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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": 2,
"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": 3,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" \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",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" \n",
" derivs = np.array([state[1], u/state[2]*dmdt, -dmdt])\n",
" return derivs"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"#Runge Kutta Method (Explicit)\n",
"\n",
"def rk_step(state, rhs, dt): #imported from notebooks\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": 5,
"metadata": {},
"outputs": [],
"source": [
"#Heun Method (Implicit)\n",
"\n",
"def heun_step(state, rhs, dt, etol=0.000001, maxiters = 100): #imported from notebooks\n",
" \n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state + rhs(state)*dt\n",
" \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",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"#Define Initial Conditions\n",
"\n",
"y0= 0 #inital y position\n",
"v0= 0 #initial velocity\n",
"\n",
"m0= 0.25 #initial mass\n",
"mf= 0.05 #final mass\n",
"\n",
"u= 250 #propelant velocity\n",
"N= 100 #number of time steps\n",
"\n",
"dmdt= 0.05\n",
"t = (m0 - mf) / dmdt #simulation time\n",
"dt = t/N #size of dt step"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"rk_run = np.zeros([N,3]) #initialize explicit solution\n",
"\n",
"rk_run[0,0]= y0 #explicit initial conditions\n",
"rk_run[0,1]= v0\n",
"rk_run[0,2]= m0\n",
"\n",
"heun_run = np.zeros([N,3]) #initialize implicit solution\n",
"\n",
"heun_run[0,0]= y0 #implicit initial conditions\n",
"heun_run[0,1]= v0\n",
"heun_run[0,2]= m0"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"#Tsiolkovsky Method\n",
"\n",
"dt_tsi = t/N\n",
"t_tsi = np.linspace(0, t, N)\n",
"m_tsi = m0 - dmdt * t_tsi\n",
"mfm0 = m_tsi / m0\n",
"v_tsi = -u * np.log(mfm0)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"for i in range(N-1):\n",
" heun_run[i+1] = heun_step(heun_run[i], simplerocket, dt) #solve Heun method\n",
"\n",
"for i in range(N-1):\n",
" rk_run[i+1] = rk_step(rk_run[i], simplerocket, dt) #solve Runge Kutta method"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Velocity (m/s)')"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize = (15,10)) #plot all methods\n",
"\n",
"plt.plot(heun_run[:,2], heun_run[:,1], label='Heun (Implicit)', color = 'black', linewidth='12', linestyle='--')\n",
"plt.plot(rk_run[:,2], rk_run[:,1], label='Runge Kutta (Explicit)', color = 'tomato', linewidth='7', linestyle='--')\n",
"plt.plot(m_tsi, v_tsi, label='Tsiolkovsky', color = 'deepskyblue', linewidth='3', linestyle='--')\n",
"\n",
"plt.title('Simple Rocket Velocity vs. mf/m0 Ratio')\n",
"plt.legend(loc='best')\n",
"plt.xlabel('Final Mass / Initial Mass')\n",
"plt.ylabel('Velocity (m/s)')"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"simpleh = heun_run[99, 0] #save data for comparison in part 2\n",
"simplev = heun_run[99, 1]"
]
},
{
"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": 12,
"metadata": {},
"outputs": [],
"source": [
"def rocket(state, dmdt=0.05, u=250, c=0.18e-3):\n",
" \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",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" \n",
" derivs = np.array([state[1], u/state[2]*dmdt-g-c/state[2]*state[1]**2, -dmdt])\n",
" return derivs"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"g = 9.81 #define extra required constants"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"for i in range(N-1):\n",
" heun_run[i+1] = heun_step(heun_run[i], rocket, dt)\n",
"\n",
"for i in range(N-1):\n",
" rk_run[i+1] = rk_step(rk_run[i], rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Velocity (m/s)')"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ijInGut53YU3BsxGrMtQK+NmP3W2vlDuxKkNbjTG7/BjHdqe/vY3oXNHp720eU2WQMea4MWYJ1uev4weKoe7m+rR/nHKM/jzZGNPdGLPQGLPTGHPMGHPaGHOaHP7RjKx/TiilspFWOJVSuZrdNXIQ1hx4AC+I0yTqtnin/dXTKdLxJfmIST3VhOMLZZbuj7Tv/3RUOmtgVTq9dRd1TGVQLyvHzQHzsebKg5QWMsfjKVJanlOxu2TutVdz4jntcfo7vWvt2O+c5xApzyun74X1yhizkZT7x/raj46BS46Qcr9xZs3C+hEkBGsUZ7AGUAqxt3/iIZ9zjMeNMV8bY542xtTD6o6biNUy/0QW48vtfO1Om9M2ktLFvZGXdI2d/t7gMVUmGWPOkDLYmgAvu0lWgZReHt5eX7WyMTR39jj97ev/hD3eEimlMk8rnEqpXM8eMdYxn2QkLq2cdiXHMVppexFx20XLnvOwnb36k8tux5xsN4iI64BCGY3XtdK5wkulc6n9mGbwmAxwDJKUz2uqDLBbIb6wV+8WkXJYLV1gTc3ibbAdx3O6Q0RKZ1dMtvVYg0hBysA3aYhINCn3hSZfa3tAqZX2ajdP82BmkvNgVb5eC8fgQd1EpAgplfqZnga/8pUx5iApz9X1R4PvPYyWml6ZiwDHqLnVshJfbmb/qNXGXvVrhdMYc5SUc97Z09yqpIzGvM/+MSMnYllHyudCWxG5ySWJ872dbt8D9iBW3bwcJjPvo1SMMXuxBj4C758TFbHmaYa0/xOUUtlEK5xKqbziHVJGzxzhuK/QieOLewTW9CfuvERKl9CpLvtmOpU/2b4fyi1PFVpnGWjpfBdrSoUQ4GOXgYzcHbuqm82O+7XKpRdXBjm6zRbEGkjIUTmb4T55snFYLTKhwPT0KnUenpNbdiuLo0txH3vUXNfyCmDNuQrWtDTzXJKMtx/LAO95+QLv07V24nzfnK/XYjZWN+QiwBRSRijNandaB8e1ihaRpqTck+j2GopIGUf3Ww/7g4Dy9mpW7xPMzaKB67Bamtf6ORaACfZjRaweH6mIyB2kjL48MYdjeYGU0XKfcdm3H+vzDFJG+HX1OhDuqXD7Pe6Y3iUrn2mO/wm3icjdrjvt0c3fxWqtvUz2veeUUi60wqmUyhOMMaeAt+3VyqQMXuPwGdbclwDPi8hEEakjIsVEpK6IfEjKPJdfGmO+dSk/ARhgr1YHfhWRgSJyo4iEiUikiHQSkVl4nufTNWbnSmdN3FQ67TkZHV0TWwIbRKS/iFSyj1vWngPvSRH5lZTpBJz9aj/easdYVEQC7SUr0yQsJ2Uuxlvtx72knrcxDWPMNlIq/TFY57Kf07ksJyL/JyIjRGQjKV8MffVfrB8HAoElIvKIiFQQkRIi0tqOz9Hy8qTdWusc3xJgur36APCdiLSzz3VREalhX/ufSTt9jrfnHUfKaKWPi0h1ESnguBYe8pzAeu1Cyms61t1gPpn0GVaFVrBeO4LVpfhzD+kbAwdEZLqIdBORKvY5ibDP7TdYvQzApcukfW0dU1/4ek9ubuXoTvu1t3lar6A5WCNgA4wXkaft13w5ERlEytQfu7AqUTnGHpDK0crZ0fleXvu9tshefUhEXrPfB8VFpImIzAOGkf7IsY4uwQNEpIGIFPT2PvJgDNZo4WANOPesiFS2Y2kOfAu0tfe/YYzZk4GylVIZYYzRRRdddPHbgnXvmrGXFumkLYI1P6fBGrxCXPYXBX50Ks/dsgwo7OUYfbC+oHsrY4xLnv729kseyvw/rAEpDNbIoSXdpHkYq6uot+MaYLWbvBFYLXnu0o/I4vV5w6W8lzOQ93GsuQXTe07fucm70d73joeyG2HND+ipzCTgWS+xBWFVdNOLrYVLvnfs7Rs9lPukl7LCPORp4ZLuwWx+j33iUv5sL2k7+nBODDDBTd4wp/0LMhnrgvTyu8To9pza6U7YaYa52TfM3nfCQ97d9v6OuSFee38pYJOXa7IHqJKF18k7vsRpp61tv8fSvJ6w7uP8x0uci7C6/3o8FlaXW0/56/p6/rF+nNyVzmt5MpAvO99zuuiiS+pFWziVUnmGsVo5HV0lawCdXPbHY3WF64vVOncE636gf4HFWNNBtDZWa6anY0zH+pLyJrAZa4Cc81hfQJdjVQy9TQngrkzXls7v3LR0vos1X91orPsU47G6eSVgVa4/xLr/tKWb8g8ATbG6Z+4jZQL57DDdZT297rTOcb2FdS7fwGqxOIH1nE5hVbynYp2XOzIalLHuJauK1b3vN7vMC1gtsB8DDY0xL3rJn2iMeQDrx4AZWF/Wz9vlbAXmYt379bOnMjyU+wZWq+lPWM/Xl9axVcBf9t/n8WEwnwxyvWYeR6fFep+0wXr9r8Y6nxfsuP7CaiVtYYwZks0x5hr2lC+RWM95mffUV44x5l+sEYyHY/VqOAWcwfp8eBGoY4zZcYVi2UxKK3k3EanstG8v1n2R72N9HiViTe3yI/AfUgae8lb+PKzP9+VYXbd9nXbGtZydWAMUDce6D/YE1ufjQayB0VoZYwYaa8RwpVQOEWOMv2NQSimlrmki8jvWjyizjTH3pJde5RwReQar2/wiY0y79NIrpZTyTls4lVJKKT8SkYakTM2gA5f4n2M0Zn9Ph6KUUlcFbeFUSiml/EhEZmJ1996FdQ+e/mNWSil11cjIaF9KKaWUygb2aJsFgV72AtZgVFrZVEopdVXRFk6llFLqChKRulgDHTlbDzQxxlxyk0UppZTKs/QeTqWUUso/DHAAmATcoZVNpZRSVyNt4cyiEiVKmMjISH+HoZRSSimllFJ+8euvvx41xpR0t0/v4cyiyMhI1q9f7+8wlFJKKaWUUsovRGSvp33apVYppZRSSimlVI7QCqdSSimllFJKqRyhFU6llFJKKaWUUjlCK5xKKaWUUkoppXKEVjiVUkoppZRSSuUIrXAqpZRSSimllMoRWuFUSimllFJKKZUjtMKplFJKKaWUUipHaIVTKaWUUkoppVSOCPR3AEoppZRSudmlS5c4fvw4J0+e5NKlS/4ORymlckxgYCDXXXcdxYoVIzAwe6qKWuFUSimllPIgKSmJ/fv3ExISQvny5QkODkZE/B2WUkplO2MMFy9e5NixY+zfv58KFSoQEJD1DrHapVYppZRSyoP4+HgCAwMpW7YsISEhWtlUSl21RISQkBDKli1LYGAg8fHx2VKuVjiVUkoppTw4ffo0YWFhWtFUSl0zRISwsDDOnDmTLeVphVMppZRSyoPz588TGhrq7zCUUuqKCg0N5dy5c9lSllY4lVJKKaU8SEpKypZ7mJRSKi8JCAggKSkpe8rKllKUUkoppa5S2p1WKXWtyc7PPa1wKqWUUkoppZTKEVrhVEoppZRSSimVI3JthVNEXhURYy/DvaTrJSI/ishJETktIutFZIiIeH1umc2nlFJKKaUskZGRiAgrV670mq5FixaICNOmTbsicfnD2rVrCQgIYMSIEam2T5s2DRGhRYsW/gnMR3379nV7jRzx9+3bN8vHEJFMddXcsGEDAQEBDB/usUqgcrFcWbkSkYbAk4BJJ90EYBbQAPgRWAZUAd4D5otIvuzMp5RSSimllCtjDEOHDqVIkSI89dRT/g4nz3H8IOHph4ubbrqJu+++m/Hjx7Nz584rG5zKslxX4RSREGAacBhY6CVdZ2AwEAfUNsa0M8Z0AioDW4FOwEPZlU8ppZRSypWjxSavLCpnfPLJJ8TGxjJ06FCKFi3q73CyVadOndi6dSujR4/Ocllbt25l69atmcr73HPPkZiYyNNPP53lONSVlesqnMCLQHVgEHDSSzrHq+0pY0zyTx3GmMPAg/bqCDddZDObTymllFJKqTTeeecdRIT777/f36Fku+uuu46oqCjKli2b5bKioqKIiorKVN5atWrRoEEDFixYwL59+7Ici7pyclWlSkQaAY8Ds40xX3lJFwHUBy4Cn7ruN8asAg4CZYDGWc2XF30fD/22QZLXTslKKaWUUv63bt06evToQUREBMHBwZQsWZL27dvz008/pUm7Z88eRITIyEiP5Xlq0XXePnfuXJo0aUKhQoUoXLgwt912m9vjpSc2NpbY2Fiio6O9xuTK+XkkJSUxduxYatSoQYECBYiIiOCxxx7j7NmzAMTHxzNs2DAiIyMJCQmhcuXKjB071m25zt1TV6xYQatWrShatCiFChWiefPmfPnllxl6fundw7l//34ee+wxqlevTsGCBSlSpAjVqlVj8ODB/P7776nSul6XlStXIiKsWrUKgJYtW6ZqkXftYtunTx8uX77M5MmTM/QclH/lmgqniOQHpgPHgUfSSV7PfvzDGHPOQ5pYl7RZyZdnGAMDtsNtm2BaHPzvkL8jUkoppZTy7K233qJJkybMmzePMmXK0KFDBypVqsSiRYuIjo5m6tSp2X7MZ599ll69ehEcHEzbtm2JiIjg+++/57bbbmPNmjUZKmvBggUAtGrVKtPx9OrVi2effZaKFSvSunVrzpw5w9tvv03nzp05fvw4jRo1Yu7cuTRs2JDmzZuzZ88eHn/8cV599VWPZX7xxRe0atWKf//9lzvuuIM6deqwevVqOnTo4LGymlFLly6lZs2avP3225w8eZKYmBhat25NgQIFmDx5MvPnz/eav0yZMvTp04fSpUsDEBMTQ58+fZKXMmXKpErvOMcLF3q8607lQoH+DsDJK0BVoIcx5mg6aSvaj3u9pHG0tVd02pbZfHmGCBQPSll/4m9oVxzKhPgvJqWUUkopdxYvXszw4cMpV64cn3/+OY0aNUret3r1au68806GDBlCdHQ0VapUybbjTpgwgV9++YX69esDkJSUxKBBg5g6dSrPPvssy5Yt87ksRytckyZNMhXL3r17yZ8/Pzt27KBcuXKA1WpYr149Fi9eTHR0NHXq1GHGjBnkz58fgEWLFtGuXTtee+01hg0bRmhoaJpyx48fz5tvvplqZNevvvqKu+++myeffJJWrVpRu3btTMUMsG/fPrp06UJCQgIvvfQSI0aMIDAwMNX+I0eOeC0jKiqKadOm0aJFCw4fPsyIESO8juZbtWpVihYtyh9//MHhw4eTK6oqd8sVLZwi0hQYBiwwxsz1IUsh+/GMlzSn7cfC2ZAvT3m2AtxofR5x4hI8vdu/8SillFLq6ubaFdJ1cXSZdPXcc88B8MEHH6SqbAI0a9aMUaNGkZiYmO1dKF944YXkyiZAQEAAL7/8MgA//vgjiYmJPpe1ceNGAKpVq5bpeMaPH59c2QS4/vrruffeewGrQjpx4sTkyiZA27ZtqV27NgkJCaxfv95tmfXr108zjchdd91Fr169uHz5Mu+++26m4wUYO3YsCQkJdO/enWeeeSZVZROgfPnyqc5xdhCR5PPsOO8q9/N7C6eIFAA+Ak5hjR7rUzb7MaN3KGY2X+pCRAYAA8B6M+U2BfLBpCpw+2boWhJezZNttUoppZTKK2JiYtJ0f3S2ePFiDh8+nGrb0aNHiY2NpUiRIrRu3dptvujoaIAMd3NNT7t27dJsK1WqFEWLFiU+Pp5jx455fT4OZ86cSb7Psnjx4pmKJSgoiFtvvTXN9kqVKgHQoEEDSpQokWZ/5cqV2bx5M//884/bch0VVlf33XcfH3/8cbpzp6Zn8eLFAPTv3z9L5WRUsWLFANK8nlTu5fcKJ/Aq1hyY9xtjfL3jMMF+LOQljWNfgtO2zOZLxRgzBZgC0KBBg1w5LE+rYrChPtTLs+20SimllMor0usK6egy6Wz37t0YYzh16lSa1jFX6XXNzChPDQZFihQhPj6e8+fP+1TOyZPWhAohISEEBwdnKpYyZcq4ff6FCllfSSMiItzmc+z3FGvFiu5bHBwDGx04cCCjoaayd691h1pmR53NrCJFigBw4sSJK3pclXm5ocLZCUgC+ohIH5d9jlfwgyLSDthljOkP7LG3V/BS7vX24x6nbZnNlydpZVMppZRSudXly5cBa9qNjh07ek3rroXPk6SkpHTTBARkz11lYWFhAFy4cIELFy4QEpLxQTPSiyW7YnWV1XlZ/TWv66lTpwCuuvlOr2a5ocIJ1r2k0V7232AvYcKoxCoAACAASURBVPb6b/ZjDREp4GHE2YYuabOS76qRmARBueLOXaWUUkpdy66/3vqNPygoiGnTpvmcz9GSePr0abf7HS1vV0JoaCgFCxbkzJkzHD9+PFvmqswue/bs8brd+Z7RzChfvjzbt29n+/btHlthc8KxY8cAqwu0yhv8XvUwxkQaY8TdgjVNCsAT9ra6dp79wAYgGOjqWqaIRAMRQByQ3Ok/s/muBqcvwWO7oNlvcCn9H/6UUkoppXJUeHg4tWrV4ujRoxm6n7BkyZIEBwdz7Ngxt11tv/nmm2yMMn033XQTAH/++ecVPW56Zs2a5XW7ty7QvoiJiQGsAZ+yyvEjwqVLl7ymM8awbds2AOrVy5MzGF6T/F7hzILR9uPrIlLJsVFESgHv26uvGWNcq1eZzZdnXUqChhvg7QMQmwDjD/o7IqWUUkopeOmllwBrgJulS5em2X/x4kW+/PLLVIMGBQUF8X//93+ANZ+mMSnDafz00088++yzORx1ai1btgSyf2CjrIqNjeXtt99Ote2bb75h5syZ5MuXj4ceeihL5T/22GMUKlSIOXPmMHr06OQu0g779+/n119/9ams8PBwALZu3eo13bZt24iPj6dGjRrawpmH5NkKpzFmPjARKANsEZGvRORzYCdQHVgAvJdd+fKywADo4zRN0ajdsMddZ2KllFJKZYgxJk8tuU2HDh146623iIuLIyYmhqpVq9K+fXu6dOlCo0aNKFWqFB06dGDTpk2p8r344osEBwczadIkatSoQdeuXbn55puJjo5m8GBfJz3IHo77T5cvX35Fj5ueoUOHMnz4cOrUqUOvXr1o3rw5bdu25dKlS4wePZq6detmqfwKFSowb948ChUqxMiRI6lQoQKdO3emS5cu1K9fn8jISL766iufyurUqRMATzzxBO3bt6d///7079+f7du3p0rnOMcdOnTIUuzqysqzFU4AY8xg4B6sbrLRQAywC3gI6GyMuZyd+fKyx6+HWgWtv88mwYM7IRf+31FKKaXUNeaxxx7j119/5YEHHuDy5cssW7aMJUuWEB8fT3R0NFOnTqVbt26p8jRt2pTvvvuO2267jf379yd3o/3444+TW02vlHr16tG4cWN++OEHj/dN+kOnTp1YsmQJxYsXZ9GiRfz22280bdqUL774gieeeCJbjnHHHXewefNmhgwZQoECBVi0aBHLli3j3LlzPPjgg2mumyft27fn/fffJyoqiuXLl/Phhx/y4YcfcuhQ6gkspk+fTr58+Rg4cGC2xK+uDMmNv3blJQ0aNDCeJtzNbdadgiYbUiYhnVUNepX2mkUppZS6pm3dujV5onmlPJkzZw49e/Zk1KhRvPjii36NpUWLFqxatYoVK1Zk+T7N3GTLli3Url2bzp07M3/+fH+Hc03IyOefiPxqjGngbl+ebuFUGdOoCAwJT1kfuhP+vei/eJRSSimlrgbdu3fn5ptv5t133yU+Pt7f4VyVXnjhBYKCghg9enT6iVWuohXOa8yrFaG8PUXUsUvw0E7/xqOUUkopldeJCOPHj+fkyZO8/vrr/g7nqrNhwwY+//xzHn74YSpXruzvcFQG5ZZ5ONUVUjgQplaFmM3W+qdH4LMj0Lmkf+NSSimllMrLGjVqRFLSVTPJQa5y00036bnNw7SF8xrUuhjcXyZlfcgOOJbov3iUUkoppVT2WLlyJcaYq+r+TZW3aYXzGvXWjVDOmmOXGwpAgvd5dpVSSimllFIqw7RL7TUqLAimVIVd5+ChcMgn/o5IKaWUUkopdbXRCuc1rG1xf0eglFJKKaWUupppl1qllFJKKaWUUjlCK5wq2WUDb+2H5cf9HYlSSimllFLqaqBdahUAf52DXn/CLwlQIQR+bwiF9NWhlFJKKaWUygJt4VQAFMpnDSAEsPcCjPjbv/EopZRSSiml8j6tcCoASgfD+Mop6xP+ge/j/RePUkoppZRSKu/TCqdK1qsUtHMaubbfNjil83MqpZRSSimlMkkrnCqZCEypAsXsezf3XYBHd/k3JqWUUkoppVTepRVOlUrZEHi/Ssr6/+Lg66P+i0cppZRSuVdkZCQikmrJnz8/5cuXp1u3bqxatcrfIeY6u3btQkQIDPQ8OuPMmTMJCgoiICCAd9555wpG5x/Tp09HRJg2bVqq7SNGjEjz+nK3DBo0yD+BAz169EBEmDNnTqrtkyZNypbYzp8/n/y+yqiff/4ZEeGZZ57JUgxZpeOQqjS6l4IvjsDcI9b6f3bA79dB8SD/xqWUUkqp3CkmJoYyZcoAEB8fz2+//cann37Kp59+ytixY3n00Uf9HGHe8f777/PQQw8REBDAhx9+SL9+/bJcZuPGjVm3bh1r1qyhcePGafZv27aNatWqUbVqVbZt25bl42VEQkICTz/9NNWqVeO+++5zm6ZKlSo0adLEYxne9l3N0ruuTZs2pW3btrz11lv079+fyMjIKx8kWuFUHkyoAqtOQtxFaxmyA+bU8HdUSimllMqNRowYQYsWLZLXExMTeeSRR5g4cSIjRoyga9euRERE+C/APGL06NGMHDmS4OBgZs+eTefOnf0dUo578803OXToEGPGjCFfvnxu07Rs2ZJJkyZd4ciypkePHrRo0YKiRYtmqZyQkBC2bt1KQEDmOqY+99xzLFq0iGeeeYaZM2dmKZbM0i61yq3iQTDVqWvtxtMQn+i/eJRSSimVdwQFBfHWW29RuHBhLl68yNKlS/0dUq731FNPMXLkSEJDQ/nqq6+uicrmhQsXmDRpEkWLFr3qnm9YWBhRUVGULl06S+WICFFRUVSpUiX9xG40bNiQWrVqMW/ePOLi4rIUS2ZphVN51K4E9C8Lj0bAbw2gqHapVUoppZSPChQokPwl+fDhw2n2R0REICIcOHDAbf7mzZsjIvz0008et8fGxnLXXXdRrFgxChQoQN26ddPcB+js8OHDDBo0iPDwcPLnz0+lSpUYNWoU58+f93g8AGMMs2fP5vbbb6d48eIEBwdToUIFBg4cyL59+zJwVtJKSkpi0KBBvPHGG1x33XUsXbqU1q1bp0nny718ZcqUQUSSKxaLFy9GRFi3bh1gdT11vvdx7dq19OjRg2rVqgGwffv2VPujoqKSy46Li2Ps2LG0bt2ayMhI8ufPT1hYGE2bNmXy5MkkJSVl+LnPmzePI0eO0L17d0JCQjKc352PPvoIESEyMpL4+LRz/Dnurbzxxhs5depU8vbGjRsnn5OlS5dy6623EhYWRuHChYmOjuabb77JUBzp3cO5Z88eHnnkEapVq0bBggUpUqQI1atX5+GHH07Vrdnddfflujrr3bs3iYmJTJ06NUPPIbtol1rl1ZQq1ui1SimllHJj4Qz4albOH+e+oRB9p29pV30DM8a733fXPdDB/X1yOeHkyZMAWW7lcWfRokWMGTOG6tWrExMTw969e1mzZg39+vXj5MmTPPLII6nSHzhwgGbNmrFv3z5Kly7NXXfdxfnz53n77bdZtWoVly65nwsuMTGRrl27snDhQkJDQ6lfvz6lS5dmy5YtTJkyhfnz57N8+XLq1auX4edw6dIlevfuzSeffEKpUqVYsmQJdevWzdT5cCc8PJw+ffqwaNEijh49yp133knJkiWT95csWZLo6GguXLjAggULKFKkCJ06dUreX7Zs2eS/v/76ax5//HHKly/PjTfeSOPGjYmLi2PNmjWsWbOG77//nrlz52YovgULFgDQqlWrLD7TFP369WPVqlVMnz6dfv36JR8DYNOmTTz66KMEBwczd+5cihQpkib/nDlzGD9+PLVr1+bOO+9k9+7d/PDDD/zwww9MmDCBwYMHZznGr7/+mh49enDmzBkiIiJo06YNAH///TcTJkwgPDycESNGeMzvy3V15ji/CxcuZNSoUVmOP6O0wqm80sqmUkoppTLjjz/+YPfu3QQFBbltscuq119/nY8++og+ffokb5s2bRr9+vXj+eefZ+DAgalahQYNGsS+ffto164dc+fOJTQ0FIB//vmH2267zeNgOU8//TQLFy6kZcuWzJw5k3LlyiXvGzduHMOGDaNHjx78+eefHu9B9KRTp058/fXXlC9fnmXLlmW626QntWrVYtq0aTRu3JijR48yatSoNIPLPPjgg7Rs2ZIFCxZQtmxZjy3EjRs3JjY2lgYNGqTafvDgQWJiYpg3bx69evWiQ4cOPsVmjOGHH34Asn/QnwkTJvDLL7+wcOFC3nnnHYYNG0ZCQgJdu3bl/PnzjBs3Ls3zcBg3bhzvvvsuDz30UPK2+fPn0717d4YNG8att96aquU3o3bt2kX37t05e/Ysr7/+Oo8//niq182ePXs4ceKE1zJ8ua6u6QsVKsRvv/3GiRMnCAsLy3T8maFdalWGGAMz42DPOX9HopRSSqncKD4+nm+//Za7776bpKQkxo0blyMDBnXr1i1VZROgb9++VK5cmRMnTrBhw4bk7X/99ReLFi0iKCiI999/P7myCVCuXDneeOMNt8c4cuQI7733HkWKFGHevHmpKpsAjzzyCDExMezYsSPD96levnyZr7/+GoAPPvgg2yub2a1mzZpuK2nh4eGMHj0asCpmvjpw4ABHjx6lSJEiac6rq8mTJ3udFmXx4sWp0hcsWJBPP/2U0NBQnnrqKWJjYxk4cCA7d+6kY8eODB061OOxmjVrlqqyCdClSxe6dOlCYmIiEyZM8Pk5ujNmzBjOnj1Lnz59ePLJJ9P8SBEZGZmtrdwA+fLlo0qVKiQlJbFp06ZsLdsX2sKpfPbvRRi0A744CtHXwXd1IZ+2gCqllFLXvJYtW6bZFhISwrfffktMTEyOHLNdu3Zut0dFRbFz507++eef5G2OlrTmzZtz/fXXuy2rcOHCJCQkpNr+/fffc+HCBdq0aUOJEiXcHi86OpolS5awZs0a7rjjDp/jDwgIoEmTJqxevZrevXuzcuVKqlat6nN+f0hMTGT58uWsW7eOuLg4Lly4gDEmuUVux44dPpf177//AlC8ePF006Y3LUp4eHiabTVq1ODdd9/lgQce4Pbbb+fkyZNERkby0UcfeT3Wvffe63b7fffdx7x581i5cmW68XrjqBz3798/S+VkVLFixQD391PnNK1wKp/tPg8Lj1p/rzoJY/bDU+X9G5NSSiml/M8xD6cxhri4OH744QfOnz9P7969Wb16NZUqVcr2Y5Yv7/5LiOO+vPPnzydvO3jwIAAVKlRwm0dEKF++PH/88Ueq7X///Tdg3fsm6dxndOTIEd8Cdzrm4sWLadOmDatXr6ZFixa5utL5xx9/0KlTJ3bu3OkxjfMgPOlx3N/r7j5KV5mdFuX+++9n4cKFfPnll4gIc+bMSbc7acWKFd1ud8xh6WmQK18YY9i/fz9AlrrlZobjPKfXXTcnaIVT+axREXimAry411oftRtuLwo3FfZvXEoppZTyL9d5OA8dOkRMTAxbtmzhnnvuYe3atelW2FylN+ppZuYl9BaDu/IuX74MWJWDRo0aeS375ptvznA8hQoVSlXpbNmyJStWrMh0pTMzI8X6Wu7dd9/Nzp076dy5M48//jhRUVEUKVKEfPnysXnzZurUqYMxxucyHRW/jFRSM2rfvn38+OOPgFXZi42NTfc6piejr+Pszp9ZjvOc1XlBM0MrnCpDRlWAJcdhXQIkGuj1J2xoAKEZu0deKaWUUlexsmXLMm/ePGrXrs0vv/zCrFmz0nRVDA4OBuD06dNuy9i7d2+2xeO4R9Bbme72ObrfpjfdSlb4Wul0nK+LFy9y8eLF5HWHs2fPcvTo0RyJcfPmzezYsYPrr7+eefPmpamc79q1K8NllipVCoBjx45lS4yuLl26RI8ePYiPj6dnz5588cUXDB8+nKZNm3LTTTd5zLdnzx6v29O739QbESEiIoK9e/eyfft2j920c4LjPDvO+5WkFU6VIYEBMLMa1F0PZ5Jg+zkY/he8n7vvc1dKKaVyRof7rug0Iz6JvtP3KVRyUFRUFIMHD2bcuHE8//zz9OjRg8DAlK+e4eHh7N69m23btqXpXrhp06ZU92Bm1S233ALATz/9xIEDB9IMYrRo0SK3LW233347gYGBLF26lFOnTvnU/TMz3FU6V65cmWogoYCAAMqUKUNcXBw7duygZs2aqcr49ttvPbYwOiqnnqZ+SW//8ePHAeuauWsJnjUr41MDRUREUKpUKf79918OHjzo9j7MrBg5ciRr1qyhWbNmfPzxx0ydOpXBgwfTvXt3NmzYQOHC7rvozZo1i4EDB7rdDqRqyc+MmJgYpkyZwgcffECzZs2yVFZ6183h8uXL7Nixg4CAAOrUqZOlY2aGjlKrMqxSKIyrnLI+8R/4Omd+UFNKKaVUHvbf//6XwoUL89dffzFjxoxU+2677TbAmt7EebCevXv30rdv32yNo1KlSrRp04aLFy8yZMgQzp1LGW7/0KFDPPHEE27zlStXjkGDBnH8+HHat2/vdlCc48ePM2XKlAzfw+nKUels1qwZhw4dokWLFmmO5zhnL7zwAomJicnbHfNLeuKozG3dutXt/jJlyhAQEMCBAwfSDJwEULVqVUSEDRs2sHbt2lT7Jk2axOeff+7bk3ThqLytWbMmU/k9+fbbbxkzZgzFihXjk08+ITAwkAcffJCuXbuya9cuBgwY4DHvjz/+yMSJE1NtW7BgAfPmzSMoKCjL83A+8cQThIaGMm3aNN5666003aD37NnDxo0bfSorvevqsHnzZs6cOUO9evWu+JQooBVOlUn3l4FOTr0A7t8Ohy/6Lx6llFJK5T4lS5Zk+PDhALz88supWmIefvhhwsPDWbt2LVWrVuXuu++mZcuWVK9enRIlSmT5XjtXkydPJiIigi+//JIbbriBbt260b59e6pUqUKxYsVo2LAhQJquqm+99RadO3dm1apV1KhRg4YNG9KtWzfatWtHnTp1KFOmDAMHDkweBCcrXCudLVu2TFXpfOaZZyhUqBDz588nKiqKrl270qxZMxo2bEjr1q0pXbq023I7deoEwNChQ+nYsSP9+/enf//+yYMihYaGEhMTw4ULF6hTpw733nsv/fv3Z9SoUYBVsXnggQe4ePEizZs3p1WrVvTs2ZPq1aszePBgnn766Uw9344dOwKwfPlyr+lWrFhB3759PS4vvfRSctqDBw/Su3dvjDFMmzYt1ajEU6dO5YYbbmDOnDlMmTLF7bGGDh3KkCFDuOmmm+jVqxdNmzalU6dOJCUlMWbMGKpXr56p5+pQqVIlZs+eTWhoKMOHDycyMpIuXbrQuXNn6tWrxw033JBmmhdP0ruuDo7z6+scqdnOGKNLFpb69euba9XRi8aUXW0MK6zlzk3GJCX5OyqllFIq+/z555/+DiFXq1ChggHMihUrPKZJSEgwpUuXNoD54IMPUu3bs2eP6dmzpylRooQJDg42VapUMS+++KK5ePGiadasmQHMjz/+mCqPp+0O99xzjwHMjBkz0uw7dOiQGTBggClbtqwJDg42N9xwgxkxYoQ5e/Zs8nP566+/3Ja7YMEC0759e1OmTBkTFBRkihcvbmrWrGn69etnFixYYBITE9M5W5adO3cawOTLl89jmoSEBNO8eXMDmHLlypnt27cn79u4caNp27atue6660z+/PlN7dq1zfvvv2+SkpKSz/OhQ4fSlDlu3DhTq1Ytkz9/fgMYwKxZsyZ5/+HDh03fvn1NuXLlTGBgoAFM1apVk/dfunTJTJgwwdSpU8eEhoaaokWLmtatW5tly5aZrVu3pknviwsXLphSpUqZsLAwc+7cuTT7n3rqqeRYvS2NGjVKjvGWW24xgHn00UfdHvOXX34xQUFBpkCBAmbz5s3J2xs1apR8Tr799ltzyy23mMKFC5vQ0FDTvHlz89VXX7ktr3v37gYwn3zySartEydONIAZOHCg23w7d+40gwYNMjfeeKMJCQkx1113nalevbp5+OGHzbZt25LTnTt3zgAmJCTEbTnpXVdjjKlZs6YJCgpy+7rwJiOff8B646G+JCYDo0mptBo0aGDWr1/v7zD8ZtlxaL3Z+rtsMKy7Ca7P79+YlFJKqeyydetWqlWr5u8wVA7766+/qFy5MmFhYRw7dsxvI4lei55//nleeOEFZs2aRa9evfwWR+PGjVm3bh1r1qyhcePGfosju/3yyy80atSIe+65h5kzZ2Yob0Y+/0TkV2NMA3f7tEutypLbi8GwCKt77ZaGWtlUSimlVO6UlJTEhg0b0mzft28f9913H8YY+vTpo5XNK2z48OGULVuWl19+OXkaGpV9XnzxRfLnz8/LL7/stxh0lFqVZW/eAPkE9PNZKaWUUrnVxYsXqV+/PhUqVCAqKoqwsDD279/Phg0bOH/+PLVr1+aFF17wd5jXnEKFCvHaa6/Rp08fZsyYke0DRl3L1qxZw6JFixg5ciSRkZF+i0MrnCrLArWdXCmllFK5XFBQECNHjmT58uVs2LCBEydOEBISQo0aNejcuTNDhw6lYMGC/g7zmtS7d2969+7t7zCuOk2aNPE4Vc6VpBVOlSMWHYMggdbF/B2JUkoppRTky5ePV155hVdeecXfoahcyHW6F5V9tG1KZasLSfDoLmi3Be7dCocu+DsipZRSSimllL9ohVNlq4RLMO9f6+8jiXDfVkjyf0u+UkoppZRSyg+0wqmyVYlgmFkNHOMHfXcCXt/n15CUUkoppZRSfqIVTpXtWhaF/1ZIWR+1G34+6b94lFJKKaWUUv6hFU6VI56rAM2KWH9fBnr9CfGJfg1JKaWUUkopdYVphVPliMAAmF0ditrjIO+9AP/ZDrlgZGallFJKKaXUFaIVTpVjyueHD6umrH92FKYc8l88SimllFJKqStLK5wqR3UqCYPLpawP2wW/n/ZfPEoppZRSSqkrRyucKseNuRFqFbT+DhLYc96/8SillFJKKaWujFxT4RSRh0VknohsFZFjIpIoIkdEZLmI3Csi4ibPNBExXpZt6Ryzl4j8KCInReS0iKwXkSEikmvOy9WgQD6YWx1ahMFvDaBdCX9HpJRSSimllLoSclPF6imgI3AO+Bn4DNgF3ArMAL7wUhFcDUx3s3zh6WAiMgGYBTQAfgSWAVWA94D5IpIv609JOVQrCCvqwo0F/B2JUkoppbJKRDK89O3bN1PHatCgASLC+vXrsxz36dOnEREKFSqUZl+JEiUQEY4ePZrl4/jT77//johQs2ZNf4eiFACB/g7ASQ/gN2PMGeeNIlID+A7oAPQBPnKT9wNjzDRfDyQinYHBQBxwizFmp729NLAC6AQ8BIzL+NNQSimllLq69enTJ822uLg4lixZQsGCBenSpUua/c2bN78SoSmlcplcU+E0xvzkYfsfdmvki8DtuK9wZtTT9uNTjsqmfazDIvIgsBIYISLvGmOSsuF4yo31p+CZ3TCvBhTJNa9EpZRSSqVn2rRpabatXLmSJUuWUKJECbf7M+uzzz7j3LlzREZGZluZSqkrJzd1qfXmkv2Y5eFmRCQCqA9cBD513W+MWQUcBMoAjbN6POXeB/9As99gSTwM0Pk5lVJKKeVBhQoViIqKIn/+/P4ORSmVCbm+wikiFYFB9upXHpK1FJGxIjJFRF4SkRgv93vWsx//MMac85Am1iWtymah+eCiXcmcewQm/ePfeJRSSil15UyfPp3o6GiKFi1KUFAQJUuWpE6dOgwdOpR9+/alSuvtHs4LFy4wduxYGjRoQOHChQkNDaVmzZqMGjWKkydPZkusly9fZvDgwYgItWvX5sCBA6n2b9y4kV69ehEeHk5wcDClSpXirrvu4vvvv09TVq1atRARvvvuO4/HGzRoECLCCy+8kLztzJkzvPTSS9SpU4eCBQsSEhJCuXLlaNasGc899xyXLl3yWJ6zY8eO0bRpU0SEnj17cuHCBZ588klEhOHDh3vMN3v2bESEW2+91afjKJWKMSZXLUA/YBrWgD6rgETgMvCqm7TTAONh+QOo5SbPUHv/F15iGGenGZNevPXr1zcqcwZuM4YV1hK80pj1p/wdkVJKKZXan3/+6e8Q8owVK1YYwFSoUMFruscff9wAJjg42LRs2dL07NnTtGnTxlSpUsUA5quvvkqVvn79+gYwsbGxqbYnJCSYxo0bG8AULlzYtG/f3nTp0sWULFnSAKZSpUpm//79afIApmDBgmniKl68uAHMkSNHkredOXPG3HXXXQYwt912mzl58mSqPJ988okJCgoygKlTp47p2bOnadq0qRERA5jXXnstVfo333zTAObee+91e27Onz9vwsLCjIiYv//+2xhjTGJiYvLzLFasmGnbtq3p2bOnadmypSlbtqwBTEJCQnIZW7ZsMYCpUaNGqrJ37dplKleubADzxBNPmKSkJGOMMXv27DH58uUzxYoVM+fOnXMbV7NmzQxg5s+f73a/ujpl5PMPWG881a087fDXAnzgUnFMBEYC+d2kHQY8DFQHCgJlgbbARjvvYSDcJc9Ie99MLzG8YqeZnF68WuHMvHOXjKkbm1LprLjGmPiL/o5KKaWUSqEVTt/5UuE8ceKECQwMNMWKFTO7d+9Os//PP/80+/btS7XNU4XzwQcfTK7oxcXFJW9PSEgwd9xxhwFMq1atUuXJSIXz8OHDpmHDhskVxIsXU39J2b17tylQoIABzKRJk1Lt++abb0xwcLAREfPDDz8kb4+LizOBgYEmNDTUnDqV9pf2uXPnGsC0aNEieduiRYsMYJo1a5amQnj58mWzcuXKVLG5q3CuW7fOlCxZ0gQEBJj33nsvzXE7duxoAPPRRx+l2bdp0yYDmPDwcJOYmJhmv7p6ZVeFM9d1qTXG9DfGCBAK1ADeAZ4H1opIOZe07xhj3jXG/GmMOWOMOWSMWQTcDKwFSpEyQJCDYz7PTN81KCID7Dk71x85ciSzxVzz7KDCQAAAIABJREFU8ueDT6tDYXsCmt3noZ/ez6mUUioPeX43yErflgHb0+YfsN33/M/vTpv/ri2+55+SC25fOX78OJcuXaJatWpuBwGqVq0a119/fbrlnDhxgv/9738ATJw4kdKlSyfvK1SoEFOmTCEkJITly5ezadOmDMe5Y8cOmjRpQmxsLCNHjmTGjBkEBQWlSjNx4kTOnTtH69atGThwYKp9d9xxB/3798cYw9ixY5O3ly5dmjZt2nD27Fk+/TTNUCLJgy05TyFz+PBhAFq0aJHmPtaAgACio6PTxObsyy+/pGXLlpw+fZrPP/+cIUOGpEnz8MMPA/D++++n2TdhwgQABgwYQGCgjvKoMi7XVTgdjDHn7IrkE1iVxjpYc2T6kvciMNpevdNld4L9mHYCphSOfQnudhpjphhjGhhjGpQsWdKXkJQHlULhf1VT1hcchbcPeE6vlFJKqbyrQoUKlC5dmp9//pn//ve/7Nq1K1PlrF27lgsXLlClShWaNGmSZn9ERAS33347YI2emxGrV6+madOm7N27l8mTJ/PKK6+4Tbdq1SoAj/OL3n///W6P70jvOpJvXFwcS5cupVChQqmmlXHcwzphwgQ++OCDDM0T+v7779OpUycKFizIihUr6NChg9t0t956KzVq1CA2NjbVvbKnTp1i1qxZBAUF8Z///Mfn4yrlLNdWOF04pkK