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+1.363636363636363757e+00,-2.880707137011690975e+02 +4.272727272727273373e+00,5.819147617112720582e+03 From a8d760feaea52b1adcb071627b231ddcf99fc8aa Mon Sep 17 00:00:00 2001 From: Nifacy Date: Wed, 19 Nov 2025 23:15:24 +0300 Subject: [PATCH 2/3] add jupyter notebook with solution --- stud/grishin/lab-1/main.ipynb | 535 ++++++++++++++++++++++++++++++++++ 1 file changed, 535 insertions(+) create mode 100644 stud/grishin/lab-1/main.ipynb diff --git a/stud/grishin/lab-1/main.ipynb b/stud/grishin/lab-1/main.ipynb new file mode 100644 index 0000000..797df38 --- /dev/null +++ b/stud/grishin/lab-1/main.ipynb @@ -0,0 +1,535 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# Лабораторная работа №1 по предмету \"математика для машинного обучения\"" + ], + "metadata": { + "id": "9NnxP3BwlQQS" + } + }, + { + "cell_type": "markdown", + "source": [ + "- **Тема работы:** Регрессионный анализ\n", + "- **Выполнил:** Гришин А.Ю.\n", + "- **Группа:** М8О-106СВ-25\n", + "- **Вариант:** 4" + ], + "metadata": { + "id": "4PVdcbntlZcw" + } + }, + { + "cell_type": "code", + "source": [ + "import csv\n", + "import numpy as np\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "import sklearn.model_selection\n", + "import sklearn.linear_model\n", + "import sklearn.metrics" + ], + "metadata": { + "id": "M7NYKxRNlY8J" + }, + "execution_count": 1, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "RANDOM_SEED = 42" + ], + "metadata": { + "id": "p3npGMXYLGnS" + }, + "execution_count": 2, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "## 1. Загрузка датасета\n", + "\n", + "Загрузим датасет, соответствующий выбранному варианту лабораторной работы. Так как в условии задания не было явно указано способа импорта датасета, то для этой задачи я выбрал стандартную библиотеку `csv`." + ], + "metadata": { + "id": "M95sbpiQlwM7" + } + }, + { + "cell_type": "code", + "source": [ + "dataset = []\n", + "\n", + "with open(\"datasets/lab1-04.csv\", newline='', encoding='utf-8') as f:\n", + " reader = csv.reader(f)\n", + " for row in reader:\n", + " dataset.append(tuple(map(float, row)))\n", + "\n", + "dataset = np.array(dataset, dtype=np.float64)" + ], + "metadata": { + "id": "mTCiw6__mBQk" + }, + "execution_count": 3, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "## 2. Визуализация датасета\n", + "\n", + "Визуализируем загруженный датасет в виде диаграммы рассеяния. Для визуализации воспользуемся библиотекой `matplotlib`." + ], + "metadata": { + "id": "HmR3bqq-nZca" + } + }, + { + "cell_type": "code", + "source": [ + "X, y = dataset[:, 0], dataset[:, 1]\n", + "\n", + "plt.figure(figsize=(8, 5))\n", + "plt.scatter(X, y)\n", + "plt.title(\"Визуализация датасета\")\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$y = f(x)$\")\n", + "plt.grid(True, alpha=0.4)\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 487 + }, + "id": "RWvN0g5sn6R3", + "outputId": "602a0ada-8750-43e4-9369-b38a893f33a4" + }, + "execution_count": 4, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Как видим, целевая функция $f(x)$ имеет форму кусочно-гладкой функции. При этом, точкой разрыва является $x = 5$." + ], + "metadata": { + "id": "RlHXXQPDKWnd" + } + }, + { + "cell_type": "markdown", + "source": [ + "## 3. Обучение модели регрессии" + ], + "metadata": { + "id": "xi5dxAyhLVP_" + } + }, + { + "cell_type": "markdown", + "source": [ + "### Бейзлайн" + ], + "metadata": { + "id": "EyIfw59rLZhk" + } + }, + { + "cell_type": "markdown", + "source": [ + "Начнем с самого базового решения: простой линейной регрессии вида\n", + "\n", + "$$\n", + "f(x) = c_1 \\cdot x\n", + "$$\n", + "\n", + "Данная регрессия имеет вид линейной функции всего с одним весом $c_1$." + ], + "metadata": { + "id": "K-ie2AwEP8Bo" + } + }, + { + "cell_type": "code", + "source": [ + "X, y = dataset[:, 0], dataset[:, 1]\n", + "X = X.reshape((X.shape[0], 1))\n", + "\n", + "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(\n", + " X, y,\n", + " test_size=0.2,\n", + " random_state=RANDOM_SEED,\n", + ")\n", + "\n", + "model = sklearn.linear_model.LinearRegression()\n", + "model.fit(X_train, y_train)\n", + "print('R2 score:', sklearn.metrics.r2_score(y_test, model.predict(X_test)))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "L17B9ecDLa-1", + "outputId": "c88da584-d867-49ed-d800-eb22f05b8227" + }, + "execution_count": 6, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "R2 score: 0.12235502001780518\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Как видим, метрика $R ^ 2$ имеет очень низкие значения, что говорит нам о том, что модель плохо справляется с поставленной задачей. Значения, которые предсказывает модель на основе данных, слишком далеки от действительных в тестовой выборке." + ], + "metadata": { + "id": "PbY4Vja9Qkyr" + } + }, + { + "cell_type": "code", + "source": [ + "X, y = dataset[:, 0], dataset[:, 1]\n", + "\n", + "plt.figure(figsize=(8, 5))\n", + "plt.scatter(X, y, label=\"Исходный датасет\")\n", + "plt.scatter(X_test[:, 0], model.predict(X_test), label=\"Предсказанные значения\")\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$y = f(x)$\")\n", + "plt.legend()\n", + "plt.grid(True, alpha=0.4)\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 465 + }, + "id": "NGWf_1uXMfFr", + "outputId": "b23b3fd9-2431-4482-d3e1-d560a6379200" + }, + "execution_count": 10, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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nYObaPMl6wiJHtqcJAIpKXd9CmojIkzB4JiKq55RU1ajN2rErW0gTEXkaBs9ERPWcq4NbV7WQJiLyRAyeiYjqOVcFtyoAmhDXtZAmIvJEDJ6JiOq5HnHhiAoNcCivWY54rpcGxzeIhh71yahRo6BSqWT/u3jxoruHSOTRGDwTEdVzPmoVpqcnALDcGCj+HNbY12pwbR4fR4YEYFivWKQm1q8W0g1FWloaCgsLTf777rvv3D0sIq/gtcGzVqvFtGnTEBcXh8DAQLRt2xazZs2CIFzb9iIIAl5++WVERUUhMDAQ/fv3x19//WVynuLiYgwbNgwhISEICwvDo48+ikuXLpkc8/vvv+Omm25CQEAAYmJi8Prrr9fJYyQicpa0pCgsGp4MTahpCocmNACLhyfjtX91AiAdXKsALHwoGV893gsLhnbFV4/3wpbnb0NitOe0T/ZqOi2QvxU48K3+X53W5Xfp7+8PjUZj8p95++nPPvsMYWFhWLVqFdq3b4+AgACkpqbixIkTJsetXr0aycnJCAgIwHXXXYeZM2fiypUrJsfMmDEDarUaAQEBUKvVUKlUuPvuu02O2b59O2699VY0btwYTZs2RWpqKi5cuAAAuPXWWzFhwgTDsf/9738RFhaGvXv3AtDHBI8++qghJrj++uuxYMECk/O/8MILiI6Ohp+fH1q2bInJkydDp9Mpvv2oUaMsxizOkfHj7Nq1q8kxW7ZsMVnRN7+NsZycHKhUKhw7dsxw2bZt23DTTTchMDAQMTExeOaZZ1BeXi55ewBYsGABYmNj4e/vj8jISDz22GO4fPkyAODYsWNQqVTIyckxuU2bNm0wf/58w89vv/02OnXqhKCgIMTExOCpp54yiY2k5kKlUmHVqlWGn0+cOIEHHngAYWFhCA8Px5AhQ0wel9L57NGjh+Hn6upqtGvXzuIbkiVLluD666+Hn5+f4RsU4+eLs3lt8Dxv3jwsWrQICxcuxKFDhzBv3jy8/vrreO+99wzHvP7663j33XexePFi7Nq1C0FBQUhNTUVl5bXNM8OGDcPBgweRmZmJdevW4ddff8WYMWMM15eWlmLgwIFo3bo19uzZgzfeeAMzZszARx99VKePl4iottKSorBtcj+TIHjb5H5IS4qyGlwvGp6MOztHIaVtMwzp2hIpbZsxVcNZ8tYA85OAzwcD3z2q/3d+kv5yD3D58mXMmTMHX3zxBbZv346LFy9i6NChhuu3bt2KESNGYPz48cjLy8OHH36Izz77DHPmzLE4V2JiIo4dO4ZTp07hgQceMLkuJycHt99+OxISEpCVlYVt27YhPT0dWq3lB4mVK1fi2WefxZo1a5CcnAwA0Ol0aNWqFb755hvk5eXh5ZdfxtSpU7Fy5UrD7QYOHIh169bhyJEj+O9//4uPPvoIS5cuVXx7dzh69CjS0tJw77334vfff8fXX3+Nbdu2Ydy4cbK36dGjB7755hv89ddf+Pbbb7Fp0ya8+eabdt2vWq3Gu+++i4MHD+Lzzz/H5s2bMWnSJMW3r6mpQWpqKoKDg7F161Zs374dTZo0QVpaGqqrq+0ai7GFCxfi9OnTJpf98ccfeOyxxzB69GgcOXIEhYWFSElJcfg+lPDaDoM7duzAkCFDMGjQIAD6T01fffUVsrOzAehXnefPn4+XXnoJQ4YMAQB88cUXiIyMxKpVqzB06FAcOnQIGRkZ2L17N7p16wYAeO+993DnnXfizTffRHR0NJYtW4bq6mp8+umn8PPzQ2JiInJycvD222+bBNlERN7AR61CSttmktelJUVhQIIG2fnFOFNWiYhg/WZABsoukrcGWDkCFoUCSwv1lz/wBZBwl1uGJqqpqcHChQvRs2dPAMDnn3+O+Ph4ZGdno0ePHpg5cyZeeOEFjBw5EgBw3XXXYdasWZg0aRKmT59uOE9VVRUCAwOh0Wjg5+eHwMBAVFVdaw//+uuvo1u3bvjggw8MlyUmJlqM53//+x8eeeQRfPPNN7j55psNl/v6+mLmzJmGn+Pi4pCVlYWVK1caAvV+/foZrtdqtQgMDDQE50pu7w5z587FsGHDDKuo7du3x7vvvotbbrkFixYtQkCA5WZg48AxICAAISEhkh9CrDFetW3Tpg1mz56NJ554wvD7CQwMRGFhoeztv/76a+h0Ovz3v/+FSqV//1iyZAnCwsKwZcsWDBw40K7xAPpMgdmzZ2Py5MmYNm2a4fLff/8dPj4+mDx5suEyPz8/u89vD68Nnnv37o2PPvoIf/75Jzp06ID9+/dj27ZtePvttwEA+fn5KCoqQv/+/Q23CQ0NRc+ePZGVlYWhQ4ciKysLYWFhhsAZAPr37w+1Wo1du3bhnnvuQVZWFm6++WaTX0RqairmzZuHCxcuoGnTphZjq6qqMnlTKC0tBaD/ZCt+ReRK4v3UxX15G86NNM6LtIY4LyoAPeOM39cE6CQ6CDbEuTGm0+kgCILhPylyl+tPoAUyJgMQJHLNBf2lGS8A198JqH2cNGrr4xN/Nn5cjRo1Qrdu3QzXXX/99QgLC0NeXh66d++O/fv3Y/v27SYrzVqtFpWVlSgvL0fjxo0BAOfOnUNISIjsGHJycnDfffdZnbPs7Gx89NFHaNKkCXr06GFx7Pvvv48lS5agoKAAFRUVqK6uRteuXU2Oe/XVVzFnzhxUVFRg7NixePjhhw3XK7n9unXr0KRJE8PPV65cQUBAgMncHThwwOQYMXA1nteSkhI0adIEarUakZGRGDx4MObNm2fxO9i/fz9+//13LFu2zGTOdDod/v77b8THx0vO1bJly/Cf//wHly9fxr333otJkyaZPFd79+4Ntfpa8sHly5dNrt+4cSNee+01/PHHHygtLcWVK1dMfqeJiYlYvnw5/v77b8TFxZmMTRAE5OTk4MiRIwgODjYZV2VlJY4cOYIBAwYomk9jM2fOxG233YY+ffqY3FebNm1QU1ODlStX4r777jME63KvTfFyqfcvpe9nXhs8v/DCCygtLUXHjh3h4+MDrVaLOXPmYNiwYQCAoqIiAEBkZKTJ7SIjIw3XFRUVISIiwuT6Ro0aITw83OQY4yeG8TmLiookg+e5c+eafIIVnThxwuKJ5AqCIODChQuGvB+6hnMjjfMijfMir6HPjVarhVarRU1NjUkQAsAi31eK6vh2+JWekr8eAlB6EtVHf4XQuk+tx2tMq9VCp9NZfH1eU1MDQJ9XWl1dbXgc1dXVko+xuroaly5dwrRp0yxyVwH9V//ifRw9ehStW7c2nNN8DAEBAdBqtbJf6et0OmRlZeG9997D999/j6eeegpffvml4fqVK1fi+eefx7x589CzZ08EBwfj7bffxu7du03OOXr0aKSnp2Pv3r14/vnnkZ6ejltvvVXR7bVaLW655RaT9NBVq1bh9ddfNzmmQ4cOJpsvs7Oz8cgjj5jMa3BwMHbu3AlBEHDo0CE89thjiIyMNKyOi8eWlZXhsccew9ixYy3mJCYmRna+0tLSsGvXLhw+fBjjx4/HN998g4ceeshw/NKlS9GxY0fD8QMHDjTM/7Fjx5Ceno4xY8Zg+vTpCA8Px/bt2/HEE0/g0qVLaNSoEYYPH47vv/8ebdu2RVBQkOE84vOitLQUycnJ+OyzzyzG1rx5c1RXVyueT0EQkJeXh08++QTZ2dn4559/TOaoS5cuePnllzF69Gg8/PDD8PX1RUVFBTp16iQ5PzU1NdBqtSgsLISPj+kH07KyMsn5NOe1wfPKlSuxbNkyLF++3JBKMWHCBERHRxu+PnKXKVOmYOLEiYafS0tLERMTg5iYGMlP3s4mrojExMRYvOE1dJwbaZwXad48L1qdgN35xTh7qRItmgSgu0T6hZJj5Hjz3DhDZWUljh07Bl9fX8mviG1+bVx5XtH9+FaeB5z8FbSPjw/UarXFGH19fQHox+7n54dGjRrhypUr+P333w2btg4fPoyLFy+iU6dO8PPzQ3JyMo4cOSK7Agro5+q3337DiBEj0KhRI/j5+VmMoUuXLvjll19k502tVuPhhx/G2LFjMXjwYHTq1Anr16/HPffcAwDYtWsXevfujaefftpwG3FznPE5xc2RnTp1wurVq7FmzRoMHDhQ0e19fHwQHBxs8lh37dplmDPxGH9/f5NjxBxd43lVq9WGYxISEvDVV18hNzcXqampJsfeeOONOHz4sNX5ldKsWTM0a9YMiYmJ2Lp1K7799luMHDnSMM64uDiTczZq1Ag+Pj7w8/PDgQMHoNPp8M477xhe2z/88IPJuPz8/LBp0yacPn3aEHB26NDB8Pvt1q0bvv32W7Rs2VI27lE6nyqVCtOmTcOjjz6K+Ph4i/kEgGeffRbLly/H6NGjcd9992H48OGSz3FA/97l4+ODqKgoi7QXMVPAFq8Nnp9//nm88MILho0LnTp1wvHjxzF37lyMHDkSGo0GgP5JGxV1rZTS6dOnDTthNRoNzpw5Y3LeK1euoLi42HB7jUZjkZwu/iweY87f3x/+/v4Wl6vV6jr7IyPeV0P8o2YL50Ya50WaN85LRm4hZq7NM2nJHRUagOnpCUhLilJ8jC3eODfOIlaMMF95N/6a2OqKfLD03w9zqmAN4KKVffPxiT8bPy5fX18888wzePfdd9GoUSOMGzcOvXr1MuRAv/zyyxg8eDBat26N++67D2q1Gvv370dubi5mz56NS5cu4ZVXXgEA9O3bF0VFRfDz80NFRQWqqqpQWlqK0NBQTJkyBZ06dcLYsWPxxBNPwM/PDz///DPuv/9+NG/eHAAQHh4OlUqFNm3a4I033sBTTz2FW265Bc2aNUOHDh3w5Zdf4qeffkJcXBy+/PJL7N69G3FxcYbH9cEHH+CWW25BUFAQtm3bhszMTCxYsAAqlUrR7aXmzXjOpP6Vm1dAn+IpCAIOHjyIHTt24JlnnrE4dvLkyejVqxeefvppPPbYYwgKCkJeXh4yMzOxcOFCyd/rkiVLkJycjLCwMOzfvx8rVqzA448/bnLfUt8YiZe1b9/ekOuenp6O7du348MPP5S8nfhhxPwcw4cPx5tvvom7774br7zyClq1aoXjx4/j+++/x6RJk9CqVStF8wnov7U4ceIEjhw5IvkYBEHAyJEjkZycjClTpgDQ52TLfSsmXi713qX0vcxr3/EuX75s8SB9fHwM+SpxcXHQaDTYtGmT4frS0lLs2rXLkEyfkpKCixcvYs+ePYZjNm/eDJ1OZ3hjSElJwa+//mr4OgsAMjMzcf3110umbBARuVNGbiGeXLrXJCgGgKKSSjy5dC8ycgsVHUMu1ro3EBINy+KAIhUQ0lJ/nBs1btwYkydPxr///W/06dMHTZo0wddff224PjU1FevWrcNPP/2E7t27o1evXnjnnXfQunVrAMCbb76JN954A2VlZWjfvj3atGmD6OhorFy5EhkZGRg/fjwA/arlTz/9hP3796NHjx5ISUnB6tWr0aiR9Brff/7zHyQlJRlWiv/zn//gX//6Fx588EH07NkT58+fx1NPPWVym/Xr1+PWW29Fx44dMXPmTEydOhWjR49WfHtnKikpQWBgIIKCgpCeno677rrL5BtrUefOnfHLL7/gzz//xE033YQbbrgBL7/8MqKjo2XPnZWVhbS0NHTo0AFPP/00hg0bZrLBzpYuXbrg7bffxrx585CUlIRly5Zh7ty5dj2+xo0b49dff0VsbCz+9a9/IT4+Ho8++igqKyvt/ga+vLwcU6dOtSilKHrttdfw119/4ZNPPrHrvLWhEqzuaPBco0aNwsaNG/Hhhx8iMTER+/btw5gxYzB69GjMmzcPgL6c3WuvvYbPP/8ccXFxmDZtGn7//Xfk5eUZlurvuOMOnD59GosXL0ZNTQ0eeeQRdOvWDcuXLwegf4Jff/31GDhwICZPnozc3FyMHj0a77zzjuJqG+In65KSkjpL2ygoKEBsbGyDXBGyhnMjjfMizdvmRasT0HfeZougWKQCEBniD0CFolL5YzShAdg2uZ/VFA5vmxtnq6ysRH5+PuLi4ky++hUEAdXV1YZ6s1YZqm0AphU3rt7OzdU2PvvsM0yYMKFWHQdnzJhh+Nd8blatWoVVq1ZJ5sU2JHY9ZxoYV8yN3GsXUB6veW3axnvvvYdp06bhqaeewpkzZxAdHY3//Oc/ePnllw3HTJo0CeXl5RgzZgwuXryIvn37IiMjw2Syli1bhnHjxuH222+HWq3Gvffei3fffddwfWhoKH766SeMHTsWN954I5o3b46XX36ZZeqIyONk5xfLBs6APjwrKq2SvV48prCkEtn5xbIl7chJEu7SB8gZkwHjzYMh0UDaa24vU+cMxpUUzAUEBCA0lI12yPt4bfAcHByM+fPnm3TEMadSqfDKK68Y8q2khIeHG1aZ5XTu3Blbt251dKhERHXiTJl84OzOc5EVCXcBHQcBx3cAl04DTSL1qRouKk9X15577jnZ69LS0pCWllaHoyFyjob3XRsRUT0VEWzZMMETzkU2qH2AuJuATvfp//WQwHnUqFG1Stkgqq8YPBMR1RM94sIRFRpgbQsaNCH+0IRYPyYqVN9ZkIiILDF4JiKqJ3zUKkxPTwBgWcNB/HnGXYmYcZf1Y6anJ7AlNxGRDAbPRET1SFpSFBYNT4Ym1DTtQhMagEXDk5GWFKXoGFLGSwtWETVYznjNeu2GQSIikpaWFIUBCRpk5xfjTFklIoL1aRjGq8lKjiF5Yje+y5cvIzAw0M2jISKlLl++DODaa9gRDJ6JiOohH7XKZqk5JceQNB8fH4SFhRm61DZu3NjQ7aympgY6nY41e81wbqRxXuQ5c24EQcDly5dx5swZhIWFwcfH8Y25DJ6JiIgcILYlFgNoQP8HWqvVwsfHh4GQGc6NNM6LPFfMTVhYmElLcUcweCYiInKASqVCVFQUIiIiUFNTA0DfebGwsBBRUVENsvOiNZwbaZwXec6eG19f31qtOIsYPBMReTGtTmDespv5+PgY/iDrdDr4+PggICCAgZAZzo00zos8T50bBs9ERF4qI7cQM9fmmbTkjgoNwPT0BFbMICJyEc8J44mISLGM3EI8uXSvSeAMAEUllXhy6V5k5Ba6aWRERPUbg2ciIi+j1QmYuTYPUtVKxctmrs2DVscaxEREzsbgmYjIy2TnF1usOBsTABSWVCI7v7juBkVE1EAweCYi8jJnyuQDZ0eOIyIi5bhhkIjIS4iVNf46fUnR8RHBAbYPIiIiuzB4JiLyAlKVNeSoAGhC9WXriIjIuRg8ExF5OLGyhpLtf2KF5+npCaz3TETkAgyeiYg8mLXKGlI0rPNMRORSDJ6JiDyYrcoaonG3tUWfdi3YYZCIyMUYPBMReQC5NttKK2a0jwxGSttmLh4lERExeCYicjNrbbaVVsxgZQ0iorrBOs9ERG5kq832hfJqRIUGwFoiRniQL25s3dS1AyUiIgAMnomI3EZJm+1Z6/MwbVA8AMgG0MXlNbjljZ+RkVvoimESEZERBs9ERG6itM120yB/LBqeDE2ofGqGuFLNAJqIyLUYPBMRuYk9bbbTkqLwy/O3ITzIT/IYcaV65to8aHVKC9sREZG9GDwTEbmJvZsB9xy/gOLyatnjxJXq7PxiZwyPiIgkMHgmInKTHnHhNjcDNgvyM2wGtGelmoiIXIPBMxGRm/ioVZiengBAfjPg+fJqw2ZAlq0jInI/Bs9ERG6UlhSleDPghfIqqyvVKujrQ/eIC3fJWImIiMEzEZHbXdsM6Ct5/bWydYcwbZD0SrX48/T0BLbnJiJyIQbPREQeQL8ZsEb2+mtl6/wkV6o1oQFYNDwZaUlRLh4pEVHDxvbcREQewJ7NgEO6tsSABA2y84txpqwSEcH6VA2uOBMRuR6DZyIiD2DvZkAftQopbZu5ckhERCSBaRtERB7AVtk6bgYkIvIMDJ6JiDyAtbJ1td0MqNUJyDp6HqtzTiLr6Hl2ICQiqgWmbRAReQixbN3MtXkoLLmWA60JDcD09ASHNgNm5BZanC+qFucjImroGDwTETlAqxNcsmEvLSnKaZsBM3IL8eTSvTBfZxbrRrM6BxGR/Rg8ExHZydWruc7YDKjVCZi5Ns8icAb0Ze9UAGauzcOABA2rdBAR2YE5z0REdhBXc40DZ+Daam5GbqGbRmaa2/zZ9nyLMRoT60Zn5xfX3QCJiOoBrjwTESnkyau5UqvhSiitL01ERHpceSYiUig7v9gjV3PlVsOVUFpfmoiI9LjyTESkkD1dAOuKtdVwa1TQV/Fg3WgiIvtw5ZmISCF7uwDWBVur4VJqWzeaiKgh48ozEZFCYhfAopJKyZVeV6zm2iqJ58gqd23qRhMRNXQMnomIFBK7AD65dC9UgEkA7YrVXCUl8ZSuck8bFI/mwf5OrUlNRNQQMW2DiMgOYhdATahp0KoJDXBq0xGlJfHE1XC5UFgFfcA9qk8chnRtiZS2zRg4ExHVAleeiYjsZN4FsHkTf0AAzpVXIevo+Vqv7NpbEq8uV8OJiBo6Bs9ERA4QuwBm5BbiuW/2O7XboD0l8VLaNjOshpuneDC3mYjI+Rg8ExE5SEytMF8hFlMrHE3jcKQknvlqOHObiYhcg8EzEZEDXNlt0NGSeOJqOBERuY5Xbxg8efIkhg8fjmbNmiEwMBCdOnXCb7/9ZrheEAS8/PLLiIqKQmBgIPr374+//vrL5BzFxcUYNmwYQkJCEBYWhkcffRSXLl0yOeb333/HTTfdhICAAMTExOD111+vk8dHRJ7LGd0GtToBWUfPY3XOSWQdPQ+tTh+KK90EyAYnRER1z2tXni9cuIA+ffrgtttuw//+9z+0aNECf/31F5o2bWo45vXXX8e7776Lzz//HHFxcZg2bRpSU1ORl5eHgAD9is2wYcNQWFiIzMxM1NTU4JFHHsGYMWOwfPlyAEBpaSkGDhyI/v37Y/HixThw4ABGjx6NsLAwjBkzxi2PnYjcr7bdBm2VoeMmQCIiz+S1wfO8efMQExODJUuWGC6Li4sz/L8gCJg/fz5eeuklDBkyBADwxRdfIDIyEqtWrcLQoUNx6NAhZGRkYPfu3ejWrRsA4L333sOdd96JN998E9HR0Vi2bBmqq6vx6aefws/PD4mJicjJycHbb7/N4JmoAatNt0GludLcBEhE5Hm8Nnhes2YNUlNTcf/99+OXX35By5Yt8dRTT+Hxxx8HAOTn56OoqAj9+/c33CY0NBQ9e/ZEVlYWhg4diqysLISFhRkCZwDo378/1Go1du3ahXvuuQdZWVm4+eab4efnZzgmNTUV8+bNw4ULF0xWukVVVVWoqqoy/FxaWgoA0Ol00Ol0Tp8Lc+L91MV9eRvOjTTOizRr89KtdRhahvrjdKl8t8HIkAB0ax1mcnutTsCstQehVkndSn+7WWsP4vaOERiYEInbO0Zgd34xzl6qRIsmAeh+dROgu39XfM5I47zI49xI47zIq+u5UXo/Xhs8//3331i0aBEmTpyIqVOnYvfu3XjmmWfg5+eHkSNHoqioCAAQGRlpcrvIyEjDdUVFRYiIiDC5vlGjRggPDzc5xnhF2/icRUVFksHz3LlzMXPmTIvLT5w4geDgYAcfsXKCIODChQtQqVRQqfi1rjHOjTTOizRb8zL1lhZYtrNAf6zR5eKRw3q1wMl/Tpjc5u+z5Yj1r0BsC2v3XIGt+/7AdS2CAADRvkB0UwAox8l/yh19OE7F54w0zos8zo00zou8up6bsrIyRcd5bfCs0+nQrVs3vPrqqwCAG264Abm5uVi8eDFGjhzp1rFNmTIFEydONPxcWlqKmJgYxMTEICQkxOX3r9PpIAgCYmJioFZ79Z5Qp+PcSOO8SLM1L7GxgDq4OWavO4SiUqPUipAAvDQ4HqmJ11IrtDoBu/OL8cupMmSftf1HYGijEMTGtnTOA3EBPmekcV7kcW6kcV7k1fXciJkCtnht8BwVFYWEhASTy+Lj4/Hdd98BADQaDQDg9OnTiIq69gfs9OnT6Nq1q+GYM2fOmJzjypUrKC4uNtxeo9Hg9OnTJseIP4vHmPP394e/v7/F5Wq1us5eGOJ98YVoiXMjjfMizda83NGpJQYmRlutr2y5OdB28BwR0tjjfxd8zkjjvMjj3EjjvMiry7lReh9e+1vq06cPDh8+bHLZn3/+idatWwPQbx7UaDTYtGmT4frS0lLs2rULKSkpAICUlBRcvHgRe/bsMRyzefNm6HQ69OzZ03DMr7/+ipqaGsMxmZmZuP766yVTNoio4RHrKw/p2hIpbZtZBM5PLt1rtaydMZahIyLybF4bPD/77LPYuXMnXn31VRw5cgTLly/HRx99hLFjxwIAVCoVJkyYgNmzZ2PNmjU4cOAARowYgejoaNx9990A9CvVaWlpePzxx5GdnY3t27dj3LhxGDp0KKKjowEA//73v+Hn54dHH30UBw8exNdff40FCxaYpGUQEYmMazdv/+scZqyRbqQihWXoiIg8n9embXTv3h0//PADpkyZgldeeQVxcXGYP38+hg0bZjhm0qRJKC8vx5gxY3Dx4kX07dsXGRkZhhrPALBs2TKMGzcOt99+O9RqNe699168++67hutDQ0Px008/YezYsbjxxhvRvHlzvPzyyyxTR0QWpGo324Nl6IiIPJ/XBs8AMHjwYAwePFj2epVKhVdeeQWvvPKK7DHh4eGGhihyOnfujK1btzo8TiKq/+RqNysxIqU17kiKssiVJiIiz+PVwTMRkSfQ6gTMXKs8PcNcaqIGKW2bOXVMRETkGl6b80xE5Cmy84sdTtUAgP9bmYOM3EInjoiIiFyFwTMRUS2dKXM8cAaA06VVeHLpXgbQRERegMEzEVEtRQQH2D7ICjHdY+baPGh1jiZ/EBFRXWDwTERUSz3iwhEVGqCg9Yk8AUBhSSWy84udNSwiInIBBs9ERLXko1ZhenqC7QMVqG0KCBERuRaDZyIiJ0hLisKi4cmICq1dCkdtU0CIiMi1WKqOiMhJ0pKiMCBBg+z8YmTmFWFVzikUl1cbrlerALmUZhX0TVLYlpuIyLMxeCYiukqrE5CdX4wzZZWICA5At9Zhdp/DR61CSttmSGnbDC8OSjA534XyKoxdvg8ATGpCsy03EZH3YPBMRATp1totQ/0x9ZYWiI117JxiIG1skVplcT9sy01E5D0YPBNRgyfXWvt0aSWW7SyAOrg57ujU0in3ZZzaIa5Isy03EZH3YPBMRA2atdba4mWz1x3CwMRopwW4UivSRETkHVhtg4gaNFuttQUARaX6+stanYCso+exOuckso6eZ0MTIqIGiCvPRNSgKa2rvDGvCBNX5pgE2lHMVSYianC48kxEDZrSusqfbD9msUJdVFKJJ5fuRUZuoSuGRkREHojBMxE1aLZaa6ugr88sRUzamLk2jykcREQNBINnImrQjFtrm8fIKugDZGtxsQCgsESfE01ERPUfg2ciavDE1toas9bakSEB6NNOWVUMpbnTRETk3bhhkIgaNLGrYNUVHd68vwsgAOfKqwwdBrfu+wOA7VVlpbnTRETk3Rg8E1GDJdVVUKygkdK2GXQ6Hdo0bwxNSABOlVRJ1oJWQd8hsEdceJ2Nm4iI3IdpG0TUIIldBW1V0FCrVHhpcDwA6ZxoAJiensAOgUREDQSDZyJqcJR0FTSuoJGaKJ0TrQkNwKLhyazzTETUgDBtg4gaHCVdBQtLKrE7vxjRvvrL0pKiMCBBg+z8Ypwpq0REsD5VgyvOREQNC4NnImpwlFbGOHupEtFNr/3so1Yhpa2y6htERFQ/MW2DiBocpZUxWjRhBQ0iIjLF4JmIGhwlXQWjQgPQnRU0iIjIDINnImpwbHUVBEwraGh1ArKOnsfqnJPIOnqerbiJiBow5jwTUYMkdhU0r/OsuVrnOS0pCjqdDgdPlWDYV0dwsqTKcEyU0TFERNSwMHgmogbLVgWNDQcLsWxnAYpKVTBeoxZrQbNMHRFRw8PgmYgaNLkKGlqdgNnrDiHW3/I2AvSh9My1eRiQoGG5OiKiBoQ5z0REErLzi1FUarsWdHZ+cd0NioiI3I7BMxGRBKW1oJUeR0RE9QODZyIiCUprQSs9joiI6gcGz0REEnrEhUMTYrsWdA/WgiYialAYPBMRSfBRq/DS4HgAympBExFRw8BqG0REMlITo6Ari8XxX86a1HnWsM4zEVGDxeCZiMiKxOhQbHk+Cb8dvyhZC5qIiBoWBs9ERDbI1YImIqKGhznPREREREQKMXgmIiIiIlKIwTMRERERkULMeSaiBkerE5CdX8wNgEREZDcGz0TUoGTkFmLm2jwUllxrqx3F0nNERKQQ0zaIqMHIyC3Ek0v3mgTOAFBUUoknl+5FRm6hm0ZGRETegsEzETUIWp2AmWvzIEhcJ142c20etDqpI4iIiPQYPBNRg5CdX2yx4mxMAFBYUons/GIA+mB759Hz2H/iInYePc+gmoiIADDnmYgaiDNl8oGz+XFiXvSZ0gr0aCEg++w/iAgJZF40ERFx5ZmI6getTkDW0fNYnXMSWRIrxRHBAYrOc+zcZeZFExGRLK48E5HXU1JBo0dcOKJCA1BUUimZ96wCEBnij6+yC2TzolXQ50UPSNCwtB0RUQPFlWci8mpKK2j4qFWYnp4AQB8EGxN/fqhHLIpKledFExFRw1NvgufXXnsNKpUKEyZMMFxWWVmJsWPHolmzZmjSpAnuvfdenD592uR2BQUFGDRoEBo3boyIiAg8//zzuHLliskxW7ZsQXJyMvz9/dGuXTt89tlndfCIiMgWeytopCVFYdHwZGhCTVM4NKEBWDQ8GW2aBym6X6X500REVP/Ui7SN3bt348MPP0Tnzp1NLn/22Wexfv16fPPNNwgNDcW4cePwr3/9C9u3bwcAaLVaDBo0CBqNBjt27EBhYSFGjBgBX19fvPrqqwCA/Px8DBo0CE888QSWLVuGTZs24bHHHkNUVBRSU1Pr/LES0TX2VNDoEReO7PxiVF3R4c37ugAq4NylKpMOg1lHzyu6X6X500REVP94ffB86dIlDBs2DB9//DFmz55tuLykpASffPIJli9fjn79+gEAlixZgvj4eOzcuRO9evXCTz/9hLy8PGzcuBGRkZHo2rUrZs2ahcmTJ2PGjBnw8/PD4sWLERcXh7feegsAEB8fj23btuGdd95h8EzkZtZSLIxtzCvCxJU5kjnRKW2bGS5TkhetCdUH20RE1DB5fdrG2LFjMWjQIPTv39/k8j179qCmpsbk8o4dOyI2NhZZWVkAgKysLHTq1AmRkZGGY1JTU1FaWoqDBw8ajjE/d2pqquEcROQeGbmFmLXuoKJjP9l+TFH1DCV50dPTE7hZkIioAfPqlecVK1Zg79692L17t8V1RUVF8PPzQ1hYmMnlkZGRKCoqMhxjHDiL14vXWTumtLQUFRUVCAwMtLjvqqoqVFVVGX4uLS0FAOh0Ouh0Ojsfpf3E+6mL+/I2nBtp3jYvGw4W4unl+yAA8LESx6oAqFSAXH8TFYBZaw/i9o4RhoB4YEIkPhjWFbPXHcLZsgqoIcBHBWhCAvDS4HgMTIj0mnlyJW97ztQVzos8zo00zou8up4bpffjtcHziRMnMH78eGRmZiIgwLPyD+fOnYuZM2daXH7ixAkEBwe7/P4FQcCFCxegUqmgUnGFzBjnRpo3zYtOELB622F0b2G9458KkEy9sFSBrfv+wHUtrm0WjA8GvhzaFvlnL+FSyUWMDg1DXIsmUKtqUFBQUJvh1xve9JypS5wXeZwbaZwXeXU9N2VlZYqO89rgec+ePThz5gySk5MNl2m1Wvz6669YuHAhNmzYgOrqaly8eNFk9fn06dPQaDQAAI1Gg+zsbJPzitU4jI8xr9Bx+vRphISESK46A8CUKVMwceJEw8+lpaWIiYlBTEwMQkJCHH/QCul0OgiCgJiYGKjVXp+Z41ScG2neNC87j55HZsEVWCZWmAoP8sNdnaPxWdYxm+cc2igEsbEtLS6PjdGhoKAAsbGxHj8vdc2bnjN1ifMij3MjjfMir67nRswUsMVrg+fbb78dBw4cMLnskUceQceOHTF58mTExMTA19cXmzZtwr333gsAOHz4MAoKCpCSkgIASElJwZw5c3DmzBlEREQAADIzMxESEoKEhATDMT/++KPJ/WRmZhrOIcXf3x/+/v4Wl6vV6jp7YYj3xReiJc6NNE+ZF61OQHZ+Mc6UVZpUwhCdLa+GVrC9AjH1zgRoQgPxyY7jNo+NCGks+7g9ZV48EedGGudFHudGGudFXl3OjdL78NrgOTg4GElJSSaXBQUFoVmzZobLH330UUycOBHh4eEICQnB008/jZSUFPTq1QsAMHDgQCQkJODhhx/G66+/jqKiIrz00ksYO3asIfh94oknsHDhQkyaNAmjR4/G5s2bsXLlSqxfv75uHzBRA6CkU6DSMnGa0EBWzyAiIqer1x9x3nnnHQwePBj33nsvbr75Zmg0Gnz//feG6318fLBu3Tr4+PggJSUFw4cPx4gRI/DKK68YjomLi8P69euRmZmJLl264K233sJ///tflqkjcjKlnQLFgFhu7VkFfcAtrlizegYRETmT1648S9myZYvJzwEBAXj//ffx/vvvy96mdevWFmkZ5m699Vbs27fPGUMkIgm2OgWqoO8UOCBBYwiIn1y612JToFRALHYVNF/R1pitaBMRESlRq+C5pqYGRUVFuHz5Mlq0aIHwcH71SUT2s6dTYErbZjYD4gEJGmQdPW/Imx6QoMGABI3VXGoiIiIl7A6ey8rKsHTpUqxYsQLZ2dmorq6GIAhQqVRo1aoVBg4ciDFjxqB79+6uGC8R1UNnypR1CvyfUepGWlKUZECcmVeEvvM2W82bJiIicpRdwfPbb7+NOXPmoG3btkhPT8fUqVMRHR2NwMBAFBcXIzc3F1u3bsXAgQPRs2dPvPfee2jfvr2rxk5E9YTSTYBfZB3HF1nHER7ki3u6tkT/BI3JCrKYN22e/lFYUoknlu7Fs/3bY1y/9lxxJiIih9kVPO/evRu//vorEhMTJa/v0aMHRo8ejcWLF2PJkiXYunUrg2cisslWVQxzxeU1+GT7MXyy/ZhhVXlAgkY2b1r0zsa/8FX2Ccy4i6vQRETkGLuqbXz11VeygbMxf39/PPHEExg9erTDAyOihsNaVQxbxGocCzcfsZo3bTi+1LR6BxERkT0cLlWntIUhEZES4iZATaiyFA6RuNK8ZEe+XbebuTYPWp2yBt5EREQih4Pnm266CUVFRc4cCxE1cGlJUdg2uR++erwXRqS0Vnw7AcDFyzV2HS9W7yAiIrKHw8HzDTfcgJ49e+KPP/4wuTwnJwd33nlnrQdGRN5LqxOQdfQ8VuecRNbR83at8PqoVUhp2wx3OJCTHBboa1fah9IqH0RERCKHg+clS5Zg1KhR6Nu3L7Zt24Y///wTDzzwAG688Ub4+Pg4c4xE5EUycgvRd95mPPTxToxfkYOHPt6JvvM2251jbKuToJRH+rSx6z6UVvkgIiIS1ao998yZMzFx4kQMGDAASUlJKCsrQ1ZWFtauXeus8RGRF1HaYlsJ402Etogtucf1a6/Pmw7xV3R8jzg2diIiIvs4HDyfPn0a48ePx+zZs5GQkABfX1+MGjUKPXr0cOb4iMhL2GqxDdi/SU/cRBhlZROheUvutKQobH/hdjzbv4Oi44mIiOzhcPAcFxeHX3/9Fd988w327NmD7777DmPGjMEbb7zhzPERkZewp8W2PYw3EY7u0wbhQX4m12tCA7BoeLJJ3WYftQrj+7fHYonAW+p4IiIipexuzy369NNPMXToUMPPaWlp+PnnnzF48GAcO3YM77//vlMGSETeQenmO0c26YmbCFPaNsOLgxIsWnLLrSDLtfDmijMRETnK4eDZOHAWJScnY8eOHbjjjjtqNSgi8j5KN9/VdpOeGEi76ngiIiJr7ErbKCgosHlMmzZtsGPHDgDAyZMnHRsVEXkdW9UxuEmPiIjqA7uC5+7du+M///kPdu/eLXtMSUkJvv32WyQlJeG7776r9QCJyDtYa7HNTXpERFRf2JW2cejQIcyZMwcDBgxAQEAAbrzxRkRHRyMgIAAXLlxAXl4eDh48iOTkZLz++utslkLUwIjVMWauzTPZPKgJDcD09ARu0iMiIq9nV/D82muvYc6cOZg9ezZ+/PFHbN26FcePH0dFRQWaN2+OYcOGITU1FUlJSa4aLxF5OG7SIyKi+syu4Hn+/Pl47rnnEBERgbVr1+KDDz5A48aNXTU2IvJSztikp9UJDMCJiMjj2BU8R0dHY9++fUhNTcWXX36JN954g8EzETldRm6hRepHFFM/iIjIA9i1YfD//u//kJ6ejptuugkAsHTpUmRnZ6OiosIlgyOihseZLb6JiIicza7g+emnn8Zvv/2GtLQ0CIKA999/H71790ZISAji4+MxdOhQvPbaa/jf//7nqvESUT3mihbfREREzmR3e+7OnTvjxRdfRNu2bbFz506UlZVh27ZtmDBhApo2bYrVq1fjgQcecMVYiaiec1WLbyIiImdxuMPgX3/9Zfj/nj17omfPnoafBYGrQkRkP1e2+CYiInIGu1eelVCpuCOeiOxXVy2+iYiIHOWS4JmIyBFs8U1ERJ6OwTMReQy2+CYiIk9Xq+D5n3/+gU6ns/h/IiJbtDoBWUfPY3XOSWQdPW+ooCG2+NaEmqZmaEIDsGh4Mus8ExGRWzm8YRAAEhISkJOTg+uuu87k/4mIrLHVBIUtvomIyFPVKng2rqrBChtEpITYBMX8HUNsgiKuLjujxTcREZGzMeeZiOoMm6AQEZG3Y/BMRHWGTVCIiMjbMXgmojrDJihEROTtGDwTUZ1R2tykeZC/i0dCRETkGAbPRFRnbDVBEf3fN/uRkVtYJ2MiIiKyB4NnIqoz1pqgGDtdqq+8wQCaiIg8Ta2C56lTpyI8PNzi/4mo/pFramIvsQlKZIh8agYrbxARkaeqVZ3nKVOmSP4/EdUvtpqaWKPVCRbNTtKSohAc4Ith/90lezvjyhus90xERJ6iVsEzEdV/SpuayN1WLuiuuqJTdP+svEFERJ6EOc9EJKs2TU3EoNu8rrMYdB87V65oDEordBAREdUFh4PnEydOOHMcROSBlDY12fn3eZPLlQTdX2UXQBMiX3lDBf0qdY847qUgIiLP4XDw3LFjR7z88su4fPmyM8dDRG5mvDFw+5Fzim4zdplpZQwlQXdRaRUe6hELwLLyhvjz9PQE+KhtFbYjIiKqOw4Hz5mZmdiwYQPat2+Pzz77zIlDIiJ32XCwEH3nbcZDH+/E+BU5WPjzEUW3u1hRY1JaTmmecpvmjbFoeDI0oaapGZrQAKu51ERERO7i8IbB3r17Y9euXfjiiy/w4osv4r333sP8+fNx0003OXN8RFRHDp4qwfi1J3BFcHyld+baPAxI0CjOU44IDkBK22YYkKCxqMjBFWciIvJEtd4wOGLECBw+fBiDBg3CHXfcgfvuuw/5+fnOGBsR1RGtTsDa/YWSOcpKGZeWs9VJ0Dyf2UetQkrbZhjStSVS2jZj4ExERB7LadU2Bg4ciMceeww//PADEhISMGnSJFy6dMlZpyciF9qdX4ySihqnnKuopMJqJ0HmMxMRkTdzOG1j8eLF2L17N3bv3o1Dhw5BrVYjKSkJTzzxBLp06YIVK1YgISEB33//Pbp16+bMMRN5NammIe4OIs9ecl4t5VnrDyHQz8fQSdC8zrNGYXMVIiIiT+Rw8Dxnzhz07NkTI0aMQK9evXDjjTciMDDQcP2YMWPw6quvYtSoUcjNzXXKYIm8XW069blSiybKcpTDg3xxobzGanrHhfJqk+YpzGcmIqL6xOHgWUmd50cffRTTpk1z9C6I6pXadOpzte5x4QgN9IUKVySvV0G/YjxtUDzGLt9n9VzGzVMGJGgM+cxERET1gUs7DEZERGDz5s2uvAuqz3RaIH8rcOBb/b86rbtH5LDadOqrCz5qFdK76AN3aznKd3aOxqLhyQgP8rV5zsKSSizc/JdzB0pERORmLg2eVSoVbrnlFlfeBdVXeWuA+UnA54OB7x7V/zs/SX+5F1LaqS87v7juBmUmMToU7/37Bps1l9OSojBtcKKic76z8S+T5ilERETezqXBsyvNnTsX3bt3R3BwMCIiInD33Xfj8OHDJsdUVlZi7NixaNasGZo0aYJ7770Xp0+fNjmmoKAAgwYNQuPGjREREYHnn38eV66YfnW9ZcsWJCcnw9/fH+3atWNTGFfLWwOsHAGUnjK9vLRQf7kXBtBKm4YoPc5VUhOjsG1yP3z1eC8sGNoVXz3eC9sm97NIJ9GEKMuRBkxX1I27F2YdPe+2lXYiIiJHOZzz7G6//PILxo4di+7du+PKlSuYOnUqBg4ciLy8PAQFBQEAnn32Waxfvx7ffPMNQkNDMW7cOPzrX//C9u3bAQBarRaDBg2CRqPBjh07UFhYiBEjRsDX1xevvvoqACA/Px+DBg3CE088gWXLlmHTpk147LHHEBUVhdTUVLc9/npLpwUyJgOyCQ4qIOMFoOMgQO2j7HzHdwCXTgNNIoGYXk4esDL2NA1xNyU5ymIdZ2ur6SJxRb2kotojN0sSERHZw2uD54yMDJOfP/vsM0RERGDPnj24+eabUVJSgk8++QTLly9Hv379AABLlixBfHw8du7ciV69euGnn35CXl4eNm7ciMjISHTt2hWzZs3C5MmTMWPGDPj5+WHx4sWIi4vDW2+9BQCIj4/Htm3b8M477zB4doXjOyxXnE0IQOlJ/XFxNrpZ5q3RB+LG52scASQ+BWhvBOL6KAvAnUAMNotKKiU/Fogb8sSmIc7m7PJ4Yh3nJ5buVXR8Zl4Rlmw/5pGbJYmIiOzhtcGzuZKSEgBAeLg++NizZw9qamrQv39/wzEdO3ZEbGwssrKy0KtXL2RlZaFTp06IjIw0HJOamoonn3wSBw8exA033ICsrCyTc4jHTJgwQXYsVVVVqKqqMvxcWloKANDpdNDpdLV+rLaI91MX9+V0ZacBlYKAtuw0YO3xHVoLfDsagGByPl3lRej+/hW6Pa/qV6JT5wDX3wkczwLKzwBBEUDrFKcH1SoALw/uiKevVqoQzK7D1etVEKCrRSqDVidgd34xzl6qRLMgfwDAlj/OYNXvJ3Gh/FoTFE1IAF4aHI/URH3A6shzZmBCJJ69vT3e3fynzWPX7D8JtUr6cakAzFp7ELd3jPC4EnZe/VpyMc6NNM6LPM6NNM6LvLqeG6X3Uy+CZ51OhwkTJqBPnz5ISkoCABQVFcHPzw9hYWEmx0ZGRqKoqMhwjHHgLF4vXmftmNLSUlRUVJjUthbNnTsXM2fOtLj8xIkTCA4OduxB2kEQBFy4cAEqlQoqlWcFIzZVhwLhNlaUxeMKCqSvE3TAju+B8L6WV6nUuNC4PVQqQCUIwOZPga0rgJrL1w4KCAOS/gVEdXHsMciIDwYWpMdg7f5Ck25+oYG+SO8ShfjgGhTIPSYFDp4qsTi3qH1jAI2v/axCBb7M3AtdWSwSo0Mdfs6kt/PFoSM+KKmQL3HX2N8H5VVVJvdvqQJb9/2B61oEKb7vuuDVryUX49xI47zI49xI47zIq+u5KSsrU3RcvQiex44di9zcXGzbts3dQwEATJkyBRMnTjT8XFpaipiYGMTExCAkJMTl96/T6SAIAmJiYqBWe9me0FYtgV+fBcoKIZ33rAKCo4Gut8qvDudvA06tlbxKp/KBIAAxF7ZBLciVvlMBp9YB930KxKfLj1WntXvFOjYWGNgjybA63KJJALo7oWnIhoOFGL/2xNUZU3YuFYDjv5zFlueToILg8HNmSF8/qyvqo1JisSTrmM3zDG0UgtjYlnbdt6t59WvJxTg30jgv8jg30jgv8up6bsRMAVu8PngeN24c1q1bh19//RWtWrUyXK7RaFBdXY2LFy+arD6fPn0aGo3GcEx2drbJ+cRqHMbHmFfoOH36NEJCQiRXnQHA398f/v7+Fper1eo6e2GI9+V1L0S1Gkh7VV9VA4BkOJY2B2hkpc7w5TOAbGAMqKGDWtBaCZ6v3teGKUD8YOmAWCqfOiQaSJun38xovEmxdW+Tc6jVQO/2Lazct320OgGvrPsDVwT7A/CTJVXIPnYBKdeFO/ycuaNTSywcppbdDBga6If/7jhu8zwRIY098vnqta+lOsC5kcZ5kce5kcZ5kVeXc6P0Prw2eBYEAU8//TR++OEHbNmyBXFxcSbX33jjjfD19cWmTZtw7733AgAOHz6MgoICpKSkAABSUlIwZ84cnDlzBhEREQCAzMxMhISEICEhwXDMjz/+aHLuzMxMwznIBRLuAh74QiY4fU1/vTVNIq1fr4iVjYliKT3zlfHSQmDlw0BgU6DiwrXLGzcHOj+gz602C6SdwVYNaVvGLtuLuf9KRHwtMoqsteHW6gS3bpYkIiJyJq8NnseOHYvly5dj9erVCA4ONuQoh4aGIjAwEKGhoXj00UcxceJEhIeHIyQkBE8//TRSUlLQq5e+XNnAgQORkJCAhx9+GK+//jqKiorw0ksvYezYsYaV4yeeeAILFy7EpEmTMHr0aGzevBkrV67E+vXr3fbYG4SEu2yu4Mpq3VsfaJfKpX7Y4ZLptw62S+nBNHAGgMvngJ0f6P8TV6dtfQCwQ21rQ1+sqMHTy/dhQXoMYmMdP49ciTuxMseTS/dCBenUjunpCR63WZCIiEiK134/sGjRIpSUlODWW29FVFSU4b+vv/7acMw777yDwYMH495778XNN98MjUaD77//3nC9j48P1q1bBx8fH6SkpGD48OEYMWIEXnnlFcMxcXFxWL9+PTIzM9GlSxe89dZb+O9//8sydXVB7aNf9e10n/5fpSu2ah99gOoM5qvYNkvp2VB6Sr7Ri4PtyJ1VG3rt/kKXNS1JS4rCouHJNrsXEhEReTqvXXkWBNt/5AMCAvD+++/j/ffflz2mdevWFmkZ5m699Vbs27fP7jGSG8mlfiim0q8St+5terH5SrSjzBu9WMuhtrFKbauGtBICgJKKGuzOL3ZqPrYxa6kdRERE3sJrV56JbEq4C5iQC4xcB/R6Sp97bCxQzLE1D97EjYmvWa52OzufGqh1O3IxLcJo5A47e8m17cHF1I4hXVsipW0zBs5EROR1GDxT/SamfqTNBZ77Exi+Ckgeof/3+SPAA18CIWYpAyHR+lVrqRVfMZ+61mEq9KvYSnKoM16wmcIhlxZhrxZN3N8enIiIyJN5bdoGkd3UPkBcX8CnQF9wWa22f2OimE+9cgRgsf3NTk0indqO3DwtonkTf0AAzpVXoXnjRli28is0unwWZxCGbF1H6Mw+Owf5++B0WSWyjp5nOgUREZEMBs9E4uq0UnL51IHhQEUxbAfVRvnUB39Qdp9Wcq21OsF6HnHeGmDdZPS5cgrw0190SgjHzJoR2KDrYTisvEqL577ZD62gMtRo5kY+IiIiUwyeiRwht2L9x3obmxTN8qmV5lDLHJeRWyjbnCQtKUq2JrUGxVjkOx9P1kwwCaBFRSWVeHLpXrz/7xvQNMifG/yIiIiuYvBM5CipFWvjoPrwj8DvXwOXz1+73rzRi82a1DJVP6APnJ9cutfiVmLgu2hYF6RlSudTq1WAABVm+n2JzMpuMM/hFm8x7qt9EKvXqaFDWvDf+M8NjdGlYwdAEPQ1rO2pwU1EROTlGDwTOZsYVMfdBAycbT2f2moOtXzVD61OwMy1ebLbDFUA1qz5Dmk18vnUKgjQ4Dx6qP/AbiFe8hgxcE5VZ2O67xeIrikGsqH/z5gLmr8QERF5IlbbIHIlJY1exBxqO6p+2GrJLQBoVH5G0RAjcNHq9anqbCzynQ8NiuUPUlhWj4iIyNtx5ZnIBpsb8pxx7uobEZH+C3r4/AGf8jM2UyGUtOQ+gzBFY7B2nBo6TPf9Qv//Vh/y1fVu8+YvRERE9QyDZyIrbG7Ic8m5+yAtzvq5lbTkztZ1RFVjDfwvn4ZU3rMAFU4jHLt1HWXLVvdQ/4FolZUVZ7MzKi2rR0RE5K2YtkEkQ9yQZ54eIW7Iy8gtdNu5xZbccovBKgCRoY3RaNDrRpeYHqECUJgyHTqoZc9jK6VDkrNamBMREXkgBs9EEmxtyAOAmWvzoNXZ3yTFGee21pJb/Hl6egJ8EodYzafuPGAEJvTvgNBAX5OrxRQNpakfJpzSwpyIiMgzMW2DSIKSDXmFJZXIzi9GSttmbjm32JLbPPVDY55WIlOTOiPvDGbO24zCkkr4qASgCRAW6IsRvePQPiIYY5fvxW5dR5wSwqFBsY2cZ8BaWT2X0WmVd4ckIiJyAgbPRBKUbMgzPs54U6FxW2ypDYb2nluKeH9VV3R4874ugAo4d0n6/gBY1KSWqxFdUlGD+Rv/wqLhyYbAfGbZCCzynQ+dYG3ToHxZPZfJW2PZkEaqZB4DbCIiciIGz0QSlGzIE4+T2vhnzHyDoT3nlmJtE6OSVXClaSPbJvfDgAQNsvO74rfDceiSOxf+l4ukT2re/MXVZDonGkrmiSX+lAbYRERECjF4Jq/jytJxInFDXlFJpVzfP2hCA3ChvBpjl1uu4BozdPwbnoy0pCjF5+4RF25x3Y+/F+Kp5Xtt3oc19qaNpLRtBrQdBaQ9fG0FN6iF+zoM6rT6gNhai5iMFwBBB3wzyvI48wCbiIjIDgyeyau4snScMXFD3pNL98r1/cO0QfGYtV56BdeYeP3UHw6gX8dI+DVS2zz39PQEiw8EP/5+CuO+2id7HyroV4wHJGisfphwOG1Eqh25OxzfYbqSbOFqybz1/webATZrUhMRkZ1YbYMU0+oEZB09j9U5J5F19LxDlSZqw5Wl46SIG/I0oabpE5rQACwanoymQf5WV3DNFZfXoNfcTcjILbR57gEJGpO5/vH3U3hq+T5Ym3LjFWNraps24nZKS+FdPmflSqOa1ERERHbgyjMp4ooVX3vSL2zl6SpddbVXWlLU1bxfy3Guzjlp9/mKy6tN0iukzp2ZV4S+V6tgiOx5SLZWlmuTNuIRnFkKjzWpiYjITgyeySa5ygz25NlKndOeYNyVpeNs8VGrJM9Zm5VZ40Df+Nxyc23PIr+tcSlJSZFKG/EYrXvrN/2VFkI6LUMFNG5mY+X5KtakJiIiOzFtg6xyRbMQR9IvlObpbj9yrs7SSmx1+ZMjl15RfUWHqT/k2syhtiZK4YqxXNpIZEiAQx+G6pTaR18tA4Bsi5g739IH2NZ6MIa0rNua1FJ0WiB/K3DgW/2/Oq17x0NERDZx5ZmscvaKr6PpF0pXeRf+fMTw/46kldiTSmJtBVcJ4w8EGbmFmPrDARSX19h5FlP2rBibpI2UXkbwlVLcdENH+Dbygg10CXfpq2VIlqG7WjJPrb5azk5mfb0ua1JLkSqj17g50PkBoH0qoFIB5WdZm5qIyMMweCarnNHQw5ijwbitPF0p9qaVOJLXLdflTwnxA4FcqoY91Cpg4UP2rxiLaSM6XVMUFGg9N1VDikznREOQqSTAdhe5OtWXzwE7P9D/Z0wMqq+/k4E0EZGbMXgmq5xdmcHRYNyRVV57NhLWJq/bfONfeGM/jP86B8Xl1ZLHG2/Is7YSb4+FD92AOzt7cKqFq9gqn2crwHYHq3WqZRgH1WzyQkTkVsx5Jqts5fWqoDzPFqhdMC6Xp2uNXH6xcdm97X+dw4w1tcvrFldwh3RtiZs6tMCr9yRBBdmMXEN6ha2VeHPm8X9UaAAWD0/GnZ2jFZ+jwRED7E736f9196qtzTrVNpSe0q9a562xfhzzqYmIXIIrz2SVsysz1LZMmvkq71+ny7Dw56M279d4JfvgqRIM++oITpZUKRqzI5U85NI5NGZpIEpX4gH93Cx8KBlNg/xc2l2RXMxZ5fGsNXlhW3IiIpdh8Ew2KQ0ElXBGMG5c3i3r6HlFwbO4kr3hYCGW7SxAUanUurB19gS6gPUa0ebjsqVZkB/m3JPk2VUwSBmnlMczavJinrYil08t1ZZcp/WslBYiIi/A4JkUURII2nMuZwXj9qxka3UCZq87hFh/u4cMwLG6zsaBvlQlDyUbIcODfJE15Xb4NWKWVb1gs061HcxXsa3mU5u1Jf9jve3VaQbXREQWGDyTYnLNQhzhrGDcnpXsrKPnUVRaidgW9o3VGR33rFXysDX+V+/pxMC5PhHrVEuW0bOT+Sq2zXzqqyvWv74JbJlred/Gq9MAUz+IiCTwLzK5jfEmu5S2zRzO3ZXbSNg0yBej+7RBaKAftDrB7rQLwDkd92w1hQEgOX5NqBc0LCHHiGX0Qhz93co0eVGaT73rA8ivTgNYO14fRJsH4mJwbWuzIhFRPcaVZ6o1exqLuIrxSnZmXhFW5ZxCcXk1Ptl+DJ9sP4ao0AAM7R5r93kdSSUxprQpzLbJ/ZyWFkNewriM3uEfgd+/Bi6fV3BDK01elOZTV1y0cqUAVBTLXyemfnS4Q9l9ERHVMwyeGyBnBruONBZxFR+1CiUV1Viy/Zhkveb5G/9EeJAvVJCvvxwZ4o+3HuiKc5eqbM6Nknm0tymMs9JiyEuIZfTibgIGzr6WX9y4ub7D4J8ZlkG1tSYvNvOpVUBgUyvBsRLiZsUswMf+D6RERN6OwXMD48xgtzaNRVxBySqvyuj/jYk/z7grEX3aNbd5X0rn0dkdGqkek2r4ct0tpkG1rU17VvOprz7Lez4BbHm19uMtPwOEOCl45sZEIvIizHluQGzl3mbkFio+l61AFbDdWMTZlKzyXrhcg/7xEYgMcTy/2J55dHaHRmqA7G3yIpdPHRKtv/zm5/T/b2epRgtBEbW7vShvDTA/Cfh8MPDdo/p/5ycxr5qIPBZXnhsIpbm3ttpYi+xNR6gLSldvmzfxx5bnu+G34xftTl2xdx5r2xSGyCG22pJbXZ0WgMBwoOICZFM/QqKB1inAPydrN06lNam5Mk1EHoTBcwPh7GC3LtIR7M3NVrp6Gxzg63DZPXvn0dkdGokUk0oDEYmr05Kl6F7T/7+11A+pzYr2UlqTWtABG6ZIl8yz9gGBiMhFGDw3EM4Odl2djuBIbraiVd6QALRp3tihMQGOzaMzm8IQOY2t1WlrwXXCXYBOV7v7V1qT+puRlleVFgIrH766+fGC2fhYh5qIXIvBcwPh7GDXlekIjm5EVLLK+9LgeKhVNXaPSeToPDqzQyOR09hanXblyq7SmtSSrr66jQNnQLoFuYipH0TkJAyeGwhnB7uuSkeobW62rVXegQmRKCgosGtMxmozj87s0EhUJ6wF17WltCa1XcxakIvBcd4a+W6JTP0gIjsxeG4gXBHsuiIdwRm52carvEWllSi+VIXwID8E+/tix5FzOH/6Ik7VBKFn2+YubQdORFbYrEntKLEO9Q594G91U+LDVzdHGtW9ZlBNRDYweG5AXBHsOjsdwVm52WLDlNcz/jB5rD4qAT1aCMg++w8iQgIdetzMYSZyAps1qWsZUF86rWBTIiwbxijNp2YaCNUBT+jgS5YYPDcwrsi9dWY6grNys+Xypo050sxFfCOruqLDm/d3AQTgXLntboS1wTdPqresVf0Y+Crw0xTHV6abRCrYlChFQT41YCUNZLD9YyWS4EkdfMkUg+cGyJNzb52Rm20tb9qYvfWtrb2RuWo++eZJ9Z61jYlqtczKtDViHerewMEfnDjQq+8Ya8dLtzcXg+v7PweCuugv4+o0OcjTOviSKXYYJI8i5hQD8i20beUU28qbNmacQ22NM7szKuWO+yRyC7kuinLdEgPFD88y7xJiHWqnb0oUpANn8ToA2PCSvjb1obXsnEgO8cQOvmSKwXM9ptUJyDp6HqtzTiLr6HmXv9CcdX9iTrEm1LEW2o40ZrF2G3e8kfHNk+iqhLuACbnAyHXAvZ/o/33+CPDAl/ItyMW8ZHFTYm1bkSsmAGUngb9+Ar4dbZkyIq5OSwXQOi2QvxU48K3+X522boZMHseejfPkHkzbqKcOnirBsK+O4GRJleEyV37d7+z0AvPc7OZB/oAKOHepCllHz1vN+3WkMcu5siqszjkpmVPsjlbkntj+nMhtpErmKalDbXVTogv9/YvMfTlQSo8NXxqcuujgS7XD4Lke2nCwEMt2FqCoVAXjFRfzXClnbURzZm6W1Jgy84rw3Lf7FQfmtvKmzalVwKz1h2TP7Y43Mr55EimgpA613KZEQ4k6FwTVNZetXGlPKT2Zhi/mmFtdr7i6gy/VHoPnekarEzB73SHE+lteZ7xBTqcTMGv9oVqvFNe2qYkxqdXrsMa+uHjZsiOgtcDcWi1mKeaZD+bndscbGd88iZxIbpX6j/V2BNVX378Cw4CKi5B+Z1EBAU2VjUlRKT2JVWpzXLWud1zZwZecgznP9YzYGESO+HX/U8v3OWUjmrNys+Q2x0kFzuJ5Afm8X7m8aWNysbz5ucU3MrnQXwX9Bw9nvpG54z6J6jWpTYmO5FOnv3v1ApnNij3GKBuPolJ6RqvUUsRVa3tyq8njOWPjPLkWV57rmdp8jW/vSrE99+fohjxrbOX9SuVNC4IO50+fQn+hCWb9eFjxueu6qyA7GRLVEUfyqeVqU6e9BnS4AziSB/lNig6U0rt02vIyZ6xak8diMy7PxuBZoffffx9vvPEGioqK0KVLF7z33nvo0aOHu4dlobZf49u7Ec0Z6QX2lJaTYi0wN69prdPpUOB3GfsvKPtjIp7bHW9kfPMkciNr+dTWgmudDkj6F3BqHWRTP+wtpSd1nD2r1rbywskjuaKpGTkHg2cFvv76a0ycOBGLFy9Gz549MX/+fKSmpuLw4cOIiIhw9/BM9IgLhyYkACpU1Oo8SleUnZGbVdtNb458YGjRxP6g3x1vZHzzJPJQ1oLrqC7AfZ8CG16QXp02L6Un20XRaJXanNRqtBSlx5FH8uSmZg0Zg2cF3n77bTz++ON45JFHAACLFy/G+vXr8emnn+KFF15w8+hM+ahVeGlwPL7M3FuryqZKA1JnpBc4ulpem00T3R0M+t3xRsY3TyIvFJ8OxA+uRSk9s1Vqc7VZtaYGy1lVtho6Bs82VFdXY8+ePZgyZYrhMrVajf79+yMrK8uNI5OXmhgFXVks/tx8GucuSW+4k+NIQFrb9AL9ark/ikqrrB5nPk4AmDYo3qE3AuYUE5HL1aaUnvkqtbnarFqTV6pt4OvsfgwNGYNnG86dOwetVovISNNP75GRkfjjjz8kb1NVVYWqqmuBYGlpKQB9vq1Op3PdYK/S6XSI1wTjxbRQPPddruLbiS/Blwd3hAoCdHZ0rxuYEInbO0Zgd34xzl6qRLMgfa288+VV2PHXWXS38iL/6WAharRa+Kgs708MbM1L1mlCAjC4cxTmrM8zqS6iCQnAS4PjkZoo/UYg/g50Oh0GJkTig2FdMXvdIclzDEyIrJPflycwnhe6hvMij3MjzaF56ThYv9HweBZQfgYIigBap1zLoZakAlJf03cyBCC5BJA6V///HvI74nNGmpJ52XCwUPZvldzfO/PbP718HwQAPkZ/is+WVmDcsj147983KDpPXavr54zS+2Hw7AJz587FzJkzLS4/ceIEgoODXX7/giDgwoULCNH5oUcL5QFwaKAv0rtEIT64BgUFBQ7dd7QvcKGiBEt3FqKk4lqwK547MTrU5PiDp0qwbGcBOgQBCLI8X2M/H/wruSXio0Jw7NxllFXWIDjAF5errmB59t+I9QdiW1w7XoUKfJm5F7qyWIv7Aq7NjUqlgkqlQnww8OXQtibnbtO8MdQqx+fAG5nPC+lxXuRxbqTVal58YoGQWP3//3PS9vFBXYCBnwK53wOVF69dHhCm37QY1AXwoPcx2bkRdMD5o0BVKeAfAjRrC6gaTiVdW88Z8e+kvX/vRDpBwOpth9FdJh5QAVi97QCub1INtYe9luv6faasrEzRcQyebWjevDl8fHxw+rTppovTp09Do9FI3mbKlCmYOHGi4efS0lLExMQgJiYGISEhLh0voP/kJAgCklrF4OVNp3G6VD6vt2mQH6be0RGRIYFWV4eV2nCwEOPXnrh6f9fOpcIVbCw4gff+3dzw6VarEzDsqyNXOyFK04T4YWCPJPioVWjTGobb3frGz7K3UwE4/stZbHk+yeLxiHMTExMDtfram7N47oZKbl4aOs6LPM6NtDqfl9hYoPud0qvWHkZybg6tBTa8CJQZpawERwOpc/R54w2AteeMrb+T1v7eiXYePY/MgiuQL58IAFcw4koT9PKw/TV1/XoSMwVsYfBsg5+fH2688UZs2rQJd999NwD9L3PTpk0YN26c5G38/f3h72/Z4k+tVtfZHxm1Wg3fRj6Ylp6IJ5fuBSCd1zvr7k5Oy3XS6gS8su4PXBHkX+SvrPsDAxOj4aNWYVf+eZwsqYK1F/TJkir8dvyiyYY5R28nEn8P/INvivMijfMij3Mjrc7nRa0G2t5cN/dVSyZzk7cG+GYkLFuT/6O/XGxNXs/aj5vnLndrHSb7nKnt3zsAOFteDa3M32Xz45z1nHXmxsS6fD0pvQ8GzwpMnDgRI0eORLdu3dCjRw/Mnz8f5eXlhuobnsxVtYKlXhj2dBtMadvM4QYrzmjMQkREbqS0yYugAzZMsd1+3EsCbKlNey1D/TH1lhaIjbU83hl/75zRj8EeDWFjIoNnBR588EGcPXsWL7/8MoqKitC1a1dkZGRYbCL0VM6uFSz3wrgjSTqNxZz4Inf0BV3XbwRERN7G40uSKW3y8s1Iy6vE9uPiynTeGplqJfPkq5W4QUZuIZ5cutfi48Lp0kos21kAdXBz3NGppcl1zvh754x+DErJPcaikko8uXQvFg1PrhcBNINnhcaNGyebpuFJtDoBu46ex9miizhVE4SebZvDR61yWq1gay+MT7cfU3QO8UXu6Au6Lt8IiIi8jVes/NWqeYvRyrROB3w7CpapH2YBtjE3rFJrdQJmrs2TXWcHgNnrDhnSGkXO+HvnytKsxh/Smjfxx4w1B619l4CZa/MwIEHjWR/kHMBEtXokI7cQfedtxsOf7sKK3Sfw8Ke70HfeZmTkFjrl/LZe/CoA1l4PKujfwMUXufiCFq8zPxaQfkE7ejsiovpOXOAwT6ETV/6c9feg1mrdvOXqyvSPEyGf+oGrAbb22sV5a4D5ScDng4HvHtX/Oz9Jf7kLKUlrLCrVpzUac9bfOzGFUxNqukKtCQ1weDVYjDke+ngnxq/IwbD/7rLar0FM3Xwn8zCyjp6H1o5yuJ6GwXM9URdvmEpe/OJrQemL3NEXtCveCIiIvJmS1c2Za/M8I2gRm7zUqhcugMvnrVx5NcA+vkP/Y94a/Wq0ebqIuErtwgC6NrnLzvp7l5YUhW2T++Grx3thwdCu+OrxXtg2uZ/F7bU6AVlHz2N1zknZIFcu5lBi4c9H8dDHO526uFfXmLZRDyhZEXbGVyVKX/yP9mmDH3OLFG9QdDQn29m53ERE3szeTdtuZbM1uRMD/EunlW9Q7DhIWQqHnakfzZtYVuCSIpe77Ky/d7ZSOJWk/FiLOezhzXnQDJ7rgbp6w1S6caF/ggZTByXY9SJ3NCfbWbncRETezusqEVlrTT7wVeCnKVbbjwuNm0F1+Zzt+2kSqXyD4vEdtluqS21QbNwM6PwgcP2dFoF0Rm4hZqw5aPWUKug7BtrKXXbm3zvzTaUXyqsw9moXQmPmQa6tmEMpb86DZvBcD7jyDdNkM0CQPzQhAVabrogbFxjUEhHVLa+sRJRwl361V2oVV62WXZkWALxYPQrjhE+hQbHMfhuVPhBv3Rs4+IOy8djayCimfpj/Fbx8Htj5gf4/sdJHx0HI3rIWP27cjTYIwxl0hE4iW1Yc+kuD4+ssgJRaYVarrK7L48UfclFRrcXRs+VOG4dHfRtiBwbP9YCr3jClXlxhjX0NLyRn7tglIqLa8dpKRGof6dVemZXpisBIPFsyFBmVyTivvoJFvvOhE8w3rF/9Ie01/fmVblC0dpzV1A8jpYXAyochBDZFj4oL6OGnv/iUEI6ZNSOwQdfDcKgaOqQG/42HOoSjd+OjgE7j8sofclWzrKXCCwDOl1fj2ZX7XTImj/k2RCFuGKwHxDdMuZDVvMqFEnKbAUou1wAAQhv7mlyudOOCko0InsKbxkpEVC8rESXcBUzIBUauA+79BNoRa9Ff+x4yrgagG3Q98GTNBBTB9O+bEBJtWqbO5gZFFRDSUn+cHJupH4Z71/9TccHkUg2Ksch3PlLV2QCAVHU2tvk/g/dqZqJV/rfA0rtdXvnDWfnK1ogxx7JHe2Lcbe0U3cajvg1RgCvP9YB5DUdjjrxhKtmAGNBIjWWP9cS5S1WKNy54Re3Rq7xprEREIld1lXUro5Xp7KPncbJ0p8nVG3Q9kFnVDT3UfyACF3EGYRifPhIp7SNMz3F1g6IA1dXEDz39z7i2Si3HztrU5n8R1Sr96u503y+hrhHwvu+Cq9cY3ae1+tRO4Kx8ZTnGMUef9s3Rq20zfLf3H+/7NsQGrjzXE84s3aasHmUV1CoVhnRtiZS2zRQFzl5RexTeNVYiInNKS5J5I7mv93VQY6cuAWt0vbFTl4Az5TWWByXchX0pC3DGbJX6NMKxL2WB7WC11rWp9QF0tOo8Zvt+avjZlEx9aidxdXqEecxRL78NAVee6xWxlM2uo+dwtugknta0NHQYtEdRSYWi45S+COuqlJ4zeNNYiYjk1NdN27XZ45ORW4gnf24OFRaYrFLv1nWE7mc1FrUstP4BQ0z9kK0AolwzVZmVa21X/nC0/bor0iPG3dYW7SODZcdRH78NYfBcz/ioVejVthkKfMsRG9sMajtSNbLzi7Exrwgr9/yj6DZKX4TeVHvUm8ZKRNTQOLop0nhhRLi6Sm1+O5sLIya1qeuATJpIbdIKbc0fcC29RKk+7VrY/HtY3/oyMG2DTFpsfrL9GMoqr1g93t4NiN5Ue9SbxkpE1NA4mgZgz8KIVWIFkJBo+wZ+lU4Azgkhio7dVuRjsVm9tmmFtuZPBWDhQ8n46vFeeOfBrggP8jU/hcnx9sQC4rchStM9PRmD5wbO0Rab9uQoeVPtUW8aK1F95ClVbup6HJ7yuL2BI3t8nLowYlwBpNdTQOPmptcHisGk6d9IASqoVCqcv+VVfTUQmcofOgCnhGYYsamRSRtrZ7Vfl5o/NXS4I/gIVt18CncGH0FKXBju6hKNkSltJM/hzfnKzsC0jQbMkZI14UG+ePWeTnblKHlT7VFvGitRfeOKKjeO5IbWdbUdVvexn71pAM5aGDF9PiWgx8C+8Bk427LJyx/rLepTq0KigbTXcH3CXYAm1KgBzDVi3Duz5mFDQxVxVXlC//ZOSys0nj+fw2vRJXcu/C8XAdkAsoGKQA1m1ozAiktdJW9f23xl8wZsUMGiepdWJ2DX0fM4W3QRp2qCHNrD5SoMnhswR0rWTBuc6NCLZWj3WLyz8U+Lyz3t06t52T82giGqG3KNG8xbA9t7TnuDUleMw9YY6/L+6hN7NkXWZmFEDPQy84qwKucUisurDdddez6Zbeyz1jlRvF5sAFN2Lbe5CM0ws+Zhk0Yq4mb1JduPKXqsPx4oNDxma3+rfNQqpFRtB7InwHwDpP/lIryK13FBPcFkLADwbP8OGNevncN/B6Vel8aiQgNwV5corNlfiDOlFejRQkD22X8QERLoMR8ombbRgDmSt6sJsb9LYd95myUDZ8CxUnqu5syyf0Rkm7O+jjbmSG6oK8ZhTV3fX0PmaK608Z6gT7cfMwmcARu5xmJ96k736f81ryEtpn8MX4XT7R7E8Oop6Fu1wCJYBfTPh4sVEuX3JHy587hJuocsKx0TxWmY7vsl1NAZLlcBWLG7QNE4AMt0pB9/P2UzVbSwpBIf/prv0eViufLcgNmTt+tIuoLcioro2f7tMa5fe49cxa1vO4OJPJmzq9w4WnKyrqvtsLpP3bK3ZJqtv2GAE0qYqn2AuL4oOvU7dulCoJPtgKgXFuiLkooaRemWhba+vbDRMVGtAqJxHj3Ufxiqk9jznDRfYVZDh57qP5Cu1pcIzNZ1NKSmKOFJ5WIZPDdgSkrWGHNWl0JA/PR6AuP6tVc63DpXX+ukEnkaZ1e5cTQoretqO6zuU/eULozYsyfIGR9yggPkq1oYe6RPHOZv/NMirdAa2WBTYcfECFy0uMzWc9L8g0eqOhvTfb9AtOpaNZNTQjhm1oyQXGmX4ykfKJm20YBZ+xrLWJSLuhQqKgtERPWes6vcOBqUKj3/ubIqp1TFYHUf95ArmWacYvDZdsu0AVtq8yGnTfPG0IQEyP4tFsvCjevXDouGJ6NpkJ+i84p/az/bnm/5nFXYMfEMwiwus/acNP/gkarOxiLf+dDA9O+9BsVY5DsfqepsReMwGZObP1By5bmBk/saq1mQH4Z0jcaABI1D6QpcUSEipZxd5cbRoFRpA4lZ6w8Zfq5NVQxW9/EctjaxKVGbDzlqlQovDY7HU8tybG5WT0uKQkW1Fs+u3K/4/JLP2QTrHRN1gn4DY7auo8lYbD0njRfP1NBhuu8XVx+j+WPW38d03y+RWdXNrhQOd3+g5MozIS0pCtsm98NXj/fCgqFd8dXjvZD9Yn+8nJ7ocCFzrqgQkVKObuaSIwaltlbxzAMAJd/GmS8012YTk7Mfd11xZU1qd9S7drTfgcjeZiFyUhOVb1bXhAY6fD+G52zeGX3HRABKSuYpfU4aL4r1UP+BaFWxReAsUquAaJU+r1oJZ811bXHlmQA4P7+XKypEZA97N3NZU5uSk3LjkGtZbL6Jyd4w157H7UjNamdzVk1qqceSmVdU5/WuHel3YMzZH3KU5mSLf2MdCfhNnrOT0+Ejlswz2jxY1Vhf53lDVVfDZUpfi8aLYlL50pK3UXCcJ32gZPBMLsF6yURkL2dWualNMG4+jnNlVSZfe5sz3sPRM66pQ2O19bilgtbwIF/c07Ul+juYXmcvZ9Wk3nCwEK+s+8PksYQ19sXFy5al2Fxd79qRfgfGrD2f7PmwoxME7Dx6HmfLqxU9743/xjoS+JtsvJOoSR3YujfmQI0hDrwWjRfPpPKlpSg5rraNWZyJwTO5jDNXkoioYXDmt2C1CcaNx7E656Si+1O6h0MuqJJ73HJBa3F5DT7ZfgyfbD/m1hVa8bIp3x9AkF8jFF+WDwAPnirB+LUncEUwvVwqcBbP7cryZI7su1HyocWeFfoNBwuxetthZBZcgfbqvCj5fcr9jbWH4fGLNamN+AAOvRaNA/vduo44JYRDA+nUDQEqVDfWIKX3YOzc/LfsOZ/p1wHjbvec0rYMnsmlWC+ZiGqrNukKzgjGHd3D4YzUBKVpBdZWaJ2R7qFkhfbC5Ro8/Om1ygnmj0urE7B2f6HdK6WuLE+m9HcbHNAI99/YStEmentW6DNyC/H08n3o3kL8mCB/rBTjv7FFJRUoLq9GeBN/FF+y/m2JSHz8zk4JMg7sZ5aNwCLf+dAJ5psGVVABaDRoHlaska83rQKw8rcCjLvdc0rbMngml2O9ZCJylLNybGvDvj0c+iOclZqgNK1AboXWWfPnyAqt+ePanV+MkooaWC+O6twx2KK038GlyitYsv2YzaDSngY9uPr/9jbzMSf1N7b6ig7vbzmC4nLpFX3j56yrXmPXAvuu+O1wHLrkzoX/5aJrB4REA2mvIdu/DwpLdsqeRwBQVOr+2s7GWG2DiIg8kiMttl3B3qoYB0+V4Onl+yzGbS01AZBuxW1PwGheP9+Z8+dIZSTzx3X2Uu2CX1dUZzL+3VqjtF26PT0OXNUPISO3ELe88bPVwBnQP2cz84pc+hoTA/sed46C/3N5wMh1wL2f6P+dcABIuMsrS9syeCYiIo+jJMfWViDjTOLX0OZlxEIDfTGhf3vDSqIzUhOMORIwFpVUOH3+bJX/k2P8uFo0cSz4dXV5MvF3Gx5kvcufkmDWnkDQFUGjkrJ7Yum7AQmaun2NiXnVne7T/6v2AeCdpW0ZPBMRkVM5o1avJ3YpFWviP9u/A8IC9YHWxYoavLPxL/SdtxkZuYVGqQmOMQ+UHAlaZ60/hIWb/3Lq/CldoZVzpqwS3ePCERro61AAPrR7rMP3rURaUhSmDU5UdKy1YLZ5kL+ic0QEBzg9aFSSH98syA+/PH8b0pKiPOY1pqQuuybEs0rbMngmIiKnycgtRN95m/HQxzsxfkUOHvp4pyGwtIenfpWbmVeE+Rv/xEWzAFn8mnvzodO1Or95oORI0HqhvBrvbPxL0bH2VAgJDfTD6D5tEBzgY9d4AP3j8lGrkN5Fn0Mrl/4S1lh69fedjX869DyyhyakdsFsRm4h/u8b613/jFfRHW3mI0dJfvz58mrsOX4BgOe8xpSkRb00ON6jCg0weCYiIqdwR45tbb/KtWeVXEkqxKrflZW1M2ctUBLTCqJClT1We9b5lcyf8QeiT7YfQ1mlFio74phmQX64sbW+/nVidCje+/cNkl30Fg9Pxp6XBuDZ/tJVFVyd616bYFZ87heVygea5vnxzu4waW8w7EnpEnJpUZEhARjWKxapiZ5V2pbVNoiIqNbsqTJgb6MFV3UptbfKgJKvuS+U1yCoaSOooFU8DiWBknFJssy8Inyz5x+UVV5RfB9S96lk/uTKrgl2ROjny6txyxs/4+XBHREfrG9DPTAxWrI0mlYnYMXuE5LnceR5ZE8JNnuaexmft3kTf8xYc9Dmh5bIEH/MuCvR5LmVlhSF9/59A1ZvOwDg2u/TkX4I9gbDntYJWKq0bbfWYTj5j/TzwZ0YPBMRUa3Zkz+ppNyUq7uUOtItT+nKXteYUGz5p1hy3AIsS9YpDZTEygUpbZuhU6swPPt1jqLxODp/SnJo5dqWmysqqcTTy/dhQXoMYmPlS5g683mk5MOReXA9IEFjs7mX1HmVeOuBrujTrrnF5amJUbi+STVGXGmiuMOgFHuDYU/sBGz+vNDpdHV23/Zg8ExERLXmivxJV3UpdXSVXOnKXkJUKN77d2uLOs/iuJ3ROEppfu6z/Ttgxe4Ch+ZPSQ6tTgCmDYpH82B/hDf2wzMr9uLCZcsVcXGu1+4vxMAeSVDLJI0663mk5MMRANngetvkfpK/I7nzKnHuUpXsdWqVCr3aNoNabmIUcCQYZidgxzB4JiKiWnNV/qQrupQ6urqpaGUvJABtmjdGm9byqQmAY22PjSldZRzXrx3G9Wvn0PwpDWSbB/tjSNeWyDp6XjJwFgkASipqsDu/GL3bt5A8xhnPIyUfjl74/gBKLtfY9c2D0m6PjozZWRwJhtkJ2H4MnomIqNZcmT/p7C6ljq5uKlnZe2lwPNSqGsPxruqIZu8qoyPjsDeQVTqv1pqlKOn4pwnxt3geGadfnCursvnhyFrDGrlvHpR2ezTnCbnDtoJhdgK2D6ttEBFRrTm7coAr1WZ1U64qgNh4oi6rAtgai62v3G1VGrG3+oTSebXWLMXa80hUeUWHzLxrbZ7NyyPOWn9I0TjkyNU3dqRkm7tzh4d0bYmUts084nVXn3DlmYiInMJb8idru0pubWXP2RucbFWLsHeVUTxfZl4RVuWcQnF5teE6qUojQ7vHSNaMlgoKlcxraKAvuttYgRWfRy98f0Byhbjkco1J3rKjOci2mAfLjqRd2Hrua3UCdh09j7NFF3GqJgg92zZnoOsFGDwTEZHTeEP+pDOqDBh/zW0c4DZr7Iuqi5ew/8JJRIQ0rtVjV1pKT+lX7raqRIj5vhP6d0BJRbVFcG1MKihUMq/pXaIUzceABA1mrMkDYBk8G6dWCILgksAZsAyWlaSUGHu2f3uM69de9vGKv48zpRXo0UJA9tl/EBES6FEfNEkag2ciInIqV+ZP2lO31xpnrZKbB6Q+KuFqIKSCVlBZrRtt67z2ltKzNjdKqkSI172z8U+rY3u2fweM69dOct6tzau+zrOy1uXZ+cVWG46IqRX2Mi4XKLVhUDxG6psHax8OpM6xYvcJjOsn3fDF+PfhYzSN1n6/nsJZr0FvxuCZiIi8gr1NTWyp7Sq5koDUkWDIkVJ61uZmQIKmVlUijOmDwgKM69dO9hi5eVVBQEFBgaL7cVVLaPHDEQCHvnkQPxxM/SFXdlUesF6P2tkNheqSs1+D3orBMxEReTxHVmLlyK2c2bOiprRsmSPBkL2l9GzNzYT+7R1apVVy33Kkvn2ouaLD32fLFaW0OLOsm1iHunkTf0AAzpVXISI4AO//Oxmz1tv/zUNaUhQqqrV4duV+m/ct9SHA2Q2F6oozX4PejsEzERE5TKsTsCv/vGzA6YyveJ25Uie3cnZXlyis2V/otFbd5mO0Jxiyp5SekrlZsv2YovPZw96V4YzcQsxaexCx/hWKUlrszS+WIqZfjOoTh8y8Ijz3zX6L3++0QfFoGuRv9/NTExqoaAxSHwJc0VDI1bx5tdwVGDwTEZFDDp4qwbCvjuBkybXOacYBkbO+4nXWSp3cyllhSSU+/DXf4nhntOp25Db2lNJTMjcXK5TlGdvDnpVhcd7VKgGxRr1RrM2vPfnFUozTLzLzimRXTMcu34dFw5MxpGtLu85fm4otrmoo5EreulruKqzzTEREdttwsBDLdhZYbOoSA6K5P+bhyaV7Lf7gitdn5BYqvi9nrNQ50h1OPHbm2jyLGsiOBDZKb2NPfWWlcxMW6Ct7PnuY13a2xdaKJSA9v8C1/OKmQX52j1OsdW0t39vW/VtTm7rm9tbP9gTeuFruSgyeiYjILlqdgNnrDskGJAKAj7fmOy1gccZKnaPd4eQaZtgKgIzZGwzZE5gpnZtH+sRJns8ejjT8sGfFUkpaUhSmDYpXdF/jbmuLBUO74qvHe2Hb5H5IS4qq9f1b42iTGm9qKCRS+jw7V1Yl23SnPmHaBhER2UUsI2b8Fbw5a3837f2K1xmtv2u7ImZPq27zsQH2B0NKS+kpnZtx/drhek0Ti/OFB/ninq4tERLoi3c2/mX1sTjS7MYZK5ZK84v7tGth8Xxy9YqpoxVbjH+/Z0orDJd7WkMhkZIcdLUKJt0d63MVDgbPRERkF2d9Nav0PM5oatI8yN/hcQLWW3VbazwiBkMDEjTIOiq/sdKYuMmy6ooOb97fxaRChPnt7JkbW4He9Zpg2eC6f4LGoc2ezvjWwNPzix2tay7+PnYdPYezRSfxtKalx3YYVPJh0fwDc32uwsHgmYiI7OKsjUz2nEcuUG16NbgLDfSDVidIBh4ZuYVXu9XZz95W3foOg2cw1DfUUI4tM68IfedtVrRx0tomS7kAzZ6GL9YCPVd0h7yxdVOEB/miuFx606IKQGSIP3SCgNU5J2v9AcGcM761cCUftQq92jZDgW85YmObQe2BgbNI7nmmVkl/01Sfq3CoBEGov0kpHqK0tBShoaEoKSlBSEiIy+9Pp9OhoKAAsbGxUKuZ1m6McyON8yKN8yJNqxNw87xNaO1fgV1Xy47ZQwxYtk3u51DZuuz8YmTmFVm0j5YKSJU0MrE2TgB2rZyZP2fk7l/q3PYcK8XTOr/Z6r5o3O3v4uVrwbUjHyyszYs4r4B04O3ulVFve58xfp6dK6sySdWQ89XjvRxana/ruVEar3HlmYiI7OKjVuGlwfH4MnOv3bet7YYoH7UKJRXVWLL9mM1mDUorbGhC/DGka7RFnWdHUi6M2VMbF1f/vzZ1dF3ZFt1eSj60hF4Nmo0DZ0D+635n5BfXphU76Rk/z1bnnFR0m/pWhcMrg+djx45h1qxZ2Lx5M4qKihAdHY3hw4fjxRdfhJ/ftZI2v//+O8aOHYvdu3ejRYsWePrppzFp0iSTc33zzTeYNm0ajh07hvbt22PevHm48847DdcLgoDp06fj448/xsWLF9GnTx8sWrQI7dtL96snImoIUhOjoCuLxeGNRTh/+Yri29U2YLEnIFVaYeOtB7qiT7vmmJQWbxGY2ZNyYc7eSg/1pY6ukg8t4UF+8JUJeq19WKhtfrEnrczXB95Ys9oZPP/7AQl//PEHdDodPvzwQxw8eBDvvPMOFi9ejKlTpxqOKS0txcCBA9G6dWvs2bMHb7zxBmbMmIGPPvrIcMyOHTvw0EMP4dFHH8W+fftw99134+6770Zubq7hmNdffx3vvvsuFi9ejF27diEoKAipqamorKxfn6KIiOyVGB2KBUNvUHTsuNvampQQc5Q9AanS1a5zl/RNXsTAbEjXlkhp28zQXMPRWtX2VHqoT3V0lXxoKS6vxumyKtnra1NCTo7575eBc+15Y81qZ/DK4DktLQ1LlizBwIEDcd111+Guu+7Cc889h++//95wzLJly1BdXY1PP/0UiYmJGDp0KJ555hm8/fbbhmMWLFiAtLQ0PP/884iPj8esWbOQnJyMhQsXAtCvOs+fPx8vvfQShgwZgs6dO+OLL77AqVOnsGrVqrp+2EREHqfndc0U/fF8dsD1dgcsWp2ArKPnTerG2hNk1mZVrDbNPaydV+64+rSC58wA35FzST1vyDW8sWa1M3hl2oaUkpIShIdf+2STlZWFm2++2SSNIzU1FfPmzcOFCxfQtGlTZGVlYeLEiSbnSU1NNQTG+fn5KCoqQv/+/Q3Xh4aGomfPnsjKysLQoUMlx1JVVYWqqmufqEtLSwHoE991Ol2tH6st4v3UxX15G86NNM6LNM6LPHFeVBDw8uCOeHr5PgDSG7JeHtwRKgjQ2RHEbDhYiNnrDpl0MNSEBOCBbrHwUdk+T4sgP3RrHYaWof44XSpfaSEyJADdWodZ/I53HT2PM6UV8LHyN/9MaQV2HT2HXkZpBMbPGXvuH4DDY/U0LYL8JH9HPioBaghW51TqXPY8XrnnzUuD45Ga6Jm5zd7+PjMwIRIfDOsqO+8DEyIdfmx1PTdK76deBM9HjhzBe++9hzfffNNwWVFREeLi4kyOi4yMNFzXtGlTFBUVGS4zPqaoqMhwnPHtpI6RMnfuXMycOdPi8hMnTiA4ONiOR+YYQRBw4cIFqFQqqFT169NebXFupHFepHFe5BnPTXywCgvSY7B2fyFKKq5t/goN9EV6lyjEB9egoKBA8bkPnirBsp0FiPWHSSMWFSqw68Bh3NrSBxXVWtkgMyTQF5pGl3Dyn3JMvaUFlu3U37dUYD+sVwuc/OeExXnOFl1Ejxa2g/SzRSdR4Ftu+Nn8OWPP/Ts6Vk+jaSRgQGwjlFbUmDwOtUpAXBNApRLQJMAXgIDSiis2f48FBeUSR1iy9rz5MnMvdGWxSIwOrcUjc4368D4THwx8ObQtjp27jLLKGgQH+KJN88ZQq+x77Zur67kpKytTdJxHBc8vvPAC5s2bZ/WYQ4cOoWPHjoafT548ibS0NNx///14/PHHXT1ERaZMmWKyol1aWoqYmBjExMTUWak6QRAQExPjFWVv6hLnRhrnRRrnRZ753MTGAgN7JGF3fjHOXqpEiyYB6O7AhiytTsCwr46gqFT6dioAYY19cOGyTrbm73v/7oQ2rfWrjLGxgDq4ud2rkadqgpB99h+b431a0xKxsaYrz+bzovT+HR2rJxrS18/i2wgfFaASBOw+p8L8hzoBgNVvLIx/j7Yoed4c/+Ustjyf5HEpBPXpfaZNa+eer67nRswUsMWjguf/+7//w6hRo6wec9111xn+/9SpU7jtttvQu3dvk42AAKDRaHD69GmTy8SfNRqN1WOMrxcvi4qKMjmma9eusmP09/eHv79lNyu1Wl1nLwzxvrz9hegKnBtpnBdpnBd55nOjVgO921vp2a3ArvzzOFlSBcsMymvOlV/Bs/07YMXuE4qqYNzRqSUGJkbbVWmhZ9vmiAgJtNlco2fb5haNLcznxZ77d2SsnuiOTi2xcJjaojxck0BfzH+oE+7o1BIAJI9xpK2zkufNyZIq/Hb8okdWK+H7jLy6nBul9+FRwXOLFi3QooWyN96TJ0/itttuw4033oglS5ZYPOCUlBS8+OKLqKmpga+vLwAgMzMT119/PZo2bWo4ZtOmTZgwYYLhdpmZmUhJSQEAxMXFQaPRYNOmTYZgubS0FLt27cKTTz5Zy0dLRETmlG4Qa9M8CNsm91McZNpb4swZLcEdvX9PqtdcG+bl4VoE+UHT6JLJarKzSsjVp2ol5Pk8KnhW6uTJk7j11lvRunVrvPnmmzh79qzhOnG1+N///jdmzpyJRx99FJMnT0Zubi4WLFiAd955x3Ds+PHjccstt+Ctt97CoEGDsGLFCvz222+GVWyVSoUJEyZg9uzZaN++PeLi4jBt2jRER0fj7rvvrtPHTETkKbQ6AbuOnsfZoos4VROEnm2bO21l1J6qE64OMtlco/aMf0f6bnGW+cvO+D3Wp2ol5Pm8MnjOzMzEkSNHcOTIEbRq1crkOrHbeGhoKH766SeMHTsWN954I5o3b46XX34ZY8aMMRzbu3dvLF++HC+99BKmTp2K9u3bY9WqVUhKSjIcM2nSJJSXl2PMmDG4ePEi+vbti4yMDAQE8AVIRA2P2CL5TGnF1VbL/yAiJLDWjU/ElcfmQf7QhARYrTqhqcO6sWyu4R3EesO20mzqW71hcg+VIEab5DJKe6U7S133gvcmnBtpnBdpnBdTxi2XfVTC1eBZBZ2gDyTN2ykrPaf5ym7Y1bbNcukSjtxPXfHW54zxBxhXfUBw9dyIz0/Au5433vqcqQt1PTdK4zWvXHkmIqK6ZU9bbKVBl3Ewbqzksr7cXejVIFqkNF2iLgLB+kTqA4wjm/bcjWk2VFcYPBMRkU32tMVWkr+qJBgPaKTGssd64tylKsVBcH0JBOuK3AcYsQW5p67WymGaDdUFBs9ERGSTs6sZKAnGi0qroFapMKRrS0XnrG+BoKu54tsET1BfqpWQ52JyDRER2eTsagZFJRWKjlMajNsKBAF9IKi1o0V4fWfPtwlEdA2DZyIiskmsZiC3/qiCPj1CSTWDjNxCzFp/SNH9Kg3GGQjaj7WRiRzD4JmIiGwSm4YAlj3clDYN0eoELNj4J55YuhfF5dVW78+eYBxgIOgI1kYmcgyDZyIiUkSsZqAJNQ2mNKEBNvOJM3IL0ee1zXhn41+K78+eDn4MBO3nzG8TiBoSbhgkIiLFxGoGu46ew9mik3ha09Jmh0G5jXxywoN88eo9neza3Hdj66YID/KTXdFmkwxLzm5BTtRQcOWZiIjs4qNWoVfbZugSE4ZebZvZTNWQ28gnZ9rgRLsC54zcQtzyxs9WA2fA8wJBrU5A1tHzWJ1zEllHz7tlM2Ntvk0gaqi48kxERC5jayOfFE2I8tQKJavantgkw5PqUbM2MpF9GDwTEZHL2LNBz97UCiWr2uFBvvjl+dvg18hzvmj1xHrUrI1MpJznvJsQEVG9Y+8GPXtSK5SsaheX12DP8Qt2jcGVWI+ayPsxeCYiIpexVdFBpAnxt3vF1RvL07EeNZH3Y/BMREQuY60+tOjZ/h2w/YXb7U5V8MbydN4Y8BORKQbPRETkUnIVHaJCA7B4eDLG92/v0OY0b6xT7I0BPxGZ4oZBIiJyOVdUdPDGOsViwF9UUimZ98x61ESejyvPRERUJ8SKDkO6tkSKjfrQSnlbnWJntDknIvfiyjMREXk1b6tTLAb85nWePbEeNRFZYvBMRERez9vqFHtbwE9E1zB4JiIicgNvC/iJSI85z0RERERECjF4JiIiIiJSiMEzEREREZFCDJ6JiIiIiBRi8ExEREREpBCDZyIiIiIihRg8ExEREREpxOCZiIiIiEghBs9ERERERAoxeCYiIiIiUojtueuAIAgAgNLS0jq5P51Oh7KyMpSWlkKt5ucjY5wbaZwXaZwXeZwbaZwXeZwbaZwXeXU9N2KcJsZtchg814GysjIAQExMjJtHQkRERETWlJWVITQ0VPZ6lWArvKZa0+l0OHXqFIKDg6FSqVx+f6WlpYiJicGJEycQEhLi8vvzJpwbaZwXaZwXeZwbaZwXeZwbaZwXeXU9N4IgoKysDNHR0VZXurnyXAfUajVatWpV5/cbEhLCF6IMzo00zos0zos8zo00zos8zo00zou8upwbayvOIibXEBEREREpxOCZiIiIiEghBs/1kL+/P6ZPnw5/f393D8XjcG6kcV6kcV7kcW6kcV7kcW6kcV7keerccMMgEREREZFCXHkmIiIiIlKIwTMRERERkUIMnomIiIiIFGLwTERERESkEIPneuTXX39Feno6oqOjoVKpsGrVKncPySPMnTsX3bt3R3BwMCIiInD33Xfj8OHD7h6WR1i0aBE6d+5sKECfkpKC//3vf+4elsd57bXXoFKpMGHCBHcPxe1mzJgBlUpl8l/Hjh3dPSyPcPLkSQwfPhzNmjVDYGAgOnXqhN9++83dw3K7Nm3aWDxnVCoVxo4d6+6huZVWq8W0adMQFxeHwMBAtG3bFrNmzQLrOOjbY0+YMAGtW7dGYGAgevfujd27d7t7WAbsMFiPlJeXo0uXLhg9ejT+9a9/uXs4HuOXX37B2LFj0b17d1y5cgVTp07FwIEDkZeXh6CgIHcPz61atWqF1157De3bt4cgCPj8888xZMgQ7Nu3D4mJie4enkfYvXs3PvzwQ3Tu3NndQ/EYiYmJ2Lhxo+HnRo34p+TChQvo06cPbrvtNvzvf/9DixYt8Ndff6Fp06buHprb7d69G1qt1vBzbm4uBgwYgPvvv9+No3K/efPmYdGiRfj888+RmJiI3377DY888ghCQ0PxzDPPuHt4bvXYY48hNzcXX375JaKjo7F06VL0798feXl5aNmypbuHx1J19ZVKpcIPP/yAu+++291D8Thnz55FREQEfvnlF9x8883uHo7HCQ8PxxtvvIFHH33U3UNxu0uXLiE5ORkffPABZs+eja5du2L+/PnuHpZbzZgxA6tWrUJOTo67h+JRXnjhBWzfvh1bt25191A83oQJE7Bu3Tr89ddfUKlU7h6O2wwePBiRkZH45JNPDJfde++9CAwMxNKlS904MveqqKhAcHAwVq9ejUGDBhkuv/HGG3HHHXdg9uzZbhydHtM2qMEpKSkBoA8S6RqtVosVK1agvLwcKSkp7h6ORxg7diwGDRqE/v37u3soHuWvv/5CdHQ0rrvuOgwbNgwFBQXuHpLbrVmzBt26dcP999+PiIgI3HDDDfj444/dPSyPU11djaVLl2L06NENOnAGgN69e2PTpk34888/AQD79+/Htm3bcMcdd7h5ZO515coVaLVaBAQEmFweGBiIbdu2uWlUpvhdGzUoOp0OEyZMQJ8+fZCUlOTu4XiEAwcOICUlBZWVlWjSpAl++OEHJCQkuHtYbrdixQrs3bvXo/LsPEHPnj3x2Wef4frrr0dhYSFmzpyJm266Cbm5uQgODnb38Nzm77//xqJFizBx4kRMnToVu3fvxjPPPAM/Pz+MHDnS3cPzGKtWrcLFixcxatQodw/F7V544QWUlpaiY8eO8PHxgVarxZw5czBs2DB3D82tgoODkZKSglmzZiE+Ph6RkZH46quvkJWVhXbt2rl7eAAYPFMDM3bsWOTm5nrMp1dPcP311yMnJwclJSX49ttvMXLkSPzyyy8NOoA+ceIExo8fj8zMTIvVj4bOeFWsc+fO6NmzJ1q3bo2VK1c26FQfnU6Hbt264dVXXwUA3HDDDcjNzcXixYsZPBv55JNPcMcddyA6OtrdQ3G7lStXYtmyZVi+fDkSExORk5ODCRMmIDo6usE/Z7788kuMHj0aLVu2hI+PD5KTk/HQQw9hz5497h4aAAbP1ICMGzcO69atw6+//opWrVq5ezgew8/Pz/Bp/sYbb8Tu3buxYMECfPjhh24emfvs2bMHZ86cQXJysuEyrVaLX3/9FQsXLkRVVRV8fHzcOELPERYWhg4dOuDIkSPuHopbRUVFWXzgjI+Px3fffeemEXme48ePY+PGjfj+++/dPRSP8Pzzz+OFF17A0KFDAQCdOnXC8ePHMXfu3AYfPLdt2xa//PILysvLUVpaiqioKDz44IO47rrr3D00AMx5pgZAEASMGzcOP/zwAzZv3oy4uDh3D8mj6XQ6VFVVuXsYbnX77bfjwIEDyMnJMfzXrVs3DBs2DDk5OQycjVy6dAlHjx5FVFSUu4fiVn369LEogfnnn3+idevWbhqR51myZAkiIiJMNoE1ZJcvX4ZabRqG+fj4QKfTuWlEnicoKAhRUVG4cOECNmzYgCFDhrh7SAC48lyvXLp0yWT1Jz8/Hzk5OQgPD0dsbKwbR+ZeY8eOxfLly7F69WoEBwejqKgIABAaGorAwEA3j869pkyZgjvuuAOxsbEoKyvD8uXLsWXLFmzYsMHdQ3Or4OBgi5z4oKAgNGvWrMHnyj/33HNIT09H69atcerUKUyfPh0+Pj546KGH3D00t3r22WfRu3dvvPrqq3jggQeQnZ2Njz76CB999JG7h+YRdDodlixZgpEjR7K04VXp6emYM2cOYmNjkZiYiH379uHtt9/G6NGj3T00t9uwYQMEQcD111+PI0eO4Pnnn0fHjh3xyCOPuHtoegLVGz///LMAwOK/kSNHuntobiU1JwCEJUuWuHtobjd69GihdevWgp+fn9CiRQvh9ttvF3766Sd3D8sj3XLLLcL48ePdPQy3e/DBB4WoqCjBz89PaNmypfDggw8KR44ccfewPMLatWuFpKQkwd/fX+jYsaPw0UcfuXtIHmPDhg0CAOHw4cPuHorHKC0tFcaPHy/ExsYKAQEBwnXXXSe8+OKLQlVVlbuH5nZff/21cN111wl+fn6CRqMRxo4dK1y8eNHdwzJgnWciIiIiIoWY80xEREREpBCDZyIiIiIihRg8ExEREREpxOCZiIiIiEghBs9ERERERAoxeCYiIiIiUojBMxERERGRQgyeiYiIiIgUYvBMRERERKQQg2ciIiIiIoUYPBMRkWJfffUVAgMDUVhYaLjskUceQefOnVFSUuLGkRER1Q2VIAiCuwdBRETeQRAEdO3aFTfffDPee+89TJ8+HZ9++il27tyJli1bunt4REQu18jdAyAiIu+hUqkwZ84c3HfffdBoNHjvvfewdetWBs5E1GBw5ZmIiOyWnJyMgwcP4qeffsItt9zi7uEQEdUZ5jwTEZFdMjIy8Mcff0Cr1SIyMtLdwyEiqlNceSYiIsX27t2LW2+9FR9++CE+++wzhISE4JtvvnH3sIiI6gxznomISJFjx45h0KBBmDp1Kh566CFcd911SElJwd69e5GcnOzu4RER1QmuPBMRkU3FxcXo3bs3br31VixevNhw+aBBg6DVapGRkeHG0RER1R0Gz0RERERECnHDIBERERGRQgyeiYiIiIgUYvBMRERERKQQg2ciIiIiIoUYPBMRERERKcTgmYiIiIhIIQbPREREREQKMXgmIiIiIlKIwTMRERERkUIMnomIiIiIFGLwTERERESkEINnIiIiIiKF/h9vid/VpmWRAAAAAABJRU5ErkJggg==\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "То же самое можно и подтвердить визуально. Мы видим, что модель, в силу ограниченности входных значений, не может предсказывать более точные значения. Модель пытается найти тот угловой коэффициент, при котором погрешность будет наименьшей." + ], + "metadata": { + "id": "4rJ0UYZmQym6" + } + }, + { + "cell_type": "markdown", + "source": [ + "### Улучшение бейзлайна: Добавление степеней" + ], + "metadata": { + "id": "VvAmfezoNIrN" + } + }, + { + "cell_type": "markdown", + "source": [ + "На прошлом шаге была выдвинута гипотеза, что столь низкие показатели метрики $R ^ 2$ были обусловлены недостаточным количеством входной информации. Попробуем расширить входные признаки, воспользовавшись feature engineering.\n", + "\n", + "При таком подходе мы пытаемся обогатить входные признаки через какие-нибудь функции (в основном, они нелинейные. В противном случае толку от дополнительных признаков мало).