{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Stock price modelling for the mathematically curious\n", "\n", "In this notebook we discuss a mathematical model for stock prices. We present some numerical approximations and illustrate these with simple plots." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bank balance as an Ordinary Differential Equation\n", "\n", "Consider the general ordinary differential equation for unknown $U : (0,\\infty) \\to \\mathbb{R}$,\n", "\n", "$$\n", "\\tag{ODE}\n", "\\frac{dU(t)}{dt} = f(t,U(t)), \\quad t > 0,\n", "$$\n", "\n", "with a given initial value $U(0) = U_0$ and function $f : (0,\\infty) \\times \\mathbb{R} \\to \\mathbb{R}$.\n", "\n", "By integrating, we see that it is equivalent with the integral equation\n", "\n", "$$\n", "\\tag{IE}\n", "U(t) = U_0 + \\int_0^t f(s,U(s)) \\, ds , \\quad t > 0.\n", "$$\n", "\n", "For example, we could be modelling our bank account balance $B$ by\n", "\n", "$$\n", "\\frac{dB(t)}{dt} = \\mu B(t) + F(t), \\quad t > 0,\n", "$$\n", "\n", "where $\\mu$ is the interest rate and $F$ stands for, say, your salary or expenses.\n", "\n", "It is easy to see that the solution to this equation is given by\n", "\n", "$$\n", "B(t) = e^{\\mu t}B_0 + \\int_0^t e^{\\mu (t-s)} F(s) \\, ds , \\quad t > 0,\n", "$$\n", "\n", "where $B_0$ is the initial balance.\n", "\n", "Remark: For a bank account, a discrete model would probably be a more realistic choice, but we wish to emphasize the analogy between this and the continuous time model for stock price." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# We inspect our model over a time frame\n", "\n", "import pandas as pd\n", "import numpy as np\n", "\n", "start_date = '2017-01-01'\n", "end_date = '2017-12-31'\n", "date_range = pd.date_range(start=start_date, end=end_date)\n", "\n", "# We assume that the daily earnings and expenses vary somewhat randomly\n", "daily_earnings_avg = 10.0 # average daily earnings\n", "daily_expenses_scale = 50.0 # scale of unexpected expenses\n", "F_df = pd.DataFrame(data=np.random.normal(loc=daily_earnings_avg, \n", " scale=daily_expenses_scale, \n", " size=len(date_range)), \n", " index=date_range)\n", "\n", "def F(s):\n", " return F_df.loc[s].values\n", "\n", "B_0 = 10000 # Initial bank balance at 10000 euros\n", "mu = 0.01 / 365 # 1 percent annual interest rate transformed into daily interest rate\n", "\n", "def integrand(t,s):\n", " return np.exp(mu * (t - s).days) * F(s)\n", "\n", "def integral(t):\n", " return sum([integrand(t,s) for s in pd.date_range(start=start_date, end=t)])\n", "\n", "def B(t):\n", " return np.exp(mu * (t - pd.to_datetime(start_date)).days) * B_0 + integral(t)\n", "\n", "bank_balance = pd.DataFrame(data=[np.round(B(t),2) for t in date_range], index=date_range, columns=['bank_balance'])" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We plot the bank balance over our chosen time frame\n", "\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "plt.figure(figsize=(15,5))\n", "plt.xlabel('Time')\n", "plt.ylabel('Bank balance')\n", "\n", "sns.lineplot(data=bank_balance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fluctuations as a standard Wiener process\n", "\n", "What if we wanted to invest in some stocks intead? It is generally agreed that stock values fluctuate quite randomly. We could therefore try to model the stock price $S_t$ at time $t$ by\n", "\n", "$$\n", "\\tag{1}\n", "\\frac{dS_t}{dt} = \\mu S_t + \\sigma S_t \\xi_t , \\quad t > 0,\n", "$$\n", "\n", "where $\\mu$ and $\\sigma$ stand for expected rate of return and volatility, respectively, and $\\xi_t$ denotes random \"noise\".\n", "\n", "It is not immediately clear how random noise should be desrcibed mathematically. The generally accepted way is to view it formally as a time derivative of a _standard Wiener process_ $W$, that is\n", "\n", "$$\n", "\\xi_t = \\frac{dW_t}{dt} .\n", "$$\n", "\n", "By definition, the standard Wiener process\n", "- has continuous paths, \n", "- $W_0 = 0$ almost surely,\n", "- has independent increments so that $W_t - W_s$ is independent from $W_u - W_v$ whenever $t > s > u > v$,\n", "- $W_t - W_s$ is normally distributed with mean $0$ and variance $t-s$, whenever $t > s$\n", "\n", "The last property has the effect that the displacement of Wiener process scales, not linearly with time, but with its square root, that is\n", "\n", "$$\n", "dW_t \\sim (dt)^{1/2}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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pkXiWnTvh5X/0UaJZs/DehAlEDz5INGUKfn7jDSjDTz+t5PAydR9W7BiGqdfk5BBduACBwZygzXgfHTpAUPEV4a6qCnlafn4QvmyF9fn7I9+uRQs0Zk5Lc8swmX8wGtHOQG6zwXgPkZFE06fD8FFfEYLoueeIPvrIeoGvqCii//wHDd7XrXPf+BjPwksWwzD1mpQUWDV79PD0SBi1tG0LgSY319MjsY0QqHpZUQFlTW1RHn9/FFSJikKZd/Ymu4/QUKJhw1ChlPE+GjRAOLav59k6gtFItHgx0fr16qq0DhhA9MknRAsXqjeECUG0ZQvRn386N1bGM7BixzBMvaWkhCg7GwUs/P09PRpGLQEBRFOn+oYyfvkyLOZ9+hA1aWLf38rK3dix8CbrdETl5a4ZJwOysogyM30rzLe+IQRCEePjPT0S97NzJyq1RkSo/5vevYkSEohuvJFozx7rn83PJ3rqKaKXX8bLF3OZ6zus2DEMU29JSUGoVadOnh4JYy/BwRDw3Gm1T02FIcAeWrQgGjkSRV8cISBAEeJOnoQl/ehRLnHuCoSAdzQ52dMjYawhSfBWXbwIY0d9YvhwoocfJho/3r6/69kT1V2/+QbeTnPI0QWHD8Mr2KEDUUGBsyNm3I0kvNgsFRMTI2JjYz09DIZh6ihFRUSFhUTt23t6JIwjHDoEr+vEia4vcFFejvM0bEi0davtz8sFHrRsal1aCqXjwgUIYW3bEnXvziGDWpGZiTk1fDi3N/B2SkvxHPbsSdSrl6dH4x7+/hsVnMeNc2y9y8lBGKtejwiA8HC8X15O9N57yF9ctAhRBi1bYo0pL8fPHTtq+lUYB5AkKU4IEWPrc+yxYxim3hIRwUqdL9OsmaKcu5rNm/FvaCiUNlskJEAQ07IaXXg40aBBCEPt0gVhgzt3cul3LRACSnNYGKoNMt5NeDiUj/PnLXug6hJ6PdF//0v03XeOH6N5cyh0ixcjzFK+bj//TLRhA5RGSVIK00gSwjKffprXGF+CFTuGYeodRiNyDa5c8fRImNpkZBC99JLSEsAa7dohD83VLQGEgPDTqxfRL7/YVuyystCDrmtXePi0JiSEqF8/omnTUOQjMBBjkj15jP3k5iLsrFs3bm/gK3TqhKJEWVmeHonr2bQJYeD/93/Ozc/gYKJbbiHauxetEnbuJJo3DwVW/vWvqz+/YAH2yTNnHD8n415YsWMYpt6Rnq5OcWDcS2Ul0RNPIMQqONj25wMD0bA4IwPWZlchSegJtXQp0cqV6BVlCZ0OeSqNG6NgiisJDkZZfiLM6dhYvNR4FJmaXLiA68kefN+hZUs8/2rWCl+mshK5cX36IEzYWW68EUahI0dQgCYoiKhvX/OfHT4crRL69IESzXg/VjpgMAzD1D2EQNGUiAiEpjDeQ1AQ0Zw5EK6PHUMOma3cjo4dIZRnZLguD+Szz4hGjUJ1udhYhC1dvHh1yJ4QEJZMJjQZd2cPtA4dIACePIn8oxEjkE/DqGPQIFw3ro7rO0gSPNZ1nZIS9FmdP18bb7IkET3zDNGtt+K4tmjcGAVboqLQP4/xblixYximXnH5MjbKmBgOufImNm3CfbnlFgjYc+eiQfQbb1j/u8hIKFiBga4Z1+nTsJY3bAjFbupUhFiaK4qi06Fa5cCBrgnBtIYkof1Dw4ZQLnfuRDVOtX3z6jN6PeYPF6HxTfLziYqLYdyoa1RU4PXWW9oeNyBAnVJHBANVjx5E//sfDG+9e2s7FkZbNLEnSpI0VZKkJEmSzkqS9LSZ398pSVKOJEnH/nkt0uK8DMMw9pKSAk9G27aeHgkjk5wMBe7AAXi7GjYkuu02on37bPeqkiR4p6KjXTM2gwFGgOuuw8/NmyO3b+PGqz8bFkY0eTJ+7ynatEHVPCIu268GnQ5GBXf16zKZUFTn5El4eDm8zXnOnYOHv6rK0yPRnnXr4KnLzPTsOO64A8Wq3nnHt4vV1IccZKcVO0mS/InoQyKaRkS9iGi+JEnmis+uEUIM+Of1hbPnZRiGsRe9Hh6VLl3cGybniwiBSpA//ojE+tdfJ9q9G/lbt98Oy+2xY0SnTuH/8uuGG4iOH4eQpaaoQWkp0b//jdDYZcuUULibb4Yg8dFH6jbjkhLr5ysrQ+6bPflnRUUIC33vPaU0OBEE8zfeQAgoEeZVXByE9IAAz3uCGzcmmjAB4YVE+O71QaCxh/x8/Lt1K+ZE06buOW9REZ6rqirk+T73HJ6Xigp4h93Zl9ERtO6fWFVF9PvvWEcqKxHibC9dukDZ2L/ftbm27kYIoh07iAYPdp3hSi1hYUT334/7dOSIZ8fiKKmpqAiakVG3C+5oIdoMJaKzQohzQogqIvqRiGZrcFyGYRhNCQwkmjIFggBjHblgyHvvEa1eDaUuPR2KV6dOEDYiIqDwDB6svAYNgsftu++gAK5bZ/08n35KdOkS0fLlRE2aKO83aICeSqGhUP5scfq0ecVNCChgf/4Jq3dhISogXrpk+5j/+x9CQmsLsxMm4Prs2IGf4+NxDm9qGt6gAZTMigqEZe7eDS/R5cu2S5cbjUqbhspKCN5HjuBv64KCeOECjBBvvok5vnWr68u5Fxaismp4OAoEDRiAnNJrr0X0wNmzRF98gTmq16MHojdhMGB+3303wgKd9Y7pdPC0+ftjXqan4/p8+qn9XszGjZHTmpcHr39dKB4kBIwPn3ziPXltU6YQffwx8hp9bR0QAs97Zibm3bx5RF9+6dveR0tokWPXhogyqv2cSUTm0lnnSpI0loiSiehRIUSGmc8wDMO4hMpKCEzh4VwgwRp6PdGzzyLXbfVqWGrDw2t6OF96qebfmBM8GjaEdTcnRxFSantFDAaU7x4yBOX7a3PddUSzZsGKHxICRcUSHTrAEpuZqVQ2rKoiOnoU1tmmTRFSGRYGJUdubB4WZv54ZWVEv/2GqnDyZ/LzoTA1b478v+3bcYyMDLRCcJfXxx6Cg9HE+cIFpWS5JOE7jBmDnysqcD1ycvDKz1fCSuXKm5mZEL5DQqCItGsHxd4XWbsWRp6xY6EM7NtHtHAh5vHQoa45Z0YGPNzDhyth4I0bI2eTCM/Yvfdi7n79Ne7B4497x1pVWUn0wAMwaIweTfTDD1DGXnnF/p5/RiO+008/oU3J888TPfYY7kd+Pp714GAYc6p7yW0RHY31JC4OBY58vajKN9/gGn31lVL51tNIEtbp//4XRon77/f0iNQjSWjnUFiIuTFlChS75GSiF16wvA/4Ilp47MwFndTW5TcSUQchRD8i+pOIvrV4MElaLElSrCRJsTlcj5xhGI1ISSHato1zWmyxejUE3fJyCBSNGjkWttq8OSykixbBs3XzzfDeyRbShARUZcvLg4BtDklC+My8eciDsnW+sDDcZ5MJ93n7dgiKvXsTXXMNBEVJgiJJRHTwoGXr/qZNEC7nz8fPly8jv8RggDDQrh36nu3di5DRHj3sv0buQJLgoZ44EUry6NFE3buj6AwRvv/mzejrePo0vl/nzjUV7cGDiWbOhEAUEYFrnJiI3/lintjDD8MTnZNDNH06PGXh4fBGaG3Bj4+Hx7NvXxhMLOX2BgWhh15AABSoWbO8Q6kjQjj2qVMY+5IlRK+9BmPJPfconl1rlJVBOUxKgmc+Lw8K7b334vvKhY8iI1FWf/NmKA/2esA7dIDBxdfzpzduJPr8c+QOy83CvQVJwt7www8wVvgC+fmYs9HR2GuCgxH+//DDCN99+WVPj1BbtPDYZRJR9ccomohqREkLIaoHFXxORCstHUwI8RkRfUZEFBMT42POXoZhPEFODjaZiAiE80VE1BSKDAaEX7RqxSXgbTFxIhQ52ZvjDJIEwa1vX7zeegvesqeeIlqxAkqBrZYTnTpBafr9dwi7lvLXJAkb+BdfQDifNAnejzZtaoZ4EkGIj4lB2FZCAqpYVkcInK9fP3jiiJSeeSYTBFSdDn3tzp2DcuTpvDo1BAYStWiBl4wQuDehoVBQg4LM/62/P75/dDQUOTl0MScH17FfPwjW3nwdhECZ99Gj4Y2sqMD3iYqCZ6SoCN9n+XJ4y7SospiejrVJr1fvFejcGZ9fuxbeVk9WIdTrYVjp0EFZE8aOhbHg2DE8S1u3Yt0oKlKUtN9/h3cyJAQGnnnz4NFu3x7PkDWFpW9frEGhofisPYYlOcxeCDT0btXKu+dkbfbtQz7z0KEwBHjj2GXPsrd4Em3x3ntEu3ZhDsoGLUlCVErnzlj38vNhsPJ1Ty+RNordESLqKklSRyLKIqJ5RHRr9Q9IktRKCJH9z4+ziOi0BudlGIYhvR75P+XlynuhoWjASqTkVen1sIgz5jEasQHeeCPC0rSkRQt4uzZsIHr/fZxnxQoIbbbCrSQJFtXayll1KitxzPXrITBGRcFbN26cZUWldWu0LUhJgcBZvZKlJBF98AE2e6MRIZnjx0OgIUKI6IQJyAn68098jwkTIOAOGaIID75AQID9OacNGigGkrAw3Bs55HXQIDx/3sjff8MzOXw45oVcXIZI+U7HjkFZf+wxhMJZC/+1RFUV0Zo1UHavuw7zw97jSBIUwsaNPafYpabCePHyy/B4V6d1a7yOH0do9po1GOsNNyj9HnNyYGAZORLHMRgQZmrLmNO2LV5Hj8Ijvnix/Qa57GwYHLp1gxfQGxUkcwiB8f7nP47NPa0wmXDNzF23yEhEMmzYAIPPzJnuH59aDh9GpM7dd5s31MTE4N/XX8c6/9BDUPh8GaenjRDCIEnSg0S0lYj8iegrIcRJSZJeJqJYIcQGInpIkqRZRGQgonwiutPZ8zIMwxAhd6i8HIJ3cDCUOLkymsGAhV0IbEbemAPlLaxdC0WlZ0/XhDJJEtHs2Urj7upeI1u0bIn7+O67qJJZO7frySeh3M+fD0E6OxsVNseMsS4g9emDcMvayt/KlfDqjBqFY8XFwUI9eDB+bzJBoWnWDMrMqFF476+/MOdmzFD/3XydsDBc59RUohMnoOj264fr5U3CtMGAQhTt2sG7lJYGb13tuTFgANGqVbjvfn5Q0iwZByyh18OjW1SEYzgSyhwQgLDHgABc206d3Hs9S0vhMTKZrFdk7N8fil1sLDx5H34IhdRoRKhz48ZECxZAyYuKQhjwxx9D+Z8/3/q1bdAAa7ojtGqFa5acDC+it4ZKFxcjHzkjA4rSffdhPfH0s7NpE67d4sWWe3Lu3Ilcy5gY7wsZJYLB7403sJ/dfrv1zz70EEJ/vfF72IskvLi0TUxMjIiNjfX0MBiG8WKEQK6TOS+JEFisCwvhVahLCdJacvEi+sYNHIiwKU8LFeZITUUvpVtugcArBLxyY8ZAoTAYkJMis24dvC8vvqjO8i0EXidPwjP36KMQ8jt2RMie7FmsqkJYT48emFNffw0vZ5s2EF6bNfPO6+cOSkuhBOt08NR40uNQmw0bkGezYgWEt5MnkedlaU0oL4eQfc01sPar5dAhCJJahQAmJ6NS5IIFNT2MrkQI5CD9/Tc87AMGWP6syYQw1o4doTAvW4bv3r07Xi1b1rwOJhOeyR07oDA++mjN59bcWC5dgtHkxhvtm1NCQOFMT4cRp2tX72hzI+dxxsUhf/G222CA0ulwLT2tXJhMiFb47juiBx+03MIlOxtj798fYfbetu4ZjUS//gpPnWyU82UkSYoTQsTY+pwXTHFGDb6YoM4wrkTefCTJcuibJEEgj45mpc4SQsBD5ecHz5e3bc4ynTsjvHbtWggUL70EIfK33xD+WFs4nDsXIWSJibDaWiuKIQQ8fnFx8CRMnozjffYZlEdZqRMCxTDKymDFbtQIlt6SEhy/eXN4rH780WWXwasJD4fXZuxYCIPl5RCqKyrgvbpyBZ4JueBGTg4Eb3c0lh4xAora2LEYU7Nm1teEkBAo699/D8OQGiorEY7711/aPUdduyI3qH9/dSXmL11SevQ5SkYGPOT3329dqSOC8BwaqoTfLlsGw8i4ceaVWz8/5DC+8w7+v3QpnjFLSBLuV0qK+vtQ/W8HD0bI6IkTeHmavDwYGE6cQP7upEm4xv36KUYHT1JZiXuTlQWlOycHP+fmXv3ZVq1QafLgQaItW9w/VmtV0Qs4AAAgAElEQVSkpWGvmD27bih19uBF9jTGEnI42aVLEDjsKQHMMNWprIQXY+hQ7xXg1ZKaisIX48f7Vk6TtyFJyIuZOtW+8EhPsGgRvGWyx6xzZ1TbtIQkQbFbvx5C8RNPmJ/3sgHg4EEc8557EL41bx7yhcrLIeAUFyNns08fZc7t3g3vxiefQDgzGrFm21v0oa4gSYrCdPYsPE61GTAAinFlJUKpQ0OVIjWuYOtWCMwLF0I5KClRl1e4eDFy8latggJvjeJihBU+8ojj4YPmkKu4Hj+OfDO5kmR1hIDS3KIF5mFEBIRyR0hPhyL0/fe2c+GSkzE+uXKsPQwbBo/Qhg1QtrdtQ27jrbfCYFL7swMH4tlKSDDfGsUSfn7IqczOVo6bmYn71bmztvfKEiYTislERCDCIDoacz44GIagkhK8rlxx/VhsUVGB51cOvzSZML8syQs33ICIGVe1CXEEIZAzl5oKmdlafnZdhBU7L0enQznWoiK4k1mpYxyluBi5P3v3Inzszjs9PSLH0elQfrtFi/q3aGtJbi7y6u66yzeqhbZogVyJZs2wYavh9tvhYfvuOwjeDz9cU0hJS4OiGBsLb5y/P7w7rVujFH6DBhAKjxzB56OiahbhGToUx5Vzy6ZMUSp02mNwSE/H3/l6qfbq9OkDYVavhxArv0JC8PvoaHzv1FSl1L/WFBYivHjgQHi95OtsLW9MpkMHeIl/+QVKYePG5j8nBNG330IIXrLENQq9fG3KyxWhW+4Jt3Ur5vBzzxHddBM8jY6Qn4/Qu5gY9PayhhwKXVEBJdKR7xwYCM86Edbzn36CrPPUU3hmq3tUg4KgBO7bh/xNe3ooSlLNfnt5eYrRoX17zL3q57p8GfulToeXwYC5bGmv2bABHq5//Qu5aRcvoj/nli34/913Y62VjT1ycaovv4R8N24c/rZdOzwLERFY46xRWopxdu6s/jrYIi8PY7zvPuW96GgUEiovRwTDzJk1r6WfH77r6dOIVLj/fs8bjauqEBo8bVr9lA9YsfNiCgrw0BsMqCrVqhUW04wMPFjelL/AeDdXrmCRO3YMws3cub7tUTh+HOMfMMDzm4gv8/bbWGNmzKhZFdKbueMO+z4vSRBUKithNZ85E9X2YmPRHPnYMfSMkkPeBg7EGlu9iEzz5lAkZW9U9TkXFob1eedOKI3+/jj+999DIFLbwFmng8HlgQd8517YQpJsf5fu3eH1PHfONVVri4pQRONf/1L2z5Yt1RdE+b//QziXJaVOZto0KDmuWlN794ZXMzcXCpifn2KgGzwYhaFCQuDJjo3FeLt3t+8c+/dDobn1VuufMxgwXxctwr9afOdHHkHho7AwKHkPPQRvUPUS9VOnYv9q1AgeLktFPWzRvz8E/5QUNEk/dw7zYeZMzNkzZ3Cd/f3hWauqgkI5ZYrSzoEISlvjxrj2cphsw4bKeIODFYXxzjtrXqeTJ9GEfMoUpaqkwQDlqFkzpQJvbQoKoKysWwcl8IUXtJMFf/8d1+K552p+T0nCfc7Nxfwwt6bFxaEHao8eyLW0F50O1/r4cRxr2jTH2ikUFuK+PvGE/X9bV2DVwEsxGLCQ+PvDmiNbp4qLYTlu2xbhGSzUMra4cAFx/JmZaHw6fToWzjvuQGKxvaXOXUFVFTweEyZgYS4ogJBnrkHvxYtK02n2YDuOyYRr3Ldv3VEkLCFJULpuuglC0d13Q1m7cAFej48+gnfmjTcgqNXu4RcQYF2IvPZaKCdyT7wePdSHAFVUwLI/diz+RvZiRUf7ruHFHpo2xb1ISYH3Qcum3Dk5EKw//RQ/CwElqLrQaouoKNz///wHBUxql0yPjYUicMst9h3XUf73P3iZpk+HZ87PD9dPDpuUPWldutin2AkBBWPUKNvzdtMmeLeffFJbj4jsfTIYMI7Vq5EnNWcOwmKDg/Hdf/kF1/yxxxyPNGjUCHOhVy8oM3L4tL8/PJYBAVD2JAlKZPUefURYN77+GvO3uodr7Fjl/+PHK/+v/Sx/8AEUuKVLlfcCAqAsN2iAPTAnB2u03Hrg0CFcj2eegUJYVARFcMwYXBdnmTMHe6u5edysGe63nx+uf//+Nb2F8+ZB0bSljOn1uMZ5eVBux45FTuqmTXjGSkpwn1u2VJRYtRQXIyw+MRHXKSpK/d/WJerBtuFbyJXZAgIQ4jN+fM2Qg4gICLQZGQglYBhrnDqFDTInB5v99Ol4PzISAo87ihZY4/hxWGrbtIHXSJJgxezVS0nibt0anrnZsxE6c+YMNmXuSec4SUnIO7vzTsfyY3yR0lIIDJIEoeSBByD4Hj6sWP+HDFFXoKI2o0bB6ycXmggNhbKXkoIwTmukpaHfVkEBLN35+RD6rBWUqGv06AFhUqfT9rgffoiwt8pK/CxJEBjtbXsiSQh1/Oyzq39XUoK55Q4lXM5na94cwv8991wdUipJjvXi+vRTtDeond9mjmHDIJu4ql9hdDSKI61eDcN2bCzmR3a2opyPGKFNflxICGSq/v0Vo0JYmLJWEGFtaNMG8yg5GcaYrCx46mv391ODwQAl5rXXrjZOtmgBOW/jRnz/zEwUt0pKwnMybRque8uWUObOnXO+WE5VFapxFhVZbwsREIDvLns609KwX+fn43p07ox5+cUXiFgoLsZ+/frr+ExcHNHTT0OpS0/Hd8zJQbTEddfh3o4eDQXzzBmiV19FiKcaLl6ElzMxEcpdfVXqiLjdgVdhMiGEx88PVl9L3jghkOSfnQ1Lja0EZ6b+8thjsOht3QrPTHWEwAL73nsoP62lpdwaublY9L/+GmFwQUFEs2ZByZg+HZtGfDwEk82bYR28cgWlt8PDUSa7RQt1AghzNfIGGBAA639drxYqV8OUK84tWoT1s0MH/KxVSHJGBqzOixYpFSFfeQVC6A03mP+brCwYLkpKas7nI0cgbBYXQ8Cs63kishiiZQTKkSPw0i5cCI+K0QgFoWtXx4otrV2L+zp7thKaduoU7q8Q3uVdLS1FaHC/fuabMtempATC9IgRqFhpiUuXMMdvvtnxMEhHqKrCvrFwIRSbRx7BfrV3L/YGS8+XswgB48Aff+BZNJkQoj14MKrxlpTAizVhAsJYp061fcx9+2C4eftt694tuWBT69bI3xw3znw+nRbrV3Y2DFMLFqjL2ausxL6dnIz8wrvuwlh//RXr2OrV8Ho++ywUwb/+guKm16Ma6LBheJYMhqsV28REyC233grZdtIkvG9NiRcCuX3nzkEZdFdbEHejtt0Bh2J6CTodNqLcXCwc1pAkPDS7dsE1P2GC6yxnjG+yfTs2w9dfR6iHuWR6SUJM/fLl+Oxrrzl3TpMJm1tBARbzykp41YYOxebYqxd+7tgRC/zgweiRNH9+TQt6t26KN27aNLyIlFywadOg5LFiZz+Fhdg0q6pw7eu6UrdnD9bVRx+F8CfPs+HDlc9oJZBfuIDqiT17woofEoJCFJYqjV65gobrU6diDa/OkCF4nj78EJ6K2gVf6hrydysuxtpgr0etNmfPIlytUyelMXF2NrwfahQdc9x4I56bnTtxf/ftwzrbvr33GVcDAyEbNGum7vuuWwcZRC7qYYnCQhgj3O0PCAqCEWbOHFTPvOsuKOeFhXgZDNrWHEhMRFj1ggV4TgcNQvpLSAgU2qws7GuTJsFQsGYNDJWpqcjltLSm6PUI946IsD3HQ0KUEPl77rH8uStXoEjNmYP5bi/FxbiWzz6r/hrKSlb37kouW7NmWPv0ekQgXLiAedKhQ805aK3y8vHjkFcqKxEWfPYsPJsGA0I9zVVD/ftvGMGefhpewQEDYAweMMC+67F3L2QXOc/Sl2HFzsMIAXd2QgL+P3SouqpogYEQTo4eVRbZnBx4QqZPx+9ll3deHha/mBgs3LUTgJm6hRDwwAmh5GFY4s47IQCsXAmP3oIFjp/z4YdhiazOkiWY088/j2O//z4UyGuvVV+yWm4yXlmJHknPPYcNNS7OPaWq6xL//S+s7u++67iA6+0UFcHoJee4ySFUriynT4T1uHakRatWEBgyMyGYyAgBZeD66y33CfPzQ/NfoxGGkrQ020Y/X0YIrEVEWB+cEa5KSiBAvvWWYrzIyECYmCMhWnl5EFj370eFzfnzlVBeb1PqiLAuvvSSOkG9vByKyciRUFLMceECoitmzULFSk+su35+uOa33Yb/v/IKlKgmTXBv9Xrn8sUNBjxrx47BENSoEbyzy5YpitqlSwiJ7NULnqdGjaBw3nUXZKzVq1Gp8rnnri7OI6fYrFyJ36kt3mOLxo2hBFrr02mNn36CQlM9188ZAgPx/ZcsQfTCTz+pMyCeOgWjY/PmkBOaN0d0zq5dUHBbtbraO7lmDfayOXNgDJbrTyQn47rYo9hduYJ7KOdZ+jIciulhUlKg1DVvDg+GvRZ0+fbJClyPHlhchg+HZyMyEpahsDBYGnNzlSa6PXtiofF16wSjcPEiFj5/fyywtiq5EcEKPXkyhKo9e+AtsJfXXoOFfMkSGA/ksuZNm+JVVITNx9ZmVn3hTk6GlV22yBJhbOfOwZK3aBHGrtUGWZcxGBCeJQSsyjE2gzk8R2oq7mnjxo6Fe128CAV24UKUKHc3ch6OHPq8fTuUsrvuwnprMiEvpVs35JOoYeNGhI8uX45nND0d3+/UKVip1R7H20lPh3Amt5uwl7IyhBffdRfWQFlAq6pCCGGnTsilUoOcuxQTg/CuFi1gnJo9G/vq6tXevXdevIiIjLlzrXuHDAbIBu3aWc6v2r4d9+Whh7yjYFV8PJSApk2hvP/yi1Igyd57UlaG5+unn2BoufVWzJVJk66OhNqwAcb0J57AOpWSAgNl165YW//3P6KPP4YyWLsdy2+/wcizbJlrIiXkoiT2RiCcO4c9VuvwxfR0yLYzZkC2GDbM8r0xGGC8eustKO/VWz2cOwdZpqKC6PHHUaVWDnndtg3P4cqV+O5ZWfgeVVWQPw4cgEdSbkFjjl27MI/69ME99GaljkMxPcjRo7AgydX95FdhISbk/PlYTMLDYTUPCMC/jmwSkoSNftIkJD/n5kIg8veHZak6ej2qr/38MyyN772HPiqHDmEB8+YJzajj2WexmWdkKL2ibBEUhDkxdCg2tthY+8oMp6bCI3frrRCozW0stnoOCYEiFllZSu+wsjIIwe3aYU5HRuI47doh32DFCnzX7dvrfkihMwiB8J+4OORqeLNSR4R8lrQ0zMt589QL4no91sJrrkEJcE8JoO++C4Hjhx9gRJs4Ec9EcTEs/LKRwp71fupUCDt+fngmjEa8f/w4ihgMGIA82mHD1PVn81aio1Ep78wZrEH2XCODAevf0aPwPlXPKc7KUtYSNQiBeVhWhuflxhtx74KDEV67YgXyhsaNs+vraUJiIhSbqVOtex+DgqCYFhVZVuyqqlBEaeZM82tofDw+c+21MB6o3VNczcCBiA554gnkCz/3HN7Ly8N9mTFDXbXMr75CDnppKdaZ7t2VPMrqmEzwxF13HeoahIVhfvn5KQYISULYb0wMFOQtW3DMVq3gsX/vPYQMuuIanj+Pwj7/93/qvVR6PXLYx493LITTFu3a4bV/PxSyyZPxfNY2xB4+jP3pnXcQaVQbeWz798MT/+qrUKC7d4eX8ehRvN+zpyK3yPc+KwvrrqUcXoMBz1OzZvY1vfd6hBBe+xo8eLDwFQwGITZvxv/HjpVrWyqviAj8e9ttQvz9txC//SZEebk2516wQIiwMCG++06I2Fgh9Hp1f7d+vRD33Yf/33WXEMOGCfH660KkpmozLl+nosLTI7CPlBQh/P2FePRRx/7++HHMoz59hMjJUfc3SUlCmExC7N0rRGWlY+cVQoiLF4VYu1aIw4fVPxe//CLE3Xern+/1lbQ0IcaNE+KTTzw9EnXodEJkZOD+Fhaq/7vjx4VYulSI5GTXjU0NGRlCXHONEMuWKe+dPCnE448LsXs37ofJhJezmEx47nQ6IZ5/Xoj9+50/pqdJTcVacPmyfX9nMgmxapUQGzde/bu9e4XYulX9NTca8Vlze4Bej33866/tG5+znDiB+/zHH0KMGIE59vbb6tdqc/z6K4