Allgoerithm/rock-paper-scissors-in-tfp.ipynb

## rock-paper-scissors-in-tfp.ipynb
{
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  "metadata": {
    "colab": {
      "name": "Rock, Paper, Scissors in TFP",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/Allgoerithm/b2b327f025585d4bbeabc48a85a7ac47/rock-paper-scissors-in-tfp.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ScpcrL6quKNs",
        "colab_type": "text"
      },
      "source": [
        "#Rock, Scissors, Paper in TensorFlow Probability"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tLg7ElixubDE",
        "colab_type": "text"
      },
      "source": [
        "Dr. Michael Allgöwer, b.telligent, michael.allgoewer@btelligent.com"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cqjnq8rjZGuk",
        "colab_type": "text"
      },
      "source": [
        "### This notebook is completely in Tensorflow 2 and uses eager evaluation throughout."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OPyMiAzoTt5g",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 403
        },
        "outputId": "18c7c53d-031e-45b8-fc04-590eb142ee21"
      },
      "source": [
        "try:\n",
        "  %tensorflow_version 2.x\n",
        "  assert tf.__version__.startswith('2.1')\n",
        "except Exception:\n",
        "  pass\n",
        "\n",
        "# install current TFP version which expects tensorflow 2.1\n",
        "!pip install tensorflow-probability==0.9.0\n",
        "\n",
        "# install package for graphical display of MCMC results\n",
        "!pip install arviz"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "TensorFlow 2.x selected.\n",
            "Requirement already satisfied: tensorflow-probability==0.9.0 in /usr/local/lib/python3.6/dist-packages (0.9.0)\n",
            "Requirement already satisfied: decorator in /usr/local/lib/python3.6/dist-packages (from tensorflow-probability==0.9.0) (4.4.1)\n",
            "Requirement already satisfied: six>=1.10.0 in /tensorflow-2.1.0/python3.6 (from tensorflow-probability==0.9.0) (1.13.0)\n",
            "Requirement already satisfied: gast>=0.2 in /tensorflow-2.1.0/python3.6 (from tensorflow-probability==0.9.0) (0.2.2)\n",
            "Requirement already satisfied: cloudpickle>=1.2.2 in /usr/local/lib/python3.6/dist-packages (from tensorflow-probability==0.9.0) (1.2.2)\n",
            "Requirement already satisfied: numpy>=1.13.3 in /tensorflow-2.1.0/python3.6 (from tensorflow-probability==0.9.0) (1.18.1)\n",
            "Requirement already satisfied: arviz in /usr/local/lib/python3.6/dist-packages (0.6.1)\n",
            "Requirement already satisfied: numpy>=1.12 in /tensorflow-2.1.0/python3.6 (from arviz) (1.18.1)\n",
            "Requirement already satisfied: netcdf4 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.5.3)\n",
            "Requirement already satisfied: scipy>=0.19 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.4.1)\n",
            "Requirement already satisfied: pandas>=0.23 in /usr/local/lib/python3.6/dist-packages (from arviz) (0.25.3)\n",
            "Requirement already satisfied: xarray>=0.11 in /usr/local/lib/python3.6/dist-packages (from arviz) (0.14.1)\n",
            "Requirement already satisfied: matplotlib>=3.0 in /usr/local/lib/python3.6/dist-packages (from arviz) (3.1.2)\n",
            "Requirement already satisfied: packaging in /usr/local/lib/python3.6/dist-packages (from arviz) (20.0)\n",
            "Requirement already satisfied: cftime in /usr/local/lib/python3.6/dist-packages (from netcdf4->arviz) (1.0.4.2)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas>=0.23->arviz) (2018.9)\n",
            "Requirement already satisfied: python-dateutil>=2.6.1 in /usr/local/lib/python3.6/dist-packages (from pandas>=0.23->arviz) (2.6.1)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=3.0->arviz) (0.10.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=3.0->arviz) (1.1.0)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=3.0->arviz) (2.4.6)\n",
            "Requirement already satisfied: six in /tensorflow-2.1.0/python3.6 (from packaging->arviz) (1.13.0)\n",
            "Requirement already satisfied: setuptools in /tensorflow-2.1.0/python3.6 (from kiwisolver>=1.0.1->matplotlib>=3.0->arviz) (45.0.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y9IXsNjrTX1O",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "tfd = tfp.distributions\n",
        "tfb = tfp.bijectors\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import ipywidgets as widgets\n",
        "from IPython.display import display\n",
        "\n",
        "\n",
        "%matplotlib inline\n",
        "import arviz as az\n",
        "az.style.use('arviz-darkgrid')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "22Y9RjpwBhn8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "beb33dbd-71cd-4c57-cf46-29985668743a"
      },
      "source": [
        "print(tf.__version__, tf.keras.__version__, tfp.__version__)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2.1.0-rc1 2.2.4-tf 0.9.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6lnERfXFOhif",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "55d24a93-5746-49a0-d572-23e99ac7ccb7"
      },
      "source": [
        "# We're in TF2, so eager execution is switched on by default.\n",
        "tf.executing_eagerly()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GfbTIZ6EVg1T",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# We calculate the joint log probability.\n",
        "# It answers the big and central question in each Markov chain simulation: What's the probability\n",
        "# that this data occurs together with these distribution parameters?\n",
        "@tf.function(input_signature=5 * (tf.TensorSpec(shape=[], dtype=tf.float32),))\n",
        "def joint_log_prob(total_rock, total_paper, total_scissors, p_rock, p_paper):\n",
        "    '''\n",
        "    Joint log probability of data occuring together with given parameters.\n",
        "\n",
        "    :param total_rock: number of rock occurences\n",
        "    :param total_paper: number of paper occurences\n",
