Untitled0.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "Y0_8TluDF45Z"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pDWm3vnrhDgF"
      },
      "source": [
        "## Сорокин Андрей\n",
        "\n",
        "## 24. Разделимые наименьшие квадраты\n",
        "\n",
        "[Каханер–Моулер–Нэш] \n",
        "\n",
        "Пусть необходимо аппроксимировать $m$ точек данных $(t_i,\\, y_i)$ $(i=1,2,\\dots,m)$ с помощью функции\n",
        "$$\n",
        "   b(t) = c_1 + c_2 t + c_3 t^2 + c_4 e^{\\lambda t}.\n",
        "$$\n",
        "Параметры $c_1,\\dots,c_4$ входят линейно, а $\\lambda$ нелинейно.\n",
        "Рассмотрим матрицу\n",
        "$$\n",
        "A(\\lambda) =\n",
        "\\left(\n",
        "\\begin{array}{cccc}\n",
        "    1 & t_1 & t_1^2 & e^{\\lambda t_1}  \\\\\n",
        "    1 & t_2 & t_2^2 & e^{\\lambda t_2}  \\\\\n",
        "    \\vdots & \\vdots & \\vdots & \\vdots  \\\\\n",
        "    1 & t_m & t_m^2 & e^{\\lambda t_m}  \\\\\n",
        "\\end{array}\n",
        "\\right)\n",
        "$$\n",
        "и векторы\n",
        "$$\n",
        "y = \n",
        "\\left(\n",
        "\\begin{array}{c}\n",
        "   y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_m\n",
        "\\end{array}\n",
        "\\right),\n",
        "\\qquad\n",
        "c = \n",
        "\\left(\n",
        "\\begin{array}{c}\n",
        "   c_1 \\\\ c_2 \\\\ c_3\\\\ c_4\n",
        "\\end{array}\n",
        "\\right).\n",
        "$$\n",
        "Тогда задачу наименьших квадратов можно поставить следующим образом:\n",
        "$$\n",
        "\\min_{\\lambda}  \\min_{c}  \\|A(\\lambda) c - y\\|_2.\n",
        "$$\n",
        "Для любого заданного $\\lambda$ внутренний минимум можно найти линейным методом наименьших квадратов.\n",
        "Для нахождения внешнего минимума можно воспользоваться методом одномерной минимизации.\n",
        "\n",
        "В таблице ниже приведены две группы данных, к которым необходимо применить описанный подход.\n",
        "Единственным ли образом определяются неизвестные параметры?\n",
        "Изобразите данные на графике и постройте графики построенных моделей.\n",
        "\n",
        "```\n",
        "       t        y         y\n",
        "             Группа 1  Группа 2\n",
        " -----------------------------------\n",
        "     0.00     20.00     20.00\n",
        "     0.25     51.58     24.13\n",
        "     0.50     68.73     26.50\n",
        "     0.75     75.46     27.13\n",
        "     1.00     74.36     26.00\n",
        "     1.25     67.09     23.13\n",
        "     1.50     54.73     18.50\n",
        "     1.75     37.98     12.13\n",
        "     2.00     17.28      4.00\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "6VMsG4mkzFUi"
      },
      "outputs": [],
      "source": [
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import minimize_scalar\n",
        "m = 9\n",
        "test = np.arange(0, 2.01, 0.25, dtype = float)\n",
        "\n",
        "y_1 = np.array([20.00,51.58,68.73,75.46,74.36,67.09,54.73,37.98,17.28,])\n",
        "\n",
        "y_2 = np.array([20.00,24.13,26.50,27.13,26.00,23.13,18.50,12.13,4.00,])"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Функции для метода"
      ],
      "metadata": {
        "id": "gvEkx8v7toUx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def f(lmd, C, x):\n",
        "    return C[0] + C[1] * x + C[2] * (x ** 2) + C[3] * (np.e ** (lmd * x))\n",
        "\n",
        "#Метод наименьших квадратов\n",
        "def get(lmd, y):\n",
        "    A =  np.ones((m, 4), dtype=float)\n",
        "    A[:,1] = test\n",
        "    A[:,2] = test ** 2\n",
        "    A[:,3] = np.e ** (lmd * test)\n",
        "    return np.linalg.lstsq(A, y)[0]\n",
        "\n",
        "#Вычисление функции, которую надо минимизировать\n",
        "def solve_1(lmd):    \n",
        "    C = get(lmd, y_1)\n",
        "    y_approx = f(lmd, C, test)\n",
        "    return np.sum((y_approx - y_1) ** 2)\n",
        "def solve_2(lmd):    \n",
        "    C = get(lmd, y_2)\n",
        "    y_approx = f(lmd, C, test)\n",
        "    return np.sum((y_approx - y_2) ** 2)"
      ],
      "metadata": {
        "id": "26yeo6vGiFnP"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Нанесём данные на график\n"
      ],
      "metadata": {
        "id": "BwE0wfMbtahs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.grid()\n",
        "plt.plot(test, y_1, 's')\n",
        "plt.plot(test, y_2, 's')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "VpMegXdWF4q_",
        "outputId": "ee121b30-856b-43eb-e424-80004540b2d6"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb36b163460>]"
            ]
          },
          "metadata": {},
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Построим график функции 1, которую надо минимизировать\n"
      ],
      "metadata": {
        "id": "v5eIq4eSupbD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_a = np.arange(-10.0, 10.0, .01, dtype = float)\n",
        "y_a = []\n",
        "for x in x_a:\n",
        "    y_a.append(solve_1(x))\n",
        "    \n",
        "plt.grid()\n",
        "plt.plot(x_a, y_a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 499
        },
        "id": "w3OS8qrqiWbl",
        "outputId": "384f6fd5-42a9-402e-aa2a-b517d6f49471"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-23-8435b0968071>:10: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
            "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
            "  return np.linalg.lstsq(A, y)[0]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb36c5c7eb0>]"
            ]
          },
          "metadata": {},
          "execution_count": 30
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAigAAAGdCAYAAAA44ojeAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABHiklEQVR4nO3deVxU9f4/8NcMDMO+7wgIiLijiRJolop7peW1TCs1yupqZfZrsVtutzKta97MUss0Sy3tpm1mkqZeBVFQ3EUFZJUBQRgWGYaZz+8Pv86NxAWbYc7MvJ6Ph4+aM2c+vt8eBl7M+XzOkQkhBIiIiIgkRG7uAoiIiIj+jAGFiIiIJIcBhYiIiCSHAYWIiIgkhwGFiIiIJIcBhYiIiCSHAYWIiIgkhwGFiIiIJMfe3AXcDr1ej5KSEri5uUEmk5m7HCIiIroFQgjU1NQgODgYcvmNPyOxyIBSUlKC0NBQc5dBREREt6GwsBDt2rW74T4WGVDc3NwAXGnQ3d3dqGNrtVps374dQ4cOhUKhMOrYUsD+LJ+192jt/QHW3yP7s3ym6lGtViM0NNTwc/xGLDKgXD2t4+7ubpKA4uzsDHd3d6v8wmN/ls/ae7T2/gDr75H9WT5T93gr0zM4SZaIiIgkhwGFiIiIJIcBhYiIiCSHAYWIiIgkhwGFiIiIJIcBhYiIiCSHAYWIiIgkhwGFiIiIJIcBhYiIiCSHAYWIiIgkhwGFiIiIJIcBhYiIiCSHAYWIJOVIUTX2XJBBCGHuUojIjBhQiEhS/rYiHf85b4dfjqvMXQoRmREDChFJUk55nblLICIzYkAhIiIiyWFAISIiIslhQCEiIiLJYUAhIkkS4CoeIlvGgEJERESSw4BCRJIkg8zcJRCRGTGgEBERkeQwoBAREZHkMKAQERGR5LQ6oOzZswf33XcfgoODIZPJsGXLlmbPCyEwe/ZsBAUFwcnJCUlJSTh79myzfSorKzFx4kS4u7vD09MTycnJqK2t/UuNEBERkfVodUCpq6tDbGwsli1b1uLzixYtwocffojly5cjPT0dLi4uGDZsGBoaGgz7TJw4ESdOnEBKSgp++ukn7NmzB1OnTr39LoiIiMiq2Lf2BSNGjMCIESNafE4IgSVLluCNN97A6NGjAQBr165FQEAAtmzZgvHjx+PUqVPYtm0bDh48iLi4OADA0qVLMXLkSLz//vsIDg7+C+0QERGRNWh1QLmRvLw8lJaWIikpybDNw8MD8fHxSEtLw/jx45GWlgZPT09DOAGApKQkyOVypKen44EHHrhmXI1GA41GY3isVqsBAFqtFlqt1pgtGMYz9rhSwf4sny30CAA6vc5qe7T2Y8j+LJ+pemzNeEYNKKWlpQCAgICAZtsDAgIMz5WWlsLf3795Efb28Pb2NuzzZwsWLMC8efOu2b59+3Y4Ozsbo/RrpKSkmGRcqWB/ls96e7zybSknJwdbG8+ZuRbTst5jeAX7s3zG7rG+vv6W9zVqQDGVWbNmYebMmYbHarUaoaGhGDp0KNzd3Y36d2m1WqSkpGDIkCFQKBRGHVsK2J/ls/YeX0jbDgCIjIzCyCEdzVyNaVj7MWR/ls9UPV49A3IrjBpQAgMDAQAqlQpBQUGG7SqVCj179jTsU1ZW1ux1TU1NqKysNLz+z5RKJZRK5TXbFQqFyb44TDm2FLA/y2ftPdrZya26P8D6jyH7s3zG7rE1Yxn1OigREREIDAzEjh07DNvUajXS09ORkJAAAEhISEBVVRUyMzMN++zcuRN6vR7x8fHGLIeILBgvdU9k21r9CUptbS3OnfvfeeG8vDxkZWXB29sbYWFhmDFjBt566y1ER0cjIiICb775JoKDgzFmzBgAQOfOnTF8+HA89dRTWL58ObRaLaZPn47x48dzBQ8REREBuI2AkpGRgYEDBxoeX50bMmnSJKxZswavvPIK6urqMHXqVFRVVaF///7Ytm0bHB0dDa9Zt24dpk+fjsGDB0Mul2Ps2LH48MMPjdAOERERWYNWB5R77rkHQojrPi+TyTB//nzMnz//uvt4e3tj/fr1rf2riYiIyEbwXjxEJEkC1/9FiIisHwMKERERSQ4DChFJElfxENk2BhQiIiKSHAYUIiIikhwGFCKSJE6SJbJtDChEREQkOQwoRCRJnCRLZNsYUIiIiEhyGFCIiIhIchhQiIiISHIYUIhIkriKh8i2MaAQERGR5DCgEJEkcRUPkW1jQCEiIiLJYUAhIiIiyWFAISJJ4iRZItvGgEJERESSw4BCRJLESbJEto0BhYiIiCSHAYWIiIgkhwGFiIiIJIcBhYgkiat4iGwbAwoRERFJDgMKEUkSV/EQ2TYGFCIiIpIcBhQiIiKSHAYUIpIkTpIlsm0MKERERCQ5DChEREQkOQwoRCRJXMVDZNsYUIiIiEhyGFCIiIhIchhQiEiSuIqHyLYxoBAREZHkMKAQkSRxkiyRbWNAISIiIslhQCEiIiLJYUAhIkniJFki28aAQkRERJLDgEJERESSw4BCRJLEVTxEto0BhYiIiCSHAYWIiIgkhwGFiCSJq3iIbBsDChEREUkOAwoRERFJDgMKEUkSV/EQ2TYGFCIiIpIcBhQikiROkiWybQwoREREJDkMKERERCQ5DChEJEmcJEtk24weUHQ6Hd58801ERETAyckJUVFR+Oc//wkh/nc+WQiB2bNnIygoCE5OTkhKSsLZs2eNXQoRERFZKKMHlIULF+KTTz7BRx99hFOnTmHhwoVYtGgRli5dathn0aJF+PDDD7F8+XKkp6fDxcUFw4YNQ0NDg7HLISIiIgtkb+wBU1NTMXr0aIwaNQoA0L59e2zYsAEHDhwAcOXTkyVLluCNN97A6NGjAQBr165FQEAAtmzZgvHjxxu7JCKyQFzFQ2TbjB5QEhMTsXLlSpw5cwYdO3bEkSNHsHfvXixevBgAkJeXh9LSUiQlJRle4+Hhgfj4eKSlpbUYUDQaDTQajeGxWq0GAGi1Wmi1WqPWf3U8Y48rFezP8tlCjwCg0+mttkdrP4bsz/KZqsfWjCcTf5wcYgR6vR6vv/46Fi1aBDs7O+h0Orz99tuYNWsWgCufsPTr1w8lJSUICgoyvO6hhx6CTCbDN998c82Yc+fOxbx5867Zvn79ejg7OxuzfCIysxfSrvzeNLydHiNC9WauhoiMqb6+HhMmTEB1dTXc3d1vuK/RP0HZuHEj1q1bh/Xr16Nr167IysrCjBkzEBwcjEmTJt3WmLNmzcLMmTMNj9VqNUJDQzF06NCbNthaWq0WKSkpGDJkCBQKhVHHlgL2Z/msvccX0rYDAKKiIjEyqaOZqzENaz+G7M/ymarHq2dAboXRA8rLL7+M1157zXCqpnv37sjPz8eCBQswadIkBAYGAgBUKlWzT1BUKhV69uzZ4phKpRJKpfKa7QqFwmRfHKYcWwrYn+Wz9h7t5HZW3R9g/ceQ/Vk+Y/fYmrGMvoqnvr4ecnnzYe3s7KDXX/moNiIiAoGBgdixY4fhebVajfT0dCQkJBi7HCKyUJwkS2TbjP4Jyn333Ye3334bYWFh6Nq1Kw4fPozFixfjiSeeAADIZDLMmDEDb731FqKjoxEREYE333wTwcHBGDNmjLHLISIiIgtk9ICydOlSvPnmm/j73/+OsrIyBAcH4+mnn8bs2bMN+7zyyiuoq6vD1KlTUVVVhf79+2Pbtm1wdHQ0djlERERkgYweUNzc3LBkyRIsWbLkuvvIZDLMnz8f8+fPN/ZfT0RWgpe6J7JtvBcPERERSQ4DChEREUkOAwoRSRJX8RDZNgYUIiIikhwGFCIiIpIcBhQikiSu4iGybQwoREREJDkMKEQkSZwkS2TbGFCIiIhIchhQiIiISHIYUIiIiEhyGFCISJK4iofItjGgEBERkeQwoBCRJHEVD5FtY0AhIiIiyWFAISIiIslhQCEiSeIkWSLbxoBCREREksOAQkSSxEmyRLaNAYWIiIgkhwGFiIiIJIcBhYiIiCSHAYWIJImreIhsGwMKERERSQ4DChFJElfxENk2BhQiIiKSHAYUIiIikhwGFCIiIpIcBhQikiSu4iGybQwoRCRJnCRLZNsYUIiIiEhyGFCIiIhIchhQiIiISHIYUIhIkjhJlsi2MaAQERGR5DCgEJEkcRUPkW1jQCEiIiLJYUAhIiIiyWFAISIiIslhQCEiSeIqHiLbxoBCRJLESbJEto0BhYiIiCSHAYWIiIgkhwGFiIiIJIcBhYiIiCSHAYWIJImreIhsGwMKEUkSV/EQ2TYGFCIiIpIcBhQiIiKSHAYUIiIikhwGFCKSJE6SJbJtDChEJEmcJEtk2xhQiIiISHJMElCKi4vx6KOPwsfHB05OTujevTsyMjIMzwshMHv2bAQFBcHJyQlJSUk4e/asKUohIiIiC2T0gHLp0iX069cPCoUCv/zyC06ePIl//etf8PLyMuyzaNEifPjhh1i+fDnS09Ph4uKCYcOGoaGhwdjlEBERkQWyN/aACxcuRGhoKFavXm3YFhERYfh/IQSWLFmCN954A6NHjwYArF27FgEBAdiyZQvGjx9v7JKIiIjIwhj9E5QffvgBcXFxGDduHPz9/dGrVy98+umnhufz8vJQWlqKpKQkwzYPDw/Ex8cjLS3N2OUQkYXiKh4i22b0T1Byc3PxySefYObMmXj99ddx8OBBPP/883BwcMCkSZNQWloKAAgICGj2uoCAAMNzf6bRaKDRaAyP1Wo1AECr1UKr1Rq1/qvjGXtcqWB/ls8WegSAJp3Oanu09mPI/iyfqXpszXgyIYRR1/I5ODggLi4Oqamphm3PP/88Dh48iLS0NKSmpqJfv34oKSlBUFCQYZ+HHnoIMpkM33zzzTVjzp07F/Pmzbtm+/r16+Hs7GzM8onIzF5Iu/J70/B2eowI1Zu5GiIypvr6ekyYMAHV1dVwd3e/4b5G/wQlKCgIXbp0abatc+fO+M9//gMACAwMBACoVKpmAUWlUqFnz54tjjlr1izMnDnT8FitViM0NBRDhw69aYOtpdVqkZKSgiFDhkChUBh1bClgf5bP2nt8IW07ACAyMhIjh3Q0czWmYe3HkP1ZPlP1ePUMyK0wekDp168fsrOzm207c+YMwsPDAVyZMBsYGIgdO3YYAolarUZ6ejqeffbZFsdUKpVQKpXXbFcoFCb74jDl2FLA/iyftfdoZye36v4A6z+G7M/yGbvH1oxl9IDy4osvIjExEe+88w4eeughHDhwACtXrsTKlSsBADKZDDNmzMBbb72F6OhoRERE4M0330RwcDDGjBlj7HKIyEJxkiyRbTN6QOnTpw82b96MWbNmYf78+YiIiMCSJUswceJEwz6vvPIK6urqMHXqVFRVVaF///7Ytm0bHB0djV0OEVkoXuqeyLYZPaAAwL333ot77733us/LZDLMnz8f8+fPN8VfT0RERBaO9+IhIiIiyWFAISIiIslhQCEiIiLJYUAhIkniKh4i28aAQkSSxFU8RLaNAYWIiIgkhwGFiIiImtHq9GjQmbcGk1wHhYiIiCyDEAKFlZeRVVSFrIIqZBVewokSNQYFyvCgGetiQCEiIrIhlxt1yCqsQsb5ShwurMKRwipU1DVes19JvXknqjOgEBERWbGLtRpknL+EjPOVyMi/hOPF1WjSN5+ErrCToUuQO3qGeiI21BPdglxxMn23mSq+ggGFiIjIihRXXUbquYs4eL4SGecvIfdi3TX7BLo7Iq69F3qHe6FnqCe6BLtDaW9neF6r1eKUmVf6M6AQERFZsIu1GqTlVCA1pwKpOReRX1F/zT4xAW6Ia++FPu29EdfeCyGeTpDJpH2tIQYUIiIiC1LToMX+3ErsO3cRaTkVyFbVNHveTi5Dj3YeiI/wQd8IL9wR5gVPZwczVXv7GFCIiIgkTAiBbFUNdmWXY1d2GTLOX7pmDknnIHckRvkgMcoHfSK84e6oMFO1xsOAQkSSxEvdky2radBi37kK7Mouw+4z5bhQ3dDs+XAfZ/Tv4IvEKF/cGekNH1elmSo1HQYUIpIkXuqebE1J1WVsP1GK7SdVOJBX2exTEqW9HAlRPrinox/uifFHe18XM1baNhhQiIiIzEAIgbNltdh+ohS/nlDhWHF1s+cjfF1wd0c/3BPjhzsjfeCosLvOSNaJAYWIiKiNCCGQVViFbcevfFKS94clwDIZEBfuhaFdAjGkS4BNfEpyIwwoREREJiSEwKkLNfjxaAl+PFKCokuXDc852MnRP9oXQ7sEYHDnAPi5Wd9cktvFgEJERGQC58pq8dP/hZKc8v99UuLsYIfBnQMwvGsg7o7xg6uSP4pbwn8VIiIiIymv0eD7rGJ8d6gYJy+oDdsd7OUYFOOP+2KDMaiTP5wcbGs+ye1gQCEiIvoLGpv02HlahW8zi/B7djl0/7f6xl4uw13RvrgvNhhDugTAzQquTdKWGFCIiIhaSQjgRIkaW46U4vusYlyq1xqe6xnqibG92+He7kHwcrG8K7hKBQMKERHRLarVNOG7zEKsOGqH4v37Ddv93ZR48I52+FvvEHTwdzNjhdaDAYWIiOgmTl1QY116PrYcLkGtpgmADA72cgztEoC/9W6H/h18YW8nN3eZVoUBhYiIqAUNWh22HruAdekFyMy/ZNge4eOMWNca/GPCQPh5OJuxQuvGgEJERPQHZTUN+CotH1+lF6CyrhHAlQmvw7oGYmJ8GOLC3PHLL7/A05mTXk2JAYWIiAhXTuOs2puHH7JK0KjTAwCCPRzxSN8wPNwnFP7ujgAArVZ7o2HISBhQiIjIZun1ArvOlGHV3jzsO1dh2H5HmCeS+0diWNcAzi0xEwYUIiKyOU06PX48WoKPf8/B2bJaAICdXIbh3QKR3D8Cd4R5mblCYkAhIiKboWnS4dvMIizfnYPCyiv3xHFT2uOR+DBMSmyPEE8nM1dIVzGgEBGR1avTNGHDgQJ8+t9cqNQaAICPiwOe6B+BxxLC4c6rvEoOAwoREVmt+sYmfJGaj5V7cgxXew10d8TUAZF4pG8Y74kjYQwoRERkdRq0OqxPL8DHu87hYu2VpcLhPs549u4oPHBHCJT2DCZSx4BCRERWQ6vTY2NGIZbuOIdSdQMAINTbCTMGd8TonsFckWNBGFCIiMji6fUCW7KKseS3syiorAcABHk44rlB0RgX1w4KBhOLw4BCREQWLTXnIt7++RROlKgBAL6uDpg2sAMe6RsGRwVP5VgqBhQiIrJI58pqsGDraew4XQbgynLhZ+6JwpR+7eHswB9vlo5HkIiILMrFWg2W/HYGGw4UQqcXsJPL8Gh8GJ4fHA0fV6W5yyMjYUAhIiKLoNXpsWbfefx7x1nUapoAAEO6BOC1EZ0Q5edq5urI2BhQiIhI8lJzLmLO9ycMl6XvHuKB10d2RkKUj5krI1NhQCEiIsm6UH0Zb/98Cj8dvQAA8HZxwGvDO+FvvdtBLpeZuToyJQYUIiKSnMYmPT7fl4cPd5xFfaMOchnw6J3heGlIDDyceVl6W8CAQkREkpKZfwmzvjuKM6orp3N6h3th/uiu6BrsYebKqC0xoBARkSTUaprw3rbTWLs/H0JcuZnf6yM748E7QiCT8XSOrWFAISIis9txSoU3thzHheorl6f/W+92+MfIzvBycTBzZWQuDChERGQ2F2s1mPfjSfx4pATAlfvmLHigB/pH+5q5MjI3BhQiIjKLX45dwD+2HEdlXSPkMuCpuyIxI6kjnBx4eXpiQCEiojZWfVmLuT+cwObDxQCAToFueO9vsejejpNg6X8YUIiIqM3sOVOOV749ilJ1A+Qy4Nl7ovDC4I5wsOfdhqk5BhQiIjK5+sYmLNh6Gl/uzwcARPi64P1xsegd7mXmykiqGFCIiMikjhdX4/kNh5F7sQ4AMCkhHK+O6MQ7DtMN8auDiIhMQgiBVXvzsPCX02jU6RHk4Yj3x8WiXweu0KGbY0AhIiKjq9UCU786jF1nLgIAhnYJwKK/9YCnM69rQrfG5LOS3n33XchkMsyYMcOwraGhAdOmTYOPjw9cXV0xduxYqFQqU5dCRERtYH9uJRYescOuMxfhYC/HP0d3xYrHejOcUKuYNKAcPHgQK1asQI8ePZptf/HFF/Hjjz9i06ZN2L17N0pKSvDggw+ashQiIjIxnV5gccoZPL4mA2qtDFF+Lvh+Wj88ltCel6qnVjNZQKmtrcXEiRPx6aefwsvrf7O0q6ursWrVKixevBiDBg1C7969sXr1aqSmpmL//v2mKoeIiEyosq4Rk1cfwIc7zkIIIMFfj++eiUfnIHdzl0YWymRzUKZNm4ZRo0YhKSkJb731lmF7ZmYmtFotkpKSDNs6deqEsLAwpKWl4c4777xmLI1GA41GY3isVqsBAFqtFlqt1qh1Xx3P2ONKBfuzfLbQIwDodHqr7dHajuGRomo89/URXKhugKNCjrmjYuCkOgaFTFhNj39kbcevJabqsTXjmSSgfP311zh06BAOHjx4zXOlpaVwcHCAp6dns+0BAQEoLS1tcbwFCxZg3rx512zfvn07nJ2djVLzn6WkpJhkXKlgf5bPenu88m0pNzcXW7eeM3MtpmXpx1AIYJ9Khu/Oy6ETMvg6CiR3bIST6hgAy+/vZqy9P8D4PdbX19/yvkYPKIWFhXjhhReQkpICR0dHo4w5a9YszJw50/BYrVYjNDQUQ4cOhbu7cT8+1Gq1SElJwZAhQ6BQKIw6thSwP8tn7T2+kLYdABAZGYmRQzqauRrTsIZjeLlRhzk/nsTmvAsAgCGd/bHwwa5wc1RYRX83Yu39Aabr8eoZkFth9ICSmZmJsrIy3HHHHYZtOp0Oe/bswUcffYRff/0VjY2NqKqqavYpikqlQmBgYItjKpVKKJXKa7YrFAqTfXGYcmwpYH+Wz9p7tLOTW3V/gOUew5Kqy5j6ZQaOF6shlwGvDO+EpwdEXjMR1lL7u1XW3h9g/B5bM5bRA8rgwYNx7NixZtumTJmCTp064dVXX0VoaCgUCgV27NiBsWPHAgCys7NRUFCAhIQEY5dDRERGdKjgEqauzcTFWg28XRzw0YReSIzihdfI+IweUNzc3NCtW7dm21xcXODj42PYnpycjJkzZ8Lb2xvu7u547rnnkJCQ0OIEWSIikob/ZBZh1nfH0KjTo1OgGz59PA6h3qaZB0hklivJfvDBB5DL5Rg7diw0Gg2GDRuGjz/+2BylEBHRTej0Agu3ncbKPbkArlwV9oOHe8JFyYuRk+m0yVfXrl27mj12dHTEsmXLsGzZsrb464mI6DbVNGjx/IbD+D27HADw3KAOeDGpI+RyXniNTIvxl4iIWnSh+jKmrD6I06U1UNrL8f64WNwXG2zusshGMKAQEdE1TpaoMWXNAajUGvi5KbFqUhx6tPM0d1lkQxhQiIiomd1nyjFt3SHUapoQ7e+K1VP6oJ0XJ8NS22JAISIig28OFuD1zceh0wskRPpg+WO94eFk3df6IGliQCEiIghx5U7ES3deub3Ag71C8O7YHnCwN+lN74muiwGFiMjGNen0eH3zMWzMKAIAPD+oA14c0vGaK8MStSUGFCIiG9ag1eGFrw/j1xMqyGXAOw90x/i+YeYui4gBhYjIVtU0aDF1bSbScivgYC/H0kd6YVjXlu+JRtTWGFCIiGxQRa0Gk1cfxLHiargq7bHy8d68pw5JCgMKEZGNKa66jMc+S0fuxTp4uzjgiyl90b2dh7nLImqGAYWIyIacK6vFY6vScaG6AcEejvjyyXhE+bmauyyiazCgEBHZiOzSGkz8bD8u1jYiys8FXybHI9jTydxlEbWIAYWIyAacLFHj0VXpqKxrROcgd3yV3Bc+rkpzl0V0XQwoRERW7lhRNR5dlY7qy1r0aOeBtU/0haezg7nLIrohBhQiIit2qOASJn1+ADUNTegV5okvnugLd0deup6kjwGFiMhKHTxficmfH0Bdow5923vj8yl94Krkt32yDPxKJSKyQmk5FXhizUFc1uqQEOmDVZPj4OzAb/lkOfjVSkRkZQ7kVRrCyV3Rvlj5WBycHOzMXRZRqzCgEBFZkcz8S5iy+gAua3UY0NEPKx/rDUcFwwlZHt5Hm4jIShwprDLMOUmM8mE4IYvGgEJEZAWOF1fjsVXpqNE0oW+ENz6bFMdwQhaNAYWIJEkIc1dgOU6XqvHYqnSoG5rQO9wLn0/uwwmxZPEYUIiILNhZVQ0mfpqOS/VaxLbzwGouJSYrwYBCRJIh/vCxiUxmxkIsxPmLdZjwWToq6hrRNdgda5+I50XYyGowoBARWaDS6gY8uiod5TUadAp0w1fJ8fBwZjgh68GAQkRkYS7VNeKxVekounQZ7X2c8WVyPLxceG8dsi4MKEREFqRW04TJaw7ibFktAtyV+DI5Hn5uvCsxWR8GFCIiC9Gg1WHq2gwcKayCp7MCXyXHI9Tb2dxlEZkEAwoRSQaXFl9fk06P5zccRmpOBVwc7LBmSl9EB7iZuywik2FAISKSOL1e4LXvjmH7SRUc7OT49PE49Az1NHdZRCbFgEJEJGFCCLyz9RS+zSyCXAYsndALiR18zV0WkckxoBARSdiKPbn4bG8eAGDh2B4Y1jXQzBURtQ0GFCKSJM5HATYfLsK7v5wGALwxqjPGxYWauSKitsOAQkQkQf89W46XNx0FADzZPwJP3hVp5oqI2hYDChFJxh8/NLHlS90fL67GM19mokkvcG+PILw+srO5SyJqcwwoREQSUlhZjylrDqKuUYc7I73xr4diIZfbcFojm8WAQkQkEZfqGjFp9QHD/XVWPBYHpb2ducsiMgsGFCIiCWjQ6vDk2gzkltch2MMRa6b0hYcTb/5HtosBhYgkyZZW8ej0As9vOIzM/Etwd7THmif6ItDD0dxlEZkVAwoRSYawpVTyf4QQmPvDiStXibWX47NJfdCRl7AnYkAhImmylVU8n+87jy/350MmA/79cE/0jfA2d0lEksCAQkRkJjuzy/HWzycBAK+P6IwR3YPMXBGRdNibuwAiIltUXAd8tPEohAAe6RuKJ++KMHdJRJLCT1CISJKseTpKWY0GK0/bob5Rh34dfDB/dDfIbOWcFtEtYkAhImpDlxt1eGbdYVQ1yhDp64KPJ/SGwo7fion+jO8KIpIMa7/UvV4vMHNjFo4Vq+FiL7DysV7wcOa1TohawoBCRNRG3tuejV+Ol0JhJ0NyjA7h3s7mLolIshhQiIjawMaMQnyyKwcAsGBMV0S5m7kgIoljQCEiMrH9uRX4x+ZjAIDnBnXA6J7BZq6ISPoYUIhIkqxlFU/exTo881UmtDqBUT2C8GJSR3OXRGQRGFCISDKsJZRcVVXfiCfWHERVvRY9Qz3xr3GxkMutcPYvkQkwoBCRJFn6Kp7GJj2e+SoTeRfrEOLphE8fj4Ojws7cZRFZDAYUIiIjE0LgjS3HsD+3Eq5Ke6yaHAc/N6W5yyKyKEYPKAsWLECfPn3g5uYGf39/jBkzBtnZ2c32aWhowLRp0+Dj4wNXV1eMHTsWKpXK2KUQEZnFij252JhRBLkMWDqhFzoFcskOUWsZPaDs3r0b06ZNw/79+5GSkgKtVouhQ4eirq7OsM+LL76IH3/8EZs2bcLu3btRUlKCBx980NilEJEFs9T5KNuOl2LhttMAgNn3dsHAGH8zV0RkmYx+s8Bt27Y1e7xmzRr4+/sjMzMTAwYMQHV1NVatWoX169dj0KBBAIDVq1ejc+fO2L9/P+68805jl0RE1CaOFVVjxjeHIQTweEI4JvfjDQCJbpfJ72ZcXV0NAPD29gYAZGZmQqvVIikpybBPp06dEBYWhrS0tBYDikajgUajMTxWq9UAAK1WC61Wa9R6r45n7HGlgv1ZPmvusbFJb/h/vV5vUT1eqG5A8hcH0aDVY0C0D2YNi75u/dZ8DAH2Zw1M1WNrxpMJYboPUvV6Pe6//35UVVVh7969AID169djypQpzQIHAPTt2xcDBw7EwoULrxln7ty5mDdv3jXb169fD2dn410qOr8W2F4kR5irQLgrEOoi4MLbZBC1mSY98FL6ld+bhrfTY0So/iavkAaNDvj3cTsU18sQ6CQwo5sOTib/9Y/I8tTX12PChAmorq6Gu/uN52aZ9C00bdo0HD9+3BBObtesWbMwc+ZMw2O1Wo3Q0FAMHTr0pg22xuf7zuP4sTM4ful/28K8ndAjxAM92nmge4g7uga5w8nBcpcKarVapKSkYMiQIVAorC99WXt/gHX3qGnS46X03wAAkZGRGDlE+hc10+kF/r4+C8X15fBxccCGp+PRzsvphq+x5mMIsD9rYKoer54BuRUmCyjTp0/HTz/9hD179qBdu3aG7YGBgWhsbERVVRU8PT0N21UqFQIDA1scS6lUQqm8domeQqEw6j/c4C5BkMlk+PXgKVzUuyK/sh4FlZdRUHkZPx0rBQDYyWWI9ndFbDtP9AzzRO9wL3Twc7W4iy8Z+99Oaqy9P8A6e9TLdIb/t7OTW0R/C386iZ3Z5XCwl+PTSXGI8L/1X5qs8Rj+EfuzfMbusTVjGT2gCCHw3HPPYfPmzdi1axciIppPEuvduzcUCgV27NiBsWPHAgCys7NRUFCAhIQEY5fTKh38XRHuFY6AqhMYObI/6rQCR4uqcbSoClmFV/5bVqPB6dIanC6twTcZhQAADycFeod7oXe4F+LCvRAb6skLMhH9RZawimd9egE+25sHAPjXuFjcEeZl5oqIrIfRA8q0adOwfv16fP/993Bzc0Np6ZVPHjw8PODk5AQPDw8kJydj5syZ8Pb2hru7O5577jkkJCRIbgWPp7MDBnT0w4COfoZtpdUNyCqswtGiKhwquISswipUX9Zi5+ky7DxdBgBQ2MnQNdgDceFeiGvvjbj2XvB15UWaiG7GEkLJVXvPXsSb3x8HAMwc0hH3xfIGgETGZPSA8sknnwAA7rnnnmbbV69ejcmTJwMAPvjgA8jlcowdOxYajQbDhg3Dxx9/bOxSTCLQwxHDPQIxvNuV01FanR4nS9TIyL+EzPxKZJy/hLIaDbIKq5BVWGX47aqDvysSIn2QGOWD+EgfeLs4mLMNIsmT8qXuz5XV4Nl1mdDpBR7oFYLnBnUwd0lEVsckp3huxtHREcuWLcOyZcuM/de3OYWdHLGhnogN9URy/wgIIVB06TIy/i+sZJy/hDNlNThXVotzZbX4cn8+AKBToBsSonyQEHklsHg4Wfd5TCJrUVnXiCfWZKCmoQlx4V54d2x3yKScpogsFBfCGZlMJkOotzNCvZ3xQK8rk4Or6huxP7cS+3MrkJZTgWxVjWEey+p95yGTAV2D3ZEY5Yu7on3Rp70357AQSZCmSYenv8xAQWU9wrydseKx3lDa871KZAoMKG3A09kBw7v977TQxVqNIayk5VYgt7wOx4vVOF6sxso9uXBUyHFnpA8GRF+Z/xLl58Lf0MjmSG0+ihACr/3nGA6evwQ3R3t8PjkOPpxbRmQyDChm4OuqxL09gnFvjyuT6lTqBuzPrcDesxex52w5VGoNdmWXY1d2OQAgxNMJAzr6YkC0HxI7+PJ0EJEZLN15DpsPF8NOLsMnE3ujg7+buUsismoMKBIQ4O6I0T1DMLpnCIQQOKOqxe4zZdhz5iIO5FWiuOoyNhwoxIYDhbCTy9A7zAtJXfwxuHMAovxczV0+kdX7PqsYi1POAADmj+6K/tG+Zq6IyPoxoEiMTCZDTKAbYgLdMHVAFC436rA/rwJ7zpRj95ly5JbX4cD5Shw4X4l3tp5GpK8LkroEYHAnf/QO94K9ndFvUE1kFlI5q5mZX4mXvz0KAHjqrghMjA83c0VEtoEBReKcHOwwMMbfcMv2wsp67Dxdht9OqbA/twK5F+uwck8uVu7JhaezAgNj/DG4sz/u7ugHN0eeCiL6Kwoq6vHU2kw0NukxtEsAXhvR2dwlEdkMBhQLE+rtjEmJ7TEpsT1qGrT479mL+O2kCjuzy1BVr8Xmw8XYfLgYCjsZ7or2w4hugRjSJQCezrzuClFrVNdrMWXNAVTWNaJ7iAeWjO8JOwu7pQWRJWNAsWBujgqM7B6Ekd2D0KTT41BBFXacUiHllAq55XWGq9vay2VI7OCLEd0CMbCjj7nLJrol5lzFo9Xp8ey6TOSU1yHIwxGfTYqDswO/XRK1Jb7jrIS9nRx9I7zRN8Ibs0Z2xllVDX45Xoqtxy7gdGkN9pwpx54z5ZDLgCg3OS75FmJkj2D4uzmau3QiAyksLRZC4I3Nx5GaUwEXBzusmtQHAe58nxC1NQYUKxUd4IboADc8PzgaueW1+OV4KX45fgHHi9U4q5Zj7o+nMO+nU0iI9MGYniEY1i2Qy5dJUsw1SXbFnlx8k1EIuQxYOqEXugTf+t2Jich4GFBsQKSfK6YN7IBpAzsgR1WNf/9nN87rvXC0SI3UnAqk5lTgje+PY1CMP8b0CsY9Mf68ki3ZpG3HL+DdX04DAGbf2wWDOgWYuSIi28WAYmPCvJ0xOERg5Mg7UVqjxQ9HSvB9VjHOqGqx7UQptp0ohZujPUZ0C8ToniG4M9KHEwPJJhwprMKMb7IAAJMT22NyvwjzFkRk4xhQbFiotzOmDeyAv98ThdOlNdiSVYwfs0pQUt2AjRlF2JhRhAB3JUb3DMG43u0QHcArZ1Lbacv5KAUV9Uj+4iAatHoMjPHDG6O4nJjI3BhQCDKZDJ2D3NE5yB2vDuuEg+crsSWrBFuPXYBKrTFcZyU21BPjerfDfbHBnK9CVqOyrhGTVh/AxdpGdA5yx9IJd/CCh0QSwIBCzcjlMsRH+iA+0gfz7u+KXdll+DazCDtPl+FIYRWOFFbhnz+dxLCugRgX1w6JUb48BURGI9C2y3guN+qQ/MVB5F2sQ4inE9ZM6QNXJb8tEkkB34l0XQ72cgztGoihXQNxsVaDLYeLsSmjCNmqGvxwpAQ/HClBsIcjxvZuh3G9QxHm42zuksmKmHoVj04v8MLXh3G4oAoeTgp88QSXExNJCQMK3RJfVyWevCsSyf0jcKy4GpsyivB9VjFKqhuwdOc5LN15DndF+2JifBgGdw6Agh+Rk4QJITD3hxPYflIFB3s5PpsUx7sTE0kMAwq1ikwmQ492nujRzhP/GNUZKSdV2JhRiL3nLuK/Z6/88XdT4uE+oXi4TyjaefFTFZKeT3bn4Mv9+ZDJgCUP90Sf9t7mLomI/oQBhW6bo8IO98UG477YYBRW1mPDgQJszChEWY0GS3eew0e/n8PAGH9M6BuGgZ38OVeFWsVUq3i+O1SERduyAQBvjuqCkd2DTPMXEdFfwoBCRhHq7YxXhnfCjKSOSDmpwrr0fKTmVBjuBxTs4YiH+4Thkb6h8Od5fjKTPWfK8cq3RwEAT90VgSf681onRFLFgEJG5WAvx6geQRjVIwi55bXYcKAAmzKLUFLdgA9+O4OPfj+LUd2DMCmxPXqFeZm7XJIYU177JDP/Ep7+MhNNeoF7ewRh1ghe64RIyhhQyGQi/Vzxj1Fd8NLQGGw7Xoq1aedxqKAKW7JKsCWrBLGhnpiS2B4juwfBwZ6Taqk5Y67iOXVBjSmrD+CyVoe7on2x+KGekPOUI5Gk8acCmZyjwg5jeoXgu7/3ww/T++HBO0LgYCc3XFq838Kd+CDlDMpqGsxdKlmh/Io6PP75AagbmnBHmCdWPNabgZjIAvBdSm2qRztPLH6oJ1JnDcJLQzoiwF2J8hoN/r3jLPq9uxMzvj6MrMIqc5dJEmCM0z0qdQMeXZWO8hoNOgW6YfXkvnB24AfHRJaA71QyC19XJZ4bHI1n7onCtuOlWJN6Hpn5lwynf+4I88RTd0ViaNdArv6h21JV34jHVx1AYeVlhPs4Y+0TfeHhzFs0EFkKBhQyK4Wd3LBU+VhRNdaknsePR0pwqKAKz647hDBvZyT3j8C4uHb8zdcGGGuOrLpBi0mrDyJbVQN/NyW+So7n6jEiC8NTPCQZ3dt54F8PxWLvawPx3KAO8HRWoKCyHnN+OIGEBTvx3q+nUabmPBVbcbuTZGsatJj0+QEcKayCl7MCXybHI9SbFwwksjQMKCQ5/m6OeGloDFJfG4R/ju6KcB9nVF/WYtnvOei/8He8vOkIsktrzF0mSVCdpglTVh803F/nqyfjERPIS9gTWSJ+Zk6S5exgj8cS2mNCfDhSTqrw6X9zkZl/CZsyi7Apswh3d/TDU3dFol8HH8hMfWc5krz6xiZMWXMQGfmX4O5oj3VPxqNrsIe5yyKi28SAQpJnJ5dheLdADO8WiMz8S/jsv7n49UQpdp8px+4z5egS5I5n7onCyG6B5i6VjKg1q3guN+qQvCYDB/Iq4aa0x5fJ8egWwnBCZMkYUMii9A73Qu/w3sivqMPne/OwMaMIJy+o8fyGw3jf2xnJ/cLhrDN3ldSW6jRNePKLDKTlVsBVaY8vkvsiNtTT3GUR0V/EgEIWKdzHBfNGd8OMpI5Ym5aPNal5VybU/ngKrgo7lLrn4vF+kfBw4rJSSyJaefGT6staTFl9AIcKquDiYIc1U/rgDt5CgcgqcJIsWTQvFwe8kBSNfa8Nwtz7uiDYwxG1Whn+9ds59Ht3JxZsPQUVV/5YpJtNK6qo1eCRlftx6P8mxK576k7Etfdum+KIyOQYUMgqODvYY3K/CPz2Yn882kGHaH8X1GqasGJPLu5a+DtmfXcUeRfrzF0mGUlpdQMeXrkfJy+o4evqgK+n3omePK1DZFUYUMiqKOzk6OMn8NO0RKyaFIc+7b3QqNNjw4FCDPrXLvx9XSaOFlWZu0y6Bdc725NfUYeHVqThXFktgjwc8c3TCegc5N62xRGRyXEOClkluVyGwZ0DMLhzAA6er8TyXTnYcboMW4+VYuuxUvTr4INn7+7AJcoWJquwCslrDqKirhFh3s5Y9yQvwkZkrRhQyOr1ae+NPpO9kV1agxW7c/D9kRLsO1eBfecq0D3EA8/cHYXh3XjPHym40RTZ306qMH3DITRo9egW4o7PJ/eBvxsvX09krXiKh2xGTKAbFj/cE7tfvgeTE9vDUSHHseJqTFt/CIP/tQvr0vPRoOUaZSlal56PqV9moEGrx90d/fDN1ASGEyIrx4BCNqedlzPm3t8Vqa8NxvODo+HprMD5inr8Y/Nx9F+4Ex/tPIuq+kZzl2nzZDJApxd4Z+sp/GPzcegF8HBcKD6bFAcXJT/8JbJ2fJeTzfJ2ccDMIR3x9IBIbMwoxGf/zUNx1WW8v/0MPt6Vg/F9wpB8VwRCPJ3MXapNqr585dL1e86UAwBmJEXjhcHRnDNEZCMYUMjmuSjtMaVfBB69Mxxbj13A8t25OHVBjc/35eGLtPO4r0cQpg6IQpdgrhRpS2v3FwAAnBR2eG9cD9zbI9jMFRFRW2JAIfo/Cjs5RvcMwf2xwfjv2YtYsScH+85VYEtWCbZklWBARz88MyASCVFc+dNWQjydsPLx3rzpH5ENYkAh+hOZTIYBHf0woKMfjhVVY8WeHGw9dgF7zpRjz5lydA/xwNN3R2J410DY23Eal7E0NumxJOWs4XHvME+sfDwOPq5KM1ZFRObCgEJ0A93beeCjCXegoKIen+3NxcaMQhwrrsb09YcR5u2MJ/q1x9/iQuHKSZt/SU55LV78JgtHi6oBAJ099fjyiTg4OzKcENkq/vpHdAvCfJwxf3Q37Ht1EF4YHA0vZwUKKusx98eTSHhnB+b/eBL5FbyUfmsJIfDV/nyM+vC/OFpUDQ8nBT5+pCee