            "Sampled another action: No-Op\n",
            "Zero support distribution. Restarting sampling.\n",
            "Sampled state 1\n",
            "Sampled action Right\n",
            "Sampled another action: Down\n",
            "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            "Sampled another state: 11\n",
            "Q(1, Right) = 33.67938474095751\n",
            "Q(1, Down) = 33.009996468666394\n",
            "reward(11) = 0.36912426349048555\n",
            "P_m[Right](1, 11) = 0.7847653520607024\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "voice_explain(M, *example)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "E1FTTpiTNvCi",
        "outputId": "4d1cf7ea-57d0-4a19-bf86-0c95425c44d7"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'In state 1, action Right is better than Down because it may eventually lead you through state 11 and that is good.'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        },
        "id": "yQLwYih7J76r",
        "scrolled": false,
        "outputId": "a9a4627f-96a2-4e00-e269-708e2acd87ac"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sampled state 6\n",
            "Sampled action Right\n",
            "Sampled another action: Left\n",
            "Zero support distribution. Restarting sampling.\n",
            "Sampled state 13\n",
            "Sampled action Down\n",
            "Sampled another action: Right\n",
            "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            "Sampled another state: 11\n",
            "Q(13, Down) = 34.66783003511473\n",
            "Q(13, Right) = 34.32115173375567\n",
            "reward(11) = 0.36912426349048555\n",
            "P_m[Down](13, 11) = 0.7957630490263938\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'In state 13, action Down is better than Right because it may eventually lead you through state 11 and that is good.'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "voice_explain(M, *sample_explain(M, echo=True))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E5_t25yaJ76r"
      },
      "source": [
        "We now run a comparative study. Every 10 steps, for each of the three approaches, we:\n",
        "\n",
        "* Estimate the reward;\n",
        "* Compute the associated \"optimal\" policy;\n",
        "* Evaluate that policy in the correct MDP.\n",
        "\n",
        "The next function is used in the last step."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "1K4B1KnTJ76r"
      },
      "outputs": [],
      "source": [
        "def evaluate_reward(M, w):\n",
        "    ''' Computes the policy from weights w in the MDP M.'''\n",
        "\n",
        "    S = M[0]\n",
        "    A = M[1]\n",
        "    P = M[2]\n",
        "    R = M[3]\n",
        "    gamma = M[4]\n",
        "\n",
        "    Raux = np.sum([w[i] * RFEAT[i] for i in range(len(RFEAT))], axis=0)\n",
        "\n",
        "    Maux = (S, A, P, Raux, gamma)\n",
        "    pol  = greedy(vi(Maux))\n",
        "\n",
        "    Ppol = policy_trans(pol, P)\n",
        "    Rpol = policy_rew(pol, R)\n",
        "\n",
        "    Vaux = np.linalg.inv(np.eye(len(S)) - gamma * Ppol).dot(Rpol)\n",
        "\n",
        "    # Compute average value\n",
        "    return Vaux.sum() / len(S)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "gamma"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HPUCphrdDwT-",
        "outputId": "624225d7-ad22-4e8d-aa0f-c12cfb1fee5a"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.99"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yzbntx4sJ76r"
      },
      "source": [
        "We can now run our comparative study."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Approach 1**\n",
        "Here we do update the weights for all the expert rewards, demonstrations and explanations."
      ],
      "metadata": {
        "id": "hxA900EjA-Yt"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "scrolled": false,
        "outputId": "fd7610fc-f2f5-41b1-aee1-497676627e9b",
        "id": "5alZ8aINAcIX"
      },
      "outputs": [
        {
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            "2\n",
            "0.057116647830065904\n",
            "11\n",
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            "Done. Step complete.\n",
            "18\n",
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            "-0.13726695356348922\n",
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            "16\n",
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            "0.002603060266226526\n",
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            "0.12148905645818267\n",
            "10\n",
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            "Done. Step complete.\n",
            "7\n",
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            "-0.01427110340106696\n",
            "9\n",
            "4\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r 97%|█████████▋| 29/30 [09:02<00:14, 14.48s/it]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Done. Step complete.\n",
            "5\n",
            "0\n",
            "-0.2774742015598143\n",
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            "Done. Step complete.\n",
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            "-1.0292369333071687\n",
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            "17\n",
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          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 30/30 [09:16<00:00, 18.56s/it]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Done. Step complete.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
          ]
        }
      ],
      "source": [
        "# Simulation constants\n",
        "NRUNS = 30\n",
        "NSTEPS = 15\n",
        "\n",
        "# For performance statistics\n",
        "perf_rl   = np.zeros((NRUNS, NSTEPS))\n",
        "perf_demo = np.zeros((NRUNS, NSTEPS))\n",
        "perf_expl = np.zeros((NRUNS, NSTEPS))\n",
        "perf_ref  = np.zeros((NRUNS, NSTEPS))\n",
        "\n",
        "# For reproducibility\n",
        "np.random.seed(40)\n",
        "\n",
        "# Run sims\n",
        "for run in trange(NRUNS):\n",
        "\n",
        "    # Initialize a random reward\n",
        "    wopt = np.random.randn(len(RFEAT))\n",
        "    ropt = np.sum([wopt[i] * RFEAT[i] for i in range(len(RFEAT))], axis=0)\n",
        "\n",
        "    #print('Reward:')\n",
        "    #print(np.round(ropt,2))\n",
        "\n",
        "    # This is the \"target\" MDP\n",
        "    Mopt = (S, A, P, ropt, gamma)\n",
        "\n",
        "    # Optimal policy\n",
        "    popt = greedy(vi(Mopt))\n",
        "\n",
        "    #print('Optimal policy:')\n",
        "    #print(np.round(popt, 2))\n",
        "\n",
        "    # Weights for 3 approaches\n",
        "    w_rl   = np.zeros(len(RFEAT))\n",
        "    w_demo = np.zeros(len(RFEAT))\n",
        "    w_expl = np.zeros(len(RFEAT))\n",
        "\n",
        "    samples_expl = []\n",
        "    samples_demos = []\n",
        "    samples_rl = []\n",
        "\n",
        "    # Collecting demos\n",
        "    expert_rewards = []\n",
        "    expert_demonstrations = []\n",
        "    expert_explanations = []\n",
        "\n",
        "    # Run test\n",
        "    for t in range(NSTEPS):\n",
        "        #print('\\n[Step %i]' % (t + 1))\n",
        "\n",
        "        # Sample a reward and update\n",
        "        # print('Sampling reward... ')\n",
        "        (s, a, r) = sample_reward(Mopt)\n",
        "        # store expert demos\n",
        "        expert_rewards.append((s, a, r))\n",
        "        # print('Updating weights for reward... ')\n",
        "        w_rl = rl_update(w_rl, s, a, r)\n",
        "        # print('Weights:')\n",
        "        # print(w_rl)\n",
        "\n",
        "\n",
        "        # Evaluate\n",
        "        # print('Evaluating reward...')\n",
        "        perf_rl[run, t] = evaluate_reward(Mopt, w_rl)\n",
        "        samples_rl.append(perf_rl[run, t])\n",
        "\n",
        "        # print(voice_reward(Mopt, s, a, r))\n",
        "\n",
        "        # Sample a demo and update\n",
        "        # print('\\nSampling demo... ')\n",
        "        (s, a) = sample_demo(Mopt)\n",
        "        # store expert demos\n",
        "        expert_demonstrations.append((s, a))\n",
        "        # print('Updating weights for demo... ')\n",
        "        w_demo = demo_update(w_demo, s, a)\n",
        "        # print('Weights:')\n",
        "        # print(w_demo)\n",
        "\n",
        "\n",
        "        # Evaluate\n",
        "        # print('Evaluating reward...')\n",
        "        perf_demo[run, t] = evaluate_reward(Mopt, w_demo)\n",
        "        samples_demos.append(perf_demo[run, t])\n",
        "        # print(voice_demo(Mopt, s, a))\n",
        "\n",
        "        # Sample an contrastive example and update\n",
        "        # print('\\nSampling contrastive example... ')\n",
        "        (s0, s1, a0, a1, k) = sample_explain(Mopt)\n",
        "        # store expert demos\n",
        "        expert_explanations.append((s0, s1, a0, a1, k))\n",
        "\n",
        "        # print('Updating weights for contrastive example... ')\n",
        "        w_expl = explain_update(w_expl, s0, s1, a0, a1, k)\n",
        "        # print('Weights:')\n",
        "        # print(w_expl)\n",
        "\n",
        "        # Evaluate\n",
        "        #\n",
        "        # print('Evaluating reward...')\n",
        "        perf_expl[run, t] = evaluate_reward(Mopt, w_expl)\n",
        "        samples_expl.append(perf_expl[run, t])\n",
        "        # print(voice_explain(M, s0, s1, a0, a1, k))\n",
        "\n",
        "        perf_ref[run, t] = evaluate_reward(Mopt, wopt)\n",
        "\n",
        "\n",
        "        print('Done. Step complete.')\n",
        "\n",
        "# Compute statistics\n",
        "rl_mean = np.mean(perf_rl, axis=0)\n",
        "rl_std = np.std(perf_rl, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "demo_mean = np.mean(perf_demo, axis=0)\n",
        "demo_std = np.std(perf_demo, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "expl_mean = np.mean(perf_expl, axis=0)\n",
        "expl_std = np.std(perf_expl, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "ref_mean = np.mean(perf_ref, axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rl_min_1 = np.min(rl_mean, axis=0)\n",
        "rl_range_1 = np.max(rl_mean, axis=0) - np.min(rl_mean, axis=0)\n",
        "rl_norm_1 = (rl_mean - rl_min_1)/rl_range_1\n",
        "rl_normstd_1 = np.std(rl_norm_1, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "demo_min_1 = np.min(demo_mean, axis=0)\n",
        "demo_range_1 = np.max(demo_mean, axis=0) - np.min(demo_mean, axis=0)\n",
        "demo_norm_1 = (demo_mean - demo_min_1)/demo_range_1\n",
        "demo_normstd_1 = np.std(demo_norm_1, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "expl_min_1 = np.min(expl_mean, axis=0)\n",
        "expl_range_1 = np.max(expl_mean, axis=0) - np.min(expl_mean, axis=0)\n",
        "expl_norm_1 = (expl_mean - expl_min_1)/expl_range_1\n",
        "expl_normstd_1 = np.std(expl_norm_1, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "\n",
        "ref_min_1 = np.min(ref_mean)\n",
        "ref_range_1 = np.max(ref_mean) - np.min(ref_mean)\n",
        "ref_norm_1 = (ref_mean - ref_min_1)/ref_range_1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "61b651c5-b6c4-4714-982d-8e5fe208c6a5",
        "id": "5YiySuE1AcId"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-61-0a3e9315431f>:19: RuntimeWarning: divide by zero encountered in divide\n",
            "  ref_norm_1 = (ref_mean - ref_min_1)/ref_range_1\n",
            "<ipython-input-61-0a3e9315431f>:19: RuntimeWarning: invalid value encountered in divide\n",
            "  ref_norm_1 = (ref_mean - ref_min_1)/ref_range_1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 470
        },
        "outputId": "824f5910-c2e8-4d87-c7bd-644b12bc60e5",
        "id": "CUsgHS7WAcId"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plot\n",
        "plt.figure(figsize=(4, 5))\n",
        "plt.fill_between(range(NSTEPS), rl_mean + rl_std, rl_mean - rl_std, color='g', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), demo_mean + demo_std, demo_mean - demo_std, color='r', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), expl_mean + expl_std, expl_mean - expl_std, color='b', alpha=0.1)\n",
        "plt.plot(range(NSTEPS), rl_mean, 'g:', label='LfR1')\n",
        "plt.plot(range(NSTEPS), demo_mean, 'r--', label='LfD1')\n",
        "plt.plot(range(NSTEPS), expl_mean, 'b-', label='LfCE1')\n",
        "plt.plot(range(NSTEPS), ref_mean, 'k:', label='Optimal1')\n",
        "#plt.xlabel('N. samples')\n",
        "#plt.ylabel(r'$||V_\\pi||_2$')\n",
        "plt.xlabel('Teaching signals')\n",
        "plt.ylabel('Average return')\n",
        "plt.ylim(0, 120)\n",
        "plt.xticks(range(0, 15))\n",
        "plt.legend(loc='best')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Approach 2**\n",
        "The learner update the weights only if the reward, demonstration or explanation is relevant."
      ],
      "metadata": {
        "id": "7wOoj7SoApVL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Simulation constants\n",
        "NRUNS = 30\n",
        "NSTEPS = 15\n",
        "\n",
        "# For performance statistics\n",
        "perf_rl   = np.zeros((NRUNS, NSTEPS))\n",
        "perf_demo = np.zeros((NRUNS, NSTEPS))\n",
        "perf_expl = np.zeros((NRUNS, NSTEPS))\n",
        "perf_ref  = np.zeros((NRUNS, NSTEPS))\n",
        "\n",
        "# For reproducibility\n",
        "np.random.seed(40)\n",
        "\n",
        "# Run sims\n",
        "for run in trange(NRUNS):\n",
        "\n",
        "    # Initialize a random reward\n",
        "    wopt = np.random.randn(len(RFEAT))\n",
