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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": 98,
"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": 150,
"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",
" #state=[y,v,m]\n",
" \n",
" dstate = np.zeros(np.shape(state))\n",
" \n",
" dstate=np.array([state[1],((u*dmdt)/(state[2])),-dmdt])\n",
" \n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 151,
"metadata": {},
"outputs": [],
"source": [
"y0=0\n",
"v0=0\n",
"m0=0.25\n",
"dmdt=0.05\n",
"\n",
"#Runge-kutta method imported from previoud notebook\n",
"\n",
"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": 152,
"metadata": {},
"outputs": [],
"source": [
"num_solRk2=np.zeros([N,3]) #initiliazes array\n",
"num_solRk2[0,0]=y0\n",
"num_solRk2[0,1]=v0\n",
"num_solRk2[0,2]=m0 #sets intitial conditions\n",
"t=np.linspace(0,4,1000) \n",
"N=int(4/dt)\n",
"dt=t[1]-t[0]\n",
"\n",
"#RK2 method integrates the simple rocket function\n",
"for i in range(N-1):\n",
" num_solRk2[i+1] = rk2_step(num_solRk2[i],simplerocket, dt)\n"
]
},
{
"cell_type": "code",
"execution_count": 153,
"metadata": {},
"outputs": [],
"source": [
"velocityRk2=num_solRk2[:,1]\n",
"massRk2=num_solRk2[:,2]\n",
"massfinalRk2=massRk2/m0 #desired quantity mass/initial mass\n"
]
},
{
"cell_type": "code",
"execution_count": 196,
"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": [
"plt.figure(figsize=(8,8));\n",
"plt.plot(vanalytical,mfinalanalytical,label='Analytical Solution');\n",
"plt.plot(velocityRk2,massfinalRk2,linestyle='dotted',label='RK2 Solution');\n",
"plt.legend(loc='best');\n",
"plt.title('Comparison of Analytical and RK2 Solutions');\n",
"plt.xlabel('Velocity');\n",
"plt.ylabel('Mass/Initial Mass');"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [],
"source": [
"#Huen's method imported from previous notebook\n",
"\n",
"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": 164,
"metadata": {},
"outputs": [],
"source": [
"num_solHeun=np.zeros([N,3]) #initializes array\n",
"num_solHeun[0,0]=y0\n",
"num_solHeun[0,1]=v0\n",
"num_solHeun[0,2]=m0 #sets initial conditions\n",
"t=np.linspace(0,4,1000)\n",
"N=int(4/dt)\n",
"dt=t[1]-t[0]\n",
"\n",
"#integrates the simple rocket function by Heun's method\n",
"for i in range(N-1): \n",
" num_solHeun[i+1] = heun_step(num_solHeun[i],simplerocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 165,
"metadata": {},
"outputs": [],
"source": [
"velocityHeun=num_solHeun[:,1]\n",
"massHeun=num_solHeun[:,2]\n",
"massfinalHeun=massHeun/m0 #the desired quantity mass/initial mass"
]
},
{
"cell_type": "code",
"execution_count": 166,
"metadata": {},
"outputs": [],
"source": [
"#Analytical solution\n",
"\n",
"manalytical=np.zeros(len(t))\n",
"manalytical[0]=0.25\n",
"t=np.linspace(0,4,1000)\n",
"dt=t[1]-t[0]\n",
"\n",
"#computes the solution analytical according to the equation of motion\n",
"for i in range(1, len(manalytical)):\n",
" manalytical[i]=manalytical[i-1]-0.05*dt\n",
" \n",
"vanalytical=-u*(np.log(manalytical/m0))\n",
"mfinalanalytical=manalytical/m0"
]
},
{
"cell_type": "code",
"execution_count": 197,
"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.plot(vanalytical,mfinalanalytical,label='Analytical Solution');\n",
"plt.plot(velocityHeun,massfinalHeun,linestyle='dotted',label='Heun Solution');\n",
"plt.legend(loc='best');\n",
"plt.title('Comparison of Analytical and Heun Solutions');\n",
"plt.xlabel('Velocity');\n",
"plt.ylabel('Mass/Initial Mass');"
]
},
{
"cell_type": "code",
"execution_count": 231,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"All three solutions clearly converge together\n"
]
},
{
"data": {
"image/png": 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8AvgEx2cXOIwQwpafiqEnKZ1M508oHMfqB7SALwCThPbxoSwIIWqhBYsC+F5KeSm7jBMwDFlcJPM7FtZYrK+DyPSLUWRlEZnHdrZ+vVlECJHl4SilPErmDJzxQgirs2yEEEH67Ae70UMht7UhI9CuEwMbsokYrrN6QojBmOdjtDdi0IIrOcJufd1O7ynNrl8V4EUbZVzR13npoXDp/UQPS/2wlXQ3tAB8kNley+R1rueDtKC93f1M5lzZU2hhgeug3QSD9N+vAH8Y5LKVIdCiPRrK+Bwt4mEJtAhhs0zS1ljQw+KcZhOZ+brMZisy4SZlhVlJi0d7qL6INqe8JPZFmNysp90FJqBZ/g+jvUEY5jwfMrefbOnnYFsy9OM2AqinH6dAtLHXD8mcC7/CRcfK7nZayN/XJP9+NMdUQ8TDZ4HLeloyUMFM/jCT/OG5qL+8Sf5P7cxTDM15VQJLLZw3883ki7F0vuTymo5xpO3YcV3pcqewEBfAWpoZ2U5khvq+gHZvqYZmdJdC898ZgWawXTeTP4TMuAEpaE7MjfXz3xDRsi/a0OJtHJz/jza9UqIFKHtTP5dD0IYyw9B6vEzDMf9BzpgyphEmU4H30IY9S+i6fmeSf4aj15leliGK5n60yLQBun4j0Ka5nsDKeYA2pVyiPVTb6+3z0BdhIheL5TgPLr2f6NtvoRnufUz2cTCaE+Uqk3wv2jz2zrgAH6QFzVv8AyzHtDddbmD+5mFPfPNfsB3f3NoJNB/nGQ9tyAylm32x9m2LKmQ+uMwtS9A8r++18WDrOEm0WBA5AvHk07Gyu51WynD42xYmecNM5MJzUXesSf6mDuT7Ws9zG5PImCjjIbt8V7Txclvn8BUr1+FhO/JnYCGQkxXd5tp5fUm04TKz0Sa5h9+20NPHWyn3MJqRYvE8QAsBnWIhf4yJnOFaOGVBD5fdT7Jtt7Z8iR3fOVHDFg4ipUyVUo5B+07DG2g3uvNoxsRtNAegVWiRF0Ok9n337GVcQ7P0BqCNa15Cs4wv6f/7AxHS9Y6SBk6ivbFPQwsslYJmFKxCC1v9iblMUus2rYfWzXge7a3iEtrF0V9K2RvthnWvqYf2vYW1aM6R13VdEtD291CgodQC0WRvQ6E4VlLKD9F6veai9RTdQTNe/0SLx19JSvmr5RLyxDP6+pSUcocD+QxDF95AT+eqdP8gpVyF1rszHi1Q0mW0c/AmWu/fErQ3yTAL+Y+ixVyIRgtA9A9ab2AKWsTPdWjfrQmRUu43V4YV3QahnXfj0O4HJ3S90tGusyNogcGeRDMs/7VQzlm0nsAX0cLmJ6JdoxfQvt/RRUrZV1oIrmSHnu+h+Wdt1vW6resWizbLwKxeJvkPovWYfou2/3L1BVEX3092oM0uew9tH59C2w8p+u+lQAcpZX8ppc2poEK3SBSKLAjts7Sb9L+PSi1WgkKhUCgUqudBoVAoFAqFYyjjQaFQKBQKhUMo40GhUCgUCoVDKONBoVAoFAqFQyjjQaFQKBQKhUOo2RZ2EBgYKMPCwlythkKhUCgU+cbevXstflRNxZS3g7CwMOLi4mwLKhQKhUJxnyCEOG0pTQ1bKBQKhUKhcAhlPCgUCoVCoXAIZTwoFAqFQqFwCGU8KBQKhUKhcAhlPCgUCoVCoXAIZTwoFAqFQqFwCGU8KBQKhUKhcAhlPCgUCoVCoXAIZTwoFAqFQqFwCBVhUqFwMSkpKSQmJpKcnEx6erqr1VEoFPcRbm5ueHt74+vrS0BAAG5uzukzKDDGgxCiMtABaADUByoBAughpfwmD+X2BYYDNQF34CgwD5gppczIq94KRV5ISUnhzJkzBAQEEBYWhqenJ0IIV6ulUCjuA6SUZGRkcOvWLa5du8b169cJCQnBwyPvj/4CYzygPeBfcmaBQojpwAjgDrARSAUigP8DIoQQPaSU6lVP4TISExMJCAggMDDQ1aooFIr7DCEE7u7u+Pn54evry4ULF0hMTCQoKCjPZRckn4eDwAdAL6AisCUvhQkhnkYzHP4Fakopn5BSPgU8BhwBngJeyJPGCkUeSU5Opnjx4q5WQ6FQ3OcIIXj44YdJSkpySnkFpudBSjnb9L8Tum7H6+uxUsq/TOpJEEIMBzYD44QQn6rhC4WrSE9Px9PT09VqKBSKBwAvLy/S0tKcUlZB6nlwGkKIskA94C6wPHu6lHILcB54BGicv9opFFlRPg4KhSI/cOa95r40HoA6+vqQlPK2BZk92WTzjWu37nLt1t38rlahUCgUCqdwvxoPj+rr01ZkzmSTveck30ll2s9/0WLSJj5afyy/qlUoFAqFwqncr8aDr76+aUXmhr72u8e6GPktPpGPfj5K5SLL+f1iX/48viO/qlYoFAqFwmncr8aDYWBH5roAIYYJIeKEEHGXLl1yilJtqgTRNnQyx8rsJr4IfL5lvO1MCoUCgIyMDMqVK4cQgqCgIFJTU12tkpH58+cjhCAmJiZf6ouNjUUIQWxsbL7Ul52YmBiEEMyfP9+hfOnp6cyaNYs2bdoQGBiIp6cngYGBVK1alR49ejBt2jScdb8NCwtDCMGpU6ecUp49CCEeGB+m+9V4SNbXvlZkDGnJ5hKllF9IKetLKeuXLFnSKUoJIWhb4Snj/z/cL3P86B4rORQKhYH169dz9uxZAC5dusTq1atdrNG94dSpUwghCAsLc7UqTiU5OZnw8HCGDRvGr7/+SqVKlYiKiqJ169Z4eXnx7bffMmrUKHbv3u1qVc2SW4PpfqXATNV0Mqf0dagVmZBssvlCz7ajWDPrS2rfSWRQ0nX+/vF9qLIiP1VQKAolc+fOBaBMmTKcP3+euXPnEhUV5WKtXMMLL7xA7969C1VwsdjYWLZt20a1atVYs2YNoaFZb88XL17k66+/plSpUi7SMO8cOXLE1SrkG/drz8Pv+rqaEKKoBZkG2WTzBTc3N16vPYlXr14jICODukkbOXVY9T4oFNZITExk1apVCCFYsmQJ7u7urFu3jn/++cfVqrmEwMBAqlSpUqiMh6VLlwIwderUHIYDQFBQEC+99BINGjTIkVZYqFKlClWqVHG1GvnCfWk8SCnPAvsAL6BH9nQhRCugLFr0yZ35qx1UbdSe/UUbAuAmJIlrJua3CgpFoWLRokWkpKQQHh5O8+bNad++Penp6SxcuNBiHtPx56VLl9KkSRN8fX3x8/MjIiKCbdu2mc23e/duxowZQ/369SlVqhReXl4EBwfTvXt3du3aZbfOCxcuRAhBhw4dLMocOHAAIQRlypQhLS2NmJgYHn1UmwB2+vRpYxuyD2PY8nk4cuQIw4YNo2LFihQtWpSAgABq1qzJ6NGjOX066yS0FStWMGjQIKpVq8ZDDz2Et7c3FStW5PnnnzcOEzmDixcvAuQqNLKUki+//JLw8HACAgLw9vamQoUKudLRli9EeHg4Qgg2b94MZA4jLViwAICBAwdmOS6mwxjWfB4uX77M2LFjqVKlCkWLFqV48eI0btyYGTNmmA3cZOpHk5yczJgxY3j00UcpUqQIZcqUYfjw4SQmJjrUdmdSqI0HIcR7QoijQoj3zCQbtk0SQlQ0yRMEzND/vu+q6JLFOkww/q57cyt//bHVFWooFIWCefPmARgdEgcOHJhluzXeeust+vbti5eXF507d6Zs2bL88ssvREREsHNnzneHN954g48++ojU1FQaNmxI165defjhh1mxYgXNmzdn+fIccefM0rt3b4KCgli/fj0nTpwwKzN9+nQAhg0bhoeHB82bN+fpp58GoFixYkRHRxuX7t2721XvwoULqV27NrNmzUJKyRNPPEGrVq3IyMhgypQpbNq0KYt8r169WLZsGcWKFaNt27a0a9eOlJQUZsyYQd26dTl+/Lhd9dqiXLlyAHz66adkZNh/25VS8swzzzBgwAB27NhBgwYNePLJJ5FSMmPGDGrXrs2ePfeu99bX15fo6GgqVKgAQLNmzbIcl4oVK9ooAU6cOEHdunWZPHkySUlJdOnShZYtW3LgwAGef/55OnbsSEpKitm8SUlJNGvWjLlz51K7dm3at2/PrVu3+Oyzz2jXrp3rHIellAViAeoCu0yW62izJY6bbs+WZ74uM99CmTP09NvAauBbIEnf9h3gbo9u9erVk/eCvZOfkHdii8sFU8rI4TPq35M6FAWbw4cPu1qFAs++ffskIP38/OTNmzellFKmpKTIhx9+WAJy69atZvPp17ksUaKEjIuLM25PT0+XQ4cOlYBs27Ztjnxr166V//77b47tq1atkp6enrJEiRJGPQzMmzdPAjI6OjrL9v/85z8SkK+++mqO8pKSkqSvr6/08PCQ58+fN26Pj4+XgAwNDbW4TyZMmCABOWHChCzbf/vtN+nh4SHd3d3l7NmzZUZGRpb0w4cP5zjnli5dmqM9qampRt07dOiQo/7o6GgJyHnz5lnUMTtTpkwxHpOwsDD54osvyi+//FIeOnQoh56mTJ8+XQKyVKlS8uDBg8btaWlp8sUXXzTuqzt37mTJFxoaKgEZHx9v13YDrVq1koDctGmTw202tC87DRo0kIDs0aOHvH37tnH7mTNnZKVKlSQgx40blyWP4ZwCZKdOnWRycrIx7fz58zIkJEQCctGiRRb1MYcj9xwgTlp4LhYkh8niQCMz2x/LbYFSyhFCiG3A80ArMj/JPZcC8EnuYh3H02XXCS54egB3+G7TZzzV+jlXqqQoYISNW+NqFXLNqfc7O6WcOXPmANCzZ098fHwALUZ/3759+fTTT5k7dy7Nmze3mH/ixInUq1fP+N/NzY133nmHWbNmsXXrVlJTU7N8X8TSMEOXLl3o0aMHixcvZtOmTXTubLt9w4cP5/3332fevHm88847eHt7G9MWLFjAjRs36NGjB8HBwTbLsod3332XtLQ0xo4dy+DBg3OkV61aNce2nj175tjm4eHB22+/zdy5c1m/fj3Jycn4+eUtJM7LL7/MzZs3ee+99zh16hSffvqpMS0wMJBevXoxfvx4ypQpkyXflClTAHj77bepVq2acbu7uzsffvghK1eu5PTp03zzzTf069cvTzreC7Zu3cqePXvw8/Pjs88+y3IOhISE8PHHH9OpUyemT5/OhAkTsqSD1vMxZ84cfH0zJw8GBwfzwgsvMHbsWDZu3OiSdheYYQsp5WYppbC1ZMsTo2+PsVLuYillMyllcSllMSllPSnldFcbDgCVqzclLKOE8f+6o18gHejOUyjud1JSUvj666+BzKEKA4b/y5cv58aNGznyGnjiiSdybAsKCiIgIICUlBSuXLmSI/3y5cvMnz+f0aNHM2TIEGJiYoiJieHgwYMAdnflBwcHExUVRWJiIkuWLMmSNnPmTACef/55u8qyRXp6Oj///DMAQ4YMcSjv8ePH+eSTTxg5ciSDBg0ytjctLY2MjAyLwy6OIITgzTff5Ny5c8yePZsBAwZQrVo1hBBcvnyZ6dOnU7NmTfbu3WvMc+7cOU6ePImbmxv9+/fPUaaXl5fxwWnwUShobNmifSC6S5culChRIkd6x44dKV26NMnJyVnabqBevXo88sgjObYbHDNd5TRckHoeHkiGNvsv8bteYOC163RPvsHBbd9To+VTtjMqFA8A3333HYmJiTz22GM0a9YsS1qdOnWoXbs2f/zxB8uWLWPQoEFmyzCMtWenePHiXL16lTt37mTZ/vnnn/PKK69w69Yti3pdv37d7jaMHDmSZcuWMWPGDKPPxqZNmzhy5AjVqlWjVatWdpdljcuXL3Pz5k08PDzsGocHSEtLY8SIEcyePdsw1GsWR9prixIlSjB48GBjz8ilS5dYvHgxEyZMIDExkQEDBnDo0CEAzp8/D0Dp0qVzvJEbMPgiGGQLGga9DI6w5ihfvjwXLlww2wZr5y+Q4/zNL5Tx4GIaVIvgvxvr0SRZC3hT5Nf/IZt3Q7gVmE4hhQtxVtd/YcUQ2yEpKcns0ERCQoJRzpLx4ObAtRQXF8fw4cPx8PDggw8+oEuXLpQtWxYfHx+EELz++uu89957Vh+02WnWrBl16tRhz549xMXFUb9+faOj5IgRI+wu514wbdo0Zs2aRXBwMFOnTqVp06YEBQVRpEgRAHKV7lMAACAASURBVJo2bcrOnTsdaq+jlCxZkpdeeoly5coRFRXF4cOH+euvv3jssceM9VqL2uhs3Rxx5rSHvLbBkfM3PymYWj1glI+aSIrUxlwrpR1n/8YlNnIoFPc/Z8+eZePGjYA2zW/79u05lgsXLgCwfft2p8wK+Oabb5BSMnLkSEaPHk3lypUpVqyY8caf2+77F198EYAZM2bwzz//8P333+Pn52e2Kz63BAYG4uPjQ1paGn///bddeQwzRz7//HN69epFSEiI0XCA3Lc3N7Rv39742xCiumzZsoDWNW9pNkJ8fDxADl8JS3h5eQFYHOrKPpU1rxjacPLkSYsyjrahIKCMhwJAqbIV+L1UZqS84jsnkZGe7kKNFArXM2/ePDIyMoiIiLA6G6pHDy2Ui6GXIi8Y5s2HhITkSLt06RIbNmzIVbl9+vQhMDCQJUuW8P7775OWlsaAAQPMOiEaHm7m5v5bw93dnbZt2wIwe/Zsu/JYa++GDRuc9p0JsN1DcObMGeNvw0O0bNmylC9fnoyMDBYtWpQjT2pqKosXLwa0+Az2YCj76NGjOdIOHjxoMW5Ebo+LYVhq9erVXL16NUf6Tz/9xIULF/D19c3i2FvQUcZDAaFi1JvckkW47ObG8oeu8cX3r7taJYXCZUgpjUF5bL2dG9IXLlxIeh6NboMT2sKFC7O8mSYnJzNo0CCuXbuWq3K9vb0ZMmQIt2/fNs4ysDRkUbJkSby8vEhISDD7sLHGG2+8YZyFYO4bDEePHs3y0DS0d+bMmVm66//++2+ee865M78aNWrE559/bnYfxsfHG508GzdunCUC5SuvvALAm2++mUX39PR0XnvtNU6fPk1oaKjdcTAiIiIAmDx5chZfjrNnzxITE2PRyDEYHY6GoG7RogUNGjQgOTmZ559/PksPyvnz5xk1ahSghRy35NdREFHGQwEh8JEQFpdtT6eQYBb5F2dl4hrupFh22FIo7mc2bdrEyZMn8fHxsfn9ig4dOhAYGMiFCxdYu3ZtnuodOHAgISEh7Nu3j/LlyxMVFcVTTz1FWFgYcXFxFv0q7GHEiBG4u7sD2lvy448/blbO09OTzp07k5aWRp06dejXrx9Dhgxh3LhxNuto2LAhX3zxhbEtFStWpFevXjz55JPUqFGDqlWrZomSOX78eDw9Pfn888+pWrUqvXv3pn379jz++OOEhITQtGnTXLc3O8ePH+e5554jKCiI+vXr06NHD3r27EmTJk2oWLEiO3bsICQkxGg0GhgxYgR9+vThwoUL1KpViw4dOtCnTx8qVarExx9/TEBAAMuXL88y3GKN559/npCQEPbs2UPlypWJioqiTZs2VK1aleLFi1tsc7du3XBzc+Pjjz8mMjKSwYMHM2TIEHbs2GGzzsWLF1O2bFm+/vprypcvT69evejSpQuVK1fm6NGjREREuOwLqblFGQ8FiMgu/8VdN3rPewrmfmf7ZqFQ3I8YIkd269bNZnwBT09PevfuDeR96CIgIIC4uDiGDRuGr68va9asIS4ujqioKPbt22e2e99eQkJCjG/6tqZnzpo1i8GDB5Oens6yZcuYM2dOjqmelhg0aBD79u0jJiaG1NRUVq5cya+//oq7uztjxoyhTZs2RtkmTZrw22+/0blzZ5KSkvj+++85d+4cb7zxBj/99FOW+Bd5ZevWrUyZMoX27dtz48YN1q9fz3fffceJEydo3rw5kydP5tChQ1SqVClLPiEEX331FQsXLqRRo0bs2rWLb7/9loyMDIYPH87+/fsd+h5GQEAA27dvp1+/fqSlpbFmzRrOnTvHmDFjWLduncU2165dm6VLl9KgQQN27NjB3LlzmTNnjl2+NhUrVuT3339nzJgx+Pr68v3337N582aqVavG//