        "    :param total_scissors: number of scissors occurences\n",
        "    :param p_rock: probability of rock\n",
        "    :param p_paper: probability of paper\n",
        "    '''\n",
        "    total_count = total_rock + total_paper + total_scissors \n",
        "    # Start by defining a prior for the rock / stone / scissor outcomes.\n",
        "    # The three parameters are proportional to the prior probabilities of rock, paper, and scissors, respectively.\n",
        "    # We want to start with a situation in which all combinations of probabilities for \n",
        "    # rock/paper/scissors are equally likely.\n",
        "    # Dirichlet is the analogue of having a beta prior in the case of only two options instead\n",
        "    # of three. In particular, Dirichlet([1, 1]) is a uniform distribution.\n",
        "    rv_rsp_prior = tfd.Dirichlet([1., 1., 1.], name='rv_rsp_prior')  \n",
        "    rv_rsp_outcomes = tfd.Multinomial(total_count=total_count, probs=[p_rock, p_paper, \n",
        "                                      tf.constant(1., tf.float32) - p_rock - p_paper],\n",
        "                                      name='rv_rsp_outcomes')\n",
        "\n",
        "    # calculate prior log probability of parameters\n",
        "    joint_log_prob = rv_rsp_prior.log_prob([p_rock, p_paper, tf.constant(1., tf.float32) - p_rock - p_paper])\n",
        "    \n",
        "    # add log likelihood of data\n",
        "    joint_log_prob = tf.add(joint_log_prob, rv_rsp_outcomes.log_prob([total_rock, total_paper, total_scissors]))\n",
        "\n",
        "    return joint_log_prob"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qoPizg6vkLda",
        "colab_type": "text"
      },
      "source": [
        "### define Hamilton Monte Carlo Chain and sample from posterior"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oJ4_s2c5Vnf4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# **** This cell takes about 17 minutes to execute.\n",
        "\n",
        "# observed data\n",
        "total_rock = tf.constant(5., tf.float32) \n",
        "total_paper = tf.constant(0., tf.float32)\n",
        "total_scissors = tf.constant(0., tf.float32)\n",
        "\n",
        "# define some constants\n",
        "number_of_steps = 10000\n",
        "burnin = 5000\n",
        "\n",
        "# Set the chain's start state\n",
        "initial_chain_state = [\n",
        "    1/3 * tf.ones([], dtype=tf.float32, name=\"init_p_rock\"),\n",
        "    1/3 * tf.ones([], dtype=tf.float32, name=\"init_p_paper\")\n",
        "]\n",
        "\n",
        "# for trainsforming contrained parameter space (in this case, [0, 1] for each parameter) to unconstrained real numbers\n",
        "unconstraining_bijectors = [\n",
        "    tfp.bijectors.Sigmoid(),   # bijector for p_rock                                    \n",
        "    tfp.bijectors.Sigmoid()    # bijector for p_paper\n",
        "]\n",
        "\n",
        "# fix data to the actually observed values in the joint log prob to optimize only over the unkown model parameters,\n",
        "# and convert to tensorflow function for speedup\n",
        "joint_log_prob_for_opt = tf.function(func=lambda x, y: joint_log_prob(total_rock=total_rock,\n",
        "                                                                        total_paper=total_paper,\n",
        "                                                                        total_scissors=total_scissors, \n",
        "                                                                        p_rock=x, p_paper=y),\n",
        "                                     input_signature=2 * (tf.TensorSpec(shape=[], dtype=tf.float32),)\n",
        "                                     )\n",
        "\n",
        "# define the Hamilton markov chain by successively adding wrappers to an inner kernel\n",
        "kernel = tfp.mcmc.HamiltonianMonteCarlo(\n",
        "            target_log_prob_fn=joint_log_prob_for_opt,\n",
        "            num_leapfrog_steps=2,\n",
        "            step_size=tf.constant(0.5, dtype=tf.float32),\n",
        "            state_gradients_are_stopped=True\n",
        "            )\n",
        "kernel=tfp.mcmc.TransformedTransitionKernel(\n",
        "            inner_kernel=kernel,\n",
        "            bijector=unconstraining_bijectors\n",
        "            )\n",
        "kernel = tfp.mcmc.SimpleStepSizeAdaptation(\n",
        "            inner_kernel=kernel,\n",
        "            num_adaptation_steps=int(burnin * 0.8)\n",
        "            )\n",
        "\n",
        "# sample from the chain\n",
        "[\n",
        "    posterior_p_rock,\n",
        "    posterior_p_paper\n",
        "], kernel_results = tfp.mcmc.sample_chain(\n",
        "    num_results=number_of_steps,\n",
        "    num_burnin_steps=burnin,\n",
        "    current_state=initial_chain_state,\n",
        "    trace_fn=lambda _, kernel_results: kernel_results.inner_results.inner_results.is_accepted,\n",
        "    kernel=kernel)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kNnZ7Nk7J7-E",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        },
        "outputId": "6edc153f-5a72-483a-a3de-1f541b968e7e"
      },
      "source": [
        "posterior_p_rock"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(10000,), dtype=float32, numpy=\n",
              "array([0.85103303, 0.60443765, 0.81940603, ..., 0.7190462 , 0.79699165,\n",
              "       0.59687734], dtype=float32)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4Rt5bCTOHOEl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "e9994973-b70c-40ad-ac73-1faa4594d1c9"
      },
      "source": [
        "az.plot_posterior(posterior_p_rock.numpy(), credible_interval=0.95, point_estimate='median')"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7efee02deac8>],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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e2LjJ16OR9FDYFhERSYM1ay2LFkN4GHRsr6At3hUdbWh8bs5t3SgZmBS2RURE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\niyhsi4iIiIi4iMK2iIiIiIiL/H+f4ic7oggoLgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gbZSvYItz_Eg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "17b181a7-adbc-46ee-b27f-d45f42c1a764"
