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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": 1,
"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": 2,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, without drag or gravity, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" \n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt) -dmdt]^T\n",
" '''\n",
" \n",
" #dstate = np.zeros(np.shape(state))\n",
" dstate = np.array([state[1], ((u/state[2]*dmdt)), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def rk2_step(state, rhs, dt):\n",
" '''Update a state to the next time increment using modified Euler's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" \n",
" mid_state = state + rhs(state) * dt*0.5 \n",
" next_state = state + rhs(mid_state)*dt\n",
" \n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def heun_step(state,rhs,dt,etol=0.000001,maxiters = 100):\n",
" '''Update a state to the next time increment using the implicit Heun's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state + rhs(state)*dt\n",
" ################### New iterative correction #########################\n",
" for n in range(0,maxiters):\n",
" next_state_old = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e=np.sum(np.abs(next_state-next_state_old)/np.abs(next_state+eps))\n",
" if e<etol:\n",
" break\n",
" ############### end of iterative correction #########################\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"y0 = 0\n",
"v0 = 0\n",
"m0 = 0.25\n",
"mf = 0.05 #estimated final mass\n",
"dmdt = 0.05\n",
"\n",
"T = (m0-mf)/dmdt\n",
"t = np.linspace(0,T,1000)\n",
"dt = t[1]-t[0]\n",
"N = int(T/dt) #tried to use round and got an error, why?\n",
"mf2 = np.linspace(0.25,0.05,N)\n",
"\n",
"#initialize solution array\n",
"num_heun = np.zeros([N,3])\n",
"num_rk2 = np.zeros([N,3])\n",
"\n",
"#Set intial conditions\n",
"num_heun[0,0] = y0\n",
"num_heun[0,1] = v0\n",
"num_heun[0,2] = m0\n",
"num_rk2[0,0] = y0\n",
"num_rk2[0,1] = v0\n",
"num_rk2[0,2] = m0\n",
"\n",
"dm = mf2/m0\n",
"vf = -250*np.log(dm)\n",
"\n",
"for i in range(N-1):\n",
" num_heun[i+1] = heun_step(num_heun[i], simplerocket, dt)\n",
"for i in range(N-1):\n",
" num_rk2[i+1] = rk2_step(num_rk2[i], simplerocket, dt)\n",
" \n",
"plt.figure(figsize=(10,10))\n",
"plt.plot(num_heun[:,2]/.25,num_heun[:,1],'b',label='Heuns Method')\n",
"plt.plot(num_rk2[:,2]/.25,num_rk2[:,1],'r.',label='RK Method')\n",
"plt.plot(dm,vf,'m--', label='Tsiokolvskys Equation')\n",
"plt.grid(True)\n",
"plt.xlabel('mf/mo')\n",
"plt.ylabel('Velocity (m/s)')\n",
"plt.title('Convergence of Heun and RK Methods to Tsiokolvsky')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1,0.5));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. You should have a converged solution for integrating `simplerocket`. Now, create a more relastic function, `rocket` that incorporates gravity and drag and returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (1). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \n",
"\\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt}-g-\\frac{c}{m}v^2 \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `rocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s, . \n",
"\n",
"Compare solutions between the `simplerocket` and `rocket` integration, what is the height reached when the mass reaches $m_{f} = 0.05~kg?$\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"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",
" g=9.81\n",
" #dstate = np.zeros(np.shape(state))\n",
" dstate = np.array([state[1], ((u/state[2])*dmdt - g - (c/(state[2]))*state[1]**2),-dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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cxHjeU3R/mVK6vFqBlNKD5AMd0Dvr9hN0tSVS6TtFdyRdLf6XvJGu59K/u9iebCWl9D/kA58AW93TGhGzyVdgQb6CaJtteEppPvXvOy/9Bz5Qp0yf6cfb2XK9Po+K+62PLnrPTyndXVkmpfQQXf9fe9PVHketce5CTkafS/5ffF5K6f9qFC/tP62g9vbgs+Skt7x8Q8V+1n8Wva+KKm3WkL97qf2KSyuG9cr8jogRwGXkq4I2AyenlM6tEfPtwJ+K3rk1Rln6/O8ppRt7EpukoaXp51D3VEQE+TIqgJ9X27EASLn18FLLss+uM8p6DeaUEoiR5Euby8d/LfkSTKj+p/188lkF2PZP4Fl0teh8ddlO7TYvup4/PLtOnL+sM+xg8nMyoWtnq5p6j2k6lryD3Qn8qU6s48iXcteL90nymeBtFH+upZ2FykZEji17f0mdWKt5ftH9AzCiTvylJCjIZ+madTD5aD/kS0irKv5Y7yl6n9ON8bdLb6+nPXVvSumuagNSSo+RrwSBbdedphWNCf2waEBobVmjMol8aSPky8DraWabUhlj+Tr00zr1/6vBtLvjLLoOrKwi3/d9ITlR/QhwTI0DX5UeJ58dAzgtIt5Tr3BPFQc3SjvhbwSI3KBWKblu2Lp3RIwFnln0/q7Bun1rUe5pNXb4u+PalFKtA8rlB6wq14/Sf9hdKaV6z6QvbX8m0JVAl9eH+tv6eutXKTH4UEQc391GqHrBQNjOlubRqyPi7cV61lPly67m9wZ+TP6PhjrfO3LjjX8kH7RZQr49469NTP9/UkpPVCtQ/CZL260jq5yAqKf0e53I1gfISkoHspaQDwKUK83v9xQNho3oxnRLxpH3FV9HvqrhxJTStxvU+VbRfUlEbNVoY0RMIV9FA/kkgyQ1rZmE+rGy9z153uKOZfWrtv5dprQjNDGqtLBdeLBO/fI/j2p/jKUz2y+PbVuCLSXZd1c5Y1O+Q/5X6p9BLLX4OaVOnLWexwr5Es+SqmcYYcsR7lo7eqV4S5dn1Yv3FQ3ifbj8bH0VpXleOb9LLTivSiktrFO/mlL8L6d+7A+V1ak3vyvNLHvf7Do5s26p3vGWlFLUe5EbIaqlt9fTnqr3W4Xa605DRYuzvyInFK8C9qoznp1qfF7SzDalctyzyt7XfHpASmkp+bLPvnYW+b7YZqwiH/BaVvR/MSLe1idRdSnthB8XEZPIVwONAG5OKf29drUt9irKQ248qN66XTprO4ytr7RqRc11oyJZqVw/StuLZrcv5XWga/1akVJaRm231xk2j/wfMYV8cPbhiPhZRJxRnAHva/11O1vuG+R5OIJ8hdAjRevT/x4Rx3Qz0SwpfYdO6v+HryZfzl9ep9JocjK9F3k7c1S1q2lKinh3K3qbnedj6MaTAYrf6y1F71YnJyJiFPkecchXnqSK6p8hH0idQD6g8HBE/HfkFu+PLE7ANPJD8tVvq8i3mv2sQXmAH5Avkx9eGXPRP4LcSNw2Vz9KUj3NJNTlSdABPZjWDmXv1zQou7pGvXLNXBoI+axlpdKZ53HkRoNywXxU+uUVZco12iGvZnStAbWOGpfFVtLobFOt+dmb8bY6v0sHRFZXFmxCr87vKlpZJ2utj/1JX8+37urJb7WR8+m6peC75FscSo0d7VC8TiuGNzoz10yclTGWP+6o0TrUaHiz/r3swMpo8nb5P8g77jsAP6k8+1JLSmkB+UqQR4qPvh4RfXa5bcrPyr6NfPXQq8mNGkLXbTqNtLJuQ8/X71bX4dL2otX/vNL61fK6lVJaBBxO/n2sJZ9RfCl5nbkuIu6OiL685aPfb2dTSuvIV9CdR070xpAPNn2CfFvM0iLZ605iXfoOTxRXcdXT6Ht30LXuP0Hj+did7VIz+1u1lB8gK/9t/gtdJ1C22ZcqDjAeQW6YdjX5u/0LcDa5RfqFEXFyZb0KpasPN9J1y1ldxZU7Pyh651YMLvX/PKX0aDPjk6SSZhLqa8mNYkG+b6dV5RvtRs/cLB/eSiJWV0rpHvJGG7Y+SvnysmlXO0JZ/se0Q6OziMVrVothlifR2zxPtUKt+VmK95EmY42U0pwW462lJztIpfjP60b8l7QQGzS/Tvb6+tgHemM9rTyjUEsrZ256RXEAbG7Re25KaW5K6ZcppXtSSo+mlNaklNbQtwcLyud1d7ZrvSKl9GRK6c6U0pnkxzpBPst0TjfGcSu59fwV5P+ESyLixN6OtUxpJ/wMcivjnXTd595I+fw+rhvbhUW9GH93lLYXrf7nrakyvFH9baSUFqaU5pLP1B8FfJB8i8NG8lVEl/bhJf8DYjubUno8pXQG+bL9Q4FTycnXavIBurOBb3ZjlKXvMDYiGu1rNfrea8kHQdaTD45cGRETa5SF1rdL3Z3vl5F/v6PYuv2V0n7VTSmlW7apBaSUlqSU3kZuAf6Z5AYqf0G+vWwmcHFEfLTOtF9Pbs1/Mvn2j6c1GfPFRffgiDgCICIOJ7d8Dl7uLakFDRPqYoe01CDPMcV9PK1YRddRxAMblD2o6D6WUlrV4vQaKe3UPT8iSvdMl47SX5uqNCDC1pdoH9pHcZUsLnu/X61CxZmoWpfil+LdOSJ2763Auqk0H3eMiD27WbcU/2G9GE+5RWXvm10nF9Ur1E/0xnq6vuiOaVBueovj7w0H0JUs/2edcgf3YQyLyt7XvIInInal9bOrzbqArkZ33lQ0CNiU4v7VF5N3xDuA/4yIf6lfq2WlnfC9iv7fptyIWDMW0XW/aV9tF3rToqLb7PalvE75+wll/1PVPKWZYFJKG1JKf0opnZ9Segl5GZTaN/hEE4lfKxaVve/329mUUmdK6e8ppa+nlF5LfszVr4rBc7vxP7ao6A6jTvsNEbEDXY13LapVLqX0G5pMqot7o0uXkTc7z9ex9e1TDaXcYOP8ovckgMgNg5buqa52pV/lODamlK5NKX0hpfRS8m0OpfYGziouH69mEbkRt1JS/dtmkuriVr7SZfBzi+5biu4D5MYdJalbmv3z/FzRDeCrTd7fQkRs2ZAX99D8seg9vlYjFEXjMccXvX+sVqaX/IB8dL4DeG3RIMU/F8Nq/QlcTT56Cl0b4L5yM11Hi19ap9zL6gz7Tdn7vo63livL3r+5m3VLf2xHt5CMN+MWuu5rrXlGLiIOIV9GDLkF5f6uN9bTpUV3Sq2dtiJh64vl0qzyHa2ql3MXjVO9vNqwXlK+Dp1Qp9wr6gzrFcU29qyitwOod3anWv1ryZfMryPfS/jjiHherwaZp7OErp1waP5yb1JKK8ntAgC8sQcNbJWuuurrBrpK24v9IqLegZ3S/aYr6Lovtbw+9MH6lfJTJr5e9E6iq0HOZpXa1ag3Hwf0drY4qP8fZR81e+tb+Xeod8XHK+jaF6v7vask1b+pc6a6NK4X12pkrfj9lNara1P1JzE0UtpfOjoiZpDPVI8iH/iqd6CzqqKtgFIL/eOAPeqUXURXUr0zTSbVdDVO9rrigMbri/7/l5p70oAkbaWphDqldBVdjwZ5IfDtOkcNieyN5MvFy5U2YrvS9aiISv9O1596dy6v6paUWxcuPXroDcBryJevbqTrHpvKOqvo+g5zG10WGRE7FmemWolvI/D9ovd1EbHNI4WKFnI/Vmccd9D1Hc+KiGc1iHdqg8vIui3l1p1LR/fPjIh/qjP9ysuHv0pODIcD3yuSo5q6c0auiG0zXS2PvyIinl9Zpjjw8+Widz1NtETcbr20npYe0xZ03edaXmc4+dmy7VTevsM2B5aKA39fpqKl/95U7ICWdihfFRHbPJmgOLPYreS2B/H8nq7W+F8X+dF53al/NXkH+0ny2f+fR8RR9Wu15LXks6pPITcu1B2fL7r7AefXO8AbER01rqoq3SPZ11dYXEpu5AjgS9XuwY2IF9F10Ofb5ffbppSup6vRqI8VB34r68+hfqLaKAEszZ/NdL/hvIbzcSBsZ7sxj6DrO9dV3FpWat36g9V+i8Xy/GTRezdbH2iqNd7ypPoIclJd7Sq10n/ARGo/tu/DdDWE1ur+1o/JB+GCnJiWrvSreeVJN+f3YzVLUTOpbnRV0vfIv8vJ5O9darTwOzVrSFI9qckHVpNbL72SrofeLyLfh3UY+Z69qcX79wM3lcpVjCPIyVVpHN8gX5I6ifwoiG+WDftljThKw+fWiXVOWblZdcq9sqzcwqL78wbzYSdyK5uJfAT2W+TnLU4j/3HtS965uZi8c/LKivpzq82bGtParRhHIv+pnEq+/GwK+Sz+bcXnjxdl5lUZxwxgeTH8SXIjTkeS/3gmk3doX08+krwOmF1Rf15peTeIdX5R7pIqw/Ys4kzke8E+VbbcdyW3WH0e+Q+4su47ypbR3cDbyTvSE4q6zwI+QE4Ab252fS4b/2RyC76JfLnrh8iXQU4u4vp92fQ/1N3v3o04ytfZmut2s+V7up4W4/hjUX8d8M5ifdyZ/Dznq8k7dPfXWe6XFMPmN/gui2qtv03Mh9K83wD8G/nSysnk9h7+uxh2KzV+czS/raj5OyBv+x4thq8s5tUM8u/0BPJj+h6nzu+0ie85qyzOuvXJj94plb2ozjyr+ZsmH6DYWPadZrcQc1PxNlgnqv6myNur0vivKubz7sV6vwf5aqOzi/F8pUr9X9K1TXkm+T7S4cUrqsyrur9t6v8WP1I2fD55uzKZvJ05k7xNTMVvaWKV+i8oq38nOfmeUnzPd5Nvp7q3rMycivqd5P/u08gJ2FTy7/hw8na3s6j3kxaW0xl0/be8irxNL83HYWXlerydbSG2eTTx2y7K3gT8jZxgPpv83zKJ/P/4wSLmRP4tD6uou6IY9t4q4z20mDep+P5zyQcfppLPTN9F1zb6hVXqv7cYvqLGerGuGH49MKFKmZ+UzYNLiuU/iXwbzAVly/6qyu9V1L+lGH5eg/n3/aLc4rJxvqlO+dXk/5B3AU8n/y/tTN4P/Az5CpIE/Lqi3uyy7/PUimGz6NpuPAwc3CDmH5WNKwG/7431zpcvX0Pz1b3C+TLAz5F3pFOD1xqqJ3gTig1pvbq/A3asEUPDpIPmd5JH0bWTW3q9uon5sCv5cqpG8yABL62oO7c0rMl5/ny6drgqX+vILWMuLvo/VmMcB5CT70axdgKHVNSdRw8T6mL4ocB9DaZ/U426pzS5zt3Q0o8g71zc32Dc51G2o92d795kDOXrbM11uzvle7KeFvUPoitRrHytJ1/VUfO7s30S6gPILVTX+l7fB95a6m8wH+ttK+r+Dsg74avqzKvje/g9Z5WNr2F94LdF2SeB3Wusr41+068hn7VMxXpQdwe1Sv2m462zTlT9TZFbCf96k+v2+VXqv7BO+TlV5lXVOKp8121+i+QDyV9sEONi4MA6438PXYlK5WsJOSndJv6K2Oq9bgSmtbCcdqHrYGnla15F2R5tZ1uIbV7ZeGv+touyNzWIK5ET4kOq1K2ZUBfDj6crIa/22gC8tUbdmgl1Mbw8qb6OiqSafKDo1w2+1x+BSTXG32xC/S8V41wLjK9Tvt78KL1uZdttV82Euhg+iyaTauBFFdN7S2+sd758+Rqar241QJJy4xFnkM9ufZS8s/EAeYdxHTlh+jlwOjAjpTSvyjhWkP/830S+R/Zh8tHIh4v+NwLHpr5rjKw8lifJRylLVpHjb1RvKfks0AlF/fvI82AD+d7Tq8hHuvdNKTUcX4NpXUluffI75Hm9oej+J/CMlNIvadBCaMqXfj+NfA/zL8g7BhvIO9tLyFcNvJu8zJp5Fmwr3+MmcvLzPvLZiEfJZ8AeJJ9d/jTwuhp1LyKfzfgM+f7Jx8g7+qvJBwouIZ9Ra+nS1JTSzeQzER8l75SsJM+fJeT5/OyU0gdTSqmV8bdLT9fTlFt/nk3XurexqHc58E8ppaq3RmxPxbpdevxKKcaHyQfl3phyo0KNHlnTG3FcAzyVfJXN/eR5/CA5oT8ypfSLvo6hwr8V3ZHks4HdVizfk8k7m5PIjSB167aKvpJy41rvIC/70jOEV5P/Sx4j/47PI1/B8sEq9X9N3qH+X3JDTK3cO9psrCml9F7yVRPfp2v9KN0PfhZwUEqp5vOCU0pfKur/nHwA6czK2sIAACAASURBVEngHnKifjhb3/5Q6QjyOvC/5DOiq8i/k+Xk/9y3kX/Py1v4bsvIZ/i/Rz4osKFO2f68nT2RfAb/x+RE7jG61qU/kpfRU1r5fyx++/uTb1W4jZxsriOf7f46edm31LJ02vry79lUXP6dcqOyLyL/t5bW9Y3k/98ryb/v56Z8C1xP/JqtGzT7WTHtWkpXlv03+UqqleT5/RD5YODpwOEp3+PftNS9y7//j7zuQU7wu3vriSRtEQMsR1CF4p7n0p/hK1NKP2lnPJIkSf1dRCwgN4T37ZRSo+deS1JNffGIDG1fx5e9v6FtUUiSJA0AEfEculqV99nTknrEhLqfi4hJdYZNITfwBXBdcbmTJEmSantP0b01pdSXj2iVNARs8wgP9TufiYiZ5Ge1lu4fngQ8j/zIrNIzGj/envAkSZL6t+KxdePJ7cmUHjX3ufZFJGmwMKHu/wJ4cfGqJgEfKBrZkSRJUpmIOBL4c8XHf2I7P/Nc0uBkQt3/XUButfgY8tnoKeQWrh8kP37sgpTSP9oXniRJ0oCQyC3t/xz4eEqpz58CIWnws5XvXrDzzjunWbNm9fl01q5dy7hx4/p8Oup/XPZDk8t96HLZD13bY9nfcMMNj6SUpvTpRCRpiPAMdS+YNWsW119/fZ9PZ/78+cyZM6fPp6P+x2U/NLnchy6X/dC1PZZ9RCzu0wlI0hBiK9+SJEmSJLXAhFqSJEmSpBaYUEuSJEmS1AITakmSJEmSWmBCLUmSJElSC0yoJUmSJElqgQm1JEmSJEktMKGWJEmSJKkFJtSSJEmSJLXAhFqSJEmSpBaYUEuSJEmS1AITakmSJEmSWmBCLUmSJElSC0yoJUmSJElqgQm1JEmSJEktMKGWJEmSJKkFJtSSJEmSJLXAhFqSJEmSpBb064Q6Ij4bEal4fbBOuddHxB8iYmVErImI6yPi9Iio+/1arSdJkiRJUr9NHCPi6cCHgNSg3FeBy4DZwB+A3wD7AV8BfhwRHb1ZT5IkSZIk6KcJdUSMAi4BlgM/q1PuROA0YBnwtJTScSmlE4B9gduBE4B39lY9SZIkSZJK+mVCDXwSOBB4B7CyTrmziu6ZKaUFpQ9TSsuBU4veD1e5hLvVepIkSZIkAf0woY6IZwAfAC5PKf2iTrndgSOADcCPKoenlK4GHgB2AY7sab1227RyE/wXPHHnE+0ORZIkSZJEP0uoI2I08F3gMeA9DYofVnRvTSmtq1HmuoqyPanXNg9+80H+tNuf4AJ44CsPtDscSZIkSRL9LKEGPgPsD7wrpfRIg7J7Ft3FdcrcV1G2J/XaZsxeY+hc2wnAsu8uY9PqTW2OSJIkSZLUbxLqiHgW8F7gipTSD5qoMr7orq1TZk3R3aEX6rXNhOdNYOwBYwHYvHozyy9d3uaIJEmSJEnD2x0AQESMAb4DrCK3vt1UtaJb97FavVhv65FEnAKcAjBt2jTmz5/fk9E19gLgjvx2wecWsOCABV3fRIPemjVr+n4dU7/jch+6XPZDl8tekgaWfpFQA58lPwP6rSmlpU3WWV10x9cpUxq2uuyzVuttJaV0EXARwOzZs9OcOXPqjK7nNh22iWu+eQ2sBxbCoR2HMuG5E/p0muo/5s+fT1+vY+p/XO5Dl8t+6HLZS9LA0l8u+T4B6ATeHBHzy1/Ai4oypxafXVz0Lyq6M+uMd0ZF2Z7Ua6vhOw3PZ6kLNk4mSZIkSe3VX85QQ07uj64zfK/iVTote2PRPSgixtRosfvpFWV7Uq/9Xg4UDxJ7+L8eZv396xm9++i2hiRJkiRJQ1W/OEOdUpqVUopqL/JjtADOKD47tKizBPgbMBJ4VeU4I+JoYHdgGfDnsmm1VK9f2AsmzCmOJ2yGB7/2YHvjkSRJkqQhrF8k1D1wdtE9NyL2KX0YEVOBC4vec1JKnb1Ur+12e/duW96vvr7mLd6SJEmSpD7Wny757raU0o8j4mvAqcDNEXElsBE4FtgRuAL4Sm/V6w92funOTD91OtNOmsaOz9qx3eFIkiRJ0pA1oBNqgJTSaRFxDXA6+R7sDvIDpr4NfK3WWeZW67VbdAT7Xbhfu8OQJEmSpCGv3yfUKaW5wNwGZS4HLm9h3C3VkyRJkiRpoN9DLUmSJElSW5hQD2Cb127mwW88yHWHXMf6xevbHY4kSZIkDSkm1APY7W+4nbvecRdr/7GWBy58oN3hSJIkSdKQYkI9gO3y1l22vF/6zaVsfmJzG6ORJEmSpKHFhHoAm/ySyYzeazQAmx7fxPLLlrc5IkmSJEkaOkyoB7DoCHZ7525b+h/48gOklNoYkSRJkiQNHSbUA9wub9mFYePyYlx7y1pW/G5FmyOSJEmSpKHBhHqAGzFhBLvM7bqXesnnl7QxGkmSJEkaOkyoB4Hd37M7RH7/2P88xtrb17Y3IEmSJEkaAkyoB4Gx+45l8ksnb+m///P3tzEaSZIkSRoaTKgHiRkfmLHl/bLvLWPD8g1tjEaSJEmSBj8T6kFip2fvxA5P34HhE4cz4/0ziOHR7pAkSZIkaVAb3u4A1Dsigqdc9hRGTR9Fx7iOdocjSZIkSYOeCfUgMnbfse0OQZIkSZKGDC/5liRJkiSpBSbUg9i6e9ex5uY17Q5DkiRJkgYlE+pBaN0967jllbfwl33/wt3vubvd4UiSJEnSoGRCPQjFiOCRKx6BTlhx1QpW37i63SFJkiRJ0qBjQj0Ijd5jNFNfPXVL/5LzlrQxGkmSJEkanEyoB6nd37/7lvcP/eAh1i9e38ZoJEmSJGnwMaEepHacvSMT5kzIPZthyfmepZYkSZKk3mRCPYjt8eE9trxfevFSNjyyoY3RSJIkSdLgYkI9iE3854mMP3Q8AJ3rOnngggfaHJEkSZIkDR4m1INYRDDjzBlb+h+44AE2rdnUxogkSZIkafAwoR7kprxyCqP3Gg3Apsc3sfTipW2OSJIkSZIGBxPqQW7Y8GHMOKPrLPXK369sYzSSJEmSNHgMb3cA6nu7vHkXVsxfwfS3T+9q+VuSJEmS1CMm1ENAx5gODvr+Qe0OQ5IkSZIGFS/5liRJkiSpBSbUQ1TqTKSU2h2GJEmSJA1YJtRDTOeGTpZ+eyl/PfCvNlAmSZIkST1gQj3E3HvWvdx58p2su3Md951zX7vDkSRJkqQBy4R6iJn+jukQ+f1jv3qM1Tesbm9AkiRJkjRAmVAPMWP3HcuUV0/Z0r/404vbGI0kSZIkDVwm1EPQzI/O3PL+kSseYc3Na9oYjSRJkiQNTCbUQ9D4g8ez88t33tK/+DOepZYkSZKk7jKhHqJmfqzrLPXDP3yYtXesbWM0kiRJkjTwmFAPUTscsQOTXjIp9yS477O2+C1JkiRJ3WFCPYSVn6Vefvly1t2zro3RSJIkSdLAYkI9hO30zJ2YcOyE3LMZ7vucZ6klSZIkqVkm1EPcrI/PomN8BzPOnMGen9yz3eFIkiRJ0oAxvN0BqL0mHD2BZ97/TIbv5KogSZIkSd3hGWqZTEuSJElSC0yoJUmSJElqQb9KqCPiXRHxw4i4PSIejYiNEfFwRFwZEW+IiKhS55KISHVedzSY5usj4g8RsTIi1kTE9RFxekT0q3mzvaxbtI67Tr+LDcs3tDsUSZIkSerX+tu1vmcCU4FbgD8Ba4GZwPOAY4FXRsQrUkqdVer+Ebi7yudLa00sIr4KnAasB34LbCym8xXg2Ih4VUppc+tfZ2BZfPZiFn1iEWlTYtjoYexz/j7tDkmSJEmS+q3+llC/FrgxpbS2/MOIOIic8L4MeDPwnSp1L04pXdLshCLiRHIyvQx4bkppQfH5NOAq4ATgncCXuv81BqZxB40jbUoAPHjhg8z44AxG7TqqzVFJkiRJUv/Ury5rTildU5lMF5/fCny16H1BL03urKJ7ZimZLqa1HDi16P3wULr0e/Lxkxl/xHgAOtd3ct85PpdakiRJkmoZSMnipqK7vqcjiojdgSOADcCPKoenlK4GHgB2AY7s6fQGiojY6lnUD37jQdbf3+PZLUmSJEmD0oBIqCNiT+AdRe8vahQ7JiI+HxEXRcSnIuKFdc4uH1Z0b00pratR5rqKskPCpBdPYodn7ABAejJx39mepZYkSZKkavrbPdQARMRbgKOBEcDuwLPIyf/ZKaWf1qj2piqf3RYRr00p3Vzxeek07OI6YZQyyT3rlBl0Smep//HCfwCw9JtL2ePMPRi9x+g2RyZJkiRJ/Ut/PUN9FLnxsdcDzy0++zjwySplbwLeDRwEjAemA8cBfwcOBK6MiN0q6owvutvcr11mTdHdobvBD3QTXzCRHY/aEYC0MbH4M/WOO0iSJEnS0BQppXbHUFNEjCGfIX4L8B7gNuAlKaUHm6g7EriafA/0V1NK7ywb9lHg08ClKaU31qj/GeAjwEUppbdXGX4KcArAtGnTjvj+97/fzW/XfWvWrGH8+PGNC/aGG4APFu87gO8Bu26fSWtb23XZq99wuQ9dLvuha3ss+2OOOeaGlNLsPp2IJA0R/fKS75Li/ubbgDMiYhlwHvkZ0a9oou6GiDgb+BnwkorBq4tuvX+s0rDV1QamlC4CLgKYPXt2mjNnTqOQemz+/Plsj+kApKMTN/38Jlb+fiVshl1+uwsHXHzAdpm2trU9l736D5f70OWyH7pc9pI0sPTXS76rKT17+viIGNFknTuKbuUl34uK7sw6dWdUlB1Sylv8Hn/oeHZ++c5tjkiSJEmS+pd+fYa6wgryo7OGA5OA5U3UmVx011R8fmPRPSgixtRo6fvpFWWHnAlHT+CQqw5hwtETiIh2hyNJkiRJ/cpAOkP9XHIyvQJ4pMk6ry6615V/mFJaAvwNGAm8qrJSRBxNbl18GfDnFuMdFCbOmWgyLUmSJElV9JuEOiKeExEnRcSoKsOOAr5V9H4rpbS5+PzQiDguIjoqyg+PiPeTW/8G+EKVSZ5ddM+NiH3K6k4FLix6z0kpdbb+rSRJkiRJg1V/uuR7b/J90l+JiL+Rzw7vUHx+YFHml+THZ5XMAn4KPBYRdwH3F3UOJj8+qxM4M6X068qJpZR+HBFfA04Fbo6IK4GNwLHAjsAV5AbQVEidiYd+8BDjDhzH+ENsfVaSJEnS0NafEuqrgU8BzwH2A54FBDmx/gn5EVdXVNT5O/Al4J/IDYwdBiRyYv0d8uOybqg1wZTSaRFxDXA6cDT5AVF3AN8GvubZ6S6rrlvFnW+7k7V/X8vEF07kkF8d0u6QJEmSJKmt+k1CnVJaCHyihTrv7eF0Lwcu78k4hoKO8R2svXktAI//+nEen/84E+dMbHNUkiRJktQ+/eYeavVv454yjl3evMuW/oVnLSSl1MaIJEmSJKm9TKjVtFnzZhEjc4vfq65dxaO/eLTNEUmSJElS+5hQq2mj9xjN9FOnb+lf+NGFpM2epZYkSZI0NJlQq1tmfmQmw8bl1WbtLWtZ/p/L2xyRJEmSJLWHCbW6ZeTUkcx4/4wt/Ys+sYjODTaGLkmSJGnoMaFWt834wAyGT84NxK9fuJ6l31za5ogkSZIkafszoVa3Dd9pODPPmrmlf9GnFrF57eY2RiRJkiRJ258JtVoy/bTpjNxtJDEymPqaqXRu9LJvSZIkSUPL8HYHoIGpY0wHB152IKNnjWb0zNHtDkeSJEmStjsTarVswtET2h2CJEmSJLWNl3xLkiRJktQCE2r1mvX3r+eBrz3Q7jAkSZIkabvwkm/1WEqJhR9byP2fv5/O9Z2MP2w8Ox25U7vDkiRJkqQ+5Rlq9VhEsO7udXSuzy1933vGvaSU2hyVJEmSJPUtE2r1ir0+uxcxIgBYec1KHvnZI22OSJIkSZL6lgm1esWYvccw/bTpW/rvPfNen00tSZIkaVAzoVavmfXxWXTs1AHAurvWsfTipW2OSJIkSZL6jgm1es2IySOYedbMLf2L5i1i0+pNbYxIkiRJkvqOCbV61W7v3o1RM0YBsPGhjSz53JI2RyRJkiRJfcOEWr2qY0wHe356zy39S85fwpMPPtnGiCRJkiSpb5hQq9dNe8M0xh86HoDOJzpZ+NGFbY5IkiRJknqfCbV6XQwL9j5vbwDGPmUsU14zpc0RSZIkSVLvG97uADQ4TTx2Ik/92VOZ9OJJDBvhcRtJkiRJg48JtfrMzi/dud0hSJIkSVKf8dShJEmSJEktMKHWdpFS4qEfPcSD33iw3aFIkiRJUq/wkm/1uQ3LN3DrK29l5TUrGTZuGJOPn8yo6aPaHZYkSZIk9YhnqNXnhk8ezqaVmwDoXOtjtCRJkiQNDibU6nPDhg9jny/ss6V/2SXLWH3D6jZGJEmSJEk9Z0Kt7WLisROZ/NLJW/rvfu/dpJTaGJEkSZIk9YwJtbabvc/bmxgRAKy8ZiUP//jhNkckSZIkSa0zodZ2M3bfsez2rt229N9zxj1sXre5jRFJkiRJUutMqLVdzfz4TEbsPAKAJxc/yX3n3tfmiCRJkiSpNSbU2q5GTBjBnp/Zc0v/knOXsG7hujZGJEmSJEmtMaHWdrfrybsy/ojxAHSu72TRJxa1NyBJkiRJaoEJtba76Aj2/cq+0AG7vn1X9v7C3u0OSZIkSZK6bXi7A9DQtNORO3HkvUcyeo/R7Q5FkiRJklriGWq1jcm0JEmSpIHMhFr9SupM7Q5BkiRJkppiQq1+YcPDG7jzbXdyx5vvaHcokiRJktQU76FW221YvoG/HvBXNq3YBMCub9uVCc+d0OaoJEmSJKk+z1Cr7UZOG8nEF07c0r/gnQvo3NTZxogkSZIkqTETavULe5+3N8PG5tVx7c1refDCB9sckSRJkiTVZ0KtfmH07qOZ+fGZW/oXfnwhTy59so0RSZIkSVJ9JtTqN2a8bwZj9h8DwOZVm7nn/fe0OSJJkiRJqq1fJdQR8a6I+GFE3B4Rj0bExoh4OCKujIg3RETUqfv6iPhDRKyMiDURcX1EnB4Rdb9jq/XU+4aNGsZ+F+63pf+h7z/EY795rI0RSZIkSVJt/S1pPBN4ObAO+BPwE+Bu4HnA94CfVkt0I+KrwGXAbOAPwG+A/YCvAD+OiI5qE2u1nvrOxOdNZOpJU7f0LzhtAZvXb25jRJIkSZJUXX9LqF8LTEwpHZ5SOj6l9NqU0jOBg4HlwMuAN5dXiIgTgdOAZcDTUkrHpZROAPYFbgdOAN5ZOaFW66nv7XP+PnTslI9lrLt7Hfedc1+bI5IkSZKkbfWrhDqldE1KaW2Vz28Fvlr0vqBi8FlF98yU0oKyOsuBU4veD1c5s91qPfWxkdNGstfZe23pX/O3NaSU2hiRJEmSJG1rICWLm4ru+tIHEbE7cASwAfhRZYWU0tXAA8AuwJE9raftZ/op05n8sskc+P0DeerPnkqd2+clSZIkqS0GREIdEXsC7yh6f1E26LCie2tKaV2N6tdVlO1JPW0n0REcfMXBTH3NVJNpSZIkSf3S8HYHUE1EvAU4GhgB7A48i5z8n51S+mlZ0T2L7uI6oyvdgLtn2Wet1pMkSZIkCeinCTVwFFs3PrYJ+Djw+Ypy44vuNvddl1lTdHfohXpqo84nO3n8qseZ/KLJ7Q5FkiRJkvpnQp1S+lfgXyNiDPkM8VuAecCrI+IlKaUHi6Kla4G722JVq/W6RhBxCnAKwLRp05g/f36ro2ramjVrtst0+qW/AV8k39l+IbB/e8PZ3ob0sh/CXO5Dl8t+6HLZS9LA0i8T6pLi/ubbgDMiYhlwHvkZ0a8oiqwuuuOrVKdi2Oqyz1qtVx7bRcBFALNnz05z5sypM6reMX/+fLbHdPqjf5z7Dx5b8hgA4y8az+F/OZxhwwdEEwC9Yigv+6HM5T50ueyHLpe9JA0sAykj+U7RPT4iRhTvFxXdmXXqzago25N6apN9v7Ivw0bn1XXN39bwwJceaHNEkiRJkoa6gZRQryDfSz0cmFR8dmPRPai4PLyap1eU7Uk9tcmYvccw8xNdxz8Wfnwh6+6t1UC7JEmSJPW9gZRQP5ecTK8AHgFIKS0h3107EnhVZYWIOJrcSvgy4M+lz1utp/aa8cEZjHvaOAA613Vy1zvuIqWWb4OXJEmSpB7pNwl1RDwnIk6KiFFVhh0FfKvo/VZKaXPZ4LOL7rkRsU9Znank5qsAzkkpdVaMttV6apNhI4ax/8X7b1lrH//N4yy/dHl7g5IkSZI0ZPWbhBrYG7gUWBYRv42IyyLi5xFxK3ANsBfwS/Ljs7ZIKf0Y+BqwC3BzRPwiIv4LWAAcCFxBbsiM3qin9trx6Tuy+3t239J/9/vuZsPDG9oYkSRJkqShqj8l1FcDnwJuAvYjt+T9z8A44CfACSml44qWv7eSUjoNOIl8GffRwAuBu4F3AidWnNHucT2116xPzmLUzHwhw6ZHN3H3++5uc0SSJEmShqJ+89islNJC4BM9qH85cPn2qqf2GT5+OPt9fT9ufvHNADx02UPsevKuTDxmYpsjkyRJkjSU9Kcz1FLTJr9oMlNPmsqw0cPY65y92OnZO7U7JEmSJElDTL85Qy111z5f2IdZ82Yxdp+x7Q5FkiRJ0hBkQq0Ba+SUkYycMrLdYUiSJEkaorzkW4NK2pzo3OiTziRJkiT1PRNqDRpP3PUENx59I4s/s7jdoUiSJEkaArzkW4PC6r+t5sajbqRzfSer/7KaKSdMYfwh49sdliRJkqRBzDPUGhTGHzKe8YfnBDptStzxlju89FuSJElSnzKh1qAQHcEB3z6AYaPzKr3mxjXcd+59bY5KkiRJ0mBmQq1BY+z+Y5n1qVlb+hd/cjFrblnTvoAkSZIkDWom1BpUZrxvBjs8YwcA0sbEnW+5k85NXvotSZIkqfeZUGtQKV36HSMDgNXXr2bJeUvaHJUkSZKkwciEWoPOuAPHMWverC39i/5tEWtvW9u+gCRJkiQNSibUGpRmnDGD8UcUrX5vSNzx1jtIm1Obo5IkSZI0mJhQa1AaNnwYB1xyADEiX/q94z/t6GO0JEmSJPWq4e0OQOor4586nn0v2JexB45lwnMmtDscSZIkSYOMCbUGtelvn97uECRJkiQNUl7yLUmSJElSC0yoNaRseGgDt77qVlZdv6rdoUiSJEka4LzkW0PG4/Mf57ZX38bGhzey9ta1HHHDEXSM6Wh3WJIkSZIGKM9Qa8gYvcdoNj+xGYAnbn+ChR9b2OaIJEmSJA1kJtQaMsbsNYZ9zt9nS//9X7ifFVevaGNEkiRJkgYyE2oNKbuesiuTXjQp9yS4Y+4dbFq9qb1BSZIkSRqQTKg1pEQE+39rf4ZPzM0HrF+0nnvef0+bo5IkSZI0EJlQa8gZNX0U+3513y39Sy9eyqO/fLSNEUmSJEkaiEyoNSRNfe1Uprx6ypb+O//1TjY+urGNEUmSJEkaaEyoNSRFBPtduB8jdxkJwIZlG7jzlDtJKbU5MkmSJEkDhQm1hqwRk0ew/8X7b+kfNmoYaYMJtSRJkqTmDG93AFI7Tf6Xycz40AzGP208006a1u5wJEmSJA0gJtQa8vY+d+92hyBJkiRpAPKSb0mSJEmSWmBCLVXYvHYzd77jTlb8YUW7Q5EkSZLUj5lQS2XW3rqW6w+/nqXfWMrtb7idjSt8lJYkSZKk6kyopTIdO3Ww8eGcRD9535MsOH1BmyOSJEmS1F+ZUEtlRu8+mv2/2fUorYcuf4jlly1vY0SSJEmS+isTaqnClBOnsMtbdtnSf9dpd7Fu0bo2RiRJkiSpPzKhlqrY50v7MHrv0QBsXrWZ299wO52bOtsclSRJkqT+xIRaqmL4DsM58LIDoSP3r/rjKhZ/anF7g5IkSZLUr5hQSzXs+IwdmTVv1pb+xZ9azONXPd6+gCRJkiT1K8O7WyEiJgBzgMOAacAE4HHgIeBvwNUpJR/gq0Fh5lkzWfG7Fay4agUkuP0NtzP7ptmMnDKy3aFJkiRJarOmEuqI6ABeAZwGPAeI0qCyYqnUjYjfAxcCP00pbe6lWKXtLjqCp1z6FK4/5Ho2PrKRsfuPJW1OjStKkiRJGvQaJtQR8TrgHGB3cgL9CHAtcBvwGLAK2BGYDBwIHEk+g300sCQiPpxS+n5fBC9tD6Omj+KA/3cAq29YzcyzZhId0biSJEmSpEGvbkIdEX8kJ8gPA18CvptS+nujkUbEocBc4HXAZRHxrpTSUT0PV2qPyS+ezOQXT253GJIkSZL6kUaNku0NvB/YI6X0/maSaYCU0k0ppfcCM4APFOORBp2UvPxbkiRJGqoaJtQppS+llDa0MvKU0oaU0heBvVqpL/VXaXNi4b8t5PY33G5SLUmSJA1RdRPqlNLa3phISumJRmUiYkREHBsR50fEtRGxNCI2RMQDEfHjiJhTo94lEZHqvO5oMN3XR8QfImJlRKyJiOsj4vSI8JFiqmrz+s3cdOxNLP7kYh66/CGWfXtZu0OSJEmS1AbdfmxWHzoa+E3xfhlwA7CW3NDZicCJEfGplNInatT/I3B3lc+X1ppgRHyV3HL5euC3wEbgWOArwLER8SpbKVeljtEdjN1vLCuvXgnAgnctYMdn7si4A8e1OTJJkiRJ21O3EuqImATMAhallB4r+3xX4GzgEGARMK/Z+63LdAI/Ab6UUvpDxXRfA1wGfDwirkopXVWl/sUppUuanVhEnEhOppcBz00pLSg+nwZcBZwAvJPcGJu0lX2+uA8r/7SSJ259gs51ndz2mts4/C+H0zG2o92hSZIkSdpOuntZ81nAdeTGxgCIiJHANcAbyQn1y4CrImK37ow4pfS7lNIrK5PpYtgPgEuK3jd0M+Zaziq6Z5aS6WJay4FTi94Pe+m3qukY28FBPziIYWPy6rH2lrUseNeCBrUkSZIkDSbdTRaPARZWnH1+DbAncDXwIuCrwATy2d3edGPR3b2nI4qI3YEjgA3AjyqHp5SuBh4AdiE/NkzaxriDxrHPl/fZ0r/s28tYhpTbVgAAIABJREFUeknNOwwkSZIkDTLdTah3Z9v7lI8DEvCvKaX/Sym9C1gIvLgX4iu3b9GtlbEcExGfj4iLIuJTEfHCOmeXDyu6t6aU1tUoc11FWWkbu568K9PeMG1L/4LTFrDm5jVtjEiSJEnS9tLdRskmAo9UfPZM4K6U0r1ln91IPpvdKyJiF2Bu0fuTGsXeVOWz2yLitSmlmys+37PoLq4z2fsqykrbiAj2+/p+rL5x9Zb7qW898VaOuP4Ihu/Yn9r8kyRJktTbunuGeh0wudQTETPIZ63/WFHuSWBUz0LbMo3hwKXATsBvU0q/qChyE/Bu4CBgPDCdfNb87+QWwq+scj/3+KJb77FgpdOMO7QevYaCjnEdHPSjgxg2Lv+c1i1Yx4J3ez+1JEmSNNh19xTaHcCzI2JS0cr368mXe/++otzuwPJeiA/g6+RHWS2hSoNkKaUvVny0FvhlRPyGfF/3keQGyMrv6Y5S9VaDiohTgFMApk2bxvz581sdVdPWrFmzXaajFr0P+DQwE5Yfs5zl83vrJ+CyH6pc7kOXy37octlL0sDS3YT6e8AFwF8j4m/kFr3XAD8rFYiIUcDhwDatdXdXRHwJOJn8aKtjU0rLmq2bUtoQEWcXsb2kYvDqojue2krDVlcbmFK6CLgIYPbs2WnOnDnNhtay+fPnsz2moxbNgWX7LWPKK6bQMa53H5/lsh+aXO5Dl8t+6HLZS9LA0t2E+mvke6ZfD+xFPhv8tpTSyrIyxwPjyGeHWxYR55Mv5X6YnEy3cg3tHUW38pLvRUV3Zp26pUeDLapTRtrKLm/cpd0hSJIkSdpOunUPdUqpM6X0BmBv4FnAbimlH1YUuxd4FfDdVoOKiP8A3g88CrwgpXRbi6Mq3e9d2exy6RFcB0XEmBp1n15RVmrJE3c/Qeps+e4CSZIkSf1U3YQ6Il4bEds0ypVSWphSujaltKrKsL+llH7SncuzK6Z5DnAG8Dg5mf57gyr1vLroXlf+YUppCfA3YCQ5+a+M4WjyfeDLgD/3YPoa4pZ+eynXH3w99517X+PCkiRJkgaURmeoLwceioj/joiTI2JKXwYTEZ8CzgRWkJPpumeHI+LQiDguIjoqPh8eEe8nXzIO8IUq1c8uuudGxD5ldacCFxa956SUOlv4KhIP/fAh7jz5TjrXd7LwYwt5/KrH2x2SJEmSpF7U6B7qM4FXAC8uXl+PiGuAnwJXpJR67bRbRLwU+FjRezfwroioVvSOlNI5xftZRSyPRcRdwP3kx1wdTH58VidwZkrp15UjSSn9OCK+BpwK3BwRVwIbyS2K7whcAXyld76dhqKdT9iZnZ69EyuvWQmdcNtrbuOIG45g9IzR7Q5NkiRJUi+om1CnlD4HfC4idiUn1q8AngMcDXwhIm4EfgL8NKV0R+0xNWVS2fv/z959hzV1tn8A/z5J2GEvAZE9RAEFS52IuK3YCn3rrgtHa22r/jrsrrXLV9u6qq+ignuPOuoWxTqqIEuqAgIO9t4Qkuf3R4AisgJoHPfnunJhznmec+7kBMx9ntWj+tGQ8wBqEuooAMsBeEE+wVh3yJfCegBgE4DVnPPwxk7IOX+3+gbBHMhfkxDyicw2AlhDrdOkLQQqArjscsF1j+uQZEggyZLgZsBNdLvQDUL19p0FnBBCCCGEEPL0tWiWb855GoDVAFYzxvQhXy7LH8AgyJfIWlzdQrwP8pbr64oGwjkPBhCsYJ0kAB8qeq56x9gOedd2QtqdmrkauuzpgijfKPAqjqJrRUh4PwFO65yUHRohhBBCCCGkjRSa5RsAOOd5nPNgzvkoAMYAxgLYA3kX688AXGWMpTDGfmWM9WeN9Nsm5GWh108Pdsvsap+nrU9D6vpUJUZECCGEEEIIaQ+KrkP9CM55CYDdAHYzxlQBDIa85doPwAeQTwr2NYDFbYyTkOeaxVwLFP5diMxtmQCA+PfiIXYXQ8dLR8mREUIIIU0LDw9nAAaIRKL/MMb6cc7Fyo6JEEKeMM4Yy5ZKpVtlMlmIp6dnfmMF25RQP3JGzisBHAVwlDEmgHxM8mgAme11DkKeV4wxOK1zQklsCUqiSsArOW4G3IRnuCdUTVSVHR4hhBDSoPDwcCYQCD7R0NAINDY25jo6OsUikSibOiASQl5knHOUl5erZWVlfZiXl+cbHh7+H09Pz8qGyirc5buFAcg45+c45+9zztc9iXMQ8rwRagrRdX9XiPTk97EqUiuQf77Rm12EEELIs2CAhoZGoL29faGhoWGBioqKlJJpQsiLjjEGDQ2NSktLyxwdHR1XyIc5N6jVLdSMsQ6Qj5tudA0gzvml1h6fkBeRhq0GOm/vjFtTb8Fluwv0ffWVHRIhhBDSKJFI9B9jY2MuEolo5RNCyEuHMQYDA4PKoqKiEQA2N1RG4YSaMfYfAIsAODZTlLfm+IS86AyHG6JnYk8ItWjpLEIIIc82xlg/HR2dYmXHQQghyqKlpVUGwK2x/QolvIyxsQC2AWAACgAkA6A/soQoiJJpQgghzwPOuVgkEmUrOw5CCFEWoVAo5ZxrNrZf0Rbkz6p/fgBgDee8qtWREUJqlT8oR+K8RDiudYSKoYqywyGEEEJq0ZhpQsjLrLm/gYom1A4ALnHOV7Y6IkLIIwouFSDWPxaSDAkkuRK4HXeDQOWJzBdICCGEEEIIaUeKfmvPBXD/SQRCyMtKkiWBJEMCAMg/m4/E/0tUckSEEEIIIYSQllA0oT4J4JUnEQghLyuj141gvci69vnDFQ+RtjFNeQERQgghpMUsLCxcGWOeR44c0W6qnJeXlxNjzHPFihWGTyu2Z9GKFSsMGWOejDFPdXV1j+zs7EYnlomJiVGrKduS97i9zJ8/35wx5jl//nzzp3G+5tS8fmXHQRqmaEL9NQAdxtjPjDGaVYmQdmL1uRWMAoxqn9+ZfQcFlwqUGBEhhBBCyJNVUVHBNm7caNDY/nXr1hk1tq8tKEEl7UmhhJpzfg9AXwB+AG4xxtYyxr5gjH3W0OOJREzIC4gJGJyDnaHlpgUA4BKOWP9YlN8vV3JkhBBCCCHtr3PnzqVCoRDbtm1rsMVeKpViz549hjo6OtJOnTpVPO34CGkpRZfNYgDeg3xyMiEAO8jXm36saPX2H9oaICEvC5FYhK6HuiLilQhIsuXjqmNHx6J7WHdlh0YIIYQQ0q5MTU0lRkZGhWFhYTo3btxQ7969+yOtCIcOHdLJyMhQmTBhQtbVq1efSldvQlpD0S7fnwKYC3myfBTAcsiT5vqP70HJNCEK07DWQJe9XcBE8un5i8OLcXv67YZvWxFCCCHkhXH27FmtkSNH2pqamrqpqKh46Ovru/v6+tqfOHFCXL/s7du3VRljnhYWFq6NHa+xbs11t69fv16/W7duzpqamt21tLS69+rVy7Gh8wFAVFSUmr+/v7W5ubmrioqKh5aWVncLCwvXwYMH2wUHB+u15jW//fbb2dVxPNZKvWnTJkMAmDFjRrProO/bt0/H19fX3tDQ0F1FRcXD2NjYzc/Pz+bvv//WqFuuZmx0zfO647Mb6wJ+//590fjx461MTU3dVFVVPSwsLFzfffddi9LS0gbXUpLJZFi9erWBl5eXk46OTjc1NTUPS0vLrpMmTeqUkJDQ6Nqof//9t8bgwYPtdHV1u2loaHR3cXHp/MsvvzyRLu+kfSm6bNZ0AKUA+nLOI59APIS89PT668F+hT3i340HAGTuyASsAAxQblyEEEIIeTK+/vpr0++++64jALi4uJR6eHgUp6WlqZ4/f173/PnzukuWLElZsGBBs4mlIj788EPzlStXmnl4eBQPGDCg4J9//tG4cuWKtp+fn+OxY8duDxo0qKSm7N9//63h6+vrXFJSIrCxsSn39fUtYIzx9PR01YsXL+qUl5cLpkyZkq9oDBMmTMhfsGCBdO/evYYrVqx4KBLJU5Ps7GzhqVOn9O3t7cv79+9f2tQxpk6dahkcHGwiFAq5q6trqZmZWWVycrLakSNHDE6dOqUfEhKSOGbMmAIA6N69e6m/v3/O/v37DQHA398/p6ljP3jwQKVHjx4unHN4enoWFxUVCcPDw8Vr1qzpcOvWLY2zZ88m1C0vk8nwxhtv2Bw+fNhAJBJxLy+vIn19fWlkZKTW1q1bjQ8fPmxw6NChO/Vf09GjR8VvvvmmQ3l5ucDa2rq8a9eupRkZGaofffSRVVxcnLqi7yt5uhRNqC0AnKNk+umTSCXKDoE8ReazzVEcWYy0dWkwm2mGNF+a9ZsQQgh5Ee3du1dn0aJFHY2NjSU7d+5M9PX1rU1kT548qRUQEODw6aefdho8eHCRm5tbu40lDg4ONgkNDf2nX79+pYB8zPLEiROtdu7cafTVV1+ZDxo0KL6m7H//+1/TkpISwaeffvrwxx9/TK97nIKCAsG1a9c06h+/JTQ0NPioUaNyt27darx//36dt956qxAANm7caFBRUcHGjRvX5E2EJUuWGAcHB5vY29uX7969O7Fut/EtW7boTZ061XbGjBk2vr6+McbGxtJJkyblT5o0KZ8xZggA+/btS27q+Hv27DEaM2ZMdnBw8D11dXUOABEREer9+vXrfO7cOd2TJ09qDRkypPZ6LVmyxPjw4cMGhoaGVcePH7/do0ePcgCoqqpCYGCgZUhIiMn48ePtEhISYjU0NDgAFBcXs2nTptmWl5cL5syZk75ixYqHAoG8E3FNot2a95Y8PYom1A8hb6EmTxHnHCO2j4BuWiVs9RahU7f+yg6JPGGMMTisdID+YH0YBxgj7Twl1IQQQp497Nvnd6Zk/jUPb8/j+fn5Obam3qJFi8wBYNWqVcl1k2kAGDJkSMm8efPSvvvuu44rV640Xr9+/YP2iBUAPv7444c1yTQACIVCLF269OHOnTuNwsPDtSsqKpiamhoHgKysLBEA+Pn5PbYEia6urqxua7aiZsyYkb1161bjkJAQo5qEeuvWrYZCoZAHBgY22oJcVVWFpUuXmgHAzp07E+uPwZ40aVL+qVOnsrds2WK8bt06w88//zxT0dg6dOhQGRQUVJtMA4CHh0f56NGjc7Zt22Z88uRJnboJ9erVq00BYOHChQ9rkmkAEIlEWLt27YMTJ07opaamqgYHB+u/8847uQAQEhKin5mZqWJpaVnx22+/1SbTAPDaa68VT5w4MSsoKMhU0djJ06PoGOpdAPozxrSeRDCkYafunsLpu6fRf98FdOjhg9BR7si6G6vssMgTJlAVwORNE8jnAiSEEELIs6xv376F/v7+OY09DA0Nq+rXSUtLE8XGxmqJxWKpv79/YUPHHThwYBEAXL9+vcGxza0VEBDwWHJsYWFRpaOjI62srGQZGRm1S+R6enqWAMA777xjdeDAAZ2ysrJ2+3Li7e1d6uDgUHb69Gm9rKwsYUREhHpMTIyWt7d3YadOnR57z2pcvnxZMysrS8Xe3r7c09OzwWVRfHx8igDgypUrrcpdevfuXSQWix+bycbZ2bkcAFJTU2vHRCcmJqo8ePBATSAQ4J133nnsRoC6ujr39/fPBYDz58/XTrJ24cIFbQB44403cmu6vNc1derUJrulE+VTtIX6OwA+AP5gjM3knCe2f0ikvjN3z8AmF5h1HVCVAT6Ho1F8whWhY/rBY9l26Bh3VHaI5CnhnCNtQxo6TOoAgZqi98MIIYQQ8qR88skn6SNHjixqbL+Xl5dTTk7OI0nxnTt3VDnnKC4uFqqoqDTZ2p+bm6vo9/Ym2dvbVza0XSwWSwsLC4VlZWW1XzS++eabjMuXL2tfvnxZ29/f30FVVZU7OzuX9u7du2jq1Km5Xl5eZW2JZdy4cTmLFi3quGHDBoPk5GQ1AJg8eXKT3b3j4+PVACAhIUG9uTWlc3JyWvXeWVpaNvge6ejoSAGgoqKi9j1KSUlRBQAjIyOJpqZmg9PJ2tnZVQBAWlpabSKempqqCgA2NjYNnsvR0bHB7eTZoeiH6w8AVZBPj/QPY+wugAcAZA2U5ZzzoW2MjwD4efDPGMNcEXt4FjyS5D1zxJWAz5Yw5OzrhNDAUej5QwjUtXSVHCl5kqRlUtyedhuZOzNRcKEAziHO1HpNCCFEqdq72/TLpqqqigHyJHbIkCFNTurVUAt3Y6RSabNlhEJhs2VqaGtryy5dunTn7NmzWkePHtW5cuWKODIyUhwdHa21du3aDgsWLEhdunRpq8enBQYG5nz//fcWW7duNcrMzFTR09OrqplIrDFVVfK3w8TERNK3b98GW/drODk5NdiC3Zy63a+bw7k8h27qu1lNGUXQd71nn6IJ9aB6dR2rHw2hhX7akcegiTgXZI5rCReg++3PcEyV/10wLOVw3nAI3cy74tOh32GS2yQIBS3/A0meH1l7s5C5Uz78J2NLBjSdNWH1mZWSoyKEEEJIa9na2lYCgEgk4s1NkFVXzdjm0tLSBjO++Ph41XYJsB5fX9+SmnHe5eXlbN26dQbz58+3+uWXX8wnTZqU6+7u3qpJ0ywtLau8vb0Lz507pwsAU6ZMyaw7brkh1tbWlQBgbGwsUeS9e1Jq4snKylIpKytjNZOO1ZWUlKQGAGZmZrWzDZuZmVUCQHJycoPX7Pbt20/kWpL2o2if0cEKPIa0X5gEAJhAgFdmfgO7lEL89f1s3DeQ3w9Z1B+4Xf4AUw9NhdtaNxy8dbBVd8DIs810oinMAs1qnyd9noTMvQrPr0EIIYSQZ4SNjY3EwcGhLD8/X3TkyBHt5mvImZmZVamoqPD8/HxRamrqYw1kBw4ceOLdFtXV1fn777+f4+7uXsI5R3h4uGZbjjd9+vQsPT29Kj09vaqWrD3dv3//Uj09vapbt25pxsbGqilyLpFIxAFAImm/VXTs7OwkHTt2rJDJZFi7du1j62pXVFSwAwcOGABA//79a4cGeHt7FwPAwYMHDWpa3esKCQl57Fjk2aJQQs05P6PI40kF/bITilTQ57M1MLmfizOfjcPBfv+u+R6XFYfRu0Yj2M8SkTuXKzFK0t4YY3BY7QC9AXq12269fQuF15rs5UQIIYSQZ9hXX32VCgDTp0+32b9/v079/eXl5Wzbtm26p0+frp1YS01Njffo0aMYAD766CNzmezf0ZcnTpwQ//zzzxbtGeNPP/1kHBUV9VjSGhcXp5qQkKABADY2Nm1a0mvChAkFeXl5UXl5eVG9e/dudky2mpoanz9/fppUKsXo0aPtz50791hCX1hYKPjf//5nEBER8chaziYmJhIAuHHjRquW+2rMu+++mwEAP/74o/mNGzdqz1lVVYV33323Y2pqqqq5uXnllClT8mr2TZ48Oc/Y2Fhy7949tQULFjx2Lbds2WLcnjGS9teukxuQp0tNUxsDv9+O2xVF+PXKr1h6aSmKKovQ8z4w9ehD4OiHuPrfH2G0Igh2fUYqO1zSDgSqAnTZ2wURPSNQFl8GWZkMsaNi4fG3B9Qt1Zs/ACGEEEKeKRMnTsxPSEh4sHjx4o4BAQEOVlZWFba2tuWqqqqy1NRU1aSkJPXi4mLhzz//fK/u8lTffvvtw9dee81p+/btxleuXNF2dHQse/DggVpcXJzme++9l7ZixQqzps6riODgYOOFCxd26tixY4Wjo2OZlpaWLCsrSyU8PFwskUjYyJEjcwcMGPDUl9b98ssvM1NSUlQ3bNhg6uvr29nR0bHMysqqQiaTIS0tTfXu3bvq5eXlgj179sR7eHjUjqMePnx43oYNG0yHDRvm2Lt37yItLS0pAOzatSulLfF88sknWZcuXRIfOXLE4NVXX3V59dVXi/T09KoiIyO1Hjx4oKajoyPdvn17Yt3u4Nra2rKgoKCkt956y2HFihVmhw8f1u/SpUtpZmamyvXr17WnTp2asWHDBlo26xlG0wS/ALTVtPFV/6+Q+H4i5vWch+9C/5284NWIDFh5++HCiC601NYLQsVABa5HXCHSl98Pq0yvRIxfDKqKWzxXCSGEEEKeId98801GWFhY3FtvvZUtk8lw6dIlnbCwMN3CwkKRl5dX0bJly1ImT56cW7fO4MGDSw4fPnynV69eRenp6aqhoaG6ALBq1aqk5cuXp7ZnfF9//fXDcePGZYnFYllERIT4+PHj+snJyWqvvPJK0YYNG+4ePHgwqT3Pp4igoKAHx44duz1y5MjcwsJCYWhoqO7Vq1e1y8rKBAMHDixYs2ZN0pAhQ4rr1vntt98eBgYGZmhqaspOnDiht3v3bqPdu3cbNXaOlhIIBDh06FDSqlWrktzc3EoiIyO1Tpw4oS+TydiECROywsPDb/bv3/+xGw+jRo0qOnfu3D++vr752dnZKqdPn9YrKCgQ/fjjj/eCgoLabe1x8mSwpsbaMsYuAPiUc36p1SdgrA+AHznn3q09xrOuR48e/Pr160/8PKGhofDx8Wm23IPov5DywdvoFXr3kTsmRapA+KSB8Fq2E5q6bf6bQZ6ihq593rk8RA+JBq+S/w4bjjJE1/1dwYQ0G+SLoqW/8+TFQ9f+5fU0rj1jLJxz3qMlZaOiopLd3d2bHc9KCCEvsqioKCN3d3frhvY110LtDCCMMXaKMTaGMdaiAf+MMTXG2DjG2GkAF9D4TODkCejo1gd9ziXizontiHDRr92uXQn4bDiDgk6mCPtmGqQSWtbueaY/QB+Oa//91cr5IwdJXyvtBjEhhBBCCCEvneYSagcAKwH0B7AdQAZj7Chj7AvGWABjzIcx5lH9M4Ax9iVj7BiATABbAfQDsByUUCuF85Bx6B6TjevrvkVCh3/vhZgVytDv201IsNHF2cgDSoyQtJXZdDNYfmQJAFCzUoPpeBpiQwghhBBCyNPS5KRknPMCAB8yxlYAmAtgMoDhAIY1UY0ByAWwDMDvnPPk9gmVtAYTCNBjxleomvwxwhbNhOOKbTAtks8eGK9ZDr9D/hgaOxRLBi+Bm6mbkqMlrWH7oy2YkMHifQuomSm0agQhhBBCCCGkDVo0KRnn/C7nfB4ACwAjAPwXwCkAUQCSAUQCOAngJ8jXn7bgnH9MyfSzQ6Sqjn6LN0Mr+SFCJ/dHgRrw8WD5vhOJJ9BtbTdMOzQND/PuKTdQojAmZLD90ZaSaUIIIYQQQp4yRdehLuOcH+ecf8o5H8Y59+Cc23HOPTnnwznnn3POT3PO27QOHXlyxAYd4BMcirK7d9BnaCAETP4R4ODYcW0TCpytETp9IMoKc5s5EnnWFUUUoSyp2WUcCSGEEEIIIa1Ey2a9pDqYO2D9qPWImh2F4fbDAQDzLgMumRw+G88i18oEl/77AXidxeXJ8yPnaA5u9LuBmBExkORJlB0OIYQQQgghLyRKqF9yXU264tiEYzg18ST+k6xZu90iX4reH69AjJMe4o6GKDFCoqjKzErcfOsmZKUylN4qRezoWMgq6MYIIYQQQggh7Y0SagIAGGQ3GG638nBh4Xhka/27jrFbQhFcRk7BRV97pN+JUGKEpKVUTVThtMGp9nnB+QLcmnYLXNb4mvOEEEIIIYQQxVFCTWoJVVTh/cM2qCQmIzTAE5XCf/f1PZcIsasnQmcMpvHVzwHTsaaw/cm29nnm9kwkfUlrVBNCCCGEENKeKKEmj9E17QSfvdeReukkrvboULtdXAn4BJ1GcucO2B2zE5xTi+ezzPJjS5jNMqt9fu+He0hdl6rEiAghhBBCCHmxUEJNGmXtNRivXktDxOYliDf/d0mmDV0kGLN/HLyDvRGeGq7ECElTGGNwWOUAgxEGtdvuvHsHOcdylBgVIYQQQgghLw5KqEmzPCZ9BJukfFz4dBz+thJhxavy7RfvXcQr61/BtEPTkJ6WoNwgSYMEIgFcdrlA7CGWb5ACN/9zE4VXC5UbGCGEEEIIIS8ASqhJi4hU1eH943Y4/pOJuX3nQyQQAZCvX339+Cao2zogdM5rqCwrVnKkpD6RWATXI65Qs5L3MpCVyhD9WjQqMyqVHBkhhBBCCCHPN4USasZYIGNM40kFQ559ehr6WDZ0GW6+exN+jn4AB345AeiVAz6/H8MDa0Nc3/S9ssMk9aiZqcH9hDtEhvIbIZ0+6gQVExUlR0UIIYQQQsjzTdEW6nUAHjDGljHGHJ5EQOT54GjoiD/G/YFzI/fCuuzf8dW2mZXoMe0LXH3FDPdvnFdihKQ+TSdNuB11g3OIMzp90gmMseYrEUIIIaRJFhYWrowxz7oPNTU1DzMzM9cRI0bYHj16VNxY3YCAAGvGmOf8+fPNG9qfk5Mj9PT0dGKMedra2nZJTExs9m74kSNHtOvGcuPGDfXGyubm5go0NDS615RdsWKFYcteddusWLHCkDHmGRAQYP00ztecmmt4+/ZtVWXHQp4/iibURwDoAJgH4B/G2HHGmB+jb+YvLZ8eAbBKysX5D95Awb95NV69ng5jLx+Evu2N0oJs5QVIHqHzqg46vN2h+YKEEEIIUUjfvn0L/f39c/z9/XP69u1bAAB//vmn/siRI52+/fZbE0WPl5qaKurXr59jRESE2MXFpfSvv/66bWdnJ1H0OOvXr280Sd60aZNBeXl5uw8BpQSVvEwU+gXinI8CYAvgJwDZAIYAOAggiTH2KWPMuP1DJM86FXVN9P/tACrjYhDma1+7Xb0K8NkShlybDrjy6/+By2RKjJI0Rlouxf3f7oNLaRk0QgghpLU++eST9H379iXv27cv+cyZM4nJycmxEyZMyAKA77//vmNLWpdrJCQkqPTp08fpn3/+0fT09CwOCwu7bWZmVqVIPJaWlhXa2trSvXv3GlZVNVx169atRkKhEJ07dy5V5NiEkH8pfEeKc36fc/4ZAEsAkwBcAdAJwPcA7jHGtjDGeil6XMaYCmNsYHV38iuMsTTGWCVj7CFjbC9jzKeZ+uMZY2GMsQLGWDFj7DpjbA5jrMnX2Np65HHGtl3R70w8Yg+tR5yVZu32jnlS9Jy/DPsPX8GbAAAgAElEQVRGWCMuK06JEZL6JPkSRA+LRuK8RCR8mEBrixNCCCHtRE1Nja9du/a+lpaWTCKRsMOHD+u0pF5MTIxa//79nZOTk9W9vb0LQkND7xgYGCjcKqGmpsb9/Pxys7KyVA4ePPjYuaOjo9UiIyO1+vTpU2BqaqpwyzchRK7VSSPnXMI538Y57wOgO4ANAKoAjAdwkTEWzhibxhhTa/JA/+oP4DSA+QCsAIQDOAAgF0AAgHOMsUUNVWSMrQawDUAPAGEATgFwBLAKwF7GmLA965GmdR0VCOfEAoR98TayteSjAWQAfu50H+5r3TH/xHwUlBcoN0gCAEhbl4aC8/Jr8XDVQ9z78Z6SIyKEEEJeHGKxmFtbW5cDQEZGRrMt1FevXtUYMGCAc2pqquqIESPyTp48mSgWi1t9tzswMDAbAIKDg43q7/vf//5nBACTJ0/Oae44Z8+e1Ro5cqStqampm4qKioe+vr67r6+v/YkTJx4ZH14zNjo1NVUVAJydnR8ZX95QF/C8vDzBrFmzOlpYWLiqqqp6mJiYuE2YMKFTRkZGo9/Dd+7cqevt7e2gr6/vrqKi4tGhQwc3f39/64iIiEbHi9+5c0d19OjR1oaGhu7q6uoednZ2Xb744gtTiYTuJZC2aZdWWM55FIBvAWwCwKof3QGsB5DMGJvegsPIAOwD4M05N+Ocj+Scj+GcuwIYC0AK4EvG2IC6lRhjAQDeBZAOwK263mgADgD+ATAawHv1T9baeqRlBEIR+n0XAtGdRJz3c8P6HsB1C6BKVoVfr/wKp1VO2By+CTKpQr2XSDuz/D9LGL/170iNpM+TkLYxTYkREUIIIS+WoqIiIQA01wp85swZrSFDhjjl5OSIxo4dm/3HH3/cVVNTa1PXsQEDBpTa2dmVnzp1Si87O7s2QZVKpdi7d6+hrq6udNy4cflNHePrr782HTRokPOxY8f0jY2NJYMGDcq3srKqOH/+vO6IESOcli1bVpusOzk5Vfj7++doaGjIAGDo0KF5NePK/f39c3R0dB5paS8sLBS++uqrzrt27TJycXEp7du3b2F5eblg+/btxr6+vo4VFRWPzdM0Z84ci3Hjxtn/9ddfOvb29uXDhg3L09bWlh44cMCwd+/eLjt37tStXyc8PFz91Vdf7Xzw4EFDVVVV2aBBg/LNzMwqlyxZYjFy5Ei71ry3hNRoc0LNGBvEGNsPIAnAHADlADYCGAfgGAATAOsYY+83dRzO+VnO+Zuc87AG9u0CEFz9dGK93Qurf37COY+vUycDwDvVTz9toAt3a+sRBeiZ26D/H1HodTgS3lbetdszSjJw+etpuOmoj3+Ob1VihC83JmDovLkz9Hz1arfdnnkb2X/QRHKEEEJIW12/fl394cOHaiKRiPv5+RU2Vu7KlStiPz8/x8LCQuHMmTMzduzYkSIUtk9HyXHjxmVXVlayDRs2GNRsO3DggE5mZqbKqFGjcjU0NBpN2vfu3auzaNGijkZGRpLTp0/fio2N/efPP/+8GxkZeevPP/+8pampKf300087RUdHqwHA0KFDi/ft25esr69fBQDLly9/UDOufN++fcn1x4GfPn1az9zcvDIlJSX61KlTiWfPnk2Ijo6+2aFDh8q4uDjNjRs36tctv2vXLt3ff/+9g4aGhuzIkSO3r127dvvw4cNJ8fHxN7/44osHFRUVbMaMGTYPHz4U1a339ttv2+Tn54veeOONnKSkpNgjR47cvXjxYvylS5firl27Jq5pUSekNVqVLDLGdBljHzLGbgE4AeANAKkAPgPQkXMeyDnfxTn3A9AbQAmAJhPqFrhR/bNjnTg6AvAEUAlgT/0KnPPzAB4C6ACgZ1vrkdZz6+CO0Mmh2BGwAxbaFjAsAb4/A7jeLYbT8Em4MKwzcu/HN38g0u4EagJ0PdAV4m7VvbakwM23biIvNE+5gRFCCHk+zJ9vDsY8W/QYN87qsfrjxlm1uH5Dy0v5+tq3uP7SpY91fX4SsrKyhLt379Z588037WUyGRYvXny/qRm6L1++rF1WViZwdXUt+d///vegPWOZMWNGjlAo5Nu2baud7XvTpk1G1fuavIO+aNEicwBYtWpVsq+vb0ndfUOGDCmZN29eWlVVFVu5cmWrJibW1NSUbd68OVlXV7e25dra2loyffr0TAA4e/bsI2O/f/vtN1MAmD59eubw4cOL6+777rvvMtzc3EqKi4uFK1asqL3Ox48fF8fFxWmKxWJpUFDQfXV19dobCD169ChfsGABdc0jbaJQQs0Y82CMBUGebC6DfLzxecjHONtyzn/mnOfWrcM5vwrgKOQTl7VFzbrXdT/03at/3uSclzVS71q9sm2pR9qAMYaxXcfi1nu38Ks4AOLq/1YEALxP3AJ3dkLYV1OoG7gSiHREcP3TFeq28qFHvIIjdlQsisKLlBwZIYQQ8nzw8/NzrBkrbGJi0m3MmDEOaWlpqnv27In/5JNPspqq261btxKRSMRjYmK0pkyZYtmecXXq1KmqX79+hTExMVrh4eHqWVlZwtOnT+s5ODiU9evXr9HZvdPS0kSxsbFaYrFY6u/v32Dr+sCBA4sA4Pr1642utd2ULl26lHbq1OmxL36dO3cuB4D09PTacecSiQQRERFiAJg5c2aDNwImTpyYDQBhYWHaNdvOnj2rDQC+vr4FhoaG0vp1Zs2a1ewYckKaomgL9XUA06r/HQT52GNfzvkBznlTsw+WABA1sb9JjLEOAKZUP91XZ5dN9c+UJqrXzLJkU2dba+uRdiBWFWPSV3uReukkrnX794amYSlHv+9CcNNJH7dP71JihC8ntQ5qcD/lDlUzea8naZEU0cOiUXKrpJmahBBCCKlZh3r06NE5ffr0KVRTU+OVlZVs5syZNrGxsU1O0jtgwIDCoKCguyKRiIeEhJhMnTq1XZPqyZMnZwPA+vXrjTZs2GBQWVnJxo8f32QieefOHVXOOYqLi4UqKiqedScXq3n4+Ph0BoDc3NxWfc+3sLCoaGh7TYt1RUVFba6Snp4uqqysZAKBAA4ODpUN1XNwcKgAgIyMjNou3A8ePFABAGtr6wbPZWRkJBWLxY8l2oS0lKIf/mQAqwFs4Jw3OYFBPTMAzFLwXAAAxpgIwFYAugDOcM4P19ldczesqW/8Nd1BtOtsa2090o6svQbDKjwdV9d8AYsvl6BjnvxvmWtiMaRDxuL8qJ/Qfd0f0DFp1/9TSBM0bDXgdtINkd6RqMqrgiRbgvg58eh2ppuyQyOEEPKs+uWXVPzyS2qr6+/YkYIdO5pq5Gja2bMJra7bjj755JP0kSNH1nbtSklJURk8eLBDfHy8xvjx420iIyNvCQSNt2VNnjw5H8DdwMBA2+DgYBMA2LRp0/32iG3s2LEF8+bNq9q/f7+BiYmJRCgU8hkzZjSZUFdVVTEAEIvF0iFDhjT5vd/Q0LBV3Qubej/qq7u0J2OPzVVWU6bhHYQ8QYom1Ha8FQvVVtdp7Z2ftQAGAriPxyckq/mlUTSm1tb79wCMzQQwEwBMTU0RGhra2kO1WHFx8VM5z1PXZQjitnghfM0XGH78JlSlgJAD/Q9FIv2sFbZ9Ng3Or05o9I/ny+CpX/vFABYA6Ajkz8l/MT93z4EX9neeNIuu/cuLrv2Lw8rKSrJr1667Xl5eLjExMVpr1641ePfdd3ObqlM/qWaMYePGjW1OqtXV1fnrr7+eGxISYpKVlaXi6+ubb2Fh0WQSbGtrWwkAIpGI79u3L7mtMbSVmZlZlaqqKq+srGR37txRdXV1fazFOTExURUATE1Na1uwLSwsJACQkpLSYC+BnJwcYXFxMS2VS1pN0YT6BGPsOOf8l6YKMcbmARjOOR/S+tAAxthyANMhX9pqIOc8vV6RmruATY3bqNlXdzBoa+vV4pyvA7AOAHr06MF9fHyaOFT7CA0NxdM4j9K89gbuXj6G/MCJ8IiTT4glBcfHhRvwyr27WD1iNTobd1ZykMrx1K+9D1DgUQBNZ02o6DW7bCZ5Ql7433nSKLr2Ly+69i+W7t27l0+aNClr06ZNJj/99JP5jBkzclVUmv5/tW5SvWnTJhMA7ZJUz5w5M/vQoUMGADB9+vRml/OwsbGRODg4lMXHx2scOXJEu27re3NUVFQ4AEgkknZrDVFRUYGHh0fxlStXtIOCggyXL1/+WK+Ibdu2GQFAv379amP19fUtWrp0Kc6cOaObm5srMDAweGSY6rp16wzqH4cQRSg6hnoQgK4tKOcCeatyqzHGlkE+M3gW5Ml0Q1NAJ1f/fHzGyH/V9BdOrrOttfXIE2bbawS6x2Tj0pK5SNcRYN5QoFgNOJd8Du5r3fHp6U9RUkljep8G3Z66DSbTreikQgghhLy0Fi9enKalpSW7f/++2u+//27YfA15Ul0zpnrTpk0m06dPb/P4t969e5fl5eVF5eXlRY0fP76gJXW++uqrVACYPn26zf79+3Xq7y8vL2fbtm3TPX36tFbd7TUtxNHR0eptjbuuDz74IAMAgoKCTE+ePPnIOb/55hvTyMhILbFYLH3vvfdqbxgMHTq02NnZuay4uFg4c+bMTnXXto6IiFBftmzZ4zPHE6KAJ7XGsiqApiYpaxJjbAmA+QByAAzmnMc1UrRmKa0ujDGNRsq8Uq9sW+qRp4AJBOj90Qpo3r2PjtM/hJDJe+FIZBL8/NfP2D7UDFdWfgIua/VHjLRS1v4s3Ay4CVklvfeEEEJIS5ibm1fNnj07HQCWLl1qJpE0unrWI+om1Rs3bmyXpFpREydOzP/6668f5OTkqAQEBDhYW1t39fX1tR82bJitm5ubs7GxsfvEiRPtIyIiNOvW8/PzyweAmTNn2g4bNsx2zJgxVmPGjLFKT09vU9fqsWPHFrzzzjvppaWlguHDhzt7eXk5+fn52Tg6Orp8++23HdXU1Pi6deuSLC0ta7uzCwQCbN68+a6urq503759hjY2Nl1Hjhxp269fP4eePXu6eHh4FJubmzc4yRkhLdHuCTWTD3T1BNBsV5JG6v8E4CMAeZAn01GNleWc3wcQAXkC/58GjtUf8nWr0wFcbms98nTpGJrjl2G/ImJWBPpY9gEADEwEZoQWoef7S3DdowNSws8qOcqXR9qmNNz8z01kH8jGrcm3wKXUUk0IIYS0xJdffplhaGhY9eDBA7VVq1a1eC3sZyGp/uabbzLCwsLi3nrrrWyZTIZLly7phIWF6RYWFoq8vLyKli1bljJ58uRHxoYvXLgw86OPPko1MTGpPHfunN7u3buNdu/ebVRQUNDmscq///77w+3btyf07t278M6dOxrHjx/XLygoEL3xxhs5f/31V9y4ceMea31/5ZVXyq9cuRL3+uuv55aXlwtOnTql9+DBA9X58+enHj16NLGtMZGXG2uu+yZj7GSdp4MApAJorMVYBPl60eYA9nLOxygUDGPfAfgCQD6AQZzz8BbUeRPAHsiT336c84Tq7SYAzkHe/fxDzvny9qjXkB49evDr16+3+HW21ss8rkrGZdgctRnOo2egZ/K/c2iUi4ArE33Qc+UBqIv1lBjhk/UsXPukr5KQ8t2/k7CazTSD41rHl3qyuCftWbjuRDno2r+8nsa1Z4yFc857tKRsVFRUsru7e6saSQgh5EURFRVl5O7ubt3QvpZMSjaozr855Mlyc2MNogF83KLoqjHGRkGeTANAAoC5jXxRv8U5/6k2IM73MsbWAHgHQAxj7DQACeRjuHUAHASwqv5BWluPKIeACTCl2xTk/eWN84F+6PdnHAQA1KsAn+BQpBwxRtbPX6PHtC+aPRZpHetvrSHJlSB1tXwOkLR1aRBqCmH3ix0l1YQQQggh5KXUkoR6cPVPBuAkgBMAljZSthLAQ8753VbEUneGvR7Vj4acB/BT3Q2c83cZYxcBzAHQH4AQwC0AGwGs4Zw3OOCztfWI8uib26L/sZuIOxoCPudddEkpBQBYZVfBavqXuLx+LWxC/kAHRw8lR/riYYzBYYUDpAVSZGzNAAA8+O0BBFoC2C62VXJ0hBBCCCGEPH3NJtSc8zM1/2aM/QXgfN1t7YVzHgwguA31twPY/rTqEeVyeW0ypEPG4fyXk+G+fBf0yuVDF3pdeYhCN0+cnxOAvkt2QihUdGU40hQmYHDa5ARpmRTZ++Q9AO99fw9CDSGsPm9q0nxCCCGEEEJePApNSsY571e3uzUhyiRUUUX/n3ZAEheDiwPsarfrVACFR/bh1aBXEZ7a7DB8oiCBSACX7S4weO3fTiVJXyTh/q9tXiKTEEIIIYSQ58qTWjaLkKfG2KYL+p5NQOSO35BoqooSFeC9EUB4egS8grzw4fEPUVRRpOwwXygCVQG67O0C/UH6tdsS5yfi4ZqHSoyKEEIIIYSQp6vJ/rCMsc+q/7mGc55X53mLcM5/aHVkhCio29gPUOE3FdtD/g8ZuZsBaQVkXIblV5fjSNQebBG/jZ7vfA8moPtI7UGoLkTXg10RPSwaBRcLACbvEk4IIYQQQsjLorkBposhn9l7L+TrQtc8bw6rLkcJNXmq1LR0MPXddeiX+zHePfouTt09BQCYcjQVvcJ+wrUNG2EWvA8d3foqOdIXg1BLCNejrogeFg3zd8zRYVIHZYdECCGEEELIU9NcQv0D5Ilxdr3nhDzT7A3scWLiCeyM3YnVm9/Dx3/lAgBeuZGJkh79EBo4HH1+2QsVdU0lR/r8E+mI0D2sO5iQWqcJIYQQQsjLpcmEmnP+RVPPCXmWMcYwznUchs/riSs3R8L7zzgAgJYE8FnzJ+4cMkTFquVwHT1TyZE+/xpKpquKqlASUwLd3rpKiIgQQgghhJAnjwaTkheenrkNvI/dROzBdbhjoV673TG1HK7+s3BhWGfkpyYpMcIXjyRPgqjBUYgaGIW8c3nKDocQQgghhJAnghJq8tLo+voM2CTkIHTOayhR+Xe794lbkDjZ4a8f3wWXyZQX4Avk9rTbKLpaBFm5DDGvxSAvlJJqQgghhBDy4lEooWaMvcMYq2SMvdZEmZHVZQLbHh4h7UtFXRM+q44g7/pFXPUwrd1uXMzR57M1+GGuO+Jz4pUY4YvBbqkdVM1VAQCyMnlSnX8+X8lREUIIIYQQ0r4UbaH2B5AL4M8myvxZXebN1gZFyJPW0a0PvK6l4sqKj5GmK/81iDQFvjaMhesaVyw6vwgVVRVKjvL5pWGngW6h3aBqVp1Ul8oQPSIa+RcoqSaEEEIIIS8ORRNqZwAxnPNG+8VyzqUAYgC4tCUwQp40JhCg59yfIU64j9A3uuGdUQxSIVAhrcDXoV/Dfa07Qm+dUHaYzy1NB82Gk+owSqoJIYQQQsiLQdGE2hhARgvKZQIwUTwcQp4+bSNz+By4gdXfXkcP8x612+9k3YZg6DBcHGCH7OR/lBjh80vTURPdznWDaofqpLpEhujh0ci/SEk1IYSQ5xtjzFPRR0BAgHVrztW1a9fOjDHPCxcutHm9z2vXrqkzxjwdHBy6tPVYzWnPuBXxNF9je6l5r5p7bNq0SV/ZsT4JyvqstIfm1qGurwCAZQvKWQAoVjwcQpTHw8wDV6ZfwZrra/DZmc/w1uUieN8DcO8ucrp0wcWFgejz2VowAc3lpwhNJ024n3NHpE8kJBkSyEpkiBkeA7cTbrSkFiGEkOeWv79/Tv1tmZmZKhcvXtTR0NCQDR8+/LEZOfv06UPfj0mTvLy8ijp27FjZ2H47O7vnbkziDz/8YPz55593mjRpUtbmzZvvKTue9qZoQn0DwADGmB3nPLGhAowxOwC9AVxoa3CEPG1CgRDveb0H/87+uHm2H4C7AADDUo6+X65HxI69MAzZA6seA5Ub6HNGy1kL3c51Q+QAeVItLZYi6YskuJ9xB2OPr2FNCCGEPOv27duXXH/bkSNHtC9evKijr69f1dD+1tq/f39iSUmJwMnJ6blLpohiZs+enTV16tSXbnmU5/kzrmhTWzAAFQAHGWMO9XcyxuwBHAQgrC5LyHPJXNscg08l4tq6b/BAX1i73SMuDya9BiF09jBIykuVGOHzR6uzFrqd7QYVExVov6KNLvu7UDJNCCGEtICjo2Nl9+7dyzU1NbmyYyHkSXieP+OKJtS7ABwD0AXATcbYWcbY79WPMwDiqved4JxvbedYCXnqXpnxNfQSHiDU3xPS6txPowrw+d8J3LU3ROzhDcoN8Dmj5aKF7he6w+2kG1T0VJqvQAghhLygVq5cafjKK6846ejodBOJRB76+vruTk5OLlOmTLGMj49XrVu2qfGlZWVl7JtvvjHt2rVrZy0tre4aGhrdHRwcunzwwQfmOTk5wvrlm5Keni7s3r27M2PM08/Pz6asrOyRO98hISF6vXv3dtDV1e2mqqrqYW5u7vrWW29ZxcbGqrX0HI6Oji6MMc9Dhw5pN1Zm/PjxnRhjngsWLDCr2VZYWCj46KOPzJycnFw0NDS6q6qqepiYmLh5eHg4z5s3z1wikbT6Nc6ePbsjY8xz5syZHRurt3btWgPGmGfPnj0d625X5Do+KWFhYZoDBgyw19HR6aahodG9a9eunVetWmVYUFAgYIx5ampqdq9bvrkx5o3VA4ATJ06Ip0+fbuni4tJZX1/fXUVFxcPU1NRt5MiRthcvXnzs86mvr+/++eefdwKALVu2GNcdD/722293qinXnp/xuq9PKpVi0aJFJo6Oji7q6uoeenp63YYOHWoXHR3d4s9scxRKqDnnHPKls9ZUb/IBMLv6MaB62xoAo9spPkKUTmzQAT77ruPOsS34x1KjdrvTw3K4jApE6BvdUFReqMQIny+aTpoNJtOV2Y0OFyKEEEJeKDNnzuz4/vvvW0dFRWm5uLiUDh8+PM/V1bW0oqJCEBISYnL9+nWN5o8iT3x69erl9O2333ZMTk5W79mzZ6GPj09BTk6OaMWKFWYeHh6dExMTW3QH++bNm2o9e/bsHBkZqTVr1qyMQ4cOJWloaNS2Fk6ePNlyypQpdn///beOs7Nz6dChQ/PU1NRke/bsMfLy8nJpKkGua+zYsTkAsGnTJqOG9peVlbEjR44YMMYwY8aMHACQSCTw9vZ2XLp0qXlGRoZqz549i4YOHZpna2tb/uDBA9XffvvNrLS0tNm8prHXOH/+/EyhUIjdu3cblZaWNth9bv369cYAMHv27Myabe11Hdti7969OgMHDnQODQ3VNTExkQwaNChfTU1N9v7771svWLDAvL3P9/HHH3cMCQkx5pyz7t27l/j6+haIxWLp0aNH9QcMGOC8c+fORybIGTVqVK6bm1sJANjY2JT7+/vn1Dx69uzZ7JwCbfmMy2QyvPbaa7Y//PBDR1NTU4mPj0++urq67OTJk3r9+/d3TkpKapfWHUXHUINzXglgDmPsOwADAVhV70oBcIZznt4egRHyrOk8bCKqEt5E6IL/4JX/HYGWRH5HKjY1CpPWdMHqEasxymmUssN8LqUFpyHhgwS4HnGFXj89ZYdDCCGEPDE5OTnCjRs3mujq6kqvXr0a5+Tk9Mgd5YiICHUdHR1pS441Z86cjlFRUVpOTk5lp06dumNpaVkFyJOQUaNG2V64cEF30qRJ1pcuXYpv6jjnzp3TDAgIcCgoKBD98MMP9xYuXJhVd39QUJD+5s2bTcRisfSPP/64M2DAgFJAnrAsWLDA/LfffjObMmWKbXx8fKyRkVGTsc+YMSPnhx9+sDhx4oReXl6eQF9f/5HleLdt26ZXVFQk9PLyKnJ2dq4EgP379+tGRUVpeXh