5S0Q8/4ST2jb7Mdxl+x77sYKXvI6f1vZ4SaOySZdSMNTpKj35F/x4wn/xKKWUUipnBAQEMGPGDIoWLcqrr75K5cqVKVOmDJ06dWLy5MmcPn3ap3IOHjwIQMWKFT2mufHGG1Ol9VWXLl04duwY48ePZ8CAAZmOwXH8EydOcPbs2eTtd911F8WLF+enn37i77//Tt4+c+ZMLl++TJcuXShYsGDy9lq1ajF69GhOnz7Nf/7zH0qWLEnlypXp27cvCxcuJCnJ/Qx+27dvZ8iQIcmDFDVq1Mjr83bXyjl9+nTOnDnD3XffTdmyZb3mV8qTvFLhPIE1NUogUMzHPMXtR9dPrt/sxxoiUsBD3oYuaVUOe/NGuLmw9fdloOsfcCzRryEppZRS6Xq+IpgWvi1TqqbNP6Wq7/mfd1Ov+aqW7/kHlEub3x9uv/129u7dy+zZsxk4cCAlS5Zk4cKFDBo0iMqVK7N169Z0yzD2/Tcikm6ajOrduzcAr776Ktu3u+kHnYEY3AkODqZXr14YY5g+fXrydsff7lpMn3rqKfbs2cN7771Hjx49OH/+PNOnT6djx440a9aMc+fSTrxQvnx5oqOjuXz5MkOHDk23Mn/vvfcSFhbGnDlziI+PB6xuwwCDBw/O0HNUylleqXDeglXZPAH42o+gm/0Y67zRGLMf2AAEA11dM4lINBABxAFrMhmvyqDgAJhfA0oEQT5gRHkoprcJKKWUUlelQoUK0bNnTyZNmsSWLVvYt28fHTp0IC4ujkceeSTd/BEREQCpWghd7d5t3fQaHu7a2c27119/nWeffZaDBw9yyy23sGXLlkzF4NgeFhZGaGhoqn2OSuXHH3+MMYZff/2V33//nYoVK3LLLbe4LS88PJwhQ4bwySefsH//fmJjY6lSpQpr167l7bffTpO+QIECfPvtt8TExLBy5Upat27tdaqYggULcv/993Pu3Dk++ugjvv/+e7Zu3UrNmjU9xqSUL3JFhVNE/k9E7hGREDf7mgEf2qsfGmMu29vrikg7Ecnnkj5QRB7Dmv4EIO07MOX+ztdFpJJT3lKAox/Ba8YY930UVI64Pr81iNCKujDsesjgD4ZKKaWUyqMiIiKS5530ZZCfxo0bExISwo4dO1i3bl2a/f/88w/Lli0DrMF2/p+9+46Pssr7//86SUijg0AghN6bSLGBFMHbFQuiqAgiKCAiLOuy6+ruunuv63dVXP253gqCqAhSVFRUBEFxA6KgUqX3FgIJJYQSSD+/P66BFJKQmUyYzOT9fDx4TK5znXOuz0iI88lp7nruued46aWXOHr0KL1792bt2rWX1OnZsyfgJI0FmT59eqHP79SpEx06dGD//v0sX7784ujmsGHDij1i2qVLl4sjj4X9N4uIiODLL7/k7rvvZtWqVdx8882cOHGi0D7Hjh1LUFAQU6ZMubhZUEGbDIm4o0wknEBTYBaQYIz5zhgz2xjzpTFmC/AD0ARYCPwtV5tGwALgqDFmlTFmnjFmMXAAeNVV52lr7ZL8D7PWfgK8BUQBm4wxC4wxnwG7cI5Y+ZxiblAk3tWrOtxUzddRiIiISGnYuXMnM2bMKHB654IFCwBnY6HLqVatGo888gjgTPfMfWpASkoKo0ePJjU1lb59+3L11Vd7FOvTTz/NG2+8QVJSEn369GHVqrwT38aMGUNERASLFy/m3XffzXPvm2++Ydq0aRhjmDBhQoH9XxjlnDZtGnPnzsUYc3E6b26LFy/m22+/JSsrK095RkYGixcvBor+bxYaGsq8efMYNGgQ69ato3fv3hd3vs2vSZMm9OvXj127dvHZZ59RpUoVHnrooUL7FimWws5LuZJ/gMbAP4FYIA44D6TibNrzCXB3IW3+A6wE4l31z+Mkje8BnYvx3MHAj8BpIAVYC4wFgoobu87hLH2pWdbuL/gcYhERkVKlcziLrzjncK5YscICNiwszF5//fV20KBBduDAgbZVq1YXy5cuXZqnTWHncJ45c8Zef/31FrCVK1e2/fv3twMHDrS1a9e2gG3WrJmNi4u7pA3FPIfzgnfeeccGBQXZSpUq2djY2Dz35syZY0NCQixgO3bsaAcPHmy7detmjTEWsC+++GKh/y2OHj1qK1SocPHs+dxnb+b2/PPPW8BWr17d9unTxw4ePNj279/f1qlTxwI2JibGHj58+GL9gs7htNY5s/ORRx6xgG3ZsqU9dOhQgc/75ptvLsY0bty4QuOXwOetczjLxCo5a+0+4O8etHmyhM+dA8wpSR9Sug6mwsAtkJwJqztD1TLxHSsiIiKeaNu2La+88grLly9ny5YtbNq0iaCgIOrXr8/YsWMZP348LVq0KFZflSpVIjY2lkmTJjFnzhyWLl1KVlYWjRs3ZtSoUfzxj3+kWrWST5saMWIEkZGRPPzww/Tr14/58+dz6623AvDggw/SqlUrXn75ZZYtW8bmzZupWrUqt99+O08++SR9+vQptN9atWrRr18/vvjiC6Dw41UGDhxIWloaK1asYMeOHfzwww9UrlyZBg0a8Lvf/Y7Ro0dTo8bl99QMCgri3XffJTIykkmTJtGjRw++++67S85D7dGjB2FhYaSlpWmzIPEKYz3cwUscXbp0sbnPKxLvyciGFr/A/lTnun9N+KwdBGltp4iIXCHbtm2jdevWvg5D5IqZPXs2Dz30EDfffDPfffedr8MRH3Ln558xZq21tktB98rKGk6RS1QIgolNcq6/OAEvHfRdPCIiIiKBLC0tjRdeeAGg0LWnIu5Swill2v21YUL9nOtn98GSJN/FIyIiIhJopkyZwvDhw+nQoQNbt26ld+/e3H777b4OSwKEEk4p815qAjdVdb62wKCtsPucT0MSERERCRhLly5lxowZnDhxgiFDhvDxxx/7OiQJINqCRcq8CkHwcRvovBYOpzsbCN29GVZ1gsr6DhYREREpkU8++cTXIUgA0win+IWoMJjfDsJcGwZtOQfDtkO29rwSERERESmzlHCK37i2CkzJtVP6/OPw/w74Lh4RERERESmaEk7xK8PrwvjonOtvTzrHp4iIiIiISNmjFXDid15pCptSoHkEvNHcWeMpIiJSWqy1GKNDoEWk/LDWe+vWlHCK36kQBIvaQ3iwryMREZFAFxQURHZ2NsHB+p+OiJQf2dnZBAV5Z1RHY0Pil5RsiojIlRAeHs65czqLS0TKl3PnzhEREeGVvpRwSkCwFiYehGf3+joSEREJJJUqVSI5Odmr08tERMoyay3JyclUrFjRK/1pSq34vdQsGL4dPjrmXLepCIPr+DYmEREJDNWrV+f06dMcOXKEmjVrEhoaqvWcIhKQrLWkp6dz4sQJMjMzqV69ulf6VcIpfq9CEJzOyrl+dDs0jYDrqvguJhERCQxBQUHExMSQlJTEwYMHyczM9HVIIiKlJiQkhKpVq1K7dm2vreFUwil+L9jA3DZwwzrYdg7SLNy9GX7pBDHhvo5ORET8XUhICLVr16Z27dq+DkVExO9oDacEhKohsKA91HD9CiUhHfpvhpSsotuJiIiIiEjpUcIpAaNpBHzaFkJcS2vWn4Vh2yBb+zyIiIiIiPiEEk4JKL2qw6TmOdefHod/7PdZOCIiIiIi5ZoSTgk4j9WD8dE5188fgA8TfRePiIiIiEh5pYRTAtKrTeHWXDs5/3Y3nNXGgiIiIiIiV5QSTglIIUHwYRtoGQExYbD0aqikPZlFRERERK4ofQSXgFWtAizqABWDoU6or6MRERERESl/lHBKQGsS4esIRERERETKL02plXJn41n41wFfRyEiIiIiEvg0winlyuITcN9WOJsF1UJgbPTl24iIiIiIiGc0winlyvQEJ9kEGL8LFp3wbTwiIiIiIoFMCaeUK9NbQdfKztfZwANb4dezPg1JRERERCRgKeGUciUyGL5sBw3CnOuzWXDHJjic5tu4REREREQCkRJOKXeiwmBhe6gS7FwfSnOSzrOZvo1LRERERCTQKOGUcqldJfikLbhyTtafhcHbIMv6NCwRERERkYCihFPKrVtqwFstcq4XnIDf7warpFNERERExCuUcEq5NqoePBWTc/1GPCxJ8l08IiIiIiKBRAmnlHsvNYH7ajlfP9cIbq3hy2hERERERAJHiK8DEPG1IAMzW8FDdeCuq3wdjYiIiIhI4NAIpwgQHqxkU0RERETE25RwihQiPRv+uFtndIqIiIiIeEoJp0gBTmVCv43w6iHn9bTO6BQRERERcZsSTpECrD8Dy5Kdr39NgYFbICPbtzGJiIiIiPgbJZwiBehVHaa1zLn+9iSM2qEzOkVERERE3KGEU6QQj9SFfzTKuZ6RCH/d57NwRERERET8jhJOkSL8vSGMiMq5fvEgvH7Id/GIiIiIiPgTJZwiRTAGprSAO2rmlD25G+Ym+i4mERERERF/oYRT5DJCguCjNnBjlZyyYdvhmyTfxSQiIiIi4g+UcIoUQ2QwLGgPbSKd6wwLE3ZDljYREhEREREplBJOkWKqUQGWdICYMGhXEZZcDcHG11GJiIiIiJRdZSbhNMb81hjzsTFmmzHmhDEmwxhzzBiz1BjzkDGm0I/2xpjBxpgVxphTxpizxpg1xpixxpgi35+n7aT8qh8O310NKzpCdJivoxERERERKdtCfB1ALk8DtYHNwEogBWgI3Az0AQYaY+6x1mbnbmSMmQQ8AaQC3wEZrvpvAn2MMfdZa7PyP8zTdiLNIwsut9bZZEhERERERBxlaSRvEFDdWtvJWnuntXaQtfYGoD2QCPQHhuVuYIy5FydpTAA6WGvvsNYOAJoD24ABwLj8D/K0nUhhvj4B/TbBOf2KQkRERETkojKTcFprf7DWphRQvgWY5Lq8Jd/tP7ten7bW7srVJhEY47p8poApsp62E7nEBwlw12ZYnAT3bYGM7Mu3EREREREpD/wlocp0vaZeKDDG1Ac6A+nAvPwNrLXLgXggCri+pO1ECnM0AzJdu9UuSnKOTNHutSIiIiIifpBwGmMaA4+7LhfkunWN63WLtfZ8Ic1X56tbknYiBfpDDPylQc713KMwbpezplNEREREpDwrS5sGAWCMeQToCVQA6gM34iTGL1pr5+eq2tj1eqCI7g7mq1uSdiKF+n+NITkTJh92rqcchhoh8K8mvo1LRERERMSXylzCCXQj7+ZAmcDfgP8vX71KrtdL1n3mctb1WtkL7UQKZQy80dxJOuccdcpeOAjVQ+CPDYpuKyIiIiISqMrclFpr7UhrrQEigbbAf4B/AD8ZY+rlqnrhAAp3Jy562i6nA2Mec53ZuebYsWOediMBJsjA+63g9ho5ZU/thXcO+y4mERERERFfKnMJ5wXW2vPW2q3W2qdwdpW9GueMzAvOuF4rXdI4x4V7Z3KVedoud2xvW2u7WGu71KpVq4hupLypEATz2kKPqjllj+2EeUd9F5OIiIiIiK+U2YQzn+mu1zuNMRVcX+93vTYsol1MvrolaSdSLBHB8GV76OT6tYUF4tN8GpKIiIiIiE/4S8KZjLOWMwS4MGFxveu1rTEmopB2XfPVLUk7kWKrGgKLO0CbSHi3JTwZc/k2IiIiIiKBxl8Szh44yWYycBzAWhsHrANCgfvyNzDG9MTZ5TYBWHWh3NN2Iu6qFQrru8CjdX0diYiIiIiIb5SJhNMYc5MxZogxJqyAe92Ad12X71prs3LdftH1OtEY0yxXm9rAZNflS9ba7HzdetpOxC2hBfwLS8mCbUXtkSwiIiIiEiDKyrEoTXHWab5pjFmHM7pY2VXexlVnIc7xKBdZaz8xxrwFjAE2GWOWAhlAH6AK8Dl5NxoqUTuRkjqdCbdvgu3nYHlHaFPR1xGJiIiIiJSespJwLgeeB24CWgA34hxfkgB8Csyy1n5eUENr7RPGmB+AsUBPIBjYDrwHvFXYKKWn7URK4r4t8MMp5+u+v8L3HaFZpG9jEhEREREpLcZaj4+jFKBLly52zZo1vg5D/MTPp51E86xrYniDMFhxDTQI921cIiIiIiKeMsastdZ2KehemVjDKVJeXFcFvmoPEa5/eQfToM+vcETHpoiIiIhIAFLCKXKF9awG89tBqHGud593Rj2Ppfs2LhERERERb1PCKeIDt9aAj9s6C4cBtp5zks4TGT4NS0RERETEq5RwivhI/6tgdpucf4QbU5ykM0lJp4iIiIgECCWcIj70QG2Y0crZkhlgw1n4/W6fhiQiIiIi4jVKOEV87KEoeLel83XHSvBqU9/GIyIiIiLiLWXlHE6Rcu2RulAlBHpXgxoVfB2NiIiIiIh3KOEUKSPurVVwubVgTMH3RERERETKMk2pFSnDPkyE/9kI57J8HYmIiIiIiPuUcIqUUbMTYcg2WHoS7tykpFNERERE/I8STpEy6nAaZLu+/m8y3LEJUpR0ioiIiIgfUcIpUkY91QBeaJxzHaukU0RERET8jBJOkTLszw3hxVxJ57Jk6LcRzmb6LiYRERERkeJSwilSxj3TECY2ybn+/hT026SkU0RERETKPiWcIn7gTw3g37mSzhWn4LZNcEZJp4iIiIiUYUo4RfzEHxvAq01zrn84Bbdvgizru5hERERERIqihFPEj0yIgddcSacBRtSFYOPTkEREREREChXi6wBExD1PxkCQgcrBMCzK19GIiIiIiBROCaeIHxpf39cRiIiIiIhcnqbUigSIkxkwdBskpvs6EhERERERhxJOkQBwOhN+sxFmJUKvDRCf5uuIRERERESUcIoEhB9Pwdozztfbz0HP9XAw1bcxiYiIiIgo4RQJALfVhA/bQIhrx9o9qdBjPew579u4RERERKR8U8IpEiAG1obP2kKoK+k8kOaMdO4459u4RERERKT8UsIpEkDuvAq+bA/hrn/Z8elO0rnprG/jEhEREZHySQmnSIC5tQYsag+Rrn/diRnQcwP8ctq3cYmIiIhI+aOEUyQA9a4OSzpAlWDn+mQm9PkV1ijpFBEREZErSAmnSIDqXg3+2xFqhjjXbSOhZaRvYxIRERGR8kUJp0gA61wZll8Dv6kBizpA5RBfRyQiIiIi5Yk+fooEuLYV4esOvo5CRERERMojjXCKlFNT4uH/Dvk6ChEREREJZBrhFCmHZiXAE7vAAqcz4a8NwRhfRyUiIiIigUYjnCLlTLaFaUecZBPgb/vhD3ucchERERERb1LCKVLOBBlY2B76VMspe+0QPLodMrN9F5eIiIiIBB4lnCLlUKUQ+Ko93HNVTtmMRLh3C5zP8l1cIiIiIhJYlHCKlFPhwfBxWxgRlVP25Qm4bSOcyvRdXCIiIiISOJRwipRjwQamtYQ/xeSULT8FvTfA0XTfxSUiIiIigUEJp0g5ZwxMbAoTm+SUrT8LfX/Vmk4RERERKRm3jkUxxlQDegHXAHWAasBJ4CiwDlhurU32cowicgX8qQHUrACP7XCun2sEIfqVlIiIiIiUwGUTTmNMMHAP8ARwE3DhtL7cp/ZdOFDBGmO+ByYD86212n5ExI+MqAs1QiA5EwbU8nU0IiIiIuLvikw4jTEPAi8B9XESzOPAT8BWIAk4DVQBagJtgOtxRkB7AnHGmGestR+WVvAi4n2FJZpp2RCmEU8RERERcUOhCacx5kecBPIY8Doww1r76+U6NMZ0BIYDDwKzjTG/tdZ28064IuILienQcz081cAZBRURERERKY6ixiuaAhOABtbaCcVJNgGstRustU8CMcAfXP2IiJ86kwn9NsKO8zByB/zrAFh7+XYiIiIiIkVNqW1qrU3xtGNrbTrwH2PM2572ISK+dz47Z5E2wLP74EgavN7cOVZFRERERKQwhY5wliTZzNfPucvVMcZUMMb0Mca8aoz5yRhzxBiTboyJN8Z8YozpVUi7940xtog/2y/z3MHGmBXGmFPGmLPGmDXGmLHGGK1UE3GpHQrLOkKfajllkw7DoK2Qqm3BRERERKQIbh2LUop6At+6vk4A1gIpOBsR3Qvca4x53lr790La/wjsLqD8SGEPNMZMwtl5NxX4DsgA+gBvAn2MMfdpl10RR5UQWNgBhm2Dj445ZZ8cg+MZ8Hk7qFpWfpKIiIiISJlS7I+JxpgaQCNgv7U2KVd5XeBF4GpgP/CP4q73zCUb+BR43Vq7It9zHwBmA38zxsRaa2MLaP+Otfb94j7MGHMvTrKZAPSw1u5yldcBYoEBwDiczZJEBGeH2jltIGo3vB7vlC1LhpvWw6L2UD/ct/GJiIiISNnjztTRPwOrcTYDAsAYEwr8AAzFSTj7A7HGmGh3grDW/tdaOzB/sum69xHwvuvyIXf6LcKfXa9PX0g2Xc9KBMa4Lp/R1FqRvIIMvNYMXmqSU7YpBa5fB5vO+i4uERERESmb3EmoegP78o1ePgA0BpYDvwEmAdVwRge9ab3rtX5JOzLG1Ac6A+nAvPz3rbXLgXggCudYGBHJxRh4ugHMbAUhrk2D4tPhtUO+jUtEREREyh53Vl7VBzbkK7sDZwPLkdbavcA3xph+wG3kjCJ6Q3PXa2FrMnsbYzoAlYBEnFHXb6212QXUvcb1usVae76Q/lYD0a66Kz0LWSSwDY2CuqFwzxa4uhJMbn75NiIiIiJSvriTcFYHjucruwHY6Uo2L1iPMxrqFcaYKGC46/LTQqo9XEDZVmPMIGvtpnzljV2vB4p47MF8dUWkAH1rwI/XQHQYhAf7OhoRERERKWvcmVJ7Hqh54cIYE4Mz6vljvnppQFjJQwNjTAgwC6gKfGetXZCvygZgPNAWZ3SzHs6o6684O9wuLWA9aSXXa1HHvlxYjVbZ8+hFyof2laBGhbxl1sK8o5BlC24jIiIiIuWDOwnndqC7a7dagME402m/z1evPs60Vm+YgnNUSRwFbBhkrf2PtfYNa+1Wa22KtfaItXYhcC3wE1CbS6f2Xjiq3uOPwsaYx1xndq45duyYp92IBKxX4uD+rXDPZkjR4UIiIiIi5ZY7CecHQEXgF2PMx8A/cUYCv7hQwRgTBnQCdpQ0MGPM68AInKNL+lhrE4rb1lqbjnNUC0C/fLfPuF4rUbgL984UdNNa+7a1tou1tkutWrWKG5ZIufBDMvzJNcn+yxPQawMkpPk2JhERERHxDXcSzreAOUATYCDOLq+jrLWnctW5EycpXV6SoIwxr+JMlT2Gk2zuukyTgmx3veafUrvf9dqwiLYXjn7ZX0QdESnAjVXhTzE512vOwHXrYEtRk9hFREREJCAVO+G01mZbax8CmgI3AtHW2o/zVdsL3AfM8DQgY8zLwATgBHCLtXarh11dWG+a/3TAC0estDXGRBTStmu+uiJSTEEGJjaFt5rDhX2EDqbBjetgaZJPQxMRERGRK6zQhNMYM8gYc8mmOdbafdban6y1pwu4t85a+6k701/zPfMl4CngJE6y+etlmhTlftfr6nwxxgHrgFCc5Dh/DD1x1qEmAKtK8HyRcu3xaFjQHiq5ss7TWXDbJnivsMONRERERCTgFDXCOQc4aoz5yhgzwhhTqosVjTHPA08DyTjJZpGji8aYjsaYO4wxwfnKQ4wxE3Cm5AK8VkDzC+s7JxpjmuVqWxuY7Lp8qZBzPEWkmG6rCT9cA9GhznWmhRE74Nm9zk62IiIiIhLYjC3kU58x5ingHpwdXwGygR+A+cDn1tqDBTb0JAhj7iJn86E1wJZCqm631r7kanO3K5YkYCdwCOcYk/Y4x6NkA3+21r5cyDMnA2OAVGApkIGzI24V4HNgoLX2svtrdunSxa5Zs6YY71Kk/IpPgzs2wYZcE9x/Gw3/19x3MYmIiIiIdxhj1lpruxR4r7CEM1fjujiJ5z3ATUAIzpEi64FPgfnW2u2F91CsAIcD04tRdbm1tperTWPgdzgJcUOcNZsWJ/FcAUyy1q69zHMHA2NxktRgnI2G3gPeKu7ophJOkeI5kwkPbIWvkyAiCJZ3hK5VfB2ViIiIiJRUiRLOfB1VB/rjJJ99gXCcJG8nTvL5ubW2XGVfSjhFii8zG57cDX2rw906UUhEREQkIHgt4czXaUXgdpzk8zac6awXRhg/w5mW+r319AF+QgmniHeczoQqIb6OQkRERETcVVTC6c45nHlYa1OstR9bawcBtXDO4HwfiMCZ6vpf4K+e9i8i5ce2FGjyE7wV7+tIRERERMSbvDKeYK1NBxYCC40xQUBPYABw1Bv9i0jgOp7ubCh0IhOe2AU7zsGrzSDY+DoyERERESkpr09gc222E+v6IyJSpAxElPUjAAAgAElEQVQL1XP9JHo9Hnadhw/bQGVNsRURERHxax59nDPGROEcPRJeWB1r7UpPgxKR8qNuGHx/DQzdBp8dd8oWJUG39bCgPTQs9KeMiIiIiJR1biWcxpj7gH8CLS5T1brbt4iUX5HBMK8tPLsPXnSd8LspBbquhc/aQvdqvo1PRERERDxT7KTQGDMImA0Y4BSwHzhbVBsRkeIKMvBCE2gZCaN2OFNtj2XAzb/C1BbwSF1fRygiIiIi7nJnFPIvrtffAW9ZazNLIR4RKeeGRUHTcLhni5NwZlh4dAdsToFXmoLRZkIiIiIifsOdY1GaAyuttW8o2RSR0tS9GqzuDB0q5pRFBCnZFBEREfE37oxwJgFxpRWIiEhuDcPhx2tg6Hbn+p+NfRuPiIiIiLjPnYTzG6B7aQUiIpJfpRD4tC2kZTtrPHOzViOeIiIiImWdO1Nq/xeoYoyZaIwJLq2ARERyCzIQke8nTmY29NsEbxxyEk8RERERKZuKPcJprT1ojOkOfAHcY4z5DjgEZBdS/wXvhCgiktdTe2FxkvNnw1mY3ALC3Pn1mYiIiIhcEe4ci2KAcTibBwUDTXHO27ykqqtcCaeIeN35LFh5Kuf6vQTYes45r7NumO/iEhEREZFLubOG8xngt0AmsBDYjc7hFJErLCIYlneEx3fCjESn7KfT0GUtzG8H11bxbXwiIiIiksOdhHMEcA7obq3dUErxyBWUnJzMqVOnaNiwoa9DEXFLeDBMbwUdK8Ef9jjz+g+nQ4/1MLWlc5aniIiIiPieO6ueooHvlWwGjpkzZ9KoUSN69OjB1KlTSUpK8nVIIsVmDDwZA0s6QHXXr87SLAzfDr/f7WwsJCIiIiK+5U7CGY8zwikBYvbs2QCsWLGCxx9/nKioKO6++27mzZvH+fPnfRydSPH0rQGrO0PbyJyy/xyCWzdCUobv4hIRERER9xLOj4CexpiKpRWMXDn7f/6RadEh/KlDY+pXDAcgIyODL774gvvvv5+oqCgeffRRYmNjyc7WUJGUbU0jYFUnGHBVTtnxDO1cKyIiIuJrxhbzEDtjTDjwHZAKPGat3VOagfmLLl262DVr1vg6DLct+/0Iep2Jz7k+ksTsPUf4ZF8CyemZeerWr1+fIUOGMHToUNq2bXulQxUptmwLzx9wzuf8ubOTiIqIiIhI6TLGrLXWdinwnhsJ5zdAGHATzk61eyn8HE5rrb3Vs3D9iz8mnDY7m4NDb6FhRIVL7qVlZbMo7hiz9hxhYdwx0rLy/vV27NiRoUOH8uCDD1K3bt0rFbKIW5IyoMal395kWQg2Vz4eERERkUDmrYTTnXmV1lob7EZ9v+WPCefmBZ/S7otpl613Mi2DefsS+GD3YX5MTM5z6GpQUBC33HILw4YNo3///kRGRhbaj0hZ8PZhmJ0IH7eFOqG+jkZEREQkcHgr4ezjzkOttd+5U99f+WPCufzxQfTMTHarzb4z55i1+wgf7D7MrtN5946qXLky9913Hw8//DA33XQTQUFaOCdly0+noMcGyLAQHQqftoPrdF6niIiIiFd4JeGUgvlbwpmRep7kUXdQK6yA+YbF9PPRZD7YfYQP9x7hRFrebUAbNmzI0KFDefjhh2nevHlJwxXxisnxMG4XF0fpQw280RxG1XWOVxERERERzynhLEX+lnAu/3gOzea/TbRrZ9qSyMjOZmHcMWbuOszCuGOkZ+f9XrrxxhsZNmwY999/P9WqVSvx80RKYvEJGLwNTubaE+uRKJjUHCLKxQIAERERkdKhhLMU+VvC+dBDDzF3zmx6RtVgSNO6DGxch6qhno92XpCUlsGHe48wc9dhfj52Ks+98PBw7r77boYPH07fvn0JDtane/GNvedhwGbYmJJTdk0l+KQtNNGOtiIiIiIe8SjhNMZ8DzxjrV1Zggd3A1601vbwtI+yzp8SzpSUFOrUqUNKSs6n7fDgIG6PqcWQpnW5PaYWocElX385Z88RhizbWOC9evXqMXToUIYNG0br1q1L/CwRd53LgjE7YWZiTln1EJjVGvrV9F1cIiIiIv6qqISzqOyiFbDCGPOtMeYBY0xYMR8WZox50BizFPgeaOF+yFIaIiMjWb58OU8++SRRUVEApGZl8+n+RO75bgNRc5Yx+octrEg4WaLnLD+SVOi9w4cPM3HiRNq0acP111/PlClTSE52bwMjkZKIDIb3W8FbzaGCa/3myUy4YxO8Fufb2EREREQCTVEjnFWB54AngGDgDPAjsArYBpwATgNVgJpAG+AGoBtQCeeszknAP6y1p0v1XfiQP41w5paZmUlsbCyzZs3is88+4+zZs3nuN6oUwUPN6jK0WT1aVK1Y7H5TM7OoO3cZyemZl6/sEh4ezoABA3jkkUe4+eabNeVWrpifT8PALXAoDUIMxF4N3bXcWERERMQtJVrDaYxpAvwWGAZUA4pqYIAk4D1gsrV2vycB+xN/TThzO3fuHF9++SWzZs1iyZIlZGbmTRa7XlWVoc3qMqhJXWpFFH2A4cd7E3gg9lePY4mJieHf//43DzzwgMd9iLjjWDo8uBXuqAlPxvg6GhERERH/461zOCOAnkAvoCNQG6gKJANHgXVALLDCWptW8rD9QyAknLkdO3aMDz/8kA8++IDVq1fnuRdiDL+pfxUPN6/HXQ1qE1bAes87vlnHwrhjxX7eS11bsDHpDPP3J3I+KxuARYsWcdttt5XsjYi4Ics66wvyH5FyMBViwnR0ioiIiEhRtEttKQq0hDO3HTt2MGvWLGbNmsX+/fvz3KsWGsL9jaN4uHk9utWpDsDR82lEz11OZjG/pxpVimDfA85+UqfSM/hobwILktKY/+s2QiqUfOdckZI4kArXrIHbasDUFlApxNcRiYiIiJRNSjhLUSAnnBdkZ2ezcuVKZs6cyccff8ypU3mPPWlWJZKhzepxLjOLiRv3Fbvfv1/TlOc6Nbv0RlR96HYr3NgHqtYoafgibkvLhh7r4ZczznXrSOfolDbFX84sIiIiUm4o4SxF5SHhzC01NZUvv/ySmTNnsnjxYrKysjzqxwB77r+JxpUjC68UFATtu0L3W6H9tRCiISa5MlKz4Le74Z0jOWWRQTCtJQyu47u4RERERMoiJZylqLwlnLklJiYyd+5cZs6cyfr1691q26tuDWL7dS1+g8rV4IY+0O0WiG7kXqAiHnr/CDyxC85n55SNqQevNYOwkh9ZKyIiIhIQlHCWovKccOa2adMmZsyYwaxZs0hMTLxs/fd7tGNY82jPHtaklTPqeW1PCC9ihFTECzadhXu3wK7zOWWdKsHHbaFphO/iEhERESkrlHCWIiWceWVmZrJkyRJmzJjBF198QXp6+iV1QowhblBPoiLDSvaw0DDo0gNuuhWatb1kK9GVK1cSGRlJx44dS/YcKfdOZ8LIHTAv1wbMVYLhvVZwby3fxSUiIiJSFijhLEVKOAuXlJTERx99xPvvv88vv/yS517FkGAGNq7D8ObR9KrrhY2BLm401BeqOrvm3njjjaxatYrOnTszcuRIHnzwQapWrVryZ0m5ZC28EQ9/3AMZuX5sru8MHSv7Li4RERERX1PCWYqUcBbPtm3beP/995k5cyYJCQl57jWpHMHS556m8ZHdkFT8MzwLFBwMHa7jQMM2NLnrPrJzfXtHRERw3333MWrUKLp164bR4YrigdWn4f6tsD8VxtaDN1v4OiIRERER31LCWYqUcLrnwpTb6dOn8+WXX5KRkUGDBg3Yt28fQVjY9iv8uATWrYTMjBI9K+7seZ5YuY2v4i5NYlu3bs3IkSN5+OGHueqqq0r0HCl/kjPgxYPwXCMID/Z1NCIiIiK+5ZWE0xgzEphtrT1/2crliBJOzx0/fpy5c+cSHh7OqFGj8t48ewZ+iYUfvoGDuz1+RufPV7HuxOlC74eGhjJgwABGjRpF7969CQrS1qPiueQM+M8h+HND7WIrIiIi5Ye3Es5s4CTwPjDFWrvLaxH6MSWcV8DBPfDDEvg5FlLOFLvZ+hOn6fT5qmLXb9q0KSNHjmT48OFERUV5EqmUY9bCwC3w2XFnF9sP20BzbaIsIiIi5YC3Es4vgduAYCAbWApMAr6y5XherhLOKygjHdavcpLPbeudT/hFGLtyK5O3xbn9mJCQEPr378+oUaO45ZZbNOopxbLgONy1Oee6UjBMaQFD6vguJhEREZErwWtrOI0xMcAY4FGgNmCBOGAK8K61toQ7vvgfJZw+cjwBfvzW+ZN09JLb5zOzqDd3GcnpmcXqrkKQoVXVimw6eTZPeaNGjRg5ciSPPPII9erV80roEpgu7GL71B5Iz/VjdXgUvNkcKmqtp4iIiASoohJOt4ZurLVx1tq/ADHAUOAnoAHwL+CgMeYDY8wNHgRYwRjTxxjzqjHmJ2PMEWNMujEm3hjziTGm12XaDzbGrDDGnDLGnDXGrDHGjDXGFPn+PG0nZcBVUdB/KLw0HX7/L+hyEwSHXLz9yf7EYiebAP0b1GbjPd1Yded1PNI8msgQJzvYv38/zz77LA0aNGDAgAF8/fXXZGVlef3tiP8zBsbXh1WdoFlETvn7CdBlLWw8W3hbERERkUBV4l1qjTFXA2OBB4ELK5Y24Ey3nW2tTStGH32Bb12XCcBaIAVoA7RzlT9vrf17AW0nAU8AqcB3QAbQB6gMzAfus9ZekiF42i4/jXCWHZknT/CvO2/m/qjKjP5xKysSTha77ZLfdOZ/onN2qz2dnsnsPYd5e8chNpzIu260YcOGjBo1ikcffZS6det6LX4JHGcyYcxOmJ1r8D3MwGvN4PF6TnIqIiIiEihK/VgUY0w08DQwLlexBY4Cz1pr371M+5txkr/XrbUr8t17AJiNs3b0ZmttbK579wKf4CSpPS5sZGSMqQPEAq2BJ621r+fr06N2BVHCWXZ89dVX3HnnnW63a1Qpgn0P9Cj0/upjp5i24xBz9x7hbEbO7yCCg4O56667GD16tNZ6yiWshZmJ8MROOJedU37vVTCrtY5TERERkcDhtSm1BXTc1xjzGbAPZ5QzFXgPZ7RzEc46z7eNMeOL6sda+19r7cD8yabr3kc4O+MCPJTv9p9dr0/n3jXXWpuIs9YU4JkCpsh62k7KsF9++cWjdiNaRhd5v2utqrzdvS2HB/ViSrc2XFOzMgBZWVnMnz+f3/zmNzRr1owXX3yRxMREj2KQwGMMDIuCtZ2hQ8Wc8ix0ZIqIiIiUH26PcBpjqgKPAI8DzQEDHATeAqZZa5Ny1b0OZ6rsUWttM4+DNGYs8CbwjbX2VldZfZwNi9KBagWdD2qMOQREA92stStL0q4wGuEsW3bv3s17773H9OnTSUhIuGz9YGM48EAPoiuGu/Wc1cdOMXV7HB/uTSAlM2fUMyQkhAEDBjB69Gid6ykXnc+CP+yBBSdgQxeoWcHXEYmIiIh4j1dGOI0xnYwx7wDxwKtAC2A5cC/QxFo7MXeyCWCt/RlYiLOxUEk0d70eyVV2jet1S0FJo8vqfHVL0k78QLNmzXjhhReIi4vjiy++4I477igy6esXc5XbySY4o57v3NSOww/2YvKNrbm6hjPqmZmZybx58+jbty8tW7bklVde4fjx4x6/HwkMEcEwuQX8WkCymZoFB1N9E5eIiIhIaXNn+GUNznEoAO8AHay1N1tr51trs4tolwKEFHG/SMaYKGC46/LTXLcau14PFNH8YL66JWknfiQkJIS77rqLBQsWcODAAf75z3/SsGHDS+ptOXmW/2w+QFJahkfPqRIawpjWDdgw4EZ+uvM6hjevR0Sw889q9+7dPPXUU0RHRzNkyBBWrFhBOT6yVoAaBYxsPrMXOqyGeZee7iMiIiLi99xJOPcDTwH1rbWjrbWbL1P/glGARxPIjDEhwCygKvCdtXZBrtuVXK8pRXRx4SCCyl5oJ36qfv36/O1vf2PPnj0sXryYe++9l5AQ53cge8+c5/c/b6fe3GUMWbaR5UeSLtNb4a6rXY3pPdpz+MFevH59K9pUcxbupaenM2fOHHr06EG7du144403SE5O9sp7E/+26AS8Hg+nsuD+rTByO6To1B0REREJIO4knE2tta9aa936pGwdnn6EmoJzVEkcl24YdOFgAXeHjDxtl9OBMY+5zuxcc+zYMU+7kSssODiYW2+9lU8++YRDhw4xceJEmjVzlhanZWUzZ88Rei1aTatPfuCVTfs4npru0XOqhVVgfNuGbLm3O9/ffi2Dm9YlzDXquXXrVsaPH090dDQjR45E63/Ltxoh0CjXjO53E6DTGlh7pvA2IiIiIv7EnYRziTFmwuUqGWN+b4z5pgQxXejndWAEztElfay1+XeAufCRrBKFu3Av98c3T9tdZK1921rbxVrbpVatWkV0I2VVnTp1+NOf/sTOnTv573//y6BBgwgNDQVgx6kUnvplJ9Fzl/Fg7K/EHvZ81POmqOrM7tWBbfd2IyjX2Yvnzp3j3Xff5a9//WtJ34r4seurOpsIDaqdU7bzPFy/DiYehCzNwBYRERE/507C2RdoV4x6bXBGJT1mjHkVGA8cw0k2dxVQbb/r9dKFeTli8tUtSTsJQMYYevfuzdy5czl06BCvvPIKLVq0ACA92/Lh3gRu/no1LT9ZUaJRz8WHjpNdQPLw+OOPlyR8CQBVQ2BOa5jeEiq5zubMtM7azj4bIE4bComIiIgfK40zG0KBojYRKpIx5mVgAnACuMVau7WQqutdr22NMRGF1Omar25J2kmAq1WrFn/4wx/Yvn07y5cvZ/DgwRdHPXeeOsdTv+yk/ofLGRzr/lrPKdsPXVJWr1497rzzTq/ELv7NGBheF9Z3hutyrRxffgo6rIGPtaGQiIiI+CmvJpzGGAN0Bjw6B8IY8xLOxkQncZLNXwura62NA9bhJLj3FdBXT6A+zpTcVSVtJ+WHMYYePXowe/Zs4uPjefXVV2nZsiXgrPWcuzdnredrm/dfdofbVUeT2Zh06ezsUaNGXdy8SASgWSSsuAb+1jDnh3NyJvznEAWOkIuIiIiUdaaoYxryrcXsCxwGChtxDME5L7Me8Im19gG3AjHmeeBZIBnoa61dW4w2A4F5OMnhTdba3a7y2kAszvTeJ621r3ujXUG6dOlitfFL4LPW8v333zN16lQ+/fRT0tNzptaGBwcxsHEdHm8VQ7c61S9pO2z5JmbuPpynLCgoiAMHDlC/fv1LH7ZjI9RrAJWref19iP/48RQ8tA1OZDjrPJsUNh9DRERExMeMMWuttV0KvHeZhDP31FhLzg6vRdkI9LfWFnXOZf7n3AV84bpcA2wppOp2a+1L+dpOBsYAqcBSIANnDWkV4HNgYEG75HraLj8lnOXP8ePHmTFjBlOnTmXXrrzLi9tVr8ToVjEMbVaXqqEVSErLIHruMlKz8s4y79+/P59//vmlnWekw1NDIfUcdO4OvW6HZm2dOZdS7pzKhF/PQo98v3vIss6IZ4XSWBQhIiIi4qaSJJwXNv8xwDfAEuCVQqqnA/HW2r0eBDgcmF6Mqsuttb0KaD8YGAu0B4KB7cB7wFvW2kLXk3raLjclnOWXtZbY2FimTp3KZ599RmZm5sV7kSHBDGoSRWRIMG9uPXhJ28WLF3Prrbde2unPsTBtYt6y6EbQ6w644WYIj/TyuxB/9PJBmHcMZrWGlvqWEBERER/zOOHM18kKYGH+EcbyTgmnACQmJjJ9+nSmTp3K/v37i6zbuHFjdu/eTVBQAcNTE/8AuwoZ4A+LgOtvdkY9Y5rkubVo0SLi4uIYMmQIlSoVdeKP+LsNZ+DadZBhISII/t0UnqinQXARERHxnaISzmJPyLLW3qRkU6RgderU4ZlnnmHPnj0sXryYu+++m+Dg4ALrjh49uuBk89C+wpNNgLTzsHwhPPcEvDTBGQ3NcNaSPv/88zz++ONER0czfvx4tm3b5o23JWXQppSctQ3ns2HcLrhtIxxO82lYIiIiIgUq9ginFEwjnFKYQ4cO8e677zJt2jTi4+MBqFChAvHx8dSqVevSBrPfhNiv3HtI5aokNOvI9c/8kwNn8x7Y2Lt3b5544gn69+9PhQoVPH0bUgZtPOtsKLQpJaesRgi83RLuLeBbS0RERKQ0eTSl1hjzF9eXb1lrT+a6LhZr7QvuhemflHDK5WRmZvLVV18xZcoUatasyezZsy+tlHoe/jjE2SzIA9nWsjDuGJO3xbHk0HFy/6uuW7cujz32GKNGjSI6OtqzNyFlTmoW/G0/vBpHnr/vh+rAG82gmn7HICIiIleIpwlnNs7nmNbW2p25ri/7PMBaawueTxhglHCKO7KysgqeapudDVvWwrKvYONqKN6eVQXac/ocU7bH8d7O+DxnhAYHBzNgwADGjh1Lz549MVr0FxCWnYSHt0Ncrim10aEwvRXcUsN3cYmIiEj54WnC+f9wEszXrLVJua6LxVr7N0+C9TdKOMXrThyFFV/D94vh9EmPu0nNzOLDvQlM3hbH6uOn8txr06YNTzzxBEOHDqVKlSoljVh8LDkDxu+GDxJzylpFwqYuEKKjU0RERKSUeWWXWimYEk4pNZkZsH6VM+q5Y2OJulp97BSTtx3kw70Jec4ErVixIkOHDmXs2LG0a9eupBGLj312DEbvhJMZsKoTdNXvEkREROQKUMJZipRwyhVx+AAsWwirlsJ5z9Z5AiSlZfCbxWsvGfEE6NGjB2PHjmXAgAHaZMiPJabDsmR4oHbecmsh00IFjXiKiIiIlynhLEVKOOWKSj3vHIey7CuI2+t286S0DOrPXcb5rMLXiF7YZOixxx6jXr16JYlWypAPEpwNhma0hqt1VKuIiIh4kVfO4TTGjDHGpBtjbi+izh2uOiM9CVRELiM8Anr249Cjf6b7wtV8sPswaUUkj/lN3xlfZLIJcOTIEZ577jkaNmzI/fffz/fff49+MeXf4lLht7vg1xToshae3w8Znu9LJSIiIlJs7kyuugdIAr4uos7XrjoDSxKUiBTt7WnT+DEhiYeXb6L+h8t4evVO9p85f9l2U7bHFfsZmZmZzJs3j549e9KhQwemTJnC2bNnSxK2+MjaM5Dm+p1BpoW/74cb1sGWlCKbiYiIiJSYOwlnK2CTtYWf12CtzQI2AW1KGpiIFK5atWrUru0s0juemsHLG/fRdN733P7NWhbGHSO7gBHJxYeOs/t08dd/Vg+tQHiw8yNi8+bNjBkzhujoaH73u9+xY8cO77wRuSLurgW/doEbcm0itPYsdFoDEw9ClgawRUREpJS4k3DWAhIvWwuOArUvW0tEPDZhwgQOHjzInDlz6N69OwDZFhbFHeeOb9bRbN4KXt64jxOp6RfbTN520K1n/G+nphwa1JOJXVvQqFIEAKdPn+b//u//aNWqFbfccgtffPEFWVlZ3ntjUmpaRMKKa+DlJhDmOoI13cIze6H7etjh+V5UIiIiIoUq9qZBxphEYLu1tudl6i0D2llrryp5eGWfNg2SsmDjxo289dZbfPDBB6Sk5MyTDA8O4v7GUQxoVJt7v9tAdjFHsiqGBBP/YE+qhjq71WZby8K4Y7y59SDfxp/IcyBvgwYNGDNmDCNGjKBWrVpefFdSWramwPDtsPpMTll4EPyrMfyuPgQb38UmIiIi/scru9QaYxYDvYE21to9hdRpCmwDvrfW9vUwXr+ihFPKktOnTzNz5kwmT57Mtm3bPO7nsZb1mdq9bYH3dp1KYdK2ON7fFc+p9MyL5WFhYTzwwAOMGzeOrl27evxsuTIys+HlOPjHfshw/W+gbihs7QrVdCqOiIiIuMEru9QC7wMVgM+NMc0LeEgz4HMg2FVXRK6wKlWqMG7cOLZs2UJsbCwDBw4kODjY7X7GtmlQ6L3mVSvyn+tbET+oJ1O6taF9deeMjbS0NGbOnMm1117Lddddx8yZM0lNTfX4vUjpCgmCvzSENZ2ho+uYlKktlGyKiIiId7kzwmmABUA/IBP4Adjuut0SuAkIARZba/t5P9SySSOcUtbFx8czbdo03n77bY4cOXLZ+t3rVGPFHde59YzvE5J4c+tB5u8/SmaunylXXXUVo0aNYsyYMcTExLgdu1wZGdmw4ATcU8CM6IQ0iAq78jGJiIiI//DKlFpXR6HAa8AonOQyt0xgGjDBWpvmYax+Rwmn+IuMjAzmz5/P5MmTWb58eaH15vbuwKAmdT16xuGUVKbuOMTb2+NIOJ+zYVFQUBAvvPACTz/9tEf9im98kwR3bYJ/NII/xjijoiIiIiL5eS3hzNVhFNAHaOgqOgB8Z61N8DhKP6WEU/zR5s2bmTx5MjNnzsyzyRDAkKZ1ebJtQ7rUqupx/xnZ2Xy6P5E3tx7kx8RkAJYsWcL//M//lChuuXJOZ0L71XDQ9evDLpXhvZbQvpJv4xIREZGyx+sJp+RQwin+7MImQ5MmTWL79u157l1bqyrj2jTg/sZRhAV7PrS14cRp5p1I4/klKwiKiCxpyHKF7D8P922FNbl2sq1g4C8NnLWfoRrtFBERERclnKVICacEAmstsbGxTJo06ZKzNWuFhzKyZTSPt4qhges8To9EVoLut0Kv26F2PS9ELaUtMxteiYP/3e+c2XlBu4rOaGfXKj4LTURERMoQryacxpiWwHigFxDtKo4HYoE3rbXbC2kakJRwSqCJi4tj6tSpTJs2jaNHj14sDzaGOxvUYlybBvSpV9PzBxgD7bvC7YOgaRsvRCylbVsKjNgBq07nlAUBE2Lgn40gwv2NkEVERCSAeHPToOHAW0AoUNDR4OnAaGvtDA/i9EtKOCVQpaWl8emnn/Lmm2+yatWqPPdaVa3IE61jGN48msqh+fcPK6bHnoFre5U8ULkisiy8GQ9/2QvnsnPKm0XAR22gU2XfxSYiIiK+5ZVzOI0xXXF2oQ0F5gN3AK2BNsDtwKc453ROc9UVET8WFrHsvFQAACAASURBVBbG4MGDWblyJevWrWPEiBGEh4cDsP1UCuN/2k70h8sYu3IrW0+eda/zqtWhU7dSiFpKS7CB39WHTV3h5mo55QnpUFNnd4qIiEgh3Nn24SlX/YestQOttYustTustduttV9ba+8DHsI5LuWPpRGsiPjGNddcwzvvvEN8fDyvvPIKTZo0AeBMRhaTt8XR9rMfuXnRaj7bn0hWdjFmTfS8HUI8y1IyMzM9aife0SQCll4N01pAlWB4qQk0DPd1VCIiIlJWFXtKrTHmMHDIWnvtZer9DDSw1np2kJ+f0ZRaKY+ys7NZvHgxb775Jl9//XWeezEVwxndqj6PtYyhVkTopY2Dg2HiTKjm/jpQay2dOnWidevWjBs3jhtuuAFjCprdL1