      },
      "source": [
        "az.plot_posterior(posterior_p_paper.numpy(), credible_interval=0.95, point_estimate='median')"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7efeaac48d30>],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NGyVJ9erVSxbaiQICAuTr66s9e/Yk3bdt2zZJ0pNPPnnT8z09PdWoUaOkZSEpdfHiRa1d\nu1aHDh3SlStXFB8fL8leKnLx4kVdvHhRuXPnTvaaQoUKqUSJEje9V/HixbV+/fqbfjj4wgsv6IUX\nXkjVuAAAANwFsZ3G/veHg4n8/Hx05IgUH59f83+w1DnwRmwnzoLHxsZKkk6ePClJmjx5siZPnnzb\nz4qJiUk6PnfunCQ79m/ldvffzi+//KLhw4ffcTY4Ojr6pti+3VKOxKUjid8xLSWev2vXrt3y8cT7\n/7l8BQAAID0Q22ns7rtteGjBIqnda5ayZbv1cy3Lvrx71apVk2a909PJkyc1ZMgQSVKPHj1Ut25d\n5c+fP2k5RqdOnbRz586kcf5TancbWbhwobZv356q19SvX1/169dPul2oUCGFhYXddplM4v3uvpc4\nAABwP8R2OitQQDp7Tvr5F6nZ87d+TuLseL169dSmTZsUvW/iDxkTZ8X/1+3uv5UNGzbo+vXratOm\njVq3bn3T4ydOnEjxe93N9u3bU/0DycKFCyeL7bJly2rNmjXav3//LZ+feH+ZMmXufaAAAAD3gNhO\nZ02bGM2YKc2Za+n55259kZuaNWtqypQpWr16dYpju1q1alqyZImWL1+uF198MdljcXFxWrVqVYrH\nePnyZUm3XhKydetWnT9/PsXvdTdBQUEKCgq6r/eoW7eupk2bpnXr1ik2NjbZXtsRERHatm2bcuXK\ndU8/xgQAALgf7LOdzho3lLJnl44ekzb+cevnVKpUSTVr1tSOHTs0cuRIRUVF3fScAwcO6Lfffku6\n3ahRI+XOnVtbtmzRkiVLku63LEtTp05N1bZ3iT/w/Pnnn5N2+pDs5Riffvppit8nvVSsWFFVqlTR\nhQsXNGHChKT74+LiNHLkSMXFxemll1666eqRgwcPVuvWrVP1DxEAAIDUYGY7nWXLJv37WWn2HGn2\nHEt1at96jfOgQYPUvXt3ff/99/rll19UtmxZ5cuXT1FRUTp48KBOnz6t1q1bJ239lz17dn344Yfq\n16+fhgwZovnz56to0aI6cOCAjh07phdeeEELFy5M0RifeOIJlSpVSnv37lXLli1VpUoVxcbG6s8/\n/1TZsmVVuXJl7dy5M83OSVoYMGCAOnXqpO+++06bN29WyZIltXfvXp04cUKVK1dW+/btb3rNqVOn\n9Pfff+vKlSs3PTZixIik5ScXL16UZC+v6dixY9Jzpk2bluw1Cxcu1KJFiyTZoS/ZM+v/fM3777+v\ncuXK3ee3BQAA7oLYdoKWLYzmzLP05xbp4KGbf2QoSXnz5tXUqVO1cOFC/frrrwoLC9POnTuVN29e\nFSlSRK1atdJTTz2V7DX16tXThAkTki7XfuTIEZUvX179+/fX33//neLYzpo1a9JOKL/99pvWr1+v\n/Pnz66WXXlLHjh3Vo0eP+z4Haa148eL66quvNGXKFP3+++9avXq1ChYsqDfeeEPt27e/6TLud3P4\n8GHt3r072X2RkZGKjIy87WvOnDlz02uuX7+e7L5b/VcKAACQcRnrVltKpIELFy444m1TxM/Pz6mf\nnxJBgxO0YqXU9F9S/w/cfzWPO5zzjIZz7hyc9/THOU9/nHPn4LynPz8/P4d/hvtXnptq1dJePvLr\ncikiwiH/3gEAAICTEdtOUqmiUaWK0vXr0g8LiW0AAICMiNh2olYv2bPbPyyQrl4luAEAADIaYtuJ\n6j0uFSkiXbwkLf3J2aMBAABAWiO2ncjT0+jlVvbs9uw5luLimN0GAADISIhtJ3u2iZQnj3TylLRq\ntbNHAwAAgLREbDuZt7dRyxb27Pas2ZYctBMjAAAAnIDYdgHNX7CvLBl2QNr8p7NHAwAAgLRCbLuA\n3LmNnnvWPv7mW2a2AQAAMgpi20W8/JJRliz2zPbuPQQ3AABARkBsu4hChYyeedo+nvEVsQ0AAJAR\nENsupF0bIw8PacPv0r79BDcAAIC7I7ZdyAMPGD3V2D6eMZPYBgAAcHfEtotp95qRMdLaddLBQwQ3\nAACAOyO2XUyJEkaNGtjHzG4DAAC4N2LbBbVra1/kZtVqZrcBAADcGbHtgkqXMmrUULIsaUoosQ0A\nAOCuiG0XFfiGURYPacNv0s5dBDcAAIA7IrZdVPFiRk2b2MchUy1ZFsENAADgbohtF/Z6eyOvrNK2\n7dIfm5w9GgAAAKQWse3CChYwat7MPg4JtZSQwOw2AACAOyG2XdxrbYx8faWwMOnX/3P2aAAAAJAa\nxLaL88tj1LaNvRXgpCmWoqOZ3QYAAHAXxLYbaNVSKlJEOndOmvkNsQ0AAOAuiG034O1t9G4Xe3Z7\n9hzpxAmCGwAAwB0Q227i8cekRx+Rrl+Xxk8ktgEAANwBse0mjDHq9o59oZu166Xffie4AQAAXB2x\n7UZKPmj0Ukv7eORnlqKiCG4AAABXRmy7mcA3jIoUkc6csXcnAQAAgOsitt1MtmxGH7xv/1hywUJp\n6zaCGwAAwFUR227o4epG/37OPv50pKVr1whuAAAAV0Rsu6mubxnlzycdPyFNmExsAwAAuCJi203l\nyGH0QR97OckPC6RVqwluAAAAV0Nsu7FaNY1efcU+Hj7C0smTBDcAAIArIbbdXOeORhUrSFeipEFD\nLMXFEdwAAACugth2c56eRoM+MsqRQ9q9h6tLAgAAuBJiOwMoXNiof197/fa8+dK8+QQ3AACAKyC2\nM4h6Txi91dkO7i/GW1q/geAGAABwNmI7A2nzivRcUykhQRr0saX9YQQ3AACAMxHbGYgxRr17GtV4\nWLp6Ter1vqXDRwhuAAAAZyG2MxhPT6PgwUYPPSRFXpTe62Hp6FGCGwAAwBmI7QwoZ06jMSONSpeW\nzl+QuvW0dPw4wQ0AAJDeiO0MKnduo7GjjR58UDp3Tnqnu6W//iK4AQAA0hOxnYH55TH64jOjkg/a\nwd2lm6XtOwhuAACA9EJsZ3B58xpN+MKociXpyhWpR29L69YT3AAAAOmB2M4EcuUyGjPKqG4dKTZW\n6jfA0n++spSQQHQDAAA4ErGdSWTLZjR0iFGz5yXLkkK/tPRBf0uXLhPcAAAAjkJsZyKenka9e3qo\nX18jr6zSht+lwDctHThIcAMAADgCsZ0JPdvEaNIEo8KFpPBw6c0uln5aRnADAACkNWI7kwp4yGja\nFKNaNe113J8MszRqTIJiY4luAACAtEJsZ2K5chmNGGbUob19e8FCqWs3SydPEtwAAABpgdjO5LJk\nMerYwUMjhxvlzCnt3Se90dnS+g0ENwAAwP0itiFJqlPbaPpUo/LlpcuXpb79LU0KSVBcHNENAABw\nr4htJClUyGjiF0YtW9i3v/lW6t7L0rlzBDcAAMC9ILaRTNasRt27eejjQUa+vtK27VKHTpa2bSe4\nAQAAUovYxi01amAUGmJUupR04YI9w73kJ4IbAAAgNYht3FbxYkYhE40aNpDi4qRhn1qaMClB8fFE\nNwAAQEoQ27ijbNmMBgfd2B7w2++kjwZZiokhuAEAAO6G2MZdeXjY2wMO/Mgoa1ZpzVqp5/uWLl8m\nuAEAAO6E2EaKPdXYaPQIo+zZpe077AvgnDlDcAMAANwOsY1Uebi60YQvjPz9pb8OS+90t3TqNMEN\nAABwK8Q2Uq1MaaOQCUZFi0jh4VK3HpZOnop39rAAAABcDrGNe1KokNEXY42K/De4O3S8pNMsKQEA\nAEiG2MY9K1jAaNx/g/vY8QS918PShQsENwAAQCJiG/elYAGjL8YYFSnioeMnpF59LUVFEdwAAAAS\nsY00UKig0dRJuZQntxQWJvX/yFJsLMENAABAbCNNPPhgFo361MjHR/pzizRkqKWEBIIbAABkbsQ2\n0ky5ckbDgo08PaWVq6Sp04htAACQuRHbSFOP1DD6oI+RJM38RvppGcENAAAyL2Ibae5fTxu1bWMf\njxhlafsOghsAAGROxDYcolNHo/r1pOvXpQ8/4iqTAAAgcyK24RAeHkYD+hk9VFaKvCgNCLIUE0Nw\nAwCAzIXYhsP4+BgNHWKUO5e0b7/02eeWLIvgBgAAmQexDYcqVMhoUJCRh4e0ZKm0aLGzRwQAAJB+\niG043KOPGHXqaO9QMvYLS3v3MbsNAAAyB2Ib6eK1V6V6T9g/mAwaZOnSZYIbAABkfMQ20oUxRv37\nGhUpIp08JQ0bzvptAACQ8RHbSDc5chh9PNAoa1Zp7XppzjxnjwgAAMCxiG2kq3IBRu90sddvT5xs\nafceZrcBAEDGRWwj3bVoJjVsIMXHSx8HW4qOJrgBAEDGRGwj3Rlj1KeXUcGC0olwaew4YhsAAGRM\nxDacImdOo4/6GxkjLf1JWrGK4AYAABkPsQ2nqVbV6LU29vGIUZZOnyG4AQBAxkJsw6k6vm5Uvpx0\n5YoUPNRSfDzBDQAAMg5iG07l6WkUNMDIJ5u0dZs0e46zRwQAAJB2iG04XbEHjN7rZm8HOHWapX37\nmd0GAAAZA7ENl/BsE6lBPSkuzt4O8OpVghsAALg/YhsuwRijPr2N8ueTjh6Txk8ktgEAgPsjtuEy\ncuUyGvDf7QAX/iitXUdwAwAA90Zsw6XUeNjoldb28fARls5FENwAAMB9EdtwOZ06Gj1UVrp4SRo6\n3FJCAsENAADcE7ENl5M1q9HAAUbe3tIfm6S53zt7RAAAAPeG2IZLKlHC6N2u9naAk6dYOnCQ2W0A\nAOB+iG24rBf+LT3+mHT9ujQ42FJMDMENAADcC7ENl2WMUd/3jfzzSkeOSBMnE9sAAMC9ENtwaX55\njPp/YC8n+f4H6bffCW4AAOA+iG24vFo1jVq1tI+Hfmrp/HmCGwAAuAdiG27hzU5GpUtJFy5Iw0ZY\nsiyCGwAAuD5iG27B29veDtArq/Tb79L8Bc4eEQAAwN0R23AbpUoZdXnbXr89YZKlvw4zuw0AAFwb\nsQ238mJzqVZNKTaW7QABAIDrI7bhVowx+vADozx5pEOHpPGTiG0AAOC6iG24nbx5jT7qby8n+WGB\ntHIVwQ0AAFwTsQ23VKum0Wuv2sfDR1o6EU5wAwAA10Nsw20FvmFUuZIUFSUNHGwpNpbgBgAAroXY\nhtvy9DQaFGSUK5e0b780eQqxDQAAXAuxDbdWsMCNy7nPmSetW09wAwAA10Fsw+09XteodSv7+JPh\nlk6dIrgBAIBrILaRIbzVyah8eenyZWnQEEtxcQQ3AABwPmIbGULWrEaDg4xyZJd27bavMAkAAOBs\nxDYyjCKFjQb8d//tud9Ly34huAEAgHMR28hQHn/M6PV29vGnoyyFHSC4AQCA8xDbyHDeeN2oTm0p\nNlbqP8BSZCTBDQAAnIPYRobj4WEU9KHRA0WlU6elgR/zg0kAAOAcxDYypJw5jYYGG/lkk/7cIoVM\nJbYBAED6I7aRYZUqeeOCN99+J/3fcoIbAACkL2IbGVrDBkavvWofDxth6cBBghsAAKQfYhsZXqeO\nRjUflWJipH4fWrrADyYBAEA6IbaR4WXJYjTooxs/mBwQZOn6dYIbAAA4HrGNTCFXLqNPhxplzy5t\n3yGNHmPJsghuAADgWMQ2Mo0SJYwGBRl5eEiLl9pXmQQAAHAkYhuZSp1aRl3esncoGT/R0h+bmN0G\nAACOQ2wj02n9ktS0iZSQIAUNsnT0KMENAAAcg9hGpmOMUe8eRpUrSVeipL4fWrp0meAGAABpj9hG\npuTlZfTJx0YFC0rHjkkDB3NJdwAAkPaIbWRaefMaDQ82ypZN2rRZGj+J2AYAAGmL2EamVras0Uf9\n7R9MzvteWrSY4AYAAGmH2EamV7+eUeAbdnCPHmNp23aCGwAApA1iG5DUvq3UuKEUH29fYTL8JMEN\nAADuH7ENyN6hpF9fo4CHpMiL0gf9LUVHE9wAAOD+ENvAf2XLZjQs2Mg/r/TXYenjTywlJBDcAADg\n3hHbwD8UKGA0NNjIK6u0br00dRqxDQAA7h2xDfyPihWM+r5v/2By5jfSL/9HcAMAgHtDbAO38MzT\nRq+9ah8P/9TSnr0ENwAASD1iG7iNzoFGj9WVYq9L/QZYOnuW4AYAAKlDbAO34eFhNHCAUamSUkSE\nHdzXrhHcAAAg5Yht4A58fY2GDzXKnUvat18aNsKSZRHcAAAgZYht4C6KFDYK/tgoSxZp+Qrpq6+d\nPSIAAOAuiG0gBapXM+rZ3d6hZOo0S6vXMrsNAADujtgGUuiFfxu1bGEfB39i6eAhghsAANwZsQ2k\nwjtdjB6pIV29Jg0IsnTlCt92rRoAACAASURBVMENAABuj9gGUsHT02hwkFHBgtLxE9Inw/nBJAAA\nuD1iG0il3LmNggcbZc0qrV0nzZrt7BEBAABXRWwD96B8OaP33rV/MBky1dKWrcxuAwCAmxHbwD16\n4d9Sk2ekhARp4MdcYRIAANyM2AbukTFGvXoYlS4tXbggBQ22FBdHcAMAgBuIbeA+ZMtm9MlgoxzZ\npZ27pImTiW0AAHADsQ3cpwceMPqwn71+e848aflKghsAANiIbSANPPG40Wuv2scjR1k6dYrgBgAA\nxDaQZgLfMKpYQboSJQ0Zaik+nuAGACCzI7aBNOLpaRQ0wMjHR9q+g/23AQAAsQ2kqaJFjHq+Z6/f\nDv3S0r59zG4DAJCZEdtAGvvXM1LDBlJ8vDQo2NLVqwQ3AACZFbENpDFjjN7vaVQgv3T8uPTFBGIb\nAIDMitgGHCBXLqMB/Y2MkX5cLK1ZS3ADAJAZEduAgzxc3eiVl+3jT0daOneO4AYAILMhtgEH6vSG\n0UNlpYuXpKGfWrIsghsAgMyE2AYcKGtWo4EDjLy8pD82SYsWO3tEAAAgPRHbgIOVKGH0Zid7O8Dx\nE7m6JAAAmQmxDaSDli2kypWkq1el4SNZTgIAQGZBbAPpIEsWo/4fGHl7S5v/lBb+6OwRAQCA9EBs\nA+mk2ANGbwbay0kmTLJ08iSz2wAAZHTENpCOWr4oVal8YzlJQgLBDQBARkZsA+nIw8Oof197Ocmf\nW1hOAgBARkdsA+nsgQdu7E4ycZKlcJaTAACQYRHbgBO0bCFVrSJdvSYNH8FyEgAAMipiG3ACDw+j\nfn3s5SRbtnKxGwAAMipiG3CSB/6xO8mkEEtnzzK7DQBARkNsA070YgupQnkpKkoaPZaL3QAAkNEQ\n24ATZcli9MH7Rp6e0rr10opVzh4RAABIS8Q24GSlShm1bWMfj/3C0sWLzG4DAJBRENuAC2jbxujB\nEtKFC9L4icQ2AAAZBbENuAAvL6MP+hgZI/20TPpjE8ENAEBGQGwDLqJSRaMXm9vHI0dbio4muAEA\ncHfENuBCOgcaFSwonTwlhX5JbAMA4O6IbcCF+Poavd/T3nt77vfS7j0ENwAA7ozYBlxM7VpGzzwl\nWZb06UhL168T3AAAuCtiG3BB73Y1ypNb+uuw9PUsZ48GAADcK2IbcEF58hh172YvJ5kx09LhI8xu\nAwDgjohtwEU1biTVrSPFxdnLSeLjCW4AANwNsQ24KGOMevcw8vWVdu2Wfljo7BEBAIDUIrYBF1ag\ngNHbb9rLSUKmWDp1itltAADcCbENuLgX/i1VrSJdvSaN/MySZRHcAAC4C2IbcHEeHkZ9ext5ZZU2\n/iH98quzRwQAAFLK09kDAO7F4cOHNX36dP3555+6dOmS/P399fjjjyswMFB58uS56fmLFy9WcHDw\nbd/vySefvOnxhIQEhYaGatGiRbp8+bIqVKignj17qmzZsje9Pi4uTu3bt5evr6+mTJkiY0yqvk/t\n2rUlSb///vstHy9e3Kh2zSVasTxYQ4c2Vc2aH8nP7/bfLUuWLMqbN6+qVaumNm3aqFy5cskeb9as\nmU6dOpXs+dmzZ5efn58CAgJUq1YtPfnkk/L29k7V9wAAAMkR23A7mzdvVu/evXXt2jWVKFFClStX\n1l9//aV58+ZpzZo1Cg0NVYECBW752rJly94ylitWrHjTfTNnztSXX36pEiVKqFy5ctq4caO6deum\nefPmKXv27MmeO3fu3KR/AKQ2tFOqdi1pxXIpNlb6fJylzz9L/vgDDzygKlWqSJKuXr2qvXv36tdf\nf9XKlSs1dOhQ1atX76b3bNiwoXx8fCRJUVFRCg8P1/Lly/XLL79owoQJGjBggOrWreuQ7wMAQGZA\nbMOtXLt2TUFBQbp27Zo6duyoTp06SZIsy9L48eP1zTff6JNPPtHnn39+y9fXq1cv6TV3EhcXp6+/\n/lply5bVtGnT5OXlpZ9//lmDBg3SggUL1KZNm6TnRkREKDQ0VM2aNVNAQEDafNFb8Pjvoi9jpP9b\nLq1eE6sqlW88XqVKFQUFBSX7DiNGjNCiRYs0YsQI1alTR1mzZk32nu+++66KFCmS7L6IiAhNnz5d\n8+bNU+/evTV69GjVqVPHYd8LAICMjDXbcCsrV67U+fPnVaJECXXs2DHpfmOM3n77bRUuXFgbN27U\ngQMH7utzwsPDdfnyZT311FPy8vKSJD399NPy9vZWWFhYsudOmDBBnp6eevPNN+/rM1PqwQft//04\nOEpRUbf/saSnp6d69OghX19fnTt3Trt3707R+/v7+6t3797q3LmzEhISFBwcrNjY2DQYOQAAmQ+x\nDbeyf/9+SVK1atXk4ZH8r6+np2fSMoo1a9bc1+dcvnxZkpQzZ86k+zw8PJQ9e/akxyRpx44d+umn\nn/T2228rd+7c9/WZKVW2jFS0iHTqdIImT73zziQ+Pj4qVqyYJOnMmTOp+pz27durUKFCioiI0PLl\ny+95vAAAZGbENtzK1atXJSWP4H9KDN7bzWzv27dP48aN0/DhwzV16lRt2bLlls8rVKiQJOno0aNJ\n9126dEmRkZEqWLCgJPsHlKNGjVK5cuX0/PPP39sXugdZskh9etvrwn9YIB07fufnR0dHS9JNS0ju\n/jlZ1LhxY0m67XkCAAB3xpptuJXEnUb+uZPGP4WHh9/x8fXr12v9+vVJt6dNm6bq1asrODhY/v7+\nSff7+/srICBAS5YsUf369VWqVCl9/vnnSkhI0GOPPSZJmj9/vg4cOKDQ0NCbZtkdrcbDRi8299L3\nP8Ro6U+3n90+fPhw0jkpU6ZMqj8n8cekR44cuadxAgCQ2RHbcCvVq1fXjBkztGHDBkVGRibb5u/M\nmTPatGmTpBuzuYny5cunwMBA1atXT0WLFtW1a9e0Z88ejR8/Xlu3blXv3r0VGhqqLFmyJL2mW7du\n6t69u956662k++rWravHH39cFy9e1JQpU/Tcc88l28kkJiZGWbNmvef4TtwCMCV69fTVqtUxOnuL\n1SFXr17Vrl27NGrUKMXHx+vRRx9NWk6SGonn99KlS6l+LQAAILbhZmrVqqWAgADt379fPXr0UO/e\nvVWyZEkdOnRIw4cPV1xcnCTdtP1e7dq1k4Vs9uzZ9cQTT6hGjRp6/fXXtXfvXi1fvlxPP/100nNq\n1KihGTNm6KefftKVK1dUsWJF/etf/5IkTZw4UZLUtWtXSdKmTZv02Wef6fDhw/L29laTJk3Uo0eP\nVO9T3bRp09s+dvz4ce3YsSPpdu5cHurZ3ahff/v20qVLtXTp0pteV758eQ0aNChV40iUeLVKR21n\nCABARkdsw60YYzR8+HD16tVLe/fuTbYjSd68eRUYGKiQkBDlypUrRe/n6+urVq1aadSoUfr999+T\nxbYklSpVKimoE+3du1c//vijevbsqTx58ujMmTPq3bu3SpcurWHDhunw4cOaNm2asmXLpu7du6fq\n+/1z677/tXjx4mSxLUn16xkFBEh7d0teXkXVuHFVGWP/WDTxojY1a9a855n2yMhISUrx+QQAAMkR\n23A7hQsX1ldffaXVq1dr586diomJUcmSJfXMM89o1apVkqSSJUum+P0Sl1dERETc9bmWZWnkyJEq\nU6aMmjdvLkn6/vvvFRsbq+DgYBUpUkQNGzbU8ePH9f333+utt95StmzZUv8lU+GZp4z27paux1VV\n2YCP9OrLaTcLnbjNYWrOJwAAuIHYhlvy9PRU48aNk3bLSLRz505J0sMPP5zi90pcj5ySKP7xxx+1\nd+9eTZ48OWl995EjR5QnT55kF4epUKGCli5dqmPHjt3yipVpKUeOG8ehX1qqW0d6sMT9B3d8fLxW\nrlwpyV5SAwAAUo+t/5BhREREaMWKFcqdO7caNGiQ4tclzobf7eqPly9f1qRJk9SkSRNVrVo12WMx\nMTHJbl+7dk2S0nWXknz57Eu5f/yJpevX77z/dkrMmDFDp06dUv78+dWwYcM0GCEAAJkPsQ23c+jQ\noZvi9syZM3r//fcVHR2tbt263TRLPWPGjKT1x4ni4uIUGhqq5cuXy9vbW88999wdPzckJESxsbE3\nreEuVaqUoqOjky6kExcXpxUrVsjLy0tFixa916+ZalUqS7lySWFh0pf/uffYjoiI0KhRozRlyhRl\nyZJFAwYMSPUe3QAAwMYyEridb775RqtXr1ZAQIDy5cun8+fPa8eOHYqNjdUbb7yhZ5999qbXTJo0\nSdOmTVO5cuVUsGBBRUVF6cCBAzp79qy8vb01aNAgFShQ4LafeeDAAf3www969913k+3HLUktW7bU\nd999pwEDBqhWrVo6fvy4Dh8+rHbt2jl8vfY/eXtLfXsbfRhk6etZUu1alqpWufNyknHjxsnHx0eS\nFBUVpZMnT+rQoUOKj4+Xv7+/PvroI9WqVSs9hg8AQIZEbMPt1K9fX+fPn9eBAwe0Y8cO5cyZU7Vr\n11br1q1vu7a4Y8eO2rlzp44ePZp0yff8+fOrefPmevnll1WiRIk7fubo0aP14IMPqmXLljc95u/v\nr7Fjx2rcuHH6/ffflSNHDrVp00adO3e+/y+bSvXrGTX9l6WlP0tDPrE0PVTKmfP2wZ24JjvxUvR5\n8+ZVo0aNVKdOHTVu3DjVWxcCAIDkjJW4kW4au3DhgiPeNkX8/Pyc+vmZEec8/d3unEdFWXo90NLJ\nk1L9elLwYMM+2WmIv+vpj3Oe/jjnzsF5T39+fn4O/wzWbAMZTPbsRh8PNPL0lFavkebNd/aIAADI\nvIhtIAMqX87onS72bPaESZb27nPIf8ACAAB3QWwDGdSLzaUG9aS4OClokKVLlwhuAADSG7ENZFDG\nGH3Qx6hIEenkKWnQEEvx8QQ3AADpidgGMrAcOYw++dgoWzbpj01SSCixDQBAeiK2gQyubBmjfn3t\n9duzvpX+bznBDQBAeiG2gUygcUOj1161j4eNsLQ/jOAGACA9ENtAJtGpo1HtWlJMjNSnn6XTZwhu\nAAAcjdgGMoksWYwGfWRU8kEpIsIO7uhoghsAAEcitoFMJEcOo5HDjfL6SYcOSUGDLcXFEdwAADgK\nsQ1kMoUKGX06zMjbW/p9ozRitKWEBIIbAABHILaBTKh8OaOBA4w8PKSlP0ljv7BkWQQ3AABpjdgG\nMql6Txj1/8DIGGn+AmnSFIIbAIC0RmwDmdi/njbq1ePGHtzTphPcAACkJWIbyOSaPW/Urasd3P/5\nihluAADSErENQK1eMur2zo0