HSE Lab (linear regression) 20-21 (2).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Лабораторная работа 2\n",
    "\n",
    "## Линейная регрессия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Метод наименьших квадратов: постановка задачи\n",
    "\n",
    "Рассмотрим систему уравнений $Xa = y$, в которой $a$ — столбец неизвестных. Её можно переписать в векторном виде\n",
    "$$x_1 a_1 + x_2 a_2 + \\ldots + x_k a_k = y,$$\n",
    "где $x_1,\\ldots,x_k$ — столбцы матрицы $X$. Таким образом, решить исходную систему означает найти линейную комбинацию векторов $x_1,\\ldots,x_k$, равную правой части. Но что делать, если такой линейной комбинации не существует? Геометрически это означает, что вектор $y$ не лежит в подпространстве $U = \\langle x_1,\\ldots, x_k\\rangle$. В этом случае мы можем найти *псевдорешение*: вектор коэффициентов $\\hat{a}$, для которого линейная комбинация $x_1 \\hat{a}_1 + x_2 \\hat{a}_2 + \\ldots + x_k \\hat{a}_k$ хоть и не равна в точности $y$, но является наилучшим приближением — то есть ближайшей к $y$ точкой $\\hat{y}$ подпространства $U$ (иными словами, ортогональной проекцией $y$ на это подпростанство). Итак, цель наших исканий можно сформулировать двумя эквивалентными способами:\n",
    "\n",
    "1. Найти вектор $\\hat{a}$, для которого длина разности $|X\\hat{a} - y|$ минимальна (отсюда название \"метод наименьших квадратов\");\n",
    "2. Найти ортогональную проекцию $\\hat{y}$ вектора $y$ на подпространство $U$ и представить её в виде $X\\hat{a}$.\n",
    "\n",
    "Далее мы будем предполагать, что векторы $x_1,\\ldots,x_k$ линейно независимы (если нет, то сначала имеет смысл выделить максимальную линейно независимую подсистему).\n",
    "\n",
    "На лекциях было показано, что проекция вектора $y$ на подпространство $U = \\langle x_1,\\ldots, x_k\\rangle$, записывается в виде\n",
    "$$\\hat{y} = X\\left(X^TX\\right)^{-1}X^Ty,$$\n",
    "и, соответственно, искомый вектор $\\hat{a}$ равен\n",
    "$$\\hat{a} = \\left(X^TX\\right)^{-1}X^Ty.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задача линейной регрессии\n",
    "\n",
    "Начнём с примера. Допустим, вы хотите найти зависимость среднего балла S студента ФКН от его роста H, веса W, длины волос L и N — количества часов, которые он ежедневно посвящает учёбе. Представьте, что мы измерили все эти параметры для $n$ студентов и получили наборы значений: $S_1,\\ldots, S_n$, $H_1,\\ldots, H_n$ и так далее.\n",
    "\n",
    "Тут можно подбирать много разных умных моделей, но начать имеет смысл с самой простой, линейной:\n",
    "$$S = a_1H + a_2W + a_3L + a_4N + a_5.$$\n",
    "Конечно, строгой линейной зависимости нет (иначе можно было бы радостно упразднить экзамены), но мы можем попробовать подобрать коэффициенты $a_1, a_2, a_3, a_4, a_5$, для которых отклонение правой части от наблюдаемых было бы наименьшим:\n",
    "$$\\sum_{i=1}^n\\left(S_i - ( a_1H_i + a_2W_i + a_3L_i + a_4N_i + a_5)\\right)^2 \\longrightarrow \\min$$\n",
    "И сразу видно, что мы получили задачу на метод наименьших квадратов! А именно, у нас\n",
    "$$X =\n",
    "\\begin{pmatrix}\n",
    "H_1 & W_1 & L_1 & N_1 & 1\\\\\n",
    "H_2 & W_2 & L_2 & N_2 & 1\\\\\n",
    "\\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
    "H_n & W_n & L_n & N_n & 1\n",
    "\\end{pmatrix},\\qquad y=\n",
    "\\begin{pmatrix}\n",
    "S_1\\\\ S_2\\\\ \\vdots \\\\ S_n\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "Решая эту задачу с помощью уже известных формул, получаем оценки коэффициентов $\\hat{a}_i$ ($i = 1\\ldots,5$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь проговорим общую постановку задачи линейной регрессии. У нас есть $k$ переменных $x_1,\\ldots,x_k$ (\"регрессоров\"), через которые мы хотим выразить \"объясняемую переменную\" $y$:\n",
    "$$y = a_1x_1 + a_2x_2 + \\ldots + a_kx_k$$\n",
    "Значения всех переменных мы измерили $n$ раз (у $n$ различных объектов,  в $n$ различных моментов времени - это зависит от задачи). Подставим эти данные в предыдущее равенство:\n",
    "$$\\begin{pmatrix}\n",
    "y_1\\\\ y_2 \\\\ \\vdots \\\\ y_n\n",
    "\\end{pmatrix} = \n",
    "a_1\\begin{pmatrix}\n",
    "x_{11} \\\\ x_{21} \\\\ \\vdots \\\\ x_{n1} \\end{pmatrix} + a_2\\begin{pmatrix}\n",
    "x_{12} \\\\ x_{22} \\\\ \\vdots \\\\ x_{n2} \\end{pmatrix} + \\ldots + a_k\\begin{pmatrix}\n",
    "x_{1k} \\\\ x_{2k} \\\\ \\vdots \\\\ x_{nk} \\end{pmatrix}$$\n",
    "(здесь $x_{ij}$ - это значение $j$-го признака на $i$-м измерении). Это удобно переписать в матричном виде:\n",
    "$$\\begin{pmatrix}\n",
    "x_{11} & x_{12} & \\ldots & x_{1k}\\\\\n",
    "x_{21} & x_{22} & \\ldots & x_{2k}\\\\\n",
    "\\dots & \\dots & \\dots & \\dots\\\\\n",
    "x_{n1} & x_{n2} & \\ldots & x_{nk}\n",
    "\\end{pmatrix} \\cdot\n",
    "\\begin{pmatrix}\n",
    "a_1 \\\\ a_2 \\\\ \\vdots \\\\ a_k\n",
    "\\end{pmatrix} = \n",
    "\\begin{pmatrix}\n",
    "y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n\n",
    "\\end{pmatrix}$$\n",
    "или коротко $Xa = y$. Поскольку на практике эта система уравнений зачастую не имеет решения (ибо зависимости в жизни редко бывают действительно линейными), методом наименьших квадратов ищется псевдорешение."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Оценка качества. Обучение и тест \n",
    "\n",
    "После того, как вы построили регрессию и получили какую-то зависимость объясняемой переменной от регрессоров, настаёт время оценить качество регрессии. Есть много разных функционалов качества; мы пока будем говорить только о самом простом и очевидном из них: о среднеквадратичной ошибке (mean square error). Она равна\n",
    "$$\\frac1{n}|X\\hat{a} - y|^2 = \\frac1{n}\\sum_{i=1}^n\\left(\\hat{a}_1x_{i1} + \\hat{a}_2x_{i2} + \\ldots + \\hat{a}_kx_{ik} - y_i\\right)^2$$\n",
    "\n",
    "В целом, хочется искать модели с наименьшей mean square error на имеющихся данных. Однако слишком фанатичная гонка за минимизацией ошибки может привести к печальным последствиям, в чём Вам предстоит убедиться в ходе выполнения этой лабораторной.\n",
    "\n",
    "Чтобы не попадать в эту ловушку, данные обычно делят на обучающие (по которым строят модель и оценивают коэффициенты) и тестовые. Лучшей стоит счесть ту модель, для которой значение функционала качества будет меньше."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Правила оформления графиков\n",
    "При работе с данными часто неудобно делать какие-то выводы, если смотреть на таблицу и числа в частности, поэтому важно уметь визуализировать данные. \n",
    "\n",
    "У matplotlib, конечно же, есть [документация](https://matplotlib.org/users/index.html) с большим количеством [примеров](https://matplotlib.org/examples/), но для начала достаточно знать про несколько основных типов графиков:\n",
    "- plot — обычный поточечный график, которым можно изображать кривые или отдельные точки;\n",
    "- hist — гистограмма, показывающая распределение некоторой величины;\n",
    "- scatter — график, показывающий взаимосвязь двух величин;\n",
    "- bar — столбцовый график, показывающий взаимосвязь количественной величины от категориальной.\n",
    "\n",
    "Ещё одна билиотека для визуализации: [seaborn](https://jakevdp.github.io/PythonDataScienceHandbook/04.14-visualization-with-seaborn.html). Это настройка над matplotlib, иногда удобнее и красивее делать визуализации через неё. \n",
    "\n",
    "При выполнении этой лабораторной Вы столкнётесь с необходимость рисовать большое количество графиков. Не забывайте про базовые принципы построения приличных графиков:\n",
    "- оси должны быть подписаны, причём не слишком мелко;\n",
    "- у графика должно быть название;\n",
    "- если изображено несколько графиков, то необходима поясняющая легенда;\n",
    "- для точек из разных выборок, необходимо использовать разные цвета;\n",
    "- все линии на графиках должны быть чётко видны (нет похожих цветов или цветов, сливающихся с фоном);\n",
    "- если отображена величина, имеющая очевидный диапазон значений (например, проценты могут быть от 0 до 100), то желательно масштабировать ось на весь диапазон значений (исключением является случай, когда вам необходимо показать малое отличие, которое незаметно в таких масштабах).\n",
    "\n",
    "Помните, что проверяющий имеет право снизить оценку за неопрятные графики."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Формат сдачи\n",
    "Задания сдаются через систему Anytask. Инвайт можно найти на странице курса. Присылать необходимо ноутбук с выполненным заданием. Сам ноутбук называйте в формате homework-practice-02-linregr-Username.ipynb, где Username — Ваша фамилия."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 1. Метод наименьших квадратов (3 балла)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Скачайте файлы ``train.txt`` и ``test.txt``. В первом из них находится обучающая выборка, а во втором — тестовая. Каждый из файлов содержит два столбца чисел, разделённых пробелами: в первом — $n$ точек (значения аргумента $x$), во втором — значения некоторой функции $y = f(x)$ в этих точках, искажённые случайным шумом. Ваша задача — по обучающей выборке подобрать функцию $y = g(x)$, пристойно приближающую неизвестную вам зависимость."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Загрузим обучающие и тестовые данные (не забудьте ввести правильный путь!)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data_train = np.loadtxt('C:/Users/Владимир/Downloads/train.txt', delimiter=',')\n",
    "data_test = np.loadtxt('C:/Users/Владимир/Downloads/test.txt', delimiter=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**0. [0 баллов]** Разделим значения $x$ и $y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = data_train[:,0]\n",
    "y_train = data_train[:,1]\n",
    "\n",
    "X_test = data_test[:,0]\n",
    "y_test = data_test[:,1]\n",
