{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Построение и интегрирование уравнений движения механической системы с двумя степенями свободы, используя уравнения Лагранжа II-го рода"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Пример построения и численного интегрирования уравнений движения механической системы с двумя степенями свободы. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Юдинцев В. В.](https://classmech.ru), [Кафедра теоретической механики](http://tm.ssau.ru), [Самарский университет](https://ssau.ru)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Символные математические преобразоания\n",
    "import sympy as sp\n",
    "\n",
    "# Для конструирования функций быстрых подстановок чисел в аналитические выражения \n",
    "from sympy.utilities.lambdify import lambdify\n",
    "\n",
    "# Для печати красивых формул\n",
    "sp.init_printing()\n",
    "\n",
    "# Массивы, матрицы\n",
    "import numpy as np\n",
    "\n",
    "# Для численного интегрирования дифференциальных уранвений\n",
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "# Для графиков\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pylab as pylab\n",
    "\n",
    "# Настройка стиля графиков\n",
    "pylab.rcParams.update({'legend.fontsize': 14, \n",
    "                       'figure.figsize': (12, 8), \n",
    "                       'axes.labelsize': 14,\n",
    "                       'axes.titlesize':14, \n",
    "                       'xtick.labelsize':14,\n",
    "                       'ytick.labelsize':14,\n",
    "                       'axes.grid' : True,\n",
    "                       'grid.linestyle' : ':'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Механическая система состоит из двух тел: однородной пластины и шарика, который рассматривается как материальная точка. Полукруглая однородная пластина массой $m_1$ шарнирно закреплена и может вращаться в вертикальной плоскости вокруг точки О (точка О находится в середине диаметра полукруглой пластины). Внутри пластины в канале АВ движется тяжёлый шарик массой $m_2$. Шарик соединён с пластиной пружиной с известной жёсткостью $c$ и свободной длиной $l_0$. \n",
    "\n",
    "Таким образом, известны следующие параметры:\n",
    "\n",
    "- $R$ - радиус пластины; \n",
    "- $m_1$ - масса пластины; \n",
    "- $m_2$ - масса шарика; \n",
    "- $a$ - расстояние от точки О до канала АВ;\n",
    "- $c$ - жесткость пружины АМ;\n",
    "- $l_0$ - свободная длина пружины;\n",
    "- $y_с = OC_1$ - расстояние от точки О до центра масс пластины.\n",
    "\n",
    "Схема механической системы приведена на следующем рисунке. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Механизм](https://github.com/Kidinnu/Kidinnu.github.io/raw/master/assets/img/blog/course_work_mech.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Параметры и обобщённые координат"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Объявляем символьные параметры, которые будут использоваться при построении уравнений движения  \n",
    "l0, c, R, a, b, m1, m2, yc, g, J1, t  = sp.symbols('l_0 c R a b m_1 m_2 y_c g J1 t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ b : \\sqrt{R^{2} - a^{2}}\\right\\}$"
      ],
      "text/plain": [
       "⎧      _________⎫\n",
       "⎨     ╱  2    2 ⎬\n",
       "⎩b: ╲╱  R  - a  ⎭"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Дополнительно введем словарь замен для тех символов, которые можно выразить через другие. \n",
    "# Выражать зависимые символы через независимые мы не будем, чтобы не усложнять вид уравнений \n",
    "# Например, расстояние b выражается через a и R:\n",
    "rules = {b: sp.sqrt(R**2-a**2)}\n",
    "rules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Обобщенные координаты: положение шарика и угол поворота пластины (функции времени)\n",
    "x      = sp.Function('x')\n",
    "phi    = sp.Function('phi')\n",
    "\n",
    "# Вектор обобщенных координат\n",
    "q   = [ x(t), phi(t) ]\n",
    "\n",
    "# скоростей (производная каждого элемента из q)\n",
    "dq  = [ sp.diff(var,t) for var in q  ]\n",
    "\n",
    "# и ускорений\n",
    "d2q = [ sp.diff(var,t) for var in dq ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Кинематические соотношения"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Запишем матрицу поворота:\n",
    "\n",
    "$$\n",
    "    \\boldsymbol A_z = \\begin{bmatrix} \\cos \\varphi & -\\sin \\varphi \\\\ \\sin \\varphi & \\cos \\varphi \\end{bmatrix},\n",
    "$$\n",
    "\n",
    "или матрицу преобразования координат между неподвижной системой координат $Ox_0y_0$ и подвижной системой координат, связанной с пластиной, $Ox'y'$.\n",
    "\n",
    "Например, в системе координат, связанной с пластиной, координатный столбец радиус-вектора точки А относительно оси вращения записывается следующим образом:\n",
    "\n",
    "$$\n",
    "    \\boldsymbol \\rho_A' = \\begin{bmatrix} -b \\\\ -a \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Другими словами, точка А по отношению к точке О смещена в отрицательном направлении оси x' на величину $a$ и в отрицательном направлении оси y' на величину $b$. \n",
    "\n",
    "Координаты точки А в неподвижной системе $Ox_0y_0$:\n",
    "\n",
    "$$\n",
    "    \\boldsymbol \\rho_A = \\begin{bmatrix} a \\sin \\varphi - b \\cos \\varphi \\\\ -a \\cos \\varphi - b \\sin \\varphi \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Последнее выражение можно переписать, используя матрицу поворота $\\boldsymbol A_z$:\n",
    "\n",
    "$$\n",
    "    \\boldsymbol \\rho_A = \\begin{bmatrix} \\cos \\varphi & -\\sin \\varphi \\\\ \\sin \\varphi & \\cos \\varphi \\end{bmatrix} \\begin{bmatrix} -b \\\\ -a \\end{bmatrix} = \\boldsymbol A_z \\boldsymbol \\rho_A'\n",
    "$$\n",
    "\n",
    "Для любого координатного столбца $\\boldsymbol \\rho'$ вектора в подвижной системе, его координаты $\\boldsymbol \\rho$ в неподвижной системе определяются выражением\n",
    "\n",
    "$$\n",
    "    \\boldsymbol \\rho = \\boldsymbol A_z \\boldsymbol \\rho'\n",
    "$$\n",
    "\n",
    "Используя матрицу $\\boldsymbol A_z$, можно записать координатый столбец шарика в неподвижной системе координат, зная координатный столбец его радиус-вектора в подвижной системе $Ox'y'$. Положение шарика относительно точки О определяется координатным столбцом вектора $\\boldsymbol \\rho_2'$, который представляет собой сумму двух векторов, имеющих простой вид:\n",
    "\n",
    "$$\n",
    "    \\boldsymbol \\rho_2' = \\begin{bmatrix} -b \\\\ -a \\end{bmatrix} + \\begin{bmatrix} x(t) \\\\ 0 \\end{bmatrix} = \\rho_A' + \\begin{bmatrix} x(t) \\\\ 0 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Координатный столбец шарика $\\boldsymbol r_2$ в неподвижной системе $Ox_0y_0$ определим, умножив его на матрицу поворота: \n",
    " \n",
    "$$\n",
    "    \\boldsymbol r_2 = A_z \\rho_2'\n",
    "$$\n",
    "\n",
    "Не будем вручную раскрывать это выражение, хотя оно и несложное, доверив эту работу библиотеке sympy. Зная радиус-вектор шарика в неподвижной системе координат, можно найти его скорость\n",
    "\n",
    "$$\n",
    "    \\boldsymbol V_2 = \\frac{d \\boldsymbol r_2}{dt},\n",
    "$$\n",
    "\n",
    "а выражение для скорости шарика будет необходимо при формировании выражения для кинетической энергии шарика $T_2$ и механической системы в целом $T$, чтобы построить уравнения Лагранжа:\n",
    "\n",
    "$$\n",
    "    T_2 = \\frac{m_2 |V_2|^2}{2}\n",
    "$$\n",
    "\n",
    "Дифференцирование координатного столбца радиус-вектора $\\boldsymbol r_2$ тоже доверим библиотеке sympy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Символьная матрица поворота или матрица преобразования координат\n",
    "Az = sp.Matrix([ [sp.cos(phi(t)), -sp.sin(phi(t))],\n",
    "                 [sp.sin(phi(t)),  sp.cos(phi(t))] ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- b\\\\- a\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-b⎤\n",
       "⎢  ⎥\n",
       "⎣-a⎦"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Координатный столбец точки А в подвижной системе координат Ox'y'\n",
    "rhoA = sp.Matrix([ [ -b ], \n",
    "                   [ -a ] ])\n",
    "rhoA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x{\\left(t \\right)}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡x(t)⎤\n",
       "⎢    ⎥\n",
       "⎣ 0  ⎦"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Координатный столбец шарика относительно точки А в подвижной системе координат Ox'y'\n",
    "# или координатный столбец радиус-вектора, проведённого из точки А в точку М\n",
    "rho2 = sp.Matrix([ [ x(t) ], \n",
    "                   [ 0 ] ])\n",
    "\n",
    "rho2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}a \\sin{\\left(\\phi{\\left(t \\right)} \\right)} + \\left(- b + x{\\left(t \\right)}\\right) \\cos{\\left(\\phi{\\left(t \\right)} \\right)}\\\\- a \\cos{\\left(\\phi{\\left(t \\right)} \\right)} + \\left(- b + x{\\left(t \\right)}\\right) \\sin{\\left(\\phi{\\left(t \\right)} \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡a⋅sin(φ(t)) + (-b + x(t))⋅cos(φ(t)) ⎤\n",
       "⎢                                    ⎥\n",
       "⎣-a⋅cos(φ(t)) + (-b + x(t))⋅sin(φ(t))⎦"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Координатный столбец радиус-вектора шарика относительно точки О в неподвижной системе координат\n",
    "r2 = Az*(rho2 + rhoA)\n",
    "r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}a \\cos{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} - \\left(- b + x{\\left(t \\right)}\\right) \\sin{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} + \\cos{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} x{\\left(t \\right)}\\\\a \\sin{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} + \\left(- b + x{\\left(t \\right)}\\right) \\cos{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} + \\sin{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} x{\\left(t \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡            d                                d                    d       ⎤\n",
       "⎢a⋅cos(φ(t))⋅──(φ(t)) - (-b + x(t))⋅sin(φ(t))⋅──(φ(t)) + cos(φ(t))⋅──(x(t))⎥\n",
       "⎢            dt                               dt                   dt      ⎥\n",
       "⎢                                                                          ⎥\n",
       "⎢            d                                d                    d       ⎥\n",
       "⎢a⋅sin(φ(t))⋅──(φ(t)) + (-b + x(t))⋅cos(φ(t))⋅──(φ(t)) + sin(φ(t))⋅──(x(t))⎥\n",
       "⎣            dt                               dt                   dt      ⎦"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Координатный столбец вектора скорости шарика относительно неподвижной системы координат\n",
    "v2 = sp.diff(r2, t)\n",
    "v2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Момент инерции и положение центра масс пластины"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Момент инерции пластины относительно оси вращения О"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Момент инерции пластины относительно оси вращения $O$:\n",
    "\n",
    "$$\n",
    "J_1 = \\int r^2 \\mu ds  = \\int_0^R \\int_0^{\\pi} r^2 \\mu r d \\gamma dr = \\mu \\int_0^R \\int_0^{\\pi} r^3 d \\gamma dr \n",
    "$$\n",
    "\n",
    "где $\\mu$ - масса единицы площади пластины. Для полукруглой пластины массой $m_2$ эта величина определяется отношением массы к площади половины круга:\n",
    "\n",
    "$$\n",
    "\\mu = \\frac{2 m_1}{\\pi R^2}\n",
    "$$\n",
    "\n",
    "Интеграл $J_0$ легко найти \"вручную\":\n",
    "\n",
    "$$\n",
    "    J_1 = \\mu \\int_0^R \\int_0^{\\pi} r^3 d \\gamma dr = \\frac{2 m_1}{\\pi R^2} \\pi \\frac{1}{4} R^4 = \\frac{m_1 R^2}{2}\n",
    "$$\n",
    "\n",
    "но можно воспользоваться возможностями sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{R^{2} m_{1}}{2}$"
      ],
      "text/plain": [
       " 2   \n",
       "R ⋅m₁\n",
       "─────\n",
       "  2  "
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r, gamma = sp.symbols('r, gamma')\n",
    "(2*m1/(sp.pi*R**2))*sp.integrate(sp.integrate(r**3, (r,0,R)), (gamma,0,sp.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ J_{1} : \\frac{R^{2} m_{1}}{2}, \\  b : \\sqrt{R^{2} - a^{2}}\\right\\}$"
      ],
      "text/plain": [
       "⎧     2           _________⎫\n",
       "⎪    R ⋅m₁       ╱  2    2 ⎪\n",
       "⎨J₁: ─────, b: ╲╱  R  - a  ⎬\n",
       "⎪      2                   ⎪\n",
       "⎩                          ⎭"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Запомним результат в словаре замен\n",
    "rules[J1] = (2*m1/(sp.pi*R**2))*sp.integrate(sp.integrate(r**3, (r,0,R)), (gamma,0,sp.pi))\n",
    "rules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Положение центра масс пластины"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Положение центра масс пластины:\n",
    "\n",
    "$$\n",
    "    y_c = - \\frac{1}{m_1} \\int_0^R \\int_0^{\\pi} r \\sin \\gamma \\mu r d \\gamma dr\n",
    "$$\n",
    "\n",
    "![Механизм](https://raw.githubusercontent.com/Kidinnu/Kidinnu.github.io/master/assets/img/blog/course_work_inertia.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ J_{1} : \\frac{R^{2} m_{1}}{2}, \\  b : \\sqrt{R^{2} - a^{2}}, \\  y_{c} : - \\frac{4 R}{3 \\pi}\\right\\}$"
      ],
      "text/plain": [
       "⎧     2           _________            ⎫\n",
       "⎪    R ⋅m₁       ╱  2    2        -4⋅R ⎪\n",
       "⎨J₁: ─────, b: ╲╱  R  - a  , y_c: ─────⎬\n",
       "⎪      2                           3⋅π ⎪\n",
       "⎩                                      ⎭"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rules[yc] = -(2/(sp.pi*R**2))*sp.integrate(sp.integrate(r**2*sp.sin(gamma), (r,0,R)), (gamma,0,sp.pi))\n",
    "rules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Кинетическая энергия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Кинетическая энергия шарика\n",
    "\n",
    "$$\n",
    "    T_2 = \\frac{m_2 V_2^2}{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{m_{2} \\left(\\left(a \\sin{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} + \\left(- b + x{\\left(t \\right)}\\right) \\cos{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} + \\sin{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} x{\\left(t \\right)}\\right)^{2} + \\left(a \\cos{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} - \\left(- b + x{\\left(t \\right)}\\right) \\sin{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} + \\cos{\\left(\\phi{\\left(t \\right)} \\right)} \\frac{d}{d t} x{\\left(t \\right)}\\right)^{2}\\right)}{2}$"
      ],
      "text/plain": [
       "   ⎛                                                                          \n",
       "   ⎜⎛            d                                d                    d      \n",
       "m₂⋅⎜⎜a⋅sin(φ(t))⋅──(φ(t)) + (-b + x(t))⋅cos(φ(t))⋅──(φ(t)) + sin(φ(t))⋅──(x(t)\n",
       "   ⎝⎝            dt                               dt                   dt     \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "  2                                                                           \n",
       " ⎞    ⎛            d                                d                    d    \n",
       ")⎟  + ⎜a⋅cos(φ(t))⋅──(φ(t)) - (-b + x(t))⋅sin(φ(t))⋅──(φ(t)) + cos(φ(t))⋅──(x(\n",
       " ⎠    ⎝            dt                               dt                   dt   \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "  2                                                                           \n",
       "\n",
       "    2⎞\n",
       "   ⎞ ⎟\n",
       "t))⎟ ⎟\n",
       "   ⎠ ⎠\n",
       "──────\n",
       "      "
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# v2.transpose()*v2 -- скалярное произведение скорости на саму себя\n",
    "# результат - квадрат абсолютной скорости скорости шарика\n",
    "T2 = m2*(v2.transpose()*v2)[0]/2\n",
    "T2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Кинетическая пластины\n",
    "\n",
    "$$\n",
    "    T_1 = \\frac{J_1 \\dot{\\varphi}^2}{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "T1 = J1*sp.diff(phi(t),t)**2/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Кинетическая энергия системы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{J_{1} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2}}{2} + \\frac{m_{2} \\left(a^{2} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + 2 a \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)} + b^{2} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} - 2 b x{\\left(t \\right)} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + x^{2}{\\left(t \\right)} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + \\left(\\frac{d}{d t} x{\\left(t \\right)}\\right)^{2}\\right)}{2}$"
      ],
      "text/plain": [
       "             2      ⎛             2                                        2  \n",
       "   ⎛d       ⎞       ⎜ 2 ⎛d       ⎞        d        d           2 ⎛d       ⎞   \n",
       "J₁⋅⎜──(φ(t))⎟    m₂⋅⎜a ⋅⎜──(φ(t))⎟  + 2⋅a⋅──(φ(t))⋅──(x(t)) + b ⋅⎜──(φ(t))⎟  -\n",
       "   ⎝dt      ⎠       ⎝   ⎝dt      ⎠        dt       dt            ⎝dt      ⎠   \n",
       "────────────── + ─────────────────────────────────────────────────────────────\n",
       "      2                                                                    2  \n",
       "\n",
       "                    2                   2             2⎞\n",
       "          ⎛d       ⎞     2    ⎛d       ⎞    ⎛d       ⎞ ⎟\n",
       " 2⋅b⋅x(t)⋅⎜──(φ(t))⎟  + x (t)⋅⎜──(φ(t))⎟  + ⎜──(x(t))⎟ ⎟\n",
       "          ⎝dt      ⎠          ⎝dt      ⎠    ⎝dt      ⎠ ⎠\n",
       "────────────────────────────────────────────────────────\n",
       "                                                        "
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = (T1 + T2).simplify()\n",
    "T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Потенциальная энергия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Потенциальная энергия пластины определяется высотой её центра масс над условно нулевым уровнем потенциальной энергии. \n",
    "Пусть плоскость нулевого уровня энергии проходит через ось вращения пластины.\n",
    "\n",
    "$$\n",
