264 lines
82 KiB
Plaintext
264 lines
82 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "fda98006",
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"metadata": {},
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"source": [
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"# Solution of second-order linear ordinary differential equation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 135,
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"id": "7fced95c",
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"metadata": {},
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"outputs": [],
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"source": [
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"def write_to_file(name: str, array):\n",
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" with open(f\"{name}\", 'w') as file:\n",
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" for element in array:\n",
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" file.write(f\"{element} \")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 136,
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"id": "d20bde93",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8af07a56",
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"metadata": {},
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"source": [
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"## Solution of $5u'' + 4u' + 1 = 0, u'(0) = u(0), u(10) = 5$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 137,
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"id": "d0fe0703",
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"metadata": {},
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"outputs": [],
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"source": [
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"def u(x):\n",
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" return (9 * np.exp(8) * (x - 30) + 155 * np.exp(8 - 4 * x / 5) - 5 * (x + 1)) / (20 - 36 * np.exp(8))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "efac514a",
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"metadata": {},
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"source": [
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"## Linear element"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 138,
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"id": "18bd929b",
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"metadata": {},
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"outputs": [],
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"source": [
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"def show_plot_linear(filename: str, elements: int):\n",
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" with open(filename, 'r') as file:\n",
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" data_str = file.read()\n",
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"\n",
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" x = np.linspace(0, 10, elements + 1)\n",
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" y = np.fromstring(data_str, sep=' ')\n",
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" y_real = u(x)\n",
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"\n",
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" plt.plot(x, y, label=\"Linear element solution\", color='red')\n",
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" plt.plot(x, y_real, label=\"Numeral solution\", color='black')\n",
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" plt.title(f\"Linear element, elements = {elements}\")\n",
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" plt.grid(True)\n",
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" plt.xlabel(\"X\")\n",
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" plt.ylabel(\"Y\")\n",
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" plt.legend()\n",
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" plt.savefig(f\"linear_{elements}.png\", dpi=300)\n",
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" plt.show()\n",
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"\n",
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" write_to_file(f\"linear_real_y_{elements}.txt\", y_real)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d9a38740",
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"metadata": {},
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"source": [
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"## Cubic element"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 139,
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"id": "73525bc7",
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"metadata": {},
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"outputs": [],
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"source": [
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"def show_plot_cubic(filename: str, elements: int):\n",
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" with open(filename, 'r') as file:\n",
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" data_str = file.read()\n",
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"\n",
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" x = np.linspace(0, 10, 3 * elements + 1)\n",
