{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cruise control\n", "\n", "Richard M. Murray and Karl J. Åström \n", "17 Jun 2019\n", "\n", "The cruise control system of a car is a common feedback system encountered in everyday life. The system attempts to maintain a constant velocity in the presence of disturbances primarily caused by changes in the slope of a road. The controller compensates for these unknowns by measuring the speed of the car and adjusting the throttle appropriately.\n", "\n", "This notebook explores the dynamics and control of the cruise control system, following the material presenting in Feedback Systems by Astrom and Murray. A nonlinear model of the vehicle dynamics is used, with both state space and frequency domain control laws. The process model is presented in Section 1, and a controller based on state feedback is discussed in Section 2, where we also add integral action to the controller. In Section 3 we explore the behavior with PI control including the effect of actuator saturation and how it is avoided by windup protection. Different methods of constructing control systems are shown, all using the InputOutputSystem class (and subclasses)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from math import pi\n", "import control as ct" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Process Model\n", "\n", "### Vehicle Dynamics\n", "\n", "To develop a mathematical model we start with a force balance for the car body. Let $v$ be the speed of the car, $m$ the total mass (including passengers), $F$ the force generated by the contact of the wheels with the road, and $F_d$ the disturbance force due to gravity, friction, and aerodynamic drag." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def vehicle_update(t, x, u, params={}):\n", " \"\"\"Vehicle dynamics for cruise control system.\n", "\n", " Parameters\n", " ----------\n", " x : array\n", " System state: car velocity in m/s\n", " u : array\n", " System input: [throttle, gear, road_slope], where throttle is\n", " a float between 0 and 1, gear is an integer between 1 and 5,\n", " and road_slope is in rad.\n", "\n", " Returns\n", " -------\n", " float\n", " Vehicle acceleration\n", "\n", " \"\"\"\n", " from math import copysign, sin\n", " sign = lambda x: copysign(1, x) # define the sign() function\n", " \n", " # Set up the system parameters\n", " m = params.get('m', 1600.) # vehicle mass, kg\n", " g = params.get('g', 9.8) # gravitational constant, m/s^2\n", " Cr = params.get('Cr', 0.01) # coefficient of rolling friction\n", " Cd = params.get('Cd', 0.32) # drag coefficient\n", " rho = params.get('rho', 1.3) # density of air, kg/m^3\n", " A = params.get('A', 2.4) # car area, m^2\n", " alpha = params.get(\n", " 'alpha', [40, 25, 16, 12, 10]) # gear ratio / wheel radius\n", "\n", " # Define variables for vehicle state and inputs\n", " v = x[0] # vehicle velocity\n", " throttle = np.clip(u[0], 0, 1) # vehicle throttle\n", " gear = u[1] # vehicle gear\n", " theta = u[2] # road slope\n", "\n", " # Force generated by the engine\n", "\n", " omega = alpha[int(gear)-1] * v # engine angular speed\n", " F = alpha[int(gear)-1] * motor_torque(omega, params) * throttle\n", "\n", " # Disturbance forces\n", " #\n", " # The disturbance force Fd has three major components: Fg, the forces due\n", " # to gravity; Fr, the forces due to rolling friction; and Fa, the\n", " # aerodynamic drag.\n", "\n", " # Letting the slope of the road be \\theta (theta), gravity gives the\n", " # force Fg = m g sin \\theta.\n", " \n", " Fg = m * g * sin(theta)\n", "\n", " # A simple model of rolling friction is Fr = m g Cr sgn(v), where Cr is\n", " # the coefficient of rolling friction and sgn(v) is the sign of v (±1) or\n", " # zero if v = 0.\n", " \n", " Fr = m * g * Cr * sign(v)\n", "\n", " # The aerodynamic drag is proportional to the square of the speed: Fa =\n", " # 1/2 \\rho Cd A |v| v, where \\rho is the density of air, Cd is the\n", " # shape-dependent aerodynamic drag coefficient, and A is the frontal area\n", " # of the car.\n", "\n", " Fa = 1/2 * rho * Cd * A * abs(v) * v\n", " \n", " # Final acceleration on the car\n", " Fd = Fg + Fr + Fa\n", " dv = (F - Fd) / m\n", " \n", " return dv" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Engine model\n", "\n", "The force F is generated by the engine, whose torque is proportional to the rate of fuel injection, which is itself proportional to a control signal 0 <= u <= 1 that controls the throttle position. The torque also depends on engine speed omega." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def motor_torque(omega, params={}):\n", " # Set up the system parameters\n", " Tm = params.get('Tm', 190.) # engine torque constant\n", " omega_m = params.get('omega_m', 420.) # peak engine angular speed\n", " beta = params.get('beta', 0.4) # peak engine rolloff\n", "\n", " return np.clip(Tm * (1 - beta * (omega/omega_m - 1)**2), 0, None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Torque curves for a typical car engine. The graph on the left shows the torque generated by the engine as a function of the angular velocity of the engine, while the curve on the right shows torque as a function of car speed for different gears." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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5Mps2beLrr7+ucIk3ODiYF198kTfeeIPCwkLuuece3NzcOHv2LGlpacZA/vfffz/33Xcfc+fO5fbbbyc2NpalS5caZ97MRaFQ8MADD/Dhhx/i6urK1KlTy7Xnk08+YdCgQQwePJjHHnuM4OBgcnNziYqKYsOGDcYd3hMnTqRz58706tULb29vYmNj+fjjjwkKCqJNmzYW1Qvg1VdfNfpWLl68GA8PD3755Rf++ecfli5dWq6e5uLi4kJQUBB//fUXI0eOxMPDAy8vrzIhm5566in69u0LUGGUCTs7Oz744APy8vLo3bu3MWrBuHHjGDRoUIX3nz9/PmvXrmXy5Mk8//zz9OnTh8LCQnbv3s2tt97K8OHDmTBhAh9++CHTp0/nkUceIT09nffff7+ckWku5oyr9u3b06pVK55//nmEEHh4eLBhwwa2bdtWrXteT02eCVPI5XKWLFnCnDlzuOOOO3jwwQfJyspiyZIlNG3aFLm8djz1goODef3113nppZe4dOkSt9xyC+7u7iQnJxMWFoaTk5PxmZSQkECKWiAhURk3Ri0QQoj09HTx6KOPiqZNmwqlUimCgoLECy+8IIqKisqch4ld8aXs379f9OvXT6jVauHn5yeeffZZsWzZsnJRC4qLi8Vzzz0nAgMDhYODgxg6dKg4ceKEyQgCqamp4sknnxQtWrQQKpVKeHh4iJ49e4qXXnpJ5OXlVdnWn376SfTu3VvY29sLZ2dnERISIpYvX278XK/Xi6VLl4qWLVsKe3t70atXLxEaGlph1ILffvutwntduHBBAJXupI+JiREPPvigCAgIECqVSnh7e4sBAwaIN99803jOBx98IAYMGCC8vLyEnZ2daN68uZg9e7a4fPlyle2tqH9Onz4tJk6cKNzc3ISdnZ3o1q1bGTmY28Yb2b59uwgJCRFqtVoAJiNABAcHiw4dOpj8fulYPHXqlBg2bJhwcHAQHh4e4rHHHivXv6bGR2ZmpnjqqadE8+bNhUqlEj4+PmLChAni3LlzxnN++OEH0a5dO6FWq0XLli3FO++8I77//vty49KcqAWlVDWuzp49K0aPHi1cXFyEu7u7uPPOO8WVK1fK7fovjVqQmppq1n2FMO+ZKI1a8N5775X7/o11EEKIZcuWidatWws7OzvRtm1b8cMPP4jJkyeLkJCQSr9bGrXgyJEjZc4rHUs7d+4sc3z9+vVi+PDhwtXVVajVahEUFCTuuOMOsX37drPbLyFxMyATogaRriUkJGqNFStWMGvWLGJiYuo0XaqEdXLq1Cm6devGF198wdy5c8t9PnPmTH7//fdybiUSDUtWVhZt27ZlypQpLFu2rKGrIyFx0yG5FkhISEg0INHR0cTGxvLiiy/StGlTk9nTJKyDpKQk3nrrLYYPH46npyexsbF89NFH5Obm8tRTTzV09SQkbkokQ1ZCQkKiAXnjjTdYuXIlHTp04LfffrM40oJE/aFWq7l8+TJz584lIyPDuAHw66+/Nob1kpCQqF8k1wIJCQkJCQkJCQmbREqIICEhISEhISEhYZNIhqyEhISEhISEhIRNIhmyEhISEhISEhISNolkyEpISEhISEhISNgkkiErISEhISEhISFhk0iGrISEhISEhISEhE0iGbISEhISEhISEhI2iWTISkhISEhISEhI2CSSISshISEhISEhIWGTSIashISEhISEhISETSIZshISEhISEhISEjaJZMhKSEhISEhISEjYJJIhKyEhISEhISEhYZNIhqyEhISEhISEhIRNIhmyEhISEhISEhISNolkyEpISEhISEhISNgkkiErISEhISEhISFhk0iGrISEhISEhISEhE0iGbISEhISEhISEhI2iWTISkhISEhISEhI2CSSISshISEhISEhIWGTSIashISEhISEhISETSIZshISEhISEhISEjaJZMhKSEhISEhISEjYJJIhKyEhIdGIeeedd+jduzcuLi74+PgwZcoUzp8/X+YcIQSvvfYa/v7+ODg4MGzYMM6cOVPmnOLiYubNm4eXlxdOTk5MmjSJ+Pj4+myKhISERDkkQ1ZCQkKiEbN7924ef/xxDh06xLZt29BqtYwZM4b8/HzjOUuXLuXDDz/k888/58iRI/j5+TF69Ghyc3ON58yfP59169axZs0a9u3bR15eHrfeeis6na4hmiUhISEBgEwIIRq6EhISEhIS9UNqaio+Pj7s3r2bIUOGIITA39+f+fPns2jRIsAw++rr68v//vc/5syZQ3Z2Nt7e3qxcuZK77roLgKtXrxIYGMimTZsYO3ZsQzZJQkLiJkaakZWQkJC4icjOzgbAw8MDgJiYGJKSkhgzZozxHLVazdChQzlw4AAAx44dQ6PRlDnH39+fzp07G8+RkJCQaAiUDV0Ba0Sv13P16lVcXFyQyWQNXR0JCQkrRQhBbm4u/v7+yOXWPy8ghGDBggUMGjSIzp07A5CUlASAr69vmXN9fX2JjY01nmNnZ4e7u3u5c0q/fyPFxcUUFxcb3+v1ejIyMvD09JT0qoSERKVYolslQ9YEpUtmEhISEuYQFxdHs2bNGroaVfLEE09w6tQp9u3bV+6zG41LIUSVBmdl57zzzjssWbKk+pWVkJC46TFHt0qGrAlcXFwAgwBdXV2rPF+j0bB161bGjBmDSqWq6+rZDJJcyiPJxDS2KpecnBwCAwONOsOamTdvHn///Td79uwp88Pg5+cHGGZdmzZtajyekpJinKX18/OjpKSEzMzMMrOyKSkpDBgwwOT9XnjhBRYsWGB8n52dTfPmzYmKisLb29u4SUyhUJQpa7VaZDKZsSyXy5HL5RWWNRoNCoXCWFYqlchkMmMZQKvVlimrVCqEEMayXq9Hp9MZy3q9HqVSWWFZp9MhhDCWTbWjNtqk0+nYunUro0ePxs7OrlG0qS77SQjB1q1bGTFiBA4ODo2iTXXdT6VjbNSoUajVaqtpU35+vtm6VdrsZYKcnBzc3NzIzs42y5CVkJC4ObEFXSGEYN68eaxbt45du3bRpk2bcp/7+/vz9NNP89xzzwFQUlKCj49Puc1eP//8M9OmTQMgMTGRZs2amb3ZyxZkJSEhYR1Yoi+kGdlaoNSXQ/KpLYskl/JIMjGNJJe64/HHH2fVqlX89ddfuLi4GH1a3dzccHBwQCaTMX/+fN5++23atGlDmzZtePvtt3F0dGT69OnGc2fPns3ChQvx9PTEw8ODZ555hi5dujBq1CiL6iPNnZiP9FxYhiQvy2kMMrP+3Qk2gFarZe/evWi12oauilUhyaU8kkxMI8ml7vjqq6/Izs5m2LBhNG3a1Phau3at8ZznnnuO+fPnM3fuXHr16kVCQgJbt24ts6z30UcfMWXKFKZNm8bAgQNxdHRkw4YNKBQKi+oj9bH5SM+FZUjyspzGIDPJtcAE0hKYhISEOUi6wnwkWUlISJiLJfpCmpGtBUrDyuj1+oauilUhyaU8lclECIFeb3jdbEhj5eZB6mPzkZ4Ly5DkZTmNQWaSj2wtoNPpOHLkCCNGjLCJWJL1hSQX0OsFsRkFXEzOJT6zkNj0PE5cjAN7V3KLtOQUacgp1FKiK6tE7JRyXNRKXOyVuDqo8HW1J6CJA83cDa+2vi4EeTqhkNumT9ONSGPl5kFKaWs+0nNhGZK8LKcxyExyLTCBtAQmUV0Ssws5fCmDo7EZnL2aw7mkXApK6uaH214lp52vCx39XekV5EGfFh40c3ewWYd9W0TSFeYjyUpCQsJcpKgF9YxeryctLQ0vLy+b/UdTF9wMciko0bLnQhqh55I5dCmDKxkF5c5RK+W09XWhuYcjAU3saaLS09LfkyaOdrg5qHB1UGGvNMin1Agt1OjIKdSQW6Qlu1BDUnYhCVlFJGQVciU9n/PJuRRp9JyMz+ZkfDarw+IA8Hezp18rT0Z18GVIW2+c1bbxiN8MY0XCgC0vYdY30nNhGZK8LKcxyMw2fuWsHL1eT0REBEOGDLHZgVAXNFa55BRp2Hw6iS1nktgXlUax9r8fZrkMugS40aeFB12aNaFjUxeCPZ1QKgzt12q17NmzhyHt2xsDSldEQBOHCj/T6QVXMgqITMzhZFwWYZczOB2fzdXsIv48nsCfxxOwU8jp29KDcZ2bMqFLU9wcrTfRQGMdKxLlkQxZ85GeC8uQ5GU5jUFmkmuBCaQlMIkb0er07I1K48/jCWw9k1TGeA30cGB0Bz8Gt/WiV5A7LvYNYzAWlGg5HpvF7gspbI9MISYt3/iZnULOiPY+TO0RwLB2PtgpbVNhWRuSrjAfSVYSEhLmYom+kAxZE1iqcPV6PYmJiTRt2tRm/9HUBY1BLul5xaw5EsfKg7Ek5RQZj7fxcWZSN3/GdPKjra+z2X6p9SmT6NQ8tp5J5q8TCZxLyjUe93FRM71vc6b3bY6Pi32d1sFcbHWsSMaZ+ZTKKjMzkyZNmjR0dWwCW30uGgpJXpZjrTKTfGTrGb1eT3R0NL6+vlY1EBoaW5bLuaQcvt8bw18nr1JybfbV3VHF5O4B3N6jGZ0DXKu1qao+ZdLK25nHhjnz2LBWnL2aw7rweNaFXyUlt5iPt1/ki51RjOvclEeGtKRzgFud1qUqbHmsSFiG5FpgPtJzYRmSvCynMchMmpE1gTTLcvMSkZDNZ6EX2XIm2XisS4AbswYGM6FrU9RKy7IYWRslWj2bzyTx44HLHIvNNB4f2d6Hx0e0pkdz9wasne0h6QrzkWQlISFhLtKMbD2j1+uJi4sjMDDQZv/R1AW2JJczV7P5aNsFtkemACCTwfjOTXlwUAt6NG9SayGtGlomdko5k7r5M6mbPxEJ2Xy79xIbTl5lx7kUdpxLYVBrL54d245ugU3qtV4NLReJ+kOakTUf6bmwDEleltMYZGabtbYy9Ho9CQkJkoK+AVuQS2J2IQt/Pcmtn+1je2QKchlM6e7PtqeH8MW9PegZ5F6rcVmtSSadA9z45O4QdiwcxrRezVDKZeyLSmPyF/t5YtVxYtPzq75ILWFNcpGoW6Q+Nh/pubAMSV6W0xhkJrkWmEBaAmv85BVr+XpXNN/tu0SRxvAAT+zmz/xRbWjl7dzAtWsY4jIK+Hj7Rf4Mj0cIUClk3NcviPmj2uLmYL2huxoSSVeYj7XKKrtQw+/H4skt0hiPOdopuC2kGd4u6mpfVwjBmas57L6QSkpOEen5JWQWlFCk0dPK24kOTV3p0NSVjv6uuNZhpJOcIg2RV3M4m5jD1axC0vNLyMgvIbNAA0KgUsixU8pRK+X4uTkQ5OlIcw9Hgj2daOvrbAwdWN17X0rNJzY9n5ScYtLyiknNLTbKoUSnp1irQ6fHWAe1Uo6LvRIvZzXezmq8XNQ0c3egpbczTV3tkV+XzVCvF6TmFZOYXURyjuGVmltMTqGG7EINOUVa8ou1aPUCjU6PRmcwd+wUMpQKOSqFDCc7pTGet6uDCm8XNX6u9oaXmz1eznZSkpkGQIpaUEMsVbg6nY6YmBhatGiBQmHbPpS1iTXKRQjBvxFJLNlwhuScYgD6BHvw4oQOdK+H5XRrlMmNnL2aw7ubz7HnQioAXs5qXp7Qgcnd/etModuCXExhrcaZNVIqq4yMDNzdrcMXe9f5FBb9ccqoC67H3VHFm1O6MKFrU4uuGZWSx98nEthwKrFMCLyKsFPImdTdn4cGt6C9X9kxVJ3nIqdIw94LaYSeS+HIZdNJWszFyU5Bz2AP+rbwoF9LT0ICm5QxJEsRQpCYXcTJuCxOxGVxMj6LqJR80vLKy7UmqBQyXO1V2KsU6PSCzIKSMqEQ6wInOwUtvJ0I9nSilbczHZq60snftdFkUawN3fvaa6+xZMmSMsd8fX1JSkqqdr0kH9l6RghBZmYmwcHBDV0Vq8La5BKXUcDivyLYed5goAV5OvLi+A6M6ehbbwrJ2mRiio7+rvz0YB/2XEjltQ1nuJSaz/y1J1h7JI43pnSmtU/tz1jbglwkagdrmDvJLdLw1j+RrDliyIgX7OnIoDZexs+PXs7kXFIuj686zr8RTXl9cmc8nOwqvWZGfgnv/hvJr0fjjcfUSjnD2nnTxscFdyc7PJxUKOVyLibncjYxl8jEHBKyCvn9WDy/H4tncBsv5g5rTf9WnoD5z0VBiZYNJ6/y98mrHL6UgVZfVsb+bvZ09HejhZcjHk5qPJ3saOKoQiGXUaI1zIwWlui4mlXIlYwCYjMKiErJI7dIy54LqcY/tf5u9kzs7s/kbgH4uqrZH53O3gup7ItKIzG7yFTV8HZR08LLCT9Xe7xd1Hg5G+5vb6fATiFHrZIjl12rh1ZPkUZHSm4REVezuZSST2J2EdlFGoQAjU6Qnl9S7h52SjleznYEezjiTAFtmvvTxFGNq4MSRzslqmuzr8bENNdmZ0t0egqKteQUacgp1JJVWEJKTjHJOUUkXZvdzS/REZGQQ0RCTpl7utor6dLMjZ5BHvQOdiekubvNZFK8ntrSvZ06dWL79u3G9/U5ISHNyJpAmmVpXOj0gu/3XeLDbRco0uhRKWQ8NrQVc4e3xl5lO7N/DUGxVse3ey7xWWgUxVqD7J4a2YZHh7aq0ZJjY0HSFeZjLbJKyi7izm8OEJdRCMDMAcEsuqU9Dnb/6YISrZ7PQy/yxa5odHqBl7OatXP6mXQ70usFa47EsXTLObIKDO4JI9r7MLm7PyM7+FZp3By/ksl3ey+xOSKJUvvzgf5BvDi+Q5X66XxSLr8cjmXd8QRyi7XG4628nRjZwZfBbbzo7O+GexVGuCn0esG5pFzCYtI5HJPBvotpZe5xIwq5jPZ+LnQLbEL3Zk1o39SFFl5OZiWIKdLoOBabaTCaL6ZxLimHGy0TO6WcFp5O+Fxz98goKOFyWj75Jboy5/m4qLmlsx8TujSlV7AHChMzyOZSrNURl1FITFo+MWl5XEjO4+zVHC6m5BrdFEopzeo4uI03g9t4EdLc3WoTz0RFRdGmTRs2btzIhx9+yMGDBwkMDOSnn36ib9++Fl/vtddeY/369Zw4caLW6ii5FtSQ6rgWXLx4kTZt2tjUsmhdYw1yiU3PZ+GvJzl6LdRU3xYevHVblzqZVTQHa5BJdYjLKODVv88Qes4Q1aFbMzc+mNaN1j4utXJ9W5WLtRhntoA1uBZodXqmf3uYsMsZBDRx4P07uxlnP01xKj6LBb+eJColj/Z+Lqx/fGAZ4zIlp4jHfjluDGXX3s+Ft27rTM8gD4vrFpdRwFe7o1l1+ApgSLry0bSuKPOSyz0Xp+Oz+XDbeePqEhhmle/q3Zxxnf0I9nKy+P4VkV2o4a8TCfxxPJ6TcdnlPne0UzCpmz9Pj26Lr6v5CVYy8kvYfjaZLWeS2B+dZtyrUEoLLyd6BrnTO9idboFNaOXtjOqGP89CCKJS8th7MY09F1M5dCm9zHW8XdRM6NKUab0C6ehfe89niVbPheRcTsRlcSw2kyOXM4jPLCxzjpOdgsFtvBnb2ZcR7X2tap/BH3/8wZ133smwYcN48cUX0Wq1vP/+++h0Onbu3Mnbb7/N22+/Xek1/v33XwYPHgwYDNn33nsPNzc31Go1ffv25e2336Zly5bVrqNkyNaQ6hiyp06domvXrjb1I1zXNKRchBCsDovjzX/OUlCiw1mtZPGtHbmzV7MG9Wuy5bEihGD9iQRe/esMOUVa7JRynhnTltmDWtZo1gNsVy6SIWs+1mDIfrj1PJ+GRuGsVrJx3iCzDL6UnCLGf7qXtLwS7u3bnLdu6wLAheRcZi0/QkJWIc5qJQtGt+WB/kE1XqnYdT6FZ347RVpeMXYKGbO6u/Lc1P4oFArOJeXw0bYLxjjXCrmMsZ18md4niAGtPE36r1YHIQRHYzNZHXaFTacTjcahTAa9gz0Y0d6H3CINvx2NJyXX4Afr7qji6dFtmd6neYUyyMwvYePpRDaevMqRyxlc7wHh46JmcBtvhrT1YkArr2pttCso1rBq+1Ei8x3YdjaZnKL/ZpC7BTbhnt6BTOzmj1MduAAkZheyPyqdvRdT2XsxjYzrXCCUchn9W3kysZs/t3T2q9PNfeawePFiPvvsMy5cuICHhwenTp1i3759fPPNN0RERJCRkUFGRkal1wgICMDBwQEwGLUFBQW0bduW5ORk3nzzTc6dO8eZM2fw9Kz4j2JlSIZsDZF+nGyb9LxinvntpHG2ol9LD96/sxvN3B0buGaNg6TsIhb9cYrd1/zmBrTy5OO7u1tNutv6RNIV5tPQsjoQlca93x9GCPjk7u5M7h5g9nf3XEjlgR/CAPhieg/cHVXM+fkYuUVaWng5sWJWb4I8a28WND2vmOd+P8WOaysgT41sTUa+hp8PxyKEwaC8rXsAT45sU6uzrxqdnk2nE1m25xJnrv7nE9rO14VpvQOZ2LUpPtfNuhZrdfx14ipf747mUqphY1trH2dentCBYe18jOdsP5vCuvAEdl9IKbMk38nflbGd/Bjd0Zf2fi61OslQotWzLyqV34/Fs+1ssvG+LvZK7u0bxKyBwRbNIFuCXi+IuJrN1jOGGeeLKXnGz9RKOaM6+DIlJIBh7bzLzTLXB5MnT8bNzY2ffvrJeGzhwoVER0ezfv36Gl8/Pz+fVq1a8dxzz7FgwYJqXUMyZGtIdWZkIyMj6dChg03NJtU1DSGXI5czmLcqnKScIuyUcp4b244HB7aotZmKmtJYxooQgrVH4nh9o2HG28vZjo/vCimzYcYSbFUuDW2c2RINOSObmlvM+E/3kppbzN29A3n39q4WX2Pp5nN8uSsae6UcrV6g1Qt6Bbnz7QO9quWDWhVCCD7ceo7Pdl4qc3xCl6Y8PbpNrbn1ABSW6FgVdoUf9sWQkGVYIrdXGZKn3N2nOSGBlSeF0er0rA67wofbLhjCemH4g9vCy4lNpxONx8BgvE7pHsAtnf0I9KjdyYWK9EhaXjF/HItnzZE4YyQJlULG5O4BPDq0Za3K0hSXUvP4NyKJdeEJRF1n1Pq4qLmrdyB39Q6s14mW4OBgFi1axGOPPWaU2bx58xg6dCivvfaaxa4Fphg9ejStW7fmq6++qlYdpagFEjcder3gmz2XeH/reXR6QStvJ764t0e5cDYStYNMJuPuPs3pFezBE6uOcy4pl/t/OMzjw1ozf1QbaSOYhNUghGDhbydJzS2mra8zr07sVK3rLBjdlq1nkoi6NvM4vosfH07rXmcbRlNzizl1w075Kd39+eiu7rU2c1ms1bH68BU+3xltDJXl5WzHjP7B3NcvyGwDXamQc3//YCZ09WfRHyfZfjaFA9HpHIhOB8DP1Z6pPQKYEhJAW9+6NRpN4eWsZs7QVjw8uCWh51JYtucSYZcz+P1YPH8ej2dK9wCeGtWmVmfVr6eltzOPD2/N3GGtOHM1h3XhCfx1IoGU3GI+C43i851RDGvrzYODWjCotVedur9lZ2cTGxtLSEhImeMnT57kqaeeAuDRRx9l2rRplV4nIKDiFY3i4mIiIyMrNXRrE6uakd2zZw/vvfcex44dIzExkXXr1jFlyhTj53l5eTz//POsX7+e9PR0goODefLJJ3nssceM5xQXF/PMM8+wevVqCgsLGTlyJF9++SXNmjUzux7SLIttkV2g4elfTxg3Ik3p7s9bt3WpEz8oifIUaXQs2XCW1WGGTSr9W3ryxb09qgxX1BiQdIX5NJSsdp5PYdbyI6iVcjbOG0SbahpS4VcyuXvZIWPc0vfu6MqdvQJrs6pGdp5LYeFvJ8nIL8FOKadfSw/2XEgD4MmRbVgwum2Nrq/TC347GsenOy5y9VrYrGbuDswd1pqpPQIsNs7zi7X8fiye5ftjuJxePm7tuM5+vH1blzqZua4u4Vcy+XJXNNvOGvyNlXIZd/YK5KmRbfBzq3s3qRKtnm1nk1kVFsv+qHTj8Xa+Lswe1IJJ3f3r5E/Snj17GDFiBLm5uUYf19jYWIKDg4mJialWGK5nnnmGiRMn0rx5c1JSUnjzzTfZvXs3p0+fJigoqFr1tERfWNW0SX5+Pt26dePzzz83+fnTTz/N5s2b+fnnn4mMjOTpp59m3rx5/PXXX8Zz5s+fz7p161izZg379u0jLy+PW2+9FZ1OZ/KatYFOpyM8PLxO72GL1IdcolLymPLlfkLPpWCnlPPO1C58dFd3qzViG+NYsVcpeGdqFz69JwQnOwUHL6Uz6fN9RCbmVP3lazRGuUiYpj77WAjBJ9svAoaQVtU1Yi+n5TP7x6MUa/W0vOaT+uW10Fy1SbFWxxsbzzJrxREy8kvo4OfC+6M9WT6jF0smGWaSP91xkY2nrlb7Hgei05jw6V6e//M0V7OL8HVV8+aUzoQuHMb0vs0tMp6yCzR8sv0iA94N5dW/z3A5vQA3BxWPDm3F7meH8dTINijlMv6NSOLWz/ZxKj6r2vU2B0v0SEhzg1vI308MZGhbb7R6weqwKwx/fxefh16kSFO349ROKWdC16b88lA/dj4zjJkDgnGyU3A+OZfn/jjFoP/tZNmeaPIrCXlWHU6ePEn79u2NRqxOp+OPP/6gSZMm1Y4lGx8fzz333EO7du2YOnUqdnZ2HDp0qNpGrKVY1Yzs9chksnIzsp07d+auu+7ilVdeMR7r2bMn48eP54033iA7Oxtvb29WrlzJXXfdBcDVq1cJDAxk06ZNjB071qx7S+G3aoe6lsvO8yk8uSqc3GItAU0c+Ob+nnQOcKv1+9QmjX2sXEjO5eGfjhKbXoCDSsEH07oxvkvVmZFsVS7SjKz5NISPbOkmLbVSzt5Fw6u1ITE9r5jbvzrA5fQCOge48sOM3oz5eA9ZBRqLN41VRlJ2EY+sPMqpeEOIq5kDgnluTBuuXL5kfC7e3hTJsj2XcFAp+OOxARaFlIrLKODtTZH8G2HItuRqr+TJkW24r1+QxTN/6XnFfL8vhp8OxpJ3zdBq4eXEgwODub1nMxzt/ptIiEjIZt7qcGLS8rFTynljcifu6t3covuZS030SFhMBu/+G8nxK1mAYYb6xfEdGNfZr94i3WQXavj1SBwrDlw2+io3cVQxe2ALHhgQXCchvKxV99rsjGxVDBo0iL///puEhASEEOzcuZMLFy4YDdRjx46h0WgYM2aM8Tv+/v507tyZAwcOVHjd4uJicnJyyrzgv5kDnU5nsqzVatHpdCgUClq3bm0c7FqtFr1eX66s0WjKlEv/Q5SWhRDlykCZsl6vL1PWarWVlnU6XZmyuW2qrB3mtkkul9OuXTv0en2ttkmr1fL1rihmrzhCbrGWXkHu/PXEQDr4Odd5m2raTzKZjNatW6NQKKymn2pz7LX2duKPOX0Z3MaLQo2Oub8c58Ot58vU11SbSp+hUqypTeb0k4T51NePpRCCT3YYZmOn921eLSNWpxc89stxLqcX0MzdgR9m9sbH1Z6HBrUA4LPQqFqZlT0Vn8Wkz/dxKj6bJo4qvn2gF69N6oSjvR3t27c3ymzRLe2Nz9YjK4+WCfFUERqdnq92RTPqw938G5GEXGaYnd797HAeGtzSIiM2p0jDh1vPM3jpTr7cFU1esZb2fi58Pj2E7QuGcn//4DJGLEDnADf+emIgozr4UqLVs+iP0zz/xymKtbX/7CgUijLysoQ+LTz447EBfHJ3d5q62ROfWcjcX44zc/kR4mqQ5tcS3BxUPDykJbueHcZ7d3SlhZcTWQUaPth2gSFLd/LVrmgKS2pXbjWRmbVgU4bsp59+SseOHWnWrBl2dnbccsstfPnllwwaNAiApKQk7Ozsyv3bryrn7zvvvIObm5vxFRho8HuKiIgAIDIyksjISABOnTrFxYsG5RgeHk5MTAxarZbt27dz+fJlAA4cOEBiYiJg8EdJSzP4NoWGhpKVlQXA1q1byc3NBWDTpk0UFRWh1WrZtGkTWq2WoqIiNm3aBEBubi5bt24FICsri9DQUADS0tLYs2cPAImJiUZjPS4ujrAwQ6iYmJgYwsPDAbh48SKnTp0yq00AYWFhxMXFVbtNeXl5hIWF1WqbtDo981Ye4t3N59ELuKWNC8/1tsfLWV0vbappPyUkJLB161a0Wq3V9FNtj70LESdYPrM3d3YxPIefhkYxZ/l+joWfrLBNWq2WHTt2EB0dbZVtqqifSnWEhPmU/hGoaw5Gp3MsNhM7pZxHh7aq1jW+2hVFWEwGTnYKVszqbTSGZwwIxtVeSVRKHptOJ9aonv+cSmTaNwdJubYZbcMTgxjd0RcwyOrIkSNGmSnkMj67J4TmHo7EZxbyxKrjaHX6Cq99Oj6byZ/v53+bz1Gs1dO/pSebnhrM65M7W+SvWqTRsWxPNEOW7uTT0CgKSnR0DnBl2f092fTkYG7t6l9pLGlXexXL7u/Js2PbIZPBmiNxzPghjOxCTYXfqQ43ystSZDJDJIMdC4fy5Mg22Cnl7L6QypiP9vDd3ku17kpSESqFnDt7BbJ9wVA+vSeENj7OZBdq+N/mcwx9bycrD8WiqaTfLaGmMrMGbMq14P333+fbb7/l/fffJygoiD179vDCCy+wbt06Ro0axapVq5g1axbFxcVlrjV69GhatWrF119/bfJexcXFZb6Tk5NDYGCgcQmsdNZFoVCUKWu1WuMsbHR0NC1atEClUqHVapHL5cjl8jJljUaDQqEwlpVKJTKZzFgGw6C6vqxSqRBCGMt6vR6dTmcs6/V6lEplhWWdTocQwlg21Q5TbSotm2qHuW2SyWTExMQQGBiIWq2ucZvyikqY/+tpQs+lIJfBK7d25P6+gcb61kebatpPGo2GmJgYWrVqhUwms4p+qsux9+vROF7+6yw6vaB/Sw++eaAXTip5uTaVPkPBwcHY2dlZdZuu76ecnBw8PDwk1wIzqG/XgmnfHCQsJoMZ/YNYMrmzxd8/fiWTO78+iE4v+ODObtzes+yG4U+2X+Sj7Rdo6+vM5qeGWBziTwjBl7uieW/LeQCGt/Pm03tCyqR01el0xMTE0KJFizIzZueTcrnty/0UlOh4Ynhrnhnbrsy1i7U6Ptx6gW/3XkIvDDN9L0/owB09LUsII4Rgw6lE/vfvOeNSdytvJ54Z045bqrnkvvtCKo//cpy8Yi3tfF1Y8WBvmro5WHwdU1Qkr+oSnZrHC3+eJizGkBygazM3PqzFjIbmotML1ocn8NH2C8YMYi29nHhpQgdGtPepketDbcustmgUcWRvNGQLCwtxc3Nj3bp1TJgwwXjeQw89RHx8PJs3byY0NJSRI0eWU5TdunVjypQpLFmyxKx7S35v1kd6XjEP/niUk3FZqJVyPrsnhDGd/Bq6WhJmsPtCKnN/PkZ+iY52vi4sn9Ub/ya188PV0NiKrrCGiDD1KatDl9K5e9kh7BRydj83zGJDKbdIw4RP93Elo4CJ3fz59O7yIa+yCzUM+l8ouUVavrq3B+PM8AUvRQjBO/+eY9keQ4zY2YNa8OL4DhZlyNt46ipPrApHIZexbu4AujZrAsC5pBzmrznBuSTDCsWkbv4sntgRL2fLMmWdiMvijY1njel3m7rZ8/TotkwNCahxeL0zV7OZufwIqbnFNHWz58cH+zRIWC5z0OsFa4/G8famSHKLtKiVcl4Y154H+gfXe3zyYq2ONWGGaBPp19xKBrfx4uUJHWnnZ53yqy6N0kdWo9EY/S6vp9TXEAwbv1QqFdu2bTN+npiYSEREBAMGDKizumm1Wg4cOGDTU/N1QW3JJTY9n9u/OsDJuCyaOKpY9XA/mzVib8axMrStN78+2h8fFzXnk3OZ+uUBolJyy5xzM8qlPrGmiDD10cefh0YBMK13s2rN9r369xmuZBQQ0MSBN6d0Njnj5eagYtZAg6/sp6FRmDsnpNcLXlofYTRiX7m1I6/c2tGkEVvZc3FrV39u7doUnV7w7G+nKCzR8u2eS0z6bD/nknLxdLJj2f09+fSeEIuM2Iz8Ep797SRTvtjPsdhMHFQKFoxuS+jCYUzrFVgrMaI7+bvx52MDaOntRGJ2EXd8dYATcVk1vm5d6BG5XMY9fZqzfcFQhrT1plir57UNZ5mxPIzknKJau485qJUKZgwIZuezw5gztCV2Cjl7L6Yx7pM9vPb3GXKKLHfVaAy616oM2by8PE6cOMGJEycAgz/aiRMnuHLlCq6urgwdOpRnn32WXbt2ERMTw4oVK/jpp5+47bbbAHBzc2P27NksXLiQHTt2EB4ezn333UeXLl0YNWpUndVbLpcTEBBQzsi+2akNuZxPyuX2rw5yOd3wo/LHYwPoGdQwedprg5t1rHTyd2Pd4wNp4+NMUk4R0745RERCtvHzm1Uu9cW4ceN48803mTp1qsnPDx48yIwZMxg2bBjBwcE88sgjdOvWjaNHjwKGIOrff/89H3zwAaNGjSIkJISff/6Z06dPs337dovqUtd9HJdRwL6oNGQymDPEct/Yjaeu8ufxBOQy+Pju7pXuFH9wYDBqpZzIxBxOXzeeK0Kj07Pg1xOsOnwFmQz+d3sXZl/bOGaKqp6L1yd3xtPJjvPJuYz5aA9vbYqkRKdnZHsfNs8fYtEffv218FMjPtjFb8fiAZjaI4CdzwzjyZFtcLCr3WXnQA9H/nh0AD2aNyGnSMv93x+usTFbl3rE19WeH2f1ZsmkToYoGBfTGPvxHnaeT6n1e1WFq72KF8Z1YPuCodzSyQ+9gBUHLjPqg938ffKq2X+qoHHoXquq+dGjRwkJCTFmnFiwYAEhISEsXrwYgDVr1tC7d2/uvfdeOnbsyLvvvstbb73Fo48+arzGRx99xJQpU5g2bRoDBw7E0dGRDRs21Knvh1wuJygoyKYHQl1QU7lEJGRz17KDpOUV06GpK+vmDqCVt3Mt17J+uZnHSkATB36d05+uzdzIyC/hnmWHOHLZ4Ht2M8vFGqiriDCmqOs+/vN4AgADW3lZnAI1p0jDkg1nAXh8eGt6B3tUen4TRzvGXjMW/7hm/FWEVqdn/poTrD9xFaVcxqd3h1QZhqqq58LDyY6ZA4IBiMssRK2U8/ZtXfhuRi+8Xcyfhb2QnMsdXx/ghT9Pk1WgoUNTV/54bAAfTutep8kB3J3sWDm7L72D3cmtBWO2rvWITCZjxoBg/nlyMJ0DXMkq0DBr+RHe23Ku0k13dUVzT0e+vr8nK2f3oYWXEym5xTy5OpwHfggjNj3frGs0Bt1rVTUfNmyYMVTO9a8VK1YA4Ofnx/Lly0lISKCwsJBz586xYMGCMss+9vb2fPbZZ6Snp1NQUMCGDRuMUQjqCq1Wy549e2x6ar4uqIlcjl/J5J5vD5FVoKFbYBPWPNwPH9e6z7ZS19zsY8XdyY5fHupLnxYe5BYbfrj2XEi96eXS0NRFRJiKwhqWbqyti9ByJSUl/HncYFBO6eZncRi2j7ddJDW3mGBPR54Y0dqsMGy3hRh8Y/8+eZXCYo3JNpWUaFj0xyn+OZ2ISiHjq/t6MLGbf5Vt0mq17N6921jP69tRUlLC17uj+fhaiDGApm5qJnf1NW4krSq0XFGJlo+2nmPCp3s5fiULJzsFr9zakfWP9aN7M9c666frw+XZyQXLZ/am13XGbPiVzGqFyyuVV1FRUbl+qs2whi29HPnjsQHc28dgW3yxM5p7vztEcnZhuX6qjxCAg9t4888TA5g/sjV2180Wf78vhuISTaVtKpVZSUlJpf1kzWENrcqQtVXkcjmtWrWy6X80dUF15XL4Ujr3f3eY3CItvYPd+Xl2H9wcaz8QdEMgjRVwsVfx46w+DGvnTZFGz0M/HmXXhbSbXi4NyaeffsqhQ4f4+++/OXbsGB988AFz586t0m1ACFHhjumKwhqeO3cOqJvQcl/9vo3YjAKc7BTo405YFIbtp7938OPBywBMDdKiVirMCsPmo8/E3V5OZoGGlTvCy7VJCMGTP+7lj+MJKOQynujhSFunYrPaJJfLycnJoaDAEMe0NLRcTkERd368hXf/PYdOL+jmocfDUcXl9EJe/HG7sU2VhZY7HZ/NhE9280loNBqdoH9zZz4Y1YTZg1oQcym6XkMAKoSW7+4LoaWLILdIywPfh/Hdb5aHy5PL5bi5uXH8+PFy/VTbYQ3VSgVDnBJ5Z2IbnOwUHI7J5NbP9hF+JbNBQmpeirrAqKYatj09hM4+dhRp9Lyx8SwTPw5l1/FzFbZJLpdTVFRERkZGlf1U320yF6uNWtCQ2MpO5MbI/qg0Zv94hCKNnoGtPfn2gV7lAmxLNA5KtHrmrw1n0+kk7BRylj3Qk2HtfBq6WhZhi7qiviLC1DSsYXVCyz332wl+PZbAHT2b8c6UjmaHYdPpdNy17BBHY7MY19mPz+7uZlEYtnc3n+fbvTGM6uDDN/f1KNOmD7Zd5Mtd0chk8NG07tzaxbdGoeWScjU8svIokYm5qBQyXp3YkWk9/NkYkcKCX0/ipFaw65nheDqpTIaWK9Zo+WJnFF/sMsRFdXdUsWRyZ8Z3Mjx7DRkCMDu/iIdWhnM0NhNfFzV/zB1AQBMHqw8/GZNewKMrj3IxxZC97K3JHbmjV3Ozxl5dtEmr1bLmSDzvbj5PXrEWO4WM525pzwN9A1EqFVYf1hAMG1QbXdQCa0ar1RIaGioti96ApXI5fCndaMQOb+fN9zN6NzojVhor/2GnlPPJ3SGM6+xHiU7PQz8eYWdkxYlLJOqGuooIo1arcXV1LfMCjEuVCoXCuHfh+rJSqSxTLq1XRWWVSmWYVdLo+DciGYDbezRDpVIhk8mQyWTlykCZ8l8nEzkam4WDyrC0XvojLZfLTZYVCkWZ8p29DLPNu86nklWoNR5ffiCWL3cZkny8NaULU0ICLGqTVqtl7969xh/38Phcpnyxn8jEXLyc7Vj9cD/u62eIvTylewBdm7mRX6zjw20XkMvlxvaV1v1Sah7Tlh3m09BodHrBhK5N2b5gKJO6+aNUKsu0yVTf1EY/lZZLZ/Kv75smzg58P6M3bX2dSc4t5oEfwsgs0JRpx41tur6s1WrZtWuXcQze2E911aZW3s6se3yQMXvZs39E8O6/59ALqhx7VbWpqrFXUTvu6x/M1qeHMKydNyU6wZv/RDJjxTGScorLtKPUrav0WTenn+qrTeYiGbK1gFwup3PnztKy6A1YIpfjVzJ5cIXBiB3Wzpuv7+9pcf5vW0AaK2VRKeR8ek8IYzr6otXDo7+Esz8qraGr1eiwpogwdTX2t55NJrdYS0ATB/q2qHyT1vVkF2p4e5NhmfnJkW2qFeO4ra8LXQLc0OoFG05eBWBzRCJvXbvuC+PaM71v5Ru7THG9vvjjWDz3fneI9PwSOvm78tcTg+h13WY0uVzGK7d2BGDtkSucS8oxfiaE4OdDsYz/dC8n47JwtVfyyd3d+WJ6DzwtjC9b17g5qvjxwT74u9lzKTWfB1ccoaDEvD/+DalfndVKlt3fk3kjDKm2v9lziUd+Omp23esC/yYOLJ/Zm7du64yDSsHBS+mM/XgPf51IMJ7TGH6TbLfmVoRcLsfHx8emB0JdYK5cIhKymfFDGPklOga08uTr+3qiVjY+IxaksWIKlULO59N7MKqDD8VaPbN/PMLB6PSGrlajwpoiwtTV2C+NGnB7jwAsCVT/9e5o0vJKaOntVGkorKq4vUeAoR7HEzgRl8X8tScQAh7oH8QjQ1pW65pyuRxvb2++3BXNwt9OotEJJnRpyu+PGpbcb6R3sAcTujRFL+DNjZEIIcgu0PDYz8d5eX2E0WVry9NDmNw9oNptrWuaujnw0+w+uDmoOBGXxbxV4Walh21o/SqXy1g4ph2f3ROCWilnx7kU7l52iNTc4qq/XEfIZDLu7RvEpqcG0z2wCblFWp5ac4JnfztJQYm2wWVWG0g+siaw1O9No9EQGhrKiBEjjNPpEubJ5VxSDvcsO0RmgYbewe78+GCfRudOcD3SWDGNRqNhy/Yd/Jbozu4LaTjZKVj9SD9jtiJrxRZ9ZBuKUlmlpaXh6elZq9dOzimi/zs70AvY9cwwgr2czPpeSm4RQ5fuolCj47sHejGqo2+165CRX0Lft7ej0QmaOKrIKtAwvJ033z7Qq9pJBAqLinn4mx3sSzT8TD86tBXPjW1XqaEel1HAyA92U6LT8+L49vx4IJaErEJUChmLbmnPgwNbWGToNyTHYjOZ/u0hirV65gxtyQvjOlR6vjXp12OxmTz04xEyCzQEejjw46w+tGzg8JFanZ7PQqP4LPQiegGtfZz5+M4uJJw9YhUyu55GmdnLmlEoFPTu3duq8hRbA1XJJTY9n/u+M/hAdQtswg8zG59P7I1IY8U0CoWCAX378PW9PRjQypP8Eh0zlx8hKiWvoasmUcvUxdhfH56AXkCvIHezjViAL3dGU6jR0T2wCSM71GyjoYeTHYNaewGQVaChY1NXPp/eo/pGbImOuatPsi9RIJPB65M78fy49lUaoYEejswcGATA25vOkZBVSHMPQ7iohwa3tBkjFqBnkDvv39kNgG92XzKGVqsIa9KvPYPc+eOxATT3cCQuo5CpXx0wpvttKJQKOU+PbssvD/XD11VNVEoet39zmDi75jY9I2uR1fD3339bfIPRo0fj4NA48qpXhFwux8PDfJ+sm4XK5JKaW8z934cZkx38NKsPLvbW82+wrpDGimmul8uyB3ox/dtDnIrP5oHvD/P7YwOq5bdoS9xMurUufjA3nTaERrqth/nL5QlZhaw6fAWAZ8e2qzCMmLno9YL0fEMsTrkMvp/RCyd19f6Y5xRpmL3iCEcuZ6JWGvzIx5qZpSu3SEN0yn/B8Ls1c2PlQ31xtVH9OrGbP+eTcvl8ZxTP/3maFl5OhDQ3nd3R2vRrS29n/pw7gNkrjnAyPpv7vz/Msvt7MaiNV4PWq38rTzY9OZiFv51k1/lU3txyifNpJbwxpbNN7k2x6CkrDddiLjKZjIsXL9KyZfX8g2wFjUbD1q1bGTNmjFVNzTc0Fcklr1jLrBVhXMkoMCy5PNi70cSJrQpprJjmerk4q1Usn9mbO785yKXUfO7//jC/PToADye7hq5mnXEz6dbSQOm1RUpuESfjDelhR1vgGvDZjouU6PT0a+nBgFY1d3X4YmcUp67VQy8gt1hL02pcJz2vmBnLw4hIyMHFXsnDbbWMaGte/S4k5/LoymNcSstHLjPUI7OgBEcbNE6uZ8HotpxPzmXb2WQeWXmMDU8MMplxzBr1q5ezmtWP9GPOymPsvZjGgyuO8Pn0EIvSB9cFns5qfpjRmy9CL/Dh9ih+OxbP2cQcvr6vp8UZ8Roai/8aJyUlGeN/VfVydLQtYVQXpVLJ4MGDjeEjJAyYkkuJVs+jK48RkZCDp5MdPz3YFx8X28/YZS7SWDHNjXLxdFazcnZfmrrZE52az6zlYeQXN+6QZTeLbq3tsb/rXCpgmHk0V5fEpOXz27XNYbUxG7vzfAofbr8AQHs/gx/kjsgUi6+TlF3EXcsOGfXj6of7MvNW8/TFP6cSmfz5fi6l5dPUzZ5fHuqLh5MdVzIK+ftaJAVbRS6X8dFd3Wnn60JqbjGP/nyMEm35lLDWql8d7ZR8N6MXYzv5UqLT89gvx1kfnlD1F+sYuVzGEyPb8s09nfFwsuPM1Rxu/Wwfuy+kNnTVLMIiQ3bGjBkWLWXdd999N8UGCJlMhqura42VYWPjRrno9YJnfjvJvqg0HO0ULJ/VmxYW+LM1BqSxYhpTcglo4sDK2X1wd1RxMj6bJ1ebt3PZFrmZdGttj/0d5wyxY0e0N3829uPtF9DpBcPbedMzqGZL0VfSC5i/xhChYHrf5tzbLxiA0Gv1MpeErELu/OYAUSl5NHWzZ+2c/nQOaFKlvtDrBR9uPc/jq45TqNExsLUnG+cNon8rLx4ebJix/zw0yuafHWe1wRh0tVdyIi6L/20+V+4ca9avaqWCL6b3YGqPAHR6wdO/nmBN2JWGrhYymYwx3YLYOG8Q3QKbkF2oYdbyML7bewlbiQVgkSG7fPlyXFxczD7/q6++wsurYX1B6gONRsNff/1V60tmts6Ncnl38zn+PnkVpVzG1/f1tPod6XWBNFZMU5FcWvu48P3M3sZQNq9vOGMzytUSbibdWptjv1irY+9FQ9zhEe3N26x1MTnXOEO5cEy7Gt2/SKNjzs/HyC7U0D2wCa9O7Gisx7HYTDKv+cxWRUJWIXcvO0hcRiFBno789mh/Wvs4V6kv8ou1PPbLMT4NjQLg4cEt+HFWH2Ns2Pv7B9HEUcWltHw2nrLtWVkwbGT7YFp3AL7fF8PmiLIJVKxdvyoVct6/oxsz+gchBDz/52nWHmlYY7ZUZt5OSn6d049pvZoZwrf9E8lzv5+iWKtr0PqZg+1uU7MilEolY8aMsbrljIbmermsDrvCsj2XAHjvzq4MaevdwLVrGKSxYprK5NKjuTsf3dUdgB8PxvLD/sv1WzmJWqU2x/7hSxkUlOjwcVHTyd+8Gepley4hBIzp6EvnALca3f/tTZFEJhrcAL66rwdqpYKAJg6093NBLzBrifZqViH3LDtkNGLXPNKPZu4G15HKnov4zAJu/+oAW84kY6eQ8/6d3XhpQscyURKc1UoeuhYb97PQKPQ2PisLBj/ohwcb2vTs7ye5kl5g/MwW9KtcLuO1SZ2YOSAYMBizvx6Ja7D6XC8ztVLB/27vyiu3dkQug9+OxTP928Ok5TVcHFxzqFFvFxUVcerUKVJSUozpzUqZNGlSjSpma1jzg9OQKJVK9kel8cr6CADmj2rDbSHNGrhWDYs0VkxTmVzGd2nKC+Pa886/53jzn7M0c3cwexe3LSLpVvMIPWfwQx3R3sessFLJOUWsv5bVaM7QVjW699YzSfx0MBaAD6Z1o6nbf64hI9r7cC4pl9BzKUwJqTiSwtWsQu5edogrGQUEeTqy+uF+Za4Dpp+LU/FZPLjiKGl5xXg5q/nm/p70DDK9k/+BAcEs23OJqJQ8/o1IYkLX6mxBsy6eu6U9x2IzOX4li8dXHef3x/obk+jYgn6VyWS8OtGQhW3Fgcss+vMUANN6BzZIfa6XmUwmY/agFrT2ceaJVcc5FpvJbV/uZ/nMPrT2adg4uBVR7RnZzZs307x5c/r168ekSZOYMmWK8VWa1vBmQavVsmnTJrTaxr0ZxVK0Wi3L/9jEY78cR6sXTO7uz1Mj2zR0tRoUaayYxhy5PDKkJdP7NkcIeGpNOCfjsuqvgvVIY9ettTX2hRDX+cea51awfP9lNDpBryD3Cg0/c0jMLuS5PwzGx8ODWzCsXdn7l8ak3XU+Ba2u/KYkMERbmP6twYht7mEwYm8MM2fqudh2Npm7vjlEWl4x7f1c+PuJgZW2xdVexYPGWdmLjcI1pzQboLujitMJ2fzv3/OAbenXUmN25oBghIBFf55qkA1gFclsaFtv1j8+kCDPa3Fwv9zPoUvWmXGx2obsE088wZ133kliYmK5HbU6nfX7VNQmSqWS8ePH28Q/wfokp1jPylgXcou09Axy53+3d7VKJ/z6RBorpjFHLjKZjNcndWJoW2+KNHoe/ukoyTlF9VjL+qGx69baGvvRqXnEZRRip5QzsHXV/sJ5xVp+OWyYQa1uyljAsFFn7QmyCjR0CXDj2bHty53TPdAdd0cVOUVak0HwswpKeOD7MC6nF9DM3YE1j5Q3YqH8c7F8fwyPrDxKoUbHkLbe/PZof7NiLM8a2AJntZJzSblGn2Jbx7+JAx9MMyRL+GF/DPsuptmcfi01Zu/vZ/CZXfjbSbadtWyTYE2pTGatvJ3587EB9GjehJwiLfd/f5h14ZUnpWgIqm3IpqSksGDBAnx9q5/SrzFhC/8A65MSrZ5Hfz5GXGYhge4OLLu/p00GWq4LpLFiGnPkolTI+eLeHrT1dSYlt5hHVh6jSGP7xt31SLrVPErDW/Vr6WlW4oE1YVfILdLS0tuJUR2qL9uvdkVx6FIGjnYKPr0nBDtl+Z9RhVxmnKUtdX8oJa9Yy8zlRziXlIuPi5pfHupbqTGq1WrR6wXvbIpkyYazCAH39GnO9zN6mZ1Exs1BxR09DS5dy/fHmNtUq2dEe1/u7dscgGd+O0lWQYnN6VeZTMaSSZ2M0QweX3Wc/VH1+2ejMpl5OqtZ9XA/JnRpikYneHrtSb7cFWVVM/vVNmTvuOMOdu3aVYtVsV20Wi1bt261uQeoLnl94xmOXM7EXiH45r4Q4y7amx1prJjGErk4q5V8+0Av3BxUnIzL4qV1EValVGtKY9ettTX2d1wzEEea4Vag0en5YZ/BgHu4BmlaIxKy+Xj7RQDemNy50vCBpe4OO64zZIs0Oh756Sgn4rJo4qhi5ey+BHlWfA2tVsu/m7fyzG8n+ObaZtlFt7Tn7ds6o7Iw9e3MAcHIZLDzfCrRqY0n9fNLEzrQwsuJpJwiXl4XwZYttqdf5XIZS2/vypiOvpRoDatNx6/UTzpbc3SvvUrBZ/eEMGeoYSVj6ebzvL7xrNVsHpSJav4CFBQUcOedd+Lt7U2XLl3KZdF48skna6WCDUFOTg5ubm5kZ2fbbKzGhmTtkSss+uM0smtpGi2J7yghYS77LqYxY3kYOr3glVs7MvuaH2B9Uhe6orHq1tqUVVZBCT3f3I5OL9j73PAqMxGtC4/n6bUn8XJWs2/R8GqtDhVrdUz6bD/nk3OZ0KUpn08PqdRVKrtQQ483tqHTC3Y/O4xm7o7M/eUYW84k42SnYNXD/egW2KTSexaUaHn8l+PsPJ+K4pqxc3vP6m+WfejHI2yPTOGB/kG8Prlzta9jbZyIy+L2rw6g0ws+vqt7pRvsrJlirY7ZK46yLyoNNwcVfzzWn9Y+5oflqw++3xfDGxvPAjCpmz/v39nN5KpETbFEX1TbkWTVqlVs2bIFBwcHdu3aVeaBlslkNqtsq4MQgtzcXFxcXG56H9ATcVm8sv4MAE+PaksvfweEEDe9XEqRxoppqiOXQW28eGl8B17feJa3/jlLO1+XBs9hXhs0dt1aG7Pnuy+kotML2vo6V2nECiFYtscwGztzQFC1XZw+2X6R88m5eDnb8caUzlWOUzcHFb2D3Tl0KYMdkcnEpBUYQ2V9N6N3lUZsVkEJs5YfITwuC3uVnK/u7clwMze1VcSDA1uwPTKF347Gs3B0u0aTGrx7YBOeHNGGj7Zf4JX1p+kV7G4MYWZLqJUKlj3Qk3u/O0z4lSxm/HCEP+cOwNe17rJfWqp7Zw9qgZezHQt/PcnfJ6+SWVDCN/f3xNGu4fySq21Gv/zyy7z++utkZ2dz+fJlYmJijK9Lly7VZh2tHq1Wy969e21uOaO2Sc0t5tGVxyjR6RnT0Zc5g4IkudyANFZMU125zBoYzB09DQG8H191vExMSVulsevW2hj7+65tWBrermrD7sjlTCITc3BQKbivX1C17nciLouvd0cD8OaULng42Zn1vdL6/XL4CisPxSKTwUd3dad/K89Kv5eaW8zdyw4RHpeFkxJ+mtWrxkYsQP9WnrT3c6FQo2Pt0YbPKlWbPD68Fd0D3cgt1vHSn6dt1t3I0U7J9zN609LLiYSsQmb8EEZuUd0leKiO7p3cPYAfZvbG0U7B3otp3P99GNmFDZeEotqGbElJCXfddRdyuZRTQaVSMWHChHJLgDcTGp2ex385TlJOEa28nfhgWjfUarubXi43Io0V01RXLjKZjDendKb7tdSKc1fZ/uavxq5ba2PsH47JAKBfFQYhwM+HDJEKJnf3p4mjeQbo9RRpdCz89QR6YbjGLZ3Nj19carBGp+YD8MqEjlXGcb2aVchd3xzkXFIu3i5q1s0bQp+WtZNARiaTMWtgMAA/HoitMDSYLaJUyHn/zu7YKeXsvphmjBdsi3g42fHjg33wclZzLimXR38+Rom2bvqqurp3SFtvfnmoL672So7FZjL920OkN1DihGpryhkzZrB27drarIvNotfrycjIKBe4/GbirX8iCbucgbNaybIHDLtpJbmUR5KJaWoiF3uVgi/v7YGHkx0RCTm8fs1/y1Zp7Lq1pmP/alYhVzIKkMugVxWxYNPyivk3IhGAe/tWbzb2o20XiE7Nx9tFzZJJnSz6blbBfylqp4YEGOO5VsTltHzu/Pogl9LyCWjiwNpH+uKl0tSqvpjcPQAPJzsSsgrrPdRTXdPSy5FHBhh8iJdsOGv1GakqI9DDkRWzeuNkp2B/VDqL/jhVJ7PMNdG9Ic3dWfNIfzyd7DhzNYe7lh1qkJCI1TZkdTodS5cuZejQocybN48FCxaUed1M6HQ6jhw50ihiPFaHjaeusuLAZcCwbNbK25D942aXiykkmZimpnLxb+LAx3d1RyaDVYev8Odx64t1aC6NXbfWdOwfjjEEZe8c4FZl+Knfj8Wj0Qm6NXOjSzPL09FGJGTz3bVoB+/c1sWiGd2olDweXxVufN+haeWbdqJT85j2zUESsgpp6eXEb4/2J7CJfa3rC3uVgul9DCGrll/T240FnU5HR1kCHfxcyCrQ8OrfZxq6SjWic4AbX93XE6VcxrrwBD4Pjar1e9RU93b0d2XtnP74udoTlWIYw1ezCmu5lpVTbUP29OnThISEIJfLiYiIIDw83Pg6ceJELVbR+lGpVIwdO/amXC6+nJbP83+cBuCxYa0Y3fG/CAU3s1wqQpKJaWpDLkPaehszx7247jTnknJqq3r1SmPXrTUd+4cvXXMraFm5W4FeL1h12OAHem81fGN1esGL606j0wsmdG3KqI7mR1/JzC9h9o9HyC3S0szdECM27HLF4ZSiUvK4e9khUnKLaefrwto5hkQHdaUv7usXhFwGYTEZjSoUl0qlYvy4W3jvzm4o5DL+OZXIljNJDV2tGjGkrTdvTDFEmPhg2wU2nrpaq9evjTHW2sfZ8MfLw4HY9ALuXnaIhHo0Zqu9zWznzp21WQ+bRq/Xk5aWhpeXV6P1azNFkUbH46uOk1espXewOwtHty3z+c0ql8qQZGKa2pLLvBFtOBabyd6Lacz9+Th/zxuEsxnB8q2Jxq5ba7pMXuof27eFR6Xn7Y1K40pGAS72SiZ29bf4Pj8dvMyp+Gxc7JW8emtHs79XotUz5+djxKYXEOjhwBuTOzNz+RGOXM5ArxflYthGpeRy97LDxpSzqx7uZ9xMVlf6ws/NnhHtfdgemcKvR+J4YXyHWrt2Q1Iqr45NvXhkSEu+2hXNK+sj6N/KE1czk0dYI/f0aU50Sh7f7Yth4a8naebuSPcqol6YS22NsUAPR9Y80p97lhnSLt+97CCrH+5XL9EjpF/SWkCv1xMREXHT+T2+9U8kZ67m4OFkx6f3hKC8IUD3zSqXypBkYprakotCLuOTu0No6mbPpbR8Fv1eN35lEtWnJn2cklNETFo+Mhn0Cq7ckP3l2iav23s0w8HOspBbV7MKeX/LecCQgMDHzPBHQgheWneasJgMXNSG3ecDW3vhaKcgq0DD+eTcMudfTM7l7mWHSMsrpmNTV1ZfZ8RC3eqLu3ob3Av+OB5fZxuJ6pvr5fXUyDa09HIiJbeYD7deaOiq1ZgXxndgZHsfirV6HvrxaK3NeNbmGAto4sDaOf0I8nQkLqOQu5cdIi6j7iPJWGzIyuVyFApFpS9byXNcWyiVSkaMGHFTtXvjqausvPZD8eG0bjR1M50n/GaTS1VIMjFNbcrFw8mOL+7tgVIu45/TiawKs40wQzeLbq1JGw5dm43t2NQVN4eKZ9gSswvZHmnYyHRfv+YW3+fVv8+QX6KjZ5C70Z/UHL7fF8Nvx+KRy+Cz6SG09XVBpZDT89qmtMOX0o3nRqXkcc+3h0jLK6GTvyurHu6L+w1hvepSXwxv542Pi5q0vBJCzzWOTV/Xy8tepTAuyf908DIRCdkNXLuaoZDL+OSeENr7uZCWV8zDPx6lsKTmvtO1Pcaaujmw9pH+tPByIj6zkOnfHapzn1mLDdl169bx559/mnw988wzqNXqm87/T6/Xk5CQcNPMsl3vF/v48FbGnOI3crPJxRwkmZimtuXSo7k7i25pD8AbG89y8YaZMGvkZtGtNenjQ9cMwb4tKvePXRMWh14Y3A8szYy05UwS284mo5TLePu2Lmans913MY23N0UC8PKEjmX0Yqk/76Fr/r2x6fnc+53BiO3Y1JVfHuprciNZXeoLpULOHdeyhK05Elfr128IbpTXwNZe3Nq1KXoBL6+PsJqUqtXFWa3k+5m98XSy42xiDs//WfMVp7oYY35u9qx5pB/B12Zm7/3uMCl1GM3AYkN28uTJ5V7t2rVjxYoVfPDBB9x5552cP3++Lupqtej1eqKjo28K46REq+eJ1Qa/2D7BHjw9qm2F595McjEXSSamqQu5zB7UgiFtvSnS6Jm3Otzq48veLLq1Jn1cOqPZt2XFbgU6vWDtNcPM0k1eRRodr28whG97ZEhL2vmZZwTHZRTwxOrj6IXBlaE0Vmsppf68YZcziMsoYPq3h0nOKaatrzM/V2DEQt3ri2m9AgFDprT63mleF5iS1yu3dsRZreREXBa/HrV9gz2giYNxxemvE1f5bm9Mja5XV2PM19WeVQ/3o5m7AzFp+Uz/7nCdhUOrkY/s1atXefjhh+natStarZYTJ07w448/0ry55Us5toxSqWTIkCGNYtmvKj7Ydp6IhByaOKpM+sVez80kF3ORZGKaupCLXC7jgzu74eVsx7mkXN65NltmCzRm3VrdPk7NLSY61eAfW9lGr4PR6STlFOHmoGJsJ/MjDQB8vTuahKxC/N3smTeijVnfKSjR8sjKY2QVaOjWzI23biufvrZrsybYq+Rk5JeUCbH1y0P9Ks0SVtf6ItjLif4tPRECfjtquyHrSjElL19Xe+aPMvTlu5vPkZFfUtHXbYZ+LT155doGxHf+jTRmuqsOdTnG/Js4sPrhfjR1M4Tmuu+7w2ViK9cW1TJks7OzWbRoEa1bt+bMmTPs2LGDDRs20Llz59qun02g1+uJjY1t9LNsB6LTWLbHkCLz3ald8XOrfAPEzSIXS5BkYpq6kou3i5r37+wGwI8HY9lu5QHgbwbdWt0+DrvmH9vO16XSeK5/XIshPLFbU9RK8zd5xWcW8NUuQxraFyd0MGuDmBCC534/RWRiDl7Odnx9f0/sVeW/Z6eU0/VaHNvE7CKaeziy6uF+eLuoK71+feiLu/sYZmV/PRqHzsaX3iuS18wBwbS/Flt26eZzDVS72uWB/kHG9NxPrK5+eu66HmOBHo788lBfvF0MWcpmLD9CfnHtpmi32JBdunQpLVu2ZOPGjaxevZoDBw4wePDgWq2UrXEz+D1mF2hY+OtJhIB7+gSalabxZpCLpUgyMU1dymVYOx9mX8uo9OzvJxsk84w53Cy6tbp9XJoIobL4sXnFWjZHGOKGTu3RzKLrv/VPJMVaPf1aejChS+VpZEtZvv8yG08lopTL+PLeniY3vZbWK/aaoWGvkvPLQ32rnAiA+tEXYzv54eagIiGrkH1R1Z/ZswYqkpdSIefNaxu/1h6N43S8bW/8gv/Sc3dr5kZWgYbHfqleeu76GGMtvZ2v+YGrOBmXxSMrj1KsrT1XL5mw0FNYLpfj4ODAqFGjUCgq/sf6559/1rhyDUVOTg5ubm5kZ2fj6ura0NVpcIQQPLEqnH9OJ9LCy4l/nhyEo520NC5hOxRrdUz98gBnruYwsLUnKx/sa/YmnsqoTV1Rl7p1z549vPfeexw7dozExETWrVvHlClTypwTGRnJokWL2L17N3q9nk6dOvHrr78a3RmKi4t55plnWL16NYWFhYwcOZIvv/ySZs3MMxhrKqsxH+3mQnIeX93bg3EVGJq/H4vnmd9O0sLLidCFQ8st8VfE/qg07v3usCGI/pODaO9Xdf2OxWZy1zcH0eoFr07syKyBptPPFml0zFp+hIPX/HubOKoIf2W02XWrD177+wwrDlxmQtemfDG9R0NXp86Yvyac9Seu0ifYg7Vz+llVH1SXxOxCJny6j4z8Eu7p05x3pnZp6CpVyIm4LKZ/e4iCEh23dPLj8+kVuydaoi8snpF94IEHmDZtGh4eHri5uVX4qg579uxh4sSJ+Pv7I5PJWL9+fblzIiMjmTRpEm5ubri4uNCvXz+uXPkvvE5xcTHz5s3Dy8sLJycnJk2aRHx83fr+6HQ6oqKiGm3a0T+OJ/DPacOsw8d3dTfbiG3scqkOkkxMU9dyUSsVfHpPCA4qQ97yFVaYmrMudWt+fj7dunXj888/N/l5dHQ0gwYNon379uzatYuTJ0/yyiuvYG//36zh/PnzWbduHWvWrGHfvn3k5eVx6623Wtxn1enjjPwSLiQbMlD1qcQ/tjQ18e09Asw2UjQ6PUs2GFKZ3t8vyCwjNj2vmCdWHUd7LevXzAHBJs/T6gwbDQ9eSsfRToFSISOrQEN0ar5ZdasvfVEavWD72WRyizR1eq+6pCp5PXdLe+xVcsIuZ/BvhG1n/Cqlqdt/6blXh13hj2OW2Tv1+ZvUPbAJ3z7QCzuFnM1nknhx3elaifNt8bTaihUranzTiihVtrNmzeL2228v93mpsp09ezZLlizBzc2NyMjIcsp2w4YNrFmzBk9PTxYuXMitt97KsWPHKp3lqAlCCDIzMwkODq6T6zcksen5vPpXBABPj25LNwuyiTRmuVQXSSamqQ+5tPJ25sUJHXhlfQT/23yOIW29ae3jXGf3s5S61K3jxo1j3LhxFX7+0ksvMX78eJYuXWo81rJlS2M5Ozub77//npUrVzJq1CgAfv75ZwIDA9m+fTtjx441uy7V+eEq9Y9t4+OMp7Npv9KErELjrOeUkACzr73q8BUuJOfh4WRXaRSWUnR6wfy1J0jMLqKltxP/u72rSaPZkBwhgm1nk7FTyvluRi8+2X6RwzEZhMVkmDX26ktfdPJ3pZW3E9Gp+Ww5k2w0bG2NquTl38SBOUNa8cmOi7y9KZIR7X1M+jTbGqXpuT/efpGX1p+mU4CrWX/IoP5/kwa29uLTe0KY+8sxfj0aj4eTmufHta/RNS2akT116pRFfhRnzpxBqzXfqXfcuHG8+eabTJ061eTn1yvbkJAQWrZsyYQJE/DxMcTrK1W2H3zwAaNGjSIkJISff/6Z06dPs337drPrYSlKpZLevXs3up3oOr1g4a8nyS/R0SfYg0eHtrLo+41VLjVBkolp6ksu9/VtzuA2XhRr9Sz89QRanXX4Kte1bq0MvV7PP//8Q9u2bRk7diw+Pj707du3zIrYsWPH0Gg0jBkzxnjM39+fzp07c+DAAZPXLS4uJicnp8wLMBp9Op3OOAt0fVmr1ZYp6/V6TsRlARgTC5QeB9BoNOj1etaHJyAE9GvpQTN3RzQaDUIIhBDlymD4Ac/ILeDj7YasT0+NaIWbowq9Xm+UranyZ6EX2XsxDXuVnK/u7YmDUmayHR9uPc/ao3HIZfDJtK70DXanV7Ch/uFXMsu1w1SblEol3bt3N07CmNOm0rJery9TrqxNMpmMSd0MaXz/OpFQYd9U1U/mtOn6dtR2m5RKJT179jSOQZ1OZzyntO5zhrbEz1VNfGYhP+yPsfo23Vg21SaAuUNbMri1J0UaPY/9fIzsgmKz2qRUKgkJCTGmp62PNt3S2c/oAvH17mh+2HfJZJvMxSJDNiQkhPT09KpPvEb//v3LLPvXhLpStlCxwjX3QdbpdJw9e9bYcbYw6M1RTt/tjeZobCbOaiXv3d4ZGcKiNmm1WiIjIykqKrKaNjW0ctJoNJw9exadTtdo2lQb/VT6DJWUlNRpm2QyGf+7vQuu9kpOxmfzxc6oWmlTTWlI3ZqSkkJeXh7vvvsut9xyC1u3buW2225j6tSp7N69G4CkpCTs7Oxwd3cv811fX1+Skkwv0b7zzjtlXCICAw2740+fNiRTiYyMJDLSEBLt1KlTXLx4EYDw8HBiYgyxMcPCwoiLi+PkNUM2+FpY1z179pCWZtiYFBoaSmZmpjFawfgOhs1gmzZtoqioCK1Wy6ZNm9BqtRQVFbFp0yYAcnNzef7HnWQWaAj2cMA7x2DQpqWlsWfPHgASExONvx1xcXGs2LSfT3YY6vlQNyfa+blw8eJFTp06VaZNvxyO5bOdhggIb07pglfxVWJiYugeaJDf0ZhUAA4cOEBiYqLJNmVlZaHT6di8eTPZ2dlmt2nr1q0AZGVlERoaWmWbwsLCAAjxMIzr/VFpHD4ZWa5N5vSTOW0C2Lp1K7m5ubXeJp1OR1hYmLFNMTExhIeHAxj7ydFOyfTOhtnwL0Kj2H043KrbdGM/mWoTwIXz53i0uwN+rvbEpBXw9M+HzGqTTqdj27ZtJCcn12ub+vkIprU3rKa/sTGSLzccLNcmsxEWIJPJxJw5c8TTTz9t1kutVovo6GhLbmEEEOvWrTO+T0xMFIBwdHQUH374oQgPDxfvvPOOkMlkYteuXUIIIX755RdhZ2dX7lqjR48WjzzySIX3evXVVwVQ7rVnzx4hhBCnT58Wp0+fFkIIcfz4cREZGSmEECIsLExcvHhRaLVasXnzZnHp0iUhhBC7d+8W8fHxQgghduzYIZKTk4UQQmzevFmkp6cLIYTYuHGjyM7OFkIIsX79elFQUCBKSkrE+vXrRUlJiSgoKBDr168XQgiRnZ0tNm7cKIQQIj09XWzevFkIIURycrLYsWOHEEKI+Ph4sXv3biGEEJcvXxb79+8XQghx8eJFERYWJoQQIjIyUhw/ftysNl1MzhWtX9goghZtFKsOx1arTbm5ueLo0aNW0yYhhNi/f7+4fPlyg/XTlStXxKZNm4RWq200baqNftJqtWLLli3iwoUL9dKmxT8YxnarF/4Ry377t9pt2rNnjwCM964uDalbExISBCDuueeeMudNnDhR3H333UKIinXrqFGjxJw5c0zep6ioSGRnZxtfcXFxAhCpqalCCCG0Wq3QarXlyhqNpky5RKMVnRZvFkGLNoozCVnG4zqdTgghRElJiTh+OV0ELdoo2r28SWQXFBuP6/V6odfry5WFECIuI1+0eWmTCFq0UWyNuGo8rtPphEajKVdOzSkUfd7cJoIWbRQL14Ybj9/Yjn9PJYgWzxvG1/ubI8u0KTm7UAQt2iiCn98ocos0ZdpxY5t0Op3QarXi6NGjxntV1abryzqdrso2XV/WarVi8ud7RdCijeLbPVEm+6ayfjLVDlNtur4dtd0mrVYrjh07JoqKioz1NdVPJSUaMfFTQ1uf/e2EVbfJVD9VNPa0Wq04EpNuHH+/H42rsk2lY6y0DvXZppKSEvHyutMiaNFG0ealTeJQdJqxHdnZ2WbrVouiFgwbNsziXX6rVq2iaVPzQplcj0wmK7Oz9urVqwQEBHDPPfewatUq43mTJk3CycmJ1atXs2rVKmbNmkVxcdnsEaNHj6ZVq1Z8/fXXJu9VXFxc5js5OTkEBgaSkZGBu7u7cdZFoVCUKZcuyZSW5XI5crm8wrJGo0GhUBjLSqUSmUxmLAPG5ZHSskqlQghhLOv1enQ6nbFcujRQUVmn0yGEMJZNtePGNukF3PXtYcKvZDG4jRc/PdgHnU5n021qjP0ktan6bdJoNDz162n+jUiijY8TG+YNxk4hs7hNOTk5eHh41DhqQUPq1pKSEpycnHj11Vd5+eWXjectWrSIffv2sX//fkJDQxk5cqRRJ5bSrVs3pkyZwpIlS6q8b3WjFlxIzmXMR3twtFNw+rWxKExEm1j8VwQ/HYxlcnd/Prk7xKzrLlh7gj/DE+jX0oPVD1e+g10IwcM/HWV7ZAotvZ3YOM905JbjVzK5Z9khirV67u4dyDtTu5S77oB3dnA1u4g1j/SrNJRYQ/Djgcu8+vcZujVz468nBjV0deqUY7EZ3P7VQeQy2DJ/CG18LUtlbM18tuMiH2y7gKOdgo3zBtHS23r2AtyITi+Y+8sxtpxJxsVeyZ+PDaCNr4tF+sIih7Rdu3bVpL41wsvLC6VSSceOHcsc79ChA/v27QPAz8+PkpISMjMzyyjblJQUBgwYUOG11Wo1anX5DQSlfknXbxK7vlz6A6nT6Th37hwdOnQoc/zG8vV50i0py2QyY7n0R9zcckV1r6xN3+yOJvxKFi5qpXEjQ3XapNPpiIyMpEOHDkZl3lBtsqRcl/0khDCOlVIjzNbbVBv9ZO4zVFttsrOz480pnTlyOZOLKfl8uO0CL47vYHGbamsDaUPqVjs7O3r37l0u/e2FCxcICjKkeO3ZsycqlYpt27Yxbdo0wLBMGBERUWaDmDlY6o5R6h/bOcDNpBGr1enZdNqw7GvuJq+IhGz+DE8A4KXxHav8E7HiwGW2R6Zgp5Tz+T09TBqxV9ILePjHoxRr9Yxo78ObU8pn+ALoFtiEq9lJnIzLqtKQvV6H1tVm5euZ0LUpr288y8n4bGLS8mnh5VTn96xNLJFXzyAPxnbyZcuZZJZuOc+3D/Sqp1rWPXOHt2Z/dBqHLmUwb3U4f84dUGFykPoeYzeikMv45O4Q7vvuMEdjM5m14gjr5g6k8lQhZalRitr6xFJlW0qpsq3MkJX4j6iUXD7YZvAVe+XWjvg3MR3gW0LC1vF0VvPutQ0H3+29xPFrG3AaI3l5eZw4cYITJ04ABj+7EydOGP1sn332WdauXcu3335LVFQUn3/+ORs2bGDu3LkAuLm5MXv2bBYuXMiOHTsIDw/nvvvuo0uXLsYoBnVFqX9s9woipoTFZJCWV0ITRxWDWntVeT0hBG/9Y/D5nNzdny7NKg9pFpGQzTubDNmgXhrfgY7+5WeHsgs0zFoRRnp+CZ38XfmskvTdpZFfSg10a8LLWW2U4V8nEhq4NnXPs2PbIZfBtrPJHIvNaOjq1BoKuYyP7wrB3VHFmas5vPuvdWczs1cpWPZAL4I9HYnPLOShn45SWGL+H16rMmRtVdkqFAo6d+7cIP9mahOtTs/C305RotUzrJ03d/aqWQiWxiKX2kSSiWkaSi6jOvoyNSQAvYDnfj9Vq9lmrImjR48SEhJCSIhh2X3BggWEhISwePFiAG677Ta+/vprli5dSpcuXfjuu+/4448/GDTov+Xljz76iClTpjBt2jQGDhyIo6MjGzZssLjPLD3/ZHwWAN2aNTH5+cZrs7FjO/qhqsB4vJ7dF1I5eCkdO6WcZ8a0q/TcwhIdT64Jp0SnZ3RHXx7oH1TunBKtnkd/PkZ0aj5N3ez5YWZvnNQVL3aWtuOkGYZsQzwXU0JKoxdcrZUYn/WJpfJq7ePCtF6GTYj/+/e8zbW3Mvzc7I3puZfvv8zO8ykmz7OW3yQPJzuWz+pjzP71wp/mb/iyKkPWmpStJeh0OsLDw20+yP2yvZc4GZeFi72Sd6eajo1oCY1FLrWJJBPTNKRcFk/siJezmqiUPD4Pjar3+9cHw4YNM0ZvuP51fezaBx98kIsXL1JYWMiJEyeYPHlymWvY29vz2WefkZ6eTkFBARs2bDBGIrAES/q4SKPjXKJh13T35k3Kfa7V6Y0paSd0rdpfWAjB+1sNq3oP9Asi0MOx0vPf3hTJpdR8fF3VLDURL1YIwQt/nubgpXSc1Up+mNkbX9fKU892beaGXAZXs4tIqSJdckM8F2M6+mGvkhOTls8pG0vlWh15zR/VFrXSkCQh9JxpY89WGdnB15is47nfT5GRX1LuHGv6TWrh5WRMmLA90vy+sNiQ3bJlS53l5LUmZWspDg62vQQfnZrHx9sMIUhendjJrDzg5mDrcqkLJJmYpqHk0sTRjjcmdwLgy13RRCQ0zI93XepWW+XM1Ry0eoGXsxp/Ezrp0KUMMvJLcHdU0b9V1RunNkckEZGQg5OdgrnDW1d67s7zKaw8FAvA+3d2w93Jrtw5X+++xB/H41HIZXxxbw86NK16E5uTWkkbH8PGopNmGIr1/Vw4qZWM7ugHwIaTV+v13rWBpfLyc7Nn5sBgAJZuPo9O33hmZQGeH9eeNj7OpOYW88Kfp0zOOlvTb1LvYA/eu7OrRd+x2JAdP368MYaahAGFQkH79u0bfGq+uuj1hlmFEp2eIW29ub2H+VlxKsPW5VIXSDIxTUPLZVyXpozv4odOL3ju91NoGiBRws2iWy3p4xNG/1g3kytE/1xzK7ilc9VuBTq9MPr/zx7cEg8Thmkp6XnFPPe7YWlz1sBgBrfxLnfO1jNJLN1i8D18bWJHhrYtf05FdAs0+OVW5V7QUM/FhC4GQ/bfiCSbWm6vrrzmDm2Nq72S88m5rAtvXL7B9ioFH93VHZVCxpYzyfx2Qwrbhta9ppjcPYAnR1b+R/N6LDZkbWlQ1xdarZYjR47UWqad+ubXo3GExWTgoFLwVgU7bauDrculLpBkYhprkMuSSZ1p4qjibGIOy/Zcqvf73yy61ZI+LjX0TPnHGtwKDIbshC7+VV5rfXgCUSl5uDmoeGhwiwrPK3UXSM0tpo2PM4tuKZ8+8+zVHOavPYEQcH+/IO7vH2xWe0op3fBV6v9bEQ31XAxt64ODSkFCViERCTn1eu+aUF15uTmqjDP0n+y40CB/ZOuSzgFuLBht8Adf8vcZrqQXGD+zBt1rikeGmJ9J1Kp8ZG0VmUyGu7t7rRmA9UlKbhFvbzLs4F04pm2VPmOWYMtyqSskmZjGGuTi7aLm1Ykd6RbYhNEdfRusHo0dS/rYuNHLRMSCg5fSySzQ4OFkR7+WHpVep0Sr56NrqWgfG9YKV3tVhef+diyerWeTUSlkfHx3d+xVZWeqUnOLefinoxSU6BjY2pPFEztWcKWKuX7Dl76SpeyGei4c7BQMa2eYYd58JrFe710TaiKvGf2D8XJWE5dRyB83zFo2Bh4Z0pI+wR7kl+h4+tcTRhcKa9C9NaVahuznn3/Oli1bboplMHNQKBS0bt3aqqbmzWXJhrPkFGnpEuBmdAqvLWxZLnWFJBPTWItcpnQP4M/HBtC2gYKj3wy61dw+zswvIfbazJGpGdl/Tv3nVlBRqKtS1h6NIz6zEG8XNTMqmT1NyCrkjQ1nAVgwuh2d/MuG5irRGvLYJ2QV0sLLiS+n9zQrUsKNtPNzQa2Uk1OkJSY9v8LzGvK5uKWz7bkX1EReDnYKHhtmmAX8LDSKEm3jmpVVyGV8MK0bLmolx2Iz+X6fYdXJWnRvTaiWIfvVV18xbtw4fH19ad68OVOmTOGNN97gn3/+MeYjvpnQarUcOHDA6qbmq2JHZDL/nEpEIZfxztQuVf4YWIqtyqUukWRiGmuRi0wmMxl0v764GXSruX1cOhvb0ssJN8eyM6ganZ7NZwzRCm7tUnm0giKNjs92GDayzhvRGgc70z/YQgie/+MUucVaejRvwiNDWpY757UNZzgam4mLvZLvZvQqVy9zUSnkdAmo2k+2IZ+LEe19sFPIuZSaz8WUvHq/f3Woqbzu7dscHxc1CVmF/Ho0rpZr1/AEejjy8q2GpDPvb71AVEqu1ejemlAty+XMmTPEx8fz999/8/DDDyOTyfjuu++YOHEizZo1w9+/an+lxoRcLicgIMCY/ccWyCvW8vL6CAAeGtSCzgGVBwWvDrYol7pGkolpJLkYuBl0q7l9XLrRy5RbwYHodLIKNHg529GnReVuBavDrpCSW0xAEwfu6l1xBJvVYXHsvZiGWinnvTu7lftDs+rwFVYdvoJMBp/eHUKrGqb9NPrJVmLINuRz4WKvYnAbQ3KEf08n1fv9q0NN5WWvUvD4NV/ZL3ZGUaRp+JBUtc20XoEMbetNidYQN14vsHnda1GKWvjPv8nf3x9/f38mTJhg/CwjI4OjR48aExrcLMjlcmN2MVvh/S3nScwuItDDgfmj2tbJPWxRLnWNJBPTSHK5eXSruT+Y/230Kv8nu3ST19hOlbsVFGl0fL07GoC5w1tVmKYzPrOAt/4xuBQ8O7ZdOSP1WGwGr/5t+OP/zJh2DG/vY1YbKsOY4auSEFwN/Vzc0tmPHedS+DcikadGtWmwephLbcjrrt6BfLUrmsTsItYeiWNGLbvcNTQymYx3b+/CmI/2cDIui+/3xxpdKmyVWo1a4OHhwZgxY3juuedqVClbQ6vVsmfPHpuZmj8Vn8WPBy8D8NaULhUutdUUW5NLfSDJxDSSXG4e3WpOHwshjDFWb5yR1euFMVj62E5+lV7nt6NxJOcU09TNnjt6ms5UqL8Wci2/REfvYHdmDSwb0SA5p4hHfz6ORicY38WPubX0o9/9mt9v5NWcCjPKNfRzMbqjL0q5jHNJuVxOq9iX11qoDXnZqxQ8PsIwK/vlrsY5K9vUzYFXJxpiZ3+47Tyr/tlp07rXYkP233//xc2t9pehbRm5XE6rVq1sYmpepxe8sj4CIQx5xodYEPvQUmxJLvWFJBPTSHK5eXSrOX0cn1lIRn4JKoWsXJKBE/FZpOYW46JW0q9lxUkQirU6vtxlmI19bFjFs7Grj1zhQHQ69io5791R1qWgdHNXam4x7XxdeO+ObrW2uzvQwwF3RxUlOr0xe9mNNPRz0cTRzpho4t8I63cvqC15TevVjIAmDiTnFLPq8JVaqp11cXuPAEa290GjE/x0XmDLeSAs7u2xY8eiVqvroi42iy359609EsfJ+Gxc1EpeGt+hTu9lS3KpLySZmEaSy82jW83p4zNXDbOxbX1dyoW/2nY2GYCh7byxU1Z8rd+PxZOYXYSvq5ppvUz7xiZmF/LOJkNSg+fGtifYy6nM52/9c5bjV7JwtVey7IGeOKkt9sarEJlMZtybcOaq6Vit1vBclEYvKHXnsGZqS15qpYK5ww0z78v2XKpwxtyWkckMm7xd7ZWcSynkx4O2a7DfvL8atYhWqyU0NNTqp+Yz8kuMmWieHt0WnypygtcUW5FLfSLJxDSSXG4ezOnjs9dmKE2lfC01ZCuL9Vui1fPlTsNs7KNDW5UzhsHgvvDyugjyirWENG9SzhdyfXgCPx40pKj96K7uBHk6lbtGTel4rX2RiaYNWWt4LsZ09EMmM6TTTcgqbLB6mENtyuuOns3wdVWTlFPEn8cbV7avUnxc7Xn+FkOihA+2nSe2klBw1oxkyNYCcrmczp07W/1s0tLN58gq0NDez4UH+tf9BgJbkUt9IsnENJJcbh7M6eNSw67jDYZsTFo+USl5KOUyhrWreMPVn8fjScgyxI29p09zk+dsOJXIjnMpqBQy/nd71zIuBeeTcnnhz9OAIWTXyA51kyCjo3/lhqw1PBfeLmp6BxkiQ2y/9ifCWqlNeamVCh4ebAjB9tWuaLSNLNtXKXf1DqRXoAtFGj0v/HnaZmIGX4/0q1ELyOVyfHx8rPpH+PiVTNYcMcTFe2NK51qPGWsKW5BLfSPJxDSSXG4ezOnjs9eW2m+ckd121uCn2a+lJ24OpmO4anV6o2/snCEtTc7GZuaXsOTvMwA8MbxNmQQYOUUaHv35GIUaHYPbeNVZVBf4r32RiTkmM3xZy3MxqqPhT8OOcykNWo+qqG15Te/bHA8nO65kFLDxlPW7VlQHhULBB3f3xF4l50B0uk3Gz5V+NWoBjUbDli1b0Gg0DV0Vk5Ru8AK4vUczegdXHnextrB2uTQEkkxMI8nl5qGqPs4u1BiXsG+ckTXHreCf04lcySjA3VHF9L6mZ2Pf2HiW9PwS2vm6lAk9JITgud9OEZOWT0ATBz65O6ROE2S09HLCTiknv0RHXGZBuc+t5bkY0d4g70PR6eQVW6/7T23Ly9FOyYMDgwFDXNnK0gnbKhqNhnNH9zF/pCFSw5v/RJKcU9TAtbKMGhmye/fu5b777qN///4kJBh8SFauXMm+fftqpXK2gkKhoHfv3lab4u2Xw7GcuZqDi72SF8a3r7f7WrtcGgJJJqaR5FKWxqxbq+rjc9eW2QOaOJTJnJWeV8yx2EwARlVgyAoh+OrabOysgS1wtCu/OWvvxVT+DE9AJoN3b+9SZsPYjwcus/lMEiqFjC/u7YGHk51ljbMQpUJOu2uzwWdNbPiylueilbcTQZ6OlOj07LtovemT60Je9/cPxkWt5GJKHlut3LWiOpTK7MGBLejazI3cIi2vXVutsBWqbcj+8ccfjB07FgcHB8LDwykuLgYgNzeXt99+u9YqaAvI5XI8PDwafPnHFGl5xby35TxgCPTt5Vx/u6KtWS4NhSQT00hy+Y/Grlur6uOziaVuBS5ljoeeS0EvoJO/KwFNHEx+d9eFVM4l5eJopzC5D6BIozNmNJzRP5iQ5u7Gz07GZfHWpkgAXhzfge4mMorVBaXtNOUnay3PhUwmY+S1WdkdkdZrzNWFvNwcVDwwwDCWvtgZZZM+pJVRKjM7lZJ3pxp8xf+NSCL0nPX2841Uu7fffPNNvv76a7799ltUqv/+NQ8YMIDjx4/XSuVsBY1Gwz///NPgyz+meH/LeXKLtHTyd+XevvWbIcaa5dJQSDIxjSSX/2jsurWqPq5oo1epW8GoSjZelc7GTu/TnCaO5WdTv9gZRWx6AX6u9jwztp3xeHaBhsdXGZIe3NLJj5n1mM2ptJ1nTRiy1vRcjOxg8JPdeT7FapfY60peDw5sgYNKwemEbPZa8Yx0dbheZh39XZk9yJAQ5JX1ZygosV43kuuptiF7/vx5hgwZUu64q6srWVlZNamTzaFUKhk8eDBKZe3FGKwNIhKyWXvNcXvJpE516utlCmuVS0MiycQ0klz+o7Hr1qr6+L8Z2f8M2SKNzmhAVOQfeyw2g7CYDFQKGbMHtyj3eVRKrjFd7WuTOuJ8LSasEIJnfz9JfGYhgR4O/O+OrrWW9MAc/tvwVT4pgjU9F72DPXBRK0nLK+FkfFZDV8ckdSUvT2c1d/cxxCJetudSrV67oblRZvNHtSGgiQMJWYV8suNiA9fOPKptyDZt2pSoqKhyx/ft20fLli1rVClbQyaT4erqWq/KryqEELy+8SxCwMRu/vSqpw1e12ONcmloJJmYRpLLfzR23VpZH2t1ei4k5wH/haYC2B+VRqFGR0ATBzr5l48tC/DVLoOBcVtIAE3dyroeCCF4aV0EGp1gZHufMqltVxy4zNazydgp5HwxvUeF0RDqig7X2pOQVUh2QdmZRGt6LuyUcmMmyFArjV5Ql/KaPagFCrmMfVFpRCRk1/r1G4obZeZop2TJJEP62u/3xnAuyXRoOGui2obsnDlzeOqppzh8+DAymYyrV6/yyy+/8MwzzzB37tzarKPVo9Fo+Ouvv6xi+aeUfyOSCIvJwF4l5/lx9bfB63qsUS4NjSQT00hy+Y/Grlsr6+NLafmUaPU42SkIdHc0Ht953mA4jWjvY9JIuZCcy/bIZGQymDO0VbnPfz8Wz+Fr+vC1SZ2M1zhzNduY2euF8e3p2qxJTZpWLVztVTRzNxjeN7oXWNtzUepesD3SOg3ZupRXM3dHJnRpCsC3exvPrKwpmY3q6MuYjr5o9YIX/zxtta4kpVR7/v25554jOzub4cOHU1RUxJAhQ1Cr1TzzzDM88cQTtVlHq0epVDJmzBirWP4BwzLc29c2LTwypFWFGyPqGmuTizUgycQ0klz+o7Hr1sr6uHTnfvumrsivuUIJIdh1PhWAYe28TX7vm90Gw+KWTn608nYu81lWQYlRH84f1ZZAD4OBXFCiZd7qcEp0ekZ18K1Xv9gb6dDUlfjMQiITc+jfytN43Nqei2HtfJDJDH7MV7MK8W+g35aKqGt5PTKkJX+fvMrGU4k8O7Ydza77s2WrVCSz1yZ1Yn9UGsevZLH2aFyFiUWsgRpt7XvrrbdIS0sjLCyMQ4cOkZqayhtvvFFbdbMprEXRAHy/L4b4zEL8XO15dGjDLkVak1ysBUkmppHk8h83q241tdErOjWf+MxC7BTyMkZeKck5Rfx90hCizNRs7HtbzpNZoKGdr4txIwvAq3+d4VJqPn6u9rxXz36xN1LZhi9rei48nOzocS3Sg7UmR6hLeXUOcGNga090esEP+y7X2X3qG1My82/iwNOjDclADFlBS+q7WmZT4xgVjo6O9OrViz59+uDs7Fz1FxohWq2WTZs2WUWe+OScIr7YafCve35ce5NxFOsLa5KLtSDJxDSSXMrTWHVrZX1saqPXrmtuBX1bepjUZz8dvIxGJ+gd7F4uZNbp+GxWhV0B4PXJnVBdy2j414kEfjsWj0wGH93VHfc6jhdbFddn+Loea3wuSt0LQq0wDFd9yOuRIYY/S2uOXCnn02yLVCazGQOCaevrTGaBxhjG0xqptpXz+uuvV/r54sWLq3tpm0OpVDJ+/Hir+Oe8dPN5Ckp0hDRvwuTu/g1aF2uSi7UgycQ0klz+o7Hr1sr62Dgje92Grt0XDG4FQ9uWdysoKNHyy2GDoTp7UNnVJ71e8MpfEQgBU7r707elYTY3LqOAl9cZYsnOG97a5CxvfVO6ge1ich4and5ocFvjczGyvS9LN59nf3Q6BSXaBp0suZH6kNeQNl6093PhXFIuPx+O5fHhrevsXvVBZTJTKeS8Prkzdy87xKqwK9zduzldmrk1QC0rp9q9vW7dujLvNRoNMTExKJVKWrVqZfPK1lK0Wm2DK5uTcVn8cTwegFcndrKKna7WIBdrQ5KJaSS5GLhZdWtKbhFpeSXIZRizXRWUaDl8KQMw+GfeyB/HE8gq0NDcw7FcWK7fjsVxIi4LZ7WSF8d3AAxREeavPUFusZZeQe48ObJNHbfKPJq5O+CiVpJbrCU6NY/2fv8Z8tb2XLT1dTaGZzp8KYPh7cv3S0NS1/KSyWTMGdqSp9eeZPn+yzw0uAVqpW1nJKxMZv1aejK5uz9/nbjKK39F8OdjA4z+69ZCtV0LwsPDy7wiIiJITExk5MiRPP3007VZR6tHq9WydevWBl3+EULw1j+GDQ1TQwLqLStNZViDXKwNSSamkeTyH3WhW/fs2cPEiRPx9/dHJpOxfv36Cs+dM2cOMpmMjz/+uMzx4uJi5s2bh5eXF05OTkyaNIn4+HiL61JRH5fGUW3h5YSDncEwOBidTolOTzN3B1p5O5U5X68X/LAvBoAHBwaXiZOdVVDC/zYblkLnj2qDj6s9AF/uiuZYbCYuaiUf3dUdpcI6MsnJZDKT7gXW+FzIZDKGtPUC/psttxbqS163dvWnqZs9aXnFbDiZWKf3qmvMkdmL4zvgZKfgRFwWvx+z/Jmva2r1KXZ1deX111/nlVdeqc3LWj0qlYrJkyeXycJT32yPTCHscgZqpZxnb2lX9RfqAWuQi7UhycQ0klwqp6a6NT8/n27duvH5559Xet769es5fPgw/v7l3ZLmz5/PunXrWLNmDfv27SMvL49bb70VnU5nUV0q6uPSiAVl/WP/i1Zw4wpT6LkUYtLycbFXcmevwDKffbD1Ahn5JbT1dWbGtWgE4VcyjQHeX5/SyRi9wFooTVVbKgew3udiSBuDm8eei9ZlyNaXvFQKOQ/0Dwbgh30xNp221hyZ+braM3+UYePXu5vPWZ1vcK3/Hc3KyiI7u/EECzYHIQQ5OTkNNpi1Oj3v/muYjZ09qEW5YOANRUPLxRqRZGIaSS5VUxPdOm7cON58802mTp1a4TkJCQk88cQT/PLLL+V+1LKzs/n+++/54IMPGDVqFCEhIfz888+cPn2a7du3W1SXivo48oaNXkIIdl0wbPQa1rb88nVpLM/pfZvjpP5vWTQyMYdfDscChhBCKoWc/GIt89eeQKcXTOzmz5TuARbVuT4wleHLWp+LAa29UMhlXErNJz6zoKGrY6Q+5XVPn0DsVXLOJuYQFpNR5/erK8yV2cyBwbTxcSYjv4SPd1yop9qZR7UdST799NMy74UQJCYmsnLlSm655ZYaV8yW0Gq17N27lzFjxjTIP+dfj8YTnZqPu6OKR4eVDz/TUDS0XKwRSSamkeTyHw2hW/V6Pffffz/PPvssnTp1Kvf5sWPH0Gg0jBkzxnjM39+fzp07c+DAAcaOHWv2vSp2LSi70etSWj5xGYawWwNal92QdTo+m8MxGSjlsjLxX4UQvL7hLHoBE7o0ZUArwxL4kg1niE0vwN/NnjendLaK/QM3UtruyESDUSGTyaz2uXBzUNE9sAnHYjPZcyGN6X2tI8ZofcqriaMdU3s0Y9XhK/ywP8a4mdDWMFdmKoWcVyd24r7vD/PTwVim92lOm2u+7A1NtQ3Zjz76qMx7uVyOt7c3M2bM4IUXXqhxxWwJlUrFhAkTGuTe+cVaPtpu+Hf05Mg2uNpbj7JrSLlYK5JMTCPJ5T8aQrf+73//Q6lU8uSTT5r8PCkpCTs7O9zd3csc9/X1JSkpyeR3iouLKS4uNr7PyTEYqnK5YSGw1CVBoVBQUKzhUlo+AG28HdHpdEa3gt4t3HG0U6LVapHL5cjlcr7fZ5iNndC1KV6OSvR6PXK5nH9OJnDwUjpqpZxnRrdGCMHWs8n8etQQauuDad1wvParJ4RAq9WiUqnQ6/XodDpjWa/Xo1QqKyzrdDqEEMZyaTsqKmu1WmQymbFc2o7ryy09HZDLID2/hKuZ+TRt4ohKpSoTrF6j0RjL12/QKW1HfbZpUCsPjsVmsvdiKtN6+pts0/VljUaDQqEwlpVKJTKZrFbbpFKpGDduHHq93jjGarufri/f18dgyG47m0xMSg7B3i613qa6HnsqlYqxY8can8vK+mlga09Gd/Rl29lkXt94lh9n9TbWvbbbZAnVdi2IiYkp84qOjubQoUO8/fbbuLhYh5VeX+j1ejIyMowPT33y3d4YUnOLCfJ05N6+QfV+/8poSLlYK5JMTCPJ5T/qW7ceO3aMTz75hBUrVlg8U1k6c2iKd955Bzc3N+MrMNDgxxoRYQh9FRkZSWSkwSVqy4FwdHqBq72Sq1FniYmJMcaP7eZj+HN+4MABEhMTScsrZuPJqwDMGtiC0NBQsrKyKNLoeHXdSQDmDGnJqYM7SUjP4YU/TwEwe2Aw3f2d2LRpEwC5ubls3boVMLhthIaGApCWlsaePXsASExM5MCBAwDExcURFhYGGPooPDwcgIsXL3Lq1KlybTp16hQXLxp8csPDw4mJMWxMCwsLIy4urkybAMIO7ifATQ3Ab1v2kpWVhV6vZ8uWLcY/AZs2baKoqKhM7M+ioqIGaZOvMCyn74tK4+ChwybbtGfPHtLS0gCM/QSwdetWcnNza71Ner2ec+fO1Wk/Xd+muIgw+gW7oRfw5tq9ddKmmvZTVW3S6/Xs3LmTlJQUs/pp0Zg2KGSCvRfT2Hw6oU7bZDZCohzZ2dkCENnZ2WadX1JSIjZv3ixKSkrquGZlSckpEh1e+VcELdooNp68Wq/3NoeGkos1I8nENLYqF0t1hTUAiHXr1hnff/TRR0ImkwmFQmF8AUIul4ugoCAhhBA7duwQgMjIyChzra5du4rFixebvE9RUZHIzs42vuLi4gQgkpOThRBCaLVaodVqhRBCrDseJ4IWbRRTv9wvNBqNyC0oFm1e2iSCFm0U565mCSGE0Gg0QqfTiU+3XxBBizaKSZ/tFUIYxo5OpxOfh14UQYs2ir5vbRf5xRpRXFwsHvnpiAhatFGM/mCXKCzWCL1ebxxj15d1Ol2ZskajqbSs1WrLlEvbUVFZo9GUKet0OpPlh1aEiaBFG8V3e6KMdfr3339FcXGxsa16vd5Y9+vL9d2mouIS0fW1LSJo0UZxODqlwjaVlkv76fp21HabSuVVUFBQp/10fTu2n00UQYs2is6vbha5hSVW109VtalUZkVFRWb301sbI0TQoo1i6NJQkVdQVCdtskS3Vtu1YMGCBWaf++GHH1b3NjZB6dR8ffPx9gsUlOjoFtiE8V386v3+VdFQcrFmJJmYRpLLf9S3br3//vsZNWpUmWNjx47l/vvvZ9asWQD07NkTlUrFtm3bmDZtGmCYXYmIiGDp0qUmr6tWq1Gr1eWO29sbQmEpFP/F3ryUanAraOvrjFKp5Gh0CiVaPQFNHGh7LaaqUqlEo9Pz87WNXDMHBgOGsWMqo+Gfx+PZciYZlULGR3d3x/5a4P5SP0CZTGYsly63mlu+vu7mlK+P0VlZuY2vC9siU7iUVmC83/V+0df7MJoq12eb1HYqBrX24p/TieyLzqRPS+9K21dV3WurTdfLq6766fo6Dm/nS0svJy6l5fNneAIP9A+2qn6qqh2WjrH/t3fmcVFV/R//zM4OAgKCLALmEoi4JpphbvkoZlmWS6ZZv6zUfLS0zZbnqTR7TMserXzMtCxa1HIXXFEpkVVQUkCQRZB932bmnt8fl7kyMsAM3GG283695vU6c++de8/5nLnf+c653/M9ALBi0gDsTypETlk9frxcgBfG++ulTdrSZUc2KSkJiYmJUCgUGDCATfd048YNiEQiDBs2jDtOl0dVMTEx+PTTT5GQkIDCwkIcOHAAs2bN0njsiy++iG+++QabN2/GypUrue1NTU147bXX8NNPP6GhoQETJ07Etm3b0Ldv3y61UxsYhkFpaSlcXV25jtE3mcW1iLzMPiJ4a9pAo5y8YAhdjB2qiWaoLnfRh22tra1FZmYm9z47OxvJyclwdnaGj48PXFzUJ6pIJBJ4eHhw13d0dMSSJUuwevVquLi4wNnZGa+99hqCg4PbOMGdoSl8JKO4FgAQ6MaGTlzMZB/djgt0VWvniatFuFPdBFc7Kf4R3IfbrlrRcFjLioa3Kxvw3h9XAQArJ92H+z2NbzUiTdzXMnlGpYex3xfj72Md2ZgbJVg1+T5DV8cgegmFAiwa64d3/7iKXRdzsGC0r9EtGNARXdHMTibGmkcGYM1vV/DFqQw8NswLrnZt/7T2FF3u6YiICDz00EPIz89HYmIiEhMTkZeXhwkTJmDGjBk4c+YMzpw5w8VJaIMx5TrUBYZhkJaW1qPxfRuP/w0lQzBpkLvRzpY0hC7GDtVEM1SXu+jDtsbHxyM0NBShoaEA2FHf0NBQnVYJ27x5M2bNmoU5c+Zg7NixsLGxwaFDh3QeQenIke3vZgcAuJhZBgAY299V7bjdsTkAgHmjfLjVlNIKqrgVDd+NYDMurPntCmqaFAj1ccKL49WXrjVmAlvan9nKkTXm+2J8y7LBV/IrUVnfbODaGE6v2cP6wl4mRnZpHS5mlfbotbtLVzV7YlhfBHs5oqZJgS0nDZyOq9Pgg3bw9PQkaWlpbbanpqaSPn36dPW0HLgnjktFfn4+8fLyImlpacTX15ds3ryZ21dZWUkkEgmJjIzkthUUFBChUEiOHz+u9bWNPe4tPqec+K49TPzfPEIy7lQbujoUisWiD1uhb9tqKNrTqkmuJAFvHiG+aw+T25X1pLSmkfiuPUx81x4mJTWN3HFpBZXEd+1hEvDmEVJU1UAIYePynvo6lviuPUxW/JRICCHk+z9ziO/aw2TAO0dJVnFNzzWQB+qbFMTvDbbtpa3absxM2nTWaOdp9CTv/cHGjT6/+7Khq9Jj/JlVqjdfRBfb2uUR2erqaty5c6fN9uLiYm6WG990N9ehvmAYBgUFBT3yL5AQgk9P/A2A/UekehRnjPSkLqYC1UQzVJe7GMK29iT39nFOWR0UDIGdTAwPByvEZrGjsQM97NUeV6pGYx8J8oB7y5Kzp9KL8dfNckjFQrw+dQDyyuux/ig7c3vN1IHw723XAy3iD2upCN692BXHMoprTeK+UI3KxhjBcrWG1GvBA2zWoFPpd1BQ2dDj1+8q3dHsAX82HZeSIfj46N96qJ12dNmRfeyxx7B48WL89ttvyM/PR35+Pn777TcsWbKkw9VjuoM+ch0CbFxtdXW12gu4m+dQqVRqLCsUCiiVSjAMg8zMTC7Rt0Kh4L4UrctyuVytTFpW0lCVCSFtygDUyuczSljDLRJi2cMB3DUZhtFYViqVamVt29RRO7Rtk1KpRGZmJpqamjpsE8MwamVjbpO2/dRemxQKBTIzM7kceubQJj76SXUPqc5vam3iE0PY1p7k3h/MjDuq+Fg7CAQCtfhYFRV1zfgjmU25pVoAQa5k8HGrFQ09Ha2xdt8V1DUrMcrPWW2hBFNCFV6hcmSzsrKM2pF9sCX8IyajxOArkBlSr0A3O4QFuIAhwI8tExJNge5q9ua0gRALBTj9dzF37/Y0XXZkv/rqK0yfPh0LFiyAr68vfH19MX/+fEybNg3btm3js44A9JfrENAt36Gm/GxisRgSiYTLM6evPHqEEGxsMdzzH/CBTFFnkHyH2rZJoVAgLCwMUVFRRp1Hj+9+6qhNJSUlEAgEEIvFZtMmPvpJLBbDxsaGa4eptEllI/ikp21rT9N65jQAZBSz/dbfzQ6EsPkpAfX42F8T8tCkYHC/pwOG+7IDFZFxubhZUgcXWyleDg/Aj3G5iM0qg5VEiI1PDDGpCTetCXRviZO9UwOxWIzx48e30cyYGN3PBVKREIVVjcgpM+xytYbWa+EYdlQ2Mi4PTQr9zcvhk+5q5t/bjhuN/uhIOpSMAf7MdDeOoba2lqSkpJDk5GRSW1vb3dNxoIdyHRLSfr5D1Xk6y8+mVCpJVlYWlwdNX3n0TqSx+eoGvnOUFFc3GjTfoTZtUigUJDs7mzQ2Nhp1Hj2++6mjNsnlcpKVlUWUSqXZtImPflIqleTmzZvc+U2lTeXl5XqLp9eXbTUUqpi3iooKte0v700gvmsPk2/OZZGc0lriu/YwCXzrCKltVOnPkIc2nia+aw+Tny7dYs/V0ExC/xVFfNceJntis0luWR0Z3JJTe+f5mz3dNF75NZ7Nqfv0138SpVJJcnJyuO+5sTLnKzZO+Ye/cgxaD0PrJVcoyeiPThLftYfJ70n5BqmDrvChWVltEwl67zjxXXuY/HI5l5d66T1GVi6XY8KECbhx4wZsbW0xZMgQhISEwNbWljcH+16eeeYZXLlyBcnJydzL09MTr7/+Ok6cOAFAPdehClWuw7CwsHbPLZPJ4ODgoPYC7uYzE4lEGstisRgikQgMw6iFLojFYi6NReuyRCJRK6tGiVVlVR621mWATbMjFImxKYqdGfjcuH7obS+DUChUywWnqSwSidTK2rapo3Zo2yZCCG7fvg2RSKSxTa1zzrUuG3ObOuunztoEsCEwDMOYTZv46CeGYVBYWMjVy9TaxBeGsK09zb2PMDNVoQXudrjQ8mgy1KcXbGWszhezSpFTVg97mRgRIWymmu1ns1Be14yA3rZ4eqQ33thv+iEFKu4NLTD2GFkACAtgR89V8c2GwtB6iUVCzBvtAwDY86dphBfwoZmzrRTLJgQCAP4TdR0NzT07Gt2lsWSJRIK0tDTec5caU65DXRCLxR06ynxw+MptXL9TAwcrMf7vwQC9XosvekIXU4NqohmqC4u+bKsx0fpPnULJ4Gbp3dRbv8az4SSt42P3/pULAHhsmBdsZWIUVTXi2wtsWM0b0wZhf1IBLmaafkiBioAWR7a0tgk1TYxJ3BdhgS7YfBL4K6sMDEMM1gfGYEeeHumNL05lIOFWBa7erjL6HMZ8abZorB/2/HkLBZUN2BWbjZfDA3monXZ0OUZ24cKF2LlzJ591Mapch7qgmtSkr1y1ciWDz6LZ0dgXHwqAo42kk08YB/rWxRShmmiG6nIXfdhWY6J1H98qr4dcSWAjFcHD/m7GgrGB7KDFnepGRKezGRzmj2bj8LacvIEmBYORfr0Q7OWAD4+w8darJw+An6vpj1zbycTwcrIGANwoqjaJ+yKkrxOsJSKU1TXjRrHhMmsYgx1xc7DCI0HsSpvfm8CoLF+aycQirJ7CLoqx/WwWKup6Lq9wlyOim5ub8b///Q/R0dEYMWJEm0dfXVk6MTw8XKdZjzk5OW22WVlZYevWrdi6davO1+8qhBBUVFTAz89PL+f/NT4ft8rq4WonNanHZvrWxRShmmiG6nIXfdhWY6K1jc+4wzo9gW52+PtODSrr5bCTiTGkrxMA4OfLeVAyBCP9emGAhz0yi2vwS8uo7dpHBmLdH1dR06hASF9HLG5ZstYcCHSzQ0FlAzKKayAUG/99IRULMbKfM2JulCA2swwDW5YV7mmMxY4884AvDl8pxMGU23h7+iDYWxnv4BOfms0a6oUd57ORXliNbWcz8fb0wd2voBZ02ZFNS0vjlku8cUN9VQdzfiymCbFYjJEjR+rl3I1yJb44xc5Ufzk8kIsbMwX0qYupQjXRDNXlLuZuW1uHFrROvaWKj33A3xkSkRAKJYOf4tiwAtVo7Mbj18EQYOr97rhT3YToa3cgFgrwyRNDIBYZ3xKuXeU+dzucu1GCrNJ6LIgwjfsiLMCFdWSzyvDcuH4GqYOx2JFR/ZwR0NsWWSV1OJhym/v+GiN8aiYUCrD2kQFYtOsydsfewrNhfujbkhdZn3TZKzpz5gyf9TBplEolMjIy0L9/f95DGH746xaKqhvh6WjFBZGbCvrUxVShmmiG6nIXc7etrR9h3l2a1p7LQTm2JT727PUSFFY1opeNBI8EeSA+pxxR1+5AKAD+b3wAXvw+HgDw8oRAg40A6ov+LQvdZNypwd9//20S90VYABsOculmGRRKxiB/LIzFjggEAswd5YMPj6Tjp7hco3Zk+dbsoft6Y4y/C/68WYbN0RnYNCeEh1p2TLe+aZWVldi0aROef/55vPDCC9i8eTOqqqr4qptJ0dDA/0oeDc1KfHUuCwCwYmJ/WEmM25BpQh+6mDpUE81QXe5iKbZV5cj6udggLrscwF1Hdm9LUvknR3hDJhZiwzF25aCnRnrjx0u5KK1tRn83O7wywTQmv+oCl0u2uNZk7ov7PR1hbyVGTZMCV29XG6wexqLX48P6QioSIq2gGqn5xn3v8qmZQCDAG9MGAgD2J+Xj7yL9fxe67MjGx8cjICAAmzdvRnl5OUpLS/HZZ58hICAAiYmJfNbR6BGJRAgNDeX9H+DeS7dQWtsMb2drzB7el9dz9wT60sWUoZpohupyF3O3rao+VjIEWSWsI6tgCJoUDFztpOjvZoe88nqcbVnydO4oH5xKL0b8rQpYSYQYG+CKfYn5EAiADbOHQCY2v+9MYEvmgqLqJgQMCjKJ+0IkFOABf3ZU1lBpuIzJjjjbSrlJXz9dzjVwbdpHH5qFeDthenAfEMKGA+mbLjuy//znPzFz5kzk5ORg//79OHDgALKzszFjxgysXLmSxyoaP0qlEmlpabzOlGw9GrtsQiAkJhj/pQ9dTB2qiWaoLncxd9uq6uO88no0KxhYSYScQzu6nwsEAgF+TcgHIezjal9nG/wniv0xXDDalys/84Avt8qXueFgJYGHgxUAIOrPKyZzX6jCC2KzDLNUqbHZkbmj2HDAP5IKUNekMHBtNKMvzVZPuQ+ilqVrE26V83rue+nWiOzatWvVAvfFYjHWrFmD+Ph4XipnyahGY/v2ssbjw0xvNJZCoXQNS7GtqrCCgN52uJzD/tA94O8MJUO4fLJPj/LBoSu38XdRDeytxCAAcsrq4eFghdenDjBU1XuE/i3hBblVPZfGqLuoFka4nFOOZoVxL+LQEzzg74x+rraoa1biUMptQ1enR/HvbYcnW54kbzx+XaeMVLrSZUfWwcEBublth8vz8vJgb2/frUqZGiKRCEFB/D3+YUdjbwIAlj9smqOxAP+6mANUE81QXe5i7rZV1cc3WlJvBbjaIuFWBQBgtL8LYjLYSV5ONhJMGNAbm1tyaD8e6oXdsTkAgPdn3m/UKY34QBVeUC92NJn74j53O7jaSdEoZ5CcV9nj1zc2O8JO+vIGAC4Dh7GhT81WTOwPqUiIS9nlXFYSfdBlD+mpp57CkiVL8PPPPyMvLw/5+fmIjIzE888/j7lz5/JZR6NHqVQiKSmJt6F5djS2yeRHY/nWxRygmmiG6nIXc7etqj7ObBmRtbUSo1HOwNmWjY/9OY4djZ011AtHrhQip6wezjYSJOdVQsEQTBnszsUemjOqzAUJmbdN5r4QCAQYwy1X2/PhBcZoR2YP6wuJSICU/CqkFRjfpC99aubpZI0FD7AZG/5zQn+jsl1Ov/Wf//wHAoEACxcuhELBxn5IJBK89NJL2LBhA28VNBWsra15OU+jXImvY9jRWFONjW0NX7qYE1QTzVBdWCzFtma0rABV18T+gI7u54yyumacbFnJ67FQLyz9IYHd5++CY2lFsJOJ8cGj9xumwj2MKrSgoMZ4nDJtCAtwwaGU24jNKsNK/a0M3y7GZkdc7GSYer8HDl8pROTlXHzoFWzoKrVBn5q9PCEAkZdzkZJfhahrdzD1fv7/hOrsJT333HOoqamBVCrF559/joqKCiQnJyMpKQnl5eXYvHkzZDIZ7xU1ZkQiEQYOHMjL0PzeS7koqTH90ViAX13MBaqJZqgulmNbRSIRCCHILqkDABRUsql/HvB3wf7EfCgYghBvJ8TfqkBhVSPc7GXcY8nXptyHPo7G5ajoi4DerCNbXKeA3ITCTUf3cwYAJOdVolHes064sdqRp0eyk74OJt/ucU06Q9+audrJ8NxYdoGMTVHXoWT4H5XV2ZHdvXu3Ws4xGxsbBAcHY8iQIbCx0f8KDsaIQqHA5cuXudGTrtIov5up4JUJgZCKTXs0li9dzAmqiWaoLpZjWxUKBUpqmlDXrIQAwLWWnKOj+vVC5GU2rOCxUE9sO5MJgH08WdOoQLCXI54Z42egWvc8vWwkcLRmH5pm3TFcXlZd6edqC1c7GZoVDK70cP5UY7UjYQEu8HKyRnWjAieuFhm6Omr0hGYvjPeHg5UYN+7U4mBKAe/n19lT0ufMM1NFIBCgV69e3V4+8seW0VgvJ2vMNvHRWIA/XcwJqolmqC6WY1sFAgFulrKjse4OMjTIlXCykaC6QYGbJXWwlohQUSdHWV0z3B1kSM6rhEAAfPRYEERCy/l+CAQC9HO1BcBmajAVBAIBNyqrykbRk9c2RjsiFAq4XPC/JeQbuDbq9IRmjtYSvPgQu3DJ5yczoFDy+4ihS0N+xvYlMTQikQiBgYHdGppvlCuxXZU39mHTH40F+NHF3KCaaIbqwmIJtlUkEiG7xZG1lrIjjqP7OePXlh/4qfe7Y/efOQAA1VPIhQ/4Ykhfp56uqsHxd2XDC3LKjWO1Km0Z1eLIXsruWUfWmO2IKhXVhcxS5FcYzx+TntJsUZgfnG2lyCmrx4Ekfkdlu+Qt3XfffXB2du7wZUkoFArExsZ2a2j+l/g8sxqNBfjRxdygmmiG6sJiCbZVoVBwjmyTgo0XHOrthCNXCgEA1lIRKuvl6GUjQUlNE3rby7DazHLGxsTEICIiAp6enhAIBPj99981HufrzMYD32yZGGcsrF+/HiNHjoS9vT3c3Nwwa9YsXL9+dwUnlSObkFPO++hbRxiDHdm+fTuGDBkCBwcHODg4YMyYMTh27Bi8nW0wxt8FhAD7Evh/vN5V+NZs/fr1EAgEbRZvsZWJ8eJ4fwDA1tOZkPP4vehS1oIPPvgAjo6OvFXC1BEKhfDy8oJQ2LVRVLmSwdcteWOXhgeYxWgs0H1dzBGqiWaoLiyWYFuFQiHnyJbWsMn+m+QMGuRK+LnYcA5tTSP7w7puxmA4mFnO2Lq6OoSEhGDx4sWYPXt2u8f5t0z4MrbQgnPnzuGVV17ByJEjoVAo8Pbbb2PKlCm4du0abG1tMcDdHg5WYlQ3KnCtsLrHRtONwY707dsXGzZsQGBgIAA29v3RRx9FUlIS5ozsiz9vluHXhDwsfzgQQiMIleFTs8uXL+Obb77BkCFDNO5/Zowvdpy/idzyeuxPzMdTLZPgukuXHNmnn34abm5uvFTAHBAKhfD19e3y539PKkBBZQNc7WTc4wdzoLu6mCNUE81QXVgswba2dmSblQwcrSW42JJz1KuXNXLK6mEjFaG+WYlxga6IGNLHkNUFAGRmZqJ///44fPgwPvvsM/z555/w9vbGnj17MHr0aJ3PN23aNEybNq3T4/q1OLLZ3XRk+a7/8ePH1d7v2rULbm5uSEhIwPjx4yEUCjDSzxmn/i5GXHZ5jzqyutoRvrWJiIhQe//RRx9h+/bt+OuvvzDvmUV4V3YV+RUN+Cu7jFsJrafhu80AUFtbi/nz52PHjh348MMPNR5jIxVj6UMB+PBIOraezsRjoX15GbjT+QyWEMOlKwqFAjExMV0amlcyhIuNfeHBfrCSGF9sT1fpji7mCtVEM1QXy7GtTc1y3Cqr494HeTngcg67sldKHjvLvb5ZCYlIgPdn3m8UuqSkpEAgEGDTpk145513kJKSAh8fH7zxxhsAgI8//hh2dnYdvs6fP6/zdb2d2HRr5XXNqKzv+lK1+q5/VRXbb61DXwwRJ9sVO6JPbZRKJSIjI1FXV4cxY8bAWirCjBBPAMCv8Yab9NW6zW+++Sb+97//wdvbu1ttfuWVVzB9+nRMmtRx8uD5o33R216G/IoG3ia+6Twiaykza3VBKBQiICCgS0PzJ64W4WZJHRysxJj/gHmNSHVHF3OFaqIZqovl2NaimibIlQQCAUAIIGxxVL2drZFX3gCJUAA5Q7BknD+3TKuhSUlJgaOjI37++Wf07t0bADBr1ixs374dALB06VLMmTOnw3N4eXnpfF17aylcbSUorZMju7QOoT5S3SsP/dafEIJVq1Zh3LhxCAoK4raPapW5gGFIjzxG74od0Yc2qampGDNmDBobG2FnZ4cDBw5g8ODBAIA5I/rip7hcHE0txAeP3m+QsJnWbXZxcUFhYSHKy8vx1VdfAdC9zZGRkUhMTMTly5c7vba1VISXwwPwwaFr+PJ0BmYP94JM3L0BPJ0dWYYxoczMPYQqxkRXCCH4b0uuxEVj+8FO1uWF1oySrupizlBNNEN1sRzbmtsyA18AgAC4XsROZCqpaQIAyBmCPo5WWP5woIFq2JaUlBRERERwjg4A3Lx5k4uD1NdEPKFQiEB3e5TeLEdOWR1CfXp16Tz6rP+yZctw5coVXLhwQW17kJcjrCXsxL3Mklrc527fpfPrQlfsiD60GTBgAJKTk1FZWYl9+/bh2Wefxblz5zB48GAM9XZCfzc7ZBTX4nBKIeaN5idOVBfubbOXlxeys7O71Oa8vDy8+uqriIqKgpWVlVafmTvKB1+dy8Ltqkb8Ep+PZ7o5iGe5wx88olAocPr0aZ0fi567UYKrt6thIxVhcZiffipnQLqqizlDNdEM1UW/dDRLXi6XY+3atQgODoatrS08PT2xcOFC3L59W+0cTU1NWL58OVxdXWFra4uZM2ciP1/3R4PZJazjyhDASixEcU0TpCIBGuUMVGN270wfDFsj+mOfkpKCMWPGqG1LSkrC0KFDAegvtEChUEDWzD62V62EZkz1X758OQ4ePIgzZ86gb1/1+R0SkRDDfVnHu6fCC7piR/ShjVQqRWBgIEaMGIH169cjJCQEn3/+OQA2hOiJlrkw+xMNE17Qus0qzRITE7vU5oSEBBQXF2P48OEQi8UQi8U4d+4cvvjiC4jFYiiVbVcys5KI8HI46zR/dTYLzYru/Yk3HkthwgiFQgQFBen8WHTbGTY2dt4oH/Sy7dojI2Omq7qYM1QTzVBd9EtHs+Tr6+uRmJiIdevWISQkBBUVFVi5ciVmzpyJ+Ph47riVK1fi0KFDiIyMhIuLC1avXo0ZM2YgISFBpxyUua1yojpYS9BY0wRVUAUBMC7QFf8I5n899q5SVVWFW7duITQ0VG17cnIyVqxYAUB/oQVCoRBD/T1xLj+PW0RCV/RRf0IIli9fjgMHDuDs2bPo16+fxs+M6ueMC5mliMsu7/aomzboakd6qm8JIWhqauLezwr1wifH/0b8rQrcKquDr4utVvXlg3vbrNIsJSUFr776KgDd2jxx4kSkpqaq7Vu8eDEGDhyItWvXtmsbnhrpjS/PZKKgsgH7E/Px9Kiuj0xTR5YHhEKhzjON47LLEZdTDqlIiOcf9NdTzQxLV3Qxd6gmmqG66JeOZsk7OjoiOjpabdvWrVsxatQo5ObmwsfHB1VVVdi5cye+//57bjLHDz/8AG9vb5w8eRJTp07Vui63WjmyFS0TmORK1pU1pgleKlJSUiASiRASEsJtu3XrFioqKrgRLF0fP9fW1iIzM5N7n52djeTkZDg7O8PH5+4PulAoRLCfOxCTx2V6MIb6v/LKK/jxxx/xxx9/wN7eHkVF7LKrjo6OsLa25o4b6ceeMy67DIQQvferrnZEH9q89dZbmDZtGry9vVFTU4PIyEicPXtWLdODu4MVxga64nxGKQ4kFWDlpPu0Pn93ubfNQqEQDQ0NXW6zvb29Wmw0ANja2sLFxaXN9tZYSUR4cbw/PjySjv+ezcTs4X0hEXVtIIMOf/CAXC7HiRMnIJfLtf6MKjZ29vC+8HDULq7E1OiKLuYO1UQzVBfjoqqqCgKBAE5OTgDYx4dyuRxTpkzhjvH09ERQUBBiY2M1nqOpqQnV1dVqLwDILqnljpErCVq7NovH9oOfsxX3OFKhUHCxw+2V5XK5Wlk1aU5VJoS0KQNQKzMMo1ZWPZpmGAaJiYkYOHAgZDIZtz0hIQFOTk7w8/ODUqnk6tteWaFQqJXj4uIQGhrKjYqtWrUKoaGhWLdunVqb5HI58v9OZHUrrUNzc7PObUpJScHAgQMhkUi47fHx8XBycoKPjw/XJqVSqVbuqE3bt29HVVUVwsPD0adPH+71888/q/VNsKcdJCIB7lQ3Iau4Wq/9pFAoIJfLcfz4cTQ0NGjVJpU2UqmU6xtV3/bt27dL3707d+7gmWeewYABAzBx4kT89ddfOHbsGCZNmqTWpkdD2LRy+xPz0dzc3G6b7i3r0k+avnvJycnc90Gl586dO7nvMx/3k6rOnbXpqeFecLWTIq+8AQcS8trUXVuoI8sDIpEII0eO1PrxWlpBFc7dKIFQACx9yDxHYwHddbEEqCaaoboYD42NjXjjjTcwb948ODg4AACKiooglUrRq5f6ZCN3d3duNO5e1q9fD0dHR+7l7e3Nnqu6Se04VViBk5UIyx8ORFJSErKzswEAcXFxyMtjf+BiY2NRWMgulhATE4PSUjb37OnTp1FZWQkAiIqKQk0NG4N79OhRNDY2QqFQ4OjRo1AoFGhsbMTRo0cBADU1NYiKigIAVFZW4vTp0wCA0tJSxMTEAAAKCwsxbNgwpKWlIS8vD3FxcQCAIUOGcJ/NyMjAlStXAADp6elIT08HAFy5cgUZGRkA0KZNAQEBIITg3LlzyM/PByEEp06dwqeffqrWJpFIBCexEiIBm5Is8o9jOrdp+fLlOH36tFqbevfujYqKCrU2ZWdnIykpSas2EUIQFxfHlS9evIicnBwsWrRIrZ/i/ryIwe7sY/M9x2L12k+xsbEQiUTw8fHh2tFZm5YvX47vv/9erZ+GDBmCioqKLn/3du7cic8//xyVlZUoKCjAihUrMGHChDZtEt5Oha1UhNzyBuw40H6bAHS5nzR99x599FGkpaVxbRKJRHjwwQe5z/JxP+3fvx/Tp0/vtE2pyQl4oeWJ9OaodCiUjFqbtEVALCXniw5UV1fD0dERVVVVnCHnk5f3JuBoahFmDfXElqdDO/8AhUIxSvRtK/SBQCDAgQMHMGvWrDb75HI5nnzySeTm5uLs2bNcm3788UcsXrxYLc4PACZPnoyAgAAubU9rmpqa1I6vrq6Gt7c3vFf+AqHMps3xG2cHY85IdoRQIBBAJBJBoVBAKBRCKBS2W5bL5RCJRFxZLBZDIBBwZYAdiWpdlkgkIIRwZYZhoFQquTLDMBCLxe2WlUolCCFqk1lEIlG75e62afKWC8gpq8cPz43A2P5uJtWmTdEZ2H7uJmYP88SnT4SYdT/p2qY3DlzDvsR8PD2yLzbMDjGLNunaT01KYNwnp1FRL8eWp4YiYggbH19XV6e1baUjsjwgl8tx5MgRrR6LZpXU4lgaO4LxUrjxpJfRB7roYilQTTRDdTE8crkcc+bMQXZ2NqKjo9V+PDw8PNDc3IyKigq1zxQXF8Pd3V3j+WQyGbfevOrVHiHejnhiODtiKxaLuZF5sVjMTdxpryyRSNTKqjhMVVkgELQpA1ArC4VCtbLqR7q9skgkUiur6tteuattksvliIqKgq8L6/jnVjSZXJtGtuSTTcqr0ns/yeVyHDt2jHsc3lP91NU2zR7GTpg6mlqERrnSIP2kCutSOb89fT/ZysTcPKEvz2QCAqHOT+aoI8sDYrEYDz74INdBHfG/89kgBJg0yA0DPPSfV8+Q6KKLpUA10QzVxbConNiMjAycPHkSLi4uavuHDx8OiUSiNimssLAQaWlpCAsL6/b1P5gZZBTrzhsbqvsiQLVUbWltJ58wPkK92XCUmyV1KK/r+upk2mBqduQBfxd4OlqhulGB038XG6QOxqDZwjG+cLSWILO4FsfTNIcqdQR1ZHlAIBDAwcGh0xmZJTVN2NeSN+7/xgf0RNUMira6WBJUE81QXfRLbW0tkpOTkZycDODuLPnc3FwoFAo88cQTiI+Px969e6FUKlFUVISioiJuEoqjoyOWLFmC1atX49SpU0hKSsKCBQsQHBzc6ZKUnTF7mBeGejt1s4Xmieq+6Mc5sl3PJWsoetlKEdCbjZNNyq3o5OjuYWp2RCgUYFYoOyprqJyyxqCZvZUEi1py6W87m6nzKofUkeUBuVyOP/74o9PHonv+zEGzgsFQbyeM9OvaCi2mhLa6WBJUE81QXfRLfHy8xlny7777LvLz83Hw4EHk5+dj6NCharPQW2ck2Lx5M2bNmoU5c+Zg7NixsLGxwaFDh7o1QU8mFmLttIHdbp+5orovfJxkANDlXLKGRrUwQsIt/TqypmhHHm8JLzh7vQRltU2dHM0/xqLZojA/2EhFuHq7GmdvlOj0WerI8oBYLMaUKVM6HJqvb1bg+79uAQBeHO9vMv8Yu4M2ulgaVBPNUF30S3h4OJcup/Xru+++g5+fn8Z9hBCEh4dz57CyssLWrVtRVlaG+vp6HDp0iMtE0FWWPxwIN3vzTD/IB6r7ItCdjS/OLauHQml6SxmP8GXjZPXtyJqiHQl0s8eQvo5QMARHUgt7/PrGolkvWynmtyzXu+1MZidHq0MdWZ7o7Evwy+U8VNbL4etigyn3G8+qNfrG0DeHMUI10QzVxbJwtJbghfHmm36QL8RiMTwcrGAlEULBEORXNHT+ISNjWMuIbEp+JeR6dsRN0Y48OpQdlf0j+XYnR+oHY9Hs+Qf9IRUJcTmnAvE52i9rTB1ZHmidV03jfiWD/11g87g9P64fRBYyqaEzXSwRqolmqC6Wx3sRgyET07zBHaG6LxhGCb+WZUxNMU7W39UWTjYSNMoZpBdW6+06pmpHIob0gUDAjljnldf36LWNSTN3Bys8MaIvAOCb8ze1/hx1ZHlALBbjH//4R7v/ao5fLUJ+RQOcbaVcihlLoDNdLBGqiWaoLpaFq50Uj4V2vD49Rf2+8G+ZMGWKcbJCoQDDfPQfJ2uqdsTNwQphAWymkIMpPTsqa2yaLR0fAJFQgNjMMq0/Qx1Znmjv3wwhBN/EsP8snnnAF9ZSyxqBMIZ/ecYG1UQzVBfL4YunQy1ingAfqO6Lfq6qEVnTS8EF9NyEL1O1I6rwgt+TCnSetd9djEkzHxcbzAzx1OkzRuXIxsTEICIiAp6enhAIBPj999+5fXK5HGvXrkVwcDBsbW3h6emJhQsX4vZt9X8vTU1NWL58OVxdXWFra4uZM2ciP1+/aS0UCgWioqI0fhn+ulmOK/lVkImFWDjGV6/1MDY60sVSoZpohupiOUiEAoQFuhq6GiZB6/vClEMLAPTIiKwp25FHgjwgFQuRUVyLv4tqeuy6xqjZS+G6pSc1Kke2rq4OISEh+PLLL9vsq6+vR2JiItatW4fExETs378fN27cwMyZM9WOW7lyJQ4cOIDIyEhcuHABtbW1mDFjBrdqhT6QSCR49NFHuZUsWvNNTBYA4MkRfeFiJ9NbHYyRjnSxVKgmmqG6WA6PD+tj6CqYDK3vC98WRza3h2Mo+SLE2xEioQCFVY24XamfCWumbEccrCR4eAC7/PDvyQU9dl1j1Ow+d3vMHaV9GKZxBEW0MG3aNEybNk3jPkdHR7VVZQBg69atGDVqFHJzc+Hj44Oqqirs3LkT33//PZek+4cffoC3tzdOnjyJqVOn6qXehBDU1NTA3t5e7XHZjTs1OHO9BAIB8Pw4y5ud254ulgzVRDNUF8vhnRlBhq6CydD6vlAtU3u7shFyJQOJyKjGoTrFRirG4D4OSC2oQsKtCng6WfN+DVO3I48O9cTxq0U4lHwba6cO7JHV7oxVs7enD8ZGLY81rTvhHqqqqiAQCODk5AQASEhIgFwux5QpU7hjPD09ERQUpJbYm28UCgXOnz/fZmheFRv7yP0e8GuJb7Ik2tPFkqGaaIbqYjnQPtae1vdFbzsZZGIhlAzR24imvtF3nKyp25EJA91gLxPjdlUj4vUcS6zC1DUDTNiRbWxsxBtvvIF58+bBwYFNFl1UVASpVIpevdRXzXJ3d0dRUfvr9zY1NaG6ulrtBYALR1AqlRrLCoUCSqUSEokEU6dO5Va4USgUKKqsxx8tjwdeeLAfADbOl2EYrqwK6FaVCSFtygDUygzDqJVVX772ykqlUq2sbZtUZVV92yt31CbVbEhVG8yhTd3tJ5FIhKlTp0IikZhNm/joJ9U9JBQKTbJNFO0xpkeYxo5EIsH06dMhkUggFArg48yOyppqeIHKkU3U01K1rfUyRawkIjwSxOaZ76nwAlPXDDBRR1Yul+Ppp58GwzDYtm1bp8cTQjocMl+/fj0cHR25l2q1mrS0NABAeno60tPTAQBXrlxBRkYGACApKQnZ2dlgGAYXL17ErVvsyl2xsbH46tQ1yJUEgU5C9LVmf/hOnz6NyspKAEBUVBRqatiA7qNHj6KxsVEtn1tjYyOOHj0KAKipqUFUVBQAoLKyEqdPnwYAlJaWIiYmBgBQWFjIjTrn5eUhLi4OALumelJSEgAgIyMDV65c0apNABAXF4e8vDyuTYWF7KojMTExKC0t7bRN9fX1KCkpMas2dbefbt++jZiYGDAMYzZt4qOfGIbBpUuXcPPmTZNqk8pGULRH9eeD0jkMw6C8vJzTTOXI3iozbUf26u1q1DfzPwJ4r16miCp7wdHUQjQr9N8Oc9AMxEgBQA4cONBme3NzM5k1axYZMmQIKS0tVdt36tQpAoCUl5erbR8yZAh59913271WY2Mjqaqq4l55eXlq51EoFEShULQpy+VyolAoSHNzMzl27BhpbGwkhBBSW99IQj84QXzXHiYHk/KIUqnk6t66zDCMWplhmDZlQohaWalUqpXlcnmHZYVCoVbW1A5NbVKVVfVtr9xRm5qamsixY8dIXV2d2bSpu/3U2NhIjh07xl3DHNrERz+p7qGGhgaTalN5eTkBQKqqqgilY6qqqgiANnab0j7Nzc3k+PHj3Hf0/YNpxHftYfLxkWsGrlnXeeDjk8R37WHyZxb/34N79TJFFEqGDP93NPFde5icTr+j9+sZq2Yqe6GNbTWpEVm5XI45c+YgIyMDJ0+ehIuLi9r+4cOHQyKRqE0KKywsRFpaGsLCwto9r0wmg4ODg9oLABcqIBKJNJbFYjFEIhEkEgkeeeQRyGRsVoIjacUor5fDy8ka04I9ucel7OOhu2XVKLGqLBAI2pQBqJWFQqFaWZXEuL2ySCRSK2vbJlVZVd/2yh21SSqV4pFHHoGNjY3ZtKm7/SSTyfDII49w1zCHNvHRT6p7yMrKyiTbRNEeU36E2dOoQm5Umpn6iCxwd7lafcTJ3quXKSISCvCPYDa84NAV/S+OYA6aGZUjW1tbi+TkZCQnJwNgH+MlJycjNzcXCoUCTzzxBOLj47F3714olUoUFRWhqKgIzc3NANjMBkuWLMHq1atx6tQpJCUlYcGCBQgODuayGOgDhmFQXFwMhmFACMG3F9lHvs+G+UJsYjNL+aS1LhQWqolmqC6WA+1j7bn3vlBlLjDVGFkACPV2AgCk5FXyfm5zsSMzhrALAkRfvYNGuX7j8M1BM6PysuLj4xEaGorQ0FAAwKpVqxAaGop3330X+fn5OHjwIPLz8zF06FD06dOHe7XOSLB582bMmjULc+bMwdixY2FjY4NDhw7pdeSEYRikpaWBYRj8mVWGv4tqYCMV4akRPnq7pinQWhcKC9VEM1QXy4H2sfbce1+0nuxFenj1J74Y2uLIJudV8t4Gc7EjI3x7wcPBCjVNCsTcKNHrtcxBMwEx1btBj1RXV8PR0RFVVVVcmIG2PL/7Mk6mF2PhGF/861GaL5FCMWe6YyssDapV92mUKzFw3XEAQOK6yXC2lRq4RrrT0KxE0PsnoGQIYt94WC/5ZM2Bfx26hm8vZmNmiCe+mBtq6Or0OLrYC6MakTVVGIZBQUEBsoprcOrvYgDAojA/w1bKCFDpYsr/9PiGaqIZqovlQPtYe+69L6wkIng4sHHkphpeYC0VYaCHPQB2VJZPzMmOzAhhV8A7mX4HDc36Cy8wB82oI8sDDMMgKysLu2NzQAgwcaAb/HvbGbpaBkeliynfIHxDNdEM1cVyoH2sPZrui7sTvuoMVa1u0zq8gE/MyY6EejvBy8ka9c1KnLlerLfrmINm1JHlAbFYjJCRY/BbIpvA+Llx/QxcI+NALBZj/Pjx3CxvCtWkPagulgPtY+3RdF/4tEz4yjPREVmglSObW8nrec3JjggEAswYwo7KHtZj9gJz0Iw6sjzAMAy+jr6C+mYlBrjbIyzApfMPWQAMw+DWrVsm/U+Pb6gmmqG6WA60j7VH031hDim4VI5sakEVFEr+vg/mZkdU2QtO/12Muib9LCFrDppRR5YHmuUK/JLEDv0/N86vw1XELAlziL3hG6qJZqgulgPtY+3RdF+YQwqugN52sJeJ0SBX4vqdGt7Oa252JMjLAb4uNmiUMziZfkcv1zAHzagjywNnM8pQ2sDA2VbKLS9HYR9ZhIWFmfQjC76hmmiG6mI50D7WHk33hbez6TuyQqEAQ7wdAQApeVW8ndfc7Ih6eEGhXq5hDppRR5YHdl5gF0CYO9IbVhK60o8KpVKJzMxMKJX6TehsSlBNNEN1sRxoH2uPpvvCt8WRLapu1HuyfH1yd8IXfyt8maMdUYUXnLtRglo9hBeYg2bUke0meeX1SMythEgAzBvV19DVMSoIIaioqDDZxN36gGqiGaqL5UD7WHs03RfOtlLYSkUgBMivaDBg7brHUG92qVo+MxeYox0Z6GEPf1dbNCsYnP6b/+wF5qAZdWS7ibezDc69Ho7PnhoKL2eacqs1YrEYI0eONOlHFnxDNdEM1cVyoH2sPZruC4FAAB8XWwCmnbkgpCW0IKO4FjWNcl7OaY52RCAQYFqwBwDgWCr/4QXmoBl1ZHmgj4MMA6xqTHpoXh8olUr8/fffVJdWUE00Q3WxHGgfa09794WPM7salinnknWzt4KXkzUIAVLz+YmTNVc7Mi2IjZM9c70Y9c38hheYg2bUkeWJhgbTfcSjT6gubaGaaIbqQqG0RdN94dsyIptbbtr3jCpONonH8AJztCP3ezrA29kajXIGZ6+X8H5+U9eMOrI8IBKJEBoaCpGITvRqDdWlLVQTzVBd9EtMTAwiIiLg6ekJgUCA33//XW0/IQTvv/8+PD09YW1tjfDwcFy9elXtmKamJixfvhyurq6wtbXFzJkzkZ+fr3NdaB9rT3v3xd3MBaY7Igvwv8KXudoRgUCAf7SMyh5LK+L13OagGXVkeUCpVCItLc2kh+b1AdWlLVQTzVBd9EtdXR1CQkLw5Zdfaty/ceNGfPbZZ/jyyy9x+fJleHh4YPLkyaipuZvjc+XKlThw4AAiIyNx4cIF1NbWYsaMGTr3Ge1j7WnvvvA1gxRcADDUxwkA68jyMdnInO3ItGDWkT2dfofXbBXmoJnpRvdSKBQKRSumTZuGadOmadxHCMGWLVvw9ttv4/HHHwcA7N69G+7u7vjxxx/x4osvoqqqCjt37sT333+PSZMmAQB++OEHeHt74+TJk5g6dWqPtYVyd3Wv3PJ6EEJMdhGeIE9HiIQClNQ04XZVI7ycrA1dJaMlpK8jPB2tcLuqETE3SjDlfg9DV8looCOyPCASiRAUFGTSQ/P6gOrSFqqJZqguhiM7OxtFRUWYMmUKt00mk+Ghhx5CbGwsACAhIQFyuVztGE9PTwQFBXHHaAvtY+1p777w6mUNoQBolDMoqWkyUO26j7VUhAHu9gCAKzyEF5izHWGzF/AfXmAOmtERWQ2oHnFUV1drdbxqaN7Uvwx8Q3VpC9VEM6aqi8pGmHIOxqIi9kfR3d1dbbu7uztu3brFHSOVStGrV682x6g+fy9NTU1oarrrZFVVsTPTy8rKANwNMRCJRGplhUIBgUDAlYVCIYRCYbtluVwOkUjElcViMQQCAVcGAIVCoVaWSCQghHBlhmGgVCq5MsMwEIvF7ZaVSiUIIVxZUzv4aBMhBFeuXEFwcDDEYrFam9xkStyuakJaThFCvOxNpk339lN/JwHScupx+UYBRnlKu9VPAoEAqampGDRoEGQymcHapK/v3ng/G+w4VY/jSTfx1mRfiFsG4rvTJtV3LCgoCBKJxGjup7o6Nv5bG9tKHVkNqOLCvL29DVwTCoViCtTU1MDR0dHQ1egW9z6e1uaRdUfHrF+/Hh988EGb7f7+/l2vJKUNE7cYugb88N4W4D1DV8KEcPvE0DXoGbSxrdSR1YCnpyfy8vJgb2+vVexRdXU1vL29kZeXBwcHhx6ooWlAdWkL1UQzpqoLIQQ1NTXw9PQ0dFW6jIcHG2tXVFSEPn36cNuLi4u5UVoPDw80NzejoqJCbVS2uLgYYWFhGs/75ptvYtWqVdz7yspK+Pr6Ijc31+Sd/p7CVO8LQ0H10h1j1UwX20odWQ0IhUL07av7crMODg5G9UUwFqgubaGaaMYUdTF1p6xfv37w8PBAdHQ0QkNDAQDNzc04d+4cPvmEHfYZPnw4JBIJoqOjMWfOHABAYWEh0tLSsHHjRo3nlclkkMlkbbY7OjqaXB8bGlO8LwwJ1Ut3jFEzbW0rdWQpFArFzKmtrUVmZib3Pjs7G8nJyXB2doaPjw9WrlyJjz/+GP3790f//v3x8ccfw8bGBvPmzQPA/qAsWbIEq1evhouLC5ydnfHaa68hODiYy2JAoVAohoA6shQKhWLmxMfHY8KECdx71SP/Z599Ft999x3WrFmDhoYGvPzyy6ioqMDo0aMRFRUFe3t77jObN2+GWCzGnDlz0NDQgIkTJ+K7774zqcl5FArF/KCOLA/IZDK89957Gh+jWTJUl7ZQTTRDddEv4eHhHc7+FQgEeP/99/H++++3e4yVlRW2bt2KrVu3dqkOtI91h2qmG1Qv3TEHzQTElPPGUCgUCoVCoVAsFrogAoVCoVAoFArFJKGOLIVCoVAoFArFJKGOLIVCoVAoFArFJKGOLA