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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Initial Value Problems - Project"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Create a `simplerocket` function that returns the velocity, , the acceleration, , and the mass rate change , as a function of the using eqn (2.a). Where the mass rate change and the propellent speed are constants. The average velocity of gun powder propellent used in firework rockets is m/s [3,4]. \n"
]
},
{
"cell_type": "code",
"execution_count": 143,
"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": 77,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, without drag or gravity, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" \n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
"\n",
" dstate = np.array([state[1], ((u/(state[2])*dmdt)), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 83,
"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",
" \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": 84,
"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": 85,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The number of time steps is 10000.\n",
"The time increment is 0.1\n"
]
}
],
"source": [
"x_0 = 0 \n",
"v_0 = 0 \n",
"m_0 = 0.25 \n",
"m_f= .05\n",
"dmdt = 0.05 \n",
"d_t = 0.1 \n",
"T = 1000\n",
"N = round(T/d_t)\n",
"\n",
"print('The number of time steps is {}.'.format( N ))\n",
"print('The time increment is {}'.format( d_t ))\n",
"\n",
"t=np.linspace(0,((m_0-m_f)/dmdt),N)\n",
"d_t=t[1]-t[0]\n",
"N =int(((m_0-m_f)/dmdt)/d_t)\n",
"mflimit = np.linspace(m_0, m_f, N)\n",
"\n",
"num_heun = np.zeros([N,3])\n",
"num_rk2 = np.zeros([N,3])\n",
"\n",
"num_heun[0,0] = x_0\n",
"num_heun[0,1] = v_0\n",
"num_heun[0,2] = m_0\n",
"num_rk2[0,0] = x_0\n",
"num_rk2[0,1] = v_0\n",
"num_rk2[0,2] = m_0\n",
"\n",
"\n",
"m=mflimit/m_0\n",
"u=-250*np.log(m)\n",
"\n",
"for i in range(N-1):\n",
" num_heun[i+1] = heun_step(num_heun[i], simplerocket, d_t)\n",
" num_rk2[i+1] = rk2_step(num_rk2[i], simplerocket, d_t)"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Velocity m/s')"
]
},
"execution_count": 111,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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rNXfuXD300EOSpPz8fE2YMEFFRUXauHGjFixYoJkzZ7YZHMePH6+KigqtXLlSqampOvPMM4PXcnNzuzS+aEDgjBWpeVLlLiVImlleriUZ6ZpeXqkj9u0L98gAAADQktaKAX2oSJCbm6tnnnlGEydO1KWXXqr8/HyNHDlS69at02233SaPx6MVK1YoMTGxWd8tW7aourpan376qQ4//HBJUm1trS666CI9+eSTOv/88/Xhhx92aXz33HOPHnroIfXv31+rVq3S2LFjg9estVq/fr2ysrLavMfFF1+sE088UStXrlRubq6WLl3apTFFGwJnrJi/Kbh40Hml5Tq3rFzpgW1SmmDxIAAAgM7pza3muvuzuvl//x1//PGtXsvIyFBJSUnwePz48br11lt100036eyzz9ZLL72kWbNmyefzafHixRoxYkSr97r55puDYVOS3G637rvvPq1Zs0YfffSR3nvvPY0bN65T38Hr9eqOO+6Q5J8q6wybkr9C29b3hB+BMwZ5rJVayJoAAABAd2hrW5SUlJRm52688Ua9/fbbWrt2rY488kiVlpbq0ksv1cyZM9v8nPPOO6/ZuYyMDE2bNk3Lly/X+vXrOx04CwsLtWfPHg0ePFhTpkzp1D1A4Iwtji1S2m5HlRMAAACdt7/bojQ8z3nQQQeptLRUhx9+uO655542+2RmZiozM7PFaw3PVH777bcdHkOoLVu2SFKXnwONdQROaE98nL5KcOvYmppwDwUAACB6dfcf7NsqFPTB4sCqVatUUVEhyR8Ut23bpoMPPrhL9zTGdMfQ0AVsixJrHP/PqdwY3ZSbrclDDtD1ebmqcv6DZIsUAACA8ErN27/zUWzDhg26+uqr5Xa7de6556qsrEwzZ85UbW1tq31KSkpUWtpy8N68ebMkadCgQZ0e07BhwyRJX375ZafvAQJnTEu1Vp8lJarOGJXHx2l1WmrjxT60+hkAAEBUmr8p8EhUyE8f2BLFqbKyUmeffbaqq6v1m9/8RsuWLdPxxx+vjz/+WPPnz2+z7/Lly5udKy0t1csvvyxJ+zWtN9RRRx2l3Nxcffvtt1q7dm2n7yP5FzOS/AsRxRoCZywK/FUsTtK5peXB08vTPfKFaUgAAACITVdccYU2btyo0047Tddcc43i4uK0fPly5eXl6Y9//KNWrVrVat9bb71VGzduDB7X1dXp6quvVmlpqY466iiNHz++0+NKSEjQjTfeKEm68MILm22x0rAtSmtVVqd+/frJ7XZr586dKi4u7vSYohHPcMYixxYpP6mo1H1ZmSqPj9Nmd4LeTU7ScdWBZzlZPAgAAACdsHDhwjb3m5w1a5YmT56sZcuW6fHHH9eQIUO0ZMmS4PWBAwfqiSee0JQpUzRnzhyNGTMmOMW1wdChQ3XUUUdp9OjROuGEE5SRkaH3339f//nPf5Sbm6tly5Z1+Xv84he/0MaNG/XII49o7Nixys/P14gRI1RUVKR//vOf2rp1q/79738rI6PthTkTEhI0depUvfjiixozZozGjRun5ORk5ebmauHChV0eZyQjcMYsI8kqxVrNqKjQ4xnpkqQnMjyNgRMAAADohPamoI4ePVpDhw7V3Llz5XK59PTTTys7O7tJm8mTJ+uGG27QwoULdc455+jtt99WQkJC8LoxRitWrNDChQv1xBNPaMuWLUpPT9d5552n2267LbhSbVcYY7R48WKdfvrpeuihh/Thhx/qs88+U3Z2tkaOHKkrr7yy1e1fQi1evFjZ2dlau3atVqxYIa/Xq2HDhvX5wGmsZUPGrsjPz7eFhYXhHkbnBKqc37nidcrgQfIFFg164dvtGllX52hHlRMAAECSNm7cqFGjRoV7GDFt8+bNOvDAAzVs2LDg4kDofvvzu26M+dham9/SNZ7hhAZ56zWpqjp4vDzDE8bRAAAAAOgrCJyxzFG5PL+0LPh+TWqqiuIcvxpt7QEFAAAAAK0gcEKSNHpfrf5r3z5JUm2c0XPpaWEeEQAAAIBoR+CMdYEqp5F0nmOLlL8mJ4W0y+zFQQEAAAAtGz58uKy1PL8ZJVilFkGTK6v0ZkWlplVW6TjHM51+LC4FAAAAYP9Q4YT89U0pQdLdu/fq+KpqxbfUbNHI3hwUAAAAgChH4IRUUNKxdpW7enYcAAAAAPoUAicAAAAAoEcQOOHn2CJFkryS1qYka9bA/troTnC0Y4sUAAAAAB1D4ESL7srO0vX9++nzpEQtzUgP93AAAAAARCECJxo5qpynV1QE369NTdH2eMcyQlQ5AQAAAHQAgRMtOqK2TkdX10iS6o3RExmeMI8IAAAAQLQhcKIpR5XzgtKy4PuVnjSVxRlHu8zeHBUAAACAKETgRKvGV9fo4NpaSVJVXJye96Q5rtrwDAoAAABA1CBwornUPEn+X44LSsuDp5ene1TnbLdoZK8OCwAAANHD5/Np6NChMsYoLy9PdXV17XfqBUuXLpUxRrNnz+6VzysoKJAxRgUFBb3yeaFmz54tY4yWLl0als8ncKK5+ZuCb6dWVCrXWy9J2uVy6dW01MZ2lbt6e2QAAACIEq+//rq2bt0qSdq9e7fWrFkT5hF1v82bN8sYo+HDh4d7KBGLwIk2uSWdW9ZY5Vya4WEyLQAAANr12GOPSZIOOOCAJsexZt68edq4caPmzZsX7qGEBYETLXMsHnRWebmSfT5J0tdut95LTnK0Y4sUAAAANFVUVKTVq1fLGKNnnnlG8fHxeu211/Tdd9+Fe2i9Ljc3V4cddphyc3PDPZSwIHCiXRk+qzPKK5To8+nssnINj5D59wAAAIhMTz75pPbt26eJEydq/Pjxmjx5surr67Vs2bIW2xtjZIx/R4Rnn31WxxxzjNLS0uTxeDRp0iS9++67Lfb7v//7P82fP1/5+fnq37+/3G63Bg0apDPPPFMffPBBh8e7bNkyGWM0ZcqUVtt8/vnnMsbogAMOkNfr1ezZs3XggQdKkrZs2RL8DqFTbNt7hnPjxo265JJLNGLECCUnJysrK0tHHnmkrr/+em3ZsqVJ25UrV2rOnDk64ogjlJmZqaSkJI0YMUJXXHFFcPpypCFwonWOKufPS8r0+tbvdPPeYg0OPNPZ2I4qJwAAABotWbJEkoIL81x44YVNzrfmlltu0axZs+R2uzV16lQNHjxYb775piZNmqT333+/WfubbrpJv//971VXV6ejjz5ap512mnJycrRy5UqNHz9ezz33XIfGe8455ygvL0+vv/66vv766xbb3H///ZKkSy65RC6XS+PHj9cZZ5whSUpNTdUFF1wQ/DnzzDM79LnLli3T6NGjtXjxYllrNW3aNE2YMEE+n09333231q1b16T9zJkztWLFCqWmpurEE0/USSedpH379umBBx7QD37wA3311Vcd+tze5Ar3ABAdsgNTagEAAIC2fPrpp/rss8/k8XiCwev0009XTk6OvvrqK7377rsaP358i33vv/9+ffjhhzrqqKMk+Ve6veyyy7R48WLdcsst+vOf/9yk/fXXX6/ly5erf//+Tc6vWbNGZ5xxhi677DJNnTpVKSkpbY7Z7Xbrkksu0e23366HHnpIv/3tb5tcLysr0/Lly+VyufTzn/9cknTxxRfrxBNP1MqVK5Wbm7vfq8B+9NFHuuiii2St1SOPPKI5c+YEq7ySv/IZ6qmnntK0adOafB+v16tf/epXuv3223X11Vfrf//3f/drHD2NwIm2FZR2rIJZkNGkIgoAABCLHvjsAT34twc71PaMkWeo4NiCJucK/lqglZtWdqj/5d+/XHNHz21ybt4b8/TWt291qP8tx9yisw45q0Nt98ejjz4qSTr77LODwcjtdmvWrFm699579dhjj7UaOH/1q18Fw6YkxcXF6fbbb9fixYv1zjvvqK6uTgkJCcHrrU2BPfXUU3XWWWfpqaee0rp16zR16tR2x3355Zdr4cKFWrJkiW6//XYlJTWuW/L444+roqJCZ511lgYNGtT+fwgd8Otf/1per1c33HCDLrroombXR40a1ezc2Wef3eycy+XSbbfdpscee0yvv/66ysvL5fF4umWM3YHAiU7ZExenvyUlalJVdbiHAgAAgAixb98+Pf3005Iap9E2uPDCC3Xvvffqueee0x//+EelpaU16z9t2rRm5/Ly8pSVlaXi4mLt3btXAwYMaHJ9z549evnll7VhwwaVlJTI6/VKkjZs2CBJ+uqrrzoUOAcNGqQZM2ZoxYoVeuaZZ5rs0/ngg/4/IlxxxRXt3qcj6uvr9Ze//EWSv1K6P7766iu99tpr+vrrr1VRUSFfYCai1+uVz+fT119/rTFjxnTLOLsDgRPtc1Q5ayXdlZOlVWmp8hmjtVu3qV99YLotVU4AAICY9uKLL6qoqEgjR47UuHHjmlwbM2aMRo8erc8++0wrVqzQnDlzmvUfOnRoi/dNT09XcXGxampqmpx/+OGHde2116qqqqrVMZWVlXV4/FdddZVWrFihBx54IBg4161bp40bN+qII47QhAkTOnyvtuzZs0eVlZVyuVwaMWJEh/p4vV7NnTtXjzzyiKxtfaPC/fm+vYHAif2SIGmj2619cf71pp5IT9e1xSXhHRQAAECEmDt6brNprvuj4NiCZtNs98d9k+7rdN/u0LDXZmlpaYvTZnfu3Bls11LgjIvr+JqmhYWFuvzyy+VyubRo0SKdeuqpGjx4sFJSUmSM0S9/+UvdeeedbYazUOPGjdOYMWP00UcfqbCwUPn5+cHFgubO7fx/r93hD3/4gxYvXqxBgwbpd7/7nY499ljl5eUpMTFRknTsscfq/fff36/v2xtYpRYdE6hcGkkXlTb+1eTZ9DSVxhlHO1asBQAAiEVbt27VG2+8IUnatWuX3nvvvWY/27dvlyS99957XV5R9fnnn5e1VldddZWuv/56HXrooUpNTQ0uvNPaarPtufLKKyVJDzzwgL777ju99NJL8ng8Ov/887s0Xqfc3FylpKTI6/XqX//6V4f6NKy4+/DDD2vmzJkaMmRIMGxKnf++PY3Aif02sapaB9fWSpKq4uK0IoIeSgYAAEB4LFmyRD6fT5MmTZK1ttWfs87yL1TUUA3trKKiIknSkCFDml3bvXt3sxVtO+qnP/2pcnNz9cwzz2jhwoXyer362c9+1uJCPG63W5KCz412VHx8vE488URJ0iOPPNKhPm193z//+c/avXv3fo2htxA40XGpeZL8vzRzSsuDp5/M8KjGOKucmb08MAAAAISTtVaPP/64JLVbCWy4vmzZMtXX17fZti2HHXZY8D4VFRXB8+Xl5ZozZ45KSjr32FdSUpIuvvhiVVdX695775XU+nTafv36ye12a+fOnSouLt6vz7npppsUHx+v3/72ty1uqfLFF1/oiy++CB43fN8HH3wwuFCQJP3rX//SZZddtl+f3ZsInOi4+ZuCb0+pqNSAwF9yiuLj9WJaqqNhZM0bBwAAQM9at26dvvnmG6WkpGjGjBlttp0yZYpyc3O1ffv2Lu0ZeeGFF2rIkCH65JNPdNBBB2nGjBmaPn26hg8frsLCwhafEe2ouXPnKj4+XpI0ceJEHX744S22S0hI0NSpU+X1ejVmzBide+65uvjii7VgwYJ2P+Poo4/Wn/70p+B3GTFihGbOnKmf/OQn+t73vqdRo0bpgw8+CLa/8cYblZCQoIcfflijRo3SOeeco8mTJ+vwww/XkCFDdOyxx3b6+/YkAif2k7+SmSBptuNZzqUZ6apzNls0sldHBQAAgPBZsmSJJOn0009vdw/IhIQEnXPOOZK6Nq02KytLhYWFuuSSS5SWlqZXXnlFhYWFmjFjhj755JMWp5521JAhQ4IVxfa2Qlm8eLEuuugi1dfXa8WKFXr00Uf1zDPPdOhz5syZo08++USzZ89WXV2dVq1apbffflvx8fGaP3++TjjhhGDbY445Rh9++KGmTp2q0tJSvfTSS/r222910003ae3atU32J40kJtJWMYo2+fn5trCwMNzD6F2BhYGqjdHJQwapOPDXnzt37dG0SseS1GyRAgAA+piNGzdq1KhR4R4Getjf/vY3jR49WoMGDdKWLVvkcsXe5h7787tujPnYWpvf0jUqnOi0ZP0LVrwAACAASURBVGs1q6zxWc5HM9ObTqalygkAAIAodMstt0jy78sZi2GzOxE4sf8clcufllUoOfDQcq0x2hmodkqSKnf19sgAAACATlm9erUuuugiHX300Vq9erWGDx+uefPmhXtYUY+4ji7J8Pl0TVGJcurrdWJVteLb7wIAAABEnE8++USPPfaYPB6PpkyZonvuuUepqantd0SbeIazi2LyGc4GgWc522/Hs5wAAKBv4BlOxAqe4QQAAAAARDQCJzqvlcqllVRljKNdByuhAAAAAPoUAie6jZX0VnKSzhvYXwv65YR7OAAAAADCjMCJrnFUOTcnuDRvQJ7+npSodakp+tK5+SxVTgAA0EewBgr6uu78HSdwotscWOfVpMqq4PHizPQwjgYAAKD7xcfHq66uLtzDAHpUXV2d4uO7Z/8JAie6zlHlvKSk8f3rqSn6JsGx8w5VTgAAEOU8Ho/KysrCPQygR5WVlcnj8XTLvQic6FaH19bpR1XVkiRrjB7JIGQCAIC+Izs7W8XFxdqzZ49qa2uZXos+w1qr2tpa7dmzR8XFxcrOzu6W+7IPZxfF9D6coQIVzM8S3Tp/0ABJUry1WvPtdg3xeh3t2JcTAABEr3379qmoqEjl5eWqr68P93CAbhMfHy+Px6Ps7GwlJiZ2uF9b+3C6WjoJdMXofbX67+oa/V9ykuqN0aMZ6SrYWxTuYQEAAHSLxMREDRw4UAMHDgz3UICIx5RadB9H5fJSx7OcL3lStd350DHPcgIAAAAxgcCJHpFfs08/qKmRJHmN0ZIMVqwFAAAAYg2BE90rNU+SZCRdUtK4gtsqT6oqjGlsR5UTAAAA6PMInOhe8zcF3x5bXaPRNfs0vbxCz23boTQWqAIAAABiCosGoQcYSVZG0pLtO1v/JSvIYMVaAAAAoA+jwonuV1ASfMtfNAAAAIDYReBEDzHtN5F4lhMAAADowwic6BmOKmeD0rg4/TErQ49meMIwIAAAAAC9jcCJHtRY5dyUkKCThwzS4swMLc7MUGmc41ePKicAAADQJxE40XMcVc6D6urU31svSaqMi9OydKqcAAAAQF9H4EQP81c54yVdVtK4Iu3yDA9VTgAAAKCPI3CiZzmqnJMrq3RQbZ0kf5XzcZ7lBAAAAPo0Aid6QWOV83JnlTPdoxKqnAAAAECfReBEzwupch5cWytJqqLKCQAAAPRpERM4jTFXGmNWGGM2GmP2GmPqjDG7jTF/McacZ4xptrGjMWapMca28fNFO585yxjzjjGm1BhTYYwpNMZcYYyJmP9c+g7/f31xki4rKQuefSrdo2KqnAAAAECf5Ar3ABxukJQnaYOkv0qqlDRM0gmSJkk60xgzw1rra6Hve5K+buH89tY+zBhzv6S5kmokvSGpLvA590maZIw5y1pb3/mvgyYKSoJhcnJllR6urdXXbnewynlNcWk7NwAAAAAQbSIpcJ4j6VNrbaXzpDHmCPkD4emSLpC0pIW+j1hrl3b0g4wxZ8gfNndIOs5auylwvr+kdZKmS5on6Q/7/zXQOiPJ+qucxaW6vn8/Sf4q589Ky5XtC/wtoSBDKiCAAgAAANEuYqaOWmvfDQ2bgfP/kHR/4PCkbvq4GwOvNzSEzcBn7ZR0eeBwAVNru5njWc6Tqqo1orZWA71ezS8qlsfXUuEaAAAAQDSLpApnW7yB15qu3sgYM1jSUZJqJT0Xet1a+5YxZpukAySNlX96L7pZnKQ/7tytAd56JbTUgConAAAAEPUivoJnjDlQ0mWBwzWtNDveGPM7Y8yfjDG3GWNObqM6OSbw+g9rbXUrbT4KaYvu4giRQ1oLmwAAAAD6hIircBpjLpQ0QVKCpMGSjpU/GN9prX2xlW4/a+HcP40x51hrPw85f2DgdUsbw/hPSFuEA1VOAAAAIKpFYoVznPyLA82SdFzg3M2Sbm2h7WeSrpJ0hKQ0SYMkTZP0N0mHS/qLMeaAkD5pgddmz4s6VAReW9wk0hhzSWALlcLdu3e3/W3QXCsh8uPERK1MS+3lwQAAAADoKREXOK21F1trjaQU+YPkPZIKJH1gjBkU0vYea+291tp/WmsrrbXbrbWvSDpa0gfyb7NyY9NPUMN+nrYLY/yTtTbfWpvfr1+/zt4mxjVuq1oaF6eLB+Rp9qD+WpiTpd3x7MsJAAAA9AURFzgbWGurA0Fyvvyh8fvy75HZkb61ku4MHP445HJ54DVNrWu4Vt5GG3SFY8XadJ9PZXH+X8WauDj9KZOQCQAAAPQFERs4QzTsvXmqMaaj68x8EXgNnVK7OfA6rI2+Q0LaokeY4P+9srgxgD7vSdM2V3xjM6qcAAAAQFSKlsBZIv/WKC5J2R3skxN4rQg5/2ng9QhjTHIrfX8Y0hY9wVHlHF9dozE1/l1vvMboIaqcAAAAQNSLlsB5nPxhs0TSng72OTvw+pHzpLV2q6RPJLklnRXayRgzQf7VcXdIer+T40WHOaucjYsJrU5L1b8THIsoU+UEAAAAok5EBE5jzI+MMecaYxJbuDZO0qOBw0ettfWB86ONMdOMMfEh7V3GmGvlX71Wkn7fwkc2PN/5G2PMCEffPEkPBA4XWmt9nf9W6BBHlfOHNfs0ttq/NarPGD1AlRMAAACIahEROCUdLOlJSTuMMW8YY5YbY1YbY/4h6V1JB0l6Rf7tURoMl7RG0i5jzPvGmOeMMa/Jv7/m3YE2N1hr14Z+mLX2eUkPShog6XNjzBpjzAuSNsm/ncoqdXCBInSD1Lzg26uKGqucr6Wl6ku345FdqpwAAABAVImUwPmWpNvk31fzEEkzJE2WlCpppaTp1tpp1tpqR5+/SfqDpC8lDZV0qqQJkqrkX2ToaGvtXa19oLV2rqRz5Z9eO0HSyZK+ljRP0hkNlVT0gvmbgm+/V1uriZVVweP7qHICAAAAUctY2+ntKCEpPz/fFhYWhnsY0W/RSKlylyTpy4QEnXXAAFnjf75z+Xc7dOS+2sa2BaUt3QEAAABAGBhjPrbW5rd0LVIqnIh1jirnoXV1mhKocp5UWaXM+pBHaReN7M2RAQAAAOgkV/tNgF6Smhescl5VXKILS8s0qrauebtAGwAAAACRjQonIoejyjnYW99y2GxQkNkLAwIAAADQFQRORJYOP5/Js8cAAABApCNwIipUGqMVnjQ1eZqTbVIAAACAiEbgROQJqXI+40nTKUMG6bbcbP05JTlMgwIAAACwvwiciHjfuVwqjo+XJN2XlSmv8yJVTgAAACBiETgRmRxVzotKy+QJbI2y2Z2gFz2p4RoVAAAAgP1A4ETEy/D5NKe0LHj8YGaGqo1pbECVEwAAAIhIBE5ELkeV89yycvXz+ifT7na5tDzdE65RAQAAAOggAieiQrK1urykMYA+lpGu0jjHry9VTgAAACDiEDgR2RxVzunllRpeWydJKo+P0yMZ6eEaFQAAAIAOIHAiargkXVVcEjx+Kt2jHYHVayVR5QQAAAAiDIETkc9R5Tyxqlrfq9knSaqNM7o/i5AJAAAARCoCJ6KKkXRNoMqZ463X9/bVNm1AlRMAAACIGARORAdHlfPomn26Y9cevfrtdzq7vKJ520Uje3FgAAAAAFrjCvcAgI4zkqwk6dTKqtabVe7qneEAAAAAaBMVTkSPgpL22wTbZvbcOAAAAAB0CIET0SU1r8XTf0t069NEt+OM7Z3xAAAAAGgVgRPRZf6mJoc74uN1TV6uzhs0QLfmZqveeZEFhAAAAICwInAi+jgWEHJZq78mJ0mSvna7tSYtNVyjAgAAABCCwImoluvzaXZpefD43qwMVRvT2IAqJwAAABA2BE5EJ0eVc3ZpmXK8/sm0u1wuPZnuCdeoAAAAADgQOBH1UqzVvJLGFWwfyUzXnjjHrzZVTgAAACAsCJyIXo4q50/KK3Vwba0kqSouTg9lETIBAACAcCNwok9wSbq2qLHK+bwnTd8kuBobUOUEAAAAeh2BE9HNUeX8UXWN/ru6RpJUb4x+n5XZtO2ikb05MgAAACDmETjRZxhJ1xUVy1grSVqfmqKPkhIbG1TuCs/AAAAAgBhF4ET0c1Q5R9XW6dSKSknShKpq9QusXtvYlqm1AAAAQG9xtd8EiAZGkr+yeWVxqU6vqNTRNfvCOyQAAAAgxlHhRN9Q0Lhg0ID6+rbDJlVOAAAAoFcQONF3OKbWAgAAAAg/Aif6vGpj9EhGuorjHL/uVDkBAACAHkfgRN8SUuV8MyVZ0wYP1B+yM/VwJiETAAAA6E0ETvR5u1z+tbGeTU/TFpdjnSyqnAAAAECPInCi73FUOY+vqtYPamokSV5jdHd2ZkjbkGMAAAAA3YbAiT7NSJq/t3EF23WpKfogKdHRwvb6mAAAAIBYQeBE3+Socv5Xba1OK68IHt+Vk6X6Jm2ZWgsAAAD0BAIn+q7UvODbq4pLlezzSZI2ud16wZMarlEBAAAAMYPAib5r/qbg2/719bqotCx4fF9WpsqNaWxLlRMAAADodgRO9G2OqbUXlJZrgNcrSSqKj9ef2CYFAAAA6FEETsSMJGt1bVHjAkJPZnj0H7ZJAQAAAHoMgRN9n6PKOaWySqNr9slT79N1RSUaGKh4NrZlmxQAAACgu7jabwL0HUbSr3fvlcfnU1ZgEaGm2CYFAAAA6C5UOBEbHFXOoV5vK2GzoS1TawEAAIDuQOBEDDHtNwEAAADQbQiciB0FJS2e3uhO0DV5uWyTAgAAAHQzAidii2NqrST9MStDMwcN0BupKVrMNikAAABAtyJwIqaNqK2TDVQ2n2CbFAAAAKBbETgRexxVzlMqq/T9mn2SJK8x+m12yLYobJMCAAAAdBqBEzHNSLphb3HweF1qit5LTnK0YJsUAAAAoLMInIhNjirn92pr9ZPyiuDxwuws1TVpy9RaAAAAoDMInIhhjavSXl1UorTA3pyb3Qlanu4J16AAAACAPoPAidjl2CYl1+fT3OLGqueDWRnaHe/450GVEwAAANhvBE7ENsfU2nPKynVwba0kqSouTr/PygppywJCAAAAwP4gcAIBCZIWOBYQejUtRdtc8Y4WLCAEAAAA7A8CJ+Coco6t2aeTKqt0VHWNnt22Qwd460PaMrUWAAAA6ChX+02A2HL77r1KttaxpBAAAACAzqDCCUhNqpwp7YVNqpwAAABAhxA4gQapea1eqjIhEXTRyB4eDAAAABD9CJxAg/mbmp2qk/R4ukcnDRmkL90JjRcqd/XeuAAAAIAoReAEnBxTayXpjpws/TYnS2Xx8bojJ6vpOrVMrQUAAADaROAE2nB+Wblc1h8zP0lK0v+mpoR5RAAAAED0IHACoRxVzoPqvDq3rDx4fHd2piqdz3NS5QQAAABaReAEWtQYKi8rLlVuYD/OXS6XHswKCZksIAQAAAC0iMAJtKSgJPg2zVpdV1QcPH4y3aNNCSwgBAAAALSHwAm0xjG1dmpllX5YXSNJqjdGt+eygBAAAADQHgIn0AFG0k17i5osILQmLTW8gwIAAAAiHIETaIujynlwnVfnlzZdQKg0jgWEAAAAgNYQOIF2ORYQKilVf69XkpTss9rhcjVtygJCAAAAQBCBE2iPYwGhFGt1495iXVpcqlXbtuvQ2rqmbVlACAAAAAgicAId4ZhaO6mqWvNKSpVkbSttmVoLAAAASAROAAAAAEAPIXACHeWocjpZSW+mJGtvnOOfE1VOAAAAgMAJ7JfUvCaH37ridWX/frq6fz/9PjuzaduCkGMAAAAgxkRM4DTGXGmMWWGM2WiM2WuMqTPG7DbG/MUYc54xxrTRd5Yx5h1jTKkxpsIYU2iMucIY0+b362w/xLD5m5oc/jshQW+lJEuSXvKk6ZPERMfVVp7xBAAAAGJEJAWrGyT9RFK1pL9KWinpa0knSHpC0ostBUFjzP2SlkvKl/SOpD9LOkTSfZKeN8bEt/Rhne0HOKfW/qi6RidWVgWPb8/NkrdJW6bWAgAAIHZFUuA8R1KWtfYH1tpTrbXnWGuPkfQ9STslnS7pAmcHY8wZkuZK2iHpSGvtNGvtdEkjJW2UNF3SvNAP6mw/oCU37C1Wss8nSdrkdmt5uqdpA/bmBAAAQIyKmMBprX3XWlvZwvl/SLo/cHhSyOUbA683WGs3OfrslHR54HBBC5XRzvYD/BxVzgH19bqspPH4/qwMfedyFMjZmxMAAAAxKloCVcMsxZqGE8aYwZKOklQr6bnQDtbatyRtkzRA0tiu9gOacSwgdH5puUbU1kqSquPidEdOdtMnOJlaCwAAgBgU8YHTGHOgpMsCh2scl8YEXv9hra1upftHIW270g9oyrGAUIKk/9lTFDx+KyVZfwksJgQAAADEqogLnMaYC40xS40xy40xb0n6StJgSXdaa190ND0w8Lqljdv9J6RtV/oBzTmm1o7eV6uzy8qDx3fmZKncubgyVU4AAADEmIgLnJLGyb840CxJxwXO3Szp1pB2aYHXZs99OlQEXp2ruHS2X5Ax5pLAFiqFu3fvbuM2iDVXF5cox1svSdrtcunhrJCQyd6cAAAAiCERFzittRdba42kFElHSLpHUoGkD4wxgxxNG0pH+7vZYWf7Ocf4J2ttvrU2v1+/fp29DfoKR5Uz3We1oKhYkjS1olIXlpSFNGZvTgAAAMSOiAucDay11dbaf1pr58u/quz35d8js0HD3MW0Zp0bNVwrd5zrbD+gdY7QeXJllZ7etkMLd+9VTmC7lKZtmVoLAACA2BCxgTPEksDrqcaYhMD7zYHXYW30GxLStiv9gA4xkv4rsGItAAAAEMuiJXCWyL81iktSduDcp4HXI4wxrS0H+sOQtl3pB7TNUeVsSX2TtlQ5AQAA0PdFS+A8Tv6wWSJpjyRZa7dK+kSSW9JZoR2MMRPkX912h6T3G853th/QMabZmQpjdEd2lq7u34+9OQEAABBTIiJwGmN+ZIw51xiT2MK1cZIeDRw+aq11ForuDLz+xhgzwtEnT9IDgcOF1trQB+k62w9oW0FJk8NKYzR98EA9neHRWynJep29OQEAABBDIiJwSjpY0pOSdhhj3gjswbnaGPMPSe9KOkjSK/JvjxJkrX1e0oOSBkj63BizxhjzgqRNkg6XtEpNFxrqUj+gQxxTa1Ot1YSq6uDxwpxslcWxNycAAABiQ6QEzrck3SbpM0mHSJohabKkVEkrJU231k6z1laHdrTWzpV0rvzTZCdIOlnS15LmSTojpCLa5X7A/rq6qET9vF5J0h5XvP6YFbIXJ6ETAAAAfZSxln0BuyI/P98WFhaGexiIRI4g+XpKsq7r79+z1VirZdt3avQ+x0q27Sw4BAAAAEQqY8zH1tr8lq5FSoUT6HscIfKkqmodF5haa43R/+TmqMnGKVQ5AQAA0AcROIFeYCT9f3uKlOLzr0P1jTtBf8oMCZmLRvb+wAAAAIAeROAEepKjyjmwvl7XFDWuYvtoZrq+SkhobFu5qzdHBgAAAPQ4AifQ01Lzgm9nlldoTE2NJMlrjP6nX7aarE7F1FoAAAD0IQROoKfN3xR8GyepYE+REgKLdSX6rMriQv4ZMrUWAAAAfYQr3AMAYkJBabB6eVCdV9cUlSjJWp1ZXtH8rz5MrQUAAEAfQYUT6C2OqbU/KyvX2S2FzQZMrQUAAEAfQOAEeotjai0AAAAQCwicQG9yrFrrVCdpabpHe+Id/ySpcgIAACDKETiBMPvSnaBZgwbo7pws3ZGT3fQioRMAAABRjMAJ9LaQKmdxXJy+SHRLkv6cmqI3UpLDMSoAAACg2xE4gXBwhM6xNfs0vbwiePzrnCyVxRlHW6qcAAAAiE4ETiACXFdUrFxvvSRpt8ul32VnNW1A6AQAAEAUInAC4eKocmb4rH65tyh4vNKTpveTEsMxKgAAAKDbEDiBcHKEzpOqqnViZVXw+H/65