Pendulum Example

example_pendulum3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pendulum Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Michael Wollensack METAS - 09.09.2022 - 21.11.2025"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from metas_unclib import *\n",
    "use_linprop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Input quantities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_periods = 20\n",
    "\n",
    "T_meas = ufloatfromdistribution(\n",
    "    StudentTDistribution(24.9060, 0.0712 / np.sqrt(10), 9), \n",
    "    desc='Time N Periods Measurement / s')\n",
    "\n",
    "dT_react = ufloatfromdistribution(\n",
    "    UniformDistribution(-0.1, 0.1), \n",
    "    desc='Time Reaction / s')\n",
    "\n",
    "dT_res = ufloatfromdistribution(\n",
    "    UniformDistribution(-0.005, 0.005), \n",
    "    desc='Time Resolution / s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Length measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "L_meas = ufloatfromdistribution(\n",
    "    StudentTDistribution(0.33316, 0.00026 / np.sqrt(6), 5), \n",
    "    desc='Length Measurement / m')\n",
    "\n",
    "dL_res = ufloatfromdistribution(\n",
    "    UniformDistribution(-0.0005, 0.0005), \n",
    "    desc='Length Resolution / m')\n",
    "\n",
    "dL_read = ufloatfromdistribution(\n",
    "    TriangularDistribution(-0.0005, 0.0005), \n",
    "    desc='Length Reading / m')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diameter measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "D_meas = ufloatfromdistribution(\n",
    "    StudentTDistribution(0.1005, 0.000058 / np.sqrt(4), 3), \n",
    "    desc='Diameter Measurement / m')\n",
    "\n",
    "dD_res = ufloatfromdistribution(\n",
    "    UniformDistribution(-0.001, 0.001), \n",
    "    desc='Diameter Resolution / m')\n",
    "\n",
    "dD_read = ufloatfromdistribution(\n",
    "    TriangularDistribution(-0.0005, 0.0005), \n",
    "    desc='Diameter Reading / m')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Start angle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha0 = ufloatfromdistribution(\n",
    "    UniformDistribution(5, 15), \n",
    "    desc='Start Angle / deg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simplified measurement model with $\\sin\\alpha \\approx \\alpha$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gravitational acceleration in $m/s^2$\n",
    "\n",
    "$$g_{\\mathrm{approx}} = \\frac{4\\pi^2}{\\tau^2} \\frac{I}{ml}$$\n",
    "with\n",
    "$$\\tau = \\frac{T}{n_p}$$\n",
    "and\n",
    "$$\\frac{I}{ml} = L + \\frac{D}{2} +\\frac{D^2}{5 (2L + D)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = T_meas + dT_res + dT_react\n",
    "tau = T / n_periods\n",
    "L = L_meas + dL_res + dL_read\n",
    "D = D_meas + dD_res + dD_read\n",
    "\n",
    "I_over_ml = L + D / 2 + (D**2 / (5 * (2 * L + D)))\n",
    "\n",
    "g_approx = 4 * np.pi**2 / tau**2 * I_over_ml"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exact measurement model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gravitational acceleration in $m/s^2$\n",
    "\n",
    "$$g_{\\mathrm{exact}} = \\frac{16 K\\left(\\sin\\left(\\frac{\\alpha_0}{2} \\frac{\\pi}{180}\\right)^2\\right)^2}{\\tau^2} \\frac{I}{ml}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha0_rad = alpha0 * np.pi / 180\n",
    "\n",
    "g_exact = 16 * umath.ellipk(umath.sin(alpha0_rad / 2)**2)**2 / tau**2 * I_over_ml"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Output quantity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.827632967475108 ± 0.050571068931520406\n"
     ]
    }
   ],
   "source": [
    "print(g_approx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.86515500432206 ± 0.055216310403278\n"
     ]
    }
   ],
   "source": [
    "print(g_exact)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uncertainty budget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Description                     Distribution  Value      Standard Unc  Sensitivity  Unc Component  Index    Dof     \n",
      "--------------------------------------------------------------------------------------------------------------------\n",
      "Time N Periods Measurement / s  StudentT      24.906000      0.022515    -0.789178       0.017769  12.345%         9\n",
      "Time Reaction / s               Uniform        0.000000      0.057735    -0.789178       0.045563  81.175%  Infinity\n",
      "Time Resolution / s             Uniform        0.000000      0.002887    -0.789178       0.002278   0.203%  Infinity\n",
      "Length Measurement / m          StudentT       0.333160      0.000106    25.282355       0.002684   0.282%         5\n",
      "Length Resolution / m           Uniform        0.000000      0.000289    25.282355       0.007298   2.083%  Infinity\n",
      "Length Reading / m              Triangular     0.000000      0.000204    25.282355       0.005161   1.041%  Infinity\n",
      "Diameter Measurement / m        StudentT       0.100500      0.000029    13.975757       0.000405   0.006%         3\n",
      "Diameter Resolution / m         Uniform        0.000000      0.000577    13.975757       0.008069   2.546%  Infinity\n",
      "Diameter Reading / m            Triangular     0.000000      0.000204    13.975757       0.002853   0.318%  Infinity\n"
     ]
    }
   ],
   "source": [
    "print_text_unc_budget(g_approx, showDof=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Description                     Distribution  Value      Standard Unc  Sensitivity  Unc Component  Index    Dof     \n",
      "--------------------------------------------------------------------------------------------------------------------\n",
      "Time N Periods Measurement / s  StudentT      24.906000      0.022515    -0.792191       0.017837  10.435%         9\n",
      "Time Reaction / s               Uniform        0.000000      0.057735    -0.792191       0.045737  68.613%  Infinity\n",
      "Time Resolution / s             Uniform        0.000000      0.002887    -0.792191       0.002287   0.172%  Infinity\n",
      "Length Measurement / m          StudentT       0.333160      0.000106    25.378883       0.002694   0.238%         5\n",
      "Length Resolution / m           Uniform        0.000000      0.000289    25.378883       0.007326   1.760%  Infinity\n",
      "Length Reading / m              Triangular     0.000000      0.000204    25.378883       0.005180   0.880%  Infinity\n",
      "Diameter Measurement / m        StudentT       0.100500      0.000029    14.029116       0.000407   0.005%         3\n",
      "Diameter Resolution / m         Uniform        0.000000      0.000577    14.029116       0.008100   2.152%  Infinity\n",
      "Diameter Reading / m            Triangular     0.000000      0.000204    14.029116       0.002864   0.269%  Infinity\n",
      "Start Angle / deg               Uniform       10.000000      2.886751     0.007525       0.021722  15.476%  Infinity\n"
     ]
    }
   ],
   "source": [
    "print_text_unc_budget(g_exact, showDof=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effective degrees of freedom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "589.9625210925616"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1./get_idof(g_approx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "825.7821343576667"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1./get_idof(g_exact)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Coverage interval 95%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[9.72831173 9.9269542 ]]\n"
     ]
    }
   ],
   "source": [
    "print(get_coverage_interval(g_approx, 0.95))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[9.75677417 9.97353584]]\n"
     ]
    }
   ],
   "source": [
    "print(get_coverage_interval(g_exact, 0.95))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Verification using differential equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simplified measurement model with $\\sin\\alpha \\approx \\alpha$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following differential equation\n",
    "$$\\frac{\\partial^2{\\alpha}}{\\partial{t^2}} + \\frac{g}{I/(ml)}\\alpha \\approx 0$$\n",
    "can be rewritten as an ordinary differential equations (ODE)\n",
    "$$\\frac{\\partial{y_0}}{\\partial{t}} =  y_1$$\n",
    "$$\\frac{\\partial{y_1}}{\\partial{t}} = -\\frac{g_{\\mathrm{approx}}}{I/(ml)} y_0$$\n",
    "where $y_0 = \\alpha$ and $y_1 = \\frac{\\partial{\\alpha}}{\\partial{t}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ode_function_approx(y, t, p, dy):\n",
    "    dy[0] = y[1]\n",
    "    dy[1] = -p[0] / p[1] * y[0]\n",
    "\n",
    "y = [get_value(alpha0_rad), 0]\n",
    "t = np.linspace(0, get_value(T), 2001)\n",
    "\n",
    "p_approx = [g_approx, I_over_ml]\n",
    "ytbl_approx = unumlib.ode_solver(y, t, p_approx, 1e-12, ode_function_approx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial conditions at $t_0$ are $\\alpha_0$ and for the first derivate $0$.\n",
    "\n",
    "At the time $T$ the start and end values of $\\alpha$ should be the same. The first derivate $\\frac{\\partial{\\alpha}}{\\partial{t}}$ should be 0 at the end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.4100055284748123e-11\n",
      "-1.4984827614861196e-12\n"
     ]
    }
   ],
   "source": [
    "print(get_value(ytbl_approx[-1][0] - ytbl_approx[0][0]))\n",
    "print(get_value(ytbl_approx[-1][1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, [get_value(yi[0]) * 180 / np.pi for yi in ytbl_approx])\n",
    "plt.xlabel('Time / s')\n",
    "plt.ylabel('α / deg')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exact measurement model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following differential equation\n",
    "$$\\frac{\\partial^2{\\alpha}}{\\partial{t^2}} + \\frac{g}{I/(ml)}\\sin(\\alpha) = 0$$\n",
    "can be rewritten as an ordinary differential equations (ODE)\n",
    "$$\\frac{\\partial{y_0}}{\\partial{t}} =  y_1$$\n",
    "$$\\frac{\\partial{y_1}}{\\partial{t}} = -\\frac{g_{\\mathrm{exact}}}{I/(ml)}\\sin(y_0)$$\n",
    "where $y_0 = \\alpha$ and $y_1 = \\frac{\\partial{\\alpha}}{\\partial{t}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ode_function_exact(y, t, p, dy):\n",
    "    dy[0] = y[1]\n",
    "    dy[1] = -p[0] / p[1] * np.sin(y[0])\n",
    "\n",
    "p_exact = [g_exact, I_over_ml]\n",
    "ytbl_exact = unumlib.ode_solver(y, t, p_exact, 1e-12, ode_function_exact)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial conditions at $t_0$ are $\\alpha_0$ and for the first derivate $0$.\n",
    "\n",
    "At the time $T$ the start and end values of $\\alpha$ should be the same. The first derivate $\\frac{\\partial{\\alpha}}{\\partial{t}}$ should be 0 at the end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5396185154846762e-11\n",
      "2.946872346837326e-11\n"
     ]
    }
   ],
   "source": [
    "print(get_value(ytbl_exact[-1][0] - ytbl_exact[0][0]))\n",
    "print(get_value(ytbl_exact[-1][1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, [get_value(yi[0]) * 180 / np.pi for yi in ytbl_exact])\n",
    "plt.xlabel('Time / s')\n",
    "plt.ylabel('α / deg')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimization of ODE system"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exact measurement model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual: 0.4481244677781388\n",
      "Residual: 0.4481244677781388\n",
      "Residual: 0.4481244677781388\n",
      "Residual: 0.061834521886088054\n",
      "Residual: 0.061834521886088054\n",
      "Residual: 5.35703661521423e-05\n",
      "Residual: 5.35703661521423e-05\n",
      "Residual: 1.2109893394831993e-12\n",
      "Residual: 1.2109893394831993e-12\n",