3f/7F27Vq7jZ+CgriXXrT3C/Xr15dxcXH5Uteb83twMPVPGl0OZmf6IJa81peiXu75Urci/zly5IjZwD2K+4/9+/dTu3ZtgoODOX36NB4earKbIv9x5J4jhNgrpaxvLk31PBQwRkfNxDvhVT5LGs3+GyWYtyPe1SopFAon8NZbbwFa3AdlOCgKO8p4KGD4Fw+kc9tI4//PNv9N0i0XffhEoVDkiVWrVjF48GAaNmzIqlWrCAsL44UXXnC1WgpFnlHGQwGkV4MQHg0sBsD1O2nM2JJ/c60VCoXz2LdvH3PnzuXo0aN06NCBdevWUaxYMVerpVDkGWU8FEA83d14tb3mNORXJJ5dJ4dx8MRuF2ulUCgcJTY2Fikl169fZ+3atVSuXNnVKikUTkEZDwWUTtVL0zLkK8Sjn3HS9xozfnnN1SopFAqFQgEo46HA4uYm6FCxHlIPi7vT6wq/H9ziYq0UCoVCoVDGQ4Gmb+SrVE/xpN7NdGqfDueLfT6uVkmhUCgUCvVVzYLO2BYL6bHgb1LxgMMX+f3MVeqUC3C1WgqFQqF4gFE9DwWc2lWr075mZlS7SeuO3tPP4yoUCoVCYQtlPBQCRrevjIeb5vuw62QiW44770t3CoVCoVA4ijIeCgGPBhajd8MQIIPavmtZ8Es30tJU4CiFQqFQuAZlPBQSXmxdgcblJvB3yBbifG4wc+VYV6ukUCgUigcUZTwUEkr5+xDqHWz8v+HqT9y5fdOFGikUCoXiQUUZD4WIl7pMp0RaBj2vJzP3wj/8/u1UV6ukUCgUigcQZTwUIoJLhjLRuztvXrlKYEYGj/81k6RE5TypuH8JCwtDCMHmzZutyoWHhyOEYP78+fmiV35z9OhRnnvuOSpXroyPjw9FixalXLlyNG3alFdffZUNGzY4pZ758+cjhCAmJsYp5dlDbGwsQghiY2PzrU5F3lHGQyGjaffxnBOPAODPTY4sm+BijRQKxb1k6dKl1KpVi88//5ybN28SHh5OVFQUVapU4fjx40ydOpXx48e7Wk2znDp1CiEEYWFhrlZF4WRUkKhChlcRbxIajKPsb6MAqHthKf/EjyT40Sou1kyhUDibf//9l0GDBnH37l2mTp3KyJEjcXd3N6ZnZGSwbds2tm3b5kIt88YLL7xA7969CQwMdLUqCgdQPQ+FkLodojnmUYVU4Nvi3nzw0xBXq6RQKO4BP/zwA7du3aJJkya8/PLLWQwHADc3N1q2bMnrr7/uIg3zTmBgIFWqVFHGQyFDGQ+FEOHmxs2I/xBVpjTvBpbg56JJ/LhtoavVUigKLLt376Z3796ULVsWLy8vSpYsSdeuXc2+sdvT1S6EQOgfrbO0fenSpTRp0gRfX1/8/PyIiIhwuIfg4sWLAAQFBTmUz8Dp06cZMWIE5cuXp0iRIgQEBNC6dWsWL17sUDm2fCE2b96MEILw8HDjtpiYGB599FGjHoZ9k33f2vJ5WLNmDR07diQwMBAvLy9CQkKIjo7myJEjZuUNfjKnTp1iw4YNRERE4O/vj4+PD40bN2bVqlUOtV1hHmU8FFLqNulCYIa/8f/KAx8jMzJcqJFCUTCZMmUKTZo0YdmyZTzyyCN069aNihUrsmbNGlq1asWsWbOcXudbb71F37598fLyonPnzpQtW5ZffvmFiIgIdu7caXc55cqVA2Djxo0cPHjQIR12795N7dq1mTlzJgBPPfUU9evXZ/v27fTr148BAwbc01D3zZs35+mnnwagWLFiREdHG5fu3bvbVcb48eN54oknWL9+PdWqVaN79+74+/uzcOFC6taty5o1ayzmnTNnDpGRkdy4cYNOnTpRpUoVdu/ezZNPPsk333zjlDY+0Egp1WJjqVevniyI7PzzJ9l8TlU5e2oZeTvWX+5bv8jVKikc5PDhw65WoUATGhoqAblp0yarcq1atZKAnDdvXpbta9eulYAMDg6Wu3btypK2bds2Wbx4cenp6SmPHTtm3B4fHy8BGRoaarE+QGq3T/PbS5QoIePi4ozb09PT5dChQyUg27Zta7Utply/fl0GBwdLQHp4eMhOnTrJSZMmyZ9//lleu3bNYr7bt2/LkJAQCchRo0bJtLQ0Y9qBAwdkUFCQBORnn32WJd+8efMkIKOjo+3abmDTpk0SkK1atcqy3Z59OWHCBAnICRMmZNm+Zs0aCchixYrJLVu2ZEmbPHmyBKS/v79MSEjIkmY4Z7y8vOTatWuzpL399tsSkBUrVrSoz/2OI/ccIE5aeC4qh8lCTOMa7Xnv10Y0T/oWgId3vktqq+54ehVxsWYKp7LpPdjyvnPKqtQB+i61XH6rcdA6m+f+4l5wfJ39dZgrI4+0bt06V/kmTNBmI82ePZtGjRplSWvWrBlvvvkmY8aM4fPPP2fKlCl51tPAxIkTqVevnvG/m5sb77zzDrNmzWLr1q2kpqbi6elpsxw/Pz9+/vlnBgwYQFxcHD/++CM//vijsczGjRszcuRIevXqlSXf8uXLOXv2LKGhoUyePDmLr0T16tWJjY1lxIgRfPjhhzz77LNOarVzMRyPl156iZYtW2ZJGzNmDCtWrGD37t3MmjWLN954I0f+F198kQ4dOmTZ9tprr/Hhhx9y4sQJzpw5Y+zZUTiOGrYo5FTr+T+SZVEAymWcZ99301yskULhfCIjI7N0e2dfSpUqlSPP5cuX2bNnD8WLF6d9+/Zmy23VqhWAQ0MJ9vDEE0/k2BYUFERAQAApKSlcuXLF7rKqVq3Knj172L59O6+//joREREEBASQkZHBjh076N27dw5fhC1btgDQr18/s0bKwIEDEUJw4sQJzp8/71jj8oG0tDS2b98OYNHPYuDAgQAWY4CYOwZeXl6UL18egH/++Sfvij7AqJ6HQk5AydLsrDCUJic/AeCxI5+SnDQEP/8SLtZMoXAe48aNy+KMl53w8HASEhKybIuPj0dKyfXr1/HwsH6ru3TJucHWLL3RFi9enKtXr3Lnzh2Hy2zatClNmzYFtCmau3btYuLEiaxfv54FCxbQuXNnevToAWA0CAwOi9nx9vYmODiY8+fPc/78ecqUKeOwPveSK1eukJKSgpubG6GhoWZlKlSoAGDR+LF2DIBcHQNFJgXOeBBC9AWGAzUBd+AoMA+YKaV0yCNQCFEOGAd0AMoA14E9wEdSSueEZCsA1Ok+ln8nf01Rt8vM83cj8ZsY3h2sPIrvG1qPd/owgEPlZx/mKCSkp6cD4O/vz5NPPmlV1pFpghl2OCa7ud3bTl03NzeaNm3Kjz/+SMOGDdm3bx8rV640Gg9Sd4Q0NyPEgEHGGdizTxzBVDdLbbCl/70+Bg86Bcp4EEJMB0YAd4CNQCoQAfwfECGE6CGlTLezrEbAWiAAOAWsAYKBSKCjEGKslHKy0xvhArx9fNlTaxCTri4iyd2dIhkn6XNiN9UrNrKdWaG4TwkJCQHA09PTobDVXl5eANy4ccNs+unTp/Osm7Nwd3enTZs27Nu3L0vvSdmyZQE4efKk2Xx37tzhwoULAHb1OuT3PgkMDKRIkSKkpKRw6tQpHnvssRwy8fHxgH36K5xPgTHNhBBPoxkO/wI1pZRPSCmfAh4DjgBPAS/YWZY38A2a4fAJUFFKGSWlbAy0BW4Ck4QQTZzfEtfQscsYHk7XnKJS3ARLfi68QWMUCmdQpkwZatSoweXLl21+G8OUkiVL4uXlxZUrV8wOZxgcFvMDe3oHzpw5A2QaDJDpy/H111+TlpaWI8+CBQuQUlKxYkW7Hr4GmaNHj5pNt7RPDEaHOR2s4eHhQbNmzQBYuNB8DBuDQWhtOEtx7ygwxgNg6DcdK6X8y7BRSpmANowBME4IYY/OTwFlgZPAaNPeCinlJsDwOcr/5FnrAoKHhyd9QgdTNjWVZy74s/1Mbw6eT3K1WgqFS3n77bcBeOaZZ1i/fn2O9Lt377Jq1aosDpOenp60aNEC0OI1mD7At23bxltvvXWPtc5kxowZDBw4kN9++y1HWlpaGrNmzTLGLDCdcdGjRw9CQkKIj49n/PjxWYYVDh8+bJyFMnr0aLv0aNCgAX5+fhw6dIivv/46h46W4iYYDLGEhASuXr1qV10GXnnlFQA+/vhjo/OkgalTp7Jz5078/f0ZMkRF2HUFBcJ4EEKUBeoBd4Hl2dOllFuA88AjQGM7imygrzdLKVPNpP+sr9sJIYo7rnHBpHf7UdTLmMDMa+OJzwjmvz8cvqdBYBSKgk63bt2YMmUK//77L5GRkVSuXJmuXbvSvXt3GjVqRFBQEN26dWP//v1Z8v33v//Fy8uLzz77jGrVqtGjRw8aNmxIq1atGDFiRL7pn5qayvz582nUqBGlS5emY8eO9OvXj44dOxIaGsqwYcPIyMjgtddeIzIy0pjP29ubZcuW8dBDD/Hhhx9SqVIl+vTpQ2RkJHXq1CEhIYH+/fszbNgwu/Tw8fExGk39+vWjefPmdO/encqVKzNq1Chee+01s/k8PT3p3LkzaWlp1KlTh379+jFkyBDGjRtns87OnTszduxYbty4QcuWLQkPD6dv377UqFGDV199FW9vbxYtWmR2po3i3lMgjAegjr4+JKW8bUFmTzZZa/jq68sW0g3bPYHqdpRXaIh5sgsebpqD0W/xiaw7+K+LNVIoXMsrr7zC3r17GTx4MOnp6WzYsIGffvqJq1evGiNM9uzZM0uepk2bsnHjRiIiIjh79qyxW37hwoXG3oz8YPDgwXz33Xc8//zzhISEcODAAZYvX86vv/6Kr68v0dHRbN26lUmTJuXI27hxY/744w+ee+450tPT+fbbb9m9ezeNGzdm0aJFLFiwwKpDZXZGjx7NnDlzqFmzJnFxcWzcuJEKFSqwbds2OnbsaDHfrFmzjPt+2bJlzJkzhyVLlthV5/vvv8/q1atp164dBw4c4JtvvuHq1av079+fvXv3mp2OqcgfREF4MxVCjASmASt1PwdzMtOAkcAUKaXVvjYhxDvAG8A3UsoeZtKfAFbrf5+RUn5lrbz69evLuLg42w0pIExcfYh5208BEFKiKOtHtaSoV4HyjVXoHDlyhKpVq7paDYVC8YDgyD1HCLFXSlnfXFpB6Xkw9BTctCJjcPP1s6O8X/R1Z31IJDvPmfy+b4YtDIyKqMRDPp74eP6Df7EJvLdkgKtVUigUCsV9REExHgx9Z07pBpFS/gL8ChQF1gsh2ggh/IQQlYQQs4DOgMH91+wEZSHEMCFEnBAiztkBZO41/j6eDKp3Fu8K0zjte42f0vdz/PQfrlZLoVAoFPcJBcV4SNbXvlZkDGnJVmRM6QFsA6qixYy4DhwDhgCfAod0uURzmaWUX0gp60sp65csWdLOKgsOw9r24RHdVfSWmxtLf/qfaxVSKBQKxX1DQRkIP6Wvzcch1QjJJmsVKeVFIURLtLgOrYFA4CLwPbAPuKaLHnBQ10KBdxEf+pbtz+oz8/G72IJ5t7oQ9U8S1YL9bWdWKBQKhcIKBcV4+F1fVxNCFLUw46JBNlmb6J8U3aAvRnSjwhc4g9YbcV/yTMexbJnThA03tc6a/64+zJJhjR3ysFYoFAqFIjsFYthCSnkWrTfAC224IQtCiFZoQZ/+BZzx+TvDJOPpsiBMN7mHjO1SF3d96ubu+ER+OpRgI4dCoVAoFNYpEMaDznv6epIQoqJhoxAiCJih/33f9ONYQoj3hBBHhRDvkQ0hRA0hhE+2bUWFEJ8CHYH9wMfObkRBo2KQL/0bZ44G/W/NAW7eNh+fXqFQKBQKeygwxoOU8htgJloUyQNCiNVCiG+Bv4DHgZVoH8gypTRQWV9n51XgohBiixDiayHEarQolS+g+Tl0lFLevTetKViMavsY/kU9qeazBf+AV/hgmQrnqlAoFIrcU2CMBwAp5QigH9oQRiu0L2CeQHvgP23vFzV1VgJbgApAFNAc7fPeLwH1pZQXnKh6geYhHy8GPb6DM6FrOVUE1mYc4PjpP12tlkKhUCgKKQXKeACQUi6WUjaTUhaXUhaTUtaTUk43Ha4wkY2RUgopZYyZtJVSys5SyrJSyiJSygApZVMp5ScPSo+DKUO7jKFsqubekQ5sWnPffBNMoVAoFPlMgTMeFPcGH+9i9AnuS6cbN1l97gJDE37l7z93uFothUKhUBRClPHwADGg0+v0TS5P6fR03ITk7urRyAyzATYVCoVCobCIMh4eMAKiPiRVugNQNfUQe9fMcrFGCoVCoShsKOPhAaNcpdrsLd3b+P/hfe9z+eoD4zuqUCgUCiegjIcHkGp93uEiD7Ha14dBZYvy/reDXa2SQmGWsLAwhBBZFm9vb8qVK0fPnj3ZsmWLxbwxMTEIIYiNjTWbnpSURPPmzRFCULVqVc6dOwfAxYsXWbBgAb1796Z69er4+flRrFgxqlevzpgxY/j3339z3Z7ly5fTuXNnHnnkEby8vAgICKBSpUp07dqVSZMmcerUqVyXbUp4eDhCCDZv3uyU8uzBcKyc1QZFwUYZDw8gfv4l+L56L14vGchlD3c2up9h559rXa2WQmGRyMhIoqOjiY6OJjIyEtAexOHh4Xz00UcOl3fp0iVat27N9u3bqVu3Llu3bqVs2bIAvPLKK8TExLB8+XLc3d3p2LEj4eHhXLx4kQ8//JBq1aqxd+9eh+pLS0uje/fu9OzZkx9//JEyZcrQtWtX2rVrh7+/P+vWrWPcuHH88MMPDrclP4iNjbVqiCkePArKty0U+czgp97jpzk/caxIBiXS0zn183s0rh6JcFP2pKLgMW7cOMLDw43/U1NTeemll5g5cybjxo2jR48exoe/Lc6ePUu7du04duwYLVq04IcffqB48eLG9BIlSjBx4kQGDx5MmTJljNtv3LjB0KFDWbJkCT179uTYsWN4eNh3C505cyYrVqwgODiYtWvXUrNmzSzpSUlJrFixgtKlzcW7Kxxs3LiR1NTULPtMcf+inhQPKG7u7gytMZaB166z+twF+lzfz/5flrpaLYXCLjw9PZkyZQp+fn7cvXuX9evX25Xvr7/+okWLFhw7doyOHTvy008/ZTEcAD755BPeeuutHA9BX19f5syZg5+fHydPnmTnTvs/s7N0qXZtTZgwIYfhAODv78+gQYPo2LGj3WUWNCpUqECVKlXw9PR0tSqKfEAZDw8wkU360ky0wkf/NljJ7RO4c/umi7VSKOyjaNGiVKpUCYCEBNsffPvzzz9p0aIFp0+fpmfPnnz//fcULVrUoTp9fHyoXLkygNFHwh4uXrwIQFBQkEP1GVizZg0dO3YkMDAQLy8vQkJCiI6O5siRIw6VY8sXwuAnMn/+fOM2IQQTJ04EYOLEiVn8T0yHMaz5PNy8eZN3332XWrVq4evrS7Fixahduzb/+9//uHXrVg75zZs3I4QgPDyc1NRU3n33XapUqYK3tzdBQUE888wznDlzxqG2K5yLMh4ecCr1nUwSxQAoIxP4fenbLtZIobCfpKQkAEqVKmVVbteuXYSHh5OQkMDQoUP5+uuvc/WGnJaWZnw4OjLEUK5cOQA+++wzUlJSHKpz/PjxPPHEE6xfv55q1arRvXt3/P39WbhwIXXr1mXNmjUOleco0dHR1KpVC4BatWoZfU+io6OpXbu2zfyXL1+mSZMm/Oc//zEOGUVGRnL69GneeOMNmjZtSmJiotm8qampdOzYkffff5+KFSvSsWNH3Nzc+Oqrr2jevDnXrl1zalsVDiClVIuNpV69evJ+ZteS96WcUFzKCcXlif+Wkgf+2u1qlR4YDh8+7GoVCjShoaESkJs2bcqRdvDgQenu7i49PT3l2bNnc6RHR0dLQEZERMhixYpJQI4ePTpP+sycOVMC8pFHHpEpKSl251uxYoUEJCBLlSolhw4dKufMmSP37dsn09LSLOZbs2aNBGSxYsXkli1bsqRNnjxZAtLf318mJCRkSWvVqpXZ/WZpuwHDPps3b16W7RMmTJCAnDBhgkVdDccqPj4+y/YePXpIQLZo0UJevXrVuD0xMVE2bdpUArJ3795Z8mzatMm4v+rXr5+lfdeuXZN169aVgHznnXcs6qMwjyP3HCBOWnguqp4HBfWiXuGwexgzHypOr7IP89EvL7laJYUJM/6YQY0FNaixoAYz/piRI/2DPR8Y0xccWpAjPXZHrDF9+fHlOdJf+/U1Y/qakznfYl/Y+IIxffPZzTnSB64baEzf8++e3DXSAa5evcratWuJiooiIyODadOmWXWW3LhxIzdv3qRhw4Z88MEHua73wIEDjBkzBoDJkyfj5eVld96oqCi++OILAgICSEhIYNasWQwePJi6desSEBBAdHQ0x44dy5FvypQpALz00ku0bNkyS9qYMWNo1KgRSUlJzJpVMIO9nT59mm+++QY3Nze++OILHnroIWNaQEAAs2bNws3NjWXLlnH27Nkc+YUQzJ07N8twj7+/P2PHjgW0Y6twDcp4UODh6cnRZs8xI+AhUtzc+K3IDZZt+MTVaikURlq3bm0cZy9RogSdOnXi9OnTrF27luHDh1vN26RJEzw9Pfntt98YOXJkruo/d+4cXbp04caNGwwZMoT+/fs7XMbQoUM5c+YMixcvZujQodSpUwcPDw+Sk5NZuHAhderU4ccffzTKp6WlsX37dkDzRTDHwIEDAfI1noMjbN26FSkljRs3pkqVKjnSH3/8cRo2bEhGRga//vprjvRy5cpRo0aNHNsNZf3zzz/OV1phF8p4UAAQ1WY4je74AlAl5S7H/txPWrr67oWiYGCI8zBgwADat2+Pt7c3KSkpDBgwgBMnTljN2759e5YsWYKnpyeffvopL73kWM/av//+S0REhNHR8rPPPst1O3x9fenTpw9ffPEF+/bt4/Lly8ybN4/SpUtz+/ZtoqOjjQ6EV65cISUlBTc3N0JDQ82WV6FCBQDOnz+fa53uJQa9Hn30UYsy1tpg8BXJjmGGzJ07d/KqoiKXqDgPCiMvt/2Eld+9yJYrzzFHhlFm52kGNbd80SvyhxG1RzCi9giL6WMajGFMgzEW02ObxhLbNNZilPkNEgAAIABJREFU+uSWk5nccrLF9P+L+D+r+s3rMM9qujPIHufhwoULREZGcuDAAfr168euXbsQQljMHxUVxZIlS+jduzeffKL1qk2bNs1mvRcvXqRNmzYcP36cbt268dVXX+Hu7p7n9hjw9/cnJiaGWrVqUbduXS5fvsz27dtp164dUp8FBVhsm6mMM8hw8ofyDPpZOzbW2uCm4s4UWNSRURipVqEBAfUXcVyGATB1w3EuXleWvaLgUbp0aZYtW2Ycjvjqq69s5jEYEJ6ennzyySeMGjXKqvylS5do06YNR44coXPnzixbtszuoFCOUqdOHQIDA431AgQGBlKkSBEyMjIshnyOj48HsDswk8FP48aNG2bTT58+7YjaNjH4opw8edKijKNtUBQMlPGgyMKQ5uWpUFKbunkjJY131jg2j1yhyC+qVKnCiBFaj0xsbCxpaWk285gaENOmTbNoQFy+fJk2bdpw6NAhIiMjWbFihUMOktmx1UOQlJTE9evXgcwHroeHB82aNQNg4cKFZvMZ4jGY9spYw/CAPnr0aI60hIQE9u3bZzafoe327GNTWrRogRCCXbt2cfz48RzpR44cYffu3bi5ueVwCFUUbJTxoMiCl4cbb3erbvy/4/g6lm2+993SCkVueOONN/Dz8+Pvv//myy+/tCtPdgPi5ZdfzpKemJhIREQEBw8epF27dqxcuZIiRYrkSc8nnniCDz/80Gwwq4SEBGJiYrh79y7lypWjSZMmxrRXXnkFgI8//tjoPGlg6tSp7Ny5E39/f4YMGWKXHhEREQBMnz6dCxcyv6abmJhIdHS0xR4Jg9HhaFCq0NBQnn76aTIyMnj22WeNcTkArl27xrPPPktGRgY9e/YkJCTEobIVrkX5PChy0LRiIJ1r+HD2yrvE+ycw74SkY4On8Cv2kO3MCkU+UrJkSUaPHs2ECRN455136N+/v11DC6Y+EB9//DGA8QNbQ4YM4c8//zTO7HjuuefMljFkyBCaN29ul57nz59nzJgxjB07lscff5xKlSrh6enJP//8w2+//UZKSgoBAQE5gld17tyZsWPHMmnSJFq2bEmLFi0IDg7mwIEDHDx4EG9vbxYtWmQzSJaBnj17MnXqVH7//XeqVatGs2bNuHv3Lnv27CE4OJgnn3ySlStX5sgXGRmJj48P3377LS1btqRChQq4u7vTtWtXunbtarXOmTNncvToUTZv3kz58uWNvSSbNm3i6tWr1KpVi+nTp9ulv6IAYSkAhFoenCBR5jga/7tsNPdxWX1+dVl9fnX55rzurlbpvkQFibKOtSBRBpKTk2WpUqUkIGfPnm3cbgh4ZC2w0YoVK6Snp6cE5KhRo6SUmYGUbC3ZAylZ48SJE3L69OkyKipKPv744zIgIEB6eHjIgIAA2ahRI/nWW2/lCPRkyurVq2VkZKQsUaKE9PT0lGXKlJH9+/eXhw4dMitvLRjUlStX5PDhw2VwcLD09PSU5cqVk6NGjZJJSUkWg0RJKeUvv/wiw8PDpb+/vxRC5Ni3loJESakdo7ffflvWqFFDFi1aVBYtWlTWrFlTvvvuu/LGjRs55A1Bolq1amW2ffHx8RKQoaGhZtMVlnFWkCghneytez9Sv359GRcX52o18p13F0WzJH0fjW5IblzuzgcvvkZICR9Xq3VfceTIEapWrepqNRQKxQOCI/ccIcReKWV9c2nK50FhkVd7zKRTYhO2nH2XXbcbMHH1YVerpFAoFIoCgDIeFBbxLuJDr6cnkaq7xvx8JIENh21/vVChUCgU9zfKeFBYpW65APo0zPSCjl11iNt3012okUKhUChcjTIeFDZ5LbIKAT6eQAZl5Tz+91U/V6ukUCgUCheijAeFTQKKeTG6tR/1Qt/kcPAf/CAOsu2PH21nVCgUCsV9iTIeFHbRq0l9hLs2MydNCBbufBPp5Dj4CoVCoSgcKONBYRceHp48V+s/eGVIBiRd56OLf7P3x9muVkuhUCgULkAZDwq7aduoB+/drs+YxGsUk5JH494hKfGSq9Uq9KhYKwqFIj9w5r1GGQ8Kh2jSbyoXKQHAwyRxbNHLNnIorOHm5ub0zyArFAqFOdLT0532SXllPCgcws+/BOea/Nf4v2Hiav6fvfsOr6JO2zj+fRKS0HuXrhRBpRhpKqgo9oKIotgLCva2iq5dF13XXlBsKIoNG9ZVeVVUigQQVARBlCZg6D0hyfP+MScYs5DkJAfmJLk/15VrmJnfmdzZayUP82s/TtLgyeKqWLEimzdvDjuGiJQDGzdupHLl2KwSrOJBotblyLOYUbkn24Cnalbn5h//wYZNa8OOVSpVrVqVtWvXqutCRHap7OxsVq9eTfXq1WPyPBUPUiwNBz7K2Y0a8UStmixINu594/ywI5VKtWrVIisri2XLlpGRkaEiQkRixt3Jyspi7dq1LFy4kCpVqlCtWrWYPDvutuQ2szOAIcB+QCIwB3gBGOHuUXUOm1kT4AagL9AMMGAxMB74t7sviGH0cqVRs9bsU6UbP2ZPB2Bh5k/8/ssMWrTpHHKy0iUhIYGmTZuyevVqFi1aRFZWVtiRRKQMSUxMpHLlytStW5dq1aphZjF5blztqmlmTwBDga0Ev+C3AX2AasA7wAB3L9LayGbWGfg/oCawBJgWuZUK7AFsBI5094mFPau87qpZmMzMDM59oSvHbFrF6es38HNyRzrc+CWWoBdaIiKlXanYVdPM+hMUDsuB/dz9OHfvB7QGfgb6AZdF8cgnCAqHZ4BW7n6Su58EtASeB6oCI2L4I5Q7yckp3Nn9SQau20QisE/mTKa+90TYsUREZBeLm+IBGBY53uDu83IvuvsKgm4MgBvNrNDMZlYR6BE5vdXdt+V53jbglsjpfmYWm6Gn5dReHQ8krdHp28/bzLyX1X8uDTGRiIjsanFRPETGJuwPZAJv5r/v7l8BS4GGQPciPDIbyO083lEHT25fzSZgS7R55e/2O3M4y6weADXZyLdjhhTyCRERKc3iongAckfZ/eTuO/tlPjVf252KvF0YHzm9w8yScu9F/nx35PQ5j6dBH6VU5ao1SO81nHUJCdxWtzY31fqNMf/9T9ixRERkF4mX4qFl5LiwgDaL8rUtzFBgHnARsMDM3jGzd4DfgIHAI8B1xcgqO7DfoQP4Z/32vF2tKgCjFo9i7YaVIacSEZFdIV6Kh6qR46YC2myMHIs0STUyDbMn8DHQBDgp8rUHMBuYkHcshJTc5Uc/QbXsYDZt68xMXv9YK0+KiJRF8VI85I5LiFkXgpn1BH4E9gJOBOoC9QgKiFrAW2Z2awGfH2xmaWaWlp6uzZ+Kok3zTpxe+RDOWlaL7xbdyr+/r8tPf6wLO5aIiMRYvBQPGyLHqgW0yb23oYA2AJhZTeBdgrcUR7n7OHdf5e4r3f094CiCgZK3mFnrHT3D3Ue6e6q7p9arV6/IP0h5d+mAx0irdR/p1CI7x/nH2Flsy9bGTyIiZUm8FA+/R47NC2jTNF/bghxL8JZh8o5WkXT3+cAUghU2DylqSClcQmIC9568LykVgv9r/fTHep75Wgt5ioiUJfFSPMyIHDuYWaWdtDkgX9uCNIscC3pnnruTU+0iPE+i0KpeVa4+ok3kzHnnu4eZOOvjUDOJiEjsxEXx4O6LgelAMjAg/30z600w6HE5MKkIj/wjctw/7zTNPM9LIlhXAoLZFxJjFx7Uko57bKJ987tZ3uArHpo8jKwsjU8VESkL4qJ4iBgeOd5nZnvlXjSz+sCTkdN7826OZWbDzWyOmQ3n7z4GNhO8gXjIzFLyfCYFeJSgG2QN8N+Y/yRChcQELu+awLJKwSSZOSnZPPL60JBTiYhILMRN8eDuYwn2mmgI/GBm75vZ2wRrNbQnGAD5eL6PNQLaRo55n/UnwToP2cClBOs8jDOz9wneNFwCZADnu7umA+wih3c7hSNzWpHgTp81yXz8S3eWrNkcdiwRESmhmBUPZlbVzPY3swbFfYa7DwUGEXRh9AaOBOYTbIjVv6g7akae9SLQFRhNsOx1X+AIglkWzwFd3P3d4maVorn5tJfos/II3l1+B/MzGnLTOz+iRT1FREq3qLbkNrNDCcYkPOPuM/JcP5dgF8uKQA5wn7v/M7ZRw6MtuUtm2sI1nPLURHL/r/bAgI70379JuKFERKRAsdyS+0LgfPJMlzSzlsBIoBLB5lUAw8ysT/RRpSzav3ktzu3ZYvv5nR/M5s912o9MRKS0irZ46ArMdPc1ea6dRbBewg3u3oxgK2wnGHMgAsB1fdvSpFYlkthKx6oPcPNrqi1FREqraIuHesCSfNcOA7YSGczo7mnARKBjidNJmVElpQJ3HrsHbVrdxoy6fzC54gZGvldmerZERMqVaIuHysD2yfpmlkCwXsJ3+bbSXky+GRAih+3TlmbU2n4+a8lY1q1aEWIiEREpjmiLhz+BvHtBdAeqAN/ma5dCMKtB5G9uOuFFGm/L4YZVa3g0fRnzXlTvlohIaRNt8TAJ6GRmp5pZdeBmgvENn+Vrtzd/rfIosl3Thq24p9mNnLl+AwlA6vrPmf7f0WHHEhGRKERbPNwPZAGvEqzOeDTwvbt/mdvAzJoQFA+a2yg7lNr3LKbW6Lv9vPmkm1mTvizERCIiEo2oigd3/w44DvgK+BkYBRyTr9lpBBtS5X8bIbJdm3OeJD0y/qEO6/i/V84POZGIiBRV1CtMuvtn7n6Yu+/j7ue7+4p89x9w91ru/mrsYkpZU6N2Pf7odS/rE4x/1q3N7bWW8NQ7w8KOJSIiRRA3e1tI+dPxsIHc0aAT71WrCsDLa8Yxf9GPIacSEZHCRFU8mFmymdU3s4r5rlc1s7sjm1k9ZmZNYxtTyqqr+42iXlawUWrPLVv4441/4Dk5hXxKRETCFO2bh1uAZUDn3AuRtR4mAMOAYwl2sZxkZnViFVLKrib1W3Bh43N4YEU6/05fRa+N3zL94+fDjiUiIgWItnjoAyx190l5rvUDOgE/Eux98Q7QmGDba5FCnXH0P6hZ8fDt53tOvY2VyxeFmEhERAoSbfHQApib79qJBGs9nOnuzxPsurmMoKgQKZK9z3mU5dQDoCYbWfzSxeq+EBGJU9EWD7WB/OsJ9wQWuvsPAO6eA0wBmpU8npQX1WrUJv2wB4CgEp2XOIsRb18fbigREdmhaIuHbUCN3BMzqw+0Ar7J124zULVk0aS82bfXiXxa91gubliPu+rW5uX1n/DzgmlhxxIRkXyiLR5+AQ7MM9uiP8E/FPMXD40I9sEQiUrnQf9hQYUUADYkJvD0J0Nx95BTiYhIXtEWD28CNYEJZvYgcB+QCbyb28DMEoEuwPxYhZTyo16txlzcYgiJ7py0NouFS/rz8uSFYccSEZE8KkTZ/iHgCOBQIBXIBq5y97xvGfoSdG1MiElCKXcGHH4Z60Zv4KFlrdlEJX7+6GcO3KsureqpJ0xEJB5Eu7dFBnA40Bs4FWjr7k/ka7YVuBrQVolSbGcO/AdNGtQHYOu2HK5+YyZZ2Zp9ISISD4qzt4W7+9fuPtbdF+zg/hfu/oi7/xabiFIeVUxK5KHTOpGUaADMXLyWB/6bf2iNiIiEQXtbSNxq37g61xzRFsimfb3neX3FUD765qWwY4mIlHvRjnnYzsz2BtoA1QHbURt319/0UiKDe7Vi4pxL+b7SUsB4bM6/6bHv0dSqUS/saCIi5VbUxYOZ9QRGAnsX1IxgCqeKBymRxATjql7DGDplKJsTEqidlcPIjz/nhoGnhx1NRKTcinZXzXbAp0B7YBKQO67hNSCNYPYFBFM3VThITOzfvjenVz6EvitrMev32xnxfXUm/JIediwRkXIr2jEPNwKVgYvd/SDgawB3H+Tu3YCOwDSC7owrYhlUyrcrT32cdXUfZANVALh+7EzWbs4MOZWISPkUbfFwCDDP3Z/Z0U13/xk4jmBfi1tKFk3kL2bGvf33pU6VZABWrM/gn+/+GHIqEZHyKdrioSHB1tu5sgHMLCX3QmTBqK/QrpoSY3WrpnBv//22ny/7/WmefPvGEBOJiJRP0Q6Y3MjfZ1asjxwbAb/nub4F2KP4sUR27Ij2DTi9UxUW/3kTM2tsYMm6HLrPPpou7XuHHU1EpNyI9s3DEqBpnvM5keOhuRfMLAnoBmhEm+wSVx3Rmj8rB3Xr5oQEnvrqSrK2afyDiMjuEm3x8C3QwcyqR84/JOi6eMjMhpjZ8cBbQBP+d6dNkZhoUGcPrmx3HRXcOXLjJv6T/jtTX7op7FgiIuVGtMXD28BSgoGTuPtSYDjBQlGPE0zRPA5YB9wcs5Qi+Rx70LncZIdwf/oqquc4XRc9y89T/ht2LBGRciHajbHGu3trdx+X59ptwADgDeBz4DFgf3f/vTiBzOwMM/vazNaZ2UYzSzOzS82syFnN7BAz8yJ+NStOTgnfyYMeZnbyvgAkmlPz40tZt2ZlyKlERMo+c/ewM2xnZk8AQwl25hwPbAP6ANWAd4AB7p698ydsf047gjUpdqYrwQqZvwKtvZD/EVJTUz0tLa1IP4PsXssXz6fSc72owSYAPqvRiz5XvEtCYmLIyURESjczm+buqTu6V+y9LWLNzPoTFA7LgV7uPi9yvQHwBcHUz8uARwp7lrvPAc4t4Hv9FPnj84UVDhLfGjbdi+nd/0XnyVfyZrWq3F9zAYPeupqrTn007GgiImVWPO2qOSxyvCG3cABw9xXAkMjpjdF0X+yImfUgWF47G3ixJM+S+NDlqHO5r0F37qpbm60JCby6aTxTfxofdiwRkTKrwDcPZvZ/JXi2u3ufojQ0sybA/kAm8OYOHvSVmS0lWDuiOzCxBLnOjxw/iQz4lDLgwtNH8cXYI/gjyWiclcWG9//BttYTSUpOKfzDIiISlcK6LQ4h2B1zh1tuFyKa7oDOkeNP7r5lJ22mEhQPnSlm8WBmlYHTIqfPFecZEp/q1mzE1e2HMS3tn1y7Zg0VfTmTXryBHhc9HHY0EZEyp6hjHr4DRhOMR9gVWkaOCwtosyhf2+IYQDD48k/ggxI8R+LQUT0HUfPXuVRcHQyL6bZkFD9N7EuHnseEnExEpGwprHh4FTiJYHZCF+ATYBQwzt2zYpijauS4qYA2GyPHaiX4PrldFi+5+7YSPEfiVNczbuPHf3/FPhnfk2BOvU8vZU3ridSq1yjsaCIiZUaBgw/dfRDBZliXAGkEC0C9CSwzs4fNrFOMcuR2i+yymQ9mthfQK3L6fBHaD46sMZGWnq6VtkuLhMREGpzzImsiNebSlI3cNvYksrNjWeuKiJRvhc5ccPcN7j7S3XsC7YB/AxnAFcA0M5thZleYWd0S5NgQOVYtoE3uvQ0FtClI7luHSZGtwwsU+ZlT3T21Xr16xfyWEoZ6jVuwuNcDPFujOuc1asAXlTdzz5hzwo4lIlJmRLvC5C/uPgxoBhwLjCUoKB4ClprZ6GLm+D1ybF5Am9wNuX4voM0OmVkicHbkVAMly4H9DjuNn6t1INuCl1r/lzmDGd9/G3IqEZGyoVhrJrh7jrt/7O6nEWyC9SGQBBxZzBwzIscOZlZpJ20OyNc2GkcSzNTYBLxejM9LKXTnGW/SOsPouDWDLot6cfknW1m3RUNdRERKqtgLLplZWzMbDswkeAsBUGh3wI64+2JgOpBMMCMi//fqTVCkLAcmFeNbXBA5vu7uGwtsKWVGlcrVuLv3M2xZdjVvZxzPkrVbGfb2LLSoqIhIyURVPJhZdTO72MwmAbOBG4AUgh0193f33iXIMjxyvC8yuDH3e9YHnoyc3uvuOXnuDTezOZEiZmeZ6xIM9AR1WZQ77dt248L+J20//+iH5bw8ZVEBnxARkcIUWjxYoK+ZjQGWASOAVOAjgrcEjd39SncvTnfCdu4+NvLshsAPZva+mb0NzCNYTvpdgiIlr0ZA28hxZ84ieKMxx91LsjKllFJH79uIs7r/NZzmvo8nMH76xyEmEhEp3QpbnvoegoGGjQmmU84mWOdhdGTPiZhy96Fm9g1wKdAbSATmEEytHJH3rUMUzoscC52eKWXXzcfuTdrCNazf8AneeBz3T3f2bb4f9evsEXY0EZFSp8Atuc0sh2DthTSComFKNA939+klCRcvtCV32TBr0QIuGn8CmxOCGRg9t1bnqYu+xhLiaX84EZH4EIstuVMjX9HwKJ4vssvt16wVg6oezjObx1MvK5uE9D0ZO20JAw5oFnY0EZFSpbBf7ovYhas+iuxuVwx4mJUjT2bKop58nLU3X46bTcdmtWjToCSrnouIlC8FdltIQN0WZcvmzCxOePxb5v8ZzNptVa8K4y47iKopelEmIpKroG4LdfZKuVM5uQJPDupCpaREABakb+LmNyeTk50dcjIRkdJBxYOUS20aVOOefvsA0DR5Nr9uHsJ9r10YcioRkdJBxYOUWyd3acI5+8wns+UoFqbAG9um8uE3o8KOJSIS91Q8SLl2zUln0TAr+M8gwWHdpOGsXbk85FQiIvFNxYOUazWq1ua2Ax+nbUYWo5ct54xNy1n47Jka/yAiUgAVD1LudWnfm5tb3kL7zGDHzY5bpzLlpZtCTiUiEr9UPIgAnY84g0mNz95+3u33p/lhwnshJhIRiV8qHkQiDjjvAX5K3heAzQnwyqzr+elXre8hIpKfigeRiApJyTQ4fwxTkmozcI+GfFgthdvGX8DmrZvCjiYiEldUPIjkUbdhMxZ1u5bFFYLVJuem5PDSi+eEnEpEJL4UtiX3ghI82919zxJ8XiQUAw6/jB9f/JqPc37kjpWrOXrTItI+GEnqcYPDjiYiEhcKW8y/RQmerU0zpNS67cwx9Hj4aI7atASADlNvZkGLjrTap1vIyUREwldY8dByt6QQiTMJiYkceOFrLHrkIJrlLKWSZZLy1lmsa/Q1Neo0CDueiEioCiwe3H3h7goiEm+q1ajN6lNfZtOrR1PFttLQVzDi5ZMZPOT/SE5OCTueiEhoNGBSpADN23Vhbs//sC4hgUsb1OPpmuu55eVTwo4lIhIqFQ8ihehy5Fk8tEdvvq1cCYCPEn/n1feHh5xKRCQ8hY152CEzOwA4BWgDVAdsB83c3fuUIJtI3LjprNeZ90JPZlXM5JQ12YxZUJcDum1kr/pVw44mIrLbRV08mNlDwBX8VTA4fy8ecs8120LKjOTkFO494TVeeeUKXll5PhuozODRabx36YFUq5gUdjwRkd0qqm4LMzsduBJYAgwGPo3cOhK4FJhIUDjcBxwWu5gi4WvaqDUnnPE625KCtw0L0jdx7RszyclRnSwi5Uu0Yx4uArKAw9z9WWAZgLt/5u4j3P0g4HbgGkBr+kqZ075xde7rv9/2809nr+CBTz4IMZGIyO4XbfHQEZjs7r8W0OYuYDFwc7FTicSxEzvtwfkHtgSyad/gGV7+cxijPrwr7FgiIrtNtMVDFYIui1wZAGZWLfeCuzswFehZ4nQicWrYMe04pMULLK79KzlmjPjzNb6ZoTcQIlI+RFs8/AnUyXOeHjnula9dDUDD0KXMSkpM4NZj76LBthwAOmwxHv8snbWbM0NOJiKy60VbPMzn70tWTyUYIHlJ7gUzawscChTUtSFS6rVqug837nMbh6+uytRFtzJ5dX0uGzODrOycsKOJiOxS0RYPnwF7mtnekfP/AkuBC83sOzN7C5gMJAOjYxdTJD4d3v1U+h7+NhuoAsA381fyr4/mhJxKRGTXirZ4eAW4FagM4O4ZwKkE3RepQD+CLosPgIdiF1Mkfh29byOu7NN6+/nz3/7GmK8nh5hIRGTXimqRKHdfBNyT79okM2sJ9AJqA3PcfUbsIorEvyv7tGbu8g188tNyutccwyPzv6dy1hWcdOjFYUcTEYm5Yi1PnZ+7byHowhAplxISjAdO7YiNvJdvqs8BEnjwt0dp1WQ/9mvdI+x4IiIxpY2xRGKkSkoFLjriCmpEBkzWyc5i/ZtD2bJpQ8jJRERiq8A3D2bWLPLHpe6enee8SCLdHCLlRpd2B3PlkiF8O/dh7lm5kiruTHvqLLpc/TaWoFpdRMqGwv42+x1YAOyZ5/y3In4tKE4gMzvDzL42s3VmttHM0szsUjMr1t+8ZlbJzP5hZlPNbK2ZbTaz38zsTTM7sDjPFCnIgMMv4/R6F1PFgz0v9t/wBZNfHBZyKhGR2ClszMMigt0xt+U73yXM7AlgKLAVGB/5vn2Ax4E+ZjbA3bOjeF5Lgs279iJY4OorglUxWwAnAjOBb2P4I4gA0O3U65ny2I90W/UuAD0WPsWUD/ek27GDQ04mIlJyBRYP7t6ioPNYMrP+BIXDcqCXu8+LXG8AfEEwDfQy4JEiPq8KkXUpCPbbuMvdt+W5X4e/r5YpElNdLh7Jjw/8zj4Z3zMzJZlblj3E5RMqcHyv88OOJiJSIvHUCZv7XveG3MIBwN1XAEMipzdG0X3xT4LC4SV3vzVv4RB57ip3/6WkoUV2Jik5haYXj2VslT04v2EDliVV4P75D/D93G/CjiYiUiJRFQ9mdquZnVCEdseb2a1RPLcJsD+QCbyZ/767f0WwkmVDoHsRnpdMsH04wL1FzSESazVq16PZUY9SMTL+wXGWvzOEDetWh5xMRKT4on3zcDtwUhHanQDcFsVzO0eOP0XWjNiRqfnaFmR/gi6Jxe7+s5n1NLN/mdnTZnaHmWnivew2Xfc9nKubD6VNRiZj/ljBUVsXsWDEqWRt0yZaIlI67apui0SiG1iZu9nWwgLa5E77bFlAm1z7Ro7zzGwUwaDIYcBgguW1J5rZWDOrFEVGkWI7pc+l/KPe5TTNygKg49apTBs5pJBPiYjEp11VPOwJrI+ife723ZsKaLMxcqxWhOfVjhx7AWcD/yGYcVGLYJbFUqA/8MTOHmBmgyPTRNPS09N31kykyLr1u4xJe5z713n6WCa9Njy8QCLmxRDqAAAgAElEQVQixVTo8tQ7GLvQqYDxDBWAvYGDgC+jyGGRY6ymgeYWRRWAZ939+jz3xpnZH8B3wDlmdre7/8+aFO4+EhgJkJqausump0r50u38B5n+0AK6bJzAisREHln3AvM/Ns46+sawo4mIFFlR9ra4neCXeu4v+E6Rr4JsBu6MIkfu+r1VC2iTe68oa/3mbfNM/pvunmZm0wh2Aj2EYi5oJRKthMRE9h4yhs8eP4R7627mzwoV+G35aJqltaV3ar+w44mIFElRioc7+at4uBX4HnhvJ20zCboE/huZYllUv0eOzQto0zRf26I8D4LVLnfkN4LioWERnicSM5WqVKP5wOfwzwcBkGnGpC8fpX3bY6hXLSXkdCIihSu0eHD323P/HOmu+N7d74hxjtwtvDuYWaWdzLg4IF/bgkzP8+c6wI4GLdSNHDfu4J7ILtWmeSf+ue8d/OuHWzlqRSNGrr+ciS9O5bXB3amcHJPNbkVEdpmoBky6e4K7x3x5PHdfTPALPxkYkP++mfUGmhCsPjmpCM9bCkyJnPbZwfNqAV0ip2nFSy1SMod1PYVbOzzNkxuuJpMkZi1Zx+VjZpAV2ZVTRCRexdMKk7nDzu8zs71yL5pZfeDJyOm97p6T595wM5tjZjsasn5P5HirmXXK85mKwAigBjCNIhQjIrtKr+4Hc9dJ+24/Hz/nT2597wdyclRAiEj8KmxL7l6RP37n7lvznBeJu0+Iou1YMxtBsBT1D2b2OX9tjFUdeJdgg6y8GgFtI8f8z3vfzP4DXAdMMbMpwCqgK9CYYGzG6e6umRQSqkHdmrNkzRZGfPkrWCYz/7iCO0Y34I5z3gg7mojIDhXWufolwWDJvYFf8pwXhRfh+X//gPtQM/sGuBToTbDY1BzgeWBE3rcORXze9WY2EbicYGXKygSLTT1I8BZDCzhIXLi+b1sWr17O/PW3sahSBotYTd2x13D5KQ+GHU1E5H8U9st9AkERsDnf+S7j7mOAMUVsey5wbiFt3gHeKXEwkV0oIcEYfmInLnwlm6WRawuWfM2k+SvpsVfdAj8rIrK7md7aFy41NdXT0jSuUna9xSt+Y8i449l7XW3eXXktFStW5K0hPWnToCgLq4qIxI6ZTXP31B3di6cBkyLlXtMGLXn82A/4austbKMCG7Zmcd4LU1mxfmvY0UREtlPxIBJnWjRuwfPndaVKciIAS9du4fxRU1m3aXMhnxQR2T2KXTyYWRMz62pmvXb2FcugIuXJPnvU4Mkz9ycxwYAc6my7m6EvH8zmrQXtHScisntEvZSdmZ1MsCbDXoU0jXq2hYj8pXebetxzYns+mHI6M2oEC6Fe9VJfnjz/SypUSAo5nYiUZ1H9cjez44E3CN5YrCPYUCqarbdFJAoDu7Vg5uwGzIysop6QvYKJzwzl4IufxhLU6ygi4Yj2zcBNBBtk/RO43923xT6SiOR1z9lvseH5PlTLXMSd6atI4g0mv9KI7mdFs3GtiEjsRPtPl/2AGe7+LxUOIrtHQmIiD57zX/pv3pvczoruvz7C1HfzL7gqIrJ7RFs8bAPm7oogIrJzyckp7HPZG/yU/Nc+GJ1n3MKkz14MMZWIlFfRFg/TgFa7IoiIFKxipSo0Hfoevya2BOCLKilct/jfvPflyJCTiUh5E23xcC/Q1cyO2BVhRKRg1WvWocYF7zG6aiOurV+X9YkJ3LfgESZMfy/saCJSjkRbPMwl2Op6nJndF1nPoYWZNdvR1y7IK1Lu1W3cnNZHPkqNnGBp+TrZ2dT46BqWL54fcjIRKS+i2tvCzHII1m8wCt8gy929TKzzoL0tJB59MvEVXpt1Jw/++Se1c3JYmNCEGkPHU7Nuw7CjiUgZUNDeFtH+cl/ELt5VU0SK5qieg2i8rQpVl50PBs1zlvDLU8dT4YpPqVq9VtjxRKQMi6p4cPcWuyiHiBTDfr1PYtrGlXT+7joSzGmT9QtfjDiWzkPHUbOatvIWkV1DS9SJlHL7H3shUzvcDMAvSUncUXctV4w5SvtgiMguo+JBpAzodur1fNxyMOc1qs+qConMqJjBdS/2JTsrK+xoIlIGqXgQKSOOPud+enqwBkTVnByap1fllvd+JJpB0SIiRVHgmAczyy7Bs8vMbAuR0uK+c8dhzx1FjRVVGLHpQpi6lGqVUrjx6HaYWdjxRKSMKOzNg5XgS281RHazhMRE7r3gE1a2vo3gP0N4esICnvzy13CDiUiZUtibgZa7JYWIxExCYiL3D+jIxsxsPpu9AoD/fPY9m1e/xvX9/xlyOhEpCwosHtx94e4KIiKxUyExgcdO78wFL05l8oLf2av5/by0MZPkN9K58tRHwo4nIqVcgV0LZvasmR1jZsm7K5CIxEbFpERGnpVKj2bP8EfFTABGbR7PuPFjQk4mIqVdYeMSzgfeB9LN7FUzG2BmVXZDLhGJgSopFRh+0jM0D2oHDk+vx3X/V53PI90ZIiLFUVjx0AX4F7AYOA14DVhpZuPM7Fwzq7OrA4pIyTRt2IoH+77CMavbMXbVNWRmG0Nfmc6Xc/8MO5qIlFJF3hjLzFoDpwD9gP0jl7OBr4G3gffcfcmuCBk2bYwlZcHydVs59elJLFq9GYCUCgk8f+4BHLiXlrEWkf9V0MZYRZ5O6e7z3H24u3cFmgFXAxOBXsBjwEIzm2xmN5hZm1gEF5HYaVijImMu6sYeNSsBkJmVyTMfDmDs+CdCTiYipU2x1mJw96Xu/qi7HwI0BAYDnwAdgeHAz2b2o5ndaWatYpZWREqkSa3KvHpRdxpWq8BBje9jWs2V3L/oSd776tmwo4lIKVLihZzcfZW7P+vuxwL1gEEE3RjNgJuBM0v6PUQkdprVqcyTp9RkUZV1AGxOSGDqrHv5ZfpXIScTkdIipqtAuvtGd3/V3QcQFBL9gEmx/B4iUnJd2nbjns73UjM7hxM2bOSOVek0HHc682d+G3Y0ESkFYrb3hJlVBdoCS9x9hbtnAONi9XwRia2DuhzPAySy57jBJALV2UT2O6fxW4W3aNmhW9jxRCSORfXmwcwONbMnzaxzvuvnAiuA74AlZnZ37CKKyK7StcsxrOn3OusJlm+pxQZqvHkKP//4TcjJRCSeRdttcSHBwlG/514ws5bASKASsDRyeZiZ9SlOIDM7w8y+NrN1ZrbRzNLM7FIzi7bQGWVmXsDXnOLkEylr9up4IMtPGMNGD2ZhfFU1m0umXMyXae+EnExE4lW03RZdgZnuvibPtbMiz7nB3e83s1RgMjAUGB/Nw83sicjntkY+uw3oAzwO9DGzAe4e7Tbh3wLzd3B9WZTPESmz2nQ5hDlZo/nxqwu4s2513IxbZv2Tu4Heqf3CjicicSba4qEeMCvftcMIftk/DuDuaWY2kWDaZpGZWX+CwmE50Mvd50WuNwC+IBh8eRkQ7a4+z7r7qCg/I1LutOt6BHM3/5NKvz3CZjMaZmXR4qMrWVCxMa320RgIEflLtN0WlQneBgAQ6UrYH/jO3bfkabcYaBTls4dFjjfkFg4A7r4CGBI5vTHa7gsRKboTDxnMTXteTactmTyz/E+a56yj1tj+/PrD5LCjiUgcifYX8Z9A6zzn3YEqBF0DeaUAWygiM2tCUIRkAm/mv+/uXxGMp2gY+Z4isouc2OtCbt7/SRKzU4BgEGWdt/prGqeIbBdt8TAJ6GRmp5pZdYJFoBz4LF+7vYE/onhu7uyNn/K9wchrar62RXWomT1oZiPN7C4zO1JvL0QK1u6APiw78TXWUxmAmmxk1YcD+e8kbectItGPebgfOAF4NXJuwAx3/zK3QeQtwt7AqCie2zJyXFhAm0X52hbV2Tu4NtvMBrr7D1E+S6TcaNPlEObZ6/DeQJYkZ3JNw2r4z/fg7hzVc1DY8UQkRFH9C9zdvwOOA74CfiYoEI7J1+w0YB3/+zaiIFUjx00FtNkYOVYr4jO/B64AOkSe35gg+0ygPfC5me0RRUaRcqd15178ceKrXFu/PusTE9mQmMDDs+/hh9n5x02LSHkS9et7d//M3Q9z933c/fzIgMa89x9w91ru/urOnrEDlvvxaPMUkPNhd3/M3We7+yZ3X+buHxJMN50M1OevQZr/G8hscGSNibT09PRYxRIpddp17s3VHW6henYO1bOzOXBZW854/Q+mLVwddjQRCUm89P1viByrFtAm996GAtoUyt0zCXb+hP99a5K33Uh3T3X31Hr16pXkW4qUen17nM7tHW7jqOX78dymC9iQkc1Zz33HxPkrw44mIiGIdtXGZDOrb2YV812vamZ3m9n7ZvaYmTWNMsfvkWPzAtrkPvP3AtoUVe7qkuq2ECmiI7qdyinnjaROlWAWxubMbM4bNZXxP2u9NZHyJto3D7cQrMy4fcZDZObCBIIugGOBS4FJZlYniufOiBw7mFmlnbQ5IF/bksjNtrHAViLyN3s3qs7rF/egQfWggMjytfz762N5+t2bQk4mIrtTtMVDH2Cpu+fdZrsf0An4kWDvi3cIBideUtSHuvtiYDqQDAzIf9/MegNNCFafjMUW36dGjlMLbCUi/2Ov+lV58+KeNKmVzV7N7uePlG2MWDuOR9+8KuxoIrKbRFs8tADm5rt2IsFAxzPd/XmCX/7LCIqKaOSOQ7jPzPbKvWhm9YEnI6f3untOnnvDzWyOmQ3P8xzMrJOZHWdmifmuVzCzawhmYQA8FGVGEQGa1anMU6c2wxIzAcgBFv36C2OmLCr4gyJSJkS7zkNtgq238+oJLMxdM8Hdc8xsCnBQNA9297FmNoJgKeofzOxz/toYqzrwLpH9M/JoBLTlf5fCbkHwBmS1mf0CLCGY4rkvwVuRHIJlsP8bTUYR+cs+LTvx6BFjuPbTQbRb04A31w5l7Ds/sGVbNhccFO1yLCJSmkT75mEbUCP3JPJWoBXwTb52myl45sQOuftQYBBBF0Zv4EiCHTEvA/pHsaPmTIINtOYCzYDjI8/bDLwAdHX3f0ebT0T+rk3z/Xiu36f8Uuk2cmdc3/XBbB7/v3kFf1BESjVzL/rSCmY2jWCFx8buvtXMhhC8DRji7iPztBsP7OnuLWKcNxSpqamelpYWdgyRuLV+6zbOf2EqaQvXAJBIJue2/z9uHvQwCYmJhXxaROKRmU1z99Qd3Yv2zcObQE1ggpk9CNxHsJnVu3m+WSLQheCNgYiUA9UrJvHSBV05aK+6GFl03+Ne3vAvufL5w8nMzAg7nojEWLTFw0PAF0AqcBVQCbjO3f/M06YvQdfGhJgkFJFSoXJyBZ49J5V+LcYyq/pmAL5MXskzTx9DZsbWkNOJSCxFu7dFBnA4wfiBU4G27v5EvmZbgauB0TFJKCKlRsWkRO4+9ym6ZwRb0JyyfgNDV6Ux56Fj2LxxXcjpRCRWohrzUF5pzINIdLKytvHIsydz1fIJ5I54mFuhHQ2HjKNGnQahZhORoonlmAcRkUJVqJDENYPf47tmg7dfa5s1h9VPHMHCRbNDTCYisRDtOg/bmdneQBuCNRhsR23c/aXiPl9ESjdLSKDH+fcz+dVadJ97HwDfVF3Ni58O4F/dHqHrvoeHnFBEiivqbgsz6wmMBPYuqBng7l4m5mip20KkZNLGPcXiuXdxa/3aANTKyuHufe+iV9eTQ04mIjsTs24LM2sHfAq0J9hj4rfIrdeANCB3Ead3Ab11EBEAUk+4hHXth5KSE/xjpUVWJnt/NJTZkz8JOZmIFEe0Yx5uBCoDF7v7QcDXAO4+yN27AR2BaQTdGVfs9CkiUu6ce+zN3NziMjpt2cbjK9KpxxZafXwmMz59OexoIhKlaIuHQ4B57v7Mjm66+8/AcQRLQt9SsmgiUtb0O/QSbj9wFJk5wSr3FW0b+317GVPe0GrxIqVJtMVDQ4Ktt3NlA5hZSu6FyIJRXxH9rpoiUg7suW93Ms7+iCXWEIBEc7J+e4Abnz+enOyibl8jImGKtnjYyN9nVqyPHPPvarkF2KO4oUSkbNujVQcqXTKeXyq04afkJK6uX5cPE39nyHO92bx1U9jxRKQQ0RYPS4Cmec7nRI6H5l4wsySgG5BesmgiUpbVadCEJld9zpO1WrElIfir6LfEVTz4/ONszMgKOZ2IFCTa4uFboIOZVY+cf0jQdfGQmQ0xs+OBt4Am/O823SIif1O5ag0eOP9LDs6oRfXsbHos6cSzi/Zh4MhJ/LlB+2GIxKtoi4e3gaUEAydx96XAcIKFoh4nmKJ5HLAOuDlmKUWkzKqYUpnHL/iCiypdwItbBgHw49L19B8xkQXpG0NOJyI7EpO9LcysP3AKUJugK+Nhd/+t4E+VHlokSmT3ePW7Rdz8zg9EloOgUbVl3Ng7iRMPOifcYCLlUEGLRBV7eeq83P0tgu4KEZFiO71rM+pXS+HSMdPJzllNSoNHuWteDumrF3DhCXeEHU9EIrQxlojElT57N+DVi7rTvsnjrEpyMhKMZ1eNZdTHH6BdgEXig4oHEYk7nZvVYthBd9Bom5PgTrdl7bj9K+PW934iKzsn7Hgi5V6B3RZm9n8leLa7e58SfF5EyrHu+/blqZqv89w7d/PK+mAg5ejJC1m8ZjOPn9GFqikx6XUVkWIocMCkmeUAzk623C6EdtUUkRLbui2b696cyQezlm2/1rnBZu48rhn7tu4WYjKRsi0WAya/A0YDy2OWSkSkCComJfLowM60qFOFx7+YTxJbSah0N5dPyGLYyps5sscZYUcUKXcKKx5eBU4CugJdgE+AUcA4d9cScCKyWyQkGNcd2ZbmdSozbuJpfF8pB0jg1jn3UHH9JnofeVHYEUXKlQIHTLr7IILNsC4B0ggWgHoTWGZmD5tZp10fUUQkMCC1Kce2G0C1yKDJi9au5+CJ1zP51XtCTiZSvkS1SJSZtQHOA84CGhOMh5gFvACMcfeVuyJk2DTmQSS+fDPjQ76ecB03rvlj+4CsKXVPpsvgp0hKTinwsyJSNAWNeYhqqqa7/+Luw4BmwLHAWKAd8BCw1MxGlzSsiEhhDup8LBcP/Iy5Ffbefq3byrf56YEjWLxsfojJRMqHYq3z4O457v6xu59GsAnWh0AScGQsw4mI7EztBk1occ3nTKsWbOrrwHtVF3HhhyfxzYwPwg0nUsYVe5EoM2trZsOBmQRvIQB+jkkqEZEiqFi5Kl2ufptJzS/h1WpVGVu9Gn8kGdd9fwP//fTpsOOJlFlRFQ9mVt3MLjazScBs4AYghWBHzf3dvfcuyCgislOWkECP8+5j417nUjGyo9Yhm7fQ59sbmPzy7XiOVqQUibVCB0yamQFHAOcCJwKVgGz+Pm1z2y5NGTINmBQpHT6b/DrvTL+dB9OXUTHyd9vUmkez3yXPk1KxcsjpREqXggZMFrbC5D3A2QQzK4zgbcMoYLS7r4h91Pik4kGk9Fi5fDErnzuVdttmb782J6k9lc4ZRfMmbUNMJlK6lKR4yF2eOo2gaJgSzTd29+nRtI9XKh5ESpeMrZuZ9dT5HLD2YwBeq1aVkTVrMqz9LRzRY2DI6URKh1gUD8Xh7h71zjVmdgYwBNgPSATmEKwjMcLdS9R5aWb/AoZFTq939/8U5XMqHkRKH8/JYcqYO/HFIxjSqB7ZZlTMca6tcyYDT7gx7Hgica8ke1ssovjFQ9TM7AlgKLAVGA9sA/oQDMjsY2YD3D27mM8+APgHxd/oS0RKEUtIoPuZtzP6oxQqrniZTWbsmbmN1yYn8luFn7n+yLZUSCz2hDORcq3A4sHdW+ymHJhZf4LCYTnQy93nRa43AL4A+gGXAY8U49kpBN0uKwg2+TopNqlFJN6ddcwwWs7Yl8e+u4FGf/ThnZz2fD9hAT/9sZ7HTu9MrSrJYUcUKXXiqezO7U64IbdwAIgMzBwSOb3RzIqT+U6gPcEeHetKlFJESp2DOh/H0wO/ZV2Lc7df+2b+So5//Bu++3Xezj8oIjsUF8WDmTUB9gcyCTbe+ht3/wpYSrBJV/con90NuJZg7433S55WREqjmjVq8uw5B3BFn9bbr2VlfsXlE/rx2NhrQkwmUvrERfEAdI4cf3L3LTtpMzVf20KZWUXgRWA1cGXx44lIWZCQYFxzRBtGnrU/daqsJGGPt9mcYIzc9Bl3PnsaWdlaUEqkKOKleGgZOS4soM2ifG2L4h6gLXB5Wd3xU0Si17dDQx7t15QakRUp62ZlM/X3jpz53BRWbcwIOZ1I/IuX4qFq5LipgDYbI8dqRXmgmfUErgLedffXS5BNRMqgA/c5jBdO+piuWyvR+o8e/JDVkckLVnP8Y98wa8nasOOJxLV4KR5yp07GZFqomVUiWBtiPcEMjuI8Y7CZpZlZWnp6eixiiUicaVi3Kc9cOJl9e96IRf4W+mPdVk4ZMYnnP32PnOxizQwXKfPipXjYEDlWLaBN7r0NBbTJ9S+gDXCNuy8rTiB3H+nuqe6eWq9eveI8QkRKgYTEBC7v05rnzzmAahWD2ev1E2czculNXPzcwaxauzzkhCLxJ16Kh98jx+YFtGmar21B+gE5wDlm9mXeL+CoSJshkWvPFiOviJQxh7arzweXH8R+DY2aTUaxKSGBySkbuO7Vw1k49/uw44nElXgpHmZEjh0iXQ47ckC+toVJAHrv4KtB5H6ryPkOl94UkfKneZ0qvHRBV5pRC4Akd65bs4J6Y/qS9uEzIacTiR9xUTy4+2JgOpAMDMh/38x6A00IVp+cVITntXB329EXwdRNCPa2MHfvFLufRERKu5rV6vLk4AmcV7EX/1i5jg6ZmVS2DFKnXseUx88jY+vmsCOKhC4uioeI4ZHjfWa2V+5FM6sPPBk5vTfv5lhmNtzM5pjZcEREYuia056g61FvssQabb/WbeXbfPvwwXw/95sQk4mEL26KB3cfC4wgWEXyBzN738zeBuYRLC39LsEGWXk1IljHoREiIjHWap/uVL/yW6ZX6QXAJjMeqrOJS7+9mJc++lfI6UTCEzfFA4C7DwUGEXRh9AaOBOYTbIjVv7g7aoqIFFf1mnXofO17TG5zHXfUqcPvyUmsT0xgxIpX+HzkJWzL1KJSUv6Y+27bcbvUSk1N9bS0tLBjiEjI3vtyJA//+ggrKyQw/M+VHLdpM3OS2lPjzFE0at427HgiMWVm09x9h5MK4urNg4hIPDvxkME81/cNzlpXheM2BQMn222bTZUXDmXGpy+HnE5k91HxICIShVZNO3Ddpd8yqeVlZHnwV2h1NtF88uXcMLIv6zauDjmhyK6n4kFEJEoJiYn0OOce5h/7BsuphwP/rFeHj1KWcfarvZk065OwI4rsUioeRESKqV3XI6h0+bc8V6szX1cO1rdbkAwTPvoPb09fEnI6kV1HxYOISAnUqNOA8y8bzxkVUklyp9/aLF5eezHXvDGTa9+YyaaMrLAjisScigcRkRJKSExk2KAXeGDv21m29So2UBmAt6Yv4fjHv2HWkjUhJxSJLRUPIiIxcmi3U3j4qgs4ufMe268tSF/PDR8cye0vDtSaEFJmqHgQEYmhKikVePC0TjwwoCOVkxPZu95ollTawlv8xLkvdGfpn+lhRxQpMRUPIiK7QP/9m/D+ZT1IqTZ/+7WGGytz9JPT+GDWHyEmEyk5FQ8iIrvInvVrMObsbzguuyUdN2fzafrlrN+azWVjZnDtGzPZsHVb2BFFikXFg4jILlS5YhWGnz+OKw//hBq16m+//tb0JZz06Ie8P+GFENOJFI+KBxGR3eCA1s346MqD6ZdnMGXjivdzy4IHuOn5k9iasTnEdCLRUfEgIrKbVK+YxEOndeKRgZ3oUftDvq+xnmwz3k/8lTcfO5jF838IO6JIkah4EBHZzU7stAc3njiIvTMSAei7cRNnbpxPndF9mPL6veRkZ4ecUKRgKh5ERELQse2BvHzuFE6lA8NWrsOAypZBt5+H89O/+7B80bywI4rslIoHEZGQJCencMs5r7H2pHH8ltB8+/V9MmZw3/vH8ODrl+kthMQlFQ8iIiHbq+OBNP7HZCY1OptsN96qVoXPq1bkha1fcd6z3Vmx7LewI4r8jYoHEZE4kFKxMj0ufoy5x7zOy9Vqb7/ePuNPkp8+mOkfa0qnxA8VDyIicaR9tyN57tTPOTSzPi0zt3HlmnXUYgNdplxF2gMns27VirAjiqh4EBGJN3VqNuTRi8ZzS+u7WOt1tl9P3TCeTY9148X37wwxnYiKBxGRuHXAIQOofNV3TK159PZr79bM4T+r3+TCkT1YsPinENNJeabiQUQkjlWvWYcDrnqN7w8cwZSk2jxTszoAU1I2MuaNCxg38w/cPeSUUt6oeBARKQU6HXEGjS/4nG6ZtQDouDWDL1aeyxWvzmDw6GmsWL815IRSnqh4EBEpJZo23JOnBn/N9fXOoPmaw/nVmwLw2ewVHP7gV4yZMk/rQshuoeJBRKSUOfuYYdx41SOc2b3Z9msbtmbx6pQhnPncAXw/95sQ00l5oOJBRKQUqlYxibtP2pdXL+pO8zqVaVR1Cr/XWMEPKdu4eOLFvPzhaHJyNBZCdg0VDyIipViPPevwyZW9OGiPBVhk4GTHzcYdX1dnwNOTmLt8Q8gJpSxS8SAiUspVSk7k/vNe5u5WV9NhKyxedjbbqMC0hWs49tGvuf+/c9i6TWMhJHZUPIiIlBEn9LqAF8+fzuG9TiQp0QDIynGe/GIulzxzMK99+mDICaWsUPEgIlKGpCQlcW3ftnx0xcGkNg+mdfao9SrTqmzgnmUvMPTpg1i1YknIKaW0U/EgIlIGtW5QjTcu7sE9J7Qhvc4Pf13fuojEEd2Y+s6jeE5OiAmlNFPxICJSRiUkGIN6tuaJI16ha0ZVmmzbxiVr11OTjRww8xZm39ubxfNmhh1TSiEVDyIiZVyb5p14bvAkbml5E2u97vbrHTJnUf2VPtz+/Mms3bAyxIRS2sRd8WBmZ9V11L4AABxRSURBVJjZ12a2zsw2mlmamV1qZlFlNbPLzewNM/vZzFaZ2TYzSzezz83sTDOzXfUziIjEo559zqbGddOY3HAQWR78lfpircq8lTiPU18/hNEf/ivkhFJaWDxtqGJmTwBDga3AeGAb0AeoBrwDDHD3Is03MrMlQH3gR2ApsAloDnQDDHgPONndC+30S01N9bS0tKh/HhGRePXrrIks/fByrmqUwbbIv6VuT19Fq5yONBjwEI1btgs5oYTNzKa5e+qO7sXNmwcz609QOCwH9nP349y9H9Aa+BnoB1wWxSMHArXcvYu7H+/uA929B7AvsAI4ETgnpj+EiEgpsed+Pel+7UQGpvSkWnYO+23NoN/GTXTePJHaow5i0gs3kLF1c9gxJU7FTfEADIscb3D3ebkX3X0FMCRyemNRuy/c/Rt337SD6z8BT0ROjyhBXhGRUi05OYV/nD6SV458i4GZ+27/hVDRttFj4VPM/U8XXvn4vlAzSnyKi+LBzJoA+wOZwJv577v7VwRdDw2B7jH4llmRo/awFZFyr+Ue7Tj+8reYc9zbzE/cc/v1MbUyuffPlznv6W7Mmjc5xIQSb+KieAA6R44/ufuWnbSZmq9tsZhZS+CSyOn7JXmWiEhZ0i61Dy2HfceUdjfyZcUafFi1CgBpFTfz4dg7ePLL+WRkaZlriZ/ioWXkuLCANovytS0SMzvPzEaZ2Stm9hXwC9AEGO7u70QfVUSk7EqsUIFuA4fR+PQPODCjBgCHbczgzXVn8+9P5tL3oQl8NnsF8TTYXna/CmEHiKgaOf7PGIU8NkaO1aJ89oH8fWBkFnALoEXeRUR2ok3z/Xhq8De89X9PkjZ9GaupDsDCVZu56KU0eu+ZzgVdatNr/xNCTiphiJc3D7lrLsS8lHX3C93dgMpAB+Bh4HZgspk13mkgs8GRNSbS0tPTYx1LRKRU6H/YUO66+g7uOKEDNSolRa7msDz7ca744SaufOZwFi9fEGpG2f3ipXjI3XC+agFtcu8Va3N6d9/i7rPd/XqCmR0dgccLaD/S3VPdPbVevXrF+ZYiImVChcQEzunZgi+uO4SzujenZc3P+KNSBtlmfJ20nNufe57RkxeSnaOujPIiXoqH3yPH5gW0aZqvbUm8EDkeb2ZJBbYUEREAaldJ5q6T9uGWww+nfUbQ691rbSXGb+jBLe/+yLGPfs2kX1eFnFJ2h7hYYdLMmhIMiMwEau5oxoWZLSYY6HiQu39bwu+XAGQQjPloGFlLYqe0wqSIyN/lZGfz3Ae38dnPLfhubaO/3Tt1r2kM6HEgB3ToE1I6iYW4X2HS3RcD04FkYED++2bWm6BwWA5MisG37EVQOKwFtBuMiEiUEhITuejEu3np2vO4rm8bKiUlApBim0iz1xk89UqufrYvS5f/GnJS2RXioniIGB453mdme+VeNLP6wJOR03vz7kVhZsPNbI6ZDc/zHMzsYDMbZGYp+b+JmR0IPBc5fa6oe2WIiMj/qpiUyGWHteaL6w7hpE6N6VrnRdIrJJBlxvSEJSQ83YvJr9yhpa7LmLgpHvz/27vzMCmqc4/j33dm2FFEZRMQZQlbUERAAgIqLlGRhCjBuGLwEi+5aqIxN3qNN4leNUYTUBFDEiRE1CiokcQYhQiRXUSBiCCgICAgqzDCDMu894+qYdpmlu6Z6a6emd/neeopu87pqmO9z0O/c+rUOe5TgfEEs0guN7PpZvYisBroArzM0QMcWwAdw32sdsDTwBYzmxnO8fCKmb0PzAHaAn8jeGVTREQqqHmjuoy58gyGnzWMjvnBT8voXZ/TwnPps/rXbP9ld9559Sm8oMy1CKUKyJjkAcDdRwNXEzzCGAhcBKwhWBDr8iR6CWYD9wLvAV8BvgVcCDQApgFDw4W3SprNUkREymFw/xE8P3IJPzxuKH1yi6blaelbOXPRD5gwphd/mTUhwhZKZciIAZOZTgMmRUSSdyA/jyXTHqbTh+M5jly2Z2dxSauT2J+VRa/8+vx44KN06nhW1M2UEmT8gEkREal+atepS5+r7sZueY/5za/i8eMasz8r+NnZZbtp88zFLHjiP9j52aaIWyrJUvIgIiIp1ej4JnztpvEMPm8ivfOD+f5u37mbenaYPp89T51xPZg/8Q5y9+yKuKWSKD22SIAeW4iIVJ435jxN69nj6HRwxZeO/+L4pmQf35dbho7lmAbHRdQ6KaTHFiIikjEuOPsaOt45l3f7jmNdVjB58KpatZh6bB2eO7yEoc/2429vTNV01xlMyYOIiKSdZWVxxoXX0Pqu91h0+n38rlET3II1EtsfOMj/zjzAJWPfYoaW/85ISh5ERCQy2Tk59B56Mz8dMZfhWd1pfLiAZtvPYDuNWLV1LzdOXsywJ+czZ/UnUTdVYmjMQwI05kFEJD127NzCM4u2MH7eFvYdKJzax+l8ys85wZxruv2Qr/e9OtI21hSljXlQ8pAAJQ8iIum1PTefx/+5hikL19Ok3lz2tn4FgNoFzoWHbufaSy+ny0nHRtzK6k0DJkVEpEo5sWEdfjakK/+8/Rx6NF+DhX/o9t1Tm2fXNuWSR99i9JR3+HDr3ohbWjOp5yEB6nkQEYnWv5a8wp/evp9tGy/lvYM9jhw3g+EdFjPkzN70Pf3iCFtY/eixRQUpeRARyQwfbN7Db974kNdXbAWgFnm0aX8P23KMPgeO45YBD9G1U9+IW1k96LGFiIhUC51bHMuE63oy/b/O5rxOTel1/J/ZWiuLAjNW5Oyk1XODWTT2Kj5dtyrqplZrSh5ERKTK6daqERNH9OLqfkM4La82ADd8vodGHKb3rr/R5KmvsWjMd9iwennELa2e9NgiAXpsISKS2V5680laL3yGnnlLv3T8seMasax+K67reSf9e1wWUeuqJo15qCAlDyIiVcO/507HZj9E1wPL2JNlXNS6JblZWZg7d+1uQa9B99KuW5+om1klaMyDiIjUCF/tdxld73qLDy5+nj816kJuuAR4m4OHGLZ7Ee2mXcS7D13M6nf/FXFLqzb1PCRAPQ8iIlXT3+ZM4s8rxjFsz0Yuy933pbIZDXqQ2+s7fPOcURG1LrOp50FERGqkS88eweRRb9PlwmksaTDgS2Wz6q3jp+sf48oJZ/CXN8ZrAa4kKHkQEZFqr91pfelxx3TWDZ/J4mMG8Ul2Dn9t2ACA9+scYunC1xj82BxeWfophw4XRNzazKfkQUREaoxTOvek5+0vsn3oC/Q50Jhsd87cn8+ruZfz/qd7uOXZdznvkdlMnvcxn+/T1Ncl0ZiHBGjMg4hI9bRk5VssWPAPHl3bj7yDRT0OTeovoW6r5xiY1Ynvff1XtG7eNsJWRkOvalaQkgcRkeptR24+f5y/nsnz17F730G6nnwvnzT4AoCBn9ehedvJjOx/Ki0a1Yu2oWmk5KGClDyIiNQMX+QfYvL893lh7dVsyzGy3Ony8WDm5/enVrbxje4t+d6AtnRodkzUTU05JQ8VpORBRKRm2Zf3BRNeuZMNWxczbdNdgB0pyyGfc095hPPaXs7wQbeSlZ0dXUNTSMlDBSl5EBGpmQoKnDdXfcb4WWtZvH4XAGc1ep4VJy0BoPt+uLnZKE6/eCR16taPsqmVrrTkISfdjREREakqsrKMQZ2bMahzMxav28mTsz9iW967R8r75u2m99K72b70YZa0uZJOg39A4yYtImxxeqjnIQHqeRARkUILlr/OMwseZEn2Vl7Z+CnHFxS9pZHntZjYrC+n9f0eZ3e/NMJWVpweW1SQkgcREYm37bMNrHntt7T7aApN2QnAF2Zc0Lole7Oz6J5Xh9Edb6fPgOFYVtWbVknTU4uIiFSyJk1b87Xr7uO4Oz9gcY9fsia7HS8f04C92cFP667sXM6adRPr7uvOwhceZl/u5xG3uPIoeRAREamA2nXq0nPITbT7n8U07H4PPfLqYu5c+/lesoBTC9Zz1vv3cujhTkx/8noWLZ8RdZMrTI8tEqDHFiIikowFy1/nwOyn6bntNepb/pHj/3Pi8Uxv2IDT8uty+akj+cb5N5GVZaWcKTp620JERCSN+nS7ELpdyJ7dO1jw6nharp5CA9vC3xs2wM1YWjefDgvf4NFlnbm2Txuu6NmKY+vWirrZCcu4ngczuwr4T+A0IBtYCTwFjHf3hJY6M7NawADgEqAf0AY4AdgGzAced/dZibZJPQ8iIlIRBYcPM2PmH5j88QSW1cmja/4BNqy7i43eBID6tbMZesZJXNR+BwO6nRtxawNV5m0LMxsHjAbygJnAQWAQcAzwEjDM3Q8ncJ7zgTfCj1uAd4AvgC7AV8Pj97r7PYm0S8mDiIhUlkXLZ/DO4n/wxPrz2Zt36MjxpvXfYX+bF+iSn82gEy/m+iH3UScnutkrq0TyYGaXA1MJfuwHuPvq8Hgz4E2gM/ADdx+bwLnOI0hCxrr7W3Flw4EpBL0a57n7m2WdT8mDiIhUtn0HDvHSu5uYPG89q7bupVvr+1nXcA8A5+6uzdw9D3JFz1Zc1ftk2pzQIO3tqyrJw2LgTOB6d58cVzYQmEWQWLRM9PFFKdf6PTASmOjuI8uqr+RBRERSxd2Zt3Ybv/3nt1hWezeHzej+8QW8lTfoSJ3+HU5kSLuNXNrn69Svm55EIuPneTCzVgSJwwHghfhyd58NbAKaA30q4ZKFc4u2qoRziYiIlJuZ0a99UyaPmsOU/pO41rvzce2LvlRn/upNjFt7D5dM6c1PJg7h44+WRdTaQKa8bXFGuH/f3feXUOdtoGVYd14Fr9ch3G+u4HlEREQqTdd2Pena7k/cdriAWau2MWXhemZ9uI3ux/ydVTnB3/sLD63hZ38cwNL6vfEzb6DbOcPIzknvz3mmJA+nhvv1pdT5JK5uuZhZc2BE+HFaRc4lIiKSCjnZWZzfpRnnd2nGxl37mDT9VbYdLGBnThZDc3Opa87p+xfCnIXMmDeZZX3G8O1erWnVOD0re2bEYwugYbj/opQ6ueH+mPJexMxygKeBRsBMd59e3nOJiIikQ6vG9bn7unH8/epF3NzoMk7LO+VL5dPzuvPoP9cw4KE3+WxPXlralCk9D4XTa6V69OaTBK9+bgCuKbVBZqOAUQAnn3xyipslIiJSuvp1GzDqm/cDsHHNv9kwczzNN7/JawW9AejT9gSaHls3LW3JlORhb7hvWEqdwrK9pdQpkZmNJXjDYgswyN23lFbf3ScAEyB426I81xQREUmFVu2/Sqv24zhw8DBjVn7Gs29v4Ns90/cOQKYkD+vCfZtS6rSOq5swM3sEuIVghslBhXNIiIiIVGW1a2VzcbcWXNytRVqvmyljHgpfnexqZvVKqNMrrm5CzOwh4DZgB3CBu68oXxNFREQEMiR5cPcNwBKgNjAsvjycJKoVwSOH+Yme18weBO4AdhEkDksrpcEiIiI1WEYkD6EHwv0vzax94UEzawo8EX58MHZ2STN7wMxWmtkDxDGze4H/BnYTJA5J9ViIiIhI8TJlzAPuPtXMxhOsqLnczGZQtDDWscDLwONxX2sBdAz3R5jZEODu8OMa4GazYtdLX+nuD1ba/4SIiEgNkDHJA4C7jzazOcD3gYEULck9kSSW5AaOj/nvnuFWnNmAkgcREZEkZMzCWJlMC2OJiEhNk/ELY4mIiEjVoeRBREREkqLkQURERJKi5EFERESSouRBREREkqLkQURERJKi5EFERESSouRBREREkqLkQURERJKi5EFERESSouRBREREkqK1LRJgZtuA9ZV4yhOB7ZV4Pqk4xSTzKCaZRzHJPKmMSRt3b1JcgZKHCJjZ4pIWG5FoKCaZRzHJPIpJ5okqJnpsISIiIklR8iAiIiJJUfIQjQlRN0COophkHsUk8ygmmSeSmGjMg4iIiCRFPQ8iIiKSFCUPaWRmV5nZW2b2uZnlmtliM/u+mSkO5WRmHc3sVjN72sxWmlmBmbmZXZHAd8sVD8WxZGZWy8wGmdkjZrbAzDab2QEz22RmU83snDK+r5ikgJndbGbPm9kHZrbDzA6a2TYzm2Fm15iZlfJdxSQNzOz+8N8uN7MflVIvM+Lh7trSsAHjAAf2A38FXgL2hMdeBLKjbmNV3IAx4T2M365IRTwUxzLjcX5MDDaH9+jPwPKY479QTNIel43AAWAJMB14DpgPFIT36WUgSzGJLD69gEMx8fhRZd7XVMQj8ptWEzbg8ph/TDvEHG8GrAjLbo26nVVxA24EHgK+DbQDZpWVPJQ3HopjQvE4D5gK9C+mbHj4D6QD5yomaY3L2UCDYo53BbaE9+kGxSSS2NQB3gc2hT/qxSYPmRaPyG9cTdiAxWGAriumbGBMYI/K/LUlfa8TSR7KFQ/FsVLi8/vwPv1BMcmMDfhpeJ+eUUwiuf+/DO/JZcCkUpKHjIpH5Deuum9AqzA4+UC9EupsDOv0jbq9VX0rK3kobzwUx0qLz/fDe/QPxSQzNuDO8B5NVEzSfu/PIuiNmxJ+LjZ5yMR4aOBK6p0R7t939/0l1Hk7rq6kTnnjoThWjg7hfnPMMcUkImZ2KnBT+HF6TJFikmJmVhf4I7ATuLWM6hkXj5xkKku5nBruS1tY65O4upI65Y2H4lhBZtYcGBF+nBZTpJikiZndQNBVXYvgr9K+BG/dPeDuL8VUVUxS7/+AjsCV7l7WwlYZFw8lD6nXMNx/UUqd3HB/TIrbIuWPh+JYAWaWAzwNNAJmunvsX7mKSfr0A66P+XyIYMzDr+PqKSYpZGZ9gR8AL7v7nxP4SsbFQ48tUq/w/WmPtBVSqLzxUBwr5klgELABuCauTDFJE3e/0d0NqE/wpsUY4GfAAjM7KaaqYpIiZlYPeIrgVcnRiX4t3GdMPJQ8pN7ecN+wlDqFZXtLqSOVo7zxUBzLyczGAiMJXgkc5O5b4qooJmnm7vvdfYW730EwYPJ04PGYKopJ6twPfAW4zd03l1U5lHHx0GOL1FsX7tuUUqd1XF1JnXXhPtl4lPd7NZqZPQLcAmwjSBxWF1NtXbhXTKLxFPAwcJmZ1XL3gygmqTSUYDKo683s+riyTuH+P81sMLDG3W8kA+Oh5CH13g33Xc2sXgkjXnvF1ZXUKW88FMckmdlDwG3ADuACd19RQlXFJFq7CcY+5ADHA1tRTFIti2Dgaknahttx4eeMi4ceW6SYu28gmBK2NjAsvtzMBhKMet5CMF2spFB546E4JsfMHgTuAHYRJA5LS6qrmERuAEHisBvYDopJKrn7Ke5uxW0Er24C3BEe6x5+J/PiEfUkGTVhA66gaBav9jHHmxJMS+poutbKutezKHuGyXLFQ3FMOAb3hvdiF3Bmgt9RTFIXj/7A1UCdYsr6AWvD+/SwYhJ5rCZR8gyTGRWPyG9WTdmAJyhamGQ6wWIkn4fHXkILxZT3vvYAFsRshYu9fBh7vLLioTiWGY8h4b1wgslnJpWw/UQxSVtMRlCUzM0EpgCvxPxwOMFiSUfNQKiYpD1Wkygheci0eER+s2rSBlwFzA1/4L4A3iGYrldzvJf/np4T8w9giVtlxkNxLPXejEgkHsAsxSRtMTkV+AXwJsGrsvuBPIIBclOBb6bi3iom5YpVqclDJsXDwpOKiIiIJEQDJkVERCQpSh5EREQkKUoeREREJClKHkRERCQpSh5EREQkKUoeREREJClKHkRERCQpSh5EahAze9rM3MyeSrD+uLD+ixW45o3hOX5f3nNUhJndF17/7iiuL1IdKXkQqVkmhvthZtawtIpmVge4Mu571YaZnR8mFTOibotIVaPkQaRmeRP4GGhAMavsxfkGwRLNm4G/p7hdqTQG6AyMj7ohItWFkgeRGsSD+egnhR9HlFH9hnA/2d0Pp6pNqebu2919pbvviLotItWFkgeRmucpoADob2btiqtgZi2BC2Lqx5Y1NLOfmNliM9tjZvvN7N9mdo+ZNUi2MWZ2tpm9aGZbzeyAmW02sxfMrHcp38kysyvN7DUz+8zM8s1so5nNMLPRcXWPGvNgZnOAN8KPg8Lywm1GeP6Pws89S2nHK2GdUcn+f4tUZUoeRGoYd99AsDSzAdeXUO06IBuY6+6rCg+a2ckES20/ALQG5gGvAycAPwfmmFmjRNtiZjcD/wKGUrTK4ybgCmCemX23mO/UIVhS+llgELAKmBbuTwMeTeDSr4bthuCxzB9jtn+4ewHBMsYAo4/++pF7cQnB0sZTErimSPUR9RKk2rRpS/9GMBDSgfUQrK4bV74yLP9uzDEDFoXHxwD1YsrqA8+EZb+PO9eNJRzvARwKt2/FlV1N0DuSD3SOKxsXnm8F8JW4shzgsrhj94X17447fn54fEYJ96gxwdLF+4DGxZTfX3gvoo6nNm3p3tTzIFIzvQTsAk4GzostMLO+QEeCH87nY4oGA72AucAP3X1/YYG77wNGAduB68zs2ATacCtB78YUd//Sq6DuPiVsY23glpi2tQivc5gg4fgw7nuH3H16Atcuk7vvIuhRqEfR+I/CdtQGRhIkDxqIKTWOkgeRGsjd8wl6CiDuhzHm8/Punhtz/JJwP9XdvZhz5gJLgFpAieMEYgwM95NKKC98PfScmGODCHoX5rj7ygSuUVGPhfubzMxijg8DmgIzPeaxjkhNoeRBpOb6Q7j/VmFPgZnVB74dHo+f26FtuP9N3ADDIxtwYVinSQLXPyncf1xC+dpw3zLmWJtwn47EAXdfDswCOlA0gBSKxkGMS0c7RDJNTtQNEJFouPu7ZvYe0B0YDvwOuBw4FvjQ3efEfSU73M8iGCtRmk8SaELhX/JH9WLElUftMYLej9HA62Z2OtAX2ABUyiMSkapGyYNIzfYUMJZgzoffUTT3Q3HTV28I98+5+28r4dqbCHoS2lJ8MnJqTL1ChfU6VsL1E/UXgmRosJm1Br4fHv+tV+H5L0QqQo8tRGq2pwneaOhrZhcC5xIMRpxcTN3CWSbLmpkyUbPD/XUllBeOvZgVc2wmwdsZ/c3sKxW8/oFwX+ofUWGCMJ6g5+XHwFXhdyNZq0MkEyh5EKnB3H0nwZwJECQSBrzm7p8WU30a8B7BpErjzKxxfAUzaxc/SVMpxhIkKteY2ZC483yH4BHKQYoGLeLumwl6SLKBF82sfdz3cszssgSvX9ij0cHMskutGVwzD/gvgqm9p7n71gSvI1Lt6LGFiEwk6E1oEvP5KO5+2My+QTDB0mjgWjNbCmwETiR4BNGB4Ef5ieLOEXe+JWb2Q4Ik4i9mtgD4KDxHL4LE4iZ3XxH31dsIHnVcBHxgZvPCazYFuhFMWFXmv23uvtbMlhFMLLXMzN4h6FFY4e6/jqu7w8yeAQonrdJASanR1PMgIq9TNJ5hO6UMAnT3Twh+2G8h6IXoStBD0JVgpsVfEcwOmRB3f4zglc2XgXYEb3q0Iejl6OfuRyUy7p5H8Nro9cBbBAnDFUAnYClFYxIS8U2CWS1PJJiYaiRFr6TGK5zOeqm7z03iGiLVjhXzuraIiMQxs+kEE2WNcvffRd0ekSgpeRARKYOZnQXMJ+iZaRM7u6ZITaQxDyIixTCzLGAC0BC4lGAw6d1KHETU8yAiUiwzyyF42+MwwTwPj7n7b6JtlUhmUPIgIiIiSdHbFiIiIpIUJQ8iIiKSFCUPIiIikhQlDyIiIpIUJQ8iIiKSFCUPIiIikpT/Bwcb53hyd2jyAAAAAElFTkSuQmCC\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.plot(vanalytical,mfinalanalytical,label='Analytical Solution');\n",
"plt.plot(velocityHeun,massfinalHeun,linestyle='-.',label='Heun Solution');\n",
"plt.plot(velocityRk2,massfinalRk2,linestyle='dotted',label='RK2 Solution');\n",
"plt.legend(loc='best');\n",
"plt.title('Comparison of All Three Solutions');\n",
"plt.xlabel('Velocity');\n",
"plt.ylabel('Mass/Initial Mass');\n",
"print('All three solutions clearly converge together')"
]
},
{
"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": 184,
"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.zeros(np.shape(state))\n",
" dstate=np.array([state[1],((u*dmdt/state[2])-9.81-(c/state[2])*(state[1]**2)),-dmdt])\n",
" \n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 185,
"metadata": {},
"outputs": [],
"source": [
"#Analytical solution\n",
"\n",
"manalytical=np.zeros(len(t))\n",
"manalytical[0]=0.25\n",
"t=np.linspace(0,4,1000)\n",
"dt=t[1]-t[0]\n",
"\n",
"#analytical solution computed from equation of motion\n",
"for i in range(1, len(manalytical)):\n",
" manalytical[i]=manalytical[i-1]-0.05*dt\n",
" \n",
"vanalytical=-u*(np.log(manalytical/m0))\n",
"mfinalanalytical=manalytical/m0"
]
},
{
"cell_type": "code",
"execution_count": 186,
"metadata": {},
"outputs": [],
"source": [
"num_solRk2complex=np.zeros([N,3])\n",
"num_solRk2complex[0,0]=0\n",
"num_solRk2complex[0,1]=0\n",
"num_solRk2complex[0,2]=0.25\n",
"t=np.linspace(0,4,1000)\n",
"N=int(4/dt)\n",
"dt=t[1]-t[0]\n",
"\n",
"#Complex rocket function is integrated by the RK2 method\n",
"for i in range(N-1):\n",
" num_solRk2complex[i+1] = rk2_step(num_solRk2complex[i],rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 187,
"metadata": {},
"outputs": [],
"source": [
"velocityRk2complex=num_solRk2complex[:,1]\n",
"massRk2complex=num_solRk2complex[:,2]\n",
"massfinalRk2complex=massRk2complex/m0"
]
},
{
"cell_type": "code",
"execution_count": 188,
"metadata": {},
"outputs": [],
"source": [
"num_solHeuncomplex=np.zeros([N,3])\n",
"num_solHeuncomplex[0,0]=y0\n",
"num_solHeuncomplex[0,1]=v0\n",
"num_solHeuncomplex[0,2]=m0\n",
"t=np.linspace(0,4,1000)\n",
"N=int(4/dt)\n",
"dt=t[1]-t[0]\n",
"\n",
"#Complex rocket function is integrated by the Heun method\n",
"for i in range(N-1):\n",
" num_solHeuncomplex[i+1] = heun_step(num_solHeuncomplex[i],rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 189,
"metadata": {},
"outputs": [],
"source": [
"velocityHeuncomplex=num_solHeuncomplex[:,1]\n",
"massHeuncomplex=num_solHeuncomplex[:,2]\n",
"massfinalHeuncomplex=massHeuncomplex/m0"
]
},
{
"cell_type": "code",
"execution_count": 199,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"These solutions do not converge like the simple method does, which makes sense because they take into account gravity and drag. Accounting for gravity and drag does not allow the rocket to reach as high velocities\n"
]
},
{
"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.plot(vanalytical,mfinalanalytical,label='Analytical Solution');\n",
"plt.plot(velocityHeuncomplex,massfinalHeuncomplex,linestyle='-.',label='Heun Solution');\n",
"plt.plot(velocityRk2complex,massfinalRk2complex,linestyle='dotted',label='RK2 Solution');\n",
"plt.legend(loc='best');\n",
"plt.title('Comparison of All Three Solutions');\n",
"plt.xlabel('Velocity');\n",
"plt.ylabel('Mass/Initial Mass');\n",
"print('These solutions do not converge like the simple method does, which makes sense because they take into account gravity and drag. Accounting for gravity and drag does not allow the rocket to reach as high velocities')"
]
},
{
"cell_type": "code",
"execution_count": 232,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Because we are taking drag and gravity into account, we should expect to see a lower final height. To find the final height, we see where the mass=0.05kg, which is the final value of our data\n",
"The final height from the simplified model is 596.0308372425369\n",
"The final height from the complex model is 424.5326641443993\n",
"This matches what was expected\n"
]
}
],
"source": [
"print('Because we are taking drag and gravity into account, we should expect to see a lower final height. To find the final height, we see where the mass=0.05kg, which is the final value of our data')\n",
"\n",
"finalheightsimple=num_solRk2[-1,0]\n",
"finalheightcomplex=num_solRk2complex[-1,0]\n",
"print('The final height from the simplified model is',finalheightsimple)\n",
"print('The final height from the complex model is',finalheightcomplex)\n",
"print('This matches what was expected')\n"
]
},
{
"cell_type": "code",
"execution_count": 233,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"As time increases, the two models split more and amore, with the simple model reaching higher heights as it does not account for gravity or drag\n"
]
},
{
"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": [
"#Comparison between simple and complex models\n",
"\n",
"plt.figure(figsize=(8,8));\n",
"plt.plot(t[1:],num_solRk2[:,0],label='Simplified Model');\n",
"plt.plot(t[1:],num_solRk2complex[:,0],label='Complex Model');\n",
"plt.xlabel('Time');\n",
"plt.ylabel('Height');\n",
"plt.title('Comparison of the Models');\n",
"plt.legend(loc='best');\n",
"print('As time increases, the two models split more and amore, with the simple model reaching higher heights as it does not account for gravity or drag')"
]
},
{
"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": 209,
"metadata": {},
"outputs": [],
"source": [
"def f_m(dmdt,m0=0.25, c=0.18e-3, u=250):\n",
" ''' define a function f_m(dmdt) that returns \n",
" height_desired-height_predicted[-1]\n",
" here, the time span is based upon the value of dmdt\n",
" \n",
" arguments:\n",
" ---------\n",
" dmdt: the unknown mass change rate\n",
" m0: the known initial mass\n",
" c: the known drag in kg/m\n",
" u: the known speed of the propellent\n",
" \n",
" returns:\n",
" --------\n",
" error: the difference between height_desired and height_predicted[-1]\n",
" when f_m(dmdt)= 0, the correct mass change rate was chosen\n",
" '''\n",
" y0=0\n",
" v0=0\n",
" deltam=m0-0.05\n",
" s=deltam/dmdt\n",
" t=np.linspace(0,s,1000)\n",
" dt=t[1]-t[0]\n",
" N=int(s/dt)\n",
" num_sol=np.zeros([N,3])\n",
" num_sol[0,0]=y0\n",
" num_sol[0,1]=v0\n",