9s27YN/fr1g5WVFYYPH47z588bukp6Yf369Rg5ciTs7e3h5uaGWbNm4fr162rHEELw/vvvw9PTE9bW1ggPD8fVq1fVjmlqasLy5cvh6uoKW1tbzJw5E/n5+T3ZFL2xfv16CAQCrFy5kttmqZoUFBRgwYIFcHFxgY2NDYYOHYqEhARuv6XqYqlYip3UFb7sqqXSVZtrafBhj40WQukWkZGRRCKRkB07dpBr166RV199ldja2pJbt24Zumq8M3XqVLJr1y6SlpZGkpOTyfTp04mPjw+pra3ljtmwYQOxt7cn+/btI6mpqeSpp54iffr0IdXV1dwxS5cuJV5eXiQ6OpokJiaSCRMmkJCQEKJQKAzRLN6Ii4sjfn5+ZMiQIeTVV1/ltluiJuXl5cTX15csWrSIXLp0iWRnZ5OTJ0+SzMxM7hhL1MVSsSQ7qSt82VVLpDs215Lgyx4bK9SR7SajRo0iS5cuVds2cOBA8sYbbxioRj1HcXExAUDOnTtHCCGEYRji4eFBNmzYwB3T2NhIHB0dyVdffUUIIaSyspJIJBISGRnJHVNQUECEQiE5fvx4zzaAR2pqakj//v1JdHQ0eeihhzijaqmarF27lowbN67d/Zaqi6ViyXZSV7piVy2R7thcS4MPe2zM0NCCbtDc3IyEhARMmTJFbfuUKVMQGxtroFr1HFVVVQAAZ2dnAOxqQUVFRWp6yGQyPPTQQ5weCQkJkMvlasd4enoiKCjIpDV75ZVXMH369DarHFmqJgcPHsSIESPw5JNPws3NDaGhodixYwe331J1sUQs3U7qSlfsqiXSHZtrafBhj40Z6sh2g9LSUiiVSri7u6ttd3d3R1FRkYFq1TMQQrBq1SqMGzcOQUFBAMC1uSM9ioqKIJVK0atXr3aPMTUiIyORmJiI9evXt9lnqZrcvHkT27dvR//+/XHixAksXboUK1aswJ49ewBYri6WiCXbSV3pql21NLprcy0NPuyxMUNX9uIBgUCg9p4Q0mabubFs2TJcuXIFFy5caLOvK3qYqmZ5eXl49dVXERUVBSsrq3aPsyRNAIBhGIwYMQIff/wxACA0NBRXr17F9u3bsXDhQu44S9PFkrFEO6krfNtVc0SfNtdc0ac9NgboiGw3cHV1hUgkavOPpbi4uM0/G3Ni+fLlOHjwIM6cOYO+ffty2z08PACgQz08PDzQ3NyMioqKdo8xJRISElBcXIzhw4dDLBZDLBbj3Llz+OKLLyAWi7k2WZImANCnTx8MHjxYbdugQYOQm5sLwDK/K5aKpdpJXemOXbUk+LC5lgYf9tiYoY5sN5BKpRg+fDiio6PVtkdHRyMsLMxAtdIfhBAsW7YM+/fvx+nTp9GvXz+1/f369YOHh4eaHs3NzTh37hynx/DhwyGRSNSOKSwsRFpamklqNnHiRKSmpiI5OZl7jRgxAvPnz0dycjL8/f0tThMAGDt2bJsUQjdu3ICvry8Ay/yuWCqWZid1hQ+7aknwYXMtDT7ssVFjgAlmZoUqrczOnTvJtWvXyMqVK4mtrS3JyckxdNV456WXXiKOjo7k7NmzpLCwkHvV19dzx2zYsIE4OjqS/fv3k9TUVDJ37lyNKZX69u1LTp48SRITE8nDDz9sVimVWs+gJcQyNYmLiyNisZh89NFHJCMjg+zdu5fY2NiQH374gTvGEnWxVCzJTuoKX3bVkumKzbUk+LLHxgp1ZHngv//9L/H19SVSqZQMGzaMS5tibgDQ+Nq1axd3DMMw5L333iMeHh5EJpOR8ePHk9TUVLXzNDQ0kGXLlhFnZ2dibW1NZsyYQXJzc3u4NfrjXqNqqZocOnSIBAUFEZlMRgYOHEi++eYbtf2WqoulYil2Ulf4squWTFdsrqXBhz02VgSEEGKYsWAKhUKhUCgUCqXr0BhZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1ZCoVCoVAoFIpJQh1Zit4IDw/HypUrDV2NduG7fsba3vDwcAgEAggEAiQnJ+vl/N1p96JFi7j6/f7777zVi0KhtI+52j9927uOoLbMMFBH1kyJjY2FSCTCI488YuiqWAz79+/Hv//9b+69sRh2AHjhhRdQWFiIoKCgHrvmokWL8MYbb3R63Oeff47CwsIeqBGFYtpERERg0qRJGvf9+eefEAgESExM7OFasbS2f4a2fXzbO2rLjBvqyJop3377LZYvX44LFy4gNzfX0NXpMs3NzYaugtY4OzvD3t7e0NXQiI2NDTw8PCAWizXu51tnhmFw5MgRPProo50e6+joCA8PD16vT6GYI0uWLMHp06dx69atNvu+/fZbDB06FMOGDTNAzYzL/nVm73SB2jLjhzqyZkhdXR1++eUXvPTSS5gxYwa+++47tf3h4eFYsWIF1qxZA2dnZ3h4eOD9999XO6ampgbz58+Hra0t+vTpg82bN7f5l+3n54ctW7aofW7o0KFtzqXi+PHjGDduHJycnODi4oIZM2YgKyurTd2WLVuGVatWwdXVFZMnT25znq+//hpeXl5gGEZt+8yZM/Hss88CAAgh2LhxI/z9/WFtbY2QkBD89ttv7YsGoKmpCStWrICbmxusrKwwbtw4XL58mdvPMAw++eQTBAYGQiaTwcfHBx999JFa3VX6LFq0COfOncPnn3/OPWr617/+BRcXFzQ1Naldd/bs2Vi4cGGHdVu2bBnGjRuncZ+fn59aPbShPZ0766O6ujosXLgQdnZ26NOnDzZt2qTx/BcvXoRQKMTo0aMBAL/99huCg4NhbW0NFxcXTJo0CXV1dTrVmUKxdGbMmAE3N7c2Nr2+vh4///wzlixZAkB3+9eZ7QO0t3+abF9OTg727Nmjs/1zc3PD//73P7Vtly9fhkwma/Pb0Rnh4eFYvnw5Vq5ciV69esHd3R3ffPMN6urqsHjxYtjb2yMgIADHjh1T+xy1ZcYPdWTNkJ9//hkDBgzAgAEDsGDBAuzatQuEELVjdu/eDVtbW1y6dAkbN27Ev/71L0RHR3P7V61ahYsXL+LgwYOIjo7G+fPnu/3Iqq6uDqtWrcLly5dx6tQpCIVCPPbYY20c0t27d0MsFuPixYv4+uuv25znySefRGlpKc6cOcNtq6iowIkTJzB//nwAwDvvvINdu3Zh+/btuHr1Kv75z39iwYIFOHfuXLv1W7NmDfbt24fdu3cjMTERgYGBmDp1KsrLywEAb775Jj755BOsW7cO165dw48//gh3d3eN5/r8888xZswY7hFXYWEhVq9eDaVSiYMHD3LHlZaW4vDhw1i8eHG79bp27Rq2b9+OTz75ROP+QYMGdSkWTJPOnfXR66+/jjNnzuDAgQOIiorC2bNnkZCQ0ObcBw8eREREBIRCIQoLCzF37lw899xzSE9Px9mzZ/H444+3+U5SKJSOEYvFWLhwIb777ju1++fXX39Fc3Nzl+1fZ7YP0N7+abJ93t7eePLJJ3W2f0FBQbh69aratjfffBP/93//h4CAAO2Fa2H37t1wdXVFXFwcli9fjpdeeglPPvkkwsLCkJiYiKlTp+KZZ55BfX099xlqy0wAQjE7wsLCyJYtWwghhMjlcuLq6kqio6O5/Q899BAZN26c2mdGjhxJ1q5dSwghpLq6mkgkEvLrr79y+ysrK4mNjQ159dVXuW2+vr5k8+bNaucJCQkh7733Hned1sffS3FxMQFAUlNT1eo2dOjQTts4c+ZM8txzz3Hvv/76a+Lh4UEUCgWpra0lVlZWJDY2Vu0zS5YsIXPnzlW7lqp+tbW1RCKRkL1793L7m5ubiaenJ9m4cSOprq4mMpmM7Nixo9063dteTe1/6aWXyLRp07j3W7ZsIf7+/oRhmHbPu2jRIjJ69Oh298+bN488+OCDWtdLtU0bnVv3UU1NDZFKpSQyMpLbX1ZWRqytrduc/7777iMHDx4khBCSkJBAAJCcnJwOrwWAHDhwoNM6USiWTHp6OgFATp8+zW0bP348Z9t0tX+d2T5CiM72rz3br6v9W7FiBZkyZQr3/sSJE8TOzo7cuXNHq3rcu731755CoSC2trbkmWee4bYVFhYSAOTPP//ktlFbZvzQEVkz4/r164iLi8PTTz8NgP0H/9RTT+Hbb79VO27IkCFq7/v06YPi4mIAwM2bNyGXyzFq1Chuv6OjIwYMGNCtumVlZWHevHnw9/eHg4MD+vXrBwBtYnhHjBjR6bnmz5+Pffv2cY+p9u7di6effhoikQjXrl1DY2MjJk+eDDs7O+61Z8+edh9HZWVlQS6XY+zYsdw2iUSCUaNGIT09Henp6WhqasLEiRO72nwA7CSEqKgoFBQUAAB27drFzXTVhEKhwL59+zB79mxu24svvoidO3dy72tqamBra6tzXTTp3FEfZWVlobm5GWPGjOGOd3Z2bvO9SE9PR35+PjcpJSQkBBMnTkRwcDCefPJJ7NixAxUVFTrXl0KhAAMHDkRYWBhn07OysnD+/Hk899xzAKCz/evM9gEwmP1rPSJLCMFbb72F119/HW5ubl26fuvfPZFIBBcXFwQHB3PbVCPMqt9CastMg+5HQlOMip07d0KhUMDLy4vbRgiBRCJBRUUFevXqBYA1VK0RCATc42PS8pjkXuNC7nl8IhQK22yTy+Xt1i0iIgLe3t7YsWMHPD09wTAMgoKC2kw00sYpi4iI4ILwR44cifPnz+Ozzz4DAK4dR44cUdMBAGQymcbzddRmgUAAa2vrTuukDaGhoQgJCcGePXswdepUpKam4tChQ+0en5WVhZqaGs7YMgyDX3/9FQ8//DB3zJUrV/D444/rXBdNOnfUR/f2dXscPHgQkydP5jQTiUSIjo5GbGwsoqKisHXrVrz99tu4dOkS5yhTKBTtWbJkCZYtW4b//ve/2LVrF3x9fTknU1f715ntA2Aw+xccHIyCggJUV1fj2LFjyM/Px6pVq7p8fU2/e623qdqr0pDaMtOAjsiaEQqFAnv27MGmTZuQnJzMvVJSUuDr64u9e/dqdZ6AgABIJBLExcVx26qrq5GRkaF2XO/evdVSjVRXVyM7O1vjOcvKypCeno533nkHEydOxKBBg7r1T9ba2hqPP/449u7di59++gn33Xcfhg8fDgAYPHgwZDIZcnNzERgYqPby9vbWeL7AwEBIpVJcuHCB2yaXyxEfH49Bgwahf//+sLa2xqlTp7Suo1QqhVKpbLP9+eefx65du/Dtt99i0qRJ7dYJACorKwEAdnZ2AIATJ06goqICUqkUABAXF4dbt25h1qxZWterPTrro8DAQEgkEvz111/ctoqKCty4cUPtPH/88Qdmzpyptk0gEGDs2LH44IMPkJSUBKlUigMHDnS7zhSKJTJnzhyIRCL8+OOP2L17NxYvXsw5Ybrav85sHwCd7V97tg/Qzf4FBQVBIBAgJSUF69atw3vvvcfZwp6A2jLTgI7ImhGHDx9GRUUFlixZAkdHR7V9TzzxBHbu3Illy5Z1eh57e3s8++yzeP311+Hs7Aw3Nze89957EAqFav/aH374YXz33XeIiIhAr169sG7dOohEIo3n7NWrF1xcXPDNN9+gT58+yM3N1SovX0fMnz8fERERuHr1KhYsWKBW/9deew3//Oc/wTAMxo0bh+rqasTGxsLOzo7LbNAaW1tbvPTSS1ybfXx8sHHjRtTX12PJkiWwsrLC2rVrsWbNGkilUowdOxYlJSW4evUqN1P4Xvz8/HDp0iXk5OTAzs4Ozs7OEAqFmD9/Pl577TXs2LEDe/bs6bCNvr6+EAgE+Omnn2Bra4vVq1fjH//4B/744w/4+fnhxRdfxMMPP4zx48d3S0ug8z6ys7PDkiVL8Prrr8PFxQXu7u54++23IRTe/T9cXFyMy5cvqyUDv3TpEk6dOoUpU6bAzc0Nly5dQklJCfcjSaFQdMPOzg5PPfUU3nrrLVRVVWHRokXcPl3tX2e2D4DO9q892wdAJ/tnZ2cHX19frFmzBgAbmtBTUFtmOlBH1ozYuXMnJk2a1MaJBdgUJx9//LHWmQc+++wzLF26FDNmzICDgwPWrFmDvLw8WFlZcce8+eabuHnzJmbMmAFHR0f8+9//bndEVigUIjIyEitWrEBQUBAGDBiAL774AuHh4V1qK8A60s7Ozrh+/TrmzZuntu/f//433NzcsH79ety8eRNOTk4YNmwY3nrrrXbPt2HDBjAMg2eeeQY1NTUYMWIETpw4wYVjrFu3DmKxGO+++y5u376NPn36YOnSpe2e77XXXsOzzz6LwYMHo6GhAdnZ2fDz84ODgwNmz56NI0eOdDqS6uHhgY8++ggbNmzAvn378OGHH2LUqFF49NFH8euvvyIiIgLbtm3TXrQO0KaPPv30U9TW1mLmzJmwt7fH6tWrUVVVxe0/dOgQRo8erRbD5uDggJiYGGzZsgXV1dXw9fXFpk2bMG3aNF7qTaFYIkuWLMHOnTsxZcoU+Pj4qO3T1f51ZvsA3exfe7YPgE72D2DDCw4dOoRffvmFl7yw2kJtmekgINoGvlEsmrq6Onh5eWHTpk3tjkBStGfy5MkYNGgQvvjiC71fKzw8HEOHDm2T81cfzJw5E+PGjeNGUHRBIBDgwIEDvIRJUCgU40Wf9o8ve0dtmelAY2QpGklKSsJPP/2ErKwsJCYmcvkJtVndhNI+5eXliIyMxOnTp/HKK6/02HW3bdsGOzs7pKam6vU648aNw9y5c3X6zNKlS3s07o1CoRiGnrJ/fNg7astMBzoiS9FIUlISnn/+eVy/fh1SqRTDhw/HZ599ppaqhKI7fn5+qKiowLp16/Daa6/1yDULCgrQ0NAAAPDx8eEmihkLxcXFqK6uBsCmgetKKjEKhWL89IT9M6S9o7bMMFBHlkKhUCgUCoViktDQAgqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSUIdWQqFQqFQKBSKSfL/pbXmM1o30OMAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure 4.2\n", "fig, axes = plt.subplots(1, 2, figsize=(7, 3))\n", "\n", "# (a) - single torque curve as function of omega\n", "ax = axes[0]\n", "omega = np.linspace(0, 700, 701)\n", "ax.plot(omega, motor_torque(omega))\n", "ax.set_xlabel(r'Angular velocity $\\omega$ [rad/s]')\n", "ax.set_ylabel('Torque $T$ [Nm]')\n", "ax.grid(True, linestyle='dotted')\n", "\n", "# (b) - torque curves in different gears, as function of velocity\n", "ax = axes[1]\n", "v = np.linspace(0, 70, 71)\n", "alpha = [40, 25, 16, 12, 10]\n", "for gear in range(5):\n", " omega = alpha[gear] * v\n", " T = motor_torque(omega)\n", " plt.plot(v, T, color='#1f77b4', linestyle='solid')\n", "\n", "# Set up the axes and style\n", "ax.axis([0, 70, 100, 200])\n", "ax.grid(True, linestyle='dotted')\n", "\n", "# Add labels\n", "plt.text(11.5, 120, '$n$=1')\n", "ax.text(24, 120, '$n$=2')\n", "ax.text(42.5, 120, '$n$=3')\n", "ax.text(58.5, 120, '$n$=4')\n", "ax.text(58.5, 185, '$n$=5')\n", "ax.set_xlabel('Velocity $v$ [m/s]')\n", "ax.set_ylabel('Torque $T$ [Nm]')\n", "\n", "plt.suptitle('Torque curves for typical car engine')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Input/ouput model for the vehicle system\n", "\n", "We now create an input/output model for the vehicle system that takes the throttle input $u$, the gear and the angle of the road $\\theta$ as input. The output of this model is the current vehicle velocity $v$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "vehicle = ct.NonlinearIOSystem(\n", " vehicle_update, None, name='vehicle',\n", " inputs = ('u', 'gear', 'theta'), outputs = ('v'), states=('v'))\n", "\n", "# Define a function for creating a \"standard\" cruise control plot\n", "def cruise_plot(sys, t, y, label=None, t_hill=None, vref=20, antiwindup=False,\n", " linetype='b-', subplots=None, legend=None):\n", " if subplots is None:\n", " subplots = [None, None]\n", " # Figure out the plot bounds and indices\n", " v_min = vref - 1.2; v_max = vref + 0.5; v_ind = sys.find_output('v')\n", " u_min = 0; u_max = 2 if antiwindup else 1; u_ind = sys.find_output('u')\n", "\n", " # Make sure the upper and lower bounds on v are OK\n", " while max(y[v_ind]) > v_max: v_max += 1\n", " while min(y[v_ind]) < v_min: v_min -= 1\n", "\n", " # Create arrays for return values\n", " subplot_axes = list(subplots)\n", "\n", " # Velocity profile\n", " if subplot_axes[0] is None:\n", " subplot_axes[0] = plt.subplot(2, 1, 1)\n", " else:\n", " plt.sca(subplots[0])\n", " plt.plot(t, y[v_ind], linetype)\n", " plt.plot(t, vref*np.ones(t.shape), 'k-')\n", " if t_hill:\n", " plt.axvline(t_hill, color='k', linestyle='--', label='t hill')\n", " plt.axis([0, t[-1], v_min, v_max])\n", " plt.xlabel('Time $t$ [s]')\n", " plt.ylabel('Velocity $v$ [m/s]')\n", "\n", " # Commanded input profile\n", " if subplot_axes[1] is None:\n", " subplot_axes[1] = plt.subplot(2, 1, 2)\n", " else:\n", " plt.sca(subplots[1])\n", " plt.plot(t, y[u_ind], 'r--' if antiwindup else linetype, label=label)\n", " # Applied input profile\n", " if antiwindup:\n", " plt.plot(t, np.clip(y[u_ind], 0, 1), linetype, label='Applied')\n", " if t_hill:\n", " plt.axvline(t_hill, color='k', linestyle='--')\n", " if legend:\n", " plt.legend(frameon=False)\n", " plt.axis([0, t[-1], u_min, u_max])\n", " plt.xlabel('Time $t$ [s]')\n", " plt.ylabel('Throttle $u$')\n", "\n", " return subplot_axes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## State space controller\n", "\n", "Construct a state space controller with integral action, linearized around an equilibrium point. The controller is constructed around the equilibrium point $(x_d, u_d)$ and includes both feedforward and feedback compensation.\n", "\n", "* Controller inputs - $(x, y, r)$: system states, system output, reference\n", "* Controller state - $z$: integrated error $(y - r)$\n", "* Controller output - $u$: state feedback control\n", "\n", "Note: to make the structure of the controller more clear, we implement this as a \"nonlinear\" input/output module, even though the actual input/output system is linear. This also allows the use of parameters to set the operating point and gains for the controller.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Xeq = [20.]\n", "Ueq = [0.16874874 4. 0. ]\n" ] } ], "source": [ "def sf_update(t, z, u, params={}):\n", " y, r = u[1], u[2]\n", " return y - r\n", "\n", "def sf_output(t, z, u, params={}):\n", " # Get the controller parameters that we need\n", " K = params.get('K', 0)\n", " ki = params.get('ki', 0)\n", " kf = params.get('kf', 0)\n", " xd = params.get('xd', 0)\n", " yd = params.get('yd', 0)\n", " ud = params.get('ud', 0)\n", "\n", " # Get the system state and reference input\n", " x, y, r = u[0], u[1], u[2]\n", "\n", " return ud - K * (x - xd) - ki * z + kf * (r - yd)\n", "\n", "# Create the input/output system for the controller\n", "control_sf = ct.NonlinearIOSystem(\n", " sf_update, sf_output, name='control',\n", " inputs=('x', 'y', 'r'),\n", " outputs=('u'),\n", " states=('z'))\n", "\n", "# Create the closed loop system for the state space controller\n", "cruise_sf = ct.InterconnectedSystem(\n", " [vehicle, control_sf], name='cruise',\n", " connections=[\n", " ['vehicle.u', 'control.u'],\n", " ['control.x', 'vehicle.v'],\n", " ['control.y', 'vehicle.v']],\n", " inplist=['control.r', 'vehicle.gear', 'vehicle.theta'],\n", " outlist=['control.u', 'vehicle.v'], outputs=['u', 'v'])\n", "\n", "# Define the time and input vectors\n", "T = np.linspace(0, 25, 501)\n", "vref = 20 * np.ones(T.shape)\n", "gear = 4 * np.ones(T.shape)\n", "theta0 = np.zeros(T.shape)\n", "\n", "# Find the equilibrium point for the system\n", "Xeq, Ueq = ct.find_eqpt(\n", " vehicle, [vref[0]], [0, gear[0], theta0[0]], y0=[vref[0]], iu=[1, 2])\n", "print(\"Xeq = \", Xeq)\n", "print(\"Ueq = \", Ueq)\n", "\n", "# Compute the linearized system at the eq pt\n", "cruise_linearized = ct.linearize(vehicle, Xeq, [Ueq[0], gear[0], 0])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Construct the gain matrices for the system\n", "A, B, C = cruise_linearized.A, cruise_linearized.B[0, 0], cruise_linearized.C\n", "K = 0.5\n", "kf = -1 / (C * np.linalg.inv(A - B * K) * B)\n", "\n", "# Compute the steady state velocity and throttle setting\n", "xd = Xeq[0]\n", "ud = Ueq[0]\n", "yd = vref[-1]\n", "\n", "# Response of the system with no integral feedback term\n", "plt.figure()\n", "theta_hill = [\n", " 0 if t <= 5 else\n", " 4./180. * pi * (t-5) if t <= 6 else\n", " 4./180. * pi for t in T]\n", "t, y_sfb = ct.input_output_response(\n", " cruise_sf, T, [vref, gear, theta_hill], [Xeq[0], 0],\n", " params={'K':K, 'ki':0.0, 'kf':kf, 'xd':xd, 'ud':ud, 'yd':yd})\n", "subplots = cruise_plot(cruise_sf, t, y_sfb, t_hill=5, linetype='b--')\n", "\n", "# Response of the system with state feedback + integral action\n", "t, y_sfb_int = ct.input_output_response(\n", " cruise_sf, T, [vref, gear, theta_hill], [Xeq[0], 0],\n", " params={'K':K, 'ki':0.1, 'kf':kf, 'xd':xd, 'ud':ud, 'yd':yd})\n", "cruise_plot(cruise_sf, t, y_sfb_int, t_hill=5, linetype='b-', subplots=subplots)\n", "\n", "# Add title and legend\n", "plt.suptitle('Cruise control with state feedback, integral action')\n", "import matplotlib.lines as mlines\n", "p_line = mlines.Line2D([], [], color='blue', linestyle='--', label='State feedback')\n", "pi_line = mlines.Line2D([], [], color='blue', linestyle='-', label='w/ integral action')\n", "plt.legend(handles=[p_line, pi_line], frameon=False, loc='lower right');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pole/zero cancellation\n", "\n", "The transfer function for the linearized dynamics of the cruise control system is given by $P(s) = b/(s+a)$. A simple (but not necessarily good) way to design a PI controller is to choose the parameters of the PI controller as $k_\\text{i}=ak_\\text{p}$. The controller transfer function is then $C(s)=k_\\text{p}+k_\\text{i}/s=k_\\text{i}(s+a)/s$. It has a zero at $s = -k_\\text{i}/k_\\text{p}=-a$ that cancels the process pole at $s = -a$. We have $P(s)C(s)=k_\\text{i}/s$ giving the transfer function from reference to vehicle velocity as $G_{yr}(s)=b k_\\text{p}/(s + b k_\\text{p})$, and control design is then simply a matter of choosing the gain $k_\\text{p}$. The closed loop system dynamics are of first order with the time constant $1/(b k_\\text{p})$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "system: a = (0.010124405669387215-0j) , b = (1.3203061238159202+0j)\n", "pzcancel: kp = 0.5 , ki = (0.005062202834693608+0j) , 1/(kp b) = (1.5148002148317266+0j)\n", "sfb_int: K = 0.5 , ki = 0.1\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/murray/src/python-control/murrayrm/control/xferfcn.py:1109: ComplexWarning: Casting complex values to real discards the imaginary part\n", " num[i, j, maxindex+1-len(numpoly):maxindex+1] = numpoly\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Get the transfer function from throttle input + hill to vehicle speed\n", "P = ct.ss2tf(cruise_linearized[0, 0])\n", "\n", "# Construction a controller that cancels the pole\n", "kp = 0.5\n", "a = -P.poles()[0]\n", "b = np.real(P(0)) * a\n", "ki = a * kp\n", "control_pz = ct.TransferFunction(\n", " [kp, ki], [1, 0], name='control', inputs='u', outputs='y')\n", "print(\"system: a = \", a, \", b = \", b)\n", "print(\"pzcancel: kp =\", kp, \", ki =\", ki, \", 1/(kp b) = \", 1/(kp * b))\n", "print(\"sfb_int: K = \", K, \", ki = 0.1\")\n", "\n", "# Construct the closed loop system and plot the response\n", "# Create the closed loop system for the state space controller\n", "cruise_pz = ct.InterconnectedSystem(\n", " [vehicle, control_pz], name='cruise_pz',\n", " connections = [\n", " ['control.u', '-vehicle.v'],\n", " ['vehicle.u', 'control.y']],\n", " inplist = ['control.u', 'vehicle.gear', 'vehicle.theta'],\n", " inputs = ['vref', 'gear', 'theta'],\n", " outlist = ['vehicle.v', 'vehicle.u'],\n", " outputs = ['v', 'u'])\n", "\n", "# Find the equilibrium point\n", "X0, U0 = ct.find_eqpt(\n", " cruise_pz, [vref[0], 0], [vref[0], gear[0], theta0[0]], \n", " iu=[1, 2], y0=[vref[0], 0], iy=[0])\n", "\n", "# Response of the system with PI controller canceling process pole\n", "t, y_pzcancel = ct.input_output_response(\n", " cruise_pz, T, [vref, gear, theta_hill], X0)\n", "subplots = cruise_plot(cruise_pz, t, y_pzcancel, t_hill=5, linetype='b-')\n", "cruise_plot(cruise_sf, t, y_sfb_int, t_hill=5, linetype='b--', subplots=subplots);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PI Controller\n", "\n", "In this example, the speed of the vehicle is measured and compared to the desired speed. The controller is a PI controller represented as a transfer function. In the textbook, the simulations are done for LTI systems, but here we simulate the full nonlinear system." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameter design through pole placement\n", "\n", "To illustrate the design of a PI controller, we choose the gains $k_\\text{p}$ and $k_\\text{i}$ so that the characteristic polynomial has the form\n", "\n", "$$\n", "s^2 + 2 \\zeta \\omega_0 s + \\omega_0^2\n", "$$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/murray/src/python-control/murrayrm/control/xferfcn.py:1109: ComplexWarning: Casting complex values to real discards the imaginary part\n", " num[i, j, maxindex+1-len(numpoly):maxindex+1] = numpoly\n", "/Users/murray/src/python-control/murrayrm/control/xferfcn.py:1109: ComplexWarning: Casting complex values to real discards the imaginary part\n", " num[i, j, maxindex+1-len(numpoly):maxindex+1] = numpoly\n", "/Users/murray/src/python-control/murrayrm/control/xferfcn.py:1109: ComplexWarning: Casting complex values to real discards the imaginary part\n", " num[i, j, maxindex+1-len(numpoly):maxindex+1] = numpoly\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Values of the first order transfer function P(s) = b/(s + a) are set above\n", "\n", "# Define the input that we want to track\n", "T = np.linspace(0, 40, 101)\n", "vref = 20 * np.ones(T.shape)\n", "gear = 4 * np.ones(T.shape)\n", "theta_hill = np.array([\n", " 0 if t <= 5 else\n", " 4./180. * pi * (t-5) if t <= 6 else\n", " 4./180. * pi for t in T])\n", "\n", "# Fix \\omega_0 and vary \\zeta\n", "w0 = 0.5\n", "subplots = [None, None]\n", "for zeta in [0.5, 1, 2]:\n", " # Create the controller transfer function (as an I/O system)\n", " kp = (2*zeta*w0 - a)/b\n", " ki = w0**2 / b\n", " control_tf = ct.TransferFunction(\n", " [kp, ki], [1, 0.01*ki/kp], name='control', inputs='u', outputs='y')\n", " \n", " # Construct the closed loop system by interconnecting process and controller\n", " cruise_tf = ct.InterconnectedSystem(\n", " [vehicle, control_tf], name='cruise',\n", " connections = [['control.u', '-vehicle.v'], ['vehicle.u', 'control.y']],\n", " inplist = ['control.u', 'vehicle.gear', 'vehicle.theta'], \n", " inputs = ['vref', 'gear', 'theta'],\n", " outlist = ['vehicle.v', 'vehicle.u'], outputs = ['v', 'u'])\n", "\n", " # Plot the velocity response\n", " X0, U0 = ct.find_eqpt(\n", " cruise_tf, [vref[0], 0], [vref[0], gear[0], theta_hill[0]], \n", " iu=[1, 2], y0=[vref[0], 0], iy=[0])\n", "\n", " t, y = ct.input_output_response(cruise_tf, T, [vref, gear, theta_hill], X0)\n", " subplots = cruise_plot(cruise_tf, t, y, t_hill=5, subplots=subplots)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/murray/src/python-control/murrayrm/control/xferfcn.py:1109: ComplexWarning: Casting complex values to real discards the imaginary part\n", " num[i, j, maxindex+1-len(numpoly):maxindex+1] = numpoly\n", "/Users/murray/src/python-control/murrayrm/control/xferfcn.py:1109: ComplexWarning: Casting complex values to real discards the imaginary part\n", " num[i, j, maxindex+1-len(numpoly):maxindex+1] = numpoly\n", "/Users/murray/src/python-control/murrayrm/control/xferfcn.py:1109: ComplexWarning: Casting complex values to real discards the imaginary part\n", " num[i, j, maxindex+1-len(numpoly):maxindex+1] = numpoly\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Fix \\zeta and vary \\omega_0\n", "zeta = 1\n", "subplots = [None, None]\n", "for w0 in [0.2, 0.5, 1]:\n", " # Create the controller transfer function (as an I/O system)\n", " kp = (2*zeta*w0 - a)/b\n", " ki = w0**2 / b\n", " control_tf = ct.TransferFunction(\n", " [kp, ki], [1, 0.01*ki/kp], name='control', inputs='u', outputs='y')\n", " \n", " # Construct the closed loop system by interconnecting process and controller\n", " cruise_tf = ct.InterconnectedSystem(\n", " [vehicle, control_tf], name='cruise',\n", " connections = [['control.u', '-vehicle.v'], ['vehicle.u', 'control.y']],\n", " inplist = ['control.u', 'vehicle.gear', 'vehicle.theta'], \n", " inputs = ['vref', 'gear', 'theta'],\n", " outlist = ['vehicle.v', 'vehicle.u'], outputs = ['v', 'u'])\n", "\n", " # Plot the velocity response\n", " X0, U0 = ct.find_eqpt(\n", " cruise_tf, [vref[0], 0], [vref[0], gear[0], theta_hill[0]], \n", " iu=[1, 2], y0=[vref[0], 0], iy=[0])\n", "\n", " t, y = ct.input_output_response(cruise_tf, T, [vref, gear, theta_hill], X0)\n", " subplots = cruise_plot(cruise_tf, t, y, t_hill=5, subplots=subplots)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Robustness to change in mass" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# Nominal controller design for remaining analyses\n", "# Construct a PI controller with rolloff, as a transfer function\n", "Kp = 0.5 # proportional gain\n", "Ki = 0.1 # integral gain\n", "control_tf = ct.TransferFunction(\n", " [Kp, Ki], [1, 0.01*Ki/Kp], name='control', inputs='u', outputs='y')\n", "\n", "cruise_tf = ct.InterconnectedSystem(\n", " [vehicle, control_tf], name='cruise',\n", " connections = [['control.u', '-vehicle.v'], ['vehicle.u', 'control.y']],\n", " inplist = ['control.u', 'vehicle.gear', 'vehicle.theta'], inputs = ['vref', 'gear', 'theta'],\n", " outlist = ['vehicle.v', 'vehicle.u'], outputs = ['v', 'u'])" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define the time and input vectors\n", "T = np.linspace(0, 25, 101)\n", "vref = 20 * np.ones(T.shape)\n", "gear = 4 * np.ones(T.shape)\n", "theta0 = np.zeros(T.shape)\n", "\n", "# Now simulate the effect of a hill at t = 5 seconds\n", "plt.figure()\n", "plt.suptitle('Response to change in road slope')\n", "theta_hill = np.array([\n", " 0 if t <= 5 else\n", " 4./180. * pi * (t-5) if t <= 6 else\n", " 4./180. * pi for t in T])\n", "\n", "subplots = [None, None]\n", "linecolor = ['red', 'blue', 'green']\n", "handles = []\n", "for i, m in enumerate([1200, 1600, 2000]):\n", " # Compute the equilibrium state for the system\n", " X0, U0 = ct.find_eqpt(\n", " cruise_tf, [vref[0], 0], [vref[0], gear[0], theta0[0]], \n", " iu=[1, 2], y0=[vref[0], 0], iy=[0], params={'m':m})\n", "\n", " t, y = ct.input_output_response(\n", " cruise_tf, T, [vref, gear, theta_hill], X0, params={'m':m})\n", "\n", " subplots = cruise_plot(cruise_tf, t, y, t_hill=5, subplots=subplots,\n", " linetype=linecolor[i][0] + '-')\n", " handles.append(mlines.Line2D([], [], color=linecolor[i], linestyle='-', \n", " label=\"m = %d\" % m))\n", "\n", "# Add labels to the plots\n", "plt.sca(subplots[0])\n", "plt.ylabel('Speed [m/s]')\n", "plt.legend(handles=handles, frameon=False, loc='lower right');\n", "\n", "plt.sca(subplots[1])\n", "plt.ylabel('Throttle')\n", "plt.xlabel('Time [s]');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PI controller with antiwindup protection\n", "\n", "We now create a more complicated feedback controller that includes anti-windup protection." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def pi_update(t, x, u, params={}):\n", " # Get the controller parameters that we need\n", " ki = params.get('ki', 0.1)\n", " kaw = params.get('kaw', 2) # anti-windup gain\n", "\n", " # Assign variables for inputs and states (for readability)\n", " v = u[0] # current velocity\n", " vref = u[1] # reference velocity\n", " z = x[0] # integrated error\n", "\n", " # Compute the nominal controller output (needed for anti-windup)\n", " u_a = pi_output(t, x, u, params)\n", "\n", " # Compute anti-windup compensation (scale by ki to account for structure)\n", " u_aw = kaw/ki * (np.clip(u_a, 0, 1) - u_a) if ki != 0 else 0\n", "\n", " # State is the integrated error, minus anti-windup compensation\n", " return (vref - v) + u_aw\n", "\n", "def pi_output(t, x, u, params={}):\n", " # Get the controller parameters that we need\n", " kp = params.get('kp', 0.5)\n", " ki = params.get('ki', 0.1)\n", "\n", " # Assign variables for inputs and states (for readability)\n", " v = u[0] # current velocity\n", " vref = u[1] # reference velocity\n", " z = x[0] # integrated error\n", "\n", " # PI controller\n", " return kp * (vref - v) + ki * z\n", "\n", "control_pi = ct.NonlinearIOSystem(\n", " pi_update, pi_output, name='control',\n", " inputs = ['v', 'vref'], outputs = ['u'], states = ['z'],\n", " params = {'kp':0.5, 'ki':0.1})\n", "\n", "# Create the closed loop system\n", "cruise_pi = ct.InterconnectedSystem(\n", " [vehicle, control_pi], name='cruise',\n", " connections=[\n", " ['vehicle.u', 'control.u'],\n", " ['control.v', 'vehicle.v']],\n", " inplist=['control.vref', 'vehicle.gear', 'vehicle.theta'],\n", " outlist=['control.u', 'vehicle.v'], outputs=['u', 'v'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Response to a small hill\n", "\n", "Figure 4.3b shows the response of the closed loop system. The figure shows that even if the hill is so steep that the throttle changes from 0.17 to almost full throttle, the largest speed error is less than 1 m/s, and the desired velocity is recovered after 20 s." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute the equilibrium throttle setting for the desired speed\n", "X0, U0, Y0 = ct.find_eqpt(\n", " cruise_pi, [vref[0], 0], [vref[0], gear[0], theta0[0]],\n", " y0=[0, vref[0]], iu=[1, 2], iy=[1], return_y=True)\n", "\n", "# Now simulate the effect of a hill at t = 5 seconds\n", "plt.figure()\n", "plt.suptitle('Car with cruise control encountering sloping road')\n", "theta_hill = [\n", " 0 if t <= 5 else\n", " 4./180. * pi * (t-5) if t <= 6 else\n", " 4./180. * pi for t in T]\n", "t, y = ct.input_output_response(\n", " cruise_pi, T, [vref, gear, theta_hill], X0)\n", "cruise_plot(cruise_pi, t, y, t_hill=5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Effect of Windup\n", "\n", "The windup effect occurs when a car encounters a hill that is so steep ($6^\\circ$) that the throttle saturates when the cruise controller attempts to maintain speed." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.suptitle('Cruise control with integrator windup')\n", "T = np.linspace(0, 50, 101)\n", "vref = 20 * np.ones(T.shape)\n", "theta_hill = [\n", " 0 if t <= 5 else\n", " 6./180. * pi * (t-5) if t <= 6 else\n", " 6./180. * pi for t in T]\n", "t, y = ct.input_output_response(\n", " cruise_pi, T, [vref, gear, theta_hill], X0,\n", " params={'kaw':0})\n", "cruise_plot(cruise_pi, t, y, label='Commanded', t_hill=5, \n", " antiwindup=True, legend=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### PI controller with anti-windup compensation\n", "\n", "Anti-windup can be applied to the system to improve the response. Because of the feedback from the actuator model, the output of the integrator is quickly reset to a value such that the controller output is at the saturation limit." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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69euF2s/Nzc2gcTg4OCAsLAxNmzbFJ598goYNG8Ld3R0zZsxARkYGAODu3bsQQsDFxQUKhUJnOX78eIG3uj969AhZWVmoXr16gXE8ePAgz9fm7u6ufT4nJycnnfXsjsApKSnPf9FPPHu+7HPkF4dGo8GjR4/0Pj4A7ZfN3r17cfjwYWRkZOCFF15At27dtH9I9+7di3bt2hWqQ39eDPGeFHS87GPqc7y7d+8CAFq2bJnrM7Np0ybtZyb7Pc/5ZZctr21A3vWzZcsWvPbaa6hWrRrWrVuHY8eO4dSpUxg+fDhSU1OfG292LIX5DOr7u3jy5EkEBAQAAH744QccOXIEp06dwtSpUwHkrp/ivO95GT58uM7737VrV+1z3bp1w/Hjx6FWq7F371688MILcHJygp+fH/bu3Yvr16/j+vXreidNz/sMPnjwABYWFrnKubq6Fum1Pe8Y2duerbvC7J+eno6kpCSd7Xn97bCwsMj1j6EkSXB1ddXr/Hfv3sW5c+dy/b7Y2dlBCKH9nbl37x7Mzc0N8p4B8t9oIYTR//6WVaa/1aOCMjc3R9euXbFr1y7cunXruUlFNkmScm3L/u8oLS1NZ7s+v6gA0LhxY2zcuBFCCJw7dw5r1qzBZ599BpVKhY8//hjOzs6QJAmHDh3K8y6lgu5ccnR0hLm5+XP/03NyckJMTEyu7Xfu3AEgJ5mG9ux7mf2HIL84zMzMULly5UKdo3r16qhXrx727t2LmjVrokWLFqhUqRK6du2K0aNH48SJEzh+/DhmzZpV9BdSCmXX12+//QZPT898y2W/59lJVk6xsbF57pPX78C6devg5eWFTZs26Tz/7O9EQQr7Gcwrjrxs3LgRCoUCv//+u05LhrHGipo5cybGjh2rXc/Zeti1a1d8+umnOHjwIPbt24cZM2Zot+/ZswdeXl7adUNwcnJCZmYmHjx4oPPFm1ddW1lZ5Vl/+f2TltcxsrfllYjqu7+lpaVOCwyQ99+OzMxM3Lt3TydxEkIgNjYWLVu2fO75nZ2doVKpsGrVqnyfB+Q7oLOyshAbG2uQf6IrV64MMzMzo//9LavY0mRCU6ZMgRAC77zzDtLT03M9n5GRgZ07dz73OC4uLrCyssK5c+d0tm/fvr1Q8UiSBF9fX3z77beoVKkSzp49CwDo06cPhBC4ffs2WrRokWtp3LhxvsdUqVTo1KkTNm/eXGCLVNeuXbF//37tL2m2tWvXwtrauki3yBb2v3Nvb29Uq1YNv/zyC4QQ2u1qtRrBwcHw9/cv0q3F3bp1w/79+xESEoLu3bsDAOrVqwcPDw9Mnz4dGRkZz/1PvrT+J5dfXD169ICFhQWuXr2a52emRYsWAOT33NXVFb/++qvO/lFRUTh69KjecUiSBEtLS50vs9jY2Dx/B/L7XJTEZzA7NgsLC5ibm2u3paSk4Oeffy7S8YDCfR6yk/XsxdvbW/tcq1atYG9vj++++w6xsbHaz2e3bt0QHh6OX3/9FT4+PtoWh+Lq0qULAGD9+vU623/55Zc8446Li9NJqNPT0/HXX3/leex9+/bplM3KysKmTZtQu3Ztvf4p3bJli06r5OPHj7Fz50506NBBp+7ykp1Urlu3Tmd7cHAw1Gq1TtKZ3+evT58+uHr1KpycnPL8fckesLRnz54AgKVLlxYYk75//2xsbNC6dWts2bJFp7xGo8G6deu0//iRjC1NJuTv74+lS5di9OjR8PPzw6hRo9CwYUNkZGQgPDwcK1asQKNGjdC3b98Cj5Pd32jVqlWoXbs2fH19cfLkyTz/ED3r999/x5IlS9CvXz/UqlULQghs2bIF8fHx2j+g7dq1w7vvvou33noLp0+fRseOHWFjY4OYmBgcPnwYjRs3xqhRo/I9x/z589G+fXu0bt0aH3/8MerUqYO7d+9ix44dWL58Oezs7DBjxgz8/vvv6NKlC6ZPnw5HR0esX78ef/zxB+bNmwcHB4fCvbmQW9C2bNmCpUuXws/PD2ZmZtov67yYmZlh3rx5ePPNN9GnTx+89957SEtLw1dffYX4+HjMnTu30DEA8h/UJUuW4P79+zojlHft2hWrV69G5cqV4efnV+Ax7Ozs4Onpie3bt6Nr165wdHSEs7NziY78rI/shHnBggUYOnQoFAoFvL29UbNmTXz22WeYOnUqrl27hhdffBGVK1fG3bt3cfLkSdjY2GDWrFkwMzPDrFmz8N5776F///4YPnw44uPjMWvWLLi5uen0LStInz59sGXLFowePRr9+/dHdHQ0Zs+eDTc3N1y+fDlXzKGhodi5cyfc3NxgZ2cHb2/vEvkMAkDv3r0xf/58vPHGG3j33Xfx4MEDfP3118UaW6pRo0YAgBUrVsDOzg5WVlbw8vLSq0UlJ3Nzc3Tq1Ak7d+6El5eXdoyndu3aQalUYt++fXj//feLHOezAgIC0LFjR3z00UdQq9Vo0aIFjhw5kmcCOWDAAEyfPh2vv/46PvzwQ6SmpmLhwoW5+hdlc3Z2xgsvvIBPP/0UNjY2WLJkCf79919s3LhRr9jMzc3RvXt3BAYGQqPR4Msvv0RiYqJercDdu3dHjx49MHnyZCQmJqJdu3Y4d+4cZsyYgWbNmmHw4MHastkt+5s2bUKtWrVgZWWFxo0bY8KECQgODkbHjh0xceJENGnSBBqNBlFRUdizZw8++OADtG7dGh06dMDgwYPx+eef4+7du+jTpw+USiXCw8NhbW2NcePGFXievAQFBaF79+7o0qULJk2aBEtLSyxZsgT//PMPNmzYoHeraoVgsi7opBURESGGDh0qPDw8hKWlpfY21enTp+vccZY9hktessc+cXFxETY2NqJv377ixo0bz7177t9//xUDBw4UtWvXFiqVSjg4OIhWrVrlGptGCCFWrVolWrduLWxsbIRKpRK1a9cWQ4YMEadPn37ua7xw4YJ49dVXhZOTk7C0tBQeHh5i2LBhucZp6tu3r3BwcBCWlpbC19c31x2B2XcuPXsbcV53hDx8+FD0799fVKpUSUiSlGucpq+++irPWLdt2yZat24trKyshI2Njejatas4cuSITpnCjAj+6NEjYWZmJmxsbHTu+soe3uDll1/Otc+zd88JIcTevXtFs2bNhFKpzHOcpmdHBNc3xoLGaXqWp6dnrjvPpkyZItzd3YWZmVmuO7q2bdsmunTpIuzt7YVSqRSenp6if//+uca/WbFihahTp46wtLQU9erVE6tWrRIvvfSSzp1vz6u3uXPnipo1awqlUikaNGggfvjhhzzvtIqIiBDt2rUT1tbWeY7TVNTPYEFWrVolvL29hVKpFLVq1RJBQUFi5cqVueonv9/xvD4P3333nfDy8hLm5uZFGqcp24IFCwQA8c477+hs7969uwAgduzYobO9oLvn9PkMxsfHi+HDh4tKlSoJa2tr0b17d/Hvv//meXfon3/+KZo2bSpUKpWoVauWWLRoUYHjNC1ZskTUrl1bKBQKUb9+fbF+/frnvv6c4zTNmjVLVK9eXVhaWopmzZqJv/76S6dsQaPvp6SkiMmTJwtPT0+hUCiEm5ubGDVqlM44TUIIcePGDREQECDs7OxyjdOUlJQkpk2bJry9vYWlpaVwcHAQjRs3FhMnTtS5MzArK0t8++23olGjRtpy/v7+OuOo5Xee543TlP33vU2bNjrHE+JpfT57h1/270Red3OWN5IQOa5DEBGVAvHx8ahXrx769euHFStWmDocKuUkScKYMWOwaNGiQu9748YNeHl54auvvsKkSZNKIDoqT3h5johMKjY2Fl988QW6dOkCJycn3Lx5E99++y0eP36M8ePHmzo8IiItJk1EZFJKpRI3btzA6NGj8fDhQ22n62XLlqFhw4amDo+ISIuX54iIiIj0wCEHiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID6UqaQoKCkLLli1hZ2eHqlWrol+/frh06ZJOGSEEZs6cCXd3d6hUKnTu3BmRkZEFHnfNmjWQJCnXkpqaWpIvh4iIiMqRUpU0hYWFYcyYMTh+/DhCQkKQmZmJgIAAqNVqbZl58+Zh/vz5WLRoEU6dOgVXV1d0794djx8/LvDY9vb2iImJ0VmsrKxK+iURERFROSEJIYSpg8jPvXv3ULVqVYSFhaFjx44QQsDd3R0TJkzA5MmTAQBpaWlwcXHBl19+iffeey/P46xZswYTJkxAfHy8EaMnIiKi8sTC1AEUJCEhAQDg6OgIALh+/TpiY2MREBCgLaNUKtGpUyccPXo036QJAJKSkuDp6YmsrCw0bdoUs2fPRrNmzfIsm5aWhrS0NO26RqPBw4cP4eTkBEmSDPHSiIiIqIQJIfD48WO4u7vDzKz4F9dKbdIkhEBgYCDat2+PRo0aAQBiY2MBAC4uLjplXVxccPPmzXyPVb9+faxZswaNGzdGYmIiFixYgHbt2uHvv/9G3bp1c5UPCgrCrFmzDPhqiIiIyFSio6NRvXr1Yh+n1CZNY8eOxblz53D48OFczz3b2iOEKLAFqE2bNmjTpo12vV27dmjevDm+//57LFy4MFf5KVOmIDAwULuekJAADw8PREdHw97evigvx+TUajXc3d0BAHfu3IGNjY2JIyIiIipZiYmJqFGjBuzs7AxyvFKZNI0bNw47duzAwYMHdTJDV1dXAHKLk5ubm3Z7XFxcrtangpiZmaFly5a4fPlyns8rlUoolcpc2+3t7cts0qRSqbB69WoAgLOzMxQKhYkjIiIiMg5Dda0pVXfPCSEwduxYbNmyBfv374eXl5fO815eXnB1dUVISIh2W3p6OsLCwtC2bdtCnSciIkIn8SrvFAoFhg0bhmHDhjFhIiIiKoJS1dI0ZswY/PLLL9i+fTvs7Oy0fZgcHBygUqkgSRImTJiAOXPmoG7duqhbty7mzJkDa2trvPHGG9rjDBkyBNWqVUNQUBAAYNasWWjTpg3q1q2LxMRELFy4EBEREVi8eLFJXicRERGVPaUqaVq6dCkAoHPnzjrbV69ejWHDhgEAPvroI6SkpGD06NF49OgRWrdujT179uhcr4yKitLpJR8fH493330XsbGxcHBwQLNmzXDw4EG0atWqxF9TaZGZmYm//voLANCjRw9YWJSqqiciIir1SvU4TaVFYmIiHBwckJCQUGb7NKnVatja2gKQh19gR3AiIirvDP39Xar6NBERERGVVkyaiIiIiPTApImIiIhID0yaiIiIiPTApImIiIhID0yaiIiIiPTAwXoqCEtLSyxatEj7mIiIiAqHSVMFoVAoMGbMGFOHQUREVGbx8hwRERGRHtjSVEFkZWXh0KFDAIAOHTrA3NzcxBERERGVLUyaKojU1FR06dIFAKdRISIiKgpeniMiIiLSA5MmIiIiIj0waSIiIiLSA5MmIiIiIj0waSIiIiLSA5MmIiIiIj1wyIEKQqFQYN68edrHREREVDiSEEKYOojSLjExEQ4ODkhISIC9vb2pwyEiIiI9GPr7m5fniIiIiPTAy3MVRFZWFs6ePQsAaN68OadRISIiKiQmTRVEamoqWrVqBYDTqBARERUFL88RERER6YFJExEREZEeCnV5bseOHYU+Qffu3aFSqQq9HxEREVFpUqikqV+/foU6uCRJuHz5MmrVqlWo/YiIiIhKm0JfnouNjYVGo9Frsba2LomYiYiIiIyuUEnT0KFDC3WpbdCgQRwMkoiIiMqFQl2eW716daEOvnTp0kKVp5KjUCgwY8YM7WMiIiIqnCJPo5KSkgIhhPYS3M2bN7F161b4+PggICDAoEGaGqdRISIiKntKzTQqL730EtauXQsAiI+PR+vWrfHNN