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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": 7,
"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": 8,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, without drag or gravity, in SI units.\n",
" \n",
" Arguments\n",
" ----------\n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" \n",
" Returns\n",
" ----------\n",
" derivs: array of three derivatives [v (u/m*dmdt) -dmdt]^T\n",
" '''\n",
" derivs = np.array([state[1], (u/state[2])*dmdt, -dmdt])\n",
"\n",
" return derivs"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def eulerstep(state, rhs, dt):\n",
" '''Uses Euler's method to update a state to the next one. \n",
" \n",
" Arguments\n",
" ---------\n",
" state: array of two dependent variables [y v]^T\n",
" rhs : function that computes the right hand side of the \n",
" differential equation.\n",
" dt : float, time increment. \n",
" \n",
" Returns\n",
" -------\n",
" next_state: array, updated state after one time increment. \n",
" '''\n",
" \n",
" next_state = state + rhs(state) * dt\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 191,
"metadata": {},
"outputs": [],
"source": [
"def heun_step(state1,rhs,dt,etol=0.000001,maxiters = 100):\n",
" '''Update a state to the next time increment using the implicit Heun's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state1 + rhs(state1)*dt\n",
" ################### New iterative correction #########################\n",
" for n in range(0,maxiters):\n",
" next_state_old = next_state\n",
" next_state = state1 + (rhs(state1)+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",
" ############### end of iterative correction #########################\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 192,
"metadata": {},
"outputs": [],
"source": [
"y0 = 0 # initial position\n",
"v0 = 0 # initial velocity\n",
"m0 = 0.25 # initial mass\n",
"N = 500 # number of steps\n",
"dt = 4/N\n",
"# initialize array\n",
"num_sol_1 = np.zeros([N,3])\n",
"num_sol_2 = np.zeros([N,3])\n",
"# Set intial conditions\n",
"num_sol_1[0,0] = y0\n",
"num_sol_1[0,1] = v0\n",
"num_sol_1[0,2] = m0\n",
"num_sol_2[0,0] = y0\n",
"num_sol_2[0,1] = v0\n",
"num_sol_2[0,2] = m0"
]
},
{
"cell_type": "code",
"execution_count": 193,
"metadata": {},
"outputs": [],
"source": [
"for i in range(N-1):\n",
" num_sol_1[i+1] = eulerstep(num_sol_1[i], simplerocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 194,
"metadata": {},
"outputs": [],
"source": [
"for i in range(N-1):\n",
" num_sol_2[i+1] = heun_step(num_sol_2[i], simplerocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 241,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(10,8))\n",
"plt.plot(num_sol_1[:,2]/.25, num_sol_1[:,1], linewidth=4, linestyle='--', label='Euler-Step Num-solution')\n",
"plt.plot(num_sol_2[:,2]/.25, num_sol_2[:,1], linewidth=3, linestyle='--', label='Implicit Heun Num-solution')\n",
"\n",
"\n",
"plt.title('Simple Rocket \\n')\n",
"\n",
"plt.xlabel('mf/m0')\n",
"plt.ylabel('$v$ [m/s]')\n",
"plt.legend();"
]
},
{
"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": 196,
"metadata": {},
"outputs": [],
"source": [
"def rocket(state,dmdt=0.05, u=250,c=0.18e-3):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, with drag, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" c : drag constant for a rocket set to 0.18e-3 kg/m\n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" derivs = np.array([state[1], (u/state[2])*dmdt-9.81-(c/(state[2])*(state[1]**2)), -dmdt])\n",
"\n",
" return derivs"
]
},
{
"cell_type": "code",
"execution_count": 197,
"metadata": {},
"outputs": [],
"source": [
"y0 = 0 # initial position\n",
"v0 = 0 # initial velocity\n",
"m0 = 0.25 # initial mass\n",
"N = 500 # number of steps\n",
"dt = 4/N\n",
"t = np.linspace(0,4,500)\n",
"# initialize array\n",
"num_sol_3 = np.zeros([N,3])\n",
"num_sol_4 = np.zeros([N,3])\n",
"# Set intial conditions\n",
"num_sol_3[0,0] = y0\n",
"num_sol_3[0,1] = v0\n",
"num_sol_3[0,2] = m0\n",
"num_sol_4[0,0] = y0\n",
"num_sol_4[0,1] = v0\n",
"num_sol_4[0,2] = m0"
]
},
{
"cell_type": "code",
"execution_count": 198,
"metadata": {},
"outputs": [],
"source": [
"for i in range(N-1):\n",
" num_sol_3[i+1] = eulerstep(num_sol_3[i], rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 199,
"metadata": {},
"outputs": [],
"source": [
"for i in range(N-1):\n",
" num_sol_4[i+1] = heun_step(num_sol_4[i], rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 200,
"metadata": {},
"outputs": [
{
"data": {
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1k+dWsfxidjrZstZ6M8b1ideBe4D/YQzcCMaY8mRNHrbN9vRgfr9myN1tCO+x+fuIh/WdIz1o8tp+Yl6r+SzpAcEoh1PDYIxitUxY7umxeNzhWsXcOhZXkh4k1sEIEou6yJtG+vuRH47F3HSS9B+iebFulu3mS/rlAc7keJL43Ka1TtNa79RaT9Ja9wQiSL8Gsp+Ty2mEExIgCq/RWp8FPjT/jcShF9H8cN9g/tvR1akBpVQgxhcG2F+rBcYE2gCVlFI5uoWYkyBxlZsg8X/m84NKqYhsLtIyKMfxyzqrLNeMtXLzRboWY+qZmxhfur0wAvTnnOXPRbbbxt01SvlBZzdpXcznFIz5KzNlBk8rzH8fN0+HeoXW+gTGxO9gXLPXwyE9BWNUPUAnJwEkYD2l287819WxeK9SqkEO2+sYJK5wtW+Tfiy2U9m4W5Ipt47FXGNe9mH58dbT/BzMTRts/nZ3+cdjubxcR7aDE7O1/bXWCRgzZ1jk1j3n72gSIApv+5j0WykNcfLFM8V8jsCY7NaZUaTf2s3x9MG3NvV/4e50lCfXpmShJ/G/GMFCAPBNZiPqlPNbtZ03n8tk1q5MfG0+BwPT3JwqXUH6taFgDCJxd92dS0qp/yil3J4yVkoFYcy/Z7HcVd584mVnPQ9KqVoY09CAMRXJRcc8bow3n0sAX7rbB5UhOgt1Z9WHpPdoDnVyWtFyLFYC/uWijrGkXxvneCzG2tQ/WSlVBBc8PBY97Un8BOMykYLA15kFUnl8LOY2y/5TFvhMubhlJGR9/zGvV7aMNn/D2WBCpVQNjMni84zW+hrpvdcut7+zmRgc2PaCnneZS6TT+WCuHXnceQ88vNWemXeETd5eDmmOd1L5HOPao6IYXwpTbNI8uZNKPEavWBTGxe6RGD1DM/DwTipmWjOMLzuNcbvADBNwY0wfYlnuH2Z9lc3llsa4oPoNjPnctrrZLolmG8MwThf7ASqL78cPNm3ZjdFbW8Gss6rZtt9Jn8vPclvCbTjMS+bh8vaY5TdhTIjeCOPDvQjGxMX9bPJonE8U7uk8iO5uH5fpXJKZLMfxTirHMHpXS5nr8xRwxsyT3Tup2N7ObTPwhLlfFsH4YRQDjDT3oQzbyYP3wqNb7Zl537XJ28UhzfZOKmkYPY41MY7FesA3NmXnuKjfdrLtg+Z+V8lc14oYx+psPLyTipnWymZ/3Y6TCbiBITbL3Ysx757lM6AMxvE8BGOEdYY5BW22y1WM+RKLkP1jMbfvpDLJZt02Ytw9pTxGoB6BMVDjHYxrkJ1NAu5uouwWpN9JJQ7jbiUlbPb903h+JxWXtyTE+Cy31JFhXlbSbyiwG2PuTsvgIz+bPDvM938IxnRnpc198x6MHzRXzToOYN59RR6Z7HveboA87swHWQsQQ0i/28kexw9ccudezH3J/P6vHt+L2Uz3JEgcjP2dBlw91jspG4Hre/9m6V7MGD2Z7u6Dannsx5jvrrPNF8MaIDCLy9vgwbIsj3k4mcSa/BUg3jC/dBJcrENO7sXsA4zB/X2CLY8Z2TgWsxIgFrVZx21O0nPjXsz/9OCY8PhezGa6J0Hia6Tf3cjdY4WTshVJDzAcH96+F7MvxsjdNA/WbYqb+l3di3mQm7pPYfzQtfyf4RjIrH4zT2YBYnc361THzOPJfZtPALWzegzdrQ85xSy8ThvXh1hOlVTH4VovbZyya4ERdP6CMYVBMkbPzVKM0bYPa61djh7VWn+N0XP1PsZtvhIwvtQPm3UOxrj7SVbabXu6uQbGdVDFHfL8F6PXcCzGBOEXMQKBKxjB8BSM02QxONBaH8eYrHYmxn1Usz3VjDbmPnwK4z6tUzDuz3od44v6KDAX47qz6tqYhmY+MNws3hxjnsKsTA/R1Cz3DsZE1vEYAXoKxhfGDuBLjAnHu2jXk1jnG1rrdUBDjFOlxzDej5MYlzHU1lr/5Lq023rTtNZDMfb9TzF+bFzG2E8uYfTs/hcjCOqTs7XItC0XSL8WsZ5S6hGH9HMYAcEzGJcknCf9WFwM9NBat9fGaUFXy/gK4zrH8RjHwBXSj8XlwAsYvapZabft6ea6ODndrLX+EOMzYBxGEHkJYxsnYGzzrzCO53Y40FofNtf7O4y7OjmdtN8btNapWut/YfTmTsDYpgkY63YRY10/wfgM/aeretzUPwFj3RdgDKy6ifFeTcToOT5qkz2n04m5asMcjO+FXzD2OWdT5nTF2He+x+glvoDxeXMBowfyTeAenfkctsKkzMhbCCGEA6XU8xiXNdzUWt8Oc+MJcUsppWIw5hkE4xKLg+7yi9uH9CAKIYQQIrs6mM+XMO40Je4QEiAKIYQQwik30wehlKqNMRk1wFwtpyTvKHLLGSGEEEK4slApdQiYg3Ht8HWMUcwdMEYMB2JMsv6e11oo8oQEiEIIIYRwpQDG4ChXA6SuA9211nJ6+Q4jAaIQQgghXHkD405BTTF6DsMxRp3HY9yl5mOt9d9ea53IMzKKWQghhBBC2JFBKkIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo4EiEIIIYQQwo6ftxtwJylWrJiOjIz0djOEEEIIITK1bdu2c1rr4s7SJEDMRZGRkWzdutXbzRBCCCGEyJRS6oirNDnFLIQQQggh7EiAKIQQQggh7EiAKIQQQggh7EiAKIQQQggh7EiAKIQQQggh7EiAKIQQQggh7OTrAFEpFaSUekMptUUpdUkpdV0pdVgpNVcp1cRFmV5KqbVKqctKqatKqa1KqYFKKbfrmt1yQgghhBB3mnw7D6JSqiLwP6AycAZYA9wEIoHHgJ3AeocyE4EXgBvACiAZaA1MAForpR7XWqc6WVa2ygkhhBBC3InyZYColCoELAeigFHAKK11sk16OBDuUKYrRpB3CmiutT5gvl4SWAV0BgYBn+RGOSGEEEKIO5XSWnu7DRkopcYCQ4BvtNZ9PSyzFagP9NVaf+OQ1gJYjREEltVap+W0nDMNGjTQWbmTSlpaGhcvXuTq1avcuHGDtDS31QshhMjHfHx8CAwMpHDhwoSFheHjI1coifxNKbVNa93AWVq+60FUSvkD/zT/fc/DMhEYQV4SMNcxXWu9Rin1N1AWaARsyEm53JCSksKxY8fw8/OjaNGiFCxYEB8fH5RSubUIIYQQt4jWmrS0NK5fv86lS5dISEigXLly+Pnlu69ZITySH3/e1Mc4fXxMa71fKfWAUmqMUuoLpdTbSqnGTsrUNZ/3aq0TXdS7xSFvTsrl2IULFwgICCAiIoLg4GB8fX0lOBRCiNuUUgpfX1+Cg4OJiIggICCACxcueLtZQmRbfvxpU9N8PqCUigUcTzH/n1LqB+BJm6Cuovns8qbTwFGHvDkpl2OXL1+mfPnyEhQKIcQdRilFeHg4R48epUSJEt5ujhDZkh97EIuaz82BPsAHGCOZwzBGL/8NdAUm2pQpbD5fc1PvVfM5OBfK5VhKSgr+/v65WaUQQoh8wt/fn5SUFG83Q4hsy48BoqVNfsAUrfXrWuuDWutLWusfgU6ABvoqpSqZeS3dcFkdcZPdcukVKPWsOWfi1rNnz2a1bHYXK4QQIh+Tz3dxu8uPAeIVm7+/ckzUWm8FtmG0vaVDmcKO+W1Y0mzrz2452/Z8qbVuoLVuULx4cTfVCCGEEELcHvJjgBhv8/dhF3ksr5dyKFPBTb3lnNSf3XJCCCGEEHes/Bggbrf5O9xFnmLms+X6wN/N5+pKqSAXZRo65M1JOSGEEEKIO1a+CxC11n8Dv5n/tnZMV0qFAfXMf7eaZY5hBJb+wONOyrQAIjAmvN5os6xslRO3RmRkJEqpTB+rV6/OleVZ6stvli1bRteuXYmIiMDf35/Q0FAqV65M27ZtGTVqFPv27fN2E7MtJSXF6XtasGBBKleuzFNPPcWuXbu82salS5eilKJt27ZebYcQ4s534Vgci/6YR3JacuaZ81h+nOYG4F3gR4wpbdZrrXcAKKUCgc+BUIzrEG2DtrEYk13/Rym1QWsdZ5YpAXxm5nnPyd1QsltO3CJt2rShVKlSLtPdpd3uBg0axMSJxoD96tWr07BhQwICAjh27Bhr1qxh2bJlXLt2jffeS59TPi4ujujoaKKiooiLi/NW07Ps8ccfp2DBggCcOXOGrVu3Mm3aNKZPn86cOXPo3Lmzl1uY90qVKsXp06c5efLkHb1fCyGcOzb0TYr+sZf3m39A1X6D6Hjv4xTwLeCVtuTLAFFrvUgp9QHwL+A3pdRvwHngPqAMxlQ3T2ib+wRqrb9XSn0ODAB2K6V+AZIxeiFDgAXABCfLylY5cesMGTKEli1bersZt9z8+fOZOHEiISEhLFq0iObNm9ulX79+nUWLFt0xt2gcP348ERER1v+vXLlCr169+Omnn3juued45JFHCAgI8GILhRAi7yTu3oP/lj0UBTotvsi/K4znum8qT977pFfak+9OMVtorV8HugDrMSbPfgS4DowH6mqtDzgp8wLwD4zTxi2ANkAcMAjoqrVOdbGsbJUTIi/Nnj0bgJdeeilDcAhQsGBBevTowRNPPHGrm3ZLBAcHM2GC8dvs7Nmz/Pbbb5mUEEKI29e5LyZZ/w5t9wjTn/2FrtFdvdaefBsgAmit52utW2mtw7TWAVrraK31a1prlxMOaq1naq2baK1DtNaFtNb1tdYTMztFnN1yIn9ZvXo1SimXPY7x8fEopYiMjMxSvcnJyUyaNIlmzZoRFhZGYGAg0dHRvPrqqzib/zI2NhalFP369eP8+fO8+OKLVKxYEX9/fzp16uTRMs+cOQOQpTsx9O7dm+joaAAOHjxod11f5cqVM+RfsmQJHTp0oGTJkvj7+1OmTBl69erF3r17M+SNi4uz1pOcnMyYMWOoVq0agYGBlCpViv79+3P8+HGP2+qJChUqEBoaCsDp06ed5jlz5gyvvfYaVatWJTAwkNDQUB544AG++OILUlNd/7bbs2cPTz/9NFFRUQQFBVG0aFHq1KnDv//9b4/X48iRI9x7770opXj55Zcz9OauX7+e7t27U6ZMGfz9/SlRogSdO3dm06ZNdvkmTZqEUsq6jqVLl7Z7706dOuVRe4QQt6cbf/7J1V9WWP8Pf+45igQWoWCBgl5rU748xSxEfpKQkED79u1Zt24doaGh1K9fnyJFirB9+3Y++ugjfvjhB9asWeM06Dx37hwNGzbk8uXLNGvWjAYNGhAe7mpwvr3y5csDMG3aNPr06UNISEimZZo3b05iYiLz5s0jODiYLl26WNNKlixpl3fgwIF89tlnFChQgAYNGhAREcGBAweYNWsWCxYsYP78+bRp0ybDMrTWdOvWjWXLltGyZUtq167N+vXriY2NZcmSJaxdu9YapOZUSkoK169fd9p+gP3799O6dWtOnjxJ2bJleeyxx7h69SqrVq1i48aNLFy4kIULF1KggP01PJMnT2bAgAGkpKRQuXJlOnbsSGJiInFxcYwbN466devSs2dPt23bvn077du35/Tp03z44Ye8+uqrduljxoxh2LBhKKWoX78+TZs25ejRoyxcuJBFixYxdepU+vTpA0DVqlXp27cvs2fP5saNG3Tv3p2goPSJFWz/FkLcec5/8YX17+CHHiSwahUvtsYgAWI+Fjnk52yVq1E2hJ8GN3Oa9uh/17Ln74Rs1Rv/Xnunr785bxezNh9zmX67e/bZZ1m3bh3dunXjyy+/JCwsDIDU1FSGDh3KuHHj6Nevn9PR1D///DMPP/ww33//PcHBWbtb43PPPce3337L9u3bqVChAh06dOCBBx6gXr161KlTx+mtGtr904UAACAASURBVJ999llatWrFvHnzKFGiBLGxsU7rnjBhAp999hk1a9bk+++/p0qV9A+j77//np49e9KrVy8OHTpk7cGzOHToENevX2fHjh1Uq1YNgJs3b9K/f39mzZpF37592bBhQ5bW1ZWlS5eSnJxMiRIluO++++zStNY88cQTnDx5kt69ezN58mTrNYrx8fG0bt2aJUuWMGbMGEaOHGktt27dOp5//nl8fHz4+uuvrUGaxd69ezMElI6WLFlC9+7dSUlJYc6cOXTr1s0ufcGCBQwbNozy5cszb9486tevb01bvXo1jz76KM899xzNmzcnMjKSmJgYYmJiWLp0KTdu3OCTTz6RQSpC3CVuHjpMwpKl1v/Dn3vei61Jl69PMQsBEBMT43KKmyJFiuTpsvft28fs2bOpUKEC33zzjTU4BPD19WXs2LHUqlWLNWvWsHv37gzlCxQowBdffJHl4BCgcePGzJ07l1KlSnHp0iWmT5/OgAEDuP/++ylSpAjdunVj27ZtWa43JSWF0aNHo5Ri7ty5dsEhQLdu3XjmmWe4cOECM2fOdFrHyJEjrcEhQEBAABMmTCA4OJiNGzfm+HrBM2fOMGvWLJ555hkCAgKYOnUqgYGBdnl++eUXdu7cSVhYGBMnTrQbwBIZGckHH3wAwCeffGJ3T9zRo0dbg3vH4BCM0eKO28TW5MmT6dixI/7+/ixfvjxDcAhYA9LY2Fi74BCgZcuWDBkyhBs3bvDVVxluFiWEuMvs/ugtMMfcFmrejKAa1b3bIJP0IIp8z900N5ZpUfLKkiVLAHj00Uednubz8fGhadOm7Nq1i40bN1KzZk279Hr16mX5ekdbnTt35pFHHmHx4sWsWLGCLVu2sHPnThITE/nhhx9YsGABX331Ff379/e4zm3btnH69Glq165N1apVneZp0aIFX3zxBRs3bmTAgAEZ0nv37p3htaJFi/LII48we/ZsVq9ezf333+/5igLlypXL8Fp4eDi//fYbtWvXzpC2Zs0awNhGzk6/d+rUiaJFi3LhwgV27txJ/fr1uXnzJqtWrQLgmWeeyVL7AEaMGMHo0aOpWLEiS5Yscbr9/v77b3bt2kWxYsVcXgvbokULADZulOlVhbibXYs/ROCKzdb/4zs1IEKn4aO8338nAaLI97w5zc2hQ4cAmDhxonU+QlecDVapUMH5XRzPnDnDG2+8keH1Fi1aZAj2AgIC6Ny5s3UewOvXr7N48WLefPNN4uLiGDBgAG3btqV06dJZWqedO3dmOjG4s3UqVqwYhQs7v325JRjOzmAVyzyIqampHDt2jHXr1nH+/Hl69OjBxo0b7XpvwQjEACpWrOi0PqUUFStW5MKFC/z999/Ur1+fU6dOkZSURKFCheym1PHEihUrWLZsGYULF2bt2rWULVvWaT7L9j137hw+Pu4/5J1tXyHE3WPHRyMpao5t211BMe7Clyy90YViQcXcF7wFJEDMx/Limj5X1ybmxNgutRjbpVau15sXsjpnoGUUbP369alRo4bbvNWrZzwt4GpwQUJCAl9//XWG1/38/DLtDSxYsCDdunXj/vvvp0qVKty4cYOlS5d63ItoWaeIiAhat85wsyI7ztbJE9m5I43jPIiWASh//vknL7zwArNmzbLLb5kG1d2ybKZKzbE6depw8+ZNdu/ezSuvvMKMGTOcXqto2b5FixalQ4cObuv0NKgXQtx5bl6/QoF16XcXntdE0a1Kt3wRHIIEiOIOYxm4cfXqVafpR44cyVJ9ltOeMTExvP/++zlrnI3KlSvnOHgpV64c1apVY8eOHVnqibKsU0REhMtBLO6cO3eOq1evOu1FjI+PB6BMmTJZrtfRPffcw7Rp02jbti3fffcdL774Io0bN7amW4JJS4+dM5b2WHr7SpUqhb+/P9euXeP48eNZ6kUMDw9n5syZtGnThrlz53Ljxg3mzp2bYfJuy/YtWLBgtravEOLusOTECsY+q2izzYfKJzV/RfrzSXXPLxfKa94/yS1ELrIEAgcPHiQ5OeO9LBcvXpyl+tq1awcYo1JtBzrcCpkFkCkpKZw4cQLALtCxBMmu2tuoUSOKFCnC1q1bOXz4cLba5mzwysWLF63bN7cuCWjTpg3t2xs96SNGjLBLs1zHN3/+fK5cuZKh7MKFC7lw4QJhYWHWaxgDAgKsbZsyZUqW21O0aFFWrFhBkyZNWLRoER06dLBOw2MRFRVFdHQ0x48fzzDfYWYye++EEHeG1LRUJu+ezPVAxfwmPrzfzZfO0V0oWSjjdF7eIgGiuKNUqFCBqKgoLl26ZB3FarFgwQI+/fTTLNVXr149OnXqRFxcHN27d3d6bd3Jkyf5+OOPc/1LvV+/frz11ltOez0vX77MCy+8wJkzZwgNDaVt27bWtBIlSuDn58eJEye4fPlyhrIBAQEMHz6clJQUHnvsMbZu3Zohz7Vr15gxYwZ//vmn07a99dZb/PXXX9b/k5KSePHFF7ly5Qr33XcfjRo1ys4qOzV27Fh8fHxYsWIFa9eutb7+4IMPUqtWLS5evMjgwYNJSkqyph05coR//etfgHEnGj+/9JMlw4cPx8fHhzFjxjgNdPfu3cuBAxlu1GQVEhLCsmXLaN26NcuXL6ddu3YZeqxHjRoFQM+ePVm5cmWGOm7evMn8+fPZsmWL3euWHzj79+93uXwhxO1vWfwyjiSkf7b7KT+eqvmUF1vkhNZaHrn0qF+/vvbUvn37PM57t6pQoYIGdJs2bXTfvn1dPpYtW2ZXbs6cOVoppQFdr1493a1bN127dm2tlNLDhg3TgK5QoUKG5QHaOCTsXb58Wbdo0UIDOjAwUN9///26e/fuum3btrp69erax8dHAzoxMdFaZtq0aRrQffv2zfb6t2/fXgNaKaWrVKmiH3vsMf3EE0/omJgYXahQIQ3ooKAgvXDhwgxlO3TooAEdGRmpe/XqpZ9++mn95ptv2uUZPHiwtf5atWrpzp0768cee0zXq1dPBwUFaUAvX77cmv/AgQMa0JUqVdIdOnTQAQEBum3btrpHjx46IiJCA7pEiRL6jz/+8Hgdk5OTrdv92LFjLvM9+eSTGtAxMTF2r+/bt0+XLl1aAzoiIkL36NFDt2/f3tr+du3a6aSkpAz1ff7559rX11cDOjo6Wnfv3l137NhR33vvvRrQs2bNsuZdsmSJdT+0lZiYaH2PGjVqpC9evGiXPmbMGOu+Ua1aNd2xY0fdpUsX3bBhQx0SEqIBPW3aNLsy//nPfzSgQ0NDdbdu3fTTTz+tn376aX358mVPN6nIR+RzXjiTkpqiOy3opGvE1rA+hq8b7pW2AFu1i5jG60HVnfSQADF3WQLEzB4fffRRhrILFy7UjRo10kFBQTo4OFi3aNFCL126VB8+fDjLAaLWWqekpOhvvvlGP/zww7pYsWLaz89PFy9eXNeuXVu/8MILGYLU3AgQjx07pqdMmaKfeOIJXbNmTV2sWDHt6+urQ0NDdb169fTrr7+u4+PjnZY9e/as7t+/vy5btqz28/PTgI6KisqQb9WqVbpHjx66XLly2t/fX4eGhupq1arpnj176pkzZ+pr165Z81oCxKioKJ2UlKTffvttHR0drf39/XWJEiV0nz599JEjR7K0jp4GiPHx8TogIEADevXq1XZpp06d0q+++qqOjo7WAQEBunDhwrpRo0Z60qRJOiUlxWWd27dv108++aQuV66cLlCggC5atKiuU6eOHjJkiP7777+t+VwFiFprnZSUpLt166YBXbduXX327Fm79K1bt+p+/frpihUr6oCAAB0cHKyjo6N1p06d9NSpUzMElcnJyXrkyJG6SpUq2t/f37ptTp486XY7ivxJPueFMxtHDNRfdr5Ht/mguq4RW0PX+rqWPnI5a5+ducVdgKiMdJEbGjRooJ2drnNm//793HPPPXncIiFyT1xcHNHR0URFRREXF+ft5giR78nnvHCUdO4s+2Na4J+sSQOG9fWlWtNHea/Ze15pj1Jqm9a6gbM0uQZRCCGEEOIW2D7+//BPNjrmjpSEw2V8eK7Wc15ulXMSIAohhBBC5LGbZ04TtGiN9f+5TX14pFJ7KoY6n+zf22QeRCGEEEKIPLb9o/+jiNl7eKgkbK/iy8J82nsIEiAKITyUG5N7CyHE3Sjl7FkK/7ze+v/cZj48GtWByNBI7zUqE3KKWQghhBAiD52fPAW/JOM2nKciCrEj2i/fXntoIT2IQgghhBB5JOXsWS5+9531/wZD32d+/UjKh5T3YqsyJwGiEEIIIUQeOT95MvrmTQACq1encExLgpXycqsyJ6eYhRBCCCHyQMqFC1z8brb1/2KDBqJug+AQJEAUQgghhMgTvmFhlJv0OUH16hFYowaFW7b0dpM8JqeYhRBCCCFyWXJaMp9u/5QeNXpQYca3pCUk3Da9hyA9iEIIIYQQuW7RwUXE7o2lw/wOvL3xbU75XvV2k7JEAkQhhBBCiFyUnJrMl7u+BCBFp/DDgR+Yunuql1uVNRIgCiGEEELkovXvDKbK+mP4pBk3F/Dz8eOZms94uVVZIwGiEEIIIUQuuXLoL4rNXcOAxWmM/yqVwtc1XaO7UrpwaW83LUskQBT5VmRkJEopVq9e7e2muBQfH49SisjIyAxplvbHx8fnaBlvvfUWSineeuutHNXjqF+/fh7Va1l+v379cnX5+YFlG9g+/Pz8KFGiBA8++CBff/21128vGBERgVKK48ePe7UdQgjP7HhvKL5pxt8XghXJwYH8s+Y/vduobJAAUYjb1OrVq1FK0fI2mjYhv6pduzZ9+/alb9++dO3alVKlSrFixQr69etHly5dvB4k3grDhw9HKcXo0aO93RQhblsX9+2k6K97rf/Pau5Dz6o9KVmopBdblT0yzY0QeWTFihUkJydTtmzZHNUzaNAgevbsSbFixXKpZcJRp06dMvSkfvvttzz55JMsWLCAuXPn0r17d+80Tghx29g9dhjFzb+3RSn+jizE0zWf9mqbskt6EIXII1FRUVSrVo0CBQrkqJ5ixYpRrVo1CRBvsd69e/Pggw8C8NNPP3m5NUKI/O7s9k0U33LQ+v93LXzoU70PYYFhXmxV9kmAKG47luvGYmNj2bt3L127dqV48eIULlyYpk2bsmrVKmven376iRYtWhAaGkpISAgdO3bkwIEDGeq0PV177do1hgwZQqVKlQgICKBcuXIMHjyY8+fPZ6md7q5B1FozZ84c2rVrR4kSJfD396ds2bK0bt2aCRMm2OV1dg1iy5YtiYmJAWDNmjV219Dd6lPOx44d46WXXqJq1aoEBQUREhJCkyZNiI2NdXpqNrNrM1u2bOn02lPb17dt20bHjh0JDw8nKCiI2rVrM2XKlFxft9q1awNw+vRpp+laa7755htatGhBkSJFCAwMpHLlygwePJi///7bZb1Xr15l3LhxNGrUiCJFihAUFESlSpXo0aMHy5Yt86htaWlpvPLKKyiluPfeezly5Ihd+rlz5xg6dCg1a9akcOHCFCpUiAYNGvDJJ5+QnJxszZeSkoJSinfffReAESNG2O1PcspZCM/sf2+E9e+N1RSXyhehz719vNiinJFTzOK2tXXrVgYOHEilSpVo3bo1Bw4cYP369bRp04YVK1awY8cOXn75ZZo0aUKbNm3YvHkzixYtYsuWLezZs4fw8PAMdSYlJdG6dWv27NlDq1atqFevHmvWrGHChAksW7aMtWvXUrJkzq4lSUpK4vHHH+fHH3/E19eXRo0aUb58eU6fPs2ePXtYuXIlgwYNcltH27ZtCQwMZNmyZZQsWZK2bdta06pVq5aj9mXFqlWr6Ny5M5cvX6Zy5cq0bduWq1evsmnTJvr378/KlSv55ptvcnWZS5cuZfz48VStWpWHH36Yo0ePsmHDBp555hkuXbrEa6+9lmvLunz5MoDT9zwtLY0nnniCOXPm4O/vT8uWLQkLC+O3335jwoQJzJo1i//973/Uq1fPrtzhw4dp06YNBw4cIDg4mCZNmhAaGsrRo0f56aefOH/+PG3atHHbrhs3btC7d29++OEHmjVrxsKFCwkLS++l2LlzJ+3atePkyZOUK1eOmJgYUlNT2bRpEy+//DKLFy/mp59+okCBAvj4+NC3b19+//13du3aRd26dalVq5a1LkuQLIRw7cT6FRTfZQwkS1Mwu7kPT9V4imD/YC+3LAe01vLIpUf9+vW1p/bt2+dx3rtVhQoVNKBXrVpl93rfvn01oAH94Ycf2qW98cYbGtBVqlTRISEh+tdff7WmJSYm6mbNmmlAv/POO3blVq1aZa2zSpUq+vjx49a0hIQE3bp1aw3oxx9/3K7c4cOHNaArVKjgsv2HDx+2e/3FF1+0Lmf//v12aSkpKXrhwoV2r40cOVIDeuTIkU7b3KJFiwzL9oRlOzrW68iy/L59+9q9fuLECR0WFqZ9fX11bGysTktLs6YdPXpU16lTRwN62rRpduVcbReLFi1aOH3fLa8DesqUKXZp06dP14AOCQnR165dc7s+ttxtg8TERB0ZGakBPXv27Azpn3zyiQZ06dKl7d7H5ORkPWDAAA3oSpUq6aSkJGtaSkqKrlWrlgZ0ly5d9KVLl+zqvHz5sv7ll1/sXitbtqwG9LFjx7TWWp87d04/8MADGtDdu3fXN27csMt/9epV6zYeN26cTklJsaadO3dOt2rVSgN61KhRduWGDRvm9HWRffI5f3dIS0vTv3ZorvdVrab3Va2mP+t2j245u6W+nnzd203LFLBVu4hppAcxP1s1Fta851neen2h46f2r/34Imz/2rPyLYZAzJv2r83sAX8t9az8ox9Dg/6e5c0ljRs35tVXX7V7bciQIYwbN46//vqLN998k2bNmlnTAgMDeeWVV1i7di2rVq1ixIgRjlUC8OGHH9oNLAkODmbSpElUq1aNH374gWPHjlGuXLlstfnMmTN8/vnn+Pj4MG/evAy9fb6+vnTs2DFbdWfX22+/zdtvv53lch9//DEXL17kjTfeoG/fvnZp5cqV46uvvqJhw4b897//zdUpcrp27cpTTz1l91rv3r0ZM2YM+/fvZ+vWrTRv3jzb9ScmJrJv3z6GDx9OfHw8//jHP+jWrVuGfOPHjwfg3XfftXsf/fz8+Oijj/jxxx85dOgQ8+bNo0ePHgDMnz+fXbt2ERUVxcyZMwkICLCrMyQkhNatW7ts26FDh2jXrh1//fUXr732Gu+//36Ge7tOnTqVI0eO0KtXL15//XW7tPDwcL7++msqVqzIhAkTGD58eNY2jhAig6O//Eixv84AkOID3zfx4dlazxLkF+TlluWMBIjitmV7WtUiLCyM8PBwzp8/7zQ9OjoagBMnTjits0iRIjz66KMZXq9cuTKNGjVi/fr1/Prrr/zjH//IVptXrlxJcnIyTZo0oXr16tmqI7fVrl2bOnXquEzfsWMHO3fuzPD64sWLAXj88cedlqtfvz6FCxdmx44d3Lhxg8DAwFxpr7P3B4xT6/v373f53rrjKkh+6623GDlyZIbX4+PjOXLkCL6+vvTu3TtDekBAAE888QQffPABq1evtgaIS5caP7h69+6dITjMzObNmxkwYADnzp3j008/ZfDgwU7zZfa+REREUKlSJf766y8OHTpEpUqVstQOIYS90+WC2di0MC02XWVNTUWBchF0i874o/J2IwGiuG1FREQ4fb1w4cKcP3/eaXrhwoUB4xouZ5xNeG2btn79+hxNWGwZSHArrxPMjLMpXmy99dZbTgPEQ4cOAdCwYcNMl3H+/PkcT/djUb58eaevh4SEAK7fW3dsg+SLFy+yadMmzpw5w6hRo6hVqxadO3e2y28ZgBIREeFylHpUVJRdXsjZ+9+jRw9SUlL48MMPXQaHkP6+OLbZmbNnz0qAKEQO3VetFbUmrWXepiks+2Mmz9d+ngK+OZu9Ij+QADE/i3kz42nfrOj4acbTzlnRa3b2y94CPj7uB+Fnlp5djqf07lapqamAEbhk1juYld6ytLQ0t+l58b46Bsk3b97k6aefZsaMGfTv35/777+fMmXKWNO1OTrb3b5gyZNb+vTpw9SpUxk3bhwPP/wwNWrUcJrP8r48+uijTgdi2SpatGiutlGIu1WgXyC9mg7ksfv7EeCbtbMD+ZUEiELYcHdbPEuabaCQVRUqVADgzz//zHYd+UW5cuWIi4tjxIgRWTpd7u/vDxhTvTjjOF2LNwQEBDB58mQ2b97MgQMH+L//+z8mT55sTbf0Th8/fpzk5GSnvYiHDx8GsOs5zcn7//bbbxMVFcWwYcNo2bIly5cvp27duhnylStXjoMHDzJo0KBMR0MLIXJXoQKFvN2EXCPzIAph49KlS9ZruGwdOnSITZs2oZTK0QCIVq1aUaBAATZs2MD+/ftz0lRroJWSkpKjerKrXbt2AMydOzdL5SwB0x9//JEhbc+ePRw7diznjcsFgYGBjBs3DoDY2Fji4uKsaZGRkVSoUIGUlBRmzpyZoezNmzeZNWsWgN28lJaAbfr06SQlJWW5TUOHDuXjjz/m/PnztGrVik2bNmXIk933xdv7kxC3k7SbNzn17hiS7uB7pEuAKISD1157jZMnT1r/v3r1KgMGDCA1NZXOnTu7vAbOEyVKlOD5558nLS2Nrl278tdff9mlp6amsmjRIo/qsgRacXFxXvlSf/311wkJCWHMmDFMnDjRaRs2bdqUIVCxjNIdN24cCQkJ1tePHTtGv3798tV9jzt16kSjRo1ITU1l1KhRdmmvvPIKAMOGDbN7H1NTU/nXv/7F8ePHqVSpkt21gF26dKFGjRocPHiQ3r17260/QEJCAitXrnTbppdeeokvv/yShIQEHnroIdasWWOX/vzzz1O2bFmmTp3KO++8Q2JiYoY6du3aRWxsrN1rlv0ppz9chLgbXJw5i4vTp3Ow3SOcnTDR283JE3KKWQgbjRs3JjU1lSpVqtCqVSv8/f1Zs2YNZ8+eJSoqiokTc/5B8P7773Pw4EEWL15M9erVady4MREREZw5c4bdu3dz5swZj4KkChUqULduXX7//Xdq1apF/fr1CQgIoGrVqhmmN8kL5cqVY8GCBXTr1o1Bgwbx7rvvUr16dcLDwzlx4gQHDx7kxIkT9OjRw25E7cCBA/nyyy/ZsmULVatWpXHjxly6dInNmzdz33338cADD7Bhw4Y8b7+n/vOf/9CiRQtmzJjB8OHDrSPhBw8ezIYNG5gzZw61atWymyj78OHDhIeHWyfRtvD19WXBggU8/PDDzJ07l2XLltG0aVNCQkI4evQoO3bsoHHjxrRq1cptm/75z38SFBREv379aNeunbVOMAbr/Pzzzzz66KOMHDmSTz/9lJo1a1KqVClOnTrF4cOHOXLkCE2aNLGbfsgy+fqcOXM4deoUUVFR+Pj40LlzZ9q3b5/7G1aI21RKQgJH/vshQQDJyfiGhnq7SXlCehCFsOHv78/KlSt57rnn2LVrFz/++CP+/v4MHDiQTZs2UapUqRwvIyAggEWLFjF9+nSaN2/Onj17+P777/njjz+oVatWloLQefPm0b17dy5cuMCsWbOYMmUKP//8c47b6KmYmBj27t3L0KFDKVGiBJs2bWLBggUcPXqU6Ohoxo4da72Fm0VYWBjr16/nH//4BykpKfz8888cP36c119/naVLl+b43