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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": 89,
"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": 90,
"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",
" \n",
" dstate = np.array([state[1], (u/state[2])*dmdt, -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [],
"source": [
"def rk2_step(state, rhs, dt):\n",
" '''Update a state to the next time increment using modified Euler's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" \n",
" mid_state = state + rhs(state) * dt*0.5 \n",
" next_state = state + rhs(mid_state)*dt\n",
" \n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [],
"source": [
"def heun_step(state,rhs,dt,etol=0.000001,maxiters = 100):\n",
" '''Update a state to the next time increment using the implicit Heun's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state + rhs(state)*dt\n",
" ################### New iterative correction #########################\n",
" for n in range(0,maxiters):\n",
" next_state_old = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e=np.sum(np.abs(next_state-next_state_old)/np.abs(next_state+eps))\n",
" if e<etol:\n",
" break\n",
" ############### end of iterative correction #########################\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"y_0 = 0\n",
"v_0 = 0\n",
"m = 0.25\n",
"m_final = 0.05\n",
"u = 250\n",
"dmdt = 0.05\n",
"T = (m-m_final)/dmdt \n",
"t = np.linspace(0, T, 100)\n",
"dt = t[1] - t[0]\n",
"N = int(T/dt)\n",
"\n",
"m_f = np.linspace(m, m_final, N)\n",
"delta_v = -u*np.log(m_f/m)\n",
"\n",
"num_heun_simplerocket = np.zeros([N,3])\n",
"num_rk2_simplerocket = np.zeros([N,3])\n",
"\n",
"num_heun_simplerocket[0,0] = y_0\n",
"num_heun_simplerocket[0,1] = v_0\n",
"num_heun_simplerocket[0,2] = m\n",
"num_rk2_simplerocket[0,0] = y_0\n",
"num_rk2_simplerocket[0,1] = v_0\n",
"num_rk2_simplerocket[0,2] = m\n",
"\n",
"for i in range(N-1):\n",
" num_heun_simplerocket[i+1] = heun_step(num_heun_simplerocket[i], simplerocket, dt)\n",
"for i in range(N-1):\n",
" num_rk2_simplerocket[i+1] = rk2_step(num_rk2_simplerocket[i], simplerocket, dt)\n",
"\n",
"plt.figure(figsize = (8,8))\n",
"plt.title('Convergence of Different Methods for Simple Rocket')\n",
"plt.plot((m_f/m), delta_v, '-', label='Tsiolkovsky')\n",
"plt.plot(num_heun_simplerocket[:,2]/m, num_heun_simplerocket[:,1],'-',label='heun')\n",
"plt.plot(num_rk2_simplerocket[:,2]/m, num_rk2_simplerocket[:,1],'--',label='rk2')\n",
"plt.xlabel('mass(t)/mass(0)')\n",
"plt.ylabel('velocity(t)')\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": 94,
"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",
" dstate = np.array([state[1], ((u/state[2])*dmdt)-g-((c/state[2])*(state[1]**2)), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"y_0 = 0\n",
"v_0 = 0\n",
"m = 0.25\n",
"m_final = 0.05\n",
"u = 250\n",
"dmdt = 0.05\n",
"g = 9.81\n",
"\n",
"T = (m-m_final)/dmdt \n",
"t = np.linspace(0, T, 100)\n",
"dt = t[1] - t[0]\n",
"N = int(T/dt)\n",
"\n",
"m_f = np.linspace(m, m_final, N)\n",
"delta_v = -u*np.log(m_f/m)\n",
"\n",
"num_heun_rocket = np.zeros([N,3])\n",
"num_rk2_rocket = np.zeros([N,3])\n",
"\n",
"num_heun_rocket[0,0] = y_0\n",
"num_heun_rocket[0,1] = v_0\n",
"num_heun_rocket[0,2] = m\n",
"num_rk2_rocket[0,0] = y_0\n",
"num_rk2_rocket[0,1] = v_0\n",
"num_rk2_rocket[0,2] = m\n",
"\n",
"for i in range(N-1):\n",
" num_heun_rocket[i+1] = heun_step(num_heun_rocket[i], rocket, dt)\n",
"for i in range(N-1):\n",
" num_rk2_rocket[i+1] = rk2_step(num_rk2_rocket[i], rocket, dt)\n",
"\n",
"plt.figure(figsize = (8,8))\n",
"plt.title('Convergence of Different Methods for Rocket')\n",
"plt.plot((m_f/m), delta_v, '-', label='Tsiolkovsky')\n",
"plt.plot(num_heun_rocket[:,2]/m, num_heun_rocket[:,1],'-',label='heun')\n",
"plt.plot(num_rk2_rocket[:,2]/m, num_rk2_rocket[:,1],'--',label='rk2')\n",
"plt.xlabel('mass(t)/mass(0)')\n",
"plt.ylabel('velocity(t)')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize = (8,8))\n",
"plt.title('Comparison of Rocket vs Simple Rocket')\n",
"plt.plot(t[:-2], num_heun_rocket[:,0],'-',label='heun rocket')\n",
"plt.plot(t[:-2], num_heun_simplerocket[:,0],'-',label='heun simple rocket')\n",
"plt.xlabel('time')\n",
"plt.ylabel('height')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The height of the simple rocket when m_final = 0.05 caluclated using heun step is 565.97 m\n",
"The height of the rocket when m_final = 0.05 caluclated using heun step is 407.24 m\n"
]
}
],
"source": [
"print('The height of the simple rocket when m_final = 0.05 caluclated using heun step is', round(num_heun_simplerocket[-1,0],2), 'm')\n",
"print('The height of the rocket when m_final = 0.05 caluclated using heun step is', round(num_heun_rocket[-1,0],2), 'm')"
]
},
{
"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": 40,
"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",
" \n",
" y_0 = 0\n",
" v_0 = 0\n",
" m_final = 0.05\n",
" h_desired = 300\n",
" T = (m0-m_final)/dmdt \n",
" t = np.linspace(0, T, 100)\n",
" dt = t[1] - t[0]\n",
" N = int(T/dt)\n",
"\n",
" h = np.zeros([N,3])\n",
"\n",
" h[0,0] = y_0\n",
" h[0,1] = v_0\n",
" h[0,2] = m0\n",
"\n",
" for i in range(N-1):\n",
" h[i+1] = heun_step(h[i], lambda state: rocket(state, dmdt = dmdt,u=250,c=0.18e-3), dt)\n",
" h_predicted = h[:,0]\n",
"\n",
" error = h_desired - h_predicted[-1]\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 45,
"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 = np.zeros(ns)\n",
" for i in range(ns):\n",
" f[i] = func(x[i])\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] )\n",
"\n",
" \n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb"
]
},
{
"cell_type": "code",
"execution_count": 46,
"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": 50,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"The upper bound of the mass change rates interval is [0.1375]\n",
"The lower bound of the mass change rates interval is [0.05]\n"
]
}
],
"source": [
"mass_change_rates = incsearch(f_m, 0.05, 0.4, 5)\n",
"print('The upper bound of the mass change rates interval is', mass_change_rates[0])\n",
"print('The lower bound of the mass change rates interval is', mass_change_rates[1])"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The root of the function, f_m, is 0.0769\n"
]
}
],
"source": [
"root_f_m = mod_secant(f_m, 0.001,0.1)\n",
"print('The root of the function, f_m, is', round(root_f_m[0],4))"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
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KF9o5QZ6GZkE47WBmnZIlMrOelP2xW5AsXX0K2+ecGs5+R9C9RsS8mOe7U7cWhNNMni+7hdOP3T1hk4rwD1BdD6GyIJxm1WenqQY+sT3QpmoLlK7I5Z5h8Q2BIyzohXZoHew7VuQunFoZGdndVwEvh7Onx02nuXtlbZoSbXMiZe/HgJqVsEF6PZy2oOxLu9aFbXgWhLNDSRDUuPtiYC7Bv68RBH1tQHrte2LvAKvNkbkzIXKJtxWp76g7OZwWE3ReWp8ix7um3+mxYy2dmDRV2WuNz5NJt1D2J+zv7l4as+5Tgks+kP53flXP6Ww4XyJ/olKV8ycEfziTqY3fj2w4FhU0ycAnjIAjt1xfYWb7pUpvZp3MrG01dvFIOC0i6H8lkRup2NC1tq0Ipx2t9oaDiLy23czsQOCIuOXlWDBURaruyHMIBhmEsvI2Ja9T9s/0VjNLWUtoZr1qUDMUCXJGEHT8tYqg76BYE8LpVeF0DfBhGvuKdEoG0CWN/Nnkv0DkLq9bLMEAmGa2O2UDm/7H3VfWV+FCkc+Omdl2KVOm4O5TKTsfrzGzCnfImFkPgl7aIejHZ3p8mvpkZnlmdgtl3RHMJOiTKSoMgv4Rzh5mZhdWss3m4euMFfuepjqns+F8idRw7WwJRqsPu4S4sZJtRM6pTnF3elZHNhyLCppk4BM6l+AfQCHBWEK3mtk+kR9qMxtgZqeZ2RMEl64qnDzJuPsU4D/h7G/N7H4LxilpF44z8gBwPuWrX+tC5AerGXCdmXWxYPywvBqcyK9Q9gXwMME/hmLK+rOJ9yNgkZk9bmY/M7P+4XHoEvZh8zxB76kAT6RZpgYrbBP1S4LLfR2BD8zsWjPbPTxOHc1soJmdYWYvENTIpHtdfkI4jdw18Xbcv2IoC44iaSZXsXF9Oe6+gaA3boALw/O/KDz36n1Mtppw903ApeHsLgTt0Y4O35vuZnYeQR87BQSB4qgMFPMjygLN68ysh5kVpPlZv5Cgq4/tCLr7+ImZdTaz7czs5wT/4tsTfO5TBhC1qCjmlvNtwj8AB5nZtQTfo5eF6eYDx3niUeBvpazdz+1m9qyZHR6+rm0sGJvsGDP7J0Fv5+VqvMJuKeaEsxeFn8sK53SWnC/PEryHBcArZnZ8+Dq7mdkZBLUqrcLXmUzk96MIuDbMH/n9qFLskCXHImHBGsSDuhmrqz8wKyZdskcpceO+UPmQFW0IhjBIts2HCEaDTtaba8rtx6QbE6abkGT9O0n2nzB9Fd+Lu+O29UqKtEOrcHydoMaoQo+caZRtAkl6E06SfkGYfnR1j22C19crnf2E6/ejauMBFQNt0zw23eO2dXGCNNvFpfl9iu2NTnWsKev1OdGjV0y6lMcmTNMrJm/Cz3Mlr310on1Xcxv1MVZX0h6KU20jXP90knKlM1bX6VRzrK6YvHXRc3Nlj00EnU62rmSbbSjrBbyyx3kJ8p+fIn2djNVVyeuJfGdclWDdFSn2vYGgc8FIz/P3JchvlA3xEf/IyFhd6R6L+EdTrvHBg0teAwmq/l8k6CdgC8EHfhHwKkFvn9096NGzOtteTdB502UEvStvJLi0MAU4w91HUD93RRxF0C/FLMr3hVIT8Ze1UjVqnkLwxX4jwZhdCwiOxebw+VPAEe7+C0+jZqGx8KCWcAeCf9BvEIzXtJXgWM0nqDI+E9jWg04h09nHIsp3uDghQZpvKd//VIU01djfvQSDCk4gqCWMr11qUNz9ZoI+jh4keE82E3x2PwVuIBhDK2GPwPXklwTjT31CcBeTp7shd3+UoM3dnQS1HBvCxxcEY/f1d/f/JN9CndpI0Hh5BkGt8/lAV3f/tSfpMDbCg5srjiMYa+sRgtqiDQSftWUEfxT/j+CP7t0J8t9F0BXHRILLuUnP6UyfL+5+I3A8wedvDWXfufcDg9z9+UryO3A4QU3Z51R9pIFE28qqz46FkZJkgJn9FzgOeMndj810eURERBq7Jl3jk0lhI6/ILcXpNB4VERGRalLgU0fCRnipbhW8hbJGqk/XQ5FERESaPAU+dedHwBdmNirmDp1tzeyQ8O6cyK2XT7j7rAyWU0REpMlQG586Ymb7AO9WkmwicHzYEFpERETqmAKfOhL22PxzglbxOxP0gltEcNveRwR91jzuFftRERERkTqiwKeGOnTo4L169cp0MUREROrNhx9+uNzdO2a6HOloUD2oZqNevXoxbdq0TBdDRESk3pjZwspTZSc1bhYREZEmQ4GPiIiINBkKfERERKTJUOAjIiIiTYYCHxEREWkyFPiIiIhIk6HAR0RERJoMBT4iIiLSZCjwERERaaw2r4OnRwRTAdRzc70rLS3lhx9+YN26dWzatInSUg3VJSJ1Kycnh+bNm9OyZUvatm1LTo7+8zYZ8yfCrOdh4E+g/1GZLk1WyJrAx8wuBA4EdiEY0LM1sAr4FBgDPOZJBhYzs9OA84CBQC7wBfAgcHeqQUDTzZeu4uJiFi1aRF5eHu3ataOoqIicnBzMrLZ3JSICgLtTWlrKhg0bWLVqFWvWrKF79+7k5WXN17/Upc9fLJsq8AGy61LXKOAEYCMwBXgOmAscBDwCjDWzCuU1szuBx4BBwCTgDWAH4A7gWTPLTbSzdPPVxMqVK2nWrBndunWjVatW5ObmKugRkTplZuTm5tKqVSu6detGs2bNWLlyZaaLJfXBHea8Fjyf82owL1kV+PwUaOvue7j7se7+U3ffl6AGaClwPDAiNoOZnQScD3wHDHT3Y9x9OLA98DkwHLggfkfp5qup1atX0759ewU7IpIRZkb79u1ZvXp1posi9WHZF1C8KXhevAmWzc5sebJE1gQ+7j7Z3dcnWP4ZcGc4e2jc6ivC6Sh3/zImz1KCS1gAlyeoKUo3X40UFxdTUFBQm5sUEamWgoICiouLM10MqQ9zXofSkuC5l8CXr2e2PFkiawKfSkQ+pZsiC8ysG7AnsAV4Jj6Du08ElgCdgX1qmq+2qLZHRDJJ30FNyKyxULI5eF68GT4bm9nyZImsb91mZr2Bc8PZF2NW7R5OP3P3jUmyfwB0DdNOqWE+ERGR7PHU6WWNlxPJjbvCsHQmjG6TPP2AY+Enj9ZO2bJY1tX4mNmvzGyMmT1mZhOBOUA34EZ3jw1Xe4fThSk293Vc2prka7jUj4OISONzyP9B510gvyjx+pItqecj8oug88Bge01A1gU+wP4EjZhPAwaHy64GrotL1zKcVmgXFCPyS9+qFvI1XJF+HOa/nemSiIhIbWnfF86ZCMOuhLxCqG6zVMsJ8g37Y7Cd9n3rppxZJusCH3c/y90NKAJ2Bv4BjAbeM7MuMUkjF6qre39euvnKNmB2jplNM7Npy5YtS3cz9Se2HweJGjNmDGbGyJEjM12UGrvvvvvYc889adGiBWaGmbFq1aoabbMxHZ/6NHr0aMyM0aNHZ7oo0hTk5MJ+F8J578C2Oyev/YmXXwTb/ijIt98F0IQ6tczaV+ruG919lrtfRnAX1q4EfexErA2nLStkLhNZtzZmWbr5Yst2r7sPcvdBHTt2TLGZLKB+HOrNggULMDN69epVr/t96aWXOPvss5k1axYHH3wwI0aMYMSIEVl3B+HQoUMxMyZMmJDpoqQtU++xSKUitT8HXgp5zVOnzWsepGtCtTyxsr5xc+hB4K/AsWaW7+5bgQXhup4p8nUPpwtilqWbr2FK1I9Dp/6ZLVOWGD58OPvssw9t2qRo7NcAPPNMcHPi7bffztlnn53h0sgFF1zAT3/6Uzp06JDpokhTk5MLnQZAbn7Z934iufnQaacmVcsTq6EEPqsIbmnPA9oRdGj4cbhuZzMrTHKH1l7h9OOYZenma5gS9eOgwAeANm3aNPigB2DRokUAbL/99hkuiQB06NBBQY9kzucv4pvXkbLTgs3rmvQQFg0l3BtMEPSsApYDuPsi4COgADglPoOZDSG4G+w74N3I8nTzNVgNrB+HSPsUgHvvvZfdd9+doqIi2rdvz4knnsjMmTOT5l24cCHnn38+ffr0oVmzZrRt25Zhw4bx+OOPJ0yfrA3LhAkTMDOGDh3K1q1bueGGG+jfvz/NmzenU6dOnH766Xz99dfl8owcOZLevXtHyxF5HdW9LLJ161buuOMO9t57b1q3bk1hYSEDBgzg8ssvrzDMwMiRIzEzxo8fD8CwYcOi+6xq+xJ35/7772ePPfagsLCQDh06cMIJJzB9+vRK837++eeceeaZ9O7dm+bNm9O2bVsOOeQQXnjhhXLpIsdz4sSJFcqZ6NLXlClTOOmkk+jcuTMFBQV07tyZk08+mffeey9hOWIvoX344Yccd9xxtG/fnsLCQnbddVfuv//+hPkWLlzIjTfeyLBhw+jevTvNmjWjXbt2Sc+Zqr7HlbXxefnllznyyCPp0KEDBQUFdO/enREjRvD5558nTN+rVy/MjAULFvDGG29w8MEH06ZNG4qKithnn30qHG9pwsKmDRbThLWEnAQNn71JN33IihofMzsQ6AE86+6b49btD0S+ue5395KY1TcSdEJ4s5lNcfe5YZ5OwF1hmpsSDDiabr7s00j7cfjd737H7bffzoEHHsjxxx/PRx99xNixY3nttdd47bXXOOCAA8qlnzp1KkcccQSrVq2id+/eDB8+nBUrVjBx4kQmTJjAq6++ykMPPVStztu2bt3KkUceydSpUxkyZAgDBgzg3Xff5bHHHuPtt99m+vTpbLPNNgAccMABrFu3jueee44WLVpw8sknR7dT1X//mzZt4sgjj2TChAkUFRUxbNgwioqKmDRpEjfffDNPPvkkb731Fn369InuE+DVV19l6dKlHH744XTu3BmA3XbbrUr7/M1vfsPdd99Nbm4uQ4YMoVOnTrz//vvsvffe/OpXv0qa78knn2TEiBFs2bKFnXfemWOOOYZly5YxadIkxo0bx9VXX8111wU3Ynbu3JkRI0YkLGdkfcTdd9/NBRdcQGlpKXvttRcHHXQQc+fO5bnnnmPs2LHcc889SS/nvfrqq/ztb39jxx135LDDDuPrr79mypQpnHXWWaxatYpLL720XPpHHnmEq6++mr59+9K/f3/2339/Fi9ezKRJk5gwYQJTp07ltttui6avjff4iiuu4KabbiInJ4cDDjiArl27Mn36dB5++GGefvppnn32WY4++uiEee+//35uuOEG9tprL4466ihmz57N1KlTOeGEE3j66afLlUeaqGVf4Fs3RWt7NngzStr1pdUxN8Ab18KKubB1Q7CyKTd9cPeMP4CRBHdZ/QCMIxg89AXgs3C5Ay8BhQny3hWu30jQweF/gNXhsrFAbpJ9ppUv/rHnnnt6Vc2aNavKaats+Vz3u/d3/1Nn92tbp//4U2f3uw8ItpdBkfe7qKjIJ06cGF1eWlrql19+uQPevXt337hxY3Tdxo0bvXv37g74xRdf7MXFxdF1M2bM8E6dOjng99xzT7l9Pfjggw74iBEjyi0fP358tByDBg3ypUuXRtetWrXK99hjDwf8T3/6U7l88+fPd8B79uyZ1mu/7LLLHPD+/fv74sWLo8s3bNjgJ554ogO+zz77VMg3ZMgQB3z8+PHV2t8LL7zggLdu3dqnTp0aXV5cXOwXXnhh9BjEH59PP/3UCwoKvGXLlv7KK6+UWzdz5szoe/HWW29Vq5yffPKJ5+XleU5Ojj/99NPl1j3xxBOek5Pj+fn5PmPGjITbBfz+++8vt+6RRx6Jvsb169eXW/f+++/7zJkzK5Rjzpw50dfw3nvvlVtXlff42muvdcCvvfbacstffvllB7xFixblzm1391tuucUBb9OmTbnzzd29Z8+eDnhBQYH/73//K7fu+uuvd8D79euXtDyJ1Ml3kWTepH/41tHtfes1bXzDNR38nhsv9tKS8PuwpNj9ndvdr9/WffQ27td1dJ98W9q7AqZ5FsQP6TwyXoDg+NGboJ+e8cCiMBjZRNC4+FnghErynwa8A6wh6J/nQ+A3QE5d5It9ZDzwca94Qlcn4Bm9TZDvnX+6l5TUTfmqIfIDdumll1ZYV1xc7H369HHAH3300ejyhx9+OPpjtGXLlgr57rrrroQ/DpUFPmbm06dPr7C9p556ygEfNuWqissAACAASURBVGxYueU1CXw2bNjgLVu2dMBff/31CuuXLVvmLVq0cMAnT55cbl26gc9BBx2U8Afa3X3Tpk3epUuXhMfn1FNPdcDvuuuuhNt95plnHPATTzyxWuU844wzHPDTTjst4frIfs8666yE2z3ppJMS5hswYIADFYKNVO69914H/Pe//3255TUJfCLH+8orr0yYb++9904YUEcCn0Sfic2bN3ubNm0c8IULF1btxbkCn8aq5J7BXnxtG59x9S4+5PJ/+3MfLqqYKPJnefQ27v8amva+GnLgkxVtfNx9vrtf4+7D3L27uxe6e3N37+XuJ7v785Xkf9zd93f31u7ewt33dPc7vZJLVenmyzqNsB+H008/vcKy3NxcfvaznwGUaxcSaTvy85//nPz8/Ar5fvWrX2FmzJ07lyVLllS5DD169GCXXXapsLx//6Bq+Jtvvqnytirz4Ycfsm7dOrp06cKhh8aPxRtcSjn22GMBauV28OLiYt555x0g8bFu1qwZp5xSoQkcpaWlvPrqq5hZ0ksrQ4YMAeDdd6vXRC7yPibrN+iMM84Akr/+Y445JuHyVO/Xpk2b+O9//8tVV13Fr3/9a0aOHMnIkSN59tlnAZgzZ051XkJSscc72euLXFqszusrKCiIXvqszfNRGqZvilvz562nceyWG9jSujfH7tqlYqLIbe+HXgcts7w7ljqSFW18pJZETujJf4e3/5L6dsZIPw4HXJJVAU9EpBFpvEgj0sWLF0eXRYKZZHmaN29Oly5dWLJkCUuWLKFr165VKkOPHj0SLm/dujUQ/GjWlspeA0Dfvn3Lpa2J5cuXs3nzZnJycujZM3HPDokaZa9YsYI1a9YA0KlTp5T7qG7nnpUdg8pef3Xfr3fffZdTTz213LkUL/Jaa2rFihWVHu/afn3StJSUOj/fcAkLS4I2PGcc0Jv83CTf7ZE/y/tdWI8lzB4KfBqbJtKPQ2wj5aDWNfWo05E01ZFTj8emrl5DbSspCe4tyM3NTVhTVBuSHYPKXn913q8NGzYwfPhwli5dyplnnsl5551Hv379aNWqFTk5Obz++uscfvjhtXbMY7dTH69Pmp7/zfyWhSuCoKdNYT4/+3HiQFkU+DROn79Y+YCkWd6Pw4IFC9h1110TLgfo0qWsCrdbt24AzJs3L+G2Nm3axLfffgtQ5dqe+hZ5DfPnz0+aJrKuNl5Dhw4daNasGZs3b+brr7+O1jbEihzr+HyFhYVs3LiRO+64g5YtU3WAXj1du3blq6++Yt68eQnLU5uv/+2332bp0qXsueee3HfffRXWz507t8b7iBV7vBcsWJCwz6XafH3StLg790z8Kjr/y3170qKZft6T0V+IxsYjQ1TE/Hu0htePw2OPPVZhWUlJCU899RQQ9N0SEWlT8sQTT1BcXFwh30MPPYS7069fvzr9UYkMEZGoDJXZc889admyJUuWLGHcuHEV1q9YsYIXXwy6LYh97enKy8tjv/32AxIf6y1btkTbucTnO+SQQwASrk+lsuMTeR8ffvjhhOsffPBBoHZef6RPpO7duydcn6zvp3Tf47y8PPbff38g+esbM2YMUDuvT5qWyXOXM3NJcFm2eX4OI/frldkCZTkFPo1N7BAVUNaA+WePB9PYhs+Rfhyy0F133cXkyZOj8+7Otddey9y5c+natSsnnXRSdN0pp5xC9+7dmT9/PldccQWlpWVt02fNmsW1114LwO9///s6LXPHjh0pKChg6dKl/PDDD9XKW1hYyLnnngvAb3/722gNFQQ1Vueddx7r1q1jn332if6A1tRFF10EwN/+9jemTZsWXV5aWsqoUaOStjW55ppryM/P57e//S1PPvlkhUs0paWljBs3jldffbXc8kjQmayjvosuuoi8vDyeeOIJxo4t39HmM888w9NPP01+fn603DURafD81ltv8cUXX5Qr+3XXXRdtiByvJu/xJZdcAsA//vGPCtv/29/+xrvvvkubNm0466yzqrVdkdjanlMHdad9y2YZLE32U11YYxMZosJyILcZDPsj7HN+0Jan9xB47y5464agN+fS7B3C4uyzz2bIkCEMHjyY7bbbjo8++ojZs2dTWFjIY489RmFhYTRt8+bNefrppznyyCP561//ytixY9lrr71YuXIlEyZMYMuWLfziF7/gnHPOqdMy5+fnc/TRRzN27Fh233139t9//2hvyDfddFOl+a+//nqmTZvGhAkT2H777TnooIMoLCxk0qRJfPvtt/To0SNh7Uy6TjjhBM455xzuvfde9t1333IdGC5ZsoTzzjuPu+++u0K+QYMG8fDDD3PGGWfws5/9jMsvv5yddtqJVq1asXjxYubMmcPy5csZNWoURxxxRDTf8OHDGTNmDJdddhlvvPFGtHH0ZZddxo477siuu+7KbbfdxgUXXMCJJ57I3nvvTd++fZk7dy7vv/8+OTk53HHHHQnvtKuuPfbYg2OPPZYXX3yR3XbbjWHDhtGmTRs++OADvv76a/7whz9wyy23VMhXk/f46KOPZtSoUdx8880MHjyYAw88kC5dujBjxgxmzpxJ8+bNefTRR9l2221r/Pqk6Zi+eBXvzF0BQG6OcfaBfTJcogYg0/fTN/RHVvTjE+tfQ4L+GVJ1RlhL/TjUBcJ+fEpLS/3OO+/0gQMHemFhobdt29ZPOOGEhP3qRCxYsMDPPfdc79WrlxcUFHibNm188ODB/uijj3ppaWmF9JX14zNkyJCE+0nVl8vy5cv9zDPP9G7dunleXl61+/XZsmWL33777b7XXnt5y5YtvVmzZr7jjjv6H/7wB1++fHnCPOn24+MedAx57733+m677ebNmjXztm3b+jHHHOMff/xx0uMTMXfuXL/ooot8wIABXlRU5EVFRd6nTx8/7LDD/LbbbvMlS5ZUyHPXXXf5rrvu6oWFhdH3Or7ckydP9uHDh3unTp08Ly/PO3Xq5CeeeKJPmTIlrdc/YsQIB/zBBx8st3zz5s1+0003+c477+zNmzf3Dh06+LHHHuvvvfdeynOgsvc4WT8+ES+++KIffvjh3q5dO8/Pz/euXbv6L37xC//ss88Spo/04zN//vy0Xn8i6sen8Tjv0Wnec9RL3nPUS37h4x/V235pwP34WFB+SdegQYM89jJBKp9//jkDBgyo2wI9fir0GlxWy5NMaUlQ+7NgEpz2dN2WqRoid7zovBSpO/XyXSR1bv7y9Rx06wQiX5evXHQgO3VpXS/7NrMP3X1QveyslulSV2NT1SCmiffjICLS0N379lfRoGfIDh3rLehp6NS4WUREpIFZumYTz31YdgPCuUMqdgEhiSnwERERaWDumzSPLSXBHay799iGffq0y3CJGg5d6pKsorY9IiKprdqwhcemfh2dP39ov5S9vkt5qvERERFpQB6aspANW4LhY3bYtiUH9089bp6Up8BHRESkgdiwpZgxU8qGtjlvaF9yclTbUx0KfERERBqIJ99fxA8btgLQrW0hxw7sUkkOiafAp56pDYuIZJK+gxquLcWl/HtS2WDM5wzuQ16ufsarS0esHuXm5lJSUpLpYohIE1ZSUkJubm6miyFpeP6TJXy7OhiLsUPLAk4dlHiQXUlNgU89KioqYt26dZkuhog0YevWraOoqKjyhJJVSkqdeyaUDUb6q/170zxfAWw6FPjUo9atW7Ny5UrV+ohIRpSUlLBy5Upat1YPvw3NqzO/Y97y9QC0apbHL/btmeESNVzqx6cetWrVio0bN7Jw4ULatWtHy5Ytyc3NVf8LIlJn3J2SkhLWrVvHypUradGiBa1atcp0saQa3J07x8+Nzv9yv560bp6fwRI1bAp86pGZ0alTJ9auXcuaNWv4/vvvVfsjInUuNzeXoqIiOnToQKtWrfRnq4GZMHsZs75dA0Dz/BzO2L93hkvUsCnwqWdmRuvWrVXVLCIilXJ37oip7fnZj3vQvmWzDJao4VMbHxERkSw1df5KPlz4AwD5ucY5g/tkuEQNnwIfERGRLBXbtuekPbqxXZvCDJamcVDgIyIikoWmL17FpC+XA5BjcO6QvhkuUeOgwEdERCQLxdb2HDOwC706tMhgaRoPBT4iIiJZZvZ3a3nts6XR+fOHqbantijwERERyTKxtT2H7bQt/TvrTuDaosBHREQki8xbto6Xpn8Tnb/goH4ZLE3jo8BHREQki9w94StKPXg+ZIeODOy2TWYL1Mgo8BEREckSi1ZuYOzHS6LzF6q2p9Yp8BEREckS/3r7K4rD6p59+rRjUK92GS5R46PAR0REJAssXbOJpz9YHJ2/8KDtM1iaxkuBj4iISBa49+15bCkpBWD3HtuwX9/2GS5R46TAR0REJMOWr9vMY1MXRucvPKgfZpbBEjVeCnxEREQy7N+T5rFpa1Dbs9N2rRm2Y6cMl6jxUuAjIiKSQSvXb+GRd8tqey46eHvV9tQhBT4iIiIZdP/keWzYUgJA/86tOGynbTNcosZNgY+IiEiGrNqwhYemlNX2XHBQP3JyVNtTlxT4iIiIZMgD7yxg3eZiAPp1asmRP9ouwyVq/BT4iIiIZMCaTVt58J350fkLD+pHrmp76pwCHxERkQx46J0FrN0U1Pb06dCCYwZ2yXCJmgYFPiIiIvVs7aat3De5rLbn/GGq7akvCnxERETq2cPvLmT1xq0A9GhXxPG7qbanvijwERERqUfrNhfz70nzovMXDOtHfq5+juuLjrSIiEg9emjKAlZtCGp7urcrZPgeXTNcoqZFgY+IiEg9Wbe5mPtU25NROtoiIiL15OF3F/BDWNvTrW0hJ+7RLbMFaoIU+IiIiNSD9ZuL+ffbqu3JtKw44maWb2YHm9mtZvaemX1rZlvMbImZPWtmQ5PkG2NmnuLxRSX7Pc3MJpnZajNbZ2bTzOw3ZpYVx0VERBqPR95bqNqeLJCX6QKEhgBvhM+/Az4E1gM7AScBJ5nZ9e5+TZL87wBzEyz/NtkOzexO4HxgEzAO2AocDNwBHGxmp7h7SRqvRUREpJz1m4u5N6a25zfD+lGQp//YmZAtgU8p8Bxwm7tPil1hZj8BHgOuNrPx7j4+Qf773H1MVXdmZicRBD3fAYPd/ctw+bbAeGA4cAFwWxqvRUREpJyH313IyvVbAOi6TSEnqbYnY7Ii3HT3t9z95PigJ1z3FDAmnD29lnZ5RTgdFQl6wn0tBc4LZy/XJS8REampdZuLufftr6LzFxyk2p5MaihH/uNwWuMQ2cy6AXsCW4Bn4te7+0RgCdAZ2Kem+xMRkabtoSnl7+Q6eU/V9mRStlzqqsz24TRZm51hZjYQaAksBSYDb7h7aYK0u4fTz9x9Y5LtfQB0DdNOSa/IIiLS1K3dtLVc254LD9KdXJmW9YGPmXUGRoazzyVJ9ssEy2aZ2U/dfUbc8t7hdGGK3X4dl1ZERKTaxryzoNyYXLqTK/OyOuw0szzgUaANMM7dX4xL8glwEbAzQW1PF+AY4FOCO8LeNLP4vsBbhtP1KXa9Lpy2Sr/0IiLSlK3ZtLXcmFyq7ckO2V7jcw/BLeaLSNCw2d3/EbdoPfCymb0BTCRoo3MFwR1aERbJnm6hzOwc4ByAHj16pLsZERFpxB6YPJ81m4oB6NW+iOG7a0yubJC1oaeZ3QacSXDL+cHu/l1V87r7FuDGcPaouNVrw2lLkousW5topbvf6+6D3H1Qx44dq1osERFpIlZv3Mr9k+dH5y88aHvyVNuTFbLyXTCzWwkuYS0jCHq+rCRLIpFem+ND7AXhtGeKvN3j0oqIiFTZfZPmsTas7endoQXH79YlwyWSiKwLfMzsFuASYAVwqLvPSnNT7cPpurjlkVvjdzazwiR594pLKyIiUiUr12/hgZjant8erNqebJJV74SZ3QRcBvxAEPR8WoPNnRpOP4hd6O6LgI+AAuCUBGUYQtBf0HfAuzXYv4iINEH/evsr1m8JRjzavlNLjt1VtT3ZJGsCHzO7HhgFrCIIelLWtpjZbmZ2jJnlxi3PM7NLCC6VAfw9QfZI+5+bzaxfTN5OwF3h7E1J+gESERFJaNnazTw8pay3lIsP2YHcHEuRQ+pbVtzVZWbHAVeFs3OBC80SnihfuPtN4fNewFhgpZnNARYT3H6+C8Ft7aUEQ1K8Fr8Rd3/WzO4mGJ5ihpm9Sdkgpa2B5wkGKxUREamyuyd8xcatQW1P/86tOPJHnTNcIomXFYEP0C7m+aDwkchEIBL4fEowiOiPCRoq705wi/pi4EHgTnf/MNkO3f18M5sM/IZgdPhcggbRDwB3q7ZHRESq47vVm3h0alltzyWH7kCOanuyTlYEPuHI6mOqmWc+cHEN9/s48HhNtiEiIgJw5/i5bCkO/jMP7NaGQ3faNsMlkkSypo2PiIhIQ7X4hw08+cHX0flLDt2BJE02JMMU+IiIiNTQP8fNZWtJMCDAnj3bMmQHdW6brRT4iIiI1MD85et59qPF0flLVduT1RT4iIiI1MDf35hDSWlQ27Nf3/bs169DhkskqSjwERERSdMX363hxenfROd/f/iOGSyNVIUCHxERkTTd+vocPKjs4eD+ndijR9vMFkgqpcBHREQkDZ8sWsUbs5ZG5y85bIcMlkaqSoGPiIhIGm59fXb0+TEDt2PnLm0yWBqpKgU+IiIi1fTevBVM+nI5ADkGvztUtT0NhQIfERGRanB3/vJaWW3PSXt0o2/HlhkskVSHAh8REZFqeOuL7/lw4Q8A5OcaFx28fYZLJNWhwEdERKSKSkvL1/b8fO+edG9XlMESSXUp8BEREamiF6d/wxffrQWgqCCX3wzrl+ESSXUp8BEREamCrSWl/O2NOdH5M/bvTcdWzTJYIkmHAh8REZEqeHraIhau2ABAm8J8zh7cJ8MlknQo8BEREanEpq0l3D7uy+j8eUP70qYwP4MlknQp8BEREanEQ1MWsHTNZgA6tWrGiH17ZbZAkjYFPiIiIims3riVuyZ8FZ2/8ODtKSzIzWCJpCYU+IiIiKTwr4lfsXrjVgB6ti/iJ4O6Z7hEUhMKfERERJJYumYTD7wzPzp/6WE7UpCnn86GTO+eiIhIEreN+5JNW0sB2LlLa47ZZbsMl0hqSoGPiIhIAvOWreOpDxZF50cd0Z+cHMtgiaQ2KPARERFJ4NbX51BS6gDs17c9B27fIcMlktqgwEdERCTO9MWreHnGt9H5PxzRHzPV9jQGCnxERERiuDs3v/pFdP7IH3Vmt+7bZLBEUpsU+IiIiMR4+8vlvDN3BQC5OcbvD98xwyWS2qTAR0REJFRa6tz0v7LanlMHdadvx5YZLJHUNgU+IiIioec/WcLn364BoDA/l98dsn2GSyS1TYGPiIgIwUCkt74+Jzp/1oG96dS6eQZLJHVBgY+IiAjwyLsLWbJqIwDtWhRwzuA+GS6R1AUFPiIi0uSt3rCVO8bPjc5fdFA/WjXPz2CJpK4o8BERkSbvrolzyw1EetrePTNcIqkrCnxERKRJW7JqI2PeWRCd/70GIm3U9M6KiEiTdutrs9lcHAxEukvXNhytgUgbNQU+IiLSZM1cspqxnyyJzl951AANRNrIKfAREZEmyd258X+f48E4pBwyoBP79m2f2UJJnVPgIyIiTdKEOcvKDU1x+ZH9M1wiqQ8KfEREpMkpKXVueqVsaIqf7NWdfp1aZbBEUl8U+IiISJPz7IeLmL10LQBFBblcrKEpmgwFPiIi0qRs2FLM394oG5ri14P70qmVhqZoKhT4iIhIk3Lv2/NYumYzAJ1aNePswb0zXCKpTwp8RESkyVi6ZhP/mjgvOn/pYTtQVJCXwRJJfVPgIyIiTcZfX5vNxq0lAPTv3IqT9+ye4RJJfVPgIyIiTcJn36zm2Y8WR+evOnonctVZYZOjwEdERBo9d+fPr5R1Vjhsx44csH2HzBZKMkKBj4iINHrjZ39frrPCK48akOESSaYo8BERkUatuKSUG17+PDr/sx93Z/tt1VlhU6XAR0REGrXH3/+ar5atB6BlszwuPmSHDJdIMkmBj4iINFqrN2wt11nh+cP60qFlswyWSDItKwIfM8s3s4PN7FYze8/MvjWzLWa2xMyeNbOhleQ/zcwmmdlqM1tnZtPM7DdmlvL1pZtPREQahtvf+pJVG7YC0K1tIWfsr84Km7ps+YEfArwJXAL0BD4ExgIrgZOA8WZ2XaKMZnYn8BgwCJgEvAHsANwBPGtmubWZT0REGoZ5y9bx0JQF0fkrjxpA83x9tTd12RL4lALPAYPdfTt3P8bdf+LuuwA/BUqAq81sWGwmMzsJOB/4DhgY5hsObA98DgwHLojfWbr5RESk4fjzK19QXBrcv/7jXu048kedM1wiyQZZEfi4+1vufrK7T0qw7ilgTDh7etzqK8LpKHf/MibPUuC8cPbyBJeu0s0nIiINwDtzl/Pm50uj81cdMwAzdVYoWRL4VMHH4bRbZIGZdQP2BLYAz8RncPeJwBKgM7BPTfOJiEjDUFLqXP/SrOj8SXt0Y2C3bTJYIskmDSXw2T6cfhuzbPdw+pm7b0yS74O4tDXJJyIiDcBTHyzii+/WAlCYn8sfjtgxwyWSbJL1gY+ZdQZGhrPPxayKNM1fmCL713Fpa5JPRESy3OqNW/nr67Oj8+cO6cu2rZtnsESSbbI68DGzPOBRoA0wzt1fjFndMpyuT7GJdeE0tovOdPPFluuc8Nb3acuWLUuxGRERqU+3j/uSleu3ANB1m0LOGdwnwyWSbJPVgQ9wD3AwsIiKDZsjrdS8mttMN1+Uu9/r7oPcfVDHjh3T3YyIiNSir+JuX7/iqP4UFuj2dSkvawMfM7sNOJPglvOD3f27uCRrw2lLkousWxuzLN18IiKSxf700qxyt68fvct2GS6RZKOsDHzM7FbgImAZQdDzZYJkC8JpzxSb6h6Xtib5REQkS42f/T3jZwdND8zgmmN30u3rklDWBT5mdgtBD84rgEPdfVaSpJFb3Hc2s8IkafaKS1uTfCIikoW2lpSWu339J4O686OubTJYIslmWRX4mNlNwGXADwRBz6fJ0rr7IuAjoAA4JcG2hhD0+/Md8G5N84mISHZ6+N2FzAtHX2/VLI9LD9Pt65Jc1gQ+ZnY9MApYRRD0VKW25cZwerOZ9YvZVifgrnD2JncvraV8IiKSRZav28w/YkZfv/DgfnRspdHXJbm8TBcAwMyOA64KZ+cCFya5NvuFu98UmXH3Z83sboJhJmaY2ZvAVoI7wVoDzxMMOlpOuvlERCS7/OXV2azdXAxAnw4tGLmful+T1LIi8AHaxTwfFD4SmQjcFLvA3c83s8nAbwhGec8FvgAeAO5OVmuTbj4REckOny5axdMfLorOX3PsThTkZc2FDMlSWRH4uPsYygYiTSf/48Dj9ZVPREQyq7TUufaFz/CwR7ZDBmzL0B07ZbZQ0iAoNBYRkQbnPx8v4ZNFqwAoyM3h6mMGZLhE0lAo8BERkQZl7aat3PS/L6LzZw/uTc/2LTJYImlIFPiIiEiDcvu4L1m+bjMAnVs35/yh/SrJIVJGgY+IiDQYXy5dy4PvLIjOX3FUf1o0y4rmqtJAKPAREZEGwT1o0Bwdj6t3O47btUuGSyUNjQIfERFpEF6e8S1TvloBQG6Ocd3xO2s8Lqk2BT4iIpL11m8u5oaXP4/O/3LfnvTv3DqDJZKGSoGPiIhkvTvGz+Xb1ZsA6NCygIsP2SHDJZKGSoGPiIhkta+WreO+SfOi85cfOYA2hfkZLJE0ZAp8REQka7k7o1/4jK0lQYPmPXu25cTdu2a4VNKQKfAREZGs9b+Z3zHpy+UA5Bj833E7k5OjBs2SPgU+IiKSldZvLua6F2dF50/fpyc/6tomgyWSxkCBj4iIZKXbx33Jd2vKGjRfetiOGS6RNAYKfEREJOvMWbqW+yfPj85foQbNUksU+IiISFZxd65+fmZZD8292nHiHmrQLLVDgY+IiGSV/37yDVPnrwTCHppPUA/NUnsU+IiISNZYvXErf4rpoflX+/VSD81SqxT4iIhI1rj19dksX7cZgG1bN+PiQ9VDs9QuBT4iIpIVPl20ikfeWxidv/bYnWnZLC+DJZLGSIGPiIhkXEmp88fnZ+BBe2aG7NCRI3/UObOFkkZJgY+IiGTcI+8uYOaSNQA0y8vhuuPVoFnqhgIfERHJqKVrNvHX1+dE5y88qB8927fIYImkMVPgIyIiGXXdS7NYt7kYgL4dW3D24D4ZLpE0Zgp8REQkY8bP/p6Xp38bnf/TCbvQLC83gyWSxk6Bj4iIZMSGLcVc/fzM6PyJu3dl377tM1giaQqqHfiY2Twzu7kK6W40s6/SK5aIiDR2t437ksU/bARgm6J8/nj0gAyXSJqCdGp8egEdq5CuQ5hWRESknFnfrOG+SWWDkF551ADat2yWwRJJU1GXl7oKgeI63L6IiDRAJaXOlWNnUBIOQrp373acsme3DJdKmoo6CXzMrA2wP/BdXWxfREQarsemLuSTRasAKMjN4Ybhu6jPHqk3VeoL3MzmxS062cyGptjmtuH0/vSLJiIijc3SNZu45dXZ0fnzhvalX6eWGSyRNDVVHQSlV8xzB1qGj2S2AM8Do9IrloiINEbX/HdmtM+ePh1acN7QvhkukTQ1VQ18eodTA+YBzwKXJUm7BVjm7mrfIyIiUa/O/I7XPlsanb9h+C40z1efPVK/qhT4uHt0uFwzewiYFLtMREQklTWbtnLNf8v67PnpXt3VZ49kRFVrfKLc/Vd1URAREWm8bv7fF3y/djMAHVo244oj1WePZIZ6bhYRkTr1/vyVPDb16+j8/x23M22K8jNYImnKql3jA2BmrYHfAAcDXYDmSZK6u6vlmohIE7W5uIQr/jM9On/IgE4ctUvnDJZImrpqBz5m1h2YBHQnaOyciqdTKBERaRzufGsuXy1bD0CLglyuO/5H6rNHlastCgAAIABJREFUMiqdGp8/Az2Aj4CbgS+ANbVZKBERafg+/3YNd00oG7LxD0f0p8s2hRkskUh6gc9hBD0yD3P3tbVcHhERaQSKS0oZ9dx0isNhKQb1bMsv9umZ4VKJpNe4uTXwroIeERFJ5oF35jN98WogGJbippMGkpOjS1ySeekEPgsANccXEZGEFixfz62vz4nO//aQ7TUshWSNdAKfR4EhZqaep0REpJzSUmfUc9PZXFwKwIDtWnPO4D4ZLpVImXQCn5uB94FXzGynWi6PiIg0YE9+sIip81cCkJtj/OXkgeTnqss4yR6VNm42s7cSLM4H9gKmm9nXwNdAaYJ07u4H16yIIiLSECxZtZE/v/J5dP7sA/vwo65tMlgikYqqclfX0BTrcghGbu+VZL368RERaQLcnSv+M6PcyOsXH7J9hkslUlFVAp9hdV4KERFp0J75cDFvz1kGgBn85ZSBGnldslKlgY+7T6yPgoiISMP03epNXP/SrOj8r/brzZ4922WwRCLJqcWZiIikzd3549gZrN0UXOLq2b6Iyw7fMcOlEklOgY+IiKTt+U+WMO6L76PzN580kMICXeKS7JXOIKWJ7vJKZAuwHPgQeMLdv6tkuzsCRxDcLTYI2IFgENRT3P3ZJHnGACNSbHa2u/dPsc/TgPOAgUAuwbhjDwJ3u3uiu9RERCT0/ZpNjH6h7BLXL/ftyT591MWbZLd0xuoaGk6d5KOzx677GXCDmV3g7g+k2O55wG/TKA/AO8DcBMu/TZbBzO4Ezgc2AeOArcDBwB3AwWZ2iruXpFkeEZFGzd25cuwMVm/cCkC3toWMOiLp/0yRrJFO4DMMOA74HTAVeAJYSNCPTy+CQGcf4B8EtT0HASOBf5nZ5+7+bpLtzgT+AkwL890PDKlime5z9zFVfQFmdhJB0PMdMNjdvwyXbwuMB4YDFwC3VXWbIiJNyX8+WsKbn5dd4vrLybvSolk6Pyki9Suds7QEuBC4yN3vSLD+n2Z2PkHQcJC7n2lmkwkCmd8CCQMfd78vdt6sTgezuyKcjooEPWEZlprZecAE4HIz+6cueYmIlPfd6k2MfvGz6PyIfXuyb19d4pKGIZ3GzVcDnyUJegBw97sIanCuCucfBOYD+6dTyNpkZt2APQnaID0Tvz68fX8J0Jmg5kpERELuzuX/mR69i6tHuyJGHalLXNJwpFPjsxfwShXSfQYcFTM/Czg0jf1VxTAzGwi0BJYCk4E3ktTW7B4pn7tvTLK9D4CuYdoptV1YEZGG6plpi5kwu6yjwr+esitFBbrEJQ1HOmdrAdCjCul6EIzpFbER2JzG/qrilwmWzTKzn7r7jLjlvcPpwhTb+zourYhIk7f4hw1cF9NR4cj9evHj3uqoUBqWdC51TQf2M7OktTdmdgjBZa3pMYu7A8vS2F8qnwAXATsT1PZ0AY4BPgV2At40s65xeVqG0/UptrsunLZKtNLMzjGzaWY2bdmy2n5JIiLZp7TUueyZ6dGxuHp3aMEfDtclLml40gl8bg3zvWhm/zKzoWbW28x6mdkQM7sHeDFM+zcAM2tDcNloaq2UOuTu/3D3f7r7LHdf7+7fuvvLwI+B94BOlDVkjoi0mk57AFV3v9fdB7n7oI4dO6a7GRGRBmPMlAW8O28FADkGt566qzoqlAap2pe63P05M7sKuA44K3zEMoJb26919+fCZZ0IblWvStugGnP3LWZ2I/BfyrczAlgbTluSXGTd2hRpRESahLnfr+PmV7+Izp87pC979GibwRKJpC+tFmnu/mcze5Wgr5vBBA2BAb4B3gbudPdpMem/JLgbrD5FPqXxl7oWhNOeKfJ2j0srItIkFZeUcukzn7K5OLhXpH/nVvz2kO0zXCqR9KXdFN/dPwLOqMWy1LZIpxLr4pZ/HE53NrPCJHd27RWXVkSkSbp7wld8umgVAPm5xt9/shvN8nSJSxquxjxI6anh9IPYhe6+CPiI4O60U+IzmdkQoBtBr87JepkWEWn0ZixezW3jon28cvEhOzBgu9YZLJFIzTXYwMfMdjOzY8wsN255npldQnC3F8DfE2S/MZzebGb9YvJ2Au4KZ29Sr80i0lRt2lrCxU99THFpcB/I7j224deD+2S4VCI1V+mlLjN7gOAOqCvDIR1SDTQaz939zKokNLM9KAs6ILgdHeDPZvb7mA1GelPuBYwFVprZHGAxwe3nuxDc1l5KMCTFawkK9ayZ3U0wMOoMM3uTskFKWwPPEwxWKiLSJN30vy/4alnQ60dRQS5/P3U38nIb7H9lkaiqtPEZSRD43EzQK/LIamzfgSoFPgQBx94JlidrRff/7d13dFzVucbh36duq7jKvRewDTaWKwSCAZPkBhxCMx1CC1wMBG4CSQgJuaQB6QTTm6khAQIEyIUAwaYX94Y7tmW5F8mS1TX7/jGjsSRLsjUa6czMeZ+1Zh1O9TeHbfnVKXsvIjge2CSCDyrnhf68TcDjBB+wntdkYc7NCI0hdi3BwVCTCT4Q/Rhwv672iIhfvb96B7M+Wh+e/9m0UQzqnuldQSJRdCjB57LQdEuD+ahyzs1mfx87h7L9l8CNrfwznwWebc0xREQSSWFpJTc9vyg8P3VED86b2L+ZPUTiy0GDj3PuiebmRUQkMTjn+OnLS9m2Nzi6ULfMNO48awxmh/w7qUjM0w1bEREB4OWFBby2eEt4/o4zR5Obne5hRSLR16ohdUNDUUwEcoENzjmNZC4iEofyd5fys5eXhefPndCfrx/Ry8OKRNpGRFd8zKxT6O2u7cCbwNPUGbrCzGaY2WYzO7qpY4iISGyorgnwP39bGB6AdFC3jtz2rVEH2UskPrU4+JhZJjCb4Ntde4D/48CHkt8AegGnt648ERFpa/fNXsvcDXsASE4y/nxeHpnprbohIBKzIrnicxNwFMGrPEOcc9MabuCcWwesAk5qXXkiItKWFmzcU7935qnDGdu/s4cVibStSILPdIKDkX7XOVfazHYbOXCAUBERiRElFdXc+LeF1IR6Z544qAszThx2kL1E4lskwWcI8LlzruIg2+1k/0ChIiISY257ZSkbdgV/f81OT+GP54wlOUmvrktiiyT4VAEZh7BdPw4cGV1ERGLAKwsL+Mf8gvD8L08/kv5dO3pYkUj7iCT4rATyzKzJ8GNmXQg+B7Qk0sJERKRtbNxVyq0vLQ3Pn5nXl9Pz9GSC+EMkwecFoAdwZzPb/AbIAv4eSVEiItI2qmoCfO+5BeFX1wd268gvTj/S46pE2k8k7yvOBL4DXG9mE4B/hJYPMrNrCD78PIXg1Z5Ho1KliIhExZ/fXsXC/EIAUpKMv5yXR5ZeXRcfaXFrd86VmtnXgeeBrwDHhFZNCX0MmAec7pyrjFahIiLSOh+t3cl9s9eG53/w9cM5Sq+ui89EFPOdcwXAV8zsv4BTCL7plQzkE+zQ8GXnnItalSIi0iq7Siq48bmF1P5kPnZYN64+foi3RYl4oFXXN51zbxDspVlERGJUIOD4wfOL2F68f9T1P54zliS9ui4+pNHZRUQS3KMffMnslTvC83845yh65hxKryQiiae1o7MnE+yksMm/Qc65ja35M0REJHIL8wu5640V4fmrjx/CCYf38LAiEW9FFHzMbDLwC+CrQHozm7pI/wwREWmdveVVXP/X+VSHhqQY278zN33jcI+rEvFWi0OJmR0LvM3+wLMH2BvNokREpHWcc/z4xcXk7y4DIDsjhXvOzyM1WU84iL9FcjXmdoKh52Hgp865HQfZXkRE2tlTn2zgX0u2hufvPHOMhqQQIbLgMwn4wjl3dbSLERGR1luyqYhfvfZFeP7iowdy6pjeHlYkEjsiueZpwOJoFyIiIq23t7yKa5+dT2VNAIAj+uRw66kjPa5KJHZEEnyWAL2iXYiIiLRO7XM9G3eXApCVnsK9F4wjIzXZ48pEYkckwedu4KtmNjbaxYiISOSe/LjBcz1njWZQ90wPKxKJPS0OPs65vwG/Bt4ys2vMbED0yxIRkZZYmF/Ir15fHp6/+OiBTBvTx8OKRGLTQR9uNrOaZlbPBGaaNdntuXPOqR8fEZE2tGdfJdc+M5+qmmB/PUf21XM9Ik05lFDSmsFcNBCMiEgbCgQc//P3hRQUBvvryclI4f4Lx+u5HpEmHDT4OOfU25WISIy6b/aaBuNwjVV/PSLNUKgREYlTH63ZyR/fWhWev3rKEL42qqeHFYnEPgUfEZE4tKWojOv/uoDQMFxMGtyVm7+ucbhEDkbBR0QkzlRWB5jxzHx27asEoHtWOjPPzyNF43CJHJT+loiIxJlfvb6cBRsLAUhOMmZekEePnAyPqxKJDwo+IiJx5B/zN/HkxxvC87d8cwRHD+nmYUUi8UXBR0QkTizfvJefvLQkPH/q6N5ccdxgDysSiT8KPiIicaCwtJL/fnoe5VXBwUeH5mZy19ljaKYDWRFphIKPiEiMqwk4bnhuYXjw0cy0ZB68eDxZ6eoYX6SlFHxERGLcH99ayZxV+zsp/P30oxjWI9vDikTil4KPiEgMe2PpFu59d214/toTh/LN0b09rEgkvin4iIjEqNXbivnB3xeF56cclsv3v6ZOCkVaQ8FHRCQGFZVVcfVT89hXWQPAgK4d+ct5eSQn6WFmkdZQ8BERiTHBh5kXsG7nPgA6pAYfZu7UMdXjykTin4KPiEiM+d2bK+uNuP676WMY2TvHw4pEEoeCj4hIDHllYQEPzKn/MPO0MX08rEgksSj4iIjEiCWbivjhC4vD81NH9OAHephZJKoUfEREYsD24nKufmouFdX7e2b+03ljSdLDzCJRpeAjIuKx8qoarn5qHpuLygHIzkjh4UsmkJOhh5lFok3BR0TEQ845fvLSEhZsLAQgyeCe8/MYkpvlcWUiiUnBR0TEQw++t45/zC8Iz9966ihOOLyHhxWJJDYFHxERj7y9fBt3vbEiPH/uhP5cfuwg7woS8YGYCT5mdriZ3WBmT5vZCjMLmJkzs7MPYd8LzOx9MysysxIzm2tm15pZs98v0v1ERFprxda93PDcApwLzk8a1JVfnn4kZnqYWaQtpXhdQB3XADe0dCczuxeYAZQD7wBVwFRgJjDVzKY752qitZ+ISGvtKK7gillzw8NR9O3cgfsvGkdain7nEmlrsfS3bCnwO+BcYBgw52A7mNlZBMPLVmCMc26ac+4MYDjwBXAGcF209hMRaa3yqhq+++RcCgrLAMhMS+bRSyfQLSvd48pE/CFmgo9z7hHn3A+dc393zq09+B4A3BKa/sg5t7rOsbYRvIIE8ONGbl1Fup+ISMScc9z0/CIW5u9/g2vmBeMY0UvDUYi0l7j9h93M+gHjgUrg+YbrnXNzgAKgF3B0a/cTEWmtP729mtcWbwnP/2zaKE4coTe4RNpT3AYfIC80XeacK2tim88bbNua/UREIvbSgk385Z3wBWYuPnogl35lkHcFifhUPAefwaHphma22dhg29bsJyISkU/W7ao3Btfxh+Xy82+N0htcIh6I5+BT263pvma2KQlNs6OwX5iZXRV69X3ujh07DlqoiPjXmu0lXP3UPKpqgu+tH9Yzi5kX5JGSHM8/fkXiVzz/zav9Vcm1035hzrmHnHMTnHMTcnNzIz2MiCS4nSUVXDbrM4rKqgDIzU7n8csmaQwuEQ/Fc/ApDk2bG9Cmdl1xnWWR7icicsjKq2q48om55O8OPkrYITWZx74zkb6dO3hcmYi/xXPwWR+aDmxmm/4Ntm3NfiIih6Qm4LjxuYXh19bN4C/n5zG6XyePKxOReA4+C0LTI8ysqV+hJjbYtjX7iYgclHOOX762nDeWbQ0v+/m0UXxtVE8PqxKRWnEbfJxz+cB8IA2Y3nC9mU0B+hHsnfnj1u4nInIoHnn/S2Z9tD48f8Vxg7n0WL0gKhIr4jb4hNwRmt5lZsNqF5pZD+C+0OydzrlAlPYTEWnSPxdt5tf/+iI8f+qY3tx6ykgPKxKRhsy5iF9uiiozG8f+0AEwiuDr5KuB3bULnXNHN9jvPoLDTJQDb7N/sNEc4GXg7CYGKY1ov4YmTJjg5s6de8jfU0QS0yfrdnHJo59RWRP8fWnSoK48ecUkMlKTPa5MJPrMbJ5zboLXdUQilkZnzwEmN7J8eHM7OedmmNkHwLXAFCAZWAE8Btzf1FWbSPcTEWnoiy17+e4Tc8OhZ1iPLB66ZLxCj0gMipng45ybzf4+dlq677PAs+21n4hIrfzdpXznsc8orqgGoEd2OrMum0jnjmkeVyYijYn3Z3xERDyze18l33nsM7YXVwCQnZ7CE5dPol+Xjh5XJiJNUfAREYlAaWU1l836nHU7g6PfpCUn8dAlExjZO8fjykSkOQo+IiItVFkdYMYz81lUp4PCP583lmOGdvO4MhE5GAUfEZEWCAQcNz2/iNkr9w9Q/IvTjuCU0b09rEpEDpWCj4jIIXLOcfury/jnos3hZdefNIyLjxnkXVEi0iIKPiIih+jPb6/miY83hOcvOnoA3//aYR5WJCItpeAjInIIZn34JXe/szo8P21Mb24/7UjMIuqFQ0Q8ouAjInIQL87bxP++ujw8f/xhufzxnLEkJyn0iMQbBR8RkWa8sXQLN7+wKDyfN6AzD1w0jrQU/fgUiUf6mysi0oT3Vu3g+r8uIBAa0nBEr2xmXTqJjmkx0+m9iLSQgo+ISCPmrt/NVU/NpaommHoGd8/kqSsm06ljqseViUhrKPiIiDSwZFMRlz3+OeVVwUFH+3TK4OkrJ5Obne5xZSLSWgo+IiJ1fLFlLxc/9ml40NHuWWk8feVk+nbu4HFlIhINCj4iIiFrthdz0SOfUlhaBUDnjqk8dcVkhuRmeVyZiESLgo+ICLB+5z4uePhTdu2rBIIjrT91+WQNOiqSYBR8RMT38neXcuEjn7K9uAKAjmnJzLp8IqP7dfK4MhGJNgUfEfG1TXtKOf/hTygoLAMgIzWJxy6dyPiBXT2uTETagoKPiPjW5sIyzn/4EzbtCYaetJQkHrp4AkcP6eZxZSLSVhR8RMSXthQFQ0/+7lDoSU7iwYvHc/xhuR5XJiJtScFHRHxn295yLnj4UzbsKgUgNdm4/6JxnHh4D48rE5G2pn7XRcRXthSVcf5Dn7C+Tui578LxTB3Z0+PKRKQ9KPiIiG/UPtNTe6UnJcm45/xxfG2UQo+IXyj4iIgvFBQGr/Rs3L3/Ss/MC8bxjSN6eVyZiLQnBR8RSXj5u0vrvb2Vmmzcf+F4TtaVHhHfUfARkYT25c59XPjwJ2wuKgeCb289cPE4Thqh0CPiRwo+IpKwVm8rrtcjc1pK8JV1vb0l4l8KPiKSkJZv3svFj+4feysjNYlHLpnIccO7e1yZiHhJwUdEEs7iTYVc/OhnFJUFR1nPTEvmsUsnMlk9Mov4noKPiCSUT9ft4oon5lJSUQ1AdkYKT1w+iXEDunhcmYjEAgUfEUkY767czn8/NY+K6gAAnTum8tTlkzXKuoiEKfiISEJ4ffEWbvzbAqpqHAC52ek8fcVkDu+V7XFlIhJLFHxEJO79fW4+P35xMYFg5qFv5w48c+VkBnXP9LYwEYk5Cj4iEtcenLOWO/5vRXh+aG4mT185md6dOnhYlYjEKgUfEYlLzjnufGMFD85ZF142qncOT14xie5Z6R5WJiKxTMFHROJOdU2AW19ayt/m5oeXTRrclUe+M4GcjFQPKxORWKfgIyJxpbyqhu/9dQH/Xr4tvOzkkT2ZeUEeGanJHlYmIvFAwUdE4kZhaSVXPjGXuRv2hJedPb4fd545mpTkJA8rE5F4oeAjInFhc2EZ33nsM1ZvLwkvu+r4IdzyzRGYmYeViUg8UfARkZi3alsxlzz6GVv3loeX/fTUkVz51SEeViUi8UjBR0Ri2ifrdnHVk3PZWx4cgiI12fj99KP49ti+HlcmIvFIwUdEYtYrCwu46flF4d6YM9OSefDiCRphXUQipuAjIjHHOcd9s9fyuzdXhpflZqfz+KUTObKvxt0Skcgp+IhITKmqCXDbK8v462cbw8uG98ji8csm0q9LRw8rE5FEoOAjIjFjb3kV1z4zn/dX7wwvO2ZINx64eDydOqhjQhFpPQUfEYkJ+btLuXzW5/VeVz8jry93nTWGtBT10SMi0aHgIyKem79xD1c9OZedJZXhZTdMHc6NJw9XHz0iElUKPiLiqX8u2szNzy+iojoAQFpyEr89ewyn5+l1dRGJPgUfEfFEIOD409uruOc/a8LLunRM5aFLJjBxUFcPKxORRBb3N87NbJaZuWY+K5rZ9wIze9/MisysxMzmmtm1Zhb350UklpVWVjPjmfn1Qs+Q3ExemnGsQo+ItKlEuuLzIbCmkeVbGtvYzO4FZgDlwDtAFTAVmAlMNbPpzrmaNqpVxLcKCsv47hNzWb5lb3jZ8Yflcs/5eXpzS0TaXCIFn0ecc7MOZUMzO4tg6NkKHO+cWx1a3hN4FzgDuA64u21KFfGnT9ftYsYz89m1b/9DzJcfO5ifnDJCo6uLSLvw60+aW0LTH9WGHgDn3DbgmtDsj3XLSyQ6nHM89fF6Lnzk03DoSUky7jxzNLd9a5RCj4i0m0S64nNIzKwfMB6oBJ5vuN45N8fMCoC+wNHAR+1boUhiqaiu4eevLOO5z/PDy7pnpXHfheOZNFjP84hI+0qk4HOimY0BsoBtwAfAW865QIPt8kLTZc65siaO9TnB4JOHgo9IxLYWlXPNM/NYsLEwvGx03048ePF4+nTu4GFlIuJXiRR8Lmlk2XIzO885t6TOssGh6YZmjlU7SNDgZrYRkWZ8sm4X1z07v16nhGfk9eWOM0eTkZrsYWUi4meJEHwWAvMIvpm1AcgBxgG/Bo4C3jazcc65gtD2WaHpvmaOWdtnfnb0yxVJbM45Hv3gS+74vxXUBBwAyUnGLd8cwRXHDVZPzCLiqbgPPs65PzdYtA943czeAuYQfE7nFoJvaQHU/tR1kf6ZZnYVcBXAgAEDIj2MSMIpqajmRy8u5vXF+3uR6J6Vxj3nj+OYod08rExEJChhX6VwzlUCd4RmT6mzqjg0zaJpteuKG1vpnHvIOTfBOTchNze3dYWKJIiVW4s5beYH9UJP3oDOvHr9cQo9IhIz4v6Kz0HU9tpcd9Cf9aHpwGb2699gWxFpxj/mb+InLy2hvGr/uwQXHT2An00bRXqKnucRkdiR6MGn9tfMkjrLFoSmR5hZhybe7JrYYFsRaUR5VQ23v7qMv362/1X1DqnJ3HnWaL49VoOMikjsSfTgc05o+nntAudcvpnNJ/gA9HTgybo7mNkUoB/BXp0/bqc6ReLOmu3FXPvMAlZu239HeGhuJg9cNJ7hPfVegIjEprh+xsfMxprZNDNLbrA8xcy+D3wvtOhPDXatffbnLjMbVme/HsB9odk7G+kDSESAF+Zt4lv3fFgv9Jx2VB/+ed1xCj0iEtPi/YrPIOAlYLeZrQI2EXwFfTTQBwgQHJbizbo7OedeMLP7CQ5PscTM3mb/IKU5wMsEBysVkTpKKqq57eWl/GNBQXhZekoS/3vaEZw3sb9eVReRmBfvwWcRwYFEJxF8WDmP4Gvqm4DHgXudc/Ma29E5N8PMPgCuBaYAyQQfhn4MuF9Xe0TqW5RfyPeeW8CGXaXhZUNzM7n3wnGM6JXjYWUiIocuroOPc+5L4MZW7P8s8Gz0KhJJPIGA48H31vGHf6+kOrC/+6uzxvXjl6cfQce0uP4xIiI+o59YItKkLUVl3PT8Ij5csyu8LCs9hV+dfiSn5+mtLRGJPwo+ItKo1xZv5taXllJUVhVeNrZ/Z/5yXh4DunX0sDIRkcgp+IhIPXvLq/j5K8t4qc4DzGYw44Sh3HjyYaQmx/XLoCLicwo+IhL20dqd3Pz8YgoK9/fr2bdzB/507lgmDe7qYWUiItGh4CMilFXWcNcbK5j10fp6y88c15f/Pe0IcjJSvSlMRCTKFHxEfG7+xj3c9PdFrNu5L7ysU4dUfnPGaE4d09vDykREok/BR8Snyqtq+NPbq3j4vXXUeUudk0b04I4zR9MzJ8O74kRE2oiCj4gPzduwm5tfWMy6Hfuv8mSlp3DbtFFMn9BPPTCLSMJS8BHxkdLKan735kpmfbQeV+cqz1eGduO3Z4+hXxe9pi4iiU3BR8Qn3lu1g5+8tIRNe/a/sZWVnsJPThnJ+ZM0zpaI+IOCj0iC272vkl+9trzewKIAUw7L5Y4zR9OncwePKhMRaX8KPiIJyjnHywsL+OVrX7B7X2V4eacOqfxs2ijOGtdXV3lExHcUfEQS0NodJfz0paV8vG5XveWnHdWH2741iu5Z6R5VJiLiLQUfkQRSXlXDfe+u4YE566isCYSX9+mUwa/PGM2JI3p4WJ2IiPcUfEQSxH9WbOP2V5ezYVdpeFlyknH5sYO48eTDyEzXX3cREf0kFIlzG3eVcvury3hnxfZ6y/MGdObXp49mVJ8cjyoTEYk9Cj4icaqssob756zlgTlrqazef1urU4dUbv7G4VwwaQBJSXp4WUSkLgUfkTjjnOPVxVu4419fsKWoPLzcDM6d0J8f/tcIumameVihiEjsUvARiSNLNhVx+6vLmLthT73lY/p14hffPpKx/Tt7VJmISHxQ8BGJA5sLy/j9mysP6ISwe1YaN3/jcM4e359k3dYSETkoBR+RGFZSUc0Ds9fy8PvrqKjzHE9qsnHZsYO57qRh5GSkelihiEh8UfARiUFVNQGe+2wjd7+zmp0llfXWnTyyJ7eeOpLB3TM9qk5EJH4p+IjEkEDA8fqSLfzh3ytZX6c/HoAj++Zw6ymjOGZoN4+qExGJfwo+IjHAOcf7q3fyuzdXsqSgqN663p0yuPkbh3P62L56PV1EpJUUfEQ89tmXu/n9myv5bP3uestzMlK49sRhfOcrg8hITfaoOhGRxKLnz+epAAAQ/0lEQVTgI+KRhfmF/PGtVby3ake95ekpSVx27GCumTKUTh314LKISDQp+Ii0s4X5hdz99ireXVk/8KQkGedO7M/1Jw2nV6cMj6oTEUlsCj4i7WT+xj3c887qAwJPksEZef248eTh9O/a0aPqRET8QcFHpA055/ho7S5m/mcNH6/bVW+dGZx2VB+uP2k4w3pkeVShiIi/KPiItIFAwPHOiu3c++4aFuYX1luXFAo81ynwiIi0OwUfkSiqqK7h5QUFPPTeOtbu2FdvXXKS8e2xfZhxwjAFHhERjyj4iERBUWkVz362kcc//JLtxRX11qUlJzF9Qj/+e8pQPcMjIuIxBR+RVli3o4THP1zPC/M2UVZVU29dVnoKF04ewOXHDaZnjt7SEhGJBQo+Ii0UCDg+WLOTJz5az39Wbse5+ut7ZKdzxXGDOX/yAA0gKiISYxR8RA5RcXkVL87bxJMfb2Ddzn0HrB/RK5srjhvMaWP7kJ6inpZFRGKRgo/IQSwtKOKZTzfyysICSitrDlg/dUQPrjhuMMcM7YaZxtISEYllCj4ijdhXUc3ri7fwzKcbWLSp6ID12ekpnD2hH5ccM4jB3TM9qFBERCKh4CMS4pxj/sZC/v55Pq8t3sy+Rq7uDO+RxSVfGcSZeX3JTNdfHxGReKOf3OJ72/aW8/KCAl6Yt4nV20sOWJ+WnMQpo3tx4dEDmTCwi25niYjEMQUf8aXSymr+vWwbL87fxIdrdhJwB24zNDeT8yYO4Kzx/eiamdb+RYqISNQp+IhvVNUEeH/1Dl5ZuJl/L9t2QL87AB3Tkpk2pjfnTuzPuAG6uiMikmgUfCShVdcE+HjdLv61ZAtvLN3KntKqA7Yxg2OGdOPMcf34ryN7kaVnd0REEpZ+wkvCqawO8NHanbyxdCtvLms87AAM65HF6WP7cMa4fvTt3KGdqxQRES8o+EhCKKmoZvbK7by5bBuzV2ynuKK60e36du7AtKN68+2j+jKyd7ZuZYmI+IyCj8StjbtKeWfFNv6zYjufrNtFVU0jTygDvXIyOGV0b04d04u8/l1ISlLYERHxKwUfiRvlVTV8+uVu5qzcwZxV21m748BhI2r169KBbxzRi1NGK+yIiMh+Cj4SswIBx/Ite/lwzU4+WLOTz77cTUV1oMntR/XO4etH9OTro3rpNpaIiDRKwUdiRiDgWLW9mE/X7ebTL3fx8dpdTT6YDJCeksRxw7pz0sgenDSiB7076QFlERFpnoKPeKaiuoalBXuZv2EPn6/fzefrdzcbdCDYqeCUw3ow5fBcJg/uSkaqRkEXEZFD5/vgY2YXANcAY4BkYAXwOHC/c67p+yrSIs45Nu0pY9GmQhblF7JgYyGLC4qobObWFUD3rDSOGdqd44Z14ytDu9O/a8d2qlhERBKRr4OPmd0LzADKgXeAKmAqMBOYambTnXMHdu8rzXLOUVBYxtKCvSzbXMTSgiKWFBSxs6TyoPt2y0xj0uCuTB7claOHduPwnnpWR0REose3wcfMziIYerYCxzvnVoeW9wTeBc4ArgPu9qzIOFBUVsWa7SWs2lbMii17+WJrcLq3vPF+dBoa1K0j4wZ2YfzALkwa1JVhPbIUdEREpM34NvgAt4SmP6oNPQDOuW1mdg0wG/ixmd3j91te1TUBCgrLWLdzH+tDnzU7Sli9rYTtxRWHfJzs9BTG9O/EUf06c1T/zowb0IXc7PQ2rFxERKQ+XwYfM+sHjAcqgecbrnfOzTGzAqAvcDTwUftW2L6qagJsLSpnS1E5mwvL2FxURv7uMvJ3l5K/p5SCPWVUNzZ8eTNyMlI4sm8njuiTE5p2Ykj3TPWnIyIinvJl8AHyQtNlzrmyJrb5nGDwySPOgk8g4Cgur6awrJKisir2lFaxe18Fu0oq2bWvkp3FFWwPfXYUl7NrXyWuZbkmLC05iSG5mQzrkcXI3jmM7J3NiF459O6UoVtWIiISc/wafAaHphua2WZjg23bVE3A8dB763A4nAuGl4CDgHNUBwJU1TiqagJU1QQorwpQVlVDRVUN5VUBSiqq2VdRTUmdT6RBpik9stMZ3D2z3md4z2z6d+lASnJSdP8wERGRNuLX4JMVmjY95gGUhKbZbVwLEHwT6q43VrTHH3UAM8jNSqdP5w706ZxB704d6N+lA/27dqR/147069KBjml+bSoiIpJI/PqvWe09mIiui5jZVcBVAAMGDIhKQUlRvi2UnZ5CTodUOnVIpXPHVLplpdMtM42umWl0y0qjR3YGPbLT6ZmTQbesNFJ11UZERHzAr8GnODTNamab2nXFDVc45x4CHgKYMGFCVG4qmcHVxw/BzEiyYBAyAzMjNclITUkiNTmJ1GQjIyWZ9NQkOqQmk5GaTGZ6MlnpqWSmJ5Mdmur2k4iIyIH8GnzWh6YDm9mmf4Nt25SZccspI9vjjxIREfEtv14WWBCaHmFmTY1sObHBtiIiIhLnfBl8nHP5wHwgDZjecL2ZTQH6EezV+eP2rU5ERETaii+DT8gdoeldZjasdqGZ9QDuC83e6fdem0VERBKJX5/xwTn3gpndT3Bk9iVm9jb7BynNAV4mOFipiIiIJAjfBh8A59wMM/sAuBaYAiQDK4DHgPt1tUdERCSx+Dr4ADjnngWe9boOERERaXt+fsZHREREfEbBR0RERHxDwUdERER8Q8FHREREfEPBR0RERHxDwUdERER8Q8FHREREfEPBR0RERHxDwUdERER8Q8FHREREfEPBR0RERHzDnHNe1xDXzGwHsCGKh+wO7Izi8fxE5y4yOm+R0XmLjM5bZGLtvA10zuV6XUQkFHxijJnNdc5N8LqOeKRzFxmdt8jovEVG5y0yOm/Ro1tdIiIi4hsKPiIiIuIbCj6x5yGvC4hjOneR0XmLjM5bZHTeIqPzFiV6xkdERER8Q1d8RERExDcUfNqQmV1gZu+bWZGZlZjZXDO71swiOu/RPl4si9Z3NbNZZuaa+axoq+/QXszscDO7wcyeNrMVZhYIfbezW3nchG5v0T5vfmhrAGaWamZTzewPZvaJmW0xs0ozKzCzF8zshFYcO2HbXFucN7+0uWhL8bqARGVm9wIzgHLgHaAKmArMBKaa2XTnXI1Xx4tlbfRdPwTWNLJ8S2tqjRHXADdE84A+aW9RP28hidzWAKYAb4X+eyswD9gHjALOAs4ys186525ryUF90Oba5LyFJHqbiy7nnD5R/hBsxI5goxteZ3lPYHlo3Q1eHS+WP21w7maF9rnU6+/WhufsSuC3wDnAUGB26DufHQv/D2L10wbnLeHbWuh7ngS8AHy1kXXnAtWh83BiC46Z8G2ujc6bL9pc1P9feF1AIn6AuaHGeEkj66bU+Que5MXxYvnTBufOdz8YovAPuG/aW5TPm+/aWhPn4ZHQeXi0Bfv4ss1F4bypzUXwifv7prHGzPoB44FK4PmG651zc4ACoBdwdHsfL5b56bvGKv0/kChYEJr2O5SN1ebCWnTeJHJ6xif68kLTZc65sia2+RzoG9r2o3Y+Xixry+96opmNAbKAbcAHwFvOuUCkxSYoP7W3tuL3tjY8ND3U50vU5oJaet7q8nubaxEFn+gbHJo2N3DpxgbbtufxYllbftdLGlm23MzOc84taeGxEpmf2ltb8W1bM7NewKWh2RcPcTfft7kIz1tdvm1zkdCtrujLCk33NbNNSWia7cHxYllbfNeFwPeAI0LH7wNMAxYRfJvibTPr2/JSE5af2lu0+bqtmVkK8DTQCXjHOffqIe7q6zbXivMGPm9zkdIVn+iz0DRaXWJH+3ixLOrf1Tn35waL9gGvm9lbwByCzwzcAlwXrT8zzvmpvUWV2hoPEHz9PB+4qAX7+b3NRXre1OYipCs+0VccmmY1s03tuuJmtmmr48WydvuuzrlK4I7Q7CmtOVaC8VN7axd+aGtmdjdwBcH+aaY657a2YHfftrlWnrcm+aHNtYaCT/StD00HNrNN/wbbtufxYtn60LS9vmttr6a6FLzf+tDUD+2tPSVsWzOzPxC83bKD4D/eq1t4iPWhqa/aXBTO28EkbJtrLQWf6Kt9JfEIM+vQxDYTG2zbnseLZe39XbuFpiXNbuUvfmpv7Skh25qZ/Rb4PrAL+JpzbnkEh/Fdm4vSeTuYhGxz0aDgE2XOuXxgPpAGTG+43symEOynYSvwcXsfL5Z58F3PCU0/j8KxEoKf2ls7S7i2ZmZ3AjcDewj+470okuP4rc1F67wdgoRrc1HjdQ+KifgBzmZ/T6PD6izvASyjke7XCd6PXQHcEY3jxesnmucOGEvwDYfkBstTCP62VRM63je8/t5RPoezOUgPxGpv0T1vfmtrwC9D32cPMP4Q9/F9m4vmefNbm4vmR291tQHn3Atmdj/BQRCXmNnb7B9wLwd4meDAe3X1Bg4PTaNxvLgU5XM3CHgJ2G1mq4BNBF+HHU3wtc8A8CPn3Jtt823ah5mNA+6rs2hUaPobM7updqFzrm6vt75vb1E+b4PwQVsDMLPTgJ+GZtcA15tZY5uucM7dWWfe122uDc7bIHzS5qJNwaeNOOdmmNkHwLUEx5pJJpjaHwPudy3sUTPax4tlUfyui4C7gUkEH5zMI/gb0CbgceBe59y8KJfvhRxgciPLhzey7JD4pL1F87z5pa0BdK3z3xNCn8bMAe5sYt0BfNDmon3e/NTmospCl8ZEREREEp4ebhYRERHfUPARERER31DwEREREd9Q8BERERHfUPARERER31DwEREREd9Q8BERERHfUPAREc+Y2Qlm5sxstte1iIg/KPiISJsys/WhcDPI61pERDRkhYh46TNgJFDqdSEi4g8KPiLiGedcKcHxmERE2oVudYlImzCzS83MERxAEeDL0C2v2s+gpp7xCa1zodtkSWb2fTNbZmZlZrbJzP5oZh1D23Yxsz+Htq0ws9Vm9v1m6jIzO8/M/m1mO0P7bDSzh3U7TiTx6YqPiLSVNcATwNlAJvAiUFJnfUljOzXiWWAaMDt0zOOB/wFGmtmFwCdANvABwRGwjwf+YGYZzrnf1D2QmaUCzwFnAmXAXGAbcCRwJXCWmX3dOTe3pV9WROKDRmcXkTZlZusJXvUZ7Jxb32DdCcC7wBzn3Al1lg8CvgzNrgROcs5tDq3rDywAugFLCd4qu9g5Vx5afyrwGlAM9ArdTqs97p3Aj4D3gAudc5vqrLsOuAdYC4xwzlVH4euLSIzRrS4RiXXfqw09AM65fODp0OxA4Jra0BNa/zqwmOBVoAm1y82sK/A9gleaptcNPaH9ZgKvA0OBb7bNVxERryn4iEgsqwL+08jyNaHpXOfczkbWrw5N+9RZdiLQgeDVpe1N/HlzQtNjWlqoiMQHPeMjIrFsaxO3nGqfD9rUyLq66zPqLBsSmp4aeui6ObmHWJ+IxBkFHxGJZYFWrq8rOTRdSfCB6OZ82oLjikgcUfAREb/ID02XOOcu9bIQEfGOnvERkbZWGZp6/YvW2wSfGTrZzDp7XIuIeETBR0TaWkFoOtLLIpxz24B7gc7AP81sRMNtQp0hXmlmPdu9QBFpF17/BiYiie8l4ATgGTP7N1AYWv4jD2r5IcE3vc4BlprZQoL9BWUA/QmGs7TQdJsH9YlIG1PwEZG2NhPIAS4k2ANzemj5r9q7EOdcFXCumT0DXA5MAsYQ7OxwC8Feol8h2ImhiCQg9dwsIiIivqFnfERERMQ3FHxERETENxR8RERExDcUfERERMQ3FHxERETENxR8RERExDcUfERERMQ3FHxERETENxR8RERExDcUfERERMQ3/h8IoVtKp3I9KQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"y_0 = 0\n",
"v_0 = 0\n",
"m = 0.25\n",
"m_final = 0.05\n",
"h_desired = 300\n",
"dmdt = root_f_m[0]\n",
"T = (m-m_final)/dmdt \n",
"t = np.linspace(0, T, 100)\n",
"dt = t[1] - t[0]\n",
"N = int(T/dt)\n",
"t1 = np.linspace(0,T,N)\n",
"\n",
"h = np.zeros([N,3])\n",
"\n",
"h[0,0] = y_0\n",
"h[0,1] = v_0\n",
"h[0,2] = m\n",
"\n",
"for i in range(N-1):\n",
" h[i+1] = heun_step(h[i], lambda state: rocket(state, dmdt = dmdt,u=250,c=0.18e-3), dt)\n",
" h_predicted = h[:,0]\n",
"\n",
"plt.figure(figsize = (8,8))\n",
"plt.title('Height vs Time with Point of Detonation')\n",
"plt.plot(t1, h_predicted)\n",
"plt.plot(t1[-1], h_desired, '*', markersize = 20, label = 'point of detonation')\n",
"plt.xlabel('time')\n",
"plt.ylabel('height')\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
}