Skip to content
Permalink
master
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
Go to file
 
 
Cannot retrieve contributors at this time
{
"cells": [
{
"cell_type": "code",
"execution_count": 147,
"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",
" mf = 0.05 \n",
" tf = (m0-mf)/0.05\n",
" N = 100\n",
" t = np.linspace(0, tf, N)\n",
" dt = t[1] - t[0]\n",
" height_desired = 300\n",
" num_sol_heun[0,0] = 0\n",
" num_sol_heun[0,1] = 0\n",
" num_sol_heun[0,2] = m0\n",
" \n",
" for i in range(N-1):\n",
" num_sol_heun[i+1] = heun_step(num_sol_heun[i], lambda state: rocket(state, dmdt = dmdt, u = u), dt)\n",
" \n",
" error = height_desired - num_sol_huem[-1,0]\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def f_dm(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",
" mf = 0.05\n",
" dm = m0-mf\n",
" T = dm/dmdt\n",
" g = 9.81\n",
" dt = T/100\n",
" \n",
" N = 100\n",
"\n",
" #create the time interval for our specifications\n",
" t = np.linspace(0, T, N)\n",
"\n",
" #set initial conditions of position and velocity\n",
" y0 = 0\n",
" v0 = 0\n",
"\n",
" #initialize solution array\n",
" num_sol = np.zeros([N,3])\n",
"\n",
" #initialize first variables using our set initial conditions\n",
" num_sol[0,0] = y0\n",
" num_sol[0,1] = v0\n",
" num_sol[0,2] = m0\n",
"\n",
" #solve and write to our solution array\n",
" for i in range(N-1):\n",
" num_sol[i+1] = rk2_step(num_sol[i], rocket, dt)\n",
" \n",
" error = num_sol[-1,0]-300\n",
" \n",
" return error"
]
},
{
"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": 358,
"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": 365,
"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-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" \n",
" dstate = np.array([state[1], (u/state[2])*dmdt, -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 366,
"metadata": {},
"outputs": [],
"source": [
"def eulerstep(state, rhs, dt):\n",
" '''Update a state to the next time increment using 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",
" next_state = state + rhs(state) * dt\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 367,
"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": 437,
"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": [
"y_0 = 0\n",
"v_0 = 0\n",
"m_0 = .25\n",
"\n",
"m_f = .05\n",
"dmdt = .05\n",
"N = 500\n",
"dt = 4/N\n",
"\n",
"num_sol_heun = np.zeros([N,3])\n",
"num_sol_euler = np.zeros([N,3])\n",
"\n",
"num_sol_euler[0,0] = y_0\n",
"num_sol_euler[0,1] = v_0\n",
"num_sol_euler[0,2] = m_0\n",
"\n",
"num_sol_heun[0,0] = y_0\n",
"num_sol_heun[0,1] = v_0\n",
"num_sol_heun[0,2] = m_0\n",
"\n",
"for i in range(N-1):\n",
" num_sol_heun[i+1] = heun_step(num_sol_heun[i],simplerocket,dt)\n",
"for i in range(N-1):\n",
" num_sol_euler[i+1] = eulerstep(num_sol_euler[i],simplerocket,dt)\n",
"\n",
"fig = plt.figure(figsize=(10,8))\n",
"plt.title('Simple Rocket')\n",
"plt.plot(num_sol_heun[:,2]/.25,num_sol_heun[:,1], 'b',label='Heuns Method');\n",
"plt.plot(num_sol_euler[:,2]/.25,num_sol_euler[:,1],'r--',label='Eulers Method');\n",
"plt.grid(True);\n",
"plt.xlabel('mf/m0')\n",
"plt.ylabel('v [m/s]')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1,0.5));"
]
},
{
"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": 370,
"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 - 9.81 - (c/(state[2])*(state[1]**2)), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 374,
"metadata": {},
"outputs": [],
"source": [
"T = 4 # simulation time, in number of periods\n",
"\n",
"# time array\n",
"t = np.linspace(0, T, N)\n",
"\n",
"#initialize solution array\n",
"num_heun = np.zeros([N,3])\n",
"num_rk2 = np.zeros([N,3])\n",
"\n",
"#Set intial conditions\n",
"num_heun[0,0] = y0\n",
"num_heun[0,1] = v0\n",
"num_heun[0,2] = m0\n",
"num_rk2[0,0] = x0\n",
"num_rk2[0,1] = v0\n",
"num_rk2[0,2] = m0\n",
"\n",
"for i in range(N-1):\n",
" num_heun[i+1] = heun_step(num_heun[i], rocket, dt)\n",
" \n",
"for j in range(N-1):\n",
" num_rk2[j+1] = eulerstep(num_rk2[j], rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 445,
"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_rk2[:,0], linewidth=4, linestyle='--', label='Euler-Step Rocket')\n",
"plt.plot(t, num_heun[:,0], linewidth=3, linestyle='-', label='Implicit Heun Rocket')\n",
"plt.plot(t, num_sol_heun[:,0], linewidth=3, linestyle='-', label='Implicit Heun Simplerocket')\n",
"plt.plot(t, num_sol_euler[:,0], linewidth=4, linestyle='--', label='Euler-Step 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": 454,
"metadata": {},
"outputs": [],
"source": [
"#A\n",
"def incsearch(func,xmin,xmax,ns=100):\n",
" '''incsearch: incremental search root locator\n",
" xb = incsearch(func,xmin,xmax,ns):\n",
" finds brackets of x that contain sign changes\n",
" of a function on an interval\n",
" arguments:\n",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\n",
" returns:\n",
" ---------\n",
" xb(k,1) is the lower bound of the kth sign change\n",
" xb(k,2) is the upper bound of the kth sign change\n",
" If no brackets found, xb = [].'''\n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = np.zeros(ns)\n",
" for i in range(ns):\n",
" f[i] = func(x[i])\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] )\n",
"\n",
" \n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb\n",
"\n",
"#incsearch(lambda x: f_dm(x), 0.05, 0.4, ns=7)"
]
},
{
"cell_type": "code",
"execution_count": 455,
"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": 456,
"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",
" mf = 0.05 \n",
" tf = (m0-mf)/dmdt\n",
" t = np.linspace(0, tf, 100)\n",
" N = 500\n",
" dt = (.2/dmdt)/N\n",
" y0 = 0\n",
" v0 = 0\n",
" m0 = 0.25\n",
" height_desired = 300\n",
" num_sol_heun = np.zeros([N,3])\n",
" num_sol_heun[0,0] = y0\n",
" num_sol_heun[0,1] = v0\n",
" num_sol_heun[0,2] = m0\n",
" \n",
" for i in range(N-1):\n",
" num_sol_heun[i+1] = heun_step(num_sol_heun[i], rocket, dt)\n",
"\n",
" error = num_sol_heun[-1,0] - 300\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 457,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"[[0.06060606]\n",
" [0.05707071]]\n"
]
}
],
"source": [
"yb = incsearch(lambda dmdt: f_m(dmdt, m0 = 0.25, c = 0.18e-3, u = 250), .05, .4)\n",
"print(yb)"
]
},
{
"cell_type": "code",
"execution_count": 478,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.05864732806758735 [m/s] mass flow rate\n",
"The solution took 5 iterations\n"
]
}
],
"source": [
"#B\n",
"I0,out = mod_secant(f_m, 0.0001, 0.04, es=0.000001)\n",
"print(I0, '[m/s] mass flow rate')\n",
"print('The solution took ',out[2],' iterations')"
]
},
{
"cell_type": "code",
"execution_count": 479,
"metadata": {},
"outputs": [],
"source": [
"#C\n",
"def rocket2(state,dmdt=0.05, u=250,c=0.18e-3):\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": 482,
"metadata": {},
"outputs": [],
"source": [
"g = 9.81\n",
"T_3 = (m0-mf)/dmdt\n",
"N_heun_3 = 100\n",
"N_eul_3 = 100\n",
"\n",
"t_heun_3 = np.linspace(0, T_3, N_heun_3)\n",
"t_eul_3 = np.linspace(0, T_3, N_eul_3)\n",
"\n",
"num_heun_3 = np.zeros([N_heun_3, 3])\n",
"num_eul_3 = np.zeros([N_eul_3, 3])\n",
"\n",
"dt_heun_3 = T_3/N_heun_3\n",
"dt_eul_3 = T_3/N_eul_3\n",
"\n",
"num_heun_3[0,0] = y0\n",
"num_heun_3[0,1] = v0\n",
"num_heun_3[0,2] = m0\n",
"num_eul_3[0,0] = y0\n",
"num_eul_3[0,1] = v0\n",
"num_eul_3[0,2] = m0\n",
"for i in range(N_heun_3-1):\n",
" num_heun_3[i+1] = heun_step(num_heun_3[i], rocket3, dt_heun_3)\n",
"for j in range(N_eul_3-1):\n",
" num_eul_3[j+1] = eulerstep(num_eul_3[j], rocket3, dt_eul_3)"
]
},
{
"cell_type": "code",
"execution_count": 525,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAocAAAJ7CAYAAACRRDuAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAgAElEQVR4nOydeXyNV/rAvyd7iESIUFvsYmktsUUQErXUUmuZVidhOi0N2tFROjpTXXRapjrttCjjJ2W6jFapKlUiCUEIZVCh9kSoCpKQhSzn98d773Vv7pKb9Qbn+/m8n3vv2d7nnPe8933ec57zHCGlRKFQKBQKhUKhAHBytAAKhUKhUCgUiuqDUg4VCoVCoVAoFAaUcqhQKBQKhUKhMKCUQ4VCoVAoFAqFAaUcKhQKhUKhUCgMKOVQoVAoFAqFQmFAKYcKRQUihIgUQkgLR6EQIkMIcUgI8U8hRKCjZbWGEOIZncwFjpalvAghftXV5YfKSF8Oeebei+XfqwghAq3cl6U5GujKmqr7nefoeikUlYVSDhWKqsEJ8AE6Ay8A/xNC/NGxIlVPhBCJuofvMkfL8qAhhPAwUoYmOloehULhGJRyqFBUHo8BtXRHHaA78A+gAHADlgkhejhOPIXigeEkd+/F4sdoo3SRNtJdqTpxFQrH4uJoARSK+5hcKeUto98HgANCiEvAYrSXsz8Bv3OEcIqqR0rZwNEyPIhIbSuwW5biik0P3y52z1oqaxmgRrUV9zVq5FChqHo+ArJ13/s4UhCFQqFQKIqjlEOFooqRUuYDZ3Q//W2lFUI4CSEihBA/CiF+E0LcEUJcEUJsFkL8TgghSjqfEOIhIcRbQoj9QohrQog8IcR5IUSMEGKmEKJ+aesghHjVyDZtkZU07YQQHwshTgghbgohsoUQyUKI94UQjSykf0cIIYGeuqDnLCwKqBYLLYQQPYUQq4QQZ4QQObr6HRZCvCGE8LWRr8QFI0KIICHEWt11zhNCnBVC/EsI0bi0NoFCiDG665wuhMjVtf/rQggvC2kTgVyjoC8stH+vks6pK+uILv23dqT9XJf2tIW4EUKIDUKIi0KI27p2PiuEiBNC/FUI0cYeeSoSWwtSii186aW7Xn/Rtcct3TX9VgjRpVi+R4UQ3+v6R64Q4qju3izxGS2EGCyE+FIIkaLrLxlCiH1CiNlCiBoVWXfFA4SUUh3qUEcFHWg2S1J39LeR7qguza820vgCu4zKs3RsA2rZKGMSkFNCGf8olucZXXiBhfIE8KFR3petnPcVNNtKa+e8CQwuluedEuSUwNxSXo9fdfl+qIj0gDPayK8tGS8DXUso32I9gCk22u03oIfR74m2ygeW2JAxCfAsljfRjvbvZWc7ztalvwPUtZHOC20UXQKvF4tbYYc8/7BHnhJkHWKrTS2kn6pLm2chLtCorKHAYSty5wB9dXlet1G/5TbkqAGsK6F9TgLNy9tG6njwDjVyqFBUMUIIV6CF7udxK2kE8BV3p52XA10APyAIiNaFDwT+Y6WMccAawBNIBZ4H2qAtjmkJPAGsBfJLIfdnwAygEJgipVxoId1LwNtoitR64FGgAVAP7YGZiKYUrBNCtDXK+jc0w/8k3e+VmC8KeM8eWSuRfwJRaA/e/0O7PvWAh4BxQDJaXTcJIeqVpmChLU5agdZuKWi2qA8BjYDJQBHwhZ3F/RGYBiwFugJ1gQ46mQG6oSlwxgxA6196IjFv//12nv9znbyuaP3MGqPRlBww6sdCiGFoLyn6svoCjYH6aP3/d8A3QHV2J/Mx0AyYCTRH6yfj0JR8T2C5EOJJtH4fjXZN6qJ5NNiiK+OPQojQ4gXr/h++BMag3b/vGeVvgnbt0tDu941CCI9KqJ/ifsbR2qk61HE/HdgxcgjMMkoz1kqacUZp3rCSZrFRmseKxdUCruvikoF6NmR2KfbbbOQQqAn8oAvPBUZaKSsAbbRIAh9YSeMK7Nal+dpCvH4Ea1kFXA/9SNo2NIW0pOMKVkYOgd5G7f0nK+fzAU5hZVQLGyOHQLwu7hrQxEJ8O0xHgW2NHErgJSsy/qiLP28hzsNW+aVs++26cnbbSKPvU4nFwj/Whe8tbx+wQ87KGjm8A3S3kGa4UZp8K/3EA+2FTgKrLMQ/aVTGGCtyNtX1JQlMr+x2VMf9daiRQ4Wi8vAUQnjpDl+dLdlC4F1d/PtSynVW8upHTdKAN62kmYf252+cXs/v0aalAZ6VUl61JqSU0qazayFEXSAGGAxkok0Hb7SS/Hk05e8y8Gcr58sH5ut+Pi6EqGnr/BXEQLSp7JIOWzagL+g+D0gp37eUQEqZCehHU5+yVzghRDOgn+7nYillqoWyk7F/lewZtJcHS6zSfQYIIWzavJYT/UhgbyFE8+KROlvXgcXS6tF70kirJNmqgtVSyiQL4ZuBLN33bLSRQxOklHmA3l6zZ/F47vbFdVLKbyydXEqZwt3+YndfVChALUhRKCqTzdxVOq6jubKZDdwGhkopZ1nKpDNC7637+a1OmTJDSpkLbNL9LL7qOVz3eVZKuausFRBCNAES0B5QvwKhUsqdNrLoH/Y7AXcj5djkQBvNBE0J6FxW+aoK3TSevk13WKuXrm56U4EGwsLCGysEG323pnjDXYWhJLZKKaWVuJNG30u9GKkUrOPuAhdLyslEtCn0AuC/xeIO6T5HCSGmV9ELREWz1VKglLIIOK/7mSClzLGSX79ozcT9kRDCB20KGSC2hL54TJeuq64PKxR2oZRDhaLqqQm8L3TbcVnAF21aGKzYJBrxs+6zXrGViS11n4fLJiKg/T/sRpsqOwv0kVL+r4Q8ehvCCdgeoTMeGSuVbV4Z2SqlFCUdWHd0XFd3ALyM7bolGOWzt27NjL6ftJYIOGFneZdsxBkrI5W2mlVKeZO7yuwkC0n0YVstjGz/H3AETXn8F5AuhNghtNXgA3X2r9UdW9dArzRftiONZ7Hw1tx9dn+E7b74uS6dG5rJg0JhF0o5VCgqjwFGSoc30AvYoIsLBD638jZfy+i7TYe8aA8AS/m8LcSXBf3UdF5JZQkhnNEU39JyLxjLl/XBam/d9O1WIKW8YyNdSf1BT6Gd6Sp7NGmN7rOtEEI/2oXOBU23YmkM6NqgH9oK9ito7TgA+Cua/eivOlc21VlJtOca2JOm+DWq7L6oUCjlUKGoCqSUN6WU+9BWF+pthAYAT1tIbqyEmfmjK4Zx/E0L340VxtJShLYF4C2gPdp0qlUbNSllIXdHO96yZ6ROd3xZDhmrCmOl7JlS1C3RzvL1TtFdhBBuNtKV1B+qGz+irc4F09FD/febWJlGl1JmSilfQVux3Ql4Dm21dibaivs3gNWVIHN1x7gvDixFX/zVYRIr7jmUcqhQVCE6O7Cp3DVIf93C6McNo/j2JRTZQfd5tZjtkt6hcLns+XT2inoFsQOagmhrqvSc7rOLjTT3IuncVbgro24XjL7bcuzc1kZctUO32Emv/E/UjS6DttoWtAUVueY5TcqQUsojUsrlUson0Vza6BXKiUKIwAoXvHpzzuj7/XafKaoJSjlUKKoYnX2V3l9fM4qNHuoM1vfofo4UQljcA13nu2y47mdCsehtus8WQohybdFnQUGMtaEg/qj7HCiEaFzGU+oX4DjbTFWF6EZFY3Q/x1fCAok9Rt9H2kj3eAWftzjGi58qqv31K5Hro/WLYO7axFr00WkLqe19/I5RULvyiXdvIaX8jbu2xBFqoYmiMlDKoULhGP6JNkIIMNdoREXPSt1nYzSXNZZ4k7tOi1cUi/uPUfmf6NzRWMSa8mlMKUYQ/4W2+tQdWF3S9l3FnGDr0bvnaViSXFWM3jWMP5oDY6vtJjRa21uwlPI82m44ALMsrXLWtdVU+8UtPTolOFP3s0LaX+fORb+QZhJ3Vy6nAbGW8tgxGtjS6Ps1q6nuX/R9sSPwd1sJhRAuQoiWttIoFMVRyqFC4QCklFmA3ldea7TVvcas4+5I1XwhxFIhRCchRB0hRGchxEru+hHcKKXcYpxZt1L0Wd3P9sBBIcRzQoiWQojaQohmQojRQojPsO5HsbjMxgpiRywoiFLKs9zdeWMA8JMQ4hkhRCvdeR8SQoQIIV4WQhxE23GlOAd1n2E6GX11DzgXR46S6Or/ge7nk8Aeoe1v3UxXt8ZCiAFCiNfQXPXYfGhb4GU0O8+6QIIQYoIQor6uzX4PxKG5E6ps9O3/B6HtIe2lb/9ylKm/zqO529c/142SWyJaCPE/oe1L3FfXBr5C27v4RbStAUGbjt9bDrnuVf6DtvsQwBwhxDYhxOO6PlhbCBEgtD2XF6J5GpjmOFEV9ySV4VlbHep4UA/s3FtZl9abu7uYHANEsfiK2Fs5Am2RiK0y7N5bWRffF83+TqLtEW22+wraFnu3Szivxd0z0EZLM62kd/Teyk5oWwMW2lG3z2yUb21v5T/aKPsq2op3/e9xpS1fl8Z4Fw+zvZLRprWt1cmuvZUtlNkMTfE1LusRG+nt2ef5CtCtAu7ZytohxWpbYccuQLbOo4v3QHP5U1I7SWBBedtJHQ/WoUYOFQoHIbXRQ/30UAe0URXj+BtAKJrCuR1NOchHW/35A9r03CCpjRJaO8enaCOTi9D8xmWhuaU5pytzBnd3bLFX7uIjiDEWRhD/BbRCGz07gDbFXYimVB5DmzYfjja6WLz8i2hOwD9H22PYlmuXKkVKWSSl/Ava9foQTTnORKtbBprz5n8BYWi71JS2/BVoCuA6tOt9G81h8jK0PZLPGCUvr5siazJsBEagOXG+iv1ucWyVeR5Tu9ijUsojNrL8Dk05WovWX66hmSvcQBspfBUIlFIeKK9s9ypSyjwp5RQ0B/Ur0Pxj3kJrp2to+2AvROtPrzpKTsW9iZDSmhN9hUKhUFQndIs59ItXOkopf7aVXqFQKMqCGjlUKBSKe4cRus9s7N8tRaFQKEqFUg4VCoWimiCEqGMjrj0wU/fzG6mtLFYoFIoKR00rKxQKRTVBCLEdbaHFl2j2i7fQdggZBvwFbZFSHtBZSmlrD2aFQqEoM0o5VCgUimqCECIObRGSNfKA30kpN9hIo1AoFOVCKYcKhUJRTRBChABj0dwFNURzcp6H5s9vO/BPKWWK4yRUKBQPAko5LCd+fn6yWbNmjhZDoVAoFAqFokQOHjyYLqW0tgUqAOXxeK8AmjVrxoEDD6yrLYVCoVAoFPcQQogLJaVRq5UVCoVCoVAoFAaUcqhQKBQKhUKhMKCUQ4VCoVAoFAqFAaUcKhQKhUKhUCgMKOVQoVAoFAqFQmFAKYcKhUKhUCgUCgNKOVQoFAqFQqFQGFDKoUKhUCgUCoXCgFIOFQqFQqFQKBQG1A4pVYyUkps3b5KVlUVOTg6FhYWOFkmhUCgUDzDOzs7UqFEDb29vatWqhRDC0SIpHIxSDqsQKSW//fYb2dnZ1KlThwYNGuDs7KxuRIVCoVA4BCklhYWF3Lp1i/T0dHJzc/H391fPpQccpRxWITdv3iQ7O5uAgACcnZ0dLY5CoVAoHnCEELi4uFC7dm1q1arFhQsXuHnzJt7e3o4WTeFAlM1hFZKVlUWdOnWUYqhQKBSKaoezszN16tQhKyvL0aIoHIxSDquQnJwcvLy8HC2GQqFQKBQW8fLyIicnx9FiKByMUg6rkMLCQjVqqFAoFIpqi7Ozs1ooqag+yqEQYoYQYq0QIlkIcU0IkS+EuCqE2C6EmCRsWMcKIZ4UQuwSQmQKIW4JIQ4IIaKEEDbrV9Z85UEZ+SoUCoWiuqKeUQqoXgtS5gD+wDFgD5ANBABhQDgwTggxRkpZZJxJCPEx8DyQB8QA+br0HwHhQojxUkqz16Cy5lMoFAqFQqG4n6lOyuFE4JCUMts4UAjRAU15exyIAFYZxY1FU/B+BfpJKU/pwusDscBoYDrwQbEyy5RPoVAoFAqF4n6n2kwrSykTiiuGuvCfgY91Px8tFv2K7nOOXsHT5bkCTNP9nGthmris+RSVTLNmzRBClHjExcU5TEa9DMXp379/hcgWHR2NEILIyMhylVOc+fPn29W2FXXeyMhIhBBER0dXSHnlRX99hBD87ne/s5l23rx5hrTNmjWrGgG52//Pnz9fZee0RmX1Q3uIi4tDCEH//v1LnVffz+fPn1/hclWncyoUlUl1Gjm0RYHuM08fIIRoDAQBd4CvimeQUsYLIdKARkAvtKnqMudTVC2DBw+mQYMGVuNtxd2vnD9/nubNmxMQEFAu5aFly5b06dPHarytuPuFDRs2kJGRQe3atc3iioqKWLNmTYWfMzo6msmTJxMREVFtFOZ7Ef2LmZTSwZIoFPcv1V45FEI0B6bqfn5nFNVF9/mzlDLXSvYkNCWvC3eVvLLmU1Qhc+fOLdOogSNZvXo1OTk5NG3atFzljB49ml69euHj41NBkpnSp0+fB1o56datGwcOHODLL79k6tSpZvHbt28nNTWV7t27k5SU5AAJFT169CA5OZkaNWo4WhSFouq4+St8PRnGRUOt+g4VpdpNmwohJgshooUQnwkh4oFfgMbA36WU642SNtd9XrBRXEqxtOXJp1DYpGnTpgQGBpb7gebj40NgYCAPPfRQBUmmMObpp5/G2dnZqoKsD3fEdKpCo0aNGgQGBpb7RUuhuKeIXwgpiRD/rqMlqX7KIRCCtvDkSaCfLuyvwBvF0um9SZvZKRpxS/dZqwLyKaohUkqGDh2KEIJnn33WLL6oqIjw8HCEEEyfPt0Qfv78eYM9WUFBAe+88w7t2rXDw8OD+vXrExERQUpKill5tijJ5nDr1q2MGTOGhg0b4ubmRoMGDQgJCeHdd98lN/fuILYlW6/IyEiaN9feVS5cuGBiI1jZNnEl2cGV1dZy3759TJw4kcaNG+Pm5ka9evUYOXIkCQkJFtMb23quXLmSnj174u3tjRCCjIwMu8/bsGFDBg0axL59+0hOTjaJy8zMZP369bRv354ePXrYLCc7O5uFCxfSvXt3vL298fT0pEOHDsyfP59bt26ZpG3WrBmTJ08G4NNPP7XLxnPbtm2Eh4fj4+NDjRo16NWrFxs3brQqT3p6OnPmzCEwMBBPT0+8vb3p1asXS5YsoaCgwGIeKSUrV66ka9eueHp64ufnx6hRozhy5IjNulti3bp1CCGYMGGCWdyYMWMQQlg0B1myZAlCCF544QVDmCWbQ71dn57itrKWuHLlCs899xyNGzfG3d2d5s2bM3fuXPLy8iymt0V+fj7/+Mc/aN++PR4eHjRo0ICnn36aCxesjzMY2yJeuHCByZMn07hxY1xcXHjxxRcN5a5Zs4bf/e53tG3bllq1alGjRg3at2/PnDlzuH79utXyz507x6RJk/D39zf0v3/84x8UFhZWK/tVRQm85Q/zfeDASpBF2ud8Hy3cQVS7aWUp5TPAM0IIT7SRu8nAfOAJIcRjUspLuqT6f4PSGp6UNd/dAoR4FngWUG+2DkYIwZo1a+jcuTMrVqxgwIABJosN3njjDXbs2EGXLl147733LJYxYcIENm3aRP/+/enUqRO7d+9m9erV/PDDD+zcuZO2bduWS0YpJc8//zzLli0DtGnN0NBQrl+/TnJyMnPnzmXChAk2lbw+ffpw69Yt1q1bR82aNRk3bpwhzs/Pr1zyOYL33nuP2bNnA9C1a1eCg4O5ePEi33//Pd9//z3Lli3jj3/8o8W8M2bMYMmSJYSEhDB8+HB++eWXUvtmmzx5Mlu2bCE6Opp33737lv7ll1+Sl5dnUOSscfHiRQYPHszx48epV68ewcHBeHh4kJSUxOuvv8769euJi4vD19cXgHHjxpGYmMju3bvNbD4t2XiuXLmSBQsW0L17dx577DFOnjzJvn37GDVqFGvXrjW5/gCnT58mLCyM1NRUGjRowIgRI8jJySE2NpaoqCjWr1/Ppk2bcHd3N8kXFRXF0qVLcXZ2JjQ0FH9/f/bv30/Pnj1LbIPihIWF4eTkxI4dO5BSGq5JUVGR4cXhypUrHD16lIcfftiQLyYmBoDw8HCb5Xfu3JmIiAg+/fRTACIiImymT01NJSgoCCklvXv3Jisri4SEBN59912OHz9uU9EuTlFREWPGjGHTpk14eHgQFhZGrVq1iImJYcuWLQwbNsxm/lOnTtGlSxc8PDwICQmhoKDAYO965coVfv/73+Pr60tgYCCdO3cmKyuLAwcOsHDhQr7++mv27dtndp8fO3bM8D/StGlTwsLCyMjI4NVXX2X//v12101RDXjhCGx9FU5sgoJccPGEdsNh0ALHySSlrPYH8BKaMveNUdhMXdh6G/k+0KX5R3nzWTuCgoKkvRw/ftzutA8qAQEBEpCxsbGlyrdr1y7p7Owsa9WqJX/55RcppZQ7duyQTk5OslatWvLUqVMm6c+dOyd111j6+/vLn3/+2RB3+/ZtOWnSJAnI7t27m51Ln684oaGhFmVfvHixBGT9+vXl3r17TeKKiorkjh07ZEZGhiFs1apVEpAREREWZQ4ICLCnScx47bXXLJZbEvprcu7cOYvx1uodEREhAblq1SqT8C1btkhANmzYUCYmJprEJSQkSG9vb+nq6ipPnjxpEqdvdx8fH7lv375S1cFYzq+++krm5eXJOnXqyIYNG8qCggJDmp49e0pnZ2d5+fJlmZSUZLG9i4qKZHBwsATk9OnTZXZ2tiEuJyfH0HeKt7O162qMvq3d3Nzkli1bTOLefPNNCchWrVqZ5evevbsE5Pjx42Vubq4hPCUlRbZp00YCcu7cuSZ5Nm7cKAHp7e1t0p4FBQVyxowZhvYuTX8JCgqSgDx06JAhTN+ODz/8sATk4sWLDXGFhYWyTp060tnZ2eQeiI2NlYAMDQ01O4e1+0+Pvp8D8plnnpG3b982xB0/flx6eXlJQCYkJNhdrw8//FACslGjRib/Jbm5uXLs2LGG87322mtWZYmMjDSRRU9WVpbcuHGjvHPnjkl4Tk6OnDx5sgTk1KlTTeKKiopk586dJSCnTJlikvfEiRPyoYceMpzX2n1rC/WscgAbX5Ryfm0p3/TXPr/7U6WdCjggS9K7SkpQHQ6gjq6j5wOuurCRurCfbOT7RpdmulFYmfJZOypSOWQ+9+xRUegfjrYOHx8fi3kXLFggAdm5c2d54cIF2aBBAwnIL7/80iytsXL4r3/9yyw+IyND+vj4WHyIlEY5zM/Pl35+fhIwe9hbo7KVw5KO9evXm+SraOWwR48eEpCbN2+2WN6iRYskIGfNmmUSrpdvwYIFpap3cTm/+uorKaWUUVFRJnIkJydLQA4fPlxKKa0qh5s3b5aA7NWrlywsLDQ7z61bt6S/v790cXGR169fN4SXRjl86aWXzOJu375t6JMXLlwwhO/cuVMCslatWvLatWtm+fTy1qpVy0RxDAsLs6jQSCllXl6ebNiwYamVw5dfflkCctGiRYawd955RwJy3bp10tXVVT722GOGuAMHDhja0piKUA6bNGkic3JyzOKnTZsmAfn666/bXa8WLVpY7MtSSnnlyhXp6elpUzmsU6eOzMrKsvt8erKzs6WLi4usV6+eSXh8fLwEpK+vr8VylyxZopTDe40vntQUwstHtM8vnqy0U9mjHFa7aWUrZKC5s3FBUxSvAId0cR2EEJ7S8srj7rrPQ0ZhZc2nqEJsubKxtuDjlVdeYefOnWzdupVHHnmEzMxMnnvuOYs2UMZMmjTJLMzHx4fhw4fz2WefERcXR0hISOkrARw4cID09HQaN27MkCFDylRGRVOSK5vKNJVIT08nKSkJb29vBg0aZDFNaGgoAHv37rUYP2bMmAqRJTIyko8//pjo6GiGDh3KqlWrDOG22Lx5MwBjx47FycncbLtmzZp069aNzZs3k5SUZLWethg+fLhZmJubGy1atODQoUNcunTJcJ3i4+MBGDFiBHXq1DHLN3ToUB566CEuX77MwYMHDdOau3fvBiz3f3d3d8aPH88HH5RuH4CBAweycOFCYmJi+POf/wxo08bu7u4MHTqUnj17snPnTvLz83F1dbV7SrkshIWF4enpaRYeGBgIwKVLl8ziLHHx4kXOnj2Lk5MTTz75pFm8v78/gwYN4ttvv7VaxqOPPkqtWrZN2A8dOkRMTAznz58nOztbP1CBm5sbV69e5caNGwYzBf01Hz58uMVyn3zySZ5//nm76qeoJkz87O734YsdJ4eOe0U57IcmawaQDiClTBVC/AR0BcYDq40zCCFC0VY5/woYnjJlzaeoWsriykZvf9iiRQsyMzNp3749//znP23mqV27tkVfd4DBBvDixYulksMYvbF6ee0WKxJHurI