    "    \\Pi_1 = m_1 g y_c \\cos \\varphi\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "P1 = m1*g*yc*sp.cos(phi(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Потенциальная энергия шарика:\n",
    "\n",
    "$$\n",
    "    \\Pi_2 = y_2 m_2 g\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "P2 = r2[1]*m2*g "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Потенциальная энергия пружины\n",
    "\n",
    "$$\n",
    "    \\Pi_s  = \\frac{c (x-l_0)^2}{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "PS = c*(x(t)-l0)*(x(t)-l0)/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Потенциальная энергия системы:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{c \\left(l_{0} - x{\\left(t \\right)}\\right)^{2}}{2} + g m_{1} y_{c} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} - g m_{2} \\left(a \\cos{\\left(\\phi{\\left(t \\right)} \\right)} + \\left(b - x{\\left(t \\right)}\\right) \\sin{\\left(\\phi{\\left(t \\right)} \\right)}\\right)$"
      ],
      "text/plain": [
       "             2                                                                \n",
       "c⋅(l₀ - x(t))                                                                 \n",
       "────────────── + g⋅m₁⋅y_c⋅cos(φ(t)) - g⋅m₂⋅(a⋅cos(φ(t)) + (b - x(t))⋅sin(φ(t))\n",
       "      2                                                                       \n",
       "\n",
       " \n",
       " \n",
       ")\n",
       " "
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = P1 + P2 + PS\n",
    "P.simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Функция Лагранжа"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{J_{1} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2}}{2} - \\frac{c \\left(l_{0} - x{\\left(t \\right)}\\right)^{2}}{2} - g m_{1} y_{c} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} + g m_{2} \\left(a \\cos{\\left(\\phi{\\left(t \\right)} \\right)} + \\left(b - x{\\left(t \\right)}\\right) \\sin{\\left(\\phi{\\left(t \\right)} \\right)}\\right) + \\frac{m_{2} \\left(a^{2} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + 2 a \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)} + b^{2} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} - 2 b x{\\left(t \\right)} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + x^{2}{\\left(t \\right)} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + \\left(\\frac{d}{d t} x{\\left(t \\right)}\\right)^{2}\\right)}{2}$"
      ],
      "text/plain": [
       "             2                                                                \n",
       "   ⎛d       ⎞                                                                 \n",
       "J₁⋅⎜──(φ(t))⎟                 2                                               \n",
       "   ⎝dt      ⎠    c⋅(l₀ - x(t))                                                \n",
       "────────────── - ────────────── - g⋅m₁⋅y_c⋅cos(φ(t)) + g⋅m₂⋅(a⋅cos(φ(t)) + (b \n",
       "      2                2                                                      \n",
       "\n",
       "                        ⎛             2                                       \n",
       "                        ⎜ 2 ⎛d       ⎞        d        d           2 ⎛d       \n",
       "                     m₂⋅⎜a ⋅⎜──(φ(t))⎟  + 2⋅a⋅──(φ(t))⋅──(x(t)) + b ⋅⎜──(φ(t))\n",
       "                        ⎝   ⎝dt      ⎠        dt       dt            ⎝dt      \n",
       "- x(t))⋅sin(φ(t))) + ─────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       " 2                      2                   2             2⎞\n",
       "⎞             ⎛d       ⎞     2    ⎛d       ⎞    ⎛d       ⎞ ⎟\n",
       "⎟  - 2⋅b⋅x(t)⋅⎜──(φ(t))⎟  + x (t)⋅⎜──(φ(t))⎟  + ⎜──(x(t))⎟ ⎟\n",
       "⎠             ⎝dt      ⎠          ⎝dt      ⎠    ⎝dt      ⎠ ⎠\n",
       "────────────────────────────────────────────────────────────\n",
       " 2                                                          "
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = T - P\n",
    "sp.simplify(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Функция построяния уранения Лагранжа по заданной функции Лагранжа L и обощенной коодинате q\n",
    "Lagrange_equation = lambda L, q : sp.diff(sp.diff(L,sp.diff(q)),t) - sp.diff(L,q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ - c \\left(l_{0} - x{\\left(t \\right)}\\right) + g m_{2} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} + m_{2} \\left(b - x{\\left(t \\right)}\\right) \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + m_{2} \\left(a \\frac{d^{2}}{d t^{2}} \\phi{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x{\\left(t \\right)}\\right), \\  J_{1} \\frac{d^{2}}{d t^{2}} \\phi{\\left(t \\right)} - g m_{1} y_{c} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} + g m_{2} \\left(a \\sin{\\left(\\phi{\\left(t \\right)} \\right)} + \\left(- b + x{\\left(t \\right)}\\right) \\cos{\\left(\\phi{\\left(t \\right)} \\right)}\\right) + m_{2} \\left(a^{2} \\frac{d^{2}}{d t^{2}} \\phi{\\left(t \\right)} + a \\frac{d^{2}}{d t^{2}} x{\\left(t \\right)} + b^{2} \\frac{d^{2}}{d t^{2}} \\phi{\\left(t \\right)} - 2 b x{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\phi{\\left(t \\right)} - 2 b \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)} + x^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\phi{\\left(t \\right)} + 2 x{\\left(t \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)}\\right)\\right]$"
      ],
      "text/plain": [
       "⎡                                                          2      ⎛    2      \n",
       "⎢                                                ⎛d       ⎞       ⎜   d       \n",
       "⎢-c⋅(l₀ - x(t)) + g⋅m₂⋅sin(φ(t)) + m₂⋅(b - x(t))⋅⎜──(φ(t))⎟  + m₂⋅⎜a⋅───(φ(t))\n",
       "⎢                                                ⎝dt      ⎠       ⎜    2      \n",
       "⎣                                                                 ⎝  dt       \n",
       "\n",
       "     2      ⎞       2                                                         \n",
       "    d       ⎟      d                                                          \n",
       " + ───(x(t))⎟, J₁⋅───(φ(t)) - g⋅m₁⋅y_c⋅sin(φ(t)) + g⋅m₂⋅(a⋅sin(φ(t)) + (-b + x\n",
       "     2      ⎟       2                                                         \n",
       "   dt       ⎠     dt                                                          \n",
       "\n",
       "                     ⎛     2             2              2                    2\n",
       "                     ⎜ 2  d             d           2  d                    d \n",
       "(t))⋅cos(φ(t))) + m₂⋅⎜a ⋅───(φ(t)) + a⋅───(x(t)) + b ⋅───(φ(t)) - 2⋅b⋅x(t)⋅───\n",
       "                     ⎜     2             2              2                    2\n",
       "                     ⎝   dt            dt             dt                   dt \n",
       "\n",
       "                                         2                                 ⎞⎤\n",
       "             d        d           2     d                 d        d       ⎟⎥\n",
       "(φ(t)) - 2⋅b⋅──(φ(t))⋅──(x(t)) + x (t)⋅───(φ(t)) + 2⋅x(t)⋅──(φ(t))⋅──(x(t))⎟⎥\n",
       "             dt       dt                 2                dt       dt      ⎟⎥\n",
       "                                       dt                                  ⎠⎦"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Уравнения движения (без правой части = 0)\n",
    "equations = [ sp.simplify(Lagrange_equation(L, q)) for q in (x(t), phi(t)) ]\n",
    "equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Разрешим уравнения относительно вторых производных"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ \\frac{d^{2}}{d t^{2}} \\phi{\\left(t \\right)} : \\frac{a b m_{2} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} - a c l_{0} + a c x{\\left(t \\right)} - a m_{2} x{\\left(t \\right)} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + b g m_{2} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} + 2 b m_{2} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)} + g m_{1} y_{c} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} - g m_{2} x{\\left(t \\right)} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} - 2 m_{2} x{\\left(t \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)}}{J_{1} + b^{2} m_{2} - 2 b m_{2} x{\\left(t \\right)} + m_{2} x^{2}{\\left(t \\right)}}, \\  \\frac{d^{2}}{d t^{2}} x{\\left(t \\right)} : \\frac{- a m_{2} \\left(a g m_{2} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} - b g m_{2} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} - 2 b m_{2} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)} - g m_{1} y_{c} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} + g m_{2} x{\\left(t \\right)} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} + 2 m_{2} x{\\left(t \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)}\\right) + \\left(J_{1} + a^{2} m_{2} + b^{2} m_{2} - 2 b m_{2} x{\\left(t \\right)} + m_{2} x^{2}{\\left(t \\right)}\\right) \\left(b m_{2} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} - c l_{0} + c x{\\left(t \\right)} + g m_{2} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} - m_{2} x{\\left(t \\right)} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2}\\right)}{m_{2} \\left(- J_{1} - b^{2} m_{2} + 2 b m_{2} x{\\left(t \\right)} - m_{2} x^{2}{\\left(t \\right)}\\right)}\\right\\}$"
      ],
      "text/plain": [
       "⎧                            2                                           2    \n",
       "⎪                  ⎛d       ⎞                                  ⎛d       ⎞     \n",
       "⎪  2        a⋅b⋅m₂⋅⎜──(φ(t))⎟  - a⋅c⋅l₀ + a⋅c⋅x(t) - a⋅m₂⋅x(t)⋅⎜──(φ(t))⎟  + b\n",
       "⎨ d                ⎝dt      ⎠                                  ⎝dt      ⎠     \n",
       "⎪───(φ(t)): ──────────────────────────────────────────────────────────────────\n",
       "⎪  2                                                                          \n",
       "⎩dt                                                                           \n",
       "\n",
       "                                                                              \n",
       "                         d        d                                           \n",
       "⋅g⋅m₂⋅cos(φ(t)) + 2⋅b⋅m₂⋅──(φ(t))⋅──(x(t)) + g⋅m₁⋅y_c⋅sin(φ(t)) - g⋅m₂⋅x(t)⋅co\n",
       "                         dt       dt                                          \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "             2                        2                                       \n",
       "       J₁ + b ⋅m₂ - 2⋅b⋅m₂⋅x(t) + m₂⋅x (t)                                    \n",
       "\n",
       "                                                                              \n",
       "                    d        d                           ⎛                    \n",
       "s(φ(t)) - 2⋅m₂⋅x(t)⋅──(φ(t))⋅──(x(t))    2        - a⋅m₂⋅⎜a⋅g⋅m₂⋅sin(φ(t)) - b\n",
       "                    dt       dt         d                ⎝                    \n",
       "─────────────────────────────────────, ───(x(t)): ────────────────────────────\n",
       "                                         2                                    \n",
       "                                       dt                                     \n",
       "\n",
       "                                                                              \n",
       "                         d        d                                           \n",
       "⋅g⋅m₂⋅cos(φ(t)) - 2⋅b⋅m₂⋅──(φ(t))⋅──(x(t)) - g⋅m₁⋅y_c⋅sin(φ(t)) + g⋅m₂⋅x(t)⋅co\n",
       "                         dt       dt                                          \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                    d        d       ⎞   ⎛      2       2                     \n",
       "s(φ(t)) + 2⋅m₂⋅x(t)⋅──(φ(t))⋅──(x(t))⎟ + ⎝J₁ + a ⋅m₂ + b ⋅m₂ - 2⋅b⋅m₂⋅x(t) + m\n",
       "                    dt       dt      ⎠                                        \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "         ⎛       2                        2   ⎞                               \n",
       "      m₂⋅⎝-J₁ - b ⋅m₂ + 2⋅b⋅m₂⋅x(t) - m₂⋅x (t)⎠                               \n",
       "\n",
       "         ⎛               2                                                    \n",
       "   2   ⎞ ⎜     ⎛d       ⎞                                             ⎛d      \n",
       "₂⋅x (t)⎠⋅⎜b⋅m₂⋅⎜──(φ(t))⎟  - c⋅l₀ + c⋅x(t) + g⋅m₂⋅sin(φ(t)) - m₂⋅x(t)⋅⎜──(φ(t)\n",
       "         ⎝     ⎝dt      ⎠                                             ⎝dt     \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "  2⎞⎫\n",
       " ⎞ ⎟⎪\n",
       ")⎟ ⎟⎪\n",
       " ⎠ ⎠⎬\n",
       "────⎪\n",
       "    ⎪\n",
       "    ⎭"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "сauchy_equations = sp.solve(equations, d2q)\n",
    "сauchy_equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\frac{- a m_{2} \\left(a g m_{2} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} - b g m_{2} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} - 2 b m_{2} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)} - g m_{1} y_{c} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} + g m_{2} x{\\left(t \\right)} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} + 2 m_{2} x{\\left(t \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)}\\right) + \\left(J_{1} + a^{2} m_{2} + b^{2} m_{2} - 2 b m_{2} x{\\left(t \\right)} + m_{2} x^{2}{\\left(t \\right)}\\right) \\left(b m_{2} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} - c l_{0} + c x{\\left(t \\right)} + g m_{2} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} - m_{2} x{\\left(t \\right)} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2}\\right)}{m_{2} \\left(- J_{1} - b^{2} m_{2} + 2 b m_{2} x{\\left(t \\right)} - m_{2} x^{2}{\\left(t \\right)}\\right)}, \\  \\frac{a b m_{2} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} - a c l_{0} + a c x{\\left(t \\right)} - a m_{2} x{\\left(t \\right)} \\left(\\frac{d}{d t} \\phi{\\left(t \\right)}\\right)^{2} + b g m_{2} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} + 2 b m_{2} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)} + g m_{1} y_{c} \\sin{\\left(\\phi{\\left(t \\right)} \\right)} - g m_{2} x{\\left(t \\right)} \\cos{\\left(\\phi{\\left(t \\right)} \\right)} - 2 m_{2} x{\\left(t \\right)} \\frac{d}{d t} \\phi{\\left(t \\right)} \\frac{d}{d t} x{\\left(t \\right)}}{J_{1} + b^{2} m_{2} - 2 b m_{2} x{\\left(t \\right)} + m_{2} x^{2}{\\left(t \\right)}}\\right]$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢       ⎛                                             d        d              \n",
       "⎢- a⋅m₂⋅⎜a⋅g⋅m₂⋅sin(φ(t)) - b⋅g⋅m₂⋅cos(φ(t)) - 2⋅b⋅m₂⋅──(φ(t))⋅──(x(t)) - g⋅m₁\n",
       "⎢       ⎝                                             dt       dt             \n",
       "⎢─────────────────────────────────────────────────────────────────────────────\n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                 d        d       ⎞   ⎛      2\n",
       "⋅y_c⋅sin(φ(t)) + g⋅m₂⋅x(t)⋅cos(φ(t)) + 2⋅m₂⋅x(t)⋅──(φ(t))⋅──(x(t))⎟ + ⎝J₁ + a \n",
       "                                                 dt       dt      ⎠           \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                      ⎛       2                        2   ⎞  \n",
       "                                   m₂⋅⎝-J₁ - b ⋅m₂ + 2⋅b⋅m₂⋅x(t) - m₂⋅x (t)⎠  \n",
       "\n",
       "                                      ⎛               2                       \n",
       "       2                        2   ⎞ ⎜     ⎛d       ⎞                        \n",
       "⋅m₂ + b ⋅m₂ - 2⋅b⋅m₂⋅x(t) + m₂⋅x (t)⎠⋅⎜b⋅m₂⋅⎜──(φ(t))⎟  - c⋅l₀ + c⋅x(t) + g⋅m₂\n",
       "                                      ⎝     ⎝dt      ⎠                        \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                               2⎞                   2                         \n",
       "                     ⎛d       ⎞ ⎟         ⎛d       ⎞                          \n",
       "⋅sin(φ(t)) - m₂⋅x(t)⋅⎜──(φ(t))⎟ ⎟  a⋅b⋅m₂⋅⎜──(φ(t))⎟  - a⋅c⋅l₀ + a⋅c⋅x(t) - a⋅\n",
       "                     ⎝dt      ⎠ ⎠         ⎝dt      ⎠                          \n",
       "─────────────────────────────────, ───────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                  2                                                           \n",
       "        ⎛d       ⎞                              d        d                    \n",
       "m₂⋅x(t)⋅⎜──(φ(t))⎟  + b⋅g⋅m₂⋅cos(φ(t)) + 2⋅b⋅m₂⋅──(φ(t))⋅──(x(t)) + g⋅m₁⋅y_c⋅s\n",
       "        ⎝dt      ⎠                              dt       dt                   \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                    2                        2                \n",
       "                              J₁ + b ⋅m₂ - 2⋅b⋅m₂⋅x(t) + m₂⋅x (t)             \n",
       "\n",
       "                                                            ⎤\n",
       "                                           d        d       ⎥\n",
       "in(φ(t)) - g⋅m₂⋅x(t)⋅cos(φ(t)) - 2⋅m₂⋅x(t)⋅──(φ(t))⋅──(x(t))⎥\n",
       "                                           dt       dt      ⎥\n",
       "────────────────────────────────────────────────────────────⎥\n",
       "                                                            ⎥\n",
       "                                                            ⎦"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Правая часть полученных уравнений (список выражений)\n",
    "сauchy_equations_right_side = list(сauchy_equations.values())\n",
    "сauchy_equations_right_side"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Численное интегрирование"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ l_{0}, \\  c, \\  R, \\  a, \\  b, \\  m_{1}, \\  m_{2}, \\  y_{c}, \\  g, \\  J_{1}\\right]$"
      ],
      "text/plain": [
       "[l₀, c, R, a, b, m₁, m₂, y_c, g, J₁]"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Список всех символов, встречающихся в уравнениях движения\n",
    "symbol_list = [l0, c, R, a, b, m1, m2, yc, g, J1]\n",
    "symbol_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ l_{0}, \\  c, \\  R, \\  a, \\  b, \\  m_{1}, \\  m_{2}, \\  y_{c}, \\  g, \\  J_{1}, \\  t, \\  x{\\left(t \\right)}, \\  \\phi{\\left(t \\right)}, \\  \\frac{d}{d t} x{\\left(t \\right)}, \\  \\frac{d}{d t} \\phi{\\left(t \\right)}\\right]$"
      ],
      "text/plain": [
       "⎡                                                   d         d       ⎤\n",
       "⎢l₀, c, R, a, b, m₁, m₂, y_c, g, J₁, t, x(t), φ(t), ──(x(t)), ──(φ(t))⎥\n",
       "⎣                                                   dt        dt      ⎦"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Объединяем список символов со списком переменных состояния, включая время\n",
    "params_and_state = [*symbol_list, t, *q, *dq]\n",
    "params_and_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Словарь значений независимых параметров системы\n",
    "#\n",
    "params = {R: 1.0, a: 0.5, m1: 5, m2: 1.0, g: 9.807, c: 25, l0: 0.7}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l_0 = 0.70\n",
      "c = 25.00\n",
      "R = 1.00\n",
      "a = 0.50\n",
      "b = 0.87\n",
      "m_1 = 5.00\n",
      "m_2 = 1.00\n",
      "y_c = -0.42\n",
      "g = 9.81\n",
      "J1 = 2.50\n"
     ]
    }
   ],
   "source": [
    "# для каждого символа из symbol_list выполним подстановку из rules (символ может зависеть от других символов), \n",
    "# а затем подставим значения из params\n",
    "params_list = [sym.subs(rules).subs(params).evalf() for sym in symbol_list]\n",
    "# \n",
    "for el in zip(symbol_list, params_list):\n",
    "    print(el[0], '= {:4.2f}'.format(el[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Функция для вычисления правых частей дифференциальных уравнений\n",
    "# При помощи функции lambdify определим функцию, \n",
    "# которая будет вычислять значения правых частей ДУ для заданных числовых параметров. \n",
    "# Первый аргумент функции lambdify -- список символов, \n",
    "# которые содержаться в вычисляемом выражении (сauchy_equations_right_side), \n",
    "# второй аргумент -- само символьное выражение.\n",
    "f_right_side = lambdify(params_and_state, сauchy_equations_right_side)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Функция правых частей дифференциальных уравнений для интегратора solve_ivp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dydt(t, y, params):\n",
    "    # t - время\n",
    "    # y[0] - x\n",
    "    # y[1] - phi\n",
    "    # y[2] - dx/dt\n",
    "    # y[3] - dphi/dt    \n",
    "    # функция возвращает\n",
    "    # res[0] - dx/dt\n",
    "    # res[1] - dphi/dt\n",
    "    # res[2] - d2x/dt2\n",
    "    # res[3] - d2phi/dt2\n",
    "    # вычисляем вторые производные\n",
    "    d2xd2phi = f_right_side( *[*params, t, *y] )    \n",
    "    res = y.copy()\n",
    "    # копируем скорости\n",
    "    res[0:2] = y[2:4]\n",
    "    # записываем ускорения    \n",
    "    res[2:4] = d2xd2phi[0:2]\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Начальные условия\n",
    "q0 = [0.8, 0.5, 0, 0];\n",
    "\n",
    "# Интегрирование\n",
    "solution = solve_ivp(lambda t, y: dydt(t, y, params_list), [0, 10.0], q0, \n",
    "                     rtol = 1e-6, method=\"LSODA\", t_eval = np.linspace(0,10,500))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Результаты "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(solution.t,solution.y[0]);\n",
    "plt.xlabel('t, c');\n",
    "plt.ylabel('x, м');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(solution.t,solution.y[1]);\n",
    "plt.xlabel('t, c');\n",
    "plt.ylabel('$\\\\varphi$, радиан');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Кинетическая, потенциальная и полная энергии системы\n",
    "Energy = [T, P, T + P]\n",
    "f_Energy = lambdify(params_and_state, Energy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_Energy = [ f_Energy(*[*params_list, state[0], *(state[1])]) for state in zip(solution.t, solution.y.transpose()) ] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(solution.t,n_Energy);\n",
    "plt.legend(['Кинетическая энергия','Потенциальная энергия','Полная энергия'])\n",
    "plt.xlabel('t, c');\n",
    "plt.ylabel('Энергия, Дж');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Анимация"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.patches import Circle, Wedge, Polygon\n",
    "from matplotlib.collections import PatchCollection\n",
    "import matplotlib.lines as mlines\n",
    "from matplotlib.animation import FuncAnimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Функция для вычисления положения шарика по заданному символьному выражению (второй аргумент функции) и\n",
    "# и фактическим значениям параметров системы и ее состоянию\n",
    "n_r2 = lambdify(params_and_state, r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Kf/7XuWBQdptK6Z9W5zjstfGXmUNaBtGUPyDcC2RzKFk1TiJ0KBrL73fNoB44LvbPORQNDBwXhBR/uZFInfOiDWoGLrXCf75dmVCb8qeAakfogmDVwYOOk477YGFQ7pz+i8i8WTNwsNeohEER1TmO6dyH4/rLkwkASt4WyMK6QamaQZFG5yTWx3/Ykc+gFIntzKTXn1XjJEL9m8vv6QlFGQZlGdBbIin9ThMzL8DYLb6OTKTOedEGNQPP9vcBVCNCl4ZoD04AuLzXQM2odg5pu91efr0eoTZrBnpta5lXVnWiPXgp/Y6FoUI5tHFEdY5jXX/6tWwGhSimcx9j11d6/Gl0TsJej9CWmENaBkNnfs6g7HfD9U8mg5JV4yQ26e+WZFCWwXB80aEEygkqidQ5L9qgZmA+PoVZMyoRoUvDeoS6tjAoq+xQ2La9/Hrg7LZBFb0ljhLelqn+5z+qcxw0EklTfYDd1H/9yF+l8afROY6J62My99dyiMNe/DIZlCIZODP0IykPhwuD0pHIoGTReOtrb0j5oY/vAtG2oUC54xepc160Qc3Ac9/+7ei1G0pVubNADcqDvbUcsgofeT777LPLr2mudL8jdw6hKFYGdfVyCKM6x7F+QgNQh0L98aeBjv+cQbno8qCKQZlG5zio43g+QtnA3Cc4m3nM7012xq6H6Tw451DL2DqQReMkCCEbi1KB3TqlXg8o0ceLRpTOLGiDmoE7d+4sDAr1I3RpsJ0ZDtoN1M3Vx6YqBlUcd+7cWX5tOy4MI8ydplR9/FGWTf3PRaircVtmVOc41k9o6NfDsYsgUMOgZGGwIUJ92LEw9wlOp2oYlGl0jmPzCc2iF79EBqUo1mtIgGinI3n2QBaNk3BcH64XxBiU8oxfFISQCznUZToUonRmQRvUDLzyyis7ZVCF+XPWuccOu9XOIX7llVeWX9vj8JZAs2YsH5OxD6sohmMXNeP8CcVhx8JwPFfeoIzqHEdcDrkfEJwpYlCysN6DN/q1KjfGptE5jk0O1TKHdAfWgM01BM1zP5MBFo2T2PT5P1xeblb9U2rH9eH6wfn1r1ve/BelMwvaoGbg2rVrO3XkO3Bm5yYTEB75VdmhuHbt2vLr8NrtxrmfV8WgTMNgce14LeJQ9BYG5elU7Q0lqnMctuPCrBm41Io4FBJG6ESxilBHjvwVO/JOo3MccScUwI5EqDek/MjY6YlF4yQ2ndDQFnq7EKG2N9SQ7DfraJhGKfNflM4saIOagTfffHPR5UCexUQk9sKginK4OPL2K2pQvvnmm8uvByP3nDEBhIuLHxA8nahtUKbBHp2/1AGoTg5hVOc4BguH6pxD0S4vh7BobGcGs2Zgv1VfPqbabZlpdI4j0aBWZPws2BtSPmQsymPROAlqNEfXwG6zDsusKb/+pWFZQxBJ+TCMRaerEhwKUTqzoA1qBo6Pj9HvNHEymVfWoIxiO+65yQSEGwohwIlER348OT4+Xn69XpAB7NZtiZvGXxWDIqpzHOs9eIFVtHZX9F8/oVAthzSNznEMHBcN08CliEPRr4hDmYb1PvQA0LFMWPWaVPOfReMkNuWQG4ZR+cJ8yqYagvD7ck6pRenMgjaoGTg6OsLhwqCUKYdMBEFAMBxfzKHud+XLoePJ0dHR8uvh+HxBBhDJIa3o+KPYY/dCyk9VDOqoznFsqiEoM4ewaNZ78ALq5ZCm0TmO4cKhMIyVQ9G2TDTrtZ2Z/w3TwH5z5VAYhiHd5UYsGiexKYecfr8T+m9IeQEWdVQl6C9KZxaEGdSGYfy4YRh3DMOYGoZxbBjG96f8ve8zDMMzDONdUe+NF1evXpXyyEsEp9MwCr+e8kF7UsqUQ8eTq1evAog4FGvj71V8/FHCa3eraVBTnZMYbIhQLz//io8/DevXLgPAnmWi1agpE6FOo3Mc6y3TgFWEcifm/+iiQwHIV0fDonES9ISiG3EogN1pnbmpbSZQnv6idGZBiEFtGMZfAPAzAH4KwJ8B8GUAv20YxvNbfq8H4PMAfk/E++LNG2+8oVwOYV6WBRkxEdqqjv+NN94AADxdpPXEpXxUdfwUPyAYVjhCTXVOYlPKy55lYq9hKj/+NAycizUEQBilVsWgSKNzHJv0B+iRtxoOBQubHAogXANl0p9F4yTsUTj+dYdiVzp92Y4Lq15DxzLPPX5YkkMhSmcWREWo/yaAf0kI+XlCyNcIIT8B4CGAv7Ll9/4FgF8C8O8EvS+u3Lp1qzIGxTbi8qeqnkN869YtAGkcimpvqCdjF4RcPO5sNUx0LFP5CB3VOQ4/IDiZzC98/oHd2lDjDUo1xr9N5ySqMH4WbGd2Yf0D5Bs/i8ZJhPrHzH/F1780DBYpXxcdiibOph5cLyj0/YjSmQXuBrVhGBaAIwBfWPvRFwB8b8Lv/TiAbwPwP/F+T6J48cUXK9PlYBtx+VM05aGqOaQvvvgigPj8uWbdRLdZVyaHNC9x4weq0Yub6hwHdSjWP/9AeTmEReL5AZ5OLuaQA1Cq09E2nZPYlEMOhJ+J3ehDHe9QyqQ/i8ZJbKohAUL9z2bFG5RFM4xzKBdOVtGNCUTpzIKICPUVACaAR2uPP0JoMF/AMIzXAHwOwH9DCPG3/QHDMP6SYRjvGIbxzsOHD/HkyRM8fPgQ9+/fx3A4xIcffojJZIL33nsPQRAsc21oVejVq1cRBAHee+89TCYTfPjhhxgOh7h//z7o63388ccYjUa4desWPM/D9evXz73G8fExHjx4gHsfvQ8A+ODuQ5yenuLu3bt4/PgxHj9+jLt37+L09BQffPABZrMZbty4ceE1AOD69evwPA+3bt3CaDTCxx9/XNqYAODGjRuYzWb44IMPlmP6xsMBAGBy8sm5MX39azex36zja3fuKTemNDo9ePAAx8fHywjspaZ5YUyXmjXce3KizJjy6PTAPgMQXuqyPqYmPAxGM+XGFNXpq1/9aqJO1259CADAbHRhTBZxMRjNpBsTz8/eF7/yDggBRva3Loxp3zLw6OlYiTF985vfzKXTR3e+gaeTOch0dGFMvY6FT06nUugk8rP3yekE+w1cGNNezcfZzMPTM0eKMX300UdCPnsP7TP0OtaFMU1Pw73xj997XwqdRH32vnUyQnehf3RMZ588AAD84b+/VuiYvva1r5U2n2IhhHD9D8CzAAiA7197/HMAbm14fhPATQD/beSxnwTwbpq/d3R0RMrCtm1CCCHf/bl/Sz73G++W9j6K4Gd//wPywltvk4nrXfjZD/z075Of+NdXS3hX4qEa/8pXvkFeeOtt8uBkfOE5P/KzXyJ/8Re+UvRbK5Tf+pMH5IW33ibv3j+58LMf+8U/Ij/8T79YwrviB9U5jn/34RPywltvky998MmFn/2Nf/PH5Hv/we+JemtS8PVvnZIX3nqb/Oa1+xd+9vf/75vku/7H3y7hXWVnm85xPDqdkBfeept8/st3Lvzsn/3e+7FrY1VwPZ+88Nbb5J/87vsXfvbLX/mYvPDW2+ThyaSEd3aRvBpv47v/7uZ9nq6NN+8/FfJ3ZeH7/9ffJ3/tVy/u81++Hb82ikSUzmkA8A7ZYI+KiFA/AeDjYjT607gYtQaAPwXgTwP43xfdPTwAfxfAq4vv/1MB75EL4/EYQHlJ+UUyGLloWyZaDfPCz2TLoeMJ1ZjmSG8syqnw+Cmbbsmj9DtN5XMIqc5xbLrUgxJW+Vc7h35TD15Kv2Nh7PqYzrceLpbONp3jiKshiT5W5TVgee32hhzqVdqjHHMgr8ZJzLwwCh83/4Fq6w/E1xCUVUclQmdWuBvUhBAXwDGAH1r70Q8h7Paxzn0ArwF4I/LfzwG4vfh60+9IQa0W/vPtQpX3cLx5MgHVNiipxrYzR7dZR7O+2aGQKYdQBHR8623TgEUOseI5pFTnOOJqCIDQyJjOA0xc+Q3KvCxz6BMMKhXWgG06x7HNoYo+p4rQ+b3ZoVrcRSBJHUlejZM4GYdjSzIoVV8Dk5h5PkYzL9ahBoqvoxKhMyv17U/JxT8C8K8Mw/gqgP8PwF9GmArycwBgGMbnAYAQ8qOEkDmAcz2nDcN4DGBGCJG6F3WjERoX/Y6Fe8NJye9GLHEtk4CwMPHd+6cFv6NioBrbzmyjMQms+pASQi5UQFeFgePGOhS9dmhQjl0PbUvUkiIWqnMc1Fg6aG/YUNqrCN1zVpv/m5MAGn1a78MOnL9++tmDvULfV1a26RzHzhvUixOK9XsIAKC/WBdliVDn1TgJekKzSX/6b2KP5Bi/CKiztN6DGgjraoDiI9QidGZFiIlPCPk1AH8dwN8BcA3A9wH4s4SQbyye8vziP6UZjUYAduOmpE3XLlP6iy4HYWpRtaAaD2JaJgGh/jMvwLjCEcq44z4gcuSrcNoH1TkO23Gx36rDql9cMnfKoIpJeQLU6HS0Tec4dt2gjmsbCsiX8pJX4ySS9D9oWzAMecYvAuosbYpQ180aDtqNwk/pRejMirCYOSHknxNCPkMIaRJCjgghX4z87AcJIT+Y8Ls/SQj5blHvjRdXrlwBsMghrahBSaFN7Tdx2LHg+gFGM6/gdyUeqnFcyyxgNzbUJIO6CuOnOscxSNC/6r3YgdChvtSqo2EmORTyR+i26RzHYBmh3ZDypJBDkZdEg3KvgZpEBmVejZNIMijNmoFeu9p1VEk1BOHjxad9itCZFfmSUBTi3r2wVdxhx8LcJziroEFJievBCciXQ8cTqnFcD05ArRzSvCQ6FBXIIaQ6x5Gk/+rzr+74t2GP5zjsbt5MD5cRSvnn/zad4xiOXRy0G6hvcCguLwzKSuvvuDCM1fF+lNrCoJRl/curcRLDBIeCPl7lU+okhwoop45KhM6saIOagZdeeglAJIdQ4SPvJMauh+k82HjcC8iXQ8eTl156CYSQ5BzyHTGoY/Vvq//5p3M5jiT9l+OvtP6zjdFZANhv1WHWDCUi1Nt0jmPguBvzx4GVQVn1COXlvc0OBRCugbJ8/vNqnMTSoYj5DPTbltIpb9vYZlCX4VCJ0JkVbVAzcPPmTQCRCGVFPdSkllmAfDl0PLl58ybGro+ZF2zPIa7g+IGwV32qCLXC46dzOY6kGoJLe3XUa0Zl9QfCNSDuuFe2CGUS23SOIynlDah+p6eklC9gVZgtA3k1TmLguDjYa8CsbS46r3LrWCDUvxZzQgGUc1usCJ1Z0QY1A6+//jqASA5hRT3UbflTVTYoX3/99a3euUo5pHkYzTy4frxDsd+so2GqbVDSubwJ6lDEff4NwwgjdBWd/0Byyg+w6MWvwPiTdE4ijUFZZYNq4My26i/L+PNqnMRW/UswKItk4LjotS3UEhyK4XiOICiujkyEzqxog5oBeh1lFYqykqCR920GZRVzCI+PjxN7EANAt1mHZdaUyCHNA82Nj9PfMAzle3HTubyJ0czD3CfbDYqKnlARQsI+9Bs6PFBUySFN0jkJe+xu7HBBKSNCVyRDZ77VoZBl/ufVOInQodzsUAPh/B+O3UINyiJJqiEBwmCbHxCcTovbA0XozIo2qBk4OjoCsDI0VI7QJWEn9OAEgLZlwqrXKrmhHB0dLccVl0McRiiLbxtUFIOEWyIpqueQ0rm8iW36A+XkEBbF2cKhiMshBuQ68k8iSec4CCEYLiJ0cVRZfyC5hgBYOVQyGJR5NN5GWEMS3/e417YQEODppJpBlUFCDQ0QraMqbg6I0JkVbVAzQD2ktmWiWa8pEaHJw7aUB8MwKnv9+vHxceTa7WQPvaob6jb9ARqhU9ehSIp2pNK/whHKbQ41/ZkK488T1TqdePACkvz571g4mczhS2BQ8iYISOJNuUCof0CAEwkMSlER6riUL6D6rTO3pXyVUUelI9QVg3pIS4NSgRzCPNhjFw3TwKVW/C14Mh358SSMUG+P0FbVoQCi127HbyiqOxRJ0Y5tLbMAuXJIebO8JXFLysfJeA7PD4p6W7nIE9VaXru9ZfyEACcVDKqcTkNHIcmglKmOhHfkkjoUyQblIu2xgvoD23PIy7jcS0eoK8aNGzeWX/cqXOVtj8LjzqRrtVU58s3KjRs3YDtzWGYN3ebuORRAJEKdlEOquEEZncvrDFIY1P2OhaeTOeaSG5R5GPZ6p2YAACAASURBVKaI0FNjU4YIZRJJOsexcqgTDMpudTsdbashCX8mTy/yPBon8XQyR0C2z39A7dti4/ADghMJHQreOvNAG9QMvPzyy8uvVTnyzMO2/DmguuN/+eWXwx68ncZOOhRAuKFaZg0dy4x9Tq9t4XTqKWtQRufyOmlSXqocoVrmkG/JIY4+V1aSdI6DGkmJOeTt6h75p6ohWOTQyhBUyqNxEmkdakD+z38eqEORnENd/Ph568wDbVAzcPfu3eXXVa7yT+rBS6mqQX337t2t+XNAOP6zqQfXU9OgTII6VIkORVftTi/RubyO7bho1mtoJzgUVd5QlznkW04oAPkjdEk6x5HmhGYn9E8RoZbBocijcRJZHGoZHArepEl5bDVMtC2z0PnPW2ceaIOagWeeeWb5db/TrGwf2uE4uWUSEC62o5mHmecX9K6K4ZlnnsFgS0EGUO0I5baWSYD6vcijc3kdWpCz7YSCPrdq2M4MrUYNbSsh5UmRy32SdI5jmUOdIuVF9vHnIY1BuYxQS7AH5tE4iTTjb9ZNdJt1KVJeeLO62G17UKnI/Y+3zjzQBjUDJycny6/7nQYc18d0Xi2DEgAGo+Sm/sAqv3BYsQXl5OQkk0FZxQ114CT34AXU70Uencvr2E5yD2YgmkOq5viTsJ15qs0UkP+22CSd47BHLtqWiVYjOeUJqKr+6QzK/WZdCv3zaJyEneKEBqjubZnDLfdQUIouzOetMw+0Qc1Aq9Vafl3V67fnfoDTqZeYPwVE+1BWa0FptVqpcsh7FTao7S09eAH1e7FH5/I6gxTjX+WQqjn+JGgNQRJLg1KCCGUSSTrHkebzb9VroUFZSf23OxQALcwvf/x5NE6CGsnb14Bq1tGkySEHim/MwFtnHmiDmhNVPfJNU+EPVNuhOJt6lU95SGJbyySgup9/INxQt33+6WYrew5xHtLUEDTMGi616pWM0KU5oQHCtJddnf9AdetoBo6LTgqHQvVOR3FQJ3mbU93vWNI71KLRBjUD0+l0+XVVc+hW146nPPKt2PgfnTgAtnvny/GPqmVQzDwfo5mXyqA0DHUdiuhcXie8dnm7QXl5r1HJHPo0NQQAcNhtSq9/ks5xbLvUhFLV1pmp9ZfkLoY8GicxTJHyBVRb//1mHc16CoeiwPWPt8480AY1AwcHB8uvq5pDl+aWNKC6OcRBow1ge4T+YGFQ2uNq5ZDTnPhtG4pZM3Cw11B2Q4nO5ShLhyLFhlrVy33S1BAAxRcl5SFO5yQGo3Tj1/rLoX8ejZMYpDihAVb6E1Kt2zKH47QORRPTeYCx6xXwrvjrzANtUDPw6NGj5ddVPfJPmz91ea+BmlE9g/rD+48BJPfgBFYGZdWOvGlOfFIPXoosOZR5iM7lKGl6MFN6FTzynM59OK6fyqDqteWIUCYRp3MStuOm+/y3q1mUZjvu1vUPWPXiL9ugzKNxEqH+yekOQDj/Z16AsVutxgRpagiASB1VQWsAb515oA1qBp5//vnl15f3GjBrhrIRujjSVHgDQK1mhBtqxcbf6IRecJojzyrmEKbVH6ARGjUNiuhcjjJIeUJDn7Pr+ss+/jid45i4PiZzP12ErhuOv2yDkjeDFDUEQPgZcb0ATskGZVaNt5GmhgCobtrjYJQu5afoOireOvNAG9QMvP/++8uvQ4OyUTmDchWh2+6hVzGH7NbH9wGkNSia0kfospK2ZRSgtkEZnctR6BF22pQPGdqG8SSLQd3vhkf+MhuUcTrHkaYHNeWwY2HuE4xmxRx5F8HY9TCdB9kMypLXwKwaJ0EICfvQp5z/QPUM6ixFqUBxrTN56swLbVAz8Nprr537vopHfrbj4qDdQN3c/lGp4vXbrctXYBhhjvQ2ZMkh5MnKoEqzoTaVvdhgfS5TMhmUC4dSZoMyK0uHKoNBeSaxQRmncxyrGpJ0n3+gWgZVJv27xRpUcWTVOImx62PmBdkMygrpTwiBnTKH+rBgh4qnzrzQBjUDx8fH574PN1Q1DYo40uYPAmpHKOP4+sf3cLBI59mGyjnEcdiOC8MIU5q20e+EXS6CQD2Dcn0uU5YpHykdKi8gOJ3Ia1BmZXlClTKHGig/QplEnM5xLGsItrQMiz6nSkGFXPqXHFTKqnESS4c65fwHqqW/4/pwvSB1DQ1QnEPBU2deaIOagaOjo3PfH3bVzSGNY+DMUnnnQDUNarN9OfX4DzsWhuO5kgZlHPRSkzQORb/ThB8QnE7VcyrX5zLFdlyYNSOlQ0E31OqsAYMMEUoaxZLZoIjTOY6sJzSA3A5FVtIWpQOr20LLTnvLqnESWca/ilBXZ/6n7fIFAJdadTRMo7D5z1NnXmiDmoFNEeqqGZRhD970BuXJ2IVfIYPyG98abL12mdLvWPADgqcT9QzKONK2zALU7nQTF+2wxy567QZqqRyKxfXrFUr7sZ0ZzJqBS63tDoUKOaRZo1pZizKB8lMeeEINqiwOVdn684xc0pqgNCkP3WYdlllTNu1tEzQ4kCaH3DDCxgRF1VHpCHXFWPeQ+m0LJ5N5pQzKtLeEAeGRT0BQKYNyXmtuvSGKIksOIU/SXLtOoUd+KhamxkaoR+laRgHyROh4Yjtz9NpWKoeC/jvJrH+eCHW9ZuBSq771uVXMoaXOYZqUj45lwqrXSl//RESo0zgUhmGg16lW69Sl/hnSPnWEWpOL69evn/u+37FACHBSEYMqCAiG4/QGRRWPvB6djFMd9wLVvNwnSw69yhHq9blMSVvhDqyu5q2W/rNU+cPAyqGUWf84neOgPZgNY7tD0aYGpcTjz8rAcdEw0zkUhmGg3y6/F3tWjZOge1kahwKghdkV0n95QpH+lLao/Z+nzrzQBjUDr7766rnv+91qVXmfTsNoe/oj/2pF6IKAYDQnqaITQCSHtiLjBxYGZcoTCpUjdOtzmTJwZqlPaJaffwXHH0cWh6Jt1dFq1KR2qON0jiPttdtAaFDKcv02L+gJTRqHApAj7TGrxklQh2K/ud2hAKp3W6adIeUFKFZ/njrzQhvUDNy+ffvc9ypH6DaRpQcxUL0c0qeTjA6FJDmEvPADgpNxeoNCZYN6fS5ThuP0NQR7lom9hil1ykNWQoMyXXQKWPRil3j8cTrHkaWGAKhe68wsKV8ALcwvd/xZNU6C6p/FoajS/LcdF1a9ho5lpnp+kZc78dSZF9qgZuC55547933VjvyzVLiHz6uYQzFOX5AERHJIK7KhPp3MEZD04281TLQtU8nP//pcBkKHYjhOn/ICyBGh40lWg7LXaUhtUGzSOYm0125TqtaLfzhWz6HIqnESaW9JpFRNf5ryl96haOJ06mHuB4LfGV+deaENagaePHly7vuqRSiXLYNSGhTLHNKKHHlmqfAHQoOyY5mVOfK1lz14q29Qrs9lIKyFIBkcCqBaG6ofEJxM5hkNSrlzSDfpnESWlA+g2BzSIsiS8gMsLjcref3LqnESYYQ+XQ0BEOp/NvXgeuINyiLIqj/9tyrCqeapMy+0Qc1At9s9931lI9QpUz6adRP7zXplDIpBhh6clH63OhtqnvGrmkO4PpeB6Oc/W4SqKvN/uHAoshiUsuu/Sec45n6Ap5P0KT/AQv+KONQAMBjNMut/NvMw83yB7yqZLBpvI0+EGqjOKWWWLl/A6jS7iDWAp8680AY1A/P5+fZwVr2G/Va9MhtqlmtnKf1u+Ud+vMiaQw6EC4rMBkUWhhlTXuhzVXQo1ucykO/zX2QOoWiyntDQ58o8/k06x3EyDp+bVX/H9TGdl2dQ8mLuBzidetkMyi5tnVhe69QsGm/DznhCoUIv9ixkj1AX1zqTp8680AY1A0Fw8VinSke+tuOibZloNdIVJACLI7+KjD9rD06A3pZYjfGverCm31B7HavUzTQvm+by8trlHc2hzuVQdyyMJTYoN+kcR5ZrtynU+KzCGrByqNOnPMhgUGbROAnXC3A29TLWEJQ/fp4MnfRtc4FiW2fy0pkn2qBmoN1uX3isSlW+dsbJBKBSbaMGIxdtq5bdoajI+Ok40l5sA9Ajf/Ui1Jvm8iDHCUWvY2Ey9zFx5TQos5DPoJTboNikcxyDXDUE4VypwhqYtSgdkCPtMYvGSWS51IZSpU5fM8/H2czL5FAXqT8vnXmiDWoGbNu+8JjsOYRZyJo/BVQtQjfD5WZ6YxpYtY0iRP3bMgeOi26zjmY9/b9Bv9PEdB5g7HoC3xl/Ns3lPBHq1YaqnlOxTpZb4iiyG9SbdI59bo4TGmp8yjr+LNh5aii65X/+s2icxCDDteuU5ed/pP78pyeNaWuoAKDXXjiUBXz+eenME21QM/Dss89eeEzVHNJNZG2ZBSyK8sbVMSg/dWkv0+/0OxZmXoBxBSKUWVtmARGDUrEI3aa5bDsu9lt1WPX0y+Qqh1C9tJd1VicU1YnQbdI5jqGT3aCsUlFanhMaGRyKLBonkaeG5KBtwTAAe6z+/KdOURaHom7WcNAupnUmL515og1qBu7cuXPhsd4iQlsFgzJrQQIQtthzvQBORQzKJrItjLJH6LKQR/+eogbFprmcZ/wyROh4MRy7uNSqo2Gm3yaW+kv6+d+kcxzUoDxoZ88hVs2h3ESeGpLLew3UjHL1z6JxEnlOaMyagYO9RiWCajQokDXts6hTal4680Qb1Ay88sorFx477FiY+wSjmVpH3psYOLNMl1oA0SMv9TcUe+Ti+Wf6mX6nL0EOIS8GoxwOleQRyjg2zeVcDkWV9M/jUEiu/yad47AdF5f3GpkcCmpQVkJ/ekKRwaEwawYO2uWmPWbROAmatpHlhAaoTtrjMkKdNe2zXUwdDS+deaINagauXbt24TEZjrx4MHY9TOdBpvwpoDoROkIIBo4LzznJ9Hv9Cl3ukytCq6hDtWkuZ73UA1jl21ZD/1lm/S+1GjBrhrQRuk06x5FH/1rNQK9kg5IXtuPioN1APYNDAZRvUGbROAnbcWEY2SO0h51mJU4o8hSlhs8vRn9eOvNEG9QMvPnmmxcekz1Ck5Y8LbOA6rSNGrs+Zl6A7/rsd2T6varoTwiBPc5uUKjqUGyay3lqCC7t1VGvGcqNfxPhCUW2zZQalLKOf5POceTRH6hOp6c8DjVQfuvYLBonYY9dHOyFDmIWZLh+nQe246JmhKcuWTjsWrALqCHhpTNPtEHNwPHx8YXHeopG6NbJ7Z22q5FDSMd/+smDTL9XZGN7kTiuD9cLMm+o+806GqYBW7ENZX0uE0LCtpEZx28YxrKOQnWGORwqIGwdJ+v4N63ZceTRHyg/QssL23Ezp/wBi178JY4/i8ZJ5HUoqjL/wxMKK7dDEQRi68h46cwTbVAzcHR0dOGx5ZG3YgbFOoOlQZ3NO1U1QrkOff9v/umXM/1ed2FQqh6hztPhAVgYlAr24l6fy6OZB9cP8hmUFTjyz+tQAHIblJvW7DjypHwANEIrZ8pLFlQ1KLNonESeGhKAXu41F25Qiia3/m0LfkBwOhUbpealM0+0Qc3A1atXLzxWlS4Pqx6k2SLUHcuEVa+pP/7F+//kfrZKYsMwKtE6MU/LJErZR755WJ/LeU9owt+R16BMy9nMw9wnufQ/7DSl1X/Tmr0JQghTyofq+gP57iEAVrfFlmVQptV4GywpL35A8HSiduu8PEXJQHG3JfLSmSfaoGbgjTfeuPBY2zLRrIBBmacHJxAalIcV2FDoYvAfvfFq5t/td5rKjz+v/gDNoVPLoVify3lrCIDwlEb1lJ88l3pQZDYoN63ZmzidevACkjtCeTKZw1c4QhkEJFcfeiDUPyDASUkGZVqNtxGOP7tDTQ1K1U+p7dwnNIs6KsFrAC+deaINagZu3bp14TEaoVQ9h3jguKjXDFxq1TP/rsxFSWmhi8GT+9/I/LuVcCiWt4Rl31B67fDIUyXW53Kea7cpVbgtlRoDWbv8AOG/2dPJHJ4f8H5bzGxaszexOqHIZ1ASApwobFCdTT34Acnc4QIo/5Q2rcZJhA7FPJdBWZXWmcOcKV9FFebz0Jk32qBm4MUXX9z4eBWqfO1ROJkMI1tBArC6fltlBo6Lhmng1Zc/m/l3y84h5MHKoMyWQw8sDErFrt5dn8t5LnWg9NqhQTmX0KBMyzJCnbMojZQYoUwibs1eh56w5M0hDl9D3TUgbw9ioHyDOq3GSTxdnDDkrSEA1C7MpycUuda/gvTnoTNvtEHNwIMHmztAqJhDuk7eghxA7iPftNAevA8fPsz8u5WIUDouLLOGbjP7CUW/08Tp1FPKoFyfyywRSmqEqOxUs0Zoo68hE3Fr9josJzT0d1ReA1hrCMLXKMepTqtxEiwO9WEFCvNPJnMEJOf6V9D856Ezb7RBzUC/v/kWvcMKFKXlzZ8DqtGHNSxIacZqnES/Y+Fs6sH11DEo16EFOXlOKGiagEqfgXWdh46LZr2GtmVmf61l60T5IrRpWRoUOYvSADkjdGnn85Ah5aUKrTOZDMqSHYo8a/Y6LDUkNOVDbYc6/wlNq2GibZnCDWoeOvNGG9QMjMfjjY/3Ouq1DVsnb4UzEB4Tn808zDyf87sqjnD8jViNk6D/birnULLqD6hVlLOu84DFoVjmEKrrVA/HLlqNGtpWjhqKjrwGRdr5vGwbmiflpaAuByKhzkCelAeaJlaWQ5FnzV5nwFCU22qY6FimlA5lWujFLHn3gCLqqHjozBttUDNQq23+5zvsWHBcH9O5ugblYJT92mHKKkKpboSORqjjNE5iZVCpu6DmbZkERI58FdpQ1nVmcigkTnlIy2CU71IPQO7bQtPOZ3vkYq9hYi/HCcVBOzQoldafIULdrJvoNuul6Z9nzV6HJeUJCPdAlU+pWSLUQDF1VDx05o1870ghGo3NBVuqX7899wOcTr38k6kCETqaQx6ncRJVMKhYDEoVI3TrOnNxKBQa/zq2M8uV7gDIfVts2vnM8vlv1k3sN+uK6++ibZloNbI7FEC5dTR51ux1WA3KvsS92NOwcqiy59ADVH+x+z8PnXmjDWoGRqPRxsdVr/KljkD+okTah1LNCLXrBThbOBRxGichc4QuLXkvtQDUNCjXdR4yFOVWoW0WPaHJQ8Os4VKrLmWELu18tsf5LjWhhBFK1fVnGH+JBnWeNXsd25mjw+BQ0MttVGV1U24+ozWsoxK7//PQmTfaoGbgypUrGx9X0aCIwlLhHf5eOAlVjVDT3Odex4rVOAnVi5Jmno+zmZfboDzYU+/Ie13nvNduA6FBeXmvodT417Fztsyi9DsWbAl7kaedz7bj5urBTFG90xGrQV1mL/48a/Y6LCc0wCKHWNGAGhDO/26zjmY95wlF2xK+//PQmTfaoGbg3r17Gx9fGlSKeqjs3mloiKu6oUTzB+M0TuKgbcEw1I1Q08hCXoOybtZw0FbLoIzqPPN8jBgcCkD91pn2iIdBKZ9DnXY+D0aMDkVbcf0ZDeoye/HnWbPXGTj5awiAVQ4xIWrelsl8QtG1MJ0HGLsex3d1Hh4680Yb1Ay89NJLGx+XuW1UGljzpw72GqgZ6hrU0YKUOI2TMGsGDvYaUhoUaVhe6qDokW8eojqzntCEv6tuhGo69+G4PlvKQ6cp5fqXdj7zSXlQc/4DfCLUZRmUedbsdXjoP/MCjF01GxPw0B8QawPx0Jk32qBm4ObNmxsfv6y4QcnSgxMAajVD6evHoxHqOI23oZpBGWXI2DIJoBuqOgZFVGfWCn/6u8qeUHEYf5lH/kmkmc8T18dk7jMd+fe7YQ6pqhHKgTNjdqhdL4BTgkGZd82OMmSoIQDUT/tkPqEpoDEDD515ow1qBl5//fWNj1ODUtUjP+pV9tr5q2hVvn472oM1TuNtHHaayo6f5dphSq8tviiFJ1GdeRmUqs5/HuPvLRwK2QzKNPOZ9k9nOvLvWHD9AKOZuCNvUUxcH9N5kDvlCyi3jiTvmk0hhIRdnlgcKsULk4fj/DUkQLSOStz4WXUWgTaoGTg+Po79mcq3BdqOi8t7DdTN/B8PlXNIB44LwwiNwiSNk+h11MohjkLfN0sObRF9SHkS1ZmbQaloDiUvh2LuE5xJZlCmmc82w6UeFJU7vfBK+Qpfq/jx512zKWPXx8wL2GoIFL5+fOlQcIhQi0x7Y9VZBNqgZuDo6Cj2Zyof+bNW+AOLtkGqjt+Z4WCvAbNmJGqcRF/hCPVw4VAcMBalDccugkANgzKqM9WNZQ4cdix4AcHpVC6DMg28Ul4A+XpRp5nPNELNEqE8VNig4lVDEL5W8WlfeddsCq/5H30tlXBcH64X8Jn/AsfPqrMItEHNwLYItUo5pFHsEVtBAqC4QxEpyMjrBYd9SOfKGJRRBouWYWYt+7XblH6nCT8gOJ2qkfaxHqGuGWEtRF5UzqFkuSWP0pf0cp9UEerlpR4sBqW6nY4GXE4owvGXUZjKGrnk6lAqqD+PE5pLrTrqNWPpnIpAR6grRmUj1IwVvoB6Ecoo0fHnj1BbShmUUfjor1Yv6qjO1KGoMTkU5UXoWBk6LsyagUstBoeiLWcv9jTzmRqBrDnUgHwORRqGPAzKbnmtY3lFqFmKUrvNOhqmoaT+NmNTAgAwDCOsoxLoUOkIdcW4ceNG7M8OOxZOJnP4ChqULNcuU/odCwEBTiZqG5RJGidRZg4hK6w9WAH1InRRnXmd0ABqts4MHYoGJ4dCrvGnmc+246JeM3Bpr5777/QkHX8aeERoO5YJy6yVsv7lXbMpywg9wxpoGIayrRNZr12niC7MZtVZBNqgZuDll1+O/Vm/Y4GQ1a17qkAIwXDMz6BQdUOhBmGSxkmoPH6Wa8cpqkXoojrbHD//KrbOs50Zu/6Spnykmc+0w4Fh5HcoOpYJq16TLkKfhoHjomEauNTK71AsDcoSHMq8azZlyCFCDdA6GvUCSjQIkPceCoro1qGsOotAG9QM3L17N/ZnqkYoTice/IBwMKjUilBSgoBgOJ4vDcIkjZNQ2aC2HZfDZiLnkX8cUZ1txpZZQCSHVJHxRxk6c+b537bqaDVq0jkUaeYzaw9eIDQoVW2dOFykPLE4FEB5vdjzrtkU6lDsN/M7FADtxa5ehHp5DwWHPUDk/seqswi0Qc3AM888E/szVTdUHj2IgdW15aotKKfTME2HOkRJGiehapV/6FCwGxSqpbxEdbYdtmu3AWDPMrHXMKXrcpGG8FIPtugUsLh+W7Lxp5nPPPQH1K2j4ZHyB5TXOjPvmk2hJzSsDoWqdzEMHBeWWUPHMplep9+xMBiJ2/9ZdRaBNqgZODk5if2ZahE6Co8exIDKDsX5DgdJGiehah/ak8kcAWHXv9Uw0bZMZcZPdfY5ORSAugaV7bhLh5iFfle+CF2a+czjhAZQtxc/j6JkAKXdlpt3zabwcqhUPaGgNSQ8TihOpx7mfsDpnZ2HVWcRaIOagVarFfszWXMIt7HqwckWoaIbsqoOBd1QkjROotUw0bFM6SJ021jqz8mgUMWgpDo/ncxBCHtBDrAYv2QpD9vwA4KTyZypZRxFxl7saeYzjz78gLqXe/EyqMvKoc67ZlN4pHwB4fjPBBqUouClP51DotJ+WHUWgTaoBXHQVqttGIVHyyAAaNZN7DfryjoUXDaUbjk5hCzwHP+hQgY1ZVnh3uVhUKo3/pOxC0LYelBTDhV0KDw/wMmYPYccUFN/YGFQctL/bObB9VQ0KPnMf0DBoNKYl0OhZh0VC8IMasMwftwwjDuGYUwNwzg2DOP7E577XxiG8QXDMD4xDOPMMIw/MgzjR0S9N15Mp9PYn1GDUrUPE4+WQRQVc8jWDcokjbfR7zQVdCj4tEwC1NKf6syjBzHlsCNfDvE2eDpUvXY5Ecokts3n4TjsysDLoRzNPMw8n/m1imLuB3g6mS9rSFgoqxc1y5oNgPnabYpqdSQUXikvyzoqQWsAq84iEGJQG4bxFwD8DICfAvBnAHwZwG8bhvF8zK/8xwB+H8APL57/WwB+PckIl4GDg4PEn4c5hOpNpr2GiT3GggRAzQjNukGxTeMk+u2GdDmk2+BxSxpFJf2pzlwNSoXGT+Gp/2HXguP6mM7lMSi3zWfe+kdfUwWo8cvFoGyX04udZc12vQBnU49bUSqglv4Anz78gPg6KhadRSEqQv03AfxLQsjPE0K+Rgj5CQAPAfyVTU8mhPz3hJD/hRDyVULIbULI3wNwDOA/F/T+uPDo0aPEn6tkUFB49CCmqHjkPxi56FgmWo3QodimcRL9TlO6CN02eNySRgmLctRwKKjONEWBVw7lZO5j4spjUG6Da8qThAbFtvnMO+Up+poqsBo/v5SHosfPsmafcGoZB6ip/8zzcTbzuEboRZ1QsOgsCu4GtWEYFoAjAF9Y+9EXAHxvhpfaBzDk9b5E8PzzcQH3kH5bvSrfAaeCDEBRh2J8vsJ/m8ZJHHbVyyEdOC66zTqadR4nFE1M54ESBiXVmTpAvKr8ASj1GVgVJVfToN42n3kVZQNq5pBydSi65Xz+Wdbs9S5PLMj4+d/GCU154mAD9BZ1ZKJOKFh0FoWICPUVACaAdffhEYBvS/MChmH8VQDPAfhXMT//S4ZhvGMYxjsPHz7EkydP8PDhQ9y/fx/D4RAffvghJpMJ3nvvPQRBgKtXrwIAjo+PAQBXr15FEAR47733MJlM8OGHH2I4HOL+/fugr/fxxx9jNBrh1q1b8DwP169fP/cax8fHeP/993Hjxg3MZjN88MEHOD09xd27d/H48WM8fvwYTcwxOJvigw8+wGw2W16VGX0NALh+/To8z8OtW7cwGo3w8ccflzYm23HRCGaxY7p79y5OT09Tjelgr44nZzOcnZ2VOiYAiTpFx/TJ2RQtwz+ncV6deu0GpvMAY9crdUxZPnvffDTE5ZbJRSfDdQAAt7/5rVLHlOaz96UvfQkA8LU797DfrOPdP7nGrNPwW98EAHz12nulI7pBMQAAIABJREFUjCnPfProfrhsP753h1mnsf04/J2bXy91TFGdbt26lTimR0/Dz2wjmDHr1DI8AMA3vjWQft2jY4oa1Kw6LR2K0azQMb377ru559MHdx8u9WfVyRufwgDwcCjvurc+pi+9E74/x37MrNPX3ruJy3t1fPTgsZAxXb16tbT5FAshhOt/AJ4FQAB8/9rjnwNwK8Xv/3kAYwA/kubvHR0dEVn5qd96j3zn//BbJAiCst9Kar73H/we+Rv/5o+5vNbP/b+3yQtvvU3OpnMur1cEP/xPv0h+7Bf/iMtr/dpX75IX3nqb3B04XF6vCP7iL3yF/MjPfonLa33h5rfIC2+9Ta5/c8jl9YrgJ/71VfIDP/37XF7r398ZkBfeepv8wa1HXF6vCD73G++S7/7cv+XyWrcfn5EX3nqb/PrVe1xerwj+8e9+nbzw1tvE9Xzm1xqMZuSFt94m/+IPP+Lwzorhl758h7zw1tvk8emU+bU8PyCf+Vtvk3/4O7c4vLNi+I1r98kLb71Nvv6tUy6v98bf+x3yt3/9T7i8VhH84fufkBfeept85cMnXF7vP/nf/oD8+C8fc3ktmQDwDtlgj4qIUD8B4ONiNPrTuBi1PodhGH8eYVT6RwkhvyngvXGFei1xHHYsuH6A0cwr6B2xw6sHJaBm26CwIGN13LtN4yRUPPLj1TILUKvKfRlVHgv4/CuU8sGrwwGwOjaXSf9t83nouLi810DDZN8aD/YaqBmK6b9MeWK/2MesGeiVkPbIsmbzrCGhrzN05lxeqwh43ZRMEZn2yaKzKLgb1IQQF2FB4Q+t/eiHEHb72IhhGP8lgF8G8GOEkP+D9/sSwdHRUeLPVbstb+L6mMx9LvlTgFoGFcUeu+hHbonbpnES/ZJyCFnYVYeK6jwYuVxa5gGRKneFClN5FiVfajVg1gyp9N82n3lduw0AtZIMShaG49ChqHNwKICFQVnw+seyZg8cF4bBp4YCoLdlqlGYDazWap7jF2X/sOgsClFdPv4RgB8zDOO/MwzjuwzD+BmEqSA/BwCGYXzeMIzP0ycbhvFfAfgVAH8LwBcNw/i2xX99Qe+PC1sj1Irdlrj0TjkbVKq0jhu7HqbzgFuEelmUpohBRQjhGqFUKUJPdebpUFzaq8OsGUqMnzLgdKkFQA3KhlTr37b5zFN/oLzbAvPCc/4DC4Oy4PGzrNm2M8PBXugI8kC1wnx74VAccHUodISaCULIrwH46wD+DoBrAL4PwJ8lhHxj8ZTnF/9R/jKAOoB/grC9Hv3v/xLx/nixzUOiG5NMEZokbM7eqWoROvo+oxsKixesWh9ax/XhegGXSx0A4FKrjoZpSGVQxXF0dARCSGhQcTqhMYwwQqmK/kBoUERPaFgJDQp5HOpt85m3Qa1aL3JePYgp/RI+/yxrtu243NY/YNE6VSH9B4tLXXg6FMOxiyAgXF4vyi5FqEEI+eeEkM8QQpqEkCNCyBcjP/tBQsgPrn1vbPjvBze9tizQStA4ZMwhTGLZMopXykdJN2XlZVPLqG0aJ7HfVMegBPjnDy4NSgUcquvXr4cOhR9wjdCp1It96VBwilAD8kXots1nnjUEgHrXr3OP0JdwuRnLmi1C/+F4LsSgFIGIExo/IDib8q8jY9FZFMIM6l3g1VdfTfy5ahFKnk39AaBjmbDMmjIGJd34ohGKbRonYRjGoihFjfHz7MFK6StiULz66qtce1BTZDMokxjNPMx9wl9/icafNJ8JIRiOeUco5Rr/NmyORbkANSjFRCjjYFmzRZxQ+AHB6VSNwkTb4VdDAkTTXvmfUrHoLAptUDNw+/btxJ93LBNWvabMgsqzqT+wMihViFACq1znqEGxTeNt9DtNdRyKxaLHPYdUgfHfvn2be4U7UE6ELi+85z99LZnGnzSfT6f8HQpqUPoKRCgJIVyLUoFQ/4AATyfFGZQsazbvExoVT6m5OhQCGzOw7s0i0AY1A88991zizw3DUOrId+C4qNcMXGrVub2mbBtqEkuDImJQbdN4G/1OQ6oc0iRoDnmVDao4nnvuOe4nNIBat6UOhBjUTZxM5tIYlEnzWYRD0etYIGR1pbXMnE48eAHhPv+BYg3KvGt2EBAMx3PuNQSAWqfUvGpIgEgdlYDxs+7NItAGNQNPnjzZ+hxVDAogzKHtdSwYBp+CBECt67cHjouGaWC/uXIo0michEpFKTTXnfeR72Akv0Px5MkTrtduU/odC08nc3h+wO01RWELcKgOFwalLHUUSfNZVIQekGf8SQg5oSnBoMy7Zp9OQ8ePdw0BoIZBHToUnLu80DoqAeNn3ZtFoA1qBrrd7tbniGwbwxveLZMAKNXlYLiocI46FGk0TkK1EwrLrKHb5HdC0etYi6N0uQ3Kbre76nLD06BcFubKn0NpC3Co6L+lLHUESfNZhEGtUqcjavTzriEAijUo867ZompIADUM6qeTOQLCWf+2uBMK1r1ZBNqgZmA+375JytY2Kgl7YVDyRKUc6k2XOqTROIleWw2DEggjlL1Og+8JhSIRuvl8DttxYdVr6Fgmt9dV6XInMQalXDmkSfNZRA1Bb5E+oIL+q7ahakdo867ZIhxqlQzqpUPB8YRizzKx1zCFjJ91bxaBNqgZCILtRpJKV4/yzp8Cwg31bOZh5vlcX1cEtjO7sJik0TgJkUdevOFdkAOs8pFl31CCIFie0IhwKFS4Lc12XDTrNbQ5OhSyGRRJ83kVoeRZlCYuh5Q3m2pIWCnjcq+8a/amewhYaTVMdCxTiRMKEQ41fT0R8591bxaBNqgZaLfbW59z2LEwUsag5J/yQRfnExWOvDcYlGk0TkK2CF0SNuf8OSCyoUq+obTbbe4dDoCoQyX/538wEulQyKF/0nweOi72Gib2eJ5QLCLUKjjUy6JUjqeUzbqJbrNeqP5512wRNSRAuAbIfkIHiDmhARZ1VAL0Z92bRaANagZs2976HFV6Uc/9AE8nc/6LCc2hktygAmgPzvMV3mk0TmJZlCS5/gD/lklAxKCWfEOxbXtjyg8rZUTo8jIc8z+holcYy/L5T5rPIvRv1k3sF2xQ5kWEQwHQU9rixp93zRYWoVWk04+9cPpViVCz7s0i0AY1A88+++zW5xwqYlAL884VGf/cD3A69S5EqNNonEQZbaPywvvaYUAd/Z999lkhDkVPYFEOb+i1wzyx6jXst+rS6J80n0XoD6hz/bjI8Rf5+c+7Zg9GLtqWiVaDv0OhgkMtKkIt6vp51r1ZBNqgZuDOnTtbn6NKDqko71zkTUk8WV67vRahS6NxEqoYlDPPx9nME2BQhhF/2U8o7ty5I8SgaJg1XJLIoEzCdmbcU36ARetEScafNJ9FGZSqtE4dOC7XgjRK0Z2O8q7ZtjMTpH9T+pQ3INS/26yjWefvUIjY/1n3ZhFog5qBV155ZetzVDGoxBUkhA6FLEe+ccS1TEqjcRJhGz75I5Q0x523/nWzhoN2Q/rP/4svfSdGM0+MQdlVoxd5eELBtygVkCtClzSfRdSQAOq0zqyKQ5F3zbbHc0HzX427GITp37UwnQeYuHzryFj3ZhFog5qBa9eubX3O8shfcg91dakF3w318l4DhiG/Q0EN/vUj7zQaJ2HWDBzsNeR3KARUuFP6bfk3lC99NdSZZ8ssigoRyunch+P6QiKU4fjlKMpMms/24mIr3qigP0BrSMQ5FIQUc1tm3jVbVIS61w4NyrHrcX9tnoj6/IvqdMS6N4tAG9QMvPnmm1ufc7DXQM2Qvw/vqgcnv2tXgdCg7ClQlBHXgzONxttQIYdSRA9Wigq9yJ/97MsAxDgUKlxuJOJSD4pMEeq4+Tyd+xi7vtAIbVEGZV5E5lDPvABjzhHKOPKu2WEffoEGpeRroKgTGlG9+HnszbzRBjUDx8fHW59TU8WgHIneUOUef1zKSxqNt3EoKIeMJ8trh3c0QvdH124CgJCUB5lyiOMYCLh2nNLvNKUxKOPms4hb8ij9jgXXDzCayRuhnLg+JnOfe5cXoPi0xzxrNiFEyE3BgFppnyLm/6qOiu/4eezNvNEGNQNHR0epnqdChG44dnF5r4GGyf8joYJBNXBcGEZ4ohAlrcZJqDD+YYxDwYPDrvwG5eGzLwAQZFB2w7ZhMhiUcdgxJzQ8OOxYmPsEZxIYlHHzWeTnf9U6U460l02IdKiL7kWeZ82ezH3MvEBMDUFX/tahYh0KMXVUPPZm3miDmoGrV6+mep4KR/6iJhMgrm0OT4ZO6FDU1xyKtBonEUbo5N1MgdCgMoxV32Ce9NrhxQYyG5R/cusjAIIcio4FLyA4nZZvUMYhqm0msEojkqGOIG4+DwQ7lOHfkPeUihr7ok4ow79RjP551mzRNSSA3JdbjV0frhcIS/kD+EfoeezNvNEGNQNvvPFGqucdduQvyhKVPwaEHrrsBnXccVdajZPodxoYjl0EgbwG5cBxcbDXgFnjd0sepd+x4AcEpxN5Dcq93qdQ23BCwQNROYQ8WaZ8CCpKA+TodBM3n0X14AUU0Z9GqAWmfBSlf541W2gNSVd+/UV1+QKAS6066jWDu/489mbeaIOagVu3bqV6ngpH/qLyp4BwQ5XfoNzcgzetxkn0O83QoJzKG6UWqr8CEboP7z9Gr22hJsKhWG6o8o7fdlyYNQOXBTgUMl0/HzefVxFKETn04WvK4FDEsTKoxLRNDP9GMZ//PGu2SINyv1lHw+RvUPJEZA2BYRjhKT3n+c9jb+aNNqgZePHFF1M9jxqUvsQGpT0WmPLRsRAQ4OlEPYMyrcZJyBShiyOs8Oa/mQJqXG7kmy2hDiUAqdN+wlsSG2IcComKsuLm83AcOhSX9urc/yZ1qGRIeYlDpEHZbdZhmbXC1r88a7Yt2KAs+vr1rIg8oQHEnNLz2Jt5ow1qBh48eJDqeb2OBUKAE0nTPgghGAqMUKpw/bbtzDeOP63GSRSdQ5gHkRHqvgJH3t8ajsSlPBUcoctDEfNfhrS3uPlsL65dNwz+DkXHMmHVa1J//m3HRb1m4FKLv0NRtEGZZ81eOhQCUl4ASN/pizr7ItcA3p9/Hnszb7RBzUC/30/3PGpQSbChbOJ04sELiPgNVdIFJQgIhuPNBkVajZNQw6EQm0NP/4asnM3FRKcAhfQXkD8NAG3LRFMSgzJuPg9G4k7oDMNAX3qDKpz/IhwKoNjC/Dxr9sBx0TAN7Df5OxTA4rZEiR1q0RFqEfrz2Jt5ow1qBsbjcarnLXPoJMgh3MRA8GSSPUJ3Op3DD8jG/MG0GiehikMhyqBQIeVFZIS2bdXRatSkyCGOY+DMhBSkAaFBedixpFj/4uazyBMaQP46GpFdnoBie7HnWbNtZybshAJY9WKXlYHjwjJr6IpyKDoWBiO++z+PvZk32qBmoFZL988nu0ElsmUWsHIoZM0hTSrISKtxErLr/3QyR0DE6d9qmGhbprTj9wOC05kv2KBoSpHyEIdwg1KSCF3cfLbHrrDjfoBGKHdY/wIdijxrdlzKHy8OJXeo7FGovziHwsLp1MPcD7i9Jo+9mTfyvSOFaDTSVcTLfuQrssIdWF1nLsOGugma27cp5SGtxkm0GiY6EhuUcdeu86TXlrcohzoUolJeALkjlH5AcDKZC+nwQOm1Ldjj8h3quPlsO66QloEUmfUHwjWwKp//PGu2LfCEBgg//7wNSp4Mx2L1p8EKnmmvPPZm3miDmoHRaJTqedSglNWgWPXgFPMBbdZNdJt1eR2KhAh1Wo23IfPlPkv9BRoUMt+WKDp/EJBb/5OxC0KAflvcBhVG6Mp3qDfNZ88PcDIWG6HsSX65leiUj37HwtnUg+uJNyjzrNkiawgA+Tu9iNa/J+CUltfezBNtUDNw5cqVVM9r1k3sS2xQ0qNoURFqAFK3DUpqGZVW420UmUOYFZEtsygyR+hoKpLIz7/MR76rDgci539TihzyTfP5ZNHOU2SE8rBjYTTzMPN8YX8jL3M/wNOJWIeiyML8PGu2XUAOOSBHp5tNFJHyA/DtRc9rb+aJNqgZuHfvXurnyhyhskcu9hom9ixT2N/oK2pQZtE4ib4kEbpNLHuwCjQo5DaoxUeoZR6/yEsdKIddC47rYzov16DcNJ8LcSiXEcry017WGY4L0J+mPRbgVGVds+d+gNOpJzTlSabLjTZBc6hFsayj4uhQ8NqbeaINagZeeuml1M+VeUMV7Z0C8o+/bZloNS46FFk0TqLfaUq5mQIrg1LokafER96DgiL0YwkMyk0MCxg//WyV3Tp003wWee06ZdXpRj6nmq5LonOogWL0z7pmLz//ggMKgJx1VK4X4GzmFROh5jh+XnszT7RBzcDNmzdTP1fmI9+BNqhjx59F4yT6nYaUmykQ6t+JcSh40e9amMx9TFz5DEoaNRJVQwDIvaEW5VAA5bcO3TSfRV/qAawcChnXQNFtU6OvXcTnP+uavfz8Cy5KBeTUX3SXLwA4WNRn8Jz/vPZmnmiDmoHXX3899XNlNijjLjXhCXUoCJHv+vWkgowsGifR7zQxnQcYux6X1+PJ0BHbMgyQO0Jnj13sN+to1sWmPAFyFiUVVZQa/VtlsWk+2wUYFLKMfxOra7eLSHkQP/+zrtlFndAYhpz6r7p8iRt/w6zh8l6D6/h57c080QY1A8fHx6mf25fZoBR4Sxil37Ew8wKMZYxQOrPYxTSLxkkUmUOYlfCEQtxmCmD5+jJuKLbjolMXOy9lvtzGdlzst+qw6uK2A1kidJvm8/KEQmiEUu7PPyA6QlmcQZl1zS6ibahZM3DA2aDkRRH6A4ugGseUH157M0+0Qc3A0dFR6uf2OxZcP8BoJl+EsogcahFtc3gxdOax+YNZNE5C5uvnRVe4A2HKC/1bsmE7Lr6tvy/0b8h8W2gh+kuS8rBpPtvODJdadTRMcdvh5b0GapJGKOl7OhDYNtGsGYte5OLHn3XNLsqglLUxQREnNMBi/BwDSrz2Zp5og5qBrBFqQL4q74nrYzL3hRakAHJH6AbOLNag4OUF9yQev+gerIDcEbrByIXpTYT+DVlyiDdhC77UAwgNSrNmlK7/pvk8cFwcCmwZCCwilG05Ox3ZjovLew2hDgUA9NrFRGjzRqgP9sReFBK2TpXQoR6Jz6Gnr89Tfx2hrhhZPCR6nCTbhLILaJkEyJtDOnY9TOdBbMoDLy942YdUMoOKEBJGKAXnUMty5L+J4djFZ5/9lNC/cakVGpQynlCIvtQBAGo1A712o3SDctN8LqKGBJC3F38R+gNhjnYRDmXWNXvouDhoN1AX7FCE+ssVUAPCNdkwwrQckfBO+dAR6opx48aN1M+VtcqbGnji86dCg7XsDXWdbQUZWTROoi9pUdLY9THzAuH6X2rVUa8Z0ulPCMHAcRFMngr9OzV65C3Z+IHkGgKeyNCLfdN8HgjuwUuRtRe/6B7ElKIK87Ou2UWkPALhKZ2M+g8WJ5RmzRD6d6hDyauOjNfezBNtUDPw8ssvp36utAblYoMTHaHsLXNo5YrQ04hh3JF3Fo2T2G/W0TAN6W7KKip/0DAM9CSM0DmuD9cL8Nlvf0b43zrsWNKlfBBCMHTmwotSgTCoUHaEbtN8th1XaMs0iqytU4dj8Sk/QBhUKOKEJuuanZTyx5N+p4Hh2EUQyNWYYDh20ROYP0/pdyx4AcHphE8dGa+9mSfaoGbg7t27qZ+7uilLrgW1iJZZANBt1mGZNQkdimSDMovGSRjGIkIpmUFVRA9WiozXr1M9yPRM+N/qdeSr8h/NPLh+sCwaFclht/wc0vX5TAgJUz4EBxQAeYvSikr56LctDMdz4QZl1jW7iBoSIIxQ+wHB6VSutI+wy5d4h3rVi5zPGsBrb+aJNqgZeOaZ9FGtjmXCqtekW1CL6EEKhAaljDmE9paUjywab0PGI98ibgmjyNiLnZ4YfOZPXRH+tw47TYlPKIrZUMvWf30+n808zH1SUA6xhZOxC1+iCGV4QlFcyocfEDydiDUos67ZtjMXfkILROpoZFsDC9Qf4NfpiufezAttUDNwcnKS+rmGYaAvYZW37bio1wxc2qsL/1sybKjrbLslLYvG2zjslp9Dus6yB2uFciizQPWo+1Phf0vG8RerfxMnk3mpBuX6fC6qhoT+jYBAuEGZhdOJBy8ghYx/VZgvdg5kWbODgBRalApIalAX4lAs0l45ndLy3Jt5oQ1qBlqtVqbny7ih0pZZhiG2IAGQM0Jrj100TAP7zc0ORVaNk+h3mhiO5dlMgZVBWaWipCzQxf2Zy23hf6vfsXAynsPzA+F/Ky1F3BJH6bcbIAQ4KTFKvz6f6XpUSA6xhL3Ii+pBHP0bovOos6zZp9PQwSvqhAaQq45q6VAUkPLS43wXAc+9mRfaoC6QMEIpz2QCFrfkFTCZADkNKnvkLq6FLcChaDcwKODq3SwMnNCh6MY4FDzpdyw8ncwxl8igLOJSC8rKoJDHqdpWQ8CTfle+XuR2wSc0gFy9yIt0qGmeskzjX33+i5v/Mn3+n07mCEgx+svamIEn2qBmYDrNdkwso0FZVP4cIOf4B1vGn1XjJPqdJk6nnlQGJdW/CIfisKAIVRbssQurXkPNF/+eZLwts6guL4Aclzutz+dCI/QS6r9qGyo+QntYUOvQLGv2Sv/iItQy7YFFXLtO2bNM7DVMbnVUPPdmXmiDmoGDg4NMz5exD21R+VNAuKCcTT24njwG5bYevFk1TkLGTi9hQYr4zQSQ8/p5exSe0PR6PeF/61DKCKWLZr2GtmUK/1sy9OJfn89FRuhljNAtuzwVGqEVe0qXZc0usoag1TDRtky51r+CunxReAbVeO7NvNAGNQOPHj3K9PzDjoXRzMPM8wW9o+wU1TIJkDNCMxzPEzfTrBonsazylmj8Zegv24bS71hcdY5Dxst97IX+hZxQSDD+dZ1tZ4ZWo4a2JT7laZlDKpNDNS4uQt2sm+g267AF9yLPMpeLPKGhf0e2+Q8UO35eDmURa3ZWtEHNwPPPP5/p+asIpRw5lHM/wNPJvDDvVMYI3WCU3NQ/q8ZJLCN0Eo2fFqUWAd20ZdpQBotr13nqHEe/XUyELgtF6i9DhHpd59ChLOaEhhqUUkWoRy72Gib2CjihAGgvdrGf/yxzuWiDUrZe/MsaggJPqXnN/yLW7Kxog5qB999/P9PzVzmEcmyoJ4viqCInEyBPhHruBzideokpD1k1TqKotlFZsHc8Qk1bZvHUOY5VyoscDjWwvYaAJ1a9hv1WvVT913UusoYEWFy/LMn6BxTXg5hSxPXbWeay7bhoWyZajWIcCtnuYqDOTZFBNV7zv4g1OyvaoGbgtddey/R8GSI0Uco47gHkMShXBSnx+YNZNU5CNoPS9QKcTb3C9KedNGQ6oaBdXnjqHEfDrOFSqy5ZhLqYa5cpZbfOXNe5yAg9IN+Rf5EOFVDM9etZ5nLRDoVst2UOHBedgh0KXuMvYs3OijaoGTg+Ps70fBlyCKMMCmyZFP07tiSt41Y9WOMj1Fk1TuJgrwHDkEf/YYE9aIHQoLy815AmQjfzfJzNPBx2LK46J3HYFR+hy8LQmRdWlAqUH6Fb17nIGgJgceQvkUNZ1KUmlCL0zzKXS9FfIod6WGBTAiB0KCZzHxOXvY6sqDU7C9qgZuDo6CjT8/uS5ZAWHaE+aFtSGZRpbknLqnES9YVBKcv4BwXeEkeRKYeQ1jL0uxZXnZPoteXRf+b5GM28QnrwUsrWf13nnY9Qjoo1KOkJBSHibsvMMpdtZ1bwCUUT03mAsesV9jeTGBTY5Qngm/Za1JqdBW1QM5DVQ7q810BNIoOyyB6sAGDWjLB1oCQRyjQ9OHl7wTId+RYdoaZ/S5aizOilHkVFO/qdpjT6rxzqYiPUZaa8RHWezn2MXb/4lIexWIMyC8XnUFuYeQHGHCKUcWSZy+EJTbH6A/LYAEXW0ACROioOdSQ6Ql0xsnpIZs3AQVueCN3y2t2CChLCvyVPhC5ND07eXrBMR35F9mClyBShi+pfVLSjiBzStJRxQkH1L8ugjOpc9Akd/VuuF8ARaFCmZeL6mMz9wnPIAbEGZZa5PCi4hkC2Xvy24xa6/68K83WEWrPG9evXM/+ObBG6y3sNNMziPgaHnaY0OYQrgyr+yDuPxkmEOYRydHmguexlROhkgC7qh12Lu85x9LthlwcZIpT0hKKoLj9AqP/cJxjNyjnyjupclkENyNE6c9WDuloR2rRzeex6mM6Dwk9oADkK8wkhYYS6yBxqjo0Zilqzs6ANagZeffXVzL/Tl8qgKPa4D5Ar5cF2XBy0G6gnOBR5NE6i7C4HUWzHhWGEue1FQYuSZDAooykPvHWOo98ODcrTafk5lEXfkgaUX0cS1bmME5qVQVX+KVWaGhLeFBGhTTuXVyc0xdYQAHI4VGPXx8wLCg6o8Jv/Ra3ZWdAGNQO3b9/O/DsyHfkW3YMVWEXoZCBN/mAejZOgfWiDQAKDcuziYK8Bsyb+ljxKv2PBCwhOJ+UblEPHRc0Iaxt46xzHKoew/DlADYoyIpRlOZVRnYuuIYn+LRnWwOgJTVEUoX/auTxM0eWJN8vL3STQv4wTmkt7ddRrBhcbqKg1OwvaoGbgueeey/w7suWQFm5Qty0Mx3MpDMqBM1veXhdHHo2T6Hea8AOC02n5aR+l6C9RhG7guDhoWzBrBned4+hLdLmP7bgwawYu7xUXoeuVHKGL6jwowaCgEToZ0t7KOaEQf1to2rlchv77zToapiHF/F+Ov0D9DcPgZgMVtWZnQRvUDDx58iTz7xwuIpS+FAZlsRW+QLh4+QHB00n5BmWaCu88GichU5V32DKruOgMIFeELupQ8NY5Dpn0t8cueu0GagWeUCzHX5L+UZ1tZwazZuBSqziHoi/RXQSrLjfFrQHdZh2WWRN6W2jauWyXcEJjGItOVxK6iH5cAAAgAElEQVQ4VMsTmgJPKIDQgOfhUBS1ZmdBG9QMdLvdzL/T71ggBKUblIQQDAu+JQyQ6/rtQYqCjDwaJyFTlXd4S1xxxgQgV4QuWkPAW+c4VkU55Ufo6S2RRVL2baFRnWmHgyIdio5lLgzK8j//tuOiXjNwaa9e2N8MI5QNoZ//tHN5GaEvIagky/4HFOtQAPzqqIpas7OgDWoG5vPsRnERR15pOJ168AJSymQCyo9QBgFJdUtYHo2TKDuHNEo4/oIj1BJF6IaRExreOsexui21/BOaMlJ+2paJZr08gzKqc9E9eIHQoJSlMJteu24YxTkUgPhe7Gnnsj120TANXGoV51AA4RpQ9v4HrGyQUuqoOOhf1JqdBW1QMxAEQebfWeaQlhyhK6MgAVhF6Moe/+l0Dj8gWyN0eTROouwIHSV0KObFO1RteRwKO3JCw1vnONpWHa1GrXSHGlj04C34uJcalGXN/6jOZZzQAPJ0Ohr8/+y9e6wk2X0e9p2u7urn3LldvSKJ9Wona6yoVRhyV3uVQJKtmBFIGBCgwICQxA/YcGJZsQUpsQ07EytWIiCKokSOLFmPMFIExbSjWI5kCMroRVEi9aJscu9oh8MdDnf2MZzd2eHMTnffubef9Tr5o/p099zbVV1V51l1+wMGi71zu6rPfHVOfb/32FWaP8sge1pm2r3MIjSqDYpuyxz+axZBp67YoBDEv6ozOwt2gpoDrVYr82dMEVS6rNOeIR7KZf7gFkGRh+MkmML/o2lkUKjmv2lbaNYs7V0uWISCGRSieU5Cr103wqAYTtROiWNgnW50YJ3nqIZEbYQGiM4cI/jXEKEAVq0zZSHtXtbRNhZYCMqRfoOa8a/DoHg09eAFfIJY5ZmdFjtBzYHBYJD5M8s+jJpDPjqmpK3fT7eHLu3Y5TwcJ6FRs9CyLe2CWkeFO4MJHrqjqYeQrj2PgnlOQpRDqnf9AUt50uCh1JlDus6zjpQXwBwP5WDsKi9IA+Tzn3YvD8ZzTedfHcczn1tQ8iJ6/vUYlAB/2qfKMzstdoKaA08++WTmz7AQo+4q31UPTrUHSr1qoVOvas8hTVuQkYfjbTBBUOriHzDDQ3c65UkGz3Fw2nXtHvqjiQtKNfHftrUZ1IxnPwjxaKrRQ2+AoNbR5QmI1n8y8+H6cgRl2r2sLUJjSC9qnfwD4J4YrPLMToudoObAm2++mfkzTFDqFhQrQaneQpVd5Z0GaSu883C8DbJzCNNAV4QCMMNDd1pQy+A5Dibwv1x/R8f+19c2jPF8NPW0GhQncx9zP1B+bwZvYVCo7vICyC9MT7uX+6O5HkEpcPw2D9ZrSFRC1CwClWd2WuwENQeee+65XJ8zwUM5GLlo1iw0bUv5vR0DckgHKT3UeTlOggkeqrQ55DJgwrTQ0zUEMniOgxH7X1PLLHbPsRtg5qkXlIxnXUXZwJqHUmOU7mgS3VvX/gfkCco0e9kLQhzPfC0pD8s0MwMaE+j0UPPyr/LMToudoObAyy+/nOtzOotyGHTlDwKmCCoXLdtCo5ZsUOTlOAkmTMtkglKXh0r3+k9HaGTwHAenbWOiSVAy6JiSx8BEjI4zkPGsY+w6w6rTjb4onU6DQnYv/jR7eTV2Xn2XFxNmMbh+iJOZry3lCeDnX+WZnRY7Qc2BF198MdfnehrbRjEMUvRglgVTPLRp1p+X4yREIX/dKS8e2ikMChlwOjamXoCpq09QsueP1TTI4DkOJnR66WuMUOhsHcp4XtYQaFy/Tg91X1OXJ0B+L/40e3mwrCHR56HW6VTTWUPTFZTyovLMToudoObA4eFhrs+Z4aHUK6j7YxeU6hu/nrZlUl6Ok+C065h5ISauL/zaaTEYz7WICcAMD11/7KJTr6JejQwKGTzHwQRBrddDrW/9jOdllxsdfZg7+p9/rSkvy5QHOetPs5cHGmtI9puREa/TqaazhqZmVXCxyd/pSOWZnRbSBDUh5LsJIW8SQmaEkENCyLds+f0/t/i9GSHkDULI35L13UTh4OAg1+dYyoNWQTnSkz8FRJt47oeYaPZQpjlM8nKcBNk5hGnQ19QyCTDDQ3faoJTBcxxMmJY5GLu40KjCrqr3qej00DGemaDSU5S1aJ2qkf+hRkG937JBCDCYyNn/afayzghN1apgv6W3daZODzW7L+/5p/LMTgsppykh5D8D8OMAfgjA1wP4DIDfIIQ8HfP7zwD49cXvfT2A/xnATxBCvkPG9xOFq1ev5vqc07bhBiHGGgWlrgpfwBwPXZrDJC/HSZCdQ5gGg7ELp6U+fxAwx0O3zr8MnuOw4t+c9avE0qDQ4KFjPA/Gc+w1qqhZ6g2Ki81aJCgNSPnREaGwKgT7TXmdntLsZZ0RGkB/HUnatrGy4Ajo9KPyzE4LWafJ3wPwf1FKf5ZS+kVK6fcCuAfgb8f8/t8C8A6l9HsXv/+zAP4ZgL8v6fsJwQsvvJDrc7qrfKdugKkXaH+h6j1Q0rVMystxEhwDPJRDrR5q/R660xXuMniOw+r5N8dDrxIXmzVUNAlKxvNg4qGnoWUgEAlK3a0jB2MXF5s1LQYFIFdQptnLK0GtyamgWVCzdButdVScESqVZ3ZaCN9NhBAbwAGAT5z6q08A+OaYj33Tht//LQDfQAjR88SnwM2bN3N9TlQfxrxgBRm6rFPdHtqJ62Pmhak89Hk5TkJPs0FFKY2a+mvOodYtKNb5l8FzHPYaNVgVotVDrWuoAwBUFoJSh0HJeB6M59rEFGCGh1KXmAKi7jqyIhRp9vJg7GK/VUNVk0FhgkFFSJR+owMievGrPLPTQsbT9AQAC8D9Uz+/D+B9MZ95X8zvVxfXewyEkO8ihLxECHnp3r17ePjwIe7du4e7d+9iOBzi9ddfx3Q6xY0bNxCG4TI0wJLYr169ijAMcePGDUynU7z++usYDoe4e/cu2PVu376N0WiEmzdvwvd9XLt27bFrHB4e4plnnsH169cxn89x69YtHB8f486dO3jw4AEePHiAO3fu4Pj4GLdu3cJ8Psf169cBAA/eegMA8LnP3wAAXLt2Db7v4+bNmxiNRrh9+7bUNV39wqsAgON33zmzJgC51nT6Gklr8kZDAMAX33xbCU+n13TnfjSytBbMt67pmWeeSbWmLDztt6rRc/BoLGxNWXiauAHmfginbSt/9m7evIlWDbAWHkrVz97du3cxGAzwcDTHXr2yXNN4PFby7B0fH+Ptt9/CxYaFuw+Pha0pK0+D0RzVYK782WP/ddo2br/zrvJn76u/+qtx7do19EcuLH+q/Nlja9pvVvHWu0dKz731Nd0fjtCuUi3P3nQ6RR0uHp5MpTx7TzzxxNY1vXH3AZyWrfTZW19TOD1Gf+38U/nsTadTvP72few3a7j28p8of/YePHgAy59hOHbx6quv5l5Ts9lUqvfW1xQLSqnQPwCeBEABfMupn/8PAG7GfOZVAN9/6md/bnGd9yXd7+DggOrCa6+9lutzX344ppcuX6H/6nN3BH+jdPj0lx7QS5ev0M+92ddy/+OpSy9dvkJ/5vde13L/a28N6aXLV+gnXvnK1t/Ny3ESwjCkz37fr9Ef/o0vCr92GtzpR8/fL35Wz/NHKaXf8IO/TS//0jUt9x7NPHrp8hX6sU+vuJXBcxI++qOfpt/18c8pvSdDGIb0a77v1+kP/foNLfenlNL/9GOfof/J//4Z5fdlPP8H/9Nv0//m/9Xz/FFK6X/58ZfoR/63T2u7/5//J79Hv/Of6Xn+KKX0v/3lz9OD//ETUq6dZi//xf/jj+l3/PQfSbl/Gvyvv/lF+qf/4a/RMAy13P9v/4uX6Lf+409puTellP7s779OL12+Qo/Gbu5rqD6z1wHgJbpBj8rwUD8EEOCsN/o9OOuFZvhKzO/7APpCv51AOI6T73MdvSHv01PiVKNTr8K2KtpyiJcts1KsPy/HSSBkkUOpKeVDZ8ssBp3jtzetXwbPSdAZ8h/NfbhBqC3lA4gKU3WkvDmOA0pplEOuKeUJiN4BulM+tPLftjGceAhD8Z2u0uxlnTUEQFRHEoQUx1M9rVOjLl96agiAtToyjjxq1Wd2GggX1JRSF8AhgI+e+quPIurisQl/DOAjG37/JUqpvsqdLZhMJrk+17Yt2FZF24G6mhKmZ0MRQtBty6vy3oYsPUjzcrwNItoG5cVSUGoUFDpzCDcZVLJ4jkOvXdfPv8YXqi7+J5MJTuY+vIBq6UHN0FsUZckQlNtAKcVQY5cnINp7QUjxaCr+9Z5mL+usIQFWExq11VGN3eVQKx1YdfrKv37VZ3YayMrI/1EAf50Q8p2EkK8jhPw4olSQjwEAIeTjhJCPr/3+xwA8RQj5scXvfyeAvw7gH0v6fkJQqeT75yOEaPVQDcYurArBXrOq5f5A9DLXtf4sPTjzcrwNvY6+8fO6WyYBkZjXNS1zU4RGFs9x0L3/Ab3899o2jqYeAsWCslKpaB3qweC0bYQUOJIgKLfheObDD6n2CAXA56GMw7a9HIYUQ42TggH9nY6i9ev3UPMUpqo+s9NAyjeilP4igL8D4B8BeBnAnwXwbZTSLy9+5enFH/b7bwL4NgD/4eL3/zsA/xWl9JdlfD9RqNXyW3g6X6jDiYtuywYhRMv9Ab1tg/pjFzWLYK+x3aDg4TgJOj20q7Hb5zXlw1t8h9ULRRbPcei2bTyaevCDUOl9gbWWYZoFJaXAkWKjslarrcZOa/VQ6kv7MyHlS9T46U3YtpdPZj6CkGrrQQ3obR0bGRSeXoeKgPWrPrPTQJrEp5T+NKX036GU1imlB5TS31/7uw9TSj986vd/j1L64uL3n6GUfkzWdxOF0WiU+7M6Q/46pyQyaPXQjdIbFDwcJ6HXttGXNHp3G5hBcaGuM0IRCUpPi6BceKjXBJUsnuPQY4JSg4fSjAiFHg/daDRaeqiLLijyQncNzfq9ZbTO27aXWZqF3pQPffw/WkSGdLdNBPgiFKrP7DQwz2deIDzxxJmOfqmhO+SrczMBmnOIM4T7eDhOgtOu43jmaxOUTltvhIL9+x9JGj+chP7YhW1V0Lat5c9k8RwHnS9UnWOnGXT1In/iiSe0T8kDxOSQ5gWL0GgVVB154+e37WUTagh0DvcaaB47DgBN20KzZnEV5qs+s9NgJ6g58Pbbb+f+rNPWmUOqt8IdiNZ/MvPh+npC3mkPEx6Ok+BIfKFsw0DjlEQGrR66kXvGoJDFcxx0jt8ejF3UqxW01gwK1dDF/9tvv73y0Gs8A5mHTougMsBDLTPlY9teNiFC06hZaNnWuU35YffnWb/qMzsNdoKaA88++2zuz/baNk7mPuZ+IPAbpcNg4mqtcAfWPZS6BGW69fNwnASd0wKj9evNP9M5LXRTQZIsnuPA8pd1GFRsSp7WGoqOHg/ds88+i+HERaNWQcvWl/LEOizocKqsBKU+o7pRs9C2LSkG5ba9bEINCaDPqdY3oCiX3Z9n/6s+s9NgJ6g58Morr+T+7PKFOlYb8vaDEEcTT/tm6mkMefVH89TeCR6Ok7D00GnyUOr2UPc0Vrlvapkli+c46Hz+TUj5kumhTMIrr7yivQcvANSrFjr1qh7+Ry6aNQtNjREKgPXiFm9Qb9vLJnio2f117X9Ab4QGWBgUHA4F1Wd2GuwENQeef/753J/tafLQDRc5q7o3U1dTyNcLQhzP/NTeCR6OkyCzbdQ26B7qAOj10A3G7pn8WVk8x6Gr3aDSy79dreBCvap8/z///PMYjOdae/Ay6KqjyVJDIhNOu46BhBqKbXt5MHbRsi00anoNiq4m/pmI1VlDALDC/PzrV31mp8FOUHOAzXfPA0eTh9qU/CldHjp2mKQVlDwcJ0FXDqnrhziZ+dr5Z4e5Lg/d6fXL4jkONauCvUZVU1GafoMK0DMt8PDw0IgIDaBRUBtgUAGsdar453/bXjZl/br4749ctEtgUKg+s9NgJ6g5cHBwkPuzqxxCtS/UpaA2JIdatYcya4U3D8dJ2G8uJmUp9lCynHXd+YM1q4KLzZoeg2LunxGUsnhOgtO2pXjotmGgeUoegw5BcXBwgMHEEIPinAvqbsuWEqHZtpdNWb+uWQyD8Vx7UwIgev6nXoCpm6+OTMeZvQ07Qc0BHgtJVw6hCWOnAWC/ZYMQ9R7KrFPSZFnBVauC/ZZ6QWlK/iD7DroiFKeffx3eDkeShy4Jcz/AaINBoQM6+D88PNwYodABnR5KI/jvRPxTKnZaZnE81HUuQZkXfUMiNMvhNjnTHnce6pKBx0JiglK9oNbfMgkArArBfrOmXFBk7cEp0wqOPJS6PPT6XyhdDVXuywr3lgke6rryCMVw2YNY/wu121LP/wc+9ALGbmDE888MCtGCchuGE3MiFHM/xNQTKyiL4qFmnZbU11G5cFpm1BAA+etIdh7qkuH69eu5P2tViJbx08wjpLsgAdDjockqKHk43oZeW07IMwkmeahN4l8mz3HQEfLtG2JQA6scapWC8jOHn4/ubcL62zZcP8RYoYdy5gWYGGJQyJqWuG0v98fpuzzJhKOp01EUodFvUPO2TtVxZm/DTlBz4P3vfz/X53UIiuHYxV6jipqln/peu65eUIyYQZHOQuflOAk6DCpTerACekL+LCJwusuNTJ7j0F20jVIpKE2KUPTaNtwgxGjuK7tn931PATBj/avWqer2gFEGtaS0x6S9PHUDzLzQiPNPR2E6pXRj21AdWNZR5YzS6jizt0G/qiow7ty5w/V5p6VeUESbSb91CkSt03R4KC82a6imNCh4OU4CyyFUif7YBSFmRChYyodSQTmKvCGn1y+T5zj02ja8gOJEoaA0SVDrqCO5+eZdAGasX0enIxYRM0JQduTwn7SXmTfUCINCg6CeuAHmfmjE+b+cFpozQqHjzN6GnaDmwHvf+16uz+sKeZvwMgEWfUg1eCizHKa8HCfB0eKhnGO/WYNV0Tclj6HXtuGHFMcztYKSkKiGYR0yeY6DjuE+A4M8lD1JgioR9Q4AMwT1SlCpy6EdZGwbKhM9SYIyaS9n7fIkEzoEtUn7f69ZhVUhudev48zehp2g5sDR0RHX552O+qIckwR1r21jOPEQhio9lNnWz8txEpx2HUFIcTxVKyhN4V/HC6W/GOpy2qCQyXMcHA3jtwdjFxUCXGyaUJSkPof0bv8YgBmCgtdDlwemFKWvfwfR/Cft5b5BEZoo9ZIo3/+AGesnhK+OTMeZvQ07Qc2BRqPB9fnewkOpVFCOXe09qBmcth0Jypm6XrxZBSUvx0nQUeVtpqBWt/5hzJQ4mTzHge1D1Tm03ZaNiiERCkCtQTH2o4LwvYZ+g2I5LVRhpx8m3nWPXgeATl2OoEzay0MDBaXK/W9K21wGnsJsHWf2NuwEtUZ0WzZCChxN1QhKSmkkKAzZTI6GF2rfKEGp3kNnoqBW6aHrj8wyKAHF/BvSgxlYG7+ucP1HEx/dVs0Ig6JTr8K2Kso9lFaF4EKjquyecSCEKO/FbpKHFoi+h+r3H6B/sBuDrl7ssrAT1ByYzWZcn1/lEKo5UI5nPryAGhHuBNQLiqVBkWH9vBwnQVYOYRJMGbsM8Fd550GcQSGT5zj0dKR8ZHz+ZaJtW7CrFaUeuoejuTHrXwpKhQblcGJOhAJgdTRiHUpJe7k/dlGzCPYMMCgA9YJyaJiHmrXOzAMdZ/Y27AQ1B/b397k+vxKUajzUJlrngDoP5fHURxDSTOvn5TgJqg2KMKQYTjxjDKplDqlqg2LDy0Qmz3Fo2VU0ahXlHjoTWmYBkaBU3Tpx5Jlz/gHqBZUpUxIZehI81El7eTCKDApCTDEoFPO/MCgu1A0xKDg6nek4s7dhJ6g5cP/+fa7Pq84hZRvXhJZJwMpDp8pDuWyZlEFQ8HKcBNUpL8czD0FIjeG/aVto1ixlHrrIoNgsKGTynASnZSszqIHoDDChZRaDakHx8GRmRP4wg+ppqSalfAHRu0g0/0l72aQIDaB+uNNgHEVoTDIoHk09+EGY+bO6zuwk7AQ1B55++mmuz6sWVCa1zAHU96FdGhQZBAUvx0lo1Cy0bEvZ+k0a6sCgUlA9mnoI6Wb+ZfKchCjkqcagDhIMCl1QnUN64tFlMaAJUG1QmCaoZUQokvayaevvLgSll0NQ5oFpBvXKqZbdqaDrzE7CTlBz4NVXX+X6vOo+tCa1TAIiQdm2LWUpHyuDIr2HipfjbXDa6qq8TUv5AdR66JYGxYYIhWye46CyF/ujqQdKzeNf1fMfhBSPJp4xNQQAlOdQm+ahddo2Tma+UEGZtJdNE9TMuFUVpTUp5Qvgc6rpOrOTsBPUHPjgBz/I9fl61UKnXlUvKEx6oSj00OVpGcTL8TaozCFlhotJLxSVHrokg0I2z3FQyf/SoDZkUiqglv/hxAWFWRGaXtvGydzH3A+k38sPQhxNPOP2PyC2dWTSXu6P5kbxr7rTk0lF6cB668zsGkDXmZ2EnaDmwOHhIfc1lL5Qxi4atQqatqXkfmngtOsY5Aj35EGelkEiOE6CjBzCODAviEkv1F7bVh6h2LR+2TzHQWUf2qVBZVLIt21jpEhQmtSDmIHVMxwpOANZWN0kD6WMtMe4vewFIY5nvjE1JID6wvT+2LCUL5bykaOORNeZnYSdoObAwcEB9zVUCqpoM5ljnQKA06op9VA3a1Ymg0IEx0kwxUOrCyqf/6T1y+Y5Dr2OjbEbYObJF5Sm8g+oERQmTcljWHroFBiVeWpIZEOGoIzby0ODxq4zqBTUrh/iZOYbyn92DaDrzE7CTlBzQISFpNpDZ9LLBFh4qBWtf5hj/bKtYJVV3v2Ri7ZtoVEzKUJhY+oFmLoqBGV8DYEub4fKFypLLTPJQ6myF7uJBoVS/g0sSpbBf9xeXvFvjlNJJf9HLEJp0P5n4j5PhGLnoS4ZRFhIzmL8uAoMxq5R4S4gern3xy4olT9+vZ+jIEO2FdxVLCiN45+9UBTsgf7YRadeRb161qDQ5e1Q2emGGa77LZO6XKjLITW1yw2QL4c0K0wbOw3IiVDE7WX2/JvU5aW72IsqnGomPv81q4K9RjUX/zsPdclw7do17muwoiQVgnJgWP4UEL1Q5n6IqaKQd1bvlAiOk8BTlJEVA4OGujCo7HSTFKGQzXMcVtNS1bxQL8QYFLqg0kPHcqhNMiplFOXFwbQuTwAWQ1bE5lDH7eVlhMYgD3XVqmC/VVPiVDMxQgMAvU6+Tke6zuwk7AQ1Bz7wgQ9wX6PbtuH6IcZKPJQGpnywkI+iHMKsBVkiOE6CSg8da+pvElR66PoJERrZPMdBdcjfJO8koHZa6mDs4kKjipplzmtvfyEoVXroTcqhtSoE+02xdTRxe9lUQckzLTALTKwhAPLXEek6s5NgzslSQLz22mvc11DloZt5ASZuYORmAhQKiozrF8FxEpSuf2RWyyRgzUOnyEMT56GXzXMcVhEKBR5aw3oQA8B+s4YKUcN/f+ziQs2MCXEMVoWgq0hQDccu9gwzKADWi1xcl5O4vcyMtq5BKU+Aul7kJna5ASIDL8/7T9eZnQSzdlbB8NRTT3FfQ1UOqbHWqaKQ99QNMPWCzB46ERwnQZWgppSiP3bhGJQ/CKzCr8oiFDHPv2ye47DXqMGqECWdbvqj7BEa2agoFJSD8RxfdbEp/T5Z0W3VlHmoewb1IGeIpmWKe/7j9vJg7OJis4aqgQaFKv4JMStCAeTvxa/rzE6CWU9WwfDw4UPua/C0jckCU61TVVX+7MDOmkMsguMkqBLUUy/A3A+N81DvNasLQSnfoEjyUMvmOQ6RoKxhINBDFwcTU74AdR66wdhDpyq/ViUreoqmZRrNv8D1x+3lwcS8GiIgqqNQUZQ9GM+x34wMeJPgdKJe/FnryHSd2UnYCWoOdDod7muoyiE0scIXUNeHNm8PVhEcJyEKwRLpHjr2fJnGPyEkd8gvCyZuZFDE5VDL5jkJkaCQa1Azg8K0HGpAXS/ywXiOXqch/T5ZocpDORi7xnkngUXrVIHrj9vLUcqbeetnw51kNyYwscsXEL2T/JDieOZn+pzOMzsOO0HNAc/j9yqp8lCaWOENABfqagTlsgdrRkEhguMkMEEpu8rf1IIcQE0v7m3rl81zElQIqrEbwA1C4wwqYMG/ZA8dMygu1s175TkddYLaVP6HEw9hKEZQxu1lkz30fkhxPM0mKLPCVP7ztg7VeWbHwbzTpUAIw5D7Gp16FbZVkZ9DPTJTUBFClHjo8jb1F8HxNjg5c8iyYOmhN4x/QI2g3BahUcFzHJTwP8oXoVEBFfyfzH14AcXFhjktAxmcVjSLQJSg3ARKaVSUamiEIggpjmdiBFLcXu4bKqiZk0d2pyNjDYplHVW29es8s+OwE9QcaLVa3NdYCkrJKR/DiQurQrDXMKsoDWAhP7nWZl4PrQiOt0GFoDBxShqDCg/dthoCFTzHIepyoKiGwEBB1VsMtwokCkr27/uefX08x8Fp2wgp8Ggq7ww8nkUGhYn7X3Snm017eWlQGLh+5uSR3ekmEtRm1dAA63VU2Z5/nWd2HHaCmgODwUDIdVTkELL8uYphBQkA4LTF9iHdhP7YRbVCsNeoZvqcKI6ToFJQm+ihUtGHdVuXGxU8x8Fp13E09aQKShPHLjN02zYoXY1GlgHGf9WfSbtHXqw8lPLWn7eGRAVEpz1u2svHUx9BSM0U1ApmMYQhxXDiGdflCcjfmEHnmR2HnaDmwJNPPinkOnnbxmRBf2Rm/hQgvihlE4aLggxCshkUojhOgooc4v7YRc0iuFDPZlCogNO28WjqwQ/khfC21RCo4DkOvYWglOmhMjpCoaAXOYsAPvvV75N2j7xQUUdjtEEteP2b9rLJERoVrWOPZ97CoDDPoHZyRih0ntlx2AlqDrz55ptCruMsQp4yEVX4mmedAooMipwFGaI4TkJ3ISg9yYIkxOAAACAASURBVIIyGvNrXoSCveSGE3kh7/7YhW1V0IkxKFTwHAcVnW5MzqFX0YucrX88+Iq0e+TFqihLXpSuCAaVqOd/01422UOvYriTqV2+AKBlV9GoVTKnveo8s+OwE9QceO6554RcR0UOddSD0zzrFIjWfzLzJQvKfPlzojhOQk+Fh27sGRnuBNR46IYL/uMMChU8x0FFL/bB2IVdraBtG1iUp2L9i73173/o66TdIy96Sw+lPIPS1C5PgHj+N+3llUFh3juwUbPQsi2pdRQmd3kCFr3YM77/dJ7ZcdgJag68/PLLQq7jtG2czH3M/UDI9TbB1ApfYOU1k32g5PHOieI4CSwMJ1dQzY0MdwJrOYSSPXRJ/KvgOQ4qBCWL0JgYocgb8s2CwdhFvVrBl165Lu0eeaFiuJepk3KBSFC2bUtYhGLTXjY55QXIP347LUzt8sWQp45I55kdh52g5sCLL74o5DrLHEJJHgo/CHE0MddDqSLklbcHpyiOk6Aqh9LE/Dlg9ZKT9fwD21N+VPAcBxXP/9BogzpKRZNpULMakoODA2n3yIt61UKnXpXOf6NWQcs2r4YCWEzLExSh27SXlwaFgSkfQBSlkMr/xGxBnacxg84zOw47Qc2Bw8NDIdeRHfI9WrRjMnUzOZI91F4Q4tE0n0EhiuMkKBPULTNz6FV46LYJShU8x2G/JT9CY2oPXiASlBdkC8pFD2adPCeh265J59/EdAcGkZ1+NnE8HLto1iw0DUx5AuTXUZmf8mFnjlCYuJd3gpoDorwdsgVVETYTIM9Dxw6qPB5qFR4t2fx7QYjjmW+sh7rbku+h3SYodXou7WoFFxpVBREKM/c/IL8XeX8RoTHRQw1EaV+yI3RG8y9wuNcmjouwfplFuf2Ri7ZtoVErj0Fh4l7eCWoOXL16Vch1VjmEcjx0bKOaWOELyO9ywNPhQBTHSeguPMeyDtTlUBND8wdrVgV7EgWl64c4mfmJL1QVPCdBdqcb0wWF7BzSwXgOp1XTznMcZLfOzFtDogpOuy6sMH8Tx/2xa2wNCRB56GU//2bzb2PiBph56evITNzLO0HNgRdeeEHIdZR5qA09UKJ2bvI8lDweelEcJ6FqVbDfqkkL+ZncMomh15HXizxN/qAKnpMg0kN3GnM/wGjum82/bEE5ijzUunmOg+zhTnlrSFSh17Ezd3mIwyaOTTconY6NqRdg6sppTDCYeEbzn6cw2cS9vBPUHLh586aQ6+wvBKWsHDp2UJlakGFVCPab8nIIeVomieJ4G2ROC2T/rib2YGWQKSjS9OBVxXMcovXLKcpkxZ6me6hk8T/zAozdAL2OrZ3nOLD1UypnWqbpgrLbsjHzQkxcn/tamziOakjMXf+yjkqSU2UwnhvN/9KpmCFKYeJe3glqDjzzzDNCrmNVCLoSBRV7SM/rC5XHQy2K422Q2Yt86aE2NEIB6OdfFc9xkOmhXk6JM3n/d+QJyvUIhW6e4+C0bcz9EBMJHsqZF2DiBkYLqmUdjYAzcBPHphsUy9apkt4BLEJjKvIYFCbu5Z2g5sA777wj7FrdVk2ioJhjr1FFzTKXbqdtS88h38/R5UIkx0nQLSh1Q6aHPk0PXlU8x8Fp16UJyhX/5r5QnZYNNwgxmvN7KE+D7f9uy9bOcxxkpv2Z3IOaQeT6T3M8dQNMvcDYlEcAcBatI2W8Aymli6JcM7s8Afk6PZm4l81VWAWA4zjCrtWTWOUdFWSY+zIF5ArK4cTFxWYtl0EhkuMkiMwhPI3+2AUhwH7T4AO1Y2MoS1COtk+JU8VzHHptG15AcSJBUBbCoJLYi3+wFqHRzXMcZHY6GhaB/464lIfTHBciQiNxuNfUCzD3Q7MN6hwRChP38k5Qc2AymQi7ltO2peUQDyfuspOEqYg8dHJySLcN9UiCSI6T0G3JE5TDcWRQVA2OUPTaNvyQ4ngmQVBOvMigSMihVMVzHGROCy2CoGbpSDI8dOspH7p5joNM/otQlMzym0WkPJzmeFlDYHAOtdQIheFdvgBgr1GDVSGZ1m/iXjb3DVsAVCri/vnyTApKi77h+VNAtNmHExdhKMNDmT9/TiTHSXCYoJzK8VCaLKYAuS+UwXiObsuGVYkfu62K5zjI9FAOxi4qpkcoJHro1gWFbp7jIJf/7REa3Vh6qAWs/zTHSw+1wSkfe40qqhkFZVoUwaCuLOrIsnS6MnEvm/eNCoRaTdwLSqqgNLxlEhAZFEFIcTyTE/LNW5ApkuMkyPTQ9cfzQvAPyJmWOBhvj9Co4jkOearc06I/dtFt2agkGBS64Ugc7jMYu7AqBHuNmnae4yBzWigzKEwWVBfqVdQsIoT/0xwXoYaAECLNqcYzh0Elsk5LNHEv7wQ1B0ajkbBrOW0bIV2NCRcFSuly7K7JkOqhmeQ3KERynAR22MvoRV0ED/WyyltC2k9/tH3ssiqe4yDTQ79t7LoJYOeTrJSHbquGSoVo5zkOnXoVtlWRk0M9WRkUpoIQIizt8TTHRfDQAvKGO6VpG2oCuu1sjRlM3Ms7Qc2BJ554Qti1egJDXus4mfvwAmp0D05gvShJ7PoppVyCQiTHSVh66CR4KAdjz/iXiUwP3XCynX9VPMdhuX4JBlXf8Cl5ANC2LdjVinSDQjfPcYg8lHJ68Q8KEKEAIKx17GmOB2MX1QrBXqPKfW2ZkFVHZfpgN4ZeO9twLxP38k5Qc+Dtt98Wdi1WMCH6hTIoQLgPyDcpKQ2Opz78kOZev0iOkyAyh3AdYUhTCUrdYB5kWR6abS8TVTzHoWVbqEsSlEVI+SKESPXQsedfN89JcDIKirSIIjRm8w8sOh0JMKhPc8xS/ggx26CQ1emqP3ZRswgu1M03KLI4FEzcyztBzYFnn31W2LVkeej6BbFOZYW8+5wFOSI5ToKslJfjmYcgpEbnDwJA07bQqFWE5xBHBoW3NUKjiuc4LAWllAiF+QYVEDkV5AiK1ZQ43TwnQaZB0TW4BzGDKIPiNMc8XZ5UwpHGf1SUXQSD4mjiwQ/CVL9v4l7eCWoOvPLKK8KutSpKE+yhLkj+lCxBvd4yKw9EcpyERs1Cy7aEh/yK0DKLodeuC095eDRlBkXy+lXxnARHkIduHUFIccRRQ6ASvY68oizGvwk8x0GWhzKqITHboAaiM0rE+k9zXBSD0mnbeDT14KUUlGlRhJQ/YC3tc5KujsbEvbwT1Bx4/vnnhV2LpXyIFlTseib34AQiQdm2LfEe6mXLrHwvFJEcb4MMD92S/4IcqMJTnibpxq6r5DkO3ZaNQcqXSVo8mnoI6fnlPwgpjqbeMkJjAs9xkCaoCyIouy0bxzOfW1Ce5nhYgBoCYOX0OBJ8BgzGc6NbBjKsBHW6PWDiXt4Jag4cHh4KuxYTlKI91EsPZQE2lIy2QauWQflCniI53oZeR3zIr0geaqn8bzEoVfIch8hDJ9ZDXYQexAwyDMqjiQtKAWfRNtEEnuPgtG2czHy4vjgPpR+EOJp4hRCUojq9nOa4KCkfXUlRWlaUajqWaY8p095M3Ms7Qc2Bg4MDoddzJIQ8B+M5GrUKWrbZBQmAnBzClaDM56EWzXESpHhoC9IyCsjehzQN0vbgVclzHJx2XXgOOW+ERiV6bRujuY+5Hwi75qrDQbR+E3iOQ1YPXRqw8HkRBKWoOpJ1jr0gxKNpsVIeRM8iKIpBkbUw38S9vBPUHBBtIcmo8o42k/kvU4AJSrGHyXDsolmz0LStXJ9XaQWfd0HttLNNykqDQcoIjQnejl7HxtgNMPPECUreGgKVWHkoxYW8T0doTOA5Dlk9dGlQKP4FtU5d55itvwiCsidhWqgXhDiZ+cYXpQNr4+dTagAT9/JOUHNAtIUkqihjHcOCVHgDkUEh8mUK8OcPKvVQSwh5D8YuWraFRi2fQaESTtvGRJKg3BbyNMHbsayjEGhU9AtkUPUkeOiGp9ZvAs9x6ErwUK+PXTcdolqnrnPM3ieFSHmRMIth+fwXJOUTSD/cy8S9vBPUHLh+/brQ68nIIYwEpfnWKQA47ZqUcBePmBDNcRKcjo2pF2Dqig15F0FMAXJ6kfdHLtopDAqVPMfBkeChZCkkRTCqZfTiP21QmMBzHGS0zizK2GlAXKendY5526aqxP4iz1/o+cee/wLkUNesCvYa1dQeahP38k5Qc+D973+/0OuxojRKqbBrFiV/Cog81DMvxMT1hV2TV1CK5jgJMjx0xeJ/8UIVKSjH81TeGZU8x0HGtNT+2MWFehX1qvkRChnrP12UagLPcVg9/+L2PxMnRTgDol7J/IJyneNV21jznUo1q4KLzWzjt7ehSCl/ANDr1FPzb+Je3glqDty5c0fo9Zy2DdcPMTmnHkoZOYS8U+JEc5wEFkkQmfYyWBtqYToYTyJ7UfdTRmhU8hwHGb3Yh5PtUyJNgSMhh3QwdnGhUYVdjV51JvAch/2FoBS7/uKkPFgVgv0m//j1dY4LJygFF+anrSExBd1WeoPCxL28E9QceO973yv0eqJfqDMvwMQNCnOYyKhy5zUoRHOcBKfNQn4ic0iL0TILkDMtdJhyqIlKnuPgSEh5KErLLAC42KyhIlxQPs6/CTzHgQlKkQblYDzHXqOKmlWMV72I1pnrHLNrsXQK0+G0baE51EUzKLI0ZjBxLxdjlxmKo6MjoddjL1RRFmrRNlO3LXb9UzfA1Au4BKVojpMgw0PXH88LEe4F5OUQpxGUKnmOw8VmDVaFiOV/VJyUH6tCsN8S76Fb3/8m8JwE0Z1+eGtIVCPy0PIZ1OscD8YuLjZr58qgWAfbS/vNYhgUWRozmLiXi/GUGYpGoyH0eqs+jGI8dEUT1MuQvyBB1ReQPyia4ySIjlBMXB8zLyxMUepeQ6ygpJRGOeQpwp0qeY5DpULQbdWEC8qi7H9gISgFGlSnawhM4DkJvXZdeMpb4fjnfP7XOS5SDQkgI+Vjjv1WDdWCGBROJ2qdmqaOzMS9LPxfmRBSJ4T8BCHkISFkTAj5VULIU1s+8w8JIZ8jhBwTQt4lhPx/hJB/T/R3Mx1LQSkoh7ZIU/KA7I3dt4HlIhflhbLXqKIqUFAWqWUWwASluF7UEzfA3A8Lwz8gthc7pRSDAuVQA4v1C055KB7/ogV1MQxqgIX8BdaQjIpnUAwFNiYYjosx1IbBadnwAorjmbjGBCohw2z5MQDfAeAvAfgWAHsArhBCksrMPwzgpwF8M4BvBeAD+CQhxJHw/YRhNpsJvZ7oHFKWi1WUHNoL9SpqFhH2Ql16qDkEhWiOk0AIERryW/ZgLgj/gNhpiVkiNCp5TkK3ZQsrSh27AVw/LETLLAaRvfgppQtBsRKUpvAch67g4Ua8Rdmq4bRrGE5chGF+QbnO8XDiFur8c9o2/FCcoCxSyh+QrRe3iXtZqKAmhFwE8DcA/ANK6W9TSq8C+KsAPgTgI3Gfo5T+eUrpz1NKv0Apvb74zFcB+DMiv59o7O/vC71eZyEoRYV8iuahJiTyUIoK+Z5umZUHojneBpEhvyIN9WDotsW1jVoK6hT8q+Y5DlHrTEEpXynHrpsEkQblaO7DDcJlsS9gDs9x6LVtDCcel6BkoJQWUFDWEYQUx7P8RuU6x0VL+RCd9lekomRgFaVO8w40cS+L9lAfAKgB+AT7AaX0LQBfROR9TosLiL7bUOi3E4z79+8LvR4hRGgO4WA8h1Uh2GsUoyABiA4U0UWZPD1IRXO8DSJDvoOCpXwAEVfCBXWKCIVqnuMgkn8RERrV6C08tIEAQbmKUKz2vyk8x8Fp2whCikdT/ijF8cyHF9CC7X/+wnTGcRShKF7KByC2jqpo+x9IZ1CYuJdFC+r3AQgAPDz18/uLv0uLHwfwMoA/3vSXhJDvIoS8RAh56d69e3j48CHu3buHu3fvYjgc4vXXX8d0OsWNGzcQhiGuXr0KYDX7/erVqwjDEDdu3MB0OsXrr7+O4XCIu3fvgl3v9u3bGI1GuHnzJnzfx7Vr1x67xuHhIZ5++mlcv34d8/kct27dwvHxMe7cuYMHDx7gwYMHuHPnDo6Pj3Hr1i3M5/PlZJ/1awDAtWvX4Ps+bt68if1mFXcfPhKypnuDES42LNy//5XUawIgfE2j0Qi3b99OtaZex8ZbDwZCeBqMXVgE2GtWc6/p6aef5l5TlmevXaV4cDQWwtM7g2MAQKcG4TzJ2E8AQGcnGIxdIc/eF167DQCYDt/duiZWMS5jTVmePX98hKOph8++9BI3T5/7/BcBAA/eekPrmrI8e3V4oBS4+cYd7mfv1S/fAwD4o+FyTU8++aSR5x67BhM/D09m3DyxsPlenWhdU5Znr1mJZjA8PJ7m5qnb7eLWrVt499EYfkjhtG3jzz22pvEgEok3b7/DzdMbb76J4diFTV2ta8ry7N1940vR97jx6laearWatjXFglK69Q+AHwRAt/z5MIC/jCj/mZz6/KcAfCzlvX4UwDsA/nSa3z84OKC68PnPf174Nf/Kz/4b+hd+6g+FXOu7Pv45+tEf/bSQa6nC9/zCVfrhH/mUkGtd/qVr9Bt+8Le5riGD4yR8/69cpx/6gd8Scq0f/o0v0me/79doGIZCrqcCP/qJL9FLl69Qzw+4r/Uzv/c6vXT5Cj2eult/VzXPcfj5P3yDXrp8hT48mXFf61997g69dPkK/fLDsYBvpga/8idv00uXr9Bb94+5r/XJG1+hly5foS/fGS5/ZgrPcfi9Lz2gly5foZ99s899rZduD+ily1fo7968L+CbqcH1t4/opctX6G9+4V7uazCO33h3RC9dvkJ/+fAtUV9POt4eTuily1fov/zsl7mvNRzP6aXLV+j/+QdvCPhmajCee/TS5Sv0pz/12tbf1bmXAbxEN+jRarzUfgw/BuBfbPmdOwC+EYAF4AkA76793XsA/P62mxBC/gmAvwjgP6KUvpHyu2nDBz/4QeHX7LZtvDWcCLlW0VomAYDTqqEvaPRuf+xyF2TJ4DgJTtvGo6kHLwi5e6eyHsyEEEHfTj5Ww308fNUFvu4E/bGLmkXQqW8/5lTzHAens+pF3uvwrT9LyospWO9F/ux7+K61qYbAFJ7jILIXe5YaAlMgIoeYcczSJor0DhQ5i2L1/Bcn5bNlV9GoVVKlvJi4l1O9sSmlDymlN7f8mQA4BOAB+Cj77KJl3tcB+EzSPQghP47Iw/2tlNKbuVekECwMIBI9gTnUUUFGcVomAVG+Y5T7F3JfS4RBIYPjJPSWglLMgVqklwkgtiiHtUxLY1Co5jkOInJIGQZjF3a1grad1GDJLIjl/6ygNoXnOPQEtg4tpKAUwD/jeNU2tDjvwKZtoVmzhGiATTUERUCvXU91/pm4l4XmUFNKHwH4OQA/Qgj5CCHk6wH8cwCfB/BJ9nuEkJuEkO9Z+/+fAvCfI2q1NySEvG/xpyPy+4nGwcGB8Gs6bRsncx+ub4agVA3mTRMxfnU45u/BK4PjJLDDT0TrtMF4XqiCFCBbUco2ZOnBq5rnOIgWlL2UBoUpYOJHROvMwdhFvVpBa82gMIXnOHSX4+f5o3Ssn3ORzoBGzULbtrief8ZxESM0gLjC5FVRfrHWn7bTk4l7WUYf6r8L4F8D+EUAfwRgBODbKaXB2u98LaK0EIbvRtTZ43cA3Fv78/clfD9hkGEhOYI8lH4Q4tHUK1TLJGBNUAny0PIeJqqt4O4iPCeiddpw4hWqZRIgdrhPlh68png7RAvqovHPnn9RHrrTBoUpPMdhJSjFGNSNWgUtO21mpxngbZ3IOGbvkCKlvACRASTKoASKFaEAIqdSGoeaiXtZ+E6jlM4AfO/iT9zvkKT/LwpkeaiBKFz13r38ozWPplG1fOGsU+ah4Xyhesyg4DxMVVvBSw+diBy6UbGa+gOrl58YD52LP9VtpfpdU7wdKw+lIIOyYN65etVCp14VlvJy2qFgCs9JcDpipmWKqCHRAd5e/EsP9chFs2ahWaCUJyA6A2SlPBUBvbaNN94dbf09E/dyMQa8GwrWWkUkRHmoCruZMjR2TwLz8PMKChkcJ0EU/14Q4njmFy5/riswhzhLhEI1z3GwqxVcaFQFprwUa/8D4kLem2oITOE5CU7KHNJtGAhIedOBiP/8BgXjuKjPv6hpsf2Ri5ZtoVErlkGRdv+buJd3gpoDH/jAB4RfU1TKQ7+AQz0AcYKS5SDzHqgyOE5Ct7UIeXOvv5j5gzWrgr1GlTuH3vVDnMz81Pyr5jkJoqZlFm2oBYMjaPz2YMPYZZN4joOo8evDDDUEJiEK+edPeWEcFzFCA4gzKIeT4u7/iRtg5gWJv2fiXt4Jag689tprwq+5FJScrePYC6loOdT7zRoI4ReUfUEV7jI4TkLVquBik3/8dlHzBwGg1+H30B1NskVoVPOchG7b5jYo5n6Ak7lfTP4FeeiGY++MoDSJ5zh0W/z8A8Ubu83gtGtcNSSM4+GkeDUEQOQEmXoBpm6yoNyG4vKfzqlm4l7eCWoOPPXUU8Kvud+yBQnKYnqohQlKQSkvMjjeBhEeSpaDXkQPRbfFz/+mHsRJ0MFzHETwv4zQFNBDx1uUBkQGxWjun+nBaxLPceh1Iv6j+RH5UcSiVCDyUM+8EBPXz/V5xnF/VFBB2RITpR6M54VzqAHpBbWJe3knqDnw8OHpCev8sCoE+82aMEFV1A1liqCWwfE2OAJ6kS8NqgIKKqddV86/Dp7jwJtDCqwiNEUUFCzlgUdQxvXgNYnnODhtG3M/xITDQznzAkzcoJD7f9mLPecZyDguag71KkrNrwGKvP5tGsjEvbwT1BzodOS0yRaRQzgYz7HXqHJP29OByEPHJyjYC5XXQyOL4ySI4b+4HmoROaRZIzQ6eI4DMyh4BOWqhqCIObQ23CDEmENQ9mMiNCbxHAcRdSRF3v+8rWM7nQ6mboCpFxQyQrMqzOd8B04K6qFfPv/J6zdxLxdPbRkEz+PvFboJvXadO4dwMPEKeZgCC0HJ2Yd1MHZxsVnjNihkcZwER0TKx+Lz+83ijJ1lcDqRQcEnKLMJCh08x8Fp1+AFFKN5vpA3sF5DUED+BXjo4rr8mMRzHBwBrROLLKh5O/14nlfoGpLlcC8Op8rE9THzwkIa1KvhXsl71cS9vBPUHAhD/mmGm5B2UlAS2NjlIkKEoBQ1dlsWx0lwFkVpvCHv/VYN1QJGKJyWDS+gOJ7xCEoXhEQ1CWmgg+c4OAJ6kRd17DCwHvLN76GLi1CZxHMcRAw3ylpDYBJ6nAZVGIaFriFhRgCPU20VoSmeQb3XqMGqkK0eahP3cvHetgah1Uo3NCIrROSQ9kfFbJkErFIewpBDUArKH5PFcRKctg0/pDie5heURc0fBESFvOfYb0YHcxro4DkOPU4PHRD921VIQSMUAviPaxtqEs9xEMO/mC5HOsBrULRarVUNQQFTPvaaVVQr5Nwa1JUKSVWYbuJe3glqDgwGAynX7YkQlAVtmQNEh0AQUhzP8od0RPXglMVxEthLgKfKu7+hB29RIMJDl9Wg0MFzHESkPLAOD5WUBoVJEDEtdDB2YVUILp4yKEziOQ5pc0iTwMLlRTwDLtSrqFkk9/k3GAwKLSgJIdydbgYZ24aaBidF60wT9/JOUHPgySeflHJdp20jpMCjaT5BSSmNenAWdDP1RHioBBkUsjhOQlfA+O3hmH/sui6I4D8yKNO/THXwHIeloOIwqDaN3S4KhBhUExfdVu2MQWESz3HoMEHJUUcyGM9hVQj2GsWLUBBCovHbOQ3KJ598ciWoC3wGcj3/BR3sxpCmMN/EvbwT1Bx48803pVw3bduYOJzMfXgBLexm6nIKKkophoIEhSyOk8CEIFcOXUGnhAFiDIpIUKYXEzp4joOQlIcCp/y0bQu2VeEWFJsMSpN4jgMhhLt1YhShOGtQFAU8dTRvvvkmBmMX1QrBXrMq+JupQbfFKahZDUFBz4Bee/twLxP38k5Qc+C5556Tcl3eF2qRCzIA/hzC46kPPxRjUMjiOAm8HrowpIUdOwust43iTflI76HWwXMcWraFepVTUBY45YsJSn7+z67fJJ6TwFtH0y9oD2KGXie/QfHcc88tIzSEFNSg6PAJ6v7YRc0i2GsU1KBI0ZjBxL28E9QcePnll6Vcl1tQs/ypgnool31Iedcv4IUii+Mk8E7KOpn5CEJayPxBAGjZVTRqldz8RwaFl0lQ6uA5DoQQ7pDvsMAeamDV6SYvBpPNERqTeE4CN/8FNqiByKAYTvKlvLz88suFNiiBBf8cKV/DRQ1FYQ2Kdh1HEw9+EN/Jw8S9vBPUHHjxxRelXLfH6aFceqgLmj/Gm/IissJdFsdJaNoWmjUrdw5hkXsQM6QJ+cXheOYtDIr0/OvgOQk8RUlFj1AAq/HbeRHnoTaN5zjwFqX1M9YQmAanVUN/lM9D/eKLLxZ27DqD07a3CsokFDnlC1hFqY8S6shM3Ms7Qc2Bw8NDKdflzSEtclN/AGjULLRsK/cLJW5KWh7I4ngbeMavF7nCnYGnF3ueHry6eI4DT8rD0dRDSIu7/wG+HNKAGRQbBJVpPMehJyDlJUsNgWlw2nUcz3x4OQTl4eFhZFAVNEILrE+LzOelL/IcCiBdlN7EvbwT1Bw4ODiQct1GzULbtnIfqMuxywU/UPK+UIcCUz5kcbwNvU7+kF/WsdsmwmnX86f85BDUuniOQ4+jKK3oBjXAl/JxNHFBYwwK03iOg9O2cTLz4frZBaUfhHg09QptUDMxnGda4MHBgbAuT7rAm/Y5LPCkZGAtSp0QpTVxL+8ENQeuXr0q7dpOJ/8LZThx0ahV0LKLWZAA8OUQrgQl/wtFJsdJ4DIoSiCoeDx0eQSlLp7jEBkUeb1T4p5/Xei1bZzMfcz9IPNnlwZ15+z6TeM5DuzZPcohKI+mHigttkHN0zrzcy8dLgyK4q6fV1D3R8WdQwCkcgzQWgAAIABJREFUW7+Je3knqDnwwgsvSLu2w5FD2h9tDncWCVwpDyMXzZqFpm1xfw+ZHCfBaW1vbB+HIo8dZhCR8pIlQqOL5zg47RpGOQUl82wXOuTPPJQ5jIq4KYmAeTzHgaeOpAwRimXaY44z8Omv+XcBFHv9PMONvCDE8cwvdIRiaVAlGJQm7uWdoObAzZs3pV3bSTF6Mw6D8bzQ+WMAX1GOyLHbMjlOAq+gbNkWGjV+g0IXnLaNiRtg5uURlIserBmMSl08x8HheKGKjNDoAnMI9HOkvSTxbxrPceDxUIqsIdEFntaZh1/4EoBir58Zw3nSvlYRyuIa1MtZFAkGlYl7eSeoOfDMM89IuzZPH9KsPXhNRBTyz5lDKrDDgUyOk+B0bEy9AFM3n6As8ssE4BcU7YwGhS6e45AmhzAO7IVaaA91m8NDnRChMI3nOPD04hdZQ6ILq6K87Otvdd/z2DWKiG6LI0Kx5L+4GqBmVXChUU00KEzcyztBzYF33nlH2rV7i8bulNLMnx1Mil2QAUSHwcwLtQtKmRwnIU3IKw5F78EK8Anq4SR7hb8unuPQ4yjK6o9dXKhXUa8WN0Kx8lDm99Bt8lCbxnMceHrxl6Eoeb9ZAyH5DMo37t4HUOwITc2q4GKzlov/og92Y9hWR2PiXt4Jag44jiPt2t2WjbkfYpJHUMaM3S0SVh6a7C/U/kicoJTJcRJ4cgjZlLAig8dD188RodHFcxxWrTPPJ/+8KS8XGlXY1bOvN9N4jsN+y44EJYegKvIzUF0Iylw5xJXo2SlyhAbIX5hdhi5fwKLTT4JDwcS9vBPUHJhMJtKunbfKeeYFGLtB4TdTl8NDKVJQyOQ4CTweujKkfKz4z7P+OZxWtpepLp7j0ONI+SgD/xcXHsq8+z9u/abxHAerQrDfrOV+/i80qqhZxX69560jefBoCiBbDYWJyFtHlKeGxEQ47Xri+WfiXi72jtOMSkXeP1/eKu8yVHgD+dc/dQNMvUDY+mVynATmocsX8i92yyRg3aDMnkM7GGX3UOviOQ4XmzVYFZL7hVp0/q0KyT3cJUlQm8ZzEvIKysHEKzz/QP7WqUezABebtXNrUKwEdbE99M6W4V4m7mXzvlGBUKvJe2BXbaPOp6BmL4TM65+IzR+UyXES8halTd0AMy8sdEEKAOw1mKDM4aGbuJkjNLp4jkOlQtBt1XLn0Bd9/wN8giJu/5vGcxJ6OQvTiz4ljyEv/8fz4FwbFIOxi/1WDdXCGxR1DCfxdWQm7uVi/4trxmg0knZtJ2eVb1kENTMosh4oogsyZHKchL1GFdUcHkqWIlLklkkAE5TZXygT118YFNn418VzErotO3MOPaV0kUNe7P0P5B+/nmRQmMhzHLpbPHRx6OeI0JiIvPz3R/NC548zsBzirI0JymJQ99o2vIDiZO5v/HsT9/JOUHPgiSeekHbtlaDM5qEri6C+UK+iZpHMB+pKUIpZv0yOk0AIyZVDt+K/DC/UWmYP/bIHb8b8QV08JyGPh27sBnD97AaFiXByGFSU0sQaChN5jkPe1qmRoCq2QQ2sBGUYZhOUJ17x339AtAYvoDiebRaUceiP54Uf7AasdXqKeQeYuJd3gpoDb7/9trRr5xeUxW+ZBCwEZQ4PnegerDI53oY8Ib8yTElk2FblvQl5DUqdPMeh18nei70MY+cZnI6dOeVrNPfhBmHs+Wciz3HotW0MJ14mQUkpjdpGlsKgriMIKU4yCsqHJ7PCv/+A/K1Dh+Nij11n2FZHZeJe3glqDjz77LPSrk0IiQRF5s3kwqoQ7DXK4aHImkO6Gjss5oUik+NtyOOhHJbEoAIiDjOnPDGDKmMOtU6e4+AsBFUWlKVlFsAEZTYPJRsEEycoTeQ5Dk7bRhBSHM/SPwMncx9eQEuy/7N3OqKU4mRekghNTkHdH2evITER23qxm7iXd4KaA6+88orU6+fJIe2PXXRbNVQqRNK3Uoc8gnKwMCguNKpCvoNsjpPAk/JRhhzCPDmkg5wpHzp5joPTigRlkEFQshSxorfMAqI1hBQ4mqYXlNtqCEzkOQ55Oh2VoQc1Q57WqcczH35Iz62gDsMoQlGG/b9t/Sbu5Z2g5sDzzz8v9fpRyDeroCpHhTeQX1B3W7Ywg0I2x0nI09i/P3ZRswj2BBkUOuG06ziaePCDMPVnlikfGT00OnmOg9O2QSlwlCFKIzpCoxO9HHUk22oITOQ5DnkEVVlS/oB8w53KUkMErPOf/vk/nnkISmJQrGYxbObfxL28E9QcODw8lHr9PEUpZanwBRaCcpS9KFPky0Q2x0lw2jYeTTMKysWUTEKKH6FgPGbzUEYGxYV6NoNCJ89xcDrZpwUOc6a8mIiVoMjGPxAvKE3kOQ55WmeWKoc+R+vUgeCidJ1gRnEeg6IMKR/NmoV6tRJrUJi4l3eCmgMHBwdSr5+nKC0SlMX3TgGRQXE88+Fl9FCKPExlc5yEZS/uDHm0g0l5DKo8Hrrhgv+sBoVOnuOQZ1pqf+zCrlbQti1ZX0sZ8njotglKE3mOAxNFWQpzy+ihzSYoo7OyDO/Apm2hWbMyGhTl6fJECFlooM3vPxP38k5Qc0C2hdRt2TiZ+XD9bIKyW4KWScAqDzLrC0Xky0SnFZwnh7BMEYo8Hrr+OF/+oIneDraOTPyPXDgliVDkE1SRQdGKMShM5DkOefgvU5efRs1Cy7Yynn+LGoLSvAOzpf0t+S9BDjUQRdp2HupzAtkWkpPRQxGEFEdTrxTWKbCysrO+UMrioV4Jimw5pGV4mQL5PNSD8TxXuNNEb8e2HMJNKCX/GQ2qXkKEwkSe49CoWWjbViaDcjCeo55gUBQNWetoVik/ZXkHZlt/3hoSU5GU9mriXt4Jag5cv35d6vV7GT100VSlchSkANlfqH4Q4tFUbA9O2Rwngb0UhllySEfz0vC/THnIHKHI/jLVyXMccnmoc4xdNxX1qoVOvZqD//j1m8hzEpI8dJswGHuJBkXRkDXtcTByUbcImufUoFjmUJfkHeC0arEOBRP38k5Qc+D973+/1OsvizJSvlDKVJACrFX5p13/ItdYpKCQzXESsuaQekGI45lfmghFN4eHMm9Rqk6e42BXK7jQqJ7blB8gn6BIWr+JPCfBadcxyFJDMZ6XxjsJ5OB/4uKJC+U4/4AcBsXYRcu20KiVxaCox+aQm7iXd4KaA3fu3JF6/aw5hGXKnwOye+iWPZgF5o/J5jgJ+60oDzAt/6spkeXIH6xZTFBmMyjy8K+T5yRkFhSjcvSgZcjai32boDaV5zg4rVrmtoHnnf9WNduocpORZ/1l4r/XsTF2A8y84MzfmbiXd4KaA+9973ulXn+V8pDuQC1ThTcAdJmgTOmhZLnGIsNdsjlOQs2q4GIz/XCTMlV4M2Tpxb2M0OTw0OnkOQlZBPXcD3Ay90sT7gVY60xxgtpUnuPgtOu5csjLgmj/ZzMo3rPXkviN1MJp25jECMpNKMuURIakOhoT9/JOUHPg6OhI6vWjfsLpPbRlauoPAFWrgv1WekG5HDss8ECRzfE2ZAn5LacEloR/gI3flv/86+Y5DlkMiqOJ+OdfN7LwP/cDjLYYFKbyHAc23IvSdF7XYc4aAlPhtOuYeSGmbkpBOXLRKZGHOutwm+EWg7JoSIpSm7iXd4KaA41GQ+r1rQrBfrOWPod48dDtlyjk47Tt1OuX0dRfNsfbkCXkN5iUUVDX0xflckRodPMch27LTt2Htp9z7LrJYAZFGkG5NKgTBKWpPMeh27Ix90NMU3goZ16AsRuUzEPJ0t7SeamHE3c5EKkMyDrcpmw1FKtpqWfXb+Je3glqw5FJUI1dXGhUYVfLQ6vTslOHPJkVX6Ycsiwh/7Kl/ADRCzVrhKZU6+9E/KcRlGXkv9u24fohxik8lP2lQV2OGgIgW6cnGTUkupGlderMCzBxA3Rb2aakmozsdVTzUhnUeVqn6kR5lJcGzGYz6ffIkkNYtvw5ILug3GtUUbPEPdYqOE5ClpA/e05Y7nkZ4LTri3aQcgWlbp7j0GvbcIMQo7m/9XeXNQSl8lCm7/SSpobAVJ7jkEVQlNGgyiIo2e90yqOnM3V6mrg+Zl5YqpSvpJQXE/fyTlBzYH9/X/o9suQQDsbzUh2mwCqHMA0GYxc9weE+FRwnwWlHIf+0gnK/VUNVoEGhG722DS+gOEklKF0Qks9Dp5vnOGTx0A1TCMqiIUsv8jSC0lSe4+AkhLxPY9mDuISCKk3KAzO6/tQTF6V+J5VgswiyRCjK5FTba9RgVchGg8LEvVyeN68G3L9/X/o9kiYFncZgLHaoiQlgBkVaQSl6/So4ToLTtuGHFMez7YJyMHFLFe4Dsnkoh2MX+83oAM4K3TzHgaUvpBVUhAAXm2WKUKT30KURFKbyHAcnQ+vQMnqou1k89AujK5ydSP1OKrHXrMKqkFROtTJ2eapUCLqtGgYbhpuZuJd3gpoDTz/9tPR7OO0ahhMPYZhGUJbPQ91t2QhCiuNpCkEpoQenCo6TkCnkOypXQQqQLeQ7GLvLF3BW6OY5Dlk81P3F85/HoDAVS/5TeugqWwwKU3mOQxYP9bKGoERGdZTCR1Lu/8jo+rpnnpL9tZSBEIJuK13a46qGpDwGNcDSPs8a1Cbu5Z2g5sCrr74q/R5Ou44gpHg0TZ6WRSnNPXbZZLDwZZoqbxk55Co4TkJWD11ZBXW6F0r+seu6eY5DlrZZO/4jg6KSYFCYynMcLtSzCUqrQkoVoVgKyhQGFTO6hvfekv21lCJtHdWqbWq5NEBcHZWJe3knqDnwwQ9+UPo90uYQnsx9eAEtVf4UkN5DRymNenAKzh9UwXESesv1bx8/XLam/kC2tlE8glI3z3HIWpRWNkHdqVdhW5V0OdQpIjSm8hwHQkish+40BmMP3VYt0aAoItK2Th2MXVgVgm88+JCCb6UOaQvzhyVsmwpE69lkUJq4l3eCmgOHh4fS75H2hcoER96Qt6nopVz/8cyHH4o3KFRwnITuMoc2+YVKKcVwUq6xs8B6hCLNC9XL7Z3RzXMcWrYFu1pJb1CUjP+loEzjoZtsF9Sm8pyEKOS/3aAuY8ofkE1Qdls2rl69quBbqYPTSWdQ9McuqhWCvUaJ2pxgVZh/Gibu5Z2g5sDBwYH0e6TNISzblESGtEUpsnqwquA4Ccsq720GxdRHENLSvVCbNQv1amWrQRGGkUGRN39QN89xIISkbp04kBChMQFpe/Gn8dCbynMSep20HuryGdRAekHdH0Upf0XkOAlOyhzqwSiqISGkbBGKOo6mHoJTdWQm8rwT1BwwyUNdxrHTQPoc0uWURMGCQrcV3LQtNGvWVg9dGXsQA+kF5fHMWxgU5fJQA+kEBTMoymZQA+l7sacR1CbzHIe0nZ7KmPIFsBzi9DUkReQ4CU7bxtHEgx+Eib9XxjkUQMQ/pTjT6cREnneCmgMqPdTb2uaUsWUSADRqFlq2lcJDHYVERR8oJljBaXIIy9gyicHpbB+/zRuhMYHnOMTlEK7j0dRDSMu3/4F0vfiDlAaFyTzHIa1BMSxhDj0QnWnHMx/eFkHJIjRF5DgJzEgaTpLTfoYpUp6KiLgotYk87wQ1B65duyb9Ho2ahbZtbU35GJS0IAGIz6Fax9JDLXj9KjjehjQeyqWgLmXId7uHbshpUJrAcxzSPP9lHLvOkCaH+tHUA01hUJjMcxy6LRsnWwRlEFIcTfPXEJgMlsa11am06MNfRI6TkMWpVsb9H1dHZSLPO0HNgQ984ANK7tNNUeU9GLuoVyto2ZaS76QSaTx0sgSFKo6TkElQlzDk67Rq0vk3gec4ZOK/hC9Up23jZO5j7gexv8POx21F2SbzHAe2p5OMqmj4VbRXyoY0nZ78IMTRJBpsVkSOk8CcJFvrqEblLUoFzvJvIs87Qc2B1157Tcl90oT8WEFG2QoSgJSCYuSiUaugZYutcFbFcRLS9CEta1EqkM5DzSsoTeA5Dr22jVFKQVnmF+owodMF2x+9LR5ak3mOQ5o6kpVBXUYP9fZpqSwdotexC8lxEtIM9/GCEMczv5T7P+75N5HnnaDmwFNPqZnIlCaHcDCel9I7CaQU1BN368s0D1RxnIR0/Lto2RYatfJFKHodGxM3wMxLEpR8gtoEnuOQxkO3qiEon6BK0zozLf8m8xyHNIXpacauFxUshzipjmSd/yJynIQ0w73Y+6GM/O+3NhtUJvK8E9QcePjwoZL7OO361hzCwcQrZcskIDok0ngoZVjnqjhOQre9XVAOS9oyC0gvKNocBoUJPMfBWfYiT1o/S3koY8g/Bf9MUGxxKpjMcxyyCOoyeijZuZZq/S27kBwnYbX++AhNmYvS7WoFFxrVM04lE3neCWoOdDodJfdx2lEOKaU09ncGHGOXTUe3bWPqBZi6yR5KGUNtVHGchDQh37K2zALSv1B5+DeB5zik8VD3xy469Srq1fJFKJa9+BM8dMzhsL8lh9hknuOQRlCXuSi1u+A0Ke1tvYakiBwnoWZVsNeoJnqo2fNfRoMa2Jz2aiLPO0HNAc/bPr1KBJx2HXM/xCRJUI7cUlqnwLqgjD9QWA65aKjiOAlpcgjLWuENpJuWyNuD1QSe45DWQ1lW/tMKygspDAqTeY5Dt2WDkC051ExQlTBKVbUq2G/VUkVonLZdSI63odepbz3/gHKmfAEs7fPx97+JPO8ENQfCMLkvpihsyyGceQHGblBaDyUzFJKKkmT14FTFcRLS5hCWXVAldjngXL8JPMchbQ5xWfnfXwjKbV0u0tSQmMxzHKwKwX6ztnX9FxpV2NVyvtK39eJn6RDdll1IjrdhWx3NsMRtc4FFp69TDiUTeS7n7lOEVqul5D7bPDRsM5XROwFsD/nOvAATN5BymKjiOAmrlIeEkN/YLWUPaiB9lwOeCI0JPMfhYrOGCjm/gtqqEHRbyZ2O0q7fZJ6TsG38elmn5DE4reRe5IPxHHuNKmpWpbAcJ2GToFxHfxmhKGfKxyaDwkSed4KaA4PBQMl94iYFMfRLOnacYZtBITN/UBXHSWBhvLgDdeoGmHpBabu87DVqsCok0aDoj+fL4r08MIHnOFQECsqiorsl5N8fpTMoTeY5CVEOaZJBPZdSQ2IKtnV6impIFrUGBeU4CU4ref2DsYuLzRqqVjklHWudul5HZiLP5fzXV4Qnn3xSyX22eeiWLZNKKqi2CeqBRINCFcdJ2GtWUa2QBIMietGW1UMVCcp4QTVxfcy8kMtDbQLPSUiaFkgpLb2HstdOziFNa1CYznMctgpKSTUkpqDXSW9QFpXjJDgdezG8Z3NjgkHp978NL6A4mfvLn5nI805Qc+DNN99Ucp9tk7LKnj8VhfLiBeVAYg9OVRwngRCCbkIOHcstL2tRKpAsKET04DWB5yQk5ZBO3ACuH5Z2/wPJ49cppdHY6RQOBdN5jkPkoVNfQ2IKWMg/SVCy9ReV4yRsEpTrKH2EakNhvok87wQ1B5577jkl97lQjwRlnIW+TPkoaQ4tIVHIO15QyZsSp4rjbXBa8Tl0/eX6y5k/B6QT1Dz8m8JzHNKsv9Qh/078+scLgyKNQWU6z3Fw2jUMJy7C8KygpJRy1xCYjm7LRhBSHE8TBOXi/VdUjpOwrdNT2QX1sjB7zalgIs87Qc2Bl19+Wcl9VoJycw7dYOzCqhBcbJZbUG01KCQcKKo43oZ0grK8L9RE/gUISlN4jkMS/2UeO8/gtOxYQZmlZZzpPMfBadcjQTk766U+mfvwAlpqg3rVOvPsO5BS+liXl6JynAR2tiWdgWUW1JsMChN53glqDrz44ovK7rXthdpt1VCpEGXfRzW2CUqrQrDXEP9CUclxEpI8dGWeksaQyP+IX1CawnMceouQd7BJUEqM0JgCp20jpMDR9KygXNYQpEj5MJ3nOCTV0axqSMpsUMcPNzqeRQYF+zcqKsdJSGqdGYb0XKT8AI+v30SehQtqQkidEPIThJCHhJAxIeRXCSGph64TQr6PEEIJIT8p+ruJxuHhobJ79RIEFW8P3iIgKYdyOInGbsswKFRynIReQg7tYOyiWiHYa1QVfyt1cNp1PJp68IOzvUeXNQQcRbmm8BwHp22DUuDRBkHJcmvLOtQBWOvFvuEMWNWQbF+/6TzHIakXu8waElOQJCiHpxwKReU4CUn8n8x8BCEttQZwNhiUJvIsw0P9YwC+A8BfAvAtAPYAXCGEbJ2JSwj5RgB/E8DnJXwv4Tg4OFB2L9Y2ZhMGY7e0PagZNo0eZZBZ4a6S4yR0WzaOJpsFJRu7TUh5IxS9haDc7KF0UbMILtTzGxSm8ByHVevMsyFv9rOyjh0Gkjv99DNEKEznOQ6bBAWDzC5HpiCpdezplK+icpyEZevUjetPH6EpKlq2hXq18lhhvok8CxXUhJCLAP4GgH9AKf1tSulVAH8VwIcAfCTFZ//vxeeHIr+XLFy9elXZvZxWLSF/al7qzQREh+WjqQcvVlDKERMqOU4C43c42Swoy+ydApJfqIORuxjPnN+gMIXnOCT1Iu+PXdhWBR0Og8J0JA03ylKUaTrPcUgyKM5DyldiysupGoKicpyEpm2hUaskP/8ldqoRQiKn2tr5ZyLPoj3UBwBqAD7BfkApfQvAFwF885bP/gyAX6KU/q7g7yQNL7zwgrJ7Oe06TmY+XH+zoCzzYQqsDstNreOiHpxywt0qOU7CthfqeeE/TlDyrt8UnuOQyP8oWn+pIxSdZEFlVyto21uDoMbzHIdED/05ENSNmoWWbcWcf4/XEBSV422I68W+Kkoub8oXwKaFrgwKE3kWLajfByAA8PDUz+8v/m4jCCF/E8CzAL4/zU0IId9FCHmJEPLSvXv38PDhQ9y7dw93797FcDjE66+/jul0ihs3biAMw6Ulw3Jurl69ijAMcePGDUynU7z++usYDoe4e/cu2PVu376N0WiEmzdvwvd9XLt27bFrHB4e4ubNm7h+/Trm8zlu3bqF4+Nj3LlzBw8ePMCDBw9w584dHB8f49atW5jP57h+/fqZawDAtWvX4Ps+bt68idFohNu3b59ZUzh9BAD47MtfeGxNn33pJRxNPbjHAyFrAqBsTVl46tQisfDlew/PrKk/noN4YylrunnzprQ1ZeFp/YV6ek33j0bYs4kRPMl69jAfAQDuPjw6s6a3HgzQ69hca/r0pz+tfE1ZePrKl18DANx4486ZNb0zOMbFhmUET7KevQd33gAAvHLr9pk19cdz7NkEs9ls65pu3LhhzJqy8DQdHaNZq+CtB8Mza+qPZrCtKCxepDVlffY61SiH+PSa3rj7LgAgnDzCnTt3cO3atcKsKQtPrWqI/snszJpevnELAHD/zmuFW1MWni42LNwbjJZr+tznPqdtTbGglG79A+AHAdAtfz4M4C8D8AGQU5//FICPxVz7awG8C+C5tZ99GsBPpvluBwcHVBcmk4mye1259g69dPkKvfHOo8d+/vBkRi9dvkJ//g/fUPZddOAzrz2kly5foX/02ruP/dzzA3rp8hX6o5/4kpT7quQ4CV+894heunyFXrn2zpm/+9AP/Bb9/l+5ruFbqcP9R1N66fIV+vE/vn3m7z78I5+i3/MLV7mubwrPcZh5Pr10+Qr9p5989czf/YWf+kP6V37232j4Vmrxgf/+N+kP/OoXzvz8v/j5z9Jv+/HfT3UN03lOwp/54d+hf+df/smZn/+9X3yZftMPfVLDN1KLb/+JP6B/7ef+7Zmf/+CVV+jX/qNfX/5/kTlOwl/7uX9L/+Of+IMzP//J371FL12+QidzX8O3Uof/+v+5Sv/s//I7y//XyTOAl+gGPZrWQ/1jAL5uy5/PAvgKAAvAE6c+/x5EXupN+KbF73+BEOITQnwAfw7Ady/+39g4xjvvvKPsXnEhv2X+XMfYfyYhiFs/yymWFe5UyXESnJiiNC8I8WjqlTrcCwD7LId2U8rHaA6nxZdDbwrPcahXLVyoV2NTHsrOPxAVXcalPKRdv+k8JyGuMHswnpd6qA9DXOvM/qmUvyJznIS4XvyDsYtmzUIzRcpTkeG064+d/ybynKqKhVL6EGfTOM6AEHIIwAPwUQC/sPjZU4gE92diPvYrAF469bOfB3ALwA8B2FyJZwAcx1F2r7gcwvMw1AFIYVBIWr9KjpPACk5O8z88By2zAMCuVnChUd1oUBzPfO4evKbwnIS4XuQsh7rsiOt0NBi7uNRrpbtGAXiOg9O28e5oc1Ha+eDfxq37ozM/P73+InOchDiD4vzwX8PYDTDzAjRqlpE8C82hppQ+AvBzAH6EEPIRQsjXA/jniNrgfZL9HiHkJiHkexafOaKUfmH9D4AxgMHi/89OMjAEk8lE2b3i+lCe7sFZVnQXHsg4QS1LUKrkOAk1q4KLzdoG/pmHvtwRCoD14n68y4mIHtSAOTwnwVkMd1mH64c4mfulN6iABf8xfYjTnn9F4DkOTru+3O/rGEzK3+UHSM9/kTlOgtO2MVkIynUMxm7pu3wBZ4f7mMizjD7UfxfAvwbwiwD+CMAIwLdTStefgq/F2bSQwqFSUTdocn8xVjzOQ112QV1dCMo4QS0r5KmS423YFPLrn4MexAynq7yBtQgFZ8sok3iOg9Oyz3Q5YQL7PIT8u62zgmruBziZ+6n5LwLPcXDatY2jtwcj93zw37Yx9QJM3ccF5emUnyJznISkKG2ZW+YxnF6/iTwLb1xKKZ0B+N7Fn7jfSezvRCn9sOCvJQW1mjoRU7Uq2G/VYgXFedhQm3II2b+HLA+NSo63YVPIb+WhPx8e6reH08d+JmqohUk8x8Fp23jlnePHfpZlqEnR0etE+59SumwRuIzQpPTQFYHnODjtOmZeiInro2VHr+6ZF2DsBueD/2Uv6jmeslcpPqdTHorMcRLWBeWT+83lzwdjF1/+czyeAAAWVklEQVTzno6ur6UMp6elmsizeRK/QBiNzuZzyUScoLrQqMKulp9Kp22fKUo7PSVLNFRznIQkQV32CAWwef3LGgLOkKdJPMeB5VCvZ8GdN/5dP8R4zUPZz2hQF4HnOGzqxb7iv/wG9emQPxAZFBM3eOz5LzLHSYgbbtMfz8/F/l8Nd4rWbyLP5VdhEvHEE2qzVjblkA3OwZQ8hk05pMOxi71GFTVLzqOsmuMkxPEPrHLMywynXcdw8rigXOZQc+4Bk3iOQ69tww0eF5SDiRiDogjYVEeStYagCDzHYbn+ySZBfX74Xz8DN9XQFJnjJGx6/qdugJkXcteQFAG9U/ybyPNOUHPg7bffVnq/TTmE0djt8m8mIC6HWG6Fs2qOk9BdGBSnPZQXmzVUJRkUJsFp1+AFFCdzf/kz5q1jNQZ5YRLPcehuaB04WHR9OA8pX86GTjf95ZS8dPwXgec4dDd4KHeC+myEssgcJ8HZwP/y+T8H+/9iswarQpacm8hz+d/CEvHss88qvV9vQ9us/nnzUG8Iect8majmOAm9tg0voDierQnKc8X/IuR7KuS93+I3KEziOQ6r1pmrOorB2AUhqz7dZYazzKF8fP1Aeg91EXiOw9JDtzHl4xzwv0FQb2obW2SOk7DXYIJy0/Nffv4rFYJuq7bk3ESed4KaA6+88orS+0UpDx7CcF1Qno/8KSBavx9SHE9XgjIS1PLyB1VznISNHppz0oMY2JxDKMqgMonnOGzKIe0vKvytSmKddykQl0NcIekjFEXgOQ5OJ52gLCui1D5yav+zCMVq/UXmOAmRoLQ3838OUj4AFqWPODeR552g5sDzzz+v9H5Ou44gpDieRXmDlFIMx965KEgB1qp8T+UQynyZqOY4CZsE9XByfgT1phxCUfybxHMcTucQAueU/1P7v9uyUUlpUBSB5zhcqEeCcv38Gy4MioucKU9FACGRoHx8/0fvwvUuR0XmeBtO19EMM0Zoio4oSh1xbiLPO0HNgcPDQ6X3Y3mCzCodzX24QZg6f7DoWFX5RhYqpRTDidwcctUcJyEu5HneBNXpHEoR+cMm8RyH7ib+R+65yJ8EgE59k4cy2/4vAs9xYIJyPeWjn9GgKDpO19EMxnNYFYILjVUH4CJzvA3ddu3M+QecjxxqgLXOjN7/JvL8/7d3rzGSXGcZgN+vLzUz3bOX6fbG9u56w0b2OsEsxKyJDNhxsJJfjpDDnxAkQgSyQI4J4iIgCYJASAQC2VgJEURCwkRCicQPFCOQAoIoIkaGHcc3lsU4rLzyrlnvTs+sPTM90z3dhx/V1V3T3VXjnrqcqvreR4q8M6OoTunt6vrOpU6xoI7gzJkzqR5vfMpX05ZJwGgUwpvyfWNrB92eSXSEOu2Mw4wKSl+HQmFBvTLWoYhjujNLOQepO2U4ldLEDVVL/iIysXXmrB3KPOQcZlpBqSV/YHLrzGkzFHnPOEyzPjfx/VcpCQ4uxP5KkUzy55/FnFlQR5B2D2l8DaGm9XPA5BrCNB7IyFIveNihGJz3G+0d7PSNmhtqzSljrlIadij6fRPbkocs5RxERCZebtTa6KjYMsvTqM9NFFSzfP/lIecw7oPpux9K03L9A5MF9cr6ZP55zzjMRIdi8JZM70VHRdeoOVhrd9Hrm0zmzII6gvRHqHevIVxNoaDMEm9ay1tDOCyoEywostQLXnDKWKiWh7lr2oMYGBWU3rrJN7d20OubWGZospRzGG+nG2DUodDSoQYGa0jH1hDrGqGew+pmd/hzK6YZmryYWEM8pUOd94zDNOoOrre72On1Abj3AE3Xf6PuwBhgbbOTyZxZUEfwwgsvpHq88TWkK8oKaq+g9KZ801g/lnbGe/FP+XojVRr2IPYs1UcjdLPuQRwmazkH8ed/vd1F32jMf3eHYpbvv7zkHKRRq2JlffcItbb8r7e76A4KymlLfvKecZhhQdl2O1Xa8m8sjpa9ZjFnFtQRnDp1KtXjzVfLqDnl4ZIPTXtQevxTXtO2TIpb2hnvxX/+3uegqWQNPTCef3zPEGQt5yC78le2ZRYwGKEcfO7XBh2KWa7/vOQcpFGfGzw70kevb7DW7qoaoWyOzdJOW/KS94zDjA+qaVvy5d86NYs5s6CO4OLFi6kfs+EboWttdDBXKaHmlFNvhy3uU77pFRQ2Mg4ztaBU9oU6kX8MBUXWcg4yvUOhJ/9G3cGb2zvY3untq0Odl5yDeNf66kZn8NZUbfmPRih3en2sbXYnzj/vGYeZeI5qfVtVh2q001cnkzmzoI7gxhtvTP2Y7hrC0XRPU9EDCYD3cpvRGvL5agk1J7knnG1kHMa/htBbS6plyyRgsIZ0I/5nCLKWc5Bm3cH6sKDUWVADwNpmd+oexHvJS85BhnuRb3ZGn/9FXTNUgHvv85Y9jA+o5D3jMMMO1WYH3V4fb2ztqLr+m76NCbKYMwvqCNbW1lI/5tLYCHWSezBnUaPm7NrlJOli0kbGYfxrSFvrHSxUy1hQNEPRqFex0elhq9uL9RmCrOUcxLveVze6qgvqlfXO6BmCGdbQ5yXnIMMRuvXO6POvqkM9Kqi8z//4GuK8ZxzGy3plMEMB6Lr+/SPUWcyZBXUE8/PzqR/Tvw+rppd6eManvJNe7mAj4zCNuoPNQUGpbcssYPeUb2ujg5pTxnw1eociazkHGa0h3E7lGYKs8RdUoyU/b32ENi85B/FG6FZ8BaXa/NenL/nKe8Zhhi93WteZv1Mp4cB8Ba2NTiZz1rEbeIF4a0iNMWhtbONks2a7SalqLDpod3tod7yCUs90J7D7oYy4XmqSJ+MjVJpuJsDuDsXKRgeLcxXMVfTMUOzqUAwKqllGqPPO//n3Xmai6TtgqTZ4W/B6B826vmdIquUSDs5X0PJ9/vV9B+7eiz9LOEIdwdbWVurHbNTnsL3TR7vbw+pGV21B2drszPxSh/2wkXGY4V7kgyk/bV+m/jV0ceaftZyD+AsqTW/J9Pg//63NDg7M2KHIS85BDi9UITLKH9C1bWKlXMLhWhWrm53RMyRj10DeM95Lc3EOrc3u6D0EymoAby/+LObMgjqCw4cPp35Mb8/d165vYX17J5Y9ePPEv4YwjT04bWQcxv/67ZX15NeQZ41/DV2czxBkLecg40setD1DcbjmDAvK/eSfl5yDVMolHFqoDs//wFwFTkXXbbxRc0cohzMUY9+Bec94L0u1qjtCvaFvhgYYzdJnMWddV2LMrly5kvoxvRHpl19f3/WzFt4I5aW1NjY7vcSnO21kHGZUUG2rXPLgX/IS5/lnLecghxeqKEn8I/R5US4JDi9U951/XnIO4z1HsqJsD2KP9xxRa2MbB+crqJZ3lzFFyDhMoz6HlfXRGnJNMxTAaOvgLObMgjqCEydOpH5M7wYyKqi1XUxuB+K7V9M5fxsZh/Gm9y6tttHu9tTdUA8tVFEuCVob21jZiG8P1qzlHKRUEix5I3QKO1SAr6Bcn71DkZecw7gjdO5Dqarz3+igOWXLwCJkHMbbOrW10cGhhepEh6LovJ2ubrnlFttNmaAriZi99NJLqR+zOVZQa3ogBUi/Q2Ej4zAHFyoolwTfvboBIJ6XmuSJW1BWcXltC1vdfmwzNFnLOcxohE7fCDXgdipb+3yGIE85B3HXkLr7cKvMf9Fx9+EOyL8IGYdpLLrvYtB7/Tvo9gyeO/fftpsygQV1BKdPn079mEtjBaW26Z6D8xVUSpJaQW0j4zAi7gil1vwB7Dr/uJ4hyFrOYZbqDi6ttbG901e3hhpw14wOlzzMeP55yjmIt8tBa2Nb7fW/OpihmHb+Rcg4TKPmFpQXW5sqr39vEOWmt99quSWTWFBHsLy8nPox3TVjo4JSWw9VRLBUd1IrqG1kvJem7/y1zVAAbuZxP0OQxZyDNFP8/GdRoz6HV1fb6Oz0Zz7/POUcxHtbbBr78GdRo+5gp2/wysrm1PtfETIO45+l1Xj9e5k/tfy85ZZMYkEdwZkzZ1I/pjdC2e72UC4JDi3oesIXcC+odrc3/HeSbGS8l4bv/LU9lAq4nYjR+ceTfxZzDtJI8fOfRc36/vPPU85BGvU59PoG3Z7Rmf+gExH0DEkRMg7T8J2/xvy9Ufkjx99huSWTWFBHYKsn7N1ElmrV4eb+mnjnXy4JDs4n26HI4miH/yaicYTCf85x3VCymHMQ/zmrz3/GEdo85Rxkd/76OtT+c9Y4Qq39+vfO/zvnsrdWngV1BLZ6wqOCWt/FBIx6qGl0KLI42uHtPV0pCQ7O63vZqX/v7bjWEGYx5yBLym+o/nOe9TswTzkH2Z2/vhnKXdf/lPyLkHEY/zlrvv4PHDlquSWTWFBH8Nxzz1k5rveB0ngxAaMeahrnbyvjMMMOVd2BiN4Zimo5vg5FFnMO0mBBPfz3rG+Jy1POQdSPUPtn6KbMUBQh4zBN5TOUNaeMuUoJ5y+8arspE1hQR3DHHXdYOa73harxgTQg3Q6FrYzDeLlrXD8HAI3B3rNLtfg6FFnMOYhXRDrlEhbnFM5Q1MMLqjB5yjlIEkue8qS5x/kXIeMwNaeC+apbumksqEUEjbqD0sJB202ZwII6gpdfftnKcb1RCY0XE+DrUKQwOmMr4zCcoYj//LOYcxB//hpnKLwOpVMpoe6UZ/r/5innINpnKOarZdQGuU87/yJkvBfv3pfGPTCLGnUHr15ds92MCSyoIzh+/LiV43rr5hra11CnsH7QVsZhvNw17kEKjNYQxllMZDHnIP4lPxoN89/HDEWecg7iFZROpTQsLLUJ+w4oQsZ78e59adwDs6hRd9DuZ++zz4I6gmvXrlk5rvYR6tEIXfK9c1sZh2koX/LhjVDG+fnPYs5BvJuo1vznq2XUnfK+8s9TzmEadQdNpTMUgPsdMF8toeZMLnkqSsZhGspHqJt1B9fe3LLdjAn6FuDFaHFx0cpxhwXlotaLyfsySb6gsJVxGO1LPrzRqTjzz2LOQeYqZRyYq6jNH3A7lft5hiRPOYdpDl5uopXboZh+/ytKxmGadQcL1TIWtM5Q1B1c3+rZbsYEFtQRdLtdK8c9ffwQHvj+m3H3yYaV49t28oY6PnTnMbz31JHEj2Ur4zA31Ofwkffcgve/60bbTbHCqZTwc/ecjPX8s5hzmJ+95yROHztkuxnWfPTu78GRA7MPKOQt5yA/+Z4Tqgvqn/jB47i81p76t6JkHObHf+Aojh1esN0Ma2572wHcdmQBO70+KuXsLLQQY/J9Ud51113m7NmzVo596dIlHDt2zMqxKR3MWAfmrANzLj5mrIPNnEVk2Rhz1/jvs1Pa51CtVrPdBEoYM9aBOevAnIuPGeuQxZxZUEfQarVsN4ESxox1YM46MOfiY8Y6ZDFnFtQRHD2avVdfUryYsQ7MWQfmXHzMWIcs5syCOoILFy7YbgIljBnrwJx1YM7Fx4x1yGLOfCgxgn6/j1KJfZIiY8Y6MGcdmHPxMWMdbObMhxIT8Oyzz9puAiWMGevAnHVgzsXHjHXIYs4coSYiIiIiegs4Qp2A5eVl202ghDFjHZizDsy5+JixDlnMmSPURERERERvAUeoE/DMM8/YbgIljBnrwJx1YM7Fx4x1yGLOHKGOgE8TFx8z1oE568Cci48Z68BdPgrm/PnztptACWPGOjBnHZhz8TFjHbKYMwvqCE6ePGm7CZQwZqwDc9aBORcfM9YhizmzoI7g8uXLtptACWPGOjBnHZhz8TFjHbKYMwvqCBqNhu0mUMKYsQ7MWQfmXHzMWIcs5syCOoLNzU3bTaCEMWMdmLMOzLn4mLEOWcyZBXUEfJK4+JixDsxZB+ZcfMxYhyzmnL0W5Ui1WrXdBEoYM9aBOevAnIuPGeuQxZxzvw+1iFwF8Iqlw98A4JqlY1M6mLEOzFkH5lx8zFgHmzm/3RhzZPyXuS+obRKRs9M296biYMY6MGcdmHPxMWMdspgzl3wQEREREUXAgpqIiIiIKAIW1NF82XYDKHHMWAfmrANzLj5mrEPmcuYaaiIiIiKiCDhCTUREREQUAQtqIiIiIqIIWFDvg4g8LCIXRGRLRJZF5F7bbaL4iMgnReQ/ROQNEbkqIk+KyPfZbhclR0Q+JSJGRL5ouy0ULxG5WUSeGFzLWyJyTkTus90uio+IlEXks7778gUR+X0RqdhuG+2fiLxXRL4uIpcG388fG/u7iMhnROSyiLRF5Jsicoel5rKgnpWIfBjA4wA+D+BOAE8B+AcROWG1YRSn9wH4EoAfAXA/gB0A/yQiDZuNomSIyN0AHgLwvO22ULxE5DCAbwMQAA8AeBeAXwTwus12Uex+A8DHAXwCwDsB/NLg50/abBRFtgjgRbh5tqf8/dcB/Crca/qH4F7X/ygiB1JroQ8fSpyRiDwN4HljzEO+3/0PgL8xxvDiLSARWQRwHcCDxpgnbbeH4iMihwA8A7eg/m0ALxpjHrHbKoqLiHwewH3GmB+13RZKjoj8HYAVY8zP+H73BICmMeaD9lpGcRGRdQCPGGP+cvCzALgM4IvGmM8NfrcAt6j+NWPMn6fdRo5Qz0BEHABnAHxj7E/fgDuaScV0AO61smq7IRS7L8PtDP+z7YZQIh4E8LSIfE1EXheRZ0XkkcHNmIrjXwH8mIi8EwBE5Hvhzi7+vdVWUZJOArgJvnrMGNMG8C1Yqse4vmg2NwAoA7gy9vsrAN6ffnMoJY8DeBbAv9luCMVHRB4CcCuAn7bdFkrMOwA8DOAxAH8A4N0AvjD4G9fLF8cfwh34OCciPbi1zeeMMV+y2yxK0E2D/06rx46l3BYALKj3a3ydjEz5HRWAiDwK4B4A9xhjerbbQ/EQkdvhPgdxrzGmY7s9lJgSgLO+5XjfEZHb4K6vZUFdHB8G8FEAPwXgP+F2nB4XkQvGmL+w2jJKWmbqMS75mM01AD2Mekaet2Gyl0Q5JyKPAfgIgPuNMf9ruz0Uqx+GO+P0oojsiMgOgPsAPDz4ec5u8ygmrwE4N/a7/wLAh8iL5Y8A/LEx5qvGmBeMMV8B8Cj4UGKR/d/gv5mpx1hQz2AwkrUM4ANjf/oA3N0+qCBE5HG4ox33G2PO224Pxe5vAZyGO5Ll/e8sgK8O/s1R62L4NoDbx353CsArFtpCyanBHezy64E1TpFdgFtUD+sxEZkHcC8s1WNc8jG7RwF8RUT+He6X9S8AOArgz6y2imIjIn8Kd13tgwBWRcTrAa8bY9bttYziYoxZA7Dm/52IbABoGWNetNMqSsBjAJ4SkU8D+BrcrU4/AeBTVltFcXsSwG+KyAW4Sz7uBPArAP7KaqsoksEOW7cOfiwBOCEi74b7PX1RRP4EwKdF5DyAlwD8FoB1AH9tpb3cNm92IvIw3P0Pb4a7R+IvG2O+ZbdVFBcRCbooftcY85k020LpEZFvgtvmFY6IPAB3vfztAC7CXTv9BcObX2EM9h3+LIAPwZ3yfw3ubNPvGWO2bLaN9k9E3gfgX6b86QljzMcGu/X8DoCfB7AE4GkAH7c1KMKCmoiIiIgoAq4vIiIiIiKKgAU1EREREVEELKiJiIiIiCJgQU1EREREFAELaiIiIiKiCFhQExERERFFwIKaiIiIiCgCFtRERERERBGwoCYiIiIiiuD/AemRoiyrDTzgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Функция создает набор координат x,y для построения зигзагообразной линии, которая изображает пружину \n",