    "# Сделайте то же для тестовой выборки\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. [0.1 балла]** Найдите с помощью метода наименьших квадратов линейную функцию ($y = kx + b$), наилучшим образом приближающую неизвестную зависимость. Полезные функции: ``numpy.ones(n)`` для создания массива из единиц длины $n$ и ``numpy.concatenate((А, В), axis=1)`` для слияния двух матриц по столбцам (пара ``А`` и ``В`` превращается в матрицу ``[A B]``). Напечатайте этот многочлен в виде $kx+b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "2.279 x + 4.433\n"
     ]
    }
   ],
   "source": [
    "M = len(X_train)\n",
    "X_t = np.concatenate((np.reshape(X_train, (M, 1)), np.reshape(np.ones(M), (M, 1))), axis=1)\n",
    "y_t = np.reshape(y_train, (M, 1))\n",
    "a = np.poly1d(np.linalg.lstsq(X_t, y_t, rcond=None)[0].ravel())\n",
    "print(a)\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. [0.15 балла]** Нарисуйте на плоскости точки $(x_i, y_i)$ из обеих выборок и полученную линейную функцию."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x190eb130820>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "plt.plot(X_train, y_train, 'o', label = 'train')\n",
    "plt.plot(X_test, y_test, 'o', label = 'test')\n",
    "x = np.linspace(-0.4, 1.2,100)\n",
    "plt.plot(x, a(x))\n",
    "plt.title(\"linear approximation\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend()\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. [0.15 балла]** Глядя на данные, подумайте, многочленом какой степени можно было бы лучше всего приблизить эту функцию с точки зрения минимизации среднеквадратичной ошибки на обучающей выборке. Найдите этот многочлен и напечатайте его в виде $a_0 + a_1 x + \\ldots a_k x^k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       2\n",
      "1.402 x + 1.158 x + 4.472\n"
     ]
    }
   ],
   "source": [
    "X = (np.reshape(X_train, (M, 1)))\n",
    "E = np.reshape(np.ones(M), (M, 1))\n",
    "X_2 = np.concatenate((X*X, X, E), axis=1)\n",
    "a = np.poly1d(np.linalg.lstsq(X_2, y_t, rcond=None)[0].ravel())\n",
    "print(a)\n",
    "\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. [0.1 балла]** Нарисуйте его график на одном чертеже вместе с точками $(x_i, y_i)$ из обеих выборок."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x190eb1a46d0>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "plt.plot(X_train, y_train, 'o', label = 'train data')\n",
    "plt.plot(X_test, y_test, 'o', label = 'test data')\n",
    "plt.title(\"second approximation\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend()\n",
    "x = np.linspace(-0.4, 1.2,100)\n",
    "plt.plot(x, a(x))\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5. [0.25 балла]** Для $k = 1,2,3,\\ldots,10$ найдите многочлен $\\hat{f}_k$ степени $k$, наилучшим образом приближающий неизвестную зависимость. Напечатайте найденные многочлены в виде $a_0 + a_1 x + \\ldots a_k x^k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "2.279 x + 4.433\n",
      "       2\n",
      "1.402 x + 1.158 x + 4.472\n",
      "         3        2\n",
      "-0.3818 x + 1.86 x + 1.065 x + 4.461\n",
      "       4         3         2\n",
      "7.918 x - 13.05 x + 6.794 x + 1.172 x + 4.341\n",
      "       5         4         3         2\n",
      "29.52 x - 51.13 x + 21.37 x + 3.275 x - 0.1306 x + 4.431\n",
      "      6         5         4         3      2\n",
      "-230 x + 581.5 x - 481.5 x + 121.3 x + 16 x - 4.597 x + 4.384\n",
      "        7         6         5         4         3         2\n",
      "-167.4 x + 238.7 x + 122.9 x - 314.2 x + 119.4 x + 7.215 x - 4.009 x + 4.445\n",
      "      8        7        6        5         4         3        2\n",
      "1729 x - 5702 x + 6761 x - 3133 x + 109.9 x + 268.9 x - 26.7 x - 5.183 x + 4.664\n",
      "       9        8        7        6        5         4       3\n",
      "903.2 x - 1522 x - 1216 x + 3913 x - 2442 x + 176.2 x + 219 x\n",
      "          2\n",
      " - 24.26 x - 4.553 x + 4.646\n",
      "       10             9             8             7             6\n",
      "-9819 x  + 4.018e+04 x - 6.362e+04 x + 4.669e+04 x - 1.297e+04 x\n",
      "         5        4         3         2\n",
      " - 1661 x + 1202 x + 44.94 x - 36.18 x - 2.16 x + 4.669\n"
     ]
    }
   ],
   "source": [
    "X_k = E\n",
    "polynomials = []\n",
    "for k in range(1, 11):\n",
    "    X_k = np.concatenate((X ** k, X_k), axis=1)\n",
    "    p = np.poly1d(np.linalg.lstsq(X_k, y_t, rcond=None)[0].ravel())\n",
    "    polynomials.append(p)\n",
    "    print(p)\n",
    "    \n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**6. [1 балл]** Для каждого из них найдите среднеквадратическую ошибку на обучающих данных и на тестовых данных: $\\frac1{n}\\sum_{i=1}^n\\left( \\hat{f}_k(x_i) - y_i \\right)^2$ (в первом случае сумма ведётся по парам $(x_i, y_i)$ из обучающих данных, а во втором — по парам из тестовых данных)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.43512020040488864, 0.3564762887831228, 0.3553464571518441, 0.44172701892836885, 0.5579732021691528, 2.5816929336968504, 2.5157829032610075, 4.357288520729052, 4.776342278511229, 14.632427976659198]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pw = [i for i in range(1, 11)]\n",
    "test_error = list()\n",
    "train_error = list()\n",
    "for p in polynomials:\n",
    "    e1 = 0.0\n",
    "    e2 = 0.0\n",
    "    for x, y in zip(X_train, y_train):\n",
    "        e1 += (p(x) - y) ** 2\n",
    "    for x, y in zip(X_test, y_test):\n",
    "        e2 += (p(x) - y) ** 2\n",
    "    test_error.append(e2 / len(X_test))\n",
    "    train_error.append(e1 / len(X_train))\n",
    "plt.figure(figsize=(15, 10))\n",
    "plt.title(\"Mean Square Error\")\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"MSE\")\n",
    "plt.plot(pw, test_error, 'o', label = 'Mean Square Error on test data')\n",
    "plt.plot(pw, train_error, 'o', label = 'Mean Square Error on train data')\n",
    "plt.legend()\n",
    "print(test_error)\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**7. [0.75 балла]** Для $k = 1,2,3,4,6$ нарисуйте графики полученных многочленов на одном чертеже вместе с точками $(x_i, y_i)$ из обеих выборок (возможно, график стоит сделать побольше; это делается командой `plt.figure(figsize=(width, height))`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x190eb573a00>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 10))\n",
    "plt.title(\"Polynomials\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.plot(X_train, y_train, 'o', label = 'train data')\n",
    "plt.plot(X_test, y_test, 'o', label = 'test data')\n",
    "x = np.linspace(-0.22, 1.05, 100)\n",
    "for k in range(6):\n",
    "    plt.plot(x, polynomials[k](x), label = str(k + 1) + ' degree')\n",
    "plt.legend()\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x190eb6072e0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 10))\n",
    "plt.title(\"Polynomials\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.plot(X_train, y_train, 'o', label = 'train data')\n",
    "plt.plot(X_test, y_test, 'o', label = 'test data')\n",
    "x = np.linspace(-0.4, 1.2, 100)\n",
    "for k in range(3):\n",
    "    plt.plot(x, polynomials[k](x), label = str(k + 1) + ' degree')\n",
    "plt.legend()\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x190ec069520>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 10))\n",
    "plt.title(\"Polynomials\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.plot(X_train, y_train, 'o', label = 'train data')\n",
    "plt.plot(X_test, y_test, 'o', label = 'test data')\n",
    "x = np.linspace(-0.25, 1.1, 100)\n",
    "for k in range(3, 6):\n",
    "    plt.plot(x, polynomials[k](x), label = str(k + 1) + ' degree')\n",
    "plt.legend()\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**8. [0.5 балла]** Что происходит с ошибкой при росте степени многочлена? Казалось бы, чем больше степень, тем более сложным будет многочлен и тем лучше он будет приближать нашу функцию. Подтверждают ли это ваши наблюдения? Как вам кажется, чем объясняется поведение ошибки на тестовых данных при $k = 10$? Как называется наблюдаемый Вами эффект?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ошибка на тестовых данных падает, на тренировочных данных (начиная с $k = 6$) ошибка резко возрастает. Более сложный многочлен лучше приближает нашу функцию на тренировочных данных, но сам по себе отдаляется от истинной функции. В данном случае происходит переобучение, связанное с тем, что при построении модели в обучающей выборке обнаруживаются некоторые случайные закономерности, которые отсутствуют в генеральной совокупности.\n",
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 2. Линейная регрессия (3.5 балла)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Скачайте файлы ``flats_moscow_mod.txt`` и ``flats_moscow_description.txt``. В первом из них содержатся данные о квартирах в Москве. Каждая строка содержит шесть характеристик некоторой квартиры, разделённые знаками табуляции; в первой строке записаны кодовые названия характеристик. Во втором файле приведены краткие описания признаков."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**0. [0 баллов]** Разделите выборку на обучающую и тестовую. Делать это лучше случайным образом (ведь вы не знаете, как создатели датасета упорядочили объекты); рекомендуем вам для этого функцию `sklearn.model_selection.train_test_split` с параметром `test_size=0.3`. Не забудьте зафиксировать параметр `random_state`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "data = np.loadtxt('C:/Users/Владимир/Downloads/flats_moscow_mod.txt', delimiter='\\t', skiprows = 1)\n",
    "names = list()\n",
    "with open(\"C:/Users/Владимир/Downloads/flats_moscow_mod.txt\") as myfile:\n",
    "    names = list(myfile.readline().split('\\t'))\n",
    "for i in range(len(names)):\n",
    "    names[i] = names[i].replace('\\\"', '')\n",
    "    names[i] = names[i].replace('\\n', '')\n",
    "X = data[:, 1:6]\n",