5d+4cUkqysrJwcbH993P16lWL4QEBARUiS7du3Xj44Yf59ttvuXr1KmvWrKFu3bqMGDHCZr6zZ88CMHv2bIPdpDWs1aEkrCno3t7eACYLKtLS0gAMC5Ys0aJFCy5fvmxIm56ezu3bt3FycrLanmVZ6NSnTx/c3d3ZtWsXd+7cQUpJQkICvXv3xtPTk4EDB5KQkEBiYiJ9+/atVOWwNG1oC/39r19IZomS2spWn7116xZPPfVUiTaQWVlZBuVQfx2tlevj44OPjw+ZmZk2y1QorFEtlEMhRF+gKfC1lPJ2sbgQYKXu50pput/x39EcWb8rhNgjpTyty+MPLNGleUcW24+5HPkqFfmarMrT3Zds2LDBsFL04sWLpKWl0bJly3KVqTait01Rkf23SWGhdvv6+PgwatQom2mtLbSxNBpUViIjI3nppZeYMmUKly9fZubMmVYVAD36OoSGhpZLKbCFpRFJa+hHmGz1U32aysbT05Pg4GDi4uJITEykqKiI3Nxcg/IXHh7O/Pnz2b59Oz179iQhIQFPT0969+5d4bKUpg0rG1t99pVXXmHjxo20b9+ed955h27duuHn54erqyugKaWXL1+2eA1tXfPqVH/FvUe1UA6Blmh7Jn+kG9X7Fc2NTEugvS7N92gubQxIKb8WQixF2/LuqBBiO5pdYjjgDWwAPip+srLmU1Rvjh07xgsvvICbmxvjx4/ns88+Y8KECezZs8fqAz8jI4PMzEyLDqf1LiAaNmxYZpn0ysHJkyfLXIaj0YuAb3MAACAASURBVLddcfcsemy58ihOkyZNAHB1da0WjrgnTZrEnDlz2LRpE2Cfb0N9HcaPH09UVFRlimcXjRs3Bu6OaFri3LlzADRq1AjQFG93d3du375NSkqKxReosrpAGThwIHFxcWzfvt2g0AwcOBCAXr164eXlxfbt2wkLCyMnJ4dHH33UbBV1dULfZpcuXeLOnTsW/0vK4y7mq6+0jbr++9//0rFjR5O47Oxsfv31V7M8+v8ka/deVlYWN27cKLNMCkV1ebWIB94EDgNtgDHAIKAmsA4YLaUcbsk+UEr5PPAU8BMQCgwGTgPTgbHFRhrLnU9RPcnOzuaJJ54gNzeXd999l9WrVzNgwAAOHjxY4tTfZ599ZhaWmZlpUBjKs1NLUFAQfn5+XLx4ka1bt5a5HLirpFnzWVdZ6B+OJ06cMIs7duwYqamppSrr4YcfJj093aH7Y+vx9/dn/Pjx1K1blz59+tClS5cS8wwdOhS4+1C3l8q6fnobze+++86iQrB161YuX76Ml5cXQUFBALi4uBhG6yz1/zt37vD111+XSR79KGFMTAwxMTH4+PjQrVs3w3n79evH/v37Wb9+vUl6e9GPqFXVfdCkSROaN29OUVERX375pVn81atX2bZtW5nL1/sx1L90GPP5559bHDHs109zAbxp0yaLL21ffPFFmeVRKKCaKIdSynNSyr9JKQdIKZtIKT2llB5SymZSynFSyg0l5P9cShkipfSWUtaUUgZJKT8uaVq4rPkU1Y+oqCiSk5MZOXIkL774Ik5OTnz22Wf4+/vz4YcfsmGD9S70xhtvmDhDzs/P54UXXiAzM5OgoKBy7TXs6urKK6+8Ami+9Yr7H5NSEhcXZ5dtUL169XBzc+PKlStVOiqgf3gvXLiQrKwsQ3hqaiqRkZGlnrJ88803AW3U7scffzSLv3PnDhs3brS6IKWi+fzzz0lPT2fXrl12pR81ahRBQUHEx8czdepUi06Kz549y8cff2wSpleyizveLi99+/ale/fu3Lx5k6ioKG7fvmuZk5aWZnC2PH36dDw8PAxxM2fOBGDx4sUcOHDAEF5UVMScOXMMdm2lpXv37vj4+LB//36SkpLo378/zs7OhviBAwdSUFDAJ598YvhdGiqrHW2hb6tXX33VZIT29u3bREVFkZOTU+ay9QtkiveXAwcOGP47ihMaGsojjzzC9evXmTVrlomifOrUKd54o/ieEQpF6agu08oKhQnvvPOOzWnHJ5980rAKdPXq1Xz66ac0adLEsOIU4KGHHmLNmjUMGTKEKVOm0KVLFzMbsKZNmxIUFETnzp0JCwvDx8eHvXv3kpKSgp+fH6tXm6xXKhN/+tOfSE5O5t///je9evWiW7dutGrViuvXr3P8+HFSU1M5d+5ciXspu7q6MmzYMNavX0+XLl0ICQkx7Grxzjvv2C1PQkKCzenTpk2bmjxcoqKiWL58OUlJSbRt25bg4GAyMjLYv38/PXr0oHfv3uzZY/8W5I8//jjvvfceL7/8MoMHD6ZNmza0bdsWNzc3UlNTOXnyJJmZmSxdupTg4GC7y60qnJyc2LBhA4899hiffPIJn3/+OZ06daJx48akp6eTkpLCL7/8Qv369U2mnXv16kWDBg346aef6NatGx06dMDV1ZWQkJBSO5wuzueff86AAQP44osviI+Pp0+fPgYn2NnZ2QZbP2NGjRrFs88+y/LlywkODjZxgp2Wlsa0adNYunRpqWXRO9TWL7AoPjKo/52Xl4evr69do7XGjB49mvfff5/w8HDCwsLw8tI2vfr3v/9dalntZcaMGfz4449s2bKFDh06GM6bkJBAXl4ev//978v8X/G3v/2N8ePHM2/ePNauXUu7du24dOkSCQkJTJw4kd27d5tNHwshDLMjK1as4McffzTcl7GxsQwfPpykpCRSUlJKtKFVKCxSkq8bdVSdn0OFfX4OAfn+++9LKTXfdDVr1pQuLi5WndrOnTvX4EtN7yzW2Gdgfn6+fPPNN2WbNm2ku7u7rFevnpw0aZJV/2B6GYpjzd+fnu+++04OGzZM1qtXT7q6usr69evLPn36yIULF5r4n7PlDy89PV3+4Q9/kI0bN5YuLi6l8ntor5/DTp06meVNSUmRTz31lPTz85Nubm6ydevWcv78+fL27dul9nOo5/Dhw/IPf/iDbNmypfTw8JBeXl6ydevWcuTIkXLFihVmPvustbu9FPdzWBLW/Bzqyc3NlR999JHs16+f9PX1la6urrJBgwYyKChI/vnPf5a7d+82y3P48GE5bNgwWadOHenk5GR2ncvqU1JKKa9evSpnz55t6MdeXl6yR48e8qOPPjJzsKynqKhILl++XHbu3Fm6u7tLX19fOXz4cHno0CG7/DJa44MPPjBcr+L/e0VFRbJ+/foSkGPGjLGY35afw5ycHDlr1izZvHlz6erqatYv9P3ckv9GKe3zN2mJO3fuyHfeeUcGBgZKNzc3Wa9ePTlx4kR59uxZq+csSRbj+g4YMEDWqVNH1qxZU3bu3Fl++OGHsrCw0GafOH36tHzyySeln5+fdHd3l4GBgfLtt9+WeXl50s3NTTo5OZn8t9iLelbd32CHn0Mhq2gV2/1Kt27dpPGUjC2Sk5Np165dJUuksIfz58/TvHlzAgIC1N6jCoXivmLXrl3069ePjh07cvTo0VLnV8+qymPDoTQWbT3JpYxcGtb2ZPbgtozq0qhKZRBCHJRSdrOVplrYHCoUCoVCobCfW7duWbS7TE5O5tlnnwXsW32vqDo2HErjlW+OkpaRiwTSMnJ55ZujbDhUNvveykTZHCoUCoVCcY/x66+/0r59e1q3bk3r1q3x8vLi/PnzHDx4kMLCQsLCwgwLaRTVg0VbT5Kbb+oIJTe/kEVbT1b56GFJKOVQoVAoFIp7DH9/f2bNmsWOHTvYt28fmZmZ1KxZk549ezJx4kSmTp1qcPujqB5cyrC0W6/1cEeilEPFA0mzZs2qbNcIhUKhqGi8vb157733HC2GohQ0rO1JmgVFsGHtitv1qaJQNocKhUKhUCgUlczswW3xdHU2CfN0dWb24LYOksg6auRQoVAoFAqFopLR2xU6erWyPSjlUKFQKBQKhaIKGNWlUbVUBoujppUVCoVCoVAoqoCs21lM/nYyR64ccbQoNlHKoUKhUCgUCkUVsDRpKdGHo+m0rBMvbHnB0eJYRSmHCoVCoVAoFJVM9p1s3tt7d4X5I/UfcaA0tlHKoUKhUCgUCkUls+KnFVzNuQpAU5+mPN3paQdLZB21IEWhUCgUCoWiAim+h/KLA5uzaM8iQ/yckDm4Obs5UELbKOVQoVAoFAqFooLQ76Gs3yovLSOXV9YfI8OpNbhc4iGvh5jSZYqDpbSNmlZWKBQKhUKhqCAs7aFcUOiEb0EEALN7z8bDxcMRotmNUg4V1YpmzZohhCAuLs7Roljl/PnzCCFo1qyZWZxe/vPnz5frHPPnz0cIwfz588tVTnEiIyPtKld//sjIyAo9f3VA3wZCCIKDg22mXbFihSGtEKKKJIT+/ftXm/sgLi4OIQT9+/ev8nPbutdKIjo6usr7sCPOqah+WNsr2Vn64VfDj2eDnq1iiUqPUg4VinsIRz6o70cSExM5ceKE1fjo6OgKP6e6hhVDRb2IKRQVjbW9kgtFOi8Fv0RNt5pVLFHpUcqhQlGBxMTEkJycTKNG5fOAP336dJKTk5k+fXoFSaYoTrdu3QDrCuAvv/zCnj176N69exVKpTCmUaNGJCcnExMT42hRFAq7sbSHchF53PH8mue7P+8gqUqHUg4VigqkZcuWBAYG4urqWq5y/Pz8CAwMxM/Pr4IkUxRn1KhR+Pr6smbNGgoLC83i9UqjmiJ0HK6urgQGBtKyZUtHi6JQ2M2oLo34+5iHaVjbA5AUiN+45vovovr1wNvd29Hi2YVSDhX3BHo7sejoaH7++WfGjh1LvXr18PLyok+fPsTGxhrSbtq0idDQUHx8fPD29mbkyJGcOnXKrEzj6b3s7Gzmzp1LixYtcHd3p0mTJsyYMYNr166VSk5bU11SStauXcvQoUPx9/fHzc2NRo0aER4ezkcffWSS1pLNYf/+/RkwYAAA8fHxJrZwVT1FmZqaygsvvEDbtm3x9PTE29ubkJAQoqOjkVKapS9pCtCajZ1x+MGDBxk5ciR169bF09OTTp06sXLlyjLXwd3dnYkTJ3Lp0iW2bdtmEldUVMTq1avx9fXl8ccft1lOfn4+y5Yto2/fvvj6+uLh4UHr1q2ZNWsWV69eNatPaa9haeudnZ3NggUL6NSpE15eXtSsWZPOnTvz9ttvk5OTYzXfhg0bCAkJoWbNmvj6+vLoo48SHx9vs+7W5BVC0LNnT7O4WbNmIYTA1dWVmzdvmsRt3rwZIYRJe1uyOdTb9V24cAGA5s2bm7SjpT528+ZNZs+eTfPmzXF3d6dRo0ZMmzaN69evl7p+UkpWrlxJ165d8fT0xM/Pj1GjRnHkiPXt0IxtEa9du8bMmTNp3rw5bm5ujBo1ypBu3bp1TJkyhQ4dOlC7dm08PDxo1aoVUVFRpKamWi3/t99+4/nnn6dx48aGPPPmzSM3N7da2a8+SIzq0oiXRmZwwXMEaR5TcK7xEzN7znS0WHajXNko7ikOHDhAVFQULVq0IDw8nFOnTrF7924GDx5MTEwMhw8f5sUXXyQkJITBgwezf/9+vvvuO5KSkjh27Bh169Y1K/POnTuEh4dz7NgxwsLC6Nq1K/Hx8Xz00Uds3bqVXbt2Ub9+/XLJfefOHcaPH8/GjRtxdnamV69eNG3alCtXrnDs2DF27NhR4hTykCFD8PDwYOvWrdSvX58hQ4YY4gIDA8slX2mIjY1l9OjRZGZm0qpVK4YMGcKtW7dITExk8uTJ7Nixg9WrV1foOX/44QcWL15M27ZtGTRoECkpKezZs4dnnnmGjIwMXnrppTKVO3nyZJYuXcqqVatM2nPbtm2kpaURFRWFu7u71fxZWVkMGzaMhIQEfHx8CAoKonbt2vz000+8//77rFu3jvj4eINyU9prWNp6p6enExYWxtGjRw0KnhCC2NhY5s2bx9q1a9mxYwd16tQxybdw4ULmzJkDQO/evQkICODo0aOEhYUxY8aMUrVply5dqFOnDgcPHiQjI4PatWsb4vTTwwUFBcTFxTFixAizuPDwcJvlt2rVioiICL7++muys7MZO3YsXl5ehnjj7wCZmZmEhISQlpZGv3796NixIwkJCSxbtoz9+/eTmJhYqpH+qKgoli5dirOzM6Ghofj7+7N//3569uzJ5MmTbeZNT0+ne/fuZGZm0rdvX7p162bynzRhwgQ8PDxo3749AwcO5Pbt2xw+fJglS5awdu1adu/eTZs2bUzKvHTpEiEhIZw/fx5/f39GjBjB7du3+fDDD5VC6ECklLy16y3D7+k9puPr6etAiUqJlFId5TiCgoKkvRw/ftzutA8qAQEBEpCxsbEm4RERERKQgHzvvfdM4l5++WUJyDZt2khvb2+5c+dOQ1xubq7s27evBOQbb7xhki82NtZQZps2beTFixcNcVlZWTI8PFwCcvz48Sb5zp07JwEZEBBgVf5z586ZhM+cOdNwnuTkZJO4goIC+e2335qEvfbaaxKQr732mkWZQ0NDzc5tD/p2LF5ucfTnj4iIMAm/dOmS9PX1lc7OzjI6OloWFRUZ4lJSUmTnzp0lIFetWmWSz1q76AkNDbV43fXhgFy5cqVJ3Jo1ayQgvb29ZXZ2ts36GKNvg0WLFkkppezQoYN0d3eX169fN6SZMGGCBGRSUpK8evWqQYbi6NONGzfOJH9BQYGhXxa/VvZcw7LWe/z48RKQffv2lTdu3DCEX79+Xfbu3VsCcuLEiSZ5fvrpJ+ns7CxdXFzkxo0bTeIWLVpkkKM0fW7s2LESkOvXrzeE/fbbb1IIIR9++GEJyJkzZ5rk6dSpkwTksWPHDGFludf0rFq1yiD7Y489Jm/evGmIS0tLk02aNJGA/M9//mN3vTZu3Gho+3379hnCCwoK5IwZMwznK37fGMsyaNAgmZWVZbH8//73v2bXND8/X7766qsSkEOGDDHL8/jjj0tADh06VN66dcsQfvnyZdm+fXvDeYvfW7ZQz6rys+nkJsl8JPORNRbUkL/d+s3RIhkADsgSdBuHK1f3+lHRyuHZs6/J2FjsOk6c+KNZ/hMn/mh3/rNnXzPLf+TIcLvzp6V9Ynfd7aUk5TA4ONgsz/Xr1w1/gK+88opZ/DfffCMBOWDAAJNwY+Xwu+++M8t36tQp6ezsLJ2cnGRKSoohvLQPrCtXrkhXV1fp5ORk8uCzRWUrh/YexR9yeoXn5Zdftlh+UlKSBGTXrl1NwsurHI4dO9Zivnbt2klAxsfH21V/Kc2VQ70CtGTJEimllDdu3JAeHh6yY8eOUkppVTn8+eefDf0gJyfH7DyFhYXykUcekYA8cuSIIbw0ymFp6n3+/HkphJBOTk5mLyB6eZ2cnMz685QpUyxeaz1BQUGl7nNLliyRgIyKijKEffnllxKQn3zyiXzooYdk+/btDXFXr16VQgjZoEEDk3IqQjn08vKSly9fNot/9913JSAnT55sd73CwsKsvlzl5eXJhg0b2lQOXV1drcpbEg0bNpROTk4miqX+mru4uFgsd/PmzUo5dABFRUWyx4oeBuVw1g+zHC2SCfYoh8rmUHFPYTwNp8fX19cwNWMpvnXr1oA2/WKJ2rVrM3z4cLPwVq1a0atXL4qKiti5c2eZZd6xYwf5+fkEBwfToUOHMpdTkXTq1ImIiAirR6dOnSzm27x5MwDjx4+3GB8UFISXlxeHDx8mLy+vwuS1dH3g7lSstWtrD08//TQuLi6GBShffPEFeXl5JS5E2bJli0E2T09z1xVOTk706dMHgL1795ZJttLUe9euXUgp6dWrl8Up6vbt29OjRw+z/qy3K5w0aZLFc1kLt8XAgQMBTFYZ678PHDiQ8PBwjh8/zuXLlwHtHpFSljilXBaCgoJo0KCBWXhp+05BQQG7d+8GLLeJu7u71ftCT9euXUv02fjLL7/w4YcfMnPmTKZMmUJkZCSRkZEUFBRQVFTE6dOnDWl37tyJlJLg4GCL5Q4dOhRf33toKvM+4cczP7I/bT8A7s7uvNS7bGYvjkTZHCruKRo3bmwx3MvLi2vXrlmM19sgWVNWbP1ZN2vWjN27d3Px4sXSC6tDbzhflXaBJTFq1CibjrDnz5/P//73P7Pws2fPAtjl3uXatWvldumjp2nTphbDvb21lX/lUUT1tn+bNm3i+PHjrFq1ChcXlxKVIn1bfPzxx3z88cc20xZfmGIvpal3WloaoC3QsEbLli1JTEw0pAUMfdtavrI4oG7dujVNmjThxIkTpKWl0ahRI2JiYmjWrBktWrRg4MCB/Oc//2H79u08/fTTdtsbloWK6jvp6encvn0bJycnAgICLKYpqa2s5QNN+Xz++ef597//rU3rWSErK8vwXX8dbZXbtGlTbty4YVMuRdkpvofynwe1YdGh1w3xzwY9S8NaDR0oYdlQymE1o3nz+TRvPr/M+du2XU7btsvLnP/hh78rc96qwMnJ9mB3SfFlpSp3x6jO6F2+6A3nbWFrIUdxioqKbMZX1nXVM3nyZDZt2sScOXNISkpi5MiRJS5C0rdFUFAQHTt2tJm2rCPGpam3XqGw1VdtKR0VTXh4ONHR0cTExNCvXz/Onj3LM888Y4gDqkQ5rOy+UxosjTDr+eCDD1ixYgUNGzZk8eLF9O7dG39/f8N91Lt3b/bu3WvxGtq65tWp/vcblvZQnvPN/0gTbuACbs5uvBzysoOlLBtKOVQ88NjaYUEf17Bh2d/89G/1J0+eLHMZ1YUmTZpw+vRp/vrXv5ZK4XFzcwPg1q1bFuP1o6uOYsSIEfj5+bFp0ybAPt+GTZo0AWDAgAEsWrSoMsWzC/2ouX5E0xLnzp0DMBnRbdSoEWfPnuX8+fMW/QmWdQeSgQMHEh0dzfbt28nPzzeE6WVt27YtMTExXLhwgTNnztC6dWuro3zVAT8/P9zd3bl9+zYpKSkV2lYAX331FQCffPKJRXMC4+lkPfr/JVv3j6PvrfsZS3so3ykAXxFBjks8f+jyBxp7W