ajSMLUWAAAA0YvACUSQm/YUKaPeP7V2u8ul32VnNm1A6AQAAEAUIXAC4eaocub6fPrl3uLg8Yp0jz5gai0AAACiFIETiASO0HlKZZVOcEytXZaRHtKWKicAAACiA4ETiDBG0s17i5RdX6+fl5Tqnp27mzcidAIAACAKEDiBSOGcWlvv06tbv9NVxaVyh3FIAAAAQFcQOIFIkprX+NbatttS5QQAAECEI3ACkWT+plYvWUl/TwypdxI6AQAAEMEInECkcUytbbAzPl5X9O+ncwcN0EesWgsAAIAoQeAEIpFjaq0k/S47U++kJEuSbs7NUZUxjRepcgIAACBCETiBSBQytfa6ohJ56n2SpG0JLv0hK7Npe0InAAAAIhCBE4hUjqm1efX1WlBUHDx+KsPD1FoAAABEPAInEMkcU2tPrajUhKrq4PEtudlMrQUAAEBEI3ACkcwxtdZIumVPUXBq7bcJCfpdNlNrAQAAELkInECka2Nq7bPpHr2XnBSOUQEAAADtInAC0SBkau0JlVXB41tys1Uax9RaAAAARB4CJxANWpham11fL0na5XLpgUym1gIAACDyEDiBaOGYWpvj8+mWPUWSpFPLK3VFSUnz9otG9tbIAAAAgBa5wj0AAPshNU+q3CVJmlRVrae37dB/1da23DbQDgAAAAgXKpxANHFMrZXUethswNRaAAAAhBGBE4g2jqm1LdkdH/LPmqm1AAAACBMCJxCNWgidlcaoIDdbpw0epO9c8Y4LTK0FAABAeBA4gT7i2rxcrfSkqSIuTjfn5sjnvMjUWgAAAIQBgROIViFVzstLShVnrSTpw+QkPZ2eFtI+ZOsUAAAAoIcROIFo5gido/fVak5pWfD491mZ+ibBuRC17cWBAQAAAAROoE+5vLhUh+zzr1y7Ly5ON/XLkdfZgKm1AAAA6EUETiDaOaqcbkl37N4rV2Bq7YbERC3OTA9pT+gEAABA7yBwAn2BI3QeWlenK4objx/OzNDfEt3hGBUAAABiHIET6IMuLC3TD2pqJEn1xujGfjmqNKaxAVVOAAAA9AICJ9BXOKqc8fJPrU3z+TdH2ZqQoD9khaxSS+gEAABADyNwAn2JI3Qe4K3XL/cUSZL+u7qmyQq2AAAAQG9wtd8EQHQxatgCZVpllTw7duu46uqW/7pUkNFsP08AAACgu1DhBPqagpLgWyNpYmthM9ieqbUAAADoGQROoC9qp2pZHBfyT78gs+WGAAAAQBcQOIG+qoXQWSfp/swMTRkySP9KcM6ot702LAAAAMQOAicQQ27LzdZDWRmqiovTgn65qnVeZGotAAAAuhmBE+jLQqqcPystl9vnr2Z+kejWfWyVAgAAgB5E4AT6OkfoHFFXp2uLi4PHSzM8+jApsWn7RSN7a2QAAADo4wicQIz5aVmFxlVVS5KsMfplvxyVxpnGBpW7wjQyAAAA9DUETiAWOKqccZJu27NXmfX1kqSdLpduzcluumwQU2sBAADQDQicQKxwhM5+9T4V7CkKHr+elqoX01JD2rNVCgAAALqGwAnEktS84NtJVdU6s6w8eLwwJ0vfsFUKAAAAuhGBE4gl8zc1Ofx/RSU6qLZOklQdF6dbcnOYWgsAAIBuQ+AEYo1jam2ytbpr1x65fVYjamtVsKdIpll7QicAAAA6h8AJxCJH6Dy0rk4P7dylp7/bqRF1dS23Z6sUAAAAdIKr/SYA+rof1uxruwFbpQAAAKATqHACscpR5WzJt654+Zq0Z2otAAAA9g+BE4hlLYROK2llWqqmHzBQSzM8Ie0JnQAAAOg4AicQ6xxbpUjSq6kpKuiXo5q4ON2blanP3e4wDQwAAADRjsAJxLqQrVImV1bpyMAznV5jdENejiqMY+1aqpwAAADoIAIngCZTaxMk/Wb3HqX5/E9wbk1I0K9zs0PaEzoBAADQPgInAD9H6BzsrdfNe4qCxy+npWpNWkpI+8zeGhkAAACiFIETgEPj1NkfV1bp9PKK4PHtOdna4nLupGR7cVwAAACIRgROAI0KSpoc/nJvsYbV1UmSquLidH1ervYZZ3um1gIAAKB1BE4ATTmm1qZYq0W79ijB+quZXyS6tSg7K6Q9oRMAAAAtI3ACaM6xVcqo2jrN31scPH7Ok6ZvElxN2/M8JwAAAFpA4ATQXMhWKeeUV+ikyir183r1yI5dOqjOG9KB5zkBAADQHIETQMscU2uNpF/t3qvntu3QDwN7dDZvz9RaAAAANEXgBNA6R+j0WKucwN6crbcndAIAAKARgRNA2xzPc4baFR+vj5ISm57keU4AAAAEEDgBtC3kec4G7yUn6awDBujqvH7a5op3XOF5TgAAAPhFROA0xiQYYyYZY+42xnxgjNlujKk1xmwzxjxvjJnYSr+lxhjbxs8X7XzuLGPMO8aY0v+fvTsPr7us8z7+/mZr2qRNm2ZrQRGVcRR1XIKP4ziig47jjKOjgCiKqIiKKCAzdcPRKC4gbriOgI4LLojbo4+OOG6I61hcB0XrxtamWZqkSdpmvZ8/zml68utJmr0nyft1XblOfr/f/T25y3WR5JN7i4iBiNgeEedHREn8d5FKRsHUWoAR4NLN9ewpL6e/vIxtjQ2MTGrv1FpJkiSVSOAETga+AVwMHAfcDHwB2AOcCnw7It4wTf33gY8W+fjCVAUR8T7gE0ArcBPw38BfAO8FPhsR5VPVSqtSQeisBN7a2UVF/nzOX1Wv4V31mam0hk5JkqRVr+LITZbEOPA54MqU0k2FDyLiDHLB8N8j4tsppW8Xqb8mpfSRmX6xiDgVeDHQDjwqpbQjf78Z+DbwFOAlwJVz+LdIK1dNEwx2APDAoWEu2tPL2zZvAuBjdRs4af8Qj96//1D7to3Q1ns0eipJkqQSUBIjnCmlb6WUTsuGzfyz64CP5C+ftUBf8lX511ccDJv5r7UbOC9/+Uqn1koZmfWcz97bz8n7DgXMSxrr2VXuek5JkiTlLJdA9bP867HzfaOIOBZ4KDAMXJ99nlK6EbgLaAEen3mQlQAAIABJREFUPt+vJ604mfM539jZTcvoKAB7y8vZ1uR6TkmSJOUsl8B5Qv511xTPHxMR74iIqyLi0oh4/DSjkw/Ov96SUto/RZufZNpKKlQQOjeOj3NFRxfl+fWcv6hewztczylJkiSWQeCMiBbgOfnLz03R7NnAy4BzgdcAXwN+FREPKNL2+PzrbdN82dszbSVlFZzP+aChYS7sObRW89q6DXx93drJ7T2fU5IkadUp6cAZERXAtUAd8M2U0pczTX4OXACcCNQCW4EnAr8A7gd8IyKOydTU5l8Hp/nSA/nX9VP06wX5I1S2d3Z2zvSfI60smfWcz+nr5zGD+yauf169JlPgek5JkqTVpqQDJ/AfwCnAHRTZMCil9K6U0ntSSr9OKQ2mlHallL4CPAz4EdDEoQ2CDoqD5XPtVErpqpRSa0qptbGxca5vIy1/2fWcXd3ce3iYN3Z28/I9RXandWqtJEnSqlKygTMirgTOIXd0ySkppfaZ1qaUhoG35C//MfO4P/9ay9QOPuufpo0kmBQ6N4wnPntXO08emGYCgaFTkiRp1SjJwBkRbyc3VbaTXNjccYSSYm7Nv2an1P45/3rcNLV3y7SVNJ2C9Zzl0zSbYOiUJElaFUoucEbEW4GLgW7gcSmlX8/xrTbnXwcy9w8esXJiRGR2NZlwUqatpOlsm/pvQoMRXNJQz6+rKic/uOKE4gWSJElaMUoqcEbEZcA2oIdc2PzFPN7uafnXnxTeTCndAfwUqAJOL9KHk8md99kO/HAeX19aXQqm1h70x8oKnrG1hS+tr+Xipkb6yuLQw8GOJeycJEmSjoaSCZwRcSnwCqCXXNicdnQxIh4UEU+MiPLM/YqIuJjclFyAdxYpP7i+8/KIuHdBbRPw/vzlZSml8Tn8U6TVKxM6yxN0VuT+F72rsoLXNGxm0v9UTq2VJEla0SqOdgcAIuJJ5M7PBPg98NKIKNb01pTSZfnP7wF8AdgTEb8D7iR3jMkDyB2PMg68IqV0Q/ZNUkqfjYgPAOeRO6/zG8AIuR1xNwBfBN67MP86aZWpaZoYvTxudJRLO7t5WXNuN+fv1KzjI3XreV5fwX5cbXVFR0clSZK0/EVKR/9svIh4DvCfM2h6Y0rp0fma44ELyR2Bchy5NZuJXPC8CXhfSunmI3zdM4HzyYXUcnIbDX0Y+MBMRzdbW1vT9u3bZ9JUWj0yI5dX1G/kY3UbAChLiWvaOzjpwNChBjVN064DlSRJUumKiJtTSq1Fn5VC4FzODJzSFApC5whwzpYmflZdDcDm0TGu37mLxrGCv+s4yilJkrQsTRc4S2YNp6QVpiBAVgJXdHRTPzYGQHdFOdsaGxiZ1N71nJIkSSuNgVPS4ikInc1jY1ze0UVZflbFzWureWf9xkx7Q6ckSdJKYuCUtMgObQD28ANDvKTnUAj9eN0G/ntd5jhcQ6ckSdKKYeCUtLjaeiddntO3l78b3AfAI/btn7x50EFXnLAUPZMkSdIiM3BKWnwFU2vLgDd1dvNv3T28f3cnG8eLbAidP1ZFkiRJy5uBU9LSKAidtSlx9t5+yqdt79RaSZKk5c7AKWnp1DRN+/hPlRWTbxg6JUmSljUDp6Sls21H0dtjwLs31fHkY7bwnbVuIiRJkrRSGDglLa2CqbUHfWBjHVdvrCNF8KqmzdxWUVGkUJIkScuNgVPS0suEzmfu7WfryCgAA2VlXNTcwL6IgvaOckqSJC1HBk5JR0dB6Nw0Ps47OzpZk9+x9vdVVby2oZ40qb2hU5IkabkxcEo6ig6NYt5veIR/7+6ZuL6htoaPbVg/ubmhU5IkaVkxcEo6etp6J10+eWCQM/b2T1y/o34jP65ek6kxdEqSJC0XBk5JR1dmPecrunv4qwNDAIxHsK2pgZ0V057YKUmSpBJl4JR09BWEzkrgHR1dNIyOAdBTXs6FTY3sdxMhSZKkZWdBAmdE3DMinhwRD1qI95O0ChWEzqaxMd7Z0UlFym0bdGdlBX+srMy0N3RKkiSVuhkHzoj4l4j4UkQ8LHP/VcBvgc8DN0fERxa2i5JWowcNDXNJ9x7uMTzCJ3e2c+Lw8OGNDJ2SJEklbTYjnGcBpwC3HLwREScCb8xf/hjYC5wVEf+yYD2UtHpk1nOe1j/I9TvbOT5/RmfxGkOnJElSqZpN4Hww8POU0mDBvWfmX1+QUnoEcBIwApy7QP2TtNpkQmd1SlM0LHDFCYvUGUmSJM3HbAJnA3BX5t6jgUHg4wAppd8D3wPutxCdk7RKZUJnoVuqKjm3pZG9ZQWbCA12LEGnJEmSNFuzCZxrKDilPSIqyY16/jClVDjfrR1oWZjuSVq1ioTOr9as4+wtzfxo7Vpe2djA2KT2Tq2VJEkqNbMJnLuA+xZcP4pcCP1+pl0NubWckjRPMemqDBgqy33bumndWt6zKRMyDZ2SJEklZTaB87vAfSPi4oi4H/AGIAE3ZNrdn8On3krS7LX1Trr8h8F9nNN7aOTzQxvr+K+adZkaQ6ckSVKpmE3gfBOwD7gC+BXw18B3Uko/PtggIk4A7kVux1pJmr/M1NqX9vTxt/v2T1y/tqGe31Rlz+jcuBQ9kyRJ0hHMOHCmlH4LPBL4BPDf5I5D+edMs8eROzblKwvVQUkqDJ3lwOUdXdxjeASAA2VlXNjcSHdZ4bezGexsK0mSpEUXaSZHDmhKra2tafv27Ue7G9LqUDBd9k+VFZy5tYWBfNB8yIEDXLOrg0ljndPsditJkqSFERE3p5Raiz2bcoQzIm6NiDdHxEmL1zVJmo1DmwgdPzLK5R1dRP6PZj+truZNm+snj226nlOSJOmomm5KbTPwSuBHEXF7RFwZEY+OiNms+5SkhZPZROhR+w9wQc+hUczPbajlh2urMzWGTkmSpKNluvDYCDwBuAaoBF4KfBPYHRHXRMQ/RUTVEvRRkg7JTJM9p28v/zQwSKTEv3X38Nf7DxSpMXRKkiQdDTNawxkRAfwN8FTgX4B7kNuVYwD4KvAF4KsppYFF62mJcg2ndJQUhMihgF+uWcNJB4amKYjDRkglSZI0f3Naw1ko5XwvpXRxSumewEOBtwB3AmcAnwI6I+LLEfHciNi8UJ2XpKIKRjrXJI4QNsGdayVJkpbenNZjppR+llJ6TUrpROAvgdcA/wv8E7kpuO0R8a2IePSC9VSSsqbZhXYo4Jq6DYxMau/UWkmSpKU07w2AUkq/Sym9JaV0EnB34GLgB8DfAo+a7/tL0mx1lZXxvJZmrqzf6M61kiRJR9GC7jibUrozpXRlSulkYAtw3UK+vyQdpsgo5w216/hl9Rogt3PttRvWZ2oMnZIkSUth0Y44SSl1pZR+u1jvL0kTMqHzzL0DPHFgcOL6bfUbucnjUiRJkpbcjHapnWgcUQ6cBjwG2ApUT9E0pZQeP//ulT53qZVKSGbn2ue1NE+MdNaOj3PtznbuNTJaUODOtZIkSfM13S61FbN4k0bg68ADgThCc7eDlLT02vomQueaBFfu7uQZx7TQXlHBQFkZL2lu5JM7d7NpfDxf4LcqSZKkxTTjwAm8Hfgr4A/AB4Ed5M7hlKTSUdMEgx0ANIyP897dnZy1pZn9ZWXcWVnJy5oauLq9g8qD7dvqpt3tVpIkSXM34ym1EdEFjAD3Syn1LGqvlhGn1EolKLM+85vr1vKypgZS5CZnPLV/gLauPZOnahg6JUmS5mS6KbWz2TRoDfA9w6akkpcJj6fs288FPYfufX59LZ9eX5upcRMhSZKkhTabwHkrsP6IrSSpFGRC5zl9e3lSf24VwAMPDPG4wX1FagydkiRJC2k2gfP9wMkRccJidUaSFlRB6AzgdV17OL+nlw+1d9AwsXFQtsbQKUmStFBmHDhTSv9JbrOg70TE2RHRsnjdkqQFUhA6q4AX9e6l+khr16/w72qSJEkLYTYjnADvBrqBDwN3RcRIRAwX+Rha+K5K0hwdYUOgH6ytZm9ZwRZC+V1uJUmSND8zDpwR8QBgO3AiudlpAZSTO1ol+1E5xdtI0lFy+PHBCbh2w3pe1NzIxU2NjBQ+dGqtJEnSvM1mhPNyYCPwWeAkYBO5YDnVhySVjrbew279uqqKyzdvIkXw47XVvLGhnkmTbQ2dkiRJ8zKbwPkIcjvVPj2ldHNKqS+lNDbVxyL1V5LmLjO19sThYc7vORREP7++lg/XZTbjNnRKkiTN2WwC5zjwi5SOtNuGJJWwTOh8Ye+h41IA3lW/iRvWrc3UGDolSZLmYjaB8yfAcYvVEUlaMpnjUtq69tC6/8DEvUsaN/OLNVWZGkOnJEnSbM0mcL4ROCkinrRYnZGkJVMQOiuBd3V0cY/h3LZBQ2VlXNDcyJ0V5ZmajUvYQUmSpOWvYhZtx4Argc9FxLXADcCd5KbaHial9IP5d0+SFlFN08QRKHXj47x/dydnbm2mt7ycPeXlnN/cxMd3tbNh/OBKAlcUSJIkzUbMdElmRIyT+20rOPJvXSmlNJswu2y1tram7du3H+1uSJqrzFTZn65Zw/O3NDESuWNUHr5/P1e1d04+VOUI53pKkiStJhFxc0qptdiz2YTCH+Cf9yWtNG19k0LnQ4aGeGNnN69oaqBqPPG0vQOHn+DZVmfolCRJmoEZB86U0iMXsyOSdNRkQuc/Du6ju7uH+w8N8eCh4SlqDJ2SJElHMptNgyRp5cqEx7P29k8dNidq3LlWkiRpOgZOSTroCCOWe8rK+En1mkyNoVOSJGkqBk5JKjRF6Ly9ooKztjZzfnMjv6ryjE5JkqSZMHBKUlYmdCbgVY2bub2ykv1lZbykpZE7KjJL4D2jU5Ik6TAGTkkqKiZ99sauburGxgDYU17OeS2N9JQVfgt1E29JkqQsA6ckFdPWO+ny+JFR3ru7kzXj4wDcVlnJS5sbORAFh6Y4tVaSJGkSA6ckTSUztfZBQ8Nc1tlNpNxo5i+q1/DKxs2MTaoxdEqSJB1k4JSk6WRC52P37ecVe3omrr9Zs4631m+aPKHW0ClJkgTMInBGxPMjYu1idkaSSlImdD5z7wBn9+2duP5k3Xo+tmF9psbQKUmSNJsRzquAOyPi7RFxwmJ1SJJKUiZ0Xrynl8cPDE5cv23zJr6/