proj_7.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# just some useful functions, imports and settings\n",
    "\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "from datetime import datetime\n",
    "def time_string():\n",
    "    # return datetime.now().strftime(\"%d %B %Y %X\")\n",
    "    return datetime.now().strftime(\"%X\")\n",
    "impath = 'trash_img'    # путь к папке, в которой будут сохраняться картинки\n",
    "#switching latex fonts\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\" : True,\n",
    "    \"font.family\" : \"serif\",\n",
    "    \"font.serif\" : \"Computer Modern\",\n",
    "    \"text.latex.preamble\" : r'\\usepackage{amsmath} \\usepackage{mathtext} \\usepackage[english, russian]{babel}',\n",
    "    \"axes.grid\": True,\n",
    "    \"axes.grid.which\": 'both',\n",
    "    'grid.linewidth': '1',\n",
    "})\n",
    "plt.rcParams.update({\n",
    "    \"figure.figsize\": (8, 6),\n",
    "    'figure.dpi': 200\n",
    "})\n",
    "\n",
    "# необходимые функции\n",
    "\n",
    "def err_pres_formatter(value, error):\n",
    "    \"\"\"Rounds value and it's error according to scientific conventions\"\"\"\n",
    "    first_digit = (np.array(error/10**np.floor(np.log10(error)), dtype=\"int\"))\n",
    "    first_digit_position = np.array(np.floor(np.log10(error)), dtype=\"int\")\n",
    "    ndigits = 1\n",
    "    if first_digit == 1:\n",
    "        ndigits += 1\n",
    "    power = np.log10(abs(value))\n",
    "    if abs(power//3) >= 1:\n",
    "        power = 3*int(power//3)\n",
    "        value /= 10**power\n",
    "        error /= 10**power\n",
    "        digit_number = -first_digit_position + ndigits+power-1\n",
    "        if digit_number <= 0:\n",
    "            return f\"({round(int(value), digit_number)} \\u00B1 {round(int(error), digit_number)})$\\cdot 10^{{{power}}}$\"\n",
    "        return f\"({round(value, digit_number)} \\u00B1 {round(error, digit_number)})$\\cdot 10^{{{power}}}$\"\n",
    "    digit_number = -first_digit_position + ndigits-1\n",
    "    if digit_number <= 0:\n",
    "        return f\"{round(int(value), digit_number)} \\u00B1 {round(int(error), digit_number)}\"\n",
    "    return f\"{round(value, digit_number)} \\u00B1 {round(error, digit_number)}\"\n",
    "\n",
    "\n",
    "def lower_upper_limits(domain, fun, popt, pcov, nsigma=1):\n",
    "    '''Вычисляет минимальные и максимальные значения функции \n",
    "    при заданных парамерах и стандартных отклонениях\n",
    "    в пределах nsigma*стандартное отклонение\n",
    "    Возвращает:\n",
    "    minA :(np.array) - массив минимальных значений\n",
    "    maxA :(np.array) - массив максимальных значений'''\n",
    "    err = np.sqrt(np.diag(pcov))\n",
    "    corr = pcov /np.expand_dims(err, 1) / np.expand_dims(err, 0)\n",
    "    deviations = np.eye(popt.size)*np.expand_dims(err, 1)  \n",
    "    df = np.expand_dims(fun(domain, *popt), 1) - fun(np.expand_dims(domain, 1), *(np.expand_dims(popt, 1)+np.eye(popt.size)*np.expand_dims(err, 1)))\n",
    "    dfmatrixes = np.expand_dims(df, 1)*np.expand_dims(df, 2) * np.expand_dims(corr, 0)\n",
    "    sigm_f = np.sqrt(np.sum(dfmatrixes, axis=(1, 2)))\n",
    "    return (fun(domain, *popt)-nsigma*sigm_f, fun(domain, *popt)+nsigma*sigm_f)\n",
    "\n",
    "def plot_approx(x, y, f, par_names_str, fun_name, yerr=None, visApproxError=True, p0=None):\n",
    "    if yerr is not None:\n",
    "        popt, pcov = curve_fit(f, x, y, sigma=yerr, absolute_sigma=True, p0=p0)\n",
    "    else:\n",
    "        popt, pcov = curve_fit(f, x, y, p0=p0)\n",
    "    err = np.sqrt(np.diag(pcov))\n",
    "    for v, er in zip(popt, err):\n",
    "        print(v,'+-',er)\n",
    "    approx_label = f\"approximation of function {fun_name}\"\n",
    "    if (err == np.inf).any():\n",
    "        print('Аппроксимация не сошлась. Попробуй задать начальные параметры p0')\n",
    "    else:\n",
    "        par_names = [x.split(',') for x in par_names_str.strip().split(\"\\n\") if (len(x) != 0)]\n",
    "        for i in range(len(par_names)):\n",
    "            t = par_names[i]\n",
    "            if len(t) == 2:\n",
    "                name, units = t\n",
    "            else:\n",
    "                name, units = *t, ''\n",
    "            approx_label += f\"\\n{name} = {err_pres_formatter(popt[i], 2*err[i])} {units}\"\n",
    "    teorPoints = 50     \n",
    "    intent = 0.0   # отступ по бокам от обласи экспериментальных данных\n",
    "    a, b = x.min(), x.max()\n",
    "    X = np.linspace(a-(b-a)*intent, b+(b-a)*intent, num=teorPoints)\n",
    "    plt.plot(X, f(X, *popt), 'r', label=approx_label)\n",
    "    if visApproxError and (pcov != np.inf).all():\n",
    "        nsigma = 2\n",
    "        minA, maxA = lower_upper_limits(X, f, popt, pcov, nsigma=nsigma)\n",
    "        plt.fill_between(X, minA, maxA, alpha=0.4, label=f\"область {nsigma} $\\sigma$ ошибки\")\n",
    "\n",
    "def make_beautiful_plot(xname, xunit, yname, yunit):\n",
    "    plt.grid(True, which='minor', linewidth=0.2)\n",
    "    plt.grid(True, which='major')\n",
    "    plt.xlabel(fr\"{xname}, {xunit}\")\n",
    "    plt.ylabel(fr\"{yname}, {yunit}\")\n",
    "    plt.title(fr\"{yname}({xname})\")\n",
    "    plt.legend()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7a. Estimate $\\pi$ using simple sampling Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_pi_randomly(N):\n",