        "    ropt = np.sum([wopt[i] * RFEAT[i] for i in range(len(RFEAT))], axis=0)\n",
        "\n",
        "    # This is the \"target\" MDP\n",
        "    Mopt = (S, A, P, ropt, gamma)\n",
        "\n",
        "    # Optimal policy\n",
        "    popt = greedy(vi(Mopt))\n",
        "\n",
        "    # Weights for 3 approaches\n",
        "    w_rl   = np.zeros(len(RFEAT))\n",
        "    w_demo = np.zeros(len(RFEAT))\n",
        "    w_expl = np.zeros(len(RFEAT))\n",
        "\n",
        "    samples_expl = []\n",
        "    samples_demos = []\n",
        "    samples_rl = []\n",
        "\n",
        "    # Collecting demos\n",
        "    expert_rewards = []\n",
        "    expert_demonstrations = []\n",
        "    expert_explanations = []\n",
        "\n",
        "    # Run test\n",
        "    for t in range(NSTEPS):\n",
        "        # Sample a reward and update if more informative\n",
        "        (s, a, r) = sample_reward(Mopt)\n",
        "        expert_rewards.append((s, a, r))\n",
        "\n",
        "        # Evaluate current performance\n",
        "        current_perf = evaluate_reward(Mopt, w_rl)\n",
        "\n",
        "        # Temporarily update and evaluate\n",
        "        new_w_rl = rl_update(w_rl.copy(), s, a, r)\n",
        "        new_perf = evaluate_reward(Mopt, new_w_rl)\n",
        "\n",
        "        # Update weights if new information is more informative\n",
        "        if new_perf > current_perf:\n",
        "            w_rl = new_w_rl\n",
        "\n",
        "        # Store performance\n",
        "        perf_rl[run, t] = evaluate_reward(Mopt, w_rl)\n",
        "        samples_rl.append(perf_rl[run, t])\n",
        "\n",
        "        # Sample a demo and update if more informative\n",
        "        (s, a) = sample_demo(Mopt)\n",
        "        expert_demonstrations.append((s, a))\n",
        "\n",
        "        current_perf = evaluate_reward(Mopt, w_demo)\n",
        "\n",
        "        new_w_demo = demo_update(w_demo.copy(), s, a)\n",
        "        new_perf = evaluate_reward(Mopt, new_w_demo)\n",
        "\n",
        "        if new_perf > current_perf:\n",
        "            w_demo = new_w_demo\n",
        "\n",
        "        perf_demo[run, t] = evaluate_reward(Mopt, w_demo)\n",
        "        samples_demos.append(perf_demo[run, t])\n",
        "\n",
        "        # Sample a contrastive example and update if more informative\n",
        "        (s0, s1, a0, a1, k) = sample_explain(Mopt)\n",
        "        expert_explanations.append((s0, s1, a0, a1, k))\n",
        "\n",
        "        current_perf = evaluate_reward(Mopt, w_expl)\n",
        "\n",
        "        new_w_expl = explain_update(w_expl.copy(), s0, s1, a0, a1, k)\n",
        "        new_perf = evaluate_reward(Mopt, new_w_expl)\n",
        "\n",
        "        if new_perf > current_perf:\n",
        "            w_expl = new_w_expl\n",
        "\n",
        "        perf_expl[run, t] = evaluate_reward(Mopt, w_expl)\n",
        "        samples_expl.append(perf_expl[run, t])\n",
        "\n",
        "        perf_ref[run, t] = evaluate_reward(Mopt, wopt)\n",
        "\n",
        "        print('Done. Step complete.')\n",
        "\n",
        "# Compute statistics\n",
        "rl_mean_2 = np.mean(perf_rl, axis=0)\n",
        "rl_std_2 = np.std(perf_rl, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "demo_mean_2 = np.mean(perf_demo, axis=0)\n",
        "demo_std_2 = np.std(perf_demo, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "expl_mean_2 = np.mean(perf_expl, axis=0)\n",
        "expl_std_2 = np.std(perf_expl, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "ref_mean_2 = np.mean(perf_ref, axis=0)"
      ],
      "metadata": {
        "collapsed": true,
        "id": "pe3u5HCX9dgc",
        "outputId": "3090c7fd-f492-4131-e2aa-ac56bc13035e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r  0%|          | 0/30 [00:00<?, ?it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "12\n",
            "2\n",
            "-0.034408627405261356\n",
            "9\n",
            "1\n",
            "Done. Step complete.\n",
            "14\n",
            "4\n",
            "-0.03832162007531013\n",
            "8\n",
            "1\n",
            "Done. Step complete.\n",
            "13\n",
            "2\n",
            "0.4629269416588988\n",
            "11\n",
            "1\n",
            "Done. Step complete.\n",
            "9\n",
            "3\n",
            "-0.655020128141129\n",
            "11\n",
            "1\n",
            "Done. Step complete.\n",
            "2\n",
            "0\n",
            "-0.7661188324640122\n",
            "12\n",
            "1\n",
            "Done. Step complete.\n",
            "2\n",
            "0\n",
            "-0.7109900523216924\n",
            "11\n",
            "1\n",
            "Done. Step complete.\n",
            "2\n",
            "3\n",
            "-0.5836576387161814\n",
            "9\n",
            "1\n",
            "Done. Step complete.\n",
            "10\n",
            "1\n",
            "1.003993174691577\n",
            "13\n",
            "0\n",
            "Done. Step complete.\n",
            "16\n",
            "0\n",
            "0.10501256825718175\n",
            "10\n",
            "2\n",
            "Done. Step complete.\n",
            "18\n",
            "1\n",
            "0.2519075530269076\n",
            "4\n",
            "1\n",
            "Done. Step complete.\n",
            "9\n",
            "4\n",
            "-0.7158987066660757\n",
            "1\n",
            "3\n",
            "Done. Step complete.\n",
            "3\n",
            "2\n",
            "0.23245177379883858\n",
            "1\n",
            "3\n",
            "Done. Step complete.\n",
            "15\n",
            "0\n",
            "-0.22502654143430703\n",
            "14\n",
            "3\n",
            "Done. Step complete.\n",
            "0\n",
            "0\n",
            "0.12634370016708824\n",
            "16\n",
            "3\n",
            "Done. Step complete.\n",
            "18\n",
            "1\n",
            "-0.022390211479049862\n",
            "12\n",
            "1\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r  3%|▎         | 1/30 [00:25<12:22, 25.60s/it]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Done. Step complete.\n",
            "10\n",
            "3\n",
            "-0.9840742835522331\n",
            "7\n",
            "0\n",
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            "Done. Step complete.\n"
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            "\n"
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "expert_rewards"
      ],
      "metadata": {
        "id": "wlVaStTb6xrx",
        "outputId": "e42f75c3-f9b4-4687-b35e-dd38ea2912d3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(5, 0, -0.2774742015598143),\n",
              " (0, 2, 0.013216260435200258),\n",
              " (16, 1, 0.3277847979307706),\n",
              " (9, 3, -1.0292369333071687),\n",
              " (1, 3, 0.28616493665976195),\n",
              " (1, 2, 0.3440117685264571),\n",
              " (11, 1, -0.19163031584891316),\n",
              " (6, 2, -0.285511515993251),\n",
              " (4, 4, -0.1127097260703764),\n",
              " (11, 0, -0.2752266633173911),\n",
              " (13, 1, -0.2094623039011431),\n",
              " (17, 3, -0.1766361099181517),\n",
              " (16, 2, -0.18180811425814775),\n",
              " (8, 2, 0.2541327232390824),\n",
              " (12, 3, 0.2916960168688812)]"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "expert_demonstrations"
      ],
      "metadata": {
        "id": "WBU42xIV8ytK",
        "outputId": "96f1d7ae-1f5c-4771-b840-1bef76f9de11",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(11, 1),\n",
              " (3, 3),\n",
              " (0, 3),\n",
              " (5, 0),\n",
              " (5, 0),\n",
              " (11, 1),\n",
              " (0, 3),\n",
              " (15, 3),\n",
              " (2, 0),\n",
              " (10, 3),\n",
              " (7, 1),\n",
              " (10, 2),\n",
              " (0, 3),\n",
              " (16, 3),\n",
              " (17, 3)]"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "expert_explanations"
      ],
      "metadata": {
        "id": "99sPzris80VV",
        "outputId": "32fc646b-c3a4-438b-cd29-f2f31b316e44",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(14, 10, 3, 0, 1),\n",
              " (11, 10, 1, 0, 1),\n",
              " (6, 10, 0, 1, 1),\n",
              " (16, 10, 3, 1, 1),\n",
              " (13, 10, 0, 4, 1),\n",
              " (1, 10, 3, 0, 1),\n",
              " (7, 10, 1, 0, 1),\n",
              " (9, 10, 0, 1, 1),\n",
              " (2, 10, 3, 0, 1),\n",
              " (3, 10, 3, 0, 1),\n",
              " (1, 10, 3, 1, 1),\n",
              " (14, 10, 3, 1, 1),\n",
              " (5, 10, 0, 1, 1),\n",
              " (15, 10, 3, 4, 1),\n",
              " (6, 9, 1, 3, -1)]"
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          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "samples_expl"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_s1vF_RpXlY8",
        "outputId": "2ccc1adb-daa6-4a89-daef-cdf9027d41bb"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[82.29851066343026,\n",
              " 82.29851066343026,\n",
              " 82.29851066343026,\n",
              " 82.29851066343026,\n",
              " 82.29851066343026,\n",
              " 82.29851066343026,\n",
              " 82.29851066343026,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339]"
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          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "samples_demos"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "81AIB4D7Z9Jb",
        "outputId": "fb5924b7-9887-4091-c981-3e863c2d2af6"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[82.34743273778683,\n",
              " 82.34743273778683,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339,\n",
              " 82.39635481214339]"
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          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "samples_rl"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PRp21MS2bJuz",
        "outputId": "6739f354-b12a-4176-c339-f0a60855c96f"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[3.95343359247816,\n",
              " 3.95343359247816,\n",
              " 3.95343359247816,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 10.305091033594506,\n",
              " 18.520448131392154,\n",
              " 18.520448131392154]"
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          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rl_min_2 = np.min(rl_mean_2, axis=0)\n",
        "rl_range_2 = np.max(rl_mean_2, axis=0) - np.min(rl_mean, axis=0)\n",
        "rl_norm_2 = (rl_mean_2 - rl_min_2)/rl_range_2\n",
        "rl_normstd_2 = np.std(rl_norm_2, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "demo_min_2 = np.min(demo_mean_2, axis=0)\n",
        "demo_range_2 = np.max(demo_mean_2, axis=0) - np.min(demo_mean_2, axis=0)\n",
        "demo_norm_2 = (demo_mean_2 - demo_min_2)/demo_range_2\n",
        "demo_normstd_2 = np.std(demo_norm_2, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "expl_min_2 = np.min(expl_mean_2, axis=0)\n",
        "expl_range_2 = np.max(expl_mean_2, axis=0) - np.min(expl_mean_2, axis=0)\n",
        "expl_norm_2 = (expl_mean_2 - expl_min_2)/expl_range_2\n",
        "expl_normstd_2 = np.std(expl_norm_2, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "\n",
        "ref_min_2 = np.min(ref_mean_2)\n",
        "ref_range_2 = np.max(ref_mean_2) - np.min(ref_mean_2)\n",
        "ref_norm_2 = (ref_mean_2 - ref_min_2)/ref_range_2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Cp7XlfPJSPym",
        "outputId": "b3fbf159-2e4d-4bca-9f96-3ddca2df0dca"
      },
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-68-cd22d9c44287>:19: RuntimeWarning: divide by zero encountered in divide\n",
            "  ref_norm_2 = (ref_mean_2 - ref_min_2)/ref_range_2\n",
            "<ipython-input-68-cd22d9c44287>:19: RuntimeWarning: invalid value encountered in divide\n",
            "  ref_norm_2 = (ref_mean_2 - ref_min_2)/ref_range_2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 748
        },
        "id": "d3cHTDXIJ76s",
        "outputId": "16afa4fd-579b-41d0-ed60-63bf0c1ad80a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-72-8c29bcf4f898>:8: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"g-\" (-> color='g'). The keyword argument will take precedence.\n",
            "  plt.plot(range(NSTEPS), rl_mean_2, 'g-', label='LfR2', color='green')\n",
            "<ipython-input-72-8c29bcf4f898>:9: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"r--\" (-> color='r'). The keyword argument will take precedence.\n",
            "  plt.plot(range(NSTEPS), demo_mean_2, 'r--', label='LfD2', color='orange')\n",
            "<ipython-input-72-8c29bcf4f898>:10: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"b-\" (-> color='b'). The keyword argument will take precedence.\n",
            "  plt.plot(range(NSTEPS), expl_mean_2, 'b-', label='LfCE2', color='purple')\n",
            "<ipython-input-72-8c29bcf4f898>:11: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"k:\" (-> color='k'). The keyword argument will take precedence.\n",
            "  plt.plot(range(NSTEPS), ref_mean_2, 'k:', label='Optimal2', color='gray')\n",
            "<ipython-input-72-8c29bcf4f898>:17: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"g:\" (-> color='g'). The keyword argument will take precedence.\n",
            "  plt.plot(range(NSTEPS), rl_mean, 'g:', label='LfR1', color='darkgreen')\n",
            "<ipython-input-72-8c29bcf4f898>:18: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"r--\" (-> color='r'). The keyword argument will take precedence.\n",
            "  plt.plot(range(NSTEPS), demo_mean, 'r--', label='LfD1', color='darkred')\n",