tW5rXnz5jzyyCOkpqbyzjvvWF/38fHhu+++IzY2loYNG7Jx40bmzZsHGEHwjh07qF+/fob6oqKi+P333xk1ahRRUVGsWbOGhQsXcvLkSTp27Mi///1vj9rVu3dvZs+eTUpKCh07duTHH3+0ptWuXZvdu3czevRooqKi2L59O/PmzSMuLo6yZcsycuRIJk2aZFdf2bJlrbem3LFjB7GxsUyZMoXff/89O5tNiDvW1vHDCbpunDE5H+bHhvsKe7lFeUPlp9M5t7sGDRrorVu3epR3//793HPPPXncIuGp1atXExMTQ4sWLTLcA1gIIbJDPufvPImnT/DXgw/in2zETp909KHgI20Y33K8l1uWPUqpbVrrBs7S5BSzEEIIIYQHto15g3AzODxcEn6r7se8uq7nJb2dySlmIYQQQohMXD6wnyLLt1n/n9nSh85VulIxtKIXW5V3JEAUQgghhMjEztFv4GvO47+nguKv6IIMqD3Au43KQ3KKWQiMuerkelwhhBDOnN6yjuK/pc+FOqOlD73vfZLiBYt7sVV5S3oQhRBCCCFc0Frz55gR1v83VlOcrxhG/xr9vdiqvCcBohBCCCGEC8euHGNK7fMcLgmpCr5r7sOztZ4l2D/Y203LU3KKWQghhBDChYk7JrK9oub3SF8qnQRVviw9qvbwdrPyXL7sQVRKxSqltJtHxpu4ppftpZRaq5S6rJS6qpTaqpQaqJRyu67ZLSeEEEKIO9P+8/tZfHgxAFopDpZRDKo7CH9f/0xK3v7yew/ieiDOyesnnbyGUmoi8AJwA1gBJAOtgQlAa6XU41rr1NwqJ4QQQog7k9aaD7d+aPda1bCqtK90d9x6Mr8HiJO11rGeZFRKdcUI8k4BzbXWB8zXSwKrgM7AIOCT3CgnhBBCiDvXli/H4B+3EVVdoZUC4KV6L+Fzl5xYvJPW8k3z+d+WIA9Aa30asExUNMTJKePslhNCCCHEHSjlwgVCvpzH4EVpjI1No2iCplHpRjQt29TbTbtl7oigRykVAdQHkoC5jula6zXA30ApoFFOywkhhBDiznVuwkT0tesAVAooS82qzXitwWsosyfxbpDfTzHHKKVqAYWB08A6YLnWOs0hX13zea/WOtFFXVuAsmbeDTksJ4QQQog70M1Dh7k4e7b1/4ghQ5kQE+PFFnlHfg8Q+zh5bZ9SqqfWerfNa5YbIR5xU9dRh7w5KSeEEEKIO9CZDz+EVGNcasH776dwy5be/ZxFdQAAIABJREFUbZCX5NdTzDuAF4HqGL2HZYBHgZ3AvcAvSqmyNvkLm8/X3NR51Xy2ndkyu+WslFLPmlPibD179qybakRWRUZGopTK9LF69epcWZ6lvvxm2bJldO3alYiICPz9/QkNDaVy5cq0bduWUaNGsW/fPm83Mcc2bdpE7969qVixIoGBgRQuXJiKFSsSExPDsGHD2Lx5s13+lJQUlFL4+eXv37iTJ09GKcUzzzzj7abkqttl+wuRVdc2b+bqihXW/0u88Xq+/F64FfLl0a21/tjhpWvAz0qp5cAajOsB38QYXQxgefeyejPd7Jaz0lp/CXwJ0KBBA7mZbx5o06YNpUqVcpnuLu12N2jQICZOnAhA9erVadiwIQEBARw7dow1a9awbNkyrl27xnvvvWctExcXR3R0NFFRUcTFOZslKn8ZN24cQ4YMQWtNVFQUDz30EMHBwZw4cYJt27axevVqDh48yHfffeftpgov6N27NzNmzGD69On07t3b280RdzCdlsaRMe9YA4PQxzoSVL26V9vkTfkyQHRFa52klBoLLAQesUm6Yj4XzljKypJ2xea17JYTt9CQIUNoeRd28c+fP5+JEycSEhLCokWLaN68uV369evXWbRoEWlpjpfk3j62bdvGkCFD8PPzY8aMGTz++ON26UlJSSxfvpyjR4/ave7n58f+/fvv2l/2Qojct3/2V6g/DgKg/f0p/tJLXm6Rd91WAaLJchcV21PM8eZzBTflyjnkzUk5IfLcbPMi6ZdeeilDcAhQsGBBevS4vW/3NHfuXLTW9OzZM0NwCODv70/79s4npa1WrVpeN08IcZdIvXGDhE8/I9T8f0H9ZELPzGdgmYFebZc35ddrEN0JN5+v2rz2u/lcXSkV5KJcQ4e8OSkn8qnVq1ejlHLZ4xgfH49SisjIyCzVm5yczKRJk2jWrBlhYWEEBgYSHR3Nq6++irNrT2NjY1FK0a9fP86fP8+LL75IxYoV8ff3p1OnTh4t88yZMwCUKFHC43b27t2b6OhoAA4ePGh3rWblypUz5F+yZAkdOnSgZMmS+Pv7U6ZMGXr16sXevXsz5I2Li7PWk5yczJgxY6hWrRqBgYGUKlWK/v37c/z4cY/bmt11BPfXwEVERKCU4vjx4yxcuJCmTZsSHBxMsWLF6N69O/Hx8QCkpqYyfvx4atSoQVBQEKVLl2bw4MFcvXo1Q53Dhw9HKcXo0aM5ePAgvXr1omTJkgQGBlKjRg0++ugjUlOzfrOlo0eP8uKLL1KlShWCgoIICQmhadOmfPPNN07zN23aFKUU69atY9WqVbRr145ixYrh4+PDTz/9ZM2XlJTEp59+yn333UdISAgFCxbk3nvvZejQoVy8eNFle86dO8eIESOoU6cOwcHBFCpUiCpVqtC/f382bdrk0TrdvHmT7t27o5SiadOmXLhwIVvrbNnfZsyYAcCTTz5ptz9/++23HrVHCE9s+2w0oReTALhcEBY09qFO8TpebpV33Y49iN3N5y2WF7TWx5RS24F6wOOA3SeNUqoFEIFxt5SNOS0n7i4JCQm0b9+edevWERoaSv369SlSpAjbt2/no48+4ocffmDNmjVOg85z587RsGFDLl++TLNmzWjQoAHh4eEZF+JE+fLlAZg2bRp9+vQhJCQk0zLNmzcnMTGRefPmERwcTJcuXaxpJUuWtMs7cOBAPvvsMwoUKECDBg2IiIjgwIEDzJo1iwULFjB//nzatGmTYRlaa7p168ayZcto2bIltWvXZv369cTGxrJkyRLWrl1rDVI9Xcc5c+bw2muvUbp0aY/KeeLTTz/lww8/pFmzZrRt25bNmzczd+5cNm3axM6dO3nqqadYvnw5LVu2pFKlSvz6669MmDCBgwcPsnjxYqd1xsXF0bBhQwoWLEjLli1JSEhg1apVvPrqq6xfv565c+d6fNp7xYoVdOnShYSEBKKjo2nbti1Xrlxh06ZN9O3bl9WrVzN16lSnZWfNmsXnn39OjRo1eOihhzh79iwFChQAIDExkbZt2/Lrr79SqFAhYmJiCAoK4tdff2Xs2LF89913rFy5MsP+um3bNtq3b8/p06cJDw+nVatWBAQEEB8fz4wZM/D19aVRI/fTwV64cIHHHnuMdevW0a1bN6ZPn05g4P+zd99xUdd/AMdfnzuGICAuXChOcA9wL0RzVaYm7spt5U7LtDRN21aWaZr9zJVWWorZ0MrMvS1z771HiCiy7vP747gT5EA4wAN8Px+Pe+D38/l+vvf+Hnfc2+/3M/LYdc5eXl706tWLDRs2cOLECZo0aULZsmWtxypXrlyaXmchHiTWFMtHPrupU1vRerfm+8YGapVpRKMSjRwdmmNprbPVA6iJecSy8b5yJ2AkEI95UEnr++pDE8ovAuUTlfsA+xPqhtt4Prva2XoEBQXptDpw4MAD96k6r6pdj84/dk7xmJ1/7Gz3cVMyYdOEVOvt5efnpwG9du3aNLdZu3atBnRwcLDN+pMnT2pA+/n5JatL+F0nK+/atasGdGhoqL5x44a1PC4uTo8ePdrm882dO9d6vFatWumIiIg0n4PF5s2btdFo1ID29vbWzz77rJ45c6betm2bjo6OTrHd0aNHNaDLlSuX4j6fffaZBnS1atX04cOHk9QtXbpUG41GXaBAAR0eHp7suIAuWrSoPnjwoLXu7t27unv37hrQDRo0SPM5njhxQufNm1cD2t3dXXfu3Fl/+umnesOGDfr27dsptouNjdWANhqNyepKlCihAZ03b169adMma/mdO3d0o0aNNKCrVq2qK1WqpC9cuGCtP3nypPb29taA3rx5c5Jjvv7669Zz79Kli75796617tChQ7pYsWIa0F988UWSdl9++aUGdL9+/ZKUnz17VufLl087OTnphQsXJqk7ffq0rlatmgaS1VniB/ScOXNsvjYvvfSSBnTlypX1+fPnreW3b9/W7du314Bu3Lhxkjbh4eHWcxg8eLCOiopKUn/58mW9ceNG67at1//kyZO6YsWKGtAjRozQ8fHxmXLOPXv2tFmeE6Tl77xwvMUHF1u/51pMraJrfVVNH75x+MENcwFgp04hp8mOt5hLAyuBK0qpLUqppUqpVZjnKrSsmv2q1np14kZa6++BmZhXPdmrlFqplFoGHMU8NU4YMP3+J7O3nXh4QkJCUpzixtvbO0uf+8CBA3z33Xf4+fmxYMEC8ufPb60zGo28++67VK9enXXr1rF3795k7Z2dnfniiy/w9LQ5S1KqGjRowNKlSylatCjh4eEsXLiQF198kXr16uHt7U1oaCi7du1K93Hj4uJ46623UEqxdOlS/P39k9SHhobSv39/bty4weLFi20eY8KECUn6ALq6ujJ9+nQ8PT3ZsmUL27ZtS1MsZcqU4ddff6V8+fLcuXOHpUuXMnz4cJo0aYK3tzdt2rRhTaIpJ9Jj5MiRNGzY0Lrt5ubGiBEjANi3bx/Tp09PcsWydOnS9OjRA4C1a9faPGbevHmZMWMGrq6u1rKAgADefPNNAKZOnZqm2KZOncrNmzcZPXp0spG5pUqVYvbs2QB89tlnNtu3bduWvn37Jiu/ffs2X3zxBQDTp0+nePHi1jp3d3e++OIL3N3d2bhxY5Lf0ZdffsnFixdp3Lgxn332WZKrfmDuAtCoUcpXU3bu3En9+vU5cuQIU6dOZerUqRgMSb9eMnrOQmSFm9E3+fyfz63bl/Mr2gV0xD+/fyqtHg3ZMUHcA3wKHAZKAe2AYOAOMBeoq7X+wFZDrfUgoCewO6FNa+AY5ulwOmmtbXYSsredeDhat25Nr169bD4sX+hZ5ddffwXgySefxM0teTdVg8FA48bmtTm3bEneCyEwMDDd/R0T69ixI6dOnWLZsmUMHjyYunXr4urqSlRUFD/88AP16tVj7ty56Trmrl27uHz5MtWrVycgIMDmPsHBwYDtcwJsTjdSoEABHn/cPLlAeuambNKkCYcOHWL16tWMGjWKxo0bkzdvXmJjY1m9ejWPPfYYkyZNSvPxLNq0aZOszNIP09XV1WY/Vcut8QsXLqR4zEKFCiUrf+aZZ1BKcejQIS5fvvzA2Cy3sG0NzAGoW7cubm5u7Nq1i9jY2GT1ibsOJLZjxw7u3LlDqVKlCLGx8kORIkVs/o5WrVoFQL9+/dI9Mvznn3+mWbNm3Lx5kyVLlliT8Ptl9JyFyAqz9swiPDrcuu3m5MaQmkNSafHoyHZ9ELXWJwHbf2HS1n4xYPuyRxa0E1nPkdPcnDhxAoAZM2ZY5yNMia3BKn5+tgfIX7lyhdGjRycrDw4Opk+fPknKXF1d6dixIx07dgTM09v88ssvjB07lmPHjvHiiy/Spk2bNPffs5zTnj17HpgM2DqnQoUK4eFhe2YoSzKc3sEqRqORVq1a0apVK8A8yGLt2rW89tpr7N69mwkTJvDkk08SGBiY5mP6+vomK7PEXbx48WRXuBLX37171+Yxy5SxvaCSm5sbPj4+XL58mXPnziXr73m/kydPAlCrVq1U9wNzv777j5fS++r8+fOpxgn3+u5Z9gU4fdq8mFR6R4bHx8fTvn174uPj+eGHH1JMXCHj5yxEZju68hvyz19A/maK/zzNfwv7V+tPYffCDo4se8h2CaK4Z2+v5LcsM2pJuyWZfsyJDScyseHETD9uVkjvnIGWkalBQUFUrVo11X2r2JhQ1dZVRzAPfJk/f36ycicnp2QJ4v3c3d0JDQ2lXr16+Pv7c/fuXVatWvXAdhaWc/L19aVFixap7mvrnNIio/MTuri40Lp1axo0aEBAQACXLl1ixYoV6UoQbSWAaanLqLScu+V30K1btyS3q21xcXFJVpbS+8rcpSj1GCz7ZAaj0UjPnj1ZsGABr732GvXq1aNEiRI2983oOQuRmXRMDNc+mEKTqybqHIaPOhq4Wt2X5yrbWuH30SQJoshVLF8stqYqgXtXStKqZEnzNJghISFMmTIlY8ElUr58+Qx/UZcsWZKKFSvyzz//2LzSl1o7MCeI8+bNS/fzXrt2jcjISJtXES1TyCTu+5YRXl5e1K9fn7CwsHSdY1axnN/9oqKirFP2pOXcfX19OXXqFBMnTkzxNr89LFdNLVeJbbFcyUucyPn5+XHs2DEOHz78wJHK95s3bx7u7u7MmjWLpk2bsmbNGpvdKrLqnIWwx84Zk/G+GgVAnBFOFFNMrD2KPE55HtDy0ZEd+yAKYTfLl97x48dt9mNKafqSlLRt2xaAsLAw4uLiMh5gOjwogYyLi7P2lUt8O9WSJKcUb/369fH29mbnzp3WZCG9bA1e+e+//6yvb1q7BKQlSbasomLrlvHDtmrVqmTz+oH59dBaExAQkKalHy3vq6VLl2ZqfJYpeM6cOcO6deuS1V+9etXm78gyndGcOXPS/R8XpRQzZ85k5MiRnDhxgqZNm3L06NFk+9l7zg96PwuRXnevXcY4b5l1+/tGBvzL1KalX0sHRpX9SIIochU/Pz/KlStHeHg4H374YZK6sLAwpk2blq7jBQYG0qFDB44dO0aXLl1s9q27ePEin3zySaZ/gfXu3ZuJEyfavOp58+ZNBg0axJUrV8iXL1+SARk+Pj44OTlx4cIFbt68maytq6sr48aNIy4ujvbt27Nz585k+9y+fZtFixZx+PBhm7FNnDiRI0eOWLdjYmIYNmwYt27dom7dumm+CjV27FhGjhzJwYMHk9VFRUUxYcIEdu/ejZOTE506dUrTMbNSZGQkQ4YMISYmxlp29OhRJkyYAJhXvUmL0aNH4+npyeTJk5k1a5bN986WLVv44Ycf0hVf3rx5GThwIABDhw7l0qVL1rqoqCheeOEFbt++TePGjalXr561buDAgRQtWpQNGzYwYsSIZH0wr1y5wqZNm1J97o8++ohx48Zx9uxZmjZtmmyydXvP2fKfPlvvESHssW3SS7hFm7sbXSgAvwUZeLXOq7J05/1Smv9GHul/ZPY8iI86yzyIrVu31r169UrxsXr16iTtlixZopVSGtCBgYE6NDRU16hRQyulrPPZpWcexJs3b+rg4GAN6Dx58uh69erpLl266DZt2ugqVapog8GggSRzx1nmQezVq5fd5//EE09oQCultL+/v27fvr3u3r27DgkJsc4d6ObmplesWJGsbbt27TSgS5curXv06KH79eunx44dm2SfoUOHWo9fvXp13bFjR92+fXsdGBio3dzcNKB///136/6WeRDLli2r27Vrp11dXXWbNm10165dta+vrwa0j4+PPnToUJrPcfDgwdbX3c/PTz/55JO6R48e+rHHHtMFChSwzrU3c+bMJO3SMg/i2bNnk9U9aI7IlOYttLxvevXqpb29vbWvr6/u2rWrbtu2rXZ1ddWA7tChgzaZTGk6ntZa//7779Z5F4sVK6Zbtmypu3btqps0aWKdk7Bnz55J2ljmQdywYYPtF1Sb53ts0qSJBrSHh4d+6qmndOfOnXXRokWt74mTJ08ma7dt2zZduHBhDehChQrp9u3b686dO+u6detqZ2fnJOeQ2uv/zjvvWI/x999/Z/icd+zYoZVS2mg06tatW+u+ffvqfv366S1btqT4GmQX8nc++4k6dEjvq1hRHwgwP54dV1lP2DTB0WE5DKnMg+jwpCo3PSRBzFyWBPFBj6lTpyZru2LFCl2/fn3t5uamPT09dXBwsF61apVdE2VrbZ4Ue8GCBbpVq1a6UKFC2snJSRcuXFjXqFFDDxo0KFmSmhkJ4tmzZ/WcOXN09+7ddbVq1XShQoW00WjU+fLl04GBgfqVV17Rp06dstn26tWruk+fPrpEiRLayckpxaRo7dq1umvXrrpkyZLaxcVF58uXT1esWFF369ZNL168OMlk1YmTq5iYGP3mm2/qChUqaBcXF+3j46Ofe+45ffr06XSd49WrV/WiRYt0nz59dM2aNXWRIkW0k5OT9vDw0FWrVtWDBg3Se/fuTdbOUQni5MmT9dGjR3WXLl104cKFtaurq65UqZL+8MMPdWxsbJqPZ3HhwgU9ZswYXaNGDe3h4aFdXV21n5+fbtasmX7//ff18ePHk+yflgRRa62jo6P1J598omvXrq3z5s2r8+TJoytWrKjHjBmjr1+/nmK7S5cu6dGjR+vKlStrNzc37eHhof39/XXfvn31tm3brPul9vprrfWnn36qlVLa29tbb926NUPnrLXW3333na5Xr571P0bkkImz5e989mIymfSp53pZk8OwJwN1va/r6qt3rjo6NIdJLUFU5nqRGWrXrq1t3a6z5eDBg1SqVCmLIxIi8xw7dowKFSpQrlw5jh075uhwHqpx48bx9ttvM3nyZMaNG+focEQOIX/ns5dbf/zBuSFDzRtGIyWXLeVMIU3lgpUdG5gDKaV2aa1r26qTUcxCCCGEyNVMMTFc/uDeTBT5u3bFI6ASj25q+GAySEUIIYQQuVrkH38QmzAjgsHLi0JDZbWUB5EriEIIIYTItbTWeD3+OMrNjcvvvkeBZ57BKX9+R4eV7UkfxEwkfRCFEEJYyN/57GHWnlkcDz/OqNqj8HHKjzIaUU5yfQxS74Mot5iFEEIIkSudjzzP//b+j1WnVvFU2FN8dWQhsSp9S64+qiRBFEIIIUSuo+PimLrpfaLjowGIioti4YGF3I2/+4CWAiRBFEIIIUQutHvWu7R743fqHDFBQne6EYEj8HLxcnBkOYMkiEIIIYTIVaKuXEL971t8bsIrP5hodEBTvVB12pdv7+jQcgzppSmEEEKIXGX7xGH43E1Ybzk/bA8wsLDeaxiUXBdLK3mlhBBCCJFrnN/2Fz5/7rVuz2tpoH3lUKoUquLAqHIeSRCFEEIIkStok4njb4yxbu+ooDhRyZthtYY5MKqcSRJEIYQQQuQK/3z1EYVP3wQgxgjzWxgYVmsY+fPIxNjpJQmiEEIIIXK8u/9dJ37mfOv2j/UVBctVJtQ/1IFR5VwySEUIIYQQOd62SSPwuR0PwFUvCGtgYE691zAajA6OLGeSK4gi2ypdujRKKf766y9Hh5KiU6dOoZSidOnSyeos8Z86dSpDzzFx4kSUUkycODFDx7lf796903Rcy/P37t07U58/u/jvv/+YOHEitWvXxsvLCxcXF4oVK0bNmjXp378/8+bNIz4+Pkkby2s3b948xwSdRkoplFKODiPT5ZTXXzw8l/7ZSqFV95a6XdDCQJuK7anpU9OBUeVskiAKkUP99ddfKKVo1qyZo0PJsQ4cOECVKlV48803OXz4MHXq1CE0NJQ6depw8+ZN5syZQ58+fYiKinJ0qMIB5DOWc2zc8QN3Xcz//re0Yn9VT14KesmxQeVwcotZiCyyZs0aYmNjKVGiRIaOM2TIELp160ahQoUyKTJh8eyzz3Lx4kV69OjBzJkz8fJKusLCoUOH+OqrrzAak96ievfddxkzZgzFihV7mOEKIVLwdP/3WVmtCtc/nsqSevEMqjWYQm7yNzMjJEEUIouUK1cuU45TqFAhSQ6zwLFjx9i9ezdOTk7Mnj2bvHnzJtunYsWKfPDBB8nKixUrJsmhENmIQRloX783NxY8ReSBr+lWsZujQ8rx5BazyHES9z/av38/nTp1onDhwnh4eNC4cWPWrl1r3fenn34iODiYfPny4eXlxVNPPcXRo0eTHTPxraTbt28zZswYypYti6urKyVLlmTo0KFcv349XXGm1gdRa82SJUto27YtPj4+uLi4UKJECVq0aMH06dOT7GurD2KzZs0ICQkBYN26dda+Zo64HXb27FmGDx9OQEAAbm5ueHl50ahRI+bNm4dOWP80sQf1zWzWrJnNvqeJy3ft2sVTTz1FwYIFcXNzo0aNGsyZMyddcV+5cgUADw8Pm8lhalLqA5f4d3Xu3Dl69+5NsWLFcHd3JzAwkO+//96676ZNm3j88ccpWLAg7u7uhISEsGPHjmTPlbifa1xcHO+99x6VKlUiT548FClShF69enHmzJl0xQ8QGxvLrFmzaNKkCfnz5ydPnjxUqFCBkSNHcvXq1WT7z5s3z9oX9fr16wwbNowyZcrg4uJChw4dkuy7efNmOnXqRNGiRXFxcaFo0aKEhoaydevWFONJz2ciNUuXLiVPnjx4enqyevVqu885O33GRNoVyFOAYYHDcDY4OzqUHE+uIIoca+fOnQwePJiyZcvSokULjh49yqZNm2jdujVr1qzhn3/+YcSIETRq1IjWrVuzfft2Vq5cyY4dO9i3bx8FCxZMdsyYmBhatGjBvn37aN68OYGBgaxbt47p06ezevVqNmzYQJEiRTIUd0xMDJ07d+bHH3/EaDRSv359SpUqxeXLl9m3bx9//vknQ4YMSfUYbdq0IU+ePKxevZoiRYrQpk0ba13FihUzFF96rF27lo4dO3Lz5k3Kly9PmzZtiIyMZOvWrfTp04c///yTBQsWZOpzrlq1io8//piAgABatWrFmTNn2Lx5M/379yc8PJxRo0al6TilSpUCIDw8nHnz5mXqIJzTp08TFBSEh4cHwcHBnDt3jk2bNtGlSxcWL16Mq6srXbt2pWbNmrRs2ZI9e/bw119/ERISwu7du/H397d53K5du/LTTz/RrFkzatSowaZNm1iwYAGrVq1i/fr1BAQEpCm+iIgInnjiCTZu3Ei+fPkICgrC29ub3bt3M3XqVH744QfWrVtnc/DVtWvXrH00mzRpQu3atZN8lmbOnMmQIUMwmUzUqVOH5s2bc+zYMX744QeWL1/OrFmzGDBgQJJjZsZnAuDjjz/m5ZdfpmjRovz888/UqlXL7nPOLp8xkbKovftQRgN5Kld2dCi5k9ZaHpn0CAoK0ml14MCBNO/7qPLz89OAXrt2bZLyXr16aUAD+qOPPkpSN3r0aA1of39/7eXlpdevX2+ti4qK0k2aNNGAnjRpUpJ2a9eutR7T399fnzt3zloXERGhW7RooQHduXPnJO1OnjypAe3n55di/CdPnkxSPmzYMOvzHDx4MEldXFycXrFiRZKyCRMmaEBPmDDBZszBwcHJnjstLK/j/ce9n+X5e/XqlaT8woULOn/+/NpoNOp58+Zpk8lkrTtz5oyuWbOmBvTcuXOTtEvpdbEIDg62+Xu3lAN6zpw5SeoWLlyoAe3l5aVv376d6vkk1q5dO+sx69Spo19//XW9fPlyffbs2VTbWV67+8/N8loBevjw4TouLs5a9/nnn2tA+/r66vz58+slS5ZY6+Lj43XXrl01oPv27ZvkmJb3GKB9fHz0/v37rXXR0dH6mWeescZ/P0u7+1meKzQ0VN+4ccNaHhcXZ/0M3f++mjt3rvV4rVq10hEREcmO+88//2gnJydtMBiSnJ/WWn/zzTfaYDBoZ2dnvXfv3iR16f1M3P/6x8fH66FDh2pAV65cWZ86dSpTzjmjnzH5O591TDEx+viTT+oDlSrri2+9reNu3XJ0SDkSsFOnkNM4PKnKTY/MThCvTPtMHwiomKbHhXHjk7W/MG58mttfmfZZsvZnnn8hze1vfPtdms89rR6UIDZo0CBZmxs3bli/xMaOHZusftmyZRrQISEhScoTJ4grV65M1u7o0aPaaDRqg8Ggz5w5Yy1Pb4J4+fJl7ezsrA0Gg963b98DXgGzrE4Q0/q4P0G0fKmOHj3a5vF37NihAR0YGJikPKMJYqdOnWy2q1Spkgb0unXr0nT+WmsdHh6uu3XrppVSyc7X399fv/fee/rOnTvJ2j0oQfTz89PR0dFJ6uLi4nTBggU1oLt3757smLt379aALlOmTJLyxAniZ58l/5yGh4frfPnyaUBv3LgxSZ2tBHH//v3WGG2dW3x8vK5evboG9L///msttySIzs7OKf7u+vbtqwHdo0cPm/VdunTRgO7fv7+1zJ7PROLX/86dO7pDhw4a0E2bNk2S/GX0nCVBzL62TnnV+v1zsFagjrmoM/DpAAAgAElEQVRwwdEh5UipJYjSB1HkWIlv+Vjkz5/fervLVn2FChUAuHDhgs1jent78+STTyYrL1++PPXr18dkMrF+/Xq7Y/7zzz+JjY2lQYMGVKmSPRaOr1GjBr169UrxUaNGDZvtfvnlFwA6d+5ss95yi/Wff/7h7t27mRavrd8P3Lvtl9Lv1pZ8+fLxzTffcOTIEaZMmUKHDh0oWbIkAEeOHGHMmDE0aNCA8PDwdMXYvHlzXFxckpQZjcYkty/v96D3JsAzzzxj8xwsr0la5gz99ddfAfPr6ObmlqzeYDDQuHFjALZs2ZKsPjAw0OatZzD31QNSvF3ft2/fZHFm5DNx7do1mjdvTlhYGN26deO3334jf/7kS6pl9JxF9nLz9DFc5/9o3f6vZyucihZ1YES5k/RBFDmWr6+vzXIPDw+uX79us97DwwMgxYQlpS8+S92mTZs4d+5c+oNNcPr0aSB79WHq0KFDqpNlT5w4kT179iQrP3HiBAB16tR54HNcv349w9P9WFj6Dt7PMkWNPclo+fLlefnll3n55ZcBOHz4MDNmzGD69Ons2bOH119/nRkzZqT5eKm9N1Oqt9RFR0fbbOvt7Y23t7fNOsv7Ni3vTcvvbcaMGQ88J1uDVfz8/FLc//z58wCUKVPGZr1lZL9lP8jYZ2Ls2LHExcXxxBNPsHjx4hQnBc/oOYvsZffYwRSNNQ+AO10YxhX4lbDIwfh62v7cCftIgpiNFR46hMJDH9wxOyXFJk+i2ORJdrcvOWum3W0fBoMh9QvgD6q3V25cmcIeltVFunbtSp48eVLd19XVNc3HNZlMqdZn1e81sYCAAKZNm4ZSimnTphEWFpauBDE7vzctv7egoCCqVq2a6r62rujZugKX1jjMd7QyT+fOnVm+fDmrVq1i8eLF9OzZ0+Z+GT1nkX0cXLGAorvvjdr/XxsjPao/J8lhFpAEUYhEUlsWz1JXvHhxu49vufpy+PBhu4+RXZQsWZJjx44xfvz4dH2pWm69RkZG2qy3XFHKDlq1asW0adOyxVWl8PBwbt68Sb58+ZLVpee9abmFHhISwpQpUzI1xhIlSnD8+HFOnDhhcx7QkydPWvezyMhnolWrVgwYMICnnnqK5557jqioKPr3759sv6w8Z/HwxN2O5OZ7H2H5BKypoYgIKM4L1V9waFy5lfRBFCKR8PBwa9+6xE6cOMHWrVtRStG0aVO7j9+8eXOcnZ3ZvHkzBw8ezEio1kQrLi4uQ8exV9u2bQHzvHPpYUkODh06lKxu3759nD17NuPBpUFarmZZ5hdM6Zbxw7Zo0aJkZTdv3uSnn34CSNP8fJbfW1hYWKa/d4KDgwFSnNpo7ty5QNI4M/qZCAkJYfXq1Xh6ejJw4EA+++yzZPvYe86O/oyJpDa/8xL5/osBIMINFjUz8Fq913B3dndwZLmTJIhC3GfUqFFcvHjRuh0ZGcmLL75IfHw8HTt2TLEPXFr4+PjwwgsvYDKZ6NSpE0eOHElSHx8fz8qVK9N0LEuidezYMYd8gb3yyit4eXnxzjvvMGPGDJsxbN26NVkC2aJFCwA++OADIiIirOVnz56ld+/emX4bMiX//vsvzZs358cffyQ2NjZZ/YYNG3jzzTcB82307GDSpElJkqjY2FiGDx/OzZs3CQoKsg60SE1gYCAdOnTg2LFjdOnSxWa/xYsXL/LJJ5+k+301bNgwnJyc+Oabb1i+fHmSuqVLl7JkyRKcnZ0ZNmyYtTwzPhMNGzZkzZo1FChQgGHDhiVb/cbec3b0Z0zcc3nfDvIv32jd/rq5gboBLWhWspnjgsrl5BazEIk0aNCA+Ph4/P39rSNR161bx9WrVylXrly6+qGlZMqUKRw/fpxffvmFKlWq0KBBA3x9fbly5Qp79+7lypUraUqS/Pz8qFWrFn///TfVq1cnKCgIV1dXAgICeOWVVzIc54OULFmSsLAwQkNDGTJkCG+//TZVqlShYMGCXLhwgePHj3PhwgW6du2aZKTz4MGDmT17Njt27CAgIMA6Snj79u3UrVuXhg0bsnnz5iyPX2vN2rVrWbt2LR4eHgQGBlK8eHGioqI4evQoBw4cAMxXqMaNG5fl8TxIqVKlCAoKombNmjRv3px8+fKxZcsWzpw5Q6FChdI1Ifn8+fN56qmnWL58Ob/++is1atTAz8+PiIgIzp49y8GDBzGZTLzwwgs4OaX9a6JGjRp8+umnDBkyhKeffpp69epRrlw5jh07xvbt2zEYDEyfPp1q1aolaZcZn4mgoCD++usvHnvsMV599VXu3LmTZPCVPefs6M+YuOfA6yMpmtA9+aAvbK/lTljdMY4NKpeTK4hCJOLi4sKff/7J888/z7///suPP/6Ii4sLgwcPZuvWrRTNhKkUXF1dWblyJQsXLqRp06bs27eP77//nkOHDlG9evV0JaHLli2jS5cu3Lhxg2+++YY5c+bw888/ZzjGtAoJCWH//v289tpr+Pj4sHXrVsLCwjhz5gwVKlTg3Xff5e23307SJn/+/GzatImePXsSFxfHzz//zLlz53jllVdYtWoVzs4PZ4msqlWr8tdffzFu3DgCAwM5e/YsK1asYNWqVURERNCuXTsWLVrEH3/8ke6l+LKCUoolS5Ywfvx4Tpw4QVhYGFFRUTzzzDPs2LGDyulYTcLLy4s1a9awYMECmjZtyvHjx1m2bBm7du3CycmJF154gdWrVz9w8JEtgwYNYsOGDXTs2JGTJ0+yZMkSTp06xdNPP83GjRsZOHBgsjaZ9ZmoWrUq69evx9fXlzfffJNXX301w+fs6M+YgM0XNjOl8X8cKQ5xBvPAlBdrDqaYh6yHnpXUw7qd8yioXbu23rlzZ5r2PXjwIJUqVcriiERaWZY5Cw4OTtNcckI8LKdOnaJMmTL4+fmlOohKZD/ydz7jouKi6LiiI+cjz6NMmvIXgar+fPfkd7LeciZQSu3SWte2VSe3mIUQQgiRLX3+z+ecjzTPm6kNimMlFAsbTJDk8CGQW8xCCCGEyHYOXN7LggNJ+9Z2r9idGoVtr+4kMpckiEIIIYTIVuJv3SKiSx/abItDmcxd4YrmLcqwwGEPaJnzXY+0vZrSwya3mIXAPC+b9McV2VHp0qXlvSkeOVc+/ph8l2/T+zJUO2Pg/VDF+Prjyevs+AFjWennrXt49ddLfNajFiEBPg6NRa4gCiGEECLbuLN7N+HffGvdrvPcywyuOZimvvYvUpAT7N+xlma/tqRb3Ar6zdvO/M2nHBqPXEEUQgghRLZgionh4vg3rNsezZrhG9qbgDSsM56TnT15GJ+fe5NXRTPOeRF5Y+/y9s9GQgJ8KFXQMSvFyBVEIYQQQmQL12d/Sczx4wAY3N0pOuENVC5PDm/+d4OYhV0oTDgA4TovP5oaMqVzdYclhyAJokNJvyIhhMid5O97+kUfP871L76wbhd+6SWci+XuybBjYmI5Pqsr5UynzNvayAuxL9GhRTDta5ZwaGySIDqI0WgkPj7e0WEIIYTIAvHx8RiNRkeHkWNok4ltI3qjE9ZFz1OjOvl7dHdwVFnvzk+vEhi93br9elw/itVoybAW5R0YlZkkiA7i7u5OZGSko8MQQgiRBSIjI3F3d9ztwZxmx+x3KHz0GgDxBoga1RuV2xPsHf/D+9851s3P457iVMmOvNepWra4rS4JooN4eXlx48YNuYoohBC5THx8PDdu3MDLy8vRoeQIN88cx3nmYut2WH3F5CsLcvdt+mN/wC+jrZux/u04XWMkXzxbG1en7JEY54gEUSn1jlJKJzxeTmW/HkqpDUqpm0qpSKXUTqXUYKVUqudpb7uM8PT0JG/evJw+fZrw8HDi4uJy94dBCCFyMa01cXFxhIeHc/r0afLmzYunp6ejw8oRFmyaTrib+fvvQgFY0diZ8Q3GZ4uraFniykFY2gd0wgWi4rVwDp3N+51rUSCvi2NjSyTbT3OjlKoDjAY0kOK7RSk1AxgE3AXWALFAC2A60EIp1Vlrnexynb3tMkophY+PD7du3SIiIoIrV67I1UQhhMjBjEYj7u7uFCpUCE9Pz9yb4GSibRe3MTvmD1z7Gem23sTWiga6VX+OygUrOzq0rPPfKYiPMf/byxe6fwsu2a87QrZOEJVSrsA84DKwHeiQwn6dMCd5l4CmWuujCeVFgLVAR2AI8GlmtMssSim8vLzkNoQQQohHzp3YO0zYPAGAaBfF/MeM+Hn5MbjmYAdHljUi7sYyaeUBxrRtTqHev8Cy/tBlAXgWdXRoNmX3W8yTgMrAC8DNVPYbm/DzVUuSB6C1vgy8mLA5xsYtY3vbCSGEECIDPt39Kecjz1u3FYpJDSeRxymPA6PKGnHxJoYs/pvvd52jw4xNHHH2h8E7oGg1R4eWomyb+Cil6gGjgMVa65Wp7OcLBAExwNL767XW64DzQFGgfkbbCSGEECJj/v5uJieWf52krGelngQWCXRQRFlHa83bYTtZf+QqAOf+i6LT55vZe/G2gyNLXbZMEJVSeYD5wA1g+AN2r5Xwc7/WOiqFfXbct29G2gkhhBDCTrcunSX+vemMDDMxclk8Hnc0vh6+DK011NGhZYnN302h956elFUXrGVlC+elvI+HA6N6sGyZIAJvAwHAUK31tQfsWybh5+lU9jlz374ZaSeEEEIIO21/ZQB5o0wAlL2kiXWCSY0m4e6c/QZqZNTuP76j/sF38DNcYZnLBCqp05TwduPLXrVxc8ke09mkJNsNUlFKNQRGAGFa6+/S0MSSgqd2rdYyI3XiOQfsbSeEEEIIO+z5bibFd9y7LvNFWwMdq3WnTtE6Dowqaxz+eyMBG4ZiVOYpfM5oH665lGBh79r4eGb/fpbZ6gqiUsoNmAtEYB5dnKZmCT/TO4mgve2SHkSpgQnzJu68evVqRg4lhBBC5Fq3r1wg5oMZ1u01NRQ3qpXkpaCXHBhV1jh/6ij5VzxLXhUNwDldiAFxo/mgRwMqFs0ZM5dkqwQReAfwB0ZqrS+msc2thJ+p3cy31N1KVGZvuyS01rO11rW11rULFy6caqBCCCHEo+rM5Il43DbP93vdExY0NzCx4cRcd2s5/L9rRC/ohA83AIjQ7vSJGc3w9o0JCfBxcHRpl91uMXcETEAvpVSv++oqJvx8USn1JHBMa90fOJVQ7pfKcUsm/DyVqMzedkIIIYRIh1tr1sDvG6zbs9sYeKJ6Z+oXy12ThNy9e5fTM0OpYTLfRo/RRp6PfYmWwcH0qFfKwdGlT3ZLEMF8VTM4lfqyCQ/vhO2/E35WUUq5pTAiuc59+2aknRBCCCHSKO6//7g4caJ1O1/79vR//nECfXLXlDameBO7P+9Dw5h7KcOY2AEUrtaSl1sFODAy+2SrW8xa69Jaa2XrgXnaG4BXEspqJrQ5C+wGXIDO9x9TKRUM+GJeLWVLoueyq50QQggh0u7SpEnEXzVPSGIsXIgiY8fQ1LcpHi7Ze5qX9NowdywNI36xbk+N7cR5vw5M6VwdgyHnLbuYrRLEDHg34ef7SqnylkKllA/wecLme1prUya1E0IIIcQDxF6+wp1t263bxSZPxujtnUqLnCkiKhrTxT3W7e/jm/JT/meZ/WxtXJ2y93Q2KckVCaLW+ntgJuZVT/YqpVYqpZYBRzEv1RcGTM+sdkIIIYRI3Z3YO4R7Ksqu/BGPx1qQL7QTns2aOTqsLOHl5krV4ctZ7vY0m+Kr8KHLIOb1rUc+d2dHh2a37NgH0S5a60FKqY3AYMx9GI3AIeArYGZKVwHtbSeEEEKIlE3ZOYXfT//OuPrjaP3ZZxAb6+iQslRhLzfavPQ/Xvt+F7Ob+lOyQM4ena20ztA0gCKR2rVr6507dzo6DCGEEMKh1p9bz+A1g63bbUu3ZXyD8Xi65KJ1J2LugLMbqJzXv9BCKbVLa13bVl2uuMUshBBCiOzh+omDfL1obJKygzcO4mTINTctIeY2zHsCfn0VTPGOjiZL5KLflhBCCCEcSZtM7BkxgOFHblChjuKbYAMmFyfeafwObk5ujg4vU0THRHNi2tNUitwNF3ZDxHno+nWOvpJoi1xBFEIIIUSm2PzJ6xQ7ch0D0Hanxvca9KvWj2qFqzk6tEyhTSZ2z+hNpcit9wrLheS65BAkQRRCCCFEJri4fyceX4VZt8MaKPJUqcwL1V9wYFSZa9OcV2hw895chzNNHdlcoIMDI8o6kiAKIYQQIkNMsbEcHjkIlzjz9skisKKpK283fhtnY86d6iWxzUs+ovH5/1m3v49vylLPXlQq6uXAqLKO9EEUQgghRIasf+8lipy+BUCsEaY/aWRQ7WFUyF/BwZFljp2/Labe/smQcCd5XXx1pjgPYknfuuTP6+LY4LKIJIhCCCGEsNupbWso+M0a6/aSJgYKVw3iucrPOTCqzLNv2xqqbBqOUZmnBfzXVIZRahRf9W2AX8G8Do4u60iCKIQQQgi7xERGcO7lURRMWFLiUAn4vZE73zd6C6MhZy4xl9jxQ/9Q/NdeuKkYAM6YCjMgbjQf9mpIdd/ct2RgYtIHUQghhBB22fBqPwpejQbgjgtMb2dkVN1XKOlV0sGRZdyF8Cgmfb8dkzbfV76uPXkudgyvdGpKswAfB0eX9SRBFEIIIUS6HT28lQLr91m357Y0ULFaMJ39OzswqswRfieGXl9tZ11kCTrFTOSgqRT9Yl6hc6tmhAb5Ojq8h0ISRCGEEEKkW3n/epz4ZBDHixvYUlGxt05BJjWchMrhcwLejY1nwIKdHL0SCcBpXZTHY96hev0WDGpWzsHRPTzSB1EIIYQQ6aaUolOLoRyt3pLFa8cyueFLFHQr6OiwMiQ+3sQbC39jxylTkvI2VYszoV2VHJ/8podcQRRCCCGE3SoUrsjC0O9p6tvU0aFkWOzvbzL+bH+C1GFrWd0yBZjatSZGw6OTHIIkiEIIIYRIo+jjx7l7+Eiy8twwYpntX5Jn6yd46ki+cX2XauoE/kU8+PLZ2uRxzgXnl06SIAohhBDigUwxMZwfOYpToaFcnzcPbTI9uFFOsT8MfnnFuulUPpi6DYKZ37cu+dxzx0ow6SUJohBCCCEe6K/X+xN9+DA6NparUz8h9tw5R4eUOU6sg2UDAPNE2BQPxNBlPuOfqk6xfG4ODc2RJEEUQgghRKoOrP6WYit33CsY9CwupUo5LqBMEn/ub/i2B8SbJ8KmYAXouRRccu8KKWklCaIQQgghUhR57SI3x79l3f67rGKQ90/EWJKqHOr4oX+ImNMeYszT2eBZHJ5dBnkLOTawbEISRCGEEELYpLVm65Bn8I6IByDCDT5/wsDr9cfhYnRxcHT2O3/mBG7fhpJf3wQg1iWfOTn0zvlXRTOLJIhCCCGEsGnztNcp8c8F6/bMJww8ViuUFn4tHBhVxly7fp3oue0pzlUAorQLPe+M4qh+NFZISStJEIUQQgiRzOmdf+E5e7l1++faimtBZRhdZ7QDo8qYiLux9Pp6P7/F1gAgVht5MXYEleq0oLyPh4Ojy15kJRUhhBBCJBF96yZnXxpBQfOdZU4UgSUtXJnfdAruzu6ODc5Od2PjGTB/J/sv3mI/3bmuPbmqvfGq9vgjt0pKWsgVRCGEEEIksWTJBLyvRQNw1xk+bW9keP2XqVSwkoMjs09cvIlh3/zNtpM3rGVfxj/JjfId+bBzDQyP2CopaSEJohBCCCGsNp3fxAdOa3jjGSNX8sH/WhsIqBlCj4o9HB2aXbTJxHfzprHmwIUk5bVKeTPrmUBcnCQVskVuMQshhBACgKt3rvLaxtcAOOqrGNXfiLd3Ub5vODnH3oL9a+54ep6djo9zEENihxKNCxV8PJjbuw7uLpIGpUTSZiGEEEJg0ibGbhzLjbv3bsPGuhp5v+n7eOfxdmBk9lv37ceEnJ0OQEvjLl50+pES3m4s6FcXb/ecO03PwyCpsxBCCCH45ePhHHPeCvnuXSl8scaLBBUJcmBU9tv803waH5wECaez1VSJb11CWdSv7iO9hF5ayRVEIYQQ4hEXuX495b78g4/mauocNgFQp2gdBlQb4ODI7HNg4wqCdozEqMzrK+83+TGc0czu24hyhWU6m7SQBFEIIYR4hMVevsKFMWMBcI8y0f2YD/ldvHmvyXsYDUYHR2eHs9uptO5FXFUcACdNRRgQP5aPn2tKdd+ceavcEeQWsxBCCPGI0nFxnB81kvgb5n6HToULEzLrB2rkicPH3cfB0dnh0l5YFIqKvQ3ADWNhno1+jXE9mtGovKyxnB6SIAohhBCPqKufTiNq5y7zhsFA8SlTcCpQgByYGsL147CwI9w1r6+MeyG8ev3EB7cK0VCSw3STBFEIIYR4BN366y+uf/mldbvwsKHkrV/PgRFlgNYQNghum9dXxtULnl2GU5GKNCzi2NByqgcmiEqpPzPpubTWOueu7i2EEELkEldPHODcyKHkSdjO26QJBQcOdGhM9roQHsWVW9HU7PQlLGgPERehxxIoVsPRoeVoabmC2CyTnktn0nGEEEIIYae4u3fZO6g3xe6YB3HEFspH8Q/eRxly3rjVq7eieeZ/27gUcZf/9apNwz6r4NoR8Gvg6NByvLTeYl4FvJ+B5xkDtMpAeyGEEEJkgj9f60PJU7cAiDPAm20jeSFiJy3zt3RwZOlz804sz321nRPXzANSes/dwec9AnmschMHR5Y7pDVBvKS1XmfvkyiletvbVgghhBCZY8v5zey98i8lE7YXhRjwCAyiWclmjgwr3W7fucP+TzuT/1ZToCoAMXEmwv45z2OVpdNhZkhLgrgHOJPB5zkL/JvBYwghhBDCTpdvX2bMxrHcaGngkC8EHdNsaVKQJU0/wNng7Ojw0uxudDT7PutCw+iNBDlvZUjsMH431aapf2E+6iL9DjPLAxNErXWtjD6J1voN4I2MHkcIIYQQ6RdnimP0+tHWdZa3VjKwrZLii6bvUyRvzrniFhcXx67PnqNR1AYAXFUcldVpwku35ItngnB1yoETe2dTMs2NEEIIkctN2/0pu6/sTlL2Yo0XaVA85wzmMMWb2DxjIE0jV1nLvoprw5oivVncuw5uLpIcZqacN2RJCCGEEGm2de77FJg0B/e79yYTaVCsAQOr55xpbbTJxMYvhtD0vx+sZUviglns/Tzz+9bDK0/OuUWeU9h9BVEpVRIIBoqDdSql+2mt9WR7n0MIIYQQ9ju5cy15PppHvTgofSWed7oYiS9ZhPea5px1lrXWrP/fKwRfWWQt+ym+Hp97DuXbAQ0p6OHqwOhyr3QniEopJ2A60B9QluL7dtMJZRqQBFEIIYR4yG5du8T5YcMpaJ7ukFgjRHgamRn8IQXyFHBscGmktWbd3HE0u/A/a9nv8UG87TqS7/o3omi+lK5PiYyy5wriRGAgEAf8AhwFIjMxJiGEEEJkgCk+ni0vdKXkjVgAolzgw05GXmw4klo+GR57+tCsX/gWzc5Mt26vi6/OOOeXWTigEaUKujswstzPngTxWeA20EhrLVPXCCGEENnM5ndeouS+K9btz58wUD2oLc9Vfs6BUaVPvElz9cYN6/aW+MqMNo5mbv/G+BfxdGBkjwZ7Bqn4AOskORRCCCGyn8h16yi4+A/r9or6iuv1/Xmz4ZsodX+PsOzLaFA8NeQjlhQcxA6TP8MNY5jdrwmVi3s5OrRHgj1XEM8A0ZkdiBBCCCEyJubMGc6/Mhq0ecRyZPUyrG4VybyQT3B3znm3ZF2cDHQc9DZvLOvMzLqlqVHS29EhPTLsSRC/BQYrpTy01tL3UAghhMgGTFFRnBs2HFNEBABOxYpRa9bX/OyZJ+ckh2e2QbEa4Hxv8Imz0cC7nQMdGNSjyZ5bzO8Ah4GflVL+mRyPEEIIIexwbcYMog8dAkA5O+M77VOcChTIMclh5P5VMP9J+LY7xNxxdDiPvHRfQdRaRyulWgFbgP1KqdPAOcBke3fdIoMxCiGEECIVt2JuUXDgQKKPnyBy7VqKjB+HW7Vqjg4rzbb/uYLq6/qBioXjf8LPo6DjTEeH9UizZx7EQsDvQBXMcx2WTXjYolMoF0IIIUQmOHD9AP1X9+flOi/TccZ0Iv9ah0dIM0eHlWa7Nq6iyroB5FEJU/K4F8ctZKyDoxL29EF8D6iB+TbzLOAYmTwPolJqKNAEqIZ51LQXEA7sAeYBi7TWNpNPpVQP4EWgOmAEDgFzgZlaa1tXOTPUTgghhHCU61HXGbF2BLdibzFh8wT2XtvL2OCxOWa08j9bfiPg997kVeaxr5d0fp6JGM0igw9FHBzbo86eBPEJ4CJQX2t9M5PjsXgVc2K4D9iMed5FP6A50AIIVUo9fX/ippSaAQwC7gJrgNiE/acDLZRSnbXW8fc/mb3thBBCCEeJvn2LmTP6cLHIRWvZ90e+J9g3mGYlmzkusDT6d+sflFv1HB4qCoCr2oueMa/xYmhLinjJCimOZk+C6An8moXJIUA34G+t9e3EhUqpKpgTuPZAL8xX+Cx1nTAneZeAplrrownlRYC1QEdgCPDpfce0q50QQgjhKFpr1g7uQqetp3Cto/i6uQGTQdGjYo8ckhyuocyvz+CZkBxe0170jHmdvh1aExrk6+DoBNg3ivkg5iQxy2itN96fHCaU7wdmJGy2vK/a0mHhVUuSl9DmMuZbxwBjlFL3n7O97YQQQgiHWPv+CPy2ngLgyR2aoKOaukXr8nKdlx0bWBrs2f4npRMlh9e1Jz1jXqPbE63pWc/PwdEJC3uSnhlAMwdOcZOw7Dh3LQVKKV8gCIgBlt7fQGu9DjgPFAXqZ7SdEEII4Si7V8yhyPzfrNt/1FRcCPTlo+CPcDY4OzCyB9ty7Br659F4KfM0Nje0Bz1jXqfz463p27iMg6MTiaU7QdRazwM+Af5SSvVLSLIeCqVUGeCFhM2ViaosK4/v11pHpdB8x337Zt5svQQAACAASURBVKSdEEII8dCd2b8N/cZHGBKGaR7yhcWP52Vai8/wzpO9VxnZeuI6fefvZED0CI6ZivNfQnLYqW1r+jdJaTIU4Sj2THOTeLDG7ISylHbXWmt7+jlanqsPEAw4A75AQ8xJ7bta6+WJdrX8t+N0Koc7c9++GWknhBBCPFSR/13h5IsD8Yk2Z4fXPOGjp428Ffwe/vmz97oVW09cp8/cHUTFxhNFfrrHjKOgiuDptq0Y0FSSw+zInuQtPWPnMzrOvhHmwSgWccB44OP79vNI+Jms32Iilql4EveftLedEEII8dCY4uPZODAUvysxAMQ4wYedjPRsOJgWftl7PYptR87TZ+FeomLvXV+6ijf929RnYNNyDoxMpMaeW8yG9DwyEpzWur/WWgHumCfm/gSYCGxVShVPtKslEU3vxNz2trt3AKUGKqV2KqV2Xr161d7DCCGEECn6fVxf/Pbe+46Z1dZAufqteL7G8w6MKg0u7aPikiY0it+epHhM24o8HyzJYXaWI0bmaq2jtNYHtNavYB51XAPzHIUWtxJ+eiRrfI+l7laiMnvbJY5ttta6tta6duHChVM5jBBCCJF+mxdOodTyewnWinqKy00CeKvRWxiy8wQbl/fDgqfIF3edWS6f8phhFwCvtqnIC5IcZnvZ+J2VIsvch+2UUpbhWqcSfqY2Pr7kfftmpJ0QQgjxUJxzjuRWwrzRf5dV/NK6ANNCpuHu7O7YwFJz+QDMbwd3rgNgdHWjQvnyvNqmIi82k+QwJ7B7AIkDhWPui+gEFAAuA38n1FVRSrmlMCK5TsLPvxOV2dtOCCGEeCi6dHuTVb5lOPL+FGY+6cTUkI/x9czGk0lf2gcLnrImh7h6oZ5dzivFgzAYcsYSgCINVxCVUiOVUq0y8iRKqVZKqZEZOUYiTTEnh+HANQCt9VlgN+ACdLbx/MGYR0FfArZYyu1tJ4QQQjxMbRr3psqcr3m5+UTqFqvr6HBSdOvkTpj/5L3k0MUTnlkGvrUlOcxh0nKL+UPMS99lRHdgSlp2VEo1UUr1VEq52qhrBMxJ2Jxz3/rI7yb8fF8pVT5RGx/g84TN9+5fvzkD7YQQQohMp00mYq9cSVZey6cWHSt0dEBEafPv1j/R85+CqP/MBa5e8OxyKFkn9YYiW8qOfRDLAV8Dl5RSa5RSi5RSPyql9gMbgbLAz5inu7HSWn8PzMS86slepdRKpdQy4ChQGQgj6cCWDLUTQgghssLVjz/mZMenufN3zunZtHvzb5T5tQdeCbPGxTp7wXMrJDnMwZTWqc/wopQyYZ4L8FoGnqcQkFdrbXxgQObVUvoATYDyCW0V5tu8O4GvtdZhqbTvAQwGqgFG4BDwFTAztauA9rZLrHbt2nrnzp1p2VUIIYRIZt0XE/GZ+h0AysUFv8WLcataxcFRpW793wepFRZiXVv5P+1B7/jXmT6yNyULZOOBNAKl1C6tdW1bdWkdpOJB6lPBpEWa5hrUWp8E3rD7SbReDCx+WO2EEEKIzLDnt28o8Ol31m23BvXJU6miAyN6sFX7LjH0+5N0oyuTnedxXXvSM+Z1Qh9vLclhDpeWBFGWmBNCCCGy0NlDO4h5dTIeCferTvlA2ON3mWXIjj3BzFbuucCI7/4h3qRZSCviMbLDFMAz7VrTq2FpR4cnMuiBCaLWOrV1ioUQQgiRATevXeDEgP74RJlvtIXnhfdDjYyqGopS2XPk7/LdZxm19F9Mie4NLo5vwTsdq9GjXinHBSYyTfb9r4kQQgiRy8VGR7G1Xyd8riassWyEDzoZ6dTkedqVa+fg6Gzb8NNCCod1JY++ay1TCj4IrS7JYS4iCaIQQgjhACaTid8Hd6LU4XBr2edPGijbsDWDaw52YGQpW7fiK+rtGE5jw37mOH9IHqIxKJjapSZdapd88AFEjpETV1IRQgghcrzfJw6gzMaT1u3vmhiIaFKdTxpnzzWW1y77giZ7xuCkzB0li6trFDTc4bVuDXiiejEHRycyW/Z7BwohhBC53M/Hf2L/8XsLdP1ZXbG5VXGmNZ+Gm5ObAyOzbe23n9B0z6vW5PCEqSjPxL/BhJ6PSXKYS8kVRCGEEOIh2nFpB+M3v0FsSwNXvDU1Tmi+bZePeS1nUdi9sKPDS0Zv/5KQQxPMMxIDx0zF6WUaz1vPPkZIRR/HBieyjCSIQgghxENyIvwEw9cOJ9YUC0rxc13Fb/WMfNFyGuW8yzk6vOQ2TkX9MdG6ecDkRz/Ta7z/XAua+me/ZFZkHkkQhRBCiIfgyqUTDFr/ArdibiUpn9z4beoUzWZL0mkNf06GDR/dKypRm0UeE/mobiUalivkwODEw2BXgqiUKgA0x7x+8QXgX631scwMTAghhMgt4iNvc7Hf83RzusC0dopYZ/P92uGBw3mi7BMOjs6GrTOTJIeUboLq/g1vu3o6LibxUKU7QVRK1QJWYV4jOXF5BLAb2IV5zeRdWuvjmRGkEEIIkVPpuDjOjxqJy/Fz1APGRxmZ0EPTKaAz/ar2c3R4SdyNjWfHqRs0qdEN/v4aruyHCq2hy3xwzn6DZ0TWsecK4hSgMLAPWAP4ALUAfyAk4aEBlFLhWuuCmROqEEIIkbNorbk0aTK31623llXsPpD2Fa7yer3Xs9VKKbej4xi4cCdbjl/ns+6BPPFcGGz6FFpMACcXR4cnHjJ7EsQg4AxQW2sdYylUSuUFAhPqg4DaQIXMCFIIIYTIia7N+JzwJUus2wWffx6fPsOY7MCYbLl5J4a+83ey6/R/AIz47m/cn61NSOu3HRyZcBR7EkQTsCVxcgigtb4NbEh4ANakUQghhHjk/Pftd1ybPt267dWuHYVHDHdgRLZdu3Gds58/je+dhuyiMQCx8ZqPfz9CsH9hDIbsc5VTPDz2JIg7Ae+07JiQNAohhBCPlE3fTMV70mzrahR5GzWi+NtvZatbygCXLl/k+hftqWU6TDXnf4mKdeU3Ux2qlvBift+6khw+wuxZSWU20EQpJRMgCSGEEPf5+7dFeLw1G4M2b7tUqYzvtE9RLtmrH9/Zs6eImNWWKqbDADgpE6XVJeqUzs/iAfUpkDd7xSsergcmiEqpM0qp75VSY5RSLYA/gJXAIqWUjHcXQgghEhze+Tvxo9/GJd68fTE/vN/FCe2Wx7GB3efIob3oOa3x1/fWgh4f25uDZfswv29dvPI4OzA6kR2k5Razb8LjacyjkzVwGigN/2fvvqOrKhY2Dv/mnPRKCIHQe+8QOtIRRUCRZhdFUUTFhnrt196v3U/sCioq2FE6CIJIB+m9hBoCKaSdMt8fiQmhqSE977NW1vHMntkzx0DyMnvvGZYZY54GvrHWJhbUIEVERIq7fcn7eGTZk9wcYAlOg2PB8NQIJ7e0Ho7T4Szq4WVbs3wR0d9fQUWT+UCKxxrudd1EcuNhvHd5a/x9is9Ypej8k4AYCbQj86nkv75qZx2rD3wAvGeM2UzmGoh/fa3UPYgiIlIWHE07yk0zb2JnYDwPX+Nk3HdePu7tYESv2xnSYEhRDy/b0l9/psHsUYSbzF/P6daXW123EdryYt4c2gIfZ17uPJPSyFhr/32jzPsPTwyNbYHKWYftCa+brbVN8mGcJUJMTIxdtmxZUQ9DREQKUYorhRtn3MiauDU5hdZyWaPLeaDDA8XmwZSF0z6n7ZLbCTSZi5Ak2UBuyLiHpp3789BFjfVAShlkjFlurY053bE8bbVnrT0MTMv6+quTypw609gwL+cXEREpCTLSU3h20mjWONfkKj+/Vj/ub39/sQmHqzdsJGbJbQQYFwCHbRgjM+6n//n9uKVH3WIzTik+8m0u2Vq731r7vbX2EWttf2ttRTLvUxQRESl13G4XM24cxNCXltNusze7vEN0B54575lidd9hi0YN+anmvQDstRUY4XqUKy8ZyNie9RQO5bQK9GYDa+2egjy/iIhIUfB6vfx826XU/SMWXw/cNdVL7QOWRuUb8UrPV/BzFq8lYowxXDJyPJ9Wuo/L3Y8z/vKLuKJDjaIelhRjebrELCIiUpZNu/9K6s3dmv1+VmuDu151PujzNiF+IUU4sixeD6QnQmBEdpHTYRhx4/202J9Iy+r/aL8LKcP0uJKIiMi/8MtTN1P3+1XZ7xc0Mfx4cTTv9nuPCoEVinBkmTLS02DKDfDRQEg9luuYn49D4VD+EQVEERGRf+jol19S89P52e+X1zN8NqQ8E/q9R9WQqkU4skyHDx9m3Qvnw7qpcHAtfH4ZuNKKelhSAukSs4iIyD+QOG0aBx59LPv9xpo+vDMsiP+74B3qlKtTdAPLsmPHNtyfXEpruzOnMLo5FLP7IaVkUEAUERH5G8m//krsvfdB1trBAU2b0viVB3nFz0vTyKZFPDr4c/VSyn9zObU5nF32smc43RrfT4xDFwvl31NAFBEROQvXgQPsvX0cuN0A+NWtS/X33sUnIuJvWhaOJfOn0WDOjUSYZADc1sF/3DdwpP5wbq4aXsSjk5JK/6wQERE5g81HN+OpUI6K99wDgG+VKtR4/71iEw7nffcRLedckx0OU6w/N7juwdnmaiZc3ZYgP80DSd7oT46IiMhprDuyjhun30iTyCa8NuI1qpQrR2DzZvhGRxf10LDWMvPTZ+m97TmcJvOyd5wN4/qM8fTqfQHjetfXAthyTjSDKCIicpJN8Zu4aeZNJLmSWHJgCWNmjcGnXw/8atYs6qHh8ngZ/+UqArf8mB0Od3orMSzjMS4ffAl39GmgcCjnTAFRRETkBFvX/MqSG0eQlpSzhuCKQyv4ZccvRTiqTMfT3Yz6eBlfr9zHGNcdrPPWZLW3DlfYx3nomgFc3l67o0j+0CVmERGRLNvXL+bQDWNol+jlwWPwzHAnqQGG65tdz6X1Ly3SsR1OSuf6j5ayNjYBgGSCuDbjfvyDQnhz5Hm0rlE87ouU0kEBUUREBNi1eTmx199IhUQvALUOQZV46NT7Ku5oc0eRXrZNid/Lx2+/ztqkbrnKg8pX5uPr21O7QnARjUxKKwVEEREp8/buWMOukSOJOuYBIMMHnhvqIKbnZdzb7t6ivafv4HqCPhvOPa49HHJ6+NLTE4DmVcP5YGQ7okL9i25sUmrpHkQRESnT9u/ewNZrriIqPnOdQ5cTXrjUQcO+Q3mgwwNFGw63zYUP+kHCHgCe8vuYKI7SrUEUX4zuqHAoBUYziCIiUmYd2reVDddcRuXDLgDcDnh5sIMafS/mkY6P4DBFOI+y4lP48Q7wZgZX/EIwQz7k5sP1uaZTTXydmuORgqOAKCIiZdLB2C2su3IolQ9kAOA18OrFDir0vZDHuzyO0+EsknFluDz4zn8as/DFnMLQKnDll/hEN2dUwyIZlpQxCogiIlLmnBIOgTcGOAg5vy/PnPcMPo6i+fWYkJjM2revomvq3JzC6OZwxZcQVqVIxiRlkwKiiIiUOfFp8bhs5gMpXgNvDnDguKAHL3R7AV+Hb5GMae/evcR/OIyunvU5hfX6wrAPwT+0SMYkZZduYBARkTKncd0OVH1/AruinVnhsCf/6/E/fJ1FEw5X7Irn6HuX0OKEcDjJ04dF7d9QOJQioYAoIiJlUrN6nan6+UTKDbqYl3u8jJ/Tr0jG8fPa/Vz+7hKeyRiGy2be9/i063K+qXwXjaqWL5IxiegSs4iIlHruuDhS16wltFfPXOXNK7eieeVWRTImay1vzdvGC9M3AbCIZtznupFU/PFpPpiJQ1sQ4Fs0D8qIKCCKiEiptm/Xeo6PuQf3zl1UffEFwvr3L+ohkZbh4rnJs/hwnTdX+VRvN8b2rMvdfRvicBTh+otS5ukSs4iIlFp7d65l01WX4d6+A7xe9t3/H1wHDxbpmA7Hx7PypUHcsvUmqhCXXe7jMDw/pAXj+zVSOJQip4AoIiKl0s7Ny9h25RVEZy2C7XVA5FP/xbdSpSIb0+Ytmzjyem86pS8iyiTwvt+LBJFGeKAvn4xqz/B21YtsbCInUkAUEZFSZ8ufC9l7zbVUPJK5C4nHwKuDHEytUXSzh0sWzqLcxH40stuzyxZ5m1KlQjm+HduFznUrFNnYRE6mexBFRKRU2bBiJkdvuoPIpMz7+9wO+N9gB5Hn92dU81FFMqaEZV/ScuYtBJjM2UyXdfKIeyR764xgyhVtCA8smuV1RM6k2M0gGmN8jTG9jTEvGWN+N8bsN8ZkGGNijTFfG2N6/E37K4wxC4wxCcaYZGPMMmPMWGPOvqFmXtuJiEjxsXrxdyTeMI6IrHCY4QPPDXVQ5cLBPHves4W/Q4q1MP95wn+8MTscHrPBXOO6H7/21/PhyHYKh1IsFccZxO7AzKz/PgAsB44DTYAhwBBjzBPW2kdObmiMeRO4BUgDZgMuoDfwBtDbGDPM2qyl8/OhnYiIFB/L503Ge8djhKVlvk/zheeGOWh2/uU80OEBHIX9731XKnw3Fv6ckl10JKAGwxPvYOTA3lzdqVbhjkfkXyiOAdELTAFetdYuOPGAMWYEMAl42Bgz11o794RjQ8gMeQeAbtbaLVnllYC5wGDgVuDVk86Zp3YiIlJ8LIxdyBe/PMOYrHCY4g9PD3fSud913NX2Lowp5KeCM1Lg4wEQuzynrHZ3yg39mFeOOmheLbxwxyPyLxW7y6fW2jnW2qEnh8OsY5OBj7LeXnXS4f9kvd73V8jLanMQGJP19v7TXDLOazsRESkGZu+azW1zbmN+Yw/vXuggMRD+e7mTPheNLZJwOHfTIdKMP5y4AHfMKLhqCs7gCIVDKRGK4wzi31mZ9VrtrwJjTDWgLZABfHVyA2vtfGNMLFAV6AgsOpd2IiJSPPy0/SceXPggnqy7gGa3cvB7Q8NNXe/mumbXFepYPF7LyzM38ebcbQxuXZWXhzyDObIFGg2E9jdCYc9iipyDkhgQ62e97j+hrHXW6zprbeoZ2i0lM+i1Jifo5bWdiIgUsdmfPMXTx7/AE5S7/I4eD3FZo8sKdSyJx1O4d/JyftmcCMA3K2NpUjmMG6/