    "y = data[:,0]\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. [0.5 балла]** Вашей задачей будет построить с помощью метода наименьших квадратов (линейную) зависимость между ценой квартиры и остальными доступными параметрами. С помощью известных Вам формул найдите регрессионные коэффициенты. Выпишите построенную модель."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price = 1.6223747524701233 * totsp + 0.9053244076194928 * livesp + 2.023873625340783 * kitsp + -3.583355224840709 * dist + -1.450316831470215 * metrdist\n"
     ]
    }
   ],
   "source": [
    "M = len(X_train)\n",
    "N = len(X_train[0])\n",
    "X_t = np.reshape(X_train, (M, N))\n",
    "y_t = np.reshape(y_train, (M, 1))\n",
    "coeffs = np.linalg.lstsq(X_t, y_t, rcond=None)[0].ravel()\n",
    "res = names[0] + \" = \" + str(coeffs[0]) + \" * \" + names[1]\n",
    "for i in range(2, len(names)):\n",
    "    res += \" + \" + str(coeffs[i - 1]) + \" * \" + names[i]\n",
    "print(res)\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. [0.25 балла]** Какой смысл имеют их знаки? Согласуются ли они с вашими представлениями о жизни?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Знаки переменных можно логично обосновать, положительные коэффициенты относятся к переменным, отвечающим за площадь квартиры и логично, что чем больше квартира, тем больше она стоит, а отрицательные коэффициенты относятся к дальности от центра и метро, чем выше эти расстояния, тем менее удобной для жизни становится квартира и логично, что с ростом этих показателей цена падает.\n",
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. [0.25 балла]** Оцените качество приближения, вычислив среднеквадратическую ошибку на тестовой выборке."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1242.3802671972699\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "c = np.array(np.reshape(coeffs, (5, 1)))\n",
    "M = len(X_test)\n",
    "N = len(X_test[0])\n",
    "X_t = np.reshape(X_test, (M, N))\n",
    "y_t = np.reshape(y_test, (M, 1))\n",
    "print(mean_squared_error(y_t, X_t.dot(c)))\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Усложнение модели"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Конечно, никто не гарантирует, что объясняемая переменная (цена квартиры) зависит от остальных характеристик именно линейно. Зависимость может быть, например, квадратичной или логарифмической; больше того, могут быть важны не только отдельные признаки, но и их комбинации. Это можно учитывать, добавляя в качестве дополнительных признаков разные функции от уже имеющихся характеристик: их квадраты, логарифмы, попарные произведения."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В этом задании Вам нужно постараться улучшить качество модели, добавляя дополнительные признаки, являющиеся функциями от уже имеющихся. Но будьте осторожны: чрезмерное усложнение модели будет приводить к переобучению."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. [0.25 балла]** Опишите признаки, которые Вы решили добавить. Объясните, чем был мотивирован выбор именно этих признаков."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Произведение общей площади квартиры на квадрат жилой площади. Понятно, что покупателю важна не только сама площадь квартиры, но и соотношение жилой площади и оставшейся площади. Если квартира большая, но жилая площадь маленькая, скорее всего это будет не лучший выбор для покупателя, точно так же, как и если жилой площади будет хватать, но оставшейся будет мало (а значит будет не хватать подсобных помещений и так далее). Жилая площадь взята в квадрате, так как мне кажется, что она имеет большее значение, чем остальная часть площади квартиры.\n",
    "2. Произведение общей площади на расстояние до центра. Пожалуй, главными параметрами, влияющими на цену квартиру являются её площадь и её расположение. Поэтому я взял произведение общих параметров (имеется в виду не площадь какой-то отдельной части квартиры и не расстояние до ближайшего метро, а более общие параметры), ведь если квартира имеет и большую площадь и хорошее расположение, это будет выгодно отличать её от просто большой квартиры и небольшой квартиры с плохим расположением. (Думаю среднестатистический покупатель ассоциирует близость с центром с хорошим расположением квартиры).\n",
    "\n",
    "\n",
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5. [2 балла]** Постройте с помощью метода наименьших квадратов (линейную) зависимость между ценой квартиры и новыми признаками. С помощью известных Вам формул найдите регрессионные коэффициенты. Выпишите построенную модель."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price = 2.2468251968568804 * totsp + -1.0674272596604193 * livesp + 2.3916770780607393 * kitsp + 4.913115594094059 * dist + -1.0949381299666914 * metrdist + 0.00022702788703062292 * totsp * livesp^2 + -0.11620358314397548 * totsp * dist\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "def log_ar(X):\n",
    "    return [math.log(i) for i in X]\n",
    "\n",
    "M = len(X_train)\n",
    "N = len(X_train[0])\n",
    "X_t = np.reshape(X_train, (M, N))\n",
    "y_t = np.reshape(y_train, (M, 1))\n",
    "a_1 = np.reshape(X_t[:,0] * X_t[:,1] * X_t[:,1], (M, 1))\n",
    "a_2 = np.reshape(X_t[:,0] * X_t[:,3], (M, 1))\n",
    "X_t = np.concatenate((X_t, a_1, a_2), axis=1)\n",
    "coeffs = np.linalg.lstsq(X_t, y_t, rcond=None)[0].ravel()\n",
    "res = names[0] + \" = \" + str(coeffs[0]) + \" * \" + names[1]\n",
    "for i in range(2, len(names)):\n",
    "    res += \" + \" + str(coeffs[i - 1]) + \" * \" + names[i]\n",
    "res += \" + \" + str(coeffs[5]) + \" * \" + names[1] + \" * \" + names[2] + \"^2\"\n",
    "res += \" + \" + str(coeffs[6]) + \" * \" + names[1] + \" * \" + names[4]\n",
    "print(res)\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**6. [0.25 балла]** Оцените качество приближения, вычислив среднеквадратическую ошибку на тестовой выборке."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "902.6384064636864\n"
     ]
    }
   ],
   "source": [
    "c = np.array(np.reshape(coeffs, (7, 1)))\n",
    "M = len(X_test)\n",
    "N = len(X_test[0])\n",
    "X_t = np.reshape(X_test, (M, N))\n",
    "y_t = np.reshape(y_test, (M, 1))\n",
    "a_1 = np.reshape(X_t[:,0] * X_t[:,1] * X_t[:,1], (M, 1))\n",
    "a_2 = np.reshape(X_t[:,0] * X_t[:,3], (M, 1))\n",
    "X_t = np.concatenate((X_t, a_1, a_2), axis=1)\n",
    "print(mean_squared_error(y_t, X_t.dot(c)))\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 3. Регуляризация (3.5 балла)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вспомним, что задача линейной регрессии формулируется как задача нахождения проекции вектора значений объясняемой переменной $y$ на линейную оболочку $\\langle x_1,\\ldots,x_k\\rangle$ векторов значений регрессоров. Если векторы $x_1,\\ldots,x_k$ линейно зависимы, то матрица $X^TX$ вырожденна и задача не будет решаться с помощью приведённой выше формулы. В жизни, по счастью, различные признаки редко бывают *в точности* линейно зависимы, однако во многих ситуациях они скоррелированы и становятся \"почти\" линейно зависимыми. Таковы, к примеру, зарплата человека, его уровень образования, цена машины и суммарная площадь недвижимости, которой он владеет. В этом случае матрица $X^TX$ будет близка к вырожденной, и это приводит к численной неустойчивости и плохому качеству решений; как следствие, будет иметь место переобучение. Один из симптомов этой проблемы — необычно большие по модулю компоненты вектора $a$.\n",
    "\n",
    "Есть много способов борьбы с этим злом. Один из них - регуляризация. Сейчас мы рассмотрим одну из её разновидностей — **L2-регуляризацию**. Идея в том, чтобы подправить матрицу $X^TX$, сделав её \"получше\". Например, это можно сделать, заменив её на $(X^TX + \\lambda E)$, где $\\lambda > 0$ — некоторый скаляр. Пожертвовав точностью на обучающей выборке, мы тем не менее получаем численно более стабильное псевдорешение $a = (X^TX + \\lambda E)^{-1}X^Ty$ и снижаем эффект переобучения. *Гиперпараметр* $\\lambda$ нужно подбирать, и каких-то универсальных способов это делать нет, но зачастую можно его подобрать таким, чтобы ошибка на тестовой выборке падала.\n",
    "\n",
    "Однако есть некоторые правила, которых стоит придерживаться при подборе коэффициента регуляризации. Обычно в такой ситуации всю выборку делят на три части: обучающую, *валидационную* и тестовую. Сначала по валидационной подбирают значение гиперпараметра, потом по обучающей строят модель, а по тестовой оценивают её итоговое качество. Кроме того, подбирать $\\lambda$ нужно по логарифметической сетке, чтобы узнать оптимальный порядок величины."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. [0.25 балла]** Почему не стоит подбирать коэффициент регуляризации по обучающей выборке? По тестовой выборке?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вполне возможно, что будет иметь место переобучение и в общем случае наше решение будет менее точным.\n",
    "\n",
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. [0 баллов]** Теперь давайте вспомним первую задачу. Если Вы её сделали, то помните, что ошибка аппроксимации многочленом шестой степени довольно высокая. Попытаемся использовать регуляризацию при построении модели. Поделите обучающую выборку из первой задачи на две части, одну из которых объявите обучающей, а другую — валидационной (будьте осторожны при выборе `train_size`, в этой выборке не так много данных)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_train = np.loadtxt('C:/Users/Владимир/Downloads/train.txt', delimiter=',')\n",
    "data_test = np.loadtxt('C:/Users/Владимир/Downloads/test.txt', delimiter=',')\n",
    "\n",
    "X_test = data_test[:,0]\n",
    "y_test = data_test[:,1]\n",
    "\n",
    "X_valid, X_train, y_valid, y_train = train_test_split(data_train[:,0], data_train[:,1], train_size=0.5, random_state=42)\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. [0.75 балла]** Убедитесь, что, используя регуляризацию с хорошо подобранным коэффициентом $\\lambda$, ошибку на тестовой выборке можно сделать не больше, чем для многочлена оптимальной степени в модели без регуляризации."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error with regularization: 0.34516361936863255\n",