    "    x = np.random.random(N)\n",
    "    y = np.random.random(N)\n",
    "    frac = np.mean(x**2+y**2<1)\n",
    "    pi = 4*frac\n",
    "    return pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.5138338008333835 +- 0.08479240628918229\n",
      "0.39762780883152665 +- 0.7150545173645493\n"
     ]
    },
    {
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PPz9iXCqFW+lU8TZRwTgUCkXHVirnXaGieJsj5knR09OTNCYUCkmSLr/8cltyAgAAAJAbr7zyimpra9Xb26sdO3bEzXjKlvnZQUr/A+ho245UeBpawBipiGL2kSy3xsZGNTc3q6GhQcFgUD6fb9S886GzszN6HN955x1LjmNra2vMMRjJ0OUrstnfVrLqHMi3XBQwzX2T6vEdSTrnyVg9JsFgUC6XK6UJbGbMSF+rT+aZZ56RpOi3DIbnMJre3t60J9l1dnbK4XAk/TnttNNGfN78SWXG6nDDi5dut1vt7e0Kh8Nx77Wj/ZEg232XD+YYSHSed3R0SIoUtsfyxEmKtzliDpqRBob5XH19vQ0ZjV8HjxzT7L96UY0bTuj+N8rUuOGEDh7JzSLSAAAAGJ8eeeQRSYk/IA7/TBAOh9XY2JhW++YHUI/Hk/YH0Gy2lU59XjFnZCViTlpJNKu2tbVVTqdTHo9Hfr9fbrdbLS0tI7aXL+aNozM5jmYRfHjcwYMH08oh2/2dC4WYU7pGmliVKXO/mAWvREKhUEzRq5jPk5GYhWRzBv5ozAL1aEX3cDgcfY8zmftkeF8dHR0pve+Ew+G0Z1N7PB719fUl/fnggw9GfN78SXW26fDXZeZgSjRz+ZVXXlFbW1vM67R63+WD+VoTXd/8fr+cTmf0vX2sonibI6O9kYbDYYVCoZTfuAAAAAAULvMDcqJv1ZkflkebQTb0653DrVq1SpKSfnU/m21Hs27duhE//IbDYbW2tsrj8cTNVO3s7JTf74/Zdv369XI6nfJ6vSlNdrFTKscxWV5m4WD47MlQKJTwK9jJ2slmf+dKIeaUiPn5OtG+HV6kskJzc7NcLpc6OjqSzpr1+XxxN46SivM8GYlZwE7nm8culyu6Xmkyc+bMkdfrjbbf0dGRdNkDv9+vpqamUfvNtFbjdDqz/knX0NrS0O3N97Kh++HZZ5/VokWLor/nYt/lQ21tbcLHW1paFAqFomNlLKN4m0PNzc0KhUIJ38TNC/+6devsTgsAAACAxb797W9LOlUoNQWDQQUCgWiBZfPmzXr++ecTfjXW6XTq+uuvjynWhMPh6AfTrq6upB9AM9nWXH9ytK9qO51OrV+/XpLiCq6hUEjXX3+9PB5PTHHY/LpuXV1d3FdZnU6nFi1apHA4rKuvvjphccp8LFnhamjOiWLMYoT5GpNtP/y1L1++XNLoxzEYDKqtrS3uOJrFDbNQmGwG30ivL5P9Pfy1JGo32WtOhdPp1Isvvph2TmYuQ38ylUo75kzo1tbWuMfN555//nm9+uqrMfshm30XCATkdrtVV1cX93xjY6Pq6uriimH5PE+Gvw6rz5VkNm7cKCn1mbdSZCbpSF/VN88Fj8cjt9utcDgsv9+v9vb2uD9omUu3jObNN9+UlHj91EJkThgcvsyBuTyFeV4Fg8GYAnEu9l2+mN+UGDruOzo6tGrVKgUCgaL4tntZvhMYa4aexJs2bUq4DoipqalJGzduVF1dXcw/lsw1npqbm5l5CwAAABSB2267TV1dXVq1apVqa2ujBcvq6upo8eTXv/617rzzTt111126//7749qoqqpSe3t7zBqFoVBIHo9n1A/O6WwbDAZjCr2hUEgOh0Mul0vNzc0JP+i63W719PSopaVFy5Ytk3Sq6LN8+fKYbRobG2M+RLe2tqqxsTH62aejoyP6/I4dO1RZWRktRLlcLtXW1sYUjRwOR/Su4+FwWHPmzIkpLFRWVsrlcqmrq0ttbW3y+XzR54PBoBwOh+rr69Xe3q66urqYb0c2NjbK5/Np3bp1qq+vV319ffQ4XnXVVbriiiskxR7HjRs3yuv1qrGxMW5GY3Nzs6qrq7Vq1aro13WHTtgxC+rJXl8m+3u0ffLkk0/qu9/9bvT5zs5OVVZWJi3sJXPZZZelnJOpuro65rWaedXX16dVDEq1nYaGBlVVVcnv90eLhdKpiVUVFRWqrKzUihUrdMMNN2j58uVpnU+J9p0Z29LSosbGRvX29qqqqkpOp1PLly9P+Jk/H+eJ+dzw1/upT30qrdebKbMIm876u3V1dWptbVU4HE74hyun0ym/36+urq5ocb69vT36uNfrlcvlUm9vb3SWdC7yzDen05lwKZ7169dr2bJlamxslNPp1MqVK2O2SWXf7d+/X6tXry74G7jt2LFDy5YtU1dXV3QMdnV1FXzeqXIYhmHkO4lCZ1bsw+Fw3Hor5pvy4sWLk04hb21tVXt7e/RNw/wr9EiFXzvt3r1bs2bNkiTt2rVLM2fOjHm+u7tb8+fPz7j9TLZPZ5vRYg8eOabalbHLV3R9x6Npp09KK6dik+1xzTW788tVf1a1m007uR6Dqca//PLL6u/vV3l5uW644Ya08ilWjEN7+rOiXbvHYLrbMQYzM17G4Pbt23XixAmVlZVp7ty5SeOOHj2qyZMnZ91frtrNpp1Mtk13m1TiDx06JMMw5HA4VFFREX08HA5HC0bprsuZzbaFIFfnnRXykVsu+mQMnpJsDI5ndp3nQ4vi6XA4HPL7/bYt/XD99ddH/xhmpfEwDlONPXTokK655hp9//vf15e+9KW08rFTqv9+Gmq0+lqmmHmbAvMvsJlqaGgoiDVmTPPmzYv5fWBgIE+ZAAAAAACAYmZ+g3nx4sVpb3v33XerubnZlppKOBzWK6+8ktFNw4BcYubtOJSoeLt9+3ZJkfV6ZsyYEfP8gQMHNH369Iz7y2T7dLYZLfZQ/6Du6Ngd89hT9TNVUV6aVk7FJtvjmmt255er/qxqN5t2cj0GU43fuXOnBgcHVVpaqtmzZ6eVT7FiHNrTnxXt2j0G092OMZiZ8TIGBwYGVFJSovLycp133nlJ48zZJVazqt1s2slk23S3SSX+2LFj0f+fNOnUt8DC4bA+9alPac6cOdqyZUtaeWazbSHI1XlnhXzklos+GYOnJBuD41kuzrlwOKybbrpJVVVV+j//5//oueee0x133KEPPvgg7RtHHThwQOedd55+9atf6bLLLrM0z+G+853v6M0334yu72yl8TAOU409duyYfv7zn+vaa6/VWWedlVY+dvr973+v/v5+nTx5UhMmTEhpm71790bXS2bmLbIy/B91Q6d119TUFOWyCVJs8bampoZlE8bJV0Xz3R/LJpyyZ88eDQ4OasKECQV97tmJcWhPfyybEMEYjDdexqD5tb+SkpIRv87IsgnZbZNK/PHjx6Nf2R4aaxaUhj+eimy2LQQsm5D7PhmDpyQbg+NZLs65H/3oR3rrrbfkcrk0efJkPffcc2pqatI555yTdlvTp09Xc3OzVqxYkdMZseFwWD/5yU/0q1/9imthhtukGnv8+HF96UtfKvhxWFJSookTJ6a1bEK6f5xIOZectAoAAAAASIl5A63hd/jO9bYAkAsul0tut1tdXV0Kh8MKBoNp3aBuOPP+Qi0tLValGMfr9UZvYAcUGoq3AAAAAJAHwWBQlZWV8nq90ccqKytVXV2d020BIJfq6+u1cOFCLVu2TF6v15IZs+3t7fL7/QoGgxZkGKulpUUulyvpTeiBfGPZBAAAAADIA7fbrb6+Ptu3BYBc8/v9lrbndDrV1dWlZcuWqb293bJ2g8GgDh48aHm+gJUo3gIAAAAAAKCgOZ1OSwu3UuQPYW6329I2AauxbAIAAAAAAAAAFCCKtwAAAAAAAABQgFg2AQAAAAAAIAfC4bBWrVqlcDgsSQqFQqqrq+PmWABSRvEWAAAAAAAgB7xer/x+v1wul6RIMXfOnDkKBAIKBAJ5zg7AWMCyCePQvHnzYn6uu+66fKcEAAAAYIwJh8Pyer35TgMFLBgMqqWlJd9p5E0wGFRnZ6eCwWD0MafTKY/HE/c4ACTDzFvE2Lp1a/TrHKYDBw6ou7s74zYz2T6dbUaLPdQ/GPfY1q1bVVFemlZOxSbb45prdueXq/6sajebdnI9BlONHxgYiP63kM89OzEO7enPinbtHoPpbscYzMx4GYMDAwMqKSlRSUmJjh49mjTuxIkTIz6fKavazaadTLZNd5tU4g3DiP43F/vabp///Oe1du3arF5Lrs47K+Qjt1z0mc8xeNFFF+mll17SunXrtGzZspz2V4hjsLy8XE6nU3v37o3p74wzzpAkffjhh3k//wt5DEr258e1MPNtUo0dK9fCkydP6vjx4+rv70/532N79+7NSS4Ub8ehLVu2xPy+e/duzZo1S5JUU1OjmTNnxjzf3d2t+fPnZ9xfJtuns81osQePHJO0O+axmpoaTTt9Ulo5FZtsj2uu2Z1frvqzqt1s2sn1GEw1fs+ePRocHNSECRMK+tyzE+PQnv6saNfuMZjudozBzIyXMbh9+3adOHFCJSUlmjx5ctK4o0ePjvh8pqxqN5t2Mtk23W3M+FAopMbGRoVCIfX29qqqqko9PT2SpOPHj8swDDkcjpzsazs1Njbq9ttv11VXXZXR9ua6n3fffbe++MUvRr9SHgqFtGnTJvn9frW3t0cfTyYYDMrr9aqrq0tOp3PUfjs6OuT3+yUp2nZjY6PcbndcrBXnrtfr1fLlyxO2n0g2fSbbF8Pb9Hq9qqqqks/nU1VVVdL9Fg6HE7aTzj6UpAcffFCXXXaZLr74Ynk8npRfTyr7YuhrnjRp0qjxra2tev755zV79mwdOXJEktI6Pum6+OKL1dfXF/f4q6++KpfLpT/90z/NSb/pyNV7v1Xszo9rYebbpBo7Vq6FJSUlmjhxosrKyjR37tyUtknlOpQJircAAAAAYBGXyyW/3y+/36+Wlpa0ilVjRUdHR7TAmqlwOKxQKKTvfOc7+s53vhP3fHNzc8LCbTgc1qZNmxQKheT3+6NfO+/t7R31Q7PX61UwGIwpboZCIdXW1qq5uVkNDQ0Zv55kzCJ+LmS6L4LBoEKhkFpbW0ftIxAIxJzDme7Dp556SldffbV27NhhSXEjGAzK7/en9BqG5r59+3b9/Oc/l9PpVEVFRc6P/3ChUEg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      "text/plain": [