dCQhrUDoWgfH8FHx+FntWgTgF//SIiIhJ4vDKlFqgJ7CxGvV1ADTf6FRE/ExQURL9+/Vi0aBG7du1iwoQJVKvmzLOMS0nl2bW7ueGH3WQNnwCNW+Zt3Lm7e8nmwT3w7r9h3w6WLVvGhg0bmDt3Lt26daNz585Mnz6d8+fPe/HdSXFFhV2abG48C0O2QetfYPoR0EboIiIi5Zs7CedJoGkx6jVx1RWRcqBZs2a8+uqrxMfHM+3/Z+8+o6us8rePf+9UCAmEHtIIJQkgIF1BKYINBAsgLSgEpSnq2GYcnXlGnXH+Mzqjg/TeiQpiFxREEBEUpErvaQRCJySk7ufFiSEnjbRDCtdnLVbI3nfZR9finOvsff/2rFm0bt0agPAxY3G+8154bSK8OhE6321bRnvXg0W7wdrPYNN38NZz+C14h+FNG+CWmXK2b9/OqFGjCAgI4JVXXuHEiROl/fKkCIyBJw9AmoHzaTDqANyzE47q+wAREZGbVlGW1K4AHgL6G2M+y+eYfsBnwCfGmAGlNspyTEtqRewZY9i4cSOhoaHUrVvXvjPhElTzsm2NUhgJl+Dl4ZCaYtd8OimZmQeimb4vipjE5Kx2JycnHnzwQSZMmEDPnj213LYMrD4HYw/CsavX2qo6wRtB8Lw/uBTla04RERGpEEplWxTLsu4E1gPpwGJgAXAMMNhmNR/HVjTIGehujNlY8qGXfwqcIg60chl8PCff7rSMDD45cZpJeyPZEGe/sOL35zwff/xxPD09HT1SyeZKOvztGLwXDdl2UKGNp63YUIfqZTY0ERERcYDS3IfzGeBd8l6Ka2ELo88bYyYXZ6AVkQKniINkpMOfw+Hs6UIdvvPsZSbvi2TJ4ViS0q/FnOrVqxMeHs7TTz9NcHCwo0Yredh6ybbEdueVa21OwLP+8Pcg8CzmFq4iIiJSvpRW0SCMMZOATthmOCOBNGwhMxJYCHS6mcKmiDjQzl8KHTYBbq3txaw7byFmaA/e6RRCI6+qAFy6dImJEycSEhJC7969+frrr8nIyLjO1aQ0dKgOW9rDvxtDlcx3mwzgf9EwfF+ZDk1ERERukCLNcEpumuEUcZDPFsGXS4td5jTDGL6KimfS3kjWxJwl+1WaNGnC008/TXh4eFZ1XXGsI0kw/iCsPm977mJLe2jrVdajEhERkdJQaktqJTcFThEHOh1LbMQsqm79gZrursW+zIELV5i8L5IFh2K4nJqe1e7h4cFjjz3GhAkTaNmyZWmMWApgDCw5BSeS4bWG9n0ZmW9FObdZERERkfKv1JbUiojcUPV8efmXg/hFrGP0j3vYde5ysS4T6l2NSZ2bEzOkB5M6Nye0RjUAEhMTmTFjBq1ataJnz56sWLGCtLS00nwFko1lwXCf3GETYFos3LHdto+niIiIVB75znBaljWzBNc1xpixJTi/wtAMp4jjnDp1ioCAAFJTU7PauvrU5JkWgTzSsB4uTsX/zuzbmDNM2hPJ19HxWbNrAIGBgYwfP54nn3ySOnXqlGT4UkixydD8F7iUbltu+3wAvB4E1ZzLemQiIiJSGMVaUmtZVkmqahhjzE3xUUGBU8RxjDF89913TJo0iS+++ILs/175ebgzrnkAY0L9qVfVvdj3mHswmic27MnV7u7uztChQ3nmmWdo165dsa8v17f8NITtg5Tswd8dJgdDP2V+ERGRcq+4gfOJktzUGJP/5nmViAKnyI1x/Phxpk6dyuzZszl//tqem+7OTjzaqD7PtGhIp7o1inzd3t/8yqroMwUe06VLFyZMmMCAAQNwc3Mr8j3k+vZfgXEHYf1F+/ZH6sDEphBQpWzGJSIiItenokEOpMApcmMlJiYSERHBpEmT2Llzp11fxzo1eOaWQAY38sHN+frLbQ9dvELo8h8p7L+CPj4+jBs3jjFjxtCgQYNijF4KYgwsPAUvHoaz2R6lreYEbzaCZ/3ARZUHREREyh0FTgdS4BQpG8YYNm7cyKRJk/j4449JT79WfbZeFTdGN/NnfLMA/KrlPzX2h837mbjnRJHv7erqysCBA5kwYQKdO3fGslRatTSdTYU/HoG5cfbtravBipbQpGrZjEtERETyVuqB07IsT6ADUBeINMb8XLIhVlwKnCJlLyYmhhkzZjBjxgxOnz6d1e5iWTzcsB7P3BJIN59aduckpKbhF7GeS6mFr0p7ay0vduaolNuuXTsmTJjAkCFDqFpVSag0/XDBtnfn3kTb74HusLeTigmJiIiUN6W2LYplWV6Z1WvPAN8BHwBjs/WPtywr0rKsTiUZsIhIUfj5+fHmm28SGRnJ4sWLuf322wFIM4blx0/R/ast3PrJT8w6EE1imm0mdOHh2CKFze4+NdnxSBc297uN4U0b4Ja5YeS2bdsYNWoUAQEBvPLKK0RGRpb+C7xJdfOG7R3gX43BwwneD1bYFBERqWgKPcNpWZYHsAFoiy1wbgPuBeYbY0ZlHtMEOAT82xjzZ4eMuJzRDKdI+bR161YmT55MREQEKSkpWe013VwZFeLHl1HxHLh4pdDXW96zDQMa1c/6/VRSMjP3RzN9fxSxiclZ7U5OThw+fJhGjRqVzgsRAE6lQP086jW9fgz614XWnjd+TCIiImJTWjOcL2ILmxFAI2PM/TkPMMYcwRY4exZnoCIipaVDhw7Mnz+f6Oho3nrrLfz9/QE4n5LKf387XqSwGVCtCg83rGfXVr+qO39t24QTg7vx4V23cmd9bwA6d+6ssOkAeYXNr87CGyeg3VZ4/jBcKvyEtYiIiNwgRQmcg4CTwBPGmII+qZ0A/Eo0KhGRUlK3bl1effVVjh07xvLly+nevXuRrzGuWQDOTnkXBnJxcmJQYx829L2N7Q935r1H7oPkqyUdtlxHhrFVswVIB/4XDaG/wNJTtmq3IiIiUj4UJXA2AX4xxlzvk9QZQFt1i0i54uLiwoABA1i3bh27du1izJgxhSry4+7sxOhQ/0Ldo03t6nTctxFeHg7LZkN83PVPkmJxsuCTlnCX97W2uBQI2wc9d8Kewk9gi4iIiAMVJXCmAu6FOM4fSCjqQCzLCrUs6znLshZblrXfsqwMy7KMZVkDCzhnfuYx+f3Zf517DrMsa4NlWRcty0qwLGurZVlPW5alnd5EKrFWrVoxY8YMYmJi+M9//kPjxo3zPXZwIx/qVs1jPWdBEhPgm+XwajhMfh32bNO0mwM0rwbf3QoRzaFBtv9F6y5Am63w8hG4rGW2IiIiZaooRYO2YAuTQcaY5My2DOyLBnljW1K73RjTo0gDsaz/Ac/l0fWoMWZ5PufMB0YAG4HDeRxyMr/iRZZlTQGeAq5iq7ibCvQCvIBPMu+bnte52alokEjFl56ezsqVK5k8eTLffPONXV9DzypMaBHIEyH+1HR3Lf5NfAKgZz/ocjdU8SjhiCWnS2nwxnGYGG1bYvs7Pzf4TxMYUj+/M0VERKSkSqto0MdAfeCfBRzzD8ATWFaE6/7uN+AdYDDQFFhfhHNnG2NG5vEnv7A5AFvYjANaG2P6GmMeAYKBfcAjwIRivAYRqYCcnZ3p27cvq1atYv/+/Tz77LN4eXkBcCLhKi//chD/D9Yz+sc97MqxD2ehxUXB0qnw0nDbz7ioUnwFUt0F/tsUdnSAbjWutcekwGdny25cIiIiN7uizHBWA7YCIcCP2ALo/4Dvse3H+Si2GcI9QMffZ0GLPTDLWgd0p3AznOHGmPlFuPZWoD0wwhizMEdfd2AdtjDqZ4zJKOhamuEUqZwuX77MwoULmTJlCvv27bPr6+ZTkwktAnmkYT1cnEqwAr9FO+j5ILTuCE72G0ympKRw8eJF6tatW/zr36SMgSWn4KUjkJAO+zuBf5WyHpWIiEjlVSoznJmVae8FfgW6Au9ldvUApgN3AzuBB0oaNh3Jsix/bGEzhTxmYo0x64EYwAe4/caOTkTKCy8vL55++mn27NnD6tWreeihh7AsW6XaH+LOM2jtThp9tIG3dhzhXGqB30vlb+822zOer46CNZ/adS1fvhx/f39GjBiBvtQqGsuC4T5w4Db4vFXusHkpDRbH2SrdioiIiGMV6at5Y0yUMaYT8CAwA/gWWAsswLYUtoMxpizWid1lWda7lmXNtCzr75Zl3VdA4Z+2mT/3GGOS8jlmS45jReQmZVkWd999N59++ilHjx7l5ZdfpmbNmgBEX7nKX349zFfdB8OolyAouHg3OXMKjh2wa5o0aRIpKSksXLiQjh07cvvtt7N48WKSk8vt93nlTg0X6Fkzd/ubx+Gx/XDndthWzBXSIiIiUjiFXlJ7oxVxSW1e9gJDjDG7c5zzLDAR+DTzuc28rjsReBb4rzHmpYLGqSW1IjefxMREIiIimDRpEjExMURFRVGlSuY02tH98N1nsHUDpBehROqf34MmzQHYunUrHTt2zPOwevXqMWbMGMaOHYu/f+G2a5Fr9l6BW7dCWuZbnwWMbgD/aAR1i1iMWERERGyKtaTWsqzllmX1tn5fQ1Y+7cAWDG/BVqzIF+iLbWlvC2CNZVl+Oc7xzPxZ0C5tv2/r4lV6QxWRysLDw4MnnniC7du3s23btmthE6BxMxj9J3h7ETz0GNSodf0LNgy2nZdpypQp+R56+vRp/vGPfxAUFMSgQYP44YcfKK9fHJZHge7wcgC4Zr6zGWDmSQj5BSZFQ1oxV0eLiIhI3gpaUtsf+BKIsizrLcuyirlWzHGMMf8zxkwyxuw1xlwxxpw0xnwFdAI2A/WAnJVqfw/Qxf6EZlnWmMw9O7fGx8cX9zIiUsFZlkVAQEDenTVqQr8w+PdCGPsqBLfM/0I9H7Q9eAjEx8cTERFx3Xunp6ezbNkyunfvzq233srMmTO5cqWg79EEwNMF/tkYfusIfbJ9F3AhDZ49bNu/c+35shufiIhIZVNQ4JwGnMc2a/gKsN+yrPWWZY2wLKtcbyJnjEkB/i/z1z45un9/YseT/P3el+fTPcaYmcaYDsaYDqogKSIFcnGBjt3gT/+B/zcFut4Pbu7X+j2rQ6fuWb/OmTOnwOc0nS2Lz+5uy8hgX6o42/4J3717N2PHjsXPz48XXniBw4fz2pZYsgvxgK9aw5etoGnVa+17EqHXThj4GxzP7yl/ERERKbR8A6cx5mlsYXMwtuJAGdiq084F4izLmmVZVpcbMsri2Z/5M+eS2uOZPxsWcO7vUxbHCzhGRKRoApvAiD/A24vh0SehTn1bAHW1PTyYlpbG1KlTC7xEv8C6PNiwHvO6tSJqSHf+r0MwgZ62Jb0XL17kvffeIzg4mD59+vD111+TkaE1ogV5oLZttvPfjcEz2840H5+BNZrpFBERKbGi7MPpi61Az+NAaGazAQ5iC6GLjDFxpTawQhQNus75nYGfgHPGmNrZ2gOASGzbonjnVanWsqwowB+40xizsaD7qGiQiBRbRjqkpoK7LTB+8skn9O/fv8BT1vTuQC/f2nZt6RmGL6JOM3lvJN/FnrPra9KkCU899RTh4eFZ1XUlb7HJ8MpRWHQKOnjBz+3AqTxXMRARESknSmsfzlhjzP8ZY5oDdwBzsC05DQX+BURalvWZZVkPWZblXNC1bpBBmT+3ZG/M3LZlG+AGPJrzJMuyumMLm3HAJgePUURuZk7OWWETYPLkyQUe3ty7Wq6wCeDsZPFww/qs6d2RvQPu4OnmgXi52v4ZPnLkCC+++CJ+fn6MHj2anTt3lu5rqER83WFhc9jYFmaE5A6bv16GLZfKZmwiIiIVVZH24fydMWaTMWY00ADbrOc6wBlbhdgVQExpDTA/lmW1sSyrb85wa1mWi2VZL2CrXgvwXh6n//58578ty2qa7dx6wO/r2f5ljNFaNBG5Ifbs2cPatWsLPObp5oHXvU5zb08md2lOzJAeTOrcnGY1qgGQlJTE7NmzadOmDV27duWDDz4gJSWlVMZe2XSpAe1y1ChPNzD6AHTaBuH74aS2QxURESmUUtuH07Kse4DFQF3AGGOKNMtpWVY7roU9sG1r4gUcArLWiBljbs88/mHgk8y+g0B05vGtsD17mgH82Rjzdj73mwqMB64Ca4BUoBdQHfgUGGiMSb/euLWkVkRKw2uvvcY///nPfPuru7oQM7Q7nq4uRb72mpizTNkXyReR8aRn+zffx8eHsWPHMmbMGHx9fYs17pvFnJPw5IFrv3s6w2uB8Ad/qFIe1vSIiIiUoYKW1JYocFqW5YmtqNBIoAvXthyJNMYEFfFaPYDvr3ecMcbKPL4R8By2LVAaArWxPVMaDWwAphhjfr3OPYcBT2MLqc7YCg3NBaYVdnZTgVNESkNGRgarVq1i8uTJrFy5Mld/53refHFPW2pXcSv2PSITkpi2L4rZB6M5czU1q93FxYX+/fszYcIE7rzzTsr39stl41AivHQEPj9r396oCrzdGAbUzdrZRkRE5KZT6oHTsqy7gHBse3VWxRY0k4HPsQW2b81NshO5AqeIlLZDhw4xdepU5s2bx8WLF7Paqzg7MaSxD8+0aEi7OtWLff3k9Aw+OHqSKXuj2HLmol1fq1atmDBhAmFhYVSrVq3Y96isVp+DPxyGvYn27V1rwHtNob1X3ueJiIhUZqUSODNnFEdk/gnk2mzmDmAesNgYc9MVkVfgFBFHSUhIYMmSJUyaNIk9e/bY9XWu582EFoE82qg+rk7FehwfgF/iLzJ5byQfHYsjOf3awo4aNWoQHh7OU089RXBwcLGvXxmlZcD0WPjbcTiXdq3dAkb4wP81Ah/3/M4WERGpfIodOC3L8sBWyXUktj04rcw/54GlwBxjzI7SHnBFosApIo5mjGH9+vVMnjyZTz/9lPT0a4+X+1R1Y3RoAOOa+eNbrUoBVylYfFIKsw9GM31/FJEJV+367rvvPp5++mn69OmDs7MeWPzd+VT4+wmYFANpmW+lrhbs7QhNPcp2bCIiIjdSsQKnZVlzsIXNathCZgbwHbYls58YY1TeEAVOEbmxoqKimDFjBjNnziQ+Pj6r3cWyeCSoHhNaBNLNp1axr38+ORWfpd+TkpH7vSEoKIjx48czatQo6tSpU+x7VDYHM5/v/OIsvOgP/2l6/XNEREQqk+IGzt/XVh0D5gPzjDHRDhlhBabAKSJlITk5mWXLljF58mR+/vlnu75WNT2Z0CKQ4U198XAp2ozkpD0neHbz/gKPcXd3Z8iQIUyYMIEOHfJ8b7kprTkHHbzA29W+fc5JCK0Kd3qXzbhEREQcrbiBcxEw1xhz3cqxNzMFThEpa1u2bGHKlCl88MEHJCdf2yDS282FkcF+PN0ikKbVC7fGs9nyHzlw8Uqhjh02bBhLliwp1phvFlFXIfQXSMqAgXXhX42hSdWyHpWIiEjpcti2KKLAKSLlR3x8PHPmzGHq1KlERUVltVvAvX51mNAigD4BdXHKZ/+ONTFnuWdV4f8927hxI126dCnpsCu1UfthXty1310teNYPXmsINV3zP09ERKQiKShwFr+0oYiIlCt169bllVde4ejRo3zyySf06tULsG1Q/E3MGfqt3k7wsg38Z/cxziWn5jp/8r7IQt+rTZs2dK7hDhfOXv/gm9jfgmBovWu/pxr4bzQ0/Rnej4aUQu34LCIiUnFphrOENMMpIuXZvn37mDp1KvPnzychISGrvaqzE0ObNGBCi0Da1q7OiYQkmny0gfRCvifMmzGdkb+thuQkaNsF7uoHIa0gn9nTm93Pl+CFw/DTJfv2plVty2z719F/OhERqbi0pNaBFDhFpCK4dOkSixYtYsqUKezbt8+ur3M9b2q7u/JlVHw+Z9urWbMmJ5ctwD1iin2HXxD06Aude0IV7QuSkzGwPB7+dBSO2e88Q5fqsPwWaKD9O0VEpAJS4HQgBU4RqUiMMaxdu5YpU6bw2WefkZFR9DWdLzz/PP/1ToHIw3kfUMUDutxtC5++gSUcceWTnAFTYmx7eF5Is7U194BdHcBFD7qIiEgFpMDpQAqcIlJRRUZGMmPGDGbNmmW3p+d1z1v3LQGL/lu4g5u1gbv6wq23g4tLMUdaOZ1LhbdOwKQYWHEL9M2xtakxWmYrIiIVgwKnAylwikhFV9Cenjn17t2brx/pDj8Xcccs79rQvQ90vd/292w+/PBDvLy8uP/++3Fyuvmm+KKvgp+7fbg0Bvrshh7etqq2VYu2naqIiMgNpcDpQAqcIlKZbN26lalTpxIREcHVq1dz9X/78TLu+XYBpOWuclsozs7Q9g7o2Q+CW5KalkZQUBCxsbE0btyYcePGMWrUKGrXrn39a1ViH8fDwD22v/u7w9+D4DEfcNaMp4iIlEMKnA6kwCkildHZs2eZO3cu06ZN49ixYwA0atSIQwcP4nzoN1j3JWz/CYrxDGgW34Zs9/an2ytvkJCantXs7u7OkCFDeOqpp+jYsSPWTbiutO8u+OqcfVuravDvxnB/LS21FRGR8kWB04EUOEWkMktPT2fVqlVMmTKFXr168eKLL17rPBcPP6y0/bl0vtj3uJySxsLDsUzbH8We8wl2fe3bt2f8+PEMHToUD4+bp/JtagbMOQl/Ow6nc0wm9/SGt5tAe68yGZqIiEguCpwOpMApIjcLY0zes41pqbBtI3z/BRzaU6J7rD95jin7Ivn0xGlSM669P3l7ezNy5EjGjx9PSEhIie5RkVxOg/9GwX+i4EqOyeTBdeEfjaDpzZPDRUSknFLgdCAFThGRbKKO2oLn5rWQklzsy5xMTKbXyi3su3AlV9/dd9/N+PHjefDBB3G5SSrfxiXDGydgViykZ2uv6gRRnaG2a5kNTUREpMDAefOVAxQREccJaAyPPwf/WQpDxoGPf7EvdehiYp7ta9asYcCAAQQFBfHGG28QGxtb7HtUFD7uMC0E9nSCR7JtnzLCR2FTRETKN81wlpBmOEVECmAM7N8B338JOzYVusjQG9sO8/r2I4U61tnZmYcffpjx48fTs2fPm6LI0OaL8PpxmNcMGrjb9/1yCW71BHd9pSwiIjeIltQ6kAKniEghnYuHH77G/LAKq4AiQ2kZGQR9+AMxiUVfkhsaGsq4ceMYMWIENWvWLMloK6RTKdD0Z6jjattKZWh9baUiIiKOpyW1IiJS9mrVhYdHsPmRpxi8difrT57L87DPI+OLFDbrVXGjqrPt7ezAgQM8//zz+Pn5MWrUKLZs2VIqQ68o/nECEtLh+FV4bD+03QpfnrFNNIuIiJQFBU4REbmhpsyYwUfH4ujx9RZartjIlL2RXE5Jy+qfui+ySNf7V8cQYob24N3bQgmubivZmpSUxLx58+jUqRMdOnRgzpw5JCbm/UxoZRJSFWplq6O0+wr0+w26bocNF8puXCIicvPSktoS0pJaEZHCM8YwZswYFi5cSEpKSla7p6szw5v4cp9/bfqv2UFh35lqurkSM7Q7VV2cs9rWxJxl2v4oPj9xmrRs73E1atRgxIgRjBs3jubNm5fWSyp3LmZupfJuHlup9KkF/2xse8ZTRESktOgZTgdS4BQRKbr4+HjmzZvHtGnTOH78eLGv83zLhrx7W7M8+2KuXGX2gWhmHYjOtUS3R48ejBs3jkceeQQ3N7di3788O5UCb52A6bGQmu2t3gKG1IPJwVBLFW5FRKQUKHA6kAKniEjxpaens2rVKqZOncrKlSspynuSBewfeCchNaoVeFxaRgZfRMYzbX8Ua2LO2s2e1q9fnyeeeILRo0cTFBRUrNdQ3h1Lgr8dh8WnyHrtTavC3o7gqgdrRESkFChwOpACp4hI6Th27BgzZsxg9uzZnD179rrH3+1bm9W983xvy9fhS4lM3xfF/EMxnE1OzWq3LIs+ffowbtw4evfujbOzcwFXqZh2J8BfjsHnZ2Fpc1sF2+yMgZtgRxkREXEABU4HUuAUESldV69eZfny5UydOpVNmzble9zHvdrQP6h+vv0F3iMtnWXHTzF9XxQ/nbavphMYGMiYMWN44okn8PHxKdb1y7Otl6CdFzhlC5fGQN/d0MELXgiAGi75ny8iIpKTAqcDKXCKiDjOjh07mDZtGosXL85VZXZYkwZMaBFI53reJbrHrnOXmb4/isWHY7mcmp7V7uLiwsMPP8y4ceO46667cHKqvOtPV52F3rttf6/lAn8MhAl+UK3yTfSKiIgDKHA6kAKniIjjXbhwgUWLFjFt2jT27dtn19emthfjmwUQ1qQB1VyLPzWXkJrGkiMnmb4/ih1nL9v1TZw4kWeffbbY1y7vhu2FiNP2bfVd4bWGMMYX3Ctv1hYRkVKgwOlACpwiIjeOMYb169czbdo0VqxYQVratf07q7u68FhTX8Y3D+CWmiXb92Pz6QtM3x/FR0fjSLWciIqKqpTLa3+XbiDilK240NGr9n0B7vDXhjDSR0WGREQkbwqcDqTAKSJSNk6ePMmcOXOYOXMmUVFRdn1dfWoyvlkAA4Lq4+Zc/JR0PjmVpRlePL3k05IOt0JIzYB5cfD3ExBtv5MMTarA60G2YkPOKi4kIiLZKHA6kAKniEjZSktL46uvvmLatGl88803dn31qrgxKsSP2CViCQAAIABJREFUsc0CCPKqWqzrb+85mLbDwktjqBXG1XSYcRL+eQJOXyvmixOwrxOEeJTZ0EREpBxS4HQgBU4RkfLjyJEjzJgxg7lz59ptreJkwf3+dRjXLIAHAuriVMj9P44lphC0eA1WJS4YVJCENJgcA29Hwfk0eKw+LGxe1qMSEZHyRoHTgRQ4RUTKn9+3Vpk2bRo//fSTXV+gZxVGh/rzZIg/Ph7uBV5nXf0Qerz1viOHWiFcSIV3o+Hx+tA0x+zmgjio6wq9a2kfTxGRm5UCpwMpcIqIlG+7du1i+vTpLFq0iISEhKx2VyeLhwLrMb55AD19a+c672p6BolvzKRWYFDhbpSRAefPQO16pTTy8u98KjTaDBfT4fbq8GYQ3F1TwVNE5GZTUOC8OdcIiYjITaN169ZMnTqV2NhYpk+fzq233gpAaoZh+fFT9Fq5lWbLf+Td345zLvnaA4tb8Sh82ATYuw1eGQET/wo7NkF6eq5DZs+ezc6dO0v6ksqN96JtYRNg8yW4dxd02wHfnQd9ny0iIqAZzhLTDKeISMVijOHnn39m2rRpfPjhhyQnXyvHWsXZiUcb+TC2mT/VRz1Pq0eGFP7CU96E7dmW79asA3feB13vh1p1OXXqFP7+/qSlpdGpUyfGjh3L4MGDqVatWim+uhvrZDL8XyTMiIWUHB8nutWAN4KgR82yGJmIiNxIWlLrQAqcIiIV17lz55g/fz4zZszg4MGDWe0tW7Zk165dWIVdG3ou3ja7mZGRu89yglYdWRZ/hSFv/ZeMbG+71atXZ/jw4YwZMyZr5rUiir4Kb0XCnJOQmuNjRQ9vW/Ds5l0WIxMRkRtBS2pFRETyUKtWLV544QX279/P2rVrGTRoEC4uLowbN67wYRPgx2/yDpsAJgN2/cyjJ3/j2KBu/LVNE3wzixVdunSJqVOn0qZNG26//Xbmzp3LlStXSuGV3Vj+VWBaCBy6DcY0AJds/+nWXYDuO2BFfNmNT0REyo5mOEtIM5wiIpVLXFwcnp6eeHp6Fu6E9HTb7Ob5M4W+R3qG4cuoeGbsj+KbmDO5Zj3DwsIYM2YMbdq0KeLoy4djSfDWCZgfB+lAgLstjLrra24RkUpJS2odSIFTROQmt2MTTH6j2KefSEhi9oFo5h6MITYx2a6vY8eOjBkzhiFDhhQ+AJcjR5PgHyegS3V40te+b8dlW8Gh7lpqKyJS4SlwOpACp4jITS76GHyzHLb8AGmp1z8+H7/Pes48EMWqaPtZT09PT8LCwhg9ejTt27cvhUGXvXt3wurztmc8Xw9S8BQRqcgUOB1IgVNERABIuAyb1sD6ryEuqkSXikxIYs7BGOYejCH6ylW7vnbt2jF69GiGDRtG9erVS3SfsvLTRbhju31b9xrwtyBbANU+niIiFYsCpwMpcIqIiB1j4NBvsP5rzK8bsNLSin2p9AzD19HxzNwfzcroM6Rne8/28PBg8ODBjBkzhttuu61oRY7K2Imr8OZxWJD5jGd2XWvA/2sIvWoqeIqIVBQVokqtZVmhlmU9Z1nWYsuy9luWlWFZlrEsa2Ahzh1mWdYGy7IuWpaVYFnWVsuynrYsq8DXV9zzRERE8mVZENIKRv+JNfeF8+LP+zlwoXiVZ52dLPoF1uOLe9uxu38XsuevxMRE5s2bR+fOnWndujXvv/8+58+fL53X4GANq8CcZnDwNnjCx76q7YaLcM8u6LIdVp615XcREam4ylOwGg/8DwgDQoFCfa9pWdYUYAnQAdgArAZCgMnAcsuynEvzPBERkcKaPH8h7/52gmYf/0iPr35h6ZGTJKfns33Kdaw/eZ78stdvv/3Gc889R4MGDRg+fDjr16+nIqxgalwVZjeDg51gdANwzfbOv/kS9NkNrxwtu/GJiEjJlafA+RvwDjAYaAqsv94JlmUNAJ4C4oDWxpi+xphHgGBgH/AIMKG0zhMRESmstLQ0kpKSsn5fH3eesHW78ItYV6xZz1kHoq97THJyMkuWLKFHjx6Ehoby9ttvc+rUqSKP/UZrVBVmhsLh2+ApX3DLFjyH1iu7cYmISMmV22c4LctaB3QHHjXGLM/nmK1Ae2CEMWZhjr7uwDpsodLPGJNR0vPyomc4RUSkIAcPHmTWrFnMnz+fM2fs9+rs7lOTsc0C6B9UH3fn/L8D3nbmEu0/21Ss+7u4uPDQQw/x5JNPcs899+DsXP4X8MQkw9uRcCoFPrjFvi8hDb48C4/WA2c94ykiUi5UyKJB1wuclmX5A1FACuBtjEnK45howA+4wxjzU0nOy48Cp4iIFEZycjKffPIJM2fO5Pvvv7frq+3uyuPBvowJ9aeZd+79Nsdv3Mv0/YWvfPtgYF0OXUpkX45Z1MDAQEaNGkV4eDiBgYHFeyE3kDG5Cwf9JxJePgrBVeHVQAirD67lab2WiMhNqEIUDSqGtpk/9+QVGjNtyXFsSc4TEREpNnd3d4YMGcLatWs5cOAAL730EnXq1AHgbHIq7/12guYfb6TbV7+w6HAsV9Ns9VuvpKax9MjJQt/HzclibteW7B1wJz/27cTIYF88XGyzmpGRkbz++usEBQXRp08fVqxYQWpq8fcOdbScYTMpHf6TmbsPJUH4AQj+GabHQHLxHo0VEREHq8iBs1HmzxMFHBOZ49iSnCciIlIqQkJCeOedd4iOjuaDDz6gZ8+eWX0b4s7z+Prd+Eas5w+b9/PvXce5lFr4rVUeCapP7SpuANxRvybzurXi5NAeTOvSgvZ1bPt2GmNYuXIlAwYMwN/fnz/+8Y8cPHiwdF+kA6QbGOcL3i7X2k4kw/hD0HgzvBcFV3LusyIiImWqIgfO39ccFVR1ISHzp1cpnCciIlKq3N3dGTx4MN999x0HDx7kj3/8I3Xr1gXgfEoqE/ec4O87jhTpmqND/XO1VXdzYVzzALY+1JltD3fmqeYBeLvZUtvp06d55513CA0NpVu3brmW+5Ynni7weiM4fjv8sxHUcb3WF5sCLxyBoM3w1gm4UH4nbkVEbioVOXD+vtCmqA+hFve8axewrDGZe3ZujY+PL+5lREREsgQHB/Pvf/+b6Oholi1bxt13313kazT2qkov39oFHtO2dnWmdGlB7NAeLOzeim4+NbP6NmzYQGJiYpHve6PVcIE/N7QFz3ebgI/btb4zqfCXY3D7Nu3hKSJSHlTkwHk582fu6grX/N53OVtbcc/LYoyZaYzpYIzp8Ps30SIiIqXBzc2NgQMHsnr1ao4cOcKrr76Kj49Poc59IiT37GZ+qro481hTX9Y/0IkDA+/kj60b0aZRQ+67777iDv2Gq+YMzwfAsdtgajA0dL/W90SD3M+AiojIjVeRA+fxzJ8NCzgmIMexJTlPRETkhmrcuDFvvfUWkZGRfPLJJ/Tp0wcrnxTlbFmEh/gV6z4hNarx744hbO3ZDJfpb8GOzZBecR6GrOIM4/3g0G0wvxl0rm571jOn96PhUPmfwBURqVQq8rYoAdiK+xS0vUkU4A/caYzZWJLz8qNtUURE5EaKjIxk7ty5zJkzh+joaLu+VjU9eTLUn8ea+lLT3TWfKxRSjVpwx71w571QL4/0VsHsTIA2W23ftA+sC38OhDaq1CAiUioq5T6cmcf8CrQDRhhjFubo6w6sA+IAP2NMRknPy4sCp4iIlIX09HS++eYbZs2axRdffEF6thnJKs5O9A+qz+hQf3o0qFXym4W2hjvvg/Z3gpv79Y8vh4buhQ9O27f1rmULnl29y2ZMIiKVRWUOnAOBZdjCYVdjzOHM9nrA90AL4A/GmImlcV5eFDhFRKSsnTx5kvnz5zN79myOHj1q1xdc3YNRIX6MDPbDx6OEYbFqNbjtLuj1EDQIuP7x5ciGC/DPSFh1LnffHdVtRYj61NJznyIixVEhAqdlWe2AqdmaWmDbluQQkPX2YIy5Pcd5U4HxwFVgDZAK9AKqA58CA40xuR5EKe55OSlwiohIeZGRkcG6deuYNWsWK1asICUlJavPxbLoG1iXJ0P9ud+vDs5OJUhW4/9im+0swPbt22nUqBHe3uVr+nDbZfhXJCyPz12uvlU1eCUQBtUFl4pc5UJE5AarKIGzB7bZxQIZY3K9Q1qWNQx4GmgFOAP7gbnAtIKWxBb3vOwUOEVEpDw6e/YsixcvZtasWezZs8euz79aFcKD/RgV4keQV9WiXdirBryzGFzyf0bUGENoaChRUVH079+fUaNGcdddd+HkVH5S3IFEeDsSFp2C1Bwfhba2h/Z6vlNEpNAqROCsqBQ4RUSkPDPG8MsvvzB79mwiIiK4cuVKVp8F9PKtzbJnn8D72F5IS73+Be/pD4PHFHjIhg0b6Natm11bw4YNGTlyJCNHjiQoKKgYr8Qxoq7Ce9EwMxauZEAvb1jTpqxHJSJSsShwOpACp4iIVBSXL1/mww8/ZNasWfzyyy8AdOzY0fb3hEuweS1sWAUxx/O/yJszwLegncUgPDyc+fPnA7YCRlfT7RcN9erVi/DwcPr370/VqkWcYXWQs6kwJQa6e9v+ZDcj1radyh/8wb9K2YxPRKQ8U+B0IAVOERGpiHbv3s2cOXPo2LEjYWFh1zqMgWMH4cdV8Mt6uJpt48rGzeDV/xV43cuXL+Pj40NiYiKd63nz9b3tWHr0JPMOxrD1zCW7Y2vUqMGQIUMIDw+nU6dO+e4xWpZSM6DxzxCdDK4WhNWHlwOgRbWyHpmISPmhwOlACpwiIlJpJV+FrT/Aj9/AoT3w+HPQrXeBp8yePZvRo0cDMOvOW3gy1D+rb/e5y8w9GMPiI7GcuWq/fLdFixaMHDmSxx57DB8fn9J/LcW0/DQ8ujd3e7/a8KdAuKPGjR+TiEh5o8DpQAqcIiJyU4iLAu86UKXgJbBdunRh06ZNeLg4Eze0B15uLrmOSc3I4IvIeOYejGFV9BnSs30WcXZ2pnfv3oSHh9O3b1/c3NxK/aUURYaBr87C21Hw48Xc/V2q24Jn39pQksK/IiIVmQKnAylwioiI2Ozbt48WLVoA8HhTXxZ0b3Xdc04mJrPocCzzDsaw/+IVu746deoQFhZGeHg4t956q0PGXBQ/XbRVtv3sbO6+Zh7wehAMrnfDhyUiUuYKCpzlpz65iIiIVGhz587N+vuoEL9CndPAw50/tm7EvoF3sqnfbYwJ9ae6q21W9MyZM0ycOJE2bdrQtm1b3n//fc6cOeOQsRdGlxrwaSvY2xHCfWzPdP5ufyIcSSqzoYmIlFua4SwhzXCKiIhAamoq/v7+nD59miZeHhwe1LXY10pKS2fF8VPMOxTD2thzZP+k4urqSr9+/Rg5ciT3338/rq757wfqaDHJ8L9oWxXbDANRnaFmjuGcSYE6ZbsqWETE4TTDKSIiIg711Vdfcfr0aQBquLmwIe58sa9V1cWZsKa+rOndkeODu/Fmu6Y08fIAbMF2xYoVPPjgg/j7+/Piiy+ye/fuUnkNReXnDu80sQXNz1vlDpt7rkCDTRC2F7ZfLpMhioiUOc1wlpBmOEVERGDEiBEsXLjQri24ugcjg/0YEeyLX7WSb2D5Q9w55h+MZdnxOBJS0+362rVrx4gRIxg2bBh16tQp8b1KQ/h+mB937fee3vBSANxfC8rhDjAiIsWmokEOpMApIiICaWlpfPvtt8yZM4cvvviC1NRr2544Wxb3+tVmVIgfDwbWw825ZAusrqSm8fHxU8w/FMu6k7mX3D7wwAOMHDmSPn36lNmS2wwDfXbBN3lM9N7iAS8GwLD64K61ZiJSCShwOpACp4iIiL34+HiWLFnC3Llzcy13re3uSljTBoQH+9GmdvUS3Sc5PYMGS9dxPiU1z/46deowbNgwRowYQdu2bbHKYFrx18vw3yj46DSk5+jzcYNn/WCsL9Qqu0dRRURKTIHTgRQ4RURE8maM4ddff2XevHksXbqUCxcu2PW3qe1FeLAfYU0aULtK0SvrfHQ0jsHf7yzUsa1atWLEiBGEhYXh4+NT5HuV1ImrMDEaZp2EhBzJ08MJDnQC/5KvOhYRKRMKnA6kwCkiInJ9V69e5dNPP2Xu3LmsWbOG7J8/3Jws+gXWIzzEj/v96uDsVLiZyAe+/ZWvo4q2TYqzszP33XcfI0aM4MEHH6RKlRub8i6kwsyTtvAZm2Jr61oDfmh7Q4chIlKqFDgdSIFTRESkaCIjI1m4cCHz5s3j6NGjdn0NPNwZ3qQB4SF+NPf2zPcacYnJ+H+wnvRCfo5xsmzPVWbXvn17yuo9PCUDPjhtW277ZiN4KEedo+WZS3AH1AEXPecpIuWctkURERGRciMwMJC//OUvHDp0iHXr1jFixAg8PGzbnpxMTOad3cdp8fFGbvt8M9P2RXIhOfczmosOxxY6bAL8rW1TNve7jfHNA6jpZntgsl+/fqXzgorBzQke94EdHaBfbfu+tAx4+SgM2QtNf7aF0otpZTNOEZGS0gxnCWmGU0REpOQuX77MsmXLmD9/Phs2bLDrq+LsxEMN6xEe7Mc9frVxsixartjInvMJhbq2BRwd1I0gr6qArdjQF5GnufOPr+PTqy+4uJT2yymR5afh0b32bZ7O8IQPPOsPjauWzbhERPKjJbUOpMApIiJSug4fPsyCBQtYsGABUVFRdn1+Hu70DqjL7APRhb5ed5+arHugU96dXjXgtrugcy8IbFouNsg8nQJTY2BKLJzJMbnrhG357Qv+cEeNcjFcEREFTkdS4BQREXGMjIwMvv/+e+bNm8eKFStISkoq1nXmdm1JeIjf9Q/0C7IFz9t7gnft6x7uaEnpsOQUvBcNexNz93fwgr82hAfr5O4TEbmRFDgdSIFTRETE8S5evMhHH33EggUL2LhxY6HP83BxJm5oD7zcirBs1nKCFm2g893Qtgu4l+1+JcbAt+fhvSj45rx939+D4C9BZTEqEZFrFDgdSIFTRETkxjp06BALFixg4cKFuZbc5jS8aQMWdW9d/Ju5V4X2d9jCZ2hrcMpdbzEtLY2kpCS8vLyKf59C2nMF/hcNi+Jsv0d1hro5tjCNvAqB2tNTRG4gVakVERGRSiM4OJh//OMfHD9+nDVr1jB8+HCqVs27ko6niwtnrqYU/2bJSfDTGvjvK/Cnx+HjuRAbaXfI6tWr8fHxISwsjFWrVpGW5riSsrdUg1mhtqC57JbcYXPfFQjaDPfuhK/P5t4KRkTkRtMMZwlphlNERKTsXbp0ieXLl7NgwQJ++OEHuz5XJ4sHAuoyItiXBwLq4epUCpV2Apvanvfs1INh458mIiIiq8vHx4ehQ4cyfPhw2rZti3UDK/uMPwjTY6/9HlIVnvGDET7gVb6K8YpIJaIltQ6kwCkiIlK+HD16lEWLFrFw4UKOHj1q1/fX55/jzb494afVcPxQie9lnJz4NvoM8w5E8eHRuFz9LVq0YPjw4QwbNoyGDRuW+H4FjsXAiP22QkMZOfqqO8MTDWCCn7ZVEZHSp8DpQAqcIiIi5ZMxhh9//JEFCxbw0UcfcfnyZXbt2kWrVq1sB8SegE3fwea1cP5Mie71Q9w5un+1pcBjunfvzvDhwxk4cCDe3t4lul9BjiXB5BiYfRIupdv3WcCDtW37ed7lrW1VRKR0KHA6kAKniIhI+ZeYmMh3331Hv379cndmpMP+nbZnNbdthJTkIl9/9I97Cr03qLu7Ow888ADDhw+nT58+uLu7F/l+hZGQBgtOwfvRcDCPHWW2tYe2jq9zJCI3AQVOB1LgFBERqUSuJtlC56bvYP8O2zrV652Slo5PxDouphS9WJC3tzePPvooYWFhdO3aFac8quCWVIaBb87BxOhr26rcXh02tSv1W4nITUqB04EUOEVERCqpc/Hw8/ewaU2uyrTZLTsWx6C1Owt92ebe1Yi+cpXLqfbrXQMCAhg2bBhhYWHXlv2Wsn1XYFIM3F0T+te175sSA9+dh2f9oLuW24pIEShwOpACp4iISCVnDEQehk1rbQH08gW77gdXb+OLyPhCX+6XB2+nZU1PPo88zZIjJ1kVfYbUHPuXtGrVirCwMIYOHUpgYGCpvIyCZBgI/QUOZy69bVXNVt12WH2o5uzw24tIBafA6UAKnCIiIjeR9HTY8yvnV35MlX3buJKWjm/EulyBMT8hNTw4MLCrXdvZqyl8dCyOJUdOsvHUhVzndOvWjbCwMAYOHEitWrVK5WXktPkidN6eu93bBZ7wgadU3VZECqDA6UAKnCIiIjefF198kVmTJtLC25Of4y8W+rw32jXl/7Vtkm//scuJLD1ykiVHTrLvwhW7PldXV3r37k1YWBh9+/bFw8Oj2OPPy94rtuq2C+PgSo59VSzggdq2bVXuqQmlsZWpiFQeCpwOpMApIiJyc0lLSyMgIIC4uNz7bl7P4Ue70qR64YLijrOXWHLkJBFHThKTaF8519PTk0ceeYRhw4Zx99134+LiUuSx5OdCKsyPs4XPI1dz93erAevbltrtRKQSKChwln4pNBEREZFKzLIspk+fzoABA3Bzcyv0ebfXq1HosAnQpnZ13ukUSuSQ7qzt3ZEnQvzwdrMFy4SEBBYtWkTv3r3x9fXlmWeeYdOmTZTGRIK3K/whAA7eBl+1gt45VvH2cNwWoiJSCWmGs4Q0wykiInLzOn/+PMuWLWPx4sVs2LChwGMnd27O0y1KVgAoOT2Dr6PiWXrkJF9GxXM13X7ta6NGjRgyZAjDhg2jZcuWJbpXdocSYWosLD4FOzuAb46tQ189Cm094eE64KrpDJGbjpbUOpACp4iIiAAcP36cJUuWsGjRIg4cOJCrv19gXUaH+nO/fx1cS2G/zcspaaw4cYqlR07yXew50nN8pmvZsiXDhg1jyJAhNGrUqMT3A0jNyB0oDydC8C+2v/u6wVhfGNMAfNxzny8ilZMCpwMpcIqIiEh2xhh+/fVXFi9eTEREBKdPn7brr+3uyqDGPgxv0oAu9WuWyj1PJSXz0dE4Io7Gsel07kq3nTt35qWXXqJ///6lcr/sXjwM70bbt7lYMKCOrbpt1xra01OkslPgdCAFThEREclPWloaq1evZsmSJXzyySckJiba9Tf2qsqwJg0Ia9KAZt6epXLPlVHx9Pl2W672iRMn8uyzz5bKPbKLSYaZsTAjFk6l5u5vWQ2e8oXh9cGr9GobiUg5osDpQAqcIiIiUhgJCQl89tlnLF68mNWrV5Oenm7X3652dcKaNmBIIx98q1Up9n1e23qIf+48atfm5ORETEwMPj4+xb7u9aRkwIp4W3XbjZdy93s5w+RgeNxxQxCRMqLA6UAKnCIiIlJUp06d4sMPP2Tx4sVs2bLFrs/Jgrsa1CKsiS8DgupT3a1o04KNP/qBY5eT7Np69erFmjVrSjzuwtqZANNibEWGsu/pubEtdKlxw4YhIjeIAqcDKXCKiIhISRw6dIilS5eyZMkSDh06ZNdXxdmJBwLqMqxJAx4IqIu7c8HFhjafvkDnL37O1T5r1iyefPLJ3CdkZEApFDDKz8U0WBRnq3DrZsH2DvbPc15Og7ej4MkG0LD4k7oiUsYUOB1IgVNERERKgzGGrVu3smTJEj744ANOnTpl11/DzYUBQfUZ1qQBdzWohVMelXie27yP9/dE2rW5urpy6tQpatbMo0DR5Nchw0Cn7tDmdqhS+H1Ci8IYOJ0K9XNsWzotBp46BBbwQG0Y7wv31QJnFRkSqVAUOB1IgVNERERKW1paGmvXrmXJkiWsWLGChIQEu/4GHu4MbuRDWJMGdKhrW6OanmHw/2AdcUkpdsf269ePzz//PPdNLl+AF4fZZjkBXN2gdSfo1ANadQS3vPc1SUtLw9nZGauEpWeNgVu3wu4r9u2Nqti2VRnVAOq55X2uiJQvCpwOpMApIiIijpSUlMSXX37J0qVL+frrr0lJsQ+UwdU9GNK4Af7V3Bm7cW+u85cuXcrQoUNzX3jdV7B4Ut43da8KbTvbZj5btAMX16yuxYsX89prrzFo0CCGDBlCu3btihU+Mwx8dgamxcLq87n7XS0YUBfG+UI3ba0iUq4pcDqQAqeIiIjcKOfPn2fFihUsXbqU77//nut9jqtatSqnT5/G0zOPLVfefhkO7r7+TT08of2d0LEbhN5K34ce4quvvsrqbtKkCYMHD2bw4MG0atWqWOHzUKJtW5V5cXAuLXd/Mw/4tCWEOmbFr4iUkAKnAylwioiISFmIiYnhww8/JCIigvw+iwwePJgPPvggd8e5ePjT47Z1rUWQ4VmdGVv3EnEklh/jzpPz7NDQUAYPHsygQYO45ZZbinRtgKR0WB4P02Php2xbq9RxhejO4O64+kYiUgIKnA6kwCkiIiJl7dChQ0RERLB06VIOHDiQ1f7pp5/y0EMP5T7hm49h2awS3TPmylU+OhbHh0fj+Dn+Yq7+W265hUGDBjF48GBCQ0OLfP1dCbZZz0WnbMtq325i3//jBdh1BcLqQ42i7RwjIqWsUgdOy7LmAyMKOOSAMaZZPucOA8YDrQFnYD8wD5hmjMnI65ycFDhFRESkvDDGsGPHDiIiIli5ciVbt27F3T2P4j8r5sO3H0Naaqnc90RCEh8djePDY3H8euZSrv7WrVszaNAgHn30UUJCQop07YQ0SDFQy9W+/eHd8NlZ8HCCofVgrC908NKzniJl4WYJnBuBw3kcctIY8+c8zpsCPAVcBb4DUoFegBfwCfCoMSb9evdX4BQREZEKKekK7NgEW36APb9C+nU/9hTKkUuJWTOfO89dztXfpk2brPDZtGnTYt0j+ioEbYacI27raQueQ+tBdc16itwwN0vgDDfGzC/kOQOA5UAc0M0YcyizvT7wPdAc+IMxZuL1rqXAKSIiIhVewiXYthF+WQ8HdkHhFnpd1/ex5+i5cku+/W3bts0Kn02aNMn3uJwup8HCU7Yltzm3VQGo5gRD69u2V9Gsp4jjKXDmPmcr0B4YYYxcltxfAAAgAElEQVRZmKOvO7AOWxj1u97SWgVOERERqVQunoNff4Sf18GR3NusFMX/fjvB8z/vL9Sxbdu25dFHHy3SzKcxsOmSLXh+FA9X8/jU1tELfmoLLio4JOIwCpz2x/sDUUAK4G2MScrjmGjAD7jDGPNTQddT4BQREZFK6+xp2PoDKRvX4BZ7vMind/5iM5tP5y4odD1t2rTJCp/BwcGFOudcqq3A0MxY2Jt4rX1gXVhW9IK5IlIEBQXOyvRdz12WZb1rWdZMy7L+blnWfZZl5fX62mb+3JNX2My0JcexIiIiIjef2vXgvoFMr9OCJh/9wKtbD7LzbO7nMvNyIiGpSGGzqvO1j207duzgtddeIyQkhDZt2vDWW2/ZVd/NSy1XeM4ffusIG9vCiPpQxcm2rDand6Pg/WhbSBURx6pMM5x52QsMMcbsznb8s8BE4FNjzCP5XHMi8CzwX2PMSwXdXzOc/7+9O4+Pqrr/P/46SQhrwpJVCAkgomwqoICyQ0BFFBBwr9qqtVVb/fb7s7Wrv67a+m37tT+X79fWpVat7ItA2AKCAq4gIKvIvoaEfQkJyfn9cSchyUy2mbkzk+T9fDzmMeTec849c+Z4zCfn3HNFRESkvhswYACrVl1c9HVFy+bc0SmV2zum0q11C595/mvDTp76dFuNr/HO0CvplRDHlB2HmLrrMBuPnfZK07NnTyZOnMikSZPo2rVrtWUeK3QemRJV5h7O/CJouxqOXYDGxpkBfbgtDG6pez1F/FXfZzi/xAkOuwMtgLbAGGAd0A1YYoxpVyZ9yajo4xbzUiUjXFxwqyoiIiJSt1hrueOOO7juuutKj205cYZfr/2G7jNW0mPGSn679hu2nSj/q9XkHYdqfI0m0VHc0j6Jrq1a8Ezvznx12wA2TRjAr3t3pkeZgHbDhg0888wzdOvWje7du/PMM8+wYcMGKptAad2ofLAJMD3XCTYBzlt4JweGfglXfArP74HDBTWutojUQJ2f4ayMMSYWWA70B16y1j7uOf5z4HfA29bab1WS9/fAz4BXrbWP+Dj/XeC7AOnp6X12797tzocQERERiSC7d+9mypQpvPfee6xZs8br/FVt4ri9Yyp9k1oyckHNV4CNzUhmVmbldzJtPX6GabsOMXXnYZ+PWunSpQsTJ05kwoQJ9OrVC1PFVOXJC/DuYfj7QVjjPYlKjIGxCfDQJTCyDURr1lOkWvV606CqGGNuBWYDO621nTzHtKRWREREJEDbt29nypQpTJkyhXXr1gVU1ttDenJP57Y1u+7Js0zb6QSfa/JOep3v2LFj6bLba6+9tsqy1pxyAs93DsMpH48hHZsAs3rWqFoiDVpDDji7AFuBAmttY8+xkiB0rbW2dyX5ZgDjgR9Ya1+s6hoKOEVERKSh27JlS2nwuXHjxlrlbRIdRc7dw4iLjan1dXeeOsv0XYeZtvMwnx45Qdnfam+++Wbmzp1bo3LOFMGUHHjtIKwsE8P+vQs8VLM4WKRBa8gB53XAKuCotTbBc6w9sIeqH4uyF0gDBlprV1Z1DQWcIiIiIhdt3LiRyZMnM3XqVLZsqf4ZnNUtp62pvafPMWN3DtN2HmJVznFee/0NHnjggVqXs/mME3hOz4X110BcmTjYWhi0Fq6NhwdToYfv/ZJEGpyGHHD+FXgSWGitvbHM8S+A3sD91tq3KuQZAnwAHALaWWt9PEL4IgWcIiIiIt6stXz11VdMnTqVyZMns22b7x1r7+yUynPXdiGjRdOgXfvg2fO0HnEzTa4fAV2uhOjoWpdhrfeutR8eh8FfXvy5bxw8eAncmQzxtZ+gFak36m3AaYy5GmcmMstaW1TmeAzOPZjP4+zEe6O1dmGZ8xOBqThB5SBr7XbP8WRgGc7utk9aa1+org4KOEVERESqZq1lw4YNpctuv/76a6801ya2ZFLHFCZ1TKVDXPCCT1rEw9X9ofdA6N7Hr+CzxJNfwwv7vY83i4JJSU7wOVCPV5EGqD4HnOOAmcBRYBuwD+dRJj1xHo9SDPzUWvsnH3lfBr4P5ANLgEJgBBAPzAImlg1iK6OAU0RERKTmrLWsX7+eqVOnMnXqVJ8zn9ckxjOxYyqTOqTQKb5ZcC7ctBn85T1oFOt3EUUWso85S25n5UKBj1+jL2sK30mF+1KhbeMA6itSh9TngLMj8ATQF8gAEgCLE3h+iPM4lC+qyH838BhOgBoNbAFeB16pbiltCQWcIiIiIv4pmfksCT63bt3qlaZXQhwTO6QyqWMKl7Vs7v/F+g2Dh3/iV9bc3FwSExPLHytwnuH5j4PwlY+nu/8qA37d0a/LidQ59TbgjAQKOEVEREQCV3LP55QpU5g2bZrPDYeubBPHpI4pTOyQwhWtarljz6O/hN4Dal2vffv2kZGRQb9+/Rg/fjzjx4+nc+fOZeoNn52C1w/Cv3PgpGd93I5+0LHCyuAd56BTEFcLi0QKBZwuUsApIiIiElzWWjZt2sTUqVOZNm2az0etdGvVnIkdU5nQIYUr28RVXWBsY/jrZGjcpGYV2LMdvt4Iva7nxXcn84Mf/KDc6Z49e5YGn1dddRXGc9Pm2SKYcQTWnYHnLy1f5I5zcOkncE0cfDsV7kqG1o1qVh2RSKeA00UKOEVERETctXnzZqZNm8a0adNYv3691/kuLZsxoUMKEzqk0icx3ruAPgPh+7+o+QX//QpkzwZgS34xb27Yzszdh9l24qxX0g4dOjB+/HjGjRvHgAEDiK5kU6Jf7YTf7r74c2MD4xLh25dAZmuI1kZDUocp4HSRAk4RERGR0Nm2bRvTp09n+vTpfPFF+a06Bg4cyIczpsCalfDFR7DDsyz3u09D36E1u4C18ONvwbFcr1Mbj51m5u7DzNyVw5q8k17nk5KSuPXWWxk3bhyZmZk0aXJxRvVH2+Gl/b43GkprDPelwAOpcFmQ9kgSCSUFnC5SwCkiIiISHjt37iwNPj/++GP++te/8uSTT15McPQIrF0FA0ZCkxpGcju3wu+fqDbZ7tPnmLU7h5m7DvPR4eMUVfidunnz5tx0002MGzeO0aNH07p1a44WOvd5vnEQvjjtu9wB8fBsJxjUqmbVFYkECjhdpIBTREREJPz27t1L8+bNadOmTWAFTX8dsqbUKktufgHv7znCzN2HWbw/j/yi8g87iImJYejQoYwbN45bb72V9u3bs/40vHEI3j4MuYXly1vZC65vGdjHEAklBZwuUsApIiIiUk9YC794CA7v97uIM4UXWLAvj1l7DjNvTy7HCgq90vTp04dx48YxduxYunTrwfyjhn8egnlHoWMT2NoXTJl7Oo8Xwl/2OctuO2vJrUQgBZwuUsApIiIiUk/s3wXPfC9oxV0oLmb5oWPM2p3DrN057DuT75WmU6dOjB07lrFjx3LZtQPYdyGGvhX2PXr1ADyyzfn3gHi4PxVuT4aWMUGrqkhAFHC6SAGniIiISD1RWABb1sGalZxYsZCWJri/J39+5ASz9+Qwe3cOG45538SZkJDAmDFjGDt2LKNGjaJ58+YAXL8GVlfYo6hJFIxPdIJP7XIr4aaA00UKOEVERETql/Pnz5OSnMSVzWIYn5HMbR1SyGjRNKjXmJj9JdN3Ha70fOPGjcnMzOTWsWOJGTKB2efbMP8oXPDxq3vbWLg3Be5Lhe7Ng1pNkRpRwOkiBZwiIiIi9UtWVhajR48ud6xXQhy3dUhhXEYyPVrHBVT+heJikt5ZxvGCCzXO069fP4ZPuJPioXew0KTy5WnfU5oLroQbAtw3SaS2FHC6SAGniIiISP2ybds2/v73vzNjxgx27Njhdb5zfDPGZyQzLiOZ61Na17r87AN5ZGb5//tjp06duO7e73F+6J2siE0jp9AJPlvFwKHroXHUxbQXiqGI8sdEgk0Bp4sUcIqIiIjUT9Za1q9fz8yZM5kxYwYbNmzwSpPaNJaxGcmMz0hh2CVtiI2uPrL7werNvLhpT43r8Xi3dJYeyGPT8TNe51omJHL1wz/h/JDb6dU+hZe7Ny53fm4u3LcF7kx2drntF19+B1yRYFDA6SIFnCIiIiINwzfffMOsWbOYOXMmq1atouLv0S1jY7gpLZFxGcmMTksiLtb3NrIZk5ez57T3jrW+dG3VnE0TBgKw/eRZ5uzJYc7uHD46fJyiCtfPysrixhtvLHds0kaYduTiz5c1hW+lOPd8dgzubanSgCngdJECThEREZGG59ChQ8yZM4eZM2eSnZ1NYWH5523GRhmGt01gXEYyY9OTSW3mzDyuzTtJ71mra3ydp6/syLPXdvE6fvR8IfP3HuH9PUdYsC+X4sZNyM3NpXHjizOcF4qhx2ew9Zzvsge1dGY9J+kRKxIgBZwuUsApIiIi0rCdPHmS+fPnM2vWLObPn8+pU6fKnTdA/+RWjM1IZueps/zvln01LnvVLf24LrlVlWkKi4vZVNSIq771MFzVH5JSS88VW/jwBPzrEEw5AqeKvPM3NnBrIvyxk2Y9xT8KOF2kgFNERERESpw/f55ly5Yxa9YsZs+ezaFDh/wuK6VpLAfuGkpUbW+6bNcBrurnvDpeDlHRAJwrgjl58NYhWHjU2UyoRIyBg9dBYqzf1ZUGTAGnixRwioiIiIgvxcXFfPbZZ8ycOZPZs2ezZcuWWuV/6PI0/j6we2CViGsJV3qCz269oYkzhXm4AP59GN46DGtPwy0JMKdn+azrT8OsXOd+z06a+ZQqKOB0kQJOEREREamJrVu3Mnv2bGbPns3q1au9Nh2qaM7IXtySnhy8CsQ0gsuvvDj7mZACwMYzcMHCVS0u1nPNmjV80GM8r+Y1AeD6eCfwvD0ZEhoFr0pSPyjgdJECThERERGprcOHD/P+++8ze/ZsFi9ezPnz573S9E9uyW0ZKYzNSKZLy+bBr0Tp0tv+cGnX0sO/+MUv+P1zf4Sp+6F1+YA3xsBNbZzg85YEaBod/GpJ3aOA00UKOEVEREQkEGfOnGHRokXMmTOHuXPnkpub65WmS8tm3JqezK3pyVyf3IroqCA+TLNLT/jx86U/Xn311az7aiMMvg0y74W+NzqzoxXERcPEJLgnBYa2gmg937PBUsDpIgWcIiIiIhIsRUVFrF69unTp7ddff+2VJrFJI0anJXFrejI3pifRPDoqsItOfBBunATA3r17SU9PL3++ZSIMux1G3AM9rvdZxNa+0KVZYNWQuquqgDPA3ikiIiIiIsESHR3NwIEDef7559m2bRubN2/mueeeY8CAARjPbrW5+YW8tf0AE5d+ye8SesITv4WhY6B1on8Xvap/6T/nzZvnff5ELsx6GX4wAO7pDG/8CvZuu3h+y2dM6NeTp59+mhUrVlBYWEhuAeys5Pmf0rBohjNAmuEUERERkVDIyclh/vz5zJkzh4ULF3L27FlWrFjBoEGDnATWwt4dsO5j57XLe3bUS9Il8IfXwRPM3nLLLcydO7fS5I93S2f4JW2Yu/cIs5t3JG/gJNj+JWS9UZqmZcuWpD/9Mhv63821TQu4Py2W25MgSY9cqbe0pNZFCjhFREREJNTy8/NZunQpo0aNIiYmxnei43mw/lMn+Nz8JRR4b0xE5ni48xEAzp49S0JCAvn5+ZVed8XNfRmU2rr05zW5J5m39wjz9h7hs9wTFJeEFq9vgI49StOZ4iL6x5zie5fFMz4pirhKqix1kwJOFyngFBEREZGIV3AetqyDdZ/A+k/gmGdjov98Frr2ApzltGPGjKm0iNaxjThyz7BKNyzKzS9gwb5cZuWcYfb9/48L14yCaO/IMvrCefoWHOSxrm2YlBFPrG7yq/MUcLpIAaeIiIiI1CnWwr6dzuznDRNKd6B99NFHeeWVVyrNdmenVP497KoaXaKo2JJ1Gl5M6suHPUZztut1PtNFnz3JY1/9k3uH9adPnz5ERSn6rIsUcLpIAaeIiIiI1HXWWjIyMti7d2+laf41pCf3dm7rV/mfmFb8KakfS7rdyMm0i8/8JGcv3JkB1pKUlMQNN9zADTeN5sZRo0hMTPDrWhJ6VQWcWj0tIiIiItLAbdiwocpgM8rAjWl+7oIL9LPHmZ6zEHIWsiY+nf9KGcC8yzKJXTmdXM8E2JEjR3j77bd5+0g0FF9Du62zGBefz31DruWaa67R7GcdpYBTRERERKSB8/k4lDKuaNmc+EbBCR16n9zDuyf3UPz1e+RHx3L0ziFk7csla+8RlhzI49SIuyHtMvanXcZLwEvrv6TZq79jZHQeEwZew6hRo0hJSQlKXcR9WlIbIC2pFREREZG6Lj8/n+XLlzNv3jzmzp3Lzp07vdLENYoms20CN7dPYnT7JC5p1jjo9TgeFUvy2LcobN7Kd4KvVsHSf9Mzbwu3DOzLI488Qnp6etDrIbWjezhdpIBTREREROoTay2bN29m7ty5zJs3j5UrV1JUVFQujQF6J8YzOi2J0e0T6ZvUkijje/fa2rp8zuds6zoURtwF/W+G2CbeiYqKYO1SFt3QgZE9LwvKdcV/CjhdpIBTREREROqzY8eOsWjRIubNm0dWVha5ubleaZKaxHJDWgKj05K4MS2R1o0b+XWtXafO0XHKiosHmsXBwHEw/C64ZmS5x6yYc6c5NbI5zWOCE+iK/xRwukgBp4iIiIg0FEVFRXz22WfMmzePefPmsXbtWq800cbQP7klo9OSuKl9Ir0S4mtc/iub9/Doqs2+T7ZMhMETnJnPq4bQeefHfN16G6S0g+59IL4Vi4/CqwfhzmQY3QaaRvv7SaU2FHC6SAGniIiIiDRUBw4cYMGCBcyfP59FixZx6tQprzRtmzXmxrREbkpLZFS7ROJjK998aOziNczZc6T6Cye249WXX+bhRa84zxUFSO/M/f2e5K3GnQFoEQ23JsAdyXBDG2isTW5do4DTRQo4RURERESgoKCAlStXMn/+fObNm8fmzd4zlTHGcH1KK0a3T+KmtESubBN3MX9RMQnvLOV0YZFXPq9yYmI4sXg2zd7+W+mx81GNSJr4Hqdim3ulbxkN45PgjiQY0RoaVQg+CwoKAIiNja3px5UyFHC6SAGniIiIiIi3Xbt2kZWVRVZWFtnZ2Zw9e9YrTbvS2c8kjIEJ2V/WqOzBgwez/P5bYNWScsc3tUznvYwhTO4whG3xaT7zJsRYbksy/DID2nv2I5oyZQoPPvggw4cPZ9SoUYwaNYrOnTtjgrQRUn2ngNNFCjhFRERERKqWn5/PihUryMrKYv78+Wzbti2g8v7w+9/z07wNcOKYz/MWWNe6E5MzhvBehyHsapFa7nyULebAudmkdO8B7S/loe9+l9dee61cmoyMDEaNGsXIkSMZMWIEbdq0CajO9ZkCThcp4BQRERERqZ1vvvmGBQsWkJWVxdKlSzl37lyt8m9eNI8rJv+t+oQ4wednCV2YnDGEKRmD2dc8iREH17Ik+6fO+RbxzP56L6+fa8HSq8dxZvG/YeOqi/eGAsYYrrnmmtLZz/79+2v5bRkKOF2kgFNERERExH9lZz+zsrLYunVrlelTUlI48PoLRM14o9bXKsawOqkrAAOObCp37ie9vsOfut8OQPyJw7RaPYtDWW9TsGFlueAToHnz5gwdOpSRI0cycuRIunbt2qCX3yrgdJECThERERGR4Nm5cydZWVksXLiQ7Oxszpw5U+78fffdxz9f/BtsWgNffQEbv4CTvpfW1pQFOo1702vpLUBU7j6Kl02FD6bA5k+8gk+Atm3bkpmZyciRI8nMzCQ11buc+kwBp4sUcIqIiIiIuOP8+fOsXLmSBQsWsGDBAjZs2MC7777LXXfddTFRcTHs2+kEnl99Dts3QdGFWl2nGMMHKVcyJWMw09MHkNukle+EOXth+VSY/gIc3lNpeT179iQzM5PMzEwGDx5MixYtalWfukYBp4sUcIqIiIiIhMa+ffto1apV1QFc/lnYss4TgH4BRw7W6hoXTBQfpFzFlIxBvNv2Os40b+2d6NvdYdcm7+M+xMTEcN1115UGoNdeey2NGjWqVZ0inQJOFyngFBERERGJYDkHYOMaJwDdss4JSGto7LINzGnTHYbeDgPHQ8sE2LURvt2jfMKkNJrd9RR/zl/Pwc+Xk70/l09yTnDBR6wVFxfH0KFDyczMZMSIEXTr1q3O3/+pgNNFCjhFREREROqICxdgx2Yn+Ny4huJd24iqLGlxMYnvLONEgWd5bnQM9B4BjWJh1fvlE0/6D3j0LwCknTnChD0fcfM3H3Bu/UcsPZDH4v25bDp+Bl9SU1MZMWJE6Ss9PT1IHzZ0FHBWwRhzN/B94EogGtgCvAG8Yq0tri6/Ak4RERERkbppeN9rSMzdx6h2idzQLoH2LZqWnlt1+BgD5n5as4JeXAXdr/M6fMnZPCbs+YhJez6k0+61LNt/hCX788g+kMf+s+d9FnXZZZeVBp/Dhg0jISHBr88WSgo4K2GMeQl4FMgHsoFCYAQQB8wEJllri6oqQwGniIiIiEjdk5OTQ0pKSrljl7dszg1pCYxsm8CKQ8d4fsOumhXWJ5O7H3yChR0Hkdekpc8kKeeOctuelfxg6xy6ntzLluOnyT5wlCUH8vjg4FGOF3hvdGSM4eqrr2bEiBEMHz6cQYMGReQGRAo4fTDGTACmAYeAwdbarz3HU4BlQFfgSWvtC1WVo4BTRERERKTu2bFjBz//+c9ZvHgxeXl5AZXVtVVzNk0YSKGJZnnKlUzNGMTM9tdzxMdut0sX/5hhh9eXO1ZUbPki7yTZB5zZz5WHj5Nf5L3YMiYmht/85jf89Kc/Dai+waaA0wdjzOdAH+B+a+1bFc4NAT7ACUbbVbW0VgGniIiIiEjdVVxczNq1a1m0aBELFy5k1apVFBYW1qqMH3ZP54X+Xcsdu2Ci+DC5B1PTBzEjfQCHm7YhKf84B6bfTUyZ8OJko2Y82ecRbtu7kpEH19K4uJD8C0WsyjlO9oGjLD2Yx2dHTlLkidveeecd7r777sA/eBAp4KzAGJMG7AUKgFbW2nM+0uwD2gEDrLWrKitLAaeIiIiISP1x+vRpli9fzuLFi1m0aBGbN2+uNs/kYVdxe6fUSs8XmShWJnXjQNME7ty9vNy5dzsM5Z6BTwMQV3CGMfs/ZcKej7jpwOc0K3Lu8zxZcIHlh46SfeAoTy9eTeollwTwCYNPAWcFxphbgDnAWmtt70rSzATGAY9ba1+qrCwFnCIiIiIi9de+fftYvHhx6Ss3N9crTZSBPgktGdkugcy2CQxIaUVsdGX735Z32+BfMjN9gNfxphfyuenA50zY8xFj9n9KfOFZtp8tpPO72QF/pmBTwFmBMeaHwAvALGvt+ErSvAD8EPiztfb/VFaWAk4RERERkYahuLiYdevWsWTJEhYvXsyHH35Ifn6+V7pmMdEMTGlFZtsEMtsl0CshvtIy17TpzJT0QUzNGMSOuLY+08QWFTDy4Foyty3kyd/8KmifJ1iqCjhjQl2ZCFGytZPvh+E4Tnve41yui4iIiIiI1AFRUVH06tWLXr168dRTT5Gfn8/KlStLZz/Xrl2LtZazF4pYtD+PRfvz4DNIbNKI4Zc4wWdm2zZ0jGtWWmbvo9vpfXQ7z375Butad2J6+kCmtx/A5lYZpWkKomOZl9aPflFHw/GxA9JQZzh/DvwOeNta+61K0vwe+BnwqrX2kQrnvgt8FyA9Pb3P7t27Xa6xiIiIiIhEutzcXJYtW8aSJUtYsmQJO3bs8JmuY1xTMtsmMKJtG0a0TSCxSaxXms3x7Z3gM30AX7bpTGxRAdsvz6V9mu9Z0HDSktoKtKRWRERERETctmPHDrKzs1myZAnZ2dk+H79igCvbxJHZNoHhbdswOLU1LRqVX4j6TYtLmN28Az/6/TMhqnntaEmtt12e94wq0rSvkFZERERERKTGOnXqRKdOnXj44YdL7/8sCUA//PBDzp49iwXWHT3FuqOn+PNXu2gUZeib1JIRbRMYfkkbrktuxaWnD9LLx3M564KGOsPZHthD1Y9F2QukAQOttSsrK0sznCIiIiIiUlvnz5/n448/Lg1AP/30U4qKirzSlWxA9MzfXub6224PQ02rpyW1PhhjvgB6A/dba9+qcG4I8AFwCGhnra30zwkKOEVEREREJFAnT55kxYoVZGdns3TpUtavX196rnHjxhw7doymTZuGsYaV05Ja354FpgJ/NMasstZuBzDGJAMve9I8V1WwKSIiIiIiEgzx8fGMGTOGMWPGAJCTk8OyZcvIzs7m/PnzERtsVqfBznACGGNeBr4P5ANLgEJgBBAPzAImWmu957XL0AyniIiIiIg0ZJrhrIS19lFjzEfAY8AQIBrYArwOvKLZTREREREREf816IATwFr7LvBuuOshIiIiIiJS30SFuwIiIiIiIiJSPyngFBEREREREVco4BQRERERERFXKOAUERERERERVyjgFBEREREREVco4BQRERERERFXKOAUERERERERVyjgFBEREREREVco4BQRERERERFXKOAUERERERERVyjgFBEREREREVco4BQRERERERFXKOAUERERERERVyjgFBEREREREVco4BQRERERERFXKOAUERERERERVxhrbbjrUKcZY44Au8NdDx8SgdxwV6KBUtuHj9o+vNT+4aO2Dx+1ffio7cNHbR8+kdr2GdbaJF8nFHDWU8aYz62114S7Hg2R2j581PbhpfYPH7V9+Kjtw0dtHz5q+/Cpi22vJbUiIiIiIiLiCgWcIiIiIiIi4goFnPXXq+GuQAOmtg8ftX14qf3DR20fPmr78FHbh4/aPnzqXNvrHk4RERERERFxhWY4RURERERExBUKOEPIGHO3MeZDY8wJY8xpY8znxpjHjDF+fQ+1Lc8Y86Yxxlbx2hLK+odSONveGDO0mnYv+0qvkDeg7ywSBKvtjTGXG2OeMMa8bYzZYowp9rTBRB/EJCQAABBJSURBVDfrUZf7PYS3/Y0xjYwxI4wxfzbGfGyMOWiMKTDG7DfGTDPGDK0ir/r+xXL86vsa88PW7zXmB9j2gYwdgdajofd7f9s+kO9M/b60jLC1odv9PiYYhUj1jDEvAY8C+UA2UAiMAF4ERhhjJllri0JU3kpgu4/jB0NV/1CKgLY/BPyziiL7Al2Bb4C9laSp9XcWCYLc9t8HnghlPepyv4eIaP8hwGLPvw8BXwBngG7ABGCCMea31tpfVVGG+n4Afd9DY35o215jfuBtH9DY0RDH/Ahoe433Ye73HpE53ltr9XL5hdNJrOfLvqzM8RRgk+fcE26XB7zpOfdAOOvfENu+mjI3evL9LFjfWSS8XGj7h4A/AbcDlwIfeMqY6EY96nK/j5T2B4YD04BBPs7dAVzwlDHMx3n1/QDaPpA2rMt9P1LavpoyNeZXX1YgY0eDG/Mjoe0D/M7U78PUhqHq92H/ohrCC/jc84Xd5+PckDJfdJSb5QXQGYNa/4bY9lWUd50nzwWgnY/zdXkQdrXfUPNfuv3976XO9vtIav9qyviHp4zXfJxT3w+w7TXmh6/tq8ivMT8I/aaasaPBjfmR0vYBfGfq92Fqw1DVP+LXo9d1xpg0oA9QAEyteN5auxzYD6QC/UNdXqRdL5jqSNt/x/O+wFq7v4Z5Il6k9Bt/6xEp9fdXHar/Ws97WhjrEFR1qO19qsv1ryN115gfnLb3OXY0xDE/UtrexXwRqw61vU+hrL8CTvf18rxvtNaeqyTNZxXSul3eMGPMX4wxrxpjfmuMuaGKm4KDXf9QisS2L2WMaYazRALgtWqS1+Y7iwSR0m/8rUek1N9fdaX+l3neq7o/R30/cBrzLwpb3TXmB7XtKxs7GuKYHyltH4x86vdVC3Ybhqz+2jTIfR0977urSLOnQlq3y7vPx7FNxpg7rbUbXLheuERi25c1CYgDcoC51aStzXcWCSKl3/hbj0ipv78ivv7GmFTgAc+P06tIqr4fOI35F4Wz7hrzy6f1SzVjR0Mc8yOl7YORT/2+Ei61YcjqH8l/NagvWnjez1SR5rTnPc7l8r4Efgh095TTFhgDrMPZAWuJMaZdEK8XbpHU9r6ULK16y1pbWEkaf76zSBAp/cbfekRK/f0V0fU3xsQAbwMtgWxr7fs+kqnvB05jvrdw1l1jvsPvtq/B2NEQx/xIaftA8qnfV8HFNgxZv9cMp/uM592Guzxr7X9XOHQGmGeMWQwsx1mf/VPg8WBcLwJETNt7FWRMZ2Cw58fXK0vn53cWCSKl3/hbj0ipv78ivf7/g7Pl+l7gXl8J1PcDpzE/cmjMD5rqxo6GOOZHStv7nU/9vlputWHI+r1mON13yvPeooo0JedOVZHGrfKw1hYAz3p+HO329UIoktu+5C/dq621m2tw7XKq+c4iQaT0G3/rESn191fE1t8Y8wLwIM4zxkZYaw/VJr/6fuA05pdLGyoa8wNs+xqOHQ1xzI+Utg9avhLq9663Ycj6vQJO9+3yvGdUkaZ9hbShLK/EFs97xel2t64XCrs87xHV9saYaC6usa9u44iqVPadRYJdnvdw9xt/6+Fvvkixy/MeUfU3xvwZZ8nPEZz/cX7tZ1Hq+4HTmB8iGvNL+d32tRg7/K2Hv/kiwS7Pe7jbPij5fFC/d68NS+rker9XwOm+ki2MuxtjmlaS5toKaUNZXokEz/vpCsfdul4oRGrb34DzH/0ZYHINrluZyr6zSBAp/cbfekRK/f0VcfU3xvwJ+BGQB4y01m4KoDj1/cBpzA8djfkOv9q+lmNHQxzzI6XtA85XCfV799owZP1eAafLrLV7gTVALM4OdeUYY4bgPE/nELA61OWVcbvn/bOyB128nusiuO0f9LxPttYGMoD6/M4iQaT0G3/rESn191ek1d8Y8xzwFHAM53+c6wIsUn0/cBrzQ0djvp9tX9uxoyGO+ZHS9oHmq4L6vUttGNJ+b63Vy+UXMBHnhtyDQOcyx5OBjZ5zT1TI8yzOFPizQSrvapzdqqIrHI/B+QtKkSffDcG4XqS8IqHtK+RPBM570l1fTd39/s4i4RXstvdR/geeMiYGux7B+K7D/Yqg9v+tJ90xoE8N666+H2DbB9KGdbnvR0LbV0ivMd///9/WeuwIpP+q3wel7TXeh6HtA2nDUPX7sH9RDeUFvOz50s4B7wMzgBOeYzN9dJI3PefeDFJ54zzn8nD+SjEVWADs9xwvAn4crPpH0ivcbV8h73940m2uQb0D+s4i4RXMtgd6Ax+XeZ30pN1W9ngwv7O63O8jof2BWz1pLM5fVt+s5PW0+n7Q215jfpjHHU9+jfl+tD1+jh2B9l/1+4DGbY334Wv7iB/vw/4lNaQXcDewEud/WGeAL4DHgCgfaX12xgDK6wj8N7DK0wHzPR3ra5wt2qv9K0ptrhdpr3C2fYV86z1lP1WDOgf8nUXCK1htDwwtMxBX+nLhO6uz/T7c7Y/zkOpq8wAfqO8Hve015kfGuKMx34+293fsCEb/bej93t+2DyCf+n0EtKHb/d54LiIiIiIiIiISVNo0SERERERERFyhgFNERERERERcoYBTREREREREXKGAU0RERERERFyhgFNERERERERcoYBTREREREREXKGAU0RERERERFyhgFNEpB4wxuwyxthqXuPKpM/0HFsS5nr/zlOPX9QiT2aFz9W5irStjDHnyqS9Nzg1Dz9jzEuez3R9DdKWtPM/gnTtzp7ytvuRN6h9T31IRCSyxYS7AiIiElQLgUOVnNsTyoqE0ANAZcHGXUCT0FUlNIwxBhiH811/HObqlGOM2Qe0A9pba/eFuz419AANrA+JiISKAk4RkfrlOWvtBzVItwroCpxxtzqu2gakAvcZY35lrS32kebbwAXgK+DqUFbOZf2BtsD/VPK53bYbp/8U+JE3kvpeQ+5DIiIhoSW1IiINkLX2rLV2i7V2b7jrEoBzwBSgPTC84kljTDfgWiALOBzaqrnuNs/7zHBc3Fpb6Ok/O/zIG0l9ryH3IRGRkFDAKSLSAFV2H13Ze/OM43FjzDrPPWzHjDGzPL+E+ypzlDHmZU/6PGPMeWPMbmPMm8aYK1z6KG943h/wce7bFdJ4McbEG2MeMcbMNsZ8Y4w5a4w5ZYxZY4z5qTHG51JKY8wVxpi3PJ+vwJNnpzFmhjFmfIW00caYx4wxHxtjTnjSHzbGfGGM+S9jTKIfn3s8cBxY5kfesnUr7QfGmFhjzC+NMVuNMfnGmBxjzL+MMWk+8nndw2mMecgYY3GW0wLsrXCfZFrFa/ooV30odH1IRCQktKRWRER8McC/gInACuBrnJmescAQY8zV1trdFfK8irM8cSOwHOePmj2A+4GJxpiR1trVwayktXaVMWYrcJsxJt5aexKcX9CBe4FcYC7wSCVF9Ab+B2f2ahvwGZAA9AP+ANxijBlmrT1fksEYczXwEdAc2Ay8D5QEWjcBsZSfefwncA9w1pMvD0gEOgP/CbznqWeNGGOuBC4F/mWtLaxpvmrE4tz/2wfn+94EXIfThoOMMVdZa09UU8Y2nM86CWgGTMX5zCVqsoRWfSgEfUhEJJQUcIqIiC+dcH4B7mqt3QngmamZBdwAPA18v0KeJ4FlZQMTY4zxpHsJ+F/gShfq+k+cX+zvAP7uOXYTTuDygrW20KmGTztwllIuL3v/njGmNTAZGAk8Dvy5TJ4f4QQKP7bWPl+2MGNMHNC9zM+dcAKFXUBfa+2RCul7AbVdWurGctpBwKdAJ2ttrqdurYAPgKuA7wF/rKoAa+0KYIUxJhMn4PyRH5sGqQ+Fpg+JiISMltSKiNQvy4zvR6K86UdZj5cEmwDW2nzgN54fR1RMbK2dVXEWzDpexglmehpjLvejHtV5Cyim/JLIkqWQb1aV0Vq7x1q7rOJmMdbaY8ATnh8nVsiW4nnP8lHeKWvtxz7SflExUPCkX1sS4NXCbTgzXQtrma8qxcC3y9bFWnsc+JPnR6/v2w3qQyHrQyIiIaMZThGR+qWyx6J8VMtyCoDFPo5v8by39ZXJGJMOjAYuB+KBaM+pJM97F2BrLetSJWvtfmPMYuAGY0wXnOWGY4AvrbVfVpffM4M2EGeWLw1oirOkuOSPsl0qZPkUGAW8aoz5FbDCWlvZbq2bcJaSjjXGPA28a631+/E0xphLgZ7ATGvt2erS18JOa+0mH8er/L7doD7kJah9SEQk1BRwiojULzV9LEp19ltri3wcP+l599oIxRjzO5ylttEVz5URH4S6+fIGzlLfB3AC7liq2OilhDHmEpylqf2qSFaxzs/hBBdDcYLy88aYtTjLT9+x1n5VktBae8IY8yDwD+BZ4FnjPKdyNc59gZPL3ttXAxM87zNqkacmKgtgKv2+3aA+FJI+JCISUlpSKyIivtTq2Y7GmDuAn+PMxDyIcw9oU2utsdYanA1kwJn1ccMs4BjwLZylkAXAuzXI9zpOoPAhzrLRZCDWU+fmnjTl6mytPWOtHQZcD/zak7cnTqC03hjz8wrpJwPpnnq9gbMcdhLOfYObjTHtqLnbgEKcQCOYwvEsz3LUh0LWh0REQkoBp4iIBMMkz/tPrLWvW2t3eu75LNHZzYt7Znjew1nOeDUwt7r72owx8TgzWheAm621S621R8rs/Fplna21q621/9daOxJoAzyEE7j9xhjTuULaY9baN62137HWXg5chrMLa0ecWatqGWPaAn1xNtU5XpM8dYz6kMt9SEQkHBRwiohIMLTxvHvtlmmM6YE7O4tW9DrOvXd5wGs1SN8KZ+bpuLX2lI/z99T0wtbaAmvtaziPxIjCma2qKv12LgYJV9XwMuNx6hvs5bTBVnIvYm1v21Efcr8PiYiEnAJOEREJhpLNZR42xjQqOWiMScHZ5bOqe/KCwlr7ubU20fOaX4MsB3HuUUw0xtxe9oQx5mYu7jBKhXOPeTaWqXi8M9DV8+Nuz7E+xphJnkfKVDSmbNoauA1n9mt2DdOHy37Pe9cqU3lTH3K/D4mIhJw2DRIRkWD4K85szlhguzHmE5xnMQ4FdgJzgFvDVjsfPM9W/APOBi6TjTFP4Pzi3hm4Fue5jD/zkfX7wIvGmG+Ar3DuOUzF2QQmFnjbWrvGk7YjMAU4Y4xZA+wDGgO9POdOAs9UV1djTBtgMLDaWutrF+JIMhOnLd4zxiwCSh5z8pTnUSGVUR9ysQ+JiISLZjhFRCRg1tqvgd44vxhH4QQGVwCvAAMAX8sNw85a+0fgduAToAdwM86S0Lup/Jf4nwGvAqdxPttEnABjmeff95dJu9KT/iOgPTAOGO7J+zzQw1q7tgZVHYvzR+JIX04L8AJO2x0EbsHZAOhBLm6g45P6kOt9SEQkLIy1Ntx1EBERkSoYY97HWT7ZyVq7M9z1ERERqSktqRUREYl8H+HsTqtgU0RE6hTNcIqIiIiIiIgrdA+niIiIiIiIuEIBp4iIiIiIiLhCAaeIiIiIiIi4QgGniIiIiIiIuEIBp4iIiIiIiLhCAaeIiIiIiIi4QgGniIiIiIiIuEIBp4iIiIiIiLji/wP4twVW6dltCwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize = (15,10))\n",
"\n",
"plt.plot(heun_run[:,2], heun_run[:,1], label='Heun (Implicit)', color = 'black', linewidth='12', linestyle='--')\n",
"plt.plot(rk_run[:,2], rk_run[:,1], label='Runge Kutta (Explicit)', color = 'tomato', linewidth='7', linestyle='--')\n",
"plt.plot(m_tsi, v_tsi, label='Tsiolkovsky', color = 'deepskyblue', linewidth='3', linestyle='--')\n",
"\n",
"plt.title('Rocket Velocity vs. mf/m0 Ratio')\n",
"plt.legend(loc='best')\n",
"plt.xlabel('Final Mass / Initial Mass')\n",
"plt.ylabel('Velocity (m/s)')"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The simple rocket solution predicted the rocket would travel faster and higher than the complex one.\n",
"This makes sense as it does not take into account the effect of gravity or drag.\n",
"\n",
"In the simple model, the rocket reached a height of 581.79 m. when it ran out of fuel\n",
"In the complex model, the rocket reached a height of 416.39 m. when it ran out of fuel\n",
"\n",
"In the simple model, the rocket reached a velocity of 392.58 m/s. when it ran out of fuel\n",
"In the complex model, the rocket reached a velocity of 225.35 m/s. when it ran out of fuel\n"
]
}
],
"source": [
"print('The simple rocket solution predicted the rocket would travel faster and higher than the complex one.')\n",
"print('This makes sense as it does not take into account the effect of gravity or drag.')\n",
"print()\n",
"print('In the simple model, the rocket reached a height of', round(simpleh, 2), 'm. when it ran out of fuel')\n",
"print('In the complex model, the rocket reached a height of', round(heun_run[99, 0], 2), 'm. when it ran out of fuel')\n",
"print()\n",
"print('In the simple model, the rocket reached a velocity of', round(simplev, 2), 'm/s. when it ran out of fuel')\n",
"print('In the complex model, the rocket reached a velocity of', round(heun_run[99, 1], 2), 'm/s. when it ran out of fuel')"
]
},
{
"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": 74,
"metadata": {},
"outputs": [],
"source": [
"def f_m(dmdt, m0=0.25, c=0.18e-3, u=250):\n",
" \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",
"\n",
" t = (m0-mf)/dmdt\n",
" t= np.linspace(0, t, N)\n",
" dt= t[1]-t[0]\n",
" \n",
" desired_h = 300\n",
" \n",
" sol= np.zeros([N, 3])\n",
" \n",
" sol[0,0]= y0\n",
" sol[0,1]= v0\n",
" sol[0,2]= m0\n",
" \n",
" for i in range(N-1):\n",
" sol[i+1] = rk_step(sol[i], rocket, dt)\n",
" predicted_h = sol[-1,0]\n",
" \n",
" error = desired_h - predicted_h\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [],
"source": [
"def incsearch(func,xmin,xmax,ns=50): #imported from notebooks\n",
" \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",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" \n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" \n",
" return xb"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [],
"source": [
"def mod_secant(func,dx,x0,es=0.0001,maxit=50): #imported from notebooks\n",
"\n",
" iter = 0;\n",
" xr=x0\n",
" \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",
" \n",
" return xr,[func(xr),ea,iter]"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"Using incsearch, the two closest mass exchange rates are [0.08888889] kg/s and [0.05] kg/s\n"
]
}
],
"source": [
"MCR = incsearch(f_m, 0.05, 0.4, 10) #search using incsearch\n",
"\n",
"print('Using incsearch, the two closest mass exchange rates are', MCR[0], 'kg/s and', MCR[1], 'kg/s')"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using mod_secant, the root of the function is 0.0588 kg/s.\n"
]
}
],
"source": [
"root = mod_secant(f_m,0.001,0.05) #solve using mod_secant\n",
"\n",
"print('Using mod_secant, the root of the function is', round(root[0], 4), 'kg/s.')"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [],
"source": [
"dmdt= root[0]\n",
"\n",
"t_all = (m0-mf)/dmdt\n",
"t = np.linspace(0, t_all, N)\n",
"\n",
"dt= t[1]-t[0]\n",
"height_desired= 300\n",
"\n",
"final_sol= np.zeros([N,3])\n",
"\n",
"final_sol[0,0]= y0\n",
"final_sol[0,1]= v0\n",
"final_sol[0,2]= m0\n",
"\n",
"for i in range(N-1):\n",
" final_sol[i+1]= rk_step(final_sol[i], rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The rocket detonates at a height of 300 m after 3.403 seconds of flight.\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,10))\n",
"\n",
"plt.plot(t, final_sol[:,0], color='black')\n",
"plt.plot(t[99],height_desired,'r*',markersize=30)\n",
"\n",
"plt.title('Rocket Altitude vs. Time with Explosion Point');\n",
"plt.xlabel('Time (s)')\n",
"plt.ylabel('Altitude (m)')\n",
"\n",
"print('The rocket detonates at a height of 300 m after', round(t[99], 3) ,'seconds of flight.')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"Math 24 Rocket Motion. https://www.math24.net/rocket-motion/\\\n",
"\n",
"Kasdin and Paley. Engineering Dynamics. ch 6-Linear Momentum of a Multiparticle System pp234-235 Princeton University Press\n",
"\n",
"https://en.wikipedia.org/wiki/Specific_impulse\n",
"\n",
"https://www.apogeerockets.com/Rocket_Motors/Estes_Motors/13mm_Motors/Estes_13mm_1_4A3-3T"
]
}
],
"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
}