518ODVvzOZhPjsMyE++gjXwxvJyBDi5ptx3w0GIQ4cEOLf/xaioMDyfpSSgu9lMgnx3ntCPPccnk9r7NmD5zcry/zvjUacX6a4WIipU4WYMUOIs2eFWLRIiMmT7Z/TaikvF+Lnn4W4dEn935w+LcQTT+B6uBKTSYhvvsF1rv1MlZcLMXOmELffLkR+vu1jFRUJ8eabQowZI8Qjj+A9a3PTZMLzmpYmxMcfC1FSory/cyeuV3l5zXvnzRBRrFChO3lcebP28iXF7sMPcTUPHhTi2DEoWKmpmKzypMnIgEK3di0eJi029kuXhAgMFGLJEiz8a9cKsWWLuoekOu++K8TgwYoiOmCAEC+/bHvBq6ts2iREgwZCvPaap0einjvvxJizsx0/xvbtMBSYTJjL1ha8s2eFCA0VYsUKx88ns3s3rrkjAsTmzULMneucYllXOXoUG1t6ujbrjavZtg3rp8zly0J8+61tI0tuLv61R7BxJZ98AoH5+HH8XF4uxIYNQixfDsHEFYKyPP99RUixhMEgxO+/wwAqK/m25u5XX2Hvs3bM4mJ156+qwpp2+LD1zwghxIsvQklw5bwzmaCsjBghxOrV+C7nz2OMo0dj3RfCvIErPh6fs7Q2rl4txAMP1Ly+JpMQf/6JNaOiQvmu3kppKcb8009CTJyIZ8xgwPd68UUoexcuCFFWBplsxAghJkwQIjNT/Zqo0wnx11/mP19Vhb3r9Oma758/D2Vm40acc9s2Z7+pbS5fVre2yGuE2mdCC0wmzMeZM4U4dEiIhATMrzNnahrwSkutj6uiAmuDPWNPTITToqQE4ygpwdzYsMHhr+MRWLFzEyYTLMRVVbCYWMJgwCSaOVOISZO0O//y5biLZ87g5ytXsMisW+fYQ3v+vBBvvSXEyJGKkvfMM9qN1xeIjxciPFyIkBB8/7/+8vSIbHP2LLx1shXLWdLShAgKgkBhjspKzP0333ROkRQCFue1ax33tHz+Oe7ToEFCTJ8uxLXXwqI3bBjmshBCDBzoW0q6FsTHCzFqFIReX8BgEOKNN+CpkzlzRogXXoAQZomsLFieDxxw/RjVotMJccMNQvz4Y833y8qc87BYw2iEkmFtH/IVrlyBgPfggxCKr7tOiCNHINTVVqJkwXn5cvOCt70GjeJieIDOnrX+ucpKIR5+GHvlwYOIOli/Xjth+fx5rG0mE57hb77B/KlORgaE1pISIWbPFuKDD+DVkElJgWexoODq4+fnm/cc63S4lr/+qs33cAcmE679229DwdPr4S0bMUJ5vfEGPrtxY81rZA2DAdfd1lz46y94Ui3NvyNH7Ps+jpCYKMRjj6mLuNq4EcYndxuBMjJgOB41Cnv0++/X/L3JBKVt40Y8X6Wl2p3bYMBzsmwZFMn8fO/1RFtCrWLHxVOcQAgk8H7+OSopWavIlJaGHJeUFMTtv/yy84nXej1Kx/fujfwKmcpKxBbLscl6vWNVMC9eRPz94MEoYvD++8gfqcuVCDMzkafi748yujt2IBG/qEhdIRJPcffdyOk5d86+/DhLCIHcg4kTURHt8GGljPOlS8hjevFF5NU5y6FDqEg1bZrjJas/+4zoo4/w98HBStWxG25ADsb06eh9VDuhvS6zdCmKeKxZ4xvtUOStSE58l6msxFqZnm5+jTUa8ZyOHu1d37OyEt8jJ8d9lRM3b0Zu4Zgx7jmfK/npJ+Ts3nAD1t9770Uu0VNPYW/79lsUAXvlFRRMeOst8+vHrl2oXKimoqjRiDx1ayXZa5OTg/zftWuxPwYF4frPmGG9YIQlLl+GTLFlC3KFvvnGdt5kXh725717kS9dWooxyXlztdsBmEwovtO1a828pqQkVJEVAn/rTb357MVkQo7hxo2YA3Pm4GUP+flEn3yCHERrOViZmdjHRo3CXPMEFRUocDNwoO384v37sedef717xlYdnQ6VZfPy8OxWL5AlX8f+/SHDGgxoBaNVkaKCAuTnxcSgQJOvobZ4ise9ctZe3uyxM5mEePppeAoeesi2VfDyZYRnmkywEpw/7/wYfv4Z57fmTk5Px+8vXnTuXB9+KETr1tYt546QkSHEjh3aHtNRioqE6NdPiIYNESYg89tvQjRujLA2b0T21j38sGuO/8ADmGfXXovQ3IEDEYJ56JA2x6+qUkLpXElFBXId9uxx/bk8TXo6rNRffOHpkajDaBTinXfM5/oIAS/ek0/WtLQbDPh+crijN/LZZ8i1Uesh0AKDwXIukC/x999IMageppWdLcT338MzJQQ8tQsXWrbsFxYiGsCWx0UmPh5ej3Pn7B+vyYRwvLfewj2fNg3eL3vufUYG8mGvuQb5X/amVBQVYRx33YXohfXrsf+vWFFTRtmzB+uDXBdACKzDzz2H0Oe6hF6vpJTYEzJbUoL7p9fblu+MRniZ9u1zfJxaUFkJ2cWaJ+rcOe8M166qQgj2n39i/Bcu4NlNS/P0yLwHUumx82F7jGdZvhwl3u+9F1ZFWxaFqCh4viQJHqCxY5XKZo6yaROqaU6fbvkzERGowrR/PzwvjnL//Sit3bAh0c03wzPkLELAqvnCC84fSwsOHIBHde3amhXVhg6Fpa9zZ/c3ZlVDbi6q4j35pGuO//77sFoeOADvcEICrtHQoc4f22iEN9nZhsRqKC9H1cQ5c7SZv97MsWPwFnnCIusI5eVKPyZzTJoEr3T1qpIVFYh+qKpy3zjtZfx4VGzbvNl951y/Ht7rigr3nVNLDAZ4rHr0gLU+IQGeE5MJ3hC5hxwRGje//77lqrjp6dhz1VYK7doVvdrat7d/3JKEMT/2GMrif/AB1rZ77kG0QFqa+b8zGuFVWrUK3rI770T0xZIl6NFmD40aYRyPP46KhK+/Do9fZKQibwgBb2fr1qh2KRMYiIqf1uQJXyQgAH3n5B6EWVnq/m7DBniBhbAt3/n5QRbLzoZHylOcPIn7bWmuFRRgbdi2zZ2jUsepU1izBg7E9WzbFvP2xAllzWdUokb789TLWz12K1fCg3HnnepidJOSanok1qzB32/Z4tw4TCZY+GxhMMAKsmWL8wUUjh4VIjJSiObNLVvX7T3eli2wKt5+u2cqUZpM8MqZTNYteseOITbc2ZwyLbl82b7Kgc5w9qwQN94oxA8/aHO80lJcd2e9yfaQnCxEkyZC9OqlzpJuNKKw0IIFvld9051eImdRm5e0bh28dKdOIVfNF3Ik5Mqx7hrrxYvwUNhzPoPBe6ohf/UVvEk7dyLHcu1avH79FXmUavewigrkm+/dq+7zaWm2vR32UlUFD+OMGYjSycioGa0j54aNGIHICC3PbTKhKNXNN2OfPX8e1/PECZxv/Xrls5mZeK7M5eLVFXQ6zCm13qqMDPtknNJSIXbt8uw1rKhAXqWleWQy4f67S2ZQS2Ulnu/aUVG5uXj2T5zwzLi8DWKPnWt47z3E+M+bR/TFF7Zj0HU69Mm4eFF5b/ZseCi+/NLxcTzzDBpdqrFE+vvDEllaivh9Zxg4EJ6bRo3Qw2fdOseOo9Oh50qjRmgemZxM9N13yIHKz3dujPaydSvuyZo11nMrKivR12f6dPRG8QaefRZWYndY5zt3Rv7GvHnaHC8lBZY4Wz3utKRrV3gbk5PxPax5zVNSkEv48MPocyM3l/Z2fvkF3ltH8mo9QV4eco7j4mx/NioKr59/hmfKF3KAunVDE93HHnOPx79VK1i7d+60bekWAh7FQ4eIPvwQHi53c+wYvCnytWneHF6z8ePRq0rOVWvbFnuZJOGz27Zh3HFx2JN278ZL5q+/4AlW27tu/37sZ85G0lQnMBAexvXr4dH59FOi225DbtHjj8OTO20aenO9/76281mSsH59/z2+20svweu9YwfudXXPXG4uZIPaPcbqEiEhmFPHjiHPytKzaDCgmXhYGOadWsLCIBN5Mhc/OBhe3l27rt6rsrMR5dWpk3v3XDUEBcF73Lt3zfebNsVzn5yMZ1ktQnhndJW78IFt0bvw90cy96pV6hp6p6bi386dlfeCg7G4//orFlRHyM5GEQu1REcjEVuLjbtbN2ykAwcS3XSTEq5gD++8A8U4MxM/L12KDejgQTSXdVeoXE4OFMt16xBiao2hQ6EUJCQQzZ3rHSFg998PIUFNM1ZvoqIChRDat3d/wYsJExAmtXkzGtzWxmhEeHX//jDKfPMN5uuyZRDStBT8tMZkQtGJggLvaSZsi+Bg3BNrxadkRo9Gk+AHH7T9vHoT4eEoQLRjh3vOl5WF4hu21tG//kJ4WteumNtt2+K9M2dcP8biYuxjCQlQzsrLYZSYOpXo6aeVzzVogP1r0CCiIUPwnsEAATYvD8coLYVSVH0t6d2baPhw9WGYN9+M9dQVBhH5mEuX4jx//onm8gYD5v8112hXIKI2/v4o6nHvvUQLFkDBHDhQUeLy8pB68NRT3lV8yFWUlWHuVVaa/31WFuSb7Gz7jy0EDNPuNk5XJz0de1vt8aekQL7yNuNkfj721LAw84aFPn2gYNuScYxGoowMyGV79lgOR60XqHHreerlraGYakNB9HqEGJorw52QAJvCO+/Yf36dzr5xyBQVaRvqodMJcdNN+B7PPaf+77Kz0U7g+uuv/t2ePQiVi4rSrjiHJfbvR0Pudevs+7uvv8Z3vuWWq8tPu5OvvkKYly8i91z0ZLjgww/jPq5apbyXlIRwWyKET1UvFvT6697fEN1oRDEiaz24vImqKhSc8IWQSmcwGBC6P2uWe3pHmUy22yqYTAjl3rBB2Uv0epSFl9s0uHKuf/cd2qnodHitXIkQQU+0l1m/3r1FlYqKtC3lrmdlSgsAACAASURBVIbCQiHy8mq+p9cL8coruBf1BTksOjv76lSW8nL8ztFn1GRC2wNPFuiqqrp6X5WfY0/KK+YoL0c6htr9ytJ6VFWFdWPtWoTC7tyJMGxvLBLjDMShmK5DrWVNth5U99bJ9O0L6+OXX9rn7TKZUCjjmWfst/A1agSrplaJqCEhKIl/zz2wuKo97gsvwGPz+utX/27MGFjLwsMR1vDrr9qMtTZGI0r1t2yJQjZqMJlg3Rw6FGGka9bgPu7apf68ZWUoulNWhlCpBQuIPv4YniF7LGlpaUSLFyM02NfQ6+HJbt0ac9JTvPkmQhYnTVJCN26/HQnoq1ahoEGbNsrnn3gCXubt23EPvZGdO2t6NrydhAQUyqjrxWz8/TF/8vPhAXY1kgQL97ffovhAbc6dQ0Gk0FB4QOW9JCAAocezZyP86dVX7YsMUYsQOMeCBdhHkpIQ/ta+PdZUd3rFTSZEzhQWuu+cjRpZLvjiCkwmojfegKewOv7+CHUdOdJ9Y/E08lxftQqROtXlrzVrsB7Zahdg7dgdO6KVQEmJ82N1hMBAyClr1igyxRdf4Lt6m0c2MRHPeo8etj977BiiCWrLy5WVaE2Vm4s2Bo0bw8tXXk509qxrxu3tONg1ilHDhQuIZW7WzPzv77kHeRcXLiA8Qg3btmHD7d/fsTGdP4+NfsoUbeLp/fygmEgSHjyj0XpcemIilNklSxD+Y47u3aHc2dtzxh5+/x3K0bp1lu8PkVIR68IFhM7o9Xh//nws4J9/TnT6NBTS0lLL8fVCYKFJSIBS3qkTlP5duxCCSoS5MnIkws1GjoTCaSnn4tVX8bvqIUu+gl6PPJru3T07joAAopUrEaISHY358M03uA+tW5v/G0nCnPnyS9zr++5z54itk5EBo8nddxMtWuTp0aijf3+sQ+aMX3WNXr0w3wYOvLqvmCsICYGAV1Z29e/KypDnbG59CQzEKyQEho2mTbH+BQdr06MrKwsGwdtvR2+5sjKEk7dqhX6UwcEwWMXEuKcfX1UVnhdvC1HTEj8/oltuqdlPsbgY++y4cXW7N605/PyQDhMeXvNZ7NkT88GZsNj27VHh8fx5673vXElhIeSS/HyELHfo4H15dVeuIGy0R4+avewsERkJg3B1eVmnQ+/GsjKEXcv7dvPmWKuSkiCn1eXcUbOocet56uWtoZhqMecSr05Zmf2haDNmCNGyJaoIOUJ+PtzVycmO/b0ljEYh+vYVYtgw6yGikycj1LJ2SIilYxYWCvH229pXy5w0SYjoaMuu/cJCIbZtUyrF5eSgD2FGhnLtDQaEEBmN6F3UsqX5Pn+xsQjvu/NO/HzmjPI7kwl9ZVatEmLxYlRrJMI1MpkQnrRgAT6bnIzzp6UJERAgxP33a3Mt6jtnz6JH386d6j5fVYXnUJLQS9JbeOcdIcaMsR2C5y1kZaGKXHm5p0fiXhIThZg7V5tepraQw87kEKySEqxrRqP68Fe9XoiXXhLik0/w8+nTzoV0paZirpaU4OfSUvRZO3YMP1dUIDTw1Ck8a66cHyUlQjz7rDYVnr0dgwGh5nJvvP370QfQV9YLV1BcjD12926ET2oVenzgAEKcPRUKaDDg+ZZ7K3pbqLvBgGromzerv0YmE/bo33/HuiAE7tuvvwpx5crVn5d7WFbvSezrEIdiehaTCVZPa6FmoaHwck2aZN6qWpvUVKI//kAStKMWiCZNYIE9e1bbqkF+figssmEDCjeUll79maNH4XF8/nlYX9QcMzYWXs3t27Uba1ISjnfffeat5rm5cPlXVSkFKJo1Qx/C6Gjl2vv74x7Hx8Myt3AhLEbffw+r9OXLsAQPGQKvkGx9ru6pkkM3br8dFdNOnsT5N2/G7yorlYqXTz6J4gbdu/uuty47GxVivaliVefOmA/jx6v7fGAgCpSMGIFQsp07XTs+NZSVoeLZhAnWPdDexOnTqEjrTXPBHbRogfv15puuP5ckYV2RowKOHUM43pUr6iswBgRgDb7+eljIv/oKxxAC+4g9nq64OKyRDz+MyJFnn8W/zzyjRKHIxcV69kR4pnydDh1CQRgihIdqFSI6ZIj6iBlfpqwMc0FOmxgxAtfdV9YLVxAWhqqply8j7UOrghtyRI7annla4++P6KDHH0dUUWKiZ8ZhiawsyIgDBqgrQkiEtax/f8hDSUl4b/BgRDZV90TLRESgIJe3hZ+6Aw7FdAFy/lRMDMJLbJGZCfdyr17WP/fxx3gIFi92bnxdumCTzM62HHLmCN26QREZMACb8tq1NYWHQYOI9u3DdVHLhAnY+GuXwXWGjz6CcG4uXO3iRVyb0FCERKrJg8jLwyK+bBlCIO67Twnl0OkgFD3/vPpQiKZNlYbdzz+vvP/vfxNNnAjhLCYGSp4vIQQ2m8BAdc+FPZw5A4VXbg7r6vyV0FDk4I0dC4F3927Mb0+RkoLre9NNnhuDvUycCKHaV6p3akXz5kQrVkDBM5lc37Jh0CDsG+fOYU3r0cN+YT48HC8hiB56CPP/wgXsSfPnQ+DS6ayvcTk5RF9/DePY009DqU9IgFI1ZIj56zBokBLenpmJ19Sp+NvsbBxnxw5cx0mT7PtOlZVQDmfPdl1FSm+iUSOif/0L+8ann0Khue46T4/Ks/j5Ke17Ro5UX0HVFs2bI+TaWvskV+PnBwWzXz/knHkT7dphPtrbGiIyEn+blIT93lYupKMpS76OJLzYXBoTEyNiY2M9PQy7SUyEoDV1qm1rgXz5jUbrORdlZVh0pkxBfoIzmEywfIaHqy8cYg/vvkv0yCOwxv7nP3jv88+hML3/vv2CXEkJcvKmT9emxPmsWYjpXr265vsZGShJ3qQJykOrzTsoLoYiHxkJr1xqKoSfoCDk1Hg6l8xbSEuDtXj48JpFSZzBYMB8W7dOKfTwwQcQXocMgQLcv796q6C9ZGXB8h0UhLwKT8Tyy2tIebnvWCcPHEB+xdy5rs8181Zyc6GY3HUX1htXcv48epc99JD6vm62MBgQYdC9O6IW1q+Hh6Bp05rPm16PXOJNmxCBIUn4bGAg9iBH7n92NhTJzp2JfvgB51i4EMViWrVCP1SjURmHyYSXXk905AiMmzodFNNHH9VOoPd2SkqwBufkIBds6FBPj4ipb+h0zu1TsseuWzd1smRVFQy/HTp4tlibFkiSFCeEsOka4VBMjTEYsIm2bq1u8koSlIJWraAM1qaiAotwcjK8QQ884PwY/fxQuCQszDUJ4w89hKqRK1YoytPly7DwOtJvLSwMm/Hy5c6P12RCuOjXX1/9uyZNIPSMHWtfMnmjRrDO5eQgvKxLF4TM/vorK3VEUHz374dAYa0wib0UFUFwu3IFVtcRI2Dhv+02/H7VKoSvys2Mt261f/7k5MDzTITCDvfeq4S1/fYbCur8+9+Y8zk5eP/ECQi6BQVQtuyteGovhw+jYEpBgevOoTWlpRhvfVXqiGBc0uth/HK0n6laCgpQ/VBLL39AAIwmDRpAyJo6FZ6KjRsRFSHP+UOHEM1w+jTm6bp1+Fzjxo7f/1atlII78+cjlN1kgmElIAD/f/VV7K2lpQg5PHgQa8FvvyGEtF07jLm+KHVEKKbx559Q6Fipcz2nT8P4wYDKSuzFzvTJbNAA645aB4EQStHA+gJ77DTm/HnkklmK+zVHdjY23CeewGZEpJR77tYNXqBvvoFgOmWKS4atOVVVsJoePIhSuwsW4AFzNOzou+9gkd2wQV34iE6HBTU/H2FHUVHwEo0YAY/dv/+Nz8l5Ih07Oi9kxsZCebXn3tcH9u5FuGr37jAoOOs9M5ngtf7yS3jnunUzf8zSUngJ+/SBYLltGwTAf/3L9jmMRjRL/vRTGGt+/BHhlvv2wRO4cCGEwuJi5fPBwVD+HnsMRpjlyxEKs2AB5uzTT7sm5Ovxx7FR/vKLb1T/yslRQgHrQwicNdLS4LHr14/onXdcH5bpDg4exLo7ejTR228TXXstjBv9+7uvrH5FBfbLbt3gvf/jD6Q6dOyIdSEsrH7OPZMJiveoUfU7t85dHDmC9I4ZM+q3EUsmIQEOjEmT3Os9O3MG8uA11/j2vFfrsWPFTkOEgDVMkpA/Ys/GMWsWFoF16yCspqejN8cXX8ADpLawgz0YjQg/bNXKNeWO8/KwmWdloe/XU085fiy9Hpt0y5bw/li7tidPwsNJBAUrPx8C79ixREuXQtheuBChk0ePIm9j8GDnE+gNBiwgPXrU70XcYMDi3bQpFOqyMihejnhra5OTA4UpNhaL9FNPqYvTN5kg6PXrh/GsWgUFz1xIaH6+oiwNG4Y5Y86qX16OOZ6TA+PMggVEL78MgdZoxDwLCUGo6IYNRA8+iN6JWpOYCI+PK9YIrSkoQHjyxIn250TVVX77Ddfkv/+tO16UykqlQMojjxDdeKOnR8Qw7icvDwbBgQOxH9RnysuxB7dp4/4+qwYDzh0WBrnBV406ahW7eix+aoPRiLj1gAAoR2FhCDWzd+Lcc49iSWvYED/r9QhpdBWlpQiP69PHNSGDTZui2uArr8BT4gyBgQiru/9+VKwcN67m700mXHNJgrcwOhoFV0JDoXDrdAgHfe899LDbu1f52759tamKFhCgJCmXl0OR8dUFxBFMJhgkTp6Exbx7dyh2WhUyEQKKXFoavF/VGyvbws+PaNo0/H/rVhgH/v4bOZt33IFcn9JSKHMDB2Lct90GZcnSOUJCMM+io/E3qakwFuTk1PTYPvkk1ogPP8TmPny4U5ehBrt3Y+727avdMV1Jo0awXntbMr8nmTULxrvevTFP1PR08naEwL1etgwFsBimPhIZiRSPEycgD3lbLzl3kpQEGaFnT/efOyAA542P175ooDfCHjs7KSqCB6q4GP8vK8Mm1rWrc80o9XokcXfvTnTnne7b3PfsgUA7dar3hwFVVECI7dcPYXVEuPbZ2fBadOuGUBu5qXh1srORU7FyJfKhcnMhgEdGalfIQ0ang+dWFrjtVe7S0vD3c+Yo1TG9GdlDd/48FNrISHxvLUMeMjNx3PR0KOvOFoDIyUGY5ebNmE9LlkBprKhAbqSjyuiKFQipO3Om5r2rqEDe0T33aLe5Z2fD8zxyJNFLL2lzTFeSmIgQ1VGjvH+t8QRff43iH/PmIZfTF41CQuC5GjsWgpQvfgeG0ZKyMhjgiGAodEeBq/x8pJhER0OJycnBnhQWVvMVHg6juavR6WBQbdcO0VGewGSCXNW6tWJYFAKyd3k5XkFB6lpxeQr22LmIwkIkxIaHwyIZHY1/mzRx7riBgQjBdDdduqBCXXa29gqO1jRogPylp55SFLlDh7BohYcrybTmhInPPoMCMmsWrDctW+LlCkJDkTOZkoKQJLncuFpKStAr6scfoQjcdJN3hnaWluK6+/mhlLpcRKZlS20FOiGIXngBx/zyS22O2bw50XPP4dpWVCj9ARctcs7DeN11RC++iDn6xRfK+/LcTU1Ftdjly53bQIqLcTw/PxSk8AVOnsQ64648K19jxgyExhcUYK7v34/QTG989i2xahVekmS7fQ/D1AfCwlAnISnJNSkvMiYTnA5nz0KxCwhQjItGIxSYrCxENMk0beqe0MSgIBh6PNmiyc8P0QMBAdiHEhKgzMn1LIgwvroQDs8eOzuRJ4Gryqe7GyHQ+iA0FA+4t1NcrORX7duHGPZ+/eCps+QF0OtR2nnAACTRuwMhsJCfPAnPlVwS3xqnTyPH8umn4aF6/30o3T17ol2EK70c58/Di5mbi+sVGooNaeBAKCVykZAGDbAopqbCYz1tGt7T611n+UtLgxd76VLf6Lv01FNEr78Ob7jclF4mKQm5fX36ICzYEYSAhzExEXlZAwc6P2ZXU1ICI4AvtWTwFCYTnq877oCF+/77MY+83fu1aRMqfE6eDEMMe2UZ5mpKSrBnarlfFhcjvaS8HPt2ly6QecydQ6+HF7G0FCkHvlBwS2vy82F4Dwmp+QoL06YWgKvg4imMapKTISROnGh/w0i9HorW8OEQPNLSsJg0bKh4c7QmNxfeikGDEK7Yvr31z//0E9EttyC3bsYM7cdjjYwMXJ/wcFxfS9cjJweFNRo1IvrkE3iUhIDVPj8f4/7kEzTDdiQ+3GBQXhUVUIhLShAWIUlo8lteDiU0OBihE2VlioVr/34odDING6LcePv2rvUoyMtTXp5z5dHdSVkZ8qXCwhDTX3vj3LcP17lzZxiI7BHY5VzS/fvhDfaF/KX0dOQX3nEHe3HUIj/7H3yASrsDBkBpcjYyxFUUFaEnYe/eRG++6Z7wLobxNeQiHg0bIiTdmoOguBh7tVyAbNcufN7PDy9/fxjJhg/HvnDkCAxB9kbM6HSotTB4sGuMbseOQVnq0UP7Y9c3OBSTUU3nznig7VXqhIDSkp+veGwSEvB/Iiw+4eE4bp8+9jcmt8aGDfBk2VLqiCBUduyIPEJ307YtvndZmWWlLi8Pity998IyLxfekCSlcXFqKvqp/fQT0c8/W26nUFWFBb6kRAkBIYI13WCo+dnwcNyroCB8LjDQ8obQuze+i06H+xkV5R4Pwl9/oQHxf/7jG0odEa77Bx/Au/jWW+ihVZ1Ro6CULV0Kgf2uu9QdVwhU2KyogFfQVzwikZHwWNf3qnD2ID/7w4ahqNaePcjNNJc/7GoqKvAMmkyKQNmpE6q/bt6MNWH2bHigLXkJGIbBHta3L/bow4cVg3h1SksRvZOeDkPvtdfimWvdGs+g0aj8KyuGfn5YKxxBr4cMt28fIqG09OCVlEB26dpVu2MytvERUYlxJf7+Sjn3K1fgTVAjNKakoEdL377KYjB9Oh7m4mLlVVqqnVBeVARrV0YG/q2+uJkjMRFC0euvey58tlkzpZCInJ8px5ofOQIh/ZlnrJcE79wZOXd790Kp+/lnFCho0UL5jNGI0M38fGwC4eHK7+Rk4YAA3KsmTWqGHNhazCMi3F/Ry2RCnprBYL/RwdPMnEl0ww1of3DLLVcrNUFByG/4/HMIw2o8bwcO4L7Pm+c7Sl1cHOba9dd7eiS+SUAAohLmzEHi//ffw3PvjvCp3FyEko8di1zmhATld5MnQ7H78kvsAZmZaG/AMIx12rWDYS8hAe2WBg2CcldWhgInFy5gfe/WDS9Jwl49aJBrxhMRAcPb3r3YY0aP1k5WOn0ax+rWTZvjMerQRNyWJGkqEb1LRP5E9IUQ4rVavw8molVENJiI8ojoFiFEmhbnZrSjsBAl4NVU+MzJQQnfNm1qWmMCAiDIVQ8Zkq3MOh3C/Ryt9FhRAauS7ImaPRsKkrWiMwcOQMHxhgITJhMU51OnsIjn5aFRetu26ipFRUVBWcjJQTGY1auRY9WhA65xXByEsaFDr05S7tzZJV/JpezciaIsy5b5jreuOu++i03NnAdDkpBLmZWFfKTdu6EEWvLIFBRg8335Zd8IvyTCfN+xA887e+ucp1EjCH6//YaiP64kPh4eZT8/nO/jjzE3ZU+BPEe/+gqGF3c2G2YYX6drVyh3ckGVPn1gPCkqwlrZo4d7c72iotBb7vBhGJuHDXM+MqCoCAb47t29O2+tLuJ0jp0kSf5ElExEk4gok4iOENF8IcSpap+5n4j6CSHukyRpHhHNEULcYuvY3phj9+uvyEl74gnvT2Z3hPh4CNMjRljO5Sovh9AdEAAhU23ozYEDRJcuYdGwN0/MZILSWVCAHnaNG6PH33ffoZl0q1Z4tWyJY1fvS1dc7D2Ch9EIBWzPHghMXbpAObPXG5aSgjxDvZ7ojTfg9dm5ExuCt8ay5+bCm9uxo+3PGo3oI+fnhyp7vlysKDER39tcNcjiYnhh/PyIFi+G16N1a3jl5DDjuDj0wlu+3HcqSsplpIVAeHBd6M3maYRAKPa117qmDUplJdEvv2ANHT4cxZtuvVWJ5mAYRjuEgLwVEQHDa2EhPPGeLC6VkgJP4rBhzj/3Bw+id/C0afWzQIsrcFvxFEmSRhDRMiHElH9+foaISAjxarXPbP3nMwckSQogoktE1FzYOLk3KnaffUb0zTeoVHbbbZ4ejfYYjfAelJWh2Ie50u+VlQgh6NXLPoWkshIet4ICVPKzx4ovK5xDhig9zM6fR1ERufGlTKtWCA+aOxdWow0bvKsSX0kJCiOsWQNvlKM92bKy0PswKgpCmE6H72nJ4GA0YqFt3dq9uTpybs6bb+JeqGlaLHsgJclzfW+0QAgosv37Q5G3RlUV0auvIq/wnXfwbG3ZgkqpUVHwmniLgcIWiYlE69ejAqilfFDGMWJjYSTRKmdYCBR0+PRTrA/XXXd1XijDMPWDK1ewZtuSD6qqIHNUVtZ8tWgBw9PBgzDAc8Es7XBn8ZQ2RJRR7edMIqqdxvn/PyOEMEiSVERETYkot/bBJElaTESLiYjaOduF2AUsWgT38kcfIQxx/HhPj0hb/P1hrdm5E6EB11xT01tiMCB0YMQI+48dHKzka8THI7RSTRPb8+eh1HXtWlMJ6tgRYY1GIwSd7Gx4BCsr8fupU7FIeYtSZzBAYI+Px/wxmfDdHJ3mbdogNO/yZczJpCSiSZPMf/boUaLX/gmQ/uYbokceQTiXpc9rRWIiFLolS2D9P3gQoYc6HfLQzGEwYIzXX69tk3NPIEkoPKEmxyAoCD3wysowZ9evh7eyWTOit9/2HaWOCOPv3t27m736Kj/9RHT8OLy3WsyJL79ESGWPHggNj7EpNjCMezEYkIP+6KO+0ZbJl4mKwr9ZWcidDQioqbgNHw6FLSkJ0WvVkSTIec2bY33y4qL7dRotFDtzYnnt26nmM3hTiM+I6DMieOycG5r2+PmhsfHlyyjsMGaMb+b/WCM8HF4SuYGjXIQjKwsCxZgxjodWBQRAKTx6FIm1TZrAw1YbOZ/D3x9jiIpSCoDUxt8fVqLqhUSIEKrpTaSmouXCzTfj+o0c6VzseWEhFtewMCgAf/yB0L65c/H70lKEDg8ZAgG7USOiBQugOBBBiThwALk0zjTlNofBgPvy0UfwmhqN8BR+9x28AStWIAzVXNjoli0QNLt3v7oPnC8yfDiUu+Bg5d5YQ74XN9yAORIU5FsKklzl9RabwfaMIyxeTLRwIUJ477vP8ePEx8NoMGMG1qObbvKdojxM/SIxEdEeL72EImJdu/p2JIclUlOR2tKuHdG330LmKi3F8xkRgT08IgJ7Z8+eULyaN9e+8bkQqMqZnY1jBwXh3yZNlDWibVvsS8HByqt2Ze26mK7kC3AopoPk5+Nff39YMWQrR12iesXJkhJ48Ro2vNqL5whCwLvWsqVSFMVgwDnlfmuhoYjPJlLC+XyRtDSE4S1ZgoWyTZuav6+shEJmT8iaToe+NpIEr7G/P9HKlfByNW+OXJn166HE/d//XV1S32DAxvH111C4Vq3SJsFZCCiYX36JNhOShM2oute0qgrhvpMnw+Na22u7aRPm2ptv1p2NYeRI3OPExLrznSzx7bfwRD//vG/nRnozL76InOOff3Ys327NGoRvjxtH9Mormg+PYTRDr8c6kp8PpaZ3b6wvL76IAlS+alg/eRL77rp1iC764APIBtOmwWnQti0UN39/yEXVufdeVMdt2RI5t//7H4ymgwYh9NGZPUYIGISnTYMhv0OHq43mdZV9+yCjzZ3rnfu0O0MxjxBRV0mSOhL9P/bOO0yq6v7/nzMzu7Ozs7v0YhdEjWKJgtiwNxQVO7EbQROTGGJF7NEYe9QYGxKNRrFHUSwgxqh8YwMEFQwKUlQW2N6mz5zfH2/Ob2aXmd0pd+q+X88zz87O3Ln33Dtnzj3v82nyk4j8QkTO6rLN6yJyvoh8LCKnici/exJ1hU7//vgBTJ6Mieqjj1pv9cg3djtE16JFWDWy2WB9sGKyplTUUmcKbToceO5w4BG7ClWsou7jj+F6WF4OS11XUSeC61tXlzimsSvBIGL0QiFMzEx9wBtuwA3gyivh7nrEEbDQxbOKORwikyYhg+ayZRB177+fmQW6pQXWuMWLYV0NBuO7mZaXQ9QtXoxY1TPPFPnd79An1q4VOeaY3BeSzzYXXICb8YIFsKCWMscdBxdoirrsMXkyxoy2ttSEXW0tFlp23BGTycsuy14bCbGCe+6B+PnPf2AR+vRT3DduuAGLiP/8Z/Fkfd64Ed4bTz+N+77DgfvdmDF4/9FHo3OEBQsgZJ1OLP62tGBxsKUlWv7nnntgvWtsFDn/fMxJt9wS99ejj4boSzXGeckSeIv88Y+ow7rPPojBLfXx3OfDnMjvR5hIUWfy1Fpn/BCR4wSZMVeKyHWbXrtFRE7c9LxCRF4SkRUi8pmIDE9mv6NGjdKFzmefaX3EEVovXJjvlmSHjg6tX39d65df1rq2Nt+tKR4iEa2fe07rAw/U+rzzur927e1av/aa1u+/r3U43PO+v/pK61de0Xr9+vjH/eADrdeuTa29S5Zovf/+Wl90kdZtbal91nDPPVqPHav1rFnJnUc4rPW992p9ySVa+3xa+/1an3SS1jfemN7xC5nmZq0rKnCupcyiRVqvXJnvVvQe6urwSIb33tP66KO1vv327LaJEKuor9e6pkbrE07Y/L2ZM7Xu21drt1vr6dNx7ytEgkH8/dOftLbbtRbRetQorR94QOsNG6w7zpo1Ws+YofUZZ2jdvz+Oo5TWRx6p9eLFPX/+rbe0vu46PH/nHa1DIa3//nfs56abrGtnoXLDDTjXOXPy3ZLEiMgCnYR2ytgVM5sUsitmLK2tsLR8+CEsKIVows2E5ma4/qVaoqA3E4kgFlMEK4vGqpaItWtRP2bXXeGa2BW/H1bTAQOwsmSKkFvJ3LlIbnLDDen14a++gvUvldgqkw7/xx+REXLZMtR/K0Wr1tlnY4W5trbIVwMToDUS9AwdurnrL7Eenw+u12PHRseaeDQ0INb17bcxaOOtWgAAIABJREFUvvzxj/E9BwgpNC6/HPeDL7+EC2ZXfvgBY8177yED78MP576NPWFcJRcvhtXx3HPjn4uVhMOIoZ09G67x8+Yh9GXWLHjVxNYZbm+Hl89jj8HT5pNPop5DWuP6Pv00rHbZTraWL1aswNg4cSIswIVKzsodZJNiEXYi+AH9+c/INnjGGfluDckXWiO+bJ994AJZVpbYjdT89IyI+vxzCLxDDolmg9QaGUGXLsW+jjkm+26pc+dCzKfSj2fPhjtJurGmr7wCt48998TNudQWR0Rwcz3qKAT/F0NikY8/hrt0bE3InvD7kezIuAqR7PLggyLvvos+1TX7byCAseLVV7Hd2WfD1ahYY5JI72L1aiTQOucc3FMTEYmgf++5J+6769bB1bgQqK9Hu264IbNER5lgShvddx8WT9eswT3eLNZPmoQ5xhVXoFZq10XHjg5kSt+4EeI0mwv8zc24d5x/vsjXX8P904TnmL8jR0Lsv/EG2mqF2NQaAnj8+MIuz0Nhl2MiEaSK/ugj1Lpj7Q5g6sulI0aKMWHKiy+i4PgvfiHy+9/H32bVKvjOt7ZilWzSJMS9vPce4s923BErapWVGEibmzHY/PznuUl5f8MN6MfPPRc/Y2lXvv8eq5BnnSXy29+mf9xFixAwXsgDayaEwyjRMXIkrCeFyk8/4Ya5bBniLq+9tmcxoDWyNO6+u8gee+SmnSQa+1xR0Xms/L//w+Rn4kSRCROwWs9C46SYOO88JAf67rvk++7kyUj8sWJF4SwumYRwVmeuTAdT6/aEE7AYK4KFu6eeQimqRHzzDUTz3nsjsZlVi0ORCDJ777ILYtDfew/f9733op5rbEK9cBiPXXYRefxxlGXp2xcLphdcAA+GMWMgQkeNSt4rZsYMiNapUws/jjCXyVN6HfGKO9tsEHZnnYVVkSeegIWlN9PWhqLKBx+MVasXXkBh6u7qtgWDuG7PPosf8SGHYOWuGGrXhEJIPlJfn3h1LhyGYOrbF+nF99sPiXgaGzHA/fKXmKzdfz8EwJAhGKy23jp3Vqzf/U5k/nxktUwmY97GjRBk55yT2XH33juzzxc6djtci+rqclsgPhWCwWhGtqOPxupsMjdxrxclYIYNy34bSZSqKkxir70WLpYDB2Jh5MMP0d+22w7fH0UdKSaWLIH74tVXp9Z3r78e4TB9+kCAHH541prYI5EIEphddBHmhYWAserPmgURtXSpyIUX9rxgvMsuWIT+5S/hqjl2bOJt6+oQMvLWWyJXXQUBWVsr8te/4nsxjzVrYHVrasKc6cQT4QpqEsBdeWX3bfrgA3xOBGPdxx9jjimCcICXXuq+nYaPP4ZL77RpPW9bLNBilyIffojVz9NPjz8xmz8fj9//vnAKY+ea5cshVEz9rr32wgTkH//A5N9uRzr+iRPhuufzwad71ix89qqrMChrjYnm/PnILFkIK16JmDsX53rffYlXCo1rVGMj/iYqvu3xYLAZNAixeTvskHvL5RNPYIL/t791L7jq6zFI2+3FZ13NF5FI/LIX+SQYxI3y0EPhDjx4MH6zfj/cZEeOxOJMIkzdQq3ZD3JNRweKN1dU4Pf417+K7LQTxku6XZJiZMYMeI4sW9Y5HixZXnkFv4nf/Q735Hz8Dsx4OnMmMj+XAqtWwcK3apXI8OGd36utRZbORx6BKB80CC6yf/sbxODVVyOjZ0sLFgJralBS4cQTRU4+uec8BMlQW4tjTZ2KNt5/PzKoxpuraw3r4E47oT1WHD/bJGux4y04RTwePLrWFTGMHYvaKkuXwtLUm9iwAX8//xxiTGusVO2yCywA11+PQcHUpampEVm4UOTmmyHuhg2Du6FZ6TrySFjqbrqpsEXd//0ffNMrKxMPDlojDuaxxyDoEok6EezniCMwuX7sMQRcJ0MoBNe59vaUT2Ezzj4bA25P9WtuuQVB64VofSpUzj4bK8mFtKb2/fcoDP+//+GGXVWF1x0OiIXm5sSfbWmBtejrrynq8oHbjZX0jRuRpnv77fEaRR0pRlpa4FK5cmV6ok4ESYWuvBKiYvz47sevbPHPf2IcnTAh98fOFsOGwTtg9GgYOETguj9lCu4bDzyA2Pw99oD30osvYh5z4om4t9TWYv4cCCCp0/PPY45olajaYguIxM8+QzmXqVPRvni8+irmpv/+d3GIulSgxS5FTMzYmjWYSMcL0vV4UOBwm22welHofrtW8Pnn+JFedhkG42RXi1eswA9vzJjEP64lSzAoFGLCicWLkTBn+HCsTnVXh27xYrinHnRQ8vtftAjWksZGWAITXaNwGAPlPffAhe7HH2ExjVfDLhVWrMAAHs+lYcECWKanTCnM76ZQmTMH7ipnnpn/seGbbzCWjRuHhZl4Qj4chmD79lusbnYV8Y2NiBk85pjuFyxI9tAaY0suYnAJyRaRCOYCu+8u8uSTme/v739HWMSIEXD7GzEi830mg8+HsfTkk+GpVEqsWAE3y5NPRhbkGTPwvZ13HtwZc3WNeyISgcV3550RAnHVVdEwoOZm5MEYMgRz12JZBKPFLkuYFenXXkPnjqeLKysx4VUKN9tSJRLBasf//gff6BNOwOpMKqvFI0bAKtfdiklzM3ygfT5r2m0lX3+NVaJ7700s6pYuFXn9ddysUhF1InCDtNkQLPzcc/G3ee01uE4OGoTB6+CD4bfe1JTaseLx4IOIs2tt7fy61iimOmQIVkdJ8hxzDIp4f/hhfo7f2gp3Fb8fYm3pUqygJrLO2u3o59OnY9tYQiFY4M8+m6IunyhFUUeKn0gEibiOO86a/U2ahOQaGzdinmGFN0syzJ6NcTbTuPNCZMQIzG+ffx6Gi/PPx33k738vHFEngnnTbrth8fLpp+FZZbjmGixkzphRPKIuFWixS5OmJlilwmEk+6io6Jy+HqUOYXp2OHp2aSs2tMak7oEH4Ppz2mnZO5bJjllICSd+/BGWxPHje/bPfustxA7+7nfpJ9T59ltYQl0uWIQHDkTduN13RzxeczOsLsYCZKwsixfDLSJdy9CKFXCFveUWxPoZli/HTXPqVAh6khoXXog4kNra7MbihsP43TQ0wKo2bhz6yuOPIwvZDjvg99VTv4xE0Jd+/nP8Bs3vcOFCxJBMmdJ9UiRCSOnyr39hTJk9G27ZRxyResKzQACLl2edZX3iuf/+V+TAA3Efu+EGa/cdj5NOgjvgDz/k3ysjW7z/PjyVttsu3y3pmbo6LHzfdBNCCx5+GFa8e+/Nd8tSgxa7LNOvHwafBx9E9h3jCrd+PSZBSmEl+1e/grm6gPVzyqxdi6BUjweBqaeemt3j2WyI2XvggcK4jlqL3HknkhS0tSUWdV4vVouOOw5lADK5We20EwamF1+EpWzZMqxCLVmCG9b48Z1vIHY7RNkzz6BQabqMGBENhK6txWtaw73h2WcR/ExS57zzsKL76qvZO8batYhr/eor9L1163DMHXaAIN9xR/STZPqlzQbr8WefRV1vRNAPTj6ZWRcJKQU8Hiw4JXOfbW8X+ctfsFAUDGKxe+VKZCY84ojU7teBAMaqCy5IPqY8FQ44QOTuu3NTY7ihAYu5Z51VuqJOROSww4pD1Ilg/hKJwPPk4YfR7j/+Md+tyh4UdhlQVoYBbL/9YNYNBDCQ+f143+nEQPXpp0hMUOxEIhArTieem5ooubCiud34cZprm098PgRFX3yxSHV14u3mzUOcQFMT6tNZwYknIiPryJEIMO8uU+GOOyLV8qhRuPGmSySCc/3zn9G/58xBhqv+/UvTjSEXHHwwAtGzEX/xww+Izdx6axxn4EB8V9deiwWCsjK4TKfzuzWu6H4/hP7334vsvz+TphBiFU1NmFOccw6sIrlCa7hBTpmCseHKK6Ox08uXw+ohgpjaP/4Rk+MrrkCYwRlnwHNkp52w+DN+PGLPzz0X84TujvnGG3CZu/tuxB0feWR2zu/KKzFuPfFEdvZvqKiAi+Lkydk9DkkNmw1GmCefRJ81CcJKEd6OMyASweTZ4cDKe20tBsRY8XHKKXCXe+ABDIjd7WvxYginQmXmTPhRDxwIM3YyxautYq+9EMdjpcUuHI5aHpLF74fl4/bb8d3GIxKB0B83DsIq3cxe8Rg4EJmclMLfnibUP/sZJvm3345sY+lgt8PVduFC1L4xBT27SxRDusdmQ2zCe+/BsmYFpi+/+y7Et9awqG6zjTX7F0GR2smTMfl84w3EWWSyaEAI6cyMGVgMfvNNLAhHIrjfLlyY3ePedRdcKn/5S/zfvz8WgETgeTR4cNT17uabES/+ySfwPoh1z+7TB/OhW2/FnOHAA5F6vitffily1FFYrLTZcL7PPpvdheIHHsACVyrzrM8/T22Mfu89LL5mmriMWI/NBmPLHnvkuyXZhcIuTXw+TG59vmjdslAIlplYYWezIVOQy4W4rER88AHS45qCi4WA1qiRtGABRNDIkYixsdnyE+v2zjtwa01UaiIVfD7cyF56KbXPvfACJuRr1iS+Bm+8ATdNny9+1tRcs9VWsA5l4gp60km4qT/8MCb2U6bQSpMp55+P39hTTyXeZtEiiKiOjs0T2MSyfj3iBdatw6TiD3/IjhuQUvj9Pf44nl96KVaoCSGZEw5jjD34YCwOXnstRNGMGXDrr69H+MP771ubTOzdd3GsiRMRhyaC/x98EM9vvx0WtVGjsMj35ZdI2rXvvvH3Z7PBtXL2bJR9GjVK5KOPou//+99YrF20CPfKr75CyEK25xV33IEwhmTHLJPtceJEfC8rV3a//erVKG/w8MMZN5WQtGHylBSJRDDB8nhgqTOxdiaubu5crFiNHt3ZTS0UwqD98stwkTrkEMRILV0KS0owiG3uuQfufbmeLHm9iMXaYQecxyOPIHZuwAC0afx41N7KJytWQFCNHZt5XTszoT744M0LbSaivl7kF7/ATerOOzd/f80afHdao61jxhROshcRrDquWZN6Zk7DggW46d93X+dEKiR9Dj8cv7tVqzYvbF9Xh8nUH/6AzLNvvgkXqA0b8BgzBmNKSwvcSh5/HKvfw4Zlv92rVsE1upTdWQjJNbNmYRHtpZc6JyTz+XAv+egjCAePB4vI++6L8fzggxFH1l1oQCJWr8Z8ZYstYIGz2hNj5UpY/J54Au33++GieccdiD3v39/a4/XE11/DzfWZZ+ACmohIBOPr6tW4d552GuYK//1v4vmH1rC2br+9yNCh2Wg96c0weUoWCIUw2fJ4ojFfxgpis8HVcuFCWOb8fqyyGxwOxCg99BCsPiJYOfriCwwa1dVYFbrjDhTVzLXeDoUQNP3tt0ibvdNOmLQNHozUsIcemv6+03UB7MqIEWiH8fVPl1dfRar5Cy7AdX7mmeRcMh99FHGUl166+XuBAG5cb7wBMbzvvoUl6kQQA/Hhh+nHKY4ejTqFnMxbxzXXIE7V7UYigjPOwGQiHMaEZ/x4jA0jR2JiUVWF1fK338aY8/bb6HdOJ1JQ50LUieA47AeEWMuDD2Lht2sJmYoK/MaPPBKeQrNm4ffu92ORcdw4LAytW4eQjo8/Tu54Xi8WcEMhuGFmw71+hx0Qbz54MBaJP/wQ86Ybbsi9qBMR2XJLiLVrr+1+u7vvxgL8kCHIpfDkk7AwXn11/O21FrntNnwPFHUkr2itC/YxatQoXUiEw1rX1Wnt8yXexu/X+ocftP7gA62vu07r2troe8Eg/u/o0PqTT7RuacH+6uqi29xxh9b776/1rbdqHYlk71wMPp/Wjz6q9apVWjc2Wn/MSETrm27S+pFHrNn3a69pPXWq1l5vep8PhbR+8kmtX38d/y9apPVtt2nd0ND95zwerSdO1Ppvf+v8us+n9dtv47v9/nt8t4WKz4f2LVqE8/B6tV62TOuZM/He999r/c47WgcC+W5p7yIYxN+77tL6pJPw/JhjtB45EuPAmjWdt49EMHZorfV//6v1ypW5ayshJDs0Nmo9dCjuR6nQ1qb13Lla3347xoZLL9W6ulrrpqaePzt3rtZlZVq/8UZ6bU6FSETrtWuzf5xk+POfUZDqo4/ivz9/vtZ2u9ann9553jJlCj73r39t/pnPPsN7M2Zkp82EiMgCnYR2oitmFmhqQiKV5cvhNrFkCVarttoK7zc3Y5XtwANFjj++82cjEZQScLlELrkEK3KZuh2KIAbHboeVMZbaWqxEnX22talrAwGc47HHwt30scdEjj4aq2SZZIhcvx7phH/2s9RjiEwAtzlPUxsvHMaKpc0Wv21aR11fwuHObrLLluH6TZ6M1O/FwJIlKNZ58cVwr5w3D+nv589HTMTtt1uXxZOkx1lnweVnzRqsMH/xRTSRASGkNAkEEJaRieWsvR1Wu/33R43RiROjCU5i+fJLJHb78UdrEywVAx4PPICGD4d7aOy1aWhA/F9ZGSx0ffpE3wsEMG9bsQJj8vbbR9+bMgXznPXrN3erJ8QK6IqZR5xO/LCPPx6i4O23kaWuowOuetXVcOc77rjNP6t1tDbaCy9AMGzcmH5bIhHE8p12GibyItjvX/+KiWP//iJXXWV9PZIHHsB5r1yJm8qvf434w8svx/mly9ChmOh++WVqn9MaouXll/G/SfxhspjecUfi+jnz5iEhRW1tVNR98w1q1ey6K0RRsYg6EZRI+M1v4B68334Ici8rQ12au++Gm8rrr+e7lb2X1lZkh/vmGwjvhgYsvFiRNIgQUng0N2Ncfv/9zN0hq6oQh97QgP1ecAFieZcvj26zbBlc6++9t/eJOhG4v994IxY4Z8+Ovq41soKuX4+asbGiTgQLni+8gHnVxIkQeiIQ4889ByFNUUfyDYVdFjAWNr8fVqU//AHCqqkJYurHHyFO4mUVtNtFJk1CPZfhwyEmLroIK0Sp0t6OjJyPPopJ+xVX4PXvvoM//b/+BevM+PEQkF9/nf45G+rq8DjvPCTamDgR4um885Ai2VyTZAzFq1cjaPzHHxGfePfdSNxx660ou7BmDdIpNzR0v59AAKJ60iQM2l2vu9uNwPN46Ym1hkVuyJDORZi/+QY3ylAIJQhKBZsNMZ9Ll3Zff4hkh//9D3Ea33+PxZ1RoxBzO2+eyJ/+lO/WEUKywYYNiG3v6lGTCYMHwwvjscdgwdtjD5GbbkJc3S674F564YXWHa/YmDQJWaunTYsumt13Hxbf77kHY288hg/H/KO2NloG4d13Me8599zctJ2Q7qArZpbYuBECZsCA6GsbNmClJ5n6b599hon11ltDkHV0YNDZfffkjh+JQPBcdBHcuk4/vbO7QSgEa9ratRB68+ZhYPr1ryEq00llv3o1LHIDB+JmEi95SCSC1bBp0/BIJKauvBIB4NdcA5eJa6+NZg4NBmFlGjAA7qp9+iDxS2Vl/HY9/zzO9aqruncxbGpC8piuKZzr6mBlHD4cwenNzbgx+v2lmeo9FMJ3EArBksci5LmjtRWr9uPHR6+71iiN8MwzSM601175bSMhxDoiEdx7YucKVrNhA+7NM2fi/8cei3rw9GZefBFj6/z5mK/suy+sbq+80nPyM48Hi8bffovwmTlzIPYYxkCyBV0x84zTiR99rG4eMiT5ot4rVsBqssMOSGM+ZozIttvCXfCtt7q3psydi0G7qgqi5owzNh+kFi7E6uBRR8Etz6T+f+qpni1g8fjqK4jCQABCNNGgaLNhm9ZWCDtT3LixEZaxm2/GZ3fYAfsbOxbujq+9hnTvc+agBs6wYRBZM2ciO5jLBevjBx90vuZawyf+sMN6HnDnz8dx2tvx//r1uDZG1InAvfTVVzePtSslHA6s6t5xR+faQyS7zJ+PRYMJEzqLaVN+ZMYM1JFMJoMrIaQ4eOstLOB+9ln2jjFkCNy7586Fd0o+slEWIqedBu+IvfdGOMXUqbDGJZPRurISFs/DDoMb5sSJFHWkMKDFLkv4fBArAwakl/zE748OErGDzNVXYwJ46qkQUMuWweplLGy1tRByu+0G98V+/Tbfd3s73L0OOACrUwatRX76CTeB66/HfhK5I8R+pr4e2w4ejJTtJklMd9TXw6o5fDiscosWwUI0ZgySrvR0zf7zH1gZr7kGAralBSJs1SoM0n/4A67/l18iPsnl6rlNXi8e/fph8nzzzRA2zz+PQTwQwLHa20vL/TIRb70FC3FvjMHINcEg+v2OO2KCkIiHHoIL9Zw5tKQSUgoccwzCIFavjpZPIrmjrQ1usNOmYc6UCt99J/L551hgvu46JKwhJFska7GjsMsSxuWwqgqDRjrMnw/L2qWXRoWb1hAr/fpB/J1/PuL1jj0W7194IbIe7rZb9xO/piaIp3jui+vXQxj99BNcFeJZGb/6CiuAXm80Ucr++6ceODxzpsg//gHXs5NPhlUyGUysXtci8E88gdWzYBCuJ/X1CB7vaSUtEEB805ZbYoL9xRewiv7yl3BnfeQRXLOpU1PPxlnMNDXBcjx2bL5bUrpEIuivSJbd/SLEM89A2D39NOvIEVLsLF+OhdlbbkFdN5Ifpk3DnOnss/PdEkISQ2FXAJhC2ukGRH/xBSbVp54af7Ln80VdMxcswDZ//3vnFLxdWbUK2595ZvfuGB4PVqIOOQTia6utEID9ySew9tXVQQAdcAAEVDoxeSKYyEYi6YmlJUsgfCdMQMDzkUdiX089BTF64YW4YX70kcgpp4j89rdos82Gc+/XD26eW24pcuKJEHcPP4yMkG1tKEp6yCFoW1MT3Ed33DG98yxW3nkHfWzatM0zhBFr+OgjuBD//vfJLQJpLfLpp+iPRx+d/fYRQrLDpZeKTJ+OWPchQ/LdGkJIIZOssKMzTxZxOuG2F4mkJ3z22guP5ub4wq6iQmTcODw2boQbRzzXy1g6OmDt6mm1v7ISoqa2FmLR64XVa6+9IIDGjEkuwLgnlErfAub3Q4BFIsic2dSEVbfrr4+266CDcE122gn/L1+Oc2ppwf8nnADRcv75cAvdcUesnIbDuKbPPYdzv+SS3nnjPewwfNc1Nen3Y9I9W22FZDzV1cl/ZsoUuAF98YX1pUoIIdmntRXeKhMn9s57CyEkO9Bil0X8fiQi6dcvuRiveHz+OeqmXHNN5nFdDQ2wutjtqQmy9eshnHbbrbAShmgdPY/Y58kQCkEIVlXF/25mzoRr5gknYNve7Dvv9SJxx6hRsNASawiFkMzg0EMTZ3RNxIoV+D5+9jNY/Bi0T0hx8eCDsNJ/9pnIPvvkuzWEkEKHWTELgPLyaAHsdNl5ZwRXJ5r4hUJwj9ywAdarf/4T2SK7Eokg/izZjE+xDB2KYqaFJOpEOp9HqufkcMBFNpHgPvRQlInYZ5/eLepE8L337Vt