    "def get_spring_line(length, coils, diameter):\n",
    "    x = np.linspace(0,length,coils*2)\n",
    "    y = [ diameter*0.5*(-1)**i for i in range(len(x))]\n",
    "    return np.array([x,y])\n",
    "\n",
    "xy = get_spring_line(10, 10, 1)\n",
    "plt.plot(xy[0],xy[1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WvCRP87HFCboMceGVkhKb3k87Gpll54lOAyuZWeONW1+auxQLsxdOq13ZNnlJnrwkTz6SJS/J03xsceYqF4ny6uy0z4lkrI3M8oT/hIGVGGd43Po7je/gibIn8FLNS9jfvn9K4/Fl2+QlefKSPPlIlrwkT/OxRQ96QkKC0SVYyvz5840uwTKGs7TCBaIcpjtuXbZNXpInL8mTj2TJS/I0H1v0oAcCAaNLsJTGRnPeTCceDWd5/ER8zH8+04bHrT9X9Ryernga7xx8Z9KhQLJt8pI8eUmefCRLXpKn+ZAdZjgpKSlRpaWlRpdhGbquy7h+JsNZ7juyD3vb9hpdTtyYaNy6bJu8JE9ekicfyZKX5MmLiMqUUiXTacMWv43+/n6jS7CUiooKo0uwjOEsu7xdBlcSX8Ydt350P3bv3m10aZYi73VekicfyZKX5Gk+0oMuhAm8UP0Cen29RpdhCTMx37oQQggxEelBj5D0oPMqKyszugTLGM7SO+A1uBJrcHQ6oh63LiYm73VekicfyZKX5Gk+0oMuhAk8UfYEFKz/XjSSQ3MgOzUby3KXTXu+dSGEEGIi0oMeIelB51VeXm50CZZRXl4OX9AnJ+dMHJ2OCX82qA/iWN+xMePWZXrLicl7nZfkyUey5CV5mo/0oIuoydXefHRdR2t3K95pfMfoUqxBAaDon5biSsGCjAVYMVfGrY8k73VekicfyZKX5MlLetAj5PP5jC7BUmpra40uwTJqa2vR4+0xugzLcPRO3IM+mf5AP+qPybj10eS9zkvy5CNZ8pI8zccWPegbNmxQ8ucbPl6vF8nJyUaXYQlerxeVbZU43HXY6FKsIQjW+yPbfdy6vNd5SZ58JEtekicv6UGP0MDAgNElWMqRI0eMLsEyjhw5IjO4MNK8vLu00ePWX6x50Vbj1uW9zkvy5CNZ8pI8zYexr8m8nE5brOaMyc7ONroEy8jOzkZda53RZViGSozdXwQVFHq8PdjTugd7WvfYYty6vNd5SZ58JEtekqf52OLMVdd1o0uwlP7+fmRlZRldhiX09/djYFD+wsOFggTlmplhe8Pj1uuP1cPlcCFvVh5WzF2BnNScGXn9mSDvdV6SJx/JkpfkaT62OEEXvORKbz6apiE4aI/hEjNBkTHX1AQGA2jpbkFLd4ulxq3Le52X5MlHsuQleZqPLU7QiaYw75qYUEJCgtElWEZCQgIG1aDRZViHCY4xw+PWj/Udw87GnUhPTsfi7MVYlrcMTi2+drnyXuclefKRLHlJnuZjgsNZ7MkQF14ej8foEiyjt6/X6BIshQbM9WF85Lj1p3Y/heeqnkNFcwX6A/Fx8zR5r/OSPPlIlrwkT/OJr+6cKZKLRHnl5uYaXYJlpKSnADLdNhs90dwfxuNt3Lq813lJnnwkS16Sp/nYogc9EAgYXYKltLS0GF2CZbS2thpdgqVwT7MYS8Pj1l+tfRVP7n4Sr+1/DYc7zTUfvrzXeUmefCRLXpKn+djiRkXFxcWqrKzM6DIsIxgMyl8lmDQda8Ku5l1Gl2EdOuK+24FASE9Ox6LsRSjMKzR03Lq813lJnnwkS16SJy+5UVGEfD6f0SVYSnV1tdElWEZzQ7PRJViKo8dhdAnTNjxuvaq1yvBx6/Je5yV58pEseUme5mOLHvSSkhJVWlpqdBlCjFF9pBo1bTVGlyHiRDyMWxdCCLuTHvQI9ffHx4wJ8UKGC/E5ckBur8zJ0Rn/PeiTmelx6/Je5yV58pEseUme5iM96EIY6N3Gd3Go85DRZYg4Z6Zx60IIYXfSgx4h6UHnJZ+0+XQekjkWOVm9B30i441b3928O+px67qu45577sHKlSuRl5eHb33rWyguLsazzz4bo8rtRfadfCRLXpKn+UgPuhAGer3udbT3tRtdhrCwSMet9/b2YsOGDRgYGMBtt92G4uJiBAIBvPDCC7j//vtx8cUX4+9///sMVi6EEPHJ1D3oRHQDETUSkY+IyohoS5jlLxxazkdEB4nouum2Oczr9U51NcQ4qqqqjC7BMvrb5a87nBzd9uxBn8xp49bLJx63fu6556KwsBD79+/Hddddh40bNyI9PR133nknqqurUVpaimuuucaANbAO2XfykSx5SZ7mE5MedCK6GsAfANwA4M2h758FsFopNWZeOSIqALAXwP8AeBjA+UPfP6aU+ttU2hxJ5kHn5ff7kZiYaHQZlrCtZhvcXrfRZVjHIAA5R4/IyHHrla9X4vrrrkdLSwtSUlJOLjPyvb57925s2bIFR48eRVpamlFlxzXZd/KRLHlJnrzM3IP+VQC/VUo9opTap5T6EoA2ANdPsPx1AI4opb40tPwjAH4H4JZptHmS3EmUV3OzzN3NJdAj2yYnrd8Wl9WwGDlu/c/P/xmf/8LnTzs5B05/r69fvx5Lly7FQw89NNOlWobsO/lIlrwkT/NhP5oRkQtAMYAXR/3oRQCbJnjaeeMs/wKAEiJKmGKbJ8ndsXjNmTPH6BIsw5kq2yYnlWT9a2pioed4D1avWj3m8dHv9RUrVqCpqWmGqrIe2XfykSx5SZ7mE4vuplyE/sg8+sq3dgBzJ3jO3AmWdw61F3WbRHQNEZUSUenRo0fhdrvR1taG1tZWdHV1oaGhAV6vFzU1NdB1HeXl5QBOXclcXl4OXddRU1MDr9eLhoYGdHV1obW1FW1tbXC73WhqaoLH40FtbS2CwSAqKytPa2P4e1VVFfx+P+rr69Hb24vm5mZ0dHSgo6MDzc3N6O3tRX19Pfx+/8lxYKPbqKysRDAYRG1tLTweD5qamgxbp+7ubsutk1G/p6A3eHLmkdO+q6G7YgYBrU8DBQhavwbyEshP0DwaMABovRqgA46ucdrA0JjswaE2BgjaCQ3kI5Bv6N8DBK1PAwZPjd8e00aXA9CHXmsA0DwayE8g71BNgaE2gkM1q3HamKl16rPgOs3A7+nKS65ET0/PmPdTXV3dae+nWbNmoaCgwLTvJ7PvI7q7uy23Tkb9no4fP265dTLy99TY2Gi5dTLy98SBfQw6Ec0H0ArgAqXUGyMevx3Ax5VSReM8pw7A75VSPxjx2IUAXgMwD6EPElG1OdK6detURUXFtNZLnNLR0YG8vDyjy7CEl8pfQrfqNroMyyAfSS/6FOx4eQfeffZdvPnGm6c9PvK93tPTg4WLFuJnj/8M5647V+ZbnwLZd/KRLHlJnrzMOgbdjdClWqN7tvMwtgd82NEJlg8COD7FNoUQQkRg44Ub0XioEY899ti4P1dK4ZZbb0HJBSVInZ16ar71PVObb10IIcTk2E/QlVIBAGUALhv1o8sAvD3B03YAuHSc5UuVUgNTbPMkXdfDLSKi4PP5jC7BOoJGF2AtNEhGlxCXnAlO3Pyjm/HFm76Iu+++Gx6PB0DovX748GF88lOfxPa3t+PTt3z6tOf1D/TjwLEDeK7qOTxd8TR2NOzAcc9xI1YhLsi+k49kyUvyNJ9YTrP4e4SmQnwLoVlaPgdgjVLqEBE9CgBKqX8fWn54msVHAPwKwGaEpln8+KhpFidsc7J61q9fr3bv3s29mrbV29uL9PR0o8uwhO17t6PD32F0GZZBAwSVIENcpuro4aN4/OePo3JnJZYULEF2VjZ2796NrR/Yio9+4aNITk2OqB0HOZCdmo1ls5dhYfbC2BYdR2TfyUey5CV58uIY4hKTAYRKqceJKAfAdxAaQ74XwFUjTqQXjVq+kYiuAvBThKZNPALgpuGT8wjbnFAwKN2UnNrb2+WNzCR4Ihijd6E9kU9O0Kdj7sK5+PI9X4an14OO1g7kJObgmgXXwJXoiqqdQTWIY55jOOY5hp2NO0/Ot273ceuy7+QjWfKSPM0nJj3oZiM3KuIlNzTgs6thF5q6m4wuwzrkRkW8YpBnSkIK5mfOx8q5K5HiSgn/BAuRfScfyZKX5MnLrBeJmo6MreJVV1dndAmW4enwGF2CpTj65OycUyzytPO4ddl38pEseUme5mOLHvSSkhJVWlpqdBlCjFF7tBZVrVVGlyGE4WTcuhDCKqQHPUL9/TIFGCcZLsSn/aDMEspp+MY7gsdM5jk8bv2dxnfwRNkTeLH6RdQerUVQt841RLLv5CNZ8pI8zUd60IUwUEtXC3Yc3GF0GUKYmp3HrQsh4o/0oEdIetB5ySdtPs11zUaXYCnSg87LLHlaZdy67Dv5SJa8JE/zkR50IQwUCAbwdOXTRpchRFyScetCCDOSHvQIeb1eo0uwlMrKSqNLsIx91fuMLsFSHF3m6PG1CrPnGW/j1mXfyUey5CV5mo8tetBlHnRewWAQTqd9bzbCKRgM4uk9T0NXutGlWIMOm3Q7zJA4ztOM49Zl38lHsuQlefKSHvQI+f1+o0uwlAMHDhhdgmUcOHAADs3cvZTxRPPYYpc2Y+I5TzOOW5d9Jx/JkpfkaT62+LjkckV3m2oxufz8fKNLsIz8/Hw0HGzAwOCA0aVYgp4sf4ngZJU8A4MBtHS3oKW7xdBx67Lv5CNZ8pI8zccWJ+jBoDnHI8Yrt9uNtLQ0o8uwBLfbjURnIvoHZKYhDppfg55gjZNKM7BinsPj1o95jmFn406kJ6VjUc4iFOYVwqnF9pAo+04+kiUvydN8bHGCrmnx+2daM5I3MZ+0tDQkDiQCch0zC5Vg/WtqZpLV81RQ6PH1oKq1ClWtVTEfty77Tj6SJS/J03xscYJuhwthZ9LAgAzH4DIwMGCaC9gswVqdvcazWZ7D49YPHDuABEcC5syagxVzViAnLYelfdl38pEseUme5mOLE3TBS9dtdtSOIV3XkZWSZXQZlkGKoCAfyLnYOc+BwYEx49YLZhdgcfbiKbcp+04+kiUvydN8bHGCLkNceKWkSI8vl5SUFKQnpxtdhmUopz1PJmNF8gwZOW59V+OuKY9bl30nH8mSl+RpPrY4c5WLRHl1dnYaXYJldHZ2YlbSLKPLsAzyk9ElWIrkOdbIcetP7X4Kz+15Drubd6M/EP5Cb9l38pEseUme5mOLHvSEhASjS7CU+fPnG12CZQxn6dAcGNQHDa4m/lllWkCzkDzDi2bcuuw7+UiWvCRP87FFD3ogEDC6BEtpbGw0ugTLGM4y0ZlocCXW4DghN33iJHlGZ3jc+qv7X8WT5U9i2/5tONR56OTPZd/JR7LkJXmaD9lhhpOSkhJVWlpqdBmWoeu6jOtnMpzltv3b4Pa4jS4n/ikAMiqDj+TJgkBIT0rHwqyFWD53ecznW7cDOQ7xkjx5EVGZUqpkOm3Y4rfR3y83geFUUVFhdAmWMZxlepJcKMrB0SU9vpwkTx7D49b3Ve+Lety6GJ8ch3hJnuYjPehCmECTuwm7Du0yugwhxAyLxXzrQghjSQ96hKQHnVdZWZnRJVjGcJbzM0+/QEfz+ZB6qM2IkuKao1N6fDlJnrzGyzPcuHUxPjkO8ZI8zUd60IUwib+V/w26Cs2a4erswdm3P4Q3H/y2wVUJIYxAIMxKmoXF2YtROCe6+daFEMaSHvQISQ86r/LycqNLsIyRWSYnJJ/8dyA7A06f34iS4pr0+PKSPHlFk6eCQq+vF1VHTs23Xt5cLuPWh8hxiJfkaT62+Egud8jitW7dOqNLsIyRWWYkZ+BE4MTJ/yuS6TOiNZglc8lzkjx5TSfP/oF+NBxrQMOxBhm3DjkOcZM8zccWPeg+n8/oEiyltrbW6BIsY2SWebPyDKzEGhy90uPLSfLkxZXnuOPWj9tr3Loch3hJnuZjix50l8tldAmWUlBQYHQJljEyywVZC1DRcmqqK92VAFd3LwKZ0U3BmPdOJRK7enH4yi1sdcaLwVTp8eUkefKKRZ6DahBujxtujxu7mnbZZty6HId4SZ7mY4se9IGBAaNLsJQjR44YXYJljMwyxZUCGnFXmN6CfOTu3hdVexn7m3DWTx/Fkmdf4yoxrmheW+zSZozkySvWeY4et/7snmctO25djkO8JE/zscXe1+m0bi+CEbKzs40uwTJGZ5mUkHTy352rlyG7+kDEbSUddePs7z2I7b+6HY6APT+UqkTrz0o1kyRPXjOdp3fAi4ZjDXiu6jn8veLveLvhbRz3HJ/RGmJFjkO8JE/zscUJuq7rRpdgKTIrDomWYJ8AACAASURBVJ/RWWanntpJHlu/ChkNLRG14+z1YMuX78ZbP7k16iExVkJBubCWk+TJy8g8BwYH0Nrdaplx63Ic4iV5mo90LYuoaZotPtfNiNFZLsxaiNbuVgCAb24unCci2GkGgth6/Q9Q+p1r0b9wbizKjBuKpMeXk+TJyyx5jjdufVH2Iiyfszxuxq3LcYiX5Gk+7L8RIkokogeJyE1EJ4joGSLKD/Oc24hoFxH1EtExIvoHEZ0xapnfEpEa9fVOhDVNZ5XEKAkJCUaXYBmjs1yQueC0/1O4G4npOrbecAf2Xvuv6Fq74uTDweQkuNzdUdez6Wv34qz/+m3UzzMNOcbwkjx5mTDP4XHre4/sjatx63Ic4iV5mk8sdhf3A/gIgI8D2AIgHcCzRDTZ/FJbATwMYBOAiwEEAbxMRKMHRb0MYN6Ir6siKUiGuPDyeDxGl2AZo7PUNA1JzqQJlh5r89d+jENXXoCjF5x+w7KeZYswe3dNVLWsv/sRnJg3GxkHmqN6npnQgHwY5yR58oqHPONl3Loch3hJnubD+rcsIsoA8DkAn1VKvTT02KcAHAJwKYAXxnueUuqKUe18CkAPgM0A/jHiR36l1NFo65KLRHnl5uYaXYJljJdldmo2jvSErqjXnU5o/T7oKWNP2kvueBhdK5eg8SOXjflZ5+qlyK4+gNbLNkVUx6pf/xVOnx+7bvsCLrzm9ijXwjz0RPkwzkny5BVveQ6PW2/tboWDHMhKzcLS3KVYnLPY6NLkOMRM8jQf7h70YgAJAF4cfkApdRjAPoR6xyM1C6HaukY9fj4RdRBRHRE9QkQR3dklEAhE8dIinJaWyC5cFOGNl2V+1qkRYX2L5yO3cuwNJM546E/QHQ7UXHf1uO0eW7864gtMl/z9FeTsrceuO74IIIJhNSYm0wLykjx5xXOew+PW3216F0+UPYEXql/AvrZ9COpBQ+qR4xAvydN8uPcWcwEMAnCPerx96GeRegBABYAdIx77J4B/B3AJgK8BOBvAq0SUOF4DRHQNEZUSUWlXVxfcbjfa2trQ2tqKrq4uNDQ0wOv1oqamBrquo7y8HABQVlYGACgvL4eu66ipqYHX60VDQwO6urrQ2tqKtrY2uN1uNDU1wePxoLa2FsFgEJWVlae1Mfy9qqoKfr8f9fX16O3tRXNzMzo6OtDR0YHm5mb09vaivr4efr8fVVVV47ZRWVmJYDCI2tpaeDweNDU1GbZOhYWFllsno35PS5cuHbNO7iY3oABHjwNdK5ZidukBUICg9WsgL6HwD/+H9AOtKP/GtdB6NUAHHF2hEWSOztD3QS0HTp8Pjm4HMAhofRpogKCd0EA+AvlC/573WjkK/r4db/7XN0PLAsDQn+GH23J0OQAdodcaADSPBvITyDtUU4Cg9WmYVXcYmZVHQrV3nl6Po9Nxcp0QHKpnxDqRn6B5htqfYJ1Ofp9knaCFhhFofRowiJPrNKaNCNcJwaGaDVwn7YRm2DoBsNw6Gfl70tN0S6yT1qmh19eLfXv34andT+GZV59BaWMpqqqrZmxfvmTJElPty+P9+JSSkmK5dTLy98SBVAS9ZUR0F4Bvh1nsIgDzATwKIEGNaJiItgHYr5S6LoLXug/AxwCcr5Q6OMly8xEaOnO1UurJydpcs2aNqq6uDvfSIkKVlZU466yzjC7DEibK8pnKZ+AP+pF2qBVrf/4Ydtx7CwBg/qs7sfzPz2P7L28Hwlx1f+E1t2P7r++Y8OdZ1QdQ/MNf4+X//SHgOjUMbNNX70XFrZ9F/7zZEa9HUvtxXPy576L9nDNR9t2wb/OYcXQ5MJgld7/kInnyskOeCY4E5M3Kw4q8FcidFbthE3Ic4iV58iKiMqVUSfglJxbp4Oz7AfwhzDLNAM4F4ACQC+DYiJ/lAXg93IsQ0U8ROjm/aLKTcwBQSh0hohYAy8O1m5ycHG4REQV5E/OZKMvZabPR0t0Cz8J5SOzqBQDk7N6HVf/zFF757V1hT87DSWltR8mdv8C2R+447eQcAHqWLUTO7n0Rn6A7Pf3Y8uW78cYDt2HDvb+ZVl3TZfWTn5kmefKyQ54jx61rpCE7NTsm49blOMRL8jSfiI7ySim3Uqo2zFc/gDIAAwBOXrU2NMXiKgBvT/YaRPQAgE8AuFgpNXbQ7djlcwEsANAWblmZgJ/X8J9yxPRNlOWKOUNTJg6diKcdasWGe/4b23/5PSDCi571BCecPWOvzHf2eLD5q/firfu/iWB62pifH1+7HNk1DZGtQCCIrdfegdJvX4O+ZQtBBs+YNPxne8FD8uRltzx1pcds3Loch3hJnubDOgZdKdUD4DcAfkxElxLRegC/B7AHoSkSAQBEVEtEXxzx/58D+CxCUzN2EdHcoa+0oZ+nEdFPiOg8IlpCRFsRmt2lA8BT4epKSUnhW0mB4uJio0uwjImyzEnLgUaht6c2EMR5X78Pb/zsWwimRb4t9y1ZMOYCU80XwNbr78C7d9w4YQ+5+6wipDdGcMGQrmPrjXei+gsfPTkHuzL4ngOD2dbvoZxJkicvO+c50XzrJ/wnptSeHId4SZ7mE4tLyr8C4EkAjwN4C4AHwPuVUiP3TCsRGgYz7AaEZm55BaEe8eGvW4Z+PghgLYCnAdQB+B2A/QDOU0r1hStIetB5ySdtPpNlmZWSBQBoP+dM7PzPL8M3JyeqtjtXLUNOVf2pB3QdF95wJ6pu/AR6ipZO+LxgRhocgYGw7W+65Sdovnwz2rZuPPkYKQVMoRd93Y9+g4X/fDPq541mtx7KWJM8eUmepwzPt/783udPzrfu7hs9v8TE5DjES/I0H/YJwpVSPgBfGvqaaBma7P/jLO8FcMVky0xGetB5ySdtPpNluSRnCY6fOI7q6z82pbbd64uQv23nyf+f/+W7cfCDl6B98/optTdSyZ2/QM/yRTj4r6e/Lf2Z6Ug93I4Ti+dF3FbRf/8NmQcOIaHfi8PvOX9addm5hzIWJE9ekuf4xhu3Xji7EAuzF074HDkO8ZI8zSd+J2WNgtfrNboESxme7khM32RZLslZMq22+xfMgas3NAb97O/8DO71q3DoAxdF9NzJhqqc8dCfoIjG/eDQXbgIsyv2RVzjkqdfRW7lfrz2i+8hpe1Y+CeEcXKqSMFC8uQleYY3PG694nDFpMvJcYiX5Gk+tjhBT0qK/NbpIrwVK1YYXYJlTJalpmlITUyd9muced/vEJiVitr/+HDEzxlMTISrs2fM40v/+gLSG1smnEqx84zlyKxtjOg15ry1GwVPv4o3H/gm4HSy3CBpcJb0UHKSPHlJnpGblzn5X+HkOMRL8jQfW5ygy51EeTU3NxtdgmWEyzI/M3/Sn4fj6vEgpf04Kr7xuaie17s0H7PLa057bP62nVj40tt4+8e3TPAs4PhZKzHr0JGw7WfWNGDtw49h+8Pfm/aUkc5eDzRf6D2u9dtilzZjJE9ekmfkiuYUTfpzOQ7xkjzNxxZ7C2eE09KJyMyZM8foEiwjXJZFcyc/SIXz9o+/hnd+9NWon9e5uhDZ1aemWsyprMXq/34S2x/67qQn1MG0FDgGJr/ANKXtGDbe8TBee/h70JNcJx9XRFFfYOr09OOKq7+GwsefD7WRNP1eeHGK5MlL8oxMgiMBaUljp4AdSY5DvCRP87HFCfrgoPxZkVN3d7fRJVhGuCxdThfSEic/UE3Gs3jBlJ7n3lCE9IOHAQCph9qw4YeP4LVf3T7mpkbRcvZ4sPnme/DWfV9HMOP09fLlZCL9YATTOw4LBnHhdXei+tr/h8z6UO8PBYyd5tFqJE9ekmdk5mWEv8hcjkO8JE/zscUJujbNP6GL08mYfj6RZFmQUzADlZzONzsbTq8Prs4ebL71x1HPwT6e0Bzsd2LX7Tegf8HY3pqe5YuRuzvCC0x1HRfe8APs+9yH0PSBi5DccRwAoBzSQ8lJ8uQleUbmjPlnhF1GjkO8JE/zkTNXIUzu5F1FZ5gWHMSFN/4A79wV3RzsA6kpSGo/fvqDQ3Ow773xY+hevWzc5x1fuxxZ+yO7wHTTrT9ByyXn4chF5wCaxnKBqRDCeMkJySwXxwsR72xxgq4bfPtxq/H5fEaXYBmRZKlpGjKTM2egmtMFU5JQ8ZVPo3fF4qie11O4ELNH9YSff/M9aPyXi3F084YJn3d87UqktrSHbb/4rl+iZ+lCNFz9njE/o8HohhAUPvY80hpbo3qOnUSbp5ic5Bne4pzI9jdyHOIleZqPLU7QHQ6Ze5ZTZubMnyxaVaRZFuYVxriSsd546Ds4dvbaqJ/XuboQWTWnLjDd+L0HcXztCjT9y8WTPk9PcoHCfJhe84s/AwqovvHjpz0+fIGpckXek774mW1Y+Yd/IP+VdyJ+jt1Ek6cIT/IMb9W8VREtJ8chXpKn+djiBD0YDBpdgqW0t4fv5RSRiTTLgtwC0CQ3DzIT97oipDeGLvZce/+jCKYkY98XPjrtdpf+9QVk1h0adw52b14OMuqaQL7IMsrbUYGlT72MNx64DZn1h6Zdm1VFmqeIjOQ5ufSkdDi1yC5El+MQL8nTfGxxgu5yucIvJCK2aNEio0uwjGiynJ02O4aV8AlkZ8Dp82P5H/+BtCMd2P3Nz0f83InGks97bRcWvfAm3vqvW8f9efeKJcitqIWeEn44W0btQZz54J+w/Re3o3dpPpI6ZfaCiUSSp4ic5Dm55XnLI15WjkO8JE/zscUJuoyt4lVXV2d0CZYRTZZn5p8Zw0p4Jbm7Me+Ncuy4J7o52AMZs5By+Ohpj2VV1WHNI0/gtYdvn3AO9tAFpk1w9E0+nC2l7RjOvv3neO0XQ3Owa1poeIwYV7g8RXQkz4kREZbOXhrx8nIc4iV5mo8tTtCTk5ONLsFS1q6NflyyGF80WWalZCEpIT6mwtr32Q/h9Ye+HfVdQrsLF512gWnqoTaU3PWrsHOwH1+zHKmt7RjMnPieB87eiedgj1owiPd86CbMfrdqeu2Y3GR5iuhJnhOblx5+7vOR5DjES/I0H1ucoPf39xtdgqWUlZUZXYJlRJtlNH8CNtKhD1wETOEOvp1rlyNr30EAgKu7NzQH+wO3hZ+D3eUEKQVH5wQ9lIEgtl5/J0q/d/24c7AjEMV1KkNzsLvPXBn5vO1xasI8xZRInhNbt3BdVMvLcYiX5Gk+tjhBT0mZ3g1WxOmKi4uNLsEyos1yRd6KuLlYdCrcZxVh1qEj0Hw+XHDDD7DzBzfBNzc3oucqIgxmj9NDqeu46LrvY+91V6NrzdjZcE7My0POvgMR17jp6/+FlovPwb7/+DAyDzRH/Lx4NG6eYsokz/GlJaZFPfe5HId4SZ7mY4sTdOlB5yWftPlEm6WmaVH/KTieBNNS4AgEsPW6O7Hnpk+iZ+WSqJ7vcI/98LL5Kz9C4wcuwtEt4x+AuosKkL2nPqL2N9z1K/QumY+Gj12FEwvnILG7N6r64o30+PKSPMcXyZ1DR5PjEC/J03xscYIuPei85JM2n6lkeVb+WTGoxDxSjh7HgY9egY5zo1tPf2Y6kvtaTnus5Pafo3NNIZo+eMmEz3OftRKZdU1h21/9y8eh6Tr2fvHfQg9EOb5+pLx3KqHFwcXr0uPLS/Icy6k5sTB7YdTPk+MQL8nTfGxxgu71eo0uwVIqKyuNLsEyppJlWlIaUl3WvRX28888hOb3XRj183qWL8act/af/P/aB/6AwSQX9l3zr5M+r3vFYqS0uyddpuBvLyGrthGl37v+tMenMgNM3o4KbPrGfZi7w/zvI0eX9PhykjzHWpKzZErPk+MQL8nTfGxxgp6UFB8zX8SLNWvWGF2CZUw1y7ULLHzF/RR7po+vXY6MQ6Gx5Mv/+BzSWo5i921fCP9Ep3PC+dcBYO7rpVj8/Ot4676vj/mZ0jRovkDENWbsb8KZD/4Ru7/2GWRXN4R/gsEGM6THl5PkOdba/Knty+Q4xEvyNB9bnKD7/X6jS7CUAwciv6BOTG6qWS7MXgiXQ27ANZL7zJVIa2rHgpfexvzXd2HHj6Kbg308WVV1OONXf8Vrvxh/DvYTC+Yge29k49eTjrpx9vcexOsPfxftZ69FRsPhadfHZTBIGO8ziuaxxSFixkiep5s9a3bEdw4dTY5DvCRP85naOyPOyJ1EeeXn5xtdgmVMJ8vV81ajoqWCsZr4pqckIcXtRtHv/4FX/ucHUfXEKyJA1097Tsrhoyi561fY9sgdE87B3lVUgNyqOrhLJu99cvZ6sOXLd+Otn9yKQGY6ACDBcyLi+ji1HJyFih1zcbA2C437snD0cBoGB0PrnZw6gEWFPVi6qguFazqxcdMRJEHufslFT5YsR9q4eOOUnyvHIV6Sp/nY4gQ9GIxijmMRltvtRlraNG/0IgBML8vlc5aj6kgVBnX5s/mwY2euxu5vfDrqOdi9s7ORUd98ctYYV3cvNt8yNAd7+sS/H/dZRVj1v09O3nggiK3X/wCl37kW/QvnRlXXGLqOC268C+/855cRyM6I/GmDwI6XF+L5x5ajfm/OhMt5TyRgf2Uu9leGpra88qqD8DoI7/u3OiwqtPaMNTNB82vQE+QkHQCyU7KjnlpxJDkO8ZI8zccWf2/TpjHbghhL3sR8pptlYd7Yeb3trPxb10FPif6ak57CxcitqAUAaL4ALrjhB3j3zi+FnYO9t3Ahko53T7yArmPr9Xdg77X/iq61K0770VQuMD3vm/fB1dOH2WXVET+n5eAsfPuzl+CBb5876cn5eA41peO1fxTg1k9cjkd/eiYCPtmXTodKmPhaB7spWVIyrefLcYiX5Gk+ttjbqkkuABPRGxgYMLoEy5hulmfMOwMa2eJtHJkpdk66z1qBrP2NobuEXn9H5HOwh/nwv/mr96LpvRfi6AVjT0aUwwGtP/KpFjf88Nfoy5+HfZ/9ELKrw48XVQp4+ncr8Y1PXoaGmuyIX2ek1NTQ9ql0wrN/XIlbP3E5DuzNmlJbAlPePq0mIykDGcmR/wVoPHIc4iV5mo8c2UXUdF2OMlymm6WmaVicvZipmvhHamp3We1aXYjU1nZsuemHaPjI5VHNwT7RDDAldzyMzlVL0fThS8f9ed/i+citrI3oNVb96i/Q/APYe9O/4dj61cg42DLp8roO/PIHJfjjg2diIDD1qf1crtO3z7bmWfj+tVtR8facKbdpZ1PdPq2mePH059yW4xAvydN8bHGCLkNceMmNn/hwZLlu0ToQ5MAPAMo5tb+W6UkuZNQfwrHiNVHPwa6IgFHXuZzx0B+hJzix79r/N+HzuooKkFMVfgaYJU++jOyaBpTecSMAIJCbCYdv8pmpfv2fxdj2TEEE1U+uo2Ps9hnwO/HjWzZj767Z027fbqa6fVpJWmIactKiG2o1HjkO8ZI8zccWZ65ykSivzs5Oo0uwDI4snZoTi3OkFx0AyD/1Dyqv/uYu1H72Q1E/r39uLrL2N538/7I/P4/0piMo/9Y1kz7Pvb4IGQeaJ11m7htlWPLcdrz1029EXM/zjxXi1aeXRrz8ZFasGH/7HAg48JNbN+F4ezLL69jFdLZPq1i/cD1LO3Ic4iV5mo8tTtATEhKMLsFS5s+fb3QJlsGVZfGiYtAULjq0mulMY+cpWDCl53WvXILcitAdTOe/uhP5r+7E2/d+LfzrLZyHxO6JZ0bJqj6AM375l3HnYJ9oWE1bcxoe+znfTax27px4++z3uPDLu6Z3oZ/d2H2axbTENMzNmOZMRkPkOMRL8jQfW5ygBwKR3+lPhNfY2Gh0CZbBlaWmaViWu4ylrXjmODHzt1J3r12JzLpG5Ozeh1X/+xS2P/zdyOZgn2SZlMNHUXLnL/DaL7477hzsgwkJcPZ4TntMKeAXd5bA7+ObPfc975l8+6zcMRev/n0J2+tZnRHbp5mcU3AOW1tyHOIleZqPLU7Qk5Kin3ZNTKyoqMjoEiyDM8uz8s+Cg+x9AjCYPvNzwnetXorM2kZs+NFvsO1X3496DvbRnD0ebL7lx3jr/m9OOAd7X8GCMReY7n5rLmoreMeF/+lP4bfPvz6yBsGg/PUmEkZsn2aRnZqN7NSpzSY0HjkO8ZI8zccWJ+j9/f1Gl2ApFRVy90ounFlqmoZVc1extRePHF0GfEBxOqEcGt548FtRz8GuNA0InLpGRvMFsPX6O/HuHTeif97EJ9udq5YhZ9RUi//35+XR1R2BL34x/PZ5vD0FO1+RuxBGwpDt0yTOW3oea3tyHOIleZoP+wk6ESUS0YNE5CaiE0T0DBFNuvcmou8TkRr1dXTUMjS03BEi8hLRa0Q0+f21h8jVybw2bNhgdAmWwZ3lqvmrkOCw7zUXg9nG9FC+/Kcfwzc7+t7B/vl5yKkemslF13HhDXdiz5c+gZ6iyS/yHH2B6fH2ZOx5l3/qw5/9LLLt87Vnl7C/thUZtX0abX7GfKS4eI/DchziJXmaTyx60O8H8BEAHwewBUA6gGeJwv7tfT+AeSO+Rl/p9HUAXwPwJQAbAXQAeImIZoUrSHrQeZWVlRldgmXEIkuuWRLikaMzvnoou1YWIGdP6ALT8798Nw5+6FJ0nLcu7PP6F8yBq/fUGPTq0tlQOv8wk5tvjmz7rCmfjUEZ5hJWvG2fHAiEjUs2srcrxyFekqf5sJ6gE1EGgM8BuFUp9ZJSqhzApwCcCWD8u3WcElRKHR3xdWxEuwTgZgD3KKX+ppTaC+DTAGYB+ES4uqQHnVdx8fRvMiFCYpHl4pzFSEu0522b462H0r2uCJn1zTj7Oz+De8NqHHr/1im1c7A2Nnf3vP/+yLbPAb8DLY3pManBSuJt++RQkFsAl9PF3q4ch3hJnubD3YNeDCABwIvDDyilDgPYB2BTmOcuJaJWImokoj8T0ci/8RYAmDuqXS+A1ydql4iuIaJSIiptaWmB2+1GW1sbWltb0dXVhYaGBni9XtTU1EDXdZSXlwM49SmyvLwcuq6jpqYGXq8XDQ0N6OrqQmtrK9ra2uB2u9HU1ASPx4Pa2loEg0FUVlae1sbw96qqKvj9ftTX16O3txfNzc3o6OhAR0cHmpub0dvbi/r6evj9flRVVY3bRmVlJYLBIGpra+HxeNDU1GTYOpWXl1tunYz6PQ3nyb1OWf2hEzZHtwMYBLQ+DTRA0E5oIB+BfEP/HiBofRowOLQsTvXynfze5QB0QOvVgAFA82ggP4G8BK1fAwWG2ggCjh4HoMZpo3Po8R4HEByqJzD0fC+B/ATNM9R+rwbop8brjmlrknVydjjjap08OQWY92Y5BhLTUPvvH4rq94QBOtnWwX1ZuPbaSiQlBXH11bWYN8+Dyy9vwurVbmzc2IbNm1uxfHkX3vveBuTmevHJT9ZA03TcdFNo2xvuKb/ppnJomo5PfrIGuble3Hvvdixf3oXNm1uxcWMbVq924/LLmzBvngdXX12LpKQgrr02tO2lehHx78mK214k6+TodFhunSb7PTl8DuRpeTHZl5eWlppqXx7vx6c333zTcutk5O+JA6kJ5tOdUmNEnwDwKIAENaJhInoVQL1S6toJnnclQr3htQDyAHwHQBGANUqp40S0CcBbABYrpZpHPO9/ACxQSl0xWV0lJSWqtLR0eisnTtJ1Xe7OyiSWWe5o2IGW7slvCW85Coi3m6ou+fsraPrgJVE/74Lr78CbP/0G9KQkXP/e9+J4O/9fCjVNh65Htn1+5PM1uPq6avYaLCUOt8/pOLfgXCzMXhiTtuU4xEvy5EVEZUqpad0oIqLfBhHdNc5FnKO/tk7WBEK7pnEppf5PKfUXpdQepdTLAN43VNunRy8aTbvDfD5fuEVEFGpra8MvJCISyyzPKTgHGtlrh+vojb8xvlM5OQcAz4K5yNkTusA04I/Nen/iE5FvnwN+e21rUxGP2+dUZSRnxOzkHJDjEDfJ03wi3aPeD2BVmK93ARwF4ACQO+r5eQDaIy1KKeUBUA1geN6w4RldRt+CLKJ2XS7+8W92VlBQYHQJlhHLLDVNw1n5Z8WsfTMaTLXPGN+uVUuRs6cOAKA5+P4SOtI//xn59qk5Y1ODldhp+zy/8PyYti/HIV6Sp/lEdIKulHIrpWrDfPUDKAMwAOCy4ecOTbG4CsDbkRZFREkIDXFpG3qoEaGT9MtGLbMlknYHBgYifWkRgSNHjhhdgmXEOsvCvEL26c3MTPPapxc3dIHpIQBAWnps7pZ8zjmRb5+xqsFK7LJ9Ls1dGvP9jhyHeEme5sO6t1BK9QD4DYAfE9GlRLQewO8B7AHw8vByRFRLRF8c8f+fENGFRFRAROcAeAJAKoDfDbWrEOrF/yYRfZiIzgDwWwAeAH8KV5dzmnf2E6fLzua7G5zdzUSWm5dtjvlrmIVKtE8vbl/BAiR1dgMAlqzojslr1NVFvn3GqgYrscP2maAloHhx7GcEkeMQL8nTfGLxcf4rAJ4E8DhCF3Z6ALxfKTXyb3srcfowmHwAjyE0F/qTAPwAzlVKHRqxzL0A7gPwcwClCM2VfrlSqi9cQbquT3llxFgyrzyfmcgyMyUTC7NiNxbUTMhOc3FrGl5/4FsAgKWrumLyEnl5kW+fS4tiU4OV2GH7jMWc5+OR4xAvydN82LuWlVI+hG4m9KVJlqFR//9YBO0qAN8f+hIGkiu9+cxUlucuPRdHK45iYNDaw70UWb+HciQ9JQkAsPyM4zFpPxCIbPuct6gPaRnW3rY4WH37zE3LxYKsBTPyWnIc4iV5mo8tfiOh+xwJLgkJ9r2VPLeZzPL8ZbG9aMsUbLFHG2vFmceRO/cEe7snTkS2fW66/DD7a1uShbdPBzmwZfmWGXs9OQ7xkjzNx8K7i1NkiAsvj8cTfiERkZnMMndWruWHutCAPT+Maxpw6YcOsrebnx9++3Q4dFzyQf7XtiIrb59nF5wNpzZz13vJcYiX5Gk+tjhBl4tEeeXmjp5FU0zVTGd57masBQAAIABJREFU9pKzkeCwbk+JnmjfD+OXf7QByam8w0yqqsJvn5uvaEbuXC/r61qVVbfPvFl5yM/Kn9HXlOMQL8nTfGxxgh4IyPRfnFpabHZ3yhia6Sw1TbP0rC52mcZuPGkZA/j0VypY27zggsm3z1mZfnzq5j2sr2llVtw+HZoDWwpnbmjLMDkO8ZI8zcd6e4txJCYmGl2CpRQWFhpdgmUYkeXsWbORnzmzvV0zRU+zZg9lpC7+YBPWbWoLv2CEnn568u3zc98oR0a2n+31rM6K2+e5BecacoGhHId4SZ7mY4sTdJ/PZ3QJllJdXW10CZZhVJbnLTsPSc4kQ147lhw99rmV+kSu+04pcubwTJn26U9PvH1e/C8Hseky6XWLhtW2z3np8zA/c74hry3HIV6Sp/lQaPZCayspKVGlpaVGlyGEqXh8Hvyz+p9QsP4+wG5am2bhjmsvRPfx5Ji0f+6lh3Hzf74DzVrnmyIKLocL7z/z/TI9nxDjIKIypVTJdNqwxTtLJuDnVVZWZnQJlmFklmlJaVi3cJ1hrx8Ljk45YwSABUv6cOd/b8O8RWHv4zapm28eu31e+uEGOTmfIittnxcVXWToybkch3hJnuYjPehC2Nz2uu3o6OswugwRAwGfhj/9fC3+7/HlUPr0pvjLzPHimm+VoeRCvjHuIj6ty1+H5XOWG12GEKYlPegRkh50XvJJm48ZstxSuMUyUy9aqYeSgytJx2e+Vok7fr0NK89yR/38m28uQ0LiIC7/6AHc95cX5OR8mqywfebNyjPFybkZ9p1WInmaj/SgCyHQ3d+Nl/a9ZHQZIsYOVGdh2zMF2PPOHLS3pk24XIJrEEtWdOO8Sw/jgvceQnqWTFUrZNy5EJHi6EG3xR18vF65iQanqqoqrF271ugyLMEsWWamZGLtgrWoaq0yupRpcXQ7MJg5aHQZplW4pguFa7oAAJ7eBDTWZqGtOQ0DAQc0TSE5bQBLlncjf1kvnE4leTKL9zwvWmnsuPORzLLvtArJ03xs0YNeXFys5M83fPx+v8wtz8RsWb514C0c6TlidBlTNwgg/kcRmIfkySuO81y/cD0K88wzV7bZ9p3xTvLkJWPQIyR3EuXV3NxsdAmWYbYsNxduRlrixEMfzE7rt8UubcZInrziNc8lOUtMdXIOmG/fGe8kT/OJz71FlJxOW4zkmTFz5swxugTLMGOWlxRdAkeczqGnkqz/F8GZJHnyisc8M5MzsXHJRqPLGMOM+854Jnmajy1O0AcH43fMnxl1d3cbXYJlmDFLl9OFi1ZeZHQZU0KB6U0lKE4nefKKtzxdDhcuKbrE6DLGZcZ9ZzyTPM3HFifoZrmoxSqSkqx3i3ijmDXLrJQsbFxsvl6zcJQj/noozUzy5BVPeWqk4bLVl5n2+GnWfWe8kjzNx5zvPCGE4ZbkLsHS3KVGlyGEMMD5y85HiivF6DKEsC1bnKDrum50CZbi8/mMLsEyzJ5l8eJizJkVP2MTaTC+hhCYneTJK17yXLtgLeZkmPt9b/Z9Z7yRPM3HFifoDkd8XvBmVpmZmUaXYBnxkOUFKy5ARnKG0WVERLniZwhBPJA8ecVDnoWzC1E0t8joMsKKh31nPJE8zccWJ+jBYNDoEiylvb3d6BIsI16yvLToUiQnJBtdRljki48eynghefIye54LMhdg/aL1RpcRkXjZd8YLydN8bHGC7nK5jC7BUhYtWmR0CZYRL1lqmobLV1+OBEeC0aVMSk+R4WycJE9eZs4zJzUHm5ZtMrqMiMXLvjNeSJ7mY4sTdBlbxauurs7oEiwjnrJ0OV24fPXl0Mi8uw1Hnwxn4yR58jJrnrOSZuHioouNLiMq8bTvjAeSp/mQUuYfEzddJSUlqrS01OgyhLCErv4uvLLvFShYf98hhNUlJSThvWe817TTKQoRj4ioTClVMp02bPGO7O/vN7oESykrKzO6BMuIxyyzUrKwdcVWEMw3ntbRac4eynglefIyW54JjgRcsfqKuDw5j8d9p5lJnuYjPehCiCk51ncM2+u2S0+6EHEowZGAq864Ci6nXKMlBDfpQY+Q9KDzkk/afOI5y9mzZuPCFReaqifdbD2U8U7y5GWWPF0OV9yfnMfzvtOMJE/zkR50IcS0dPR14PW616UnXYg44HK4cOUZV8b1ybkQZic96BHyer1Gl2AplZWVRpdgGVbIMm9WHrYs32KKnnRHlzl6KK1C8uRldJ5WOjm3wr7TTCRP87FFD3pxcbGSP9/wCQaDcDqdRpdhCVbKsr2nHW8ceMPYnnQdNul2mCGSJy8D83Q5XbhyjTVOzgFr7TvNQPLkZcoedCJKJKIHichNRCeI6Bkiyg/znCYiUuN8PTdime+P8/OjkdTk9/unu1pihAMHDhhdgmVYKcs5GXNwcdHFhs6TrnnkbJKT5MnLqDyTEpIsdXIOWGvfaQaSp/nEYm9xP4CPAPg4gC0A0gE8S0ST/W1vI4B5I742AFAA/jJquf2jllsbSUFyJ1Fe+fmTft4SUbBaltmp2bhi9RVwasb0xOjJ5r1TYzySPHkZkeespFl47xnvtdTJOWC9fafRJE/zYT1BJ6IMAJ8DcKtS6iWlVDmATwE4E8ClEz1PKXVMKXV0+AvAVQB6Afx11KLBkcsppY5FUlcwGJzS+ojxud1uo0uwDCtmmZaUhivXXolEZ+KMv7bmlx5fTpInr5nOc3babLxnzXvicp7zcKy47zSS5Gk+3O/aYgAJAF4cfkApdRjAPgCbImmAiAihk/w/KKVGz4+4lIhaiaiRiP5MREsjadOKOycjpaWlGV2CZVg1yyRnEq5aexVSXakz+roqwfrX1MwkyZPXTOa5MGshtq7cOmOvN9Osuu80iuRpPtxnrnMBDAIY/VGsfehnkbgMQAGA/x71+E4AnwFwJYAvDLX3NhHljNcIEV1DRKVEVNrR0QG32422tja0traiq6sLDQ0N8Hq9qKmpga7rKC8vB3BqLtDy8nLouo6amhp4vV40NDSgq6sLra2taGtrg9vtRlNTEzweD2praxEMBk9eBT3cxvD3qqoq+P1+1NfXo7e3F83Nzejo6EBHRweam5vR29uL+vp6+P1+VFVVjdtGZWUlgsEgamtr4fF40NTUZNg6DQwMWG6djPo9BQIBy63T8O/JqTmR589DVnJWaP5nBTh6HEAQ0Po0UICg9WsgL4H8FBqfOwBovRqgn5rxYnju6JPfux3A4FAbAwTthAbyUeirn0KP9WnA4NCy47XR5QD0odcaCI0NJj+BvEM1BYbaCA7VrMZpY4bWSTuhGbdOJyy4Tkb+nvSZWadFqYswV5tr+n3EyDai3e/5fD7LrZORv6ejR49abp2M/D1xiGgWFyK6C8C3wyx2EYD5AB4FkKBGNExE2wDsV0pdF8Fr/RXAYqXU2WGWSwNwEMA9Sqn7Jlv2rLPOUjKFEJ/W1lYsWLDA6DIswS5Zvt3wNlq7W2P+Olq/Bj1Fxk1zkTx5zUSe6xeuR2FeYUxfwwzssu+cKZInL45ZXCK9kut+AH8Is0wzgHMBOADkAhg5PjwPwOvhXoSI8gD8C4Abwy2rlPIQUTWA5eGWlSEuvFJSUowuwTLskuWmZZtQ21aLqiNVMX0d5ZQhGZwkT16xzFMjDecvOx9zMubE7DXMxC77zpkieZpPRGeuSim3Uqo2zFc/gDIAAwgNUwEADE2xuArA2xG81GcA+AH8OdyCRJQEoAhAW7hl5SJRXp2dnUaXYBl2yrJoXhG2FG6J6TSM5Df+ZklWInnyilWeic5EXHnGlbY5OQfste+cCZKn+bAeKZVSPQB+A+DHRHQpEa0H8HsAewC8PLwcEdUS0RdHPnfo4tDPA/izUqpvdNtE9BMiupCICojoHABPAEgF8LtwdSUkJExntcQo8+fPN7oEy7BblnMz5uI9a94DlyM2U77JtIC8JE9escgzJzUH71v7PqS47NUDard9Z6xJnuYTi66srwB4EsDjAN4C4AHwfqXU4IhlViI0DGakrQgNV3lkgnbzATyG0FzoTyLU036uUupQuIICgUAU5YtwGhsbjS7BMuyYZWpiKt5/5vuRmZzJ3rbjhNyanpPkyYs7z8LZhaGbg9lwGKcd952xJHmaT0QXica7kpISVVpaanQZlqHrui0PCLFg9yxLD5Wi0c14YFAAZFQGH8mTF1OeBMLGgo1YnL14+o3FKbvvO7lJnrw4LhK1xW+jv3/0dOpiOioqKowuwTLsnmXJ4hJsWrqJbVz68PR4gofkyYsjz0RnIi5fc7mtT84B2XdykzzNR3rQhRCG8wV92Fa7DR6/x+hShDCt+Rnzcd7S86SnUwiTkx70CEkPOq/hCfnF9EmWIUnOJFx5xpUoyC2YVjvDN3IRPCRPXlPNk0DYuHgjNhdulpPzIbLv5CV5mo/0oAshTOVI9xHsOLgDupIZRIRITkjGxUUX226WFiHimfSgR0h60HkN3yZXTJ9kOdb8zPl4/5nvR0ZyRtTPlR5fXpInr2jzXJS9CO87035TKEZC9p28JE/z+f/t3X10XHd95/H3V0+WZVl2FD8ojuPH2E7sKI5jhdRJCXbAgLNJQwhdYJdTUnbJobQsW9qyJ4eW5LRpabtdSA7bbaF7dmkLC1kWeralyxLIkoVN0oBk4hgbxY6xo/ghdoSt2IqePJ7f/nHHYazoYSR/pd/VvZ/XOXNsje6Mf/PW1finn+7c0Qq6TJhe7e1HLce27/g+nj38LIEKn6d01hFf6umrwp41VTXctOqmXL3x0ETpudOXevrSCnqFBgYGYg8hUzo7O2MPITPUcmxrF6/l9tbbmVs/t6Ltq09rxdeTevqqpOfl8y7nzo13anI+Dj13+lLP9MnFCvr1118f9OsbP/39/cyePTv2MDJBLSv3k2M/Yc/RPWOvpheAmmkbUvapp68xetZU1XDT6ptY3KSJeSX03OlLPX1pBb1CZ8+ejT2ETDl69GjsIWSGWlbu6suu5rbW22ic1TjqNlX9uXhKmzbq6Wu0nkvnL01WzTU5r5ieO32pZ/rkYm2kpiYXD3PaNDc3xx5CZqjlxDTUNbDjmh3sP76fZ488+7ozvYRZ2f+N4HRST1/De9ZV17Fl9RYWzV0UaUQzl547faln+uRieaRY1OnaPOmsOH7UcnLWLF7DndfdyZJ5Sy643gp6RaMn9fR1vqdhrGtZx53X3anJ+STpudOXeqaPlpZlwvRKbz9qOXk1VTXcfOXNnHr1FE8ceIL+s/0E04qvJ/X0FSywoHEBN6++mbqautjDmdH03OlLPdMnF18RM60CeaqtrY09hMxQy4t3yZxLuP3a22m9vBWr0ve6q1z8DzE96mvquW7ZdWxbt02Tcwd67vSlnumTi6dfHeLiq7e3N/YQMkMt/VzVchWbLtvE0vlLYw8lM+ysfuC5WFVWxfrL1nPHxjuoKeqX1l703OlLPdMnF88WepGorwULFsQeQmaopa9FCxexqnEVfUN9PH3wabp7u2MPaUYrztLixsVY1ryMG5bf8NrhA/p+96OWvtQzfXKxgj40NBR7CJly+PDh2EPIDLX0db5nQ10D29Zt461Xv5Wm+qbIo5q5dJrFyVk0dxF3bLyDG1feeMGxvfp+96OWvtQzfXLxRkWbN28OHR0dsYeRGYVCQb+VcKKWvkbr+dIrL9H+Qjv9Z/sjjGoGK5KTZRwfl865lDeseAON9SOfq1/f737U0pd6+tIbFVVoYGAg9hAyZc+ePbGHkBlq6Wu0ni3zWrj92tvZsmoLDbUN0zyqmav6lfHfml5g/uz5vHX9W7n1qltHnZyDvt89qaUv9UyfXKygt7W1hfb29tjDEJGUOP7KcXa+uJPeQb0wSiZvYeNC2pa3jTkpF5H80Qp6hXQCfl86XMiPWvqqtOfieYvZcc0Obr3qVubPnj/Fo5q5qk9qBX04w7h8/uXcsfEOtq7bOqHJub7f/ailL/VMH62gi0june4/TUdXh876IqOqsipWXLqCjVdspKZKx+qKyOi0gl4hraD70k/aftTS12R7Ns1uYtu6bdy18S5WL1ytCViJVtChvrae1iWt3HXdXWxevvmi9g19v/tRS1/qmT5aQRcRGcGLJ1/kx0d/rOPUc2ph40I2Lt3IJXMuiT0UEZlhtIJeof5+nVrN0+7du2MPITPU0pdnzyuar2DHNTvYsWEHS+Ytocpy8XR5geqefK2g11XXsa5lHXdvuput67a6T871/e5HLX2pZ/rkYgVd50H3NTg4yKxZs2IPIxPU0tdU93zhZy+w7/g+evp7puzfSJVzQMbn6FVWxaVzLmX9kvUsmrtoSv8tfb/7UUtf6ulLK+gV0juJ+urq6oo9hMxQS19T3XP5pcvZvn47d2+6m/WXrc/8OdWr+rL7X8QlDZfwhhVv4O7rk9XyqZ6cg77fPamlL/VMn1y8EkrvjuVr8eLFsYeQGWrpa7p6VlVVsWHJBjYs2UDfUB97j+3laM9RBguD0/LvT5dQn63fsDbOamTVwlWsWbiGqqrp/+FD3+9+1NKXeqZPLmau586diz2ETOnp6aGpqSn2MDJBLX3F6NlQ10Db8jZYDgNDAzx3/DkO9xymb2jmnz3KhoxQO3Mn6WbG/NnzWda8jFULV0U/O4++3/2opS/1TJ9cTNBjrJRkWX19fewhZIZa+ords76uno1XbGTjFRspFAscfPkgL5x8gVf6X6EYilHHNhmheuZNzmura1nYuJDVC1fTMq8l9nAuEHv/zBK19KWe6ZOLCbqIyHSrqaphzeI1rFm8BoCTr57kYPdBTpw5wauDrxKYeZPfNKqyKubWz2Vx02LWLFpDQ122XxcgIvmQiwl6sTjzVq7SbGBgIPYQMkMtfaW5Z/OcZprnNL/2cfeZbg797BAnzpygb6gvlRN2O2epG1d1VTVN9U20NLWw4tIVNNY3xh5SxdK8f840aulLPdPHfYJuZvcC7wU2AfOAlSGEQxXc7m7gD4DVwAHgEyGEvyv7vAH3A/cClwBPA78eQtgz3n1XV2f8PGHTbP78+bGHkBlq6Wsm9VwwdwEL5i547eOevh4OnzrMy70vc2bgTCpecBrq4k7OzYz6mnrmzZ7HwrkLWda8bEavkM+k/TPt1NKXeqbPVKygNwCPAv8T+EwlNzCzLcAjJBPwrwPvBL5qZjeHEJ4ubfZx4LeAe4DngE8C3zazdSGEM2Pdf6FQmMTDkNEcP35cLyZxopa+ZnLP+Q3zmd9w4X+SJ189yZGeI3T3dtM72MtQYWhaj2W3gel7kWi1VVNfW8/82fNZOHchl19y+YyejI9kJu+faaOWvtQzfabsjYrMrA34IRWsoJvZI0BzCGF72XXfAV4OIby3tHp+FPiPIYQ/LH1+NnAC+O0QwufGun+9UZEvvaGBH7X0lYeexWKRn736M7rPdHOq/xRnBs7Qf7afQrGA+/O58xsVVVkVdTV1NNQ10FTf9NpkfPgPJlmVh/1zuqilL/X05fFGRWk5Bn0L8Nlh130L+I3S31cCLSQr8wCEEPrN7HvATcCYE3QdW+Vr3759tLa2xh5GJqilrzz0rKqqYuHchSycu3DEz/cN9dHT38OZ/jP0DvbSN9THwNkBhs4NUSwWORfOUQxFiqE47oS++kw15+aPfJpawzBLLlVUUVVVRW11LbNqZjG7djYNdQ3MmTWHubPmMm/2POrrdJaIPOyf00Utfaln+qTl/IMtwPFh1x0vXU/Zn2NtcwEzu9fM2s2svaenh+7ubo4dO8aRI0c4deoUBw4coL+/n71791IsFtm5cycA51fad+7cSbFYZO/evfT393PgwAFOnTrFkSNHOHbsGN3d3Rw6dIje3l46OzspFArs2rXrgvs4/+fu3bsZHBxk//79nD59mq6uLk6cOMGJEyfo6uri9OnT7N+/n8HBQXbv3j3ifezatYtCoUBnZye9vb0cOnQo2mNqbW3N3GOK9XXasGFD5h5TzK/TvHnzMveYJvp16vppF03VTcwamMXyOcu5svFK1s9bz01Lb2J943retu5tXDXrKt553TtZbav55c2/zMqwkjta72BFWMGODTtYW7eWN1/5Zq5eejU3L72Z65uv54ZFN3DL0lu44dIb2LFuB9fMuYY7r72T1VWrecemd3B54XJ2XLODea/OY8vqLVT1VHHFvCs4feI0QwNDmd/3KnlMra2tmXtMsb5OV199deYeU8yvU3Nzc+YeU8yvk4eKDnExsweBT4yz2bYQwuNlt5nIIS5DwL8KIfxt2XXvBz4XQqg3s5uAJ4BlIYQXy7b5r8BlIYS3j3X/69evD3v37h1n+FKpjo4ONm/eHHsYmaCWvtTTl3r6Uk8/aulLPX1N5yEuDwFfHGebrosYx0u8fiV8ET9fMX+p9GcL8OIo24yqoSFbLzSKTd/EftTSl3r6Uk9f6ulHLX2pZ/pUdIhLCKE7hNA5zuVi3tf6KWD7sOu2A0+W/n6QZJJe/iLSeuCNZduMqq9v5r/ldproBbd+1NKXevpST1/q6Uctfaln+rifxcXMWkhWutcDXwL+GckZWLpCCCdL2zwG/CCEcF/p45uA7wG/B/wdcBfw+8Avnj/Nopn9O5LDbO4B9gG/C9wCjHuaxba2ttDe3u76OEVEREREhvM4xGUqXiT6IeBHJJNzgH8sffxLZdusBi47/0EI4UngPcD7gWeBXwHeXXYOdIA/BT4N/DnQXrr9W8ebnAP09/dP9rHICM6/OEIunlr6Uk9f6ulLPf2opS/1TJ8pOw96mug86L4KhQI1NWk5Q+fMppa+1NOXevpSTz9q6Us9faV1BT11vE55I4nnn38+9hAyQy19qacv9fSlnn7U0pd6pk8uJuh1dXWxh5ApS5cujT2EzFBLX+rpSz19qacftfSlnumTiwl6oVCIPYRM6e7ujj2EzFBLX+rpSz19qacftfSlnumTiwl6VVUuHua0aWxsjD2EzFBLX+rpSz19qacftfSlnumTi5lrHl4IO53Onj0bewiZoZa+1NOXevpSTz9q6Us90ycXE3TxVSwWYw8hM9TSl3r6Uk9f6ulHLX2pZ/rkYoKuQ1x8NTQ0xB5CZqilL/X0pZ6+1NOPWvpSz/TJxcxVLxL1dfLkydhDyAy19KWevtTTl3r6UUtf6pk+uZig19bWxh5CpixZsiT2EDJDLX2ppy/19KWeftTSl3qmTy4m6ENDQ7GHkCkHDx6MPYTMUEtf6ulLPX2ppx+19KWe6WN5OMNJW1tbaG9vjz2MzCgWizqu34la+lJPX+rpSz39qKUv9fRlZh0hhLaLuY9cfDX6+vpiDyFTnnnmmdhDyAy19KWevtTTl3r6UUtf6pk+WkEXEREREXGiFfQKaQXdV0dHR+whZIZa+lJPX+rpSz39qKUv9UwfraCLiIiIiDjRCnqFtILua+fOnbGHkBlq6Us9famnL/X0o5a+1DN9tIIuE6ZXe/tRS1/q6Us9famnH7X0pZ6+tIJeoYGBgdhDyJTOzs7YQ8gMtfSlnr7U05d6+lFLX+qZPrmYoNfV1cUeQqasXLky9hAyQy19qacv9fSlnn7U0pd6pk8uJuhnz56NPYRMOXr0aOwhZIZa+lJPX+rpSz39qKUv9UyfXEzQa2pqYg8hU5qbm2MPITPU0pd6+lJPX+rpRy19qWf65GKCXiwWYw8hU3RWHD9q6Us9famnL/X0o5a+1DN9cjFBF196pbcftfSlnr7U05d6+lFLX+qZPrn4iphZ7CFkSm1tbewhZIZa+lJPX+rpSz39qKUv9UyfXEzQdYiLr97e3thDyAy19KWevtTTl3r6UUtf6pk+uZig60WivhYsWBB7CJmhlr7U05d6+lJPP2rpSz3TJxcT9KGhodhDyJTDhw/HHkJmqKUv9fSlnr7U049a+lLP9LEQQuwxTLnNmzeHjo6O2MPIjEKhoN9KOFFLX+rpSz19qacftfSlnr7MrCOE0HYx95GLFfSBgYHYQ8iUPXv2xB5CZqilL/X0pZ6+1NOPWvpSz/TJxQp6W1tbaG9vjz0MEREREck4raBXSCfg96XDhfyopS/19KWevtTTj1r6Us/0cV9BN7N7gfcCm4B5wMoQwqFxbvNB4FeADSQ/NPwI+L0Qwv8r2+YB4P5hNz0eQmgZb0xaQRcRERGR6ZDWFfQG4FHggQncZivwCPBm4EbgOeBbZrZm2HbPAZeVXVoruXOtoPvST9p+1NKXevpST1/q6Uctfaln+kzZMehm1gb8kApW0Ee4rQHHgD8MIXy2dN0DwLtCCNdMdCxaQRcRERGR6ZDWFXQPdUA9cGrY9avM7IiZHTSzr5jZqkrurL+/332AebZ79+7YQ8gMtfSlnr7U05d6+lFLX+qZPmmdoD8I9AJ/X3bd08A9wA7gg0AL8KSZXTrSHZjZvWbWbmbtPT09dHd3c+zYMY4cOcKpU6c4cOAA/f397N27l2KxyM6dO4Gf/5pn586dFItF9u7dS39/PwcOHODUqVMcOXKEY8eO0d3dzaFDh+jt7aWzs5NCocCuXbsuuI/zf+7evZvBwUH279/P6dOn6erq4sSJE5w4cYKuri5Onz7N/v37GRwcfO2bZPh97Nq1i0KhQGdnJ729vRw6dCjaY1q7dm3mHlOsr9OVV16ZuccU8+s0Z86czD2mmF+nurq6zD2mmF+ntWvXZu4xxfo6rVq1KnOPKebXae7cuZl7TDG/Th4qOsTFzB4EPjHOZttCCI+X3WZSh7iY2UeBPwDeEkL4wRjbNQI/Bf44hPDpse6ztbU16KdDP/v372fNmuEvD5DJUEtf6ulLPX2ppx+19KWevjwOcan0baMeAr44zjZdFzMQeG1y/iCwY6zJOUAIodfM9gDj7lF6dyxfixcvjj2EzFBLX+rpSz19qacftfSlnulT0cw1hNANdE/lQMzsY8DvA7eVn15xjO3rgauA74637blz5y5+gPKanp4SifnEAAAOtklEQVQempqaYg8jE9TSl3r6Uk9f6ulHLX2pZ/q4H4NuZi1mdh2wtnTVejO7zsyay7Z5zMw+Vfbx7wB/DHwA2Fe6jxYzm1e2zZ+Z2ZvMbKWZ3Qj8D2AO8NfjjamqKq2H2s9M9fX1sYeQGWrpSz19qacv9fSjlr7UM32mYub6IZI3GvpS6eN/LH38S2XbrCY5j/l5vw7UkpwL/VjZ5eGybZYCXyY5F/rXgUHgF0IIL/g/BBERERGRONwPzg4hPMA4b1IUQlgx1sej3OY9kx1TsVic7E1lBAMDA7GHkBlq6Us9famnL/X0o5a+1DN9cnHsR3V1dewhZMr8+fNjDyEz1NKXevpST1/q6Uctfaln+uRigl4oFGIPIVOOHz8eewiZoZa+1NOXevpSTz9q6Us90ycXE/S6urrYQ8iUZcuWxR5CZqilL/X0pZ6+1NOPWvpSz/TJxQRdx1b52rdvX+whZIZa+lJPX+rpSz39qKUv9Uyfit5JdKZra2sL7e3tsYchIiIiIhnn8U6iuVhB7+vriz2ETOno6Ig9hMxQS1/q6Us9famnH7X0pZ7poxV0EREREREnWkGvkFbQfeknbT9q6Us9famnL/X0o5a+1DN9tIIuIiIiIuJEK+gV6u/vjz2ETNm1a1fsIWSGWvpST1/q6Us9/ailL/VMn1ysoG/evDno1zd+CoUCNTU1sYeRCWrpSz19qacv9fSjlr7U05dW0Cs0ODgYewiZ8vzzz8ceQmaopS/19KWevtTTj1r6Us/0ycUEXe8k6mvp0qWxh5AZaulLPX2ppy/19KOWvtQzfXIxQS8UCrGHkCnd3d2xh5AZaulLPX2ppy/19KOWvtQzfXIxQa+qysXDnDaNjY2xh5AZaulLPX2ppy/19KOWvtQzfXIxc83DC2Gn09mzZ2MPITPU0pd6+lJPX+rpRy19qWf65GKCLr6KxWLsIWSGWvpST1/q6Us9/ailL/VMn1xM0HWIi6+GhobYQ8gMtfSlnr7U05d6+lFLX+qZPrmYuepFor5OnjwZewiZoZa+1NOXevpSTz9q6Us90ycXE/Ta2trYQ8iUJUuWxB5CZqilL/X0pZ6+1NOPWvpSz/TJxQR9aGgo9hAy5eDBg7GHkBlq6Us9famnL/X0o5a+1DN9LA9nOGlrawvt7e2xh5EZxWJRx/U7UUtf6ulLPX2ppx+19KWevsysI4TQdjH3kYuvRl9fX+whZMozzzwTewiZoZa+1NOXevpSTz9q6Us900cr6CIiIiIiTrSCXiGtoPvq6OiIPYTMUEtf6ulLPX2ppx+19KWe6aMVdBERERERJ1pBr5BW0H3t3Lkz9hAyQy19qacv9fSlnn7U0pd6po9W0GXC9GpvP2rpSz19qacv9fSjlr7U05dW0Cs0MDAQewiZ0tnZGXsImaGWvtTTl3r6Uk8/aulLPdMnFxP0urq62EPIlJUrV8YeQmaopS/19KWevtTTj1r6Us/0ycUE/ezZs7GHkClHjx6NPYTMUEtf6ulLPX2ppx+19KWe6eM+QTeze83su2bWY2bBzFZUcJt7StsOv9QP2+7DZnbQzAbMrMPM3ljJmGpqaib3YGREzc3NsYeQGWrpSz19qacv9fSjlr7UM32mYgW9AXgUeGCCt+sDLiu/hBBeO3jczN4NPAz8EbAJeBL4ppktG++Oi8XiBIciY9FZcfyopS/19KWevtTTj1r6Us/0cV9aDiE8BGBmE331agghvDTG5z8GfCGE8Feljz9iZm8Hfg24b+IjlcnSK739qKUv9fSlnr7U049a+lLP9EnTV2S2mb1gZofN7Btmtun8J8ysDthMsjJf7lHgpvHu2Mx8R5pztbW1sYeQGWrpSz19qacv9fSjlr7UM33ScnD2c8AHgF3AXOCjwBNmtjGEsB9YAFQDx4fd7jjwlpHu0MzuBe4tfThoZj+eioHn1AKgO/YgMkItfamnL/X0pZ5+1NKXevpad7F3UNEE3cweBD4xzmbbQgiPT2YQIYSngKfK/r0ngWeAjwD/pnzT4UMb4brz9/l54POl+2u/2BPGy8+ppx+19KWevtTTl3r6UUtf6unLzC763TErXUF/CPjiONt0XeRYXhNCOFd6cGtKV3UD54CWYZsu4vWr6iIiIiIiM1ZFE/QQQjfT+KsPSw4av5bkkBdCCENm1gFsB75atul24GvTNS4RERERkanmfgy6mbWQrHSvLV213szmA10hhJOlbR4DfhBCuK/08f3APwH7gSaSw1quJTlDy3mfBv7WzH4APAF8CFgC/GUFw/r8xT4uuYB6+lFLX+rpSz19qacftfSlnr4uuqeFMOIh3JO/Q7MHgPtH+NSvhhC+UNrmEPB4COGe0sefAd5JMrF/BfgR8EDp2PTy+/4w8HGS86T/GPjNEML3XB+AiIiIiEhE7hN0ERERERGZvDSdB11EREREJPc0QRcRERERSZHMTdDNrNnMPmtmnWbWb2YvmtlfmNmlFdz2bjPba2aDpT/vmo4xp5mZ3Wtm3zWzHjMLZraigtvcU9p2+KV+6kecbpPpWbqd9s0RmNms0vd7t5m9amZ/b2ZLx7nNAyPsmy9N15jTxMw+bGYHzWzAzDrM7I3jbP+m0nYDZvZTM/vQdI017SbS0sy2jvIcedV0jjmtzOyW0vfykVKXeyq4TauZ/d/S//tHzOyTprcRn3BLM1sxyr759mkacqqZ2X1m9kMzO21mL5vZP5jZNRXcbsL7Z+Ym6CRndrmc5MWkrcD7gFuAL491IzPbAjwCfAm4rvTnV83sxikdbfo1AI8CD0zwdn0kL+Z97RJCGPAd2ow04Z7aN8f0EHA38F7gjSRngfqGmVWPc7vnuHD/bJ3KQaaRmb0beBj4I2AT8CTwTTNbNsr2K4H/VdpuE/Ap4LNmdvf0jDi9JtqyzAYu3A/3T+U4Z5BGkhNBfBToH29jM2sCvk3yvig3kJwJ7neAj03hGGeKCbUs83Yu3Df/j//QZqStwH8CbgJuBQrAd8ysebQbTHr/DCFk/gLcBhSBpjG2eQT49rDrvgN8Ofb403AB2kjetXVFBdveA/TGHnOaLxPsqX1z5C7zgCHgX5Zdd0Xpe/1tY9zuAeDHsccf+wI8DfzVsOv2A58aZfs/AfYPu+4/A0/FfiyxL5NoubX0/b8g9tjTfgF6gXvG2ebXgNPA7LLrfhc4QulkGLpU3HJFad9siz3emXAh+QHoHHDHGNtMav/M4gr6SJqAQZJV3dFsIVnZLPctkp+SZOJmm9kLZnbYzL5hZptiD2gG0745ss1ALWVtQggvAj9h/DarSr9mPGhmXzGzVVM4ztQxszqSfsP3q0cZvd1o+2GbmdX6jnDmmGTL89rN7JiZPWZm26ZkgPmwBfh+CKF8hfhbJL9RXxFlRDPf183shJk9YWbvij2YFJtLcjTKqTG2mdT+mfkJuiVvkvQHJKsbhTE2bSH59UO546XrZWKeAz4A3Ely6MEA8ISZrYk6qplL++bIWkhWLoa/y/F4bZ4m+S3PDuCDpW2ftApep5IhC4BqJrZfjbYf1pTuL68m0/IYyara3STvAfIc8JiZ3TJVg8y40fbN85+TyvUCvw38c5KjDx4DHjGz90UdVXo9DDwDPDXGNpPaP2fMBN3MHhzlhQvll63DbjMH+AeSXyN8vIJ/ZvhJ4W2E62a8ybSciBDCUyGEvw4hPBNC+D7wbuAA8BGvx5AmU92zJBf7Jrj0HLNNCOGbIYT/HkJ4NoTwHeB2kufC9/s+khlhovvVSNuPdH0eVdwyhPBcCOEvQwgdpefLDwP/m2RiJJOjfdNBCKE7hPAfQgj/FEJoDyF8Evgclc2hcsXMPg38InB3COHcOJtPeP+suYixTbeHgC+Os03X+b+YWSPJC5oAbg/jv0DxJV7/k8wiXv9TTxZMqOXFCiGcM7N2IKsr6FPdM0/7JlTe8xdIVi4XAC+XfW4RUPE7DIcQes1sD9ndP0fSTfLbh4nsV6PthwXgZ66jm1km03IkTwPv8RpUzoy2b0J2nyen09PAr8YeRJqY2WdIvl+3hRB+Os7mk9o/Z8wEPYTQzet/lT0iM5sLfJPkJ5S3hxB6K7jZU8B24N+XXbed5NX4mTKRlh5KpxK6Ftg1Xf/mdJqGnrnZN6HynmbWAZwlafHfStctBa5mAm0sOf3nVcB3JzPemSiEMFTqtx34atmntgNfG+VmTwHvGHbddqA9hHDWf5QzwyRbjuQ6kkNfZOKeAv7EzOrLFuO2A0eBQ9FGlR3aN8uY2cMkk/OtIYTOCm4yuf0z9itgp+AVtXNLMc6viLWUXerKtnuMslfYk7yYpwDcR/Kf9X0k//nfGPsxRe7ZQvLN+S9IfhVzW+nj5jFa3g+8DVhV2va/lFq+IfbjiX2ZZE/tm6P3/AuSQ9jeQnJ6u++SHA9YXbZNJ/AbZR//GfAmYCVwI/ANklfYL4/9eKa53btJzoLzr0l+qHmY5PjT5aXP/w3wN2XbrwReJfkNx9Wl2w2R/Ho3+uOZYS3/LckPO2tITrX4qdLzwTtjP5Y0XEjOjHFd6dIHfLL092Wlz38KeKxs+3kkq5RfAa4hOa7/NPBbsR9L7MskWr6/9P/T1cA6ksOuhoDfjP1Y0nAB/ry0b93KhfPLxrJtXPbP6A92CuJtLT3RjXTZWrbdIeALw277rtJ/5kMkZ4LI/ZMlySnpRmp5z2gtgc8AL5CcOecEyauVt8R+LGm4TKZn6TrtmyP3rAc+S3KIRR/Ja06uGLZNAB4o+/grJCsXQyST+68B62M/lkj9Plza3waBDuCWss89Djw+bPs3ATtL2x8EPhT7MaTlMpGWJMfzPk9yXuqTwPeB22I/hrRcxvh//Aulz38BODTsNq0kh7YNkKz23o9OsTjhliQT9L0kP4yfBtqB98V+HGm5jNJy+P8xLvunlW4oIiIiIiIpMGPO4iIiIiIikgeaoIuIiIiIpIgm6CIiIiIiKaIJuoiIiIhIimiCLiIiIiKSIpqgi4iIiIikiCboIiIiIiIpogm6iIiIiEiK/H/qEtGNRJ67nQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# матрица поворота \n",
    "nAz = lambda x: np.matrix([ [np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)] ])\n",
    "\n",
    "# создаем рисунок \n",
    "fig, ax = plt.subplots();\n",
    "plt.xlim(-2,2)\n",
    "plt.ylim(-1.5,0.5)\n",
    "ax.set_aspect(1)\n",
    "\n",
    "# полукруг (пластина) с центром в начале координат\n",
    "body1 = Wedge([0,0], 1.0, -180+np.degrees(q0[1]), np.degrees(q0[1]), fc='#AACCAA')\n",
    "# шарик\n",
    "body2 = Wedge([0,0], 0.1, 0, 360, fc = 'b')\n",
    "# пружина\n",
    "spring_xy = get_spring_line(1, 10, 0.1)\n",
    "spring    = mlines.Line2D(spring_xy[0], spring_xy[1], lw = 0.5, color = 'r')   \n",
    "\n",
    "# Функция init добавляет к рисунку четыре объекта: \n",
    "# пластину (полукруг), шарик (круг), пружину (ломаная линия) и еще один круг, \n",
    "# изображающий ось вращения.\n",
    "# Далее в функции get_frame СВОЙСТВА этих объектов будут изменятся (обычно это положение объекта)\n",
    "def init():    \n",
    "    # Пластина\n",
    "    ax.add_patch(body1)    \n",
    "    # Ось вращения\n",
    "    ax.add_patch(Wedge([0,0], 0.03, 0, 360, ec = 'black', fc = 'white'))\n",
    "    # Шарик\n",
    "    ax.add_patch(body2)    \n",
    "    # Пружина\n",
    "    ax.add_line(spring)    \n",
    "    return spring, body1, body2, \n",
    "    \n",
    "def get_frame(i):        \n",
    "    phi = solution.y[1, i] \n",
    "    x   = solution.y[0, i] \n",
    "    t   = solution.t[i]\n",
    "    \n",
    "    # положение шарика относительно неподвижной системы координат\n",
    "    r2 = n_r2(*[*params_list, t , x, phi, 0, 0]).astype(np.float).flatten()\n",
    "    \n",
    "    # положение точки А относительно неподвижной системы координат    \n",
    "    rA = nAz(phi)*(rhoA.subs(rules).subs(params).evalf())\n",
    "    \n",
    "    # Повророт пластины имитируем изменением углов, обозначающих начало и конец сектора\n",
    "    body1.set_theta1(-180 + np.degrees(phi))\n",
    "    body1.set_theta2(np.degrees(phi))        \n",
    "    body1.get_path()\n",
    "    \n",
    "    # Изменяем координаты центра шарика\n",
    "    body2.set_center([r2[0], r2[1]])    \n",
    "    body2.get_path()\n",
    "    \n",
    "    # Точки ломаной (пружины) заданы в системе координат, связанной с пластиной\n",
    "    # Используем матрицу преобразования координат для определения координат ломаной в \n",
    "    # неподвижной системе - в системе координат рисунка \n",
    "    spring_xy = nAz(phi)*get_spring_line(x-0.1, 10, 0.1)\n",
    "    # Подменяем спискок координат ломаной, которая еще в функции init была добавлена к рисунке\n",
    "    # Не забываем, что пружина начинается в точке А (добавляем координаты точки А)\n",
    "    spring.set_xdata(spring_xy[0] + rA[0])\n",
    "    spring.set_ydata(spring_xy[1] + rA[1])\n",
    "    \n",
    "    return spring, body1, body2 \n",
    "    \n",
    "anim = FuncAnimation(fig, get_frame, init_func=init, frames = len(solution.t), interval=50, blit=True)\n",
    "\n",
    "anim.save('animation.mp4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}