4FIeFhd2p2y1YKpXi+PHjYnV19Sa7Cjf1Gh0dHSsHDBiQf/r0ab2goCCD999//5EJ565evaoREREhNjExkUyYMCEfaN/r2Fo5OTnCmTNn2kgkEvbxxx8//Pnnn2vzsH379umMGzfOvr3PuXDhwrT+/fuXmJmZVdXdHhQUpD9r1izb999/32r06NExampqHABCQkLu//DDD8bR0dFaffv2LVJ0UrK2fMbv3r2rLpPJEBsbG2Nvby8BgKKiIsHgwYPtr169qr148eIOGzZsuN/6d0NO4YS6RnXivK2tARDyPBGpqsNn5WHcn34BcZMDYJaUjc8GAkWFD/D6ztcR0DkAK4avgLl2u98QfGFl7s7E7Wm3AQ5ED4uG6xFX6A94IVeEIISQF1LC/ATzB78+MGu+JGAy1iTbZYdLSt1tcePirDJ3ZjbYWllfx3kd0+x/sU+tuy3SN9I+/1x+i5aNsP2vbUqn/+uU3ZKyT0pWVpZQKpUyOzu7svpJGAB4eHiUt+Q42dnZwj179hgBwKpVq1JqEg0A0NXVlW3cuDHFxcXF9fLlyzqXL1/W6NWrV1lDx9m2bZtuYGCgLQCEhIQkTpw48bG1LVesWGEKAO+99156TTINAAKBAMuWLUs9evSoXnx8vMaaNWsMv/zyy8z69euytLSs8vb2Ljx37pxuSEiI/ocffvhI8rplyxZDAJg4cWLt9vT0dBEA9OnTp6j+GFuhUIjXXnutyZbOlrzGuXPnZp4+fVpv/fr1JvUT6uXLl5sAwKRJk7JUVOSNmu11HeubNm2a7bRp0xrdX1lZGV4TQ1BQkEFeXp7IwcGh7Mcff3ykUTMgIKDwzTffzNmxY0eLfrdaauzYsQUNbQ8MDMzbsWNH/tmzZ/VOnz6t1dw1aYn2+IyvXLnyXk0yDQDa2tqyzz77LO3111/XDgsLa1GviubQ+j+EtIJlN2/0uJGB6/tXQd3AuHb7vn/2od/PTjj/2QTIpFVNHIHU0OqqBVXT6nWqS2WIGRGD3JO5So6KEEIIeTIcHBwqDQ0Nq27cuCGeO3euhSLjj+sKDQ3VqqysZFZWVhWDBg0qqb/fzs5O0qdPn0IAOH36dIOJw08//WT89ttv22toaMiOHj16p6FEs7CwUHDz5k0tAJg9e/ZjS4UJBAKMGzcuBwAuXLjQoiG3NUcAACAASURBVATl7bffzgaArVu3PpLs3bt3T/TXX3/pampqyiZPnlw703WvXr1KGWMIDg42+eWXX4zS0tJa3CjYktcIAKNGjSqyt7cvj42N1aw7jjc3N1dw8OBBA5FIxOfOnVt7M6a9rmN9Xl5eRXW7Rdd/COos31qTEL755pu5ggaWdZ08efJj16s93L9/X/Trr78azZgxo+OYMWOsAgICrAMCAqxTUlLUAeDWrVvq7XGetn7GNTU1ZSNHjiyqv93Nza0cALKystqly3erEmrGmBNjbDVj7CZjLL/6cZMxtoox5twegRHyrGMCAd4YNAe33ruFad3+vZP47R/F6P/jdsQ6GyDhwiElRvh80HLRQrfz3aBqUZ1Ul8sQ4xeDnKNP5P8AQgghRKmEQiHWr1+fpKOjI121alUHV1fXrkZGRu6DBw+2++9//2tUUFDQou/n9+/fVwUAS0vLRpcZsra2rgCAhw8fPjY5VlJSktrChQs7McZw/PjxO76+vo8lLNXnUZHJZFBTU+OWlpYNzvxlb29fAQDp6ektmoRr7NixBXp6elURERHiuLi42jpBQUGGUqkUw4cPz9PR0antCu7l5VW2cOHCh6WlpYIFCxZYmZubu1tZWXUNCAiw3rp1q55U2nDP6pa+xhozZ87MAICVK1ea1Gxbs2aNUVlZmWDo0KH5VlZWta+/va5jfbNnz87at29fcmMPofDfObjS0tJUAMDGxqbBz0DNdWlP3377rYm9vb3b/PnzrYKCgkx3795ttH//fsP9+/cbJiYmqgNAYWGhQpPhNaatn/EOHTo0OEGPvr6+FAAqKirapXFZ4S7fjLEpkE88pgqg7qB9HQCdAQQyxmZxzkPaI0BCnnUGGgbY8PoGTHSbiE2/TMLEmIcAALeEIlT6voHQ8f3Q8/c/oC6mscGN0XTURPfz3RHpG4mKexXglRyxo2PhstsFxm8YN38AQgghSmP/i31q/W7YinDZ4ZJSvxu4Irqd7ZbQ2rrKMnr06EJfX9/onTt36p0/f158/fp18ZkzZ/ROnz6tt2TJEvMTJ07caa7LsHyuYDS5BGVNmYaYmZlVmpmZSa5duyaeO3eu5cmTJxN0dXVl9cvVOQ9vqBW0ufM0RF1dnb/++uu5ISEhJuvXrzf69ddfUwFg586dhgAwderUx7rlf//99+mBgYE5O3fu1Lt06ZL42rVr2jWJ3NKlS0suXrx4WywWPxJIS19jjVmzZuV+9913HY8cOaKflZV139jYWLpx40ZjAJgzZ85jXdnb4zo+ixq7QXH06FHxN998Y6mqqsoXL158f9SoUQXW1tYSLS0tmUAgwJQpUyxDQkJMFP08NKatn/HGPq/tTaGzMMZeAbAe8mT6AICRkCfRLgBeA7AP8nWq11eXJeSlMcBmANb9GIvQiX0hqf7NUpUCPlvCkGZngsidy5Ub4DNOw04D3c53g7qNvJcQl3DE/ScOmXuaHIpFCCGEPJd0dXVls2bNyt2+ffu9O3fuxMXHx0cPHDgwPzs7W2Xu3LmWzdXv1KlTJQDcu3ev0a7GKSkpagBgYWHxWEuduro6P3v27J2+ffsW/v3339o+Pj6ODS1B1KlTJ4lAIEB5ebkgJSWlwS6yd+/eVQMabxFsSGBgYA4A7N6921AmkyEsLEwzPj5ew8LConL48OENjr+1sbGRLFy4MOvw4cNJ6enp0efPn//HysqqIioqSmvx4sWmrX2NNXR0dGRjxozJLi8vF6xevdrojz/+0L579666g4NDWWMxtfU6tkWHDh0kAJCcnNzgZyAhIaHB7TUThjU2M3pj9Xbt2mUAAHPmzEn//PPPM11dXSu0tbVlNYlrUlJSuy1FBbT9M/60KJq2f1RdZyLn/E3O+THO+W3O+S3O+Z+c8/8AmAh5y/f/tXewhDzr1MV68NkShuSz+xFjJ67dbpMpQbdxHyJssBPyHiYqMcJnm4a1PKnWcJCvMsGrOOLGxiFje4aSIyOEEEKeLDs7O8l3332XCgC3bt16bC3e+nx8fEpUVVV5SkqK2tmzZ7Xq709OTla5dOmSDgAMGjTosXGkACAWi/mpU6cSBg0alB8ZGanl7e3tmJ6e/kjCqaOjI+vSpUsJAKxbt86w/jFkMhl27NhhCADe3t4Nnqchffv2LXV0dCxLTU1VPXbsmPaGDRsMAWDMmDHZLW1Z9Pb2Lp0+fXomAMTExDT4nrXkNdY1b968TIFAgODgYOPVq1ebAEBgYGBWY+XrU/Q6tkW/fv2KAGDv3r0GMtnjDe+bN282aKiepaWlhDGGjIwMlby8vMfe7EOHDjU4yV9eXp6wuv5jyWtiYqLKtWvXGhxDr6qqygGgqkqx+YXa4zP+NCiaUPcFEM4539FYgep91wB4tyUwQp5nDv1Ho8vtPFz4eCwK69xT63f6DqqcHfDX0g/AG/jDRwB1S3V0C+0GTefq/4NkwK2pt1B+/7nrMUUIIYQ8Jjo6Wm3lypWGDY2xPXDggB4AmJubN9vaZmRkJH3zzTezAWDu3LmdUlNTa4dyFhYWCqZNm2ZVUVHBevXqVdjYDN+AvBX32LFjiSNHjsyNi4vT9Pb2drp///4jw0Lnzp2bAQCrVq3qEBYWVpskymQyfPLJJ2Z37tzR0NPTq3rnnXcUmgBl/Pjx2QCwbt06o0OHDj2y9nRde/fu1Tlw4IBO/YSsoqKCnTp1ShdoOMlT5DXWcHH5f/buPC6rMv3j+OdmBxERVNxFRRHFDcFdwWmzsszMyaZs3zTNalqtcX7NVLaMrZpN+2qbo5XW2DKFu6KAoIi44b4rCiiy3r8/QHBXEHhYvu/X63mduM65z7meHgEvz33uq2NOZGTk4S1btrj/8ssvvt7e3vn33XffaTmV1+d4Me6+++6Dvr6+eevWrfN85plnGp+Sg8+MGTPOuMJ3/fr1Czp37nwkPz/fPPHEEye1pvn+++/rvvHGG2dctT84OPgYwOeff+6fmZlZPA97//79zqNGjWqdlZV1xtqyefPmuQDr168vVV/u8vozXtFK+wy1P/D7BRy3HuhW+nREag4nZxcGvvQlu+74K2tuG0rvmMLHyxpmWho+9iZPpC1l9GNfE+gb6NhEqyD3pu50i+7GyktWcjT5KB0+6oBHi3JZMFJERMShdu3a5frggw8GPvroo61CQkKOtmjRIjsvL8+kpKR4pqamehQ9n7r9Qs719ttvb09KSvJKSEio0759+869e/dOd3V1tTExMXUPHjzo0rJly+zPPvts8/nO4+rqynfffZc6cuRIO2PGDP+BAwcG//777+tat26dC3DPPfekLVy4cO+nn37aaNCgQSEREREZDRo0yE1KSvJKTU318PT0LPj44483na8H9anuueeeg88991zz2bNn+0HhCtfHe0+fKCYmps4rr7zS1MfHJ79Tp05HGzRokHv06FGnlStXeh84cMClcePGOU899dQ5p7Od7z2eaNy4cXv/+OOPegDXX3/9gTM9d12en+OJ3nnnnYZz5sw5axu4a6+99tBtt912CAoLzmnTpm0eNWpU20mTJjX79ttv/Tt06HB0165dbnFxcd533nnnng8++OC0qfAA//jHP3YMHz68/XvvvRcQHR3t07Zt22Pbtm1zX7Nmjde4ceN2vfnmm6cV1ePHj9/38ccfN4qLi/Nu3bp157CwsCP5+fksW7asbt26dfOHDh168Pvvvz/trviVV16ZUa9evfwVK1Z4d+3atUNQUNAxFxcXO2jQoIz777//nK1dyuvPeEUq7R3qNKDtBRzXpuhYkVqvSYdwei/bwbK3nmRXvcJvudnt4WXXGDq93YlXl7xKXoFabJ3KLcCNbtHd6PSfTgT85Yy/C0RERKqdsLCwrIkTJ27v169f+oEDB1z+97//+S5YsKCeMYZRo0btW758edLQoUMvaPpqvXr1ChYvXpwyceLE7a1atTq2ePFinz/++MPX19c3b9y4cbtiY2OT27Zte8aVuU/l7OzM119/vXnUqFH7Nm/e7DFw4MDglJSU4pWTP/nkk20fffTRxp49e2YkJSV5zZ07t35WVpbTDTfccGDZsmVrLjTnEzVt2jQvMjKyuK/xib2nT3TTTTelPfjgg7uCg4OzNm3a5PHzzz/Xj42N9Q4ICMh58sknd6xcuXLNiStwl/U9Hjd48OCM49OUx48ff8bp3uX5OZ4oJiameLG1M71iY2NPmkY+cuTIw7/99tvayMjIw7t373b97bfffLOyspxee+21zZMnTz7rYoFDhw7NmDlz5rqIiIjM7du3u8+bN6+ei4uL/fDDDzf+4x//2H2mMS1atMhbsWLFmuHDhx9wc3Oz0dHR9ZKTk72GDh16cMWKFcmNGjU642dQr169gu+//35d//790zdv3uwxa9Ys/2+++abB4sWLvc90/Kljy+vPeEUxpVmFzRgzExgKXG+tPWM/IGPMNcD3wCxr7fByybKKCw8PtytWrKjw60RHRxMVFVXh15GKk75vO7H3XM3trRPZesKi32FNwnj/8ql0D+x9xnH67E+Wl5GHs7fzOVd9rAn0udde+uxrr8r47I0xsdba8As5NiEhYXPXrl1PW3FZpCabNm2a35gxY1r37t07Y8mSJescnU9ZHT582MnX17e7p6dnwdGjR+MdnU91lpCQ0KBr166BZ9pX2jvUrxZtvzXGfGiMiTTGtDTGtCj67w+AGUDBCceKSBGfhs0Z9F0CX/91CaGNQovja7bG4RHRh+gRERxJ06rW55J7IJf4vvFsenxTqdt0iIiIiJxLVlaWmTx5chOA8ePHa1VUOa9SFdTW2oXAQxT2n76NwuepU4HNRf99R9E5H7LWLirXTEVqkN7NexN7byzP/+l53J3deWY+hOyHqBkrOBjUlBUfPe/oFKukvIw8Eq9M5MjqI2z71zbW3b8Om6+iWkRERC7Oyy+/3HD48OGBISEhnTZu3OjRq1evjJEjRx4+/0ip7Urd7dpa+xbQE/gc2ArkAflF//0p0NNaO6U8kxSpidyc3ZgwYAKr7kvgskMl6ze0OJhP+J3PsGhAIHtTVzsww6rHyc0J9+Yly6bvencXyaOSKcjViukiIiJSdr///nvdmTNn+h8+fNj52muvPThr1qxNjs5JqofSrvINgLU2nsI71CJykdo1DMau3MfC5+6l40sf4ne08I5rv4VbSOvUhQWP344deIuDs6wanNyd6PhNR1LuTGHPZ4WzsPZ+uZf8zHw6ftMRZ4+ztpUUEREROau5c+fWuAK6Xr16BdbaWEfnUdOV+g61iJQ/4+RE/4nvk796FYsGBhbH62dZBjz7EXXuG0rqsp8dl2AV4uTiRIePO9B0TEnbxAOzD7Dq6lXkZWq1dBERERGpPCqoRaqQhq070W9eKis+fI5tfiUTSHpuyKRJ/8H8+sCV5OSf1p6x1jFOhnZT2tHiiRbFsUO/HyLxskRy0xzaOUFEREREapFzTvk2xrx7Eee21tr7LmK8SK0VfsfTHLnuHqLvG0L//yzHpQA88uDn9XN5+N9hvHfNe/Rp0cfRaTqUMYa2L7bFpZ4LqRNSAUhfms7KQSvp+ktX3Bqd1lZSRERERKRcne8Z6rsv4twWUEEtUkZ16jci6psY1v7yJXl33UFuXjav94b8fUn0+7Afo8NHM+nSSfi4+zg6VYdq9VQrnOs6s2HcBgCOJBwh9ZlUgt8NdnBmIiI1g7UWY4yj0xARcYjztWk9X0F9T/mlIiJl0eHym/j9I382Zi3BY9UrHMk9gsXy9oq3WT1/Bi+3vIteD7zg6DQdqvnY5rjUdWHtnWvx6eVD21fbOjolEZEawRiTmZeX5+zq6prv6FxERBwhPz/f2Rhz9Gz7z1lQW2s/KP+URKS0nFzcuOeav3P5gNsZ89MYflr/E6YAnvtqL722TmLJZ5/S+rPZNG7X3dGpOkzj2xrjGuCKT28fXLzL1MBAREROYa1dkJ6efqm/v7/68YpIrXTkyBFPYOXZ9mtRMpFqpJVvK+bcNIevhn/F+OS6DNhaGO+zbAeeXcKYP+EWCvJr70rX/oP9cfV1PS2etTHLAdmIiFR/eXl53+7bt8/k5eXp74wiUutYazl48KBbbm7uT2c7psw/HI0x3saYKGPMCGNMr7KeR0RKxxjDjaE3MvG1eBZc0q44Xu8YDJz0BYkd/dm4+EcHZli1bH9rOzEhMez5co+jUxERqY7+yMrKen/Dhg0+Bw4c8M3NzXU53/OEIiLVnbWWrKwst23btvmnp6cnAl+d7dhSz4s0xtQFJgO3AsdvBX0CLCvaPxp4CrjBWhtT2vOLyIWp36wtA35bR/z0V6n/0JME7itsF9VtXTrZA4fwx6go+k79AXevug7O1HH2/WcfGx4sXKws+eZkcvfn0nxccwdnJSJSffTo0cPGxsa+dOTIkZjs7OwRxpgB1lpfR+clIlLBrDFmf35+/vsFBQWf9ujR46x9a0tVUBtjvIBooDuwH4gDLj/lsF+AqcAwQAW1SAXr/pdHyBpyO9Gjr6HfV4txLQD3fBj0cTQb5jbg6JTX6TJ8tKPTdIi6veri1dGLo2uOgoUND24gd18ugc8GasVaEZEL1KNHDwv8XvQSEZETlHbK918pLKa/BFpbawefeoC1diOwHvjTxacnIhfC08ePqC8Wkfrbt6xuXac4HrQ7h44jxvD0Bzdz+FjtW0/Go7kH3Rd0x6d3SWuxLf/cwvox67H5mrIoIiIiIhentAX1n4FdwF3W2iPnOG4L0KzMWYlImbQfdAMhKQeZ9/BwMt0KY9Mi4IXt0+n4dkdmJc9ybIIO4OrnStffuuI32K84tvOdnawZuYaC7AIHZiYiIiIi1V1pC+q2QIy19th5jtsPNChbSiJyMZxd3Yh8dQbpsUv4JaoFEy4pjO/M2Mn131zPsK+HsePgFscmWcmc6zgT+kMojW5uVBzbN2MfiVclkpdRe1dFFxEREZGLU9qCOhdwv4DjmgOZpU3GGBNsjBlvjPncGLPWGFNgjLHGmBvOMebjomPO9lp7nmv+xRizwBhz2BiTaYxZYYx5wBij9hBSrTUN7c1lv2/hw5u/IaBOQHF80YrvyA1qzbwnRtaqFltOrk6EfBpCs/Elk2cO/X6IlVErydlz1nUmRERERETOqrRF4zqguzHmrEW1McYX6AqsLkM+o4HXgZuBYKA0qwYtonC18VNfZ53jaoyZCnwBhAMLgF+B9sAUYIYxxrn0b0Gk6jDGMKLTCJIfSObu7ncD8PpcCEyzRL78Nas7+LFh4Q8OzrLyGCdD0GtBtH6+dXHsSNIRsjapT7WIiIiIlF5pC+r/AAHAC+c45jnAG/i2DPmsBl4BbgSCgHmlGPu+tfb2M7yeOtPBxpjhwBhgN9DFWjvEWjsMaAckU7hK+dgyvAeRKqe+Z33eu/Y9FgybQ5+9rsXxLhsyaBk1lOjbIsk+ku7ADCuPMYZWE1rR/t32GFdDx+kdqdennqPTEhEREZFqqLQF9VtACvCQMWaeMebBongrY8w9xphfKLzLnAS8X9pkrLXvW2sft9Z+U7RaeEU6Xmg/Ya1df0IOeyh8DwBPauq31CT9u1xNk417ib6lP7lFf7Ld8iHq0/nsaNOQhG+nODbBStT0nqb02tCLhtc3dHQqIiIiIlJNlapYLFrZ+3IgFhgAvFa0Kwp4B7gUSACuttZml1+a5csY0xzoAeRwhjvp1tp5wA6gMdC7crMTqVge3r5EfbaAzb/PZFVb7+J4m705dP3zOOYPDuHw7tqxaJlHS4/TYlkbs9j1wS4HZCMiIiIi1U2p775aa7dZa3sC1wL/Bn4BfqfweeUbgXBr7bZyzfLCDDLGvGqMedcY809jzBXnuLvcvWibZK0928OTy085VqRGaRc5jE4pacx7dATpJ6yKMPDntRxr34ZFbz+FtbWrV3POvhwSByeScncKm57eVOvev4iIiIiUjktZB1pr5wBzyjGXi3XrGWJrjDEjrbWrTokfX5HoXLfhtp5yrEiN4+TsQuQr37DrzuWsufVaeq/YDUBARgFjo1/kZb81TL1qKs19mjs408qR+kwqWRsK/41t6wtbyd6eTfB7wTi56ckPERERETndOf+WaIyZYYy50hhTmtW2K9tK4EGgE4WLoTUFhlA49bwj8JsxptkpY47Pcz1yjvMeb/tVt/xSFamamoRE0GvZDpa8/ii7fZz4oT3M6Ag/pPxAx6kdmRIzhfyCfEenWeHaTm6L31V+xV/v+XQPq4asUq9qERERETkjc64pjcaYAsACuyic0v3xiQt4VTRjTDQQCYyw1s4o5Vg3ClcJ7w1MtdaOPWHf0xSuRv65tXbUWcY/D0wA3rXW3neG/fcC9wIEBAT0+Oqrr0qTXplkZmbi7e19/gOlxqnMz/7Yod1M3/ARnx355aT4jQcDubH9ndTvNKBS8nCYfOBV4KcTYkHAi4B/5aai7/naS5997VUZn/2gQYNirbXhFXoREZFa4nxTvqdR+Fx0U+BJCle9Xgh8CHxrrT1awfmVmbU2xxgzCfgeuOqU3RlF23P9xjq+L+NMO6217wLvAoSHh9uoqKiyJ3uBoqOjqYzrSNVT2Z/9YEZyz5YF3DvnXtbuX4tHLjz32WZaHZ7Iopv60fudOXh4+1ZaPpXN/smy5R9b2Px/mwsDG8D9r+50+W8X6oTUqbQ89D1fe+mzr7302YuIVC/nnPJtrX2AwmL6RgoXHyugcHXvD4Hdxpj3jDF9KzzLsltbtD11yvfmom2rc4xtccqxIrXKgFYDWHnfSiYOnMj/zXciKA1cCyDqi0XsatuIlV+94egUK4wxhsC/BxL8fjA4F8ayt2QT3zeetOg0xyYnIiIiIlXGeVfasdbmWGu/tdZeSWEB+jSwjsI7uHcBC4wxycaYx4wxjSs23VI7PkEz85R4fNG2kzHG8yxjI045VqTWcXdx59lBz3LD87NIDCpZTqD13ly63fQQ8y/vwKGdqQ7MsGI1uasJnX/ojJNX4Y/KvEN5JF6eSPrydAdnJiIiIiJVQWn7UO+01k6y1oYA/YAPKJwSHUzhE4ZbjTHfG2OGGmOcyz/dUvtz0Xb5icGitl5xgBsw4tRBxphIoDmwG1hSwTmKVHltB1xL6NqDzH985Mkttn5NISc4iMWTH8YWFDguwQrkf5U/3ed3x62xW+HXQ/yp20NrFYqIiIhIGfpQH2etXWKtvQdoAtwGRFM4OXIIMBPYUR4JnosxppsxZsipxbsxxsUY8wiFq38DvHaG4ZOKti8ZY4JOGNsIeLvoyxettTWzShApJSdnFwa+9CVHVi5nWUST4nijzAL6Pvo6y8ObsCNpqQMzrDh1e9QlbFkYAbcFEPJ5CMapKjc+EBEREZHKctHNVa21Wdbaz6y1lwCDgf2AARqW9lzGmDBjzNLjLyCsaNcLp8SPCwRmA3uNMUuMMd8aY+ZS2F96ctExT1hrfz5D3jMoXHStMbDKGDPbGDMTWE9hu63vgCmlfQ8iNV2TDuH0itnJ0jcfZ7dPyY+QnvF7cendl6nz/lUjW2x5tPQg5OMQnL1Onnxj8y25abkOykpEREREHOmiC2pjjLcx5i5jzAJgLiWF9LYynM4H6HXC6/i8ynanxI9LAN4AUoCWwDUUttk6CnwE9LTWvny2i1lrxwA3Uzj9OxK4AtgAjAWGW2trXlUgUk56j3sJz3WpzL+qU3HslT6WsdGP0ffDviTuSXRgdpVnw183ENczjqPrq2zTAxERERGpIOdrm3VWxphBwB3A9YAnhXels4EfKFwF/Jezjz4za2100Xku9PhU4KHSXueUc0wHpl/MOURqq3oBLRn442oS/zONrZOe5PXehYt1xeyIoce7Pfhrn78yccAzeLnXzH6629/azo43Cp9uiesdR+h3ofgOqLntxERERETkZKW6Q22MaW2M+T9jTCrwG3AL4EXhneLxQFNr7Y3W2p+ttbb80xWRqqjL8NFctnQvEy95FjfnwsW78gry+GHWS+xs6ceKj15wcIYVw72pO04eRSuAH8wj4dIE9kzf4+CsRERERKSynLegNsZ4GWNuM8b8QeHzxX+jsH3WIWAqEGatDbPWvmWtVYNWkVrK3cWdiZETSbg/gYGtBmIK4N3ZELQ3l/A7n2bRgED2bVrt6DTLVcPhDekW3Q3XRq4A2BxL8s3JbP7nZvRviiIiIiI13zkLamPMBxS2jvqQwmeMofDO9E1AE2vtOGvtyopNUUSqkw4NOvDHbX/wdbfn6LS/5AmOfgu34BLahQV/u42C/DwHZli+fHr5ELYsDK+OXsWxzRM3s/b2tRRkq0mAiIiISE12vjvUdwDewGbg70CgtfYKa+3X1tqcik5ORKonJ+PEiGFPk5e0ikUDA4vj9bMsA577lFUd/dm4aI7jEixnnoGedF/UHd9LSp6f3vPpHlZespKcvfpRKSIiIlJTna+g/gK4xFrb1lr7T2vt9spISkRqhoatO9FvXiqxH73AFv+SNRC7rkunReQ1/HHbQI5lHnJghuXH1deVLv/tQuO7GhfH0helE9szliNJRxyYmYiIiIhUlHMW1NbaUdbaPyorGRGpmXrc/hQNN+4iemRvcot+6rjlw6BPF7CrbSNiZ051bILlxMnVieD3gmk7uW1xv4KCIwU4eV10h0IRERERqYL0tzwRqRRe9RoQ9eUSUv83g9VtStpotdqby+j/juWO7+/gwNEDDsywfBhjaPFICzrP7oyLvwudZnXCs7Wno9MSERERkQqgglpEKlX7qOF0XJfG/Mdv5LA7TOkJy5vDxys/psPUDnyW8FmNWCHb/2p/em/ujW//0/tS14T3JyIiIiIqqEXEAZycXRj40ldkJcYSO+a64vj+o/u59btbmfBodzbH/OrADMuHi7fLabFDCw+RcGkCOfu0WJmIiIhIdaeCWkQcpnH7MD65bRazb5pNy3otAWiUCY+/nUDjfpcTfc9l5GRlEeESigAAIABJREFUOjjL8pOVmkXSsCQO/X6IuJ5xZK6uOe9NREREpDZSQS0iDjek/RCSxiTxSO9HePUXqH8MPPIg6v3f2NqmAYn/meboFMvF4QWHyT2QC8CxzceI7xPP/jn7HZyViIiIiJSVCmoRqRK83byZfMVkwl7+nDUtvYrjQbuz6XLDGOYPDuHwrs0Oy688NL61MaE/hOLs7QxAfmY+q69dzdZ/bdVz1SIiIiLVkApqEalSQq64meD1B5k3/joy3UriA39eS3b7tiz+13hsQYHjErxIDYY0oPuS7ngEehQGLGx6bBNrb11Lfla+Y5MTERERkVJRQS0iVY6zmzuRr88iPXYJMWEBxfFGmQX0fexNYrsHsD1hgQMzvDjeod6ExYRRr3+94tiez/cQPyCeY9uOOTAzERERESkNFdQiUmU1De1NxPKdLH3jMXb5lPy4Ck/cz7FLIpm84GXyCvIcmGHZuTV0o+tvXWlyT5PiWGZsJrHhsRxacMiBmYmIiIjIhVJBLSJVmnFyoveDL+O1LpX5QzpzfLL3E5dYHv39CcLfDWfZ9mUOzbGsnNydaP/v9rR7ux3GxQCQuzeXoylHHZyZiIiIiFwIFdQiUi3UC2jJwNmJrPnhfT65tAEzQwrjCXsS6PNBH0bPGU3a/u2OTbIMjDE0G92Mrv/rimtDV5qOaUrTu5s6Oi0RERERuQAqqEWkWgm95i7+MncnL132Ep4ungBYLBu/foe81i1Z9MLoarlome9AX8Ljwwl6PcjRqYiIiIjIBVJBLSLVjquzK4/3e5w1D6zh6nZX45ELb/8IDTMt/Z5+h/jODUhdOtfRaZaaezN3nFxP/rGcl5lH4tWJpK9Id1BWIiIiInI2KqhFpNoK9A1k9k2zmd3zdeoUOBfHw9ak0bT/lUTfFsmxzGq8wJeFlDtSOPjTQeL7x7P7s92OzkhERERETqCCWkSqNWMMl147Hu8NW5k3LIz8wrW9cM+HqE/ns7tNI2I/edGxSZbVTkj7LQ0Am21Ze+taNjyygYK86jelXURERKQmUkEtIjVC3QZNiZwZy4afv2R16zrF8cB9ufS4/SkWDQhk78ZEB2ZYBs0gbHkYXh29ikPbX9tO4hWJ5OzLcWBiIiIiIgIqqEWkhgm+bCQhKQeZ/+RNHPYoifdbuAX30K78+MZY8gvyHZdgKXkFeRG2NAz/of7FsUO/HyI2LJb0GD1XLSIiIuJIKqhFpMZxdnVj4KTpZK9OYNHAwJJ4PozePJW+H/Ylfle84xIsJZe6LoTODCXw/wKLY9nbs4kfEM/O93Y6LjERERGRWk4FtYjUWI3adqHfvFTiPn2Z1Iau/H0QbPOFmB0xhL8XzsNzHyYjO8PRaV4Q42QI/Hsgned0xsXXBQCbY1l37zrW3r2Wgmw9Vy0iIiJS2VRQi0iNFzbqMZps2ovvY3/DzdkNgAJbwOvLXue1Ec1Z8vpj1aZ3tf/V/vRY0YM6XUqeE8/elo1xMQ7MSkRERKR2UkEtIrWCh7cvf7v0H6wavYpL21wKQMe98NSP6fR5+F+s6NGYbSvnOzjLC+PZ1pOwJWEE3BKAeyt3Ok7viHFWQS0iIiJS2VRQi0it0t6/Pb/c8gvTr5/OSwvccS26MR2xch/+PSOJvn8wOVmZjk3yAjh7OdPh0w70iOmBq7/rSftsvsVa66DMRERERGoPFdQiUusYY7ip800M+CWFeVd34vhkb69ciPr3z2xt04CEb6c4NMcLYYzBrZHbafHUiakkXZ9EXnqeA7ISERERqT1UUItIrVWvcSsi56xmzQ/vs7aFZ3E8aHc2Xf88jgWXtGP/5mQHZlh6+7/fz9YXtrL/u/3ERsRyZM0RR6ckIiIiUmOpoBaRWi/0mrsI2nCQeeOvI+OEG74Dft+Ac8dOzH/qL+Tn5jguwVJIX17SmzprXRaxPWPZ89UeB2YkIiIiUnOpoBYRAVzcPIh8fRaZK2NY2rNpcbx+lqXOJ1/S98O+rNi5woEZXpg2z7UhZHoITl6FP94LjhSQfFMy68asU2stERERkXKmglpE5ARNQiLovWwHy997li0NXCgAxlwNMbtj6fleT0bPGU1aVpqj0zyngJsCCFsahmdQyTT2ndN2Et8/nqzULAdmJiIiIlKzqKAWETmDiLsnEpC6j6+fv4mEVu4AWCzvxL5DyJvt+f3VcRTkV91Fv7w7e9MjtgcNb2hYHMtYkUFsWCz7Z+93YGYiIiIiNYcKahGRs/Dw9uWmCdNJGpPElUFXFseHLtzPn/46hdUd/Fj3xwwHZnhuLj4udPymI0FvBGFcCvtU5x3KY/W1q9n+1nYHZyciIiJS/amgFhE5j7Z+bfnxLz8y888z6erUlEm/Fca7bMigzaUjmDcsjPR9VbNANcbQ/MHmdFvQDfcWhXfanes643eFn4MzExEREan+VFCLiFwAYwzDQoaxaGw8idf1Jse5MO5SAJHfxXM0qBWLXx6HLaiaC3/V612P8Phw/K7yI/iDYLzaezk6JREREZFqTwW1iEgp1KnfiKgvl7Bt3mziOtYvjjdOL6DvE1OI79yATYt/dGCGZ+fq70rnOZ1pNKLRafsyYjOwBdYBWYmIiIhUXyqoRUTKoG2/IXRftZ/FL49jt0/Jj9KwNWk0HziE6JF9OJK214EZnpkx5rRYRlwGcX3jSLwykZx91aPftoiIiEhVoIJaRKSMjJMTfR97E68NW5h3XXfyin6iuuVD1NdLeW9kO75b+x3WVt07v3mH80gakYTNsaT9ksaK7is4tPCQo9MSERERqRZUUIuIXCSfhs2JnBXHpt++JTGoLgA7vWFiWDrDvh7GkC+HsPHgRgdneWZOdZxoNLJkCnjOjhxWRq1kywtbNAVcRERE5DxUUIuIlJP2g24gdO1BFj57F09eX5cMj8L4T+t/otPbnXjphyc4llm17v46uTjR5vk2dP6xMy5+LoXBfEh9OpXEKxLJ3p3t2ARFREREqjAV1CIi5cjJ2YX+E9/n9Xc2c3+P+zEUPrOcnZ9N4ISX2RPYkJhpf4MqNg3c/yp/wuPD8ennUxxL+y2NFV1XcPDXgw7MTERERKTqUkEtIlIB/Dz9mDZkGsvuXkZ403Au2Qg3JkGrA3n0HPMcy8MC2Bzzq6PTPIlHSw+6RXej5YSWFP07ALl7c0m8IpFNEzZRkFc1W4KJiIiIOEqVKqiNMcHGmPHGmM+NMWuNMQXGGGuMueECxv7FGLPAGHPYGJNpjFlhjHnAGHPO91jWcSIiFyKiWQRL71rKEyF3k+ZZssJ2xMp9NOl7OdE396tSq4EfnwLe5ZcuuAa4FgYtbH15K0dWHXFsciIiIiJVTFUrGkcDrwM3A8EU3yM5N2PMVOALIBxYAPwKtAemADOMMc7lOU5EpDScnZy57Kn3KFibzPzBIRy/z+ueD1HTF3O4TVOWTH4YW1B17gD7XepH+Mpw6l9W2Gu7zfNtqNu9roOzEhEREalaqlpBvRp4BbgRCALmnW+AMWY4MAbYDXSx1g6x1g4D2gHJwDBgbHmNExEpK/+WwQz87xpS/vsZq9p4F8ebHsqnz6OvszLUn40LfnBghidzb+xOl7ldCPkihBaPtXB0OiIiIiJVTpUqqK2171trH7fWfmOtvdAeM08VbZ+w1q4/4Vx7KLzjDfDkGaZwl3WciMhFCRl8C53WpbHw2bvY510yEad78iFaRQ1l0vu3c/jYYQdmWMI4GQL+EoBxOnnC0LEtx1h56UqOrj/qoMxEREREHK9aF4vGmOZADyAH+PbU/dbaecAOoDHQ+2LHiYiUl+OrgbutT2Xe0G7kFf00ntMOJuz4hOApwfy8+2cKbNWZBn5cQW4Ba25aw6H/HSI2LJY90/c4OiURERERh6jWBTXQvWibZK3NOssxy0859mLGiYiUq3qNWxH5XTypv88kJrQ+j1xRGN9zZA8vprzIgI8GsHLjYscmeYqM5RlkxGYAkJ+ZT/LNySTfnkxeRp6DMxMRERGpXNW9oG5dtN1yjmO2nnLsxYwTEakQ7SKHEZF4gEn3fEWzus2K4/EbF1MvvB/zrw4lbceFPglTser1rUfYkjA8gzyLY3s+2cOK7itIj0l3YGYiIiIilau6F9THV/U5Vy+XzKLticvTlnWciEiFMcZwY+iNrB27lif7PYmLcWHCAmh9CAb+lERB+3bMf/oW8nNzHJ0qdcPq0iOuBwG3BBTHjm08Rny/eLa8sAWbbx2YnYiIiEjlcHF0Ahfp+Co5pf2bW1nHlZzAmHuBewECAgKIjo4u66kuWGZmZqVcR6oeffa1zxUuVxAY0ooOM54CDgHgf9Qy8IUvWP3pDFIeHId/xNWOTRLgLqAlhQ0Pj4LNs6Q+nUrqN6kwAWjk2PSqK33P11767EVEqpfqXlBnFG29z3HM8X0ZJ8TKOq6YtfZd4F2A8PBwGxUVdc5Ey0N0dDSVcR2pevTZ11LRMHDlAZZNe4amE1+hxcHCZ5RDt2cT+vi/WPCn7wh+byaN2nR2bJ5RkHV3Fsk3J5O+pGjKdwK43O9Cz7U9cWvk5tD0qiN9z9de+uxFRKqX6j7le3PRttU5jjnePHXzCbGyjhMRqVTGyYleD7xAg9Q9RN8eRdYJ/ww64PcNeHTsQvTYIeRkZZ79JJXAs7Un3eZ3o9XEVsW/WQJuDlAxLSIiIjVadS+o44u2nYwxnmc5JuKUYy9mnIiIQ3j6+BH10R8ciF3A0ogmxXGfbIia+iNrQhryY8ocB2YITi5OtH62Nd3mdcPvaj/avNzGofmIiIiIVLRqXVBba7cBcYAbMOLU/caYSKA5sBtYcrHjREQcrXmX/vSO2UnsRy+wsXHJ3d8POh5jyFfXcNUXV7F2/1oHZgi+/X3pMqcLzp7OJ8Vz03LZ/tZ2bIEWLBMREZGaoVoX1EUmFW1fMsYEHQ8aYxoBbxd9+aK1tqCcxomIOFyP25+iZWoa8x4axpJWzkwLL4z/d8N/6TytM4/8/AiHDu9xbJInsNay7t51bHhwAwmXJ5C9I9vRKYmIiIhctCpVUBtjwowxS4+/gLCiXS+cEi9mrZ0BTAMaA6uMMbONMTOB9UBH4DtgyqnXKus4EZGqwtXDi8jXZhK0eid397wPU9TAIK8gj3kzXyOneRPm/+3WKtFma//M/eybsQ+AQ/87xPIuy9k7Y6+DsxIRERG5OFWqoAZ8gF4nvI73gG53Svwk1toxwM0UTuOOBK4ANgBjgeHW2vwzXays40REqpKG3o14Z8g7xN0Xx8BWA8HCG/+FRpmWgc99xrq2viTMmOrQHP2v9afl0y2LmxbmHcxjzYg1JN+aTN7hPIfmJiIiIlJWVaqgttZGW2vN+V5nGTvdWtvPWutjra1jre1hrZ16vinbZR0nIlLVdGvcjejbovmh/1RaZ5Q8vxyyLYuuI8ayuH8rdiYtc0huTq5OtHmuDd3+6IZ7S/fi+J7P9rC8y3LSotMckpeIiIjIxahSBbWIiFwcYwzXXDqG+pt3E317FEddS/b1XbQV3+69ib7zTxxNP+CQ/HwjfYlIjCBgVEBxLHtrNgl/SmDDoxvIP6aJQSIiIlJ9qKAWEamBvOo1IOqjP0iLW8zivi1K4rkQ9dEfHAwMYPGrD2MLKn8yjks9F0I+DaHjNx1x8StqrG1h++TtxEXEkXswt9JzEhERESkLFdQiIjVYs9A+9F20lYSv32RtC8/iePO0fPr+9XW+uaoVCbsTHJJboxGNiFgVQf0r6hfHPNt54lLfxSH5iIiIiJSWCmoRkVqg65/H0W7jIeZPuJn9dQqXosg38Hzr7YS9G8b9c+5n35F9lZ6Xe1N3uvy3C+2mtsOjjQft322PMWdcKkNERESkylFBLSJSSzi7ujHw+c9xWb+Jedd15+1ehlWNocAW8O/YfxP0VhCToyeRfSS9UvMyxtBsTDN6JvfErYHbSfvys/LZ+81erLWVmpOIiIjIhVBBLSJSy/g2CSRyVhyXfr+ay9teXhxPz05n9wsT2N3KnyWvP1bpz1c7uZ3+K2nTU5tYc+MakoYnkbPP8f20RURERE6kglpEpJYKadSRuTfPZfZNswn2D6ZhJjwzH1odyKPPw/8ioaMfyXM/d1h+adFp7HhjBwD7Z+1neefl7P9hv8PyERERETmVCmoRkVrMGMOQ9kNYNXoV77QeS75zyfPL3VIOE3zlKBb+KYjd6+IqPTefCB+a3t+0+OvcPbmsHrqa5NuTyT2klcBFRETE8VRQi4gIrs6uXD/mLcy69URf143cot8OTkD/PzZSN7RHYf/qw5V3h9i5jjPtp7Wn84+dcWtc8mz1nk/2sDx0OQd/PlhpuYiIiIiciQpqEREpVr9ZW6JmxbNt8X9Z1iOgOF6nqH/1ocDGLHphNAX5eZWWk/9V/kSsjqDRTY2KYzk7ckgcnEjKvSnkZVReLiIiIiInUkEtIiKnadNrML1W7Cbu05dJaeZRHG96KJ9+T7/DpDvasWjrokrLx9XflY7TO9JpRidcG7gWx3e9t4vlnZeTtTmr0nIREREROU4FtYiInFXYqMcISj3M/KdHsc+78PnqzfXgny030/+j/tw440Y2H9pcafk0HN6QiKQIGlzfoDjm3swdjxYe5xglIiIiUjFUUIuIyDk5u7ox8LlPcd+0lT9G9uHJK13ILrpJ/E3SN3SY0oFJXz5A+r7tlZKPWyM3Os3oRMgXIbg1c6PDxx0wJyymJiIiIlJZVFCLiMgF8WnYnEFfLubFaev5c6c/F8ez87PpNvFtstu0ZP4zt5KfW/H9oo0xBPwlgN6beuPVzuukfTbfsv3N7eRn5Vd4HiIiIlK7qaAWEZFSCfQN5OsbvmbhHQuJaBrBFevhyg3QMNMy8PnP2BTow4oPn8MWFFR4Lk5up/8a2zZ5GxvGbyA2LJb0mPQKz0FERERqLxXUIiJSJv1a9mPp3Ut5otcj7PR1Lo6325lN+F1/I65LQ1J++7pSc8ralEXq31IBOLr2KHF94tj45Ebyj+lutYiIiJQ/FdQiIlJmTsaJQeMm47t5N9F3/onMknbR9Eg6SLvLRrLgkiB2JS+vlHw8WnvQ7s12ONUp+vVWANte2saKbis4vPhwpeQgIiIitYcKahERuWhe9RoQ9cH/OLomgfmDQ8gvWiPMCRjw+0bqde3JHzf3q/CFy4wxNL2vKRGrIvAd5Fscz0rJIr5/POsfWk/+Ed2tFhERkfKhglpERMpNo7ZdGPjfNaTO/56Y7o2K4165MGj6Ym74Z2feXv42ufm5FZqHZ2tPuv7WlfbvtMe5btF0dAs73tjB8i7LSfs9rUKvLyIiIrWDCmoRESl3Qf2vpWfcHuK/mExyS08AvgyFX/0P8cBPDxA6LZTv136PtbbCcjBORXerV0fgN9ivOH5s0zESLklg38x9FXZtERERqR1UUIuISIXp/pdHCN6UzsIX7mfqdU2L4+sOrOO6r6/j6fGhJM35qEJz8GjpQeefOtPh4w64+LoA4NneE78r/c4zUkREROTcVFCLiEiFcnJ2of9T0/h14gZevORFfNx9APA5Bg9/sIZO19zJ4v6t2LZyfoXlYIyh8W2NiVgTQYNhDQj+IBhnT+fzDxQRERE5BxXUIiJSKTxdPXmi/xNsfHAj43qOY8IiQ8Ojhfv6LtpKo/BIom8I59DO1ArLwb2JO6EzQ/Ht73tS3FpLyr0p7PtO08BFRETkwqmgFhGRStXAqwFvXvkmN/7rZ5b0KpkG7p4PUf+JxQa1JfrBoWQfSa+0nPZ+tZdd7+0iaVgSSSOTyNmXU2nXFhERkepLBbWIiDhEYM/L6LN0B4kz3mZVG+/ieP0sS9RbP7CvhR8Ln7+f/NyKLW5tgWXrpK3FX+/7eh8xITHs/mx3hS6aJiIiItWfCmoREXGoLsNHE7r+MEsmP8wWf5fiePO0fPo/8282tK7HvF/eq7Di1jgZus3rRuM7GhfH8g7ksfbWtSQOTiQrNatCrisiIiLVnwpqERFxOOPkRJ9HXqXxlgPMe2gYB7xM8T6fw8e4at69DPpkEMu2L6uQ67vWd6XDhx3oMrcL7i3di+Npv6SxvNNytv5rKwV5BRVybREREam+VFCLiEiV4V7Hh8jXZuK6eSvRowZwxBX+LwqOusG8LfPo/UFvbvjmBlL2JlfI9f2u8CMiKYJm45tBUU1fkFXApsc2Edcrjoy4jAq5roiIiFRPKqhFRKTK8WnYnKhP53MkOQHXu+/F2ZS0uPpP8n9YNagj86/syJ71K8v92i7eLrR7vR1hS8Oo07lOcTwzLpPtb24v9+uJiIhI9aWCWkREqqxGbbswZei/WfPAGkZ0HAFAn61wwxoYODeZup26E31zPw7v2XqeM5WeT08fesT2oPULrTHuBtcGrrT9V9tyv46IiIhUXyqoRUSkymvv355vRnxDzN0xPLSzRXHcKxeipi8mr00g0eOvK/dWW06uTrR6qhURqyIImR6CWwO3k/bnHc4jZ79abImIiNRWKqhFRKTaiGgWwYgfN7Piw+dZ28KzOO5/1BL15vdFrbbuK/dWW17tvPC7zO+0+MYnNrI8ZDl7vtijFlsiIiK1kApqERGpVoyTE+F3TKB9ajqLJo1h62mttt5lQ+t6LH/vWWxBxa3MfWjBIXb9exe5+3NJviWZxCsTydqsFlsiIiK1iQpqERGplpycXej35FQab0tj3iPD2V+npNVW8I5jRNz7f9z9XASLty2ukOvbPIt7ixNabP18QoutXLXYEhERqQ1UUIuISLXm5ulN5OQZuKVuJfrWgWQWPeb8fTB8aOPo92E/hkwfwsrd5bsieP1B9QtbbD14Qouto4UttmJ7xHJ48eFyvZ6IiIhUPSqoRUSkRvBp2JyoT+aRtSaR+VeHMvGyklZbP67/ke7/7s4Lf4siddnP5XZNl7outHujHWFLTm6xdWTVEeL7xZNyXwq5B3PL7XoiIiJStaigFhGRGqVh284MnLOKmc+mcEuXWzBFt4+9cuDO1+bRou9g5l/egZ1Jy8rtmj69CltstXm5DU5eJb9ad727i5gOMWSl6tlqERGRmkgFtYiI1Eht/dry2bDPSBydyHUdrmNsDDQ+Ai4FMPDXFPy79mbesDD2pSaVy/WcXJ1o+VhLeq7pif81/sXxOqF18Aj0KJdriIiISNWiglpERGq00EahzLpxFrc+9BFxHUtaX7nnQ+R38Xh2CCV61AAO795SLtfzaOVB5x86E/pdKJ5BnrSf1h5jzPkHioiISLWjglpERGqFTlffTljSAeI/e4XVrUued/bOgajPF1LQpjXRo6/k6OH95XK9BkMb0HNtT7yCvU6KF+QUsOraVRz85WC5XEdEREQcRwW1iIjUKt1veZROG9JZ9vYE1jctaXtVP8sS9c5cMloE8O1Hj5GTn3PR1zLOp9+Z3vbqNg7MPkDiFYkkjUwie1f2RV9HREREHEMFtYiI1DrGyYleo5+n7ZYMFk0aw5YGLsX7nPMKuGvdvwieEswnKz8hvyC/3K5bkF3Ajrd2FH+97+t9xHSIYcfUHdh8W27XERERkcqhglpERGotJxdX+j05labbDjN/ws3squfEpAGQ4QGbD23m9u9vp/O0zsxa+gkF+XkXfz13J8Ljwgm4JaA4lp+ez/qx64nrHUf68vSLvoaIiIhUHhXUIiJS67l6eDHw+c/x3bqPlhNewt+zZJXu5P3J5N51Oxta1WXZW09iCwou6lpuAW6EfBZC1/91xbO9Z3E8Y0UGcb3iSLkvBQ5f1CVERESkkqigFhERKeLp48f4yMfZNH4Tz0Y9S123unTZDX9eA+13HKPXgy+REujN8n///aIL6/p/qk9EYgSBzwZi3IuetbaFvau5FXZ/svvi35CIiIhUqBpRUBtjPjbG2HO81p5j7F+MMQuMMYeNMZnGmBXGmAeMMTXi/42IiJSej7sPEyMnkjo+lQm+13DEtWRfh21ZRNz/D5KCfFjx0fMXVVg7uTsRODGQnkk98buqpKUX6ZC9XYuViYiIVHU1rWhcBHxyhtesMx1sjJkKfAGEAwuAX4H2wBRghjHGuRJyFhGRKsrfy58bJ/3A0ZTVRA/vQVbJ2mWEph4h/M5nWBXsS/wXky/qOp5tPek8pzOh34fiEegBzaDFoy0uMnsRERGpaDWtoH7fWnv7GV5PnXqgMWY4MAbYDXSx1g6x1g4D2gHJwDBgbKVmLyIiVVLD1p2ImrGC9DXxzBvajWMnFNZdNmTQ/ZZHiQ+pT9yP75f5GsYYGlzbgIg1EfBC4d3rEx1dd5Sd7+/EFmg1cBERkaqiphXUpXG8yH7CWrv+eNBauwcYXfTlk5r6LSIixwW060bkd/GkJcYw7+pQck6Yx9R97SEennEPl392OUu3Ly3zNZw9naHlyTFrLevHrWfdPeuI6xtHRmxGmc8vIiIi5adWFovGmOZADyAH+PbU/dbaecAOoDHQu3KzExGRqq5JSASRc1axN24h8y/vQK4T/NYa5gfCr5t+pc8Hfbh6+tWs2LG8XK534IcDpP2SBkDGsgxiI2JZN3oduQdzy+X8IiIiUjY1raAeZIx51RjzrjHmn8aYK85yh7l70TbJWpt1lnMtP+VYERGRkzTv0o+BPyeza8Uf/P7IdTid8Cvnp/U/MW1MT5aFNyHlt68v6jr1L6tPq7+1wriVrAa+852dLGu/TNPARUREHKimFdS3Ag8D9wDPAHOBVcaYzqcc17pou+Uc59p6yrEiIiJn1LJ7FC+MnUXyA8nc3PlmDAbXPPjbPOgVu5vgy0aytGfTMhfWzl7OtP5HayKSIvC7smQ18LwDeYXTwPvEkb4svbzejoiIiFygmlJQrwQeBDoB3kBTYAiQAHQEfjPGNDvheO+i7ZFznDOzaFu3fFMVEZGaqr1/ez6//nNWj1nN3xlI4OGSfb2X7yL4spEsi2jCmp+/KNP5vYK86PxjZzrN6oR7K/fieEZMBnFpgN3sAAAgAElEQVS940i+PZns3Wq3JSIiUlmMtTV3mpgxxg2YR+Fz0FOttWOL4k8DzwGfW2tHnWXs88AE4F1r7X1n2H8vcC9AQEBAj6+++qpi3sQJMjMz8fb2Pv+BUuPos6+d9LlXf2mr5+P//psMTDhw2r6Fneqz54578e8x+LR9F/TZHwOmA18BJz5KPZXCf0qWaqkyvu8HDRoUa60Nr9CLiIjUEjW6oAYwxlwLfA+kWmvbFMUeBN4AvitqlXWmcW9QeNd7srX20XNdIzw83K5YsaJ8Ez+D6OhooqKiKvw6UvXos6+d9LnXHCn/+4aDTz9Cn2U7Ttu3vGtDPP/5IqHX3FkcK81nn7Upi41/3cj+7/YTcGsAIZ+ElFfa4gCV8X1vjFFBLSJSTmrKlO9zWVu0PXHK9+aibatzjGtxyrEiIiJlEnzJn+mzdDvro2eyuE8LCk7YF5Gwj1n/uovBnw9mybYlpT63ZxtPQmeF0uXXLrR5sc1p+w/89wBH1x29iOxFRETkbGpDQe1ftM08IRZftO1kjPE8y7iIU44VERG5KO0ih9F38VY2zfuOxf1aUgCku8FrveHnjT/T98O+XPbZZaw6vKrU5/a71A/3Ju4nxXLTckkelczy0OVsfHwjeel55fROREREBGpHQf3nom1xM1Br7TYgDnADRpw6wBgTCTQHdgOlv10gIiJyDkEDh9J34RZSF83howcHcLhOya/j3zb9xhv/e5AVoX6s/OqNi7rO5r9vJu9AHjbXsu2VbSxrv4zdn+xWmy0REZFyUu0LamNMN2PMEGOM8ylxF2PMIxQ+Bw3w2ilDJxVtXzLGBJ0wrhHwdtGXL1prCxAREakAbftezfhX5rNmzBpGdRlV3Mf66QUQnpRGt5seYmUHX+Knv4otKP2vo8a3N8ann0/x17l7cll7+9rCNlsxarMlIiJysap9QQ0EArOBvcaYJcaYb40xcynsMT256JgnrLU/nzjIWjsDmAY0prBX9WxjzExgPYXro34HTKmk9yAiIrVYcINgPh32KSljU3ig7U2MXF2yr1vKYbrf/FcSQ+oT+8mLpSqs64bVpfuC7oR8EYJbM7fieEZMBnG94lh7x1q12RIREbkINaGgTqBwxe4UoCVwDRAJHAU+Anpaa18+00Br7RjgZgqnf0cCVwAbgLHAcGttfoVnLyIiUiTIL4gpt0znl3+/yoJL25N7wm/pruvS6XH7UyQF+bBs6gQK8i/seWhjDAF/CaDn2p60nNAS42aK9+3+eDcx7WLYMmkL+cf0K09ERKS0qn1Bba1NtdY+ZK3ta61tZq31sNZ6WmvbWWvvtNbGnmf8dGttP2utj7W2jrW2h7V2qqZ6i4iIo9Rr050Bv6awO3Ye8y/vcFJhHZp6hF5jJ7GxpTeLXxpH/gUW1i7eLrR5vg09k3vS4LoGxfH8zHx2TNkBqqdFRERKrdoX1CIiIjVVi24DGfhzMnviFzLv6lCOuZTsa7czGzNlCh2mduCDuA/Iyc+5oHMWt9n6pQteHb0AaPNCG5zrOJ9npIiIiJxKBbWIiEgV17xLPyLnrOLwmnjmDQ8ns+hx6OcHwIa0jdw9+26C3gzirWVvkZWbdUHn9LvMj/CEcEKmhxAwKuC0/dvf2M6xbcfK822IiIjUOCqoRUREqomAdt2InLGcnA3r+GnsFSzqUq9437b0bTz004OsDK5H9OgrSd+3/bznc3JxIuCmAIyTOSme9kcaGx7aQExwDKkTU8nLVP9qERGRM1FBLSIiUs34tWjHVW/NZcvDW3nxkhdpVKcRACOSoE9qLlHvzKWgZUuib4vk4Lb1pTq3tZaNf90IQEFWAVv+uYWY4Bj1rxYRETkDFdQiIiLVlI+7D0/0f4LU8am8OfhN7k3yKN7ne8wS9el83ILaEz0igr0bEy/onMYY2r7aFu/u3sWxnJ05rL19LbE9Yzm04FC5vw8REZHqSgW1iIhINefl6sW4XuPoH7ePBX+7jc0NXYv3eedA1IwV+HToyrwhndmeuOi856sfVZ8ey3sQ/GEwbo1L+ldnxmaycuBKVt+wmqxNF/astoiISE2mglpERKSGcPP0ZsA/Pqb59nQWvziW9U3di/d55EHkj6sJ6N6fhVFtWZvwv3OeyzgbmtzRhJ7re9LqmVY4eZT8lWH/f/YTExLDxsc3ahq4iIjUaiqoRUREahgXNw/6PvEWbbdmsmzKU//f3p3HWVnW/x9/fQZGFkdARAUEWVxQwIXNHUFTU8vU1DR/maZlP9f8urT90rTc0qz8aupXS82vWW65VFaaCIIgCoKgorJvigICguwz1++PcwaGkZngcObMDOf1fDzmcXHu6zrXfd1zcWbu99wbb3fddl1daQX0fWUaA/94FCf86QRGzBpRe19lTen2824c8N4B7HTmTuuWp9WJFVNWfO6GZpIkFRMDtSRJW6mSJk058KIb6Tn1U8Y+eBPj9moDwP19YMG28Lf3/8bABwZy6P2H8vc3HqWivOa7eTfftTk9/9iTPqP60OqgVkRp0P2W7oXaFEmSGiQDtSRJW7koKaHf2T+kz6RFvPXs73jz7C8SrD+yPHL2SGaffwbTOpUx4mffYfXKz2rsq/VBrekzsg99X+tLy91bblC3dulaJp40kSWjltTZtkiS1JAYqCVJKiK9TziP+y76J5MumsR5fc6jtKSUnZfCOeNh93mrOOynv2N+h9YMu+xkln0yb6N9RATb7b/d55bPvnU2C59ZyLhDxvHWqW+xfMryut4cSZLqlYFakqQi1KNdD373ld8x/XvTuaHNV1nTZH3dLovLGXT706zp1JGh3zycBTMm/cf+ypeXM/eOueteL3hyAa/v/TqTL53M6gWr62ITJEmqdwZqSZKK2C6tduG8nzxJ+fRpDP3O0cwvW38q+PYrEoP/dzgt9+zJsBP2Zc6Emm9g1qRlE/qN7ceOp++4bllam5h7x1xG7zaamTfPpHxFeZ1uiyRJhWagliRJtOnYjcH3Pk/Z3AW8/IMzmLlD03V1LdfAoL9NpH2fgTz+9X2Z8NGEjfbRonsLev25F31H96X1wNbrlpd/Ws70H03ntR6vMe+heT5qS5K01TBQS5KkdVq0asvhN/+JXT5YyshbL2VS5xbr6ppWwJ8rJrLfPftx7MPH8sLUF0jp8+G41QGt2H/Y/vR+ujcteqx//6rZq3j37HeZcNzGA7kkSY2NgVqSJH1O022ac8iVt7PXjGWMfeBG3ui5Pe/tAE/vlan/19R/cczDx9D37v0YdstFrF6xbIP3RwTtTmzHgIkD2OOuPSjdqXRdXbsT2xVyUyRJqjMGakmSVKMoKaHfOT+i79uf8NnLL3Jyr1MoifW7D92GTWTQD+5iYfvWvHTB8SyZN3OD95eUlrDLBbtw4JQD6XJ1F8r6lNHhOx0+t57V871xmSSp8TFQS5KkTdK355E88bUneP/i97l4wMW0LG3JlSMzdR0+reCIe/5BSZeuDDu57+duYNZ0u6Z0+1k3+r3ej5LSDXc/loxawqhOo5h82WSDtSSpUTFQS5KkzbJb29244/g7mH3pDFYfdzQfl63fndhuNQx6ehwd9h/IyEN35Z3n/rDBe6NJbPA6pcS0H04jrU7MvT1zR/AZP5vB2mVrC7ItkiRtCQO1JEnKSduyHRl87/O0nreI4T/9FlPaN1tX1yTBISNn0/NL5zB+rza8dvfVVJR/PiSvXbKWtGb9jc3Kl5Yz46czGL3baObcOYeK1RUF2RZJknJhoJYkSVuk2batGHjt/ew2dzljfv9z3ui5/Qb1+7+3hH0vuZ7DbtmLe8fey4o1K9bVlbYppc8rfej9dG9a9my5bvmaj9cw5ZIpvLb3a3z0yEc+akuS1CAZqCVJUl5ESQn9z/0Jfd/+hHef/xMjDu/KmuyexkP7wajVU/nu375Ll9904bqh1zH/s/mZ91XeEXzCAHrc34Nmndcf6V45bSWT/s8kxvQdw8J/LKyPzZIkqUYGakmSlHd7HX0Ghw2bzvyJoxl62gDuHbTturr5y+dz7bBr+fPRHXj56B68P/RJIHN9dYdvdeCA9w9gt1/uRtO2Tde957M3P+ODuz4o+HZIklQbA7UkSaozHXsewODHXmPITR9w2zG30blVZwDaLofzXi/n8H+/z55HnMrYXm0Zfc81VJSvpUnzJnS+ojMHTTuIXX+8KyUtSiCg243d6nlrJEnakIFakiTVuVbNWnH5wZcz9dKpPPLVR7hsXhdaVrlHWb93FnHgBT9nZoeWDLvyNJYu/JCmrZvS/YbuHDj1QPZ6YC/K9inboM/y5eVMuWIKK2evLPDWSJKUYaCWJEkFU9qklK/v83V+8sA0Jv7lHkYd1Im1VfZGus1fw6DbnqC8U0eGntqfORNG0KxDM9qf3f5zfc29Yy5zfjWH0XuMzjzD+iOfYS1JKiwDtSRJKrgoKWGfk7/LwaNmM2/8K7z0tQNY3Hz9M6rbrITBT46lw/4DeezUnoyYNYKU1t/pe+3Stcy6eRYAaVXmGdavdn+VaT+exppFawq+PZKk4mSgliRJ9arTPodwxKOjafrBhwz7/ulM36l0XV2TBE/EJAY+MJAB9w3g4QkPs7p8NU23a0qvJ3qx3YHbrWtbsbyCWTfN4tVurzLj+hmsXfr5515LkpRPBmpJktQglG2/M4N+8We6fLCc1++7jjG9d2Bma/jL3pn6sR+O5aynzqLrr3bl+UuOp7z7h/Qd1Zfez/Zm233X30W8fEk5M66ewejdRjP717MpX1leT1skSdraGaglSVKDUtKkKQO+fQ39Jy7gszEjOXfAd2jetPm6+n7jPuKYO/9B2Z69GHF0DxY0e4H+4/qz95/2psWeLda1WzN/DVMvn8q4g8dtcLq4JEn5YqCWJEkNVs/dD+beE+5l9n/N5oYjb6Djdh257NVMXfO1MPDFyez1xTOZ2KM1U2ffwP5jetLj9z1otmuzdX3sfNbOREQNa5AkKXcGakmS1OC1a9mOHw/8MdMvnUbz8y/knS4tN6jfd8pSDvn+HSzq1Ib3hp9J1+eas/sdu1PWr4yOF3T8XH9LXl3iUWtJ0hYzUEuSpEZjm6bNOPSHv2XvaUuZ+NT/8MrALqxusr6+/acVDH5wKDvs15eZjx4G/z2LkuYb7u4sHbeUcQePY2z/sSz8x0KDtSQpZwZqSZLU6ERJCfucdD6HvjyDxe+9ydBvHcG8Vut3a7Yph/6jZnL8U6fQ/77+PDDuAVasWQHA9J9MB2DZG8uYePxExg0cx6IhiwzWkqTNZqCWJEmN2k677cvg+4eww0dLGXXr93hzj1YAPNoL5pfBGx++wbnPnkvnX3fmxkcuomKnxZS0WL8L9Okrn/LmF95k/ODxLB62uL42Q5LUCBmoJUnSVqG0eUsOvvI37Pf+Et574c+8e8GpG9wdfOGKhbT+zV3s84dBbLPHdyk96iOidP3Nypa8vITxg8cz/sjxLB5usJYk/WcGakmStNXpcdTp3Ph/H2fu5XO55ahb6NqmK61WwtnjoUmCgya8y6H/PoP2bb4B+74NTde/d/FLixl/+HjGHzWe8uU+w1qSVDMDtSRJ2mq1bdGWqw69iimXTOHJL/wP7/Vou0F9j/lzGDzhYvaJr8MuI6Fk/XXU0TRo0rJJ9S4lSVrHQC1JkrZ6TUqacNRR59Nv4kKmjfw7w768D0u3WV+/w5p5DJ77/ziw4hs0K3sRSiroePXnH7e1ZvGaAo5aktTQGaglSVJR6X7w8Qz66wTSnNkMu/I0Jndotq6uBR9w8LLrabrz6ez1yl5c+fyVTF44GYCKVRWM2XcME0+YyNI3ltbX8CVJDYiBWpIkFaVWO3Zi0K2Psfuc5bz52B28ctj6Z1rfc9ACPlnxCbeNuo0979yTY/73GF68/FFWzV7Fwr8tZGy/sUw8aSJLxxusJamYGaglSVJRi5IS9jvtYg4dPoMlk99iyIXH8fohu27Q5t9TXmD7378CVKxbtvCZhYztM5a3TnmLZROXFXjUkqSGwEAtSZKUtWO3Xhz52+eYdMV0njvzOU7Y8wRKooSjpkH/Vb9lAOexI0M3eM+CvyxgzL5jeOuUtzxiLUlFxkAtSZJUTUmUcNwex/Hs159l+vem8+0uJ/FxWQnbMoNeXEd/zqMdL2/wngV/WcDYPmOZ+JWJrJy1sp5GLkkqJAM1EBFnRsTwiFgSEcsiYkxEXBQRfn8kSSpyu7bela9d/xRtPl7CyF9exri921DGNHrzU/rxbdoxfIP2C4d8TEkrdyEkqRgU/U/7iPgt8EegPzAceAHYE7gTeCIifAClJElimxZlHHLFr+nzzqLMo7dO3J+K5lPpzTX059vZU8ErmLrjQ/R8qCc3j7iZecvmAVC+srxexy5JqhtFHagj4hTgQmAesG9K6csppZOBPYBJwMnAxfU4REmS1AB1P/h4Bj09jtJ58xl+zTnM6DaPXlxHH87j5uOfZOqiqfzoxR/R+dedOeWxU3jl6GcYN3gci15aREqpvocvScqTog7UwI+y5Q9SSpMrF6aUPgIuyL78oad+S5KkjWnZuh0Dr3uA3tOW8f6Qx/nHxV1ZsGvpuvq1FWv5+NnXqRjRmiXDlvDmkW/y2oDhfPLCJwZrSdoKFG1QjIhOQD9gNfB49fqU0jBgLtAeOKiwo5MkSY3Nnkecyhl3vMQHl3/AQyc9xGG7HgbAua/2JlgfnleMrWDCMRMYvtuzfPzMhwZrSWrEijZQA32y5dsppRU1tHm9WltJkqRatShtwVn7ncXwbw3nnQvfYedDl9Cj+TfpwF8J1qxrVzG9Ne+c9B7D2j3Ce/893GAtSY1QMQfqbtlyZi1tZlVrK0mStMn23nFvjv/DK7SZ/w4Lb15N2e4X0pGnCFavb/TJLnz4vXKGt/wDcx8ZwpryNTV3KElqUIo5UJdly89qabMsW25Xx2ORJElbseZlbTjkB3fQb/Jkthn9ZdKXb6Vt6ZOUsGpdm4qVXfn7nL9z3B+Pq8eRSpI2R9P6HkA9imyZ0/lVEXE+cD7AzjvvzNChQ/M0rJotW7asIOtRw+PcFyfnvXg591u7Urji//HxxctZ/NSf2Pnx1qRPjiVKp/KnAW9wccnFzr8kNRLFHKiXZsuyWtpU1i2tXpFSuhe4F6B///5p8ODBeR3cxgwdOpRCrEcNj3NfnJz34uXcF5EvHg/3wIwhwxgyZAodW3bkulOuo22LtvU9MknSJijmQD0jW3appU3nam0lSZLyruuRgzj3yEF0e+lEw7QkNSLFfA31uGzZKyJa1NBmQLW2kiRJdSYi/nMjSVKDUbSBOqU0G3gD2AY4rXp9RAwCOgHzgFGFHZ0kSZIkqaEr2kCddVO2/EVE7F65MCJ2Au7Kvrw5pVRR8JFJkiRJkhq0Yr6GmpTSExFxN3ABMDEi/g2sAb4AtAKeBu6sxyFKkiRJkhqoog7UACmlCyNiBHARMAhoArwL3A/c7dFpSZIkSdLGFH2gBkgpPQI8Ut/jkCRJkiQ1HsV+DbUkSZIkSTkxUEuSJEmSlAMDtSRJkiRJOTBQS5IkSZKUAwO1JEmSJEk5MFBLkiRJkpQDA7UkSZIkSTkwUEuSJEmSlAMDtSRJkiRJOTBQS5IkSZKUAwO1JEmSJEk5MFBLkiRJkpQDA7UkSZIkSTkwUEuSJEmSlAMDtSRJkiRJOTBQS5IkSZKUg0gp1fcYGr2ImA/MLMCq2gELCrAeNTzOfXFy3ouXc1+8CjH3XVJKO9bxOiSpKBioG5GIGJNS6l/f41DhOffFyXkvXs598XLuJalx8ZRvSZIkSZJyYKCWJEmSJCkHBurG5d76HoDqjXNfnJz34uXcFy/nXpIaEa+hliRJkiQpBx6hliRJkiQpBwbqehIRZ0bE8IhYEhHLImJMRFwUEZs8JxFRGhFfiIjbIuLViPgwIlZHxNyIeCIiBtfhJihH+Zj7Wvq+MSJS9uvKfIxX+ZHveY+IFhHx/Yh4PSIWR8TyiJgeEY9HxKH5Hr9yl8+5j4hOEXFHRLwXESsiYmVETI6IeyKie12MX5svInpExPci4uGIeDciKrI/l0/dwn7r7PeHJCk3nvJdDyLit8CFwErgRWAN8AVgO+Ap4LSUUvkm9HMU8EL25TxgLPAZ0BPonV3+85TSNXndAOUsX3NfQ98DgFFk/lAWwFUppV/mY9zaMvme94joBjwP7A58DLwKrAK6AvsDP0spXZ/HTVCO8jn3EdEHGAK0AeaQ+ZkP0B/YBVgGfDGlNDKf26DNFxG/Ab63karTUkpP5Nhnnf3+kCTlzr9oFlhEnELmF+I8YN+U0pdTSicDewCTgJOBizexuwrgSeDwlFKHbF+np5T2Ac4AyoGrI+KIvG+INlue5756382AB4GPgGfyMmDlRb7nPSK2JfOHtN2BnwOdUkonppS+llI6AOgAPJbnzVAO6uAz/1syYfo+oHtK6aSU0klAN+B+oAy4O4+boNy9BdwKnE7mszpsSzqry98fkqQt4xHqAouIMUA/4OyU0kPV6gYBQ8n8wtwlpVSxhev6HXAecH9K6bwt6Utbri7nPiJ+AXwf+ApwCnA2HqFuEPI97xFxE/BD4KGU0tn5H7HyJZ9zHxHNgRXZlx1SSvOq1XcE5mZfbptSWr7lW6B8iYihwCByPEJdyH0HSdLm8Qh1AUVEJzK/EFcDj1evTykNI7ND1B44KA+rHJctO+WhL22Bupz7iDgQuAJ4JKX01y0frfIl3/MeEdsA38m+vDl/I1W+1cFnvhxYW9n9Ruor/zr+GeuDt7YC9bDvIEnaDAbqwuqTLd9OKdW0w/N6tbZbYo9s+WEe+tKWqZO5zx61+gPwCRu/Xk/1K9/z3g/YAZidUpoUEYdkb0T3PxFxXUQcvKUDVt7kde5TSmvIXDcLcF1ElFbWZf9dec3875Onnm1tCr3vIEnaDE3rewBFplu2nFlLm1nV2uYkItoD52RfPrklfSkv6mrubwB6AGeklBbkMjDVqXzP+z7ZcnJEPEjm1P6qromIJ4GzatnxVmHUxWf+QuCfZM5SOC57GjDAAGB74Hbgqs0cpxq+gu07SJI2n4G6sMqy5We1tFmWLbfLdSUR0RR4GGgNvOhpwA1C3uc+Ig4BLgOeTik9ugVjU93J97y3zZaHA02AXwL3AAuzy+4icw39p8C5mztY5VXeP/MppWnZz/1DwHFseDnPGODl7JFsbV0Ksu8gScqNp3wXVuV1b3V9Ot49ZB6lMRv4Rh2vS5smr3MfES2AB8gEpwvz0afqRL4/85U/s5uSObX3qpTS1JTS4pTSs8BJ2XWd7TOJ613ef95nw/RbZO4afSLQDtiRzLxvDzwZET4mcetTqH0HSVIODNSFtTRbltXSprJuaS1tahQRt5O5s/c84AvV7wSrepPvub8R2BO4PKXkNfINV77nvWqb+6pXppTGkHk2cQkweBP6U93J69xHRBvgaTJHII9NKT2bUlqYUlqQUnoGOJbMzciujog9autLjU6d7ztIknJnoC6sGdmySy1tOldru8ki4jbgUmA+mTA9eXP7UJ2ZkS3zNfcnk3kO+dkRMbTqF5kda4ALsst+l8N4lR8zsmW+5r1qm+k1tKlc3n4T+lPdmZEt8zX3XyJzNPrVlNK06pUppSnAaDJnLwze1EGqUZiRLetk30GStGW8hrqwKh9j1SsiWtRw06AB1dpukoi4BbiczLWUR6eU3sl9mKoDdTH3JWSea1qT7tmvNpvYn/Iv3/P+RpV/70Dmj2fVtcuWyzZSp8LJ99zvmi2X1NJmcbZsW0sbNT51tu8gSdpyHqEuoJTSbDI7xNsAp1Wvj4hBZG4yMw8Ytan9RsTNZO7suohMmH4zLwNW3uR77lNKXVNKsbEvMo/RArgqu2z//G2JNkcdzPtcMkchIXOfhOr9bQ/0zb4cU71ehVMHP+8/yJb9qj4yq0p/pWQeqwY1n72gRqiu9h0kSflhoC68m7LlLyJi98qFEbETmTv0AtycUqqoUndTRLwbETdRTUT8HPgBmSMTR6eU/Ot0w5XXuVejke95vyFbXhMR+1d5T3PgbjJ39x+LO9YNQT7n/h/AcjJHqn8dEc2qvKcZ8N9kTvtdBPwr71uiOvcfPveb/X9JklQYnvJdYCmlJyLibuACYGJE/BtYQ+ZoUysyN525s9rbOpB51nCHqgsj4ivAT7IvpwCXRAQb8W5K6ea8bYRyks+5V+OR73lPKf01In4JXAmMjojRZC71OADoCMwFvp5S8o7A9Syfc59S+jgiLgR+D1wEnBwRY8ncAbpftv0q4NyUUm2nhasAIqIv64MuQM9seWNEXFm5MKV0UJU2tX3uc/m/JEkqAAN1PUgpXRgRI8jsFA0i8zzZd4H7gbs34y/MVa+T65/92phhgIG6Acjj3KsRyfe8p5SuioiRwCVAH6AlMAv4FZmjVBu7tlr1IJ9zn1L6Q0RMJPP8+YHAMdmquWSC9q+8f0aD0Qo4cCPLc74Du78/JKlhCg9iSJIkSZK0+byGWpIkSZKkHBioJUmSJEnKgYFakiRJkqQcGKglSZIkScqBgVqSJEmSpBwYqCVJkiRJyoGBWpIkSZKkHBioJamAIqJzRPwxIj6IiLURkSLiNxtp91/Zum/WxzglSZL0nzWt7wFIUrGIiACeBAYA7wAvAWuA1zbS/KvAWuBvBRugJEmSNkuklOp7DJJUFCKiGzANmAXsllJaW0O7nYEPgCEppaMLOERJkiRtBk/5lqTC6Zwtp9cUprNOIvPz+am6H5IkSZJyZaCWpI3IXr+csv8+JyLGRMRnETEvIn4fETtm65pHxHUR8X5ErIyIWRFxQ0SUVumra7avYdlFgyr7r1xHNV8FEvB0lT6uzba/NiI6RcSDEfFhRCyPiDci4tQqbQ+NiOciYmG2/qWIGFDLtvaKiIciYnZErIqIBdn3H7dF30RJkqStnKd8S9JGVAzsiqkAAANVSURBVAm6twCXkQnDS4FDgPbABOBQ4F/A3tn6ZsAgoCVwX0rp/Gxf7YBfZt/3ReAj4J+V60opnVNlva2B+cCYlNIhVZZfC/wUeBA4HlgGvA50yo4jAWcCq4BHgfFkTi/fD9gL+Azom1J6v9p2fgV4LDv2t7PbVdlnCXB9SunqzfvuSZIkFQcDtSRtRJVA/RFwREppUnb59sAooAfwFrAY+HJKaUm2fn8yQbcJ0C2lNLNKn4PJ3IhsWEppcA3r/Qbwv8D3U0q3Vll+LZlADXA7cEVKqTxbdwFwFzAH2Bb4bkrp8WxdCfAIcDpwf0rpvCp9tgfeA1pl+/tVtbH+ncwfB45NKf1r075zkiRJxcNTviWpdtdUhmmAlNIi4J7sy57A+ZVhOls/HngOCDJHqzfXV7PlX2qon0kmbJdXWXYvsJDMkeV/Vobp7HgqgF9kXx5Rra/vkAnTI6uG6ez7hgJ3Zl9euZnbIEmSVBQM1JJUu39uZNmUbDmzatiuYnK27Lg5K4qIlmROCZ+YUppaQ7MhKaXVVRdkw/WMWsZb03gqA/+DNazr/mx5WEQ0qaGNJElS0TJQS1Lt5mxk2bJa6qrWN9/MdR1L5hTrmo5Ob8o6P1efUqqsa1atapdsOb2GPqcDFWS2Y4daxiRJklSUDNSSVIvsKdM1qa0uF//pdO9NWefmjCmypTfTkCRJyoGBWpIagOxjtr4ETEspTSjQaiuPZnevob4rmd8TK4FPCjEgSZKkxsRALUkNw5FAG2o/Op1vlc/F/mYN9d/KliNSSmsLMB5JkqRGxUAtSQ1D5eneTxVwnfeRebb2YRFxadWKiDgcuCT78rYCjkmSJKnRMFBLUj3LPiv6ROBDMs+4LoiU0jzgLGAVcHtETIiIRyJiKJnnZW8LXJ9S2tidwyVJkoqegVqS6t+hwM7A0ymlgt4gLKX0DNAfeJjMnbxPBfYBnge+lFK6upDjkSRJakyiwPtukqRqIuLXwGXAMSmlF+p7PJIkSdo0HqGWpPo3CbiWzGnWkiRJaiQ8Qi1JkiRJUg48Qi1JkiRJUg4M1JIkSZIk5cBALUmSJElSDgzUkiRJkiTlwEAtSZIkSVIODNSSJEmSJOXAQC1JkiRJUg4M1JIkSZIk5eD/Azt/WHc2pe3qAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"y0 = 0\n",
"v0 = 0\n",
"m0 = 0.25\n",
"mf = 0.05 #estimated final mass\n",
"dmdt = 0.05\n",
"\n",
"T = (m0-mf)/dmdt\n",
"t = np.linspace(0,T,1000)\n",
"dt = t[1]-t[0]\n",
"N = int(T/dt) #tried to use round and got an error, why?\n",
"mf2 = np.linspace(0.25,0.05,N)\n",
"\n",
"#initialize solution array\n",
"num_heun_2 = np.zeros([N,3])\n",
"num_rk2_2 = np.zeros([N,3])\n",
"\n",
"#Set intial conditions\n",
"num_heun_2[0,0] = y0\n",
"num_heun_2[0,1] = v0\n",
"num_heun_2[0,2] = m0\n",
"num_rk2_2[0,0] = y0\n",
"num_rk2_2[0,1] = v0\n",
"num_rk2_2[0,2] = m0\n",
"\n",
"dm = mf2/m0\n",
"vf = -250*np.log(dm)\n",
"\n",
"for i in range(N-1):\n",
" num_heun_2[i+1] = heun_step(num_heun_2[i], rocket, dt)\n",
"for i in range(N-1):\n",
" num_rk2_2[i+1] = rk2_step(num_rk2_2[i], rocket, dt)\n",
" \n",
"plt.figure(figsize=(10,10))\n",
"plt.plot(num_heun_2[:,2]/.25,num_heun_2[:,1],'g',label='Heuns Method')\n",
"plt.plot(num_rk2_2[:,2]/.25,num_rk2_2[:,1],'r--',label='RK Method')\n",
"plt.plot(dm,vf,'m--', label='Tsiokolvskys Equation')\n",
"plt.grid(True)\n",
"plt.xlabel('mf/mo')\n",
"plt.ylabel('Velocity (m/s)')\n",
"plt.title('Convergence of Heun and RK Methods to Tsiokolvsky')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1,0.5));"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The final height from the simple rocket is 596.03 m\n",
"The final height from the realistic rocket is 424.53 m\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Comparison\n",
"plt.plot(t[0:-1], num_heun[:,0], label = 'Simple Rocket')\n",
"plt.plot(t[0:-1], num_heun_2[:,0], label = 'Realistic Rocket')\n",
"plt.xlabel('Time (s)')\n",
"plt.ylabel('Height (m)')\n",
"plt.title('Simple Rocket Height vs. Realistic Rocket Height \\n')\n",
"plt.legend()\n",
"plt.grid();\n",
"print('The final height from the simple rocket is {:.2f} m'.format(num_heun[-1,0]))\n",
"print('The final height from the realistic rocket is {:.2f} m'.format(num_heun_2[-1,0]))"
]
},
{
"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",
"__Using 10 subintervals, the two closest mass change rates to get the desired height are 0.05 and 0.0889 kg/s.__\n",
"\n",
"b. Use the modified secant method to find the root of the function $f_{m}$.\n",
"\n",
"__The root of the function is about 0.0789.__\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": 9,
"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",
" T = (0.25-0.05)/dmdt\n",
" t= np.linspace(0,T,1000)\n",
" dt=t[1]-t[0]\n",
" N=int(T/dt)\n",
" height_f = 300\n",
"\n",
" #initialize solution array\n",
" height = np.zeros([N,3])\n",
"\n",
" #Set intial conditions\n",
" height[0,0] = y0\n",
" height[0,1] = v0\n",
" height[0,2] = m0\n",
"\n",
" for i in range(N-1):\n",
" height[i+1] = rk2_step(height[i],lambda state: rocket(state,\n",
" dmdt=dmdt, u=250,c=0.18e-3),dt)\n",
" height_predicted = height[:,0]\n",
" error = height_f - height_predicted[-1]\n",
"\n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def incsearch(func,xmin,xmax,ns=50):\n",
" '''incsearch: incremental search root locator\n",
" xb = incsearch(func,xmin,xmax,ns):\n",
" finds brackets of x that contain sign changes\n",
" of a function on an interval\n",
" arguments:\n",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\n",
" returns:\n",
" ---------\n",
" xb(k,1) is the lower bound of the kth sign change\n",
" xb(k,2) is the upper bound of the kth sign change\n",
" If no brackets found, xb = [].'''\n",
" x = np.linspace(xmin,xmax,ns)\n",
" #f = func(x)\n",
" 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": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"number of brackets: 1\n",
"\n",
"The mass change rate to get the desired height is between [0.05] and [0.08888889] kg/s.\n"
]
}
],
"source": [
"#incsearch(f_m, 0.05, 0.4, ns=10)\n",
"print('The mass change rate to get the desired height is between {} and {} kg/s.'.\n",
" format(incsearch(f_m, 0.05, 0.4, ns=10)[1],incsearch(f_m, 0.05, 0.4, ns=10)[0]))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def mod_secant(func,dx,x0,es=0.0001,maxit=50):\n",
" '''mod_secant: Modified secant root location zeroes\n",
" root,[fx,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):\n",
" uses modified secant method to find the root of func\n",
" arguments:\n",
" ----------\n",
" func = name of function\n",
" dx = perturbation fraction\n",
" xr = initial guess\n",
" es = desired relative error (default = 0.0001 )\n",
" maxit = maximum allowable iterations (default = 50)\n",
" p1,p2,... = additional parameters used by function\n",
" returns:\n",
" --------\n",
" root = real root\n",
" fx = func evaluated at root\n",
" ea = approximate relative error ( )\n",
" iter = number of iterations'''\n",
"\n",
" iter = 0;\n",
" xr=x0\n",
" for iter in range(0,maxit):\n",
" xrold = xr;\n",
" dfunc=(func(xr+dx)-func(xr))/dx;\n",
" xr = xr - func(xr)/dfunc;\n",
" if xr != 0:\n",
" ea = abs((xr - xrold)/xr) * 100;\n",
" else:\n",
" ea = abs((xr - xrold)/1) * 100;\n",
" if ea <= es:\n",
" break\n",
" return xr,[func(xr),ea,iter]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The root of the function is 0.07890352694481415\n"
]
}
],
"source": [
"fm_secant = mod_secant(lambda x: f_m(x), 0.00001, 0.1)\n",
"print('The root of the function is',fm_secant[0])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"y0 = 0 \n",
"v0 = 0 \n",
"dmdt = fm_secant[0]\n",
"T = (0.25-0.05)/dmdt\n",
"t= np.linspace(0,T,10000)\n",
"dt=t[1]-t[0]\n",
" \n",
"N=int(T/dt)\n",
"height_f = 300\n",
"plotc = np.linspace(0,T,N)\n",
"\n",
"#initialize solution array\n",
"height = np.zeros([N,3])\n",
"\n",
"#Set intial conditions\n",
"height[0,0] = y0\n",
"height[0,1] = v0\n",
"height[0,2] = m0\n",
"\n",
"for i in range(N-1):\n",
" height[i+1] = rk2_step(height[i],lambda state: rocket(state,dmdt=dmdt, u=250),dt)\n",
"height_predicted = height[:,0]\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 27,
"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(plotc, height_predicted,'y-')\n",
"plt.plot(plotc[-1],height_f, 'm*', markersize = 40, label = \"point of detonation\")\n",
"plt.xlabel('Time (s)\\n')\n",
"plt.ylabel('Height (m)\\n')\n",
"plt.xlim(0,3.5)\n",
"plt.ylim(0,400)\n",
"plt.legend()\n",
"plt.title('Height of Rocket vs Time\\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
}