" num_sol[0,2]=m0\n",
" \n",
" \n",
" rhs=lambda state: rocket(state,dmdt,u,c)\n",
" for i in range(N-1):\n",
" num_sol[i+1] = rk2_step(num_sol[i],rhs,dt)\n",
" \n",
" desiredheight=300\n",
" error=desiredheight-num_sol[-1,0]\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 235,
"metadata": {},
"outputs": [],
"source": [
"#Incsearch function imported from earlier notebook\n",
"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": 213,
"metadata": {},
"outputs": [],
"source": [
"#Modified secant function imported from earlier notebook\n",
"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": 236,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"The range of masses in which we reach our desired height is between [[0.08571429]\n",
" [0.07857143]]\n"
]
}
],
"source": [
"#I used incsearch to find the range of masses that the desired height is between\n",
"desiredrange=incsearch(f_m,0.05,0.4)\n",
"\n",
"print('The range of masses in which we reach our desired height is between',desiredrange)"
]
},
{
"cell_type": "code",
"execution_count": 219,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.07890352691884071 4.690708970588359e-07 7\n",
"The modified secant value gives a result of 0.07890352691884071 for dmdt, with an error of 4.690708970588359e-07 and was obtained after 7 iterations\n"
]
}
],
"source": [
"#The mod scand method is used to make a guess of what dmdt is for our desired height\n",
"modsecantdmdtguess,error=mod_secant(lambda t:f_m(t),0.0001,0.1)\n",
"\n",
"errorvalue=error[1]\n",
"iteration=error[2]\n",
"\n",
"print(modsecantdmdtguess,errorvalue,iteration)\n",
"\n",
"print('The modified secant value gives a result of',modsecantdmdtguess,'for dmdt, with an error of',errorvalue,'and was obtained after',iteration,'iterations')"
]
},
{
"cell_type": "code",
"execution_count": 230,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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dG/AmcgM4zMx+FaXM/XitdwCxp6yuuB8pPbV0RpQyf6L8ltR4n28syT4WNSHwHBsB90YpM4bSFqZkXMAw4f+lEo/k+D+8N3JjvOtX3GtmgwJflGbWx8xGmdmLeKdOesS7Y+fcHOBVf/Va864VcZCZtTGzg83sSbwX7LLoe6kSX/jLTOBW865l0cC86yIk2gryNt4vT/DmC2iI9wvqX1HKHwjkmtkLZvYLM+vtH4eO/hwW/6H0jRur+bhO8vvEXIR3uqkd8LmZjTezQ/zj1M7M+pvZpWb2Bt70yhXqwOZ3nFvkr17jvxab+K+DjJBy+XgjkMBrXp5tZqf6MXQysyvwRlNk4n0B/o7KyQgb9trBzPqa2UVmNgX4ktL33e3OuX+G78Cf6+ESvGbuXsDXZna9v5/WZtbezAaY2Rgz+xCIdOXRwPuku5ld5f/QyPBvoZ/Pj+DNLAvwDzO7M+T1PMjMXqP0FOQjzrlvqEJ+J/NX/NWLzOwBMzvQ/7waaN51ZcZT/iiMwPMdbWZH+sc+8Hzj7cCY1GNRE/z5iwItbJeYd92UI/zn2MfM7gL+5m//guQkV4H/ZS/zrhvTLsprd28VnXGsPt6onmu19MZ7k7pybiWEXWeD8qdMb4k3hXa0fT6NN+2xA5bGir+c5zmZGLMu4p32ifT4EcvH+b94JGxfb8coOyyO4+vwWkz2mhk0gdhmEGOmwgjlV/jlJ1T02EZ4fl0TeRx/+1FEvx5P6K0IaJ3Acbk8xj67hpWtqWu1xHNbDIyMY5+nU9qyE+u2KULdxpROyR5+mxxWtqquTzIsxnO5OFAuwrb2eD9Yoj32TLyZnaO+JvE6dUerPyyk3GRif7Yk9VhUx+dBhPo1cq2WcmKItY8meKMJI8UV81otavFIEuedcumPdwGwN/HGkxfgdaDMBabhTYmb45ybF20/Ufa9DW8CmpvwZhfdgzf74hzgUufcaGqmx/dI4G68BCvSkLFEhJ9WidWpdA7eJE934l0LYwXescj3//43cJJz7kIX37DhOsl5rWS9gGvwTi9swDt/uwfvg+V1vCn82zvvHHtF9/8Y3rn/GXiJQ7QZPnHO3YPXWfNJ/7Hz8Fo4vsGbQbWXizDTZCUV470/VuK1qkzEm6+nt3Mu1mRmgZjfwBv5MhZv0qqf8JK0XcD3eC1yv6B0jp3QunvwRlb9A69FKS/G4+TiXargGrzX82a8/9M6vNa705xzo1zIJHpVyXmTcg0E/or3vyn0Y/jEj+lYypkR2Tn3Lt4p0nfwWn1jzdkSaz9JPRY1wTmX55w7GzgL7zIb6yk95jPxWq4Pd87FmsOnOuPbjffafRTvtZsfb13zMxepZ8zsdbxfam85505LdjwiIlI/qMWjHjJvGufh/uoXscqKiIhUJSUedZDfYathjCJ3UdpJ8KUaCElERARQ4lFXHQgsNrObQ0YotDez4/zRCYEhiS8658rrhS4iIlJl1MejDjKzQZQ/udJM4AwX4fLjIiIi1UWJRx3kT750Ad7Qtb5ANt7Qp0148xO8CLzgnIs6ukBERKQ6KPGopKysLNe1a9dkhyEiIlJjvvjii4QvdKqr01ZS165dmTt3brLDEBERqTFmtrL8UpGpc6mIiIjUGCUeIiIiUmOUeIiIiEiNUeIhIiIiNUaJh4iIiNQYJR4iIiJSY5R4iIiISI1R4iEiIiI1RomHiIhIXZW/E14a7S1TRMrMXGpm1wDHAP3wri3SAtgKzAMmA8+7KPO7m9kovCuu9gfSgcXAU8Ajsa5Hkmi9yigpKWHLli3s3LmTvLw8Skp0uRSR+io9PZ3mzZvTpk0bMjMzkx2O1EXLZ8LC/0D/86H3yGRHA6RQ4gHcjJdwLADmALuALsCxwAjgHDP7WXhCYGYPAWOAPOBDoNAv/yAwwszOdc4Vhz9YovUqo6ioiNzcXDIyMmjTpg1NmjQhLS0NM6vKhxGRWsA5R2FhIdu3b2fVqlV07txZyYdUvUVvli6VeOzl58BXzrldoXeaWV+8xOAMYDRei0Rg29l4ycN6YIhz7nv//vbAdOAs4GrggbB9JlSvsjZv3kxmZib77LOPkg2Res7MaNiwIVlZWYD3+bDPPvskOSqpU5yDJe96fy+Z5q2nwHdPyvTxcM7NDk86/Pu/BR7yV48P2zzWX94cSB78OhvwTqEA3GJm4c8z0XqVsm3bNtq2baukQ0TKaNGiBTt27Eh2GFLXbFwMRXne30V5sPG75MbjS5nEoxxF/jIvcIeZdQIOAwqAl8MrOOdmAmuADsCgytarCkVFRTRs2LAqdykidUCDBg0oLq7SM7sisOQ9KPFfV64Yvn8vufH4Uj7xMLNuwP/5q2+GbDrEX37rnNsTpfrnYWUrU69KqLVDRMLpc0GqxcLXoDjf+7soH759Lbnx+FKpjwcAZnYJMBRoAHQCjsJLkO50zoUetW7+cmWM3a0KK1uZeiIiIqnj378s7TwaSXpYC/uGBTChZfTyfU6D85+rmthiSMUWj6PxOpGOAob49/0RuDWsXDN/uVe/kBCBgcvNq6Be7ZWC47hFRKSSjvszdOgHDZpE3l5cEHs9oEET6NDf218NSLnEwzl3mXPOgCZAX+B+YALwqZl1DCkaaJuMOLdHDInWK92B2eVmNtfM5m7cuDHR3dScwDju5bOSHYmIiFSVtj3g8pkw/PeQ0RgqOh7C0rx6w//g7adtj+qJM0zKJR4Bzrk9zrmFzrmb8EahHIQ3x0ZAoAt4s70qlwpsC+0unmi90Ngec84NcM4NaNeuXYzdpIjQcdwprmvXrphZ8JaWlkaLFi3IycnhuOOOY+zYsXzzzTfJDrPWmjFjBmbGsGHDkh1KVBMmTCjzGjAz0tPTycrK4thjj+Wpp54iylyCFTZs2DDMjBkzZlTJ/kRqXFo6HHUNXPkxtO8bvfUjXIMm0P5Ar95RV0NazaUDKZt4hAnM3XGamTXw/17hL7vEqJcTVrYy9WqnSOO4a4ETTzyR0aNHc9FFF3HSSSfRs2dP5s6dy8SJEznooIM4/fTTWb9+fZU9XuDLbsKECVW2z2QIJG4rVqxIdiiV1qNHD0aPHs3o0aM577zz6Ny5M9OnT+fSSy/lrLPOSslRIHXldSS1UKD145gbIKNR7LIZjbxyNdjKUebha/wRE7MVb0htBtAG2AB85W/ra2aNo4xQGegvvwq5L9F6tVOkcdzZvZMbUxxuueWWvX6Vl5SU8Oabb3L99dfz5ptvMnToUObMmUPbtm2TE2QtdPjhh7No0SKaNInzV1ESDR48mMmTJ5e577XXXuOcc87h9ddf56mnnuKyyy6r1GM888wz7N69m86dO1dqPyIpIS0dsvtAeoPSz/1I0htA9gE12soRqra0eAzBSzq2Aj8BOOdygS+BhsC54RXMbCjeqJj1wCeB+xOtV2ul6DjuRKSlpXHGGWcwd+5cevbsyZIlS7jhhhuSHVat0qRJE3r37l1rv2jPOussLrjgAgBefnmvaXgqrHPnzvTu3btWJGIicVn0Jq68gQT5O5N66j0lEg8zO8bMLjCzvS5UYGZHA//0V/8Zdv2UO/3lJDPrGVInG3jYX50Y4YJvidarfVJ0HHdltG7dmvvvvx+A5557LuIpl02bNjFu3Dj69etHs2bNaNq0KYceeih//etfKSwsLFPWzPjzn73e3H/+85/L9C0IbzJfuXIlY8aMoXv37mRmZtK6dWuGDx/OCy+8EDHW0Kb3DRs2cMUVV9CpUycyMzPp1q0bt9xyC3l5e/8y2bFjB4899hhnnnkmPXv2pEmTJjRr1oxDDjmE22+/nT17yjbUTZ48GTNj5UpvlHi3bt3KPI/AqZfy+nh8++23XHTRReTk5JCZmUlWVhYjR47knXfeiVj+4osvxsyYPHkyS5cuZdSoUbRv357MzEx69+7NpEmTqvxCiAMGDAAIPtdQU6dO5eSTTyYrK4uGDRuSk5PD6NGjWbRoUcR9RevjkcjzqsjrSKRa+KfWLWTsRDFpETqeuqSeek+VUy098PpxPGhmX+K1NjT37z/ALzMVb1htkHNuipk9gjfN+Xwz+4DSi721AP5D2Q6plaqXkmrpOO7KGjlyJG3atGHz5s1Mnz6dX/ziF8Ft8+fP56STTmLt2rV06tSJYcOGUVJSwmeffcb111/P1KlTefvtt4OzyI4ePZqvv/6aefPmcdBBB3HwwQcH9xX692effcZJJ53E1q1b6datG2eddRabNm1i5syZzJgxg2nTpvH0009HnAwqNzeXww47DOccRx11FNu3b2f27NlMmjSJhQsX8sYbb5QpP2/ePK644gqys7PZf//9GTBgAJs2beKzzz5j3LhxvPHGG8ycOZNGjbxzuT179mT06NFMmTKFXbt2cfbZZ9OsWWn/6dC/o3njjTc477zzyM/Pp2/fvhxzzDGsXr2ad999l3feeYdx48Zx2223Raz79ddfc+2115KVlcXw4cPZsGEDs2fP5pZbbmH16tX8/e9/L/fx47V9+3aAvS6oNnbsWCZOnEhaWhqDBw9m33335ZtvvuGZZ57hpZdeYsqUKZxyyikVeqyKPK94X0ci1WbjYlxhXnDo5m6XSXGbHjQ/9XZ4fzxsWgqFu72NyTz17pxL+g1voq5b8S7QlgvswZsefQUwBTiznPqjgI+B7Xjzc3wBXAWkVUe90Nthhx3m4rVw4cK4y8btp6XOPXK0c3/p4Nz4Fonf/tLBuUcGe/tLoi5dujjATZ8+vdyyI0aMcID7wx/+ELxv9+7drlu3bg5wd9xxhyssLAxu27RpkzvuuOMc4MaPH19mX+PHj494f8CePXtcTk6OA9x1113nioqKgtvmz5/vsrOzHeD+8Y9/RNwv4C677DKXn58f3LZw4ULXrFkzB7jZs2eXqZebm+s+/PBDV1xcXOb+LVu2uJNOOskBbuLEiXvFGTh+y5cvj/g8pk+f7gA3dOjQMvevW7fOtWjRwgHu3nvv3atOkyZNHOCmTZtWZtvo0aODz2/8+PFl4p05c6ZLS0tzaWlpbtWqVRHjiSRwzEaPHr3XtuLiYjdgwAAHuIsuuih4/9SpUx3gmjZt6mbOnFmmzl133eUA17JlS7dhw4Yy24YOHRrx9Zbo8yrvdRRLtXw+SP3y0f2ucEJbV/inlm73n7LcoxN/60qK/c+q4iLnPv6bc7e1d25CK+dubefc7AcSfihgrkvwOz8lTrU455Y75/7knBvunMtxzjV2zjVyznV1zp3jnPtPOfVfcM4d7Zxr4Zxr6pw7zDn3kCvnVEmi9VJKLR3HXRUCQ5k3bdoUvG/y5MksX76c8847j7Fjx5KRUdqo16ZNG55++mkaNGjAQw89VKEhmS+//DK5ubl06dKFu+66i/T09OC2Aw88MNiUfs8990Ssn5OTw9/+9rcy1+rp06cPF154IQAffvhhmfKdOnXi2GOPJS2s81erVq3429/+BsCUKVPijr88jz/+ONu3b+eoo47i+uuvL7Nt2LBhXH311UD05zdw4EDGjx9fJt4hQ4Zw4oknUlJSwvTp0ysVX0FBAfPnz+f8889n7ty5pKenB2MCuPfeewG49tprGTJkSJm6N910E0cccQTbtm3j8ccfr9DjVvfzEqlKxQtexVwRi11nTi64k/Yn3oCl+Z9V4cNuSwqTduo9JRIPqaRaOI67KgTOsYd+Kbz99tsAnHvuXv2GAejYsSP77bcfP/30E99//33EMpHMnDkTgAsuuIAGDRrstf2SSy7BzFi6dClr1qzZa/uxxx5L48aN97q/d2+vmXPt2rV7bXPOMXv2bO644w7GjBnDJZdcwsUXX8xf/vIXAJYsWRJ3/OUJPL+LL7444vZLL70UgNmzZ0ccxjpy5MiIp5hiPb/yBE5bmRmZmZn079+fKVOm0Lx5c5599lkGDvQGnxUVFfHxxx/HjP+SSy4BqPB8HdXxvESqy9qiFtxROIrTCm6nsGV3RvbbZ+9CgR+rx98KzZIzD1Wq9PGQqhB4Qc3+K8y6O/ZwqsA47sHX17qEI+Cnn34CvJaMgGXLlgHRE49QGzdupFevXnE9ViCZ6NYt8uV7GjVqRMeOHVmzZg1r1qxh3333LbM92iiSFi1aAOzVwXTDhg387Gc/Y86cOVFjCq8DRicAACAASURBVPR1qArlPb9u3bqRlpZGXl4emzZtIjs7u8z2ij6/ePTo0YPBgwcDkJ6eTqtWrYJzuLRq1SpYbtOmTeTn55OWlkaXLpGn5+nRw2vJi5QUxlIdz0ukOhQVlzBq92/JLfY6nl92TDcapEf5bA/8WD3qmhqMsJQSj7qmlozjriznHF995U2z0q9fv+D9gV/jp5xyCllZWTH3UZH5PwKnZWJdRTTWqZvwUyblueyyy5gzZw5HH300EyZM4KCDDqJVq1Y0aNCAgoKCvTpWVlY8zy+Wij6/eESaxyOS0OMeLf6KnFYLVR3PS6Q6vLNgPbmbvaSjVZMGnD8wp5wayaPEoy5a9Gb5F4QLjOPuPbJmYqpiU6dOZcuWLWRkZJQZGpqTk8N3333HlVdeWeERDLF06tQJKG1RCZeXl8e6desA9mrtqKhdu3bx9ttvk56ezltvvVXm1z3A0qVLK7X/SDp16sR3333HsmXLGDFixF7bV6xYQUlJCY0aNSrTwpQKsrKyyMzMJD8/nxUrVrDffvvtVWb58uVA5f83IqnIOcejs34Irl90ZFeaNEzdr3el83VNcIr0kF94lnrjuCtjy5Yt/Pa3vwW8IYyhzf4nn3wyUPHJpQKdPouKiiJuHzp0KAAvvvhixDJPP/00zjl69uxZ6S+3bdu2UVJSQvPmzfdKOgCef/75qHXLex7RBJ7fM888E3H7U095Vy0YPHhwmQ67qSAjI4Ojjz4aiB5/oOWkuq9Rk+jxF6mMj5duYsEaf5h5Rhqjj4x1RZDkU+JR14ROkQ6lHUh/8YK3DO14GhjHXUuUlJTwxhtvMHDgQJYuXUrv3r25++67y5S5/PLLycnJ4emnn2b8+PHs3r17r/0sWLAg+EUaEEgWok00de6555KTk8Py5csZO3ZsmcmjFi5cyPjx4wG48cYbK/UcAdq3b0/r1q3ZunXrXhOTTZs2jfvuuy9q3fKeRzS//vWvad68ObNnzw6OmgmYNWtWcL6KVJ0pNjAS5/777w92NA247777+OSTT2jZsmWlp1gvT6LHX6QyQls7zhuQQ9tmVXsqtqql1k8XqbzAFOmWBumZ3jDZQWO8vhzdhsKnD8N/b/dmMy3xp1BPwWu3TJw4MfgrNS8vj40bN/Lll1+ydetWAM4880weffRRWrduXaZes2bNmDp1Kqeeeiq33norDz74IP3796dDhw5s2LCB5cuXs2LFCo444ojgSAfwLkrXpEkTXn31VYYMGUKPHj1IT0/n9NNP5/TTT6dRo0a89NJLnHzyydxzzz289tprDBw4kM2bNzNjxgwKCgq48MILufzyyyv93NPT0/nDH/7AjTfeyAUXXMCDDz5I165d+eGHH/jf//7H73//e+64446Idc866yxmzJjBBRdcwAknnBBsMZk0aVLMPi0dOnTg2Wef5fzzz+faa6/liSee4MADD2Tt2rV89NFHlJSUMG7cOE466aRKP7/qcMopp3DzzTczadIkhgwZwjHHHEPHjh2ZP38+CxYsoFGjRjz33HO0b9++WuMo73UkUtUWrNnGR997He3TDH59TPckR1Q+JR51zcLXvPHZ7Q+EcyeXnZcj0JN5/5Hw8mjY8K03jvvo3yQt3Gjefde7oq6Z0bRpU1q1asVhhx3G4YcfzqhRozjwwAOj1u3Xrx/ffPMNDz/8MK+//jpffvkleXl5tGvXjpycHC688ELOOeecMnU6dOjAW2+9xa233spXX33F7Nmzcc7RqVOn4BfGoEGD+Prrr5k4cSLTpk3j1VdfpXHjxgwaNIjLL7+cUaNGJdw5M9wNN9xA165dueeee/j2229ZsGABBx54IM899xwXXHBB1MTj6quvZvv27Tz//PO89dZb5Od70+WPGzeu3M60gevgTJo0if/+97/BoasnnHAC11xzDSNHpnZ/oIkTJzJ48GAefPBBPv/8c+bMmUN2djYXXnght9xyCwcccED5O6mkeF5HIlXp0Vml/c5G9tuHzm1T/7pDlmhvb/EMGDDAzZ07N66yixYtok+fPtUb0AvnQdchpa0c0ZQUe60fKz6CUS9Vb0wiUq4a+XyQOiV3826G3j2dEv9r/M2rB9OvU4xLYlQhM/vCOTcgkbpq8ahr4k0ikjyOW0REKufRWT8Ek46je7atsaSjstS5VEREpJb5cUceL81dHVy/cmjPGKVTixIPERGRWuafs5dTUOSNruvfqSVH94x/QsRkU+IhIiJSi2zbU8jzn64Kro8Z1rPKOrbXBCUeIiIitcizn6xgZ743SV3P7GaccED1DhOvako8REREaok9BcU8+fGK4PqVQ3uQllZ7WjtAiYeIiEit8a/PV7F5VwEA+7ZqzOkHd0xyRBWnxKOGad4UEQmnzwWJR0FRCY+HTBh2xdDuNEivfV/jtS/iWiw9PT142XYRkYCSkhLSYk34JwL85+s1rN3mXYsrq1lDzhuQk+SIEqNXeg1q0qQJO3eWc7l6Eal3du/eTePGjZMdhqSw4hLHP2aWXgzukqO70ahBehIjSpwSjxrUokULNm/erFYPEQlyzrF161aaNm2a7FAkhb377XqWbdwFQPPMDC48skuSI0qcEo8a1Lx5c5o2bcrKlSvZunUrRUVFOrcrUk8558jPz2fdunUUFRXtdaVlkQDnHA/PWBpcv/DILrRo1CCJEVWOrtVSg8yM7OxsduzYwfbt2/nxxx/V+iFSj2VkZNCyZUuys7PVx0Oi+uj7n1iwZjsAmRlpXDq4W5IjqhwlHjXMzGjRogUtWrRIdigiIlILPDS9tLXj5wNzyGqWmcRoKk8ptoiISIr6YuUWPlu+GYCMNOPXQ7onOaLKU+IhIiKSoh4J6dtxxsH70ql1kyRGUzWUeIiIiKSgxeu388GiHwEwgyuH1f7WDlDiISIikpIemVE6b8eJB3SgZ3bzJEZTdZR4iIiIpJiVm3bx5ry1wfUxw3skMZqqpcRDREQkxTw8/QdK/GmeBvfMon+nVskNqAop8RAREUkha7bu4ZUvVwfXrz62ZxKjqXpKPERERFLIP2b8QJHf3HF41zYM6t42yRFVLSUeIiIiKWLD9jz+PTc3uH7NiLrV2gFKPERERFLGozOXUVBUAsDBOa0Y3DMryRFVPSUeIiIiKeCnnfm88L+VwfXfjOiJmSUxouqhxENERCQFPP7RMvIKvdaOvh1bMHz/7CRHVD2UeIiIiCTZll0FPPtJaWvHNcfWzdYOUOIhIiKSdE9+vJzdBcUA7N++OScc0CHJEVUfJR4iIiJJtG1PIZM/XhFcv+rYnqSl1c3WDlDiISIiklRPz1nBjvwiALq3a8op/fZJckTVS4mHiIhIkuzML+LJj5cH168a1pP0OtzaAUo8REREkubZT1aydXchAJ3bNOGMgzsmOaLqp8RDREQkCXYXFPHER8uC62OG9SAjve5/Ldf9ZygiIpKCXvhsFZt2FQCwb6vG/OzQTkmOqGYo8RAREalheYXFPDartLXj/4Z2p2FG/fhKrh/PUkREJIW8NDeXH3fkA5DdPJNzB+QkOaKao8RDRESkBuUXFfPIjB+C65cP6U6jBulJjKhmKfEQERGpQS/NXc26bXkAZDVryKgjOic5opqlxENERKSG5BcV8/D0pcH1K4b0oEnDjCRGVPOUeIiIiNSQlz7