\n", + "\n", + "Попробуем добавить кроме исходного входного признака значения переменной $x$ также значения ее квадрата $x ^ 2$ и константу $1$ для воозможности смещения значений." + ], + "metadata": { + "id": "xKomT0x1RDbK" + } + }, + { + "cell_type": "code", + "source": [ + "X, y = dataset[:, 0], dataset[:, 1]\n", + "X = np.array([\n", + " [x, x ** 2, 1]\n", + " for x in X\n", + "], dtype=np.float64)\n", + "\n", + "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(\n", + " X, y,\n", + " test_size=0.2,\n", + " random_state=RANDOM_SEED,\n", + ")\n", + "\n", + "model = sklearn.linear_model.LinearRegression()\n", + "model.fit(X_train, y_train)\n", + "print('R2 score:', sklearn.metrics.r2_score(y_test, model.predict(X_test)))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "J1qwQySINKbV", + "outputId": "de271685-3a1d-4bf2-d924-c5ac26f00e8e" + }, + "execution_count": 11, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "R2 score: 0.25375726131861287\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Как видим, гипотеза подтвердилась! Показатель метрики $R ^ 2$ стал значительно выше в сравнении с прошлыми результатами. Однако, показатель метрики все еще далек от идеала (модели, которые хорошо решают задачу регрессии, обычно имеют показатели данной метрики $\\ge 90\\%$)" + ], + "metadata": { + "id": "2gT2dWzHRuWT" + } + }, + { + "cell_type": "code", + "source": [ + "plt.figure(figsize=(8, 5))\n", + "plt.scatter(X[:, 0], y, label=\"Исходный датасет\")\n", + "plt.scatter(X[:, 0], model.predict(X), label=\"Предсказанные значения\")\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$y = f(x)$\")\n", + "plt.legend()\n", + "plt.grid(True, alpha=0.4)\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 465 + }, + "id": "DdxM7zeLNp7D", + "outputId": "9a4b5c8a-8e65-4b64-e2c5-0dbab3ddcda5" + }, + "execution_count": 13, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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gmYiomjNXkk4CAFYUXhIA5Cjs30KaiMiZMHgmIqrm0jJzK6w46xIA3C4ss/r89mwhTUTkbBg8ExFVc/YObu3VQpqIyBkxeCYiqubsFdxKAMhl9mshTUTkjBg8ExFVcx2ighAWYHlJOlM055rWN6ZGNPSoToYPHw6JRGL03+3btx09RCKn5rLBs1KpxPTp0xEVFQVvb280btwYc+bMgW63cUEQMGPGDISFhcHb2xs9e/bE2bNn9c6Tm5uLwYMHQyaTITAwECNHjsSdO3f0jvnrr7/QrVs3eHl5ISIiAgsWLKiS50hEZAtuUglm9osFgAoBtObrQB93k8F1+fg4VOaFwZ0ikRhXvVpI1xRJSUnIzs7W+/fjjz86elhELsFlg+f58+dj6dKl+PTTT3Hq1CnMnz8fCxYswCeffKI9ZsGCBfj444+xbNkyHDx4EL6+vkhMTERR0f38v8GDB+PkyZPYtm0bNm/ejN27d2P06NHa+xUKBXr37o0GDRrg8OHD+OCDDzBr1ix8+eWXVfp8iYgqI6l5GJYOiYc8QD+FQx7ghWVD4vH+Uy0AGA6uJQA+HRSPNaM6YcnA1lgzqhN2vfkw4sKdp32yS1Mpgcw9wIn/qf+rUtr9kp6enpDL5Xr/yref/uabbxAYGIgNGzYgOjoaXl5eSExMxKVLl/SO+/nnnxEfHw8vLy80atQIs2fPRlmZ/gbUWbNmQSqVwsvLC1KpFBKJBP3799c7Zt++fejevTt8fHxQu3ZtJCYm4tatWwCA7t27Y/z48dpj//Of/yAwMBBHjhwBoF5QGzlypHZBrWnTpliyZIne+adMmYLw8HB4eHigXr16mDx5MlQqlejHDx8+vMKYNXOk+zxbt26td8yuXbv0VvTLP0bXsWPHIJFIcOHCBe1te/fuRbdu3eDt7Y2IiAi8+uqrKCgoMPh4AFiyZAkiIyPh6emJ0NBQvPTSS7h79y4A4MKFC5BIJDh27JjeYxo2bIjFixdrv/7oo4/QokUL+Pr6IiIiAq+88orewqKhuZBIJNiwYYP260uXLmHAgAEIDAxEUFAQnnjiCb3nJXY+O3TooP26pKQETZo0qfAJyYoVK9C0aVN4eHhoP0HR/XmxNZdtkrJ//3488cQT6NOnDwD1N37NmjVIS0sDoF51Xrx4MaZNm4YnnngCAPDtt98iNDQUGzZswMCBA3Hq1CmkpKTg0KFDaNeuHQDgk08+wWOPPYaFCxciPDwcq1atQklJCb7++mt4eHggLi4Ox44dw0cffaQXZBMRObuk5mHoFStHWmYuruUXIcRfna+sSbtYOiS+QhMVeYAXZvaLRVJz/RVmTdBBlZSxEUiZDCiu3L9NFg4kzQdiH3fcuO65e/cu3n33XXz77bfw8PDAK6+8goEDB2Lfvn0AgD179mDo0KH4+OOP0a1bN5w/f177t3HmzJl654qLi8OWLVvg4eGB8ePHo7i4WHvfsWPH8Mgjj2DEiBFYsmQJatWqhd9//x1KZcU3EuvWrcOECROwZcsWxMfHA1D/PNavXx8//PAD6tSpg/3792P06NEICwvDgAEDAAC9e/fGgAEDULduXZw8eRLPP/884uLiMHToUFGPd4Tz588jKSkJc+fOxddff43r169j7NixGDt2LFasWGHwMR06dMAPP/yAsLAwXLx4EUOHDsXChQsxY8YM0deVSqX4+OOPERUVhX/++QevvPIKJk2ahM8//1zU40tLS5GYmIiEhATs2bMHtWrVwty5c5GUlIS//voLHh4eosei69NPP8XVq1f1bvv777/x0ksvYd68eRg0aBA8PDzw1FNPWXV+sVw2eO7cuTO+/PJLnDlzBg888ACOHz+OvXv34qOPPgIAZGZmIicnBz179tQ+JiAgAB07dkRqaioGDhyI1NRUBAYGagNnAOjZsyekUikOHjyIJ598EqmpqXjwwQf1vtGJiYmYP38+bt26hdq1a1cYW3Fxsd4vBYVCAUD94q6KPzia6/CPW0WcG8M4L4ZVx3mRAOgYpft7S4DqXpOT3rGheKRZCA5l5uL6nSIE+3mh/b3guvwcVMe5sYRKpYIgCNp/hhi7XevURmDdMACC3oq/oMgG1g0FBvwXiLFfAF1+fJqvdZ9XaWkpPvnkE3Ts2BGAemUwNjYWBw8eRIcOHTB79mxMnjwZQ4cOBQBERUXhnXfeweTJk/WCtaKiInh7e0Mul8PDwwPe3t4oLi7WXnPBggVo164dPvvsM+1jYmNjK4zrl19+wYsvvoh169ahW7du2vtq1aqFWbNmaR/bsGFD7N+/H+vWrcOzzz4LAHj44Ye195eVlcHb2xtlZWUQBEHU4w3Nm+7YDP3X2Lwamn9Dx86bNw/PP/88XnvtNQBAkyZNsGTJEnTv3h2ff/45vLwqbgbu1KmT9v89PT0hk8m0z7P8+ctfW3Ob5noA0KBBA8yZMwdjxozRfn+8vLxQWFho9Bxr166FSqXC8uXLIZGof7q//vpr1K5dG7///jt69+4taj513bx5E3PnzsWkSZMwY8YM7bWOHz8ONzc3TJo0SXush4eH0dem5nZDv7/E/j5z2eB5ypQpUCgUaNasGdzc3KBUKvHuu+9i8ODBAICcnBwAQGhoqN7jQkNDtffl5OQgJCRE7/5atWohKChI75ioqKgK59DcZyh4fu+99zB79uwKt1+6dAn+/v7WPF2LCIKAW7duaT+6oPs4N4ZxXgyrqfMS7g6E1waAAlz+1/DHwzV1bjSUSiWUSiVKS0shlepnQJZPWTBIpYTHr1NQPnAGAAkE9a2/TkFJVC9A6mazcQPqsatUKpSUlOjdXlqq7jZZUlKCkpISlJWVoVatWmjVqpX22EaNGiEwMBAnTpxA69atcfz4cezbtw/z5s3TO39RURFu374NHx8fAMD169fh5+ennZvyYzh69CieeuqpCmPSUKlUSEtLw/Lly+Hn54c2bdpUOHbZsmX473//i0uXLqGwsBAlJSV6YwfUKZ/vv/8+CgsLMWbMGAwcOFB7v7nHK5VKbN68We/veFlZGby8vPSOOXHihN4xmtVz3XnNy8uDv78/pFIpQkJC0KdPH7z77rsVvgfHjx/HiRMnsHr1au35NIHfmTNn0KxZM4PztWbNGiQnJ+Pu3bt48sknMWHCBO05AaBLly56P7d3796FUqnU3r9jxw588MEHOHPmDBQKBcrKyvS+pzExMVizZg1Onz6tFyOVlZWhpKQER48exblz5yCTyfTGVVRUhDNnzqB79+6i51MQBJSUlGDWrFl46KGHtG/kNM+nfv36KC0txZo1a/DUU09BIpFoA2NDP0+lpaVQKpXIzs6Gm5v+ays/P9/gfJbnssHzunXrsGrVKqxevVqbSjF+/HiEh4dj2LBhDh3bW2+9hYkTJ2q/VigUiIiIQERERIUfJHvQrIhERERU+KVe03FuDOO8GObK86JUCQZXkG3FlefGFoqKinDhwgW4u7sb/Aja7MfSF/ZAkn/F6N0SCED+FXjk/Ak07FbZ4epxc3ODVCqtMEZ3d3WLdg8PD3h4eKBWrVrar8t/j2vVqgUPDw/cuXMHs2bNMvgxuUwm0z7u4sWLaNSokfZx5cfg4+MDNzc3o/MmlUpx4MABfP755/jxxx/x+uuv6wWUa9euxZQpU7Bw4UIkJCTA398fH3zwAdLS0vTOmZycjGeffRaHDx/GhAkT8Mwzz+Dhhx8W9Xg3Nzc8/PDDeqkLP/30E9577z29Y5o2bYqff/5Ze8zBgwfxwgsv6M2rv78/Dh8+DEEQkJGRgeHDh6N+/fraT8s1xxYUFGD06NF49dVXK8xJZGSk0fl66qmnkJCQgL///htjx47Fli1bMHjwYO3xa9euRUxMjPb4hx9+WDv/Fy5cwFNPPYWXX34Z8+bNQ1BQEPbu3YuXXnpJO7ZRo0Zh06ZNiImJga+vr/Y8mu/v3bt30bZtW6xcubLC2IKDg7U/A2LmUyKR4OLFi1ixYgWOHj2Kf//9V2+OOnfujNmzZ2P06NF48cUX4e7ujsLCQrRp08bg/KhUKri5uSEsLKzCyr0mU8Aclw2e33zzTUyZMgUDBw4EALRo0QIXL17Ee++9h2HDhkEulwMArl69irCw+7l6V69e1Sbzy+VyXLt2Te+8ZWVlyM3N1T5eLpdXyK/RfK05pjxPT094enpWuF0qlVbZHxnNtWriHzVzODeGcV4Mc8V5SUnPrpC7HGYgd1mpEozmP4vhinNjK5pNb+VX3nU/Jja5In/nmvH7dEjuXAPstLJffnyar3WfV1lZGQ4fPqzdtHX69Gncvn0bsbGxkEgkiI+Px5kzZxAdHW30OkVFRUhLS8OQIUOMjqFly5bYuXMn3nnnHaPneeGFFzBmzBg89thjaN68OTZs2IAnn3wSgHofVOfOnZGcnKw9/p9//qnwPOvUqYM6deogJiYGP/74I3766Sf06NFD9ON9fX31nqvmk2jdufPw8NA75vLlyxXmVSqVao+Jjo7GI488guPHj6NXr156x8bHx+PUqVMm59cQmUwGmUyGpk2bYteuXVi7di2GDBmiHWdkZKTeOWvVqqW95pEjR6BSqfDRRx9pX9s//PCD3rh8fHywfft2XL16VbtaGx0drb2/bdu2WLduHUJDQ00uGpqbT40pU6bgpZdeQnR0dIX5BNRpJt999x1GjhyJZ555BoMHDzb6qZju96D87y6xv8tc9jfe3bt3KzxJNzc3bb5KVFQU5HI5duzYob1foVDg4MGDSEhIAAAkJCTg9u3bOHz4sPaYnTt3QqVSaT8WSEhIwO7du7UfpQDAtm3b0LRpU4MpG0REjpSSno0xK49UaMedk1eEMSuPICU9W3tc1/k7MWj5Aby29hgGLT+ArvN3au8nO/MLNX+MJcfZibu7O8aNG4eDBw/i8OHDGD58ODp16qQNpmfMmIFvv/0Ws2fPxsmTJ3Hq1CmsXbsW06ZNAwDcuXNHm/vctWtX5OTkICcnB4WFhSguLkZeXh4A9Se2hw4dwiuvvIK//voLf//9N5YuXYobN25ox6KpBtKgQQN88MEHGDNmDG7evAlAHbj9+eef2Lp1K86cOYPp06fj0KFDes/l888/x8mTJ3HhwgWsXLkS27ZtQ5s2bUQ/3taKiopQWFiIw4cPY//+/YiLi6twzOTJk7F//36MHTsWx44dw9mzZ/Hzzz9j7NixRs+7YsUKHD9+HBcvXsTGjRuxZs0a7fMUo0mTJtpc93/++Qffffcdli1bZvDY0NBQNGnSBE2aNNG7ffDgwahbty6eeOIJ7NmzB5mZmdi1axdeffVV7cqxWOfPn8euXbuMbngUBAFDhw5FfHw8pkyZgiZNmsDb29uia1jKZYPnfv364d1338WWLVtw4cIFrF+/Hh999JH2XaimTMncuXOxceNGnDhxAkOHDkV4eLi2NEpMTAySkpIwatQopKWlYd++fRg7diwGDhyI8PBwAMDzzz8PDw8PjBw5EidPnsT333+PJUuW6KVlEBE5A6VKwOxNGTC0TU1z2+xNGfjlL3EBNtlRg87qqhpGq2tLAFk99XEO5OPjg8mTJ+P5559Hly5d4Ofnh++//157f2JiIjZv3ozffvsN7du3R6dOnbBo0SI0aNAAALBw4UJ88MEHyM/PR3R0NBo2bIjw8HCsW7cOKSkp2o1pDzzwAH777TccP34cHTp0QEJCAn7++Wdt6kh5//d//4fmzZtj3Lhx2q+feuopPPfcc+jYsSNu3ryJV155Re8xW7ZsQffu3dGsWTPMnj0bU6dOxYgRI0Q/3pby8vLg7e0NX19f9OvXD48//rjBuKJly5b4448/cObMGXTr1g1t2rTBjBkztDGKIampqUhKSsIDDzyAcePGYfDgwZg+fbrosbVq1QofffQR5s+fj+bNm2PVqlV47733LHp+Pj4+2L17NyIjI/HUU08hJiYGI0eORFFRkcXpqwUFBZg6dWqFUooa77//Ps6ePYuvvvrKovNWhkQwux3YOeXn52P69OlYv349rl27hvDwcAwaNAgzZszQ5rgIgoCZM2fiyy+/xO3bt9G1a1d8/vnneOCBB7Tnyc3NxdixY7Fp0yZIpVI8/fTT+Pjjj+Hn56c95q+//kJycjIOHTqEunXrYty4cZg8ebLosSoUCgQEBCAvL6/Kcp6zsrIQGRlZIz9ONYVzYxjnxTBXm5fU8zcxaPkBs8cF+Xogt8DwxiwJ1OXp9k7uYTKFw9XmxtaKioqQmZmJqKgovbxJzeYmTb1ZkzI2qqtqqB+pc8e9xw341qHl6r755huMHz++Uh0HNRUsZs2aVWFuNmzYgA0bNuCbb76xyXhdlUU/MzWMPebG2GsXEB+vuWzOs7+/PxYvXqxX1Ls8iUSCd955x2QOVVBQkN6mA0NatmyJPXv2WDtUIqIqcS2/yPxBgNHAGVCHcNl5RUjLzEVC4zo2GhkZFPu4OkA2WOf5faeo81xZugtR5Xl5eSEggI12yPW4bPBMRET6Qvwr1ny1lthAnCop9nGgWR/g4n7gzlV1jnODzjYvT+cob7zxhtH7kpKSkJSUVIWjIbKNmvdZGxFRNdUhKghhAV6msmgR5Osu6ly2DMTJDKkbENUNaPGM+r9OEjgPHz68UikbRNUVg2ciomrCTSrBzH7qrmwVG2+ozX2iudkAOyxAXbaOiIgqYvBMRFSNJDUPw9Ih8ZAH6K8cywO8sHRIPB5rGW42wJ7ZL9amDVWIiKoT5jwTEVUzSc3D0CtWbrQBiibALt9IRW6gkQqZ5qIFq4hqLFu8Zhk8ExFVQ25SiclqGeYCbDJN08r67t27dm/IQES2c/fuXQD3X8PWYPBMRFRDmQuwyTg3NzcEBgbi2jV1m20fHx9IJBIIgoDS0lKoVCrW7C2Hc2MY58U4W86NIAi4e/curl27hsDAQLi5Wb8xl8EzERGRFeRyOQBoA2hA/QdaqVTCzc2NgVA5nBvDOC/G2WNuAgMDta9dazF4JiJyYUqVwNQLB5FIJAgLC0NISAhKS0sBqDsvZmdnIywsrEZ2XjSFc2MY58U4W8+Nu7t7pVacNRg8ExG5qJT07Aqb/sK46a/Kubm5af8gq1QquLm5wcvLi4FQOZwbwzgvxjnr3DjPSIiISLSU9GyMWXlEL3AGgJy8IoxZeQQp6dkOGhkRUfXG4JmIyMUoVQJmb8qAoYJLmttmb8qAUsUyakREtsbgmYjIxaRl5lZYcdYlAMjOK0JaZm7VDYqIqIZg8ExE5GKu5RsPnK05joiIxOOGQSIiF6GprHH26h1Rx4f4e5k/iIiILMLgmYjIBRiqrGGMBOpW2x2iguw/MCKiGobBMxGRk9NU1hCz/U9T4Xlmv1jWeyYisgMGz0RETsxUZQ1D5KzzTERkVwyeiYicmLnKGhpjH26MLk2C2WGQiMjOGDwTETkBY222xVbMiA71R0LjOnYeJRERMXgmInIwU222xVbMYGUNIqKqwTrPREQOZK7N9q2CEoQFeMFUIkaQrzvaNqht34ESEREABs9ERA4jps32nC0ZmN4nBgCMBtC5BaV46IPfkZKebY9hEhGRDgbPREQOIrbNdm1fTywdEg95gPHUDM1KNQNoIiL7YvBMROQglrTZTmoehj/efBhBvh4Gj9GsVM/elAGlSmxhOyIishSDZyIiBxG7ya+unycA4PDFW8gtKDF6nGalOi0z1xbDIyIiAxg8ExE5SIeoILObAQHg9XXHkJKebdFKNRER2QeDZyIiB3GTSjCzXywA45sBAeCqohhjVh7BhRsFos7LsnVERPbD4JmIyIGSmodh6ZB4hMqMB7yaDOY1aVmQy4yvVEugrg/dISrI1sMkIqJ7GDwTETlYUvMwfPhsK5PHCAByFMUY1CESQMWVas3XM/vFsj03EZEdMXgmInICNwqKRR3XsK6PwbJ18gAvLB0Sj6TmYfYYHhER3cP23ERETsCSNtwJjeugV6wcaZm5uJZfhBB/daoGV5yJiOyPwTMRkRPQVN7IySsy2HFQAvXqsiaf2U0qQULjOlU6RiIiYtoGEZFTMFV5g/nMRETOg8EzEZGT0FTesHU+s1IlIPX8Tfx87DJSz99kB0Iiokpg2gYRkRNJah5m03zmlPRszN6Ugey8+41TwgK8MLNfLDcXEhFZgcEzEZEVlCrBbhv2bJXPnJKejTErj1TIoc7JK8KYlUdYnYOIyAoMnomILOQKq7lKlYDZmzIMbj4UoM6jnr0pA71i5cyjJiKyAHOeiYgsoFnN1Q2cgfuruSnp2Q4amX5u8zf7MiuMUZcAIDuvCGmZuVU3QCKiaoArz0REIjnzaq6h1XAxruVbdjwRUU3HlWciIpHSMnOdcjXX2Gq4GGKbsxARkRpXnomIRBK7SluVq7mmVsNNKd90hYiIxGHwTEQkkiUttG3FXFUPc6vhhrDpChGR9Rg8ExGJZGkL7coSU9XDmlVuuZNVBiEiciUMnomIRNK00B6z8ggkgF4AbevVXLE1msWuck/vE4O6/p42r0lNRFTTcMMgEZEFjLXQDvL1wItdGiLA26PS7a/NVfUA1FU9lCpBuxpuLBSWQL1aPbxLFJ5oXQ8JjeswcCYiqgQGz0REFkpqHoa9k3tgzahOGNmlIYJ83XGzoARf77uAQcsPoOv8nZWq92xJVQ/NajiACgE0c5uJiGyPwTMRkRXcpBLkFaoD5tyCUr37KtswxdKqHsZWw+UBXmzBTURkY8x5JiKygj0bplhT1SOpeRh6xcpNVuYgIqLKc+mV58uXL2PIkCGoU6cOvL290aJFC/z555/a+wVBwIwZMxAWFgZvb2/07NkTZ8+e1TtHbm4uBg8eDJlMhsDAQIwcORJ37tzRO+avv/5Ct27d4OXlhYiICCxYsKBKnh8ROS9bNEzRbaedev6mNldabB5z+aoeblIJEhrXYW4zEZEduezK861bt9ClSxc8/PDD+PXXXxEcHIyzZ8+idu3a2mMWLFiAjz/+GP/9738RFRWF6dOnIzExERkZGfDyUq/YDB48GNnZ2di2bRtKS0vx4osvYvTo0Vi9ejUAQKFQoHfv3ujZsyeWLVuGEydOYMSIEQgMDMTo0aMd8tyJyPEq2zDFXBm6qqrqQURElnHZ4Hn+/PmIiIjAihUrtLdFRUVp/18QBCxevBjTpk3DE088AQD49ttvERoaig0bNmDgwIE4deoUUlJScOjQIbRr1w4A8Mknn+Cxxx7DwoULER4ejlWrVqGkpARff/01PDw8EBcXh2PHjuGjjz5i8ExUg1WmYYrYMnRLh8RXCLBZo5mIyLFcNnjeuHEjEhMT8eyzz+KPP/5AvXr18Morr2DUqFEAgMzMTOTk5KBnz57axwQEBKBjx45ITU3FwIEDkZqaisDAQG3gDAA9e/aEVCrFwYMH8eSTTyI1NRUPPvggPDw8tMckJiZi/vz5uHXrlt5Kt0ZxcTGKi4u1XysUCgCASqWCSqWy+VyUp7lOVVzL1XBuDOO8GGZqXto1CES9AE9cVRhvmBIq80K7BoF6j1eqBMzZdBJSieFydhIAczadxCPNQtA7NhSPNAvBocxcXL9ThGA/L7S/l8fs6O8Vf2YM47wYx7kxjPNiXFXPjdjruGzw/M8//2Dp0qWYOHEipk6dikOHDuHVV1+Fh4cHhg0bhpycHABAaGio3uNCQ0O19+Xk5CAkJETv/lq1aiEoKEjvGN0Vbd1z5uTkGAye33vvPcyePbvC7ZcuXYK/v7+Vz1g8QRBw69YtSCQSSCT8WFcX58Ywzoth5uZl6kPBWHUgS32szu2aIwd3Csblfy/pPeaf6wWI9CxEZLCpKxdiz9G/0SjYFwAQ7g6E1waAAlz+t8Dap2NT/JkxjPNiHOfGMM6LcVU9N/n5+aKOc9ngWaVSoV27dpg3bx4AoE2bNkhPT8eyZcswbNgwh47trbfewsSJE7VfKxQKREREICIiAjKZzO7XV6lUEAQBERERkEpdek+ozXFuDOO8GGZuXiIjAal/XczdfAo5Cp3UCpkXpvWNQWLc/dQKpUrAocxc/HElH2nXzf8RGFhLhsjIerZ5InbAnxnDOC/GcW4M47wYV9Vzo8kUMMdlg+ewsDDExsbq3RYTE4Mff/wRACCXywEAV69eRVjY/T9gV69eRevWrbXHXLt2Te8cZWVlyM3N1T5eLpfj6tWresdovtYcU56npyc8PT0r3C6VSqvshaG5Fl+IFXFuDOO8GGZuXh5tUQ+948JNloiruDnQfPAcIvNx+u8Ff2YM47wYx7kxjPNiXFXOjdhruOx3qUuXLjh9+rTebWfOnEGDBg0AqDcPyuVy7NixQ3u/QqHAwYMHkZCQAABISEjA7du3cfjwYe0xO3fuhEqlQseOHbXH7N69G6Wl95sgbNu2DU2bNjWYskFENY+pEnGazYGmytrpMlaGjoiInIPLBs8TJkzAgQMHMG/ePJw7dw6rV6/Gl19+ieTkZACARCLB+PHjMXfuXGzcuBEnTpzA0KFDER4ejv79+wNQr1QnJSVh1KhRSEtLw759+zB27FgMHDgQ4eHhAIDnn38eHh4eGDlyJE6ePInvv/8eS5Ys0UvLICLS0K3dvO/sDczaaLiRiiEsQ0dE5PxcNm2jffv2WL9+Pd566y288847iIqKwuLFizF48GDtMZMmTUJBQQFGjx6N27dvo2vXrkhJSdHWeAaAVatWYezYsXjkkUcglUrx9NNP4+OPP9beHxAQgN9++w3Jyclo27Yt6tatixkzZrBMHRFVYKh2syVYho6IyPm5bPAMAH379kXfvn2N3i+RSPDOO+/gnXfeMXpMUFCQtiGKMS1btsSePXusHicRVX/GajeLMTShAR5tHsZ22kRELsClg2ciImegVAmYvUl8ekZ5iXFyJDSuY9MxERGRfbhszjMRkbNIy8y1OlUDAF5fdwwp6dk2HBEREdkLg2ciokq6lm994AwAVxXFGLPyCANoIiIXwOCZiKiSQvy9zB9kgibdY/amDChV1iZ/EBFRVWDwTERUSR2ighAW4CWi9YlxAoDsvCKkZebaalhERGQHDJ6JiCrJTSrBzH6x5g8UobIpIEREZF8MnomIbCCpeRiWDolHWEDlUjgqmwJCRET2xVJ1REQ2ktQ8DL1i5UjLzMW2jBxsOHYFuQUl2vulEsBYSrME6iYpbMtNROTcGDwTEd2jVAlIy8zFtfwihPh7oV2DQIvP4SaVIKFxHSQ0roO3+8Tqne9WQTGSVx8FAL2a0GzLTUTkOhg8ExHBcGvtegGemPpQMCIjrTunJpDWtVQqqXAdtuUmInIdDJ6JqMYz1lr7qqIIqw5kQepfF4+2qGeTa+mmdmhWpNmWm4jIdTB4JqIazVRrbc1tczefQu+4cACwSdBraEWaiIhcA4NnIqrRzLXWFgDkKIrw6c6zWHvokt6xYUy3ICKqcViqjohqNLF1lRdtP1shyM7JK2JbbSKiGobBMxHVaJWpq8y22kRENQ+DZyKq0SrbWptttYmIahYGz0RUo+m21i4fQFsSULOtNhFRzcDgmYhqNKVKQIC3B0Z0aYjavu5694XKvNAzJlTUedhWm4ioZmC1DSKqsQw1Rgny9UD/1uHoFStHuwaBuHQpC18fU+BKXrHBcnZsq01EVLNw5ZmIaiRNY5TyFTRuFZRgxb4LyCssgZtUAqlEgml9YwAYT+tgW20iopqDwTMR1ThiGqPoVtBIjAvD0iHxkAfop2bIA7ywdEg86zwTEdUgTNsgohpHTGOU7LwiHMrMRfi9NGi21SYiIoDBMxHVQGIrY1y/U4Tw2ve/ZlttIiJi2gYR1ThiK2ME+7GCBhER6WPwTEQ1jrnGKBIAYQFeaM8KGkREVA6DZyKqccQ0RmEFDSIiMoTBMxHVSEnNxVfQUKoEpJ6/iZ+PXUbq+ZvaKhxERFTzcMMgEdVYYiponLySh8FrzuFyXrH2trAAL8zsF8sSdURENRCDZyKq0UxV0Nh6MhurDmQhRyGBboJHTl4Rxqw8whrPREQ1ENM2iIgMUKoEzN18SnQjFSIiqhkYPBMRGZCWmYschflGKmmZuVU3KCIicjgGz0REBohtpCL2OCIiqh4YPBMRGSC2kYrY44iIqHpg8ExEZECHqCDIZeYbqXRgIxUiohqFwTMRkQFuUgmm9Y0BwEYqRER0H0vVEREZkRgXBlV+JC7+cV2vzrOcdZ6JiGosBs9ERCbEhQdg15vN8efF20YbqRARUc3B4JmIyAxTjVSIiKhmYc4zEREREZFIDJ6JiIiIiERi2gYR1ThKlYC0zFzmMBMRkcUYPBNRjZKSno3ZmzKQnXe/M2AYq2cQEZFITNsgohojJT0bY1Ye0QucASAnrwhjVh5BSnq2g0ZGRESugsEzEdUISpWA2ZsyIBi4T3Pb7E0ZUKoMHUFERKTG4JmIaoS0zNwKK866BADZeUVIy8wFoA62D5y/ieOXbuPA+ZsMqomICABznomohriWbzxwLn+cJi/6mqIQHYIFpF3/FyEyb+ZFExERV56JqHpQqgSknr+Jn49dRqqBleIQfy9R57lw4y7zoomIyCiuPBORyxNTQaNDVBDCAryQk1dkMO9ZAiBU5ok1aVlG86IlUOdF94qVs7QdEVENxZVnInJpYitouEklmNkvFoA6CNal+XpQh0jkKMTnRRMRUc1TbYLn999/HxKJBOPHj9feVlRUhOTkZNSpUwd+fn54+umncfXqVb3HZWVloU+fPvDx8UFISAjefPNNlJWV6R2za9cuxMfHw9PTE02aNME333xTBc+IiMyxtIJGUvMwLB0SD3mAfgqHPMALS4fEo2FdX1HXFZs/TURE1U+1SNs4dOgQvvjiC7Rs2VLv9gkTJmDLli344YcfEBAQgLFjx+Kpp57Cvn37AABKpRJ9+vSBXC7H/v37kZ2djaFDh8Ld3R3z5s0DAGRmZqJPnz54+eWXsWrVKuzYsQMvvfQSwsLCkJiYWOXPlYjuO/DPTdEVNDpEBSEtMxfFZSosfKYVIAFu3CnW6zCYev6mqOuKzZ8mIqLqx+WD5zt37mDw4MFYvnw55s6dq709Ly8PX331FVavXo0ePXoAAFasWIGYmBgcOHAAnTp1wm+//YaMjAxs374doaGhaN26NebMmYPJkydj1qxZ8PDwwLJlyxAVFYUPP/wQABATE4O9e/di0aJFDJ6JHCglPRtTfjwh6tjtGTmYuO6YwZzohMZ1tLeJyYuWB6iDbSIiqplcPm0jOTkZffr0Qc+ePfVuP3z4MEpLS/Vub9asGSIjI5GamgoASE1NRYsWLRAaGqo9JjExEQqFAidPntQeU/7ciYmJ2nMQUdXT5DnfLiwVdfxX+y6Iqp4hJi96Zr9YbhYkIqrBXHrlee3atThy5AgOHTpU4b6cnBx4eHggMDBQ7/bQ0FDk5ORoj9ENnDX3a+4zdYxCoUBhYSG8vb0rXLu4uBjFxcXarxUKBQBApVJBpVJZ+Cwtp7lOVVzL1XBuDHOleVGqBMzZdBJSifmmJRIAEglgrL+JBMCcTSfxSLMQbUDcOzYUnw9ujbmbT+F6fiGkEOAmAeQyL0zrG4PesaEuMU/25ko/M1WJ82Ic58YwzotxVT03Yq/jssHzpUuX8Nprr2Hbtm3w8nKu/MP33nsPs2fPrnD7pUuX4O/vb/frC4KAW7duQSKRQCLhCpkuzo1hrjQv/1wvQKRnISKDbXXGQuw5+jcaBd/fLBjjD3w3sDEyr9/BnbzbGBEQiKhgP0glpcjKyrLVhV2aK/3MVCXOi3GcG8M4L8ZV9dzk5+eLOs5lg+fDhw/j2rVriI+P196mVCqxe/dufPrpp9i6dStKSkpw+/ZtvdXnq1evQi6XAwDkcjnS0tL0zqupxqF7TPkKHVevXoVMJjO46gwAb731FiZOnKj9WqFQICIiAhEREZDJZNY/aZFUKhUEQUBERASkUpfPzLEpzo1hrjQvx29dRtp1879EA33c0b9VPXyTesHssQNryRAZWa/C7ZERKmRlZSEyMtLp56WqudLPTFXivBjHuTGM82JcVc+NJlPAHJcNnh955BGcOKG/WejFF19Es2bNMHnyZERERMDd3R07duzA008/DQA4ffo0srKykJCQAABISEjAu+++i2vXriEkJAQAsG3bNshkMsTGxmqP+eWXX/Sus23bNu05DPH09ISnp2eF26VSaZW9MDTX4guxIs6NYc4yL0qVgLTMXFzLL9KrhKERIvOBUjAfPH88sC2kUgm+2n/R7LEhMh+jz9tZ5sUZcW4M47wYx7kxjPNiXFXOjdhruGzw7O/vj+bNm+vd5uvrizp16mhvHzlyJCZOnIigoCDIZDKMGzcOCQkJ6NSpEwCgd+/eiI2NxQsvvIAFCxYgJycH06ZNQ3Jysjb4ffnll/Hpp59i0qRJGDFiBHbu3Il169Zhy5YtVfuEiWoAW3UKlAd4odO9KhqsnkFERLZUrd/iLFq0CH379sXTTz+NBx98EHK5HD/99JP2fjc3N2zevBlubm5ISEjAkCFDMHToULzzzjvaY6KiorBlyxZs27YNrVq1wocffoj//Oc/LFNHZGO27BSoqYjB6hlERGRrLrvybMiuXbv0vvby8sJnn32Gzz77zOhjGjRoUCEto7zu3bvj6NGjthgiERlgrlOgBOpOgb1i5XCTSrSdAsuvUsvLrVIDsOhYIiIic6pV8ExEriktM1d0p0BNU5Ok5mHoFSs3mB9dPm+6V6zc6LFERESWYPBMRA53Ld944Kzr13upG5rA100q0esQCIjLmyYiIrIWg2cicrgQf3G12r9NvYhvUy8iyNcdT7auh56xcr0VZE3edPn0j+y8Iry88ggm9IzG2B7RXHEmIiKrVWrDYGlpKS5duoTTp08jNzfXVmMiohpGU0FDbEibW1CKr/ZdwKDlB9B1/k6kpGebzJvWWLT9LLq8v1OvJTcREZElLA6e8/PzsXTpUjz00EOQyWRo2LAhYmJiEBwcjAYNGmDUqFEG22UTERljqiqGOZpqHJ/uPGcyb1p7vEK/egcREZElLAqeP/roIzRs2BArVqxAz549sWHDBhw7dgxnzpxBamoqZs6cibKyMvTu3RtJSUk4e/asvcZNRNWMpiqGPEBcCoeGZqV5xf5Mix43e1MGlCpT69REREQVWZTzfOjQIezevRtxcXEG7+/QoQNGjBiBZcuWYcWKFdizZw+io6NtMlAiqv50K2j8mp6Nb1PNdwcE1AH07buloq9jqHoHERGRGBYFz2vWrBF1nKenJ15++WWrBkRErs9ci21TdCtoiA2eNQK93ZFXWGoy71mX2CofREREGlZX28jPz4e/v78tx0JE1YCtSsWZa8NtyItdGmLxdvHpYmKrfBAREWlYXW2jW7duyMnJseVYiMjFiW2xLYbuJkJzJFAH6GN7RKvzpmWeoo7vEBUkejxERERAJYLnNm3aoGPHjvj777/1bj927Bgee+yxSg+MiFyLuRbbgOWb9DSbCMNMbCLUJIPM7Berbd29b8ojmNDzAVHHExERWcLq4HnFihUYPnw4unbtir179+LMmTMYMGAA2rZtCzc3N1uOkYhcgCUtti2R1DwMeyf3wJpRnTCiS0ME+Xro3S8P8MLSIfF6KSFuUgle6xmNZQYCb0PHExERiVWpDoOzZ8+Gp6cnevXqBaVSiUceeQSpqano0KGDrcZHRC5C7OY7azbpaTYRJjSug7f7xIrejKhbvcOazYtERETlWR08X716FfPmzcPy5csRGxuLv//+G8OHD2fgTFRDid18V9lNerrVOOxxPBERkSlWp21ERUVh9+7d+OGHH3D48GH8+OOPGD16ND744ANbjo+IXIS5FtvcpEdERNWB1cHz119/jaNHj6JPnz4AgKSkJPz+++9YtGgRkpOTbTZAInINplpsc5MeERFVF1YHzwMHDqxwW3x8PPbv34+dO3dWalBE5JqMtdjmJj0iIqouLMp5zsrKQmRkpMljGjZsiP379wMALl++jHr16lk/OiJyObbapFeZLoVERET2YlHw3L59e/Tv3x8vvfQS2rdvb/CYvLw8/O9//8OSJUswevRovPrqqzYZKBG5jspu0rNVl0IiIiJbsyh4PnXqFN5991306tULXl5eaNu2LcLDw+Hl5YVbt24hIyMDJ0+eRHx8PBYsWMBmKURkMU2XwvKtVDRdCpn+QUREjmRRzvP777+Pd999F9nZ2fjss88QHR2NGzdu4OzZswCAwYMH4/Dhw0hNTWXgTEQWs0eXQiIiIluyaOV58eLFeOONNxASEoJNmzbh888/h4+Pj73GRkQ1jCVdClm7mYiIHMGilefw8HAcPXoUAPDdd9+hoKDALoMioprJnl0KiYiIbMGi4Pn1119Hv3790K1bNwDAypUrkZaWhsLCQrsMjohqlqrqUkhERGQti4LncePG4c8//0RSUhIEQcBnn32Gzp07QyaTISYmBgMHDsT777+PX3/91V7jJaJqjF0KiYjI2VncJKVly5Z4++230bhxYxw4cAD5+fnYu3cvxo8fj9q1a+Pnn3/GgAED7DFWIqrm2KWQiIicnUUbBnVpKmwAQMeOHdGxY0ft14LAnfBEZJqxJiiaLoXl6zzLWeeZiIicgNXBsykSCVeFiMg4c01QbNWlkIiIyNbsEjwTERkjtglKZbsUEhER2YPFOc9ERNZiExQiInJ1lQqe//33X6hUqgr/T0RkiCVNUIiIiJxRpYLn2NhYXLhwocL/ExEZwiYoRETk6ioVPOtW1WCFDSIyR2xzk7q+nnYeCRERkXWY80xEVcZcExSN1384jpT07CoZExERkSUYPBORKEqVgNTzN/HzsctIPX/Tqk19ppqg6LqqUFfeYABNRETOhqXqiMgsc3WZLaFpgjJr40nkKIoNHiNAHVzP3pSBXrFy1ncmIiKnwZVnIjJJU5e5fJUMTV1mc6vDhlask5qH4cMBrU0+jpU3iIjIGXHlmYiMMleX2dzqsKkV6+IycaUtWXmDiIicCVeeicioytRlNrdifeFGgagxiK3QQUREVBUqFTxPnToVQUFBFf6fiKoHsau+OQr948R0ElyTlgW5zHjlDQnUq9Qdovh7hYiInEelgue33noLgYGBFf6fiFyXbo7yjXzDG/rKm7P5pF7us5gV6xxFMQZ1iARQsfKG5uuZ/WK5WZCIiJwKc56JSGvryWy8s/lvvcBXKgHMVaXLLSjFmJVHsHRIPJKah4lesW5Y1wdLh8RXyIuWW1nJg4iIyN4YPBMRAODklTy8tukSygT9lV5LyjlrNg+KzVMO8fdCQuM66BUrR1pmLq7lFyHEX52qwRVnIiJyRlYHz5cuXUJERIQtx0JEDqJUCdh0PNtgjrKGuRVozebBA+dvolPjOggL8EJOXpHBc0qgXl3W5DO7SSVIaFynEs+AiIioalid89ysWTPMmDEDd+/eteV4iMgBDmXmIq+w1OQxYlegk1cfwbaMHKOdBJnPTERErszq4Hnbtm3YunUroqOj8c0339hwSETVmy3aXNva9Tu2q6V8u1Cd/wwAS4fEQx6gn8IhD/DS5kYTERG5GqvTNjp37oyDBw/i22+/xdtvv41PPvkEixcvRrdu3Ww5PqJqxZZtrm0p2E9cjnKQrztuFZSaTO8A1CkcszdlYO/kHsxnJiKiaqXSTVKGDh2K06dPo0+fPnj00UfxzDPPIDMz0xZjI6pWKtvm2p7aRwUhwNvdbM3luU80F33O7LwifLrzrDaf+YnW9ZDQuA4DZyIicmk26zDYu3dvvPTSS1i/fj1iY2MxadIk3Llzx1anJ3JpYpqGzN6U4bAUDjepBP1aqVe+TeUoP9YyHEuHxCPQ213UeRdtP+vQNwVERES2ZnXwvGzZMowcORItW7ZEQEAAHnnkEezZswcvv/wylixZgj///BOxsbH4888/bTlerffeew/t27eHv78/QkJC0L9/f5w+fVrvmKKiIiQnJ6NOnTrw8/PD008/jatXr+odk5WVhT59+sDHxwchISF48803UVZWpnfMrl27EB8fD09PTzRp0oQ53mSxyrS5ripx4QH45Pk2ZnOUk5qH4bPB8aLP68g3BURERLZmdc7zu+++i44dO2Lo0KHo1KkT2rZtC29vb+39o0ePxrx58zB8+HCkp6fbZLC6/vjjDyQnJ6N9+/YoKyvD1KlT0bt3b2RkZMDX1xcAMGHCBGzZsgU//PADAgICMHbsWDz11FPYt28fAECpVKJPnz6Qy+XYv38/srOzMXToULi7u2PevHkAgMzMTPTp0wcvv/wyVq1ahR07duCll15CWFgYEhMTbf68qHoS2zRE7HH2khgXht5x4WZzlDs1UpeiM/WGQEPzpiChcR0oVYL5/GeVEri4H8jPBgquA77BgG8IIJGov/ape///fYMBQQDu3jB/+52rlp9PAHD1JlB2Qb0EX3DN8Dl0H2dsTLr/7xcKNOgMSN1s9r0jIqKqUak6z+aMHDkS06dPt/YSJqWkpOh9/c033yAkJASHDx/Ggw8+iLy8PHz11VdYvXo1evToAQBYsWIFYmJicODAAXTq1Am//fYbMjIysH37doSGhqJ169aYM2cOJk+ejFmzZsHDwwPLli1DVFQUPvzwQwBATEwM9u7di0WLFjF4JtEsaRpiD6KC1nvE1Fx2k0ows18sXr5XVaM8KVToIP0bIbiN65BBeb4Ix0/n4ssjd5B7twTBUOA6ZAjy8cDoeD+0ahqtDizPpAB/fQ/cvVnp52wTEjcgqBuQuwcQlLY9t09doMWzQGCEOuD2CzUcgDPQJiJyKnbtMBgSEoKdO3fa8xJaeXl5AICgIHXThcOHD6O0tBQ9e/bUHtOsWTNERkYiNTUVnTp1QmpqKlq0aIHQ0FDtMYmJiRgzZgxOnjyJNm3aIDU1Ve8cmmPGjx9v/ydF1UaHqCCLmoZYy1CQvC0jx/YVPlRKJPmew9JW/+DbE+pa7yG4jToSBerhOvrX2o86kvz7x+9X/+czAPDQOU8ZgLR7/2qauzeAg0vFHetTB2j5HBCdyJVsIiIHs2vwLJFI8NBDD9nzEgAAlUqF8ePHo0uXLmjeXF0NICcnBx4eHggMDNQ7NjQ0FDk5OdpjdANnzf2a+0wdo1AoUFhYqJeqolFcXIzi4mLt1wqFQjtOlUpViWcqjuY6VXEtV+OouZEAmNG3GcatPgoAegG0Zv13Rt9mkECAysr84K0nszF38ynkKO4HyX6etXCnWJ3D76az0HxdUYixqw7jk+fbIDEuTH9eVErgYqo6RcGnrnoFtPAm4F1HHayd/Q048QNQeBOJABI9DY9HBdcP5FQSN6gghUri4OdSeBs4+IX6nzFetYH2LwGRCerAXPP9untDnWLSIMGmwTV/zxjGeTGOc2MY58W4qp4bsdexa/BcVZKTk5Geno69e/c6eigA1JsZZ8+eXeH2S5cuwd/f3+7XFwQBt27dgkQigUTCsmC6HDk3Mf7Akn4R2HQ8W6+bX4C3O/q1CkOMfymysrKsOvfJK3lYdSALkZ5AZLDuPRW7BkohoKEkB/64i6O7c9C0MBKSEgVu3SmBJONnSC7/CZSYqZTjHQtUfN9Y7QgSKW75REMiASSCC/xhO3lA/c8QDz+gfjsgNE797q0kH/DwV797K84HPGVAncaARNw+cv6eMYzzYhznxjDOi3FVPTf5+fnmD0I1CJ7Hjh2LzZs3Y/fu3ahfv772drlcjpKSEty+fVtv9fnq1auQy+XaY9LS9D8v1lTj0D2mfIWOq1evQiaTGVx1BoC33noLEydO1H6tUCgQERGBiIgIyGQy65+sSCqVCoIgICIiAlKpzaoRVguOnpvISKB3h+Y4lJmL63eKEOznhfaVbBqiVAkYvOYcchT655BChfbS0whGHm5A/abtYekxPO62H3V1Uyp+Va+wCrW7IuLWXkhtndvrwlQSNwgCqs+85Pxq+n7vukDzp3TysOVGV6wd/VpyVpwX4zg3hnFejKvqudFkCpjjssGzIAgYN24c1q9fj127diEqKkrv/rZt28Ld3R07duzA008/DQA4ffo0srKykJCQAABISEjAu+++i2vXriEkJASAuu24TCZDbGys9phffvlF79zbtm3TnsMQT09PeHpW/CxbKpVW2QtDcy2+ECty9NxIpUDn6GDzB4p08Pw1ROQfRVuJenMeADwiPYL+bvv0g2RdBjJDpFBBKiirR5BoQzVqXu5eBdLK5WH71AVaDtDPt/YLBSI6Ofy15Kw4L8ZxbgzjvBhXlXMj9houGzwnJydj9erV+Pnnn+Hv76/NUQ4ICIC3tzcCAgIwcuRITJw4EUFBQZDJZBg3bhwSEhLQqVMnAOrGLrGxsXjhhRewYMEC5OTkYNq0aUhOTtYGvy+//DI+/fRTTJo0CSNGjMDOnTuxbt06bNmyxWHPnWqw8mXcbl9C/NG1WOtxy9Ejo+rq7g3gwOfqf7o8awONBgGX6wEhMUDRLW5cJKIawWWD56VL1asj3bt317t9xYoVGD58OABg0aJFkEqlePrpp1FcXIzExER8/vn9PwBubm7YvHkzxowZg4SEBPj6+mLYsGF45513tMdERUVhy5YtmDBhApYsWYL69evjP//5D8vUkX1pguQ7V++XLTu71WAZNyP79Yjsq0QBXMsA/v5Cv4yfT517Jfgi1T+7/mEMqImoWnHZ4FkQzFck8PLywmeffYbPPvvM6DENGjSokJZRXvfu3XH06FGLx0hkEU3AfPoX4K916hU/Ildz9yZwcJn+bcZSPxhUE5ELctngmchlWbCqXGOVbyDi6A6DoRNs12HQ2RrBVAVjqR+aoLrpYwykichlMHgmqioqJbB7oboxRmENyFHWBEYPJIkPcJ1tRVKlAmplqcuk2GqzSqOHgN5zK7YgN9Rh8OzW6v0phG5QzdVpInIRDJ6JbE13ZVl3tfHIt+brJ7uS8sGO7sou81xNk7oBUd3MH9e4+/1AW/fnSbOSfTEVOLRM3UTF1XF1mohcBINnIlvQy1d2/Y/kcyGDIvpJNEx42vlXh6s7U4F24+5A90nGg+vqkCaiG1R71wY6/N/9Lor8OSQiB2DwTGQJo/nKrvXR+g1Bhg1lXbBDaAMACJXkoYnSD+dK4pAj1MYhVTOoTkjxWYto1Pb1xDVlEULghQ4NK9fQhezA3Cq2bpqI7s+t7hsiVwmwC28Bf7yvf5tPHaDlc1yZJqIqw+CZyBxXXlU2kHes9A3BWWUz1Mkvwektp5BbUAI3iYAOKgFpKgmUwv3geOyao1DpFLYJC/DCzH6xSGoe5oAnQ1azJMDW1hDPAk784Pw/73dvVsybZiBNRHbE4JnIGO0Gv8+dPqf0hiDDBmVn7FDFAwCCoUCZbwg+mZgMt1r6L3M3AAkAUs/fRG5BicnzqspVhMzJK8KYlUewdEg8A+jqxlCAnTivYkrIgc+As9scM0Zz9DYg3luR1t2wyjQPIrIBBs9ERjf4fQeUGGlv7Ug+dXElog/+k67ETUGGqwhCmqoZVChXDSIfeOFiHhIa1zF4mmv5RRZfWoC6YtvsTRnoFStnCkd1ZyigbvQQUFYCpC0HcguB+F7qDoPntztX+pLuirQu79pAxzHAg28wiCYiqzB4pppJpQQu7nPuhiSGSr3dWzk79FcOvj5+zOwpTAXIIf5eVg1LAJCdV4S0zFyjgTlVc7U8gE5jgCydMn7Rj1RM/biVBaQ7WepH4S1g1zxg/ydA/AtM8SAiizF4pppDpQQy9wF/HwbWfQ7cveboEVWQCxkUTZ5Ewy7PmvyDLjbwNXVch6gghAV4ISfP8hVowLqVa6rmDK1UJxlI/XCGDYol+RVTPBhIE5EIDJ6peivf8rrwFhDUDSh0/ErYLcEPK8p645DQDMFQ4BoC1VUu0qVY2roJkkz8AdcNfA01qpcAkAd4oUNUkNFzuEklmNkvFmNWHoE1yRfWrlxTDWMs9UOzSu0MG3ENbTpksxYiMoLBM1VPxjb7SRz8x8+nLlQtnsXYI2FIyW9UMU8Z4nKKywe+QrnHA8DMfrFmc5J7xcoxvucD+Hb/PwDubx6USipuFtQ9v7nAnMgsTVAd1c1wIxhH7Tsw2qyFq9NEpMbgmaoP3VXmo98BxQ7c7Gdi9epg5m388scBow8Vm1Oc1DwMS4fEY/amDGTrpF7IRZaTS0nP1j7WTSIAfkCgtzuGdo5CdIg/klcf0Y5Hw5LAnEg0U6vTzlLxhiXxiOgeBs/keoxVx3DwR78lnkHIqt8XhVGJUAS3x43CMoONRcTmCps6TqkSkJaZi+IyFRY+0wqQADfuFCPEX70ibC6wTUnPxpiVRyqkfOQVlmLx9rNYOiS+UoE5kU1I3YDuk9WVMZypOZFe18NAoOMrrN5BVIMweCbXUD532YHVMRSCN9aVdccOoQ2mPRaLMkUOvjh6Fyl5jaDKkwInAeBP7fHlG4tUdrOf7opx+WuIqX6hVAmYvSnDYK605rbZmzKwd3IP9IqVIy0zF9fyi0QH5kQ2Z2hlunF358ibLrytrt6R+gnQ5gUg+lFAWr/qx0FEVYbBMzkvJwqYAfUGv6/LkvCZsj8ESCEP8MJFWSySN1dcwdVVvrFIZTb7/fJXNl65l05h6hqmpGXm6gXe5ZVPG2E5OnJahvKmHfX7ovhe9Y6DXwDyR4HIBkCzR5nWQVQNMXgm5+JkAfMNQYYNZV2wXWirbUSiWXed3icGc7YYXsHVpbl/6voT6NEsFB61pFZt9vvlrysYu+ao0WuIbV5ii7QRIqdjbAOib7D6/9OWVV3edMkd9fUOfsaNhkTVEINnEk2TZ2uXj/Ad3QrbyAa/P+9E4avNpw3m/QZ4e5hcwS0vt6AUnd7bgXlPNje72a9XrByp529q5/pWQTFeWW04cNYQu9HQFjWiiZxa+TSPRg8BD01yTIoHNxoSVTsMnkkUU3m21m4eU5aV4e+DW+H5TwoaZv2EWqV3bDVccUT8IUsC0CuunsE3DT8fu2zxJXMLSvTSKwzlFG/LyEHX+Tv15tqS9yjmVoxtUSOayOU4Q4qH7kZDrkgTuSwGz2SWscoMluTZat1Ly7iw/wfIzq5HHBQ2H69JHv5Ao+7AY68DUV1E/cFyk0oMruRWZmVWN71C99zG5tpYzWVDzI3LVjWiiVyW0UDaQSvS3rWBjmNYsYPIRTB4JpPMVWYQlWdrII+5of2GbJh3ENDxZaDrRODfy0BkJCCt2KDEEuZWcI0xll5RUqbC1PXpFp2rvDCRK8bG0kZCZV6Y3i+Opeio5hDTrMXeq9OFt9QVO/Z/DMQP5Wo0kZNj8EwmWVqZQcsJNv7lQgZF9JNo2PnZ+3+IVCqTj7Ekr9vUCq4YuukVKenZmLr+BHILSi08iz5LVoz10kYUd+FfpkC3Ns3gXot/sKmGEtNK/Mi36g2B9lByh/nRRC6AwTOZZFVlhoyNQMpkQHHFTqMyTrc6xiFVM6hOSLG0VRMkifjDY01et7EVXDE06RXGUjUsIZUAnw6yIH3mHk3aiEpVG1lZSqZqEBlSfnV690Lg4FL1irG96OVHM5AmciYMnskkiyozaCpm7Jpn51HdC5KVnbFDFQ8ACIYC1xCoLSenYSytRKkScDBTt5pFCZJXW5fXXX7jX5CPB177/hhyC0oMHq+7Ic9UWowlPh3UBo+1ZKoFkd2V73pYFbnSDKSJnAqDZzJJTGWGcJk7OmQtB/631L5l5nzq4kK9PlhwoTFS8hvpBcnGGEorOXklD4PXnMPlvGLtcVKJ4bQLsXnd5Tf+zXuyOcasPKI9h0b5DXmp529atGItlehvHqxsxRMispLRTYf/s+91WbGDyOEYPJNJxvJ6pVChg/Rv9JT+iWGqPXD7o8A+A/DwB+Jf0P5xaCh1wyc6eclnr+bj09/Pmz2NJq1k68lsrDqQhRyFBPdDWdPVLMTWT9Zlro6zJti1pBGJBOrUjNq+HmyXTeRMdAPpnu8Ax3YB1+OAE9/bd7+HbsUOWTiQNB+Ifdx+1yMiAAyeSQRNIDhn4wlE3DmOnpLDeLLWXtSR5KsPKLPDRTXVMQyUbtJd5U09f1NU8Bzi7wWlSsDczacQ6WndkCztuFc+naOunycgADcKipF6/iY6RAWJToup4+uBd+81VyEiJyZ1A+pGA/GPAIlzqi61Q3EFWPcC0H0qS94R2RmDZzLtXtWMpH9/QWKt7yHxsN8vf4PVMcywpOFHWmYuchRFiAy2bnzW1HXWBPop6dl444fjFTYjTu8Ta7bcXZCvO1LfegQetSpXWo+Iqpix1I6j3wHF+fa55q556s2MrBtNZDcMnqkivTJz91dL7JEcUOJZB1n1+6C4URKadUxEUC3LfiTNlYsTAAxsHwHA8pVjjcp23DPVZCZ59RGMfjAKX+7ONNqwZN6TLRg4E7k6gxU7PrfPPhHWjSayKwbPpGYkYLYLnd3iHg06o0klf6GbKxe3aPtZrD10CQPbR1p87sp23BPTZGbj8Wx89nwbzNlyymR+NBFVEwYrdtihHr5e3WhuLiSyFQbPVDV1mb3rAK3s94tbk1/86c5zWLT9TIX7c/KKsHj7GQT5ukMCwyXkgIrVLEwFsGIaqohtMlPb1xN7J/cQ3aCFiKqBqmwTrru5kOXuiCqFwXMNpA36FAVok/kVIv5abJeUDK0q3MCy9lCWwds1q7wSnf/Xpfn600FtUNvX02wAK7ahiiVNZsqXuyOiGqRKA+kbrNJBVAkMnmuYlPRszNl4Ak8VrMWIWimoLbFTiTkAxR6B8Oz/SZX9Uhazynvrbil6tgtBVnG+Xp1nS1IkTOUwl2+oYlGTGSIioGoDaVbpILIYg+eaQqVE2q5N+HfHWqTU2gV/90K7XeqW4Ievy5Lwk8dz2N2sF6rqV7HYVd66fp7Y9WY7/HnxtsUpEmJymHUbqlhSDYSIqAJjgfTx74FCGwbSu+YBaV8wL5pIBAbP1ZlKCVzcB5z+BcJf36PD3Zvo4G6fS90QZNhQ1gXbhbb3W2QrSi1qLFKemJxiXWJXb/293K1OkRCbw6x53qaqgVR2MyIR1TCGKnbsmme78+vmRXvXZrk7IiMYPFdX2ceBn/oCiksA7FNm7oYgwwZlZ2xXtbsfMJdjbXk4sTnFukSt8sq80LCuj1VjAizLYdYQ222QiEg0TcWOkBhg02tAYa5tz89yd0RGMXiublRK4I+FQPp+IN8O1TPu7dI+6d8V/TapDAbMuqzJ5bUkp1iXmFXeaX1jIJWUWjwmDWtzmMt3G2Q1DSKyidjHgWZ97Fc3WrfcHTcXEgGAmciHXEvGRmBRHLB7vm3P61MX6PQKMGwz8MYZIOk9NEt4DKEBPkZXtCVQrxRbmstrLqcYUOcUK1WG+/FpVnnlAfrBqzzAC0uHxCMxrnKrvJrVbWuetyZV5InW9bQpHURElaZZhX7zH/Xv6U6vqH9v25pmc+Gu+eqFGqIaiivP1UXGRmDdUAACILHBx2pm6oDaK5fX0pxiQ3RXeXMURci9U4wgXw/4e7pj/7kbuHn1Nq6U+qJj47oWj485zETktIxW6bBxA5Zd84CDX9i1dj+RM2PwXB2olOomJwbXa8XT1j8WWbLIHrm81uQUG+ImlSCvsAQLUv7WG5ubRECHYAFp1/9FiMzbqnEyh5mInJ7RKh1rbZMfXXiT3QurgKUb56lqMHiuDi7ut0l3QIl3ENBviUX5bLbO5bVVXWRjedO6zOVQm1KVOcz85UlElVKVVTqYF20z1mycp6rB4Lk6uHO1Ug8XvGtDUomSRLbsjGeLusim8qZ1GarLbE5VB7L85UlENqVbpSNlsk0WXvSw6YpNWLtxnqoGg+fqwC/U8sfo5DRLnOhjNlvkFJvLm9YlJodao6oDWf7yJCK70VTp0KRzHPkOKMm33fkN5UXbpWhq9WNpMy6qeqy2UR006Kz+qMzMLybBQNUMRHVzmsBZw1zFDHMBozW1pc09RhPIlg/KNYFsSnq2xdc0pbJVR4iIzNKkcyS9B0y5qF4t9g603fk1edH/7Qt80Aj44wNAUNnu/NWUJRvnyTG48lwdSN3UOWbrhqJ8AK2JrRaVPY2fygZiev0WSIqyz2qlLVMayucU1/X1BCTAjTvFSD1/0+S5raktbeoxjlgFsEXVESIi0TTpHA++oVOl43t1PrMtFN5Wl1E9fRzo9hwQ94RtzlsN2WrjPNkPg+fqIvZxYMC36hy2/Ps50Dmog9mlL2CrqgMkilK9j/ttGezaKqXB0Ji2ZeTgjf8dF31uc3nTujQ51CqVgJ+PXTY4D44IZPnLk4gcwt6bC0sLgP+9CFyfzJxoI2y1cZ7sh8FzdRL7OJQPPIZXF3yGiDIBf5V0xQHl/bbZuqukKpWAOVtO2SR/11a5uYYC8EAfd9y+W7EjoKlzm8qb1qW5r7BUicFfHdTeXn4eHBHI8pcnETmcPTcX7poHHFwGtBrIEnfl2GLjPNkXc56rmbSLeUjJb4zjQmMcVMVUaJ+tWSV9ZfVRm+Tv2io311hOsaHAWcy5jeVN6wr0cTd4jfLz4IhAtjKdDImIbCr2cWB8uk73QhulihXm3s+JXtxc3eyLtAtAQMWdTGzG5RwYPFczlVn9tGYjmi02NogtLWfpuZOah2Hv5B5YM6oTlgxsjVUjO+K/L3bAwPYR+O+LHeBZy/CPf/l5cEQgy1+eRORUdDcXvnHW9oE0W3/rqezGebIvpm1UM5Vd/bQ0f9cWKQ2WlJaz9Nzla1CrVCpkedzFlVIJchTFRh9Xfh4c0ZKbnQyJyCnZMy961zwg7Qt2LETVNuMiyzB4Fumzzz7DBx98gJycHLRq1QqffPIJOnTo4OhhVdAhKghymRckKKzUecQGxbZIaahsrrA1bxiu37Es6HdUIMtfnkTk1OyRF82OhVq2bEJGtsPgWYTvv/8eEydOxLJly9CxY0csXrwYiYmJOH36NEJCQhw9PD1uUgmm9Y3Bd9uOVKocvdiA1BYbG6xdLa/MpolgP8uDfkcFsvzlSUROr0LTlW+BkjuVPy87FpITYs6zCB999BFGjRqFF198EbGxsVi2bBl8fHzw9ddfO3poBiXGhWFwp0gE+npY/FhL83dtkZurXi33tHicYs5tTHsr85g1gewTreshoXEdrgATEWnoNV3Jutd0pbZtzr1rHrCgEXOiK0mpEpB6/iZ+PnYZqedvstGWlbjybEZJSQkOHz6Mt956S3ubVCpFz549kZqaavAxxcXFKC6+n0+rUCgAqPNtVSr7d1dSqVSIkfvj7aQAvPFjuujHacLAGX2bQQIBKpEvqt6xofh8cGvM3XwKOYr7KQ1Bvh54vGU4ZJ61UFqmNBpo/nYyG6VKJdwkFa+nyTEuX7JOLvPCtL4xeKRZCPafvY7rd4oQ7OeF9mZWgjXfAwkEzOjbDONWHwVgOI/Z0nlwZZp5qYqfT1fCeTGOc2MY50VDAjz4JtB1IrDnI2D3fKgkblBBCpXEytXj4nzgj/nAweVA3w+BmH62HbKDiP2ZUaoEHMrMFf33rrytJ7Mr/J3W/C1NjHPOPTRV/XoSex0Gz2bcuHEDSqUSoaGhereHhobi77//NviY9957D7Nnz65w+6VLl+Dv72+XceoSBAG3bt2CTOWBDsHiA78Ab3f0axWGGP9SZGVlWXTNGH/gu4GNceHGXZzKzsPRS7dRUFyMjHOZyDiXqT13XHiA3uNOXsnDqgNZeMAXgG/F8/p4uOGp+HqICZPhwo27yC8qhb+XOxrW9cGp7BsYt/wE8grvB9XGrqOhmRuJRIIYfwmW9IvApuPZBs9hzTy4Kt15kUi4mq7BeTGOc2MY58WAqOcAr2YQ0jfgllswJBJAUtk23Tu/Bi5nA9G9AYlrf4gu5mfm5JU8o3+rjP29K//4VQeyEOkJRAbfv12CQny37QhU+ZGizlPVqvr1lJ+fL+o4Bs928NZbb2HixInarxUKBSIiIhAREQGZTGb366tUKgiCgOb1IzBjx1VcVRjPR67t64GpjzZDqMzb4nexhpy+k41FqZn3rnf/XBKUYXvWJXzyfF3tO1ylSsDgNeeQozB+TbnMA707NIebVIKGDe7fvvVkNl7bdEnUdXRp5iYiIgJSqRSRkUDvDs0r9W6+Oig/L6TGeTGOc2MY58WIyEio2iZBOP4HIq67Q3piHVBUydbfqXuAowuBlgOAB5KABgkumRNt7mfG2r93Gub+1koAXPzjOna92dzp/vZV9etJkylgDoNnM+rWrQs3NzdcvXpV7/arV69CLpcbfIynpyc8PSvm8Eql0ir7ZSqVSuFeyw3T+8VhzMojAAynJszp38JmlSKUKgHvbP4bZYLxF+g7m/9G77hwuEklOJh5E5fzilExW/q+y3nF+PPibb0Nc5ZepzzN90HzvZBKgc7RwRWOq2nKzwupcV6M49wYxnkxopY7pMEPQNq2J6RJ79imxF3hdeDgZ+p/LlKZQ6kS9Daet2sQaPRnprJ/7wBY/be2Mso/x8psrq/K15PYazB4NsPDwwNt27bFjh070L9/fwDqd0I7duzA2LFjHTs4EexVYs3QC8OShikJjetYXSPa0usQEZGTsUeJOxeozJGSnl3h73G9AE9MfSgYkZEVj7fF3ztb9GOwhKHnGFbN+hMweBZh4sSJGDZsGNq1a4cOHTpg8eLFKCgowIsvvujooYli6xJrxl4YjzY3vBJfnuYFam2N6Kr+RUBE5GpsufJnV+VL3P31vbrOc2U4aaOVlPRsjFl5pEIa5VVFEVYdyILUvy4ebVFP7z5b/L2zRT8GsYw9x5y8IoxZeaTadEdk8CzCc889h+vXr2PGjBnIyclB69atkZKSUmEToTNQqgQcPH8T13Nu40qpLzo2rgs3qcRmtYJNvTC+3ndB1Dk0L1Bra0RX5S8CIiJX43Irf/boWOhkjVaUKgGzN2UY/FunuW3u5lMV0i9s8ffOFv0YjNF9k1bXzxOzNp40+hwlAGZvykCvWLlzvpGzABOyRBo7diwuXryI4uJiHDx4EB07dnT0kCpISc9G1/k78cLXB7H20CW88PVBdJ2/Eynp2TY5v7kXvwSAqddD+drJ1taI7mBljWYioupOs8BR/qN+zcqfrf4e2I0mnWPAd7arEa1J53BgjWgx6Rc5CnX6hS5b/L2zRT8GQzQxx6DlB/Da2mMY/J+DyFEUGz1ek2KyaNtpl68xzeC5mqiKX5hiXvya14LYF6gmJ1seoP+uWR7gZfTjHXv9IiAicmViVjdnb8pwjaAl9nHgzfO2b7SyKA7I2Gib81nA2vQLW/29s+RvrZhGKsZiDjE+/f08Bi0/YNPFvarGtI1qQMyKsC0+KhH74h/ZpSF+Sc8RvUHRmpxse22EJCJyVdVuM7VmFfrBN2yTygEA+dkO2VRY109cF11D6Re2+nsn5m+tmJQfUzGHJVw5D5rBczVQVb8wxeZe9YyVY2qfWIuCYWtysm29EZKIyJVV283U9qjMsWueOh+60yt2D6JT0rMxa+NJk8dIoO72Zyz9wlZ/73T/1pbfVHqroBjJq4+a3exnLuYQy5XzoBk8VwP2/IWptxnA1xNymZfJpiuaTQe22qBoTlVdh4jI2VX7zdQ6lTku7PsBAed+Qm2I6whnUNFtdRB9cBnQb4ldNhQa22SvSxMyTusbY/NFJlPjKr/CLJXA5CfYb69PR2GJEuevF9hkDJpzu9SnIfcweK4G7PUL09CLK9DHXftCMtR0hbnGRESOYc+qCk5D6oaUgiYYk54ICXoh2W0DJtb6HwSY3rBuUmGuXVI5xKY3hMq8MLhTsMkugbZkLKA3lQovALhZUIIJ647bZUyu9mkINwxWA/aoPmFsM0De3VIAQICPu97tpjb46RKzEcFZuNJYiYhqwmZq3YBUBSk+UT6Fl0vHIwc2eEOwax7wQTSQ8haQuafSlTnEpjfMf7ol4sIDKnUtsWyVr2yKJuZYNbIjxj7cRNRjXO3TEK48VwOaX5hjVh6xyS9MMRsQvWpJseqljrhxp1h07pUr1R51pbESEWlU983UhgLSraoO2FbcDh2kf6On5DCerLUXdSRWpnMU2q4+tNjV1JsFxajvYdUlLGarfGVjdGOOLtF10alxHfx45N9q92kIV56rCWtKvhkjrh5lMaQSCZ5oXQ8JjeuICpxdpfaoK42ViKi8pOZh2Du5B9aM6oQlA1tjzahO2Du5h8sHzoDxgFQFKQ6oYjFX+QLaFy/FqWZjK3+xStaHFruaGuxXdauu9k6PKB9zVNdPQ7jyXI1oduMePH8D13MuY5y8nrbDoCVy8gpFHSf2RVhVpfRswZXGSkRkTHXdTC0mIFVBitvtJwItO9qmOseuecCRbyxehRabg94+KgiX/7VsE5617dftkR4x9uHGiA71NzqO6vhpCIPnasZNKkGnxnWQ5V6AyMg6kFqQqpGWmYvtGTlYd/hfUY8R+yJ0pdqjrjRWIqKaxqJNkdJ71Tl2L4Rwr0a01UsemlVoCzYVlk+ptNUm+8qkFZqbP0C98dKSLT5dmgSb/XtY3UrLMm2D9FpsfrXvAvKLykweb+kGRFeqPepKYyUi++GGYedkcRrAvRrRZx76HLcEv8oPwMIuhdakVJr62atsWqG5+ZMA+HRQPNaM6oRFz7VGkK97+VPoHW9JLKD5NERsuqcz48pzDSemBqUhlrxbdqXao640VqLqyNqPo215PkdsGLb1867OrEkD+Lt2dzxavAzJbhswotavqC2pRK1iC7sUWrLqaupnr1es3CZphWLnT6kSkHWzAIu2n61wjqrIV1aqBBw8fxPXc27jSqmvVWmo9sLguQazpmRNkK875j3ZwqI/IK5Ue9SVxkpU3dg6aLXmfMYWFOzZSpjVfSxnaRpAiL+XtrTdZ8r+SHZbjwm1fgRQifrQu+ZBOLAUkk5jzAbRYnLQt57Mxiurjhn92RvfM1pUWuGBf26iS5O6Jq9lbv4M/Uzqqmy+cvkGbJBAr3rXtowczN6UgWuKQnQIFpB2/V+EyLyd5jXB4LkGs6ZkzfS+cVb94A5sH4lF289UuN3ZdtvaK0eNiEyzddBqzfkcsWHYEcF6dWHJpkjdhRF1EP00zggRmOn+LcKRa/UYJEW37nUpXAr0+9jqsnYqQcDczadM/uyt2HdB1LlG/fdP/N9DjTC2R7RVHQvNfSI9oecDGNujidWvAXOBeaCPO27f6ynhpnMJZ3pNMOe5BrMmb1cus7xLYdf5Ow0GzoB1pfTszZZl/4jIPHNBK6AOWsXmHVt7Pks2DNuCrZ83GWco13erqgO6Fn+MgSXT8J+yJBS717b6/ELhrUqVtbtw4y5yFKZ/9m4Xloo6191SJRZtP4u2c7dZXFrV3CfSEgBrD2VZdD7d/O1f/rpiMGdblyZwLs+ZXhNcea7BLMnbtSZdwfy712iz74wdpbrtDCZyZraucmPt+ap6wzCr+1QtQ7m+Kkhx0T8e9fsNgWdsCLB7oXol2ULavwy75gGHVwCPLrBoFTq/SFxgHOjtjrzCUlHplrfvllq8UmvLn0lDK8xSCSxKFa3M9e2JwXMNJqZkjS5bdSkENO9eL2Fsj2ixw61y1bVOKpGzsXXQau1xYhcUbuQX4+djlyv9pprVfaqe2YWR7pOBkBgIv06GJN/K+tAWbigEAH8v41UtdL3YJQqLjXySa4gAy1KNbPUzaWzxzFYLxo5+TTB4rsFM5ffqsmbjCldUiEgsW1e5sfY4sTVw52w5pf26Mhv7WN3HMYwtjGg3sZW0xc32G3Fr63uV21RoQXOVhnV9IJd54UpescnN6mN7NEFTuR+m/HhCdBpHdl4RvtmXibr+nqI2Voph6jhrihFYytGvCQbPNZyxkjV1fD3wROtw9IqVW7WywhUVIhLL1lVurD2fmAWF8itnldnExOo+zsPwJjbNpsL/Ihy3rDuxyOYqUokE0/rG4JVVx8xuVk9qHgZ/T3cM/uqg6GGIfcNni59Ja4oRiOUsrwluGCQkNQ/D3sk9sGZUJywZ2BprRnVC2ts9MaNfnNWFzLmiQkRiWdz4wo7nM7Zh2NilK7OJydbPu6rYs4GMI5rTGGs8Amg2FX6CD0ufgSAAgrXD2TUP+KAJkPIWkLnH4KbCxDjxm9U7Na6DsADr/n6aaqhii59Jey2KOdNrgivPBMD2+b1cUSEiS1jT+MJe5yufF3sjv1hv5a483TS0jlGWVWywZJzO0EjFVjWpDT0XTW3fqm5OYy7FQFMf+oxQH++5/wdBuGPdxQpzgQOfq//Jwg2mc4jdrK4Jcl9eecTiYZgru1jZ16KtFsV8Pd1QVHK/43Fla0vbkkQQrH4fRSIpFAoEBAQgLy8PMpnM7tdTqVTIyspCZGQkpFLHfbigeTcPGP4IyhFl35xlbpwN58Uwzotx9pobZ+gwWN7Pxy7jtbXHzB63ZGBr9GsZZtW8mBunoaA1yNcdT7auh55WptdZqrIVlDQ/M6fy3fHO5r/1notubV9d9v57kXr+JgYtPyD6eClUSHZbjxG1UirXpVCj+1Souk7EhUv/IqfMD9cLSiz6OU1Jz8aUn04YLe9mzppRnYwunFn72lGqBHSdv9Ps3gExHyrU9XPH8JZ+iI+JrpIOg2LjNa48k93YeiWJiKo/W38KZovzWZuGZiz4MHa7sXEaC1pzC0rx1b4L+GrfBZMrtLZ4AyFmhXbR9rP4b+pF9DexX+bklTy8tukSygT9203V9rVHcxoNS1MMVJBilddAFLYaj6HKHxFxfHGF9AaL7JqHwoPfYIPfOHz2bySU9+ZF7Iq7ZqX6053nsGJfpuhNhBqmnr+1rx0xzcY+HRSP2r4e2g6Dhy7kYvGOim3AbxeUYP+5m2gc1cDhqRq6GDyTXbFeMhFVlqPTFSxLQ1MfsfVkdoXV1bAALzzeKgwbj2eLTk0QW7nA2MZFW6VZiN0ElltQgq/3XcDXBgJ6pUrApuPZFldhsGd1JktTDPS767UEmrYFfp2kLk9nJa/Cq3jSeysEt2B8VvYEVJBatBHVTSrBaz2jMbZHE+3r5JqiGO/+YjzVSEPz/G39GrM0HemN/x03eB7Nz8rczafQOy7caWIHBs9kd6yXTETWslXwVxliVtI0m5hUKsHo6mp2XhG+2J1Z4fymAiWxQauhFVpbtv62ZhNYdrnrHMrMRV5hKSpuRRPHHhvRLOl3oOmuN7ZHk/s3xj4ONOujba6i+T5YQiJR/5vg/hMGuW3H7NJh2KrqYPGKu+ZvbUp6Nr7aW/HnrPxz0bzhs9drTOzimZjStjkK5yptyyQ+IiJySsaqIJiqFmAvxqpwBHi7Y3zPaPSKlQOwbnXVVMUOSwJGzQrtgXtVKmzZ+rsym8A017l+p3LBrz2qM+lWlzDHaHt2qZu6ucqA71DkFVqp8chxC0vdFyNJesCqdvCa14ypVt+6b/i2ZeTY9TWmCeifaF3PaPUuVyxty+CZiIicjq2DP1vQlPWc0PMBBHqrO8LdLizFou1n0XX+TqSkZ+usrlrGWKBkTcCYvPoIPt15VnSjKjE0K7SWrqrqXifYz/rgt46vB9o2sKySiViaN0aa76k5RoO42Mdx5Mk9+LD0aagE67rpSSXqf5+5f4pHpQdNX68csSk+oTJPLB0Sj16xcqd4jbliaVsGz0REZFO2qNVrSZfSqrQtIweLt5+psDFLs1K389TVSp2/fKBkTdCqCeituZ4xlqzQGrtO+6ggBHi7W5W0cbOgBA998LvdPm1Iah6GzwbHizrWWBCXkp6N139MxyfKpzGmdDxyYH0pVjeJCp+7L8E4t58Q4isuqBeb4vPhgNZIah7mNK8xcz/jEgBymXOVtmXwTERENpOSno2u83di0PIDeG3tMQxafkC7KmsJZ/woV8xq+Ia/LlfqGuUDs8oGrZZezxilSkCAtwdGdGmI2j6Wb5eq6+cJN6kE/Vqpc2iNNeAI9DEeKNo7XadTozpmg7gwI/0JyqdLqJurfIyBJdPwn9JHcVPws3g8Egnwuvv/0Gnjg0DGRrPHi30t3LhTbNHx9n6NiWnMMq1vjNNsFgQYPBMRkY3YMke5qj7KtWSVXMxK3a2CUvh61rJ80xiMB2aatAJrO8pZer3ydN8QfbXvAm7dLYOfp2UB9OvrjmHryWzEhQfgk+fbGOyit2xIPNKm9kSQkZVWa1IJLPn+WtJdT/e8+87dwKyNJyu8qVJBigOqWMxVvoD2xcvwpfQ5iyuNAIAkP1vd4nvXfIOdCTUsfc04U7qEsT0FoTIvDO4UicQ45ypty2obRERUaeZWZS2tHFAVXUotrTIgdgWudUQAdv2bW6EyhzFi2g7rVi7YlpGD7/+8hIJi44FU+fObqhBiirGKHQXF6s5vxpqblHdVUYxxq49iSb8IPNqpBXrHhRuswpB6/iZyC4yfz5KydWK+v+VLtPWKlZstsWbovOaoIEXc8/MgKekLpEwGFFdEP1Zr1zzgyDcGOxMClr9mnK0TsKHqHO0aBOLyv5eq5PqW4MozERFVmq3zJy1ZBbSGNavkYlfgYsMMr66GBXjh/x6MqrCCLA/wEl3PN6FxHczoF4cvX2gnaiwTej5gcJVXzPXEvCHyqiXFqpc6YmSXhqhtIuVCc45Nx7OhVAlGqzDYKpVAzPfXWIoRAOyd3ANrRnXCkoGtsWZUJ+yd3EMbOBs6rxg37hSrg97x6UD3qRY/HoA66DayCm3pa8berzFriKnO4Qy48kxERJVmj/xJe3UptXaVXNRKncwLDev6oGGDMKOrq5OSYirdkEKTn2tu1XBsjyZ6zTMsuZ64+rvFkEokmN4vDj2ahWLwVwdNHp9XWIpDmbnoHB1s8BhbpBKI+f5O+ekE8u6WWlQDW2w1C7Nj1pS2q9sU+PFF6062ax5weAXw6AK9VWhLXzPsBGwdBs9ERFRp9sqftEeXUktWyXVTA8Q0S5nWNwZSSan2eEOpBbZoHGVJ4xYAVl3P0jdENwqKRR1vqt6zmKYlcplnhVQC3fSLG/nFZr+/1rQDF1vNojyj6Q/N+6vv/N8Ii88JQN3VcN0L6lXsB99QB+Ww/DXDTsCWY/BMRESVZs/8SVt3Ka3MKrm5lbresaHIysqy2VhNqeyqobmWzPbagGaq3rOpNwUaRWUqbMvI0T4/a3KQTTH25smaqhNm0x/i+quP2v+TNUNVM5ALbelrhp2ALcPgmYiIKs3SlVBHquwquamVOpVKZcuhmmXpqqEmYN6WkYMNx64gt6BEe1/5zXRtG9RGkK+70Q181mxAC/B2R3szb6A0bwqm/HTC4Apx3t1SbWoFAIMbGm2hfLBsTdUJc29klCoBBz0643qzCKBuFBocX2Rd83JNLnS5VWiyDwbPRERkE66SP2mLVXLdlTrdFdw6Pu4ovn0Hx29dRojMp9Iff5tbHS4/FlPMrdBq8n3H93wAeYUl94Jr44EzYHgDmqk3UP1ahYmaj16xcszamAGg4vV1UysEQbBL4AxUDJbFpJTomtAzGmN7RBt9vprvxzVFIToEC5h4vR2e9Z2EmbX+C+8iK5vtGMmFJtti8ExERDZj7/xJMcGkObZcJS8fkLpJBHQIFpB2XQKlIDFZ+s7ScwOmS+mZmhtjJed0ae5btP2M2bFZswFtRt9miPEX17o8LTNX23DE2FitzT8WoC6xZ2jDoOYYQ2+exKSU6J5j7aFLGNsj2uD9ut8PN50fs+/vtMYPaImU+IOIzvjEkqd2nyYX+pn/qvOqbcwWr0FXx+CZiIhsyl75k5YGk6bYYpVcTEBqqnqDNec2dj5Tc9MrVl6pKhHl1fH1wB9vPgyPWoar3Rp7AyWBIDof3F5d7TTfXwBWvXnS/NxMXZ+ul/JSnql61OaqgaggxdDzD2Pvs+3htnWKdTWhAXUlDwnu5VXbhi1fg66MwTMRETk9S4NJUzQrZ8VlKix8phUgUdfgrevnCQjqqhGp52+azR0WE5Ba0yDG0lJ65uZmfM9om22mA4CbBSU4fPGWyTdIht5AlZap8M/1AlEpLbbsaje9Twzq+nvqfX9D/L3w2fPxmLPF8jdPSc3DUFiixIR1x81e29CbANHVXry6ImF8OrB7oTodw1KCCvhhGHDdNnnQtnwNujoGz0REZDWlSsDBzJtGP8K1xUe8tuxeaGzl7PFWYdh4PFv0ipolZcss6Yon5ty65+sQFWR2blbsuyBqnJawdGU4JT0bczadRKRnoaiUFrH5xabSJzTpF8O7RGFbRg7e+OF4he/v9D4xqO3rafHPpzzA2+wxgOE3ARZVe9HUhA6JAX6dpE7JsJQN8qBt3UHU1TF4JiIiq5y8kofBa87hct79+r66AZGtPuK1ti5zecZWzrLzivDF7swKx5taUbMmrcDWjWSu5ReJmpvbheLyjC1hycqwZt6lEgGROr1RTM2v2PxiU4EzoE6/2JaRY3TFNHn1USwdEo8nWtcT/XyAym06taraS+zjQLM+1q9CG6kJLZatXoPVBdtzExGRxbaezMaqA1kVNnVpAqL3fsmwuP21MbYIOq3pDqc5dvamDChV+o+0Jq3A1o1kQvy9RM9NoLe7dSXQypFA/QZIbL1ucyuWgOH5Be7nF4fKzM9H+cVOTQtyU/ne5q5vSmVaW2sCb2PfD6NzrFmFHvAdIAu3aLxau+YBi+KAjI0WPcweHURdGYNnIiKyiFIlYO7mU0YDEgHA8j2ZNgtYbBF0WtsdTndFTZe5AEiXpQGnJcGV2Ll5sUuU9rHWsqZetyUrloYkNQ/Dh8+2MnsdlaDObV4ysDXWjOqEvZN7IKl5WKWvb4omuJcH6H8PNIG7sU9XKhN4A1CvQo9PV68iW0OzCr1rPqBSinqI2J+zG/nF+PnYZaSev2nxGxJXwrQNIiKyiKaMmO5H8OWZ+rtp6Ue8tqjLXNkVsfKPF5tWYE3AaUkpPbFzM7ZHEzSV+1VIownydceTretB5u2ORdvPmnwu1tTrtsWKpdi233X9PSukX9h7xdTa0oy61V6uKQq1t4ueY80qdN2m6qoaghXNeSzIhRaTgy6VAHO2nNJ+XZ2rcDB4JiIii9jqo1mx57FFXea6vp5WjxMwvPJmrNydLrlOubjU88Y3VupSqgQEeHtgRJeGWH/ssl6jkvLBlSVzYy7Qayr3Nxpc94yVW7XZ0xafGlTmHLZOlTHE2tKMmu/HwfM3cD3nMsbJ66Fj47qWzXHz/upv9A/DLL4+ANG50GLeLJZ/w1ydq3AweCYiIovYqoyYJecxFqjWvhfcBXh7QKkSDAYeKenZ97rVWc7cqnb5gFTdYfAaBroHaMuxbcvIQdf5O0VtnDS0yTLI1wP9W4ejl5EA1pKa1aYCPXs0uBHT4jtU5gmVIODnY5cNXrMynzzY4lMLe3KTStCpcR1kuRcgMrIOpNbMdVx/QPIdkDLZ+prQu+YBR74BkuYbXYU29nMmlRj+pKk6V+Fg8ExERBbpEBUEucwLEhSaP9gAawMW3eBuW0bOvfbRJfhq3wV8te+CwYBUTCMTU+MEzK9q6wakKpUKWVl3ERlZD1Kp1KLauMaOvVVQghX7LpgMZG0V+NqywY3mjYCpwFkAUFSmwuD/HNTeXv77WJlPHmzZTdKpVbYaB6AOvM2sQpf/ObuRX6yXqlFeda3CwQ2DRERkETepBNP6xlj12MoGLG5SCfIK1cFk+Q5v5St5iK2wIZd54v8ejEKYkY1fmpQLSzdCWVJpojJVKTQ0ge8TreshoXEdhwaEmjcCpjbrBfi4AwBu39UPrg1VZLF2c15lH+tSbFGNA1AH34ubG63IoftzVtdfXDpUdavC4ZIrzxcuXMCcOXOwc+dO5OTkIDw8HEOGDMHbb78NDw8P7XF//fUXkpOTcejQIQQHB2PcuHGYNGmS3rl++OEHTJ8+HRcuXEB0dDTmz5+Pxx57THu/IAiYOXMmli9fjtu3b6NLly5YunQpoqMN96snIqoJEuPCoMqPxOntObh5t0z046zZdKbLkmYNYitsfDigNbo0qYtJSTEVVm4tSbkoz9JKD9Wljq6YNy1Bvh5wNxLcG/u4vzKr6/ZISXFaVbQKDVRNTrkzcsmV57///hsqlQpffPEFTp48iUWLFmHZsmWYOvV+2RaFQoHevXujQYMGOHz4MD744APMmjULX375pfaY/fv3Y9CgQRg5ciSOHj2K/v37o3///khPT9ces2DBAnz88cdYtmwZDh48CF9fXyQmJqKoqHq9iyIislRceACWDGwj6tixDzfWKyFmLUsCUrGrXTfuqKs5lF+51TTXsLZWtSWVHqpTHV0xb1pyC0pwNd94FQ1jJeQqs7ruTCvzdmfLVWgTdaGtrlnt4lwyeE5KSsKKFSvQu3dvNGrUCI8//jjeeOMN/PTTT9pjVq1ahZKSEnz99deIi4vDwIED8eqrr+Kjjz7SHrNkyRIkJSXhzTffRExMDObMmYP4+Hh8+umnANSrzosXL8a0adPwxBNPoGXLlvj2229x5coVbNiwoaqfNhGR0+nYqI6oP54TejW1OGBRqoQK6RKWBJmVWRWzRRqFJdevTit4tgzwrTmXoZ+bGquyNaGB+xU50jdUuKvSNatdlEumbRiSl5eHoKD772xSU1Px4IMP6qVxJCYmYv78+bh16xZq166N1NRUTJw4Ue88iYmJ2sA4MzMTOTk56Nmzp/b+gIAAdOzYEampqRg4cKDBsRQXF6O4+P47aoVCAUC9kUSlsqIWo4U016mKa7kazo1hnBfDOC/GaeZFAgEz+jbDuNVHARjekDWjbzNIIEBlQRCz9WQ25m4+pdfBUC7zwoB2kXCTmD9PsK8H2jUIRL0AT1xVGK+0ECrzQrsGgRW+xwfP38Q1RSHcTPzNv6YoxMHzN9BJJ41C92fGkusDsHqszibY18Pg98hNIkAKweScGjqXJc/X2M/NtL4xSIxzztxm+/+ekQAPvgkENwNSpgJ3xHf31PPTS+r/lqvG0Ts2FJ8Pbm103nvHhlr93Kr6d7DY61SL4PncuXP45JNPsHDhQu1tOTk5iIqK0jsuNDRUe1/t2rWRk5OjvU33mJycHO1xuo8zdIwh7733HmbPnl3h9kuXLsHf39+CZ2YdQRBw69YtSCQSSCTV691eZXFuDOO8GMZ5MU53bmL8JVjSLwKbjmcjr/D+5q8Ab3f0axWGGP9SZGVliT73ySt5WHUgC5Ge0GvEIkEhDp44je713FBYojQaZMq83SGvdQeX/y3A1IeCseqA+tqGAvvBnYJx+d9LFc5zPec2OgSbD9Kv51xGlnuB9uvyPzOWXN/asTobeS0BvSJrQVFYqvc8pBIBUX6ARCLAz8sdgABFYZnZ72NWVoGBIyoy9XPz3bYjUOVHIi48oBLPzD6q7PeMbyvgqU3A2d+A079ad47fVwBXcoDo3oDkfvJCjD/w3cDGuHDjLvKLSuHv5Y6GdX0glVj22i+vqn8H5+fnizrOqYLnKVOmYP78+SaPOXXqFJo1a6b9+vLly0hKSsKzzz6LUaNG2XuIorz11lt6K9oKhQIRERGIiIiATCaz+/VVKhUEQUBERASkUpfMzLEbzo1hnBfDOC/GlZ+byEigd4fmOJSZi+t3ihDs54X2VmzIUqoEDF5zDjkKw4+TAAj0ccOtuyqjpcc+eb4FGjZQrzJGRgJS/7oWr0ZeKfVF2vV/zY53nLweIiP1V57Lz4vY61s7Vmf0RFePCp9GuEkAiSDg0A0JFg9qAQAmP7HQ/T6aI+bn5uIf17HrzeZOl0JQ5b9nGowG6oVZvwqdugc48QmQNA+I6ad3V8MGNhrjPVU9N5pMAXOcKnh+/fXXMXz4cJPHNGrUSPv/V65cwcMPP4zOnTvrbQQEALlcjqtXr+rdpvlaLpebPEb3fs1tYWFhese0bt3a6Bg9PT3h6VmxfItUKq2yP8Caa/EPfkWcG8M4L4ZxXowrPzdSKdA52kTPbhEOZt7E5bxiVMygvO9GQRkm9HwAaw9dElUF49EW9dA7LtyiSgsdG9dFiMzbbHONjo3rVmhsUX5eLLm+NWN1Ro+2qIdPB0srNNTw83bH4kEt8GgLdRttQ8dY09ZZzM/N5bxi/HnxtlNWK6ny3zNxTwAxfa2vyJH/L/DDULPVOGyhKudG7DWcKngODg5GcLC4X7yXL1/Gww8/jLZt22