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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Initial Value Problems - Project\n",
"\n",
"![Initial condition of firework with FBD and sum of momentum](../images/firework.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are going to end this module with a __bang__ by looking at the flight path of a firework. Shown above is the initial condition of a firework, the _Freedom Flyer_ in (a), its final height where it detonates in (b), the applied forces in the __Free Body Diagram (FBD)__ in (c), and the __momentum__ of the firework $m\\mathbf{v}$ and the propellent $dm \\mathbf{u}$ in (d). \n",
"\n",
"The resulting equation of motion is that the acceleration is proportional to the speed of the propellent and the mass rate change $\\frac{dm}{dt}$ as such\n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt} -mg - cv^2.~~~~~~~~(1)\n",
"\\end{equation}$$\n",
"\n",
"If we assume that the acceleration and the propellent momentum are much greater than the forces of gravity and drag, then the equation is simplified to the conservation of momentum. A further simplification is that the speed of the propellant is constant, $u=constant$, then the equation can be integrated to obtain an analytical rocket equation solution of [Tsiolkovsky](https://www.math24.net/rocket-motion/) [1,2], \n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt}~~~~~(2.a)\n",
"\\end{equation}$$\n",
"\n",
"$$\\begin{equation}\n",
"\\frac{m_{f}}{m_{0}}=e^{-\\Delta v / u},~~~~~(2.b) \n",
"\\end{equation}$$\n",
"\n",
"where $m_f$ and $m_0$ are the mass at beginning and end of flight, $u$ is the speed of the propellent, and $\\Delta v=v_{final}-v_{initial}$ is the change in speed of the rocket from beginning to end of flight. Equation 2.b only relates the final velocity to the change in mass and propellent speed. When you integrate Eqn 2.a, you will have to compare the velocity as a function of mass loss. \n",
"\n",
"Your first objective is to integrate a numerical model that converges to equation (2.b), the Tsiolkovsky equation. Next, you will add drag and gravity and compare the results _between equations (1) and (2)_. Finally, you will vary the mass change rate to achieve the desired detonation height. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Create a `simplerocket` function that returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (2.a). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt} \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `simplerocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s. \n",
"\n",
"_Hint: your integrated solution will have a current mass that you can use to create $\\frac{m_{f}}{m_{0}}$ by dividing state[2]/(initial mass), then your plot of velocity(t) vs mass(t)/mass(0) should match Tsiolkovsky's_"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, without drag or gravity, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" \n",
" Returns\n",
" -------\n",
" dstate: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
"\n",
" dstate = np.array([state[1], ((u/(state[2])*dmdt)), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def rk2_step(state, rhs, dt):\n",
" '''Update a state to the next time increment using modified Euler's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" \n",
" \n",
" mid_state = state + rhs(state) * dt*0.5 \n",
" next_state = state + rhs(mid_state)*dt\n",
" \n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"def heun_step(state,rhs,dt,etol=0.000001,maxiters = 100):\n",
" '''Update a state to the next time increment using the implicit Heun's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state + rhs(state)*dt\n",
" \n",
" ### New iterative correction\n",
" for n in range(0,maxiters):\n",
" next_state_old = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e=np.sum(np.abs(next_state-next_state_old)/np.abs(next_state+eps))\n",
" if e<etol:\n",
" break\n",
" \n",
" ### end of iterative correction\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The number of time steps is 10000.\n",
"The time increment is 0.1\n"
]
}
],
"source": [
"x_0 = 0 \n",
"v_0 = 0 \n",
"m_0 = 0.25 \n",
"m_f= .05\n",
"dmdt = 0.05 \n",
"d_t = 0.1 \n",
"T = 1000\n",
"N = round(T/d_t)\n",
"\n",
"print('The number of time steps is {}.'.format( N ))\n",
"print('The time increment is {}'.format( d_t ))\n",
"\n",
"t=np.linspace(0,((m_0-m_f)/dmdt),N)\n",
"d_t=t[1]-t[0]\n",
"N =int(((m_0-m_f)/dmdt)/d_t)\n",
"mflimit = np.linspace(m_0, m_f, N)\n",
"\n",
"num_heun = np.zeros([N,3])\n",
"num_rk2 = np.zeros([N,3])\n",
"\n",
"num_heun[0,0] = x_0\n",
"num_heun[0,1] = v_0\n",
"num_heun[0,2] = m_0\n",
"num_rk2[0,0] = x_0\n",
"num_rk2[0,1] = v_0\n",
"num_rk2[0,2] = m_0\n",
"\n",
"\n",
"m=mflimit/m_0\n",
"u=-250*np.log(m)\n",
"\n",
"for i in range(N-1):\n",
" num_heun[i+1] = heun_step(num_heun[i], simplerocket, d_t)\n",
" num_rk2[i+1] = rk2_step(num_rk2[i], simplerocket, d_t)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Velocity [m/s]')"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x1080 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,15));\n",
"plt.plot(num_heun[:,2]/m_0,num_heun[:,1],'o-',label='Implicit')\n",
"plt.plot(m,u,'--',label='Analytical')\n",
"plt.legend();\n",
"plt.xlabel('Mt/M0')\n",
"plt.ylabel('Velocity [m/s]')"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Velocity [m/s]')"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x1080 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,15));\n",
"plt.plot(num_rk2[:,2]/m_0,num_rk2[:,1],'s-',label='Explicit')\n",
"plt.plot(m,u,'--',label='Analytical')\n",
"plt.legend();\n",
"plt.xlabel('Mt/M0')\n",
"plt.ylabel('Velocity [m/s]')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. You should have a converged solution for integrating `simplerocket`. Now, create a more relastic function, `rocket` that incorporates gravity and drag and returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (1). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \n",
"\\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt}-g-\\frac{c}{m}v^2 \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `rocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s, . \n",
"\n",
"Compare solutions between the `simplerocket` and `rocket` integration, what is the height reached when the mass reaches $m_{f} = 0.05~kg?$\n"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"def rocket(state,dmdt=0.05, u=250,c=0.18e-3):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, with drag, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" c : drag constant for a rocket set to 0.18e-3 kg/m\n",
" Returns\n",
" -------\n",
" dstate: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" dstate = np.array([state[1], (u/state[2])*dmdt-9.81-(c/state[2])*state[1]**2, -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"num_heun2 = np.zeros([N,3])\n",
"num_rk22 = np.zeros([N,3])\n",
"num_heun2[0,0] = x_0\n",
"num_heun2[0,1] = v_0\n",
"num_heun2[0,2] = m_0\n",
"num_rk22[0,0] = x_0\n",
"num_rk22[0,1] = v_0\n",
"num_rk22[0,2] = m_0\n",
"\n",
"\n",
"m=mflimit/m_0\n",
"u=-250*np.log(m)\n",
"\n",
"for i in range(N-1):\n",
" num_heun2[i+1] = heun_step(num_heun2[i], rocket, d_t)\n",
" num_rk22[i+1] = rk2_step(num_rk22[i], rocket, d_t)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Velocity [m/s]')"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x1080 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,15));\n",
"plt.plot(num_heun2[:,2]/m_0,num_heun2[:,1],'o-',label='Implicit')\n",
"plt.plot(m,u,'--',label='Analytical')\n",
"plt.legend();\n",
"plt.xlabel('Mt/M0')\n",
