Baseball_Pitch_Sequence_Simulator.ipynb

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      "source": [
        "# Tutorial: Generating Synthetic Baseball Pitch Sequences Using Markov Models\n",
        "\n",
        "Name: John Hodge\n",
        "\n",
        "Date: 04/18/24"
      ],
      "metadata": {
        "id": "a9HC56hzKyYn"
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      "cell_type": "markdown",
      "source": [
        "In this tutorial, we'll explore how to simulate realistic baseball pitch sequences using Markov models. By the end, we will have a synthetic dataset of baseball pitch sequences, including ball and strike counts and pitch outcomes. This dataset can be used to train machine learning models to predict the type of pitch based on the count and pitch history.\n",
        "\n",
        "## Conceptual Overview\n",
        "A Markov model is a stochastic model that describes a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. For our baseball simulation, each \"state\" will be defined by the current count of balls and strikes, and each \"event\" will be a pitch with a specific outcome (ball, strike, hit).\n"
      ],
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    {
      "cell_type": "markdown",
      "source": [
        "## Initialize environment"
      ],
      "metadata": {
        "id": "YyNStGIyLbWC"
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    },
    {
      "cell_type": "code",
      "source": [
        "!pip install pandas matplotlib seaborn"
      ],
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          "name": "stdout",
          "text": [
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          ]
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    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "from typing import Dict, Tuple, List, Union\n",
        "import random\n",
        "from matplotlib import pyplot as plt\n",
        "import seaborn as sns"
      ],
      "metadata": {
        "id": "o-jtq_hId1R1"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Step 1: Define Transition Probabilities\n",
        "\n",
        "First, define the transition probabilities, which are the core of the Markov model. These probabilities dictate the likelihood of moving from one state (e.g., the count) to another state based on the outcome of a pitch (ball, strike, or hit)."
      ],
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      "source": [
        "transition_probs = {\n",
        "    (0, 0): {\n",
        "        'pitch_probs': {'Fastball': 0.50, 'Slider': 0.25, 'Curveball': 0.15, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.30, 'strike': 0.60, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.40, 'strike': 0.50, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.45, 'strike': 0.45, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.35, 'strike': 0.55, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (0, 1): {\n",
        "        'pitch_probs': {'Fastball': 0.45, 'Slider': 0.30, 'Curveball': 0.15, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.32, 'strike': 0.58, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.42, 'strike': 0.48, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.47, 'strike': 0.43, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.37, 'strike': 0.53, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (0, 2): {\n",
        "        'pitch_probs': {'Fastball': 0.40, 'Slider': 0.35, 'Curveball': 0.15, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.34, 'strike': 0.56, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.44, 'strike': 0.46, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.49, 'strike': 0.41, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.39, 'strike': 0.51, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (1, 0): {\n",
        "        'pitch_probs': {'Fastball': 0.55, 'Slider': 0.20, 'Curveball': 0.15, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.28, 'strike': 0.62, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.38, 'strike': 0.52, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.43, 'strike': 0.47, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.33, 'strike': 0.57, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (1, 1): {\n",
        "        'pitch_probs': {'Fastball': 0.50, 'Slider': 0.25, 'Curveball': 0.15, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.30, 'strike': 0.60, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.40, 'strike': 0.50, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.45, 'strike': 0.45, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.35, 'strike': 0.55, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (1, 2): {\n",
        "        'pitch_probs': {'Fastball': 0.45, 'Slider': 0.30, 'Curveball': 0.15, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.32, 'strike': 0.58, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.42, 'strike': 0.48, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.47, 'strike': 0.43, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.37, 'strike': 0.53, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (2, 0): {\n",
        "        'pitch_probs': {'Fastball': 0.60, 'Slider': 0.20, 'Curveball': 0.10, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.25, 'strike': 0.65, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.35, 'strike': 0.55, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.40, 'strike': 0.50, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.30, 'strike': 0.60, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (2, 1): {\n",
        "        'pitch_probs': {'Fastball': 0.55, 'Slider': 0.25, 'Curveball': 0.10, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.28, 'strike': 0.62, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.38, 'strike': 0.52, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.43, 'strike': 0.47, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.33, 'strike': 0.57, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (2, 2): {\n",
        "        'pitch_probs': {'Fastball': 0.50, 'Slider': 0.30, 'Curveball': 0.10, 'Changeup': 0.10},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.30, 'strike': 0.60, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.40, 'strike': 0.50, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.45, 'strike': 0.45, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.35, 'strike': 0.55, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (3, 0): {\n",
        "        'pitch_probs': {'Fastball': 0.80, 'Slider': 0.10, 'Curveball': 0.05, 'Changeup': 0.05},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.20, 'strike': 0.70, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.30, 'strike': 0.60, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.35, 'strike': 0.55, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.25, 'strike': 0.65, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (3, 1): {\n",
        "        'pitch_probs': {'Fastball': 0.75, 'Slider': 0.15, 'Curveball': 0.05, 'Changeup': 0.05},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.25, 'strike': 0.65, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.35, 'strike': 0.55, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.40, 'strike': 0.50, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.30, 'strike': 0.60, 'hit': 0.10}\n",
        "        }\n",
        "    },\n",
        "    (3, 2): {\n",
        "        'pitch_probs': {'Fastball': 0.70, 'Slider': 0.20, 'Curveball': 0.05, 'Changeup': 0.05},\n",
        "        'outcomes': {\n",
        "            'Fastball': {'ball': 0.28, 'strike': 0.62, 'hit': 0.10},\n",
        "            'Slider': {'ball': 0.38, 'strike': 0.52, 'hit': 0.10},\n",
        "            'Curveball': {'ball': 0.43, 'strike': 0.47, 'hit': 0.10},\n",
        "            'Changeup': {'ball': 0.33, 'strike': 0.57, 'hit': 0.10}\n",
        "        }\n",
        "}\n",
        "}"
      ],
      "metadata": {
        "id": "uNdzAxMyc1EK"
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      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Step 2: Simulate a Pitch\n",
        "\n",
        "Using the defined probabilities, simulate a pitch based on the current count. This involves selecting a pitch type according to `pitch_probs` and determining the outcome (ball, strike, hit) based on `outcomes`.\n",
        "\n",
        "```python\n",
        "def simulate_pitch(self, state):\n",
        "    pitch_probs = self.transition_probs[state]['pitch_probs']\n",
        "    pitch_type = random.choices(list(pitch_probs.keys()), weights=pitch_probs.values(), k=1)[0]\n",
        "\n",
        "    outcome_probs = self.transition_probs[state]['outcomes'][pitch_type]\n",
        "    outcome = random.choices(list(outcome_probs.keys()), weights=outcome_probs.values(), k=1)[0]\n",
        "\n",
        "    return pitch_type, outcome\n",
        "```\n",
        "\n",
        "## Step 3: Update the Count\n",
        "\n",
        "After each pitch, update the count of balls and strikes based on the outcome.\n",
        "\n",
        "```python\n",
        "def update_count(self, state, outcome):\n",
        "    balls, strikes = state\n",
        "    if outcome == 'ball':\n",
        "        balls += 1\n",
        "    elif outcome == 'strike':\n",
        "        strikes += 1\n",
        "\n",
        "    # Rules to determine next state or end the at-bat\n",
        "    if balls >= 4:\n",
        "        return 'walk'\n",
        "    elif strikes >= 3:\n",
        "        return 'strikeout'\n",
        "    else:\n",
        "        return (balls, strikes)\n",
        "```\n",
        "\n",
        "## Step 4: Simulate an At-Bat\n",
        "\n",
        "Combine the pitch simulation and count updating in a loop to simulate an entire at-bat.\n",
        "\n",
        "```python\n",
        "def simulate_at_bat(self):\n",
        "    state = (0, 0)\n",
        "    sequence = []\n",
        "\n",
        "    while True:\n",
        "        pitch_type, outcome = self.simulate_pitch(state)\n",
        "        sequence.append((state, pitch_type, outcome))\n",
        "        new_state = self.update_count(state, outcome)\n",
        "        if isinstance(new_state, tuple):\n",
        "            state = new_state\n",
        "        else:\n",
        "            sequence.append(new_state)\n",
        "            break\n",
        "\n",
        "    return sequence\n",
        "```"
      ],
      "metadata": {
        "id": "ORQyJlSQL1wI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Step 5: Combine components into a baseball pitch simulator class"
      ],
      "metadata": {
        "id": "LUx7Gg9HMfN4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class BaseballPitchSimulator:\n",
        "    def __init__(self, transition_probs: Dict):\n",
        "        self.states = [(balls, strikes) for balls in range(4) for strikes in range(3)]\n",
        "        self.pitch_types = ['Fastball', 'Slider', 'Curveball', 'Changeup']\n",
        "        self.transition_probs = transition_probs\n",
        "        self.pitch_count = 0\n",
        "\n",
        "    def simulate_pitch(self, current_state: Tuple[int, int]) -> Tuple[str, str]:\n",
        "        \"\"\"Simulates a pitch and determines its outcome based on probabilistic pitch type selection.\"\"\"\n",
        "        pitch_type_probs = self.transition_probs[current_state]['pitch_probs']\n",
        "        pitch_types = list(pitch_type_probs.keys())\n",
        "        pitch_probabilities = list(pitch_type_probs.values())\n",
        "        pitch_type = random.choices(pitch_types, weights=pitch_probabilities, k=1)[0]\n",
        "        probabilities = self.transition_probs[current_state]['outcomes'][pitch_type]\n",
        "        self.pitch_count += 1\n",
        "        fatigue_factor = 1  # Static fatigue factor, modify if needed\n",
        "        outcome = random.choices(['ball', 'strike', 'hit'],\n",
        "                                weights=[probabilities['ball'] * fatigue_factor,\n",
        "                                          probabilities['strike'] / fatigue_factor,\n",
        "                                          probabilities['hit']],\n",
        "                                k=1)[0]\n",
        "        return pitch_type, outcome\n",
        "\n",
        "\n",
        "    def update_count(self, current_state, outcome):\n",
        "        balls, strikes = current_state\n",
        "        if outcome == 'ball':\n",
        "            balls += 1\n",
        "            if balls == 4:\n",
        "                return 'walk'\n",
        "        elif outcome == 'strike':\n",
        "            strikes += 1\n",
        "            if strikes == 3:\n",
        "                return 'strikeout'\n",
        "        elif outcome == 'hit':\n",
        "            return 'hit'\n",
        "\n",
        "        return (balls, strikes) if (balls < 4 and strikes < 3) else None\n",
        "\n",
        "    def simulate_at_bat(self):\n",
        "        state = (0, 0)\n",
        "        sequence = []\n",
        "\n",
        "        while True:\n",
        "            pitch_type, outcome = self.simulate_pitch(state)\n",
        "            sequence.append((state, pitch_type, outcome))\n",
        "            new_state = self.update_count(state, outcome)\n",
        "            if isinstance(new_state, tuple):\n",
        "                state = new_state\n",
        "            else:\n",
        "                sequence.append(new_state)\n",
        "                break\n",
        "\n",
        "        return sequence"
      ],
      "metadata": {
        "id": "myIGzlmJcFsJ"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Example usage:\n",
        "simulator = BaseballPitchSimulator(transition_probs)\n",
        "for i in range(5):\n",
        "    print(i, simulator.simulate_at_bat())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hHe6D-jWJVOW",
        "outputId": "d46b1f34-0c4b-4530-c0c7-606bcad2208f"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 [((0, 0), 'Changeup', 'ball'), ((1, 0), 'Fastball', 'strike'), ((1, 1), 'Fastball', 'strike'), ((1, 2), 'Slider', 'ball'), ((2, 2), 'Fastball', 'strike'), 'strikeout']\n",
            "1 [((0, 0), 'Fastball', 'ball'), ((1, 0), 'Curveball', 'hit'), 'hit']\n",
            "2 [((0, 0), 'Fastball', 'strike'), ((0, 1), 'Slider', 'strike'), ((0, 2), 'Changeup', 'ball'), ((1, 2), 'Curveball', 'strike'), 'strikeout']\n",
            "3 [((0, 0), 'Fastball', 'strike'), ((0, 1), 'Changeup', 'strike'), ((0, 2), 'Fastball', 'ball'), ((1, 2), 'Slider', 'strike'), 'strikeout']\n",
            "4 [((0, 0), 'Fastball', 'hit'), 'hit']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Step 6: Generate Dataset\n",
        "\n",
        "Simulate multiple at-bats to generate a dataset."
      ],
      "metadata": {
        "id": "jZpe5FzCMx_B"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def generate_dataset(num_at_bats):\n",
        "    simulator = BaseballPitchSimulator(transition_probs)\n",
        "    data = []\n",
        "\n",
        "    for _ in range(num_at_bats):\n",
        "        at_bat = simulator.simulate_at_bat()\n",
        "        for state, pitch_type, outcome in at_bat[:-1]:  # Exclude the final result like 'walk' or 'strikeout'\n",
        "            balls, strikes = state\n",
        "            data.append([balls, strikes, pitch_type, outcome])\n",
        "\n",
        "    df = pd.DataFrame(data, columns=['Balls', 'Strikes', 'PitchType', 'Outcome'])\n",
        "    return df"
      ],
      "metadata": {
        "id": "8Qp_dtP_bdDT"
      },
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate the dataset\n",
        "dataset = generate_dataset(100000)\n",
        "\n",
        "# Save to CSV (for ML model training)\n",
        "dataset.to_csv('baseball_pitch_data.csv', index=False)"
      ],
      "metadata": {
        "id": "IoX2kFVBJX-7"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## View Data"
      ],
      "metadata": {
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      "cell_type": "code",
      "source": [
        "dataset"
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          "height": 424
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        "id": "nPwgsNu5LK3H",
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      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "        Balls  Strikes PitchType Outcome\n",
              "0           0        0  Fastball  strike\n",
              "1           0        1  Changeup    ball\n",
              "2           1        1    Slider     hit\n",
              "3           0        0  Fastball  strike\n",
              "4           0        1  Changeup  strike\n",
              "...       ...      ...       ...     ...\n",
              "378195      1        0  Fastball  strike\n",
              "378196      1        1    Slider  strike\n",
              "378197      1        2  Fastball    ball\n",
              "378198      2        2  Fastball    ball\n",
              "378199      3        2  Fastball  strike\n",
              "\n",
              "[378200 rows x 4 columns]"
            ],
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Balls</th>\n",
              "      <th>Strikes</th>\n",
              "      <th>PitchType</th>\n",
              "      <th>Outcome</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>Fastball</td>\n",
              "      <td>strike</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>Changeup</td>\n",
              "      <td>ball</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>Slider</td>\n",
              "      <td>hit</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>Fastball</td>\n",
              "      <td>strike</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>Changeup</td>\n",
              "      <td>strike</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>378195</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>Fastball</td>\n",
              "      <td>strike</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>378196</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>Slider</td>\n",
              "      <td>strike</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>378197</th>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>Fastball</td>\n",
              "      <td>ball</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>378198</th>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>Fastball</td>\n",
              "      <td>ball</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>378199</th>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>Fastball</td>\n",
              "      <td>strike</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>378200 rows × 4 columns</p>\n",
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            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
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          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "source": [
        "# @title PitchType vs Outcome\n",
        "\n",
        "from matplotlib import pyplot as plt\n",
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "plt.subplots(figsize=(8, 8))\n",
        "df_2dhist = pd.DataFrame({\n",
        "    x_label: grp['Outcome'].value_counts()\n",
        "    for x_label, grp in dataset.groupby('PitchType')\n",
        "})\n",
        "sns.heatmap(df_2dhist, cmap='viridis')\n",
        "plt.xlabel('PitchType')\n",
        "_ = plt.ylabel('Outcome')"
      ],
      "cell_type": "code",