LFihUVnnBCQgLefvttlJaWwt1dXUty27ZtaNq0KWrXrq09ZseOHRg/frz2cdu2bUNCQgIAICoqCnK5HDt27NAGywqFAgcPHsSYMWMq+WyJiKg8sRvEGtb1xd7JPUQHmZY2/7B1cw1Lrm/LRiWOVL48XLCvB+S17uitJtuqhFx1qlZSZTQVOUJirO9OuGsecHgF8OgCo50JqyOXXEq5fPkyunfvjsjISCxcuBDXr19HTk6OXh7y888/Dw8PD4wcORInT57E999/jyVLluilU7z22mtISUnBhx9+iL///huzZs3Cn3/+ibFjxwIAJBIJxo8fj7lz52Ljxo04ceIEhg4divDwcPTv37+qnzYRkVNQqgQcOH8Txy/dxgEbVzOwpOqEvUuP1ZjmGnak+z3q1LgOpAbyVm3xfaxO1UqqXGUrcmiqceyaD6iUth2bk3KqlWextm3bhnPnzuHcuXOoX7++3n2CoP4lHhAQgN9++w3Jyclo27Yt6tatixkzZmD06NHaYzt37ozVq1dj2rRpmDp1KqKjo7FhwwY0b95ce8ykSZNQUFCA0aNH4/bt2+jatStSUlLg5cUXIBHVPJqWy9cUhegQLCDt+r8IkXlXuvGJZuWxrq8n5DIvk1UnrGntba0a1VzDhWnqDZtLs6lu9YZtRrMKXbcp8OOLgGBFdYtd84Aj3wBJ86v9KrRE0ESbZDcKhQIBAQHIy8ursg2DWVlZiIyMZJ5mOZwbwzgvhnFe9GlaLgtQlx1TB88SqAR1IGnNaqwmGNfNeQ30ccftu6VG0yXMXUc3GK/qYNdVf2aqYs7sPTean0/Aup8bR3G6n5mTG4AfhlXuHDbKha7quREbr7nkyjMREVUtS9piiw26dINxXXl31eXuAu4F0RpiWnsbCsat2YBWk1SXOdOk2ZR/LpVtCV/jxPUHJN9ZnwcNVPtcaAbPRERkliVtscVsdhMTjHvVkmLVSx1x406xqNVQY8G4pp22s648OlJ1mzOm2dhI7ONAsz7WV+MA7uVCDwUGfFvtAmgn+HyAiIicna2rGYgJxnMUxZBKJKI2ktminXZNU13nzN4bSWsMTR70gO8AWbiVJxGAzROAshKbDs3RGDwTEZFZtq5mkJNXKOo4WwbjmpVxUuOckSiVrcZx9wbwUQyQsdG243IgBs9ERGSWppqBsTU8CdR5smKqGaSkZ2POllOiris2GGedX8txzkg03VVofyvSeO7eUJezS99g86E5AoNnIiIyS9M0BKjYw01s0xClSsCS7Wfw8sojyC0w/TGuJcE4wDq/1uCckcViHwcmnLR+FfrHF9XVPFwcg2ciIhKlMk1DUtKz0eX9nVi0/azo61nSwc+WK+M1BeeMrFKZXGhBpS6D5+INVRg8ExGRaEnNw7B3cg98N6IjBraPwHcjOmLv5B5mA+cxK48gRyHu4/8gX3erqjwMbB9ptEEGYFkwXhPY4tMEqsEqkwu9ax6wKM5l86AZPBMRkUXcpBJ0alwHrSIC0akSVTCMmd43zqLAOSU9G13n78Si7WcM3u+s7bSVKgGp52/i52OXkWrjNudisQU5VYruKrSP+RKVely4rTfrPBMRkd2Yq+hgiFwmPsfWWJ1ijQk9ozG2R7TTrZ46U2MS1kamSot9HHggSV1V4+4Nyx7rgg1VuPJMRER2Y0mlBktzbM2taksArD10SfT1q4om4C//pkLTmCQlPbvKx8TayFRptTyAvouse6ymoYqLpHEweCYiIruxtFKDJTm2rlinuLo2JiECoF45fua/gMSa8NJ1GqoweCYiIrsxV9FBQy7ztDjH1hXrFLtiwE9kkeb9gWdWWPdYF2mowuCZiIjsxlRFB40JPR/AvimPWJzr64p1il0x4CeyWFx/69t6axqqOPFGQgbPRERkV8YqOoQFeGHZkHi81tO6DX2uWKfYFQN+IqtUtq33rnnAx22A7OO2HZcNsNoGERHZnT0qOmhWtcesPAIJoJdH7Kx1ijUBf05ekdGa1HInC/iJrKYpZRcSA6RMBhRXLHt8/hXgz6+Bor+Bh95Qn88JcOWZiIiqhD0qOrhanWI2JqEaqbKr0LvnO1VTFa48ExGRS3O1OsWagL98nWe5g+o8E1UJ3VXozeOBuzcte7ymnN2Abx1eD5rBMxERuTzNqrarcLWAn8hmKtNQBQBSpgDN+jg0hYNpG0RERA7AxiRUY2kbqlj6My8AisvAxf32GJVoDJ6JiIiIqGrFPq5OwfC3Ik3pzlXbj8cCDJ6JiIiIqOrFPg5MOGn5RkK/UPuMRyQGz0RERETkGJqNhKKaqkgAWT2gQecqGZoxDJ6JiIiIyLHMlrO7lx+d9L7D6z0zeCYiIiIixzO1Ci0Ld4oydQBL1RERERGRM4l9XF2OLnMfkHMdkL8ORHVx+IqzBoNnIiIiInIuUjcgqivglgVERgJS50mWcJ6REBERERE5OQbPREREREQiMXgmIiIiIhKJwTMRERERkUgMnomIiIiIRGLwTEREREQkEoNnIiIiIiKRGDwTEREREYnE4JmIiIiISCQGz0REREREIrE9dxUQBAEAoFAoquR6KpUK+fn5UCgUkDpRO0tnwLkxjPNiGOfFOM6NYZwX4zg3hnFejKvqudHEaZq4zRgGz1UgPz8fABAREeHgkRARERGRKfn5+QgICDB6v0QwF15TpalUKly5cgX+/v6QSCR2v55CoUBERAQuXboEmUxm9+u5Es6NYZwXwzgvxnFuDOO8GMe5MYzzYlxVz40gCMjPz0d4eLjJlW6uPFcBqVSK+vXrV/l1ZTIZX4hGcG4M47wYxnkxjnNjGOfFOM6NYZwX46pybkytOGswuYaIiIiISCQGz0REREREIjF4roY8PT0xc+ZMeHp6OnooTodzYxjnxTDOi3GcG8M4L8ZxbgzjvBjnrHPDDYNERERERCJx5ZmIiIiISCQGz0REREREIjF4JiIiIiISicEzEREREZFIDJ6rkd27d6Nfv34IDw+HRCLBhg0bHD0kp/Dee++hffv28Pf3R0hICPr374/Tp087elhOYenSpWjZsqW2AH1CQgJ+/fVXRw/L6bz//vuQSCQYP368o4ficLNmzYJEItH716xZM0cPyylcvnwZQ4YMQZ06deDt7Y0WLVrgzz//dPSwHK5hw4YVfmYkEgmSk5MdPTSHUiqVmD59OqKiouDt7Y3GjRtjzpw5YB0HdXvs8ePHo0GDBvD29kbnzp1x6NAhRw9Lix0Gq5GCggK0atUKI0aMwFNPPeXo4TiNP/74A8nJyWjfvj3KysowdepU9O7dGxkZGfD19XX08Byqfv36eP/99xEdHQ1BEPDf//4XTzzxBI4ePYq4uDhHD88pHDp0CF988QVatmzp6KE4jbi4OGzfvl37da1a/FNy69YtdOnSBQ8//DB+/fVXBAcH4+zZs6hdu7ajh+Zwhw4dglKp1H6dnp6OXr164dlnn3XgqBxv/vz5WLp0Kf773/8iLi4Of/75J1588UUEBATg1VdfdfTwHOqll15Ceno6vvvuO4SHh2PlypXo2bMnMjIyUK9ePUcPj6XqqiuJRIL169ejf//+jh6K07l+/TpCQkLwxx9/4MEHH3T0cJxOUFAQPvjgA4wcOdLRQ3G4O3fuID4+Hp9//jnmzp2L1q1bY/HixY4elkPNmjULGzZswLFjxxw9FKcyZcoU7Nu3D3v27HH0UJze+PHjsXnzZpw9exYSicTRw3GYvn37IjQ0FF999ZX2tqeffhre3t5YuXKlA0fmWIWFhfD398fPP/+MPn36aG9v27YtHn30UcydO9eBo1Nj2gbVOHl5eQDUQSLdp1QqsXbtWhQUFCAhIcHRw3EKycnJ6NOnD3r27OnooTiVs2fPIjw8HI0aNcLgwYORlZXl6CE53MaNG9GuXTs8++yzCAkJQZs2bbB8+XJHD8vplJSUYOXKlRgxYkSNDpwBoHPnztixYwfOnDkDADh+/Dj27t2LRx991MEjc6yysjIolUp4eXnp3e7t7Y29e/c6aFT6+Fkb1SgqlQrjx49Hly5d0Lx5c0cPxymcOHECCQkJKCoqgp+fH9avX4/Y2FhHD8vh1q5diyNHjjhVnp0z6NixI7755hs0bdoU2dnZmD17Nrp164b09HT4+/s7engO888//2Dp0qWYOHEipk6dikOHDuHVV1+Fh4cHhg0b5ujhOY0NGzbg9u3bGD58uKOH4nBTpkyBQqFAs2bN4ObmBqVSiXfffReDBw929NAcyt/fHwkJCZgzZw5iYmIQGhqKNWvWIDU1FU2aNHH08AAweKYaJjk5Genp6U7z7tUZNG3aFMeOHUNeXh7+97//YdiwYfjjjz9qdAB96dIlvPbaa9i2bVuF1Y+aTndVrGXLlujYsSMaNGiAdevW1ehUH5VKhXbt2mHevHkAgDZt2iA9PR3Lli1j8Kzjq6++wqOPPorw8HBHD8Xh1q1bh1WrVmH16tWIi4vDsWPHMH78eISHh9f4n5nvvvsOI0aMQL169eDm5ob4+HgMGjQIhw8fdvTQADB4phpk7Nix2Lx5M3bv3o369es7ejhOw8PDQ/tuvm3btjh06BCWLFmCL774wsEjc5zDhw/j2rVriI+P196mVCqxe/dufPrppyguLoabm5sDR+g8AgMD8cADD+DcuXOOHopDhYWFVXjDGRMTgx9//NFBI3I+Fy9exPbt2/HTTz85eihO4c0338SUKVMwcOBAAECLFi1w8eJFvPfeezU+eG7cuDH++OMPFBQUQKFQICwsDM899xwaNWrk6KEBYM4z1QCCIGDs2LFYv349du7ciaioKEcPyampVCoUFxc7ehgO9cgjj+DEiRM4duyY9l+7du0wePBgHDt2jIGzjjt37uD8+fMICwtz9FAcqkuXLhVKYJ45cwYNGjRw0Iicz4oVKxASEqK3Cawmu3v3LqRS/TDMzc0NKpXKQSNyPr6+vggLC8OtW7ewdetWPPHEE44eEgCuPFcrd+7c0Vv9yczMxLFjxxAUFITIyEgHjsyxkpOTsXr1avz888/w9/dHTk4OACAgIADe3t4OHp1jvfXWW3j00UcRGRmJ/Px8rF69Grt27cLWrVsdPTSH8vf3r5AT7+vrizp16tT4XPk33ngD/fr1Q4MGDXDlyhXMnDkTbm5uGDRokKOH5lATJkxA586dMW/ePAwYMABpaWn48ssv8eWXXzp6aE5BpVJhxYoVGDZsGEsb3tOvXz+8++67iIyMRFxcHI4ePYqPPvoII0aMcPTQHG7r1q0QBAFNmzbFuXPn8Oabb6JZs2Z48cUXHT00NYGqjd9//10AUOHfsGHDHD00hzI0JwCEFStWOHpoDjdixAihQYMGgoeHhxAcHCw88sgjwm+//eboYTmlhx56SHjttdccPQyHe+6554SwsDDBw8NDqFevnvDcc88J586dc/SwnMKmTZuE5s2bC56enkKzZs2EL7/80tFDchpbt24VAAinT5929FCchkKhEF577TUhMjJS8PLyEho1aiS8/fbbQnFxsaOH5nDff/+90KhRI8HDw0OQy+VCcnKycPv2bUcPS4t1nomIiIiIRGLOMxERERGRSAyeiYiIiIhEYvBMRERERCQSg2ciIiIiIpEYPBMRERERicTgmYiIiIhIJAbPREREREQiMXgmIiIiIhKJwTMRERERkUgMnomIiIiIRGLwTEREoq1Zswbe3t7Izs7W3vbiiy+iZcuWyMvLc+DIiIiqhkQQBMHRgyAiItcgCAJat26NBx98EJ988glmzpyJr7/+GgcOHEC9evUcPTwiIrur5egBEBGR65BIJHj33XfxzDPPQC6X45NPPsGePXsYOBNRjcGVZyIislh8fDxOnjyJ3377DQ899JCjh0NEVGWY80xERBZJSUnB33//DaVSidDQUEcPh4ioSnHlmYiIRDty5Ai6d++OL774At988w1kMhl++OEHRw+LiKjKMOeZiIhEuXDhAvr06YOpU6di0KBBaNSoERISEnDkyBHEx8c7enhERFWCK89ERGRWbm4uOnfujO7du2PZsmXa2/v06QOlUomUlBQHjo6IqOoweCYiIiIiEokbBomIiIiIRGLwTEREREQkEoNnIiIiIiKRGDwTEREREYnE4JmIiIiISCQGz0REREREIjF4JiIiIiISicEzEREREZFIDJ6JiIiIiERi8ExEREREJBKDZyIiIiIikRg8ExERERGJ9P8RVnpPMJHhYQAAAABJRU5ErkJggg==\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Как видим, полученная модель имеет вид гиперболы с направленными ветвями вниз. Интересно, что модель не решила полностью воспроизводить одну из частей кусочно-гладкой функции, а остановилась на \"средне-оптимальном\" представлении." + ], + "metadata": { + "id": "e6jIM4J3R_t_" + } + }, + { + "cell_type": "markdown", + "source": [ + "## Улучшение бейзлайна: добавление коэффициента" + ], + "metadata": { + "id": "LEWWTDoEN2Ow" + } + }, + { + "cell_type": "markdown", + "source": [ + "Ранее было отмечено, что целевая функция имеет форму кусочно-гладкой функции. Однако, до этого мы использовали для решения задачи регрессии только непрерывные функции.\n", + "\n", + "Попробуем снова воспользоваться feature engineering и обогатить в этот раз входные признаки информацией о том, что целевая функция кусочно-гладкая.\n", + "\n", + "Для этого введем переменную-коэффициент:\n", + "\n", + "$$\n", + "a = \\left\\{\n", + " \\begin{matrix}\n", + " 1, & x \\ge 5 \\\\\n", + " 0, & x < 5 \\\\\n", + " \\end{matrix}\n", + "\\right.\n", + "$$\n", + "\n", + "И попробуем представить модель следующим образом:\n", + "\n", + "$$\n", + "f(x) =\n", + "a \\cdot \\left[ c_1 + c_2 \\cdot x + c_3 \\cdot x ^ 2 \\right] +\n", + "(1 - a) \\cdot \\left[ c_4 + c_5 \\cdot x + c_6 \\cdot x ^ 2 \\right]\n", + "$$\n", + "\n", + "Иными словами, мы представляем модель в виде двух компонент, играющих\n", + "роль квадратичных функциий, но помноженных на введенный коэффициент.\n", + "Именно он и хранит информацию о кусочной гладкости функции: если входное значение $x \\le 5$, то учитывается только первая компонента, иначе - только вторая." + ], + "metadata": { + "id": "nDv1J5Q0SU78" + } + }, + { + "cell_type": "code", + "source": [ + "def get_features(x):\n", + " a = int(x >= 5.0)\n", + " return [a, a * x, a * x ** 2, (1 - a), (1 - a) * x, (1 - a) * x ** 2]\n", + "\n", + "\n", + "X, y = dataset[:, 0], dataset[:, 1]\n", + "X = np.array([get_features(x) for x in X], dtype=np.float64)\n", + "\n", + "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(\n", + " X, y,\n", + " test_size=0.2,\n", + " random_state=RANDOM_SEED,\n", + ")\n", + "\n", + "model = sklearn.linear_model.LinearRegression()\n", + "model.fit(X_train, y_train)\n", + "print('R2 score:', sklearn.metrics.r2_score(y_test, model.predict(X_test)))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "qQOrr0a8N4Pd", + "outputId": "8c121c78-e88a-4e3e-c57b-ae25550cc586" + }, + "execution_count": 14, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "R2 score: 0.9836822750509996\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Как видим, модель показала прекрасные результаты, что говорит нам о том, что\n", + "гипотеза подтвердилась! Об этом свидетельствует значение метрики $R ^ 2$,\n", + "возросшее до $98\\%$." + ], + "metadata": { + "id": "i5PlFZO8TlLC" + } + }, + { + "cell_type": "code", + "source": [ + "plt.figure(figsize=(8, 5))\n", + "plt.scatter(dataset[:, 0], y, label=\"Исходный датасет\")\n", + "plt.scatter(dataset[:, 0], model.predict(X), label=\"Предсказанные значения\")\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$y = f(x)$\")\n", + "plt.legend()\n", + "plt.grid(True, alpha=0.4)\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 465 + }, + "id": "r1eoUkQ9OIpB", + "outputId": "8a2228c6-6b0a-4189-eb2e-a22087f2c643" + }, + "execution_count": 16, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Как видим, визуально также модель теперь учитывает кусочно-гладкий характер целевой функции." + ], + "metadata": { + "id": "vm5bPCtQTycD" + } + }, + { + "cell_type": "markdown", + "source": [ + "## Итоги\n", + "\n", + "| Модель | Значение $R ^ 2$ |\n", + "|----------|---|\n", + "| Бейзлайн | $0.12$ |\n", + "| Квадратичная функция | $0.25$ |\n", + "| 2 квадратичные функции с коэффициентом | $0.98$ |\n" + ], + "metadata": { + "id": "GKL_ZxuMT3gz" + } + } + ] +} \ No newline at end of file From 12487b8c735828d92f1ad8bec2d236025eb10dda Mon Sep 17 00:00:00 2001 From: Nifacy Date: Wed, 3 Dec 2025 18:43:50 +0300 Subject: [PATCH 3/3] fix: use pandas to read dataset --- stud/grishin/lab-1/main.ipynb | 35 +++++++++++++++-------------------- 1 file changed, 15 insertions(+), 20 deletions(-) diff --git a/stud/grishin/lab-1/main.ipynb b/stud/grishin/lab-1/main.ipynb index 797df38..be4abb8 100644 --- a/stud/grishin/lab-1/main.ipynb +++ b/stud/grishin/lab-1/main.ipynb @@ -40,6 +40,7 @@ "source": [ "import csv\n", "import numpy as np\n", + "import pandas as pd\n", "\n", "import matplotlib.pyplot as plt\n", "\n", @@ -50,7 +51,7 @@ "metadata": { "id": "M7NYKxRNlY8J" }, - "execution_count": 1, + "execution_count": 3, "outputs": [] }, { @@ -69,7 +70,8 @@ "source": [ "## 1. Загрузка датасета\n", "\n", - "Загрузим датасет, соответствующий выбранному варианту лабораторной работы. Так как в условии задания не было явно указано способа импорта датасета, то для этой задачи я выбрал стандартную библиотеку `csv`." + "Загрузим датасет, соответствующий выбранному варианту лабораторной работы.\n", + "Для более оптимизированной загрузки датасета я решил использовать библиотеку `pandas`." ], "metadata": { "id": "M95sbpiQlwM7" @@ -78,19 +80,12 @@ { "cell_type": "code", "source": [ - "dataset = []\n", - "\n", - "with open(\"datasets/lab1-04.csv\", newline='', encoding='utf-8') as f:\n", - " reader = csv.reader(f)\n", - " for row in reader:\n", - " dataset.append(tuple(map(float, row)))\n", - "\n", - "dataset = np.array(dataset, dtype=np.float64)" + "dataset = pd.read_csv('datasets/lab1-04.csv', header=None).to_numpy()" ], "metadata": { "id": "mTCiw6__mBQk" }, - "execution_count": 3, + "execution_count": 11, "outputs": [] }, { @@ -123,9 +118,9 @@ "height": 487 }, "id": "RWvN0g5sn6R3", - "outputId": "602a0ada-8750-43e4-9369-b38a893f33a4" + "outputId": "2ca9727f-d8d6-4077-82b2-4fe4663dab58" }, - "execution_count": 4, + "execution_count": 12, "outputs": [ { "output_type": "display_data", @@ -202,9 +197,9 @@ "base_uri": "https://localhost:8080/" }, "id": "L17B9ecDLa-1", - "outputId": "c88da584-d867-49ed-d800-eb22f05b8227" + "outputId": "05470730-130f-4d79-f3a0-a911a54d5ce5" }, - "execution_count": 6, + "execution_count": 13, "outputs": [ { "output_type": "stream", @@ -246,7 +241,7 @@ "id": "NGWf_1uXMfFr", "outputId": "b23b3fd9-2431-4482-d3e1-d560a6379200" }, - "execution_count": 10, + "execution_count": null, "outputs": [ { "output_type": "display_data", @@ -317,7 +312,7 @@ "id": "J1qwQySINKbV", "outputId": "de271685-3a1d-4bf2-d924-c5ac26f00e8e" }, - "execution_count": 11, + "execution_count": null, "outputs": [ { "output_type": "stream", @@ -357,7 +352,7 @@ "id": "DdxM7zeLNp7D", "outputId": "9a4b5c8a-8e65-4b64-e2c5-0dbab3ddcda5" }, - "execution_count": 13, + "execution_count": null, "outputs": [ { "output_type": "display_data", @@ -451,7 +446,7 @@ "id": "qQOrr0a8N4Pd", "outputId": "8c121c78-e88a-4e3e-c57b-ae25550cc586" }, - "execution_count": 14, + "execution_count": null, "outputs": [ { "output_type": "stream", @@ -493,7 +488,7 @@ "id": "r1eoUkQ9OIpB", "outputId": "8a2228c6-6b0a-4189-eb2e-a22087f2c643" }, - "execution_count": 16, + "execution_count": null, "outputs": [ { "output_type": "display_data",