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February 17, 2021 05:12
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Sympy_test.ipynb
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| { | |
| "nbformat": 4, | |
| "nbformat_minor": 0, | |
| "metadata": { | |
| "colab": { | |
| "name": "Sympy_test.ipynb", | |
| "provenance": [], | |
| "collapsed_sections": [], | |
| "toc_visible": true, | |
| "authorship_tag": "ABX9TyPPbnTBdZdNn+V8Mdv8+4e3", | |
| "include_colab_link": true | |
| }, | |
| "kernelspec": { | |
| "name": "python3", | |
| "display_name": "Python 3" | |
| } | |
| }, | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "view-in-github", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "<a href=\"https://colab.research.google.com/gist/awnion/3db791d560db3cf6bda9106c43fa6d3e/sympy_test.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "jcHKeNYdzoRh" | |
| }, | |
| "source": [ | |
| "#!pip install -U sympy\r\n", | |
| "#!pip install \"antlr4-python3-runtime>=4.7,<4.8\"" | |
| ], | |
| "execution_count": null, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "lPK9WLePi4AO" | |
| }, | |
| "source": [ | |
| "from sympy import *\n", | |
| "from sympy.plotting import plot, PlotGrid\n", | |
| "from sympy.parsing.latex import parse_latex\n", | |
| "init_printing()\n", | |
| "t = Symbol('t', positive=True) # введем переменную" | |
| ], | |
| "execution_count": null, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Rj8BgNv3RIOJ" | |
| }, | |
| "source": [ | |
| "" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "cssNaEheRXf-" | |
| }, | |
| "source": [ | |
| "# Задача 1\r\n", | |
| "\r\n", | |
| "Из графика следует следующее выражения для функции $p(t)$\r\n", | |
| "\r\n", | |
| "$$\r\n", | |
| "p(t) = \\begin{cases}\r\n", | |
| " - 0.08 t + 1, &0 \\leq t < 5 \\\\\r\n", | |
| " 0.6, &5 \\leq t < 8\\\\\r\n", | |
| " -0.3 t + 3, &8 \\leq t < 10\r\n", | |
| " \\end{cases}\r\n", | |
| "$$\r\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "dT-Xk-cWTq8s" | |
| }, | |
| "source": [ | |
| "## Посчитаем $T_1$\r\n", | |
| "\r\n", | |
| "По определению\r\n", | |
| "\r\n", | |
| "$$\r\n", | |
| "T_1 = \\int_{0}^{\\infty} p(t) dt\r\n", | |
| "$$\r\n", | |
| "\r\n", | |
| "В данном случае проще посчитать площать под графиком геометрически.\r\n", | |
| "Нам нужно сложить площать трапеции со сторонами 1 и 0.6 и высотой 5,\r\n", | |
| "площадь прямоугольника со сторонами 0.6 и 3 и площадь прямоугольного треугольника со сторонами 0.6 и 2. Получаем:\r\n", | |
| "\r\n", | |
| "$$\r\n", | |
| "T_1 = \\frac{1}{2}\\cdot (1 + 0.6) \\cdot 5 + \r\n", | |
| " 0.6 \\cdot 3 + \r\n", | |
| " \\frac{1}{2}\\cdot 0.6 \\cdot 2 = \\\\\r\n", | |
| " \r\n", | |
| " \\boxed{\\large T_1 = 6.4}\r\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "7WCk-rIdVS1U" | |
| }, | |
| "source": [ | |
| "## Найдем $\\lambda(t)$\r\n", | |
| "\r\n", | |
| "$$\r\n", | |
| "\\lambda(t) = \\frac{(1 - p(t))'}{p(t)} = - \\frac{p(t)'}{p(t)}\r\n", | |
| "$$\r\n", | |
| "\r\n", | |
| "$$\\Large\r\n", | |
| "\\lambda(t) = \\begin{cases}\r\n", | |
| " -\\frac{(- 0.08 t + 1)'}{- 0.08 t + 1}, &0 \\leq t < 5 \\\\\r\n", | |
| " -\\frac{(0.6)'}{0.6}, &5 \\leq t < 8\\\\\r\n", | |
| " -\\frac{(- 0.3 t + 3)'}{- 0.3 t + 3}, &8 \\leq t < 10\r\n", | |
| " \\end{cases}\r\n", | |
| "$$\r\n", | |
| "\r\n", | |
| "Упростим\r\n", | |
| "\r\n", | |
| "$$\\Large\r\n", | |
| "\\lambda(t) = \\begin{cases}\r\n", | |
| " -\\frac{-0.08}{- 0.08 t + 1}, &0 \\leq t < 5 \\\\\r\n", | |
| " 0, &5 \\leq t < 8\\\\\r\n", | |
| " -\\frac{- 0.3}{- 0.3 t + 3}, &8 \\leq t < 10\r\n", | |
| " \\end{cases}\r\n", | |
| "$$\r\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 58 | |
| }, | |
| "id": "5cuBgrMbW_cY", | |
| "outputId": "97c381e1-17aa-464b-f7e4-953401051004" | |
| }, | |
| "source": [ | |
| "parse_latex(r'''-\\frac{-0.08}{- 0.08 t + 1}''').simplify(rational=True).factor(),\\\r\n", | |
| "parse_latex(r'''-\\frac{- 0.3}{- 0.3 t + 3}''').simplify(rational=True).factor()" | |
| ], | |
| "execution_count": 18, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "image/png": "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\n", | |
| "text/latex": "$\\displaystyle \\left( - \\frac{2}{2 t - 25}, \\ - \\frac{1}{t - 10}\\right)$", | |
| "text/plain": [ | |
| "⎛ -2 -1 ⎞\n", | |
| "⎜────────, ──────⎟\n", | |
| "⎝2⋅t - 25 t - 10⎠" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 18 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "ISNT0eZrXgfZ" | |
| }, | |
| "source": [ | |
| "$$\\boxed{\\Large\r\n", | |
| "\\lambda(t) = \\begin{cases}\r\n", | |
| " \\frac{2}{25 - 2t}, &0 \\leq t < 5 \\\\\r\n", | |
| " 0, &5 \\leq t < 8\\\\\r\n", | |
| " \\frac{1}{10 - t}, &8 \\leq t < 10\r\n", | |
| " \\end{cases}}\r\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "92Kzonq0koc-" | |
| }, | |
| "source": [ | |
| "# Задача 2\r\n", | |
| "\r\n", | |
| "$$\r\n", | |
| "\\lambda(t) = \\begin{cases}\r\n", | |
| " 3, &0 \\leq t < 1 \\\\\r\n", | |
| " \\frac{3}{2}(3-t), &1 \\leq t < 2\\\\\r\n", | |
| " 3/2, &2 \\leq t\r\n", | |
| " \\end{cases}\r\n", | |
| "$$\r\n", | |
| "\r\n", | |
| "\r\n", | |
| "---\r\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "_AaU2WKrHRS9" | |
| }, | |
| "source": [ | |
| "## Для $0 \\leq t < 1$\r\n", | |
| "\r\n", | |
| "$$\\Large\r\n", | |
| "p(t) = e^{-\\int_{0}^{t} 3dt} = \\boxed{ e^{-3t} }\r\n", | |
| "$$\r\n", | |
| "\r\n", | |
| "Проверка: $p(0) = e^{-0} = 1 \\color{green}{\\checkmark}$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "iyAVUjrxHX8F" | |
| }, | |
| "source": [ | |
| "## Для $1 \\leq t < 2$\r\n", | |
| "\r\n", | |
| "$$\r\n", | |
| "p(t) = e^{-\\left(\\int_{0}^{1} 3dt + \\int_{1}^{t} \\frac{3}{2}(3-t)dt \\right)}\r\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 55 | |
