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@jlmcgehee21
Created May 23, 2018 18:53
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Digital Twins -- A Simple Example for Engineers\n",
"\n",
"This notebook contains some scratch code used to generate the figures for the blog post that shares its title. I have provided notes/comments where I thought they might be useful."
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [],
"source": [
"from scipy.integrate import odeint\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"from cycler import cycler\n",
"\n",
"monochrome = (cycler('color', ['k']) * cycler('marker', ['', '.']) *\n",
" cycler('linestyle', ['-', '--', ':', '-.']))\n",
"plt.rc('axes', prop_cycle=monochrome)\n",
"\n",
"sns.set_style('ticks')\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Functions that will need to be re-used, and \"global\" variables that will be referenced across cells. Of course, all of this is bad practice for production code, but this is a notebook to make pretty pictures for a blog post."
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"x_0 = 0 # initial position\n",
"xd_0 = 0 # initial velocity\n",
"\n",
"state_0 = [x_0, xd_0] # intitial state\n",
"\n",
"t = np.arange(0, 100, 0.01) # time vector\n",
"\n",
"def bump(t, height=0.1):\n",
" '''\n",
" Create a bump of a given height that starts at t=5 seconds, \n",
" and ends at t=5.2 seconds.\n",
" '''\n",
" if 5 < t < 5.2:\n",
" return height\n",
" return 0\n",
"\n",
"def eqn(w, t, m, c, k, bumpsize=0.1):\n",
" '''\n",
" Callable with ODE to solve.\n",
" \n",
" Note `xdd` is the main equation shown in the blog\n",
" '''\n",
" x, xd = w\n",
" road_d = bump(t, bumpsize) - bump(t - 0.01, bumpsize)\n",
" \n",
" xdd = (c/m)*road_d + (k/m)*bump(t, bumpsize) -(c/m)*xd - (k/m)*x\n",
" \n",
" return xd, xdd\n",
"\n",
"def format_plot(fig, ax, size=(8, 6)):\n",
" fig.set_size_inches(*size)\n",
" ax.set_xlabel('time (s)', fontsize=12)\n",
" ax.set_ylabel('displacement of mass (m)', fontsize=12)\n",
" sns.despine(fig, trim=True)\n",
" ax.grid()\n",
" \n",
" return ax\n",
"\n",
"def title_string(desc='', m=0, c=0, k=0):\n",
" return f'{desc}: m={m}kg, c={c}N*s/m, k={k}N/m'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sample plot of the results of the ODE solver. Note how we can pass parameters for our system into `odeint`. This is useful for simulating across a wide array of parameters, or more interestingly, _finding optimal values for our parameters based on external constraints_."
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {},
"outputs": [
{
"data": {
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ENkaqqtgIpFIpbrnllmj+kUceYe7cuZ1YIhER2VgpcNgIvPPOO8ybN6/Jsueff76TSiMiIhszBQ4bgTfeeGODZf/+9787oSQiIrKxU+CwEXjvvfc2WObunVASERHZ2Clw2Ag0FyQocBARkUJQ4LARmDNnzgbLPvroI9atW9cJpRERkY2ZAoeNwKeffrrBslQqtUGDSRERkVwpcChyDQ0NLFq0KJrfZZddounmAgoREZFcKHAockuWLKGhoQGAwYMHs/XWW0frPvnkk84qloiIbKQUOBS5+fPnR9MjRoxg5MiR0bwyDiIikm8KHIrcggULounhw4ezxRZbRPPKOIiISL4pcChy8YxDZuAQXyciIpIPChyKXDzjMGLECDbbbLNofsmSJZ1RJBER2YgpcChy8eBgs802Y8iQIdH84sWLO6NIIiKyEevQ22qbWSlwE7AzsA44092rYuvPAs4G6oEr3P3R2LrzgeHuflE4fxRwSbjtbe5+i5n1Bu4GhgLVwKnuvlF/ey5fvjyaHjRokDIOIiJSUB2dcfgS0Mvd9wIuAq5NrzCz4cB5wD7AYcAvzaynmfU2s3uAb8e2rQCuA74A7A9MMbNhwDnAm+4+CbgT+EnHPK3Okxk4ZGYcUqlUZxRLREQ2Uh0dOOwLPAHg7jOBibF1uwMz3H2du68EqoCdgF7AHcAvYtuOB6rcfbm7rwdeBPaLHx94HDgkacHMrPyTTz6hvr6+XU+ss2QGDr1796Zv374A1NXVsWrVqs4qmoiIbIQ6tKoC6A+sjM03mFm5u9c3s64aGODuy4F/mNlprRynGhiQsTy9bANmNgWYkrG4x8EHH8zvf/97hg0blt2zakFtbS2VlZV5OVZL4o0jV6xYQWVlJQMGDGDNmjUAzJw5k9GjRxe0DIXUEdewO9B1zJ2uYe50DXOX72s4fvz4rPfp6MBhFdAvNl8aBg3NresHrEh4nPS28eUt7u/uU4Gp8WVmNgb4YOzYsU0GUcpFZWVlu16UbNTU1ETTn//859lqq63YfPPNo/tUDBgwoOBlKKSOuIbdga5j7nQNc6drmLuucA07uqpiBjAZwMz2BN6MrXsFmGRmvcxsAEF1xFstHKcS2NbMBptZD4JqipfjxweOAF7I/1PoWjKrKoAm7RzUQFJERPKpozMODwKHmtlLQAlwupl9l6C9wiNm9huCL/tS4MfuXtvcQdy9LtzvyXDb29z9UzO7GbjDzF4E1gMndcBz6jR1dXWsXr0agJKSEvr37w8ocBARkcLp0MDB3RuBb2Ysfje2/hbglhb2vT1jfhowLWNZDfCVfJS1GKxY8VlNzMCBAyktDRJI6cxD5jYiIiK50gBQRay5agoIgog0BQ4iIpJPChyKmAIHERHpaAocilhLgYOqKkREpFAUOBSxlSs/G8oinmVQxkFERApFgUMRq66ujqb79ftsWAsFDiIiUigKHIpYuismwCabbBJNxwOHeHWGiIhIrhQ4FDFlHEREpKMpcChi8YyDAgcREekIChyKWDzjEK+qSI8gCbBq1SoaGho6tFwiIrLxUuBQxFqqqigrK9sgeBAREckHBQ5FrKWqClB1hYiIFIYChyLWUlUFaBAoEREpDAUORay1jMOAAQOiaXXJFBGRfFHgUMRayzjE2zjEtxMREcmFAoci1lLjyMx5BQ4iIpIvChyKWGtVFQocRESkEBQ4FKlUKpW4qkLdMUVEJF8UOBSp9evXU19fD0BFRQU9e/Zssl4ZBxERKQQFDkWqtWwDKHAQEZHCUOBQpFpr35C5TIGDiIjkiwKHItVajwpQd0wRESkMBQ5FKpuqCjWOFBGRfFHgUKTWrFkTTauNg4iIdBQFDkWqpqYmmu7Tp88G6xU4iIhIIShwKFJr166NppsLHNTGQURECkGBQ5HKJuOgNg4iIpIvChyKVDxw6N279wbrM6sqUqlUh5RLREQ2bgocilRbGYeePXtSUVEBQH19PevWreuwsomIyMZLgUORaitwADWQFBGR/FPgUKTaahwJaiApIiL5p8ChSLXVxgHUQFJERPJPgUORUlWFiIh0BgUORUqBg4iIdAYFDkUqSeCgNg4iIpJvChyKVJLGkfF7WMRvwy0iItJe5R19QjMrBW4CdgbWAWe6e1Vs/VnA2UA9cIW7P2pmQ4B7gd7APOB0YBzw69ih9wS+BLwCvAe8FS5/0N2vL+iT6gRJGkf27ds3mo7fFEtERKS9OjxwIPhy7+Xue5nZnsC1wDEAZjYcOA+YCPQCXjSzfwKXAPe6++1mdhFwtrtfBxwQ7vcV4FN3f8LMDgH+5O7ndvQT60hJqioUOIiISL51RlXFvsATAO4+kyBISNsdmOHu69x9JVAF7BTfB3gcOCS9g5n1BS4D/idcNAGYYGbPmdn9ZjaikE+ms2QbOKiqQkRE8qEzMg79gZWx+QYzK3f3+mbWVQMDMpanl6WdAdzv7kvC+XeBWe7+lJmdDNwAHB8vgJlNAaZklKsHQFVVVd4aEtbW1lJZWZmXY2VaufKzy/Tpp582u008y/Dxxx8XrCyFVMhr2J3oOuZO1zB3uoa5y/c1HD9+fNb7dEbgsAroF5svDYOG5tb1A1bElq+NLUs7maaBwXQg/XP8QeDyzAK4+1RganyZmY0BPhg7diwjR47M7hm1oLKysl0vShL19fXR9E477cTQoUM32GbrrbeOpnv27FmwshRSIa9hd6LrmDtdw9zpGuauK1zDzqiqmAFMBgjbOLwZW/cKMMnMepnZAGA8QSPHaB/gCOCFcP8BQE93/zh2jFuB48Lpg4FZBXoenUpVFSIi0hk6I+PwIHComb0ElACnm9l3gSp3f8TMfkMQGJQCP3b3WjO7Argj7HGxBDgpPNY44MOM418E3GZm3wLWAGcW/Bl1sFQqpV4VIiLSKTo8cHD3RuCbGYvfja2/BbglY5+FwOHNHOvfBL004ss+AA7MV3m7otra2mi6Z8+elJWVNbtdfBwHBQ4iIpIPGgCqCMUHf2op2wDKOIiISP4pcChCSdo3gNo4iIhI/ilwKELtCRyUcRARkXxQ4FCEkgYOauMgIiL5psChCCnjICIinUWBQxFK2jgyHlTU1NTQ2NhY0HKJiMjGT4FDEUqacSgtLW0SWMT3ExERaQ8FDkUoyeBPaWrnICIi+aTAoQjFB4BqK3BQl0wREcknBQ5FaN26ddF0z549W91WDSRFRCSfFDgUocwhp1ujwEFERPJJgUMRyibjoDYOIiKSTwocilB7qyrUxkFERHKlwKEIqY2DiIh0FgUORSgeOPTq1avVbRU4iIhIPilwKELKOIiISGcpb22lmfUEpgDHAeOABuBd4H7gdndfX/ASygba2zhSbRxERCRXLWYczGx/4N/AeOAq4EDgMOB6YCfgVTM7qCMKKU2pO6aIiHSW1jIORwH7uvuqjOXvAI+a2QDgEmB6oQonzVNVhYiIdJYWAwd3/35rO7r7SuB7eS+RtEndMUVEpLO02sYBwMyGA6cBg+PL3f2HBSqTtEEDQImISGdJ0qviEWB3oCTjIZ1E3TFFRKSztJlxAHq4+7EFL4kkpqoKERHpLEkyDrPMbIeCl0QSa2/gUFNTU7AyiYhI95Ak4zADeN3M5gN16YXuvnXBSiWtyqY7Zp8+faJpBQ4iIpKrJIHDpcBJwPuFLYokpYyDiIh0liSBwzJ3/0vBSyKJZRM4KOMgIiL5lCRw+LuZXQM8AETfWO4+u2ClklZl06tCgYOIiORTksDhpPDvcbFlKUBtHDpJNhmH3r17R9M1NTWkUilKStSbVkRE2qfNwMHdt+qIgkhy2QQOFRUVVFRUUFdXR2NjI+vWrWszSyEiItKS1m5y9Ydw1MiW1o8wsz8WpljSmmx6VYCqK0REJH9ayzjcQHAzq/8CjwJVQBlBFcURBLfZPqvgJZQm6uvraWxsBKCkpITy8rZrm/r27cvKlSuBIHAYPHhwG3uIiIg0r7WbXL1uZrsBXwWOBz4HNALvAX8F7nf3xg4ppUQyqymStFdQxkFERPKl1Z+r7p4C7gsf0gVk074hTYGDiIjkS5Ihp6ULyaYrZpoCBxERyZck3THzysxKgZuAnQnGhTjT3ati688CzgbqgSvc/VEzGwLcC/QG5gGnu3uNmV0P7AtUh7sfA1Q0t22HPLkOoIyDiIh0ps7IOHwJ6OXuewEXAdemV4S9OM4D9gEOA35pZj2BS4B73X0S8BpBYAEwATjM3Q8IHytb2XajoMBBREQ6U6LAwcy2Dv8ea2aXmNmAHM65L/AEgLvPBCbG1u0OzHD3dWEQUAXsFN8HeBw4JMxcbAtMNbMZZvaNzOOnt82hrF1Otl0xoWngsGbNmryXSUREuo82qyrM7Pfh318DNwJPAn8g6GnRHv2BlbH5BjMrd/f6ZtZVAwMylqeX9SXoMvp/BN1EnzGzV1vYNvM5TQGmZCzuAVBVVUV1dXXmLu1SW1tLZWVlXo6V9u6770bTqVQq0fHr6qKbmvL+++/nvUyFVIhr2B3pOuZO1zB3uoa5y/c1HD9+fNb7JGnjMIEgE3ARcIe7X2xm/876TJ9ZBfSLzZeGQUNz6/oBK2LL18aW1QDXp9svmNl0gnYTzW3bhLtPBabGl5nZGOCDsWPHMnLkyBye3mcqKyvb9aK0ZsmSJdH0gAEDEh1/8803z3qfrqIQ17A70nXMna5h7nQNc9cVrmGSqorScLyGQ4Hp4bK+rWzflhnAZAAz2xN4M7buFWCSmfUKq0PGA2/F9yEYfOoFggGoZphZmZlVEFRRzG5h242G2jiIiEhnShI4VJnZYwQjRj5nZvcAb+RwzgeBWjN7CbgOuMDMvmtmR7v7AuA3BF/204Efu3stcAVwopnNAPYCbnT3SuAuYCbwHHCnu7/d3LY5lLXLUXdMERHpTEmqKk4Hvgy86O7rzewF4M72njDMXnwzY/G7sfW3ALdk7LMQOLyZY10NXJ1k242FMg4iItKZ2sw4uPsa4CV3/9DMjgWGEoyVIJ1AgYOIiHSmNgOHsFfFhWY2niDtvxVBrwrpBLl2x1TgICIiuUjSxmECcA5BdcUd7n46sGVBSyUtak/GoW/fz9qyahwHERHJRWf0qpAcqKpCREQ6U7a9Kp7NQ68KyYF6VYiISGdKEjicTnDTqP3dvY6gq+TpBS2VtEgZBxER6UxJe1U8RjA09GiCIaf3LXTBpHkKHEREpDMluVfF5cDF4Ww9wT0d3gF2LGC5pAXqVSEiIp0pSVXF14HRwF8J7kZ5KvB2IQslLVPGQUREOlOSwGGRu88HKoGd3f1uYGxhiyUtUXdMERHpTEkChzoz2wZwghtQlQODClssaYkyDiIi0pmSBA6/JLgF9aPAccDHwDOFLJS0rD3dMSsqKigrKwOgvr6eurq6gpRNREQ2fm02jnT3RwmCBsxsZ2Bbd/9PoQsmzWtPxqGkpIQ+ffpQXV0NBFmHAQMGFKR8IiKycUvSq2I4cBowOLbsZHf/YQHLJS1oT+AAKHAQEZG8SFJV8QiwO1CS8ZBO0J7umKB2DiIikh9tZhyAHu5+bMFLIonkknFIU+AgIiLtlSTjMMvMdih4SSSR9gYO8S6ZChxERKS9kmQcZgCvm9l8IGqO7+5bF6xU0qL29KqAphkHjeUgIiLtlSRwuBQ4CXi/sEWRJIqpqmL69OnceuutjB07lh/+8IdssskmHXJeEREpnCSBwzJ3/0vBSyKJFEvg8Mwzz3DooYfS2NgIwMyZM3nyyScpKVG7WhGRYpYkcPi7mV0DPABE31ruPrtgpZIWFUOvilQqxfe///0oaAD45z//yaOPPspRRx1V0HOLiEhhJQkcTgr/HhdblgLUxqETFEPG4c0332T27A3jyqlTpypwEBEpcklGjtyqIwoiyRRDr4q//vWv0fTuu+/OK6+8AsATTzzBsmXLGDx4cEu7iohIF5ekO6Z0EalUqigyDtOnT4+mv//97zNx4kQguE9GfJ2IiBQfBQ5FpL6+nlQqBUBZWRnl5UlqmgIdFTisW7eOV199NZrff//9+cIXvhDNP/OM7o8mIlLMWgwczGyPjiyItK292QbouHEcXnvttaicY8eOZejQoRx00EHRegUOIiLFrbWMw+8AzOzpDiqLtCGmb8vxAAAgAElEQVRfgUMhMw7/+te/oum99toLgL333ju6rXdlZSWrVq0q2PlFRKSwWst1l5vZP4DPm9kjmSvd/ejCFUua096umNBxgcPbb78dTe+6664A9O7dm+2335433ngDCLIS+++/f8HKICIihdNa4HAEcBBgBGM4SCcrhozDO++8E01vt9120fSECROiwGHWrFkKHEREilSLgYO7fwLcaWZz3f1ZM9sSqHD3qo4rnsTlEjh0RHfMVCrVJOOw/fbbR9MTJkzgj3/8IxAEDiIiUpySNMv/1MzeBjYHSs1sCXCku79b2KJJpq6ecViwYAErVqwAoH///myxxRbRugkTJkTTr732WkHOLyIihZekO+YNwFXuPsjdBwBXADcVtljSnPbeGRM6JnDIrKaI35cinn2YM2cOdXV1iIhI8UkSOAxz9zvSM+7+R2CzwhVJWtLVu2NWVX1Wi2VmTdb169ePkSNHAsF4FO+/r5utiogUoySBQ7mZRWMEm9kQgntVSAfr6lUVH374YTS91VYbjlQebyxZWVlZkDKIiEhhJa2qmGlmPzeznwMvATcXtljSnK7eHTMeOIwZM2aD9ePHj4+mFTiIiBSnJDe5mmpmVcBhBIHGt9z9qfaczMxKCdpH7Exwi+4z4700zOws4GygHrjC3R8NMxz3Ar2BecDp7l5jZhcAJ4a7Pubul5lZCfAJMCdc/rK7X9yesnZFXT3j8MEHH0TTbQUO8fYQIiJSPBLd7MDdpwP5uDvRl4Be7r6Xme0JXAscA2Bmw4HzgIlAL+BFM/sncAlwr7vfbmYXAWeb2cPAycAeQGO47YNADTDb3TfKezfnEjj06tWLkpKS6EZZDQ0N0WiO+aKqChGRjV9H3+RqX+AJAHefSRAkpO0OzHD3de6+EqgCdorvAzwOHAJ8DBzu7g3ungIqgFpgArCFmT1jZo9ZZgu9IpdLr4qSkpImWYe1a9fmrVzp4y1cuBCA8vJyNt988w22iWcc3D26YZeIiBSP5LdXzI/+wMrYfIOZlbt7fTPrqoEBGcurgQHuXgcsCasmrgZec/f3wqzFL939fjPbF7gb2C2zEGY2BZiSsbgHBD0Dqqurc32eQNAmIZ+/rD/66KNouqamJutj9+zZM+pR8frrr7PpppvmrWzxXhLDhw9nzpw5G2yTSqXo168f1dXVrFmzhhdffJEhQ4a0etx8X8PuStcxd7qGudM1zF2+r2H8B11SbQYOZnaMuz+csewUd78r67PBKqBfbL40DBqaW9cPWBFbvja2DDPrBdxGEEx8K9znVYL2Ebj7i2a2uZmVhFmJiLtPBaZmPKcxwAdjx46Nug3mqrKysl0vSksGDRoUTQ8fPjzrY/fr149ly5YBMHLkyGbbIbRXvJpi3LhxLZZt2223Zfbs2UBwa/C2nkO+r2F3peuYO13D3Oka5q4rXMMWAwczO4qgCuBqM4tXhlcAVwLtCRxmAEcBfwnbOLwZW/cK8IswIOgJjAfeCveZDNxOcP+MF8JMw8PAdHf/VewYPwOWAleZ2c7Ax5lBQzHLpVcFFHYsh7lz50bTW265ZYvbbbPNNlHgUFVVxd57753XcoiISGG1lnHYheAmV0OBc2PL6wmqB9rjQeBQM3sJKAFON7PvAlXu/oiZ/QZ4gaDtxY/dvdbMrgDuCHtcLAFOImhkuT/Q08yOCI99MfC/wN1mdmRYztPaWc4uKZfGkVDYnhXz5s2LpuNDTWfaZpttomkNAiUiUnxau8nVz4Gfm9m33D0vQ0y7eyPwzYzF78bW3wLckrHPQuDwjH0eJOh50Zwjcyxml5XPwCHfGYd44NBcw8g0BQ4iIsUtSePI283sVGAwQZYAAHf/v4KVSpqVa+BQyDtkKnAQEekekgQOfwa2IGiPkG4vsNG0GygmuXTHhMJWVcyfPz+aHjFiRIvbKXAQESluSQKH8cD4WO8H6ST5zDh0VlXFFltsQY8ePVi/fj2LFy9m1apV9O/fP69lERGRwkkyANTHBS+FJNJVG0fW1dWxaNEiIBhoatiwYS1uW1ZW1mRUSWUdRESKS5KMw5vAM2b2BMFYCoDaOHSGXLtjFirjsHDhwmgUyKFDh1JRUdHq9ttssw3uDsB///tfdt1117yVRURECitJ4NCfYPjnsbFlauPQCbpqxiFpNUVaPOMQHw1TRES6viR3xzwdwMwGuvuKwhdJWtJV2zhkGzjEB4iKjzgpIiJdX5Ihp8cRjJsw0Mx2A54Gvuzu77a+p+RbV+1VkW3gEB/qWhkHEZHikqRx5I3A+cAid58H3EDGfR6kYyjjICIinS1J4LCpu/8zPROOIqn+c52gq7ZxiI/hMHz48Da3V8ZBRKR4JQkcUuGNp1IA4a2ry1rfRQqhq/aqWLx4cTTdWlfMtM0224zevXsDsHLlSlasUNMZEZFikSRwuAl4EhhqZr8EZobLpIN11YxDegwHCIKCtpSUlDSprlDWQUSkeLQZOLj7bcAlwD0Et9Se4u43F7pgsqGu2sYhnnEYOnRoon3UzkFEpDglGccBd3/OzP6dnjezPu6e35sdSJu6asYhHjgkyTiA2jmIiBSrJN0xvwtcAaS/qUoI2juonUMHy7U7ZiEyDrW1tVRXVwNQXl7OwIEDE+2njIOISHFKknG4ANgT0E0FOllXzDhkZhtKSkpa2fozyjiIiBSnJIHDHHd/o+AlkValUqku2cYh24aRaZ2RcUilUsyaNYu5c+eyyy67sPXWW3fIeUVENiZJAocbzew+4B9AXXqhu99ZsFLJBtavXx9Nl5eXU1qapENMU5kZh1QqlThD0JL2NIyEjs84LF26lBNOOIGnn346WnbOOedw/fXXt3lTLhER+UySwOHbwDCgT2xZClDg0IFyzTYAVFRUUFFRQV1dHQ0NDaxfv77dx0prb8Zh+PDh9OjRg/Xr17N06VJWr17NJptsklNZWrJ+/XomT57MK6+80mT5zTffzIoVK7jnnntyDqBERLqLJIHDaHfftuAlkVblI3CAIOuwcuVKIMg65Bo4tDfjUFpayujRo6mqqgKCrMP222+fU1lacsUVV0RBQ0lJCePHj+edd94B4E9/+hMHHHAAU6ZMKci5RUQ2Nkny3R+aWds3IJCCyrVHRVq+2zm0pytmWke0c1iwYAHXXnttNH/11Vfz1ltvNQkUvve97zXJnIiISMuSBA5rgbfM7EkzeyT9KHTBpKl8ZhzS8tGzor1VFdAx7Ryuueaa6HnuvPPOXHDBBZSUlPDrX/8aMwNg9erVXHHFFQU5v4jIxiZJ4PAAQZfMe8Pp9EM6UL4Ch0JmHLKpqoDCZxxqa2u5/fbbo/nLL788alTau3dvrrnmmmjd7373Oz755JO8l0FEZGOTZMjpO4CngcXA3cD0cJl0IGUcsvfggw+ydOlSIAhSvvjFLzZZf+SRR7LPPvsAUFdXx4033pj3MoiIbGzaDBzMbDLwEvBbYChQaWbHFLpg0lSud8ZM60oZh3jg8MEHH+Rclkx33XVXNH3GGWds0IW1pKSEH/zgB9H873//e1avXp33coiIbEySVFVcCuwBrHD3+cC+wOWFLJRsKB445NI4sitlHLbaaqtoOt9VFatWreKpp56K5k855ZRmtzvqqKMYO3YsACtWrODOO9XLWESkNUkCh9IwYADA3V8nGMdBOtDatWuj6d69e7f7OPnMOKxduzY6RkVFBQMGDMhq/xEjRkSDLy1evDivd+x87LHHqKsLxivbddddm2Q34kpLS/mf//mfaP7WW2/NWxlERDZGSQKHGjMbTRgsmNkkoLb1XSTf8hU45DPjsGTJkmh6yJAhWQ+iVFZWxujRo6P5fLZzePDBB6PpL3/5y61ue/LJJ0dZnNdee43Zs2fnrRwiIhubJIHDRQTDTW9jZi8DDwIXFrRUsoGumHFINzwE2HTTTdt1jEK0c6ivr+fJJ5+M5r/0pS+1uv2gQYM4/vjjo3llHUREWpakV8VLBHfHPBH4BWDu/lyhCyZNdcWMw7Jly6Lp9gYOhWjnMHv27Gh0zC222IIddtihzX3OPPPMaPree+/N291DRUQ2Nkl6VewE3OPujwMfAU9beuQc6TDxwCH+5Z+tfGYc4oHD4MGD23WMeMYhX4FD/EZWBx98cKIqlP322y9qJLly5UoeeKCwQ5WsWLGCq666ir322otBgwYxYMAAdtttN372s58xd+7cgp5bRCQXSaoqbgZuBXD3Nwl6Wfy+gGWSZnTFjEO8qqIrBw5JlJSUcMYZZ0Tzf/jDH/JSluY88MADjB07lgsvvJCZM2eyYsUKVq1axauvvsrll1/Otttuyw9+8IO8NhYVEcmXJIFDX3ePWpq5+0NA/8IVSZrTFds45KOqIt+BQ21tLTNmzIjmDzrooMT7nnrqqZSVlQHw3HPPMWfOnJzLE5dKpbjssss4/vjjmwRdmdavX88111zDhAkTeO211/JaBhGRXCUJHFJmtmN6xszGAw2FK5I0pztkHPLROPLll1+OxrwYN24cI0eOTLzviBEjmDx5cjR/22235VyeuJ/+9Kdceuml0fyoUaP4wx/+wLx581iwYAF/+ctf2GOPPaL17s7ee+/Nfffdl9dyiIjkIslttX8KPG9mb4bznwNOLlyRpDnV1dXR9CabbNLu43S1Ng4jRoygR48erF+/nqVLl1JdXU2/fv3aXaYXXnghmj7wwAOz3v+MM85g2rRpANxxxx38/Oc/p7w8yb9J626//XZ+8YtfRPNf+MIXuO+++xg4cGC07Ctf+QrHH388f/zjHznvvPNYs2YNtbW1nHjiibz77rtccsklWXd5TerTTz9lxowZuDuffPIJ69ato6ysjM0224zRo0ez3XbbMXHixJzeeyKycWjzE9HdHw0bQ+4D1AP/cvd234PYzEqBm4CdgXXAme5eFVt/FnB2eK4rwvMPIbjJVm9gHnC6u9dks217y9tVxL+kBw0a1O7jdLVeFaWlpWy55ZZRtcBHH32UqBdES15++eVoOn0fimxMnjyZYcOGsXDhQubPn8/jjz/OUUcd1e7yALzyyitNbuM9efJk/va3vzU7dHhJSQnf+MY32HfffTn66KNxdwAuvfRSKisrue2223JqHBtXU1PDXXfdxQ033MDbb7/d5valpaXssMMOTJo0KXpsvvnmeSlLpoaGBlasWMGyZctYsWIF9fX1QHB9evbsyYABAxg4cCD9+/fPS2AnIskl/Y/bAlgClADbm9kx7n5LO8/5JaCXu+9lZnsC1wLHAJjZcOA8YCLQC3jRzP4JXALc6+63m9lFwNlm9qek2wLXtbOs7fbCCy8wdepU+vXrRyoVDLSZSqWaPJIsS8/H09Xt/XUPhRvHIZcyjRkzJgocPvzww3YHDo2NjcycOTOa32uvvbI+RkVFBaeeeipXXXUVEDSSzCVwqKmp4ZRTTolGsdxpp53485//3Ob9RsaNG8fLL7/MV7/61Wjo7Pvuu4+qqioeeuihrKpgMn366afceOONTJ06tUnw15bGxkbeeOMN3njjDX77298CMHbsWCZNmsR+++3HpEmT2HrrrRNnRdasWUNVVRVz5szh/fffp6qqKvr7ySefRO//tvTr14/Bgwez6aabtvp34MCB0f1K0mVcu3YtNTU1rFmzhjVr1kTTNTU10br0Y9GiRZSVlVFTU0NjYyMlJSUbPMrLyykrK6O8vHyD6Wzmy8rKaGxsJJVK0djYGD3amm9pm/S1TJczPp1kPnNZa1p73ZYtW9bmD5+kr3tX0dHlHTx4MBdffHFOVda5ajNwMLNbCL7YewOfAmOBF4H2Bg77Ak8AuPtMM5sYW7c7MMPd1wHrzKwK2Cnc58pwm8fD6fez2LZDA4dly5Zx6KGHNrmjZT4NGzas3fsWKuOQa+CQlks7B3dnxYoVQDCS5TbbbNOu45xxxhlR4PDoo4+yYMEChg8f3q5jXXzxxbz33ntAUMX00EMPJa6KGTRoEI899hjnn38+N910EwCzZs1i4sSJ3H///UyaNCmrsrz66qtcd911/OUvf4l+waf17t2bPffck4kTJzJq1Cg22WQT6uvrWbBgAf/973959dVXefvttzf4kKyqqqKqqoo//vGPAGy++ebss88+jB49mqFDh9K7d29SqRTr1q1j8eLFLF68mI8++oj33nuPTz/9NKvyt6S6uprq6uqC3GFVpCsaMmQI5513XqedP0nG4VBgK4LqhcuBkeQ2cmR/YGVsvsHMyt29vpl11cCAjOXNLWtr2ybMbAowJWNxDwg+COPtCdqjpqaGHj16FCRwGD16NOXl5VRWVrZr/wULFkTTy5cvb/dxoOkNrpYtW9buY8WzILNmzWpynNra2sTHjY+9sOOOO/Luu++2qzwAEyZMYNasWTQ0NHDNNdc06aqZ1MyZM/nNb34TzV944YVZPZ+073znOwwZMoQrr7yS+vp6Fi5cyP77788pp5zCd77znVbbHdTV1TF9+nTuuOMOXn/99Q3Wjxw5kq997Wsce+yxbbZfWLNmDf/5z3+YNWsWr776Km+88cYG7/F58+Zx//33Z/X8mlNSUkK/fv3o378//fv3p6KiIgpa1q1bR3V1NatXr6a6urrofqGK5Kqmpianz+648ePHZ71PksBhvruvMbN3gR3d/SEzuzrrM31mFRD/yVUaBg3NresHrIgtX9vMsiTbNuHuU4Gp8WVmNgb4YOzYsTmlgdPefvttbr31VoYOHZo4/dfWNj179uTQQw/NqY1D/Eu6vr6+XW8aCNJz6dEZAfbYY492p8523333aLq6urpJmSorKxOXMf6L89BDD233cwM499xzOe200wCYNm0aV199dVYNE1euXNmkB8WRRx7Jj3/843Y3brzssss48MADOe6441i2bBmpVIo777yTadOmcc4553Dcccexww470KNHD1atWsVrr73G3//+d+66664mwWLapEmTuOCCCzj66KOjLqhJTJw4MQqi1q1bx6uvvsoLL7zA888/z4wZM1i1alXiY5WXl7P11luz7bbbMnbsWLbZZpvo75gxY+jRo0ebx2hsbGTVqlUsXbqUZcuWtfo3/X6NVwH26tWLvn370qdPH/r27RtNN/dYunQp48aNo3fv3pSVlW1QzZhKpWhoaKC+vj76m360Nt/cuoaGBkpKSigtLY0ebc23tk1JSUmb1aHZVKG29T5uaf3ChQsZNmxYu/fvqjqyvH379uW0007r1GuUJHBYb2b7Ae8AR5jZM8CQHM45AzgK+EvYxuHN2LpXgF+YWS+gJzAeeCvcZzJwO3AE8EKW23a4UaNGceKJJ+b05VUI+WrjsGbNmqjevlevXjnVt+VrLId4w8j2tG+IO/744zn33HOprq7mvffe47HHHuPII49MvP8FF1wQjQA5ePBgbrnllpz/0Q844ABef/11zjrrrOheHMuXL+fKK6/kyiuvpLS0lIqKihYzXeXl5Zx44omcf/75TJgwIaeyAPTs2ZN99tmHffbZh4suuoiGhgbefPNNXn/9dRYuXMiiRYtYv349ELQd2Wyzzdhss83YfPPNGTduHFtuuWV0d9T2Ki0tZeDAgQwcOLDdVVNJZRPESvN0DXNXWVnZ6YFVksDhQuBc4DTgRwSNJH+ZwzkfBA41s5cIGluebmbfBarc/REz+w3Bl30p8GN3rzWzK4A7wl4US4CTwixIom1zKOtGJ19tHPLRoyItH20cVq5cyTvvvAMEd93cbbfdcipT3759OfPMM7nuuqB5zK9+9avEgcO0adOiOn+Am2++mREjRuRUnrRRo0bx+OOPc88993DppZfy/vvvR+saGxubDRpGjBjBMcccw09/+tOC9YKA4Lrvsssu7LLLLgU7h4h0Ac2l21p7jBs3bmC2+xTDY9y4cWPGjRuX+vjjj1P58s477+TtWPnS2NiYKikpSRHcJj1VX1/fruPMnj07OsaOO+6YU5kaGhpSPXv2jI63YsWKaF3Sa/jkk09G+++66645lSdt7ty5qfLy8ui4M2bMaHOfRYsWpYYOHRrtc8IJJ+SlLM2pq6tLPfDAA6kTTzwxNWbMmOicPXr0SG233Xapb37zm6lp06al1q9f3yXfi8VG1zB3uoa5K8A1zPr7ssWMg5lNCz+ImluHux+dx/hFOkhJSQl9+vSJqilqamraNeBSPjMOpaWljBkzJhqz4MMPP2TnnXfO6hj5rKZIGzVqFCeffDJ33HEHEPSQePbZZ1tME6ZSKaZMmRI1Gh0xYkTUbbEQysvLOfbYYzn22GOBoCFkXV0dPXv2zKrdgohINlobcvqvwAOtPKRI5aOdQ766YqZtvfXW0XRVVVUrWzavEIEDwI9+9KNogKHnn3+ev/3tby1ue9NNN/HQQw9F87fddlvOQVU2Kioq6NOnj4IGESmoFgMHd78j/QAeJeitsBx4KFwmRSof7RzyNfhT2rhx46LpbG8u1djYyL/+9a9oPp+Bw7hx4/j2t78dzZ977rksXrx4g+2eeeYZzj///Gj+nHPO4fDDD89bOUREuoo2b3JlZl8GqoDzgR8CVWaW/U0ApMvId8YhH7+qt91222g6PWBSUnPmzGky8FM8e5EPl1xyCUOHDgVg/vz5fPWrX20ScD333HMcffTR0aBKEydO5Nprr81rGUREuookd8f8BbCfu+/v7vsChxEMEy1FKh44tDfjkO+qinjGIdvAIZ5t2GOPPfLeVWnw4MFROweAZ599lr333ptbbrmF8847j4MPPpjVq1cDMHz4cP72t7916nCwIiKFlCRwqHH3aKwFd59NC40mpTjEqyram3HId1VFPOOQbVVFZuBQCIcffji/+tWvovn//Oc/TJkyhRtuuIGGhuAu88OGDWP69OmMGjWqIGUQEekKkozj8IyZXQjcCDQAXwfeMrNBQIm7J79LjnQJ+c445KOqYtSoUfTs2ZN169axaNEiVqxY0eSW062J39iqUIEDwA9/+EM22WQTvve971FbW9tk3b777ss999zD6NGjC3Z+EZGuIEngcD5QxoaDPp1CkHlQE+4ik4+MQ76rKsrKythmm22iQZzmzJmTaBCntWvX8sYbb0Tz8eGrC+Fb3/oWX/ziF7nrrruorKxk0KBBHHnkkRx22GGdPpqbiEhHaDNwcPfcxoSVLicfGYd8V1VA0M4h28Bh9uzZUaPEz33uc4mzFLkYPXo0P/7xjwt+HhGRrihJr4phZnZ0OH2dmU03s50KXzQplHxnHPI1VkF7elZ0RPsGERH5TJLGkbcD25jZQcBBwJ3ADYUslBRWrhmHVCqV96oKaF/Pio5q3yAiIoEkgcOm7n4dwZ0m73X324E+re8iXVmuGYfVq1dHd8bs06cPvXr1yku5zCyaTldZtEUZBxGRjpUkcOhhZhUEgcNTZtYH2KSwxZJCyjXjUIhsA8AOO+wQTb/zzjtRcNKSBQsWRLeu7t27NzvuuGPeyiIiIs1LEjg8DCwGlrj7LOAV4N6ClkoKKteMQyEaRgIMGjQoGgOhrq6uzeqKeDXFhAkTqKhQO14RkUJrM3Bw958BOwDpYaZPcvefF7RUUlC5DjldiIaRafGswZtvvtnKlvDCCy9E03vvvXdeyyEiIs1rMXAws6+Ff78LfBW4IJw+JPwrRSqfgUM+Mw7QNHCIj8/QnOeffz6a3m+//fJaDhERaV5r4zik+8ap4ngjs8kmnzVRSd9jIRuFqqoA2Gmnz3r6tpZxqK6u5rXXXgOgpKSEffbZJ6/lEBGR5rUYOIRVFLj76R1XHOkI/fr1i6arq6uz3r+jqipayzi8/PLL0T0idtpppw4Z+ElERFoJHMzsGVq5mZW7H1SQEknB5ZpxKGRVxec+9zl69epFbW0tc+fOZcmSJc1uF6+mmDRpUl7LICIiLWutceSNwG+BecAagkGfrgOWAFWFL5oUSleuqqioqGDChAnR/Ouvv97sds8++2w0rcBBRKTjtFZV8QCAmf0A2NvdG8P5vwMvd0zxpBDyWVWR78ABYK+99mLGjBlAcPvqTMuXL+fll4O3YElJCQceeOAG24iISGEkGcdhCBAfGrAfkP9vC+kw+ayqyHcbBwgCh7TmMg5PP/00jY2NAEycOJHNNtss72UQEZHmJbmt9r3Av8zsb0AJ8BVgakFLJQXVu3dvSkpKSKVSrF27loaGBsrKkt8dvSMyDmlvvfUWtbW1TYa1fuKJJ6Lpww8/PO/nFxGRliUZAOoS4CfAIGAA8F13v7rQBZPCKS0tzWksh+XLl0fThQgcRowYEd3wat26dTz33HPRuvr6eqZNmxbNK3AQEelYSTIOuPvDBENPy0aiX79+UTVFdXU1/fv3T7Rf5p0xBw0aVJDyTZ48ORpy+u9//zuHHXYYANOnT2fRokVAEGDoxlYiIh0rSRsH2Qi1t51DTU0N69evB6BXr1707t0772UDOPLII6Pphx9+OGrTcPfdd0fLTzjhhKyqWEREJHcKHLqp9gYOhW7fkDZp0qTo+HPnzuWpp55iwYIF3HfffdE2J510UsHOLyIizVPg0E21t0tmRwUOPXv25Otf/3o0f+WVV3LZZZdF2Y4999yT3XbbrWDnFxGR5ilw6Ka6esYB4JxzzqG8PGiG89xzz/G73/0uWnfRRRcV9NwiItI8BQ7dVDEEDuPGjeOUU07ZYPlRRx3F0UcfXdBzi4hI8xQ4dFPFEDgAnH/++Zx66qnR/BFHHMHdd99NSUlJwc8tIiIbUuDQTXX1Ng5pFRUV3H777cybN4+PPvqIxx57LHHXURERyb9E4zjIxqdYMg5pI0aM6LBziYhIy5Rx6KbaGzjER40s1OBPIiLSdXVoxsHMegN3A0OBauBUd1+csc3PgCOBeuB8d3/FzMYCtwMp4C3g2+7eaGZXA/sSPI+p7n6LmQ0G3gu3A3jQ3a8v/LMrLvHAoStXVYiISNfS0RmHc4A33X0ScCfBPTAiZvZ5YH9gD6EDx2IAAA+uSURBVOBE4Lfhqv8DfhLuVwIcY2YHAmPdfS+C4OFCMxsEfB74k7sfED4UNDQj3sahGKoqRESka+jowGFfIH1rw8eBQ5pZ/w93T7n7XKDczDYDJgDPZez3MvCNcFkKKAPqwm0nmNlzZna/malyvBnF1sZBRES6hoJVVZjZGcAFGYsXAivD6WqCu23G9QeWxubT25S4eyq+zN1rgVozqwDuIKiqWG1m7wKz3P0pMzsZuAE4Pl/Pa2OhwEFERNqjYIGDu/8B+EN8mZn9DUjnyPsBKzJ2WxVbH9+msZllhFUTfwWedfdfhuunAzXh9IPA5ZllM7MpwJSMxT0Aqqqqsqrzb01tbS2VlZV5OVa+LV36WXy2aNGixOVcsmRJNL148WLWrl2b97LFdeVrWEx0HXOna5g7XcPc5fsajh8/Put9Oro75gxgMvAKcATwQjPrrzKza4CRQKm7LzGz18zsAHd/NtzvmbCh5dPAte5+T+wYtwIPAH8BDgZmZRbC3acCU+PLzGwM8MHYsWMZOXJkzk8UoLKysl0vSkeoq6uLphsaGhKVc926dVGgUFZWxsSJEws+EFNXvobFRNcxd7qGudM1zF1XuIYdHTjcDNxhZi8C64GTAMzsKuCvYQ+KFwjaL5QC3w73+x5wi5n1ACoJsgznAVsDZ5nZWeF2pwMXAbeZ2beANcCZHfLMikx7qiriXTEHDx6s0RtFRLqhDg0c3L0G+Eozy38Ym74UuDRj/XsEvS3irgsfzTkwl3J2B+3pjqn2DSIiogGguqn2dMfU4E8iIqLAoZvq1asXpaXBy79u3bombR5aooyDiIgocOimSkpKsm7noMBBREQUOHRj2VZXKHAQEREFDt1YPOOwatWqNrdX4CAiIgocurEBAz4buFOBg4iIJKHAoRuLBw4rV65sZcuAAgcREVHg0I0pcBARkWwpcOjGFDiIiEi2FDh0Y/3794+mk7Rx0ABQIiKiwKEbU8ZBRESypcChG8smcGhoaGDFis/ugj5w4MCClUtERLouBQ7dWDaBw/Lly0mlUkBQTVFe3tE3VhURka5AgUM3lk3gsGTJkmh6yJAhBSuTiIh0bQocujEFDiIiki0FDt1YNr0qFDiIiAgocOjWlHEQEZFsKXDoxhQ4iIhIthQ4dGOZgUO610RzFDiIiAgocOjWevXqRY8ePQCoq6ujtra2xW3jgcOmm25a8LKJiEjXpMChm0taXaGMg4iIgAKHbi8eOLTWs0KBg4iIgAKHbi/eJVMZBxERaYsCh25OVRUiIpINBQ7dXJLAoa6uLlpXWlqqG1yJiHRjChy6uXgQsHz58ma3ybyddllZWcHLJSIiXZMCh25u8ODB0XQ8QIhTNYWIiKQpcOjm4mMyKHAQEZG2KHDo5uKBw9KlS5vdRoGDiIikKXDo5pJUVSxatCiaVuAgItK9KXDo5pJkHBYuXBhNDxs2rOBlEhGRrkuBQzcXzzgkCRyGDx9e8DKJiEjXpcChm0vSOHLBggXRtDIOIiLdmwKHbi6zqqK5W2sr4yAi8v/bu/sgu+rygOPffTHJRhdSQaQZggayfYRmNCx2iCmGdEYKBKudtpmxnU6rtE3rhLYwOhQZHJjWtlNG7dRqi0SD2Jdpp4BTpUUyk6ITEMnIUJtofOQlGclAt8YUSZq3zWb7x7l7uXtzNzm7d+/LJt/PTIZzfud39j734b489/c7L5pg4XCGGxgYYP78+QAcOXKEQ4cOndDHEQdJ0oT+dj5YRAwAfw+cB+wHfjMzf1jX5w7geuAYcFNmbouIZcAXgHFgB7AhM49HxL8C5wKjwKHMvG6qvu14fnNRT08P55xzDi+++CJQjDosXLiwun18fNwRB0lSVbtHHD4IbM/MdwJfBG6v3RgRw8BVwBXA+4DPVDZ9Eri9sl8P8N5K+xBwZWauyczrTtFXUzjZAZIHDhzg4MGDACxYsIDBwcG2xiZJ6i7tLhyuBL5aWX4YeFeD7ZszczwzfwD0R8QbgMuBr9fuFxFvBBYBX4mIxyLi3ZXtJ/RtzVM5fZzsAMn6UzF7enraFpckqfu0bKoiIn4LuLmueQSYuAXjfuDsuu1nAbU/eSf69GTmeF3bPOATwF8Brwcej4htU/TVSZxsxKH2+AanKSRJLSscMvPzwOdr2yLiQWBirHsQeLlut1dqttf2Od6g7b+BuzPzGPA/EfE0EFP0nSQi1gPr65rnATz77LPs37//VE+vlMOHD7Nz585Z+Vut1N//6stg+/btLF++vLr+1FNPVZcXLlzY9uczV3LY7cxj88xh88xh82Y7h5dccsm092nrwZHA48BaYBtwHbC1wfa7IuLjwAVAb2bujYinI2JNZn6tst+jFFMQvw+sjYjXAcuBnUCjvpNk5j3APbVtEdG/ZcuW0fPPP3/SF2kzdu7cOaP/Ke1WH2Pt+qOPvpq+oaGhtj+fuZLDbmcem2cOm2cOm9cNOWx34fC3wH0R8RhwFPg1gIi4C7i/cgbFVuAJiuMvNlT2+xCwMSLmURQH92fmWERcExHfpBhluK1SZJzQt0xglZGLM1LtFETt1ARQPduivp8k6czU1sIhMw8C6xq031KzfCdwZ93271OcbVG/300N2hr21dRqC4KXXnpp0rY9e/ZUly+44IK2xSRJ6k5eAEonHXF44YUXqstLlixpW0ySpO5k4SALB0lSaRYOmlQ4jIyMcPx4cWLK+Pj4pMLBqQpJkoWDGBgY4Oyzi8tdjI6OVi8CtW/fPg4fPgzA4OBgtY8k6cxl4SCg8XSF0xSSpHoWDgImFw4Tp2BaOEiS6lk4CIALL7ywurx79+5J/63fLkk6c1k4CICLLrqourxr1y4AnnnmmWrbsmXL2h6TJKn7WDgIgKVLl1aXn3/+eWBy4TA0NNT2mCRJ3cfCQcDkwqHRiIOFgyQJLBxUUV84jI6OTjrG4eKLL+5AVJKkbmPhIAAWL17MvHnzANi7dy9PPvkkY2NjQHFg5MDAQCfDkyR1CQsHAdDX18ell15aXb/33nuryytWrOhESJKkLmThoKrLLrusurxp06aG7ZKkM5uFg6qGh4en1S5JOvNYOKhq5cqVJ7T19fWxevXqDkQjSepGFg6qGh4eZvHixZPaVq1axaJFizoUkSSp21g4qKq3t5f169dParvxxhs7FI0kqRv1dzoAdZdbb72VPXv2sHnzZm644QbWrVvX6ZAkSV3EwkGTzJ8/n40bN3Y6DElSl3KqQpIklWbhIEmSSrNwkCRJpVk4SJKk0iwcJElSaRYOkiSpNAsHSZJUmoWDJEkqzcJBkiSVZuEgSZJKs3CQJEmlea+KFjl27BgjIyMMDg52OpQ5zRzODvPYPHPYPHPYvJGREYaGhujv79zXd8/4+HjHHvx0FhFvBnZ1Og5J0mlnaWbu7tSDO+LQOnuA7cB7Oh3IHPdlzOFsMI/NM4fNM4fN+zLF90vHWDi0SGYei4ijnawKTwfmcHaYx+aZw+aZw+ZVcniskzF4cKQkSSrNwkGSJJVm4SBJkkqzcGitezodwGnAHM4O89g8c9g8c9i8jufQ0zElSVJpjjhIkqTSLBwkSVJpXsehBSKiF/gb4G3AEeC3M/PZzkbV/SLiNcAm4M3AfOBjwHeBLwDjwA5gQ2Ye71CIc0ZEnAc8BVwNHMMcTltEfITiYkXzKN7PX8c8llZ5P99H8X4eA34HX4ulRcQVwF9k5pqIWEaDvEXEHcD1FHm9KTO3tSM2Rxxa4xeBBZn5DuBW4BMdjmeu+HXgR5n5TuBa4NPAJ4HbK209wHs7GN+cUPnA/ixwqNJkDqcpItYAq4CfBa4ClmAep2st0J+Zq4A/Bv4Uc1hKRNwCfA5YUGk6IW8RMUzx2rwCeB/wmXbFZ+HQGlcCXwXIzG8Cb+9sOHPGvwAfrSz3UFTRl1P80gN4GHhXB+Kaaz4O3A28WFk3h9N3DcUl478EfAV4CPM4Xd8H+isjsGcBo5jDsp4DfqlmvVHergQ2Z+Z4Zv6AItdvaEdwFg6tcRbw45r1sYhwWugUMvNAZu6PiEHgfuB2oCczJ0792Q+c3bEA54CIeD/ww8x8pKbZHE7fuRQF/zrg94B/AHrN47QcoJim+B6wEfgUvhZLycwHKAqtCY3yVv8907Z8Wji0xitA7b1jezt9bfG5IiKWAI8Cf5eZ/wjUzn8OAi93JLC54wbg6oj4GrAC+CJwXs12c1jOj4BHMvNoZiZwmMkfyubx1G6myOFPURzvdR/F8SITzGF5jT4H679n2pZPC4fWeJxifo+IWEkx5KlTiIg3ApuBP8rMTZXmpyvzzQDXAVs7EdtckZmrM/OqzFwD/CfwG8DD5nDaHgOujYieiFgMvBbYYh6n5X959RfxPuA1+H6eqUZ5exy4JiJ6I+JCih+oe9sRjMPnrfElil9936CYq/9Ah+OZK24DfgL4aERMHOvwh8CnImIesJNiCkPT8yFgozksLzMfiojVwDaKH1gbgF2Yx+n4S2BTRGylGGm4DfgW5nAmTngPZ+ZYJbdP8OprtC28cqQkSSrNqQpJklSahYMkSSrNwkGSJJVm4SBJkkqzcJAkSaVZOEiakYjYHBHnVpb/PSIubeFjfTAi1p9ke19EPFS5uZekFvI6DpJm6uqJhcxc26oHiYg3Ae8HVk7Vp3JO+10Ud7H8lVbFIsnrOEiagYi4l+LLfAfFVVK3Unxhvw74c4obbP00cBC4A/gDIIAHMvPmyt/4BYr7kcyr9PtwZj7R4LHuBnZk5qcr93z5a4ob/BwFngc+kJkHKn2/C/xqZn67Nc9cklMVkqYtMyeuhvpzmflC3eafAT6WmW8BRoCPANcDw8CGiFgcEUPAnwFrM/MyYD3wYES8tvYPRUQP8MsUd6cEeAewBnhrZl5OUTi8tWaXf2PyXQUlzTKnKiTNtl2Z+XRl+Tngx5l5FNgbEa8ArwdWAz9Jcf+Hif2OA8uA2tGCc4BFmbm7sr4dGAOejIhHKEYwttX0f46isJDUIo44SJptR+rWRxv06QO2ZOaKiX8UxzDsqOt3HOiJiF6AzHyZ4k6LH6YoIP45Im6u+7tjs/AcJE3BwkHSTI1R3PFwJv4D+PmIeAtARKwF/gtYUNspM/dR3GXxTZV+7wa2AN/IzDspbhv+tppdLgK+N8OYJJVg4SBpph4EHouI5dPdMTO/Q3Fcwz9FxLeBPwHek5n/16D7A8C1leWHge8AOyLiW8Aq4M6avtfgHRellvKsCkldLSKWUhQDb8/MKT+wImINsCEz17UrNulM5IiDpK6WmbuA+4DfnapPRPQBt1Cc9imphRxxkCRJpTniIEmSSrNwkCRJpVk4SJKk0iwcJElSaRYOkiSpNAsHSZJU2v8DmqNNKb2YbhoAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m = 1000 #kg\n",