"plt.ylabel('Velocity [m/s]')"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Velocity [m/s]')"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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G28tzxRVXMHToUPLy8jjiiCPo2LEjL7/8MgMHDuStt97aaP/LL7+cP//5z6xZs4a9996bo446im222YZHH32Ufv368fDDD1cq78knn0y7du14/vnnmTFjRpn73H777QCcddZZ5Obm0q9fP44/PvWMlKZNm3Laaaet+3PCCSdU6nvHjRtHr169GD16NDFGBg8eTP/+/SkuLuaPf/wjkyZN2mD/IUOGMGHCBJo2bcrBBx/MIYccwqpVq7jjjjvYa6+9mD59eqW+d4uKMfqnGn/69OkTs86k62O8drsYn744xu/+m3QaSZKkrDF16tSkI2S8KVOmRCA2b948Llu2LMYY46pVq+I222wTgfj6669vNAeIQGzdunUsKChYt72oqCj+9Kc/jUA8+OCDN5r3zDPPxDlz5my0/YknnogNGzaMrVu3XpdhrTFjxkQgnnbaaRts/81vfhOB+Mtf/nKj4y1atCg2a9Ys5ubmxi+//HLd9v/9738RiF26dCn3n8eVV14ZgXjllVdusP2dd96Jubm5MScnJ957772xuLh4g8+nTp260d+3v//97xv9njVr1qzLPmjQoI2+/7TTTotAHDNmTLkZy7I5f9eBglhOX8ro93Cqlux7DuxzNjRulXQSSZKkumXS9fDqqMrtu9dpcNQtG2574nyYUsnnbPS/FA68bMNtfx0C05+t3PzBN0H+6ZXbdzPcd999AJx00kk0adIEgLy8PIYOHcqtt97K/fffT79+/cqc+7vf/Y4+ffqsGzdo0IBrr72W0aNH8/rrr7NmzRoaNmy47vPyLoE98sgjOfHEE/nrX//KpEmTOOKIIzaZ+5xzzmHUqFGMGTOGa6+9lq222mrdZw888ABLly7lxBNPpEOHDpv+h1AJv//97yksLOSSSy7hjDPO2OjzHj16bLTtpJNO2mhbbm4u11xzDffffz/PP/88S5YsoXnz5jWSsSZYOOujrVomnUCSJEl10KpVq/jb3/4GlFxGu9bpp5/OrbfeysMPP8wtt9xCs2bNNpo/ePDgjba1a9eOrbfemgULFvDdd9/Rvn37DT6fN28eTz31FB9//DELFy6ksLAQgI8//hiA6dOnV6pwdujQgeOOO44JEyYwfvz4Dd7TeeeddwJw7rnnbvI4lVFUVMSLL74IwJlnnrlZc6dPn86zzz7LjBkzWLp0KcXFxQAUFhZSXFzMjBkz6N27d43krAkWTkmSJEk14rHHHmP+/PnstNNO9O3bd4PPevfuTa9evfjggw+YMGECw4cP32h+586dyzxuixYtWLBgAStXrtxg+913382FF17I8uXLy820ePHiSuc///zzmTBhAnfccce6wjlp0iSmTZvGbrvtRv/+/St9rIrMmzePZcuWkZubS/fu3Ss1p7CwkBEjRnDvvfeSuoq1bJvze7cEC6dgyTfw7Sew40FJJ5EkScpuB1628WWum+OoWza+zHZzDP171efWgLXv2ly0aFGZl81+88036/Yrq3A2aFD5Z5oWFBRwzjnnkJuby//93/9x5JFH0rFjR5o0aUIIgV//+tdcf/31FZaz0vr27Uvv3r159913KSgoID8/f93DgkaMGFHp49SGm2++mdGjR9OhQwf+9Kc/sf/++9OuXTsaNWoEwP77789bb721Wb93S7Bw1mcrF8Ezl8LHj0DDxnDhNMhrmnQqSZIkZaHZs2fz0ksvAfDtt9/y7bfflrvvm2++yfTp09l5552r/H2PPPIIMUbOP/98Lrrooo0+L+9ps5ty3nnnMXz4cO644w6uvfZaHn/8cZo3b86Pf/zjKmctrU2bNjRp0oTly5fzn//8hx133HGTc9Y+cffuu+8u89Ljqv7e2uZrUeqzvOYwezIUrU6Vzw/+mnQiSZIkZakxY8ZQXFzMwIEDK3zLw4knngiUnA2tqvnz5wPQqVOnjT6bO3cuL7zwQpWO+6Mf/Yg2bdowfvx4Ro0aRWFhIT/5yU/KfBBPXl4ewLr7RisrJyeHgw8+GIB77723UnMq+r0vvPACc+fO3awMW4qFsz5r0AD2Oadk/PZdkL7pWJIkSaqsGCMPPJB6uu6mzgSu/XzcuHEUFRVV+Tt33XXXdcdZunTpuu1Llixh+PDhLFy4sErH3WqrrTjzzDNZsWIFt956K1D+5bRt27YlLy+Pb775hgULFmzW91x++eXk5ORw4403Mnbs2I0+//TTT/n000/Xjdf+3jvvvHPdg4IA/vOf/3D22Wdv1ndvSRbO+q7XUGiUfmrtdzNgxovJ5pEkSVLWmTRpEv/9739p0qQJxx13XIX7Dho0iDZt2vD111/zzDPPVPk7Tz/9dDp16sSUKVPYYYcdOO644zj22GPp2rUrBQUFZd4jWlkjRowgJycHgAEDBtCzZ88y92vYsCFHHHEEhYWF9O7dm1NOOYUzzzyTSy+9dJPfsffee3PPPfes+y3du3dnyJAhHHPMMey+++706NGDyZMnr9v/sssuo2HDhtx999306NGDk08+mUMPPZSePXvSqVMn9t9//yr/3tpk4azvGjWDvdb7r1CTb08uiyRJkrLSmDFjADj66KM3+Q7Ihg0bcvLJJwPVu6x26623pqCggLPOOotmzZrx9NNPU1BQwHHHHceUKVPKvPS0sjp16rTujOKmXoUyevRozjjjDIqKipgwYQL33Xcf48ePr9T3DB8+nClTpjBs2DDWrFnDxIkTee2118jJyeHiiy/moINKHuq533778c4773DEEUewaNEiHn/8cb744gsuv/xynnvuuQ3eT5pJQqY9xSjb5Ofnx4KCgqRjVM/Cz+HmPSGmT82f8xZsW/Z/xZEkSarPpk2bRo8ePZKOoVr24Ycf0qtXLzp06MCsWbPIza1/z1rdnL/rIYT3Yoz5ZX3mGU5Bq87Q48iS8dt3JpdFkiRJStgVV1wBpN7LWR/LZk2ycCpl3/VuhP7w77BsXnJZJEmSpC3siSee4IwzzmDvvffmiSeeoGvXrowcOTLpWFnPwqmUTvtAh71S60WroGBMsnkkSZKkLWjKlCncf//9fPrppwwaNIhnn32Wpk19R311WTiVEsKGZzn/81JyWSRJkqQt7KqrriLGyOLFi3nmmWfYZZddko5UJ3hBskr0PBo+fQr2GAI7H5Z0GkmSJElZzsKpErl5cNIDSaeQJEmSVEd4Sa0kSZIkqVZYOCVJkqTN4HvsVdfV5N9xC6fKVlQInzwGow+Crz9MOo0kSVJGyMnJYc2aNUnHkGrVmjVryMnJqZFjWThVtucug4eHwZfvwb9uTTqNJElSRmjevDmLFy9OOoZUqxYvXkzz5s1r5FgWTpWt19CS9Y//AQtnJ5dFkiQpQ7Ru3ZoFCxYwb948Vq9e7eW1qjNijKxevZp58+axYMECWrduXSPH9Sm1KluH3tD1BzDzdYhFMPlOGHRd0qkkSZIS1ahRIzp37sz8+fOZOXMmRUVFSUeSakxOTg7Nmzenc+fONGrUqEaOaeFU+fY/P1U4AaY8AP1/BY1bJZtJkiQpYY0aNWK77bZju+22SzqKlPG8pFbl634wtN01tb56Kbw3NtE4kiRJkrKLhVPla9AA9j+vZPz2XVC4Ork8kiRJkrKKhVMV2/1EaLZtan3J1/DxI8nmkSRJkpQ1LJyqWG4j2OdnJeN/3Qo+jU2SJElSJVg4tWn5w6Fh09T6t1NhxkvJ5pEkSZKUFSyc2rTGW8NeP4HcrVLls033pBNJkiRJygK+FkWVc8BFqT9N2ySdRJIkSVKWsHCqciyakiRJkjaTl9RKkiRJkmqFhVNVs/RbmPZk0ikkSZIkZTAvqdXmKVwFz/0a3v8LxGK44CNo3j7pVJIkSZIykGc4tXly8uDrD6FwJRSthrduTzqRJEmSpAxl4dTmCQH6/aJkXHA/rFiQXB5JkiRJGcvCqc238+HQdtfU+uql8O59yeaRJEmSlJEsnNp8DRpA3wtKxpPvhDUrkssjSZIkKSNZOFU1u58ALTqm1pfPSz1ESJIkSZLWY+FU1eQ0hP3PKxm/eQsUrUkujyRJkqSMY+FU1e31E2iyTWp90efwyWPJ5pEkSZKUUSycqrq8JrDP2SXjN/4MMSaXR5IkSVJGsXCqer5/JjRsmlovXAmLv0o2jyRJkqSMkZt0AGW5Jq3h4KugWVvocRQ0yEk6kSRJkqQMYeFU9e1zVtIJJEmSJGUgL6mVJEmSJNUKC6dqXoywamnSKSRJkiQlzMKpmhMj/PtZuPdg+IeX2UqSJEn1nfdwquZ8NwP+NqRkPOdjaP+95PJIkiRJSpRnOFVz2uwEuw4uGb9+Y3JZJEmSJCXOwqmadcDFJeufTIS505PLIkmSJClRFk7VrA69YKdD04MIr/8x0TiSJEmSkmPhVM1b/yznRw/D/P8ml0WSJElSYiycqnmd9oZu/VPrsQjeuCnZPJIkSZISYeFU7Vj/LOcHf4WFs5PLIkmSJCkRFk7Vjq79oPN+qfXiNfCvW5LNI0mSJGmLs3CqdoQAB1xUMn7/IVi5OLk8kiRJkra43KQDqA7bcSB02if1fs5+F8JWLZJOJEmSJGkLsnCq9oQAw/4JOf41kyRJkuojL6lV7bJsSpIkSfWWhVOSJEmSVCs8/aQtZ/l8eOt2aNQM+v0i6TSSJEmSapmFU1vGN1PhvkNh9RLIaw57nQZNWiedSpIkSVIt8pJabRltd4EWHVLrq5fA5DuSzSNJkiSp1lk4tWU0yIH+vyoZT74rdYmtJEmSpDrLwqktZ7djoc0uqfXVS+Ct25LNI0mSJKlWWTi15TTIgQGXlIzfvtuznJIkSVIdZuHUltXzWGi7a2p99VL4163J5pEkSZJUazKmcIYQzgshTAghTAshfBdCWBNCmBtCeDGEcGoIIZQxZ2wIIVbw59NNfOfQEMLrIYRFIYSlIYSCEMK5IYSM+edS5zRoAP3XO8v5zj2w7Lvk8kiSJEmqNZn0WpRLgHbAx8C/gGVAF+AgYCBwQgjhuBhjcRlz3wRmlLH96/K+LIRwOzACWAm8BKxJf89twMAQwokxxqKq/xyVq+cx0PYPMHda6iznW7fCwVclnUqSJElSDcukwnky8H6Mcdn6G0MIu5EqhEcDpwFjyph7b4xxbGW/KIRwPKmyOQc4IMb4WXr7tsAk4FhgJHDz5v8MbVKDBql7OR8elhq/fQ/sNxKatkk0liRJkqSalTGXjsYY3yhdNtPbPwFuTw8PqaGvuyy9vGRt2Ux/1zfAOenhpV5aW4t6HA3tekLLTnDY76FRi6QTSZIkSaphmXSGsyKF6eXK6h4ohNAR6AOsBh4u/XmM8dUQwpfA9sC+pC7vVU1r0ABO/iu02B5y85JOI0mSJKkWZHzhDCF0A85OD58sZ7cDQwh7AM2Ab4A3gBfKud+zd3r5SYxxRTnHe5dU4eyNhbP2tO6WdAJJkiRJtSjjCmcI4XSgP9AQ6AjsT+rS3+tjjI+VM+0nZWybGkI4Ocb4Uanta1vOrApifF5qX0mSJEnSZsq4wgn0JfVwoLUKgd8Cfypj3w+A90g9VGgW0ALYC/g9sCfwYghhrxjjl+vNaZZebnS/6HqWppfNy/owhHAWcBZA586dK/ot2hyz/gXzPoM+p216X0mSJEkZL+MeihNjPDPGGIAmwG7ATcBVwOQQQodS+94UY7w1xjg1xrgsxvh1jPFpYG9gMqnXrFy24Tew9n2esRoZ74kx5scY89u2bVvVw2it5fPhgaNgzOHwzCWwZE7SiSRJkiTVgIwrnGvFGFeki+TFpErjnqTekVmZuauB69PDH5b6eEl62Yzyrf1sSQX7qKY03hpWLkytF66A125MNo8kSZKkGpGxhbOUte/ePDKE0LCScz5NL7cvtX1metmlgrmdSu2r2hQCHPTbkvF7Y2FBRbfYSpIkScoG2VI4F5K6lzMXaF3JOdukl0tLbX8/vdwthNC4nLnfL7Wvalv3g6HTvqn14jXw6h+SzSNJkiSp2rKlcB5AqmwuBOZVcs5J6eW762+MMc4GpgB5wImlJ4UQ+pN6Ou4c4K0q5tXmCgEGrneW88O/ph4gJEmSJClrZUThDCH8IIRwSgihURmf9QXuSw/vizEWpbf3CiEMDiHklNo/N4RwIXB+etOfy/jKtfd33rDsowkAACAASURBVBBC6L7e3HbAHenhqHLe46na0rUf7DAgtR6LYdJ1SaaRJEmSVE2Z8lqUHUndp3lbCGEKqbOLzdPbe6b3eZrU61HW6go8BswPIUwHvkjP2R3oABQDl8QYnyv9ZTHGR0IIdwLnAB+FEF4E1gADSb1aZSKVfECRathBV8B/X0mtf/IP+MGF0H73RCNJkiRJqpqMOMMJvApcQ+q9mjsDxwGHAk2BR4FjY4yDY4wr1pvzIXAz8G+gM3Ak0B9YTqq87h1jLPdGwBjjCOAUUpfX9gcOA2YAI4Hj155J1RbWsQ/sst6DhT3LKUmSJGWtEGOVX0cpID8/PxYUFCQdo26Z8zHc1Y91r0o98yXomJ9oJEmSJEllCyG8F2Ms8/+wZ8oZTqlE++/B945Lrfc8OvWeTkmSJElZJ1Pu4ZQ2NPAK6Ptz2G7PpJNIkiRJqiILpzLT1l2TTiBJkiSpmrykVpIkSZJUKyycyg6rlsC790Gxr0aVJEmSsoWX1CrzvTMaXrkeln8HTVrDbscmnUiSJElSJXiGU5lv0exU2QR4+VooKkw2jyRJkqRKsXAq8/W9ABq1TK1/NwPefzDZPJIkSZIqxcKpzNekNfT7ecn4lVGwenlyeSRJkiRVioVT2WGfc6BZ+9T60jnw9p3J5pEkSZK0SRZOZYe8JjDg0pLxGzfD8vnJ5ZEkSZK0SRZOZY/eP4ZtuqfWVy2CN/6UbB5JkiRJFbJwKnvk5MLAK0rGb98Di75ILo8kSZKkClk4lV16HAXb90mtF62CSdcnm0eSJElSuSycyi4hwMFXpdabtoPt90oyjSRJkqQK5CYdQNps3Q6AY++BXY+ARs2STiNJkiSpHBZOZac9hySdQJIkSdImeEmtJEmSJKlWWDhVN8x+Fz6fnHQKSZIkSeuxcCq7LfoCxp8C9x0MT/0CiouSTiRJkiQpzcKp7JaTB/+ZlFr/dip8OD7ZPJIkSZLWsXAquzVrB/ufVzJ++VpYvTy5PJIkSZLWsXAq++1/XuqdnABLvoLJdySbR5IkSRJg4VRd0KgZHHR5yfiNP8PSb5PLI0mSJAmwcKqu6HUqtN01tb56KbwyKtk8kiRJkiycqiNycuGQa0rG742FudMTiyNJkiTJwqm6ZKdDoFv/1HosghevTDaPJEmSVM9ZOFV3hACHXgOE1Pjf/4SZbyQaSZIkSarPLJyqW7bbE/Y8ObW+8yBo1j7ZPJIkSVI9lpt0AKnGHfRb6DUUuh2QdBJJkiSpXrNwqu5puX3qjyRJkqREeUmtJEmSJKlWWDhV961eDq//CZZ9l3QSSZIkqV7xklrVbZ8+DU9fBEu+gqXfwOE3JJ1IkiRJqjc8w6m6b8lXqeW798J3/0k2iyRJklSPWDhVt+3yQ+i8f2q9uBCe/22yeSRJkqR6xMKpui0EOOzakvG/n4b/vpJYHEmSJKk+sXCq7tu+D+z5o5Lxs7+G4qLk8kiSJEn1hIVT9cPAK6Bhk9T6t5/AlHHJ5pEkSZLqAQun6ocWHaDfhSXjl6+FlYuSyyNJkiTVAxZO1R/7j4QWHVPry+fBa/+XbB5JkiSpjrNwqv5o2BgO+V3JePJdviZFkiRJqkUWTtUv3zseOu0DW7WEQ6+BVp2TTiRJkiTVWblJB5C2qBDgmDthq1bQdJuk00iSJEl1moVT9c82OyadQJIkSaoXvKRWkiRJklQrLJzS1x/C+FN8TYokSZJUwyycqt9eugbu7g+fPgWv3Zh0GkmSJKlOsXCqfmvXA4ip9cl3+poUSZIkqQZZOFW/fe946Lh3ar14DTz/22TzSJIkSXWIhVP1WwgwaFTJ+N9Pw4wXk8sjSZIk1SEWTqljH+h1asn4mUuhcHVyeSRJkqQ6wsIpARx8JTRqkVr/7jN4+65k80iSJEl1gIVTAmjWDgZcVjJ+9QZYMie5PJIkSVIdYOGU1tr7p9B219T66qXwwpXJ5pEkSZKynIVTWiunIRx+Q8n4o4dhwazk8kiSJElZLjfpAFJG2WEA9DgKln8Hh/8Btu6SdCJJkiQpa1k4pdKOuRPymqZemSJJkiSpyiycUmmNmiWdQJIkSaoTvIdTqozVy5JOIEmSJGUdC6dUkaI18K/b4E89Yc5HSaeRJEmSsoqFU6rIPy+C5y+HlQvhn7+CGJNOJEmSJGUNC6dUkX3PhQbpW50//xd8/GiyeSRJkqQsYuGUKtJ2Z9jn7JLx87+BVUuSyyNJkiRlEQuntCn9L4Fm26bWl3wNr4xKNo8kSZKUJSyc0qZs1QIOvbZkPPlO+GZqcnkkSZKkLGHhlCpj9xOh6w9S67EInv6lDxCSJEmSNsHCKVVGCPDDGzd8gNCH45PNJEmSJGU4C6dUWe12hf3OLRk//xtYsSC5PJIkSVKGs3BKm+OAX0GL7VPreU1h0RfJ5pEkSZIyWG7SAaSs0qgZHP4H+PpD+MGF0LBx0okkSZKkjGXhlDZXj8GpP5IkSZIq5CW1kiRJkqRaYeGUqitG+PRpWDo36SSSJElSRrFwStWxYCb87WQYPxRevDLpNJIkSVJGyZjCGUI4L4QwIYQwLYTwXQhhTQhhbgjhxRDCqSGEUMHcoSGE10MIi0IIS0MIBSGEc0MIFf6+qs6T1pn3GUx/NrX+wUMw661k80iSJEkZJJOK1SXAMcAK4F/Ao8AM4CDgQeCxsopgCOF24CEgH3gdeAHYGbgNeCSEkFPWl1V1nrSBnQ6BHkeWjJ/+JRQVJpdHkiRJyiCZVDhPBraOMe4VYzwyxnhyjHE/YHfgG+Bo4LT1J4QQjgdGAHOAPWKMg2OMxwI7AdOAY4GRpb+oqvOkMg0aBQ2bpta//QTevjPZPJIkSVKGyJjCGWN8I8a4rIztnwC3p4eHlPr4svTykhjjZ+vN+QY4Jz28tIwzo1WdJ22sZUfo/6uS8aTrYOHnyeWRJEmSMkS2FKq11yiuXLshhNAR6AOsBh4uPSHG+CrwJdAe2Le686QK7XcutOuZWl+zHP55cerptZIkSVI9lvGFM4TQDTg7PXxyvY96p5efxBhXlDP93VL7VmeeVL6chnDkzSXj6c/CtCeSyyNJkiRlgIwrnCGE00MIY0MID4UQXgWmAx2B62OMj623a7f0clYFh1t7XWO39bZVdZ5UsU57Q/7wkvE/fwUrFyWXR5IkSUpYxhVOoC+phwMNBQ5Ib/stcHWp/Zqllxvd97mepell8xqYt04I4az0K1QK5s6dW8FhVO8MvBKatkutL50Dr/4h2TySJElSgjKucMYYz4wxBqAJsBtwE3AVMDmE0GG9Xde+l3Nzb5Sr6rz1M94TY8yPMea3bdu2qodRXdS4FRw+KrW++0nQ94Jk80iSJEkJyk06QHnS91dOBS4OIcwBbiT1jszj0rssSS+blTGdUp8tWW9bVedJlbPbcbB1V9i+T9JJJEmSpERl3BnOcoxJL48MITRMr89ML7tUMK9TqX2rM0+qnBAsm5IkSRLZUzgXkno1Si7QOr3t/fRytxBC43Lmfb/UvtWZJ1VPcVHSCSRJkqQtKlsK5wGkyuZCYB5AjHE2MAXIA04sPSGE0J/U023nAG+t3V7VeVKVrVycei/n+KG+m1OSJEn1SkYUzhDCD0IIp4QQGpXxWV/gvvTwvhjj+qeJrk8vbwghdF9vTjvgjvRwVIyxuNRhqzpP2jyrlsAd+8E796TezTl1YtKJJEmSpC0mIwonsCPwF2BOCOGl9Ds4nwghfAK8AewAPE3q9SjrxBgfAe4E2gMfhRCeDCH8A/gM6AlMJPWgIWpinrTZGjWHXQaVjJ+5BFYsTC6PJEmStAVlSuF8FbgG+ADYmdSTaA8FmgKPAsfGGAenn1y7gRjjCOAUUpfJ9gcOA2YAI4HjS50RrfY8abMNvAKatU+tL/0GXir9SllJkiSpbgrRe8qqJT8/PxYUFCQdQ5nuk4nw8GnpQYDhz0HnfRKNJEmSJNWEEMJ7Mcb8sj7LlDOcUt3W82jY6bD0IMIT50HhqkQjSZIkSbXNwiltCSHAEX+EvGap8bx/w2s3JptJkiRJqmUWTmlLadUJDr6qZPzGn+CbT5JKI0mSJNU6C6e0JeWfAZ32Ta0XF8LjI6HY51NJkiSpbrJwSltSgwZw1K2Qk5caN2zsa1IkSZJUZ+UmHUCqd9runLq0tmFj2GtYqoRKkiRJdZCFU0rCfucmnUCSJEmqdZ5akSRJkiTVCgunlAmK1sCbt8CSb5JOIkmSJNUYL6mVkjbnI5h4Tmr5ZQGcNC7pRJIkSVKN8AynlLTl36XKJsDUx2Hak8nmkSRJkmqIhVNK2g4DoPepJeOnL/JVKZIkSaoTLJxSJjj0Wmi2bWp96Rx44bfJ5pEkSZJqgIVTygSNt4Yf/l/JeMo4+M+k5PJIkiRJNcDCKWWKnkdDjyNLxk+cB6uWJJdHkiRJqiYLp5RJjvhT6mwnwKLZ8MIVyeaRJEmSqsHCKWWSZu3ghzeWjAvuh/++klgcSZIkqTosnFKm+d7xsOvgkvFbtyeXRZIkSaoGC6eUaUJIXVrbtC384Jcw5C9JJ5IkSZKqJDfpAJLK0HxbOP99aNQ86SSSJElSlXmGU8pUlk1JkiRlOQunlC1ihC8Kkk4hSZIkVZqFU8oGi7+Cv54E9w6E/72edBpJkiSpUiycUjZ44Qr47PnU+uPnwuplyeaRJEmSKsHCKWWDQ66BrVqm1hfOghd/l2weSZIkqRIsnFI2aLEdDLqhZPzO3TDzjeTySJIkSZVg4ZSyxZ4nw86DSsaPnwurliaXR5IkSdoEC6eULUKAwTeVXFq7YGbq3k5JkiQpQ1k4pWxS+tLagvtgxovJ5ZEkSZIqYOGUss2eJ8Oug0vGj4+EFQuSyyNJkiSVw8IpZZu1l9Y2aZMaL/kaJl2fbCZJkiSpDBZOKRs1awtH3pRa3+NkOPDXyeaRJEmSypCbdABJVdTjSPjpy7B9n6STSJIkSWXyDKeUzSybkiRJymAWTqmuWTIn6QSSJEkSYOGU6o5VS+CJ8+C278PCz5NOI0mSJFk4pTpjwk9gyjhYtRgmjoDi4qQTSZIkqZ6zcEp1xYDLIKT/lZ75OrxzT7J5JEmSVO9ZOKW6otPe0PeCkvGLV8Lc6cnlkSRJUr1n4ZTqkgGXwrbfS60XroTHfgZFhclmkiRJUr1l4ZTqktxGcOzd0KBhavzVFHj9xmQzSZIkqd6ycEp1TfvvwYG/Lhm/+geY/W5yeSRJklRvWTiluqjvz6Hz/qn1WAT/+GnqtSmSJEnSFmThlOqiBjlw7F3QqEVqvOB/8NLVyWaSJElSvWPhlOqqrbvAD9P3b3brv+ETbCVJkqQtIDfpAJJq0R4nwVYtYKfDoIH/fUmSJElbloVTqstCgF0OTzqFJEmS6ilPeUj10bLvkk4gSZKkesDCKdUnRWtg0nVw8x7w7adJp5EkSVIdZ+GU6pOnLoBXb4DVS+EfZ0LhqqQTSZIkqQ6zcEr1yX4jIadRan3OR/DytcnmkSRJUp1m4ZTqk3Y94JD13sf5r1vhf68ll0eSJEl1moVTqm/2Pgt2HJgeRHjsbFixINFIkiRJqpssnFJ906ABHHMHNG6dGi/+Ep68AGJMNpckSZLqHAunVB81bw9H3VoynjoR3n8wuTySJEmqkyycUn3VYzD0GVYyfuYSmDs9sTiSJEmqeyycUn122PXQZpfU+prl8Pi5XlorSZKkGmPhlOqzvCZwwv2pV6W06wlH3QIhJJ1KkiRJdURu0gEkJaz99+DH/4Dt+0DDxkmnkSRJUh1i4ZQEXfslnUCSJEl1kJfUSirbgplQXJx0CkmSJGUxC6ekDcUI7z0At+8L/7ol6TSSJEnKYhZOSRv66BF48nwoXAEvXwNfvJd0IkmSJGUpC6ekDe12DGyfn1ovLoRHz4CVi5PNJEmSpKxk4ZS0oZyGcMJ90KhFarzgf/DPi5LNJEmSpKxk4ZS0sa27wuA/l4z/39/hw/GJxZEkSVJ2snBKKtvuJ0CvU0rGT/8SvvtPcnkkSZKUdSycksp3+B+g9Y6p9dVL4eHTYM3KZDNJkiQpa1g4JZWvUTM4cQzk5KXGcz6C5y9PNpMkSZKyhoVTUsW22xMOu65kXHA/zJ2eXB5JkiRlDQunpE37/pnQ82ho1h5+8gS03TnpRJIkScoCuUkHkJQFQoCjboXC1dCsbdJpJEmSlCUsnJIqZ6uWSSeQJElSlvGSWklVt/hrmPlG0ikkSZKUoSyckqpmxotwVz8YPxQWzEo6jSRJkjJQRhTOEELDEMLAEMIfQwiTQwhfhxBWhxC+DCE8EkIYUM68sSGEWMGfTzfxvUNDCK+HEBaFEJaGEApCCOeGEDLin4uUsQpXw1MXwvJ5sHIRPHJ6apskSZK0nky5h7M/8EJ6fQ7wHrAM6AkcDxwfQrgmxnhFOfPfBGaUsf3r8r4whHA7MAJYCbwErAEGArcBA0MIJ8YYi6rwW6S6LzcPTrgf7j8Migvhy/fgpd/BYb9POpkkSZIySKYUzmLgUeDmGOPr638QQhgCPAT8NoQwKcY4qYz598YYx1b2y0IIx5Mqm3OAA2KMn6W3bwtMAo4FRgI3V+G3SPVDx3w4+Cp4/jep8Vu3Qdd+sMvhSaaSJElSBsmIS0djjC/HGE8oXTbTn/0dGJsenlpDX3lZennJ2rKZ/q5vgHPSw0u9tFbahP1Gws6DSsaPnQ0LZyeXR5IkSRklWwrV++llx+oeKITQEegDrAYeLv15jPFV4EugPbBvdb9PqtNCgGPuhBbpfzVXLoRHhkPRmmRzSZIkKSNkS+HcKb0s757MA0MIfwoh3BNCuCaEcFgFZyd7p5efxBhXlLPPu6X2lVSeJq1T93OGnNT4i3fghfJut5YkSVJ9kin3cJYrhNAeGJYePlrObj8pY9vUEMLJMcaPSm3vll5W9B6Hz0vtK6kinfeBg68sKZqT74BO+8BuxySbS5IkSYnK6DOcIYRc4C9AS+ClGOOTpXb5ADgf2A1oBnQABgMfknrC7YshhO1LzWmWXi6r4KuXppfNy8l1VvoVKgVz586t7M+R6rb9z4ddjigZz34nuSySJEnKCBldOIG7SL2qZDZlPDAoxnhTjPHWGOPUGOOyGOPXMcangb2ByUA7Sh4QtFZYO72qoWKM98QY82OM+W3btq3qYaS6JQQ45g5o1zN1X+eg65JOJEmSpIRl7CW1IYSbgTNIvbpkYIxxTmXnxhhXhxCuBx4Hfljq4yXpZTPKt/azJRXsI6m0xq3g7DegQU7SSSRJkpQBMvIMZwjhj6QulZ1Lqmx+tokpZfk0vSx9Se3M9LJLBXM7ldpXUmVZNiVJkpSWcYUzhPAH4ELgO+CQGOPUKh5qm/Ryaanta1+xslsIoXE5c79fal9JVbVqSer9nF99kHQSSZIkbWEZVThDCKOAi4EFpMrmh9U43Enp5bvrb4wxzgamAHnAiWVk6E/qfZ9zgLeq8f2S5k6H0QfBh3+DCT+BFQuSTiRJkqQtKGMKZwjhGuASYCGpslnh2cUQQq8QwuAQQk6p7bkhhAtJXZIL8Ocypl+fXt4QQui+3tx2wB3p4agYY3EVfoqktRrkwJL07dcLZ8HEEVDsv1aSJEn1RUY8NCiEcBTwm/RwBnBeCKGsXT+NMY5Kr3cFHgPmhxCmA1+Qeo3J7qRej1IMXBJjfK70QWKMj4QQ7gTOAT4KIbwIrCH1RNwWwETgtpr5dVI9ts2OcPTtMOHHqfG//wn/ugX6XZBsLkmSJG0RGVE4gdbrreen/5TlVWBt4fwQuJnUK1C6AL1JverkC2AMcHuM8b3yvjDGOCKE8AZwLtAfyCH1oKH7gTs9uynVkJ5HwX4j4a30f8N56XfQMR+69ks2lyRJkmpdiLHKr6MUkJ+fHwsKCpKOIWW2ojUwdjDMnpwaN20HZ78Ozdsnm0uSJEnVFkJ4L8ZY5knDjLmHU1IdltMQThwDTdqkxsu+hUeGp4qoJEmS6iwLp6Qto0UHOOE+COn/2Zn1JrxwZbKZJEmSVKssnJK2nB0GwIGXl4wn3w5TH08qjSRJkmqZhVPSltXvQth1cGp9x4Og6w+SzSNJkqRakylPqZVUXzRoAMfcCVP2hX1HpN7VKUmSpDrJwilpy9uqBex/XtIpJEmSVMu8pFZS5pj3WdIJJEmSVIPKPcMZQpheQ98RY4y71NCxJNVFxUUw6ffw+p/gR3+DXQ5POpEkSZJqQEWX1Havoe+INXQcSXXVK6Pg9T+m1v9xFpz1CmyzY5KJJEmSVAM2dQ/no8Cl1Tj+DcCx1ZgvqT7Y52z4cDws+hxWLYbxp8CZL0KjZkknkyRJUjVsqnAuiTH+p6oHDyEsqepcSfVI021gyINw/2FQuBLmToMnRsIJYyCEpNNJkiSpiip6aNDTwAfVPP4HwD+reQxJ9UGHXjD4zyXjTx6Dt25LLo8kSZKqrdzCGWM8MsZ4S3UOHmO8OcZ4ZHWOIake6TUUvn9myfiFK+C/ryaXR5IkSdXia1EkZZbDroeOe6fWYzE8cjos/DzZTJIkSaoSC6ekzJKbByeNg2bbpsbLv4PxQ2H18mRzSZIkabNVunCGELqEEI4LIXQqtX33EMIrIYQFIYT3QwiH1nxMSfVKi+3gpAehQcPUeMEsmPtpspkkSZK02TbnDOdFwMNAo7UbQgjNgReBA4CWwJ7A4yGEnWsypKR6qPM+cMSNsM1O8NOXYfu9kk4kSZKkzbQ5hfMA4NMY44z1tp0KtAUmALsCvyJVSM+vsYSS6q8+w+Ds16HNTkknkSRJUhVsTuHcDphZatthQDFwQYxxeozxRmAqcGDNxJNU7zVsnHQCSZIkVdHmFM5WwIJS2/aD/8/efYfZVZZ7H/8+KUMbehKQRJPQixwkDAhKhwAyhN6kI71YsBzjIZ7XI1HHhqJ0CB2UDkIUCD0gQiYgUqWYoUQCJEhJSDLJzPP+sfawh8nMZGb22rN2+X6ui2vPevZaa268ztH8cj+FZ2KMs9qNPQcML7QwSerUv5+Cq/aB+e9nXYkkSZKWojeB8yOSLicAuXWaQ4G/drivtZfvlaSeeeYmuGwP+NeDcMsJ0NqSdUWSJEnqRm+C4T+AL4cQRueujwMi8GCH+0YBs5CktIUAixckP798D9x/Vrb1SJIkqVu9CZyXADXAkyGEJ0h2rZ0N3Nl2QwihFticZFqtJKXr8wfAtmfkrx/5TdL1lCRJUknqceCMMV4H/BRYFqgDZgIHxRjnt7vtIJJQ+mCKNUpS3s4/hPXaHfd7++nw1tPZ1SNJkqQu9WqtZYxxArAasFaM8XMxxoc73PIAsCVweUr1SdKnDRgIB1yanM8JsHg+/PFwmPtutnVJkiRpCV0GzhDC+NzGQJ8SY5zfYVfa9t81xRinxxg/TLNISfqUZVeGr/4Bllkpuf7gDbjhKFjcnG1dkiRJ+pTuOpw/BV4IITwXQjgrhDCmv4qSpKUash4cMAkIyfXrf4U/fxdizLQsSZIk5XUXOA8BbiA5U/NMYFoIoSmEcHYIYbsQQuiXCiWpK+vvBrv8b/76ySvh1fuzq0eSJEmf0mXgjDHeGGP8KslZm+OAK4DlgW+RbAr0VgjhohDCHiGEwf1QqyQtadszYNODgQC7TYR1ds66IkmSJOWE2IvpZyGEAcB2wAHAPsBnSc7i/IjkeJRbgb/EGD9Ov9TSVFdXFxsbG7MuA4BR4ycv9Z6mhvp+qETqZ4sWwJvTYPR2WVciSZJUdUII02OMdZ1919tdaltjjA/FGL8RYxwJfBH4JTALOIxkCu67IYRbQwhHhRBWKbR4pWvU+Mk9CqZSWRm8rGFTkiSpBPUqcHYUY5wWYxwfY9wQ+DzwI+Alku7n5cA3Cq5QRWHwVMVbtACmnu3OtZIkSRkalNaLYozPA88DZ4UQRgP7ATPTer+Koy10OtVWFWXuO/DHw5Jptv9pgnHngPucSZIk9bvUAmd7McYZwNnFeLeKY9T4yQRghsFTleC5W5OwCcnOtUM3hG1OzbYmSZKkKtTrwBlCqAHGAGsBy3Z1X4zxugLqUgYiSfC026myt9WJMHM6/OP65PqeM5NzO9cbm21dkiRJVaZXgTOE8F3gf4CVe3C7gbNMOc1WZS8EGPc7eO9fSacztsJNX4PjpsCwDbOuTpIkqWr0+FiUEMI3gN/mLp8HXgbmdnV/jPHIgqsrA6V0LEqbtDcDMniqbM19By7eCT58M7ledRQcfz+ssHqmZUmSJFWS7o5F6U3g/CcwGjggxnhHivWVtVIMnG0MnhIw6xmYtDssmpdcj/wyHHkbDKrJti5JkqQKkdY5nCOBhwyb5aOpoT7VkOhRKipLa24K+18M5Hapfe1RmPxt6OFftkmSJKnvehM4ZwFzilWIisfgqaq30V6wy//mr5+6GqZdml09kiRJVaI3gfN2YNsQwuBiFaPiKkbwrJs4JbX3SUW17Rmw2VeTn4fXwcb7ZFuPJElSFejNGs5VgWnA48BpMcb3i1lYuSjlNZxLk2aX0vWdKguLF8Kj58CXvg6Dl8u6GkmSpIqQyqZBuRetDjwAjACeAN4EWju5NcYYT+pDrWWnnAMnwOjxk0lzJZvBU5IkSaouae1SuyxwPbAXn+y+0aUYYxzYqyrLVLkHzjbuaKuq9sp9MHwLWG6VrCuRJEkqO90FzkG9eM9ZwDjgP8B1wCt0cw6nyktbQEwreLa9x+CpkhYjPH4h3PUDGL09HHEzDHSZuiRJUlp60+F8HagFNosxvlHUqspIpXQ4O0qz4xmAGQZPlaKZT8IlO+WvNz8S9v49hKVN4pAkSVKbtM7hHAI8bNisDmnuaBtJf8qulIrhY2CnM/PXT10Nj/42u3okSZIqTG8C579Y+tpNVZg0g6fnd6okbf+9/HEpAPf+CJ67NbNyJEmSKklvAucVwI4hhGFFqkUlrKmhniG1Nam8y+CpkhICjPsdjNw2P3bryfDG3PM64AAAIABJREFUtOxqkiRJqhC9WcM5gGSX2g2B02OMDxWzsHJRqWs4u+OOtqpIH78Hk8bCnFeS6xWGwvH3wqqjMi1LkiSp1KV1LMpLJFNq184NLQT+TdfncG7Qh1rLTjUGzjZpBs8htTU0Thib2vukPnnvX3DJLjD/veR6yAZw3D0elyJJktSNtAJnZ8GyK57DWUXSDJ52O5W51x6Dq/aGlubkeu0d4cjb3LlWkiSpC2mdw7leSvWowqR5hqfndypzI7eBfS+Am4+DgctA3dcMm5IkSX3U4w6nOmeH89PqJk5h9tzm1N5n8FRmHjs/OTblc1tnXYkkSVJJS2VKrTpn4Oyc6zslSZKk6tBd4OzNsShSj6V5fufsuc0eo6LSMG82zJiadRWSJEllo8vAGUK4JYRweiEvDyF8PYRwSyHvUHlLM3h6fqcyNefV5NiU6w6GN6dnXY0kSVJZ6K7DuS8wpsD3jwH2KfAdqgAGT5W1GOGWE5NjUxZ9nITO9/6VdVWSJEklb2lTapcPIazV13+A5fvjX0LlI81NgEaNn0zdxCmpvU/qUgiw34Ww3KrJ9cez4ZoDYd6cbOuSJEkqcV1uGpQ7dzOVHYUq+UxONw3qO8/vVNl5/fHkjM7FC5LrEVvB0X+CwctlW5ckSVKG+rRLbQjhTdILnJ9N4z2lyMBZOIOnysrzf4IbjuKT/3rccC84+CoYULF/ryZJktQtj0UpIgNnegyeKht/uxDu+n7+equT4Cs/T6beSpIkVRmPRVFZSHt9p1Q0W58M27TbxPuJi+Cxc7OrR5IkqUTZ4SyQHc7isNupktfaCjd/DZ67NT92xM2w7q7Z1SRJkpQBO5wqOx6jopI3YADseyF87kvJ9YZ7wcgvZ1uTJElSibHDWSA7nP0jrcA4pLaGxgljU3mXBMDH78ETl8D233XjIEmSVJXscKrspdXtnD232W6n0rX8arDj9w2bkiRJnTBwqmw4zVZlpfEy+OjtrKuQJEnKlIFTZSft4Dna4Kk0tbbC3WfCnWfAtQfCgg+zrkiSJCkzBk6VraaGeobU1hT8nojHqChFb/0d/nZ+8vOsf8D1h8PihdnWJEmSlJEeB84QwvEhhOWKWYzUW40TxjrNVqVl+BgYd07+esbDcOtJSedTkiSpyvSmw3kx8GYI4dchhPWKVZDUF06zVUkZcxTsPCF//dytcNf3wV3BJUlSlelN4LwTWAk4A3ghhHBXCGFcCCEUpzSp99IKnk6zVcG2+y5sdWL++omLYeqvs6tHkiQpAz0OnDHGvYG1gQZgNrAbcBswI4QwPoQwtDglSr3nNFtlLgTYowE22S8/dv9Z8ORV2dUkSZLUz0LswxSvEMJg4GDgVGAbkoZQM3ATcH6M8bE0iyxldXV1sbGxMesy1I00A2NaQVZVZPHCZLfaGQ8n12EAHHodbPCVbOuSJElKSQhheoyxrrPv+rRLbYxxUYzx2hjjl4HNgUnAYuAw4JEQwvQQwtdCCMv0sMDBIYRdcutD/xZCeCuE0BxCmBlCuCmEsONSnj8shDA1hPBBCGFuCKExhHBaCKHbf7++Pqfykvb6TqlXBi0Dh1wLa26aXMdWuO1UWPhRtnVJkiT1gz51OJd4SQjDge8Dp7cbjsA7wIQY46SlPL8rMCV3OQuYDswDNgY+nxs/K8b4v508ex5Jp3UBcB+wCNgFWBG4FTgoxtiS1nMd2eEsL6PHTyatbVvsdqpXPnobLtsN5r8Ph98In90q64okSZJS0V2Hs6DAmQuKpwJ7AQOBhcB1JOHxCGDP3K1nxBh/1817ds6955wY49QO3x0CXJt7/84xxgfafXcAyTTeWcD2McaXc+NrAA8AGwHfijGe0+GdfXquMwbO8uQ0W2VizqvQsgiGbZh1JZIkSalJNXCGEFYGjgVOBtYDAvA6cAFwSYzxvXb3fpEkfL4TY1y3b+VDCOFS4Djgshjjce3GG4EtgKNjjFd1eGYH4EGSUDk8xtha6HOdMXCWt7SCp6FTkiRJ1SqVNZwhhDG54DcT+DWwPvAQcACwdozx5+3DJkCM8XFgMvC5vhaf81Tuc0S7ekaQhMZm4MaOD8QYH8rVuiawdaHPqTI1NdSTxrk+7marPpv9MlxzIHz83tLvlSRJKjO92RynEfha7udLgf+KMe4cY7x1KV3AecCgvhaYs17u8612Y5vnPp+LMc7v4rlpHe4t5DlVqBkpbyo02uCpnvr33+GyPeCVKXDtQbBwbtYVSZIkpao3gbMJ+B4wIsZ4Uozx2R4+dwIwuLeFtQkhrAkck7u8ud1Xo3Ofr3Xz+Osd7i3kOVW4tHazjbibrXpozivw8Zzk55mNcP3hyTEqkiRJFaI3gXOdGOOvY4zv9+YXxMRSd3vtTAhhEHANsDJwX4zxjnZf1+Y+53XzirZ2wYopPNe+rhNzR6g0vvvuu928RuXIabbqN5seCPW/yl//60G4+ThoWZxZSZIkSWnqTeC8O4Tw7aXdFEI4I4RwTwE1tXchyVElb5DsevupX5X77O02u3197hMxxotjjHUxxrqhQ4f29TUqYU6zVb/Z8njYeUL++oU74M5vQgpHVkmSJGWtN4FzV/JnYnZnY5KQWJAQwjkkO9POAnaJMc7qcEvbqem1dK3tu/YnrPf1OVUhp9mqX2z3Xdim3THGT10D90wwdEqSpLLXm8DZUzVAt0eJLE0I4dfAN4B3ScLmy53c1pT7HNnNqz7b4d5CnlMVa2qoZ0htTcHvcZqtOhUC7DYRvtBuIsdj58IjZ2dXkyRJUgpSDZwhhEBy5MjsAt7xC+DbwBxgbIzx+S5ubTsqZZMQwnJd3LNlh3sLeU5VrnHC2FSn2dZNnJLKu1QhQoBx58CGe+XH7vsxTLs0u5okSZIK1G3gDCHc0/ZPbmi39mMd/rmfZHfXjYCH+1JMCKGBZCfc/5CEzae7ujfG+AbwJElH9aBO3rUDybmds4DHCn1OapPWNNvZc5vtdurTBg6CAybB6O3zY68/7tRaSZJUtkLs5g8yIYT2U2Mj9Gjzzn8A+8QYuzt2pLPfdRYwAXgf2DXGOL0HzxwI3EgSDreLMb6SGx8GPECynvRbMcZz0niuM3V1dbGxsbHH/56qLKPHT+777lMdpNU9VQVY+BFcuTestTns+SsYUIzVD5IkSekIIUyPMdZ1+t1SAmfb5j8BuAe4G/hVF7c3AzNjjP/qQ4F7A7fnLhuB57q49cUYY0OHZ88HTgEWAPcCi0g2LVoJuA04sLNjWfr6XEcGTkF6GwIZOvWJhXOhZoVkqq0kSVIJ63Pg7PCSqcDkjoEvDSGEY4DLe3DrQzHGHTt5/jDgNGBTYCDwInAZcEGMscsNjPr6XHsGTrVn8FRRxQjvvwarjsq6EkmSpE+kEjjVOQOnOkpzXabBU59obYU/fxeeuRGOvgPW+kLWFUmSJAHdB04XBkkpS2tTIfDsTrVzzwRonAQLP4Sr94N3Xsi6IkmSpKXqssMZQvif3I8XxBj/0+66R2KMPy20uHJgh1NL4zRbpWLWs3BFPSx4P7muXQOO/Qusvk62dUmSpKrXpym1uR1qI7BRjPGldtdL/X1AjDEO7GvB5cTAqZ5IK3QOqa2hccLYVN6lMjRzOly5DzR/lFyvNAK+9hdY5XPZ1iVJkqpaXwPnRJKA+ZsY43vtrnskxvjDvhRbbgyc6g27nSrYa3+Fq/eHxfOT69XWTjqdK66ZbV2SJKlquWlQERk41RcGTxXk1fvhukOgpTm5HrohHPNnWGH1bOuSJElVyU2DpBLjpkIqyDo7w0FXQsitXHj3Rbh6X5j/frZ1SZIkdWDglDKS1m62o8ZPNnhWow33hP0vJlk2D8z6B9xyQqYlSZIkddTjwBlCOCWE0BxC6PJPyCGEvXL3HJ9OeVLla2qoZ0htTcHvMXhWoU0PhL1/n/y8/Oqwc1UsnZckSWWkx2s4QwhTgE2BtWKMrV3cMxCYCfw9xrhHalWWMNdwKk2u7VSfPHkVfPaLMHSDrCuRJElVKJVNg0IIbwAvxhi7PZMhF0w3iDFWxT79Bk4Vg8FTkiRJ5SKtTYOGAm/34L53gGG9eK+kDtxUSAV76x9w++nQsijrSiRJUhUb1It7PwA+24P7hgNz+1aOpDZtobPQ0Nj2vN3OKvLvp+CqfWHB+9A8F/a/FAb25r/uJUmS0tGbDudTwNYhhHW6uiH33ZeAvxdamKSEmwqp116cnIRNgOduhdtOhtaWbGuSJElVqTeB8wpgMHBbCGG9jl+GENYFbgMG5u6VlJLGCWOdZque2+lM2Oqk/PUzNybTa1s73e9NkiSpaHqzaVAA7gD2BBYDjwAv5r7eANiOZIruXTHGPdMvtTS5aZCy4KZCWqoYYfK3ofGy/NiYo2Cvc2CARzBLkqT0pLJLbe5FNcBvgBNYcv3nYuAS4NsxxoV9rLXsGDiVldHjJ9Pz/+/t2pDaGhondLv5tMpVayvc+c3k2JQ2dcdB/a8hhOzqkiRJFSW1wNnuhWsCuwAjc0OvAffFGGf1ucoyZeBU1ux2qlutrXD7afD0dfmxrU6Cr/zc0ClJklKReuBUnoFTpcLgqS61tsCtJ8MzN+THtjkddpto6JQkSQVL6xxOSSXMTYXUpQEDYd8LYJP982OL5ifrPCVJkoqo1x3OEMIGwDeAHUnO3ASYCTwAnBtjfLGLRyuSHU6VIrud6lTLIrjpa7DSWrBHg91NSZKUijQ3DToGuACoATr7k0ozcFKM8co+1FmWDJwqVWltKmTorDAti5OOp2FTkiSlJJUptSGELUl2oa0BbgX2AjYCNgbqgZtJzum8JHevpAzNaKhPJSyOGj/ZabaVZOCgJcNmawu8cGc29UiSpIrWm3M4bwAOAI6IMf6hi3u+ClwL3BhjPCS1KkuYHU6VC6fZqlOtLbldbP8AO3wfdvyB3U9JktQraW0atC0wvauwCZD7bhqwfe9KlFRsbiqkTj1xcRI2AR76OTzwUzcTkiRJqelN4FwdeKkH970MrNa3ciQVU5PTbNXRFsfCumPz1w//Au6faOiUJEmp6E3g/A+wTg/uWzt3r6QS1dRQ3+muX71l6KwAg5eFQ6+F9XbLj039Fdx/lqFTkiQVrDeB86/AViGEfbq6IYQwDtgaeLTQwiQVl5sK6RODloFDroH1ds+PTf013Pd/hk5JklSQ3mwatC3wENACXANcCcwAIklX8yjgCGAgsEOMsSpCp5sGqVKkERoDSZBVmVq8EG44Cl66Kz/25W/Crv/nRkKSJKlLqWwaFGN8BPgWyZ8pjwbuJwmcTbmfj82971vVEjalSpJGtzPiNNuyNmgZOPgqWP8r+bFHz4Ep/2unU5Ik9UmPO5yfPBDC5iTBc3tgLZIAOpOk+3lOjPGptIssZXY4VYk8QqXKLW6GG4+Bf+b+72CFYXDyI7DiGpmWJUmSSlN3Hc5eB059moFTlcrQWeUWN8NNx8Ibj8PRd8KwDbOuSJIklSgDZxEZOFXpDJ5VbHEzfDgTVhuddSWSJKmEGTiLyMCpapFG8BxSW0PjhLFLv1Glbc6rsNrabiQkSZKAPgbOEMLFBfzOGGM8qYDny4aBU9XEbqd4czpctQ9seiDUnw0DenO6liRJqkR9DZytBfzOGGMcWMDzZcPAqWpk8KxSc16FS3aCBR8k1184HPb+PQyoiv+6lyRJXegucA7q5rkTilSPpDLX1FCfSugcNX6yobOcrDIS1t8D/nF9cv33a5OzO/e7CAZ29z8nkiSpWrmGs0B2OFXt7HZWmdYWuOOb8NTV+bGNxsEBl8GgmuzqkiRJmemuw+niG0kFaWqoZ0ht4UEjreCqIhswEMb9DrY8Pj/2wh1w/RGwaEF2dUmSpJLUpw5nCKEWqAOGAq/HGB9Pu7ByYYdTyrPbWUVihLvPhL+dlx9bZ2c45FqoWT67uiRJUr9LrcMZQlgxt3vtbOA+4I/ASe2+PyWE8HoIYatCCpZUnpoa6lMJi6PGT2a0Hc/SFgLs/hPY7jv5sVfvh+sOhoVzs6tLkiSVlB4HzhDC8sCDwPHAh8AUoOMhbPcAI4D9UqpPUhlKI3RGnGZb8kKAXf4XdjozP9Y0FZ65IbuaJElSSelNh/M7wObAH4DRMcY9Ot4QY3wVeBnYOZ3yJJWrNLudBs8St8N/w67/l/y8zemwxbHZ1iNJkkpGbwLnwcBbwHExxnnd3PcaMLygqiRVjKaG+iWmQvSFobPEbfstOPoO2G1i0vmUJEmid4FzHeCJGOPStiGcDQzpe0mSKs0Mu53VYfT2S4bNlkUwb3Y29UiSpMz1JnAuApbpwX0jAHeMkLSENKfZqgy0LIabj4dJu8H7b2RdjSRJykBvAudLwOYhhC5DZwhhFWAz4NlCC5NUuex2Vok7vgnP3wbvvQqXfwXmvJp1RZIkqZ/1JnDeDKwB/LSbeyYCtcCNhRQlqfJ5hEoV2GAPGDA4+fmDN+CyPeDt57KtSZIk9aveBM7fA/8EvhVCeCiE8I3c+MgQwgkhhHuAU4DngEtTrlNShfIIlQq20Tg47I8waLnket47cPme8GZjtnVJkqR+E2KMPb85hM+SdDrrSP6MF3Kf5H7+O7BPjLFqFuvU1dXFxkb/8CSlIa3QmEaIVYpeewyuOxgWfphc19TCV/8Io7fLti5JkpSKEML0GGNdZ9/1psNJjPGNGONWwN7ARcA9wP3AlcAhQF01hU1J6fIIlQo1cpvkyJTlVkuum+fCNQfAP+/Kti5JklR0vepwakl2OKXisNtZgd55Ea7eFz56K7keMAj2vxg+f0C2dUmSpIL0qcMZQrgphPCVEDzBW1L/8wiVCjRsQzj2L7DKyOS6dTHc92NYtLTjnSVJUrnqbkrt/sCdwBshhJ+EENbrp5ok6RMeoVJhVhsNX7sLhmwAtWvCkbfC4GWzrkqSJBVJl1NqQwjnkazLXI38xkCPAJcBN8YYP+6XCkucU2ql/pNGaAzADKfZZm/eHPh4NgzdIOtKJElSgfo0pTbGeBqwFknovAdoBbYjCZyzQgiXhBC+VIR6JalTHqFSQVZYvfOw+c6L4N4CkiRVjB5vGhRCWAs4GjgKaPtTQgReIgmhV8cYZxWjyFJmh1PKhpsKVaCmR5Pda//rINjrtzBgYNYVSZKkHkjlWJQY479jjD+LMW4EfBmYBHxEEj4bgNdDCLeHEPYJIfinBElF1dRQz5DamoLfY7ezRMx+Ga47BBbPhyevgpu+BosXZl2VJEkqUEHHooQQlgMOBI4Bdmz31bsxxjULqqxM2OGUsme3swK0LIY/fR2evi4/tvZOcMg1sExtdnVJkqSl6q7Dmdo5nCGEscA1wFAgxhirostp4JRKRxrBc0htDY0TxqZQjXqttRXu/gE8fmF+bPgWcNiNyZpPSZJUklKZUtvFi2tDCMeFEKYCd5GETYA3CnmvJPVFGh3K2XObnWablQEDYI8G2OnM/NjM6XD5HvDBm9nVJUmS+qxPHc4Qwk7AsSRndS5HctLAQuBPJBsI3RPTap2WODucUmnyCJUyN+1SmPxdPjmVa6URyZmdQ9fPtCxJkrSkVDqcIYTRIYQfhRBmAPcCRwDLA08D3wTWijEeEmO8u1rCpqTS5REqZW7L4+HAy2DA4OT6wzeTTufMJ7OtS5Ik9cqg7r4MISwPHESyKdB2JH/hH4D/ANcBk2KMfy9yjZLUJ22hs9DQ2Pa8mwr1s8/vD8uuDNcfAYs+ho/nwBtPwPAxWVcmSZJ6qMsOZwhhEjCLZIrsDrnhe4GvAp+JMX7dsCmpHDQ11BNSeI/dzgysuwsc9SdYblXY9tuw9clZVyRJknqhyzWcIYTW3I8zgCuAy2OM7trQgWs4pfLiESpl6oOZsNJaENL4qwNJkpSmvq7hvBbYJca4TozxLMOmpErQ1FCfSli029nPVh6+ZNhs/hj+/gdw2wBJkkpWl4EzxnhkjPGB/ixGkvpLWqHT4JmRlkVw07Fw28lw95nJGZ6SJKnkFHQOpySVszS7naMNnv3rb+fDS3flfj4PbjslCaGSJKmkGDglVT2PUClDW50EG43LX//jj/DHw6B5XnY1SZKkJXS5aZB6xk2DpMripkJlpLUF7vwWPHlVfmz4FnDYjbDC6tnVJUlSlenrpkGSVHU8QqWMDBgI434H230nPzZzOly2G/ynKbOyJElSnh3OAtnhlCqX3c4y8sQl8OfvkUxuBmrXgMNvhM9slmlZkiRVAzucktQHHqFSRrY6AQ6+EgYuk1zPfRsur4fXH8+2LkmSqpyBU5KWwiNUysTG+8CRt8IyKyfXK64JQ9bLtiZJkqqcU2oL5JRaqbqkERoDMMNptsXz9vNw+2lJx3OVz2VdjSRJFa8sptSGEDYIIXwzhHBNCOHFEEJrCCGGEA7s5pkrcvd09c+LS/mdh4UQpoYQPgghzA0hNIYQTgshlMx/LpJKi0eolIE1NoYT7jdsSpJUAgZlXUA7pwDf7OOzjwKvdDL+VlcPhBDOA04FFgD3AYuAXYBzgV1CCAfFGFv6WI+kCtYWOgsNjW3Pu6lQEYRO9hp+9hZ46S7Y+1wYVNP/NUmSVIVKKXA+C/wSaASmA5OAHXr47KUxxit6+otCCAeQhM1ZwPYxxpdz42sADwD7AacD5/T0nZKqT1NDPaPHT6bQhQmjxk82dBbbjIfh1pOgpTnZUOjgq2HZlbKuSpKkilcyU0djjJfGGP87xnhDjPHVIv+6H+Q+v98WNnM1vE3SaQUY79RaSUszI8WdbJ1mW0Qv35OETYB/PQhX1MNHb2dakiRJ1aDqAlUIYQSwBdAM3Njx+xjjQ8BMYE1g6/6tTlK58giVEjf2LNhpQv561j9g0liY3dlqDEmSlJZKCZw7hRDODiFcHEI4K4Swezfdyc1zn8/FGOd3cc+0DvdKUo/Y7SxRIcAO34O9fw9hYDL2/mtJ6PSsTkmSiqaU1nAW4qhOxp4PIRwaY3ymw/jo3Odr3bzv9Q73SlKPpbmpkEeopGzMUbDCMLjxGFg8H+a/B1eOg/0vhk32zbo6SZIqTrl3OP8OfAPYBKgF1gL2Ap4GNgbuDSEM7/BMbe5zXjfvnZv7XLGzL0MIJ+aOUGl89913+1q7pArnESolaoM94JjJsPyQ5LplYRJA/3oueDa1JEmpKuvAGWP8bYzx9zHG52OM82KMb8UYJwNbAX8DhpHfIKhN2175ff5TRYzx4hhjXYyxbujQoX19jaQqkObaToNnikZsAcffC6uvmxuIMOWH8M4LmZYlSVKlKevA2ZUYYzPws9zlnh2+/ij3WUvX2r77qJt7JKnHmhrq6eRkyF4zdKZotdFw3BT43DbJ9Z6/gjU2zrYmSZIqTKWs4ezMi7nPjlNqm3KfI7t59rMd7pWkgs1IcW0npDNlt+otvxoceRu8eCdsemDW1UiSVHEqssOZs3ruc26H8adyn5uEEJbr4tktO9wrSanxCJUSM3jZzsPmR2/D7JeXHJckST1WyYHz4NzntPaDMcY3gCeBGuCgjg+FEHYARgCzgMeKXKOkKubazhK2cC5cd3BybMpr/k+BJEl9VbaBM4TwhRDCXiG0Haj2yfigEMK3SXavBfhNJ4+3re/8eQihbccIQgjDgPNzlw0xxta065ak9txUqET96XR46+8w/z9w1T7w7C1ZVyRJUlkKsUS2gA8hjCEf9iA51mRF4GXgvbbBGOPWufv3BW7NffcS8Gbu/k1JjkdpBX4QY/xFF7/vfOAUYAFwL7AI2AVYCbgNODDG2LK0uuvq6mJjY2Nv/lUlqVNpBUbXdqZg5pNJh3Neu6Ovxp4FX/o6hDS2f5IkqXKEEKbHGOs6/a6EAueOwANLuy/GGHL3jwa+SXIEykiSNZuRJHhOBc6LMU5fyu88DDiNJKQOJNlo6DLggp52Nw2cktJm8CwR/2mCaw6EOe3WcW55Anzl5zBgYJePSZJUbcoicJYrA6ekYqibOIXZc5sLfo+hs0Afvwd/PBxe/2t+bP2vwAGXwjLdna4lSVL1MHAWkYFTUjHZ7SwBixbA7afCszfnx9bcFL56Pazc8eQtSZKqj4GziAyckvpDGsEzkD8LVL3U2gr3/QgePSc/tuJn4Ng/w2prZ1aWJEmloLvAWba71EpSNUmjQxnx7M4+GzAAxv4Yxp0DAwYlY6utAyuNyLYuSZJKnB3OAtnhlNTfnGabsVcfgPt+DEfcDMuvlnU1kiRlzg6nJFWQtIKi3c4+WmcnOOH+JcNmjNCyOJuaJEkqUQZOSSpDTQ31qQTPUeMnGzz7orOzOB85G647CBZ80P/1SJJUogycklTGmhrqGVJbU/B7Ro2fTN3EKSlUVKWeuzWZZvvq/TBpd/jPa1lXJElSSTBwSlKZa5wwNpVu5+y5zXY7+2rOK/mf330BLt0F3piWXT2SJJUINw0qkJsGSSo1HqGSkaevhz+dDi3NyfWgZWHfC+Dz+2dblyRJReamQZJURTxCJSObHQJH3Q7L5TYTWrwAbjoWHv5VsqGQJElVyA5ngexwSiplHqGSgTmvwnUHf3qa7WaHJWd4Dip8va0kSaXGDqckVammhno62U+11+x29sLq68Dx98Ko7fJjT18HV+0D82ZnV5ckSRkwcEpShZvhESr9b7lV4YhbYPMj8mNvPQ1z386uJkmSMuCU2gI5pVZSuXFToX4UIzz6W7jvLDjkGthwz6wrkiQpdU6plSR9wk2F+lEIsO0Z8PVGw6YkqSoZOCWpCjU5zbZ/rbb2kmNvPweTvwOLF/Z/PZIk9RMDpyRVsbR2nzV09tLcd+G6Q2HapclmQnPfzboiSZKKwsApSVXObmcGnr4OPng9+fn1x+CSnZOOpyRJFcZNgwrkpkGSKk0aoXFIbQ2NE8amUE2FihEeOxfu+SHJiligphb2v8S1npKksuOmQZKkHkuj2zl7brPdzu6EAF/6Ohx2PdSsmIw1z4U/HgZTz04CqSTjxKv8AAAgAElEQVRJFcAOZ4HscEqqZGmFxrTWilakd16A6w6B91/Lj/3XoTDuHBi8bHZ1SZLUQ3Y4JUl94qZC/WDYRnDCAzDyy/mxf/wRrtwLPno7u7okSUqBgVOS1C03FeoHK6wOR94GY47Kj705DZ65IbuaJElKgYFTktQjTQ31DKmtKfg9o8ZPZrTBc0mDamDc72CPBggDYJP9YJvTs65KkqSCuIazQK7hlFSNXNtZZE2PwFpjoGb5rCuRJGmpXMMpSUqV02yLbNS2S4bNxc1w349hwQfZ1CRJUh8YOCVJfeamQv3oru/D1F/DJTvDuy9lXY0kST3ilNoCOaVWkhJOsy2iN6fDpTvnr5dZCQ64FNbfPbuaJEnKcUqtJKnomhrqCSm8x02FOjFiCzhgEgxaLrle+GFydufDvwL/4liSVMIMnJKk1MxIaW1nxGm2S9j0QDjublj5s7mBCPefBTcdC83zMi1NkqSuOKW2QE6plaSuOc22CObNhhuOgtcezY+tsSkcei2sOjK7uiRJVcsptZKkTLipUBGsMASOuh22PCE/9vYzcPGOMGNqZmVJktQZO5wFssMpST1jt7MIpl8Jk78DrYuS6+F1cPy9ENJYTStJUs/Y4ZQkZa6poZ4htTUFv8ezO9vZ4mg4ZjKsMAyWHwIHXWHYlCSVFDucBbLDKUm9Z7czZR/MhI9mJbvZSpLUz7rrcBo4C2TglKS+M3gW2fQrYfV1YdSXs65EklTBnFIrSSpJaW4qVDdxSirvqhhNj8CdZ8BVe8PfLvS8TklSJgyckqRMNaV0dufsuc2u7WzT2gp//h7EFmhdDHd9H245EZo/zroySVKVMXBKkkqCmwqlaMAAOPwmGN5uTeczN8Ck3eC9GdnVJUmqOgZOSVLJaJww1rM707LycDj2LzDmqPxY23mdL9+bWVmSpOripkEFctMgSSoeNxVKyfQrkim2Lc25gQA7nwnbfifphkqSVAA3DZIklaU0u52jq7njucUxSbdzxbVyAxHunwjXHwELPsiyMklShTNwSpJKWlqbCkWqfJrtiDo46SEYuW1+7JUpMOfV7GqSJFU8A6ckqSykFTyrelOh2mFw1G2w9WnJ9Z6/guFjsq1JklTRDJySpLLipkIFGjgY9vgpHH8/bHF01tVIkiqcgVOSVHbsdqZgxBZLjs15FW44GubN6f96JEkVycApSSpbTQ31hBTeU9XBs03zPLj+SHj+Nrhoe3hzetYVSZIqgIFTklTWZqTU7YQqnmYL8PIUeOe55OcP34TLdocnLgGPT5MkFcBzOAvkOZySVFo8u7MAL90Nt5wIC97Pj216EOz1W1imNru6JEklzXM4JUlVw2m2BVh/9+TolM9slh975ka4dBd496Xs6pIklS0DpySp4jjNtgCrjoKv3QNj2u1g++6LcMlO8OwtmZUlSSpPTqktkFNqJan0Oc22j566FiZ/GxYvyI9tfSrs/lMIafSRJUmVwCm1kqSqlma3s27ilFTeVRY2PxyOvxdWHZ0fGzjYsClJ6jE7nAWywylJ5cVuZx/Mfx9uPy35POp2GDgo64okSSWkuw6ngbNABk5JKj91E6cwe25zKu+qmuAZIzTPhWVW/PT4wrkweHkY4KQpSapWBs4iMnBKUvlKq9s5pLaGxgljU3lXWWlthesOgjAQ9r8Ills164okSRlwDackSZ1oSmk329lzm6tvN1uAh38Jr9wLL98NF+0A//571hVJkkqMgVOSVPU8u7OPFs3L//z+azBpLEy7NJl+K0kSBk5JkgDP7uyTsT+Gg6+Gmty6zpZmmPwduOlrsODDbGuTJJUE13AWyDWcklSZ3M22F+a8CjccDW8/kx9bbR04+EpYc9Ps6pIk9QvXcEqS1EtpdjsrvuO5+jpw/BTY4tj82HuvwiW7QOPlTrGVpCpm4JQkqQtpbSoEVTDNdvByMO63cMAkqKlNxloWwp3fgsZJ2dYmScqMU2oL5JRaSaoeTrPtodkvw43HwNvPwurrwokPLnl+pySpYjilVpKkFDjNtoeGrAfH3wtbHg8HXWnYlKQqZuCUJKkXnGbbQ4OXg/pfw5qfX/K7p66BhXP7vyZJUr8zcEqS1AdpBc+K73Z29PT1cPtpcMlO8PbzWVcjSSoyA6ckSQVwmm0vfDQL7jwj+Xn2S3DJzkm3U5JUsQyckiQVyGm2PbTimsk028HLJ9eL5yfdzltPgeZ52dYmSSoKd6ktkLvUSpI6cjfbpXjnRbjxaHj3xfzYkA3goMthjU2yq0uS1CfuUitJUj9ymu1SDNsQTrgfNjssPzb7n8kU28bLwL8Ml6SKYeCUJKkInGa7FDUrwH4XwD7ntZtiuyBZ43nDUTD//WzrkySlwsApSVIRNTXUM6S2puD3VGy3c/Mj4MQHYVi7qbSv/TUJn5KksucazgK5hlOS1FNpBsaKW9+5aD7cfSY0ToLDb4b1ds26IklSD3W3htPAWSADpySpt9xUqBtvPw9rbLzk+KL5MHi5/q9HkrRUbhokSVIJSWt9Z0VOs+0sbM54GM75ArxyX//XI0kqSMkEzhDCBiGEb4YQrgkhvBhCaA0hxBDCgT149rAQwtQQwgchhLkhhMYQwmkhhG7//fr6nCRJaXA32x6YNxtuORHmzoJr9ocp/w9aFmVdlSSph0opWJ0C/BY4HNgACD15KIRwHnAtUAdMBaYA6wPnAjeFEAam+ZwkSWlKezfbuolTUnlXyXj/dYit+etHfwuXfwX+05RZSZKkniulwPks8EvgEGBd4KGlPRBCOAA4FZgF/FeMca8Y437AesALwH7A6Wk9J0lSsaQVPGfPba6sbufwMXDyo7DOLvmxN6fBhdvDc7dmV5ckqUdKdtOgEMKDwA7AQTHGm7q4pxHYAjg6xnhVh+92AB4kCZXDY8z/9Whfn+uMmwZJktLmbradaG2Fx34P9/0YWhfnx7c4Fvb4mRsKSVKGynKX2qUFzhDCCOANoBlYJcY4v5N73gSGA1+OMf61kOe6YuCUJBVLWsEzADMqJXi+2Qg3HZtMtW0zdCM48LLONxySJBVdpe5Su3nu87nOQmPOtA73FvKcJEn9Kq1ptpF0u6aZGlEHJz8Cm+yXH3v3BbiiHhbOza4uSVKnyjlwjs59vtbNPW1//Tm63Vhfn5MkKRPuZtvBsivDgZfDuN/BoNxU2l3/HyxTm21dkqQlDMq6gAK0/a/KvG7uafurzhVTeE6SpMy0hc40AmPbO8p6fWcIsMXR8Lmt4ek/wJijs65IktSJcu5wth2b0ttFqH19Lv+CEE7MndnZ+O677/b1NZIk9Vrax6iUvaEbwK4/SgJoe28/D/dMgMULs6hKkpRTzoHzo9xnd/Nn2r77qN1YX5/7RIzx4hhjXYyxbujQoUstVJKktDnNthuL5sPNx8Fffw+X7ALvvJh1RZJUtco5cDblPkd2c89nO9xbyHOSJJWUtLudFRM8n/4DvPN88vPbz8DFO8C0SVCiO/NLUiUr58D5VO5zkxBCV4dvbdnh3kKekySpJKUdPOsmTknlXZnZ4ljY81cwcJnkevECmPxt+OPhMG9OtrVJUpUp28AZY3wDeBKoAQ7q+H0IYQdgBDALeKzQ5yRJKnVNDfWEpd+2VLPnNpd3tzME2OoEOPFBGNbubM5/ToYLvgT/ejCjwiSp+pRt4Mz5We7z5yGEddsGQwjDgPNzlw0xxtaUnpMkqaTNcJpt3hobwwkPwBdPzo/NnQVX7Qv3/BAWN2dXmyRViRBLZD1DCGEM+bAHsDHJsSQvA++1DcYYt+7w3PnAKcAC4F5gEbALsBJwG3BgjLGlk9/Xp+c6qquri42NjT3+95QkqT+lGRjL+hiVl+6B206Bj2fnx9YaA8fdAwMHZ1eXJFWAEML0GGNdZ9+VUodzJeCL7f5pOwNzvQ7jnxJjPBU4nGSa7A7A7sArwOnAAV2Fxr4+J0lSOWlqqGdIbU0q7yrrbuf6u8Epf4V1d82PrTfWsClJRVYyHc5yZYdTklQu7HYCra3w+IXwzz/DkbfBwEFZVyRJZa+7DqeBs0AGTklSuTF4kgTPAR0men3wJrz9fNINlST1WLlMqZUkSf0g7WNURpfjVNuOYbO1FW49Ga47CO48A5rnZVOXJFUYA6ckSVUqrdAZKfP1nQCNk6Bpau7ny+DC7eDN6dnWJEkVwMApSVIVS7vbWbbB8/MHwEZ756/fexUmjYUHG6BlcXZ1SVKZcw1ngVzDKUmqJFW9vjNGePoP8Of/huaP8uPD62D/i2H1dbKrTZJKmGs4JUlSj6R9jErdxCmpvKtfhABfOAxOeQQ+t01+fGYjXLgtNF6ehFJJUo/Z4SyQHU5JUqWq6m5naws8eg488FNoXZQfX/8rcMjVnt8pSe3Y4ZQkSb1W1es7BwyE7b4NJ9wHQzbIj9cONWxKUi/Y4SyQHU5JUrWo2o7novlw74/g5XvgpKmwTG3WFUlSSemuw2ngLJCBU5JUTUaPn0xaf3IYUltD44SxKb2tHyycu2TYnP8+zHkVRmyRTU2SVAKcUitJklIxI8VptrPnNpfXNNvOOpt/+W+YtCvcdxYsbu7/miSpxNnhLJAdTklSNavaabYAz94CNx2bv15zU9jvIlhjk+xqkqQM2OGUJElFUdUbCw3fAkZum7+e9QxctANMPTvZ5VaSZOCUJEmFS7M7WTbnd646Eo6+A3b/GQxaNhlrXQT3/R9ctnuytlOSqpyBU5IkpSLNbmfZrO8cMAC2OTXZvXatMfnxN6fBBV+Gxy+G1tbs6pOkjLmGs0Cu4ZQkqXNVt76zZTE88ht4qAFaF+fHR+8Ah14Ly6yYXW2SVESu4ZQkSf2u6tZ3DhwEO3wPTrgfhm2cHx+0LNR4dqek6mTglCRJRZX2+s7RpR48P7MZnPggfPlbsPwQ2Pt3EELWVUlSJpxSWyCn1EqS1HNVN812wQew7MqfHlu8EP71IKy/eyYlSVLanFIrSZJKQtVNs+0YNgEe+AlcdzDcfDzM/0//1yRJ/cgOZ4HscEqS1HdV1/F8/fHkyBRyf/5a8TOw9+9hvbGZliVJhbDDKUmSSlLa6ztLvuM5dAPY7Kv564/egmsPhNtPT6bfSlKFMXBKkqRMpTnNFtLtmqZuuVVgvwvgkGthhaH58aeuhvO3gVfuza42SSoCp9QWyCm1kiSlq2qm2c6bDXeeAS/86dPjY46C3SZ2vv5TkkpQd1NqDZwFMnBKklQcVRM8n70F/vxd+HhOfmyl4XD0HbD6OtnVJUk95BpOSZJUdpoa6knr9MqSXt/5+f3h1Mdh433yY7XDYJWR2dUkSSmxw1kgO5ySJBVfmmExADNKteP53K1w1//AkbfAsI2yrkaSesQOpyRJKmtpbiwUKeGNhTbZD7759JJhs7UVHvmNO9lKKjsGTkmSVDbSDJ4lO812UM2SY09cDPf+KNnJ9mV3spVUPgyckiSp7DQ11DOktpNg1gclGzzbfDQrCZsAH86Eaw+A20+z2ympLLiGs0Cu4ZQkKVtph8WS3NH2uVth8neW3Ml23Dmw3tjs6pIkPBalqAyckiSVhorfWGje7CR0Pn/bp8c3PwJ2+wkst0o2dUmqem4aJEmSKl7Fbyy0whA4+Eo46ApYfkh+/KlrkrWd/7wrs9IkqSt2OAtkh1OSpNKUZmAsuWm282bDn7+bTLVtb7+LYLNDs6lJUtWywylJkqpORW8stMKQpNN50JWwwtBkbJXPwUbjMi1Lkjqyw1kgO5ySJJW+it5Y6OP34K7xsNlXYZ2dsq5GUhVy06AiMnBKklQ+Kjp4dub202FEHYw5GkLIuhpJFcrAWUQGTkmSyk/F72gL8Pyf4IYjk59HbQd7/w5WWzvbmiRVJNdwSpIktVPxO9oCPH5h/uemqXD+l+Cx86C1JbuaJFUdO5wFssMpSVL5q8gdbRfNhwd/Bn/9PcTW/PjwOtjnXBi2UXa1SaoodjglSZK60dRQT1orHEtmR9vBy8HYH8Px98Ean8+Pz2yEC7eDh34Bi5uzq09SVbDDWSA7nJIkVZaK3FhocTM8eg48/AtoaRcyh22SdDuHj8muNkllz02DisjAKUlSZarI4PnOi/Cn0+HNafmxjfeFg6/MriZJZc/AWUQGTkmSKlvF7Wjb2gJPXAz3/RgGDobTpsGKa2Rbk6SyZuAsIgOnJEnVoeI2FnpvBrz3Kqy766fHF85Npt0uv1o2dUkqO24aJEmSVKCmhnqG1Nak8q6S2FhotdFLhk2AB34C524Jz9wENiYkFcgOZ4HscEqSVH0qcn0nwMzpcOmu+WNU1h0L9b+GVUdmW5ekkmaHU5IkKUVNDfWphsSS6HgCNM+DFT+Tv35lCpy/NTx2HrQszq4uSWXLDmeB7HBKkqSK6ngu/AjuOyvZWIh2f078zBdg79/BZzbLrDRJpclNg4rIwClJktpUVPB8Yxrc8Q145/n8WBgI25wGO/4AapbPrjZJJcXAWUQGTkmS1FHFHKXSsggePQce+gW0LMyPrzISjpkMq3w2m7oklRTXcEqSJPWjNNd4RpIAWzdxSirv65WBg2H778Kpj8Go7fLjtWvASsP7vx5JZcfAKUmSVCRNDfWElN41e25zdhsLrb4OHH0H7HMerDAMxp0DA/xjpKSlc0ptgZxSK0mSeqJi1ncuWgCDl/30WGsL3P0/8MWTYLW1s6lLUmacUitJkpSxijlKpWPYBHj8Inj8Qjj/SzD17GTtpyRhh7NgdjglSVJfVEzHc8GH8JtNYOGH+bGhG8Fev4GR22RTk6R+5S61RWTglCRJhaiI4DnzyeQIlVnPfHp88yNh7I9h+dX6vyZJ/cbAWUQGTkmSlIayD54ti+GJi+D+n8Ciefnx5VeH3X4Cmx0KIa0tlCSVEgNnERk4JUlSmso+eH7wJvzl+/DinZ8eH7Ud1J8NQ9fv33okFZ2bBkmSJJWJst9caOURcOi1cOgfYKUR+fGmqfD0H/qvDkklwcApSZJUgtI8wxOS4Fk3cUqKb1yKDfeE0x6HL30dwkBYZSRs/73++/2SSoJTagvklFpJklRsaXcoh9TW0DhhbKrv7NasZ2Dh3CV3rf3wLQgDYMU1+q8WSalzSq0kSVIZS3ua7ey5zf07zXbNTTs/ImXyt+HcLWHapdDa2n/1SOo3djgLZIdTkiT1t7LfWAjghTvh+sPz18PrkrM7P/Nf/V+LpILY4ZQkSaogZb+xEMByq8Bqa+evZzbCxTvC3Wcm028lVQQ7nAWywylJkrJWth3PRQvgkbPhkd9AS3N+fKXhsMfPYKO9PbtTKgOew1lEBk5JklQqyjZ4zn4Z7jwjOTqlvXV2gT1/Cauv0z91SOoTA2cRGTglSVKpKcvgGSP84/pkSu3Hs/PjA5eBrzfCKp8rfg2S+sQ1nJIkSVWkLNd4hgCbHZqEyy2Ph7ZTSDcaZ9iUypgdzgLZ4ZQkSaWuLDue/34K7v0R7HshrPSZT3/XsggGDi5+DZJ6xA6nJElSFWtqqGdIbU1q7+uXjudam8NRty8ZNhd8mJzd+fAvYfHC4tYgqWB2OAtkh1OSJJWTYgTFfj3H864fwN/OT35efd1kU6F1du6/3y9pCXY4JUmSBKS/vhP68RzPlkXw+mP56zmvwNX7wQ1Hwwczi//7JfWaHc4C2eGUJEnlrOw6ni2LoXES3D8RFn6YHx+8Auz4fdj6VNd3Sv3MY1GKyMApSZIqQdkFz4/ehik/TI5SaW/ohlD/axi1bfF+t6RPqegptSGEK0IIsZt/Xuzm2cNCCFNDCB+EEOaGEBpDCKeFEMr+PxdJkqTeKLuptiuuAftfDMdMhqEb5cfffRGuqIc//3dxfq+kXhmUdQEpehR4pZPxtzq7OYRwHnAqsAC4D1gE7AKcC+wSQjgoxthSpFolSZJKUlvoTDMotr2rKB3PUdvCyVPhbxfAgw2waF4yvsbG6f8uSb1W9lNqQwhXAEcDx8YYr+jhMwcANwGzgO1jjC/nxtcAHgA2Ar4VYzxnae9ySq0kSapkZTXV9oOZcM+Z8P4bcNwUGOCkNak/VPSU2j76Qe7z+21hEyDG+DZwSu5yvFNrJUlStSurqbYrD4eDroCj/7Rk2Hz98WQ32/ffSP/3SupS1QWqEMIIYAugGbix4/cxxoeAmcCawNb9W50kSVJpKqvgWbPCp69bW/5/e3cepkdV5238/nV3CAlhD8i+yCagApIg+xYBNTiIigsOEBEZxUGUQYmKOghKhhEQERAcNTqK4yvIoggCQUDWIWwDBFAwzSYBwpoEsnXO+0dV0wvdT3qp6me7P9dVV9G1njopup/vc06dgj+eALMugx9OhJv+E5YsLP68kt6kkQLnPhFxZkRcGBGnRMQB/bRQ7pDPH0wpvd7Pse7sta0kSZKos+DZafZNMOf/sv9e+nr2SpXz3g2PXF3eOSUBjTVo0OF9LJsVER9PKd3fbdmm+fzxCsd6ote2kiRJ6qauBhfabB/41FXZyLXP5h8LX2qHX38Mttgf3jsN1tys2HNKAhqjhfNe4AvAtsA4YD3gQOA+YBvguohYv9v24/L5ggrHnJ/PVy62qJIkSY2lblo8N94Vjr4B3v89WHG1ruV/uwbO2xmuOxkWze9vb0lDVPeBM6X0/ZTSOSmlWSmlBSmlZ1JKVwI7AbcDa9M1SBBAdO461HNGxNH5OztnPv/880MvvCRJUoOoi+DZ2gY7fQaOvRt2nMIbHws7FsPNZ2bPd87+S3Hnk1T/gbM/KaXFwGn5j+/vtmpePh9H/zrXzetrZUrpwpTShJTShLXWWmt4BZUkSWogdRE8V1oTPnA2HP1n2GBi1/IFz8PK6xR3HkmNGzhzD+fz7l1q2/P5xhX227DXtpIkSRqEugie6+0AR14DHzwfVlobdjkGxm9R3PElESkNuWdpzYuIXYBbgRdTSmvmyzYkGxRoMbBaXyPVRsSTwAbA7imlWyqdY8KECWnmzJmFl12SJKmRlDEKbaGBduErEK0wulcnuDsuhLbRsMNhb363pyQAIuKulNKEvtY1+v81H83nna85IaX0JHA3sAJwSO8dImIvsrA5B7htBMooSZLU8Gq+xXPFVd8cNl9+Eq79Jvz+C/Bf+8ITdxRzLqmJ1HXgjIjtI+LAiGjttbwtIo4nG70W4Kxeu3Y+2/kfEbF5t/3WBs7Lf5yWUlpWRrklSZKaVc0Hz+5uPit7byfAP+6Bn+4PlxwFrzxd/LmkBlXXXWoj4oPApcCLwF+Bp8heZfIOstejLAO+mlI6vY99zwM+BywErgOWAJOAVYDLgI+klDqWVwa71EqSJA1dTXe1XfxaFjpvORs6FnUtHzUWdv8S7HosjBpTzLmkOlapS229B85NgePIXoGyMbAm2etOngL+ApybUrqrwv6HAp8nC6itZIMM/RQ4f6CtmwZOSZKk4avp4PnS41nX2lmX9Vy+6oaw37dh24Mhou99pSbQsIGzFhg4JUmSilPTwbP9ZrhqKjx7f8/lG+0Kh/zMV6qoaTXzoEGSJEmqIzX9jOcmu8O/3AgHfh/Grtm1fMHzPX+W9AZbOIfJFk5JkqTy1GyL5+svw42nw/9eAJ/4H9hiv+EfU6pTdqktkYFTkiSpfDUbPF95ClbdoOeylODyf4WtPwBbHuDznWp4Bs4SGTglSZJGTs0Gz+4evBR+OyX7780mwXtPg7W2KvYcUg0xcJbIwClJkjTyajZ4pgQ/2qPnwELRCjsdDXufCGNWH/45pBpj4CyRgVOSJKl6ajJ4LpgL158Kd/8cur9pb8wasO/X4V1ToLVteOeQaoiBs0QGTkmSpOqryeA55364+qvQ/peey9feBvY/FTafNLzjSzXCwFkiA6ckSVLtqLngmRI8dAVccxK8/ETPdVu+Dz7+K2hpHV4BpSqrFDhty5ckSVLD6AyHRQbPzmONH7cCM08a5OtPImCbg2CLA+C2H8LNZ8Hi+dm6ldcxbKrh2cI5TLZwSpIk1a4yWjxhGK2e856F60+BWVfAsTNh3No916fka1RUd+xSWyIDpyRJUu2rueD52oswdo2ey+Y/D7/8EOzxb1mrqMFTdcLAWSIDpyRJUv2oueDZ3R+Oh5k/yf57o13ggO/A+jsO/7hSyQycJTJwSpIk1Z9Np15JGZ+Chxw8F82HH2wPC57vufydH4NJ34RVNxh+4aSSGDhLZOCUJEmqXxNOvZa58xcXftwhBc/XX4Kbvgd3XADLlnQtbxsDux4Lux0Ho8cVV0ipIAbOEhk4JUmSGkPNvFLlhcfg2m/Cw3/ouXzcW2Dfb8D2hzq6rWqKgbNEBk5JkqTGUjPBc/Zf4E9fgzn/13P5VpPhExcVUzCpAJUCZ8tIF0aSJEmqZe3TJhczCFA3m0y9cvBBdtM94Ogb4aDzYNw6Xcvf8eFCyyaVyRbOYbKFU5IkqbGV0eIZwOzBhNrFC+CWH8CTt8Nhl/V8ZUpKsPBlGLN64eWUBsIutSUycEqSJDWHmnilSkpvfj/nX6+Bi4+E3b8IOx8DK4wttoDSchg4S2TglCRJai41ETw7dSyFH+0Ozz+U/bzyerDvSbDdxx1YSCPGZzglSZKkgpTxjCcM8TnPec9A6uj28z/g8mPggj3h0RnFFlAaAls4h8kWTkmSpOZW9RbPjqVwzy/gz6fBgud6rttsX9jvFFjn7cUXUMrZpbZEBk5JkiQBbDr1Ssr4ZD3g4LloHtx6TjYtea3bisje3bnP12HV9UsooZqdgbNEBk5JkiT1Vkar5/hxKzDzpP2Wv+Grz8AN34V7fglpWdfy7f8ZPnhu4eWSDJwlMnBKkiSpP1XtbvvcQ3DtN+Fv10DraDj2Llhtw1LKo+Zm4CyRgVOSJEnLU9Xg+fcb4YVHYeKney5//SVovxneduCbX7UiDYKBs0QGTkmSJA1U1QcY6u6ak7LnPTfcGfY/FTacWHzB1BQMnCUycEqSJGmwqh48X2KpIbgAAB2FSURBVHocfjgBOhZ3LdvmIJj0LVhzs1LKpsblezglSZKkGlL1d3mOXhkmHgUto7qWzboczt0Jrvw3mPds4WVTc7KFc5hs4ZQkSdJwTTj1WubOX7z8DYegYrB9cTbM+DY8+Luey0etBLt8HnY9FlZcpZRyqXHYpbZEBk5JkiQVqSrdbZ+aCdd+Cx6/uefysWvC/t+B7T9RSpnUGOxSK0mSJNWJqnS33WACTPkDfPJiWHvbruWvvQDYQKWhs4VzmGzhlCRJUplGvMVzWQfc/1u4/jswehx89mZoaS2lDGoMdqktkYFTkiRJI6Gs4BnA7L7C59JF8OrTsMZbey7/+41w03/CfifD+juWUibVFwNniQyckiRJGkllBU8YwGtVUoIf7wP/uCf7eZuDYN9vwvjNSyuTap+Bs0QGTkmSJFXLiHe3/ce98ON9IXV0LYtW2PEI2OtEWHmdUsqj2mbgLJGBU5IkSdU2osFz7qNw/Skw67Key0eNhZ2Pgd2+ACuuWkp5VJsMnCUycEqSJKlWlBU8x49bgZkn7ddz4VN3wXXfgva/9Fw+Zg3Y8wSYeBS0jS6lPKotBs4SGTglSZJUa0bsOc+U4LEZcO2/w7P399xw4lEw+YzSyqHaYeAskYFTkiRJtWrTqVeW9hbNHsFz2TJ44OKsq+3LT0BLG3z+f2HNzUo6u2qJgbNEBk5JkiTVgxF5znPpIpj5M3htLux7Us8NF74CT98Fb90HIkopi6rDwFkiA6ckSZLqyYi/z7PT9adm7+/cZA+Y9C3YcGIp5dDIM3CWyMApSZKkejSi7/Oc/xycvT0sWdC1bKv3Z62gb9m2tHJoZFQKnC0jXRhJkiRJ1dc+bTLt0yZTRufWTaZe2SvQBrzzkOydnZ0e+SOcvxtc8hl48e8llEK1wBbOYbKFU5IkSY2i9Oc8X3gM/vzdbICh7lra4F2Hw55fgVXWLaUMKo9daktk4JQkSVKjKb277Zz7s2c6/3p1z5VtK8LeX4Xdv1ja+VW8SoGzbaQLI0mSJKm2dbZIlhE8O4/ZPu038MTtMOPb8Pgt2cqlC2HFVQo/p6rHFs5hsoVTkiRJja7U93me9n54bEYWPBe+Cv96J7SO6rlRx5I3L1PNsEttiQyckiRJaibldbdNtH91B1h1/Z6Ln7gdLv407H0ibHcotNpJs9YYOEtk4JQkSVIzGpHXqqQE0yd3dbldc/PsGc9tPwQtvnCjVhg4S2TglCRJUjMrNXh+bQe4YE9Y8HzPFWtvkwXPrT8AUcaLXTQYBs4SGTglSZKkTBnhcywLmdJ6NV8Z9ydY9ErPletuB/t8HbbY3+BZRQbOEhk4JUmSpJ7KCJ6rMJ/PtP2RY8dcC0sW9Fy5wcQseG62T+Hn1fJVCpx2fJYkSZJUqPZpk7uewyzIq4zjjKUf5V3zzuCCpZOhbUzXyqfuhDv/q9DzqRi2cA6TLZySJEnS8hXd6rkWL3FM2xUc2jqD0dEBn7sF3rJtoefQwNjCKUmSJKmqim71fJ7VOXnpEey96Cy+suQoNjmrvecGi+bDJZ+BZ+4r7JwaPFs4h8kWTkmSJGnwyhzdNoDZkx+BGSdnC7b+J9jna7D21qWds5nZwilJkiSppnS2eI4ft0Lhxx7FEl647syuBQ9dAeftAhd/GuY+Wvj51D9bOIfJFk5JkiSpGEW2em4ZT/Kltot5X+udPVdEC2z3CdjrK7D6JoWdr5n5WpQSGTglSZKkYhUZPLeN2RzfdjGTWu/puaKlDXY4DPb8Mqy6fmHna0YGzhIZOCVJkqTyFBU+d4i/cXzbb9mj9YGeK1bdCI67F1paCzlPM/IZTkmSJEl1qajRbe9JW3DYkq/xsUXf4I5lb3tj+Slz92TTr1097OOrb7ZwDpMtnJIkSdLIKabFM7F7ywMc0fonjl1yLAsZ/caa9mmTYeZPYcv3wirrFXCuxmeX2hIZOCVJkqTqKOPVKtvGbK4c/XUWMYrROx0Ju38JVlm38PM0ErvUSpIkSWo4RXW37e6LbZcAMJol8L8XsOiMd8BVJ8KrzxR6nmZh4JQkSZJU14p8p+evOt7Dvcs2e+Pn0bEE7vgRC894B1w1FebNGfY5moldaofJLrWSJElS7Rled9vE3i338cW2i9m+5e891ixMo7ioYxJHnng2rLzO8ArZIHyGs0QGTkmSJKl2DT943ssX2y7pM3jus+hMbpt2+PAK2AAMnCUycEqSJEn1YejhMwueX2q7hO3y4Hljxzs5YsnUHlsV/TxpvTBwlsjAKUmSJNWX4QTPffIWz5OXHM7dacsea3eMR3g8rcPMaYcOv5B1xMBZIgOnJEmSVL+GFj4TED2WjGYxN4w+ntWYzy873sOFSw/keVZrilbPSoGzbaQLI0mSJEm1ojMQDi54xpuWfLT1BtaNFwH4TNsfOaz1Wi7qmMS7p77Is6zRFMGzLwZOSZIkSU2vMxBOOPVa5s5fPOj9Z6d1eWDZJry9pR2AFWMJR7ZdzSdbr+P/dezNrlPn8g/G9zhXM7BL7TDZpVaSJElqTIPvbpvYr+Uujm27lHe2zO6xZnFq5ZKOPTmv4594Mr0FaJzg6TOcJTJwSpIkSY1t06lXMrjUlI1qe1zbpezQ8miPNUtTC59d8iWuW7Zjj+X1HD4NnCUycEqSJEnNY3CtnondWx7gC22/Y6eWRwB4NY1lt0U/YB5j+9yjHoOngbOCiDgU+BzwTqAVeBj4GXB+SmnZ8vY3cEqSJEnNZ3CtnomdWx7i2NZLmZm24qylH+mxdsN4lpVYxMNpox7L6yV8Gjj7ERHnAscAC4EZwBJgErAycClwSEqpo9IxDJySJElScxtMq2cLy1hGS49lZ406l4Nbb+FPHRP4wdKDeTBt2mN9rQdPA2cfIuLDwMXAHGDPlNLf8uVvAf4MbA18MaV0dqXjGDglSZIkwdDe6blJPMOMFU6gNbpy2YyOHThn6cHcmzZ/0/a1GD4NnH2IiJnAjsARKaVf9Fq3F3ADWRhdv1LXWgOnJEmSpN4GGj43jjlMbfs172u9803rbup4Bz9YejAz09vetG78uBWYedJ+wy5nEQycvUTEBsCTwGJgtZTS631s8xSwPrBbSunW/o5l4JQkSZLUn4EGz63iCf617TImt9xBS/TMaLd1bMMPOg7mtmXbAPHG8lpp7awUOFv6WtgEdsjnD/YVNnN39tpWkiRJkgalfdrkN6ZKHkkbceySL7Df4tP5XcfudKSuYLlL6yx+vcJ3+FbbLyocoTY1a+DsfAr38QrbPNFrW0mSJEkass7gGRW2eSytz/FLjmHfxWfwm6V7syS1vrFuxrJ3lV/IgrVVuwBVMi6fL6iwzfx8vnLvFRFxNHA0wEYbbdR7tSRJkiT1a3a31s7+utw+ntbhxKVHc07HwXyu9Qo2b3mam5e9faSKWJhmDZydXyoM6QHWlNKFwIWQPcNZVKEkSZIkNZfOrrYTTr2WufMXv2n9U2ktvr7007SwDCq2jdamZg2c8/L5uArbdK6bV2EbSZIkSRq27iPO9tXq2fvdnfWiWQNnez7fuMI2G/baVpIkSZJK1z6ALrf1olkD5z35fNuIGNPPSLUTe20rSZIkSSOqVl59MlT12S47TCmlJ4G7gRWAQ3qvj4i9gA2AOcBtI1s6SZIkSWoMTRk4c6fl8/+IiM07F0bE2sB5+Y/TUkrLRrxkkiRJktQAmrVLLSmliyPifOBzwP0RcR2wBJgErAJcBvywikWUJEmSpLrWtIETIKV0TETcDHwe2AtoBR4Gfgqcb+umJEmSJA1dUwdOgJTSRcBF1S6HJEmSJDWaZn6GU5IkSZJUIgOnJEmSJKkUBk5JkiRJUikMnJIkSZKkUhg4JUmSJEmlMHBKkiRJkkph4JQkSZIklcLAKUmSJEkqhYFTkiRJklQKA6ckSZIkqRQGTkmSJElSKQyckiRJkqRSGDglSZIkSaUwcEqSJEmSSmHglCRJkiSVwsApSZIkSSqFgVOSJEmSVAoDpyRJkiSpFAZOSZIkSVIpDJySJEmSpFIYOCVJkiRJpTBwSpIkSZJKYeCUJEmSJJXCwClJkiRJKoWBU5IkSZJUCgOnJEmSJKkUBk5JkiRJUikipVTtMtS1iHgeeLza5ejDeGButQvRpKz76rHuq8v6rx7rvnqs++qx7qvHuq+eWq37jVNKa/W1wsDZoCJiZkppQrXL0Yys++qx7qvL+q8e6756rPvqse6rx7qvnnqse7vUSpIkSZJKYeCUJEmSJJXCwNm4Lqx2AZqYdV891n11Wf/VY91Xj3VfPdZ99Vj31VN3de8znJIkSZKkUtjCKUmSJEkqhYFTkiRJklQKA2cdiIhDI+IvEfFKRMyPiJkR8fmIGPC/X0SMiohJEXFGRNweEc9ExOKIeDoiLo6IvUu8hLpVRN3nxzk2Iv5fRDwUES9ExJKIeD4irouIf46IKOsa6lVRdd/Psb8bESmfTiiivI2mwHt/ere67mt6uKxrqFdF3/sRMSYivhIRd0bEyxHxWkTMjojfRsRuRZe/nhX093bv5dzz3aeNyryeelLkfR8RG0TEORHxSES8HhELI+JvEfGjiHhrGeWvZwXX/UYRcV5E/D0iFuWfdf4YEfuVUfZ6FRFbRcRxEfHLiHg4IpblvxM+MszjlvbZaVjl8hnO2hYR5wLHAAuBGcASYBKwMnApcEhKqWMAx3kPcG3+4xzgLmABsA3w9nz5KSmlbxZ6AXWsqLrPj/UUsDbwAPA0Wd1vDLwbCOBy4EMppWUFX0ZdKrLu+zj2ROA2si/cAvhySul7RZS7URR8708HjgBuAR7tY5NnUkpfLaDYDaHoez8iNgWuATYHngNuBxYBmwDbA99OKZ1a4CXUrQL/3r4NmFphk52ArYHHgC2SH8SK/p2zA3A9sBrwFNnnHYAJwPrAfOCAlNKtRV5DvSq47t8NXAWsDrQD9wDrARPJ/uaemFI6veBLqEsR8X3guD5WHZJSuniIxyzts9OwpZScanQCPgwk4BmyP0qdy98CzMrXHTfAY+0LXAzs0ce6jwFL8+PtU+3rroWpyLrP99sdWKmP5duSfQGQgE9V+7prYSq67nsdezTwIFnovzQ/1gnVvuZamkq496fn+0yp9rXV+lRC3a9EFvIT8G1gVK/1awJbVvu6a2Eq8/dOH+d6MD/e16p93bUwlXDf35rvc2H3ex4YBfwkX3dfta+7FqaCP2euCDyZ73M20Npt3T5kQT8Bu1T7umthAo4CTgc+CmwG3JDXz0eq/W9ZyvVWu8KdKvzjwMz8Bjm8j3V7dbuxWgo413/lx/tJta+7FqYRrvtv5Me7qNrXXQtTmXUP/Ee+/wfoCkIGzhLrHwNnNev+tHyfn1f72mp9Gqnf+cAu+bGWAutX+7prYSqy7vPQk/JpnT7Wr9dt/dhqX3u1p4Lr/hP59o/R68utfP238/VXVvu6a3Fi+IFzxD63DmXyGc4aFREbADsCi4Hf9l6fUrqRrJVmHWDnAk55Tz7foIBj1bUq1P3SfL6wgGPVtTLrPu/q829kwf73wy9t46nCva9c0XUfESsAn8l/nFZcSRvPCN/3R+bzq1NKTw/zWHWvhLrvoOtval9jI6R8vgB4fbDlbSQl1P3EfH5DSmlJH+uvy+f7RcQqgy+x+lMPf7sNnLVrh3z+YEqpv1+Kd/badji2yOfPFHCsejdidZ8/X/XZ/EdDUEl1HxErAj8HXqTvZyaUKfPe3ycizoyICyPilIg4oNqDGNSYout+R7Ius0+mlB6KiF0jGyzrgog4OSJ2GW6BG8iI/M6PiLFkj7BA1rVTBdd9HnRm5D+eHBGjOtfl/935vPJPUt7008SKvu/H5fO5/azvXD6KrrFDVIyRzgyD1laNk2pANs3nj1fY5ole2w5JRKwDTMl/vGQ4x2oQpdV9RHyKrGvDKLLW5F3Jvvg5LaV06SDL2YjKqvvvAFsBH08p9ffHUOX+3jm8j2WzIuLjKaX7B3msRlR03b8jn/+t28BN3X0zIi4BDqvwAaVZjNTf20PIBu94DvjDMI7TSMqo+2OAq8la+N8XETPz5RPJBrM5G/jyIMvZiIqu++fyeX+jAHdfvinZs7YqxohlhqHy2+Xa1flN0YIK28zP5ysP9SQR0Qb8ElgVmGFXQ6Dcut+N7IPfocCe+bJvkD3boBLqPiJ2Bb4IXJZS+s0wytYMyrj37wW+QDZA1jiyZ6gOBO4jGyX7uohYf/BFbThF1/0a+XxPsrD/PbKRalcHDiLrXvVh4NxBl7TxjMjfW7q60/6iny6Hzajwuk8p/Z3sy9yryL7Y/WA+rU82eMpN1j9QfN1fn88n5108e/tst/+2S22xRup32JAZOGtX57MHZXf5+BHZkMlPAv9c8rnqRWl1n1I6KqUUwFiyD+DfB/4duD0i1iv6fHWo0LqPiDHAz4BXyb71VmWF3/sppe+nlM5JKc1KKS1IKT2TUrqS7NUQt5O9LsjXohRf951/39vIug9+OaX0WErp5ZTSFWQfwBNwhO8lLP/vbURsTteXjD8t6zx1qPC6z79kfIDsC5aDgPHAWmT3/OrAJRHhK+AKrvuU0vXATcAY4JqI2DciVo6ILSPix8Bkup6v9RVwxRqpzDBkBs7aNS+fj6uwTee6eRW26VdEnA18muy1HJNSSnOGcpwGVHrdp5Rezz+Af5nsw/Z2wA+HcqwGU3TdfxfYEjg+peTzyctX+r3fKaW0mGwUVYD3D+dYDaLouu++zY97r0wpzSR7P2ELsPcAjtfIRuK+72zdvC2l9NAQj9GICq37iFgNuIysFee9KaUrUkovpJTmppQuB95LNljQNyJii0rHagJl3PeHADeTvWd2BtmXvY+QvQLkHLJXAkE2noKKM2J/u4fKZzhrV3s+37jCNhv22nbAIuIMsm5uz5OFzb8N9hgNrD2fl1L3ffgZWXe3D0TEqCbv6tOez4uq+4PJvkk9IiJ6P8P2tnz+uYg4EHg0pXTUAMvZqNrz+Ujd+w/nc7vUFl/33beZ3c82s4EJZCMXNrP2fF7W39tWup5hdrCgntrzeVF1P5msNfP6vGttDymlRyPiDrIvWfYGmvmzT3s+L+y+Tyk9FxF7Au8he/fmeLJnOy8H7gZezjf1uf1itefzkfrbPWgGztrV+ZqSbSNiTD+DOkzste2ARMTpwPHAC8B+KaVZQy9mQyqt7vvxMlk3kzay566eLeCY9aqMum8hG6ipP2/Np9UGeLxGNtL3/pr5fH7FrZpD0XV/d7f/XpPsy8XexufzZq//su/7A8i+VFkA+Bx5T0XX/Ub5/JUK23SGnjUqbNMMSrnv89F/r82nN+RBdBzZ4DWPDL64qmCk/3YPml1qa1RK6UmyDwwrkHVR6CEi9iJ7GH4OcNtAjxsR08hGZ3uJLGzeV0iBG0hZdV/BnmRh82X6H068KRRd9ymlTVJK0ddE9poUgC/ny7Yv7krqUxXu/Y/m8zsrbtUESrj3nwbuyH+c1MfxVgfelf84s/f6ZjIC9/2n8/lvUkrNHu57KKHu/5HPd+z+SpRuxxtF9sog6L/lvylU4ff91Hx+rq+kKVYV/i0HL6XkVKMT8BGyB4CfATbvtnxtsn7wCTiu1z6nkXVTO62P452S7/MSsGO1r6+WpyLrHtgD+CQwuo/z7AY8lh/ve9W+7lqYir7vK5xnen6sE6p9zbU0FXzvb082Im1rr+VtZL0sOvLjHVDt666FqYTf+R/I93kW2L7b8hWB/8nXzQSi2tde7ams3ztkrciL8v13rfZ11uJU8O+ctclakhPZuAiju60bDZyfr3sRWLXa117tqYTfOe8AxvZaNobs+c1ENmr5CtW+7lqcgBvyOvpIhW0q1f2g/y1H9PqqXcFOy/kHgvPym+R14PfA78i6iiTg0j4+yE3P103vtfyf8uWJrDVhej/T1Gpfc61MBdb9FLqC/gzgV8AV3X4BJLJ3so2p9jXXylRU3S/nHJ37GDhLqn+6RkJ9gexb1d+SvR/v6Xx5B/CVal9vLU1F3/vAf+brF5GNIHlpt/p/Ctii2tdcK1MZv3eAL+XbPFTt66vlqci6J3v12NJ8/dP539vfk7V+JmAh8MFqX3OtTAXX/XSyLvo3Ar/Oj/divv3/AetW+3prZSLrYXJ7t+nVvJ7+2n35QOt+KP+WIzn5DGeNSykdExE3A58new6tlezbjZ8C56eUBjq0dPdnFSbkU19uBKYNsbgNpcC6v5GsdXkPshFTdyUbwnoOcAnwy5TSZQUXv64VWPcaggLr/z6yl6zvRDaYwQ50BZ2fkXWtuqvg4te1ou/9lNKXI+JW4Fiy+h9L9gzVmcC0lFJfz3Y2pZJ+73wqn/sqlAqKrPuU0s8j4n6y9y/vAeyfr3qabNCmM5NjV7yh4Pv+MrJBm7YDdgZeAx4i61Hxo5SNTq7MKsC7+1g+5NGTa/mzU+SJWJIkSZKkQjlokCRJkiSpFAZOSZIkSVIpDJySJEmSpFIYOCVJkiRJpTBwSpIkSZJKYeCUJEmSJJXCwClJkiRJKoWBU5KkYYqI9ohI+XTacrb9VbdtbxjGOcdHxNKIuL7bstRt+pfl7H9Lt22n97PN6Ij4ekQ8EBGvRcSLEfGniDhgqOWWJDUXA6ckScU6PCJa+1oREasAB/e3Y2cAHOB5DgJagUv7Wf+pCufZAti10sEjYiXgJuBUYG3gSuBuYBJwdUQcP8BySpKamIFTkqTizATWA/brZ/3HgTHAnQWc60NAou/AORN4d0S8rZ99O8NopXJMA3YCbgTemlI6JKX0HmA34DXgexGxw5BKLklqGgZOSZKKMz2fT+ln/RSgA/jv4ZwkIlYma2mcmVJ6ajDliIgW4DDgJeDyfo6/BvAvwDLgyJTS/M51KaU7gNOBAL465IuQJDUFA6ckScW5A5gFHBQRq3VfERFbAbsAfwKe6bXu37t3pe31LGZfXWwPBEYDv+unHJeRBcrD+ujeux+wAfBrYFE/+78fGAXcmlL6ex/rf9W5XUSM6ucYkiQZOCVJKth0YEXgE72WT8nnP+tjn3uBn3f7+ee9pt46nwPtL3AuIguU6wH7D6IcnTq7yvbZ5Tal9ChZoF0J2LLCcSRJTc7AKUlSsf6brNvslM4FeSvj4cCLwBW9d0gpXZZSmtLt5yndp+7bRsSKwPuAWSmlv1Yox/R83r0cqwEfBB5MKc2ssO+m+fzxCts82WtbSZLexMApSVKBUkpzgKuBnSJi63zx/mStjRellBYP8xT7A+Pov3Wzsxx3Ag+Sde9dPV/8CbLW10qtm+THB1hQYZvO5zpXXs6xJElNzMApSVLxpufzKb3m0xm+D+Xz/l6H0rsco8lGx+0sx1Lgl8vZL/L5QF/RIklSnwyckiQV7wrgBbJBe8aTvTPz/pTSXcM5aES0AR8A2lNKdw9gl/8mC5ifyltbdwKuSik9u5z95uXzcRW26Vw3r8I2kqQmZ+CUJKlgebfZi4B1ybqvjmb53VgHYm9gDQbWukkeLK8CJpK9yoQBlqM9n29cYZsNe20rSdKbGDglSSrH9Hx+IFkr46/633TAOkenHVDg7KMcc4E/DGCfztbTiX2tjIjNgdWB14BKAxdJkpqcgVOSpBLkXV5vJuta+9uU0nMD2G0JvNF1toeICLIRZp8DbhlEUX4PPJqX4ycppSUD2OePeVl2jYi+RqH9ZD6/soBBkCRJDczAKUlSSVJKe6SUxqeUDh3gLk/n8637WLcz2Ui3l6eUlg2iDEtSSlvk5Zg6wH1eBC4k+5zw04h441nOiHg38BWyAYVOG2g5JEnN6U3foEqSpKq5FPgSMCMirid/9UhK6Si6Rqet+DqUAp1INsjQ3sBjEXEjsBqwL9AKnJBSumeEyiJJqlMGTkmSasfXyVoODyYLmKPy5Ufly14Brh+JgqSUFkTEnsAJwKFko+MuzM9/RkrpTyNRDklSfYuUfMWWJEm1LCK2A+4FLkopfXJ520uSVCts4ZQkqfaNBk5mYCPMSpJUM2zhlCRJkiSVwlFqJUmSJEmlMHBKkiRJkkph4JQkSZIklcLAKUmSJEkqhYFTkiRJklQKA6ckSZIkqRQGTkmSJElSKf4/WPhMd+HfwSEAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1080x1080 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,15));\n",