433+xs3Yt3FxXrkz9syNGIIusmRTOm2d58wghWWTePKTXp6gjhFgJhV0WUQriLhBIfx81NSKHH47Jn88Xfd3rhaug3y8yaxZcsurrsV04jBS+990HwWcSM5xwAgQL6Zktt4xfY683ohQKr+6xB6yYJHPWrUPJjmuuSb42ZVdOOUXk5Zfh0nXUUUhAtGKFte0khGSH115DPDchhFgJhV2WcTphVQuH09/HTz/BF3/JEuxLBFkan3tOxO1G8pJjjsFE8cYbURMnEsGx+/SBO+f99+P1nXe25LRIL+T99+GSaZICkfRoaEAm2XnzMq8ndeqpIt98I3LXXbDc+3xwm9640Zq2EkKs55xzRO6+GyWCCCHESpg8JcuYemx+f+pxNIZttkHB8Q0bUDR66lSszpv9xWbdNMktRozAQwQZIocNQxIWpkgn6TJ2LPriwIGwGKcbN9qbiUQg5iZMgAXUCioqRK66CllfKytRdPfjj5EBl7F3hBQWgQDmA5FIvltCCClFKOyyjMMBsZWJsFMKljaHA+6BwWBqlrdhw/AgJBNcLvS/uXNRXmPKFFiMSXKEw4hx3XXX7NQFNOPLbbehzqTDgYx706ezVAUhhYDWKET+0kt4TgghVkNXzCyjFKx2fn/mA/kOO2A1Pl2BSIgV7LwzMqS6XJycpEIoBAtatq1oO++McWLxYpEXX0QMLiEk/7z1FhbH5s3LvFQQIYTEg+UOcoDHAzfIQYNQa46QUuCrr0Tmz0cheONy3Fv5738h3A4+OP77X38NN+jttsvdhE5rHO/nP2eSBkLyTSSC36LHg7hYzgUIIanAcgcFRGycHSGlgtaZJwYqdj76SKSxEcXCly/Ha88+K/L223geDGJC9847WK3PJUrBcjdnjkhLS26PTQjpzMyZWAz7058o6ggh2YMxdjnAbke8i9/P5CWkdNhjD7hk1tVBuJx0UjR5T2+gtRXn3doqcv75ELla47fucOD5HXdglf43v8H7uXa/Ou00lD2ZPVvk7LNze2xCCAgERG64AWPBGWfkuzWEkFKGwi5HOJ1wwdCavvVW4fOJtLejeLaDPTkv2GyonbZkicghh4gMGJDvFuWGDRtwrpdfjv4nEu2DEyfibygkst9+Ilttlb+4WHP8l16isCMkX0yfjqQpb7/duxa/CCG5h0NMjigvh6jLpFg5AVqLtLXBBS4QEOnoyHeLejcHHihy9dXIkPnJJ6WfUMXnQx3JF1+EuLPb42/ncKBw+K675rZ9sdhsqHX3zjv4zRBCckt7u8itt4oceijqzRJCSDbJSNgppforpd5VSn236W+/BNuFlVKLNz16ZRg/4+ysIRIRaWrCJNXlgmD2+UpfTBQ6RtS99JLITz/luzXZIxxG3biTTxY54oh8tyY5Jk7EpJKF5QlJng8/xIJIpouxjY0iu+8ucvvt9NYhhGSfjLJiKqXuEpFGrfUdSqlrRKSf1npqnO3atdYpR5eVSlZMQ309JoaDB3OAT4dgEDfJcFikpgZiwutFxtEBA5iZMd+EQiINDSJDhuS7JdkhEhF5+mn0tRNOyM0xPR6MFVYUg/f5IEpPX18qAAAgAElEQVQJId2zZg3KEvh8Iv36iZxyCmLjDj88Nbf/xkYkLmIdWUJIpuQqK+YEEXlq0/OnROSkDPdX0rjdECUeT75bUnx4vRDGWmNiXVWFCa+ZqPp8+W0fwYSnogLiZ+3afLcmO/Tti0WFWIJB9E+/H8/DYWssyB0dWLRoboaozIRHHhEZOhRuYYSQ7nE4kHjo6adFjjtO5IUX4EY5dCjczpPl9tvhik1rOSEkV2SacmKI1rpWRERrXauUGpxguwql1AIRCYnIHVrr1xLtUCl1sYhcLCKy7bbbZti8wqKiAmmO29qQTIFWu57RGlkHOzpw7fr37xzTZLPhunq9mHDzmuYXpxOirr5epJR+vkuWoG+d1GXpSmtYKeMJL5sND7tdpLo6tcLkPh9W+svKIBY9nswy6u69t8jkydgvM/MSkphFi/C7/uc/8f+55+L+MmcO4mrNwuzxx8PF+cor8fuPlxTlD39A5uBBg3LWfEJIL6dHV0yl1DwRGRrnretE5Cmtdd+YbZu01pvF2SmlttRar1NKDReRf4vIEVrrlT01rtRcMUWwqt/QABHCCVb3aA1XFr8fQrhPn/jCzetF3B3dMQuDSATfUzCYmpjJFsEgHokyU4ZC6GMuV+fJmdYiGzeiXz3+OM7rkks6b9PRAQHWty8EXCQCi10kEn1uatn17ZtcdkwzRpSV4djG/ThTF26tRVatEhk+PP19EFLqjBuHAuIrViSuNxcIiJx3nsjYsSIXXSQyYgSen3yyyLHHYiHnnnuQlXbs2Ny2nxBSmiTritmjxU5rfWQ3B9mglNpik7VuCxHZmGAf6zb9/V4p9R8R2UtEehR2pYjTicluezsmeUx9HB+tMWH2+yHo3O7E2zqdmPB6vRR2hcJf/4o0+6edlpvjRSKIiykrE9l6a5FXXoEQOuggFATefXe05W9/Exk5EqUZli/H4oqxAIfDcMH68kuRnXcWqa0V+fvfUYNu8mRM5roKv/Z2HNPlSiy6IhGIs+ZmiMjq6sTbmjhSux3WaZsNbWxsRP/OpGzCtdfie6mry1/5BUIKnRdeEFm5svsi4uXlIs8/j+f19XDTnDULrzmdIocdJjJ3rsiUKRR2hJDckqmseF1Ezt/0/HwRmdV1A6VUP6WUc9PzgSJyoIgsy/C4RU1NDSZ7TNOfmI6OqPtZd6JOpLM7JrNj5h+bDeIplwkDWlpEXntN5L338H9jI1x4RRAjs+eeEFU1NegjP/4o8sQTyOTpdqOA97Jl+MxLL4l8+y3af/rpEIhlZZv3Q58PYtDEeybCZoPlzeWCEGxujt9PTfIZpTqXUXA6ITg7OjLr30cdhd/U22+nvw9CSpXWViwELVkC1+VkGThQZMYMkfXrRT74AFb9b77Bwsy0adlrLyGExCPTrJgDRORFEdlWRNaKyOla60al1GgR+bXWerJS6gAReUxEIgIheb/W+u/J7L8UXTENxsVw8ODEdbB6Kz4frk9FBTKSJeN+Zj7Tvz8z/xUKfr/IunXZF3hLl4pssQV+R+Ew+kAspu6hEUY2G1bcN2zAti4XkovstZfImDGwzA0a1H2/0xor9ZFI8i6SxsLX1rZ5vGg4DFEXDmOi2NVaYFw+M3E3DoVwnY48UuS559LbByGlytSpInfdJfLZZyL77JPZvrQuHFd0QkhpkKwrZkbCLtuUsrALBuES5XbD1ZCAYBATZrsdE9xkXVW1xoqpEYNWozUm3eEwJsjhMCbzPVlrejMzZ8IKduON2ZvgBIMit90G8Xj++Zu/b1x6PR70jcrKqOtuV5qbsd3gwT2nNDdxcD25CcfDxIQad0u7HfsKBhMLN60hRMvLNxeuqfCrX4k8+yzGHitKKBBSCqxcieyVZ54p8o9/5Ls1hBCyOZbF2JHsYOJyOjo6x/nkg3AYlgRT8DtfmFgkpaLxRclian0Zd8xMxZbJxmnS14fD8bcrL2dcXyIOP1zkgAOy16dCIfSRSy+NHw9jvkPj0ttdbJsItvF48Fvo2zfxdiLYxmZLL1bN5cLvvbERixgOB/pZv36J+5JSOFZ7O847lVpasZx2msj06cjw1zXDJyG9lSuvxBjy5z/nuyWEEJIZTN2RR6qr8betLb/t6OjAo74eloNAIPdtMBkwjStdOhPXigrsx4qadi0tUde98nJM+vv0gUVl8GDUM1KKcZLdMXQo+vgbb0CMWM2bb4o89BDi5rrWlostk+F29yzqRNDn3G6Iu+7aGwzCYud2p7+AUF4Oi7Tdjv316dOzBc1YBjOpRXfYYejDL7+c/j4IKSX+/W/E5153nciWW+a7NYQQkhkUdnkk2YlkNtEax3c6MfkNBPIj8FpacLy+fdO38DidsKJ4vZm1xevFNXG7EWvVrx+Eg9sdTWRhrDUmgQaJz8aNIvPnI1mJ1Wy/PdKMd7XWdRV1qdQ3NK613S22tLdjm1RdMLvicEDcDRyY3L7sdvQ5jyf9PudwICX7nDn5G3MIKRRCIdSaGzZM5LLL8t0aQgjJHAq7PGMmkiaDX67x++ECWVkJYTdkSGeB19iYfYFnMmC63ZmlYVcKVjtzTukQDiPWqqxscytQV8xk3BSsJZvzs5+JXH89RJhV4bxtbRAmI0ci42UssYlSUhV1IhBPbjfEfTC4+fvhcLTsgBWlSkwil2RJpc+Fw9iu62/h5ptFvvsufXdOQkqFr74S+f57kbvvZtItQkhpQGGXZ8xE0ueLP5GMJRt5bjyeaLkAETyPFXh+PwRec7P1xxbBebe0wBLWk5BKBpcL18nvT/2zWiOphUhy2TgdDrQ70zT0pYxSEBYPPYQU4Fbw1Vdwn2po6Py6EXWmRmSqos7QndXOuEFmaq1Ll7Ky5PpcIIAEKc3NSLrS2hq18m21FYTxX/4S/7ORCM6zro6LFqR08flQBuX770VOOSXfrSGEEGugsCsAulrtIhFMzEyK8/p6ZHxcvz49wZKIcBg3t3jFlWMFnnH/svLYxl2usRECKdmyBj1RXp6+O2Z7O657nz7JWzPcbnxfVsT1lSpVVbhGPS1chMM9W1qbm5GQZepU9M1YYkVdnz7p9ydTFNzn62ytjkTwO3C58mvtMtczXh83JRXq63H+JiFLezvcYltacJ3nzEF2TCMOzWJIUxPGmdZWuKk1N/f8vRFSjFx+OcaSvn2Z2ZgQUjrQGacAMCKqtRWr67HxM0phEmlcDBsb49e5SgczMezO/dFmwyTZ50P7Bg7M/CYYDmMCGQhgktynjzVubSLR7JgdHZj8Jrtfvx/CwOVKzR3U6YTVtaOD6eMTYbcjc2UohGtcXY2/Dgf64FtviRx8MPrFjBki55wjst12cBfcccfo97F+vch992F1fd99o/uPjanLVNQZ3G7sr60NyUZEolayqqrM9p0p5eW4diaTrTnXSATCzetFv+zXD/3f5YI4a2+PJkq65RYIY62jrtChUDT7ptuNz9bVYcwZNMi63yghhcChhyIRFmvNEUJKCd6qCwS3G+KtrAwT3379otkXBw3CquKAAZh4mULGmWCSppSV9SwSlUKbTDbATPD5MFkMBnFOZvJpJUZgJWtFi0RgmbDbU68paCbCgQAtG92htcj994u8+y6sSTffLPLll+h7q1dDmG2xhcjee2PxYPVqkaefhphbu1bk8cfxPR1yCGLrDKEQ9mdi6qwQdSJRq53fj4cRQE6nNYsqmWDqJ4ZC0d+jqf/o9eK32rVcSFlZdEwxou2aa1D7r64O++zbF2Kvb19sb7fjM+EwBCPdjUkp0NQkcuutIhMmYBwihJBSgsKuQDC12/r3x8TMuHvFTlIdDog7rSHu0k0QIoKJYCiUvHWqshITvdbW9CZ4sa6XNhsm75kkSukOMylNxh1Ta4i6cDh9kWnOg6UPEqMU3J4GD0YfnzABmeiqq5FcZbfdsLBx6qlYyNhpJ2Sr22YbfI8tLRAzxx0XtZiZRYJQCN+dVaLOYBKktLVFk5DkK7auKy4X2tbRgetTX4/2DRjQfWkHhwPXyVjrnnkG9QbnzMH179r/TbZckylWBL/hO+8UOeEEPCekmPjd72Cx/t//8t0SQgixHgq7IqOsDBPjUAiTqnRX0T2eqNtiMiiFZBShUOrxa+EwhKiJf7LKlTQR5rz8/p4tmx4PBEJ1dfouOXZ7tDh6JmK71DngAJGxYyEeDj4YIi8RDgdEXVmZyM47o4CwSa6jNYSeic8cNCg7brDGRToQwKKESZZTCJhyCyYurqwM1yHZ9tntSJ4ydy5E8bnnwlr6zjubjylVVfhtLFgg8qtfiWy9Nax9s2cjTo+QYuHFF0VmzhS58UYkTiGEkFKDwq4IMfEzgQAmdamKO60hQuKt0HeHcRVta0v+mCY7n3G97Ns3N7E6ybhjBoOYsJsC5JngdkevK8kesa6XZpEgm4lMjKXaxNYVUpIFtztaC3PAALQzVY46CoLtuefwuz72WFjwYjOOrl6NuMdDDxV56imRM8+EG+1f/iJyzDFWnQ0h2WXdOpFLLhEZM0Zk2rR8t4YQQrIDk6cUKS4XrFGtrbBepOKG5vViopqqK6Sx2jU0YGLdkxgyVkWlsj8B74rDgUdHB9oRieCcI5HOD5vNmoycJlbRCI5CEgC5wuuFODD1CK2+Bj5f53IUuUhWoxR+WyYbZiFhs3Vv9UxlP7/4BZLSTJ8u8vbbuL6PPSay5ZaIa1y9WuSmm+Aqu/XWWKAZORLF510uWFcJKVS0Fpk8GWPU00+zhiMhpHShxa6IqarCw+OJ1tdKBo8Hq/vpuB46nfhce3v3bofG/VIE1oRc30hNUpNQCOcbCOC5SDTLaFVV+paOeMdzu3GMbBd0L0Ta2yG6TKKNhobo9bYCnw+LBHZ79lwvE1FRAffnUhfr5eWIP3rzTVizb7kFrms1NahBePPNyFbq9eKxcaPIYYchsQ0hhYxZsLjrLrh2E0JIqcJ1qyKnuhqT6bY2rLz3lNzBCI/uEiz0RE1N1B2uunrz9yORaHKXfIg6Q1UVrkeuJuQuF0SNyZ7YG4gtNVBRAUuO14vXNm5E/8jUhTEcRoKbsjJrym2QnnE6RX76Kepyba65iTlsacF3MWeOyP7756+dhPSE1oirO+ookd/8Jt+tIYSQ7EKLXZFj0pQ7nZhs9WS5M5ntMrF4lJdjEt/evnlyEq1hWTGZCvNdIyiXIsBYCX2+zMtR5BrjpmrcVpP9TFNTtNSAySrqdsNFsKICCw51delbMU3W0kiEhYTzQdfrbYqeK4XvfswYxN198UV+2kdId4TDIrW1IvPmIY6UtRgJIaUOh7kSwJRKqKiIxtzFS25ikns4nZlb0aqrsb9YIWkm+oEAJuEVFZkdoxgxFtNCLX1grF8NDbC6btyIWnG1tfhr/m9shEBNlCTHWGV9Plhwu8Z42u3ok/36Ydv6evTLVLOGejzI/FhTk//6cQTE1rfbuFHkqqtEHnkk360iZHPuvVdk112ROGXAgHy3hhBCsg9dMUsEs5Ju3OLiWTgCAUzG4rlPpkpZGaxTxlpjatyZiX62atQVOiYlvseTmbtrtjA12RwOrF6bv7GPYBALAD4fvtfKymh2SJFoUhxjle3O+uty4XqYfunzJe+eGwpFs5YWSv04ApxOxDqWl4uMG4dYvHvvtWZsISQZPB6UT/nyS4xNNhv+mudnnilyxRUYc7bdNt+tJYSQ3EBhV0KYrJWmqHIk0rnodqq163oiNnGL3R4VeZmWDih23O6oxauQMimaRDJuNyxs3VFTg/Z3dKAvtbVhMm/cK7WGQEsmltBmwyKDywWLbn09rHndueka66+INVlLifU4HPgezz9f5F//Enn+eZGJEwtzQYOUFpEIFpsuukhk2TLcc8JhPCIR/N1nH5EddkDNOkII6S1Q2JUYSmFiZbNFsxMaFxSv19o09KaGlnE7dLmiRaR7M05n1IJZXm5N1k0rMG6zyQhvswDgckUFoXGLtNvRp1J1jXQ68bnGRvTL/v0TC8P29mjtw0K5fmRzlBI57jiRoUNFZs0SGT8e44yJ+yXEaiIRlOfYay/WoyOEkK4wxq5EMcksgkFYSMyk3moXyaoqiEink8ktDCahTSQCEZNqXFk2CIchzGJdKpPF4YBgHzIEYmzgwPTj3UxmS7sd4i5eQfdAAFZBl6v3uvQWEw6HyFlnicydG32toQGxnIliNDOhowOLVqQ4mDVLZOVK6/YXDuN+w4UDQgjZHAq7EsblgoUkHIawczisT0BhtyMDYm+o85UKTmdUWDc2ZmeCmwqpWOsSoRRcMTO1oNntEHfl5XC37JqAp7kZiwU9uYuSwuHcc9HXZ83CeOB2YyHBSnGnNQSdKSnSG+tFFhsvvyxy0kkiBx1kzQLX44+LfPABioxfdlnm+yOEkFKDwq7EcToxiXY4Mq8nlgibjaIuHqauWyCQX3FnrHUuV/5qCnbFZsOig8nk2toarYkXCuG6MTV58bDnniInnxyNr+vTB8+9XmvEXSQSLa1h3MlN6RZSmHz/vcikSVj0e/11fF+LF6e/vzfeEPn1r5GBVSnecwghJB4FMs0j2aSsDKvoJPdUVkYtDc3N+XFX7ehAGwotqY3J5GrqLwaDiOFzu3tnqYxiRikkUAkG8V1WVUUzZLa1RcVeOn0/HMbCSDCIfZgMqV5vNFkUKSwCAcTBKSWycKHI9tuLXHihyKuviqxahXEwFRYswP723hvWOkIIIfHhLZGQLON2R60XxjKVKyIRCLuKisKsA2cm/FVVEHUmno8UH+3tSCt/773R16qro9lzE9XX7A4TIxwKwfJjRJ1ZMIkXo0nyz7RpIp9/LvLEExB1IiJ/+hP+79MHmSyTZfVqkeOPR3mNN95g6RNCCOkOCjtCckBVVTSDaGxMWbYx1rpCri9mynT0789YzWKmqgqucgcd1Pn1dMWd3w9RZ0prxFpxy8rwMP2bFA6zZ4v85S8iv/2tyCmnRF/fcku46z74IDJazprV874aGpB11e8XefttZF8lhBCSGAo7QnKAES8uF1zTTIkIreFqZtwQvV68Z5JDZDJpjUQgIp3OwrTWdaWionBiAEl63HSTyE47ifzwQ/Q1U4LFiLuerNZaY7uGhs6JdmJRCla7UAi/HVI4/OxnqG14zz3x3z/3XAi7U09F7cOufPaZyHvvoR/stZfIihUir70msssu2W03IYSUApxGEZIjTBkEE3OXjFumUhBl5eXRR7IxRR5P4VvrSGnh9UYn9g89FH3diDuto4sa1dUQZvEeIujr/fsn7u8uF35DHR3dF7snuSEUErn8cpErrhD5xz8Sb9evn8i778K98qyzRNavh4BvaRG5/nqRq6/G4tfChSJ33omFglGjcnYahBBS1ChdwH4so0eP1gsWLMh3MwixFK0xcdEak9Z4D61hiQgE8Ii1SjgcsMJVVSUuPaC1yIYNEIWmQD0hueAXv8DEvbZ2c8FlMp8acReL3Y6+bcqyuFw9u+U2N2MBY+hQJlHJN19+CTfcRx8VOfPMnrf3eOCaaeof/vznIosWifzvf4inGzgwu+0lhJBiQim1UGs9uqftaLEjJMcYt8yecDgwuRWBW2Ws0OvowMTI7Y4WiY+lowOfKbRMmKT0OfdckRdeEHnnHZETT+z8nun7Dgf6pxFyDkd6sZWmXp7Hw76eCUuXimyzTfqJi775Bq6S332XfAbmykqUQXj/fZGddxYZNgyv0+WSEELSh2uchBQBNhusdNXVsMANGoSYtPZ2WOba2qIFgLXG6+Xl+AwhueToo9E/H388flFqpaKZYl0uWOfSTZhjkqgYt+NsEwohJraUCIfhPrnddiLTp6d+fuvXixx6qMjkyamX1XE6RcaNi4o6QgghmUFhR0gRUlaGWJVBgzA5amuLCjxa60g+KStDRsTZs5EVsaUlu8dzuyG4AoHsHiccFqmrQ1KXAo5gSIn6epQeuOcexLL96ldIWDJvXs+fXbsWMXF77olx5+qrs99eQggh3UNhR0gRU1aGBBMmc2BbG2KYysporSP548YbRe6/X+TNNyHysomJxfN4snscU6ohFIofI1iMXH014uK23lrkk09EXnoJ1v6jjhI54QSR5cs7bx+JICbupJNgZbv9dpF994UQHDkyP+dACCEkCpOnEFJC+P2YdFZVMVMgyT/z56NAtc+HxBhnnJGd47S0oN8PGZI4oVAm+HwijY1wHzVxroMHZ+dYuSISgfXx4487x0L6fCIPPCBy2214vnIl4uFaWjCmbLcd3MEvukjk4ovxPyGEkOySbPIUCjtCCCFZ5aKLRF59FTXJ+va1fv/BINwkq6utL+8RiWDfSsH1ORwW2bgRlsJ+/aw9Vq5YskTkvPNQRy5RspING+BOO2mSyIQJeG3WLJEPPhDZbz96BBBCSC5JVtjRFZMQQkhWefhhCAKnU+SSS5Bww0pMrcdsJFFpb4eY69MH4s7hgEXc64WFvNjo6EBJio0buy8pMGQIRF0wCCF36614/ZBDKOoIIaRQobAjhBCSVcrKEIO1eLHIU0+J7L03nluJ2w0BZqXYCgYh7CorO4sZU0PSxN0VE5ddhti5Z56BBbInyspEpk0T2WOP7LeNEEJIZmQk7JRSpyulliqlIkqphOZBpdQ4pdRypdQKpdQ1mRyTEEJIcbL//kjSEYlYn0WxogJlQaxKoqI1CqDbbJvXdzOvFVsilZdfRhmKqVNFjjgi360hhBBiNZla7L4WkVNE5MNEGyil7CLykIgcKyK7isiZSqldMzwuIYSQImSPPeCO+e67IqtWWbdfpWBZ8/msqTXn8cBiV1MDIdeViopoqZFiqG23Zg1iHceMEbnllny3hhBCSDbISNhprb/RWi/vYbMxIrJCa/291jogIs+LyIRMjksIIaR4ufBCCLEnnrB2v5WV+Ftfj0djo0hTE1wmW1ujdR57EmLhMLYvL0eSlHgohbg7rbFtIRMKiZx9Ns7ruefgXkkIIaT0yEWM3VYi8kPM/z9ueo0QQkgvZJttRMaNg7ALhazbr8OBrJgOR7TmXCAA61t7O4RdSwsyPjY1wSIXj9ZWfL5vXwi47o5nEqlku0B6qmgtsm6dyL33itTWiowfLzJ9usjw4fluGSGEkGzh6GkDpdQ8ERka563rtNazkjhGvNtiwnBzpdTFInKxiMi2226bxO4JIYQUGxddJHL66ahvN2aMdftNVO7AJDkxcXFeLx7l5RBnTidEnM+H16uqINx6oqoKwrG5GclIuhOC2SIQQDmJRYtQymDJEpEnn0StvSuvFNlhByRAIYQQUtr0eNvSWh+Z4TF+FJFtYv7fWkTWdXO86SIyXQR17DI8NiGEkALk+ONF1q4V2XLL3BzPCK6yMljiamog8Do64LJpt0OktbfjebL18Gw2uGQ2NUHgud3ZO4d4aA3X1mefxbntuqvI0UejiPgee6CsQTLZLwkhhBQ/uXDF/FxEdlRKDVNKlYvIL0Tk9RwclxBCSIFSVgZBdeKJcBnMNTYbxNuQISg0brPBTTMc7tkFsysVFbD8tbbmPpHK449D1N1wA0SpKSmxzz6wOFLUEUJI7yHTcgcnK6V+FJH9ReRNpdScTa9vqZR6S0REax0Skd+JyBwR+UZEXtRaL82s2YQQQoodp1Nk4UKRb7/NXxuUQoKUgQPx6Ncv9QLcsYlUmppyV9tu9WqR3/9e5JhjRG6+GeKSEEJI70XpAq6uOnr0aL1gwYJ8N4MQQkiWCIchjMyjmDGxdm43hF42MbfuZ55BIhpa5gghpHRRSi3UWiesGW7IhSsmIYQQEpfly0VGjBD597/z3ZLMqayEqOvosK5Qejy0Fpk4UeTPfxY591yKOkIIIYDCjhBCSN4YPhxWrscfz/6xVq+GdeuOO1DnLhvU1MAlsrk5eyUQgsFogXRCCCHEQGFHCCEkb1RUwOr06qvZE1siEFlnnAHL4LRpIltvLTJzpvXHUUqkf39k1mxstD6ZymeficyfjwQpV1xh7b4JIYVDKATLfwFHTJEChMKOEEJIXrnoIgivf/4ze8eYOlXk889FXnhB5OuvRSZNQubI+fNF9t9fZMUK645ls0HcaQ1xZ9XErKEBtf8uvhiTvmKPSSSExMfvF6mrg+U/m27dpPSgsCOEEJJXdttNZL/94I6ZjdXp114Tuf9+kSlTRE4+WWTkSJGHHhLZcUeUCIhERLbYQuS550Ruu80aK5uplxcMYnKW6XlFIiLnnSeyfr3I889j/4SQ0qOjA4s4dnu0jEoolO9W5QazGNbUJOLz0VqZDhR2hBBC8s7kySLffCPy3/9av+/ycpQEuOuuzd8bN07k00+R9OTTT0Wuv17krLOwYp4pLhdq5Xm9mKxlwl13ibz1lsh994mM7jEvGiGk2NAatTRbWhA/a8qviOS2jEo+8fmij8ZGkQ0bIGyDwXy3rHigsCOEEJJ3Jk4UqaoSefJJ6/YZCEAQHX64yDvv9Fzn7f77Re6+W+TFF0XGjxdpa8u8DVVViCNsbU1fLC5ZAsE5caLIJZdk3iZCSGERiUDIdHRgkal/f7h02+1Ry78V41EhozXO0eEQGTIEorasDF4VdXV4dHTgWpHEUNgRQgjJO1VVIrNni9x7r3X7fOcdxNZ9+GHyn7nySiQm+c9/RA47TGTjxszaoBQmZg4HJm6tram5emot8tvfYqL3yCOMqyOk1AiFkDjK70f9yz59Ov/OXS6UUmlvt8aToFDx+3Etqqogal0ukQEDIPJqaqIWzfXr4QVB4kNhRwghpCA46CCRV14RmTWr8+sNDSIvvyzym9+I7LyzyO23R2MxElFbK3LiiUiUcvTRqbXjvPPQhmXLRMaOFVm1KvVzicVmwwTF6cTkbMMGxN0lEzezbJnIokUo0WDcsgghpYFJkhIOY4xwu+NvV1MD611zc2larIy1zm6HoIvFbofYGzwYNTvLyuCaSnEXH0e+G0AIIYSIYJX6r39FwY+Cu6UAABeTSURBVPLycpH33sNjyRLc+KuqIP7OOktkzhyRU08Vef99ZLeMXeFetUpkr71EbrpJ5LLL0mvL+PEi8+aJTJgg8tVXIsOGZXZudjusbqEQxJ3Hg0dFBc4rnpuozyeyyy4i332H5C6EEOvROj+W8GAQi1YOB8YGRzczcpsNCzv19bBa9e2bvTZrDZdHpRILTasJBHA9uloru1JWBgFsEqyIbC4EezsUdoQQQgoCpUTmzsWq7JZb4uZ9wAEif/yjyBFHQMCZbJB+P8ok/PznIg88AIF3+eXIrjlxIrY56aTM2nPAASIrVyIByjXXQOwddFBm+3Q4MCmrrsbkqaMDAq68HK/FFh2fNk1kwQLU3rPRv4YQS9AaFjK/H7+9QACujn365LYdbW0Y8wYMwMJPT5gxoq0N40RlpfVtCoVgFQwE8H9FRXJty5S2NoxxyZyTKSdDcRcfCjtCCCEFw+DB+PvuuyLDhye+0e+0E5KdiGDi8X//J/L66yJDhyIG41//ytzKJgIXqOZmlEyw2SD2lMpcaNnt2HdVVVTgNTRgIlVTAwG49944f5Y2ICQzIhEIOfMwca52O35rJmlJd1YzKwkEICqrq1MTTlVVaH9LC4Sele31eLBfEYxBra24LjU11h0jHoEAHjU1yVshu4o7rbMjdIsRpQs4f+ro0aP1ggUL8t0MQgghBY7HI/LMMyIPPyxy/PEif/qTtftvacHEY8YM1Nu76y6RQw+1bv9aw0XT1NV7/XWRCy7gSjQhmaB1VKCIQDg4ndGHwwGRt2EDfmu5iGPVGos4oRAWslJdJAqFEJdn3BIzdcmMRDC+eb0Qi7HJnvx+JC/JpsdAQwOEXTrHMdlEAwG0u5TFnVJqoda6x2I3dO4ghBBS9FRWilx8scjixdaLOpFo7MeAAbAIHnaYyAkniCxdas3+lcLq/eDBqFf3m99ARHo8vaN+FSFWEw5DNHR0YHwYMAAW/f79O1vn7Hb87/XmphC43w8hUl2dnmByODAeBQJwYcxkfDDJW7xetGfAgOh1qarCvj2e9PffE8Eg2mAyYaaKsdyVl8OzIpttLRYo7AghhJAkOeUUkeXLRe68U+Sjj0T22AOxfuvWWbP/jg4kfRk1SuT00zFZManQCSHJEQzid2MsOX37wkKXyLpVVYX3sl0rzlgQ7fbMrEuVldESCC0tqYs7046GBvw/cCCEXez1KS/Ho709e4tL7e2ZJ2mJzTpMcUdhRwghhKSEyyVy9dVIrDJlCurejRiBLJobN8KKFwymt+9bb0WphocegmtS375Ry0NrK613hPSE1wtRpzUESzICKtZql+5vNxl8PlgFu4qodOjTB4LU48H4kGwZhGAQVrr2dlybQYPiZ+UVwf4jkeyUFgiFsF+3O3NXT6VguTPirjcvhFHYEUIIIWkwYIDIX/4CC94554iMGYN6e7vthonlk0+KbL+9yP77w9J35ZVICpNo0rFsGRLCTJoksu++mKxUVsI906zONzdT3BESD2OFamqCO2F3giUebnd2rXamfQ6HNbGzSiHut29fWCbr67t3JTW14urqINb69cNnuxNVJg4xG1a79nb8taqkglI4JxMfmAu32kKEwo4QQgjJgGHDRKZPxyTr2GNFnn8eYmybbUQOPhir3suXi/ztbyiWPnCgyGmnQeCZVXatRS69FNvefnvn/dtsWJ2vrsYKd2NjaRYpJoWNiYcqRCIRCDpjhRo4MPU0/cZq5/Nlx2rn8cD6nkr2x2Qw8YPhcNT9tCvGNbWtDaJy8ODkxKVSGJNCIWu/+1AI18Pttracgom5E+m94yTLHRBCCCEWMWxYtMzCkUfiYfB4UJNu9myR1auxGj55sshPP4n8+td476GHYGnoikmuYrfDatfQgAlMLmpMEWLcgY2lp5CytYZCUQtNTU3U8pYOpvxIW1tUIFhBJIJ9lpd3rlVpFU4nxo2GBgg4kyHSZNs1deLS+e5cLny+vR3lWKzAZCnNRgF0hwPn2diIsbJfv/wUoM8XFHaEEEJIDqisRCmG44+PvrbnniJbbSUybpzIY4/BDbOnfdhssE7U13fOYkdItmhthThxOND3bLbsCJRU8XoxeTcZazNtk80GcdfWBiuXVTUkOzpw/ayIrUuEcT81giYYhPUuGIQ4q6lJbyHIJDdpbYXVLtNrHA7jerhc2Ru7TD3Q1lYI0urq7BynEGEdO0IIIaTICAQwgROJpvsmJBt4vRBz1dWY4NfXY3I+YED++p2JF2tvh/gysVVWEImgrl15Oc6x0PbXE1pD2Hm9UTfuTC2s5hyczswsmVoji6fHA3fQbC5KxV6H/v2tszbmC9axI4QQQkqU8nLEESkF9yufL98tIqWIKV7tcERrjQ0YgL/5SlBh3EJj4+msFAjGamfqzWWKSTxSU5P5vpJBKbhi9u8PC54VbrM2mzXxh21t0di6bHsamOtQVoaFiWxmOy0kKOwIIYSQIsThiE5qGxt7z8SF5I6WlmhcnXEhtNujlqeGBgitXGEKasfWp8uGa6NJwZ8oQ6bWsAQ1NMCS1dCAa9XRgbaZpB2xbodWuXUmg1KwUFkZg2vi4Ux8XKoYC2tlZW5Fbv/++NtbkqnQM58QQggpUswke8MGxJPkwtWL9A58PoiXqqrNRYnDgQlzQwMeAwdmXousO7SGoDDFvQcNyq5QMhaqtjYINeNyGgqhHV4vRILNhvfCYViiYqObjKjSujRivExRdY8nmsgpWUwCF5cLrqG5TGZit2NhoqEBljsj9EoVCjtCCCGkiLHZMNFqbcVkvNhjSQxaY8IcO1numhagrKy0J2n5IhJBfJLDkViUlJdHxV1jI55nS9yZuKyKip5rr1mF2x0Vk0bQGNfMigq85nRG+5/pr6EQrOfmb3V16SQ4MgXROzqSt7qZa2i+u3z8Xp1OCMqWFgjMXFkM80GJdDVCCCGk9xI7CY2dbBYrkQgEQ0/upQ4HrJQs+2AtJgtmT9YNpxPWkKam7FlDAoFoXJbVNeC6w8TatbaiDXY7RFplZfz+phT6o8NROosrXTHn1tERjbnsDo8HYsr0k3yOS243vsf2drSnELK6ZgMKO0IIIaTIUQqT3qam6CS4WDHJMUxdsthJdOzE0FiVGhoo7qzE50MfqqpKLuulyxVNspINa0hHR7SOY66FgdsNS1x5OR7FvmBiBVVV6CN1dRB5TieuTVeR5/Hg92kyaRbCtevTB+KuuRnuvLmw/OYaCjtCCCGkBKiogGuiiWUpxklLMAihpnVydcnsdrgBUtxZQ2wWzFTiwmKtIW63dd9DJIJ4NlO/MdcYQUmilJfDpdLrjbplikStYE4nFmWam7Ftvi11sZgi7fX16Of9+uW7RdZThMM+IYQQQrqiFFakIxFMsIuNQAATLhEk40jGVcpYA4yVL5cZGkuR1lZcw3RioYwAam21rj1GNBSzBboUqazEQsrQofj9ud3oN62tsOQ1NWGRKZtxl+lSXo6+6vXiUWrQYkcIIYSUCOXl0RgYKy0n2cbnw2TQ1ElLJdmEEXe5sNyZNPdtbZunTu+aEbHYXL2MBcbtTq/wuMMRjfWMl0kzVbRGe8rLc1sqgCSPKatgYgpDIZSkCIeTi8HLF8adtLkZfatUktuI0GJHCCGElBQ1NZgUW2k5ySYeD0RZbF2+VIm13NXXZ8dyFw5DfDY3Y8JaWdn54XZjwmisF+nW+8o1WsPCa6wsmbgemjg4K/qez4frSGtd8WDEfU1N4Yo6EfRR44bZ3Lx5tt1ipoQ0KiGEEEKstpxkA61h8fJ4YP0yqfMzmQzGWu7q6yESrbLceb3RYt01Nbi+3bkqmnpnptB1oaJ151ICmcZDxZbe8PszyzzY0YH9lWqGSZJfHA64rjc3Y2GjVGIpKewIIYSQEqO6OppqfMCA3Ccv0BoTe+OWFYngYQRd7Aq5FYLC4HTifBsaIO6qq7H/dMVVOIxr6PNBIA8YkJxQrq7G8Ts6CnfCGInASuf3YwHAqqyTsaU3Bg5Mb5/BIGIu85EJk/QeXC78ttvaotk9ix0KO0IIIaTE6Go5yYXVIxzGJMkIOiPeHA5Mzu12tCv2YbdbX3evvBwCzLhNiuAYJhYoWSterJWuuhriJ9l2lpfjmIVqtYstKdGnj7XujiaTZHMz+oPLlfo+jBtrZaV17SKkK0ohUdDGjeivAwcW3m81VSjsCCGEkBIk20XLtYZlxefDIxTC63Y7JvMVFfHrW+WC8nKRwYOj7TMiraUlmmCmvDxqQez6CIdhMTIF0NNxZzVWO1MTrlCILSnRv392RL/LBfe21lbsP5W+Z0ocuFzFk/yHFC+mBEJDA/pr3775blFmUNgRQgghJUg2ipaHw7DGGcucscqZFOIVFVELXb5RKlpYuroawtPrRdsTJfdQKmpNTNVK1xVjtWtvz18dtlgiEXxnzc04p4EDsxd/afpeY2M01jNZvF70KyZNIbnC6YwuhMVm+SxGKOwIIYSQEsVYplpaYP1IdcISa5Xz+/FcJJrUoqICk6J8i5aeUAoipqwMgiMUwrl0dQ21WpDm2moXieDcQiGI8Ni/pjyDsUJm2xpm+kYqwlZrTK7Lykoj3okUDzU10cWgYiYjYaeUOl1EbhaRXURkjNZ6QYLtVotIm4iERSSktR6dyXEJIYQQ0jMmrXdDA6wnqbjeaQ3rjiniW4hWuXRxOHJTuyrXVrvGRriQGmw2nKeJLXQ4civEa2pQsLq9Hc97wu+HCC12dzhSfBgrc7GT6bD2tYicIiKPJbHtYVrr+gyPRwghhJAUsNvhdpeKuAuHsW0wCDFXiAlAioVcWe1CIYg6txsishDEd1lZNN7O7e7ZSujxoJ+lk3CFEJJhgXKt9Tda6+VWNYYQQggh1mOzRZOANDZGrXDxCARgZQmFIAKrqynqMiHWamfcIbOB+U7dbnzP+RZ1BlPuoaei5aEQXH4rKwun7YQUG7kaqrWIzFVKLVRKXdzdhkqpi5VSC5RSC+rq6nLUPEIIIaS0iRV3TU3xxZ3HA+uSSa5RzEkEComqqmhB9u4IBuH+ajKMJovW2Hd5eW5cTFPB4YDY9HphNe7ogEW4K+baMGkKIenT489fKTVPRIbGees6rfWsJI9zoNZ6nVJqsIi8q5T6n9b6w3gbaq2ni8h0EZHRo0freNsQQgghJHWMuGtshLgTgdub1ijS294OcdCvH1PNW4kpfpwo1i4UwvU3YltrfAfJEghALBVqMXRTaLxr2QlTFsNmi2YkZL8jJH16FHZa6yMzPYjWet2mvxuVUq+KyBgRiSvsCCGEEJI9bDa4WBpxF4lEs15WVqJgNV3hrKe6Ghar2Fi7cBhizxTkjrXs1dSkVkxdqcK1sNpsOJ+uZSeMyLPbWeKAECvIusFeKeUWEZvWum3T86NF5JZsH5cQQggh8YkVdy0teK1PH06ss0ms1c7lgnhrb4egqayE6LHbIXw8Hoi9ZLL0aQ2hZCxfhUzXshOxBeRNzUFCSPpkNAQopU5WSv0oIvuLyJtKqTmbXt9SKfXWps2GiMh8pdQSEflMRN7UWr+TyXEJIYQQkhnGLbOqCn8p6rJPdTUschs2wPXS6RQZNAjp/Y11zpQn6OhILtmKzxcVh8VGWRmuyeDBiOmkpZiQzMjIYqe1flVEXo3z+joROW7T8+9FZM9MjkMIIYQQ6ymV2k3FgtMJa104jOueyELldkctWT0JblMigNYuQkiB5U4ihBBCCCldkkmKUl4Oa5ZJtpLIkhUOIzayqorWLkJI7sodEEIIIYSQJFAKYs0It0SYLJos6E0IEaGwI4QQQggpOEwylPb2xNt4PNFkJIQQQmFHCCGEEFJgKIX4ukAA2SO7Egwig2YxJk0hhGQHCjtCCCGEkALE7YbAi2e183jwt1Br1xFCcg+FHSGEEEJIAWKzwSLn9SLezhBbuy7ZIuaEkNKHwo4QQgghpEAx5Q46OqKv+f2occekKYSQWCjsCCGEEEIKFFOw3OOBpU4kWruObpiEkFgo7AghhBBCChi3GxY6jwd/fT5Y61i7jhASCwuUE0IIIYQUMKZgeaw7Jt0wCSFdocWOEEIIIaSAMaUPQiGRtja4Z7J2HSGkKxR2hBBCCCEFjsuFuDqTNIVumISQrlDYEUIIIYQUOEqJVFXhOYuSE0LiwRg7QgghhJAiwO2GtY616wgh8aDFjhBCCCGkCFCKoo4QkhgKO0IIIYQQQggpcijsCCGEEEIIIaTIobAjhBBCCCGEkCKHwo4QQgghhBBCihwKO0IIIYQQQggpcijsCCGEEEIIIaTIobAjhBBCCCGEkCKHwo4QQgghhBBCihwKO0IIIYQQQggpcijsCCGEEEIIIaTIUVrrfLchIUqpOhFZk+92xGGgiNTnuxGkpGEfI7mA/YzkAvYzkm3Yx0guyGc/205rPainjQpa2BUqSqkFWuvR+W4HKV3Yx0guYD8juYD9jGQb9jGSC4qhn9EVkxBCCCGEEEKKHAo7QgghhBBCCClyKOzSY3q+G0BKHvYxkgvYz0guYD8j2YZ9jOSCgu9njLEjhBBCCCGEkCKHFjtCCCGEEEIIKXIo7AghhBBCCCGkyKGwS4BSapxSarlSaoVS6po47zuVUi9sev9TpdT2uW8lKXaS6GeXK6WWKaW+VEq9p5TaLh/tJMVNT/0sZrvTlFJaKVXQ6ZxJ4ZFMH1NKnbFpPFuqlJqZ6zaS4ieJe+a2Sqn3lVJfbLpvHpePdpLiRSn1hFJqo1Lq6wTvK6XUXzf1wS+VUnvnuo3dQWEXB6WUXUQeEpFjRWRXETlTKbVrl80miUiT1nqEiNwnInfmtpWk2Emyn30hIqO11nuIyMsiclduW0mKnST7mSilqkXk9yLyaW5bSIqdZPqYUmpHEZkmIgdqrUeKyB9y3lBS1CQ5ll0vIi9qrfcSkV+IyMO5bSUpAf4hIuO6ef9YEdlx0+NiEXkkB21KGgq7+IwRkRVa6++11gEReV5EJnTZZoKIPLXp+csicoRSSuWwjaT46bGfaa3f11p7Nv37iYhsneM2kuInmfFMRORWwcKBL5eNIyVBMn3sIhF5SGvdJCKitd6Y4zaS4ieZfqZFpGbT8z4isi6H7SMlgNb6QxFp7GaTCSLytAafiEhfpdQWuWldz1DYxWcrEfkh5v8fN70WdxutdUhEWkRkQE5aR0qFZPpZLJNE5O2stoiUIj32M6XUXiKyjdZ6di4bRkqGZMaynURkJ6XU/ymlPlFKdbciTkg8kulnN4vIOUqpH0XkLRG5NDdNI72IVOduOcWR7wYUKPEsb13rQiSzDSHdkXQfUkqdIyKjReSQrLaIlCLd9jOllE3gTn5BrhpESo5kxjKHwHXpUIHnwUdKqd201s1ZbhspHZLpZ2eKyD+01vcqpfYXkX9u6meR7DeP9BIKev5Pi118fhSRbWL+31o2N+f//22UUg6Byb870y0h/6+9+2WRKoziOP49iGLQNi9gDQbBF7BVFINhksHkH6wWEZNBsPoGFNEqaNFpW8RmcKuCsKhsMYhhiyAqP8MdyzK4z2yYy7N+P+mGCSf84M6595zn7taSM6rqHHAHmCb5saLadHDslbPjwGngdVV9BtaBmQeoaAmt98yXSX4m+QR8YGj0pFYtObsOPANI8gY4CkxWUp3+F03/3cZiY7fYW+BkVZ2oqiMMC7izXb+ZAVfm1xeBV/Fr71rOnjmbj8g9ZGjq3EnRfvwzZ0l2kkySrCVZY9jlnCbZHKdcdajlnvkCOANQVROG0cyPK61SvWvJ2TZwFqCqTjE0dl9XWqUOuhlweX465jqwk+TL2EX95SjmAkl+VdUNYAM4BDxJ8q6q7gGbSWbAY4ZX/FsMb+oujVexetSYs/vAMeD5/Gye7STT0YpWdxpzJu1bY8Y2gPNV9R74DdxO8m28qtWbxpzdAh5V1U2G8birPnTXMqrqKcPI+GS+q3kXOAyQ5AHD7uYFYAv4Dlwbp9LFyrxLkiRJUt8cxZQkSZKkztnYSZIkSVLnbOwkSZIkqXM2dpIkSZLUORs7SZIkSeqcjZ0kSZIkdc7GTpIkSZI69wfzmMd1X4FagAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here we plot a few sample paths of a discretized Wiener process over (0,1)\n", "\n", "N = 100\n", "K = 5\n", "\n", "dt = 1 / N\n", "dW = np.random.normal(loc=0.0, scale=np.sqrt(dt), size=(N,K))\n", "W = np.cumsum(dW, axis=0)\n", "\n", "W_df = pd.DataFrame(data=W, index=np.array(range(100)) / N)\n", "\n", "plt.figure(figsize=(15,5))\n", "\n", "sns.lineplot(data=W_df, \n", " palette=sns.light_palette(\"blue\", n_colors=K), \n", " legend=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Stock Price as a Stochastic Differential Equation\n", "\n", "Proceeding formally, we may then multiply both sides of equation (1) by $dt$ and arrive at\n", "\n", "$$\n", "\\tag{SDE}\n", "dS_t = \\mu S_t \\, dt + \\sigma S_t \\, dW_t, \\quad t > 0,\n", "$$\n", "\n", "which can be interpreted rigorously as the integral equation\n", "\n", "$$\n", "S_t = S_0 + \\mu \\int_0^t S_s \\, ds + \\sigma \\int_0^t S_s \\, dW_s , \\quad t > 0.\n", "$$\n", "\n", "It remains to be defined what we mean by the stochastic integral on the right-hand side. We will interpret it as an _Itô integral_, that is, as the limit of approximating sums\n", "\n", "$$\n", "\\int_0^t S_s \\, dW_s \\sim \\sum_{k=0}^N S_{s_k}(W_{s_{k+1}} - W_{s_k})\n", "$$\n", "\n", "with increasingly fine-grained partitions $0 = s_0 < \\cdots < s_k < s_{k+1} < \\cdots < s_N = t$.\n", "\n", "\n", "### Itô's formula\n", "\n", "Recall the Taylor expansion of a smooth function $f$ around $(t',x')$:\n", "\n", "$$\n", "f(t,x)-f(t',x')=\\frac{\\partial f}{\\partial t}(t',x')(t-t')+\\frac{\\partial f}{\\partial x}(t',x')(x-x')+\\frac{1}{2}\\frac{\\partial^2 f}{\\partial t^2}(t',x')(t-t')^2+\\frac{1}{2}\\frac{\\partial^2 f}{\\partial x^2}(t',x')(x-x')^2+\\cdots\n", "$$\n", "\n", "As $(t,x)$ approaches $(t',x')$ we arrive at the first order approximation\n", "\n", "$$\n", "df(t,x) = \\frac{\\partial f}{\\partial t} (t,x) \\, dt + \\frac{\\partial f}{\\partial x}(t,x) \\, dx\n", "$$\n", "\n", "A stochastic version of this arises from substituting $W_t$ for $x$. Now, since $dW_t \\sim (dt)^{1/2}$, also the second order terms contribute to the first order approximation:,\n", "\n", "$$\n", "\\frac{1}{2}\\frac{\\partial^2 f}{\\partial t^2}(t,W_t)\\,dt^2+\\frac{1}{2}\\frac{\\partial^2 f}{\\partial x^2}(t,W_t)\\,dW_t^2\\sim\\frac{1}{2}\\frac{\\partial^2 f}{\\partial x^2}(t,W_t)\\,dt .\n", "$$\n", "\n", "This leads us to Itô's formula:\n", "\n", "$$\n", "df(t,W_t) = \\frac{\\partial f}{\\partial t}(t,W_t) \\, dt + \\frac{\\partial f}{\\partial x} (t,W_t) \\, dW_t + \\frac{1}{2} \\frac{\\partial^2 f}{\\partial x^2} (t,W_t) \\, dt\n", "$$\n", "\n", "\n", "### Solution to our SDE\n", "\n", "We are now ready to face the SDE modelling our stock prices. Indeed, let us use Itô's formula to compute the differential of\n", "\n", "$$\n", "S_t = e^{W_t} .\n", "$$\n", "\n", "Without difficulty, we see that\n", "\n", "$$\n", "de^{W_t} = e^{W_t} \\, dW_t + \\frac{1}{2} e^{W_t} \\, dt\n", "$$\n", "\n", "so that we've arrived to the solution of\n", "\n", "$$\n", "dS_t = \\frac{1}{2} S_t \\, dt + S_t \\, dW_t .\n", "$$\n", "\n", "This is a special case of our equation with\n", "\n", "$$\n", "\\begin{cases}\n", "\\mu = 1/2, \\\\ \\sigma = 1, \\\\ S_0 = 1.\n", "\\end{cases}\n", "$$\n", "\n", "With some thought, we notice that the general case is solved by\n", "\n", "$$\n", "S_t = S_0 \\exp((\\mu - \\sigma^2 / 2)t + \\sigma W_t) .\n", "$$\n", "\n", "This process is known as _Geometric Brownian motion_." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here we plot a few sample paths of the solution S_t\n", "\n", "N = len(date_range)\n", "K = 5\n", "\n", "dt = 1 / N\n", "dW = np.random.normal(loc=0.0, scale=np.sqrt(dt), size=(N,K))\n", "\n", "W_df = pd.DataFrame(data=np.cumsum(dW, axis=0), index=date_range)\n", "\n", "def W(t):\n", " return W_df.loc[t]\n", "\n", "# Try out different values for the parameters\n", "S_0 = 100 # Initial stock value at 100 euros\n", "sigma = 0.1\n", "mu = 0.0055\n", "\n", "def S(t, mu, sigma, W):\n", " return S_0 * np.exp((mu - sigma**2 / 2) * (t - pd.to_datetime(start_date)).days + sigma * W(t))\n", "\n", "stock_price = pd.DataFrame(data=[np.round(S(t, mu, sigma, W),2) for t in date_range], \n", " index=date_range)\n", "\n", "plt.figure(figsize=(15,5))\n", "plt.xlabel('Time')\n", "plt.ylabel('Stock value')\n", "\n", "sns.lineplot(data=stock_price, \n", " palette=sns.light_palette(\"blue\", n_colors=K), \n", " legend=False)" ] }, { "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }