notebooks/Classical-Search-and-PPO-in-AC-Environment.ipynb

{
    "cells": [
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {},
            "outputs": [],
            "source": [
                "## Imports\n",
                "from collections import defaultdict\n",
                "from importlib import resources\n",
                "import numpy as np\n",
                "import torch\n",
                "import matplotlib.pyplot as plt\n",
                "from ac_solver.envs.ac_env import ACEnv\n",
                "from ast import literal_eval\n",
                "\n",
                "## Load data\n",
                "filename = \"greedy_search_paths.txt\"\n",
                "with resources.open_text('ac_solver.search.miller_schupp.data', filename) as file:\n",
                "    gs_paths = [literal_eval(path) for path in file]\n",
                "\n",
                "filename = \"greedy_solved_presentations.txt\"\n",
                "with resources.open_text('ac_solver.search.miller_schupp.data', filename) as file:\n",
                "    gs_solved = [np.array(literal_eval(presentation)) for presentation in file]\n",
                "\n",
                "filename = \"bfs_solved_presentations.txt\"\n",
                "with resources.open_text('ac_solver.search.miller_schupp.data', filename) as file:\n",
                "    bfs_solved = [np.array(literal_eval(presentation)) for presentation in file]\n",
                "\n",
                "filename = \"all_presentations.txt\"\n",
                "with resources.open_text('ac_solver.search.miller_schupp.data', filename) as file:\n",
                "    all_presentations = [np.array(literal_eval(presentation)) for presentation in file]"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Section 3"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "## how much does the length of a presentation have to get before it is simplified in greedy search\n",
                "\n",
                "n_to_gs_excess_lengths_dict = {} \n",
                "lengths_to_gs_excess_lengths_dict = {} \n",
                "for presentation, path in zip(gs_solved, gs_paths):\n",
                "    \n",
                "    # compute total length of the presentation\n",
                "    max_relator_length = len(presentation) // 2 \n",
                "    first_relator = presentation[:max_relator_length]\n",
                "    second_relator = presentation[max_relator_length:]\n",
                "    presentation_length = np.count_nonzero(first_relator) + np.count_nonzero(second_relator)\n",
                "\n",
                "    # compute n\n",
                "    n = (np.count_nonzero(first_relator) - 3) // 2\n",
                "\n",
                "    # compute the maximum value presentation length took during greedy search\n",
                "    max_length_in_path = max([y for _, y in path])\n",
                " \n",
                "    # record\n",
                "    if presentation_length not in lengths_to_gs_excess_lengths_dict.keys():\n",
                "        lengths_to_gs_excess_lengths_dict[presentation_length] = []\n",
                "\n",
                "    if n not in n_to_gs_excess_lengths_dict.keys():\n",
                "        n_to_gs_excess_lengths_dict[n] = []\n",
                "        \n",
                "    # record\n",
                "    lengths_to_gs_excess_lengths_dict[presentation_length].append(max_length_in_path - presentation_length)\n",
                "    n_to_gs_excess_lengths_dict[n].append(max_length_in_path - presentation_length)"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [
                {
                    "data": {
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",
                        "text/plain": [
                            "<Figure size 640x480 with 2 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# Example data - replace with your actual data\n",
                "data = lengths_to_gs_excess_lengths_dict\n",
                "\n",
                "# Determine the maximum frequency to set color map size\n",
                "max_freq = max([values.count(value) for _, values in data.items() for value in set(values)])\n",
                "\n",
                "# Create a color map with sufficient colors\n",
                "colors = plt.cm.viridis(np.linspace(0, 1, max_freq))  # Adjusted to max frequency\n",
                "\n",
                "fig, ax = plt.subplots()\n",
                "\n",
                "for key, values in data.items():\n",
                "    value_count = {val: values.count(val) for val in values}\n",
                "    for val, count in value_count.items():\n",
                "        ax.scatter(key, val, s=100, color=colors[count-1], alpha=1.0)  # Index adjusted for count\n",
                "\n",
                "# Create a colorbar as legend\n",
                "sm = plt.cm.ScalarMappable(cmap='viridis', norm=plt.Normalize(vmin=1, vmax=max_freq))\n",
                "cbar = plt.colorbar(sm, ax=ax, ticks=range(0, max_freq + 1, 20))\n",
                "cbar.set_label('Frequency')\n",
                "\n",
                "ax.set_title('Increase in presentation length')\n",
                "ax.set_xlabel('Initial length of presentation')\n",
                "ax.set_ylabel('Increase in length')\n",
                "ax.set_xticks([7, 10, 13, 16, 19, 22, 25])\n",
                "plt.grid(True)\n",
                "# plt.savefig(\"./Images/gs_length_increase_vs_length.pdf\")\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 2 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# Example data - replace with your actual data\n",
                "data = n_to_gs_excess_lengths_dict\n",
                "\n",
                "# Determine the maximum frequency to set color map size\n",
                "max_freq = max([values.count(value) for _, values in data.items() for value in set(values)])\n",
                "\n",
                "# Create a color map with sufficient colors\n",
                "colors = plt.cm.viridis(np.linspace(0, 1, max_freq))  # Adjusted to max frequency\n",
                "\n",
                "fig, ax = plt.subplots()\n",
                "\n",
                "for key, values in data.items():\n",
                "    value_count = {val: values.count(val) for val in values}\n",
                "    for val, count in value_count.items():\n",
                "        ax.scatter(key, val, s=100, color=colors[count-1], alpha=1.0)  # Index adjusted for count\n",
                "\n",
                "# Create a colorbar as legend\n",
                "sm = plt.cm.ScalarMappable(cmap='viridis', norm=plt.Normalize(vmin=1, vmax=max_freq))\n",
                "cbar = plt.colorbar(sm, ax=ax, ticks=range(0, max_freq + 1, 20))\n",
                "cbar.set_label('Frequency')\n",
                "\n",
                "ax.set_title('Increase in presentation length')\n",
                "ax.set_xlabel('n')\n",
                "ax.set_ylabel('Increase in length')\n",
                "ax.set_xticks([1, 2, 3, 4, 5, 6, 7])\n",
                "plt.grid(True)\n",
                "# plt.savefig('/Users/alishehper/work/ac_paper/fig/gs_length_increase_vs_n.png')\n",
                "# plt.savefig(\"./Images/gs_length_increase_vs_n.pdf\")\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "gs_excess_lengths_to_gs_path_lengths_dict = {}\n",
                "for path in gs_paths:\n",
                "    path_length = len(path) - 1\n",
                "    max_length_increase = max([pres_length for _, pres_length in path]) - path[0][1]\n",
                "    if max_length_increase not in gs_excess_lengths_to_gs_path_lengths_dict:\n",
                "        gs_excess_lengths_to_gs_path_lengths_dict[max_length_increase] = []\n",
                "    gs_excess_lengths_to_gs_path_lengths_dict[max_length_increase].append(path_length)\n",
                "\n",
                "# Example data: a dictionary where the keys are values of n and the values are lists of data points\n",
                "data = gs_excess_lengths_to_gs_path_lengths_dict\n",
                "xs = sorted(list(data.keys()))\n",
                "ys = [data[x] for x in xs]\n",
                "\n",
                "# Colors for each box plot\n",
                "colors =['#ADD8E6']*7\n",
                "\n",
                "# Prepare the plot\n",
                "fig, ax = plt.subplots()\n",
                "\n",
                "# Create a boxplot with colors\n",
                "boxplots = ax.boxplot(ys, patch_artist=True)\n",
                "\n",
                "# Coloring each box\n",
                "for patch, color in zip(boxplots['boxes'], colors):\n",
                "    patch.set_facecolor(color)\n",
                "\n",
                "# Setting the labels for each box based on the dictionary keys\n",
                "ax.set_xticklabels(xs)\n",
                "\n",
                "# Labeling the axes\n",
                "ax.set_xlabel('Increase in length')\n",
                "ax.set_ylabel('Path length')\n",
                "\n",
                "# Adding a title\n",
                "ax.set_title('Distribution of Greedy Search path lengths as a function of n')\n",
                "\n",
                "# plt.savefig('/Users/alishehper/work/ac_paper/fig/path_lengths_vs_length_increase.png')\n",
                "# plt.savefig(\"./Images/path_lengths_vs_length_increase.pdf\")\n",
                "# Display the plot\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# how \n",
                "n_to_gs_path_lengths_dict = {}\n",
                "\n",
                "for presentation, path in zip(gs_solved, gs_paths):\n",
                "\n",
                "    # compute n\n",
                "    max_relator_length = len(presentation) // 2 \n",
                "    first_relator = presentation[:max_relator_length]\n",
                "    n = (np.count_nonzero(first_relator) - 3) // 2\n",
                "\n",
                "    if n not in n_to_gs_path_lengths_dict.keys():\n",
                "        n_to_gs_path_lengths_dict[n] = []\n",
                "    n_to_gs_path_lengths_dict[n].append(len(path)-1)\n",
                "\n",
                "## making the boxplots\n",
                "data = n_to_gs_path_lengths_dict\n",
                "xs = sorted(list(data.keys()))\n",
                "ys = [data[x] for x in xs]\n",
                "\n",
                "colors =['#ADD8E6']*7\n",
                "fig, ax = plt.subplots()\n",
                "boxplots = ax.boxplot(ys, patch_artist=True)\n",
                "\n",
                "# Coloring each box\n",
                "for patch, color in zip(boxplots['boxes'], colors):\n",
                "    patch.set_facecolor(color)\n",
                "\n",
                "# Setting the labels for each box based on the dictionary keys\n",
                "ax.set_xticklabels(xs)\n",
                "\n",
                "# Labeling the axes\n",
                "ax.set_xlabel('n')\n",
                "ax.set_ylabel('Path length')\n",
                "\n",
                "# Adding a title\n",
                "ax.set_title('Distribution of Greedy Search path lengths as a function of n')\n",
                "\n",
                "# plt.savefig(\"./Images/gs_path_lengths.pdf\")\n",
                "# Display the plot\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Section 4"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "The loaded checkpoint of PPO agent solved 431 presentations.\n"
                    ]
                }
            ],
            "source": [
                "import torch\n",
                "import requests\n",
                "from pathlib import Path\n",
                "\n",
                "# URL of the file on Google Drive\n",
                "url = \"https://drive.google.com/uc?id=1hjCReTkrrNKGbz2X0jEhpAPKBby0MczQ&export=download\"\n",
                "filename = \"ppo.pt\"\n",
                "\n",
                "# Define the path where the checkpoint will be saved\n",
                "ckpt_path = Path(\"/tmp\") / filename\n",
                "\n",
                "# Download the file if it does not exist\n",
                "if not ckpt_path.exists():\n",
                "    print(f\"Downloading {filename} from Google Drive...\")\n",
                "    response = requests.get(url, stream=True)\n",
                "    with open(ckpt_path, 'wb') as f:\n",
                "        for chunk in response.iter_content(chunk_size=8192):\n",
                "            if chunk:\n",
                "                f.write(chunk)\n",