| }, | |
| "id": "u-epNx76jbeb", | |
| "outputId": "e94ba1d2-6088-468f-e261-562713145cbe" | |
| }, | |
| "source": [ | |
| "p_0_1 = -3 + 0*t\n", | |
| "p_1_2 = -3/2*(3-t)\n", | |
| "(\n", | |
| " p_0_1.integrate((t,0,1)) + \n", | |
| " p_1_2.integrate((t, 1, t))\n", | |
| ").simplify(rational=True).factor() # тут я кстати обсчитался на бумажке" | |
| ], | |
| "execution_count": null, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "image/png": "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\n", | |
| "text/latex": "$\\displaystyle \\frac{3 \\left(t^{2} - 6 t + 1\\right)}{4}$", | |
| "text/plain": [ | |
| " ⎛ 2 ⎞\n", | |
| "3⋅⎝t - 6⋅t + 1⎠\n", | |
| "────────────────\n", | |
| " 4 " | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 3 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "uowjOPxGo4rA" | |
| }, | |
| "source": [ | |
| "Таким образом\r\n", | |
| "$$\\Large\r\n", | |
| "p(t) = \\boxed{e^{\\frac{3}{4}(t^2 - 6t + 1)}}\r\n", | |
| "$$\r\n", | |
| "\r\n", | |
| "## Для $2 \\leq t$\r\n", | |
| "\r\n", | |
| "$$\\Large{\r\n", | |
| "p(t) = e^{-\\left(\r\n", | |
| " \\int_{0}^{1} 3dt + \r\n", | |
| " \\int_{1}^{2} \\frac{3}{2}(3-t)dt + \r\n", | |
| " \\int_{2}^{t} \\frac{3}{2}dt\r\n", | |
| " \\right)} \\\\= e^{-\\left(\r\n", | |
| " (3 - 0) + \\frac{3}{2}((3 \\cdot 2-2^2/2) - (3 \\cdot 1-1^2/2)) +\r\n", | |
| " (\\frac{3}{2}t - 3)\r\n", | |
| " \\right)}\r\n", | |
| "}$$\r\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 80 | |
| }, | |
| "id": "IT_sSnTskMkF", | |
| "outputId": "56dbcb93-e5a0-4566-d953-9b958ae68af1" | |
| }, | |
| "source": [ | |
| "expr = parse_latex(r'''-(\r\n", | |
| " {\\int_{0}^{1}3 dt} +\r\n", | |
| " {\\int_{1}^{2}\\frac{3}{2}(3-t) dt} +\r\n", | |
| " {\\int_{2}^{t}\\frac{3}{2} dt}\r\n", | |
| " )''') # хз почему их так странно сортирует\r\n", | |
| "expr" | |
| ], | |
| "execution_count": null, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "image/png": "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\n", | |
| "text/latex": "$\\displaystyle - (\\int\\limits_{2}^{t} \\frac{3}{2}\\, dt + \\left(\\int\\limits_{1}^{2} \\frac{3}{2} \\left(3 - t\\right)\\, dt + \\int\\limits_{0}^{1} 3\\, dt\\right))$", | |
| "text/plain": [ | |
| " ⎛t 2 ⎞\n", | |
| " ⎜⌠ ⌠ 1 ⎟\n", | |
| " ⎜⎮ 3 ⎮ 3 ⌠ ⎟\n", | |
| "-⎜⎮ ─ dt + ⎮ ─⋅(3 - t) dt + ⎮ 3 dt⎟\n", | |
| " ⎜⎮ 2 ⎮ 2 ⌡ ⎟\n", | |
| " ⎜⌡ ⌡ 0 ⎟\n", | |
| " ⎝2 1 ⎠" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 4 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 53 | |
| }, | |
| "id": "5wRRTXqTyyjq", | |
| "outputId": "7066bf16-7701-4617-c7c8-0ec86aaaa907" | |
| }, | |
| "source": [ | |
| "expr.simplify().factor() # оаоаоаоаоа" | |
| ], | |
| "execution_count": null, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "image/png": "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\n", | |
| "text/latex": "$\\displaystyle - \\frac{3 \\left(2 t + 3\\right)}{4}$", | |
| "text/plain": [ | |
| "-3⋅(2⋅t + 3) \n", | |
| "─────────────\n", | |
| " 4 " | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 5 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "q8Y-ugcd43Xw", | |
| "outputId": "d2c444b4-7ff5-4ae0-a02c-7ef2dc6db8c0" | |
| }, | |
| "source": [ | |
| "print(latex(expr.simplify().factor()))" | |
| ], | |
| "execution_count": null, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "- \\frac{3 \\left(2 t + 3\\right)}{4}\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "IoxTsjF25XGM" | |
| }, | |
| "source": [ | |
| "$$\\Large\r\n", | |
| "p(t) = \\boxed{ e^{- \\frac{3 \\left(2 t + 3\\right)}{4}} }\r\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Z9E4fHar7Gjx" | |
| }, | |
| "source": [ | |
| "## Посчитаем среднюю наработку до отказа $T_1$\r\n", | |
| "\r\n", | |
| "$$\r\n", | |
| "T_1 = \\int_{0}^{\\infty} p(t) dt = \r\n", | |
| "{\\int_{0}^{1} e^{-3t} dt} +\r\n", | |
| "{\\int_{1}^{2} e^{\\frac{3}{4}(t^2 - 6t + 1)} dt} +\r\n", | |
| "{\\int_{2}^{\\infty} e^{- \\frac{3 \\left(2 t + 3\\right)}{4}} dt}\r\n", | |
| "$$\r\n", | |
| "\r\n", | |
| "Подынтегральная функция во втором интеграле не берется в элементарных функциях.\r\n", | |
| "\r\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 80 | |
| }, | |
| "id": "uJFdPHsd46Sw", | |
| "outputId": "ded70b8a-d627-4ff6-9670-fd804a3538b6" | |
| }, | |
| "source": [ | |
| "expr = parse_latex(r'''\r\n", | |
| "{\\int_{0}^{1} e^{-3t} dt} +\r\n", | |
| "{\\int_{1}^{2} e^{\\frac{3}{4}(t^2 - 6t + 1)} dt} +\r\n", | |
| "{\\int_{2}^{\\infty} e^{- \\frac{3 \\left(2 t + 3\\right)}{4}} dt}\r\n", | |
| "''').subs({Symbol('e'): E})\r\n", | |
| "expr" | |
| ], | |
| "execution_count": null, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "image/png": "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\n", | |
| "text/latex": "$\\displaystyle \\int\\limits_{2}^{\\infty} e^{- \\frac{3 \\left(2 t + 3\\right)}{4}}\\, dt + \\int\\limits_{1}^{2} e^{\\frac{3}{4} \\left(\\left(t^{2} - 6 t\\right) + 1\\right)}\\, dt + \\int\\limits_{0}^{1} e^{- 3 t}\\, dt$", | |
| "text/plain": [ | |
| "∞ 2 \n", | |
| "⌠ ⌠ \n", | |
| "⎮ 3⋅(2⋅t + 3) ⎮ 3 ⎛ 2 ⎞ 1 \n", | |
| "⎮ -─────────── ⎮ ─⋅⎝t - 6⋅t + 1⎠ ⌠ \n", | |
| "⎮ 4 ⎮ 4 ⎮ -3⋅t \n", | |
| "⎮ ℯ dt + ⎮ ℯ dt + ⎮ ℯ dt\n", | |
| "⌡ ⌡ ⌡ \n", | |
| "2 1 0 " | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 7 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 69 | |
| }, | |
| "id": "QA08gb5N8RGQ", | |
| "outputId": "632e782d-4553-47cb-ba2c-599fbd5e10e9" | |
| }, | |
| "source": [ | |
| "expr.simplify()" | |
| ], | |
| "execution_count": null, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "image/png": "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\n", | |