57tqu6oVwrFA09GRobBls6Ys2fPkpiYiBCCfv36lbn8sLAwXF1d2bNnD8nJyeUR1aBkFRQUlKucsjJ06FDg7oPMXvTKiKWt6o4dO2bTh1tV4OrqypQpU6hbty6tWrWyautnjL4tNmzYUKrrUVnXsG/fvgghSExM5JdffjGLT05OZt++fTg5OZn059DQUAA+++wzi+VaCy8J/ShgTEwMMTExCCEICwsziU9LSzP4+CztqGFV3wsuLi707t0bsNwmd+7c4euvvy5z+Xqfi/qXDmO2bdtm0TRBf8337NljUQncunVrmXw5KuzD1h7Krk6uzO0zt4olqjiUcqhQAC+99JLBOB60Ea5p06ZRWFjI6NGjyzWi4e/vz9SpUykqKmLs2LFmD+7CwkK++86+6Xy9knX69GmHKIizZ8/G29ubt99+m48//tiiDImJiWbKo/7Bv3DhQhObqdTUVCIjI6t0utMa7777Lunp6Zw6dcouv3ddu3Zl1KhRnD59mieeeMKiXerly5f55z//adJOlXUNAwICGDt2LEVFRTz33HNkZmYa4jIyMnjuuecoKiriiSeeMFFAoqKicHJyYs2aNWYvSe+//z4HDhwokzwNGjSgffv2XLp0ifXr1/PII49Qr149Q7x+FFGvHOp/24u+Hcv7wlUaZs7UnBgvXrzYpF2KioqYM2eOiS1nadHbJC9dutTEzOLMmTNMnTrVYp7mzZszbNgwCgoKiIqKMnFyfuXKFf785z+XWR5FydjaQzmycyRNfarvSHhJqGllxQNPcHAwhYWFtGnThrCwMNzc3IiPj+fq1au0bNmyxMUG9rBo0SLOnDnD5s2b6dChA8HBwTRu3JjffvuNo0eP8ttvv9mlIAUEBNClSxcOHTrEI488QlBQEO7u7rRt25bZs2eXW86SaNKkCRs2bGDcuHFMnz6dBQsW0KFDB+rWrculS5c4c+YMly5dYsKECSYrN6Oioli+fDlJSUm0bduW4OBgMjIy2L9/Pz169KB3797s2bOn0uWvaD799FNGjhzJ+vXr2bJlC506dSIgIICsrCxSU1NJTk6mqKiIqVOn4uKi/d1W5jVcunQpJ06cIC4ujhYtWhh2XYmNjeXGjRt06tTJrD8HBQXx1ltv8Ze//IXhw4ebOMH++eefmTlzJh9++GGZ5Bk4cCDHjx8nLy/PbGRwwIABODs7k5eXh5OTk2HnGHsZPXo0cXFxPPXUUwwaNMjgbPvdd9+16Oy+Ihg1ahTPPvssy5cvJzg42MQJdlpaGtOmTWPp0qVlKvuVV17hhx9+4JNPPiE2NpYuXbpw/fp14uPjCQ4OpkGDBhbvkaVLl3LkyBG+//57WrRoQb9+/bh9+zaxsbF06NCBXr16kZiYaBhpVVQcswe3NbE5BG0P5UyXNbzSp+y7N1UH1Mih4oHHzc2NHTt28Nxzz3HkyBE2btyIm5sbUVFRJCYmWnSDUVrc3d357rvvWLNmDf369ePYsWN8/fXXnDhxgkceeaRUCug333zDE088wfXr1/niiy9YuXIl33//fblltJcBAwbw888/85e//AV/f38SExPZsGEDKSkptG7dmr///e8sWLDAJI+vry+7d+/mqaeeoqCggO+//56LFy8ye/Zsfvjhh3LvRe0ovL29iYmJYfXq1fTr148zZ87wzTffcPDgQVxcXJg6dSpbt241W7xTWdfQz8+PvXv38uabb9KoUSO2bNnCli1baNKkCQsWLGD37t1mu6OAppisW7eOXr16cejQITZt2kS9evXYtm0bo0ePLrM8xgph8ZHB2rVr07VrVwA6d+5sUS5bTJ8+3VDPTZs2sXLlSlauXGm2LV9Fs2zZMpYvX27YaeWHH36gXbt27N27lx49epS53ODgYPbv38+wYcPIzMzk22+/5eLFi8ybN4+tW7davUcaN27M/v37ee6553BycuLbb7/l6NGjTJs2jZiYGMN0tNqnveLR76HcqLYnxnsoj+/WjOa+1r0G3AuI6jCdcy/TrVs3ae+0S3JyMu3atatkiRT2EhcXx4ABAwgNDVXbTCkUivuO8+fP06pVK2rWrMmNGzfsXrmsnlWlY2/qXnr/n2aP6iScODn9JK3qtHKwVNYRQhyUUnazlUaNHCoUCoVCcY8ipbRoF5qamsrTTz9NYWEhv//975VLm0rkzZ1vGr4/9fBT1VoxtBdlc6hQKBQKxT1KYWEh3bt3p2nTpgQGBuLr60tqaio//fQTeXl5dOzYkbfeesvRYt63JKUlseW0tluSQDCv7zwHS1QxKOVQoVAoFIp7FGdnZ+bNm8f27ds5dOgQGRkZuLu70759e8aMGcMLL7xg2CVKUfG8sfMNw/eJHSfS1q+tA6WpOJTNYTlRNocKhUKhuJ9Qzyr7OHDpAN1XaFuJCgRHpx2lg3/ZdkOqSuyxOVQjhwqFQqFQKBQ2KL6H8uzBbVl54u4eyk90eOKeUAztRSmHCoVCoVAoFFawtIfyy+sOkyZugos2avjXfn91sJQVi1q+pFAoFAqFQmEFq3soF0QA99+oISjlUKFQKBQKhcIqtvZQvh9HDUEphwqFQqFQKBRWsbWH8v04aghKOVQoFAqFQqGwyuzBbfF0dTYJKyKPDJfV9+WoIagFKQqFQqFQKBRWGdWlEaDZHqZl5FAgrnLD5VNGdGpwX44aglIOFQqFQqFQKGwyqksjGte/TPcV4YB+hfJRB0tVeahpZYVCoVAoFIoSeD3+/vVrWBylHCoUCoVCoVDY4MClA2z6ZRNwf/o1LI5SDhXVimbNmiGEpsq4pQAAIABJREFUIC4uztGiWOX8+fMIIWjWrJlZnF7+8+fPl+sc8+fPRwjB/Pnzy1VOcSIjI+0qV3/+yMjICj1/dUDfBsZHjRo1aNCgAT179uT5559n69atFBUVOVrUexZ9uyoU9wvz4+Ybvt/vo4aglEOF4p4iLi4OIQT9+/d3tCj3PJ06dSIiIoKIiAhGjx5Nly5dSEtLY+nSpQwZMoSHH34Ye/dNt4f75drplevo6GhHi6JQVAn7Lu7j+1PfAw/GqCGoBSkKRYUSExNDfn4+jRo1Klc506dPZ+LEifj5+VWQZIrijBo1yuII6sGDB5k7dy7bt2+nX79+xMbG0rNnz6oX8B4mOTnZ0SIoFGXC0h7Knxyfb4if2HHifT9qCEo5VCgqlJYtW1ZIOX5+fkoxdBBBQUFs3bqVCRMm8PXXX/PUU09x4sQJXFzU36W9BAYGOloEhaLUWN9DORdcwEk48bfQvzlYyqpBTSsr7gmMp7J+/vlnxo4dS7169fDy8qJPnz7ExsYa0m7atInQ0FB8fHzw9vZm5MiRnDp1yqxM42m+7Oxs5s6dS4sWLXB3d6dJkybMmDGDa9eulUpOWzaHUkrWrl3L0KFD8ff3x83NjUaNGhEeHs5HH31kktaSzWH//v0ZMGAAAPHx8SY2c1U9VZmamsoLL7xA27Zt8fT0xNvbm5CQEKKjo5FSmqUvyRazf//+Fm1NjcMPHjzIyJEjqVu3Lp6ennTq1ImVK1dWQu3AycmJpUuX4uHhwZkzZ9iwYYNZmvz8fJYtW0bfvn3x9fXFw8OD1q1bM2vWLK5evWpWD3uvXXZ2NgsWLKBTp054eXlRs2ZNOnfuzNtvv01OTo6ZHMb9OD8/nwULFhAYGIiHhwf+/v5MmjSJlJQUi/Vct24dU6ZMoUOHDtSuXRsPDw9atWpFVFQUqampJmn1traffvopAJMnTzaph/E0sy2bw/T0dObMmUNgYKCh7/Tq1YslS5ZQUFBglj46Otpg/3rz5k1mz55N8+bNcXd3p1GjRkybNo3r169bPJdCURpK2kP5qYefItDvwXjxUa/C9zmWhsj1Dj3vRQ4cOEBUVBQtWrQgPDycU6dOsXv3bgYPHkxMTAyHDx/mxRdfJCQkhMGDB7N//36+++47kpKSOHbsGHXr1jUr886dO4SHh3Ps2DHCwsLo2rUr8fHxfPTRR2zdupVdu3ZRv379csl9584dxo8fz8aNG3F2dqZXr140bdqUK1eucOzYMXbs2MH06dNtljFkyBA8PDzYunUr9evXZ8iQIYa4qhypiY2NZfTo0WRmZtKqVSuGDBnCrVu3SExMZPLkyezYsYPVq1dX6Dl/+OEHFi9eTNu2bRk0aBApKSns2bOHZ555hoyMDF566aUKPR9oo7dDhgxhw4YNbNu2jXHjxhnisrKyGDZsGAkJCfj4+BAUFETt2rX56aefeP/991m3bh3x8fGGRUv2Xrv09HTCwsI4evQovr6+PProowghiI2NZd68eaxdu5YdO3ZQp04dM3nz8/MZOnQo+/btIzQ0lHbt2rF3714+++wzdu7cyZEjR6hdu7ZJngkTJuDh4UH79u0ZOHAgt2/f5vDhwyxZsoS1a9eye/du2rRpA4CXlxcREREkJCRw5swZQkJCaNWqlaEs4+/WOH36NGFhYaSmptKgQQNGjBhBTk4OsbGxREVFsX79ejZt2oS7u7tZ3szMTEJCQkhLS6Nfv3507NiRhIQEli1bxv79+0lMTMTV1bVEGRQKa9jaQ9lZOD8QtoYGpJTqKMcRFBQk7eX48eN2p60I1v90UQa+ukUGzNlkOAJf3SLX/3SxSuUoDQEBARKQsbGxJuERERESkIB87733TOJefvllCcg2bdpIb29vuXPnTkNcbm6u7Nu3rwTkG2+8YZIvNjbWUGabNm3kxYt32yUrK0uGh4dLQI4fP94k37lz5yQgAwICrMp/7tw5k/CZM2cazpOcnGwSV1BQIL/99luTsNdee00C8rXXXrMoc2hoqNm57UHfjsXLLY7+/BERESbhly5dkr6+vtLZ2VlGR0fLoqIiQ1xKSors3LmzBOSqVatM8llrFz2hoaEWr7s+HJArV640iVuzZo0EpLe3t8zOzrZZH2PsbQMppXzzzTclIENCQkzCJ0yYIAE5btw4ef36dUN4QUGBoT8Wv0b2XLvx48dLQPbt21feuHHDEH79+nXZu3dvCciJEydaLBeQ3bp1k1euXDHEZWRkyK5du0pAvvXWW2bn++9//2vWdvn5+fLVV1+VgBwyZIhZHn37Fb/GxujlKU737t0N91Rubq4hPCUlRbZp00YCcu7cuSZ5Vq1aZSjvsccekzdv3jTEpaWlySZNmkhA/uc//7Eqj6J0VPWzqrrQ++8xJs9L/dFo7v/JyA2RjhavwgAOyBJ0GzWtfB9jaYg8N7+QRVtPOkii8hMcHMysWbNMwubOnQvAL7/8QlRUFH379jXEeXh48Kc//Yn/Z+++w6Mss/+Pv+80EgghoQRI6EWkCTEBaQKBr1JUxAL2BcsKCpZ1jYKuimBBFBcUFMUCuODPhliBdaVIVcCGAioKAgHpobck9++PyQwpM+nJM0k+r+uaa/LUOZMZzeF+nvscIMul5+wmTpyYZRJJ1apVmTZtGoGBgXzwwQc5LrEVxJ49e3j55ZcJCAhg7ty5OUb5AgMDGTBgQKHPXxiPP/54jnIumR+PP/641+MmTZrEwYMH+ec//8mQIUOyXDqsX78+06dPB+DFF18s1nivuuoqbrnllizrbrzxRlq2bMnhw4eLdVZxZrVq1QLIcnvBhg0beOedd2jYsCGzZs0iKirKsy0wMJCnn36a8847j6VLl7J+ff47KPz555+8//77BAQE8Oqrr2YZ5YuKimL69OkEBATw7rvvev0+GmN44403iI6O9qyrVq0aDz74IOCaLJXd4MGDqVy5cpZ1QUFBjBs3jpiYGP773/9y5MiRfL+H3Cxbtow1a9Z4/tsKDQ31bKtfvz6TJk0CYOrUqZw8eTLH8eHh4bz++uuEh4d71sXExHhG3L29P5GC8NVD+VDQWxVr1BBdVi7XfA2R+1pfFmS+HOcWFRVFjRo12L9/v9ftzZs3B2Dnzp1ezxkZGcmll16aY32zZs3o1KkTK1as4KuvvuKGG24oVMyLFi3izJkzdO3aldat/WOWW7t27Wjfvr3P7d9//z0//PBDjvWff/45AIMGDfJ6XHx8POHh4Xz//fecPHkySwJQFN4+H3Bdkt24caPPz7ao3LUOAwLO/jt6/vz5npjCwsJyHBMQEEC3bt348ccfWbVqFW3bts3Xay1btgxrLZ07d/Z6m0CrVq3o2LEjq1ev9vp9bNCggdfXcp/L1+/o119/ZcGCBWzevJmjR4963nNqairp6els3ryZuLi4fL2H3CxduhSAyy67zOtl8X79+lG3bl127drFunXr6Nq1a5bt8fHx1KlTJ8dxeb0/kfw620N5E8kpJzw9lK/v0JwmUU0cjq50KTksx2Iiw0j2kgjGROb8g1ZW1KtXz+v68PBw9u/f73W7e6TB22gE4LWYdeZtK1asYMeOHQUPNsOff/4J+NcMTl9lXNzGjBnjNTn8448/AOjQoUOer7F///4il/Rxa9Cggdf1ERERgO/Ptqj27dsHkCWZcf8Opk6dytSpU3M9PvvElNwkJycD0LhxY5/7NG3alNWrV3v2zaygv6PU1FTuvPNOXnvtNa+TiNwOHz6cZ+z5kZ/316RJE3bt2lUs70+kMAbGxRJebSMXvXUZAMEBwTzcfYazQTlAyWE5ltSnRZZp+QBhwYEk9WnhYFRFk3kEpzDbC0vdHlzS0lzfJfdEhtx4m1TgS17dSErqc83LunXrALKMyLl/B/Hx8bRp0ybX4wsyUuxO0HL7ruWWxBX0dzR58mSmT59OTEwMzz//PF26dCE6OtrzuXXp0oVVq1bl+poFUdrvT6QwrLU8uvhsuZpb4m6hUWQj5wJyiJLDcuzsEHn5ma1cEnJrdefeFhMTU+jzN2zYEIBffim793q61a9fn82bN/PII48UKPEJCQkB4OjRo163u0dX/cnevXtZuHAhABdddJFnff369QFITEzk2WefLbbXc496u0cmvdmyZQtAsYzIvvfeewC88sorXi/bb968ucivkVlpvz+Rwlj4+0JW7VgFQEhgCA9d+JDDETlD/xQr5wbGxbJiVC+2jL+EFaN6KTH0IiUlxXMvXWZ//PEHq1evxhhD9+7dC33+Xr16ERwczMqVK4vcOcKdZHmrB1ca+vXrB5xNLPLL/cd+06ZNObb99NNPRZrwUxLS09O58847OXnyJOecc06WCUPu38G8efMK9Dnk9dldeOGFGGNYvXo1v/76a47tGzdu5OuvvyYgIKBI30c3d21Ad7Kb2RdffOHzknhhv4M9evQA4JNPPuHgwYM5ti9cuJBdu3YRHh5OfHx8gc4tUhystTyy+OzEk9vibqNBNe+3M5R3Sg5FgH/+85/s2rXLs3z06FHuuOMO0tLSuOKKK3ze75Qf0dHRDB8+nPT0dK666qocf/jT0tL45JNP8nUud5K1efNmRxLEpKQkIiIieOqpp5g6darXGFavXp0jeezduzcAEyZMyHIP2/bt2xk6dGixXbosDt9++y19+vTh/fffp0qVKsyePZvAwLMzGM8//3wGDhzI5s2bGTx4sNf7UXft2sWkSZOy/H7y+uwaNmzIVVddRXp6OsOGDePQoUOebSkpKQwbNoz09HQGDx7sNaErKPc9sC+//HKWy/q///47w4cP93mc+30U9B86F154IR06dODIkSOMGDGCU6dOebYlJydz7733Aq7WkcU1kUmkID7+5WPW7nRVPggNCuXh7g87HJFzdFlZKrzOnTuTlpbGOeecQ69evQgJCWHp0qXs3buXpk2b5jnpID+effZZfv/9dz7//HNat25N586dqVevHnv27GH9+vXs2bMnXwlSw4YNiYuL47vvvuO8884jPj6eSpUq0aJFC5KSkoocZ17q16/PvHnzuPrqqxk5ciRPPvkkrVu3pkaNGuzcuZPff/+dnTt3cs0112SZ0TxixAheffVV1qxZQ4sWLejcuTMpKSl88803dOzYkS5durBy5coSjz+zefPmeW4bOHPmDCkpKaxfv94zitmmTRtmzpzJ+eefn+PYmTNnMmDAAD788EPmz59Pu3btaNiwIYcPH2b79u1s3LiR9PR0hg8f7mm7l5/P7uWXX2bTpk0sWbKEJk2aeLqnLF68mIMHD9KuXbti+T4CjB49mgULFvDKK6+wePFi4uLiOHDgAEuXLqVz587UqVPH62dy+eWXM3bsWCZNmsRPP/1EvXr1MMZwyy230KVLl1xfc86cOSQmJvL222+zdOlSunXr5imCfezYMXr37p3rRCmR4pK9QcT9FzdnzDdn7zW8I+EOYqoW/naisk4jh1LhhYSEsGjRIoYNG8aPP/7Ixx9/TEhICCNGjGD16tVey2cUVKVKlfjkk09466236N69Oz/99BPvv/8+mzZt4rzzzivQH/y5c+cyePBgDhw4wNtvv83rr7/OZ599VuQY8ysxMZGff/6Zhx56iOjoaFavXs28efPYtm0bzZs35+mnn+bJJ5/MckxUVBQrVqzghhtuIDU1lc8++4wdO3aQlJTEggULHOls8cMPPzBz5kxmzpzJ3LlzWbt2LTExMdxxxx0sXLiQH3/80WtiCK4Zsl9++SWzZs2ie/fu/P7778ydO5d169YRFBTE8OHDWbhwYY4RsLw+u5o1a7Jq1SrGjRtHbGws8+fPZ/78+dSvX58nn3ySFStWeC0DUxidO3fmm2++4ZJLLuHQoUN89NFH7Nixg4cffpiFCxf6/Ezat2/PO++8Q4cOHVi5ciVvvPEGr7/+utdL4dk1a9aM7777jqSkJMLDw/noo49YsmQJrVu3ZsqUKcyfP79AE5lECsPdQzk55QQWdw/lH9ic7KpZWjm4MqO6jXI2SIcZf7qcUxYlJCTY/Bbg3bhxIy1btizhiCS/lixZQmJiIj169MjR01dEpKIq73+ruo5f5LXMW6rZQ3LoLYzuNpqnej/lQGSlwxizzlqbkNs+fjFyaIwJNsb0NsZMNMasNsbsMsacNsYkG2PeN8