            "<ipython-input-72-8c29bcf4f898>:19: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"b-\" (-> color='b'). The keyword argument will take precedence.\n",
            "  plt.plot(range(NSTEPS), expl_mean, 'b-', label='LfCE1', color='darkblue')\n",
            "<ipython-input-72-8c29bcf4f898>:20: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"k:\" (-> color='k'). The keyword argument will take precedence.\n",
            "  plt.plot(range(NSTEPS), ref_mean, 'k:', label='Optimal1', color='black')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x500 with 1 Axes>"
            ],
            "image/png": 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9gKnTJ7PH3tu1GnvcSbOYOn0yd917W+bY199+wdTpk9l5j21ajT3tzOOZOn0yN996febYr4t+Yer0yUzfaYtWY8+efSpTp0/mb3+/InOstm5V5vNsyQUXn8vU6ZO57KoLM8fC4VBmbFoZhEJJzjj7fKZOn8z+h5zGZVd+lrmlx17w19czxw47whq79/7Hc/lVn2Vu22y/BVOnT+ZPF7yYOXbqGdfwvxcWkyvsnUCW8HrtPq7dRRo6IhzO9MjN4HJlbPEKtk3eJn+QUlJTF808P//Cj1mwMM6KFREgCMCyZUkeXbZgvdf+74VlQGPqWRyAVTU6jzy2/tiXX1kBRDNjP/60lnOy92e0QpGyLU/ahkUwGKS4uJjm5maKioq6/Lp40uCLr5cihaSqunztVs82B7UamzEHCQG6QbipESMRw+3x4fb5UFQ1KyYB2xxkm4OyaQ7SdcGPP9bxw/w1LFgYYeGvUebPb6I5mADSO0Un6WiCoUNdbDyhgHHjyvD7vJn3SyQi1kiXF1Wxvie6kUCYBorqwOlwtRgbTY31ZMYGgxF22HEjTjlta7pDV+WarQTouRIIBOP8vDBAebnHjiLpCMNApMw+CDPVDF2z/89s8oZQKMn8nwPMn9/E/J+s24KFzei6WG+sw6EwflwxkyaVMmliKZMnljJx41KKi3MTGr5mdYihw0sYPb6qW6/rqlyzzUFZwBZmbZAy8Yhk0rL7CwGaI2PqCQQS3HPffL74cg1DhngZPtzP8OEFjBjmtx4P8+P12l/PDY1o1KC+IU5DQ4yGhgT1DXHqG2I0Zh7HCYf1zi/UDUKhJCtWRto8V1DgZNLEUiZNLGHypDImTSxl3Lgi3C4tq3PoT+xfmU12kRJ0A5GIW8IfwOFESZkUYjGD/z78M3fd+yPBYMc/5opyD8OH+xmRUhDDh6UfW0rC48nt19c0BYmEoOVmOeOraKH3FaX1OetJq7v1z+cp2TYMSCCWEezWLS3MGxvj1NfHaWiMZ87HYmZW3787DBvqSwn80swqf8Rw/4D43HqDrQRssoNpgmEiEgkwdCt2v0WWrWEInn52Ebf9+zvqVscAmLhxCccevTHhsM6KlWFWroywclWE5SvCRCJGRlh8821Dm2/ZlpKoGuIlqQvicYN43CQeN4nFUo8TBrGYmTkXi1uPYzGTRGL9cW2ZAmxyj8ejUVHuoazMQ0WFh4pyD+VlHsrLreeFBU6yKZfdHge/GV/c/YKP0kARCaTqtfJUAC1Zg0OvIZ19rtBaqSY8k5CaPzV2Fc7kypYXbDU26Z2I0Lpunu4pthKw6R1t2ftbRPdIKXn19eX881/fsHiJ5XgbMdzPuWdtzgH7j0ZV1/81SykJBlOKYVWEFSvCrEgpiJUrreeRaOdKwiZ/KCx0WsK83EN5mYuKMieV5S7KSx1UlGtUlmlUlKlUlCq4yn6T+f444wvRjHoUGUSRTSB1FGkCVsJgpGQfUCwx5gl/gjOxCEUKwEzdC5AmCoLmimMtgQ34mufiiX6dOmeihGMowTiKiKPKOKtHXo9wlAJQUnc7RQ1PosjUeWHdK1gRbUsnf4DuHmONrX+A0rrbaI/lG79KwreZ9X/S+CwVNde1O3bFhGeJF2zbi//1rmErgTzBjBv8/N9vCC+1IkNky1VBy4ey7eNdGtOSDrb9nRoE0vV2zHTWrrRWQgq0NID8sCbOkz8EWRywzD6FLpWDNi5kt9F+nB8v45OPl3X2ThQCk1I3ioFiP3KSj4guqY8arIma1EcN6qMm9VGT5riJU1NwrXNzawrO1H2n5xwKLjV9b5lxhEjXE1r7P5Q5lP4PSx1otX/IjEmdE3RtFSvlgA6OVWTCWunqNbiIoZeuzS3whD/AEVwDS9aOF8Dq1C1csv/asZHPcei17b5PuNgFimWfd0e/xplc0e7YSPHbSMWVGvsdzuTyNkapgI9I0ftI1YrYcsUErsRW7V43Wvg1QvsVAGeiAmfiWGjn04v7FyK0Omts0oszfny71437lyO0EImEQXD3MYye0z3HcFexlUAe0PTjGj4891UCPw+OFe0qVN7ExSKsH6cLyXbobJ/UcX8XYvl32Xuv8tRt4yxdzwRiqZtNb1GB4anHLZOdhqRu7dFybPoTbo+WC4ni1K09WppeCoBNOhhb1+Kxp5Ox9albmrHdGDu6g7FNqRsUDfF3MK532EqgHxGmYP7dX/LNjfMQSRNPhY/xszZFdbZR0KzFykJp7W1s5zggJFLXrTo7bZAZ39bSv6NlqKKk6vW0HlTTlOCRD1fzwc9W0oxDVZi5RSm/nV5JiW/gftXWfgTrO4XXLzjX+nmr63RwLq/owfS84Y/xN7+GIpKZY7p7IxK+LUm6x2I6K9ZeXlo7Q4kKrP89smlNOJRg1NbDcnb9fv1lvvfee/z973/niy++oKamhueee46DDz44c15KyWWXXcbdd99NIBBghx124I477mDChAmZMY2NjZx11lm8+OKLqKrKYYcdxr/+9a9WySz5SGRlkA9nv8bqj63VyYg9xzL9bzPwVPg6eWU3SOqIcAgczrZ/2G0Kqu7/INesiXHbHd/z5NO/YhgSRYED9x/N2WduzqiR+f052PQMV2w+pqMU01kNgD+wgqGLPyTpGk2o7HBCZYdiuDfq51kODtJ5ArmiX5VAJBJhiy224MQTT+TQQw9d7/wNN9zALbfcwoMPPsiYMWOYM2cOM2fO5Mcff8TjsQqPHXXUUdTU1PDGG2+g6zonnHACp556Ko8++mhf/zldQkrJkud/5tNL30IPJnH4nEy9dBfGz9qE1aujLPh2DQ6HisOh4nRaN4cz9dzR4rFT7VRgC9NyXClabkpEhUJJ7r5vPg/896dMaN8uOw3lT+dtyaSJpTl5T5v+Q9PrKGx8jsKmZ3DHfqSx6hwah10AQKRoN1b85n/EfVPtlf0Ao1+VwD777MM+++zT5jkpJTfffDOXXHIJBx10EAD//e9/qaqq4vnnn2fWrFnMnz+fV199lc8++4ytt7ZSqm+99Vb23Xdf/vGPfzBsWO62UD0h0Rzn04vfYumLvwBQsVU1O9y8N4WjS1i+LMg+ez5NPN71OOl07wKnK6UgHOsoDBX8fgcVFd5MuF15mZuKci/lLR4XFTm7tQNIJEweeewX7rzrR5oCVoXDLbco5/zZW7LtNrlxXtn0D4oZxd/8KoWNz+ALvYeScntLxYkqQmsHqi7i/u6VNbDJD/LWULt48WJqa2uZMWNG5lhxcTHbbrst8+bNY9asWcybN4+SkpKMAgCYMWMGqqryySefcMghh7R5bau2ytryrMFgMHd/SIqaD5Yx70+vE60No2gKm50znU3P2AY11YDmgfu+Jx438fudeH0ODF2gGwJDFxiGwDTXN9ybpsQ0rRj33uB0qJSVuykvS8VkV3jWPs6E9XkoL3fzwYe1/OvWb6mptWqcjBtbxJ/O3YIZe4wY9Ek1GxxSMGr+zjj1msyhmH8qobLDCZcckAmhtBnY5K0SqK21wsKqqlqvLKuqqjLnamtrGTKkdZSBw+GgrKwsM6YtrrvuOq644op2z2cTM27w1Q0f8tO9XwFQOLaUHW6eScUW1ZkxweYETz3xMwC3/2cGO+40Yr3rCCExDIGeUgrrKonM8dRjPZogGYoQSSpWdmYqpr6hMU5DiyzNUEhHNwR1dTHq6roeE1Nd7ePsMzbjkIPG2J3UBgnO+EL8gVcJVJ2R6samEi3aHV/oA0JlhxEqOzQTD28zeMhbJZBLLrroImbPnp15HgwGGTlyZNbfp+nHNXxwzqs0/2KFfk44ejOmXrwzDl/rstNPPPYT0ajBbzYuZYcdh7d1KVRVweXScHWxZokIh8EoypRraI9EwrTS91uk9Dc0JlrVbkmn9zc2JSgudnHqSZM5+vcTcl62wSb3qGaQgqb/UdTwJJ7olwDECrcn4bd6NdQPv8yKl7d3eYOWvP0VV1dbK+W6ujqGDh2aOV5XV8eWW26ZGbN69epWrzMMg8bGxszr28LtdmfKzeaCTOjnPz5C6AJPhY/pN+zJiD3WX0XpuuDBB34A4MSTN8uOSUUIqwWj2rnCcLs1hg71M3Ro53HIpilQFKXNLF+bAYQ08YY+pKjxCfyBV1GlVdteohEt2h2UtQuHdIkDm8FL3iqBMWPGUF1dzdy5czNCPxgM8sknn3D66acDsN122xEIBPjiiy+YOtXqXvXWW28hhGDbbXOfbt0W4RVBPvpTi9DPvVKhn+Vth36+9spiamsiVFR6OeCg8dmZhGlaJRwc2a10qOUoysimb/GG5zH8199lnic8GxMqO4JQ2aGYzo6SuGwGI/2qBMLhMAsXLsw8X7x4MV9//TVlZWWMGjWKc889l6uvvpoJEyZkQkSHDRuWySWYNGkSe++9N6eccgp33nknuq5z5plnMmvWrD6PDJJSsvi5n/js0rfRQ1bo59aX7cK4Izdpd3UvpeTeu78F4KhjJuN2Z0doi1SXLttRa6OYEQoCL6HIBMEKq91prGA7Ep5JxAqmESo7goRvC9vcswHTr0rg888/Z7fddss8T9vpjzvuOB544AEuuOACIpEIp556KoFAgB133JFXX301kyMA8Mgjj3DmmWeyxx57ZJLFbrnllj79OxKBOJ9ePJelL1lt4iqmDGWHm2dSuFFJh6/74vM6vvu2Hpdb4/dHT8rOZFKlnLtiCrIZpEiBJ/wJRY1PUBB4GVVEMRwVBMt/Z5l6FI3lE9+wBb8N0M9KYNddd+2wfrmiKFx55ZVceeWV7Y4pKyvr18Sw+k9W8N6V77Yb+tkR991tFdE55NAJlJd7OxndRdKmIFsJbHA4kisobHiKosancCaXZo4n3WMIlR2JInSklrL32wrAJkXe+gTyHT2m8+6Fb/L1HV8AbYd+dsTSpUHeeH0JAMefuGn2JiYkCNFpVJBNP5IucdwuaqY+vVWitKM8kLVjS1bfTcmaewAQagGh0gMJlR1hJXHZQt+mHWwl0EM+vvnjjAL4zdGbM+XindYL/eyI/97/PVLCLruOZMJvspd0I/Sk/YPPc7yh9xn+6+/bPb9m+OU0DzkFsEopj1hwcLtjG4b+habqswEIlh2BKzafYPmRREr2zdTOt7HpCFsJ9JDp505nwWu/UnnIJCYfMrFbr22ZHHbCydncBXQ9NNSm79D0OjR9DUlfFj/rNkj6NmHVhCdz+h42gw9bCfQQp9fJoS/M4ueFgW6/tivJYT3CNME0wOXK3jVteoU/8BpDlv0JoRWwfOLrCK2IWOH2LNrs+3Zf03IFH/dv2clYT7vnbGy6gq0E+picJIelMS07sx0a2v8oZpSKlZdT3PAIAIZrGKrRbPWMVZxdr7vTnbE2Nj3AVgJ9zKv/tyj7yWEphJ60mr3Y9Cvu6DdULTkTV2IREoXAkD/QMPTPoOYuS93GpqfYSqAPkVJy3z1WWOjRWUwOA1KmINsf0K9IQUndvymv+TsKBoazmrqN/kWscMf+npmNTbvYSqAPaZkc9rtsJYelSTd9d9gfaf+h4Il+iYJBuGRfVo+8wTbl2OQ9tsToQ3KSHJYi00XM9gf0PVJPZeIqrB71DyLBfQmVHmaH6toMCGwDch+Rs+QwWFsqQrN1el+imCGGLD2HqqXnZY4JRxmhssNtBWAzYLClRh/x4H25SQ4D1oaG2qagPsMT/oyqpWfjTC5DotJU9UeS3sn9PS0bm25jS40+oLk5wdNPWslhJ56yWfbfwBQgJYodGZR7pEFZ7b8orb0ZBYHuGkndRrfYCsBmwGIrgT4gnRy28cQytt8h+yWu7dDQvsGRWEr1kjMzHbiCpYdSP/IaK/bfxmaAYiuBHKPrgv+mksNOOGnT7Dtu7VIRfYMUDPv1WFyJhZhqIWtGXke47JD+npWNTa+xl485JpfJYUCL0tG2IzKnKCprRlxFrGA7lk9601YANoMGeyeQQ3KaHJZ+D9MqM2yHhnYRkUAVcYSjOHPI1/wWmrEG1QyimiG01L1qBgmX7EO47FAAYkU7s7JwJzvyx2ZQYSuBHPL5Z7V892097lwkhwFIiUzqtikIq1aP1Nb2ca5cdj7OxHJUEcoId9UMocoECc8klk96MzO2YuVluBKL2ryuL/Qecf9UDPdGqTeyFYDN4MJWAjkkvQs4OAfJYcAG3UXMkViONzwPb/hjvOF5GM4hrPzN/zLnveFP2hXsqgi3eh4rmI7uHo1QCxFaIUIrytybjjJMR2VO/xYbm/7EVgI5YunSIG++brX4y3pyWJoNrItYQdP/8DXPxRv+GKe+stU5TV+NIuKZ0soNQy9AkcmUQF8r1C1BX9DqtWtG/b3P/gYbm3zDVgI5IqfJYSmEoQ9O84SUOBOL8ES+IFT228zfWND0IgXNr1hDcBD3b0G8YDtiBdOJ+bdpVVs/UnpAv0zdxgbosHd6vmErgRyQ8+QwWFsqYjCYgqTEmVhomXdC8/CGP8Fh1AEQK5iG4R4NQKjsEJKe8cQKtifu37qVD8DGpj/RdUEyaaLrAqkoQBaVgFzbcjoX2EogB+Q6OQwAwxgUXcQKG56gfNW1OIz6VseF4ibhn4JmhjBSxyIl+xEp2a/vJ2lj0wIpJbou0HWBYUiElDgcKm63RkmpG7dLw+HomtTuyoYhGYtTUJy7XhS2Esgyui548P4cJoelGahdxKQEDKvqJiC0YhxGPULxEPdPIVawPbGC6ST8W9mtE23ygpZCX9clEonToeJya5SUOvC4HbhcKk6nmpPfo0NxdFmp9Oj6ObvyBsorLy+irjaHyWEpBlypCCnxhj+gfNUNRIt2pnHonwGIFu7AignPEfdtYXfesskL0kI/qQsMXSIViVNTcXv6Ruj3NbYSyCJSSu6/N7fJYUCqaqgYMP4AT/gTymv+jjc8DwBHcjmNVeeA6kJqhcQLpvXzDG0GEtl2ulrutZR5p4XQ93g1vKUO3C4Nt1vD6UgJ/PTbC4mUYu1FejOBDs+Lnl+7C9hKIIvkPDksjRBWfoAjv5WAO/IV5TV/xxd6FwCpuGiuOJqmqjNBdRGPG0RjZibASVUUNIeCQ1PQNBWHQxkUK60NHSlla0HXkcyTEiEkprn23jRMTCGRUqJA64i4dgVo94Sy06HidqmUFjtwuy3B73Smd9oipSnWeW9aPE4f78n3tb3XZK6pomq5+63bSiCLpJPDDjksR8lhKYSR/13EilffS+XKSwErnDNYPoum6rMxXMORUhIKJlFUhepqL26XA8MU6ElBPGFg6JJEwiQcFUgJKgqaBpqmtlISNvmNNAUYuvVEUTJCzTQlppCIlvdy7YJX0RQcDhVNVXA4VXwFTpwu1TqmqTic6wjEdsyiSouQGqX1ifXGOpwqzvR1M8K3jdcoHQv+XPwmhSlQcvh9t5VAlliypDn3yWGQ313EpAmK9UOKFO9J+aprCZceSGP1uZmyC8mkSTiiU1jooqLci8+3/t8hhMQwrMgLwxAYpiCZMEkkBYYuSCQEprCEi0rbu4e0ycBahErSi1EppbVGTC0U2zqXWVy2OJcmj/VuXiClTPW7Nqy4RpcL1enAFGsFpqoqaE4FzaHhdSq4nBpOtwNNU1I3y96uaSqqXRgx5+ShJBmYtEwOGz8hh83F87CLmDO+iLLaf4I0qRvzbwAM9yiWbPoZwlEGWMIhHDEQUjJkiI+yUne7q3lVVXC5tDajXy3lkFIQpmXHTcSt+OxEwiQSkxkFoCiKtQAlfb92pWYtTC2FoaigqQqqmh5rPbZu2V+BSSnzehfXE2R6cSJNUN0onkJwOFFS31NLqFsCvqWwt4V8/5M/kmQA09yc4JmnfgFymByWJo+6iDkSyymr/SeFjU+jYCJRaEhchOEeCZBRAIYhCIV1vB4HlZVeCgp6XubC4VDbDJdruXtIC9m0BWLtY6XVDr7lcZueIYUAXbe2Sw4/qscDLmdefD9tuoatBLJAtpLDpJQYomOHlkgmrQzCTsblEkdyFRWrb6Wk8XEUaZllQoV7UF99PnHnCKumUYpo1EDXTUpK3JSXe3E6VfQczV1xqDg7+UbLde5b239suoo0TMveryiWycflBqcDoSjW/6mZ24iWDYlcl6CwlUAvMVokh5148mY9XlUKYWUeutT2t8hSCIQwwenMuqNIEVEUoYM0UGQSJXWPNJCqO1O6wRt8j6pfj0OVCQCihTvRNPTPJAq2BiAd6W+aglDIwO1SGVHlp6jIaa+4BzpSgmEgDQNF06DAj+JygcNhf7Y5Rsvh/6+tBHrJ3DeXZpLD9j9wXPcvkFr9Kwp4HBoOtf2wSGkamFKguLogUKWkePkcPMEPMoK9pYCPF+1E47i7M8OHf7UJSkqwr0u8cHvqN34GAFG4DVIrJOHZkubhF5As3B6Alub7eMIkHjOoKHFRWeHNXb6ETZ+QNvlIIVAcDpSiQhS321IENjlDSklYD1Mfqcfj8DC0cGhO3sdWAr1ASsmjD88HepgcJiW6kDgUBVdKAXQ4vBtdxByJxRSuvrfd86oZan1txZlRAhINqTpBcSIVB1IrXDtO81E3+XWEs3q9UBkpJcGQjqooVA/xUlrqsR1/AxhpmpbwBxSnE83jAZfLtvfnGCklIT3EmvAa6qP1RPQIY0vG5uz9bCXQCz76aBU//9TYo+QwKSWGKXFqCm6HhtqJYJdSIpNJlC5mCRuesdRs9in++seJF+2UEujWDdWJUFvX1K/Z4huk4gDF0WnJQuFaf0WSCf0scFFZ4cHn2zB6HAxGpGEgdd1abLjdlvB32ua8XCOlJJgMUhepoynahCENilxFGNLo/MW9wFYCveCOf38DdD85TAiJKSUuTcXt6GL9ESGs8NBubMFN90iCw//cpbE9LcsspSQSMTBMyZBKK/Qzl8WubHKDTNv7dd0y+fj9qG53JsTTJncIIdYK/1gTAkGhsxCP0yqgGEwGc/r+9ifcQxYubOL/XrbaF3YnOcwQAkVa9n/nOvZ/XTcJhZLAWpNPOtxRJpOIcBzV40ZR0mahlsmNrcMdFQVIPVcVMnHZ2cQwBKGQjterMbTaR2HhwC5rvSGyrr1fKyqyTD62vT/nCCFoTjZTF7aEv0RS5C7C7ejbQoq2Eughb765FClhux2GdS05LGX/1xQFt1PF0YZdNRo1KC31UFjoapXpCmCEwgivB8XjsUoHCZHJZm39GHzN/0dh4+MES35LuGg/kqZVg6VlqJmiKmiqlbSjamsfd3XLH40aJJMmZWVuyss8uFy20BhISNOEpLXgaGXyse39OUcIQVOiibpwHYFYABQodhfjcvTPIspWAj3kD3/Ykq2nVbHg1+ZOx7a0/7s0Da0NZ6lMFc4qLHRRVORe/5yMQkFBl/oJK1++iRKai3fIplSO/h2mKax6LS1uuiFIJg10XWAakqQpMkW6LE8gOBwKmqq2UhIAwVASp0Nj+DA/RUUu21Y8QJAtQzxVFbxeK7krByGeUkrMRAIjHsdMJPCWl6Nu4KYlwzQIJAPUhetojjejKAql3lIc/VwCZsP+VHrJ+PGlmHT84xHCKpLl0qwIoPYcwImEiduttu1QNQzLH9CVLmLShNVvWI+r9kFVFVRVoz3dkVY+hiFbKQvDFCST1s00BQldZHYThYVOKiu8eDz212cgYJV00JGmmVN7vxQCIx5Hj8XQQyGMeNwqdiglisOBr7w8q+83UDBMI7Pyb443o2kapZ7+F/5p8mMWgxQzZaZxO1RcWscO4HjcMq206VQ1TaSUXatj0/Q5it6IdJZAaed1+hUlXccFoG2TjlXSd62C8HoddujnAKBViKfDgeb3Zz3EUxhGRvAng0HMRAKkRHO5cPp8qA4HRixGvLERd2Eh2gBvh9oddFOnKZ4y+yQCuDQX5d5ytDzzt9hKIBdk7P/gdmo4O/nRWbZ/SUFB2z8QkUx2+Yer1L1qPRgyA9TsfLyd7SZs8gtpGFY9nxyFeJrJpCX4IxGSkQgikQBFQXO7cRcVrfdddXi9xBsbiTc346+szMoc8pm08K8N19KcaMbj8FDprcw74Z/GVgLZJqUAnGr79v91icdNPB4Nr3f9jyNToKurX6DVr1mvGzKzW9O2Gdi0svdrGvj9qFkq6dDSvp8MhTBiMWthomlobjfOkpJO38Pp95NoasJdWIjDM3h7RyeNJAubFtIQa8Dj8DDENyQnlWizia0EsoiQltnEpakd2v/XJR43qKz0th3CaRiWLbcry/DocpTg90hUaydgk3fIdL5HNhFibYhnYWFWQjzbs+9rTiea242roKDzi7RAc7tJRiIkmpsHrRLQTZ0lgSXUR+sZ4huStyv/dbGVQJZIR9a4HBruTuz/LRGpipp+f9tCXuh6qzr4HaIHkOU7WY9dG6YTLp+Rum6t1LNtV0uXdMhCiKep6ySam0k0N7dp3+8NroIC4k1NuIqKcHpz13mvPzBNk6XNS6mJ1FDpy1/TT1vYSiALGKZAVcDt0HB2MyErHjfweh14vesLBimlFcvd1S9U8WbI7V+2IoRs8obM5wioBQUoXm9ehtXqsRjRujr0cBjN68VVWJjV3raay4UejRJvasLh8eTl/0FPEEKwrHkZq0KrqPBW4NQGlvPMVgK9RFGsMq9uR9fs/+uSSJhUV/vajrYxTevW3ZWjMnBWIYMdKQQykUBxOi0FkKfe9WQoRLiuDplM4i4tzZmAdvr9JJqbcRcX4/L7c/IefYkQguXB5awMr6TMW9ZvCV+9Ib89FnmOgoJDVfA4e6YATFOgqrRfbM0wLFtvV7b4sRWQWNPtOdjkDqnrlgLwelGLivJSAUgpiTY0EFyxAoTA3QUnb2/QnE4UKUk0NeW8WUquEUKwKrSKFcEV/VLuIVvYSqAXaGrXKoC2Rzxu4vU62026EulKjl1AWXAjyuvjYcFNPZqLTfaQUiITCRACtaDA2gHkoY1YmCbR1auJ1NTg6IGzt6c4CwtJBIPokUifvF+uqIvUsSy4jEJ3IV7nwPVx2OagfiSRMKioKGxT0HcrNFRKqHsNBYksmpyDmdp0lYFi/jGTSSJ1dSSam3EVFqL14TxVTUNRVeKNjTh9vgFZr2h1ZDVLA0vxOr0DWgGAvRPoN3TdxOFQ28wNACxfgGFAVyIyQj+gxFcgVS9U7JLdidp0mYFg/gHQo1HCK1eSaG7GU1LSpwogjauggGQoRDIc7vP37i0NsQYWBxbjdDgpcPXN7imX2DuBfiIeN/H7ne13IzMMJHTN1FRnJYhRsTNoA3tVMhCRUkI6a7awEPI48iXR3Eykrg4pBJ4cOoA7Q1FVVKfT2g34/VmNQsolgXiARU2LUBWVIndRf08nK9g7gX5C102Kitzt/gjTGZldIV0qQlbtnbX52XQNKQQyHgeHA7W4OG/DP6UQROvrCa1ciaKqVnmHfp6n0+dDD4fRB8huIJgI8mvTrwgpKPGU9Pd0skZeKwHTNJkzZw5jxozB6/Uybtw4rrrqqlZRBVJKLr30UoYOHYrX62XGjBksWLCgH2fdOcmkicvVdpkIWFv4q0v+gEQDNH1mPR6yVxZnadMZA8X8IwyDSF0d0dpanF4vTl/PushlG0VV0dxuovX1VrXRPCacDLOoaREJM0GZt6y/p5NV8loJXH/99dxxxx3cdtttzJ8/n+uvv54bbriBW2+9NTPmhhtu4JZbbuHOO+/kk08+we/3M3PmTOLxeD/OvGPicQO/39l+I5Z0aGhXlMCaN1AQyKJNwTcyuxO1aRMppbX6FwKtsDBvo38AjESC8KpVxBoacBUVobnzK4zR4fNhxGIkgrltodgbonqURU2LiOgRKn2DrwBeXvsEPvroIw466CD2228/AEaPHs1jjz3Gp59+Clg/xptvvplLLrmEgw46CID//ve/VFVV8fzzzzNr1qx+m3t7SGnV7u+oFaMwjE66FLSgck/ElneAOvCSVAYiAyX6ByAZDhOpq8NMJPrV/t8RiqJYVUabmvo8SqkrxPU4i5oWEUqEqPBV9Pd0ckJe7wS233575s6dyy+//ALAN998wwcffMA+++wDwOLFi6mtrWXGjLXF0oqLi9l2222ZN29eu9dNJBIEg8FWt74i3TymXVNQusRAV+u0uMth5FEw/LdZnKVNW7Qy/xQX560CkFISDwQIrVyJNAw8OU4A6y1Or9faDTR33qWvL0kaSRYFFtEcb6bCV5H31UB7Sl7vBC688EKCwSATJ05E0zRM0+Saa67hqKOOAqC2thaAqqqqVq+rqqrKnGuL6667jiuuuCJ3E++AeNyktNSN09m+KQjD6FoXMZs+oVX0T1ERuNt36Pc3aQdwbM0aHB4PjgFSqM2Z2g24i4ryovHMuhVBB6sCgDzfCTz55JM88sgjPProo3z55Zc8+OCD/OMf/+DBBx/s1XUvuugimpubM7fly5dnacYdk24e05EpKN1FrEsJNEsfhF9vgWjfzH9DQUppmX1ME2kYraN/8jj809R1wjU1RFevxun3DxgFAFbjGZFIEA8E+nsqrSqCVvgqBlRF0J6Q1zuBP//5z1x44YUZ2/5mm23G0qVLue666zjuuOOorq4GoK6ujqFDh2ZeV1dXx5Zbbtnudd1uN+5+cJB11DwmTbe6iC26HSX8E8IzzHYKt4GU0sqmbnmzTrS6rVvBRlEUqzJgStgrXi+q39/rzNZ0K0aRavTe0a27tKwA6i4uHjBx9y1x+v0kAgHcRUX91nNgoFcE7Ql5rQSi0eh62zBN0xBCADBmzBiqq6uZO3duRugHg0E++eQTTj/99L6ebqdYZSLaaR5DN0tFRJeghH9CKhpU7pHlmQ48ZKriqmzRsEWBtcK85U3TQFUhJXDVtsa0VAK9EP6mrmPG4yQjEZLhsNWKsYXiURQlM4/MTVFQHQ5UhwMlfd9SQShKq+dmPN4nFUBzjeZ2o0ejJAIBHKkFXl+Srgi6IrxiwFYE7Ql5rQQOOOAArrnmGkaNGsUmm2zCV199xU033cSJJ54IWD+gc889l6uvvpoJEyYwZswY5syZw7Bhwzj44IP7d/LrIIREyvabxwDd6yKWzhIunQ6u0uxMcgAhpcyU1siYzzQN1eu1wjXbEep9ISDTPXiToRB6NGrt7hQFzeNZrxVjerciU93BpBBr2znGYpljgNUwPv3CFoog3fHLVVKS878t1zj9fuKBAK7i4j5tPNOyImixu3jAVgTtCXmtBG699VbmzJnDH//4R1avXs2wYcM47bTTuPTSSzNjLrjgAiKRCKeeeiqBQIAdd9yRV199FU+etbCLx42UKagDAZ9axXZFUCkpJSCrNpxewlIIy2lumsiUEMTjscIKHQ7QtH5ZBUspLcEfi2V68JrJJKrDgcPttoqktTOvtOmpu7uNlkrD4fH0uutXvtBfjWdqw7WDoiJoT1DkQC/qnQWCwSDFxcU0NzdTVNT1eiDhcJKlS4OUlnaucBobY1RX+6moaD9b02xuBl1H6cxfYURQXhuNIhKIXT+FwoldnvNAIrPaT5