Z7s/HE9wAAKQFYhuAJKlVS6PePe3gnve9NHwk2wICAHC/iG0ASZo9\nb/ThB/YuJUuWcuEbAADuF7ENIJkm/zIaGmyULZv0xyapazdL584R3AAA3AtiG8BNHq9rNG6skZ+f\ndOCgFPiWpV27CW4AAFKL2AZwS+XLGYVMNHqwhHTunPRud0sLfyS4AQBIDWIbwG0VKWw0ZZJR/XrS\n9evSyNGWPh2ZoJgYohsAgJQgtgHcka+vUfBgozc72T+c/HGJ9E53S6fPENwAANwNsQ3growxatvG\naNSnRrlySXv3Sh07W9qyleAGAOBOiG0AKVbzUaPQEKOyZaTISKl7L0vTpiewHzcAALdBbANIlSKF\njSaNN2ryjJSQIE2fIb3znqUT4QQ3AAD/i9gGkGrZshl92M9DAz8yypFd2rVb6hBo6adlXOYdAIB/\nIrYB3LOnGhv9Z5pR1SpSdLT0yTBLgz62dOkywQ0AgERsA7hPhQoZfTHGqFNHoywe0vKV0usdLW3+\nk+AGAIDYBnDfsmQxat/WaNIEo6JFpDNn7B9PjvosQdHRRDcAIPMitgGkmQrljaaHGjVvZt9esEhq\n14FZbgBA5kVsA0hTvr5Gvbp76PPPjAoXkk6dtme5R45mlhsAkPkQ2wAcosbDRjO+vDHLvfBHqW0H\nS5s2E9wAgMyD2AbgMImz3F+MMSpcWDp9WurR257ljooiugEAGR+xDcDhHq5uNGOaUYt/zHK3e4NZ\nbgBAxkdsA0gXvr5GPW8xyz2CWW4AQAZGbANIV4mz3C82t28vYpYbAJCBEdsA0p2vr1GP9+xZ7iJF\nbsxyfzqKWW4AQMZCbANwmv+d5f5xsb1jyR+bCG4AQMZAbANwKh8fe5Z73Fh7lvvMGann+5Y+Hcks\nNwDA/RHbAFxC9Wr2LHfLFvbtH5fYs9wb/yC4AQDui9gG4DJ8fIy6d0s+y92rj6XgYQmKjCS6AQDu\nh9gG4HKSZrlflIyRfl4mtWln6edfLFkW0Q0AcB/ENgCX5ONj1P1dD02eYFS6lHTxkhQ81FKP3pZO\nnCC4AQDugdgG4NIqVjCaNsXozU5GXl7S5j/ttdxfz7IUF0d0AwBcG7ENwOV5ehq1bWM0c7rRIzWk\n2Fhp8hRLr3e0tPlPghsA4LqIbQBuo2hRozGjjD7sZ5Qnj3Tkb6l7L0sDBibo1GmiGwDgeohtAG7F\nGKMmzxjNmmlvE+jhIa1abf+AcsZMSzExRDcAwHUQ2wDcUq6c9jaBX041qlZViomRpk6z1K6DpdVr\n2LUEAOAaiG0Abq1MaaNxY40GfmSUL590Ilz6MMhS4JuWfttIdAMAnIvYBuD2jDF6qrHRrK+M2r0m\n+WST9odJ7/e11OVdS1u2EtwAAOcgtgFkGL6+Rp0DPTRnttHLrSQvL2nnLqlbD0vdeiRo+w6iGwCQ\nvohtABmOXx6jd7p4aM4soxebS56e0patUtdulrq8m6D1GywlJBDeAADHI7YBZFj58hn1eM9Ds782\n+vdzUtas0o6dUt/+9g8pv5trKTKS6AYAOA6xDSDDK1TIqG9vD8391ujVlyVfX3uP7nETLDVrae/T\nvfEPS/HxhDcAIG15OnsAAJBe8uUz6vKWUbvXLP3fcunHJZb2h9n7dK9abalAAenZJpaeamxUvLhx\n9nABABkAsQ0g08mRw6jZC1KzF4wOHLS0ZKmlZb9KZ85I02dI02dYKlPaUqOGRnXrSKVL2TueAACQ\nWsZy0Ca0Fy5ccMTbpoifn59TPz8z4pynP8552oqJsbRmnfTzMkub/5Ti42885p9XevRRqeajRk82\nyiMPj4vOG2gmxN/19Mc5dw7Oe/rz8/Nz+GcQ20gTnPP0xzl3nIsXLa1dJ61ea2nrNunateSPP/SQ\nVL2aVLGCUcUKUsECzHo7En/X0x/n3Dk47+kvPWKbZSQA8D9y5zZ67lnpuWeNYmMt7dwlbdxk6Y8/\npIOHpLAw+49kz1Xkz2epYgWpQgWjCuWlh8rae34DAEBsA8AdeHkZ1XhYqvGwUZc3pbj43FqxIlI7\nd1vavVs6dEg6e05atUZatcaOb2OkBx6w9FBZKeAho4CHpLJlpVw5CXAAyGyIbQBIhfz5PPT0U0ZP\nP2WH89Wr9o4mu3ZLu3fbx2fOSseO2X+Wr7ixUq9IkRsB/lBZezmKXx4CHAAyMmIbAO6Dj49RtapS\ntaqSZIfzhQt2dIcdkMLCLO0/IJ08KYWH239Wrb4R4AUKWAooKz303xnwihXsZSwAgIyB2AaANObn\nZ1S7llS7lpQY4JcuWTpwUNofJu0PsxR2wJ75PnPG/rN2/Y0AL13a0sPVpOrVjKpVY/kJALgzYhsA\n0kGuXIlrv6XEAI+KsnTw0I0A37/fvrLloUP2n7nfWzJGKlPa0iM1pDq1jSpXkrJmJb4BwF0Q2wDg\nJNmzG1WtIlWtIv1zCcqWbdLWbZa2bpX+PiodOGj/+fY7S76+Us1HLTWoZ19wh11PAMC1EdsA4EL8\n/IwaN5QaN7Qj+lyEvdf3H39Y+v0P6cKFG5eX9/KSatey1LSJUe2akqcn4Q0ArobYBgAXls/f6KnG\n0lONjRISLO3bL61dZ2nlKun4CWnNWmnNWkv+/lKTZyw929So2ANENwC4CmIbANyEh4d90ZwK5Y06\nB9rrvZf9YunnZVJEhPT1LOnrWZaqVbWju1EDydub8AYAZyK2AcANGWNUtoxUtozRm50srd8gLV5q\n6Y9N0rbt0rbtliZMlF543lLzZkb5/IluAHAGYhsA3FzWrEYN6ksN6hudOWNp6c/Sj0ssnT4tzZgp\nffOtpWeettSujVHRokQ3AKQnD2cPAACQdgoUMHq9ndF33xgNGWRUpbIUFyctWSq92tbSJ8MSdOy4\ndfc3AgCkCWIbADIgT0+jhg2MJo7z0OQJRrVqSvEJ0k/LpDbtLA35JEFHjxLdAOBoxDYAZHCVKhqN\nHuGhKZOM6taWEhKkZb9Kbdrb0X3qFNENAI5CbANAJlGhvNGI4R4KDTF6/DHJsuzofrWtpYmTE3T5\nMtENAGntnn4gee3aNYWEhGjp0qUKDw9X7ty59cQTT6h79+4qWLBgqt7r0qVLCg0N1Zo1axQRESF/\nf3/Vr19fgYGBypkz5y1fEx8frzlz5mjx4sU6fvy4fHx8VKNGDQUGBqpkyZK3/ay1a9dq1qxZ2r9/\nvyQpICBAr732mh577LGbnnvy5EmtXbtWGzZsUFhYmC5evKgcOXKofPnyatGiherVq5ei73f06FG1\nbdtWMTExeuSRRzR+/PgUvQ4AbufatWv66quv9Ouvv+r06dPKlSuXateurc6dO6tAgQJ3fX25AKPg\nwfEaOWq6Vq3ao4sX/9ZX/4nUV/+JU548BdSgQU21b99WhQsXvu17REdHa9asWVq5cqXCw8Pl4eGh\nggULqnr16uratat8fX3T8isDgNsylmWlaiojJiZG7dq107Zt25Q/f3498sgjOnHihHbs2KG8efNq\nzpw5KlasmC5cuHDX94qMjFRgYKCOHz+uokWLqly5cjp8+LD++usvFS9eXFOnTlXu3LmTvSYhIUH9\n+vXT6tWrlTNnTj3yyCOKjIzUtm3b5O3trQkTJujxxx+/6fNnz56tsWPHKkuWLHr00Ufl5eWljRs3\nKiYmRr169dJLL72U7PmdO3fWjh075OXlpYoVK8rf31/h4eHas2ePJOnll19W9+7d7/odu3Tpoq1b\nt8qyrAwd235+fin6/xxph3PuHM4+7zExMeratat27dqlfPnyqWrVqjp58qT27NkjPz8/hYaGqmjR\nond9n+joaDVq1Ei+vr4qUKC0zkbkU3TUdVkJBySdlrd3dk2aNE4VKlS46bXh4eF65513FB4erqJF\niyogIECxsbE6evSojh49qkWLFqUo+lPK2ec8M+KcOwfnPf35+fk5/DNSPbM9ceJEbdu2TdWrV9e0\nadOUPXt2SdL06dM1fPhw9e/fXzNnzkzRe40ZM0bHjx9XgwYNFBwcLE9PezijR4/W3Llz9fnnnyso\nKCjZa3788UetXr1axYoV0+TJk+Xv7y9JWrFihfr376+BAwdq2bJlyV7z999/a9y4cfLy8tKECRNU\nuXJlSfasc6dOnTR27FjVrl1bxYoVS3pNgQIF1KtXLzVt2jTpO0rS+vXr1adPH82ePVt16tRRrVq1\nbvv9Fi1apC1btqhZs2ZasGBBis4JANzJ9OnTtWvXLlWuXFmff/550gzyrFmz9MUXXyg4OFiTJk26\n6/t4eXkpJCREFStWlKenp+Li7C0DQ6fF6eyZKYqJmal33h2h0KnTVarUje0CY2Nj1aNHD50+fVp9\n+/ZV8+bNk73voUOHlCtXrrT90gDgxlK1Zjs2NlbffPON9P/t3Xt4VNW9//H3zj0hIZkESMiFJIDD\nVUBBBIVHgQoexFI9UMGqBTxo8WgRqrX1drCtrdXnaBXQ4yXqT4stRYoUC0JR5CqikoZLAsgtISTh\nlvudSfbvj50JCUmAhJlchs/refYzk71nr732l/1svrNm7bWAZ599tl4SOnPmTPr06cOOHTvYs2fP\nRcs6ffo0//rXv/D19eXxxx+vTbQBHnnkEWw2G2vXriU3N7fefn/5y18AePjhh2sTbYCxY8cyevRo\nMjMz+fzzz+vts3TpUqqqqrjjjjtqE22AHj16MGPGDKqqqli6dGm9fX73u98xderUeucIcOONN3L7\n7bcDsG7duibP78yZMyxatIjhw4dzyy23XDQeIiIXc/bsWT7++GMAHnvssXpdNe6++2569+5NcnIy\n+/btu2hZPj4+DB48uPbe6+Nj8MNJBn9d4sOsWbMBP0pL9jHj/iJeXXiuP/fSpUtJT09n2rRpDRJt\ngF69ehEQEOCCsxUR8QzNSrZ37txJUVERPXr0aPSnxQkTJgCwYcOGi5a1fft2qqurGTx4cL2kGawW\nl1GjRlFVVcW2bdtq12dlZXH06FH8/f0b7Wc9duzYRo/vLGPMmDFN7rNly5aL1tmpd+/egPWFoSmv\nvPIKFRUVPP7445dcrojIhezatYvi4mJiY2Pp06dPg+3O+9nmzZtbfIygIINZM7wJCPAGDKqqfVm2\nHO6+z2T1GpOVK1cC8OMf/7jFxxARuZI0qxuJs7WksUQbYMCAAQC1DyBeyPfffw/Q6H8YzvWrVq3i\n4MGDDfbp1atXvZbwuvucf/yioiJycnKaPFZkZCRhYWHk5ORQUlLSoCW7MVlZWQANviQ4bdu2jfXr\n1/PAAw8QFxfHyZMnL1qmiMjFXMp9E6h332wu0zT58MMPKS8vY9iwYdz30wD+9JpJxjF4/oUcqioy\nCQ/vRmRkJCkpKWzevJmSkhK6d+/OmDFj6nXHExGRZibb2dnZAERFRTW63bnemYxeiDMBbuohGud6\n5+fqvu/atesF96l7fOc+nTt3JjAwsMn98vPzyc7Orm21bkpRURFr1qwBYPTo0Q22l5WV8eKLLxIf\nH8+99957wbJERJrjUu+Bde+bl2LRokXk5uZSUlLCoUOHyMzMJCEhgSeffJLoaIP/9y4sWw5vv3OE\nsgrIy+vC3T95kcOH/l6vnDfffJOHHnqIn/zkJy04OxERz9SsZLu0tBSgyf54zmS2pKTkomWVlZVd\nsCzneucxm7NP3eM79/H392+yLo0dqyl//OMfycvLY+DAgdx8880Ntr/55pvk5OSwePFifH19L1qe\niMilasl981J8+eWXnZqjmQAAHhBJREFUZGZm1v7du3dvFixYQHR0NAC+vgZ3TwN/32JeeglMcz+H\nD+0jIOh+Zs74If9xqzdr167h//7v/1i4cCEJCQmNdvUTEbkSaVKbZvjggw9Yv349nTt35rnnnsMw\njHrb09LS+Nvf/sbEiRMZOnRoG9VSRKR5Pv74Y7Zv385nn33Gn/70J3x8fJgxYwb//Oc/630uONg5\nUmwVYbbJOKrv5+13u/LEk+EMHnIP06ZNA+D9999v3RMQEWnHmpVsO598Ly8vb3S