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" y = np.fromstring(data_str, sep=' ')\n",
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" y_real = u(x)\n",
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"\n",
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" plt.plot(x, y, label=\"Cubic element solution\", color=\"green\")\n",
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" plt.plot(x, y_real, label=\"Numeral solution\", color='black')\n",
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" plt.title(f\"Cubic element, elements = {elements} \")\n",
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" plt.xlabel(\"X\")\n",
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" plt.ylabel(\"Y\")\n",
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" plt.grid(True)\n",
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" plt.legend()\n",
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" plt.savefig(f\"cubic_{elements}.png\", dpi=300)\n",
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" plt.show()\n",
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"\n",
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" write_to_file(f\"cubic_real_y_{elements}.txt\", y_real)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3584baa4",
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"metadata": {},
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"source": [
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"## Main part"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 140,
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"id": "b8a772e3",
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"metadata": {},
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"outputs": [
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{
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"data": {
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uMLghIiIiu8LghoiIiOyKw03iJ2u23LhxQ01iZaop4YmIiMi8ZPyTzEot64fJhKTvOlhT165d07Vo0UJNHCWTMfn7+78xwZUxw+RYMbebN2/G6/lkAre3TfDGjRs3bty4cYPVbnIdfxdNW26Cg4PVlOyVK1dWq9/KPBUyhb1MWf8uZ8+eVVPFG6+3Ex+GFWZl5Vnjx5vCixcv1Iq6hun4yTxYz5bBerYM1rPlsK5tu55lPitfX983VoqPjabBzejRo1VBZ8+eHbVPVsGNDwlmZJ2UhDJ0RUlgY47gxtPTU52X/3HMh/VsGaxny2A9Ww7r2j7qOT4pJZoGN7J4Xc2aNdWCbdu2bVML+HXq1EktSPcuhQsXVivW+vv7qwXzpAUoNnKM8cq2EvkZKl82UzKcz9TnpehYz5bBerYM1rPlsK5tu54Tcj5NZyj28PBQP3v06KECnAMHDqgVm2XVWllJOa7uqK1bt6rVhCVokRWOZQXbffv2oWjRom8cb1gpOKb58+eryJKIiIis35MnT9C8eXOEhIS8s+dF0+DGzc1NBSm7d++O2telSxcV5OzZsyfe55Fl7zNnzqyCnPi03EhX2L1798zSLbVhwwZUr16dTZ5mxHq2DNazZbCeLYd1bdv1LNfv1KlTxyu40bRbKkOGDMiXL1+0fbLo3ZIlSxK8GvDOnTtjvc/d3V1tMUmFm+vDbc5z02usZ8tgPVsG69lyWNe2Wc8JOZemk/hJnox0Mxk7d+4csmTJkqDzyErAEigRERERadpy0717d5QtWxYjRoxAkyZNsH//fsyYMUNtBn379sX169fx559/qtsTJ05UI6ry58+P8PBwlXOzefNmNeyMiIiISNPgpkSJEli2bJkKYIYMGaKCFgleWrRoEXXMzZs3ERQUFHX7+fPn6Nmzpwp4JCG4YMGC2Lhxo5orh4iIiEjz5Rc+/vhjtcVlzpw50W736dNHbURERESx4cKZREREZFcY3BAREZFdYXBDREREdoXBDREREdkVzROKiejdIiMj8fLlS7XJ7J+G32WT+9KnT89JyYiIXmFwQ2RG9+/fV3MwrV27FhcuXIg1OIm5xXb/u1ZJkcAmd+7casZvmeVbfsom+2KboZuIyJ4xuCEyIWlFOXjwINasWaM2mZjSnMu3Gf4DS0B06tQptRlzcXFBjuzZkS9//qiAR7Y8efJw4VgislsMbog+kCzCum7dOhXMyE+5bayAtzdqPX2Kkk+fwv3Vf7q4tkQJuF8S5pwkoHJxwbWICJwG3thCIiJw7vx5tS1fvjyqTE5OTsjm64t8BQpEC3zy5s0LLy8vDWqRiMh0GNwQJVBERES01hlZxd64dcbL0xPV06dH7bt3USssDJkePHj94CRJgKRJY98kqIjrvri2JEng7OKCzLdvI/P586h1/jwg27lz0J07h5uBgTgdHv5G0HNfp8PFoCC1rVy1Ktrry5w2rT7QKVQI8qqKFCmCzJkzW7KKiYg+CIMboni4c+dOVOuM5NBILo2xgjlyoHby5Kh9+TLKPniARBcv6u9ImRJo2BBo0gSQJULMlfSbPr1+q1Ahape06vhERsLnxg1UMwp65OfdM2dw+tIlnH75MlrQcwtA0J07alu7das6z6RJk1A4Z07UbtAAtT/5BGXKlIGrK/90EJH14l8oojhaZyRfxtA6c+jQoWitM8mTJ0f1IkVQ28UFNU+cQMYLF14/OEUKoEEDfUBTtar5Apr4cHYGMmXSb0brr6UBUDEiAhWvXtUHPa8CnwenTuFMQABO37iBU5GR2A3gIICjgYE4OnYsRo4di+QeHqhWoQJqN2mCWrVrI2PGjNq9PiKiWDC4IXrl2bNnWLRoEVatWqVaZx4YdycBKFy4MGoXKIDa4eEovWsXEr1q2VCSJwfq19cHNNWqAW5usHouLkDWrPqtenW1yxtAOdlevMCL8+dxbNYsZLp6FRs3bMCakBCsky6t8HAs2bBBbaJg5syoXa8eajdqhLJly3JIOhFpjsENEYBjx47h888/x4kTJ6L2pUiRAtWrV0ft3LlR684dZFizBpg79/WDkiWLHtDY05BrCVBy5cL1ihVRqE4dtHR1RcuTJxGxdi0OLl6MNYcOYU1EBA4AOB4UhONTpmD0lClI5u6OaiVLonbz5qj18cfIJC1GREQWxuCGHJrMITN27FgMHDhQDadOnTo1vuzQAbWzZkXpgAC4LlkCLFr0+gGS9Fuvnj6gqVHDvgKat3FyAgoUgEuBAijVuzdKPX2KQTt34u7y5Vj/339Yc/WqatW59+wZlu7YoTZ8/TX8M2RA7dq1UbtFC5QrXx5uttCiRUQ2j8ENOazz58+jVatW2Lt3r7pdr3ZtTM+eHenmzweuXHl9oIxK+vRTfUBTsybg4aFdoa1F4sSqKytN9epo8fPPaHHzJiLXr8ehBQuwZscOrHn8GPsAnLx5Eyd//x1jf/8dXokSoap07TVtitqNG8PX11frV0FEdoprS5HDkcTgX375ReXQSGCTLFkyzOnfH8uOH0e6n3/WBzYyZLtpU2DpUhkqBcybp2+xYWATuwwZ4Ny6NUqsWYMfQ0Ox5+hR3B04EPP9/fG5s7NKYA578QLLDxxAx5491dDyEpkyYcqgQbh7967WpSciO8PghhzKtWvXULNmTXTu3BlPnjxBlSpVcKJ7d7QeNQpO168DuXMDixfrA5q//9aPepJWCkrYCK1ChZBq0CA0O3ECf4aF4dbq1TjQvDmGpE2LMq/+8By8fh1dBg+GT7p0+LRQISyeMwfh4eFal56I7ACDG3KY1pq//voL/v7+2LBhAzw8PDB5zBhsSJUKmQcPluQboHFj4OBBoFEjgEsTmI6nJ5xr10bxefMw4PZt7L52DTfHj8ekXLlQXPKedDr8d/w4Grdpg/TJkqFjjRrYuXmzWZetICL7xuCG7J50ezRu3FiNhgoJCUHJkiVxdNEifPvbb3CWZGGZkG7iROCff/QJw2ReGTMibY8e6HLuHA5cvYpTPXvi+zRpIOOqQl68wIwNG1ChalXkTJ4cg9q0wQWZg4eIKAEY3JBd+/fff1VrzZIlS9SsukOHDsWuzp2R57PPgLNn1YUW27cDXbvqRwSRZWXKhHzjxmHknTu4cuQINn32Gb7w9ERSABfDwjB4zhzkzJ0b5TJlwvRBgxAcHKx1iYnIBjC4IbsUGhqKtm3bol69emrphPz582P/zp3of+MGXFu3Bp480c9Nc+QIUEayQEhrzoULo8qCBZgtOTqrVmFexYqo6eKi/kjtvn4dXw0ejPSpUuF/hQphxezZeP78udZFJiIrxeCG7M7WrVtRsGBBzJ49W61+3bt3bxxcsgRFvv0WmDZNf9CAAcDatUAaGcdDVsXZGUnq1EHzrVuxNiwM16ZPx7h8+VAQwHOdDkuOH0f9tm3hkzQpvqlWDfu3bGF+DhFFw+CG7MbTp0/RvXt3VK5cGVeuXEG2bNmwbds2jKlUCR7SOnPgAODtDaxeDQwZol9+gKxb4sTI8OWX6HnqFI7du4ej/fqhp48P0ssyEC9e4OdNm1CqShX4JU+O4a1a4UpgoNYlJiIrwOCG7MKBAwdQtGhRTJTEYABffvkljh0+jArr1gF16wKSq1GiBHD4MFC7ttbFpfeRKhUKDRuGcdev4+rZs1jbqhVaeHlBBuqfDQtD/7lzkTVXLlTOlAkLx49XM04TkWNicEM2TS5ggwYNQpkyZRAQEIAMGTJg9erVmD50KLz+9z9g+HD9gZ06AbIkQJYsWheZTMA1d27U/OMP/BUSgttbt2J29eqokigRJCV86/Xr+KxXL2RJmhSDGjfGDePZponIITC4IZt1+vRpFdQMHjwYERERaNq0KU6ePInaskJ30aLApk36+WpkdmGZedhR1oFyJE5O8KpYEV+sX49NT57g8pw5GJg3r+q2uvn8OQYvXowsWbOiqb8/dixdytwcIgfB4IZsTmRkJFasWIFSpUrh0KFD8Pb2xoIFC/D3/Pnw/vNPoGJFQGYbzptXn2fTvLnWRSZLcHVF5tatMejMGVy5cAF/N2iA8okS4SWAf06dwkeNGqFwypSY0bMnHj96pHVpiciMGNyQTXn27Bk++eQTNRJKfq9Tp45qrflM8mhkYcvu3fWzDcs8Nvv3A/nyaV1k0oBb9uxounQpdjx6hKOjR6ND+vQqN+d4SAg6/vQTMiZPju5VquC8TAVARHaHwQ3ZlB49ekQtnzBt2jSsXLkSGe7d0ycLy5pQiRIBU6bo14XibMPk5oZCffpgxs2buL5zJ34qWxY5nJwQEhmJiVu2IHfRoqiVOTP+mzpVdW0SkX1gcEM2Y+7cuWo1b8PcNe3atYPTX38BpUoB584Bvr762Ya/+YazDdMbUpYrh+67duHcgwdY8/XXqJs0qUpAXnf1Kj799lvkTJIEY1q0wP2bN7UuKhF9IAY3ZBOOHTuGjh07qt/79euHEgUKwLlzZ6BVK5ngBqhRQz/Mu3RprYtKVs45RQrU+uUXrAwNReBff6FX7txICeDys2f4bv58ZPLxQZvChXFI5kMiIpvE4Ias3sOHD9GoUSM1SV/t2rXRv0ULVOjbFy4zZ+pbaAYO1E/Mlzq11kUlW+LkhOwtWmDs2bO4dv48fvv0UxRxdUU4gDnHjqF43boo7e2Nv/r2xbNw2UtEtoLBDVn9yKhWrVrhwoULyJo1K/4aPx5ulSohxYUL0KVKBaxZAwwaxNmG6YN45syJtitW4NDjx9g9dChapE2LRAD2BQfj81Gj4Js0KX6oUQNXT53SuqhEFA8MbsiqjRw5Ev/99x/c3d2xZPFiePfoAafbtxHq64uX+/YBNWtqXUSyI05ubijTvz/+un0bV7dswdCSJZHRyQl3IyIwcsMGZPf3x+f58uGYzHxNRFaLwQ1ZrfXr12OALHAJqETionv2qMUudR4eONi7N5A5s9ZFJDuWrlIl9N+3D5fv3cOSDh1Q0dNTzZnz15kzKFyrFmr6+GDjr79yYkAiK8TghqySLHzZvHlzdeFo37492kqisAQ00lU1ciTCGNiQhbh6e6PhjBnYGhaGAxMnoknatOoP5/qbN1H9669RNFkyzPv+e7x4/lzrohKRtQQ3169fR8uWLZEqVSokTpwYBQoUwMGDB9/6mK1bt6pFEqWrImfOnJgzZ47FykvmFx4ejv/973+4f/8+ihUrhinjxgEtWsgdQK1aiJR1oogszdkZxbt2xT+3b+P88uX4NlcueAI4+ugRWo4ejZxJk2JC8+YIu39f65ISOTxNg5vg4GCUK1cOiRIlwpo1a9RaQePHj0fKlDIwM3aXLl1C3bp1UblyZRw9ehTdunVT3+zXsQ/cbnTt2lUFuLKswpIlS+AxYgRw9Kh+NNTvv3MOG9Jc9nr1MPncOQQdPoyhZcogLYCgFy/Q4++/4ZsmDb6vXBk3AgK0LiaRw9I0uBk9ejR8fX3VVPolS5ZEtmzZUKNGDeTIkSPOx/z666/qOAmC/Pz88M0336hv+RMmTLBo2ck85LMwY8YMNVHf/PnzkeXSJWDsWP2dMvQ7Qwati0gUJVWRIui/ezeu3LiBGQ0bIreLC0J0OozeuhVZ/fzQ1t8fpzdu1LqYRA5H0+Dm33//RfHixdG4cWOkTZsWRYoUwUy5gL3Fnj17UK1atWj7atasqfaTbTty5Ag6vepykpW+a5YsCXz+OSAJm+3bA/Xra11Eolh5ZMiADkuW4ExYGJZ/+y3KeXrihQTrp04hf/Xq+DhjRmybNYvJx0QW4goNXbx4Ua0PJOsF/fDDDzhw4AC6dOkCNzc3tG7dOtbH3Lp1C+nSpYu2T26HhoaqSd4kb8eYLK4om4EcJ168eKE2UzKcz9TndQQPHjxQE/VJvo0shtmnd29Etm4N52vXoMuZEy/HjJGKVceyni2D9fweXF1RZ/x41Bk3DnsnTcKEsWOx/O5drLpxA6s6dECJHj3Q/euvUX/gQLjKOmisZ4tiXdt2PSfkfE46Db9KSBAjLTe7d++O2ifBjQQ5cbXE5M6dG23atEHfvn2j9q1evVrl4Tx58uSN4GbQoEGqFSAm6fLw9JR0QLKGifqGDx+OQ4cOqUBVuhzzHjqEYhMmINLZGTtHjUJw7txaF5PovYTt3Yt1f/yBxTdvqtmPRRYXF3xWvjyKtW8Pdy7wShQvco2XUbQhISFIliyZ9bbcZMiQAfny5Yu2T/JoJIk0LunTp8ft27ej7ZPb8kJjBjZCgiBpGTJuuZE8H8nteVflvE9UKStWV69eXSVJU/wMGzZMBTay0rdM2Fc4RQq4vuqe0g0YgDLdukU7nvVsGaxnE6lTB58NGYJRR47g12+/xbT9+3ElIgJjtm2D9/bt6PjRR8jfpAkafPEF69nM+Jm27Xo29LzEh6bBjYyUOnv2bLR9586dQ5YsWeJ8TJkyZVRLjTGpRNkfGxkuLltMUuHm+nCb89z2Zu3atRg6dGhUsniJokWBypXlUwyULQuX/v3h4hr7x5T1bBmsZ9PIWLIkhu7bh743bmBO584Y/99/uCgzH2/bBvdt27Brxgx8N3MmspQooXVR7R4/07ZZzwk5l6YJxd27d8fevXsxYsQIBAYGqq4iGSnTWVZ7Nmp5kbWFDL766iuVq9OnTx8EBASomWsXLlyozkW2RYb1GybqkxW/VZ6V5Nbs2AFIU/3cuSqHgcieePr4oNOyZTgXFoZFnTujZOLEkKzAaceOIWfJkmjj54dzW7ZoXUwim6ZpcFOiRAksW7YMf//9N/z9/dU3+IkTJ6KFTNj2ys2bNxEUFBR1W4aBr1q1SrXWFCpUSOVnzJo1S42YItubqE/mOpLPwaRJk4BDh4Aff9QfMGUKkD271sUkMhuXxInxv6lTsSM4GFNbtkTVZMnU8g5zAgKQt0oVfJYtG46tWKF1MYlskuZfiz/++GO1xSW22YcrVaqkhg2T7ZL5iQ4fPqxmpl68eDHcIyL0sxC/fAn873+AUWsdkT1zcnZGpv/9D2t++w2HZ83C8IED8d+9e1h4+TIW1q+PjzNkQL9Ro1Ca/yeIbGf5BXI80tL222+/wdnZGQsWLEBmWSeqVy9A8q98fIDp0zkLMTkeJyeU6tQJ/969i2Nz5+IzHx/I/4KVN2+iTOvWqJo6NTZPmcK5cojigcENWZQsqyCtNkK6IdWEjCtXAtOm6Q/44w/A21vbQhJprGDLllhw/ToC/v0XbbJlU03sm+/fR9UuXVA2RQqsHDYMushIrYtJZLUY3JDFyEKYkmcjkyp++umn+P7772UcP9C2rf4AGbIfY/ZpIkeW+5NP8PvFiwjcsgWd/fwg4z73hobikwEDUMTLCwt790YEJ6QjegODG7KIiIgIlSh+5coVtXbYH3/8AWfpemrXDrh7FyhQABg+XOtiElmlLJUqYerp07h88CB6Fy2KpACOPXmCz8aNQ/6kSTHnq6/wItwwRSARMbghi5BZomXldplocenSpUiRIoVMbAOsWiWTEQHz5gEeHloXk8iqpS9WDGMOHcKVgAAMLFcOKQGcff4cbaZPRy4vL/zSogXCEzDRGZG9YnBDZrdy5cqoifpkHqOCBQsCAQFAz576A0aN0rfcEFG8eOfJg0E7d+JKUBBG16iBtE5OuPLyJTrPn49sKVNiXP36eHTnjtbFJNIMgxsyK5lw8XNZ2RtQK363bNkSeP5cP+z76VOgenVZUEzrYhLZJC9fX/RZtw6Xb9/G5AYN4OvigluRkei9YgWypE+PIdWqIfjKFa2LSWRxDG7IrIucNWzYEA8fPkTp0qUxYcIE/R2DBgGHD+tHRck8Rs78GBJ9iMRp0uDbpUsRGByM3z7/HDldXfFAp8PATZuQNWtWDKhYEQ8uXdK6mEQWw6sKmYXMxSEtNceOHUOaNGmwaNEitQo8tm/Xd0OJmTP189oQkUm4eXmh7Z9/IuDRI/zdqRP83d0hGTjDtm9H1uzZ0a9CBdy/eFHrYhKZHYMbMou5c+fqR0S9mqgvU6ZMQEgIIF1UMgmZDP9u2FDrYhLZJRd3dzT9+WccCwvD4u7dUdDdHWEARuzciaw5cuCH8uVx7/x5rYtJZDYMbsjkXr58qUZHCflZpUoV/R2yIKqsE5YjBzBxoraFJHIAzokSodFPP+HIo0dY2qsXCnt44BGAkbt2IWvu3Pi+bFnclZnBiewMgxsyORnqLYnEsm5UD5mYT/z9t364t4sL8Ndf+lW/icginF1d0WDsWBx+9AjL+/RBEQ8PPAYwes8eZMubF9+VKYO7MoKRyE4wuCGT59qMGTNG/S7LLHh6eupba77+Wn9A//5A6dLaFpLIQTm5uKDe6NE49OgRVnz/PYomTqyCnDF79yKrnx96lyqFO2fOaF1Mog/G4IZMasuWLTh06JCarK+zdEPJat+ymrHk25QqpQ9uiEjzIOfTkSNx8NEj/NevH4p7euIJgHH79yNbvnzoVbIkbp86pXUxid4bgxsyqbFjx6qfbdu2VaOkMH48sG0bkCSJvjvKVZYAJCJr4OTsjI+HDcP+sDCsGjAAJV4FOeMPHEA2f3/0KF4ct06c0LqYRAnG4IZM5vjx41i7dq0aIaVybY4ced1SM3kykDOn1kUkojiCnDpDhmBfWBhWDxyIUkmS4CmACYcOIVvBguherBhuHjumdTGJ4o3BDZm81UZW/s6ePr1+FmJZsViGfLdpo3XxiCgeQU7tQYOwJzQUa4cMQZmkSSHLcU48fBjZCxdG1yJFcEO+tBBZOQY3ZBJBQUFqPhvRu3dv/UR9kpiYIYMsKAXICuBEZDNBTs0BA7ArJATrhw9H2VdBzuSjR5G9aFF0KVwY1w8d0rqYRHFicEMmMXHiRDW/TeXKlVHc3x+YNu11d1SqVFoXj4jeM8ip/sMP2BkSgg0jR6K8lxeeAZhy7BhyFC+ugpybR49qXUyiNzC4oQ8WHBysVvsWffr0ARYtAu7dA3x9gfr1tS4eEZkgyKn2/ffY/vAhNo0Zg4+SJYsKcrIXKYIexYrh9smTWheTKAqDG/pgv/76Kx4/fowCBQqgZs2awM8/6+/46iuOjiKysyCnSu/e2BocrIKcsl5eqrtqwuHDyFagAPqUKsXJAMkqMLihDxIeHo5JkyZF5do4yWrf+/YBskhm+/ZaF4+IzBjk7Hz4EOuGDYsaXTVW5snx88MP5crhfmCg1sUkB8bghj54gczbt2/D19cXTZs2fd1q07gxkDat1sUjIjMHOTX69VOjq1YNHIhir2Y8Hrl7N7LlyoUfP/oID69c0bqY5IAY3NB7i4yMxLhx49Tv3bt3R6LQUP0aUkJmJyYix5knZ9AgHJBlHfr2RSEPD7UK+dAdO5A1a1YMrVoVodeuaV1MciAMbui9/fvvvzh37hySJ0+O9tIFNXu29FMBRYpw/SgiBw1yPh0xAofDwrCkVy/4u7sjBMCPmzcja+bMGFGzJsJu3NC6mOQAGNzQezMskNmpUyd4yQKZhuHf0mrDeW2IHHoV8oZjx+LYo0f4p2tX+Lm5IVinQ7/165EtUyaMqVsXj+/c0bqYZMcY3NB72bVrF/bs2QM3Nzd06dIFWLsWuHgRSJkSaNZM6+IRkZUEOU0mTsSJsDDM69QJuRIlwn2dDt+tXq1mMf+pXj08uX9f62KSHWJwQx/UatOqVSukl6UWDInEssyCtOIQEb3i4uaG5j//jNOhoZjTvj2yu7rijk6Hnv/+ixxp02Jyo0YIf/hQ62KSHWFwQwl25swZlW/j5OSEXr16ARcu6FtuxNdfa108IrJSrh4eaD1zJgJCQjCrdWtkcXHBrchIdF26FDlTpcIvTZvimQxMIPpADG4owcaPH69+1qtXD3ny5NHn2uh0QK1aXPmbiN4pkacn2s2Zg3MPH+LX5s2RycUF1yMj0fmff5DL2xszWrbEiydPtC4m2TAGN5QgN27cUHPbRC2QKX+Afv9df+c332hbOCKyKW5Jk6LjvHkIfPAAUxs3ho+zM65GRKh9eZMnx59ffomI58+1LibZIAY3lCCTJ0/G8+fPUa5cOZQtWxaQlcCDg4Fs2fQtN0RECeSeLBk6L1yIwLt3MbFBA6R1csLFly9VF5a/lxcWduuGyJcvtS4m2RAGNxRvoaGhah2pqAUypSvKkEgsuTYuLtoWkIhsWmJvb5V/c/HWLYyqVQveTk4IeP4cn02ahCJeXvi3Xz/oIiO1LibZAAY3FG8zZ85ESEgI8ubNi48//li/hpSsJeXhAbRtq3XxiMhOJEmbFt+tWYNLQUEYXLkykgE4Hh6OeiNGoJSXF9YNH84gh96KwQ3Fi3RFTZgwQf0uI6ScnZ1ft9rImlKpUmlbQCKyO8kyZVKzG18KDETfMmUgk0wcePIEtfr3x0cpU2Lbq0V7iWJicEPxsmDBAly/fl3NadOyZUtAZhdduFB/J9eRIiIz8s6RAyN278alkyfRvWhRuAPYGRqKSt26oXqqVNg7a5bWRSQrw+CG3kmn00VN2tetWze4u7sDv/0mzTlAyZJA8eJaF5GIHEDa/Pnx06FDuHDgAL7Onx+JAGx88ABlOnTAJ+nS4Yhh4V5yeJoGN4MGDVITwRlvks8Rlzlz5rxxvIfke5BZrVmzBqdOnUJSGbbZsSMQEQG8Sixmqw0RWVrG4sXxy8mTOLt9O9rkyqUuZCvv3EHR5s3xv0yZcGrFCq2LSI7ecpM/f37cvHkzatu5c+dbj0+WLFm0469cuWKxsjqqsWPHqp8S2KRIkQJYuRIICgJSpwaaNNG6eETkoLJVqIDfz53DmbVr0TxLFshyvUuuX0eB+vXRMls2nN+wQesikqMGN66uriqPw7CllgvmW0hrjfHx6dKls1hZHdH+/fuxdetW9T5Jl5RiSCRu104/UoqISEO5a9bEvMuXcXzpUjT08YEOULf9atRA+zx5cOUdX5rJ/mge3Jw/fx4+Pj7Inj07WrRogSBpEXiLR48eIUuWLPD19VXT/0t3CZm/1aa5TJGeKRNw7hwg34acnICvvtK6eEREUfwbNFAtNwf/+gt10qRBBIDfzp1DrgoV8E2BArghU1eQQ3DV8slLlSql8mhkfSLpYho8eDAqVKiAkydPwsvL643j5bjff/8dBQsWVPOtjBs3Ts2SKwGOuvDG4tmzZ2oznohOvHjxQm2mZDifqc+rlcDAQCxdulT93rVrV/W6nKdOhUzVF1mnDiIyZpQXa/Fy2Vs9WyvWs2Wwnk2vYJMmWN6kCfbMnInB/ftjc3Awfj55Er+VLo0WOXKgSObMyODvr3Ux7dYLM32mE3I+J50MhbESDx8+VK0yP/30E9pJl0c8Xqifnx+aNWuGoUOHxpm0LEFTTPPnz4enp8yaQHGR2YjXrl2LYsWKYcCAAXAJD0fNtm2R6MkT7B44EHeLFNG6iERE7xS0YgX+WrAA+58+VbeTAmjl54eK3bvDPW1arYtH8fTkyRPViyCNG5J/azPBjShRogSqVauGkSNHxuv4xo0bq3yQv+MYAhhby410ad27d++dlZNQEmxt2LAB1atXR6JEMkjRdt25cwc5c+ZEeHi4ek0VK1aE06xZcO3UCbqcOfHy5ElAJvLTgD3VszVjPVsG69kyZEbjNcOG4ccxY3D81WKcKZ2c0KtaNXSaPVvNikzW/ZmW67fk5cYnuNG0Wyq2fJoLFy7g888/j9fxEREROHHiBOrUqRPnMTIni5qXJQapcHP9ITHnuS1lxowZKrCRYLNq1apqFIJh+LdTp05IFEudWpo91LMtYD1bBuvZ/Or8+CMiixTB8x07MPiXX3Dm+XP027ABkzNnRr8GDfDl77+rRTzJOj/TCTmXpgnFMo3/tm3bcPnyZezevRsNGjSAi4uL6mYSrVq1Qt++faOOHzJkCNavX4+LFy/i8OHDaqZcGQrevn17DV+F/Xn8+DGmTp0atUCmjFDDrl3A8eNA4sTAF19oXUQiovfi7OKChmPG4ERYGP748ktkc3XF7chIdFmyBLm9vfFb69Z4GR6udTHpA2ka3Fy7dk0FMpIo3KRJE6SSabT37kWaNGnU/TJyShKNDYKDg9GhQweVZyOtNdJEJUFRvnz5NHwV9keSth88eIAcOXKogDPa8O8WLYCUKTUtHxHRh3Jxc0Or6dMR8PAhpjVvDh9nZwRFRKD9n38iX7JkWPDtt4h8+VLrYpItBjeyXtGNGzdUTowEOnJbLqgGMr+KjKYykIUbpaVGjr916xZWrVqFIkxqNamXL1+qhG7Rs2dP1ZKGW7eAJUv0B3BGYiKyI25JkuCrefMQePcuxn/6KVI7OeH8ixdoNnUqinh54d9+/bgCuQ3SfJ4bsi6LFy9W3YTSevaFoftp5kz9kO+yZYHChbUuIhGRySX29kaPFStw8do1DKlSBZJ5czw8HPVGjECZZMmwSdbXs67xN/QWDG4o1gUyv/nmGySW/Bpplp0+XX8AW22IyM55+fhgwKZNuBQYiO/LlIFMGLLv8WNU++47VPH2xp4ZM7QuIsUDgxuKsnnzZhw5ckTN/9PZEMjIAnTXrwMyTLJRI62LSERkEd45cmDk7t24cPw4uhQqBDcAWx4+RNmOHfFx2rQ4umCB1kWkt2BwQ1EMrTYygaIkd0dLJO7QQcbVa1g6IiLLS1+gACYdPYrzu3erdapkhvZVd++iSLNm+MzXFwGrVmldRIoFgxtSjh49qobZSwJxjx499DtPnwa2bNFP1texo9ZFJCLSTOYyZTAzIABn1q9Hs1crkC+8dg35P/4YbXLmxOUdO7QuIhlhcEOKrNNlmPE5a9as+p2//KL/Wa8e4OurYemIiKxDrurVMf/yZRxbvBj10qeHjKOac+ECcn/0kVqc8+bRo1oXkRjckJDh9TIMX/Tu3Vu/MywM+PNP/e9MJCYiiqZAo0ZYfvMm9v3+O6p7e0OWdJTFOXMUKYLvS5fGg8BArYvo0BjckJo/SJaykDW9ihYtqt85d64+wMmbF6hSResiEhFZpZJt2mD9/fvYMmECyiRNClmac/S+fciWKxeGVa2KsBs3tC6iQ2Jw4+BkJuJZs2ZFb7WRuRwMicSdOgGy/AIREcWpUrdu2BUSgpUDB6KQhwdCAQzYvBk5MmXCxPr1Ef7wodZFdCgMbhzctGnT1FpShQoVUiu4Ktu26ZOJkySRBb60LiIRkU1wcnZG3UGDcDgsDAu6dEGuRIlwV6dD9xUrkCt1asxq1Qovn0rbDpkbgxsHJstYTJ48OfoCmcLQaiOrsydPrmEJiYhsj7OrKz6bNAmnQ0Mxs1UrZHJxwbWICHSYOxf5kifnulUWwODGgcmK7Hfu3EH69OnVKClFJuxbtkz/OxOJiYjem6uHB9r/8QfO37uHCfXrI02MdatW/vgj160yEwY3DmzNmjXqZ926dZEoUSL9TplaPCIC+OgjwN9f2wISEdkBjxQp0G3ZMly4dg1Dq1aNWrfqk6FDUS55cmydMEHrItodBjcOzBDc1K5dW7/j+XN9cCPYakNEZPJ1q/pv3KjWrfquVCkkBrDn0SNU7tEDNVKlwoE5c7Quot1gcOOgLl26hLNnz8LV1VUNAVeWLgVu3QIyZAAaNNC6iEREdrtu1ai9e3HhyBF0LlAA0m6+4cEDNay8oY8PTi1frnURbR6DGwdvtSlbtiySG5KGDYnEX34JGLqpiIjILDIULoypx4/j7LZtaJ0jh7ogL7t5EwUaNECr7NlxUZa/offC4MZBvdEldfw4sHMn4OqqD26IiMgisn30EeYEBuLEihVolDEjdDKP6qVLyFOlCjrlz48bhw5pXUSbw+DGAYWHh2Pz5s3RgxtDq410R/n4aFg6IiLHlO/TT7H42jUc+OMP1EyVCjJYfNrp08hZvDi+K1kS98+f17qINoPBjQPavn07njx5Ah8fHxQsWBCQmTP/+kt/JxOJiYg0VbxVK6y9dw9bJ05EWS8vtaTDmAMHkD13brWkw6ObN7UuotVjcOPAXVK1atXST9z3xx/AkydA/vz6IeBERKS5il27YufDh28s6ZA9Y0ZMatCASzq8BYMbR8+3kQmkfvnldasN15EiIrLKJR3+/vZb5Hy1pEO35cuRO3Vq/N6mDV6Gh2tdTKvD4MZBh4C7uLjoh4Bv2gScOwd4eQEtW2pdPCIiimNJh6aTJ+P0w4eY8fnnyOjsjKsREWg3Zw78kyfHoh49uKSDEQY3DjwEPEWKFK8TiVu31gc4RERktRJ5eqLDn3+qJR3Gf/opUjk54ezz52gyYQJKJEuGtcOGcUkHBjcO3iUlE/b995/+jk6dtC0YERHFW+KUKdFjxQpcDArCwIoVkRTA4adPUXvAAFRKmRK7pk2DI2Nw48hDwKVLSiL8okUBPz+ti0dERAmULFMmDNq6FZcCAtCjWDG4y4jY0FCU79QJH6dNi2P//ANHxODGgezYsUMNAc+QIQMKFSoEvAp0ULWq1kUjIqIPkDpPHow/eBCB+/ejQ968cAGw6u5dFG7aFM2yZMH5DRvgSBjcOOoQcPlFWm5ElSqalouIiEwjU4kSmHHmDM5s2ICmmTOrfQuCguBXowa+9PPDtQMH4AgY3Dhqvs2lS8CVK/rlFipU0LpoRERkQrmqVcPfV67gyIIFqJs2LSIAzAwIQM6SJdGzeHHcO3sW9ozBjYO4fPkyAgIC1BDw6tWrv+6SKl0aSJJE6+IREZEZFP7sM6y8fRs7fv4ZFZIlwzMAPx06hOx582JQpUoIvXYN9ojBjYO12pQpU0Y/BNzQJcV8GyIiu1e+UydsCw7GmmHDUCRxYoQBGLxtG7Jnzoyf6tWzu9mOGdw4YpeUTve65Yb5NkREDjPbca1+/XAwLAwLe/RAHjc33Nfp0PPff5ErdWrMat3abmY7ZnDjAJ49exY1BLxOnTrAqVPAnTtA4sT6bikiInIYzi4uaDx+PE6GhGDWF18gk4sLrkVEqMkB8ydLhoXdu9v8bMcMbhxkCPjjx4/fHAIuicRubloXj4iINODq4YF2s2er2Y6layq1kxPOvXiBzyZORHEbn+2YwY0jrgLOIeBERPSKR4oU6L58OS5eu4bBlStDFuI5Ypjt2Nsbu6dPh61hcONo+TbS1Lh1q/4OJhMTEdErXj4++HHzZlwMCEBPw2zHISEo99VX+CRdOhxbuBC2gsGNnbty5QrOnDnzegj44cNAaCggI6aKFNG6eEREZIWzHY+LMdvxyjt3UOSzz9A8a1YEGlr/rRiDG0cbAm7It6lUCXCRjywREVHcsx2fXrsWn2XODB2gJgb0q1YNX+XLhxvyZdlKaRrcDBo0SOWAGG958+Z962MWLVqkjvHw8ECBAgWwevVqi5XX5rukBIeAExFRAuSuWRMLrlzB4b//Ru00aSDjqKafOYMcxYqhT8mSuH/+PKyN5i03+fPnx82bN6O2nTt3xnns7t270axZM7Rr1w5HjhxB/fr11Xby5EmLltmWhoBvetV8qIKbZ88AQ/0y34aIiBKgSNOmWH3nDrZPmYJyyZJBZsQZe+AAsufOjWHVquHRrVuwFpoHN66urkifPn3Uljp16jiPnTRpkhrx07t3b/j5+WHo0KEoWrQopk6datEy2woJFGUIuNRr4cKFgb17gadPgXTpAD8/rYtHREQ2qMI332BHcDBWDhyIQh4eCAUwYNMm5PDxweRGjfBM8jo15qp1Ac6fPw8fHx/VzSR5ISNHjkTmVyuZxrRnzx706NEj2r6aNWti+fLlb229kM0g9FWlv3jxQm2mZDifqc/7vlatWqV+1qhRAy9fvoTz+vUqMSyyUiVE2PAETdZWz/aK9WwZrGfLYV2bVo1+/VDtu++wuFcvDJo5E4EvXqDr0qX4acUKfFG5MqpUrGjStQsT8r5pGtyUKlUKc+bMQZ48eVSX1ODBg1GhQgXVzeTlJSPto7t16xbSSauDEbkt++MiwZKcN6b169fD09MT5rBhwwZYg8WLF6ufadOmVblJ5ZctQyoAx1KnRpAd5CpZSz3bO9azZbCeLYd1bVpJa9TA6I8+wpFp0/Db9u24EhGB+Vu3otCGDXA24USxT548ifexTjqdLDRkHR4+fIgsWbLgp59+Unk1Mbm5ueGPP/5QeTcGv/zyiwpebt++He+WG19fX9y7dw/JkiUzafklqpT/NDLkOlGiRNBSUFAQcubMCWdnZxU4pkyUCK5p08Lp5Uu8kKXus2WDrbKmerZnrGfLYD1bDuva/J4+eIBfvvgCLl5e6DxnjknrWa7fkroSEhLyzuu35t1SxmSocu7cuREYGBjr/ZI7EjOIkduyPy7u7u5qi0kq3FwfbnOeO742btyofkpXn7TcQEZNSVdUtmxIlDs37IE11LMjYD1bBuvZcljX5pMoXTq1EKf0Fpi6nhNyLs0Tio09evQIFy5cUGsgxUYu1IbRPwYShct+escQcC65QEREDkLT4KZXr17Ytm0bLl++rIZ5N2jQQM2ka+h2atWqFfr27Rt1fNeuXbF27VqMHz8eAQEBap6cgwcP4ptvvtHwVVif58+fRx8Cbjy/DYeAExGRndO0W+ratWsqkLl//z7SpEmD8uXLY+/evep3Q96I5IwYlC1bFvPnz0f//v3xww8/IFeuXGqklL+/v4avwjqHgEsrmCRbqyHg9+8DR4/q76xcWeviERER2W9ws2DBgrfev9WwwKORxo0bq43itwq4Cg6lHiVvPF8+SVzSunhERERmZVU5N2TmJRfYJUVERA6AwY2duXr1Kk6dOqVabNQq4ILJxERE5EAY3Nhpq03p0qXh7e0NXL8OyLw20j0lK4ETERHZOQY3jtIlVbSoTCSkYcmIiIgsg8GNnQ0BN0zex3wbIiJyVAxu7MiuXbvUEHCZkbhIkSL6EVLMtyEiIgfD4Maeh4BfuCAZxjJnNVCunNbFIyIisggGN46QbyPLU5hw2XkiIiJrxuDGjoaAnzx5UrXY1KhRQ7+TXVJEROSAGNzYCVlzS5QqVUo/BDwyEtiyRX8nk4mJiMiBMLix1y6pkyeBu3cBT0+gZEltC0dERGRBDG7sfQj4Rx8Bbm4alo6IiMiyGNzYgd27dyMsLEwNAS8qk/UJ5tsQEZGDYnBjB1avXq1+1qxZUz8E/OVLYNs2/Z0MboiIyMEwuLHHfJtDh4CwMCBlSqBwYW0LR0REZGEMbux5CLgslOniomn5iIiILI3BjZ0MAS9ZsiRSpUql38n1pIiIyIExuLG3LqnwcFlkSv87822IiMgBMbixtyHge/boA5wMGYC8ebUtIBERkQYY3NjBEPA0adKgWLFibw4Bd3LStHxERERaYHBjB11SUUPABfNtiIjIwTG4sad8m9BQYP9+/e/MtyEiIgfF4MZGXbt2DSdOnICTk9PrIeA7dgAREUD27ECWLFoXkYiISBMMbuxgFfDUqVPrd7JLioiIiMGN3XRJCa4nRURExODGFr148eLNIeD37gHHjul/r1xZw9IRERHZSHBz48YN85aEEjQEPDQ0NPoQ8C1b9D/9/YF06TQtHxERkU0EN/nz58f8+fPNWxqKFw4BJyIiMkFwM3z4cHTs2BGNGzfGgwcP4vswMgPm2xAREZkguOnUqROOHz+O+/fvI1++fPjvv//i+1AyoevXr6v3IdoQ8KtXgfPnAWnF+egjrYtIRESkKdeEHJwtWzZs3rwZU6dORcOGDeHn5wdX1+inOHz4sKnLSHGsAv7GEPDixYEUKTQsHRERkY0FN+LKlStYunQpUqZMiXr16r0R3JAGXVKG4IZdUkRERAkLbmbOnImePXuiWrVqOHXqlBqtQ5YdAr5hw4bowY1Ox2RiIiKi9wluatWqhf3796suqVatWsX3YWRCe/bsUUPApTuquHRBCcm1uXYNcHMDypbVuohERES2E9xERESoRNZMmTKZt0T0fkPAJbDx9NSwdERERDYW3Bi6Q0g7HAJORET0blx+wUbIDNHHjh1TQ8Cl5UaJjHw9MzGDGyIiIusKbkaNGqUu3N26dYvzmDlz5qhjjDcPDw840hDwEiVKvB4Cfvw4cP8+kCSJjA3XtoBERERWwirGcR84cADTp09HwYIF33lssmTJcPbs2ajbEuDA0YeAy8R9iRJpVDIiIiLronnLzaNHj9CiRQs1zFzmznkXCWbSp08ftaVzgEUiX758+eYQcON8Gw4BJyIisp6Wm86dO6Nu3bpq7pxhw4bFKxjKkiULIiMjUbRoUYwYMUIt6hmXZ8+eqc1AhlIb5oyRzZQM5zP1eXfu3ImQkBCkSpUKhQoV0p//xQu4bt8Oabd6UaGCuu0ozFXPFB3r2TJYz5bDurbtek7I+TQNbhYsWKCWa5BuqfjIkycPfv/9d9V9JRf7cePGoWzZsmpCwbiGqI8cORKDBw9+Y//69evhaaah06YeWTZ37lz1U4K4devWqd9TBgTgo0eP8NzLC2uuXwdu3oSj4Qg+y2A9Wwbr2XJY17ZZz0+ePIn3sU46nUxxa3lXr15VE9HJizfk2lSqVAmFCxfGxIkT4x3FyfpWzZo1w9ChQ+PdcuPr64t79+6p/B1zzCBcvXp1JDJhDoy0am3fvl113bVu3Vrtcx4xAi6DBiGyQQNE/PMPHIm56pmiYz1bBuvZcljXtl3PhklspXHjXddvzVpuDh06hDt37qiuJeOJAuUiLrMgS0Di4uLy1nNIpRUpUgSBgYFxHuPu7q622B5rrg+3Kc8tsadMnmgYKRV13m3b1A/natXg7KD/Sc35HtJrrGfLYD1bDuvaNus5IefSLLipWrUqTpw4EW1fmzZtkDdvXnz33XfvDGwMwZCco06dOrBX0sL18OFDtUCp1I3y9Cmwe7f+dyYTExERWUdw4+XlBX9//2j7kiRJopJmDftlDauMGTOqvBkxZMgQlC5dGjlz5lQX/LFjx6pVytu3bw97ZWi1ke63qBYoCWykq83HB8idW9sCEhERWRnNR0u9TVBQ0Os1lAAEBwejQ4cOuHXrlho2XqxYMezevRv58uWDvZJZiUW0OYCMh4A7yDw/RERENhncbN269a23J0yYoDZHYmi5kSHgb0zexyUXiIiIrG8SP4pfy01UcBMSIlM6639ncENERPQGBjdWTMb0nz9/Pnq31Pbt+gUzc+YEMmfWtoBERERWiMGNFZPJCWUm5rRp06qlJhR2SREREb0Vgxtb6pISXE+KiIjorRjc2EAycVSX1J07gGFuoMqVNSwZERGR9WJwY0stN1u26H9KsJMmjYYlIyIisl4MbqyULLvwxhw3zLchIiJ6JwY3VrzsgiwOJmtpyOzECvNtiIiI3onBjZUytNpIYOPm5gZcuQJcuADImlsffaR18YiIiKwWgxsrFWeXVIkSwDuWeiciInJkDG5sZdkF5tsQERHFC4MbWxgppdMxuCEiIoonBje2sOzC2bPAjRuAuztQtqzWxSMiIrJqDG6s0MmTJ9VQ8HTp0qktqtVGApvEibUuHhERkVVjcGMLycTbtul/skuKiIjonRjc2EIy8cmT+p/Fi2tYKiIiItvA4Mbak4mfPwfOndPfkS+ftgUjIiKyAQxurIzk2kRbMDMwEHj5EkiaFPD11bp4REREVo/BjZUJCgqKWnYhb968wOnTr1ttnJy0Lh4REZHVY3BjpV1S+fLl0y+7cOqU/g52SREREcULgxsrE61LShi33BAREdE7Mbix5mRi4+Amf34NS0VERGQ7GNxY8xw3L17oZycWbLkhIiKKFwY3VuTx48cIlNFRhpabCxf