b09HHcDGOMzeWR8+73rMdfb4xZZow5ZIw5aoxZa4wZYYzxi9+LiIiIFK/ceihHVIrg/i73l3JE/sdf7jnsAXyR8fNfwDrgGNAKuAq4yhgzzlr7qI/jVwDe6i7s8rIOAGPMVOBO4CTwJXAG6A1MAXobYwZZa9N8HS8iIiJlj68GEWlmH/d1uo/qYcVz60ZZ5i/JYTrwATDZWrss8wZjzDXAbOARY8xia623BrmvWWtn5PfFjDFX4UoM/wK6W2t/y1hfG1gMXAGMBCYX4r2IiIiIn/LWICKdk5yp/AH3dprtYGT+wy8un1prF1lrr86eGGZseweYkbF4YzG95OiM5wfdiWHGa+0G7shYHKXLy+Vbz549sdbqfkMRkQpkYFwsT1/ZlphqoVgsqWYP+4Nf5L7EC6kWWs3p8PyCv4wc5uW7jGfvjXULwBhTD4gHTgM5Kvlaa5caY5KBWKATULr1NURERKREDYyLZfvpudy94G4AoqtEM7Jj6VV98HdlJTlsnvHs6x7CRGPMeUA4sBtYDnxhrfXWsDUu4/lna633u1JhDa7kMA4lhyIiIuXK8TPHeWr52RnJo7uNpkpIFQcj8i9+nxwaY+oAQzMWP/Cx29+8rNtgjLnWWrs+2/rGGc+5NXPdlm1fERERKSemfjOVv47+BUBs1ViGJ/juClQR+fU9dcaYIOA/QDXgS2tt9h5j3wN3A61xjRrGAJcCP+Ca6fw/Y0z2ZsLhGc/HcnnpoxnPVQsfvYiIiPibw6cOM37FeM/ywxc+TGiQWjZm5u8jh9NwlZfZjpfJKNbaSdlWHQM+M8Z8ASzFdc/gaFwzj92M+/DCBmWMuR24HShSz10REREpOdnb5CX1acH3h6Zz4MQBABpHNubW8291OEr/47fJoTFmMnArrnIzva21f+X3WGvtaWPM08BHQP9sm49kPIfjm3vbEW8brbWvAq+Cq0NKfuMSERGR0uFuk+cuWZOccoJRc39kb9Bqzz6P93yckMAQp0L0W355WdkYMxHX5eK9uBLD3/I4xBt3d5Tsl5W3Zjw3zOXY+tn2FRERkTLk2YW/ZKllCHDyTDphJ68BoFWtVlzf9nonQvN7fpccGmMmAPcB+4GLrLUbCnmqGhnPR7Otd5fFaW2MCfNxbIds+4qIiEgZklubPIBxieMIDAgszZDKDL9KDo0x44Ek4CCuxPCHIpxucMbzmswrrbXbgW+BEGCQlxh64Kqn+BewqgivLyIiIg6JifQ+/pNm9hFfN54rzr2ilCMqO/wmOTTGjAMeBFJwJYa5jtoZY9obYy41xgRmWx9kjLkP12VpgH97OfzpjOdnjDHNMh0bDbyUsTjeR51EERER8XNJfVoQFpx1ZDCdkxwMmslTvZ/CGOPjSPGL5NAYMwD4V8biZuAuY8wML49RmQ5rBHwC7DHGrDLGvGeMWYCrfuHEjH0etNYuzP561tr3gZeBOsB6Y8wnxpi5wG+4SuDMA6aUwFuVPDRq1AhjTJ4PJ1veuWPIrmfPnsUS24wZMzDGMHTo0CKdJ7sxY8bk63dbXK87dOhQjDHMmDGjWM5XVO7PJ/MjPDycmJgYunfvzj/+8Q9WrlTN+8LaunUrxhgaNWrkdCgiwNk2ebGRYZCpTV5CU8tFTS5yOjy/5i+zlatn+jkh4+HNUsBdnOgHYDLQEdfkkjhc5Wl2AG8CU62163y9oLX2TmPMcmAE0AMIxDWJ5Q3gZY0aOqtPnz7UqVPH5/bctpVXW7dupXHjxjRs2JCtW7cW+jxNmzalW7duPrfntq086Nq1K82auS4YnDp1in379vHDDz+wbNkyJk2aRJcuXZg5c6Znn6KaMWMGN998M0OGDPGbRLkwevbsydKlS1m8eDE9e/Z0OhyRfBkYF0vz2BTavtwWm1HB7sleyzRqmAe/SA6ttTOAGQU8ZgtwbxFfdw4wpyjnkJIxatSoMvcHaNasWRw/frzItS+vuOIKOnXqRLVqJdMAvlu3bmU6SSmq2267zevo6OLFi7n//vtZuXIlXbp0YfXq1TRp0qT0AyyjYmNj2bhxI8HBwU6HIpLFo0se9SSG/Zv3p1uD8v0P4OLgF8mhSHlQXAXRq1WrVmKJofiWmJjIypUrSUxMZNWqVdxyyy2O3r5Q1gQHB3Puuec6HYZIFmt3rmXuxrme5ScSn3AwmrLDL+45FCksay39+vXDGMPtt9+eY3t6ejq9e/fGGMPIkWcb5WS+Pyo1NZXx48fTsmVLQkNDqV27NkOGDGHbtm05zpebvO45XLhwIVdeeSUxMTGEhIRQp04dunbtyjPPPMOJE2dLLni753Do0KE0buxq9f3nn39muW+upO/xct8H6utSdmHvtfz666+59tprqVevHiEhIdSqVYsBAwawfPlyr/tnvtfz9ddf54ILLiAiIgJjDCkpKQV6bV8qVarEq6++CsDSpUtZu3Ztjn2OHTvGhAkT6NChAxEREYSFhdG6dWvGjBnD0aNZK2c1atSIm2++GYCZM2fmem/nvn37ePDBBzn33HMJCwsjIiKCTp068dJLL5GampojjszfkyNHjpCUlETjxo2pVKkSsbGx3HHHHRw4cCDHcWfOnOGtt97iuuuuo0WLFlStWpXKlSvTqlUrHnzwwRzHLFmyBGMMS5cuBVxJtLf7f/O65/DPP//kzjvvpEmTJlSqVImoqCgSExOZM8f7xRv3PbJjxoxh9+7dDBs2jHr16lGpUiUaN27MqFGjOHnypNdjRdwe+vIhz8+DWg0irm6cg9GUHRo5rAiO/AXv3wxXz4CqtZ2OplgZY3jrrbdo374906dPJzExkeuuu86zfezYsSxatIi4uDgmTpzo9RzXXHMNn376KT179qRdu3asWLGCWbNmsWDBAr766itatGhRpBittdx5551MmzYNgISEBHr06MGBAwfYuHEjo0aN4pprrsk1yevWrRtHjx7lgw8+oEqVKlx99dWebTVr1ixSfE6YOHEiSUlJAJx//vl07tyZHTt28Nlnn/HZZ58xbdo0/v73v3s99q677uKll16ia9euXHrppfz666/Fev9QmzZtaN++Pd9//z1ffPEFCQlnb4HesWMHffr0YcOGDdSqVYvOnTsTGhrKmjVrePzxx/nwww9ZsmQJUVFRAFx99dWsXr2aFStW5LjXM/PPmzdvplevXmzfvp06depw2WWXcfz4cRYvXsyIESP48MMP+fTTT6lUqVKOeA8dOkTXrl1JTk6me/futGnThuXLlzNt2jS++eYbVq9eneVS7+7du/nb3/5GVFQU5557Lu3bt+fw4cOsXbuWCRMm8P777/P11197vld16tRhyJAhLFiwgN27d+e4Hzg/9/9+/fXX9O3bl5SUFBo3bswVV1zB/v37Wbp0KUuWLGHBggWe5Dm77du3Ex8fj7WWLl26cPjwYZYvX84zzzzDhg0b+Pjjj/N8famYFm1ZxBd/fAFAgAlgbOJYhyMqQ6y1ehThER8fb/Nrw4YN+d63WH3yD2vHRLqe/VzDhg0tYBcvXlyg45YtW2YDAwNt1apV7a+//mqttXbRokU2ICDAVq1a1f72229Z9t+yZYvFNYHJRkdH259//tmz7dSpU/bGG2+0gO3QoUOO13Ifl12PHj28xv78889bwNauXduuWrUqy7b09HS7aNEim5KS4ln35ptvWsAOGTLEa8wNGzbMz68kh8cee8zrefPi/ky2bNnidbuv9z1kyBAL2DfffDPL+vnz51vAxsTE2NWrV2fZtnz5chsREWGDg4PtL7/8kmWb+/derVo1+/XXXxfoPWSOM3s83tx6660WsDfccINnXXp6uu3cubMF7MiRI+2xY8c8244fP+75zmT//fr6PDPr0KGDBeygQYPsiRMnPOu3bdtmzznnHAvYUaNGeT0vYPv372+PHDni2ZacnGzr169vAfuf//wny3GHDx+2H3/8sT19+nSW9cePH7c333yzBezw4cNzxOjrc3bz9f08ceKEJ5Z7773XpqameratX7/eRkdHW8BOmzYty3Hu7ytgb7vtNnvq1CnPtg0bNtjw8HAL2OXLl3uNRwrPsb9VRfDhtztsl6e/tI0e/NR2efpLO3fddttxekfLGCxjsLd9dJvTIfoNYK3NI7fRZeXy7IloGFMN1r4ONt31PKaaa72fy37pKvMjMjIyx/7dunVj7NixHDlyhMGDB7Nt2zauv/560tPTmT59eq4zTx955BFatWrlWQ4JCWHKlClUq1aNNWvWsGLFikK/j9TUVJ566inAdRmwU6dOWbYbY0hMTCzVewyzX97M/pg3b16Jvv5jjz0GwGuvvcYFF1yQZVvXrl155JFHOHPmDK+88orX4x944AE6duxYojHWqlULgP3793vWLViwgFWrVtGpUycmT55M5cqVPdvCwsKYNm0a0dHRzJ49m4MHD+b7tZYtW8aaNWuoWrUq06ZNIzQ01LOtfv36TJo0CYCpU6d6vYwaHh7O66+/Tnj42XbxMTExntsovvzyyyz7V61alcsuuyzHxJGwsDCmTJlCUFAQH3zwQb7jz8t7773H9u3badiwIRMmTCAw8GzduTZt2jBmzBgAnnvuOa/H169fnxdeeIGQkLP9b1u2bMlNN90E5Hx/UvG4eygnp5zA4uqh/MAH3/PTn64i2JUCK/FYz8ecDbKM0WXl8uyeH2Hhv2DTp5B6AoLCoOWlcPGTTkeWp9xK2WT+o5zZ6NGj+eqrr1i4cCHnnXcehw4dYtiwYVxzzTW5vtaNN96YY121atW49NJLmT17NkuWLKFr164FfxPA2rVr2bdvH/VeaSLTAAAgAElEQVTq1aNv376FOkdxy6uUTXFNrPFm3759rFmzhoiICC6++GKv+/To0QOAVau8Nyi68sorSyw+t/R0VyWrgICz/37+/PPPAbjqqquyrHerUqUKCQkJfP7556xZs8bn+8vOfS/fZZddRvXq1XNs79evH3Xr1mXXrl2sW7cux3cxPj7e638r7skhO3fu9Pq63333HV9++SVbt27l2LFjuAYUXP842rt3LwcPHvRcHi8K9/u74YYbvM5kvvnmmxkxYgSbN28mOTmZ2NjYLNt79epFWFjOThd5vT+pOLz1UD6TZohKH8LxoKWM7DiSehH1HIqubFJyWJ5VrQOVqkLaKQgKdT1XiigT9x0WppSN+/7DJk2acOjQIVq1auUZdfElMjLS60gk4LkHcMeOHQWKI7M///wToMj3LRYnJ0vZbNmyBWsthw8fJigo9//97N271+v6hg0blkRoWezbtw8gS7L2xx9/AJCUlOS5X9IXX7F7k5ycDOCZcORNkyZN2LVrl2ffzHwl8xEREQA5RhuPHj3KDTfckOe9eocPHy6W5DCv9xcaGkpMTAzJyclek8OCvj+peHLroRxRKYLR3UaXckRln5LD8u7YHoi/GRJuhrVvwtHdTkdUoubNm+eZMbpjxw6Sk5Np2rRpkc6pYqm5c4+y5Udamutf99WqVWPgwIG57utroo23UaTitm6dq35+27ZtPevcsffo0SPPGeIFSWDdI3a5fc/c+3jjbRQzN6NHj+bjjz+mVatWjB8/noSEBGrWrOkZ1YuJiWHXrl25vmZBlPb7k4onJjKMZC8JYprZR1KXJGpUruFAVGWbksPy7trZZ3++9Hnn4igFP/30E/fccw8hISEMGjSI2bNnc80117By5cos9ytllpKSwqFDh7ze8+cu3RITE1PomNxJwi+//FLoczjN/bvLXqbFzT06mh/169cHXDXx/LUQ9/r16/nhhx8AuOiisy223LEPGjSIESNGFNvr1avnutzlHpn0ZsuWLQA5RtUK47333gPgnXfeoU2bNlm2HTt2jL/++qvIr5FZXu/v5MmT7Nq1Cyie9ycVT1KfFoyeuz7LpeV0TpJe5UPu7aQ+F4Whf5JJuXDs2DEGDx7MiRMneOaZZ5g1axaJiYmsW7cuz0uAs2fPzrHu0KFDfPrppwBF6tQSHx9PzZo12bFjBwsX5mjzXSDuJM1bzbuS5P6DvWnTphzbfvrpJ7Zv316gc7Vt25Z9+/b5ZYHpU6dOMWzYMAB69+5NXNzZmmj9+vUDziZX+ZXX5+a+x/KTTz7xOpFl4cKF7Nq1i/DwcOLj4wv02t646xi6k93M5syZ43MUr7DfP/f7e/vtt70eO3PmTKy1NGvWTMmhFIq7h3LdapWwmXooj77oIsJDwvM+geSg5FDKhREjRrBx40YGDBjAvffeS0BAALNnzyY6OpoXXngh1xm4Y8eOZePGjZ7lM2fOcM8993Do0CHi4+OL1Gs4ODiY0aNd97vcfPPNfPPNN1m2W2tZsmQJhw4dyvNctWrVIiQkhN27dxdoNmxR9e7dG4AJEyZw+PBhz/rt27czdOjQAl9+HDduHOCaCPTf//43x/bTp0/z8ccf+5yQUlKWLFlCly5dWLVqFbVr1+a1117Lsn3gwIHEx8ezdOlShg8f7rXA9B9//MHUqVOzrHMnPJm/Y5ldeOGFdOjQgSNHjjBixAhOnTrl2ZacnMy997q6hI4cOTLLTObCck/kyB7n2rVrPd9Vb/J6H74MGjSI+vXrs2XLFkaPHp3lNoQNGzZ4Zq/ff//9BTqvSGYD42Lp03k528IuIzn0FqJr/snt8TkbI0j+6LKy+KXx48fnetnx+uuv98wGnTVrFjNnzqR+/fq8+eabnn3q1q3LW2+9Rd++fbnllluIi4vLcS9YgwYNiI+Pp3379vTq1Ytq1aqxatUqtm3bRs2aNZk1a1aR38s//vEPNm7cyGuvvUanTp1ISEigWbNmHDhwgA0bNrB9+3a2bNmSZzmb4OBgLrnkEj788EPi4uLo2rUrYWFh1KxZk/Hjx+c7nuXLl3vtLezWoEEDxo49Wyx2xIgRvPrqq6xZs4YWLVrQuXNnUlJS+Oabb+jYsSNdunRh5cqV+X79yy+/nIkTJ/LAAw/Qp08fzjnnHFq0aEFISAjbt2/nl19+4dChQ7z88st07tw53+fNr9dee80zann69Gn279/P999/z549ewBXsvbmm2/muK8wICCAefPm0b9/f1555RXmzJlDu3btqFevHvv27WPbtm38+uuv1K5dO8tl506dOlGnTh2+/fZbEhISaN26NcHBwXTt2tXTPWXOnDkkJiby9ttvs3TpUrp16+Ypgn3s2DF69+7tKflSVI8++iiDBg3i4Ycf5t1336Vly5bs3LmT5cuXc+2117JixQqvtwpcccUVzJgxg6SkJL744guio10lsZKSknKdcBUaGsq7775Lv379eO655/jwww/p0KEDBw4cYMmSJZw+fZqbbrrJa4cjkfzac2wPE1edbXQwtudYKgXlLBov+ZRXIUQ9ykER7DLEXXA5r8e///1va621GzdutFWqVLFBQUE+i+GOGjXKArZTp06ewr+ZC/aeOXPGjhs3zp5zzjm2UqVKtlatWvbGG2/0WfTZHUN2eRUJ/uSTT+wll1xia9WqZYODg23t2rVtt27d7IQJE7IUPs6taPK+ffvsrbfeauvVq2eDgoIKVBQ7c1Hh3B7t2rXLcey2bdvsDTfcYGvWrGlDQkJs8+bN7ZgxY+ypU6cKXATb7fvvv7e33nqrbdq0qQ0NDbXh4eG2efPmdsCAAXb69Ol2//79Wfb39XvPL3ecmR+VK1e2devWtd26dbP33nuvXblyZZ7nOXHihJ0yZYrt3r27jYqKssHBwbZOnTo2Pj7e3n///XbFihVe3+sll1xiq1evbgMCArx+vnv37rVJSUme72F4eLjt2LGjnTJlSo6C1dbmXVx78eLFFrA9evTwui0xMdFWr17dVqlSxbZv396+8MILNi0tLdei5y+99JJt166dDQsL8/wO3Z97XkXat27daocPH24bNWpkQ0JCbLVq1Wz37t3tf/7zH5uenp5jf/f39bHHHvN6vvwUF5fCKYt/q+7+/G5Pwes2L7WxqWmpeR9UQZGPItjGFtOMtIoqISHBeuu/6s3GjRtp2bJlCUck+bF161YaN25Mw4YNffYMFhGpiMra36o/Dv7BuVPO5Uz6GQA+uvYjBrQY4HBU/ssYs85am5DbPrqsLCIiImXCvO+SeXbhL+xMOUFMZBhJfVrw3pZHPIlhtwbduOycyxyOsuxTcigiIiJ+z90mz12yJjnlBA9+8AM7TLInm3nm/55RbdpioNnKIiIi4ve8tck7lWqJSh0CwOUtLqdL/S5OhFbuaORQKqRGjRoVWwcIEREpebm1yQswATzV+6lSjqj80sihiIiI+L2YSO+tM9PMPm5ufzOtarUq5YjKLyWHIiIi4veS+rQgLDgwy7p0TnIsZA5jeo5xJqhySpeVRURExO8NjHN16ZmwcBM7U06QavZyMGgmI7tdQL2Ieg5HV74oOSxl1lrNpBIREb/k7/diD4yLZVfqx9z5+Z0ARIZGMqrbhw5HVf7osnIpCgwMJC0tLe8dRUREHJCWlkZgYGDeOzrk6OmjPL70cc/yQ90eIiosysGIyiclh6WocuXKHD161OkwREREvDp69CiVK1d2Ogyfnl/1PLuP7QagXkQ9RnYc6XBE5ZOSw1IUERHBgQMHNHooIiJ+Jy0tjQMHDhAREeF0KF7tPrqbCSsmeJYf7/k4YcHeZzBL0eiew1JUtWpVTpw4wZ9//kn16tUJDw8nMDBQ9yCKiIgjrLWkpaVx9OhRDhw4QJUqVahatarTYXltk/ffnU9y7MwxANpEt2FIuyEOR1l+KTksRcYYoqOjOXLkCIcPH2bPnj0aRRQREUcFBgZSuXJlatasSdWqVR0fsPDVJm+n2eTJWib83wQCA/z33siyTslhKTPGEBER4bfD9iIiIk7y1SavmrmJo0GL6dW4F32b9XUouopB9xyKiIiI38itTR7Asxc96/joZnmn5FBERET8Rm5t8m5oewPn1z2/lCOqeJQcioiIiN/w1SbvSMhsnuj1hENRVSy651BERET8hq82eXd0TaBRZCNng6sglByKiIiIXxkYF0vymXmMnO8qch0ZGslDF851OKqKQ5eVRURExK8cPnU4S5u8f134L6qHVXcwoopFyaGIiIj4lWeWP8Pe43sBaFitISM6jnA4oopFyaGIiIj4je2HtvP86uc9y0/2epLQoFAHI6p4dM+hiIiIOMJbm7y5Wx/mZOpJABJiEriu7XUOR1nxKDkUERGRUue9Td737DDbPNnJcxc9R4DRRc7Spt+4iIiIlDrvbfIgKnUIAJe3uJwejXo4EVqFp+RQRERESl1ubfKCAoKYcNGEUo5I3JQcioiISKnLrU3e8PjhnFPjnFKOSNyUHIqIiEip89Um72Touzza41GHohLQhBQRERFxgLtN3jMLNrLz0EnSMtrkPfZ//alVpZbD0VVsGjkUERERRwyMiyWx4yK2hV1Gcugt1KyxhbsvuNvpsCo8JYciIiLiiG2HtvHv1f/2LD/d+2kVvPYDSg5FRETEEaO/HO0peN0hpgPXtrnW4YgEdM+hiIiIlDBvnVDq1trBnPVzPPtMvHiiCl77CSWHIiIiUmK8dUIZPfdHKlX/wLPPVS2v4sKGFzoVomSjFF1ERERKjLdOKCfOpLNvT1cAQgJDVPDazyg5FBERkRKTWycUgHsuuIcmUU1KMyTJg5JDERERKTG5dUKpWbkmD1/4cClHJHlRcigiIiIlxlcnlINBMxnbcyzVQqs5FJn4ogkpIiIiUmLcnVCeXfgLySnHSc3ohNKo7l7+Hv93h6MTb5QcioiISIkaGBdLk5j9xL0SR7pNB2DixfMJClAa4o90WVlERERKlLWW+xbe50kM+zbrS99mfR2OSnxRcigiIiIl6tNfP+XLLV8CEGgCmXjxRIcjktwoORQREZESczrtNP/87z89y7fH306rWq0cjEjyoov9IiIiUiy8tcn7/cT/47cDvwEQGRrJ2MSxDkcpeVFyKCIiIkXmrU3eqLk/si/of559HuvxGDUr13QqRMknXVYWERGRIvPWJu/kmXRCTw4GoEWNFozoMMKJ0KSAlByKiIhIkeXVJu/5Ps8THBhcmiFJISk5FBERkSLLrU1e32Z96d+8fylHJIWl5FBERESKzFebvMPBb/H8xc87FJUUhiakiIiISJG52+RNWLCJnYdOeNrk/b1Le1rWaulwdFIQSg5FRESkWAyMi2Xj0Vk8tOghAGqE1eCxHh86HJUUlC4ri4iISLHYdWQXTy1/yrM8NnEsUWFRDkYkheEXyaExJtgY09sYM9EYs9oYs8sYc9oYk2yMed8Y0zOP4683xiwzxhwyxhw1xqw1xowwxuT6/gp7nIiIiOQ06stRHD19FIA20W24Pf52hyOSwvCXy8o9gC8yfv4LWAccA1oBVwFXGWPGWWsfzX6gMWYqcCdwEvgSOAP0BqYAvY0xg6y1acV1nIiISEXnrRNK7ZrbmPXDLM8+k/pMIijAX9IMKQh/+dTSgQ+AydbaZZk3GGOuAWYDjxhjFltrF2fadhWuBO8voLu19reM9bWBxcAVwEhgcrZzFuo4ERGRis5bJ5TRc38kKOo9zz5XtryS3k16OxWiFJFfXD611i6y1l6dPTHM2PYOMCNj8cZsm0dnPD/oTvAyjtkN3JGxOMrLZeLCHiciIlKheeuEcuJMOgf3XghAaFAoEy+e6ERoUkzKSvLzXcZzPfcKY0w9IB44DbyX/QBr7VIgGagDdCrqcSIiIpJ3J5SkLkk0imxUihFJcSsryWHzjOddmdbFZTz/bK31/k2FNdn2LcpxIiIiFV5unVDqR9RnVLdRpRyRFDe/Tw6NMXWAoRmLH2Ta1Djj+c9cDt+Wbd+iHCciIlLh+eqEcjBoJs9e9CyVgys7FJkUF3+ZkOKVMSYI+A9QDfjSWvtJps3hGc/HcjnF0YznqsVwnIiISIXn7oTy7MJNJKec7YSS0NQyuPVgh6OT4uDXySEwDVd5me3knIxiMp5tAc9Z2OPOnsCY24HbARo0aFDY04iIiJRJA+NiMWFrGfjOQAACTAAv9P0WY0weR0pZ4LeXlY0xk4FbcZWb6W2t/SvbLkcynsPxzb3tSKZ1hT3Ow1r7qrU2wVqbUKtWrVxOIyIiUv6cTD3Jff+9z7M8LH4Y7eq0czAiKU5+mRwaYyYCdwN7cSWGv3nZbWvGc8NcTlU/275FOU5ERESA51Y+xx8H/wAgKjSKcYnjHI5IipPfXVY2xkwA7gP2AxdZazf42NVd3qa1MSbMx8zjDtn2LcpxIiIiFYq3TihxjVN5atnZ/snjEsdRo3INB6OU4uZXI4fGmPFAEnAQV2L4g699rbXbgW+BEGCQl3P1wFUX8S9gVVGPExERqUjcnVCSU05gcXdCWc/Qt6dwItU1rtK+TnuGJwx3NlApdn6THBpjxgEPAim4EsP8jNo9nfH8jDGmWaZzRQMvZSyOt9amF9NxIiIiFYL3Tihp/LatlWd5Sr8pBAYEZj9Uyji/uKxsjBkA/CtjcTNwl48ZT5ustePdC9ba940xL+NqebfeGPM/4AyuGc4RwDxgSvaTFPY4ERGRiiKvTih/a/c3ujboWpohSSnxi+QQqJ7p54SMhzdLgfGZV1hr7zTGLAdGAD2AQGAT8Abwsq/Rv8IeJyIiUhHERIaR7CVBTDP7qBpSlWf+7xkHopLSYKwtdLk/ARISEuzatWudDkNERKRYue85zHxpOZ2T7A9+kSf6X84/Ov/DweiksIwx66y1vgbhAP8ZORQRERE/crYTyi8kpxz3dEJpVHcvIzuOdDg6KUlKDkVERMSrgXGxVK/+Oz1mXOZZN6XfIoIDgx2MSkqa38xWFhEREf+Smp7KyM/PjhJe0/oaEhsnOhiRlAYlhyIiIuLVlG+msH7PegAqB1fmuYufczgiKQ26rCwiIlLBeeuE0rGZ4dHFj3r2eaT7I9SLqOdglFJalByKiIhUYNlnJbs7odSrt5Qjp48AcG7Nc7mv831OhimlSJeVRUREKjBfnVA2bj3Hszy1/1RCAkNKOzRxiJJDERGRCiyvTijXtrmWXo17lWZI4jAlhyIiIhVYTGSY1/XuTigTL55YyhGJ0wp8z6ExphbQHqgNRAIHgT3Ad9bafcUbnoiIiJSkpD4tvHZCORg0kyd6Pk5M1RgHoxMn5Cs5NMbUA4YBlwOtc9nvZ2Ae8Kq1dkexRCgiIiIlxlcnlKYxB7jrgrscjk6ckGtyaIxpCjwNDMy070FgI3AAOAxEADWAc4E2GY9RxpgPgdHW2j9KJnQREREpDgPjYgmr+hN9Z5/thPLSJcsIClBRk4rI56dujJkA3A2EAGuBmcD/rLW/5HLMucBFwBBgEHC5MeYFa+0DxRq1iIiIFJuTqScZOf9sJ5Qh7YbQrUE3ByMSJ+U2IeWfwCfAedbajtbaqbklhgDW2k3W2hettQlAO+BTQIWRRERE/Ngzy59h84HNAESGRjLhogkORyROym28OMFa+11hT2ytXQ9cbYyJK+w5REREpPh464TSusFxnl7+tGefJ3s9SXSVaAejFKf5TA6LkhiWxHlERESk8Lx3QvmRatGfcSrtFAAdYjowLH6Yk2GKH9CdpiIiIhWA904o6RzZGQ+hEGACmHbpNAIDAh2KUPyFimCLiIhUAHl1QhnZYSTn1z2/NEMSP1WgkUNjTBRwJ5AIxAChPna11tqmRYxNREREiklMZBjJXhLENLOPuuF1GddrnANRiT/Kd3JojGkGLAXqACaP3W1RghIREZHilVsnlBl9JxNRKcLB6MSfFGTkcCJQF1gG/Bv4DThaEkGJiIhI8XJ3QpmwcBM7U054OqFc2CKUq1td7XB04k8Kkhz2BLYCF1lrT5dINCIiIlJiBsbFsuPMh9w139UWr1JgJab2/xlj8rogKBVJQSakWOAbJYYiIiJl084jO3l40cOe5YcvfJim1TVFQLIqSHL4Pa77DUVERKQMumfBPRw+dRiAc2qcwwNd1d1WcirIZeXngHnGmC7W2pUlFZCIiIgUjbdOKEFVvuP9De979pl2yTQqBVVyMErxV/lODq21nxpj/gF8ZoyZAiwEdgDpPvbfVjwhioiISH5564Qyau6PnAh707PP0PZDSWyc6FSI4ucK2iHlO2A38FDGwxdbiHOLiIhIEXnrhHLyTDppqZdC6FxqVq7Jcxc951B0UhYUpM5hT2ABEJKxaj8qZSMiIuJX8uqEMvHiidSoXKM0Q5IypiCje+NwJYYTgPHW2pSSCUlEREQKK7dOKL0a9+Km825yICopSwoyW7k9sM5aO0qJoYiIiH9K6tOCsODALOvSOcnRkNlMu2SaahpKngoycngCV1cUERER8VPuTihPz/+Zvw6fIs3s42DQTEb3/j+a12jucHRSFhRk5HAZ0LqkAhEREZHicXn7GOo2eYltYQNIDr2FhnX2qKah5FtBksNHgKbGmHtKKhgREREpurkb5/LRLx95ll+97FVCAkNyOULkrIJcVk4A3gSeN8ZcTd51DmcVPTwRERHxxVux654tqzBy/kjPPn8//+90a9DNwSilrDHW2vztaEw6rvqF7jtZcz3QWhuY2/byIiEhwa5du9bpMEREpILJXuwaICw4kGaNvuHTHY8BUCe8DhtHbCQyNNKpMMXPGGPWWWsTctunICOHs8gjIRQREZHS4a3Y9YkzaXy3uT6Eupan9JuixFAKrCDt84aWYBwiIiJSAHkVu768xeVc2fLK0gxJyomCTEgRERERPxETGeZ1fZrZR0SlCKb2n6qahlIoSg5FRETKIF/Frg8GzWR87/HERsQ6FJmUdT6TQ2PM7caYIk0qMcYEGmNuL8o5REREJKeBcbE8fWVbYiJDAUuq2cP+4BeJa5zKsIRhTocnZVhuI4fTgA3GmCHGGO9j1z4YY8KMMUOBjcDLRYhPREREfBgYF8u1iT/zZ9hlJIfeQmqlVUy/bDoBRhcGpfBy+/Zch2u+0xvAX8aY14wx1xljGnnb2RjT2BhzvTHmDeAv4HUgBLi2eEMWERERgK0pW3noy4c8yw91e4iWtVo6GJGUBz5nK1tr3zHGfATcB9wJ3ALcDGCMOQUcAA4DEUANXIkguOog7gCeAiZba0+WWPQiIiIVgLdi15e3j2HYp8M4duYYAK1qtWJUt1EORyrlQb6KYGfce3glMBDoDni7y3U7sBiYB3xsrfXaOaW8URFsEREpSb6KXfeLP8i/f7geAINh5a0r6VSvk1NhShlRbEWwrbVpwHsZD4wxNYFooBqQAuyx1u4vWrgiIiKSna9i1+9/cwoquZbvueAeJYZSbArSIcXDWrsP2FfMsYiIiEg2vopdm/QaADSObMwTvZ4ozZCknNN0JhERET+WW7FrgOmXTadKSJXSDEnKOSWHIiIifiy3Yte3xd1G7ya9HYpMyqtCXVYWERGR0jEwzjUH9NmFv5CccpxUs5eDQTOJjPqNZy+e53B0Uh4pORQREfFzA+NiCa26nn6zL/Ose/uSj4gMjXQwKimvdFlZRETEzx0+dZhhn55tiXdN62sY0GKAgxFJeabkUERExM898MUDbDu0DYAaYTV4od8LDkck5ZkuK4uIiPiR7N1Q+sWd4ZV1r3i2v9jvRaKrRDsYoZR3GjkUERHxE+5uKMkpJ7BAcsoJXlt8jMqpPQAYeO5Arm1zrbNBSrmn5FBERMRPeOuGApWISh1CVGgUL1/yMsYYR2KTiqNAyaExppEx5hVjzGZjzHFjTJqPR2pJBSwiIlJe+eqGEmhr8kK/F6gTXqeUI5KKKN/3HBpjWgPLgQggr3+26J81IiIiBRQTGUaylwQxJPgYN7S9wYGIpCIqyMjhk0A1YD5wAVDNWhvg61Ei0YqIiJRj3rqhWE7xUP82upwspaYgSVx3YCtwhbV2jbX2SMmEJCIiUjENjItlSPcgUs0eLOmkmj1c1ekUN3du43RoUoEUpJRNJWCNtfZMSQUjIiJSkR07fYzXNg4nOfR3APo378/Eyz91OCqpaAoycvgrrsvKIiIiUgJG/W8Uvx90JYYRlSJ45dJXdDlZSl1BRg6nA88ZYxpZa7eWUDwiIiIVQvZi1/3PT2XKmime7ZP7TqZeRD0HI5SKKt8jh9bal4B3gf8ZY/oZYzTpREREpBC8Fbuevuiop9j1pedcypB2Q5wNUiqsgpSy+SPjx0bAp0CqMWYXkO5ld2utbVr08ERERMqf3IpdVwr/kVcvfVWXk8UxBbms3CjTzwYIBhr42NcWNiAREZHyLrdi11P7T6Vu1bqlHJHIWQVJDhuXWBSAMaYF0BfoACQA5+BKQgdZa9/3ccwMILdx91+stefm8prXA3cA5wGBwCbgTeBla623EVEREZEi81XsulLwcfVOFsflOzm01v5ZkoHgStLuKeSxK4DNXtbv8nWAMWYqcCdwEvgSOAP0BqYAvY0xg6y12cf8RUREiiypTwtGz12f5dKy5RT/uuQ8XU4WxxVk5LCk/QQ8C6wF1gGvAz3yeexr1toZ+X0hY8xVuBLDv4Du1trfMtbXBhYDVwAjgcn5PaeIiEh+DYyLZd2ub3lz2T4CbU3SzD6GdIvib51aOh2aSOGSQ2NMZ6AnEJuxKhlYYq1dVdhArLWvZXuNwp4qP0ZnPD/oTgwzYthtjLkDWAKMMsa8qMvLIiJS3PYe28v0DX9nd+huAK5vez1PXjLb4ahEXAqUHBpjGgGzgU7uVRnPNmP7KuBGf66DaIypB8QDp4H3sm+31i41xiTjSnw7AStLN0IRESlPstczvP/ic/jP5nvYfcyVGNYNr8uL/V50OB+MwicAACAASURBVEqRswpSyiYK1yXXhsAx4BPgd1wJYmPgMqALsMgYE2+tPVj84fqUaIw5DwgHdgPLgS98jPrFZTz/bK31Pl0M1uBKDuNQcigiIoXkrmfovrcwOeUED3zwPTsD9nv+Ar8+4HWqh1V3MEqRrAoycvgArsTwA2C4tXZ/5o3GmOrANOBqIAl4qLiCzIe/eVm3wRhzrbV2fbb17lnXuU2w2ZZtXxERkQLzVs/wTJohKn0Ix4OWMix+GP2a93MoOhHvCtLl5HJcs39vzJ4YAlhrDwA3ZewzsHjCy9P3wN1Aa1yjhjHApcAPQCtc3Vxisx0TnvF8LJfzHs14rlp8oYqISEWTWz3DplFNee7i50o5IpG8FSQ5bAQss9ae8rVDxrZlZC2YXWKstZOstS9aazdYa49Za3dZaz8DOgKrgWjOTj5xy3KfZGEYY243xqw1xqzdu3dvYU8jIiLlXExkmNf1aWYfs66YRXhIuNftIk4qSHJ4Bqicj/3CMvZ1jLX2NPB0xmL/bJuPZDzn9l+ke9sRbxutta9aaxOstQm1atUqfKAiIlKuJfVpQVhwYJZ16ZzkwtYH6VK/i0NRieSuIMnhRlwTP+r42iFjW6+MfZ22KeM5+2XlrRnPDXM5tn62fUVERApsYFwsTwxsSUBQCpZ0Us0eqtT8mJnXjXQ6NBGfCjIh5T/AC7ju47vbWrso80ZjTCKuotGVgbeKL8RCq5HxfDTb+u8ynlsbY8J8zFjukG1fERGRQvnpyAy2BI+BYAgJDGH+TWsJCQxxOiwRnwqSHE4DrsLVteQLY8xOYAuue/ca4xqhM7jK3Uwr5jgLY3DG85rMK621240x3wLnA4OAWZm3G2N6APVwdU8pdFFvERGRr3d8zbivxnmWn0h8gra12zoYkUjeCtJbOdUY0xcYBwzHlQxmvmR7FFdS+Ehp9CQ2xrTHlcTNz/x6xpggXDOY785Y9W8vhz+NqwD2M8aYldbazRnHRgMvZewzXt1RREQkv7IXu76rd0MeWX0jaRl/oi5scCH3db7P4ShF8masLfikXWNMKK4uI+7Rwh3AOmvtyUIHYsz5nE3MwFWKpirwG3DAvdJa2ylj/4HAhxnbfs2IoSrQFldJm3RgtLV2go/Xewm4AzgJ/A/XJJreQAQwD7g6P0luQkKCXbt2bUHeqoiIlDPZi10DBASksjvw3xwPWkpEpQh+GP4DjSIbORekCGCMWWetTchtn0L1Vs5IAlcUKirfIoALvKxv7mP/H3Dd49gR1+SSOFyXuHcAbwJTrbXrfL2YtfZOY8xyYASuS+WBuCaxvAG8rFFDERHJL2/FrtPTg4iyrmLXU/pNUWIoZUahksOSYK1dwtkahPnZfwtwbxFfcw4wpyjnEBERya3Y9eDWg7nxvBtLOSKRwvOZHBpjumf8+I219mSm5Xyx1n5VpMhERETKiJjIMJK9JYgBB3n5kpcxJt9jHyKOy23kcAmuy7Qtcd3T517OD5vHuUVERMqNpD4tctxzmM5Jbu9Rm+ph1R2MTKTgckvgvsKV5B3PtiwiIiKZDIyLJflIMuPn/0yArUma2Ufnc/fyrz4POB2aSIH5TA6ttT1zWxYRERGXU6mneH3jcHaEunontI1uy1s3fONwVCKFo0u/IiIiBZC9nmFSnxas2DuJ7/5yJYYhgSHMvnI2oUGhDkcqUjj5Tg6NMW8Ay621b+Sx31Cgu7X2liLGJiIi4ley1zNMTjnBAx98T7JZ4/mLOuH/JqgLipRpAQXYdyjQLR/7dQWGFCoaERERP+atnuHpVIhKdf3Z69usL3dfcLe3Q0XKjIIkh/kVjKs7iYiISLmSWz3D6CrRzLh8hsrWSJlXEslhayClBM4rIiLiqJjIMK/r08w+3rz8TWqH1y7liESKX673HGbcZ5hZNy/rMp+rJXA+8FkxxCYiIuJXfNUz7NjiL/o3v9nByESKT14TUoZm+tkCzTIeufkLeLgIMYmIiPilgXGxnEk7zQMfriA9rRppZh/h1Rcx58bpTocmUmzySg7d/wwywBvAcuB1H/ueBpKB1dba08UTnoiIiH9ZsW8yW0MmAxAaFMrCIWtVtkbKlVyTQ2vtTPfPxpgxuBK/mb6PEBERKb8+/fVTJn892bM88eKJtI5u7WBEIsUv33UOrbWNSjAOERERv5K92PVt3WuRtHyoZ/uAFgO4I+EO5wIUKSElMVtZRESkTHMXu05OOYHFVex67Ce/c+JIGwBiq8byxoA3VLZGyiWfI4fGmL9l/PihtfZIpuV8sdbOKlJkIiIiDvFW7NraYKJSh3AyeBlzrppDjco1HIpOpGTldll5Bq4ZyquBI5mW80vJoYiIlEm5Fbt+pPsjdG/YvZQjEik9uSWHs3Alg4eyLYuIiJRrMZFhJHtJEIOCjvCv7v9yICKR0uMzObTWDs1tWUREpLxyFbv+kRNnznaDtZzi4f5tCArI91xOkTJJE1JERESyGRgXS+/2u0k1e7Ckk2r28LcLg7ily3lOhyZS4ortnz/GmBpAirU2Lc+dRURE/Nh3u75j+sZhnA519XS4q+NdjOv3gsNRiZSOfCeHxpj2wMXAx9baTZnWX4yra0oMcMgY86C1Vn2ERESkTMhez3BkrwY8+vVgTqe5EsP2ddoz4aIJDkcpUnoKcln5LuAp4LB7hTGmNjAXiMU1WSUSmGaM6VCcQYqIiJQEb/UMH573Mzv3xAIQHhLOu1e/q/Z4UqEUJDnsAvxord2Zad1NQGVgEhAKXImrD/NdxRahiIhICfFWzzA9PYio1CEAvHrpqzSv0dyJ0EQcU5DkMBrYnm3dRcAZ4HFrbaq1dh6wFrigmOITEREpMbnVM7z9/Nu5ru11pRyRiPMKkhxWBY5mW9cR+NZaeyjTut9xXWYWERHxazGRYV7XBwQeYlLfSaUcjYh/KEhyeBBo6F7ImKBSDVjh5Zxnih6aiIhIyUrq04Kw4Kx/Ci0neaBPC8KCvSeOIuVdQZLDtcAFxhj3JeN/4JqEsijbfs2BXcUQm4iISIkaGBfLxXH7s9QzHNw5jTu6a16lVFwFqXM4GegHrDTGpABRwB/AQvcOxpiaQFvgveIMUkREpCR8t+s7XtlwG6dCTwFwW9xtPDtA1dikYst3cmit/a8x5hbgUVyTU5YAd2Yren0TEJixTURExG9kr2c4olc9Hl09iFNprsSwTXQbJveb7HCUIs4z1triO5kxYUAIcLSidEpJSEiwa9eudToMERHJhbueYeayNcacYU/QJI4HLSU8JJy1f19Li5otHIxSpOQZY9ZZaxNy26dYeytba09Yaw9VlMRQRETKBm/1DK0N9tQzfH3A60oMRTIUqreyMSYW6M7ZkjXJwFfW2uTiCkxERKS45FbP8K6OdzG49eBSjkjEfxUoOTTGRAJTgcHkHHVMN8a8A4y01qYUU3wiIiJFFhMZRrKXBDEw6DDPXfycAxGJ+K98X1bOuJ9wEXAtrhZ5XwNzgLeB1RnrrgO+zNhXRETEL3ivZ3iKh/u3ISQwxKGoRPxTQe45vBdoD6wC2lpru1hrb7LW3mit7YqrhM2KjH3uLv5QRURECuf/t3ffcXaVdeLHP98pyaQnGEIgEDqhYyAo0iFAkBo6goKwygoWFAhlXddd/UkR/QkriGJHRH+aREBRpKwEWdZdSigWFF0RiCIEiBLSpjy/P+6dYTI592bKnVs/79drXoc59zlnvufhSeabp525M6cxa4en19rP8OwDRvIPe+9W6dCkqjOQYeWTyb0l5cg+r8sDIKX0m4g4htzr804FripNiJIk9V/fLWvmzZnBiLGP8+2nP0xqy+3Q8dH9PsrHDz6rwpFK1WkgyeG2wJ1ZiWG3lNKyiPgZcPiQI5MkaYD6blmzZNlKLlnwOK+OuJ5ELjE8eMuD+bcD/62SYUpVbSDDyoncvEJJkqpS1pY1qzsSI1aeCMCm4zflOyd8h+am5kqEJ9WEgSSHfwAOiIhxhQpExHjgQOD3Q4xLkqQBK7ZlTWtTK/NPms+UMVPKHJVUWwaSHH4f2AC4PSK27fthRGwD/IDcO5e/V5rwJEnqv00mZm+W0RlLufbwa3nrpm8tc0RS7RlIcvg54JfAAcCvI+LnEXFTRHwzIn4O/AY4KF/mmtKHKklScbkta9YeMu5iFTtv9QfeN+t9FYpKqi39XpCSUloREQcBNwAnAPvkv3qKAPOBc1NKK0oapSRJ/TB35jReW/Ma/3zb/0DXJDpjKePedB8L330DEU6bl/pjQG9ISSm9DJwcEdOB/ci9Pi+A54Gfp5SeLX2IkiT1T0dXBzf97oM8O/IeACaMnMCisx9hdOvoCkcm1Y5BvVs5nwR+u8SxSJLUb1n7GT649Fru+d97esrcfPzNbL3B1hWMUqo9600O8+9TngNsDqwGHkspLRruwCRJKiRrP8N58xfz56b/6fnN9vEDPs5R2x1VwSil2lQ0OYyIk4EbgXF9zi8GjkspPTeMsUmSlClrP8P2zmBS15msaFnE0dsdzb8c8C8Vik6qbQVXK0fEbsDNwHhgBfAY8L/kFp7sDiwoR4CSJPVVbD/D7d60Hd867ls0xUA25JDUrdifnAvI9SzeDGycUtojpbQtMAv4I7BHRBw4/CFKkrS2QvsZdsXL3HrKrUxom1DmiKT6USw53A/4C/DelNLy7pMppceAj5Bbpbzf8IYnSdK6Cu1neMa+k9hhwx0qFJVUH4olhxsDD6WUVmd8dn/+uEnpQ5Ikqbi5M6cx960r6YgXSXTRES+y387P8akjj610aFLNK7YgZSTwStYHKaVl+c1ERw5HUJIkdcvasmbLjZfy70+8kxVtuXcuHLHtEdx06u0VjlSqD4Pa51CSpHLI2rLm0oVPsGrUV1nRnksMt9lgG759/LdpbmouditJ/bS+5HBqROw/mM9TSvdnnZckqb+ytqxZ1d5FR8eR0LaAcSPGcfuptzOxbWKFIpTqz/qSwzn5ryypyOepH/eWJKmoYlvWBMEtJ9ziAhSpxIolcM+SS/IkSaqITSaOYklGgtgZS/nUwZ/yDSjSMCiYHKaUtihjHJIkrWPenBlrzTmE3JY122/xOy7d9/IKRibVL7ePlyRVrbkzp3Hh4RvT1bS0Z8uacZN/yO1nf4z8rhmSSsx5gZKkqrV8zXI+/+QZPDfyCQCmjJnCT977EKNbR1c4Mql+mRxKkqpC3/0MLzpsW775uw/yxF9ziWFrUysLTl7A9AnTKxypVN9MDiVJFZe1n+FF8xfzQvOynt9UXzzqi+w7fd8KRik1BuccSpIqLms/w86uZiZ1nAnAhW+7kLNnnl2J0KSGY3IoSaq4YvsZHrntkVx1yFVljkhqXCaHkqSK22TiqMzzTc1/45YTbvHVeFIZmRxKkipu3pwZtLWu/SspsZp/evtOjB85vkJRSY2papLDiJgREedHxM0R8VREdEVEiogT+3HtaRHx84j4W0Qsj4iHI+L9EVH0+QZ7nSSptI7ebSobTr2LjnixZz/Dc2dP4L37zqx0aFLDqabVyucC5w/0ooi4HjgPWAXcC7QDs4HrgNkRcVJKqbNU10mShqbvljXz5sxg0V8/wwNLr4G2XJmvHfM1zpo5u7KBSg2qmpLDXwJXAw8DjwBfBQ4odkFEnEAuwXsB2D+l9HT+/EbAz4DjgA8A15biOknS0GRvWfMof2la3PMb6eK9L+asmWdVMEqpsVXN8GlK6SsppYtTSt9LKf2hn5ddlj9e0p3g5e/1V3I9kQCXZgwTD/Y6SdIQZG1Z09HZ1LNlzfE7HM8Vh1xRidAk5dVs8hMRmwJ7AGuA7/f9PKW0CFgCTAX2Gup1kqShK7ZlzZ6b7Mm3jvsWTf67XKqoWv4T2D1L+Vcppey/beChPmWHcp0kaYgKbVlD06vc/o7bfWeyVAVqOTncMn/8U5Eyz/YpO5TrJElDVGjLmosO25apY6dWKCpJvdVycjg2f3y9SJnl+eO4ElwnSRqio3ebykab3LvWljVnH9jGBw98W6VDk5RXTauVByryx1Sm6964QcQ5wDkA06dPH+xtJKmuFdqy5v4X39iy5vojrue8PY+obKCS1lLLyeFr+ePYImW6P3ut17nBXtcjpXQjcCPArFmzBp1kSlK96s+WNRfsdQHn7XleBaOUlKWWh5WfyR83L1Jmsz5lh3KdJKmf1rdlzQk7nMDVh11didAkrUctJ4eL88edIqLA8jf27FN2KNdJkvqp2JY1e2+2t1vWSFWsZv9kppSeAx4FRgAn9f08Ig4ANiX3FpT/Gup1kqT+K7RlTTQv47ZTb2NUa6F/m0uqtJpNDvO6t9G/KiK26T4ZEVOAL+S/vTKl1FWi6yRJ/VBoy5rL3r4jk0dPrlBUkvqjahakRMTuvJGYAeyYP14eERd1n0wp7dXrv+dHxA3kXnn3ZETcA7QDs4HxwK3AdX1/1mCvkyStK2tV8mE7T+Lj9y1g+Yv70Jwm0xVLOf+QLfnHffeodLiS1iNSqo7FthFxIPCz9ZVLKUXfcxFxGvB+YBegGXgK+BpwQ7Hev8Fe19usWbPSww8/3J+iklR3+q5KBmhrbWLy1Lv4z6XXABAE80+ez/E7HF+pMCXlRcQjKaVZxcpUTc9hSuk+3tiDcKDX3gLcUq7rJEk5WauSV7V38czzu/bsZfjvb/93E0OphtT6nENJUgUVW5UMcOk+l/KBt3ygnCFJGiKTQ0nSoBValdwZSzljtzO4fPblZY5I0lCZHEqSBm3enBmMam1e61wXq5g+bTFfOforRAxqtpCkCjI5lCQN2tyZ0zjrwJF0xoskuuiIF5kw5Q7uOudyWptbKx2epEGomgUpkqTqlrVlzdabvMIVDx/PsrZlAGw9aWvu/YcHGTui2OvrJVUzk0NJ0nr13bJmybKVXLLgcV4fdSPLOnKJ4ZQxU7jznXcyZcyUSoYqaYgcVpYkrVfWljWrOxIsPxaA8SPHc+fpd7LNBttkXS6phpgcSpLWq9iWNSObR3L7qbczc+OZZY5K0nAwOZQkrVexLWu+e+J3OWCLA8ockaThYnIoSVqv3JY1a//K6GIVJ75lBHO3n1uhqCQNB5NDSdJ6HfPmjdly8/+io9eWNYe++SWuOe70SocmqcRcrSxJWkvfLWsuOmw77n/xs/xkyTU970u+8G0XcvWhV1c2UEnDwuRQktQja8uai+Y/ygvNi3t+Y5z15rP49KGf9u0nUp1yWFmS1CNry5rOrmYmdZwJwIk7nsiXj/4yTeGvD6le+adbktSj2JY1h29zON8+/ts0NzVnlpFUH0wOJUk9Cm1Z09LyGgtOXsCI5hFljkhSuZkcSpJ6zJszgxF9OwZjDZ88Zk9Gt46uSEySyssFKZLUoPquSp43ZwbjJjzFiy2fY2zX6TSnyTQ1L+Pfjp7FaW/ZttLhSioTk0NJakBZq5IvXvAYS1uu5W9N9/K3tnvZcuKW3H/W/Ww6ftMKRyupnBxWlqQGlLUqeU0HjF79DgA2Hb8p955xr4mh1IBMDiWpARVblTx17FTuPeNetpy0ZZmjklQNTA4lqQEVWpWcml7hnnfdw3Zv2q7MEUmqFiaHktSA5s2ZwciWtd9wkljNBYduw05TdqpQVJKqgQtSJKnOZa1K3mn6Cl4fdSMsP5bmNJmueJnzD9mSDx+0T6XDlVRhJoeSVMeyViVfsuBxVoz6Mks6boO22xjdOpo7T7+T/Tbfr8LRSqoGDitLUh3LWpW8uiORlh8DwKiWUdxx2h0mhpJ6mBxKUh0rtiq5raWNH532Iw7c4sDyBiWpqpkcSlIdK7QquSuW8sN3/JCDtzy4zBFJqnYmh5JUx7JWJXexinMOnMohWx1SoagkVTMXpEhSnchalbzbFmtYPfprdLx2JM1pMp2xlPcesBEfm/P2SocrqUqZHEpSHSi0KnnV6K/ybPtCaFvAiOYRLDx5IUdud0SFo5VUzRxWlqQ6UGhVcudrRwEwsnkkt55yK0dud2QlwpNUQ+w5lKQ6sL5VybedehuHbX1YmaOSVIvsOZSkOlB4VfLL/OgdPzIxlNRvJoeSVAey35W8inMPnsbsrWZXKCpJtchhZUmqMVmrkjfb6AWWjfwCrZ0n9Lwr+f0Hb8alh5oYShoYk0NJqiFZq5IvXvAYr7Rex8vcCW13MH7keH582o/ZZ/o+FY5WUi1yWFmSakjWquQ1HdC26mQANhi1Afeeca+JoaRBs+dQkmpIsVXJU8ZM4e533c2uG+1a5qgk1RN7DiWphhRalUzTqyx69yITQ0lDZs+hJFWprIUn8+bMYN78xbR39l6ZvJqPHrEL20/evmKxSqof9hxKUhXqXniyZNlKErmFJ5ctfJK7/vBT/tz0GTriRRJd0PwKHztmG87Zd2alQ5ZUJ+w5lKQqlLXwZGV7J7c/EqxoW8SKlkXsMmUX7nrXXUwdO7VCUUqqR/YcSlIVKrbwBOBtm76NRe9eZGIoqeRMDiWpChVaeNIZSzls68O4+113M2nUpDJHJakRmBxKUhWaN2cGba1r/xXdxSq23fw33H7q7YwZMaZCkUmqd845lKQKy1qVfOAOYxg7+TaWv/BWmtNkOmMpu23zJ24/6wqam5orHbKkOmZyKEkVlPU6vEsXPE5M/C5Pvf4taPsSABe+7UKuPvRqIqLY7SRpyBxWlqQKylqVvKoj8drLB/V8f9UhV5kYSiobew4lqYKKrUpujma+esxXOfPNZ5Y5KkmNzJ5DSaqgQquSu+Jlbjv1NhNDSWVnz6EklUl/X4eXWM2HDtmCI7c7sHLBSmpYJoeSVAZZC08uW/gEb9vpGf7c9P+Y1HVmboPrple5+PAZvH//t1Y4YkmNyuRQksog+3V4Xdz1eFvP6/B2nrIzPz7tx2w2YbMKRSlJJoeSVBbrex3eQVscxMJTFjKxbWI5w5KkdbggRZLKoNjr8E7f5XR+cvpPTAwlVQWTQ0kqg3lzZjCyZe19CrtYxX47vsJNx93EyJaRFYpMktbmsLIklVjWquSJk57m1RHXM6LzxJ7X4c2dFVx3woWVDleS1mJyKEkllLUqed78xbzY/Dn+3vwf0PZjRreO5pbjb+HY7Y+tcLSStC6HlSWphLJWJbd3BuPa3wnAxmM35v53329iKKlq2XMoSSVUbFXyLlN24Y7T7nCrGklVzZ5DSSqhQquSW1uX88DZD5gYSqp69hxK0iBlLTw5Za82PnvnMoI3Vh83N3Xw6bn7MH7k+ApGK0n9Y3IoSYNQaOHJy62fZ3XraiZ15F6HN35UJ584ehbH7b5phSOWpP4xOZSkQSi08GR016m82nY2zaMf5bsnfpcjtj26QhFK0uCYHErSIBRbeLLVpK344Tt+yI4b7ljmqCRp6Go+OYyIbwBnFiny25TS9gWuPQ04F9gVaAaeAr4O3JBS6ipxqJJqVNbcwk0mjmJJRoLY0vIa//2e/2by6MkViFSShq7mk8Ne/hP4fcb5v2QVjojrgfOAVcC9QDswG7gOmB0RJ6WUOrOuldQ4suYWXrbwSfad0czzy1avtfCkqamDq47bx8RQUk2rp+TwKymlb/SnYEScQC4xfAHYP6X0dP78RsDPgOOADwDXDk+okmpF1tzCle2d/ORXf+HV1m+68ERS3amn5HAgLssfL+lODAFSSn+NiHOB+4BLI+LzDi9Lja3Y3MIVLYtoG/ck3zvxe8zeanaZI5Ok4dFwm2BHxKbAHsAa4Pt9P08pLQKWAFOBvcobnaRqU2hT685Yyq4b7crD733YxFBSXamnnsODImJXYCzwV+AB4O6Mnr+Z+eOvUkrZXQLwEDAtX/bB4QhWUvXJWngyb84MLl7wGGs63ijXxSpmbPEUt5/1IGNGjKlcwJI0DOopOTwj49yvI+LUlNKTvc5tmT/+qci9nu1TVlKdy1548gSHznyJvzbfxLjO02lOk+mMpczZbRVfOeVKIqLCUUtS6dVDcvgY8Ai5Fcd/AsYDuwOfAnYD7omI3VNKS/Llx+aPrxe55/L8cVzpw5VUjbIXnnSx8KFO/t52L39vu5eJbRP59vHf5ohtj6hQlJI0/Go+OUwpXdPn1OvAHRFxN7CI3LzBy8itPgbo/qd+GuzPjIhzgHMApk+fPtjbSKoixRaeAOy20W4sPGUhW03aqpxhSVLZ1e2ClJTSGuCK/Le9/5n/Wv44lsK6P3st68OU0o0ppVkppVkbbrjh0AKVVBWKLTw5c7czefAfHjQxlNQQar7ncD2eyh+n9Tr3TP64eZHrNutTVlIdyVp4cuGh2zBvwWN0djX3lOtiFcft2cy/H/t15xdKahj1nhy+KX9c3uvc4vxxp4gYVWDF8p59ykqqE1kLTy5d8DhjN7ydF5qfYlLKbWpN06t8aPbmXDT7hApHLEnlVe/J4cn540PdJ1JKz0XEo+QWrZwE3NT7gog4ANiU3NtT/qtMcUoqk6yFJ6s6EstfeCsr2r7EipZFHLrVodx8/M1MGTOlQlFKUuXU9JzDiHhzRBwVEc19zrdExAXAh/KnPtfn0u65iFdFxDa9rpsCfCH/7ZW+HUWqP8UWngTBJw78BD85/ScmhpIaVq33HG4B/AB4JSJ+BzxPbvuZXYBNgC5yr8j7ae+LUkrzI+IG4FzgyYi4B2gHZpPbCudW4LpyPYSk4ZE1t3CTiaNYkpEgpqZXuPtdd/u2E0kNr9aTw8eBa4G3kFtgMpPcFjXPA18Hrk8pPZJ1YUrpvIh4AHg/cADQTG4By9eAG+w1lGpb9qbWT/KWbTp5ftlqgpE9ZSPa+cTRezB7q50rFa4kVY2aTg5TSn8EPjyE628BbildRJKqRfam1p3c+9SLvNr6TSZ15BaejGlbw/85ek+O38M9SyUJajw5lKRCis0tXNGyiPETf8s3jvsWh2x1dJkjk6TqVtMLUiSpkGKbWs/Zeg6Pv+9xDtnqkDJHJUnVz55DSTUva+HJBw6ezkdv/RVd8pIT5AAAGLlJREFUXW/8NdfFKt4+s50vnfRjmsJ/G0tSFpNDSTUta+HJxQseY82Yb/BS80s9m1pH8zLOn705Fx7sptaSVIzJoaSalrXwZE0HdPz9CFa0nc