                "    print(f\"Downloaded {filename} to {ckpt_path}\")\n",
                "\n",
                "# Load the checkpoint\n",
                "ppo_checkpoint = torch.load(ckpt_path, map_location=\"cpu\")\n",
                "\n",
                "id_to_ac_seq_dict = ppo_checkpoint['ACMoves_hist']\n",
                "print(f\"The loaded checkpoint of PPO agent solved {len(id_to_ac_seq_dict)} presentations.\")"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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4AUDs2rVLCCGEh4eH8PHxeeQ2fXx8hKen5yPLPIgBVwiRl5cnAIhevXppVf7UqVMCgHj99ddl0ydOnCgAiP3790vTvL29BQBx5MgRadru3bsFAGFlZSUuXbokTf/8888FAHHgwAFpmuaD9/bbb0vT1Gq16N69u7CwsJAdOHfu3JHVp7i4WNSvX1+0b99eNh2AMDExEWfPni23bw8GGpVKJUaPHv3Q16K4uFi4uLiI+vXri8LCQml6YmKiACCmTZtWbl8e/PBoTlKPkpubKywsLETnzp1lfwAsWbJEABD//e9/pWkP+1A96NdffxUAxLvvvltu3vXr18W1a9ekR1FRkTRv2rRpAoCwsbERXbt2FR999JE4fvz4I7dVFgABQPzyyy/StEuXLglLS0vx8ssvS9MefD+FECIlJUUAkAKMEPeD8IPHjYbm+Dt06JA0LTc3VyiVSjFhwgSt6lr2eBg+fLhwd3cXf//9t6xc3759hUqlkuqs+QIKCAiQvXaLFy8WAKQgX1RUJKpXry6aNm0q7t27J5X76quvBADZl8nPP//80JN827Zty70uRUVFws3NTfTu3Vua1qtXL9mXvC4AlPssvPvuuwKASE5OlqbdunVL+Pr6Ch8fH+lY1bwetWrVqvB9fZAmoFlZWYk///xTmn7s2DEBQIwbN06apvlcvf/++7J1JCcnCwAiLi5ONn3Xrl2y6Vu2bBEAxM8///zQ+mi7LiG0P+YeddxW9Bq9+eabwtraWty9e1ea1r17d+Ht7V2ubEUBt1GjRsLFxUX2h+mvv/4qTExMxODBg6VpmvPHa6+9Jlvnyy+/LKpXry49X7hwoVbnmQdps9yiRYsEAFlDQnFxsQgJCRG2trYiPz9fmv7gZ7Rfv37CxcVFlJSUSNOysrKEiYmJ7NzboUMHERQUJHs91Wq1aNmypahTp440TXOMHzt2TJqWm5srVCqV1gH3gw8+qPB9epCuAfdx55eTJ08KAGLTpk0P3aYu3+cP1kPznV22YUIIIQIDA2Xfux9++KGwsbERv//+u6zc+++/L0xNTcXly5eFEEJs3bpVABBz5syRypSUlEh/3GgbcIODg2V/dM6ZM0cAENu2bRNC3G+o8fT0FH369JEtv2DBAqFQKMQff/zxyO1oAq7m+/HChQti9uzZQqFQiAYNGkjlNJ+l8+fPi2vXromLFy+Kzz//XCiVSuHq6ipu374tbt68qVX+0jSklD32H4ddFADpZ8KKfqKuyI4dOwAA48ePl02fMGECAJT7eTIwMBAhISHS8+bNmwO430xfs2bNctMrump/zJgx0v81P3EXFxfjhx9+kKZbWVlJ///nn3+Ql5eH0NDQct0JAKBt27YIDAx8zJ7e78d67NgxXL16tcL5v/zyC3JzczFq1ChZn7fu3bvD39+/wn7Lb731lux5aGhohftc1g8//IDi4mK8++67sj6LI0aMgL29/RP1j9a877a2tuXm1apVC87OztKj7M92MTExWL9+PRo3bozdu3fjP//5D4KDg/Hiiy+W+7nzYUJCQhAcHCw9r1mzJnr16oXdu3dLP8OWfT/v3buH69evw8/PDw4ODhW+pw8TGBiI0NBQ6bmzszPq1av32Nf8QUIIbN68GT179oQQAn///bf0CA8PR15eXrl6DRs2DBYWFtJzTT002/7ll19w/fp1jBgxQnZx44ABA1CtWjWd6mdrayvrE2ZhYYFmzZrJ9tPBwQF//vknfv75Z53W/TA7duxAs2bN0Lp1a1k93njjDWRmZuK3336TlR8yZIjsfX2ciIgI1KhRQ3rerFkzNG/eXDoHlTVy5EjZ802bNkGlUqFTp06y9yo4OBi2trY4cOAAgP/1VU9MTKzwJ0td1qVR2WOu7Gt069Yt/P333wgNDcWdO3eQlpam1TrKysrKwqlTpzB06FA4OjpK0xs0aIBOnTpV+HpWdJ66fv26dN7QvG7btm3T6ed6bZbbsWMH3Nzc0K9fP2maubk53nnnHRQUFFTYBUGjT58+yM3NlXVTio+Ph1qtRp8+fQAAN27cwP79+/Hqq69Kr+/ff/+N69evIzw8HOnp6VIXsx07dqBFixZo1qyZtD5nZ2epG4w2duzY8djuCU/icecXlUoF4P4Fbg92LylbN0D77/OyIiMjYWZmho0bN0rTUlNT8dtvv0mvNXD/8xMaGopq1arJPj8dO3ZEaWmp1D1tx44dMDMzk32WTU1N8fbbbz/mlZB74403ZBdYjhw5EmZmZtK+mpiYYMCAAfjuu+9w69YtqVxcXBxatmwJX1/fx27j9u3b0vejn58fpkyZgpCQEGzZsqVc2Xr16sHZ2Rm+vr5488034efnh+3bt8Pa2lra/uPyl2b+w7p1VYQBF4C9vT0AyN7oR7l06RJMTEzKXaHv5uYGBwcHXLp0STa9bIgF/veh8/LyqnD6g33aTExMynWsrlu3LgB5X5fExES0aNEClpaWcHR0hLOzM5YvXy7ra6ShzQEM3O+bnJqaCi8vLzRr1gwzZsyQfUlp9rWiPjv+/v7lXgtLS8tyfWyqVatWbp8f9LDtWFhYoFatWuW2ow3NB6agoKDcvG3btmHv3r2YN29ehcv269cPycnJ+Oeff7Bnzx70798fJ0+eRM+ePXH37t3HbrtOnTrlptWtWxd37tzBtWvXANwf0WLatGlSny0nJyc4Ozvj5s2bFb6nD/Pg8Qdo95o/6Nq1a7h586bUT6rsY9iwYQDKX2T34LY1oVWzbc379uBnyczMTOcr6z09PWV9YzXbK7ufkydPhq2tLZo1a4Y6depg9OjROHz4sE7bKevSpUsVHvsBAQHS/LK0/dxpPOw4ebCPm5mZGTw9PWXT0tPTkZeXBxcXl3LvV0FBgfRetW3bFr1790ZMTAycnJzQq1cvrF69Wtb/UNt1aVT2mDt79ixefvllqFQq2Nvbw9nZWfrjRZdjX+NR56mAgAD8/fffuH37tmz6447dPn36oFWrVnj99dfh6uqKvn374ttvv31s2NVmuUuXLqFOnTrlLkB82HFVVpcuXaBSqWSha+PGjWjUqJH0vXHhwgUIIfDBBx+Uez811zBo3lNNXR6kbT/N7OxsnDhxQi8B93Hvka+vL8aPH48vvvgCTk5OCA8Px9KlS2XHkK7f52U5OTmhQ4cOsqHPNm7cCDMzM0RGRkrT0tPTsWvXrnKvdceOHQHIX2t3d/dyjS669ol98P2ytbWFu7u77LwxePBgFBYWSoH0/PnzOH78OAYNGqTVNiwtLbF3717s3bsXhw4dwpUrV3D48OEKLwLbvHkz9u7di6SkJFy4cAGpqalSA4/me/hx+UvbIFwWR1HA/YDr4eFR7uKNx3nwy/RhNBcoaTtdPHDxmDaSk5Px0ksvoU2bNli2bBnc3d1hbm6O1atXV3gBjbatSK+++ipCQ0OxZcsW7NmzB3PnzsUnn3yChIQEdO3aVed6PmyfDcHPzw9mZmYVvu9t27YFgMcOmWZvb49OnTqhU6dOMDc3x5o1a3Ds2DFp+cp4++23sXr1arz77rsICQmBSqWCQqFA3759dWoxqqrjTLPNgQMHYsiQIRWWadCggV62rQ1tthUQEIDz588jMTERu3btwubNm7Fs2TJMmzatwotFqpourbe6UCqV5cKQWq2Gi4sL4uLiKlxG84emQqFAfHw8jh49iu+//x67d+/Ga6+9hvnz5+Po0aOwtbXVel0alXnfb968ibZt28Le3h4zZ85E7dq1YWlpiRMnTmDy5Mk6HfuV8bh9sLKywqFDh3DgwAFs374du3btwsaNG9G+fXvs2bPnocs/6XLaUiqViIiIwJYtW7Bs2TLk5OTg8OHDmD17tlRG8xpOnDgR4eHhFa5HmyEWtbFz505YWlqiXbt2jy37sO/U0tLSCl8XbY6z+fPnY+jQodi2bRv27NmDd955B7GxsTh69Kjsj0Jtv88f1LdvXwwbNgynTp1Co0aN8O2336JDhw7SqAHA/de7U6dOeO+99ypch+YPj6cpMDAQwcHBWLduHQYPHox169bBwsICr776qlbLm5qaSgH9cdq0aSN7PcpSqVRwd3fH6dOnH7mO06dPo0aNGlKDpDYYcP9fjx49sHLlSqSkpMi6E1TE29sbarUa6enp0l/UwP2rKm/evAlvb+8qrZtarcYff/wh+xD8/vvvACC1cm3evBmWlpbYvXs3lEqlVG716tWV3r67uztGjRqFUaNGITc3Fy+++CI++ugjdO3aVdrX8+fPS1dGapw/f77KXouy2yn7F2JxcTEuXryo9QetLBsbG4SFheHgwYP466+/ZD8FP4kmTZpgzZo1yMrKemzZ9PT0ctN+//13WFtbS2EhPj4eQ4YMwfz586Uyd+/eLXdF7ZOemHXl7OwMOzs7lJaWPtHrXRHN+3rhwgXZF2BJSQkyMzNlgbmq9tPGxgZ9+vRBnz59UFxcjMjISHz00UeIjo7WeWgpb29vnD9/vtx0zc/olT3+H3acaNO6Xbt2bfzwww9o1aqVVsG6RYsWaNGiBT766COsX78eAwYMwIYNG/D666/rvC5tPOz9TEpKwvXr15GQkIA2bdpI0zVXXGuzjgeVPX88KC0tDU5OTk80rJqJiQk6dOiADh06YMGCBZg9ezb+85//4MCBA4/8jDxuOW9vb5w+fRpqtVr2h4u2x1WfPn2wZs0a7Nu3D+fOnYMQQvaTueYcam5u/tjPsre3d4XHYUWvZUW2b9+Odu3aaXXcVKtWrcIRAy5duqTT8FAPCgoKQlBQEKZOnYojR46gVatWWLFiBWbNmlXp7/OIiAi8+eabUov577//jujoaFmZ2rVro6CgQKvXet++fSgoKJC14mr7Wmukp6fLzqcFBQXIyspCt27dZOUGDx6M8ePHIysrC+vXr0f37t117hpWFXr06IFVq1bhxx9/lHX30khOTkZmZibefPNNndbLLgr/77333oONjQ1ef/115OTklJufkZGBxYsXA4B0kDx4B50FCxYAgF5+iik73IgQAkuWLIG5uTk6dOgA4P5fUwqFQjaMTmZmJrZu3frE2ywtLS33c6CLiws8PDykny+bNGkCFxcXrFixQvaT5s6dO3Hu3Lkqey06duwICwsLfPrpp7K/zr/88kvk5eU98XamTZuG0tJSDBw4sMKuCg+2ON25cwcpKSkVrmvnzp0AtPs5KSUlRdZf9cqVK9i2bRs6d+4stUqYmpqW2/5nn31Wbkg1zRezrkPJ6MrU1BS9e/fG5s2bK2z11nSt0EWTJk1QvXp1rFq1CiUlJdL0uLi4cj9nV8V+Xr9+XfbcwsICgYGBEEI8tP/po3Tr1g0//fST7Ji4ffs2Vq5cCR8fH636uT/K1q1bZcPt/fTTTzh27JhWv568+uqrKC0txYcfflhuXklJifQ6/vPPP+WOM82NNDSfaW3XpYuHvZ+a479snYqLi7Fs2bIK16FNlwV3d3c0atQIa9askW0vNTUVe/bsKffFr40bN26Um/bg6/aky3Xr1g3Z2dmybgYlJSX47LPPYGtr+9hfiDp27AhHR0ds3LgRGzduRLNmzWTdY1xcXBAWFobPP/+8wj/Iy36Wu3XrhqNHj+Knn36SzX9Ya35Z9+7dw969e7U+P9euXRtHjx5FcXGxNC0xMRFXrlzRavkH5efny84rwP2wa2JiInutgSf/PndwcEB4eDi+/fZbbNiwARYWFoiIiJCVefXVV5GSkoLdu3eXW/7mzZtSHbt164aSkhIsX75cml9aWorPPvvs8TtbxsqVK2Xns+XLl6OkpKTceaNfv35QKBQYO3Ys/vjjD9k1DE/TpEmTYGVlhTfffLPcOfrGjRt46623YG1tjUmTJum0Xrbg/r/atWtj/fr16NOnDwICAmR3Mjty5Ag2bdokjc/XsGFDDBkyBCtXrpR+Tvvpp5+wZs0aREREaPVTjC4sLS2xa9cuDBkyBM2bN8fOnTuxfft2TJkyRWrt6969OxYsWIAuXbqgf//+yM3NxdKlS+Hn5/fYpv+HuXXrFjw9PREVFYWGDRvC1tYWP/zwA37++WepVdHc3ByffPIJhg0bhrZt26Jfv37IycnB4sWL4ePjg3HjxlXJa+Ds7Izo6GjExMSgS5cueOmll3D+/HksW7YMTZs2feIPZmhoKJYsWYK3334bderUke5kVlxcjN9//x1xcXGwsLCAm5sbgPsBt2XLlmjRogW6dOkCLy8v3Lx5E1u3bkVycjIiIiLQuHHjx263fv36CA8PxzvvvAOlUil9eZf9mbxHjx74+uuvoVKpEBgYiJSUFPzwww+oXr26bF2NGjWCqakpPvnkE+Tl5UGpVKJ9+/Zajcmrq48//hgHDhxA8+bNMWLECAQGBuLGjRs4ceIEfvjhhwq/vB/FwsICM2bMwNtvv4327dvj1VdfRWZmJr766ivUrl1b1kJXu3ZtODg4YMWKFbCzs4ONjQ2aN2+uU7/Wzp07w83NDa1atYKrqyvOnTuHJUuWoHv37jr17dJ4//338c0336Br165455134OjoiDVr1uDixYvYvHlzpW/i4Ofnh9atW2PkyJEoKirCokWLUL169Yf+1FlW27Zt8eabbyI2NhanTp1C586dYW5ujvT0dGzatAmLFy9GVFQU1qxZg2XLluHll19G7dq1cevWLaxatQr29vbSl7+269LFw47bli1bolq1ahgyZAjeeecdKBQKfP311xV2bwgODsbGjRsxfvx4NG3aFLa2tujZs2eF25s7dy66du2KkJAQDB8+HIWFhfjss8+gUqkeOVb2w8ycOROHDh1C9+7d4e3tjdzcXCxbtgyenp4VtkLpstwbb7yBzz//HEOHDsXx48fh4+OD+Ph4HD58GIsWLXrssWpubo7IyEhs2LABt2/frvBagqVLl6J169YICgrCiBEjUKtWLeTk5CAlJQV//vknfv31VwD3G380t6YeO3YsbGxssHLlSqmV+VF+/PFH5Ofnax1wX3/9dcTHx6NLly549dVXkZGRgXXr1qF27dpaLf+g/fv3Y8yYMXjllVdQt25dlJSU4Ouvv5b+WAeq5vu8T58+GDhwIJYtW4bw8PByN7OYNGkSvvvuO/To0QNDhw5FcHAwbt++jTNnziA+Ph6ZmZlwcnJCz5490apVK7z//vvIzMxEYGAgEhISdO53XlxcjA4dOuDVV1+Vvidbt26Nl156SVbO2dkZXbp0waZNm+Dg4KCXxjlt1KlTB2vWrMGAAQMQFBRU7k5mf//9N7755hvdjwOtx1v4l/j999/FiBEjhI+Pj7CwsBB2dnaiVatW4rPPPpMNp3Lv3j0RExMjfH19hbm5ufDy8hLR0dGyMkLcH/ake/fu5baDCoYc0gxtM3fuXGmaZjiOjIwM0blzZ2FtbS1cXV3F9OnTZcNlCSHEl19+KerUqSOUSqXw9/cXq1evlobpeNy2y87TDDlTVFQkJk2aJBo2bCjs7OyEjY2NaNiwYYVj1m7cuFE0btxYKJVK4ejoKAYMGCAb3qjsvjyoojo+zJIlS4S/v78wNzcXrq6uYuTIkbKxdsuuT5fhe06ePCkGDx4satasKSwsLISNjY1o0KCBmDBhgrhw4YJU7t69e2LVqlUiIiJCeHt7C6VSKaytrUXjxo3F3LlzZUPWPIzm9V+3bp30fjVu3LjccEn//POPGDZsmHBychK2trYiPDxcpKWlVTiUzqpVq0StWrWEqampbOilhx1/Dw5386i6lh2CSIj746aOHj1aeHl5CXNzc+Hm5iY6dOggVq5cKZXRDOPz4PA8FQ3fJIQQn376qfR6NmvWTBw+fFgEBweLLl26yMpt27ZNBAYGCjMzM9l62rZtW+HwX0OGDJENT/T555+LNm3aiOrVq0tjx06aNEnk5eVp9VpU9LnJyMgQUVFRwsHBQVhaWopmzZqVG3v6Ya/Hw5Q9F8yfP194eXkJpVIpQkNDy43r/LDPlcbKlStFcHCwsLKyEnZ2diIoKEi899574urVq0IIIU6cOCH69esnatasKZRKpXBxcRE9evSQDWOn7bqE0O2Ye9hxe/jwYdGiRQthZWUlPDw8xHvvvScNr1j2c1JQUCD69+8vHBwcBADpvX7YcfbDDz+IVq1aCSsrK2Fvby969uwpfvvtN1mZh50/NEMwaYbF2rdvn+jVq5fw8PAQFhYWwsPDQ/Tr16/cUFAP0na5nJwc6fNvYWEhgoKCKhwmqqLPqBD/G+tUoVCIK1euVFiXjIwMMXjwYOHm5ibMzc1FjRo1RI8ePUR8fLys3OnTp0Xbtm2FpaWlqFGjhvjwww/Fl19++dhhwiZOnFjhOLGPMn/+fFGjRg2hVCpFq1atxC+//PLQYcIed375448/xGuvvSZq164tLC0thaOjo2jXrp344YcfZMtp+33+sPNmfn6+sLKyKje0W1m3bt0S0dHRws/PT1hYWAgnJyfRsmVLMW/ePNmQXtevXxeDBg0S9vb2QqVSiUGDBknDnWk7TNjBgwfFG2+8IapVqyZsbW3FgAEDHjpu+7fffivw/+OLa+tx5xwNXb+LT58+Lfr16yfc3d2l75Z+/fqVG4ZNWwoh9HC1B1WZoUOHIj4+vsKfz+n5pFAoMHr0aFm3E5JTq9VwdnZGZGQkVq1aZejqPHWZmZnw9fXF3LlzMXHiRENXh+iJBAYGokePHrrfgYqemm3btiEiIgKHDh2SDe1nDNhFgYgM6u7du1AqlbLuCGvXrsWNGzdkt+ckoudHcXEx+vTpo/VV+WQYq1atQq1atR7ZreZ5xYBLRAZ19OhRjBs3Dq+88gqqV6+OEydO4Msvv0T9+vXxyiuvGLp6RPQELCwspDF16dmzYcMGnD59Gtu3b8fixYuf2mg8TxMDLhEZlI+PD7y8vPDpp5/ixo0bcHR0xODBg/Hxxx/L7lJERERVo1+/frC1tcXw4cMxatQoQ1dHL9gHl4iIiIiMCsfBJSIiIiKjwoBLREREREaFfXBxf0iiq1evws7Ozig7WhMRERE974QQuHXrFjw8PB57Ix0GXABXr16Fl5eXoatBRERERI9x5coVeHp6PrIMAy4g3fbwypUrsLe3N3BtiIiIiOhB+fn58PLy0urW6gy4gNQtwd7engGXiIiI6BmmTXdSXmRGREREREaFAZeIiIiIjAoDLhEREREZFQZcIiIiIjIqDLhEREREZFQYcImIiIjIqBg04C5fvhwNGjSQhucKCQnBzp07pflhYWFQKBSyx1tvvSVbx+XLl9G9e3dYW1vDxcUFkyZNQklJydPeFSIiIiJ6Rhh0HFxPT098/PHHqFOnDoQQWLNmDXr16oWTJ0/ihRdeAACMGDECM2fOlJaxtraW/l9aWoru3bvDzc0NR44cQVZWFgYPHgxzc3PMnj37qe8PERERERmeQgghDF2JshwdHTF37lwMHz4cYWFhaNSoERYtWlRh2Z07d6JHjx64evUqXF1dAQArVqzA5MmTce3aNVhYWGi1zfz8fKhUKuTl5fFGD0RERETPIF3y2jPTB7e0tBQbNmzA7du3ERISIk2Pi4uDk5MT6tevj+joaNy5c0eal5KSgqCgICncAkB4eDjy8/Nx9uzZp1p/IiIiIno2GPxWvWfOnEFISAju3r0LW1tbbNmyBYGBgQCA/v37w9vbGx4eHjh9+jQmT56M8+fPIyEhAQCQnZ0tC7cApOfZ2dkP3WZRURGKioqk5/n5+VW9W0RERERkIAYPuPXq1cOpU6eQl5eH+Ph4DBkyBAcPHkRgYCDeeOMNqVxQUBDc3d3RoUMHZGRkoHbt2k+8zdjYWMTExFRF9YmIiIjoGWPwLgoWFhbw8/NDcHAwYmNj0bBhQyxevLjCss2bNwcAXLhwAQDg5uaGnJwcWRnNczc3t4duMzo6Gnl5edLjypUrVbErRERERPQMMHjAfZBarZZ1Hyjr1KlTAAB3d3cAQEhICM6cOYPc3FypzN69e2Fvby91c6iIUqmUhibTPIiIiEg3paWlSEpKwjfffIOkpCSUlpYaukpEAAzcRSE6Ohpdu3ZFzZo1cevWLaxfvx5JSUnYvXs3MjIysH79enTr1g3Vq1fH6dOnMW7cOLRp0wYNGjQAAHTu3BmBgYEYNGgQ5syZg+zsbEydOhWjR4+GUqk05K4REREZtYSEBEyYMAGZmZnSNB8fH8yfPx+RkZGGqxgRDNyCm5ubi8GDB6NevXro0KEDfv75Z+zevRudOnWChYUFfvjhB3Tu3Bn+/v6YMGECevfuje+//15a3tTUFImJiTA1NUVISAgGDhyIwYMHy8bNJSIioqqVkJCAqKgoBAUFISUlBbdu3ZJGNoqKipIuBicylGduHFxD4Di4RERE2iktLYWfnx+CgoKwdetWmJj8r61MrVYjIiICqampSE9Ph6mpqQFrSsbmuRwHl4iIiJ59ycnJyMzMxJQpU2ThFgBMTEwQHR2NixcvIjk52UA1JGLAJSIiIh1kZWUBAOrXr1/hfM10TTkiQ2DAJSIiIq1pRjJKTU2tcL5muqYckSEw4BIREZHWQkND4ePjg9mzZ0OtVsvmqdVqxMbGwtfXF6GhoQaqIREDLhEREenA1NQU8+fPR2JiIiIiImSjKERERCAxMRHz5s3jBWZkUAa/VS8RERE9XyIjIxEfH48JEyagZcuW0nRfX1/Ex8dzHFwyOA4TBg4TRkRE9CRKS0uRnJyMrKwsuLu7IzQ0lC23pDe65DW24BIREdETMTU1RVhYmKGrQVQO++ASERERkVFhwCUiIiIio8IuCkRERPRE2AeXnlVswSUiIiKdJSQkwM/PD+3atUP//v3Rrl07+Pn5ISEhwdBVI2LAJSIiIt0kJCQgKioKQUFBsnFwg4KCEBUVxZBLBsdhwsBhwoiIiLRVWloKPz8/BAUFYevWrTAx+V9bmVqtRkREBFJTU5Gens7uClSldMlrbMElIiIirSUnJyMzMxNTpkyRhVsAMDExQXR0NC5evIjk5GQD1ZCIAZeIiIh0kJWVBQCoX79+hfM10zXliAyBAZeIiIi05u7uDgBITU2tcL5muqYckSEw4BIREZHWQkND4ePjg9mzZ0OtVsvmqdVqxMbGwtfXF6GhoQaqIREDLhEREenA1NQU8+fPR2JiIiIiImSjKERERCAxMRHz5s3jBWZkULzRAxEREekkMjIS8fHxmDBhAlq2bClN9/X1RXx8PCIjIw1YOyIOEwaAw4QRERE9Cd7JjJ4mXfIaW3CJiIjoiZiamiIsLMzQ1SAqh31wiYiIiMioMOASERERkVFhwCUiIiIio8KAS0RERERGhQGXiIiIiIwKAy4RERERGRUGXCIiIiIyKgy4RERERGRUGHCJiIiIyKgw4BIRERGRUWHAJSIiIiKjwoBLREREREaFAZeIiIiIjAoDLhEREREZFQZcIiIiIjIqDLhEREREZFQYcImIiIjIqDDgEhEREZFRYcAlIiIiIqPCgEtERERERoUBl4iIiIiMCgMuERERERkVBlwiIiIiMioMuERERERkVBhwiYiIiMioMOASERERkVFhwCUiIiIio8KAS0RERERGhQGXiIiIiIyKQQPu8uXL0aBBA9jb28Pe3h4hISHYuXOnNP/u3bsYPXo0qlevDltbW/Tu3Rs5OTmydVy+fBndu3eHtbU1XFxcMGnSJJSUlDztXSEiIiKiZ4RBA66npyc+/vhjHD9+HL/88gvat2+PXr164ezZswCAcePG4fvvv8emTZtw8OBBXL16FZGRkdLypaWl6N69O4qLi3HkyBGsWbMGX331FaZNm2aoXSIiIiIiA1MIIYShK1GWo6Mj5s6di6ioKDg7O2P9+vWIiooCAKSlpSEgIAApKSlo0aIFdu7ciR49euDq1atwdXUFAKxYsQKTJ0/GtWvXYGFhodU28/PzoVKpkJeXB3t7e73tGxERERE9GV3y2jPTB7e0tBQbNmzA7du3ERISguPHj+PevXvo2LGjVMbf3x81a9ZESkoKACAlJQVBQUFSuAWA8PBw5OfnS63ARERERPTvYmboCpw5cwYhISG4e/cubG1tsWXLFgQGBuLUqVOwsLCAg4ODrLyrqyuys7MBANnZ2bJwq5mvmfcwRUVFKCoqkp7n5+dX0d4QERERkaEZvAW3Xr16OHXqFI4dO4aRI0diyJAh+O233/S6zdjYWKhUKunh5eWl1+0RERER0dNj8IBrYWEBPz8/BAcHIzY2Fg0bNsTixYvh5uaG4uJi3Lx5U1Y+JycHbm5uAAA3N7dyoyponmvKVCQ6Ohp5eXnS48qVK1W7U0RERERkMAYPuA9Sq9UoKipCcHAwzM3NsW/fPmne+fPncfnyZYSEhAAAQkJCcObMGeTm5kpl9u7dC3t7ewQGBj50G0qlUhqaTPMgIiIiIuNg0D640dHR6Nq1K2rWrIlbt25h/fr1SEpKwu7du6FSqTB8+HCMHz8ejo6OsLe3x9tvv42QkBC0aNECANC5c2cEBgZi0KBBmDNnDrKzszF16lSMHj0aSqXSkLtGRERERAZi0ICbm5uLwYMHIysrCyqVCg0aNMDu3bvRqVMnAMDChQthYmKC3r17o6ioCOHh4Vi2bJm0vKmpKRITEzFy5EiEhITAxsYGQ4YMwcyZMw21S0RERERkYM/cOLiGwHFwiYiIiJ5tz+U4uEREREREVYEBl4iIiIiMCgMuERERERkVBlwiIiIiMioMuERERERkVBhwiYiIiMioMOASERERkVFhwCUiIiIio8KAS0RERERGhQGXiIiIiIwKAy4RERERGRUGXCIiIiIyKgy4RERERGRUGHCJiIiIyKgw4BIRERGRUWHAJSIiIiKjwoBLREREREaFAZeIiIiIjAoDLhEREREZFQZcIiIiIjIqDLhEREREZFQYcImIiIjIqDDgEhEREZFRYcAlIiIiIqPCgEtERERERoUBl4iIiIiMCgMuERERERkVBlwiIiIiMioMuERERERkVBhwiYiIiMioMOASERERkVFhwCUiIiIio8KAS0RERERGhQGXiIiIiIwKAy4RERERGRUGXCIiIiIyKgy4RERERGRUGHCJiIiIyKgw4BIRERGRUWHAJSIiIiKjwoBLREREREaFAZeIiIiIjAoDLhEREREZFQZcIiIiIjIqDLhEREREZFQYcImIiIjIqDDgEhEREZFRYcAlIiIiIqPCgEtERERERoUBl4iIiIiMCgMuERERERkVgwbc2NhYNG3aFHZ2dnBxcUFERATOnz8vKxMWFgaFQiF7vPXWW7Iyly9fRvfu3WFtbQ0XFxdMmjQJJSUlT3NXiIiIiOgZYWbIjR88eBCjR49G06ZNUVJSgilTpqBz58747bffYGNjI5UbMWIEZs6cKT23traW/l9aWoru3bvDzc0NR44cQVZWFgYPHgxzc3PMnj37qe4PERERERmeQgghDF0JjWvXrsHFxQUHDx5EmzZtANxvwW3UqBEWLVpU4TI7d+5Ejx49cPXqVbi6ugIAVqxYgcmTJ+PatWuwsLB47Hbz8/OhUqmQl5cHe3v7KtsfIiIiIqoauuS1Z6oPbl5eHgDA0dFRNj0uLg5OTk6oX78+oqOjcefOHWleSkoKgoKCpHALAOHh4cjPz8fZs2efTsWJiIiI6Jlh0C4KZanVarz77rto1aoV6tevL03v378/vL294eHhgdOnT2Py5Mk4f/48EhISAADZ2dmycAtAep6dnV3htoqKilBUVCQ9z8/Pr+rdISIiIiIDeWYC7ujRo5Gamooff/xRNv2NN96Q/h8UFAR3d3d06NABGRkZqF279hNtKzY2FjExMZWqLxERERE9m56JLgpjxoxBYmIiDhw4AE9Pz0eWbd68OQDgwoULAAA3Nzfk5OTIymieu7m5VbiO6Oho5OXlSY8rV65UdheIiIiI6Blh0IArhMCYMWOwZcsW7N+/H76+vo9d5tSpUwAAd3d3AEBISAjOnDmD3NxcqczevXthb2+PwMDACtehVCphb28vexARERGRcTBoF4XRo0dj/fr12LZtG+zs7KQ+syqVClZWVsjIyMD69evRrVs3VK9eHadPn8a4cePQpk0bNGjQAADQuXNnBAYGYtCgQZgzZw6ys7MxdepUjB49Gkql0pC7R0REREQGYNBhwhQKRYXTV69ejaFDh+LKlSsYOHAgUlNTcfv2bXh5eeHll1/G1KlTZa2uly5dwsiRI5GUlAQbGxsMGTIEH3/8MczMtMvvHCaMiIiI6NmmS157psbBNRQGXCIiIqJn23M7Di4RERERUWUx4BIRERGRUWHAJSIiIiKjwoBLREREREaFAZeIiIiIjAoDLhEREREZFQZcIiIiIjIqDLhEREREZFQYcImIiIjIqGh3L1siIiKiB5SWliI5ORlZWVlwd3dHaGgoTE1NDV0tIrbgEhERke4SEhLg5+eHdu3aoX///mjXrh38/PyQkJBg6KoRMeASERGRbhISEhAVFYWgoCCkpKTg1q1bSElJQVBQEKKiohhyyeAUQghh6EoYWn5+PlQqFfLy8mBvb2/o6hARET2zSktL4efnh6CgIGzduhUmJv9rK1Or1YiIiEBqairS09PZXYGqlC55jS24REREpLXk5GRkZmZiypQpsnALACYmJoiOjsbFixeRnJxsoBoSMeASERGRDrKysgAA9evXr3C+ZrqmHJEhMOASERGR1tzd3QEAqampFc7XTNeUIzIEBlwiIiLSWmhoKHx8fDB79myo1WrZPLVajdjYWPj6+iI0NNRANSRiwCUiIiIdmJqaYv78+UhMTERERIRsFIWIiAgkJiZi3rx5vMCMDIo3eiAiIiKdREZGIj4+HhMmTEDLli2l6b6+voiPj0dkZKQBa0fEYcIAcJgwIiKiJ8E7mdHTpEteYwsuERERPRFTU1OEhYUZuhpE5bAPLhEREREZFbbgEhER0RNhFwV6VrEFl4iIiHSWkJAAPz8/tGvXDv3790e7du3g5+eHhIQEQ1eNiAGXiIiIdJOQkICoqCgEBQXJhgkLCgpCVFQUQy4ZHEdRAEdRICIi0lZpaSn8/PwQFBSErVu3wsTkf21larUaERERSE1NRXp6OrsrUJXSJa+xBZeIiIi0lpycjMzMTEyZMkUWbgHAxMQE0dHRuHjxIpKTkw1UQyIGXCIiItJBVlYWAKB+/foVztdM15QjMgQGXCIiItKau7s7ACA1NbXC+ZrpmnJEhsCAS0RERFoLDQ2Fj48PZs+eDbVaLZunVqsRGxsLX19fhIaGGqiGRAy4REREpANTU1PMnz8fiYmJiIiIkI2iEBERgcTERMybN48XmJFB8UYPREREpJPIyEjEx8djwoQJaNmypTTd19cX8fHxiIyMNGDtiDhMGAAOE0ZERPQkeCczepp0yWtswSUiIqInYmpqirCwMENXg6gc9sElIiIiIqPCgEtERERERoUBl4iIiIiMCgMuERERERkVBlwiIiIiMioMuERERERkVBhwiYiIiMioMOASERERkVFhwCUiIiIio8KAS0RERERGhQGXiIiIiIwKAy4RERERGRUGXCIiIiIyKgy4RERERGRUGHCJiIiIyKiYPemCxcXFyM3NhVqtlk2vWbNmpStFRERERPSkdA646enpeO2113DkyBHZdCEEFAoFSktLq6xyRERERES60rmLwtChQ2FiYoLExEQcP34cJ06cwIkTJ3Dy5EmcOHFCp3XFxsaiadOmsLOzg4uLCyIiInD+/HlZmbt372L06NGoXr06bG1t0bt3b+Tk5MjKXL58Gd27d4e1tTVcXFwwadIklJSU6LprRERERGQEdG7BPXXqFI4fPw5/f/9Kb/zgwYMYPXo0mjZtipKSEkyZMgWdO3fGb7/9BhsbGwDAuHHjsH37dmzatAkqlQpjxoxBZGQkDh8+DAAoLS1F9+7d4ebmhiNHjiArKwuDBw+Gubk5Zs+eXek6EhEREdHzRSGEELos0LRpUyxcuBCtW7eu8spcu3YNLi4uOHjwINq0aYO8vDw4Oztj/fr1iIqKAgCkpaUhICAAKSkpaNGiBXbu3IkePXrg6tWrcHV1BQCsWLECkydPxrVr12BhYfHY7ebn50OlUiEvLw/29vZVvl9EREREVDm65DWtuijk5+dLj08++QTvvfcekpKScP36ddm8/Pz8SlU8Ly8PAODo6AgAOH78OO7du4eOHTtKZfz9/VGzZk2kpKQAAFJSUhAUFCSFWwAIDw9Hfn4+zp49W6n6EBEREdHzR6suCg4ODlAoFNJzIQQ6dOggK1PZi8zUajXeffddtGrVCvXr1wcAZGdnw8LCAg4ODrKyrq6uyM7OlsqUDbea+Zp5FSkqKkJRUZH0vLLBnIiIiIieHVoF3AMHDui7Hhg9ejRSU1Px448/6n1bsbGxiImJ0ft2iIiIiOjp0yrgtm3bVvr/5cuX4eXlJWvRBe634F65cuWJKjFmzBgkJibi0KFD8PT0lKa7ubmhuLgYN2/elLXi5uTkwM3NTSrz008/ydanGWVBU+ZB0dHRGD9+vPQ8Pz8fXl5eT1R3IiIiInq26DxMmK+vL65du1Zu+o0bN+Dr66vTuoQQGDNmDLZs2YL9+/eXWz44OBjm5ubYt2+fNO38+fO4fPkyQkJCAAAhISE4c+YMcnNzpTJ79+6Fvb09AgMDK9yuUqmEvb297EFERERExkHnYcI0fW0fVFBQAEtLS53WNXr0aKxfvx7btm2DnZ2d1GdWpVLBysoKKpUKw4cPx/jx4+Ho6Ah7e3u8/fbbCAkJQYsWLQAAnTt3RmBgIAYNGoQ5c+YgOzsbU6dOxejRo6FUKnXdPSIiIiJ6zmkdcDU/6SsUCnzwwQewtraW5pWWluLYsWNo1KiRThtfvnw5ACAsLEw2ffXq1Rg6dCgAYOHChTAxMUHv3r1RVFSE8PBwLFu2TCpramqKxMREjBw5EiEhIbCxscGQIUMwc+ZMnepCRERERMZB63Fw27VrB+D+zRlCQkJk48taWFjAx8cHEydORJ06dfRTUz3iOLhEREREzzZd8prWLbiakRSGDRuGxYsXMwgSERER0TNJ5z64q1ev1kc9iIiIiIiqhM4BNzIyssLpCoUClpaW8PPzQ//+/VGvXr1KV46IiIiISFc6DxNmb2+P/fv348SJE1AoFFAoFDh58iT279+PkpISbNy4EQ0bNsThw4f1UV8iIiIiokfSuQXXzc0N/fv3x5IlS2Bicj8fq9VqjB07FnZ2dtiwYQPeeustTJ48+anclYyIiIiIqCytR1HQcHZ2xuHDh1G3bl3Z9N9//x0tW7bE33//jTNnziA0NBQ3b96syrrqDUdRICIiInq26WUUBY2SkhKkpaWVC7hpaWkoLS0FAFhaWlZ4MwgiIiJ6tt25cwdpaWlaly8sLERmZiZ8fHxgZWWl1TL+/v6y8fSJqprOAXfQoEEYPnw4pkyZgqZNmwIAfv75Z8yePRuDBw8GcH+s3BdeeKFqa0pERER6l5aWhuDgYL1u4/jx43jxxRf1ug36d9O5i0JpaSk+/vhjLFmyBDk5OQAAV1dXvP3225g8eTJMTU1x+fJlmJiYwNPTUy+VrmrsokBERHSfri24586dw8CBA7Fu3ToEBARotQxbcOlJ6JLXdA64D24IwHMfChlwiYiInsyJEycQHBzMVlnSO732wS2LYZCIiIiInjU6j4Obk5ODQYMGwcPDA2ZmZjA1NZU9iIiIiIgMSecW3KFDh+Ly5cv44IMP4O7uztESiIiIiOiZonPA/fHHH5GcnIxGjRrpoTpERERERJWjcxcFLy8vVOK6NCIiIiIivdI54C5atAjvv/8+MjMz9VAdIiIiIqLK0bmLQp8+fXDnzh3Url0b1tbWMDc3l82/ceNGlVWOiIiIiEhXOgfcRYsW6aEaRERERERVQ+eAO2TIEH3Ug4iIiIioSujcBxcAMjIyMHXqVPTr1w+5ubkAgJ07d+Ls2bNVWjkiIiIiIl3pHHAPHjyIoKAgHDt2DAkJCSgoKAAA/Prrr5g+fXqVV5CIiIiISBc6B9z3338fs2bNwt69e2FhYSFNb9++PY4ePVqllSMiIiIi0pXOAffMmTN4+eWXy013cXHB33//XSWVIiIiIiJ6UjoHXAcHB2RlZZWbfvLkSdSoUaNKKkVERERE9KR0Drh9+/bF5MmTkZ2dDYVCAbVajcOHD2PixIkYPHiwPupIRERERKQ1nQPu7Nmz4e/vDy8vLxQUFCAwMBBt2rRBy5YtMXXqVH3UkYiIiIhIazqPg2thYYFVq1bhgw8+QGpqKgoKCtC4cWPUqVNHH/UjIiIiItKJzgFXo2bNmqhZs2ZV1oWIiIiIqNK0Crjjx4/XeoULFix44soQEREREVWWVgH35MmTWq1MoVBUqjJERERERJWlVcA9cOCAvutBRERERFQldB5FgYiIiIjoWcaAS0RERERGhQGXiIiIiIwKAy4RERERGRUGXCIiIiIyKk90o4f09HQcOHAAubm5UKvVsnnTpk2rkooRERERET0JnQPuqlWrMHLkSDg5OcHNzU029q1CoWDAJSIiIiKD0jngzpo1Cx999BEmT56sj/oQEREREVWKzn1w//nnH7zyyiv6qAsRERERUaXpHHBfeeUV7NmzRx91ISIiIiKqNK26KHz66afS//38/PDBBx/g6NGjCAoKgrm5uazsO++8U7U1JCIiIiLSgVYBd+HChbLntra2OHjwIA4ePCibrlAoGHCJiIiIyKC0CrgXL17Udz2IiIiIiKqEzn1wZ86ciTt37pSbXlhYiJkzZ1ZJpYiIiIiInpTOATcmJgYFBQXlpt+5cwcxMTFVUikiIiIioielc8AVQshu7qDx66+/wtHRsUoqRURERET0pLS+0UO1atWgUCigUChQt25dWcgtLS1FQUEB3nrrLb1UkoiIiIhIW1oH3EWLFkEIgddeew0xMTFQqVTSPAsLC/j4+CAkJEQvlSQiIiIi0pbWAXfIkCEAAF9fX7Rs2bLc+LdERERERM8CrQOuRtu2baX/3717F8XFxbL59vb2la8VEREREdET0vkiszt37mDMmDFwcXGBjY0NqlWrJnvo4tChQ+jZsyc8PDygUCiwdetW2fyhQ4dK/X41jy5dusjK3LhxAwMGDIC9vT0cHBwwfPjwCkd5ICIiIqJ/B50D7qRJk7B//34sX74cSqUSX3zxBWJiYuDh4YG1a9fqtK7bt2+jYcOGWLp06UPLdOnSBVlZWdLjm2++kc0fMGAAzp49i7179yIxMRGHDh3CG2+8oetuEREREZGR0LmLwvfff4+1a9ciLCwMw4YNQ2hoKPz8/ODt7Y24uDgMGDBA63V17doVXbt2fWQZpVIJNze3CuedO3cOu3btws8//4wmTZoAAD777DN069YN8+bNg4eHh/Y7RkRERERGQecW3Bs3bqBWrVoA7ve3vXHjBgCgdevWOHToUNXWDkBSUhJcXFxQr149jBw5EtevX5fmpaSkwMHBQQq3ANCxY0eYmJjg2LFjVV4XIiIiInr26Rxwa9WqhYsXLwIA/P398e233wK437Lr4OBQpZXr0qUL1q5di3379uGTTz7BwYMH0bVrV5SWlgIAsrOz4eLiIlvGzMwMjo6OyM7Ofuh6i4qKkJ+fL3sQERERkXHQuYvCsGHD8Ouvv6Jt27Z4//330bNnTyxZsgT37t3DggULqrRyffv2lf4fFBSEBg0aoHbt2khKSkKHDh2eeL2xsbG8rTARERGRkdI54I4bN076f8eOHZGWlobjx4/Dz88PDRo0qNLKPahWrVpwcnLChQsX0KFDB7i5uSE3N1dWpqSkBDdu3Hhov10AiI6Oxvjx46Xn+fn58PLy0lu9iYiIiOjp0TrgqtVqzJ07F9999x2Ki4vRoUMHTJ8+Hd7e3vD29tZnHSV//vknrl+/Dnd3dwBASEgIbt68iePHjyM4OBgAsH//fqjVajRv3vyh61EqlVAqlU+lzkRERET0dGndB/ejjz7ClClTYGtrixo1amDx4sUYPXp0pTZeUFCAU6dO4dSpUwCAixcv4tSpU7h8+TIKCgowadIkHD16FJmZmdi3bx969eoFPz8/hIeHAwACAgLQpUsXjBgxAj/99BMOHz6MMWPGoG/fvhxBgYiIiOhfSuuAu3btWixbtgy7d+/G1q1b8f333yMuLg5qtfqJN/7LL7+gcePGaNy4MQBg/PjxaNy4MaZNmwZTU1OcPn0aL730EurWrYvhw4cjODgYycnJstbXuLg4+Pv7o0OHDujWrRtat26NlStXPnGdiIiIiOj5phBCCG0KKpVKXLhwQdZX1dLSEhcuXICnp6feKvg05OfnQ6VSIS8vj7caJiIi0sGJEycQHByM48eP48UXXzR0dciI6ZLXtG7BLSkpgaWlpWyaubk57t2792S1JCIiIiLSA60vMhNCYOjQobLuAXfv3sVbb70FGxsbaVpCQkLV1pCIiIiISAdaB9whQ4aUmzZw4MAqrQwRERERUWVpHXBXr16tz3oQEREREVUJnW/VS0RERET0LGPAJSIiIiKjovOteonoyZSWliI5ORlZWVlwd3dHaGgoTE1NDV0tIiIio8MWXKKnICEhAX5+fmjXrh369++Pdu3awc/Pj6OOEBER6QEDLpGeJSQkICoqCkFBQUhJScGtW7eQkpKCoKAgREVFMeQSERFVMa3vZGbMeCcz0pfS0lL4+fkhKCgIW7duhYnJ//6mVKvViIiIQGpqKtLT09ldgYieS7yTGT0termTGRHpLjk5GZmZmZgyZYos3AKAiYkJoqOjcfHiRSQnJxuohkRERMaHAZdIj7KysgAA9evXr3C+ZrqmHBEREVUeAy6RHrm7uwMAUlNTK5yvma4pR0RERJXHgEukR6GhofDx8cHs2bOhVqtl89RqNWJjY+Hr64vQ0FAD1ZCIiMj4MOAS6ZGpqSnmz5+PxMREREREyEZRiIiIQGJiIubNm8cLzIiIiKoQb/RApGeRkZGIj4/HhAkT0LJlS2m6r68v4uPjERkZacDaERERGR8GXKKnIDIyEr169eKdzIiIiJ4CBlyip8TU1BRhYWGGrgYREZHRYx9cIiIiIjIqDLhEREREZFQYcImIiIjIqDDgEhEREZFR4UVmRE9JaWkpR1EgIiJ6CtiCS/QUJCQkwM/PD+3atUP//v3Rrl07+Pn5ISEhwdBVIyIiMjoMuER6lpCQgKioKAQFBcnuZBYUFISoqCiGXCIioiqmEEIIQ1fC0PLz86FSqZCXlwd7e3tDV4eMSGlpKfz8/BAUFIStW7fCxOR/f1Oq1WpEREQgNTUV6enp7K5ARM+lEydOIDg4GMePH8eLL75o6OqQEdMlr7EFl0iPkpOTkZmZiSlTpkAIgaSkJHzzzTdISkqCEALR0dG4ePEikpOTDV1VIiIio8GLzIj0KCsrCwCQkZGBfv36ITMzU5rn4+ODWbNmycoRERFR5THgEumRu7s7AGDgwIHo0aMHJk2aBCsrKxQWFmLnzp0YOHCgrBwRERFVHgMukR61bNkSZmZmsLGxQWpqKhITE6V5Pj4+UKlUuH37Nlq2bGnAWhIRERkX9sEl0qMjR46gpKQEeXl5KCwsxMqVK3H16lWsXLkShYWFyMvLQ0lJCY4cOWLoqhIRERkNtuAS6dFff/0FAGjcuDFu3LiBN954Q5rn4+ODxo0b4+TJk1I5IiIiqjy24BLp0bVr1wAAo0aNQkZGBg4cOID169fjwIEDuHDhAt566y1ZOSIiIqo8tuAS6ZGzszOA+zd7eO211xAWFibNU6vV2Lp1q6wcEZE+pKen49atW3pZ97lz52T/VjU7OzvUqVNHL+sm48WAS6RHNWrUAADs3LkTERERiI6ORv369ZGamorY2Fjs3LlTVo6IqKqlp6ejbt26et+OZlQYffj9998ZckknDLhEehQaGgofHx84OTnh9OnTstESfHx80KRJE1y/fh2hoaEGrCURGTNNy+26desQEBBQ5esvLCxEZmYmfHx8YGVlVaXrPnfuHAYOHKi31mcyXgy4RHpkamqK+fPnIyoqCt26dUNERAQKCwthZWWFCxcuYMeOHYiPj+dteolI7wICAvR2K91WrVrpZb1ET4oBl0jPIiMjMXHiRCxcuBDbt2+XppuZmWHixImIjIw0YO2IiIiMDwMukZ4lJCRg3rx56N69O7p27Sq7k9m8efPQokULhlwiIqIqxIBLpEelpaWYMGECevToga1bt8LE5H8j87311luIiIjAxIkT0atXL3ZTICIiqiIcB5dIj5KTk5GZmYkpU6bIwi0AmJiYIDo6GhcvXkRycrKBakhERGR82IJLpEdZWVkAgPr166O0tBTJycnIysqCu7s7QkNDUb9+fVk5IiIiqjwGXCI9cnd3BwAsWbIEn3/+OTIzM6V5Pj4+0q17NeWIiIio8hhwifQoNDQUzs7OiI6OLjc+ZE5ODqZMmQIXFxeOg0tERFSF2AeXSM+Ki4sB3L/d5MqVK3H16lWsXLkSdnZ2AICioiJDVo+IiMjosAWXSI+SkpKQl5cHf39/3L17V+qSAAC+vr7w9/dHWloakpKS0KFDBwPWlIiIyHiwBZdIj5KSkgAAS5cuxYULF3DgwAGsX78eBw4cQHp6Oj777DNZOSIiIqo8tuASPSWmpqYICwszdDWIiIiMHltwifRIE2inT58OtVotm6dWqxETEyMrR0RERJXHFlwiPQoLC4OzszN+/PFHvPTSS+Vu1fvjjz/CxcWFAZeIiKgKMeAS6ZGpqSlWrFiB3r17Y8eOHdi+fbs0T6FQAACWL1/O2/QSERFVIYN2UTh06BB69uwJDw8PKBQKbN26VTZfCIFp06bB3d0dVlZW6NixI9LT02Vlbty4gQEDBsDe3h4ODg4YPnw4CgoKnuJeEGlHqVTKnltaWhqoJkRERMbNoAH39u3baNiwIZYuXVrh/Dlz5uDTTz/FihUrcOzYMdjY2CA8PBx3796VygwYMABnz57F3r17kZiYiEOHDsmGYiIypNLSUkyYMAE9e/ZEfn6+bBSFvLw89OzZExMnTkRpaamhq0pERGQ0DNpFoWvXrujatWuF84QQWLRoEaZOnYpevXoBANauXQtXV1ds3boVffv2xblz57Br1y78/PPPaNKkCQDgs88+Q7du3TBv3jx4eHg8tX0hqkhycjIyMzPxzTffwNzcvFxf2+joaLRs2RLJycnsh0tERFRFntlRFC5evIjs7Gx07NhRmqZSqdC8eXOkpKQAAFJSUuDg4CCFWwDo2LEjTExMcOzYsadeZ6IHZWVlAQDq169f4XzNdE05IiIiqrxnNuBmZ2cDAFxdXWXTXV1dpXnZ2dlwcXGRzTczM4Ojo6NUpiJFRUXIz8+XPYj0wd3dHQCQmppa4XzNdE05IiIiqrxnNuDqU2xsLFQqlfTw8vIydJXISIWGhsLHxwezZ8/GvXv3kJSUhG+++QZJSUm4d+8eYmNj4evri9DQUENXlYiIyGg8s8OEubm5AQBycnJkrVs5OTlo1KiRVCY3N1e2XElJCW7cuCEtX5Ho6GiMHz9eep6fn8+QS3phamqK+fPno3fv3lCpVCgsLJTmacbD3bx5M4cJIyIiqkLPbAuur68v3NzcsG/fPmlafn4+jh07hpCQEABASEgIbt68iePHj0tl9u/fD7VajebNmz903UqlEvb29rIHkT5pxrx9cFpF04mIiKhyDBpwCwoKcOrUKZw6dQrA/QvLTp06hcuXL0OhUODdd9/FrFmz8N133+HMmTMYPHgwPDw8EBERAQAICAhAly5dMGLECPz00084fPgwxowZg759+3IEBXomaIYJ69GjB/Ly8mTDhN28eRM9evTgMGFERERVzKBdFH755Re0a9dOeq7pNjBkyBB89dVXeO+993D79m288cYbuHnzJlq3bo1du3bJBsiPi4vDmDFj0KFDB5iYmKB379749NNPn/q+EFWEw4QRERE9fQYNuGFhYRBCPHS+QqHAzJkzMXPmzIeWcXR0xPr16/VRPaJK4zBhRERET98z2weXyBhwmDAiIqKnjwGXSI84TBgREdHT98wOE0ZkDDTDhEVFRVU4TNjdu3cRHx/PYcKIiIiqEFtwiZ6CivqaKxSKR/ZBJyIioifDgEukR5phwnr27FnhMGE9e/bkMGFERERVjAGXSI80w4RNmTIFJibyj5uJiQmio6Nx8eJFJCcnG6iGRERExod9cIn0SDP8V0ZGBvr164fMzExpno+PD2bNmiUrR0RERJXHFlwiPdIM/zVo0CAEBQUhJSUFt27dQkpKCoKCgjBo0CBZOSIiIqo8BlwiPWrZsiXMzMzg4uKCTZs24e7du/j+++9x9+5dbNq0CS4uLjAzM0PLli0NXVUiIiKjwS4KRHp05MgRlJSUICcnB9WqVSs3TJjm+ZEjR3irXiIioirCFlwiPXpU31qFQqFVOSIiItINAy6RHrm4uAAAWrduXeEwYa1atZKVIyIiospjwCUyoLKtuERERFQ12AeXSI9yc3MBAD/++GOFt+rVPNeUIyIiospjCy6RHmmG/6qopVahUEjTOUwYERFR1WELLpEeaYYJq169Oi5duoSUlBRkZWXB3d0dISEh8Pb2xvXr1zlMGBERURViCy6RHpUdJiwqKgpnz55FYWEhzp49i6ioKOTk5KCkpARHjhwxdFWJiIiMBltwifRIM/zX2LFjsXTpUiQmJkrzzMzMMHbsWCxevJjDhBEREVUhBlwiPdL0rf3000/RvXt3dO3aVbq4bOfOnfj0009l5YiIiKjyGHCJ9KhsH9wtW7bAzOx/H7k33ngDnp6e7INLRHqlKLmLxm4msLr5O3D1+eqZaHXzdzR2M4Gi5K6hq0LPGQZcIj0q2wc3MjIS0dHRqF+/PlJTUxEbG4ucnBypHG/VS0T6YFlwGSfetAUOvQkcMnRtdBMA4MSbtjhXcBkAGwJIewy4RHqk6Vu7bt06TJ06VdZS6+vri3Xr1mHgwIHsg0tEenPXtiZe/LwAcXFxCPD3N3R1dHIuLQ0DBgzAl91qGroq9JxhwCXSI03f2tq1a+PChQtITk6WhgkLDQ3FTz/9JCtHRFTVhJklTmarUehQF/BoZOjq6KQwW42T2WoIM0tDV4WeM89XZxyi50xoaCh8fHwwe/Zs3Lt3D6dOncKRI0dw6tQp3Lt3D7GxsfD19UVoaKihq0pERGQ02IJLpEempqaYP38+evfuDWtrawghpHnjx4+HEAKbN2+GqampAWtJRERkXNiCS6RnR48eBVD+dr0mJiay+URERFQ1GHCJ9Ki4uBgLFy6ESqWCh4eHbJ67uztUKhUWLlyI4uJiA9WQiIjI+DDgEunRsmXLUFJSgry8PFy/fl027/r168jLy0NJSQmWLVtmoBoSEREZHwZcIj1KT0+X/t+hQwekpKTg1q1bSElJQYcOHSosR0RERJXDi8yI9EhzUZmfnx+2bdsm9btt0aIFtm3bhrp16yIjI0N28RkRERFVDltwifRIpVIBuN8dQa1Wy+ap1WrcuHFDVo6IiIgqjy24RHpkZnb/I/bPP//A09MTAwYMQK1atfDHH38gLi4O//zzj6wcERERVR6/VYn0KCwsDLNmzYKjoyNycnKwYMEC2XxHR0fcuHEDYWFhhqkgERGREWIXBSI9CgsLg0qlkroiPOjGjRtQqVQMuERERFWIAZdIzx43xi3HwCUiIqpaDLhEerRv3z4UFhY+skxhYSH27dv3lGpERERk/BhwifRo9erVAABTU1PcunULCxcuxJgxY7Bw4ULcunULpqamsnJERERUebzIjEiPjh49CgBo2rQpgoKCkJmZKc1bvHgxgoOD8dNPP0nliIiIqPIYcIn0yMLCAsD9oGtlZSWbl5OTIwVeTTkiIiKqPHZRINKjNm3aSP9/sC9u2edlyxEREVHlMOAS6VFkZGSVliMiIqLHY8Al0qMff/yxSssRERHR4zHgEunR5cuXAQA1a9ascL6Xl5esHBEREVUeLzIj0iNNsL18+TLCw8ORlZWF69evo3r16nB3d8fu3btl5YiIiKjy2IJLpEdt27aV/r9nzx6cPn0af/31F06fPo09e/ZUWI6IiIgqhwGXSI80N3IAACGEbF7Z52XLERERUeUw4BLp0dWrV6X/PzjWrVKprLAcERERVQ4DLpEeHTt2DADw8ssvw93dXTbP3d0dERERsnJERERUebzIjEiPNN0QCgoKkJ6ejsOHDyMrKwvu7u5o1aoVunfvLitHRERElccWXCI9qlOnDgBg79696N27N5RKJXr06AGlUonevXtj7969snJERERUeQy4RHo0atQomJmZQaVS4fTp02jZsiXs7e3RsmVLnDlzBiqVCmZmZhg1apShq0pERGQ0nukuCjNmzEBMTIxsWr169ZCWlgYAuHv3LiZMmIANGzagqKgI4eHhWLZsGVxdXQ1RXaJyLCwsMG7cOMydOxeWlpYYP348atWqhT/++ANxcXHIy8vDpEmTyl2ARkRUVe7cuQMAOHHihF7WX1hYiMzMTPj4+MDKyqpK133u3LkqXR/9ezzTARcAXnjhBfzwww/SczOz/1V53Lhx2L59OzZt2gSVSoUxY8YgMjIShw8fNkRV6V/ozp070h9cD9O3b1/k5OQgLi4OCxYskKabmppi8ODB6Nu37yO/ePz9/WFtbV1ldSaifxfNOWrEiBEGrsmTs7OzM3QV6DnzzAdcMzMzuLm5lZuel5eHL7/8EuvXr0f79u0BAKtXr0ZAQACOHj2KFi1aPO2q0r9QWloagoODn2jZ0tJSrF27FmvXrn1kuePHj+PFF198om0QEWlGa9HXH8vnzp3DwIEDsW7dOgQEBFT5+u3s7HidAunsmQ+46enp8PDwgKWlJUJCQhAbG4uaNWvi+PHjuHfvHjp27CiV9ff3R82aNZGSksKAS0+Fv78/jh8/rnX5J/ki8Pf3f9LqERHByckJr7/+ut63ExAQwD/G6ZnxTAfc5s2b46uvvkK9evWQlZWFmJgYhIaGIjU1FdnZ2bCwsICDg4NsGVdXV2RnZz9yvUVFRSgqKpKe5+fn66P69C9gbW39RCd0fhEQERHpzzMdcLt27Sr9v0GDBmjevDm8vb3x7bffVqoje2xsbLmL14iIiIjIODxXw4Q5ODigbt26uHDhAtzc3FBcXIybN2/KyuTk5FTYZ7es6Oho5OXlSY8rV67osdZERERE9DQ9VwG3oKAAGRkZcHd3R3BwMMzNzbFv3z5p/vnz53H58mWEhIQ8cj1KpRL29vayBxEREREZh2e6i8LEiRPRs2dPeHt74+rVq5g+fTpMTU3Rr18/qFQqDB8+HOPHj4ejoyPs7e3x9ttvIyQkhBeYEREREf2LPdMB988//0S/fv1w/fp1ODs7o3Xr1jh69CicnZ0BAAsXLoSJiQl69+4tu9EDEREREf17PdMBd8OGDY+cb2lpiaVLl2Lp0qVPqUZERERE9Kx7rvrgEhERERE9DgMuERERERkVBlwiIiIiMioMuERERERkVBhwiYiIiMioMOASERERkVFhwCUiIiIio8KAS0RERERGhQGXiIiIiIwKAy4RERERGRUGXCIiIiIyKgy4RERERGRUGHCJiIiIyKgw4BIRERGRUWHAJSIiIiKjwoBLREREREaFAZeIiIiIjAoDLhEREREZFQZcIiIiIjIqDLhEREREZFQYcImIiIjIqJgZugJEz5r09HTcunVLL+s+d+6c7N+qZmdnhzp16uhl3URERM8LBlyiMtLT01G3bl29b2fgwIF6W/fvv//OkEtERP9qDLhEZWhabtetW4eAgIAqX39hYSEyMzPh4+MDKyurKl33uXPnMHDgQL21PhMRET0vGHCJKhAQEIAXX3xRL+tu1aqVXtZLRERE9/EiMyIiIiIyKmzBJSIiIsmdO3eQlpamdfknuXjW398f1tbWOteNSFsMuERERCRJS0tDcHCwzsvpcvHs8ePH9dYNjAhgwCUiIqIy/P39cfz4ca3LP8nFs/7+/k9aPSKtMOASERGRxNraWufWVV48S88aXmRGREREREaFAZeIiIiIjAoDLhEREREZFfbBJSpDUXIXjd1MYHXzd+Dq8/X3n9XN39HYzQSKkruGrgoREZFBMeASlWFZcBkn3rQFDr0JHDJ0bXQTAODEm7Y4V3AZQEtDV4eIiMhgGHCJyrhrWxMvfl6AuLg4BDxnw9icS0vDgAED8GW3moauChERkUEx4BKVIcwscTJbjUKHuoBHI0NXRyeF2WqczFZDmFkauipEREQG9Xx1MiQiIiIiegwGXCIiIiIyKgy4RERERGRUGHCJiIiIyKgw4BIRERGRUeEoCkRl3LlzBwBw4sQJvay/sLAQmZmZ8PHxgZWVVZWu+9y5c1W6PiIioucVAy5RGWlpaQCAESNGGLgmT87Ozs7QVSAiIjIoBlyiMiIiIgAA/v7+sLa2rvL1nzt3DgMHDsS6desQEBBQ5eu3s7NDnTp1qny9REREzxMGXKIynJyc8Prrr+t9OwEBAXjxxRf1vh0iIqJ/I15kRkRERERGhQGXiIiIiIwKuygQVcKdO3ekC9O0oRnpQJcRD/TVH5iIiMhYMeASVUJaWhqCg4N1Xm7gwIFalz1+/Dj76xIREemAAZeoEvz9/XH8+HGtyz/JOLj+/v5PWj0iIqJ/JYUQQhi6ElVh6dKlmDt3LrKzs9GwYUN89tlnaNasmVbL5ufnQ6VSIS8vD/b29nquKRERERHpSpe8ZhQXmW3cuBHjx4/H9OnTceLECTRs2BDh4eHIzc01dNWIiIiI6CkzioC7YMECjBgxAsOGDUNgYCBWrFgBa2tr/Pe//zV01YiIiIjoKXvuA25xcTGOHz+Ojh07StNMTEzQsWNHpKSkVLhMUVER8vPzZQ8iIiIiMg7PfcD9+++/UVpaCldXV9l0V1dXZGdnV7hMbGwsVCqV9PDy8noaVSUiIiKip+C5D7hPIjo6Gnl5edLjypUrhq4SEREREVWR536YMCcnJ5iamiInJ0c2PScnB25ubhUuo1QqoVQqn0b1iIiIiOgpe+5bcC0sLBAcHIx9+/ZJ09RqNfbt24eQkBAD1oyIiIiIDOG5b8EFgPHjx2PIkCFo0qQJmjVrhkWLFuH27dsYNmyYoatGRERERE+ZUQTcPn364Nq1a5g2bRqys7PRqFEj7Nq1q9yFZ0RERERk/IzmTmaVwTuZERERET3b/nV3MiMiIiIi0mDAJSIiIiKjwoBLREREREaFAZeIiIiIjAoDLhEREREZFQZcIiIiIjIqDLhEREREZFSM4kYPlaUZCjg/P9/ANSEiIiKiimhymja3cGDABXDr1i0AgJeXl4FrQkRERESPcuvWLahUqkeW4Z3MAKjValy9ehV2dnZQKBSGrg4Zsfz8fHh5eeHKlSu8ax4RGQWe1+hpEULg1q1b8PDwgInJo3vZsgUXgImJCTw9PQ1dDfoXsbe35xcBERkVntfoaXhcy60GLzIjIiIiIqPCgEtERERERoUBl+gpUiqVmD59OpRKpaGrQkRUJXheo2cRLzIjIiIiIqPCFlwiIiIiMioMuERERERkVBhwiYiIiMioMOASPYOSkpKgUChw8+ZNvW5n6NChiIiI0Os2iIi0FRYWhnfffVev28jMzIRCocCpU6f0uh0yLAZcMlpDhw6FQqGAQqGAhYUF/Pz8MHPmTJSUlEgBUvNwdXVF79698ccff8jWceTIEXTr1g3VqlWDpaUlgoKCsGDBApSWlhpor4jIWPGcRVR1GHDJqHXp0gVZWVlIT0/HhAkTMGPGDMydO1eaf/78eVy9ehWbNm3C2bNn0bNnT+mLYMuWLWjbti08PT1x4MABpKWlYezYsZg1axb69u0LDkBCRFWN5yyiqsGAS0ZNqVTCzc0N3t7eGDlyJDp27IjvvvtOmu/i4gJ3d3e0adMG06ZNw2+//YYLFy7g9u3bGDFiBF566SWsXLkSjRo1go+PD15//XWsWbMG8fHx+Pbbbx+57WXLlqFOnTqwtLSEq6sroqKipHlFRUV455134OLiAktLS7Ru3Ro///xzhevJz8+HlZUVdu7cKZu+ZcsW2NnZ4c6dOwCAK1eu4NVXX4WDgwMcHR3Rq1cvZGZmSuVLS0sxfvx4ODg4oHr16njvvff4hUf0jDHkOUuhUGDr1q2yaQ4ODvjqq68A/O+n/YSEBLRr1w7W1tZo2LAhUlJSpPKXLl1Cz549Ua1aNdjY2OCFF17Ajh07pPkHDx5Es2bNoFQq4e7ujvfffx8lJSUV1mfKlClo3rx5uekNGzbEzJkzpedffPEFAgICYGlpCX9/fyxbtkxW/qeffkLjxo1haWmJJk2a4OTJk498Hcg4MODSv4qVlRWKi4sfOg8AiouLsWfPHly/fh0TJ04sV65nz56oW7cuvvnmm4du55dffsE777yDmTNn4vz589i1axfatGkjzX/vvfewefNmrFmzBidOnICfnx/Cw8Nx48aNcuuyt7dHjx49sH79etn0uLg4REREwNraGvfu3UN4eDjs7OyQnJyMw4cPw9bWFl26dJH2d/78+fjqq6/w3//+Fz/++CNu3LiBLVu2PP5FIyKDeVrnLF385z//wcSJE3Hq1CnUrVsX/fr1k0Lq6NGjUVRUhEOHDuHMmTP45JNPYGtrCwD466+/0K1bNzRt2hS//vorli9fji+//BKzZs2qcDsDBgzATz/9hIyMDGna2bNncfr0afTv3x/A/fPgtGnT8NFHH+HcuXOYPXs2PvjgA6xZswYAUFBQgB49eiAwMBDHjx/HjBkzKnyNyAgJIiM1ZMgQ0atXLyGEEGq1Wuzdu1colUoxceJEceDAAQFA/PPPP0IIIa5evSpatmwpatSoIYqKisTHH38sm/+gl156SQQEBDx025s3bxb29vYiPz+/3LyCggJhbm4u4uLipGnFxcXCw8NDzJkzRwghytVvy5YtwtbWVty+fVsIIUReXp6wtLQUO3fuFEII8fXXX4t69eoJtVotrbOoqEhYWVmJ3bt3CyGEcHd3l9YvhBD37t0Tnp6e0mtERIZlyHOWEEIAEFu2bJFNU6lUYvXq1UIIIS5evCgAiC+++EKaf/bsWQFAnDt3TgghRFBQkJgxY0aF658yZUq589TSpUuFra2tKC0tFUII0bZtWzF27FhpfsOGDcXMmTOl59HR0aJ58+bS89q1a4v169fLtvPhhx+KkJAQIYQQn3/+uahevbooLCyU5i9fvlwAECdPnnzk60HPN7bgklFLTEyEra0tLC0t0bVrV/Tp0wczZsyQ5nt6esLGxgYeHh64ffs2Nm/eDAsLC2m+0OIn/Li4ONja2kqP5ORkdOrUCd7e3qhVqxYGDRqEuLg4qStBRkYG7t27h1atWknrMDc3R7NmzXDu3LkKt9GtWzeYm5tLP1Vu3rwZ9vb26NixIwDg119/xYULF2BnZyfVw9HREXfv3kVGRgby8vKQlZUl+7nPzMwMTZo00f7FJCK9M9Q5SxcNGjSQ/u/u7g4AyM3NBQC88847mDVrFlq1aoXp06fj9OnTUtlz584hJCQECoVCmtaqVSsUFBTgzz//rHBbAwYMkH69EkLgm2++wYABAwAAt2/fRkZGBoYPHy7bn1mzZkmtvufOnUODBg1gaWkprTMkJESn/aXnk5mhK0CkT+3atcPy5cthYWEBDw8PmJnJD/nk5GTY29vDxcUFdnZ20vS6desCuH9ybNmyZbn1njt3DoGBgQCAl156SRYca9SoASsrK5w4cQJJSUnYs2cPpk2bhhkzZjy0n+3jWFhYICoqCuvXr0ffvn2xfv169OnTR9qfgoICBAcHIy4urtyyzs7OT7RNInr6DHXOAu73wX0wIN+7d6/cuszNzaX/a8KqWq0GALz++usIDw/H9u3bsWfPHsTGxmL+/Pl4++23tX8RyujXrx8mT56MEydOoLCwEFeuXEGfPn0A3D/vAcCqVavK9dU1NTV9ou2R8WALLhk1Gxsb+Pn5oWbNmuW+KADA19cXtWvXln1RAEDnzp3h6OiI+fPnl1vmu+++Q3p6Ovr16wcAsLOzg5+fn/TQ9IszMzNDx44dMWfOHJw+fRqZmZnYv38/ateuDQsLCxw+fFha57179/Dzzz9LX0AVGTBgAHbt2oWzZ89i//79UisGALz44otIT0+Hi4uLrC5+fn5QqVRQqVRwd3fHsWPHpGVKSkpw/PhxLV9JInoaDHnOcnZ2RlZWlrRcenq69MuTLry8vPDWW28hISEBEyZMwKpVqwAAAQEBSElJkYXow4cPw87ODp6enhWuy9PTE23btkVcXBzi4uLQqVMnuLi4AABcXV3h4eGBP/74o9x5z9fXV9rm6dOncffuXWmdR48e1Xmf6PnDgEtUARsbG3z++efYtm0b3njjDSmgfvnllxg6dCiioqLw6quvPnT5xMREfPrppzh16hQuXbqEtWvXQq1Wo169erCxscHIkSMxadIk7Nq1C7/99htGjBiBO3fuYPjw4Q9dZ5s2beDm5oYBAwbA19dX1mIxYMAAODk5oVevXkhOTsbFixeRlJSEd955R/rpb+zYsfj444+xdetWpKWlYdSoUXq/kQQRPR2VPWcBQPv27bFkyRKcPHkSv/zyC9566y1Za6023n33XezevRsXL17EiRMncODAAQQEBAAARo0ahStXruDtt99GWloatm3bhunTp2P8+PEwMXl4HBkwYAA2bNiATZs2yf6wB4CYmBjExsbi008/xe+//44zZ85g9erVWLBgAQCgf//+UCgUGDFiBH777Tfs2LED8+bN02mf6Dll0B7ARHpU9oKNBz14wcbDHDp0SISHhwt7e3thYWEhXnjhBTFv3jxRUlLyyOWSk5NF27ZtRbVq1YSVlZVo0KCB2LhxozS/sLBQvP3228LJyUkolUrRqlUr8dNPPz22fu+9954AIKZNm1Zum1lZWWLw4MHSOmvVqiVGjBgh8vLyhBD3LyobO3assLe3Fw4ODmL8+PFi8ODBvMiM6BlhyHOWEEL89ddfonPnzsLGxkbUqVNH7Nixo8KLzMpenPXPP/8IAOLAgQNCCCHGjBkjateuLZRKpXB2dhaDBg0Sf//9t1Q+KSlJNG3aVFhYWAg3NzcxefJkce/ePWn+gxeZabahVCqFtbW1uHXrVrl6x8XFiUaNGgkLCwtRrVo10aZNG5GQkCDNT0lJEQ0bNhQWFhaiUaNGYvPmzbzI7F9AIQQHwiQiIiIi48EuCkRERERkVBhwiYiIiMioMOASERERkVFhwCUiIiIio8KAS0RERERGhQGXiIiIiIwKAy4RERERGRUGXCIiIiIyKgy4RERERGRUGHCJiIiIyKgw4BIRERGRUWHAJSIiIiKj8n/h/2KQ6oRo+gAAAABJRU5ErkJggg==",
                        "text/plain": [
                            "<Figure size 800x600 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# What are the GS-path-lengths for presentations solved / unsolved by PPO?\n",
                "gs_path_lengths_for_ppo_solved = []\n",
                "gs_path_lengths_for_ppo_unsolved = []\n",
                "\n",
                "for i, path in enumerate(gs_paths):\n",
                "    if i in ppo_checkpoint['success_record']['solved']:\n",
                "        gs_path_lengths_for_ppo_solved.append(len(path)-1)\n",
                "    else:\n",
                "        gs_path_lengths_for_ppo_unsolved.append(len(path)-1)\n",
                "\n",
                "# Creating the boxplot\n",
                "plt.figure(figsize=(8, 6))  # Set the figure size\n",
                "plt.boxplot([gs_path_lengths_for_ppo_solved, gs_path_lengths_for_ppo_unsolved], labels=['PPO-solved', 'PPO-unsolved'])  # Plot boxplots for both lists\n",
                "plt.title('Comparison of GS path lengths for presentations solved / unsolved by PPO')  # Add a title\n",
                "plt.ylabel('Path length')  # Label the y-axis\n",
                "\n",
                "#plt.savefig('/Users/alishehper/work/ac_paper/fig/path_lengths_ppo_solved_vs_unsolved.png')\n",
                "# plt.savefig(\"./Images/path_lengths_ppo_solved_vs_unsolved.pdf\")\n",
                "# Show the plot\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 11,
            "metadata": {},
            "outputs": [],
            "source": [
                "# What are the lengths of paths found by PPO itself?\n",
                "ppo_path_lengths_for_ppo_solved = []\n",
                "\n",
                "for i, path in enumerate(gs_paths):\n",
                "    if i in ppo_checkpoint['success_record']['solved']:\n",
                "        ppo_path_lengths_for_ppo_solved.append(len(id_to_ac_seq_dict[i]))"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 12,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 800x600 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# Example data\n",
                "x_values = gs_path_lengths_for_ppo_solved\n",
                "y_values = ppo_path_lengths_for_ppo_solved\n",
                "\n",
                "# Creating the scatter plot\n",
                "plt.figure(figsize=(8, 6))  # Set the figure size\n",
                "plt.scatter(x_values, y_values)  # Plot the data points as a scatter plot\n",
                "plt.plot(y_values, y_values, linestyle=(0, (5, 10)), label='y = x', color='black')\n",
                "plt.title('Scatter Plot between Two Lists')  # Add a title\n",
                "plt.xlabel('GS path lengths for PPO solved')  # Label the x-axis\n",
                "plt.ylabel('PPO path lengths for PPO solved')  # Label the y-axis\n",
                "\n",
                "# Set axis limits and ticks\n",
                "axis_limits = [0, 200]  # Define common limits for x and y axes\n",
                "ticks = [0, 25, 50, 75, 100, 125, 150, 175, 200]  # Define ticks\n",
                "\n",
                "plt.xlim(axis_limits)  # Set the x-axis limits\n",
                "plt.ylim(axis_limits)  # Set the y-axis limits\n",
                "plt.xticks(ticks)  # Set the x-axis ticks\n",
                "plt.yticks(ticks)  # Set the y-axis ticks\n",
                "\n",
                "# plt.savefig('/Users/alishehper/work/ac_paper/fig/path_lengths_gs_vs_ppo.png')\n",
                "# plt.savefig(\"./Images/path_lengths_gs_vs_ppo.pdf\")\n",
                "# Show the plot\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Section 1"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 13,
            "metadata": {},
            "outputs": [],
            "source": [
                "## For each n and presentation, get the number of examples that each of the three algorithms solve\n",
                "\n",
                "## Initiate data\n",
                "# GS\n",
                "n_to_gs_num_solved = [0]*7\n",
                "length_to_gs_num_solved = defaultdict(int)\n",
                "\n",
                "# BFS\n",
                "n_to_bfs_num_solved = [0]*7\n",
                "length_to_bfs_num_solved = defaultdict(int)\n",
                "\n",
                "# PPO\n",
                "n_to_ppo_solved = [0]*7\n",