7s9XlUvo9O1vB\nmyrLub7u0/aXuk/d4zv3qaioaLIujR3rfGvWrOGNN94gMDCQl19+ucE4tg6Hgz/84Q8EBwfzyCOP\nNFmOiEhLteS+2RxhYWGMGDGCRYsWERERwYsvvsiJEycaHB/gpRcnMW+uQXAwfH8QHnrE5FjWbQCk\npqZe8J4rInIlaVY3EudsYk31B3Sud/70eCHO/t1NPTzoXF+3f7jz/alTpy64T93jO/cpLCykrKys\n0X7bzv2ami1ty5YtteOAv/DCCwwcOLDRMg4cOEBERARPPvlkvW3FxcWA9eDmnDlzAC5pHFwRkbou\n9R7Y1HM1lyo4OJhRo0axfPlyduzYUTvcad17ZGxsNFdfbTB2DLz1jsmn/4St26ztVVVV5OUVEBXl\nuoltREQ6qmYl23379gWonUXxfHv37gWaflK+rquuugpoeuQS5/q6Dyw69zl06BAOh6PBiCR1p2F3\nCgkJISoqipycHPbv38+QIUPq7XPixAny8/OJiopqtEV+586dPPXUUwA899xzF5zEBqzxtc+cOdPo\ntqKiIpKTky+4v4hIU1py32ypsLAwgHqz2cXHx+Pv709FRQVFRUXYbDZsYQZPPGbww0kmf3ypkH3W\nfwPMfyyQeY+aXDfMaKx4EZErRrO6kVx77bWEhISQkZFBWlpag+3OmRsbG8/6fCNGjMDLy4uUlJQG\nE9dUVlayZcsWvL29ueGGG2rXR0dHk5CQQEVFBVu3bm1Q5hdffNHo8Z1lNDb+t3OfUaNGNdi2b98+\nHn/8cSorK/n1r39dO4ZtY6Kjo9m+fXujy+LFiwEYNmxY7ToRkeYaNGgQwcHBZGZmcuDAgQbbnfez\nxkZKaq6dO3cCEBsbW7vOz8+vtsHBud2pX1+DaVOtxgQv72gyMjsx7zGTp5+tJifHRETkStWsZNvP\nz692SKfnnnuu3hPv7733Hvv372f48OH1ulksW7aMu+66i9dff71eWV26dOGWW27h7NmzvPTSSzgc\njtptixYtIi8vjwkTJhAeHl5vv+nTp9d+pm6SvmHDBjZv3kxsbCzjxo2rt89dd92Ft7c3K1asqDe7\nZUZGBu+//z7e3t7cdddd9fZJT09n3rx5lJSUMG/ePCZNmtScUImIuJyvry9TpkwB4KWXXqp9Tgas\n6doPHjzINddcU/srJDR9D966dSu7du1qcIzy8nLeeOMNkpOTiYiIYMSIEfW233PPPQC8++67ZGRk\n1K7Pysri7bffBuD+WXcw5T/Bywu+3ATT7zV5+U/VnDyppFtErjzN6kYC8NBDD/HVV1+RnJzM+PHj\nGTZsGFlZWaSkpBAeHs7vf//7ep/Pz88nPT290dkW582bx969e9mwYQPTpk2jb9++HDlyhEOHDhEX\nF8fcuXMb7HP77bezbds2Nm7cyLRp0xg2bBj5+fkkJyfj7+/PggULGnQviY+P5+GHH+bVV1/lwQcf\nZPjw4fj6+vL1119TUVHB/PnzG0zE8Mwzz5CXl4fNZmPfvn385je/aVCXhIQE7rvvvuaGUESkxWbO\nnMk333zD7t27mTp1KoMHDyYnJ4e9e/dis9l4+umn632+qXtwamoqSUlJdO3aFbvdTqdOncjNzeXA\ngQMUFhYSHBzM888/3+Bhy0GDBnH//feTlJTEfffdx6BBg/Dy8mLXrl2UlpYycuRIZsy4G29vLyZN\nNHltkcnOZPj7J7Dqnya332Zyz90G3bqpe4mIXBmanWz7+/vzwQcf8Oabb/Lpp5+yfv16wsLCuPPO\nO5k7d26zHswJCwsjKSmJd955h02bNrFx40bCw8P58Y9/zOzZswkJCWmwj5eXF7///e9ZunQpn376\nKVu3biUgIIAxY8Ywe/ZsEhMTGz3W9OnTiY2NZcmSJaSkpADQr18/7rnnnka7kBQWFgJWf8XVq1c3\nWuY111yjZFtEWpW/vz+LFy/mgw8+YN26dWzatInOnTtz22238eCDDzY5Udj5br75ZkpLS0lJSSE1\nNZXCwkL8/f2JjY3ljjvuYOrUqXTp0qXRfWfPnk3v3r1ZunQpe/bsoaqqivj4eCZOnMiUKVPw9vYG\noHcvg9deMdiZbPLu+yb/TjmXdP9wkpV0d+2qpFtEPJthmqZbfter+1BNa7PZbG16/CuRYt76FPO2\nobi3jGmaJP8bkt4zSanpveLjA+PGwtQ7Dfr2bTrpVsxbn2LeNhT31mez2dx+jGa3bIuIiDSXYRhc\new1cM4R6SffadbB2ncnAASaTbjMYezMEBam1W0Q8h5JtERFpNc6k+9prDFLTTJb/3eTzDbBnL+zZ\na/Lqa3DzTSZjxxgMvRb8/JR4i0jHpmRbRETaRP9+Bv2fMpjzM5M1n8E/15hkZsKatbBmrUlgIIwc\nYTLmpnL69TWJilLiLSIdj5JtERFpU10iDO79Cdxzt9XCvW69yeYtcPo0fLEBvthQAkB0tMnVA6F/\nX4N+/aBXT/D3VwIuIu2bkm0REWkXDMPg6oFw9UCDeT832X8Atmw1Sdntw+5dDrKyICvL6uNtfR4i\nu5nExUFcLPToYRAXCzHR0LWrEnERaR+UbIuISLvj5WXQr681M6XNFsrx47ns2g2paZC2zyQtDfIL\nIOeEtXzzLUD9wbVCQky6RFiJd5cI6NIFunQxzr2PgPBw8PFRUi4i7qNkW0RE2r2gIIMR18OI6wEM\nTNMkvwCOHYOMY3DsmGm9ZkJ2NlRUQFGRtRw5Wrek+gm5YYAtzCQyEqKioHsUREYadI+y/o6JVgu5\niFweJdsiItLhGIaBLQxsYTDoaoBzCbFpmhQXw+kzVr/v06fh1Gk4ddrkjHPdGThzBqqqIDfPWtL2\n1ZZQ5zgQE22SmACJiZCYaNAzEXrEga+vknARuTgl2yIi4lEMwyAkBEJCIDGh3pZ6n6uuNikogJOn\n4MQJyMmBnBMm2TnW++xsKC6BzOPWsnkrOBNxHx+4qrdJ/341o6r0h9gY69giInUp2RYRkSuSl5eB\nzQY2G/SxO9fWbyHPy4PDR6yuKEeOmhw5AkeOWEl42j5rWb7CSsA7d4Z+fWsS8P4G/ftCaKiSb5Er\nnZJtERGRRhiGQXi49RDlsKHgTMRN0yQr23pYMzXVJDUNvv8eCgvh6x3W4mwBj401GVCTfA/oB717\n64FMkSuNkm0REZFmMAyDmGjr4clbxlmJ89mzJgcPQWoqpKaZ7E2DzMxzy9p/Wcm3nx/0sZv07w8D\n+hv07weR3dT9RMSTKdkWERG5TL6+zqEK4T9rWsALC61W7701rd+padboKLv3WIuz9TsiAvr3MxnQ\n3yqjZ0+whSn5FvEUSrZFRETcoHNn53CF57qfHMuEvc7W71Q4dMgaFWXzFti85dwoKOE2k549rVky\ne/a0RkCJi4XgYCXhIh2Nkm0REZFWYBgGPeKsYQP/Y4KVNJeXWzNlOlvAv/8esrJrhiP8Dr79DuoO\nRRgWZhIbA7GxEBtjEBsD3btb44PbbOqOItIeeWSyferUKfLz89u6GlcUh8OhmLcyxbxteGLcu3Tp\n0tZVuGIFBBgMHgSDB4HzAcyyMpMjR+HwYTh42OTwYTh61ErA8/OtZc9eOH+CHj8/iIo0iaqZkCcq\n0qh5tZLxiAhrBBYRaV0emWx369atrasgItJh5ObmtnUVpI7AQKNm/G6oOxRhaalZO+Z3ZiZkHjc5\nfhyyc6yJeiorrdk0M44596ifjPv4QGS3c8l49yiDyJpEPCrSmsJeI6WIuJ5HJtsiIiKeJijIwH4V\n2K9yrjmXGDscJidP1UzMkwPZOWbNJD3W3ydPgsMBx7OsxVI/Gff2gq5drWQ8Pr6YqEiThHhISIDo\n7uDtrURcWs40TXJzrdlbc/MgLxeKiqGsDErLTLpHGfzoh57ZFUrJtoiISAfn42MQ3d1Kii31ExaH\nw+T0GWumTOcMmTk51myZJ05YSbnDUZOcn4B/p1TU29/PF+LinMm3UZuEx8Zo2nqpr7zc5Gj6uYmg\njh6FrCzruquouNCeJjeONPDEzglKtkVERDycj49BVKTVXcTqHw51E/LqaqvVMTvHWvLzA9i3r4yj\n6ZCeYSVJhw5bS90WcW9v6BFnkpgIPRMNEhMgMdEag1wt4Z6tvNzk2DErqT58xKxJriE7G0yz8X28\nvKwHecNrZm7t3BmCgiAwEHolGnTt2oon0IoM02wqJJcnLy/PHcVeEk98gKm9CwsLU8xbmWLeNjwx\n7u39AUmbzdam/6dcierGvLraJOeE9ZDm0XQ4etTkSDqkp0NpaeP7+/lCfDw1ybc1dGFiopXse/JD\nmlVVJgUFcCYXcnOhoBBKS6CkFIpLzNr35WVQVQXVJlRX17yvBh8fXwzjLP5+4O8P/gHUvu/UySAk\nBEJCoHMIhARb70M6Q3An98S1stL6EpaVDRkZkJ5hkp4Bx45Zv4A0lUGGhVq/fCQmQmKCQVys9atL\nt27t75cQm83m9mN4ZMt2165d8fHxyFNrt2w2m2LeyhTztqG4y5XGy+tcF5UbRkLdaetPnKzpLnAE\njhwxOXzESsgrKuD7g9ZStyU8IABiok2io7GW7gbRNbNxdutqjc7S3pimSWkp5OWdS6Jzc+F0rln7\n/swZa1t+HlRVX87Rzl6oJk1uMQzo1MmsTcZDgq1WY+f74GADb2/rc15edV6BikooL7dGwcnPt/pU\nnzljvRYWXri2ISHWF6qeNUm1lVyDzdb+/h3bkv7HEBERkWYzjHNdU0ZeD84kvLraJDvb2b3A6rd7\n+IjVMlpeXrc7CpyfQAYFmYSHQ0S4NVRheDiEhRoEB2MtnazXTp2sxdfHGmXl/MU8r8XYNK33FZVW\na3xZ2bmltMya2TM/H/ILzNrhFa2/oaAAzl4oB24QFwgLs+oe2tmqZ3BNfYOCrBbqgACrC463F3h5\nW4mvtxd0Cu5Efn4JFRVWrCoroaLCpLwcSkqsehYVW0mw8315uXV+xcXWkp3dWK1a3onB19f6IhTf\nA3r0gPgeBj1q3oeFeuYDja6mZFtERERcxsvLICYGYmJg1I3gTMIdDpOsbGs0lKwsyMo2rdeapazc\nSoRLS62hDc9xS2/XZgsI4NwXgfCa9xFGnffW+rCwlg+haLP5k5d3ft+cC5dVWWnWJt5FReeWwtr3\nJiUlVou7WW1F0/kFpLra6qYSGGidX2ioQZcIaxjIiHDrNSRECfXlUrItIiIibufjc24GTcu5BM7Z\nVcPZTeOMs2vGGZPConOttsUl1mtJsdX32eGwWqwvlZcXBAVayaVzsVqbrVbasDAICzOs19C669pn\nFxcAPz/DSvQjmvpE+6z3lUTJtoiIiLQpwzBqu4acS8bhUhJF0zRxOKzE+6wDqhw1fZJrumkYhtVl\nw8vL6mKiVlppbUq2RUREpMMyDANfX6tvcWBbV0akEV5tXQEREREREU+lZFtERERExE2UbIuIiIiI\nuImSbRERERERN1GyLSIiIiLiJkq2RURERETcRMm2iIiIiIibKNkWEREREXETJdsiIiIiIm6iZFtE\nRERExE2UbIuIiIiIuImSbRERERERN1GyLSIiIiLiJkq2RURERETcRMm2iIiIiIibKNkWEREREXET\nJdsiIiIiIm6iZFtERERExE0M0zTNtq6EKxUVFfHdd98xdOhQQkJC2ro6VwTFvPUp5m1DcW99innr\nU8zbhuLe+lor5h7Xsl1cXMzGjRspLi5u66pcMRTz1qeYtw3FvfUp5q1PMW8binvra62Ye1yyLSIi\nIiLSXijZFhERERFxE+8FCxYsaOtKuJqfnx8JCQn4+/u3dVWuGIp561PM24bi3voU89anmLcNxb31\ntUbMPe4BSRERERGR9kLdSERERERE3ETJtoiIiIiImyjZFhERERFxEyXbIiIiIiJuomRbRERERMRN\nfNq6Apdi165dLFy4kOTkZBwOB3a7nRkzZjBx4sRLLqOyspK33nqLf/zjH2RnZxMaGsqYMWN49NFH\niYiIcGPtO6bLjXlGRgYrV65k