      "best error without regularization: 0.35534645715184415\n"
     ]
    }
   ],
   "source": [
    "lam = 0\n",
    "lam_err = 10000000\n",
    "delta = 0\n",
    "M = len(X_valid)\n",
    "X_v = np.concatenate((np.reshape(X_valid, (M, 1)), np.reshape(np.ones(M), (M, 1))), axis=1)\n",
    "y_v = np.reshape(y_valid, (M, 1))\n",
    "N = len(X_train)\n",
    "X_tr = np.concatenate((np.reshape(X_train, (N, 1)), np.reshape(np.ones(N), (N, 1))), axis=1)\n",
    "y_tr = np.reshape(y_train, (N, 1))\n",
    "L = len(X_test)\n",
    "X_te = np.concatenate((np.reshape(X_test, (L, 1)), np.reshape(np.ones(L), (L, 1))), axis=1)\n",
    "y_te = np.reshape(y_test, (L, 1))\n",
    "for k in range(2, 7):\n",
    "    X_v = np.concatenate((np.reshape(X_valid, (M, 1)) ** k, X_v), axis=1)\n",
    "    X_tr = np.concatenate((np.reshape(X_train, (N, 1)) ** k, X_tr), axis=1)\n",
    "    X_te = np.concatenate((np.reshape(X_test, (L, 1)) ** k, X_te), axis=1)\n",
    "'''while delta < 1:\n",
    "    delta += 1e-3\n",
    "    A = np.transpose(X_v).dot(X_v) + np.identity(7) * delta\n",
    "    B = np.transpose(X_v).dot(y_v)\n",
    "    a = np.linalg.inv(A).dot(B)\n",
    "    mse = mean_squared_error(y_v, X_v.dot(a))\n",
    "    if mse < lam_err:\n",
    "        lam_err = mse\n",
    "        lam = delta\n",
    "'''\n",
    "lam = 0.2\n",
    "A = np.transpose(X_tr).dot(X_tr) + np.identity(7) * lam\n",
    "B = np.transpose(X_tr).dot(y_tr)\n",
    "a = np.linalg.inv(A).dot(B)\n",
    "\n",
    "mse1 = mean_squared_error(y_te, X_te.dot(a))\n",
    "y_old_pred = [polynomials[2](x) for x in X_test] # приближение многочленом 3 степени без регуляризации\n",
    "mse2 = mean_squared_error(y_te, y_old_pred)\n",
    "\n",
    "print('error with regularization: ' + str(mse1))\n",
    "print('best error without regularization: ' + str(mse2))\n",
    "\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. [0.25 балла]** Для этого $\\lambda$ сравните $\\det(X^TX)$ и $\\det(X^TX + \\lambda E)$. Чем можно объяснить такой результат?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.441254371592972e-15 0.03685469388776301\n"
     ]
    }
   ],
   "source": [
    "det1 = np.linalg.det(np.transpose(X_tr).dot(X_tr))\n",
    "det2 = np.linalg.det(np.transpose(X_tr).dot(X_tr) + np.identity(7) * lam)\n",
    "print(det1, det2)\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5. [0.25 балла]** Нарисуйте на одном чертеже графики многочленов шестой степени, приближающих неизвестную функцию, для модели с регуляризацией и без."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00628418 0.03220246 0.0978189  0.27145681 0.71435569 1.29961238\n",
      " 4.48171155]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x190ee07a670>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cpbz0BN164RxdfnK+02VNTKO8lm4kQvcuUG/FPnXv96q72auevsuQv2/rcJdLccXFip87V/Hz5so3b57i58+XJyNjXOuMVsaYddbaZUM9xkgfAAAARt1j66t0+1/fU5c/KEmqau7S7X99T5IIfuNtDLYnO5ZAU5N6tm1Td+lW9WzbGr4skxTMlSQZd0i+tIBSi/yKX/Uhxb//Ovlmz5YrIWFM6pnoCH0AAAAYdT94dttA4OvX5Q/qB89uI/SNtzHYnqyf9fvVs3u3erZtC4e8reHLQH39wDGe3Fz55s5R8qpVik/cL1/NXxRna2QynBlxnIgIfQAAABh11c1dWu16TV/xPKo806Bqm63vB67Rk81nOl3axDMK25NZaxWor1fP9h3hgLd9m7q371Dvzp0D2yMYr1dxM2cqacUK+ebOVfyc2fLNnStPZuYhr3b3CD8RjBShDwAAAKPuhuS39RX/g0o0vZKkAtOge7wPKtMbJ+kSZ4sbZ12BLrX0tCgQCsgf8h90GQgFFLRBpfnSNDlpslK8KaPfoOQ4tycLdXaqZ+dO9Wzfru7t2weCXnD//oFjPLm58s2ereSVK+SbMyf8UVws4/WObu0YFYQ+AAAAjLqveP+kxEDvQfclml59xfsnSd90pqgx4g/6tbd1r6o7qlXdHv6oaq8KX++oVlN307BfK8GToEmJkzQpaZImJU7S5KTJKkgu0LLJy1SYUjiyAo+wPZk952vq7Q93O3aEw9327fJXVg5sjWASEuSbNUsp7z9Pvtlz5Js9W77Zs2iuEmUIfQAAABh1iV37juv+aBEIBVTWXKYtjVu0uXGztjRu0bambeoNHQi4ca445SXnKS85T3Oz5io/OV9pvjR5XV55XV55XJ6DLt3GraaeJtV21Kq2s1b7OvaptrNWb9W8pfqueoVsSJI0NWWqzsg7QyvyVujUyacqOS55WDXbhVfJX9uknqd+qp7qZvV0pamnN1c9f/yu1Dc1U2634oqKFL9wgdKuuFzxs2fLN2uWvIWFMi7XqJ9HjC9Cn4Muvvhi/f73v5ck/f73v9fNN98sSVqzZo3uvfdePfXUUyf8HmvWrFFcXJxWrFhxwq91PG688UZdeumluuqqq4b9nF/+8pdKTEzU9ddff1zvdejnONLXAQAAo+g4pxRGqpaeFpXsK9E7te9oU8MmbWvapu5gtyQp2Zus+Vnz9dF5H9WczDkqTClUfnK+MuMz5TKjE5QCoYDKW8u1tmat3qh+Q0+UPaE/bfuTPMajxTmLtSJvhc6bep5mZsyUDYXkr65Rb9nO8PTMHX2XZWWyXf2jfKny5ufJN2uWki+cJd+smfLNnq244mK5fL5RqRmRh9DnoGeeeUaStGfPHt1///0DoW80rVmzRsnJyccMfYFAQB6Pc18OgUBAN91004iee+jnONLXAQAAo+gIUwp13h3O1TQMnf5O/avuX3q75m29te8tlTaWysoqwZOgeZnzdPWcq7Uga4EWZC3Q1NSpoxbujsTj8mh6+nRNT5+uj837mHqDvXq3dr3+9d4/Vf7u69r75E/0z/ofq7I1Rbl1vTJd3Qeem5sr38yZyrjmmnC4mzVLcTNmyp2cNKY1I/IQ+sbI97//fcXHx+vzn/+8vvSlL+ndd9/Viy++qBdeeEEPPfSQHnnkERUVFamkpES33XabysrKtGTJEp1//vm65JJL1N7erquuukqbNm3S0qVL9cgjj8gYoxdeeEFf/vKXFQgEtHz5cv3iF7+Qz+cbeK3s7GyVlJToy1/+sh5++GH98pe/lNvt1iOPPKKf/vSnOuusswZqvOuuu1RdXa09e/YoOztbP/7xj3XTTTepvLxckvSjH/1IK1euVH19vT760Y+qsbFRy5cv1z/+8Q+tW7dO7e3tuvTSS7Vp0yZJ0r333qv29nbdddddB52Lu+++W08++aS6urq0YsUK/c///I+MMVq1apVWrFih119/XatXr1ZbW5uSk5P10Y9+VBdffPHA89977z3t2rVLGzdu1P/7f/9Pvb29ysrK0u9+9zt1dXUd9jm+8MILSk5O1pe//GVt2LBBN910kzo7OzVjxgz95je/UUZGhlatWqXTTjtNL730kpqbm/XrX//6oHMDAABOUH8bfoc3BD+WkA2ptLFUr1S+orU1a/Ve/XsK2IC8Lq9OyjlJ/7HkP3Ta5NO0KHuRvO7xbVJig0H5KyvVU7ZLPWU71buzTD1lZUrZtUtnd3YOHNeTnqiyjC6tWxCQe8Z0nbHyGi099YPypKePa72IXBMi9H3v7e9pa9PWUX3NuZlz9dVTv3rEx88++2zdd999+vznP6+SkhL19PTI7/frtddeOyxc3HPPPdq0aZM2bNggKTxytX79em3evFl5eXlauXKlXn/9dS1btkw33nijXnjhBc2ePVvXX3+9fvGLX+iLX/zikDUUFRXppptuGghAQ1m3bp1ee+01JSQk6KMf/ai+9KUv6cwzz1R5ebkuvPBClZaW6pvf/Kbe97736fbbb9c//vEPPfDAA8d1rj772c/qjjvCf9X7+Mc/rqeeekqXXXaZJKm5uVkvv/yyJA2Exby8vIFz8fOf/1wvv/yypk2bptTUVL355psyxujBBx/U97//fd13332HfY4vvPDCwHtff/31+ulPf6pzzjlHd9xxh775zW/qRz/6kaTw6OLbb7+tZ555Rt/85jf1/PPPH9fnBQAAjmHxNREX8iSpw9+hN6vf1CtVr+iVylfU0NUgI6MFWQt0w4IbdOqUU3Vy7slK8IzPRuGh3l717tmj3l271LOzTL27ytRTtku9u3fL9h5YK+iZNCk8cnf1VYqbMUO+mTPlmz5d7vR0zfZ36s/b/6zfbv6tfl1zrxa89nd9atGndO7Uc8d8NBKRb0KEPicsXbpU69atU1tbm3w+n0455RSVlJTo1Vdf1U9+8pNjPv/UU09VQUF4zvuSJUu0Z88epaSkqLi4WLNnz5Yk3XDDDfr5z39+xNA3HKtXr1ZCQvh/aM8//7y2bNky8Fhra6va2tr02muv6W9/+5sk6QMf+IAyjrNb00svvaTvf//76uzsVFNTkxYsWDAQ+q699tojPu/111/Xgw8+qFdffVWSVFlZqWuvvVY1NTXq7e1VcXHxUd+3paVFzc3NOueccySFz9fVV1898PiVV14pKfxvtWfPnuP6nAAAQHSpaq/Smoo1eqXyFb2z7x35Q36leFO0In+Fzik4RyvzVyoz/tD95EZXsLU1HOzKdql3d9/lrl3qrayUgn0b2Rsjb0GBfNOnK2nlSvlmTFfc9OnyzZwpd0rKEV870Zuo6xdcrw/P/bCeLHtSv970a31xzRc1PW26bl1+q87MZ3/EiWxChL6jjciNFa/Xq6KiIj300ENasWKFFi9erJdeekllZWWaN2/eMZ/vG7SQ1u12KxAIyPa1zh2Kx+NRKBTu7NTd3X3E4w6VlHRgTncoFNLatWsHQmC/I73v4Pc80vt2d3fr5ptvVklJiQoLC3XXXXcddNzg9x+spqZGn/zkJ/XEE08oOTncmepzn/ucbrnlFq1evVpr1qw5bBrp8eo/x/3nFwAAxA5rrXY079CL5S/qxfIXVdpUKkkqTivWR+d+VOcUnqMluUvkdY3ulM2BZiq7wyN1Pbt2qXfXbvXs3qVgfcPAccbrVVxRkXxz5yrl4ovkmz5DvpkzFFdUJFfCyEcY49xx+tDsD+mDMz+o5/Y+p1+8+wv9x/P/oevmXacvLv2ifG6atUxEEyL0OeXss8/Wvffeq9/85jdatGiRbrnlFi1duvSwDTdTUlLU1tZ2zNebO3eu9uzZo507d2rmzJn63//934FRrKKiIq1bt04XXXSR/vKXvxz02q2trcOq94ILLtDPfvYz3XrrrZKkDRs2aMmSJTrzzDP16KOP6qtf/ar++c9/an/fxpyTJk1SXV2dGhsblZycrKeeekof+MAHDnrN/oCXnZ2t9vZ2/fnPfz5mR0+/369rrrlG3/ve9wZGNaXwyF1+fr4k6be//e0xP8e0tDRlZGTo1Vdf1VlnnXXQ+QIAALEnZEPaWL9RL5S/oBfKX1BFW4WMjE7KOUn/ufQ/9b6p79PU1Kmj8l7B9nb17t6j3j27w+Fu92717tqt3j17ZHt6Bo5zpaXJV1ys5LPODo/aFU+Xb8Z0efPzZcawiZ7H5dFFxRfp3MJz9d/r/luPlD6it/e9re+d9T3NzJg5Zu+LyEToG0NnnXWWvv3tb+uMM85QUlKS4uPjh2wWkpWVpZUrV2rhwoW66KKLdMkllwz5evHx8XrooYd09dVXDzRy6e9Ueeedd+qTn/ykvvOd7+i0004beM5ll12mq666So8//vhhjVwO9ZOf/ESf+cxntHjxYgUCAZ199tn65S9/qTvvvFMf+chH9Kc//UnnnHOOpkyZopSUFHm9Xt1xxx067bTTVFxcrLlz5x72munp6frUpz6lRYsWqaioSMuXLz/meXvjjTf0zjvv6M4779Sdd94pKdzp9K677tLVV1+t/Px8nX766dq9e/eQn+Ngv/3tbwcauUyfPl0PPfTQMd8fAABEj0AooJLaEj2/93m9WP6i6rvq5XF5dNrk03Tjghv1vqnvU3ZC9ohe2/r98ldVqWfPnnDA290X8PbsPmjUTi5XeEpmcbGSVqxQ3PRi+YqLFTd9utwZGYf9wX88xXvidftpt2tl/kp94/Vv6MNPf1hfXvZlXTvnWkfrwvgyR5syGC2WLVtmS0pKDrqvtLR0WNMocWw9PT1yu93yeDxau3at/uM//mOg0Uqs4+sIAIDI0xvs1Zs1b+q5vc/ppYqX1NLTogRPgs7MP1PnTT1PZxWcpdS41GG9lrVWgbq6cKjbuzfcUGV3eMSut7JSGrQExJ2errji4r6PonCwKy6Wt7BQrri4sfp0R01DV4O+/vrX9XrV61pVsErfXPnNMV/HiPFjjFlnrV021GOM9OGYysvLdc011ygUCikuLk6/+tWvnC4JAABMMJ3+Tr1R/Yae2/ucXql8Re3+diV7k3VO4Tk6f+r5WpG/4ojdNq21CjY1hUNdf7jrD3jl5YM2LpeMz6e4adPkmzNHKRdeqLiiIsUVTVNcUZE8x9nMLtJkJ2Tr/vPu1+9Lf68frvuhPvTEh/TtM7+tFXlH388Z0Y/Qh2OaNWuW1q9f73QZAABggmnpadErla/ohfIX9HrV6+oOdivdl64Lii7QeVPP0+lTTlecOzzCZq1VoKlJvXv6At3ePfKXl4dvl5cr1N5+4IU9HsUVFChu2jQlnX5aONhNm6a4adPkmTJFxhW7Wxy4jEvXzb9Oyycv11df+apueu4mfXPFN3XFrCucLg1jiNAHAACAiNHQ1aAXy1/UC+Uv6O2atxWwAeUm5uqKWVfo/YXnabF7qkIVVep9q1zN5fert3yv/HvLDw92bre8+fmKmzpVaSef3BfqpiquqGjMm6hEgzmZc/SHS/+gL635ku58I9xDgeAXuyb2VzsAAAAcZa3V7tbdeqn8Ja2pWKP3ajcoq8VqUU+OvqZlmteVrtT6Lvkr3lJvxZ+1e9BUTHk88ubnKW7aNKWdcoriphYqbto0eadOVVx+vkwUrLNzUoInQT8+98f6wotfIPjFOEIfAAAAxlVvW6s2vfeCNr/7gvZt3yDvviZNapZuavUqvTkkVzAkaZ+kfTI+n3oLCxRXOFVJZ5weDnRTw6N23ilTZLyju8/eRONz+/Tj9x0IfsYYXT7zcqfLwigj9AEAAGBU2WBQgdpa9VZUyl9Zod7KSnXu3aXmXdsUqtqnhLYeJUjqbzMYSEmQr3CqkuZNl7egMBzoCgsVN3WqPLm5Mb3GLhL0B7/Pv/h53fH6HTIy+uDMDzpdFkYRoc9BF198sX7/+99Lkn7/+9/r5ptvliStWbNG9957r5566inHaisqKlJJSYmys4e/r82///u/65ZbbtH8+fOP670efvhhXXDBBcrLyzuh1wGAieCx9VX6wbPbVN3cpbz0BN164RxdfnK+02VhgrHWKtjcLH9llfxVleqtqAhfr6xUb2WF/NU1kt8/cHzIJdWnSrXpRs0z45RcPF+Fc0/VwsXnKW36bLlTh7e9wrEM+f3hfl164W6ppVJKK5DOu0NafM2ovF8s8bl9+vG54eD3jde/IUkEvxhC6HPQM888I0nas2eP7r///oHQNxKBQEAeBxckB4NBPfjggyN67sMPP6yFCxcOhL6Rvg4AxLrH1lfp9r++py5/UJJU1dyl2//6niQR/DDqQh0d6u0LdQPhrrJK/qpwuDuoaYrCe9iZvMlqmZqpPfMT9K53n8oS21SbbpRbPF8rpp6ls/LP0sLshfK4Rv93lqG+P1772/261PugPMHu8EEtFdKTnw9fJ/gdJt4Tr5+87ycEvxhE6Bsj3//+9xUfH6/Pf/7z+tKXvqR3331XL774ol544QU99NBDeuSRRwZG02677TaVlZVpyZIlOv/883XJJZeovb1dV111lTZt2qSlS5fqkUcekTHmoPdYtWqVVqxYoddff12rV6/WqlWrdMstt6i9vV3Z2dl6+OGHNWXKFL3zzjv65Cc/qaSkJJ155pn6+9//rk2bNunhhx9WSUmJfvazn0mSLr30Un35y1/WqlWrDnqfyy+/XBUVFeru7tYXvvAFffrTn5YkJScn65ZbbtGzzz6r++67T1//+td17733qrq6WnfccYckqaurS729vdq9e7fuvvtuPfnkk+rq6tKKFSv0P//zP/rLX/6ikpISfexjH1NCQoLWrl2riy66SPfee6+WLVumP/zhD/rOd74ja60uueQSfe973xt47y984Qt66qmnlJCQoMcff1yTJk0a439VAHDWD57dNvALbb8uf1A/eHYboQ/HLdTRIX91tXqr+oJcVXXfZTjUBZubDzreJCQoriBf3rx8JS5dKm9hgezkHG1LaNbbZo9eb16vbfu3SZJS4lK0Iu9MXZt/llbmr1R2wvBnDo3UUN8fX9QfDwS+fv6u8MjfeIa+jY9GzWjjocHPZVy6bMZlTpeFEzQhQt++73xHPaVbR/U1ffPmavJ//dcRHz/77LN133336fOf/7xKSkrU09Mjv9+v1157TWedddZBx95zzz3atGmTNmzYICk8vXP9+vXavHmz8vLytHLlSr3++us688wzD3uf5uZmvfzyy/L7/TrnnHP0+OOPKycnR3/605/0ta99Tb/5zW/0iU98Qg888IBWrFih22677bg/19/85jfKzMxUV1eXli9frg996EPKyspSR0eHFi5cqLvvvvug41evXq3Vq1dLkq655hqdc845kqTPfvazA2Hw4x//uJ566ildddVV+tnPfjYQ8garrq7WV7/6Va1bt04ZGRm64IIL9Nhjj+nyyy9XR0eHTj/9dH3729/WV77yFf3qV7/S17/+9eP+3AAgmlQ3dx3X/ZjYgm1t4QBXXX0g0FUfuAzu33/Q8SYuTt78fHnz8xW/YIG8BfmKy8+Xt6BA3oICuTMy1BXo0nsN76mktkRv1byo9+reU8AGFOeK08m5J+tzJ39Op005TQuyFozJaN7RDPV9kGcahj64pXKMqxlk46Ph0UV/X31RMNrYH/w+++Jndccbd6gotUiLchY5XRZOwIQIfU5YunSp1q1bp7a2Nvl8Pp1yyikqKSnRq6++qp/85CfHfP6pp56qgoICSdKSJUu0Z8+eIUPftddeK0natm2bNm3apPPPP19SeLrllClT1NzcrLa2Nq1YsUKS9NGPfvS41wr+5Cc/0d/+9jdJUkVFhXbs2KGsrCy53W596EMfOuLzvv/97yshIUGf+cxnJEkvvfSSvv/976uzs1NNTU1asGCBLrvsyH85euedd7Rq1Srl5ORIkj72sY/plVde0eWXX664uDhdeumlksLn+rnnnjuuzwkAolFeeoKqhvrFNj3BgWrgJBsKKdDQoEB1tfw1NQeC3aDboba2g55j4uPlzcsLh7qFC/sCXl442OXny52VdVjDlLrOOq2tW6/1O5/R+rr12ta0TUEblMu4tDBroW5ceKNOm3KaluQsUbwnfjxPwWGG+v6ottkqGCr4pRWMU1UKj/D5D/m+dWK08TjFe+J13zn36Zonr9Gtr9yqRy97VKlxo7P2EuNvQoS+o43IjRWv16uioiI99NBDWrFihRYvXqyXXnpJZWVlmjdv3jGf7/P5Bq673W4FAoEhj0tKSpIUXlC9YMECrV279qDH9x/yV7zBPB6PQqHQwO3u7u7DjlmzZo2ef/55rV27VomJiVq1atXAcfHx8XK73UO+9gsvvKD/+7//0yuvvDLw2jfffLNKSkpUWFiou+66a8j3G8xae8THvF7vwHTXo50fAIglt14456A1S5KU4HXr1gvnOFgVDjMKU/lCXV3y1+yTvyYc5AI1NfJX14QDXU2NAjU1soMapUiSKyUlHOry8pS4bJm8eVMGRu68eXlyZ2YetlRksE5/p7Y1bNPmhs3a1LhJG+o2qKq9SpIU747XopxF+uSiT+rk3JN1Us5JSolLOf5zM4aG+v74kT6se9wPHjzF05sQ/jcZL0caVRzP0cYRSvOl6Qfn/EA3/P0G3fH6HfrvVf991K8hRK4JEfqccvbZZ+vee+/Vb37zGy1atEi33HKLli5detg3S0pKitoO+Wvc8ZozZ47q6+u1du1anXHGGfL7/dq+fbsWLFiglJQUvfnmmzr99NP1xz/+ceA5RUVFuv/++xUKhVRVVaW33377sNdtaWlRRkaGEhMTtXXrVr355pvHrGXv3r26+eab9Y9//EMJCeG/PvcHvOzsbLW3t+vPf/6zrrrqqqN+/qeddpq+8IUvqKGhQRkZGfrDH/6gz33ucyM6PwAQC/rX7cV6986o7lA6jKl8NhBQoL5+INQF9u07EOj21ShQXXPYejoZI09urrx5eUpYuFDeC86XZ8qUvpCXL2/eFLlTUg6u44W7pYpBwTPrQPDs9Hdq2/5t2tK4RVsat2hzw2btbt2tkA3/MTg7IVsn556sj879qE6ZdIrmZM6R1xXZ++EN9f1x5oU3y+M+ydn1dGkF4a+Doe6PAotzFuuLS7+oe0vu1e+3/l4fm/cxp0vCCBD6xtBZZ52lb3/72zrjjDOUlJSk+Pj4w9bzSVJWVpZWrlyphQsX6qKLLtIll1xy3O8VFxenP//5z/r85z+vlpYWBQIBffGLX9SCBQv061//Wp/61KeUlJSkVatWKS0tTZK0cuVKFRcXa9GiRVq4cKFOOeWUw173Ax/4gH75y19q8eLFmjNnjk4//fRj1vLwww+rsbFRV1xxhSQpLy9PzzzzjD71qU9p0aJFKioq0vLlyweOv/HGG3XTTTcNNHLpN2XKFH33u9/VueeeK2utLr74Yn3wg3SQAjCxXX5yfvQEoBGI9g6l9vlvKtDao0CnV/4utwKdbvk73fK/fpcCqX+Tf98+BerqpEEzbSTJlZws75Qp8uRNUcKixfJOmSLvlMny5uXJMyVP3km5w9+EfFDw7DJGu7v2qeyFW7Wz6gWVxXm1s3mnqturZRWeUZOdkK35WfN1ftH5mp85XwuyFyg3MXe0T824GPr74xpnp1Ged8fBfwiQxn+08QRdP/96vbPvHd1Xcp+W5C7RgqwFTpeE42SONoUuWixbtsyWlJQcdF9paemwplFOBO3t7UpOTpYUbhpTU1OjH//4xw5XFR34OgKA8bXynheHXLeYn56g1297nwMVHWCDQQUaGhWo3RcOb/tq5a/dp0DNPvlra8NTMGuqJHvwjB7jtvImBuVZcKa8kyfLM2WyvJPDoc4zebK8Uw4ZpTtO3YFuVbZVqrK9UhVtFap89XuqCHVrj9ejSo9Htm+GkcdaFWXM0oz0GZqRPkNzM+ZqftZ85SbmMmVvrEVR984jae5u1tVPXS2P8ejRyx6NuOm9kIwx66y1y4Z6jJG+CeDpp5/Wd7/7XQUCAU2bNk0PP/yw0yUBAEbIH/Sr3d+uDn+HOgOd6vSHPzoCHerwd6gr0KXeYK96g73qCfaoN9Q7cLs32Ct/yB/eWNsGFbKhAx8KKWjDo2suuWSMkUsuyUhGRi7jksu45DZueVyeAx8mfOl1eeVxeRTnjpPP7TvoMs4dJ5/LJ5/bJ5/Hp3hPvOLd8Yr3xMvn9g1c97g8jnUoDfX2KlBXF55qWVurwL5aBepq5a8ddF9dnRQ8eEsA4/WGg9vkyUpYtlSp5TXyuPfLmxgMB72EkNy+kEx6ofSlh467ru5At+q76lXXWaf6znrVdtaqvjN8u7azVpVtlarrqjvoOclxVoV+t+b19Oqy9g7N6PVrpt+vQn9Q3hs3ndB5wggtdni0cRSkx6frB2f/QDf+40bd+caduu+c+/hjQRQh9E0A11577UCXTwBA5AjZkJp7mtXQ1aDGrkY1dDWoqbtJTd1NaulpUWtvq1p6WsIfveHLrsDxhZ84Vzh8ed1e+dw+eVweuY1bxhi5jXsgzLmMKxzyJFnZgbVdIRuS7fsvFAoHQ3/Ir0AoEP6wgYHr/pB/4Hkj4XF5lDzHq1DQK1mvbChOCoUv4z3x+srLL4cDoydeCZ6E8KU74UB47AuTPo9v4NLn8snX3it3Y4tcDc0yDU1SfaNC9Q0K1NbJX1enQG2tgk1Nh9VjEhPlzc2VZ9IkJZ16al+4myTPpL7LyZPlzsg4+Bffjcv6pvL1SJICktriEtV51hfV2bJLXf6ugwJ7W2+bmnua1dzTrJaeloMu9/fsV1vv4WvefW6fchNzNSlxklbkr1BBcoEKUwpVmFKogpQCpf/iLJmWfYef4LTCEf/bAJK0JHeJPnfy5/Sjf/1If9r2J3147oedLgnDFNOhz1rLXyAwYrEw9RmAc/whv+o767WvY5/2dexTTUfNwPXaztqBgNc/ujaY1+VVui9dab40pcalKi85T/N885QWl6ZUX6qSvElK8iYp0ZMYvvQmKtGTOHDpc/sGAt54/xwMhAJDjjT2BHvUG+xVV6BLPcEedQe61R3sVnegWz3BHnUFutQd6Nbmmga9satGQfVILr+M8cvt7lV2ekilTaXqCnQNHGu6e5TeLmW2S5ltVhmHXGa2Sxltkv/wU6yWRGl/ilFLqlstxR61LElWS6pHbWletaXHqT09Tv54r9xuj4zaZbVD0o5w/G2zUpukHeGfFQEbkD/oHwi+/qkF8ge75ZcU6j//m38c/jiCRE/iwL95ui9d+cn5SvOlKScxRzkJOZqUOEm5ibnKScxRalzq0f9dY2ANGSLXJxZ+QiW1Jfr+O9/XSTknaV4Wy2CiQcyu6du9e7dSUlKUlZVF8MNxs9aqsbFRbW1tKi4udrocABGqtbdVFW0VqmitCF8O+qjvqj9s1CslLkVTkqZoUuIk5STmKCs+S1kJWcpOyFZ2Qray4sPXk7xJ0fezaxTXLD3+ZpkeeqJEgbo6zXB368qpPs3z9YZH5erqw9Mw6+oUam8/7Lk23iebnaFgVpoCmanqzUxWT2aiujKS1J2eoM70eHWkxanHFVJvqFf+oF/+kF9BG1QwFAxfDroeCB3YEsgo/G9ijDnoev/01v4prl6XV153+HacK+6gUJ7kTVKCJ0Fvl3Xof9+oUV2LNDk5S1+5cMHoNqoZ4t/jseDK6O2KiojS1N2kq5+4WvGeeP3p0j8pOS7Z6ZKgo6/pi9nQ5/f7VVlZecy94IAjiY+PV0FBgbzD7ZYGICYFQgFVtlVqd8tu7WrZpd0tu7W7Zbf2tu1VS0/LQcdmh6wKU6aqcPLJmpI0RZOTJg9cTk6arCRvkkOfxRg7dJsCKTyydNlPDmxTYK1CHR3h0FZ/lI+6usM2FZf61s7l5h74yMnpu54jT06OvJMmyTNpklzJyREfmA/tUCqF91v87pWLxiyEOfGeiG3ratfp3579N10560rdecadTpcDTdDQBwDA8QjZkCraKrRj/w5t379dO5t3alfzLu1t23vQaE9uQq6K04o1LXWaprY3qWDjX1TY3amCQECJ1h4WdmKdDQQUuOckBev3KdDlVqDbdeAykKxAxinhMNfQINt1+HpE4/OFA1x29uGBLidnINS509MjPswNlxMdSiO5Kyqi1/fe/p5+V/o7PXrZo5qbOdfpciY8uncCADBIW2+btjZt1fb92w8Kef1NUoyMClMKNT19us4pPEfFacWanjZdxWnFB7cp/++FUtvBo33yd4Wn1UVx6LPWKtjcrGBjowINDQrUNyjQ2KBg//WGAx/BpibJWkkH7+vm8obkSQjIk+tVwuLF4QA3KMT1f7hSUmImzA2XEx1KneqKith200k36eldT+uet+/RQxc+NOG+l6MJoQ8AMGYeW1/l+Bqi5u5mbWnaotLGUpU2lWpL4xZVtFUMPJ7hy9DsjNn60KwPaXbGbM3OmK3p6dOV4Ek49ou3VB7f/Q6yoZCCLS19Qa4xHOL6rzf0h7pGBRrDH/L7D3sN4/XKnZMtT3aOvPn5SjjppPAI3cZfyK1GeeKD8sSH5IkPyuVRuFvklx4e3080CvZDy0tPGHLULS99GF9zUfSeiH1pvjR99uTP6ltvfkv/3PtPXVh0odMl4QgIfQCAMXHoGqKq5i7d/tf3JGnMgl+Hv0NbGrdoY/1GbWrYpC2NW1TdUT3weH5yvuZnzdeVs67U3My5mps5V1nxJ9DwK61AaqkY+v5xYP1+BZr2K9jUqEBjk4KNDQo0Nh0W4IKNjQo0NUmBwOEv4vHIk5UlT1aW3NlZ8s2ZE76dky13VpY82TnyZGfJk50tV+oRukZunNS3pm9QUHSiW+ShawtbKsK3pYgKfrdeOGfI9XW3Xjgnpt4TE8OHZn1If9r2J91Xcp/OKThH8Z54p0vCEFjTBwAYE2O9higQCmjH/h16r+E9bWrYpPca3lNZc5mswj/XClMKtSBrgeZnzde8rHmalzlPab60E37fgwyjgcnxsNYq1NJycJBrCge2YGNT3+WBIBdsaRnydUxcnNzZWfJkZYfDXFZm+Hp2VjjIDbruTkuTcblGegYOiIQRtv9eeIQQXih9KbI2JXdiFDwSRt4Rm97Z947+7dl/02eWfEY3nXST0+VMWDRyAQCMu+LbntZQP2GMpN33XHLcr9fc3ayNDRu1oW6DNtRv0KaGTQNr8NJ96VqYvVCLsxdrYfZCLcpepPT49BOqf9iOEnastQq1tobDWlNfaGvar+D+pr5A16RAU6OCTfvDl/ubhx6Nk+ROSwuHtMyMQ8Jcf5DLkiczU+6srKjoYDkm7kqXjvRVd1fz+NYCTDC3rLlFr1a+qieveFKTkyY7Xc6ERCMXAMC4O5E1RNZa7W7drfW167WhfoM21G3QntY9kiS3cWtO5hxdMfMKLc5ZrMXZi1WQUjAuIcf6/Qo2Nyuwf/+B8LY/oKD3PxR0NSlYsV+BH/5dwabfKbC/6aghzpWUFA5rGRny5ucrftFCeTL7Ql1fePNkZcmdmSlPRoYM28ccm8PTbYGJ7D+X/adernhZ/73uv/W9s7/ndDk4RMSGPmPMHkltkoKSAkdKrQCAyHQ8a4j8Qb9Km0q1vm691tWu0/q69WruaZYUbhSwJGeJPjjzgzop5yQtyFqgRG/iCddnQyGF2toU3L8/HOL2Nyu4f7+CzfsP3NcUvt5/O9TaesTXc6WmypORIXdmprwFBYpfvOjgEJeR2TdKlyV3RoZcPt8Jfw44xHl3DD3ddrzXFgITUH5yvm5ceKMe2PiAPjz3wzo592SnS8IgETu9sy/0LbPWNhzrWKZ3AmOLdSAYqSN97XT6O/Vu/bsDAW9j/UZ1B7slSVNTpurk3JN1yqRTtCR3iYpTi485imeDQQVbW8PBrbnvY//+vuv7D4zONTcfdIyCwSFfz3i9cvcFOHdGujwZmeHbGRnh4NZ/PSNTnsyM8B5yjMRFhkhYWwhMUJ3+Tl322GXKTsjWHy75g1xmFNYLY9iick0foQ8RgV8eDuvAKIVHa7575SKCH4atpadlYBRvXe06lTaWKmADchmX5mTM0dJJSweCXqaSwqGspeVAgBv4GOq+8LE60s8zr1ee9HS509MPBLe+257MjEH3hS89GekyiYkTc00cAJygp3c9rdtevU13r7hbV8y6wulyJpRoDX27Je1XeEX2/1hrHzjk8U9L+rQkTZ06denevXvHv0jEtlHuyhetxroDY9ThDwHD0tDVoH+Vr9WmXW9pZ/l6NdXuVVK3VVq3WzNdk1VksjUlmKyMXo9MS/uBgNfSItvTc8TXNYmJ4YYm6elyp4cvPYNC3OBAF76dKVcSAQ4Axou1Vtf//XpVtFXoqSueUnJcstMlTRjRGvryrLXVxphcSc9J+py19pWhjmWkD2NimK2/Y33q42h3YByxSAhbE/APAQPr3lpaFGxpVbClRaHWlr7bB+7rbKxVa2ONevY3yrS1K6EzqLih+5dI6ps+mZ4uV1rqgYDWH+bSDgS68PX0gZDHOjgAiHybGzbrw09/WJ9Y+AndsvQWp8uZMKKye6e1trrvss4Y8zdJp0oaMvQBY6Kl8pj3Hzz1MaTq9n26/Zlt2rA/UZOzulTVXqXq9mq19rYqEAooaIMK2dCB66GQgjaoRG+i0n3pSvWlKi0uTem+dKX50pTmS1OGL0N5yXkqSCk4sU2kR+hEOjCOmkjZcPmFuw8OfFL49gt3R3Tos6GQQu3t4TVvLS0KtbaGw1rr4OuDA92g221tR542KSkQ51Z7vNQcH1R7vFFPikfx03KVkVOoSZNnaPKUWYpLzzg42KWlySQkMPo2miLhjyIA0GdB9gJdPvNy/e+W/9U1s69RQQoddJ0WkaHPGJMkyWWtbeu7foGkux0uCxPNMVp/N3Q16NuvPCKbvUVJCeUycftlTHjd218qJFVIOQk5ykvO0+TEyfK4PHIZl9wutzwmfN3j8sgYo05/p1p6WtTS3aLy1nI19zSrrbftsLdO8CQoPzlfBSkFKkguUGFKoaalTtPM9JnKTcwdk1+ij6cD45iJlLA1jD8EjJVQb69CLS0KtrWFg1prq4KtbX3BrU3BttYDAa6tVaH+4NbWFg5uodCRX9zrlTs19cBHdpbipk8PX09Lkys1VY1xPdoZ2Kct/nKt79quvaZJHfFSclKGTsk9RcsmL9OyScs0O2O23C73mJ8PDBIpfxQBgEE+d/Ln9NSup/Tbzb/V107/mtPlTHgRGfokTZL0t75fYD2Sfm+t/YezJWHCOaT1d5cx+ldSitbOPUNrn/iQtu/fLqVL7kCigp3FCrUtkPVnKOTPlPVnqPTOj8jnHvlUtGAoqLbeNjV2N6qqvUoVbRWqbKtUZXulKtsq9VbNWwMbU0tSalyqZqbP1KyMWZqdMVsz02dqZsZMpcalntBp6J+q6ugUVgfD1kFGuAeYtVa2pyc8TbI/tLW1KdjaOui+/uB2yDF99x1tnZskGZ9P7tRUufqCmycnR3EzZvQFt1S5UlIPXO8Lc+60NLlTUw8bdfOH/CptHHr7hNyUXC2ddbo+OGmZlk5aquK0YrqzOS1S/igCAIPkJubqsumX6bGdj+nmJTcrIz7D6ZImtIhd03c8WNOHsRJ69096+dVv6Y/ubpUkxKvXGHldXp2Se4pOzztdDz7r1b6GTEkH/9I7Hk1OrLVq7G7U7pbd2rF/h3Y079DO/Tu1s3mn2v3tB2pJztf8rPmalzlP87Pma37W/Oj7H+8w11eOFev3K9jertA7f1LwH99SqKtXQb9LoV6jUMin4PRLFEqYqmB7m0Jt7eGgdtBlm+T3H/1NPB65U1IOBLeUlEGXKXKnpsmVkix3aprcqSkHBTxXSsoJrXXr3z7hX3X/0vra9drYsHHgDwr92ycsnbRUyyYvU0Hy+GyCjuNwV7p0pJW3dzWPby0AMMiu5l364OMf1M0n3az/WPIfTpcT86JyTR/gpK5Al54se1L/u+sR7UkxmpI0XR+ZdoHOyDtDp0w6RQme8Hq27MDQ2xmMx9RHY4yyE7KVnZCt5ZOXD9xvrdW+jn3a0bxD2/dv19amrdrSuEXP7X1u4JjJSZM1PzMcABdkL9DCrIVKj08f85pHbIQbLltrZbu6FGxrV6ijPbyurS0czEIdg663tw8EtlB7W/j4trZw0Gs7dJRtiJHTkpfkSkwMh6+UZLlTUuXOzFDctGkDt10pKXKnJPeNuKWEb6emypWcIndqikx8/LiEKWutqjuqtaFugzbUbdC79e9q2/5tCtnQwPYJV866UqfknqKTc09WTmLOmNeEEzTCEWgAGGvT06frnIJz9Ietf9CNC28c+P0J44+RPmCQhq4G/WHrH/TotkfV3NOshVkLdcOCG/T+ae+XxzX030iipXtna2+rtjaGA+CWpi0qbSzVntY9A4/nJ+drYfZCLcxaqAXZCzQ/a76SvEmO1GqtVaijU6GOjoGwFtr4tIJvPaJQS5NCngyFCs9VMLnoQGjraFeovSN8bFubgh3h60fafHswk5god3JyOLQlJ8md3De6lpxyIKwl9we6lIGg5kpJCT8vOVnGE5l/Q+sKdGlr01ZtrN+od+vf1Ya6DarvqpckJXoStThnsZbkLtFJOSdpSc4SWmtHownYVRZA9FhXu043/uNGff20r+vaudc6XU5Mi8otG44HoQ8nanfLbj206SE9tespBUIBrSpcpRsW3KBTck+J6als7b3t2tK4RZsaN2lzw2ZtbtysqvYqSZKRUXFasRZkLdCC7AVakLVAczLnHPGvdAOjau3tfWFtUGjrC2Chjo6+MNZx4L7+wNZ/f99xR+sY2c/4fHIlJw8Er/4Pd3JSOKQlJ4dDXEqKXEnJ4dDWH+6SkvvCXLKMOzYajwRDQe1q2aVNDZu0sWGjNjVs0o79OxS04eBbkFygJblLtCRniZbkLtHM9Jk0XYkVdO8EEKGstbrumeu0v2e/nrz8SX7ujCFCH3AEgVBAD216SL949xdyG7c+OPOD+vj8j2ta6jSnSxtz1lrZ3t6+YNb30dmplv37VL5vm6rry9TQUKH9TdUKdXYovkdK8