                "length_to_ppo_num_solved = defaultdict(int)\n",
                "\n",
                "# All presentations\n",
                "length_to_num_presentations = defaultdict(int)\n",
                "\n",
                "for id, presentation in enumerate(all_presentations):\n",
                "\n",
                "    # compute n\n",
                "    max_relator_length = len(presentation) // 2 \n",
                "    first_relator = presentation[:max_relator_length]\n",
                "    n = (np.count_nonzero(first_relator) - 3) // 2\n",
                "\n",
                "    # compute total presentation length\n",
                "    presentation_length = np.count_nonzero(first_relator) + np.count_nonzero(presentation[max_relator_length:])\n",
                "\n",
                "    ## record info\n",
                "    length_to_num_presentations[presentation_length] += 1\n",
                "\n",
                "    # record info for GS\n",
                "    if any(np.array_equal(presentation, arr) for arr in gs_solved):\n",
                "        length_to_gs_num_solved[presentation_length] += 1\n",
                "        n_to_gs_num_solved[n-1] += 1\n",
                "\n",
                "    # record info for BFS\n",
                "    if any(np.array_equal(presentation, arr) for arr in bfs_solved):\n",
                "        n_to_bfs_num_solved[n-1] += 1\n",
                "        length_to_bfs_num_solved[presentation_length] += 1\n",
                "\n",
                "    # record info for PPO\n",
                "    if id in ppo_checkpoint[\"success_record\"][\"solved\"]:\n",
                "        n_to_ppo_solved[n-1] += 1\n",
                "        length_to_ppo_num_solved[presentation_length] += 1"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 14,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "n = ['1', '2', '3', '4', '5', '6', '7']  \n",
                "X_axis = np.arange(len(n)) \n",
                "\n",
                "# Width of the bar\n",
                "barWidth = 0.25\n",
                "\n",
                "# Set position of bar on X axis\n",
                "r1 = X_axis - barWidth\n",
                "r2 = X_axis\n",
                "r3 = X_axis + barWidth\n",
                "\n",
                "# Make the plot\n",
                "plt.bar(r1, n_to_gs_num_solved, width=barWidth, label='GS', color='blue')\n",
                "plt.bar(r2, n_to_ppo_solved, width=barWidth, label='PPO', color='green') \n",
                "plt.bar(r3, n_to_bfs_num_solved, width=barWidth, label='BFS', color='grey')\n",
                "\n",
                "# Adding xticks\n",
                "plt.xticks(X_axis, n)\n",
                "plt.xlabel(\"n\")\n",
                "plt.ylabel(\"Number of presentations\")\n",
                "plt.title(\"\"\"Number of presentations solved by Greedy Search, Proximal Policy\n",
                "Optimization and Breadth First Search as a function of n\"\"\")\n",
                "plt.legend()\n",
                "\n",
                "# plt.savefig('/Users/alishehper/work/ac_paper/fig/performance_vs_n.png')\n",
                "# Display the figure\n",
                "# plt.savefig(\"./Images/performance_vs_n.pdf\")\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 15,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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hQTx79kx6JSYmStMU+0jHjh2VPqPptklPTxclSpQQAQEB0rlQiA/nJ3d3d9GgQQOprGXLlsLExETa/kIIcfXqVaGvr6+0n8bHxwsTExMxatQopWUPGjRImJmZKcWvjuIHslChQqJVq1Zi5syZ4tq1ayrzTZw4UZiZmYmbN28qlY8ePVro6+uLe/fuKa3Px1JTU0WZMmVEvXr1lMozOg917dpV6OnpqT3vKbabYj/29/dX2pZDhw4V+vr6SvuEphRJQFhYmHj27Jl48uSJOHjwoKhYsaIAILZs2aK07Jo1a0qJlRAf9j0jIyPRsGFDkZaWJpUvXLhQABC//vqrVBYVFSUAiEmTJol///1XmJubqyQpGSVmAMSGDRuksuvXr0vb8sSJEyrL+DipUfdbePz4cZUkXtvE7HN5hTbnUk0Ss9q1awsLCwulY0MIobQfZOfc8LFcS8w+fbm6uorIyEghhBCzZ88WMplM3Lp1S+nk9OzZM1GqVCnh7+8v1efn5yeMjY1VfhCbNm0q7OzslJKbTw0aNEhYWVmJuLg4leWYm5srfYGurq7Cx8dHpY5y5copnaQ/l5h9THHiXbdunQAgoqOjhRBCHD16VAAQy5YtU5r/3bt3olChQko7S2BgoChdurRK7Ddv3pQOtowcO3ZMABCLFy9Wmebt7S18fX2l91lJzKKiopTKr127JgCIqVOnSmUARN26dZXmS09PF9bW1qJPnz4q66WI48iRI0KID//9WFlZqbSyZKUuxQlg+vTpSnWcO3dOABA7duyQyjJKzD6WlpYmXrx4IZ49eyaaNm2q9OOrTWI2ZcoUAUBcvXpVab7Hjx8LAEqJjKb7qJ+fn3Bzc1P5cctMZp9TtHyMHDlSZVpAQICws7OT3n+amAnxIQkoWrSo0onN19dXVKtWTXqv6blBsX9/+g9bamqqsLKy0jgx+3jZCu3btxempqbSj6Fi316xYoU0z4IFCwQAcevWrc8uQ19fX9SsWVOlvEWLFkrnxwEDBkjTFPvIoUOHlD6j6bZR7NOrV69Wma9Xr17C2NhYpKWliffv3wu5XC610HysSZMmKi277du3F8WKFZO+v/fv3wtHR0fRuXPnz24DIT4cL4oW3o/Xu169euLBgwfSfOXKlRONGjVSiXvfvn0CgFi3bp3a+l++fCmePXsm+vXrJ6ytrZWmqTsPpaWlCUtLy0yvPCj24z/++EOpfOvWrSr/iGpKkQR8+rK0tBTTpk1TWfbq1auVPr9hwwYBQPzvf/9TKk9JSRGWlpYqLTh9+/YVRkZG0pWAp0+fKk3PKDEzNzdXOlaFEMLa2lrln+X4+HgBQIwbN07t+qampornz5+LZ8+eCWtrazFkyJDPLlsdTfIKbc6lmSVmcXFxAoBKK+2nsnNu+Fiu9TpetGgRSpYsCQMDAzg6OsLLywt6eh+6uN26dQtCCJQoUULtZz+9M6Jw4cIqd4zcuXMHXl5en+1IfevWLbx+/VqlD4OCotO7QrFixVTmKVSokEp/tIxcuXIFP//8M/7++28kJCQoTXv9+jWAD9feAcDT01NpuoGBgcpdnrdu3cK1a9ekPkuZxf8xxXK8vLxUpnl7e2f7Fv1PvzsPDw/o6emp9CFwd3dXev/s2TPEx8dj2bJlKh2BFRTrNWrUKOzbtw9VqlSBp6cnGjZsiE6dOkl9VbSpS+HT77hQoUIAoPF3vHr1asyaNQvXr1/Hu3fvMlxPTd29exd6enoq+4OTkxOsra2l71FBk310woQJaNGiBUqWLIkyZcqgUaNG6NKlC8qVK/fZWDL73Of2qVKlSiEqKuqznZPbt2+P7du34/jx46hevTru3LmDs2fPKg1Noum5QRHLp/MZGhpm2JdNHXXLKVmyJJKTk/Hs2TM4OTnB29sblStXxvr169GzZ08AH/qlffvttyrf26csLCyQmJioUj5hwgRpDLUGDRqo/eyn+5Sm2+bWrVsAIPUdVef169dISUnBmzdv1Nbn5eWF//3vf0plXbt2xcaNG/HPP/+gdu3a2LdvH54+fYouXbpkuBwFPT09DBgwAAMGDMCLFy9w9OhRhIeHY/fu3ejQoYPUN/DWrVu4ePGiRue8Xbt2YdKkSYiOjlbqQ6Ru/DV156GEhASUKVMm09iB7J831OnTpw/atWsHPT09WFtbS/3FPvVp7Bkdh0ZGRihevLjKOWPmzJnYsWMHoqOjsWHDhgx/Dz9VpEgRlW1pZWWFokWLqpQBytvizZs3mDp1KiIiIvDw4UMIIaRpit/CrPhcXqHtufRz/v33XwDIdP/IzrnhY7mWmFWpUkWlQ69Ceno6ZDIZdu/eDX19fZXp5ubmSu8zu2MpI+np6XBwcMD69evVTv/04FcXCwClnSoj8fHx8PPzg6WlJSZMmAAPDw+YmJjg3LlzGDVqlErHVU3jL1u2LGbPnq12+qcHSF7KaDDKT787xXb47rvvMvzhUCQCpUqVwo0bN7Br1y5ERkZiy5YtWLx4McaPH4+wsDCt6lLIzne8bt06dOvWDS1btsSIESPg4OAAfX19TJ06VemGk6zQdDBPTeKvXbs27ty5gx07dmDPnj1YsWIF5syZg/DwcPTq1SvDurP6OU01b94cpqam+OOPP1C9enX88ccf0NPTk26oAbQ/N+SWrl27YvDgwXjw4AFSUlJw4sQJLFy4MNPPeXt748KFC3j37p3SP5yZJcmA+mNHk22jOC5mzJiR4bAL5ubmGt9ApBAQEABHR0esW7cOtWvXxrp16+Dk5KT1EDu2trYIDAxEYGAg6tSpg0OHDuHu3btwdXVFeno6GjRogJEjR6r9bMmSJQEA//zzDwIDA1G7dm0sXrwYzs7OMDQ0REREhMrNQUDWf0MUsnPeyEiJEiU02nbZjf38+fNSQnvp0iWN717MaJ012RY//PADIiIiMGTIEFSrVg1WVlaQyWTo0KFDln4LFT6XVyjk9sDIWT03fCxf3Kfv4eEBIQTc3d2lAy0rdZw8eVLlhPfpPPv27UONGjWyvXMrZPSlHzx4EC9evMDWrVuVxiP6+C5U4MN4KQBw+/Zt1K1bVyp///49YmNjlU7YHh4euHDhAurXr6/1zqZYzo0bN6Q7VxRu3LghTc+qW7duKf0nd/v2baSnp2c6tpu9vT0sLCyQlpam0UnJzMwM7du3R/v27ZGamorWrVtj8uTJGDNmjNZ1aSqjbb1582YUL14cW7duVZonJCREo8+ro/gxunXrFkqVKiWVP336FPHx8Vn+nmxsbNC9e3d0794diYmJqF27NkJDQzNNsD73uY/3qU9dv34ddnZ2n72V38zMDM2aNcOmTZswe/ZsbNy4EbVq1YKLi4s0j6bnBkUst27dUtq/3717h5iYmAzvIPyUonXpYzdv3oSpqanSP24dOnTAsGHD8Ntvv0njHbVv3z7T+ps1a4YTJ05g27ZtCAoK0iimjGi6bTw8PAAAlpaWnz0uFHeaqdsG6r5jfX19dOrUCatWrcK0adOwfft29O7dO8Mfak1UqlQJhw4dwuPHj+Hq6goPDw8kJiZmejxv2bIFJiYmiIqKUmplioiI0Gi59vb2sLS0xOXLl7Mce175+Dj8uHU4NTUVMTExStsuKSkJ3bt3h4+PD6pXr47p06ejVatWSncB54TNmzcjODgYs2bNksrevn2bo0+U0eW5VLFdNdk/snpu+Fi+eCRT69atoa+vj7CwMJX/OIQQePHiRaZ1tGnTBs+fP1ebmSrqDAoKQlpaGiZOnKgyz/v377O0kyh+eD79rOLk9PH6pKamYvHixUrzVapUCba2tli+fDnev38vla9fv16lWTwoKAgPHz7E8uXLVeJ48+YNkpKSMoyzUqVKcHBwQHh4uNJ/xrt378a1a9fQtGnTTNb08xYtWqT0fsGCBQA+jDPzOfr6+mjTpg22bNmidqf/+Bb0T/cDIyMj+Pj4QAiBd+/eaVWXNszMzNQ2t6v7jk+ePKlyS7RijD1N9q8mTZoAgMqTBhStpFn5nj7dbubm5vD09My0hSSzzzk7O6NChQpYvXq10rpdvnwZe/bskdblc9q3b49Hjx5hxYoVuHDhgsoJTNNzQ6VKlWBvb4/w8HCloQ1WrVql1XF9/PhxnDt3Tnp///597NixAw0bNlRKOOzs7NC4cWOsW7cO69evR6NGjWBnZ5dp/f369YOjoyOGDh2KmzdvqkzXpsVF023j6+sLDw8PzJw5U+1lVMVxoa+vj4CAAGzfvh337t2Tpl+7dg1RUVFqY+jSpQtevXqFvn37IjExUWkcrow8efIEV69eVSlPTU3F/v37lS4/BQUF4fjx42qXHx8fL50z9fX1IZPJlIYiio2Nxfbt2zONB/hwabVly5b4888/1T5uKTstYTnN398fRkZGmD9/vlKcK1euxOvXr5XOGaNGjcK9e/ewevVqzJ49G25ubggODta6tVRb+vr6KttwwYIFaoeO0hVdnkvt7e1Ru3Zt/Prrr0rHBqC6b2T13PCxfNNiNmnSJIwZMwaxsbFo2bIlLCwsEBMTg23btqFPnz4YPnz4Z+vo2rUr1qxZg2HDhuHUqVOoVasWkpKSsG/fPvTv3x8tWrSAn58f+vbti6lTpyI6OhoNGzaEoaEhbt26hU2bNmHevHlo27atVrFXqFAB+vr6mDZtGl6/fg1jY2PUq1cP1atXR6FChRAcHIxBgwZBJpNh7dq1Kl+ikZERQkND8cMPP6BevXoICgpCbGwsVq1aBQ8PD6XWli5duuCPP/7A999/jwMHDqBGjRpIS0vD9evX8ccffyAqKirDZl1DQ0NMmzYN3bt3h5+fHzp27IinT59i3rx5cHNzw9ChQ7Va70/FxMQgMDAQjRo1wvHjx7Fu3Tp06tRJo5aKX375BQcOHEDVqlXRu3dv+Pj44OXLlzh37hz27duHly9fAgAaNmwIJycn1KhRA46Ojrh27RoWLlyIpk2bwsLCQqu6tOHr64uNGzdi2LBhqFy5MszNzdG8eXM0a9YMW7duRatWrdC0aVPExMQgPDwcPj4+Sj+AcrkcPj4+2LhxI0qWLAkbGxuUKVNGbX+F8uXLIzg4GMuWLZMuh586dQqrV69Gy5YtlVpVNeXj44M6derA19cXNjY2OHPmDDZv3pzpcyE1+dyMGTPQuHFjVKtWDT179sSbN2+wYMECWFlZSWO1fU6TJk1gYWGB4cOHS4n1xzQ9NxgaGmLSpEno27cv6tWrh/bt2yMmJgYRERFa9TErU6YMAgICMGjQIBgbG0v/SCme3PCxrl27SucLdf/sqWNjY4Nt27ahefPmKF++PDp06IDKlSvD0NAQ9+/fx6ZNmwCo7zv4KU23jZ6eHlasWIHGjRujdOnS6N69OwoXLoyHDx/iwIEDsLS0xJ9//imtZ2RkJGrVqoX+/fvj/fv30tiBFy9eVImhYsWKKFOmDDZt2oRSpUrhm2++yTTuBw8eoEqVKqhXrx7q168PJycnxMXF4bfffsOFCxcwZMgQ6YdsxIgR2LlzJ5o1a4Zu3brB19cXSUlJuHTpEjZv3ozY2FjY2dmhadOmmD17Nho1aoROnTohLi4OixYtgqenp9q41ZkyZQr27NkDPz8/9OnTB6VKlcLjx4+xadMmHDlyROsBt1etWoXu3bsjIiLis2NBZpe9vT3GjBmDsLAwNGrUCIGBgbhx4wYWL16MypUrS8ny33//jcWLFyMkJET6niIiIlCnTh2MGzcO06dPz7EYmzVrhrVr18LKygo+Pj44fvw49u3bB1tb2xxbpq7PpfPnz0fNmjXxzTffoE+fPnB3d0dsbCz++usvlUdnZeXcoETj2wSySJs7/LZs2SJq1qwpzMzMhJmZmfD29hYDBgwQN27ckObx8/PLcMiE5ORk8dNPPwl3d3dhaGgonJycRNu2bcWdO3eU5lu2bJnw9fUVcrlcWFhYiLJly4qRI0eKR48eSfO4urqqHSrg07s3hPgwpk/x4sWlW8oVd5QcPXpUfPvtt0IulwsXFxcxcuRI6VbiT+86mT9/vnB1dRXGxsaiSpUq4ujRo8LX11c0atRIab7U1FQxbdo0Ubp0aWFsbCwKFSokfH19RVhYmHj9+nVmm1hs3LhRVKxYURgbGwsbGxvRuXNnpbughMjaXZlXr14Vbdu2FRYWFqJQoUJi4MCBSsNyCCFU7jb72NOnT8WAAQNE0aJFpe+ufv36SnerLl26VNSuXVvY2toKY2Nj4eHhIUaMGKGy3prUpbj7Z9OmTUqfVXebdGJioujUqZOwtraW7vwR4sNdoFOmTJG+t4oVK4pdu3aJ4OBglbs4jx07Jnx9fYWRkZHSHZrqxjF79+6dCAsLk/bjokWLijFjxkhDrChouo9OmjRJVKlSRVhbWwu5XC68vb3F5MmTMx1LS9PP7du3T9SoUUPI5XJhaWkpmjdvrnInlLq7MhU6d+4s8H9DEGREk3ODEB/GBHR3dxfGxsaiUqVK4vDhw2qPWXUU++e6detEiRIlpO80ozvEUlJSRKFChYSVlZXKvp6Zx48fixEjRggfHx8hl8uFsbGxKF68uOjatavS8CdC/P995NmzZ2rr0nTbnD9/XrRu3Vo6flxdXUVQUJDYv3+/0nyHDh2S9tXixYuL8PBwtfupwvTp0wUAMWXKFI3WPSEhQcybN08EBASIIkWKCENDQ2FhYSGqVasmli9frnLn33///SfGjBkjPD09hZGRkbCzsxPVq1cXM2fOVNoXV65cKX1v3t7eIiIiQm3cnzsP3b17V3Tt2lXY29tL38mAAQOkUQAyOjequ5tQcTee4i7BjGQ0jtmnMjsvL1y4UHh7ewtDQ0Ph6Ogo+vXrJ42/lpCQIFxdXcU333yjMnLB0KFDhZ6enjh+/HiG65LR725G56BPt/GrV69E9+7dhZ2dnTA3NxcBAQHi+vXrwtXVVQQHB0vzZXccs09pei7VZLgMIYS4fPmyaNWqlbC2thYmJibCy8tL7d2n2Tk3CCGETIh83EZbgKWnp8Pe3h6tW7dWe+kyvwgNDUVYWBiePXumdXMt0Zfs/fv3cHFxQfPmzbFy5cq8DifPzJs3D0OHDkVsbKxGLX0FheLqx6lTp/I6FMpl2T035ItLmQXd27dvYWxsrHTZcs2aNXj58qXKI5mIKH/Yvn07nj17hq5du+Z1KHlGCIGVK1fCz8+PSdlHhBA4ePAg1q1bl9ehUB7I7rmBiVk+cOLECQwdOhTt2rWDra0tzp07h5UrV6JMmTJKQwcQUd47efIkLl68iIkTJ6JixYrw8/PL65ByXVJSEnbu3IkDBw7g0qVL2LFjR16HlK/IZLLPjitJXyddnRuYmOUDbm5uKFq0KObPn4+XL1/CxsYGXbt2xS+//KIykC4R5a0lS5Zg3bp1qFChgspDjguKZ8+eoVOnTrC2tsbYsWMRGBiY1yER5TldnRvYx4yIiIgon8gX45gRERERERMzIiIionyDiZkaq1atgkwmU3kAd3aEhobm+jO78nK5uelrXUdt1ksx7/Pnz3Mklpw4JgoKmUyW6WC+X7K1a9fC29sbhoaGWg/CmltiY2Mhk8nyfZ/AyMhIVKhQASYmJpDJZDn6yKLs0nSbHjx4EDKZDAcPHsyVuLIjvxyrX0RiduXKFXz33XcoXLgwjI2N4eLigs6dO+PKlSvZqnfKlCkaP7IjP0tOTkZoaOgXsePnpW7dukEmk0kvAwMDFC1aFB06dFD7iJj8KKf22U+3zcevyMhInS/v0aNHCA0NVRkx+3MuXbqEtm3bwtXVFSYmJihcuDAaNGggPf6Lct/169fRrVs3eHh4YPny5Vi2bFmexrNhwwaVR/B8KV68eIGgoCDI5XIsWrQIa9euzfBZs8eOHUNoaGi2ErfFixfn+0Q1J+hi2+W0fH9X5tatW9GxY0fY2NigZ8+e0mMQVq5cic2bN+P3339Hq1atslT3lClT0LZtW7Rs2VKpvEuXLujQoYPSw3Cz6+eff8bo0aN1Vt/HkpOTpUfGfDruWU4u90tkbGyMFStWAPgwCOCdO3cQHh6OyMhIXL16VekB2vlRRvusLny8bT5Wvnx5NGjQQKfHxKNHjxAWFgY3NzdUqFAh0/mPHTuGunXrolixYujduzecnJxw//59nDhxAvPmzcMPP/ygk7hIOwcPHkR6ejrmzZsnPd8yL23YsAGXL1/GkCFDlMpdXV2lB0rnV6dPn8Z///2HiRMnZvrQ9mPHjiEsLAzdunXLcivl4sWLYWdnl6OPi8qPdLHtclq+Tszu3LmDLl26oHjx4jh8+DDs7e2laYMHD0atWrXQpUsXXLx4Uavn4WVGX19f6YHFumBgYAADg9zf3Hm13PzKwMBA5UHL3377LZo1a4a//voLvXv3zvCzSUlJGf4H+zVQt20+ltkxIYTA27dvIZfLdR0aJk+eDCsrK5w+fVrlZJoX40V97fuCphTbPr/+wCnIZDKYmJjkdRif9aVsS8p5+fpS5owZM5CcnIxly5YpJWXAhye4L126FElJSUoPX1X0tbl+/TqCgoJgaWkJW1tbDB48GG/fvpXmk8lkSEpKwurVq6VLNor/HNT1p3Fzc0OzZs1w8OBBVKpUCXK5HGXLlpUuH27duhVly5aFiYkJfH19cf78eaV4P+0v9LlLR4qHP6empmL8+PHw9fWFlZUVzMzMUKtWLRw4cECqJzY2Vto2YWFhKnWo66f0/v17TJw4ER4eHjA2NoabmxvGjh2LlJQUpfkU63zkyBFUqVIFJiYmKF68ONasWZPJN/fBzJkzUb16ddja2kIul8PX1xebN29WmU9xXX/79u0oU6YMjI2NUbp0abWX0I4cOYLKlSvDxMQEHh4eWLp0qUaxfI6TkxMAKCWwin3g0KFD6N+/PxwcHFCkSBFp+u7du1GrVi2YmZnBwsICTZs2Vbm0fvHiRXTr1g3FixeHiYkJnJyc0KNHD7x48SJL6/W5fVYhPj5e+k/QysoK3bt3R3JycnY2j9L2UHdMREVFSceEIu69e/eiZs2asLa2hrm5Oby8vDB27FgAH1pZKleuDADo3r27tC6fu6xy584dlC5dWu2PloODg0rZunXr4OvrC7lcDhsbG3To0AH3799Xmueff/5Bu3btUKxYMRgbG6No0aIYOnQo3rx5ozRft27dYG5ujjt37kgPXe/cuTMASK1FimPf3t4ejRo1wpkzZ1Ri0mT//pQm5wCF33//Hb6+vrCwsIClpSXKli2LefPmZboMTY/TT7m5uSEkJATAhwdpf3ze+fjvTz/z8T6r2K+OHj2KYcOGwd7eHmZmZmjVqhWePXum8vndu3fDz89PWsfKlStjw4YNAD5cLfjrr79w9+5daZ9yc3MDkHF/qL///ls6jq2trdGiRQtcu3ZNaR7FOfT27dtZPrY2bdok7Y92dnb47rvv8PDhQ2l6nTp1EBwcDACoXLmy2mP743hGjBgBAHB3d5fWVXFsanJ+d3Nzw5UrV3Do0CHp84qrLS9fvsTw4cNRtmxZmJubw9LSEo0bN8aFCxc0WldNnTx5Eo0aNYKVlRVMTU3h5+eHo0ePqqyrptv+zZs3GDRoEOzs7GBhYYHAwEA8fPhQ5ffwc9tOISvHqi7l66aUP//8E25ubqhVq5ba6bVr14abmxv++usvlWlBQUFwc3PD1KlTceLECcyfPx+vXr2Skoq1a9eiV69eqFKlCvr06QMA8PDw+Gw8t2/fRqdOndC3b1989913mDlzJpo3b47w8HCMHTsW/fv3BwBMnToVQUFBuHHjBvT01Oe+ffv2VWmujoyMxPr166UfmoSEBKxYsQIdO3ZE79698d9//2HlypUICAjAqVOnUKFCBdjb22PJkiXo168fWrVqhdatWwMAypUrl+F69OrVC6tXr0bbtm3x448/4uTJk5g6dSquXbuGbdu2qaxz27Zt0bNnTwQHB+PXX39Ft27d4Ovri9KlS392e82bNw+BgYHo3LkzUlNT8fvvv6Ndu3bYtWsXmjZtqjTvkSNHsHXrVvTv3x8WFhaYP38+2rRpg3v37sHW1hbAhz5GDRs2hL29PUJDQ/H+/XuEhITA0dHxs3F8StFBPi0tDf/++y9GjRoFW1tbNGvWTGXe/v37w97eHuPHj0dSUhKAD/tOcHAwAgICMG3aNCQnJ2PJkiWoWbMmzp8/L/0Y7N27F//++y+6d+8OJycnXLlyBcuWLcOVK1dw4sQJKWHWdL002WeDgoLg7u6OqVOn4ty5c1ixYgUcHBwwbdo0rbaNgqGhIaysrDKc/8aNG+jYsSP69u2L3r17w8vLC1euXEGzZs1Qrlw5TJgwAcbGxrh9+7Z00i1VqhQmTJiA8ePHo0+fPtLxXb169QyX4+rqiuPHj+Py5csoU6bMZ9dh8uTJGDduHIKCgtCrVy88e/YMCxYsQO3atXH+/Hkpudu0aROSk5PRr18/2Nra4tSpU1iwYAEePHiATZs2KdX5/v17BAQEoGbNmpg5cyZMTU0BAD179sSqVavQuHFj9OrVC+/fv8c///yDEydOoFKlStLnNdm/1dHkHAB82Nc6duyI+vXrS9/1tWvXcPToUQwePPiz20ub4/Rjc+fOxZo1a7Bt2zYsWbIE5ubmnz3vfM4PP/yAQoUKISQkBLGxsZg7dy4GDhyIjRs3SvOsWrUKPXr0QOnSpTFmzBhYW1vj/PnziIyMRKdOnfDTTz/h9evXePDgAebMmQMAMDc3z3CZ+/btQ+PGjVG8eHGEhobizZs3WLBgAWrUqIFz585Jx7FCVo+tVatWoXv37qhcuTKmTp2Kp0+fYt68eTh69Ki0P/7000/w8vLCsmXLMGHCBLi7u2f4e9S6dWvcvHkTv/32G+bMmSM9o1jxD7om5/e5c+fihx9+gLm5OX766ScAkM43//77L7Zv34527drB3d0dT58+xdKlS+Hn56ez7h5///03GjduDF9fX4SEhEBPTw8RERGoV68e/vnnH1SpUkVpfk22fbdu3fDHH3+gS5cu+Pbbb3Ho0CGV/TezbQdk/VjVKa0fe55L4uPjBQDRokWLz84XGBgoAIiEhAQhhBAhISECgAgMDFSar3///gKAuHDhglRmZmam9GR7BcWT62NiYqQyV1dXAUAcO3ZMKouKihIAhFwuF3fv3pXKly5dKgCIAwcOSGWKuDJy69YtYWVlJRo0aCDev38vhBDi/fv3IiUlRWm+V69eCUdHR9GjRw+p7NmzZwKACAkJUan30+VGR0cLAKJXr15K8w0fPlwAEH///bfKOh8+fFgqi4uLE8bGxuLHH3/McF0UkpOTld6npqaKMmXKiHr16imVAxBGRkbi9u3bUtmFCxcEALFgwQKprGXLlsLExERpW1+9elXo6+t/dtsqBAcHCwAqr8KFC4uzZ88qzavYB2rWrCl9H0II8d9//wlra2vRu3dvpfmfPHkirKyslMo/XX8hhPjtt99Utqk265XRPqv4nj/eL4QQolWrVsLW1vYzW+WDjLaNn5+f0vZQd0xERkYq1TVnzhwBQDx79izD5Z0+fVoAEBEREZnGJoQQe/bsEfr6+kJfX19Uq1ZNjBw5UkRFRYnU1FSl+WJjY4W+vr6YPHmyUvmlS5eEgYGBUrm672fq1KlCJpMpfReKbTN69Gilef/++28BQAwaNEilnvT0dOlvTfdvdTQ9BwwePFhYWloq7aua0vQ4VUex3336XWd0PnJ1dVXafxX7lb+/v9I2Gzp0qNDX1xfx8fFCiA+/BxYWFqJq1arizZs3SnV+/LmmTZsKV1dXleXGxMSo7G8VKlQQDg4O4sWLF1LZhQsXhJ6enujatavKOmbl2EpNTRUODg6iTJkySnHv2rVLABDjx49X2RanT5/+bJ1CCDFjxgyV41EI7c7vpUuXlo7vj719+1akpaUplcXExAhjY2MxYcIEpTJNjuEDBw4o/R6mp6eLEiVKiICAAKXvLjk5Wbi7u4sGDRpIZZpu+7NnzwoAYsiQIUrzdevWTWVfzGjbCZG9Y1WX8u2lzP/++w8AYGFh8dn5FNMTEhKUygcMGKD0XtE5+H//+1+WY/Lx8UG1atWk91WrVgUA1KtXT+kBvoryf//9V6N6k5KS0KpVKxQqVAi//fab1JdHX19feiRTeno6Xr58iffv36NSpUo4d+5cltZBsf7Dhg1TKv/xxx8BQKX10cfHR6nF0t7eHl5eXhqt28d9jV69eoXXr1+jVq1aamP39/dX+g+xXLlysLS0lJaTlpaGqKgotGzZUmlblypVCgEBAZnGomBiYoK9e/di7969iIqKwtKlS2Fubo4mTZrg5s2bKvP37t1bqW/V3r17ER8fj44dO+L58+fSS19fH1WrVlW6xPTx+r99+xbPnz/Ht99+CwDSNtDVeil8//33Su9r1aqFFy9eqBwf6ny8bRSvWbNmffYz7u7uKnEqWqR27NiB9PR07VYgAw0aNMDx48cRGBiICxcuYPr06QgICEDhwoWxc+dOab6tW7ciPT0dQUFBSt+Pk5MTSpQokeH3k5SUhOfPn6N69eoQQqh0RQCAfv36Kb3fsmULZDKZdDnvY592H8hs/86IpucAa2trJCUlYe/evZ+tTx1tjtOc0qdPH6VtVqtWLaSlpeHu3bsAPhx3//33H0aPHq3SVywrQ+U8fvwY0dHR6NatG2xsbKTycuXKoUGDBmp/J7JybJ05cwZxcXHo37+/UtxNmzaFt7e32qs92aHt+V0dY2Nj6UpPWloaXrx4IXVH0MU+ER0djVu3bqFTp0548eKFdIwmJSWhfv36OHz4sMp5I7Ntr7jUqLhqpZCVm4KyeqzqUr69lKlIuBQJWkYySuBKlCih9N7DwwN6enrZGofp4x9OANIlnqJFi6otf/XqlUb19u7dG3fu3MGxY8dUmkpXr16NWbNm4fr163j37p1U7u7urnX8AHD37l3o6emp3EHl5OQEa2tr6USo8Ok6A0ChQoU0Wrddu3Zh0qRJiI6OVurfoO5Emtlynj17hjdv3qh8rwDg5eWlccKtr6+vcgm5SZMmKFGiBMaMGYMtW7YoTft0O9+6dQvAh2RcHUtLS+nvly9fIiwsDL///rtKB/XXr1/rdL0UPt2OhQoVAvBhX/w4NnXUbZvMqNsP27dvjxUrVqBXr14YPXo06tevj9atW6Nt27YZXtrXROXKlbF161akpqbiwoUL2LZtG+bMmYO2bdsiOjoaPj4+uHXrFoQQarcnAKW78u7du4fx48dj586dKvuz4vtRMDAwUOpjCHzo9+bi4qL0w56R7BxHmpwD+vfvjz/++AONGzdG4cKF0bBhQwQFBaFRo0aZ1q/NcZpTPrffAh+2NYBML2NrSnGe8/LyUplWqlQpREVFqdzgkZVj63PL8fb2xpEjR7K2AhnQ9vyujqLf5OLFixETE4O0tDRpmi4u5SnOoYo+deq8fv1a2r5A5ttesd6fno+ycqdwdo5VXcm3iZmVlRWcnZ1x8eLFz8538eJFFC5cONMfHV2cZDK6Ky2jcqHBY0jnzZuH3377TXrw6cfWrVuHbt26oWXLlhgxYgQcHBygr6+PqVOnSieqrNJ0e2R13f755x8EBgaidu3aWLx4MZydnWFoaIiIiAips64ulqMLRYoUgZeXFw4fPqwy7dM7DBX/ya1du1a6aeBjH99AEBQUhGPHjmHEiBGoUKECzM3NkZ6ejkaNGumsJelTub0d1d2BKZfLcfjwYRw4cAB//fUXIiMjsXHjRtSrVw979uzJ9h3PRkZGqFy5MipXroySJUuie/fu2LRpE0JCQpCeng6ZTIbdu3erXY6iz1FaWhoaNGiAly9fYtSoUfD29oaZmRkePnyIbt26qXw/H7ciZEVWvxdNzwEODg6Ijo5GVFQUdu/ejd27dyMiIgJdu3bF6tWrM6xf2+M0uz7+kf9YXh7/mvoSYlTIzu/dlClTMG7cOPTo0QMTJ06EjY0N9PT0MGTIEJ2ctxR1zJgxI8Ohcj7tG5ib2z4/fM/5NjEDgGbNmmH58uU4cuQIatasqTL9n3/+QWxsLPr27asy7datW0rZ8+3bt5Genq7UoTOvR4v/559/MHz4cAwZMkS6y+tjmzdvRvHixbF161alWD+9dKLNeri6uiI9PR23bt1CqVKlpPKnT58iPj4erq6uWVgTVVu2bIGJiQmioqKUxr6KiIjIUn329vaQy+XSf1sfu3HjRpbjVHj//j0SExMznU/RxO3g4PDZ1qVXr15h//79CAsLw/jx46XyT+PXdr3yep/VlJ6eHurXr4/69etj9uzZmDJlCn766SccOHAA/v7+OlsPRQf7x48fA/jw/Qgh4O7ujpIlS2b4uUuXLuHmzZtYvXo1unbtKpVrcynQw8MDUVFRePnypUatZlmh6TkA+JCwNm/eHM2bN0d6ejr69++PpUuXYty4cRm2HOj6OFUoVKiQygCeqamp0vekLcVxd/ny5c+2gmi6XynOc+qOsevXr8POzk4nw6F8vJxPW9lv3LiR5fNtRuupzfk9ozo2b96MunXrYuXKlUrl8fHxUmf57FB8l5aWllq30GdEsd4xMTFKreW3b99WmfdLOIfm2z5mADBixAjI5XL07dtXZYiBly9f4vvvv4epqal0++vHFi1apPReMTp448aNpTIzM7M8G/338ePHCAoKQs2aNTFjxgy18ygy948z9ZMnT+L48eNK8ynuENNkXZo0aQIAKqNjz549GwA+exeWNvT19SGTyZT+Q46Njc3yqPX6+voICAjA9u3bce/ePan82rVriIqKylasN2/exI0bN1C+fPlM5w0ICIClpSWmTJmidFlJQXGLv7rvDlDd7tquV17us5p6+fKlSpniP2PFpTLFj56m63LgwAG1/7EqLvUqLhW1bt0a+vr6CAsLU5lfCCGdR9R9P0IIjYaXUGjTpg2EENLgzp8uSxc0PQd8en7U09OT7pD8dBicT+vX5XGq4OHhodICvWzZsgxbzDLTsGFDWFhYYOrUqUrDHgHK28bMzEzlMrQ6zs7OqFChAlavXq20D16+fBl79uyRzpPZValSJTg4OCA8PFzpe9i9ezeuXbuW5fNtRsePNuf3jM4l+vr6Kvvvpk2blIb3yA5fX194eHhg5syZav8ZVjdMSmYU/VwXL16sVK7uqSDannvyQr5uMStRogRWr16Nzp07o2zZsioj/z9//hy//fab2tuKY2JiEBgYiEaNGuH48eNYt24dOnXqpPTj6+vri3379mH27NlwcXGBu7u71HE/pw0aNAjPnj3DyJEj8fvvvytNK1euHMqVK4dmzZph69ataNWqFZo2bYqYmBiEh4fDx8dHaYeWy+Xw8fHBxo0bUbJkSdjY2KBMmTJq+2OUL18ewcHBWLZsGeLj4+Hn54dTp05h9erVaNmyJerWrauT9WvatClmz56NRo0aoVOnToiLi8OiRYvg6emZ6eXpjISFhSEyMhK1atVC//798f79eyxYsAClS5fWuM73799j3bp1AD40qcfGxiI8PBzp6elqWyE+ZWlpiSVLlqBLly745ptv0KFDB9jb2+PevXv466+/UKNGDSxcuBCWlpaoXbs2pk+fjnfv3qFw4cLYs2cPYmJisrVeebnPamrChAk4fPgwmjZtCldXV8TFxWHx4sUoUqSI1PLt4eEBa2trhIeHw8LCAmZmZqhatWqGfSd/+OEHJCcno1WrVvD29kZqaiqOHTuGjRs3ws3NDd27d5fqnTRpEsaMGYPY2Fi0bNkSFhYWiImJwbZt29CnTx8MHz4c3t7e8PDwwPDhw/Hw4UNYWlpiy5YtWvUjqVu3Lrp06YL58+fj1q1b0iXqf/75B3Xr1tXJM/c0PQf06tULL1++RL169VCkSBHcvXsXCxYsQIUKFZRaTj6VE8epIp7vv/8ebdq0QYMGDXDhwgVERUVlucXF0tISc+bMQa9evVC5cmV06tQJhQoVwoULF5CcnCxdrvX19cXGjRsxbNgwVK5cGebm5mjevLnaOmfMmIHGjRujWrVq6NmzpzRchpWVldox2LLC0NAQ06ZNQ/fu3eHn54eOHTtKw2W4ublh6NChWarX19cXAPDTTz+hQ4cOMDQ0RPPmzbU6v/v6+mLJkiWYNGkSPD094eDggHr16qFZs2aYMGECunfvjurVq+PSpUtYv369zgZx19PTw4oVK9C4cWOULl0a3bt3R+HChfHw4UMcOHAAlpaW+PPPP7XeHm3atMHcuXPx4sULabgMxQ1dH7eSZbTt8tWA0bl2/2c2XLx4UXTs2FE4OzsLQ0ND4eTkJDp27CguXbqkMq/i9tqrV6+Ktm3bCgsLC1GoUCExcOBAldusr1+/LmrXri3kcrkAIN3GndHQAE2bNlVZHgAxYMAApTLFbcQzZsxQiUvBz89P7fAE+OjW3vT0dDFlyhTh6uoqjI2NRcWKFcWuXbtEcHCwyi3hx44dE76+vsLIyEipDnXDdLx7906EhYUJd3d3YWhoKIoWLSrGjBkj3r59qzRfRuvs5+en9jbrT61cuVKUKFFCGBsbC29vbxEREaE2HnXbULH8T4eGOHTokLSexYsXF+Hh4ZkORaKgbkgIS0tLUb9+fbFv3z6leTO7df3AgQMiICBAWFlZCRMTE+Hh4SG6desmzpw5I83z4MED0apVK2FtbS2srKxEu3btxKNHj9QOJaDpemW0z2Y0bIG6fTmjbWNmZpbhdG2Oif3794sWLVoIFxcXYWRkJFxcXETHjh3FzZs3lebbsWOH8PHxEQYGBpnedr97927Ro0cP4e3tLczNzYWRkZHw9PQUP/zwg3j69KnK/Fu2bBE1a9YUZmZmwszMTHh7e4sBAwaIGzduSPNcvXpV+Pv7C3Nzc2FnZyd69+4t3Rr/cSyf2zbv378XM2bMEN7e3sLIyEjY29uLxo0bKw2/os3+/SlNzwGbN28WDRs2FA4ODsLIyEgUK1ZM9O3bVzx+/Piz9Quh+XGqTkb7XVpamhg1apSws7MTpqamIiAgQNy+fTvD4TI+Pc4+HWJBYefOnaJ69epCLpcLS0tLUaVKFfHbb79J0xMTE0WnTp2EtbW1ACBto4yGdti3b5+oUaOGVF/z5s3F1atXNVpHTY8tIYTYuHGjqFixojA2NhY2Njaic+fO4sGDB2rr02S4DCGEmDhxoihcuLDQ09NTikPT8/uTJ09E06ZNhYWFhdLQOG/fvhU//vijcHZ2FnK5XNSoUUMcP35c5byf1eEyFM6fPy9at24tbG1thbGxsXB1dRVBQUFi//790jzabPukpCQxYMAAYWNjI8zNzUXLli3FjRs3BADxyy+/aLTtsnOs6pLs/4L5aoSGhiIsLAzPnj3TyfVwIiIi+vJER0ejYsWKWLdundp+3PlVvu5jRkRERJSZTx+lBnzoa6enp4fatWvnQURZl6/7mBERERFlZvr06Th79izq1q0LAwMDadiYPn36qIw1mt8xMSMiIqIvWvXq1bF3715MnDgRiYmJKFasGEJDQ6VngX5Jvro+ZkRERERfKvYxIyIiIsonmJgRERER5RPsY4YPA40+evQIFhYWX8TjGoiIiOjDkx/+++8/uLi4ZOt5tvkJEzMAjx49+uLu2iAiIqIP7t+/jyJFiuR1GDrBxAyAhYUFgA9frKWlZR5HQ0RERJpISEhA0aJFpd/xrwETM/z/52hZWloyMSMiIvrCfE3dkL6OC7JEREREXwEmZkRERET5BBMzIiIionyCfcyIiIhyWVpaGt69e5fXYeR7hoaG0NfXz+swchUTMyIiolwihMCTJ08QHx+f16F8MaytreHk5PRVdfD/HCZmREREuUSRlDk4OMDU1LTAJBtZIYRAcnIy4uLiAADOzs55HFHuYGJGRESUC9LS0qSkzNbWNq/D+SLI5XIAQFxcHBwcHArEZU12/iciIsoFij5lpqameRzJl0WxvQpKnzwmZkRERLmIly+1U9C2FxMzIiIionwiTxOzw4cPo3nz5nBxcYFMJsP27duVpgshMH78eDg7O0Mul8Pf3x+3bt1Smufly5fo3LkzLC0tYW1tjZ49eyIxMTEX14KIiIhIN/I0MUtKSkL58uWxaNEitdOnT5+O+fPnIzw8HCdPnoSZmRkCAgLw9u1baZ7OnTvjypUr2Lt3L3bt2oXDhw+jT58+ubUKRERE2SaT5d4rq548eYLBgwfD09MTJiYmcHR0RI0aNbBkyRIkJycDAC5cuIDAwEA4ODjAxMQEbm5uaN++vXRnJWUuT+/KbNy4MRo3bqx2mhACc+fOxc8//4wWLVoAANasWQNHR0ds374dHTp0wLVr1xAZGYnTp0+jUqVKAIAFCxagSZMmmDlzJlxcXHJtXYiIiL5W//77L2rUqAFra2tMmTIFZcuWhbGxMS5duoRly5ahcOHCqFatGurXr49mzZohKioK1tbWiI2Nxc6dO5GUlJTXq/DFyLfDZcTExODJkyfw9/eXyqysrFC1alUcP34cHTp0wPHjx2FtbS0lZQDg7+8PPT09nDx5Eq1atcqL0ImIiL4q/fv3h4GBAc6cOQMzMzOpvHjx4mjRogWEENixYwdev36NFStWwMDgQ3rh7u6OunXr5lXYX6R82/n/yZMnAABHR0elckdHR2nakydP4ODgoDTdwMAANjY20jzqpKSkICEhQelFREREql68eIE9e/ZgwIABSknZx2QyGZycnPD+/Xts27YNQohcjvLrkW9bzHLS1KlTERYWlivLyvB6fqj6CaEIVVseEhLC+nOhfhGi3ckkz+oHwPMeEeWG27dvQwgBLy8vpXI7Ozupz/eAAQMwbdo0jB07Fp06dcL333+PKlWqoF69eujatatKIwtlLN+2mDk5OQEAnj59qlT+9OlTaZqTk5NKh8L379/j5cuX0jzqjBkzBq9fv5Ze9+/f13H0REREX7dTp04hOjoapUuXRkpKCgBg8uTJePLkCcLDw1G6dGmEh4fD29sbly5dyuNovxz5NjFzd3eHk5MT9u/fL5UlJCTg5MmTqFatGgCgWrVqiI+Px9mzZ6V5/v77b6Snp6Nq1aoZ1m1sbAxLS0ulFxEREany9PSETCbDjRs3lMqLFy8OT09P6bFJCra2tmjXrh1mzpyJa9euwcXFBTNnzszNkL9oeXopMzExEbdv35bex8TEIDo6GjY2NihWrBiGDBmCSZMmoUSJEnB3d8e4cePg4uKCli1bAgBKlSqFRo0aoXfv3ggPD8e7d+8wcOBAdOjQgXdk0ldPFqaby6VERJ9ja2uLBg0aYOHChfjhhx8y7GemjpGRETw8PHhXphbyNDE7c+aM0t0aw4YNAwAEBwdj1apVGDlyJJKSktCnTx/Ex8ejZs2aiIyMhImJifSZ9evXY+DAgahfvz709PTQpk0bzJ8/P9fXhYiI6Gu1ePFi1KhRA5UqVUJoaCjKlSsHPT09nD59GtevX4evry927dqF33//HR06dEDJkiUhhMCff/6J//3vf4iIiMjrVfhi5GliVqdOnc/euSGTyTBhwgRMmDAhw3lsbGywYcOGnAiPiIiIAHh4eOD8+fOYMmUKxowZgwcPHsDY2Bg+Pj4YPnw4+vfvjydPnsDU1BQ//vgj7t+/D2NjY5QoUQIrVqxAly5d8noVvhgF8q5MIiKi/ORLuMva2dkZCxYswIIFC9ROL168OJYtW5bLUX198m3nfyIiIqKChokZERERUT7BxIyIiIgon2BiRkRERJRPMDEjIiIiyieYmBERERHlE0zMiIiIiPIJJmZERERE+QQTMyIiIqJ8gokZERERUT7BRzIRERHlMVmYLNeWJUK0f/5Tt27dsHr1agCAoaEhihUrhq5du2Ls2LE4cuQI6tatK83r4OCAmjVrYsaMGShevLhUfuzYMUyaNAnHjx/HmzdvUKJECXTv3h2DBw+Gvr5+9lfsK8EWMyIiIspUo0aN8PjxY9y6dQs//vgjQkNDMWPGDGn6jRs38OjRI2zatAlXrlxB8+bNkZaWBgDYtm0b/Pz8UKRIERw4cADXr1/H4MGDMWnSJHTo0AHiS3hYaC5hixkRERFlytjYGE5OTgCAfv36Ydu2bdi5cyeqVasG4ENLmbW1NZydnTF+/Hh07twZt2/fRpEiRdC7d28EBgYqPeS8V69ecHR0RGBgIP744w+0b98+T9Yrv2GLGREREWlNLpcjNTU1w2kAkJqaij179uDFixcYPny4ynzNmzdHyZIl8dtvv+VorF8SJmZERESkMSEE9u3bh6ioKNSrV09l+uPHjzFz5kwULlwYXl5euHnzJgCgVKlSauvz9vaW5iFeyiQiIiIN7Nq1C+bm5nj37h3S09PRqVMnhIaG4vTp0wCAIkWKQAiB5ORklC9fHlu2bIGRkZH0efYj0wwTMyIiIspU3bp1sWTJEhgZGcHFxQUGBsopxD///ANLS0s4ODjAwsJCKi9ZsiQA4Nq1a6hevbpKvdeuXYOPj0/OBv8F4aVMIiIiypSZmRk8PT1RrFgxlaQMANzd3eHh4aGUlAFAw4YNYWNjg1mzZql8ZufOnbh16xY6duyYY3F/aZiYERERUY4xMzPD0qVLsWPHDvTp0wcXL15EbGwsVq5ciW7duqFt27YICgrK6zDzDSZmRERElKPatm2LAwcO4N69e6hVqxa8vLwwZ84c/PTTT/j9998hk+XeALv5HfuYERER5bGsjMafm1atWpXhtDp16mjUsb9WrVqIjIzUYVRfJ7aYEREREeUTTMyIiIiI8gkmZkRERET5BBMzIiIionyCnf+JPhIWFqa2PCQkJJcjISKigogtZkRERET5BBMzIiIionyCiRkRERFRPsHEjIiIiCifYGJGRERElE/wrkwiIqI8ltEd4TkhK3eZd+vWDatXr5be29jYoHLlypg+fTrKlSsHAGqfd1mjRg0cOXIEALB8+XIsXLgQd+7cgYGBAdzd3REUFIQxY8ZkcU2+TmwxIyIiokw1atQIjx8/xuPHj7F//34YGBigWbNmSvNERERI8zx+/Bg7d+4EAPz6668YMmQIBg0ahOjoaBw9ehQjR45EYmJiXqxKvsYWMyIiIsqUsbExnJycAABOTk4YPXo0atWqhWfPnsHe3h4AYG1tLc3zsZ07dyIoKAg9e/aUykqXLp07gX9h2GJGREREWklMTMS6devg6ekJW1vbTOd3cnLCiRMncPfu3VyI7svGxIyogJPJ1L+IiD62a9cumJubw9zcHBYWFti5cyc2btwIPb3/n0p07NhRmsfc3Bzbt28H8KFfm7W1Ndzc3ODl5YVu3brhjz/+QHp6eh6tTf7FxIyIiIgyVbduXURHRyM6OhqnTp1CQEAAGjdurNQKNmfOHGme6OhoNGjQAADg7OyM48eP49KlSxg8eDDev3+P4OBgNGrUiMnZJ5iYERERUabMzMzg6ekJT09PVK5cGStWrEBSUhKWL18uzePk5CTN4+npCTMzM6U6ypQpg/79+2PdunXYu3cv9u7di0OHDuX2quRrTMyIiIhIazKZDHp6enjz5k2WPu/j4wMASEpK0mVYXzyN7sqsWLGi2vFJ1Dl37ly2AiIiIqL8JyUlBU+ePAEAvHr1CgsXLkRiYiKaN2+e6Wf79esHFxcX1KtXD0WKFMHjx48xadIk2Nvbo1q1ajkd+hdFo8SsZcuW0t9v377F4sWL4ePjI23MEydO4MqVK+jfv3+OBElERER5KzIyEs7OzgAACwsLeHt7Y9OmTahTp06mn/X398evv/6KJUuW4MWLF7Czs0O1atWwf/9+je7qLEg0Ssw+HiW4V69eGDRoECZOnKgyz/3793UbHRERUQGQldH4c9OqVauwatWqz84jhMhwWps2bdCmTRsdR/V10rqP2aZNm9C1a1eV8u+++w5btmzRSVBEREREBZHWiZlcLsfRo0dVyo8ePQoTExOdBEVERERUEGn9SKYhQ4agX79+OHfuHKpUqQIAOHnyJH799VeMGzdO5wESERERFRRaJ2ajR49G8eLFMW/ePKxbtw4AUKpUKURERCAoKEjnARIREREVFFl6iHlQUBCTMCIioiz4XCd5UlXQtleWBpiNj4/HihUrMHbsWLx8+RLAh/HLHj58qNPgiIiIvhaGhoYAgOTk5DyO5Mui2F6K7fe107rF7OLFi/D394eVlRViY2PRq1cv2NjYYOvWrbh37x7WrFmTE3ESERF90fT19WFtbY24uDgAgKmpqcaDtxdEQggkJycjLi4O1tbW0NfXz+uQcoXWidmwYcPQrVs3TJ8+HRYWFlJ5kyZN0KlTJ50GR0RE9DVxcnICACk5o8xZW1tL260g0DoxO336NJYuXapSXrhwYelRDURERKRKJpPB2dkZDg4OePfuXV6Hk+8ZGhoWmJYyBa0TM2NjYyQkJKiU37x5E/b29joJioiI6Gumr69f4BIO0ozWnf8DAwMxYcIEKdOXyWS4d+8eRo0axcctEBEREWWD1onZrFmzkJiYCAcHB7x58wZ+fn7w9PSEhYUFJk+enBMxEhERERUIWl/KtLKywt69e3HkyBFcvHgRiYmJ+Oabb+Dv758T8REREREVGFonZvfv30fRokVRs2ZN1KxZMydiIiIiIiqQtL6U6ebmBj8/PyxfvhyvXr3KiZiIiIiICiStE7MzZ86gSpUqmDBhApydndGyZUts3rwZKSkpOREfERERUYGhdWJWsWJFzJgxA/fu3cPu3bthb2+PPn36wNHRET169MiJGImIiIgKhCw9KxP4MExG3bp1sXz5cuzbtw/u7u5YvXq1LmNDWloaxo0bB3d3d8jlcnh4eGDixIlKDzQVQmD8+PFwdnaGXC6Hv78/bt26pdM4iIiIiHJDlhOzBw8eYPr06ahQoQKqVKkCc3NzLFq0SJexYdq0aViyZAkWLlyIa9euYdq0aZg+fToWLFggzTN9+nTMnz8f4eHhOHnyJMzMzBAQEIC3b9/qNBYiIiKinKb1XZlLly7Fhg0bcPToUXh7e6Nz587YsWMHXF1ddR7csWPH0KJFCzRt2hTAhxsPfvvtN5w6dQrAh9ayuXPn4ueff0aLFi0AAGvWrIGjoyO2b9+ODh066DwmIiIiopyidYvZpEmTULVqVZw9exaXL1/GmDFjciQpA4Dq1atj//79uHnzJgDgwoULOHLkCBo3bgwAiImJwZMnT5TGULOyskLVqlVx/PjxDOtNSUlBQkKC0ouIiIgor2ndYnbv3j3IZLKciEXF6NGjkZCQAG9vb+jr6yMtLQ2TJ09G586dAUB6aLqjo6PS5xwdHT/7QPWpU6ciLCws5wInIiIiygKNErOLFy9qXGG5cuWyHMyn/vjjD6xfvx4bNmxA6dKlER0djSFDhsDFxQXBwcFZrnfMmDEYNmyY9D4hIQFFixbVRchEREREWaZRYlahQgXIZDKluyE/ppgmk8mQlpams+BGjBiB0aNHS33FypYti7t372Lq1KkIDg6Gk5MTAODp06dwdnaWPvf06VNUqFAhw3qNjY1hbGyssziJiIiIdEGjxCwmJian41ArOTkZenrK3eD09fWRnp4OAHB3d4eTkxP2798vJWIJCQk4efIk+vXrl9vhEhEREWWLRolZTnXuz0zz5s0xefJkFCtWDKVLl8b58+cxe/ZsaSBbmUyGIUOGYNKkSShRogTc3d0xbtw4uLi4oGXLlnkSMxEREVFWad35HwDu3LmDuXPn4tq1awAAHx8fDB48GB4eHjoNbsGCBRg3bhz69++PuLg4uLi4oG/fvhg/frw0z8iRI5GUlIQ+ffogPj4eNWvWRGRkJExMTHQaCxEREVFO0zoxi4qKQmBgICpUqIAaNWoAAI4ePYrSpUvjzz//RIMGDXQWnIWFBebOnYu5c+dmOI9MJsOECRMwYcIEnS2XiIiIKC9onZiNHj0aQ4cOxS+//KJSPmrUKJ0mZkREREQFidYDzF67dg09e/ZUKe/RoweuXr2qk6CIiIiICiKtEzN7e3tER0erlEdHR8PBwUEXMREREREVSFpfyuzduzf69OmDf//9F9WrVwfwoY/ZtGnTlAZtJSIiIiLtaJ2YjRs3DhYWFpg1axbGjBkDAHBxcUFoaCgGDRqk8wCJiIiICgqtEzOZTIahQ4di6NCh+O+//wB8uHuSiIiIiLJH6z5mb968QXJyMoAPCdnLly8xd+5c7NmzR+fBERERERUkWreYtWjRAq1bt8b333+P+Ph4VKlSBUZGRnj+/Dlmz57NRyERfSVkYTK15SJE/TNziYgo+7RuMTt37hxq1aoFANi8eTOcnJxw9+5drFmzBvPnz9d5gEREREQFhdaJWXJystSnbM+ePWjdujX09PTw7bff4u7duzoPkIiIiKig0Dox8/T0xPbt23H//n1ERUWhYcOGAIC4uDhYWlrqPEAiIiKigkLrxGz8+PEYPnw43NzcULVqVVSrVg3Ah9azihUr6jxAIiIiooJC687/bdu2Rc2aNfH48WOUL19eKq9fvz5atWql0+CIiIiIChKtEzMAcHJygpOTk1JZlSpVdBIQERERUUGl9aVMIiIiIsoZTMyIiIiI8gkmZkRERET5BBMzIiIionxC68Rs9erV+Ouvv6T3I0eOhLW1NapXr84BZomIiIiyQevEbMqUKZDL5QCA48ePY9GiRZg+fTrs7OwwdOhQnQdIREREVFBoPVzG/fv34enpCQDYvn072rRpgz59+qBGjRqoU6eOruMjIiIiKjC0TszMzc3x4sULFCtWDHv27MGwYcMAACYmJnjz5o3OAyT6moSFhaktDwkJyeVIiIgoP9I6MWvQoAF69eqFihUr4ubNm2jSpAkA4MqVK3Bzc9N1fET0hZPJ1JcLkbtxEBF9CbTuY7Zo0SJUq1YNz549w5YtW2BrawsAOHv2LDp27KjzAImIiIgKCq1bzKytrbFw4UKV8owu0RARERGRZrL0rMz4+HicOnUKcXFxSE9Pl8plMhm6dOmis+CIiIiIChKtE7M///wTnTt3RmJiIiwtLSH7qAMJEzMiIiKirNO6j9mPP/6IHj16IDExEfHx8Xj16pX0evnyZU7ESERERFQgaJ2YPXz4EIMGDYKpqWlOxENERERUYGmdmAUEBODMmTM5EQsRERFRgaZ1H7OmTZtixIgRuHr1KsqWLQtDQ0Ol6YGBgToLjoiIiKgg0Tox6927NwBgwoQJKtNkMhnS0tKyHxURERFRAaR1Yvbx8BhEREREpDta9zEjIiIiopyRpcTs0KFDaN68OTw9PeHp6YnAwED8888/uo6NiIiIqEDROjFbt24d/P39YWpqikGDBmHQoEGQy+WoX78+NmzYkBMxEhFlSCZT/yIi+hJp3cds8uTJmD59OoYOHSqVDRo0CLNnz8bEiRPRqVMnnQZIREREVFBo3WL277//onnz5irlgYGBiImJ0UlQRERERAWR1olZ0aJFsX//fpXyffv2oWjRojoJioiIiKgg0vpS5o8//ohBgwYhOjoa1atXBwAcPXoUq1atwrx583QeIBEREVFBoXVi1q9fPzg5OWHWrFn4448/AAClSpXCxo0b0aJFC50HSERERFRQaJ2YAUCrVq3QqlUrXcdCREREVKBxgFkiIiKifEKjFjMbGxvcvHkTdnZ2KFSoEGSfGSTo5cuXOguOiIiIqCDRKDGbM2cOLCwspL8/l5gRERERUdZolJgFBwdLf3fr1i2nYiEiIiIq0LTuY6avr4+4uDiV8hcvXkBfX18nQREREREVRFonZkIIteUpKSkwMjLKdkBEREREBZXGw2XMnz8fACCTybBixQqYm5tL09LS0nD48GF4e3vrPkIiIiKiAkLjxGzOnDkAPrSYhYeHK122NDIygpubG8LDw3UfIRFpJSwsTG15SEhILkdCRETa0jgxUzygvG7duti6dSsKFSqUY0ERERERFURaj/x/4MCBnIiDiIiIqMDL0iOZHjx4gJ07d+LevXtITU1VmjZ79mydBEZERERU0GidmO3fvx+BgYEoXrw4rl+/jjJlyiA2NhZCCHzzzTc5ESMRERFRgaD1cBljxozB8OHDcenSJZiYmGDLli24f/8+/Pz80K5du5yIkYiIiKhA0Doxu3btGrp27QoAMDAwwJs3b2Bubo4JEyZg2rRpOg+QiIiIqKDQOjEzMzOT+pU5Ozvjzp070rTnz5/rLjIiIiKiAkbrPmbffvstjhw5glKlSqFJkyb48ccfcenSJWzduhXffvttTsRIREREVCBonZjNnj0biYmJAD4MZJmYmIiNGzeiRIkSvCOTiIiIKBu0vpRZvHhxlCtXDsCHy5rh4eG4ePEitmzZAldXV50H+PDhQ3z33XewtbWFXC5H2bJlcebMGWm6EALjx4+Hs7Mz5HI5/P39cevWLZ3HQURERJTTspSYvXjxQqU8Pj4exYsX10lQCq9evUKNGjVgaGiI3bt34+rVq5g1a5bSUwemT5+O+fPnIzw8HCdPnoSZmRkCAgLw9u1bncZCRERElNO0vpQZGxuLtLQ0lfKUlBQ8fPhQJ0EpTJs2DUWLFkVERIRU5u7uLv0thMDcuXPx888/o0WLFgCANWvWwNHREdu3b0eHDh10Gg8RERFRTtI4Mdu5c6f0d1RUFKysrKT3aWlp2L9/P9zc3HQa3M6dOxEQEIB27drh0KFDKFy4MPr374/evXsD+PD8zidPnsDf31/6jJWVFapWrYrjx48zMSMiIqIvisaJWcuWLQEAMpkMwcHBStMMDQ3h5uaGWbNm6TS4f//9F0uWLMGwYcMwduxYnD59GoMGDYKRkRGCg4Px5MkTAICjo6PS5xwdHaVp6qSkpCAlJUV6n5CQoNO4iYiIiLJC48QsPT0dwIdLiadPn4adnV2OBfXxMitVqoQpU6YAACpWrIjLly8jPDxcJTnUxtSpUxEWFqarMImIiIh0QuvO/zExMbmSlAEfBrD18fFRKitVqhTu3bsHAHBycgIAPH36VGmep0+fStPUGTNmDF6/fi297t+/r+PIiYiIiLSnded/4MODzPfv34+4uDipJU3h119/1UlgAFCjRg3cuHFDqezmzZvSsBzu7u5wcnLC/v37UaFCBQAfLkuePHkS/fr1y7BeY2NjGBsb6yxOIiIiIl3QOjELCwvDhAkTUKlSJTg7O0Mmk+VEXACAoUOHonr16pgyZQqCgoJw6tQpLFu2DMuWLQPwob/bkCFDMGnSJJQoUQLu7u4YN24cXFxcpD5xRERERF8KrROz8PBwrFq1Cl26dMmJeJRUrlwZ27Ztw5gxYzBhwgS4u7tj7ty56Ny5szTPyJEjkZSUhD59+iA+Ph41a9ZEZGQkTExMcjw+IiIiIl3SOjFLTU1F9erVcyIWtZo1a4ZmzZplOF0mk2HChAmYMGFCrsVERERElBO07vzfq1cvbNiwISdiISIiIirQtG4xe/v2LZYtW4Z9+/ahXLlyMDQ0VJrOB5kTERERZY3WidnFixelOyAvX76sNC0nbwQgoq+LLEz9+UKEiFyOhIgo/9A6MTtw4EBOxEFERERU4Gndx0zh9u3biIqKwps3bwB8eKA4EREREWWd1onZixcvUL9+fZQsWRJNmjTB48ePAQA9e/bEjz/+qPMAiYiIiAoKrROzoUOHwtDQEPfu3YOpqalU3r59e0RGRuo0OCIiIqKCROs+Znv27EFUVBSKFCmiVF6iRAncvXtXZ4ERERERFTRat5glJSUptZQpvHz5ks+fJCIiIsoGrROzWrVqYc2aNdJ7mUyG9PR0TJ8+HXXr1tVpcEREREQFidaXMqdPn4769evjzJkzSE1NxciRI3HlyhW8fPkSR48ezYkYiYiIiAoErVvMypQpg5s3b6JmzZpo0aIFkpKS0Lp1a5w/fx4eHh45ESMRERFRgaB1ixkAWFlZ4aefftJ1LEREREQFmtYtZpGRkThy5Ij0ftGiRahQoQI6deqEV69e6TQ4IiIiooJE68RsxIgRSEhIAABcunQJw4YNQ5MmTRATE4Nhw4bpPEAiIiKigkLrS5kxMTHw8fEBAGzZsgXNmzfHlClTcO7cOTRp0kTnARIREREVFFq3mBkZGSE5ORkAsG/fPjRs2BAAYGNjI7WkEREREZH2tG4xq1mzJoYNG4YaNWrg1KlT2LhxIwDg5s2bKk8DICIiIiLNad1itnDhQhgYGGDz5s1YsmQJChcuDADYvXs3GjVqpPMAiYiIiAoKrVvMihUrhl27dqmUz5kzRycBERERERVUWreYAcCdO3fw888/o2PHjoiLiwPwocXsypUrOg2OiIiIqCDROjE7dOgQypYti5MnT2Lr1q1ITEwEAFy4cAEhISE6D5CIiIiooND6Uubo0aMxadIkDBs2DBYWFlJ5vXr1sHDhQp0GR0T5T1hYmNpy/mNGRJR9WreYXbp0Ca1atVIpd3BwwPPnz3USFBEREVFBpHViZm1tjcePH6uUnz9/XrpDk4iIiIi0p3Vi1qFDB4waNQpPnjyBTCZDeno6jh49iuHDh6Nr1645ESMRERFRgaB1YjZlyhR4e3ujaNGiSExMhI+PD2rXro3q1avj559/zokYiYiIiAoErTr/CyHw5MkTzJ8/H+PHj8elS5eQmJiIihUrokSJEjkVIxEREVGBoHVi5unpiStXrqBEiRIoWrRoTsVFREREVOBodSlTT08PJUqUwIsXL3IqHiKifEUmU/8iIsoJWvcx++WXXzBixAhcvnw5J+IhIiIiKrC0HmC2a9euSE5ORvny5WFkZAS5XK40/eXLlzoLjoiIiKgg0Toxmzt3bg6EQURERERaJ2bBwcE5EQcRERFRgad1YgYAaWlp2LZtG65duwYA8PHxQYsWLWBgkKXqiIiIiAhZSMyuXLmCwMBAPHnyBF5eXgCAadOmwd7eHn/++SfKlCmj8yCJiIiICgKtE7NevXqhdOnSOHPmDAoVKgQAePXqFbp164Y+ffrg2LFjOg+SiEhbsjD1Y1qIEJHLkRARaU7rxCw6OlopKQOAQoUKYfLkyahcubJOgyMiIiIqSLQex6xkyZJ4+vSpSnlcXBw8PT11EhQRERFRQaR1YjZ16lQMGjQImzdvxoMHD/DgwQNs3rwZQ4YMwbRp05CQkCC9iIiIiEhzWl/KbNasGQAgKCgIsv97LokQH/psNG/eXHovk8mQlpamqziJiIiIvnpaJ2YHDhzIiTiIiIiICjytEzM/P7+ciIOIiIiowNO6jxkRERER5QwmZkRERET5BBMzIiIionxCo8Rs586dePfuXU7HQkRERFSgaZSYtWrVCvHx8QAAfX19xMXF5WRMRERERAWSRomZvb09Tpw4AeD/j1FGRERERLql0XAZ33//PVq0aAGZTAaZTAYnJ6cM5+WgskRERERZo1FiFhoaig4dOuD27dsIDAxEREQErK2tczg0IiIiooJF4wFmvb294e3tjZCQELRr1w6mpqY5GRcRERFRgaP1yP8hISEAgGfPnuHGjRsAAC8vL9jb2+s2MiIiIqICRutxzJKTk9GjRw+4uLigdu3aqF27NlxcXNCzZ08kJyfnRIxEREREBYLWidnQoUNx6NAh7Ny5E/Hx8YiPj8eOHTtw6NAh/PjjjzkRIxEREVGBoPWlzC1btmDz5s2oU6eOVNakSRPI5XIEBQVhyZIluoyPiIiIqMDI0qVMR0dHlXIHBwdeyiQiIiLKBq0Ts2rVqiEkJARv376Vyt68eYOwsDBUq1ZNp8ERERERFSRaX8qcN28eAgICUKRIEZQvXx4AcOHCBZiYmCAqKkrnARIREREVFFq3mJUpUwa3bt3C1KlTUaFCBVSoUAG//PILbt26hdKlS+dEjJJffvkFMpkMQ4YMkcrevn2LAQMGwNbWFubm5mjTpg2ePn2ao3EQERER5QStW8wAwNTUFL1799Z1LJ91+vRpLF26FOXKlVMqHzp0KP766y9s2rQJVlZWGDhwIFq3bo2jR4/manxERERE2aV1i1leSExMROfOnbF8+XIUKlRIKn/9+jVWrlyJ2bNno169evD19UVERASOHTsmPXSdiIiI6EvxRSRmAwYMQNOmTeHv769UfvbsWbx7906p3NvbG8WKFcPx48dzO0wiIiKibMnSpczc9Pvvv+PcuXM4ffq0yrQnT57AyMhI5YHqjo6OePLkSYZ1pqSkICUlRXqfkJCgs3iJiIiIsipft5jdv38fgwcPxvr162FiYqKzeqdOnQorKyvpVbRoUZ3VTUSkDZlM/YuICqYsJWbx8fFYsWIFxowZg5cvXwIAzp07h4cPH+o0uLNnzyIuLg7ffPMNDAwMYGBggEOHDmH+/PkwMDCAo6MjUlNTER8fr/S5p0+fwsnJKcN6x4wZg9evX0uv+/fv6zRuIiIioqzQ+lLmxYsX4e/vDysrK8TGxqJ3796wsbHB1q1bce/ePaxZs0ZnwdWvXx+XLl1SKuvevTu8vb0xatQoFC1aFIaGhti/fz/atGkDALhx4wbu3bv32cFujY2NYWxsrLM4iYiIiHRB68Rs2LBh6NatG6ZPnw4LCwupvEmTJujUqZNOg7OwsECZMmWUyszMzGBrayuV9+zZE8OGDYONjQ0sLS3xww8/oFq1avj22291GgsRERFRTtM6MVOMJ/apwoULf7bDfU6ZM2cO9PT00KZNG6SkpCAgIACLFy/O9TiIiIiIskvrxMzY2FjtXYw3b96Evb29ToL6nIMHDyq9NzExwaJFi7Bo0aIcXzYRERFRTtK6839gYCAmTJiAd+/eAQBkMhnu3buHUaNGSf28iIiIiEh7Widms2bNQmJiIhwcHPDmzRv4+fnB09MTFhYWmDx5ck7ESERERFQgaH0p08rKCnv37sWRI0dw8eJFJCYm4ptvvlEZlZ+IiIiItJPlkf9r1qyJmjVr6jIWIiIiogJN68Rs/vz5astlMhlMTEzg6emJ2rVrQ19fP9vBERERERUkWidmc+bMwbNnz5CcnIxChQoBAF69egVTU1OYm5sjLi4OxYsXx4EDB/ioIyIiIiItaN35f8qUKahcuTJu3bqFFy9e4MWLF7h58yaqVq2KefPm4d69e3BycsLQoUNzIl4iIiKir5bWLWY///wztmzZAg8PD6nM09MTM2fORJs2bfDvv/9i+vTpHDqDiIiISEtat5g9fvwY79+/Vyl///69NPK/i4sL/vvvv+xHR0RERFSAaJ2Y1a1bF3379sX58+elsvPnz6Nfv36oV68eAODSpUtwd3fXXZREREREBYDWidnKlSthY2MDX19fGBsbw9jYGJUqVYKNjQ1WrlwJADA3N8esWbN0HiwRERHR10zrPmZOTk7Yu3cvrl+/jps3bwIAvLy84OXlJc1Tt25d3UVIREREVEBkeYBZb29veHt76zIWIiIiogItS4nZgwcPsHPnTty7dw+pqalK02bPnq2TwIiIiIgKGq0Ts/379yMwMBDFixfH9evXUaZMGcTGxkIIgW+++SYnYiQiIiIqELTu/D9mzBgMHz4cly5dgomJCbZs2YL79+/Dz88P7dq1y4kYiYiIiAoErROza9euoWvXrgAAAwMDvHnzBubm5pgwYQKmTZum8wCJiIiICgqtL2WamZlJ/cqcnZ1x584dlC5dGgDw/Plz3UZHRJRPycJkastFiMjlSIjoa6J1Yvbtt9/iyJEjKFWqFJo0aYIff/wRly5dwtatW/Htt9/mRIxEREREBYLWidns2bORmJgIAAgLC0NiYiI2btyIEiVK8I5MIiIiomzQOjErXry49LeZmRnCw8N1GhARERFRQaV15//ixYvjxYsXKuXx8fFKSRsRERERaUfrxCw2NhZpaWkq5SkpKXj48KFOgiIiIiIqiDS+lLlz507p76ioKFhZWUnv09LSsH//fri5uek0OCIqeMLCwtSWh4SE5HIkRES5T+PErGXLlgAAmUyG4OBgpWmGhoZwc3PDrFmzdBocERERUUGicWKWnp4OAHB3d8fp06dhZ2eXY0ERERERFURa35UZExOTE3EQERERFXhaJ2bAhweZ79+/H3FxcVJLmsKvv/6qk8CIiIiIChqtE7OwsDBMmDABlSpVgrOzM2Qy9Y8lISIiIiLtaJ2YhYeHY9WqVejSpUtOxENERERUYGk9jllqaiqqV6+eE7EQERERFWhaJ2a9evXChg0bciIWIiIiogJN60uZb9++xbJly7Bv3z6UK1cOhoaGStP5IHMiIiKirNE6Mbt48SIqVKgAALh8+bLSNN4IQERERJR1WidmBw4cyIk4iIiIiAo8rfuYKdy+fRtRUVF48+YNAEAIobOgiIiIiAoirROzFy9eoH79+ihZsiSaNGmCx48fAwB69uyJH3/8UecBEhERERUUWidmQ4cOhaGhIe7duwdTU1OpvH379oiMjNRpcEREREQFidZ9zPbs2YOoqCgUKVJEqbxEiRK4e/euzgIjIiIiKmi0bjFLSkpSailTePnyJYyNjXUSFBEREVFBpHViVqtWLaxZs0Z6L5PJkJ6ejunTp6Nu3bo6DY6IiIioINH6Uub06dNRv359nDlzBqmpqRg5ciSuXLmCly9f4ujRozkRIxEREVGBoHWLWZkyZXDz5k3UrFkTLVq0QFJSElq3bo3z58/Dw8MjJ2IkIiIiKhC0bjEDACsrK/z000+6joWIiIioQNO6xSwiIgKbNm1SKd+0aRNWr16tk6CIiIiICiKtE7OpU6fCzs5OpdzBwQFTpkzRSVBEREREBZHWidm9e/fg7u6uUu7q6op79+7pJCgiIiKigkjrxMzBwQEXL15UKb9w4QJsbW11EhQRERFRQaR1YtaxY0cMGjQIBw4cQFpaGtLS0vD3339j8ODB6NChQ07ESERERFQgaH1X5sSJExEbG4v69evDwODDx9PT09G1a1f2MSMiIiLKBq0SMyEEnjx5glWrVmHSpEmIjo6GXC5H2bJl4erqmlMxEhFRPiWTqS8XInfjIPpaaJ2YeXp64sqVKyhRogRKlCiRU3ERERERFTha9THT09NDiRIl8OLFi5yKh4iIiKjA0rrz/y+//IIRI0bg8uXLOREPERERUYGldef/rl27Ijk5GeXLl4eRkRHkcrnS9JcvX+osOCIiIqKCROvEbO7cuTkQBhERERFpnZgFBwfnRBxEREREBZ7WfcwA4M6dO/j555/RsWNHxMXFAQB2796NK1eu6DQ4IiIiooJE68Ts0KFDKFu2LE6ePImtW7ciMTERwIdHMoWEhOg8QCIiyjqZTP2LiPInrROz0aNHY9KkSdi7dy+MjIyk8nr16uHEiRM6DY6IiIioINE6Mbt06RJatWqlUu7g4IDnz5/rJCiFqVOnonLlyrCwsICDgwNatmyJGzduKM3z9u1bDBgwALa2tjA3N0ebNm3w9OlTncZBRERElBu0Tsysra3x+PFjlfLz58+jcOHCOglK4dChQxgwYABOnDiBvXv34t27d2jYsCGSkpKkeYYOHYo///wTmzZtwqFDh/Do0SO0bt1ap3EQERER5Qat78rs0KEDRo0ahU2bNkEmkyE9PR1Hjx7F8OHD0bVrV50GFxkZqfR+1apVcHBwwNmzZ1G7dm28fv0aK1euxIYNG1CvXj0AQEREBEqVKoUTJ07g22+/1Wk8RERERDlJ6xazKVOmwNvbG0WLFkViYiJ8fHxQu3ZtVK9eHT///HNOxCh5/fo1AMDGxgYAcPbsWbx79w7+/v7SPN7e3ihWrBiOHz+eYT0pKSlISEhQehERERHlNa1bzIyMjLB8+XKMHz8ely5dQmJiIipWrJjjDzRPT0/HkCFDUKNGDZQpUwYA8OTJExgZGcHa2lppXkdHRzx58iTDuqZOnYqwsLCcDJeIKFtkYepvnRQhIpcjIaLcpHFilp6ejhkzZmDnzp1ITU1F/fr1ERISovJIppwyYMAAXL58GUeOHMl2XWPGjMGwYcOk9wkJCShatGi26yUiIiLKDo0vZU6ePBljx46Fubk5ChcujHnz5mHAgAE5GZtk4MCB2LVrFw4cOIAiRYpI5U5OTkhNTUV8fLzS/E+fPoWTk1OG9RkbG8PS0lLpRURERJTXNE7M1qxZg8WLFyMqKgrbt2/Hn3/+ifXr1yM9PT3HghNCYODAgdi2bRv+/vtvuLu7K0339fWFoaEh9u/fL5XduHED9+7dQ7Vq1XIsLiIiIqKcoPGlzHv37qFJkybSe39/f8hkMjx69EipFUuXBgwYgA0bNmDHjh2wsLCQ+o1ZWVlBLpfDysoKPXv2xLBhw2BjYwNLS0v88MMPqFatGu/IJCIioi+OxonZ+/fvYWJiolRmaGiId+/e6TwohSVLlgAA6tSpo1QeERGBbt26AQDmzJkDPT09tGnTBikpKQgICMDixYtzLCYiIiKinKJxYiaEQLdu3WBsbCyVvX37Ft9//z3MzMyksq1bt+osOCEyv/vIxMQEixYtwqJFi3S2XCIiIqK8oHFiFhwcrFL23Xff6TQYIqKcltFQOSEhIbkcCRGRKo0Ts4iIiJyMg4iIiKjA03qAWSIiyhhb5IgoO7R+JBMRERER5QwmZkRERET5BBMzIiIionyCiRkRERFRPsHO/0RElG/JZOrLNRjmkuiLxMSMiKgAkoWpz3hECDMeorzES5lERERE+QQTMyIiIqJ8gokZERERUT7BxIyIiIgon2BiRkRERJRPMDEjIiIiyieYmBERERHlE0zMiIiIiPIJJmZERERE+QQTMyIiIqJ8gokZERERUT7BZ2USEVGBxYekU37DxIyI6AsSFhamtjwkJCSXI/m8jB6SHopQteX5LX6ivMJLmURERET5BBMzIiIionyCiRkRERFRPsHEjIiIiCifYGJGRERElE/wrkwiIqIcwuE4SFtsMSMiIiLKJ5iYEREREeUTvJRJRET0heKl0q8PW8yIiIiI8gkmZkRERET5BBMzIiIionyCfcyIiEjypTwkPafxIeyUV9hiRkRERJRPMDEjIiIiyieYmBERERHlE0zMiIiIiPIJJmZERERE+QQTMyIiIqJ8gokZERERUT7BxIyIiIgon2BiRkRERJRPMDEjIiIiyieYmBERERHlE3xWJhERfXEyepalCBG5HAmRbjExIyIi+sowcf1y8VImERERUT7BxIyIiIgon2BiRkRERJRPMDEjIiIiyifY+Z+IiL4aYWFhastDQkJyOZLPY+d8yghbzIiIiIjyCSZmRERERPkEL2USERHlEzl9KfZLudRbkLHFjIiIiCifYIsZERERqSVTf48CEMqbF3IKW8yIiIiI8omvJjFbtGgR3NzcYGJigqpVq+LUqVN5HRIRERGRVr6KS5kbN27EsGHDEB4ejqpVq2Lu3LkICAjAjRs34ODgkNfhERERFQi8uSD7vooWs9mzZ6N3797o3r07fHx8EB4eDlNTU/z66695HRoRERGRxr74xCw1NRVnz56Fv7+/VKanpwd/f38cP348DyMjIiIi0s4Xfynz+fPnSEtLg6Ojo1K5o6Mjrl+/rvYzKSkpSElJkd6/fv0aAJCQkJBzgX7qbUbF6idoHRvr/7rrz41lsH7Wz/pZf17VryFFvUJ8PXeDysQXvjaPHj1C4cKFcezYMVSrVk0qHzlyJA4dOoSTJ0+qfCY0NDTD6+BERET0Zbl//z6KFCmS12HoxBffYmZnZwd9fX08ffpUqfzp06dwcnJS+5kxY8Zg2LBh0vv09HS8fPkStra2kGU4aEvOSEhIQNGiRXH//n1YWlqyftaf75bB+lk/62f9eVV/ZoQQ+O+//+Di4pLry84pX3xiZmRkBF9fX+zfvx8tW7YE8CHR2r9/PwYOHKj2M8bGxjA2NlYqs7a2zuFIP8/S0jJHd2rW/3XXnxvLYP2sn/Wz/ryq/3OsrKzyZLk55YtPzABg2LBhCA4ORqVKlVClShXMnTsXSUlJ6N69e16HRkRERKSxryIxa9++PZ49e4bx48fjyZMnqFChAiIjI1VuCCAiIiLKz76KxAwABg4cmOGly/zM2NgYISEhKpdWWT/rzy/LYP2sn/Wz/ryqvyD64u/KJCIiIvpafPEDzBIRERF9LZiYEREREeUTTMyIiIiI8gkmZnnEzc0NMplM5TVgwACd1J+WloZx48bB3d0dcrkcHh4emDhxok4fW/Hff/9hyJAhcHV1hVwuR/Xq1XH69Oks1XX48GE0b94cLi4ukMlk2L59u9J0IQTGjx8PZ2dnyOVy+Pv749atWzqrf+vWrWjYsKE0yHB0dLTO4n/37h1GjRqFsmXLwszMDC4uLujatSsePXqks/hDQ0Ph7e0NMzMzFCpUCP7+/mqfepHV+j/2/fffQyaTYe7cuTqrv1u3birHQqNGjXQa/7Vr1xAYGAgrKyuYmZmhcuXKuHfvnk7qV3csy2QyzJgxQyf1JyYmYuDAgShSpAjkcjl8fHwQHh6uUd2a1P/06VN069YNLi4uMDU1RaNGjbQ6vqZOnYrKlSvDwsICDg4OaNmyJW7cuKE0z9u3bzFgwADY2trC3Nwcbdq0URkYPDv1L1u2DHXq1IGlpSVkMhni4+N1Fv/Lly/xww8/wMvLC3K5HMWKFcOgQYOkx/npIv6+ffvCw8MDcrkc9vb2aNGiRYaPFcxK/QpCCDRu3DjT41zb+uvUqaOy/3///fca1U/KmJjlkdOnT+Px48fSa+/evQCAdu3a6aT+adOmYcmSJVi4cCGuXbuGadOmYfr06ViwYIFO6geAXr16Ye/evVi7di0uXbqEhg0bwt/fHw8fPtS6rqSkJJQvXx6LFi1SO3369OmYP38+wsPDcfLkSZiZmSEgIABv32bwwDYt609KSkLNmjUxbdo0rWPPrP7k5GScO3cO48aNw7lz57B161bcuHEDgYGBOqkfAEqWLImFCxfi0qVLOHLkCNzc3NCwYUM8e/ZMJ/UrbNu2DSdOnNB6lG1N6m/UqJHSMfHbb7/prP47d+6gZs2a8Pb2xsGDB3Hx4kWMGzcOJiYmOqn/47gfP36MX3/9FTKZDG3atNFJ/cOGDUNkZCTWrVuHa9euYciQIRg4cCB27tyZ7fqFEGjZsiX+/fdf7NixA+fPn4erqyv8/f2RlJSkUf2HDh3CgAEDcOLECezduxfv3r1Dw4YNlT4/dOhQ/Pnnn9i0aRMOHTqER48eoXXr1jqrPzk5GY0aNcLYsWM1qlOb+h89eoRHjx5h5syZuHz5MlatWoXIyEj07NlTZ/H7+voiIiIC165dQ1RUFIQQaNiwIdLS0nRSv8LcuXO1fsKNpvX37t1b6TiYPn26Vsuh/yMoXxg8eLDw8PAQ6enpOqmvadOmokePHkplrVu3Fp07d9ZJ/cnJyUJfX1/s2rVLqfybb74RP/30U7bqBiC2bdsmvU9PTxdOTk5ixowZUll8fLwwNjYWv/32W7br/1hMTIwAIM6fP691vZrUr3Dq1CkBQNy9ezdH6n/9+rUAIPbt26ez+h88eCAKFy4sLl++LFxdXcWcOXO0rjuj+oODg0WLFi2yVJ8m9bdv31589913OVb/p1q0aCHq1auns/pLly4tJkyYoFSW1WPt0/pv3LghAIjLly9LZWlpacLe3l4sX75c6/qFECIuLk4AEIcOHRJCfDheDQ0NxaZNm6R5rl27JgCI48ePZ7v+jx04cEAAEK9evcpS7JnVr/DHH38IIyMj8e7duxyp/8KFCwKAuH37ts7qP3/+vChcuLB4/PixRvuxNvX7+fmJwYMHZ6k+UsYWs3wgNTUV69atQ48ePXT2rM7q1atj//79uHnzJgDgwoULOHLkCBo3bqyT+t+/f4+0tDSVFge5XI4jR47oZBkKMTExePLkCfz9/aUyKysrVK1aFcePH9fpsnLL69evIZPJcuRRYKmpqVi2bBmsrKxQvnx5ndSZnp6OLl26YMSIEShdurRO6vzUwYMH4eDgAC8vL/Tr1w8vXrzQSb3p6en466+/ULJkSQQEBMDBwQFVq1bV+DKOtp4+fYq//vpL49YUTVSvXh07d+7Ew4cPIYTAgQMHcPPmTTRs2DDbdaekpACA0rGsp6cHY2PjLB/Likt8NjY2AICzZ8/i3bt3Ssewt7c3ihUrlqVj+NP6dU2T+l+/fg1LS0sYGGg/HGhm9SclJSEiIgLu7u4oWrSoTupPTk5Gp06dsGjRogyfI52d+gFg/fr1sLOzQ5kyZTBmzBgkJydnazkFFROzfGD79u2Ij49Ht27ddFbn6NGj0aFDB3h7e8PQ0BAVK1bEkCFD0LlzZ53Ub2FhgWrVqmHixIl49OgR0tLSsG7dOhw/fhyPHz/WyTIUnjx5AgAqT3JwdHSUpn1J3r59i1GjRqFjx446fbbcrl27YG5uDhMTE8yZMwd79+6FnZ2dTuqeNm0aDAwMMGjQIJ3U96lGjRphzZo12L9/P6ZNm4ZDhw6hcePGGl3GyUxcXBwSExPxyy+/oFGjRtizZw9atWqF1q1b49ChQzqIXtnq1athYWGh8WU6TSxYsAA+Pj4oUqQIjIyM0KhRIyxatAi1a9fOdt2KBGnMmDF49eoVUlNTMW3aNDx48CBLx3J6ejqGDBmCGjVqoEyZMgA+HMNGRkYq/4hk5RhWV78uaVL/8+fPMXHiRPTp00en9S9evBjm5uYwNzfH7t27sXfvXhgZGemk/qFDh6J69epo0aKF1jFrUn+nTp2wbt06HDhwAGPGjMHatWvx3XffZWtZBdVXM/L/l2zlypVo3Lix1v12PuePP/7A+vXrsWHDBpQuXRrR0dEYMmQIXFxcEBwcrJNlrF27Fj169EDhwoWhr6+Pb775Bh07dsTZs2d1Uv/X6N27dwgKCoIQAkuWLNFp3XXr1kV0dDSeP3+O5cuXIygoCCdPnoSDg0O26j179izmzZuHc+fO6axF91MdOnSQ/i5btizKlSsHDw8PHDx4EPXr189W3enp6QCAFi1aYOjQoQCAChUq4NixYwgPD4efn1+26v/Ur7/+is6dO2vcf00TCxYswIkTJ7Bz5064urri8OHDGDBgAFxcXJRaobLC0NAQW7duRc+ePWFjYwN9fX34+/ujcePGWbpZaMCAAbh8+bLOW87zS/0JCQlo2rQpfHx8EBoaqtP6O3fujAYNGuDx48eYOXMmgoKCcPToUa32JXX179y5E3///TfOnz+vdbyaxv9xklq2bFk4Ozujfv36uHPnDjw8PLK93AIljy+lFnixsbFCT09PbN++Xaf1FilSRCxcuFCpbOLEicLLy0unyxFCiMTERPHo0SMhhBBBQUGiSZMm2aoPn/R9uHPnjtp+X7Vr1xaDBg3Kdv0fy8k+ZqmpqaJly5aiXLly4vnz5zqv/1Oenp5iypQp2a5/zpw5QiaTCX19fekFQOjp6QlXV9ds158ROzs7ER4enu36U1JShIGBgZg4caLSfCNHjhTVq1fPdv0fO3z4sAAgoqOjta43o/qTk5OFoaGhSn/Onj17ioCAgGzX/7H4+HgRFxcnhBCiSpUqon///lrVPWDAAFGkSBHx77//KpXv379fbb+vYsWKidmzZ2e7/o9lp49ZZvUnJCSIatWqifr164s3b97ovP6PpaSkCFNTU7Fhw4Zs1z948OAMj2E/P78ciT8xMVEAEJGRkRrXTx/wUmYei4iIgIODA5o2barTepOTk6Gnp/z16uvrS60HumRmZgZnZ2e8evUKUVFR2W4q/5S7uzucnJywf/9+qSwhIQEnT55EtWrVdLqsnKJoKbt16xb27dsHW1vbHF9menq61H8oO7p06YKLFy8iOjpaerm4uGDEiBGIiorSQaSqHjx4gBcvXsDZ2TnbdRkZGaFy5coqt/ffvHkTrq6u2a7/YytXroSvr6/O+vYBH/add+/e5crxbGVlBXt7e9y6dQtnzpzR+FgWQmDgwIHYtm0b/v77b7i7uytN9/X1haGhodIxfOPGDdy7d0+jYziz+rNLk/oTEhLQsGFDGBkZYefOnVq1YmUlfiEEhBAaHcOZ1T969GiVYxgA5syZg4iIiByJX7EMXRzDBQ0vZeah9PR0REREIDg4OEsdSD+nefPmmDx5MooVK4bSpUvj/PnzmD17Nnr06KGzZShu6fby8sLt27cxYsQIeHt7o3v37lrXlZiYiNu3b0vvY2JiEB0dDRsbGxQrVgxDhgzBpEmTUKJECbi7u2PcuHFwcXFBy5YtdVL/y5cvce/ePWlsMcWPuJOTk0YdZT9Xv7OzM9q2bYtz585h165dSEtLk/rV2NjYaNSH5HP129raYvLkyQgMDISzszOeP3+ORYsW4eHDhxoPv5LZ9vk0kTQ0NISTkxO8vLyyXb+NjQ3CwsLQpk0bODk54c6dOxg5ciQ8PT0REBCgk/hHjBiB9u3bo3bt2qhbty4iIyPx559/4uDBgzqpH/jww71p0ybMmjVLozq1qd/Pzw8jRoyAXC6Hq6srDh06hDVr1mD27Nk6qX/Tpk2wt7dHsWLFcOnSJQwePBgtW7bU+OaCAQMGYMOGDdixYwcsLCyk/dvKygpyuRxWVlbo2bMnhg0bBhsbG1haWuKHH35AtWrV8O2332a7fuBDP7YnT55I63np0iVYWFigWLFimd4kkFn9iqQsOTkZ69atQ0JCAhISEgAA9vb20NfXz1b9//77LzZu3IiGDRvC3t4eDx48wC+//AK5XI4mTZpke/tkdB4rVqyYRklWZvXfuXMHGzZsQJMmTWBra4uLFy9i6NChqF27NsqVK5dp/fSJPGurIxEVFSUAiBs3bui87oSEBDF48GBRrFgxYWJiIooXLy5++uknkZKSorNlbNy4URQvXlwYGRkJJycnMWDAABEfH5+luhSXHz59BQcHCyE+DJkxbtw44ejoKIyNjUX9+vW12m6Z1R8REaF2ekhISLbrV1weVfc6cOBAtut/8+aNaNWqlXBxcRFGRkbC2dlZBAYGilOnTuls+3xK2+EyPld/cnKyaNiwobC3txeGhobC1dVV9O7dWzx58kSn8a9cuVJ4enoKExMTUb58ea26D2hS/9KlS4VcLs/SMZBZ/Y8fPxbdunUTLi4uwsTERHh5eYlZs2ZpPLxOZvXPmzdPFClSRBgaGopixYqJn3/+WatzRUb7d0REhDTPmzdvRP/+/UWhQoWEqampaNWqlXj8+LHO6g8JCcl0nqzWn9H2AyBiYmKyXf/Dhw9F48aNhYODgzA0NBRFihQRnTp1EtevX9fZ9lH3GU2Hy8is/nv37onatWsLGxsbYWxsLDw9PcWIESPE69evNaqflMmE0OFQ8ERERESUZexjRkRERJRPMDEjIiIiyieYmBERERHlE0zMiIiIiPIJJmZERERE+QQTMyIiIqJ8gokZERERUT7BxIyIiIgon2BiRvSFk8lk2L59e4bT69SpgyFDhuRaPJ9z8OBByGQyxMfH67zu0NBQODo6Zro9KGtWrVoFa2vrvA6D6KvHxIxIR2Qy2WdfoaGhGX42NjYWMplMevDv1yA3E8Jr164hLCwMS5cuxePHj9G4ceNcWW5+l9Uk1c3NDXPnzlUqa9++PW7evKmbwIgoQ3yIOZGOPH78WPp748aNGD9+vPQwdAAwNzfPi7AKhDt37gAAWrRoAZlMlqexpKWlQSaTQU/v6/q/Vy6XSw8MJ6Kc83WdOYjykJOTk/SysrKCTCaT3js4OGD27NkoUqQIjI2NUaFCBURGRkqfdXd3BwBUrFgRMpkMderUAQCcPn0aDRo0gJ2dHaysrODn54dz585lK86UlBQMHz4chQsXhpmZGapWrYqDBw9K0xWXrKKiolCqVCmYm5ujUaNGSonn+/fvMWjQIFhbW8PW1hajRo1CcHAwWrZsCQDo1q0bDh06hHnz5kkthrGxsdLnz549i0qVKsHU1BTVq1dXSmDVuXTpEurVqwe5XA5bW1v06dMHiYmJAD5cwmzevDkAQE9PL8PELC0tDT179oS7uzvkcjm8vLwwb968zy5Xcen1r7/+Qrly5WBiYoJvv/1/7d19TFPXGwfwb+nKu3WwYZH4UsNbCmEbmM5f2y3O+MJ0I4i6LUIAl+nmIBQ3UGfCFoJbmEFYdDLn3urCsuk/NYOwSYXBTJoMOx0IrrbKsCyu0Fg7XR2RUJ7fHws3XAEp7I3fz+eTkPSce+45T8+9CU/vPbf9D7q7u8fNV319PZKSkhAUFIS+vr4p59nhcCAjIwMREREICwtDcnIyvvrqK2F7d3c31q5di/DwcCgUCuTm5uLatWvC9ieeeAJ6vR67du1CZGQkoqOjRVdllUolACArKwsSiUQo9/T0IDMzEwqFAuHh4VCr1Whubhb163A48MorrwjHbuz7HOvw4cOIjY1FYGAgEhMTUVdXJ9oukUjw0UcfISsrC6GhoYiPj0d9ff1d55yxe96//SvqjP0/MhgMNHfuXKFcU1NDcrmcvvjiC7p48SLt2rWLZDIZ2e12IiI6c+YMAaDm5mZyOp3kdruJiKilpYXq6urIarXSjz/+SC+88AIpFAq6efOm0DcAOnHixKSxLF++nIqLi4Xy1q1bSavV0unTp+ny5ctUVVVFQUFBQiwGg4FkMhmtWrWKLBYLnT17llQqFWVnZwt9vPnmmxQZGUlGo5GsVitt376d5HI5ZWZmEhHRr7/+ShqNhrZt20ZOp5OcTicNDw9Ta2srAaBly5ZRW1sbXbhwgR5//HHSarWTxu/1emn+/Pm0YcMG6urqopaWFlqyZAnl5+cTEdFvv/1GBoOBAAhjTWRoaIjeeOMNslgs9NNPP9Fnn31GoaGhdPz48UnHHo1XpVKRyWSi8+fP09NPP01KpZKGhoZE86XVaslsNtPFixfp1q1bU87zU089RatXr6bz589TT08PNTQ00LfffktERB6Ph6KiomjPnj1ktVrp3LlztHr1alqxYoXouMrlciovLye73U6ffvopSSQSMplMRETkcrkIABkMBnI6neRyuYiIqKOjg95//33q6uoiu91OZWVlFBwcTA6Hg4iI3G43LViwgCoqKkTzeec5bTQaSSaTUW1tLdlsNqquriapVErffPON0AYALViwgD7//HO6dOkS6fV6Cg8PF85vxth4nJgx9je4859YTEwMvfXWW6I2arWaCgoKiIiot7eXANAPP/xw1359Ph/NmTOHGhoahLrpJGYOh4OkUildvXpV1GblypW0Z88eIXYAdPnyZWF7bW0tKRQKoaxQKKiqqkooDw8P06JFi4TE7M5xR40mOs3NzUJdY2MjAaDBwcEJ4//ggw8oIiKCvF6vaJ+AgADq7+8nIqITJ07QTD5nFhYW0saNGyfdPhrvsWPHhDq3200hISFCQjc6Xx0dHUIbf+Y5JSWFysvLJxx37969tGbNGlHdzz//TADIZrMR0R/z+9hjj4naqNVq2r17t1Ce6twYlZycTO+++65QXrx4Mb3zzjuiNnee01qtlrZt2yZq88wzz9C6detE45eVlQllr9dLAOjrr7+eMibG7lW8xoyxv9nNmzfxyy+/QKfTiep1Oh06Ozvvuu/AwADKysrQ1tYGl8sFn8+H33//HX19fTOKpaurCz6fDwkJCaL627dv44EHHhDKoaGhiI2NFcrz58+Hy+UCANy4cQMDAwN49NFHhe1SqRRLly7FyMiIX3E89NBDor4BwOVyYdGiRePaWq1WPPzwwwgLCxPqdDodRkZGYLPZoFAo/BoTAGpra/HJJ5+gr68Pg4ODGBoawiOPPDLlfhqNRngdGRmJxMREWK1WoS4wMFD0nvyZZ71ej5dffhkmkwmrVq3Cxo0bhT46OzvR2to64brEnp4eod+xYwLi4zQZr9eL8vJyNDY2wul0Ynh4GIODg9M+p6xWK1588UVRnU6nG3d7eGyMYWFhkMvlU8bI2L2MEzPGZrH8/Hy43W4cOHAAixcvRlBQEDQaDYaGhmbUn9frhVQqxdmzZyGVSkXbxiYBMplMtE0ikYCIZjTmRMb2P7qGyd+kbqaOHTuG0tJSVFdXQ6PRYM6cOaiqqkJ7e/uf7jskJES0ts2fed66dSvS09PR2NgIk8mEyspKVFdXo6ioCF6vFxkZGdi3b9+4sUYTWWDi4zTVPJaWluLUqVPYv38/4uLiEBISgk2bNs34nJrKTGJk7F7Gi/8Z+5vJ5XLExMTAbDaL6s1mM5KSkgD8ccUF+GOB+p1t9Ho91q1bh+TkZAQFBYkWgE9XamoqfD4fXC4X4uLiRH/R0dF+9TF37lwoFApYLBahzufzjXsoITAwcNz7mQmVSoXOzk7cunVLqDObzQgICEBiYqLf/ZjNZmi1WhQUFCA1NRVxcXHC05xT+e6774TXHo8HdrsdKpVq0vb+zvPChQuxfft2GI1GlJSU4MMPPwQApKWl4cKFC1AqleP2H3vlcCoymWzCc2rLli3IyspCSkoKoqOjRQ9mAP4dO5VKdddzmjE2M5yYMfYP2LlzJ/bt24fjx4/DZrPhtddeQ0dHB4qLiwEA8+bNQ0hICE6ePImBgQHcuHEDABAfH4+6ujpYrVa0t7cjJyfnT31lQUJCAnJycpCXlwej0Yje3l6cOXMGlZWVaGxs9LufoqIiVFZW4ssvv4TNZkNxcTE8Ho/oqpFSqUR7ezuuXLmCa9euzfgqSU5ODoKDg5Gfn4/u7m60traiqKgIubm507qNGR8fj++//x5NTU2w2+14/fXXRcnl3VRUVKClpQXd3d3YsmULHnzwQeEJ1In4M887duxAU1MTent7ce7cObS2tgrJXmFhIa5fv47NmzfDYrGgp6cHTU1NeP7556eV7CqVSrS0tKC/vx8ej0eYB6PRiI6ODnR2diI7O3vcsVEqlTh9+jSuXr066QeBnTt34ujRozh8+DAuXbqEmpoaGI1GlJaW+h0fY2w8TswY+wfo9Xq8+uqrKCkpQUpKCk6ePIn6+nrEx8cDAO677z4cPHgQR44cQUxMDDIzMwEAH3/8MTweD9LS0pCbmwu9Xo958+b9qVgMBgPy8vJQUlKCxMRErF+/HhaLZcL1XZPZvXs3Nm/ejLy8PGg0GoSHhyM9PR3BwcFCm9LSUkilUiQlJSEqKmrG6+JCQ0PR1NSE69evQ61WY9OmTVi5ciUOHTo0rX5eeuklbNiwAc899xyWLVsGt9uNgoICv/Z9++23UVxcjKVLl6K/vx8NDQ3CVc7JTDXPPp8PhYWFUKlUePLJJ5GQkID33nsPAIQrrD6fD2vWrEFKSgp27NiB+++/f1rfj1ZdXY1Tp05h4cKFSE1NBQDU1NQgIiICWq0WGRkZSE9PR1pammi/iooKXLlyBbGxsYiKipqw7/Xr1+PAgQPYv38/kpOTceTIERgMBuGrXhhjMyOhv3LhCGPsnjQyMgKVSoVnn30We/fu/bfD+cu0tbVhxYoV8Hg8/HNEjLF/BC/+Z4xNm8PhgMlkwvLly3H79m0cOnQIvb29yM7O/rdDY4yx/2l8K5MxNm0BAQE4evQo1Go1dDodurq60NzcfNcF8YwxxqbGtzIZY4wxxmYJvmLGGGOMMTZLcGLGGGOMMTZLcGLGGGOMMTZLcGLGGGOMMTZLcGLGGGOMMTZLcGLGGGOMMTZLcGLGGGOMMTZLcGLGGGOMMTZLcGLGGGOMMTZL/BfYo1KOTOgT8QAAAABJRU5ErkJggg==",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "lengths = sorted(list(length_to_gs_num_solved.keys()))\n",
                "Y = [length_to_gs_num_solved.get(length, 0) / length_to_num_presentations[length] * 100 for length in lengths]\n",
                "Z = [length_to_bfs_num_solved.get(length, 0) / length_to_num_presentations[length] * 100 for length in lengths]\n",
                "W = [length_to_ppo_num_solved.get(length, 0) / length_to_num_presentations[length] * 100 for length in lengths]  \n",
                "\n",
                "X_axis = np.arange(len(lengths))\n",
                "\n",
                "# Width of the bar\n",
                "barWidth = 0.25\n",
                "\n",
                "# Set position of bar on X axis\n",
                "r1 = X_axis - barWidth\n",
                "r2 = X_axis\n",
                "r3 = X_axis + barWidth\n",
                "\n",
                "# Make the plot\n",
                "plt.bar(r1, Y, width=barWidth, label='GS', color='blue')\n",
                "plt.bar(r2, W, width=barWidth, label='PPO', color='green')\n",
                "plt.bar(r3, Z, width=barWidth, label='BFS', color='grey')\n",
                "\n",
                "# Adding xticks\n",
                "plt.xticks(X_axis, lengths)\n",
                "plt.xlabel(\"Total length of a presentation\")\n",
                "plt.ylabel(\"Percentage of presentations solved\")\n",
                "plt.title(\"\"\"Percentage of presentations solved by Greedy Search, Proximal Policy\n",
                "Optimization and Breadth First Search as a function of total length\"\"\")\n",
                "plt.legend()\n",
                "\n",
                "# plt.savefig('/Users/alishehper/work/ac_paper/fig/performance_vs_length.png')\n",
                "\n",
                "# plt.savefig(\"./Images/performance_vs_length.pdf\")\n",
                "# Display the figure\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": []
        }
    ],
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