"k = 500 #N/m\n",
"c = 250 #Ns/m\n",
"\n",
"road = np.array([bump(t_i) for t_i in t])\n",
"road_d = np.diff(road)\n",
"states = odeint(eqn, state_0, t, (m, c, k), hmax=0.01)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.plot(t, states[:, 0], linewidth=3)\n",
"format_plot(fig, ax);\n",
"ax.set_title(title_string('0.1m Bump', m, c, k), fontsize=14)\n",
"fig.savefig('./images/single_bump.png', transparent=True)"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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yuKrQNJ+u3fl0F2CjEwD71zenlPmDaT5duirJp4NFO98O4ydAoTEm30nDQGAH9sFOWdeRCm/bGPOaiPwXW9vhnAjS+V9sLYkvRGQdNg98wXNM+2IfFHn5rxelnsMRegx7HrltaiM81jHZv2Xck52OLYDwXmcrez0v1YlcHfoHoJE4VYUczbBPJyrayUPwKxLKVUcf21HNRmPMN8Z2LDAMW83G3xNm8A1mqIcU5UlD8LxJZczvNR+42tl/v3Q+IyItsY3/+2LbLdxBYA+JcDzDAMAYs95Z5pfYjPo/3kwvSKj2egme75IQNL4sf8JWG3tajvdgGIlQr8MIt+/OCPMXtvG/x17s/mrmHyG2g45M7AWorPP4B++ynuk7PJ+3Y58+9heRKzzjj1FyH0ZarSRcu0r/9sLtk2f8M4nITdgn348bY/7gXUGIm81s7E1WFpF9Z69JzrIlevwMZozxGWOuxrajexlb7Wy5iFwmtrrh+djqOF6VvS54vY+tanivpyoSlPMcM8bkGU87ZCfT2Iwt6f7BGe3dh/5h/zlXnv1bgtj2SO9gb86HeINnY6sdett6+oNyf9pK23aF02Zs9bPfYavrRRIEV+VxVaFpPl278+nS8pFIaD5dukrn08FimG8HMMbk+gM05/MujrcXrYr9X5rbsA+mbo0gnUewNRAvwOZ/12AD4m4ikuVsN7gDrarMa17EduI3XUT8NRjKPNYx3r/h7sling+fyCXBX2IvAP+P4zet5wOrTM15318x9kGE/zgUYKuO+LWr5PrP8A84N/BnYJ9SReJ/TvruwD5V8i/3C+yTxcs9676dsi/K87BP2Jtg2zyU10bs/jkbGyjgDJflNWxVNoNtu/FsBbZdKlOJ9xA7T/5XYM9Nf7WaXtgf/hfYYxD2PBaRZcAkEUnzBD3nYzvt8PvEGLPQqTryuIj8zykt+Aq7D18HEJGGQIcIk/4N0FBE2hnnlTJie4r8lTHmEuzxCktEfoFtvzXVGHN30LRfYtuOtPJUCTsTOICt0hPJd3Y5T87/gO04aSeBnTsEp6sz9h2zY7FVdqeIyAfY8z4H+MYYc7C071ZJ/4fNxG7C3rQOdr5DxOeYc3O2FduDsv+muAG2mtQGY6slb8PuM/96zwe2G2O+c86pliLS1hyvNhx2/4bY/rnY392rwG+8Aa/zJP1DQIwx/jZE/o5lvsEen9K2vQz7aoYEp2Q4AfsqpYiuKcaYJSIyC1sq7E9THexvrtTX8qio0Hy6dufT3wDtRaSh/7oqIvcCbUzoDv8qTPPp8ufTwWKZbwetuxn2Hq6fOV7N/hTsebrBmVbZ/R+WMWaTiDyE7T8kVGd93rT2AvoaY+4DPhaRiU4a+2NrJC4sT42qCngdW7tkGLbDrYnOtTTssY71/i3lnqwPZTcDqVInbBBsjDni3Ow8JbYXwWbYTlFu9s/jHPgc50ITC008VXIaYttTJGFvfMFWIRomIu9jnzDeWcntnS8i47DVMW4D0jj+pLgBUM8EtoFzGWOKROSf2Ab/C4wx/mqTe7E3qZdiq0Rdi23/8UUZaZmHrRJZgO1KvlycapQvAY85TyLBVmuEkk/mg5fdLiIPAA+KyGvGmD1iO/EoKuVJdyw9BTwnImuwVVieAl40x9tqlXYeL8YGPDPFtnm8AtthQKh33t6LfcXBROzT7yew72D9ApvR3ottR+pztlsPyDAh2lIZY9Y7weELYtvMpGMvuE+X9WWdc28G9jx4wvkd+u1zvlMCtsODB7HB2yPYjqJ8IlKe7+xP7ywn8y+rJ8oDwCgROYR9111bbHW0+VTy/cDOU9TG2LanYTNS54br98BSEXnOlP5an1DLH3Oqbz0gItux+/QB7FNZf7uip4GpTjBchO218W/O8t86y/9DRG7D3oD9CttxlP9GPQvbUUZASYMTlL6IPZ8mAFni9sdFDrAa+9T4BbGvFsnEPph60RizB9hT2raxnfA8hD1vnsL+DtIJ8zqdMP6Azdj9zsW2ywxXXVJFiebTQO3Op/+LbabxnHMtb4ttkzgKQPPp6sung0U73y4tfzT2FU2rsA8HRjnbeRz4wBjzhbN8Ve3/cB7CdlJV1gOIo8A9IrILe36fge0HYxVOZ3Pl2GaA0o61l3NdHQfMEpFZxpgNZcwf8/0bfE/mHP9zsb3Yx8yJXB0abOa0Alvy8AzwZxPYEHsH9qSMlU+dbe7AljK1B37mKfH4I/Z1A6uwF77Kvj/ubWyVjC+Bs7BPp/xtG+8isN1OKPOwF1vvDeYr2JLVV5x09sE+he7s/EBDMvadX59zvM1SRdyF/S4fYEua/G2HIqlS9Rh23z7sfH4dT2lQdXJK6+7HZkwfACux757zC3seO5nF1dge+lZh25r8woR4FYVzIzEJ2/tmR2e7j2Az88+wnW1s5vj+HETp1YWGYjO/T7DByTzCd6TidRH2CeOVHP89+P8ucKpU/Qxogz1nZjjfe2p5v3OQWzjeBjYkJ3P5pbP+9dgq0U8DL1D598j+P+x3bFXWjM7T2DnY1/qklDV/CLdjq2It4Hg7wH6e0rVHsG0AX3P+/B1O+P0a+0DgM+yN2E3+J8RO+v1thYJ1xbZDOxsb7HqP7a+coPly7HFYiv0dvuekt8xtO6VFP3e2/Tm2FPhyE/hqhlI5AcVEzyh9P3D10ny6lubTnmt5Y2e7/uPv76hQ8+nqy6eDXUR08+2y8sdB2BLJ/2Kv1xsJvC5Uyf4Px9iqwpFUh/4SWwo7Bvuw9a/YWlkfUPm8pqxj7U3HfOz58vdyrDvW+9d7T9YT24FdRfuCqJAEny+apfKquojtFKOOMWZIKfO8Z4y5LEbpScD+qG4zTscMFVjHAOyTKf+T13OwN9JpnifgKkIiciHwrTHmO+dzHWAPMMAYs8gZF7NzpDZwnqaOL+tJbgXWO5Myfu9VvL17gXfM8VeO1RgS9B5XpWoqzadVWaoznxbbk/kSY0xlH/REur2o5I8RbnsRMfyuFaX3ZFXrhK0OrUon9t1zS2O0rcuxT8CSsKU+FfUn4EqxXc6nY59m/p9mrBU2APh/TvWXQ9jXXBzEacchIr2xVdVUFRCR9kBWFDP4VKeKWqnVrStLbJu0PthXKNQYYt+xeRIRvDtcqXig+bSi+vPpNBFpFu3ANAb5Y7jtJmObNVSkxlVM6T1Z1TvRq0Or8F4xxpTZW24VuQPbxmV4JW/Of4VtM/QFtjrSt+i7OivjHmz1l/exbTU7Y6vM+nsN/RTdv1XpW0q+mqcq+V9pUGZ168pwqiRfbDw9SdYQ12C//ynVnRClqojm06q68+kxlOPNAJUQ7fwxnHOx369XNWy7vPSerIppdWillFJKKaWUUrWGlgQrpZRSSimllKo1YtomWEQSsT3cnY59yfJNxvPuNhG5GRiJfffa/caYt0SkObaH1hRsD3dDytMTqFJKKaWUUkop5RfrkuABQKoxphf2HZLT/BOcDl1+j33lxc+w77CsC4wHZhljemPbmJS3PryvKv62bNlSJevRv5r/p8e69vzpsa49f1V8rFXl1cTjqn81+E+Pde3502Nde/6qM2+OdRB8PvAugPNqje6eaT2ApcaYfOc9aRuBbtjOGl52SpFbYd8fGXNHj1b0lXkq3uixrj30WNceeqxPTHpcaw891rWHHuvaozqPdayD4IZAjudzkfPOs1DTDgEZxhgftsv+dcDF2Bc1R0RE6nz//fccO3ascqlWSimllFJKKXVCiPV7gg9i3xvnl2iMORZmWjpOqa/zfrkuItIX+AdwYfCKRWQEMCJodEqfPn149tlnadq0aaUSnpeXR3Z2dqXWoeKDHuvaQ4917VGVx/rUU0+tkvUopZRSqnrEOgheClwJvCIiPYG1nmnLgQdEJBWoC5wKrBORp4BXjTELsaXDxaFWbIyZAczwjhORtsDmDh06cMoplXt1ZHZ2tt741BJ6rGsPPda1hx5rpZRSSvnFOgh+A7hURD4BEoDfiMidwEZjzJsi8jjwMbaa9t3GmDxn3DMicg82AP5djNOslFJKKaWUUuoEEdMg2BhTDIwKGr3BM/054LmgZTYAF0U9cUoppZRSSimlTnix7hhLKaWUUkoppZSqNhoEK6WUUkoppZSqNTQIVkopFdLrr7/Oo48+GtG8Pp+P3r17M3ToUIYOHcq0adMA+PDDDxk4cCCDBg3ilVdeAWxPzbfffjs33HADN998M/v27SuxvoKCAsaNG0dxcTFDhw7lwQcfdKfl5+dzySWXuJ/fe+89/vnPf5aZRmMMTz75ZETfRymllIo3hw4dYtSoUQwZMoRBgwbxxRdfAPD+++/Tt29fN49evnw5xcXF3HPPPQwaNIihQ4eydevWEuvz+XxMmDCBw4cPM2HCBG677baA6eeddx4A33//PdOmTePrr7/m4MGDYdP31Vdf8be//a3M77Fnzx7+/Oc/l+erl5sGwUoppSpt27ZtdO3aldmzZzN79mzGjh1LYWEhU6dO5cUXX2T27NksWLCAPXv2MG/ePDp16sTcuXMZMGAATz31VIn1zZw5k/79+5OYaLOpt99+m+XLl4fc9uLFi7nooovKTKOIsHXrVrZt21ap76qUUkrVRC+99BI9e/bk5ZdfZurUqW4guW7dOsaNG+fm0T169OCDDz6goKCABQsWMHbsWB566KES63vnnXfo2rUraWlpAKxatYp//etfJeZbs2YNb7/9No8//njIB9t+Cxcu5OKLLy7zezRp0oS0tLSw+X5ViHXv0EoppeLMvn37+N3vfsfo0aPJyclhzpw5AdPHjRvH999/z86dOxk6dCipqalMnDiRgoICWrduTUZGBgBnn302K1asYNWqVdx0000AXHDBBSWCYJ/Px5tvvskbb7zhjrv77ruZPHkyr7/+OnXq1AmYd+/evTRp0oQrr7yS7t27Y4yhXbt2ZGZmsnLlSlJSUrjzzjsB6N+/P3PmzGHixIlR2VdKKaVUVcrLy2PixIls376dwsJCJk+ezM6dO0PmxcOGDSMlJQWAoqIi6tatC9gS2OzsbGbNmkW3bt246667WLVqFb179wbgjDPOYN26dSW2PXv2bP7+97+7n++8806eeOIJevbsSbNmzdzxIsLIkSPZsmULbdu25b333uO5556jTp06nHzyyTz22GMkJiaybt06br31VoYOHYqI8OWXX5KVlUX37t1ZsmQJBw8e5MUXXyQjI4MrrriCJ554gh49elT5PgUtCVZKqbgwbdo00tPTSUhIqLK/9PR0t9pyOHv37uWWW25h4sSJ9OrVi379+rlPkv1/3bp1IysrixEjRjB79mxGjhzJuHHjyM3NJT093V1XWloaubm5AePT0tI4dOhQwDa3bNlCgwYNSE5OdseJCAMGDCjxpHrt2rWcdtppABw+fJgrrriCuXPnsnLlSs466yzmzJlDYWGhW/orIlF9sqyUUurEVR158fz582nZsiULFizgr3/9K6tXrw6bFzds2JDU1FR2797NuHHj3AfA5513HpMnT2bOnDkcOXKE+fPnk5ubS4MGDdztJCUlcezYMfdzXl4eO3bsoHHjxu64pk2bMnr0aO6+++6ANLZv355BgwYxfvx4AN566y2GDx/OvHnzuPjii8nNzWXPnj1kZmaSkJAAQLdu3bjvvvsoKCggNTWVl156iQ4dOrBixQoAOnTowKpVqyp5xMLTIDhObdq0ifvuu4+PPvqoupOilIqBadOmkZubW6XrzM3NLTMI/vjjjykoKKC4uBiAd999121T5P9bs2YNp512Gn369AGge/fu7Nq1iwYNGnD48GF3XYcPHyY9PT1g/OHDh2nYsGHANvfv30+TJk1KpGXEiBEYYwKue8FVq7p27QpAw4YNad++vTtcWFgIQFZWFgcOHIhsBylVRY4ePcozzzzDtGnT2LNnT3UnRylVQdWRF3/77becccYZALRt25Zhw4aFzYvB9n8xbNgw7rjjDrcUdeDAgbRq1YqEhAT69OnD+vXrS+TRxcXFATWtcnJyaNSoUYn0XHXVVaSlpTF37tywaZ44cSLLli1jyJAhfP755yQmJrJo0SIuvPBCdx5vft2hQwd3OD8/H7BBeZ06ddz7j6qm1aHj0LFjx/jZz37Gpk0CujjuAAAgAElEQVSbSE5OZvXq1Zx66qnVnSylVBSNHTuWKVOmVGnm26BBA8aOHVvqPAMGDODqq69mzJgxvPrqq/Tr149+/fqVmO+RRx7hpJNO4uabb2bDhg00b96c9u3bs3XrVg4cOED9+vVZuXIlw4cPZ/v27SxevJhu3brx0UcfcfbZZwesKzMzM2THGklJSTz00ENuVWqA7OxsRo8e7X72P2EO5+DBgwFPtZWKNp/Px7XXXsvbb78N2DZ7K1euJDU1tZpTppQqr+rIi9u3b8/atWvp27cv3333HdOnT2fatGkh8+KNGzcyevRopk+fTufOnQF7DbrqqquYP38+zZo149NPP6Vr1640adKEhQsXcvnll/Pll1/SqVOngHU1atQoIEj2mjJlCtddd13Y6QsWLOD2228nMzOTe+65h/fff59PPvmE++67L9Ldgs/no06dOm7fIFVNg+A49Nlnn7Fp0yYACgsLeeONNzQIVuoEN3bs2DID1mjp2LEjV111FVOnTg2bgY0YMYJx48axePFikpKSmDp1KsnJyUyYMIHhw4fj8/kYOHAgTZs2ZfDgwYwfP57BgweTnJxc4gl4mzZt2LdvH8eOHQt4Kg3Qrl07brzxRmbNmsXOnTs5+eSTy/VdVq9eTa9evcq3A5SqhMWLF7sBMNi2ebNmzWLkyJHVmCqlVEVUR158/fXXM2nSJIYMGUJRURGTJk0KO++0adMoKCjggQceAGyA/fTTT3P//fdz2223kZqaSvv27bnuuutISkpi6dKlXH/99fh8voC3MACkpKTQpEkT9u7dS2ZmZsC0xo0bM2HCBG699daQ6ejWrRsjR44kLS2N+vXr07t3bz788EO3g61IGGPcEvBoSPD5fFFbeXUTkbbA5v/973+ccsoplVpXdnZ2jQk0n3nmGW655Rb388CBAyN6PYiKTE061iq69FjXXM8++yzt2rXj0ksvrZL1+Y/12LFjGTNmDK1atarM6kovblaRqJKbj3j4DY8cOZIZM2YEjOvZsyeffvppNaUoPsXDsVZVQ491zfHWW2+xZ88ehg0bFpX1l3asH374YS655BK6d+8e6erKlTdrm+A4lJ2dHfB58+bN1ZQSpZSKjhtvvJF33323StsCbdiwgdatW1c2AFYqYj6fj//85z8lxn/22WelvkZEKaVqgp///Od89dVXYas9R8vu3bvJzc0tTwBcbhoEx6Ht27cHfN6/f381pUQppaIjNTWVadOmVWlboM6dOwe0H1Yq2rZs2cL3338PQEZGBmeeeSZgg+NFixZVY8qUUqpsCQkJPPLII+WqxlwVsrKy3HccR4sGwXHoxx9/dIdff/11vv3222pMjVJKKaVC+eKLL9zh7t27B1Tv11d1KaVU9dEgOA7t3LnTHRaRakyJUkoppcL5/PPP3eEzzzwzoCd07zSllFKxpb1Dx6GRI0eyefNmdu7cSYsWLao7OUoppZQKwVsSfOaZZ7rVof3TfD5fma/1UkopVfU0CI5D1fWaFKWUUkpFbv369e7w6aefTvv27UlPT+fQoUPs2bOHHTt26MNspZSqBlodOo4dPXqUrVu3smLFCrfjDaWUqiqvv/46jz76aETzHjp0iFGjRjFkyBAGDRrkloC9//779O3bl6FDhzJ06FCWL19OcXEx99xzD4MGDWLo0KFs3boVgC+//JJrr72W66+/nieffDLkdlauXMmsWbP4/vvv6dq1K+vWrXOnzZs3jyeeeML9PGbMGI4ePVpm2h9//HE2btwY0fdUKlIFBQVs27bN/dyuXTsSExMDXgfy9ddfV0fSlFInKJ/PR+/evd08d9q0aQB8+OGHDBw4kEGDBvHKK68AkJeXx+23384NN9zAzTffHLLH+oKCAsaNG0dxcTFDhw4NeJdwfn4+l1xyCQDfffcdEydOZNeuXeTn54dN33vvvRfRa12NMWHvA6qKBsFx7O6776Zt27b06NGDuXPnVndylFK12EsvvUTPnj15+eWXmTp1qtur47p16xg3bhyzZ89m9uzZ9OjRgw8++ICCggIWLFjA2LFjeeihhwD405/+xLRp05g3bx6rV68OKEUDm7k/8cQTDB48GIAGDRowceJECgoKSqQnPz+f4uJi6tWrV2bahw0bxl/+8pfK7gKlAmzdutV9xVfLli3dc7FTp07uPBoEK6Wq0rZt2+jataub544dO5bCwkKmTp3Kiy++yOzZs1mwYAF79uxh3rx5dOrUiblz5zJgwACeeuqpEuubOXMm/fv3d9/U8Pbbb4fs1O+jjz5i0aJFTJ8+nUOHDoVN3+LFi7nooovK/B4iwtatWwMeJFY1rQ4dxzIzM91hfU2SUipa9u3bx+9+9ztGjx5NTk4Oc+bMCZg+btw4hg0bRkpKCgBFRUXUrVsXgK+++ors7GxmzZpFt27duOuuu1i1ahW9e/cG4IwzzmDdunXk5uZSUFBA69atATj//PP55JNP6NKli7udpUuX0qFDB3c7bdq0oXv37jz22GOMHz8+IE3Lli3j3HPP5bPPPmPGjBnk5+eTm5vL9ddfz7Jly9iwYQO//vWvueGGG2jYsCGpqals2LCBzp07R2cnqlpn06ZN7nD79u3dYQ2ClVLlkZeXx8SJE9m+fTuFhYVMnjyZnTt3hsyLv//+e3bu3MnQoUNJTU11HxS3bt2ajIwMAM4++2xWrFjBqlWruOmmmwC44IILSgTBPp+PN998kzfeeMMdd/fddzN58mRef/116tQ5Hka2a9eOyZMn880339CkSRPmzJnDv/71LxITE/npT3/KH//4R3w+H3v37qVJkyZceeWVdO/enS+++ILTTjuNzMxMVq5cSUpKCjNmzCA5OZn+/fszZ84cJk6cGJX9qiXBcWbZsmVcc801/Pa3v3WrMwDk5ORUY6qUUrEwZcoUEhISIvobMWJEieVHjBgRMM+UKVPK3ObevXu55ZZbmDhxIr169aJfv37uE2b/X7du3dxAcvfu3YwbN44777wTgPPOO4/JkyczZ84cjhw5wvz588nNzaVBgwbuNpKSkkqMS0tLK/E0efny5SV6xB8zZgxLly5l5cqVAeMXLVrExRdfDNjXyo0fP54pU6bw9NNP8/DDD/Pcc8+xYMECd34R0VfWqCoVLgju2LGjO6xBsFLxJ9Z58fz582nZsiULFizgr3/9K6tXrw6bF2dlZTFixAhmz57NyJEjGTduHLm5uaSnp7vrS0tLIzc3N2B8qDx3y5YtNGjQgOTkZHeciDBgwAC3Bpdfr169uPzyyxk9ejRgm1NNnjyZBQsW0K5dO44dO8batWs57bTTADh8+DBXXHEFU6dOZeXKlZx11lnMmTOHwsJCt3lStPNlLQmOM5s2beK1114rMV6DYKVUNHz88cdkZWW51TrffffdkE+fu3XrhjGGO++8kz/84Q/06NEDgIEDB9KwYUMA+vTpw3//+1/S09M5fPiwu3xxcTENGjQIGHf48GF3Ob/9+/dz+umnB4xLSUlh6tSpjB07luuuu84d7+9w6LvvvqNjx47UqVOH+vXr07p1a1JSUsjIyAhot5SVlRXw+jmlKktLgpVSVeHbb7/lggsuAKBt27YMGzYsbF582mmnkZSUBNh3k+/atStk/pqenh4wPlye26RJkxLpGTFiBIMHD+ajjz4Km2Z/9euHH36YM844A5/Px8KFC+nbt687T9euXdm8eTMNGzZ0r5ENGzZ08+asrCwOHDgQ8X4qLw2C44w32G3evDk7duwoMV4pparKgAEDuPrqqxkzZgyvvvoq/fr1o1+/fiXm27hxI6NHj2b69OlulWKfz8dVV13F/PnzadasGZ9++ildu3alSZMmLFy4kMsvv5wvv/ySTp06uU+bt23bRqtWrViyZAm33XZbwDYaN24csq1R165dueKKK3juuee44YYb2LBhQ0CgEckraHJycgKamChVWZs3b3aH27Vr5w536NDBHd6yZYu+JkkpVar27duzdu1a+vbty3fffcf06dOZNm1ayLz4kUce4aSTTuLmm29mw4YNNG/enPbt27N161YOHDhA/fr1WblyJcOHD2f79u0sXryYbt268dFHHwW8xxxss8uDBw+W2EZSUhIPPfSQW5U6lFdeeYV7772XunXrMnz4cL744guys7PdkmIoO28+ePAgjRs3Lmv3VJgGwXHGezK2atXKDYJDnaRKqRPLlClTIqrCHM6MGTOYMWNGuZfr2LEjV111FVOnTuW+++4LOc+0adMoKCjggQceAGynVU8//TT3338/t912G6mpqbRv357rrruOpKQkli5dyvXXX4/P53N7m7z33nu56667KCoq4vzzzy9R6nvuuefy/vvvM2DAgBLbHzVqFAsXLgRsVehIOt7wWrNmDXfccUe5lqnJRCQReAo4HcgHbjLGbPRMvxkYCRwD7jfGvOWZNgZoZoyZ4Hy+ErjHmfdFY8xzIlIPeBk4GTgE3GiM2R2TLxcntm/f7g63atXKHW7YsCEZGRnk5OSQn5/P7t27Ofnkk6sjiUqpCoh1Xnz99dczadIkhgwZQlFREZMmTQo774gRIxg3bhyLFy8mKSmJqVOnkpyczIQJExg+fDg+n4+BAwfStGlTBg8ezPjx4xk8eDDJycluT9J+bdq0Yd++fRw7diyg/S/YB3s33ngjs2bNCpkOEeGGG24gLS2Npk2b0qZNm3Jf51avXk2vXr3KtUx5JPh8vqitvLqJSFtg8//+9z9OOeWUSq0rOzs74LUG1WXSpElMnToVsNUM/VWju3XrxurVq6szaSeMmnKsVfTpsY4vxcXF3Hjjjbzwwgtu51iRKu1YHzhwgAkTJvDMM89EuroaX2wnIr8ErjLGDBORnsBEY8zVzrRmwPtAdyAVWOIMJwLPAz2A14wxE0QkGcgGzgEOA0uBK4BfAQ2NMVNE5HqglzFmNJGrkpuPmvwbbtWqlfv6wm+//Zaf/OQn7rRu3bqxdu1aAFasWEH37t2rJY3xpCYfa1W19FjXHM8++yzt2rXj0ksvjcr6SzvWY8eOZcyYMQEPEctQrrxZO8aKM95qz96TQqtDK6VOdImJidx6661V/kq4mTNnnlClwI7zgXcBjDHLsEGuXw9gqTEm3xiTA2wEumED4lnAA555TwU2GmP2G2MKsAHzBd71A+8AfYmQiNT5/vvvOXbsWIW+WDwoLi52a2qBbb7k5e8FHYjqK0CUUqoybrzxRt599123X5BY2bBhA61bty5PAFxuWh06zgRXhw41XimlTlQ9e/akZ8+eVbrOMWPGVOn6aoiGgPfpaJGI1DHGHAsx7RCQYYzZD7wnIsNKWc8hICNovH9cCSIyAgjuHjWlT58+PPvsszRt2rR83ypIXl4e2dnZlVpHNOzevZuioiIAMjIyAtoHAwEd0KxYsUJLvSJQU4+1qnp6rGuWm266CWNMVNZd2rG+7LLLynUelPc6qkFwnAlXEnzw4EHtXEMppZTfQSDd8znRCYBDTUsHwnXBGW5e7/iwyxtjZgABjd/8TZU6dOhwwjRVCnb06FF3uFWrViXSePrppzNv3jwA8vPza+R3qGlq6rFWVU+Pde1Rncdag+A44y3xzczMdHtUzcjIIC8vj3r16lVj6pRSStUQS4ErgVecNsFrPdOWAw+ISCpQF1vleV2Y9WQDHUWkMZCLrQr9KNAGuNxZV3/g42h8iXjl7RSrZcuWJaZrdWillKpeGgTHGW8Q3LBhQw4ePKilv0oppYK9AVwqIp9gOwv5jYjciW3f+6aIPI4NXBOBu40xeaFWYowpdJb7rzPvi8aYH0TkaWCWiCwBCoAbYvCd4oY3CG7RokWJ6d4geOvWrTFJk1JKqeM0CI4z3pddp6enawCslFKqBGNMMTAqaPQGz/TngOfCLDsz6PO/gX8HjTsCXFsVaT0R/fDDD+5wqCDYWzrsDZiVUkrFhgbBcWby5Mns2rWLI0eO6HsFlVJKqRqorJLgZs2aucM7d+6kuLiYxER9YYdSSsWKBsFxZsiQIdWdBKWUUkqVYufOne6wN+D1S01NpVGjRuzfv5+ioiL27NmjD7aVUiqGNAiOc+vXr+eHH37g8OHD9OjRI+QTZ6WUUkrFzp49e9zhrKyskPM0a9aM/fv3A7Bjxw4NgpVSKoa07k2cu/vuu7nsssv4xS9+wbJly6o7OUoppVStt3v3bnc4XBDcvHlzd3jHjh1RT5NSSqnjNAiOc2lpae6wt9MspZRSSlUPb0lwkyZNQs7jDYJ//PHHqKdJKaXUcVodOo7s3buX/v37U79+fZo3b868efM0CFZKKaVqkMLCQg4cOABAYmIijRo1CjmflgQrpVT10SA4jhw6dIgVK1YAx98xqEGwUkopVXPs3bvXHW7cuDFJSUkh5/N2mKVBsFJKxZZWh44jR44ccYfr168PaBCslFJK1SSRtAcGrQ6tlFLVSYPgOKJBsFJKKVWzRdIeGLQ6tFJKVScNguOIBsFKKaVUzRZpEKzVoZVSqvpoEBxHNAhWSimlajatDq2UUjWfBsFxRINgpZRSqmYLVRK8efNmNm/eHDBfRkYGycnJgM2/jx49GrtEKqVULadBcBzRIFgppZSq2YJLgkePHk27du3o2LEj33zzjTstISEhoLq0N3hWSikVXRoEx5FQQXBmZiYiwllnnUX79u2rK2lKKaWUIjCY3b59O48//jgA9957Lx07dgyY11td2hs8K6WUii59T3Ac8Zb0+oPgXr16sWHDhupKklJKKaU8vMHsRx99BNj3Bffv37/EvBoEK6VU9dCS4DgSqiRYKaWUUjXHvn373OGVK1e64zIyMkrM660OrUGwUkrFjpYEx5FrrrmGzp07c+TIEbp06VLdyVFKKaVUkAMHDrjDRUVFAJx99tkhmyxpSbBSSlUPDYLjiIggItWdDKWUUkqFsX///hLjLrzwQgB8Ph9btmxh586d9OzZU4NgpZSqJhoEx7nCwkLmzZtHXl4eRUVF3HLLLdWdJKWUUqpWKi4uJicnp8T43r17Y4zhoosu4scff0RE2LBhQ0AQrL1DK6VU7GgQHOeKi4u58cYbAUhOTtYgWCmllKomhw4dwufzlRh/zjnnkJmZyd69ewEwxrB3714tCVZKqWqiHWPFuZSUFBISEgBbKuxvf6SUUkqp2ApVFTojI4MWLVqQmprKWWed5Y5fvny5BsFKKVVNNAiOI7/5zW9o27YtnTt3ZuHChQAkJCSQmprqznP06NHqSp5SSilVq3k7xfLr2rWr+7D67LPPdsevWbNGe4dWSqlqEtPq0CKSCDwFnA7kAzcZYzZ6pt8MjASOAfcbY94SkdbAi05aE4ARxhgTy3TXFDt27GDr1q0A5Ofnu+Pr1avnBr95eXk0aNCgWtKnlFJK1WbekuCEhAR8Pl/A2xx++tOfusNr1qzhN7/5jftZg2CllIqdWJcEDwBSjTG9gAnANP8EEWkG/B44D/gZMFVE6gL3AU8aYy4CHgSmxjjNNUZeXp477C391ZJgpZRSqvp5S4KvvPJKvv76ayZMmOCO8wbBa9euJTMz0y0l3r9/P4WFhbFLrFJK1WKxDoLPB94FMMYsA7p7pvUAlhpj8o0xOcBGoBswFnjbmacOkEct5S39rVu3rjtcr149d1iDYKWUUqp6eEuCGzVqRMeOHQPeD3zaaae5wxs2bKC4uJjGjRu74/bt2xebhCqlVC0X696hGwLedwcUiUgdY8yxENMOARnGmD0AYl+Q+yi2NLkEERkBjAganQKwceNGDh06VKmE5+XlkZ2dXal1VJb3CfP27dvd9CQmHn+W8dVXX2nnWJVUE461ig091rVHVR7rU089tUrWo0483ny6UaNGJaZnZGTQunVrtm3bRmFhIV9//TVZWVlur9G7d++madOmMUuvUkrVVrEOgg8C6Z7PiU4AHGpaOnAAQEQuxrYlHhquPbAxZgYwwztORNoCmzt06MApp5xSqYRnZ2fXqBufLl26uOk56aST3PEtWrSoUemMRzXtWKvo0WNde+ixVrHgLQn25s1enTt3Ztu2bQB888032jmWUkpVg1hXh14KXA4gIj2BtZ5py4HeIpIqIhnAqcA6JwD+G9DPGLMyxumtUcJVh9Y2wUoppVT185YE5+fnc/jw4RLzdOzY0R3euHEjmZmZ7udQr1hSSilV9WIdBL8B5InIJ8BjwB0icqeIXGWM+RF4HPgY+BC42xiTB0zHVmueJSKLROTZGKe5xgjXMZa2CVZKKaWqnzeInTp1Kueff36JeTp27Ej9+vXp1q0b6enp2iZYKaWqQUyrQxtjioFRQaM3eKY/BzwXtMzpMUhaXAhXEtyjRw+SkpKoV69eQLUqpZRSSsVO8HuC27ZtW2KeW265hd///vdur9DffPONO02DYKWUio1YtwlWlRCuJPi+++6rjuQopZRSyiO4OnOoIDglJSXgs5YEK6VU7MW6OrSqhHAlwUoppZSqfsElwa1atSpzGQ2ClVIq9rQkOE74fD4+/fRT8vPzyc/Pp04dPXRKKaVUTRJcEty8efMyl9EgWCmlYk8jqTiRkJDAOeecU93JUEoppVQYwSXBzZo1CznfV199xZo1a9i2bVvA+4Q1CFZKqdjQIPgEsGTJEhYuXMjRo0e56KKLuOyyy6o7SUoppVStUlBQUOINDeGC4OnTp/P8888D8Ic//MEdr0GwUkrFhgbBJ4BFixZxzz33uJ81CFZKKSUiicBTwOlAPnCTMWajZ/rNwEjgGHC/MeYtEWkCzAXqAduB3wCdsK8r9OsJDACWA18D65zxbxhj/hbVL1WDHTp0qMS4cNWh27Rp4w57S481CFZKqdjQIDhO+Hw+APeVCl76nmCllFIhDABSjTG9RKQnMA24GkBEmgG/B7oDqcASEXkfuAeYa4yZKSITgJHGmMeAi5zlrgV+MMa8KyJ9gXnGmNtj/cVqouAguG7dumRkZISc1xsE79692x3WIFgppWJDe4eOE+vXrycxMZF69epx7rnnBkzzBsHe1ygppZSq1c4H3gUwxizDBrx+PYClxph8Y0wOsBHo5l0GeAfo619ARNKAe4HRzqizgbNFZLGIvCoiZfcCdQI7ePBgwOfmzZuHfHAN0Lp1a3d4+/btbmeXhw8fDngThFJKqejQkuA44c8U8/LyKCgoCJimJcFKKaVCaAjkeD4XiUgdY8yxENMOARlB4/3j/IYDrxpj9jifNwCrjDEfiMivgCeAa7wJEJERwIigdKUAbNy4MWQV4vLIy8sjOzu7UuuoKmvWrHGHk5OTyczMDJu2wsJCd3jTpk1kZGSwd+9eAD777DOysrKim9g4VJOOtYouPda1R1Ue61NPPbVc82sQHCe8JbypqakB07yfNQhWSinlOAikez4nOgFwqGnpwAHP+KOecX6/IjDI/RA44gy/Afw5OAHGmBnADO84EWkLbO7QoQOnnHJK+b5RkOzs7HLf+ETLli1b3OFLLrmEd955J2xJcIcOHUhMTKS4uJg9e/bQqVMnNwjOzMysMd+pJqlJx1pFlx7r2qM6j7VWh44T3upRdevWDZimJcFKKaVCWApcDuC0CV7rmbYc6C0iqSKSAZyK7eDKXQboD3zsLJ8B1DXGfOdZx/PAQGe4D7AqSt8jLnirQzds2DBsAAy2pLhly5bu57S0NHdY2wUrpVT0aRAcJ0orCY5Wm+CjR4+yc+fOKlufUkqpmHoDyBORT4DHgDtE5E4RucoY8yPwODbI/RC42xiTB9wPXC8iS4FewJPOujoBW4LWPwG4RUQWAaM43la4VgoOgsvi7RwrJSXFHdYgWCmlok+rQ8eJ0kqCo1Edeu3atVx44YUkJSWxfv16bZ+klFJxxhhTjA1OvTZ4pj8HPBe0zE6gX4h1rcD2Nu0dtxm4uKrSG++87ZvT09NLmdNq06YNS5YsASAx8XiZhAbBSikVfVoSHCdiXRI8YcIECgoK+Pe//60BsFJKKVUGb0nwjh07Al59FIq3JLi4uNgd1iBYKaWiT4PgOOENboNLgr2fq+LVCseOHWPRokWceeaZLF26lD179pS9kFJKKVWLeYPgBQsWsHr16lLnP/PMM7n88su56aabaN++vTteg2CllIo+rQ4dJ7zBbXBJcFZWFr/97W+pW7curVq1qvS2srOzOXLkCEuWLGHz5s2MHTu20utUSimlTmTB7wnOzMwsdf5rrrmGa66xnW3//e9/Z+7cuYAGwUopFQsaBMeJ0qpDt2jRghdeeKHKtrV+/Xp3+Kyzzqqy9SqllFInquB3HpcVBHs1btzYHdYgWCmlok+rQ8eJ0jrGqmpbt251h9u3b8+xY8fYvn17VLeplFJKxbOcnJyAz02aNIl4WQ2ClVIqtjQIjhO33nor3333Hd988w3jxo2L6ra2bNniDk+fPp169eppibBSSilVigMHDrjDKSkp1K9fP+JlvUHw3r17qzRdSimlStLq0HEiLS2NtLS0mGzLWxIMtqOsnTt3UlhYSHJyckzSoJRSSsUTbxB80kknRbTM008/zfr16zHGhFyPUkqp6NAg+ATg8/m49dZbyc/Pp6CggH/84x8kJCRUeH3BQbDfjz/+WCUdbymllFInGm91aG/JbmlmzpzJ8uXLA8ZpEKyUUtGnQfAJICEhgRkzZlBUVATAiy++WKkS2507d7rDLVq0cNsDb9++XYNgpZRSKoTc3Fx3OCsrK6JlWrZsWWJcTk4OxcXFJCZqizWllIoWvcLGif3797Nr1y4OHDhAYWFhienezrK8PUmXV1FRUUB7pJ/+9KfusHaOpZRSSpXk8/k4cuSI+/nkk0+OaLkWLVq4wykpKQAUFxcHBNRKKaWqngbBcWL06NE0bdqURo0aMW/evBLTva9N8vYkXV4HDx6kcePGJCQkcNJJJ9GmTRt32g8//FDh9SqllFInqry8PIqLi93PFSkJ9gfBYB98K6WUih4NggTJOkcAACAASURBVONEQUGBO+zNKP28JcGVCYIbNWrEnj17KCwsZOPGjTRr1sydtmvXrgqvVymllDpRHTx40B2uU6cOXbt2jWg5bxCclJTkDmu7YKWUii4NguNEWUFwVZUE+yUlJZGZmUlmZqY7Tl/boJRSSpV06NAhd7hVq1bcdtttES3nDYJ9Pp87rEGwUkpFlwbBcaI8JcGVaRMcrEmTJu7wnj17qmy9Siml1InCWxLcsGHDiJfztgk+duyYO6xBsFJKRZcGwXEiVtWhg2lJsFJKKVW6igbB3pJg7wNsDYKVUiq69BVJcSJW1aG/+uorduzYQVZWFm3atAkoCdYgWCmllCrJWx06PT094uUaNmxIgwYNyM3NDehYSzvGUkqp6Co1CBaRusAIYCDQCSgCNgCvAjONMQWlLK6qUKyqQz///PNMnz4dgEcffZRbb70VYwyZmZmcdNJJFV6vUkqp8DS/jW/ekuDt27ezb98+GjduHNGyLVq04Ouvvw4YpyXBSikVXWGrQ4vIhcAK4FTgYeBi4GfA34BuwEoRuSQWiVSxKwnOyclxhzMyMkhNTaVTp05kZmYG9FyplFKqamh+G/+8QfCXX34ZUDJcllGjRnHfffdx7bXXuuM0CFZKqegqrST4SuB8Y8zBoPHrgbdEJAO4B/gwWolTx5UVBA8ZMoTzzjuPunXr0rFjxwpvJzgIVkopFXWa38a5w4cPB3wuT/55xx13APDiiy/y6quvAhoEK6VUtIUNgo0xd5W2oDEmBxhb5SlSIXlLd0MFwUOHDq2S7XiDYK3+rJRS0af5bfzzlgRD+TrH8mvUqJE7rEGwUkpFV5kdY4lIM2AYENC4xRjzhyilSYVQWFjoDocKgquKN+P1P8k+dOgQ+/fvJycnh5/85Cc0aNAgattXSqnaSvPb+LVv3z53ODU1lcTE8r98w/vgWYNgpZSKrkiu0m8CPYCEoD8VQ5s2baKgoIDc3Fzatm0bte2Eqg7dr18/2rRpQ7du3fj888+jtm2llKrlNL+NU97enOvVq1ehdXiDYO0dWimloiuSVySlGGN+GfWUqFIlJCSQnJxMcnJyVLcTKgj2Zsze6UoppaqU5rdxyltyW97aUuvWrWPixIls3bo15PqUUkpVvUhKgleJyGlRT4mqlJkzZ/Lzn/+cvn37smDBggqvJ1QQ7O3gQ4NgpZSKGs1v45S3TXB5g+DCwkLeeust1q5d647TIFgppaIrkpLgpcCXIrIDcBumGmPaRS1Vqty+/vpr/vOf/wBwySUVe5NGXl6e2wt1cnKy+9olbxCsGbNSSkWN5rdxyvtKpPJ2itWsWbMS4w4ePEhRUZG+mlAppaIkkiB4CnADsCm6SVGlWbFiBSkpKaSkpNC5c2cSEgKbidWtW9cdruh7goNLgf3b0JJgpZSKiSlofhuXvK9IKu+bFbKyskhISMDn8wWMP3jwYECP0UoppapOJEHwPmPMK1FPiQqrqKiIHj16ALZtcFFRUYl5vEFwXl5ehbZTWFjIGWecQU5ODpmZme54bROslFIxofltnDpy5Ig7XN7AtU6dOmRlZbFr166A8fv379cgWCmloiSSIPhtEXkUeA1wixiNMdpNcIz4qyiDfT1ScCkw4FZdhoqXBJ9yyil88cUXJcZrSbBSSsWE5rdxyluK639oXR7NmjUrEQRr8yOllIqeSILgG5z/Az3jfIC2UYqR4CA4lKooCQ5H2wQrpVRMaH4bp4qLi93hQYMGlXv5Zs2asWbNmoBxmt8qpVT0lBkEG2N+EouEqPDKGwRXtCQ4HC0JVkqp6NP8Nn7l5ua6w+XtHRpCd46lQbBSSkVP2FckicgLIlLyqnx8enMReSk6yVJe3iDYG+x6VUV16HC0TbBSSkWP5rfxrbi4OKBNcFpaWrnXoUGwUkrFVmklwU8Ab4nIt8BbwEYgCVstqz/QCbg56ilUMasOvWbNGlatWkWDBg3o0qULXbt2BY6XBKenp1OvXr0KrVsppVRYmt/GsaNHj7ptglNTUyv0WiMNgpVSKrbCBsHGmC9F5BzgOuAaoDNQDHwN/BN41RhTHG55VXViVR367bffZtKkSQCMHz+ehx56CIAuXbpw7NgxfV+hUkpFgea38c37eiSAH374gZYtW5ZrHaGC4P3791cqXUoppcIrtU2wMcYHLHD+VDWJVUlwuDZNiYlha80rpZSqAprfxi9v3pmXl1ciKI7Eeeedx8svv8wnn3zCU089BWhJsFJKRZNGN3EgkiC4S5cuPPvss/x/9s47PMpi7cP3bjoh9N6FkBGE0KSDhSKoIIqIChwFFTx60M8aEERFARGwK4qIooIgSBeQiCC9SCcQXkLoNZRAElJI2e+PzY7vJrubrSky93XlYt42O8tCnv3N07766itatWrF1KlTOXv2rEuvozfc7uQ0KRQKhUJxs6EXwWBOHXKVOnXqMHDgQKv2SkoEKxQKhe9wpkWSoohxRgTXrFmTO++8k+7du3Pq1CkAoqKiWLBgAT169HDqdTytbqlQKBSK4oMQwghMBZph7jv8jKZpR3TXhwLPAlnAOE3TfhNCVAJ+BkKAs8AQTdNShRCfAp2A5NzH+wABtu4tlDdXjMjr+XVHBFvQF6JUIlihUCh8h/IElwAMBgPVq1enYsWKVgZST0ZGBg8//LAUwGA2zA8//DDHjx936nUceYL37dvHX3/9xbJly9wK9VIoFApFofMgEKxpWntgJPCh5UJuNeoXgY5AD+B9IUQQ8Bbws6ZpnYHdmEUyQCugh6Zpd+X+XHNw701F3q4JnkRSKRGsUCgUhYNTIlgIUT/3z75CiLeEEGULekbhPdq1a8fZs2e5dOkSK1eutHnP119/zYEDBwAICAiQO9HXr1/n5Zdfdup1HHmC+/fvz913380DDzzAyZMn3XkbCoVCoSgAL9vbTsDvAJqmbQVu111rA2zSNC0jV9AeASL1zwArgW65HuWGwDdCiE1CiKfyzm+514O1llguX74sx/7+/hgMBrfn0otgVRhLoVAofEeB4dBCiGm5f34CfAGsAmZgrmCpKAZkZmby0UcfyeOJEyfSoUMH2rdvD8DixYvZv38/TZs2dTiPIxGsP05OTkahUCgU3sUH9rYMoHdTZgsh/DVNy7JxLRkom+e85Vwo5jZOH2Fu3bRWCLHDzr1539MwYFie04EAR44c8diepKenExsb69EcnhITEyPHfn5+bq8nKiqKjRs3yuOLFy8W+XsrThSHz1pROKjP+ubBm591o0aNXLrfmZzgVph3jEcCP2ia9oYQ4m831uZWfpLu2ktANU3TRrrz2v9moqOjpXfWz8+PuXPn8sorr/Dggw+yePFiAD7//HO++eYbh/M4CofW5zjlLQLiKdnZ2Zw/f97llhIKhULxL8Nr9jaXJECfoGrMFcC2roUBV3Xn03TnUoFPLfm+Qog1mO24rXut0DTtG8DK+Agh6gHHwsPDqVWrlgdvD2JjY13+4uNt9LU6goOD3V6P0Wi0CoG+fv16kb+34kRx+KwVhYP6rG8eivKzdiYc2pjbn7A7sCb3nLsJLy7nJwkhQoQQs4H/ufma/3p++eWfjhrZ2dkcPnwYgFdffdXqnrS0NIfzFLYn2GQysXDhQpo2bcoTTzzhlTkVCoWiBONNewuwCbgPQAjRDtivu7Yd6CyECM4NuW4ExOifAe4FNgARwCYhhJ8QIgBzGPQuO/fedOjDloODg92eJ2+v4OvXr5OVlWXnboVCoVB4gjMi+IgQYgVQH1iXK0j3ufl67uQnBQM/AOPdfM0Sz4kTJ1i2bBmrVq3i4MGDVtcyMjJYsmRJvnNg7jsYHh4OQFJSEkuXLnX4OoXtCT537hwPP/wwsbGxrFu3TuU/KRSKmx1v2luARUC6EGIz8DHwshDiFSHEA5qmnQc+wyxc1wCjNU1LB8YBjwkhNgHtgS80TYsFfgK2AuuAHzVNO2DrXg/WWmLRe2+9KYIhf9EthUKhUHgHZ8KhhwAPARs1TbshhNgA/Ojm67mcn6RpWiIQLYQY7Gjif3Pe0YIFCxgzZgwAffv2Zdy4cfLatm3bSEpKsro/PT2dgwcPYjAY6NGjB0eOmCPOf/zxRyIjI+2+TrNmzahRowZpaWmcO3fOynOs340+fPiw1/4ubrvtNg4cOEB2djbz5s3jjjvu8Mq8nqByUW4e1Gd981CUeUcu4E17S65X+b95Th/SXZ8OTM/zzAWgp425JgOTnbn3ZkNvg0uVKuX2PFWrVs137urVq1SsWNHtORUKhUJhmwJFsKZp14UQmzVNOy6E6AtUwdwb0B3cyU9yin9z3lGFChXkuEqVKlbr+Pnnn+XYaDSSk5MDQHh4OIGBgQwdOpQvv/wSgM2bNxMeHk5AgO2Pz5GnuHbt2nIcFhbm0d9FYmIicXFxNGnShLvuuktWtb548WKxyAFRuSg3D+qzvnkoCZ+1l+2topDQR061a9fO7XlseYJVmySFQqHwDQWGQ+dWqxwhhGiEOdTpFszVKt3Bnfykm54bN27Isb4AB8Cff/4px3pxawmJjoyMlAL26tWrbN682a016MOhPfWqr127lrZt2xIWFsbUqVPl+d27d3s0r0KhUJRkvGxvFYWEv/8//gRPopnseYIVCoVC4X2cyQluBTyHOUTrB03ThgB13Xw9d/KTbnrsieDk5GS2b98uj/VhWOnp5r86g8FAr1695PkVK1a4tQZ9YSxPc4It7SRycnLo3LmzPG8p6KVQKBQ3Kd60t4pCwlFRSVdQOcEKhUJReDiTE2zUNC1HCNEdmJB7zq1qle7kJ+muzXTnNf8N6EVwUFCQHG/fvp3s7GzA7PG9ePGivGbxBAP06NGDr776CoB169a5tQZveoKPHTsmx/feey/r168HzLnbOTk5GI3O7M0oFArFvw6v2VtF4aEXwXmLSrqC8gQrFApF4eFqdei/vFCtUuEi9jzBf//9T/vIdu3aWQlkvQju3LkzBoMBgB07dtgUsQkJCbz11ltMmjSJ2bNn57teuXJl6tevT2RkJDVq1PDo/Zw4cUKOmzdvLot+pKenc+bMGY/mVigUihKMsrclEH1nBU88waVLl84nopUIVigUCt/gjAgeAvwM3KlpWibmcOUhPl2Vwgp7InjHjh1yfPvtt9sVwRUqVJBVobOzs9m0aVO+1zh9+jTvvfceI0aMYMqUKfmu9+3bl/j4ePbu3cs777zj0fvRi+C6devSsGFDeRwXF+fR3AqFQlGCUfa2BGLpwADIQo/uktcbrESwQqFQ+IYCRbCmadeBFZjbGdUBVmHu96soJJzxBLdu3dquCAa466675Pivv/7K9xqOegR7k+zsbE6ePCmP69SpQ/369eWx/ppCoVDcTCh7WzLRh0Nb6nG4y6JFi3jjjTfkscoJVigUCt9QYE6wEOJdwPIbOQtz792DQFMfrkuhw5YITkhIkIIxODiY2267jc8//5y0tDSCgoIIDw+3muPOO+/k008/BZA5uHq8VdijIM6dOyd7DleqVInQ0FCr9lWnT5/22WsrFApFcUbZ25JJZmamHHva0zcyMpKdO3fKY+UJVigUCt/gTGGsJ4A6wEfA68BdQC9HDyi8iy0RrDeSzZs3JyAgwGFrho4dO8rxrl27yMzMtGqpVFieYL2nt25dc9HTxx9/nNatW1OrVi2r0GiFQqG4yVD2tgRi2dgF8+aup5QrV06OlQhWKBQK3+BMTnCCpmnngFigmaZps4DwAp5ReJHatWvTsmVLmjRpIg3svn3/1Epp2bJlgXNUqVKFevXqAeZQaf3zULAnOD09nfnz5/P9998zY4b7bSvPnz8vx5YCW82bN6dfv360a9fO4110hUKhKMEoe1vCMJlM5OTkyOPKlSt7PKcSwQqFQuF7nPEEZwohGgAa0FkIsQoo79tlKfSMGTOGMWPGWJ3TF99o0qSJU/O0adOG48ePA7Bt2zZatWolrxXkCU5PT6d///6AuV3S008/7fT69Vy4cEGObbWDUCgUipsYZW9LGHnrb5Qv7/nHpa/9oXKCFQqFwjc44wl+H/gG+A14GDgFrPXlohQFoxfBt912m1PPtG3bVo63b99uda0gT7D+XEpKCiaTyem16jGZTFSuXBmDwaBEsEKhUFij7G0JIzU11eo4LCzMo/mWLVtGp07/1EJTnmCFQqHwDc5Uh/5N07SuuVUrmwE9NU17xvdLU9gjJyeH2NhYeWwRwcOHD6dSpUqULl2aOXPm5HtOL4K3bdtmdU1vyEuVKpXvWX9/f0JCQgCzkM1r+J3l+eefJyEhgRs3bjB69GirayaTiatXr5Kdne3W3AqFQlGSUfa25KGPogLPRXCVKlWsjpUIVigUCt/gTHXoasBgoILu3EBN06J8uC6FA44dO0ZaWhpgDim25NFev36dy5cvA8jrelq2bImfnx/Z2dkcOnSIq1evytyjgkQwmL3BlnmTk5M9KqDl7++Pv/8///y6dOnC9u3buX79OvHx8VZtkxQKheJmQNnbkkfecOXg4GCP5ssbIZWUlEROTg5GozOBewqFQqFwFmd+qy4F2gCGPD+KQmLx4sVMnz6dH374gQsXLtgNhdb3CbbVqzAkJITIyEh5rK8wrRfN9oy4foc7OTnZxXfhmKSkJLmjnpCQ4NW5FQqFooSg7G0J49KlS3JsNBoxGDz7uPKKYJPJ5HV7q1AoFArnCmMFaprW1+crUdhlypQpbNq0CYCNGzc6JYLzFuuw0KpVK3bv3g3Anj176Nq1KwAdOnQgPT2dtLQ0GjVqZPNZX4pgveHXF89SKBSKmwhlb0sYlugrwCq6yV1CQkIoW7aslYf56tWrlC1b1uO5FQqFQvEPzvzG3imEaKJpWozPV6OwSd4+wZ6I4ObNm8vxnj175HjAgAEMGDDA4Tr0xbHy5kE5y5w5c6hUqRJVq1aladOmctdcnwelPMEKheImRdnbEkZAQIAcR0REeGXOqlWr5hPBdevW9crcCoVCoTDjjAjeBOwRQpwDMi0nNU1TSZuFRF4RfPjwYXms99o6I4JbtGghxxaPsLPkrRDtKmlpaVJoBwQEWK1ReYIVCoVC2duShr5Twi233OKVOatVq2Zl51VxLIVCofA+zojgd4ABQLxvl6KwR14RfOTIEXkcHh4ux/pcXnsi2OJ9NZlMHDp0iLS0NFn1uSD0hbDcEcF6cVulShWr3CnlCVYoFAplb0sazhSVdJW8ecHFvVdwWloaX3zxBZs3b0YIwcsvv6xaICoUimKPMyL4iqZp83y+EoVd9CI4NTWVxMREwJw7VL16dXnNGU9wWFgY4eHhxMXFkZ2dTUxMDK1bt3ZqHZ56gq9cuSLHlorWFnzlCT558iRnzpyhbdu2qrqmQqEo7ih7W8LQi2BPOiboqVatmtVxcfYEp6am0r17dzZv3izP/fTTT2zatIl69eoV3cIUCoWiAJwRwcuFEFOABYBUVpqm7fLZqhRW6EXw2bNn5Tg8PNzKm+qMCAZzSHRcXBxgzgtu3bo17777LufOnSMkJIRXXnmFWrVq5XuuadOmdO3aldKlS1OjRg2X34d+N9vSmsmCLzzBX3/9Nc899xwAXbt25ffff/dK4RKFQqHwEcreljB84QkuSSJ45MiRVgIYzN9T+vXrx7Zt2/Dz8yuilSkUCoVjnFEElmpJD+vOmQCVo1RI6EXw6dOn5VgfCg3Oi+DmzZszb57Z2WApjjV//nxiYsy1WAYPHmxTBL/22mu89tprbrwDM3pDnrfSpd4T7A0RnJCQwKuvviqP//zzT77//nuGDh3q8dwKhULhI5S9LWFYOjcA7Nrlnb2KvKHExVUEa5rG1KlT5XH//v1ZtGgRmZmZ7Ny5k++++07ZXIVCUWwpUARrmuadSg8Kt9GL4JMnT8qxuyLYVnEsfZ9gZ3OEXcVZT7A3wqHnzp1rtUMPMG3aNGWQFQpFsUXZ25KHXqBmZWV5Zc5BgwaRkJDAqFGjgOKbE/z555+TnZ0NQJcuXZg7dy7vvfceb7/9NgATJkzgqaeeUt5ghUJRLFFJkiUAvaA9fvy4HOcVwb169WLPnj3ExsYyefJku/Pp2yTt3buX7OzsQhHBjjzBlSpVkqHdV65c8fjLxNKlS/Od27lzJ2fOnPFoXoVCoVAoLPgiHDooKIhKlSrJ4+LoCU5JSeHHH3+Ux2+++SYGg4HXXnuNChUqAObvK7ZssUKhUBQHlAguAeg9wY5EcMWKFWnWrBm33nqrw8qM1apVk9dTU1M5evRokXuC/f392bNnD2fOnCE9Pd2j3N2MjAw2bNggj4UQcrxmzRq351UoFAqFQo8vCmOBtY0sjiJ4xYoVJCcnA3Drrbdy1113AeaNgGHDhsn7ZsyYURTLUygUigKxqzSEEG01TdtWmItR5MdkMtGrVy9u3LhBRkYG+/btk9fyimBXaNq0qQw7jomJcUoEx8XFsXDhQlJSUmjYsCFPPPGES6+pF8F5PcEAkZGRLs1nj/3798uNgwYNGvDss8+ycuVKunXrRocOHbzyGgqFQuEtlL0tuehFsL6DgqcUdxG8ePFiOX7sscesinQOHTqUiRMnArBq1SquXLkivcMKhUJRXHDkCf4aQAjxZyGtRWEDg8HAokWLWL58OQsXLuTixYuAuV9wzZo13Z63SZMmcrx//37S09Plsb7fsJ5Dhw4xcuRIxo0bJwtruYLekOf1BHuTwMBAHn/8cRo2bEjr1q15+eWXiY6OJioqigYNGvjsdRUKhcJNlL0toehtZ1hYmNfm1W8a69sLFgdu3LjB8uXL5fGDDz5odb1+/fq0adMGMOdJL1iwoFDXp1AoFM7gKObUXwgRDbQUQuRL6tA07QHfLUthi/j4eDmuX7++zWITWVlZZGRkkJ2dTZkyZezO1bRpUzneu3evHAcFBdntp+tpn+C6dety++23c+3aNYfh2p4SGRnJzz//DCCLdigUCkUxRtnbEoq+Zoc3RfAbb7whx5cuXfLavN5g69atJCUlAVCvXj2bUVyPP/4427dvB2DJkiWqKKVCoSh2OBLB9wJdAIG5Z6GiiNHnA99yS/4iojt27KB169YAtGzZkp07d9qdS+8JtrRGAsf5wJ6K4LfffltWjbRFVlYWV65c4dKlS1SoUCFfr0R3UFUpFQpFCUDZ2xKKvmaHrTQfd6lWrRpHjhwBil916HXr1slx9+7drUKhLTzwwAO8/PLLgLkWR3p6ut0oM4VCoSgK7IZDa5p2WtO0H4EnNU37AfgL2KRp2g+5x4pCRt8eqW7duvmuO9siCaBx48ZybDG04FsRXBCjRo2iatWq3HbbbcycOdPr8ysUCkVxRNnbkouvRHCNGjXkOCUlBZPJ5LW5PUUvgu+44w6b99SvX5+IiAjA3IJx/fr1hbI2hUKhcBZnqkOfEUIcAPYAO4UQ8UKIW328LkUuV65c4c033+Tdd99l2bJl8nydOnXy3euKCC5dujT169cHICcnR54vShFcsWJFOb58+bJX5163bh2DBg3i9ttvZ+zYsV6dW6FQKLyEsrclDH07P2/WutDX/DCZTFy/ft1rc3vCjRs32Lx5szy+88477d7bs2dPOV65cqVP16VQKBSu4kwfms+BSZbdaCHEEGAq5tAthY+5dOkS48ePB6xFaO3atfPd64oIBnNI9NGjRwHo168fERERDneyS4IIjomJ4cMPPyQiIoI2bdrQtWtXAM6cOcPs2bMBPCooplAoFD5E2dsShl4Ely9f3mvz5k0HunbtmlerT7vLrl27ZDeJevXq2fwuYuHee+/ls88+A+CPP/4olPUpFAqFszjjCa6qD8fSNO17oLLvlqTQow+10hd5KsgTrK9YaQ99XnCDBg0YP348UVFRdu/X90B0NTzLZDIxefJkpk2bxty5c20+qxfB7hYC2blzJzNnzmTUqFFMmzZNntf3CtY0za25FQqFwscoe1vC0G8cN2rUyGvz5i0eWVzaJP39999y3LFjR4f3du7cGX9/s6/lwIEDXo/wUigUCk9wRgT7CyFkgzchRCWg+CSn/MvRi2D9jrOn4dBgXSFaXxzLHoGBgQQGBgJmQe7Ma1hIT08nKiqK//73vwwePNhmIQ1veILj4uLk2JKPBNYiOD4+nszMTLfmVygUCh+i7G0JQ2+jK1f23n5FXk9wcRHB+oKbt99+u8N7Q0NDadWqlTzeuHGjz9alUCgUruKMCP4c2CqEeE8I8R6wGfjKt8tSWNALTYtwMxgMNkN63QmHtuCMCAb3Q6L11S3thVx7QwRbwrsBwsPD5bh06dLy7ywrK8vqPk9Ys2YNQ4cOZcqUKU553xUKhcIByt6WMFJTU+W4VKlSXpu3uHqCd+3aJcctW7Ys8H594SxVHEuhUBQnCswJ1jTtGyHEEaAHZtH8vKZpq32+MgVgvctsoXr16gQEBOQ7n1cEm0wmmx5XCxEREQQEBJCZmcmJEydISkpy2FsYzGLyypUrgFkEV6pUyan3oTfg9kSwfi57IjgjI4OzZ89SoUIFm/OcO3dOjvNuFAghOHPmDGD2GOu9w+6wfPlyevXqJY/XrFnD8uXLHf6dKxQKhT28aW+FEEbM+cTNgAzgGU3TjuiuDwWeBbKAcZqm/Zbref4ZCAHOAkM0TUsVQrwMPJb76ApN08YKIQzAacASfrNF07R/mtveBGRmZsrNaaPRKCOlvIGtnOCiJi0tjYMHD8rjFi1aFPjMHXfcweTJkwElghUKRfHCmcJYaJq2Bljj47UobGBLBNsKhQZzT1x/f38ZNp2ZmenQKAcGBiKEkF7gBx54gH79+jF8+HC7zzzyyCOyQIejStJ50RtwexU0K1SQUYBcuXKFnJwcjEZzsMLBgwcZM2YMS5cule+vbdu2jBo1it69e0vhefbsWTmHvsUEmFs2rFlj/md87Ngxp9duj3vuuYfx48czduxYbty4wcqVK5kzZw4DBgzweG6FhctneQAAIABJREFUQnFz4kV7+yAQrGlaeyFEO+BDoA+AEKIa8CJwOxAMbBRC/AG8BfysadpMIcRI4FkhxBJgINAWyMm9dxGQCuzSNK23F9ZaItF7gUNDQ726AVq5cmUMBoOsn1Ec8mn37dsna5NEREQQFhZW4DMdO3aU72P37t0kJyc79ZxCoVD4GmfCoRVFiC0R7Kgaoych0evWrbMKdbLFlClTmD59Oh9//HG+cC1HOOMJDggIkJ7onJwc+czs2bNp1aoVCxcutMqL3rZtG3369OHJJ5+Uoch6T3D16tWt5r/lllvk+Pjx406v3R4BAQGMGjWK1157TZ6bMmVKsernqFAoblo6Ab8DaJq2FbPgtdAGcx/iDE3TrgFHgEj9M8BKoBtwCuipaVq2pmkmIABIB1oBNYUQa4UQK4SnoTUlEP2mq7dbGPn5+VnlGCckJHh1fnfQfz/Q5/o6onz58vJ7RnZ2tlVOsUKhUBQlTnmCFUWHLSFrzxMMZhFsMcYZGRkF7rg2bdqUuXPnymNv5jTpcSYnGMx5wUlJSYB55zs6Opr//Oc/VsKyRo0aJCQkSEH8008/cebMGX755ReSk5MB899D3nYVehHsDU+whddee42PPvqI9PR0du/eze7du53KlVIoFAofUgbQx9BmCyH8NU3LsnEtGSib53wyUFbTtEzgUm7482Rgt6Zph3O9ye9rmjZfCNEJmAW0zrsIIcQwYFie04EAR44ckb+z3SU9PZ3Y2FiP5nCXvILO2+sYOHAgH3/8MWAW3EX1Pi2sW7dOjmvUqOH0eoQQ7N+/H4Bly5a5tIGupyg/a0Xhoj7rmwdvftauVugvUAQLIfpomrYkz7n/aJr2k4trU7iBq57gQ4cOERAQQFBQEMHBwQXOr/cEAy6FOLuC3hNsLxwazCL4zJkzVKpUiX379jFkyBApgBs3bszs2bNp3rw5CQkJREVF8cMP5m4ia9asYeDAgXKe6tWr5wtN85UILl++PA8//LDsQ7xkyRIlghUKhct42d4mAfpdUGOuALZ1LQy4qjufpjuHECIY+A6zMH4+95kdmPOJ0TRtoxCihhDCkOstlmia9g3wTZ73VA84Fh4eTq1atdx4a/8QGxvr1dZErqDvRuDv7+/1dTRs2NCn87uKPtKqa9euTq+nR48e/Prrr4A5Csvd91GUn7WicFGf9c1DUX7WdkWwEKI35rCnyUIIP92lAGACoERwIeBKTjC43qJB3yYJcEo4u4OznuANGzYQFBREZmYmLVu2lGHOjRo1Yt26dbJ4VpUqVfj+++8JDw9nzJgxAERHR8t58oZCg/dE8MmTJwkNDbWqZv3ggw9KEbx06VLGjh3r9vwKheLmwkf2dhPQG5iXmxO8X3dtOzA+V9wGAY2AmNxn7gNmAvcCG3I9wEuANZqmfaCb423gMjBJCNEMOJVXAP/bSUxMlGNLP1xvot8wLg7VofVFsRo3buz0c23atJHj7du3e3VNCoVC4S6Ofms3B7oAVYAXdOezMIdEKQqBhg0b8txzzzF37lxpcB2JYFepW7eurBANyKIX9vj1119ZvXo1KSkpDBo0iJ49ezr1Os6KYIsI/+yzzzhw4ABg9k7/+uuv+SpRGwwGRo8ezcWLF/nss8+srtkSwVWqVOGrr76iXr163HLLLQVWz7bHu+++y3fffUebNm2YOHEid911Fz169CAwMJAbN26wZ88ezp8/n6+6p0KhUNjBF/Z2EdBdCLEZMABDhBCvAEc0TVsqhPgM2IC5NshoTdPShRDjgB9yK0dfAgZgLrB1JxAkhLg3d+43gInALCHE/bnrHOzmOkssN5MIvnjxIpcuXQLMRcAcRaTlpXHjxpQqVYrU1FROnz7N2bNn8xWuVCgUisLG7m9tTdPeA94TQjyvadrUQlyTQkf79u1p3749c+bMkedcMT4FYTQaqVChAhcuXACsjbottmzZwrRp0wBo3ry50yLY2XBogAsXLvDuu+/K43HjxtnddTYYDEyZMoW///6bLVu2AObw5O7du9u897///a9T63XE1q1bMZlMbNu2TVavDgsLo127drIFxIYNG3jkkUc8fi2FQvHvxxf2VtO0HCDvL7xDuuvTgel5nrkA5P2lvghzBWlb3O/hMks0lvoVgFfbI1nQF9vyVm97d9F7gRs1aiRtnzP4+/vTqlUrNmzYAMDff/9Nnz59vL5GhUKhcAVnti5nCiGeBCpg3k0GQNO0j3y2KoUVSUlJUkQGBQU5DHm+cOECycnJZGRkUK9ePUJDQwucv1y5clIEW3Z67VG6dGk5TklJcWb5ALRs2ZL+/ftz9epVwsPDHd47efJkWSylUaNGvPDCCw7vDwgIYM6cOTRp0oSUlBQSExM5f/6802tzheTkZPllwGg0WlXIvOOOO3wqgqOjo+nevbvqQ6xQ/HtR9rYEoY9w8oUI1gtfi40uKtwNhbbQpk0bKYItnR0UCoWiKHFmK28u5n6CzYCmuT9NHD6h8CqnTp2S4zp16jgUQf369aNhw4Y0adKEHTt2ODW/voJ0QeLRXRH81FNP8csvv7Bq1Sruu+8+u/fFx8fz5ZdfyuOJEycSEBBQ4Px169bl/fffl8cTJkzg8OHDTq/PWXbu3CkLdTVp0sRqk+GOO+4gIiKCZ555hh49enj1dY8cOUKPHj0K3BBQKBQlGmVvSxD6ytb69oTeom7dunJsqY9RVHhDBFtQecEKhaI44IwnuBHQSFdVUlHI6EVwQaHQrvYJBuu2SPq+h7ZwVwQ7S1RUlDT2ZcqUoVevXk4/+9xzz/Hzzz+zZcsWMjMzef3111myZInNezMzM0lOTqZChQourU9vvPVGHaBbt25omubSfM4yfbo5avHLL7/kzjvvVKHWCsW/E2VvSxB6EeyLopL169eXY0tLwKLCUxHcuvU/3bN27drldk0OhUKh8BbOeIJPFXyLwlfMmjXLKj+2oKJYekPsrAjWh3GdOnXKYXEsvefT2yI4IyOD1atXy+NatWq5lHfk5+fH559/Lg3r0qVLWbNmjdU9f/31F7Vr1yY4OJgnn3zS5TXqvet5RbCvDLrJZLIKhRsxYoTNquEKhaLEo+xtCUJvA33RXrBevXpybDKZitQb7KkIrlevnqwHkpiYyMmTJ722NoVCoXAHZxTGfmCtEGK0EOIVy4+vF6Yws3nzZlnwCQoWwe54gkeMGEGZMmUAs4c0Pj7e7r2+9AQvXLjQqtCIn5+fg7vzc+edd/LWW29Z5Ry//PLLVqI+LCyM06dPk5OTw/Hjx11eo6ViNUCzZs1cft4ZcnJyeOuttzh0yFzDxmAw8Omnn8qWTMeOHWPWrFk+eW2FQlGkKHtbgtAXrtJHVHkLfRs+KLq84JSUFJkqFRAQYCXOncVgMNC8eXN5vGfPHm8tT6FQKNzCGRFcBjgChKNylAqdtLQ0q2NfhEN369aNtm3byuP9+/fbvdddEfzSSy8xcuRI3n//fbteTEvVaQtXrlxxev60tDTWr1/PihUrOH78uNyV37dvHzNnzpT36Y338ePHZX6vM2RlZREXFyePb731VqefdYU//viD9957j0aNGvHoo48C5rZSr7/+urxn6lTvFWw/d+4cy5YtY/v27eTk5HhtXoVC4TLK3pYg8hZG9DZGo9FqM9jRBrUv0b9u/fr1Xd6gttCiRQs53r17t8frUigUCk8oMCdY07QhAEKIcpqmFX239puM1NRUq2NfeIIBmjZtyh9//AGYRfDDDz9s8z53RHBOTg6fffaZFJx6MWfh0KFDrFu3zurc5cuXnZofzELOQrVq1XjmmWd4++23ARgzZgyPPfYYoaGhVKhQgdKlS5OSkiIrSTubF3z06FHZT7lmzZrSe64nOTmZjz/+mB07dnD58mU2bdrk9Huw8Msvv8ixvpei5T1lZGSwc+dOduzYwe233+7y/BYsHucPPvhA5ps1b96cOXPm+EzgKxQK+yh7W7LQb+g66trgCUFBQfJ7wLFjx3zyGgVx5MgROW7QoIHb8ygRrFAoihMFeoKFEBFCiAPAASFEDSFErBBCfUMuJPKKYFc8wa7kDzVt2lSOve0JTk5OlgK4dOnS+Pvn33v5/vvv5diSB5yenp7v/dtDX9CrevXqvPrqq1SvXh0wC+SPPjJ3GDEYDFYVN10JiY6NjZXjRo0a2bwnKCiI8ePHs2zZMjZv3lygNzsrK4s1a9YwZswYHnzwQVq3bs2PP/4or5cpU4aLFy8C5tA4i2cY8Dgk+pVXXmH8+PFWBVf27NlD586dfVJZW6FQOEbZ25KF3j75IhwarHON9UUyCxO9J7igFoeOUCJYoVAUJ5wJh/4CeAlI0DTtLPA58I1PV6WQFEY4NPhWBFt6HIM5rDcvOTk5zJkzRx5bimdAwX2LLeg9wTVq1CA0NNSqoNikSZNkPlXekGhnSU5OplKlSoB9ERwYGGiVK2yvTVVKSgrjx4/nlltuoWvXrowbN44lS5awY8cOqxzmd999l2rVqtGtWzcWL17MgAED5LV58+Y5LGLmiLS0NKtc80aNGsmiapcuXeLhhx92egPCGXJycqQXXaFQ2EXZ2xKEr3OCwbqFYUHdG3yFtzzBQgj5HeXUqVMuRXspFAqFt3FGBFfUNO0Py4GmaVMx5y0pCoFr167JcVhYmJUItYU7Irhjx448/fTT8vjIkSN2BVClSpV44403GD9+PKNHj3Zqfv170AtcC5s3b5Y73BUqVLAKAXbWSOpFsMUDPGTIEG677TbALDrfeecdwH0RPGjQIC5evMjFixcZNWqU3fv0Icp///231TWTycRPP/1Ew4YNefPNNzl9+nSBr5uTk8Off/7JQw89xPPPPy/DsM+dO8eGDRucXr+ekJAQ1q9fz9NPP03fvn3Zv38/a9askf9+YmJiGDdunFtz69m7dy99+/YlLCyMwMBAbr31VmbMmOHxvArFvxRlb0sQevvkiz7BYL1xXFSFsfQi2BNPcEBAgNWGu/IGKxSKosQZEWwSQgQDJgAhRDXAvaoICpfRC8hq1aoVeL87Injv3r3s3btXHptMJqt2CHrKlCnDhAkTGDVqFEOHDnVqfv17sOUJ1nuB+/XrJ72t4LwIzhsODebq0pMnT5bnp0+fzqFDh9wWwRYqVark8LPQi+CdO3fKcWJiIo8++ihPPPGErLQJ5lyy5557jtmzZ3PLLbfI80888QQdO3a0ar109OhRqwra+r87VwkKCmL69OnMnTsXPz8/2rdvzyeffCKvT5kyxSoE3FWmT59O69atWbRokdxU0TTNqiWXN8nIyHCp0JlCUQxR9rYEod/kPHr0qE9eQ18HJG+16MLCWyIYVEi0QqEoPjgjgqcCq4AqQoj3ga255xSFQGJiohzXr1+/wPtDQkIICgqiTJkyNnNv82IymfKFXIPjkGhXcRQOnZmZyfz58+XxgAEDrAy9O55gvSe5Z8+edO3aFYDs7GxGjBhhlRN84sQJJ9+F89gSwXFxcbRp08bqvdaoUYMZM2Zw+vRppk6dSpcuXWThk8DAQL766is2btzIiRMneOONNyhfvny+19q/f79HIXIGg4GAgAB5PGzYMDp06ACYP5s33njDrXm///57hg0bZhUCbTAYaNWqFW3atOHEiRNWoYTusmPHDgYPHky1atUIDg4mMDCQtm3bMmXKFKvNF4WihKDsbQlC//vN1gavN9D3o3dmI9zbpKeny4glo9HoVnskPUoEKxSK4oIz1aG/E0LEA/cBAcAwTdOi3X1BIYQRs1FvBmQAz2iadkR3fSjwLJAFjNM07TchRCXgZyAEOAsM0TTNewmLxZjk5GQ5joiIKPD+UaNGOQzVzUtmZqZsi2M0GuXYmyLYUTj0n3/+KQs/1axZk86dO7N8+XKEEFSsWNEqH8oRtsKhwSy8Jk+eTKtWrTCZTCxdupT77rtPXnfHE1wQjRs3Jjg4mPT0dE6ePMmyZcsYPHiwVZGsZ599lg8//JDQ0FB5bs2aNXLcvn17mWNWu3ZtJkyYwIgRI5g8eTIfffSR3LjYsmULQgjGjh3LCy+8YCVobZGVleVwc8RoNDJ16lRatmxJ//79rfKqCyInJ4eYmBhmzJjB559/nu+6yWRi586dVpWnQ0JCqF69OuHh4URERBAREUGTJk1o0aKFzdB5C8nJybz66qtMnz493/vbvn0727dvZ/369SxdutTp9dsjOjqa77//nvj4eDIzMylfvjyRkZF069aN7t27ey0MMiMjw2chlYqSgbftrcK36IsKOvp95Qn6eYtiY+/YsWMywqZOnToeR/IoEaxQKIoLBbsKAU3T1gkhZNyPEKKUByL0QSBY07T2Qoh2wIdAn9x5qwEvArcDwcBGIcQfwFvAz5qmzRRCjMQskj928/WLDJPJhMlkIicnx+aflrGfnx9+fn7cuHHDKqS5cePGXl+TPvc3KChIiitfieC8u+W//vqrHD/66KMYjUYmTZrEpEmTXHoNW+HQFlq0aMGgQYP46aefAPjqq69srs0RcXFxbNiwgVtvvZXGjRs7/MLj7+9P8+bN2bp1K2AO8ba00ggJCeHHH3+kX79++Z5bvXq1HFu813rKli3LuHHjeP7553n99df5+eefAXO+86uvvsqMGTP45JNP6N69u9213X333VSvXp0XX3wxX6i1hWbNmnH06FErj7k9rl27xtKlS1m0aBHr1q1zqbczmAt0HT16lKNHjxIdbf1d/5ZbbqFFixa0bNmSFi1aEBkZSc2aNTl16hS9e/dm3759VvfrN3H8/f15//33XVqLLbKzs9E0jblz51qdX7t2LZ9++imBgYHUrl2bevXqUblyZfn3aTAYCAkJITQ0lFKlSsmf0NBQSpcuTVhYGMnJyezatYu///6buLg4DAYDp06dstqkSE1N5dtvv6VDhw40a9aswE2OvKSlpXH48GEOHTrEoUOHZKSBv78/lSpVombNmtSsWZNatWpRq1YtgoKC5O+djIwMqy/5+vdm+dNkMpGamsqlS5eoX78+QUFBsrep0Whk27ZthIWFUblyZSpVqkRYWJj8/WY0GjEajTb/Deb9DFJSUkhKSiIpKYn09HT5Gv7+/gQFBcnNlILmKgl42d4qfIi+MKGvRLDeZuqjqgoLb4ZCA0RGRsrf1Zqmcf36davNYIVCoSgsChTBQohXgHGAxUVhwJyv5G6eUifgdwBN07YKIfSNTtsAmzRNywAyhBBHgMjcZybk3rMyd1xoInjKlCm8+eabTufYGgwG+QUR8FqeYuvWrb0yjx59KHSpUqWcEsEvvPAChw8fJiUlhVmzZlnlsdrCXjh0dna2lafukUcecXn9FuyFQ1sYN24c8+bNIyMjg7179zJx4kSee+45m71+bREdHc3w4cMBGDx4sFVLJ1vcfvvtUgRbBHCVKlVYtmyZVXibBZPJxJ9//imPbYlgCzVq1GD27NkMHTqU//3vfzJ/++DBg9xzzz307t2bKVOm5Isc2L59Oxs3bgRgyZIlnDlzxir/Wo8jAZyYmMiSJUv49ddfiY6Odqrqc4UKFShfvjxGo1GG4CckJDh89tixYxw7doyFCxfKc6VLlyYjI8Pqubvvvpu3336bTp06kZSUxIIFC0hJSZFF0SxkZ2eTk5NDQEAAJpOJxMREDh8+zPHjxzlz5gxnzpwhPj6ey5cvc+7cOc6dO0dCQoIU1ra4ceMG8fHxVi1EPCEgIIDg4GBZBM9oNMq5/fz8qFy5MrVq1aJatWqEhYURFBSEyWQiIyNDCsL09HT5s379eqtokuKKwWDA398ff39/KXBzcnKcrkAP5lx9y2ecnZ1NZmam1e/s0NBQvv32Wx577DFfvAWv4AN7q/AhehHsbL95V9GL66IQwfrfbZ5UhrZQqlQphBDExsZiMpnYv38/7dq183hehUKhcBVnPMEvA+0A73zLM1e61LvfsoUQ/pqmZdm4lgyUzXPecq5QyM7OZuzYsS61G7J4db1J5cqVrVrveAu9CC5dujSpqamkpaVx4cIFLl68SOXKlfM9s2nTJhnGdOXKlQJFsL1w6K1bt8pQ6GrVqtkUh86yYMECzp49y9mzZ20Kuzp16vDSSy/xwQcfAPD111/z0ksvOT2/vkCUPpzXHnn/3qpXr866deto2LCh3WemT5/On3/+yZYtW5za8LjrrrvYs2cPH3/8Me+++67MsV22bBm///47Tz31FFFRUTKX/LPPPpPPPv7443YFsC0uX77MkiVLmD9/PqtXr7byENpjzJgxPPPMM9SoUcNmCPYff/xBjx495P+Vhg0b0r59e/bv309MTIxNgWxLFK1du5a1a9dSsWJFGUIfFhZGdHQ02dnZ8ic+Pp4LFy4QHBzM9evX3W4v5WssAtbyf8NCdnY258+ftyqq9m/BZDKRmZnpURutgtqpXb9+nS+++KJYi2C8b28VPkRv5wtDBG/ZsqXQPafeFsFgjs6y2NQ9e/YoEaxQKIoEZ0RwnKZp+wq+zWmSAH2ipzFXANu6FgZc1Z1P052zQggxDBiW53QgmMN5PPGGPPbYY8yYMaPQKs9aPCEWj3KZMmUYPXo0cXFxBT579epV4uPjuXHjBmXLli0whFo/p5+fHw0aNCAmJgaA3377zaZxMhr/qad24MCBAvsjhoeH88wzz5CcnEzlypWl8dO3yuncuTOaphX4/uxRtWpVqlatSosWLTh8+LDNe/r27cu0adO4evUqx48fZ8yYMQwZMiTffenp6fmqIuv7/ZYuXdph1eS4uDimTJkijw0GA9OmTSMrK8vhc7Vr12bw4MEMHjzYKgTNHqdOnWLOnDmsWrWKu+++m8DAQBYtWiQFxbRp05g+fTo9evTg7rvv5pdffpHP9u7du8DKz+fOnWP9+vWsWLGCHTt22P33f9ttt8nXiIuLY+zYsXTv3p3HH3+c69ev2/13W6tWLcaMGSPzjuPi4mjQoIH0ssfHx3Pw4EFiY2M5dOgQcXFxDv8fX7582alCahbPvLOUK1eOypUry5DesmXLyvDma9euceDAAfbv309qaiqDBg0iMjKSnJwcMjIySE9P58svv7Sq6G3BYDAQGhpq5c1NTU0tsgrXgYGBBAcHExAQQGBgIIGBgZw6dcqhJxzM78PPz4+yZcsSEBBATk4OOTk5ZGVlkZKSYpXuUZSUKlWKBx980KOK5xbs9Qn3At62twofUtgiODExkfPnz3tNjDqDvnikp0WxLDRv3lym8+zZs8crc/qS8+fPs2PHDjIyMmjcuDG33nrrvyL1QqG42XFGBH8hhPgFiAbkNr2maT+6+ZqbgN7AvNycYH3c7XZgfG6LiCCgERCT+8x9wEzgXiBfc1RN074BvtGfE0LUA46Fh4dTq1YtN5dr9tANHTqUevXqSQGoz2czGAxWY0vOm+XYgl48+opFixbxn//8B4AHHniAJUuWOLxfX6G3bNmyNG/eXIrgpKQkm1/2qlSpIscVK1Ys8Atho0aNGDbMen/CZDJZ9bgdPHiwnOfq1ausXLmSy5cvExQU5HQrJmd49913efHFFwHz5zpy5Mh8X15iY2PzvSdLH2OAe+65x65H9/DhwwwbNkyKtdKlSxMdHU379u299h4sJCYmMnPmTMDsITh37hz79u3jpZdekmHPOTk5rFy5kpUrV8rnGjRoQMWKFQkODiY0NBSDwcCVK1c4e/YsBw4cYO/evfz1118OhXibNm3o168f/fr1yxcJ8Oijj1KmTJkCe1oDjB07FqPRKHs4//7771y+fJmPPvqI+++/n+rVqzNy5Ej8/f0xmUycPn2amJgYduzYQVxcHMeOHePUqVOcOXPGKe+0MzRu3Jivv/6aevXqUbVqVacKwWRkZLBixQruvfdegoODra4tXLhQiuA6derQs2dPevXqRdeuXfNtIFlybFNSUkhOTpZ/Jicnc+LECfbu3UtsbCxnz54lKSmJ1NRUjEYjAQEBNGnShAEDBhASEkJwcLDdn6CgIKufwMBA/PzyR9tmZWURFRUljy25vZUrV6ZatWpUr15dhmU784VQnz9s2bC4fPky2dnZmEwmHnjgAfz9/WVIc2ZmJklJSYSEhABIj75FZFt+B1t+3+p/jEYjN27c4OLFizK/OTs7W1Y+L8Z4294qfETe6LDCKIwF5voXRSWCnakT4QzNmzeX4+Isgk+cOMGrr77KwoULrTY8WrZsyaRJkxymLSkUiuKPMyL4f0BVQP9tzQS4a5QXAd2FEJsx5zsNyc2DOqJp2lIhxGeYRa4RGK1pWroQYhzwQ27l6EvAADdf223CwsKsxF9xxdU+wfpw6JCQEKtG9nkLD1nQixtXcvb0xMbGSpEVGhpKly5d5LULFy4wYID5I27QoIFXRfCzzz7LZ599xpEjR7h69SpDhw7ljTfesGprlJdr167JwluBgYF2w7+PHz9O165duXDhAmD+N7N69WqPwrwd0a5dO2rVqsXp06e5fPkya9eu5Z577mH9+vWsXbuW999/36rYloX4+Hjuvvtut16zRYsWLFy40KFHwFZOtiPeeustLl++LCtK//3333Tu3Flenzt3Lo8++igGg4HatWtTu3Zt7r33Xqs5srOzSUhI4Nq1a1I0pqWlWQmjS5cuMWvWLKKjo/P93/D396dnz568/vrr3HHHHS6tH8z/7x566CGb10aOHEmZMmVo2rQp4eHhDgWjxTscGhpK1apVXV6HN/H39+ejjz7y2nz69+bsl2lXQvYLet4bHuBCwNv2VuEj8kad+GqTO28xSUu7osLCFyJYn9q1b98+srOzbW7EFSUbN26kT58+Nos97tq1i27duhEVFcX7779fKA4OhULhfZwRwXU0TbOfyOgimqblAP/Nc/qQ7vp0YHqeZy4APb21hn8znopg/Q6tvfYF3hDBeg91z549rbxnrvYJNplMTocmBQYGMnHiRFmdeeHChVy4cEF6Tm2hD9Nu2LChzfzW06fqUNz9AAAgAElEQVRP06VLF/kFpVSpUqxYscIpAZycnIzRaHQ5z8toNNKvXz8++eQTAObNm8c999yDwWCgS5cudOnShb179xIVFZWv8rIzhISE0KlTJ+rWrcu3334LmP9N/Pbbb7JI2OLFi2nXrp1H/SsNBgOffvop9evX5/XXX8/n0Z0yZQr9+/d3+Bn7+flRvXr1fJXB89K/f3+uXr3K1q1bOXLkCOfOnaNjx460a9fOZ+GMgwcP9sm8in8lXrW3Ct+hF0e+DI3NG1Fz8uRJn71WXq5duyZregQHB3vNEVClShVq1KjB2bNnZQV7H6YYuMzu3bvp2bOnVaRcx44dKVOmDGvXriU9PR2ASZMmkZCQwIwZM5QQVihKIM78rz0uhHDNtaMoMlwVwa1atSI6OpolS5bw9ttvW/Xwi4mJsTmHN0Tw4sWL5fjBBx+0ula+fHn5peLq1asFhrmOGTOGihUr0qRJE9kGyRF9+/alY8eO8nj79u02czYt6D1Itgz12bNnufvuu2X7maCgIJYsWUKnTp0KXAvADz/8QLly5ejYsWO+VjwF0b9/fzleuHCh1aYGmNtRnDlzRh7ff//9DBw4kLZt21K7dm0qVapEhQoVCA8Pp127djz55JNMnjyZv/76i8TERKKjo5k+fTpPP/20nOOFF15gyJAhPPnkkzz00EO0adPG436PBoOBl156iQMHDvDUU09RvXp1jEYjNWrUIDIyMt/78oRy5crRs2dPhg8fzqBBg7jvvvt8JoAVChdR9raEkJiYKMe+FEBGo1GmBAAcPXrUZ6+VF70XuE6dOl4V+/rvGsUpJPrSpUv07t1bCuAqVaqwfv16Nm7cyIoVKzh27Bj33XefvH/mzJmMHDmyqJarUCg8wBlPcBoQk9u3UCoiTdMe8NmqFG6j96g6I4IrVqyYr69sgwYNiI+PJzMzk5iYGFq1amV13VUR/Nhjj5GTk0O5cuWYMmUKKSkpbN++HTB78PQGxXKuXLly8kvGlStXHO5Anz17litXrnDlyhWnxJLBYOCrr74iMjISgMzMTJ566inmz59v08g7EsEXLlygS5cuMrQ7ICCABQsW0K1bN3nPxYsX2bNnD926dbM5/9q1a8nKymLz5s08/vjjBa5fT9u2balXrx7Hjx8nMTGRWbNmWYWPr1q1igMHDgDmsPNZs2a5lbv26aefsn//fvm5WXKRwZwvPXz4cDZu3Ojxl6SIiAirgmkKxU2GsrclBH3Ekq9zdEuXLi1tW2F6gn0RCm2hefPmLF++HDCLYFdtn6948cUX5cZx2bJlWbt2rVWB0WrVqrF06VKGDRvGd999B8DkyZNp2bJlca88r1Ao8uDM9uUCzG0bfs4dW34UxRBXPcG2aNmypRzv3Lkz33VXRfDSpUuZP38+06dPx2g0WvUGvvPOO2164VwJibbk64Lz+ahNmjSxKni0YMECxo0bZ/PeQ4dktL5Ve6SjR4/SqVMnGS7t7+/PvHnzuP/++wFzmHaTJk2oUqUK99xzj9U6LeTk5PDXX3/JY1dzdY1GIy+88II8/vjjj2U1X5PJxJgxY+S1p556yu3iLaGhoaxatSpfLi5Ar169WL58uaqWqVB4jrK3JQR9qKwzRQA9QZ8XbMuO+ApPRPClS5eIiopi//79Nq8Xx+JYv/32G3PmzJHHP/30k80OG35+fkybNo0+ffrIc0OHDrXbmUKhUBRPChTBmqb9APwJXARmAWtyzymKId4QwXrP765du/Jdd0UE37hxQ+5g+/n5ERoaapUPrDcielwRwefOnZPjgnJCLRgMBtk/18Jbb73FF198ke9eW57grVu30r59e+kB9vPzY86cOVah3QaDwep9bN26Nd/c+/fvl7llVapUKbCllS2efvppwsLC5Fotu9MGg4Fvv/2Wnj17EhISwogRI1yeW0+5cuVYvnw5q1evZtSoUYwePZp169axdOlSn1VGVShuJpS9LTmkpqbKsa/79urtiN7e+RpnRPC1a9dsbpavXbuWyZMnExkZSe/evWW6kIW89UeKuoVaVlYWr7/+ujx+4okn6N27t937/f39+fHHHwkPDwfM34WefPLJYtt/XqFQ5KdAESyEuA/YDHwJVAFihRC2lYuiyPG2CPbUE2wpqgFQpkwZUlJSWLNmjTz3wAO2o/z0VV19IYLBds/DF154gU8++cTKkD388MP07t2bhg0bUr9+fSZNmkTnzp1JSEgAzCHo8+fPl8W29OjzgteuXZvv+qpVq+T4rrvucsubWrZsWV5++WV5/Morr/D3338D5iqcK1eu5MCBA9SsWdPlufNiMBjo2rUr48ePZ9y4cdxxxx3KA6xQeAllb0sOehGct9WZt9GnA125cqXA3t3eoiARfPr0aTp27Ej//v1lsSgLenv322+/cdttt8kNWoD69evLzduLFy8Wqri3xcyZM2XUV5kyZfjwww8LfKZMmTLMmzdPRpVt3brV5ka6QqEonjgTDv0O0Ba4qmnaOaAT8K4vF6VwH70IzmuUbDFp0iQqVKhAzZo15S99fcGKffv2cePGDatnOnXqxPTp05kzZw7/+9//HM6vF8HlypUjOjpaztesWTO7rXac9QRbeoGCOTTYleqV+tfWj7/55hvatm3L0qVLycjIYMKECfzwww+MHj2aDh06MGLECFmsq3z58vzxxx922+Pow5v14t+CJScKsBlq7CwjRoyQrZvS0tIICAiwum6vrZNCoShWvIOytyUCfasiX28E6u2hpR1cYeBIBF+9epUePXpw4MABjh49ygcffGB1/ZFHHqFfv37y7yYtLY2nn36a5557jqysLIxGo1WrpKIMib5x4wZjx46Vx1FRUU63Z2vRogWjR4+Wx6NGjcrn9VYoFMUTZ0SwMdcYA6Bp2h7MfQsVxRBXPcHXrl0jMTFRtioAs8G1iMIbN25w8OBBq2ciIiJ45plneOyxxxz217XMb6Fs2bJW+cD2vMCWNVhwJIItPXnBvFtuq32RPfTC97777qNHjx7yeOfOnfTp04fQ0FAqVKhAhQoVGDx4sNXfRZs2bdi1a5fDKtAdOnSQu8SxsbGcP39eXktMTGTTpk3y2BMRXKpUKRYvXky5cuUYPXq0VaiZQqEoMSh7W0KwFAkEfJ4Lqs8JHjhwoM/Dry3YE8Emk4kBAwZIexgQECDDgi3cfffdzJ8/ny1btlil+Xz99dc88sgjpKenF5u84Hnz5slNjSpVqvDSSy+59PzIkSNp0qQJYI4QcPV5hUJRNDgjglOFEHXINcRCiM5AwS5GRZEQHBxM3bp1iYiIICIiosD78/YJtlBQSLSzXL16VY7Lli1r5fn0hgh2NxQarI36uXPnWL58OePGjbPaSMjOzrZqhQHmcPCJEyeyYcMGu55sC6VKlaJdu3byePXq1XL8+++/y7Dr1q1bU7VqVZfWn5fIyEj27NnDqFGjPJpHoVAUGcrelhCSk5PlWN+VwRfoay7ow4h9SXp6utxk9vPzs0qn+frrr1m5cqU8njlzJgMHDrQ5T9u2bdm+fTuPPvqoPLd48WLuv/9+q0KTRSWCTSaTVejzCy+84PImQ2BgIN9++608Xrp0KdHR0V5bo0Kh8A3OiOCRQDTQQAixBVgEeFZhR+EzQkJCOH78OJqmybxQR9gTwQVViHYWvSc4OztbCtoaNWpYvUZeGjduzL333sugQYOswrPz4k5laAt6AXv8+HH8/PwYPXo0K1asICoqyqrthZ+fH7fffjsTJ07k6NGjjBgxwqq6tCP0HuYFC/4p9Przzz/Lca9evVxauz3q1q3r9LoUCkWxQ9nbEoK+t7yvPbN6EazfWPYl+lZMNWvWlFFWp06d4rXXXpPXXn31VQYMGOBwrtDQUObMmWP13Jo1a/j+++/lcVGJ4LVr18rXDgkJ4bnnnnNrnrZt2zJkyBB5/H//939kZmZ6ZY0KhcI3FBg7qmnaZiFEO6A94Ads0TTNcaUiRYnBngjWhzlv27bN7fn1IljvUe3VqxdGo/09mIceeshunq0eTzzB9erVIzQ0lHr16ln1/61evToffPABH3zwAQMHDsTPz4+mTZsybNgwq7A0Z+nXr5/MGVq5ciVJSUlkZGTw+++/y3vs7aIrFIqbB2VvSw562+brFkl6Eax/XV9iLxR69OjRsihY48aN7bYWzIvBYJA1SCzRSrGxsfj5+ZGdnU1cXBzJycmF4uXW8+WXX8rx4MGDraLQXGXChAn8+uuvJCcnc+jQIb744guropUKhaJ44Ux16EhgtqZpK4ETwJ9CCOHzlSkKBXsiuG3btrKgxd69e62qQF+6dImWLVsSERHh0EsL1rvWlgb04DgU2hU8EcFVq1YlOTmZmJgYZs+ene96VlYWv/76Kz/99BNRUVFurzEiIkLmPmVkZDBjxgwCAgKIiooiLCyMDh06WHmdFQrFzYmytyUHvSfYVq97b6LffC0sT7AtEbxr1y5mzZolz3/55ZcuhYIbDAbeeOMNPvjgA0qXLs3vv/9ulS+8b98+L6zceRISEqzqlAwfPtyj+apVq8Zbb70lj995551CK2LmChkZGSxfvpz//e9/tG/fnipVqhAWFka5cuVo2rQp/fv358svv+To0aNFvVSFwqc4Ew79FfAtgKZp+zFXr5zmwzUpChF7Irhs2bKy0EN2draVNzgwMJDdu3cTFxdHfHy8w/n1u9YW412qVCm6dOnilfWPGjWK+Ph4Nm7cyJNPPunSswaDwWFVz6NHj8pK1jVr1nTLC2xh2LBhcjxv3jzKli3L+PHjOXHiBF9//bXb8yoUin8Vyt6WEK5fvy7HvhbBek/w6tWr6du3r09fD6zDoS0i+O2335b9fB944AHuuusut+aOiori0KFDdO7cuUiLY/3000+y00P79u2tBLm7vPjii7IeS1JSklXl6KImOTmZcePGUa9ePXr16sXUqVPZunUrFy9eJCUlhWvXrhETE8P8+fMZPnw4DRo0oFOnTsycOTNflxCF4t+AMyI4VNO0RZYDTdMWA2V8tySFpyxfvpzZs2fz3XffFdjH154IBujYsaMcb968WY71+U8pKSkOm9z36dOHadOmcf/998tz99xzT77Xcpfg4GDq169Px44dve5N1VeC9tQ4DhkyhBo1avDQQw+xcuVKKb7Lly9P06ZNPZpboVD8a1D2toSg7xPsbDsdd9GL4NTU1HwdG3yBvgVU7dq1iYmJ4bfffgPMG8jvv/++R/NbCm3pRfDGjRsLTWyZTCZmzJghj59++mmvzBsYGMgnn3wij2fMmOFRXRVvYDKZmD17NkIIxowZY9WloiA2bdrEkCFDaNCgAZ988olTrTcVipKCMyLYJISQ39KFEI2AbN8tSeEpw4cPZ9CgQTz99NMFhuI4EsEdOnSQY30rHz8/P3mvyWSymiMvLVq0YNiwYVahY86EQptMJsaPH88rr7zCkCFDHAptX7F//3459lQEBwcHs3nzZhYsWGD1hUahUCh0KHtbQtDbPVf607tDXptx+vRpn9tEffpSrVq18Pf3p2/fvhgMBvr06eMVrylYi+AFCxbQr18/p9o7esrWrVuJjY0FzBv7/fv399rc9957L/fddx9g/i7zf//3f0XyHQbMEXiPPPIIgwYNskofq1GjBq+99hqrVq3i1KlTJCUlkZCQwPbt2/n888+5//77rVpOnj59mpdffhkhBLNnzyYnJ6co3o5C4VWcaao6BlgvhLAoglsBVcWnGONKr2BnPcFbtmwhJydHFrMqXbq0fDYlJYVSpUrZfY2LFy9KEW0wGKy8wvYwGAxMmDBB7rZ/+umnlCnjfYdIUlISa9as4eDBgwQGBlpVr9y1a5ccF5T77Az64iIKhUJhA2VvSwh6j1jt2rV9+lp5RfD169dJSkryKEWnIPSe4Jo1a3LrrbeyYMECDh8+7FVBpxfBmZmZLFu2jIceeoiFCxf6tPWUvg7Io48+6vWCXB9//DF//PEHmZmZbNq0iTlz5hRYRdvbHDhwgF69enH8+HF5rnr16kyYMIGBAwcSEBBgdX9YWBiVK1emdevWDB8+nISEBGbMmMEnn3wiHSonT55k0KBBfPzxx0yZMsXtkHhfkJqaSlxcHP/f3p3HR1ndexz/TFYSSJAlCQQChMXDDpXdBRQVFBGhiqWt63XhItYNK63XVry94lKX1qVaq61i3eq+ICqKS1kkFVFB4SD7ZoAkLCGQfe4fk3mcyUImmck2832/Xrw8zzpneCQnv+ec8zvWWrZt20ZeXh55eXkcPXqU6OhooqKiaNOmDSkpKaSkpJCenk6fPn3o2bOnVtWIUIFkh36nIjHHSUApsNJa2/xm+ovDNwiubejKsYLgzMxM0tLS2LNnD4cOHeLbb791hu62adOGffv2AZ4g+Fhvwl9//XXnreGJJ54Y8FvzDh06OEFwbm5ulSC4rKyMTZs2kZ6eXu/snNu3b3eyUPfo0aPGIPhYyzmJiIRCqNtbY0wU8BdgCFAEXGmt3ehz/CpgZsVn/V/F53cEngcSgN3A5dbaI3U5t771bUl8h+36rnfbEKp7Abxjx45GC4K7du3qlL3zXUOlffv2ZGRksGPHDmffokWLOOOMM3j99ddJSUkJ6eeB53cH3+UKL7rooirnFBQUsH79etavX4+1liuuuKLKi+xBgwaRm5tLfHw8rVu3dv507NiR1NRURowY4UwlmzNnDuedd16DL6fltWrVKiZOnOgsSwkwa9Ys7rnnnoAD/tTUVH77299yww038OSTT/K///u/5OTkOPc/7bTTOOecc7jnnnsYMGBAg3yPY9mxYwdLlixh+fLlLFu2jO+++65eL2iioqLo3r07xhj69etH//796devH/369Wvw+f6BKi0tpaCgwO/P0aNHcbvdzvQ6l8tFVFQUCQkJzv+LiYmJJCYmEh0d3cTfoHkKpCcYoAuQA7iAAcaY86y1f2u4akkw6tITvHDhQvLz8zl69Cg9e/b0O+ZyuTjppJN47bXXAPjkk0/8gmCv2uYdv/zyy055+vTpgX0JPI2jt2HMyckhMzPT73h2djbexKmZmZn1ymR4/PHHExMTQ2lpKVu3bnW+S05OjpMYpFWrVn5LKImINKBQtrdTgVbW2jEVSy/dD5wHYIzpBFwHDAdaAUuNMYuB3wPPW2ufNsb8BphpjHkh0HOBB+tZ1zpbs2YN1113HTk5Objdbr9fgL1l3/9mZGTQo0cPv33fffed80LX93xv2Xe7Z8+epKenV2nzGjqBd3R0NElJSeTn5zv7tm3b5iSvDLX8/HxnClN8fHxQywYF4ic/+YlfEAyeKVijR49m4cKFIX/JsGzZMmdebGpqKmPHjmXv3r18+OGHLF++nOXLl/PNN99QVvbjTISxY8dWCYKzs7OdoLA22dnZ3HXXXX5LSo0ePZrk5GRSU1NJSUkhNTWV5ORkvwCmdevWJCQkMGLECL9lJY8ePcq6desoKSmhuLjY788333zD/PnznU6Q+Ph4nnvuOc4//3zn+m+//ZannnqK4uJiSkpKnPt4y97/710uFz169OCBBx7gkksu4Z577uHBBx907r1w4UIWLlxIjx49GDhwIImJiURFRTmJR10uF4MHD66ywsY777zD66+/7nee758DBw7Qvn17XC4Xo0eP5qKLLsLtdvPll1/y9ttvs2DBArZs2RLQ331tysvL2bJlC1u2bPFbuhI8iVyPP/54xowZ4xcgv/jii34Z1I/liiuuYPDgwX77fv/73zu91EeOHDnmn/Ly8qCzwsfHx9OmTRuSkpJISEggLy+PuLg4YmNjiY2N9Sv7/omLi+PGG2904gqXy8W+ffucLPFut5vy8nLKysqq/CkvLyc6OpoJEyZQWFjo/Nm9e7fz76u0tJQePXrwyCOPNMnv2bUGwcaYv+FpNBOAXUBvYCmgILiZqksQXDmwrGz8+PFOEPzhhx/yq1/9Cgg8CB43bhyfffaZs+37Q7g2aWlpTrm6uc27d+92yvUdKh0XF8fxxx/vJBr5+uuvad++vV8v8ODBg/3mxoiINIQGaG9PBt4DsNZ+bowZ7nNsJLDMWlsEFBljNgKDK66ZX3HOoorypjqc2yhBcFlZGWeffbbf3NXaWGuD+kzfYaVevXr1apT24bjjjvMLgqurS6j4/p2mpaVRUlLSoMNFhw4d6ixV5P2dwe12s3nzZoYPH85DDz3E5ZdfHrLP830x3717d0466SSysrKO2Yvo+6LEq67P/b777uOKK64gMzOTgoICv1U3alNYWOj3u93GjRsZNmxYQNcmJiZW+d1r69atPPhgYP9UvQFc27ZtmT9/PrNmzeLnP/+5X66YrVu31vj/ZE5OTpUg+KuvvuLvf/97QJ+/YcMGli1bxttvv12nf+9ekydP5qc//SllZWXO3OcXXnjBLwN6TY4cOcJXX31VJXO5d33rQOzcuZP09HQOHTrEnj17yM7OZs2aNY06r7qoqIiioiK/kQGB8ibEq6+PPvromMc3b97MnDlzePfdd4P6nPoI5F/wmUAmniFV/wt0BeY2ZKUkOHUJgmtz5plnOuWPP/6YkpISYmNjAw6CfbMiDh8+3G9YVW06derklKvLZuj7w9CbabI+RowY4QTBK1as4JxzzmHp0qXO8eHDh9d0qYhIKIW6vU0GDvpslxljYqy1pdUcywfaVtpf3b7azvVjjLkauLrS7jjw/CLvG9jVhdvt9mvrmsrEiROdBEsNqfJ0pS+//LLBPtd3NYj8/HzS09M577zzuPjii/1eToeKb3btwsJCHnroIW655RaOHj1KQUEBV1xxBc8++yw33HBD0J9VXl7OSy+95Gz/5z//qfY8bw9oz549yczMpHXr1lX+vl944QXcbjfFxcUcPXrU6dXbv38/eXl55ObmkpubywcffEB+fj5FRUVceeWVPPzww3UO5tavX+/3IqK25Sl9lZWVVam7b5Ks2hQVFVW5/qyzzvILgo+loKCgyvV1WT958eLFLF68OODzK0tPT2f06NF++7744ouAguCaBBoAA05HUjBcLhcJCQkkJCSQmJhYZeRES9e5c+eQ/Dyra29yIEHwD9baAmPMemCQtfYNY8wf61U7aRS+ySSCDYL79OlDt27d2L59O/n5+WRlZXHSSScFFAS73W6/ZSTqmn2xsYLgE088kWeeeQbwNP7nnHOOX+/12LFj631vEZE6CHV7ewjwnQAYVREAV3csCTjgs/9oNfsCOdePtfYJ4AnffcaYHsCW3r171+nFaGUrV67kN7/5jTN01ztc1DtHrvJ2RkaGM+3Hu2/9+vXk5eX5zavzXUPed7tHjx6kp6c7+9PT0xk3blyjzLdLTU1lw4YNznZ+fn6DDR/MyspyygcPHqS8vJy///3v3HTTTQ3ymQkJCVx33XUAfP/998yePZtTTjmFGTNmsH79esAzHevLL7/khx9+OGYizsq2bdvGxx9/TKtWrZgxYwZLly51enUTExOd31GioqI48cQTOf300znxxBMZNWpUrXOuA/27WLFihbPaxpIlS1izZg1Tp07liy++YO/evezdu5d9+/axd+9e8vPzOXLkiDPv0zskdsCAAX49z9HR0QwZMoS4uDji4+M5cOAA3377rdObnZCQwFlnnUXHjh1JTk6uUtfExETuu+++GofERkVFOfeq7vpf/vKXzjD1r7/+mmeffbba4cHHHXccSUlJZGVlMXToUDIzM0lOTubyyy9n4MCBHDlyhJycHHbt2sX27dvZsGGD33z0ytq3b88555xDjx49iI+PrzZ5mvffrtfIkSOr1P+6666rNUlreXk5eXl5pKWlOS8CvvvuO9atW+e34kkwEhMTSUpKIjk5meTk5GrLv/zlL+nfv7/fz5lHH3004J7kSy+9lJiYGA4fPszhw4fJycnhhRdecHqHff8UFhZSXFzslIuKiujQoQPl5eXO9JCSkhK/aQAxMTE1/omPj2f48OHOs2rVqpUz3957zoABA7jxxhurPLfGEEgQXGyMGQt8B5xtjPkYaNhF8SQogfYEu91u8vPzSUhIqJIl0MvlcnHmmWc66+ktXrw44CB48+bNfsOLZsyYUafvUVsQ7DscOpggeMyYMU552bJllJeX8/rrr7N06VI+/fTTZpX9UETCWqjb22XAucC/KuYEr/E5lgXcaYxpBcQD/YC1FddMAp4Gzgb+XcdzG03Hjh2ZM2dORORsqJwhOtD5iPXhG4R4f9E+4YQTGiz5Uffu3Wnbti0HDx4kLy+PnTt3MmTIEFatWsXNN9/MY489BsBll11WJQB+6623iIuLo3Xr1hQWFpKXl8fGjRv59ttvWbFihTNEd9CgQcyYMcNvKPSkSZOIi4tj8uTJTJw4scGSII0ZM4Yrr7ySJ598EoDZs2dz6qmnBjycuTrHH3+8M0R3wYIFfktJZmZm8tFHHx1zulv37t2ZM2dOvT8/MzPTuf8FF1zAHXfcwZtvvskDDzzgN5LuwIEDLFq0iEWLFjn7YmJiiI2NpaioKKBArkePHkybNo2pU6dy4oknhmT6QSBLddbE7Xbzww8/sG7dOvbs2UNeXh779+/nwIEDzlxY7/fyzsP1/jctLY20tDQ6depEampqvacZzJ49u87XJCYmkpqaSs+ePRk5cmS9PrchrFu3rkkCYAgsCJ4L/Aq4DLgVT8KO4FZJlwYVaBB8+PBh501ncnIyBw8erPY83yB40aJFzJs3jzlz5nDppZfSpk0bevfuXe11Tz/9tFOOjY2t8zISjdUT3L9/fzp06EBubi579+5lzZo1DBgwgHPPPZdzzz233vcVEamjULe3rwNnGmOW40m0dbkx5iZgo7X2LWPMQ3gC1yjgf6y1hcaY/wOeqcgGnQP8oqJ3OqBzg6irHENjBsHVDdWt60vsunC5XAwdOpRPP/0U8MwXzcjIIDExkb/85S/813/9F/fddx+XXXaZ33Vut0nbJakAACAASURBVJvLLruM/fv31/oZa9asYdOmTbzyyivOvpkzZ3LGGWeE9LvU5P7773fW5M3NzWXmzJlOYqhgPPbYY1xzzTXOtjGGDz/8MKgRFvURFRXFtGnTmDZtGllZWTzzzDO8/PLL1c6lLi0tpbS0tJq7/HivgQMHOvcbPHhwkwVJ1fGOAvGOCpGWK5Alkj4HPq/YHGWMOc5aG1yaMmlQgQbBvssj1dQTDDBhwgQng3JWVhY7duxgyJAhx6yD2+3mxRdfdLbr84a1c+fOTrm2IDiYH0bR0dFMmTKFf/zjH4An0G/IBl9EpDqhbm+tteXAf1favd7n+N+olHTLWrsHOKuaewV8roSebxB83XXX+S3nF2rVDUf92c9+1mCfB1QJgn1fQA8fPpwXX3yxypzBPXv21BoAJyYmctJJJ3H66aezbt06ZwRZx44dG3WUV3JyMk899RQTJkwAcHpNg+mNvffee5k798eUAYMHD2bx4sUBL0PZUEaOHMnIkSP585//zPLly1m6dCnLly9n48aNbN261e/30uTkZDp16kT//v0ZNGgQI0eOZOzYsezatSsiRnhI06oxCDbGvA1UmyrPGIO1tv5jCaRB9evXj7FjxxIfH+/Xm1rZsdYI9tWuXTvGjx/PBx98AHgm+V9//fXHrMOqVavYuNFZjrJebyUbqycYPEs3eYPgPn36UFZWpnXVRKRRqL2V2vjOT+3QoUOdR1bVReUg+KSTTqJbt24N9nngWSbJ64svvgjomqKiIn7+85+Tk5NDQUEB8fHxtGvXjoyMDAYMGMCgQYMYNmyY85LfN7HWtGnTGn3VhzPPPJNrr72WRx55BIC5c+fyk5/8hPHjx9fpPm63m7lz5/LHP/6YLmDkyJEsWrSo2axrC55hz2PHjvXLq+J2uyktLaW4uNiZM1qd+mSBFqmrY/0EeOUYx6QZu+WWW6qko69OoEEweJY28gbBr7zySq1BsHcOj1d9fjB36dKFmTNn0qlTpyrr80Ho5gSDJ8Pn0KFD+eqrr1izZo0CYBFpTGpv5Zh8e4KDXTO0NpUDkMYYGTVixAinvHLlStxud61DYLt3787zzz8f0P3Ly8v9hkJfcMEF9atokO6//36++OILPv/8c8rKypg6dSpLliwJeBWKo0ePcvXVVzvrtIJnWam33nqr3ktFNiaXy+Uk3xJpajUGwdbaZ7xlY0wHYCxQBnxqra1+8qi0KL5BcG3ZFqdOncqsWbMoLy9n6dKlbNq0iV69ejkLZfsGjXv37uW5557zu77yfKZAJCUl8fjjj1d7rKCgwJnDHB8fT4cOHep8f19RUVE899xznHvuubz22mvs2LGjQd+0i4h4qb2V2jRWEFxUVOS3fE1UVFSjBIx9+/YlOTnZWUt127Zt9OjRI2T3//zzz53gvn379px22mkhu3ddxMXF8corrzB8+HCys7PJz89nwoQJvPHGG7WuRLFp0yamT5/O6tWrnX1Tp07lhRdeqDZLsogcW1RtJxhjpgEbgRuAW4CNxpim+ekhIVWXnuDU1FTOPvtsZ/vmm2+mXbt2xMXFcfHFF/ud+9hjj1WZi1zbUgN1lZubS1pampOgIBRJE/r378/69ev56KOPgu5ZFhGpK7W3UhPfIPjgwYNOsBhqviOswJPZ+FjTqkIlKiqKUaNGOduff/75Mc6uO99e4GnTpjVpT2SXLl1YvHixM0Ju//79nHHGGdx1112UlJRUOb+goIC7776bQYMG+QXAV111FS+//LICYJF6qjUIBu4Exlprx1lrTwYmAvc3bLWkMdQlCAZPJkWvJUuWcODAAUpLS/2WSNq/fz9/+tOfqlxbn57gY+nWrRvZ2dkUFRWFtLGMjY0lJSXFWV9SRKQRqb2Vavm+SH7rrbdo27YtN910U8g/p/JQ6MZcIWH06NFOOZTteuWh0NOnTw/Zvetr4MCBfPDBB6SlpQFQUlLCrbfeSs+ePfn1r3/NM888w5NPPsnMmTPp3r07v/3tb53f2WJjY3nsscf461//2ujzmkXCSSD/eo5Ya521Ba21Xxpjqk3gIc3D6tWrWbJkCUVFRQwbNoyJEydWe15dg+BJkyaRkZHBjh07/BYK9w2C7777bmeoVvfu3Xn88cc5fPhwjcsoBSs2NrbJMyGKiISI2luplu+LZO/yMlu2bAn551ROihUOQbB3VQvwDIWuayKqhjJs2DCysrI4//zznWRgO3fu5L777qvxmiFDhvDUU08FtcawiHgEEgR/bIyZCzyCZ47SJcBaY0w7wGWtzWvICkrdLV261Fk+Yfbs2SELgqOjo5k7dy7XXnut335vEPzVV1/xwAMPOPvvvfdezjoruNUz3njjDZ5//nm2bt3KlVdeydVXXx3U/UREmjG1t1Kt6kZTbdq0KeSf4xsEX3755Y26TM3IkSOd8urVqykqKqoxe3BdvPzyy0556tSpzSopU7du3VixYgUPP/wwd999t998bF89evTglltu4corr2xW9RdpyQIJgm8AooG7Ku2/GM+SDkqj28zUZ53gQIJggCuvvJI//vGPbNu2zdmXn5/P7t27Of/885031CeeeGJIkmls3LjRacB83xKLiIQhtbdSreqC4L1793Lo0KGQZgX2HQ7dt2/fkOTbCFTHjh3p3bs3GzdupLi4mNWrVwfd7rvd7mY3FLqymJgYbrzxRq655href/99li5dyu7du4mKiqJXr16cfvrpjBkzRqtWiIRYrUGwtVavnFqYhgyC4+Pj+etf/+rXw/v9998zaNAg8vLynHv94x//CMm8Wt+lkbZu3eqU33jjDRISEsjMzKRnz56aFyMiLZ7aW6lJTcklv//++5AOjfXtCe7atWvI7huo0aNHs3HjRgBWrFgRdBCclZXF9u3bAc+LhOYyFLo68fHxTJkyhSlTtCy4SGMIJDt0mjFmSkX5QWPMEmPM4IavmtRXoEHwlVdeyaFDh8jOzubuu+8O+P4TJ070Wye4rKzMCYCjo6N56aWXOP7443G7g5/K5rtEgm/v87XXXstZZ52FMcYvOBYRaanU3kpN4uLiqn1Z/f3334fsM9xut19PcFOskjBmzBinvHTp0qDv969//cspT506lbi4uKDvKSLhIZCuuqeBXsaY8cB4YAHwcENWSoLjGwQXFhbWeF50dDRJSUmkpaU5qfoDVV3QnJGRwXvvveck0hg8eDAdOnSgV69ezpvduvLtCfYGwUVFRc4yDi6Xi27dutXr3iIizczTqL2VGlQ3JLq+bWt17r77bidBEzRNT/C4ceOc8ieffEJ5eXm971VeXu43H/hnP/tZUHUTkfASSBDcwVr7IHA28Ly19mkgsUFrJUEJtCc42M/wHYL8ySefsGnTJs444wxnX25uLnl5eWzevLne69ilpKQ4b78PHjzIgQMH2Lp1q9PL3LVrV73ZFZFwofZWalRdEBzKnuA33njDb53apugJ7t+/PykpKQDk5eWxZs2aWq6o2cqVK/2yQp9++ukhqaOIhIdAguA4Y0wsnkb5Q2NMItCmYaslwWiMINjlctGmzY//GwwaNKhKxkLvUklQ/3WCXS6XX2/wli1bWLdunbPdt2/fet1XRKQZUnsrNWrIIDg7O5usrCxnu127dvV+eR0Ml8vFqaee6mx//PHH9b6X71Don/70p8qqLCJ+AgmC3wT2ATnW2lVAFvB8g9ZKghJoELxr1y42bNjAzp07/ZJkBco3CPZdK9j7ud57RkdH07p16zrf38sY45S/++47vvvuO2e7f//+9b6viEgzo/ZWalRdcqxQBcELFy70227KaUannXaaU65vEFx5KPSFF14YdL1EJLzUGgRba28HBgLen0q/sNb+oUFrJUHxfXt7rCD4d7/7HcYYMjIyeP75uv+etXjxYjZt2sSePXuqDJs6ePCgUz7uuOOCWmZhwIABTnnt2rUKgkUkLKm9lWPx7QmOjY0lKiqKpKQkjhw5EvS93377bb/tphgK7eUbBH/66aeUlZXV+R4rVqxwknx16NDB754iInCMINgYc1HFf28CLgRurCifUfFfaabqs0RSYmLdp5317duXnj17kpqaWmX9uv379zvl+g6F9ho4cKBT/vbbb1m7dq2z3a9fv6DuLSLS1NTeSiB829LbbruNI0eOsHnz5nq1376OHj3K4sWL/fY1RVIsL2MMnTp1Ajwv1H2TdQXK98X++eefr2UURaSKY/1U6FPx30GNUREJnQ4dOnDhhRcSHx9/zCFNvm+PA10nOFChmA/s5dsTvGrVKrKzswHP3KEhQ4YEdW8RkWZA7a3UyrctjYmJ8XvhHYwlS5ZU6U1uyiDY5XIxceJEnnnmGQDeeecdRo0aFfD1hYWFfkHwL37xi5DXUURavhqD4IphWVhrL2+86kgopKen89JLL9V6nm9PcEMGwe3atQvqXn379uXWW2/ltNNOo6ioiMmTJwOeHuLk5OSg7i0i0tTU3kogfOcE+7axwao8FBqadjg0wLnnnusEwW+//TZ/+EPgswLeeust5+8nMzOTU045pUHqKCItW41BsDHmY8Bd03Fr7fgGqZE0mmCD4NLSUg4fPszhw4dJTk72C0hD2RMcFxfHnXfeCcDNN9/s7D/ppJOCuq+ISHOg9lYC4duWhioIdrvdvPPOO1X2N3UQPGHCBOLi4iguLubrr79m+/btAV/79NNPO+VLL72UqKhAcsCKSKQ51k+GR4BHgd1AAfAw8CCQA4RudXZpMsEGwbNmzaJdu3ZkZGRU6XkOZRDsa+7cudxwww3ExcUxZcqUkN1XRKQJqb2VWlUOgrdt28bChQt59NFH633P1atXOwmkfIPFpg6Ck5KS/JZKqq63ujq7du3i/fffd7YvueSSUFdNRMLEsYZDvwpgjPk1cKK1trxieyGwonGqJw0p2MRYx1oiqaGC4JSUFB588EFuuOEG0tPTQ3ZfEZGmovZWAuHblu7fv58+ffpQUlICwMUXX1yv6UG7d+8mPT2d3bt3+63i0NRBMMCUKVP44IMPAHjxxRcZP772ARGPP/445eXlAJx66qlkZmY2aB1FpOUKZIxIR8B3xfQkoH3DVEdCwe128+tf/5rrrruOmTNn4nZXP8ou2MRYxwqCr732WjZt2sSqVauYPXt2ne9dm+7du2vhexEJN2pvpUa+c4IPHTpE3759ne1vv/22XvecPHkyO3bsYMmSJc5SRAkJCSF9eV1fF1xwgbPyxNKlS2sdEl1YWMhf//pXZ/uaa65p0PqJSMsWSM7454GVxpjXABcwHXiiQWslQXG5XDz44INOg/bwww8TFxdX5bxgh0P7BsH5+fl+x1q3bk3Pnj3rfE8RkQim9lZqVHk49LBhw1izZg0Aa9euZcyYMfW6b1RUFKmpqc52ly5d/HqFm0paWhpnnXUWCxcuBDxDoidOnFjj+S+88AL79u0DICMjg2nTpjVKPUWkZaq1J9ha+3vgNqAd0Ba4yVr7x4aumAQnkLWCgw2CKw/NEhGR+lN7K8dSOQgeOHCgs7127dqg7u2dFwzNYyi0l++c3ldffZXi4uJqzystLWX+/PnO9uzZs7U2sIgcU0A/Iay1bwJvNnBdJIRatWrlDHcuKioiKSmpyjkJCQkUFxdTWFhYryC4ffsfR+kpCBYRCZ7aW6mJ73KDeXl5DBr047LSq1atCurezTUInjJlCqmpqezdu5fs7GxefPHFapNdLViwgI0bPTnk2rZty9VXX93YVRWRFkZ548NUID3B2dnZHD16lLKysmqHS9emcoPsa+fOnRw4cKDG+cgiIiISuFatWjlJLEtLS+nXr59z7Msvv3SSZAUiPz+fqVOn8uSTT5Kdnd1sg+BWrVpx/fXXO9vz58+v0ht84MAB/ud//sfZ/vWvf+33+4mISHUUBIepQIJgr6ioqHrN//HtCa4cBI8dO5Z27doRFxfHpk2b6nxvERER8dehQwenHB0dTbdu3QDP9Ka6JMd67733ePPNN7nqqquYNGkSu3fvdo41pyAYPMsxekezWWu5//77nWNut5vrr7+e7OxsADp16uQXNIuI1ERBcJiqSxBcX75vWisPh87NzQU8b6v1RlZERCR4vkFwbm4uI0aMcLb/85//BHyfV1991Smfe+65zbYnGDy/a9xxxx3O9u9//3veffdd3G43f/jDH1iwYIFz7NFHH/VL2ikiUhMFwWHKNwguLCxskM+oqSe4uLiYQ4cOAZ5e5uaw1IKIiEhLVzkIHjlypLOdlZUV0D0KCgp4++23ne3p06c36yAY4Fe/+pWTCKy0tJTJkyeTnp7O7bff7pxzySWX8NOf/rSpqigiLUyjps4zxiQA/wRSgXzgUmvtvkrn3A6cA5QCN1hrs3yOPQhYa+3jjVfrlqm2nuD8/HxWrFhBYmIi7dq1Y8CAAXX+jOTkZKKjoykrKyMmJoaSkhJiY2OdXmDwNNhRUXrXIiIiEqxj9QSvXLkyoHu8++67TuLMfv36MWDAgGYfBMfExPDQQw9x6aWXsmPHDtxutzMEGmD8+PF+awSLiNSmsaOTWcAaa+0pwAI8S0E4jDEnAOOAUcAM4NGK/SnGmEXAlMatbstVWxC8ceNGJk6cyCmnnMIvf/nLen2Gy+Vi7969lJaWsn//fmJjYwH8guCOHTvW694iIiLiz7dNzcnJYcSIEWRmZnLppZdyyy23BJSM8qWXXnLKP/vZzygtLWXPnj2Ap13v3Llz6CseAp06dSIrK4vzzjvP2ZeQkMDcuXNZtGgRrVq1asLaiUhL09iLqJ0M3FtRXgT8rprjH1hr3cB2Y0yMMSYFaAPMA85urIq2dLUFwb5rBHuzTdaH75Bor5ycHKfs+9ZaRERE6q9yT3CbNm3YvHlzwNfn5+ezcOFCZ/vCCy8kOzvbCZ5TU1OdF9rNUadOnXjjjTfYt28fe/bsoVevXvVa4lFEpMGCYGPMFcCNlXbvAQ5WlPOBtpWOJwO5Ptv5QFtr7UZgizGmxiDYGHM1UHlhuDjw9Hrm5+fX7QtUUlhYyLp164K6R2M65ZRT6N69O3FxcZSVlVWpu+92eXl5SL/bV1995ZTj4+Nb1N8btLxnLfWnZx05QvmsfZemEWlMlYPgunrppZecPCGDBg2iX79+fP75587x5jgUujopKSmkpKQ0dTVEpAVrsCDYWvsU8JTvPmPMa0BSxWYScKDSZYd8jtd0Tk2f9wTwRKXP6wFs6d27N127dg247tVZt25di/rFxzdZRHW8i8qDZ3hVKL/bZ5995pQzMzNb1N8btLxnLfWnZx059KwlHAQbBD/55JNO+fLLLwdo9vOBRUQaQmMPh14GTAKy8Axt/nc1x+81xtwHdAWirLU5SMj5DocOZijRvn372L17N3l5efTq1Ytu3bppOLSISBOrbyJKY0xv4GnADawFZltry40xf8QzZSkGeMJa+zdjTHtgQ8V5AK9ba//c8N8uctUWBB89epSioqJqV2VYs2aNkzwrLi6Oiy++GFAQLCKRqbETYz0GDDDGLMUzdPkOAGPMvcaYkdbaVXgC4xXAq8DsRq5fxAhVEHzHHXcwdOhQxo8fz+uvvw4oMZaISDNQr0SUwAPAbRXXuYDzjDGnAb2ttWPwBMJzjTHtgBOAF6y1p1b8UQDcwGoKgleuXMmMGTNISUnhwQcfrPbaH374gU6dOgEwbdo0p31WECwikahRe4KttUeA6dXsv8WnPA9PEqzqrq92v9RdqBJjVc5UCVBSUuIsnaQgWESkSdQ3EeUw4FOf6yYAcwBvsgc3EA2UVJw7zBjzKbAXuM5a+0MDfR+h5iB4586dTtbnF198kXnz5uFyufyunTBhAlu2bOHZZ59l8ODBzn4FwSISiRp7OLQ0kn/+85+89dZbFBUVcdlllzFt2jS/4941AiG4nuC0tDSn7F2z7+GHH+ZPf/oTOTk5QQXYIiJSu1AmogRcFYGxs89aWwgUGmNigWfwDIc+bIxZD6yy1n5ojPkl8DBwQai+l1RVUxB89tln06ZNGw4fPsyGDRtYvHgxEyZMqHJ9q1atuOqqq/z2KQgWkUikIDhMrVmzhpdffhmAMWPGVDkequHQ3qFVgN/C9dHR0X4BsoiINIwQJ6Isr2YfFcOfXwE+sdbeVXF8CeB9o/o68L+V66aVG0LL7XY7I60OHz7M119/TVxcHABTp07ln//8JwC///3v6dq1a5Xe4Ops2bLFKTfnv8/mXDcJLT3ryNGUKzcoCA5TdVknuCGCYBERaVL1SkRpjFltjDnVWvtJxXUfVyTZ+gi431r7nM89nsSTv+NfwOnAqsqV0MoNode+fXv27fPkOEtNTaVz584AzJs3j+eff57y8nJWrlzJqlWrOO+883juueeYOXMmUVFV08C43W6/ZJannHIK7dq1a5wvUkeR+KwjlZ515GjKZ60gOEy1atXKKXvXBPTVvn17+vbty9GjR4Oat6sgWESkWXoMeKYiEWUx8AvwJKIEXqnIBO1NRBnFj4ko5wB/M8bEAevw9P5eB/QErjLGeMfSXg78Bvi7MeYaoAC4slG+WYTr0KGDEwTn5uY6QXCvXr2YNWsWjz7qyXF22WWXOee++eabPPvss1XW1j106BAFBQWA54V4dVmlRUTCkYLgMOXbu+vb6+t10003cdNNNwX9Ob5Dnvfs2cPBgwdZtmwZnTt3pkuXLqSmpgb9GSIiUjf1TURprd2AJ2u0rwcr/lTntGDqKXXnOy/YtxcX4M477+TDDz/EWkt5ebkTLL///vu89957zrJIXpXnAwcyfFpEJBw09hJJ0kh8E1JVFwSH8nOSk5MBT1bozz77jHPOOYcTTjiByZMnN9jnioiIRKJjrRXctm1bFi9ezOjRo/32Pf3001UCYFBSLBGJXOoJDlO+PcG+maAbQqdOnTh06BAAWVlZzv709PQG/VwREZFIc6wgGCAjI4Ply5fz9ddfc/DgQYYNG0abNm2qvZeCYBGJVAqCw1Rj9QQDdO3alQ0bNgCwZMkSZ3/Pnj0b9HNFREQiTW1BMIDL5WLo0KG13ktBsIhEKgXBYaq2nuB3332X3NxcEhISGDduXJVkGXXRp08f1q1bR+/evdm+fbuzX0GwiIhIaAUSBAdKQbCIRCrNCQ5TtfUEz58/n0suuYTp06ezfv36oD7rL3/5C7t37+azzz6jV69ezn4FwSIiIqGlIFhEJHgKgsNUbT3BvvuCWScY8Ft70FrrlBUEi4iIhJbvyC1v9uf6UhAsIpFKw6HDVGZmJvfddx8JCQnVNmy+QXDr1q1D8pn79u1zGtRWrVrRu3fvkNxXREREPHyXHty7d29Q91IQLCKRSkFwmEpLS2POnDk1Hi8oKHDKoQqCfTNDDxo0iJgY/e8lIiISSmlpaU45mCC4uLiYPXv2AJ5EWp07dw66biIiLYWGQ0eoUAfB27Zt44svvmDcuHEAjB07Nuh7ioiIiL/KPcFut7te99m9e7dzbadOnYiNjQ1J/UREWgJ11UWoUAfB7733HvPmzXO2L7zwwqDvKSIiIv7atGlDq1atKCws5OjRoxQUFNS4DvCx7Nixwyl369YtlFUUEWn21BMcgUpLSykuLgY8Sa3i4+ODvucVV1zBzJkz6dKlC/Pnz2fkyJFB31NERET8uVwuv95g75DmuvINgjMyMoKul4hIS6Ke4DDldrs5/fTTKSgo4OjRo6xevZro6Gigai+wy+UK+vNiYmJ4/PHHg76PiIiIHFtaWhrbt28HPEOifZcnDJT3elAQLCKRR0FwmHK5XHz++efOGsGFhYXOsOeGSIolIiIijSMUGaLVEywikUzDocNYTWsFKwgWERFpuRQEi4gERz3BYSwxMZG8vDwAp0cYIC4ujkmTJlFQUEB6enpTVU9ERETqQUGwiEhwFASHsZp6grt3787ChQubokoiIiISJAXBIiLB0XDoMJaYmOiUfXuCRUREpOVKS0tzyvXJDn3kyBFyc3MBiI2NpVOnTiGrm4hIS6AgOIzV1BMsIiIiLVewPcG+vcBdunQhKkq/DopIZNFPvTCmnmAREZHwE8ogWEOhRSQSaU5wGKupJ3jlypW8//77tG7dmuHDhzNu3LimqJ6IiIjUg4JgEZHgKAgOYzX1BC9fvpzbb78dgOuvv15BsIiISAuSkpLilHNycigrKyM6Ojrg6xUEi0ik03DoMKZ1gkVERMJPTEwMHTp0AMDtdpOTk1On67dv3