"plt.plot(num_rk22[:,2]/m_0,num_rk22[:,1],'s-',label='Explicit')\n",
"plt.plot(m,u,'--',label='Analytical')\n",
"plt.legend();\n",
"plt.xlabel('Mt/M0')\n",
"plt.ylabel('Velocity [m/s]')"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The height of the simple rocket is: 597.4795789904731 The height of the rocket is: 425.35224719755064\n"
]
}
],
"source": [
"simple_rocket_height = num_heun[-1,0] \n",
"rocket_height = num_heun2[-1,0] \n",
"print('The height of the simple rocket is:',simple_rocket_height, 'The height of the rocket is:',rocket_height)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3. Solve for the mass change rate that results in detonation at a height of 300 meters. Create a function `f_dm` that returns the final height of the firework when it reaches $m_{f}=0.05~kg$. The inputs should be \n",
"\n",
"$f_{m}= f_{m}(\\frac{dm}{dt},~parameters)$\n",
"\n",
"where $\\frac{dm}{dt}$ is the variable we are using to find a root and $parameters$ are the known values, `m0=0.25, c=0.18e-3, u=250`. When $f_{m}(\\frac{dm}{dt}) = 0$, we have found the correct root. \n",
"\n",
"Plot the height as a function of time and use a star to denote detonation at the correct height with a `'*'`-marker\n",
"\n",
"Approach the solution in two steps, use the incremental search [`incsearch`](../notebooks/04_Getting_to_the_root.ipynb) with 5-10 sub-intervals _we want to limit the number of times we call the function_. Then, use the modified secant method to find the true root of the function.\n",
"\n",
"a. Use the incremental search to find the two closest mass change rates within the interval $\\frac{dm}{dt}=0.05-0.4~kg/s.$\n",
"\n",
"b. Use the modified secant method to find the root of the function $f_{m}$.\n",
"\n",
"c. Plot your solution for the height as a function of time and indicate the detonation with a `*`-marker."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"def heun_step3(state,rhs,dt,etol=0.000001,maxiters = 100):\n",
" '''Update a state to the next time increment using the implicit Heun's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state + rhs(state)*dt\n",
" \n",
" ###New iterative correction\n",
" for n in range(0,maxiters):\n",
" next_state_old = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e=np.sum(np.abs(next_state-next_state_old)/np.abs(next_state+eps))\n",
" if e<etol:\n",
" break\n",
" \n",
" ### end of iterative correction\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"def f_m(dmdt,m0=0.25, c=0.18e-3, u=250):\n",
" ''' define a function f_m(dmdt) that returns \n",
" height_desired-height_predicted[-1]\n",
" here, the time span is based upon the value of dmdt\n",
" \n",
" arguments:\n",
" ---------\n",
" dmdt: the unknown mass change rate\n",
" m0: the known initial mass\n",
" c: the known drag in kg/m\n",
" u: the known speed of the propellent\n",
" \n",
" returns:\n",
" --------\n",
" error: the difference between height_desired and height_predicted[-1]\n",
" when f_m(dmdt)= 0, the correct mass change rate was chosen\n",
" '''\n",
" m_f= 0.05\n",
" height_desired=300\n",
" y_0 = 0 \n",
" v_0 = 0 \n",
" T_2=(m_0-m_f)/dmdt\n",
" t=np.linspace(0,T_2,1000)\n",
" dt=t[1]-t[0]\n",
" N =int(T_2/dt)\n",
" \n",
" num_sol=np.zeros([N,3])\n",
" \n",
" num_sol[0,0] = y_0\n",
" num_sol[0,1] = v_0\n",
" num_sol[0,2] = m0\n",
" \n",
" for i in range(N-1):\n",
" num_sol[i+1] = rk2_step(num_sol[i], lambda state: rocket(state, dmdt=dmdt, u=250, c=0.18e-3), dt)\n",
" height_predicted=num_sol[:,0]\n",
" error = height_desired-height_predicted[-1] \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n"
]
}
],
"source": [
"def incsearch(func,xmin,xmax,ns=50):\n",
" '''incsearch: incremental search root locator\n",
" xb = incsearch(func,xmin,xmax,ns):\n",
" finds brackets of x that contain sign changes\n",
" of a function on an interval\n",
" arguments:\n",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\n",
" returns:\n",
" ---------\n",
" xb(k,1) is the lower bound of the kth sign change\n",
" xb(k,2) is the upper bound of the kth sign change\n",
" If no brackets found, xb = [].'''\n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = np.zeros(ns)\n",
" for i in range(ns):\n",
" f[i] = func(x[i])\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] )\n",
"\n",
" \n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb\n",
"\n",
"The_change_of_mass = incsearch(f_m, 0.05, 0.4, 5)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The Root of the function is 0.07890352693388984\n"
]
}
],
"source": [
"def mod_secant(func,dx,x0,es=0.0001,maxit=50):\n",
" '''mod_secant: Modified secant root location zeroes\n",
" root,[fx,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):\n",
" uses modified secant method to find the root of func\n",
" arguments:\n",
" ----------\n",
" func = name of function\n",
" dx = perturbation fraction\n",
" xr = initial guess\n",
" es = desired relative error (default = 0.0001 )\n",
" maxit = maximum allowable iterations (default = 50)\n",
" p1,p2,... = additional parameters used by function\n",
" returns:\n",
" --------\n",
" root = real root\n",
" fx = func evaluated at root\n",
" ea = approximate relative error ( )\n",
" iter = number of iterations'''\n",
"\n",
" iter = 0;\n",
" xr=x0\n",
" for iter in range(0,maxit):\n",
" xrold = xr;\n",
" dfunc=(func(xr+dx)-func(xr))/dx;\n",
" xr = xr - func(xr)/dfunc;\n",
" if xr != 0:\n",
" ea = abs((xr - xrold)/xr) * 100;\n",
" else:\n",
" ea = abs((xr - xrold)/1) * 100;\n",
" if ea <= es:\n",
" break\n",
" return xr,[func(xr),ea,iter]\n",
"\n",
"The_root = mod_secant(f_m, 0.001,0.1)\n",
"print('The Root of the function is',The_root[0])"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x1080 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"m_f= .05\n",
"m_0= .25\n",
"y_0 = 0 \n",
"v_0 = 0 \n",
"dmdt_final=The_root[0]\n",
"height_desired=300\n",
"T2=(m_0-m_f)/dmdt_final\n",
"t=np.linspace(0,T2,1000)\n",
"dt=t[1]-t[0]\n",
"N =int(T2/dt)\n",
" \n",
"num_sol=np.zeros([N,3])\n",
"num_sol[0,0] = y_0\n",
"num_sol[0,1] = v_0\n",
"num_sol[0,2] = m_0\n",
" \n",
"for i in range(N-1):\n",
" num_sol[i+1] = rk2_step(num_sol[i], lambda state: rocket(state, dmdt=dmdt_final, u=250, c=0.18e-3), dt)\n",
" height_predicted=num_sol[:,0]\n",
"\n",
"plt.figure(figsize=(15,15));\n",
"plt.plot(t[:-1], height_predicted)\n",
"plt.plot(t[-1], height_predicted[-1], '*', label = 'detonation')\n",
"plt.xlabel('Time (s)')\n",
"plt.ylabel('Height (m)')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"1. Math 24 _Rocket Motion_. <https://www.math24.net/rocket-motion/\\>\n",
"\n",
"2. Kasdin and Paley. _Engineering Dynamics_. [ch 6-Linear Momentum of a Multiparticle System pp234-235](https://www.jstor.org/stable/j.ctvcm4ggj.9) Princeton University Press \n",
"\n",
"3. <https://en.wikipedia.org/wiki/Specific_impulse>\n",
"\n",
"4. <https://www.apogeerockets.com/Rocket_Motors/Estes_Motors/13mm_Motors/Estes_13mm_1_4A3-3T>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}