l5FFW1hL3LhZoS/P1VgVJKiRGPY8bjJIJBq/l6ix68+RDhMlARhkEyHKZoo42y3njGNE0MaWAIA1OaGMIgbsRZGliKx+nJy4JwqyOrGV4wnNGlo7v1uq7KtcGxfMhzTFOgaUqHpqDMKrcr/oD6d1FEAundCAo2zuJM+59MI/ZUAT1F08DlsoRqP67203PLNF8PBtHjcTBNVJcLh9ebd4lOAxXV4UBRlLWlpjv5vIUQGaGeFuyGNDBNE13oJI0kCZEgaSatMcJESIFpmkgkAoHf6c9LBdAX2EqgD+iseQzQvVaSsWVI1QNVMzPOy4FKq9W+ENYP3uEAvz9j5unPevNSCEvoR6Mkg0HMRMIywaSasAzEKJyBgDNValoPh3EVFgKWsI/oEcLJMAkjgS504kYcU1rCvqVgl0iUlAdFVVU0VUNTrJtDc+BQHWiKNqjj/7uKrQT6gETCpKKik+qSptn10tFj/oAceSyY0azNsT+Quo40jLxa7a9LdM0aYg0NICWax2NV37QFR85JN56JrFlDVDMI6WGa4k1Ek1F0oaOqKg7VgapY927NbQl5lzbo4/qzja0EcoxhCBwOpcPcAEi1kuyOcHH4rNsARJomMlUqWyssBJcrLwuwJcNhYql697app+/QTZ2oHiVkBlmzbDkyVoxa6MXtcFPkKdogYvf7ElsJ5JhYzMDn66B5DC3yA7qiBIzowBX+Qlh1kQDF51sbzpmHCNMkVl9vhXbaCiDn6KZOJBkmlAjTnGwmpscAcDhU/DGFwiEVeftdGejYSiDH6LpJVVUnzq20P6ALWczKxweAEUVueRuUTM3iTHOHlBJ03YrwcbtRfb68Lb6WJh4IkAyH8ZRueDkYfUXSSBLRw4TiYQLJAAkjAYDH4aHUU4qqqkivxGgOYYQjOIsHRyevfMNWAjkk3TzG5+tE4KXqBXXqD0jUQ9PnVkN599COx+YJ0jAs04/TiVZcbJl+8sTe3x5GPE68oQFnnnYJG8jE9TgRI0IwHiSYDJIwEigoeJ1eyrylKErr3bCiKCguJ8nGAJrfN2jyIfIJ+380h8TjBoWFrvabx6QQut41YbP6dUsBFG0B3mFZmmVukEJYlTdVFaWgwDL9DACHqpSSWEMDQtdxFWyYIYPZJq7HCOsRgvFmgskQCTOBpqh4HV4KvGXrCf510bwe9EAQPRTGXVrSN5PegOi2Eqirq+P8889n7ty5rF69mnVzzcwWtVs2ZLrSPCY9rqv1gpTVr1sPqvK3jWSmH4IQ4PVawn8Ard6SoRCJQABXN5IGbdpGCEFDrIGVoZUkjAQOzYHX4e12g3ar5IYbvTGAs8BvJQraZI1u/zqPP/54li1bxpw5cxg6dKi9XW6HZFJ02DwmQ9of0FmGqdBh9ZtA/jaUz4R8ulyoPh84nQPq+2HqOtE1a9BcLjv+v5fE9Tg14Rrqo/V4HB4q/b1ry6h5PSSbmtGDIdzlg6vHb3/TbSXwwQcf8P7773dYqtnGigrqsHlMmrQ/oDNTSePHKEYQ6arIO4dwq5DPoiLL7j8ATD/rEm9qwojFbGdwL2mON7MqtIpgIkiJpyRrIZ2az4MeaMZRUIDm3nDKchjCyDjNc0G3f6kjR45czwRk0xopJUIICgo6/6IKw+hiwbhXrQdD9oJObKh9hRTCarii61bIZ0mJ1XRlACoAPRol3tiIq6BgQO1e8gnTNKkJruLXpl+JGlEqfOVZjenX3G6EbqAHQ1m7Zj6zMriSf877J4c9cRhP/fhUzt6n2zuBm2++mQsvvJD//Oc/jB49OgdTGvhYZSIcnZqCMvbzLpgeZOXukGxADjs4S7PsOQMx5LMjpBDE6uutrGC78FuPiOsxVoVqWBNbQ4HTj9eZm1wWy0ncjOp04PD7Bp1/wBAGj375KA989AArWJGpHf7qr69yyS6X5OQ9u60EjjzySKLRKOPGjcPn8+Fc50NobGzM2uQGKunmMQ5HJyvi7tQLGrIHckhum8e02uG19Thd+17XB1TIZ2ckmptJBoO4B0E9/v4gEGtiZWglET1KqacUh5q7QADV5UIYJrFVdWhuJ46iIstZ7Mnfvs9doSZUw5M/PMlTPzzF6l9XgwmUwXa/2Y59JuzDkZOPzNl792gnYNM+XWoekyZVNC1XRayklBCPr9c+sT1aNixpdb/OsYEU8tkZRiJBtL4ebZD8PX2JaZrUhmupDdeiqArlXQj3zAYOnxd8XsxEgmRDI3pTAK3Ah7OwEIffN2A+R1OYPPz5wzz2+WMsEUsQ0moe5Cn2UOWqYvZes9lnk31YHVmNS8vdDrVbSkDXdd59913mzJnDmDFjcjWnAU0i0YXmMSmEYdCltcvyx6BwEhRv0b2qoYYBDgear8XWvC3B3t7jds4PlB9ZZ0gpiTc2YiYSeMvsiJPuEE1GWRVaRX2sniJ3ER5H3zdx0txuy09gGBjhKEYwjOb14iwuzGtTUV24jqd/fJonvnuC2l9qrYNDYNqYaczadBZ7jdsrp0J/XbqlBJxOJ8888wxz5szJ1XwGPLGYQXW1H1XtWFh32R9ghFC+ORNF6ojdvoCCCV2fjGGA34+SZ13W8gU9HCbe1ITbzgnoMlJKGuONrAqtIq7HqfBW9Hs5ZtXhQC0sQAqBGY/npanIFCYPff4Qz377LAviCzCllU/lLHQyvHA4F+59IbtvvHu/zK3b5qCDDz6Y559/nvPOOy8X8xnQmKZAVZXOy0SAlUxlmlbp5I5Y8zaK1JG+MeAf3+W5SCmRitLatm+TQRgGsfp6VE2zSxF0Ed3UqQ3VUhepxaE5KfeV9/eUWqGoKg6fD3ysNRUFmnH4fTgKC/rFVLQmsoanf3yaR798lLpFddbBoTB1xFRmbTqLmeNm4nH27yKt29/+CRMmcOWVV/Lhhx8ydepU/Ou0fzv77LOzNrmBRjxu4vM5O08Qg7X+gE52AulewlTt3W1TkB6LEWtuxldejnudBucbOvFAgGQkYucEdJFIMsLK0EoaYg0Uu4v7xfzTHVqaivRwBD0YQvN6cZUUofm8OTUVmcLkwU8f5NVfXuX70PcYwrDm5NHYqHwj5hwwhx3G7JCz9+8u3VYC9957LyUlJXzxxRd88cUXrc4pirJBK4FEwqS8vGvNsYWud+4PkAJSpSK621DejMWINjcjVZVwTQ1CCLxlZbYiAEs5NjTg8vvt/49OEELQGG9kRXAFhqlT6a3sd/NPd1jXVBRdWZtTU9EHyz7gLy/8hTXL14AGVMNWQ7fiyE2PZObYmfjd2e2ZnA26rQQWL16ci3kMeNLNY7pkCoKu1Qtq/holUYfUCqCs6ysHYZpE6+sxTRNfdTVmIkG0thakxFtevkELvkxOgGmidaF094ZM0khSG6pldbQOp8NFWZ6Zf7pDZ6aibOwMXlv0On9++y/owkBxKIytGsMV+1/G1GFTrAESzHj3M39FPIH05q4mm20MzRLxeOfNY9LIdH5AZ0ogbQqq3A20rguseEMDiVAIz8iRgLU1RlGI1NYihcBXUTFoIny6SzIUItHcjLu4uL+nktcE40FWhVfRnGim2F3cp9EquaaVqSgURg+Gev17uGv+I9y97FEEgplDd+Gvu59FgcsPBkSXrejVtePRBhJKCVT06jLt0m0lcOKJJ3Z4/r777uvxZAYyyaTJkCGdNI9JY5pWtm0nqw+l4QOgewXjkuEwsbo6nCUlrTpiaS4XrsJCYqtXg5T4Kis3OEVgJpNE6+txeDyDqkBcXI+nHrUOAhDrBAXIdc63TA5Mx6gDxIwYNeEaDKFT4S3vk9j//kB1OFCLCq3/h14EUFz49pW8+t1cKIJDNtuPS6b8CU3J4vcr0mAFkuSIbiuBpqamVs91Xef7778nEAiw++79E+LU3ySTJk5nFyqGppCpctudKQw5/Xlk4zwo2qRL1zWTSSJr1iABp39926PmdKIUFRFds8baEQwZMqiEYUdIKYk3NWHGYngGUU5AINbEsuByhBStBHlbSLGuUhDrPLcQCHwOH0XeDSN0VlGU7gVdtOD+nx/h1WVzAZhQMI45U/+Mpg6s31S3lcBzzz233jEhBKeffjrjxo3LyqQGGunmMW53F5VAMtm1VbjqhIqdu3ZNIYjW12NEIniKitoNPVUdDtzFxcQaGpBC4K+q2iBCJPVIhFhDA87Cwv6eSlZpjDWSMBIUuq2/S1kn3GDdhYbaombkunJvsK74c4GUkn//eC93zX8QCmHfsTO4Zqc5A8ppniYrv35VVZk9eza77rorF1xwQTYuOWCwmsfQafOYzHghrCSuLK/A401NJJqbcfl84HB02JRb1TTcxcXEm5osRVBdPaibqWeaxqvqoPo7I8kIgUQzfpd/UNns8x0hBH98/XzmhT4DBc7e9DROmnh0f0+rx2RNbf36668YhpGtyw0outQ8Jk3KH9ChEhBJlHd3QPn+z2CEO71kMhwmVl+Pw+tFwSqy1RmqpuEpKSHZ3EykpgYzmeza/Acg6abxrkG2CwjGm9FNPe9j9gcTpjT57dPHM++nz6AR/rLFOQNaAUAPdgKzZ89u9VxKSU1NDS+//DLHHXdc1iY2kCgocHXePCZNSlF26A9o+BAl+B0yUQebXN/h5dJ+AFQVzeHoWhZyCkVVcZeUEA8ErB3B0KE4BlnY5GBtGq+bOvXxBnw5Ktlssz66MLj0s2tZmLDC5A/ceB9+P+Hwfp5V7+m2Evjqq69aPVdVlcrKSm688cZOI4cGIy6X1qXmMWmErnfqD8hkCXfSQCbtBzBjMasMsq5bCqAbpiZFVfGUlpIIBIisWmUpgj6oNSQMAz0SIR4IoLlcOP1+HB5PVuv5D+am8cFkkLgep8xrZzz3BUkzyQWfXMbbqz7A4dP4y7bncsRvDu7vaWWFbiuBt99+OxfzGLB4PJ03j0kjhehakthqq4tYZ6GhGT9AURGKoiCEsCKAurniVRQFd8o0FFq5koJhw3B6vd26RlcxEgmS4TCJQAAzFkN1OjGiUeINDaguFw6vF1dhIQ6vF62XvQoGa9N4IQQN0QZUVbWduX1AU7yZWc+cSK1jNS6ni39Mv5JdhuVP2Yfe0u1v0O67704gEFjveDAY3OBCRD0eB2Vlns6bx6TpSpJYeAFKZBFScVpJYu3Q0g+gahpSCEtg9jDSJ60IRDJJeNUqkpFIj67TFlJKkpEI4ZoampcsIVpTA4C7tBRXYSHu4mI8ZWVoLhdGNEpoxQqaFy8muGwZ8aYm9FjMUqDdYDA3jY/qUULxEAXOwbW7yUfCeoRDHj+a2jWrURtVbt3+b4NKAUAPdgLvvPMOyTaciPF4nPfffz8rkxooOBxqt0xBmCYSUDta3aZNQeU7gqNtR2ZLP0DGhp+OOOpluKe7uJhEMEh41SoKhg7tlRlFmCZ6JEIi5ZhVAIfPh9aOg1ZzuTLmIFPXMRMJwitXgqbh9HispiFeb5eSvQZz0/imWBMCkdX+vTbrE0g088cPzqfJHUBxKFy0y7lMr96mv6eVdbosMb799tvM4x9//JHa2trMc9M0efXVVxk+fHh2ZzfI6JI/YLWlBGTVXm2eX88P0OK4miXnp7uoiGQ4THjVKvzV1d2ut9+WycdVWNitFbnmdGbCOYVpWvWP6qxSvJrHg6uwEKfPZymEdRRfMhIZtE3j43qcpkQTXmduzHU2Fmti9fzh/T+xMLiIEn8xt+91A5uWT+7vaeWELiuBLbfcEkVRUBSlTbOP1+vl1ltvzerkBhPp5ux0pASkhMLJyMgiq3R0G6zrB0hfWwGULCZ9uQoK0CMRwqtWgZSd1tqRUmLEYla/3lAIM5nE4fXiLi3ttSBWNQ3V58Pp8yGFwEgkiK1ZQwxQ3W5cfr/lWE6ZxuINDYO2aXxYDxPTY1QM4GJu+c63q3/k5OfOIlGUpLKwnP/s/E/GFQ3eTopdlhqLFy9GSsnYsWP59NNPqayszJxzuVwMGTIEbZDZXrNK2h/QkWBSFOSm18Mmf2szjX1dP0CGLJmC1sXp96PHYoRWrUIK0WZPgnVNPgBOrzdn0TiKquL0enF6vUgpMRMJEoGA5VhOFQbTB2nTeCEEayJrcDlctkM4RywLr+CUF84mEUvilE7u2/82RhWO6O9p5ZQuS42NNtoIsL6INj3AMJBSdi2tvA0F0KYfIHPSBF8Xi9d1E2cqAS28alWrngRmMkkiFX1jxuOoDke3TT69RVEUHB5PJqTVTCQwYzGcfv+gLI4XSoaIJMMUeewKqLlgYfNiTnv/XOJFCbx4uevAmwa9AoAeZgw/9NBD7LDDDgwbNoylS5cC8M9//pP//e9/WZ3cYEIYRsdCWgpo/BjE+lnXLf0A6xaGk9KqDZnL+j8OrxeH10u0tpZofT2RujqalywhUlNjmYpKSvpcAbSF5nbjKiwctH0CGmONSMChDv5aT33Nl6u/4aR3z6I+3siE0rG8fPTjbD5k0/6eVp/QbSVwxx13MHv2bPbdd18CgQBmqiJmaWkpN998c7bnNyjoUlP55m9QP9wL5a2t1itr25YfIINhWHWCclwEzuHx4PT7idbVEWtoQHM68ZaV4czRDsSmNXE9RnOqTtBAQApB8IefCf20sL+n0ilPzX+eEx8/k0BzM5uUTuLeXW6l3DN4Ks12Rrclx6233srdd9/NwQcfzN/+9rfM8a233przzz8/q5MbNHTFH9DwoXVfOLGVOahdP0AaIcDj6RPzh+Zy4R1EZZgHEs2JIAkzQZE7fxPf9OYQDfM+o/79edS//wnJxiaqZu7OFjde0d9Ty9AUb+aHNfNp1oMklAQrIzXc//GjSAGFiQL+s9NNFLo2rPyLHrWX3GqrrdY77na7iWQxwWhQYZqd+gMyDWTKd1z7slQTlDb9AKRMQVJaNYNsBi2madIQa8Ddje5yfYWUkiX3Pcqadz+i+ZsfMr0yADSfF83bd3MWUlAfb6Q2Wsey0Ape/+ktasOrGTq0itrYamqjqwmsboYwUACUpF5YDCOLhvPfA+7Y4BQA9EAJjBkzhq+//jrjKE7z6quvMmnSpKxNbDDRNX/AR9bj8h1ShwTRhgaMaLT9SBfTtHYAthIY1ISSQSLJCKWe/k98M8IRgvN/oWwbayGoKAp1b75L8Lv5APjHjaZip+lU7rwdJVttlundqwdDJFbXUzC+d6GWy4MreX3RWxQXFlEbW0NtrI5vln7PqroaTK9AFqVMqRJYaT382VxoNX0H616BEncxm1VPZqivivHFYzlk9H4bbDnuHlURPeOMM4jH40gp+fTTT3nssce47rrruOeee3IxxwFNl/wBwR9Q9IDVUL54SyDlB0jVvWlXgZgmuN0d9g6wGfg0xhpRFPqlYYmUkvDCxdS//zH1739M4CsraXTX91/CWWitmjc65giMYIiKnabjHT50vWs0fv41X5/9V9xDKtj+mfu7/X2NmwneXfUhz/36EvO+/sw6OJS1gj0E6IADNEVjiLeCam8VDUYjxe5Cdp+4M+NLxzLUV0WFp4ISVwe/qQ2QbiuBk08+Ga/XyyWXXEI0GuX3v/89w4YN41//+hezZs3KxRwHNkJ0Xt45ZQqibFtQHVYXrI78ACmklIOqSYrN+qQbx/icfesQDnzzA6uef4X69+cRr13d6pxvoxHEV9binDgegKH7zujwWoUTxgGSyMLF1Lz0BsMO6rxntiEMnvjxOd5a/j4/JX4hbKRMzS5wSAdblG3KuPLRVPuq8OJBNRU2HTKJieW/saOnukm3/rcMw+DRRx9l5syZHHXUUUSjUcLhMEOGDMnV/AY+hmGVdOhAmCspp7As37FTP0AaaZuCNgjSjWNKPCV9+r6h+b+w4ikr5Ft1uSidthWVO02nYqfp+EZ1L3beWVzImJOOZsE/72Thv++jet89MmaidVnYvJiXl73Gc/NfomlVsxW/OBSG+qvYd+Se7LbrTmxWMTjLN/QX3ZIgDoeDP/zhD8yfb9n/fD4fPp/d1KIjhGHQ2cZTjj8HWbwFsnIvog0N6NFop2Ua0rsL2xQ0eOnLxjHxmjqMSDRjs6/YZXtG/rqEip2mU7bNVmje3vWYGPX7w1j28FPEV9aw4qkXGPX7wzLnfmlYyL8/v5efwwtZJVM1yRRQHAqjykcwe7s/svPw7VHtLOmc0O1l5LRp0/jqq6/WcwzbtENn/gCA0m2gdBuMSIRE7XJchYWd2iylEIOyNo7NWvqqcUzol1/58vQ/g5RMe+ROvEOr8A6tYtLF52XtPTSvh7F/OJ75V93IojsfpHT/XXm36XNeWvYaHy/8HNksLVNPlcaO1dux/0Z7sWP1dLwOu1Berum2EvjjH//In/70J1asWMHUqVPxr5PBuvnmm2dtcgMdmc4P6KLJxojHQcpOM2+lafaqd4BN/tNXjWMaP/2Kr8/5K0YojH/c6E53rb2h6uC9+e6uu6GuiSsvOozXd0uFk/rAp3vZcex2XLTjuZTlQRTUhkS3pUja+Xv22WdnjimKYlWyVJRMBrENVn6AEB0nci17CBwFyIpdSYbDXXP0phWLbQoatGQax7hzF7de+9rbfHfhVUhdp2TK5mx163U4i7ObjCal5KfAAl5a9hqvLn+TEVsG+d3r4G42Gekfzv4bzWTfUXsyqmDw1+jJV3qULGbTNWTKH9CuaUdKlJ+uREnUoW/9PGZiRJf6+0oh0AZZ43Sb1uS6cczSh5/m5+tvASkZMmMXNvvbHDRPdhO7Pln1Bee99FciRdGMpIlP8/HE+DIO2O0ortp4P/s7nAd0WwnYvoCuIzvrJxxZiJKoQ6puDO+miEBDu1ETmWv2so2kTf6Tbhzjy1HjmBXPvMTPf/sXACNnHcLEi87JeoDBS0tfY87L1yCSEs2pscekndlv1F7sUL0tTtUOa84nbEmSI6QQVp3/jkxB6XpBJVujxzsxG6VJ9yi2lcCgJdeNY6pn7sbyx56lauZujDn56KyuxiN6lGu/uomXlr0GJVAYLeDf+/29zYqc4V+XEPjqW0YcfmDW3t+m+9iSJFcYhuXA7WBln6kXVLY9ejTapWgfaZooduXOQUuuGseYiQSqy2X1YCjws+2jd6JmObrsxQWv8a9v7mQN9aionLbl8Zwy6Vg0Zf1dRnTZCj465DgURaF0m63wbzQyq3Ox6Tp24G2uSDnIO/IHpHcCRuE0RDLZqRJIt5HszGRkM3BJN47xZzFDOFHfwKdHn87SBx7PHMumAhBScM3HN3HJy1ezZmU9lY5y7t31Vv4w+YQ2FQCAb9QIKnaYhjRNfr3t3qzNxab72EogR4hksmPzTmwpSnwlUnGguzexBHxn5qActZG0yR+y3TgmsmQZnx59OqH5C1hy/2PowVBWrpumId7IGR/8mSeXPwdOqCyp4IHd/82Uis5DxSeccxoAta/MJTj/l6zOy6br9EgJBAIB7rnnHi666CIaGxsB+PLLL1m5cmVWJwewcuVKjj76aMrLy/F6vWy22WZ8/vnnmfNSSi699FKGDh2K1+tlxowZLFiwIOvz6A4Zf0BHzram1N9QMgU9JrrWGSxdMM42BQ1Kst04JvDtD3x6zB+JrajBO2IY0x7+N86iwqxcG+Dx+c9y2OvH8VHdp7g1F3+ecRavH/MMI4qGden1hRPHU52qO7TwlruzNi+b7tHt5ca3337LjBkzKC4uZsmSJZxyyimUlZXx7LPPsmzZMv773/9mbXJNTU3ssMMO7LbbbrzyyitUVlayYMECSkvXJpPccMMN3HLLLTz44IOMGTOGOXPmMHPmTH788Uc8XQi3zAnpJLGOzDbDD0eUbosZXY3RlOiwThCsbSNp9w4YvGSzccyadz7km/MvQ8QTFG0yka1uvx53RXYaAulC54T/ncl3S3+EEpgwfCx/m3Y544u7XyZ6/JknUff629S//zGNn39N2dZbZmWONl2n2zuB2bNnc/zxx7NgwYJWQnbfffflvffey+rkrr/+ekaOHMn999/PtGnTGDNmDHvttRfjxo0DLMF48803c8kll3DQQQex+eab89///pdVq1bx/PPPt3vdRCJBMBhsdcsqpomkA39AGt9ITPdvEIbRuZ3fMOyCcYOYbDaOWfHMS3x9zsWIeILyHaax9f3/ypoCWBZewXFv/5HvAj8CsHHBBB7e/a4eKQCwfAPDD9kfgIU3/8cqvW4DWL6WmBHFaKPveDbpthL47LPPOO2009Y7Pnz4cGpra7MyqTQvvPACW2+9Nb/97W8ZMmQIW221FXffvXbbuHjxYmpra5kxY20p2+LiYrbddlvmzZvX7nWvu+46iouLM7eRI7MbmSB0vcvtHvVYrGvmHSHA5eqTNpI2fU+6cUyBs/cZwiKZRJomww7am61uux5Hloo8PrvoRY5880R+aPqJorJCztrtFJ48/D48vVRcY08/HndVJZW779iqM9mGiClMwnqYhmgDTbEmTFNQ7avKaUOhbi8r3W53myvnX375hcrKyqxMKs2iRYsyje3/+te/8tlnn3H22Wfjcrk47rjjMkqnqqqq1euqqqo6VEgXXXQRs2fPzjwPBoNZUwRSCND1jvMDal5AWf4wcujhJI1t0LpiCrJ7Bwxqstk4ZtTvDsU3agTl22+TFf/R6kg9xz//R1YGa6ACtq7ckmunzaHKl50S8p4hFez06pOozg1zl6sLnZgRI2kkUVHwOr0M9Q+lwF2Az+FDRqJ4PNnz5axLt//XDzzwQK688kqefPJJwDJ5LFu2jL/85S8cdthhnby6ewgh2Hrrrbn22msB2Gqrrfj++++58847Oe6443p8XbfbjbsTwdtjutBUXln9Bkrdq5iesQjX5rgKO/mA7d4Bg4JEMEjdF1+gahpDpkzBVWCt+tONYwpcPfuhm7E4C265i3F/OD5T+6dih2lZmfMPjT8x+/2Lqa1fDRIOGb4/c7Y7v93Qz56yQSkAKYmLBHEjjm7oOFUnPqePqqIq/E4/PqcPh7b2/yNBNKfT6fb//I033sjhhx/OkCFDiMVi7LLLLtTW1rLddttxzTXXZHVyQ4cOZfLk1g0kJk2axDPPPANAdXU1AHV1dQwduratXV1dHVtuuWVW59JlutBUPt1JzPBvjUx0IVNYCHA67d4BAwwpJY0//cSyt95i2VtvUff55wjDsu/+9o03KE99t7/892388sDDeMrKcJYU4SwpxllchKu0BGdJEdX7zMjY9I1IFCkEjgI/iqKQDDTz1RkX0vzN94QXLGbq3TdlZfUvpOChX57glu//gyFNSqqLOWOzkzhi8iG9vnZ7SCmpf/cjVjzzElvcdOWgyoeRUhA3E8SMGMIUuDQXha5CiguL8Tv8+Fz9lwDabSVQXFzMG2+8wQcffMC3335LOBxmypQprezy2WKHHXbg559/bnXsl19+ydQvGjNmDNXV1cydOzcj9IPBIJ988gmnn3561ufTFYSud/xhxmtRIr8iUUhok7v0RZdC2KagAcaC55/n46uvJlJT0+p40ejRODwePOVWSQjd1GlatRx9TSP6msY2r1W27dSMElj28FMsvPUeFIeGs6gIaZrozUEcRQWM++MJWREkvzQu5LQXzqPRHQAn7Dl8Vy6degFFPdypdBURT/DDZTeQbGhkxTMvMWpW7hROXyCEIGbGiOtxJBK35qbMXUaxpxi/w4fb6cmLcO8e78F23HFHdtxxx2zOZT3OO+88tt9+e6699lqOOOIIPv30U+666y7uuusuwDJFnXvuuVx99dVMmDAhEyI6bNgwDj744JzOrS2klJY/oKMVe7peUNFm6Lqz8yzhtCnIVgJ5iZSSpl9+YdnbbzNixx2p2NSqkeMqLCRSU4PD42HYDjswavfdGbXbbhStU4AxmAxSccxBjDhgb4zmEHpTM8lAED3QjN4cRG8K4K5cW0NID4Wt9zVMko1NAKiVpYz410UERhfTGFxMXWgNoUSYEm8RBe4CTGmSMBL82rAEJIytHI2UAlMKlgdW0hBpZEhhBWX+UgLJZq6b+0+SYR3FrXDJXn/isLEH9omwshrPHMdP1/yTRXc+wLAD98bhG3hNZaJ6lKgeRUnZ96v91RS6C/A5/bgc+dcISpHdjMm65ZZb2r6QouDxeBg/fjw777wzWpZMFy+99BIXXXQRCxYsYMyYMcyePZtTTjklc15KyWWXXcZdd91FIBBgxx135N///je/+c1vuvwewWCQ4uJimpubKSrqeYy2NAxEU1OHUTzKt+ehLL0XY8TJNHlP7bSNpEwmweFA68W8bLKLHomw8sMPWTZ3LsvefptwKklyyzPOYPpf/2qNicWo+fhjhk2fjsPbtiATQrCwaSGhZKhb0R9mIoEeCPLBD29x2+u3sbISki11SwMQA0qAdLCRAdQCCjC8xdhGIAoUpW4AJniDHv6212XsulFuF3rrInSdDw84itiKGiacexpjTj66T9+/V0hJUyKApmhUeispcBfgd/pb2fd7QiIQwFNRgb+bvdy7Kte6rQTGjBnDmjVriEajmaStpqYmfD4fBQUFrF69mrFjx/L2229nPfQyV2RNCSQSmM3NqO386AGUt6ehhH8i9pt/ExJT8ZSUdHhNEY+jFRSg9Ffim02GWGMjb/7xj9R88gkimcwc19xuhm23HRsfcQTjDzqoy9cLJ8L8XP8zBe6CHvUNOOm1s/h8wddgQMFoP6qioioqsfoYyYhOQbkff7EPVdEQhqB+udWpbMS4YWiKiopKw5omwqEIFeVlVJSXoaAypWJzTpt8fFZyFnrCqhde5fu/XoOjqICdXnkSZ3FuzVDZQAhBU9wq/z2iaCTFnk56hHeDXCuBbquoa6+9lrvuuot77rknk7S1cOFCTjvtNE499VR22GEHZs2axXnnncfTTz/d3csPaIRhdLxtFklwVyKjS4mpk3E4OwkNtXsH9CuJQIDl776bEeyekhIa589HJJMUjhqVMfEM22EHnB0o/vboTeOYBc2L+Dz0NVTBA7v8m62GbNbta+QrQ/fbkyX3P0Z4wSKW3PcIE877Q39PqUN0UyeQCFDqKWVE4Qh8ruzkZfQV3d4JjBs3jmeeeWa96JuvvvqKww47jEWLFvHRRx9x2GGHUbOOUyxfycZOQEqJCASsbmGd2O/1SDPB5TU4Cwo67Ccsk0lQVdTi4rxwIG1ovHrCCaz++muO+eKLjHlv2dtvUzRyJMXjxvXqM4nrcX5p/AVNUfE6uy80/vLJ5by6fC57Dt+Vf2x3VY/nka+sfvsDvj7rIlSPm51eewp3eX72HY4bccLJMEN8QxhWOCwnNv+82wnU1NRgGOunMRuGkUnQGjZsGKFQdqsV5j1dqReUHqpbyV+dNpS320j2G0vnzmXJ66+jqCqhlSspSpk2R+22W1au35vGMR8u/4RXf5kLHjhlUs/zZfKZyl13YNjB+zJk9x1xlZX093TaJJQMoRtJRhQMp6qgOmt+0L6m2+mJu+22G6eddhpfffVV5thXX33F6aefzu677w7Ad999x5gxPaslMmDpSlN5vRmAZCTSadVQ2xTUfxjxOB9eeikAm596akYBZIveNo655r0boQFGGMPZuGR8VueWLyiKwqZXX8SQ3XfKu0WQlILGWANSSsaUjWVY8fABqwCgB0rg3nvvpaysjKlTp2Yyb7feemvKysq4916rOURBQQE33nhj1iebz4hUU/l2STaivLoRytvTMSKNnXcRs9tI9hvf3HknwSVL8FVVMfW887J+/d40jlkcXMrKeA0o8MdtTsj63PIVM5Ho7ykAlgJviDXic/oZVzKOcm9uWoD2Jd2WMNXV1bzxxhv89NNP/PKL1Qhi4403ZuONN86M2S1LW+aBgpQSksmO8wMaP0ZBIEQCYTpwdmY2Mk2w20j2OaEVK/jq1lsB2G7OnExph2zSm8Yx9/38MBTDDhO2Zb/xM3s9FykBmb/fMSklq55/hRXPvMCmV/0V/5hR/TYXXeg0J4KUesoY6q/G5fCQaMM0nm2SQqDoOlo83uq40+nMyg6kx8vMiRMnMnHixF5PYFAghCW0O1i1p/sJm4XTQFE6FO5274D+46MrrsCIxxm63XaMz0HCYW8axywPr+TlZW8AcPqmJ/Z6LlKCMDyoikbH29j+QwEqd96T8mk7obrdIPsn8kZKiSY9VHpK0BSNxlgSYsnOX5iN9xYCpakJtY3CnSUlJVRXV/dqsdgjKbNixQpeeOEFli1bRjLZ+j/ipptu6vFkBiwpf0CHjt5UpnDCtUXnJSAMw6oTZCuBPsVM9XlWHQ52uvrqnOzC6qMNPW4cc+m712ImTXYYsS2blU3u/AUdYCkAF16PjyFVlVltap9tRHWS6DIrIc9XOQTV27c5M0IIQOJQHVlr+9kdpBAomtZKbkgpiUajrF69GqBV7bTu0u2/aO7cuRx44IGMHTuWn376iU033ZQlS5YgpWTKlCk9nshARnbmD9CbofkbAJKOzbrmD/D57N4BfYzmcjHj9tsJXnDBeuUdskFzvJnV0dUU9qAGz5e13/Dlgm8BOGj6vlmZj6I4KSsv678OfF3F7YLSYvSmZkRTAG9J35mEDGHiVBy4VBea2j/OX2maKA7HeotHbyo3ZfXq1QwZMqTHpqFuS5mLLrqI888/n++++w6Px8MzzzzD8uXL2WWXXfjtb3/bo0kMdGRn9YLS/gDPRhhaRYeRQWlTUJd6DneAMAy+vecevn/gAbtbUzfJhQLQTZ1VoVVIJB5H94XuE78+Bx4oLixi5pjdez8hqaAAzgGy2/RUVoCiYEZjGKFIzt9PSjCEgaaouDV3vymAzvClGgbput7ja3RbCcyfP59jjz0WAIfDQSwWo6CggCuvvJLrr7++xxMZqEjT7LSpvJIyBRn+rTvNDchG74BIbS0vHnEEH112GR9cfDE/PPhgj6+1IRBetYq5Z52VqQGUC1aHVxNIBChxd7+cQG20jjdr34UK+Pv+V2ZvUgowQAIPFKcDV5mVMBavrbOaN+UIKSWmNHCoDlyaGzWPTWXZMFl2+6/z+/0ZP8DQoUP59ddfM+fq6+t7PaEBh2laiqAD040s3x4xfBZx7w6oXTEF9bKNZHTNGuq++ipTpvqjyy6j5tNPe3y9wc68K69kwbPP8s755+fk+sF4kLpoHcXu4h7Z3u/7+VEMabBN5RS2rZqagxkODNyVZSiqijQFSo482SJVXdWpOnFpLtQBoiR7Q7e/kdOnT+eDD6xIl3333Zc//elPXHPNNZx44olMnz496xPMe1I9UTvUyFV7o2/8T+KeHTr0B6TbSPa2mUblZpuxxy23cMTcuYw78ECEYfD6qacSHiBlPPqSlR98wK8vvoiiqky/+OKsX183dVaFVyGk2SMz0I/1P/PUN8+DgNMmHZ/1+Q0kFE3DN2oE7iEVoKZ+bxKiS5aTWNOA1A1qa+vYf/+DqKyoZtjQ7iX5mcJqCOXWXLg0V84UTb7RbSVw0003se222wJwxRVXsMcee/DEE08wevToTLLYhoRIJru0atdTMb4dKosemoJiDQ28cvzxrPn228yxcQccQMm4cex6442UTZpEbM0a3jj1VMxe2A4HG6au88GcOQBMPvbYTC+AbLI6vJrmeDMl7p7Vvrn87esRAUFxuIitK7fM7uQGIJrfy5kXXsiRR/wOACMaxYhESayuJ/TLr9x87d+oXbWKefM+4OtvvgRg0sRN8fuK8PuKqCivYpttpvPA/a1NpO+88y6zjvw9vxk/kbLySqZusw2PPvZYn/99/UG3pI1pmqxYsYLNN98csExDd955Z04mNhCQQnTqD6DxE6TqQQ8Vdh4aKgQ4HN1qI1nz6ae8efrpRGprCS1fzm/feKOVUnL6fMy85x6eP+ggfnP44b12OA8mvr/3Xpp++QVPeTnT/vznrF8/bQYqcPl71EB+TayeX+OLwAEnTP29nTjYBg6vF+/woSSbApjRGIsWLWbTceOplipORUUa1k59zpyLOf6E44lGIzz77POcccZZVA2tYs+99gQkn376KVtstgUX/vkvVA0Zwsv/938cf+KJFBUVsf9++/XvH5ljuiURNE1jr732Yv78+ZR0Ugd/gyDlD+ioaqgy/1LUxnk4quZgDp3V4eW600ZSSsk3//kPn1x7LdI0KRk/nhm3397mrqR49Gh+/9FHOP3dT1AarETq6vg8ldMy/a9/xZ3l77Nu6tREajCFidfTswSnB395HMNrsvmwTThus99ldX6DBlVJ9WUuYtLGm7Bs+XIAnnr5ZY7Ybz/+c//dgMRX4KNiSAUKFcz+07n86+Z/8e7b77LfPvuioHDJhRe3UrJnn3UWb7z5Js//73+2EliXTTfdlEWLFm14BeLaIhV62e4KzYxB4AsAku4tOgzHy4RxdmEXkAgEePu881jy+usAjD/4YHa54YYOhXzLc4lAgHBNDeWTJnX6XoOVr267DT0SYchWW7HxEUdk/fr1kTU0xZqo8Fb06PUN8SaeWvQ8AH/Y5IQe7SS6g5SSqB7N6Xu0h8/Zs/IoQorUT1Aikbz93lxOO/V0igoLuXbOJTiFxF1QCCg4FCc0hTBNwWsffEBTUwCP24tTbX/R1RwMbhBVEbqtBK6++mrOP/98rrrqKqZOnYp/HcHTm85cg46mz1BEEuEcgnB3kuDSRX9AuKaG/x1yCKHly1FdLna44gomH3NMl39EzYsX8/LRR2PG4xz2yiv4ulmjfLCw7UUX4fT5GLPvvllPygsnwtRFV1PoKuix8L747auIhxNsMnQi21dNy+r82iKqRxlyc8+zTnvD6nNrulRGwwrdFKlcGmvRpCoKqqKhKCojqkfg9Xjx+woYN3mzjFtXURQuvuQSLrvsMpLJJIZpUlpSwrEdKP+nnn6azz//nDtuvz0bf2Je020lsO++VrbigQe2bj4tpURRFMxUtIzN2npBuncKWmdZmWl/QCdCw19VRcmECaAo7HXXXVRu1r2OUt7KSjSnk+CSJbx+2mkc8MQTnWcwD0KcPh/bXnRR1q9rmiarwqvQTb1HpSEAFgeWMu+Xz0DC7pvtvGH7AiSW4EegoOJQHWiKhqqoeBze9eJ3FKy6XOse/9N55zHr4INZtmABl91wA8cdfjgVikLDTz/hKS7GXVKS6QU99803Oenkk7nl+usZU1FBNFWaIY2zoABnKklLGAbxxsZ2p+/0+zO7cGGaxDsIo3f4fLgKrWxyaZpEU2MdHk/WzZWt3re7L3j77bdzMY/BSbpekLvzekEd+QOS4TCKpuH0elFUlT1uuQVFVTttUt8WroICZt5zD8/uvz+1n37KvCuvZMerr+72dQYqjb/8Qun48TkrybE6spqmeBPlnp6XGH568QvgB5/wcuLmR2Vxdu3jc/pYfW7/hBD72uisll71K4CqqGiq2+qLrKgpId+9AM6Kigo2mTKFTaZMYeLUqUydPp0tN92U32y0EdE1a1CdThxeL+++9x6HHnEEl597LgftuCORVKOslvirq9cqAV1vc0zmb6uqyigBaRhE6uraHeutrMwoASEE0dRYb1lZfimBXXbZJRfzGHyYCWj6DADdsyXOjpLJOvAHNMyfz+unnkr11luz2z//CYCntHet9krGj2f3W27h1RNO4Pv776dy881zYhfPN6KrV/P8gQdSMn48e99/P77KyqxeP5KMUBetw+/sWTQQQHMyyHNLX4ISuGa7S3LuC0ijKEqPKptmlTZW/Q5FQ1W1rEbsjxk/niOPOIJ/PPAAj91zD0YkgsPj4Z133+WgQw7hmiuu4LhDDmn39Y4W/aQVhwNPWVnXxmoa3pZj19nhpRULgKKqeMuthYTDl9vKqT2KF3z//ff5z3/+w6JFi3jqqacYPnw4Dz30EGPGjGHHHXfM9hwHJoEvUEQc4SgD/286HtuOP+CnJ57gg7/+FSMex4hGidXX463omaNxXUbvtRdTZ8/mi5tu4r0LL6Rs4kQqU6G/g5WPr7mGZCiEFKLDH25PME2TlaGVGL0wAwE8suApIkaUjYvHs9uwnbI4w/ylo1V/ezQHg3z9zTetjpV34zM966yz2GKrrfh+0SK2njqVt995h4MOOYSzzjyTw3/7W9LViVwuF2UdXFdzOikcMaJL76k6HBR0daymUTB8OJAqTZNDur3MeOaZZ5g5cyZer5cvv/ySRKrjT3NzM9dee23WJzhgKdkKfeozhCv/hOZ2dzx2HX+AHovx9uzZvDN7NkY8zshdd+Xw11/PmgJIs/V557HRjBmYiQQfXX75oC40V/PZZ/zy9NMA7HjNNZ3XcOom9bF6muJNFHm6b6JLszJUw30fPwwGnDrpuMHtC5BgCoEhDIS0yjS7NTduhwen6ui0Xs+7777L1tOmtbpddc01XX77yZMmseeMGVx+xRUAPPTww0SjUa6/4QZGbLRR5nb4kUf26s8cCCiym7/8rbbaivPOO49jjz2WwsJCvvnmG8aOHctXX33FPvvsk2k2P5AIBoMUFxfT3NzcregmmUxiBgKoLbZ8LUkEg4RWrsTTiT1PxONofj+K10vg1195/bTTaJw/H0VV2fpPf2LK2WfnzIadCAaZd9VVbHvRRa23qoMIYZo8s88+NPzwAxN/9zt2/cc/snr9SDLCgsYFaIrWK5PKyS+ew2e/fonL7eLj017PaeVKKRSQPkaNGoXb3XeBAeuv+h2drvo3dNorJQ0Qj8dZvHgxY8aMWa8keFflWrfNQT///DM777zzeseLi4sJBALdvdygRo/FOhXeLf0BwjD4v2OOIbh0Kd7KSmbcdhvDc2xecxcVsevf/57T9+hvfnzoIRp++AFXcXHWI4JM06QuXGtFA/l6bgYK6xF+jP0EHjh88wPztnRxj+gjW79Nz+i2+q2urmbhwoXrHf/ggw8YO3ZsViY14An+AN9dCHVvdKmBTNofoDoc7HTddQzbfnsOf+21nCuAtpj/2GMs/N//+uS9hGlixGI5fY9YQwOf3nADANMuuCDjbMsWjfFG6mMNFPfCDATw+MJniKhRxo7ZiPO3OzNLs+t/hBQY0kBVFFyaG4/DjVuzGrTYCiA/6PZO4JRTTuGcc87hvvvuQ1EUVq1axbx58zj//POZkyrGtcGz+g3UJf/G7d8FWb5bx2PX8QeM3GUXRuzcP7HhS15/nXfPPx+Hx0PJ+PFUbLJJzt5r1bx5vHXOOYRXrWLU7ruzyXHHMXLXXbNuq080NVE8ejTCMJh8zDFZvXY0GaUmXIPX4e1V28GIHuW/C54A4JRJx6Epg2AXIMGUJqCkmrI4bKGfp3T7m3vhhRcihGCPPfYgGo2y884743a7Of/88znrrLNyMccBRzpJLOndqnNzUCo/QI9GMyFi/eUQHLXHHozcbTeWv/02r518Moe9/HJWo2hMXc/YNQtHjbLiq6Vk2dy5LJs7l8JRo5h8zDFMnDUra/6JkvHjOeTFF4nV12dVwQghqA3XkDASlPt6t7uY8841NDcEGVk1nJkjs9A1rJ+x7P4mmuLApTlte3+e0+1PR1EULr74YhobG/n+++/5+OOPWbNmDVdddVUu5jfwkCY0fgyAUbBNx0NT/gDTNPnvVlvxzL77EuvHxjyqpjHjttso2mgjQsuW8eaZZyJ6GZ4mpWT5u+/y8jHH8Popp2SOFw4fzn6PPMIRc+ey+amn4iouJrRsGZ9ccw0Pb701tZ9/3ts/J4OqafirqrJ2PcieGagh1shb89+HZphWOHXA7wJMYSKkwKW6cDtctgIYAHT7E3o4FUrlcrmYPHky06ZNo6CgIBdzG5g0f4tiBBFqARR2Yk5J+QPqvvkGPRwmvHJl1uPXu4u7pISZ99yDw+tlxbvv8lnKnt5d9FiMHx96iCd3352Xf/97lr/1FsveeqtVxuSInXaibOJEtr/sMo754gt2vekmKjffHFdhYauchYYff0SPdq+42U9PPMGn11+PngOfQzQZZVVoFW6Hu1dmIIAXlr6CLJa4fW4u2O7sLM2w75FSYggDNdWT16k5N5imLAOdbiuB8847jyFDhvD73/+e//u//7NrBa1LqlSE7tkCzd126GiGlD9gxfvvA1i+gD7KEO2I8smT2fXGGwGr2uavL77Y5deGV63ik+uu4+Gtt+a9Cy+k6ZdfcPr9bHrSScx69912V+ROr5eJRx7JYa+8wm/fWOtQF6bJqyedxENTpvDBpZfS1EZQwrrEGxuZd+WVfHnLLSxI5QZkC8sMVEvciFPoKuzVteJmgocWPAl+uGjP8/A4OsknyVPSLRkdqhNXHjdlt2mbbkucmpoaHn/8cRRF4YgjjmDo0KGcccYZfPTRR7mY34AjUzTON6XTsVIIVKeTFe+9B1hKIF8Yf9BBbPGHP4CiEEzVaO8Ky+bO5avbbiMRCFA4ahTbX345R3/+OTteeSXFXSw/3rKyaaSmBkVVSYZCfH/vvTyxyy688Nvf8utLL7XbJe3T668nEQhQNmkSE3+X3Tr8jfFGGmINFPegYfy6PLPoRRoSjQzzVbP/RjOzMLs+RoIhTKQEt+bCvYH05B1sdHsv63A42H///dl///2JRqM899xzPProo+y2226MGDGiVeP5DZLoEgDMwmkdbobT/oB4MJhpC5lPSgCscsujZ85k6LS2Sxmbus7i//s/HF4vo/faC4AJhx/O0rlzmThrFhvtuWevnbGFI0bwu/ffZ8X77/PDgw+y9I03WPXRR6z66CN8VVXsePXVjE1VtgVY8+23/PjIIwDsePXVWe2kFtdj1IRrcGpOnFrv+kAHEyFufucO8MKJWx2Ns5dmpb7Gdv4OHnr1zfP5fMycOZOmpiaWLl3K/PnzszWvAUty2luEF36IVjyhY4toyh+w8sMPQUrKJk3KuvOyt6gORysFYMRiaG43iUCAHx95hB8eeIBIbS2lEyaw0Z57oigKTq+XfR54IKvzUFSVkbvswshddiG0ciXzH36Y+Y8+SrSurlURuGQ4zPt//StIyYRDD2XY9OlZm4MQgppwLTE9RoWv9+U7rnr/HyQjSdSEyn6j9szCDPsOU1gmYJfqwqE58sr2X1tby3EnnMC8jz/G6XTSsE4ZaJv16ZESSO8AHnnkEebOncvIkSP53e9+x9NZtr8ORMxkEtMxHGdn9t11/AEj82wXsC7B5ct57aSTcPr9rPn2W8x4HLDK34476CBEMtl5jaQsUDh8ONP+8hemnncey995h6qtt86ce/X441n91Vc4/X6mX3xxVt+3KdFEQ7Q+K2agpJnky8g3UAD7jNujzVLK+Uh69a8qKi7V1W+2/xNPPplAIMCzbcibm2+5hdraWr749FOKU6XWx/3mNyxduhQAj8dDVVUV22y9Naeecgq777Y2j+ebb7/lhr//nQ8/+oj6+npGb7QRp55yCmcP8tD3biuBWbNm8dJLL+Hz+TjiiCOYM2cO2223XS7mNiBJhsOoXegTnM4PGLXbbhjRKBvtmd+rwbrPP6fhhx8yzys23ZTNTj6Z8Qce2CfCf100lytjggKruUdg8WIAtrngAvzV1Vl7r7geozZUgyMLZiCA/y19hXq9gSFDK7l85wuzMMPcI6RApJy/TtWZt7b/RYsWMWXKFCZMmNDq+OWXXcbJJ55IMplkydKlPProo8zcZx+uuPxy/nqh9Rl8+eWXDKms5MH772fkiBHM+/hj/vDHP6JpGmf88Y/98ef0Cd1WApqm8eSTTzJz5ky0dey933//PZtuumnWJjegkBLlnWl4leHERswB2g+bzdQLcjgYu99+jB0AjawnHHIIsYYG6r//nkm/+x3V06blVZVL1eFg1rvvElyyhIosfgfTZqBwMkKlv/f9B3Shc+9PDwFwwsa/x6XleVc3CYY0UVKZv70Nic0lLVf8Dz38MMcecwz33XMPAIUFBVSnFgajRo1i5512onroUC6/4goOO+QQNt54Y044/vhW1xs7diwff/wxz/3vf7YSaMkjKadbmlAoxGOPPcY999zDF198seGGjIZ/Qgn/jEtZQryzrlLpekFZLpGQazY/+eT+nkKHuAoKsqoAoIUZqJdJYWmufv9GalbWUVpRzKFjDsjKNbOKEck8XOv81XBpLlSp0EpktBi7HooKmhcphPVUtJOv4cheI5uPP/yQ4088kaKiIv55441426num+bsM8/kmmuv5YUXX+TPG2/c5pjmYJCyXjZxynd6rNbfe+897r33Xp555hmGDRvGoYceyu0bQFPmdsnkB2yGonXNH7Dk9dcpHjuW0gkT8mpVbWMRSUZYGVyJQ3NmZcUeNxK8+P2roMMWozbD09n3pB/wvdh+s3lZvTdix7XFBdUXR6CYbSfxiYqdMHd6zfpeKwrq//0GJbl+Nrx5eKL3k05RWVmJ2+3G6/VmVv0dUVZWxpAhQzK7h3X5aN48nnzqKV54/vmszTEf6ZYSqK2t5YEHHuDee+8lGAxyxBFHkEgkeP7555k8eXKu5jgwqLfyA4yCrTsZaPkDEIK5Z56JEYtx+Ouv57RYm033SRpJlgeXZ6U2UJqnF/8Ps8TEFXVy+c5/yco1pRTEjHirhkACsc6Yteck1mNFavgdXoQwM9E+2URRFDS3G0VRMruBfERK2eYC7PsffuDQww9nziWXsFee++t6S5eVwAEHHMB7773Hfvvtx80338zee++NpmnceeeduZzfwEDKTJKYWdyxkzz9g6z79luMWAxvRQXlkyblfIo2XUcIwcrQSgLxAJVZCAcFWND8K//67j/ghj9PP5tSb0lWrtsYa8Lj9LTqRaym/rWk5XkFBUVqqFJBVbVWUT7RA2pQUHC01d1L0UBKZOom9l2aWekrmmY1gFfTjeDVtdnvqorY9xerOUoemUAbGhpYs2YNo0ePbnX8x/nz2WvvvTn5pJO4OMv9J/KRLiuBV155hbPPPpvTTz99Pc/7Bk9kIUpyNRInsmirjsem/AErPrTMR/lSKsJmLXXhWtZE11DqKUXJQhJUIBFk9gdzSIokOw/dnt+OPSgLs4S4EUdTNTYq2ogiT/ca2iQMg9pgEJfqxN3SLNWGiUoKYQl/QBECVBVV01BcpRnB3xGKoqC4ixDJpDU2T0yft9x2G6qqctCBB2aO/fDjj+w5cybHHH00V195ZT/Oru/oshL44IMPuPfee5k6dSqTJk3imGOOYdasWbmc28ChwSqZYXg3BbV7+QH5liW8odMUa6QmUovf6ctKOCjAyf87i2U1yykYUsDlUy/Miv9HSkEoGWJ4wfBuK4DOry0zK35ICXFNQ1XVjBDv7t+gpBRHtnYD3W00HwqHqa2tRdd1Fi9ZwqOPPsq999/PNVdfzfjx4wHLBLTnzJnsteeenHfOOZlWuZqmUVnZ+8iwfKXLSmD69OlMnz6dm2++mSeeeIL77ruP2bNnI4TgjTfeYOTIkRQW9q6g1kBFqj507+YYRZ3nS0ghSIZCeVsqYkMmmoyyIrQSRVHwZimBa+6K91hQvwgkHDdxFuWe7ESahJJhCpz+rGQvt0SapiXkVdUyIbUw8fSGtCIRpmmZT3t5vXSj+ZaceMIJ7Y6//IoruPyKK3C5XFRXV7PttGm8/uqr7Lbrrpkxzzz7LGvWrOGRRx/lkUcfzRzfaKON+PWXX3o133ym243mW/Lzzz9z77338tBDDxEIBNhzzz154YUXsjm/PqG3jeYN0yS4fDnu4uIOv9xSSmQiweL33mPuWWdRNmkSR7z5Zjb+BJtekjSSLG5eTCgepCxLjuD6eAOHv3E8TfEAu5XtyM17XJeV6xrCoDnezNiysZR7ezbXtDlo9KhRmQblaQWgOp1Z7/CWxkwmEaaZs+sPRnLdaL5XBs+NN96YG264gRUrVvDYY4/15lIDGiNhhbl1urpJ1wtKVVzN91IRGwpCCGpCNQTiAUqytFIXUnDpZ9fRlAjwm5JxXL/r5Vm5LkAw3ky5t4xSd/bi10VaAbhcORXQisNhRQz1fO1pk2Wykv6naRoHH3wwBx98cDYuN6CQsVXozXE0l6fzwSl/wA5XXcXY/fajcMSI3E/QplPqwnXUResocZe0iqLpDRfMvYwPV3yCq9DJddMua+187QUxPYpDc1JVUJ21uYrU4kRzOnMepKCqKlLTEIaRV5FCGzJ2WEovURZcS8kPO+BtfrLTsen+AU6vl1G77UapHWXV7wRiTdREarLqCH532Ye88f07EIADq/ZhfHHX+ih0hpSCcDJClW8IflcWMm2lRAjRZwogjZoKJ7V3A/lB/hYCGSCozfNQEEjf2A7HtawXZJMfRJNRVoZWAmTNERw3E/xz/h1QDBVqORdv/6esXBegORGkyF1ERRZqGCElsh8UAFiRQoq9G8gbbInUG6LLURMrkGiYBZ10EkttuT+66ipUl4tNjj2WolGj+maeNuuhmzorQiuI6rGsZQQD3PTtv1kcWkp5RRlPzLgvayYb3dQRwqS6oKrXOxYpBInmZksBOBz9kqeSDhdNKyKb/sNWAr1A1r2DApjeSaC1XzUUACEwpWT+o49ixGJMOOSQPpmjzfoIIagJ1tAQa6DSm7347yd/ep4nFj4LCly1zV+p8LYft95dmhPNVPoqKXaX9Oo6UggSgQCuwkKUWKzfBLCiqigOB0LX86glzYaJrYJ7gVxt9QY2i9puv9hqrBCsSZeKqKy0S0X0I2uia6iL1lHqKc3aSv2XxoVc+/pNsAYOH3UAO1Rvm5XrglXIzuPwUOWv6tV8pRDEAwFcxcV4Kyr6vWihmso/yOfaQhsCthLoBUqqcqhZ2LESSPsDlqdCQ0fstJO9Be4nmuPNrAytxOv0Zq2Wv5CCy+b9DSklLsXFOVucnpXrgrVriRpRqvxV+Fw991sI0yQeCOApLaVg6NA2Y877GkVVUR0O20HczwwoSfS3v/0NRVE499xzM8fi8ThnnHEG5eXlFBQUcNhhh1FXV5f7ycRqUKO/IlEwCqZ2PDadH/CBVWRu5C675H5+NusR12OsCC4HyGpLx8cWPsOPsZ9xDXVy4/5XUeTOXuZ8INFEiaeECm/PM4OFaZJobsZTWoq/qgo1j4IT0oXn7N1A/zFglMBnn33Gf/7zHzbffPNWx8877zxefPFFnnrqKd59911WrVrFoYcemvsJaV70yf8gWvg7cHSSZSwE8XCYNd99B8DwnXbK/fxsWqGbOsuCy4nqMUo8JVm77i+BhfzzuzsAOH/qWew8cvusXTtuxFGkSrW/er0ufl1FGIalAMrK8FdX55UCACvBMpu7gdraWmbusw9FpaWUDxmSlWsOdgaEEgiHwxx11FHcfffdlLbo8tPc3My9997LTTfdxO67787UqVO5//77+eijj/j444/bvV4ikSAYDLa6dRtXCWLUCYSLT+t0qBSCVZ9+ClJSNmkS/qqq7r+fTY8RQlAbqqUh1kBpljKCwaoOevyzZ6AndHYZugNHjD04a9cGCCVCljO4h13NhGGQCAbxlpdbO4A8DcdUNA1FVbu8Gzjx5JM59PDD2zzXstH8/O+/zxz/6uuvOfJ3v2PYyJH4i4qYOHkyp51+Or+kagItWbIEh9vd5u3jTz4B4Lnnn2fmPvtQPXw4pRUV7LDzzrz2+uu9/Ov7nwGhBM444wz2228/ZsyY0er4F198ga7rrY5PnDiRUaNGMW/evHavd91111FcXJy5jRw5Mmdzl1KiAHrKIWyXiuh7GmIN1EZqs+oIBjjtpfOIBKOoDSpzppyfVUdrMBHE5/IxpKBnq1lT10kGg/gqK/NaAUB2dwMtG80PSe0EXnr5ZXbYaScSiQT/feABvv/mGx584AGKioq47IorWr3+tVdeYcXSpa1uU6dY4d/vv/8+M/bYgxf/9z8+nTePXXfZhYMPPZSvvv661/PuT/Jrb9gGjz/+OF9++SWfffbZeudqa2txuVyUlJS0Ol5VVZUpA9sWF110EbNnz848DwaDuVMEpgmqyqSjjmLS0UdjxOO5eR+bNkk7gj0OT1abur+76kN+Mn4BD5yx7clU9sJmvy6GMEiaScYWjcXj7EI5knUwdR09FMJbWYmvsnJABCGkq5b2ptR0W43mb7vlFk4+9VT22XtvnnnqqczYMWPGsO20aQQCgVbXKC8vb7c15U033tjq+TVXXcWLL77ISy+/zFZbbtmjOecDea0Eli9fzjnnnMMbb7yxXoW83uB2u3G7+6i/qxDQIiPT2Unza5vsEddjrAytxJQmRe7s1dyvjzdw2efXgQZHTf8tJ295TNauDZbiKvP0rECcmUySDIfxDRmCr6KiywpASoke1bv9ftnA6XNapaYdDqvxTA+v01aj+dffeIP6+nrO/1PbmdvrLiC7gxCCUDg84BvR57US+OKLL1i9ejVTpqzNxjVNk/fee4/bbruN1157jWQySSAQaPVh1tXVdanRdF8ghcCIRFD9/gGxIhss6KbOiuBKwskw5VlM2jKEwez3LqEp2czGxeM5d7M/ZO3asLZbWHVB953BZiJBMhLBV1VlKYBumKf0qM51Bdkpdd1dLgpfhMvv6nXjmbYazS9YsACAiRtv3KVr7LTLLuuZDJsbG9sce+NNNxEOh/ltO/6JgUJeK4E99tiD71IRNWlOOOEEJk6cyF/+8hdGjhyJ0+lk7ty5HHbYYYDV42DZsmVst13nDV5yTdof8Nb557Pm++/Z9e9/Z6NB3rQ6H2jpCC73lmelRWSa89+8lG9+/B6tROO6vS7ttolJ6AZSmGs7dKlre/FKKWhONDOqcBQF7k4y0NfBTCTQo1H81dV4y8v7PRGsJ7RsPKNImZU2lN31Mjz68MNMmjix03GPPf44V11zDc8+/XTG9zBQyWslUFhYyKabbtrqmN/vp7y8PHP8pJNOYvbs2ZSVlVFUVMRZZ53Fdtttx/Tp0/tjyq0xTUzDYNXHH2PEYviHDevvGW0QNMYbqYvUUuguzKoj+OfAQt5ZauV6zBi5C+OKOq8OKgwDkdSRumVqUTQHiqYiTR0pACkyUTHBRBC/5qbI48zU9lFUFdLN21PP123xaMTjGPE4vupqvGVlPVIATp+Ti8L901Td6VubuJbeDWSr8cxvUpV6f/r5Z7brgkwYOXJkpt1kezzx5JOc+oc/8PijjzJjjz16Pcf+Jq+VQFf45z//iaqqHHbYYSQSCWbOnMm///3v/p6WhRDUff+9XSoixwghMISBIQwSZpwVwRW4HR48juz5keJmggs/vQJZKtlixKb8bbfL2hwnTROR1BFJHZBWb16nE62oEM3jRnO7UBwOS/ALgRRWNc+knkCLORldOo4SdwnCMJCGYSkRw0BKidB1pBBrX5vuAayq+KqqeqwAwFqFu/zZc5z3lPRuQDFNayfdy93AnjNmUFFRwT9uvLGVYzjNuqbkznj8iSc4+dRTefShh9hv3317Nbd8YcApgXfeeafVc4/Hw+23387tt9/ePxPqACkEK1P5CnapiJ4hpcQQBqYwMISJIXQMaVoCX08QF3EMU0cXBkIKTGGiqmpWHcEAN317O4uCS6jwlHHz7tdmdhjSNBG6gUgmQUgUh4bqcOAqK0HzeFDdLlSXcz1htu53oTEcYmjVaKpLR7e5e0kL/7ZuiqriKuie+SifUTXNajzTgW+gq43m/X4/d91xB0f+/vccfOihnHnGGYwfN476hgaeevppli9fzqMPP5wZ39DQsF5kYUlJCR6Ph8cef5wTTjqJf954I9OmTcuM83q9FBf3LJcjHxhwSmCgkPYHrLBLRayHSJk/pJQILMFtpgS7IQ0M0yBpJEmIBAkzgSmsc0KYCCQSiSIVVFVFUzUcigOX5kJTNByqllUfAMBtn9/NE18/B8Vw1dS/UowPPRRGpkwWqtOJq7gIzee12jO6ulefP5wM43K4GFo4tF3zVUvfwYaAmtottbcb6E6j+QMPPJD3332X62+4gWOOO84KCR8xgt123ZUrL7+81diZ++yz3usfeeghjjziCO6+914Mw+Csc87hrHPOyZw/9phjuO+ee3rwV+YHthLIFaZJvLmZ+lTWYr6WijBNE4H1YxNSIGRKzGaem0ikJXylxBQmQEoUS4RpvQasQmrpa1mvAFNa44UQmdeQMmOIFu/Tch4ooKBYAl51oCkabqcbTdGyauPvCkubl3HPRw+BgC3LN2Eb/2QQEmdhAY600He7eiygTdMklAgxtmQsBa7Bs5rvLR01nrnvnnu6LXS3njqVp554ot3zo0ePzvQKb4+33nijW+85ULCVQK4QgpWffw5SUt5PpSJM06Q+Vo9hWqYSQxqY0lp1C2EJbCHXKgCwBLkUa4W4TMVXKCitHq+LopBZgafPK4rS6jGAitrisQKKiktz4XA6+lzAd4aQgmu/vBFZKvElfPzn8NvxFZRadv0sZeAGkgFKPaVUFdilRNYl03gmC74Bm/axlUCOkEJQPmkSW55xRr/VCmqONbG0YRGKw5ER0goKqmIJ4rRA1lRLoKmp85qitRLqGyr3/vAgHzd8iafAw9MnP01pWXajuxJGAmEKhpcNz1p/48GE3Yayb7CVQA5I+wPKJk1i+jpVT3P1futGkyAl9eEazGiMiuJqNG/2ImU2BG77/B7u/vVB0ODinS9mfFnHYYM9oSnWxIjCEZT0slvYYMZuQ5l7bCWQC1L1gsjB6kUKgdD1taGDpmnFjDscqA4HzoICHF4vcZkkEWikrHQ0oj7YK7v1hsazP73E3R8+CCoctvOhHLnpkVl/j+ZEMz6Xj+rC6rwzg+UTdhvK3GMrgVwgBDVff40Ahk6fjtPXswYmwjBaC3wprWQapxPN6cRVVITmdmeeqy2ahjc0r0B3QHlxJbGkiRGK4CzOXrOTwcrKSA03/3AHqFBWWMYVM67M+nuYpklCTzC+bDxep11LqjNUTUMahr0byBG2EsgBUgi+vfdelr3zDtMv+f/2zjs8qir945/pmcwkk04KqSRUaRJEYF1XRFixrAVBZRFEsGzoiogIqICsoAisgHVBERFYxYIFAQVWAalZRfkhKAICgfQyfebe3x8hYwJpUwIJOR+eeR7unXPf+85k5rxzznnP+32KLo/UT25QliQcZeWph4Bno5HaYEAdFIRKq63S4deE0+0kz5pHsDa4PIc8PBy3xY7kcKDUXvoNQY2VUmcZY76dTLFcQqv0FN66cwVadeDfr3xbPuH6cL/UwpoTFaWm3WI00CCIIBBgZFlGcjg4dU6IoqUX+gEuqxWVVktQeDhKjcbT4Xv766fEUUKZo4zo4GgA1MF6tBEmbGfy0Ggu3LgkAKvTxpitj/NLyVGidZG8fvOrxJgCv6BvdVpRK9UkhCT4rBbWHPHsIhajgYAjgkCgcbs588MPPpWKcDudBIeHE+RHaVpJksg356NWVU251JhCcZmtuM0W1EaDz/YvRyRJ4t4PRvFrzm9oojX864YXaBlTd10gb3G73RTbikkyJfmsFtZcUSgUKFUqMRpoAERIDTQ+loqQ5fIaMmo/dRMsLguF9kKMmqobj5RqNbqIsHMLyy6/7nG5sezQSn7N/w1kGJpyJ51TuzfIffKseUQHRxMfIgoJ+oK3MpSC+iGCQICRJYnft28HvJsKkpxOVFotKj/FbgosBTjdTnTqC+2oDMFow8Nwm80BE/Zu6nx1chv/+vF1iIbbOvVnwnUTUOkCvw5QYC3AqDWSHJYs9gT4SGUZyob8/D4zcybdujfMD4FLcZ+6EEEggMiyjK2ggLwffwS8CwJuh6N88VfjewfhcDnIs+Vh0FY/3aNQKNCGm1DqdLitVp/vc7mQnfsDU3bNREZmYPLNTO/9OFpTYAvPQXltIICUsBSRDeQnFaWmTxw/zgMjR5KYnIzeaCQtI4MJEyeSn5/vlT21TsdHH31U5dyjEybw5RdfBNLtevHGm29ybZ8+RLVoQVSLFvT761/ZVY2sbqARQSCQuN3k7N8PskyEl6Ui3A4HGj8rQRY7ijE7zASra05JVWo06KIikZ3nNpU1U74/+yP3rx6NrdhG7xZX8VjGg+giwgO+M9XhcmB2mGlpbElYUFhAbTdHFAoFv504wdV/+hNHfv2Vd95+m4MHDvDywoV89fXX/OnPf6agBiWw+mI0GomMjAyQx/Vn67Zt3D1oEJu+/JJvtm4lMTGRG2+6iZMnTzbofUUQCCSSRMqNNzJ4yxaumT273pdV1EbxZypIkiTOms+iVWnr3HykDjGgMYXiNlt8vl9Txuy0MG7jFCSXhNaqYUabCejDwlCHBHbBXJIkCmwFxBvjiQuJC6jt5szo0aPRarVs3LiR6/r2JbVVKwbcdBNffPopJ0+d4qlp05BlmVatWzPruecYMnQooeHhJKWmsmTpUo+dVq1bA3DnoEGodTrP8fnTNCNGjuSOgQOZ8/zzxCcmEhkTw8zZs3G5XDz+xBNEx8aSnJbG8rfequLnE08+SbsOHQgJCyOjTRumP/00TmfNOs4r3nqLRx5+mC6dO9O2bVtee+UVJEniq/PK5wcaEQQCiCxJqLRawjMyiOvRo97Xue12lDodaj+CQKmjlFJb6QULwtWhUCjQRoSj1KhxW20+37Mp4pJcTP5uBgXaQoIj9Lx66wtEBoejCTMFPHU2z5pHeFA4LUNbNpldwQ6HA4fDUWXO3e1243A4cJ03cgxEW28pKChgw4YN/OMf/0Cv13uyhlQaDQnJydx7772sff/98sVjWebF+fPp1KkTe777jscfe4wJjz7Kxk2bgHJheoA3X3+d348d8xxXx9dbtnD61Cm+3rSJF+bO5Zlnn+XW224jPDyc7f/9Lw+OGsUjWVn8/vvvnmtCQkJ48403+CE7m/kvvsib//43CxYurPdrtVgsOJ3OBheybxqfzCZARb0gX0pFuB0ONHp9rRvA6qLQWohbdtd7c5NKp0UbGYFkdzSrbIsXvn+Z/+bsJEit4/WbF9LR0AqNKRR1cGDn6otsRQSpg0gJS2mQDWcNxZw5c5gzZw4Wyx+jxG+//ZY5c+bw2WefVWn7wgsvMGfOHIqLiz3ndu/ezZw5c/j444+rtF24cCFz5swhNzfXcy47O9tr/w4fPowsy7SrJvVaoVDQvn17CgsLKSguBoWCXj17MmniRNJbtSLrkUe48447WLhoEVAuTA8QZjIRGxvrOa6OiIgIFrz0Em3atOH+4cNp07o1FquVKZMnk5GRwROPP45Wq+Xbc0khAFOnTKFXz56kpKRwy803M3H8eP7z/vv1fq1TnnyS+Lg4ru/Tp97X+ILYJxAo3G4OffQRv+/aRbt77iHxL3+p96WSy4XG4PtUhM1pI9eaW+OCcE1oQkNwmc3NpqTEoxufYtOxrWCC2d2fop0+FWQZbVhgF4OtTitOl5OMqAyhEdBA1JUdVJGa3bNXL1RabblAjdtNj6uu4l8vv+x1eer27dpVGc3FtGjBFe3be45VKhWRkZGcPXvWc27N2rX8a/Fifv31V8rKynC5XISG1u+z9vy8eaxeu5bNGzcS5GfaeF2IIBAoJImjmzdzYutWYrp0qXcQqNgB6c96QLG9GJvTRlhImFfXNaeSEu8f/oRNP24F4KaMflyfcC2uohKC4lsE9HU73U6KbEWkmFI8O7abElOmlIvNayplqfXu3Zurr776gimtxx577IK23bt358orr7yg7bhzSlyV23bp0sVr/9LT01EoFBw8eJDbb7/9gucPHjxIeHi451d9xXQRKhWyWv2HeL0sexTu6oPmvKw9hUJR7bkKmzt27mTosGHMmD6dfjfcgCk0lNVr1/LSggV13uvF+fOZO28eGz7/nE4dO3rKyDQUIggECJfNxulduwAvU0PtdlR+rAe43W7Oms+i0/h2fXMoKXGo6AjzDvwLIiBNl8ysa6biNltQGQ1oQgL3S12SJAqsBcQaYkkISQiY3YuJtpqAqFKpqi1xEYi23hIZGckNN9zAkiVLmDBhAnr9H9N4OTk5rFy5kvvuu8/zOd55buMmlHfS3+3aRbv27T2jA41Gg9PlQqrU0VbIWlacq9iXULkNdZzbvn07yUlJPDFpkufpY7/9BvCH3fPuA/DC/Pn8c+5cPv34Y67s0sXzXEN+K8WaQACQZZmz2dm+lYpwONAYDD7XQyl1llJiL6nXgnBNaEyhqI2GyzJb6Kw1jzHfTsbqttIjpRtr7loO5wTateGmgKaEFtoLCdWFkmhKFHWBGpCXX34Zu91O//792bZtGydOnOCLL77ghhtuICEhgdmVMvO+/fZb5s6dy88//8zixYtZu3Yt48aNK99voFaTkpLClm3byC0ooMRsLi/SeG5nskqrRaXVevSdK45VWm25ap5KVeUcFYvUWi2t27bl+IkTrF23jt9OnGDJq6/y0SefAHjan3+fFxcs4Olnn+WNN94gLT2d3IICcgsKsDocfq0X1oUIAoHA7eZkRcE4L0pFQPmvAl9LTQPkWfJAgV+7UC/XkhL51gIGvz+CM+azpIUk88LVM9Eo1bjN1nKN4ADWUCpzlKFAQZIpSWwIa2AyMjLYs2cPaWlpDBo0iFatWvHggw9y3XXXsWPHDiIiIjxtH330Ufbs2UPXrl2ZNWsW8+fPp3///p7nX3zxRTZt2kRySgrdMjM9HTOUl7BWqlTlHf65Dr7iQXXn+GMz22233caECRMYO3YsV3brxo6dO5k2bVpVu+fd55VXX8XhcDBo0CASWrb0POa/9FKDjtAVsqgfQElJCSaTieLi4nov3ADYCwooOnCAoIgI1t19N3k//kifhQtpPXBgva6XXC6cFgumlBSfagZZnBZ+zP0RnUrnd8cjyzL23Hwc+QVowpp+cTO37Kb/ioHkFuSh1qv56O8raWmIR3I4kBwuglvGBUxtze6yU2wrJj0ivcloBdtsNo4ePUpqamqDLzxeKlJSUhg/fjzjx4+/1K40GLX9Hevbr4mRQACw5OWR99NPACRcc029r3M7HH7VCyq2FWNz2QLyy7NySQmXpelPC730/VJyVXmgginXTqClobxom8tsRRMeGrAA4Ha7ybfmE2+Mb5ILwQKBWBgOALb8fKI7dUJyOr0rFWG3o4+O9mmo53a7ybXkBnTqobykRATWUznIbneTFfde88uHrDi8GnQw+5anuDmlfPjvslhRBekCWh+owFZAVHAULU1NZ0OYQFAZEQQCQETbttyxfr1PtXg0et868WJHMaX2UiL1ga1xog4xogkNwVlSiqYBiqk1NMu/f5eFB18FFYzuMMoTAGRJQnY4y1NC/SjSV5lCWyFBmiBSTCmiMmgj5Ldz2TiC2hFBIBCcU/9SeZFv7nY6y5XDfJwKyjPnoVAqAp6FUlFSwm214rbZUQX5V9q6NmRJQrI7UKhVPnfMpY4yzlhzOWk+xS/Fv7FwyysA9OlyDSPbDvW0c5ktqI3BqAOUEmp1WpHcEsnhyV5v0hMIGhMiCPiJ02xGbbWi8rICqHRuPcCXzq/MUVaejqhtmF/qqiAdmohw7Dm5KLXey1vWheRyldcskiRUOh2S3YHbYkMVrEepqfqRdEpO9p/5gQNnD6LRaShwFnDSfJqDp3/mxO8nkTUyVJbqVYJRZ2B2z6c802ySy1W+Mzg8LCCvxel2UmwvJtWUGvCRmEBwsRFBwE+OfPEF+5Ys4YoRI+g1Y0a9r3M7HOgiInxaDyi0FuJwOYjQR9Td2Ee0plDcFktAS0pIDgduqx2FUoHaoEcTGooiSEtO0Sl+yznC/h/2sf3Ybqw4CAoP4qT5NGetucg5Mrgo7+wr1nNtgBtQQIjGSLwhjoTgOBThCh69KotgzR9pt26zBW2YCZXB91Rcz2uQJPIt+cQaY4kzisqggqaPCAJ+cnrPHiSXi2AvFoQrsnJ92SXsdDt9qhNUH2RZxuKwYJfslDnKKJby2Xv0W/IdhcRExIISbG4bZ0pyOXjqZ4K0WtLiUnBKLhySkwO//USJpZSWsfHo9XockoOishKOnTiOWq0iOj4KF26cuMn7PQ+nxYkySolbe27HpA3Io/xTWWkjplKrRKVU0jqsFVckdCDBEEekNgKlS0HnmA4khNYs1+i221Go1QGrEppvyycsKIzEULEhTHB5IIKAH7hdLs7s2weUbxKrLxV1enxZDyiyF2F1WIkKjqqz7Wc/fsZXh75CrVETFx2H2WmmzFHGrgO7KLWUEtsyFkklYXaaKSgowJJjAR1QOdMxhwt/hVuBfEAD/y39Y1s+ZwEHnJJzoGK92wZYADWUlJX90dYJSOB2uFEHqYkzxhEdHU2hrpCEsHhubnM9LQgjXt+C6LA4nxTXZFnGbbURFBMVkLWNUnspGqWGJFMSQZrLM7de0PwQQcAPTu/Zg8tm86lUhDo42OuOTZIkcs25qFSqOtMRT5WcYsLqCch2+cKO/SzggkJ14R8de4XWxbmaWsGaYAwaA5ZgC26Hi2RTS+Ii4tCrg7DabBzTnCBUH0KX1CvQKDVolBp+jfgNm91GRmQysYZodHoDklrFieLThBpMdErqhEapQavSkleaBxK0DG9JelQ6KmXVX9WyLOO2WHEWl+AsLUOy2lAbgr1KW3VbraiDggKS5WR32bG5bKRHpGMKavqb6QSCCkQQ8IPjmzcDPpSKcDrR+iAlaXaaKbGVEKKre47+rf+9hRwlE2IPIT4knm5tu2HQGDBqjRzLOYZSVtIluQsJ4QkYtUZUqJAkiWhDNDEhMVU6ZVeZGcvJ06j0Fy7cel6Tw4E7wYZCqURtNKAOMZZ32jW9L7G1+69QKFAbglEF69GEhuAoLsZVZgGFAnWwvs5gIEsSksNJUEKU33VXKjaEJYcmE6WvewQmuHTk5OQwdOhQtm/fjkajoaio6FK71OgRQcAPTnz9NQCJ115b72tkSQIfS0cXWAvqJRxTaC3kvQPvgQJeGvQSf06uf1XT6lAZgtGGh+HIL0BZqaSELMtINjtumx2lVoM2IhxNiBFlkC5gtU4UCgVqowGVIRi32YKjqBhXmbm8eFewvsYg4yozowkNTH2gfGs+0cHRJIQmiA1hjYDhw4dTVFTEhx9+eMFzL730EqdPnyY7OxuTqfyzmpKSwrFjxwDQ6/W0atWKcePGMXLkSM91NpuNhx9+mL1793Lw4EFuvvnmau1fjohPtI9YcnM5e04ZyetSETqd10HA5rSRZ80jWFt3hsuC/y7A6rTSPro91yTV37eaUCgUaMNCPSUlZEnCZbbgKi4FICg2muDEhPK5d31QgxS7qggG+vhY9AlxqIJ0uErLcJWZL1BGk5yucz77nxJaYC1Ar9WTbEoWG8KaAL/88gvdunUjIyODmJgYz/lnn32W06dPc+DAAf7+978zatQoPv/8c8/zbrcbvV7P2LFj6du376Vw/ZIhgoCPqLRa/vLii7S7917vSkVUSEl6mVlS4ijB7DATrK49CJwpPcOqr1fBGRjUdlDAOmSlVosuKgLZ6cJVZkap1aJPiCU4KQFdRDgq3cURpFEolWhCjOgT4tDHx6HU6XCWlOIyWzzBwG02owkNQeWnZGSRrQilQkmKKUVsCGsCpKSk8P777/P222+jUCgYPny457mQkBBiY2NJS0tj8uTJREREsHHjRs/zBoOBpUuXMmrUKGJj65irvMwQ00E+ojOZ6DRqFCX9+nl1nS9SkpIkcdZ8liBNUJ3TEUu2LwEZNEoNA6+oXzXT+qIOMRIUG4NSra51KuZioFAqz033BOMqOzdNVFJWXtNdq0ETHuZXACy1lyLJEmnhaQ26H6OxYbabAQjWBnveP4fLgdPtRK1UVxEvqmir1+g9n0uny4nD7UClVFXJoKqprUYduNHV7t27ue+++wgNDWXhwoVVBGcqkCSJdevWUVhYWK3QTXNEjAQuItK5omzeTgWVOEoosdUtHGNz2dj4+0aIg6wbswIucF4+xWJCbfRdBCfQVASD4IRY9AmxqPRBaMLD/BqZmB1mbE5bk5WI9AfjaCPG0UbyyvI85+ZtmIdxtJHRq0ZXaRszMQbjaCPHC457zi3eshjjaCMPLH+gStuUJ1IwjjZy8PRBz7nl25cH1Pfo6Gh0Oh16vZ7Y2FjPmgDA5MmTMRqN6HQ6Bg4cSHh4eJU1geZM4/gmNxM8paO9/AVSaCmsl3DM+z+9T54lj3hTPKN6jPLH1SaHQqVCExpCcGI82vAwn+1YnVbMDjNJpqQmow0gqJtJkyaRnZ3NV199RY8ePXjppZdIT0+/1G41CsR00EVEstsJioz06le01Wklz5aHUVv7KMDisLB0x1IARl45stkuYvozQrG77JTYS0gKTSI+pOZdyJczZS+Xb+irnIAwqf8kxvcdj1pZtbs4O/8sQJVy5ll/yWLUNaMu2Pfx2z9/u6Dt8F7DA+l6rURFRZGenk56ejpr166lY8eOZGZm0r59+4vmQ2NFjAQuIrIkofaydHSRrQir01qnbsDsDbM5++tZdKU6BrYP7FpAc8DhclBgLaBlSEtahjZfbQCDzoBBZ6iynqJVazHoDFXWAyq3rfxeadQaDDrDBTuqa2p7KUhMTGTw4MFMmTLlkty/sSFGAhcJyeVC4WXp6PoKx7glN1/+35cA9EjqQZBalDTwBqfbSZ41j4SQBBJDE5ttAGhKFBcXk30uRbuCyMj6V3QdN24cV1xxBXv27CEzMxOAn376CYfDQUFBAaWlpR77Xbp0CZDXjRMRBC4SbocDtU7n1XpAsaOYMkcZEUG1Z6ds+nUTxUHFGBINzLp1lr+uNivcbjd5ljziDHEkm5JFUbgmwpYtW+jatWuVcw888EANrS+kffv29OvXj+nTp/PZZ58BMGDAAM+mMsBj/3KXYRdB4CLhdjjQhXmXtlhgLUBGrrVjkmWZpXvK1wKGZw4nNrR55Tj7gyRJ5FvziQqOIiVMqIM1FZYvX87y5cvr3b4mhbEvvviiXu0ud8S49yIgy3L5ekBQ/adpzA4z+dZ8QrS11wn6z/f/4aczPxGsCea+zvf562qzQZIk8ix5mIJMpIWlBTydViBoKoggcBGQnM7y1FAv1gMqhGPqWg+Y88kcOA29onoRrg/319VmQ541jxBdCKlhqaIstKBZI4LARcDtcKAOCqp36eiKhUq9tvYAsOWXLZRZy0CGR3o9EghXmwX51nwMGgNp4WmiHISg2SOCwEXA7XCg9qJURImjhDJHGSGa2qeCVhxYAS2gX89+dIzv6K+bzYJCWyEapYbUsNQ6914IBM0BEQQaGFmWyytg1nM9QJIk8sx5qFXqWlMVfzz7I/89/l+USiWPX/d4oNy9rCmyFaFAQWpYqhCGEQjOIYJAA+O221HqdPXWE7a4LBTZi+qsE/T818+DDDe3vpkkU1IgXL2sqSgIlxKW0qwKwgkEdSGCQAMjOZ3lpaPrqW5VYCnA6XaiU9ccNLYe3srOfTvhDNzXUWQE1UVzLggnENSFCAINjOR01rt0tMPlIM+WV+di5Ru73gAFRIVG0SmuUyDcvGwRBeEEgtoRQaAB8UZKUpIkTpacpMxeVqtwzO8lv7OncA/EwbO3PxtIdy87KgrCJYYmNtuCcAJBXTTqIDBnzhy6d+9OSEgIMTEx3HbbbRw6dKhKG5vNRlZWFpGRkRiNRu68807OnDlziTyuittuL5eSrEepiDxrHqfKThGhj6h1QfjNfW/ilt30Su5F39bNSwbPGyoKwiUYE5p1QbjmRk5ODjfccAMGg4GwsLBL7U6ToFF/M7Zu3UpWVhY7d+5k48aNOJ1O+vXrh9ls9rSZMGECn3zyCWvXrmXr1q2cOnWKO+644xJ6/QduhwNNcHCdUpIl9hKOFR9Dr9HXuhZwOPcwa/63BoCHMx8OqK+XExX7LOJD4kkyJYkAcJkxfPhwbrvttmqfqyw0//PPPwPlspMKhQKFQoFeryclJYVBgwbx1VdfXXD92LFj6datGzqd7rIvHFdBo/52fPHFFwwfPpwOHTrQuXNnli9fzvHjx9m7dy9QXknwzTffZP78+fTp04du3bqxbNkytm/fzs6dOy+x9+VKYprg2jWB7S47x4qO4ZSchOhq3xfw5IdP4jzlpIW7BT0SegTS1csGURCueVOX0PyhQ4d4++23CQsLo2/fvsyePfsCGyNGjGDw4MEX0+1LSpMqIFdcXAxARER5it/evXtxOp307fvHtEjbtm1JSkpix44dXH311dXasdvt2O12z3FJSUnAfZVcrnIt3lrWAyRJ4kTJCYpsRcQYYmpsB1BsK+bHnB8BuLPznQETkG+qSJKEU3LilJy4JBdOyYkkScjIoiCcHzgqjbLPR6lSVdnvUltbhVKJppJ2Rk1ttV7qbddGSkqKpwro22+/zbBhwzyF5iqE5gGSkpL485//TFxcHNOnT2fgwIG0adMGgEWLFgGQm5vL999/HzDfGjNNJghIksT48ePp3bs3V1xxBVA+/6fVai+Y+2vRogU5OTk12pozZw7PPPNMQ7r7h5RkLUHgdOlpcspy6lwHAHjn+3dwhblITUhlzJ/HBNrdRkltHb0KFRq1BpVSRbAmmGBVMEGaILRqLSGaEFEQzkcWGWven5I6YAB3fvqp53hJTAwui6Xati2vvZa7t2zxHL+ekoI1L++Cdo8FsExzfYTmKzNu3DhmzpzJRx99xOOPN98Nl00mCGRlZXHgwAG++eYbv21NmTKFiRMneo5LSkpITEz0225lJIeDoKioGn+xF9mK+L3sdwxaQ50dltlh5q3/vQXAmD+NuSymOGRZ9jxcssvrjl6r1KJWqtEqtZfF+yHwn/OF5usiIiKCmJiYZltCuoImEQRGjx7N+vXr2bZtGy1btvScj42NxeFwUFRUVGU0cObMmVo/BDqdDp0XFT19QZblKsPhylidVo4XH0dGrlf9mgXbFlBkKSI5PJkb028MtKtVkCQJt+xGlmXcshugyrHMuc4bGUmWgHOiG/IfJTIAJFkqX4xDUX4NMsrzlqAUKFAqlKhUKtRKNcGaYAxqAzq1TnT0l4ixZWU1Pnd+gsM/zp6tse35Ws+jGmlHW/kz21xp1EFAlmXGjBnDunXr2LJlC6mpqVWe79atGxqNhs2bN3PnnXcCcOjQIY4fP07Pnj0vhcsAuJ1OFDWsB7jdbk4Un6DEXlKv3atl9jJWfL0C3DCgy4ALBLzrwuww45JdSLL0R0cuy8hS+YdfQkJB+ZdAce5fRYerVCjLO2mFCqVSiU6pQ6VQeR6V26hVao8NpaK8A6jIyPAcc+H/FQoFKoVKdPSNBG/m6Buq7cUiPz+f3NzcC/qV5kajDgJZWVm8++67fPTRR4SEhHjm+U0mE3q9HpPJxAMPPMDEiROJiIggNDSUMWPG0LNnzxoXhS8G0jkpSWU1paNPlp7kjOUMkfrIeqUuvrX3LSQklColo64e5ZUfpfZSnJKTYHUwSqWyvKNVlP/qVqvUqBSq8k5YqSrv/BUqT6de0flXdNIizVJwubFw4UKUSmWN6abNhUYdBJYuLZdN/Mtf/lLl/LJlyxg+fDhQnhesVCq58847sdvt9O/fnyVLllxkT6vidjjQhYdfMMzMt+ZzqvQUJp2pXpkrLsnFB4c/gBbwcNeHMerqX/rY7XZjdppJD08nLiTO69cgEDRmvBWaLy0tJScnB6fTydGjR3nnnXd44403mDNnDunp6Z52R44coaysjJycHKxWq+ce7du3R+uFPnhTolEHgfoIPAcFBbF48WIWL158ETyqmwqfzy8dbXaYOVZ8DKVKWadaWAWfHf6MEyUnCNeH89DVD3nlR7GjmDBdGFHBUV5dJxA0BbwVmp8+fTrTp09Hq9USGxvL1VdfzebNm7nuuuuqtBs5ciRbt271HFfc4+jRo6SkpATuBTQiGnUQaIpIDgfK81JDnW4nx4qPYXVYiTHWvh+gApfbxfyv54MMw7sMr3fggPKSCW7JTXxovMiVF1x2BEpovjq2VEprbS6IIBBg3A4H6uBgj5SkJEmcKj1FviXfqzLGi7Yu4tTRUyh1Su7teK9XPhTbi4nSRxGuE5rDAoGgdsRqX4CRXC60lTbc5NvyOVlyElOQqd7ZL7Is88nBT0ABnRI7eaWCZXVaUSlVxIXEicVcgUBQJ6KXCCCyJIFC4ZkKKnOUcaz4GBq1xqvpnO0ntnNSOomupY7n73jeKx+KbcW0CG5RZx0igUAgABEEAoq70nqAw+XgWPEx7C47YUFhXtl5de+rAAzuNJjUyPrnMJfaSwnWBgvxFIFAUG9EEAggbocDbXAwKBScLDlJgbWAyKCa09aq49MfP2Xn0Z2olWoe6FpztsP5SJJEmaOMeGO8V6MOgUDQvBFBIIBILhcag4FcSy6nyk4RHhTu9S7Y2Z/OhjPQMbijV/n9RfYiwoPCRUqoQCDwCpEdFCAktxuFSkWZZOW4+USdAjHVceDMAfLM5ZUWR/95dL2vc7qdIiVUIBD4hAgCAcLtcOBWypyxncEpOQkLDvPaxpv734QouC7xOq5pdU29ryu0FhIdHC1SQgUCgdeI6aAA4bJayZVLKHaUeL0OAPDd79/x+ZHPARjfe3y9r7M6rahVapESKhAIfEL0GgHibNlZ8tzF9RKIOZ9tR7YxYtkIJLfE39r8jXbR7ep9rUgJFQj+QAjNe48IAgGgoCyPs448QoxhXita5ZnzeOTtR3CWOYmwRzCzz8x6XytSQgXNEW+F5gH279/PXXfdRYsWLQgKCiIjI4NRo0Z52vz222+e0ufnPyr0yk+fPs29995L69atUSqVjB8/vqFf6kVBBAE/sblsnCw4hkKjJsTo3Zy83WVn9OejcZqcaPVaVty/giB1UN0XIlJCBYLqqE5ofv369Vx99dXY7XZWrlzJwYMHeeeddzCZTEybNq3K9Zs2beL06dNVHt26dQPKtcmjo6N56qmn6Ny580V/bQ2FWBj2A7fbTU5pDqW2ImIT071SKJJkicmbJrPv9D5CQ0JZNXwVGZEZ9b5epIQKAoksy1gszkty7+BgTUDUvaoTml+yZAn3338/AwYMYN26dZ62qamp9OjRg6Kioio2IiMja1QlTElJYeHChQD8+9//9tvfxoIIAn5Q5iyl0FaISRt6Qenounhw1YNsO7MNtVbNywNe9ioAiJRQQaCxWJwYjYsuyb3LysZiMPhfq786ofkNGzaQl5dXo5C8WDcQQcAvJFlCliQ0QXpUuvp/iGd8OoNt/9sGSpgyaApXt/ROBa3QVki0XqSECgSVqU5o/vDhwwC0bdu2XjZ69ep1QWJHWS26y5cDIggEAFWQDmU9VYd2nNjBmiNrQANdU7oytOtQr+5ldVpRK0VKqCCwBAdrKCsbe8nu3VDUR5iqMqtXr6Zdu/pn510OiCDgL0olquD6Lcz+UvALYz4fg1vppt/V/Vhw4wKvb1dsKyYxNFGkhAoCikKhCMiUTGOjdevWAPzf//0fPXv2rLN9YmJiFbnJ5oD4KeknSo26iopYTfya9yvD1gyjxF7ClXFX8uJfX0St8i4Gi5RQgcA7+vXrR1RUFHPnzq32+fMXhpsjYiTgJwqNBmUd6wHF1mLuXHon5jIzUYlRLLlpidd1hSpSQtPD00VKqKDZU1+heYPBwBtvvMFdd93FrbfeytixY0lPTycvL481a9Zw/Phx3nvvPU/7/Px8cnJyqtgICwsj6FziR8U9y8rKyM3NJTs7G61WS/v27QP7Ai8iIgj4gVKjQWXQo1TX/DZKssSTm5/E7DKDEmb1m0WEPsLre1WkhEYb6i9RKRBcrngjNP+3v/2N7du3M2fOHO69915KSkpITEykT58+zJo1q0rbvn37XnD9qlWruPvuuwGq3HPv3r28++67JCcne6Vj3NgQQcAPVDodmvDapR8X7FzAxqMbUUermfXnWfRp3cfr+4iUUIHgD7wVmgfIzMzk/fffr/H5lJSUei0ie7vQ3BQQQaABeWPXG7yy5xUAZl0/izva3eGTHZESKhAIGgqxMNxA/Hvnv5n7/lwogUcyH/E5AFSkhMYaY0VKqEAgCDiiV2kAjhQcYf7X8wGIC4pj7FW+518X24qJ0ccQGhQaKPcEAoHAg5gOCjD5lnwe/ORBHEYHqZGprBm6xmuJyQoqUkJjQ6qvZSIQCAT+IkYCAaTUXsrD6x/m95LfSTIlsWroKkz62heOa0KSJMwOM3GGOJESKhAIGgwxEggQLreLm1++mdNlpwmNDeW1W17zKRW0gmJHMWFBYSIlVCAQNChiJBAgnvziSU6fPQ0WmNBtAmnhaT7bcrqdOF1OkRIqEAgaHDESCABrf1zLh79+CFEwuN1ghmQO8cteoU0IxwsEgouDCAJ+svvUbmZsmQFA1jVZjLt6nF/2REqoQCC4mIhexg82/N8GHlv1GC6ni1ta38LYHv6X4hUpoQLBpeXpp5+mS5cul8196kIEAR/JKc1h+L+H47a4CbeH89z1z/ktkVdoKxQpoQJBPThx4gQjRowgPj4erVZLcnIy48aNIz8/3ys7CoWCDz/8sMq5xx57jM2bNwfQ2/rx448/cuedd5KSkoJCoWDBggUX5b4iCPjIyh9W4jA50AXrePeBd72uCno+RbYiFChIDUsVKaECQS38+uuvZGZmcvjwYVatWsWRI0d45ZVX2Lx5Mz179qSgoMAv+0ajsdqKpA2NxWIhLS2Nf/7znzXqHDcEIgj4yMSeE3mu/3MsG7mMVlGt/LJVZCtClmXSwtP8SisVCPzFbDZjNpurFEpzOByYzWbsdnu1bSVJ8pxzOp2YzWZsNlu92vpCVlYWWq2WL7/8kmuvvZakpCRuvPFGNm3axMmTJ5k6dSpQXhRu5syZ3HPPPRgMBhISEli8eLHHTkpKCgC33347CoXCc3z+NM3w4cO57bbbeO6552jRogVhYWE8++yzuFwuJk2aREREBC1btmTZsmVV/Jw8eTKtW7cmODiYtLQ0pk2bVutr7t69O/PmzePuu+9GVw+NkkAhgoCPKBQKHsp8iCRTkl92iu3FSLJEq4hWROov/q8PgaAyRqMRo9FIXl6e59y8efMwGo2MHj26StuYmBiMRiPHjx/3nFu8eDFGo/GCss4pKSkYjUYOHjzoOedtJVCAgoICNmzYwD/+8Q/0+qoj5tjYWIYMGcLq1as9QWzevHl07tyZ/fv388QTTzBu3Dg2btwIlAvTAyxbtozTp097jqvjq6++4tSpU2zbto358+czY8YMbr75ZsLDw/nuu+94+OGHeeihh/j9998914SEhLB8+XJ++uknFi5cyOuvv85LL73k9WtuaEQQuIQU24txS27SwtNEABAI6sHhw4eRZblGHeB27dpRWFhIbm4uAL179+aJJ56gdevWjBkzhoEDB3o64ujo8o2YYWFhxMbGeo6rIyIigkWLFtGmTRtGjBhBmzZtsFgsPPnkk2RkZDBlyhS0Wi3ffPON55qnnnqKXr16kZKSwi233MJjjz3GmjVrAvVWBAyRInqJKLGX4JbcpIalEh0sdgULGgdlZWUABAcHe85NmjSJ8ePHoz5PPOns2bMAVX6RZ2VlMWrUqAvqZVWIrlRuO3z4cJ/9rG9d//N1hXv27OnTgmuHDh2qpGy3aNGCK664wnOsUqmIjIz0vCdQLlq/aNEifvnlF8rKynC5XISGNr6sPzESuASUOcpwup2khqUSY4i51O4IBB4MBgMGg6FKpptWq8VgMFwwT13RtnLnqNFoMBgMHjnGutp6S3p6OgqFosq0UmUOHjxIeHh4rb/qfeF8XxUKRbXnKtY8duzYwZAhQxgwYADr169n//79TJ06FYfDEVC/AoEIAheZMkcZdqed1HARAAQCb4mMjOSGG25gyZIlWK3WKs/l5OSwcuVKBg8e7AliO3furNJm586dVaaSNBoNbrc74H5u376d5ORkpk6dSmZmJhkZGRw7dizg9wkEIghcRMwOM1aHldTwVFoYWlxqdwSCJsnLL7+M3W6nf//+bNu2jRMnTvDFF19www03kJCQwOzZsz1tv/32W+bOncvPP//M4sWLWbt2LePG/bGrPyUlhc2bN5OTk0NhYWHAfMzIyPCI2P/yyy8sWrSIdevW1XqNw+EgOzub7OxsHA4HJ0+eJDs7myNHjgTMr+oQQeAiYXaYMTvM5QHAKAKAQOArGRkZ7Nmzh7S0NAYNGkSrVq148MEHue6669ixYwcREX+kWT/66KPs2bOHrl27MmvWLObPn0///v09z7/44ots3LiRxMTEC4Tr/eHWW29lwoQJjB49mi5durB9+3amTZtW6zWnTp2ia9eudO3aldOnT/PCCy/QtWtXRo4cGTC/qkMhX47KyV5SUlKCyWSiuLjYq4WbAmsBB3MPEmOsfVrH7DBjcVpICk2ipamlv+4KBH5js9k4evQoqampF8zfXy6kpKQwfvx4xo8ff6ldaTBq+zvWt18TI4EGxuq0YnaYSQpNIj4k/lK7IxAIBFUQQaABsTqtlNpLSTYlEx8SL6qCCgSCRofYJ9BAVASAxNBEEQAEgktAxd4EQe2InqkBsDqtlNhLSAxNpGVoSxEABAJBo0X0TgHG5rKJACBoMoi8kKZNIP5+oocKIHaXnWJbMS1DWpIYmigCgKDRUlHWoTHuYBXUH4vFAvi2+7oCsSYQIOwuO4W2QloaRQAQNH7UajXBwcHk5uai0WjE57WJIcsyFouFs2fPEhYWdkGtJm8QQSAAOFwOCqwFJIYkkmRK8usPIhBcDBQKBXFxcRw9erTRljMQ1E1FBVR/EEHAT2Rk8q35IgAImhxarZaMjAwxJdRE0Wg0AelvRBDwE7VCTbQxWgQAQZNEqVRetjuGBfXjspkIXLx4MSkpKQQFBdGjRw927drV4PfUqXTEhcSRbEoWAUAgEDRJLosgsHr1aiZOnMiMGTPYt28fnTt3pn///lUEHhoCg9ZAclgyapUYUAkEgqbJZREE5s+fz6hRo7j//vtp3749r7zyCsHBwfz73/++1K4JBAJBo6bJ/4R1OBzs3buXKVOmeM4plUr69u3Ljh07qr3Gbrdjt9s9x8XFxUB51T2BQCC4HKjoz+raUNbkg0BeXh5ut5sWLarW6G/RogX/93//V+01c+bM4ZlnnrngfGJiYoP4KBAIBJeK0tJSTCZTjc83+SDgC1OmTGHixImeY0mSKCgoIDIysoq2al2UlJSQmJjIiRMnAiIgLew1LnsNYVPYE/Yulk1ZliktLSU+vvYS9k0+CERFRaFSqThz5kyV82fOnKlxE4VOp7tANDssLMxnH0JDQwP2Bxf2Gp+9hrAp7Al7F8NmbSOACpr8wrBWq6Vbt25s3rzZc06SJDZv3kzPnj0voWcCgUDQ+GnyIwGAiRMnMmzYMDIzM7nqqqtYsGABZrOZ+++//1K7JhAIBI2ayyIIDB48mNzcXKZPn05OTg5dunThiy++uGCxONDodDpmzJhxwdSSsHd52GsIm8KesNcYbFZGCM0LBAJBM6bJrwkIBAKBwHdEEBAIBIJmjAgCAoFA0IwRQUAgEAiaMSII+EggS1dv27aNW265hfj4eBQKBR9++KFfvs2ZM4fu3bsTEhJCTEwMt912G4cOHfLZ3tKlS+nUqZNns0rPnj35/PPP/fKxMv/85z9RKBSMHz/ep+uffvppFApFlUfbtm398unkyZP8/e9/JzIyEr1eT8eOHdmzZ49PtlJSUi7wT6FQkJWV5ZM9t9vNtGnTSE1NRa/X06pVK2bOnOmX6HhpaSnjx48nOTkZvV5Pr1692L17d72vr+szLMsy06dPJy4uDr1eT9++fTl8+LDP9j744AP69evn2eWfnZ3ts39Op5PJkyfTsWNHDAYD8fHx3HfffZw6dcpn/55++mnatm2LwWAgPDycvn378t133/lsrzIPP/wwCoWCBQsW1Pqa64sIAj4Q6NLVZrOZzp07s3jx4oD4t3XrVrKysti5cycbN27E6XTSr18/zGazT/ZatmzJP//5T/bu3cuePXvo06cPf/vb3/jxxx/99nX37t28+uqrdOrUyS87HTp04PTp057HN99847OtwsJCevfujUaj4fPPP+enn37ixRdfJDw83Cd7u3fvruLbxo0bAbjrrrt8svf888+zdOlSXn75ZQ4ePMjzzz/P3Llz+de//uWTPYCRI0eyceNGVqxYwQ8//EC/fv3o27cvJ0+erNf1dX2G586dy6JFi3jllVf47rvvMBgM9O/fH5vN5pM9s9nMn/70J55//nm//bNYLOzbt49p06axb98+PvjgAw4dOsStt97qkz2A1q1b8/LLL/PDDz/wzTffkJKSQr9+/cjNzfXJXgXr1q1j586ddZaC8ApZ4DVXXXWVnJWV5Tl2u91yfHy8PGfOHL9tA/K6dev8tlOZs2fPyoC8devWgNkMDw+X33jjDb9slJaWyhkZGfLGjRvla6+9Vh43bpxPdmbMmCF37tzZL18qM3nyZPlPf/pTwOydz7hx4+RWrVrJkiT5dP1NN90kjxgxosq5O+64Qx4yZIhP9iwWi6xSqeT169dXOX/llVfKU6dO9dre+Z9hSZLk2NhYed68eZ5zRUVFsk6nk1etWuW1vcocPXpUBuT9+/f77F917Nq1SwbkY8eOBcRecXGxDMibNm3y2d7vv/8uJyQkyAcOHJCTk5Pll156qU5b9UGMBLykonR13759PefqKl19qakolR0REeG3LbfbzXvvvYfZbPa7LEdWVhY33XRTlffSVw4fPkx8fDxpaWkMGTKE48eP+2zr448/JjMzk7vuuouYmBi6du3K66+/7rePUP75eeeddxgxYoRXxQor06tXLzZv3szPP/8MwP/+9z+++eYbbrzxRp/suVwu3G73BTKTer3erxFVBUePHiUnJ6fK39lkMtGjR49G/Z1RKBR+1RSrwOFw8Nprr2EymejcubNPNiRJYujQoUyaNIkOHTr47VNlLosdwxcTX0pXX0okSWL8+PH07t2bK664wmc7P/zwAz179sRms2E0Glm3bh3t27f32d57773Hvn37vJp3rokePXqwfPly2rRpw+nTp3nmmWe45pprOHDgACEhIV7b+/XXX1m6dCkTJ07kySefZPfu3YwdOxatVsuwYcP88vXDDz+kqKiI4cOH+2zjiSeeoKSkhLZt26JSqXC73cyePZshQ4b4ZC8kJISePXsyc+ZM2rVrR4sWLVi1ahU7duwgPT3dZz8ryMnJAaj2O1PxXGPCZrMxefJk7rnnHr+KwK1fv567774bi8VCXFwcGzduJCoqyidbzz//PGq1mrFjx/rsT02IIHCZk5WVxYEDB/z+RdemTRuys7MpLi7mP//5D8OGDWPr1q0+BYITJ04wbtw4Nm7cGBCR88q/gDt16kSPHj1ITk5mzZo1PPDAA17bkySJzMxMnnvuOQC6du3KgQMHeOWVV/wOAm+++SY33nijX3O6a9asYeXKlbz77rt06NCB7Oxsxo8fT3x8vM/+rVixghEjRpCQkIBKpeLKK6/knnvuYe/evT772RRxOp0MGjQIWZZZunSpX7auu+46srOzycvL4/XXX2fQoEF89913xMTEeGVn7969LFy4kH379vk8eqwNMR3kJb6Urr5UjB49mvXr1/P111/TsmVLv2xptVrS09Pp1q0bc+bMoXPnzixcuNAnW3v37uXs2bNceeWVqNVq1Go1W7duZdGiRajVatxut1++hoWF0bp1a44cOeLT9XFxcRcEt3bt2vk1xQRw7NgxNm3axMiRI/2yM2nSJJ544gnuvvtuOnbsyNChQ5kwYQJz5szx2WarVq3YunUrZWVlnDhxgl27duF0OklLS/PLV8DzvWjs35mKAHDs2DE2btzodylog8FAeno6V199NW+++SZqtZo333zTazv//e9/OXv2LElJSZ7vy7Fjx3j00UdJSUnxy0cQQcBrmkLpalmWGT16NOvWreOrr74iNTU14PeQJKmKRKc3XH/99fzwww9kZ2d7HpmZmQwZMoTs7GxUKpVfvpWVlfHLL78QFxfn0/W9e/e+IKX2559/Jjk52S+/li1bRkxMDDfddJNfdiwWC0pl1a+uSqVCkiS/7EJ5xxUXF0dhYSEbNmzgb3/7m982U1NTiY2NrfKdKSkp4bvvvms035mKAHD48GE2bdpEZGRkwO/h63dm6NChfP/991W+L/Hx8UyaNIkNGzb47ZeYDvKBQJeuLisrq/Kr9ejRo2RnZxMREUFSUpLX9rKysnj33Xf56KOPCAkJ8cy7mkwm9Hq91/amTJnCjTfeSFJSEqWlpbz77rts2bLF5w9gSEjIBesTBoOByMhIn9YtHnvsMW655RaSk5M5deoUM2bMQKVScc899/jk34QJE+jVqxfPPfccgwYNYteuXbz22mu89tprPtmD8g5g2bJlDBs2DLXav6/dLbfcwuzZs0lKSqJDhw7s37+f+fPnM2LECJ9tbtiwAVmWadOmDUeOHGHSpEm0bdu23p/puj7D48ePZ9asWWRkZJCamsq0adOIj4/ntttu88leQUEBx48f9+TyVwTt2NjYakcXtdmLi4tj4MCB7Nu3j/Xr1+N2uz3fmYiICLRarVf2IiMjmT17NrfeeitxcXHk5eWxePFiTp48WWNacF2v9/ygpNFoiI2NpU2bNtXa84qA5Bg1Q/71r3/JSUlJslarla+66ip5586dPtv6+uuvZeCCx7Bhw3yyV50tQF62bJlP9kaMGCEnJyfLWq1Wjo6Olq+//nr5yy+/9MlWTfiTIjp48GA5Li5O1mq1ckJCgjx48GD5yJEjfvnzySefyFdccYWs0+nktm3byq+99ppf9jZs2CAD8qFDh/yyI8uyXFJSIo8bN05OSkqSg4KC5LS0NHnq1Kmy3W732ebq1avltLQ0WavVyrGxsXJWVpZcVFRU7+vr+gxLkiRPmzZNbtGihazT6eTrr7++1veiLnvLli2r9vkZM2Z4ba8izbS6x9dff+21PavVKt9+++1yfHy8rNVq5bi4OPnWW2+Vd+3a5fPrPZ9ApoiKUtICgUDQjBFrAgKBQNCMEUFAIBAImjEiCAgEAkEzRgQBgUAgaMaIICAQCATNGBEEBAKBoBkjgoBAIBA0Y0QQEAgEgmaMCAICQSVSUlJqle377bff6iVn2JBcSh8CIX8qaFyIICBoVFSnxVv58fTTT19S/xITEzl9+rRf2gyXgw+CywdRQE7QqDh9+rTn/6tXr2b69OlVKnoajcZL4ZYHlUp1ycsfNwYfBJcPYiQgaFRUVIGMjY3FZDKhUCiqnHvvvfdo164dQUFBtG3bliVLllS5fvLkybRu3Zrg4GDS0tKYNm0aTqezSptPPvmE7t27ExQURFRUFLfffnuV5y0WCyNGjCAkJISkpKQq1UPPn4rZsmULCoWCzZs3k5mZSXBwML169bqgFPWsWbOIiYkhJCSEkSNH8sQTT9ClS5ca34fCwkKGDBlCdHQ0er2ejIwMli1bVq0PUC6JmZGRQVBQENdddx1vvfUWCoWCoqIiAJYvX05YWBgbNmygXbt2GI1G/vrXv1YJurt37+aGG24gKioKk8nEtddey759+2r00eFwMHr0aOLi4ggKCiI5OdkvTQPBpUEEAUGTYeXKlUyfPp3Zs2dz8OBBnnvuOaZNm8Zbb73laRMSEsLy5cv56aefWLhwIa+//jovvfSS5/lPP/2U22+/nQEDBrB//342b97MVVddVeU+L774IpmZmezfv59//OMfPPLIIxd06uczdepUXnzxRfbs2YNara5S1nnlypXMnj2b559/nr1795KUlFSnatW0adP46aef+Pzzzzl48CBLly6tUZrw6NGjDBw4kNtuu43//e9/PPTQQ0ydOvWCdhaLhRdeeIEVK1awbds2jh8/zmOPPeZ5vrS0lGHDhvHNN9+wc+dOMjIyGDBgAKWlpdXed9GiRXz88cesWbOGQ4cOsXLlyoCInAguMgGpRSoQNADLli2TTSaT57hVq1byu+++W6XNzJkz5Z49e9ZoY968eXK3bt08xz179pSHDBlSY/vk5GT573//u+dYkiQ5JiZGXrp0qSzLsqfs8P79+2VZ/qME8KZNmzzXfPrppzIgW61WWZZluUePHnJWVlaV+/Tu3Vvu3LlzjX7ccsst8v3331/tc+f7MHnyZPmKK66o0mbq1KkyIBcWFsqy/Efp5colthcvXiy3aNGiRh/cbrccEhIif/LJJ55zgLxu3TpZlmV5zJgxcp8+fWRJkmq0IWj8iJGAoElgNpv55ZdfeOCBBzAajZ7HrFmz+OWXXzztVq9eTe/evYmNjcVoNPLUU09VkYXMzs7m+uuvr/VenTp18vy/Yjrq7Nmz9b6mQtGs4ppDhw5dMNo4//h8HnnkEd577z26dOnC448/zvbt22tse+jQIbp3716n/eDgYFq1alXFz8qv68yZM4waNYqMjAxMJhOhoaGUlZXVKKs5fPhwsrOzadOmDWPHjuXLL7+s9TUJGiciCAiaBGVlZQC8/vrrVWT2Dhw4wM6dOwHYsWMHQ4YMYcCAAaxfv579+/czdepUHA6Hx059lNU0Gk2VY4VCUad0Y+VrKsTA/ZF7vPHGGzl27BgTJkzg1KlTXH/99VWmbnyhutclV5ITGTZsGNnZ2SxcuJDt27eTnZ1NZGRklfevMldeeSVHjx5l5syZWK1WBg0axMCBA/3yUXDxEUFA0CRo0aIF8fHx/Prrr6Snp1d5VGgob9++neTkZKZOnUpmZiYZGRkcO3asip1OnTpV0bq9GLRp04bdu3dXOXf+cXVER0czbNgw3nnnHRYsWFCjvGWbNm3Ys2eP1/bP59tvv2Xs2LEMGDCADh06oNPpyMvLq/Wa0NBQBg8ezOuvv87q1at5//33KSgo8PregkuHSBEVNBmeeeYZxo4di8lk4q9//St2u509e/ZQWFjIxIkTycjI4Pjx47z33nt0796dTz/9lHXr1lWxMWPGDK6//npatWrF3Xffjcvl4rPPPmPy5MkN5veYMWMYNWoUmZmZ9OrVi9WrV/P999+TlpZW4zXTp0+nW7dudOjQAbvdzvr162nXrl21bR966CHmz5/P5MmTeeCBB8jOzmb58uXAH6OS+pCRkcGKFSvIzMykpKSESZMm1Tpymj9/PnFxcXTt2hWlUsnatWuJjY0lLCys3vcUXHrESEDQZBg5ciRvvPEGy5Yto2PHjlx77bUsX77cMxK49dZbmTBhAqNHj6ZLly5s376dadOmVbHxl7/8hbVr1/Lxxx/TpUsX+vTpw65duxrU7yFDhjBlyhQee+wxzxTK8OHDCQoKqvEarVbLlClT6NSpE3/+859RqVS899571bZNTU3lP//5Dx988AGdOnVi6dKlnuwgnU5Xbz/ffPNNCgsLufLKKxk6dChjx44lJiamxvYhISHMnTuXzMxMunfvzm+//cZnn32GUim6laaE0BgWCC4BN9xwA7GxsaxYsaJB7M+ePZtXXnmFEydONIh9weWDmA4SCBoYi8XCK6+8Qv/+/VGpVKxatYpNmzaxcePGgN1jyZIldO/encjISL799lvmzZvH6NGjA2ZfcPkigoBA0MAoFAo+++wzZs+ejc1mo02bNrz//vv07ds3YPc4fPgws2bNoqCggKSkJB599FGmTJkSMPuCyxcxHSQQCATNGLGCIxAIBM0YEQQEAoGgGSOCgEAgEDRjRBAQCASCZowIAgKBQNCMEUFAIBAImjEiCAgEAkEzRgQBgUAgaMb8P4JmW2Ih61YHAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plot\n",
        "plt.figure(figsize=(4, 5))\n",
        "\n",
        "# Approach 2\n",
        "plt.fill_between(range(NSTEPS), rl_mean_2 + rl_std_2, rl_mean_2 - rl_std_2, color='lightgreen', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), demo_mean_2 + demo_std_2, demo_mean_2 - demo_std_2, color='lightcoral', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), expl_mean_2 + expl_std_2, expl_mean_2 - expl_std_2, color='lightblue', alpha=0.1)\n",
        "plt.plot(range(NSTEPS), rl_mean_2, 'g-', label='LfR2', color='green')\n",
        "plt.plot(range(NSTEPS), demo_mean_2, 'r--', label='LfD2', color='orange')\n",
        "plt.plot(range(NSTEPS), expl_mean_2, 'b-', label='LfCE2', color='purple')\n",
        "plt.plot(range(NSTEPS), ref_mean_2, 'k:', label='Optimal2', color='gray')\n",
        "\n",
        "# Approach 1\n",
        "plt.fill_between(range(NSTEPS), rl_mean + rl_std, rl_mean - rl_std, color='darkgreen', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), demo_mean + demo_std, demo_mean - demo_std, color='darkred', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), expl_mean + expl_std, expl_mean - expl_std, color='darkblue', alpha=0.1)\n",
        "plt.plot(range(NSTEPS), rl_mean, 'g:', label='LfR1', color='darkgreen')\n",
        "plt.plot(range(NSTEPS), demo_mean, 'r--', label='LfD1', color='darkred')\n",
        "plt.plot(range(NSTEPS), expl_mean, 'b-', label='LfCE1', color='darkblue')\n",
        "plt.plot(range(NSTEPS), ref_mean, 'k:', label='Optimal1', color='black')\n",
        "\n",
        "# Labels and legend\n",
        "plt.xlabel('Teaching signals')\n",
        "plt.ylabel('Average return')\n",
        "plt.ylim(0, 120)\n",
        "plt.xticks(range(0, 15))\n",
        "plt.legend(loc='best')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Approach 3**\n",
        "We use BEC to evaluate the expert rewards, demonstrations and explanations."
      ],
      "metadata": {
        "id": "K9HVBKVQBt6o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Import necessary libraries\n",
        "import numpy as np\n",
        "from tqdm import trange\n",
        "\n",
        "# Simulation constants\n",
        "NRUNS = 30\n",
        "NSTEPS = 15\n",
        "\n",
        "# For performance statistics\n",
        "perf_rl = np.zeros((NRUNS, NSTEPS))\n",
        "perf_demo = np.zeros((NRUNS, NSTEPS))\n",
        "perf_expl = np.zeros((NRUNS, NSTEPS))\n",
        "perf_ref = np.zeros((NRUNS, NSTEPS))\n",
        "\n",
        "# For reproducibility\n",
        "np.random.seed(40)\n",
        "\n",
        "def compute_BEC(policy, Mopt, feature_expectations):\n",
        "    S, A, P, ropt, gamma = Mopt\n",
        "    BEC = []\n",
        "\n",
        "    for s in S:\n",
        "        for a in A:\n",
        "            mu_sa = feature_expectations[(s, a)]\n",
        "            for a_prime in A:\n",
        "                if a != a_prime:\n",
        "                    mu_sa_prime = feature_expectations[(s, a_prime)]\n",
        "                    half_space = np.dot(ropt, (mu_sa - mu_sa_prime)) >= 0\n",
        "                    BEC.append(half_space)\n",
        "\n",
        "    return BEC\n",
        "\n",
        "def calculate_BEC_for_trajectory(trajectory, policy, feature_expectations):\n",
        "    BEC_trajectory = []\n",
        "\n",
        "    for (s, a, r) in trajectory:\n",
        "        mu_sa = feature_expectations[(s, a)]\n",
        "        for a_prime in policy[s]:\n",
        "            if a != a_prime:\n",
        "                mu_sa_prime = feature_expectations[(s, a_prime)]\n",
        "                half_space = np.dot(ropt, (mu_sa - mu_sa_prime)) >= 0\n",
        "                BEC_trajectory.append(half_space)\n",
        "\n",
        "    return BEC_trajectory\n",
        "\n",
        "def set_cover_greedy(U, T):\n",
        "    C = set()\n",
        "    D = set()\n",
        "\n",
        "    while U - C:\n",
        "        max_intersection = 0\n",
        "        best_trajectory = None\n",
        "\n",
        "        for tau in T:\n",
        "            intersection = len(U.intersection(tau))\n",
        "            if intersection > max_intersection:\n",
        "                max_intersection = intersection\n",
        "                best_trajectory = tau\n",
        "\n",
        "        if best_trajectory:\n",
        "            D.add(best_trajectory)\n",
        "            C = C.union(best_trajectory)\n",
        "\n",
        "    return D\n",
        "\n",
        "def compute_feature_expectations(policy, Mopt):\n",
        "    S, A, P, R, gamma = Mopt\n",
        "    feature_expectations = { (s, a): np.zeros(len(RFEAT[next(iter(RFEAT))])) for s in S for a in A }\n",
        "\n",
        "    for s in S:\n",
        "        for a in A:\n",
        "            discount_factor = 1.0\n",
        "            state = s\n",
        "            action = a\n",
        "\n",
        "            for t in range(NSTEPS):\n",