PLdPa8ctBXZIcUc1LicTDzBqY2Qgzu9fMPjWzdWZWYGZrzGyKmQ2LUm+ymbkYt8XlPO4oM/vIzLaZ2U4zm2tmV5lZShwXERGpO/IKi3loemnfjv8b2oPGDetP346AVGnfGQq87/+9HvgC2AUcAJwNnG1mtznn/hSl/sfA0gj3r4v2gGb2EDAGyAM+BAqBEcCDwAgzO9c5V5zAcxEREdnLS3NzWb890NqRyQVH1L/WDkidxKMEeAV4wDn3UegGMzsfeB74o5lNd85Nj1D/Cefc5HgfzMzOxks61gNDnHPf+/e3B6YDZwFXAw8k8FxERETK8Fo7Sn8fXzmsfrZ2QIqcanHO/dc5d0540uFv+zcw2V/9ZRU95Fh/eXMg6fAfawNwpb96i065iIhIVfj357ls2O7N29GueSYX1LORLKFqyxfrV/6y0vPJmlkn4DCgAHg5fLtzbiawBugADKrs44mISP2WV1jMwzNCWjuG9qhX83aES5VTLeXZz19G67Mx3Mz6A82ADcBs4H3nXEmEsof4y2+dc3ui7O9zYF+/7JzEQhYREYF//W9VsLUju3lmvZu3I1zKJx5m1gG42F99JUqxiyLct9DMfu6cmx92fzd/uTLGw64KKysiIlJhXmtH6UiWK4fV79YOSPFTLWaWATwHtAQ+dM69GVbka+A3QF+81o6OwKnAPLwRMR+Y2b5hdZr5y10xHnqnv2yeePQiIlLfvfi/VWWuyfKLw+t3awekfovHP/CGuOYSoWOpc+7+sLt2AVPN7H1gJl4fjbF4I1QCLFA90aDM7HLgcoDOnfUiEhGRvYW3doxRaweQwi0eZvYA8Cu8Ia8jnHPr463rnCsA7vRXR4Zt3uEvmxFdYNuOSBudc4855wY45wa0a9cu3rBERKQeeeGzVWz0Wzvat8jk52rtAFI08TCze/FOoWzESzq+L6dKJIFZS8NPtazwl7Fmbglcn3hFjDIiIiIR5RUW88jM0NaOnmrt8KVc4mFmdwHXA5uA451zCxPcVVt/uTPs/sDQ3L5m1jhK3YFhZUVEROL2fEhrR4cWjTh/YE45NeqPlEo8zGwicBOwBS/pmFeJ3Z3nLz8PvdM5lwt8CTQEzo0Qw1C8+ULWA59U4vFFRKQeyiss5h+hrR3D1bcjVMokHmZ2G3AzsBUv6YjZ2mBmB5vZqWaWHnZ/hpldj3eqBuCvEaoH+n9MMrOeIXWzgYf91YlR5gERERGJ6tlPVqq1I4aUGNViZqcD4/zVpcA1Zhap6GLn3ET/767Aa8BmM1sCrMYb/toPb1htCd6U6O+G78Q5N8XMHsGbHn2+mX1A6UXiWgD/wbtYnIiISNx25heV6dtx1fAeZGaotSNUSiQeQJuQvwf4t0hmAoHEYx7eRdwOx+soegjeENnVwFPAQ865L6I9oHNujJnNBq7CuzpuOl6H1CeBR9TaISIiFTX54+Vs3lUAwL6tGnP+QI1kCZcSiYd/ZdnJFayzHLiuko/7AvBCZfYhIiICsG13IY/OWhZcv/a4/WiYkTI9GlKGjoiIiEgVePyjZezIKwKge1ZTfnZI+GwOAko8REREKm3Tznye/Hh5cP2643uRka6v2Eh0VERERCrpkRk/sLugGIDeHZpzar99khxR6lLiISIiUgnrt+Xx7KelFzy//vhepKVFHJkpKPEQERGplIemLyW/yBsI2b9TS44/oH2SI0ptSjxEREQSlLt5N//6fFVw/YYT9ifKPFTiU+IhIiKSoL99+D2FxQ6Aw7u2Ych+WUmOKPUp8RAREUnAso07eeXL1cH1G07opdaOOCjxEBERScD9H3xPidfYwTH7ZXFE97axKwigxENERKTCFq/fzpvfrA2u33DC/kmMpnZR4iEiIlJB9723BOe3dhzXpz0H57RKbkC1iBIPERGRCvhm9VbeW7ghuH798b2SGE3to8RDRESkAu55b0nw71P678MBHVskMZraR4mHiIhInD75YROzlmwEIM3gt8eptaOilHiIiIjEwTnHpGmLg+tnH9qJntnNkhhR7aTEQ0REJA7vLdzA17lbAWiYkcZ16tuRECUeIiIi5SgqLuHud78Lrl80qAv7tmqcxIhqLyUeIiIi5Xj1qzUs/XEnAM0yMxgzvGeSI6q9lHiIiIjEkFdYzP3vl45kuXxId9o0bZjEiGo3JR4iIiIxPPfpStZuywMgq1lDfjW4W5Ijqt2UeIiIiESxPa+Qh6YvDa5fc+x+NM3MSGJEtZ8SDxERkSiemLWMLbsLAejUujG/OLxzkiOq/ZR4iIiIRLBxRz5PzF4eXL/hhF40zNDXZmXpCIqIiETw4H+/Z3dBMQC9OzTnjIP2TXJEdYMSDxERkTCrNu3mhf+tCq7/7qT9SUuzJEZUdyjxEBERCXPf+99RWOxd935g19YM3z87yRHVHUo8REREQixcu53X560Nrt98Um/M1NpRVZR4iIiIhLjnve9wXmMHx/XJZkDXNskNqI5R4iEiIuL75IdN/HfxjwCYwY0n7p/kiOoeJR4iIiJASYnjzncWBdfPOnhfendokcSI6iYlHiIiIsBb89fxzeptgHfZ+xvU2lEtlHiIiEi9l19UzN3vLg6uX3p0N132vpoo8RARkXrv2U9Wkrt5DwCtmzTgymE9khxR3aXEQ0RE6rVtuwv5+3/LXgiuZeMGSYyoblPiISIi9drDM5aybY93IbjObZrwy0FdkhxR3abEQ0RE6q3VW3bz1JwVwfWbTtxfF4KrZjq6IiJSb9333hIKikoAOKhTS07tv0+SI6r7lHiIiEi9tGDNNl77ek1w/fcj+2hq9BqgxENEROod57zJwkqnRm/PEd3bJjeoekKJh4iI1Dszl2zk46WbAEhPM245WZOF1RQlHiIiUq8UlzgmvlM6Wdj5A3Pomd08iRHVL0o8RESkXnnly9UsXr8DgCYN07nuuP2SHFH9osRDRETqjT0Fxdz33pLg+q+P6U5280ZJjKj+UeIhIiL1xuMfLWP99jwAspplcvmQ7kmOqP5R4iEiIvXChu15PDLjh+D69cf3omlmRhIjqp+UeIiISL1wz7vfsaewGIDeHZpz/sCcJEdUPynxEBGROm/Bmm1M+XJ1cH3cKQeQnqbJwpJBiYeIiNRpzjlue2thcLKwEb2zGbxfVnKDqseUeIiISJ323sINfLZ8MwAZacbYkX2SHFH9lhKJh5k1MLMRZnavmX1qZuvMrMDM1pjZFDMbVk79UWb2kZltM7OdZjbXzK4ys5jPL9F6IiJSOxQUlXDn24uC678c1IWe2c2SGJGkyhfsUOAD4HqgC/AF8BqwGTgbmG5mt0aqaGYPAc8DA4CPgPeBXsCDwBQzS6/KeiIiUns888kKVmzaDUCLRhlcO0KThSVbqiQeJcArwBDn3D7OuVOdc+c75/oBPweKgT+a2fDQSmZ2NjAGWA/09+udBewHLALOAq4Of7BE64mISO2xeVcBD3z4fXD9NyP2o3XThkmMSCBFEg/n3H+dc+c45z6KsO3fwGR/9Zdhm8f6y5udc9+H1NkAXOmv3hLh1Emi9UREpJZ44IMl7MgrAqBbVlMuOrJrcgMSIEUSjzh85S87Be4ws07AYUAB8HJ4BefcTGAN0AEYVNl6IiJSeyz9cQfPfbYquD725N40zKgtX3l1W235LwROyq0Lue8Qf/mtc25PlHqfh5WtTD0REaklbp+6iOISb/zsoO5tOP6A9kmOSAJSPvEwsw7Axf7qKyGbuvnLlTGqB9LdbiH3JVpPRERqgVlLNjL9u40AmMEfTz0AM00WlipSOvEwswzgOaAl8KFz7s2QzYHxULti7GKnv2xeBfVERCTFFRWXcPvU0uGz5x7Wib4dWyYxIgmX0okH8A9gBJDL3h1LA+mrq+A+E61XugOzy/05P+Zu3Lgx0d2IiEgVe/HzXL7bsAOAJg3TufGE/ZMckYRL2cTDzB4AfoU35HWEc259WJEd/jLWTDCBbTtC7ku0XpBz7jHn3ADn3IB27drF2I2IiNSUrbsLuPe974LrVw7tQXaLRkmMSCJJycTDzO4FfgNsxEs6vo9QbIW/7BJjV4FLD64IuS/ReiIiksL++v4Stu4uBKBT68b8ekj3JEckkaRc4mFmd+HNYLoJON45tzBK0cAQ275m1jhKmYFhZStTT0REUtTi9dt59tPSMQPjTjmARg00AXUqSqnEw8wmAjcBW/CSjnnRyjrncoEvgYbAuRH2NRRv3o/1wCeVrSciIqnJOcef31iIP3qWo3u25cS+Gj6bqlIm8TCz24Cbga14SUc8rQ13+stJZtYzZF/ZwMP+6kTnXEkV1RMRkRQzbcF6Plm2CYD0NGP8aX01fDaFZSQ7AAAzOx0Y568uBa6J8qJZ7JybGFhxzk0xs0fwpjmfb2YfAIV4I2FaAP/Bu+hbGYnWExGR1JJXWMxfQobPXjioC73aayaEVJYSiQfQJuTvAf4tkpnAxNA7nHNjzGw2cBXeVW7TgcXAk8Aj0VotEq0nIiKp49GZy1iz1ZuEunWTBvz2uF5JjkjKkxKJh3NuMqUXgkuk/gvACzVVT0REkm/N1j08MnNpcP3GE/enZZMGSYxI4pEyfTxEREQq4o63F5FX6DVOH7BPC34+sHOSI5J4KPEQEZFa59Nlm5j6Tel1Qyec3pf0NHUorQ2UeIiISK1SVFzChDe+Da6fdlBHDu/WJkYNSSVKPEREpFZ58fNcFq/3rmjRuEE6Y0/uneSIpCKUeIiISK0Rfj2WMcN60LFVtEmoJRUp8RARkVrj3vdKr8eS00bXY6mNlHiIiEitMH/1Np77rPR6LH8Yqeux1EZKPEREJOWVlDjGvb4A51+PZWivdroeSy2lxENERFLeS3NzmZe7FYCG6WlMOF3XY6mtlHiIiEhK27KrgEnTFgfXrxjanW5ZTZMYkVSGEg8REUlpd7/3HVv8DqWdWjdmzLCe5dSQVKbEQ0REUta83K28+L9VwfXxp/WlcUN1KK3NlHiIiEhKKi5x/DGkQ+mxvbM5rk92coOSSlPiISIiKelfn6/im9XbAGiYkcb40w5Qh9I6QImHiIiknM27CrhrWukMpVcO7UGXtupQWhco8RARkZRz17TFbNtTOkPplcN6JDkiqSpKPEREJKV8uWoL//o8N7g+4bS+mqG0DlHiISIiKaO4xPGn1xcE14/r054RfTRDaV2ixENERFLGC5+tZMGa7QBk+h1KpW5R4iEiIinhx+15ZTqUXjW8JzltmiQxIqkOSjxERCQl3PrWQnbkFwHQLaspl+uS93WSEg8REUm6Gd/9yFvfrAuu337mgepQWkcp8RARkaTaU1DMH0M6lP7skH05qmdWEiOS6qTEQ0REkurv//2e3M17AGjZuAG/P6VPkiOS6qTEQ0REkmbJhh08NmtZcH3syb3JapaZxIikulU48TCzi8zsqDjKDTKzixILS0RE6rqSEsfvX51PUYl3FbgBXVpz3oCcJEcl1S2RFo/JwGVxlPsV8FQC+xcRkXrgpbm5zF25BYCMNOOOn/UjLU0XgavrqvNUi149IiIS0U8787nzncXB9cuHdKdX++ZJjEhqSnUmHp2AndW4fxERqaVun7qozEXgrjl2vyRHJDUlI55CEfpq9IzRfyMD6AOMAD6vRGwiIlIHfbz0J177ak1w/bYzDqRxQ83ZUV/ElXjg9etwIetH+7doDCgB7kksLBERqYvyCosZ95/SOTtO7b8Pw/bPTmJEUtPiTTyeoTTxGA38AHwcpWwBsAZ43Tk3r3LhiYhIXfLwjB9Y/tMuAJpnZvCnU3URuPomrsTDOXdx4G8zGw3Mds5dWl1BiYhI3bNkww4embE0uP67k/Ynu0WjJEYkyRBvi0eobqjTqIiIVEBxieN3U76hsNhrPD+kcytGHdElyVFJMlQ48XDOrayOQEREpO565pMVfJ27FYAG6caks/uTrjk76qVEWjwAMLNGwACgIxC1rcw590yijyEiIrXf6i27ufvd74LrVw3vqTk76rGEEg8z+y3wJ6BFHMWVeIiI1FPOOX7/2gJ2FxQD0Kt9M8YM65nkqCSZKpx4mNmlwL3+6iJgMbC9KoMSEZG64T9fr2HWko0AmMGdP+tPwwxdn7Q+S6TF4zd4Q2svdM69UMXxiIhIHbFpZz63vrkwuD76yK4c1qV1EiOSVJBI2tkLmKOkQ0REYrn1rYVs2e1Ni75vq8bcdOL+SY5IUkEiicduYFVVByIiInXHfxdv4PWv1wbXbz/rQJpmJjyeQeqQRBKPOcCBVR2IiIjUDTvzixj3Wum06Gcdsq+mRZegRBKPPwO9/RlMRUREyrh72mLWbssDoE3ThvxR06JLiHLbvcxsSIS77wOeNLORwFS8Uy8lkeo752ZVKkIREak1vli5mWc+LZ1ncvxpB9CmacMkRiSpJp4TbjMoe2XaAAPO8W/RuDgfQ0REarm8wmJuevkbnP+NMXz/dpx+UMfkBiUpJ56kYBaREw8REZGg+95fwjL/yrPNMjP4y1n9MNO06FJWuYmHc25YDcQhIiK12Bcrt/D4R8uC6384pQ/7tmqcxIgkVWn6OBERqZS8wmJumjIveIplcM8sfj4wJ7lBScpS4iEiIpXy1/eXsGxj6SmWiWfrFItEl8i1WiKNcomkAPjJObc0zv3uD5wEDMS76m0vvA6s5zrnpkSpMxmINaz3O+dc7xiPOQq4EugPpONdd+Yp4BHnXMRROiIiUurLVWVPsfx+ZB86tW6SxIgk1SUy4mQGFehsambbgaeBPzrndsQoeiVwbQLxAHwMREpw1sWI6yFgDJAHfAgUAiOAB4ERZnauc644wXhEROo8bxTLPEpCTrH84nCdYpHYEkk8Zvn1jvLXt1A6j0cXoA1eYvIZ0A7oClwDDDOzo5xzu6PsdwFwNzAX+AL4JzA0zpiecM5NjvcJmNnZeEnHemCIc+57//72wHTgLOBq4IF49ykiUt/c/8H3/OCfYmnaMJ07f6ZTLFK+RPp4nOQvFwIjnXNtnXOHOOcOc85lAScD3+IlH/2A/fCmWe+Hd2XbiJxzTzjnfuece8k590MCcVXEWH95cyDp8GPYgNfyAnCLmakPjIhIBF/nbuWxWaUf1WNH9iGnjU6xSPkS+WIdh5dEHOucmxa+0Tn3LnA83vVc/uScWwGMAvKBsxMPtWqYWSfgMLw+KC+Hb3fOzQTWAB2AQTUbnYhI6gs/xXJUj7aMOrxzcoOSWiORxON8YLpz7sdoBfyWg+nAef56LvAlXofR6jDczO4zs8fM7DYzOzFGa8Uh/vJb59yegKJlEgAAIABJREFUKGU+DysrIiK+v334Pd//uBOAJg3TmXR2f9LSdIpF4pNIH49OeElEefKBfUPWc/FGq1SHiyLct9DMfu6cmx92fzd/uTK8QohVYWVFRAT4atUWHp1VOopl7Mm9dYpFKiSRFo+fgCFmFnVKOn/bEGBTyN2tga0JPF4sX+P1G+kLNAM6AqcC84ADgA/MbN+wOs385a4Y+93pL5tXXagiIrXbnoJibnhpHsX+OZZB3dtwwRFdkhyV1DaJJB5vAu2Bl8xsr3FT/n3/BrKBN0I29QaWhZevDOfc/c65vzvnFjrndjnn1jnnpgKHA5/6MYwNqxZoD0z4+jNmdrmZzTWzuRs3bkx0NyIitcqkaYuD12Jp2jCdu885SKdYpMISOdUyHm/kyinAUjP7BO+0hcMbTnsU0MC/bzyAmR0GdAaeqYKYy+WcKzCzO4HXgZFhmwNziTQjusC2iPOOOOceAx4DGDBggC6gJyJ13uzvf2LynBXB9fGn9dUpFklIhRMP59xGMzsKeAQ4De+USpkiwFvAlc65jX6dL8ysQQ1PyLXYX4afalnhL2O1DwZaclbEKCMiUi9s21PITVPmBdeP65PNuQM6JTEiqc0SafHAObcOONPMOuMlHoEv97XAR/4Q2vA6NT0LaFt/uTPs/q/8ZV8zaxxlZMvAsLIiIvXWn9/4lnXb8gBo3aQBd2iiMKmEhBKPAOfcKuC5Koqlqp3nLz8PvdM5l2tmXwKHAucSdvrHzIbijdxZD3xSA3GKiKSsd+av49Wv1gTX7zirH9nNGyUxIqntau3MnGZ2sJmdambpYfdnmNn1lM6S+tcI1e/0l5PMrGdI3WzgYX91oi4UJyL12cYd+fz+tdIZCc46ZF9O7rdPEiOSuqDcFg//dArAGudccch6XPxWkXKZ2aGUfumDNxwW4A4zuzFkf4HZRLsCrwGbzWwJsBpv+Gs/vGG1JXhTor8bIaYpZvYI3vTo883sA0ovEtcC+A/exeJEROol5xxjX/2GLbsLAejQohETTu+b5KikLojnVMsKvC/xA4Al/nq8IzlcnI8B3hf+ERHu3y9K+Xl4F3E7HK+j6CH+463Gu7T9Q865L6IG5twYM5sNXIV3Mbp0vA6pTwKPqLVDROqzl79YzQeLSieovvvc/rRs3CCJEUldEU9SsArvC70wbL1KOedmUDrHRjzllwPXVfIxXwBeqMw+RETqmtzNu7n1zYXB9dFHduGY/dolMSKpS8pNPJxzXWOti4hI3VFc4rjx5XnszC8CoHtWU245uU+So5K6pNZ2LhURkar36Kwf+Gz5ZgDSDO497yAaN0wvp5ZI/JR4iIgIAN+s3sp97y0Jrl89vCeHdG6dxIikLko48TCznmZ2t5nNNrPvzOyukG2D/OuZtKqaMEVEpDrtLiji2n99TZF/AbhDOrfiNyOi9e0XSVxCE4iZ2a+Ah4CG/l0OyAop0g5vSvVCvBEmIiKSwm57ayHLQy4Ad//5B5ORrkZxqXoVflWZ2dHAo0AecBPeENjw0SjTgO3A6ZUNUEREqte0Bet58X+5wfU/n3EgXdo2TWJEUpcl0uLxO7wWjpOdc58Ae83Z75wrNLPvAHWFFhFJYRu253HLq98E10/pvw9nHxp+bU2RqpNIO9qRwP8CSUcMuYDm1hURSVElJY4bXprHVn920n1aNuKOM3UBOKleiSQeLfFmBy1PQyp5EToREak+T368nNlLfwLADP56/sG0bKLZSaV6JZJ4/Ah0i6Pc/sCackuJiEiN+3btNu6a9l1w/cqhPRjUvW0SI5L6IpHE42PgUDMbEK2AmR0P9AJmJBiXiIhUkz0FxVz7r68pKPYuSdW/U0uuO65XkqOS+iKRxOOveKNYXjWzE8yszD7MbAjehdaKgL9XPkQREalKt7+9kKU/7gSgcQNv6GzDDA2dlZpR4Veac+4zvJEtnYB3gE14o1zONLMNwHRgX+B3zrn5VRiriIhU0jvz1/Hcp6uC6+NPO4Du7ZolMSKpbxJKcZ1z9wIjgbl4l7M3oBXexGELgDOdc/dXVZAiIlJ5uZt387tXSofOnnxgB84fmJPEiKQ+SnjUiXNuGjDNzNridTZNB3Kdc//f3n3HV1Xn+R9/fdJIQgk19F4FpYPOqiCCo47OOo6gjl2x/BQHyzqj7szu/n7jzFpmdHQsrA4qlgXr6M7KqNhAsSC9Su89EAikkXK/vz/uzU0ISUi5ueeW9/PxyOPkfE/J5x6+wDunfM/uUBUnIiKhUVzq45ezlnK00P/W2S6t0njkssF6dFbCrsGPuzrnDuK/3CIiIhHqT3PWsWzHYQCSEoy//GIYGWl6dFbC76TBw8yua8gPcM692pDtRUSkYeatz+L5eZuD8/ed35/heuuseKQ2Zzxm4L95tL4UPEREPLL/SCH3vrksOD+mXztuPbuXhxVJvKtN8PiS6oPHWGAfsDZkFYmISEiU+hx3v7mMg3lFALRr3oQnLh9CQoLu6xDvnDR4OOfOqW6ZmfmAD51zN4WyKBERabhpczfyzSb/LXhm8OQVQ2nbrInHVUm804gxIiIxaOHWbJ74ZH1w/s5xfTizT1sPKxLxU/AQEYkxh/KKmDprKb7ARfJRPVpx1/i+3hYlEqDgISISQ3w+x71vLWNPTiEAGWnJPHXlMJIS9c+9RAb1RBGRGDJt3ia+WJcVnP/TpCF0apnmYUUix1PwEBGJEd9sOsDjc8pfdX/bmF6cN7C9hxWJnEjBQ0QkBuw/UsjUWcuOu6/jvvP7e1uUSBVqM3LpmJOs0qGmdZxzX9a5KhERqbWSUh93zlrKgdxjALRtlsIzVw0nWfd1SASqzQBic6l+ADEHnB/4qm55g98HIyIi1Xv8k/V8vyUb8I/X8dSVw2jfItXjqkSqVptQsJ2GDZkuIiKN5LMf9jFt7qbg/L0T+mm8DolotRm5tEcY6hARkTrakZ3PPRXewzK2XzumjOvjYUUiJ6cLgCIiUehYSSlTZi7hSGEJAJ0yUvnzFUP1HhaJeAoeIiJR6Pcf/MCKnTkAJCcaz1w9nNZNUzyuSuTkFDxERKLM35bs5LXvtgXn//UnpzC8WysPKxKpPQUPEZEosmpXDg/+bWVw/qLTOnLDP/XwriCROlLwEBGJEtl5Rdz22mKOlfgA6JvZjEcnDsZM93VI9FDwEBGJAiWlPqbOWsquwwUANG+SxPPXjqBZEw2VJNFFwUNEJAr8cc465m88EJx/4oqh9GrXzMOKROpHwUNEJMLNXrGH5+dtDs5PHd9XL3+TqKXgISISwdbtPcqv3lkenD93QCZ3j+/rYUUiDaPgISISoXIKirnttUXkF5UC0KNNugYJk6in4CEiEoF8Pse9by5j68F8ANJTEnn+2pFkpCV7XJlIwyh4iIhEoCc/28Bna/cH5x+bOJj+HZp7WJFIaCh4iIhEmA9X7uEvn20Izt82phcXD+7kYUUioaPgISISQVbvzuHet8pvJj2zTxt+dX5/DysSCS0FDxGRCJF19Bi3vLKIguLym0mfvWo4SYn6p1pih3qziEgEOFZSyu2vL2Z3TiHgH5l0+vUjaZmuN85KbFHwEBHxmHOOf3t/FYu2HQLADP7yi2H0ydTNpBJ7FDxERDz28tdbeWvRzuD8gxcOYNyATA8rEmk8Ch4iIh76cn0Wv5+9Jjj/8+GdueXsXh5WJNK4IiZ4mFl/M7vLzF43s7Vm5jMzZ2YTa7HtVWb2lZnlmFmumS0ysylmVuPnq+92IiKhsDkrlztnLsHn/PPDurXkPy89Ta+5l5gWSe9Tvh24q64bmdmzwB1AIfAZUAyMB54BxpvZJOdcaai2ExEJhZyCYm5+dRFHCksA6JiRyvPXjiA1OdHjykQaVyT9Zr8K+CNwBdAHmHeyDczsMvzhYS8w2Dl3sXPuUqAv8ANwKXBnqLYTEQmF4lIfU/57CZuz8gBITU7ghWtHktk81ePKRBpfxAQP59x059yvnXNvOec21XKzBwPT+51zwWH+nHP78J9BAXigiksn9d1ORKRBnHP8+/+sYv7GA8G2P04cwmldMjysSiR8ovY/VjPrAowAioC3Ky93zs0DdgEdgDMaup2ISCi88OVmZn2/Izh/z4R+/HSIhkOX+BG1wQMYFpiuds4VVLPOwkrrNmQ7EZEG+WjVHh75aG1w/ufDOjN1fB8PKxIJv2gOHj0D0201rLO90roN2U5EpN6W7zjM3W8uwwWeYBndszUPX6YnWCT+RHPwaBaY5tWwTm5gWnH4v/puJyJSLzsP5TP5lUUUFvsA6Nm2Kc9fM4ImSXqCReJPNAePsl8TXJi2K9+B2a2BMT8WZWVl1Xc3IhIHjhQWc9OMhRzIPQZAy/RkXrphFK2a6h0sEp+iOXgcDUyb1bBO2bKjFdrqu12Qc+4F59xI59zIdu3anbRQEYlPZY/Nrt/nP4makuh/bLZn26YeVybinWgOHlsD0+41rNO10roN2U5EpNacc/zH31fz1Ybyx2YfnXgao3u29rAqEe9Fc/BYGpgOMrO0atYZVWndhmwnIlJr/zVvMzMXbA/O3zW+L5cO6+JhRSKRIWqDh3NuB7AESAEmVV5uZmOBLvhHJ/22oduJiNTW35bs5NEKj83+bGgn7p7Q18OKRCJH1AaPgIcD00fNLPgwvJllAs8FZh9xzvlCtJ2ISI2+2pDFr99ZEZw/o1drHp04WI/NigSYc/V+uCOkzGw45f/pAwzE/zjrBiC7rNE5d0al7Z7DP8x5IfAp5S97awG8D0ys5iVx9dquspEjR7pFixbV+nOKSOxatSuHK57/lrwi/z8dAzo0583bfkRGWrLHlYmElpktds6NrM+2kfR22hbA6VW013h+0jl3h5nNB6YAY4FEYC3wEjCturMW9d1ORKQqO7LzuXHGwmDo6JSRyowbRyt0iFQSMcHDOTeX8jE26rrtTGBmuLYTEanoUF4R17/8PVlH/WN1tEhNYsZNo+mQobfNilQW7fd4iIh4qrC4lMmvLAy+4j4lMYG/XjeSfu018LFIVRQ8RETqqdTn+OWspSzZfhgAM/jzFUM5vVcbjysTiVwKHiIi9eCc47fvr+KTNfuCbf9+8UAuGtzRw6pEIp+Ch4hIPfzx43XM+r58gLDbxvTixjP1QmuRk1HwEBGpo79+uZnn5m4Kzl86rDP3XzDAw4pEooeCh4hIHby1aAd/+McPwfnxAzJ5bOJgEhI0QJhIbSh4iIjU0ker9vLAu+Wjko7u0Zpnrx5OcqL+KRWpLf1tERGphW82HmDqrKX4AoM9D+zYguk3jCQ1OdHbwkSijIKHiMhJrNh5mFteXURRqX9A4x5t0nnlptG0SNWopCJ1peAhIlKDjftzueHl8qHQO7RI5bXJp9OueROPKxOJTgoeIiLV2JGdz7UvLiA7rwiAlunJvDZ5NF1bp3tcmUj0UvAQEanC7sMF/OKv37EnpxCA9JREXr5hFH01FLpIgyh4iIhUsv9oIVdPX8DOQwUApCT5378yrFsrjysTiX4KHiIiFWTnFXHN9AVsOeB/6VtyovH8NSM4s09bjysTiQ0KHiIiATn5xVwzfQHr9+UCkJhgPP2L4YwbkOlxZSKxQ8FDRAQ4WljMdS9/z5o9RwD/m2afuHwIF5zawePKRGKLgoeIxL38ohImz1jE8h2Hg22PXjaYS4Z29rAqkdik4CEica2wuJRbX13M91uzg20PXTKIy0d29bAqkdil4CEicauwuJRbXl3E/I0Hgm2/+ckpXPujHt4VJRLjFDxEJC6VhY6vNpSHjn85rx+3jOnlYVUisU/BQ0TiTlWh4+4Jffnl+L4eViUSH5K8LkBEJJwKik68vHLPhH7cNUGhQyQcFDxEJG4UFJVy86sL+XrjwWDbvef1Y6rOdIiEjYKHiMSFgqJSJr+ykG82lYeOfzmvny6viISZgoeIxLyqQsd9P+7HnecqdIiEm4KHiMS03GMl3DRjId9vKR+n41fn92fKuD4eViUSvxQ8RCRm5eT7h0GvOCKpQoeItxQ8RCQmHcg9xrUvfs8PgXevADx44QBuG9vbw6pERMFDRGLO3pxCrp7+HZuy8oJtD10ySCOSikQABQ8RiSk7svO5evoCtmfnA5Bg8NjEIUwc0cXjykQEFDxEJIZszsrl6ukL2JNTCEBSgvHklUO5eHAnjysTkTIKHiISE9btPcrV0xdwIPcYAClJCUy7ejjjT2nvcWUiUpGCh4hEvcXbDnHTjIXkFBQDkJacyF+vG8lZfdt6XJmIVKbgISJR7Yt1+7n99cUUFvsAaN4kiZduHMWoHq09rkxEqqLgISJR672lO/nV2yso8TkA2jRNYcaNozmtS4bHlYlIdRQ8RCQqvTh/Cw99sCY436VVGq9NPp2ebZt6WJWInIyCh4hEFeccf/x4Hc/N3RRs69++Oa9OHk37FqkeViYitaHgISJRo6TUx2/eW8Wbi3YE20Z2b8WL148iIz3Zw8pEpLYUPEQkKhQWlzJ11lLmrNkXbBs/IJNnrhpOWkqih5WJSF0oeIhIxMvOK+LmVxayZHv5y94uG96FRy47jeTEBA8rE5G6UvAQkYi29UAeN7z8PVsP5gfbbh3TiwcvHICZeViZiNSHgoeIRKwl2w9x8yuLyM4rAsAM/u2igdx0Vk+PKxOR+lLwEJGI9NGqvdz1xlKOlfgHBmuSlMBTVw7jglM7eFyZiDSEgoeIRJyX5m/hodlrcP5xwWjdNIXp149keLdW3hYmIg2m4CEiEcPnc/x+9g+89PWWYFuPNunMuHE0PTQwmEhMUPAQkYiQd6yEu99cxicVHpcd3q0l068fReumKR5WJiKhpOAhIp7bdbiAyTMWsnbv0WDbBYM68OSVQ0lN1hgdIrFEwUNEPLV42yFue20RB3KLgm23nN2TBy48hcQEPS4rEmsUPETEM+8t3cn976ykqNT/5EpyovGHn53G5aO6elyZiDSWqB/yz8xmmJmr4WttDdteZWZfmVmOmeWa2SIzm2JmUX9cRCKZz+f448druefN5cHQ0So9mdcnn67QIRLjYumMx9fAxira91S1spk9C9wBFAKfAcXAeOAZYLyZTXLOlTZSrSJxK7+ohHveXMbHq8tvIu2b2YwXrx9FtzbpHlYmIuEQS8FjunNuRm1WNLPL8IeOvcAY59yGQHt74AvgUuBO4KnGKVUkPu3IzufW1xbzw54jwbZz+rfj6V8Mo3mq3i4rEg/i9ZLCg4Hp/WWhA8A5tw+4PTD7gC65iITOVxuy+Okz848LHZPP6smL149S6BCJI7F0xqNWzKwLMAIoAt6uvNw5N8/MdgGdgTOAb8JboUhscc7x/JebeeyjtfgCI5GmJCbwu0sGceXobt4WJyJhF0vBY5yZDQaaAfuA+cAnzjlfpfWGBaarnXMF1exrIf7gMQwFD5F6yztWwq/fWcHsleW3WrVv0YRp14zQ8OcicSqWgsd1VbStMbMrnXMrK7SVvdZyWw372l5pXRGpo60H8rjttcWs21c+KNioHq149urhZDZP9bAyEfFSLASPZcBi/E+mbANaAMOBPwBDgE/NbLhzbldg/WaBaV4N+8wNTJuHvlyR2PfFuv3cNWspRwpLgm3X/ag7v71oIClJunVKJJ5FffBwzj1ZqSkPmG1mnwDz8N+n8SD+p1QAyoZCdPX9mWZ2K3ArQLduukYtUqbU53jq0/U8/cXG4JtlU5IS+P3PTuXykRqfQ0RiIHhUxzlXZGYPA/8D/KTCorLzvs1O3CqobNnRqhY6514AXgAYOXJkvQOMSCzZf7SQu2Yt49vNB4NtHTNS+a9rRjCka0sPKxORSBKzwSOgbNTSzhXatgam3WvYruxXs601rCMiAd9uOsjUN5aSdfRYsO3MPm146sphtG3WxMPKRCTSxHrwaBOY5lZoWxqYDjKztGqebBlVaV0RqYLP55g2bxOPz1kXfFTWDKae25ep4/vqJW8icoJYDx6XB6YLyxqcczvMbAn+G1AnAa9W3MDMxgJd8I9q+m2Y6hSJOofyirjnrWXMXZcVbGvTNIUnrxzK2X3beViZiESyqL693MyGmtnFZpZYqT3JzO4Fpgaa/lxp04cD00fNrE+F7TKB5wKzj1QxBoiIAIu2ZnPRX746LnSM6tGK2VPPVugQkRpF+xmPHsB7QLaZrQd24n8E9jSgE+DDPyz6xxU3cs69Y2bT8A+PvtLMPqX8JXEtgPfxvyxORCooKfXx9OcbefrzDcFLKwD/Z2xv7vtxP5ISo/p3GREJg2gPHsvxv8htNP6bRYfhf0x2J/Ay8KxzbnFVGzrn7jCz+cAUYCyQiP9m1JeAaTrbIXK8nYfyufuNZSzadijYlpGWzBOXD2H8Ke09rExEoklUBw/n3Bbg7gZsPxOYGbqKRGLT/y7fzb++t5KjFQYEO71na/58xVA6tUzzsDIRiTZRHTxEpHHlHSvh//59NW8v3hlsS0ww7pnQl9vP6aOnVkSkzhQ8RKRKK3Ye5q43lrHlQPnbBbq2TuOpK4fpBW8iUm8KHiJynOJSH898vpFnvthIaYU7SC8Z2omHfnYqLVKTPaxORKKdgoeIBG3Yd5R731rOyl05wbamKYk89LNT+fnwLh5WJiKxQsFDRCj1OV6cv5k/zVlPUUn5A12jerTiT5OG0L1NUw+rE5FYouAhEue2H8znvreX8/3W7GBbSmIC953fj8ln9dINpCISUgoeInHKOcfM77fzh9k/kF9UGmw/tXMLnrh8KP3aN/ewOhGJVQoeInFo64E8HvjbCr7bXH6WIzHBmDKuD788tw/JGoFURBqJgodIHCkp9fHi/C088cl6jlW4l6N3u6Y8cflQhnRt6WF1IhIPFDxE4sSa3Ue4/90Vxz2xkphg3Hx2T+6Z0I/U5MQathYRCQ0FD5EYV1hcytOfb+D5eZspqTAux8COLXhs4mBO7ZzhYXUiEm8UPERi2HebD/Kb91ayKat89NGUpATuGt+XW8f00r0cIhJ2Ch4iMSjr6DH+8x8/8N7SXce1j+7RmocvO43e7Zp5VJmIxDsFD5EYUupzzFywjcc+Xnfcm2SbNUni/gsHcPXobiRoXA4R8ZCCh0iMWLHzML95b9VxN48CXDy4I7+9aCAdMlI9qkxEpJyCh0iUy8kv5k9z1vH6gm248ntH6dEmnd9dcipj+rXzrjgRkUoUPESiVEmpjzcW7uDxOes4lF8cbE9JSuDOcX24dUwvPSIrIhFHwUMkCn2z8QC/+2ANa/cePa79nP7t+H//PEgvdRORiKXgIRJFth3M4w+zf2DOmn3HtXdplcZvLzqF8wd1wEw3j4pI5FLwEIkCRwuLeeaLjbw8fytFpeVDnaenJDJlXB8mn9VTl1VEJCooeIhEsKISH28s3M5fPtvAgdyi45b9fHhn7r9gAO1b6GkVEYkeCh4iEcjnc8xeuYc/zVnHtoP5xy0b1q0l//HTQQzVC91EJAopeIhEmK83HuCRD9eeMB5Hp4xUfn3BAC4Z2kn3cYhI1FLwEIkQq3fn8OhH6/hyfdZx7RlpyUwZ15vrftRD93GISNRT8BDx2Lq9R3nqs/X8Y+Xe49qbJCVw45k9uX1sbzLSkz2qTkQktBQ8RDyycf9Rnvx0A7NX7jluxNEEg0kjunL3eX3pmJHmXYEiIo1AwUMkzDZl5fKXzzbw9+W7jwscAOcNbM+vzu9Pv/bNvSlORKSRKXiIhMmmrFye/Xwj7y/bha9S4Bg/IJO7J/TjtC4Z3hQnIhImCh4ijWzlzhyem7uRj1bvPeEMx7j+7bh7Qj+G6NFYEYkTCh4ijcA5x7ebDvLc3E3M33jghOVj+rXj7gl9Gd6tlQfViYh4R8FDJIR8PscnP+zjubmbWL7j8AnLzx2QyZRxvRnRvbUH1YmIeE/BQyQE8otK+NuSXbz89RY2ZeUdtyzB4OLBnbj9nN6c0rGFRxWKiEQGBQ+RBth9uIBXv93GrO+3k1NQfNyylKQEJo3owm1jetOtTbpHFYqIRBYFD5F6WLL9EC/N38KHq/ZSWukRlWZNkrj6jG5MPrMnmXqBm4jIcRQ8RGqpsLiUD1bs4fXvtrGsivs3urVO58YzezBxRBeap2qkURGRqih4iJzExv25zFywnXeX7DzhcgrAGb1ac9OZPRl/SnsSE/TyNhGRmih4iFThWEkpH6/ex39/t40FW7JPWJ6SmMA/D+3EjWf2YFAnDfolIlJbCh4iFfyw5wjvLt7Je0t3cTCv6ITlXVuncdXo7kwa2YW2zZp4UKGISHRT8JC4dzD3GH9fvpt3Fu9k9e4jJyxPTDAmnJLJ1ad356w+bUnQ5RQRkXpT8JC4VFTi44t1+3l38U4+X7ufksovTwE6ZqRy5ahuXDGqKx0y9HSKiEgoKHhI3Cgp9fHd5mw+WLGbD1ftrfJG0ZSkBH48sD0TR3ThrD5tSUpM8KBSEZHYpeAhMc3ncyzcms0HK/bw4ao9HMg98b4NgOHdWjJxRFcuGtyRjDQ9Cisi0lgUPCTmlJT6WLj1EHPW7OUfK/ew78ixKtfr3DKNnw3rxGXDu9CrXbMwVykiEp8UPCQm5BeV8OX6LOas2cfna/dzOP/EyygAmc2b8JPTOvLTIZ0Y1rWlbhQVEQkzBQ+JWntzCpm7bj+frNnHVxsPUFTiq3K91k1TuPDUDlw8uBOje7bWIF8iIh5S8JCoUVhcyqKth/hyQxbz1mWxbt/Ratft0CKVCQMz+fHADvxT7za6SVREJEIoeEjEcs6xKSuXrzYc4Mv1WXy7+SCFxVWf1QDo37455w1sz3kD23Na5wxdRhERiUAKHhIxnHNs2J/Lgs0H+W5zNgu2HKz2KRTwD1s+skcrzh2QyXkD29O9TdMwVisiIvWh4CGeKSrxsXbvEZZsO8T3W7NZsDm7ymHKK+rZtilj+rZlbP92nNGrDekp6sIiItEk7v/VNrOrgNuBwUAisBZ4GZjYcON0AAAMo0lEQVTmnKv+vL7U2Z6cApZuP8zS7YdYuv0wK3flcKyaG0LLZKQlc3rP1pzdrx1j+7ajW5v0MFUrIiKNIa6Dh5k9C9wBFAKfAcXAeOAZYLyZTXLOlXpYYlRyzrEju4A1e3JYs/sIq3cfYdXunGrH06ioVXoyo3u25oxebTijVxv6t2+uezVERGJI3AYPM7sMf+jYC4xxzm0ItLcHvgAuBe4EnvKsyCiQU1DMxv25bNqfyw97/SHjh91HOHqspFbbd22dxrCurRjerSVn9G5Dv0wFDRGRWBa3wQN4MDC9vyx0ADjn9pnZ7cBc4AEzezreL7mUlPrYk1PIlgN5/pCR5f/auD+PA7knP4tRJj0lkSFdWjKsW0uGdWvF0K4taddcr5YXEYkncRk8zKwLMAIoAt6uvNw5N8/MdgGdgTOAb8JbYXgdKyll/5Fj7DtSyI5D+ezILmBHdn7w+71HCimt4u2tNWmZnsygTi0Y2LEFAzu1YGDHDHq3a6rxNERE4lxcBg9gWGC62jlXUM06C/EHj2FEWfAoKfWRU1DM4YJiDucXc6SgmMMFRRzKKyYr1x8wso76p/uPHqt2ePHaSElKoFfbpvTObEa/zOb+sNGpBR0zUjHTJRMRETlevAaPnoHpthrW2V5p3UZVUurjxflbKHWO0lLnn/ocJT6HLzAt9TmKS30UFJWSX1RKQXGp//viEgqK/N8fLSyp9f0VdZHZvAldW6fTp10z+mQ2o3dmU/q0a07nVmkaglxERGotXoNH2atI82pYJzcwbd7ItQDggIc/XBuOH3WCxASjbbMU2rdIpUurNLq2SqdLqzS6tE4Pfp+anOhJbSIiElviNXiU/YpetxsXyjY2uxW4FaBbt24hKSgxhJclzPzjX7RMSyYjPYWWacm0TE8mIy2Zts2a0L5FEzKbp9KueRPat0ilddMUnbUQEZGwiNfgUfZ2sWY1rFO27IQ3kTnnXgBeABg5cmS9wktlCQnGLWf3JDEhgcQE/FMzkhKNBDOSEozEBP98WnIi6SlJpKckkpqcSHpKYvD75qlJtEhN1iOpIiISkeI1eGwNTLvXsE7XSus2ut9cNDBcP0pERMQT8fps49LAdJCZpVWzzqhK64qIiEgDxWXwcM7tAJYAKcCkysvNbCzQBf+opt+GtzoREZHYFZfBI+DhwPRRM+tT1mhmmcBzgdlH4n3UUhERkVCK13s8cM69Y2bT8L+ZdqWZfUr5S+JaAO/jf1mciIiIhEjcBg8A59wdZjYfmAKMBRKBtcBLwDSd7RAREQmtuA4eAM65mcBMr+sQERGJB/F8j4eIiIiEmYKHiIiIhI2Ch4iIiISNgoeIiIiEjYKHiIiIhI2Ch4iIiISNgoeIiIiEjYKHiIiIhI2Ch4iIiISNgoeIiIiEjYKHiIiIhI0557yuIaqZWRawLYS7bAscCOH+4o2OX8Po+DWMjl/D6Rg2TLiOX3fnXLv6bKjgEWHMbJFzbqTXdUQrHb+G0fFrGB2/htMxbJhoOH661CIiIiJho+AhIiIiYaPgEXle8LqAKKfj1zA6fg2j49dwOoYNE/HHT/d4iIiISNjojIeIiIiEjYJHIzKzq8zsKzPLMbNcM1tkZlPMrF7HPdT7i3Sh+rxmNsPMXA1faxvrM3jBzPqb2V1m9rqZrTUzX+BzTmzgfuOi/4X6+MVh/0s2s/Fm9riZfWdme8ysyMx2mdk7ZnZOA/Yd832wMY5fpPXBpHD+sHhiZs8CdwCFwGdAMTAeeAYYb2aTnHOlXu0v0jXS5/0a2FhF+56G1BqBbgfuCuUO46z/hfz4BcRL/xsLfBL4fi+wGMgDBgKXAZeZ2UPOuX+vy07jqA82yvELiIw+6JzTV4i/8HcOF/jD7FuhvT2wJrDsLq/2F+lfjXD8ZgS2ucHrzxam43cz8BhwOdAbmBv4/BMj4c8j0r8a4fjFW/87F3gHOLuKZVcAJYHjMa4O+4ybPthIxy+i+qDnBcTiF7Ao8Id8XRXLxlb4C5Tgxf4i/asRjl9E/aXz4Hg29D/OuOp/jXD84rr/VXE8pgeOx4t12Cau+2AIjl9E9cGYuS4WKcysCzACKALerrzcOTcP2AV0AM4I9/4iXbx93kinPw9pBEsD0y61WVl98AR1On6RSPd4hN6wwHS1c66gmnUWAp0D634T5v1Fusb8vOPMbDDQDNgHzAc+cc756ltsHIi3/teY1P/8+gamtb2vQH3weHU9fhVFRB9U8Ai9noFpTS+O215p3XDuL9I15ue9roq2NWZ2pXNuZR33FS/irf81prjvf2bWAbghMPtuLTdTHwyo5/GrKCL6oC61hF6zwDSvhnVyA9PmHuwv0jXG510GTAUGBfbfCbgYWI7/TvFPzaxz3UuNC/HW/xqD+h9gZknA60AG8Jlz7n9ruan6IA06fhBhfVBnPELPAtNQDQkb6v1FupB/Xufck5Wa8oDZZvYJMA//deEHgTtD9TNjSLz1v5BT/wv6L/yPv+4ArqnDduqDfvU9fhHXB3XGI/SOBqbNalinbNnRGtZprP1FurB9XudcEfBwYPYnDdlXDIu3/hc28dT/zOwpYDL+cSnGO+f21mHzuO+DDTx+1fKqDyp4hN7WwLR7Det0rbRuOPcX6bYGpuH6vGUj9sX8qe562hqYxkv/C7eY739m9jj+0/xZ+P/T3FDHXWwNTOOyD4bg+J1M2PuggkfolT3qNMjM0qpZZ1SldcO5v0gX7s/bJjDNrXGt+BVv/S/cYrr/mdljwL3AQeA859yaeuwmbvtgiI7fyYS9Dyp4hJhzbgewBEgBJlVebmZj8T9/vRf4Ntz7i3QefN7LA9OFIdhXzIm3/ueBmO1/ZvYI8CvgEP7/NJfXZz/x2gdDdfxqIfx90OsRzGLxC5hI+Uh6fSq0ZwKrqWJ4X/zX2dYCD4dif9H8FcrjBwzFf/d2YqX2JPy/SZQG9ne+15+7EY/nXE4y8qb6X+Mcv3jtf8BDgc91CBhRy23UBxvh+EViH9RTLY3AOfeOmU3D/7KplWb2KeUvNGoBvI//xUYVdQT6B6ah2F/UCvHx6wG8B2Sb2XpgJ/5H7k7D/0iZD7jfOfdx43ya8DOz4cBzFZoGBqb/aWb3lTU65yqO8qj+FxDi49eD+Ot//wz8NjC7EfilmVW16lrn3CMV5tUHaZTj14MI64MKHo3EOXeHmc0HpuB/l0Ai/jT6EjDN1XGkuFDvL9KF8PMuB54CRuO/OW0Y/nS/E3gZeNY5tzjE5XutBXB6Fe19q2irlTjrf6E8fvHY/1pX+H5k4Ksq84BHqll2gjjqg6E+fhHXBy1wykVERESk0enmUhEREQkbBQ8REREJGwUPERERCRsFDxEREQkbBQ8REREJGwUPERERCRsFDxEREQkbBQ8RCRkzc/X4mhHY9pzA/FxvP4WINCaNXCoiofRKFW0dgPOBPOCdKpbPb9SKRCSiaORSEWlUZnYO8AWwzTnXo4b10oFuQL5zbnt4qhORcNMZDxGJCM65fPzv3hCRGKZ7PEQkIlR3j4eZ9Qi0bzWzBDO718xWm1mBme00sycCZ0sws1Zm9mRg3WNmtsHM7q3hZ5qZXWlmc8zsQGCb7Wb2VzPr0agfWCROKXiISDSZCfwO2ALMAZoC9wDvmllrYAFwBbAQ/70jPYDHzexfK+/IzJLx33MyCzgLWAP8Hf+9KDcDS8ysujeDikg96VKLiESL7kAh0M85txvAzLoCS4EL8L8mfDlwrXOuMLD8IuAD4AEzezJwOafMQ8DPgS+Bq51zO8sWmNmdwNPAG2Y2wDlX0uifTiRO6IyHiESTqWWhA8A5twN4PTDbHbi9LHQEls8GVgDNgeDZi8DZkalALjCpYugIbPcMMBvoDVzYOB9FJD4peIhItCgGPq+ifWNgusg5d6CK5RsC004V2sYBacA859z+an7evMD0R3UtVESqp0stIhIt9lZzySM3MN1ZxbKKy1MrtPUKTC8ys5ONKdCulvWJSC0oeIhItPA1cHlFiYHpOuC7k6y7oA77FZGTUPAQkXi0IzBd6Zy7wctCROKN7vEQkXj0Kf57RiaYWUuvixGJJwoeIhJ3nHP7gGeBlsDfzWxA5XUCg5HdbGbtw16gSAzTpRYRiVe/xv+ky+XAKjNbhn9gslSgK3AKkBKY7vOqSJFYozMeIhKXnHPFzrkrgEvwDzLWKfD9P+H/pWwmcCmwybMiRWKQ3k4rIiIiYaMzHiIiIhI2Ch4iIiISNgoeIiIiEjYKHiIiIhI2Ch4iIiISNgoeIiIiEjYKHiIiIhI2Ch4iIiISNgoeIiIiEjYKHiIiIhI2/x9E3srRbXxjngAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"deltam=0.25-0.05\n",
"dmdt=modsecantdmdtguess\n",
"s=deltam/dmdt\n",
"t=np.linspace(0,s,1000)\n",
"dt=t[1]-t[0]\n",
"N=int(s/dt)\n",
"c=0.18e-3\n",
"u=250\n",
"\n",
"num_sol=np.zeros([N,3])\n",
"num_sol[0,0]=y0\n",
"num_sol[0,1]=v0\n",
"num_sol[0,2]=m0\n",
" \n",
"#The rocket function is integrated using our guessed dmdt from the desired height \n",
"rhs=lambda state: rocket(state,dmdt,u,c)\n",
"for i in range(N-1):\n",
" num_sol[i+1] = rk2_step(num_sol[i],rhs,dt)\n",
" \n",
"y300=num_sol[:,0]\n",
"\n",
"\n",
"plt.figure(figsize=(8,8));\n",
"plt.plot(t[2:],y300);\n",
"plt.plot(t[-1],y300[-1],'*',markersize=20,label='Detonation Point');\n",
"plt.ylabel('Height');\n",
"plt.xlabel('Time');\n",
"plt.title('Height vs Time to Detonation Point');\n",
"plt.legend(loc='best');\n"
]
},
{
"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
}