| "text/latex": "$\\displaystyle - \\frac{1}{3 e^{3}} - \\frac{\\sqrt{3} \\sqrt{\\pi} \\operatorname{erfi}{\\left(\\frac{\\sqrt{3}}{2} \\right)}}{3 e^{6}} + \\frac{2}{3 e^{\\frac{21}{4}}} + \\frac{\\sqrt{3} \\sqrt{\\pi} \\operatorname{erfi}{\\left(\\sqrt{3} \\right)}}{3 e^{6}} + \\frac{1}{3}$", | |
| "text/plain": [ | |
| " -6 ⎛√3⎞ \n", | |
| " -3 √3⋅√π⋅ℯ ⋅erfi⎜──⎟ -21/4 -6 \n", | |
| " ℯ ⎝2 ⎠ 2⋅ℯ √3⋅√π⋅ℯ ⋅erfi(√3) 1\n", | |
| "- ─── - ────────────────── + ──────── + ────────────────── + ─\n", | |
| " 3 3 3 3 3" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 8 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 37 | |
| }, | |
| "id": "En9Genv28VjU", | |
| "outputId": "6b6cf602-acbc-47fd-b2f6-cce64c07ab60" | |
| }, | |
| "source": [ | |
| "expr.evalf()" | |
| ], | |
| "execution_count": null, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "image/png": "iVBORw0KGgoAAAANSUhEUgAAANMAAAASCAYAAADBs+vIAAAABHNCSVQICAgIfAhkiAAABiVJREFUaIHt2nmsXVUVBvAftRUElSpGXlQi9kG1DKEqQYwilkSN0TYMgUQjUCMoRlTCmJAYi4mBqsEBJ4jiSCQRlMGnCCoYBgVREEvDJDyGWJTSgCAV++r1j7Uv7/S8c+69Z59TSMz9kpv9svdaZ631vbOHtfZhjDHG2Gp4Fc7H3/A0pvElvKThc1bj13gQG7EBt+DT2KkD+ZXoDfltrtDbBsfiRjyJf+FmHId5NbHkcNJEJyeWnXAMfop7BGeP4zp8qCKWHBs5sZDH8fQAvx7uyC94D67EQ4Kze/FjvLmtzjYlpUncgJfjUtyB/bAMd+IteHSA0SL+gz9hLf6BHbA/9hXB7y8mTq78UhxcY/sAHIQpvLc0dgHen2xchqfwDizBD3BUST6Hk6Y6ObEch29gHa7GA9gZh2JHXIzDxcuYayM3/qYcExNhoZgMZTyJL3Tg12qcmvovwXrshhWYn/z6YQc64JeC/I+X+s9O/d+sUqrBdjX9n03P+npL+UH4XdJZUeo/JPXfi5cV+p+Py9PYoSWdHE665LEuloOw3NyVfkJMrB4Oa2mD5rHkcExMpukR/c3xa0LsvA+LCVjEsoLPbXUQM72H+8z9B73I7Ha9Q5VyA+yT7Fy1leT3TvIP4Xmlse+nsY9V6C1NY78p9OVw0iWPg2IZhNOT3jktbeTE0pTjPqaNPply/HpT0rm05pn/xBOlvkY6RUeWpfZK/Lek9ASux/biuNUGy1N721aS/3Bqv21uDjCR2qrVpN93gFhFyeOkSx4HxTIIm1I709JGTixNOS5iW3xALAafTParFpEcv+4WqcR+ttwx4W1iEv6q1N9IZ35h8LWpvavC+f6D34nFolAwKk7GC8U5fl+8VUyMszqSL+IF4p+xGd+qGF+f2tdUjC1K7fz09x3yOOmKx2Gx1KF/jocrhsgOs5ETS1OOi5gQOVUR9+GD+G1LvzbgNHEMXCvyn0fFLrdCnHw+UnpOI53iZNoxtY/XONjvX1gzXoeTRWLcxxWisvRIR/JFHJH8m7JlsaKPKbwPJ+JCQRYswBkFuX41KIeTrngcFksdzsJe+LnIK9rYyImlKcd9fAfX4naxuyzC8WLn/IWonP25hV9EcWNaVACPLfTfg++KgkkZI+vUlSm7xISoGk6IxHORKHm/oSP5IvpHlnNrxi8UL9ikWGnOxZdxqzh6PJDkykeH5wLDYqnCJ3CSWPGP3Eo2hiGX4zNELvV3Uf1bIyqWZ4sddFUHvp2Ki8QkmBQ51RvF8fMCfK4jHZ8XydZJNY58NY1/NCeKAl4t7gTWdCy/p/DvQYOT9QVi6/4L/o3HxPb9umSjZ/aIksNJFzyOGksRxyed283mLYMwio3cWJpwPAy7JflimTvHr7envp9UyG8vCjCbzR5FG+sUd6Y7U7u4xsHdU1t3Th0V94sVa09zk7o28qMm65vE3cHeohy/UNy/TIsY14tzOnmcdMFj08LDCaJyt0Yk53WXnE1t5MbShONh6B/vi5W5HL/692dXV8g/hZvEfHh9Sx08e6VxYivvGf2rimHy24mz+Qx2yfRpZbLxlULfc1EabxrLacneLUZbnJrY6PqdWGkux8PwrqSztqVf5ySdz9TYuTaNLy/05eg8g6YXYZNi615Q6l9sNkksYp7ZS9jrW8iXcWSSuXyATB8vruhbKlbADXhFaezZvrRtEsunkuzNeOkI8jk2cmJpyvES1RNyV1GZ64lyeRu/jjD7adIrS2PvFjncRlt+upaj8wwmze4Cl+BMkRT2xNZaVppOY7uW+k9IRq7Ceek55+OvSX4d9mghX8bAFaKEG3GNOFefmeLcJC7gDqyQb8pJrk7TWI5OcjP4okjQy7+VLW2QF0tTjleJCt6U+NJltUj6NyY7U+beSzX1a554v3rJj+8lO5eJSdETd1ttdbbALqJMuU5cWN2v/uPBadWTaS9B5K3ifDwjypV/EMSVV9Gm8kUs0SxZPwV/FEnx06Iq8zXx0WQdmnDSRqdJLKvUfxja/13T0kYfTWNpyvGB+JGoQj4mJt4j4kU+ytxvSHP9WiAW7t+LyTEjSts/E/dSXemMMcYYY4wxxhhjjPH/g/8B00AWUc+4JjwAAAAASUVORK5CYII=\n", | |
| "text/latex": "$\\displaystyle 0.337900727095088$", | |
| "text/plain": [ | |
| "0.337900727095088" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 9 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 723 | |
| }, | |
| "id": "3oI9DXZR91JX", | |
| "outputId": "4f550266-1efe-496c-8aad-2e139af851f3" | |
| }, | |
| "source": [ | |
| "e1 = exp(-3*t), (t, 0, 1)\r\n", | |
| "e2 = exp(3/4*(t*t - 6*t + 1)), (t, 1, 2)\r\n", | |
| "e3 = exp(-3/4*(2*t + 3)), (t, 2, 5)\r\n", | |
| "\r\n", | |
| "p1 = plot( *e1, show=False)\r\n", | |
| "p2 = plot( *e2, show=False, line_color='red')\r\n", | |
| "p3 = plot( *e3, show=False, line_color='blue')\r\n", | |
| "\r\n", | |
| "p = plot(show=False, ylabel='p(t)', title='Нормальная шкала')\r\n", | |
| "p.append(p1[0])\r\n", | |
| "p.append(p2[0])\r\n", | |
| "p.append(p3[0])\r\n", | |
| "\r\n", | |
| "p_log = plot(show=False, ylabel='p(t)', yscale='log', title='Логарифмическая шкала')\r\n", | |
| "p_log.append(p1[0])\r\n", | |
| "p_log.append(p2[0])\r\n", | |
| "p_log.append(p3[0])\r\n", | |
| "\r\n", | |
| "pg = PlotGrid(1, 2, p, p_log, size=(8, 10))" | |
| ], | |
| "execution_count": null, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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X3270XQqAAwhVuGlvuWkm3ADwYMqoSs0YO0BLCTdATgtVuEnu75ZizA2Avje0vEhvN+7Rsys2+y4FwAGEKtwUJFIDiunvBuDJtFGVqntrK7M2gRwWrnVuGFAMoI/V1taqtrZWjY1BV9T7jhyotxv3aM2W3Ro9sNRzdQA6E66WG8bcAOhj7VPBy8vLJUnHDa/Q86u26sU1TAkHclWowk37mBumYQLw5eihZSpNxlX31hbfpQDoQqjCTQEDigF4Fo+Zpoyq1NK3t/suBUAXQhZu2lcopuUGgD8zjxioxWu3acfeFt+lAOhEqMJN+yJ+jLkB4NPxI8rV5qSX1rLeDZCLQhVu9ndLMeYGgEcnjKqQJC1eyyaaQC4KVbj5x/YLjLkB4E//ogLNGDtAz61iUDGQi0IVbljnBkCuOGpIPy1es02tbXzYAnJNyMJNMKCYMTcA+kptba2qq6v3L+LXrmpMpXY07dMbG3Z4qgxAV8IVbmIxFRfEZb4LAZA3Oi7i127qqEoNLivUC28x7gbINaEKN8lETHtaWrWzaZ/vUgDkuVEDSuSctIhwA+Sc0IUbiTE3APwzM506fpC2s9YNkHNCFW4K2H4BQA45emiZHnttoxp2NPkuBUCakIWb9gHFzE4A4N+00QMkSXWrN3uuBEC6UIUbM5OJbikAueHYw/trwrD+WsxKxUBOCVW4kYKAQ7cUgFxQWBBXSTKuOgYVAzklhOGGlhsAueOUowYpGY+paV+r71IApIQv3IhwA6DvdLWIX7sJh/fX31du1qvr6JoCckX4wo2ZmuiWAtBHulrEr93UUZWSxGJ+QA4JYbhh40wAuWNwWaE+OmmoVm3a5bsUACmhCzcxmVpouQGQQ0qTcT26dIOc44MXkAtCF27M2DgTQG6ZNqZSm3Y2a82W3b5LAaCQhhsGFAPIJdNGVWr6mAF6uZ5BxUAuCF+4EevcAMgt4w4r02vrt+vvK1mpGMgF4Qs3dEsByDHxmGnK6Ep2CAdyRCjDDd1SAHLNqeMGqby4QI27m32XAuS98IUbuqUA5KCjh/bXc6u2aDHjbgDvwhduWOcGQA46YVSFYsZifkAuCF24ibFxJoAc1K8woVmThmrZ+u2+SwHyXsJ3AT3FgGIAfam2tla1tbVd7i2VbmC/Qv1hUb32tbYpEQ/dZ0cgMkL308fGmQD60sH2lko3bXSlChIxvbFhRx9UBqAr4Qs3xvYLAHLT1FEV2ra7hXE3gGchDDd0SwHITSMHlGhIWSHhBvAsfOFGwWwpNqgDkGvMTLOOHapdza2+SwHyWvjCjZkkpoMDyE2jBpTo0aUbtHH7Xt+lAHkrhOEm+JOuKQC5aOqoCg2vKNLitdt8lwLkrdCFm7iZThxTqeZ9NPsCyD3HDq9Qw85mPbdqi+9SgLwVunAjSQtXb6VbCkBOSiZimjyinEHFgEehCzf7u6WYDg4gR00fO0CtbW3a27zPdylAXgpfuFGQbhhzAyBXnTCyUq+s265X3mYrBsCH0IWbGC03AHLc1FEVkqS61XRNAT6ELtzQLQUg1w3sV6hZxx6mNxt2+i4FyEshDDft69wQbgDkrn6FBXri9Y0sOAp4EL5wk/qTlhsAfaG2tlbV1dXd2hU83bTRlWrZ16pVm3ZlqTIAXQlfuEm13DTRcgOgD/RkV/B000ZVakdTK1PCAQ9CGG6CP9kZHEAuO2pIP/UvSmjRGsIN0NdCF25iTAUHEAKxmGnO5MO1ZVez71KAvBO6cMNsKQBhMbS8SA8v2aDGPS2+SwHySmjDDbOlAOS6qaMrJUkv0jUF9KkQhptUtxQtNwBy3AkjKzRz7AAte2eH71KAvBK+cJP6s4lwAyDHlSQT2tm8T0+/0eC7FCCvhC7cxIwBxQDCY9qoSi1eu037uGcBfSZ04eYfU8FZ9RNA7nvfkQM1tH+RXl9P1xTQV0IXbiQpHjM1t7b6LgMADuq4ERVauWmXXmBQMdBnQhlukvEYA4oBhMLh5UUa2r+IlYqBPhTOcJOIqaWVbikAuc/MdNZxQ7Vj7z7fpQB5I5ThpiAeY7YUgNAYUVmiJ5dt1DuNe32XAuSFUIabwgTdUgDCY1pqMT+6poC+EcpwE3RLEW4AhMPEw/vr/UcO1Gvrt/suBcgLoQw3BXGj5QZAaBTEY2ptc/rrchbzA/pCKMNNMhFjET8AoTJtdKWWvL1de5pZxgLItnCGmzjdUgD6Rm1traqrq9XY2Nir61SNHqAJw8r06tu9uw6AgwtluOlXlFDMDn4eAPTW7NmzVVNTo/Ly8l5dZ8qoCr2ybrsWrt6SocoAdCXhu4BD4Zy0nTUjAIRIZWlSRw4u1QurmTEFZFsoW26YCg4gjD50zGFqbXNyjkVIgWwKZbhhQDGAMDpqSD899UaDVm7a5bsUINLCGW7YWwpACE1tX8yPrikgq8IZbuiWAhBCRwwq1clHDdTqzbTcANkU3nBDtxSAkInFTMlEXA8vecd3KUCkhTPcxOO03AAIpWmjK/Vmwy5t3dXsuxQgssIZbuiWAhBSJ46p1PQxA/RS/TbfpQCRFd5w09rGdEoAoXPc8Aq9sGYri/kBWRTKcFOYCMpm3A2AsClOxjXp8P5a9BYzpoBsCWW4ScZT4YauKQAhdOr4wXrtnR3skQdkSTjDTYJwAyC8jh5apm27W/Ta+u2+SwEiKdzhhk89AEJo6qgKjRpQrCXrCDdANoQz3NAtBSDEDq8o0b5Wp2ff3OS7FCCSwhluUi03TYQbACE1bcwABhUDWRLqcEPLDYCwOvmogTq8slhvb93juxQgckIdbmi5ARBWE4eVq271VtWtofUGyLRQhptCxtwACLljhpWpanSlVjXs9F0KEDmhDDfMlgIQdgXxmAriMT322kbfpQCRE+5wQ8sNgBCbNrpSS9dv166mfb5LASKFcAMAnpw4plJTR1XolXWNvksBIiWc4aZ9zE1rq+dKAODQTR5ZoYWrt6qOTTSBjApnuKHlBkAEVJQkNW5IP1pugAwj3ACARycdOUgLVm5RW5vzXQoQGaEMN4WJuCTWuQGQfbW1taqurlZjY3ZaVyYO76/GPS16kynhQMaENNwwFRxA35g9e7ZqampUXl6eletXja6UJL3AVgxAxoQy3BTETDPGDtgfcgAgrMYOKtX0MQP0cv0236UAkRHKdBCPx/TCW1u1eWez71IAoFfMTP2LE1qwihlTQKaEMtxIwaBiBhQDiIKpoyu1smGXtuziAxuQCaENN4WJGAOKAUTCtNGVmnR4f7qmgAwJbbih5QZAVEweUaFl7+zQc3RNARkR2nBTmIgzWwpAJBQVxDVpeLleWM2MKSATQhtukomYmvax/QKAaPjwMUMkY3FSIBPCG27idEsBiI4jh/TT86u2aOn67b5LAUIvtOGmsIABxQCiYxqL+QEZE9pwk4wTbgBEx2H9i3TKUYOYMQVkQHjDDbOlAETMgH5JLVi5Wc6xiSbQG6ENN4WJOC03ACJl2uhKbdjepLVbdvsuBQi1EIebmJqZLQUgQqpGV2pEZbFeXEPXFNAboQ03yUSMdW4ARMr4w8q0dVezXljDoGKgN0IbbgoTMTW1EG4AREciHtMJoyqYMQX0UmjDDS03AKLotPFDVJKMa1fTPt+lAKGV1XBjZrPMbJmZrTCzb3by/Cgze3LKlCk6/vjj9eCDD3b72oXMlgIQQeOHlmnh6q1avJZxN8Chylq4MbO4pOslnSlpoqQLzWxih9O+LemeF198UXfddZe+9KUvdfv6SXYFBxBBJ4yskBmL+QG9kc2Wm+mSVjjnVjrnmiXdJencDuc4Sf0lqbGxUYcffni3L56Mx9Xa5rSPrikAEVJeXKAzJhympW83+i4FCK1EFq89XNLatMf1kmZ0OOc/JD0yYsQI7dq1S4899linF6qpqVFNTY0kqaGhQVKw/YIkNbe2KREP7dAhAHiPgf0Kdf9Lb6utzSkWM9/lAKHjOxVcKOnm+vp6Pfjgg/r0pz+ttrb3tsRUV1errq5OdXV1Gjx4sKRg+wWJHXQBRM+00ZVqaW3T8o07fJcChFI2w806SSPTHo9IHUs3T9I9kvS+971Pe/fu1aZNm7p18WSCcAMgmqaNrlBza5teeItBxcChyGa4WShpnJmNNbOkpLmS5nc4Z42kD0nSa6+9pr179+5vmTmYssKEThhZoSZWKQYQMWMGlqqyJKm6t7b4LgUIpayNuXHO7TOzL0t6WFJc0k3OuSVm9j1Jdc65+ZKukvSbyZMny8x08803y6x7/csWMy1eu01N+9hgDkC0mJmmjq7UImZMAYckmwOK5Zx7UNKDHY59J+3vSyWdpGDWVI+0j7mh5QZAFJ06frDWN+5Rw469GlxW5LscIFR8Dyg+ZO2zpVjrBkAUHTO0TK+u284mmsAhCG+4YUAxgAg7dni5CuLGYn7AIQh9uKHlBkAUFRXEdfZxw9Sws8l3KUDohDjcxCVJTS2MuQEQTYPLCnX/y+sZWwj0UIjDDS03AKJt2uhKNe9r05K3t/suBQiVEIeboOWGMTcAomrq6EqVFMS0ZB37TAE9Edpwk6TlBkDEDSkr0uD+RXp2xWbfpQChEtpw849uKfqiAUTX1FGVemHNVjnHgqVAd4U33BQwFRxA9E0dXamGHU2q37rHdylAaIQ23PxjhWLCDYDomjqyQkP7F+qlehbzA7ortOEmEY8pHjO6pQBE2jHD+mtnU6sWrGTcDdBdoQ03UjDupqmFlhsA0RWPmaaMqtALb9FyA3RX6MNNcyvhBkC0nTJukMqLEtq+p9l3KUAohDrcJGm5AXCIzOyIefPm6WMf+5jvUg5qwrD+WrBqi16qZ70boDtCHW4KE3HG3AB5yMxuMrONZvZqh+OzzGyZma0ws28e6BrOuZU33nhjdgvNkBNGVshMbKIJdFPCdwG9UZiIMVsKyE83S/qFpFvaD5hZXNL1ks6QVC9poZnNlxSXdE2H13/eObexb0rtvbKiAp117FCtb9zruxQgFMLdclMQY50bIA85556RtKXD4emSVjjnVjrnmiXdJelc59wrzrlzOnx1K9jU1NSoqqpKVVVVamhoyPB30TMVJUk98PJ6tbaxmB9wMKEON8k4LTcA9hsuaW3a4/rUsU6Z2cAvfvGLevHFF3XNNR0bdgLV1dWqq6tTXV2dBg8enNlqe2ja6ErtbNqnNzbs8FoHEAYh75ZizA2AQ+OcC9XCMdNGV+rEMZVasq5RE4b1910OkNNC3XJTWEDLDYD91kkamfZ4ROpYJIwaUKJVm3br2TdDlckAL8IdbhKMuQGw30JJ48xsrJklJc2VNN9zTRljZpo2uoIZU0A3hDrcDK8s0egBJb7LANDHzOxOSX+XdLSZ1ZvZPOfcPklflvSwpNck3eOcW+Kzzkz7wLjBqiwp0MbtzJoCDiTUY26272nRK+tY1ArIN865C7s4/qCkB/u4nD5zzLD+eqm+UYvWbNWsY4f5LgfIWaFuuSlizA2ALKutrVV1dbUaG/1/kDp2eH8l4zG6poCDCHW4CWZLEW4AZM/s2bNVU1Oj8vJy36WoMBHX7MnDtHrzbt+lADkt5OEmxlRwAHllUL9CPb2sQXtbuPcBXQl5uImrpdWxYieAvDF1dKWaW9v0KuMNgS6FO9wUBOUzHRxAvpg2ukLTRlfqZcIN0KVwh5tEUD7NswDyxaB+Rdq8s0kLWMwP6FLIw01ckhhUDCCvTBlVofXb9so5uuSBzoQ83ATlM6gYQLbk0lTwdlWjB+iVtxv1FrOmgE6FO9wUtIcbWm4AZEcuTQVvN21MpSSx3g3QhXCHm/ZuqRbCDYD8MX5ImY4ZVqZVm3b6LgXISaEON0UFdEsByD+xmGlIWZEee22j71KAnBTqcMOAYgD5atqoSi3bsEONe1p8lwLknJCHG1puAOSnqjGVck5avHab71KAnBPucNPeLcWYGwB5ZvLICsVMWsSgYuA9wh1u6JYCkKf6FSZ08lGDmTEFdCLk4YYVigHkrzGDSvTimq3a18oHPCBdJMINLTcAsiUXF/FrN210pXY1t2rZhh2+SwFySrjDTUF7txQtNwCyIxcX8Ws3ZVSFjhveX0vXbfddCpBTwh1uEgwoBpC/RlaWaMP2Jv3tzU2+S9ELEnAAACAASURBVAFySqjDTSJmihndUgDyk5mpakwlg4qBDkIdbsxMRQVxuqUA5K2poypVv3WPNmzf67sUIGeEOtxIQdcULTcA8tWJYyo1Y+wALV5L6w3QLvThpqK4QG1kGwB5asKwci1eu03PryLcAO1CH26cpB1N7K0CID8lEzFNHlHBuBsgTejDTWEiziJ+APLazCMGSM5pT/M+36UAOSH04aaogDE3ALInlxfxa3fciAotrm/UK6x3A0iKQLgpLKDlBkD25PIifu2mja6UJLqmgJTwhxtmSwHIcwNKkxo7qERvbKDlBpAiEG6KCuLaywrFAPLc9LED9fQbm+Sc810K4F3ow01hIqYmuqUA5LkpIyu0ZVezVm3a5bsUwLvQh5tghWJabgDkN8bdAP8Q+nBTmIgxoBhA3jtycD+9/8iBWr2Zlhsg9OGGlhsAkGIxU2EipkeXbvBdCuBdBMINLTcAIAVdU29s2KnG3azajvwW+nBTmIhrX5vTvlZabwDkt6oxAzRj7AC9VM+4G+S30IebooLgW6BrCkC+O35Euere2qqFqwk3yG+hDzeFibgk0TUFIO+VJBOaOKy/6gg3yHOhDze03ADIpjDsLZXuv22ZbvrV5dI+NtFE/gp9uKHlBkA2hWFvqXRHDipV8eJF0ksv+S4F8Cb04aa95YYtGABA0kknBX/+7//6rQPwKPThpr3lpmkfLTcAoJEjpeOPl1as8F0J4E34ww0tNwDwbhMmSH/4g+8qAG9CH26KCmi5AYB3Oekkqb5eWrPGdyWAF6EPN4UJWm4A4F1OPjn489ln/dYBeBL6cEPLDQB0cNxx0qmnSsuW+a4E8CL04aa95aaJlhsACCQSUjIp/elPvisBvAh9uClKxFWajLPODQCkO/lk6eWXpZAsPghkUvjDTTKuXc2t2ku3FAD8w0knSc5JCxb4rgToc+EPNwwoBoD3mjFDOu00adEi35UAfS704SYRjykRM7qlACBdv37Szp3Sww/7rgToc6EPN1IwY4qWGwDo4OSTpeeek5qbfVcC9KmIhJsYY24AZEXYdgV/l9NPD7qn6JpCnolEuClMMFsKQHaEbVfwd5kxQ3r6aemZZ3xXAvSpSISbooIY69wAQEeHHSaNGyctXOi7EqBPRSTc0HIDAJ0680zp8celNj4AIn9EJ9ww5gYA3mvaNGnrVmnJEt+VAH0mIuEmxmwpAOjMKadI8XgwawrIE9EIN4m49jTTcgMA7zFmTPD1+OO+KwH6TDTCDd1SANA5M2n69GDGlHO+qwH6RCTCTSGzpQCgax/4gPT229LKlb4rAfpEJMINs6UA4AA+8AHp1FPZRBN5IxrhhkX8AKBrEyYEs6UefdR3JUCfiEa4KYhp7z66pQCgU2ZB683TT/uuBOgTEQk3cbW2ObW0EnAAoFNnnSVVVEhvveW7EiDrIhJugm+DrikA6MK0adLixdJf/+q7EiDrIhJu4pLEQn4A0JXjj5cqK6UXXvBdCZB10Qg3ifZwQ8sNAHQqFpM+/GHpgQd8VwJkXSTCTUlhXIP6JQk3AHAgM2dKy5dL69b5rgTIqkiEm2Q8pk07m9XEjCkA6Nppp0nvf7/097/7rgTIqkiEm+Jk0C21h5YbABlWW1ur6upqNTY2+i6l9yZPZr0b5IVIhJt/DCgm3ADIrNmzZ6umpkbl5eW+S+m9eDxY7+bJJ31XAmRVJMJNcSrcsDM4ABzEqadKLS2Mu0GkRSLc7F/nhjE3AHBgp58urV4tPfWU70qArIlIuEl1S9FyAwAHNnlysFIxXVOIsEiEm/3dUoy5AYADi8el2bOlhgbflQBZE4lww4BiAOiBadOk+fOlNWt8VwJkRaTCDS03ANANp58e/EnXFCIqEuEmHjMl4zH2lgKA7jj2WGnWLOmVV3xXAmRFJMKNFMyYolsKALohFpPKyqS775ac810NkHERCjdxwg0AdNcHPyjV10srVviuBMi4yISb4mScMTcA0F0f/KB08snSM8/4rgTIuMiEm6IELTcA0G3jxkmrVkkPP+y7EiDjohNuknHtYUAxAHSPmfShD0lPPCG1ce9EtEQn3CQYUAwAPTJrljRpkvTyy74rATIqMuGmOEm3FAD0yCmnBGNuHn/cdyVARkUn3BTE2RUcAHpixAjpmGMIN4icyISbIWWF6l9c4LsMAAiXuXOld96Rmpt9VwJkTGTCTXOr01ubd/suAwDCZfJk6cUXpQULfFcCZExkwk0xi/gBQM+ddlqwYvFTT/muBMiY6ISbZEx7WlrlWEocALqvoiKYNfXQQ74rATImOuGmIK7WNqeWVsINAPTI1KnS889LjY2+KwEyIqvhxsxmmdkyM1thZt/s4pxPTJw4UZMmTdJFF110yO9VVBCXJLZgAICeOuOMYFE/tmJARCSydWEzi0u6XtIZkuolLTSz+c65pWnnjJP0rWeffVaVlZXauHHjIb9fcTIIN3tbWlXOrCkA6L6ZM6UBA4KuqdmzfVcD9Fo2W26mS1rhnFvpnGuWdJekczucc4mk6ysrKyVJQ4YMOeQ3K25vuWGtGwDomWRSmj5devRR35UAGZHNcDNc0tq0x/WpY+nGSxp/0kknaebMmXqoiwFtNTU1qqqqUlVVlRoaGjo9p5huKQA4dGecIS1fLq1e7bsSoNd8DyhOSBr31FNP6c4779Qll1yibdu2veek6upq1dXVqa6uToMHD+70QkVJwg2AzKutrVV1dbUaoz7Y9qMflSZMkB55xHclQK9lM9yskzQy7fGI1LF09ZLmFxQUaOzYsRo/fryWL19+SG/W3nKzl24pABk0e/Zs1dTUqLy83Hcp2TV+vLRzp/Tww74rAXotm+FmoaRxZjbWzJKS5kqa3+GcP0k6TZI2bdqkN954Q0ccccQhvRndUgDQC2bSRz4S7DO1b5/vaoBeyVq4cc7tk/RlSQ9Lek3SPc65JWb2PTObkzrtYUmbJ06cqNNPP10//vGPNXDgwEN6v2K6pQCgd2bPlsaODda8AUIsa1PBJck596CkBzsc+07a352kKyVd0dv3YrYUAPTSKadIL78cdE29//2+qwEOme8BxRnTvogf+0sBwCEaMCAYWPzmm74rAXolMuHmH4v4tXmuBABCbMYM6Y47pM2bfVcCHLLIhJuiRPCtMOYGAHph1izJORb0Q6hFJtwk4jGdOKZSBTHzXQoAhFdVVbCg31NP+a4EOGSRCTeStOydHdqwo8l3GQAQXvG4NHCg9Kc/SW108yOcIhVuSpIJ7W5mfQYA6JUzz5QOOyyYOQWEUKTCTXEyrj0MKAaA3vnoR4Ng8+CDBz8XyEHRCjcFce2h5QYAeueww6Rp0wg3CK1ohZtknNlSAJAJH/uYlExKW7b4rgTosUiFm5JkXLtZoRgAeu/UU6Unn2RKOEIpUuGmqCDO9gsAkAnTpwezph57zHclQI9FKtyU0C0FAJkRj0tz50p//rPUyn0V4RKpcFNMyw0AZM5JJ0kNDdLChb4rAXokWuEmSbgBgIz5yEek004Lxt4AIRKtcFNAtxQAZMzAgUGX1D33+K4E6JFIhZuSZFz72pya97GQHwBkxJw5kpm0dq3vSoBui1S4KSqIS2JncADImLPOkl58kQX9ECqRCjclyYQkMe4GADJlwoRgYDH7TCFEIhVuipPBt0PLDQBkiFmwFcNNN0m7d/uuBuiWaIWbgqDlhp3BASCD5syRjj+eWVMIjWiFm2Qw5mYvLTcAkDmnnCK9/rr0xz/6rgTolkiFm5JUuGF/KQDIoGRSuugiaf16qY3ZqMh9kQo3xQVxjagsVlMLP3wAkFGnnBLMmHruOd+VAAcVrXCTjKt+6x7tbGLMDQBk1FlnBZtpPv2070qAg4pUuKFbCgCypKJCKiuTfv9735UABxWtcMNsKQDInn/6J2nHDumNN3xXAhxQpMJN+2wpFvEDgCyYM0dat45ZU8h5kQo3yURMBXHTbqaCA0DmjRolnX669OqrvisBDihS4UYKZkztZkAxAGTHhz4k3XZb0IID5KjIhZuSZIIBxQCQLeedJ40cKT36qO9KgC5FMNzE6ZYCgGyZMEEqKZFuv913JUCXohduCuMMKAaAbDGTLrxQammRNm/2XQ3QqeiFm4IEU8EBIJvOOitYzK+21nclQKciF26Kk3HG3ABANlVVSe9/v7Rwoe9KgE5FLtyUEG4AILvMpBkzpN/+Vtq+3Xc1wHtELtwUJxlzA+DgzOyfLrnkEv3zP/+zHnnkEd/lhM/HPx604DzwgO9KgPeIXLgpTTLmBog6M7vJzDaa2asdjs8ys2VmtsLMvnmgazjn/vSb3/xGN9xwg+6+++7sFhxFM2ZI9fVspImcFLlwQ7cUkBduljQr/YCZxSVdL+lMSRMlXWhmE83sODO7v8PXkPbX/eAHP9Dll1/el7VHQywmXXCBdPPNwX5TQA5J+C4g04qTcTXta1Nrm1M8Zr7LAZAFzrlnzGxMh8PTJa1wzq2UJDO7S9K5zrlrJJ3T8RpmZt/4xjd05plnaurUqZ2+T01NjWpqaiRJDQ0NmfsGouKCC6RFi6S//EX6xCd8VwPsF8mWG4mdwYE8NFzS2rTH9aljXfnKY489pnvvvVc33HBDpydUV1errq5OdXV1Gjx4cAZLjYj3vU9avly6807flQDvEsGWm+Bb2tPcqrKiAs/VAMhVzrnrJF3ru45Qi8Wkyy4Lws327VL//r4rAiRFsOWmdH/LDeNugDyzTtLItMcjUseQTR/8oLR0qTR/vu9KgP0iF25KCDdAvlooaZyZjTWzpKS5kviNm20zZ0of/rDEjDPkkMiFm/3dUi2MuQGiyszulPR3SUebWb2ZzXPO7ZP0ZUkPS3pN0j3OuSU+68wLsZg0fXowY4q9ppAjIhdu2ltudjXRcgNElXPuQufcMOdcgXNuhHPuxtTxB51z451zRzrn/tN3nXnj/POD9W7++EfflQCSIhhuigviiplYpRhARtTW1qq6ulqNjY2+S8ldU6cGi/o995zvSgBJEQw3pcm42py0m24pABkwe/Zs1dTUqLy83HcpuctM+uhHpRtvlN5+23c1QATDTWEw5oZuKQDoQxdeGOwUzqwp5IDIhZuSVLhhET8A6EPHHCPt3RvsFA54FrlwU1zAgGIA8OKSS6R4XHr9dd+VIM9FLtzEY6bigjgtNwDQ12bPlurqpDvu8F0J8lzkwo0klRbGtYvZUgDQtw4/XPr856V775Wc810N8lgkw01JMqHdTbTcAECfO+UU6bXXpGef9V0J8lhEww0tNwAyg3Vueuj886XjjpNuucV3JchjkQw3pYUJxtwAyAjWuemhfv2kKVOke+6R9uzxXQ3yVMJ3AdlQkoxrx17CDYADmzVrljZt2tStc1955RVVVVVluaLMaGho0ODBg/0VsGOHtG+fdOyxUmXlAU/1XmsPUGt29KTWF1544SHn3KyDnRfJcFOaTGjD9r2+ywCQ4x566KFun1taWqq6urosVpM5VVVVfmttbZXGjpVOPln6/e8PeKr3WnuAWrOjh7UeNNhIEe2WKimMs84NAPgSj0vV1dJtt0nr1vmuBnkokuGmNMmYGwDwau7cYObU3Xf7rgR5KJLhpoR1bgBk2KBBg3yX0G3V1dW+S5COOipY6+bWWw+45k1O1NpN1Jod2ajVXG4stNTtIrrTN3fd48v1s0ff0Ir/PFOJeCTzG+Cb+S4gQzJ670EHd98tffaz0iOPBK04QO91694Tyd/8Jclgf6ndLbTeAOgd1rnphXPOkZJJ6Y9/9F0J8kwkw01p+87gDCoG0Eusc9MLpaXS5z4n3XCDRDhEH4pkuGlvudnFoGIAGfDQQw/p1Vdf1VFHHaUf/vCHvsvp0uc//3kNGTJExx57rO9S/uGTn5RGjZL+8Id3HV67dq1OP/10TZw4UZMmTdK1117rqcCD27t3r6ZPn67Jkydr0qRJ+u53v+u7pINqbW3VlClTdM455/gu5YDGjBmj4447TieccEJG15GKZLgpLyrQccP7axf7SwHopdbWVl1++eUaN26cli5dqjvvvFNLly71XVanPvvZz/Zo7Z4+UVUllZRI1133roHFiURCP/3pT7V06VItWLBA119/fc7+uxYWFuqJJ57QSy+9pMWLF+uhhx7SggULfJd1QNdee60mTJjgu4xuefLJJ7V48eKMjmmLZLhJFsT0yrrt2km4AdBLzz//vI466igVFhYqmUxq7ty5+vOf/+y7rE594AMf0IABA3yX8W5m0le/Goy9Wbhw/+Fhw4Zp6tSpkqSysjJNmDBB63J0TRwzU79+/SRJLS0tamlpkVnujqmvr6/XAw88oC984Qu+S/EmkuGmH2NuAGTIunXrNHLkyP2PR4wYkbO/hHPW+edLS5YEY286sXr1ar344ouaMWNGHxfWfa2trTrhhBM0ZMgQnXHGGTld69e+9jX96Ec/UiyW+7/izUwf+chHNG3aNNXU1GTsurn/nR+CkmQQbhhzAwA5oH9/6YorpL/+Vdq27V1P7dy5UxdccIH++7//W/379/dU4MHF43EtXrxY9fX1ev755/Xqq6/6LqlT999/v4YMGaJp06b5LqVb/va3v2nRokX6y1/+ouuvv17PPPNMRq4byXDT3nLDFgwAemv48OFau3bt/sf19fUaPny4x4pC6rzzpI0bpXvv3X+opaVFF1xwgT75yU/q/PPP91hc91VUVOj000/PvbFNKc8++6zmz5+vMWPGaO7cuXriiSf0qU99yndZXWr/WRoyZIjOO+88Pf/88xm5biTDTWlharYUY24A9NKJJ56o5cuXq6mpSc3Nzbrrrrs0Z84c32WFz9Sp0uTJ0o03Ss7JOad58+ZpwoQJuvLKK