Btl2URlhhKUGvAqodfI2x2Q7XvuUTtE9nO55EpKCn8kJ8md1BfWkpIGQporKSkczvofS046ONglJcmdlCQTFzf2JypCBUIB7WnZo9Km0vBHY6m2NG5RZ6BTkpTiTdHC7IValLNIi7IXaWH2QmUnZDtcNQBgInpu73O6Zc0tuu+c+3RB0QVOlxOzWNMHDGHH/h36+utf15bGLbqw6ELdfurtykrIcrqsI7J+v0KdnQPh7KCPjqHu7xttG/ycQy4VGHr37FQdsnLN61UoIU49Ppc6vCG1uJtV6wmoK0HqTpM8yalKTp+ujMwpys4s1OSc6UrLmBSeHpmcLFdS3/TJpCT2ZxuBTn+nyprLtG3/NpU2lmpr01Zt279NPcHwWsN4d7xmZ8zWB2d+UIuywyFvaupUumoCACLC+wrfp6kpU/XQpod0/rTz+T3AAYQ+TDiDR/dS4lJG/a9ONhhUqKtLoY5O2a5BIazvvlBXl0KdHbJdXQcCW//1Q0NbZ6dsX3Czx+r+OIhJSAg3FklMDI+gJSbKnZYm75QpA7cPujzoev9j4etDjahZa1XbWautTVtV2lSqLU3btLVpq6ra10paK3VKmaFMzQzO1AwzQzM8MzQjYYZmuGYowySO2rmONd2Bbu1u2a2dzeEurGXNZdrZvHNgyq0UHsGbmzVX1865VnMz52p+1nxNS512xDWnAAA4ze1y64YFN+hbb35LJbUlBzWgw/hgeicOF8NrQ/pH90rrN+uSvPfrlgWfUVrINxC6bFdX3/UuhboG3e4PZv33dXYdCGpdnbKDbh9rP7WDGCNXQoJMUl9AS0w6ENYGglvCgVA2KKyZgeMGBbek8POcWqPW2tuq7U3btW1/OATuat6lspYydfg7Bo7JjM/UjPQZKk4t1tTUqSpICW8yX5BcoERv7AdCf9CvyvZKlbeWa2/rXpW3lau8tVzlbeWq6ahRyIanyHpcHhWnFYf3W+z7mJUxiy0TAABRqTvQrQv/cqEWZi/Uz8/7udPlxCTW9GH4IqQLnA0E+kJWl2x3t0Jd3eFRs+5uhTq7ZLv7QlZXd18Q6x4UyroPPLfvMtjVqbaWBvk72+TzS3FDz2o8Mrf7oDBmEhMOBK6EhPBHX3AzCQnh+/sDW/99/aEu6UCgG1ab/igP4f2jgv2jVrtadmln807tbtmttt62g47NTshWYUqhClMKNSVpinITczUpcZJyEnOUm5irzPjMiJ6yaK1VS0+L9nXu076OQR+Dbg8OdpKUEpeiaSnTVJhaqKLUIs1In6FZ6bNUmFoor8vr4GcTJaL8+wMAJpJfvPsL3b/hfj32wcc0I32G0+XEHEIfhu8Ym2DbUCgcwrq7w4Gqp+fgYNbTd9ndF8i6u8IhrLvvvu6eA8Gs/zW6Bx3Xd/uYG1kPwcTHy+/1qTnkVofLq1CcT5Ny05WVnaqN7dtUFWhQbuZULStaqcSUzL7glRAOZPEJBwe0hL7A1hfoHGsYEiEhfKy09LSooq1iyI/6znrZQzac9rg8yknIUU5ijtJ96UqLS1OqL3XgMjUuVWm+NCV7k+Xz+ORz+RTnjlOcO04+t08+d/i2y7jC20IoFL60IYVsSFbh692BbnUFutQZ6FRXoEtd/gPX2/3tau5u1v6e/drfvX/gsv8+f8h/WM2TEidpUuIkTU6arIKUAk1LnaapKVM1LXWa0n3pjNyNVIx/fwBArGnubtYFf7lAFxZdqG+t/JbT5cQcQl+Ms4GAQt09BwJXT1+g6unpC2g9A4Er/Nig24dchjY+Lhs0CgVN+DJgDtxWvGxv74hqDAereJn4+HCQio8/cF9CfDh0JcTL+OIPhLG++1wJQ1xP7HtuYuLA6z6+ofrwjdJ9PZq+8E+q7Nqqr5/+dV09++rROu3j4xghPJYFQgE1dDWorrNO9Z31qu2sVX1Xveo661TXWaeWnha19raqtadVbf62Y7/gKEuNS1VGfIYyfBlKj09XZnym0n3pyk7I1uSkyZqcOFmTkyYrKyErokcno9oE/v4AgGj1nbe+o//b/n/6x5X/0KSkSU6XE1Po3umAUFeXgk1NCvX0DgphvQdCV29P3+jXwddDPX3HdXcr1B/aegY91t1zyGM9R+zAeEwej1w+Xzh8+XzhQOaPl1GP3N6QTLyVy21lPFauhGS5zvh4OHDF+wZCmImPPyjMGZ+vb8rjwfeNx0jGD57ddlDgM+42mbxfq7yjXvet+kF0tghuqTy++2OIx+UJh6ekycc8NhAKqL23XS29LQMhsDfYq55gj3qDvQdd7w52y1orY4xcxiWXccnIhG/LJWOMEjwJSvAkKNGTGL7uPXA90ZuoNF8aUy8jwQT+/gCAaHX9/Ov1p21/0u+2/k63LL3F6XImDELfGGl56int+8Ydx/ckr/dA+Oq7NL44uXzxMvE+edPSDjzm8w2MjJl438Axrvi+0bL+YHbQ5aCA5vPJeIf4pfWI06XuivjpUtXNB2o23iYlTv21jKdNXRU3Rmfgk8JrlIYcySgY/1oimMflUXp8utLj050uBeOJ7w8AiDoFKQU6f9r5+r9t/6dPL/q0kuOSnS5pQiD0jZHEZcs05dv/TybOdyCMxfnC4as/tPUHsLi4cMBzqOPiQfqDXRQ2RshLT1BVc5dcvn1KKPy1jCugzr3/rinxc5wubeTOu2PoEH7ecf5B4UTRLAORKFK+PwAAx+UTCz6hZ/c8qz9v/7NuXHij0+VMCKzpQ8x4bH2Vbn/6Kbnzfi0b8qqr/JPy2Tx998pFuvzkfKfLGzmnAxfNMhDJnP7+AACMyCef/aT2tu7Vsx96Vm5XBAx8xADW9GFCyM3dq4Spv1LQn6K2vf+mKUn5uvXCOdEd+KTwL7BO/hL7wt0HBz4pfPuFu/nleiKLlLDl9PcHAGBErplzjb788pf11r63tCJvhdPlxDxCH2LCutp1+syLn9GM9Bn65fm/VHZCttMlxQ6aZeBQh47+tlSEb0sEMADAsKwqXKWUuBQ9UfYEoW8c0EcckWnjo+F27Helhy83PnrEQ2vaa3TLmltUkFygX1/4awLfaDtSU4wYa5bx2PoqrbznRRXf9rRW3vOiHltf5XRJketoo78AAAyDz+3TRUUX6YW9L6i9t93pcmIeoQ+Rp38UoaVCkj0wijBE8OsKdOkLL31BvcFe/fh9P1aaL2386411590RXsM3WIw1y3hsfZVu/+t7qmrukpVU1dyl2//6HsHvSBj9BQCMgtUzV6s72K3n9j7ndCkxj9CHyDPMUQRrre58405tbdqq7539PU1Pmz6ORU4gi68JN21JK5Rkwpcx1sTl0D0eJanLH9QPnt3mUEURboKM/gIAxtbi7MWaljpNj5c97nQpMY81fYg8wxxFeHjzw/r77r/rC6d8QWcXnD0OhU1gMd4sY/Aej8O5f8JjqwQAwCgwxmj1jNX66fqfqrKtUgUp/PFwrDDSh8gzjFGE16pe03+v+29dWHShPrnwk+NUGGJVXnrCcd0/4U2A0V8AwPi4bPplMjJ6suxJp0uJaYQ+RJ5jrCHb07JHX3n5K5qdMVt3r7hbxhgHikQsufXCOUrwHrxHUILXrVsvnONQRVFg8TXSlzZJdzWHLwl8AIARmJI8RadOPlVPlD2hWNg/PFIR+hB5jjKK0N7bri+89AV5XB79+H0/VqI30elqEQMuPzlf371ykfLTE2Qk5acn6LtXLor+PR4BAIgCq2euVmV7pdbXrXe6lJhlYiFRL1u2zJaUlDhdBsZYyIb0hRe/oFerXtWvLviVlk9e7nRJgDMiZWN0AABGQae/U6seXaWLiy/WXSvucrqcqGWMWWetXTbUY4z0IWr84t1faE3lGn1l+VcIfJi4jmNLEwAAokGiN1HnTztfz+55Vt2BbqfLiUmEPkSFLY1b9MDGB7R6xmp9ZO5HnC4HcA4bowMAYtDqGavV7m/Xi+UvOl1KTCL0IeIFQ0F9c+03leHL0FdP/SqNWzCxsTE6ACAGLZ+8XFOSpuiJsiecLiUmEfoQ8f6w9Q/a0rhFt516m1LjUp0uB3AWG6MDAGKQy7h06fRLtbZmreo665wuJ+YQ+hDR9nXs00/X/1Rn5p+pC4sudLocwHnH2NIEAIBotXrGaoVsSE/vetrpUmIOoQ8R7TtvfUchG9LXTvsa0zoBiY3RAQAxqyitSCflnMSefWPA43QBwJG8UP6CXqp4SV9a+iUVpDB1DRiw+BpCHgAgJq2esVrfevNb2tK0RQuyFjhdTsxgpA8Rqb23Xd956zuanTFbH5//cafLAQAAwDj4QPEHFOeK0xM7aegymgh9iEg/2/Az1XfW684z7pTX5XW6HAAAAIyD1LhUnTv1XD2z+xn5g36ny4kZhD5EnE0Nm/T70t/r2jnXanHOYqfLAQAAwDhaPWO1mnua9UrVK06XEjMIfYgogVBA31z7TWUnZOvzp3ze6XIAAAAwzlbkrVBmfKb+vvvvTpcSMwh9iCi/K/2dtjZt1W2n3qaUuBSnywEAAMA487g8OrfwXL1W9RpTPEcJoQ8Ro7q9Wj/f8HOdU3COzp92vtPlAAAAwCGrClepw9+hktoSp0uJCYQ+RIyfrP+JJOm/Tvsv9uQDAACYwE6bcpri3fFaU7HG6VJiAqEPEWF3y279ffff9eE5H1Zecp7T5QAAAMBBCZ4EnZ53utZUrGGj9lFA6ENEeGDjA/K5fbphwQ1OlwIAAIAIsKpglao7qrV9/3anS4l6hD44bk/LHj2z+xldM/saZSVkOV0OAAAAIsA5hedIElM8RwGhD4771Xu/UpwrTjcuvNHpUgAAABAhshOytTh7MaFvFBD64Kjy1nI9vetpXT3namUnZDtdDgAAACLIqsJV2tS4SfWd9U6XEtUIfXDUAxsfkMfl0b8t/DenSwEAAECEWVW4SpL0cuXLzhYS5Qh9cExFa4We2vWUrp7NKB8AAAAONzN9pvKT85nieYIIfXDMr977ldzGrU8s/ITTpQAAACACGWO0qnCV3qx5U53+TqfLiVqEPjiisq1ST5Y9qatmX6XcxFynywEAAECEWlW4Sj3BHr1Z86bTpUQtQh8c8eB7D8oYw1o+AAAAHNXSSUuV4k1hXd8JIPRh3FW1V+nxnY/rQ7M+pElJk5wuBwAAABHM6/LqzPwztaZijUI25HQ5UYnQh3HXP8r3yUWfdLoUAAAARIFVhavU1N2k9xrec7qUqETow7iqbq/WYzsf05WzrtTkpMlOlwMAAIAosDJ/pdzGTRfPESL0YVw9+N6DkqR/X/TvDlcCAACAaJHmS9PSSUsJfSNE6MO4qe2o1d92/k1XzmSUDwAAAMdnVeEq7WzeqYq2CqdLiTqEPoybv+z4i4KhoG5ceKPTpQAAACDKrCpYJUl6uYIunseL0IdxEQgF9Ncdf9WKvBUqTCl0uhwAAABEmcLUQs1Mn8kUzxEg9GFcvFb1mmo7a3XV7KucLgUAAABR6pyCc1RSW6KWnhanS4kqhD6Miz9v/7OyE7J1TuE5TpcCAACAKLWqcJWCNqjXq153upSoQujDmNvXsU+vVr2qK2ZeIa/L63Q5AAAAiFKLshcpMz6TKZ7HidCHMffXHX+VtVZXzrrS6VIAAAAQxdwut84pOEevVb0mf8jvdDlRg9CHMRUIBfSXHX/RirwVKkgpcLocAAAARLlVhavU5m/T+tr1TpcSNQh9GFOvVb2mus46XT37aqdLAQAAQAw4dfKpchu33tr3ltOlRA1CH8bU/23/P2UnZOvswrOdLgUAAAAxIDkuWfOz5uudfe84XUrUIPRhzNS01+i1qtdo4AIAAIBRtXzycr3X8J46/Z1OlxIVCH0YM3/dGW7g8qHZH3K6FAAAAMSQ5ZOXKxAKaEP9BqdLiQqEPoyJQCigv+74q1bkr1B+cr7T5QAAACCGnJJ7ijzGwxTPYSL0YUy8WvlquIHLLBq4AAAAYHQlehO1IHuB3t73ttOlRAVCH8bEn3f8WTkJOTRwAQAAwJg4dfKp2tywmXV9w0Dow6jrb+By+czLaeACAACAMbFs8jIFbVD/qvuX06VEPEIfRh0NXAAAADDWTs49WR6Xhymew0Dow6gKhAL663YauAAAAGBsJXgStDh7sd6poZnLsRD6MKperXxVdV11uno2DVwAAAAwtpZNXqYtTVvU3tvudCkRjdCHUTXQwKWABi4AAAAYW6dOPlUhG2Jd3zEQ+jBq9nfv1+tVr2v1jNU0cAEAAMCYOynnJHldXr1dw7q+oyH0YdS8VPGSgjaoC4sudLoUAAAATADxnnidlHOS3qllXd/REPowav6595/KT87X3My5TpcCAACACWL55OXa2rRVrb2tTpcSsQh9GBUtPS16q/otXTDtAhljnC4HAAAAE8TyycsVsiGt27fO6VIiFqEPo2JNxRoFbEDnTzvf6VIAAAAwgSzOWSyf28d+fUdB6MOoeH7v85qcNFkLsxc6XQoAAAAmEJ/bp5NyTlJJbYnTpUQsQh9OWHtvu16vfl3nTzufqZ0AAAAYd8snL9e2pm1q6WlxupSIROjDCXu58mX5Q35dMO0Cp0sBAADABHTq5FNlZVWyj9G+oRD6cMKe2/ucchNytThnsdOlAAAAYAJalL1I8e54tm44AkIfTkinv1OvVb2m9097v1yGLycAAACMP6/bqyW5S2jmcgT8lo4T8krVK+oJ9tC1EwAAAI46dfKp2rF/h5q6m5wuJeIQ+nBCntvznLLis3Ry7slOlwIAAIAJbPnk5ZLEur4hEPowYl2BLr1a9areP+39crvcTpcDAACACWxB9gIleBL0zj7W9R2K0IcRe73qdXUFuvT+ae93uhQAAABMcF6XV6fknkLoG0LEhj5jzAeMMduMMTuNMbc5XQ8O98+9/1S6L13LJi1zuhQAAABAyycvV1lLmRq6GpwuJaJEZOgzxrgl/VzSRZLmS/qIMWa+s1VhsJ5gj16pfEXnTT1PHpfH6XIAAAAAnTr5VElSSS3r+gaLyNAn6VRJO621u6y1vZL+KOmDDteEQdZWr1WHv4OunQAAAIgY87LmKcmbpHdqmOI5WKSGvnxJFYNuV/bdN8AY82ljTIkxpqS+vn5ci0N4Q/bUuFSdOuVUp0sBAAAAJEkel0en5J7Cfn2HiNTQZ4a4zx50w9oHrLXLrLXLcnJyxqksSJI/6NdL5S/p3MJz5XV5nS4HAAAAGLB00lLtad2j5u5mp0uJGJEa+iolFQ66XSCp2qFacIg3a95Um79NFxRd4HQpAAAAwEEW5yyWJL3X8J7DlUSOSA1970iaZYwpNsbESfqwpCccrgl9ntv7nJK9yTp9yulOlwIAAAAcZH7WfBkZbWrY5HQpESMi2y5aawPGmM9KelaSW9JvrLWbHS4Lkvwhv16seFGrClcpzh3ndDkAAADAQZK8SZqRPkMbGzY6XUrEiMjQJ0nW2mckPeN0HTjYO/veUUtPC107AQAAELEWZS/SSxUvyVorY4ZqFzKxROr0TkSoF8tfVIInQSvyVjhdCgAAADCkhdkL1dzTrMr2SqdLiQiEPhyXN6rf0GmTT1O8J97pUgAAAIAhDTRzqaeZi0Tow3GoaK1QRVuFzsg7w+lSAAAAgCOakT5D8e54Onj2IfRh2NbWrJUkQh8AAAAimtfl1byseXTw7EPow7CtrV6rKUlTVJRa5HQpAAAAwFEtyl6k0qZS+UN+p0txHKEPwxIIBfRWzVs6I+8MOiABAAAg4i3KXqSeYI927N/hdCmOI/RhWDY3blabv42pnQAAAIgKi3IWSRJTPEXowzC9Uf2GjIxOn3y606UAAAAAx5SXlKfM+ExtrGeTdkIfhuXN6jc1P2u+0uPTnS4FAAAAOCZjjBZmL2SkT4Q+DEN7b7verX+XDdkBAAAQVRZlL9Kull1q7213uhRHEfpwTG/ve1tBG2Q9HwAAAKLKouxFsrLa3LjZ6VIcRejDMa2tXqsET4JOyjnJ6VIAAACAYVuYvVCSJvwm7YQ+HNPamrVaNmmZ4txxTpcCAAAADFuaL03TUqfpvXpCH3BEVe1V2tu6l/V8AAAAiEo0cyH04RjWVq+VJEIfAAAAotKi7EWq66pTbUet06U4htCHo3qj+g3lJuaqOK3Y6VIAAACA47YoO7xJ+0Re10fowxEFQ0G9VfOWVuStkDHG6XIAAACA4zYnc448Lg+hDxjKlsYtau1t1RlT2KoBAAAA0cnn9mluxtwJva6P0IcjWlsTXs93et7pDlcCAAAAjFx/M5dgKOh0KY4g9OGI3qh+Q/My5ykzPtPpUgAAAIARW5SzSJ2BTu1u2e10KY4g9GFIHf4OvVv3rs7IY2onAAAAottEb+ZC6MOQSvaVKGADbNUAAACAqDctdZpSvCmEPmCwN6rfULw7Xifnnux0KQAAAMAJcRmXFmQvmLDNXAh9GNLamrVaOnmp4txxTpcCAAAAnLBF2Yu0ff92dQW6nC5l3BH6cJia9hrtbtnNVg0AAACIGYuyFylog9ratNXpUsYdoQ+H6d+qgfV8AAAAiBWLcvqaudRPvHV9hD4cZm31WuUk5Ghm+kynSwEAAABGRXZCtqYkTZmQzVwIfThIyIb0Zs2bOiPvDBljnC4HAAAAGDULsxcS+oDSplI19zSzPx8AAABizqLsRapqr1JTd5PTpYwrQh8Osr52vSRp2aRlDlcCAAAAjK7+Tdon2tYNhD4cZH3dek1JmqLJSZOdLgUAAAAYVfOz5stlXBNuiiehDwOstdpQt0FLcpc4XQoAAAAw6hK9iZqeNl2bGzY7Xcq4IvRhwL6OfarrqtOSnCVOlwIAAACMiTmZc7R9/3anyxhXhD4MWF8XXs/HSB8AAABi1eyM2artrFVLT4vTpYwbQh8GbKjfoARPgmZnzHa6FAAAAGBM9P+uO5FG+wh9GLChboMWZy+Wx+VxuhQAAABgTMzJmCOJ0IcJqNPfqe37t+uk3JOcLgUAAAAYM9kJ2crwZWjH/h1OlzJuCH2QJL3X8J6CNkgTFwAAAMQ0Y4xmZ8xmpA8Tz4a6DZLESB8AAABi3qyMWdrZvFPBUNDpUsYFoQ+SpPX16zUzfaZS41KdLgUAAAAYU7MzZqsr0KXK9kqnSxkXhD4oZEPaWLdRJ+UwygcAAIDYNztzYnXwJPRBu5p3qc3fppNzT3a6FAAAAGDMzUibIZdxEfowcWyo3yCJTdkBAAAwMcR74jUtdZq2NW1zupRxQeiD1tetV2Z8pqamTHW6FAAAAGBcTKQOnoQ+6N36d3VSzkkyxjhdCgAAADAu5mTMUVV7ldp7250uZcwR+ia4pu4m7W3dy9ROAAAATCizM8LNXHY273S4krFH6Jvg+vfnY1N2AAAATCT9oW8iTPEk9E1wG+o3yOPyaEH2AqdLAQAAAMbN5KTJSvGmEPoQ+96te1fzs+bL5/Y5XQoAAAAwbowxmpUxi9CH2NYb7NWmhk1M7QQAAMCE1N/B01rrdCljitA3gZU2lao31Mum7AAAAJiQZmfOVoe/Q9Ud1U6XMqYIfRNYfxOXk3JOcrYQAAAAwAEDzVyaYnuKJ6FvAttQt0H5yfnKScxxuhQAAABg3M1KnyUjE/Pr+gh9E5S1VhvqNzC1EwAAABNWojdRhSmFhD7Epqr2KjV0NdDEBQAAABNafzOXWEbom6DW162XJC3JXeJsIQAAAICDZmfM1t7WveoKdDldypgh9E1Q79a/qyRvkmamz3S6FAAAAMAxszNmy8qqrLnM6VLGDKFvgtpQt0GLsxfL7XI7XQoAAADgmIEOnjE8xZPQNwG197ZrR/MOpnYCAABgwstPyVeCJ4HQh9iysWGjQjZEExcAAABMeC7j0qyMWYQ+xJZ3696VkdHinMVOlwIAAAA4rr+Dp7XW6VLGBKFvAtpQv0GzMmYpOS7Z6VIAAAAAx83OmK2WnhbVddY5XcqYIPRNMCEb0sb6jTop5ySnSwEAAAAiwpyMOZJit5kLoW+CqWirULu/XQuzFzpdCgAAABARZmXMkkToQ4wobSqVJM3NnOtwJQAAAEBkSIlLUV5SHqEPsWFr41Z5jIdN2QEAAIBB+pu5xCJC3wRT2lSqmRkzFeeOc7oUAAAAIGLMypilPS171BvsdbqUUUfom0CstdratJWpnQAAAMAhZmfOVsAGtKtll9OljDpC3wRS11mnpu4mQh8AAABwiNkZsyXFZjMXQt8E0t/EZX7WfIcrAQAAACLL1JSp8rl92t5E6EMUK20qlZEZ2IcEAAAAQJjH5dGM9BmM9CG6bW3cqmmp05ToTXS6FAAAACDixGoHT0LfBFLaVKp5mfOcLgMAAACISHMy5qixu1ENXQ1OlzKqCH0TRHN3s2o6ajQ3iyYuAAAAwFBitZkLoW+C2Lp/qyQx0gcAAAAcwYz0GZKk3S27Ha5kdBH6JojSxnDnTkIfAAAAMLTM+EylxKUQ+hCdSptKNTlpstLj050uBQAAAIhIxhgVpxVrT8sep0sZVYS+CWJr01ZG+QAAAIBjKEot0u5WRvoQZTr9ndrTsofQBwAAABxDcVqx6jrr1OHvcLqUUUPomwC2798uK6u5mXTuBAAAAI6mOLVYkrSndY+zhYwiQt8EUNrU18Qli5E+AAAA4GiK0ookxVYHT0LfBFDaWKoMX4YmJU5yuhQAAAAgohWmFMpt3DHVzIXQNwFsbdqquZlzZYxxuhQAAAAgosW545SfnM9IH6KHP+jXjuYdTO0EAAAAhqkorYg1fYgeO5t3KhAK0LkTAAAAGKbi1GLtbd2rkA05XcqoIPTFuK1NWyWJzp0AAADAMBWlFakn2KOajhqnSxkVERf6jDF3GWOqjDEb+j4udrqmaFbaVKpET6Kmpk51uhQAAAAgKhSn9W3bECPNXCIu9PX5b2vtkr6PZ5wuJpqVNpZqbuZcuUyk/lMDAAAAkaUotUhS7GzbQBKIYcFQUNv2b2NqJwAAAHAcMuMzlRKXEjPNXCI19H3WGLPRGPMbY0zGUAcYYz5tjCkxxpTU19ePd31RobytXF2BLjp3AgAAAMfBGKPitGJG+k6EMeZ5Y8ymIT4+KOkXkmZIWiKpRtJ9Q72GtfYBa+0ya+2ynJyc8Ss+ipQ2lkoSnTsBAACA41SUWhQza/o8xzrAGPNZSb+z1u4frTe11r5/OMcZY34l6anRet+JZmvTVnldXk1Pn+50KQAAAEBUKU4r1hNlT6jD36Ekb5LT5ZyQ4Yz0TZb0jjHmUWPMB4wxZiwLMsZMGXTzCkmbxvL9YtmWpi2alTFLXpfX6VIAAACAqFKcGjsdPI8Z+qy1X5c0S9KvJd0oaYcx5jvGmBljVNP3jTHvGWM2SjpX0pfG6H1imrVWW5u2MrUTAAAAGIGitCJJ0u7W6F/Xd8zpnZJkrbXGmH2S9kkKSMqQ9GdjzHPW2q+MZkHW2o+P5utNVPs69qmlp4XOnQAAAMAIFKYUym3cMdHMZThr+j4v6QZJDZIelHSrtdZvjHFJ2iFpVEMfRseWpi2SROdOAAAAYATi3HHKT86Piemdwxnpy5Z0pbV27+A7rbUhY8ylY1MWTtTWpq1yGZdmZ8x2uhQAAAAgKhWnFcfE9M7hrOm749DAN+ix0tEvCaNha+NWFaUWKcGT4HQpAAAAQFQqSi1SeWu5QjbkdCknJFI3Z8cJ2tK0hamdAAAAwAkoSitST7BHNR01TpdyQgh9Maipu0l1nXV07gQAAABOQHFaeNuGaG/mQuiLQVsbt0oSnTsBAACAE1CUWiQp+vfqI/TFoP7OnYQ+AAAAYOQy4zOVGpfKSB8iz/am7cpLylOaL83pUgAAAICoZYxRUVqR9rTucbqUE0Loi0FlLWWamTHT6TIAAACAqFeUWsT0TkSWQCig3S27NSNthtOlAAAAAFGvOK1YdV11au9td7qUESP0xZjKtkr5Q35NT5/udCkAAABA1CtODXfw3Ns65NblUYHQF2PKWsokSTPTmd4JAAAAnKj+bRt2texyuJKRI/TFmF3N4S/G/i9OAAAAACNXmFIot3FHdTMXQl+MKWsp05SkKUryJjldCgAAABD1vG6v8pPzo3rbBkJfjNnVvIv1fAAAAMAoKk4rZqQPkSEYCmpXyy46dwIAAACjqCi1SOWt5QqGgk6XMiKEvhhS3VGtnmCPZqQT+gAAAIDRUpxWrJ5gj2o6apwuZUQIfTGkv4nL9DSmdwIAAACjpSitSJKidoonoS+G9G/XwJo+AAAAYPQUpRZJUtQ2cyH0xZCy5jLlJuQqNS7V6VIAAACAmJEZn6nUuFTtadnjdCkjQuiLIXTuBAAAAEafMUZFaUXa3cpIHxxkrVVZSxlNXAAAAIAxUJxazEgfnLWvY5+6Al00cQEAAADGQFFakeq76tXe2+50KceN0Bcj+pu4MNIHAAAAjL7i1GJJ0dnBk9AXI8qa+0IfG7MDAAAAo644LRz6orGDJ6EvRpQ1lykrPkvp8elOlwIAAADEnMKUQrmNm9AH59DEBQAAABg7XrdXBSkFTO+EM6y14e0aaOICAAAAjJmi1CJG+uCMus46tfvbGekDAAAAxlBRapHKW8sVDAWdLuW4eJwuACeOzp0AAADA2Fs6aamaupvUFehSclyy0+UMG6EvBuxq3iVJTO8EAAAAxtC5U8/VuVPPdbqM48b0zhhQ1lKmdF+6MuMznS4FAAAAQIQh9MWA/iYuxhinSwEAAAAQYQh9Uc5aq53NO1nPBwAAAGBIhL4o19jdqNbeVkIfAAAAgCER+qIcTVwAAAAAHA2hL8qxXQMAAACAoyH0Rbmy5jKlxKUoJyHH6VIAAAAARCBCX5Tb1bJLM9Jm0LkTAAAAwJAIfVGurLmMqZ0AAAAAjojQF8WaupvU1N1EExcAAAAAR0Toi2L9nTsZ6QMAAABwJIS+KLarhdAHAAAA4OgIfVGsrLlMiZ5ETUqc5HQpAAAAACIUoS+KlbWEm7jQuRMAAADAkRD6otiu5l00cQEAAABwVIS+KNXS06L6rnrW8wEAAAA4KkJflNrdslsSTVwAAAAAHB2hL0qVNZdJEtM7AQAAABwVoS9KlbWUKcGToLzkPKdLAQAAABDBCH1RalfzLhWnFctl+CcEAAAAcGQkhihV1lKmGWms5wMAAABwdIS+KNTe2659Hfs0PZ31fAAAAACOjtAXhQY6dzLSBwAAAOAYCH1RaHdrOPQVpxU7XAkAAACASEfoi0LlreVyG7fyk/OdLgUAAABAhCP0RaHy1nJNSZoir9vrdCkAAAAAIhyhLwqVt5VraupUp8sAAAAAEAUIfVHGWqvy1nIVphQ6XQoAAACAKEDoizItPS1q87dpWuo0p0sBAAAAEAUIfVGmvK1ckjQ1hemdAAAAAI6N0Bdl+kNfYSrTOwEAAAAcG6EvylS0VsjIqCC5wOlSAAAAAEQBQl+UKW8Lb9cQ545zuhQAAAAAUYDQF2XKW8uZ2gkAAABg2Ah9Uaa8rZwmLgAAAACGjdAXRVp6WtTc08x2DQAAAACGjdAXRSrbKiWJjdkBAAAADBuhL4qwRx8AAACA40XoiyLlreHQV5DCdg0AAAAAhofQF0XK28o1KXGS4j3xTpcCAAAAIEoQ+qJIeWu5pqYytRMAAADA8BH6ogjbNQAAAAA4XoS+KNHe266m7iZG+gAAAAAcF0JflKhoq5BE504AAAAAx4fQFyX6t2tgjz4AAAAAx4PQFyX6R/oIfQAAAACOB6EvSpS3lisnIUeJ3kSnSwEAAAAQRQh9UWJv615G+QAAAAAcN0JflKhoq6BzJwAAAIDjRuiLAp3+TtV31Wta6jSnSwEAAAAQZQh9UYAmLgAAAABGitAXBdijDwAAAMBIEfqiAHv0AQAAABgpQl8UKG8tV2Z8ppLjkp0uBQAAAECUcST0GWOuNsZsNsaEjDHLDnnsdmPMTmPMNmPMhU7UF2kq2iqY2gkAAABgRJwa6dsk6UpJrwy+0xgzX9KHJS2Q9AFJ9xtj3ONfXmTZ27qX7RoAAAAAjIgjoc9aW2qt3TbEQx+U9EdrbY+1dreknZJOHd/qIkt3oFu1nbWM9AEAAAAYkUhb05cvqWLQ7cq++w5jjPm0MabEGFNSX18/LsU5obKtUpIY6QMAAAAwIp6xemFjzPOSJg/x0NestY8f6WlD3GeHOtBa+4CkByRp2bJlQx4TC/o7dzLSBwAAAGAkxiz0WWvfP4KnVUoavC9BgaTq0akoOvXv0VeQUuBwJQAAAACiUaRN73xC0oeNMT5jTLGkWZLedrgmR5W3livdl640X5rTpQAAAACIQk5t2XCFMaZS0hmSnjbGPCtJ1trNkh6VtEXSPyR9xlobdKLGSFHeVs7UTgAAAAAjNmbTO4/GWvs3SX87wmPflvTt8a0ocpW3luvkSSc7XQYAAACAKBVp0zsxSG+wVzUdNYz0AQAAABgxQl8Eq2yvlJVluwYAAAAAI0boi2AVreHOnYz0AQAAABgpQl8EY48+AAAAACeK0BfBylvLlRKXwnYNAAAAAEaM0BfBKtoqNDVlqowxTpcCAAAAIEoR+iLY3ta9TO0EAAAAcEIIfRHKH/SruqNahamFTpcCAAAAIIoR+iJUdUe1QjakaanTnC4FAAAAQBQj9EWo8lY6dwIAAAA4cYS+CNW/XUNhCtM7AQAAAIwcoS9CVbRVKMmbpMz4TKdLAQAAABDFCH0Rqry1nO0aAAAAAJwwQl+EqmirYGonAAAAgBNG6ItAwVBQle2VhD4AAAAAJ4zQF4HqOusUCAVUkFLgdCkAAAAAohyhLwJVd1RLkvKS8hyuBAAAAEC0I/RFoOr2cOibkjzF4UoAAAAARDtCXwSq6aiRJE1JIvQBAAAAODGEvghU3V6trPgsxXvinS4FAAAAQJQj9EWg6vZq5SWzng8AAADAiSP0RaCajhqmdgIAAAAYFYS+CGOtVU1HDSN9AAAAAEYFoS/CNHY3qifYQ+gDAAAAMCoIfRGmf7sG9ugDAAAAMBoIfRGmf2N29ugDAAAAMBoIfRGmpj28Rx8jfQAAAABGA6EvwlS3Vys1LlXJcclOlwIAAAAgBhD6Ikx1B3v0AQAAABg9hL4IU91ezR59AAAAAEYNoS+CsEcfAAAAgNFG6Isgrb2t6vB30MQFAAAAwKgh9EWQgT36GOkDAAAAMEoIfRGEPfoAAAAAjDZCXwRhjz4AAAAAo43QF0GqO6qV4ElQui/d6VIAAAAAxAhCXwSpbq9WXlKejDFOlwIAAAAgRhD6Ikh1ezXr+QAAAACMKkJfBKnpqGE9HwAAAIBRReiLEJ3+TjX3NDPSBwAAAGBUEfoiRP8effnJ+Q5XAgAAACCWEPoixMAefUmM9AEAAAAYPYS+CDGwR18ya/oAAAAAjB5CX4So7qiW1+VVdkK206UAAAAAiCGEvghR3V6tKUlT5DL8kwAAAAAYPSSMCFHdwR59AAAAAEYfoS9C1LSzRx8AAACA0UfoiwC9wV7Vd9Uz0gcAAABg1BH6IkBNR7hzJ3v0AQAAABhthL4I0L8xO3v0AQAAABhthL4I0D/Sxx59AAAAAEYboS8CVLdXy2Vcyk3MdboUAAAAADGG0BcBqturNSlxkrwur9OlAAAAAIgxhL4IUN1RzXo+AAAAAGOC0BcBatprWM8HAAAAYEwQ+hwWCAVU21nLSB8AAACAMUHoc1h9Z72CNsgefQAAAADGBKHPYVXtVZKkKcmM9AEAAAAYfYQ+hw3s0ZfEmj4AAAAAo4/Q57Dq9mpJjPQBAAAAGBuEPofVdNQoKz5LPrfP6VIAAAAAxCBCn8Oq2qto4gIAAABgzBD6HFbTUcPUTgAAAABjhtDnoJANhTdmp4kLAAAAgDFC6HNQU3eTekO9jPQBAAAAGDOEPgf179HHmj4AAAAAY4XQ56Ca9vAefVOSGOkDAAAAMDYIfQ6q7gjv0ZeXzJo+AAAAAGOD0Oeg6vZqpcalKsmb5HQpAAAAAGIUoc9B1e3VrOcDAAAAMKYIfQ6q6ahhPR8AAACAMUXoc4i1VtXt1aznAwAAADCmCH0Oae1tVWegk5E+AAAAAGOK0OcQ9ugDAAAAMB4IfQ4Z2KMvmZE+AAAAAGOH0OeQgT36kljTBwAAAGDsEPocUt1erQRPgtJ8aU6XAgAAACCGEfocUtNRo7ykPBljnC4FAAAAQAwj9DmktqNWk5MmO10GAAAAgBhH6HNIXWedchNznS4DAAAAQIwj9DkgEAqoobuB0AcAAABgzBH6HNDQ1aCQDRH6AAAAAIw5Qp8D6jrrJEmTEic5XAkAAACAWEfoc0B/6GOkDwAAAMBYI/Q5oLazVpI0KYmRPgAAAABji9DngLrOOnldXmX4MpwuBQAAAECMcyT0GWOuNsZsNsaEjDHLBt1fZIzpMsZs6Pv4pRP1jbX+7RrYmB0AAADAWPM49L6bJF0p6X+GeKzMWrtkfMsZX7WdtaznAwAAADAuHBnps9aWWmu3OfHekYCN2QEAAACMl0hc01dsjFlvjHnZGHPWkQ4yxnzaGFNijCmpr68fz/pOiLWW0AcAAABg3IzZ9E5jzPOSJg/x0NestY8f4Wk1kqZaaxuNMUslPWaMWWCtbT30QGvtA5IekKRly5bZ0ap7rLX529QV6GKPPgAAAADjYsxCn7X2/SN4To+knr7r64wxZZJmSyoZ5fIcU9fBxuwAAAAAxk9ETe80xuQYY9x916dLmiVpl7NVjS42ZgcAAAAwnpzasuEKY0ylpDMkPW2MebbvobMlbTTGvCvpz5JustY2OVHjWOnfmJ3QBwAAAGA8OLJlg7X2b5L+NsT9f5H0l/GvaPwQ+gAAAACMp4ia3jkR1HXWKcOXoTh3nNOlAAAAAJgACH3jjO0aAAAAAIwnQt84q+us06QkOncCAAAAGB+EvnFW21nLSB8AAACAcUPoG0e9wV41dTcR+gAAAACMG0LfOKrvqpfExuwAAAAAxg+hbxyxMTsAAACA8UboG0fs0QcAAABgvBH6xlFdR3ikj+mdAAAAAMYLoW8c1XXWKd4dr9S4VKdLAQAAADBBEPrGUf92DcYYp0sBAAAAMEEQ+sZRXWcd6/kAAAAAjCtC3zhiY3YAAAAA443QN06starvrKeJCwAAAIBxRegbJ809zeoN9TLSBwAAAGBcEfrGSf/G7JOSGOkDAAAAMH4IfeOEjdkBAAAAOIHQN076Qx9r+gAAAACMJ0LfOKnrrJORUVZCltOlAAAAAJhACH3jpK6zTlkJWfK6vE6XAgAAAGACIfSNE/boAwAAAOAEQt84qeusYz0fAAAAgHFH6BsndZ11jPQBAAAAGHeEvnHQHehWS08LI30AAAAAxh2hbxz0b8zOSB8AAACA8UboGwdszA4AAADAKYS+cdA/0sf0TgAAAADjjdA3DpjeCQAAAMAphL5xUNdZpyRvkpLjkp0uBQAAAMAEQ+gbB2zMDgAAAMAphL5xQOgDAAAA4BRC3zio66yjiQsAAAAARxD6xljIhtTQ2cBIHwAAAABHEPrGWFN3kwI2QOgDAAAA4AhC3xjr35id6Z0AAAAAnEDoG2O1HYQ+AAAAAM4h9I0xNmYHAAAA4CRC3xir66yT27iVGZ/pdCkAAAAAJiBC3xir7axVdkK23C6306UAAAAAmIAIfWOMPfoAAAAAOInQN8bqOus0KYnQBwAAAMAZhL4xVttZSxMXAAAAAI4h9I2hDn+HOvwdhD4AAAAAjiH0jaH+jdkJfQAAAACcQugbQ/179NHIBQAAAIBTCH1jiI3ZAQAAADiN0DeGCH0AAAAAnEboG0P7OvYpNS5VCZ4Ep0sBAAAAMEER+sZQXWcdo3wAAAAAHEXoG0N1nXU0cQEAAADgKELfGGKkDwAAAIDTCH1jJBAKqLG7kdAHAAAAwFGEvjHS0NWgkA0R+gAAAAA4itA3Rmo7ayVJk5MmO1wJAAAAgImM0DdG2KMPAAAAQCQg9I0Ra62mpkwl9AEAAABwlMfpAmLVBUUX6IKiC5wuAwAAAMAEx0gfAAAAAMQwQh8AAAAAxDBCHwAAAADEMEIfAAAAAMQwQh8AAAAAxDBCHwAAAADEMEIfAAAAAMQwQh8AAAAAxDBCHwAAAADEMEIfAAAAAMQwQh8AAAAAxDBCHwAAAADEMEIfAAAAAMQwQh8AAAAAxDBCHwAAAADEMEIfAAAAAMQwQh8AAAAAxDBCHwAAAADEMEIfAAAAAMQwQh8AAAAAxDBCHwAAAADEMEIfAAAAAMQwQh8AAAAAxDBjrXW6hhNmjKmXtNfpOoaQLanB6SImKM69szj/zuHcO4dz7xzOvXM4987h3DsnUs/9NGttzlAPxEToi1TGmBJr7TKn65iIOPfO4vw7h3PvHM69czj3zuHcO4dz75xoPPdM7wQAAACAGEboAwAAAIAYRugbWw84XcAExrl3FuffOZx753DuncO5dw7n3jmce+dE3blnTR8AAAAAxDBG+gAAAAAghhH6AAAAACCGEfpGkTEm0xjznDFmR99lxlGOdRtj1htjnhrPGmPVcM69MabQGPOSMabUGLPZGPMFJ2qNFcaYDxhjthljdhpjbhvicWOM+Unf4xuNMac4UWcsGsa5/1jfOd9ojHnDGHOSE3XGomOd+0HHLTfGBI0xV41nfbFuOOffGLPKGLOh7//zL493jbFqGP/fSTPGPGmMebfv3H/CiTpjjTHmN8aYOmPMpiM8zs/aMTKMcx9VP2sJfaPrNkkvWGtnSXqh7/aRfEFS6bhUNTEM59wHJP2ntXaepNMlfcYYM38ca4wZxhi3pJ9LukjSfEkfGeJcXiRpVt/HpyX9YlyLjFHDPPe7JZ1jrV0s6VuKwgXnkWiY577/uO9JenZ8K4xtwzn/xph0SfdLWm2tXSDp6vGuMxYN82v/M5K2WGtPkrRK0n3GmLhxLTQ2PSzpA0d5nJ+1Y+dhHf3cR9XPWkLf6PqgpN/2Xf+tpMuHOsgYUyDpEkkPjk9ZE8Ixz721tsZa+6++620Kh+788Sowxpwqaae1dpe1tlfSHxX+Nxjsg5L+fzbsTUnpxpgp411oDDrmubfWvmGt3d93801JBeNcY6wazte9JH1O0l8k1Y1ncRPAcM7/RyX91VpbLknWWv4NRsdwzr2VlGKMMZKSJTUp/MdWnABr7SsKn8sj4WftGDnWuY+2n7WEvtE1yVpbI4UDhqTcIxz3I0lfkRQap7omguGee0mSMaZI0smS3hr70mJSvqSKQbcrdXiAHs4xOH7He14/KenvY1rRxHHMc2+MyZd0haRfjmNdE8VwvvZnS8owxqwxxqwzxlw/btXFtuGc+59JmiepWtJ7kr5greX3nLHHz9rIEPE/az1OFxBtjDHPS5o8xENfG+bzL5VUZ61dZ4xZNYqlxbwTPfeDXidZ4b/Cf9Fa2zoatU1AZoj7Dt3/ZTjH4PgN+7waY85V+AfRmWNa0cQxnHP/I0lftdYGwwMeGEXDOf8eSUslnScpQdJaY8yb1trtY11cjBvOub9Q0gZJ75M0Q9JzxphX+Tk75vhZ67Bo+VlL6DtO1tr3H+kxY0ytMWaKtbamb2h9qGklKyWtNsZcLCleUqox5hFr7XVjVHLMGIVzL2OMV+HA9ztr7V/HqNSJoFJS4aDbBQr/dfd4j8HxG9Z5NcYsVngK+UXW2sZxqi3WDefcL5P0x77Aly3pYmNMwFr72LhUGNuG+/+dBmtth6QOY8wrkk6SROg7McM595+QdI8NbwC90xizW9JcSW+PT4kTFj9rHRRNP2uZ3jm6npB0Q9/1GyQ9fugB1trbrbUF1toiSR+W9CKBb1Qc89z3rTP4taRSa+0Px7G2WPSOpFnGmOK+hfofVvjfYLAnJF3f11nsdEkt/VNwcUKOee6NMVMl/VXSxxnhGFXHPPfW2mJrbVHf/+P/LOlmAt+oGc7/dx6XdJYxxmOMSZR0mmiaNhqGc+7LFR5hlTFmkqQ5knaNa5UTEz9rHRJtP2sZ6Rtd90h61BjzSYX/53e1JBlj8iQ9aK292MniYtxwzv1KSR+X9J4xZkPf8/7LWvuMA/VGNWttwBjzWYW7E7ol/cZau9kYc1Pf47+U9IykiyXtlNSp8F+BcYKGee7vkJQl6f6+EaeAtXaZUzXHimGee4yR4Zx/a22pMeYfkjYqvG7+QWvtkO3WMXzD/Nr/lqSHjTHvKTzl8KvW2gbHio4Rxpg/KNwNNdsYUynpTkleiZ+1Y20Y5z6qftaa8Cg8AAAAACAWMb0TAAAAAGIYoQ8AAAAAYhihDwAAAABiGKEPAAAAAGIYoQ8AAAAAYhihDwAAAABiGKEPAAAAAGIYoQ8AgBEyxiw3xmw0xsQbY5KMMZuNMQudrgsAgMHYnB0AgBNgjPl/kuIlJUiqtNZ+1+GSAAA4CKEPAIATYIyJk/SOpG5JK6y1QYdLAgDgIEzvBADgxGRKSpaUovCIHwAAEYWRPgAAToAx5glJf5RULGmKtfazDpcEAMBBPE4XAABAtDLGXC8pYK39vTHGLekNY8z7rLUvOl0bAAD9GOkDAAAAgBjGmj4AAAAAiGGEPgAAAACIYYQ+AAAAAIhhhD4AAAAAiGGEPgAAAACIYYQ+AAAAAIhhhD4AAAAAiGH/f8s+gGuQXnEEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 10))\n",