0AY6nJ5A5s9bFIyIisgkMbqxw2YX06dMjbdq00fNtnPlWERERxQevmNacTMyRUkRERAnG4MaKMJmYiIjowzG4seYFMzkMnIiIKMEY3Fjhsguq5UaWXAgI0N/J4IaIiCjeGNxYiStXriA0NPT1sgsXL+oXzUycGMiaVeviERER2QwGN1a47IIEOFFdUn5+HClFRESUALxqWoloXVKCI6WIiIjeC4MbK8GRUkRERKbB4MZKcMFMIiIi02BwY43LLkREcKQUERHRe2JwYwVOnDgRtexCmjRpgEuXgPBwwMMDyJZN6+IRERHZFAY31pxMLEPCXVw0LBkREZHtsZrgZtSoUXByckK3bt3eetyiRYvUPDAeHh4oUKAAVq9eDbtNJmaXFBERkW0GNwcOHMD06dNfJ9PGYffu3WjWrBnatWuHI0eOoH79+mqT1bTtctkFjpQiIiKyveDm0aNHaNGiBWbOnImUKVO+9dhJkyahVq1a6N27N/z8/DB06FAULVoUU6dOhd0suyA4xw0REdF7c4XGOnfujLp166JatWoYNmzYW4/ds2cPevToEW1fzZo1sXz58jgf8+zZM7UZyBIH4sWLF2ozJcP5EnLeS5cuISwsDG5ubsiePTtehIfD9cwZOMl5cueWk5m0jPbgfeqZEo71bBmsZ8thXdt2PSfkfJoGNwsWLMDhw4dVt1R83Lp1C+nSpYu2T27L/riMHDkSgwcPfmP/+vXr4enpCXPYsGFDvI/dt2+f+pkxY0b1OM9bt1A9PBwRiRJhTUAAdOfPm6WM9iAh9Uzvj/VsGaxny2Fd22Y9P3nyxPqDm6tXr6Jr167qxUtysLn07ds3WmuPtNz4+vqiRo0aSJYsmcmjSnk91atX168PFQ8S3Iny5cujTp06cFq5Ut12zpsXtT/5xKTlsxfvU8+UcKxny2A9Ww7r2rbr2dDzYtXBzaFDh3Dnzh2VM2MQERGB7du3qxwa6UpyiTEMWuaBuX37drR9clv2x8Xd3V1tMUmFm+vDnZBzG5KhCxcurH/MuXPqtpO/P//zvYM530N6jfVsGaxny2Fd22Y9J+RcmiUUV61aVU1ed/To0aitePHiKrlYfo8Z2IgyZcpg06ZN0fZJdCj7bdUbycQcBk5ERPRBNGu58fLygr+/f7R9SZIkQapUqaL2t2rVSuWiSN6MkG6sihUrYvz48SoJWXJ2Dh48iBkzZsAWyUixCxcuRB8GzpFSREREtj0U/G2CgoJw8+bNqNtly5bF/PnzVTAjLR2LFy9WI6ViBkm2QrqkZCh4hgwZ9MsuREYCZ87o7+QcN0RERLY5FNzY1q1b33pbNG7cWG324I2ZiYOCJB1cOhaBHDm0LRwREZGNsuqWG3v3RnBj6JLKkwdwtaq4k4iIyGYwuLGCZGIuu0BERGQ6DG40EhkZyZFSREREZsDgRiOXL1+OWnYhtyyzIDhSioiI6IMxuNGIodUmf/78+omJdDp2SxEREZkAgxtrSSa+ehV4/FifSJwzp7aFIyIismEMbqwlmdjQJSVdVJwWnIiI6L0xuLGWlht2SREREZkEgxsNSCIxl10gIiIyDwY3GjCsBO7j44PUqVPrd7LlhoiIyCQY3FhDl5TxSCm23BAREX0QBjcaBjdRXVLXrklflX6kVK5c2haOiIjIxjG40UCcMxNLYOPmpmHJiIiIbB+DGwvjsgtERETmxeBGg2UXHj16BHd3dy67QEREZAYMbjTKt5FlF1wlx0ZwpBQREZHJMLjROpmYI6WIiIhMisGNhb2Rb3PjBhASAri46JdeICIiog/C4MZall2QxTLd3TUsGRERkX1gcGPhZRcuXrwYvVuKXVJEREQmxeDGgk6cOKF+ZsyYEalSpdLv5EgpIiIik2JwY0FvdEkJjpQiIiIyKQY3GiQTc6QUERGR+TC40bLl5tYtIDgYcHYG8uTRtnBERER2gsGNBssuvJFMnCMH4OGhYemIiIjsB4MbC7l06RIeP34cfdkFdkkRERGZHIMbC3dJ+fv7v152wTBSisnEREREJsPgxkLe6JISbLkhIiIyOQY3WiUTy0gpznFDRERkcgxutApu7twBHjwAnJyAvHm1LRwREZEdYXBjAaGhoSqhONaRUtmzA4kTa1g6IiIi+8LgxoLLLmTKlAne3t76neySIiIiMgsGNxbskoo1mZgjpYiIiEyKwY0FR0rFuqYUW26IiIhMisGNVgtmsluKiIjILBjcWGDZBUPOTVS31N27wL17+pFSfn7aFpCIiMjOMLgxs4sXL6plFzw8PJArV67oXVJZswKenpqWj4iIyN5oGtxMmzZNtWYkS5ZMbWXKlMGaNWviPH7OnDlwcnKKtknQYAtdUvnz5+eyC0RERBbw6mqrDRkaPWrUKNWiodPp8Mcff6BevXo4cuSICgZiI0HQ2bNno25LgGPNmExMRETkQMHNJ598Eu328OHDVWvO3r174wxuJJhJnz49bDqZmMENERGRfQY3xiIiIrBo0SKVnyLdU3F59OgRsmTJohJ1ixYtihEjRsQZCIlnz56pzXi2YPHixQu1mZLhfMbnNbTc5MuXL2q/66lTkPaml3nyQGfiMjiC2OqZTI/1bBmsZ8thXdt2PSfkfE466Q/SkIwkkmAmPDwcSZMmxfz581GnTp1Yj92zZw/Onz+v8nRCQkIwbtw4bN++HadOnVJdXLEZNGgQBg8e/MZ+eR5PMyfzPnnyBM2bN1e///XXX+r1uYWGonarVmrfyr//RgSXXiAiIor3NVWu/5KiYtXBzfPnzxEUFKQKu3jxYsyaNQvbtm1TLR3xieL8/PzQrFkzDB06NN4tN76+vrh37947KyehpDwbNmxA9erVkShRIuzatQuVK1dWz3fhwgV1jNPOnXCtUgW6LFnw8vx5kz6/o4hZz2QerGfLYD1bDuvatutZrt+pU6eOV3CjebeUm5sbcubMqX4vVqwYDhw4gEmTJmH69OnvfKxUWpEiRRAYGBjnMe7u7mqL7bHm+nAbzn36VW6NtDRFPderZGin/Pn5n+sDmfM9pNdYz5bBerYc1rVt1nNCzmV189xILo1xS8u78nSkWytDhgywRkwmJiIisjxNW2769u2L2rVrI3PmzAgLC1N5MFu3bsW6devU/a1atULGjBkxcuRIdXvIkCEoXbq0aul5+PAhxo4diytXrqB9+/awuQUzGdwQERHZX3Bz584dFcDcvHkTyZMnV0GABDbSTyckF8fZ+XXjUnBwMDp06IBbt24hZcqUqhtr9+7d8crP0XLZhVjXlOIEfkRERPYX3Pz2229vvV9acYxNmDBBbbZAEoglszvasgsPHgC3bul/55pSREREZmF1OTf2wjC/jb+/P1xcXKJ3Sfn6Al5eGpaOiIjIfjG40SKZmF1SREREZsPgxkw4UoqIiEgbDG7M3C0VbaQUk4mJiIjMjsGNGcjsiZcvX1a/cxg4ERGRZTG4MQPDEHBZdkGGrCsPHwI3buh/50gpIiIis2FwYwaxzm9jaLWRBT6TJ9eoZERERPaPwY0Z822YTExERGR5DG7M2HLDfBsiIiLLY3BjYrKY58mTJ9XvXHaBiIjI8hjcmJiseyXLLiROnFgt8BmFLTdEREQWweDGxGSV8jeWXQgNBa5d0//O4IaIiMisGNyY2KVLl+JOJvbxAVKk0KhkREREjoHBjZlabphMTEREpA0GN5ZsuWFwQ0REZHYMbkzo4cOHuHv3rvqda0oRERFpg8GNCRmGgGfOnBkpjHNr2HJDRERkMQxuzDAzcYECBV7vDAsDgoL0vzO4ISIiMjtX8z+Fgwc3Z87of6ZPD3h7a1QyIjL35J0vXrx4r8fK41xdXREeHq7OQ+bDurb+enZzc4Oz84e3uzC4MSEuu0DkWHQ6nZq4U/LtPuQc6dOnx9WrV+Hk5GTS8lF0rGvrr2cJbLJly6aCnA/B4MYMyy4wmZjIMRgCm7Rp08LT0/O9LpiRkZF49OgRkiZNapJvrBQ31rV117M87saNG7h586bKXf2QAJTBjYlcuHABT58+VdFmjhw5Xt/Blhsiu/1CYwhsUqVK9d7nkT/oz58/h4eHBy+4Zsa6tv56TpMmjQpwXr58iUSJEr13GfjumnDyPnd3d2TJkuX1sguCwQ2RXTLk2EiLDRGZhqE76kNzothyYyLVq1dHcHAwFi5c+Hrno0fA5cv639ktRWSXmLtBZH3/n9hyY0KSHR5tfpuAAP3PtGmBD2i2JiKy9AVm+fLlsFVffPEF6tevr3Ux7PI9zZo1KyZOnAhrx+DGnNglRUQ2ePGXhM7atWtbtEyOatCgQShcuDCszZw5c6J/WX/lwIED+PLLL2Ht2C1lThwpRUQ2SIbxWsNwYsm7kBZxsh5p0qSBLWDLjTmx5YaIbLwL4/Lly+r20qVLUblyZZVALQsD79mzJ9pjdu7ciQoVKiBx4sTw9fVFly5d8Pjx46j7586di+LFi8PLy0sFT82bN8edO3ei7t+6dat6njVr1qBYsWJqgIacMzYyf0qTJk1Uy4K3tzfq1aunyvm20TsjR45UI1kzZMiAIkWKYPHixW8897p169R98hqqVKmiyifl8fPzQ7JkyVSZnzx58sZ5ZV4WeYzUS2zn3bRpk3rtUndly5bF2bNno1pHBg8ejGPHjqnjZJN9sZFzlSxZEkmSJFGvu1y5cmogi8G0adPU65OE3Dx58qj6jouhXMbzMx09elTtk3qU+9u0aYOQkJCockkLU2zdUkFBQar+Zdi31JG8L7dv336jZUrKI49Nnjw5mjZtijCZvd+MGNyYE4MbIsei0wFyQddik+c2o379+qFXr17qIpg7d240a9ZMDdc1TIVRq1YtNGrUSM3U/s8//6jA5Jtvvok2umzo0KHqQi6Bk1xEpXsspu+//x6jRo3CmTNnos8ZZnSemjVrqiBpx44d2LVrl7qwyvPL8OPYSADy559/4pdfflFBWdeuXdGyZUts27Yt2nFyIZ46dSp2794dFUDJhXz+/PlYtWoV1q9fjylTprxx3l9//RWnTp1C9+7dYz2v1N348eNx8OBB1RLVtm1btf+zzz5Dz549kT9/ftUVKJvsi0nqWboRK1asqOpXXoN0DRmSb5ctW6Zek5xL5lvr2LGjCk62bNmC9yEBmLxuCVYM5ZL3PiYJ7iSwefDggXrNGzZswMWLF9Vnw5h8PuQ9X7lypdrkWHmPzUrnYEJCQuQvgPppas+fP9ctX75c/dQ9fqzTOTnJnxud7s4dkz+XI4tWz2Q2rOe3e/r0qe706dPqZ5RHj/T/57XY5LnjqXXr1rp69erFeb/8jVy2bJn6/dKlS+r2rFmzou4/deqU2nfmzBl1u127drovv/wy2jl27Nihc3Z2jl4/Rg4cOKDOERYWpm5v2bJF3ZbP3