tjpTY+iUJEmr22wC5/8DNgAvA34TEV+LiH+OKNwxQ5JWsILQWQa8qaubhxw4AMDfDe7joQeGitQYOiVJ0uo148CZUnoScE/gMqAL+Hvgi8CfIuKVEdG4OF2UpBJSEDrXJHj37i5e3NPLOzq6qE5THI1i6JQkSavUrDYNSindkVJ6NXA34CzgR8DdgTcBt0fExyPirxe+m5JUQmqaJj6tGx/nvN69lB+ppm3jonZJkiSpFM1pl9qU0khK6RMppb8BHgx8CBgFzgS+FxE3R8TzImLNAvZVkkrDth1HbPKZ9bV0lRd+i01whcvfJUnS6jLvY1FSSr8AXg/8JxD5jwcDVwN/johz5vs1JKnkZDYROmgcuKJ+I5c21PPi5iYGCpe5D3YsTd8kSZJKxLwCZ0Q8NiI+D/wJOB84AHwYeAbwVaAJuCoiLphvRyWp5BQJnb+pquLa/BEpv1lTxUXNjQxPqnE9pyRJWj1mHTgjoi4iLoqIW4EbgH8BdgKvBo5NKT0/pXRdSumfgUcAg4CBU9LKlAmdJw4P87quPRPXP15bzasbNzM+qcbQKUmSVocZB86IeEhEXAPcBbwd+AvgRuBU4J4ppctTSnsKa1JKPwa+Qm5jIUlamTKh86kDg7x0T+/E9Q21NVxWv4lJe9gaOiVJ0iowmxHO7cDz8p9fAzwwpfR3KaUvpJTGp6kbBCrm2kFJWhYyofPcvr08o69/4vpTdeu5pm5DpsbQKUmSVrbZBM4/A9vITZt9YUrpf2dYdy5QOduOSdKyUxA6A3jFnh4ePzA4ce/d9Rv5fG1NpsbQKUmSVq7ZBM57pZTenlLqPXLTQ1LO2Cz7JUnLU0HoLAfe3NnN/9l/YOLe6xvq+c7atZkaQ6ckSVqZZhM4b4iIi4/UKCJeFhFfn00nIqIyIk6JiLdHxI8iYldEDEfEXRHx2Yh49BHqz4yImyKiLyIGImJ7RJwfEdP+++ZaJ0nTKgidVcC7dnfyl0O5vWrHI/j3xnoGC49LAUOnJElakWYTrB4L3H8G7e4HnDLLfpwMfAO4GDgOuBn4ArCH3KZE346INxQrjIj3AZ8AWoGbgP8mt6HRe4HPRkT5QtZJ0ozUNE18WpsSH9jdwbEjI2wYG+M9uzupSenwGkOnJElaYRZjJK8KmG4ToWLGgc8Bj0opbUkpPTGldEZK6QHA04Ex4N8j4jGFRRFxKvBioJ3cJkZPTCk9BTgB+A3wFOAl2S821zpJmrFtO8it5MxpGBvng+2dfGzXbh40NDx1naFTkiStIAsaOCMigIcCXbOpSyl9K6V0WkrppiLPrgM+kr98Vubxq/Kvr0gp7Sio2Q2cl798ZZEpsnOtk6SZa5u85P3uo6Pca2R0BnUbF6lDkiRJS+tIaxy/fvAjf+vvC+9lPr4F3A7cF/juAvfzZ/nXYwv6diy5cDsMXJ8tSCndSO7M0Bbg4fOtk6Q5yRyXkvWnygrOa26kr6zw23EydEqSpBXhSOdjPrbg8wRszX9M55fAy+fTqSJOyL/uKrj34PzrLSml/VPU/QQ4Jt/2B/Osk6S5aesrOlX211WVnNfSxJ7ycl7c3MjV7R2sm1jbmeCKE/JTcyVJkpanIwXOx+VfA/g6cAPwtinaDgN3pZT+uEB9y33hiBbgOfnLzxU8Oj7/ets05bdn2s6nTpLmrkjovK2ykp78yOYvq9dwYXMD72vvpOpgg8GOpe2jJEnSAps2cKaUvnnw84j4PnBj4b3FFhEVwLVAHfDNlNKXCx7X5l8HDys8ZCD/un4B6gr79QLgBQB3v/vdp3kbSSqQCZ1PGNzH3rIy3thQD8CP1q7lFU0NXNHRdeibc1vdEaflSpIklaoZb4qTUvrblNJli9mZIv6D3BErd3D4hkEHt38scrbAtOZaNyGldFVKqTWl1NrY2DjXt5G0GmXC4xn9A7x0z6HNhb5Rs443NNRP/gblzrWSJGmZKtldWCPiSuAcckeXnJJSas806c+/1jK1g8/6C+7NtU6SFkYmdJ7bt5dn9+2duP7C+lreXr/R0ClJkpa9KafURsSr859+IKXUU3A9IymlN8+1UxHxduACoJNc2Cy2a8af86/HTfNWd8u0nU+dJC2cgum1Afzbnl72lpXxxfW5v3d9tG4DG8fGeX5BEHV6rSRJWm4ipeIzSyNinNy00/umlH5XcH3E9wRSSql8Th2KeCuwDegmFzZ/MUW7u5Hb3GcY2Fhsx9mIuIPcUSqPTCl9fz51U2ltbU3bt2+fxb9QkgoUjFyOAv/a1MC3atZN3HtN1x7O6B/I1Bg6JUlS6YiIm1NKrcWeTbdp0JvJBcyuzPWiiYjLyIXNHuBxU4VNgJTSHRHxU+AhwOnAxzLvdTK50NgO/HC+dZK0KApGOiuAt3Z2cX5ZEz9eWw3Az6rX8LT+gYnF57kaRzolSdLyMOUI51KLiEuB1wC9wGNTSjfPoOY04Hpy4fBvU0q/z99vAr4N3A+4KKV05ULUFeMIp6R5u+KESUegDEbw/C1NnDg0zKu7e6ZebG/olCRJJWC6Ec6SCJwR8STg/+YvtwO3TNH01uxOuRHxfuA84ADwDWCE3M62G4AvAqellMaKfM051WUZOCUtiLaNFE4i2RfB2pQmj2wWrTN0SpKko2s5BM7nAP85g6Y3ppQeXaT+TOB84AFAOXAr8GFyGx6NT/N151RXyMApacFkQmdWAu6qKOfY0czfwgydkiTpKFqQwBkR5wFXAk9JKX1lijZPBD4PvDildM0c+7usGDglLagpjj8ZB968eRNfqa3hQ7t2c7/hkUydoVOSJB0d0wXO2ZzD+VRgD/Bf07T5r3yb02bxvpKkg6YIjm+r38h1G9YzUFbGC1ua+H1lZabOczolSVLpmU3g/EvgV9NNNc2vefwVuU13JElzUSR0Prl/kA1juam0veXlnNvSxG0VmY3GDZ2SJKnEzCZwNgK7Z9CuA2iaW3ckScBhofM+IyN8sL2TmvHc3/y6Ksp5/pYmdlZkjjw2dEqSpBIym8DZB9xtBu2OAQaO2EqSNL1M6Lz/8DDva++kOh862ysqOLelic7yzLdyQ6ckSSoRswmcPwMeHhH3mqpB/tkjgJ/Pt2OSJA4LnQ8dGuLK3V1U5jd8u72yknNbmugpM3RKkqTSM5vA+RGgEvhiRJyQfRgR9yZ3fmV5vq0kaSFkQucjDhzg7R1dlOdD5x+qqnhhSxN7yzKndrZtXKoeSpIkFTWbwHkd8FXgROCWiPhWRLw///FN4Nf5ZzeklK5dhL5K0uqVCZ2P2beft3R2E/nQ+Zs1VbyysSFTlOCKw/4+KEmStGRmHDhT7sDOpwIfyN96NPCi/Mdj8vc+ADxlAfsnSTooEzqfMLiP13ftAWDT2BgX9PQeXjPYYeiUJElHTaT8X8dnVRTRApwCHJe/dRvwzZRS+wL2bVlobW1N27dvP9rdkLSaZNZnfr62hgcNDXHPkdGpa2qaYNuORe6YJElajSLi5pRSa7FnFcVuHkk+WH5iXr2SJM1NW9+k0PnUgcEj1wx2LGKHJEmSipvNGk5JUqnITK/NurWqktc11DMyqcadayVJ0tKadeCMiPtExPsi4paI6M1/3BIR742Iv1yMTkqSipgidN5SVck5LU18fn0tr2rczKSJtoZOSZK0hGYVOCPiOeTO2HwRcF9gQ/7jvsCLgZ9HxNkL3EdJ0lSKhM5vrVvH3vJyAG6oreGSxs2MTaoxdEqSpKUx48AZEScBVwNVwBeAJ5ILmvcD/gn4HLlzOq/Ot5UkLYVM6HxJbx9n9vVPXH+1tobXNtQzPqnG0ClJkhbfbEY4t+XbPyuldFpK6asppd+mlG5NKf1XSul04FnkNiL6t8XorCRpCgWhM4BX7unhaXsPhc4vra/lDYZOSZK0xGYTOB8J3JxS+tRUDfLPfgI8ar4dkyTNUiZ0XtLdw6n9AxP3Pre+ljdv3sSkw7AMnZIkaRHNJnBuBn43g3Y7gPq5dUeSNC8FobMMeG3XHp5UEDqv27Cey+oNnZIkaWnMJnD2APeaQbt75ttKko6GTOh8Q9ce/qngrM5P1q3nbfUbDZ2SJGnRzSZw/gB4WEQ8eaoGEfHPwMOB78+3Y5KkeSgIneXAGzu7+YeC0DkUMTlwgqFTkiQtuNkEznfkX6+PiA9HxMkRcfeIuFv+8w8BnwXGC9pKko6WmqaJTyuAN3d287jBfTyzr59LunuK/wAwdEqSpAUUKR32N+6pG0e8lFyYLPZ7SgBjwMtSSu9dmO6VvtbW1rR9+/aj3Q1JKu6KE2CwY+JylNyIZxyprsj5npIkScVExM0ppdZiz2YzwklK6T3Aw4BrgdvJ/e4ylv/8Y8DDVlPYlKSSt23HYSOd2bA5Bnxz3drJNx3plCRJC2BWgRMgpfSzlNLZKaXjU0prUkpV+c+fk1L62WJ0UpI0D5nQWWgMeG1DPRc1N/K+jXVuJCRJkhbUrAOnJGkZmiJ0fmrDer60vhaA/9hUZ+iUJEkLysApSatFkdB5en8/j9y3f+L6g5vqeM8mQ6ckSVoYU24aFBFXzeN9U0rphfOoXzbcNEjSspPZSGgYuKi5kZsK1nGe29vHS3v6Jq/3dCMhSZJUxHSbBk0XOMfn8TVTSql8HvXLhoFT0rLUthEKxjGHgZc1N/LdgtB5Tm8fFxo6JUnSEUwXOCumqTt3kfojSTra2nonhc4q4J27O7m4uZEb86HzQxvrGCd4WU/vodDZVmfolCRJMzarczh1OEc4JS1rRUY6/7Wpge/UrJu499zevZNDJxg6JUnShAU7h1OStMK09VJ4MmcV8I6OLh4zuG/i3pdqa+guz/y4cCMhSZI0A3MKnBFRGxGPjojTI+L/LHSnJElLKBM6K4G3d3Txd4P7qB8b40Ptu2kYK7Ks39ApSZKOYFaBMyLW53ev7QK+CXwaeGHB8/Mi4vaIeNjCdlOStKjaeicdmVIJvK2ji2t3tnOvkdFp6gydkiRpajMOnBGxDvgO8HxgL/DfMHlJD/B14FjgKQvUP0nSUsmc01kJ3G107LBmt1dUeE6nJEmakdmMcP4r8GDgU8DxKaV/yDZIKf0B2AH83cJ0T5K0pLbt4PC/JR7yq6oqnnZMC5du3sSkSbaGTkmSVMRsAufTgF3AOSmlwWna3QYcM69eSZKOnsyazoNur6jghS1NDJaVcf2G9by2oZ5J45+GTkmSlDGbwHkv4H9SSgeO0K4LaJh7lyRJR11mTSfA1tFRTt6/f+L6/66v5VWNm5m0wrOtDq44YWn6KEmSSt5sAucIsGYG7Y4FBubWHUlSycis6awA3tjZzVP7D32L/6/aGrY1NTBSWDfYYeiUJEnA7ALn74AHR8SUoTMiNgJ/BfzvfDsmSSoBmdBZDryuaw9n7O2fuPeNmnVc1NzIUOEs3MEOaNu4dP2UJEklaTaB83NAM/Dmadq8EagFrp9PpyRJJWTbDmjrm7gsAy7p7uGsvr0T9767bi0XNDWyPwpTZzJ0SpK0ys0mcL4H+C1wUUTcGBEX5O8fFxHnRsTXgfOAW4BrFrifkqSjrSB0BrBtTy/n9h6694N1azm/uZF9h4VONxOSJGm1mnHgzO9M+/fAzcDfAu/MP3o08B/AY4FfAP+UUhpa2G5KkkpCJnRe0NPH+T29E/d+sraa/1dbU6TO0ClJ0mo0mxFOUkp3pJQeBjwJ+CDwdeBbwEeBM4DWlNIdC95LSVLpKAidAC/q3cvL9vQA8Oy+vZzeP8W+cYZOSZJWnUgpHe0+LGutra1p+/btR7sbkrT0MgHyf6rXcNKBoSIneGbr+o7UQpIkLSMRcXNKqbXYsylHOCPisxGIjr+zAAAgAElEQVTxhIg44u8OkqRVKBMcH1YkbI4Ae8oyP2oc6ZQkadWYbkrtU4H/B9wREW+KCA9VkyRNNs1o5SjwysbNPHtrM7vKyzN1hk5JklaD6QLnB4AeYCvwSuDW/O60Z0fEuiXpnSSp9E0ROl/fUM/Xa2u4rbKSs7c2c1tFRabO0ClJ0ko3ZeBMKZ1PLmyeQW5zoHFyu9N+GGiPiKsj4hFL0ktJUmkrEjofvW8/Ffl9AnZVVHD2lmZ+V1mZqTN0SpK0kk27S21KaTildH1K6QnAccAlwO+AWuAc4KaI+E1EbIuIlsXvriSpZGVC5yn79vPe3Z1Uj48D0F1RznO3NPHLNVWZOkOnJEkr1WzO4dyZUnpLSum+wN8AHwL6gfsAlwG3R8T/jYgnR0T5dO8lSVqhMqHzb/Yf4IPtndTmQ+fe8nLObWniJ9VrMnWGTkmSVqJZncN5UErphymlc4EtwNnAd4By4InA54G7FqqDkqRlJhM6HzI0xId27Wbj2BgA+8rKeFFzEzeurc7UGTolSVpp5hQ4D0op7U8pfTyldArwD0AXEEDjQnROkrRMZULn/YZH+Miu3TSNjgIwXBZc1NzI12oye9AZOiVJWlHmFTgjojYizomIm4CvcSho3jHvnkmSlrdM6LzXyCgf2bWbY0ZyoXM0gis31TGUPbzT0ClJ0ooxp8AZEY+JiI8B7cBV5NZ0DgPXA08Ajl+wHkqSlq9M6Lzb6Bgf3bWbew6P0Dg6ylXtnaxJxeoMnZIkrQSRUrGf9EUaRhxPbr3m2cDdyU2dBfg58J/AtSmlnsXoZClrbW1N27dvP9rdkKTSlgmQPWVl9JSXcc/8aOfUdcXP+JQkSaUjIm5OKbUWezbtCGdErIuIsyPi28AO4N/JHY/SC7wPeEhK6SEppfesxrApSZqhTHDcND5eNGz+obKCSX8GdaRTkqRlbcrAGREfIjdl9sPAyfnb3wCeAWxJKb00pfTzxe+iJGlFOMJo5fbqNTx9awuvb6hnbFJdHVxxwqJ2TZIkLY7pRjifC9QCfwZeB9wjpfT4lNJ1KaXhpeicJGmFmSJ0/qmygpc0N3KgrIzPra/l5Y2bmfSDZrDD0U5Jkpah6QLnJ4BTUkr3SildmlK6c6k6JUlawYqEzruNjHLK4L6J66/X1vCSlkb2RWYLW0OnJEnLypSBM6V0Vkrp20vZGUnSKtHWx6G956ACuLRrD8/s65+498O1a3l+SxM9ZZkfVYZOSZKWjXmdwylJ0py19UJN08RlGfCKPT2c39M7ce9X1Ws4e0sz7eXlmVpDpyRJy4GBU5J09GzbMSl0BvCi3r28pmsPkT+2609VlZy1tZk/VlZMrjV0SpJU8gyckqSja9uOw9Z1ntE/wFs7u6nIh872igqes6WZW6qqJtcaOiVJKmkGTklSaciEzn8Y3Mf7dneydnwcgJ7ycn5eXVWkztApSVKpMnBKkkpHJnQ+Yv8Brm7voG5sjOf39vHMvQNT1Bk6JUkqRQZOSVJpyYTOvxoa5rN3tXNBT/EzPA/VGTolSSo1Bk5JUunJhM6WsTEyJ3KyP4Iv1daQJtUZOiVJKiUGTklSaWqbekRzBNjW1MAljZu5on4j45Pq6qBt42L3TpIkzYCBU5JUuqYIndfWrefGdWsB+HjdBl7TsJmRSS2SoVOSpBJg4JQklbYiofPMvf08dnDfxPWX19dwYXMj+6Jw4m1yiq0kSUeZgVOSVPoyoXNNgrd1dHFq/6Fda29at5bntzTRU5b50WbolCTpqDFwSpKWh7Y+KNg6qBx4Xdcezu09FEZ/Vb2GZ29p5s6K8kytoVOSpKPBwClJWj7aeqGmaeIygAt6+nh11x4i5far/XNVJWdtaeE3VZWZWkOnJElLzcApSVpetu04bIrtM/oHeHtHF1XjudDZVVHOc7c08/M1VZNrDZ2SJC0pA6ckaXnKhM7H7dvPB3d3sH4sd0hK4+gY9xgZLVJn6JQkaakYOCVJy1cmdLYeGOKju3Zz/6EhPri7g43j41PUGTolSVoKJRM4I+I+EXFhRFwbEbdGxHhEpIg4bZqaj+TbTPVx6xG+5pkRcVNE9EXEQERsj4jzI6Jk/rtIko4gEzpPGBnhkzt3s3V07Ah1dZ7VKUnSIqs42h0ocB5w4Rxrvw/8vsj9XVMVRMT7gBcDB4BvAiPAKcB7gVMi4vSU0hF+W5EklYS2vkmjllGkyddq1nHjurW8obObQ9sJ5c/qLHLWpyRJmr9SCpz/C1wBbAduBj4EnDzD2mtSSh+Z6ReKiFPJhc124FEppR35+83At4GnAC8Brpzpe0qSjrJM6Cz0P9VreHXjZkYi6Cov4527u6jN72qbqzV0SpK0GEpm6mhK6ZqU0stTSp9JKf1hkb/cq/KvrzgYNvN92E1upBXglU6tlaRlZorQeNPatYxEbtzzR2vX8rwtzXSVZ77Fu65TkqQFt+oCVUQcCzwUGAauzz5PKd0I3AW0AA9f2t5JkuatSOi8uKeXl/T0Tlz/Zk0Vz9rSwp8rMhN9DJ2SJC2olRI4HxMR74iIqyLi0oh4/DSjkw/Ov96SUto/RZufZNpKkpaTtj4KV3IG8MLevby+s5vy/FTauyorOGurZ3VKkrSYVkrgfDbwMuBc4DXA14BfRcQDirQ9Pv962zTvd3umrSRpuWnrPWy086kDg1y5u5Pq/HEpveXlnNPSzNfXrc3UGjolSVoIyz1w/hy4ADgRqAW2Ak8EfgHcD/hGRByTqanNvw5O874D+df1xR5GxAvyR6hs7+zsnGvfJUlLIRM6T95/gA/v6qB+LLcR+XBZ8G9NDXx0w3rSpLo6uOKEpeunJEkr0LIOnCmld6WU3pNS+nVKaTCltCul9BXgYcCPgCYObRB00ME5Vok5SildlVJqTSm1NjY2zvVtJElLJRM6HzA8zLU727nH8AgAKYJ31G/k95WVk+sGOxztlCRpHpZ14JxKSmkYeEv+8h8zj/vzr7VM7eCz/mnaSJKWk0zovNvoGB/ftZuHHDgAwCXdPZwwMjJFraFTkqS5WJGBM+/W/Gt2Su2f86/HTVN7t0xbSdJKkAmdG8fHuaq9g8s7unha/8AURQdrDZ2SJM3WSg6cm/Ov2d8gfpZ/PTEiMrtETDgp01aStFJkQueaBP84uO+wZl3lZfyp0mNTJEmaj5UcOJ+Wf/1J4c2U0h3AT4Eq4PRsUUScDBwLtAM/XOQ+SpKOhiJndRbaF8H5zY2ctaWZn65Zk6k1dEqSNFPLNnBGxIMi4okRUZ65XxERF5PbvRbgnUXKD67vvDwi7l1Q2wS8P395WUppfKH7LUkqEW19UNNU9NFrG+r59Zo19JWXc25LE1+rWZepNXRKkjQTkdKcN2tdUBHxEA6FPcgda7Ie2AHsOXgzpfTwfPt/Ab6Qf/Y74M58+weQOx5lHHhVSumtU3y99wPnAQeAbwAjwCnABuCLwGkppbEj9bu1tTVt3759Nv9USVKpyQTIW6qqeHFLI3vKD/1N81+7ezh7b//EVudALrBu27E0fZQkqURFxM0ppdaiz0oocD4a+PaR2qWUIt/+eOBCckegHEduzWYiFzxvAt6XUrr5CF/zTOB8ciG1nNxGQx8GPjDT0U0DpyStEJnQeWdFOec1N/HnqkNHpTx9bz+v7O6h/LDa6afoSpK0ki2LwLlcGTglaQXJhM6+sjIuaG7gp9XVE/cePbiPyzu7WZf9+WnolCStUtMFzmW7hlOSpAWXCY11+WNTnjAwOHHvOzXrOHtLM+3lmXFO13VKknQYA6ckSYWKHJtyWWc3z+3dO3Hv1jVVPHNrM3dUeGyKJEnTMXBKkpSVCZ1lwMU9vbyuq5uK/FTau4+M0jI6WqTW0ClJ0kEGTkmSiilybMpp/YO8v72D+w8N8c6OLiqnKKWtDq44YdG7KElSqTNwSpI0lW07Dhvt/OsDQ3xy5242jk/ezDwBk8Y7Bzsc7ZQkrXoGTkmSjiQTOqNIkw/VbeD85kb6I/PU0ClJWsUMnJIkzcQ0x57csG4tV9Zv5Afr1vLsrc3cVeEOtpIkgYFTkqSZmyJ03lZ5aDXn76uqOHNrC79YU5WpNXRKklYfA6ckSbNRJHS+oG8vb+7oojK/g+2e8nLOaWniazXrMrWGTknS6mLglCRptorsYPvPg/u4elcHG8fGABgqK2NbUwNX120gTaqtM3hKklYNA6ckSXNRZAfbhw4N8Ymdu7nH8MjEvXfXb+Q1DfWMZOsNnZKkVcDAKUnSfGRC591HR7l2VzsP239g4t6X1tfy/C1N7CnL/Ng1dEqSVjgDpyRJ85UJnXXjif9o7+Ap/QMT935TVUVXeXm20tApSVrRDJySJC2ETOisBF7ftYeL9vRQnhKXd3bzFyOHTazN1xo6JUkrk4FTkqSFkgmdAZzT18+X79zFY/btP0JtHbRtXLy+SZJ0FBg4JUlaSG19hwXPu42OHtbsd5WVvHHzJoYn3U2OdkqSVhQDpyRJi6HIeZ0HdZeV8dLmRq7bsJ5ztzTR7WZCkqQVysApSdJimSJ0fml9DTsrKwD4aXU1Z25t4XeVlZlaQ6ckafkzcEqStJiKhM7n9PXzb909REoA7Kys4KytzXx73dpMraFTkrS8GTglSVpsRTYTOntvP+/d3UnN+DgA+8rKuLCpgWvqNpAm1dYZPCVJy5aBU5KkpdDWBzVNk249av8Brt25m2NGcpsKpQiurN/IJQ2bGYpsvaFTkrT8GDglSVoq23YcNtp575ERPrWznYfuPzBx78vra3heSzNd5W4mJEla3gyckiQttUzo3DQ+ztXtHZzaPzBx75fVa/hKTU2RWkOnJGn5MHBKknQ0ZEJnJfC6rj28oruHspR4/MAgz97bP0VtHVxxwuL3UZKkeTJwSpJ0tBTZTOhZe/u5pr2DS7v2kF3GOclgh6OdkqSSZ+CUJOloaus7LHiedGCItWnSXrWMAO/eVEd/ZGKooVOSVMIMnJIklYIi53UWumzzJq7eWMeZW1v4Y2VFptbQKUkqTQZOSZJKxRSh81dVVXxmw3oA/lxVyTO3tvDdtdWZWkOnJKn0GDglSSolRULnA4aHeWtHF9Xj4wAMlJXxkuZGrq7bwKSJt211Bk9JUkkxcEqSVGra+qCmadKtJwzu42O7drNldBSAFMG76zeyrXEz+1zXKUkqUQZOSZJK0bYdh4123nd4hE/f1c5D9x+YuHdDbQ3P3tLMXRXlk+sNnZKkEmDglCSplGVCZ/34OFe3d/D0gjM6f7umiqdvbeEn1WsytYZOSdLRZeCUJKnUZUJnJXBJdw9tnd1U5I9P6S0v512bNk5e0wmu65QkHVUGTkmSloMimwmdOjDIf+7azebRMerHxnhbRxdRpDRXb+iUJC09A6ckSctFW99hwfNBQ8N8emc7723vZMvY2BHqDZ2SpKVl4JQkabnJhM6WsTEeMDx8WLPP1daw3XWdkqSjyMApSdJyVGSKbaGfVK/h0oZ6zm1p4hMbaj2vU5J0VBg4JUlarqYInePAmzdvYiyC0Qgu21zPqxo3s9/zOiVJS8zAKUnSclZkXWcZ8IH2Th5wYGji3ldqazhrSzN3eF6nJGkJGTglSVoJiqzr/Miu3ZzaPzBx7+B5nd9bW52prYMrTliKXkqSVhkDpyRJK0UmdFYBbV17eF1XN5X58zr3lpfz4uZGrqrbwHhh48EORzslSQvOwClJ0kpSZF3naf2DfGTXbppGRwFIEbynfiMXNTXQ77pOSdIiMnBKkrTStPVBTdOkWw8cGua6u9pp3X9g4t731q3l9srKIvWGTknSwjBwSpK0Em3bcdhoZ8P4OFe1d3BW314ALunaw4lFzu8E8kenbFzsXkqSVjgDpyRJK1kmdFYCL9/TyyfvaufUgcEjFCdHOyVJ82LglCRppSuyrvMBRUY2b6+o4F8bN9NTlvn1wNApSZojA6ckSatBkfM6C+2L4KLmBr5eW8PTjmnhV1VVmXpDpyRp9gyckiStJlOEzu+trWZHPmS2V1Tw7K3NfHp9LWlSbZ3BU5I0KwZOSZJWmyKh8+/37ed97R1sGBsDYDSCNzXU88rGzezz6BRJ0hwZOCVJWo3a+oDJQfJR+w9w3c527jt0aH3nV2trOHNrM3+srMjUGzolSUdm4JQkabVq6z1stPPY0TE+vqudU/cOTNz7Q1UVz9jawtdq1mXqnWIrSZqegVOSpNUuEzrXJGjr3sOlnd2sGR8HYF9ZGduaGri8fuPkdZ1g6JQkTcnAKUmSiq7r/JeBQT6xazd3GxmZuFeZshNxD9YbOiVJhzNwSpKknCJHp9xneIRP72zn7wb30br/ABf09E5TXwdXnLDInZQkLScGTkmSNFkmdG4YT7yro4v37u4ks3UQ+yIYL7wx2OFopyRpgoFTkiQdLhM6A6hJk1dvjgMXNzXw0uZG+so8OkWSdDgDpyRJKq6tD2qapnz8wY0b+P66tXx33VrO2LqFX1dVZuqdYitJq52BU5IkTW3bjqIbCgHsj0O/RtxVWcGztrZw3fraybvYOsVWklY1A6ckSTqyIqHz4p5e3rm7k5r80SkjEbyxoZ6XN25mIJxiK0kycEqSpJkqEjofu28/193Vzn2Ghifufa22hqcf08Jvi02xlSStKgZOSZI0c0WOTjludJRrd+3m9L39E/duq6zkzC0tXL++ZvIU27Y6g6ckrSIGTkmSNHuZ0FmdEq/t7uHyji7W5afYDpcFb2jYzGfW1xapN3RK0mpg4JQkSXNTZIrtPw7u49M72/mL/BTbewyP8MSBwSnqDZ2StNJlz2+WJEmauYOhsyA8Hj8yyid27eZt9Rs5fe/AYed3Tq6vm/w+kqQVxRFOSZI0f0Wm2L6mu4f7jIwc1vQLtTXscxdbSVoVDJySJGlhzGCU8ss163ht42aevrWFHZXuYitJK52BU5IkLZwiu9ge1FlexqUN9QD8qaqSM7c284Xamky9u9hK0kpi4JQkSQuvSOhsHBvnNd09rM3vYnugrIzXNm7mkoZ6p9hK0gpl4JQkSYujSOh80sAgn9rZzr2GhyfufWl9Lc/Y2sLvnGIrSSuOgVOSJC2etj6oaZp0614jo3xy526e1D8wce+P+Sm2n1lfy6Q9bZ1iK0nLmoFTkiQtrm07DhvtXJcSb+rawxs6uyem2A6V5dZ4/mtTA3vLnGIrSSuBgVOSJC2NIlNsnzIwyKd3tnNCwRTbm6vXMJRd0wn50c6Ni9lDSdICM3BKkqSlU2QX23vmp9iesbcfgDd1dtM4Nj7FGyRHOyVpGTFwSpKkpZcJndUp8ZruHj5/5y4euf/AYc0PuIutJC1LBk5JknR0FJlie8LIyGH3/qd6Df947BZ+sLY6U+8UW0kqdSUTOCPiPhFxYURcGxG3RsR4RKSIOG0GtWdGxE0R0RcRAxGxPSLOj4hp/31zrZMkSQukyBTbQnvKynhV42Y6Kyp4YUsT79xUx+RI6hRbSSplpRSszgPeBTwTuA9QZLeAw0XE+4BPAK3ATcB/A38BvBf4bESUL2SdJElaBFOEzl0VFYwX/Erw4Y11PGdLM3dWZH5MGzolqSSVUuD8X+AK4Azg3sCNRyqIiFOBFwPtwANTSk9MKT0FOAH4DfAU4CULVSdJkhZRkdB54vAwn71rF3+zb//EvV9Wr+FpW7dww7q1mXrP7JSkUhMppSO3Ogoi4jvAycDpKaXPTtFmO/BQ4OyU0scyz04GvkMuVB6TUhqfb10xra2tafv27bP6t0mSpCPIBMdx4KN163n3po2MFmwgdPrefl6+p5fq7O8z00zTlSQtrIi4OaXUWuxZKY1wzkpEHEsuNA4D12efp5RuBO4CWoCHz7dOkiQtoUxgLAOe29fPR3ft5piR0Yn7129YzzO2NrOjsjJTXwdXnLAEHZUkTWfZBk7gwfnXW1JK+6do85NM2/nUSZKkpVRklPKBQ8Ncf9cuHj8wOHHv91VVPG9LE/uyR6cMdjjFVpKOsuUcOI/Pv942TZvbM23nUydJkpZakV1s16fEFZ3dtHV2Uz2eW/lyYU8v66ZaJmTolKSjZjkHztr86+A0bQbyr+sXoE6SJB0tmdAZwKkDg1y3s51zevs4tX+6H+u4oZAkHSXLOXAenDcz212P5lp36A0iXpA/s3N7Z2fnXN9GkiTNRlsf1DRNunXPkVEu6uk77Cy1HZWVvH3TRoYPew9DpyQtpeUcOPvzr7XTtDn4rL/g3lzrJqSUrkoptaaUWhsbG4/YUUmStEC27TjiDrQHInh502Y+snEDZ25t4Q+VFZMbGDolacks58D55/zrcdO0uVum7XzqJElSqZgmdH6ptobfV1UB8Ns1VZyxtYXPrK+dPLXJKbaStCSWc+D8Wf71xIhYO0WbkzJt51MnSZJKSZENhQBO7x/g1V17qBrPRcyhsjIubajnwqYGesoyv/oYOiVpUS3bwJlSugP4KVAFnJ59HhEnA8cC7cAP51snSZJKVJENhZ7RP8Cnd7Zz7+FDqzi/XbOOU49p4UfVazL1jnZK0mJZtoEz7y3518sj4t4Hb0ZEE/D+/OVlKaXxBaqTJEmlqK0PMlsHnTAywqd3tvPMvkNbMnRWVPCClibesWkjI4e9h6FTkhZapKnOrFpiEfEQDoU9gPuRO5ZkB7Dn4M2U0sMzde8HzgMOAN8ARoBTgA3AF4HTUkpjRb7enOqyWltb0/bt22f875QkSYusSHD87tpq/r1xM3vKyyfu3X9oiI/t3E1ltnFNU25zIknSjETEzSml1mLPSmmEcwPwfwo+Dp6BeULm/iQppRcDzyQ3TfZk4PHA74GXAKdOFRrnWidJkkpckXWdj9p/gM/dtYu/2bd/4t4j9x04PGwCDHY42ilJC6RkRjiXK0c4JUkqYZngOA58YsN6vrNuLR9s76CieFVB/fRHsEiSls8IpyRJ0sLKBMYy4Ky9/VxdJGy2l5fz3bXVmXo3FJKk+TBwSpKkla3IhkLZX4DGgUsaN3N+SxOXbt7Evpjc3tApSXNj4JQkSStfW++002OvW1/L/+RHNz+zYf3/b+++wyM767uN3z+1lbapbC/GMbEhQGhhTQ2mOMSEboNN6DWAbQIJicG8IaDQDDHNgA0xYAwBE6pNJ7RQDcFr0zFgIDbeXWm1TVqtdrVqz/vHOdodzc5oi2Y0I+n+XNdcZ+eUZ848O5c0Xz2N8zas5ectLUVltEN3RzXvUpLmHQOnJElaOMqEzr8Z2s8jhvYfen5bczPPWL+G93QsZ2zKmcnWTkk6DgZOSZK0sHQPHBE8OyYmeGvfTl6/YxdLJrJluMcjuKKzg2etW8NtTUUjPrvb4dLTZuuOJWnOMnBKkqSFqSh0BvD4fUN8amsPfzE8fGj/z1oXce6GtXxy2RKmzO3v8imSdFQGTkmStHB1D8CS1VN2bRwb56qePl66u5+mfPm4Aw0NvHblCl6yeiWjR5Rh6JSkcgyckiRpYbvoliNaOxuB5w/s5Zptvdxx5HDEXDExQXOpMlw+RZJKMnBKkiRByQmF7jIyyse39fK0gUHuMDrKy3ftOUoZhk5JKhQppaOfpbI2bdqUNm/eXOvbkCRJlVQiOO6PYHHR96a9DcFtTc3cfWSkRBnll2GRpPkkIm5MKW0qdcwWTkmSpGIlwmJx2AS4ZEUXT1+/hnd2tju2U5JKMHBKkiSVUmL5lEJfWbKYLyxdwkQE7+to56nr1/Lb5qIRnt3t0N1R5RuVpPpl4JQkSZpOmdB594MH2XTg8PIpv17UwpM3rOX97csZn3JmsrVT0oJl4JQkSTqaEsunbBgb5wO9fbx81x4WTUwAMBbBZV0dPHPdGm5raioqox0uPW227liS6oKBU5Ik6ViUWD6lAXjG3kE+sa2XPz948ND+n7Uu4kkb1nLNsqVMFF4w1Gdrp6QFxcApSZJ0PLoHgJiy646jY/zntu28eE8/TfnkQsMNDVyysosXrF3NUERRGbZ2SloYDJySJEnHq7v/iNbOJuCF/Xu5ZlsvpxYsk7IopZIz3NraKWkhMHBKkiSdqBITCt1lZJSPb+3luf0DdI2P071zV1F7aHEZhk5J81ekUn9x0zHbtGlT2rx5c61vQ5Ik1VqJ4DgYwbKi71ojwA/bWjmjYIbbw2WUX4ZFkupVRNyYUtpU6pgtnJIkSZVQIiwWh02Ad3d2cOHa1bxi1QoGGkqM7ZSkecTAKUmSVCndA9O2Uv5kUQtXty8D4EtLl3DOhnV8t621qIx2g6ekecPAKUmSVGllQucdR0d57L6hQ8/7mpq4YO1qXrOyi8FSM9lK0hxn4JQkSaqGEq2dyycSb9i5m3ds30HX+Pih/Z9ZtpSzN67j+7Z2SppnDJySJEnVVKK188z9B7h2Sw+PGNp/aN/2piZetHY13bZ2SppHnKV2hpylVpIkHbMSwfErSxbzxhWd7GlsPLRvzdgYV/X0cYexsRJlOJOtpPriLLWSJEn1oERYfOTQ/iNaO1eOj7O+VNgEWzslzSkGTkmSpNlUYmzniokJ3ta3k7ds38HqsTFev2M3TdOW4dhOSXODgVOSJKkWSrR2nrX/AF+5fRunjo5O2T8BfKB9mWM7Jc05Bk5JkqRa6R6AJaun7GoucdrHli/lHV2dnL1xHd9zJltJc4iBU5IkqZYuumXaiYB2NDbwjs4OIJvJ9vy1q3m1M9lKmiMMnJIkSfWgRGsnwKrxCV6/YxedBet2Xpuv2/ldWzsl1TkDpyRJUr0o09p51v4DXLelh7/eN3Ro3/amJi7IWzv3NtjaKak+GTglSZLqTfcAMDVEdk1M8NYdu3jL9h10Fbd2bljHt23tlFSHDJySJEn1qLu/bGvntVt6OKugtbOvqYkXr13N55cuLlFOO1x6WjXvVJLKMnBKkiTVsxJjO7smJnjLjl28taC1c8PoGGcOHShdxlCfrZ2SasLAKUmSVO/KjO386/0H+CgyH10AACAASURBVOyWHh6zb4jX7NzF4pSmL8fWTkmzzMApSZI0V3QPHBE8OyYmuGTHLh4wfPCI01+zsotPLVvClBhqa6ekWWTglCRJmmumWbdz0tcXt/GZZUv5t5UreP7a1dze1FRUhpMKSao+A6ckSdJcVKK1s9BHli879O8ftbVyzoa1fHj5MsaLTzR0SqoiA6ckSdJcViZ0vnf7Dp7Tv5eGfFzncEMDl67o5Jnr1vC75uaiMmztlFQdBk5JkqS5rkRrZ2tKvGxPP9ds286dDo4c2v+z1kWcu2Et7+1YzugR5Rg6JVWWgVOSJGm+KNHaebeREf5rWy8v3tNPc97aORbB5Z0dPHnDWn7Z0lJUhq2dkirHwClJkjSflGjtbAZe2L+XT27t4R4Fs9ne0tLCVe3LKMnQKakCDJySJEnzUYnWzj8dHePDPdt5xa49tE1MsGx8glfu3jNNGbZ2SpqZpqOfIkmSpDlpMnQWhMZG4Ol7B3nI/v38sbmZleMTUy7ZH8FIBB0TBfu722HJarjollm4aUnziS2ckiRJ812J1s6TxsZ50IHhI/a/q7Odx29cx5eWLCYVHhjqs7VT0nEzcEqSJC0ER1m3E+AXLS1cs3wZuxsbecXqlVywZhVbmxqLyrGbraRjZ+CUJElaSLoHgCh5aH9DsGp8/NDz7y1u4+wN6/jw8mWMHVGOoVPS0Rk4JUmSFpru/pKtnfcdPshnt/Tw1IFBIl9C5UBDA5eu6ORp69dwc0tzUTm2dkqanoFTkiRpoeoeyCYDKrAkJV65ew//2bOdU0dGDu3/1aJFPGX9Wt7W2cGBKGohNXRKKiNSSkc/S2Vt2rQpbd68uda3IUmSNDMlQuMocHX7ct7b0c5Iw+GQuWF0jA/2bGddQffbw+VMP05U0vwTETemlDaVOmYLpyRJkkpOKtQM/N3AXj6ztYf7Fsxou3J8nDWlwibk3Ww7qnijkuYSA6ckSZIOK9FCefLYGO/v7eO1O3axYmyc1+zcfZQvkclutpIAu9TOmF1qJUnSvFUiNB4MWFT09XEcuLSrk6ftHeSksSPms7WbrTTP2aVWkiRJx6/EEirFYRPgmuXL+Gj7Ms7ZsJb3ty9n9IhybO2UFioDpyRJksors4TKpH0RXNGZBcrhhgYu6+rgvA1ruWnRoqJyXEJFWogMnJIkSTq6EkuoACxNiff39PFnBw8vofK7lhaetX4Nr1nZRX9D0ddNJxWSFhQDpyRJko7NRbeUbO2828gIH9vWy0W79tA2MXFo/2eWLeVxG9fxuaVLmNoT10mFpIXCSYNmyEmDJEnSglUiNPY2NnLJik6+uWTxlP2nHxjmVbt2c8dRJxWS5hsnDZIkSVLllQiKa8fHuaxvJ+/cvoO1BTPW3tDWyueXLilTjq2d0nxl4JQkSdKJ6x4oGTwftv8An93Sw7P799KYEhtGx3hB/95pynFSIWk+skvtDNmlVpIkKXfpaTDUd8Tu37Q0MxQN/MXBg1P29zU20kBi5fjEEdfYzVaaO+xSK0mSpOorM6nQnUdGjwibAK9b0cnjNqzn48uWckTktLVTmhcMnJIkSaqsMt1sC31jcRvfWrKYwcYGXr+yi2esW8OvW5qLyrGbrTTXGTglSZJUHdOEzuUTE9xhdPTQ85+1LuJv16/l0q4O9kcUldOeddeVNOcYOCVJklQ9ZVo7Tx8+yGe29vCiPQM053OKjEfw4fblPG7jOr62uG3q2p1DfbZ2SnOQgVOSJEnV1z0AS1ZP2bUowYX9A3x6aw/3PTB8aP/2piZetmYV569ZxW1NTUXl2M1WmksMnJIkSZodZSYVOmV0jPf39vHGHTvpGh8/tP/7i9s4Z8M6tjU1HlmWoVOaEwyckiRJml0lutkG8Nh9+/nclm08ee8gkXezPXP/ftaPjZcoBFs7pTnAwClJkqTaKNHa2T6ReNWuPXxsWy/3P3CAf97df8Q5o8U7DJ5S3TJwSpIkqXbKTCp0t5FR3te7g9XjU1s390Xw+I3ruLJ9OSNHlGXolOqNgVOSJEm1dwxrdwJc3tnO7c3NvKurgyduWMf1ra1F5djaKdUTA6ckSZLqxzShcxT4ceuiQ89vbWnmhetW80+rVtDbWDSxkMFTqgsGTkmSJNWXMq2dzcBHtm3n4l27WToxcWj/V5cu4XEb1/HB9mWlx3dKqplIKR39LJW1adOmtHnz5lrfhiRJ0vxVIjTubGzgrV2dfGHpkin7/3RkhH/ZtYfThw+WKOfoXXYlHb+IuDGltKnUsTnfwhkRV0dEmubx62mufWpEfDciBiJiX0RsjogLI2LO14skSdK8USIorhyf4JIdu7iqZzunjhyePuj3LS08d90aLunqLFGO3Wyl2dZU6xuooO8Dvyuxv6fUyRFxOXABMAx8g2xYwJnAu4EzI+LclFKZRZ8kSZI0qyZDZ1FgPH34IJ/Y2stHly/jis52DjRk7QanjR4xh21BWe22dkqzZD4FzvenlK4+lhMj4olkYbMXOCOldEu+fw3wP8DZwIuBy6pzq5IkSToh3QNw6Wkw1HdoVzPw7L2DPHJoP2/p6qCnqYlzBoeOUk774fIkVc1C7Tr6ynz7ismwCZBS2g6cnz+92K61kiRJdeiiW0oGxbXj47xlxy7e19t3xJfcnyxq4Z9WraDH2WylWbXgAlVEbATuA4wAnyw+nlL6NrAVWAvcf3bvTpIkSceszGy2i4smxRwH3rii69Bstle2L+dgFJdl6JSqYT4FzodFxNsi4sqIeF1EnFWmhfLe+faXKaUDZcq6oehcSZIk1asywXPSj1oXcfOiFgCGGxp4V1cHT9iwjm+3tRaVY2unVGnzKXA+E/hH4O+AVwFfAX4eEXcvOu+UfHvbNGX9sehcSZIk1bsyofMBwwe5ett27nzw8ERCW5qbefHa1VywZhW3NRVNa2LwlCpmPgTOnwAvAe4GLAXWA48BfgrcFfh6RGwoOH9pvp1uJPm+fLussrcqSZKkqirT2nmfgwf5r229/MvO3SwfP7wQwXcXt3H2xnVc1tnO/ijqZ9vdDt0d1b5jaV6b84EzpfSOlNK7Ukq/SikNpZR6UkpfBO4L/BBYzeFJggAmf5Kk4rKOVUS8IF+zc/OOHTtO/OYlSZJUHSWCZxPwt4P7+MKWHp60d5DIx3qORvD+jnYeu3EdN7QuKioo2dopzcCcD5zlpJRGgEvyp48qODSYb5dS3uSxwVIHU0pXppQ2pZQ2rVq1amY3KkmSpOop0drZOTHBa3bt4WPbernH8MFD+3c3NrJyvMwy7HazlU7IvA2cuV/n28Iutbfm25Onue6konMlSZI0V5XpZnu3kVH+s2c7r9+xixVj4zxjYJBTRseOUpbBUzoeTUc/ZU5bkW/3Fez7cb69W0S0lZmp9vSicyVJkjTXTYbOgsDYADx+3xAPH9pPY4lLrlm2lEUpcfa+oaktNd3t086MKykz31s4z8u3k8uckFK6HbgJaAHOLb4gIh4CbAR6gR/Mwj1KkiRpNpUIistSOmL9zp7GRt7e1UH3qhU8df0afpIvrXK4HFs7paOZ04EzIu4VEY+JiMai/U0R8TKy2WsB3l506eTYzjdHxKkF160GrsifvimlNFGN+5YkSVKNHWXtToAPdCxnuCH7uvzLRYt4xvq1vGLVCnobi9pCDZ5SWZHSCU/WWnMR8QTgWmA38FtgC9lSJncnWx5lAnhlSunfS1x7BXA+MAx8HRgFzgSWA9cBT0oplRk1ftimTZvS5s2bK/J+JEmSVCMlAuOBCD7QvpwPti9npOHwkiltExM8d2Avzx4YpPWI79IB3f1VvlmpvkTEjSmlTSWPzfHAeQrwUrIlUE4mG7OZyILnd4HLU0o3TnP9U4ELyQJqI9kkQ1cB7znW1k0DpyRJ0jxRppVya1Mjb+vs4KtLl0zZv25sjJft7uesof1E8UWO79QCMm8DZz0wcEqSJM0zZYLnDa2LeHNXJ78pGsv5F8PDvKVvJ6vGS7RXGDy1AEwXOOf0GE5JkiSp4sqM7zx9+CAf39bLq3fuorNgvc7dDY10lAqb4PhOLXgGTkmSJKmUEsGzETh3cIgvbNnGMwb20pQSL9+9h+ajltUOl55WrTuV6paBU5IkSZpOidbO5ROJl+/u58u3b+PBB4anHEvAv67s4tttrUwZvDbUZ2unFhwDpyRJknQ0ZbrZrh0/clGDry5u47plS3nx2tWcv2YVf2huKirLbrZaOAyckiRJ0rE6yvqdCXhfx+Ew+f3FbZyzYR1v7upgoKFoLluDpxYAA6ckSZJ0vLoH4MjFUAjgyt4+zt07SEO+GsR4BB9pX85jNq7n48uWMnZEWY7v1Pxl4JQkSZJORHd/ydbOrokJXr1rD5/Y1svpBeM7+xsbef3KLs7dsJbr21qnXuT4Ts1TrsM5Q67DKUmSJKBkYEzA1xe38dauTrYWjeV86NB+3tG3k8aSZbl+p+YO1+GUJEmSqq3E+M4AHrH/AJ/duo2X7O5n8cTh9TpXjY+XDpvg+E7NGwZOSZIkqZJKjO9clODvBvbyxS3bOGdwH8vGJ7hgz5GtmEf0Pexuh+6Oqt2qVG0GTkmSJKnSyozvXDk+wb/t3M2Xt2xjZUFrJ8CuhgaevH4tX13cVhQ8k62dmrMMnJIkSVK1lFlGpb0obAK8p7Odmxe18E9rVvHsdav5RUtLUVl2s9XcY+CUJEmSqu0o63fuj+BrSxYfen5TaytP2bCWV65aQW9j0UhPg6fmEAOnJEmSNFvKrN+5OCU+t2UbzxzYS1PBKhJfWLqEx25cx7s72tkfRdcZPDUHuCzKDLksiiRJkk5ImbB4W1MTb+/q4BsFLZ4AK8fGecmefh63b+jI2W2XrIaLbqnOfUpH4bIokiRJUr0p08325LEx3tG3k6t6tnOXgyOH9u9sauTVq1bwj6tXHlnWUJ+tnapLBk5JkiSplsoEz9OHD/Jf23p53Y5drBobO7T/UUP7pynLbraqLwZOSZIkqR50D2RdYws0AE/YN8QXtvRw/p4B7n/gAGcVBc4EDDQ4vlP1yTGcM+QYTkmSJFVcmbCYOHLKoe+0tfLy1St5Xv9enr53kLZS3++nmSFXminHcEqSJElzSZlutsVhcwx4e1cHQw0NvLOrg8dsXMd1S5cwfkR5tnaqNgyckiRJUr06yvqdOxobGS+IoX1NTfzrqhWct34t17e1FpVlN1vNPrvUzpBdaiVJkjRrSgTGMeAzy5ZyRUc7u5qmLpjywP0HeNnufu48OlqiLLvZqjLsUitJkiTNByVCYhNw3uA+vrhlGy/aM0DbxMShY9cvbuPcDWt51couehuLVu+0xVOzwMApSZIkzSVlutkuSYkL+wf4wpYenji4j4a8J2OK4LPLlnJ5Z5lwafBUFRk4JUmSpLmoTPBcPT5O987dfHprLw/efwCAlonEBXuO0oW2ux26O6pxp1rADJySJEnSXFYmeJ46OsoV23fw/p7tvGL3HtaNT527dqAh+MbiNqbO6JJs7VRFGTglSZKk+aBM8Lzf8EHOG9x3xP73t7fzD2tW8ax1q/npopaisuxmq8owcEqSJEnzSfcAR67YOdXWpkY+2r4MgB+3tvL09Wt52eqV/LGpqagsg6dmxsApSZIkzTfd/dMue7J0IvHkvYM0FSyR+LUli3n8xnW8fkUnOxuLYoLBUyfIdThnyHU4JUmSVPfKhMXbmxp5Z2cHX1m6ZMr+tokJnjkwyLMH9rK0VF5wDU8VmG4dTgPnDBk4JUmSNGeUCZ4/W9TC2zs72NzWOmV/5/g4/7y7n8ftGypTnsFT0wdOu9RKkiRJC0WZiYXucXCEq3r7uKK3j9NGRg7t39PYyLTNU93tcOlplb9PzRsGTkmSJGmhKRE8A3jwgWE+ubWXN+7YyfrRMU4dGeEx5Vo3Jw31Ob5TZRk4JUmSpIWqxIy2jcBj9+3n81u28c7tO2ksuuR/WxfxvLWr+UWLS6no6AyckiRJ0kJWZkbbFuCksbEp+xLw9q4OftTWylM2ZEup3OpSKpqGgVOSJElS2fGdhW5uaebXBS2bX1uymCdsXMfrVnSyw6VUVIKBU5IkSdJh0wTPu46Mct2WHv66YFzneASfWL6MR29czzs72xmMqV10DZ4Lm8uizJDLokiSJGleKxMWf97Swjvy7rWFOsbH+bv+vfzt3kFaSl3oUirzjutwVpGBU5IkSQtCieCZgOvbWnl7Zwe/WTQ1Xj557yCv2rVnmvIMnvOF63BKkiRJmpnuAViyesquAB50YJhPbOvlkr6dbBjNJhlqSolnDAwepTzX8FwIDJySJEmSjs1Ft5RcSqUBeMzQfj63ZRsX79rNc/v3cnLRDLeDEVzf2sqU/pWu4TnvNR39FEmSJEkq0N2fb6eGxRbgaXv3lbzk6vblXNnZzukHhnnpnn7ueXCkoLy8HLvZzju2cEqSJEk6McewlArAzoYG/rN9GQA3tLXy9PVr+fvVK/ltc3NRec5oO98YOCVJkiTNzFGCZwCP3jdEY8GEpd9aspgnbVjLxatWcHtTUcdLg+e84Sy1M+QstZIkSVKRMmHxtqYmLu9s58tLl0zZ35QS5wzu44X9e1k9Pl6iPLva1jOXRakiA6ckSZJURpng+ZuWZt7V2cG3F7dN2b9oYoIL+gd4brkZbg2edcllUSRJkiTNvjJdbe88Msq7t+/gw9t6uc+B4UP7DzY0sHRimgYxu9rOObZwzpAtnJIkSdIxKhEWE3B9WyuXdXawryH47JYeiqYSYhSO2JeVZ4tnPbCFU5IkSVLtdQ/AktVTdgXwoAPDfHxbL1f19B0RLH+8qIVHnbSezyxdwljRMVs865+BU5IkSdLsueiWki2TAawtmjAoAZd1dtDb1MRrVq3g7A3r+NKSxUwUX2zwrFsGTkmSJEmz7xjW8OxrbOT/Wg63ed7a0swrVq/kiRvW8vXFbRwxOLC7Hbo7Kn+vOmGO4Zwhx3BKkiRJFVCmhXJ/BB9dvowPti9nsHFqe9ldDo7w4j39PPjAMFF84ZLVWWuqqs5lUarIwClJkiRVUJngOdAQfKh9OR9ZvowDDVOD5z2GD/LiPf08YPjgkRcaPKvOSYMkSZIkzQ1lutq2TyResmeAr9y+jWf376V14vBIzp+1LuLjy5eVLm+oz/GdNWTglCRJklR/ygTProkJ/mlPP1/aso2nDgzSnBKREhfsOcoSKU4sVBN2qZ0hu9RKkiRJs6BMWOxtbOT6tlbO2Tc0Zf/+CF67sotnDezlLiOjJcpzDc9KcQxnFRk4JUmSpFl0jK2U729fzmVd2Yy1jxjazwV7Bjh11OBZDY7hlCRJkjQ/HMNyKiPAh9sPj+n82pLFnLNhLS9ftYJbm5qKyrOrbTUZOCVJkiTNPdMEzxbgAz19/NXQ/kP7UgRfXrqEx29cx6tWdrGlqbGoPINnNdildobsUitJkiTVgTJh8VctzVze2cF3FrdN2d+UEmcP7uMF/XtZOz5eojy72h4ru9RKkiRJmt+6B7I1N4vcdWSUy7fv4CPbern/gQOH9o9F8Mnly3jWujWUiJu2eFaIgVOSJEnS/HDRLWWD5z0PjvC+3h1c1bOdvxgePrT/aXsHaTzi7AIGzxkxcEqSJEmaX6YJnqcPH+Tqnj7+o6ePhw7t59zBfUec84llS9ne6BjPSnAM5ww5hlOSJEmqc5eeBkN9x3Tqr1qaefKGdbRMJJ40uI/nDexltWM8p+UYTkmSJEkL12SL5zF4T0fWijnSEFzTvoy/2bieN3V10meL5wkxcEqSJElaGI5hDc/zBvdx9+GDh56PNAQfbV/Gozau481dHexoLIpQBs9p2aV2huxSK0mSJM1RZYJiAr7X1soVne38YtGiKccWTUxw7uA+njuwl1XjEyXKXHhdbafrUmvgnCEDpyRJkjTHTRM8v9vWynvKBM8vbOkpvYYnLKjg6RhOSZIkSSqnTFfbAM44MMw127ZzeW8fdzt4uKvtpuGD5cMm2NU211TrG5AkSZKkujAZOouC4mTwfPCBYb6bd7V9Uf+RAfXHi1o4aXSMlRMFXW0ny1pALZ6F7FI7Q3aplSRJkuapabraRtG+gwGP2rievQ0NnDe4j+cM7GXlAhnjaZdaSZIkSTpe03S1LfaZpUvpa2piuKGBD7cv55Eb1/Pmrg62L/DlVAyckiRJkjSdY1hO5eTRMe5ycOTQ84MNDXykfTl/c9J6Xr+ik54FGjztUjtDdqmVJEmSFphputr+z+I2/qNjOb8qmtW2KSUev2+I5/UPcNJYicmG5nBXW5dFqSIDpyRJkrRAHWU5lf/oaOdnrVODZ2NKvL1vJw/bf6BMmXMveE4XOJ2lVpIkSZJOxDHMavuD1lb+o3M5N7W2ArB4IrHpwPA0Zc6vWW0X/BjOiHhqRHw3IgYiYl9EbI6ICyNiwdeNJEmSpGMwzeRCDxwe5uqePq7q2c79DgzztL2DLCvqZXp7UyO/aW4uKnN+jPFc0F1qI+Jy4AJgGPgGMAqcCSwDrgXOTSlNs5qrXWolSZIkFZkmKI4DRdMHcfGqFXxx6RIePrSfF/YPcNeR0SMvXLIaLrqlordZKY7hLCEingh8CugFzkgp3ZLvXwP8D3AX4B9SSpdNV46BU5IkSVJJx9BCeVtTE4/buI6JOLzYyhn7D/DC/gHuUTDr7SF1GDxdh7O0V+bbV0yGTYCU0nbg/PzpxXatlSRJknRCDnW1LbVyZyaAhxdNIPSdxW08bf1aXrB2FTcVzXbLUF/e3baj8vdbBQsyTEXERuA+wAjwyeLjKaVvA1uBtcD9Z/fuJEmSJM0r3f1lg+cdxsZ4e99OPr2lh0fuGyIKeqD+oK2NZ61fw3PXruZHrYuY2jd1bvRUXZCBE7h3vv1lSqnMfMTcUHSuJEmSJJ24yeC5ZPURh+40OsqlO3Zx3dYeHrNviIaC4HlDWyvPW7eGN3d1zubdVsRCDZyn5Nvbpjnnj0XnSpIkSdLMXXRL2eB5x9ExLtmxi89v6eHswX00FQTPM8qt3VnHFuo6nEvz7dA05+zLt8uKD0TEC4AXANzhDneo7J1JkiRJWhgKJ/8pmmDoDmNjvHbnbl7YP8AH2pfzh+ZmHjA8zfqddWqhBs7JztMn1PE5pXQlcCVks9RW6qYkSZIkLVCT63gWBc8NY+O8etcexplu6qH6tVC71A7m26XTnDN5bHCacyRJkiSpcg7NbDtV8dqdc8VCDZy35tuTpznnpKJzJUmSJGl2lAmec81C7VL743x7t4hoKzNT7elF50qSJEnS7JrjoXNBtnCmlG4HbgJagHOLj0fEQ4CNQC/wg9m9O0mSJEmaHxZk4Mxdkm/fHBGnTu6MiNXAFfnTN6WUJmb9ziRJkiRpHlioXWpJKX0qIt4DnA/8PCK+DowCZwLLgeuAd9fwFiVJkiRpTluwgRMgpXRBRHwPuBB4CNnkT78GrgLeY+umJEmSJJ24BR04AVJK1wDX1Po+JEmSJGm+WchjOCVJkiRJVWTglCRJkiRVhYFTkiRJklQVBk5JkiRJUlUYOCVJkiRJVWHglCRJkiRVhYFTkiRJklQVBk5JkiRJUlUYOCVJkiRJVWHglCRJkiRVhYFTkiRJklQVBk5JkiRJUlUYOCVJkiRJVWHglCRJkiRVhYFTkiRJklQVBk5JkiRJUlUYOCVJkiRJVWHglCRJkiRVhYFTkiRJklQVBk5JkiRJUlUYOCVJkiRJVWHglCRJkiRVhYFTkiRJklQVBk5JkiRJUlUYOCVJkiRJVWHglCRJkiRVhYFTkiRJklQVkVKq9T3MaRGxA7it1vdRwkpgZ61vYoGy7mvHuq8t6792rPvase5rx7qvHeu+duq17k9OKa0qdcDAOU9FxOaU0qZa38dCZN3XjnVfW9Z/7Vj3tWPd1451XzvWfe3Mxbq3S60kSZIkqSoMnJIkSZKkqjBwzl9X1voGFjDrvnas+9qy/mvHuq8d6752rPvase5rZ87VvWM4JUmSJElVYQunJEmSJKkqDJySJEmSpKowcM4BEfHUiPhuRAxExL6I2BwRF0bEMf//RURzRJwZEW+NiB9GRE9EjETE1oj4VEQ8tIpvYc6qRN3n5fx9RHwiIm6OiF0RMRoROyLi6xHx9IiIar2HuapSdV+m7DdGRMof/1yJ+51vKvjZv7qgrks9fl2t9zBXVfqzHxFtEfHyiLghIvojYn9E/F9EfDIiHlTp+5/LKvT79qFH+cwXPu5Qzfczl1Tycx8RGyPiXRHxm4g4EBHDEXFLRLw3Iu5Yjfufyypc93eIiCsi4g8RcTD/rvOliHhENe59roqIO0fESyPiIxHx64iYyH8mPGmG5Vbtu9OM7ssxnPUtIi4HLgCGgW8Ao8CZwDLgWuDclNL4MZTzV8DX8qe9wI3AEHBX4M/z/a9LKb26om9gDqtU3edlbQFWA78AtpLV/cnA/YAAPguck1KaqPDbmJMqWfclyj4d+AHZH9wCuCil9JZK3Pd8UeHP/tXAs4DvA78rcUpPSumVFbjteaHSn/2IOAX4KnAq0Af8EDgI/AlwL+C1KaXXV/AtzFkV/H37Z8DF05xyX+AuwO+B05JfxCr9M+fewDeBDmAL2fcdgE3ABmAfcFZK6fpKvoe5qsJ1fz/gy0AncCvwY2A9cDrZ79xXpJT+vcJvYU6KiHcALy1x6NyU0qdOsMyqfXeasZSSjzp9AE8EEtBD9ktpcv8a4Ff5sZceY1kPBz4FPLjEsScDY3l5D6v1+66HRyXrPr/uL4ElJfbfjewPAAl4Tq3fdz08Kl33RWUvAn5JFvqvzcv651q/53p6VOGzf3V+zbNr/d7q/VGFul9CFvIT8Fqguej4CuBOtX7f9fCo5s+dEq/1y7y8/1fr910Pjyp87q/Pr7my8DMPNAMfyI/9tNbvux4eFf6e2Qrcnl9zGdBYcOxhZEE/AQ+o9fuuhwfwfODf78KicwAAEdFJREFUgfOAPwW+ldfPk2r9f1mV91vrCvcxzX8ObM4/IM8scewhBR+shgq81vvz8j5Q6/ddD49Zrvt/zcu7ptbvux4e1ax74M359Y/lcBAycFax/jFw1rLuL8mv+VCt31u9P2brZz7wgLysMWBDrd93PTwqWfd56En5Y22J4+sLji+u9Xuv9aPCdf+U/PzfU/THrfz4a/PjX6z1+67HBzMPnLP2vfVEHo7hrFMRsRG4DzACfLL4eErp22StNGuB+1fgJX+cbzdWoKw5rQZ1P5ZvhytQ1pxWzbrPu/r8E1mw//zM73b+qcFnX7lK131EtAB/lz99U+XudP6Z5c/9c/PtV1JKW2dY1pxXhbof5/Dv1FJzI6R8OwQcON77nU+qUPen59tvpZRGSxz/er59REQsP/47Vjlz4Xe3gbN+3Tvf/jKlVO6H4g1F587Eafm2pwJlzXWzVvf5+KoX5U8NQVWq+4hoBT4E7Kb0mAllqvnZf1hEvC0iroyI10XEWbWexKDOVLru70PWZfb2lNLNEfHAyCbL+o+I+LeIeMBMb3gemZWf+RGxmGwIC2RdO1Xhus+Dzjfyp/8WEc2Tx/J/T45X/kDKm34WsEp/7pfm251ljk/ub+bw3CGqjNnODMetqRYvqmNySr69bZpz/lh07gmJiLXAs/Onn55JWfNE1eo+Ip5D1rWhmaw1+YFkf/i5JKV07XHe53xUrbp/A3Bn4G9TSuV+Gaq6P3eeWWLfryLib1NKPz/OsuajStf93fPtLQUTNxV6dUR8GnjGNF9QForZ+n17LtnkHX3AF2ZQznxSjbq/APgKWQv/30TE5nz/6WST2VwGXHSc9zkfVbru+/JtuVmAC/efQjbWVpUxa5nhRPnX5fo1+ZeioWnO2Zdvl53oi0REE/ARoB34hl0NgerW/YPIvvg9FTgj3/evZGMbVIW6j4gHAv8AXJdS+vgM7m0hqMZn/yfAS8gmyFpKNobqMcBPyWbJ/npEbDj+W513Kl33Xfn2DLKw/xaymWo7gceTda96InD5cd/p/DMrv2853J32w2W6HC5EFa/7lNIfyP6Y+2WyP+w+IX9sIJs85TvWP1D5uv9mvn103sWz2IsK/m2X2sqarZ9hJ8zAWb8mxx5Uu8vHe8mmTL4deHqVX2uuqFrdp5Sen1IKYDHZF/B3AN3ADyNifaVfbw6qaN1HRBvwQWAv2V+9Nb2Kf/ZTSu9IKb0rpfSrlNJQSqknpfRFsqUhfki2XJDLolS+7id/vzeRdR+8KKX0+5RSf0rpc2RfwBPwLNclrP7v24g4lcN/ZLyqWq8zB1W87vM/Mv6C7A8sjwdWAqvIPvOdwKcjwiXgKlz3KaVvAt8B2oCvRsTDI2JZRNwpIt4HPJrD42tdAq6yZisznDADZ/0azLdLpzln8tjgNOeUFRGXAc8jW5bjzJRS74mUMw9Vve5TSgfyL+AXkX3Zvifw7hMpa56pdN2/EbgT8LKUkuOTj67qn/1JKaURsllUAR41k7LmiUrXfeE57ys+mFLaTLY+YQPw0GMobz6bjc/9ZOvmD1JKN59gGfNRRes+IjqA68hacR6ZUvpcSmlXSmlnSumzwCPJJgv614g4bbqyFoBqfO7PBb5Hts7sN8j+2PsbsiVA3kW2JBBk8ymocmbtd/eJcgxn/bo13548zTknFZ17zCLirWTd3HaQhc1bjreMeezWfFuVui/hg2Td3R4bEc0LvKvPrfm2UnV/NtlfUp8VEcVj2P4s354fEY8BfpdSev4x3ud8dWu+na3P/q/zrV1qK1/3hef8X5lz/g/YRDZz4UJ2a76t1u/bRg6PYXayoKluzbeVqvtHk7VmfjPvWjtFSul3EfG/ZH9keSiwkL/73JpvK/a5Tyn1RcQZwF+Rrb25kmxs52eBm4D+/FTH7VfWrfl2tn53HzcDZ/2aXKbkbhHRVmZSh9OLzj0mEfHvwMuAXcAjUkq/OvHbnJeqVvdl9JN1M2kiG3e1vQJlzlXVqPsGsomayrlj/ug4xvLms9n+7K/It/umPWthqHTd31Tw7xVkf1wstjLfLvT6r/bn/iyyP6oMAY4jn6rSdX+HfDswzTmToadrmnMWgqp87vPZf7+WPw7Jg+hSsslrfnP8t6tpzPbv7uNml9o6lVK6newLQwtZF4UpIuIhZIPhe4EfHGu5EfEmstnZ9pCFzZ9W5IbnkWrV/TTOIAub/ZSfTnxBqHTdp5T+JKUUpR5ky6QAXJTvu1fl3sncVIPP/nn59oZpz1oAqvDZ3wr8b/70zBLldQJ/kT/dXHx8IZmFz/3z8u3HU0oLPdxPUYW635Zv71O4JEpBec1kSwZB+Zb/BaEGP+8vzreXuyRNZdXg//L4pZR81OkDeBLZAOAe4NSC/avJ+sEn4KVF11xC1k3tkhLlvS6/Zg9wn1q/v3p+VLLugQcDTwMWlXidBwG/z8t7S63fdz08Kv25n+Z1rs7L+udav+d6elT4s38vshlpG4v2N5H1shjPyzur1u+7Hh5V+Jn/2Pya7cC9Cva3Av+VH9sMRK3fe60f1fq5Q9aKfDC//oG1fp/1+Kjwz5zVZC3JiWxehEUFxxYB78mP7Qbaa/3ea/2ows+cuwOLi/a1kY3fTGSzlrfU+n3X4wP4Vl5HT5rmnOnq/rj/L2f1/dW6gn0c5T8Irsg/JAeAzwOfIesqkoBrS3yRuzo/dnXR/sfl+xNZa8LVZR4X1/o918ujgnX/bA4H/W8AHwU+V/ADIJGtydZW6/dcL49K1f1RXmPyGgNnleqfwzOh7iL7q+onydbH25rvHwdeXuv3W0+PSn/2gUvz4wfJZpC8tqD+twCn1fo918ujGj93gH/Mz7m51u+vnh+VrHuypcfG8uNb89+3nydr/UzAMPCEWr/nenlUuO6vJuui/23gY3l5u/Pzfwasq/X7rZcHWQ+THxY89ub19NvC/cda9yfyfzmbD8dw1rmU0gUR8T3gQrJxaI1kf924CnhPSulYp5YuHKuwKX+U8m3gTSd4u/NKBev+22Styw8mmzH1gWRTWPcCnwY+klK6rsK3P6dVsO51AipY/z8lW2T9vmSTGdybw0Hng2Rdq26s8O3PaZX+7KeULoqI64G/J6v/xWRjqN4GvCmlVGps54JUpZ87z8m3LoUyjUrWfUrpQxHxc7L1lx8M/HV+aCvZpE1vS85dcUiFP/fXkU3adE/g/sB+4GayHhXvTdns5MosB+5XYv8Jz55cz9+dIk/EkiRJkiRVlJMGSZIkSZKqwsApSZIkSaoKA6ckSZIkqSoMnJIkSZKkqjBwSpIkSZKqwsApSZIkSaoKA6ckSZIkqSoMnJIkzbKIeHJEpIh40XFetzgieiLihoiIYzi/KSJ2RcQfTvxu566IaIiICyNic0Tsi4iBiPhuRDyl1vcmSQuFgVOSpFkUEW3ApcDvgQ8UHevOg2h3qWtTSvuBNwCbgGcew8s9BOgCrp3JPc9FEdFI9r7fDZwGfBX4HnA6cE1EvLOGtydJC4aBU5Kk2fWPwEnAG1NKoydw/ZVAL/DGiGg5yrnn5NvPnMDrzHX/ADwO+BVwp5TSOSmlRwN3B7YDfx8Rj6/lDUrSQmDglCRplkREE3AhsA/4+ImUkVIaAT4CrAfOnea1AngCWbj6wYm81lyVt26+PH96fkpp++SxlNItwCvyp/8y2/cmSQuNgVOSVHN5N9KU//vZ+Zi7oYjojYgPRMSq/FhrRPxbRPw2IoYj4o8R8YaIaC5R5qqIeGlEfCUi/i8/fyAifpiP62sscy/3jYhPRsTWiBjNr/ldRFwTEQ8vOrc1Ii6OiJvyMYIH8zGWP4iI10dEa1HxZ5MFxU+llIaK6wB4Tf70NZN1UqaL7Yfy7QXTVOv989e6LqU0Ufg6C6CuHwCsBraklL5T4qU/CYwCp0fEhmnqUJI0Q021vgFJkiZFxJvJukJ+G/gK8EDgucCmiHgQ8N/AXfLjvyMbo/j/gFXAC4qKOwt4B7AlP/d/gTVkYeR+wCMi4uyUUip4/UcAXwSagZ8A38//vRF4ErAX+GZ+bkN+7sOBgfyeBvLXuDNZ69m7ybq/TnpCvv16ibf/IeBewD2Bn+avP6nw36SUfhER24EHRMSqlNKOEuWdnW9Ldqed53V973x7Q6n3nlLaHxG/JKvvewFbS50nSZo5A6ckqZ48C7hXSulmgIjoJOsOeo982w+cklIayI/fiyxUPD8i3pBSuq2grBuB+6eU/rfwBSJiHfAl4PHAeUzt2vpKstDz1JTSx4quWwH8ScGuvyQLQDcBZxS2WObdWR9IFpoKPSTfHtHFNaX07Lwl855krZLdxecU+QFZgH0Y8IkSx88mq6//KXP9fK7rU/Jt4T0W+yNZ2DxlmnMkSTNkl1pJUj159WQAAkgp7QHemz+9K/CCyQCUH/8JWaAJDoe5yWM3FwegfH8Ph8f3Pano8Jp8++US1+1KKd1Y4tzvFnePTZnv57PKAlm3U2ADcDClVIllSn6Vb+9dfCAi7gGcCnxhmomJ5m1dA0vz7ZRzi+zLt8umOUeSNEO2cEqS6slXSuz7Xb69rTAgFbgl364vPpBP0vNwsq6da4FWssA0GTLuVHTJj8jC1jUR8Qbghyml8TL3ehMwDjwvIn4LfLpwcpoSVufb3dOcczwmy1lT4tjk7LTTLYcyn+t6co3SNM05kqRZYOCUJNWTLSX27ZvmWOHxKRP0RMSdgOvIxiGWs7zo+SvJuln+Tf4YiogbycYS/mdhy2RK6fcR8Y/AW4DLgcsj4g/A9cBngWuLAlR7vi3uZnuiJsvpKHHsHGA/pUPlpPlc14P5dinlTR4bnOYcSdIM2aVWklQ3CmdTLWG6Y6V8iiwAfY5sDOAKoCmlFGQTzcDhlrDJ1+8F7gOcCbyJrGXtfkA38JuIeG7R+e8CTgbOBz4KNAJPJ5sFdXNEFIas/nxbHLxO1GQ5ewp3RsSfkq01+d9F3UynmOd1fWu+PXmaez6p6FxJUhUYOCVJ805E/BlZ6OoDzsnH+O0uaAU7tdy1KaWJlNI3U0qvTCmdQRaeLibrFXR5UbAhpdSbUnpvSunpKaU/IWu1+3m+vbjg1L58u6ICb7GwnL6i/cfSnbZi6rSub8q3p5e558XAn+dPf3wcb1eSdJwMnJKk+agr324rMy7wacdaUEppKKX0ZrJupq0cbrErd/5Pgcvyp/cs2L8TuB1oyVshSxnJt8cy5OWu+famov3nkK0x+fljKKMS6q6uyWbZ7QM2RsQZJS49l2yG3BtSSi6JIklVZOCUJM1Ht5B1C/3z4sAREc8BnlLqooj454g4qcT+TcC6vMwt+b6HR8Sj8slyCs9tBB6VPy1elmNyiZIHlLnvyfAz3VjISfcnmxTnWwWvvZ6sW+q3Ukr9Za6rtLqr6zz4Xpo/fU9ErC645jSyLrwAbzjWNylJOjFOGiRJmndSSjsi4grgxcD/RMS3gV6yrp9/DlxCNmlNsVcBl0bEzcDNwEGysX4PJPsj7ZvypT4gW6/y7cBARNwE9ACLyQLfuvz13lxU/nXAM4G/Aj5S4vX/m2yyn3Mi4jvA78lmZ/1cSulzkydFxN3JZqe9PqW0o+D6s8nGSn5m2gqqoDqu67cDZwCPBW6JiG+QtWr+FVnr6btSSp+deQ1IkqZj4JQkzVcvBX5GNsnMfcm6md4IXAT8mtIh6ELgEcAm4GFAG1m4+TxwRUrpqwXnfp5shtgzyMYpPpBsFtc/kq1n+Z6iMAjZpDpbgCdGxIUl1pTsjYjHAK8mW1/zL8kC5Jb82knPyrdXFJV/Dlmr53Ula6R66q6uU0rjEfEE4ALgOcBZZOH9xrz8a2b8riVJRxUpuUSVJEmzJSIuJmv1e15K6aoTuL6FrPvoBHBKSmkk398FbAd+lFJ6UAVvWZKkE2bglCRpFkVEG1mr3yhwl5TS6HFe/2LgXcCzU0ofKth/J+CpwPdSSl+v4C1LknTCDJySJM2yiDgP+Dhwfkrpvcdx3WKycZ1bgPsmf4lLkuqcgVOSJEmSVBUuiyJJkiRJqgoDpyRJkiSpKgyckiRJkqSqMHBKkiRJkqrCwClJkiRJqgoDpyRJkiSpKv4/28i7oCcIIdkAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1080x1080 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,15));\n",
"plt.plot(num_heun[:,2]/m_0,num_heun[:,1],'o-',label='Implicit')\n",
"plt.plot(num_rk2[:,2]/m_0,num_rk2[:,1],'s-',label='Explicit')\n",
"plt.plot(m,u,'--',label='Analytical')\n",
"plt.legend();\n",
"plt.xlabel('mass(t)/mass0')\n",
"plt.ylabel('Velocity m/s')"
]
},
{
"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": 87,
"metadata": {},
"outputs": [],
"source": [
"def rocket(state,dmdt=0.05, u=250,c=0.18e-3):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, with drag, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" c : drag constant for a rocket set to 0.18e-3 kg/m\n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" dstate = np.array([state[1], (u/state[2])*dmdt-9.81-(c/state[2])*state[1]**2, -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [],
"source": [
"num_heun2 = np.zeros([N,3])\n",
"num_rk22 = np.zeros([N,3])\n",
"num_heun2[0,0] = x_0\n",
"num_heun2[0,1] = v_0\n",
"num_heun2[0,2] = m_0\n",
"num_rk22[0,0] = x_0\n",
"num_rk22[0,1] = v_0\n",
"num_rk22[0,2] = m_0\n",
"\n",
"\n",
"m=mflimit/m_0\n",
"u=-250*np.log(m)\n",
"\n",
"for i in range(N-1):\n",
" num_heun2[i+1] = heun_step(num_heun2[i], rocket, d_t)\n",
" num_rk22[i+1] = rk2_step(num_rk22[i], rocket, d_t)"
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Velocity m/s')"
]
},
"execution_count": 110,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x1080 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,15));\n",
"plt.plot(num_heun2[:,2]/m_0,num_heun2[:,1],'o-',label='Implicit')\n",
"plt.plot(num_rk22[:,2]/m_0,num_rk22[:,1],'s-',label='Explicit')\n",
"plt.plot(m,u,'--',label='Analytical')\n",
"plt.legend();\n",
"plt.xlabel('mass(t)/mass0')\n",
"plt.ylabel('Velocity m/s')"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The height of the simple rocket: 597.4795789904731 The height of the rocket: 425.35224719755064\n",
"<class 'function'>\n",
"<class 'function'>\n"
]
}
],
"source": [
"simple_rocket_height = num_heun[-1,0] \n",
"rocket_highet = num_heun2[-1,0] \n",
"print('The height of the simple rocket:',simple_rocket_height, 'The height of the rocket:',rocket_highet)\n",
"print(type(rocket))\n",
"print(type(rk2_step))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3. Solve for the mass change rate that results in detonation at a height of 300 meters. Create a function `f_dm` that returns the final height of the firework when it reaches $m_{f}=0.05~kg$. The inputs should be \n",
"\n",
"$f_{m}= f_{m}(\\frac{dm}{dt},~parameters)$\n",
"\n",
"where $\\frac{dm}{dt}$ is the variable we are using to find a root and $parameters$ are the known values, `m0=0.25, c=0.18e-3, u=250`. When $f_{m}(\\frac{dm}{dt}) = 0$, we have found the correct root. \n",
"\n",
"Plot the height as a function of time and use a star to denote detonation at the correct height with a `'*'`-marker\n",
"\n",
"Approach the solution in two steps, use the incremental search [`incsearch`](../notebooks/04_Getting_to_the_root.ipynb) with 5-10 sub-intervals _we want to limit the number of times we call the function_. Then, use the modified secant method to find the true root of the function.\n",
"\n",
"a. Use the incremental search to find the two closest mass change rates within the interval $\\frac{dm}{dt}=0.05-0.4~kg/s.$\n",
"\n",
"b. Use the modified secant method to find the root of the function $f_{m}$.\n",
"\n",
"c. Plot your solution for the height as a function of time and indicate the detonation with a `*`-marker."
]
},
{
"cell_type": "code",
"execution_count": 138,
"metadata": {},
"outputs": [],
"source": [
"def heun_step3(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": 139,
"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",
" m_f= 0.05\n",
" height_desired=300\n",
" y_0 = 0 \n",
" v_0 = 0 \n",
" T_2=(m_0-m_f)/dmdt\n",
" t=np.linspace(0,T_2,1000)\n",
" dt=t[1]-t[0]\n",
" N =int(T_2/dt)\n",
" \n",
" num_sol=np.zeros([N,3])\n",
" \n",
" num_sol[0,0] = y0\n",
" num_sol[0,1] = v0\n",
" num_sol[0,2] = m0\n",
" \n",
" for i in range(N-1):\n",
" num_sol[i+1] = rk2_step(num_sol[i], lambda state: rocket(state, dmdt=dmdt, u=250, c=0.18e-3), dt)\n",
" height_predicted=num_sol[:,0]\n",
" error = height_desired-height_predicted[-1] \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 140,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n"
]
}
],
"source": [
"def incsearch(func,xmin,xmax,ns=50):\n",
" '''incsearch: incremental search root locator\n",
" xb = incsearch(func,xmin,xmax,ns):\n",
" finds brackets of x that contain sign changes\n",
" of a function on an interval\n",
" arguments:\n",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\n",
" returns:\n",
" ---------\n",
" xb(k,1) is the lower bound of the kth sign change\n",
" xb(k,2) is the upper bound of the kth sign change\n",
" If no brackets found, xb = [].'''\n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = np.zeros(ns)\n",
" for i in range(ns):\n",
" f[i] = func(x[i])\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] )\n",
"\n",
" \n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb\n",
"\n",
"The_change_of_mass = incsearch(f_m, 0.05, 0.4, 5)"
]
},
{
"cell_type": "code",
"execution_count": 141,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The function root is 0.07890352693388984\n"
]
}
],
"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]\n",
"\n",
"The_root = mod_secant(f_m, 0.001,0.1)\n",
"print('The function root is',The_root[0])"
]
},
{
"cell_type": "code",
"execution_count": 142,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x1080 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"m_f= .05\n",
"m_0= .25\n",
"y_0 = 0 \n",
"v_0 = 0 \n",
"dmdt_final=The_root[0]\n",
"height_desired=300\n",
"T2=(m0-mf)/dmdt_final\n",
"t=np.linspace(0,T2,1000)\n",
"dt=t[1]-t[0]\n",
"N =int(T2/dt)\n",
" \n",
"num_sol=np.zeros([N,3])\n",
"num_sol[0,0] = y_0\n",
"num_sol[0,1] = v_0\n",
"num_sol[0,2] = m_0\n",
" \n",
"for i in range(N-1):\n",
" num_sol[i+1] = rk2_step(num_sol[i], lambda state: rocket(state, dmdt=dmdt_final, u=250, c=0.18e-3), dt)\n",
" height_predicted=num_sol[:,0]\n",
"\n",
"plt.figure(figsize=(15,15));\n",
"plt.plot(t[:-1], height_predicted)\n",
"plt.plot(t[-1], height_predicted[-1], '*', label = 'detonation')\n",
"plt.xlabel('Time (s)')\n",
"plt.ylabel('Height (m)')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"1. Math 24 _Rocket Motion_. <https://www.math24.net/rocket-motion/\\>\n",
"\n",
"2. Kasdin and Paley. _Engineering Dynamics_. [ch 6-Linear Momentum of a Multiparticle System pp234-235](https://www.jstor.org/stable/j.ctvcm4ggj.9) Princeton University Press \n",
"\n",
"3. <https://en.wikipedia.org/wiki/Specific_impulse>\n",
"\n",
"4. <https://www.apogeerockets.com/Rocket_Motors/Estes_Motors/13mm_Motors/Estes_13mm_1_4A3-3T>"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}