        "                feature_expectations[(s, a)] += discount_factor * RFEAT[state]\n",
        "\n",
        "                # Move to the next state according to the policy\n",
        "                next_state_probs = P[state][action]\n",
        "                next_state = np.random.choice(list(next_state_probs.keys()), p=list(next_state_probs.values()))\n",
        "\n",
        "                # Select the next action based on the policy\n",
        "                action_probs = policy[next_state]\n",
        "                action = np.random.choice(list(action_probs.keys()), p=list(action_probs.values()))\n",
        "\n",
        "                # Update the discount factor\n",
        "                discount_factor *= gamma\n",
        "\n",
        "    return feature_expectations\n",
        "\n",
        "# Main simulation loop\n",
        "for run in trange(NRUNS):\n",
        "\n",
        "    # Initialize a random reward\n",
        "    num_features = len(RFEAT[next(iter(RFEAT))])\n",
        "    wopt = np.random.randn(num_features)\n",
        "    ropt = np.sum([wopt[i] * RFEAT[state][i] for state in RFEAT.keys() for i in range(num_features)], axis=0)\n",
        "\n",
        "    # This is the \"target\" MDP\n",
        "    Mopt = (S, A, P, ropt, gamma)\n",
        "\n",
        "    # Optimal policy\n",
        "    popt = greedy(vi(Mopt))\n",
        "\n",
        "    # Compute feature expectations for optimal policy\n",
        "    feature_expectations = compute_feature_expectations(popt, Mopt)\n",
        "\n",
        "    # Use Theorem 1 to compute BEC\n",
        "    BEC_popt = compute_BEC(popt, Mopt, feature_expectations)\n",
        "\n",
        "    # Initialize sets for SCOT algorithm\n",
        "    U = set(BEC_popt)\n",
        "    T = []\n",
        "    expert_rewards = []\n",
        "    expert_demonstrations = []\n",
        "    expert_explanations = []\n",
        "\n",
        "    # Run test\n",
        "    for t in range(NSTEPS):\n",
        "        # Sample a reward and store\n",
        "        (s, a, r) = sample_reward(Mopt)\n",
        "        expert_rewards.append((s, a, r))\n",
        "\n",
        "        # Sample a demo and store\n",
        "        (s, a) = sample_demo(Mopt)\n",
        "        expert_demonstrations.append((s, a))\n",
        "\n",
        "        # Sample a contrastive example and store\n",
        "        (s0, s1, a0, a1, k) = sample_explain(Mopt)\n",
        "        expert_explanations.append((s0, s1, a0, a1, k))\n",
        "\n",
        "        # Compute BEC for each type of expert information\n",
        "        BEC_reward = calculate_BEC_for_trajectory([(s, a, r)], popt, feature_expectations)\n",
        "        BEC_demo = calculate_BEC_for_trajectory([(s, a)], popt, feature_expectations)\n",
        "        BEC_explain = calculate_BEC_for_trajectory([(s0, s1, a0, a1, k)], popt, feature_expectations)\n",
        "\n",
        "        # Add to set of constraints\n",
        "        T.extend([BEC_reward, BEC_demo, BEC_explain])\n",
        "\n",
        "        # Perform SCOT algorithm\n",
        "        D = set_cover_greedy(U, T)\n",
        "\n",
        "        # Update weights based on the selected most informative examples\n",
        "        for (s, a, r) in expert_rewards:\n",
        "            if (s, a, r) in D:\n",
        "                w_rl = rl_update(w_rl, s, a, r)\n",
        "\n",
        "        for (s, a) in expert_demonstrations:\n",
        "            if (s, a) in D:\n",
        "                w_demo = demo_update(w_demo, s, a)\n",
        "\n",
        "        for (s0, s1, a0, a1, k) in expert_explanations:\n",
        "            if (s0, s1, a0, a1, k) in D:\n",
        "                w_expl = explain_update(w_expl, s0, s1, a0, a1, k)\n",
        "\n",
        "        # Evaluate performance\n",
        "        perf_rl[run, t] = evaluate_reward(Mopt, w_rl)\n",
        "        perf_demo[run, t] = evaluate_reward(Mopt, w_demo)\n",
        "        perf_expl[run, t] = evaluate_reward(Mopt, w_expl)\n",
        "        perf_ref[run, t] = evaluate_reward(Mopt, wopt)\n",
        "\n",
        "        print('Done. Step complete.')\n",
        "\n",
        "# Compute statistics\n",
        "rl_mean = np.mean(perf_rl, axis=0)\n",
        "rl_std = np.std(perf_rl, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "demo_mean = np.mean(perf_demo, axis=0)\n",
        "demo_std = np.std(perf_demo, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "expl_mean = np.mean(perf_expl, axis=0)\n",
        "expl_std = np.std(perf_expl, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "ref_mean = np.mean(perf_ref, axis=0)\n"
      ],
      "metadata": {
        "id": "SabPmjHBB7FL",
        "outputId": "d7bb80df-c67e-492e-880f-3e31444208f2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        }
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "  0%|          | 0/30 [00:00<?, ?it/s]\n"
          ]
        },
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "only integer scalar arrays can be converted to a scalar index",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-59-7688d69af252>\u001b[0m in \u001b[0;36m<cell line: 93>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     94\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     95\u001b[0m     \u001b[0;31m# Initialize a random reward\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 96\u001b[0;31m     \u001b[0mnum_features\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mRFEAT\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0miter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mRFEAT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     97\u001b[0m     \u001b[0mwopt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_features\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     98\u001b[0m     \u001b[0mropt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mwopt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mRFEAT\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstate\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mRFEAT\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_features\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mTypeError\u001b[0m: only integer scalar arrays can be converted to a scalar index"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rl_min = np.min(rl_mean, axis=0)\n",
        "rl_range = np.max(rl_mean, axis=0) - np.min(rl_mean, axis=0)\n",
        "rl_norm = (rl_mean - rl_min)/rl_range\n",
        "rl_normstd = np.std(rl_norm, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "demo_min = np.min(demo_mean, axis=0)\n",
        "demo_range = np.max(demo_mean, axis=0) - np.min(demo_mean, axis=0)\n",
        "demo_norm = (demo_mean - demo_min)/demo_range\n",
        "demo_normstd = np.std(demo_norm, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "expl_min = np.min(expl_mean, axis=0)\n",
        "expl_range = np.max(expl_mean, axis=0) - np.min(expl_mean, axis=0)\n",
        "expl_norm = (expl_mean - expl_min)/expl_range\n",
        "expl_normstd = np.std(expl_norm, axis=0) / np.sqrt(NRUNS)\n",
        "\n",
        "\n",
        "ref_min = np.min(ref_mean)\n",
        "ref_range = np.max(ref_mean) - np.min(ref_mean)\n",
        "ref_norm = (ref_mean - ref_min)/ref_range"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "236bef4a-4d8c-4fad-cabb-0edfcb57adc1",
        "id": "CYideCpjCSzL"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-41-a6cb8b7f165e>:19: RuntimeWarning: divide by zero encountered in divide\n",
            "  ref_norm = (ref_mean - ref_min)/ref_range\n",
            "<ipython-input-41-a6cb8b7f165e>:19: RuntimeWarning: invalid value encountered in divide\n",
            "  ref_norm = (ref_mean - ref_min)/ref_range\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 470
        },
        "outputId": "820d9a16-885f-47a6-e42d-a88f3c6ea1a7",
        "id": "mQAJvpH2CSzM"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plot\n",
        "plt.figure(figsize=(4, 5))\n",
        "plt.fill_between(range(NSTEPS), rl_mean + rl_std, rl_mean - rl_std, color='g', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), demo_mean + demo_std, demo_mean - demo_std, color='r', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), expl_mean + expl_std, expl_mean - expl_std, color='b', alpha=0.1)\n",
        "plt.plot(range(NSTEPS), rl_mean, 'g:', label='LfR')\n",
        "plt.plot(range(NSTEPS), demo_mean, 'r--', label='LfD')\n",
        "plt.plot(range(NSTEPS), expl_mean, 'b-', label='LfCE')\n",
        "plt.plot(range(NSTEPS), ref_mean, 'k:', label='Optimal')\n",
        "#plt.xlabel('N. samples')\n",
        "#plt.ylabel(r'$||V_\\pi||_2$')\n",
        "plt.xlabel('Teaching signals')\n",
        "plt.ylabel('Average return')\n",
        "plt.ylim(0, 120)\n",
        "plt.xticks(range(0, 15))\n",
        "plt.legend(loc='best')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot\n",
        "plt.figure()\n",
        "plt.fill_between(range(NSTEPS), rl_norm*100 + rl_normstd*100, rl_norm*100 - rl_normstd*100, color='g', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), demo_norm*100 + demo_normstd*100, demo_norm*100 - demo_normstd*100, color='r', alpha=0.1)\n",
        "plt.fill_between(range(NSTEPS), expl_norm*100 + expl_normstd*100, expl_norm*100 - expl_normstd*100, color='b', alpha=0.1)\n",
        "plt.plot(range(NSTEPS), rl_norm*100, 'g:', label='RL')\n",
        "plt.plot(range(NSTEPS), demo_norm*100, 'r--', label='Demo')\n",
        "plt.plot(range(NSTEPS), expl_norm*100, 'b-', label='Contrastive Example')\n",
        "plt.plot(range(NSTEPS), ref_norm, 'k:', label='Optimal')\n",
        "plt.xlabel('N. samples')\n",
        "plt.ylabel(r'$||V_\\pi||_2$')\n",
        "plt.legend(loc='best')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "wEPI3fNMSSTN",
        "outputId": "6d3a1b44-a890-4139-d0e3-79a13f847774"
      },
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SW_VyigwJ76s",
        "outputId": "ffbda8db-3c82-45fb-c4df-0ce63fd2901d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimal:\n",
            "[ 0.77400935  0.19217953 -1.08031784  0.86528134]\n",
            "Contrastive Examples:\n",
            "[ 0.0042135  -0.01617479  0.0039453   0.57847882]\n",
            "Demos:\n",
            "[ 9.58074360e-05 -2.26440269e-04  0.00000000e+00  1.41656361e-02]\n",
            "RL:\n",
            "[ 0.          0.05082654 -0.20584739  0.        ]\n"
          ]
        }
      ],
      "source": [
        "print('Optimal:')\n",
        "print(wopt)\n",
        "print('Contrastive Examples:')\n",
        "print(w_expl)\n",
        "print('Demos:')\n",
        "print(w_demo)\n",
        "print('RL:')\n",
        "print(w_rl)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "wopt = [ 0.77400935, 0.19217953, -1.08031784, 0.86528134]\n",
        "w_expl = [ 0.00405971, -0.01627153, -0.50089822,  0.87839342]\n",
        "w_demos = [-0.20741821, -0.01244667,  0.01091068,  0.05925187]\n",
        "w_rl = [ 0.,0.05082654, -0.20584739, 0.        ]\n"
      ],
      "metadata": {
        "id": "nNU5CvwDF2BN"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy.stats\n",
        "from scipy.stats import f_oneway\n",
        "from scipy.stats import normaltest, ttest_rel, shapiro, mannwhitneyu, wilcoxon, ranksums, ttest_ind, kruskal, sem"
      ],
      "metadata": {
        "id": "VQfsUdTyul_5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ttest_rel(perf_demo[5], perf_rl[5])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a2xUe-m2e87z",
        "outputId": "2188ba55-1359-40b5-da48-6d02ccf256da"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "TtestResult(statistic=9.534616572884282, pvalue=1.6801336791089284e-07, df=14)"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mannwhitneyu(rl_mean,demo_mean)"
      ],
      "metadata": {
        "id": "KOxoPso6utXY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d2fdd3dd-07a4-4c59-c73e-fdbcc5aae14d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "MannwhitneyuResult(statistic=123.0, pvalue=0.6783024655972324)"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mannwhitneyu(rl_mean,expl_mean)"
      ],
      "metadata": {
        "id": "L2ltypYFu0f4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "adff8d97-5c98-413a-86b6-11e350a98912"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "MannwhitneyuResult(statistic=0.0, pvalue=3.3833394126542183e-06)"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mannwhitneyu(demo_mean,expl_mean)"
      ],
      "metadata": {
        "id": "wXeM5X1gu6o4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e259a532-6456-4202-bd53-b5f3a4c20377"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "MannwhitneyuResult(statistic=0.0, pvalue=3.3833394126542183e-06)"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ttest_rel(rl_mean,demo_mean)"
      ],
      "metadata": {
        "id": "ueGaHcIQFivE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9dfac0bd-f3bb-4fbf-ed1e-2ef2fe7d8294"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "TtestResult(statistic=0.9274795151197749, pvalue=0.36939206304515015, df=14)"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ttest_rel(rl_mean,expl_mean)"
      ],
      "metadata": {
        "id": "tYcAfUjWuFHJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c526e352-f498-45cb-b54d-4d2f1ab80fc5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "TtestResult(statistic=-11.509656338736663, pvalue=1.5948655358133367e-08, df=14)"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ttest_rel(demo_mean,expl_mean)"
      ],
      "metadata": {
        "id": "a5EWFCCrvOhQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ea2e55cb-c9b7-45b5-9a15-f1e8c38f6d98"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "TtestResult(statistic=-32.05173041281676, pvalue=1.673105598909057e-14, df=14)"
            ]
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          "execution_count": 44
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