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "metadata": {
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 696
        },
        "id": "qImrPSmWH-z_",
        "outputId": "a02b4db9-476c-4c1d-eaf1-89f06caa2ea8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Violin Plot\n",
        "\n",
        "A violin plot plays a similar role as a box-and-whisker plot. It shows the distribution of data points after grouping by one (or more) variables. Unlike a box plot, each violin is drawn using a kernel density estimate of the underlying distribution.\n",
        "\n",
        "More information: https://seaborn.pydata.org/generated/seaborn.violinplot.html"
      ],
      "metadata": {
        "id": "PV1luMeWNiA9"
      }
    },
    {
      "source": [
        "# Violine plot of PitchType vs Balls\n",
        "figsize = (12, 1.2 * len(dataset['PitchType'].unique()))\n",
        "plt.figure(figsize=figsize)\n",
        "sns.violinplot(dataset, x='Balls', y='PitchType', inner='box', palette='Dark2')\n",
        "sns.despine(top=True, right=True, bottom=True, left=True)"
      ],
      "cell_type": "code",
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-33-fdee93e4505f>:4: FutureWarning: \n",
            "\n",
            "Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `y` variable to `hue` and set `legend=False` for the same effect.\n",
            "\n",
            "  sns.violinplot(dataset, x='Balls', y='PitchType', inner='box', palette='Dark2')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x480 with 1 Axes>"
            ],
            "image/png": 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GYYDZRDg/g9DgnFijZ0vPCxlNngDW8jqs5XVYmrwAuFwuDj30UI4++mgmT56shq/SpxmGwZYtW1ixYgVffPEFX3zxBVu2bPnqBjsHCu3NXVPdRFOcnbPKlGFgCoQxN3kwN3qwNLRhbvBg9gY63Cw3N5exY8cyZswYxo4dS3FxMRZLD1vlqptR0CAJdd111/HRRx/FpkmMG0y4IEtfNr4nc7MX27rt2LbUQSRKSmoqp55yCqeddpqWw5SEqKqqYsGCBfz3v/9l9erVAIT7pREaMYBIbqr2+a+LRLFuqsW2qQZLQxsQW3Zv1jGzOP744xk2bFiCCxT5btFolNWrV/Pxxx/z0UcfffXFwmQinJMSa+o4KKtX9WExtXhjUyvK6+PLZqalpTFlyhQmTZrE5MmTyc3NTXCVIl2rra2N1atXs3LlSlatWsUXK1bQ2tLy1Q1sVsJZyUSyU4hmpxDJTAZbAr7QB0JYGjyYG9uwNLRhqW/D5A/Fr3a73YwePToePowaNQq3WwdC94aChr00c+ZMxo0bx7333rvPj/Hhhx9y2GGH0djYSHp6OnPnzmXOnDm7DhnqA84880zWbd6I54QJiXmT+Q6uN5dhCoQTXca+MQxMkSiEo7R/jXM4HDgcDh1dkS4XDocJBoOEQiEikUj8csNsAqsldirfyRQ1IBKFyFf7scViweFwYLfbNT1KupVIJEI4HI7v/zt/xDTMJrCYY6cJDBcNhxXfrHFd/CQG5gYP1vI6bFvrMXmD8asGDRrE5MmTmTRpEuPHj1dfB+nRotEomzdvZuXKlbFpEKtWsnnT5g77fjTZSSQ7JRYsZKXs/6aue8owMHkCWGpbsdS1YK5rxdLii19tMpsp3NHnoX0bNmyYRg1/i17xbWP27Nk88cQTu1xeVlbG0KFD9+kxvx4GSBcym7plyADEhlrtlG72dIFAgEAg8N03FOkipqgBwTDd7SPGI488AsD555+f4Eq+WyQSwev14vV6E12KyB4zRQ2IRhK+70f3x5OYTESzkglmJRMcNxhTqx9rdROW6mbKt2+j/MUXefHFFzGZzYwcMYIxY8ZQVFREYWEhQ4YMITk5eX9UKbLHotEolZWV8SaNmzdvZuPGjWzavJmA3//VDW0WwrmpRLOSiWSlEMlK7jmjlkwmjGQn4WQn4cIdzSIDISz1bVjqWrHUtbKxYgsbN27k9ddfj93FbGbIkMGMKB3B8OHDKSoqYsCAAfTr10/TLuglQQPArFmzePzxxztcpo6iIiIiIpIwJhNGqotQqotQSR5EDcwNbViqm7FWN7NqzWpWrVrV4S45OTkUFhZSVFTEkCFDGDx4MFlZWWRkZJCcnKyVpaTTBYNB6uvrqauro7a2ltraWurq6qiurmbz5s1s2bJl1wNVVjORFBfRvFwi2cmx0QoprtgBxN7CYSOSn0EkPyP2s2FgavPHp1yYGz1sqihn08ZN8fABwGq1kpeXx4ABAxg4cCADBgxgwIABlJaW9qnpU70maHA4HPTv37/DZX/+8595/PHH2bhxI5mZmZxwwgn86U9/iifFW7Zs4bLLLmPevHkEg0GGDBnCnXfeyciRIznssMMAyMiI/WKdffbZzJ07F4gNCb7ssst46qmnsNlsXHzxxdxyyy3xN/6nnnqK++67jy+//JKkpCQOP/xw7r333n3+xdrdUej2IfAiIiIismdMgTCut79IdBlxkVRXbJpjJAqR2JTHmvrYl732prlfZ7VasVgsWCyW+Hmz2YzZbMZkMn3jKdDh9OuXSffXPiVh59OvbztfHo1Gv3GLRCJEo1FCoRDR6LeP9TEsZrBbMSztU6DM8eat5iYP5iYPrK/uwlf+zaIpLgJTS/bPk5lMGCkuwikuGLyj71l7+NDowdTqw9wWINLmp7y2ioqKig53t9lsvP76631mylSvCRp2x2w285e//IXCwkI2btzIJZdcwrXXXssDDzwAwKWXXkowGOTjjz8mKSmJ1atXk5ycTEFBAS+99BKnnnoqX375JampqbhcX63j/MQTT3DeeeexcOFCFi9ezAUXXMCgQYP4xS9+AUAoFOLWW29l+PDh1NTUcNVVVzF79uwOSdfeuP3227n55ps7XPa73/2Om266ad/+YURERET6IJNhYGn0JLqM76W9D4bI/mL6Wq8g2cnO4cPXhSOY2/yY2gLY126D+jba2toUNPQ0//3vfzvMafvBD37ACy+8EP95yJAh3HbbbVx00UXxoKG8vJxTTz2VAw44AICioqL47dvXLs/Nzd2lR0NBQQH33HMPJpOJ4cOHs2LFCu6555540HDuuefGb1tUVMRf/vIXJk2aRFtb2z7Nu7v++uu56qqrOlym0QwiIiIie8cwmYimd+PO8e2NnNu/2EWiEDViPS5EuphhMsWmPphNscatZhOYzbERDWYz3TFpiO7uC34iRQ1MvgDmtgCmNj/mHZupre/1SOs1QcNhhx3Ggw8+GP85KSmJd999l9tvv521a9fS0tJCOBzG7/fj9Xpxu91cccUVXHzxxbz99tsceeSRnHrqqYwZM+Y7n2vKlCkdhplNnTqVu+++m0gkgsViYcmSJdx0000sX76cxsbG+HCk8vJyRo4cudevTdMkRERERL4/w2HFd/R3f9bbH0zeAJbqZsyNHswtPiwtPky+4C63y83NJTs7m4yMjN1u6enpJCUl4XQ6cTgcOJ1ObDabpkQIoVAIr9eLx+PpcNp+vrm5mfr6+nhPhvb+DKFQaNdMwWImkuwkmuYimuqOnxrJzt7Vl2FPGQYmXxBzowdLoye+H5u9AdhNMOh2uzngoPF9qodgrwkakpKSOqwwsXnzZo4//nguvvhifv/735OZmcm8efM477zzCAaDuN1uzj//fI455hhee+013n77bW6//XbuvvtuLr/88n2uw+PxcMwxx3DMMcfw9NNPk5OTQ3l5OccccwzB4K5/PKR7MxzW/dOhej8wRQ0IR3Y5KmIymbBardhsNqxWq5a+lD3SPrczEonEt52H8hoQ++DRDZaz2xPnXnZx7Iyzm3fHNgxMkdiSl6avrU5tNpvj+3D7vG190ZDOsvO87p2Xsfy6jkdEu98RUMORwL9xwTCWmhYs1U1Yq1swt+60dJ7JRH5+PoWFhfFGkIWFhQwePLjD9F2RvWGz2UhLSyMtLW2P72MYBi0tLR2aQbavNrFx0ya85fVA/Vd3sFoIZybFV5qIZiZjuOyd/2ISzOQNxEKFhrZ4uGD62sp0mVmZDCwa1qEBZPv59PT0Pvc3udd+o1iyZAnRaJS77747vs74P//5z11uV1BQwEUXXcRFF13E9ddfz8MPP8zll1+O3R7bQXZe/73d//73vw4/f/bZZ5SUlGCxWFi7di319fX88Y9/pKCgAIDFixd39suT/aTL19ruaoaBpbIR27rtWGtagNjv/IQJExgzZgxjxoxhwIABfe6NT7qG3+9nyZIlzJ8/n/nz51NdXR1bzs4EkawUwvkZhIpye85SV91F1MBS04x1Uw22bY0QiWI2mzlw/HhGjx7NqFGjGDlyJNnZ2YmuVPqYaDTKli1bWLVqFatXx1ZPWL9+feyzUwRMNgjlpRMZkEk4Lx1svfZj5+5FDcx1LVirm7FUNWNpbNuRwoI7KYmJhxzCpEmTGDNmDIMHD8bpdCa2XhFioVd7OFFcXMy0adPi1xmGQW1t7VfBw8aNrFmzhvUbNmDs+JwJEE1yEMmKrUQRyUommp4Ubx7ZI0QNzM1eLHUtmOtasda1YfJ2nPqQl5/PiNJSSktLGT58OKWlpXsV6PQFvfYdf+jQoYRCIe6//35OOOEE5s+fz0MPPdThNnPmzOEHP/gBw4YNo7GxkQ8++IARI0YAMHjwYEwmE//973859thjcblc8f4K5eXlXHXVVVx44YV8/vnn3H///dx9990ADBo0CLvdzv33389FF13EypUrufXWW/fvi+9hTKEIlm0NsaVj9IW3c4QjWDfXYl+3HXNrbH3jadOm8dOf/pSJEycqWJAu4XQ6mT59OtOnT8cwDDZu3Mj8+fNZsGABX3zxBZa6VhyrtxEsyiU0PA/DrSlh38bU6sO2qRbb5tr4cOohhYWccPzxHHPMMQoWJOHMZnP8CPzxxx8PxALH1atXM2/ePD766CO2lW/DVl4PZhPh3FTCAzKJDMjslUc8ATBiy1dat9Rhq2jA5I/tu1arlQPGHcikSZOYPHkypaWlGkEoPY7JZCI3N5fc3FwOOuig+OVer5c1a9awatUqVq5cyYoVK2gsr4fyHSMfLGYimUlEslKIZMe2bnXQIRSJjVSoa8FS24q1oQ1CXx1szszKZOxB0xgxYkQ8WFCo8N1MhmH0+O4ys2fPpqmpiX//+98dLr/nnnu48847aWpq4pBDDuGMM87grLPOorGxkfT0dC6//HLeeOMNtm7dSmpqKrNmzeKee+4hKysLgFtvvZUHHniA6upqzjrrLObOncvMmTMZNWoU0WiUZ555BovFwsUXX8xtt90W//L27LPPcsMNN7B9+3bGjx/P9ddfz4knnsjSpUsZN24cH374IYcddli8jrlz5zJnzhyampr2879c4r344ovcc++9RMJhwnnpBMYXxuZ6yT4x+YLYyqqwb6iGYBi73c6xxx7Lj3/8YwoLCxNdnvRhLS0tvPHGGzzzzDOxkQ5mE6HB2QRLB2Ckaljwziw1zdhXVGCpawUgOSWFY44+muOPP57S0lIFhdJjGIbBpk2b+Oijj/j4449Zs2ZN/LpIVgqhITmEB2WBved/4TY3e7GW12Etr8fcFgv409PTOfLII5k+fTrjxo3TFAjpMwzDYPv27axatYovvviCFStWsG7dug7LaEZTnPHgIZruJprqBpul64sLR77qq9DQhqXB02EaE0BhUSFjx4xlzJgxjB07lvz8fP3t3Qe9ImiQnq28vJy77747NiXFYiY4PI/giAFg3Q9vNr2FYWDdVINz6RYIR0jPyOBHp53GKaecQkZGRqKrE4kLh8O8/fbbPPnUk2zetDl22cBMgiMGEM3c+1V5ehNTixfH8nKslY1ArNHw8ccfz4wZM9QQWHqFmpoaPv74Yz7++GMWLV6MEY3GRjrkZxAakkMkLz3W2b6HMHkCsXBhSx2WZi8ALrebw2bO5Oijj2bixIkatSCyg8/nY/Xq1fHg4YsvvqCtra3DbaJux44mkx0bTu51ABGOYPKHYs0afcHYaZM3Fiy0+uJTmACSk5MZMWIEI0eOZMyYMYwePVqjFTqJggbpFgzD4MMPP+Tee++luroaI8mB/8Ahmk6xJ4JhHIs3YquoJyU1hcsuvYxZs2bpi4l0a9FolHnz5vHEE0+watUqAML90ggeUEA0q2+sL93O5AtiX7UV28YaMAwmTpzI5ZdfzvDhwxNdmkiXqaur4+233+aNN96grKwMAMNhIzQoi/CQHKIZSd3z738wjLWiHtuWWiy1sVFHNpuN6dOnc/TRRzNt2jT1WhDZA+09XlasWMHGjRvZvHkzGzZupLamZtcb260Yltgym4bVDBZL7NS6Y+lNkykeLFj8IQju2qgWYr1R2vsqlJaWMmLECPUq60IKGqRb8fl8zJ07l6efeZpwaMd0igOHYHS3NXK7CXNtC67/rcfkCXDggQdy8803k5ubm+iyRPaYYRh8/vnnPPXUU3z22WcAhIr7ERgzqFcMp/5W4Qi2LytxrN0O4QiFhYVcfvnlTJ06VR96pE8pKyvjjTfe4M0336ShoQGAaKqL8MBMwgOziKa7Exs6RKJYtjdi21IXG3EUNTCZTEycOJFjjjmGmTNnxvt4icj34/F44s0m2xtONjQ04Pf78fv9+Hw+/H4/oVBol/umpaWRk5NDdnZ2/LR9KywsZODAgfFFAqTrKWiQbunr0yn8E4sID+k7685+p6iBbc1WHKu2YjaZ+cUvfsFZZ52FxaLpJtJzLV++nDvuuIONGzdiOG0Exg2Jzd/ubV+6o7GpTo5VWzH5gmRlZXHBBRdw3HHHaZi19GnhcJhFixbxxhtv8NFHHxEIxLq8R5OdX4UOmftppEMkiqWuFWt5HbatDfEjpCUlJcyaNYujjjpKwb5IAoXDYQKBAH6/n0gkQnp6enzVQOkeFDRIt9U+neIPt/+B1pZWAqMLCI0c0Pu+dOwlkyeA839lWGpb6Z/Xn1tvuZUDDjgg0WWJdIpwOMxzzz3Hw488TMAfINwvjcCEwl4zqsnc5MWxaD2WBg9Op5MzzzyTn/3sZ2oSJ/I1fr+fTz/9lA8++IBP5s3D5431QDDcDkIDMwkPzCSaldx5PR2iUcwNHiw1zViqm7HWt0Ek1rguNzeXWbNmccwxx1BcXNw5zyci0sspaJBub8uWLVx55ZVUVlYSKswhMLGoRzWL6kyWinpcizdCMMxRRx3Fddddp+Ga0itt376du+++m3nz5oHFTGBEPqHSAT1rHe6dRaLY12zDvmYbRA2OPfZYLr300vgqRyLyzQKBAIsWLeKDDz7g448/prU11hsBs4lIspNo2ldN46Jp7tjqVeZvOCgRNWKN4kIRTP4gltoWLNUtWOtaIRxbzs5kMjF8+HAmTJgQXzFCw61FRPaOggbpERoaGvjVr37FqlWrCPdLwz9tWO+fv70zw8C+sgL76m04nU6uueYajjvuOM3jll7v448/5q677qKmpoZoipPAhCIi/XpWN2hzfSvORRswN/vo178/N1x/fYf1x0Vkz4XDYZYsWcInn3zCunXr2Lhx4y6d6zGbiKS4MJy2WKAQimDaES60hwlfV1xczIQJE5g4cSLjxo0jNTV1P7waEZHeS0GD9Bh+v5/f/e53fPTRR0TT3PgOKcVw94GVFQwD+7It2NdtZ+DAgfz5z39m0KBBia5KZL/xer088sgjPPfcc0SjUUJDcgiMGwwOW6JL+3bhCPYVFdjXbcdkMvGjH/2Iiy66CLfbnejKRHoNwzCoq6tj48aN8cZxmzZtYsPGjXg9sSlKSUlJJCUlkZycjNvtjv+cmprK6NGjGT9+PJmZmYl+KSIivYqCBulRIpEI999/P8899xyGy47v4NLYEli9lWHgWLIJ24ZqioqKuP/++zXUWvqsdevWcfvtt7NmzRpw2PAfOJjwoOxu2bfFUt2Mc9EGTJ4AgwcP5oYbbmDs2LGJLkukzzAMg0gkogarIiIJoqBBeqTnn3+ee++9F8NixjethEheRqJL6nxRA8eiDdg21zJ8+HD+8pe/kJbWs4aMi3S2SCTCCy+8wEMPPYTf748tgTuhECOpe6xbb/IHsX9Rjm1TLRaLhTPPPJNzzjkHh6MPjL4SERER2UFBg/RYH330Eb+98UaCwSD+SUWEC3vRMlPRKI7P1mOrqGf06NHcc889pKSkJLoqkW5j+/bt/OlPf+LTTz8Fq4XA6IGESvK+uQFcV4tEsZVtx7F6G4QiDB8+nN/85jcMGzYsMfWIiIiIJJCCBunRVq1axVVXX01zUxP+ycW9I2yIRHEuWIe1spHx48dz1113aU63yG4YhsE777zDn//8Z5qamohkJBGYVLx/p1MZBpZtjTiWb8Hc5ic9PZ2LLrqIE044AYvFsv/qEBEREelGFDRIj7dhwwYuueQSmpub8R80lPCQnESXtO/CEZzzvsRa3cyUKVP44x//iNPZPYaEi3RXzc3N/OUvf+G1114Dk4lQQSah4flEM7t26Vdzkwf7si1Yq5uxWK38+PTTOffcc7XkrIiIiPR5ChqkVygrK+OSSy+htbUV/0ElhAdnJ7qkvReK4PpkDZbaVg499FBuvfVW7HZ7oqsS6TEWLVrEX/7yF8rKygAI56YSKs0n0j+9cxtGBkI4VlRg21gNBsyYMYMrrrhCq8GIiIiI7KCgQXqNL7/8kksvvZQ2Txv+KSWxbvQ9RTCM6+M1WOrbOProo7nxxhvVKVtkHxiGweLFi3n66af57LPPAIimuQgOy48FkBbzvj1wMIy1qglLZSO2ykYIRRhSOIQr51zJQQcd1ImvQERERKTnU9AgvcqaNWu47LLL8Hi9+KaWECnoAUtBBsO4PlqDpaGN4447jhtuuEFzu0U6wfr163n22Wd58623iITDGE47wZL+RPLTiTrt4LB+60gHU6sPa2UjlspGrLWtsOPPZb9+/fj5z3/OySefrEBQREREZDcUNEivs2rVKi6/4nK8Ph++acOIDMhMdEnfbKeQ4fjjj+eGG27AbN7HI64islu1tbW88MILvPTSS3g8nq+uMJkwXDaiThuG047hshN12jCFIli3N2Ju9e+4mYlRo0Zx8MEHM336dIqLizF15lQMERERkV5GQYP0SitWrOCKK67AF/Djmz6cSH5GokvalUIGkf3K4/Hw9ttvs2nTJurr66mrq4tt9fUE/P4Ot3W73UydOpXp06czdepUMjK64XuIiIiISDeloEF6rWXLljFnzhz8wSC+GcOI5HWjLwo7hQwnnHAC119/vUIGkQQxDAOv10tdXR319fWYTCZGjx6NzWZLdGkiIiIiPZKCBunVli5dypwr5xAIhvAfVNw9GkQqZBARERERkV5M326kVzvwwAO59557SXK5cH5ahu3LysQWpJBBRERERER6OY1okD5hw4YNzLlyDrU1tQSH5REcN/hbu813CYUMIiIiIiLSByhokD6jpqaGK6+8kg0bNhAemIl/SglY9s8XfZMviHPeWiwNHoUMIiIiIiLSqylokD6lra2N6667jiVLlhDJScE3fTg4urbhm6WyEdfCDRAIceKJJ/LrX/9aIYOIiIiIiPRaChqkzwkGg9x22228/fbbRFNd+A4ZgZHk6PwnikSxL9+CvawKu93OnDlzOPnkkzHt7ykbIiIiIiIi+5GCBumTotEoDzzwAP/4xz8wXHZ8B5cSzUjqtMc3tfhwflqGpclDYWEht912G8XFxZ32+CIiIiIiIt2Vggbp01544QX+/Oc/Y1jNBEYOJFSUC3brvj+gYWDdVItz6WYIRzjllFO44oorcDqdnVaziIiIiIhId6agQfq8Dz74gFtuvRWf1wtWC8HCHELD8jCS9zIcCIZxLN6IraKe5JQU/t9vfsPMmTO7pGYREREREZHuSkGDCLEmkf/5z394/vnnqa6uBiA8IIPgsHyiOSm7XwrTMDD5Q5ibvJibPdjXV2PyBBg3bhw333wz/fr128+vQkREREREJPEUNIjsJBwO89FHH/Hss8+ycuVKACIZSYSG5RFNde0IFbyYmzxYmn2YAqH4fU1mM+efdx6zZ8/GYrEk6iWIiIiIiIgklIIGkW+wcuVKnnvuOd5//32i0WiH60wmEwUFBQwdOpShQ4dSXFzMiBEjyM3NTVC1IiIiIiIi3YOCBpHvUFVVxb///W98Pl88WCgsLFSDRxERERERkd1Q0CAiIiIiIiIincac6AJEREREREREpPdQ0CAiIiIiIiIinUZBg4iIiIiIiIh0GgUNIiIiIiIiItJpFDSIiIiIiIiISKdR0CAiIiIiIiIinUZBg4iIiIiIiIh0GgUNIiIiIiIiItJpFDSIiIiIiIiISKdR0CAiIiIiIiIinUZBg4iIiIiIiIh0GgUNIiIiIiIiItJpFDSIiIiIiIiISKdR0CAiIiIiIiIinUZBg4iIiIiIiIh0GmuiCxDp7iKRCF9++SWLFy+mqamJkpISSktLGTRoEBaLJdHliYiIiIiIdCsKGkS+xjAMNm3axOLFi1m8eDGfL1lCm8ezy+2cTgclJcMoLS1l+PDhlJaWMmTIEKxW7VYiIiIiItJ3mQzDMBJdhEiihcNh3n77bT777DMWL15EQ0Nj/Lose5ihyQGKkwKk2iJs99mo9NvY5rNRHbAT2WkPcjjsHHvscVx00UWkpaUl4JWIiIiIiIgkloIG6fNWrVrF7bf/gfXrNwCQaotQnBSIb+n26DfeNxyF6kAsdNjms7HB46A+aCU1JYWLL7mEE088UdMrRERERESkT1HQIH2W1+vl73//Oy/8859EDYODMj1Mz2oj2x7BZNq3x4wY8L+GJN6pScUfMTF8+HCuueYaDjjggM4tXkREREREpJtS0CB90oIFC7jjjjuorq4mxxHmlPwmhiQFO+3xW8Nm3qpKZUmTG4DjjjuOSy65hKysrE57DhERERERke5IQYP0KQ0NDdxzzz288847WEwwM7uVmTmtWLtooddyr41XKtOo9NtJcru54MILOfXUU9UwUkREREREei0FDdInGIbBa6+9xn333UtraxuD3UFOzm+inzPc5c8dNWBxo5u3qtPwRkwMHVrMH/5wO4MGDery5xYREREREdnfFDRIr9fW1saNN97IggULcFgMZuU2MznTi3kf+zDsK0/YxNvVqSxsTCI5OYnf//4PHHTQQfu3CBERERERkS6moEF6tW3btnHN1VezafNmhiX7OWVAE2m2b15FYn9Y2uTiX9syiGLil3PmcPrpp2Pa1+6TIiIiIiIi3YyCBum1li5dyq+vu47mlhYOyW7jmH4t+30Uwzep8Nr4R0UWLSEzJ5xwAr/61a+w2+2JLktEREREROR7U9AgvdKrr77KHXf8ESMS4aT8RiZm+BJd0i5aQmaeKs9kq8/OAQccwB//+EetSiEiIiIiIj2eggbpVSKRCH/729945plnSLIanFFQT2EnLlvZ2UJReLkynaVNbnJzcvjTnXdSWlqa6LJERERERET2mYIG6TU8Hg833ngj8+fPp58jzFmD68m0RxJd1ncyDPikPok3q9KwO+z8v//3W4466qhElyUiIiIiIrJPFDRIr1BZWck111zDxo0bGZ7s5ycFjTgtPetXe22rg+e3ZuKPmDjnnHP4xS9+gdlsTnRZIiIiIiIie0VBg/R4y5cv59prr6W5uZkZWW38oH/3afq4t2oCVp7akkld0MoRRxzBb3/7W5xOZ6LLEul1DMOgoaGBiooKtm7dyrZt23A6neTn55OXl0d+fj4ZGRlaEUZERERkHyhokB7ttdde44+3304kEuakvCYmZXoTXdL35g2beLoik40eByNHjuTOO+9Uk0iR76GqqopFixaxdevWeLBQUVGBz/ftTWJdTid5+fnk79gGDRrEIYccQm5u7n6qXERERKRnUtAgPVIkEuGBBx7g6aefxr2j6WNRN276uLfCUXilMo3FTUn0y83lrrvvpqSkJNFlifQYXq+XDz74gNdff53PP/+cnf/UOcwGWfYQWfYIWfYwWY4wmfYIoaiJxqCFxpCVhqCFhh3nfZGvpjCZTCYmTpzIrFmzmDlzJklJSYl4eSIiIiLdmoIG6XE8Hg+/+93vmDdvHrmOMGf3kKaPe2vnJpFOl5Nbb72NGTNmJLoskW4rEomwZMkS3njjDT54/338gQAARUkBxqT56OeIhQrJlih7MyPCHzHRELRQ4bOzrMnFZq8DAIfDzqGHzmTWrFlMnjwZq9XaFS9LREREpMdR0CA9SmVlJb/61a/YsGEDw5L9/LQHNn3cW6tbnDy/NYOQYeaKK67gJz/5ieaNi+xky5YtvPbaa7z55hvU1NQCkG0PMz7dy7h0HxmdHEQ2Bi0sa3KxtNlNbSAWLqSnp3P00Udz4oknMnTo0E59PhEREZGeRkGD9BjLly/nuuuupampmelZbRzbg5s+7q1Kn5UnyrNpCZk56aSTuOaaa3T0VPq8devW8dhjj/Hhhx8C4LIYjEnzMj7dS4ErtFejFvaFYUCl38bSJhfLm920hWNTLA455BDOPfdcSktLu7YAERERkW5KQYP0CL2x6ePeagmZebI8k20+OxMmTODWW28lMzMz0WWJ7Hdr1qzhscce45NPPgFgsDvI9Kw2RqT4sSZoRdiIAWVtDj6qTY5PrZg2bRrnnnsuo0ePTkxRIiIiIgmioEG6tWAwyEMPPcQzzzyD27Kj6WNy72n6uLeCURMvbE1nZYuLzIwMfnvjjUydOjXRZYnsFytXruSxxx5jwYIFABS6AxyR20pRUrDLRy/sKcOATR4779WmsNETCxwmT57Mueeey7hx4xJbnIiIiMh+oqBBuq2ysjJuvvkm1q/fQK4jzJmD6sl29L6mj3vLMGBBQ6xJZNiA008/nUsvvRSHw5Ho0kS6xLJly3jsscdYuHAhAMVJAQ7fETB0Z5s9dt6vTaaszQnAgQceyLnnnsvEiRPVZ0VERER6NQUN0u1EIhGeeeYZ/u/vfycUDjMl08MP+rdgN+tXdWdVfivPVWRQHbBRXFzMLbfcQnFxcaLLEuk0S5cu5ZFHHmHJkiUAlCT7OTynjSHdPGD4ugqvjfdrU1jbGgscxowZw/nnn8+kSZMUOIiIiEivpKBBupVt27Zx880388UXX5Bqi3JqfiPDUgKJLqvbCkXhjapUPm1Ixm63cfnlV3Daaafpy4v0aEuWLOGRRx5h6dKlAAxL9nNEbiuD3KEEV/b9VPqsvFeTwupWF6DAQaQrRSIR2traaG5uxufzkZSURHp6OklJSdrfRET2AwUN0i0YhsErr7zCfffei8/vZ2yalx/mN+Pq5UtXdpa1rQ5e3JaBJ2xm+vTp/OY3v1GjSOlRDMOIBwzLli0DoDTFz+E5rRT08IDh67b7rLxXm8KqlljgcMABB3D++eczefJkfQES2QPhcJjNmzezbt061q1bR01NDS0tLbS2tsZOW1po83h2e1+LxUJqaippaWmkpaWRnp5Oamoq/fv3Z/jw4QwfPpzs7GztiyIi35OCBkm4+vp6/vCHPzB//nzcFoMf5jcyJs2f6LJ6nNaQmRe3pbOuzUlmRga/uvZaZs6cqQ9L0q0ZhsGiRYt49NFHWb58OQAjUnwckdvGAFfvChi+7uuBw+jRo/nFL36hwEFkJ16vl/Xr18dDhXXr1rFxwwaCoV3fH5wWA6c5gtsSxWUxcFmiuCxR7GaDQNSEN2zGG2nfLHjDJqLsuq9lZmYwfHhpPHgYPnw4eXl52i9FRPaCggZJGL/fzyuvvMJjjz5Kc0sLw5L9nDqgiVRbNNGl9VhRAz6tT+KN6jQiBowoLeWCCy9kypQp+oAk3UooFOLDDz/kn//8JytWrABgZIqPI3JbyXeFE1zd/rXdb+X9mhRW7ggcRowYwWmnncaRRx6pJq/S5/h8PpYvX87ixYtZvHgx69Z9STT61UdVq8mgvzNEvjNEvitEnjNEpj2CyxLFspd/5gwDAlETnrCZ+qCVSr+NbT4blX4bDUFrh9umpqYwbtyBTJgwgUmTJlFYWKi/qyIi30JBg+x3Ho+Hf/3rXzzzzNM0NjbhsBj8oF8zkzO83WaJup6uLmDhvZoUlje7MYjNBb/wwguZMGFCokuTPq66upp///vfvPLKv2loaARgVKqPw3P6XsDwdVU7AodVrS6iBqSlpnLCiSdyyimnkJ+fn+jyRLpEMBhk5cqVLFmyhMWLF7Nq1UrC4dgKU1aTQYEryEBXiDxXLFzIdoT3OlDYF76IicodoUOlz0aFz079TuFDZmYGEydOigcP2kdFRDpS0CD7TWtrKy+88ALPPfssLa2tuCwG07JamZ7lUS+GLlLtt/LuTkdKJ06cyEUXXcTo0aMTXJn0JdFolEWLFvGvf/2LTz75mGjUwG0xmJDh4aAMD1latraD5pCZ/zUksagxibawGZPJxLRp0zjttNM46KCDMJvNiS5RZJ9FIhHWrVvHokWLWLx4McuXLyMQiK0kYzbBQGeQ4uQAxUkBBrmD2LrRr3tzyMyGNgcbPLGtOWSJX5eX15+JEycxceJEJk6cSFZWVgIrFRFJPAUN0uWampp47rnneOGf/8Tj9ZJkjTIjq40pmR6cChj2i20+G+/UpPDljuX1pk+fzi9+8QtKS0sTXJn0Zo2Njbz55pv866WXqNi6FYACV5ApmR4OSPN1qy8Q3VE4CitbXHzWkMQWrx2AgQMHcsopp3DkkUeSm5ub4ApFvpthGFRUVLBw4UIWL17MkiVLaG1tjV+f5wxRnBSgODlAoTuIo4d8LjAMqA9aYqHDjvDBG/nqTa2oqIhJk2LBw/jx40lKSkpgtSIi+5+CBulS//jHP3j0kUfw+f2k2KIcktXK5EwvdrN+7RJhi9fGO9WpbPDE5n0XFxdz2GGHMXPmTIqLizXfVL4XwzAoKytj/vz5zJ8/n1WrVmEYBjazwdg0L1Myvb2+wWNXqfRZ+awhiWXNbkLR2H5aUlLCwQcfzIwZMygtLdVIB+kWotEoW7ZsYcWKFSxbtozFixdRU1Mbvz7LHqY4KcDQ5ABFSUGSrL2jL1PUiI0iXO9xsL7NwWavg+COfdVsNjNy5EgmTpzI2LFjGTlyJGlpaQmuWESka3X7oMFkMvHyyy9z0kknJboU2QdHHnEEIV8rx/RrYWKGV0cwu4mNbXbm1yexzuMkvOODUEHBQGbOPIzDDjuMESNGKHSQPeLz+Vi0aBELFixg/vx51NbWAbEh0EPcAUam+hmf7tX0qE7ii5hY3uRiTauTjR4HYSO2n2ZlZjJ9xgxmzJjBpEmTcLlcCa5U+oqWlhZWrVrFypUrWblyJatWruywtGSyNUpxkp+hyQGKk4Jk2PvGVKlwFLb67Kz32NnQ5qDC5yCy09vgoEGDGD16NKNGjWL06NEUFxdjtVq/+QFFRHqYhAcNVVVV/P73v+e1115j27Zt5ObmMm7cOObMmcMRRxyhoKGHO+Lww0k3mrisuC7RpeyTe8ty8ER6cTpiQNgw7dgAvjr6YrfbsdlsWCwWHSmVuEgkQiQSIRwOE4lECO20xJwJA4sp1sDNYjJ6dHPXJEuUOSW1333DBApETGzwOFjT6mBtq4u2cGw/tdvtjBkzhmHDhlFSUkJJSQlDhgzRlxj5XsLhMNu2bWPz5s1s2bKFTZs2sXr1arZs2dLhdrmOEINcQQrcIQa5g/RzhHv0e0FnCUZNbPbYKffZqPDaqfDZ8e30+cLpcDBi5EhKS0sZPHgwQ4YMYfDgwaSnpyv4lz4jFArh8/nw+/3x0/bPG9FoNP75o/18NBrFMAysVisWiwWr1dpha7/M6XTidrtxOp3Y7XbtU/tJQj91bN68menTp5Oens6dd97JAQccQCgU4q233uLSSy9l7dq1iSxPBE/ETFs41uzpkUceAeD8889PZEn7RTQaxe/34/f7E12K9CAGscCq/Si7dC2HxWBkqp+RqX6iRjPbfDbWtjpZ0+pkyY6lAdvZrFaKiovjwUNJSQl5eXlkZWVht9sT+CqkO/F6vdTV1VFfX09VVRWbN2+OBwtbt24lHO64MozLYlCSHGvaOMgVosAd1Oilb2A3GwxLCTAsJQDEejzUBS1UeO2U++xUeIMsX7qUpUuXdrhfamoKgwfHQof2rV+/fmRlZZGRkYHFYtnd04nsV6FQiLa2tvjW2tra4WePx9Ph5/bN6/XGAgWfD5/fTyTS9SOezGYzbpcLl9sdDx/cbjfJycmkpKSQlJTU4TQ5ObnD+fZNfzu/W0KDhksuuQSTycTChQs7NMkZNWoU5557bvznuro6Tj75ZN566y0GDBjA3XffzYknngjEjq5dcMEFvP/++1RVVTFo0CAuueQSfvnLX8bvP3v2bJqampgxYwZ33303wWCQn/zkJ9x7773YbDYAtm/fzvnnn8/7779P//79+f3vf88NN9zAnDlzmDNnDhBranjNNdfwyiuvEAgEmDhxIvfccw9jx47t8Dz//ve/4889Z84cli1bxocffgjAzJkz4x3/n3rqKWw2GxdffDG33HKL0jUREdknZhMUuEMUuEMc1a+VQMREVcDKdp+N7f7YtrFsLV9++eUu901PSyM7J4fs7GxydpxmZ2eTkZGBe8cHMZfLRVJSEi6XC7fbrSNC3ZhhGAQCAbxeLx6PB4/Hs8v5trY2GhoaqK+vjwcLdXW1eL2+3T6m2xJlgCNEbkqYHEdsy3WESbdFMOvXYJ+YTJDjiJDj8DE+I/bvHoyaqPZbqQ1YqQ3uOA2EWL2yhRUrVuzyGGaziYz0DLKys8nKyopvmZmZJCUlxfffnc+3/6wRTn1T+0jEQCBAIBDA7/fHz+/8s9/vj79v7O60/X3E09ZGa1trfOWYveG0GNjNUewmg1RzlGyHgd0c22w7Tu07jZA0mwzMxP7e7XweYj1SIoYpfhoBooaJyI6fQ1ETwZ22QMRPsLmZxkYTQcNMIGJibyNSu91OcnISyclfBRA772ftfzvb9zmXy4XL5cLhcHzr1ptGESfsXaahoYE333yT3//+97vtxJuenh4/f/PNN/OnP/2JO++8k/vvv58zzjiDLVu2kJmZSTQaZeDAgbzwwgtkZWWxYMECLrjgAvLy8jj99NPjj/HBBx+Ql5fHBx98wPr16/nxj3/MuHHj+MUvfgHAWWedRV1dHR9++CE2m42rrrqKmpqaDjX96Ec/wuVy8cYbb5CWlsbf//53jjjiCNatW0dmZuYev/YnnniC8847L96B+YILLmDQoEHxWr6ufeffWfsvo4iIdD5v2Mz967MTXUanyrGHCO/4wBUyTPEPZW0tTTQ3N7F+/fpElygJYib2Yd5hBospNgXKYjKw7pgKZTYZhKImtvlsbPPZEl3uPslxhPlJQVOiy/hWdrMRDwx3FjGgMWiJBxAtIQut4diIy9a2asqb61m3TomP7D82s4HDbOAyR8i1GDiTozjNBi5LFKcldt5pieK0GDjNO04tUVw7LrebjW4VUhpGLOjzRUz4o2b8ETP+qAlfxIw/Yor/HDttvyyI3+OhqaWOqqg53vz1+zCbzbz88sv069evE15V4iUsaFi/fj2GYezR8nqzZ8/mpz/9KQB/+MMf+Mtf/sLChQuZNWsWNpuNm2++OX7bwsJCPv30U/75z392CBoyMjL461//isViobS0lOOOO4733nuPX/ziF6xdu5Z3332XRYsWMXHiRCA2TL6kpCR+/3nz5rFw4UJqamriX/Dvuusu/v3vf/Piiy9ywQUX7PFrLygo4J577sFkMjF8+HBWrFjBPffc841Bw+23397hNQL87ne/46abbtrj5xQRkT0XxUSlX8MipW+IYiJqmNjrQ3qyX1hMkO2IkO2IUBIN0BY20xqOhQ3tpw1BK9v9Nqr8PTMIku7LhEGKNUqqLUKqNUKqrWOY4LJEY6HD1y6zmugx/VlMpth0xNjyuh1XwjEMCBt8LXzYKXjYEU54I2ZaQ2Za2vfNkIUoe/cPEI1Gqa2tVdDwfe1ND8oxY8bEzyclJZGamtphtMHf/vY3HnvsMcrLy/H5fASDQcaNG9fhMUaNGtVhHlteXl58GNqXX36J1Wpl/Pjx8euHDh1KRkZG/Ofly5fT1tZGVlZWh8f1+Xxs2LBhj18LwJQpUzoMOZ06dSp33303kUhkt3Ptrr/+eq666qoOl2k0g4hI1zFj0N/ZO5bijI9i2DGSIRQ1feuHH5PJFG+i1d4M1mQyYTabd9lMJlOHrf3+X79Mvp/2z0w7n37bFo1Gd7u1N09rP/9tTBhY20c1mA1sJgOrOXZZT5TjCH/3jboJw4j1iIpNnbBSF7BSs2MqRWPQ+q15kMNhJyM9g6Qdw7iTkpJ2mTrRPi/dZrNhtVqx2+1YrVZsNlv8fPt7wO7291iNxnfu3991mz19jO5if73enf+Nv+k20Wg03hSxfX/+esPEUChEKBTa7flgMBifIrHzdImdL9t5qkRLMEhLeO/6gVhMBk6LgcMcxbXTqIb4aAezgWPH6Aab6atpE7EtGp8+YTF91WzaxI5pEyYw81WQYRixkT+x0HTH9AkjNqUiytemTewYfRA7byIYMROImnYKDsz4vjZ6IbIPvafsNltsf9ux/+08dcJut+922kRubi4jR47c6+fqrhIWNJSUlGAymfao4WN7H4V2JpOJaDSWNj333HNcc8013H333UydOpWUlBTuvPNO/ve//+3xY+yJtrY28vLy4r0WdtY+zcNsNu/yprBzR/Z9pWkSIiL7l9sa5fKhPW+1HE/YzJetDrZ47bGjmwEboa8N58zPy2NoSQn5+flkZWV16M2Qk5OD2+1WQNAHRCIRmpqadurRUBff6uvr2b59O+VbtuALBDoc4DMDmfYwOY4Q+a6QmkB+Tzs3hazw2an02agLWvHuZsWrrKwsDhw8mP79+5OZmUn213ozZGdna/+VLhEOh3fbo2F3W3sjyNbW1ngTyMa2Vrye3feA+T52RDIYezly4Lu4XC6S05Lpt6Mp5NcbRe7cFHLnbecwT31QEhg0ZGZmcswxx/C3v/2NK664Ypc+DU1NTR36NHyT+fPnM23aNC655JL4ZXs7wmD48OGEw2GWLl3KhAkTgNjUjsbGxvhtxo8fT1VVFVarlSFDhuz2cXJycli5cmWHy5YtW7ZLyPH1EOSzzz6jpKREnYO7oSTLV5+u5lx0DgDJvfB9I2KYCEdjRz53frPe+ahG+6YPMH2PYRgdlrRsP78zM18d7exO8y731c77fndmGFATsLKm1cnaViflXnv8aKfNaqWopLjDMpdDhw4lJSUloTVL92CxWOJfUL9JNBqlurqaLVu2xFefaF+JYk1jI2taXfHbfn1Zy1xHuFe8F3Q2X8S0I1SwUe61s9Vn7xAqWK1WCgYVdFhlon1LTk5OYOXSl1mtVlJTU0lNTd3nx4hEIni93g4BRHzViR3LWX59aUufzxf/3LHztvMoDiC+jOXXl7hs/7l9NEH7tvMIg/af28MCNUvtPAn9V/zb3/7G9OnTmTx5MrfccgtjxowhHA7zzjvv8OCDD7JmzZrvfIySkhKefPJJ3nrrLQoLC3nqqadYtGgRhYWFe1xHaWkpRx55JBdccAEPPvggNpuNq6++GpfLFf9SdeSRRzJ16lROOukk/vSnPzFs2DAqKyt57bXXOPnkk5k4cSKHH344d955J08++SRTp07lH//4BytXruTAAw/s8Hzl5eVcddVVXHjhhXz++efcf//93H333Xv3j9eD+COxbq6OHni0Y05JbaJL6BKGAZu9dla2OFnV4qItHPuQ43a7mDHjYGbOnMnUqVNxuVzf8UjSV0UiEbZs2cKnn37K/PnzWb58OcFIhCCQZoswPNlPaYqf4uQgdnPP2/e7s3AUNnkdrGlx8GWbi4ZgLKQ2m80cOH5c/O9qYWGhPizJ92I2m8nLyyMvL48pU6Z0uK6pqYk1a9awcuVKVqxYwapVK1nc5GVxU+x6h9mgwBWgODlIcVKAAa5QnwwefBETGz0O1rc52OixUxPoePCpoKCAQ0ePZtSoUYwePZqhQ4dqv5VeyWKxkJKSorC7D0noO1lRURGff/45v//977n66qvZvn07OTk5TJgwgQcffHCPHuPCCy9k6dKl/PjHP8ZkMvHTn/6USy65hDfeeGOvannyySc577zzOOSQQ+jfvz+33347q1atwul0ArGpFq+//jq/+c1vOOecc6itraV///4ccsgh8YYdxxxzDL/97W+59tpr8fv9nHvuuZx11lm7LEl01lln4fP5mDx5MhaLhV/+8pd71UyyJ8nLy2P9Bi9/WtefaVmtTMvyaHhlAhkGfNnm4J3qlHiju9TUFI4/5lAOO+wwJk2apHWBZY9YLBaKioooKirijDPOoLW1lf/9738sWLCABQsWsLCxiYWNSTjMBgemezko00N/Z8+ZI90dVfutfNaQxLJmN/5I7BtbSkoyR8+cxowZM5gyZcr3OtoksjfS09OZOnUqU6dOBWKjHzZv3szKlStj24oVbNi8mfWe2Ocol8WgKMlPcVKAockBsu2RHtMobm+EorDZ62BDm531HgeVvq9GGbndbg466ABG7wgWRo0aRVpaWkLrFRHpKiajO3VZ6Ua2bt1KQUEB7777LkcccUSnPe7MmTMZN24c9957b6c9Znfm8Xh48cUXefaZZ2hqbsZpMZia2cb0LA9J1p4xNLk3MAzY4LHzdnUqFT47ZpOJo485huOOO44DDzxQR0+kU0UiEdasWcO8efN48803qaqqAqDQHeCgTA+jUv1Ye88y0V0qYsDqFiefNSSx0RPr1dO/f3+OOOIIpk+fzpgxY7T/SrfV3NzMkiVLWLRoEYsWLWLr1q3x61JtkVjokBSgODlAmq1nfiaIGLDVZ2Njm4P1HgflXjvhHY3jbFYrY8aOZeLEiUyaNInS0lLtryLSZyho2OH999+nra2NAw44gO3bt3Pttdeybds21q1bt0uPhe+jrwUN7Xw+Hy+//DJP/+Mf1Dc0YDcbHJTp4eCsNlJ66IeLnmKzx847NSnxLylHHHEE559//l5NLxLZV5FIhE8//ZSXXnqJzz77DMMwSLZGmZThYXKGl3T7t3e+76taQmYWNbpZ2JhMSyiWykyZMoVTTz2VadOmqaeP9EhVVVUsXryYhQsXsnjxIhoavuqFlWUPMzQ5QHFSgMKkIMnd9GBE1IiNLtrgiQULmz0OAtGvVlwpLS2NBwtjxoyJj4wVEelrFDTs8NZbb3H11VezceNGUlJSmDZtGvfeey+DBw/u1Ofpq0FDu0AgwKuvvspTTz5JdU0NVrPB5AwPR+S04rbqV7EzbfXZeKc6hXVtsQ85Bx98MBdccAElJSUJrkz6qm3btvHyyy/z6n/+Q3NLCyagNMXHwdkeCpOCiS6vW9jitbGgPpmVLS6iBiQnJXH8CSdwyimnMGjQoESXJ9JpDMNg06ZNLF68mCVLlrBkyRLa2tri1/d3hihOClCUFGSAK0iqNZqQqRbhKFQHbGz12djQ5mCj14En/NWQrMLCIUyYEAsWDjzwQE1fEhHZQUGDJEQoFOL111/niSeeoLKyklRblFPzGxmWEkh0aT1eW9jMK5VprGyJNXI86KCDuOCCCxg1alSCKxOJCQQCvP/++7z00kvxlXqKkgIckdtKUR8NHDZ77LxXk8L6HSOPSkpKOPXUUznmmGPUlFX6hEgkwrp16+LBw7KlS/EHvvpMkGSNku8MkucMke+MLa2ZZY90aoPJYNTEdr+VbT4blT47lX4b1QEb0Z0+Kefl9WfixElMnDiRiRMnfuuqHSIifZmCBkmocDjMs88+y//9/e+EwmGmZHr4Qf8WdanfR1+2OnhxWwZtYTNjx47loosu2mXVE5HuZNWqVTz22GPMnz8fiPVxODK3laLkvhE4bPbYebcmhQ07AoYpU6Ywe/Zsxo4dq6VkpU8LhUKsWrWKZcuWsW7dOtatW9ehxwOA3WzQ3xEi0x7GZYnithi4LNH45rZGcZkNHJYo/ogZT8SMN2zGG9lpC5vxRkzUB63UBmzs/OnD5XQybPhwhu/YDjzwQPLz8/fvP4SISA+loEG6hbKyMm6++SbWr99Atj3MjwY2MsgdSnRZPUYoCm9Wp7KgPhmb1cpll1/Oj370I8xmddyTnmHNmjU8+uijzJs3D4gFDu0jHHrj9+1NO0Yw7BwwnH/++YwePTrBlYl0Xx6Ph7Kysnjw8OWXX7Jp0ybC4e+/ok1ycjKlpaXxUGH48OEMHDhQ/VBERPaRggbpNoLBII8++ihPPfkkhmEwM6eVw3Na1Z3+O1T7rTy3NYMqv43CIUO45dZb1YdBeqy1a9fy2GOP8fHHHwMwZEfgUNxLAoevBwxTp07lvPPOU8Agso9CoRCNjY20trbS0tISP91583q9JCcnk5aW9o2b2+3WKCIRkU6koEG6neXLl3PzzTdTWVlJvjPE6QMb6ef8/kcrehvDgM8a3LxenU44CqeddhqXXXaZOlxLr/Dll1/y2GOP8dFHHwEw2B3k8JxWSpIDPS5wMAzY6LHzfu1Xq79MmzaN8847T71TREREpFdS0CDdktfr5f777+fll1/GaoJZ/ZqZluXpcV8wukpb2MxL29JZ2+okPT2N3/72RqZPn57oskQ6XVlZGY8//jjvv/8+AANdQY7IbWV4DwgcDAPK2hy8X5vCFq8dgOnTp3PuuecqYBAREZFeTUGDdGsLFizg97fdRn1DAxPSvZyU39Tnp1JsbLPz3NZMWsNmpkyZwm9/+1t1vZZeb8OGDcydO5d3330XwzDIdwY5IreNESn+bhc4GAasbY0FDFt9sYDh0EMP5ZxzzqG0tDTB1YmIiIh0PQUN0u3V19dz7bXXsmrVKoa4A5wxqJFkazTRZSXEogY3/96ejsVi5dLLLuP0009Xw0fpUzZt2sQTTzzB22+/RTRqkOcMcXhOKyNT/Z26zN2+iBqwusXJB7UpVPptmEwmjjjiCGbPns3QoUMTW5yIiIjIfvS9goZgMMimTZsoLi7GarV2Zl0iHQQCAf7whz/w1ltvkWGPcNagevr3ob4NUSO2qsQndcmkp6dxxx1/YuzYsYkuSyRhysvLmTt3Lm+++SbRaJR0W4QD070cmO4lxxHZr7U0Bi0sa3KxtNlNbcCK2Wzi6KOP4eyzz6awsHC/1iIiIiLSHexT0OD1ern88st54oknAFi3bh1FRUVcfvnlDBgwgF//+tedXqiIYRg88cQTPPTQQzjMBj8e2MCI1ECiy+pygYiJ57ems6bVReGQIdz95z9rHW+RHbZt28Y//vEP3nn7bdo8HgAKXEEmZHgZk+bDZemaQXu+iIkVzS6WNrnY7I01eHQ47Bx99DGcddZZFBQUdMnzioiIiPQE+xQ0/PKXv2T+/Pnce++9zJo1iy+++IKioiJeeeUVbrrpJpYuXdoVtYoA8MEHH3DzTTcRCASY1b+Zg3txk8imoJkny7PY7rcxZcoUbrvtNpKTkxNdlki34/f7mTdvHq+//jqfffYZ0WgUiwlGpPgYn+5lWEoAy/d8nwhH4cs2J0ubXKxtdRExwGQyMXHiRH7wgx9w6KGHkpSU1DkvSERERKQH26egYfDgwTz//PNMmTKFlJQUli9fTlFREevXr2f8+PG0tLR0Ra0icV9++SW/uuYaampre22TyAqvjafKs2gNmznttNOYM2eOpiiJ7IH6+nreeust3njjDcrKygBwWgyy7SGy7GGy7JHYqSN2PskSjYeVUSO2qktD0EpjyEJD0ELjjvPb/XZ8kdgNS0pKmDVrFkcddRS5ubmJeqkiIiIi3dI+BQ1ut5uVK1dSVFTUIWhYvnw5hxxyCM3NzV1Rq0gHdXV1XHfddb2ySeSKZif/3JZJ1DBx5VVX8aMf/SjRJYn0SGVlZbz22mssXLiQrVu3EgwGd7mN02KQaQsRMkw0Bq2EjV2HPpjNJvLy8jnssMOYNWuWmjuKiIiIfIt9ChoOOeQQfvSjH3H55ZeTkpLCF198QWFhIZdffjllZWW8+eabXVGryC78fj9/+MMfePvtt3tFk0jDgA9rk3m7JpUkt5vbfv97pk6dmuiyRHqFaDRKXV0dW7dupaKigq1bt3bYHA4H+fn5Hba8vDwGDBhAv379sNlsiX4JIiIiIj3CPgUN8+bN4wc/+AE///nPmTt3LhdeeCGrV69mwYIFfPTRR0yYMKErahXZLcMwmDt3Ln//+99xWAx+MrCB0pSe1yQyGDXxr21pLG92k9e/P3f/+c8UFRUluiwREREREZG9sk+z2mfMmMGyZcsIh8MccMABvP322+Tm5vLpp58qZJD9zmQycc455/CHP/wBrA6e3JLFJ3VJ7PvCrftfc8jM/23KYnmzm3HjxvHoY48pZBARERERkR5pn0Y0iHRXa9eu5VfXXENtXR2TMjycmNfc7ZtEbvHa+Ed5Fm1hMyeddBJXX321hmiLiIiIiEiPtc9BQyQS4eWXX2bNmjUAjBw5kh/+8Ifqii8JV1tby7XXXsuaNWso3NEkMqmbNolc0uji5coMDJOZq666ilNPPRVTb12rU0RERERE+oR9ChpWrVrFiSeeSFVVFcOHDwdg3bp15OTk8OqrrzJ69OhOL1Rkb/j9fm677TbeffddMnc0iezXjZpERgx4syqVefXJpKak8Ifbb2fixImJLktEREREROR726egYerUqeTk5PDEE0+QkZEBQGNjI7Nnz6a2tpYFCxZ0eqEie8swDB599FEeeeQRnBaDH3eTJpG+iIlnKzIoa3NSWFjIXXfdxYABAxJdloiIiIiISKfYp6DB5XKxePFiRo0a1eHylStXMmnSJHw+X6cVKPJ9vfvuu9xyyy0Eg0EmZng4tn8LLktiWpNU+a08XZFJXcDKwQcfzE033URSUlJCahEREREREekK+9Qmb9iwYVRXV+9yeU1NDUOHDv3eRYl0piOPPJJHH32U4cOHs7gxiT+X9eOLZud+XZXCHzHx2vZU7t+QS13AyuzZs7njjjsUMoiIiIiISK+zTyMaXn/9da699lpuuukmpkyZAsBnn33GLbfcwh//+EdmzJgRv21qamrnVSvyPYTDYZ5//nn+7//+TiAQZESKnxPzmki3d12jSMOApU0u3qhOoy1spmDgQK66+mqmTp3aZc8pIiIiIiKSSPsUNJjNXw2EaO+Q3/4wO/9sMpmIRCKdUadIp9m2bRt33HEHCxcuxGE2OLpfM1MyvZg7ebGHSp+V/2xPY4vXgdPh4NzzzuMnP/kJdru9c59IRERERESkG9mnoOHDDz/c4yX4Dj300L0uSqSrGYbBm2++yb333ENzSwsFriCnDmjqlJUpvGET79Sk8r+GJAxiUzeuuOIKcnNzv3/hIiIiIiIi3dw+BQ0ivUVjYyP33Xcfb775JhYTDE3yU5wcoDgpQH9neI9HOUQNqA9aKGtz8H5tGp6wicLCQq655homTJjQtS9CRERERESkG9mnoKGwsJBzzjmH2bNnM2jQoK6oS2S/+uyzz/jb3/5GWVlZ/DK3JUpRUix0KE4OkG2PYDLFQoXagJVtPhuVfhvbfDa2++0EorFUIsnt5hcXXMBpp52G1WpN1EsSERERERFJiH0KGu69917mzp3LypUrOeywwzjvvPM4+eSTcTgcXVGjyH5TX1/PkiVLWLRoEUsWL6Zy+/b4dWm2CKnWCFUBG6HoV0MdzGYzRUVFlJaWMnz4cA4//HCysrISUb6IiIiIiEjCfa+pE59//jlz587l2WefJRKJ8LOf/Yxzzz2X8ePHd2aNIglTWVnJ4sWLd2yLaGlpjYcK7cHC0KFDFbKJiIiIiIjs0Ck9GkKhEA888ADXXXcdoVCIAw44gCuuuIJzzjlnj5tGinR3hmEQiUQ0HUJERERERORbfK+gIRQK8fLLL/P444/zzjvvMGXKFM477zy2bt3K3/72Nw4//HCeeeaZzqxXRERERERERLqxvQoannzySX784x+zatUqHn/8cZ599lnMZjNnnXUW559/PqWlpfHbrly5kkmTJuHz+bqkcBERERERERHpfvYqaLBYLGzfvp28vDyOOuoozjvvPE466SRsNtsut/V4PFx22WU8/vjjnVqwiIiIiIiIiHRfexU0mM1mqqqq8Pl8DB48uCvrEhEREREREZEeyLy3dzCZTAoZRERERERERGS39npEw+jRo7+z6/7nn3/+vQsTERERERERkZ5nr9fpO+aYY0hOTu6KWkRERERERESkh9unHg25ubldWZOIiIiIiIiI9FB71aPBZDJ1VR0iIiIiIiIi0gvsVdCwF4MfRERERERERKQP2qugYdOmTeTk5HRVLSIiIiIiIiLSw+1Vj4Z2kUiEuXPn8t5771FTU0M0Gu1w/fvvv99pBYqIiIiIiIhIz7HXq04A/PKXv2Tu3Lkcd9xxjB49Wr0bRERERERERATYxxEN2dnZPPnkkxx77LFdUZOIiIiIiIiI9FB71aOhnd1uZ+jQoZ1di4iIiIiIiIj0cPsUNFx99dXcd999WoVC+gTDMNiyZQtNTU36nRcREREREfkOezx14pRTTunw8/vvv09mZiajRo3CZrN1uO5f//pX51UokiDhcJj33nuPf/zjH5SVlQGQkpLCoEGDGDRoEAUFBRQUFMTPu93uBFcsIiIiIiKSeHvcDDItLa3DzyeffHKnFyPSHfh8Pv7zn//w7LPPUlVVhclkIjenBACvt5E1a9ayatWqXe43ceJEbrjhBvLz8/d3ySIiIiIiIt3GPjWDFOmNGhoaeOGFF3jppZdoaWnBYrExIO8ABhVMwOX8KmgzDAN/oAWvtxGvtxGPr5HW1hqamrfidru5+uqrOfbYY7Uai4iIiIiI9En7FDRs2rSJcDhMSUlJh8vLysqw2WwMGTKks+oT6XLV1dXMnTuX1157jWAwiN3upmDAeAoGjMVmc+3x42yvXsPade8SDgc47LDDuO6660hPT++6wkVERERERLqhfWoGOXv2bBYsWLDL5f/73/+YPXv2961JZL9ZvXo1Z599Ni+//DJWi5sRw45ixpRfUDRkyl6FDAB5/UYwddLZZKQX8MEHH/Czn/1st/uJiIiIiIhIb7ZPIxpSU1P5/PPPd1nicv369UycOJGmpqbOqk+ky8yfP58bbvgNwWCQ4SWHMTB/LCbTPmVvHRiGQfnWJazf+AnRaIRTTjmFyy+/HJdr74ILERERERGRnmifvlWZTCZaW1t3uby5uZlIJPK9ixLpaq+88gq/+tWvCIcjjB39QwoGHNgpIQPE9o/BBRM5aMLPSUnO4V//+hdnnXX2bhtIioiIiIiI9Db7NKLhhBNOwOVy8eyzz2KxWACIRCL8+Mc/xuPx8MYbb3R6oSKdwTAMHnnkER599FHsdjfjDjiZtNS8Lnu+aDTMhk3z2Vy+GIvFzM0338yRRx7ZZc8nIiIiIiKSaPsUNKxatYpDDz2U9PR0Dj74YAA++eQTWlpaeP/99xk9enSnFyryfYXDYe644w5effVV3K50Dhx7Gm5X+n557obGcpavfIVoNMRNN93E0UcfvV+eV0REREREZH/b5+UtKysr+etf/8ry5ctxuVyMGTOGyy67jMzMzM6uUeR783q9/OY3v+HTTz8lNaU/B445BbvdvV9raG6pYunyF4lEg/z2t7/lBz/4wX59fhERERERkf1hn4KG8vJyCgoKMJlMu71u0KBBnVKcSGeor6/n6quvYe3aNWRnFTFm1PFYLPaE1NLSWs3ny18gHA7wm9/8huOPPz4hdYiIiIiIiHSVfQoaLBYL27dvJzc3t8Pl9fX15ObmqiGkdBtVVVVceumlbNu2jQH5YygtORKzuXOaPu6r1rYaPl/2AqGwn1//+tf88Ic/TGg9IiIiIiIinWmfvnEZhrHb0QxtbW04nc7vXZRIZ6iuruaSSy5h27ZtFA2ZxohhRyU8ZABISc5lwrjTsdlc3H777bz88suJLklERERERKTTWPfmxldddRUQW77vt7/9LW73V3PcI5EI//vf/xg3blynFiiyL2pqarj44ouprKxkaOEMCodMSXRJHSQn5zBh3Ol8vuwF7rjjDiKRCKeddlqiyxIREREREfne9ipoWLp0KRAb0bBixQrs9q/mudvtdsaOHcs111zTuRWK7KWdQ4biwundLmRol5yUzYRxp7Nk+QvcddddhMNhfvKTnyS6LBERERERke9ln3o0nHPOOdx3332kpqZ2RU0i+6ympoZLLrmUrVsrKBoyjeLCaYku6Tt5vI18vux5/IE2LrvsMn7+858nuiQREREREZF9ts/LW4p0N7W1tVxyySVUVFRQNGQqxYXTE13SHvP6mliy7J/4/S1ccMEFnHPOObvtgyIiIiIiItLd7XHQcMoppzB37lxSU1M55ZRTvvW2//rXvzqlOJE9VVdXx8UXX0xFRQWFg6dQXDi9x31R9/mbWbLsBXy+Js4++2wuuuiiHvcaRLq7uro6qqqqaGxspLGxkaamJhoaGuLnGxsbcTgcjBkzhnHjxjFmzBjS0tISXbaIiIhIj7LHPRrS0tLiX3raz2swhHQH9fX18ZEMPTVkAHA505h44I/5fNkLPPHEE/j9fubMmdMjX4tId+LxeHjvvfd4/fXXWbZs2bfe1mp1EImEWLFiBU8//TQARUVFjBs3Lr59fWlnEREREelor6ZORCIR7rrrLv7zn/8QDAY5/PDDuemmm3C5XF1Zo8g3qqur49JLL2XLli0MGXQQQ4tm9Pgv5sGghyXLX6StrZaTTz6ZX/3qV91iWU6RniQSibBkyRJef/11PvjgAwKBAGAiM2MQqSn9sNvd2G3u+KnN7sJuc2E2W4lEQjS3bKepeRuNTVtpbqkkEgnFHzs/P59TTjmFk08+maSkpMS9SBEREZFuaq+ChltvvZWbbrqJI488EpfLxVtvvcVPf/pTHnvssa6sUWS3Nm7cyJVXXkl1dTVDBk1maNHBPT5kaBcK+fh8+Yu0tFZz7LHHcsMNN2C17