+Dhy6ACUlT4n6U2uMiQZGZr2dcsKh2lmvu87SfPdJdc+lnYiIFKH4TydS5emJPPQVBKRbABzGwRNdnij0cLh91y62v9SXATueAGx2+UszN3HoeEahjkUkv5SYgGiM8QEmAuHAbGvtDyccDsl6PX6WUyRnvYbmQzsRESkC1loOv/4GB596CoBa+9xcN9+Jj/HhufOe45J6lxTqeJYsmkvAB71o5f2TAc4l3OL8DoAKIf5MuqEDFUMDCnU8IvmlJF1i/j8yl57Zw6kPqPx1Y4fl38lru5wTGDMaGA1Qo0aNvJ5GRET+hvV6OfjU0xydNCm7LLBVK9o9OpoWwb50rdq18MZiLdMnv0X3DY8RaDJnCb3WAIaW1cJ55+oYosMVDqXkKhEB0RjzKjCKzKVoeltrD5xUJSnrNYQz++tY0glleW2XzVo7AZgAEBMTk+egKSIiZ2ZdLvY98CCJP+RcPAru0oVqr79GraCgs7TMf8dT01k4YRwXHP08e5ohyQYyzjWWiFaDmDy4GQG+zkIdk0h+K/YB0RjzEnA7cJjMcLjlNNV2Zr3WPMup/toBfecJZXltJyIiheRYwiGW3jiCamty5gZCL7yAqs89h/HzK9Sx7Indy/4Pr6GfO2d9w23eytzsvpvL+/fhui61Cn/NRZECUKwDojHmeeAu4AjQ11q7/gxV/1r6pqkxJvAMTyS3O6nuubQTEZFCcPDgdlZcO5RaO3N+PJcbMYLoRx7GOAt3lm7JorlUnTGa9hzKLpvrackjPnfy7DXn0aVehUIdj0hBKrYPqRhjngXGA0fJDIerz1TXWrsHWAH4AcNOc67uZK6beABYfK7tRESk4O3YvpI/h1+SKxwuPr8aEQ/fX+jhcOaPk2k5fRjVTgiHb7kH8UL5//LZbf0UDqXUKZYB0RjzBHAfcIzMcPhPZu+eyXp9zhhT74RzVQTeynr7rLXWm0/tRESkgKw+vJpRv91Ggq8ru+zj3g7mX1gFl9d1lpYFo17LzsRRDsi83/CmjDtY1/hOvh57HtXLF+49kCKFwVhbvJ6rMMYMAr7LersMWHeGqhuttc+e1PYtMrfHSwNmAS4yn3wOA74Fhlqbtdx+PrQ7WUxMjF22bNnfVRMRkbOYt2ce4+ePJ82TRnCq5dHPPPzY3gEX9uDF7i8S6BNYJOP6bcFsQmfezd3usYy4sDejutbW/YZSohljlltrY057rBgGxJHAh/+g6nxrbY/TtL8CGAs0B5zARuAD4O2zzQLmtd2JFBBFRM7Nl5u+5KklT+E94ceuw2sZWP8SHu38KL4O38IZyNGdEFHrlOI352yhba3ydKwTWTjjEClAJSoglmQKiCIieWOt5dvnb2bproX80CH33U83tbiJsa3GFspsXVqGm7RfX6Xcb0/BsA+hycUF3qdIUTlbQCzWTzGLiEjpl+HJ4Pvxw2k6bRONgKPBsLCZA4dx8GCHBxnecHihjCP24CF2vj+SLhm/ZRZ8ewtENYaoBoXSv0hxUiwfUhERkbLheEoCP1x3Pk2nbcou67vSS6DDn1d6vFJo4fCPP34j/e0eOeEQsBWbgP/Z9lEQKb00gygiIkXi0KGdLLlhGE02J2eXLa9r+HBEed694E1aRrUs8DG4PV5mfPY/em59NnvLPICP3X1xNn6Gq8KqFPgYRIojBUQRESl0rthYEkaPpd62nHA4u6Vh2pDqvN/vHWqF1yrwMRw8Es+6926if+qM7C3zUq0fD7hGkdRwKC+1KfgxiBRXCogiIlKoUteuZc+YW/DExWWXfdnVwfqLm/JJn7eoEFjwi04vW76Ecj/cQC92Z5dt9VbhVvc4Bvbtw5judXE4tISNlF0KiCIiUmgSZ85k3/h7sWlpmQW+vqSPH8XR6jv4sOvTBPkW7KLTHq/l9RnrGbb4CqqanIA61dOVV/1v5rmRnbWEjQgKiCIiUkg8x46x//7/ZIdDR3g41V5/jeD27XmlEPo/lJTGuM9XsXj7EdY6ruV9v5dIt7484h5JbK2hfH1Za6JC/QthJCLFn55iFhGRApXiSuHBhQ+y2xylyosvgMOBb40a1Pr8c4Lbty+UMSzaGkf/VxeyePsRAGZ72/KE60oGux6nSs+b+HhUB4VDkRNoBlFERArMoZRD3DbnNtYfWc+KgyuYdNEkqr78MkEd2uMTEVEoY/hz1ie8OCeeOG/9XOXfBV7Ka5e1onO9gr/nUaSk0QyiiIgUiA3r5nP3+8NYf2Q9AHuT9zJuzjj8+/YonHDoSoUf76LZwtt4J+ANypGUfahTnUimjeuqcChyBgqIIiKS7+b9+DaJV49h9KeHCD+es6VrqjuVpIyks7TMJwfXw4SesOx9AKK8h3kw4CuMgdt712fiDR2oGBpQ8OMQKaF0iVlERPKN13r59pXbqf/ubHy8mWXjvvXy+BUOulXvzvPdnifYN7jgBmAtLPsApj8A7rSc8iYXE9XgYT4JLsd59aMKrn+RUkIBUURE8sXxtCR+vGc4LWbtzC5LCILJ3R1c2eQq7om5Bx9Hwf3a2b57D/7T7qDqgVk5hT6BcOGz0OZaehitayjyTykgiojIOdt3YAvLbrqCFptydkbZWRFeHu7Pzec/zJAGQwqsb2stc2Z8S+NFd1PFHMk5ULEpDP0AKjYqsL5FSisFRBEROSerl//MkXHjqR/nyS77o4Fh4pBInr3gFdpWaltgfSekupj7/gMMPPwuTpNzr2NGm1H4XfgU+AYWWN8ipZkeUhERkTyb8fVLZIy6i8onhMMpnQ3fX9+Qj4Z8UaDhcPmuePq/uoBl+13Z4fCYDWZ0xp1Mjrpd4VDkHGgGUURE8mTOrPep8vB7OLMm7jKc8PZFDvwu6M2n5z1bYNvmuT1e3pq3jVdnb8HjtUykD10dfxJhkrjf3sYtl3ZnaNtqBdK3SFmhgCgiInnSpcdVfNf6fZqvOEp8CLwwxEmvfqO5tfWtOEzBXKDavf8AT3+9kF9iT5wdNNzlGkOd6EjeuzKGulEhBdK3SFmigCgiInni7+NPt9c+54fbB/NlV7jzgifpX6d/gfRlrWXW9O9ovPge7rABzOUJ0vHLPn5Zl8bcd2FD/H2cBdK/SFmjgCgiIv9IytKlBLRogcM/Z8/i6Ao1affKB3R2+tI0smmB9BuXkMSSD+7lgmOfZ95raOAeny95yn0VkcF+vDCsBb0aVSqQvkXKKgVEERE5qzR3GhtfeQr/96cQPngwlZ96EnPCmoKtKrYqsL6XLv2dkJ/GcBHbIavLBBvEGm8d+jSuyLNDWlAhxP/sJxGRf00BUUREzmj/oe0svvVKGq85BkDC1KkEtWlNuaFDC7Zja2Hpe7SZ/hBOcnZE+c3TlIe4hdGXdOOydtVzBVURyT8KiCIiclrLln5Pwl0P0PhwzhI2Pq1bENKjR8F2nHQAvhsLW2fx1x2F6daH590jWFH5cj64rA21KxTgdn0iooAoIiK5WWv5/v0HqPb6t1RJzyn/ua0h7oZaPF2hQsF1vuEH+P52SI3PLvJWbMK41DE0atmRr3rWw8epJXxFCpoCooiIZDuWHMcv46+g5dw92WUZPvDOBQ4cF/bk6S4PFki/G/YnEhrgQ7VDG3OFQzrdiqPXw7xm/PDzUTAUKSwKiCIiAsDaP+ey9847aLknI7vsUDi8dKmTC/uN5aaWN+X7+oZuj5f/m5+56HW7WuWZOHIcjo0/wvHDcMnbUKc7wAkL2ohIYVBAFBEp46y1fLbxM9wPPk37Pd7s8qX1DZ8ODufh85+jW7Vu+d7v1t17eWLqMuYf8AVg0bYjTFq+n6uHfwwB5SCwXL73KSL/jAKiiEgZlpSRxKOLHmXmrpmUO9/QYC+EpsBnPR3s7N+Cj3u8RJWQKvnap9vj5ZdvJ9JuzSPc7K3MrzyAJXNm8plpG7igaU+iArV0jUhRBES9nwAAIABJREFUUkAUESmjNsZv5O55d7M7aTcAx0IM/7vEiddAu/Ov5uO2d+Hr9M3XPrft3c+2ieMYkDYdDFRyHuUa70w+9vQjMtiPJy9pRlSowqFIUVNAFBEpg2J/nc6nX9/L7rbeXOV76obyeJfH6Vuzb7725/Fafvn+C1qtfIjzTVx2eZwNY5+NpH/zaJ64uBmRWvRapFhQQBQRKUOs203c/71D4ltvcaX1sj3SwZ+1Mi/vNi7fmJe6v0T1sOr52ue2vfvYOuluLkqdlr0bCsBPnva86DOau0Z0YWDL/L2MLSLnRgFRRKSMcO3fT+z48aQuWw5kZrWb5/lz27UZDG04nPva34e/M/9m8DLcXn6Z+hHt1j1BP5OzdM1RG8LDrutIb3QJkwc3o2JoQL71KSL5QwFRRKQMSJw5k/0PPYw3ISG7LCgmhgZP3s9zdjcX1r4wX/tLOJ7O8leGM8g1L9es4UxPW55x3sTtw7pycasq2ipPpJhSQBQRKcUOxu9h5cPjqDl7Q06hw0GFW8dS4aabME4nlWma7/2GBflBQDi4Mt/H2TAec11Lav1BfD6kBZXCNGsoUpwpIIqIlFILfp1E+oPPUPPEvZSrVKbqiy8S1KZNgfZtjKHpNS+z743fWOxtxJu+o7jj0o4MbFFZs4YiJYACoohIKZPmTuPzt2+nzTsL8HPnlHu6t6fB86/hDA/P3w69XljxMTQeCME5+zRXiqrAV32/ZXGshykDmhARrP1QREoKBUQRkVJk69Gt3LvgXlIyNtMqa6Iu3Qc+6usg5NJqPJmP4dBay4LFi6i1+AFqJK2CXb/BkPdy1RnapRnDNGMoUuIoIIqIlAJe6+XT9Z/y2orXyPBmQAXDh30d9F/q5Y1L/Bh8/u1c1+y6fOtvz6F4Vk56hH7HPsffZE1Trv0KWl4O9Xpn19PlZJGSSQFRRKSE2xe3gwmfj2dK2KZc5XNbGLZ1qMEzvV6gRVSLfOnL5fHy8/df0GLVfxlkDmQ/oezGibfzOPxqdsmXfkSkaCkgioiUUNZaZvzyFn5PvsWlx7z8cZ2TPVE5M3b961zEwx0fJsQvJF/6W7lhE/FTxzPINT/X0jUrvfV4xHMDd9UcQk9fPZ0sUhooIIqIlEDxyYf56bHraf3TVpw2s+y27z38Z6SToMAwHurwEP3r9M+Xvo4mpzHnsxfpE/smrU1KdnmiDeJ59wg2Vx3Ci5e2omF0aL70JyJFTwFRRKSE+XPFDHaPv5uY2JxHlFP9YFo7B+2qduSJrk8SHRx9zv1Ya5myIpaZP33JO94Xcs0afufpzGs+Ixl9SSceb1sdh0P3GoqUJgqIIiIlhLWWY198gc9zz1E7LSccbqgG714cyFV97ubyRpfjMI5z7mvroSQe/OZPluyIBxoy07ctfZ3L2emtxMPu66jYqj9f9m9EZEj+bc0nIsWHAqKISAng2reP/Q89zPFFi7LL3A6Y3M3B1v5NebP7s9QJr3PO/WS4PEz4+XdeXZKAy2Ozyx9zXcN6W5Nfyl3GI4Nj6FQ38pz7EpHiSwFRRKSYS5w+g/0PPID3+PHsMv/69Zh7TWMq16/Joy1G4+vwPfeODm/G9+d7GbFzHW94nsNFzuxgnE8lnL0e4LtudfHzOfcZShEp3hQQRUSKqUX7FpGckcx5VSrjTU3NLDSG8tdeS9SddzDGzy9/1hlMT4L5z8Pvb2G8bqKAW3y+52X3MAC6NYjiiYubUjMy+Nz7EpESQQFRRKSYScpI4qVlLzFlyxRCfUP55uJviBw1iqRZs6j81FMEtWmdPx1ZC2u/hhkPQfKBnHLjoG2VACod8+ehi5owQPsni5Q5xlr797XkH4mJibHLli0r6mGISAn229Jv+GLmS8yrmpBd1r1ad17t+hLGWhwB577OoNdrmTF3Fs1WP0W1xJW5D9boBP1fIKlcIxzGEOyveQSR0soYs9xaG3O6Y/qbLyJSDBxLPcr3L4yh+VerudYBq290cjQ0c9bu172/sjF5K00jm55zP2u37mLX1w9yYeqPOM0JEwQhlaDvE9BiOBiDVjQUKdt0p7GISBGy1jL7149ZcHF32n22mgAXBKfDDdO9ANQKq8UnF35yzuHwYGIa90xeSeAnFzAg7YfscOjGie10G9y6DFqOAF1KFhGKaUA0xjQ0xowzxkw0xmw0xniNMdYYM/QftL3CGLPAGJNgjEk2xiwzxow15uwLg+W1nYhIXsUe2cknd/Wn4s3PUm+3K7t8dwX4pouT65pdx1cDv6JVxVZ57iM1w8Ors7bQ44V5fL1yHxM9fbKPLfQ0ZaD7eTa3vA8Cws7ps4hI6VJcLzGPAcb920bGmDeBW4A0YDbgAnoDbwC9jTHDrLWe/GonIpIXbq+bH75+lrBXP6f9EW9OuQO+72hY0b8ej3d/iuZRzfPch9dr+fmPNTw5N479CWnZ5RM9fejlWMnnnl7YRoOYMKAJ1csHndPnEZHSp7gGxD+BF4BlwHLgfaD72RoYY4aQGfIOAN2stVuyyisBc4HBwK3Aq/nRTkQkL9bv+IMVj95B2z+O5irfXAXev8iPvr1u4PMWN+Hn9MtzHys3bWfPN4/RL/Un3s54jP3kLKDtxocnIp7i4QFN6NYgKs99iEjpViKeYjbGzCMzIA6z1n59hjrLgLbAtdbaT0461h2YR2YIrGqt9Z5ru9PRU8wicjYprhTm9etA7X052+Sl+MHnPRwc7teGR7o8Rt1ydfN8/j2HE/j9y+fpc+gjIkwyAEu8jRiR8TBgiAjy5a6+Dbi8fQ18nLp7RqSsK/VPMRtjqpEZ8jKAr04+bq2db4yJBaoCHYFF59JORCQvgnyDMNcPhyc/A+CPBoYv+4cxstfdDKk/JO97KFvLlt+m4Jz5MMPMPjjpOZPyzlSGdG7Krb3qEx6YDzuuiEipVyoCIvDXqrHrrLWpZ6izlMyg15qcoJfXdiIif8tmZICvb65Fpvtd+SCT5s9iblQc5ftdyEft7iMq6Bwu9caugJmPUH/nglzBcLc3iqfdV0KjgUzt35haFbQLioj8c6UlINbOet11ljq7T6p7Lu1ERM4o3ZPOzpnf4vO/D6k4/h5C++Q8OewwDrq88CE1k/fSrVq3vHcSvx1mPwHrpuYqTrKBvO6+hCUVh/OfgS3pWCcy732ISJlVWgJiSNbr8bPUSc56PXH917y2ExE5rYUrvmXvU0/Qcl0KGcCBp58muEsXHIGB2XXqlKtDnXJ1znySs51/SxytapQj5JcHYPPPOQeME9vmWl5IHETzhvW4v001HA6taSgieVNaAuJfPwX/7RM3eW2XcwJjRgOjAWrUqJHX04hICbf36E5mPHcbrX/aSsucJQ3xJiWTtnEjQa3Pbf/kP2MTeO6XjSzYEse43vW5s9dDsPkXwELjgdD7UUyF+jx+bh9DRAQoPQExKes15Cx1/jqWdEJZXttls9ZOACZA5lPMZx+miJQ26Z50vvnsv0T937d0OpL7R8D85g56PfsGQXXzHg53H05kwZQ3eHxnY9LJXPrm3QXbuapjT6L6PAY1O0P19ufwCURETlVaAuLOrNeaZ6lT/aS659JORMo4ay3zl37F/uefp9Wfue9S2RUFH/bzoXmfEVSq1jBP5z+UkMLcb96j3Y63uNLsZ5fzciZ4BgKQkuHh9TlbePziO875c4iInE5pCYgrs16bGmMCz/BEcruT6p5LOxEpwzbFb2LKB/dz0YcbqXTCHkspfjC5m4P9/VrxWOeHaBzZ+F+f+0hSGrO//4Tmm99ghNmVfSPMWJ/vmOzpSQIhdKoTyZA21fLp04iInKpUBERr7R5jzAqgDTAMON2C19XIXPB68bm2E5Gy6UjqEV5f+TpTt0wlNMhLPx/wywqIC5oafriwPNd3v5uL6138r9c0TDiewfQfJ9Nw/SsMN1tzLVmTaAN5xz2QWtGR3NW/Jd3qV8i1dI6ISH4rFQExyzNkLnb9nDFmkbV2K4AxpiLwVladZ0+zG0pe24lIGZHhyWDSn5/yzrp3Oe7KvJycGGyY0sVBp/VePjnfh1a9LmNi61sJ9w//V+dOSnPxy7RvqbXmZYazPlcwTLV+fOTpx/fBQxl9QQz3tKyqJ5NFpFAUy632jDFtyAlnAE3IXGZmCxD/V6G1tuNJ7d4CxgBpwCzABfQGwoBvgaHWWg8nyWu7k2mrPZHSxxUby67nnuKXuAW80y/3MYfX0qFyJ8Z3uJf6EfX//bk9XmY/dQkXeOfnKk+3Pkzy9OGrgKFc0bsdw9tVx9/HeS4fQ0TkFCVxq70woMNpys/6E9hae4sxZiEwlsy9m53ARuAD4O0zzQLmtZ2IlF6e5GSOvPce8R9+hE1Pp5cx/Nzawe6KmTN4tcJqMb7deM6rel6eL/f6Oh34V2sBuzMDoss6+dLTg0l+w7i0Twe+6ViTAF8FQxEpfMVyBrGk0gyiSMlnMzI4OvlL4t5+G098fK5j3/cJ5bsuPtzS8hZGNBqBr+Nf7mt8ZBtE1s1VdCzhGGkvt+E3bxPed47gou6dGNm5FsH+xfXf7yJSWpTEGUQRkUIVlxLHT+89SJtv1+OzLy7XsYCmTan0wH+4sIYvN4XWoFxAuX983qQ0F9On/0i3Ax9Rcf88GD0fqrTKPl4uvBwf9viBY25fvjivNmEB/zJ0iogUAAVEESnTUlwpfPfVU4S99y3t9+W+m8SnSmWibr+d8EGDMA4HLf7FeRNSXUz/+VuqrXmdoazOOfDrC3DZpFx1r+vZ9Bw+gYhI/lNAFJEyyeV1MXXzVH758VXufe9ormPukECqjLmViKuuxOHv/6/OezQ5nRnTplBr3RsMN+tyHbMYjNMPPG5w6seviBRf+gklImWK13qZvnM6b656k12Ju6CCZUM1aLwXMpzwc4xh28CGTBhy3b96+ORQQipzpk2m3sa3GWE25lquxmMN33s782ula/nfsBEF8KlERPKXAqKIlAnWWuatnMrU395lXlhszgFjmNjLyfkrvPzcpxzDut3CXQ2H/+NwuP1wMh/OW8+IP0dzmdmRKxi6rYNvvV352Hkpvbt34bHOtfP5U4mIFAwFRBEp1ay1LFw3jU2vPUu7RXFcGgILRjvxOHOS3J4agWRccDUTm11HqF/oPzrvqj3H+L9525i+/gDWQi/fsMwFsshcruZrTzcm+Q7hwh6d+KxTTUL18ImIlCAKiCJSav2+eTZrX3uSmPkH6OLKLIs+Bt3XWua0MjiMg8H1BnNLq1uoGFTxH53TdfwoT3z0LZ/syV3/bfcgOjnW84WnJ1/7D2ZQ7w5M7lBTy9WISImkn1wiUup4ko9z9NNPCJjwFl1T3bmObYuGQxGG/rX7M6blGGqF1/pnJ03cD7+/ie+yj7jb48tkXiYdv+zDf9hGDA58n8u7t+SrttUJ9NMC1yJScikgikip4UlO5ujEScR/9BGeY8c48fnj3VEwuZuDcn3O54lWY6kXUe+fnfTgevj9TVjzJXgyAAgHLnUu4HNPbwCaVA7j5h516d8sGh+nI38/lIhIEVBAFJESzVpLijsFlq9l7+3j8CYm5jp+rFIwH3VMxa9PT8a3GUvjyMZ/e85dcUks/GUyA1O+IWzfwlMrVGhIhKcanYMiubl7Xc6rXyHP2+2JiBRHCogiUiJZa5m/dz4T1kwgMjCS/7V+HOvOuZzsW7UqFcaOJahHK8Z6kmgRdfZlrq21LN0Sy+YZ79Lx0Jdc6dh3aqVq7aHrndDgAm51ewny049QESmd9NNNREoUr/Uye+UUPls3kWXe7dnl21odIuLyy0iaNYsKo28ifNBAjK8vf7cpXobby49r9vH+wh20Ofg1T/h+BCdcJbbGgWk0ADqNheodIGumMMhPl5JFpPRSQBSREsHlcTFjyWccePf/iPnjGG2bGZb1z3kQ5N217/L82MepeOedGJ+//9F2OCmdL/7YzSe/7+JwUjoAOzmP8T6TCTOpJNlAJnt6YNuN5saLexXY5xIRKY4UEEWkWEvOSOanGW+R9ukXtF2TSh2bWd59rWVKF0tceOaMntvrxhvgh4/jzD/WrLWs2H6AdTM/ofm+r5jvupzDtlH28eME8rp7MF4crIoaxBXnNWVAy8oF+vlERIojBUQRKZYOHj/Iz1NeIGjydFpsc59yfGdFCEkztG3Zjxub30jD8g3PeK7j6W5mLl5G2u/v0Sd1Om1NIjjgap9ZLHPlBERjYGfDUYzqWpuHapfXgyciUmYpIIpIsbIlbhNzJz5Dle/+oMN+e8rxP2safuzoQ7U+A3i1xQ3UCa9z5pN5vbB9Lmnz3mLgntk4jc21FV4fx3KCScX6hTA8pjojO9eiVoXgAvhUIiIliwKiiBQb1lpW3HYt561MyFXuNbCkoeGXzgG06j6UJ5tcTfXQ6mc+UeoxWPUZLH0P4rcRCbmCYayNZJK7N4vD+3Nnn5YMi6lOeKC2whMR+YsCoogUG8YYKg4aAis/ACDDB+Y2NyzoGkHfrlczoeFllAs4/XPJO+OOs2L3US5tEgb/awYZSafUWeBpxkRvX2hwIVd2qsM99SrgcOgysojIyRQQRaTQHUg+gF27HqbNI/qRhzG+ObN3XYbdzvSPJrGqWgZru1dnaIdRTKo7iACfgFPOk+byMH3dAb74Yw+Ltx/Bx2Ho+p9eVKzZCbbMyKzkHw6triCp+TX8sd7JI+1rULVcYGF9VBGREkkBUUQKhbWW1fuW8/vEl6j2y2rqZt1fGNShA+EDLsqu5+fjj9//PUtHh5MHqvfC6Th1T+ON+4+xZPZ3VNw6mR3uSix2DwXA7bVMXRHLzW2ugcR90O4GaDEc/IIJBe6uVigfVUSkxDPWnnoTuORNTEyMXbZsWVEPQ6RYSfekM3vlFHZ++i6tFh4g4nju4wEtW1B78uS/PU9yuptZS1aT9PvHdEv+mZqOQwActuF0Sn8dd9a/d2tXCGbOXedhjCN7UWsRETmVMWa5tTbmdMc0gygiBWJnwk7mfPc6zu9m0WZDBrW9uY9nOCGpRytibn/sjOfweC2LNsWydcFX1I79jgGsxsd4c+10EmUSaO/YyCJvM9rWjGBEu+p4rMFH9xaKiOSZAqKI5BuX18Xc3XOZM/dDer+3ik5HTq0THwLT2zjY0q0mI7uOJKDWqesXprs9TJ4yhZBNX9Hbs5DzTEqup5ABEmwQUz3n8bNvX5p37sJ/21WnfqXQAvpkIiJliwKiiJyzfcn7+Hrz13yz9RviUuMIdFlGJOaus7EqTG/rwLdPNy5vejX/rdLpjAtR+zkddNr0DPW9208Jhku8jfjc3YuE2hcypEM9Pm1SCX+fU+9TFBGRvFNAFJE88yQns+qzN3js2CR2VsopT/U3LGxq6LLe8mtTw+IOocR0Gcp/Gg6nZljN7Hrpbg/+7uOQGAsVG2eXG2M4UHsw9be9BMAub0Wmes5jUXAfOsa05e6Y6lQvH1Ron1NEpKxRQBSRf8VaS8rSpSRMmUri9OkEpaVxcUs/Xu2f+ybDyd0crBregktaXs7NNftmL1OT7vawcP1edv0+leqx0+jjsxpToT6M+S1X+3q9R/LF5hX8ZLoT3awnl7atzrja5bVuoYhIIVBAFJG/lZCewJZNv1Nr0Q6OTf0G1+7duY53XO/hvZ5wPNAQ7BvMgDoDGNZgWPb+yG6Pl4Wb9rF50fdE7fqRnnYpvU1a5uVjD3DwT9i/Biq3yD5n5So1qHL1u0yoVZ5AP11CFhEpTAqIInJabq+bP3b9xqpv3qX8rJU03+Hl8GlWxfJv0ABv/x7Ui1zIxS0vo3/t/gT7BuP1WpbtiGPNb9MI3/Y9Pb2L6WqSMxudPAkY3RzSjp1y7m4NovL/g4mIyN9SQBSRbNZa1h1Zx0/bf2LWpmk88b9D9Ew5tZ4jNJTwgQMIv3QIAU2bYIxhInfi8Vr+2BHP9HU7mb7uAK+n3s/1js2ZjU4Khdu90fzg7cziwB68c+0V2gtZRKQYUUAUEfYk7uGnLd/x0+7p7EzcmV2+o5Kh1Y6cacNdDcPpdOPDhPbpjSMgZ+s7d0Y6L3yzkK83ezlyPCO7fJlPQ2L+CojAPlueHzyd+NWvG3VadmFgq6rcVjNC9xWKiBQzCogiZdSR1CPMXvEVB779mnp/xJJQy7CzV+57/RY0NVSJt8xr7mBTx8r0bD+Cfs37Zy5P406HbXNhw/f4bJrGAFdV3jn+QK7233s6Mcw5j2meDszyOY9KTbszoFU1RtWNxMfpQEREiicFRJEy5lDsFj6fcCdVft9O012W5lnlYSmWST0s9oTZvFWtQig/qA8XN7iEMcHNWLl5L2b9t7DhB9g8AzKSsus24xgVSCCO8OyyHT51+G+DbxjQqjoTGkZpvUIRkRJCAVGkDHDHx5M0cxaJv/xMyh9LOd/jOaVOaApUi4P90T50rdqVAbUHEO3XhtWr17N64lekJ95BT7MBzKltAdwhlamRfpB0/0j6Nq5Ev2bRdG8QRYCvQqGISEmjgChSCsWlxrExfiOdI2PYM2YMKX8shdOEQi+wrmbmotZpXVtxVeNBlPPG8PvWVB6ffIh9x35nqf8tVDCJufY/zhZRG5oMgsYX41u1DeO3x9O2ZgR+Prp8LCJSkikgipQSOxJ2MG/XXObGzmPVoVX4Of34dcSveI4lnBIO3c3q82n0Ng62r03LRhfR/HgjvBtXMG3VfhZmbDyhpoO5nlYM8/k1px/fetTuPBQaD4RKTeGE7fI61Y0s6I8pIiKFQAFRpITyeD2sPbyGpQu/JmXOPOr9Gc+uBg5Wds2cvUv3pPPr3l+JueACDm/YQGDbtoT160dov/M55BtI5C+TaLRzDS22fkArsxUf46Wabc9C7sjVz8/e9kR6EpntbcOeqG60a96M23rWL4qPLCIihUQBUaQESXGlsGTPItbP+RoW/EGzjal0TTihgvEypWvO5d0Zu2bQZ/jDhF9yMb5BFrbOhgX/ofLWOdyXdjSz0glXg7s51uKHiwwy1yT093FAvQvY3/gabmtUiejwAEREpPRTQBQp5uJS45ixfDKH5s4gfMU2mu3w0Cvt9HWrH4bQFEtSkCE6oC4mrRY+njiYOjJzO7ssJ98h6LWGtbY2870tqBpi6NikOr0bVaJLvQra5k5EpAxSQBQp5g5tXEXrG9444/Hj/rCyrmF5fScHa1eD9DYkxzZmizsCT1Qw9KoCcZtPaZfsW57paU1ZaFuSWKUrbRrXp2f9KG6tEqaFq0VEyjgFRJEi5vF62BC/AfehQ9TalEhw5874VqqYfbxhy54sCXMQkejNLosLhWX1Dasa+JNaoRydjifzZOpOKhzYzfUZndnnjQBg++HjHExzUqlGJ9i1CGp0hHq9oV4fDphahMYd5/G6kYQGaJs7ERHJoYAoUsistWxP2M7SLXPZv2AWvis30nB7OtWOwH4g+rFHibjssuz6ToeT2JbV2bdrF6vqONhS04+oQMOlaYe4NS0J37jc5+/sWMccb5vs94u3HeGSga9CcBT4h2SX1wPqVQot4E8rIiIlkQKiSAGz1hKbHMuyXYvYufBnWLaWuluP0/wgtLSn1k/+dUGugAhwsHVFQhut44bUFGqmuzHpp+9rm7cyR2w4fj4O2taIoFPdSJpXC4fyIadvICIichoKiCL5zGu9bDm6hRWHVrDiYOZXs8UHuH6Gl4an34QEgAwn2LoVqVTl1NQYU7E1Hf/87pTyWBvJIk9TltCMxOiONGzQiPPqRjKuRoR2MBERkTxTQBTJJ+74eFKWL+fLua/zasMduY4dDge/k8Kh18D2aFhby7C9BkREpnPV8fWUd+4Ba3MtQB3drCf8+RibvNVY5m3IChqSXKkdteo2onO9KP5bM4Jgf/11FhGR/KHfKCL/grWWvUl7WXNwFd09dXCtXU/q6tWkrlxFxrZtAHQ2hnfudJDmnxPwNlc1eAzsL58ZCDfXAP9KGbTxpjE4LY2GGS4c8X/VPgJxWyCqQXb7GvVbcE+db6ldvToxNSMYUr2cZghFRKTAKCCKnEVCegJr49ay9tAakufMwblhO9V3p1H3gGVPxunbGGtpGGtZXScnIKb5+PL66AxamVR6pKZzW3o6vsdytztky7E3qAltOvcB/9wPjzicDl68pmd+fzwREZHTUkAUyXI45TAb4zeydddKNh/bypr0bexO2p19/M3JbqISz3IChyWwvAvfqAyOBkfhTqqLJ6U27tRaeFOrcovfY7R0HAQg1fqx0tZmlbceGxz1SY9uQ/Va9elYtwI0rHiWTkRERAqeAqKUWdZalq/+hTmz38exeSeVYlOoddDSMQk29Xawu33u/Ua2VjFEJeY8QJISbKkUkUZgpIuAyAwCy2fgyPobdUFSL16KH56r/cfu8wk0LhLKtyC8Vgta1KhAt+rlGFUxFKcWphYRkWJEAVFKLa/1si95H9sTtlO3XF2ijrhJWbaM9C1bSdu4kfQNGwhOSGDgadrWPnDqk8SLGxkOhcOeyuAT6aK9M4W2icm5K/kEQnQzOFIZnwRD/UqhNK0SlvXViWZVwwjy0187EREp3vSb6gTGmCuAMUALwAlsBD4E3rbWes/WVoqOy+Nib/JediXuYsf+DRzduIZDR3Yzp+JhUt2pANze8h4uXe7m0Asv/u35MpzgzPpuW2vwpkfjSa1OWkQSQ0LnUMflwnkc4kwE1OkJFZtA5ZaZX5H1wOnD4KMp3BjirwdJRESkRFJAzGKMeRO4BUgDZgMuoDfwBtDbGDPMWnuWVeykoCVmJLLy4Ep2H9lO/Pb1pO7Yjt27n+ADCVQ6aqkcb+mYdY/gvvLw0005f7x/3LiKy32jTjmnw9fLxmgHW6INeyoC5d1EBmcQ7fbl+I7b8KZHg/UDYK/Zz6eOKiSG1cdZqTE1qlVnXJ/6px1rtYigfP/8IiIihUUBETDGDCEzHB4Aullrt2SVVwLmAoOBW4FXi2yQpVyaO4358vWiAAAQ+klEQVT9x/ezP3k/lYMrU92WwxkejnHk3Ae4ftmv2LvG0yYBHKfZgeRE0UfB121x+WTe23c4fTf+LS8itPoE/MNd+Ie7CYhw4Rvs4VigP009XkIygtiVXpntqZXZZqtQJaQ+DWqF06BSKA2jQ6hfsSv1Kl6nWUERESn1FBAz/Sfr9b6/wiGAtfagMWYMMA+43xjzui41/zte6yU+LZ4jqUc4nHqYwymHOZxwgKN7d5G8by92/0H8jsQTfjSVCgkQlWhJSnSyJcNDvenf41szZ4auYrlKpB87S2eA2wEHImBPlCEwHTJMIJ70SlhHDXwbtadaj3QoXxcq1Mu8HBxZnz83ONjsrkTl6GhqVwimWYUQBkYF85AWnhYRkTKqzP8GNMZUA9oCGcBXJx+31s43xsQCVYGOwKLCHWHx4vK4OJZ+LPMr7RjRwVWoHlYV63bjSUjAc+wY7iNH+HPDHzya/Dn7QpKx5GTq19520+hvQh5kXsl3bVqeKyDWbtSWZQEQlAZx4XAgwnAgAvaXN6SGefENdRMe5CLK40NQRhhm33Uku2sT6OtDdOVQCAiD/8SCI/fTyaNa5tf/HRERkdKhzAdEoHXW6zprbeoZ6iwlMyC2phgFRGstXuvF7fXi9npweTx4vF481oPL6yHD7eK4K43jGWmkuNJoFFWTyqERp5xneewmJq79kYyURNzJCdjkRExKIkcCPRwIhQybgtum4eY4/ZanUne/JTQVQlItJsWHlDSLNy337ZlhQK1BDmKb5g5jrn/4J874ePEc3JO7zOHg52GGlCBLsPXHLyMUd0YUTndV/ANrQkRNMirUwhMZQbnyQbweEUj18kFEBvth/tq27qRwKCIiIqdSQITaWa+7zlLnr9WSa5+lTqF44X+jSd7wGw5v5o4dDkv2l7Hg8Ga998K2yob5LXIC0dW1H2HUvDkkzl2MdXnxur1Yt5cAl2VUBjhPuq/v6y6GTd2y7rfLylctd1jabj2xopszXXMvd/zUsqMhhipHLMdC4GgwHAk3HA6DI2GQEWLxBBvCAwP4b522mPbdT2lfo/uPuC1UCgsgOjyAquUCqRQWoHUERURE8pECIoRkvZ4mzmT7a7G70LPUKRTVtu2g1a//7DbIhU1gfouc96nudNz7Y0nbn56r3pnm1ALTTy1LDDxTbxann8Xp7838CvAQF5b5v9Z6AvC6Q7HuUD7tm0IwBoejHL6OKAJ9qxAUVIfwsLpUDosgMsSPGuWDMA1OfeIYYGTXOmf/0CIiInLOFBCz58b4m+diz9DYmNHAaIAaNWrk15jO1t8/ruvrzv0+3Z2O8fM9Y/0MH0jxgzQ/SPGHYyGn9jW/mWFbVQfpAU7S/PyoHlKVB7tcgrN8NCYkEgLLQUA5CAin/twVdAgoR1RIKJEhfkQG+1MhxI+IYD98nbrUKyIiUlwpIEJS1mvIWer8dSzp5APW2gnABICYmJg8hcx/Y3/tmmzrvBcLeB3gNQZrwGvAnvDfGDgQ4QPuUAy+OKwvIf4hRIy+h9B+GzFBwTgCgjGBQWxOS+exdd/h8AvD3zecQL9wgv1CCPMLYaR/MOUCwijnH0JkUDiRfcII9fcj2N+H8EBf/HzOHPTu69uxoP93iIiISAFQQISdWa81z1Kn+kl1i8yY297E47X4Op34OBw48vDQhW/TTrneNwW+6nBBPo1QRERESjoFRFiZ9drUGBN4hieZ251Ut8gE+PoV9RBERESklCvzN4JZa/cAKwA/YNjJx40x3YFqZO6ysrhwRyciIiJS+Mp8QMzyTNbrc8aYen8VGmMqAm9lvX1Wu6iIiIhIWaBLzIC19mtjzNvAGGCtMWYW4AJ6k7nm87fAG0U4RBEREZFCo4CYxVp7izFmITAW6A44gY3AB8Dbmj0UERGRskIB8QTW2s+Az4p6HCIiIiJFSfcgioiIiEguCogiIiIikosCooiIiIjkooAoIiIiIrkoIIqIiIhILgqIIiIiIpKLAqKIiIiI5KKAKCIiIiK5KCCKiIiISC4KiCIiIiKSiwKiiIiIiORirLVFPYZSwxhzGNhVCF1VAOIKoR8pXvR9L7v0vS+79L0vuwrje1/TWht1ugMKiCWQMWaZtTamqMchhUvf97JL3/uyS9/7squov/e6xCwiIiIiuSggioiIiEguCogl04SiHoAUCX3fyy5978sufe/LriL93useRBERERHJRTOIIiIiIpKLAmIJYYy5whizwBiTYIxJNsYsM8aMNcboe1hKGWMaGmPGGfP/7d15rFxlHcbx7yOLVtmFCrIVsYBiQdZiEay2Vf9ADFJCoyRgRKIoLsgiRkAhArIYTNgiAm1sEBBki5EoqA0oi4KgraBYoCp6EZClrC3w+Md7Jr0zzL2XwsycYe7zSSbvnHPec85v7s2993ff7Wi+pHskvSTJkmbXHVt0j6TVJM2QdIakWyT9R9IySQ9KulzS9LpjjO6RdJikyyTdLelRScslPSzpekkHSFLdMUZvSDqp+p1vSUf0/P7pYu5/ks4GDgWeA24AlgMzgDWBK4H9bL9YX4TRDZLOBL7c5tB+ti/vdTzRG5JmAr+sNoeA24GngXcD76n2n2j7uBrCiy6T9C9gIrAQeJDyvd8cmAoIuBr4hO2Xagsyuk7SLsDNlIY8AUfaPr2XMaT1qc9J2peSHA4B29ney/Y+wGTgbmAf4Is1hhjdsxA4DdgfeCewoN5wokdeAq4A9rS9UfUzv7/tKcAc4EXgWEkfrDXK6JY5wLq2d7T9MdtzbL8PmAI8BHwcOLDWCKOrJL0RmEv5fl9dVxxJEPvfMVV5tO17GzttPwR8vtr8erqaB4/tH9o+yvZlthfXHU/0hu1f2Z5t+8Y2xy6l/OEAOKCngUVP2L7J9tNt9i8Czq42Z/U2quixEyg9Bp8DnqgriCQVfUzSJsBOwDLgJ63HbS+gdEFsCOzW2+gioiZ/rMpNao0i6vBCVT5XaxTRNZKmAl8DLrZ9bZ2xJEHsbztU5SLbz45Q5/ctdSNisE2uyv/UGkX0lKQtKC1KALUmDtEdkt4EzAP+R/vx5z21at0BxKi2qMolo9T5R0vdiBhQkjYEDqo2r6gxlOgySZ8GPgCsRmktnkZp1DnZ9pV1xhZd8x1ga2CO7UfqDiYJYn9boypfNh5lmKeqcs0uxxIRNZK0KjAfWBu4oe7up+i63WmejPICcCzwvXrCiW6SNA34CnBVNda4duli7m+N9a6yFlFEnEdZ3uqfZILKwLN9sG0Bbwa2Bc4EvgXcIuntdcYWnSVpAnAR8CRl1ZK+kASxvy2tyjVGqdM4tnSUOhHxOibp+8BnKMtdzbA9VHNI0SO2n7X9F9tHUla12B44q+aworNOArYCDrfdN2OL08Xc3x6oys1HqbNpS92IGCCSzgC+BDxMSQ7vHeOUGFwXAacDH5O0mu3ldQcUHbEPZf3TAyW1rnG5TVV+XtJewN9tH9yLoJIg9rfGchbbSpowwkzmXVrqRsSAkHQqcDjwKDDL9l9qDinq9ThlLOKqwHqUhZRjMLyBMilpJO+oXuv0Jpx0Mfc12/8E7gBWB/ZrPS7pA5TZbUOUR/JExICQdApwJPAYJTm8q+aQon57UpLDx4HaZ7lGZ9ieZFvtXpRlb6A8ak+239uruJIg9r+Tq/K7kt7Z2ClpInBOtXlKnssZMTgknQgcTUkEZtlOD8E4IGkPSZ+qHrXWemx34IJq8wLbL/Y2uhhvZGeCbL+TdA7lsXrPAdcDyymzGdcCrgJm55fF4JG0Iyv+CYDy6KU1gXspC6kCYDtP0RkgkvZmxfNX/wAsGqHqPbZP6U1U0QuSDqKMM3yc0ns0RPmZ35Ly8w/wM2C/UR6eEANE0lzKckdH2j69l/fOGMTXAduHSroJ+AJljMIqwD3AhcC5aT0cWGsBU9vsn9xmXwyO9Ya937l6tbMASII4WBYAJwJ7UGa1TqMsdzZEWRh9vu2r6gsvxpO0IEZEREREk4xBjIiIiIgmSRAjIiIiokkSxIiIiIhokgQxIiIiIpokQYyIiIiIJkkQIyIiIqJJEsSIiIiIaJIEMSIiIiKaJEGMiIiIiCZJECNiXJJ0pySv5Oum6twNqu1/1P05VoakSW0+0xGv8ZqtX8ffdCjciKhRnsUcEeOOJAG/B+5sObQ1sBvwEHBdm1N/XZXTqvLmrgTYfU8Dl1fvF77Ga11D+TpuCHzkNV4rIvpEnsUcEVGRdBpwBDDP9kGj1FsXeBvwqO2HexTeayZpEnA/sMT2pA5fezolgV5ge3onrx0RvZcWxIiIFXaoyj+OVsn2Y8Bj3Q8nIqIeGYMYEbHCe6tyxARR0iqSnpG0TNIb2+x/QdIESQdJ+p2kpZIelvQjSetXdSdIOkbSn6tz7pN0nKS2/7RXYx6Pl3S7pCclPSvpDkmf7einX3G/rSXNk7Sk+pxLJT0g6UpJ+3bjnhHRX9KCGBEBSNoMeCtg4K5Rqr4LmADcZfv5NvvvBS4GZgK/Aa6njM07ANhA0iHAL4C1gRsp4x0/BHybMjbwjJa4ZgKXAusBi6vrrQXsAfxA0hTbX3q1n7uVpCnAb4E1gXuAaylfk42rzzEBuKJT94uI/pQEMSKiaHQv32f7iVHq7ViVt4+wfzLwADDJ9qMAknYFbgE+DPyKknQdbXtZdfxzwLnAHIYliJJ2Aq6i9PZ8Cvixq4Hjkt5FSeQOk3Sh7dYJN6/WVynJ4Tdsnzz8gKQ1gCkduk9E9LF0MUdEFK9o/CErEsE7Rti/GJjdSA4BbN8GDAECFtn+aiM5rFxTlRs3dkhaBZgHvAWYY/tiD5tVaPtu4Kxqs5Ozh99WlT9vPWD7Kduv15nbEbESkiBGRBSdShBPtf1km/PWqMpj2xxbuyr/O2zf/sC2wA22r3n5KUBpqQRYf8RoV95tVXmepFnDx1lGxPiRLuaIiGLMBLFaP3F74EWGjVMcth/gp23O25LSbbvY9p/aXHq7qhx+bHZVzpA01npknZxRfRplfOMMyljJ5yXdCSwA5tv+cwfvFRF9KgliRIx7kt4KbFptjtaCOJkyQWSR7Wfa7F9s+5E25+1clbeOcN2dqnL4uMZGwnoJ8Dyju2GM469Y9blmSpoKfBTYHXgfMBU4StLxtk/o1P0ioj8lQYyIWJGMDdkeGqXeWN3LrRNXGhoJ4B/GuO7w8ydW5YEt4xV7wvatVAmtpNWBTwLnA9+SdKntv/Y6pojonYxBjIhY+fGHI81gHikBbNdC2Hr+SzQ/+q8xk3rbMWLqOtvLbM+lzMQWK7rEI2JAJUGMiOjcBJXRWgjd7vqS3gGsC/zV9lPDDjVmEZ8jaaM2502U9EVJq40R80qRdKikrUeIs5GsLunkPSOi/6SLOSLilSeIO1ASvdY1Bxv7X9ZCWE1QWYeSAC5tc82RWiWPpSygvRtwn6RbKEvlrEdZDmcb4AHbZ9FZhwBnS7oPWAg8BWwIvB9YHbikWrYnIgZYEsSIGNckvRnYqtoccbFpSZtTkrO/DU/0Wva3W95mrO7lxvGmVknb/5a0I3AEsDewK+V39iPAg8D3aDNjugO+CexFmZQyjTL55iHKLObzyVNUIsYFDVt3NSIiBpikScD9wBLbkzp87enAr4EFtqd38toR0XtpQYyIGH/WlzS3en+J7ete7YUknQBsRumGjogBkQQxImL8eQtwYPV+IfCqE0RK9/f2Y9aKiNeVdDFHRERERJMscxMRERERTZIgRkRERESTJIgRERER0SQJYkREREQ0SYIYEREREU2SIEZEREREkySIEREREdEkCWJERERENPk/VbHswdDR2gEAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 720x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(10,8))\n",