NvMnTtXlydPHl1kZGTUvmfPnukSJ06sW7du3RuvLzw8XOfp6anbvXu3LiIiQhccHKx+SpmbNWsW7bk3btwYdc6RI0eqfRcuXIja17FjR13NmjXfOK+xd5131apVap+hXgYOHKgrVKjQW1/z/fv31WO2bt0a6/1ly5bVdejQIdq+xo0b6+rUqRPre2ool9SFwZEjR9Q+eb/F7NmzdcmTJ3/jubJkyaKbMGGC+n39+vU6FxcXXVBQ0BufjU2bNql6ltcn9RQaGhp1TO/evXWlSpWK//+r97h+s+XGXGSklHyeUqeWTkqtS0NE9EGMW1Gka0cYupWkNUa6U6QFxbBJ64p8s7906ZI65tChQ/jkk0/UzLPS6iKtEIZuDWPSffM28lyBgYHqHIbnkq4pWcdIWghikmOlK0mm65CWiEyZMqmf0uIS83jj15guXTrVjZQ9e/Zo+wyv2fi8xq/7XeeNWXfxIa9PWrmkTqUOJ02apFpTDKSVS7qpjJUrV07tNyc5v3RBymaQL18+1W127ty5qH3SHSXvl3EdJOT1vw9mapkLu6SIHI9M6CfzWyWABAChoaHqgvtBs+aaeTJB49liDd0hUnYhU+1LV4jk2cQkwYzk3siFWbZ58+appFQJauR2zK4kySl5G3kuycmR88Qn2VWOF9KtJBdV42UBJK/nba8x5gy5ss/4NRvOmzFjxmjHveu8wnCe+Jo9e7aq37Vr16puv/79+6tuoNKlSyOhnF99zvQNOnrvu/BrfLytHs2FwY25cKQUkeORC9c7Ls5vkD/yMhurPM5GlwQoWrQoTp8+jZw5c8a5qPD9+/dVnoXhW77kn7zvc8nFXZa9kIDwXaQlQYINCaYk4dkkgWSM8xpaod6HJADHdzZeSXaWrW/fvihTpozKBZLgRhKeJfeodevWUcfu2rVLlTE2hiBQWn9SpkypfpdcqoSWS55XcpNkM7yv8jmQRGVJatYSgxtzYcsNEVkxGQkT84Ima2QZdzHE13fffacuspJA3L59e9X6Ihc5aVmQBF1pvZGLpSTjfvXVVyrpVZKL30eLFi0wduxYlcg6ZMgQ1c0ko4ZkNFefPn3UbWPSHSLJsJLsK4m5MnJHLtqSlCtBjnFAkBDG55VWiPLly6s6laAiIeeVLhvpupP3Qsou543Z8iP3z5gxA59++il8fHzUaKvz58+jVatW6v7evXur5GcJfKpVq4b//vtP1cfGjRtjfU4JQuV9lgTq4cOHqy4kSXiOWS5pnZKRXjIKTLroYi41Is9VoEAB9Z5IArLUb6dOnVSwJ2XRkm1+TbCl4IYtN0RkhWS4r6ElwLDJsOT3ITklMgJGLpLSOiLn+vHHH9WF2NBSIDk5ixYtUq0J0oIzbty493ouucBu375dBUwNGzZUrQft2rVTOTdxteRIIDVgwACMHj0apUqVQp06dVR3kgzh/hCG88qoKSmHjNhK6HllhJk8TobZSz39/fffsb7mgIAAdayMVJORUp07d1ZdgUJGUkkejtSpjLyaPn266saqVKlSnN1E8jxyTnnvpF6GDRv2xogpCURl9JaUa8yYMW+cR7qXVqxYoVp/PvroIxXsSI5SbK/B0pxeZVE7DGmSlHH2EmHHp0kzIaTPcvXq1ahTuTISycyOUrW3bkkWmkmfx9FF1XOdOh+0aiy9Hev57eRiKt+o5UImqx+/L5Pl3NA7sa6tv57f9v8qIddvTd9dmXRIokYppGzShygTJr2NRP558+ZVL1qaw+SPr9WRCZoksPH21q8rRURERBajaXAj/YvSPClDBCW5TGaElH5UmQwpNjKxkkwOJE2QR44cUU1xskn/rTVxMgy/ky4prhhMRETkOMGNjNeXJu9cuXKpfkRJbJIhenv37o31eOlTlL5JSZ6S/k3p75TMeUlYsyZOTCYmIiLSjNV0Okr2+oIFC9R8CNI9FRvJbpeEJWMyT0LMNU6spuWGwQ0REZHjDQWX+Q8kmJEkImm1kTUy4hqbf+vWLTVDpDG5Lfvj8uzZM7UZJyQZkiVNPWlR1Pletdy8zJMHOjNOjOSoDPVszkmniPX8LlIvMh5Dkic/ZEIyw5gOw7nIfFjX1l/Pcrw8Tv5/ubi4RLsvIX+LNA9uZKIfGd8v2c+ymqrMDSBDCuMKcBJKhujFNrxRFkCLOWbfFJyfP4fTxYvq9403buCZNSY82wmZQ4PMj/UcO1kAUVa3lrlA4lqwMSHMvUoyvca6tt56lv9LT58+VcP9DQuzGhivyG71wY1M7GSY1VKm1D5w4IDKrZFx+jHJHxLjpdSF3Jb9cZGZHHv06BGt5UYmL6pRo4ZZhoLvmzkTThJ5pkiBqi1aMKHYDKSe5YIra7pwiLL5sJ7fTlqbZWZWaXH+kKHg8i1VLgIyeZthan4yD9a19dez/L9KnDixmjcntqHgNhPcxNYkZdyNZEy6r2S2xG7dukXtkz++ceXoCJnpMeZsj0L+WJvjD7bXq0XgnPLnRyI3N5Ofn8z/HlJ0rOe48wTlD7fM4/Ehc6YYmu0N5yLzYV1bfz3L8YZ1vWL+3UnI3yFNgxtpValdu7aaaVKiPFknQ2bNXLdunbpfppaWBcmka0l07dpVTess00TXrVtXJSDLEHKZltpaeF29qv+FycRERESa0DR0lSXPJYCRvJuqVauqLikJbKQZXMiCZMbLust00BIASTAja11Ijs7y5cvh7+8Pa8HghohIO/IFWb75y+KN5iDLSKSQGeitvJyOTtOWm99+++2db35MjRs3Vpu1igpuuKYUEVmpL774An/88YdqFf/++++j9suXxQYNGkSNdiHTkDWeZMFOWVzS+Mu6fHmX5QTI9NjpaErPniGJoaWJLTdEZMUkWVMWTAwODoYtMMWINGsig2lkMAwTm82DwY0pnT8PZxkpJZH4q9VwiYiskUyIKhdXQ05jbAYNGqRaHIxJ60PWrFmjtQLJMjgjRoxQ845Jl82QIUPUMF6ZTd7b21sttSOrVBuTkWZNmjRRx8sxsvTO5cuX3zivzFwvq4tL+oKYO3cuihcvrkbiSPmbN2+uUhziS1qlZHoQyfWUwSZy7i5dukTdL8GepEvIStcyXYjkhZ4/fz7O8xnKaUwGvRhW5Jb7ZXoTGQUsgYxs8jpj65ZasmSJWtVbyiV1LPmlxmSf1HPbtm3V65fXYE05p9aEwY0Zll3Q+flxCDiRA5ILp8yyrsWW0K4kmSBNLpRTpkzBtWvXPuh1b968GTdu3FBzk/z0008YOHAgPv74YxUg7Nu3D1999RU6duwY9TwyzYDMLi8X6B07dmDXrl1qSL0sr2PcQiOjY8+ePatGxa5cuTLqsbL0zrFjx1Q3mgQKEkDE17///qsCNJluRIIWOYcswmwg55KBKnKczH4v9SrLBL3vZJYS1MiI3g4dOqhuKNlkOpKYZI1FCfaaNm2qJreVwHLAgAEqx8eYBDwS3Mn6ip06dcLXX3+t6oisfCi4LYtadkGCGyJyODLJmFyktSCTCSZJkiRBj5H8GmmZkWDkXTmQbyMtL5MnT1bDeKWFZcyYMaoufvjhh6iRsbJI8s6dO9XF+59//lHDhWfNmhXVLSMtO9KKIy0aMg+ZkNcjx0gXjoG0Whhkz55dPW+JEiXU649P3UuAJS0+0nIlQ4ul9aNkyZLqPgl2JKiRYEtyYsS8efNUMCJB0Pvke0pOjZRfWoHeNiebBIUysEYCGiHrLZ4+fRpjx46NFrxJoCVBjfjuu+8wYcIEbNmyJapli/TYcmOG4EbHfBsishGSdyPJxWcMX87eg3SlGM9nIt1Txq0h0kqUKlWqqO4jaXUJDAxULTcSkMgmAZJM4HbhwoWox8k5jAMbQwuHLLosQYk8XqYHMYyujQ/p/pIZcCUwktYUWfLHMBOu1IHMPF2qVKmo46XcEjh8SP3Eh5y/XLly0fbJbQm4ZE4lg4IFC0b9LoGhBEwJ6ZZzFGy5MVe3FBE5HPl2Li0ICSEtGDLzqsyY/iETy73vcjIyE6x0EUnrSszuHSlPzO6u2LpnYk6uZpiELeY+w+RuUkcyI720isSUJk2aqN9jtkRJ95uUVTZ5rBwrQY3cjm/CseT/SCAhXWnS3SWtINI6Inkx7yO+dWQqb6tXeo3BjanIf6zAQPUrgxsixyQXmoR2DcmFSb6Zy+O0mjVXuoykeypm14YED7IwsVy8Dd1HshbghypatKjqmkqbNm2ClsEJCAjA/fv3VXkNeSuSH5NQMr2/tP7I1rlzZ+TNm1flufj5+alWHMkTMnRLyfNJTktc6x1KHZ08eTLaPqkj4yBEWp+MW19iI88t3WHG5LZ0T8VcQJLejd1SphIYCKeXL/EicWL5aqB1aYiI4k26f1q0aKHyV4zJiJ+7d++qHBrpLvr555+xZs2aD34+ea7UqVOrLiJJKL506ZLKtZFRS29LbpauKAkUJAn64sWLKj9GkosTQiaClfwiCUjkHH/99ZcKdrJkyYJcuXKpMkl3leQHSfdZy5Yt1Uz5sj82VapUUQHWn3/+qbqQJH8pZrAjo5wkYJLk53v37sXa0tKzZ0+VQC2v59y5c6qrcOrUqejVq1eCXh/pMbgxldu3ofP2Rph8m+BIKSKyMTJ8O+ZFV1oTfvnlFxXUyKzw+/fvN8nFVrrQZGSVBCsNGzZUz9OuXTuVc/O2lhxpJZHRQ4sWLVItKdKCM27cuAQn+EpwI/kskr+yceNG/Pfffyq3xpDYLF1mMtpLRjlJq9Xq1avjXNdIusQkCbhPnz4qsVmWEpKh5MakzqT1Rcps6EqLrTVr4cKFalkhmXX/xx9/VO9JQkaC0WtOOgebilL6tuXDHRISYvpVwZ8/x7qlS1GzUSMuNGhG0p8tf2xk1ADr2XxYz28nF2JpcciWLdsHrQpuqpwbejfWtfXX89v+XyXk+s1315ScnBAh3VJERESkGQY3REREZFcY3BAREZFdYXBDREREdoXBDREREdkVBjdERB/AwQacEtnE/ycGN0RE78EwPF4WiCQi0zAso/GhszJz+QUiovcgf3xlFWvDooUyMZ1hiYKEzgkif9Blfg/OvWJerGvrrmd5nMyILf+XZAHTD8HghojoPcmKzOJDVmWWZnhZpVqWAHif4Ijij3Vt/fUswZDMXP2h7w+DGyKi9yR/gDNkyKAWgHzflaDlcbIUgazOzZmgzYt1bf31LGuHmaJVjcENEZEJuqjeN0dAHicrUctU87zgmhfr2nHqmZ2OREREZFcY3BAREZFdYXBDREREdsXVUScIkqXTzZFEJXNeyLnZn2s+rGfLYD1bBuvZcljXtl3Phut2fCb6c7jgJiwsTP309fXVuihERET0Htfx5MmTv/UYJ52DzR0ukwTduHEDXl5eJp/nQKJKCZquXr2KZMmSmfTc9Brr2TJYz5bBerYc1rVt17OEKxLY+Pj4vHO4uMO13EiFZMqUyazPIW8m/+OYH+vZMljPlsF6thzWte3W87tabAyYUExERER2hcENERER2RUGNybk7u6OgQMHqp9kPqxny2A9Wwbr2XJY145Tzw6XUExERET2jS03REREZFcY3BAREZFdYXBDREREdoXBDREREdkVBjcm8vPPPyNr1qzw8PBAqVKlsH//fq2LZHdGjhyJEiVKqNml06ZNi/r16+Ps2bNaF8uujRo1Ss3k3a1bN62LYpeuX7+Oli1bIlWqVEicODEKFCiAgwcPal0suxIREYEBAwYgW7Zsqo5z5MiBoUOHxmt9Iorb9u3b8cknn6jZguVvxPLly6PdL/X7448/IkOGDKreq1WrhvPnz8NSGNyYwD///IMePXqooW+HDx9GoUKFULNmTdy5c0frotmVbdu2oXPnzti7dy82bNigFmerUaMGHj9+rHXR7NKBAwcwffp0FCxYUOui2KXg4GCUK1dOLSy4Zs0anD59GuPHj0fKlCm1LppdGT16NKZNm4apU6fizJkz6vaYMWMwZcoUrYtm0x4/fqyudfLFPjZSx5MnT8avv/6Kffv2IUmSJOq6GB4ebpkCylBw+jAlS5bUde7cOep2RESEzsfHRzdy5EhNy2Xv7ty5I1+9dNu2bdO6KHYnLCxMlytXLt2GDRt0FStW1HXt2lXrItmd7777Tle+fHmti2H36tatq2vbtm20fQ0bNtS1aNFCszLZGwC6ZcuWRd2OjIzUpU+fXjd27NiofQ8fPtS5u7vr/v77b4uUiS03H+j58+c4dOiQanIzXr9Kbu/Zs0fTstm7kJAQ9dPb21vrotgdaSGrW7dutM81mda///6L4sWLo3HjxqqbtUiRIpg5c6bWxbI7ZcuWxaZNm3Du3Dl1+9ixY9i5cydq166tddHs1qVLl3Dr1q1ofz9kTShJ2bDUddHhFs40tXv37qk+3XTp0kXbL7cDAgI0K5cjrO4ueSDSrO/v7691cezKggULVPeqdEuR+Vy8eFF1l0iX9g8//KDqu0uXLnBzc0Pr1q21Lp7d+P7779Uq1Xnz5oWLi4v6ez18+HC0aNFC66LZrVu3bqmfsV0XDfeZG4MbstmWhZMnT6pvYGQ6V69eRdeuXVVOkyTHk3kDdGm5GTFihLotLTfymZYcBQY3prNw4ULMmzcP8+fPR/78+XH06FH1xUgSYVnP9ovdUh8oderU6tvA7du3o+2X2+nTp9esXPbsm2++wcqVK7FlyxZkypRJ6+LYFelilUT4okWLwtXVVW2SyC2JgfK7fOsl05BRJPny5Yu2z8/PD0FBQZqVyR717t1btd40bdpUjUb7/PPP0b17dzX6kszDcO3T8rrI4OYDSRNysWLFVJ+u8TcyuV2mTBlNy2ZvJG9NAptly5Zh8+bNamgnmVbVqlVx4sQJ9e3WsEnrgjThy+8SyJNpSJdqzKkMJC8kS5YsmpXJHj158kTlQRqTz7H8nSbzkL/NEsQYXxela1BGTVnqushuKROQPnNp3pSLQMmSJTFx4kQ1TK5NmzZaF83uuqKkaXnFihVqrhtD360kqsk8CvThpF5j5jDJEE6Zh4W5TaYlrQeS7CrdUk2aNFFzY82YMUNtZDoyF4vk2GTOnFl1Sx05cgQ//fQT2rZtq3XRbNqjR48QGBgYLYlYvgDJAA+pa+n6GzZsGHLlyqWCHZlrSLoCZX4yi7DImCwHMGXKFF3mzJl1bm5uamj43r17tS6S3ZGPa2zb7NmztS6aXeNQcPP577//dP7+/mqIbN68eXUzZszQukh2JzQ0VH1+5e+zh4eHLnv27Lp+/frpnj17pnXRbNqWLVti/XvcunXrqOHgAwYM0KVLl059vqtWrao7e/asxcrnJP9YJowiIiIiMj/m3BAREZFdYXBDREREdoXBDREREdkVBjdERERkVxjcEBERkV1hcENERER2hcENERER2RUGN0RERGRXGNwQkU2TxTxlGYOGDRtG2x8SEgJfX1/069dPs7IRkTY4QzER2TxZcLJw4cKYOXOmWuRTtGrVCseOHcOBAwfUArdE5DgY3BCRXZg8eTIGDRqEU6dOqUUoGzdurAKbQoUKaV00IrIwBjdEZBfkT1mVKlXg4uKCEydO4Ntvv0X//v21LhYRaYDBDRHZjYCAAPj5+aFAgQI4fPgwXF1dtS4SEWmACcVEZDd+//13eHp64tKlS7h27ZrWxSEijbDlhojswu7du1GxYkWsX78ew4YNU/s2btwIJycnrYtGRBbGlhsisnlPnjzBF198ga+//hqVK1fGb7/9ppKKf/31V62LRkQaYMsNEdm8rl27YvXq1Wrot3RLienTp6NXr14quThr1qxaF5GILIjBDRHZtG3btqFq1arYunUrypcvH+2+mjVr4uXLl+yeInIwDG6IiIjIrjDnhoiIiOwKgxsiIiKyKwxuiIiIyK4wuCEiIiK7wuCGiIiI7AqDGyIiIrIrDG6IiIjIrjC4ISIiIrvC4IaIiIjsCoMbIiIisisMboiIiMiuMLghIiIi2JP/A6lgikNI8VG7AAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"N = 20\n",
|
||
"show_plot_linear(\"matrix_linear.txt\", N)\n",
|
||
"show_plot_cubic(\"matrix_cubic.txt\", N)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "22fe3de6",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Errors"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 142,
|
||
"id": "e0e9266d",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def read_data_from_file(filename):\n",
|
||
" with open(filename, 'r') as file:\n",
|
||
" content = file.read().strip()\n",
|
||
" data = np.array([float(x) for x in content.split()])\n",
|
||
" return data\n",
|
||
"\n",
|
||
"def show_error(program_file: str, analytical_file: str):\n",
|
||
" # Считывание данных из файлов\n",
|
||
" real = read_data_from_file(analytical_file)\n",
|
||
" matrix = read_data_from_file(program_file)\n",
|
||
" \n",
|
||
" # Расчет абсолютных разностей\n",
|
||
" absolute_errors = np.abs(real - matrix)\n",
|
||
"\n",
|
||
" # Расчет относительных погрешностей (в долях)\n",
|
||
" # Добавляем маленькое значение к знаменателю для избежания деления на ноль\n",
|
||
" relative_errors = absolute_errors / (np.abs(real))\n",
|
||
"\n",
|
||
" # Расчет относительных погрешностей в процентах\n",
|
||
" relative_errors_percent = relative_errors * 100\n",
|
||
"\n",
|
||
" # Нахождение максимальной относительной погрешности\n",
|
||
" max_relative_error = np.max(relative_errors)\n",
|
||
" max_relative_error_percent = np.max(relative_errors_percent)\n",
|
||
" max_error_index = np.argmax(relative_errors)\n",
|
||
"\n",
|
||
" # Вывод результатов\n",
|
||
" print(f\"\\nМаксимальная относительная погрешность: {max_relative_error:.6f} ({max_relative_error_percent:.2f}%)\")\n",
|
||
" print(f\"Индекс точки с максимальной погрешностью: {max_error_index}\")\n",
|
||
" print(f\"Значения в точке с максимальной погрешностью:\")\n",
|
||
" print(f\" cubic_real: {real[max_error_index]}\")\n",
|
||
" print(f\" matrix_cubic: {matrix[max_error_index]}\")\n",
|
||
" print(f\" Абсолютная разность: {absolute_errors[max_error_index]:.6f}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 143,
|
||
"id": "89918171",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"\n",
|
||
"Максимальная относительная погрешность: 0.107830 (10.78%)\n",
|
||
"Индекс точки с максимальной погрешностью: 0\n",
|
||
"Значения в точке с максимальной погрешностью:\n",
|
||
" cubic_real: 3.1950864987612366\n",
|
||
" matrix_cubic: 2.85056\n",
|
||
" Абсолютная разность: 0.344526\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"show_error(\"matrix_linear.txt\", \"linear_real_y_20.txt\")"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": ".venv",
|
||
"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": "3.12.3"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|