31Xd0ANDQ3almpx2rNnjx599FEdc8wxnqvq3DXXXKP6+nqtXr1ad911lz74wQ/qtttu811Wp3bt2qUdO3bs//sjjzySsZl+kQw37d1SDCgG0FuJREK/+MUvtHz5ck2YMEGf+MQnNGnSJN9lderCCy/U+973Pi1btkwjRozQjTfe6Lukd7v8cqmuTnr8cT377LO69dZb9cQTT+iEE07QCSecoAcffNB3hZ1av369Tj/9dB1//PE68cQTdcYZZ+T8FOsw2LBhg04++WRNnjxZ06dP19lnn61Zs7q16fdBRXL7BUma8H8e0qdmjtK/nz2xV4UB6FTuThXpmYPee2pra1VbW6snn3xSy5cv74uaomvv3mBw8eDB0u9/77sahFP+br8gBV1TOxlzA6CXWKE4g4qKpClTpDfekFat8l0NIizC4SbBmBsAyDVf/GKw3k2OjgNBNEQ33CQT2s1UcADILSNHBvtN/exn0q5dvqtBREU33BTGGVAMALlo3jxp/Hjpllt8V4KIinC4SbDODQDkohkzpIEDpccfl9rafFeDCIp2uKFbCgByj5l08cXSww8HX0CGRTfcJOMMKAaAXHX++dKoUdr2P7f6rgQRFN1wQ7cUAOSuZFKPf61Ww568XRlacR8RtXDhQh1//PHau3evzKzUzJaY2QGXMo5suBlWXqzxh/VTjixSCADoYPrcI1RYaPrJT3xXglx24oknas6cOfr2t78tST+SdJtz7oA7l0Y23LQ5p0Vrtml3M603AJCLysqkSy+V7rtPWrnSdzXIZd/5znf06KOPSlKVgoBzQJENN6X7dwZn3A2AQ1dbW6vq6mo1Njb6LiWS/uVfpHhc+vnPfVeCXLZ582bt3LlTksokFR3s/MiGm7JCNs8E0Htsv5Bdhx8e7Kf58svS5s2+q0GuuvTSS/X9739fkm6X9H8Pdn5kw00p4QYAQmHePOmZZ6Rf/cp3JchFt9xyiwoKCnTRRRdJ0g8lnWhmHzzQayIbbvoRbgAgFI49VjrzTOl//ifYOBxId/HFF+u+++6TJDnnWp1zM5xzTxzoNZEPN0wHB4Dc9/WvSxs3Srey7A0yILLhprQwLkna2dTiuRIAwMGcfro0dWrQNcWODOityIabfkXt3VK03ABArjOT/v3fpRUrpPvv910Nwi664Yap4AAQKnPmSAMGSD/+se9KEHaRDTfFBXHFTNq5l3ADAGGQSEhXXCH97W/SggW+q0GYRTbcmJlKCxPMlgKAEJk3T6qoEFsyoFciG26koGuKbikACI9+/aTLLpP+8Idg/A1wKKIfbpoJNwAQJl/5ijRmDNPCcegiHW6OPqxs/zYMAIBwGDZMOu20YGDxpk2+q0EYRTrcNO5t0Rsbd/ouAwDQQ1//urRnj/TLX/quBGEU6XDTrzDBbCkAvcKu4H5MnCidfbb0i18EIQfoieiHGwYUA+gFdgX35+qrpYYG6ZZbfFeCsIl2uCmi5QYAwuoDH5Auuki64w62ZEDPRDrclBUmtLN5n9ranO9SAAA9ZCade670zDPS/Pm+q0GYRDrc9CtKyDlpdwv7SwFAGJ1/fjAtnC0Z0BPRDjeFBZLYggEAwiqRkK68Uvrf/w2+gO6IdrjZvzN4i+dKAACH6nOfkyor2ZIB3RfpcNO+gN8OWm4AILT69ZO++U3prbekN97wXQ3CINLh5h8tN4QbAAiziy+WXn1V+vnPfVeCMIh2uEm13DDmBgDCbejQIODcfLO0caPvapDr8iLc0C0FAOF35ZXS3r3S9df7rgS5LtLhpizVLbWDbikACL0JE6TZs6W//U3avdt3NchlkQ43/QoTmjKyQm0sbQkAkXD11dITTwTdU0BXIh1uEvGYXn9nhzZsb/JdCgAgA04+WZo+XfrZz6RW1mdFFyIdbqSga4oxNwAQDWZB682bb0p/+pPvapCrIh9u+hUltINF/AAgMs47TzriiGBLBsfWgehE5MNNWVEBLTcAECHxuHTFFVJTE1syoHORDzf96ZYCgMj53OektWvZUBOdy2q4MbNZZrbMzFaY2Te7Ou++++6Tmamuri7jNQRjbuiWAnBoamtrVV1drcbGRt+lIE1pqfSlL0nz50vLlvmuBrkma+HGzOKSrpd0pqSJki40s4mdnFd27bXXasaMGVmpo18hLTcADt3s2bNVU1Oj8vJy36Wggy9/WUompZ/+1HclyDXZbLmZLmmFc26lc65Z0l2Szu3kvO//67/+q4qKirJSRFlRAXtLAUAEDRkifeYz0i23SO+847sa5JJshpvhktamPa5PHdvPzKZKGnn22Wcf8EI1NTWqqqpSVVWVGhoaelREWVFCu5tbta+VhfwAIGquvFKaMoUtGfBu3gYUm1lM0s8kXXWwc6urq1VXV6e6ujoNHjy4R+9TVlQgiZ3BASCKjj5aOuww6Ze/lHbt8l0NckU2w806SSPTHo9IHWtXJulYSU+NGTNGCxYs0Jw5czI+qLiypEDHDO2n7XsINwAQRVdfLW3ZIv3ud74rQa7IZrhZKGmcmY01s6SkuZLmtz/pnGt0zg1yzo1ZvXq1Zs6cqfnz56uqqiqjRZQk43r9nZ0s5AcAEfX+90szZwZbMuzjcyyUxXDjnNsn6cuSHpb0mqR7nHNLzOx7ZjYnW+/bUXu3FDOmACCa2rdkWLVKuu8+39UgFySyeXHn3IOSHuxw7DudnfvUU09lpYb+hBsAiLxzz5XOP1/69a+lT3wiCDzIX5FfobisKMhv2/fQLQUAURWPSx/+sPTkk9Jf/+q7GvgW+XDTv7i95YZwAwBR9pnPSIMGST/5ie9K4Fvkw83+lhu6pQAg0kpKpMsvl2prpdde810NfIp8uCmIx1RcEKflBgDywOWXS1OnSr//ve9K4FPkw43UvnkmLTcAEHWDB0szZkg//zlbMuSzvAk322m5AYC8cMUVUkuL9Itf+K4EvuRFuJk8smL/ejcAgGgbN04677xgS4adO31XAx/yItxs3tms19dv910GAKCPXH21tHWrdNNNviuBD3kRbvoXFzBbCgDyyMyZ0kknSffey5YM+Sgvwk15cYJF/AAgz3zrW8GCfmzJkH/yItz0LyrQ9r0tcs75LgUA0EfOPFMaP1768Y8lbv/5JT/CTXGBWlqd9rS0+i4FANBHYjHpqqukF16Qnn7adzXoS/kRblIzpbbvoeMVAPLJpz8drH3Dlgz5JT/CTXH7FgyMuwGAfFJcLH3lK9KKFdKSJb6rQV/Jj3Czv+WGcAMA+eayy6S1a6Wf/tR3JegreRFuylM7g9NyAwD5Z9Ag6XOfk267TVq/3nc16At5EW7KihI6rKxQu5oYcwMA+eiKK6TWVum663xXgr6QF+GmvLhAG3Y0afPOZt+lAAiZ2tpaVVdXq7Gx0Xcp6IUjj5TOP1/61a+kHTt8V4Nsy4tw039/txQtNwB6Zvbs2aqpqVF5ebnvUtBLV10lTZgg3X6770qQbXkRbgriMZUm42pkQDEA5K2ZM6VEQrrmmmDXcERXXoQbKeiaItwAQH67+mppzZpgzylEV96Em/6EGwDIe+ecIx19NFsyRF3ehBtabgAA7VsyvPii9OSTvqtBtuRVuGERPwDApz8tDRkStN4gmvIm3NAtBQCQpKIi6d/+TVq3TnrlFd/VIBvyJtzQLQUAaPepT0lvvsmWDFGVV+Fmd3OrWlrbfJcCAPBs4EBp3jzpjjuCFhxES16FG0m03gAAJLElQ5TlTbgZWJrUpMP7M6gYACBJGjtW+tjHpBtukLZv910NMilvwk1pUUJL3t6ubYQbAEDK1VcHe03dcYfvSpBJeRNuKtq7pXYTbgAAgaoq6dxzpf/6L7ZkiJL8CTclSUnStj3sDA4A+IcvfEFau1a65x7flSBT8ifcpFputtFyAwBIc+aZ0sSJ0k9+wpYMUZE34aY/s6UAAJ1o35Jh8WLp8cd9V4NMyJtwE4+ZyooStNwAAN7jk5+Uhg4NWm8QfnkTbiSpooRVigEA71VYKH31q0HLDVsyhF9+hZvipLbtZkAxAOC9Lr1UGj2aDTWjIL/CTUkB69wAADo1YIB0zjnSnXdKMq9z3AAAIABJREFU9fW+q0Fv5FW46V9cwDo3AIAufe1rwYypa6/1XQl6I6/CzdiBpRrQL+m7DABAjhozRvr4x6Vf/1pqbPRdDQ5VXoUbSVr01la1tbGQAQCgc1//ujRlivS73/muBIcqr8JNRUmB2py0o2mf71IAADlq2jQpHg+mhTczByWU8izcpLZgYMYUAOAArr5aWrdOuvtu35XgUORVuKksCVYp3sqgYgDAAcyaJU2aFEwLZ0uG8MmrcEPLDQCgO8ykb3xDqqyUHnvMdzXoqTwLN2yeCQDonn/+Z2n5culHP/JdCXoqr8JNZarlZistNwCAgygslP7lX4KWmxdf9F0NeiKvwk15MS03AIDuu/RSqbRUuukm35WgJ/Iq3MRjpuOGl2tPM1PBAQAHV1EhXXWV9KtfSWvW+K4G3ZVX4UaSdjbt0/rtTb7LAACExLx5wZ9syRAeeRduKksKtHUXY24AAN0zapQ0d65UUyNt2+a7GnRH3oWbAaVJbSHcAAB64KqrgrE3d9zhuxJ0R96Fm4qSJOvcAAB6ZMoUafJk6Qc/YEuGMMi7cDOgNKkthBsAQA9deaW0fj2tN2GQd+GmsiSpvS1t2tPc6rsUAECIfOQj0nHHBRtqsiVDbsvDcBOsdUPrDQCgJ8ykr39dWrJEeugh39XgQPIv3JSmVilmUDEAoIfmzpVmzw7WvUHuyrtwM6CULRiAfGdmE8zsho997GP6Fb+l0APJpHTKKVJtrbRoke9q0JW8CzeVJUkdN7xcjWzBAISSmd1kZhvN7NUOx2eZ2TIzW2Fm3zzQNZxzrznnvnjPPffo2WefzW7BiJzqaqmsLBh7g9yUd+FmQGlSr6xrVMNOVikGQupmSbPSD5hZXNL1ks6UNFHShWY20cyOM7P7O3wNSb1mztlnn62zzjqrr+tHyJWXBwHnnnukt97yXQ06k3fhpry4QDETC/kBIeWce0bSlg6Hp0ta4Zxb6ZxrlnSXpHOdc684587p8LUxdZ35f/nLX3T77bf38XeAKPja16Tp09lQM1flXbiJx0wVJUltJtwAUTJc0tq0x/WpY50ys9PM7LpLL730gC03NTU1qqqqUlVVlRoaGjJXLUJvxAjpqKOkn/5U2rrVdzXoKOG7AB8GlCaZLQXkMefcU5KekvSVA51XXV2t6upqSVJVVVXW60K4XHWVdOut0g03SN/6lu9qkC7vWm6kINzQcgNEyjpJI9Mej0gdA7Jm8uRgYb/rrpOaGMaZU/Iz3JSweSYQMQsljTOzsWaWlDRX0nzPNSEPXH21dMQREkO3cktehpujhvTTiIpi32UAOARmdqekv0s62szqzWyec26fpC9LeljSa5Lucc4t+f/bu/PwKqt77ePflYnMCZmAhCEMMioEDYNKUXEoVINV1DI4D/GoqJTB1572tO85vZzqSJ1OU9GKqGCpVYKKttVKRQWCVgVkFJRAgDAFAoQMPOePRTRiAknIztrD/bmufW32zib7RnBz8zzrWT+XOSU0nHsu7N9vLws/fNh1GqkVkmtujIH315ZSc9gjPMy4jiMiTeB53rgGnn8TeLOV40iIqx3JcNVV8NZbcOGFrhMJhOiRm9S4KDwP9miXYhE5jsLCQvLz8ykrK3MdRfzUz35mr57Spn7+IzTLTXwbAC0qFpHjysvLo6CggKSkJNdRxE9FRsKdd8KePVBU5DqNQKiWmyPzpXaWq9yIiMiJu+km+OorePBB10kEQrXcfHvkRtfuiYjIiUtKgptvhrlzYcMG12kkJMtN7WRwXQ4uIiIt5c47ITwcHn3UdRIJyXLTNjYSY2CHTkuJiEgLycqC8eNhxgzYudN1mtAWkuUmIjyMs3umg+e5jiIiIkFkyhQYOBD+8AfXSUJbSJYbgOLdB1mzrdx1DBERCSKnnAIJCXYkQ0WF6zShK2TLTWp8FDvKtaBYRI5N+9xIU02dCtu2waxZrpOErpAtN2nxbVRuROS4tM+NNNWIEfbUlEYyuBPS5Ub73IiISEurHcmwejUsWOA6TWgK4XITxb5D1VRU1biOIiIiQebyy+FHP4L773edJDSFcLmxG/np1JSIiLS0yEi45BL4179g8WLXaUKPyo1OTYmIiA/ceKPduVgDNVtfyJab9IQ2dEiKZpdGMIiIiA8kJMAtt8Crr8L69a7ThJaQLTep8VGUlFVQuk/lRkREfOP22yEmBmbOdJ0ktIRsuak9LaVyIyLHon1u5ERkZsJVV9lp4RrJ0HpCttxER4aTGB2hciMix6R9buRETZwIBw/CU0+5ThI6QrbcgF13U6qrpURExIf69YOf/AQef1wjGVqLyo2O3IiIiI9NmwalpVp701pCvNxEq9yIiIjPnXUWjBkD8+ZpJENrCOlykxYfpXIjIiI+Z4zdtfiNN6Cw0HWa4BfS5SY9oQ37K2vYf6jadRQREQlyY8ZAdra9ckp8K6TLTce2MWSnxrJ9r1Z4iYiIb0VEwM9/DkuW2Jv4TkiXm+SYKDbuPECpRjCIiEgruO46e/TmgQdcJwluIV1uMhLtRn7b9+nIjYiI+F5Cgl1789e/wrp1rtMEr9AuNwnRAGzfq0XFIlI/7VAsLW3iRDs1/JFHXCcJXiFdbtrGRhIZbtiuK6ZEpAHaoVhaWocOdiTD88/bvW+k5YV0uTHGkJEQrdNSIiLSqqZOhfR0jWTwlZAuN6BdikVEpPX17g2nnAJPPAEHDrhOE3xCvtxkJLRhmy4FFxGRVjZ1KuzYoZEMvhDy5aZPh8RvFxaLiIi0luHDYdAgePhhqKlxnSa4hHy5iQw3fLBuBxVV+pMlIiKtxxg7UHPjRnjrLddpgkvIl5t2ifaojU5NiYhIa7v0Uhg4EO6913WS4BLy5aZ9ki03W8tUbkREpHWFh8PVV8NHH8GiRa7TBI+QLzffHrnRFVMiIuLAdddBSgo89JDrJMFD5aa23OjIjYiIOBAXB7feCu+8A2vWuE4THEK+3CRGRxATGc5WrbkRkXpo/IK0httug8REjWRoKSFfbowxtE+KVrkRkXpp/IK0hvbtIS8P/vQn2L7ddZrAF/LlBqBXuwTCMK5jiIhICJsyBSor4cknXScJfCo3QHRkGJ98s9t1DBERCWG9esHo0bbcaCTDiVG5ATokx7BtbwWHD3uuo4iISAibOhVSU2HOHNdJApvKDdAhKZrqwx47ynU5uIiIuHPmmfay8Hvu0UiGE6FyA3RIigGgRJeDi4iIQ8bYozfr18Nrr7lOE7hUbrBHbgBKyg46TiIiIqHupz+F7t3hwQfB02qJZlG5oW650ZEbERFxKzwcJk+GxYs1kqG5VG6AlLgooiLCVG5ERMQvXHstZGXB7NmukwQmn5YbY8xIY8xqY8w6Y8zd9Xx9sjFmZf/+/Tn33HP5+uuvfRmnQcYYzuqZTkWVVm+JiIh7sbFw0032svBVq1ynCTw+KzfGmHDgSWAU0BcYZ4zpe9TLPgVyP//8cy677DLuuusuX8U5rvKKalZs2evs/UVEROq65RaIjtZIhubw5ZGbwcA6z/O+8jyvEpgNXFz3BZ7nved53gGAoUOHUlxc7MM4x5aZHMOWPVpQLCIi/iEjA665BmbOhG3bXKcJLL4sN1nApjqPi488V68ZM2YwatSoer9WUFBAbm4uubm5lJaWtmzKI7KSo9m2t4KqmsM++f4iIiJNNXkyREXBCy+4ThJY/GJB8axZsygqKmLatGn1fj0/P5+ioiKKiopIT0/3SYbM5BgOe7BNAzRFpA5NBReXevaEUaPg3nth/37XaQKHL8vNZqBTnccdjzz3PcaY8+655x7mzZtHmzZtfBjn2DKT7UZ+W/ao3IjIdzQVXFy7807YvRuefdZ1ksDhy3KzFDjJGNPVGBMFjAXm1X2BMWYg8Id58+aRkZHhwyjHl9U2htwubdmuIzciIuJHzjgDTj8dHn0UqqtdpwkMPis3nudVAxOBt4EvgVc8z1thjPkfY8zoIy97EIi//PLLycnJYfTo0Q19O5/LSo6h6OvdbNyp434iIuJfpk2DjRuhsNB1ksAQ4ctv7nnem8CbRz336zo/Pq/2h77M0RjRkeGkxUexWVdMiYiInxk92g7VvO8+O57BGNeJ/JtfLCj2F1nJMRTvVrkRERH/Eh4OEybA0qWwcKHrNP5P5aaOgZ2TiYvy6cEsERGRZrnmGkhPh4cecp3E/6nc1NEmIpx3V2/n8GHnZ8lERES+JyYGJk6E+fNh5UrXafybyk0dHdvGUFl9mNLyQ66jiIiI/MCtt9qRDM895zqJf1O5qaNjSiwAm3YdcJxERETkh9LS4I474Pe/h5IS12n8l8pNHZ3a2o38tKhYRET8VX4+VFXB44+7TuK/VG7qyEqOYUjXFHYfqHQdRUREpF7du8Oll8LTT0N5ues0/knlpo6YqAg27NjPyi17XUcRERFp0NSpsGcPzJjhOol/Urk5SueUWL7RmhsREfFjQ4fCsGF2JENVles0/kfl5iidU2K1oFhERPzeL34BiYkwd67rJP5H5eYofTMT6ZwaS0WVppOJiIj/GjkSDh2ym/p52p7te1RujtI2NoqPv9rF5j2aDi4iIv4rLAymTIFPPoF//tN1Gv+icnOU7DS7183Xmg4uIiJ+7uqrISMDHnzQdRL/onJzlM4pcQB8vVPrbkQECgsLyc/Pp6yszHUUkR+IjobbboMtW2DFCtdp/IfKzVHS4qNIjolg+16dlhIRyMvLo6CggKSkJNdRROp1662wZo0GatalcnMUYwyZybGs2rrPdRQREZHjSkuD66+HF1+0R3BE5aZe2WmxbNRpKRERCRCTJ0NNjZ05JSo39cpOjWPTrgNU1xx2HUVEROS4unWDMWPgf/8X9unEg8pNfbLT4qg+7GmApoiIBIwpU6BvX5g1y3US91Ru6tE9PY6stjFs2KGJZCIiEhiGDIHISLjvPo1kULmpR3ZqHJt3H+SrHVp3IyIigWPqVNi0Cf78Z9dJ3FK5qUdKXBSJ0RE6ciMiIgHlwguhd2+7qV8oj2RQuamHMYau6fFs2KFdikVEJHDUjmRYvRref991GndUbhowtGsKFVW6WkpERALLlVdCp07wwAOuk7ijctOAxJhIln29m/JDmg4uIiKBIzrazpxasAC++MJ1GjdUbhrQPT0egK9Kte5GREQCyy23QFwcPPyw6yRuqNw0oEeGHaC5XuVGREQCTEoK3HADvPQSFBe7TtP6VG4a0LltLN3S4li/XYuKRUQk8EyaBKedBo8/7jpJ61O5aUBUZDjGwJpt2sdaREQCT9eu0KWLHcmwd6/rNK1L5eYYTspIYN12nZYSEZHANHWqLTZ//KPrJK1L5eYYemTEsa+imopKXTElIiKBJzcXzj4bpk+HykrXaVqPys0x9GqfSGn5ITbs1BgGEREJTL/4hd3c75VXXCdpPSo3x9CzXQKgdTciIhK4zjvPXhYeSiMZVG6OoWtaHBFhRuVGREQCVu1Ihs8/h7//3XWa1qFycwxREWF0S49jVYnKjYiIBK4JE6BDB5gxw3WS1qFycxy52Sl8pQGaIiISwNq0gbvvhjlz4LPPXKfxPZWb48hKjmHDjv3sq6hyHUVERKTZrrrKrr156CHXSXxP5eY4ere3i4pXb9WpKRERCVxt28JNN8Hs2bBpk+s0vqVycxy9OyQCsGpriG3vKCIiQWfSJOjcGWbOdJ3Et1RujiMzKZrOKbGs1KJikZBUWFhIfn4+ZWVlrqOInLAuXWDoUHjgAQjmP9IqN8dhjCEzOZqVW3TkRiQU5eXlUVBQQFJSkusoIi1iyhTYtw8KClwn8R2Vm0bol5nEqq17qTkcIrsfiYhI0Dr1VBgxAh57LHhHMqjcNMLATsl0S4tj/XadmhIRkcB3992QkAAvv+w6iW+o3DTCSe0SWFmyjxUlOjUlIiKB77zzIDLSXhYejCMZVG4aoXt6HNGRYSzfrHIjIiKBzxiYOhWWL4e333adpuWp3DRCRHgYo07uwJ4DQXpyUkREQs64cZCZGZyb+qncNFJidARvLd+qRcUiIhIUoqLgzjthyxb49FPXaVqWyk0j9e+YzIHKGtaXlruOIiIi0iLy86G4OPiO3qjcNNKAjkkM6ZrCl1pULCIiQSI52Y5kmDMHvv7adZqWo3LTSN3S41m5ZS9LN+5yHUVERKTF3HmnvX/sMbc5WpLKTSOFhRn6d0ri35v2uI4iIiLSYjp3hrFjYcEC2L3bdZqWoXLTBMNPSmdfRTUHK2tcRxEREWkxd90Fa9YEz0gGlZsm6JERz9c7D/B5sY7eiIhI8Ojf345kmD4dDh1ynebEqdw0wcDObWkbG6khmiIiEnSmTYOSkuAYyaBy0wQpcVG0jYti0fodrqOIiIi0qPPPhwEDoLAw8EcyqNw0UW6Xtqzauo+amsOuo4iIiLQYY+zRm1dftYuLA5nKTRMN6ZpC8e6DrN+x33UUERGRFnXFFZCVBQ8+6DrJiVG5aaLc7BQAFm/QfjciIhJcIiNh0iR47z1Ytsx1muZTuWmizimxZCVHs0Y7FYuISBDKz4cuXeCll1wnaT6VmyYyxjAoO4UFK7fhBfqKKxERkaMkJtrTU489Bhs3uk7TPCo3zTCkWyql+w7xldbdiIhIELrjDggLg0cfdZ2keVRumuH0bqmclBHPh+t0SbiIiASfjh1h3Dh45hnYFYBLTFVumqFLaiwHKmtYtG6n6ygiIiI+MXUqHDgAzz/vOknTqdw0gzGGi3My2VdRRc1hrbsREZHg078/TJgADzwAFRWu0zSNyk0z9emQyKL1OzVnSkREgta118K2bfDii66TNI3KTTMN65FGfFQ4SzcG4MlIERGRRjj3XMjJgYcfhsMBtDG/yk0ztY2LoleHRN78YqvrKCIiIj5hjF178+WX8OabrtM0nsrNCRh+UjqfFe9hZ3kQzIcXERGpxxVX2KGagTQtXOXmBIzok86g7LYs0iXhIiISpCIjYdQou2Px0qWu0zSOys0J6NchiY07DvD2im2uo4iIiPjMjTdCUlLgDNRUuTkBYWGGnw7MpOxgJYeqa1zHERER8YmEBPiP/4C5c2H9etdpjk/l5gSd3i2ND9bt5MP12tBPRESC1+23w4ABduaUv1O5OUFn9EjlzO6pfKRyIyIiQSwry14W/uyzsNPP/8pTuTlBbSLCSUtowytFm6iqCaBNAERERJpoyhQ7kuHpp10nOTaVmxZw8YBMuqTE8tF6XTUlIiLB6+STYeRIeP11/x7JoHLTAs48KY31peW8t6rUdRQRERGfuvtuKCqCF15wnaRhKjctoE1EOJcO7MjcZcVUVOmqKRERCV7Dh8PAgf49kkHlpoX8+OR29GqfwHurtruOIiIi4jPGwLRpsHo1FBa6TlM/lZsWMrRbGlv2HOSVok2uo4iIiPjU5ZfDxRfD44+7TlI/lZsWEh5muPbMbDbs3E9J2UHXcUTkOIwxcbm5ucyfP991FJGAExEBZ58N//gHfPyx6zQ/pHLTgkb268DGHQf4c1Gx6ygiQcsY86wxZrsxZvlRz480xqw2xqwzxtzdiG/1/6644gofpRQJfjfcAMnJ8NBDrpP8kMpNC+qcGsvPBnXiL58UU3PYcx1HJFj9CRhZ9wljTDjwJDAK6AuMM8b0NcacYoyZf9QtwxhzPrAyIyOj1cOLBIvakQyvvQbr1rlO830qNy3s3N4ZpMZF8Y8vNUxTxBc8z1sI7Drq6cHAOs/zvvI8rxKYDVzsed4XnudddNRtO3A2MPSll17ij3/8I4f99ZIPET93++2QnQ2PPuo6yfep3LSwEb0zqD7sqdyItK4soO5q/uIjz9XL87xfep43afz48dx0002EhdX/UVhQUEBubi65ubmUlmofK5GjZWbCWWfBc8/BDj/ax1blpoVFhIcx8uT2LFixlVUle13HEZFjuPbaa7nooosa/Hp+fj5FRUUUFRWRnp7eislEAseUKXDwIDz1lOsk31G58YHxgzsTZgzP/3ON6ygioWIz0KnO445HnhMRH+vbF66+GhYtsiXHH6jc+EBybBQzM3dzzx0/gY0bXccRCQVLgZOMMV2NMVHAWGCe40wiIeP66+Gdd2DmTNdJLJUbHzll5JmE9eoJTz7pOopIUDHGvAx8BPQyxhQbY27wPK8amAi8DXwJvOJ53gqXOUVCyfDhkJtrRzLU+MEUIpUbX+nYEQYMgMWL4auvXKcRCRqe543zPK+D53mRnud19DxvxpHn3/Q8r6fned09z7vHdU6RUFI7kmHtWv8YyaBy40v/+Z/2d/rpp10nEZFmKiwsJD8/n7KyMtdRRPzapZfCOefA3Lmuk6jc+FZWlj0ROWsWLFvmOo2INENeXh4FBQUkJSW5jiLi1yIi4JJL4MUX4cMP3WZRufG1u+6C+Hj4/e/9dza8iIhIC7juOmjb1v1IBpUbX0tKgt/8Bj77zH+WkYuIiPhAfDzceqsdybB2rbscKjetYfx46NoV/vQn2KytN0REJHhNnAjR0W7/Pa9y0xrCwuD+++1pqV/+EjwN1RQRkeDUvr2dGP7QQ+BqaonKTWvp1cuejJw/H555xnUaERERn7ntNqiocLfVm8pNa7r2Whg5EmbMgI8/dp1GRETEJ3r3hrw8eOIJOHCg9d9f5aY1GWOvmgoPt5PGiotdJxKR49A+NyLNM20a7NwJzz/f+u9tPP9Y/9HoELm5uRQVFfkyi+99/jlMnWrX3vzlL5CY6DqRSFMZ1wFaSGh99oi0Is+DK6+019H84x/23/UtoFGfPTpy40L//rbcbNkCN9/s5pidiIiIDxljN/V7/314/fXWfW+VG1cuuAD+67/s1PA77oD9+10nEhERaVGXXALdusGDD7buhcIqNy6NHQuTJ8OqVXZMw44drhOJiIi0mPBw+9fcxx+37kgGlRvXLr/cnqIqKoLLLoMVK1wnEhERaTHXXQcpKXYf29aicuMPfvpTeOkliIuz1869+KLrRCIiIi0iNtaOWZwxA1avbp33VLnxF0OGQEEBDB0KTz0FP/+5TlOJiEhQuO46iIqCRx5pnfdTufEnWVl2GMfll9tBm+PH26M4miYu4oz2uRE5cRkZcM01ds+bbdt8/34qN/4mIgImTYLp0yE1Ff7wB5gwARYs0EwqEQfy8vIoKCggKSnJdRSRgDZ5sp0aPmuW799L5cZfnXKKPWpzxx12QMc998CYMfDqq1Bd7TqdiIhIk/TqBWefDffe6/vdT1Ru/FlYmL2Cas4cyM+3pWb6dLtxwKOPwoYNrhOKiIg02s9/Drt2wXPP+fZ9NH4hkNTUwBtvwOzZsGgR7NsHgwfDqFFw4YXQo4frhBI6NH5BRJrM8+CMM+y6m7VrmzWSoVGfPSo3geqbb+x+1gsX2sEdERGQlGSP+/3oR7b0dOjgOqUEL5UbEWmWV1+1qyz+/Gd7cqKJVG5CxoYN8M47sHgxrFljq/GhQ9CxI2RmQp8+dv587972ORMsfy+JQ8Hyh0ifPSKtrKYGLroIEhLsqosm/pXUqFdHNCuZ+JeuXe0Azptvhqoq+PRTe1uxAlautLddu+yfpNhYe01e+/aQng6dO0NmJlsyc0nKiicuzvUvRkREgll4OFx8MdxyC0ycCMOHt/x76MhNKNi1yxacdetg/Xp7snPLFvs8QGQkOVvf4rM1sVxwARQX270EKyu/60Dp6dCunb1PTYW0NHtJX5iWpIcqHbkRkWY7cAC6dIHTT4d585r0U90fuTHGjASmA+HAM57n3X/U19sAM7t3705qaipz5swhOzvbl5FCU0oKDBtmb3VVVsKmTbBlC7/6Jpx1m+zZrM8+sxdmffCBfcmWLXY5T+0eZu3a2X6UnAyRkfZsV2UlnHyyXePcqZM9zJiVZV+fmmp3pkxIsIUoLs7eYmLs45gYiI5WURIRCRWxsXDbbfDf/w1ffmlXT7Qknx25McaEA2uA84FiYCkwzvO8lXVecyvQ3/O8m2fPns1f//pX5syZc8zvq389tS7Pg/Jy2LoVdu6E0tLv7nftgt277TY8JSW2vCxfbgvLypXQr5+dB3rqqfDJJ/b7JSXZ2zff2EORCxfa9c//+heMGGHPpmVlwUkn2RkkXbvCnj22RLVrZ9t+drZ9706d7Pu3a2czxsfbzZzj4ux9TIwtWbGx9nFExHe32Fh73jcmxt63aWN/rVFRNmdkpL0PD7e3sDB7b8x3j42x97U3Y77/3NE/rnur77mGbvDdfW0BbOjrx7tvQSFz5KawsJDCwkLee+891q5d2xqZREJCaaldGTFhAjzzTKN/mtsFxcaY04H/73nej488/gWA53n31XnN20de82F1dTXt27entLQUc4xPYpWbwFFVZUvH3r32vrzcHtk5dMg+V1Njy0lYGGzfbgtGSYl9Pi7OrpOOibFlqrwcEhPthWFdu8Lnn9vytHixPWK0eLE9ZbZxoy0933xjT6lt3Wpft2KFLS6VlTZbbbGqva8tYLVFq/b5lJTvzt4NG2aPZmVn2/dJTLS/DrDLmLZvt0egcnLg448hN/f75a5tW/vrHTwYliz57vvVvmft/dHPn3UWvP/+d5nOPNPuBNCzp10/npVl/7vUft/a19fe136fM86ADz+0h4E/+sieWty5036/Dz+0s1t/9rNG//aGTLmppc8ekZZ32232s/OVVxr9jzDn5eYyYKTneTceeXwVMMTzvIl1XrMcGPnjH/94044dO/jiiy/o06cPERHfP1tWWlrKjiNDJA8dOkROTo5PMre00tJS0tPTXcdolGDL6nkN3+p+vfbHDd0f7zX1/dgYe6QoLAzKyvaRmJjA4cP2+aO/XntfU/P9x3WfDw//4dfrPq79vrWP676+7s8/+r7259U+ht1kZrZt1O/BsmXL3vY8b2SjXuzfVG5EHKr9TGsC92tuGmvBggUAdO/enb///e+kpaU1+Nq4uLiA+YAJpA+tlUAPAAAFZElEQVRDZfWNIM4aDMVGRBzz1VpLXy7h3Ax0qvO445Hn6n1NdXU1ZWVlpKam+jCSiIiIBDtflpulwEnGmK7GmChgLHD0BV/zgGsA5s6dy4gRI4653kZERETkeHx2WsrzvGpjzETgbeyl4M96nrfCGPM/QJHnefOAGcALPXr0ICUlhdmzZx/3+x7rlJW/yc/Pdx2h0ZTVN5RVRKT1aRM/EWmOYDnEqs8ekcDSqM8ebZsmIiIiQUXlRkRERIJKQJWbBQsWsHz5cnr06MH9999//J/gyPXXX09GRgYnn3yy6yjHtWnTJs455xz69u1Lv379mD59uutIDaqoqGDw4MEMGDCAfv368Zvf/MZ1pOOqqalh4MCBXHTRRa6jHFN2djannHIKOTk55Obmuo4jInJCAmbNTU1NDT179iQ2NpZly5YxaNAgXn75Zfr27dsa+Zpk4cKFxMfHc/XVV7N8+XLXcY6ppKSEkpISTj31VPbt28dpp53Ga6+95pf/XT3PY//+/cTHx1NVVcWwYcOYPn06Q4cOdR2tQY888ghFRUXs3buX+fPnu47ToOzsbIqKipqyYD9k1txo/IKIXwmuNTdLliyhR48etGnThqioKMaOHcvrr7/uOla9hg8fTkpKiusYjdKhQwdOPfVUABISEujTpw+bNx+9HZF/MMYQHx8PQFVVFVVVVX69dUBxcTFvvPEGN954o+socgLy8vIoKCggKSnJdRQRaaSAKTebN2+mU6fv9gTs2LGj3/4lHKg2btzIp59+ypAhQ1xHaVBNTQ05OTlkZGRw/vnn+3XWSZMm8bvf/Y6wABh3bozhggsu4LTTTqOgoMB1HBGRE+L/n7rSKsrLyxkzZgyPPfYYiYmJruM0KDw8nH//+98UFxezZMkSvz3tN3/+fDIyMjjttNNcR2mUDz74gE8++YS33nqLJ598koULF7qOJCLSbAFTbrKysti0adO3j4uLi8nKynKYKHhUVVUxZswYJkyYwKWXXuo6TqMkJydzzjnnfDuXzN8sWrSIefPmkZ2dzdixY3n33Xe58sorXcdqUO3/SxkZGVxyySUsWbLEcSIRkeYLmHIzaNAg1q5dy6FDh6isrGT27NmMHj3adayA53keN9xwA3369GHy5Mmu4xxTaWkpe/bsAeDgwYP87W9/o3fv3o5T1e++++6juLiYjRs3Mnv2bEaMGMGsWbNcx6rX/v372bdv37c/fueddwLiSj8RkYYETLmJiIjgiSeeYO3atfTp04crrriCfv36uY5Vr3HjxnH66aezevVqOnbsyIwZM1xHatCiRYt44YUXePfdd8nJySEnJ4c333zTdax6lZSUcM4559C/f38GDRrE+eef7/eXWAeCbdu2MWzYMAYMGMDgwYO58MILGTlSQ79FJHAFzKXgtbQFuohf8N/L1JpGnz0igSW4LgUXERERaQyVGxEREQkqKjciIiISVFRuREREJKio3IiIiEhQUbkRERGRoKJyIyIiIkFF5UZEGmXp0qX079+fiooKjDFxxpgVxpig38q4sLCQ/Px8ysrKXEcRkUZSuRGRRhk0aBCjR4/mV7/6FcDvgFme5/nn5NIWlJeXR0FBAUlJSa6jiEgjRbgOICKB49e//jWDBg0CyAXucBxHRKReOnIjIo22c+dOysvLARKAaMdxRETqpXIjIo12880389vf/hbgReABx3FEROqlciMijTJz5kwiIyMZP348wP3AIGPMCMexRER+wF+mgjeaMWaB53kjXecQkdCizx6RwBFw5UZERETkWHRaSkRERIKKyo2IiIgEFZUbERERCSoqNyIiIhJUVG5EREQkqKjciIiISFD5PyxNJdZD1l4aAAAAAElFTkSuQmCC\n", | |
| "text/plain": [ | |
| "<Figure size 576x720 with 2 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [], | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "iMGoN0kVKyb8" | |
| }, | |
| "source": [ | |
| "#end" | |
| ], | |
| "execution_count": null, | |
| "outputs": [] | |
| } | |
| ] | |
| } |
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