6ayHgp9OEdk0/tpH1Ao+rkq8OKQjnrk7CpsyC7Fm33nkXqzD5/vysDo1D4M7+WNyYgSvUHsLSqsb8I/Nx7DjdBkAoH8HX7w/LhY+znbYet68tRGR+TGgEN0GJwc7PJ7QHo/Gh2PP2XKsST2PXdnl+O1UGX47VYZof1dM7tceD/QKgbMD32Z/pNMLrEvPx6Jt2ajVNMHBTo5XhsfgiX4RkMtl0Gq15i6RiCSA3zmJ/gK5XIZ7YvxxT4w/cstr8UXqeXybWYSzZbX4x+bjePeX03igVwjG9wnjMmUApy6o8frmYzhcUAUA6BXmiXcf7IGYQDfzFkZEksOAQmQkkX6umDe6G14aFoNNGUX4IvU8CirrsTYtH2vT8hEb6olH+oTivthgm7sSallNAxZvP4ONGYXQC8BVaY9Xh8dgQnw474FERC2yre+SRG3A3VGB5P4RmJLYHqk5FdhwoADbT5biSGEVjhRW4Z8/ncT9PUPwt94huCPMy6rnqtRpmvD53jx8sjsH9Y1X7nM0qnsQ3ry3CwI9eC8dIro+BhQiE5HLZegf7Yv+0b64WKvBfzKLsOFAAc5X1GPDgQJsOFCAUG8njOkZgtE9Q9DB39XcJRtNTYMWa9Py8dl/c3Gp/sqckp6hnnhjVGfEtfc2c3VEZAkYUIjagK+rEk/fHYWpAyKxP7cSGzMK8euJUhRWXsbSneewdOc5dA/xwP2xwRjWNRBhPs7mLvm2lFRdxrr0fHyZlg91QxMAoL2PM14c0hH3xwZb9adFRGRcDChEbUgmkyEhygcJUT6ob2xCykkVvs8qwe4z5ThWXI1jxdV4e+spdAp0w9AuARjSJRDdQtwl/YNdpxdIzbmIL9Py8dspFfTiyvYO/q6YPrAD7u0RxCvuElGrmTWgLFu2DO+99x5KS0sRGxuLpUuXom/fvuYsiajNODvYY/T/nd6pqNXg52MXsO14KdLzKnG6tAanS2vw4c5zCPJwRL8OvujXwQf9onzh5WRn7tIhhEBWYRV+OFKCn49eQFmNxvBcQqQPJiWGY0iXQE6AJaLbZraA8s0332DmzJlYvnw54uPjsWTJEgwbNgzZ2dnw9/c3V1lEZuHjqsTjCe3xeEJ7VNU3YufpMmw/ocLuM+W4UN2AbzOL8G1mEQAgys8FgXI5Gg4Xo3d7H0T6ukLeBkGgolaD1JwK7D5Tjt1nylH+h1Di4aTA6J7BeOzOcEQHcMkwEf11ZgsoixcvxlNPPYUpU6YAAJYvX46ff/4Zn3/+OV577TVzlUVkdp7ODnjwjnZ48I52aNDqcCCvEvtyLmLfuYs4UaJGTnkdciDHvu9OAADclPboFuKB6ABXRPld+RPh5wJ/N+VtXS6+SadH0aXLyLtYh5zyWhwpqkZW4SUUVl5utp+zgx2SOgdgdM9g3BXtBwd7nsYhIuMxS0BpbGxEZmYmZs2aZdgml8uRlJSEtLS0a/bXaDTQaP7325parQYAaLVao1918up41no1S/ZnWewAJER4IiHCE/8vqQOq6rXYd64M3+89BrXCCycv1KBG04S03Aqk5VY0e61MBvi4OMDfTQkfFwc4OdjBWWEHRwc72Mtl0OoEtDo9tDo9quq1qKxvREVtIyrqGqHViRbr6ejviruifTAg2he9w72gvBpKhA5arc4oPVvbMWyJtffI/iyfqXpszXgyIUTL34lMqKSkBCEhIUhNTUVCQoJh+yuvvILdu3cjPT292f5z587FvHnzrhln/fr1cHa2zNUORMagE0BpPVBUJ0PZZRlUlwHVZRkuagC9uP3TPgqZgK8T4O8o0M5FINwVCHMVcOK0eiL6C+rr6zFhwgRUV1fD3f3GV9e2iG83s2bNwsyZMw2P1Wo1QkNDMXTo0Js22FparRYpKSkYMmQIFAqFUceWAvZn+W6lR71eoLK+EWU1GpTVaFBZ14jLWj0atDrUN+qg0wso7OSwl8ugsJPBw0kBbxcH+Lg4wM9NiQA3ZZvMa2kJj6HlY3+Wz1Q9Xj0DcivMElB8fX1hZ2cHlUrVbLtKpUJgYOA1+yuVSiiVymu2KxQKk31xmHJsKWB/lu9mPQYpHRDkZbkXf+MxtHzsz/IZu8fWjGWWWW0ODg7o3bs3duzYYdim1+uxY8eOZqd8iIiIyDaZ7RTPzJkzMWnSJMTFxaFv375YsmQJ6urqDKt6iIiIyHaZLaA8/PDDKC8vx+zZs1FaWoqePXti27ZtCAgIMFdJREREJBFmnSQ7ffp0TJ8+3ZwlEBERkQTxykpEREQkOQwoREREJDkMKERERCQ5DChEREQkOQwoREREJDkMKERERCQ5DChEREQkOQwoREREJDkMKERERCQ5Zr2S7O0SQgBo3W2bb5VWq0V9fT3UarVV3qWS/Vk+a+/R2vsDrL9H9mf5TNXj1Z/bV3+O34hFBpSamhoAQGhoqJkrISIiotaqqamBh4fHDfeRiVuJMRKj1+tRUlICNzc3yGQyo46tVqsRGhqKwsJCuLu7G3VsKWB/ls/ae7T2/gDr75H9WT5T9SiEQE1NDYKDgyGX33iWiUV+giKXy9GuXTuT/h3u7u5W+4UHsD9rYO09Wnt/gPX3yP4snyl6vNknJ1dxkiwRERFJDgMKERERSQ4Dyp8olUrMmTMHSqXS3KWYBPuzfNbeo7X3B1h/j+zP8kmhR4ucJEtERETWjZ+gEBERkeQwoBAREZHkMKAQERGR5DCgEBERkeTYXEB5++23kZiYCGdnZ3h6era4T0FBAUaNGgVnZ2f4+/vj5ZdfRlNT0w3HraysxMSJE+Hu7g5PT08kJyejtrbWBB20zq5duyCTyVr8c/Dgweu+7p577rlm/2eeeaYNK7917du3v6bWd99994avaWhowLRp0+Dj4wNXV1eMHTsWKpWqjSpunfPnzyM5ORkRERFwcnJCVFQU5syZg8bGxhu+TsrHcNmyZWjfvj0cHR0RHx+PAwcO3HD/TZs2oVOnTnB0dET37t2xdevWNqq09RYsWIA+ffrAzc0N/v7+GDNmDLKzs2/4mjVr1lxzrBwdHduo4taZO3fuNbV26tTphq+xpOMHtPw9RSaTYdq0aS3uL/Xjt2fPHtx3330IDg6GTCbDli1bmj0vhMDs2bMRFBQEJycnJCUl4ezZszcdt7Xv49ayuYDS2NiIcePG4dlnn23xeZ1Oh1GjRqGxsRGpqan44osvsGbNGsyePfuG406cOBEnTpxASkoKfvrpJ+zZswdTp041RQutkpiYiAsXLjT78+STTyIiIgJxcXE3fO1TTz3V7HWLFi1qo6pbb/78+c1qfe655264/4svvogff/wRmzZtwu7du1FSUoIHH3ywjaptndOnT0Ov12PFihU4ceIEPvjgAyxfvhyvv/76TV8rxWP4zTffYObMmZgzZw4OHTqE2NhYDBs2DGVlZS3un5qaikceeQTJyck4fPgwxowZgzFjxuD48eNtXPmt2b17N6ZNm4b9+/cjJSUFWq0WQ4cORV1d3Q1f5+7u3uxY5efnt1HFrde1a9dmte7du/e6+1ra8QOAgwcPNusvJSUFADBu3LjrvkbKx6+urg6xsbFYtmxZi88vWrQIH374IZYvX4709HS4uLhg2LBhaGhouO6YrX0f3xZho1avXi08PDyu2b5161Yhl8tFaWmpYdsnn3wi3N3dhUajaXGskydPCgDi4MGDhm2//PKLkMlkori42Oi1/xWNjY3Cz89PzJ8//4b73X333eKFF15om6L+ovDwcPHBBx/c8v5VVVVCoVCITZs2GbadOnVKABBpaWkmqND4Fi1aJCIiIm64j1SPYd++fcW0adMMj3U6nQgODhYLFixocf+HHnpIjBo1qtm2+Ph48fTTT5u0TmMpKysTAMTu3buvu8/1vh9J0Zw5c0RsbOwt72/px08IIV544QURFRUl9Hp9i89b0vEDIDZv3mx4rNfrRWBgoHjvvfcM26qqqoRSqRQbNmy47jitfR/fDpv7BOVm0tLS0L17dwQEBBi2DRs2DGq1GidOnLjuazw9PZt9IpGUlAS5XI709HST19waP/zwAyoqKjBlypSb7rtu3Tr4+vqiW7dumDVrFurr69ugwtvz7rvvwsfHB7169cJ77713w1NymZmZ0Gq1SEpKMmzr1KkTwsLCkJaW1hbl/mXV1dXw9va+6X5SO4aNjY3IzMxs9m8vl8uRlJR03X/7tLS0ZvsDV96TlnSsANz0eNXW1iI8PByhoaEYPXr0db/fSMHZs2cRHByMyMhITJw4EQUFBdfd19KPX2NjI7766is88cQTN7w5rSUdvz/Ky8tDaWlps2Pk4eGB+Pj46x6j23kf3w6LvFmgKZWWljYLJwAMj0tLS6/7Gn9//2bb7O3t4e3tfd3XmMuqVaswbNiwm95sccKECQgPD0dwcDCOHj2KV199FdnZ2fjuu+/aqNJb9/zzz+OOO+6At7c3UlNTMWvWLFy4cAGLFy9ucf/S0lI4ODhcMwcpICBAcserJefOncPSpUvx/vvv33A/KR7DixcvQqfTtfgeO336dIuvud570hKOlV6vx4wZM9CvXz9069btuvvFxMTg888/R48ePVBdXY33338fiYmJOHHihMlvjNpa8fHxWLNmDWJiYnDhwgXMmzcPd911F44fPw43N7dr9rfk4wcAW7ZsQVVVFSZPnnzdfSzp+P3Z1ePQmmN0O+/j22EVAeW1117DwoULb7jPqVOnbjqRy5LcTs9FRUX49ddfsXHjxpuO/8f5M927d0dQUBAGDx6MnJwcREVF3X7ht6g1/c2cOdOwrUePHnBwcMDTTz+NBQsWSPpS1LdzDIuLizF8+HCMGzcOTz311A1fa+5jSMC0adNw/PjxG87RAICEhAQkJCQYHicmJqJz585YsWIF/vnPf5q6zFYZMWKE4f979OiB+Ph4hIeHY+PGjUhOTjZjZaaxatUqjBgxAsHBwdfdx5KOnyWxioDy0ksv3TDdAkBkZOQtjRUYGHjNTOSrqzsCAwOv+5o/TwxqampCZWXldV/zV91Oz6tXr4aPjw/uv//+Vv998fHxAK789t4WP9z+yjGNj49HU1MTzp8/j5iYmGueDwwMRGNjI6qqqpp9iqJSqUx2vFrS2h5LSkowcOBAJCYmYuXKla3++9r6GLbE19cXdnZ216yYutG/fWBgYKv2l4rp06cbJsy39rdohUKBXr164dy5cyaqzng8PT3RsWPH69ZqqccPAPLz8/Hbb7+1+lNHSzp+V4+DSqVCUFCQYbtKpULPnj1bfM3tvI9vi9Fms1iYm02SValUhm0rVqwQ7u7uoqGhocWxrk6SzcjIMGz79ddfJTVJVq/Xi4iICPHSSy/d1uv37t0rAIgjR44YuTLj++qrr4RcLheVlZUtPn91kuy3335r2Hb69GlJT5ItKioS0dHRYvz48aKpqem2xpDKMezbt6+YPn264bFOpxMhISE3nCR77733NtuWkJAg2UmWer1eTJs2TQQHB4szZ87c1hhNTU0iJiZGvPjii0auzvhqamqEl5eX+Pe//93i85Z2/P5ozpw5IjAwUGi12la9TsrHD9eZJPv+++8btlVXV9/SJNnWvI9vq1ajjWQh8vPzxeHDh8W8efOEq6urOHz4sDh8+LCoqakRQlz5wurWrZsYOnSoyMrKEtu2bRN+fn5i1qxZhjHS09NFTEyMKCoqMmwbPny46NWrl0hPTxd79+4V0dHR4pFHHmnz/q7nt99+EwDEqVOnrnmuqKhIxMTEiPT0dCGEEOfOnRPz588XGRkZIi8vT3z//fciMjJSDBgwoK3LvqnU1FTxwQcfiKysLJGTkyO++uor4efnJx5//HHDPn/uTwghnnnmGREWFiZ27twpMjIyREJCgkhISDBHCzdVVFQkOnToIAYPHiyKiorEhQsXDH/+uI+lHMOvv/5aKJVKsWbNGnHy5EkxdepU4enpaVg599hjj4nXXnvNsP++ffuEvb29eP/998WpU6fEnDlzhEKhEMeOHTNXCzf07LPPCg8PD7Fr165mx6q+vt6wz597nDdvnvj1119FTk6OyMzMFOPHjxeOjo7ixIkT5mjhhl566SWxa9cukZeXJ/bt2yeSkpKEr6+vKCsrE0JY/vG7SqfTibCwMPHqq69e85ylHb+amhrDzzoAYvHixeLw4cMiPz9fCCHEu+++Kzw9PcX3338vjh49KkaPHi0iIiLE5cuXDWMMGjRILF261PD4Zu9jY7C5gDJp0iQB4Jo/v//+u2Gf8+fPixEjRggnJyfh6+srXnrppWYJ+vfffxcARF5enmFbRUWFeOSRR4Srq6twd3cXU6ZMMYQeKXjkkUdEYmJii8/l5eU1+zcoKCgQAwYMEN7e3kKpVIoOHTqIl19+WVRXV7dhxbcmMzNTxMfHCw8PD+Ho6Cg6d+4s3nnnnWafdv25PyGEuHz5svj73/8uvLy8hLOzs3jggQea/cCXktWrV7f4NfvHD0At7RguXbpUhIWFCQcHB9G3b1+xf/9+w3N33323mDRpUrP9N27cKDp27CgcHBxE165dxc8//9zGFd+66x2r1atXG/b5c48zZsww/HsEBASIkSNHikOHDrV98bfg4YcfFkFBQcLBwUGEhISIhx9+WJw7d87wvKUfv6t+/fVXAUBkZ2df85ylHb+rP7P+/OdqD3q9Xrz55psiICBAKJVKMXjw4Gv6Dg8PF3PmzGm27UbvY2OQCSGE8U4YEREREf11vA4KERERSQ4DChEREUkOAwoRERFJDgMKERERSQ4DChEREUkOAwoRERFJDgMKERERSQ4DChEREUkOAwoRERFJDgMKERERSQ4DChEREUkOAwoRERFJzv8HT6tXIyA6P8YAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Построим аппроксимацию"
      ],
      "metadata": {
        "id": "NfmkY5vCvlUJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lmd = minimize_scalar(solve_1, bounds=[-10, 10], method='bounded')['x']\n",
        "\n",
        "x_v1 = np.arange(0, 2.01, 0.01, dtype = float)\n",
        "C_result = get(lmd, y_1)\n",
        "y_v1 = f(lmd, C_result, x_v1)\n",
        "plt.grid()\n",
        "plt.plot(x_v1, y_v1)\n",
        "plt.plot(test, y_1, 's')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 499
        },
        "id": "ILg3Kn7Qiz8V",
        "outputId": "af430c87-4b06-4fda-e28d-bee294728fe4"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-23-8435b0968071>:10: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
            "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
            "  return np.linalg.lstsq(A, y)[0]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb36b486fe0>]"
            ]
          },
          "metadata": {},
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAh8AAAGdCAYAAACyzRGfAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABUBUlEQVR4nO3dd3wUZf4H8M9syW56r6SQ0HsJLYTeERQERQUVEc8GnMB53vm7U0HvTvA8sWFH1PMQQUEEBYRAggRCCTWUQEJCQiotvW2Z3x+brEQgZJPdnS2f9+uVl2Z2Mvl+Mwn5ZOZ5nhFEURRBREREZCUyqQsgIiIi58LwQURERFbF8EFERERWxfBBREREVsXwQURERFbF8EFERERWxfBBREREVsXwQURERFalkLqA39Pr9cjPz4enpycEQZC6HCIiImoGURRRXl6OsLAwyGRNX9uwufCRn5+PiIgIqcsgIiKiFsjNzUV4eHiT+9hc+PD09ARgKN7Ly8usx9ZoNPjll18wbtw4KJVKsx7bFjh6f4Dj98j+7J+j98j+7J+leiwrK0NERITx93hTbC58NNxq8fLyskj4cHNzg5eXl0N+Uzl6f4Dj98j+7J+j98j+7J+le2zOkAkOOCUiIiKrYvggIiIiq2L4ICIiIqti+CAiIiKrYvggIiIiq2L4ICIiIqti+CAiIiKrYvggIiIiq2L4ICIiIqti+CAiIiKrYvggIiIiq7K5Z7sQOZ2SXKDqquH/tVp4V2UDBccBRf2Pp5s/4MMnPROR42D4IJJSSS7wfiygrQUAKAGMAID0G/ZRqID5qY0CiE4vorCsBoWlNSitrkNJlQal1YY3jU4PvQjo9SL0oghBEODmIoeHSgE3FwXcVXL4u6sQ4q1CsJcaHipFsx4ERURkLgwfRFKqumoMHrelrcVPB9Kwt7IEF69W4tL1auSXVEOrF81SgpuLHKHearQL9ED7IA90CPZA+0BPdAj2gFopN8vnICK6EcMHkR34IDETp0R9o21KuYBgLzV83Vzg7aqEt5sSXmolVAoZZIIAuQyQCQL0ooiqOh0qa7WoqDX890pFLQrLalBeo0VVnQ6ZlyuRebkSv5wuMh5fIRPQJdQLvSN80DvCB32jfNHW341XSYio1Rg+iCRUq9VD1Yz9+kf5YkR0O8QEeCDCzw0Rfq4I8lRDLmtdEKiq06KorBaXrlcho7gC54srDP8tKsf1Kg1O5pXiZF4p/ptyEQAQ5q1GfPsADOkQgCHtA+Dv0ZzqiYgaY/ggsrKyGg0SzhRhe1oRLp87gO+bcWdjyT3dgLDOZq/FzUWB6AAFogPcMbRDoHG7KIq4dL0ax3JLjG8nL5Uiv7QG61MvYX3qJQBAr3BvjO8eggndQhAT6GH2+ojIMTF8EFmBXi8i5cJVrDuci22nClGjMdxC6SboARscViEIQv0VFjfc3SsMAFBdp8PB7GtIzriCX89fwZmCMhy/VIrjl0rxxrZ0dAz2wITuobi3TxtEB7j/djDO5iGi32H4ILKg4vIafHMgF+tTc3HperVxe7tAd9zVIxRTgr2BjRIWaAJXFzmGdwzE8I6GKyTF5TXYeboY204VYl/GFZwrqsC5ovN4N+E8YqN8cV9sOCZH6eD56UCTZ/MQkWNj+CCygPTCcnz26wVsOpaPOp3hKoenSoG7e4dhRr8I9Ar3NgzczK++w5FsV5CnGjMHRmLmwEiUVmmQcLYIPx7Px55zl5F68TpSL17HOsVFbFTceTYPqq4yfBA5EYYPIjPal3kFHyZm4tfzV4zb+kb64NG4tpjQPeTmqatu/oa//JuabqtQGfazYd5uSkzrG45pfcNRXFaDjUfz8P2RS6gr1vNfGSK6Cf9ZIDKD1IvX8Ob2c9h/wTC2QSYAE7qHYO6QGMRG+d7+A30iDLcc6sdEaLRaJCcnIz4+Hko7HRMR5KXGU8Pb4clhMTh3TAZskroiIrI1DB9ErZCWV4o3f0lHYvplAICLXIYHB0TgiSExiPR3a95BfCJ+CxcaDUrd8oDQXoBSaaGqrUMQBHQK9pS6DCKyQQwfRC1QXFaDZdvOYsORPACAXCZgRr9wzB/VAW18XCWuzv58kJiJ+yZ3RpCXWupSiMgKGD6ITFCr1WF1cjbeSziPyjodAODePm3w3OgOaHvj9FIyyU8nC/Dumd2YHdcWTw9vB193F6lLIiILYvggaqbE9GIs3XwaWVcqAQC9I3yw9J5u6BXhI21hDqBLqBdO5evx8Z4LWHMgB08MjcETQ6PhruI/UUSOiD/ZRHdQUlWHV7ecNt5iCfBQ4cWJnXFvnzaQtXJ5c4fXzNk8/350BO4qVOHN7edwuqAMK3aew/8OXMQLEzpjGr/ORA6H4YOoCdtPFeLvP6ThcnktBAF4bHBbLB7bEZ5q+x4MajXNnM0j+ERglA8womMQfk4rwBvb0pFzrQrPrz+Or/Zn46XJXdG/rZ90fRCRWTF8EN3C9co6vLQpDVtOFAAwrEj6xn09ERvFX4AmM2E2j0wmYHLPMIztGowvkrPx3q4MnLhUivs/2o+7e4XhpUldOCiVyAHIpC6AyNYcuHAVd737K7acKIBcJuDZEe3w0x+HMnhYkUohx1PD22H38yPw0IBIyARg8/F8jP5PEr7anw2dXpS6RCJqBYYPonpanR4rdpzDQ5+moKC0BjEB7tj47GC8MKHzzSuTklUEeqrw+rQe+HH+EPSK8EF5rRYvbzqFez9IxslLpVKXR0QtxPBBBCC/pBozPz2AdxLOQy8C98WGY/OCIegZ7iN1aQSgextvbHhmMF6b2h2eagVOXCrFlJV78a+fz6BGo5O6PCIyEcMHOb19mVcw+b29OJh9DR4qBd55sDfevL8Xp3naGLlMwCODopDwp+G4p1cY9CLwyZ4LuOudX5F68ZrU5RGRCRg+yGmJoohVe7PwyKqDuFZZh+5tvPDTH4dgSu82UpdGTQjyVOPdh/pg1ex+CPJU4cKVStz30X78Y8tpVNfxKgiRPWD4IKdUo9HhT+uO47Utp6HTi7i3Txt89/RgRPlzlVJ7MbpLMHYsGo77YsMhisBne7Mw6b1fORaEyA4wfJDTKSytwf0f7ceGo3mQywS8NLkr3prRi4NK7ZC3mxJv3t8Lqx/rj2AvFS5crsS9HyTjw8RMzoghsmEMH+RU0gvLDTMl8krh66bEV48PwNwh0RAErqBpz0Z2DsL2hcMwsXsItHoRy7edxazPUpBfUi11aUR0Cwwf5DT2ZV7BfR/tM0yjDXTHpnlDEN8+QOqyyEx83Fzwway+eOO+nnBzkSPlwjVMeHsPtqUVSl0aEf0Owwc5hR+O5mH25wdRXqNF/7a++P7pwYj0d5O6LDIzQRAwo18Efv7jUPSK8EFZjRZPf52KVzefRp1WL3V5RFSP4YMc3kdJmVj47TFodCIm9QjFf+cO5CPbHVzbAHd893QcnhwWAwD4PDkLMz7ej0vXqySujIgAhg9yYKIo4s3t6Vi29SwA4Ikh0XjvoT4cWOoklHIZ/u+uLvj00X7wUitwLLcEk97di4QzRVKXRuT0GD7IIYmiiNe2nMH7uzMAAH+d2Bl/n9yVj2Z3QmO7BuOnPw5Fr3BvlFZrMPfLw3h75znoORuGSDIMH+Rw9HoRf/shDZ8nZwEAXp3SDU8PbydxVSSlCD83rH96MB6NiwIAvL3zPJ78byrKazQSV0bknEwKH23btoUgCDe9zZs3DwBQU1ODefPmwd/fHx4eHpg+fTqKiniJk6xHq9Pj+fXHseZADmQC8MZ9PfFoXFupyyIb4KKQ4dUp3fHGfT3hIpdh55kiTFmZjIziCqlLI3I6JoWPQ4cOoaCgwPi2Y8cOAMD9998PAFi0aBE2b96M9evXIykpCfn5+Zg2bZr5qya6BZ1exJ+/O2FcPOztB/tgRr8IqcsiGzOjXwTWPR2HEC81LlyuxNSVydh9tljqsoiciknhIzAwECEhIca3LVu2oF27dhg+fDhKS0uxatUqvPXWWxg1ahRiY2OxevVq7Nu3DykpKZaqnwiAYYzH3zaexMajeVDIBKyc2Rf39AqTuiyyUb0jfLB5wRAMaOuHilot5n55CJ/vzYIochwIkTW0+LGddXV1+Prrr7F48WIIgoDU1FRoNBqMGTPGuE/nzp0RGRmJ/fv3Y9CgQbc8Tm1tLWpra43vl5WVAQA0Gg00GvPej204nrmPayscvT/g1j2KoojXfk7H2kO5kAnAm/f1wOhO/nb5dXD0c2hL/fmoZVg9uy+WbDmD9al5eHXLaZwvKsNLkzpDKW/5cDhb6tES2J/9s1SPphxPEFsY9detW4eZM2ciJycHYWFhWLNmDebMmdMoSADAgAEDMHLkSCxfvvyWx1myZAmWLl160/Y1a9bAzY2LQFHTRBHYnCNDQr7hl8WsdjoMCOJfr9R8ogjsLhDw40UZRAjo5K3HYx31cGvxn2ZEzqmqqgozZ85EaWkpvLy8mty3xT9eq1atwsSJExEW1rpL2y+++CIWL15sfL+srAwREREYN27cHYs3lUajwY4dOzB27FgolUqzHtsWOHp/wM09vrc7Ewn5mQCAV+/pgof62/cYD0c/h7ba3yQAE88UY/F3J5FeCnyW7YnPH+2LMB9Xk49lqz2aC/uzf5bqseHORXO0KHxcvHgRO3fuxIYNG4zbQkJCUFdXh5KSEvj4+Bi3FxUVISQk5LbHUqlUUKlUN21XKpUWO/GWPLYtcLj+SnKBqquG/9dq4V2VDeWV09hx9jISdmciDJ6YO3kYHh0cLW2dZuRw5/B3bLG/CT3bICLAA098eRiZlysx49OD+PLxAegc0rI/gmyxR3Nif/bP3D2acqwWhY/Vq1cjKCgIkyZNMm6LjY2FUqlEQkICpk+fDgBIT09HTk4O4uLiWvJpiAzB4/1YQGu4nacEMAIA0oG7ANylArSCCxTdj0hXIzmMbmHe+P6ZwZj9+UGcL67A/R/tx6eP9sOgGH+pSyNyKCaPqtLr9Vi9ejVmz54NheK37OLt7Y25c+di8eLF2L17N1JTUzFnzhzExcXddrAp0R1VXTUGj9tRiHW/XRkhaqUwH1d89/Rg9G/ri/IaLR5ddRA/nyyQuiwih2Jy+Ni5cydycnLw+OOP3/TaihUrMHnyZEyfPh3Dhg1DSEhIo1szRET2wNtNif/OHYjx3YJRp9Nj3poj+HJfttRlETkMk8PHuHHjIIoiOnbseNNrarUaK1euxLVr11BZWYkNGzY0Od6DiMhWqZVyfDArFg8PioQoAq/8eAr/3n6Wa4EQmQGf7UJEdBtymYDXpnTH8+MMf2yt3J2Jv35/Ejo+lI6oVRg+iIiaIAgC5o/qgOXTe0AmAN8ezsWib49Bo9NLXRqR3WL4ICJqhgf6R+K9h/pCIRPw4/F8zF9zBLVandRlEdklhg+yafsyr0hdApHRpJ6h+PiRWLjIZdh+qghP/TcVNRoGECJTMXyQzUrLK8XffylEjXiHhWsUKsCN6zCQdYzuEoxVj/WDWilDYvplzFl9CJW1WqnLIrIrfHoB2aRrlXV46r+pyNP44q/Rq/HmpHAoZAI0Wi2Sk5MRHx8PZcM6M27+gI99L6tO9mVoh0B8OWcAHv/iEPZfuIrFn27BfyaHw8NFYVyFFwXHAX6PEt0SwwfZHJ1exHNrjyKvpBrRAe5Y+mg8FK71Vz80GpS65QGhvQAHX/qYbNvAGH98/cRA/OXzn/HO5eeg/sLwRM8bV+E1UqiA+akMIET1eNuFbM47O8/h1/NX4KqU46OHY+HtypBBtqlPpC8+nBYFtXCHR4lra7kKL9ENGD7Ipuw6W4R3d2UAAF6f1gOdQjwlroioae0CPKQugcjuMHyQzci9VoVF3x4HADwaF4WpfdpIXBEREVkCwwfZhBqNDk9/nYrSag16R/jgb5O6SF0SERFZCMMH2YR//HQap/LL4Ofugg9m9YVKIZe6JCIishCGD5Lc9lOF+DolBwCw4oHeCPNxlbgiIiKyJIYPklR+STVe+O4EAOCpYTEY3jFQ4oqILEOj48PoiBowfJBkdHoRC789htJqDXqGe+NP4zpJXRKR6dz8Det4NKFGVOLVXYV8Gi5RPS4yRpJZuTsDB7Ouwd1Fjncf7AMXBbMw2SGfCMMCYvXrePx+Fd7UnOtYtDkXOWf00G9Kwz+mdocgCBIXTSQthg+SxOHsa3h75zkAwGtTu6NtgLvEFRG1gk/Eb6uX/m4V3tgw4M+u+fjj2qP434Ec+Lu7YDGv8pGT45+aZHXlNRo8t/YY9CJwb582mNY3XOqSiCzq7l5heHVKdwDAu7sy8PneLIkrIpIWwwdZ3T+2nEFeSTUi/Fzx6pRuUpdDZBWPDIrCn8Z2BAC8uuU0Nh69JHFFRNJh+CCr2nW2CN8ezoUgAG/e1wueaj63hZzH/FHtMSe+LQDg+fUnsOtskbQFEUmE4YOs5nplHf7y/UkAwNz4aAyM8Ze4IiLrEgQBL03qinv7tIFOL+KZr4/gYNY1qcsisjqGD7Kal388hcvltWgf5IHnx3PAHTknmUzAG/f1xKjOQajV6jH3y0M4V1QudVlEVsXwQVax5UQ+Nh/Ph1wm4K0ZvaBWcvl0cl5KuQwrZ/ZFvyhflNdoMWf1IRSX1UhdFpHVMHyQxRWX1+DvP6QBAOaNbI+e4T7SFkRkA1xd5Pj00X6IDnBHXkk1Hv/yECprtVKXRWQVDB9kca9sOoWSKg26hXlh/sj2UpdDZDN83V3wxZz+8Hd3QVpeGeavOQKtTi91WUQWx/BBFrUtrRBb0wqhkAn49329uIop0e9E+bvjs9n9oFbKsDv9Ml7adAqiyGXYybHxNwFZTGm1Bi9vMtxueWp4DLqGeUlcEZFt6hPpi3cf7ANBAL45mIMPkzKlLonIohg+yGKWbzuL4vJaxAS4Y8GoDlKXQ2TTxnULwSuTuwIA3tiWjk3H8iSuiMhyGD7IIg5cuIo1B3IAAP+a1oOzW4ia4bH4aDwxJBoA8Of1J5By4arEFRFZBsMHmV2NRocXNxgWE3toQAQGcTExomb7v7u6YGL3ENTp9Hjqv6nIvlIpdUlEZsfwQWb3/q4MXLhSiUBPFf46sYvU5RDZFZlMwIoHeqNXhA9KqzWY++UhlFZrpC6LyKwYPsisMorL8VH9YLnXpnSDtyuf3UJkKrVSjk8fiUWotxqZlyux4JujnIJLDoXhg8xGFEW89MMpaPUixnQJwoTuoVKXRGS3grzU+PRRwxTcPecu458/n5G6JCKzYfggs9l8ogD7L1yFSiHDK3d3k7ocIrvXvY03VszoDQBYnZyNbw7mSFsQkZkwfJBZlNdo8I8tpwEYllCP8HOTuCIixzCxRygWj+0IAHjphzTOgCGHwPBBZvH2zvMoLq9FW383PDksRupyiBzKglHtcXevMGj1Ip75OhU5V6ukLomoVRg+qNXOFpbhi33ZAIAl93Tjmh5EZiYIAv59X0/0CvfG9SrDDJjyGs6AIfvF8EGtIooiXv7hFHR6ERO6hWBEpyCpSyJySGqlHJ882g8hXmqcL67AwrXHoNfzGTBknxg+qFV+OJaHg9nX4KqU4+W7u0pdDpFDC/ZS45NHY+GikCHhbDHe3XVe6pKIWoThg1qsqk6LZVvPAgDmj2qPMB9XiSsicnw9w33wz6ndARjGWiWcKZK4IiLTMXxQi32UdAFFZbWI8HPF3PrnURCR5d3fLwKPDIoCACz89hiyuAQ72RmGD2qRvJJqfFy/kun/TezCQaZEVvbS5K7oF+WL8hotnvzqMCprtVKXRNRsDB/UIm9sO4tarR4Dov0woXuI1OUQOR0XhQwfzOqLIE8VzhdX4M/fHYcocgAq2QeGDzJZ6sXr2HQsH4IAvDy5KwRBkLokIqcU5KXGhw/HQikX8PPJQny854LUJRE1C8MHmUSvF/Fq/Uqm98eGo3sbb4krInJusVG+xscZvLHtLH49f1niiojujOGDTLLpeB6O55bA3UWO58d1krocIgIwa2AkZvQLh14EFnxzFLnXuAIq2TaTw0deXh4efvhh+Pv7w9XVFT169MDhw4eNr4uiiJdffhmhoaFwdXXFmDFjcP4856I7ghqNDsu3pgMAnh3ZHkFeaokrIiLAsALqq1O6o1e4N0qqNJi/5gjqtHqpyyK6LZPCx/Xr1xEfHw+lUomtW7fi9OnT+M9//gNfX1/jPm+88QbeffddfPTRRzhw4ADc3d0xfvx41NTUmL14sq7VydkoLKtBGx9OrSWyNWqlHCtn9YW3qxLHL5XiXz+fkbokottSmLLz8uXLERERgdWrVxu3RUf/9ktIFEW8/fbb+Pvf/44pU6YAAL766isEBwfjhx9+wIMPPmimssnaSqrq8EFiBgBg8diOnFpLZIPCfd3w1oxemPvlYXyxLxv92/phUs9QqcsiuolJ4ePHH3/E+PHjcf/99yMpKQlt2rTBs88+iz/84Q8AgKysLBQWFmLMmDHGj/H29sbAgQOxf//+W4aP2tpa1NbWGt8vKysDAGg0Gmg05n1wUsPxzH1cW2HJ/t5LOIfyGi06BXtgUvcgyb6GPIf2zdH7A6TvcVh7Pzw5tC0++TUbL3x/HB2DXNHW391sx5e6P0tz9P4Ay/VoyvEE0YSJ4Wq14R7/4sWLcf/99+PQoUN47rnn8NFHH2H27NnYt28f4uPjkZ+fj9DQ39L2jBkzIAgCvv3225uOuWTJEixduvSm7WvWrIGbm1uzGyHLuVYL/POoHFpRwFOddejqy7UEiGyZTgRWnpIjs1xAmJuIRd11cOHFSrKwqqoqzJw5E6WlpfDy8mpyX5OufOj1evTr1w//+te/AAB9+vRBWlqaMXy0xIsvvojFixcb3y8rK0NERATGjRt3x+JNpdFosGPHDowdOxZKpdKsx7YFlurvLxvSoBXzMTDaF3+a2U/SdT14Du2bo/cH2E6PA4bW4J4P9iO/UoNDuij8s346bmvZSn+W4uj9AZbrseHORXOYFD5CQ0PRtWvjJ5d26dIF33//PQAgJMSw0mVRUVGjKx9FRUXo3bv3LY+pUqmgUqlu2q5UKi124i15bFtgzv7OFpZh47F8AMCLd3WFi4uLWY7bWjyH9s3R+wOk7zHcX4l3H+yLRz4/gHWpeRgYE4DpseFmO77U/Vmao/cHmL9HU45l0myX+Ph4pKenN9p27tw5REUZHnAUHR2NkJAQJCQkGF8vKyvDgQMHEBcXZ8qnIhvx723pEEXgrh4h6B3hI3U5RGSCIR0CsHB0RwDA3344ifTCcokrIjIwKXwsWrQIKSkp+Ne//oWMjAysWbMGn3zyCebNmwfAMNd84cKF+Mc//oEff/wRJ0+exKOPPoqwsDBMnTrVEvWTBR24cBUJZ4shlwlcUIzITs0f1R5DOwSgRqPHs/9LRVUdH0BH0jMpfPTv3x8bN27EN998g+7du+O1117D22+/jVmzZhn3eeGFF7BgwQI8+eST6N+/PyoqKrBt2zbjYFWyD6Io4s1fDFe5HuwfgZhAD4krIqKWkMsEvP1AbwR7qZB5uRJLfjwldUlEpo35AIDJkydj8uTJt31dEAS8+uqrePXVV1tVGElrb8YVHMq+DheFDAtGdZC6HCJqBX8PFd5+oA9mfpaCdYcvYUiHQNzTK0zqssiJ8dkudBNRFPGfX84BAB4eGIUQb161IrJ3ce38MX9kewDA3zacRM5VPv+FpMPwQTfZnV6MY7klUCtleGZEO6nLISIzeW50B8RG+aK8Vos/rj0KjY7PfyFpMHxQI6Io4q0dhqses+PaItDz5mnQRGSfFHIZ3nmwN7zUChzLLTH+rBNZG8MHNbL9VBHS8srg7iLHU8N51YPI0YT7umHZ9J4AgI+SMrH3/BWJKyJnxPBBRnq9iBX1fwnNiY+Gn7ttLChGROZ1V49QPDQgEqIILFp3DFcqau/8QURmxPBBRj+dLEB6UTk81Qr8YWiM1OUQkQW9PLkrOgR54HJ5LZ5ffxx6PZ/ZRNbD8EEAAJ1exNs7DVc9nhgSA283x15WmMjZubrI8d7MPlApZEhMv4zPk7OkLomcCMMHAQC2phUg83IlvF2VeHxIW6nLISIr6Bzihb9PNjyv641t6ThT0PwHgxG1BsMHQa8X8f6uDADA4/HR8FTzqgeRs3h4YCTGdAlCnU6PRd8eQ41GJ3VJ5AQYPgg7zxThbGE5PFQKPDa4rdTlEJEVCYKAZdN7IsDDBWcLy/Hm9vQ7fxBRKzF8ODlRFPH+bsNVj0fjojjWg8gJBXiosLx++u1ne7OwL4PTb8myGD6c3J7zV3DiUinUShnmDomWuhwiksjoLsGYOTASAPCn9cdRWqWRuCJyZAwfTkwURbyXcB4AMGtgFPw9uJopkTP7+6QuiA5wR0FpDV7alCZ1OeTAGD6c2IGsazh88Tpc5DI8OYzrehA5OzcXBVY80BtymYAfj+dj07E8qUsiB8Xw4cQaZrjM6B+OYC8+uZaIgN4RPvjjqA4AgL//kIa8kmqJKyJHxPDhpI7kXMfejCtQyAQ8NYzPcCGi38wb2Q59In1QXqPFn9Yd4+qnZHYMH07qw8RMAMDUPm0Q4ecmcTVEZEsUchlWzOgNNxc5Ui5cw6q9XP2UzIvhwwllFFdgx+kiAMDTfHItEd1C2wB3vFS/+um/f0lHRnG5xBWRI2H4cEKf7rkAABjbNRjtgzwkroaIbNWD/SMwolMg6rR6/GndcWh1eqlLIgfB8OFkispqsPGoYQT708M5w4WIbk8QBCyb1hMd1SXQ5h3D9z/9BBQch3dVNlBwHMg/ZngryZW4UrI3CqkLIOtanZyNOp0e/aJ8ERvlJ3U5RGTjQsTL2CpbCLmqDjgC4AgwAgBuXIVdoQLmpwI+EZLUSPaHVz6cSHmNBv9LuQgAeIpjPYioOaquQq6va3ofbS1QddU69ZBDYPhwIt8czEF5rRbtAt0xunOQ1OUQEZGTYvhwEnVaPT7fmw0AeGpYO8hkgrQFERGR02L4cBI/Hs9HYVkNgjxVmNInTOpyiIjIiTF8OAFRFPHJHsOiYo8PiYZKIZe4IiIicmYMH05gz/krOFdUAQ+VwvjIbCIiIqkwfDiBz+uXRp7RLwJeaqXE1RARkbNj+HBwGcXlSDp3GYIAPDa4rdTlEJG9cfM3rOPRBK3gYtiPqJm4yJiDW52cDQAY2yUYkf58gBwRmcgnwrCAWP06HhqtFsnJyYiPj0dKVgmWbTuLMsELn1R7o4uPtKWS/eCVDwdWUlWH749cAmAYaEpE1CI+EUBYb8NbaC+UurUFQnthyLDRCO86CLl6f7zw3Qk++4WajeHDga05mIMajR5dQ70wMJpLqROReQmCgNemdIeXWoGTeaX4rH58GdGdMHw4KI1Oj6/2GZZSnzskGoLARcWIyPyCvNR4aXJXAMCKHedw4XKFxBWRPWD4cFBb0wpRWFaDAA8VJvcKlbocInJg98WGY2iHANRq9fjr9yeh14tSl0Q2juHDQTVMr31kUBQXFSMiixIEAf+6twfcXOQ4mH0N/ztwUeqSyMYxfDigo7klOJZbAhe5DLMGcVExIrK8CD83/GVCZwDAsq1ncel6lcQVkS1j+HBAX+3PAQDc0zsMAR5Nz88nIjKXRwZFoV+ULyrrdPi/jWkQRd5+oVtj+LB3JblA/jHDW8FxKEqzkXs6Bd2ELDzdsdzwOhGRFchkApbf1xMuChn2nLuMTcfypS6JbBQXGbNnJbnA+7GAthYAoAQwCcCkhhXUN8KwMuH8VMM8fSIiC2sX6IHnRnfAv7en49UtpzG8YyB83V2kLotsDK982LOqq8bgcVvaWuPKhERE1vCHoTHoGOyBa5V1+NfPZ6Quh2wQwwcREZmVi0KG16f1AACsT72EfZlXJK6IbA3DBxERmV1slB8erp9t97eNaajR6CSuiGwJwwcREVnECxM6I8hThawrlfhgd4bU5ZANYfggIiKL8FIrsfSebgCAD5Mycb6oXOKKyFYwfBARkcVM6B6CMV2CoNGJeHEDl14nA4YPIiKyGEEQsHRKd7i5yHH44nWsPcS1h4jhw765+UNU3GEFU4UKcPO3Tj1ERLfQxscVz4/rBAB4fesZFJfVSFwRSc2k8LFkyRIIgtDorXPnzsbXa2pqMG/ePPj7+8PDwwPTp09HUVGR2Yumej4ROHlvAibV/hPTda+jZNZ2JHZ6FZrHE4AnkwxvXGCMiGzA7MFt0TPcG+U1WizdclrqckhiJl/56NatGwoKCoxve/fuNb62aNEibN68GevXr0dSUhLy8/Mxbdo0sxZMjX15So9TYjRiesbDvW0sSt3aAqG9gLDehjcGDyKyAXKZ4cm3cpmAn04UYM+5y1KXRBIyOXwoFAqEhIQY3wICAgAApaWlWLVqFd566y2MGjUKsbGxWL16Nfbt24eUlBSzF05AabUGP500PDvhoYF8ei0R2bbubbwxO64tAODlTVz7w5mZ/GyX8+fPIywsDGq1GnFxcXj99dcRGRmJ1NRUaDQajBkzxrhv586dERkZif3792PQoEG3PF5tbS1qa39bIrysrAwAoNFooNFoTC2vSQ3HM/dxpbIhNQc1Gj06BXuge4i7w/V3K47eI/uzf47eY2v7mz8iGltO5CP7ahU+2H0eC0a2M2d5rebo5w+wXI+mHE8QTXjm8datW1FRUYFOnTqhoKAAS5cuRV5eHtLS0rB582bMmTOnUZAAgAEDBmDkyJFYvnz5LY+5ZMkSLF269Kbta9asgZubW7MbcTaiCCw/IUdBlYDpbXUYFsrpa0RkH45cEfDleTkUgogXe+sQoJa6IjKHqqoqzJw5E6WlpfDy8mpyX5OufEycONH4/z179sTAgQMRFRWFdevWwdXVtUXFvvjii1i8eLHx/bKyMkRERGDcuHF3LN5UGo0GO3bswNixY6FUKu/8ATbsWG4JClIOQqWQ4cWZI+HtqnSo/m7H0Xtkf/bP0Xs0R38TRREZXx5BcuZVJFUE47N7+0IQBDNX2jKOfv4Ay/XYcOeiOUy+7XIjHx8fdOzYERkZGRg7dizq6upQUlICHx8f4z5FRUUICQm57TFUKhVUqpuniyqVSoudeEse21rWHzGM9ZjUMxQBXo2vEDlCf3fi6D2yP/vn6D22tr/XpnbHhLd/xZ7zV7Hr3FVM6B5qxupaz9HPH2D+Hk05VqvW+aioqEBmZiZCQ0MRGxsLpVKJhIQE4+vp6enIyclBXFxcaz4N/U5ZjQabjxcAAGYO4EBTIrI/MYEeeHp4DABg6ebTqKzVSlwRWZNJ4eP5559HUlISsrOzsW/fPtx7772Qy+V46KGH4O3tjblz52Lx4sXYvXs3UlNTMWfOHMTFxd12sCm1zKZj+ajW6NAhyAOxUb5Sl0NE1CLPjmyPCD9XFJTW4J2E81KXQ1ZkUvi4dOkSHnroIXTq1AkzZsyAv78/UlJSEBgYCABYsWIFJk+ejOnTp2PYsGEICQnBhg0bLFK4sxJFEWsO5AAAHhoQaTP3SYmITKVWyvHqPd0BAKv2ZiG9kA+ecxYmjflYu3Ztk6+r1WqsXLkSK1eubFVRdHsnLpXiTEEZXBQyTOvbRupyiIhaZWTnIIzvFoztp4rw9x9OYt1Tcfyjygnw2S52puGhTBO7h8DHzUXiaoiIWu/lu7vBVSnHoezr+C71ktTlkBUwfNiR6jodthw3zHJ5oD+XTScix9DGxxXPjekAAFi+7SxKqx13gS8yYPiwI9tOFaC8VotwX1cMiuaTaonIcTweH42YQHdcqajD2zvPSV0OWRjDhx1Zf9hwOfK+2HDIZLwnSkSOw0Uhw5K7uwEAvtp/kYNPHRzDh53IvVaFfZlXIQiG8EFE5GiGdQzE+G7B0OlFvPJjGkx4+gfZGYYPO/H9EcNVj8Ht/BHuy2feEJFj+vukrlApZEi5cA0/nSyQuhyyEIYPO6DXi8YR4PfHcqApETmuCD83PDuiPQDgnz+d4cqnDorhww6kXLiKS9er4alSYHy32z8nh4jIETw1PAbhvoaVT1fuzpC6HLIAhg87sL7+qsfkXmFwdZFLXA0RkWWplXK8PLkrAOCzX7OQdaVS4orI3Bg+bFxZjQZb0wz3PWf040BTInIOY7sGY1jHQNTp9Hh18ympyyEzY/iwcT+dKECNRo/2QR7oHeEjdTlERFYhCAJeubsrlHIBu9MvI+FMkdQlkRkxfNi49YcNy6nfHxvO5x0QkVNpF+iBx4dEAwCWbj6NGo1O4orIXBg+bNiFyxU4klMCuUzAvXyIHBE5oQWjOiDYS4Wca1VYtTdL6nLITBg+bNjGo3kAgKEdAhDkqZa4GiIi6/NQKfDixC4AgJW7M1BUViNxRWQODB82ShRFY/i4tw+vehCR85rSOwx9In1QVafD8m1npS6HzIDhw0Ydvngdl65Xw0OlwLiuXNuDiJyXYfCp4bkvG47k4VhuibQFUasxfNioDUcMVz0mdA/h2h5E5PR6R/hgWv1V4Fc3n+JzX+wcw4cNqtHo8NOJfAC85UJE1OCFCZ3h5iLHkZwS/Hg8X+pyqBUYPmzQ7rPFKKvRIsRLjUEx/lKXQ0RkE0K81Xh2RDsAwLKtZ1FVx+e+2CuGDxu0oX6g6ZQ+YZDLuLYHEVGDJ4bGoI2P4bkvHyddkLocaiGGDxtzvbIOienFAIBpfbicOhHRjdRKOf7vLsPU24/3ZCK/pFriiqglGD5szJaTBdDoRHQN9UKnEE+pyyEisjl39QjBgLZ+qNHosWwrp97aI4YPG7PxiOEJthxoSkR0a4Ig4OW7u0IQgB+P5yP14jWpSyITMXzYkOwrlTiSUwKZYFhUh4iIbq17G2/MiI0AYHjui17Pqbf2hOHDhvxwzDDQNL59AIK8uJw6EVFTnh/fCR4qBU5cKjX++0n2geHDRoiiaJy3PrU3b7kQEd1JoKcKz440TL399/Z0PvXWjjB82IhT+WW4cLkSKoUM47oFS10OEZFdeDw+2jj1lk+9tR8MHzZic/1Vj1Gdg+CpVkpcDRGRfVAr5fjz+E4AgA8TM3Glolbiiqg5GD5sgF4vYsuJAgDAPb040JSIyBT39ApDz3BvVNRq8fbOc1KXQ83A8GEDjuRcR16J4Qm2IzsHSV0OEZFdkckE48Jj3xzMRUZxucQV0Z0wfNiAhlsu47oGQ63kE2yJiEw1KMYfY7sGQ6cX8frPXHjM1jF8SEyr0+Onk4ZbLndzbQ8iohZ7cWJnKGQCEs4WY1/GFanLoSYwfEhs/4WruFJRB183JYa0D5C6HCIiuxUT6IFZAyMBAP/8+QwXHrNhDB8Sa7jlMrFHKJRyng4iotb44+gO8FQpcCq/DBuPcuExW8XfdhKq1eqwNa0QAGe5EBGZg7+HCvNGtQcAvPlLOqrruPCYLWL4kFBS+mWU12gR7KXCgLZ+UpdDROQQHhvc9oaFxy5IXQ7dAsOHhDbXr+0xuWcYZDJB4mqIiByDWinHCxN+W3jscjkXHrM1DB8SqarTYufpIgC85UJEZG539wxDr3BvVNbpuPCYDWL4kMjus5dRrdEhws8VPcO9pS6HiMihNF54LAfni7jwmC1h+JDIz/Vre9zVIxSCwFsuRETmNjDGH+O6BkMvAq9v5cJjtoThQwLVdTrsOlsMAJjUI1TiaoiIHNdf6xce23W2GPsyufCYrWD4kMDu9GJUa3QI93VFjza85UJEZCkxgR6YWb/w2PKtZyGKXHjMFjB8SKBhOfVJvOVCRGRxC0Z1gJuLHMcvlRrXViJpMXxYWXWdDrvOGG653MVbLkREFhfoqcITQ2MAAG9uT4dGp5e4ImL4sLKkc7/dcuEsFyIi6/jD0Gj4u7vgwpVKrDucK3U5To/hw8p+Omm45MdZLkRE1uOpVmJ+/bLr7+w8z2XXJdaq8LFs2TIIgoCFCxcat9XU1GDevHnw9/eHh4cHpk+fjqKiotbW6RBqNDoknDF8LXjLhYjIumYOjES4ryuKy2vxeXKW1OU4tRaHj0OHDuHjjz9Gz549G21ftGgRNm/ejPXr1yMpKQn5+fmYNm1aqwt1BInpl1FVp0MbH1f04i0XIiKrUinkeH6cYdn1jxIzcb2yTuKKnFeLwkdFRQVmzZqFTz/9FL6+vsbtpaWlWLVqFd566y2MGjUKsbGxWL16Nfbt24eUlBSzFW2vfltYLIS3XIiIJHBPrzB0CfVCea0WHyRmSF2O01K05IPmzZuHSZMmYcyYMfjHP/5h3J6amgqNRoMxY8YYt3Xu3BmRkZHYv38/Bg0adNOxamtrUVv720N/ysrKAAAajQYajaYl5d1Ww/HMfdzmuPGWy9gugRapQcr+rMXRe2R/9s/Re3SE/p4f2x5zvzqCL/Zl4+EB4QjzcTW+5gj93YmlejTleCaHj7Vr1+LIkSM4dOjQTa8VFhbCxcUFPj4+jbYHBwejsPDWc6tff/11LF269Kbtv/zyC9zc3Ewtr1l27NhhkeM25cQ1AZV1cvi4iMg/sQ8FJy33uaToz9ocvUf2Z/8cvUd77k8UgfZeMmSUyfDnr5Iwq/3NU2/tub/mMnePVVVVzd7XpPCRm5uL5557Djt27IBarTa5sFt58cUXsXjxYuP7ZWVliIiIwLhx4+Dl5WWWz9FAo9Fgx44dGDt2LJRKpVmPfSe7vjsJoAD39muLSRM7WeRzSNmftTh6j+zP/jl6j47SX5ueJbj/k4M4dEWGVx6IR8dgTwCO019TLNVjw52L5jApfKSmpqK4uBh9+/Y1btPpdNizZw/ef/99bN++HXV1dSgpKWl09aOoqAghISG3PKZKpYJKpbppu1KptNiJt+Sxb6VOq8fu9MsAgEk9wyz+ua3dnxQcvUf2Z/8cvUd7769/TCAmdg/B1rRCrEjIxGez+zd63d77aw5z92jKsUwacDp69GicPHkSx44dM77169cPs2bNMv6/UqlEQkKC8WPS09ORk5ODuLg4Uz6VQ0m5cBVlNVoEeKjQN9L3zh9AREQW9/z4TpDLBOw8U4xD2dekLsepmHTlw9PTE927d2+0zd3dHf7+/sbtc+fOxeLFi+Hn5wcvLy8sWLAAcXFxtxxs6iy2nzKMdxnbNRgyGWe5EBHZgnaBHpjRLwLfHMzBsq1n8d3TzvtHsrWZfYXTFStWYPLkyZg+fTqGDRuGkJAQbNiwwdyfxm7o9SJ2nDbMchnfLVjiaoiI6EYLx3SAWilD6sXr2Fn/3C2yvBZNtb1RYmJio/fVajVWrlyJlStXtvbQDuFobgmKy2vhqVJgcLsAqcshIqIbBHupMSc+Gh8mZuKNbWcxJMZ5r9JbU6vDBzXtl/pbLiM7B8FFwUfpEBHZmmf6qHAkJRcVl7X49dcqeFdlAwXHAUX9r0g3f8AnQtIaHQ3DhwWJomgc7zGh+61n+xARkYRKcuH16UB8i1pABSC5fnv6DfsoVMD8VAYQM+Kf4haUXlSO7KtVcFHIMLxjoNTlEBHR71VdBbS1Te+jrTXsR2bD8GFB29MMA02HdQiAu4oXmYiIiACGD4tquOUyrhtvuRARETVg+LCQ3GtVOF1QBpkAjOnCKbZEREQNGD4spOGqx4BoP/i5u0hcDRERke1g+LCQX041LCzGWy5EREQ3YviwgCsVtTh00fCcAIYPIiKixhg+LGDX2WKIItC9jRfCfFylLoeIiG7Hzd+wjkcTRLnKsB+ZDed/WkDCGcMtFw40JSKycT4RhgXE6tfx0Gi1SE5ORnz8YLyw4RTOFVVgbL+uWMgFxsyKVz7MrEajw55zVwAwfBAR2QWfCCCst+EttBdK3doCob1x712TcEqMxgdHa1FQWi1xkY6F4cPM9mdeRbVGh1BvNbqFeUldDhERtdDQDgEYEO2HOq0e7+3KkLoch8LwYWY76m+5jO4SBEEQJK6GiIhaShAE/Hl8JwDAukO5yLlaJXFFjoPhw4xEUeR4DyIiB9K/rR+GdwyEVi/i7Z3npC7HYTB8mFFaXhmKymrh7iJHXDuOjCYicgR/GtcRALDxWB7OF5VLXI1jYPgwo4ZbLsM6BkKlkEtcDRERmUPPcB+M7xYMUQTe2sGrH+bA8GFGO083jPfgLRciIkfyp3GdIAjA1rRCpOWVSl2O3WP4MJP8kmrjg+RGdgqUuhwiIjKjjsGeuKdXGADgnYTzEldj/xg+zKRhoGlslC/8PZpeLY+IiOzPglEdIBOAHaeLePWjlRg+zGTHmWIAvOVCROSo2gd5GK9+cOZL6zB8mEFFrRYpmYaleTnFlojIcf1xtOHqx84zxTh5iVc/Worhwwx+PXcZdTo9ogPc0S7QXepyiIjIQmICPTC1dxsAvPrRGgwfZrCz4ZZLZ65qSkTk6OaPag+ZACScLcaJSyVSl2OXGD5aSa8XkXTOED5GdQmSuBoiIrK0mEAPTO3TcPWDM19aguGjlU7kleJKRR08VAr0b+sndTlERGQFC0Z1gFwmYNfZYhzLLZG6HLvD8NFKu88arnoM7RAApZxfTiIiZxAd4G4c+/EOx36YjL8tW2l3uiF8jOzMWy5ERM5kwaj2kMsE7E6/jKM516Uux64wfLTC5fJanKifajWCq5oSETmVtgHuuLd+7AdXPTUNw0crJNZf9ejRxhtBnmqJqyEiImtruPqRmH4ZR3j1o9kYPlohMf0yAD7LhYjIWUX5u2Naw9UPznxpNoaPFtLo9Nhzrj58cLwHEZHTWjCqAxQyAUnnLiP1Iq9+NAfDRwsdzr6O8lot/Nxd0DPcR+pyiIhIIpH+bpjeNxwAVz1tLoaPFmoY7zGiYyDkMq5qSkTkzOaPag+FTMCv568g9eI1qcuxeQwfLbTrLKfYEhGRQYSfG+6Lbbj6wbEfd8Lw0QK516pwvrgCcpmAYR042JSIiIB5I3n1o7kYPlqg4ZZLbKQvvN2UEldDRES24MarH+8mZEhcjW1j+GiBhlsuIzrzqgcREf3m2RGGdT+Szl3mE2+bwPBhohqNDvsyrwIARnG8BxER3SDS3w1TeoUBAN7bxasft8PwYaIDWddQq9Uj1FuNTsGeUpdDREQ25tmR7SEIwI7TRThTUCZ1OTaJ4cNESfWrmg7rEAhB4BRbIiJqrH2QByb1CAUAvL+bVz9uheHDRHvOG8LHcC6pTkREtzF/VHsAwM8nC5BRXC5xNbaH4cMEeSXVyCiugEwA4tsFSF0OERHZqM4hXhjXNRiiCKzcnSl1OTaH4cMEDc9y6R3hwym2RETUpAWjOgAANh3Lw8WrlRJXY1sYPkzQMN5jeEfOciEioqb1CPfGyE6B0IvAB7z60QjDRzNpdXokZ14BAAzryFsuRER0Z/Prr358f+QSLl2vkrga22FS+Pjwww/Rs2dPeHl5wcvLC3Fxcdi6davx9ZqaGsybNw/+/v7w8PDA9OnTUVRUZPaipXAstwTlNVr4uCn5FFsiImqW2ChfxLf3h1Yv4uOkC1KXYzNMCh/h4eFYtmwZUlNTcfjwYYwaNQpTpkzBqVOnAACLFi3C5s2bsX79eiQlJSE/Px/Tpk2zSOHWllQ/3mNI+wA+xZaIiJqtYezHt4dzUVRWI3E1tsGk8HH33XfjrrvuQocOHdCxY0f885//hIeHB1JSUlBaWopVq1bhrbfewqhRoxAbG4vVq1dj3759SElJsVT9VtMw2HR4R06xJSKi5hsU448Bbf1Qp9Xz6ke9Fo/50Ol0WLt2LSorKxEXF4fU1FRoNBqMGTPGuE/nzp0RGRmJ/fv3m6VYqVyrrMOJvFIAwDCGDyIiMlHDuh9rDl7ElYpaiauRnsLUDzh58iTi4uJQU1MDDw8PbNy4EV27dsWxY8fg4uICHx+fRvsHBwejsLDwtserra1Fbe1vJ6KszLAUrUajgUajMbW8JjUcz9TjJp4thCgCnYI94OcqN3td5tLS/uyJo/fI/uyfo/fI/lpmUFtv9Az3wolLZfgkKQN/HtfRrMc3haV6NOV4giiKoikHr6urQ05ODkpLS/Hdd9/hs88+Q1JSEo4dO4Y5c+Y0ChIAMGDAAIwcORLLly+/5fGWLFmCpUuX3rR9zZo1cHNzM6U0i/k6Q4ZDl2UYFabHlCi91OUQEZEdSrsu4NOzcqhkIl7pq4O7gy0XVVVVhZkzZ6K0tBReXl5N7mty+Pi9MWPGoF27dnjggQcwevRoXL9+vdHVj6ioKCxcuBCLFi265cff6spHREQErly5csfiTaXRaLBjxw6MHTsWSmXzzrpeLyL+30m4UlGHLx+LxeB2/matyZxa0p+9cfQe2Z/9c/Qe2V/LiaKIKR+k4ExhOeaPiMFzo9ub9fjNZakey8rKEBAQ0KzwYfJtl9/T6/Wora1FbGwslEolEhISMH36dABAeno6cnJyEBcXd9uPV6lUUKlUN21XKpUW+8Y25din8ktxpaIOrko5BrUPhFIht0hN5mTJr52tcPQe2Z/9c/Qe2V/L/HF0BzzzvyP4MiUHT45oDy+1dF9Dc/doyrFMCh8vvvgiJk6ciMjISJSXl2PNmjVITEzE9u3b4e3tjblz52Lx4sXw8/ODl5cXFixYgLi4OAwaNMjkJmzFnnOGhcXi2vlDZQfBg4iIbNf4biHoGOyBc0UV+O/+i5g3UpqrH1IzabZLcXExHn30UXTq1AmjR4/GoUOHsH37dowdOxYAsGLFCkyePBnTp0/HsGHDEBISgg0bNlikcGv5tf4ptsM6cFVTIiJqHZlMwDMj2gEAVidnoUajk7giaZh05WPVqlVNvq5Wq7Fy5UqsXLmyVUXZiuo6HQ5nXwcADOnAKbZERNR6d/cMw39+OYdL16ux7nAuHo1rK3VJVsdnuzThUPY11On0CPVWo12gu9TlEBGRA1DIZXhqWAwA4OOkC9DonG8WJcNHE5IzDOM94tsHQBC4pDoREZnH/f0iEODhgrySamw+ni91OVbH8NGEX88bwsdQjvcgIiIzUivleHxINADgw8RM6PWtWvXC7jB83MbVilqcLjCstjq4HcMHERGZ18ODouCpUuB8cQV2nnGMJ8A3F8PHbSRnXgUAdA7xRKDnzeuQEBERtYaXWolH4qIAAB8kZqKVa37aFYaP29hbP8WWt1yIiMhSHh8SDZVChmO5Jdh/4arU5VgNw8ctiKKIved/G2xKRERkCQEeKjzQPwKAYeyHs2D4uIWsK5XIL62Bi1yGAdF+UpdDREQO7A9DYyCXCfj1/BWcvFQqdTlWwfBxCw1TbPtG+cDNpdWPvyEiIrqtCD83TOkVBgD4IDFD4mqsg+HjFn6bYstVTYmIyPKerl9yfdupQmQUV0hcjeUxfPyOVqc3DvrheA8iIrKGjsGeGNs1GKIIfJzk+GM/GD5+50ReKcprtPB2VaJHG2+pyyEiIifxbP3Vj41H85BfUi1xNZbF8PE7yfW3XAa384dcxiXViYjIOvpE+iIuxh9avYhPf70gdTkWxfDxO79mcIotERFJ49mRhqsf3xzMwdWKWomrsRyGjxtU1mpxNOc6AC4uRkRE1jekfQB6tPFGjUaPL/ZlS12OxTB83OBQ9jVodCLa+Lgi0s9N6nKIiMjJCIJgHPvx5b5slNdoJK7IMhg+brA/s2GWiz8EgeM9iIjI+sZ3C0FMoDvKarRYezBX6nIsguHjBg1TbPkUWyIikopMJuCpYTEAgM+Ts1Cn1UtckfkxfNQrrdIgLc+wrG1cO3+JqyEiImc2tU8bBHqqUFBag83H86Uux+wYPuodyLoKvQjEBLoj2EstdTlEROTEVAo55sS3BQB8sucCRFGUtiAzY/ioty+z4ZYLr3oQEZH0Zg2MgruLHOlF5Ug8d1nqcsyK4aPe/kyO9yAiItvh7arEQwMiATjekusMHwCuVNQivagcADAohlc+iIjINjw+JBoKmYCUC9dwPLdE6nLMhuEDQEr9LJfOIZ7wc3eRuBoiIiKDMB9X3NM7DIBh7IejYPjAjeM9eMuFiIhsy5P10263phXg4tVKiasxD4YP3Djeg7dciIjItnQO8cKIToHQi8Bnv2ZJXY5ZOH34KCitRtaVSsgEYECMn9TlEBER3eSpYYYl19cdznWIB845ffhouOrRI9wHXmqlxNUQERHdbFCMH3qGe6NWq8eX+y9KXU6rOX344PoeRERk6wRBMF79+O/+bFTVaSWuqHWcOnyIomi88hHHKbZERGTDJnQPQaSfG65XabD+8CWpy2kVpw4fOdeqkFdSDaVcQL+2vlKXQ0REdFtymYA/DI0GAHy29wK0Ovt94JxTh4+GWy59Inzh5qKQuBoiIqKm3RcbAT93F+Req8bWtEKpy2kxpw4fDbdcBnG8BxER2QFXFzkejYsCAHy8J9NuHzjntOFDFEUcyOJ4DyIisi+PxrWFWilDWl6Z8Y9oe+O04SP7ahWKymrhIpehT6SP1OUQERE1i5+7Cx7oFwEA+MhOl1x32vBxoP55Lr0jfKBWyiWuhoiIqPmeGBoDmQDsOXcZp/PLpC7HZM4bPrKuAQAGclVTIiKyMxF+bpjYIxSAYeaLvXHK8CGKovHKx8BojvcgIiL784ehhgfObT6ej6KyGomrMY1Tho9LJdXIL62BQiagb5SP1OUQERGZrHeED/q39YVGJ+Kr/dlSl2MSpwwfB7OuAwB6hntzfQ8iIrJbc4cYrn58nZJjV0uuO2f4yDaEj4GcYktERHZsbNdgRPm7obRag+9T7WfJdecMH/WDTQcxfBARkR2TywQ8Hm9Ycn3V3izo9Pax6JjThY9rtcClkhrIZQJio/g8FyIism/39wuHt6sS2VerkHCmSOpymsXpwkdmmQAA6N7GGx4qjvcgIiL75uaiwMyBkQCAz37Nkria5nG68JFRHz4GRXN9DyIicgyz49pCIRNwMPsajueWSF3OHTlt+ODiYkRE5ChCvNW4p1cYAOCzvbZ/9cPxw0dJLpB/DMg/hmsZhxBcm40esiwMUNdvL8mVukIiIqJWmzvUMPD055MFyCuplriappkUPl5//XX0798fnp6eCAoKwtSpU5Gent5on5qaGsybNw/+/v7w8PDA9OnTUVQk0QCYklzg/Vjgk+HAJ8MR/O1E/KT6Gza7/A0eX4w2bH8/lgGEiIjsXrcwbwxu5w+dXsQXybZ99cOk8JGUlIR58+YhJSUFO3bsgEajwbhx41BZWWncZ9GiRdi8eTPWr1+PpKQk5OfnY9q0aWYvvFmqrgLa2qb30dYa9iMiIrJzT9Rf/Vh7MBflNRqJq7k9k6Z7bNu2rdH7X3zxBYKCgpCamophw4ahtLQUq1atwpo1azBq1CgAwOrVq9GlSxekpKRg0KBB5quciIiIGhnRMQjtAt2RebkS3x7KxRP1z3+xNa2aa1paWgoA8PMzDN5MTU2FRqPBmDFjjPt07twZkZGR2L9//y3DR21tLWprf7s6UVZmeDSwRqOBRtPK1KbVQtmM3TRaLdDaz2UDGr5erf662TBH75H92T9H75H92b7H4qLw0o+nsTo5C7P6t4FC3vgmh6V6NOV4giiKLVoOTa/X45577kFJSQn27t0LAFizZg3mzJnTKEwAwIABAzBy5EgsX778puMsWbIES5cuvWn7mjVr4Obm1pLSjLyrsjEi/eU77pfY6VWUurVt1eciIiKyBXU6YMkROSq1Ah7roEOfAOuselpVVYWZM2eitLQUXl5eTe7b4isf8+bNQ1pamjF4tNSLL76IxYsXG98vKytDREQExo0bd8fi76jgOJB+593i4+OB0F6t+1w2QKPRYMeOHRg7diyUyuZc87E/jt4j+7N/jt4j+7MPF90y8H7iBRyp9sX/TRwIQRCMr1mqx4Y7F83RovAxf/58bNmyBXv27EF4eLhxe0hICOrq6lBSUgIfHx/j9qKiIoSEhNzyWCqVCiqV6qbtSqWy9V8URfPaUyoUgB1/k/2eWb52Ns7Re2R/9s/Re2R/tm12fAw+2ZuNE5fKcCK/Av3a3ry2lbl7NOVYJs12EUUR8+fPx8aNG7Fr1y5ER0c3ej02NhZKpRIJCQnGbenp6cjJyUFcXJwpn4qIiIhaKNBThXt7twFgm0uum3TlY968eVizZg02bdoET09PFBYWAgC8vb3h6uoKb29vzJ07F4sXL4afnx+8vLywYMECxMXFSTPTxc0fUKianm6rUBn2IyIiciBzh0bj28O52H66EBevViLK313qkoxMCh8ffvghAGDEiBGNtq9evRqPPfYYAGDFihWQyWSYPn06amtrMX78eHzwwQdmKdZkPhHA/FTjOh4arRbJycmIj4833GoBDMHDJ0Ka+oiIiCykY7AnhncMRNK5y1idnI0l93STuiQjk8JHcybGqNVqrFy5EitXrmxxUWblE/FbuNBoUOqWZxhcasf38oiIiJpj7pBoJJ27jPWHc7F4XEd4qW3jd5/jP9uFiIjISQ3tEID2QR6orNNh3SHbeZQIwwcREZGDEgQBj8cbJod8sS8bOr111vy4E4YPIiIiBzatbxv4uilx6Xo1dpwulLocAK1cXp2IiIhsm1opx1O9XbB5/zns3n0Vo726wrsq27AQp0STLxg+iIiIHFlJLp46PgNPq2qBqwA+B0YAjVcAV6gMs0OtFEB424WIiMiRVV2FoGtivSvAsB5W/bIU1sDwQURERFbF8EFERERWxfBBREREVsXwQURERFbF8EFERERWxfBBREREVsXwQURE5Mjc/A3reDRFoTLsZyVcZIyIiMiR+UQYFhCrX8dDo9UiOTkZ8fHxUHKFUyIiIrIIn4jfwoVGg1K3PCC0F6BUSlIOb7sQERGRVTF8EBERkVUxfBAREZFVMXwQERGRVTF8EBERkVUxfBAREZFVMXwQERGRVTF8EBERkVUxfBAREZFV2dwKp6IoAgDKysrMfmyNRoOqqiqUlZVBKdGqbpbk6P0Bjt8j+7N/jt4j+7N/luqx4fd2w+/xpthc+CgvLwcARERYb415IiIiMo/y8nJ4e3s3uY8gNieiWJFer0d+fj48PT0hCIJZj11WVoaIiAjk5ubCy8vLrMe2BY7eH+D4PbI/++foPbI/+2epHkVRRHl5OcLCwiCTNT2qw+aufMhkMoSHh1v0c3h5eTnsNxXg+P0Bjt8j+7N/jt4j+7N/lujxTlc8GnDAKREREVkVwwcRERFZlVOFD5VKhVdeeQUqlUrqUizC0fsDHL9H9mf/HL1H9mf/bKFHmxtwSkRERI7Nqa58EBERkfQYPoiIiMiqGD6IiIjIqhg+iIiIyKrsOnysXLkSbdu2hVqtxsCBA3Hw4MEm91+/fj06d+4MtVqNHj164Oeff270uiiKePnllxEaGgpXV1eMGTMG58+ft2QLd2RKj59++imGDh0KX19f+Pr6YsyYMTft/9hjj0EQhEZvEyZMsHQbt2VKf1988cVNtavV6kb72Ps5HDFixE09CoKASZMmGfexpXO4Z88e3H333QgLC4MgCPjhhx/u+DGJiYno27cvVCoV2rdvjy+++OKmfUz92bYUU/vbsGEDxo4di8DAQHh5eSEuLg7bt29vtM+SJUtuOn+dO3e2YBe3Z2p/iYmJt/z+LCwsbLSfrZw/wPQeb/XzJQgCunXrZtzHVs7h66+/jv79+8PT0xNBQUGYOnUq0tPT7/hxtvC70G7Dx7fffovFixfjlVdewZEjR9CrVy+MHz8excXFt9x/3759eOihhzB37lwcPXoUU6dOxdSpU5GWlmbc54033sC7776Ljz76CAcOHIC7uzvGjx+Pmpoaa7XViKk9JiYm4qGHHsLu3buxf/9+REREYNy4ccjLy2u034QJE1BQUGB8++abb6zRzk1M7Q8wrMh3Y+0XL15s9Lq9n8MNGzY06i8tLQ1yuRz3339/o/1s5RxWVlaiV69eWLlyZbP2z8rKwqRJkzBy5EgcO3YMCxcuxBNPPNHoF3RLvi8sxdT+9uzZg7Fjx+Lnn39GamoqRo4cibvvvhtHjx5ttF+3bt0anb+9e/daovw7MrW/Bunp6Y3qDwoKMr5mS+cPML3Hd955p1Fvubm58PPzu+ln0BbOYVJSEubNm4eUlBTs2LEDGo0G48aNQ2Vl5W0/xmZ+F4p2asCAAeK8efOM7+t0OjEsLEx8/fXXb7n/jBkzxEmTJjXaNnDgQPGpp54SRVEU9Xq9GBISIv773/82vl5SUiKqVCrxm2++sUAHd2Zqj7+n1WpFT09P8csvvzRumz17tjhlyhRzl9oipva3evVq0dvb+7bHc8RzuGLFCtHT01OsqKgwbrOlc3gjAOLGjRub3OeFF14Qu3Xr1mjbAw88II4fP974fmu/ZpbSnP5upWvXruLSpUuN77/yyitir169zFeYmTSnv927d4sAxOvXr992H1s9f6LYsnO4ceNGURAEMTs727jNVs9hcXGxCEBMSkq67T628rvQLq981NXVITU1FWPGjDFuk8lkGDNmDPbv33/Lj9m/f3+j/QFg/Pjxxv2zsrJQWFjYaB9vb28MHDjwtse0pJb0+HtVVVXQaDTw8/NrtD0xMRFBQUHo1KkTnnnmGVy9etWstTdHS/urqKhAVFQUIiIiMGXKFJw6dcr4miOew1WrVuHBBx+Eu7t7o+22cA5b4k4/h+b4mtkSvV6P8vLym34Gz58/j7CwMMTExGDWrFnIycmRqMKW6d27N0JDQzF27FgkJycbtzva+QMMP4NjxoxBVFRUo+22eA5LS0sB4KbvtxvZyu9CuwwfV65cgU6nQ3BwcKPtwcHBN917bFBYWNjk/g3/NeWYltSSHn/vL3/5C8LCwhp9E02YMAFfffUVEhISsHz5ciQlJWHixInQ6XRmrf9OWtJfp06d8Pnnn2PTpk34+uuvodfrMXjwYFy6dAmA453DgwcPIi0tDU888USj7bZyDlvidj+HZWVlqK6uNsv3vS158803UVFRgRkzZhi3DRw4EF988QW2bduGDz/8EFlZWRg6dCjKy8slrLR5QkND8dFHH+H777/H999/j4iICIwYMQJHjhwBYJ5/t2xJfn4+tm7detPPoC2eQ71ej4ULFyI+Ph7du3e/7X628rvQ5p5qS+axbNkyrF27FomJiY0GZT744IPG/+/Rowd69uyJdu3aITExEaNHj5ai1GaLi4tDXFyc8f3BgwejS5cu+Pjjj/Haa69JWJllrFq1Cj169MCAAQMabbfnc+hM1qxZg6VLl2LTpk2NxkRMnDjR+P89e/bEwIEDERUVhXXr1mHu3LlSlNpsnTp1QqdOnYzvDx48GJmZmVixYgX++9//SliZZXz55Zfw8fHB1KlTG223xXM4b948pKWlSTZ+yFR2eeUjICAAcrkcRUVFjbYXFRUhJCTklh8TEhLS5P4N/zXlmJbUkh4bvPnmm1i2bBl++eUX9OzZs8l9Y2JiEBAQgIyMjFbXbIrW9NdAqVSiT58+xtod6RxWVlZi7dq1zfqHTKpz2BK3+zn08vKCq6urWb4vbMHatWvxxBNPYN26dTdd4v49Hx8fdOzY0S7O360MGDDAWLujnD/AMOPj888/xyOPPAIXF5cm95X6HM6fPx9btmzB7t27ER4e3uS+tvK70C7Dh4uLC2JjY5GQkGDcptfrkZCQ0Ogv4xvFxcU12h8AduzYYdw/OjoaISEhjfYpKyvDgQMHbntMS2pJj4BhlPJrr72Gbdu2oV+/fnf8PJcuXcLVq1cRGhpqlrqbq6X93Uin0+HkyZPG2h3lHAKGqXC1tbV4+OGH7/h5pDqHLXGnn0NzfF9I7ZtvvsGcOXPwzTffNJoifTsVFRXIzMy0i/N3K8eOHTPW7gjnr0FSUhIyMjKa9QeAVOdQFEXMnz8fGzduxK5duxAdHX3Hj7GZ34VmG7pqZWvXrhVVKpX4xRdfiKdPnxaffPJJ0cfHRywsLBRFURQfeeQR8a9//atx/+TkZFGhUIhvvvmmeObMGfGVV14RlUqlePLkSeM+y5YtE318fMRNmzaJJ06cEKdMmSJGR0eL1dXVVu9PFE3vcdmyZaKLi4v43XffiQUFBca38vJyURRFsby8XHz++efF/fv3i1lZWeLOnTvFvn37ih06dBBrampsvr+lS5eK27dvFzMzM8XU1FTxwQcfFNVqtXjq1CnjPvZ+DhsMGTJEfOCBB27abmvnsLy8XDx69Kh49OhREYD41ltviUePHhUvXrwoiqIo/vWvfxUfeeQR4/4XLlwQ3dzcxD//+c/imTNnxJUrV4pyuVzctm2bcZ87fc1sub///e9/okKhEFeuXNnoZ7CkpMS4z5/+9CcxMTFRzMrKEpOTk8UxY8aIAQEBYnFxsc33t2LFCvGHH34Qz58/L548eVJ87rnnRJlMJu7cudO4jy2dP1E0vccGDz/8sDhw4MBbHtNWzuEzzzwjent7i4mJiY2+36qqqoz72OrvQrsNH6Ioiu+9954YGRkpuri4iAMGDBBTUlKMrw0fPlycPXt2o/3XrVsnduzYUXRxcRG7desm/vTTT41e1+v14ksvvSQGBweLKpVKHD16tJienm6NVm7LlB6joqJEADe9vfLKK6IoimJVVZU4btw4MTAwUFQqlWJUVJT4hz/8QbJ/FETRtP4WLlxo3Dc4OFi86667xCNHjjQ6nr2fQ1EUxbNnz4oAxF9++eWmY9naOWyYevn7t4aeZs+eLQ4fPvymj+ndu7fo4uIixsTEiKtXr77puE19zazJ1P6GDx/e5P6iaJhaHBoaKrq4uIht2rQRH3jgATEjI8O6jdUztb/ly5eL7dq1E9Vqtejn5yeOGDFC3LVr103HtZXzJ4ot+x4tKSkRXV1dxU8++eSWx7SVc3irvgA0+pmy1d+FQn0DRERERFZhl2M+iIiIyH4xfBAREZFVMXwQERGRVTF8EBERkVUxfBAREZFVMXwQERGRVTF8EBERkVUxfBAREZFVMXwQERGRVTF8EBERkVUxfBAREZFVMXwQERGRVf0/F2gACJyntMQAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Построим график функции 2, которую надо минимизировать"
      ],
      "metadata": {
        "id": "WcLlOdWiyNIp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_a = np.arange(-50, 10, .1, dtype = float)\n",
        "y_a = []\n",
        "for x in x_a:\n",
        "    y_a.append(solve_2(x))\n",
        "    \n",
        "plt.plot(x_a, y_a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 514
        },
        "id": "QP4MIecykJgJ",
        "outputId": "5608b815-93c9-4da2-fdf5-0d2d9c478f39"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-23-8435b0968071>:10: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
            "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
            "  return np.linalg.lstsq(A, y)[0]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb36b50b880>]"
            ]
          },
          "metadata": {},
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Построим сразу обе выборки.\n",
        "\n",
        "Функция возрастает идя к нулю, тогда пусть лямбда будет равна -50\n"
      ],
      "metadata": {
        "id": "2HzKIIDayyVS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lmd = -50\n",
        "x_v2 = np.arange(0, 2.01, 0.01, dtype = float)\n",
        "C_result = get(lmd, y_2)\n",
        "y_v = f(lmd, C_result, x_v1)\n",
        "\n",
        "plt.grid()\n",
        "plt.plot(x_v1, y_v1)\n",
        "plt.plot(test, y_1, 's')\n",
        "plt.plot(x_v2, y_v)\n",
        "plt.plot(test, y_2, 's')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 499
        },
        "id": "Y5TJXVNokPrW",
        "outputId": "8922d5b0-b941-42ee-dba0-c774b4ee9f87"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-23-8435b0968071>:10: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
            "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
            "  return np.linalg.lstsq(A, y)[0]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb36b37bc40>]"
            ]
          },
          "metadata": {},
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "В первой функции минимум можно определить одним способом(внешняя функция имеет определённый минимум), а во второй это сделать не получится(она возрастает на этом промежутке), поэтому мы нашли приближение."
      ],
      "metadata": {
        "id": "DlQIFeYNp528"
      }
    }
  ]
}