79697N27l5MnTxITE8MXX3zh5pp3XJcTc9M02bRpE1988QU7d+4k\nKysLh8NBfHw8EydOZObMmRpKqgmXe61v3LiRTz75hLS0NE6fPs3Zs2fp3r071157LbNnzyYxMdHN\nZ9DxuOKeXldBQQGTJk3i5MmTjBo1iqSkJBfXuOO73Jj//e9/59e//nWT2z/44AOuv/56V1XXI7jq\nOj9z5gxvvvkmX375JdnZ2QQFBZGQkMDkyZO5++673VT7juty4z527FiOHz9+wc8sWbKEYcOGXXKd\n2n2yvX37dv7rv/4LPz8/brvtNjp16sS6deuYN28eOTk5zJo166JlVFdXM2fOHLZs2cKQIUMYP348\n6enpLFu2jK+++oq//e1vhIeHt8LZdAyuiPm3337LokWL8Pb2plevXpw+fboVat5xXW7MKysreeCB\nB/Dz82P48OGMGjWKyspKtmzZwiuvvML69ev58MMPCQwMbKUz6hhcca1v2rSJlJQUBg0aRLdu3fDx\n8eHw4cN88sknrFq1irfeeouRI0e2wtl0DK6I+fl+85vfaIrrC3BlzMeNG0e/fv0arI+JiXFllTs8\nV8U8LS2NWbNmUVhYyE033cSECRMoLS3l0KFDbNiwQcn2eVwR9/vuu4+ioqIG6/Py8liyZAmhoaFc\nffXVzauY2Y6dPXvW/MEPfmAOHDjQTE1NrV1fWFhojh8/3hwwYICZmZl50XI+/vhj0263m/Pnzzer\nq6tr13/00Uem3W43n3nmGbfUvyNyVcwzMjLM5ORks6yszDRN0xw4cKA5ZswYt9W7I3NFzCsrK83X\nX3/dzM/Pb7D+wQcfNO12u/n222+7pf4dlauu9fLy8kbXb9u2zbTb7eadd97psjp3dK6KeV2fffaZ\nabfbzT//+c+m3W43Z82a5epqd2iuivny5ctNu91uLl++3J3V9QiuinlRUZF58803myNGjDDT0tIa\nPY6c4477S11JSUmm3W43f/vb3zZ733bdZ3v79u1kZGQwadKket+kQ0JC+NnPfsbZs2dZsWLFRctZ\ntmwZAPPnz8cwjNr106ZNIy4ujlWrVlFeXu76E+iAXBXzuLg4hgwZQkBAgDur6xFcEXNfX1/mzJlD\naGhog/UPPvggAN98843rK9+Buepab6p7zsiRIwkNDSUjI8Nlde7oXBVzp9zcXBYsWMDkyZO56aab\n3FHlDs/VMZeLc1XMP/roI7KysvjFL35B3759G2z38Wn3nRNalbuv9Y8//hiAKVOmNHvfdv0vtWPH\nDgBGjRrVYJtz3cUSiIqKClJSUkhMTGzwM5dhGNxwww0sXbqUPXv2NKv/jadyRcyledwdc+cN2dvb\nu8VleCJ3xz05OZmCggKGDh3a4jI8jatj/j//8z94e3vz1FNPNfqzr7g+5qmpqeTn5+NwOIiNjWXk\nyJHYbDbXVNZDuCrmq1evxjAMJkyYwOHDh9m6dSvl5eX07NmT0aNH4+fn59qKd3DuvKfv3LmTQ4cO\nMXDgwEa/+FxMu062jx49CkB8fHyDbV27diUoKIj09PQLlpGRkUF1dTUJCQmNbneuP3r0qJJtXBNz\naR53x3z58uUA3HjjjS0uwxO5Ou5btmwhOTmZyspK0tPT2bBhAzab7YIPlV1pXBnzlStXsm7dOhYv\nXkxoaKiS7Sa4+jr/8MMP6/0dEBDAf//3f/PAAw9cVj09iStiXllZyYEDBwgPD+fDDz9k4cKFVFdX\n126Pi4tj8eLF9OnTx6V178jc+X+ps1V76tSpLdq/XSfbzgdeQkJCGt0eHBx80Rusc3twcHCTZdQ9\n1pXOFTGX5nFnzDdu3MjSpUvp1atXi28SnsrVcd+6dSvvvvtu7d/x8fG8/PLLDBw48PIq6kFcFfMT\nJ07w/PPPM2nSJH7wgx+4tI6exlUxj42N5ZlnnmHUqFFERUVRUFDAV199xcsvv8z//u//EhgYyL33\n3uvSundUroh5QUEBVVVV5Ofn8/rrr/P4448zefJkHA4Hf/3rX3njjTeYM2cOa9as0UhTNdz1f2lJ\nSQlr1qwhMDCQSZMmtahu7brPtoi03K5du5g3bx4hISG8+uqr+snRzZ544gn279/Pzp07WbZsGYmJ\niUyfPp1Vq1a1ddU8ztNPP42Pjw9PPfVUW1flijF8+HDuueceEhISCAgIIDIykh/96EckJSXh7+/P\nokWLcDgcbV1Nj+Fsxa6qqmL69OnMmjWLiIgIIiMjmTt3LrfeeivHjx/ns88+a+Oaer7Vq1dTWlrK\nrbfe2mTD7cW062TbeVJNfRMpLi5u8huMk3N7Uy3XzvUtDaCncUXMpXncEfPdu3dz//334+XlxTvv\nvMNVV1112fX0NO661jt16sSgQYNYvHgxPXv25NlnnyU3N/ey6uopXBHzFStWsGnTJp599lkN2XoJ\n3H1Pv+qqqxg6dCj5+fkcOnSoxeV4ElfmLmCN+3w+57o9e/a0tJoex13XurMrZksejHRq18m2sz91\nY31sTp06RWlpaaN9c+qKi4vDy8urti/P+Zzrm+rTfaVxRcyleVwd8927dzNr1iyqq6tJSkpi0KBB\nrqqqR3H3te7j48P1119PaWkpu3fvbnE5nsQVMU9NTQVg7ty59OnTp3YZN24cYPWd79OnD5MnT3Zt\n5Tuo1rinOx+QLCsru6xyPIUrYh4UFERkZCQAnTt3brDdua6iouIya+s53HGtHzx4kOTkZHr27HlZ\nz/W162T7uuuuA6yb5/mc65yfaUpAQACDBg3iyJEjDWYEMk2Tbdu2ERQUpH6VNVwRc2keV8bcmWhX\nVVXxzjvvMHjwYNdV1MO0xrV+8uRJwBqCUVwT82uuuYYpU6Y0WJyzw0VFRTFlyhRuueUWF9e+Y3L3\ndV5VVVXbuhodHd3icjyJq2I+YsQIwEr4zudcp8mEznHHtX45w/3V0+LRvVvB2bNnzXHjxl1wgPJj\nx47Vrj9x4oR58OBBs7CwsF45mtTm0rkq5ufTpDZNc1XMd+/ebQ4bNswcMmSI+e2337Za/TsqV8V9\n165djZa/adMmc8CAAeawYcPMkpIS95xEB+Ou+4tpmuaxY8c0qU0jXHl/OZ/D4TBfeOEF0263m/fe\ne6/7TqKDcVXMv/vuO9Nut5u33XabWVBQULv+5MmT5ujRo82+ffuahw8fdv8JdRCuvr9UVlaaI0aM\nMAcMGGCePn36supmmKZpXl667l5NTb15/PhxnnjiiXpTb/7qV79ixYoV/OEPf+DOO++sXV9dXc3s\n2bNrp2u/7rrryMjIYN26dcTExLBs2TL1/avDFTHPzc3lxRdfrP175cqVBAQEMGHChNp1v/zlLxX3\nGpcb8/z8fMaPH09BQQGjR49utEU7JCSEGTNmtNYpdQiuuNb79OmD3W7HbrcTFRVFWVkZ+/fv59tv\nv8XX15dXXnlFrax1uCLmjcnMzGTcuHGMGjWKpKQkd59Gh+Kq69y5REZGUlBQwI4dOzh69ChRUVH8\n+c9/Ji4uri1Or11y1XX+wgsv8N5779G9e3fGjBmDw+Hg888/58yZM8yfP7920jKxuPL+snbtWn7+\n858zfvx4Fi5ceFn1atdD/4H1M8pHH33Ea6+9xurVq3E4HNjtdh577LHanw0vxsvLizfeeIO33nqL\nlStX8v777xMWFsaUKVN49NFHlfCdxxUxLy0tbTBT0/nrHn74YcW+xuXGvLi4mIKCAgA2b97M5s2b\nG3wmJiZGyfZ5XHGtz58/n6+//ppvvvmG3NxcvLy86N69O3fddRc//elP6dWrl5vPomNxRcyleVwR\n81mzZvHvf/+bbdu2UVBQgK+vLz169GDOnDnMnDmzwey1VzpXXee/+tWvsNvtLFmyhBUrVmAYBv36\n9eO5557Tl/hGuPL+4rIuJEC7b9kWEREREemo2vUDkiIiIiIiHZmSbRERERERN1GyLSIiIiLiJkq2\nRURERETcRMm2iIiIiIibKNkWEREREXETJdsiIiIiIm6iZFtERERExE2UbIuIiIiIuImSbRERERER\nN1GyLSIiIiLiJkq2RURERETc5P8DxInkq38/h78AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o3vgX6NUIQ-U",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "6dc074ff-7f4a-4377-a14c-398de608f1fa"
      },
      "source": [
        "posterior_p_scissors = 1 - posterior_p_paper.numpy() - posterior_p_rock.numpy()\n",
        "az.plot_posterior(posterior_p_scissors, credible_interval=0.95, point_estimate='median')"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7efeaa9bad30>],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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HbDnJf1+GL78yuCVJknKbsV2INDoh0OSi2OMHe0esX29wS5Ik5SZju5C5uW2g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\nERER8RIl2yIiIiIiXvL/Jv7zBtfCO7wAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u01ADn6_2Hr7",
        "colab_type": "text"
      },
      "source": [
        "### Let's check the correctness of our result with mathemagic"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "--m_e_xc4SyI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "p_exact_posterior = tfp.distributions.Dirichlet([1 + 5, 1, 1]).sample(10000)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xYv9qNPx-LBm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "12f8dda1-95c8-4e0a-bc30-958d5a76350b"
      },
      "source": [
        "# exact posterior for p_rock\n",
        "az.plot_posterior(p_exact_posterior[:, 0].numpy(), credible_interval=0.95, point_estimate='median') "
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7efeaa6ec358>],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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bAIDrdOaMVf+BVklJ0q3Npfv/5e4RwR/d3MzZlWT3bungIYLbUxDbAABcB2ut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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g-XooDOEB4HW",
        "colab_type": "text"
      },
      "source": [