9/gpZdeYgsTERERlTtFTprOnj2LDh06AAB+++03uLi44ObNm1i7di0WLlxosADJMDQaDSIjIxEZGQmNRmPqcIiIiMqcIk+jkpycDDs7OwDAnj178PLLL8PMzAxt2rTBzZs3DRYgGUZKSgoaNWoEgNOoEBERFUWRW5rq1KmDbdu2ITo6Gn/99Ze2H1NcXBz7/RAREVG5U+Skafr06Zg0aRJq1qyJ1q1bw9/fH4Dc6tSsWTODBUhERERUGhT58lz//v3Rvn17xMTEwNfXV7u9a9eu+L//+z+DBEdERERUWhS6pemTTz7ByZMnAQCurq5o1qwZzMyeHqZVq1aoX7++4SIkIiIiKgUKnTTFxMSgT58+cHNzw7vvvos//vgDaWlpJREbERERUalR6KRp9erVuHv3Ln799VdUqlQJH3zwAZydnfHyyy9jzZo1uH//fpGDCQoKQsuWLWFnZ4eqVauiX79+uHTpkk4ZIQRmzpwJd3d3qFQqdO7cGZGRkc89dnBwMHx8fKBUKuHj44OtW7cWOU4iIiKqeIrUEVySJHTo0AHz5s3Dv//+i5MnT6JNmzb44Ycf4O7ujo4dO+Lrr7/G7du3C3XcsLAwjBkzBsePH0dISAgyMzMREBAAtVqtLTNv3jzMnz8fixYtwqlTp+Dq6oru3bvj8ePH+R732LFjGDBgAAYPHoy///4bgwcPxmuvvYYTJ04U5eWXSQqFApMmTcKkSZM4jQoREVERFHkalfzcu3cPO3fuxPbt29GhQwdMmjSpWMeqWrUqwsLC0LFjRwgh4O7ujgkTJmDy5MkAgLS0NLi4uODLL7/Ee++9l+dxBgwYgMTEROzatUu77cUXX0TlypWxYcOG58aRPQz7nTt3OJwCERFRGZGYmAh3d3eDTaNS5LvnACA1NRXnzp1DXFyczijTzs7O2L59e7GDS0hIAAA4OjoCAK5fv47Y2Fidue2USiU6deqEo0eP5ps0HTt2DBMnTtTZ1qNHD3z33Xd5lk9LS9Ppp5WYmAgAcHd3L/JrISIiorKtyEnT7t27MWTIkDz7MEmShKysrGIFJoRAYGAg2rdvrx3JOjY2FgDg4uKiUzZ7Cpf8xMbG5rlP9vGeFRQUhFmzZhUnfCIiIipnipw0jR07Fq+++iqmT5+eKyExhLFjx+LcuXM4fPhwruckSdJZF0Lk2lacfaZMmYLAwEDtemJiImrUqIG1a+/A2rpsXJ4TAkhOBh49kpe4ODWWLpXrae7cuxg7ltOoEBmKEEBcHHD1KnD9OnDzJnDnztMlJgZ48MCw57S2BlQqwMrq6U+l8ulPS0v5Z/bj7HWFQn6c86eFhfwz52Nzc/mxuXnuRZIAMzN5yX6c/edUkgq/FLRfzueyH2fL789+zk4nQjxdz/lTCECjyf18zm3PPs5ecq7nLJfXc88eJ+eS1zSgeXWYeXZbzpiffV15vc78yj3vvEDe73d+9VKYes3+zOj7uKBj5RVLNrU6Ef/3f4a7SlTkpCkuLg6BgYElkjCNGzcOO3bswMGDB1G9enXtdldXVwByy5Gbm5tOLAXF4erqmqtVqaB9lEollEplru0vvWQDe/uymWyo1cDSpfLjlStt8OGHNjAr8njwRBVTejpw+TJw4cLT5dIl4MoV+XdMH5UrA87OgJMT4OgIVKqku9jbA3Z2uouNjbxYW8s/lcr8EwYieioxsXhXvZ5VrBHBQ0NDUbt2bYMFI4TAuHHjsHXrVoSGhsLLy0vneS8vL7i6uiIkJEQ7VUt6ejrCwsLw5Zdf5ntcf39/hISE6PRr2rNnD9q2bWuw2MuSy5eB3buBXr1MHQlR6fXgARARobv8+y+QmZl3eTMzoEYNoE4doGZNoHp1oFq1pz9dXeUkyaJYPUmJyJSK/Ou7aNEivPrqqzh06BAaN26c6zb2999/v9DHHDNmDH755Rds374ddnZ22tYhBwcHqFQqSJKECRMmYM6cOahbty7q1q2LOXPmwNraGm+88Yb2OEOGDEG1atUQFBQEABg/fjw6duyIL7/8Ei+99BK2b9+OvXv35nnpr6L47jsmTUTZHj8Gzp4FTp6Ul1On5EtsebGzA3x8gIYN5Z/16z9NlPJooCaicqTIQw78+OOPGDlyJFQqFZycnHT6B0mShGvXrhU+mHzam1evXo1hw4YBkFujZs2aheXLl+PRo0do3bo1Fi9erO0sDgCdO3dGzZo1sWbNGu223377DdOmTcO1a9dQu3ZtfPHFF3j55Zf1iit7yAFD3bJoCmq1Gra2tgAASUqCEDY4fx7I8bYRVRjR0cDhw0+X8+fz7tNRuzbQtOnTpUkTuTWJl8aIygZDf38XOWlydXXF+++/j48//lhn7rnyqLwlTS+9lITt220wYgTwww8mDozICG7dAvbtk5fQUDlpelaNGkCrVkDLlvLP5s0BBwejh0pEBmTo7+8iX55LT0/HgAEDyn3CVB6NGQNs3w78/DMwZw5QpYqpIyIyrORkOUHavVv++cxsTDA3B5o1A9q3B9q1k5cc95YQEeWpyEnT0KFDsWnTJnzyySeGjIdKiIWFBUaPHg0A6NDBAi1aAKdPA8uXA9OmmTg4IgO4dQv44w9g5045UUpNffqcmRng5wd07Qq88ALg7w88aXglItJbkS/Pvf/++1i7di18fX3RpEmTXB3B58+fb5AAS4PycHnuWevXA4MGyXf03LjBDqxUNsXEAL/+CmzYADw7laSHB9CnD9C9O9C5s3w7PxFVLKXm8tz58+e1t/3/888/Os89b6BJMr1XXwU++kgeeO/XX4HBg00dEZF+EhKAzZvlRCk09OkAgZIEtGkD9O0rJ0uNGrHDNhEZlsEn7C2PykNLkxBCO+WNs7MzJEnCnDnA1KlA69bA8eMmDpDoOc6cAZYtA375Re6zlK1NG2DgQPkfAfZLIqKcSs3dcxVJeUiact49l5SUBBsbG9y8KY8to1DIoxk/c4WVyORSUuQkadkyuQ9etgYNgCFDgAEDgGfGwCUi0jL093ehbn07d+4cNHlNlpOPyMhIZOY3fC6ZnIeHPFBfRoY8SjhRafHgATB7NuDpCYwYISdMlpbAG28ABw8CkZHAxx8zYSIi4ypU0tSsWTM8KMSsk/7+/oiKiip0UGQckiSPagwAz3RLIzKJmzeBCRPkhH76dODePTlxmjdPvjtu/XqgQwf2VSIi0yhUR3AhBD799FNYW1vrVT49Pb1IQZHxNGok92f65x/gtddMHQ1VVDdvyi1La9YAWU/m12zaVL5Z4dVXOV8bEZUOhfpT1LFjR1x6dpS4Avj7+0OlUhU6KDKe7JamyEjTxkEV05078gCrK1bIl4kBeSylyZOBbt3YokREpUuhkqbQ0NASCoNMJXvuOV6eI2N6+BAICgIWLXo6CGXXrnJrk7+/aWMjIsoPG70ruOyWpitX5C8vKyvTxkPlW0aGPAr9jBly4gTISdIXXwBdupg2NiKi52HSVEFYWFhg6NCh2sfZXF0BR0f5C+zff+V+JEQl4a+/gIkTgYsX5fVGjYAvvwR69uRlOCIqG5g0VRBKpRJr1qzJtV2S5C+vgwflS3RMmsjQrl4Fxo+X54UDAGdn+TLciBHs4E1EZUuhhhyg8omdwakkZGQAc+fKSfkff8gJUmCgPCbYyJFMmIio7Cnyn63r16/DiyPLlRlCCCQ/mXvC2tpaZ35AdgYnQzt+HHj3XeD8eXm9a1dg8WLA29u0cRERFUeRW5oaNGiACRMmaOczo9ItOTkZtra2sLW11SZP2TjAJRnK48fAmDFA27ZywuTsDKxdC4SEMGEiorKvyEnToUOHEBkZidq1a+OLL77I9UVMZUd20nTjBpCUZNJQqAw7fhxo1gxYsgQQAhg2TO70PXgwO3oTUflQ5KSpZcuWCAkJwebNm7Ft2zbUqVMHK1asKNTcdFQ6ODvLd9EBwIULpo2Fyp7MTGDWLKB9e7nTt4cHsHcvsHq1/NkiIiovit0RPCAgAKdOncK3336Lb775Bj4+PtiyZYshYiMjYmdwKopr14COHYGZM+XpT954A/j7b7kPExFReWOwu+d69+6NlStXwtHREa+++qqhDktGws7gVFjr18tDVBw7BtjbA+vWydsqVTJ1ZEREJaPId8+tWrUKkZGRuHDhAiIjI3H79m1IkgQPDw/06dPHkDGSEbAzOOkrKQkYOxb46Sd5vX174OefgZo1TRoWEVGJK3LSNGXKFDRq1AiNGzfGK6+8gsaNG6NRo0awsbExZHxkJNktTbw8RwWJiAAGDAD++w8wMwOmTwemTQPMzU0dGRFRySty0nT37l1DxkElzNzcHP3799c+flZ2S9Pt20B8PC+xkC4h5Ml1J00C0tOBatWAX36R+zMREVUUHJO3grCyssLmzZvzfd7eHqhRA4iOllub2rUzYnBUqt27BwwfDvz+u7zet698Z5yTk2njIiIyNk6jQlrsDE7P+usvoHFjOWFSKoEFC4Dt25kwEVHFxKSJtNgZnLKlpcnzxL34InD3LuDjA5w8Cbz/PgeqJKKKi0lTBaFWqyFJEiRJglqtzrMMO4MTII/i3aYN8O238vqYMcDp00CTJqaNi4jI1IqcNA0bNgwHDx40ZCxkYrw8V7EJASxfDvj5yXfJOTsDO3bIHcBVKlNHR0RkekVOmh4/foyAgADUrVsXc+bMwe3btw0ZF5lAgwbypZd794C4OFNHQ8b04AHwyivAyJFASgrQvTtw7pzc6ZuIiGRFTpqCg4Nx+/ZtjB07Fps3b0bNmjXRs2dP/Pbbb8jIyDBkjGQk1tZArVryY16iqzgOHAB8fYGtWwGFAvj6a2D3bsDNzdSRERGVLsXq0+Tk5ITx48cjPDwcJ0+eRJ06dTB48GC4u7tj4sSJuHz5sqHiJCNhZ/CKIyMD+OQTeZ6427eBevWA48eBDz6QB64kIiJdBvnTGBMTgz179mDPnj0wNzdHr169EBkZCR8fH3yb3ZuUygR2Bq8Yrl6Vpz8JCpL7Mr39NnD2LNC8uakjIyIqvYqcNGVkZCA4OBh9+vSBp6cnNm/ejIkTJyImJgY//fQT9uzZg59//hmfffaZIeOlEpadNJ0/b9o4qOSsWwc0ayYPIVCpErB5M/DjjwBnQCIiKliRRwR3c3ODRqPBwIEDcfLkSTRt2jRXmR49eqAS5+MoFbJbALMf5yf78tyFC3ILBMfkKT8SE+XhA9atk9c7dJAfe3iYNi4iorJCEkKIouz4888/49VXX4WVlZWhYyp1EhMT4eDggISEBNjb25s6nBKVmiq3OGg0cj8Xd3dTR0SGcOIE8MYbwLVrcn+lGTPk/kwWnEiJiMoxQ39/F/nyXKdOnaBUKnNtF0IgKiqqWEGR6VhZAXXqyI8vXDBtLFR8WVlyv6X27eWEydMTOHgQmD6dCRMRUWEVOWny8vLCvXv3cm1/+PAhvLy8ihUUmVb2JTp2Bi/bbt0CunWTW5QyM4EBA+RBKzkZMxFR0RQ5aRJCQMqjw0tSUlKRL9kdPHgQffv2hbu7OyRJwrZt23Sev3v3LoYNGwZ3d3dYW1vjxRdffO6wBmvWrNFOH5JzSU1NLVKMZZVarYaNjQ1sbGzynUYlm4+P/JNJU9m1das89lJoqHy5dfVqYMMGueM3EREVTaEb6AMDAwEAkiTh008/hbW1tfa5rKwsnDhxIs9O4fpQq9Xw9fXFW2+9hVdeeUXnOSEE+vXrB4VCge3bt8Pe3h7z589Ht27dcOHCBdgUcOuPvb09Ll26pLOtIvTFelZycrJe5XJ2BqeyJTlZnmh3+XJ53c8P+OUXeQwmIiIqnkInTeHh4QDkJOb8+fOwtLTUPmdpaQlfX19MmjSpSMH07NkTPXv2zPO5y5cv4/jx4/jnn3/Q8Mm3+pIlS1C1alVs2LABI0aMyPe4kiTB1dW1SDFVRDkvz/EOurLj77+BgQPlCXcB4MMPgc8/B3L8ihIRUTEUOmk6cOAAAOCtt97CwoULYWdnZ/Cg8pKWlgZAt4XI3NwclpaWOHz4cIFJU1JSEjw9PZGVlYWmTZti9uzZaNasWYnHXFbVqyffYRUfD8TGcjqN0k4IYOFC4KOPgPR0ub7WrpX7MxERkeEUKmkKDAzE7NmzYWNjg0qVKmHGjBn5lp0/f36xg8upfv368PT0xJQpU7B8+XLY2Nhg/vz5iI2NRUxMTIH7rVmzBo0bN0ZiYiIWLFiAdu3a4e+//0bdunXz3CctLU2bpAHyLYsVSfYddP/9J7c2MWkqve7eBd56C9i1S17v2xdYuRKoUsW0cRERlUeFSprCw8O1k/FGRETkWy6vDuLFpVAoEBwcjLfffhuOjo4wNzdHt27d8r2cl61NmzZo06aNdr1du3Zo3rw5vv/+eyxcuDDPfYKCgjBr1iyDxl/WNGz4NGlii0XptHs3MHQoEBcnJ7pffw2MHs3LqUREJaVQSVP2pblnHxuLn58fIiIikJCQgPT0dFSpUgWtW7dGixYt9D6GmZkZWrZsWeBdd1OmTNF2eAfklqYaNWoUK/ayxsdHvgOLncFLn7Q04OOPge++k9cbNZLvjMueAoeIiEpGmRzezsHBAYDcOfz06dOYPXu23vsKIRAREYHGjRvnW0apVOY5cGdZZmZmhk6dOmkfPw/HaiqdLlyQR/b++295fdw44MsvAZXKtHEREVUERU6agoKC4OLiguHDh+tsX7VqFe7du4fJkycX+phJSUm4cuWKdv369euIiIiAo6MjPDw8sHnzZlSpUgUeHh44f/48xo8fj379+iEgIEC7z5AhQ1CtWjUEBQUBAGbNmoU2bdqgbt26SExMxMKFCxEREYHFixcX8ZWXTSqVCqGhoXqXzzlWE++gMz0hgBUrgIkTgZQUwNkZWLMG6N3b1JEREVUcRR7ccvny5ahfv36u7Q0bNsSyZcuKdMzTp0+jWbNm2jvbAgMD0axZM0yfPh0AEBMTg8GDB6N+/fp4//33MXjwYGzYsEHnGFFRUTodw+Pj4/Huu++iQYMGCAgIwO3bt3Hw4EG0atWqSDFWFN7eunfQkencvw/83/8BI0fKCVNAAHD+PBMmIiJjK/KEvVZWVrh48WKuKVOuXbsGHx+fcjXidkWasDcnb2+5M3hICDuDm8r+/cDgwcCdO4BCIV+KGz9eTmiJiKhgpWbC3ho1auDIkSO5th85cgTu7u7FCooMT61Wo0qVKqhSpcpzp1HJln2Jjp3BjS89HZg8WU5W79wB6tcHTpyQL88xYSIiMo0i92kaMWIEJkyYgIyMDLzwwgsAgH379uGjjz7CBx98YLAAyXDu379fqPINGwLbtrEzuLH995/c2fvMGXn93XeB+fPlOeSIiMh0ipw0ffTRR3j48CFGjx6N9PR0APIlu8mTJ2PKlCkGC5BMh3fQGZcQ8sS648bJc8g5OgI//ij3ZyIiItMrcp+mbElJSbh48SJUKhXq1q1b7m7VB8pHnya1Wg1bW1sAcp0VNMFxtr//Bpo2BSpXBh484B10JenRI7lF6bff5PUuXeSpUKpXN21cRERlmaG/v4s9TpOtrS1atmxZ7ECo9Mm+g+7RI85BV5IOHgQGDQKiowELC3mS3UmTAHNzU0dGREQ5FStpio+Px8qVK3Hx4kVIkoQGDRrg7bff1g4+SWUb56ArWRkZwKxZwJw58qW5OnWAX34B+D8IEVHpVOT7cE6fPo3atWvj22+/xcOHD3H//n18++23qF27Ns6ePWvIGMmEeAddybh6FejQAfjiCzlhGj4cCA9nwkREVJoVuaVp4sSJ+N///ocffvgBFhbyYTIzM7V31R08eNBgQVLxmZmZaefo02calWy8g86whAB+/hkYMwZISgIqVZJH+n71VVNHRkREz1PkpOn06dM6CRMAWFhY4KOPPirUBLpkHCqVCqdOnSr0fmxpMpz4eHlU702b5PWOHeUEysPDpGEREZGeinx5zt7eHlFRUbm2R0dHw87OrlhBUemRc9iB4t1nWbEdOgT4+soJk7m5fFlu/34mTEREZUmRk6YBAwbg7bffxqZNmxAdHY1bt25h48aNGDFiBAYOHGjIGMmEnr2DjgonMxOYPh3o3BmIigJq1QKOHAE++YR3xxERlTVFvjz39ddfQ5IkDBkyBJmZmRBCwNLSEqNGjcLcuXMNGSMZQHJyMnyeXGu7cOECrK2t9drPygqoXRu4fFm+RMc76PR37Rrw5pvA8ePy+tChwPffA2yIJSIqm4qcNFlaWmLBggUICgrC1atXIYRAnTp19P4yJuMSQuDmzZvax4XRsKGcNEVGAl27lkR05YsQwLp1cmfvx48BBwdg2TLg9ddNHRkRERVHoZKmwMBAvcvOnz+/0MFQ6cQ76PQXHw+MGgVs3Civd+ggd/b29DRpWEREZACFSprCw8P1Kidxvo1yJfsOuvPnTRtHaXf4sDyy982bcn+lmTOBKVPYd4mIqLwoVNJ04MCBkoqDSrFWreSfZ84AKSmASmXaeEqbzEzgs8/kO+I0Grmz9/r1QJs2po6MiIgMqch3z1HFUbs2UK0akJ4OHD1q6mhKl+yRvWfPlhOmoUOBiAgmTERE5VGxkqZDhw5h0KBB8Pf3x+3btwEAP//8Mw4fPmyQ4Kh0kCSgSxf5cWioSUMpNYQA1q4FmjaV745zcJD7Ma1Zw7vjiIjKqyInTcHBwejRowdUKhXCw8ORlpYGAHj8+DHmzJljsADJMCRJgo+PD3x8fIrU5yw7aeIVWrmz98CBcqtSUpLc0nTuHDBggKkjIyKiklTkpOnzzz/HsmXL8MMPP0ChUGi3t23blhP2lkLW1taIjIxEZGRkkYaF6NxZ/nnyJKBWGza2suTgQd2RvT//XE4kObI3EVH5V+Sk6dKlS+jYsWOu7fb29oiPjy9OTFQKeXnJiUFGhjyidUWTkQFMmya3uEVFyf28jh4Fpk7l3XFERBVFkZMmNzc3XLlyJdf2w4cPo1atWsUKikqfityv6coVoH37p3fHvfUWEB7+9K5CIiKqGIqcNL333nsYP348Tpw4AUmScOfOHaxfvx6TJk3C6NGjDRkjGUBycjIaNmyIhg0bIjk5uUjHyL5EV1H6NQkBrF4td/Y+eRKoVAn49Vdg1Sp29iYiqoiKPI3KRx99hISEBHTp0gWpqano2LEjlEolJk2ahLFjxxoyRjIAIQQuXLigfVwU2S1Np07J04OU58Th4UPgvfeA336T1zt1kkf2rlHDtHEREZHpSKKQ36ARERFo2rSpdj05ORkXLlyARqOBj48PbG1tDR2jySUmJsLBwQEJCQmwt7c3dThFolartXWTlJQEGxubIh2nVi3g+nVg1y7gxRcNGWHpceAAMHgwcPs2YGEhj8H04Yfsu0REVNYY+vu70JfnmjdvDj8/PyxduhQJCQmwtrZGixYt0KpVq3KZMJGu8nyJLj0dmDxZnpT49m2gbl3g2DHg44+ZMBERURGSpiNHjqB58+b4+OOP4ebmhkGDBnF6lQqkvI7X9O+/gL8/MG+e3JdpxAi5s3eLFqaOjIiISotCJ03+/v744YcfEBsbi6VLl+LWrVvo1q0bateujS+++AK3bt0qiTiplMhuaTpzBkhMNGkoBiEEsGwZ0Lw5cPYs4OQEbNkC/PADUMQrmEREVE4V+e45lUqFoUOHIjQ0FP/99x8GDhyI5cuXw8vLC7169TJkjFSK1Kghj1Gk0QCHDpk6muK5dw/o1w8YNUqeiLh7d3lk7//7P1NHRkREpZFBJuytXbs2Pv74Y0ydOhX29vb466+/DHFYMiBJkuDp6QlPT88iTaOSU3m4RLd7N9C4MbBjB2BpCcyfL29zdzd1ZEREVFoVO2kKCwvD0KFD4erqio8++ggvv/wyjlTEIaNLOWtra9y4cQM3btwo0jQqOZXlpCklBRg/HujZE7h7F/DxkcdgmjgRMDPIvxBERFReFWmcpujoaKxZswZr1qzB9evX0bZtW3z//fd47bXXinwrO5Ud2f2awsPlyWsrVTJhMIVw7hzw5pvAP//I62PHyh2/VSrTxkVERGVDoZOm7t2748CBA6hSpQqGDBmC4cOHw9vbuyRio1LK3R2oVw/47z95Atv//c/UERVMowEWLpSHE0hPB6pWlUf6Ztc7IiIqjEInTSqVCsHBwejTpw/MOXhNmZGSkqKdYPngwYNQFbN5pUsXOWk6cKB0J0137gDDhgEhIfJ6797yNChVq5o0LCIiKoMKPSJ4RcQRwXP79VdgwADA0xO4erV0Dv64bZs83tKDB/IluG++AUaOlCcfJiKi8s/kI4ITAUDfvvKYRjdvAr//bupodKnVwLvvykMHPHgANGsmjys1ahQTJiIiKjomTVQkKpXcigMA339v2lhyOnVKTpJ++EFOkD76CDh+HGjQwNSRERFRWcekiYps9Gj5Nv19+4DISNPGkpUFfPEF0LYtcPkyUL26HNeXX8rjMBERERUXkyYqMg8PeURtAFi0yHRx3Lwpd0yfNg3IzARee00eXiB7PCkiIiJDKFVJ08GDB9G3b1+4u7tDkiRs27ZN5/m7d+9i2LBhcHd3h7W1NV588UVcvnz5uccNDg6Gj48PlEolfHx8sHXr1hJ6BRXPuHHyz7VrgUePjH/+9euBJk3kKV3s7ICffgI2bgQqVzZ+LEREVL6VqqRJrVbD19cXi/JothBCoF+/frh27Rq2b9+O8PBweHp6olu3blCr1fke89ixYxgwYAAGDx6Mv//+G4MHD8Zrr72GEydOlORLKZWcnZ3h7Oxs0GN26gQ0agQkJ8tjHxlLfDzwxhvAoEHyxMFt2wIREcCQIezsTUREJaPUDjkgSRK2bt2Kfk+u//z333/w9vbGP//8g4YNGwIAsrKyULVqVXz55ZcYkd0r+RkDBgxAYmIidu3apd324osvonLlytiwYYNesZSHIQdK0g8/yHereXnJ/YlKeviBsDBg8GAgOlo+14wZwJQpgEWRxrcnIqLyqsIOOZCWlgYAsLKy0m4zNzeHpaUlDh8+nO9+x44dQ0BAgM62Hj164OjRowWeKzExUWeh/L35pnw57Pp14M8/S+486elyctSli5ww1akDHDkCfPopEyYiIip5ZSZpql+/Pjw9PTFlyhQ8evQI6enpmDt3LmJjYxETE5PvfrGxsXBxcdHZ5uLigtjY2Hz3CQoKgoODg3apUaOGwV5HeWRtDbz9tvy4pIYfuHgRaNMGmDsXEEI+X3g40Lp1yZyPiIjoWWUmaVIoFAgODsZ///0HR0dHWFtbIzQ0FD179nzudC7SM51chBC5tuU0ZcoUJCQkaJfo6GiDvAZTSklJQefOndG5c2ekpKQY/PhjxsjDD4SEyAmOoQgBLF4MNG8uJ0lOTsCWLcCPPwJPBjgnIiIyijJ1UcPPzw8RERFISEhAeno6qlSpgtatW6NFixb57uPq6pqrVSkuLi5X61NOSqUSSqXSYHGXBhqNBmFhYdrHhlazpjxK+PbtwOzZ8l1txe2QffcuMHz400t+AQFyZ3N392KHS0REVGhlpqUpJwcHB1SpUgWXL1/G6dOn8dJLL+Vb1t/fHyHZs7U+sWfPHrRt27akw6xwPvxQTpQ2bAA+/7x4x/rjD6BxYzlhUiqBBQuAXbuYMBERkemUqpampKQkXLlyRbt+/fp1REREwNHRER4eHti8eTOqVKkCDw8PnD9/HuPHj0e/fv10OnoPGTIE1apVQ1BQEABg/Pjx6NixI7788ku89NJL2L59O/bu3Vtg53Eqmnbt5EEux4wBpk+XE5zsvk76SkmRk6/Fi+X1xo2BX36RhzUgIiIyKVGKHDhwQADItQwdOlQIIcSCBQtE9erVhUKhEB4eHmLatGkiLS1N5xidOnXSls+2efNm4e3tLRQKhahfv74IDg4uVFwJCQkCgEhISCjOyzOppKQk7fuZlJRUouf65BMhACHMzYX4/Xf994uIEMLHR94XEGLiRCFSUkouTiIiKt8M/f1dasdpKk3KwzhNarUatk96TiclJcHGxqbEziUE8NZb8ujcKhVw4EDBd7k9eCDPEbdggTysgKsrsGYN0KNHiYVIREQVQIUdp4nKDkmSB7x88UX5clufPnIH8QcPdMs9fix3Gq9VC/jqKzlh+t//5HnjmDAREVFpU6r6NFHJsra2Ntq5FApg82agc2fgzJmnE/vWqyePt1S9OrBiBXD/vrzd1xeYMwfo2ZPToBARUenEpKmCsLGxKXCOvpJgayvf8fbpp0BoKHDpEvDff/KSrW5dubXp1VflcZ6IiIhKKyZNVKKqVAGWLZMfP3gAnDgBHD8uJ1DduwPDhnEKFCIiKhv4dUVG4+QE9OolL0RERGUNL4hUEKmpqejduzd69+6N1NRUU4dDRERU5rClqYLIysrCn0/mI8nKyjJxNERERGUPW5qIiIiI9MCkiYiIiEgPTJqIiIiI9MCkiYiIiEgPTJqIiIiI9MC75/SQPadxYmKiiSMpupyjgScmJvIOOiIiKveyv7ezv8eLi0mTHh48mWm2Ro0aJo7EMNzd3U0dAhERkdE8ePAADg4OxT4OkyY9ODo6AgCioqIM8qZT0SUmJqJGjRqIjo6Gvb29qcOp8FgfpQfrovRgXZQeCQkJ8PDw0H6PFxeTJj2YPZlJ1sHBgb8ApYS9vT3rohRhfZQerIvSg3VRepgZaEZ4dgQnIiIi0gOTJiIiIiI9MGnSg1KpxIwZM6BUKk0dSoXHuihdWB+lB+ui9GBdlB6GrgtJGOo+PCIiIqJyjC1NRERERHpg0kRERESkByZNRERERHpg0kRERESkByZNeliyZAm8vLxgZWUFPz8/HDp0yNQhlXsHDx5E37594e7uDkmSsG3bNp3nhRCYOXMm3N3doVKp0LlzZ0RGRpom2HIuKCgILVu2hJ2dHapWrYp+/frh0qVLOmVYH8axdOlSNGnSRDtoor+/P3bt2qV9nvVgOkFBQZAkCRMmTNBuY30Yx8yZMyFJks7i6uqqfd6Q9cCk6Tk2bdqECRMmYOrUqQgPD0eHDh3Qs2dPREVFmTq0ck2tVsPX1xeLFi3K8/l58+Zh/vz5WLRoEU6dOgVXV1d0794djx8/NnKk5V9YWBjGjBmD48ePIyQkBJmZmQgICNCZBJr1YRzVq1fH3Llzcfr0aZw+fRovvPACXnrpJe0XAOvBNE6dOoUVK1agSZMmOttZH8bTsGFDxMTEaJfz589rnzNoPQgqUKtWrcTIkSN1ttWvX198/PHHJoqo4gEgtm7dql3XaDTC1dVVzJ07V7stNTVVODg4iGXLlpkgwoolLi5OABBhYWFCCNaHqVWuXFn8+OOPrAcTefz4sahbt64ICQkRnTp1EuPHjxdC8PfCmGbMmCF8fX3zfM7Q9cCWpgKkp6fjzJkzCAgI0NkeEBCAo0ePmigqun79OmJjY3XqRalUolOnTqwXI0hISADwdCJr1odpZGVlYePGjVCr1fD392c9mMiYMWPQu3dvdOvWTWc768O4Ll++DHd3d3h5eeH111/HtWvXABi+HjhhbwHu37+PrKwsuLi46Gx3cXFBbGysiaKi7Pc+r3q5efOmKUKqMIQQCAwMRPv27dGoUSMArA9jO3/+PPz9/ZGamgpbW1ts3boVPj4+2i8A1oPxbNy4EWfPnsWpU6dyPcffC+Np3bo11q5di3r16uHu3bv4/PPP0bZtW0RGRhq8Hpg06UGSJJ11IUSubWR8rBfjGzt2LM6dO4fDhw/neo71YRze3t6IiIhAfHw8goODMXToUISFhWmfZz0YR3R0NMaPH489e/bAysoq33Ksj5LXs2dP7ePGjRvD398ftWvXxk8//YQ2bdoAMFw98PJcAZydnWFubp6rVSkuLi5X1krGk31XBOvFuMaNG4cdO3bgwIEDqF69unY768O4LC0tUadOHbRo0QJBQUHw9fXFggULWA9GdubMGcTFxcHPzw8WFhawsLBAWFgYFi5cCAsLC+17zvowPhsbGzRu3BiXL182+O8Fk6YCWFpaws/PDyEhITrbQ0JC0LZtWxNFRV5eXnB1ddWpl/T0dISFhbFeSoAQAmPHjsWWLVuwf/9+eHl56TzP+jAtIQTS0tJYD0bWtWtXnD9/HhEREdqlRYsWePPNNxEREYFatWqxPkwkLS0NFy9ehJubm+F/LwrddbyC2bhxo1AoFGLlypXiwoULYsKECcLGxkbcuHHD1KGVa48fPxbh4eEiPDxcABDz588X4eHh4ubNm0IIIebOnSscHBzEli1bxPnz58XAgQOFm5ubSExMNHHk5c+oUaOEg4ODCA0NFTExMdolOTlZW4b1YRxTpkwRBw8eFNevXxfnzp0Tn3zyiTAzMxN79uwRQrAeTC3n3XNCsD6M5YMPPhChoaHi2rVr4vjx46JPnz7Czs5O+z1tyHpg0qSHxYsXC09PT2FpaSmaN2+uvdWaSs6BAwcEgFzL0KFDhRDybaQzZswQrq6uQqlUio4dO4rz58+bNuhyKq96ACBWr16tLcP6MI7hw4dr/xZVqVJFdO3aVZswCcF6MLVnkybWh3EMGDBAuLm5CYVCIdzd3cXLL78sIiMjtc8bsh4kIYQoZksYERERUbnHPk1EREREemDSRERERKQHJk1EREREemDSRERERKQHJk1EREREemDSRERERKQHJk1EREREeihTSVNQUBBatmwJOzs7VK1aFf369cOlS5eeu19YWBj8/PxgZWWFWrVqYdmyZUaIloiIiMqTMpU0hYWFYcyYMTh+/DhCQkKQmZmJgIAAqNXqfPe5fv06evXqhQ4dOiA8PByffPIJ3n//fQQHBxsxciIiIirryvSI4Pfu3UPVqlURFhaGjh075llm8uTJ2LFjBy5evKjdNnLkSPz99984duyYsUIlomLo3LkzmjZtiu+++87UoeSpc+fOCAsLAwCEh4ejadOmz91n2LBh+OmnnwAAW7duRb9+/UowQiIyBAtTB1AcCQkJAABHR8d8yxw7dgwBAQE623r06IGVK1ciIyMDCoUi1z5paWlIS0vTrms0Gjx8+BBOTk6QJMlA0RMRADg4OBT4/MCBA7FmzRooFAokJiYaKaqnJk+ejKioKGzYsCHfMpmZmRg6dCimTp0KJycnveKcPXs2pk6dinr16iE5Odkkr42ovBNC4PHjx3B3d4eZmQEurhlgrjyT0Gg0om/fvqJ9+/YFlqtbt6744osvdLYdOXJEABB37tzJc58ZM2bkO0kpFy5cuHDhwqVsLdHR0QbJPcpsS9PYsWNx7tw5HD58+Llln20dEk+uSObXajRlyhQEBgZq1xMSEuDh4YHo6GjY29sXI2rTUavVcHd3BwDcuXMHNjY2Jo6IiIioZCUmJqJGjRqws7MzyPHKZNI0btw47NixAwcPHkT16tULLOvq6orY2FidbXFxcbCwsICTk1Oe+yiVSiiVylzb7e3ty2zSpFKpsHr1agCAs7NznpcliYiIyiNDda0pU0mTEALjxo3D1q1bERoaCi8vr+fu4+/vj507d+ps27NnD1q0aFGhEgeFQoFhw4aZOgwiIqIyq0wNOTBmzBisW7cOv/zyC+zs7BAbG4vY2FikpKRoy0yZMgVDhgzRro8cORI3b95EYGAgLl68iFWrVmHlypWYNGmSKV4CERERlVFlKmlaunQpEhIS0LlzZ7i5uWmXTZs2acvExMQgKipKu+7l5YU///wToaGhaNq0KWbPno2FCxfilVdeMcVLMJnMzEz88ccf+OOPP5CZmWnqcIiIiMqcMj1Ok7EkJibCwcEBCQkJZbZPk1qthq2tLQAgKSmJHcGJiKjcM/T3d5lqaSIiIiIyFSZNRERERHpg0kRERESkByZNRERERHpg0kRERESkByZNRERERHpg0lRBWFpaYtGiRVi0aBEsLS1NHQ4REVUAN27cgCRJiIiIKNZxOnfujAkTJhgkpuJg0lRBKBQKjBkzBmPGjKlQ08cQEZlKbGwsxo0bh1q1akGpVKJGjRro27cv9u3bZ+rQqIjK1NxzREREZcGNGzfQrl07VKpUCfPmzUOTJk2QkZGBv/76C2PGjMG///5r6hCpCNjSVEFkZWUhNDQUoaGhyMrKMnU4RETl2ujRoyFJEk6ePIn+/fujXr16aNiwIQIDA3H8+HEAQFRUFF566SXY2trC3t4er732Gu7evas9xsyZM9G0aVOsWrUKHh4esLW1xahRo5CVlYV58+bB1dUVVatWxRdffKFzbkmSsHz5cvTp0wfW1tZo0KABjh07hitXrqBz586wsbGBv78/rl69qt3n6tWreOmll+Di4gJbW1u0bNkSe/fu1TluzZo1MWfOHAwfPhx2dnbw8PDAihUrdMqcPHkSzZo1g5WVFVq0aIHw8PBc782FCxfQq1cv2NrawsXFBYMHD8b9+/e1z6vVagwZMgS2trZwc3PDN998U/SKMDAmTRVEamoqunTpgi5duiA1NdXU4RARFZ1anf/y7N+3gsrmmOy9wLKF9PDhQ+zevRtjxozJc8qqSpUqQQiBfv364eHDhwgLC0NISAiuXr2KAQMG6JS9evUqdu3ahd27d2PDhg1YtWoVevfujVu3biEsLAxffvklpk2bpk3Ess2ePRtDhgxBREQE6tevjzfeeAPvvfcepkyZgtOnTwMAxo4dqy2flJSEXr16Ye/evQgPD0ePHj3Qt29fnblcAeCbb77RJkOjR4/GqFGjtK1marUaffr0gbe3N86cOYOZM2di0qRJOvvHxMSgU6dOaNq0KU6fPo3du3fj7t27eO2117RlPvzwQxw4cABbt27Fnj17EBoaijNnzhS6HkqEoOdKSEgQAERCQoKpQymypKQkAUAAEElJSaYOh4io6ID8l169dMtaW+dftlMn3bLOznmXK6QTJ04IAGLLli35ltmzZ48wNzcXUVFR2m2RkZECgDh58qQQQogZM2YIa2trkZiYqC3To0cPUbNmTZGVlaXd5u3tLYKCgnK8PRDTpk3Trh87dkwAECtXrtRu27Bhg7Cysirwdfj4+Ijvv/9eu+7p6SkGDRqkXddoNKJq1api6dKlQgghli9fLhwdHYVardaWWbp0qQAgwsPDhRBCfPrppyIgIEDnPNHR0QKAuHTpknj8+LGwtLQUGzdu1D7/4MEDoVKpxPjx4wuMNy+G/v5mnyYiIiIDEkIAkC+T5efixYuoUaMGatSood3m4+ODSpUq4eLFi2jZsiUA+ZKYnZ2dtoyLiwvMzc1hZmamsy0uLk7n+E2aNNF5HgAaN26ssy01NRWJiYmwt7eHWq3GrFmz8Pvvv+POnTvIzMxESkpKrpamnMeVJAmurq7ac1+8eBG+vr6wtrbWlvH399fZ/8yZMzhw4IB2Avmcrl69ipSUFKSnp+vs5+joCG9v71zlTYFJExERlS1JSfk/Z26uu/5MMqHD7JkeKjduFDmknOrWrQtJknDx4kX069cvzzJCiDyTqme3P3u3syRJeW7TaDQ623KWyT5eXtuy9/vwww/x119/4euvv0adOnWgUqnQv39/pKen53vcZ8+dnSwWRKPRoG/fvvjyyy9zPefm5obLly8/9ximxKSJiIjKljz6CRm9bAEcHR3Ro0cPLF68GO+//36ufk3x8fHw8fFBVFQUoqOjta1NFy5cQEJCAho0aGCQOArj0KFDGDZsGP7v//4PgNzH6UYhk0gfHx/8/PPPSElJgUqlAoBcfa2aN2+O4OBg1KxZExYWuVOQOnXqQKFQ4Pjx4/Dw8AAAPHr0CP/99x86depUhFdmWOwITkREZGBLlixBVlYWWrVqheDgYFy+fBkXL17EwoUL4e/vj27duqFJkyZ48803cfbsWZw8eRJDhgxBp06d0KJFC6PHW6dOHWzZsgURERH4+++/8cYbb+RqvXqeN954A2ZmZnj77bdx4cIF/Pnnn/j66691yowZMwYPHz7EwIEDcfLkSVy7dg179uzB8OHDkZWVBVtbW7z99tv48MMPsW/fPvzzzz8YNmyYzuVIUyodURAREZUjXl5eOHv2LLp06YIPPvgAjRo1Qvfu3bFv3z4sXboUkiRh27ZtqFy5Mjp27Ihu3bqhVq1a2LRpk0ni/fbbb1G5cmW0bdsWffv2RY8ePdC8efNCHcPW1hY7d+7EhQsX0KxZM0ydOjXXZTh3d3ccOXIEWVlZ6NGjBxo1aoTx48fDwcFBmxh99dVX6NixI/73v/+hW7duaN++Pfz8/Az2WotDEvpchKzgEhMT4eDggISEBNjb25s6nCJJT0/HggULAADjx4/nVCpERFTuGfr7m0mTHspD0kRERFTRGPr7m5fniIiIiPTAu+cqiKysLJw9exaAfPeC+bO35RIREVGBmDRVEKmpqWjVqhUA+VbSvIb2JyIiovzx8hwRERGRHpg0EREREemBSRMRERGRHpg0EREREemBSRMRERGRHpg0ERERlUEzZ85E06ZNtevDhg1Dv379inXM0NBQSJKE+Pj4Yh2nvOKQAxWEQqHAjBkztI+JiKhkHT16FB06dED37t2xe/fuEj/fggULwEk+ShaTpgrC0tISM2fONHUYREQVxqpVqzBu3Dj8+OOPiIqKgoeHR4mez8HBoUSPT7w8R0REZHBqtRq//vorRo0ahT59+mDNmjXa57Ivgf3xxx/w9fWFlZUVWrdujfPnz2vLrFmzBpUqVcK2bdtQr149WFlZoXv37oiOjs73nM9enhNCYN68eahVqxZUKhV8fX3x22+/6ezz559/ol69elCpVOjSpQtu3LhhqLegXCpzSdPBgwfRt29fuLu7Q5IkbNu2rcDy2R/OZ5d///3XOAGXEhqNBpGRkYiMjIRGozF1OEREhSYEoFabZinsVa9NmzbB29sb3t7eGDRoEFavXp3r0tmHH36Ir7/+GqdOnULVqlXxv//9DxkZGdrnk5OT8cUXX+Cnn37CkSNHkJiYiNdff13vGKZNm4bVq1dj6dKliIyMxMSJEzFo0CCEhYUBAKKjo/Hyyy+jV69eiIiIwIgRI/Dxxx8X7oVWMGXu8pxarYavry/eeustvPLKK3rvd+nSJZ0ZjqtUqVIS4ZVaKSkpaNSoEQBOo0JEZVNyMmBra5pzJyUBhfmzuXLlSgwaNAgA8OKLLyIpKQn79u1Dt27dtGVmzJiB7t27AwB++uknVK9eHVu3bsVrr70GAMjIyMCiRYvQunVrbZkGDRrg5MmT2mmx8qNWqzF//nzs378f/v7+AIBatWrh8OHDWL58OTp16oSlS5eiVq1a+PbbbyFJEry9vXH+/Hl8+eWX+r/QCqbMJU09e/ZEz549C71f1apVUalSJcMHRERElMOlS5dw8uRJbNmyBQBgYWGBAQMGYNWqVTpJU3YyAwCOjo7w9vbGxYsXtdssLCzQokUL7Xr9+vVRqVIlXLx48blJ04ULF5CamqpNyrKlp6ejWbNmAICLFy+iTZs2kCQpz5gotzKXNBVVs2bNkJqaCh8fH0ybNg1dunTJt2xaWhrS0tK064mJicYIkYiICmBtLbf4mOrc+lq5ciUyMzNRrVo17TYhBBQKBR49elTgvjkTmLzW89v2rOxuGH/88YdOHACgVCq1MVHhlPukyc3NDStWrICfnx/S0tLw888/o2vXrggNDUXHjh3z3CcoKAizZs0ycqRERFQQSSrcJTJTyMzMxNq1a/HNN98gICBA57lXXnkF69ev13aVOH78uPaOukePHuG///5D/fr1dY51+vRpbavSpUuXEB8fr1MmPz4+PlAqlYiKikKnTp3yLfNsv+Djx4/r/VoronKfNGV3xMvm7++P6OhofP311/kmTVOmTEFgYKB2PTExETVq1CjxWImIqGz7/fff8ejRI7z99tu5hgDo378/Vq5ciW+//RYA8Nlnn8HJyQkuLi6YOnUqnJ2dde5+UygUGDduHBYuXAiFQoGxY8eiTZs2z700BwB2dnaYNGkSJk6cCI1Gg/bt2yMxMRFHjx6Fra0thg4dipEjR+Kbb75BYGAg3nvvPZw5c0bnLj/KrczdPWcIbdq0weXLl/N9XqlUwt7eXmchIiJ6npUrV6Jbt255jpn0yiuvICIiAmfPngUAzJ07F+PHj4efnx9iYmKwY8cOWFpaastbW1tj8uTJeOONN+Dv7w+VSoWNGzfqHcvs2bMxffp0BAUFoUGDBujRowd27twJLy8vAICHhweCg4Oxc+dO+Pr6YtmyZZgzZ04x34HyTRJl+KKmJEnYunVroYeN79+/Px4+fIj9+/frVT4xMREODg5ISEgoswmUWq2G7ZPbTnj3HBGR6YSGhqJLly549OhRvjcorVmzBhMmTOB0JsVk6O/vMnd5LikpCVeuXNGuX79+HREREXB0dISHhwemTJmC27dvY+3atQCA7777DjVr1kTDhg2Rnp6OdevWITg4GMHBwaZ6CSahUCgwadIk7WMiIiIqnDKXNJ0+fVrnzrfsvkdDhw7FmjVrEBMTg6ioKO3z6enpmDRpEm7fvg2VSoWGDRvijz/+QK9evYweuylZWlriq6++MnUYREREZVaZvjxnLOXh8hwREVFFU+Evz1HRaDQabQuch4cHzMwq5D0ARERERcakqYJISUnR3jHBjuBERESFZ5TmhocPHxrjNEREREQlxigtTc7OzqhevTp8fX11lrp16+o1HDwRERGRqRklabpw4QIiIiIQHh6OU6dOYfny5Xj48KH2brYTJ04YIwwiIiKiIjNK0lS/fn3Ur18fr7/+OgB5ksDdu3dj3Lhx6Nq1qzFCICIiIioWk9xCJUkSevbsiXXr1uHOnTumCIGIiIioUIySNGk0mjy3t2nTBqGhocYIgYiIiKhYjHJ5ztbWFo0aNULTpk3h6+uLpk2bwtvbGydPnkRSUpIxQqjwLCwsMHr0aO1jIiIiKhyjfHtu2bIFf//9N/7++28sXrwYly9fhkajgSRJmD17tjFCqPCUSiUWL15s6jCIiIjKLJNMo5KamoqrV6/CyckJrq6uxj59oXEaFSIiorKnXEyjYmVlhYYNG5ri1BWWEAL3798HII+bxfGxiIiICoedWyqI5ORkVK1aFQCnUSEiIioKztpKREREpAcmTURERER6YNJEREREpAejJU2HDh3CoEGD4O/vj9u3bwMAfv75Zxw+fNhYIRAREREVmVGSpuDgYPTo0QMqlQrh4eFIS0sDADx+/Bhz5swxRghERERExWKUpOnzzz/HsmXL8MMPP0ChUGi3t23bFmfPnjVGCERERETFYpQhBy5duoSOHTvm2m5vb4/4+HhjhFDhWVhYYOjQodrHREREVDhG+fZ0c3PDlStXULNmTZ3thw8fRq1atYwRQoWnVCqxZs0aU4dBRERUZhnl8tx7772H8ePH48SJE5AkCXfu3MH69esxadIk7SSyRERERKWZUVqaPvroIyQkJKBLly5ITU1Fx44doVQqMWnSJIwdO9YYIVR4QggkJycDAKytrTmNChERUSEZdcLe5ORkXLhwARqNBj4+PrC1tTXWqYulPEzYq1arte83p1EhIqKKoExP2GttbY0WLVoY85REREREBlFiSVNgYKDeZefPn19SYRAREREZRIklTeHh4XqVY98aIiIiKgtKLGk6cOBASR2aiIiIyOiMMuRAVFQU8utvHhUVZYwQiIiIiIrFKEmTl5cX7t27l2v7gwcP4OXlZYwQiIiIiIrFKHfPCSHy7LuUlJQEKysrY4RQ4Zmbm6N///7ax0RERFQ4JZo0Zd9BJ0kSPv30U1hbW2ufy8rKwokTJ9C0adNCHfPgwYP46quvcObMGcTExGDr1q3o169fgfuEhYUhMDAQkZGRcHd3x0cffYSRI0cW9uWUaVZWVti8ebOpwzCs2FggNRVITwcyMwEzM8DcXP6pVALVqz8tm5YGWFjIzxMRERVBiSZN2XfQCSFw/vx5WFpaap+ztLSEr68vJk2aVKhjqtVq+Pr64q233sIrr7zy3PLXr19Hr1698M4772DdunU4cuQIRo8ejSpVqui1P5lIejoQEgLs3g3cugXExAA1awIbNz4t4+8P3LiR9/516wL//fd0vU0bICJCTqisrOSkSqmUH1evDhw69LTsxInyvlZWgEql+9PBAZg27WnZXbuAuDjA0lI+XvZPKyt5adnyadnkZDlxy/F7QEREZUeJJk3Zd9C99dZbWLhwIezs7HSeF0IgOjq6UMfs2bMnevbsqXf5ZcuWwcPDA9999x0AoEGDBjh9+jS+/vprJk2lUVgY8MsvwG+/AQ8f6j737Lq1tZzMKBRyMqLRyEtWlvxcTunp8k+NRk5enkwpo92W05EjwKlTecfn5KSbNH31FZDfnaKWlnILV7aBA4EdO+RYs2PPTq6USuDs2actYXPmAEePyq9NqXxaXqWSH3/yibwfAJw+Ddy5I69bWDx9P7ITtIYN5ceA/LqzW+I43AcRUaEYpU/T2rVr8eWXX+ZKmh4+fAgvLy9kZWWV2LmPHTuGgIAAnW09evTAypUrkZGRAYVCkWuftLQ0pOX4sktMTCyx+IyltE+jcuUKsGQJkLT+ERDnB8BPThC8vIDKleVEwcYWeDfHTu0igXYFHDRn2VYRgF8WoMmSk6qsJ8lV9mcvZ1nH34COyU+fz8wCsjLln+bmumUfBgHVHz45ribH8bPk5CRn2TPvAugNZAJIfLJoScCoHJcOQ1oAN5zzf223LYDs4gceA1di8y872BuwevKrfvgMcPGinDBZKOQES/EkwTIzBwICtAmndOU/mN2Kgpm5GczMJZhZSLB8ksNZKQWUHVrByskGNjaAXeJt2D6OgZ2TJeyclahcwxZOtSvB2tkakhmTMyIqH4zWETwvxugIHhsbCxcXF51tLi4uyMzMxP379+Hm5pZrn6CgIMyaNatE4yKZSM/AmnUWGPe+BLUaAPo9fTIFwAVDnUnxZNGHR8FPR+RcaV1w2R9yrvQuRNmA/ErJVuVc6fJkycfPOVc6yIsAkPFkyWl9zpV6T5Z87M+5Uu3JokuJVDiaxcOplgOcqqng5AQ4pdyC06MrcHICHKuYw8nNEk7VVXDysIFjTXs41nGEwop9z4io9DFaR/Dp06cbpCN4UTx75152EpffaORTpkzRmQYmMTERNWrUKLkAK6iH527h3c7/IfjRCwCADh3khg4qQZosICMDSEuXL1lmL5kZcmf6OnW1l/LEtevQ3ImFJlMDkZmFrAwN0tOBtHQJqekS0nxbIUVjBbUaSLp0C4/vPEZSphUSs2zwSOOAdCiRBivEaFwRcwXAlewgqj9Z8mdnBzg6Ao54CMfEG6hsnYbKdhmobK9B5cpAZSczODhZwKFtQzh4OMDBAXBQJMNOlQlbV1uYK4wymgoRVTBlriN4Ybm6uiI2VvfSRVxcHCwsLODk5JTnPkqlEkqlskTjquj2B53AkKk1cFu8AAtkYPZMDT6cpuTNbSXO/MmiTwuv15NFH7pJkNAIqOOS8PB6Ah7ceIwHlWrjQaICDx4AD479hwf/xOBBgjkeJCnxIFmFh+m2eJDpgEeiMgDg8WN5uQlHAI7Ao3xO+33Olaf/lNkgCfZmSbAzT4GdIgW2inTY+XrB1t0BdnaAbeJt2Ny+DFtbwNZOgo29ubw4WMCmkgI2TWrDxtUONjaAjUUarK00sKpkxUuNRBWc0TqCL1iwAPb29iV5ujz5+/tj586dOtv27NmDFi1a5NmfiUre4tfCMG5zBwiYwdvqBtZvUsDvf7kv7VDZJZlJsHW1ha2rLTz8n3lydP6X/bLSsxCfIOFhvBkePgQenr2BB+duI/5+Jh49FHgUDzxKNMejJEskpFoioZoPElKUSEgAEh5lIVMjZ91q2EKtsUWMBk8vQR7Meaa8LyfmTf4HSoIG1lBDJaXC2iwVKvN0WJunQVW7Gqyq2st9+pPuwermf1BaaqBUCFgqBJSWApaWcp98ha8PFNWqyn31H92D4spFWCgk7WJuIcHCUoK5hRks6tWCuWsVeaSMpASY3bwOcwsJ5goz7U8zc3kfM3dXmDlWkkfcSEuB2f04+TmFGcwssvukPXlsZwMzW2tIEmCmyYRZavLT5yzMIJk9LSuZy+u8Z4BIJon8OhyVUklJSbhyRW7nb9asGebPn48uXbrA0dERHh4emDJlCm7fvo21a9cCkIccaNSoEd577z288847OHbsGEaOHIkNGzboffdcYmIiHBwckJCQYJLEzxBKS0fwpQMPYvTGjgCAEfUP47sjLWHjyFY9Kj6hEUhLTEPinSQ8jlUj8W4KEuNSkfQoA0nxmXjs1QRJwgaPHwPqyBtIuhAFdYqEpBQLJKVZQJ1uCXWGJdRZSqgrV4c63RLJybo3QFZkkiQgCQ0kCEh40sXhyWMJQr5JwkIhJ1hCAykt9em+OcoDABQKSMqnySiSknTPhRxfS5aWgJXqyXEFUNCNOZYKSNpuIAJISMi/rIUCyPl3MCE+VxEhnmSLFha6ZRMTkDNEnS9Rc7ms9ptVnZT7Dt3s/czMAescx01WQ2jy+Uo2MwNUT1tTRUpKruMKPIlXkgAr1dMn0lLzjQEAoLJ+Gm96WsFls+siu2xBN3KpVEB2TE/KSsj9+iSIJ+9vjrIZz3a4zPG5sLEBJPkSvJSe+vTu6DwIaw2Skisb7PvbaElTfHw8Vq5ciYsXL0KSJDRo0ABvv/02HBwcCnWc0NBQdOmSu9Pr0KFDsWbNGgwbNgw3btxAaGio9rmwsDBMnDhRO7jl5MmTCzW4JZMmw1gx6CDeWy8nTB+1OoC5xzrzcgeVeplpWUh5kAz1/RQkP0xFSkI6kuPTkZKYgeSEDKTUqIdUS3ukpgIpV24j9Z/LSE152l1M7j4mIT1DQoZ3I2TaOyIjA8iMuYeMS9eQpZGQkWWGTI0ZMjRmyNKYIUuYIcu9BrJsHZCZCWgSk5B15668XZghC2bQCAlZMIdGSNDYOSBLoZJH3UjPgCYpGVkwRxbMISBBAzPtIowzexZRKZEIwHDf30ZJmk6fPo0ePXpApVKhVatWEELg9OnTSElJwZ49e9C8efOSDqFYykPSlJqaqm1ZCw4ONvr0NStXAiNGyI8Dm4fi61OdmDARmYDQCDmR0gCaTA00qenISs+C0Ai5079GQJP15LHSCuJJK4RIz4Dm/kN5f42Qtz15DACwtYWwl/8JFukZwN27uc6rfWxjC1SuLLduZGYCt28/fe7ZbyQbGwinJ8NvZGUBT8b2y7NFxsYGqFr16YHyG/wWkIfWyHln9fXr+ZdVqQBXV+2qFHUzV6Da1helEsh5V3Z0tE7Ljc6lToUCcHd/uu3ObXlokzxIFuZAtRyXlGNjIWVl5h2vmRng7v5033tx+bfGSJLuce/dK7h5NedMC/fvy7My5EEIyMfNfnEPHgApKbnLZdeju7t2nDpx/wGe3E6dN3d3wMJCPsfDh3IHyJznzeGxnQ2at65StpKmDh06oE6dOvjhhx9g8eTOnMzMTIwYMQLXrl3DwYMHn3ME0yoPSZMprVkDDB8uf5jHvxyNbzdXZ8JEREQlztDf30ZJmlQqFcLDw1G/fn2d7RcuXECLFi2QnHN05lKISVPR7VxwDS9N9IIQEsaNAxYs4EDURERkHIb+/jbKxW17e3tERUXl2h4dHZ1rlHAqP26disGwiZUghIR33lAzYSIiojLNKEnTgAED8Pbbb2PTpk2Ijo7GrVu3sHHjRowYMQIDBw40RggVnlqtho2NDWxsbKAu6FqxgWSlZ2FQ97t4KBzhZ30Bi5YrmDAREVGZZpRpVL7++mtIkoQhQ4YgM1PuuKZQKDBq1CjMnTvXGCEQYNTLoEG9DiEsoTNs8RgbtlnD0tbyufsQERGVZiWeNGVkZKBHjx5Yvnw5goKCcPXqVQghUKdOHZ1pVaj8OLL0HGbuaw8AWPLu36jbvb2JIyIiIiq+Ek+aFAoF/vnnH0iSBGtrazRu3LikT0kmFH8zAW+Mc0QWLDDI6zAGL2fCRERE5YNR+jQNGTIEK1euNMapyISEAN7p/B+isqqjtsVNLD7YxNQhERERGYxR+jSlp6fjxx9/REhICFq0aJFrNOr58+cbIwwqYZs2Ab/daAkLKRMbflTDvrqnqUMiIiIyGKMkTf/884921O///vtP5zmJt1SVC2lpwJQp8uNp083RcqiPaQMiIiIyMKMkTQcOHDDGaagAZmZm6NSpk/axoS3+OgU3bqjg7g58+BETYSIiKn+MkjSR6alUKp1JjA3p0bVH+PxTAFBh9tQUWFurnrcLERFRmWO0pGnfvn3Yt28f4uLioMkxeSEArFq1ylhhUAmYM+BvPBKd0Uh5GUNH1DJ1OERERCXCKEnTrFmz8Nlnn6FFixZwc3NjP6Zy5MbhW1h42h8AMO+TeJhbmps4IiIiopJhlKRp2bJlWLNmDQYPHmyM01Ee1Go1atasCQC4ceNGrjsYi2ra4JtIR3W8UPksXpzWwiDHJCIiKo2MNuRA27ZtjXEqKsD9+/cNeryz6y9i/Y12AICvvldBMmMLIhERlV9GGdxyxIgR+OWXX4xxKjISoRH4cFwKAODNmkfQ/M0GJo6IiIioZJVYS1NgYKD2sUajwYoVK7B37140adIECoVCpywHtyx79v98G/sfNYcl0vDFOg5iSURE5V+JJU3h4eE6602bNgUgD3SZEzuFl00Lt1QHALz7f/fg2a66iaMhIiIqeSWWNB04cADDhw/HggULYGdnV1KnIRO4cQPYuVN+PDaICRMREVUMJdqn6aeffkJKSkpJnoJMYOm8xxAC6N4d8PY2dTRERETGUaJ3zwkhSvLwVAhmZmZo0aKF9nFRpTxMwcpl6QCAsa/fB+BsiPCIiIhKvRIfcoB9lkoHlUqFU6dOFfs4mz46gweiPTzNb6H3IDcDREZERFQ2lHjSVK9evecmTg8fPizpMMgAhEbg+1+cAACjul+BuSX7MxERUcVR4knTrFmz4ODgUNKnISM4sSoSZ1MaQYlUvP1dY1OHQ0REZFQlnjS9/vrrqFq1akmfhp4jOTkZPj4+AIALFy7A2tq60MdY/EU8AGBgnVNw9u5gyPCIiIhKvRJNmtifqfQQQuDmzZvax4V19597+PVGSwDAmE+dDBobERFRWVCiQw7w7rny48eP/kM6lGht8w9aDPExdThERERGV6ItTRqNpiQPT0aSmQksOy9PuDx2HFsPiYioYjLKhL1Utu3eDdy6JaFKFeDVmQ1NHQ4REZFJMGmi59q8Wf45cCCgVJo2FiIiIlMpk0nTkiVL4OXlBSsrK/j5+eHQoUP5lg0NDYUkSbmWf//914gRl13pSenYvv4xAKB/r2QTR0NERGQ6JT7kgKFt2rQJEyZMwJIlS9CuXTssX74cPXv2xIULF+Dh4ZHvfpcuXYK9vb12vUqVKsYIt9SQJEk75EBh7mrcO/8cErJawM0sFu1eqFjvGRERUU5lrqVp/vz5ePvttzFixAg0aNAA3333HWrUqIGlS5cWuF/VqlXh6uqqXczNzY0UcelgbW2NyMhIREZGFmqMpt/WyRMuv9zwEswUFes9IyIiyqlMJU3p6ek4c+YMAgICdLYHBATg6NGjBe7brFkzuLm5oWvXrjhw4ECBZdPS0pCYmKizVEQZyRnYdqURAKD/cI7qTkREFVuZSpru37+PrKwsuLi46Gx3cXFBbGxsnvu4ublhxYoVCA4OxpYtW+Dt7Y2uXbvi4MGD+Z4nKCgIDg4O2qVGjRoGfR1lxf7vzuGRqIyq0j10GM1pU4iIqGIrc32agNx9coQQ+fbT8fb2hre3t3bd398f0dHR+Prrr9GxY8c895kyZQoCAwO164mJiWU+cUpOTkbLlvKI3qdOndLrEt1va9UAgJcbXIS5Zd7vFRERUUVRppImZ2dnmJub52pViouLy9X6VJA2bdpg3bp1+T6vVCqhLGf31gshcOHCBe3j58lMzcTW/+QxmfoPsy3R2IiIiMqCMnV5ztLSEn5+fggJCdHZHhISgrZt2+p9nPDwcLi5uRk6vHIl7K9UPBBOcDZ/iE7jmpg6HCIiIpMrUy1NABAYGIjBgwejRYsW8Pf3x4oVKxAVFYWRI0cCkC+t3b59G2vXrgUAfPfdd6hZsyYaNmyI9PR0rFu3DsHBwQgODjblyyj1Nu+SW5f+763KsLDi1ClERERlLmkaMGAAHjx4gM8++wwxMTFo1KgR/vzzT3h6egIAYmJiEBUVpS2fnp6OSZMm4fbt21CpVGjYsCH++OMP9OrVy1QvodTLygK2bJEf93+VCRMREREASEKfDi4VXGJiIhwcHJCQkKAzQGZZolarYWsrtx4lJSXBxsYm37Kha6PQZagHHB0FYmMlKBTGipKIiMhwDP39Xab6NJFxbP7qBgCgn+txJkxERERPlLnLc1Q0kiRpL2EWNI1KVnoWtlyQh2joP4AfDyIiomz8VqwgrK2tcePGjeeWO7TkPGI1TVFJikfXQN+SD4yIiKiM4OU50vHzkscAgFfqnoelraWJoyEiIio9mDSRVvL9ZGy+LLcuDR1XNju8ExERlRQmTRVESkoKWrZsiZYtWyIlJSXPMttmhOMx7OFlEYV2IznXHBERUU7s01RBaDQanD59Wvs4Lz9tk1uXhrS9CjMLD6PFRkREVBawpYkAALdvA3tjGwEABs9pYOJoiIiISh8mTQQAWL8e0GgktGsH1G7naupwiIiISh0mTQShEfhpjXzJbuhQEwdDRERUSjFpIpzd8C8uXDSD0jwDr75q6miIiIhKJyZNhLVfxQEA+rmfQqVKpo2FiIiotOLdcxWIs7Nzrm3pSen45VxDAMCQERzMkoiIKD9MmioIGxsb3Lt3L9f23UHhuC9aw8UsDgEfNTV+YERERGUEL89VcD+tEQCAN5tdgIUVc2giIqL8MGmqwK6FRmHnneYAgKEfu5s4GiIiotKNSVMFkZKSgs6dO6Nz585ISUnBjRtAl94qZMASbWzPo0n/eqYOkYiIqFTj9ZgKQqPRICwsDABw/boGvXoBUclVUM8+BsEHqpg4OiIiotKPSVMF1LMnEBUF1K0LHAh1gzuvzBERET0XL89VQNqE6QCYMBEREemJLU2F0NU9EhaSbe4nJAlo2OjpetRNIDEx/wM1bAhIT/LVW9FAfHz+ZRs0AMyfVNOd28DDh/mX9a4PKBQAABETg8x7j5CapUCaRoHkrExtsVoWN3FgpweqVcvjtRAREVGeJCGEMHUQpV1iYiIcHBwAJACwN3U4RaQGICdJl8KuoF7H2qYNh4iIqIRlf38nJCTA3r74399saSqEXwJPw1ppk/sJSQJatXq6/t9/wKNH+R+oZQvAzFx+fOUK8OBB/mWbN9e2HuHaNSCPASq1mjYFlEr58c2bUDyKg9LaHFa2FhCKDHR4R36qmp9r/scgIiKiPLGlSQ+GzlRNQa1Wo2rVqgCAuLg42NjkkfwRERGVI2xpoiKxsbGBWq02dRhERERlFu+eIyIiItIDkyYiIiIiPTBpqiBSU1PRu3dv9O7dG6mpqaYOh4iIqMxhn6YKIisrC3/++af2MRERERUOW5qIiIiI9MCkiYiIiEgPZTJpWrJkCby8vGBlZQU/Pz8cOnSowPJhYWHw8/ODlZUVatWqhWXLlhkpUiIiIiovylzStGnTJkyYMAFTp05FeHg4OnTogJ49eyIqKirP8tevX0evXr3QoUMHhIeH45NPPsH777+P4OBgI0dOREREZVmZGxG8devWaN68OZYuXard1qBBA/Tr1w9BQUG5yk+ePBk7duzAxYsXtdtGjhyJv//+G8eOHdPrnOVlRHBbW3nuuaSkJI4ITkRE5V6FHhE8PT0dZ86cwccff6yzPSAgAEePHs1zn2PHjiEgIEBnW48ePbBy5UpkZGRAkT2vWw5paWlIS0vTrickJACQ3/yyKudo4ImJibyDjoiIyr3s721DtQ+VqaTp/v37yMrKgouLi852FxcXxMbG5rlPbGxsnuUzMzNx//59uLm55donKCgIs2bNyrW9Ro0axYi+9HB3dzd1CEREREbz4MEDODg4FPs4ZSppyiZJks66ECLXtueVz2t7tilTpiAwMFC7Hh8fD09PT0RFRRnkTaeiS0xMRI0aNRAdHV1mL5WWJ6yP0oN1UXqwLkqPhIQEeHh4wNHR0SDHK1NJk7OzM8zNzXO1KsXFxeVqTcrm6uqaZ3kLCws4OTnluY9SqYRSqcy13cHBgb8ApYS9vT3rohRhfZQerIvSg3VRepiZGea+tzJ195ylpSX8/PwQEhKisz0kJARt27bNcx9/f/9c5ffs2YMWLVrk2Z+JiIiIKC9lKmkCgMDAQPz4449YtWoVLl68iIkTJyIqKgojR44EIF9aGzJkiLb8yJEjcfPmTQQGBuLixYtYtWoVVq5ciUmTJpnqJRAREVEZVKYuzwHAgAED8ODBA3z22WeIiYlBo0aN8Oeff8LT0xMAEBMTozNmk5eXF/78809MnDgRixcvhru7OxYuXIhXXnlF73MqlUrMmDEjz0t2ZFysi9KF9VF6sC5KD9ZF6WHouihz4zQRERERmUKZuzxHREREZApMmoiIiIj0wKSJiIiISA9MmoiIiIj0wKRJD0uWLIGXlxesrKzg5+eHQ4cOmTqkcu/gwYPo27cv3N3dIUkStm3bpvO8EAIzZ86Eu7s7VCoVOnfujMjISNMEW84FBQWhZcuWsLOzQ9WqVdGvXz9cunRJpwzrwziWLl2KJk2aaAdN9Pf3x65du7TPsx5MJygoCJIkYcKECdptrA/jmDlzJiRJ0llcXV21zxuyHpg0PcemTZswYcIETJ06FeHh4ejQoQN69uypM6wBGZ5arYavry8WLVqU5/Pz5s3D/PnzsWjRIpw6dQqurq7o3r07Hj9+bORIy7+wsDCMGTMGx48fR0hICDIzMxEQEKAzCTTrwziqV6+OuXPn4vTp0zh9+jReeOEFvPTSS9ovANaDaZw6dQorVqxAkyZNdLazPoynYcOGiImJ0S7nz5/XPmfQehBUoFatWomRI0fqbKtfv774+OOPTRRRxQNAbN26Vbuu0WiEq6urmDt3rnZbamqqcHBwEMuWLTNBhBVLXFycACDCwsKEEKwPU6tcubL48ccfWQ8m8vjxY1G3bl0REhIiOnXqJMaPHy+E4O+FMc2YMUP4+vrm+Zyh64EtTQVIT0/HmTNnEBAQoLM9ICAAR48eNVFUdP36dcTGxurUi1KpRKdOnVgvRpCQkAAA2gkwWR+mkZWVhY0bN0KtVsPf35/1YCJjxoxB79690a1bN53trA/junz5Mtzd3eHl5YXXX38d165dA2D4eihzI4Ib0/3795GVlZVrMmAXF5dckwCT8WS/93nVy82bN00RUoUhhEBgYCDat2+PRo0aAWB9GNv58+fh7++P1NRU2NraYuvWrfDx8dF+AbAejGfjxo04e/YsTp06les5/l4YT+vWrbF27VrUq1cPd+/exeeff462bdsiMjLS4PXApEkPkiTprAshcm0j42O9GN/YsWNx7tw5HD58ONdzrA/j8Pb2RkREBOLj4xEcHIyhQ4ciLCxM+zzrwTiio6Mxfvx47NmzB1ZWVvmWY32UvJ49e2ofN27cGP7+/qhduzZ++ukntGnTBoDh6oGX5wrg7OwMc3PzXK1KcXFxubJWMp7suyJYL8Y1btw47NixAwcOHED16tW121kfxmVpaYk6deqgRYsWCAoKgq+vLxYsWMB6MLIzZ84gLi4Ofn5+sLCwgIWFBcLCwrBw4UJYWFho33PWh/HZ2NigcePGuHz5ssF/L5g0FcDS0hJ+fn4ICQnR2R4SEoK2bduaKCry8vKCq6urTr2kp6cjLCyM9VIChBAYO3YstmzZgv3798PLy0vnedaHaQkhkJaWxnowsq5du+L8+fOIiIjQLi1atMCbb76JiIgI1KpVi/VhImlpabh48SLc3NwM/3tR6K7jFczGjRuFQqEQK1euFBcuXBATJkwQNjY24saNG6YOrVx7/PixCA8PF+Hh4QKAmD9/vggPDxc3b94UQggxd+5c4eDgILZs2SLOnz8vBg4cKNzc3ERiYqKJIy9/Ro0aJRwcHERoaKiIiYnRLsnJydoyrA/jmDJlijh48KC4fv26OHfunPjkk0+EmZmZ2LNnjxCC9WBqOe+eE4L1YSwffPCBCA0NFdeuXRPHjx8Xffr0EXZ2dtrvaUPWA5MmPSxevFh4enoKS0tL0bx5c+2t1lRyDhw4IADkWoYOHSqEkG8jnTFjhnB1dRVKpVJ07NhRnD9/3rRBl1N51QMAsXr1am0Z1odxDB8+XPu3qEqVKqJr167ahEkI1oOpPZs0sT6MY8CAAcLNzU0oFArh7u4uXn75ZREZGal93pD1IAkhRDFbwoiIiIjKPfZpIiIiItIDkyYiIiIiPTBpIiIiItIDkyYiIiIiPTBpIiIiItIDkyYiIiIiPTBpIiIiItIDkyYiIiIiPTBpIiIiItIDkyYiKvU6d+6MCRMmmDqMfHXu3BmSJEGSJEREROi1z7Bhw7T7bNu2rUTjIyLDYNJERCaVnTjktwwbNgxbtmzB7NmzTRLfhAkT0K9fv+eWe+eddxATE4NGjRrpddwFCxYgJiammNERkTFZmDoAIqrYciYOmzZtwvTp03Hp0iXtNpVKBQcHB1OEBgA4deoUevfu/dxy1tbWcHV11fu4Dg4OJn1dRFR4bGkiIpNydXXVLg4ODpAkKde2Zy/Pde7cGePGjcOECRNQuXJluLi4YMWKFVCr1XjrrbdgZ2eH2rVrY9euXdp9hBCYN28eatWqBZVKBV9fX/z222/5xpWRkQFLS0scPXoUU6dOhSRJaN26daFe22+//YbGjRtDpVLByckJ3bp1g1qtLvR7RESlA5MmIiqTfvrpJzg7O+PkyZMYN24cRo0ahVdffRVt27bF2bNn0aNHDwwePBjJyckAgGnTpmH16tVYunQpIiMjMXHiRAwaNAhhYWF5Ht/c3ByHDx8GAERERCAmJgZ//fWX3vHFxMRg4MCBGD58OC5evIjQ0FC8/PLLEEIU/8UTkUnw8hwRlUm+vr6YNm0aAGDKlCmYO3cunJ2d8c477wAApk+fjqVLl+LcuXNo3Lgx5s+fj/3798Pf3x8AUKtWLRw+fBjLly9Hp06dch3fzMwMd+7cgZOTE3x9fQsdX0xMDDIzM/Hyyy/D09MTANC4ceOivlwiKgWYNBFRmdSkSRPtY3Nzczg5OekkJS4uLgCAuLg4XLhwAampqejevbvOMdLT09GsWbN8zxEeHl6khAmQk7quXbuicePG6NGjBwICAtC/f39Urly5SMcjItNj0kREZZJCodBZlyRJZ5skSQAAjUYDjUYDAPjjjz9QrVo1nf2USmW+54iIiChy0mRubo6QkBAcPXoUe/bswffff4+pU6fixIkT8PLyKtIxici02KeJiMo9Hx8fKJVKREVFoU6dOjpLjRo18t3v/PnzOi1ahSVJEtq1a4dZs2YhPDwclpaW2Lp1a5GPR0SmxZYmIir37OzsMGnSJEycOBEajQbt27dHYmIijh49CltbWwwdOjTP/TQaDc6dO4c7d+7AxsamUEMEnDhxAvv27UNAQACqVq2KEydO4N69e2jQoIGhXhYRGRlbmoioQpg9ezamT5+OoKAgNGjQAD169MDOnTsLvFT2+eefY9OmTahWrRo+++yzQp3P3t4eBw8eRK9evVCvXj1MmzYN33zzDXr27Fncl0JEJiIJ3v9KRFQsnTt3RtOmTfHdd98Vel9JkrB161a9Rh0nItNiSxMRkQEsWbIEtra2OH/+vF7lR44cCVtb2xKOiogMiS1NRETFdPv2baSkpAAAPDw8YGlp+dx94uLikJiYCABwc3ODjY1NicZIRMXHpImIiIhID7w8R0RERKQHJk1EREREemDSRERERKQHJk1EREREemDSRERERKQHJk1EREREemDSRERERKQHJk1EREREemDSRERERKQHJk1EREREevh/yZyV8OmKCtcAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.suptitle('Cruise control with integrator anti-windup protection')\n", "t, y = ct.input_output_response(\n", " cruise_pi, T, [vref, gear, theta_hill], X0,\n", " params={'kaw':2.})\n", "cruise_plot(cruise_pi, t, y, label='Commanded', t_hill=5, \n", " antiwindup=True, legend=True);" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 2 }