tUiMSJ9Unl5Oa+99hpvvPEmNTXVALjdmeT3H0Vev5E4nSl7/ZjRaJTWthqamrfS1LSNhqYthMNBkpKSOe20Uzn99NPJysrq7JciIiIi0mPtVdBQUlLCNddcw4UXXgjAu+++y3HHHYfP59MRV9mvFi5cyK9/fT1er4ehRQczZNDkXhMytAuFAyxd/hLNLZUcccQR3HzzzQobRL7BunXr+Pvf/878+fMBsFmd9MsdTn7/0aSm9u/U94dQOMC2bcsp37qEQNCDzWbjhBNO4IwzzmDAgAGd9jwiIiIiPdVeBQ0Oh4P169dTUFAQv8zpdLJ+/XoGDhzYJQWKfN1//vMf7rjjDgwDRo84ln65wxNdUpcJh4MsW/EyjU0VHHzwwfz+97/HbrcnuiyRbmPLli08/PDDvPvuuwBkpBcwcMBYcrKGYrF0bTAXiYTZXr2aLeUL8fqaMJvNHHHEEZx55pkMGzasS59bREREpDvbq6DBYrFQVVVFTk5O/LKUlBS++OILCgsLu6RAkXbRaJSHHnqIJ598ErvNxdgDTiY9LT/RZXW5SCTE8pWvUN+wmYkTJ3LbbbeRnp6e6LJEEmr79u089thjvPbaa0SjUdJS8xhadDCZGYP2ey2GEaWmtoxN5QtpbY1N15gxYwYXXXQRQ4cO3e/1iIiIiCTaXgUNZrOZH/zgBzgcjvhlr776KocffniHhlha3lI6m9/v59Zbb+W9994jyZ3JuDGn4HalJ7qs/SYaDbNi9WvU1JaRnZ3NLbfcwvjx4xNdlsh+V19fzxNPPMG//vUy4XCI5KRshhYdTHZWUcKnTxmGQUNjOZu2fEZjUwUmk4kf/OAHnH/++eTn9/5QVERERKTdXgUN55xzzh7d7vHHH9/ngkS+rrGxkV/96lesXLmSjPSBjB39Q2y2vrfSiWEYlFcsoWzjx5hMcN555zF79mwsFkuiSxPpcs3NzTzzzDM899zzBAJ+3K50igqn0z+3NOEBw9fFAoctlG34hNa2aqxWG6eeegqzZ88mIyMj0eWJ9Hp+v5/t27fT3NyMy+XC5XLhdrtxu904nU71FRMR2Q/2KmgQ2d82b97MVVddRWVlJXn9RzJy+DGYzX37i3Vzy3ZWrP4vPl8zEyZM4KabbuownUmkN2ltbeW5557j2Wefxev14nSkUDhkKvn9R3X79wLDMKiu+ZINm+bh9TXhcrk444wz+OlPf6plMUW+p+bmZsrLy9m6dSuVlZVs27YtvtXV1X3rfZ1OJ263m6SkJIqKihgxYgQjR45kxIgRpKTs/co0IiKyKwUN0i35/X6efvppnnjiCYLBIEVDplE0ZGq3O3KZKKGQn9Vfvk1N7TrS09P53e9+x9SpUxNdlkin8Xg8PP/88zz99DN4PG047EkMGXwQA/LGdHmTx84WjUbYtn0FmzZ/SiDoIT09nXPOOYcf/vCHOJ3ORJcn0iP4fD6WLVvG4sWLWbhwIWVlZbvcxmQy43Sm4nKm4XKlY7e5iEbDhCMhIpEgkR2n4XDsfDjsJxD0dHiMQYMGxUOHUaNGMWzYMDVhFhHZBwoapFsxDINPPvmEe+65l+3bK3E6khlWcjj9ctTB/esMw2Br5XLWrf+AaDTCz3/+cy666CItgSk9mtfr5cUXX+Qf//gHLS0t2O1uhhRMZuCAsVgstkSX971EIkHKKz5nc8UiwuEAqalp/OhHp3HaaadpSoXI14TDYVatWsXixYtZtGgRK1euJBwOA2A2W0lPG0BqSj9crnRczjTcrjQcjtS9nhYRCHpoaamiuWU7La1VtLRUEQr749c7nU4mTZrE9OnTmTZtGrm5uZ36OkVEeisFDdJtlJeXc8899/Dpp59iNpkZVDCRwsFTsFp1JOHbtLbVsGLVf/F4Gxg1ajRXXjmH0aNHJ7oskb3S2trKf/7zH5588kmam5ux2VwMKZhEwcBxWCy96z0gGPJRsXUpW7ctJRjy4XA4OP744/npT3+qpaKlT2toaGDBggV88sknLFy4EJ/PB4AJE6mp/cnMGExmxiDSUvO7bGSTYRj4/M2x4KFlO/WNW/B46uPXl5SUMG3aNKZPn86oUaPUJ0lE5BsoaJCE83q9zJ07l2eeeZZwOERW5hCGlxxOkjsz0aX1GOFwkLVl77G9ahUABx54IGeeeSZTp2q6iXRfhmGwdOlSXn31Vd577z2CwSA2q5NBBRMZNHB8rw8ZI5EQlVWr2FKxCJ+vGbPZzGGHHcYZZ5zByJEjE12eSJczDIP169czb9485s2bx+rVq2n/WOp2Z5KVOYTMjEFkpBdgszq+49G6js/XTF3DRurqNtLQVEE0GhtZkZaWxpQpU5g2bRoHHXSQlp4WEdmJggZJqPfee497772X2tpaXM40hg09jJzsYn053keNTVvZXL6QuvqNQOzIy89//nOOOOIITamQbqO+vp7XXnuNV199lYqKCgCS3Jnk5x3AgPwxCf1CkQiGEaWmtozN5Ytoaa0CYmHh8ccfz4wZM0hLS0twhSKdx+PxsGzZMhYsWMC8efOorq4GYv0VMtIHkp1VTE5WEW5395xOFImEaGgsp65+I3UNm/D7WwAwmUyMHDmSqVOnMnXqVEaMGKHVLUSkT1PQIAlTVlbGmWeeidlsZcigyQwZNKnHz8HuLlrbatlSvoiqmjUYhkFeXh4/+9nPOOGEE9R8ThIiHA7z2Wef8eqrr/LJJ58QjUaxWGz0yxnGgLwxpKXl9/mA0TAMGpu2sqViUTwsNJvNjB8/npkzZ3LIIYdofrj0OH6/ny+++IIlS5awePFi1qxZQzQaBcBmc5GdWUh2dhFZmYU9LmQ0DAOPp466hk3U1W+iqXkbhhF7bWlp6UyZchBTp05lwoQJWh1KRPocBQ3fwmQy8fLLL3PSSSexefNmCgsLWbp0KePGjdvt7T/88EMOO+wwGhsbNXxuDyxbtoyLLrqIwsFTGFo0I9Hl7NanC+cSDHkTXcY+MwyDSCQUH+ZpMpmw2+3YbDZsNluf/2InXSscDhMKheKn7UwmM2azFbPZSnf9FbTb3EydPDthz+/1NVFTW0ZNbRnNLduB2J/qkSNHMnPmTGbOnMmgQYMSVp/IN2ltbaWsrIylS5eyePFiVq5cGd//TSYzaan5ZGYUkJkxmPS0fEym3nPUPxwO0tC4hbqGTdTXb8IfaI1fl5vbjwMOGM2oUaMYPXo0w4cPx+HoWcGKSFeJRqN4PB5aW1tpa2ujtbW1w3mPx0MkEiEajRIOh4lGo/Gf209tNhtOpxOn04nL5drlfFJSEunp6aSnp5OSkqIRR/tBnx5LXVtby4033shrr71GdXU1GRkZjB07lhtvvJHp06d3uG1BQQHbt28nOzs7QdX2Xt35y24w5CUYjAUNjzzyCADnn39+Ikv6XgzDIBAIEAgEEl2K9GGGEd2x1Fww0aV0W25XOkMGTWLIoEkEAm3U1K2ntnY9a9asZfXq1TzwwAP079+fkpISSkpKGDp0KEOHDmXAgAFqTif7RTgcpry8nPXr17NhwwbWr19PWdl6amqq47cxYSIlpR8D8gaRmTGI9LT8XtfcdWdWq53cnBJyc0p2Gu2wmeaWSpqbKnnvvfd47733dtzWSklJSTx0GDhwIAMHDiQrK6tbfy4S2VN+v5/GxkYaGxtpaGj41q21tZX9eezbbDaTlpZGRkYG6enpZGRkkJaWRmZmJllZWR1OMzMzNRp4H/XpoOHUU08lGAzyxBNPUFRURHV1Ne+99x719fW73NZisdC/f/8urykYDGq9ZhERiXM4kikYMI6CAeMIhfzU1W+kpq6MxsbtfPLJJ3zyySfx2zqdToqKiigpKaGoqIjs7GwyMjLIzMwkIyOD1NRUfYmR72QYBs3NzdTW1lJXV0ddXV2H85WVlWzZsqXDSCUApyOF7MxCkpNzSE8bQHr6wB43HaKzmEwmkpNzSE6OTZmIBf2tNLdsp6mlkubm7Xz55TrWrFnT4X5Op5P8/HwKCgoYMGBAfEtPTyctLY3U1FTcbrf2Y9mv/H5/fJRBS0tLh9Pm5uZdAoXGxka83u8eEWy3u7Hb3KSnDcRmdWK1OrDaHF+dt8bOWyx2zGYzJpMZk8kUO8UEpq8ui0YjRCKhHSN5Q/HzkR3nw+EgwZCPUMhLMOgjGPCytWI7Gzdu/M463W53/O9o+6iItLS0Dufb/8YmJSWRlJSEw+Ho8/tpnw0ampqa+OSTT/jwww859NBDARg8eDCTJ0/e7e13N3Xi9ddfZ86cOVRUVDBlyhTOPvvsXe43b948rr/+ehYvXkx2djYnn3wyt99+O0lJSQAMGTKE8847j7KyMv79739zyimnMHfu3A6Psbsj0A6HQ0PuRES6SCjk57NFTyW6jG9ltyVhs7qIRsNEoiGikTDBYJjVq1ezevXqb7yfxWLBarVitVp3fHAzYTKZOpzfHZPJ1OGI09dvtydHo3Z+jL72Aeyb/n2+6d+hK4/uRaPRXTbDMOLDkCORyHc8ggmz2YrN5sJstmKJT4UyEwh6CTRsob5hS5fVvy+SkjI5YORxCXt+k8mE05mK05lKv9zhAESjEVrbamhrq8Pra8Lnb8Lra6KifNu3fvmxWq2kpqaSmpraIXyw2+04HA7sdjt2u71bNoHuK/v93u6/3+e9cW+fyzAMwuFwfFqjz+fD7/fj9/vj53c+bWtrIxjcsxGIZrMFu82NzZ5Cdma/WJBgd2O3Je04n7TTZa5uMXXKMKKEQv74KObY5iEQ9Ox03kttbROVlduJRr/r/THGbDbjdrtJSkomOTkJt9tNamoqF1xwAcOHD+/iV9U9dL93oP0kOTmZ5ORk/v3vfzNlypS9/tJeUVHBKaecwqWXXsoFF1zA4sWLufrqqzvcZsOGDcyaNYvbbruNxx57jNraWi677DIuu+wyHn/88fjt7rrrLm688UZ+97vf7fa5br/9dm6++eYOl/3ud7/jpptu2quaRURkzxhGlNa26u++YQ/U/kVSU6hk3xlEo7GjhrLvzGYLaal5pKXm7XJdKOTD62uiqWkbDU3leLwN+HxNQGzaSvuRY5H9yW5z43Kl43Kl4XKm4d5x3m5Pxm53Y7XYe1yYZDKZ4+EHSd9+2/beZ6GQl2DIh9/fgsfbENs8DXh9jfFpodFolLa2Ntra2qje6eNEYWGhgobezmq1MnfuXH7xi1/w0EMPMX78eA499FB+8pOfMGbMmO+8/4MPPkhxcTF33303AMOHD2fFihXccccd8dvcfvvtnHHGGcyZMweILTX4l7/8hUMPPZQHH3wwPt/n8MMP3yWk2Nn111/PVVdd1eEyjWYQEek6JpOZ5KSe0iXeIBINE43sGNkQDROJhGlvICnSedpHvlhioxgsX41mgO795SIpKTPRJexWNBrF52/G52vC52v6amSDtwmfvznezPnbmM0WzOZv//c3DKPDF8DdHQX/ri+IX3+M3V0ve64z/r335TF2Hjnx9VFq7SOcvkkw5CUY8tLcUrnTpab4CIX4qAWbe6eRC+745Q67e8f7RfcUjUYIhnwEg54dm7fDyIbY1IvYFgz59mj/3JnL5WL06NFdVH33033/p/eDU089leOOO45PPvmEzz77jDfeeIM//elPPPLII8yePftb77tmzRoOOuigDpdNnTq1w8/Lly/niy++4Omnn45f1j40cdOmTYwYMQKAiRMnfutzaZqEiMj+ZbM5mTLpzESXsVs+fwu1detpaq6kra0Gr6+xw4dFs9nM4MGDdunR0D6/tP1nl8vV4448SdcwDINgMIjX68Xr9dLY2Ljb3gy1tbXU1tbS2toaO2q3Y0CDyWQmyZ0Z60mQlE1Kcg5pqXnYbK7EvrBuKBDwxJpDtmynuWU7La1VRCK7jgxJS0ujdMgwBg4cSF5eHpmZmR2mSrSfT05OVgNY6VThcDg+bcLn8+HxeGhpaYn3ZGjvz/D1Hg0NDQ00NNZ95+NbrY4d4UPHaRRWqxPbjr4MVqsDm629T4Nzr0ZKtI86iE0pbO/VECYcCcSCgmBsNMLO/RpCIW88PPguKSkp5OSmk54+JN6nof105x4NX99cLle3nM7UlfrWq90Np9PJUUcdxVFHHcVvf/tbzj//fH73u999Z9CwJ9ra2rjwwgu54oordrlu52XJ2vs1SPdjt7nj5y+5JPb/aLe7v+nm3ZcBUSNKJBLCMDrOLWufr22z2eJztkX2Rvu87p2Xs9xZbN6/JXbUzWTp7gc+gY77fqIZhoHHW09N7Xpq6spobf1qDGZycjLjxo1j6NCh8dUnioqK1CFb9orJZIof1MjIyGDAgAHfevvW1lY2bNgQX22i/bSqeufGhiZSknN3LGU5iPS0gVitfavZtWFEaWmtpqm5Mh4u+P0t8evNZjPFxcWUlpYycOBABgwYED9NSUlJYOXSl1mt1vgU870VDodpamqKN4TceWWJnX+ur6+nsbHyW0dP7GrHiCpMmMxmTJihvTHkTs0g93aUgdlsJj09nX798+Kh/NdXnmg/TUtL63Nhwfehf6mvGTlyJP/+97+/83YjRozgP//5T4fLPvvssw4/jx8/ntWrVzN06NDOLFH2o6mTZye6hO/FMKLU1K5nc/lCWlqrABg6dCjjx49n3LhxHHjggWRkZCS4SultQqEQa9asYenSpSxdupTly5fj88WGGNptLvr3G8mAvANITtJywd/EMAxaWqqoqSujpq4Mr7cRAJvVxtSpUzn00EM56KCD6N+/v0YlyH6XkpLCuHHj4s2xIfY7u337djZs2MC6detYunQpX3zxBVsqqtlSsRiTyUxqSn8yM2JLXaal5mOx9L6PocGgl/qGzdQ1bKK+YTOhnY6QZmZmctBBhzJq1ChGjx5NaWkpbnf3CTVFvi+r1Up2djbZ2d/99z0ajdLS0kJDQ0OH0RKtra20tbV1OO/xeOL9hSKRSIfGte3nbTYbLpcLp9OJ0+mMn3e5XLhcLtxud4elLNtXkEhOTtZBti7S+97h91B9fT0/+tGPOPfccxkzZgwpKSksXryYP/3pT/zwhz/8zvtfdNFF3H333fzqV7/i/PPPZ8mSJbusFnHdddcxZcoULrvsMs4//3ySkpJYvXo177zzDn/961+76JX1HO2JYFX1WjLSY0c8pHNEo2Eqq1azpWIRXm8jZrOZI444gp///OfxKTsiXcVmszFmzBjGjBnD2WefTTgcpqysjPfee4/XX3+d8oollFcsIS01nwH5B9AvZ3ifO9L5TUIhP1srl7O1chl+fysQm9N5xBFHMHPmTKZNm6ZRcNItmUwm8vPzyc/P5+CDDwZiq2atXLmSJUuWsHjxYlatWkVzSyWbtnyGxWIjM2MQ2VnF5GQV4XDs/dHT7sAworS0VFPXsJG6+k20tFbT3h+lX79+TJs2i/HjxzN69GgFgyI7aR9JkJ6enuhSpIuYjD7auSUQCHDTTTfx9ttvs2HDBkKhEAUFBfzoRz/ihhtuiM9dffnllznppJN2u7zlf//7X6688koqKiqYPHky55xzDueeey6NjY3xnWbRokX85je/4dNPP8UwDIqLi/nxj3/MDTfcAMSWt5wzZ068YWRfEg6Hue+++3jppZeIRqP0yx3OsOJDcTpTE11ajxUKB9i6bRkVWz8nEPRgs9k4/vjj+dnPfkZBQUGiyxMhHA4zf/58/vOf//Dpp58SjUaxWOz0zy1lQP4BpKb0zQ/ifn8r5VuXsG37F4TDQZKSkjj88MM59NBDmTRpkvr0SK/g9Xr54osvWLRoEZ9++mmHJRxTU/rFQofsYlKSc7v1+0Ao5I+NWqjfSH3Dpvi8bqvVyrhx45g6dSrTpk1jyJAh3fp1iIh0pT4bNEj3UVZWxl133cXy5cuxWGwUDjqIwYMmduuutN2NYRhUbl/Jug0fEg4HSEpK5rTTTuX0008nKysr0eWJ7FZNTQ3//e9/efXV/7J9e6yDdUb6QIoLp5OR3jeCsda2WraUL6KqZi2GESUnJ5ef/OTHnHTSSRq5IL1eZWUl8+fPZ968eXy+5HNC4VhTRIcjmeysIrIyhpCZUZDwppKGYeDx1FFbHxu10NyyLd6ANTe3H9OnT2Pq1KlMmDBB+62IyA4KGqRbMAyDN998k/vvv5+GhgbcrnSGlRxOTlZRokvr9sLhAGu+fIeqmrWkpKRw9tlnc/LJJ+vDjvQY0WiUJUuW8PzzzzNv3jwAMjMGU1w4nfS0/ARX1/kMw6CxqYLN5Qupb9gMQFFRET//+c856qijsNlsiS1QJAE8Hg8LFy5k3rx5zJ8/n6amph3XtDeVHERW5mDS0wZgsXT9PuIPtNLSUhXvt9DexNFsNjNmzBimTZvGtGnTKC4u1qgFEZHdUNAg3YrH4+HRRx/l+eefJxKJkJ1VzPCSw3C70hNdWrfU0lrNilWv4vU1MWbMGG699Vb69euX6LJE9tmaNWt4+OGHWbBgAQBZmYUUF04jLTUvwZV1jsamrZRt+Di+BvmECRM444wzmDp1qr6siOwQiURYu3YtixcvZtGiRSxfvpxQKDbawWy2kJaaR2bGYFJS+uF2peNypn6vUZChkJ+W1ipaWqpobq2ipbWKQKAtfn1qahpTp05h+vTpHHTQQaSlpX3v1ygi0tspaJBuadOmTdx9990sXrwYq9XBmFEnkJU5JNFldRuGYVCxbSllGz7CMKKcffbZnH/++VpyR3qNFStW8PDDD7Nw4UIAsrOKKS6cRmpKzwzSWttqWb/xE+rqY3PSZ86cydlnn63mrCJ7wO/3s2LFinjwsHbt2l2WxXM6UnA602LBgysNlysdu81NJBIiEgkSiYQI7zht/zkU9tPaWoPX19jhsfr168eoUaMYOXIkY8aMYdSoUVgslv35kkVEejwFDdJttU+n+MMf/kA4HKF02JEMzB+T6LISLhTysWrtW9TWrScjI5Obb76JyZMnJ7oskS6xdOlS/u///o+lS5cCkJtTQnHh9B6zNKbP18SGTQvYXr0GMJgwYQKXXnopI0eOTHRpIj1Wa2srS5cuZfPmzVRWVrJ161YqKyupqqraJYD4LqmpqYwcOTK+jRgxQr2NREQ6gYIG6fZWrFjBNddcQ3NzM0MGTWZo0cF9dohxU/M2Vqx+Db+/hUmTJnHTTTfpA5H0CUuWLOHvf/87X3zxBSaTif79RlA8ZBqubjqtKhj0sHHL/9i2bRlRI8rw4cO55JJLmDx5cp99/xLpauFwmOrq6njw0NTUhNvtxu1243K54qft55OSksjMzNQ+KSLSBRQ0SI+wbds2rrzySsrLy+mXO5xRpbP2SzOo7qS8YgnrNnyEyQQXXHABZ511FmazOdFliew3hmHw6aef8tBDD7Fu3TrMJjP5eQdQOGQqTkdyossDIBjyUbH1c8orlhCOBBk4cCAXXnghRxxxhPZXERER6TMUNEiP0dzczK9//WuWLl1KWmo+4w44CbvdneiyupxhGGzcvICNmz8lJyeHW2+9lXHjxiW6LJGEiUajfPDBB/z973+nvLwcs9lKwYADGTJ4MvYELYPn97ewpWIJ27Z/QSQSIjMzk/PPP58TTzxRvVNERESkz1HQID1KKBTi9ttv5/XXX8flSufAMaeQ5M5MdFldxjAM1m/8mM3lixg4cCB//etf6d+/f6LLEukWwuEwb775Jg8//DDV1dVYrXYGDZzAgLwxOJ0p+6WGNk89W8oXsr16DYYRpV+/fpxxxhmceOKJOJ3O/VKDiIiISHejoEF6HMMweOyxx3j44Yex2ZyMGfVDMjMKEl1WpzMMgy/L3qdi21KGDCnkr3+9n+zsntEAT2R/CgaDvPLKKzz++OM0NDQAJrIyBpOXN4rc7KFdMs2qqbmSzeULqa1bD0BRURFnnnkmRx11lEYwiIiISJ+noEF6rDfeeIPf//4PRCMRDhh1Irk5QxNdUqcxjChrvnyHbdtXMHRoCfff/xcyMjISXZZIt+bz+XjnnXd4/fXXWbZsGQBWq4N+OcPI7z+atLT8fW76Fo1GafPU0Ni0jZraMpqatwIwduxYzjrrLKZNm6aGciIiIiI7KGiQHm3p0qVcddVVBPwBDhh9IrnZPT9siEajrF77JturVzNixAjuu+8+UlNTE12WSI9SUVHBG2+8weuvv05VVRUAblc6ef1HkZrSD5vNjd3uxm5z7XbEQyQSormliqbmrTQ1baOppZJIJBi/fvr06Zx55pnqlyIiIiKyGwoapMdbvnw5c+bMIeAPMGb0D8nJLk50SfssGv3/7d15fFTlvcfxz5ktCySBAFmQJIBAIGyBAILcCooCSq3LVau1qK+igtVbKaLi0iptRduiKMu1rV6LW4uKihapS1UUZVMI+74jJgRC9m2W89w/gJQgVJZJZib5vl+veZ3J5JlzficnZ2bOd87znABrN8yn4MBWevfuzVNPPUWzZs1CXZZIxLJtm9zcXN577z0++eQTqqurv9PG6fTgccfg8cTidsfi81VRVr4f2w7UtunYsSPZ2dm1t6SkpIZcDREREZGIoqBBGoVVq1Yxfvx4vDXeiA0bAgE/a9a/y8HCHeTk5DB16lRiYkIzgr5IY1RZWcnixYvJy8ujuLiYoqKiOrdDhw7h8/lwOp1069aN3r17k52dTa9evUhISAh1+SIiIiIRQ0GDNBq1YYPXdzhsaNUx1CWdskDAx6q18zhUtJvzzz+fKVOmaMR6kQZmjKGyshKn06n9T0REROQsKGiQRiU3N5fx43+Jz+ejd48rad2qQ6hL+l6BgJfcNW9TVLyXIUOG8Lvf/Q63O/ij5IuIiIiIiDQER6gLEAmmPn36MG3aU7jdblavm8fBwp2hLuk/8vu9rFz9FkXFexk2bBiPPfaYQgYREREREYloChqk0enbty9PPfUkbreL1evmUXhoV6hLOiG/v4bcNW9SXPINw4cPZ/LkybhcrlCXJSIiIiIiclbUdUIara+//pp77rkHny9A7x5XhFU3Cp+/htzVcykpzePSSy/l4Ycfxul0hrosERERERGRs6agQRq1r776iokTJ+L1+sjqOoK2Kd1DXRI+XzUrV8+ltCyfUaNG8eCDDypkEBERERGRRkNBgzR6a9as4Z57JlJWVkqnjj+gffoALMsKSS0+XxUrVs+lrGw/P/rRj5g0aRIOh3owiYiIiIhI46GgQZqE3bt3c/fd48nPz6Nd29507TIMy2rYA3yvt5KVq9+grPwAV111Fffee69CBhERERERaXQUNEiTUVhYyC9/+Uu2bNlCm9ad6Jk1CqezYa7wUOOtYOWqNyivOMg111zDPffcE7KzKkREREREROqTggZpUioqKnjwwQdZtmwZCfFtye55JR5PbL0u88DB7WzY/AFebyU//vGPGT9+vEIGERERERFptBQ0SJPj9/uZMmUKCxYsIDa2JX17/TcxMS3qYTletmxfyL5v1+B2u7nrrru47rrrFDKIiIiIiEijpqBBmiRjDH/+85+ZPXs2UZ5mZPe6ivi4lKDNv7jkW9ZvXEBlVTFdunRh8uTJdOgQPpfXFBERERERqS8KGqRJe+utt5g6dSoYSEnuRkZ6f5o3a33G87PtADt2LWHXnmVYlsXo0aO59dZbcbsbZiwIERERERGRUFPQIE3e4sWLmTFjBjt37gSgdauOtE/vT4uEdqfVzaGi8hDrNrxHadl+UlPb8sgjvyY7O7ueqhYREREREQlPChpEONyVYsmSJbz88svk5uYCkBCfSkZ6f5JadzrhpTADAR+VVcVUVhZRVl7Anm++JhDwc/nllzN+/HiaNWvW0KshIiIiIiIScgoaRI6zbt06Xn31VRYuXIgxhtiYlqS164MxhsrKQ4fDhaoiqqtL6zwvISGBBx98kCFDhoSochERERERkdBT0CByEnv27OHvf/878+fPx+fz1T5uWRbJycmkp6eTnp5OWloa6enp9OjRg7i4uBBWLCIiIiIiEnoKGkS+R2FhIYsWLSIhIYH09HTOOeccoqOjQ12WiIiIiIhIWFLQICIiIiIiIiJB890R7kREREREREREzpCCBhEREREREREJGgUNIiIiIiIiIhI0ChpEREREREREJGgUNIiIiIiIiIhI0ChoEBEREREREZGgUdAgIiIiIiIiIkGjoEFEREREREREgkZBg4iIiIiIiIgEjYIGEREREREREQkaBQ0iIiIiIiIiEjQKGkREREREREQkaBQ0iIiIiIiIiEjQKGgQERERERERkaBR0CAiIiIiIiIiQeMKdQEi4aygoIC///3vrFu3jqSkJFJSUkhNTa29paSkEBsbG+oyRUREREREwoaCBpET2LNnD6+88goLFizA7/djAeYkbRPiEzin3Tlce+21jBw5EsuyGrJUERERERGRsGIZY052/CTS5GzdupUXX3yRTz7+BNvYpFhxjHRn0s+ZRiVeCu1KCk0lh0zF4emRnwtMOX5s/uu//otJkybRunXrUK+KiIiIiIhISChoEAFWr17Niy++yOLFiwHIcLRkpCuT3s62OE7hDIVDdiWveFewwS4grnkcE++dyPDhw3V2g4iIiIiINDkKGqRJKy4u5te//jXLly8HINPRhpHuTLo6kk47JDDG8EVgF3N9a6gxfoYMGcJ9991Hq1at6qN0ERERERGRsKSgQZqsffv2Mf7uu9n7zTd0dyQzyt2Njs6zDwUK7Qpe8q5gs32AhPh47r3vPi6++OIgVCwiIiIiIhL+FDRIk7Rp0yZ+Of6XFBUXcZmrK5e7s4LazcE2hkX+HbzlX0eN8TNs2DAmTpxIy5Ytg7YMERERERGRcKSgQZqcJUuW8OADD1BdXcNPPNn8wNWx3pZ1wC7nJe8KttoHSWrThpmzZpGenl5vyxMREREREQk1BQ3SpMyfP58pU6bgMha3ugfQy9W23pdpG8OH/i3M862jVWIiM2fNokOHDvW+XBERERERkVBQ0CBNgjGGv/71r/zlL3+huRXFnZ7z6eBMbNAaFvq2M8e3ihYtWjBjxgw6d+7coMsXERERERFpCAoapNHz+/1MnTqVefPm0drRjP/xDCbZEReSWr707+QV70ri4uKZPmM6Xbt2DUkdIiIiIiIi9UVBgzRq1dXV/OpXv2LRokWkO1pwV9Rg4q3okNa0zL+H2d6vadYslqefeYYePXqEtB4REREREZFgUtAgjVZ1dTX33HMPK1asoLsjmduiBhJtuUJdFgAr/N/wgnc5nphopk2bRnZ2dqhLEhERERERCQoFDdIoHRsy9HWewxjPAJyWI9Rl1bHK/y3Pe5fhinLzx6lT6d+/f6hLEhEREREROWvhdeQlEgSREDIAZLvackfUIAJeP/dMmMDixYtDXZKIiIiIiMhZ0xkN0qhESshwrE2BAv7XuwTjhMemTOGCCy4IdUkijVZJSQn79+/n4MGDFBYWnnAaFxdHv3796NevH9nZ2cTGxoa6bBEREZGIoqBBGo1IDBmO2ho4yEzvl/gdhsmTJ3PxxReHuiSRRiMQCLB06VLmzp3L0qVLOdnbngsH8VY0ZaYGHwEAnE4n3bt3p3///uTk5NCjRw88Hk9Dli8iIiIScRQ0SKMQySHDUTsChczwfkkNAR7+1cNcdtlloS5JJKKVlJTwj3/8g7fefJNv8/IAONfRigxHSxKsaBKsaOKPTFtYMcTixrIsfCbADvsQmwMFbLIPsMs+hM3ht8qoqCj69u3LT3/6U3JyckK5eiIiIiJhS0GDRLzGEDIctccuYnrNl1Tg5f777+fKK68MdUkiEWfDhg3MnTuXf330EV6fjyjLxQBnGkNd53KOI+G051dtfGy1D7I5cIBNgQK+MSUA9OvXj3HjxukStSIiIiLHUdAgEa0xhQxH7bNLeKbmC0pNNRMmTOC6664LdUkiYc8Yw2effcaLL77Ixo0bAUix4hji6shAVwYxljtoy9pjF/GudwPr7HwABg8ezNixY+nSpUvQliEiIiISyRQ0SMQqKSnh/vvvZ9WqVY0mZDgq3y7j6ZpFFJsq7rzzTkaPHh3qkkTC1vbt23nqqadYsWIFFha9nakMdZ1LpqMNlmXV33IDhbzrW89m+wAAw4YN47bbbqN9+/b1tkwRERGRSKCgQSLSnj17uGfCBPZ+8w39nWnc4unXaEKGow7Y5Txds4hCU8mtt97KmDFj6vWgSSTSlJSU8Nxzz/HWW29h2za9nKlc4+5FkqN5g9axKVDAO7717LQP4bAcjLx0JLfddhupqakNWoeIiIhIuFDQIBEnNzeX+++7n9KyUi5zdeWH7iwcjfQA/JBdydPeRRTY5YwePZqf//znChukyQsEArzzzjv8+U9/oqS0lBQrjms9vejuTAlZTcYY1tn5vOtbz167BI/Hwy233MKNN95IVFRUyOoSERERCQUFDRJRFixYwJTHpmACNqM9fRnoygh1SfWu2K7iae8i8u0yLr/8ciZOnKgDF2mycnNzeerJp9i6bSsxlptRrm5c6Do3bM5oso1hReAb3vStpdhUcc455zBhwgQGDx4c6tJEREREGoyCBokIxhiee+45XnjhBZpZHsZ5BtLZ2SbUZTWYUlPNzJov2WMX07lzZ6ZMmUJaWlqoyxJpMHl5ecyaNYt//etfWMD5zvZc4elOvBUd6tJOqNr4eM+3iU/8WwlgGDx4MBMmTOCcc84JdWkiIiIi9U5Bg4S9mpoafve73/HRRx+R5GjOnZ7zSXbEhbqsBuczAeb61vCZfwexMbE89PBDDBs2LNRlidSryspKXnrpJf72t7/h9Xrp6Ejkx55sMhwtQ13aKcm3S5njXc0muwCP283om25i9OjRREeHZ0AiIiIiEgwKGiSsFRUVce+997Ju3To6O1ozLmoQzSxPqMsKqa/9e3nFl0u18XHNNdfwi1/8Ao+naf9NpPGxbZsFCxbw7P/+L4WHDtHSiuVqdw/6OdtF3DglxhhyA9/yhm8NRaaS1JRUfnH3Lxg6dGjErYuIiIjIqVDQIGFr2bJlPPH4E+Tl5zHQmcFPPX1xhUk/7FDbb5fxvHc5e+1iMjMzmTJlik7JlkYjNzeXp59+ms2bNxNluRjh6sLFri54LGeoSzsrNcbPP32b+Jd/K35ssrKyGDt2LAMGDFDgICIiIo2KggYJO/v27WP69Ol89tlnOLD4kTuLEa5MfRA/js8EeN23mkX+nTRv1oyHHn6YCy+8MNRliZyxffv2MXPmTD799FMABjkzuMLdnRaOmBBXFlwFdjn/8G3g68BeDJCdnc24cePIzs4OdWkiIiIiQaGgQcJGdXU1L730Eq+8/DJen49MRxuu8/TmHEdCqEsLa1/59/KKbyU1xs9///d/M2bMGBITE0Ndlsgp27FjB6+//jrvzX8Pn99HJ0crrvX0jphxGM7UPruEd30bWB34FoCBAwdy++23k5WVFeLKRCJDIBCguLiYwsJCDh06RGFhYZ37ZWVleDweoqKiTniLjo4mKSmJ9PR02rVrp7FTRESCSEGDhJwxho8//pgZ06ezv6CAllYs17h70td5js5iOEX5dhnPeZexzy4hyhPFlVddyY033khSUlKoSxM5Idu2Wbp0KXPmzGH58uUAJFnNucLdvcnt+7sCh3jXt4EN9n4ALrjgAm6//XY6deoU4spEwoNt2+zbt4+tW7fWuR04cADbtoOyDMuySE5OJj09nfT0dNLS0khPT6dDhw4kJyc3qdckEZFgUNAgIbVt2zaeeuopVq5ciQsnw12dGenOxGO5Ql1axPGZAEv8u/nAv5lCU4nL5WLUqFHcdNNNGr9BwkZVVRXvvfcer7/2Gnv27gWgq6MNF7k708ORgqMJf5jfGjjIu771bLUPAtC3b19GjhzJRRddRPPmzUNcnUjD8Pv9bN++nY0bN7Jlyxa2bt3Ktm3bqKqqqtOupRVDG6s5CVY0cVYUCVY08VY08VbUkWk0sbjxY+MjgNcE8BGoc7/GBDhkKtlvythvl1NgyjlkKr9TU8uWLcnKyiIrK4tu3bqRlZVFixYtGugvIiISmRQ0SMh88MEHTJ48Gdu26e1sy7XuXrR2NAt1WREvYGy+Cuzlfd9m8k0ZDoeD4cOHc/PNN9OhQ4dQlydN1N69e3nnnXeYN28e5eXluHBwnjOdi9yd1D3qGMYYNtkFvO/bzBb7AAbwuN384IILGDlyJAMHDsTtdoe6TJGgMMaQl5fH+vXrWb9+PRs2bGDz5s3U1NTUtnHiINWKo50jgXaOFkemCTS3ouqlJq/xU2Aq2G+Xsd+Us88uYbddxEFTUaddampqbfDQrVs3unbtSrNm+gwjInKUgobTNHToULKzs3n66afPeB4LFy7kwgsvpKioiBYtWjB79mzGjx9PcXFx0OqMBL///e95++23udUzgH6utFCX0+jYxpAb2Mc//Zv4xi7BsiyGDBnC8OHD6du3r76NkXpVUVHBihUrWLZsGUuXLmXfvn0AxFvRDHV15AeujsTV04FCY3HIruSrwF6W+ffwrSkFICE+gUuGX8LIkSPp3r27TueWiGHbNnl5eWzZsoVt27axadMm1q9fX+ezjxOLcxwJtHck0t7RknRHC1Ks+LC44lS5qWG3XcQuu4hdgUPsNsWUmuo6bdLT02vPeOjatStdunQhJqZxDWYrInKqwvL89Pz8fB577DHee+899u3bR1JSEtnZ2YwfP55hw4aFujwJsvQwHvDtN1UfUW5qvr9hmIvBjdf4WbhwIQsXLgTA6XTidrtxu924XC4dsMhZ8/v9+Hw+fD4ffr+/zu9cOHDjwBjDQt92Fvq2h6jKU9PciuLXMZeEtIZERywjHJkMd3VhnylhqX8PX5XtZe7cucydO5fExMTa07mPfrOakKCzQyT0qqur2b59e53xFLZt20ZlZd1uCa2tZvR3ptHe0ZIOjkTaOVqE7WVsm1tRdHem0N2ZAu7DZ2MUmSp220X/vu3N54M9e/jggw8AcDgctG/fnk6dOtG+fXsyMjLIyMggLS2NqCgFrSLSuIVd0LBr1y4GDx5MixYt+OMf/0jPnj3x+Xx88MEH3HnnnWzatOm052mMIRAI4HKF3epKmCs3NZRyOGh4/vnnAbj11ltDWVLQBAIBAoEA1dXV399Y5Cz5sfFjA/7vbRsWwuhcP8uyaGe14BpPC642PdlkF7Dcv5etRQf44osv+OKLL2rbtmvXrjZ4yMzMJDk5mVatWumgRoLK7/dTUFDAt99+e8LboUOH6rR3YpFixdHTmV7b9SHN0aLeuj80BMuySLRiSXTE0ofD4yAZYzhoKthtF7PbLmKPXcTunXvZsWPHd57bNjWVjCPhQ1paGq1bt669JSYm6jOrNDq2bVNdXU1VVRWVlZV1plVVVdTU1FBTU4PX662dHr1fU1ODbdsYY2pvRweCPfq4w+HA5XLhcrnqfJF27P3o6GhiYmJqp0fvx8bG1k5jYmJwOsMz8Iw0Yfcq9vOf/xzLsli+fHmdvm7du3fnZz/7Gbt27aJDhw7k5ubWXnO8uLiYli1b8umnnzJ06NDargkLFizg4YcfZu3atcycOZOxY8eyceNGunbtWjvfadOmMXPmTLZvP/zt2rp167j33ntZtGgRzZo1Y/jw4UybNo3WrVvXPsfv93PXXXfx8ssv43a7ueOOO/jNb35T+43wyy+/zDPPPMPmzZtp1qwZF110EU8//bSuACAiImfFYVlkOZPJciYDUGZq2GUfYlegiF32IXbvO8CH33zIhx9+WOd58fHxtGnThjZt2tC6devaafPmzet86IqOjq7zASwqKgqHw4HDEfpT1+Xs2LZdGzAf/eBeXV39nfvV1dWUl5dTUlJCSUkJpaWllJSUUFxcXOexE13twYWDRCuWLEcSKY742kAhxYrDHaZnKgSTZVm0sZrTxtGcfrQDDndjLDZV5Jsy9ttl5Jsy8u0y9ucVsfjbb1m8ePEJ59OiRYs64UPz5s1p1qwZsbGxJ5xGR0ef9OBKZyzK8Y4eqNu2XedsxGPPSjx6/9iD/WNfM479+fjQoE6QUFlFVVUlVRH0xVZUVBQxMTE0a9aMmJgYYmNja0OI498rj71/9NK5brcbj8eDx+PB7XbXeawpBYlhtZaHDh3i/fff57HHHjvhgDotWrQ4rXEMJk2axNSpU+nYsSMtW7bkueee49VXX+W3v/1tbZtXX32Vn/zkJ8DhwOKiiy7i1ltvZdq0aVRVVXH//fdz3XXX8cknn9Q+58UXX2TMmDEsX76cr7/+mttvv5309HRuu+02AHw+H7/97W/JzMykoKCACRMmcMstt7BgwYIz+rsc3ZmPdfQfWUREgq8cL1OqPg51GaetJTHEW1HU4MdnAgQwBLCpKi1nZ2lZbaguciYcWDixcOPAhQsXDlyWAycOXByeWkC58bItcJBtgYOhLrlWsiOOMVEDGny5jqNnPhBbGxAeVWV87LfLOGAqKDHVlJiqI9NqSoqr+aZ4F1u3bm3wmkXOlgsHUZaLKFx4cBJvxRDliKt9LPrINAoXUdbhNh7LiRsnbhy4a+87cVsOXDhxcjgws7Cwjp9aYBsIYBM4cgZlABu/+ffPPmy8JoAXPzXGj5fAv6f48ZrD02rjp8bnp8brp6qkiGIOUGP8R87KPHt9+vTh2WefDcq8wl1YBQ3btm3DGFPnjIOz8Zvf/IZLLvl3H9sbb7yRmTNn1gYNW7ZsYcWKFbzyyisAzJw5kz59+jBlypTa57zwwgukpaWxZcsWunTpAkBaWhrTpk3DsiwyMzNZu3Yt06ZNqw0afvazn9U+v2PHjkyfPp3+/ftTXl5+Rpcoe/zxx5k8eXKdxx555BEeffTR056XiIh8PxvDHlMc6jJEwoqNwcYANrVff4RRN6P/KDjHCEHlwoHHcuExzsMHWkcOyo4edHmMkyp8oS5T5LR5LGft//LhIOHw//bhcMFZ9/8cJ9GWC9d3QobD9w+P8eTEaR2NFU4cNhjL4MciYCwcWASwcFoO/Ng4jY0DG8vi8GvW8VMO3zfGYFtHumdYBtsYDAZjgd94g/K38XmDM59IEFZBQ7AvgNGvX786P19//fVMnDiRpUuXMnDgQF599VX69u1bG2ysXr2aTz/99IRhwPbt22uDhoEDB9Y5DW3QoEE8+eSTBAIBnE4nK1as4NFHH2X16tUUFRXVnl64Z88esrKyTns9HnjgASZMmFDnMZ3NICJSfxxYtLPCf2BFG4OXAF7jp4bD39QETnDkZ1lWbd/VY29Hu0U4HA4syzrhz0eff+xUIsfRz1bHTo/t63z0/rHTY7tZnOh2ss9rFocPno8eMBz9htJV+11k6CQ74kK27HJTc7i7xJFuE/lHulAcNJWYkyQ1MTExtG7dho6tW9OqVSvi4uJqu0kc33XiaP/yo90lju8+4Xa7cTqd2n+buKNj1gUCgTrdJgKBwHe6T5yo68TJulod7TpxfPeJqqoqqiorKamspLq6OujHefUtJjqamNhYmsUm0OaY/ezYroXH34+Ojq7tMnG028SxP3s8HpKTk79/4Y1EWAUNnTt3xrKs/zjg49EPPcf+s/p8J057j+9+kZKSwkUXXcTf/vY3Bg4cyN/+9jfuuOOO2t+Xl5dz+eWX8/vf//4780pNTT2ldaioqGDEiBGMGDGCV199lTZt2rBnzx5GjBiB9wwTLHWTEBFpWM3x8GBM+F3lyBjDdruQrwJ72RI4QL4pq3OY0rpVK7K6dycrK4suXbqQkpJC69atiYuL00GGBE1VVRV5eXl1BoDMy8tj3759fPvtt4cPNqD2m0KP5eQc6/AgkO2sBNo5WnCOI4FoK6w+hgZFiak+fAWKwJHBIE9wGUyAVomJ9GmfSUZGBu3atSMpKYlWrVrVjskQGxsbguqlMTs2cG5oxhiqq6tPPo5DVdV3Bn88flDIoyHniQaCPHpcePTg/mQDQh4bDhw7xsLxg0HGxMRobKIgCKtX+MTEREaMGMGsWbP4xS9+8Z2goLi4mDZt2gCQl5dHnz59AFi1atUpL+PGG2/kvvvu44YbbmDHjh1cf/31tb/r27cvb775Ju3bt/+PO+GyZcvq/Lx06VI6d+6M0+lk06ZNFBYW8sQTT5CWlgbA119/fcr1SXhpbkXVflCacOudAMQTeaGPH5ua477pdDgcdV6E9YIqZ8vv9+P1evH5fAQCgdrHj/+WMxKE22j4++0ylvn3sDywl4OmAoBmsc3IyepX5xKXGnRYGkJMTAwdO3akY8eO3/mdMYaSkhK2b9/Otm3b2LJlC1u3bmXnjp3s9P/7ahQWFqlWHB0cibR3Hr68ZaoVj9OKjNcIOHymQp3LW9rFFJuqOm3aprald6dzad++fZ1LXMbFhe4MC5GGZllW7QG8NB1hFTQAzJo1i8GDBzNgwAB+85vf0KtXL/x+Px999BHPPvssGzduZODAgTzxxBN06NCBgoICHn744VOe/9VXX80dd9zBHXfcwYUXXkjbtm1rf3fnnXfy3HPPccMNN3DfffeRmJjItm3bmDNnDs8//3ztpU727NnDhAkTGDt2LCtXrmTGjBk8+eSTAKSnp+PxeJgxYwbjxo1j3bp1dQaflO/61i4lyXH6Y1c0hF/HXPL9jcKUMYZ1dj7/9G1mh10IHO72c8kll5CTk0NKSkqIK5TGrLi4mOXLl7Ns2TKWLV3KwcJCfNjEWrFc6OrEYFd7Yix3qMsMa2Wmhq/9e1ke2MtO+/ABWmxsLKMuHMWll15Knz59dAkuCTtHr5iQk5NDTk5O7eN+v59duw4Pbrht2zY2bdrEhg0b+LZqF18GdgGHz3xIt1rS3tGS9o5E0hwJtLGa4wiDs3GqjZ+9dhG7joQKu+yi2tDvqOSkJIZ0G0C3bt3o1q0bXbt2JSEh/LtgiYjUh7ALGjp27MjKlSt57LHHuOeee8jLy6NNmzbk5OTUjtD5wgsvMGbMGHJycsjMzOQPf/gDw4cPP6X5x8XFcfnll/P666/zwgsv1Pld27Zt+fLLL7n//vsZPnw4NTU1ZGRkMHLkyDrf9t50001UVVUxYMAAnE4nd999N7fffjsAbdq0Yfbs2Tz44INMnz6dvn37MnXqVH70ox8F6S/UeHTv3p158+bxJ+8S+gfSuNrdk5YOJZ1nyzaGVYFv+advE3uPDGY3dOhQbrnllqANtCryfVq0aMHw4cMZPnw4xhi2bdvGO++8w3vz5zO3eg3/8G/gfGcGF7o6hW3QGCrbAgf50L+F9YF8Ahy+NvjgwYMZOXIkP/jBD4iOjg51iSKnzeVy0alTJzp16lT7WCAQYPfu3WzYsIH169ezfv16tm/bxjb/v69WEWW5OMeKP9LtogXtHAmc40ggqp66XQSMzSFTyX5Tzn67jH12CbvsIvJMWZ3xFFq2bMngrGy6detGVlYWmZmZtGrVql5qEhGJRJaJtJE5pFHZsGEDTz75JOvXryfKcnGZqysXuTo1iettB1vA2Hwd+Ib3/ZvJs0txWA4uGX4JN9988wlPbxUJhbKyMt59911ef/119u/fjwX0dKYyzNWJLo42TXocgd12Ee9617Pe3g9At27dGDlyJJdccgmJiYkhrk6kYVRXV7N582Y2bNjA1q1bD3e72LkTv99f28YCkqzmJFnNibeij9yi6txPsKKJwoUBvATwEcB35NJ2Xuza+4Wmkv12OftNGQV2OQdMBYHjLlERGxtbe5bC0W5KycnJTfr1SkTk+yhokJCzbZsFCxYwa+YsioqLSLKac62nFz2dpzYAp8BBu4LnvMvYbRfhcrkYNWoUo0ePpl27dqEuTeSE/H4/n3/+OXPmzGHNmjUAtHMkcIW7Oz0cKU3qA/w+u4T5vg3kBr4FYMCAAdx+++306NEjxJWJhAefz8euXbvqjPmwdctWSkpL/uPzHFhHLsd5alokJJCWnk5GRgbp6emkpaXRoUMH0tPTNY6RiMhpUtAgYaO8vJz/+7//4/XXXycQCNDTkcK1nt46rfp7rPLv4yXfSiqNl8suu4yxY8c2qUvnSOTbuHEjr732Gh9++CG2bZPlSOYaTy/aOuJDXVq92m+XMd+3ka8DezFAr169GDduHH379g11aSIRobKykkOHDnHo0CEKCwspLCykqKio9n5ZWRkej6f26l0nuiUnJ9eGChpPQUQkeBQ0SNjZuXMnTz31FF999RUuHFzl7sFFrk5N6hvOU+E3Nm/71vKxfxvRUdHcP+l+Lr300lCXJXLGdu7cyfTp01myZAkOLH7g6sDl7qywuwLE2TpkV/KebyNLAruxMXTt2pWxY8cycOBAvc6JiIhIo6CgQcKSMYbPP/+cP/7xjxw8eJAhro5c5+4dUZe9qk+FdgXPe5ez0z5Exw4deGzKFDp06BDqskSCYsmSJTzzzDPs2rWLGMvNKFc3hrrOxRXh+7/PBPjIv5X3/ZvwmgAdO3Zk7NixXHDBBQoYREREpFFR0CBhraCggIkTJ7Jlyxa6O5K5Neq8Jn9JvDWBPGZ7v6bSeBk1ahQTJ07UdYml0fH7/cybN4+//PkvlJaVkmQ15xp3T3o6UyPyoHxdIJ/XvKs5YMpplZjIXf/zPwwfPlyXpxQREZFGSUGDhL3KykoeeeQRFi1aRFtHPHd6zqeVo1moy2pwAWMzz7eOj/xbifJEce999/LDH/4w1GWJ1KvS0lJeeOEF3njjDQKBAF0dSVzn6R0x4zcctCt4w7ea1YE8nE4nP/7xjxkzZgzNmjW91zARERFpOhQ0SEQIBALMnDmTv//978Rb0dzhGUQHZ9O53FuF8fJszWK22YVkZGQwZcoUzj333FCXJdJgdu/ezfTp0/nyyy9xYDHE1ZEfurNoZnlCXdoJeU2AD/2b+cC/BZ8JkJOTw8SJE9XFSURERJoEBQ0SUd566y2mTp2K01jc4u5HjqvxX76xzNTwTM0ivrFLGD58OJMmTSI2NjbUZYmExJIlS5g2bRp79uyhuRXFFe4sBjs74AiT7hTGGNYE8njDt4aDpoI2rdtw9/i7GTZsWER2+RARERE5EwoaJOIsW7aMBx94gIrKSq5y92C4q0uj/QBfYqp4uuYL8uxSrrnmGiZMmKBreUuT5/P5eP3113nh/16gorKCNEcLrnP3prOzdUjr2hwo4B3fBnbYhbhcLn7yk59wyy23KBgUERGRJkdBg0SkHTt2MOGXE8jfn89/OdvzE0/fsPlGM1gO2ZU87V1EgV3OjTfeyF133dVoAxWRM1FYWMif/vQn5s+fjzGGfs52XO3uSaKjYQ/sdwQKede3nk32AQAuuugixo0bR3p6eoPWISIiIhIuFDRIxCosLOTee+9lw4YNDHRmcJMnp9GEDQftCqbVLKLQVDBmzBhuvfVWhQwiJ7Fx40aefPJJ1q1bhwsHOc52DHF1pIMjsV73m712Me9617PWzgdg8ODB3H777WRmZtbbMkVEREQigYIGiWgVFRWMHz+etWvXNpqwYb9dxrSaRRSbKn7+859z0003hbokkbBn2zYffvghL734Ijt27gQgzWrBUHdH+jvT8FiuoC0rzy7lH74NrAzsAyAnJ4exY8fSq1evoC1DREREJJIpaJCI15jChm/tUp6uWUSpqWb8+PFcf/31oS5JJKIYY8jNzeXNN99k4cKFBAIBYi0P5zszuMDVkSRH89Oep88E2GEXsjlwgE12ATvtIgyGHj16MG7cOPr161cPayIiIiISuRQ0SKPQGMKGvXYxz9R8Qbmp4f777+eqq64KdUkiEe3AgQPMmzePefPmUVhYCECWI4l0R0sSrGgSrJgj08M3t+UEIGBs9tjFbLYL2BQ4wHa7EB8BAJxOJ7169eKnP/0p559/vro0iYiIiJyAggZpNCI5bNgZOMQM75dU4+ehhx9i1KhRoS5JpNHw+/0sXLiQuXPnsmrVqpO2i7XcxBNNCdVUGR8AlmXRuXNn+vXrR79+/cjOztZVJERERES+h4IGaVQiMWzYFjjITO9ivFaAyZMnc8kll4S6JJFGq6CggPz8fA4ePEhhYSEHDx78zv34uHhy+uXQv39/cnJySEhICHXZIiIiIhFFQYM0OpEUNmwOFPC/3iUEHPC7x37H0KFDQ12SiIiIiIjIWVHQII1S3bAhnZs8/cIubFgfyOdP3qVYLgePP/EEgwcPDnVJIiIiIiIiZ01BgzRax4YN2c62/MwzAM+Rwd5CbU0gj7/ULMXpcfOHP/6B8847L9QliYiIiIiIBIWCBmnUKioqmDRpEl999RUdHa34edQgmltRIa1ppX8f/+ddhic6iiefeoq+ffuGtB4REREREZFgUtAgjZ7P5+Oxxx7j/fffJ9kRx/94BtPa0SwktXzl38tfvV8RExvDtKefplevXiGpQ0REREREpL4oaJAmwRjDs88+y0svvUS8Fc3/RA0mzdGiQWtY4t/NS94VNGvejOnTp5OVldWgyxcREREREWkIChqkSZk7dy5PPvkkUbi43XMeWc7kel+mMYaF/u287ltNfHw8M2bOpEuXLvW+XBERERERkVBQ0CBNzsKFC/n1r39NwOtjtCeHga6MeltWkV3FK94VrLf3k9gykRkzZ3DuuefW2/JERERERERCTUGDNElr1qxh4j0TKS0r5Up3D0a4umAF8fKXxhiWBvbwum81VcbHoEGDeOCBB0hKSgraMkRERERERMKRggZpsnbt2sX48ePJz8+nj7Mto9xZtHMknPV8S0wVr9SsZK2dT7PYZoz/5Xh++MMfBjXIEBERERERCVcKGqRJO3jwIA888ABr164FoKcjhZHurpzrbHXa8zLGsDywl9d8q6k0Xs477zwefPBBkpPrfxwIERERERGRcKGgQZo8YwzLly/nxRdfZOXKlQB0drRmpDuTLEfyKZ2JUGqqedWby+rAt8TExHD33XdzxRVX6CwGERERERFpchQ0iBxj7dq1vPjii3zxxRcApFstGOHOpI/zHLz4KTSVFJpKDtmVFJqKw/dNJXmmjBrjp1+/fjz00EOkpqaGeE1ERERERERCQ0GDyAls27aNl156iX999C9sY+PBiZfACdt6PB7atm3Ltddey9VXX62zGEREREREpElT0CDyH3zzzTe8+uqrrF+/njZt2pCamkpKSkrtNCUlhcTERIULIiIiIiIiRyhoEBEREREREZGgcYS6ABERERERERFpPBQ0iIiIiIiIiEjQKGgQERERERERkaBR0CAiIiIiIiIiQaOgQURERERERESCRkGDiIiIiIiIiASNggYRERERERERCRoFDSKnqKamhkcffZSamppQlyINQNu7adH2bjq0rZsWbe+mQ9u6adH2Dn+WMcaEugiRSFBaWkpCQgIlJSXEx8eHuhypZ9reTYu2d9Ohbd20aHs3HdrWTYu2d/jTGQ0iIiIiIiIiEjQKGkREREREREQkaBQ0iIiIiIiIiEjQKGgQOUVRUVE88sgjREVFhboUaQDa3k2LtnfToW3dtGh7Nx3a1k2Ltnf402CQIiIiIiIiIhI0OqNBRERERERERIJGQYOIiIiIiIiIBI2CBhEREREREREJGgUNIiIiIiIiIhI0ChpEjjFr1izat29PdHQ05513HsuXL/+P7d944w26du1KdHQ0PXv2ZMGCBQ1UqQTD6Wzv2bNnY1lWnVt0dHQDVitn6vPPP+fyyy+nbdu2WJbFvHnzvvc5CxcupG/fvkRFRdGpUydmz55d73VKcJzu9l64cOF39m3LssjPz2+YguWMPf744/Tv35+4uDiSkpK48sor2bx58/c+T+/dkedMtrXetyPXs88+S69evYiPjyc+Pp5Bgwbxz3/+8z8+R/t1+FHQIHLEa6+9xoQJE3jkkUdYuXIlvXv3ZsSIERQUFJyw/eLFi7nhhhsYM2YMubm5XHnllVx55ZWsW7eugSuXM3G62xsgPj6evLy82tvu3bsbsGI5UxUVFfTu3ZtZs2adUvudO3cyatQoLrzwQlatWsX48eO59dZb+eCDD+q5UgmG093eR23evLnO/p2UlFRPFUqwfPbZZ9x5550sXbqUjz76CJ/Px/Dhw6moqDjpc/TeHZnOZFuD3rcjVbt27XjiiSdYsWIFX3/9NRdddBFXXHEF69evP2F77ddhyoiIMcaYAQMGmDvvvLP250AgYNq2bWsef/zxE7a/7rrrzKhRo+o8dt5555mxY8fWa50SHKe7vf/617+ahISEBqpO6gtg3n777f/Y5r777jPdu3ev89iPf/xjM2LEiHqsTOrDqWzvTz/91ACmqKioQWqS+lNQUGAA89lnn520jd67G4dT2dZ6325cWrZsaZ5//vkT/k77dXjSGQ0igNfrZcWKFVx88cW1jzkcDi6++GKWLFlywucsWbKkTnuAESNGnLS9hI8z2d4A5eXlZGRkkJaW9h+TdYls2rebpuzsbFJTU7nkkkv48ssvQ12OnIGSkhIAEhMTT9pG+3fjcCrbGvS+3RgEAgHmzJlDRUUFgwYNOmEb7dfhSUGDCHDw4EECgQDJycl1Hk9OTj5pP938/PzTai/h40y2d2ZmJi+88ALvvPMOr7zyCrZtc/755/PNN980RMnSgE62b5eWllJVVRWiqqS+pKam8qc//Yk333yTN998k7S0NIYOHcrKlStDXZqcBtu2GT9+PIMHD6ZHjx4nbaf37sh3qtta79uRbe3atTRv3pyoqCjGjRvH22+/TVZW1gnbar8OT65QFyAiEgkGDRpUJ0k///zz6datG3/+85/57W9/G8LKRORsZGZmkpmZWfvz+eefz/bt25k2bRovv/xyCCuT03HnnXeybt06vvjii1CXIvXsVLe13rcjW2ZmJqtWraKkpIS5c+dy880389lnn500bJDwozMaRIDWrVvjdDrZv39/ncf3799PSkrKCZ+TkpJyWu0lfJzJ9j6e2+2mT58+bNu2rT5KlBA62b4dHx9PTExMiKqShjRgwADt2xHkrrvuYv78+Xz66ae0a9fuP7bVe3dkO51tfTy9b0cWj8dDp06dyMnJ4fHHH6d3794888wzJ2yr/To8KWgQ4fCLWU5ODh9//HHtY7Zt8/HHH5+0P9igQYPqtAf46KOPTtpewseZbO/jBQIB1q5dS2pqan2VKSGifVtWrVqlfTsCGGO46667ePvtt/nkk0/o0KHD9z5H+3dkOpNtfTy9b0c227apqak54e+0X4epUI9GKRIu5syZY6Kioszs2bPNhg0bzO23325atGhh8vPzjTHGjB492kyaNKm2/ZdffmlcLpeZOnWq2bhxo3nkkUeM2+02a9euDdUqyGk43e09efJk88EHH5jt27ebFStWmOuvv95ER0eb9evXh2oV5BSVlZWZ3Nxck5ubawDz1FNPmdzcXLN7925jjDGTJk0yo0ePrm2/Y8cOExsba+69916zceNGM2vWLON0Os37778fqlWQ03C623vatGlm3rx5ZuvWrWbt2rXm7rvvNg6Hw/zrX/8K1SrIKbrjjjtMQkKCWbhwocnLy6u9VVZW1rbRe3fjcCbbWu/bkWvSpEnms88+Mzt37jRr1qwxkyZNMpZlmQ8//NAYo/06UihoEDnGjBkzTHp6uvF4PGbAgAFm6dKltb8bMmSIufnmm+u0f/31102XLl2Mx+Mx3bt3N++9914DVyxn43S29/jx42vbJicnm8suu8ysXLkyBFXL6Tp6+cLjb0e3780332yGDBnynedkZ2cbj8djOnbsaP761782eN1yZk53e//+97835557romOjjaJiYlm6NCh5pNPPglN8XJaTrSdgTr7q967G4cz2dZ6345cP/vZz0xGRobxeDymTZs2ZtiwYbUhgzHaryOFZYwxDXf+hIiIiIiIiIg0ZhqjQURERERERESCRkGDiIiIiIiIiASNggYRERERERERCRoFDSIiIiIiIiISNAoaRERERERERCRoFDSIiIiIiIiISNAoaBARERERERGRoFHQICIiIiIiIiJBo6BBREREmqRHH32U7Ozs2p9vueUWrrzyypDVIyIi0lgoaBAREZGIc8stt2BZVu2tVatWjBw5kjVr1oS6NBERkSZPQYOIiIhEpJEjR5KXl0deXh4ff/wxLpeLH/7wh6EuS0REpMlT0CAiIiIRKSoqipSUFFJSUsjOzmbSpEns3buXAwcOAHD//ffTpUsXYmNj6dixI7/61a/w+XynPP+5c+fSs2dPYmJiaNWqFRdffDEVFRX1tToiIiKNhivUBYiIiIicrfLycl555RU6depEq1atAIiLi2P27Nm0bduWtWvXcttttxEXF8d99933vfPLy8vjhhtu4A9/+ANXXXUVZWVlLFq0CGNMfa+KiIhIxFPQICIiIhFp/vz5NG/eHICKigpSU1OZP38+DsfhEzYffvjh2rbt27dn4sSJzJkz55SDBr/fz9VXX01GRgYAPXv2rIe1EBERaXzUdUJEREQi0oUXXsiqVatYtWoVy5cvZ8SIEVx66aXs3r0bgNdee43BgweTkpJC8+bNefjhh9mzZ88pzbt3794MGzaMnj17cu211/Lcc89RVFRUn6sjIiLSaChoEBERkYjUrFkzOnXqRKdOnejfvz/PP/88FRUVPPfccyxZsoQbb7yRyy67jPnz55Obm8tDDz2E1+s9pXk7nU4++ugj/vnPf5KVlcWMGTPIzMxk586d9bxWIiIikU9Bg4iIiDQKlmXhcDioqqpi8eLFZGRk8NBDD9GvXz86d+5ce6bD6cxv8ODBTJ48mdzcXDweD2+//XY9VS8iItJ4aIwGERERiUg1NTXk5+cDUFRUxMyZMykvL+fyyy+ntLSUPXv2MGfOHPr378977713WiHBsmXL+Pjjjxk+fDhJSUksW7aMAwcO0K1bt/paHRERkUZDQYOIiIhEpPfff5/U1FTg8BUmunbtyhtvvMHQoUMB+OUvf8ldd91FTU0No0aN4le/+hWPPvroKc07Pj6ezz//nKeffprS0lIyMjJ48sknufTSS+tpbURERBoPy+g6TSIiIiIiIiISJBqjQURERERERESCRkGDiIiIiIiIiASNggYRERERERERCRoFDSIiIiIiIiISNAoaRERERERERCRoFDSIiIiIiIiISNAoaBARERERERGRoFHQICIiIiIiIiJBo6BBRERERERERIJGQYOIiIiIiIiIBI2CBhEREREREREJmv8HTalRGd2/tAwAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 536
        },
        "id": "UssRUwvrH3uP",
        "outputId": "0f3bcb20-66f0-43bc-c4ee-fce49c8f0da7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Conclusion\n",
        "\n",
        "This tutorial demonstrates how to use Markov models to generate realistic baseball pitch sequences. The resulting dataset provides a detailed sequence of pitches, including pitch types and outcomes, based on the count during the at-bat. This synthetic dataset can be used for training predictive models in sports analytics, particularly for predicting the type of pitch based on historical data."
      ],
      "metadata": {
        "id": "IYe9cSFUMLfN"
      }
    }
  ]
}