+6UFQSLSCRST3AYu+aaa5gyZQqJiYkMHjzY2a8gWEREpGVLS0tzMjxnZ2f7ZYyujW9PcLdu3UJeNxGR5k5BcBgbNWoUo0aNqrLfNwj2HTItIiIiLUOXLl347rvvANi1axdDhgwJ+FoNhxaRSKfh0BFIPcEiIiItW3p6ulPevXt3wNe53W62bdvmbKsnWEQikYLgCKQgWEREpGXr0qWLU961a1fA1+3du9fJE5KcnEy7du1CXjcRkeZOQXAE8k2SpSBYRESk5alvT/CWLVuccmZmJi6XK6T1EhFpCRQEh7FXX32Vnj17kpKSwqxZs5z96gkWERFp2UIVBIuIRCIlxgpjJSUlTmOXl5fn7FcQLCIi0rLVdzi0gmAREfUEh7U2bdo45fz8/GrLSUlJjVonERERCZ56gkVE6k89wWHMN8A9fPiwU54+fTrbtm0jPz+flJSUpqiaiIiIBCEtLQ2Xy4Xb7Wbv3r2UlJQQGxtb63Vbt251ygqCRSRSKQgOYzX1BM+bN68JaiMiIiKhEhsbS1paGtnZ2bjdbrKzswNa81c9wSIiGg4d1mrqCRYREZGWz3dIdCDzgsvKyti+fbuz3aNHj4aolohIs6cgOIzV1BMsIiIiLZ9vcqxA5gXv2rWLkpISAFJTU5UcU0QiloLgMKaeYBERkfDl2xO8c+fOWs/3HQqtXmARiWSaExzGfN/wFhQUUF5ezg8//MCtt95KcnIyPXv25MYbb2zCGoqISEMwXrDD1wAAD2RJREFUxiQA/wRSgXzgUmvtvkrn3A6cA5QCN1hrs4wxvYGnATewFphtrS03xrwJdARKgKPW2rNrOrcxvp94dO/e3Slv27at1vM3b97slDUfWEQimXqCw1hUVFSVQHj37t0sWLCARx55hOeee64JayciIg1oFrDGWnsKsAC4zfegMeYEYBwwCpgBPFpx6AHgtorrXMB5Ffv7ACdba0+11p5dy7nSSHx7c317eWuyYcMGp3z88cc3RJVERFoEBcFhzndIdH5+vtYIFhGJDCcD71WUFwFnVHP8A2ut21q7HYgxxqQAw4BPfa8zxqQBxwFvG2OWGmMmVxyvcm7DfBWpiW9vru/SRzVRECwi4qHh0GHujTfeICYmhqSkJFJSUsjKynKOJScnN2HNREQkFIwxVwCV57bsAQ5WlPOBtpWOJwO5Ptvec1zWWnelfXHA/cCfgfbAMmNMVg3nSiPy7QlWECwiEjgFwWFu1KhRftuHDh1yyuoJFhFp+ay1TwFP+e4zxrwGeH/IJwEHKl12yOe47znl1ezLBh631pYCe40xqwFTw7l+jDFXA1dX2h0HsHHjxqBXLigsLGTdunVB3aMlc7vdxMfHU1RUxP79+8nKyqqxbS8vL/cLgsvLy1vU312kP+tIomcdOUL5rPv161en8xUERxjfXzjUEywiEraWAZOALOBs4N/VHL/XGHMf0BWIstbmGGNWG2NOtdZ+UnHdx3iGOf8KmGSMaQMMBNYB1Z3rx1r7BPCE7z5jTMxHH31U0qlTJ2Jigvs1ZN26dXX+xSfc9OjRA2stAPHx8TX+fWzbto3i4mIAUlJSGD16dKPVMRT0rCOHnnXkaMpnrTnBEUY9wSIiEeExYIAxZimentg7AIwx9xpjRlprV+EJjFcArwKzK66bA9xhjFmBp8f2FWvtImCDMeZz4APgVmttTnXnBlIxa21p165dgw6AxSPQecEaCi0i8iO1QBHA7XZz6NAhYmJiOHjwoLNfPcEiIuHJWnsEmF7N/lt8yvOAeZWOb8CTNbrydTdUs6/ac6VxBZohWkGwiMiP1BMc5m688UZiYmI47rjjWLBgAfv373eOtW/fvglrJiIiIsEKNAj2DpkGBcEiIgqCw1x8fDzl5Z7cJfv37ycvL885piBYRESkZevdu7dT9g10K1uzZo1THjBgQIPWSUSkuVMQHOZ8A928vDwFwSIiImHEN6lMTVlW3W4333zzjbM9aNCgBq+XiEhz1qhzgo0xCcA/gVQ8awpeaq3dV+mc24FzgFLgBmttljFmKPAwUAYUAZdYa/c0Zt1bqspB8H//939z2mmnkZeX5/f2WERERFqe3r17Ex0dTVlZGdu3b6egoIDWrVv7nfPDDz84L8GTkpLo3r17U1RVRKTZaOzEWLOANdbaecaYGcBtwPXeg8aYE/Ak2RgFZODJWDkC+DPwK2vtV8aYmcBc4KZGrnuL1K5dO6e8f/9+pk+vkidFREREWqi4uDh69+7tDIW21nLCCSf4neM7FHrgwIG4XK5GraOISHPT2MOhTwbeqygvwrP2YOXjH1hr3dba7UCMMSYFmGGt/arinBigsFFqGwYq9wSLiIhIeKltSLTvUOjBgwc3Sp1ERJqzBusJNsZcAdxYafcewLtGTz7QttLxZCDXZzsfaGut3VhxzxOBa4GxIa9wmFIQLCIiEt769u3rlKsLgr/66iunrPnAIiINGARba58CnvLdZ4x5DUiq2EwCDlS67JDPcb9zjDE/A/4HOKfyPOKK41cDV1faHQewceNG8vPz6/dFKhQWFtaYcKI5y8nJccr79u1rkd+hsbXUZy11p2cdOUL5rH173USag/79+ztl315fr5UrVzrl4cOHN0qdRESas8aeE7wMmARkAWcD/67m+L3GmPuArkCUtTbHGHMRMBM41VpbbXemtfYJ4AnffcaYmI8++qikU6dOxMQE91XXrVvXIn/xycjIcMp79uzhiiuuoF27dgwcOJB77rmnCWvWfLXUZy11p2cdOfSsJZwNGzbMKf/nP//B7XY7835zcnLYtGkT4Jk/PHTo0Capo4hIc9LYQfBjwDPGmKVAMfALAGPMvcArFZmg/w2swDNfebYxJhp4CNgOvGaMAfjUWnt7bR9mrS1tmK/RcrRu3ZrY2FhKSkoAWLFiBQAFBQVNWS0REREJEWMMbdq04fDhw2RnZ7Nr1y66du0KQFZWlnPeT37yE+Lj45uqmiIizUajBsHW2iNAlfTE1tpbfMrzgHmVTtGCtvXkcrlIT09n27Ztfvs7d+7cRDUSERGRUIqOjmbYsGF8+umngCfw9QbBy5cvd84bNWpUk9RPRKS5aezs0NIEPvzwQ3Jycrj77rudfQqCRUREwseIESOcsnfUF8AHH3zglE8++eRGrZOISHOlIDgC9O7dmw4dOvDDDz84+xQEi4iIhI9TTjnFKXsD35ycHL744gsAoqKiOOOMyitTiohEpsaeEyxNaMeOHU65S5cuTVgTERERCaXx48c7OUC++eYbdu3axYcffojb7QZg5MiRtGvXrolrKSLSPKgnOIJs2LDBKffp06cJayIiIiKh1KZNG8aOHets/+tf/2LBggXO9nnnndcU1RIRaZYUBEeIAwcOsHbtWmdbQbCIiEh4mTFjhlO+6aabWLJkCeBJknnRRRc1VbVERJodBcERIDc3128IVEZGBscdd1wT1khERERC7ec//3m17fv555/vZIsWEREFwRGhQ4cODBkyxNmePHlyE9ZGREREGkLr1q256667/PYlJSUxf/78JqqRiEjzpMRYEWLBggVcddVVdO7cmTvvvLOpqyMiIiINYObMmRQVFfHYY4+RkpLCPffcoylQIiKVKAiOEIMHD2blypVNXQ0RERFpQC6Xi+uvv57rr7++qasiItJsaTi0iIiIiIiIRAwFwSIiIiIiIhIxFASLiIiIiIhIxFAQLCIiIiIiIhFDQbCIiIiIiIhEDAXBIiIiIiIiEjEUBIuIiIiIiEjEUBAsIiIiIiIiEUNBsIiIiIiIiEQMBcEiIiIiIiISMRQEi4iIiIiISMSIaeoKtASlpaXs2bOHpKSkpq6KNAI968ihZx059uzZQ58+fYiJUbMXLtQ2RxY968ihZx05mrJtdrnd7kb/0JbGGNMD2NLU9RARkaBkWmu3NnUlJDTUNouIhIUmaZv1SjwwO4E1wJSmrog0irfQs44UetaR4y08P8slfKhtjiz6eR059KwjR5O1zQqCA2CtLTXGFKsHITLoWUcOPevIUfGsS5u6HhI6apsji5515NCzjhxN2TYrMZaIiIiIiIhEDAXBIiIiIiIiEjEUBIuIiIiIiEjEUBAcuCeaugLSaPSsI4eedeTQsw5Peq6RQ886cuhZR44me9ZaIklEREREREQihnqCRUREREREJGIoCBYREREREZGIoXWCa2GMiQL+AgwBioArrbUbm7ZWEirGmFjg70APIB74P+A74GnADawFZltry5uoihJixphUYBVwJlCKnnVYMsb8FpgCxOH5Gf4petZhQ21zeFPbHHnUNkeG5tQ2qye4dlOBVtbaMcBvgPubuD4SWhcBudbaU4CzgEeAB4DbKva5gPOasH4SQhW/WP0VOFqxS886DBljTgVOBE4CxgEZ6FmHG7XN4U1tcwRR2xwZmlvbrCC4dicD7wFYaz8HhjdtdSTEXgZ+V1F24Xn7OAzPmymARcAZTVAvaRj3AY8Duyu29azD00RgDfA68DbwDnrW4UZtc3hT2xxZ1DZHhmbVNisIrl0ycNBnu8wYo2HkYcJae9ham2+MSQJeAW4DXNZab9r0fKBtk1VQQsYYcxmwz1r7vs9uPevw1BFPUDQd+G/gOSBKzzqsqG0OY2qbI4fa5ojSrNpmBcG1OwQk+WxHWWtLm6oyEnrGmAzgY+BZa+3zgO9chCTgQJNUTELtv4AzjTGfAEOBBUCqz3E96/CRC7xvrS221lqgEP+GVc+65VPbHObUNkcMtc2Ro1m1zQqCa7cMmARgjBmNpxtfwoQxJg34AJhrrf17xe7VFfMWAM4G/t0UdZPQstaOtdaOs9aeCnwFXAIs0rMOS0uBs4wxLmNMOtAa+EjPOqyobQ5japsjh9rmiNKs2mYNHard63jeUC3HMy/l8iauj4TWrUA74HfGGO/8o+uBh4wxccA6PEOxJDzNAf6mZx1erLXvGGPGAll4XvbOBragZx1O1DaHN7XNkU1tcxhqbm2zy+12136WiIiIiIiISBjQcGgRERERERGJGAqCRUREREREJGIoCBYREREREZGIoSBYREREREREIoaCYBEREREREYkYCoJFWjBjzAfGmI4V5XeNMf0b8LNmGWOuPsbxaGPMO8aY1JrOERERCXdqm0WaP60TLNKynektWGsnNdSHGGO6A5cBo2s6x1pbZoy5F/gLcEFD1UVERKSZU9ss0sxpnWCRFsoY8w88jd9aYBLwbzwNXBvgLmA3MAA4AtwOXAcY4FVr7Y0V9zgXuA2IqzjvZmvtimo+63FgrbX2EWNMDPAwcDJQDGwGLrfWHq449zvg59barxvmm4uIiDRPaptFWgYNhxZpoay1l1cUT7PW7qh0eATwf9bavsAe4LfAOcAJwGxjTLoxpg8wH5hkrf0JcDXwmjGmte+NjDEu4HzgnYpdY4BTgcHW2mF4GtrBPpcsBH4amm8pIiLScqhtFmkZNBxaJDxtsdaurihvAg5aa4uBHGPMIaA9MBboDHxkjPFeVw70BnzfFHcAjrPWbq3YXgOUASuNMe/jeXud5XP+JjwNsYiIiPxIbbNIM6GeYJHwVFRpu6Sac6KBj6y1Q71/8MwrWlvpvHLAZYyJArDWHgCGADfjaXBfMsbcWOm+ZSH4DiIiIuFEbbNIM6EgWKRlKwNi63ntEmCCMaYvgDFmEvAN0Mr3JGttHrAf6F5x3mTgI2C5tXYesABPw+vVE1hfzzqJiIi0dGqbRZo5BcEiLdtrwFJjzMC6Xmit/RbPXKMXjTFfA38AplhrC6o5/VXgrIryIuBbYK0x5gvgRGCez7kTgVfqWh8REZEwobZZpJlTdmgRqZUxJhNP4zncWlvjDw1jzKnAbGvt9Maqm4iISCRS2yxSf+oJFpFaWWu3AM8AM2s6xxgTDdyCZ7kHERERaUBqm0XqTz3BIiIiIiIiEjHUEywiIiIiIiIRQ0GwiIiIiIiIRAwFwSIiIiIiIhIxFASLiIiIiIhIxFAQLCIiIiIiIhFDQbCIiIiIiIhEjP8HyHohpQS2XncAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1152x432 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure()\n",
"ax = fig.add_subplot(121)\n",
"\n",
"k_array = [500, 2500]\n",
"for k in k_array:\n",
" c = 250\n",
" states = odeint(eqn, state_0, t[t < 60], (m, c, k), hmax=0.01)\n",
" ax.plot(t[t < 60], states[:, 0], linewidth=3, label=f'k={k} (N/m)')\n",
"\n",
"ax = format_plot(fig, ax)\n",
"ax.set_title(title_string('0.1m Bump, varying k', m, c, k_array), fontsize=14)\n",
"ax.legend()\n",
"\n",
"ticks = ax.get_xticks()\n",
"\n",
"ax = fig.add_subplot(122)\n",
"c_array = [250, 500]\n",
"for c in c_array:\n",
" k = 500\n",
" states = odeint(eqn, state_0, t[t < 60], (m, c, k), hmax=0.01)\n",
" ax.plot(t[t < 60], states[:, 0], linewidth=3, label=f'c={c} (N*s/m)')\n",
"\n",
"ax = format_plot(fig, ax, (16, 6))\n",
"ax.set_title(title_string('0.1m Bump, varying c', m, c_array, k), fontsize=14)\n",
"ax.set_xticks(ticks)\n",
"ax.legend();\n",
"fig.savefig('./images/k_and_c.png', transparent=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation of Pat's design\n",
"\n",
"To generate this, I simply iterated manually until I found `k` and `c` that met the design criteria. In practice, we would use an optimization algorithm to find the best possible options automatically."
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"approximate 5 second decay: 0.9401445331394807\n",
"damping ratio: 0.578351744823806\n",
"damped natural frequency: 0.9991315673568164\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m = 600 #kg\n",
"k = 900 #N/m\n",
"c = 850 #Ns/m\n",
"\n",
"wn = np.sqrt(k/m)\n",
"zeta = c/(np.sqrt(k/m)*m*2)\n",
"wd = wn * np.sqrt(1 - zeta**2)\n",
"\n",
"road = np.array([bump(t_i) for t_i in t])\n",
"road_d = np.diff(road)\n",
"states = odeint(eqn, state_0, t[t<15], (m, c, k), hmax=0.01)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.plot(t[t<15], states[:, 0], linewidth=3)\n",
"format_plot(fig, ax);\n",
"ax.set_title(title_string('0.1m Bump -- Pat\\'s Design', m, c, k))\n",
"fig.savefig('./images/optimal_output.png', transparent=True)\n",
"\n",
"print(f'approximate 5 second decay: {1 - abs(states[1020, 0])/states[:, 0].max()}')\n",
"print(f'damping ratio: {zeta}')\n",
"print(f'damped natural frequency: {wd}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Track Test\n",
"\n",
"I adjusted the mass here to account for the unexpected design changes. As you can see, the results are still close to ideal.\n",
"\n",
"Because this is a simulation, I set these parameters in order to generate this data, but if this were real data, it would still be easy to infer all of these parameters from the data. That's one of the advantages of a physics-based model."
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"approximate 5 second decay: 0.9327406706974997\n",
"damping ratio: 0.5689470246392699\n",
"damped natural frequency: 0.9908202490204198\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m = 620 #kg\n",
"k = 900 #N/m\n",
"c = 850 #Ns/m\n",
"\n",
"wn = np.sqrt(k/m)\n",
"zeta = c/(np.sqrt(k/m)*m*2)\n",
"wd = wn * np.sqrt(1 - zeta**2)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"\n",
"bump_array = [0.1, 0.2, 0.3]\n",
"for bumpsize in bump_array:\n",
" states = odeint(eqn, state_0, t[t<15], (m, c, k, bumpsize), hmax=0.01)\n",
" ax.plot(t[t<15], states[:, 0], linewidth=3, label=f'{bumpsize}m bump')\n",
" \n",
"format_plot(fig, ax);\n",
"ax.set_title(title_string('Test Course', m, c, k), fontsize=14)\n",
"ax.legend()\n",
"fig.savefig('./images/suspension_test.png', transparent=True)\n",
"\n",
"print(f'approximate 5 second decay: {1 - abs(states[1020, 0])/states[:, 0].max()}')\n",
"print(f'damping ratio: {zeta}')\n",
"print(f'damped natural frequency: {wd}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Production Errors\n",
"\n",
"Here, I'm simply swiping the parameters from the track test, and adding some random noise sampled from a normal distribution in order to mimic production errors."
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x432 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"target_wd = 0.991\n",
"target_zeta = 0.569\n",
"\n",
"fig = plt.figure()\n",
"\n",
"ax = fig.add_subplot(121)\n",
"ax.hist(np.random.normal(target_wd, 0.05, size=5000), bins=30, edgecolor='w');\n",
"format_plot(fig, ax)\n",
"ax.set_ylabel('Count of Cars')\n",
"ax.set_xlabel('Damped natural frequency: $\\omega_d$, Hz');\n",
"ax.axvspan(0.9, 1.1, alpha=0.2, color='green', label='acceptable\\nvariance')\n",
"ax.legend()\n",
"\n",
"ax = fig.add_subplot(122)\n",
"ax.hist(np.random.normal(target_zeta, 0.05, size=5000), bins=30, edgecolor='w');\n",
"format_plot(fig, ax, (16, 6))\n",
"ax.set_ylabel('Count of Cars')\n",
"ax.set_xlabel('Damping ratio: $\\zeta$');\n",
"ax.axvspan(0.5, .64, alpha=0.2, color='green', label='acceptable\\nvariance')\n",
"ax.legend()\n",
"\n",
"fig.suptitle('Distribution of Production Suspension Parameters', fontsize=14)\n",
"fig.savefig('./images/parameter_distributions.png', transparent=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Warranty Claims\n",
"\n",
"Here, I artificially introduce a second, undamped [mode of vibration](https://en.wikipedia.org/wiki/Normal_mode). Because it is supposed to represent a failing part, I also add in some random noise.\n",
"\n",
"Again, this is a simulation, so I am _creating_ the \"problem\", but it is also easy to infer the frequency, etc. of this extra vibration from real data."
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m = 620 #kg\n",
"k = 900 #N/m\n",
"c = 850 #Ns/m\n",
"\n",
"wn = np.sqrt(k/m)\n",
"zeta = c/(np.sqrt(k/m)*m*2)\n",
"wd = wn * np.sqrt(1 - zeta**2)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"\n",
"states = odeint(eqn, state_0, t[t<15], (m, c, k), hmax=0.01)\n",
"ax.plot(t[t<15], states[:, 0] + (np.random.random(t[t<15].shape[0])*0.0003*np.sin(10*t[t<15])), linewidth=3, label=f'{bumpsize}m bump')\n",
" \n",
"format_plot(fig, ax);\n",
"ax.set_title(title_string('Warranty Claim Data', m, c, k), fontsize=14)\n",
"ax.legend()\n",
"fig.savefig('./images/warranty_claim.png', transparent=True)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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