    "plt.title(\"Polynomials\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.plot(X_train, y_train, 'o', label = 'train data')\n",
    "plt.plot(X_test, y_test, 'o', label = 'test data')\n",
    "x = np.linspace(-0.4, 1.2, 100)\n",
    "plt.plot(x, polynomials[5](x), label = 'without regularization')\n",
    "a = np.reshape(a, (1, 7))[0]\n",
    "print(a)\n",
    "plt.plot(x, np.poly1d(a)(x), label = 'with regularization')\n",
    "plt.legend()\n",
    "#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**6. [0.25 балла]** Чем первый из них выгодно отличается от второго?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Его значения не начинают резко падать при выходе за область, где находятся данные.\n",
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**7. [0.75 балла]** Пусть заданы $X\\in \\text{Mat}_{n \\times k}(\\mathbb{R})$, $\\lambda \\geqslant 0$, а также известно, что $\\text{rk}~X = k \\leqslant n$. Решите следующую задачу оптимизации:\n",
    "$$|Xa - y|^2 + \\lambda|a|^2\\rightarrow\\min\\limits_{a \\in \\mathbb{R}^k}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Интуитивно это можно понимать так: мы ищем компромисс между минимизацией длины разности $|Xa - y|$ (то есть точностью решения задачи регрессии) и тем, чтобы компоненты вектора $a$ не становились слишком большими по модулю."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**8. [0.25 балла]** Почему регуляризовать (штрафовать за слишком большую абсолютную величину) коэффициент при константном признаке (который состоит из одних единиц) — плохая идея?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**9. [0.5 балла]** Пусть теперь $\\text{rk}~X < k$. Всегда ли в этом случае существует решение? Если существует, то является ли оно единственным? Ответ обоснуйте."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**10. [0.25 балла]** Покажите, что если решений бесконечно много, то среди них обязательно найдутся решения со сколь угодно большими по модулю компоненты вектора $a$. Почему большие веса в линейной модели — плохо?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 4. Онлайн-обучение линейной регрессии (3 балла)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Раньше мы работали в ситуации, когда объекты $x_i$ и значения $y_i$ даны с самого начала и всегда доступны. Допустим теперь, что пары $(x_i, y_i)$ поступают к нам по одной, и мы не можем себе позволить хранить их все в памяти (это может быть актуально, например, если Вы пытаетесь обучить модель на устройстве со сравнительно небольшим количеством оперативной памяти: скажем, на мобильном телефоне или на бортовом компьютере спутника связи). В этом случае нам нужно уметь решать следующую задачу:\n",
    "\n",
    "**Известно:** решение задачи регрессии для датасета $(x_1, y_1),\\ldots,(x_t,y_t)$;\n",
    "\n",
    "**На вход поступает:** новая пара $(x_{t+1}, y_{t+1})$;\n",
    "\n",
    "**Требуется:** быстро (за время, не зависящее от $t$) отыскать решение задачи регрессии для расширенного датасета $(x_1, y_1),\\ldots,(x_t,y_t),(x_{t+1}, y_{t+1})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Обозначим $X_{(t)} = (x_1\\ldots x_t)^T$ и $y_{(t)} = (y_1,\\ldots,y_t)^T$. Тогда, как мы хорошо помним, решение задачи регрессии для датасета $(x_1, y_1),\\ldots,(x_t,y_t)$ имеет вид $\\hat{a}_{(t)} = \\left(X^T_{(t)}X_{(t)}\\right)^{-1}X^T_{(t)}y_{(t)}$. Размеры матриц $X^T_{(t)}X_{(t)}$ и $X^T_{(t)}y_{(t)}$ не зависят от $t$, поэтому их мы, пожалуй, можем себе позволить хранить в памяти."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. [1 балл]** И вот Ваше первое задание в этом разделе: придумайте алгоритм, принимающий на вход матрицы $X^T_{(t)}X_{(t)}$ и $X^T_{(t)}y_{(t)}$, а также пару $(x_{t+1}, y_{t+1})$ и вычисляющий матрицы $X^T_{(t+1)}X_{(t+1)}$ и $X^T_{(t+1)}y_{(t+1)}$. Сложность вашего алгоритма не должна зависеть от $t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Обозначим за $n$ высоту столба $x_i$. Далее воспользуемся блочными формулами умножения, а конкретно:\n",
    "\n",
    "$X^T_{t + 1}X_{t + 1} = (x_1...x_{t + 1}) \\cdot (x_1...x_{t + 1})^T = x_1 x_1^T + ... + x_{t+1}x_{t + 1}^T = X^T_{t}X_{t} + x_{t+1}x_{t + 1}^T$\n",
    "\n",
    "Матрица $X^T_{t}X_{t}$ нам известна и имеет размер $n \\times n$, матрица $x_{t+1}x_{t + 1}^T$ тоже является матрицей размера $n \\times n$ и её нахождение асимптотически не будет зависеть от $t$. Таким образом мы найдём $X^T_{t + 1}X_{t + 1}$ за время, которое не зависит от $t$.\n",
    "\n",
    "Аналогично имеем:\n",
    "\n",
    "$X^T_{t + 1}y_{t + 1} = (x_1...x_{t + 1}) \\cdot (y_1...y_{t + 1})^T = x_1 y_1^T + ... + x_{t+1}y_{t + 1}^T = X^T_{t}y_{t} + x_{t+1}y_{t + 1}^T$\n",
    "\n",
    "Точно так же нам уже известна матрица $X^T_{t}y_{t}$, вычисление $x_{t+1}y_{t + 1}^T$ и последующее сложение матриц не будет зависеть от $t$.\n",
    "\n",
    "\n",
    " ╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. [2 балла]** Теперь настало время написать немного кода и порисовать красивые картинки. Вам нужно будет реализовать симуляцию онлайн-обучения регрессии для задачи приближения функции (в данном случае $f_{true}(x) = 2x\\sin(5x) + x^2 - 1$; все значения искажены небольшим нормальным шумом) многочленом степени не выше 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import clear_output\n",
    "\n",
    "f_true = lambda x: 2*x*np.sin(5*x) + x**2 - 1 # this is the true function\n",
    "\n",
    "# We need this to make the plot of f_true:\n",
    "x_grid = np.linspace(-2,5,100) # 100 linearly spaced numbers\n",
    "x_grid_enl = np.hstack((x_grid.reshape((100,1))**j for j in range(6)))\n",
    "y_grid = f_true(x_grid)\n",
    "A = np.zeros((6, 6));\n",
    "B = np.zeros((6, 1));\n",
    "\n",
    "for i in range(200):\n",
    "    x_new = np.random.uniform(-2, 5)\n",
    "    y_new = f_true(x_new) + 2*np.random.randn()\n",
    "    #╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ\n",
    "    x_cur = np.array([x_new ** i for i in range(6)])\n",
    "    x_cur = np.reshape(x_cur, (1, 6))\n",
    "    x_curT = np.reshape(x_cur, (6, 1))\n",
    "    A += x_curT.dot(x_cur)\n",
    "    B += x_curT * y_new\n",
    "    a = np.linalg.inv(A).dot(B) \n",
    "    # the rest of code is just bells and whistles\n",
    "    if (i+1)%5==0:\n",
    "        clear_output(True)\n",
    "        plt.plot(x_grid,y_grid, color='blue', label='true f')\n",
    "        plt.scatter(x_new, y_new, color='red')\n",
    "        #╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ\n",
    "        \n",
    "        y_pred = x_grid_enl.dot(a)#╰( ͡° ͜ʖ ͡° )つ──☆*:・ﾟ\n",
    "        plt.scatter(x_grid, y_pred, color='orange', linewidth=5, label='predicted f')\n",
    "        \n",
    "        plt.legend(loc='upper left')\n",
    "        plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Добавление. QR-разложение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**QR-разложением** матрицы $A$ (не обязательно квадратной) мы будем называть её представление в виде $A = QR$, где $Q$ — матрица с ортонормированными столбцами, а $R$ - верхнетреугольная матрица.\n",
    "\n",
    "Смысл QR-разложения следующий. Пусть $a_1,\\ldots,a_m$ — столбцы матрицы $A$, $q_1,\\ldots,q_t$ — столбцы матрицы $Q$. Тогда $q_1,\\ldots,q_t$ — это ортонормированный базис в подпространстве, являющемся линейной оболочкой векторов $a_1,\\ldots,a_m$, а в матрице $R$ записаны коэффициенты, с помощью которых $a_i$ выражаются через $q_1,\\ldots,q_t$.\n",
    "\n",
    "Находить QR-разложение заданной матрицы можно разными способами. Мы познакомим Вас не с самым лучшим из них, но по крайней мере с наиболее простым концептуально. Заметим, что ортогональный базис линейной оболочки можно найти с помощью ортогонализации Грама-Шмидта. При этом коэффициенты из матрицы $R$ получаются в качестве побочного продукта этого процесса:\n",
    "\n",
    "```python\n",
    "for j = 1...n:\n",
    "    q_j = a_j\n",
    "    for i = 1,...,j-1:\n",
    "        r_ij = (q_i, a_j)\n",
    "        q_j = q_j - r_ij * q_i\n",
    "    r_jj = |q_j|\n",
    "    if r_jj == 0: # a_j in <a_1,...,a_j-1>\n",
    "        # What would you do in this case?..\n",
    "    q_j = q_j / r_jj\n",
    "```\n",
    "\n",
    "Для нахождения QR-разложения Вы можете использовать библиотечную функцию `scipy.linalg.qr`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Поскольку лабораторная про линейную регрессию, не так-то просто замять вопрос о том, какое же отношение QR-разложение имеет к задаче регрессии. Упомянем одно из возможных применений.\n",
    "\n",
    "Допустим, мы нашли QR-разложение матрицы $X$, а именно: $X = QR$. Тогда\n",
    "$$X^TX = (QR)^T(QR) = R^TQ^TQR = R^TR$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Поскольку в задаче регрессии матрица $X$ обычного полного ранга (то есть её столбцы линейно независимы), матрица $R$ будет квадратной. Благодаря этому нашу обычную формулу для набора регрессионных коэффициентов $\\hat{a}$ можно переписать в следующем виде:\n",
    "\n",
    "$$\\hat{a} = (X^TX)^{-1}X^Ty = (R^TR)^{-1}(QR)^Ty = R^{-1}(R^T)^{-1}R^TQ^Ty = R^{-1}Q^Ty$$\n",
    "\n",
    "Как видите, формула стала проще. Более того, зачастую обращение матрицы $R$ может быть численно более устойчиво, чем обращение матрицы $X^TX$."
   ]
  }
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