2KlkW8a9d3cd0R1zF+5PgKRSlJtcPkUFJNK7bwZGLbRL545Bc5ZedTyhyVJNUuk0NJNaXv/MKJo1t5dUX7OuVaWl7jifc9wWYTNqtAlJJUu0wOJdWMrPmF0EEiEbT2lGtp7uLTx+1nYihJg+ByPUk1I2t+IbTQxQo64kUgseG4Jj5z4u4cv4eJoSQNhj2HkmpGofmFTYzj5IMW88mDP0lbS1uZo5Kk+mJyKKkqZe1dOGFMF8teX3fAY/LYZq4+7OoKRClJ9cdhZUlVp3tu4ZJlK0nk5hZe8L2HeXblHXSxaq2yba1NfOzI3SoTqCTVIZNDSVUna25hV2phdHorL7d+ntT0MgDTJo7iyuN3Ze7MaZUIU5LqksPKkqpOsb0LT9tzWz5z2LFMaJtQ5qgkqTGYHEqqqL5zCy86bFvGje7g7yvW/evpTWOb+PIxX65AlJLUOBxWllQxmXMLv/8Iz6/6Sebcwn858s2VCVSSGojJoaSKyZpbmFJrz9xCml8BnFsoSeXksLKkssjamqbY3MLzD9ybj+1/IqNaR5U5UklqbCaHkoZd1mvvLl34BC0tq2nvGLlO+SnjWrl89uXlDlOShMmhpDLIGj5e1d5FJ6sIEk288VaTUa1NfPSIXcodoiQpzzmHkoZdsdfevdz6eVpbXyPIzS28wrmFklRR9hxKKqmsuYVTJ4zkL39bvW7hplf5zjsv4JgZx5Q/UElSJpNDSSWTNbdw3vzFrGz5GU3svdbwcXNTJ5cfty/HzNiqUuFKkjI4rCypZLLmFrZ3BqzZmZdbP09HvAgkNhzXzGdP2oNT9jQxlKRqY8+hpJIptjXNxElP8+lDR/KOnY8kIsocmSSpv0wOJQ1K37mFHzl0a8aOaue1la3rlB3Ttob/+cBvGTtibAUilSQNhMPKkgYs67V3F81/lCWr71zntXcjW4LLj93LxFCSaoTJoaQBy5pbSBrR57V3iWkT27jqhN3cmkaSaojDypKKGuhr7z515FzO2/MURjSPKHOkkqRSMDmUVFDW1jQXfv8ROnmdJsavU37jCW18eK8PlztMSVIJOawsqaCs4ePOrmYSaZ25haNam7n08B3LGZ4kaRjYcygJGNjwcRPjGLfhQkauPIlXlqee8s4tlKTaZ3IoqeCbTVLTCugas075SWPg0Qu+SlM4+CBJ9ca/2SUVfLNJZ1fHOsPHba1N/OtRu5sYSlKdsudQajADHT5ePup6pqZzWLFqpMPHktQATA6lBpI1fHzxgseI5hWkztHrlB8zcg2PzLuZyaMnlztUSVKFOC4kNZCs4eM1HdDe2Z79ZpO5e5kYSlKDsedQqlMDHT5+dcTn2CTOZfXq0Q4fS1IDMzmU6lCh1ccUWH08auQq7vvwV9ly0pblDlWSVGUcVpbqUKHVxx0Zq49HtgRXzt3bxFCSBNhzKNW8gQ4f/23ktUzlHx0+liRlMjmUaljBdx/HCprSuHXKj2lbwy8u/BYbj9u43KFKkmqEw8pSDSv47uPUlbl59eXH7mViKEkqyp5DqUb0HT6+6LDtWFJk+Dgm3MS4NaezfGWrw8eSpH4zOZRqQNbw8Ue+/xCdrKSZCeuUnzQGHr7kO7Q0+UdckjQw/uaQqkzWApOs4WPSCGAlXayiibae06Nam/jXo95sYihJGhTnHEpVpLuHcMmylSTe2J9wybIVmeWbGMes7X/LlPEtBDBt4iiuOH5Xh48lSYNm14JUIf3tIWzvDBKdBM3r3GOTCaNY+O5/KlfIkqQGYHIoVUDWHMLLFj7ByvauAldExvBxM5ccvkMZopUkNRKHlaUKyOohXNneRaIzs/yYtjX881FbMW3iqF7Dx7s4fCxJKjl7DqVhNpA3mGT1EHbvTzh35jTO2bc8MUuSGpc9h9IwylpgcsH3H6Yz/p5ZPjW9wlt3+ANTxjX39BBe6QITSVIZ2XMolUh/F5h0dbWQSOv0ELY2J644/kBO3GPzcocuSVIPk0OpBLIWmFw0/1E6OgOIdco3MY6WSbcwauXJvL5qhG8wkSRVDZNDaYD620PY0dlUcAuaDce18NDFtxCxbuIoSVIlmRxKAzDQHsJCW9D88xG7mBhKkqqSyaFUQHYP4VMD6iGcODpx6eG7cd1/PLvWfRw+liRVq0gpVTqGmjZr1qz08MMPVzoMlVjfHkKA5qZOOruayOohTHSRWLNOD6F7EUqSqklEPJJSmlWsjD2HanhZPYRX3vnrdXoIO7uai/QQdnHRnJ344s/+bA+hJKmm2XM4RPYc1o6sJBBYp4eQWENKrUSBHkJYQ9hDKEmqQfYcSnlZC0kuWfA4TU0drGzv0xOYRgCdkNFD+KYxTVz29t255p4/2kMoSapLJoeqO/3damZ1RyLRlLnGGAJiTT5RzBnV2sy/HJXrITxp1pbD+gySJFWKyaFqVn+GibtfV9fV1Uz2VjPZNp7QxqWH77jO/e0hlCTVO+ccDpFzDodff+cKjmyBaOpk1Zp1h4MLLSSJphU0RxsdnW+8Ztw5hJKkeuWcQ9W8rLmCly18ghEtkTFMTNFh4r6bUbe1NnHl8XsD2EMoSVJewyeHEXEacC6wK7kVCE8BXwduSCl1VTK2RtPfTadXtnexoj1lriYuZPLYZi49vPBCEpNBSZJyGnpYOSKuB84DVgH3Au3AbGAc8APgpJRSZ+E7OKw8GIWGiS9d+ASr2t/IxyPa6UotBbaUyU4Om5tXEYxwmFiSpAwOKxcRESeQSwxfAPZPKT2dP78R8DPgOOADwLUVC7JGZCV7c2dO61cSuGTZSj7yvYdIrIY0dq37ptRKoS1lEq/RFKPyZXJySeBegMPEkiQNVsP2HEbEw8AewJkppZv6fHYAcB+5xHFaseHlRuo57O/CkFGtTbx91w340eNLWdPR6waxhi5W05TGrXPvQj2BuU2n2wlG9pwb2RJcefwuRDSZBEqSNAD96TlsyOQwIjYFngPWABNTSiszyjwPTAP2SSk9WOhetZwcDrTHr28SOKIFmpu6WLmmaZ17F1odXDgJzD6/0fhWLj18Rz5z1+9MAiVJGiKTwwIi4mjgdmBxSmn3AmV+AMwFPpBSur7QvYY7ORxoAjfUZO9t28KDv0u0d76RqEW0Q7STukavE99Ak71C58eNDNq7Yq05h84VlCSptEwOC4iID5GbS3hrSum4AmWuBT4EfDaldFGhew1ncnjr4iXMm/8o7b0WV7Q0d7Hz9OX88tmxay26iOgigK70xrmmpg42mvy//PWlrehKvaaXxhoSq4nM4d3S9PgVus/4tibaO3Mrjrt1J4HgXEFJkoaTC1IK61758HqRMsvzx3UzqDK5+qe/XSsxBOjobGLxH8cQrH0+pSb6pvldXS38+cWt103S0giglWzrDhEX09K8GlIrnV1v/Iy21iZO3GM6Cx5Z0mcuYjOfOLZ4EmgyKElSZTVqctjd1TWobtOIOAc4B2D69Omlimkdf162zlTIvIEkcANL9oJE1mvmxo4MOjqD1R1vVNn6VgfP2nwDk0BJkmpMoyaHr+WPY4uU6f7stb4fpJRuBG6E3LByaUN7wyYTR7EkI0EslMBlaQrImjkwoa2ZNZ2sM8fvhAI9fp+aO/Aev7kzp5kESpJUYxo1OXwmf9y8SJnN+pQtu3lzZmRsE5OdwLU2BQS0d6Y+ZacNeHjXHj9JkhpXoyaHi/PHnSJiVNZWNsCefcqWXXci1t8EbiBl7fGTJElZGnK1MuRW6wC74ybYkiSpQfRntfLAVivUlyvyx6siYpvukxExBfhC/tsriyWGkiRJ9aZRh5VJKc2PiBuAc4EnI+IeoB2YDYwHbgWuq2CIkiRJZdewySFASum8iHgAeD9wANAMPAV8DbjBXkNJktRoGjo5BEgp3QLcUuk4JEmSqkEjzzmUJElSHyaHkiRJ6mFyKEmSpB4mh5IkSephcihJkqQeJoeSJEnqYXIoSZKkHiaHkiRJ6mFyKEmSpB4mh5IkSephcihJkqQeJoeSJEnqYXIoSZKkHiaHkiRJ6mFyKEmSpB4mh5IkSeoRKaVKx1DTIuIl4E9l+FGTgaVl+Dm1zDrqH+upf6yn/rGe+sd66h/rqX+GUk+bp5Q2LFbA5LBGRMTDKaVZlY6jmllH/WM99Y/11D/WU/9YT/1jPfXPcNeTw8qSJEnqYXIoSZKkHiaHtePGSgdQA6yj/rGe+sd66h/rqX+sp/6xnvpnWOvJOYeSJEnqYc+hJEmSepgcVkBEnBYRP4+Iv0XE8oh4OCLeHxGD+v9R6vtVg1I9U0R8IyJSka+nhusZhlNEzIiI8yPi5oh4KiK68s9z4hDvW1dtqdT1VI/tKSJaI2J2RHw2In4REX+JiDURsSQi5kfEgUO4d920p+Gop3psTwAR8cGI+F5E/CYiXo6I9oh4KSLuiYh3RkQM8r51056g9PVUyvbUMvDH0VBExPXAecAq4F6gHZgNXAfMjoiTUkqdlbpfNRimZ/pP4PcZ5/8ylFgr6Fzg/FLesB7bEsNQT3n11J4OAO7O//cLwCPA68COwAnACRHxyZTSvwzkpnXYnoalnvLqqT0BXAJMAX4JPEiunjYHDibXBk6MiONTSl39vWEdticYhnrKG3p7Sin5VaYvcn+BpPz/oG17nd8I+HX+s/Mrdb9q+BqGOvpG/pp3V/rZSlxP7wE+DZwMbA3cl3/OE6uh3qvlaxjqqe7aE7lfRPOB/TI+OwXoyD/zQY3cnoapnuquPeWfa19gTMb5ncgl1gk4q5Hb0zDVU8naU8Urp5G+gIfz/+POyPjsgF6Nv6kS96uGr2Goo7r8yzfjOYea9NRdWxqmemqI9tTnmb+Sf+avDuCahmhPJainRmxPH8s/8y0DuKYR29Ng6qlk7akmx+lrUURsCuwBrAG+3/fzlNIiYAkwFdir3PerBvX4TLXAetd6LM4fN+1P4QZuTwOqpwbWkT+u6k/hBm5PA6qnUnPOYfnMzB9/lVJaWaDMQ8C0fNkHy3y/ajCcz3RQROwKjAX+CjwA3J0GPpejHtVjWxpujdSets0f+ztfqVHb00DrqbeGaE8RsSXwvvy3P+znZQ3XngZZT70NuT2ZHJbPlvnjn4qUebZP2XLerxoM5zOdkXHu1xFxakrpyQHeq97UY1sabg3RniJiKvDu/LcL+nlZw7WnQdZTb3XZniLiLHLDvq3kelT3JrdLyhUppR/08zZ1355KVE+9Dbk9OaxcPmPzx9eLlFmeP46rwP2qwXA802PAh8hN8B0LbAIcBTxObpXhPRExbeCh1pV6bEvDpWHaU0S0ADcDE4B7U0r97cFoqPY0hHqC+m9P+wBnAqcB++fPfQz4xADu0QjtqRT1BCVsTyaH5dO9X1GpXklT6vtVg5I/U0rpmpTS51NKv04pvZ5S+ktK6Q7gLcAvyG0jcFmpfl6Nqse2NCwarD19kdx2Gs8B7xzAdY3WngZbT3XfnlJK70kpBTCaXMJyDfCvwC8iYpN+3qbu21OJ6qmk7cnksHxeyx/HFinT/dlrRcoM1/2qQdmeKaW0Brgi/+0RQ7lXHajHtlRW9daeIuJa4B/IbacxO6X0wgAub5j2NMR6Kqje2lNKaWU+YZlHLjnZjdz+hP3RMO1piPVU7L4Dbk8mh+XzTP64eZEym/UpW877VYNn8sdyPVP3bvG1PGxTCs/kj/XUliqhLtpTRHyW3NDUS+QSnqcHeItn8se6bk8lqKf1qYv2lOHr+ePREdHaj/LP5I913Z4yDLSe1mdA7cnksHy6tznYKSJGFSizZ5+y5bxfNSj3M70pf1xetFT9q8e2VAk1354i4tPABcDLwKEppV8P4jZ1355KVE/rU/PtqYBl5LZpaQE26Ef5um9PBQy0ntZnQO3J5LBMUkrPAY8CI4CT+n4eEQeQW6X0AvBf5b5fNajAM52cPz5UgnvVrHpsSxVS0+0pIq4E5gGvkkt4Hh/Mfeq9PZWqnvqhpttTEfuTS3iWAUvXV7je21MRA6qnfhhYeyrXbt9+JYATeWMn9216nZ8C/IqMVwCRmyfwFLkl7UO+X7V/lbKOgDeTW6nV3Od8C7l/9Xfm7zen0s9dgnq7j/W8+aPR2lKp66me2xPwyXzsrwJ79POahmtPpaynem1PwH7A6cDIjM/2Af6Qf67PNHJ7KnU9lbo9uc9hGaWU5kfEDcC5wJMRcQ9vvDx8PHAr604+3RiYkT+W4n5VrcR1tAXwA+CViPgd8Dy5rQ52IbfEvwu4JKX00+F5muETEbsDX+h1asf88fKIuKj7ZEqp9xsDGqotQcnraQvqsD1FxDHAP+e//T3wwYjIKvpUSunKXt83VHsahnragjpsT+TeYf514LqIeJRcj964/PnuP393kNuqpbeGak+Uvp62oITtyeSwzFJK50XEA8D7yW162UzuXwFfA25IA9wRv9T3qwYlfKbHgWvJLePfnNzu+YncH5qvA9enlB4pcfjlMh54a8b5bTPO9Us9tiVKW0/12p56z2ealf/Ksgi4ssBn66jD9lTqeqrX9rSIXA/rfsB25DZ0DnLJzwLg5pTSrQO9aR22p1LXU0nbU+S7HSVJkiQXpEiSJOkNJoeSJEnqYXIoSZKkHiaHkiRJ6mFyKEmSpB4mh5IkSephcihJkqQeJoeSGk5EpEF8fSN/7YH57++r7FP0T0Rcko/38CHcY/eI6IqIz5QyNknVyTekSGpE38w4NxWYA7wOzM/4/IFhjWgYRMTGwEeB+1NKdw72PimlRyNiIfChiPhSSunpkgUpqer4hhRJItcjCPwM+FNKaYsi5UYD04EVKaVnyxPd4ETEjcB7gdkppf8Y4r12AZ4AFqSUTixFfJKqk8mhJNH/5LBWRMSbyL1X9c/ANqkEf9lHxEPk3tm6VbUnxpIGzzmHkjQAheYcRsQW+fPPRERTRFwQEb+KiJUR8XxE/N98ryMRMSkirsmXXR0RT0fEBUV+ZkTEqRFxV0QszV/zbER8OSK2KHDZ2UAbcFNWYhgREyPi8nyMK3rFeV9EXFbgnt8EmoF/XG9FSapZJoeSVHq3AJ8A/gjcBYwBPgIsiIgNgP8GTgEeIjeXcQvgsxHxT31vFBGt5OZAfgfYF/g1cDu5uZHvAR6NiFkZMczNH+/JuOdo4D+By4DJ+TK3Ar8HdgQ+XuC5uu91bMEnl1TzXJAiSaW1ObAK2C6l9GeAiNgMWAwcDiwCHgfelVJalf/8SOBHwKURcU1KaUWv+30SOB64Hzg9pfR89wcR8QHg88B3I2L7lFJH/vxoYE+gHXgkI8YTySWBdwBzu6/LX9sMHFDg2X4LvArsFBEbpZT+2v9qkVQr7DmUpNL7UHdiCJBSeg64Of/t5sC53Ylh/vM7yC32GAf09ALmexk/BCwHTuqdGOavu45cgrc18PZeH+0EtAJ/7P1zetkof7ynd2KYv2dnocUr+eHp3+S/fXNWGUm1z+RQkkqrHchKrn6fPz6cUlqa8Xn39jCb9Dp3EDAKWJRSerHAz1uUP76t17kp+ePLBa75n/zxkoh4Z0RMLFAuyyv540ZFS0mqWQ4rS1JpvdC3Ny5vef74fMZnvT9v63Vuq/zxyIhY32rjDXv994T88e9ZBVNKiyLi08BFwLeAFBFPkZv/uCCl9NMiP6f7ngNJKCXVEJNDSSqtriF+3ltz/vhb4BfrKfvfvf57Wf44vlDhlNIlEfFFcotL9gX2Ibcn4nsj4i7gyAJJbvc9X11PPJJqlMmhJFWv5/LHJ1NK7x7Add1D0G8qViil9EfgmvwXEbEvuVXRh5HbCufGjMu671lomFtSjXPOoSRVr3vIzWE8ZIDzAn8FrAa2jIhR/b0opfQA8I38t7v1/TwiAtg+/+3iAcQjqYaYHEpSlcpvFXM9ufl9t0fE9n3L5DfUfk9EbNTrupXkhplbgT0yrjkuIvaPiKY+50cBh+S//VNGSNsDk4BfFVkgI6nGOawsSdXtYnIrmE8GfhkRj5HbXLsN2AzYARiRP/bed/BWYH9yyd4Dfe55AHA+8FJELAZeIreIZW9gA+Ap4EsZsXQnjrcN+akkVS17DiWpiqWU2lNKp5BbOPIjconiseQSuRZyb2M5DvhDn0u/AawEzsgPB/f97Crgd8DOwEnAW8htt/MR4C0ppb9lhHMm0El24iipTkQJ3sUuSapC+dXI/wjMLrSx9QDutQu5jboXpJROLEV8kqqTyaEk1amImEqud3BxSqnQK/H6e6/5wDHATimlp9dXXlLtclhZkupUSukF4P8A+0fE4YO9T0TsTu79zp83MZTqnz2HkiRJ6mHPoSRJknqYHEqSJKmHyaEkSZJ6mBxKkiSph8mhJEmSepgcSpIkqYfJoSRJknr8f1q2mG8IT/AOAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize = (10,10))\n",
"plt.plot(t_eul_3[0:85], num_eul_3[0:85,0], 'g', label='Explicit Euler Method with drag')\n",
"plt.plot(t_eul_3[85], 300, 'y--', label='Implicit Heun Method with drag')\n",
"plt.plot(t_heun_3[0:85], num_heun_3[0:85,0], 'o', label='Implicit Heun Detonation')\n",
"plt.plot(t_heun_3[85], 300, '*', label='Explicit Euler Detonation')\n",
"plt.legend();\n",
"plt.xlabel('Time(s)')\n",
"plt.ylabel('Position (m)')\n",
"plt.title('Rocket Height vs Time');"
]
},
{
"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
}