      "Residual: 1.0889466101733717e-21\n",
      "Residual: 1.0889466101733717e-21\n",
      "Residual: 1.0889466101733717e-21\n"
     ]
    }
   ],
   "source": [
    "def numerical_function_exact(x):\n",
    "    _g = x[0]\n",
    "    _T = x[1]\n",
    "    _I_over_ml = x[2]\n",
    "    _alpha0_rad = x[3]\n",
    "    _p = [_g, _I_over_ml]\n",
    "    _y = [_alpha0_rad, 0]\n",
    "    _t = np.linspace(0, _T, 2001)\n",
    "    _ytbl = unumlib.ode_solver(_y, _t, _p, 1e-12, ode_function_exact)\n",
    "    return get_value(_ytbl[-1][1])\n",
    "    \n",
    "def objective_function_exact(x, p):\n",
    "    _g = x[0]\n",
    "    _T = p[0]\n",
    "    _I_over_ml = p[1]\n",
    "    _alpha0_rad = p[2]\n",
    "    _f = unumlib.numerical_step(numerical_function_exact, [_g, _T, _I_over_ml, _alpha0_rad], [1e-9, 1e-9, 1e-9, 1e-9])\n",
    "    print('Residual: ' + str(get_value(_f[0] * _f[0])))\n",
    "    return _f\n",
    "\n",
    "x_start = [10.0]\n",
    "x = unumlib.optimizer(objective_function_exact, x_start, [T, I_over_ml, alpha0_rad], epsx = 1e-9)\n",
    "g_exact_opt = x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.865155004321421 ± 0.05521868932688879\n"
     ]
    }
   ],
   "source": [
    "print(g_exact_opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.86515500432206 ± 0.055216310403278\n"
     ]
    }
   ],
   "source": [
    "print(g_exact)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]\n",
      " [1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(get_correlation([g_exact_opt, g_exact]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-6.394884621840902e-13 ± 2.7170482392903897e-06\n"
     ]
    }
   ],
   "source": [
    "print(g_exact_opt - g_exact)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison of simplified model and exact model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{g_{\\mathrm{exact}}}{g_{\\mathrm{approx}}} = \\frac{16 K\\left(\\sin\\left(\\frac{\\alpha_0}{2} \\frac{\\pi}{180}\\right)^2\\right)^2}{4 \\pi^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha0_range = np.linspace(0, 45, 1001)\n",
    "alpha0_range_rad = alpha0_range * np.pi / 180 \n",
    "f = 16 * umath.ellipk(umath.sin(alpha0_range_rad / 2)**2)**2 / (4 * np.pi**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(alpha0_range, [get_value(fi) for fi in f])\n",
    "plt.xlabel('α_0 / deg')\n",
    "plt.ylabel('g_exact / g_approx')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Damped pendulum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following differential equation\n",
    "$$\\frac{\\partial^2{\\alpha}}{\\partial{t^2}} + 2\\beta\\frac{\\partial{\\alpha}}{\\partial{t}} + \\frac{g}{I/(ml)}\\sin(\\alpha) = 0$$\n",
    "can be rewritten as an ordinary differential equations (ODE)\n",
    "$$\\frac{\\partial{y_0}}{\\partial{t}} =  y_1$$\n",
    "$$\\frac{\\partial{y_1}}{\\partial{t}} = -\\frac{g_{\\mathrm{damped}}}{I/(ml)}\\sin(y_0) - 2\\beta y_1$$\n",
    "where $y_0 = \\alpha$ and $y_1 = \\frac{\\partial{\\alpha}}{\\partial{t}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The attenuation coefficent $\\beta$ can be computed with\n",
    "$$\n",
    "\\beta = \\frac{1}{T}\\ln{\\left(\\frac{\\alpha_0}{\\alpha_{\\mathrm{end}}}\\right)}\n",
    "$$\n",
    "where $\\alpha_0$ is the start angle and $\\alpha_{\\mathrm{end}}$ is the end angle after the time $T$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ode_function_damped(y, t, p, dy):\n",
    "    dy[0] = y[1]\n",
    "    dy[1] = -p[0] / p[1] * np.sin(y[0]) - 2 * p[2] * y[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual: 0.13299350420081263\n",
      "Residual: 0.13299350420081263\n",
      "Residual: 0.13299350420081263\n",
      "Residual: 0.03907242621765137\n",
      "Residual: 0.03907242621765137\n",
      "Residual: 0.0002829986683234565\n",
      "Residual: 0.0002829986683234565\n",
      "Residual: 1.750666547805865e-11\n",
      "Residual: 1.750666547805865e-11\n",
      "Residual: 9.545793072260758e-22\n",
      "Residual: 9.545793072260758e-22\n",
      "Residual: 9.545793072260758e-22\n"
     ]
    }
   ],
   "source": [
    "def numerical_function_damped(x):\n",
    "    _g = x[0]\n",
    "    _T = x[1]\n",
    "    _I_over_ml = x[2]\n",
    "    _beta = x[3]\n",
    "    _alpha0_rad = x[4]\n",
    "    _p = [_g, _I_over_ml, _beta]\n",
    "    _y = [_alpha0_rad, 0]\n",
    "    _t = np.linspace(0, _T, 2001)\n",
    "    _ytbl = unumlib.ode_solver(_y, _t, _p, 1e-12, ode_function_damped)\n",
    "    return get_value(_ytbl[-1][1])\n",
    "    \n",
    "def objective_function_damped(x, p):\n",
    "    _g = x[0]\n",
    "    _T = p[0]\n",
    "    _I_over_ml = p[1]\n",
    "    _beta = p[2]\n",
    "    _alpha0_rad = p[3]\n",
    "    _f = unumlib.numerical_step(numerical_function_damped, [_g, _T, _I_over_ml, _beta, _alpha0_rad], [1e-9, 1e-9, 1e-9, 1e-9, 1e-9])\n",
    "    print('Residual: ' + str(get_value(_f[0] * _f[0])))\n",
    "    return _f\n",
    "\n",
    "alphaend = ufloatfromdistribution(\n",
    "    UniformDistribution(2.5, 7.5), \n",
    "    desc='End Angle / deg')\n",
    "\n",
    "beta = umath.log(alpha0 / alphaend) / T\n",
    "\n",
    "x_start = [10.0]\n",
    "x = unumlib.optimizer(objective_function_damped, x_start, [T, I_over_ml, beta, alpha0_rad], epsx = 1e-9)\n",
    "g_damped_opt = x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.848198453590038 ± 0.0513963133689297\n"
     ]
    }
   ],
   "source": [
    "print(g_damped_opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.86515500432206 ± 0.055216310403278\n"
     ]
    }
   ],
   "source": [
    "print(g_exact)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Description                     Distribution  Value      Standard Unc  Sensitivity  Unc Component  Index    Dof     \n",
      "--------------------------------------------------------------------------------------------------------------------\n",
      "Time N Periods Measurement / s  StudentT      24.906000      0.022515    -0.790827       0.017806  12.002%         9\n",
      "Time Reaction / s               Uniform        0.000000      0.057735    -0.790827       0.045658  78.918%  Infinity\n",
      "Time Resolution / s             Uniform        0.000000      0.002887    -0.790827       0.002283   0.197%  Infinity\n",
      "Length Measurement / m          StudentT       0.333160      0.000106    25.336423       0.002689   0.274%         5\n",
      "Length Resolution / m           Uniform        0.000000      0.000289    25.336423       0.007314   2.025%  Infinity\n",
      "Length Reading / m              Triangular     0.000000      0.000204    25.336423       0.005172   1.013%  Infinity\n",
      "Diameter Measurement / m        StudentT       0.100500      0.000029    14.005645       0.000406   0.006%         3\n",
      "Diameter Resolution / m         Uniform        0.000000      0.000577    14.005645       0.008086   2.475%  Infinity\n",
      "Diameter Reading / m            Triangular     0.000000      0.000204    14.005645       0.002859   0.309%  Infinity\n",
      "Start Angle / deg               Uniform       10.000000      2.886751     0.002568       0.007414   2.081%  Infinity\n",
      "End Angle / deg                 Uniform        5.000000      1.443376     0.002977       0.004296   0.699%  Infinity\n"
     ]
    }
   ],
   "source": [
    "print_text_unc_budget(g_damped_opt, showDof=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Description                     Distribution  Value      Standard Unc  Sensitivity  Unc Component  Index    Dof     \n",
      "--------------------------------------------------------------------------------------------------------------------\n",
      "Time N Periods Measurement / s  StudentT      24.906000      0.022515    -0.792191       0.017837  10.435%         9\n",
      "Time Reaction / s               Uniform        0.000000      0.057735    -0.792191       0.045737  68.613%  Infinity\n",
      "Time Resolution / s             Uniform        0.000000      0.002887    -0.792191       0.002287   0.172%  Infinity\n",
      "Length Measurement / m          StudentT       0.333160      0.000106    25.378883       0.002694   0.238%         5\n",
      "Length Resolution / m           Uniform        0.000000      0.000289    25.378883       0.007326   1.760%  Infinity\n",
      "Length Reading / m              Triangular     0.000000      0.000204    25.378883       0.005180   0.880%  Infinity\n",
      "Diameter Measurement / m        StudentT       0.100500      0.000029    14.029116       0.000407   0.005%         3\n",
      "Diameter Resolution / m         Uniform        0.000000      0.000577    14.029116       0.008100   2.152%  Infinity\n",
      "Diameter Reading / m            Triangular     0.000000      0.000204    14.029116       0.002864   0.269%  Infinity\n",
      "Start Angle / deg               Uniform       10.000000      2.886751     0.007525       0.021722  15.476%  Infinity\n"
     ]
    }
   ],
   "source": [
    "print_text_unc_budget(g_exact, showDof=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_damped = [g_damped_opt, I_over_ml, beta]\n",
    "ytbl_damped = unumlib.ode_solver(y, t, p_damped, 1e-12, ode_function_damped)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZTXvHyhgapFFb//lnT2DfeBmf/Onj+ItXrEJPYU79+GEwGHMYc0pZklEul/H1r38df/EXfxF7Qx0bG8Ohhx6KFStW4A1veAMeffTRxNobN27E4OCg/2fFihWUR28D1bqTVvUHAIoEk3au6wYtvgaZIVv+Ww4nYfXGBJ8NJv0gzRSUJcmzRFkXCGIJDp7f06hbsY5+AIBKre6fsdDwyVH5oVzXxR+2B79UsB+KwWB0EuYsWfr+97+PAwcO4JJLLol8zJFHHomvfvWruPXWW/H1r38d9Xodp556Kp577rnY2hs2bMDw8LD/Z9u2bcSnb0aQ4E1DDuQpOAoiVqrW/QkqQTy6iBSrQFlqrgsEfib72s2p49STdsJATteG88jSQQ1lqe7CTyK3wf4Jz/vkOEGLb/fYVNxTlLFnrNyUufX4TiZLDAajczBndfCvfOUrePWrX43ly5dHPmbdunVYt26d//app56Ko446Cl/60pfw4Q9/OPJ5xWIRxWKR9LxxoPIViXUpxSbPkr2yJPuSunLNytIkWeq4VzefzSCfdVCpeWrWIMzzkCb9fXbCZ5Vr+pw2kD1LguSOELThStWa/zpY0l9ELuOgWncxOlXxyZ4pDjSWCA925zE0UMQfttMpS1v3TTS9/fQeWrL03w9vx5bdY/jL0w9DPjtnfwdkMBgzhDlJlp599ln87Gc/wy233KL1vHw+jxNPPBFPPvlkSiczA1XAo8hpKko3E6Gq2BAxQS4K2Qxy2eacJSqflexv6cpnUalVCVWr5hYfReq4rCwVGmSJwgslq1P9XXkMdOexb7yMkckqlg3a1d7f2F23oKfgJ5oPEwVpylN2ALBrhM6UvmtkClfc/CDqLlDMZXH5aavJajMYDAYwR9twN954I5YsWYLXvva1Ws+r1Wp4+OGHsWzZspROZgbhHylZenSEx6dI3IYLa++JaThrshTis/JN6baTdi1ErKdAQ/CAYB1LXzFHOg3nT/AVc8hmHMkPZU9qRBtuXo9HwrzPR7srT6A1WNMGm57aC7Gh5r6n95LVZTAYDIE5R5bq9TpuvPFGXHzxxcjlmoWziy66CBs2bPDf/tCHPoSf/vSneOqpp/Dggw/irW99K5599lm8/e1vn+5jx0IkS5erdSsjr1CWCtmw6AD7Npw8ZSdIGBWhaZrgE4GXFbsb+ZRv8BZtOKEs2dWVDe/dhazkWbI3YospO0FmBgj9UPsbbbgFvQWf4FG0Dr3aHhFbtagXAC1ZkhcJb25ZMsxgMBgUmHNk6Wc/+xm2bt2Kv/iLv2j72NatW7F9+3b/7f379+Pyyy/HUUcdhde85jUYGRnBPffcg6OPPno6j5wIoSwBdhNgocoSgbcobMpOJHhTBWmGK0s06eBdLZN2tj6rqUqz4V2Qsbprb9L3p+waZKmfkNQEylJBUpZoyNK+ca/OkUsbQZqjNMZxoHmR8LZ9k9ZkV0a97uJnv9+JnSN052UwGJ2HOedZOueccyJ/e7/rrrua3v70pz+NT3/609NwKjsUZbJUNV94W64KZUkmS/btMkEAulIgNJONG19PoV0No/IstSpL9mpYcLPuzmebXo+T5VrTddLFSEvqOOXeOWHwnt+T9xUrqn12wg91+JI+4FFg33jZOidL4Nm9zX6onSMlrFpE86PtxnuewYd/9HscsqAHd1x7OpvHGYwXKfh/fgdAJjdlC2UimIYL6gnVykax8uvm2hUrKs9SKBEjqt1TaFWW7AjCRDnwcGUzDnLZjP89nLA885hkHAfkNpy9AnSgSVlqkDAqZalR+9CFXjZU3aUxvANoU312EapAP37YU6K37pvA719IN3yWwWDMXjBZ6gBkMg7yWe83cFNSU6+7qDSSpGXy5ZMlGxImvFASWaJO8O4J8SxNEfuh6JSl9gm+oLYdQRhvqS38UBRG7PGSV9szpQtliciz1FCWls/r9l9/FKqV67rY16gtFgvvJAzSfFzyQG3ewX4oBuPFCiZLHQLZ5G0CmWTJOUuipVey8BaJNpzcHhRkqVp3rfaLTVVCDN5EytJUC/Ggig4QbTjZZ9VToKnd2pbsLdKQMAAYl2pTT8MJP9SC3sAPNTxhT8QmyjX/9bdmyPNDUSlL+8bLTcb5P+ygVZb2jpXw220HSGsyGIx0wGSpQ2CrAMnGYllZKlIoSyFtOLnVZ2NqFipPV47Ws+S6rt8SE8SDKjpgMkYNsyVLrcqS+Jsiwbs57oBOWarX3eZJu0aLjyLDSahKhVwGhzRafHvGytZ1AeAZyTgOANsP0LX3anUXf/alTXjDDf+L7/w63Q0ADAbDHkyWOgR+1pIxWQpupqKlB9grVvKZmrxQEiGzCdMMq91D0C4r1+qoNcJ5BPnqIlOW2smSf2YiIiYUJYprISDacD3FnO+JmijXrJRBABgtVf1rPa8nj8FuOiImyNLC3oJflypIc/twMznaQeiFevj5YT/y4JYH49crMRiMmQeTpQ6BrRG77LfKMk0TSEWCvXN+Mrik/mQyjk+YrGqHtfgIFCCZXLQqS9ZTdnGtQ1tlqaH+tPqsKMblRRuut5D1yRJgn+EkzlzIZlDMZX3VilJZmt9TwDzyuIOGz2qwC0C7kdwGj0lLhR/bMUqyCJnBYKQHJksdAlsFSJAO2YRNUder3d6Gkz8X9QSf2D9nowCJ5+azjj8OTkHCgMA/1Ntk8A6UGhuI5/e2pI7TtOGEapVDLpvxYyXGLafWxPOFGjZISGp8ZamvgMEeWmVJtPOOXu7tkdk1WvIVMls8vSdo8R2YqJCqVq7r4p4n92Bbyz4+BoNhDiZLHYKCb8S2VZaaM34ECbGLDghUq6balq1DQFatZD+U9zXYkLCwSIKevEdAKjU7U7ogHbKy1JOnMWL75nFh8BbLfwk9S70tfihbgjfmk6VG3AFhLIGsLFG34faNe1N1RyztA+D5jKhqP7Wn2Q/1woFJkroA8IPfvoA3/9t9+NN/+V+SSAkGg8FkqWNAZfBuU3+yYkmvRTK47ytqIWI+WaINvCSpW2mv21UIro1NK641v0n+N5XBWxAaqjZcrR6saGn1Q43bxh2Ums9MSWrkKTt6suTVXjrQhf4inSkdAHa0+KFa/VE2uP33OwF4yth9T+0jq8tgvJjBZKlDULSNDogiSwRLeiOJGEEbTrTEwpQlG8VKrGHpajGlZxp2LhulZsIfwW/PWbKPDgif4KOKOwACBYhKtRpracNRpoOPSRN81GRJtOHkuAMR3GmLvWOeanXIAm+Cr5U82eA3Ww/4/36UgzQZDBIwWeoQBO0ysxuXUGFaPUtpRQd4b9uTmjCDN217L6jrOA6JETts+S9VLMF4S84SHVnynp/NOP71Feen8yzlmv62rQtIZKkrF2RDTVVQJ/AWyZN28xp+qAMERMx1Xexp1D5m+QAAOrI0Ua7ieaml9xhxNtQjzw/jc3c8QZa+zmB0CpgsdQisQymTlCWCllYbEctTtOFClCWS9l4EwRN+KIIgzZ6QFS10ylKzr4hK/ekpZP1pSaEE2bcOA/WHsi7QTMSEsuS69hN8gGweL/pkiSJIc7RU9f8/rhkaaPpctmj1PlF6oep1F2//2q/xqdsfxwd/8ChZXQajE8BkqUNg29IqR0zD0ShL4eZxW4Lnum5ozpKvWFn4rKZCPEtAMGlnowCF1aaahhPkoKfFV1Su1a1M6RPSqhOBtAzeQZAmZRsui2Iu65NS21ac67rSrrw8aYtvb6O911vIYmiwCCDwXtni+QPpeaGe3D3mT+3duXk3WV0GoxPAZKlDYB9KGREdQNHSilRp7GpXai5E/ExTG44iGypBWbLyQ1Xa/VBBhhPNkt6elpwl+WMmkJUlgR4i87icDA4EXihB0Gww5pM8j8z4k3aWU2CTlRpEJ6+/K4fB7gIAb8zfFsKv5ClWjbpEPiuhJJ1wsBd3sHusZPWLkIwHn93v/3vPWAl7xmh28DEYnQAmSx0CX6WxDqUMn1ijTvCWP5epAiS32bryxG24CGXJr22lWgkiJq9osa9brtZRbdzBhTpTyGaQbbjSKUzpaShLQX5TQw0r0kzZebWbzeO9VGpYo42XcbwWauBZsleAhHF8YV8QpEnR3gOAPY0lwkcO9aOQzcB1gV2jNOrSM3ubc5seJ1wsvHeshDd9aRPe893fkmVZMRiUYLLUIbCPDmgYvLPhhMaKLIWYpeXPZTppl7TPLl1liXZFiyBlUxZ1ZTIk2k2O45AoQK075wCvTeR9jNjgTURogIDU9BGbx0clNcxxnKANR6EsNfKbFvbSK0v7/CiFIhb0erX3j9PUfm5/M1l6gbDF961fbcN9T+/Ddx94Dr98cg9ZXQaDCkyWOgRUbbhW9YfE4J3UhjP0/8ixAU0rWgg8S0lBmlMEylJYNpRV3cZ1zjjN+/0oJuJaFZqmupbtsiiDN8U0XFuLj0i1aiVhQgGiIDUjk17teT15zO8JIgkoJvgO+AuL874aRuWHem6/1+ITq3C2E5rH73s6yIOS230MxmwBk6UOAVUoZauyJN6uu0DVUgGKavFZE7zIZHAbE3Y7oaGrHZ06TnVmmTz6cQcWpvRW9QfwFuoCFAbv5lBK8XepWjd+zQGeCXuslYgVaJSlcSmSAAD6G9lQYyTZUB6h6SsGcQd1N1CzbCAnms9vqFZUZGn7sEeOXrZyAQBaZemR54dD/02BiXIVv3h8t/VCaMaLG0yWOgRkoZStviLpbWs/VIRqZUzwBOloIzSU+U1pZEO1E7GunMhZSmGCT7T4rMhSdBuOyuDtT8NJ6tWExZknyjV/AECQmqANZ0fwRlsUK3FminwhEWvQ35VDV16a4CNo8cmJ5vN7hWpFkw0liNixjWwoqsXCY6VqU3TC03vHYx6tj7/8/x7ARV+9Hx/+0e9J6zJeXGCy1CGw3YcWKEvhviLAxoidDvFIa8oOiFaWuixbh17tkBUtBJlT/pkjfFY2RCxsRUu3P+JPE3cgiEchm0GuYUq3afGJusKEDdC1+Pw2XENREmcniTuQyBKAoBVHYB7f78cdFHw/FIWyNFqqolLzmOlhS/rI6gJoW/j7woFJuC6NyfvARBn/84Tngbr5vq1kdRkvPjBZ6hCQTcO1qD85aZrKtHZAamhbWkltuFrdJWgdhhO8KWLzOI2yFEHwSLKh2uMOfGXJlni0+KFkU7oN+fDrFnJBkCYRwRO1+4nbe4CsWom4AzoFSJi5F/QGk3Y0dT1i1FPIYtlgN1ldIPBCrRnqB+D9H9lPVPsByf9UrbttE30MhiqYLHUI0pqGk99n3S4j3g0XtkTX+zzZtsfowjePt9YmGPEPiyWwNbsDAYFrPXMXZTZUU9yB/QQf0K4sAUG7zEZZGmvxFQGBz8paWWoheOLsNG24hmfJ90PRnLlcrfvnW0DsWdrb5IXySBhV6vjuRtzBwfN7sKTfC+mkSh7fsnus6e3fE+7KG52q4MJ/vRdv/9qvrdcYMWY/mCx1CGyn4aISvJtr2ylA7englm24kCW6rZ9nVprHQ5b0BsSDNuxSfptCWZJDLot+XTtjrB9L0JThRKgsSXX7iKbhRqea1R9BmqYqdqZ0QFKtWnxWtgZvkTiecbzawTQcnbK0sK+A+Y1IguHJivW1AKSQzt4CFjfIElXg5daWFt/zB+iUpe8/9AI2PbUXP/vDTvzod9vJ6jJmJ5gsdQhs23BR5EB+nwnxqNdd/0zRxMNQ/YmYsstmHH903pjgRZjHbVWaWt31vR1dIct/y9W68Yh4mPrj1bY3eE+FXA8K43i97vpEvVuqTZGH1DreD0irVIin4WRCZt3im2pu8fURqWEj0vXIZBxfWTpArCyJ9h5AtP5FImIiG4pKtXq20XZb1OeRsOf308Ud/PKJYOXLAxx3MOfBZKlDELS0zH5QRy3Sba6tTxBk8hbV0jI9s68s5cMInl3Wkq/+ROYs2WVDAeGhlIAF4fXbe+HKkk0bbjLEPN5NYByXW3jdIUTMKu4gJHW8jyzuoJnQFHOSKZ1ItepvMY/bxhIEipVXd7ChLFEsFfaVpd4CctkMBhokkqLFJ4jRgt6gdUhFlsTE3imr5gMAnifMhvr99qCl99ttB8jqAsAze8bx8f9+DE/voZ0MZJiDyVKHgMqz1KrSeO8zv9nKZKWtXZa1u4mnpYYB6cUSyM9r8v9IX4MxEQuJJJDfpm7D+SqbRV05dbxITMTGWtaoAEF7z9Zb5LfhGqTAcRz6dPCuZmVpjChIs7+1LmV+U0P5EX9TtPj8RHNJWaKatBOrZY49yNuVt4Mo7qBcrTepVM/sHSedtLv2u7/FF+/egqu++SBZTYYdmCx1CKw9S7U4z5J5LEFJSpUWv3kL+EGM1pEEcQTPknhQtw4rgZE+I10PeerQtnYqZEmY6UP22dmoP1MS4ZWvB0ntkBUtfQTGcSAIjuwNUa3GLGqXqjX//1nrihZ7ZSkIu5T/pgjSFIuJxdoXSgVo71iwoiWoa0/CqrW6T7qOWOJN2u0bI4o72D+BugtJbayRTfDtHSv5bb1Hnh/xPV2MmQWTpQ4BWSglcRtONnfLqdLy57KNJGhtOwFyIjatsmRLPKYiTOmA/Yj/VFQbjmKVSjk6SLNqEdEwGVIXCJQlK9UqhDx2E+2za23DATQZTjJxaSU1ZJ6lFmVpslKzNmKPtKhWwjxOsysvaPEtaARp7icgYfsnKnBdwHGCbKi942USBUioSoct7vMn+Fp355nit88daHr7IeIW30PbDuBXz+xLfiCjCUyWOgQFa+IRrSzZqCmBubtd/bGesotY0Ou9z27EPzLwkmwHX8iZLQleQMRavWEUylL0BJ/3cbszd7eSpQapmbTwFk2G1BZ1bSf4BKnpDYk7sGlrBdlQWV9pFOTGtl0WtVQYsE80H4vwWdlO8Lmu2zRpt6DXIx77SEzpniKzoCeYsitV61ZqpoCIO1jcX8RB873cKaq4g6d2N/uUHt85FvFIfTyxcxRv/Jf/xQVf3IR7n9pLVvfFACZLHYJ8Q1mq1sx+K4qLDggUIP0fImLfUj4kv8me0Kh4lmxVmqicJTtlKUwNo1OWaHfwyWcKW/4rf9y8blT4p70fqrsQ5oWyuyEKg7jsh6JQgFq9UN7nICJLLQbvQi7jfw9HS3YKkMiG6ifelTderqHamA6d1x2saKFo7+0ZDUhYbyHr/+zbS9CKE9EGi/oK/qTdHqIW31Mtpu5tRIoVAPzXw9shhnF/9LsXyOq+GMBkqUOQJ4sOCFGAsuakplJ1GzWcto+Jz2V65imVaThi83iXZd2wJboCtmtJwtQf72266ACZLGUyjvV0YFirDJCVJXuC16QsSVN2Nu2WMNUqyIYyv86tk3BA0OqzVn9a8pvkf1MZ3sVZg7p2JGykET2QyzjoymeI4w5EflMRjuNgIWEsQUCWin5dChIGBOtfXrbSm+B7jjDu4P6ng/YbdXuvWqvjvqf2Wk+LzlbMKbL0gQ98AI7jNP1Zs2ZN7HO++93vYs2aNejq6sJxxx2HH//4x9N0Wj0Uch4ZMd2crRJKWTHI/xFEKB+n/lgqS6377AA5lsAu8DJKWTIlB2FLdP3a1mpYgsGbIjqAmIgJEiZP2QHS+hcbZSnkenQ1Po+cd2VU21etZLLkEYQpC7IUFqRJpSz5yeAhpnTrCb6ouAOiugPdeTiO45OwEQJTulB6FvR5ZIYyw0nUXtRfxMI+UZfGiC1afCcdugAA8Nw+OmVJTjR/bPsoaoaZb2H46I//gDf96734y//vAbKaswlziiwBwDHHHIPt27f7f375y19GPvaee+7BhRdeiMsuuwy/+c1vcN555+G8887DI488Mo0nVoNtGy4gHu3f8ryFeVypDWd4Q6zETPClt3fObmFxVKtMfp+psuTnLLWqYZYELyo4srm2ocE7IkhTtM5siEcYoZE/j6k3pVKr+62hnnxAPCiyoSb8bCg5oJM47iCEiNlmLbWqVlSkJqq9V67WrVL0AWC4oU4t6EmDLAXKkvBZ7SXKhhK1jz1oAACwm2gabnSqgp0jQa1q3cX2YRrVqlKr47u/fg4A8D9P7CGrO5sw58hSLpfD0NCQ/2fRokWRj/3MZz6Dc889F+95z3tw1FFH4cMf/jBe+tKX4vOf//w0nlgNtm24OOIhapuoVnFkyTYbKqgd3eKzTR2n9v9EGcebaxMrS35Apx1xDKtt6wEKy2+SPw+FsiQTvHzW8Y3Ttq1DAOgK8UPZkSVxZnr1J2xXHoUCVKu7bbWpYglGI7Kh5I+ZYsRXrbyalGRJqD+L+gqk7b1qre6TrjVDHlkanapaE0cA2LbPIzALegtYtagXQPs6GFM8tn206TX2m60HSOoK/P6FEfz7pmdIa+pizpGlJ554AsuXL8fq1avxlre8BVu3bo187KZNm3D22Wc3vW/9+vXYtGlT7OcolUoYGRlp+pM2ZEJj4sXwyVIoqWm0+CyUpTDPUnBmMzWsErFGRX6fSYtPJget5DFYd2I3wZeGspQcSmmn/qRRO3qfnf00XJhnyXEce4JXDrLD5P8vQg2zmuDzs6HaJ/hsfVata1QAyVtkQTzkm2CrsmSrhon8poGGopTNOOgVwaLWZKm5tvhbqFk2EIRmUV/QhqPwLO0bL8N1vdfeyoU9fo4TBRHbNeoFci4d6MLBjQm+5/bRKEBP7Bptevvh54dJ6gLArpEp/NmXNuH6HzyKe57cQ1ZXF3OKLK1duxY33XQTbrvtNnzhC1/A008/jVe+8pUYHR0NffyOHTuwdOnSpvctXboUO3bsiP08GzduxODgoP9nxYoVZF9DFMQPbdeFUZ/ZV2ly7aSmYKEsCdUoVlkyJHgqtU1uiLLSFRUdQG3ClmvbT/BFtOEsFStZlRGwjSWIylmiaGn5Lb4I1cq0dqD+ZJuyw4RniTruQNR1XbuJxrCFxRTKkniuN12XbdSlmYZrzW/y/k2zpmVkMvBDeX/TtA5d1/Xzpeb3BqnjFG24XaMizbyIXDZDSsRE7SX9RQwNdDXeR5No/uSu5ngDKsUKAH70u+0YK1Vx6IIerFk2QFZXF3OKLL361a/GBRdcgOOPPx7r16/Hj3/8Yxw4cADf+c53SD/Phg0bMDw87P/Ztm0baf0wyCRHV6lx3cDsmsvEeJYMFCDxnDBCI7/PRF2Kq+2b0k0InvSc9tRxolZZyNQhlUoTtaLFfrw/5Mw5u6TtKA8XxbqTyXI78QDsFSCf0EjJ4ACtZ0luS8rnt9lpN9moLatWFObxUV+haVesbFWawLMkTQcS1W5VlsTnGLGsO1Wp+z9DBrvzWNjwLO2fsA+8FP6kxY04AlF7D4FvabdElhb108YdbGtM7J2yyjOlbyMkS/c97eVBXXjKIT4xnQnkkh/SuZg3bx6OOOIIPPnkk6EfHxoaws6dO5vet3PnTgwNDcXWLRaLKBaLZOdUgUwYyrU6utF+Y4uCTFRCDd4WxEO07sKm4QpNZKke6pdSqR06wSfiDizIUnjqeLZxXhe1utumtCQhSAaPVpasSU2uVUmxVMOUWoeWxCPSOG4fd9BGlixJTUCWmr+HFJ4lEZUgE5psxkEhl0HZMjBxPIQ89hCEf7aGXQKBd8k2lFKoP2FxB7YKkIglaG0d2nuhvLqiZZht/Ayp1V2Ml2tN10kXe4QXqkFmSJWlxl68JQPBWhkKEgYAO4e92mtXLcD9T+/Ds3vpyNITjVDOY5YPktU0wZxSlloxNjaGLVu2YNmyZaEfX7duHe64446m991+++1Yt27ddBxPC7ICoktqqvXg8WFtOAqDd5hnSSY51OZxn+BVDVqSMZOBclvOZv1LWJ5V4IeyJTW0Pquo2ABAUoCoE7wJsqECUkO7siZJsbI7czW8tu/hMr+RT/pBmsHNWqhjNorVeMgOvn5JsbJRU0Zb1B8A6CPyFsmxBIDc3rOrOzwZKG2O4+VDiSEUQdBsa89vrJMRgZd7CWIJgjZcl59oTkaWGu284w+eB8D7OmyDYQHvZ9oze72QziOW9lnXs8GcIkt/8zd/g7vvvhvPPPMM7rnnHvzpn/4pstksLrzwQgDARRddhA0bNviP/+u//mvcdttt+NSnPoXHHnsMH/jAB/DrX/8aV1555Ux9CZFwHMf/D6lLPGRCEdrSatSljg7IZhwIjmdSO1CAon1WJqnj8UuF7chSXO0uy3TwqAynoqQsmdy4ShGExvtc6SSak3iWIkhNYB6322fX2oYTE2w2xGMiJO4AkBUgszO7ruu3+HoK7coSRXuvKc28K/BZ2dRunYaT/21tHp9sbh8OUClLom6DhDmOI5nH7WofmGheWLyAMPBS9iz5JIygruu62NlQrY5Y2uf/bKbwcO0YnkLd9f6PC4I3U5hTZOm5557DhRdeiCOPPBJ/9md/hoULF+Lee+/F4sWLAQBbt27F9u3b/cefeuqpuPnmm/Gv//qvOOGEE/Af//Ef+P73v49jjz12pr6EWPgKkKaaEufRkeuaxBLE+Yqsa6uYx00IjV+3/VrI16dkQsRiatt7i8LbZfLbJqpV1JSd/D7qBG9b/5brupHnJmvDtRA8kn12ISqN97kEqTG72ZaqdX+NRXcIWRKKlglEsrhMHuVWsA1ZCksdpyA1tbrrtwhblSVbz5J4viA0Xu1c08dMIZQlUVv8bVsXAPaOBS2+YEWLvbI0MlX1/x8vHejyW4eipWiD7Y323tBgV5tlYroxpzxL3/rWt2I/ftddd7W974ILLsAFF1yQ0olo4ZGGmjbxkPOKwl5wNiP+ccoS4JGaUrVupVqFxh1YnDlO/XGcwD9ipSyFpI7bLkMu+y2+8BUtgOeZCiM9cRBqRpwp3dzgnbDuxCIbyg0hB4B9iy/KZ0XbOgwnYhOWrUMA6AlZ/2KlhjXOJNfNZBz0FLKYKNesyON4SKI5RbtMntLrJ1aWgjZcQJYEIaNqw7WRpUn7RPMDjdrzuvOY31Cs9k9UUKnVI39+q0CoSoPdeXTls1jUV8T24SnfUG4DUXvpwMyqSsAcU5bmOky9RSqEBjDMWYoxYQM0pCbUPG6hLFViFCsAKNqcWWGtjIn647puJMnLZ4N2p0l8gE9oCu1kqWid4B2RDC59/+oGURgyYWlNNBfEw9azFKX+UIdSep+rcWZD4iEITSGbQa4pG4qALDUITU+x+XsY7Mozv5H7C4ula00RdyCUmKIUdyBHEtj4rARxkZWlASLVarilxRfEHdjVrdfdgIj15DG/p+D/zNhv2S4ThGZJo01G6Yfa0VCWlg12W9eyBZOlDoLwFumuPKkktMpscpbiDN6A3Yh/sKQ3Lu7ARv2JJ4/ULT7fZ2WhWMnnE3AcJ0g0NyA1fjsrhOBRJXhHKUvy59fBZAQ5kD+XbXRA+5m9z2Pn/2kPpZQ/l2ntyZBIAvnz2Kg/ExFnpiBi4yn5rELbew3iUau7VoQ3IDTttW0VoFZlSZCwYUvFyiOI8GtnMw5ZW1IEZor226I+ukk70YZb2siFmkkwWeog5A3bOEnKkpiQS9OzZKKmpLVKJW71C1XtsNRxChIGRKWwmxveBcEKN6XTZEO1tp3klp9JbXHzD4toEGZyY89SOfzMwrNDEaQZSWosgzTbCI1vSrdRfxqtshalTezNsyJipXYVT/xbeKWM6pbb23vd+awfBWLTims1eANAf5Fm0m6klSwRt/d6Cln/FyvxOWyJ2LDf3hNkyVOWKNtwQ9yGY+jAtg0Xpf6Q7IaLIB6mE3yA2tSaTep4orJkYfCOW/5rY3YH4iMPTIhH2Sd40aGU1AnemUa2EGBGEKJ8RfL7bA3eUW24crVuvK3dD6WMjA6wTB2PIGE24Z+RtYv2bThfWQpZLGxjSh8LIWGO45C2+Jo9SzTZUL6vqKfV4G1bt9xUDwjObEuWDvhp5l7thX10i4X9IE1Wlhg6sCVLre2K1rrU0QEAUPBDHqlbWuZxB2mqYSoEz6YNl886yIRMNNqYx2MJnm02lL9YmJaIRS3oBQgM3hEETyY49n6o1paWnWoVVTdoadH6iuTapgTPiztor02iLAnjeMv1EG9PWNQe988c1PY9SxbEw3XdyDbcyGTFymfVGkkg/9u2dbh/QhCxQlNdWxIGAPsatUWI5kyCyVIHoWCo0pSrghxE+IoIpuEiPUsEGU7xbSdaciB/PjvPUoyyZFE3TZ9V7MJiw8DLuNo2o/higi9UWbK8iUepVvLXYJ8OHkVqLNtwLcZxEoN3hB/KNneqXAsUOllZoiB4PqFpSdMWe/Os1LDQCT57I/ZEueZfj8EWg3fV0mfVqljJn8O6DSeUpUbteUStQ6BdtZpJMFnqIAQKkB6pEQneSUqKmfqjptLo1q7VXT83JozUpKuGEcQSTDPB8w3eRqnjtcjaNiRMPk9YOrhN8ri4cbTuyZPrWnuWWs6cyThW7bJKre6/ptpIjWWCdxShESpNyap1GK5aiXaZKamR1R05loDC4B0QmghliYAsNa9/yTc+Zm9KzzjB66E7n/Wz32wUoOGJ9jYcFVkSypLfOmz8fcCybr3u4gArSwwT5EwTvFUNzRa+oiTiobukV/4aw1PH7YlHmNoB0Kg04fvssk2P0UEpSQ1LSbWyIWHNtUNiCSyiFII1KnETfKZxB+GeJcAuH0p+TptKY2nwDs4crljZ1A7IUngbzpTUCHWnmGueaBSKDc2UXeuZ7Vt8vh9KIkuChI1bLSwOFCuRh+c4DgmpCWvDUbQOAVm1om3DjUxV/F+YZUVspsBkqYNgqtIkqz/mJuy4Rbry59S9ics30NjdcFY758Jbh4ERm9bgTeNZis+GsqlNPcEHSLvyQhcLmxOxgPDGKEvGY/jRuVM2ypJ4TjbjtL32bMMjo0zYxVwGIofWWAFKnLSzO3Nrq0xcCxviIVSr1qW2tmqYfK6+JlO6aO/Zq2GtZw4WAJuTDz/NPCRIk8zg3UKWRiYrRhlqAvsbdXulCb6ZBJOlDoJpHpJv8A4xBgPma1Tk2tSTds3KEm1mUaJKQ9Dii2vD2ZCDyDac2OFm0NKKux42nqWq5EmJvR4GClDcmf19doZJ6X7OUkxtE5Um8BVl25L0g6k12ugAx7FrHXq1I1paYmrNkHgIctDe3rNvHYblN3lvi2k42lgCcS1sCF4UWeolmOATz+2TcqeoFKADrW24Rt26C4xZkNKgvTfzLTiAyVJHIQhiNGtpJbVwbMb7IxUPw9oy6Qhb0WJjlk7MnSIweIe34Qg8SwnBotRntmmVyV9nuLJkQ/DElF2MYmWxSgUI35VnZ0qPmeCzbGlNRrSdvPcRqVYR5nFTNSVpys57jB0Ra1WtfGWJgHiETfDZKFZjkWcmaB1OtRMxCrLkuq4fayBUq6581v9/KczfJvD9SrPA3A0wWeooiNZTVfNmW1VddpsK8TCbhouLDZA/H/VKEvn9syo6QNVnZUDE4lSaNIM0rYhYTBsuUNlMW4fRRKzLYhmyyA2Kizuw9RXFTQcak6UIBajHUrEShCasdZjxW4emfqj28X5A8iwZ1q3W6r4XTiY1FPlNY1HKEoEfKtyUbj8ZOFUJ1L9+YtVq33hze2+mwWSpg2DqLSoneHR8QmPk/1EkYqap4ymmbCeHUpoTj7joABMlJY6ENdU2CaVMyeAtnpPNOKEZXxS1Y9UwU2WpInxW0X4oozM36oYtLBY3cVufVWurDLBL2nZdN1ik27obrminpkxEnNlxHF+1MSUIwT67cOJhrFhJ17A3JO5AJg/ataehDRdK8CwCL0dLHqFxnGYyTUGWWjOnZhpMljoIpnlIiaPyFLvhcgm74TT9UKqRBOVaXTusTVVZsvNwpaPSpDLRWI0mB2lmQwkFyMx3ptCGszWlE3u44szutita1JQl/ZviVKXu7xSLmoazbcOFtg6LdmqYaFm1tfgsW1riGuazTpOqKZMQU6VG+Kha23B9lqTUq93uWeol8G/J7T3ZLkFBlkTt/i4mSwxNmLbLVHOF6i60fyuKC2GU3687Waaq/niP1Tyz4mJhm2m40MmybHCddVupqqGUVq3DBDVMl5TG5Te11tZFoP7Qtvfk84S24SxiCfylwjETfMYLi8Uy5BCyZLN3Tr5BtxIx2wTvYOdc+5l7fQ+QXSwBdc5SlBeqmMv4e+dM08HDpuzkz2VDasJUK9E2s2nv+QuLWwlel70aNuqvlWkn0zMBJksdBPPJsvgEb5k0mBqxqQMeVdtO8hmUa6eUWVSt1WODNOX36SpApcTrYR7wGEvwJCJd1STScQqNXNuodSjiDkJedzZhl97zkpW2tJQl47UyMSGdNgZv8ZyufEAGBGyX9I6H5BX5tX3VyrbFF5GzZEjCxiIUK691mG08xlRZSjJ405rSRd3JSk37lze/7lS7YgXQtPiiPFwzBSZLHYR8zi6UMkn9AUy8RY3RcOIxfD+/SYHgkSttxgpeQCZCgzRzFmf2CV543khaLT651WBq0k8ldTzGV1SUCLquUuq6bvz6FwtlSaV1aKos+RN8sWfWrz0VsfoFkKMD0lOWTGuPRcYS2E3DRSWDe++zI49hrTIgUJpIFCC5DSd9DabkcTSC0PQRELzRCCI2U2Cy1EFIy7MkE5KKIfGIag+ZGryTlKVsxvF/09WunZL/p2n6K6R2LuP4Uz7axCOpLWmVO5W87sR7nKYalqAspRYdkM+0PU4VTXEHaXmWYib4PI+QvldOkLewNlwwwWfSOow+s61nadxf0RLtWbI1eLfexO2VpXD1R36fqbKUlsE7aoKvmMv6PzdMr/PYVPj1oJgOHPUJHnuWGJrIZUwny+LVH8dxjCfiEomYUMMMVZqout7HzGIJEpf/GnpeSg2Pk+OEB4A6jmNcWz2UkjaWIJtx/K/FXFkKV8OsErzjUsel14xui08+S2wsgYVnKbwNJyl4RlOYcT4rQcQMlKVq0IZrr2unhsUtQ7ZpHdbr0gRfoZV4WO6zK0e3hnw/lKG3KKxVJn8u05akbGaPChY1JUviTP2taphIHbdRwxqeJW7DMbRhSjzETSsqwRswT/FOykMyDWJMMo5b1U4K6TRU8OQzhwVpyrVNr0ek/4dg3Qm1ETtRWbIgHuI5oQpeNuO/1rUJb6Ou44S/pn2VxsaUHmbwlt5n1OKLU5by5mf2TekJMQomay3iiFigABlM8FVr0gRfRM6SMaEJT0oH5JUntG0426k1kaJdyGbaXnvizKakZjQk7FJ+2yqWwA+7ZLLE0ITtupN4lcZOtUo2eNO292xqJxGxwP+jO8HnXYsw03FQO9t0BlWoEhqr9S/Ek3bJniWz15x8lqidUeYEL1BoQpPjbQheDHnMZ4MWrUk+lH/uOPO4TRsuLJJAep+Z7yzaD+XnFlkkpYfV7rVM2o6ahgPsiVhUG862JRm0ytqvs623KDBhN7fKKDxLUeRxpsBkqYPgqz+av8VVE9pw8sdMAy+TDd6003DNtWeH/yeJHADmpCYxs4hgGi7JiK2/DDm6NSTXtSIHkaqVWYsviYQFypJFqyyE0DiOI5m8zUlNaCyBhXlcnDl8T56shpmoVipqmP61EBEJhVwGmRY1Xc5vMlHDJiJaZUBgxLadDozMWbIlNCGkw5osRU3DEbThRjlniWGKoFVmqixFt+FMVKtaPZg2ok7wTmrvAeYTYMrp4MTGcZvaict/Deu6rptY23RJr+qKljQWC4ubu7ZnqRJ/5kBZsiAHUUTMYhmyih+KmtBkM4HX0STDKWjxRZ/ZZBpOnDlOsQLMzjxZiW7D9ViamgOVJipnyVINCyF4fhvOsF0WmbNk2Yar112ODmCYw37dSbJZWqe2/NjIEf+cLcFLoXVYjW+XmZIwEWKp5LNKq6VlEXcQpaaIM1OrNGlNlgHSuLxpGy7kBi5/PmplCTAPvKzW6n4GVnjgZTBpp4s4QuO932ZXXnQ2lE2ieSwJy9GoYWFnDpK27aIUWk3pgcFbPxgWCI8NaKtt61lqqd1vuXdOfl7YuWcCTJY6CKYBj1rEQ6Nd1kyWkszS6XmWTNtwkcqSMaFRb3eStw4t6wIKakpKBM9mN1w0qTFUlpLacBbKkip51Cd40vcwLNGcwOAdfT3SSTTvTikbKpNx/OtsoyyFrpXJm3uLKrW6/3O9PRvKIwu1umv0fyU+7sAu/mGsFD6x1mupLAkS5q2VmR00ZXacgqEEexN28jScTu2kEEYg2BlHHXcgf07TqbXkRbqGPisFgqdPPOJXh9iasIFkD5c+8ajF1vV9RRbLf6kznJKzoQiCNKNah4bXQz4L9SoVP+wyUlmyUYCia9uQpcmYCT5AXnprQ5baz2yzVkY+S+u5e6S3TVpxYxETa9778sZ15edFJXibepbGpIylqMni6QaTpQ6C+boTBWXJoF0m6soBkW11DVUa8UM6tqVlqywRT8MpeZayZjfxtEzYcqxEqxm2rbZp3EGS+mMRSkmdDl7ylZR4cmCXWZTQOtSsLR5fyLYbmoHAv2XXhgs/c7dP8My/h90h/h/fs0TsswKCM4ucJ63a5egzdxOQMMdpf+1lMk6QO2UwaRc1Zee9r7GixdSzFEHE+hskrFytG03ojs6yjCWAyVJHwdSzpEKWCga1lUzYKRK8YK2FYYsv4oZoruCl3zqkNksnkQ7A3NRcSrgeVtEBMZlFgLkpPblVZkZKAQXzuGUbLkmxsmlpRREPuwynmAk+i/beZIxnCQC6LBSgONVKkDATz5Iwsnfns6FKik+WKgbKUjmuDUcVHRAe/mlaO5iEY7LEMIBpcKRKGrbJNJWOYqVvwk5WaUxVq+Qx/HRM2PLHqEM6TU3YemqY4WRZglnaKLMogTya1k7yQtkoS0lxB6YEIW6JrlzXpHUYEJqIM+fMVZpY4iEIjdE0XLSvSH4/uWfJ4sxxU3a2tePacLaTdlGhlLlsxv+/YtQ6nGWTcACTpY6CbRtO+Ifia+sYvBu+IoXpL32CJwhNsmpVIlaWjNUfHbJETfDyZq3DJFXCq20ZpJmNmLIzVMPkZbfU61+Us6EsiEckqUnJZ0VC8KLObNh6qtTqfuxI+NSaRbtTsXVoRGrKycqSURsupq5c2+TMcW04G59VpVb3X3vhk3ZeK26k0VLTwWzLWAKYLHUUTPe3Bb4UFbM0rbJkG3ZJ7bOq191Ew7vpNFzJP3M0wStaergSwz+JQ0Xl2vTKkh05kGtE1da9cSW296wm+KIDHgF7ZSmN8f4k/0+XYeswztAM2Pl/EpUli9ri+x7nWTJqwyWe2TyWwK8dlg1lcWa5vRbW4usrmtce4zZcuti4cSNe9rKXob+/H0uWLMF5552HzZs3xz7npptuguM4TX+6urqm6cR6MFWWqgnBkYCZtygYwVeYsjMcw48a7wfMCEKlLk1/EQc8Bq3D8B94gKwA0ZIa+Sauk8WSpFgBBGdOUMN0z5y07FZ+v3k2FD3xCFp8CdEBhgbvxNTxFHOWdBUP+Sxh19qqVVZOUPCsaidHB9hMw4URGiCYiDOpPRF3ZgsSJlplhVwm9N5iU1sYvJkspYS7774bV1xxBe69917cfvvtqFQqOOecczA+Ph77vIGBAWzfvt3/8+yzz07TifUgbpRVw5yl+Dac/mb5isKN1lQNUzNL6y8Wlr++pNTxSs3VIx4qZ7ZMNE+a/nLdgByroKRA8Ewn+PzJsgTPkuvqtX+bv4dRE3ymqlXSmRv/B+suqoYp7InRAYYEL2m831swq/ezY8o/c8I0nOaZZRIWZmi2ym+qJqg0Nm04BZ+VWRsuYYKPwMMVmjru1zVYWJyghvVa1B6LWP0yk5g9JyHAbbfd1vT2TTfdhCVLluCBBx7AaaedFvk8x3EwNDSU9vGsYZ5YrdDSsshZSqUNJ85MrSxJN+WknCVRO+pG0YqZ9Cw1nblaj/2ehNZVmYajVpakz1mq1mLPICNp2S1gvvA2OZQy2/TYnOJ1BlQmy8SZiZWlQkBKdV7Pcu1EIqbb7kyIUZDVH9d1tbJ2Av9P+JlJDN5hbTiLabggvTueLJnsnRPn6SI/s5op3WSx8GRj6q8n4vUxE5hTylIrhoeHAQALFiyIfdzY2BgOPfRQrFixAm94wxvw6KOPxj6+VCphZGSk6c90wHzdSTKpCfw/+gneKn6Xugut38SVDN4GxEMtVyjT9ngV6JzZlHgkRQfo1k4Kd/Q+ZmbwLiUYmk2vs4opvcs4Z0mt3WlUWzHwUp94JChLTSs+dK+H8FklkBrNm62vpEQpVoVmUqqDUpKyZKgA1erBYEHsNFzFQMFLUGkEaZiw2WcXsyvPRLGaiMmckmubnDmp9kxgzpKler2Oq6++Gn/8x3+MY489NvJxRx55JL761a/i1ltvxde//nXU63WceuqpeO655yKfs3HjRgwODvp/VqxYkcaX0IaC1B7SQVqLdFWCI+WPabVaUtoNp5Y5ZXYTVxvDbxAP4jZcNuMgl9FvpYp9dvFkyayllaQsOY5jRB6DsMtkb5hxGy7iemQyjv/16Nxs5Qm+5Kk1M0ITpRjlsw7E7wX6qlWCwdswZykI6IwieMH7dUlN0mSZuc8qeHycZ8l19QlessG7cZ1N2nAxxEPsoZswIHiTCcqSWNw7YRAdMD4L23BzlixdccUVeOSRR/Ctb30r9nHr1q3DRRddhD/6oz/C6aefjltuuQWLFy/Gl770pcjnbNiwAcPDw/6fbdu2UR8/FOIGX6u7/titCqoqBMGgXaZEwlpaWrq1qVtaSVNlgHdD9ImHAXlMow2X1vVQMngbnjmJeADBdKDOzaWkdGYzz0tSG877mPmZAZU8JFplyXEcYw9QKYnUWE/whV+LXDbj/1zRbZf5BC+qPWTYhpPJUpwpHbBQ2hLbcAYqjUI2VK3uav8C57fh8uGExm46ML4tOROYPbSNEFdeeSV+9KMf4Re/+AUOPvhgrefm83mceOKJePLJJyMfUywWUSwWbY+pDdm/U6nVkc2ovZBUvEUmRmwVlSYntbpMbuIqyhJ13AHgEY9quaap0oibeIxZ2oB4yHEHSengE+Wa1s1Wx2dlGngZn+GUwWhJjyAkGcflz0mdWSQ+r/6Zg2sXFR1QTIl4iI9NlGsGI/5JypL3tZgSmjh1sCufRaVW1ScefuswwrNUMDvzZCUg/2Et/Fw2g0I2g3KtjslKDfMNake34QIFSBeTscpSM8HT8bMJ/1RUq0yoQtQTfDOFOaUsua6LK6+8Et/73vfw85//HKtWrdKuUavV8PDDD2PZsmUpnNAOMvFQJQiu62q1tEyIR9wN3HEcoxafCjkwUTxUbuCA4fXwTenEPivpDLFGbAvFg7ouoGgeN0jaTkv98c6hQsT0SY0gVtmME2kKT2vdCWAe8pjYLjPcDRd4dGLObEkeo27ipuGRSXUBc/I4mWjwbnz/NIljre4G2VAhxCMvKXi6CpBqUrrJupOgxTd79Jw5RZauuOIKfP3rX8fNN9+M/v5+7NixAzt27MDk5KT/mIsuuggbNmzw3/7Qhz6En/70p3jqqafw4IMP4q1vfSueffZZvP3tb5+JLyEWJv4feYw8fsTf5CaerFgBZgRBp+2klzqe3DqUa2t5aRTIY9HAZ6VKlkzyoZSUFFODd0qkRm2CT5+EyeeIPbPB1JoSoTE8s6qy5D3WrHZSdEAaaphtuywtU3qc2mE64h8XSeDVNcsskglhFPEwnYhLmoZL0zw+E5g9tI0AX/jCFwAAZ5xxRtP7b7zxRlxyySUAgK1btyIjJVnv378fl19+OXbs2IH58+fjpJNOwj333IOjjz56uo6tjGzGQTbjoFZ3lRUP+XE5JYO3BvFQGO8HzKb4dNQw6hstYJbiraJa2fiK5HOF1hbXQ+PGpdeG0zR4p1RbjeClY/AGpJBHje/hVEWlbnrKUtFATXFdV2qXxZvSqQmNXFtfAWqQmqQ9a4ZtuDiy5BGSkkHteCJmOg0nE6Co10dPIYeRKf12Z+I0nFjSaxR3IJb/MllKBSpu/rvuuqvp7U9/+tP49Kc/ndKJ6JHPOk0jrEmQyU96niU1lUZLTakm1zbJWVIhYYBdi0/FSG/kK8pG5woBkgJkcD3ifFbmBm/1m7ieSV+BeFgGPCZ5lgAzZSlOSbH1LMX7f/SJh3ztos5tQsK8x8eb0gHzdlmg0kR4lnzFymxiTUXB01etElqHhtNwcqssKiolWHmiR2qSlv/2GCpW8nOizOMzgTnVhnsxQNyIVVOaZTUnjniY7FlT8Sx5n9e8DUe9G05ZWTIheBq5U9SRBPLHyeMOUvUsmauD6XiWko3HZt4wdWVJVw3z1R8FNUxH8Wg2pafj/1EiHsS1/TMTExqvtvc9IPf/+JlFeoRGpZ3VbZiHFBi8wwmNUIV0iaPrurHhnzMFJksdBl2ztKz+xKkSZrvhFD1LJi2+xmNjW1oppY4Ds4t4qJCw5to66kEtsbbJnrW6NIpM3S7TacOZJkurqFZaKk3Cgl65rr7PSoV46LdoRTsw40T/omXshVI6czr+ny7DNlxSjAIQ+IJ0X3eCeESd2VSlUWkdijwk0zZctCldtOH0yb9oEs2m6AAmSx0GXZVGJHKrkgMzs7RqbeqWlokXKvlmKH9eE59V0ni//Filugq5QkB604HTMsFnMFmmYkpPpQ1nQHgFOYibsjNd0qukLBmER5ak2ICoX7RsfUUqBm8dbxgQnDtxN5xh2GUc8TBVw0RLMGl1CHV7T/4YtRpmuhtO9jhxdADDGHlNglCpe4/LRfSr/bomrTKFUXnT2r63SCUNW+vMemqYzg2xonBmE0KjMt5vWltt3Ym5+uM9P66lpU9qggRvWl+RfA4VBchEWYozNNuqYWrTcOq1VdQf+zZcjGfJwKcjhyuSt+FUJvhsiUfSZJk2CWu0ymJN6WakJqnF5++GMyV4MT6rmQCTpQ5DPqOnAKmM4AOSklJPw7OkZx53XVfJPG6U4K14Zps2XFFFWUrRs0Td4rPxFQHx30MbIqaSwZVOzpKJZymZ4Jma0lVUGpNVKsHEWvKZdfehqZml9clj0koSoNmjY3LmWOJhakpPUK1MowP8uIMUlKXk6IB02nszBSZLHQbd9pCqkmI23p8cHCl/btXatbrr96yLMVNaRhN8inEHVu0yFWUplQk+faVNpcVnS8JiJ/jy5kpbUvqzeKzODVErD4l8gi8Y3tBZOq2TlaVHPBSuc6Nu3dVr4QdKmxoRU4X82OgdfF7dmpSMr4K4HWsCqeUsSVOjOquufBO2grKkT8TiSU2vNGWn838wKRl8psBkqcOg24ZTvdH6JuyqgWdJkXjontmrHTPBl5KvSP64yaRd/JJeC0Kjmg1FvM9OJmGqP/SC5a5qBE+LeCjUlj+mo2hqBWmaEA+FliSg59MpKak0+kZspWyoQvAxHT9UWqGU8pmjWjhNO9wMiFgqnqWkzKKC2ZnF9YhTaXwFyHQaLmE3XF1zsXASCZspMFnqMOQM23BJWUg5E+KhQA4AfSImPy6udjGndy282oIcpJANJZS2mJuLIH/U7T358xq1h2Ju4vLXo1pbZRJO/jh5UrpMPBQJgvy9Vll3YqQsKbT3gDTSwRstLWJC42V/NT9eqXY1WaWxIXhxZ85nvXBf+fEqUGkdmqg01Vrdf+31RNQu5oLrrJOHpLJjLUjw1sxZUmzDyedQwbhfd/ZkLAFMljoOuiP+VcVReZtQykICEctrKh7icY4Tb0y3MY6rKkt6pCZ5DF/UrdZd1BXldDHBN1M5SyYqjcqovPx5jcbwY4iHF5UhHq9Wu9mUrkA8iKMDMhknuB4G6eD0Bm/hhYq+Fo7jBInmZZ0zJ18PE/P4VMIkHOCd2VetNG7iWhN8BtcZiCaPpmdWySsybsMl1M5mHP//kc5+uImEPXkzBSZLHQbtaTjFNpzNIt3E2po3cblubDZUiv4fXwHSUK10ogPkxyfW1TZ4q//QU8qGkr4e1e+hajaUzXRg3I3WcRxt1UqOL1BRrUyUlCSlzWThrc4qFa2cJQUSBkhTa0aqVVyLz5wcxNX1Pm7uh4pd/mtyZoWVJIDZRJxK3IHpDjcV1crmzEyWGFYISI2qKqHWhjPJWVINpdQ1j6vmCsnKkqqXRt3/YxBLoNCGsyJLaahhCgQvk3EC5VGTeCSRA6OJRoW2k/fxxvdQVQ2TCE0cSRc3Yi1vmIIa5n3cIJZAYZWKUdyBqJugDpoQPKVpOF9lo20dAkB3w2ul5f9RMHib7HCT84riXncmU2tJK0m8uvqTdrV64O9T8UPp1A4iCbgNx7BA4FmaBcqS6mSZReq4Sl1Af/2LqrKkM8EnplRUlt0CGsQjxXUnKgnegH7ulGrr0Mb/o6paqaopuiRML0hTkXjk9a5ztVb3X/v0oZSaKo3GDbGk0tKyUGkSyZJB1pJOzpJOXZWVJADM2nDieii04UwUPO/50aTGb/GZtOFmUSAlYLBI97Of/Wzo+x3HQVdXFw4//HCcdtppyMaMfDPMoZtarZ6zpB8doOpZCtplemqYKjkQZ0kiQIC6slTUVGnkx8XVdhwHhWwG5Vo9vZaWgUk/kSDksxgv11JTlqhN6YAUTKlIEFT2wsl1tYiHgsEb0CdiKstuvY8J9Ye+DRcQMZPa0dfDxv+TlPxsMmmnMg2XVl3ATAGaUDmzwd45QWgcJ2H9S9FcWeopzi4OoU2WPv3pT2P37t2YmJjA/PnzAQD79+9HT08P+vr6sGvXLqxevRp33nknVqxYQX7gFzt023DKu9CM9relo1qpTtnJylO5WkdPIbl2RTEbSlelUSVLgHfuck1/ZU2aBu9EUqNLHjUJHvVuOEBfDVPJQpI/ruf/USN4ulNrMpGIjVLws6FM4g6SlCVznxX1GP5UOZmEmdZWWR0i6upMlqnUBQKlxeR6xLbKDPbOyV6ouNahqD1uMMHX8Z6lj33sY3jZy16GJ554Anv37sXevXvx+OOPY+3atfjMZz6DrVu3YmhoCO9+97vTOO+LHqZtONV1J3I7KQnqnqXGmZUN3mqEJpsJJp6ozdLaBE96XNK11s+darSdUtwNR20eV52Gs1l3Qt3i027DEYdSNtXWVJYK2ehcISBo/6WqLBlN2hGrYQqRBPLH9abh1A3NJtc5WVkSZ9YnHvFxB/pJ26pqmFGLb5ZGB2if5v3vfz/+8z//E4cddpj/vsMPPxyf/OQncf755+Opp57CJz7xCZx//vmkB2V48NtwyqqEmq8o39LSymaSWb3yIl3NWALVuqKlVarqt7RUl/+WNMlSUmJ1U21N1UrZLG0S0kk8tZbmWhll4qG5H065vWehhiUTD73a/iRconHcQP3xW4dqZEmV4FVqQQp1nIfLhIT5Hp1EU7pJ61DdZ6WlLGmSJTODd/St3qSuqs/KqA2neD2mG9rK0vbt21Gttr8QqtUqduzYAQBYvnw5RkdH7U/HaEOww02vDZd005LVEH0/lJpqpavSJN3AAf32obaypEtoFHxTuqRGd4JPlYTVpXUPqqRGmTwqqz8GniVVb5F2dIAe8TA6c0rKUmJ7z0ANC8iBYhtOkeA1rSRR2JWnl1jdOLOiskRu8DYI0lQxYQP27bIo9BbNW4dJrbIeg7akMIN3fBvuzDPPxF/+5V/iN7/5jf++3/zmN3jXu96FV73qVQCAhx9+GKtWraI7JcOHKfFImiyTlRZlP5Sqt8hXD/QITdKZAf2WlvKknSGhSVLwAAv/D7XPSvraqP1QqupPUFcjG0o5HVwv/iHNaTjVnCVd1UrFKC1/PJ3oAD0FSDzOcRR38OkQj4qismRjxFbwLOksFhZKStL0l0/wiM/c01hXUqm5yj9HVcf7e4r6BC8weM+uNpw2WfrKV76CBQsW4KSTTkKxWESxWMTJJ5+MBQsW4Ctf+QoAoK+vD5/61KfID8sAclm9Npxqgnc2E6wAUCdiuuZx2jac/BhdI7bqTUs3SDOJ0ABAwfAmTk9ogsept55mg7KkGR2g/dqgbZUBaqPy8sdVlQl1E7YBwVP0LBU1zyyrbLG5QmJ5bE19eazv/ynQksda3fVfHyqTZYD6604lv0n+OLW3SN7vp0oeVcf7TdLBVcnjdEObug0NDeH222/HY489hscffxwAcOSRR+LII4/0H3PmmWfSnZDRBHldhgr0iIfT9EOBqnbeUP1RacMFSdvEZ9YkeKqEBpA8XMTEQ3eRrvz5k5U2U5Um/gdemqGU2qb0WWHw1j2zIqGRlNJa3fV/MYqDrmqleqNVNTTLn3eqUkOvgtIwpags6Y74y6QqlnhI39/Jci3x+yKfQTUbijoNu5DNIJvxfvZPlmsY6Mon1lVZ0Ot9XHiWdFp8s7MNZ6xzrV69Go7j4LDDDkMuN7vksrkM3T1rqm0nUXuqUtcmYsnJ0nrkwB+VV1FpNL1FyiqNoWKlRJbS8iwZtuGUTOkpXQ9d4uG6rtSGo520KykamgXxmGq0WpKunXwGVbN0WsoS4H1vklQMwEQNUyUeinWbliHrkSXVgEfVMzf5rGKudS6b8XPUJis1zNeorZwNpajSuK6r1IZzHAc9+SxGS1Xl2hOKPqtgSa86wRsvqX0PpxvabbiJiQlcdtll6OnpwTHHHIOtW7cCAK666ip8/OMfJz8goxm6bTjV6S9Av12ma5ZWXjth0oYjVpZ0gzR1FDz96AA1UqrbOtQxpWsHPKakpFRqLoQVJJGI+dNw6XiW6q66wqtKatJWlryzKJIa5X12egRPVUkxWSwsatOT0uBaxEU0eLX1lLYgZyn+OuvuWZPbl4nEVLNd5vuK0ogOUJjgmwlok6UNGzbgt7/9Le666y50dXX57z/77LPx7W9/m/RwjHbMFv9Pve76NwpV87jymXXM0qbEQ5XgKd60tJQl3dUhusqS5i40lTObJprrRBKoGGJlEkFOPFQJjdQe0lWtVEmN7vLfpLq5bMafeNUNvFSOO9BsaSVdZyBoa6nebAX5SWzxad7EVRUrQD+3SDVXSNeUPlUOXkPJ7TJRW61dpjoNZxZLMDvbcNpk6fvf/z4+//nP4xWveEWT/HzMMcdgy5YtpIdjtEM3OqCqsNzVr62xSqVSl/wuijdx9dRxDbO05k1ctcWn3Sqrqas0pung5CnbinUBc/M4tUrTbEpXq60/wZfgs5K+x/oZTklETK89pKrgAfomb/XoAJFZREvCmmprtsuSzqzr/5ksq5EwQH9qTVVp011KK9aX5DJO4i/LQYuPeBpOnFnxWtTrrv+663iytHv3bixZsqTt/ePj40q9e4YdTNtwSanSgN4qFfkxyZ4l0/ae+pnJ9875XijNuAOdMxOvDtE1NOuoYeaTZWpnlp+jUreQTfZZaas0vq8o/syZjKOlDtaloQl1NUyX0KgQD9HS0lWA1JQl5ZZWVY2EAQHxUFcH9czjuoRGhSzpKkDqoZSaZ1acspMfo2rEFgqUsmKlXDf42jq+DXfyySfjv/7rv/y3xQ+sf/u3f8O6devoTsYIhXZLS3G8H9AjNTJZU50so56yAyTVSjfRPCVlSS06wMzgrXrmSs1FXUGlSdOUrjsNJz9Hra76mal9VoBeMKV8zdS9NCmcWdNbpJ46bpazpEQ8cnqKh+5kGbX649XWbR2qxh2Y+YpUrrOuHyqtNty44oLemYA2dfvYxz6GV7/61fj973+ParWKz3zmM/j973+Pe+65B3fffXcaZ2RI0I4O0PD/5DTWkghCk3GQOIac11x3oprfJD9Gm9Sotg5TmIYzNWKrtg4B7+vsSlhZU1K8FvJjqD1L2YyDXMZBVTGyIphYo1fDVPfZiceMoqpExOS2V9cMKku6619UowOKmqGUJa02nJ6aono99Ntw+iqNdm3FNpwuCVNpZ+lO2qnsnJM/t65/K2lB70xAm7q94hWvwEMPPYRqtYrjjjsOP/3pT7FkyRJs2rQJJ510UhpnZEgwVWkKitEBgBpB0JmySzNnqaDhs5LHzpNN6d7H9dd7JP9g0m1L6sYdAGrkUdzEVdSwYAw/zRZfcm3V4EggUHGop+Hkx6jUFl9XNuMglzTRqO0r0jFLC2+R2v8V3X121NNw8mN0V6kkEjzDaTglz5KmaqVKPFJVwzT9UJOKREykg2tP2c2yFhxgmLN02GGH4ctf/jL1WRgK8D1LqsSjrq/S6HiW9LKQdNed0Bq8a/Vg7LyYVWsPiSmtpN9ydPKsbPKQYuvKZEmD8KoQD93lv3otrSzGyzWtNhw1CZMfp6RaaSgeqrEBQKA8qZID1fwmQE+l0THS6xu81T1LXZqKhyqpMQ2lTPPMSQRBN7NIddktEEQAqCd467XhJis11OtuYuyCat2ZgBJZGhkZUS44MDBgfBhGMnQXxwqVKOk32uba6m24NMb7TdQwFSVFfkySEVsmHtW6m0iCTCbLqM3SwnhcrtX1zNIacQfUK1p0a6uO98uPofZZyY9RI3h6xBFIR1nSaZfJj1H1LOmfWceUrlc7UaXRXKSr51kSBEFPaUs2eAfEQ+UXOK02nGa7TH0aLvjcU9VaIiGcrbEBgCJZmjdvnnL/sFZTz1Ng6EPf4K1DPNRVK51lt2n5igCpxaegWsmP0fL/VOuJKpeOwVv7evieJTUFKA2ypGNolmurtcvUFSATQ7NyG86AiOmoYUptJ0NlScf/o3Jmof5kFcbOTX1FSv4fn4gl167W6v4vkcrTcJrtPZ3oAO1puASDd+veuaTvuY7BW9eIrbqSRP7cE2UVsqSuhk03lMjSnXfe6f/7mWeewfve9z5ccskl/vTbpk2b8LWvfQ0bN25M55QMH9ptOINQSrU2nE5d3TPrT/CVFUh6qfEYR8GULpMeHfKYilla14hdUlTaNEIpp0NZUposSzHuQI+IpUTwDFUanfaQCvEIdqxpeKE0k8GT9rcBei0tWX1S9f9Uai4qteRfhlSX3cq1dUf8Vc8MeKQi6fGTiuoPoN+GUyWPmYyDrry3Rkvle6g6ZTcTUDJ4n3766f6ff//3f8c//dM/YePGjXj961+P17/+9di4cSM++clP4sYbb0z7vEq44YYbsHLlSnR1dWHt2rW4//77Yx//3e9+F2vWrEFXVxeOO+44/PjHP56mk+pDh9AAmpNlGu0yE8+S+iSV9x9Gb3WIns8qSSnNZhyIh+j4f9LwWYmVBeQtLY11J2mFUgJ6qpVeq0zXs6Tu/9EhNVNaU3a6BE+/toqpWU+xUjeOe59fn+CpKEAyOdHZladCaoxylhTIQa0eGOmTamel9S8qpCY4c/J17tbMQ9LyQ2mYx2ezwVt7Gm7Tpk04+eST295/8sknJ5KS6cC3v/1tXHPNNbj++uvx4IMP4oQTTsD69euxa9eu0Mffc889uPDCC3HZZZfhN7/5Dc477zycd955eOSRR6b55GrwowMUVZqqwU1cy7OkoVjVXfg3/vja6RAx1RF8wMsPS1vx0LnOqrV1/FB6Z9adhktHtUorC0l+nI4RW8uzRKz+AIbKkgbx0Gnv1equ0mvaLME7ua4gJyr724q5jP/LkFJtrckydZVGJmoqBCEY8U8mNaprVACTNpx+LIFK4OVs9ixpk6UVK1aETsL927/9G1asWEFyKBv80z/9Ey6//HJceumlOProo/HFL34RPT09+OpXvxr6+M985jM499xz8Z73vAdHHXUUPvzhD+OlL30pPv/5z0d+jlKphJGRkaY/0wVhTNZf8KruWdIxSyslVks3Hx2CoORZ0vD/6NQF9MhjWm04+WasFXipNQ2Xpllah4ipX2e1nCXd6ACDdplGzpJK2ylNZUmHePgmbA0SJj8vvrbONJy6kiK+Fypqh+M4Wu1Df92JTmaRhvoDqL3ugtyi5O+haiQBoHfmcrXu5/yJaIA46GQtdfw0nIxPf/rTOP/88/Hf//3fWLt2LQDg/vvvxxNPPIH//M//JD+gDsrlMh544AFs2LDBf18mk8HZZ5+NTZs2hT5n06ZNuOaaa5ret379enz/+9+P/DwbN27EBz/4QZIz6yKX0TV4G0QHKJilTcb7gUZYYsJ/3pJGbX+fncaNVqUuoOn/SSnBWyY9SrEEOtOBKRE8Oc9KyzyuMdKulg2l2YZLqV02ZaAsiY3xSd46HWUpaMOp+390CJ5Xu47+rpgHw1RZUic0KmcGPOIzWampKUC+z0qhpSXOrOHR6conq2FybR0ipkI8dAiN/Bi1Npy6ahWY0udAG+41r3kNnnjiCbz+9a/Hvn37sG/fPrzuda/D448/jte85jVpnFEZe/bsQa1Ww9KlS5vev3TpUuzYsSP0OTt27NB6PABs2LABw8PD/p9t27bZH14R2nvWjAze1G244IeACqnRyizSUX90lSWdSTsDNUxnVUYhl+yzkj+/jmpFnTpeqUl5VhohnUpBmgbj/do+K2LiYTJlB+i1lnVCOnX8PyrXwnEcPSJmMIav5A3TUJYAafJQ5cwaHp0uDXKgE3YJyCtPkltaWkGaOr4iaUGvys8Ov8WnRHhnbxvOiL4dfPDB+OhHP0p9lo5BsVhEsVickc8tlJSqZhtObSmt+tRaRaOF4zgO8lkHlZqr1S7TyXDSUVJUSJj3OFFbTZoG0vNZqZiwAUOypBhJID8nDk270IgnwLQIjbZnqeGz0ko0T8eULs6TdHPW8ywJBU/DV6So0nTlsyhV64p+KB3zuIahWfIsqaBLR00xylmiNY4DAYlQIXiCUHURT/DprH4B5DUtKp6lhhpWnH1kSVtZms1YtGgRstksdu7c2fT+nTt3YmhoKPQ5Q0NDWo+faYg2XLnmJUsnoZrSnjWhtqi2tHRafOIxSlNaPvGgjTsA9AiC1qi8jq9Ioy5gtjokrTMDmuRRSVlSJzTyHsWkgQh5vYcWEdNYd6JSN5fNINdoxyh5i3Q8SxrrTkoaviL5cWpn1ogl0LiJBwtpFdtwKZEaHeKhmyukYx4XoZg9Cmc2a5XpnVlNtWqQJcXa04k5RZYKhQJOOukk3HHHHf776vU67rjjDj8TqhXr1q1rejwA3H777ZGPn2m0JksnQdyAVBK8ddpwqjvWWmvrmcdpCZ5OyrZcmzp3SifRXJcsaalWWgZv9ZZWyY9+cJR8GFrEo6JPaIDk14du61CHlOpEB+jWLul4lnRWtFTVlRT5cTotLXLPkoEa5tVWn7RTW6SroYZpErygDafe0tJZ/qvS3tPxQgEB8VEiSyXRhpt9nqXZdyJLXHPNNbj44otx8skn45RTTsE///M/Y3x8HJdeeikA4KKLLsJBBx3kB2j+9V//NU4//XR86lOfwmtf+1p861vfwq9//Wv867/+60x+GZGQp8+qNRdxP29c19Xz/zR+SKu0+ExVGr10cBWDt1CsaH1WQHoKkM5kmWgB6vqsyEMpTSIJFK9zcD3UDd46XijAI1k9hbi6elNJaa07Abwb4ni5lpqypHRmjVaZXFvnzDpkSWV1iDizrrKkpVoR5yxNaao0WkZsDSLWrUEcVVedCJhMw3VsgjcATExMoKenJ82zkOBNb3oTdu/ejeuuuw47duzAH/3RH+G2227zTdxbt25FJhP80Dr11FNx88034/3vfz/+7u/+Di95yUvw/e9/H8cee+xMfQmxkG/05Vod3Yh+UcmLY9XWcKhHBwRrVPQUD63oAOJsKJ1WGRC0AanN48IjpOcrmlmCJ7fKkvZS6YQ7yp9fRVnSObNoaVWl4L8o6CyOBfRWh+gSD1VlqdqYmJPPEweTlpZ+G462tp9npaMsKZ9ZJw9J/Xto0t5TfW10axAxnXaZIDTlWh3VWj22E6FrwtYxj+uqVtMJZbK0aNEivOpVr/JTu2erpwcArrzySlx55ZWhH7vrrrva3nfBBRfgggsuSPlUNMhJbY2km7jcPqJfd6LrWdI3j6uY0gs5HYKneWZRm9iIbVJXtw2nY8TWCXgUz4tTMvSVpfRUmmIug2q5lnitZSKtMnUYZDjpqGGKZ1b8LV9nvYf8+ZXWnfjXWZHgKU7aua6rOaVlQvBUW1rqBM8klJI6GVyurUTwNDKL5K9rslJDf8z/Xd0sJF9ZqmgYvGdhG07Zs/TYY49h/fr1+M53voOVK1di7dq1+OhHP4qHH344zfMxWiAmywAFslQPPq6Xs6TRKlMgNHJtnTaOlik9ReKhOi4PKE7wpXhmQWqUVKuKvoIHJH8PdQzNgF4sgU4bzjuDIGLxNxdBIHRIGKBmltYZw5drq54ZUPseBgneKmdW94bJtZMIXqXmQlgtVZRHHfXHWKUh9ha17p2LratJPNIypRdzGYjfw5NUK9MJPj3P0uxTlpTJ0iGHHIKrrroKP/vZz7Bz505cffXVePjhh/HKV74Sq1evxtVXX42f//znqCn4Dhh2EAQhyVskkx7qzCJd/09aqpXOJJV269AglkAnlLKkZaRXJXiBnK5aW+WG2BQsqqrSaHqWdCb4VEmNqtKmT8LUVRpjgqeoLBUU1nsAhq0yVbO0YmaRrDypteE0vFDCs6Sp0iSFR9bqrv+60/EseWdKIB6603AmbTjFRHPVHW7aZzaZhutksiRjcHAQF154Ib71rW9h9+7d+NKXvoRarYZLL70Uixcvxje+8Q3qczIkiFacyoSPeLxKayGv1dLSuyGqGrF10591lv/qqjQ6qpVpdEBS/IM2OTDxLCnkLGUyjrIipjOCD+iR0pKGKV0+Q6JKo9sqM2gdKntpfNWKVg3TW3eiafBW9EMJYuI4impYIbgWSf9X9H1WalEK8tekqtKIH7dJCpC2GqbYhqtrLOgVUFXxTNtwarvhZq/B24gsycjn8/g//+f/4HOf+xyeffZZ3HHHHTjiiCMozsaIgOpkma76o7NKRdf/o2qW1vVZ+WqYyooWzbgDvQk+MS6v4P+RyElS/IOu/yfNDCfViTjTaTitUErd3KmE2iXjVplGS4taWTI0jisleOsSPEXDu3/mXFbpFzjxtbmuSm299pDq1Jru/jbHcaSVJwltOFPPksaZ1cMj1RQg3ZUk4nFJdWUFr3cWepbIT3TiiSdSl2S0QLUNZ5qFpNIq020PqapWMjFJa89amp4llR+m8ucvV+ux11B3RYuJ/0eLLJU0lCXlXCH11mGQs6RXm7wNp5OFpBsdoEhqpgwiCQC9PCtd/49qG05dZQs+f6kSv1cyLc+S7v42UXuinLx3TpfgKZ9Z+rhqK1V1xF93Gq63qFZXVp7mpLLEmH7kFEf8BZlSvxlqTKwZGryTiJj8uVVIno4p3ThniTg6QP66koiHMcHTiVLQzUOiPrNOdIBm+1dVATKdWEtFDVOsrR1JkA9IWFJLS7t1qEqWNMlBPuv4y4QTyWNK03AlzYBO+bGqLS1d9SeZ0OgTvLTPrKpYZRz1/yvTidl3IkYiVAlCmiZs3ZuWqv9H1M04aqnj06IsJdSu1V0/70bleuSyweRJUu10c5b0Wk8FRTUlzRUt2pN2yp4lXZVGvQ1nnrOUZPDWneALWlpJrztdg7dy3IHmtXAcx1fakltP6ahhk2U97w+g0S7TJB6qhCbIK1JvHql6i3SzkFTbcHJsgEqLdrrBZKkDIe+8ikOw6kRX/UlBpVGsrRMb4D0uUNmSfls2NaUnEY8mNYzYiJ2WrwjQJ7zqBm+9m7jWDj7f/6N35kRlybi9p5NZpEfEEhUPbRN28PmVvUXEKs2k7w3TV2lUlSXqzCJdX5H8WNXroT6GL5bSqvqK9M+sTPC0U8fjSdiExnqWmYA2WZqYmIj82I033mh1GIYaVPehVbSJh46hOZ1QSqFq6d7AXRe+uhMFU3KQdGb5xqNbO9EsrelZ0mnD6U7a+SqNIuFVV5ayTc+Lre0HaablWUrBlJ6az0qvVVbIBlNaqu0ydZ+V3mSZ6pm9x6qqVnq1i4qxBLpeKEDdW5SaZ8lgqkyVPBq34Srx7V/dzKnphjZZWrx4Mc477zx87Wtfw759+/z3//znP8f/+3//j/RwjHAIpSi5DWdGPHT8P9Q7y0zrqtT2CV5K6g+gM2knguvUCK++/yf+B161VvfDAbXTwZO8NJpm6TSVJdU8JJNkcMB7zdUTSLouEdNVllSvs+M4yiTPV8OoowM023tebbU2nLGyRNwqA4Auzam1LuXMIu9aJLW0dK8FoOEt0mzxieuWNNE4PovTuwEDsvTEE09g3rx5+Iu/+AsMDQ3h2GOPxcDAAC688EJ86lOfSuOMjBYom6XrphNrOot0NVt8CSP++m244HGJtVNqO8l1VXvtymZpoaQQm9Kb1DBiwqutWOmQJUNSQx9KGTwu+VrrKROqypLuZJl8hqT2YdCGS4fgaREPxTacbotPeYLPqA2XaTpTFHTbZWLPGnVd+bHU03Ay+YkjYqJu7yxVlrQp3De/+U18+9vfxpve9CaccsopWLx4MW699Vb85Cc/QblcTuOMjBYEniXVNlx6niVdg3eiZ0mQMMUpOy9wU820Gkzw6ZGDRFKqqf4A6kuLTT1LOmqY7g43as9SQBzV1TDtWAJlz5LemcVz44iQthqmvO5Ej+ABQtGpaLS09JQlVcVKh+B1+7XVCJ56zpIaobFpw6mGdOq24cpVb4lyNmLSzcT/o03EFGtnMw4KuQzK1TomylUs6C2EPm68pK/gTSe0ydInP/lJfO9738O5557rv+8tb3kLfvvb3+Kcc87BxRdfTHpARjv86ADFNpzKVBkA5DVCKcuaoZTKbThNZcnblef9R0wkHpoqjeo+O11fkfxYaoN3UVMNy2Yc5ddHWtNwqm04EzVMXVnSI3i5jIOMA9Rd8dx86OPqdVfyWamqNIrEw8j/o6gAVQ0N3qrj/VptOEX/T1nveugqS1oET7MNp7sbTjy3rxh+C9etKz9Wdd2JTnBkTyGLcrUeez1Ee282BlICBm248fFxDA0Ntb3/yCOPRLWaHGfOsIduZpH69JdJzpLm1Bqxz0p+rHKUgqJqpZrgrZtYLddOVDxS2meX6pktVofEGUBtWofq6050/D/J7TL5+6Bu8FY7czBlp35DVDE116Uk5S5VgpdTIx5iDF9vGk4QPFXVinYMX3e9h0ltk4nGWOJhYvBWJI/jmm04AOjJJxMxf4lucXYqS9pk6fzzz8eFF16I73znO9i6dSt27NiB//mf/8F5552HV77ylWmckdEC1TacTYK36hg+dYuv3FjEbKLSqE6tqexCA9QJnm7r0DuDomrlqzR6ZmnlZbca11lZtTJUloD4XwAEeZCDCpOgO1mmE4bXpZDhJN94lImH4vSXbuvQq518ZvlaqQdeKk6sWfis4m7ilVrdf+2o3sTl6xz3887Ms5RMluT9bapnblqlElPbhOAFC2+jRY963Q3anUa1o888Ptem4T7/+c/jmGOOwYUXXohVq1bhoIMOwplnnomBgQF8+ctfTuOMjBao3sSrmq2yJrM0sWqlrtLondl7rHc9km6IugSvOA0qjbJqRTyGr7uQFghuyvTrTiT/T8xN3OQ6B9Nw9MRDRaUR10Kn3ZmqsqRAauSbsO4EH/WovFc7mXg0kVLNaTgg/meHn4ZNrNKY7G8D1NplU34bTr2l1a2g/shn1mvxCT9UNBELDN6zsw2nfare3l78x3/8B/bu3Ysnn3wSxWIRq1atwuDgYBrnY4Qgp9mGUzY0Sz/Mq/U6CjFcWneRbkH3zIqERj4DNfHQJzTqPzwKiqQmbYO3SbtT1VukG0kgnyuurk4LR9ksrUnwvHMoqDSa5u7mumoET0el8ZfpxhEPScFTJXja0QHEbTjxMUdjVYas9E2Wa5FnMgqlVPAsmexvA9TIo1CHdK6zID8qipXj6J1ZT1maI2RJYOHChVi4cCHlWRiKUCUHPvFQbFnIBKVSdYHwoQUABot0FVs4Qc6SDvHQrE29osWgpVVQnYYzVPBUgyN1lBRlP5TmmTMZB4VsBuVaPZYgGBGPFNtwKplFuundgLr/RwRAmtxo466HHxtgUldx3YlJSytuGk42jqvGd+SyGeSzDio1F5OVGuZHPM6KLMUpSwb72+Tace0yuzZcMgnrzme1zqyihs25UErGzEPcaKuqY/iKN61sYwxffm4UAlKj51lSb2np+3+SVKu0dsMFJEzjzJoKkO56j3KCWVqX0HhnUB3DF3k3+sQjrrbws5kQmlQ8XApETHclCaCuLJmpNArtobJeXhEQqDTlWj02SX9Sc2LNe6wC8RCERvNGq3I9pgxqB56lmPaeQavMe7z691CLLCnkLJmQMPnxcbXH55rBmzHzyPk38aT8H73EajGGD6gnS9OvO9GrC6i3y7Rbh5rBkXrK0syapXVJmFw7MTrAgIipxAcI4mHis1LNLNIiNQrXw0RZKqoqS5orSeTHxo3425iwAbXrkRbB01F/5MerKUAGniWViTXNM/vksRz9f8Wkdo9CzpLJlJ13juRluqZEbLrAZKkDoUpoxLSc0Rg+sWql7P8R0QFaAY/peGlU23DBlF2KLS3NXKGk2iZKinIekgmpUSAeutk/gI7PyoB4KChAJiSsS9uzRO3/MSc0adaOqxsER+rd0lSImFF0gEYbTp94JLfhJg38PyptOL9u3kwNi1umO+FHEsxOzxKTpQ6EfhtOxyydrAC5rmtu8E5YSWKiLKWlWhVVCZ6mygbot+F0r3NSbROfle6KFi1So1DbjNDoeWn0lKXk2r76Q1wXMFSA/NZhsildR5XIZhz//2H8BJh+bZVJO5NWmXwOFYJHHR0gJsN0lSUlI3ZFPwtJxZTuExrNVpmKZ0l8bLZOwzFZ6kDkNdtwqhMt8mPLMaRGbu9om6VTIR56k2WqN1t9U7qOgtc4s2I2lOqZMxkHuUxytERwLfQJjapKQ+7/sSB4ydNw6eQs6X7/gECxmqrGb2m3UWlUCJ62SqPQPiyZnFmhrgmhAdQW3hoZvBX8P6KNZkrwqNtlIjiyXKtH/iJu2irzVasUWnzTBSZLHYicqq/IxP+jUFv+mGoQY15RlTAyS6ekLKnuhjNRafylxYkET594pKXSqPqsTKbWlM5ssAtNf5EuLcEzITSirusmhXQKNczAs6QQHaBzZkAtwykwYqufWdw84wieyf42IDCmq5jHtXKWlMbwzZQlrXaZwZmB6OsReKFM23DJ16OXDd4MKmi3nTRGPFVqN5ElYoO3zZ61uNr1uotqXc8PJfuKYifLTG60mjvczMzSyYqHnllacRrOJLNI6czmZumkM5u14ZKJhwkJk8lPrBHbN3jTRgf4K0k06nq1FczjRmdWIDRl/e8foEZqfAWIuA0XBEemYEo3qF3MZfxp6ChSM2Gw6gQIlvTG+azEIl1uwzHIIG5w1cSAR3OzdFx7SHzMceC3fJKgbBw3aMOpGLzlr0fX4N36/Kja1HvWXNc1m1pTuB4mN/GgbsI0nEXrifrMygGPNjlLxMqS/DqKb5fZGLwVMotSMEubmJpV2nAmrTL58dQtPjnuIOoXLdNpODVvkf7rznEcvxUXRcRMs5CSdsPV665x/MN0gclSByKXUfP/mJmlk4mYbO5WDYBTbWmZ+H9UFguXm9QwvXUnibUtJsvivofVugsRWUNd28rgnWD+t2nxqZElk2m4JM9So7ZWHpJCG87gWnhLepPPbRYdoEAODNtwXQqrZfwgTR3iIdQfhWthPIYfcT1c1+wmLh7rutGvD1NykESWatIiZN3JsqQWn2nKdlIbTr7+rCwxyKDdhtPy0iQrQCarMtI1eKufGdA3pbc+vxVGY/gqCp70OU2M2EqrQwxaZXF1ZYKnV1vB4G0SdikpS1G/4csKnuqyW0BO8E6eLDNXacKvh0dKDVqHCkqbSco2kKwAyTdxLZUmJ260ChNrxqGU4bXlkE09NUxqpSaoNNTZUHKry9SIHa0smbbh4klY0xoVzf8r04XZeSpGLFTbcGZp2OqepTT2t/mtQwNTutKovIYals0E2+1jiZjfhlP/AaJieG8ieMRGbBs1TEX9AQxXqVC34RTM0s1npjWP+yqNpv8nSVmSP6dJeKTaxJohwYs8c016rMHUIXFwJJBMPKYkgqZDanLZjP//MJJ42HqWolQaiXjo/F8BgvykaM+SGSlNCrz0vVB59XU10w0mSx0IZZXGog0XF0tgtgtN0dBsMlmmQPACxUrvP2JqxEOlbuPrkUmbClSM2EatMl2Cp7VKRd2UbqKGxdWW20Z6RmwVNUy092iVJZnsmJnSaX1W3uPja8s3YJMlrHFtOPNQykzb2cLq5jKO1s9Rldq+r4hY/fHH+w2IR1eSAmRI8IKcpXCDtzB39xRnZwsOYLLUkcgpqB3yx03IUiXmBmBUN6c3DWfShou7aZl4obxzOIm1rTxLimqYDooaLT6TLCQVEpbPOlqLNlMLpZQTzSNqi7oZjYEFubbKBF9aylJW8yaepP4A5mP4xQTVakp6zem8NsS1q9TcyPwfW4N31HU2rQsotLQqAanRqpvYhhPqjz7xUDV46/qKktpwkwYhmtONOUOWnnnmGVx22WVYtWoVuru7cdhhh+H6669HuVyOfd4ZZ5wBx3Ga/rzzne+cplObQcVX5H1cL2VbfmxanqVKzVUawzczeNP6irzHix/U02+WNgl3lB+volqltb9Nd+xcZymtjkrjOE7iueWpMp3fxFWStk2VpSRvka/+aL421EIp9dud3lni1TBTj07TKpWE60Ftlp40VH+A5Ek743UniWZpc+IR1I5SgKpNj1NFksHbV5ZmqbkbAGbvyTTx2GOPoV6v40tf+hIOP/xwPPLII7j88ssxPj6OT37yk7HPvfzyy/GhD33If7unpyft41pB3OCSowPETZw6Z0mfhLUueI06k4kfSsngbagsCQ+XGvGgVlLMblpaAY/EK0nEtdA9c1FhksqkDQd4Slu5Wo8kHiaKFdCctB0F48kyn4hFqDQGsQHe49Wn7MzbcFFnNmuVyd+XqUoNfSGtGtPrUUxSUiyUpaSFt5OGClBPogm73vQ4HSQrQKbRAd7XWG2Y/Ft/DgerTmavsjRnyNK5556Lc88913979erV2Lx5M77whS8kkqWenh4MDQ2lfUQy+OssUswsivMsma33kMlS+38WAZtcobibeMXgWgB6k3ZG606I23te7cYNUYE8Fg18RSKkM0yFMVmiC8jTgcktLRNSM1pKbmnpq2HJBM9UpVFVlrTrJqg/QKDemCpAUeTRdLw/k/GiFErVeqICZJ6zRKuGAQreIsu4g+jJsmrT43SQ1IYzNXg3pYOXayFkyUyxmk7MmTZcGIaHh7FgwYLEx33jG9/AokWLcOyxx2LDhg2YmJiIfXypVMLIyEjTn+mEehvOwrOkcKM1mYYDEkiN1ZmTc5Z0/T963iKNaTgNU3oabTifeBhMrAHRRN1WpVFSlrSVifjWk+8rMq2rcJ1NlaVklWb2KUtR19lU/ZGfQ+0tSvL/2AQlJk/amZqlc03Pb4Wp+gOotyV122WFXMb/JV8s+ZUxbuiFmk7M3pNZ4sknn8TnPve5RFXpzW9+Mw499FAsX74cv/vd7/De974Xmzdvxi233BL5nI0bN+KDH/wg9ZGVod6GM2mXOY3aKpNl6nWzGQcZB6i79N4inRBG3Zt4XkGlKZkobQr+n+kheGbqYKlaD1ViTFUaldwpcz+UmmfJvG4c8UhJWTII0QSazdK1uhs6ZWkcHZBA8MRNXPfMgEc8hicridOB1K1DK4O3UK0iJ8vMFCBVg3cabTh/f5th7dGpamhtP79plu6FAzpAWXrf+97XZsBu/fPYY481Pef555/HueeeiwsuuACXX355bP13vOMdWL9+PY477ji85S1vwb//+7/je9/7HrZs2RL5nA0bNmB4eNj/s23bNpKvVRU5zVBKs/BI2jZcc+10lCUVcmDchktrGk6JHKShLOmrNCqTZaZqmJ+GHassmalWSbvyTFQ2+fEqypIuQUhK2jb2/8h75xIIgj7xUDtzt0HoYNJ+OJMFvd5ZEs5s2HYCAlM4tbdInLkqhXzKsJuGi89DGre4HnEm78DgPXvJ0qxXlq699lpccsklsY9ZvXq1/+8XXngBZ555Jk499VT867/+q/bnW7t2LQBPmTrssMNCH1MsFlEsFrVrU0GFHABygjdteKQJCQO8m1apWldrl1HnLKVI8Mpias3E/6NkljZVaaIVD5PWoeM4KGQzKNfqiWP42kqKirJk6i1KyJ0yJaUq03B+68lwKW1069CwrvT4UrWO3pAfY0G7THfSTqg0Ef4fQxImP4e8Lak43m+jLCWlYZvuhhO1W3+mTUoBj7oQZDOM0NisUQmeUwpXlirchrPG4sWLsXjxYqXHPv/88zjzzDNx0kkn4cYbb0Qmo/8bzEMPPQQAWLZsmfZzpwt+G66uluBNnbNUNmjvAWrLdCtV/QRvJeJhqngo+MNMFhanafBWMR6b+n8KOY8sRU+WGfqKFLw0xrUT9s5Z70JTyFky9lklRQdo1s1kAsKbRDxMSWlkgjfBZBl5LEHCKhUbgheXtC3vnNNVU/JZL6S2VncxValhsDvf9HFTE7b3nFyjRruvyGaNivwcET8gwzSSYDox69twqnj++edxxhln4JBDDsEnP/lJ7N69Gzt27MCOHTuaHrNmzRrcf//9AIAtW7bgwx/+MB544AE888wz+MEPfoCLLroIp512Go4//viZ+lISke7qEIXoAEHCTFUa4vBIHVO6thqm0eIzSsNO0+BNnJUFJBPTNCfL/N1wxv6fqJu4nbIUn4ZtpgAVE7w0JYubeFJt+z1rtO097znxbTh/n53hlFZUREMw3q9/q/STx0Nql6p1f4eiboaT4zg+EQtTaWw8Sz0xdW3WqABAf5dHxMZiyFJYLMRswew9mSZuv/12PPnkk3jyySdx8MEHN31MhCBWKhVs3rzZn3YrFAr42c9+hn/+53/G+Pg4VqxYgfPPPx/vf//7p/38Ogg8S27kCLf3cQv/j0KrTHd1iGgHqtzETTKcYn1WKRI8m9ZhrR5jtE2R4JkqHkl+qJIhCVPycKVExKzrVmsxUQppKUtmBE/UHkU12iwtWnzaKk18G45iGi6MeFRrdf91k9o0nE3OUkht+eswjSUYK1VDVatJC7LUWxTKUoivyGKNCgD0FT0FLIwsifcJQjUbMXtPpolLLrkk0du0cuXKpvToFStW4O677075ZPSQiURUwGO97vptOh1Sk1NqldlNlsW3+MyVpXJMO8QkV0g+h9KuPOOQzjqymZDJssYP1HSiA+xITbRKY0kOlEIp02lpmZ657not8bD/Z6bEI9jhRuvR8Z4T/T2sS74U03TwZGXJQKXJRytAcqq3aSu1WndRqdXbfkkzDY4E4ttwgozks/o755pqh4zh2yh4QtkZm4pRfwwJja8shdQenRLKUr7tY7MFc6YN92KCfIOr1sNvABXp/TpqilqCt+FkWUIekuu6VhlOscbxFDOLbKbhgOibuGkatk9oVFQaw5t4chsuDWXJlNQkEDxj43j891AmHtqrQxKW9Jr6rOTnhClAst/IdBouiZRSqzQyGTG9zvL5mmpbGbyjW4c2dQF5six6Gs7EhN0X0yoT7+s1bJUJIjY6VYmsbUrEpgNMljoQOYlICEN0K2TiYKJ4xPt/DA3eCbVrdRdC+DMxeKcR8Jjkh5IJnmmiOfUYfhLBc13X2LOURMTK1q2ycEJTq7v+a9qU1FBP8DXlToWcWyZ+pspSFMHz23AGKo2vWoXUlglUeutOzNWwUIInEQ/d9lAxl4F4SjypofUsme6FE4gjj+M+qbFQlsLIUkP96TclSw0iNBpDxGazZ4nJUgdC3owe9Zu43OoyyyxKVml0yVLSGL78frM2HD3BS1JSTM8sxvBbazTVNp6Gi5+0kz+ftmdJTJYl+H+oTeny10LdhisZemnEZFlUbfkmad7Siid4usZxuXbY91CcWUxcmdSNJktmvqKk2qaGdMD7f+iHaYaoNFY5S3FqmKWyFBi8w9KwzYmHTJZaF56LurbKUlgbbmyKyRIjBcg32sg2XOOmk3Gg9UMvn1BXrq2v0sS3+GSVTI/gqRvHTc+schOnTtpOS1myObNPxKjXnSiuJDGpnZSWPmV4ZiA+mFK8L5txfC+gcl1FZYnas2Sj/qjuWTPxLKVKPIQCFHI90ooOsG1pxQU82tQW6o8XS9D8fRy1JDQDMS2+UW7DMdKCTzwiFKCyoa9Ix7NU0J2GS1CASrVgNDWnQfCUfEU1/eBIldo2xCPpWvteGtNpuIS6AH06uHUbLsELZUU8IsfwbVpaQrWKIR4GJCxJWTLNWQLi08FtSJgfSdCYDmyrbeOziolpsCFhgJoR226RboivqJFYbUyWGs8bD03DNic13qSb9+9WUmM73h/lhypVa/7PDVaWGOTIJdwQTTKW5MdHkTD5c1KHUsq77HS8Byphl8YqTTZeSZEN6RnNtoUy8SA2Yct+JV2PR/LqEPs2XNiN1jQLSX5OYpCmQUsrmFqLVpZMdqGp7rMj9/8YLhWWz+K64f9fAlJjniwdRnhtlt0CAckLU60mLFpPAQmLniwz2bEGAH3FuIBHcyKWyTh+inYrqbE1YYtJt9GpVhJWkx7DZIlBjCTjcbDqhNZXBFB4liLUMFMlpfE11l1PPg6DKXkU2VBRcQemRmkguT2U1iJd04k1+TnUteXHh7e0LFplKaVhA1IbLsZLY6IsJU/wmV+Prjg1TBAaEy+U9JxwImbvWYrLLDI5s3yeMKXNZmdZj0866NtwUUbset2VvEWmRCzcW5TWmcXn6SlktX1y0wkmSx0K0QKrJhAP/eDIZJXG1LOUtJTWluABKfh/UjJhN9VOy7OUxpmTyJJhZpF8lrBzW6k/idNwNspSNBELJtZoTdhebZsE7+ToAJO6+awDca8LJY8WylJXTOvQH5U3vInHt+HMW08iVyhuvYepktIbQTwmKjV/orjfMLMoql1ma8IW16M1OmC0VLGqO11gstShSG7DpelZMlRpEtQwU5WmiSwl+HSozdIlQ5XNq51klrYkeMQkDEhuD9ku/wXCCYJpxpJ3lvRUmrjrYVU3YUWL6bJb+TzxniX9uo7jKGU4GbX4CtF15WRpE/TG+X8siJioO1mptSne4xZZSEC0+iNIWMYx93BFETGbKTv5eW2K1dTsN3cDTJY6FomTZdaEJmZ1iK8A6fpd4s9cNqwrq2dRBME+SDOhVZaGSlO1M6VHe3TsW1rRypLZ9XAcJ1YRs/EsJU7D2ZiaY4iYlbKUsHfOpvUUFx5po1jJzwubLLNa8CpG5cOUpcZNvcew7dQb4f+p1Or+69zEWyS3wcbLUWZpu1ZZ65nlVpnJShIgyFFqrW07DecrbeVm8uivOmFliZEG/BH/CFJjriwlT5aZqilJtU2VJTlKIVG1Ih47t2vDJZBH3yBsqoaFqxIkbTji6AD5OWEtHJJWWeJuOBMFKLp2kIVEryzZmMfjwiNtiCMg74eLDmLsNVBTBFmZCGlpTVjUlZ/XSmgmJK+RiQJUzGX9X+Raice4rf8nIuCRYiGtn7Sd0pmB5mvdCendAJOljkVSGratSqMWHUBr8DYleID69ZgtrUNAYRrOcpFuGtNfSS0+O/N4tOJB0ypLwywdfa3tFCvvOZWaGzq0QBMdEDKxZqssCVLT0tJy3cB4TL3gVfiKzJWlcCVFnLeQzRj9YqFS29RnFVXX1oQtPzfK4G267LaYy/o/P+TatorVdIHJUodC5BAlJXhTt53kj5kasZMm+ExuWn54ZKIClNJ4/ywyeBcl9Sd0DJ/Es0SvWsVN2pUMVTavbjoJ3t55oifLrEhY09452vDIuFBKMeZuOtIuVJpWs3SpWveNx2b+n0arLDSx2lJZ8ttwzWe2JWHymVon4sTnMm3D9Uf5iizzm4BoY7ogODa1w8zjwaqT2btEF2Cy1LFIJh5m6z2S2ntAkMFk6qVJUmlMlKWkyINADTMzHiflLNm0tJL2rJm2Dl3X26beCpubeLIfyqZdFmOWrljUVd0NZ2WWTkdZAiLWkliQdKUQRkOyJJ4X5dGRP78ORBtsImQM3/csGZ5Z1G5XaexIGKDgLTImeBGKlaUXyntuQs4SRYtPmogT/zZVrKYLTJY6FOKmleRZ0s8ViicHcm191SrJ4N0gYRY38Shjui3xiExKt/L/JJilDW+ITWP4IbVTjQ4gIGLhylI6E2uAJRGLUdpszpzNOL5a2mqWrtWDRcgmXpruiFaZ/D5T4tEbUXtCStk2ydIRpKIsma4FfGXJckqr7cwWC2kFxHPbRvyJ9qy1BjzakjD5THJt13VJyFIQHxDUHp70yNJANytLjBSQ1IaTk6V1oOJZMm3j5BO8NDbKkqqXhjyzyJCUys9JNrybj+HHtrRSCHgUn89mpD2ceFBMwyWYpYmvRzANZ/ZjNmoiTl6eahOWGDpZ5vuK7NZwtBqxJyxH5WWlq1URm7DwQsnPax+VtzszEKcA0RC8UrXe9LOaxOAd0oabqtQhRGob8himWh2Y8MjSPCZLjDSg6v8xzeiJT8M2JWLx6o+NwVs50Zx4n52dSpPgs6qZ3Wxz2YwfDhhG8oIzGxi8FXOndAleUu20puFqdde/Rjb70EJbZRW7m21glm6+0QoTtuOYEbxefwlr9GSZ6VJakXXUmllkS2gKuYz/s6m9xUeTWdR6nccJlKWkNpxpu0wmWXJt24k1INwPJdSfbMZJTVkaZLLESAP5pDac5Xg/oEDEDFt8SatDqFs4gByWaEYek9OwzSfL0pi0i8tDolBpEluHxEZs02Rwr260oil/HTarQ0I31lskVgPRm+UnJUJjkqUT14abtG3DiSDGiDacaV0gMFq3kpoJS1N6j08OWkzYliobIAc8RpFHs9qFXDCh12yWtjd4h4VS+q2yLvP8JgAY7C4ACNQkufa8HiZLjBSgupQ2jTTsiqG3qJiS+iM/J5HU6La0FNUfq+iAFNeSxBEEmxUtYS2taq3uq5HUI/4k++xqddRb1FI5D8jILN1Y8DqVgv/HD2IkJh5+Gy4Fg3dPhMHbtg0HSHlIbcTDbt1JXxQJ8yfWaA3epWrN/xlKrQCNlezN0mEm7JEpGvVHEKIDE2X/fawsMVKFumdJlywFRCVJAdKunYs/s81Iu+qknX5bUuTdpEdowohYXWoPUdemWMMR2t6T3kd/ZptpuOA5recWLa1CNuOvENJBFKEBAiJm3NJKMEvbEppWcgAEPiZjz1KEGmbbhpOf29rSCkIpaafhbHKhBMIM3jLZMz2zV7v93COT3r9tzNKCtIzIrbIJGkIzv0GW9ktkyfcssbLESANBSythka5mrpDjOD4RC/MWua5rQcRUlSWL6IAI4iFG6HVVq3RzlqLbTtbEI6Z9aJWFFHOdZd+OWeswJjqAIDgSaE+WnrQIdwSAbpErFGOWNidLonbzTdz3QuXtCM1Upd7mS5y0NkuH71mjUJaEctRaW5AFc2UpXLGi8P+EERrx72LOjKALiHOPhE2WWShLgrQMT1T8nDaqibV5PV4bbn+DINXrrq9a8TQcIxWIm1G1nh7xCCM1cm6PcYJ3KqtDos9sQzwEuarW3bYWjlybWkmRz2zVeiJWaeLae+J9uYxjdBOIqz1poabksoE5uJXU2NQFpMyisPUeFcvavkrTOg3XIHiWhAZoP7d1dIBoaUXk/1ipNCGKWLVW918vxkGaEQtvxwl8Vj4Rk84szM39XXbkIMwsTdEuE2SpXKv7rweqVtn8HuFZ8pSl0amqH1bKbThGKkhM8Lbw0sT5fyoWxCMgNLTZUPJZwlap2JClpsyiOJWG+DrLJId6lYqNGhZnHLchu4C04DVmZ5nJLjSvtnem1pYWVassLOBxsnFm09pBiy/c0NxjcS2ER7e9tu2If7gfyt8LZ5VZ1K4AyfEHtq1DoPl6TBCM4YcleAdKil0Io68ATbabpW1Umu58sJbkQKMeHVkSbbhKo37Z/5wmv7xNJ5gsdSiS2nCmCd5AfOClfJM0jw6gV5biVKumM2doyRLF6pAwb5hMwkymTwLySBuWGEfCxESY6fSXIAdTYcqSJanpjposs92FFqcsiTacpbcoahrOVPFwHCcyxdvWWxSm/gCBStNt2DqMqi1M2PmsY0zSi7mM/8unTMTGLCMJAGnhrWyW9ltldsRDEJdhyf8zQkBqHMfBYIsRm4ostdYVpGn+LPcrAUyWOhb5hDacqa9Ifk5cS8txoJ3EmxzwaE7w4s4sT9llNM8sk6tYUmNDPIhJGBAfeGnTOozzFfmj8qY3rZg1HNZkSRAx4jZcvLJE04ZrDY+0rQuEm8frdddX8MyvR7ivyN85Z6Es9YQoS+OWvjDAIwdhU3wUazgEIRqZlCfL7E3YQOD/EUSmXncx2lDDbInYfMm3BNCQMK9uEB3gui52j5YAAIv6i1Z1pwNMljoU+Ux80rafs6Rp8Abi96zJipWu4pGUDm4apCk/J7Y9ZEDCMtLaibgJsLRaZcZkSWHPmpEJu9HOaiUd8vtMvTRx/p+SpRE7SgEiU6xClaV0Wny2wZFe7fYgxsmmlhbtmcctSSkQryzZmLCB8BF/ClLjqz+T8sSavQm7ubZXb7QU+H+sW3wiD4m8DefVrTaI3Z4xjywt7mOyxEgJ/g63yDacvZcmTEkR7yvaqD9JE3xGq0OiiZgt8Yg7d7nResqbELxssv/HpFUGxJMlm3aZuEFX627btRbtsy5D70F3PtyELb+Pug1n61mK8hXJn8s+D6klwZsi4DFEWZL/bfo9FMpRa86Sf2YCgifXHiMwjgOB2Vo2S1MoS6LtNDIZTJZRTX8J4nKgRf3pymes/T9Bu8yruXfca5vN7y1Y1e0uZH1iunu05CtLi1lZYqSFpDacjWcpbi2J394jbjt5ny+dlpZNS7K5dvtNvGxBHn1CE3rmWtNjdBE3DSdaLSYqjUywolpa5mP4jVZZTEuLWrXyz2zZKpuqNAdeuq5L1jqMzlkyv4mHpXjLSphuu1ogKvDSzyyyGsMXk3ZB7YDQ2BEPocQ0tcsIFCDx3LI0tednIVF5llrUH9u6QLCnTeQhCQVoEYECtHTAq7FzeCpow7GyxEgLcUoKkKJnyVd/zNt7SWGXBYvaqbS0YhYA2/h//PZeTKvMVFkq+ktYY9plJrvQmjKLms8tjOOmrZYu3+Ad1tKimSxrz1myqysrGvK5S9Vg8aj5iH/UmemUJVlpm6jQBUeWWxa8Uqw7Ea220VLYGL5d20kQDEE4XNf1VSsb8tFXzPneTlE7rWm4EaIsJABY0FCQ9o2X4bouabts6UAXAGDn6FRQl5UlRlrI+eSAdtmt/Jy46AAzEqaWOm4zDZdqGy5mOpA6dZxqsiy0DWdBlhzH8ZWjSGXJsAXQFWPwLllOrSVNw5nexOWvVa4tXxvb1mH7GL69qTmspWWbDC7XlesBRAte/VZZoP6If9uqKQN+arVXb7xc88mujWrlOI6vLrWRGmJlSbTKFli2yoCAvOwaLWG8XPN/MVrUb197qEGWdgxzG44xDVBNw6YmHqZ74eTnJEUH2MQdxE5/Gbbh4lpaFMtuw3ahTVkqS1GERq5tPeLfUpvO4J1CdIBoaUWc2bRuJhOQR7nFJ4hCPusYt3+T23DEypIwS1u09wq5jP9L0URIECNFS2tkkl5Z8ld8NGoLQpPPOsZtZYGBFlJDtmetZSntXr9VZk9oljQIza6RKexpEJqeQtYqRkFg6WBDWRqZwi5uw80MVq5cCcdxmv58/OMfj33O1NQUrrjiCixcuBB9fX04//zzsXPnzmk6sTmCZOmoaTj7nKVYlcbIhO09p+6ibc2C/PnMDN7R6o8NcZTPE3Y9hHJj09IqhZCDkqWy1BVBaJpr202WtbbhrA3eEW2nSq3uJ8fbqjStfihxQze9zvKZZOJhS+4Aad0JsRomP7fZ4G2XCyXgb62fajdi9xXNCYKvLJUkZalE1YYTq0Mak2VSyrZJzpmMIA9JeItozrygQYomKzVMlKu+skTiK5KUJUq/EhAoS88fmMQLByYBACsWdJPUThNziiwBwIc+9CFs377d/3PVVVfFPv7d7343fvjDH+K73/0u7r77brzwwgt44xvfOE2nNUfiZBmJZ4mW0MjPoc7/UUnDNlWWlBa8Wpil49Qf06mWYoShWa5tPrWWYJY2NXhHtOHk62NynZtqt53ZLlcIkHe4hZilLeoGOUtRKds2BK/diC3+bZNYDQQkQIzeu65LM1nWHaYsURm8m/OQfF+RJaEB5MW0Xs39DVKzsNeOfPQWsv7rerdEamzrAi3KEqFiBQDLGsrSfU/tRbXuopDLYGl/F0ntNGH/Sphl6O/vx9DQkNJjh4eH8ZWvfAU333wzXvWqVwEAbrzxRhx11FG499578fKXvzzNo1ohLgsJoPEsxYVS2hi8RZ1uNP+wF8TPLLMoegzfhtB4tWPG8EXryYB4+K2yWF+RbRuO1rMEBESsrQ1XtVNTgusRrqQ4jk1bMpws2bbhvNremSbIlaUIn1XZ7vsHSJNlcquMYL0HAPQX8wAmfSJTqtb9X7woAh5Hp7wxfMdxfEJGZfAW9ahIGBAQMRHEuHfcIx8LLMmH4zhYMlDEs3snGgpQg4RRtOEaytJ4uYan9owDoFOWDl/SByC41ocs6DGevpxOzDll6eMf/zgWLlyIE088Ef/4j/+IarU9/0TggQceQKVSwdlnn+2/b82aNTjkkEOwadOmyOeVSiWMjIw0/ZluJLbhrHKWoqfW7LxQwX+IOCJmUzuuVWas0vhkKaylZa8slav1tiW9tspSV8Q0XFVqadkSsVbiUbL0QkUZvKekSTjTlkjUUlrSdlmosmR+Ew9rlcmfx2oNR1irrPHvPkvi0brgVfztOHZ+KEFc6m4Qckm1lFZMpgUmbBoSBgCLGobrveMljExVfeK4kMKI3SAwu0dLkmfJntT0FnP+a+SBZ/YDAFYs6LGuC3jkSP4Zf+TSfpK6aWNOkaW/+qu/wre+9S3ceeed+Mu//Et87GMfw9/+7d9GPn7Hjh0oFAqYN29e0/uXLl2KHTt2RD5v48aNGBwc9P+sWLGC6ktQRiGhDefnLBmFJcYleJu34RzHkbxFcbEEtD6rgCzZqRJh3iIbZUk+T6tqlbavSH6MLpJWh9i24Uot5NF2f5tcO/LMVi2tELO0n1lk/iNWTgcXgYaAPFlmfmZ/Z1lJ9hV5RMG+Ddcc8Oj7lQo5KwWhKx+Yx0W7jKK9B7SvJdlHFMIIBJNeu0dLft2+Ys7q9SywpJFZ5LXLhGeJpl120DzPR/TLJ/cA8EgOBXLZDI4/aNB/+6WHziepmzZmPVl63/ve12babv3z2GOPAQCuueYanHHGGTj++OPxzne+E5/61Kfwuc99DqVSifRMGzZswPDwsP9n27ZtpPVVkEuYhkttsszS/xOkg7eTPBtSE7cLTYydm2cWhbeHABplyavT2h6ynFgrhKthTf4fS/IY1YazHe+Xa8mfx0b9ifQsUbThQtplUwTqj3iu6zaT3jGCdlnYGP4YWUureXms+NtWsXIcp42IkeUsiVZZC1miUH+E0rNnrOyrPxStMiBQlnZJadhU7bLDlvQCCH7GUZqw/+T4ZQCAjAOceeRisrppYtZ7lq699lpccsklsY9ZvXp16PvXrl2LarWKZ555BkceeWTbx4eGhlAul3HgwIEmdWnnzp2xvqdisYhicWZHHZMyi2w8S3HLUm2W3QINpatci1gea05qBFkJ3YVm2YaLUpaqtbo/1Wdy5nw2g2zGQU1aYCowZUnwotpwcl3jllaEamXrpZHVualKHY01UpKyZP67XRih8T4PQRsuJJaAQg3ryWfhOB5ZGitV0V3IolZ3SYzY/aINV0rBsxTRhqNoaQ105bBvvCxNrdFkFgnysm+8jHrdTSWzaLfkK6KoCwRG7Md2jGKyUoPjAMvm0ZilD1vc1/T2S5bQtcve8vJDUa7VcfiSPqxu+TyzFbOeLC1evBiLF5sxz4ceegiZTAZLliwJ/fhJJ52EfD6PO+64A+effz4AYPPmzdi6dSvWrVtnfObpgL/uJGRiDbDzLKW54DUuaTtQaUxaWtGtMl9ZsjZLtyop9i2trlymEfrW4v+xiCSQn9dOwuzqAsF1bDNLV+3SsDMZB4VcBuVqvdn/IwiNzcRaRM5SUNu+XSbHEowT7CzLZBz0FXIYLVUxVqpicX+xKUTSRqlpJTQApWepWbUSn8OWhAGBAiRM3vsb4/gizdoUYoKsVndxYLKCfeNisoxSWSpJihXNL9vLG8TofxutsqX9XdZ74QT+aMU8/9+L+4s4eD6dspTPZvCO0w4jqzcdmPVkSRWbNm3CfffdhzPPPBP9/f3YtGkT3v3ud+Otb30r5s/3eqLPP/88zjrrLPz7v/87TjnlFAwODuKyyy7DNddcgwULFmBgYABXXXUV1q1bN6sn4QCVPWvmClAQlkir/gCI9Cy5rmu1PLYrH9528t5HszqkzVck3XhN25Jd+axHllrOXbJUU4pRBI9ApUkMpbRsl5Wr9SYFyL8WFjeBqJwliskyUTtswast8ejrapAl4f9p/J3POlY3RXGu8CwkamWJcLKsK5gsGy/X/J8ZtkpNIZfBYHcew5MV7B0rYa+vANmTGqEs7RkLWmUUJAwAVi/yVJk0WmV/fPgi9Be9198ZRyy2zpvqdMwZslQsFvGtb30LH/jAB1AqlbBq1Sq8+93vxjXXXOM/plKpYPPmzZiYmPDf9+lPfxqZTAbnn38+SqUS1q9fj3/5l3+ZiS9BC3EeHfn9Oeo2nO2etYjaMukzasPlwpUU+XOZZxbFK0uFXMbYuBptxKYJpWybWLOsKz83qnVoS8SGJytN15pCWYq6HhSeJdHSGpdaWuNExKPP34dWSaduCFmybZf1t4zhU9UFmttlIq+oK58hSZZe2FfA8GQFuyUFiKJdJs5cqbl49IVhAMDyeTSkZvXi3qa3xVg+BbryWXz54pPxi8d34x2nhVtdXkyYM2TppS99Ke69997Yx6xcubJpqgQAurq6cMMNN+CGG25I83jkKMSMs7uu65MPE4IQV5tqDL+V5MnkyYSIxY/32xq845Ul07ryc0ttKo3lBF8EebQNpASSlSWKzKLmMXz71mGYwdt1XZLwyL4Q/88YweoQoF0BGiVSrAShKdfqKFVrKOayQRvOImVbPptQlMQ6DsoFr3vGyoGvqIdGpVnUV8RTu8ebalNMlhVzWSzqK2DPWBn3PrUXAMhaWv1deaxc2INn9noCwIkraCfLXr56IV6+eiFpzU7FrJ+GY4RD3EQrNbcto0dWaeyIB72yFEVqZK+R3Z61MM+SXShlpGeJxP/TIB6R0QF2AY/tJIzALJ1wPUw8Z0HtdiJG0t4LMXiXqkHmlN2C13aVhmK8H2gnYoLQWJMw6esdbSVilqpVkFjt1ds/QT9Ztm+85CtLtuGOAmKybOfwlJ+3RGXEXrXIU4DENaH0/7xqzVL/32tXLyCry2jGnFGWXmyQyUq5VkdXJvihLKs2RmP4sWnYKak0Ul2T3nhXitNwKmc2RSLxsJzga/VCURKaqJaWVRsuhNQErTLzuoK0jJerqNddZDJOU9vMhnz0NVSasRTacIKIidrjRC2tbMZBb8Hzy41NVbGor0gWHSCUHmGSDkzYBC0tEfAoqT/ziZQl0S57pNEqK2QzZLVXLuzFrxrhjgCwclFvzKP18M4zVmPPWAmnrFqAQxfS1WU0g8lSh6KNLDVl9tiqNCkqSxFGbBtzt/c87+uv1V1UavUmY7t9wGM4obE1jgPJI/62AY+Vmota3UW24amiUGkic5ZSykPyW2VWviKP0LiuNxHXV8xJwZFZ//qYICwNe9RXlmi9RVTqD+C1y8bLNYyVqk0TiFQLXveNl72JNd//Y9+GWygmyyTPEpVZemljDP/XDVKzfF4X2RqOI4eCsfulA0X/c1FgSX8XPnvhiWT1GOHgNlyHQiZBrePyQSClY/SfPYgOSGOyLN6zZKp4yC22dgWIRllqbZXREA/RLovKWbJTluRagGQct1LDBKGhvx5hadhiyqzHgiB05TMQ/xWEOjNG1CqLa8PZG7GbVSu/DUdAlvql1OoDkx7xyDj2mUVCWarUXIyWqkEaNoFKs8BXlkqBskREllY2VJnnD0wCAA4ibJW98iVB/M1JHZJYzWgGk6UOheM4kfEBtinbKsoSfRvO7szN5DHcD2WeWB3u/yFRlvwVH1E5S3bfQ6DV/0Nnlpbreoqe2Dln7y2S96FNlOxDGB3HaVNpxonVn9A2HEF0ABCQJKo2HADMb2QT7Z+oYP+41yob7M5bqyndhaz/Gtk3VvY9SxT+n0WSakWdWH3owuZ1HgfPo1nvAQBHLO3D609YjsX9Rbzr9MPJ6jKmD9yG62AUs16AX6tKY7OQFgjUndjgSNultC2qhG1wpBxoGGWWNq2dprLkr1IhDo+MCnhMy+At/9umdqtHB5CUJYuJNa92HiNTVZ9wiGWsVBNrTatDiKbhWpO2fTWMYFReKD37JgJCQ+XRWdBbwPMHJrF3nLa2IEYT5Ro27xwBEOwws8XKRb1+YjoAHL18gKQu4JF1bpV1NlhZ6mAk+X+Ms5Cy0+9ZsiVh3nOTFCDayTJKZanND0UQS9AVQsRKhK0y+cyC0DiOnbdIkICwzCJbgiDaba1maes2nERoRDQJWRsuYgzfNrEaCJSe/eNlHJigbWkJs/TzByb91x9F7d5izvcoPfK8R5aoMov6ijkcvSwgSMcfPBjzaMaLDUyWOhhRwZTBlJad/2daM4sIiEdUbes9a/mIM1v6iuTabVNrpOGRsmfJvg3XFdMq8/aZmbdxesNaWkIBIm6XjVG14RqEpu56xvRa3fXVPFsiJvxDYpRdqDQUk2WCLO0bL/sTa/MJSJhc+8ldYwC8n1W9lsqgwIoFze0xSm/Ra47zFryuXNiDYw9issQIwG24DkbUDrcSkbKUxm64KD+UrRcKiI4PoGsd0vqKADkdPDgzlf8nzA/lt+EsrrMgHU1kqfFvGxO2XFtWliZ8g7fdzba3ZWptgogsdeezyDgeWRqbqqKSD3LPbGvP7w18RUBKytJE2TdhU5AwINh99sjz3hj+0sEi2bqMQxb04KFtBwB4//eW9tMtNX/X6Yfh6OUDOGbZgPGycMbcBL8aOhhRSoqtwTvdzKIo4iF8RRT+n4h2mXF0QFRwpH3rsCvXTmjkf9PscAvO7e9Cs1lKW2huZwEBobFVDwJlSV5KS+T/ac0salyLPsu6TebxUtVvmXn72+x+xAqfjxiTF1NrFP4f37Mkt+GIlCWx4PVXz+zz3h6kU3+OkxSfY5cPIkdIajIZB2ceuQRLCEf7GXMDTJY6GFHKkr36E23wtvcspTMNB6S3liR6JQmFWbqd0Mj/tmvxNVaHhChAViGMDWJQrtb9hciCeNju6BItrVDPEnUadolGsQKCMfyxqarfMpvXU7BWUwShOTBZ8TKLUlKW/DYckWdJJFSLyUMqEzYArDssWL/BY/iM6QK34ToYSUtpTclBVF35fdbEI4rQELS06A3eCcoSsRomlKV81rEKS/TTsCsyWbKfLJMJ0USphsGejNTSsiU0YaoVjbLU6oeaIDJhyzXGSlWI79g8gl1oghTV6i5GJqu+AkTRLhPEaN9YGXvGvDF8qoDHFfObfUVUJmwAOGb5AC5edyi27B7H21/JC14Z0wMmSx2MpD1rtr6iWt1FtVZvkrltW1qRZ6ZMw5ZITbUW7P+yJXit6eAU/p8wZclvlVmoSkBALgRBAmgUoEIug0I2g3KtjrFyFYM9eTJlqXUaznVdKZSSZmotCKWkOTPQPLUmVjVSqD9d+Sx6CllMlGt47sCE72WjaJeJzKLdYyX07vfOP0TULmtd5yEnWNvCcRx88A3HktVjMFTAbbgORmQbjkhZkmsJCJJjHnjZaJVFpI5bRQeEKEvy+W09S0CzIlYi2bPWTh79NRyW/h/x/HHJ/zPpG7FtvUWidkOlIcpCalV/Jis1P/fGVgFqNXiLdtkggQIk/FAjU1XfhD3YTaPSiFbcM3u8zfKFXMYqnkFgaKAL2YyDSs3FE42pteWDNF6d5fO6sVgyXh/Hk2WMDgeTpQ6GP7UWleBtOQ0HhIRHEq0lSSc6oL12icD/I1+PsHYZdc6SaJtZE4+GYjIZkofUY3mz7W1RacaJVJrWaThR13Hslba+FoP3CCFZ8r1FE2XfhE2hLAHBRNxTuz1CM687TzJZlstmMNRiZF5G2C475+ilAIDDl/S1pWMzGJ0GbsN1MHyzNLFKk8tmkM04qNXdJiLmui7hKpWIaTiS1SESWZL25Jn6f+Q0bLn2lOUaFSBivYevLNn99+xpUX+AQFmiyiwSZMafhiMa7x8v11Cvu4Filc9ar+FoNXhTkppgZ1nZfx+FZwkIiNhjO0cB0K33ALyMIrELbV5PnsS/JfD/XnsUjl4+gDOOXEIWG8BgzBRYWepgRClLtq0yIHwtCUVLK91QymiztE17L6r2JEEatq/+lOVWGU1LqyeEiAniZNvia40PmCDyLMk7zyYqNX+aimJxbCtZomzDicTqveNlvw1HNVkmNtQ/tPUAgGAsnwJHLg28RMcQrvcAvNfCW9YeSjoJx2DMFJgsdTDSig4AAnJQrkn+H+nzWCtLbbvhKCbLopUl27ybrhAVb5KAIAjSMV5un/6yJ0vtY/hkLT4/mLLZs2Sbs1TMZXwFcGyqipEpOkLTukiXkiwtaoQw7h0r+YoVRV0gmCQTCtAQka8IaB69P3Y5+4oYjCgwWepgRLa0LBfpys9t2itWlf0/1Lvh7NtwYdejRNAqA6TMImJvUZj647fhbH1FonbjnF4uktv4vOl4i2wTvB3H8c89Vqr6vqIBAuIhr/eYqtT81/YgZRtOWh1CRZYOalGSWn1GNjj9iMVY1FdATyGLP33pQWR1GYy5BvYsdTCKCcoS9Z412a9k6kGITB23nOADwtUfsWPNhjgC4ctjhZpi04brkdpwruvCcRxJsbJUloT6IybLJEJGpVqNtXqWCPZ/9RVzGJmqYrxUJVV/BKEZnqxgbyMRO5tx/EgBG/htuLGy/1pbTLSG46B5zebo1t1oNpjfW8DPrjkdlZpLdl4GYy6CyVIHI802XFjttCbWAPtsqOba7aPytmbpbj+zSN6z5p3ZhngI71C1YaYv5rJ0Bm+/xdcgNBWP0BSyGeu9VyI8UpAk0dqyVZaA5kk7SrLkJWoDrgs8u2ccADDQlSMxHwvT9Z6xEjKNelQK0FHLmjOKqL1FVPvgGIy5DG7DdTAiiQehZ0kmHjReKKH+0KZsA3LOkuQrqoiWlt1LXYzaTzR5iyjSsIPnTraQGrLogEZd0SqzNXcD7XlIIw2yRJtZVCElS9mM40+WbWmQJbLFsQ1lqVSt+685Km/Rwr6iHyAJAKsW9ZHUZTAY6mCy1MFIVJYs1INwZYnAVxSZs0ThWRIJ3iEhjEQqTdieNZs2XD6b8b9Poh5ZG67FPO7HBhCSpfGWzKKBLntlKdhZFpAlirpy7S2NEEYKLxTgvb4WSNNv83ryVq+LVlz1qpcAAP7mnCOsVuAwGAwzcBuugyFusqWIUEqKnWWhniUCxaraskrFzyyyUIC6QwgNxXi/XFsQmnrd9a+Nvbcoi/JEXZoso1GABEGcaChKgjSRKEstLT4xtUZBPoT6s2+8jOHJKlldICBLj+0YAQAsJswsWrmwB/saXqhDCH1FAHDxqSvx56essI7AYDAYZmBlqYMRGUopzNJWOUtxY/j24/1Ac25T0C4z5+/d+WZCA8ieJRqVRpxTnoqzrt1ybl9ZsiR4fihlWUys0S2OlZWlWt31PUuURuz942XSNhwQLIr9w3Yv4HFokI4sye2xo4ZofUWAfVYYg8EwB5OlDkZa607k55aJlSX5uU1TaxV7UtNKaOR/WxOPQmuuUPA5bNdwtKpWgReKZintRGPSjlL96e8KMovErjX5/TaQR/wpV5LItQUJW9pPN4Z/3EEBQTrmIHqyxGAwZg5MljoYAaEJzyyiNnhT1M1mHOSznudC9hZN+e0y4jYc8VJaQWh8ckewhqM94JHmzAPdXt1a3cVEuYaRRkuLgtAIY/T+ibJPwrryGRL1QyRf75ugV5YOmt+cJr2UMLPoT05YjqGBLhy6sAevPW4ZWV0GgzHzYM9SByNqGo4iZylMWRK+ItuwxK5cFpVatSnwcpIgiDG0DUfkWRLKlD+xRkRogPZzU6Vsd+ezyGUcVOueqjQqlKUuulbZgQnaiTUAWNATtOF2j5YAAIuIMoBWLextevvg+XSrOBb1FfE/7z0TDuB78RgMxtwA/4/uYERNw9FEB7R7liYJ1B8A6GpRgFzXlTxL9gGPYfvbbAleVKvMti7QnuItxvFt96E5juMTmOHJij/eT9GGE8tnD0yUsX/CMzVTkDAAWNAYk3/+wKR/LZYQkaVDW8jSkUP9EY80Qz6bYaLEYMxB8P/qDkZkdEDNPjogLB18ikql8b1F3o2wXKuj7m3h8ImUTd2m4EjiPWvU6g8QBDkKA7YwS1O0ywQxGpkMVodQJFaLibW6Czy3f7Lpc9lCKEt7xjwS1p3PkpjSAWD14oAs5bMOFhJOwzEYjLkLJksdjKjVIamlYVON4fstLe+cU+V628dMIM41Wamh3mBf/pnJpuGaM4so2nAiQ0gYpYPMInvyIWqPTFZ8EkZBavLZjE+6ntkbpGFToNVHtHSgSJKyDXivkf/fSQcDAN55+mEkNRkMxtwHe5Y6GFG74QTBsbmRh/mhyDxLEqmR/85lHKs1HLLKU6rW0V2QVocQt+Go2nsA0N8gRaOlKsrVun/NKZUlrw1XIasLeEbs0VLVD3hc0Euj0nQXsljSX8Suhl+JKglbYOMbj8Nlr1iFNcQtOAaDMXcxZ5Slu+66C47jhP751a9+Ffm8M844o+3x73znO6fx5Obw23At0QGC1NiMtAslRvb/UEysAXK7rNpSl4aEybWp2mWtCd6iZUbRhmtWfyr++ylaT34bbqpCqlgBwdTa5p1eZtGSAbqW1qELg1DHI5fS+4qOWjZAplYxGIy5jzmjLJ166qnYvn170/v+/u//HnfccQdOPvnk2Odefvnl+NCHPuS/3dNDm76bFnz1p2XPGgX5CJssm6IyS+ebiRhVey+bcVDMZVCq1jFRrmEh6M7c6ocKfEUErTKJ0Ii6vYUsiVFYEKNh4jYcAMxvmLy37fM8S5Rp2Ict7sOvntkPADiCFSAGgzHDmDNkqVAoYGhoyH+7Uqng1ltvxVVXXZX4G2RPT0/Tc5NQKpVQKpX8t0dGRvQPTIAwZalaq6Pa8OtYZRblo5UlmzUqQPs0nN/SKtiTg55CFqVqPSBiBPvbvLopmrC7AhM2JQkDgnH+kckqeRtuUQs5olSWTj9iMb71q23IOMDLVy8kq8tgMBgmmDNtuFb84Ac/wN69e3HppZcmPvYb3/gGFi1ahGOPPRYbNmzAxMRE7OM3btyIwcFB/8+KFSuojq0FMe1Wqbm+oXlK8hhZKUuhadg0niV/vUej9hSRr0iuMUGchyTUGEFmxEh7HwHxEORFzkKiIjQimPLAZBkHJrzaYuzfFq37z5YQpmGfe+wQNr7xOHz1kpfhsMV9yU9gMBiMFDFnlKVWfOUrX8H69etx8MEHxz7uzW9+Mw499FAsX74cv/vd7/De974Xmzdvxi233BL5nA0bNuCaa67x3x4ZGZkRwiQrPMLQLKdX24RS+ibskDYc1VLaqRTM0lFGbFtvkSAv5ZqnWlEGPAbj/UEWEpkJuzGG/9TucV9xXEhkxF6xoDnQcdWi3ohH6sNxHFx4yiFk9RgMBsMGs54sve9978M//MM/xD7mD3/4A9asWeO//dxzz+EnP/kJvvOd7yTWf8c73uH/+7jjjsOyZctw1llnYcuWLTjssPDR4mKxiGJx5vNZuiQyNFWpobuQDVpluYyVgdUf7w/d32YnSLaqVlSeJaA9mFKM49uapfsKOTgO4LqeAjRGuJTWb8NNVSVliUb9EWGOv9/utYrn9eStIiVkyMrSvJ48FjXCJBkMBmOuYdaTpWuvvRaXXHJJ7GNWr17d9PaNN96IhQsX4vWvf73251u7di0A4Mknn4wkS7MFuWwG+ayDSs3196xRxAbIzw+dhrNdHNvSKvOn94jbcKVqzfdz2bbLMhkHfcUcRqeq/h+AarxfLKWlV5ZEZpGIl6A0YR+9bND/96pFvTxdxmAw5ixmPVlavHgxFi9erPx413Vx44034qKLLkI+r//b+UMPPQQAWLasMxZhduW9PWuTrcSDiNBMprBnrTsiZ4miDddb9GqMlSq+qgQAvQUaBaidLFEER3o1KjUXu0amyOoC7WtCFhOtDQE8Qn3lmYfjm/dvxXvWH0lWl8FgMGYb5pzB++c//zmefvppvP3tb2/72PPPP481a9bg/vvvBwBs2bIFH/7wh/HAAw/gmWeewQ9+8ANcdNFFOO2003D88cdP99GN0Eo8qLKQWoMjvdo0ClBPi2o1KfasEWQW+QGPU9Vgx1ohi2zGXvUQas+oZMSmaMP1SOd7ao+Xhk3V0lrYV2z62pcN0i2OBYC/WX8kHvj7/4NTD1tEWpfBYDBmE+YcWfrKV76CU089tcnDJFCpVLB582Z/2q1QKOBnP/sZzjnnHKxZswbXXnstzj//fPzwhz+c7mMbo7VdRkVoQqfhyrRELFgc6/0tVCEbBJNlgfpDMbEGNI/4CyJG0S5zHAcLRMDjDi/gsXUs3xTZjNMU8Hj4Ep4sYzAYDF3M+jacLm6++ebIj61cuRKu6/pvr1ixAnffffd0HCs1iHabIElUWUhCsSpX66jVXWQzDpkfSpiwW9OwewlUmkBZojVhA83eIkrPEuC1y3aPlrB1n0fkFxKapY9aNoCndnuKFZMlBoPB0MecU5ZebGgNeBRG7y7LiSfZP9QW8Gjrh2pM0wnVSpClfhKyJAhN1a/bR+T/EUTswGTFV8XS8hZRKUsAcPKh8wEAGQc48ZB5ZHUZDAbjxYI5pyy92NCdbyYeVG04OaNpslJDTyHrB17a1hZma6H8jBIqSwOSr2iMkIQBARHbtm+i7X22aDVeU47hv3ntIRidquK4gwdJSRiDwWC8WMBkqcORlsE7k3HQlc9gqlLHZLmGUtFrxwFAj6W3SDZhA4GyRNEuk2uPEmUsCYjVIaKlNa8njzzB/jYAGBoI0q8dBzh4Pt1+wmIui7866yVk9RgMBuPFBm7DdTiEyjPVQpYoV4dMVWo+oQHsx/DlqTKALjiyubY0DUdEloQqs3mnZ8IWpmwKvGRpsCz2oHndJJlTDAaDwaABk6UOR+vCW6qVJHLtyUoN46VAsbIdwxeEZqpSR6VWJ96zJhm8iU3YgiztGy97bxOtDQGANUMBWVq5kG5tCIPBYDDswWSpwxEYvMU0HF0adpe0Z228TKf+yErPGLECJIjRWKlKmoUEtPuKKCfWVi/u83et/cnxnRGIymAwGC8WsGepwxHlWSpaepaAgGSMl6rINdQkCkKTz2bQnc9islLDWKlK7FkKcpb2TXhkaV4PzcRauwmbTlnKZhx86x3rsGXXGF75Eg54ZDAYjNkEJksdjtY23HhjpL2PYL2HIC9jparfeqNYGwJ4LbfJSg0jUxW/xUeylLZhwi5X63jhwCQAOm/R0oFmciSHPVLgoHndOGgebcI2g8FgMOzBbbgOh5h6m2rJLOohIB6CvHiZRXSEBggUoH3jZX/ZLUkbrphDoRF78DixEbunkMPB8wMys2oRe4sYDAbjxQAmSx2O1h1uE+VgH5othFlabpVRrCQBguyj7cNT/vsoiJjjOFjcaI+J6ICFhEbsl0gJ2KsXcxo2g8FgvBjAZKnD0d2S4D3u71kjNEtLJmwKxcqr7RGx7Qc8stSdp1l2C7QHOi4gNGKvP2YIAHDM8gGsJG7DMRgMBmN2gj1LHY6eQvNSWjG1RqEAyZ4l0e6j8ELJtcUuNMrMorapNcLab3rZChy+pA+HLe6D49CQOwaDwWDMbjBZ6nD0FYNWGSB5ligM3v5kWcVv91EFPArV6tm9Xhr2/F6aiTUAWCKlYQ8NdJEGPDqOg5NXLiCrx2AwGIzZDyZLHQ5Z/QEChYnC/+PXnqqityDG+2mIh2iNPbl7DAAwv4dO/Tlc8hJRT6wxGAwG48UH9ix1OGRfESArSxQG74CIjROvDhEm7AONLCRKsnQkp2EzGAwGgxBMljocvZKy5Lqun7NEnoad0p41AUrP0nEHD/rTgGeuWUJWl8FgMBgvTnAbrsMht+GmKnXU6i4AGmXJ90NNVVHMefvQqNKwW8kSpQl7oCuP77xzHXYMT+FVTJYYDAaDYQkmSx0OeUnsnrGS/28Sg3cxWB2SaYz1U7XLFvU311mxgNZbdMzyQRyzfJC0JoPBYDBenGCy1OEo5jLIZRxU6y52jNBmFgkVaXiyDMBtep8tDlnQA8cBXK+sv0SWwWAwGIzZBvYsdTgcx/FH/Hc2yBJVyrbwEVVqLvaMeW04KmWpp5BrStZeMZ+n1hgMBoMxO8FkaQ5AtMt2DAuyRCMYduWz/loSAcqptZMOnQfA81e1BkkyGAwGgzFbwG24OQBBlp7bPwkAmNdNF/C4sK/gT8J15TP+ehUKvO/VRyGXzeDClx3CadgMBoPBmLVgsjQHIEzegiwNEqo/i/qKeGavt5LkoHm0vqJVi3pxw5tfSlqTwWAwGAxqcBtuDiBQljxSQ6ksLR0MVocczL4iBoPBYLwIwWRpDmB+w4j91B5vzxrVxBoAvGRJsDrk4Pk8scZgMBiMFx+YLM0BiIDHcrUOgFZZOnJpsDpktbRzjcFgMBiMFwvYszQH0Jp+PUBIll6+eiEGu/MoVWs45+ilZHUZDAaDwegUMFmaA1jYsjpk6UBXxCP1Mb+3gJ9cfRrqrovlxAZvBoPBYDA6AUyW5gAW9jUrS9SkZmiQjnwxGAwGg9FpYM/SHMDBLeSIesSfwWAwGIwXM5gszQGsXNTb9DanYTMYDAaDQYeOIUsf/ehHceqpp6Knpwfz5s0LfczWrVvx2te+Fj09PViyZAne8573oFqtxtbdt28f3vKWt2BgYADz5s3DZZddhrGxsRS+gvSQz2awqNGKWzpQJFmiy2AwGAwGw0PHkKVyuYwLLrgA73rXu0I/XqvV8NrXvhblchn33HMPvva1r+Gmm27CddddF1v3LW95Cx599FHcfvvt+NGPfoRf/OIXeMc73pHGl5AqPvD6YzA00IWPnHfcTB+FwWAwGIw5Bcd1XXemD6GDm266CVdffTUOHDjQ9P7//u//xp/8yZ/ghRdewNKl3oj7F7/4Rbz3ve/F7t27USi0rwD5wx/+gKOPPhq/+tWvcPLJJwMAbrvtNrzmNa/Bc889h+XLlyudaWRkBIODgxgeHsbAwIDdF8hgMBgMBmNaoHr/7hhlKQmbNm3Ccccd5xMlAFi/fj1GRkbw6KOPRj5n3rx5PlECgLPPPhuZTAb33Xdf5OcqlUoYGRlp+sNgMBgMBmNuYs6QpR07djQRJQD+2zt27Ih8zpIlS5rel8vlsGDBgsjnAMDGjRsxODjo/1mxYoXl6RkMBoPBYMxWzChZet/73gfHcWL/PPbYYzN5xFBs2LABw8PD/p9t27bN9JEYDAaDwWCkhBkNpbz22mtxySWXxD5m9erVSrWGhoZw//33N71v586d/seinrNr166m91WrVezbty/yOQBQLBZRLPJ4PoPBYDAYLwbMKFlavHgxFi9eTFJr3bp1+OhHP4pdu3b5rbXbb78dAwMDOProoyOfc+DAATzwwAM46aSTAAA///nPUa/XsXbtWpJzMRgMBoPB6Gx0jGdp69ateOihh7B161bUajU89NBDeOihh/xMpHPOOQdHH3003va2t+G3v/0tfvKTn+D9738/rrjiCl8Fuv/++7FmzRo8//zzAICjjjoK5557Li6//HLcf//9+N///V9ceeWV+PM//3PlSTgGg8FgMBhzGx2zG+66667D1772Nf/tE088EQBw55134owzzkA2m8WPfvQjvOtd78K6devQ29uLiy++GB/60If850xMTGDz5s2oVCr++77xjW/gyiuvxFlnnYVMJoPzzz8fn/3sZ6fvC2MwGAwGgzGr0XE5S7MRnLPEYDAYDEbn4UWXs8RgMBgMBoORBpgsMRgMBoPBYMSAyRKDwWAwGAxGDJgsMRgMBoPBYMSAyRKDwWAwGAxGDJgsMRgMBoPBYMSgY3KWZjNE+sLIyMgMn4TBYDAYDIYqxH07KUWJyRIBRkdHAQArVqyY4ZMwGAwGg8HQxejoKAYHByM/zqGUBKjX63jhhRfQ398Px3HI6o6MjGDFihXYtm0bh12mDL7W0wO+ztMHvtbTA77O04c0rrXruhgdHcXy5cuRyUQ7k1hZIkAmk8HBBx+cWv2BgQH+TzhN4Gs9PeDrPH3gaz094Os8faC+1nGKkgAbvBkMBoPBYDBiwGSJwWAwGAwGIwZMlmYxisUirr/+ehSLxZk+ypwHX+vpAV/n6QNf6+kBX+fpw0xeazZ4MxgMBoPBYMSAlSUGg8FgMBiMGDBZYjAYDAaDwYgBkyUGg8FgMBiMGDBZYjAYDAaDwYgBk6VZjBtuuAErV65EV1cX1q5di/vvv3+mjzSn8IEPfACO4zT9WbNmzUwfa07gF7/4BV73utdh+fLlcBwH3//+95s+7rourrvuOixbtgzd3d04++yz8cQTT8zMYTscSdf6kksuaXudn3vuuTNz2A7Gxo0b8bKXvQz9/f1YsmQJzjvvPGzevLnpMVNTU7jiiiuwcOFC9PX14fzzz8fOnTtn6MSdCZXrfMYZZ7S9pt/5znemei4mS7MU3/72t3HNNdfg+uuvx4MPPogTTjgB69evx65du2b6aHMKxxxzDLZv3+7/+eUvfznTR5oTGB8fxwknnIAbbrgh9OOf+MQn8NnPfhZf/OIXcd9996G3txfr16/H1NTUNJ+085F0rQHg3HPPbXqdf/Ob35zGE84N3H333bjiiitw77334vbbb0elUsE555yD8fFx/zHvfve78cMf/hDf/e53cffdd+OFF17AG9/4xhk8dedB5ToDwOWXX970mv7EJz6R7sFcxqzEKaec4l5xxRX+27VazV2+fLm7cePGGTzV3ML111/vnnDCCTN9jDkPAO73vvc9/+16ve4ODQ25//iP/+i/78CBA26xWHS/+c1vzsAJ5w5ar7Xruu7FF1/svuENb5iR88xl7Nq1ywXg3n333a7req/hfD7vfve73/Uf84c//MEF4G7atGmmjtnxaL3Oruu6p59+uvvXf/3X03oOVpZmIcrlMh544AGcffbZ/vsymQzOPvtsbNq0aQZPNvfwxBNPYPny5Vi9ejXe8pa3YOvWrTN9pDmPp59+Gjt27Gh6fQ8ODmLt2rX8+k4Jd911F5YsWYIjjzwS73rXu7B3796ZPlLHY3h4GACwYMECAMADDzyASqXS9Lpes2YNDjnkEH5dW6D1Ogt84xvfwKJFi3Dsscdiw4YNmJiYSPUcvEh3FmLPnj2o1WpYunRp0/uXLl2Kxx57bIZONfewdu1a3HTTTTjyyCOxfft2fPCDH8QrX/lKPPLII+jv75/p481Z7NixAwBCX9/iYww6nHvuuXjjG9+IVatWYcuWLfi7v/s7vPrVr8amTZuQzWZn+ngdiXq9jquvvhp//Md/jGOPPRaA97ouFAqYN29e02P5dW2OsOsMAG9+85tx6KGHYvny5fjd736H9773vdi8eTNuueWW1M7CZInxosWrX/1q/9/HH3881q5di0MPPRTf+c53cNlll83gyRgMOvz5n/+5/+/jjjsOxx9/PA477DDcddddOOuss2bwZJ2LK664Ao888gh7HFNG1HV+xzve4f/7uOOOw7Jly3DWWWdhy5YtOOyww1I5C7fhZiEWLVqEbDbbNkWxc+dODA0NzdCp5j7mzZuHI444Ak8++eRMH2VOQ7yG+fU9M1i9ejUWLVrEr3NDXHnllfjRj36EO++8EwcffLD//qGhIZTLZRw4cKDp8fy6NkPUdQ7D2rVrASDV1zSTpVmIQqGAk046CXfccYf/vnq9jjvuuAPr1q2bwZPNbYyNjWHLli1YtmzZTB9lTmPVqlUYGhpqen2PjIzgvvvu49f3NOC5557D3r17+XWuCdd1ceWVV+J73/sefv7zn2PVqlVNHz/ppJOQz+ebXtebN2/G1q1b+XWtgaTrHIaHHnoIAFJ9TXMbbpbimmuuwcUXX4yTTz4Zp5xyCv75n/8Z4+PjuPTSS2f6aHMGf/M3f4PXve51OPTQQ/HCCy/g+uuvRzabxYUXXjjTR+t4jI2NNf2W9/TTT+Ohhx7CggULcMghh+Dqq6/GRz7yEbzkJS/BqlWr8Pd///dYvnw5zjvvvJk7dIci7lovWLAAH/zgB3H++edjaGgIW7Zswd/+7d/i8MMPx/r162fw1J2HK664AjfffDNuvfVW9Pf3+z6kwcFBdHd3Y3BwEJdddhmuueYaLFiwAAMDA7jqqquwbt06vPzlL5/h03cOkq7zli1bcPPNN+M1r3kNFi5ciN/97nd497vfjdNOOw3HH398egeb1tk7hhY+97nPuYcccohbKBTcU045xb333ntn+khzCm9605vcZcuWuYVCwT3ooIPcN73pTe6TTz4508eaE7jzzjtdAG1/Lr74Ytd1vfiAv//7v3eXLl3qFotF96yzznI3b948s4fuUMRd64mJCfecc85xFy9e7ObzeffQQw91L7/8cnfHjh0zfeyOQ9g1BuDeeOON/mMmJyfd//t//687f/58t6enx/3TP/1Td/v27TN36A5E0nXeunWre9ppp7kLFixwi8Wie/jhh7vvec973OHh4VTP5TQOx2AwGAwGg8EIAXuWGAwGg8FgMGLAZInBYDAYDAYjBkyWGAwGg8FgMGLAZInBYDAYDAYjBkyWGAwGg8FgMGLAZInBYDAYDAYjBkyWGAwGg8FgMGLAZInBYDAYDAYjBkyWGAzGnMQll1zC61MYDAYJeDccg8HoODiOE/vx66+/Hp/5zGcwkwsK7r77brz1rW/Ftm3bZuwMDAaDBkyWGAxGx2H79u3+v7/97W/juuuuw+bNm/339fX1oa+vbyaO5uPWW2/F6173uhk9A4PBoAG34RgMRsdhaGjI/zM4OAjHcZre19fX19aGO+OMM3DVVVfh6quvxvz587F06VJ8+ctfxvj4OC699FL09/fj8MMPx3//9383fa5HHnkEr371q9HX14elS5fibW97G/bs2ZN4xh/84Ad4/etfH/qxZ599Fq973eswf/589Pb24phjjsGPf/xjq2vCYDDSA5MlBoPxosHXvvY1LFq0CPfffz+uuuoqvOtd78IFF1yAU089FQ8++CDOOeccvO1tb8PExAQA4MCBA3jVq16FE088Eb/+9a9x2223YefOnfizP/uz2M/z6KOPYteuXXjVq14V+vErrrgCpVIJv/jFL/Dwww/jH/7hH2ZcCWMwGNHgNhyDwXjR4IQTTsD73/9+AMCGDRvw8Y9/HIsWLcLll18OALjuuuvwhS98Ab/73e/w8pe/HJ///Odx4okn4mMf+5hf46tf/SpWrFiBxx9/HEcccUTo57n11luxfv16FAqF0I9v3boV559/Po477jgAwOrVqym/TAaDQQxWlhgMxosGxx9/vP/vbDaLhQsX+oQFAJYuXQoA2LVrFwDgt7/9Le68807fA9XX14c1a9YAALZs2RL5eW699dbIFhwA/NVf/RU+8pGP4I//+I9x/fXX43e/+53V18VgMNIFkyUGg/GiQT6fb3rbcZym94kpu3q9DgAYGxvD6173Ojz00ENNf5544gmcdtppoZ9j+/bt+M1vfoPXvva1ked4+9vfjqeeegpve9vb8PDDD+Pkk0/G5z73Odsvj8FgpAQmSwwGgxGBl770pXj00UexcuVKHH744U1/ent7Q5/zwx/+EKeeeioWLFgQW3vFihV45zvfiVtuuQXXXnstvvzlL6fxJTAYDAIwWWIwGIwIXHHFFdi3bx8uvPBC/OpXv8KWLVvwk5/8BJdeeilqtVroc+Km4ASuvvpq/OQnP8HTTz+NBx98EHfeeSeOOuqoNL4EBoNBACZLDAaDEYHly5fjf//3f1Gr1XDOOefguOOOw9VXX4158+Yhk2n/8Tk+Po477rgjkSzVajVcccUVOOqoo3DuuefiiCOOwL/8y7+k9WUwGAxLOO5MRtwyGAzGHMItt9yC97///fj9738/00dhMBiEYGWJwWAwiNDX14d/+Id/mOljMBgMYrCyxGAwGAwGgxEDVpYYDAaDwWAwYsBkicFgMBgMBiMGTJYYDAaDwWAwYsBkicFgMBgMBiMGTJYYDAaDwWAwYsBkicFgMBgMBiMGTJYYDAaDwWAwYsBkicFgMBgMBiMGTJYYDAaDwWAwYvD/B1qv6W7YRGmBAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, [get_value(yi[0]) * 180 / np.pi for yi in ytbl_damped])\n",
    "plt.xlabel('Time / s')\n",
    "plt.ylabel('α / deg')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.997023429742508 ± 2.0393463067631097\n"
     ]
    }
   ],
   "source": [
    "print(ytbl_damped[-1][0] * 180 / np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.089626688171365e-11 ± 0.14171281413414447\n"
     ]
    }
   ],
   "source": [
    "print(ytbl_damped[-1][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.02783053001525517 ± 0.016391710482837378\n"
     ]
    }
   ],
   "source": [
    "print(beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison of damped model and exact model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual: 0.0057526456229040936\n",
      "Residual: 0.0057526456229040936\n",
      "Residual: 0.0057526456229040936\n",
      "Residual: 0.0025020875903158523\n",
      "Residual: 0.0025020875903158523\n",
      "Residual: 6.213113044383658e-05\n",
      "Residual: 6.213113044383658e-05\n",
      "Residual: 3.262956784042257e-10\n",
      "Residual: 3.262956784042257e-10\n",
      "Residual: 8.983943584260442e-19\n",
      "Residual: 8.983943584260442e-19\n",
      "Residual: 6.616013413716122e-30\n",
      "Residual: 6.616013413716122e-30\n",
      "Residual: 6.616013413716122e-30\n",
      "alphaend/alpha0: 0.1, beta: 0.09245101955328218 ± 0.016393181411171895, g: 9.838993414362067 ± 0.05082643807294858\n",
      "alphaend: 0.9992156296434231\n",
      "Residual: 0.022742410600294905\n",
      "Residual: 0.022742410600294905\n",
      "Residual: 0.022742410600294905\n",
      "Residual: 0.009314973229841811\n",
      "Residual: 0.009314973229841811\n",
      "Residual: 0.00018897196165260527\n",
      "Residual: 0.00018897196165260527\n",
      "Residual: 5.567735014812304e-10\n",
      "Residual: 5.567735014812304e-10\n",
      "Residual: 6.2857109138554e-19\n",
      "Residual: 6.2857109138554e-19\n",
      "Residual: 6.2857109138554e-19\n",
      "alphaend/alpha0: 0.2, beta: 0.064620489538027 ± 0.016392354169082923, g: 9.840417924820144 ± 0.05092595155879274\n",
      "alphaend: 1.9984776190716182\n",
      "Residual: 0.05022078994913972\n",
      "Residual: 0.05022078994913972\n",
      "Residual: 0.05022078994913972\n",
      "Residual: 0.01870522502101341\n",
      "Residual: 0.01870522502101341\n",
      "Residual: 0.0002794822305633265\n",
      "Residual: 0.0002794822305633265\n",
      "Residual: 3.3558571215610685e-10\n",
      "Residual: 3.3558571215610685e-10\n",
      "Residual: 7.622359803828812e-21\n",
      "Residual: 7.622359803828812e-21\n",
      "Residual: 7.622359803828812e-21\n",
      "alphaend/alpha0: 0.30000000000000004, beta: 0.04834067310390813 ± 0.016392006146076183, g: 9.84268962600761 ± 0.051047536714650045\n",
      "alphaend: 2.997834458924861\n",
      "Residual: 0.08730368906921895\n",
      "Residual: 0.08730368906921895\n",
      "Residual: 0.08730368906921895\n",
      "Residual: 0.029057202530635567\n",
      "Residual: 0.029057202530635567\n",
      "Residual: 0.0003055108935679785\n",
      "Residual: 0.0003055108935679785\n",
      "Residual: 1.1508078613411196e-10\n",
      "Residual: 1.1508078613411196e-10\n",
      "Residual: 5.497060607748725e-20\n",
      "Residual: 5.497060607748725e-20\n",
      "Residual: 5.497060607748725e-20\n",
      "alphaend/alpha0: 0.4, beta: 0.03678995952277183 ± 0.01639182005264276, g: 9.845323686842663 ± 0.051204989199848866\n",
      "alphaend: 3.997333836141084\n",
      "Residual: 0.13299350420081263\n",
      "Residual: 0.13299350420081263\n",
      "Residual: 0.13299350420081263\n",
      "Residual: 0.03907242621765137\n",
      "Residual: 0.03907242621765137\n",
      "Residual: 0.0002829986683234565\n",
      "Residual: 0.0002829986683234565\n",
      "Residual: 1.750666547805865e-11\n",
      "Residual: 1.750666547805865e-11\n",
      "Residual: 9.545793072260758e-22\n",
      "Residual: 9.545793072260758e-22\n",
      "Residual: 9.545793072260758e-22\n",
      "alphaend/alpha0: 0.5, beta: 0.02783053001525517 ± 0.016391710482837378, g: 9.848198453590038 ± 0.0513963133689297\n",
      "alphaend: 4.997023429742508\n",
      "Residual: 0.18618206441871263\n",
      "Residual: 0.18618206441871263\n",
      "Residual: 0.18618206441871263\n",
      "Residual: 0.047902005723360584\n",
      "Residual: 0.047902005723360584\n",
      "Residual: 0.00023476012687034112\n",
      "Residual: 0.00023476012687034112\n",
      "Residual: 8.074512793741047e-13\n",
      "Residual: 8.074512793741047e-13\n",
      "Residual: 4.225024152652048e-21\n",
      "Residual: 4.225024152652048e-21\n",
      "Residual: 4.225024152652048e-21\n",
      "alphaend/alpha0: 0.6, beta: 0.020510143088652965 ± 0.016391643511440346, g: 9.851267309231291 ± 0.05162826476138853\n",
      "alphaend: 5.9969509860038155\n",
      "Residual: 0.2456538019173423\n",
      "Residual: 0.2456538019173423\n",
      "Residual: 0.2456538019173423\n",
      "Residual: 0.054776032015986555\n",
      "Residual: 0.054776032015986555\n",
      "Residual: 0.00017846608112107162\n",
      "Residual: 0.00017846608112107162\n",
      "Residual: 8.350421293852825e-15\n",
      "Residual: 8.350421293852825e-15\n",
      "Residual: 1.844574081346511e-23\n",
      "Residual: 1.844574081346511e-23\n",
      "Residual: 1.844574081346511e-23\n",
      "alphaend/alpha0: 0.7000000000000001, beta: 0.014320844131483669 ± 0.016391602712272923, g: 9.854507816531541 ± 0.05189627165417047\n",
      "alphaend: 6.997164355439631\n",
      "Residual: 0.3100907784894051\n",
      "Residual: 0.3100907784894051\n",
      "Residual: 0.3100907784894051\n",
      "Residual: 0.05941034648511739\n",
      "Residual: 0.05941034648511739\n",
      "Residual: 0.00012682741412947774\n",
      "Residual: 0.00012682741412947774\n",
      "Residual: 1.7041173110207555e-13\n",
      "Residual: 1.7041173110207555e-13\n",
      "Residual: 1.0710912976991834e-21\n",
      "Residual: 1.0710912976991834e-21\n",
      "Residual: 1.0710912976991834e-21\n",
      "alphaend/alpha0: 0.8, beta: 0.008959429507516653 ± 0.01639157909050573, g: 9.857907413965423 ± 0.05222358804289996\n",
      "alphaend: 7.997711521561181\n",
      "Residual: 0.378080149333449\n",
      "Residual: 0.378080149333449\n",
      "Residual: 0.378080149333449\n",
      "Residual: 0.06174221662277561\n",
      "Residual: 0.06174221662277561\n",
      "Residual: 8.4845157178805e-05\n",
      "Residual: 8.4845157178805e-05\n",
      "Residual: 5.372533398359084e-14\n",
      "Residual: 5.372533398359084e-14\n",
      "Residual: 4.628198673819643e-22\n",
      "Residual: 4.628198673819643e-22\n",
      "Residual: 4.628198673819643e-22\n",
      "alphaend/alpha0: 0.9, beta: 0.004230326654534103 ± 0.01639156728564398, g: 9.861458252831856 ± 0.05260013239221051\n",
      "alphaend: 8.998640627478071\n",
      "Residual: 0.4481244677781388\n",
      "Residual: 0.4481244677781388\n",
      "Residual: 0.4481244677781388\n",
      "Residual: 0.061834521886088054\n",
      "Residual: 0.061834521886088054\n",
      "Residual: 5.3997315297776526e-05\n",
      "Residual: 5.3997315297776526e-05\n",
      "Residual: 2.261218631588929e-14\n",
      "Residual: 2.261218631588929e-14\n",
      "Residual: 7.503781628764268e-23\n",
      "Residual: 7.503781628764268e-23\n",
      "Residual: 7.503781628764268e-23\n",
      "alphaend/alpha0: 1.0, beta: 0.0 ± 0.016391563898814066, g: 9.86515500432572 ± 0.05304026135779055\n",
      "alphaend: 10.000000001455385\n"
     ]
    }
   ],
   "source": [
    "alphaend_alpha0_range = np.linspace(0.1, 1.0, 10)\n",
    "alphaend_range = np.zeros_like(alphaend_alpha0_range, dtype=ufloat)\n",
    "beta_range = np.zeros_like(alphaend_alpha0_range, dtype=ufloat)\n",
    "g_damped_opt_range = np.zeros_like(alphaend_alpha0_range, dtype=ufloat)\n",
    "\n",
    "for i in range(len(alphaend_alpha0_range)):\n",
    "    alphaend_i_value = alphaend_alpha0_range[i] * get_value(alpha0)\n",
    "    alphaend_range[i] = ufloatfromdistribution(\n",
    "        UniformDistribution(0.5 * alphaend_i_value, 1.5 * alphaend_i_value), \n",
    "        desc='End Angle / deg')\n",
    "\n",
    "    beta_range[i] = umath.log(alpha0 / alphaend_range[i]) / T\n",
    "\n",
    "    x_start = [10.0]\n",
    "    x = unumlib.optimizer(objective_function_damped, x_start, [T, I_over_ml, beta_range[i], alpha0_rad], epsx = 1e-9)\n",
    "    g_damped_opt_range[i] = x[0]\n",
    "    print('alphaend/alpha0: ' + str(alphaend_alpha0_range[i]) + ', beta: ' + str(beta_range[i]) + ', g: ' + str(g_damped_opt_range[i]))\n",
    "\n",
    "    p_damped_i = [g_damped_opt_range[i], I_over_ml, beta_range[i]]\n",
    "    ytbl_damped_i = unumlib.ode_solver(y, t, p_damped_i, 1e-12, ode_function_damped)\n",
    "    print('alphaend: ' + str(get_value(ytbl_damped_i[-1][0] * 180 / np.pi)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(alphaend_alpha0_range, [get_value(gi / g_exact) for gi in g_damped_opt_range])\n",
    "plt.xlabel('α_end / α_0')\n",
    "plt.ylabel('g_damped / g_exact')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}