"plt.plot(t, num_sol_3[:,0], linewidth=4, linestyle='--', label='Euler-Step Rocket')\n",
"plt.plot(t, num_sol_4[:,0], linewidth=3, linestyle='--', label='Implicit Heun Rocket')\n",
"plt.plot(t, num_sol_1[:,0], linewidth=4, linestyle='--', label='Euler-Step Simplerocket')\n",
"plt.plot(t, num_sol_2[:,0], linewidth=3, linestyle='--', label='Implicit Heun Simplerocket')\n",
"plt.title('Rocket & Simple Rocket Heights\\n')\n",
"\n",
"plt.xlabel('$Time$ [s]')\n",
"plt.ylabel('$h$ [m]')\n",
"plt.legend();"
]
},
{
"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": 207,
"metadata": {},
"outputs": [],
"source": [
"def incsearch(func,xmin,xmax,ns=50):\n",
" '''incsearch: incremental search root locator\n",
" xb = incsearch(func,xmin,xmax,ns):\n",
" finds brackets of x that contain sign changes\n",
" of a function on an interval\n",
" arguments:\n",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\n",
" returns:\n",
" ---------\n",
" xb(k,1) is the lower bound of the kth sign change\n",
" xb(k,2) is the upper bound of the kth sign change\n",
" If no brackets found, xb = [].'''\n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = func(x)\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] )\n",
"\n",
" \n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb"
]
},
{
"cell_type": "code",
"execution_count": 208,
"metadata": {},
"outputs": [],
"source": [
"def mod_secant(func,dx,x0,es=0.0001,maxit=50):\n",
" '''mod_secant: Modified secant root location zeroes\n",
" root,[fx,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):\n",
" uses modified secant method to find the root of func\n",
" arguments:\n",
" ----------\n",
" func = name of function\n",
" dx = perturbation fraction\n",
" xr = initial guess\n",
" es = desired relative error (default = 0.0001 )\n",
" maxit = maximum allowable iterations (default = 50)\n",
" p1,p2,... = additional parameters used by function\n",
" returns:\n",
" --------\n",
" root = real root\n",
" fx = func evaluated at root\n",
" ea = approximate relative error ( )\n",
" iter = number of iterations'''\n",
"\n",
" iter = 0;\n",
" xr=x0\n",
" for iter in range(0,maxit):\n",
" xrold = xr;\n",
" dfunc=(func(xr+dx)-func(xr))/dx;\n",
" xr = xr - func(xr)/dfunc;\n",
" if xr != 0:\n",
" ea = abs((xr - xrold)/xr) * 100;\n",
" else:\n",
" ea = abs((xr - xrold)/1) * 100;\n",
" if ea <= es:\n",
" break\n",
" return xr,[func(xr),ea,iter]"
]
},
{
"cell_type": "code",
"execution_count": 209,
"metadata": {},
"outputs": [],
"source": [
"def f_m(dmdt,m0=0.25, c=0.18e-3, u=250):\n",
" ''' define a function f_m(dmdt) that returns \n",
" height_desired-height_predicted[-1]\n",
" here, the time span is based upon the value of dmdt\n",
" \n",
" arguments:\n",
" ---------\n",
" dmdt: the unknown mass change rate\n",
" m0: the known initial mass\n",
" c: the known drag in kg/m\n",
" u: the known speed of the propellent\n",
" \n",
" returns:\n",
" --------\n",
" error: the difference between height_desired and height_predicted[-1]\n",
" when f_m(dmdt)= 0, the correct mass change rate was chosen\n",
" '''\n",
" y0 = 0 # initial position\n",
" v0 = 0 # initial velocity\n",
" m0 = 0.25 # initial mass\n",
" N = 500 # number of steps\n",
" dtt = (.20/dmdt)/N\n",
" # initialize array\n",
" num_sol = np.zeros([N,3])\n",
" num_sol = np.zeros([N,3])\n",
" # Set intial conditions\n",
" num_sol[0,0] = y0\n",
" num_sol[0,1] = v0\n",
" num_sol[0,2] = m0\n",
" for i in range(N-1):\n",
" num_sol[i+1] = heun_step(num_sol[i], rocket, dtt)\n",
" error = num_sol[-1,0] - 300\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 217,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-14.54607432797377"
]
},
"execution_count": 217,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f_m(0.06)"
]
},
{
"cell_type": "code",
"execution_count": 218,
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "operands could not be broadcast together with shapes (3,) (50,) ",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-218-e15f6fcb2903>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mxb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mincsearch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf_m\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.04\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.06\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m<ipython-input-207-e3f9108b648e>\u001b[0m in \u001b[0;36mincsearch\u001b[0;34m(func, xmin, xmax, ns)\u001b[0m\n\u001b[1;32m 15\u001b[0m If no brackets found, xb = [].'''\n\u001b[1;32m 16\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxmin\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mxmax\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mns\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 18\u001b[0m \u001b[0msign_f\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msign\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0mdelta_sign_f\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msign_f\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0msign_f\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m<ipython-input-209-98bd27dfa6e2>\u001b[0m in \u001b[0;36mf_m\u001b[0;34m(dmdt, m0, c, u)\u001b[0m\n\u001b[1;32m 29\u001b[0m \u001b[0mnum_sol\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 31\u001b[0;31m \u001b[0mnum_sol\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mheun_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_sol\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrocket\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 32\u001b[0m \u001b[0merror\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnum_sol\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m300\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 33\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m<ipython-input-191-01230f21be6d>\u001b[0m in \u001b[0;36mheun_step\u001b[0;34m(state1, rhs, dt, etol, maxiters)\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0meps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfinfo\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'float64'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meps\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m \u001b[0mnext_state\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstate1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mrhs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mdt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 18\u001b[0m \u001b[0;31m################### New iterative correction #########################\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmaxiters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,) (50,) "
]
}
],
"source": [
"xb = incsearch(f_m,0.04,0.06,50)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3b"
]
},
{
"cell_type": "code",
"execution_count": 213,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.05864732806758735 m/s is the correct mass flow rate\n",
"the solution took 5 iterations\n"
]
}
],
"source": [
"h0,out = mod_secant(f_m,0.0001,0.04,es=0.000001) # <-- solution line\n",
"print(h0, 'm/s is the correct mass flow rate')\n",
"print('the solution took ',out[2],' iterations')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3c"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def rocket2(state,dmdt=0.058647, u=250,c=0.18e-3):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, with drag, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" c : drag constant for a rocket set to 0.18e-3 kg/m\n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" derivs = np.array([state[1], (u/state[2])*dmdt-9.81-(c/(state[2])*(state[1]**2)), -dmdt])\n",
"\n",
" return derivs"
]
},
{
"cell_type": "code",
"execution_count": 219,
"metadata": {},
"outputs": [],
"source": [
"dmdt=0.058647\n",
"y0 = 0 # initial position\n",
"v0 = 0 # initial velocity\n",
"m0 = 0.25 # initial mass\n",
"N = 500 # number of steps\n",
"dtt = (.20/dmdt)/N\n",
"t = np.linspace(0,.20/dmdt,500)\n",
"# initialize array\n",
"num_sol_5 = np.zeros([N,3])\n",
"# Set intial conditions\n",
"num_sol_5[0,0] = y0\n",
"num_sol_5[0,1] = v0\n",
"num_sol_5[0,2] = m0"
]
},
{
"cell_type": "code",
"execution_count": 228,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[3.00885067e+02 1.92322278e+02 7.96000000e-02]\n"
]
}
],
"source": [
"for i in range(N-1):\n",
" num_sol_5[i+1] = heun_step(num_sol_5[i], rocket, dt)\n",
"print(num_sol_5[426])"
]
},
{
"cell_type": "code",
"execution_count": 238,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(10,8))\n",
"plt.plot(t, num_sol_3[:,0], linewidth=4, linestyle='--', label='Euler-Step Rocket')\n",
"plt.plot(t[426],num_sol_5[426,0],'*',linewidth=6)\n",
"plt.title('Rocket Detonation={:.2f} meters\\n'.format(*num_sol_5[426,:]))\n",
"plt.xlabel('$Time$ [s]')\n",
"plt.ylabel('$h$ [m]')\n",
"\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"1. Math 24 _Rocket Motion_. <https://www.math24.net/rocket-motion/\\>\n",
"\n",
"2. Kasdin and Paley. _Engineering Dynamics_. [ch 6-Linear Momentum of a Multiparticle System pp234-235](https://www.jstor.org/stable/j.ctvcm4ggj.9) Princeton University Press \n",
"\n",
"3. <https://en.wikipedia.org/wiki/Specific_impulse>\n",
"\n",
"4. <https://www.apogeerockets.com/Rocket_Motors/Estes_Motors/13mm_Motors/Estes_13mm_1_4A3-3T>"
]
}
],
"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
}