        "This fits the curve we calculated with MCMC pretty well. The latter is a bit less smooth, which is caused by the relatively low sample size we used."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "38o_ARumJALZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "3c0ae091-533a-4261-dbd7-716a25182655"
      },
      "source": [
        "# exact posterior for p_paper\n",
        "az.plot_posterior(p_exact_posterior[:, 1].numpy(), credible_interval=0.95, point_estimate='median') "
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7efeab20b470>],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AgCMQ24hXp3YW3R9g37u9aAmxDQAAkFbENuLdelXJpculixcJbgAAgLQgtpHA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\nIiIi4iEK2yIiIiIiHqKwLSIiIiLiIf8ffv3btDjnZoEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uMNieYV1RKWz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "62252a31-001d-4f36-bc29-b1997a2597a3"
      },
      "source": [
        "# exact posterior for p_scissors\n",
        "az.plot_posterior(p_exact_posterior[:, 2].numpy(), credible_interval=0.95, point_estimate='median') "
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7efeac08e438>],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5cpmPpaenM2LECJ566imGDh1K7969d/r969evz6uvvkqJEiUAmDlzJh06dODFF1+kXbt2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\norAtIiIiImKT/w/0aZ2D8pXQDQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rpmE9D0DKXwA",
        "colab_type": "text"
      },
      "source": [
        "# Let's play!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YMLULn0wAeEm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from ipywidgets.widgets.interaction import show_inline_matplotlib_plots"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AArDSNdVlNtb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%matplotlib inline\n",
        "\n",
        "show_plot = True\n",
        "\n",
        "class ButtonReaction():\n",
        "    def __init__(self, moves_widget, game_statistics_widget, plot_widget, show_plot):\n",
        "        self.moves = moves_widget\n",
        "        self.game_statistics = game_statistics_widget\n",
        "        self.plot = plot_widget\n",
        "        self.history = {'rock': 0, 'paper': 0, 'scissors': 0}  # initialize history of moves of our human opponent\n",
        "        self.wins = [0, 0, 0]\n",
        "        self.show_plot = show_plot\n",
        "\n",
        "    def on_button_clicked(self, button_info):\n",
        "        actual_human_move = button_info.description.lower()\n",
        "        self.history[actual_human_move] += 1\n",
        "        history_list = [val for (key, val) in self.history.items()]\n",
        "        history_list_plus_one = [val + 1 for val in history_list]  # compute parameters for Dirichlet distribution\n",
        "        no_rounds = sum(history_list)\n",
        "        probs = tfp.distributions.Dirichlet(history_list_plus_one).sample()\n",
        "        hypothetical_human_move = list(tfp.distributions.Multinomial(total_count=1, probs=probs).sample().numpy())\n",
        "        if hypothetical_human_move == [1.0, 0.0, 0.0]:\n",
        "            our_move = 'paper'\n",
        "        elif hypothetical_human_move == [0.0, 1.0, 0.0]:\n",
        "            our_move = 'scissors'\n",
        "        else:\n",
        "            our_move = 'rock'\n",
        "        if actual_human_move == our_move:\n",
        "            result = 'draw'\n",
        "            self.wins[2] += 1\n",
        "        if (actual_human_move, our_move) in [('rock', 'paper'), ('paper', 'scissors'), ('scissors', 'rock')]:\n",
        "            result = 'computer wins'\n",
        "            self.wins[1] += 1\n",
        "        else:\n",
        "            result = 'you win'\n",
        "            self.wins[0] += 1\n",
        "        if self.show_plot:\n",
        "            p_exact_posterior = tfp.distributions.Dirichlet(history_list_plus_one).sample(10000)\n",
        "            plot_probs = pd.DataFrame({'p_rock': p_exact_posterior[:, 0].numpy(), 'p_paper': p_exact_posterior[:, 1].numpy(), 'p_scissors': p_exact_posterior[:, 2].numpy()})\n",
        "            self.plot.clear_output(wait=False)\n",
        "            with self.plot:\n",
        "                fig, ax = plt.subplots()\n",
        "                ax.set_yticklabels(labels='')   # the y-axis-labels are the concrete counts of rock/stone/scissors\n",
        "                                                # which are irrelevant here, so we switch y-axis-labels off\n",
        "                plot_probs.plot.kde(alpha=0.5, fig=fig, ax=ax)\n",
        "                show_inline_matplotlib_plots()\n",
        "        moves.value = f\"result in round {no_rounds}: your move is {actual_human_move}, computer's move is {our_move}, {result}\"\n",
        "        game_statistics.value = f'you won {self.wins[0]} times, computer won {self.wins[1]} times and we had {self.wins[2]} draws'\n",
        "\n",
        "\n",
        "moves = widgets.HTML(\n",
        "    value='no moves yet',\n",
        "    placeholder='',\n",
        "    description='',\n",
        ")\n",
        "\n",
        "game_statistics = widgets.HTML(\n",
        "    value='no game statistics yet',\n",
        "    placeholder='',\n",
        "    description='',\n",
        ")\n",
        "\n",
        "plot = widgets.Output()\n",
        "\n",
        "reaction = ButtonReaction(moves, game_statistics, plot, show_plot)\n",
        "\n",
        "rock_button = widgets.Button(description=\"Rock\")\n",
        "rock_button.on_click(reaction.on_button_clicked)\n",
        "paper_button = widgets.Button(description=\"Paper\")\n",
        "paper_button.on_click(reaction.on_button_clicked)\n",
        "scissors_button = widgets.Button(description=\"Scissors\")\n",
        "scissors_button.on_click(reaction.on_button_clicked)\n",
        "\n",
        "top_row = widgets.HBox([rock_button, paper_button, scissors_button])\n",
        "\n",
        "display(top_row, moves, game_statistics, plot)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cy4AtZsZyMXc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}