       "<Figure size 1600x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best estimate is 3.14202\n"
     ]
    }
   ],
   "source": [
    "repeats = 20\n",
    "Ns = np.array([10**i for i in range(1, 7)])\n",
    "pis = np.array([[count_pi_randomly(N) for N in Ns] for _ in range(repeats)])\n",
    "\n",
    "errors = np.abs(pis - np.pi)\n",
    "avg_errors = np.mean(errors, axis=0)\n",
    "er_error = np.sqrt(np.mean(np.square(errors - avg_errors), axis=0))\n",
    "\n",
    "plt.errorbar(Ns, avg_errors, yerr=er_error, fmt='o')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "\n",
    "plt.grid(True, which='minor', linewidth=0.2)\n",
    "plt.grid(True, which='major')\n",
    "\n",
    "plt.ylabel(\"absolute error\")\n",
    "plt.xlabel(\"Number of samples\")\n",
    "plt.title(\"Pi by Monte Carlo determining precision\")\n",
    "\n",
    "\n",
    "\n",
    "# function to approximate\n",
    "fun_name = r\"$f(x) = kx + b$\"\n",
    "def f(x, k, b):\n",
    "    return np.exp(b + k * np.log(x))\n",
    "par_names_str = fr'''\n",
    "$k$, \n",
    "'''\n",
    "\n",
    "plot_approx(Ns, avg_errors, f, par_names_str, fun_name, yerr=er_error, visApproxError=False)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print(\"Best estimate is\", pis[0, -1])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Slope of error function in log-log scale, as expected, is approximately -0.5\n",
    "\n",
    "With $10^6$ samples precision is about $10^{-3}$\n",
    "\n",
    "Best estimate is $\\pi \\approx 3.1420$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7b. Midpoint integration "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def integrate(func, H, xlims, ylims, Nx:int, Ny:int):\n",
    "    \"\"\"compute Simpson integration in 2d\n",
    "\n",
    "    Args:\n",
    "        func : integrated function\n",
    "        H: indicator function of integrating region.\n",
    "        xlims ([float, float])\n",
    "        ylims ([float, float])\n",
    "        \"\"\"\n",
    "    dx = np.abs(xlims[1]-xlims[0])/Nx\n",
    "    dy = np.abs(ylims[1]-ylims[0])/Ny\n",
    "    \n",
    "    x = np.linspace(*xlims, Nx, endpoint=False) + dx/2\n",
    "    y = np.linspace(*ylims, Ny, endpoint=False) + dy/2\n",
    "    \n",
    "    X, Y = np.meshgrid(x, y)\n",
    "    int_sum = np.sum(H(X, Y)*func(X, Y))*dx*dy\n",
    "    return int_sum\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.2"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = lambda x, y: np.ones_like(x)    # function is always 1, only area limits circle\n",
    "def H(x, y):\n",
    "    return x**2+y**2<1\n",
    "integrate(f, H, [-1, 1], [-1, 1], 10, 10)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.16      , 3.16      , 3.14      , 3.141875  , 3.14265625])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ns = np.array([2**i for i in range(1, 6)])*10\n",
    "pis = np.array([integrate(f, H, [-1, 1], [-1, 1], N, N) for N in Ns])\n",
    "\n",
    "error = np.abs(pis-np.pi)\n",
    "\n",
    "pis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EPWzZw2otlUpZuVzOKpVKVqlUBuFKP2zph7z7hQrH/Uz6wVetVhu8X6lUykql0qEB97O2trYGtff/FIvFbHl5+cAaj/L5HLZM/7MuFotH+j52q9VqgzorlcoLBeHjWo+TrEP/NcVicRDcH/Y997eT/nbX//Ps+pTL5cFrtra2Dt1H9gtbd1tbW8vK5fJQjbu3o90B7mGB9VE+n+Puo6e9nb/INnxUJ6n5sHqKxeIL1dO3+/vpf8/79d3nfUcvur0dt57DPptnw99nxz7qfgcAqZrKsiwLAAByV61WY2VlJSqVyoEXh+Ls6nQ6MT8/H8ViMdbW1g6c+7ndbke1Wo319fUolUqHTkkCAMDLzZy3AAAjNjs7O+4SSNDCwsJg3s7DLtpXKpWi2WxGqVSKdrudy0X1AABIg/AWAAAS0G63j3URpf7F9oS3AACTS3gLAAAJKBQK0Wg0jrz85uZmRERcuXIlr5IAABgz4S0AwIh1u91xl0CC7ty5E51OJ6rV6nOXbTQasbKyEsvLy4dOsQAAwMvNBcsAAEagfzGqTqcThUIhWq1WFIvFcZdFYjqdTiwtLUW3242bN29GpVIZbCedTifW19djbW0tOp1O1Ov1Y02zAADAy0d4CwCQo16vF6+99tqBz29tbTlzkj16vV7cu3cvNjc3B3Pazs7OxsWLF4cCXQAAJpvwFgAAAAAgQea8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAOAl0+v14uLFi/Haa6/F1NTU4M/KysqBr1lYWBhatv9nfn5+hJVPpk6nE/Pz84Pv5Kx/ptVqNebn52NpaSkWFhai0+mMu6RDra6uxmuvvXbo/gMAMC7CWwCAl0yhUIjNzc3Y2tqKtbW1wePVavXAoGxtbS22traiVqtFRMTy8nJsbW1Fs9kcSc2TrFgsRq1Wi3K5HL1eb9zljNXFixej3W5Hs9mMy5cvR6PRiIWFhXGXdah6vR69Xi9u37497lIAAPYQ3gIAvMSKxWIsLy9HsViMiDg0KCsUCrG8vByFQiFqtVoUCoURVTn5SqVSVKvVcZcxVv1/POj/g0KxWIxisRg3b94cc2WHu3XrVhQKhbh161Yu45/1M7EBgBcjvAUAmAD9wKzdbj/359/9oJfTNTs7O+4Sxmp9fT2KxeLgHwXK5XJsbm7G8vLyeAt7jkqlEltbW7nV2e12cxkXADgbhLcAABOgVCoNpkSoVqvRbrfHXBFnTepz245Do9EYdwkAwEtOeAsAMCGWl5ejVCpFxOHTJwCjUa/Xx10CAPCSE94CAEyQ/vQJnU7nzM/BCs/TaDRidXU1qtXqqe8v1Wo11tfXT3VMAODsOTfuAgAAOD3FYjFqtVpUq9VYWVmJmzdvDs7GTUWv14uFhYXodDrR7XajWCxGq9WKdrsdt2/fHiwTEVGr1Ybq7/V6ceHChaFlsiwbPN9oNOL27dvR6/Wi2+3GjRs3Bmc/HvS+6+vrg2U6nU7Mzs5GvV4fzA28uroazWZz8Hy5XB5MUXGYlZWV+MlPfhK9Xi86nc7guznsQnG9Xi9u3749qGO/13U6nVhaWhqsR38dq9Vq9Hq9ePToUSwtLcXi4uJzazzI6upqtFqt6Ha7g895aWkpKpXKnnovX748uN3r9eLixYuD5zc3N5/7Xs+uz5UrV6LZbMbKykpsbm4OpmM4yud3nNojIprNZqyvr0en0xlcyG/3up1kO+1vg/2pS9rtdkxNTQ3GLZfLg+2pr9FoxN27dwfr2ev1olAoRLvd3rMPAABnTAYAwEur1Wply8vLex4vlUpZRGTFYnHf58at1WpltVoti4isVCpla2trWa1WG1qmvw5bW1t7Xr+2tpZFRLbf4ezW1lZWqVSyiMgWFxdP9L6FQiHb2trKFhcXs1arNXhuc3Mzi4isXC7v+779z7xSqWSbm5tDzy8vL2eFQiFrNpv7fibNZjMrFAp7vs/FxcWsUCgMjddqtbLFxcXBOlYqlazVamWtVuvAz+UoNjc3s1KplFUqlT3rtt/juxUKhaxQKJz4fZeXl4c+v92fe5ZlWblczgqFQra2tnbqtUfEvrW/yHba31aet7/VarV9t6dms5lFxJ7PAQA4W4S3AAAvsYPC235wtF+AmUJ429cPzZ6tMcuyQZhXr9cPfO1BIWU/3N1v3Oe977Nh3bOKxeK+YV0/vD0ocM6yfwz6ng12+6896LspFAp7nut/x8VicShQLJfL+24TR7Hf+zxb40Eh6IuEt7vH3+/z6T/f/+z3e/5Faj8ovH32+eNsp0cNbw8LpPcLsQGAs8WctwAAE6j/E/OIj35GnvLcm71eL5aWlvY83v/5/VF+en+a79ufLqHT6ez7U/vdz++nWCwe+NP+W7duRcTeC8q99dZbQ88/q1wuR7vdHvwUPyJidnZ23zqbzeaRpnV4Vn/ahf0+k4iIQqEQi4uL0Wg0ct2eisXi4DN+9v37tT37+b1o7c+biiEiv+201+sdeGGz+fn5I9UGAEwu4S0AwIRaXl4ezJV5UKiViv3m9OyHk/15RUf1vv2w7MqVK/u+pv98t9s99vuVy+WI+Gge1N3r1Wg0DqwnImJubi4iIh49erRvPfuFnce1uroaEQevd0QM5rc9KGzMWz+kfvbzG1XteWyn5XI51tfX47XXXouFhYVYXV0dhPSLi4un8t0CAC8vFywDAJhga2trcfHixcFFoU4aXPUvHrWfy5cvv9DFsVKVxxmPu8d89OhRlMvloTN4q9XqIAx81uLi4iD83e00wr3+xcaeN16/tt1nAI/S7tr6n9/LUvtB1tbWolqtxr1796LRaAyC/GKxGPV6fd/vHAA4O4S3AAATrB8ALS0txerq6p6fmx9Vs9k88KfylUplIsPbg0LUPNVqtbGcaXncs4hPctZxXl622nu93lCIXygUol6vR71ej/X19VhbW4v19fXodDoxPz8fzWZTgAsAZ5hpEwAAJtzi4uLg594LCwsn+nl3s9mM7KOL3e75s7a2dsoVv7hxB3QH2f3Z93/ivzusPcl3cxoh8+4aDvvs+mcJHzY9QZ52n6W83+eXcu19q6urQ+vRn/Ih4qMpFOr1emxubkaz2YyIONH8xQDA5BDeAgCcAf2AtdfrJRtsnqa8LnL2ovpz1pbL5aGzL/tnLh92IbBOp5PrhcL688ke9h79z/WkZ3C/qP6UAs9+finWftBcuD/5yU8Gt3u9XlSr1X1fXy6XY3Fxcd95jgGAs0N4CwDwEut0Okc6W7M/fcIk6Z9NvN/690O+ceh0OkNnVu7WD+qe/S5qtdrg5/MHWVpayvWs0Tt37kShUDjwTM9erxerq6uDUDEvh23Tt2/fjojYc7b3i9aex0Xx+uHys9tCp9PZc7b1QaFzoVAwZQIAnHHCWwCAl1Sv14vbt2/HvXv3jnQRpoMueDUuu0Ot/cKz/vMHBaFLS0sRMfyz8/7j/efu3bs3mD/0qO/b/ywPOuPxeXXVarV9p6dYWFiITqcTzWZzz7y2hUIhWq1WRHx0Abjdr+31ejE/Px9LS0t7Lnh2WB3HVSgU4u233x7UuruGTqcTX/rSl6JcLu87TUb/omG7Lx72InV86Utf2vMZXL58OSIiWq3WnovJvWjtu//7rBfZTpeXlyPiH/8xodfr7TvNxcLCwp59uNPpRKPRMG0CAJxxU1mWZeMuAgCAo+v1enHhwoU9QVKhUIg7d+4MfkJ+0Gu/9KUvDYLCcTio/mKxGK1WK+7duxfVanXo+f4ZiM+Gb41GI+r1+lCYV6vVotPpxMLCQszOzg5ee+vWrWO/b8RHP8lfW1uL+fn5PWdI7v7M+2F6rVYb3N49TUWxWIxbt27tCR6ftbKyMpjvtL/srVu3Bmcat9vtPeFmf/xarXbo939UKysrsbGxERH/GFguLS3tO/bFixf3BJfFYjEqlcqxgsderxevvfZaFIvFaDabQ6/tdDpRKpWONN5Ra+8Hws/WXi6Xo9lsntp2urq6GvV6fbAt9s8S7tfwpS99Kd5+++24fft2dDqdoXC3Wq2O5QJ2AEA6hLcAAMDY7Q5vU52zGABg1EybAAAAAACQIOEtAAAAAECChLcAAAAAAAkS3gIAAGPXvxhcp9PZc5EwAICzygXLAACAsWm32/GlL31pT2DrwmUAAMJbAAAAAIAkmTYBAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBB58ZdALyIy5cvx507d6JUKh24TKPRiHq9HhERxWIxIiKWlpYOfc2LvA5IW7vdjoWFhWi1WlEoFI78mtu3b0en04nZ2dmIiJifn4/l5eUDX6P3wNl0kn6xH8c4cHatrKzE3bt3B32kVCpFrVYb7K/P6nQ6MT8/H0tLS1EulwfLdTqdePToUdTr9VhbWzvw9RGOdWBSHffvPifdP4/btw7jGGgfGbyk6vV6FhFZs9k8cJlKpZIVi8Vsa2tr8Njm5mZWKBSyer1+6q8D0rO1tZU1m82sXq9npVIpi4gsIrLNzc0jvX55eTkrFArZ2tra0OOVSiWr1Wr7vkbvgbPpJP1iP45x4Gza2trKSqXSUA9pNptZsVjMIiJbXl7e93WtVmtwfLPfn+f1H8c6MDle5O8+J9k/T9q3DuIYaH/CW15KW1tbgyZ00E5dq9UObFL9htBqtU7tdUCa1tbWskqlki0vLw/+53zUA5jl5eV99/l+LygWi3teo/fA2XSSfrEfxzhwdj0bgPRtbW0Njl/2e/6g8LZUKj13n3asA5PlpH/3Oen+edK+tR/HQAcT3vJS6v+LyWE7daFQyEql0oFj9A9oTut1wMvhqAcwm5ubB/5r8draWhYRWaVS2Xd8vQfOlpP2i/04xoGzqdlsHrr/9UPWQqGw57lWq5VVKpXBGXetVmvozLKDONaByXfUv/ucZP98kb61H8dAB3PBMl466+vrMTc3d+jcKevr69Hr9eLKlSsHLlMsFqPdbkev13vh1wGTp1qtRsRHcyA9q1KpxNbWVqytrQ09rvfA2XSSfrEfxzhwdrXb7Wi32/Haa6/t+/z8/HxERPR6veh0OvsuUygUolwuR6lUOtLclo51gIiT75+n0bd21+AY6GDCW146tVrtuRf9aDabERFx8eLFA5fpN4X19fUXfh0wWTqdTjQajSgUCgceQOz3lyK9B86ek/aL/TjGgbPrJz/5SUQcHHLs7i/tdvuF38+xDtB30v3zNPuWY6DDnRt3AXAc1Wo1arXac5c7ygFN/2Bkd5M56euAydJoNCIiBldb7v8F5yc/+UlcvHgxbty4se9faPQeOHtO2i+e5RgHzralpaXodDoHnnm2e788ydXbn+VYB+g76f55Wn3LMdDzCW95afRPYS+VSs9dtr/DHeUvS/1/LXqR1wGTZXNzMyI+6gWNRiM2Njbi1q1bERFx7969uHDhQrz99tt7+pHeA2fPSfvFbo5xgGKxeOj0KrvDh4N6RafTGQQgnU4nut1u3Lp1KyqVyp5lHesAfSfdP0+jbzkGOhrhLS+NarV6pPniIiK63e5zl9n9r8wv+jpgsuzev5vNZtTr9cH9xcXFaLVacfny5Wi1WkMHGnoPnD0n7Re7OcYBnqffWw76WfH6+nrUarWhHtRut+Py5cuxvLy856w2xzpAX1775/P6VoRjoKMy5y0vhdXV1VhaWjrynHF9/R3wuE76OmAy9P+n3W63Bxfz2K3/2FtvvbXv6/UeODtetF84xgGeZ3V1NTqdThSLxX1/WlwsFuPWrVtDAWzER2e6LS4uxsrKymCahD7HOsCzTnP/fF7f6i/jGOhohLckr9frRbPZ3PfnPgc5izszcHr6BxDFYnHf+Zn6j/WvsNqn98DZc9J+EeEYB3i+TqcTS0tLUSwWo9Vq7btMoVA48My2hYWFiIg9Aa1jHaDvtPfPo/Qtx0DHI7wleW+99daRJq/erX8wcpzT41/kdcBk6e/fh02s3+8Xjx492vOY3gNnx0n7RYRjHOD5FhYWBgHIcc9Oi/jH3tTpdIZ+DuxYB+g77f3zKH3LMdDxCG9J2vr6+oFXLjxMf4fr9XoHLtPfcXc3k5O+DpgsR+k5/X6x+1+T9R44e07aLxzjAM+ztLQUvV7vucHt+vr6gfv27iBi9xm0jnWAvtPcP4/StxwDHZ/wlqTVarVDJ7c+SL8JHHalwP6OOz8//8KvAybLUfbv/v/gL168OHhM74Gz56T9wjEOcJiVlZVYX19/bnC7uroa8/PzceHCheeOuXscxzpA32ntn0ftW46Bjk94S7La7XZ0Op24ePHivn/W19cj4qNT8vuP9fV3uMOuFNj/+c+VK1de+HXAZCmXyxFxeC/o/w9+9xWY9R44e07SLxzjAIdpNBpRr9f3DUAajcagR0REbG5uRsTBP/Xd/TPh3fu2Yx2g7zT2z6P2LcdAJ5TBS6pQKGQRkTWbzT3PbW1tZRGRFYvFfV/bf75UKp3K64CXR793bG5uHrpcqVTKIiLb2tra89zm5mYWEVmhUBh6XO+Bs+kk/eIwjnHg7Gq1WlmpVNq3n2RZli0vLw8dw6ytrWWLi4sHjre2tnbgvu1YBybfUf7u86L753H71lHqdQw0zJm3TKRCoRC1Wi06nU40Go09z9++fTsiIu7cuXMqrwMmT38C/dXV1T3P9fvDafUQvQdebifpFyelz8Dk6nQ68dZbb8WdO3ei2+0OLjLW/7O+vh6rq6tD80RWKpXodDoHzuXY37fX1tb2POdYB4h4sf3zJH1r1HVORP8Zd3oMJ9H/l5GIyOr1+oHLVSqVrFgsDv0LUKvVyu11QNr6+/FR9+Xl5eUsIrK1tbU9Y9RqtQNfp/fA2XPSfvEsxzhwNm1tbWXFYnGw/x/0Z78zx1qtVlYul7NWqzX0eKVSyQqFwr5nsPU51oHJddy/+xx3/3yRvrUfx0AHm8qyLMspF4ZTt7KyEvV6fc9cJYVCIYrF4tCVUPsajUbcvXs3Ij6aC6rb7catW7eG5m7az0lfB6Sl0WhEtVqNbre756yUQqEQs7OzsbS0dOCk+evr61GtVqPX6w3mb6rVaoO54g57X70HzpaT9osIxzhw1lWr1VhZWXnucuVyOZrN5p7He71eVKvVoR5SKpXi1q1bz716umMdmBwv+nef4+yfL9q3+hwDPZ/wFgAAAAAgQea8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPCWM+EHP/hBTE1NxdTUVPzgBz8YdznAhNFjgLzpM0De9Bkgb/rMyQhvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHnxl0A49fr9eK//tf/GhERFy9ejJmZmfEWlIN33313cPudd96JH/3oR2OsBpg0egyQN30GyJs+A+Rt0vvM9vZ2bG5uRkTEv/gX/yIKhcKpjDuVZVl2KiPx0vrP//k/x7/+1/963GUAAAAAwEvvj//4j+Nf/at/dSpjmTYBAAAAACBBpk0gLl68OLj9x3/8x3Hp0qUxVpOfd955J1555ZX48MMP48033xx3OcCE0WOAvOkzQN70GSBvk9xnHj9+PPhl++6s7UUJbxma4/bSpUsxNzc3xmry87/+1/8a3J7UdQTGR48B8qbPAHnTZ4C8nZU+c5rXkzJtAgAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJOjfuAhi9S5cuDd1/+vTp4PbDhw+j2+2OuqSRe/DgwbhLACaYHgPkTZ8B8qbPAHmbtD7z5MmTXMYV3jJkZ2cntre3x11G7s7COgLjo8cAedNngLzpM0DeJq3P7Ozs5DKu8PYMevz48dD9jY2NuHr1akRETE9Px8zMzDjKyt3upjCp6wiMjx4D5E2fAfKmzwB5m+Q+Mz09ncu4wluGXLt2Lebm5sZdRi7u378/uH39+vUxVgJMIj0GyJs+A+RNnwHyNsl9ZnZ2NpdxXbAMAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS85Uz46fYv4sPso9sfZh/dBzgtegwAAAB5EN4ysbIsi7/c/If4yp+24s3fb8b7P//o8fd/HvHm7zfj3/yXVvzl5j9ElmXjLRR4KekxAAAA5O3cuAuAPHzvh+/F7917J/763Z/t+/wHH2bxzb/6cXzzr34cv/7GJ+MPbrwZn//M+RFXCbys9BgAAABGwZm3TJy/+Ju/jxv1hweGKs/663d/FjfqD+Mv/ubvc64MmAR6DAAAAKMivGWifO+H78XSn7Ti6c8/ONbrnv78g1j6k1Z874fv5VQZMAn0GAAAAEZJeMvEyLIsfu/eO8cOVfqe/vyD+Hf3/rv5KYF96TEAAACMmvCWifGw85Mj/4z5IE/e/Wl8t9M9pYqASaLHAAAAMGrCWybGn373fyY1DjBZ9BgAAABGTXjLRPjp9i/iweN3T2Wsbz3+cfx0+xenMhYwGfQYAAAAxkF4y0T48Xvb8cGHpzOP5AcfZvHu+9unMhYwGfQYAAAAxkF4y0T43ye8gNBBfrZzuuMBLzc9BgAAgHEQ3jIR/snHXz3V8T45fbrjAS83PQYAAIBxEN4yET59fiZefWXqVMY698pUvPFLM6cyFjAZ9BgAAADGQXjLRPjUzMfi+qU3TmWs65c+HZ+a+dipjAVMBj0GAACAcRDeMjF+54u/ltQ4wGTRYwAAABg14S0T41rx9fj1Nz75QmP8xhufii8WZ0+pImCS6DEAAACMmvCWiTE1NRV/cOPN+MQJLyz0iY+/Gv/xxj+LqanTmdcSmCx6DAAAAKMmvGWifP4z56P+u5ePHa584uOvRv13L8fnP3M+p8qASaDHAAAAMErCWybOb37ul+Pe0rUj/7z5N974VNxbuha/+blfzrkyYBLoMQAAAIzKuXEXAHn4/GfOx4N/+8/ju51u/Ml3vx8PHr879Py5V6bi+qVPx+988dfii8VZP2MGjkWPAQAAYBSEt0ysqampuHbx9bh28fX46fYvYv1b34yIiF/6eMR/+w/z8amZj425QuBlpscAAACQN9MmcCZ8auZj8cr/OfHtlakQqgCnSo8BAAAgD8JbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABJ0btwFsL9qtRqdTic6nU5ERCwtLcXi4uKYqwIAAAAARkV4m6D5+fmo1WpRKpUiImJ9fT3m5+ej2WzG2tramKsDAAAAAEbBtAmJWVlZiaWlpUFwGxFRLpdjeXk5Go1GNBqNMVYHAAAAAIyK8DYxzWYzFhYWotfrDT1+8+bNwfMAAAAAwOQ7c+Ftu92Oixcv7glHD7K6uhrz8/OxtLQUCwsLsbCwEO12O7f6SqVSFAqFPY/3H+vPgQsAAAAATLYzM+dtu92Oer0eq6urR37NwsJCdDqdePvtt4fC08uXL0etVsvlAmK1Wi1qtdqex9fX1yPio/lwAQAAAIDJN/Fn3q6srMTly5ejXq/HwsLCvme17md1dTUajcZQcBsRUSwW486dO7G0tJTrGbjPqtVqUSwWY3l5eWTvCQAAAACMz8Sfebu8vHyiwLNarUa5XN437K1UKoNlRjEHbT90fvvtt3N/LwAAAAAgDRN/5u1JtNvt6PV6USqVDlymVCrF+vr6nrlz5+fnY2pq6sh/XnvttUNrWVhYiIiIVqt15LOGAQAAAICXn/B2H3fv3o2IiNdff/3AZWZnZyPiH+ei7Ws2m5Fl2ZH/bG1tHfgeCwsLMT8/H2tra4PHnn0/AAAAAGAyCW/30Q9IDzvTtf/cxsZGLjUsLCzErVu3hi6K1uv1hoJcAAAAAGByTfyctyfRnwqhf3btfvrPPTttwmm4fPlyRETcvn176PFOpxM3b9489ng/+MEPDn3+3XffPfaYAAAAAEC+hLf76Ha7uSx7FAsLC9FutyMiBv/drVarHXvMX/3VXz3ysg8fPjz1dUrRgwcPxl0CMMH0GCBv+gyQN30GyNuk9ZknT57kMq7wNjHjnhZhZ2cntre3x1rDKJyFdQTGR48B8qbPAHnTZ4C8TVqf2dnZyWVc4e0Z8Hd/93eHPv/OO+/Eb/3Wb0VExPT0dMzMzIyirJHb3RQmdR2B8dFjgLzpM0De9Bkgb5PcZ6anp3MZV3i7j9nZ2ej1ekeaPuCweXFT8Su/8iuHPv+jH/1ocPvatWsxNzeXd0ljcf/+/cHt69evj7ESYBLpMUDe9Bkgb/oMkLdJ7jN5ZYSv5DLqS65QKDx3mX6we5RlAQAAAACOS3i7jytXrkRExObm5oHLdDqdiIiJPUsVAAAAABgv4e0+5ufnIyKi1+sduEz/uUqlMoKKAAAAAICzRni7j34gu76+vu/zvV4vOp1OlEqlUZYFAAAAAJwhwtsD1Gq16HQ6g+kRdrt3715ERNy5c2fUZQEAAAAAZ8SZCm87nc5guoNHjx4duuzy8nJUKpWYn58fmj6h3W5HtVqNWq3mzFsAAAAAIDfnxl1A3hqNRty+fTt6vV50u90oFAoREbGwsBCzs7NRKBTi5s2bsby8vOe1a2trsbq6GgsLC1EsFqPb7Uav14u1tbUol8sjXhMAAAAA4CyZ+PC2Uqm80EXFFhcXY3Fx8RQrAgAAAAB4vjM1bQIAAAAAwMtCeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACTo3LgLYPQuXbo0dP/p06eD2w8fPoxutzvqkkbuwYMH4y4BmGB6DJA3fQbImz4D5G3S+syTJ09yGVd4y5CdnZ3Y3t4edxm5OwvrCIyPHgPkTZ8B8qbPAHmbtD6zs7OTy7jC2zPo8ePHQ/c3Njbi6tWrERExPT0dMzMz4ygrd7ubwqSuIzA+egyQN30GyJs+A+RtkvvM9PR0LuMKbxly7dq1mJubG3cZubh///7g9vXr18dYCTCJ9Bggb/oMkDd9BsjbJPeZ2dnZXMZ1wTIAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBB58ZdAKN36dKloftPnz4d3H748GF0u91RlzRyDx48GHcJwATTY4C86TNA3vQZIG+T1meePHmSy7jCW4bs7OzE9vb2uMvI3VlYR2B89Bggb/oMkDd9BsjbpPWZnZ2dXMYV3p5Bjx8/Hrq/sbERV69ejYiI6enpmJmZGUdZudvdFCZ1HYHx0WOAvOkzQN70GSBvk9xnpqencxlXeMuQa9euxdzc3LjLyMX9+/cHt69fvz7GSoBJpMcAedNngLzpM0DeJrnPzM7O5jKuC5YBAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgs6NuwBG79KlS0P3nz59Orj98OHD6Ha7oy5p5B48eDDuEoAJpscAedNngLzpM0DeJq3PPHnyJJdxhbcM2dnZie3t7XGXkbuzsI7A+OgxQN70GSBv+gyQt0nrMzs7O7mMK7w9gx4/fjx0f2NjI65evRoREdPT0zEzMzOOsnK3uylM6joC46PHAHnTZ4C86TNA3ia5z0xPT+cyrvCWIdeuXYu5ublxl5GL+/fvD25fv359jJUAk0iPAfKmzwB502eAvE1yn5mdnc1lXBcsAwAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgASdG3cBjN6lS5eG7j99+nRw++HDh9Htdkdd0sg9ePBg3CUAE0yPAfKmzwB502eAvE1an3ny5Eku4wpvGbKzsxPb29vjLiN3Z2EdgfHRY4C86TNA3vQZIG+T1md2dnZyGVd4ewY9fvx46P7GxkZcvXo1IiKmp6djZmZmHGXlbndTmNR1BMZHjwHyps8AedNngLxNcp+Znp7OZVzhLUOuXbsWc3Nz4y4jF/fv3x/cvn79+hgrASaRHgPkTZ8B8qbPAHmb5D4zOzuby7guWAYAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACTo3LgLYPQuXbo0dP/p06eD2w8fPoxutzvqkkbuwYMH4y4BmGB6DJA3fQbImz4D5G3S+syTJ09yGVd4y5CdnZ3Y3t4edxm5OwvrCIyPHgPkTZ8B8qbPAHmbtD6zs7OTy7jC2zPo8ePHQ/c3Njbi6tWrERExPT0dMzMz4ygrd7ubwqSuIzA+egyQN30GyJs+A+RtkvvM9PR0LuMKbxly7dq1mJubG3cZubh///7g9vXr18dYCTCJ9Bggb/oMkDd9BsjbJPeZ2dnZXMZ1wTIAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgASdG3cBjN6lS5eG7j99+nRw++HDh9Htdkdd0sg9ePBg3CUAE0yPAfKmzwB502eAvE1an3ny5Eku4wpvGbKzsxPb29vjLiN3Z2EdgfHRY4C86TNA3vQZIG+T1md2dnZyGVd4ewY9fvx46P7GxkZcvXo1IiKmp6djZmZmHGXlbndTmNR1BMZHjwHyps8AedNngLxNcp+Znp7OZVzhLUOuXbsWc3Nz4y4jF/fv3x/cvn79+hgrASaRHgPkTZ8B8qbPAHmb5D4zOzuby7guWAYAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgoS3AAAAAAAJEt4CAAAAACRIeAsAAAAAkCDhLQAAAABAgs6NuwBG79KlS0P3nz59Orj98OHD6Ha7oy5p5B48eDDuEoAJpscAedNngLzpM0DeJq3PPHnyJJdxhbcM2dnZie3t7XGXkbuzsI7A+OgxQN70GSBv+gyQt0nrMzs7O7mMK7w9gx4/fjx0f2NjI65evRoREdPT0zEzMzOOsnK3uylM6joC46PHAHnTZ4C86TNA3ia5z0xPT+cyrvCWIdeuXYu5ublxl5GL+/fvD25fv359jJUAk0iPAfKmzwB502eAvE1yn5mdnc1lXBcsAwAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEiS8BQAAAABIkPAWAAAAACBBwlsAAAAAgAQJbwEAAAAAEjTS8PbOnTvx6quvxte+9rVRvi0AAAAAwEtnpOFtvV6PLMui1WqN8m0BAAAAAF46Iw1vr1y5Eq1WKx48ePDcZb/xjW+MoCIAAAAAgDSNNLwtFAoxNTV1pGWr1WrO1QAAAAAApOvcKN/s61//ety4cSOuXr0alUolPvvZzx64bKfTGV1hAAAAAACJGWl4+5WvfCVef/31qNfrUa1Wo1AoRLFYjIiI2dnZwXKCWwAAAADgrBtpeHv37t147733IsuyiIjY2to68OJlR51eAQAAAABgEo10ztvZ2dlYXFyMzc3N2NraOvDPt7/97VGWBQAAAACQnJGeeVssFmNpaSkuXLhw6HLlcjnOnz8/oqoAAAAAANIz0vC2Xq8/N7jte/vtt3OuBgAAAAAgXSOdNuGowW1ExBe+8IUcKwEAAAAASNtIw9vdvvOd78TNmzfjc5/7XLz++utx/fr1+KM/+qNxlQMAAAAAkJSRTpvQd/PmzWg0GpFl2eCxZrMZ6+vrsba2Fvfu3Ytf+qVfGkdpAAAAAABJGHl4e+PGjWg0GrG4uBiXL1+O2dnZiIjodDrxP/7H/4g7d+7EjRs34lvf+taoSwMAAAAASMZIw9s/+7M/i06nE1tbW3H+/Pl9l6nValEul+PP//zP41/+y385yvIAAAAAAJIx0jlvV1dX4zvf+c6BwW1ERKFQiHv37sV/+k//aYSVAQAAAACkZaThbZZlR5rLtlgsDs2HCwAAAABw1ow0vC0UCkde9rXXXsuvEAAAAACAxI00vO1fnOx53nvvvZwrAQAAAABI20jD28uXL8fNmzefu9zi4mLMzc2NoCIAAAAAgDSNNLx96623YnNzM65evRp/9Ed/FO+88068//778f7778f3v//9+MM//MP43Oc+F+12O7761a+OsjQAAAAAgKScG/Ub3rt3Ly5fvhyLi4v7Pn/+/Pn4zne+M+KqAAAAAADSMtIzbyMiisVibG1txVe/+tU4f/58ZFk2+PPbv/3b8bd/+7fx5ptvjrosAAAAAICkjDy87avVatHtdmNrays2Nzfjww8/jHv37sX58+fHVRIAAAAAQDJGPm3Cs86fPy+wBQAAAAB4xkjPvL1z5068+uqr8bWvfW2UbwsAAAAA8NIZaXhbr9cjy7JotVqjfFsAAAAAgJfOSMPbK1euRKvVigcPHjx32W984xsjqAgAAAAAIE0jDW8LhUJMTU0dadlqtZpzNQAAAAAA6RrpBcu+/vWvx40bN+Lq1atRqVTis5/97IHLdjqd0RUGAAAAAJCYkYa3X/nKV+L111+Per0e1Wo1CoVCFIvFiIiYnZ0dLCe4BQAAAADOupGGt3fv3o333nsvsiyLiIitra0DL1521OkVAAAAAAAm0UjnvJ2dnY3FxcXY3NyMra2tA/98+9vfHmVZAAAAAADJGemZt8ViMZaWluLChQuHLlcul+P8+fMjqgoAAAAAID0jDW/r9fpzg9u+t99+O+dqAAAAAADSNdJpE44a3EZEfOELX8ixEgAAAACAtI00vL1z5068+uqr8bWvfW2UbwsAAAAA8NIZaXhbr9cjy7JotVqjfFsAAAAAgJfOSMPbK1euRKvVigcPHjx32W984xsjqAgAAAAAIE0jDW8LhUJMTU0dadlqtZpzNQAAAAAA6To3yjf7+te/Hjdu3IirV69GpVKJz372swcu2+l0RlcYAAAAAEBiRhrefuUrX4nXX3896vV6VKvVKBQKUSwWIyJidnZ2sJzgFgAAAAA460Ya3t69ezfee++9yLIsIiK2trYOvHjZUadXAAAAAACYRCOd83Z2djYWFxdjc3Mztra2Dvzz7W9/e5RlAQAAAAAkZ6Rn3haLxVhaWooLFy4culy5XI7z58+PqCoAAAAAgPSMNLyt1+vPDW773n777ZyrAQAAAABI10inTdgd3L7zzjvxh3/4h/H9739/8Nh3vvOdeP/99yMi4gtf+MIoSwMAAAAASMpIw9uIiO9///sxNzcXly9fjqWlpajVaoPnLly4EJVKJf78z/981GUBAAAAACRlpNMmvPfee1EqlSIi4rd/+7djbm4uOp3O4PkLFy7Et7/97fjyl78cFy5ciDfffHOU5QEAAAAAJGOkZ95Wq9W4ceNGdLvduHfvXvz7f//v913u3r17cfv27VGWBgAAAACQlJGeedvpdOLb3/72c5crFAqRZdkIKgIAAAAASNNIz7wtFotHXva9997LsRIAAAAAgLSNNLzd2to60nLvvfeeM28BAAAAgDNtpOHthQsX4mtf+9pzlyuXy/HlL395BBUBAAAAAKRppHPe3rp1Ky5cuBDr6+tx69at+MIXvhDdbje+//3vR6/Xi/X19ajX6xER8dWvfnWUpZ0ply5dGrr/9OnTwe2HDx9Gt9sddUkj9+DBg3GXAEwwPQbImz4D5E2fAfI2aX3myZMnuYw70vD2/Pnzce/evfjyl78clUpl8Hij0Rhapt1uj7IsdtnZ2Ynt7e1xl5G7s7COwPjoMUDe9Bkgb/oMkLdJ6zM7Ozu5jDvS8DbioykRut1uvPXWW/Fnf/ZnQ88tLi5GrVaL8+fPj7qsM+Xx48dD9zc2NuLq1asRETE9PR0zMzPjKCt3u5vCpK4jMD56DJA3fQbImz4D5G2S+8z09HQu4448vI2IKBQKsba2FhERf/u3fxsRH82Hy/hdu3Yt5ubmxl1GLu7fvz+4ff369TFWAkwiPQbImz4D5E2fAfI2yX1mdnY2l3HHEt7uJrQFAAAAANjrlXEXAAAAAADAXsJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAgMT9dPsX8WH20e0Ps4/uAwAw+YS3AACQoCzL4i83/yG+8qetePP3m/H+zz96/P2fR7z5+834N/+lFX+5+Q+RZdl4CwUAIDfnxl0AAAAw7Hs/fC9+79478dfv/mzf5z/4MItv/tWP45t/9eP49Tc+GX9w4834/GfOj7hKAADy5sxbAABIyF/8zd/HjfrDA4PbZ/31uz+LG/WH8Rd/8/c5VwYAwKgJbwEAIBHf++F7sfQnrXj68w+O9bqnP/8glv6kFd/74Xs5VQYAwDgIbwEAIAFZlsXv3Xvn2MFt39OffxD/7t5/NwcuAMAEEd4CAEACHnZ+cuSpEg7y5N2fxnc73VOqCACAcRPeAgBAAv70u/8zqXEAABg/4S0AAIzZT7d/EQ8ev3sqY33r8Y/jp9u/OJWxAAAYL+EtAACM2Y/f244PPjyduWo/+DCLd9/fPpWxAAAYL+EtAACM2f8+4UXKDvKzndMdDwCA8RDeAgDAmP2Tj796quN9cvp0xwMAYDyEtwAAMGafPj8Tr74ydSpjnXtlKt74pZlTGQsAgPES3gIAwJh9auZjcf3SG6cy1vVLn45PzXzsVMYCAGC8hLcAAJCA3/niryU1DgAA4ye8BQCABFwrvh6//sYnX2iM33jjU/HF4uwpVQQAwLgJbwEAIAFTU1PxBzfejE+c8OJln/j4q/Efb/yzmJo6nblzAQAYP+EtAAAk4vOfOR/137187AD3Ex9/Neq/ezk+/5nzOVUGAMA4CG8BACAhv/m5X457S9eOPIXCb7zxqbi3dC1+83O/nHNlAACM2rlxFwAAAAz7/GfOx4N/+8/ju51u/Ml3vx8PHr879Py5V6bi+qVPx+988dfii8VZUyUAAEwo4S0AACRoamoqrl18Pa5dfD1+uv2LWP/WNyMi4pc+HvHf/sN8fGrmY2OuEACAvJk2AQAAEvepmY/FK//n5NpXpkJwCwBwRghvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAAASJLwFAAAAAEiQ8BYAAAAAIEHCWwAAAACABAlvAQAAAIBc/XT7F/Fh9tHtD7OP7vN8wlsAAAAA4NRlWRZ/ufkP8ZU/bcWbv9+M93/+0ePv/zzizd9vxr/5L634y81/iCzLxltows6NuwAAAAAAYLJ874fvxe/deyf++t2f7fv8Bx9m8c2/+nF8869+HL/+xifjD268GZ//zPkRV5k+Z94CAAAAAKfmL/7m7+NG/eGBwe2z/vrdn8WN+sP4i7/5+5wre/kIbwEAAACAU/G9H74XS3/Siqc//+BYr3v68w9i6U9a8b0fvpdTZS8n4S0AAAAA8MKyLIvfu/fOsYPbvqc//yD+3b3/bg7cXYS3AAAAAMALe9j5yZGnSjjIk3d/Gt/tdE+popef8BYAAAAAeGF/+t3/mdQ4k0B4CwAAAAC8kJ9u/yIePH73VMb61uMfx0+3f3EqY73szo27APbq9Xpx+/bt6PV6ERHR6XRifn4+lpeXx1sYAAAAAOzjx+9txwcfns5ctR98mMW772/Hp2Y+dirjvcyEtwlaWFiIer0exWIxIj4Kcy9cuBDNZjOazeaYqwMAAACAYf/7hBcpO8jPdk53vJeVaRMS0263Y319Pdrt9uCxQqEQ5XJ5z+MAAAAAkIJ/8vFXT3W8T06f7ngvK+FtYgqFQhQKheh2h6+qNzs7GxGx53EAAAAAGLdPn5+JV1+ZOpWxzr0yFW/80sypjPWyO3PTJrTb7VhYWIhWqxWFQuG5y6+ursba2loUi8VBcHrr1q0olUq51FcsFmNra2vP4+vr61EsFqNcLufyvgAAAABwUp+a+Vhcv/RGfPOvfvzCY12/9Gnz3f4fZya8bbfbUa/XY3V19civWVhYiE6nE2+//fYg6O10OnH58uWo1WqxuLiYU7X/qNPpRLVajUKhEG+//Xbu7wcAAAAAJ/E7X/y1Uwlvf+eLv3YK1UyGiQ9vV1ZW4u7du3HlypVYWFiIe/fuRa/Xe+7rVldXo9FoxNbW1tAZusViMe7cuRMLCwtx5cqV3M7A7fV6cfv27ej1etHpdOLmzZu5vA8AAAAAnIZrxdfj19/4ZPz1uz878Ri/8can4ovF2VOs6uU28XPeLi8vR6vVinq9fqwpB6rVapTL5X2nVqhUKoNl8lIoFKJWq0W9Xo9WqxXNZjMuXLgQnU4nt/cEAAAAgJOampqKP7jxZnzihBcv+8THX43/eOOfxdTU6cydOwkmPrw9iXa7Hb1e79CzakulUqyvr+85i3d+fj6mpqaO/Oe11147Uk3VajV6vV4sLS29yKoBAAAAQG4+/5nzUf/dy8cOcD/x8Vej/ruX4/OfOZ9TZS8n4e0+7t69GxERr7/++oHLzM5+dPr2+vr60OPNZjOyLDvyn2cvTrawsBAXL17c837FYjEiwpm3AAAAACTtNz/3y3Fv6Vr8+hufPNLyv/HGp+Le0rX4zc/9cs6VvXyEt/voB7L7TZnQ139uY2PjVN+73W5Ht9vdc0ZvP7TNa45dAAAAADgtn//M+Xjwb/95/L9vfTH+73/66Xj1leGpEM69MhX/zz/9v+L/feuL8a1/+5vOuD3AxF+w7CT6wWn/7Nr99J87ysXPjqNarcbm5uae4LharUahUIg7d+4ce8wf/OAHhz7/7rvvHntMAAAAADjM1NRUXLv4ely7+Hr8dPsXsf6tb0ZExC99POK//Yf5+NTMx8ZcYfqEt/vodru5LHsUi4uLsb6+PjS3bafTiXK5HLdu3Tr0bOCD/Oqv/uqRl3348OGpr1OKHjx4MO4SgAmmxwB502eAvOkzQB76J9++MhXxl//fd8ZbzCl78uRJLuMKbxNULpejXC6P5b13dnZie3t7LO89SmdhHYHx0WOAvOkzQN70GSBvk9ZndnZ2chlXeHsG/N3f/d2hz7/zzjvxW7/1WxERMT09HTMzM6Moa+R2N4VJXUdgfPQYIG/6DJA3fQbI2yT3menp6VzGFd7uY3Z2Nnq93pGmDzhsXtxU/Mqv/Mqhz//oRz8a3L527VrMzc3lXdJY3L9/f3D7+vXrY6wEmER6DJA3fQbImz4D5G2S+0xeGeEruYz6kjvKvLL9YPckc9ACAAAAADyP8HYfV65ciYiIzc3NA5fpdDoRERN7lioAAAAAMF7C233Mz89HRESv1ztwmf5zlUplBBUBAAAAAGeN8HYf/UB2fX193+d7vV50Op0olUqjLAsAAAAAOEOEtweo1WrR6XQG0yPsdu/evYiIuHPnzqjLAgAAAADOiDMV3nY6ncF0B48ePTp02eXl5ahUKjE/Pz80fUK73Y5qtRq1Ws2ZtwAAAABAbs6Nu4C8NRqNuH37dvR6veh2u1EoFCIiYmFhIWZnZ6NQKMTNmzdjeXl5z2vX1tZidXU1FhYWolgsRrfbjV6vF2tra1Eul0e8JgAAAADAWTLx4W2lUnmhi4otLi7G4uLiKVYEAAAAAPB8Z2raBAAAAACAl4XwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASNC5cRfA6F26dGno/tOnTwe3Hz58GN1ud9QljdyDBw/GXQIwwfQYIG/6DJA3fQbI26T1mSdPnuQyrvCWITs7O7G9vT3uMnJ3FtYRGB89BsibPgPkTZ8B8jZpfWZnZyeXcYW3Z9Djx4+H7m9sbMTVq1cjImJ6ejpmZmbGUVbudjeFSV1HYHz0GCBv+gyQN30GyNsk95np6elcxhXeMuTatWsxNzc37jJycf/+/cHt69evj7ESYBLpMUDe9Bkgb/oMkLdJ7jOzs7O5jOuCZQAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQILOjbsARu/SpUtD958+fTq4/fDhw+h2u6MuaeQePHgw7hKACabHAHnTZ4C86TNA3iatzzx58iSXcYW3DNnZ2Ynt7e1xl5G7s7COwPjoMUDe9Bkgb/oMkLdJ6zM7Ozu5jCu8PYMeP348dH9jYyOuXr0aERHT09MxMzMzjrJyt7spTOo6AuOjxwB502eAvOkzQN4muc9MT0/nMq7wliHXrl2Lubm5cZeRi/v37w9uX79+fYyVAJNIjwHyps8AedNngLxNcp+ZnZ3NZVwXLAMAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAEnRt3AYzepUuXhu4/ffp0cPvhw4fR7XZHXdLIPXjwYNwlABNMjwHyps8AedNngLxNWp958uRJLuMKbxmys7MT29vb4y4jd2dhHYHx0WOAvOkzQN70GSBvk9ZndnZ2chlXeHsGPX78eOj+xsZGXL16NSIipqenY2ZmZhxl5W53U5jUdQTGR48B8qbPAHnTZ4C8TXKfmZ6ezmVc4S1Drl27FnNzc+MuIxf3798f3L5+/foYKwEmkR4D5E2fAfKmzwB5m+Q+Mzs7m8u4LlgGAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACTo37gIYvUuXLg3df/r06eD2w4cPo9vtjrqkkXvw4MG4SwAmmB4D5E2fAfKmzwB5m7Q+8+TJk1zGFd4yZGdnJ7a3t8ddRu7OwjoC46PHAHnTZ4C86TNA3iatz+zs7OQyrvD2DHr8+PHQ/Y2Njbh69WpERExPT8fMzMw4ysrd7qYwqesIjI8eA+RNnwHyps8AeZvkPjM9PZ3LuMJbhly7di3m5ubGXUYu7t+/P7h9/fr1MVYCTCI9BsibPgPkTZ8B8jbJfWZ2djaXcV2wDAAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASNC5cRfA6F26dGno/tOnTwe3Hz58GN1ud9QljdyDBw/GXQIwwfQYIG/6DJA3fQbI26T1mSdPnuQyrvCWITs7O7G9vT3uMnJ3FtYRGB89BsibPgPkTZ8B8jZpfWZnZyeXcYW3Z9Djx4+H7m9sbMTVq1cjImJ6ejpmZmbGUVbudjeFSV1HYHz0GCBv+gyQN30GyNsk95np6elcxhXeMuTatWsxNzc37jJycf/+/cHt69evj7ESYBLpMUDe9Bkgb/oMkLdJ7jOzs7O5jOuCZQAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACRLeAgAAAAAkSHgLAAAAAJAg4S0AAAAAQIKEtwAAAAAACTo37gIYvUuXLg3df/r06eD2w4cPo9vtjrqkkXvw4MG4SwAmmB4D5E2fAfKmzwB5m7Q+8+TJk1zGFd4yZGdnJ7a3t8ddRu7OwjoC46PHAHnTZ4C86TNA3iatz+zs7OQyrvD2DHr8+PHQ/Y2Njbh69WpERExPT8fMzMw4ysrd7qYwqesIjI8eA+RNnwHyps8AeZvkPjM9PZ3LuMJbhly7di3m5ubGXUYu7t+/P7h9/fr1MVYCTCI9BsibPgPkTZ8B8jbJfWZ2djaXcV2wDAAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJbAAAAAIAECW8BAAAAABIkvAUAAAAASJDwFgAAAAAgQcJb+P/bu4PQxu47D+A/TyaZods0skuZQlpKZNoeEtggJyWzkF1YbHIq9OCZU3vooWN2T0sXZHzZQy9FA9u75truIWNfSiE0SD0VmsBE3i7tHNIisUtbyLSNpSTd4CRk3h6yUu0ZybZkvae/7M8HQjyS/3/9DM9f630tPwEAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgi7OegCK9/TTTx/69/vvvz/4+LXXXou9vb2iRyrcq6++OusRgDNMxgB5kzNA3uQMkLezljNvvvlmLvsqbznkgw8+iP39/VmPkbvz8DUCsyNjgLzJGSBvcgbI21nLmQ8++CCXfZW359Ddu3cP/fvOnTvxta99LSIiLl26FJcvX57FWLk7GApn9WsEZkfGAHmTM0De5AyQt7OcM5cuXcplX+Uth1y9ejWef/75WY+Rix//+MeDj1966aUZTgKcRTIGyJucAfL03v5H0fzpK3FhIeJ+FvF3//CP8fjlR2c9FnDGnOXnM0tLS7ns6w3LAAAA4BzKsix+0f5z/NOPWvHs9xrx7oef3P7uhxHPfq8R//wfrfhF+8+RZdlsBwU4x7zyFgAAAM6ZX//hnfju7V/Gb+79Zej9H9/P4pVfvRWv/Oqt+MqVT8cPrj8bzzz5RMFTAuCVtwAAAHCO/Py3f4rr9ddGFrcP+s29v8T1+mvx89/+KefJAHiQ8hYAAADOiV//4Z3Y+GEr3v/w47HWvf/hx7Hxw1b8+g/v5DQZAMMobwEAAOAcyLIsvnv7l2MXt33vf/hx/Ovt/3INXIACKW8BAADgHHit8/aJL5Uwypv33ovXO3tTmgiA4yhvAQAA4Bz40ev/k9Q+ABxPeQsAAABn3Hv7H8Wrd+9NZa+f3n0r3tv/aCp7AXA05S0AAACccW+9sx8f35/OtWo/vp/FvXf3p7IXAEdT3gIAAMAZ978TvknZKH/5YLr7ATCc8hYAAADOuL957JGp7vfpS9PdD4DhlLcAAABwxn3+icvxyIWFqex18cJCXPnM5ansBcDRlLcAAABwxj1++dF46ekrU9nrpac/H49ffnQqewFwNOUtAAAAnAPffOFLSe0DwPGUtwAAAHAOXC1/Nr5y5dOn2uOrVx6PF8pLU5oIgOMobwEAAOAcWFhYiB9cfzY+NeGbl33qsUfi36//bSwsTOfauQAcT3kLAAAA58QzTz4R9W+tjF3gfuqxR6L+rZV45skncpoMgGGUtwAAAHCOvPjlz8XtjasnvoTCV688Hrc3rsaLX/5czpMB8KCLsx4AAAAAKNYzTz4Rr/7L38frnb344ev/Ha/evXfo/osXFuKlpz8f33zhS/FCecmlEgBmRHkLAAAA59DCwkJcXf5sXF3+bLy3/1E0f/pKRER85rGI//y3tXj88qMznhAAl00AAACAc+7xy4/Ghf9/ce2FhVDcAiRCeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACTo4qwHYPb29/cHH9+9e3eGk+Trj3/8Y1y4cCHu378fd+7cmfU4wBkjY4C8yRkgb3IGyNtZzpmDndrBru20lLdEu90efPztb397hpMAAAAAwHxrt9vx4osvTmUvl00AAAAAAEiQV94S3/jGNwYfLy8vx+XLl2c3TE7u3bsXX//61yMi4ic/+UlcuXJlxhMBZ4mMAfImZ4C8yRkgb2c9Z/b39wd/3X6wazuthSzLsqntBon6/e9/H1/84hcjIuJ3v/tdfOELX5jxRMBZImOAvMkZIG9yBsibnJmMyyYAAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAghayLMtmPQQAAAAAAId55S0AAAAAQIKUtwAAAAAACVLeAgAAAAAkSHkLAAAAAJAg5S0AAAAAQIKUtwAAAAAACVLeAgAAAAAkSHkLAAAAAJAg5S0AAAAAQIKUtwAAAAAACbo46wGYDzs7O1Gv1yMiolwuR0TExsZGVCqVqey/u7sb165di1arFaVSKbd5ilxX9Iww7/I69sfdt9PpxNraWmxsbMTq6upgTafTiTfeeCPq9Xpsb28Pbp/W1yFnIH+p5EzfzZs34+WXX45OpxNLS0tRqVSiVquNzJdZ5JOcgfGkljN9455vFZlPcgbGk1rOnGae3d3d+P73vz/ImoiItbW1qFarI9eMk0+zOrebugyOsb6+npXL5azb7Q5ua7fbWalUyur1+kR7drvdrNFoZPV6PatUKllEZBGRtdvt3OYpcl3RM8K8y+vYn2TfVqs1yKRh/9Vqtal/HXIG8pdSznS73axSqWTb29uD2xqNRlYul7OIyKrV6tB1ReeTnIHxpJYzk5xvFZ1PcgbGk1LOnHaearWalUqlQ3nT33NYZkyST7M4t8uD8pYj1Wq1kT/k6/V6FhFZq9Uae9/t7e1sfX09q1arg4P/JE8mJp2nyHVFzwjzLq9jf9J9R/2Ar1QqR84hZyBdqeXMgycefd1ud/CcaNj9ReaTnIHxpJYzk55vFZlPcgbGk1rOnGaearU69P7+unK5/NCaSfKp6HO7vChvOVKpVMoqlcrI+/sH/TQe5yRPJiadp8h1Rc8I8y6vY3/SfVutVra+vj54xUqr1Tr029ZpP56cgfyllDONRuPINf2TmVKp9NB9ReaTnIHxpJQzo/Y57nyr6HySMzCe1HJm0nXtdnvkK2W3t7eziMjW19cP3T5pPhV9bpcXb1jGSM1mM3q9Xjz33HMjP6dcLsfu7m70er1k5ylyXdEzwrzL69ifxr6lUilWV1ejUqkce204OQPpSi1ndnd3Y3d3NxYXF4euWVtbi4iIXq8XnU5n6OfknU9yBsaTWs5Mqsh8kjMwntRy5jTzbG5uRsQn14590Pr6enS73dje3j50+2nzqYhzuzwpbxmp0WhERMTy8vLIz+lfsLnZbCY7T5Hrip4R5l1ex37R31NyBtKVWs68/fbbETH65OLgG2bs7u6eeJ5pzilnYDyp5cykiswnOQPjSS1nJl3X6XRiZ2cnSqXSyDcJG1auzkM+5eliIY/CXDrJAd//phr1m9dpmnSeItcVPSPMu7yO/aK/p+QMpCu1nNnY2IhOpxPPP//8yHdF7ht1UjMOOQP5Sy1nJlVkPskZGE9qOTPpup2dnYiIWFpaGty3s7MTb7/9diwvL8f169eHlrfzkE95Ut4yUv8gPO4l5RF//S1Iniadp8h1Rc8I8y6vY38a+3Y6najVaoOP9/b2YmtrK9bX16f2eHIG8pdazpTL5Yf+FPCggycMlUpl5GPnmU9yBsaTWs5Mqsh8kjMwntRyZtJ17XZ7sG5nZyfu3LkTW1tbERFx+/bteOqpp+JnP/vZQxlz2nwq4twuT8pbRtrb2zv2cw7+tiRvk85T5LqiZ4R5l9exf9p9m81m1Gq1qNfrg9t2d3djZWUlqtXq4Af/aR9PzkD+Us2ZUfq5U61Wh95fRD7JGRjPvOXMpKaZT3IGxpNazky67uDHjUbjUF7cuHEjWq1WrKysRKvVGvlLomGOyqeizu3y5Jq3HKt/UKZi0nmKXFf0jDDv8jr2J9m3XC7H1tbWoR/uEZ/8BvfGjRtx8+bNwZ/7TOPxJl0nZ2A8KeXMKLdu3YpOpxPlcvmhE4mI4vNJzsB45iFnJpVXPskZGE9qOTPuuoOXaOq/cdlB/du+853vnHjPo/JpFud2eVDeMlJKB2qE0hbOotSefER88ucxo15Rcu3atYiIh55oyBlIV4o5M0yn04mNjY0ol8vRarWGfk5R+SRnYDzzkjOTyiOf5AyMJ7WcmXRd/1IE5XJ56LVp+7ft7u6e6Nqzx+VTked2eVLeMlL/m2qcl4znadJ5ilxX9Iww7/I69vPat/9kotPpHPoTGTkD6ZqXnLl27drgxOMk11h70DTzSc7AeOYlZyaVRz7JGRhPajkz6br+x0e9qVh/7zfeeOPYvU+TT9M+t8uT8paR+gdhr9cb+Tn9g3mSH+JFzVPkuqJnhHmX17F/mn2bzebIdQd/OB/8TbCcgXSlmDMP2tjYiF6vd+yJR1H5JGdgPPOQM5PKK5/kDIwntZyZdN1Rpe2De496pX/fSfKpyHO7PClvGan/TXXUu+f1D+a1tbVk5ylyXdEzwrzL69ifdN9bt27F2tpaPPXUU8c+xrAnIXIG0pNazjzo5s2b0Ww2jy1GiswnOQPjST1nJpVnPskZGE9qOTPpupPM1i9Gl5eXR37OSfKp6HO7PClvGal/EB717nn9l7E/99xzyc5T5LqiZ4R5l9exP+m+7XY7Ikb/+cvBP52RMzAfUsuZg3Z2dqJerw898djZ2Ylmszn4d5H5JGdgPCnnzKTyzic5A+NJLWcmXbe6unrsun4xWqlUht5/0nwq+twuVxmM0O12s4jIyuXykfdXKpVTP1apVMoiImu321Ofp8h1Rc8I8y6vY3/Sfbe3t7MbN26M3Hd7e1vOwJxJLWf6Wq1WVqlUsm63O/T+arV66HlRkfkkZ2A8qebMQSc53+orIp/kDIwntZw5zTyVSiWLiKEZ0263s4jISqXS0H3Hyaeiz+3ypLzlSLVaLYuIbHt7+6H7qtVqFhFZq9V66L5Wq5WVSqVsdXX1RI9z0icTk85T5LqiZ4R5l1fOTLrv6urqyCcD/Scaw7JKzkC6UsuZdrudVSqVrNVqZe12+6H/Go3G0JOWIvNJzsB4UsuZB530fKvIfJIzMJ7UcmbSdY1GI4uIrFarjbXnJPlU9LldXpS3HGt9fT0rl8uHDvhWq5VFRFav14eu6R/MJzmg+3sdtd9p5yl6XdEzwrzLK2cm2bfVamWrq6sP7bm+vp6VSqWs0WhM9euYdJ2cgfGkkjPdbjcrl8uDfUf9N+zVHkXnk5yB8aSSMw866fnWLPJJzsB4UsuZSdf1ZzpYjvbXDSt1J82nWZzb5WEhy7Is4Bg7Ozvx8ssvR8Qn1wvZ29uLra2tkdcg6XQ6sba2FuVyORqNxtD9Njc3Y29v76F38CuVSrG0tBQbGxtRrVanMs8s1hU9I8y7aefMpPtGfHKdpc3NzUPXOapUKrG1tXXsO4rKGUhXCjmzubkZN2/ePHbW1dXVoY9ZdD7JGRhPCjnT//xxz7dmlU9yBsaTSs6cdl2z2YzNzc3o9XqDjKjVaoPr4h50mnyaxbndtClvAQAAAAASdGHWAwAAAAAA8DDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAAAAACRIeQsAAAAAkCDlLQAAAABAgpS3AAAAAAAJUt4CAEAier1erK2txcrKSiwuLsby8vKsRwIAYIaUtwAAkIhSqRS1Wi1WV1ej1+vF3t7erEcCAGCGFrIsy2Y9BAAAcNjCwkKUSqXodruzHgUAgBnxylsAAAAAgAQpbwEAAAAAEqS8BQAAAABIkPIWAAAAACBBF2c9AAAAcLRmsxn1ej0iInq9XkRE1Gq1qFQqM5wKAIC8KW8BACBht27dil6vF9vb24PbVlZWYmVlJbrdbpRKpdkNBwBArlw2AQAAEtXr9aLVakW1Wj10++rqakRE3L59exZjAQBQEOUtAAAkbGNj46HblpeXIyKi3W4XPQ4AAAVS3gIAQMKGXdd2aWkpIv56/VsAAM4m5S0AAAAAQIKUtwAAAAAACVLeAgAAAAAkSHkLAAAAAJAg5S0AAAAAQIKUtwAAkJherzf0475Op3Po/wAAnE3KWwAASESv14vl5eVYXFwc3La4uBjLy8vR6/Xi1q1bsbi4GJubmxER0Ww2Y3FxMa5duzarkQEAyNFClmXZrIcAAAAAAOAwr7wFAAAAAEiQ8hYAAAAAIEHKWwAAAACABClvAQAAAAASpLwFAAAAAEiQ8hYAAAAAIEHKWwAAAACABClvAQAAAAASpLwFAAAAAEiQ8hYAAAAAIEHKWwAAAACABClvAQAAAAASpLwFAAAAAEiQ8hYAAAAAIEHKWwAAAACABClvAQAAAAASpLwFAAAAAEiQ8hYAAAAAIEHKWwAAAACABClvAQAAAAASpLwFAAAAAEiQ8hYAAAAAIEHKWwAAAACABClvAQAAAAAS9H+7ZylMMAfK8gAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1600x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax2 = ax1.twiny()\n",
    "x = np.arange(len(Ns))\n",
    "ax1.plot(x, error, 'o')\n",
    "plt.title(\"Mid point integration of circle\")\n",
    "ax1.set_yscale(\"log\")\n",
    "ax1.set_ylabel(\"error\")\n",
    "\n",
    "hs = 2/Ns\n",
    "ax1.set_xticks(x)\n",
    "ax1.set_xlabel(\"h\")\n",
    "ax1.set_xticklabels([f\"{x:f}\" for x in hs])\n",
    "\n",
    "ax2.set_xlim(ax1.get_xlim())\n",
    "ax2.set_xticks(x)\n",
    "ax2.set_xlabel(\"N - number of points\")\n",
    "ax2.set_xticklabels([x**2 for x in Ns])\n",
    "None"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $10^5$ points integration error is approximately $10^{-3}$\n",
    "\n",
    "Last value is $\\pi \\approx 3.1426$\n",
    "\n",
    "Monte Carlo need 10 times more computations for the same precision. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Same midpoint plot with more points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ns = np.array([2**i for i in range(1, 8)])*10\n",
    "pis = np.array([integrate(f, H, [-1, 1], [-1, 1], N, N) for N in Ns])\n",
    "error = np.abs(pis-np.pi)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax2 = ax1.twiny()\n",
    "x = np.arange(len(Ns))\n",
    "ax1.plot(x, error, 'o')\n",
    "plt.title(\"Mid point integration of circle\")\n",
    "ax1.set_yscale(\"log\")\n",
    "ax1.set_ylabel(\"error\")\n",
    "\n",
    "hs = 2/Ns\n",
    "ax1.set_xticks(x)\n",
    "ax1.set_xlabel(\"h\")\n",
    "ax1.set_xticklabels([f\"{x:f}\" for x in hs])\n",
    "\n",
    "ax2.set_xlim(ax1.get_xlim())\n",
    "ax2.set_xticks(x)\n",
    "ax2.set_xlabel(\"N - number of points\")\n",
    "ax2.set_xticklabels([x**2 for x in Ns])\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "LabaEnv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}