{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Mine management model\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demddp03.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2021-Oct-01\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## About\n", "\n", "A mine operator must decide how much ore to extract from a mine that will be shut down and abandoned after $T$ years of operation. The price of extracted ore is $p$ dollars per ton, and the total cost of extracting $x$ tons of ore in any year, given that the mine contains $s$ tons at the beginning of the year, is $c(s, x)$ dollars. The mine currently contains $\\bar{s}$ tons of ore. Assuming the amount of ore extracted in any year must be an integer number of tons, what extraction schedule maximizes profits?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from compecon import DDPmodel, getindex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assuming a market price $p=1$, initial stock of ore $\\bar{s}=100$, and annual discount factor $\\delta = 0.9$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "price = 1\n", "sbar = 100\n", "delta = 0.9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State Space" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a finite horizon, deterministic model with time $t$ measured in years. The state\n", "variable $s \\in \\{0, 1, 2, \\dots, \\bar{s}\\}$ is the amount of ore remaining in the mine at the beginning of the year, measured in tons." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "S = np.arange(sbar + 1) # vector of states\n", "n = S.size # number of states" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Action Space" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The action variable $x \\in \\{0, 1, 2, \\dots, s\\}$ is the amount of ore extracted over the year, measured in tons." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "X = np.arange(sbar + 1) # vector of actions\n", "m = X.size # number of actions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reward Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The reward function is $f(s, x) = px − c(s, x)$. The cost of extraction is $c(s, x) = \\frac{x^2}{1+s}$.\n", "\n", "Here, the reward is set to negative infinity if the extraction level exceeds the available stock in order to preclude the choice of an infeasible\n", "action:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "f = np.full((m, n), -np.inf)\n", "for c, s in enumerate(S):\n", " for r, x in enumerate(X):\n", " if x <= s:\n", " f[r, c] = price * x - (x ** 2) / (1 + s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State Transition Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state transition function is $g(s, x) = s − x$\n", "\n", "Here, the routine `getindex` is used to find the index of the following period’s state." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "g = np.empty_like(f)\n", "for r, x in enumerate(X):\n", " snext = S - x\n", " g[r] = getindex(snext, S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Structure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The value of the mine, given that it contains $s$ tons of ore at the beginning of year $t$, satisfies the Bellman equation\n", "\n", "\\begin{equation} V_t(s) = max_{x\\in\\{0,1,\\dots,s\\}} \\left\\{px−c(s, x) + \\delta V_{t+1}(s−x)\\right\\} \\end{equation}\n", "\n", "subject to the terminal condition $V_{T+1}(s) = 0$\n", "\n", "To solve and simulate this model, use the CompEcon class ```DDPmodel```. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": "A deterministic discrete state, discrete action, dynamic model.\nThere are 101 possible actions over 101 possible states" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = DDPmodel(f, g, delta)\n", "model.solve()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default, the `solve()` method uses Newton's algorithm. This and other default settings can be changed when solving the model. For example,\n", "```python\n", "model.solve(algorithm='funcit', print=True)\n", "```\n", "solves the model by function iteration, printing a summary of each iteration to screen.\n", "\n", "In either case, `solve()` updates the model itself, storing the $n$ vector of values `.value`, the $n$ vector of optimal actions `.policy`, and the $n\\times n$ controlled state `.transition` probability.\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "solution = pd.DataFrame({\n", " 'Stock': S,\n", " 'Extraction': X[model.policy], \n", " 'Value': model.value}).set_index('Stock')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulate Model\n", "The path followed by the stock level over time is computed by the `simulate()` method. Here, the simulation assumes an initial stock level of 100 and 15 years in duration." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": " Stock Extraction\nYear \n0 100 24\n1 76 18\n2 58 14\n3 44 11\n4 33 8\n5 25 6\n6 19 5\n7 14 3\n8 11 3\n9 8 2\n10 6 2\n11 4 1\n12 3 1\n13 2 1\n14 1 1\n15 0 0", "text/html": "
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" }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sinit = S.max()\n", "nyrs = 15\n", "t = np.arange(nyrs + 1)\n", "spath, xpath = model.simulate(sinit, nyrs)\n", "\n", "simul = pd.DataFrame({\n", " 'Year': t,\n", " 'Stock': S[spath],\n", " 'Extraction': X[xpath]}).set_index('Year')\n", "simul" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot Optimal Policy" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": "
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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = solution['Extraction'].plot(title='Optimal Extraction Policy')\n", "ax.set(ylabel='Extraction');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot Value Function\n", "The value of the firm is very nearly proportional to the stock level." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = solution['Value'].plot(title='Optimal Value Function')\n", "ax.set(ylabel='Value');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot State and Extraction Path\n", "As seen in this figure, the content of the mine is optimally exhausted in 15 years." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": "
", "image/png": 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BpW19dru90mvKjpVdY6SyjYYsziJ8U9cZXI2I1AUK5h4U7OdDbONQQA+AikjtduzYMcaMGcO6deu46aabeO6557BYSicmoqOjAThy5Eil16WlpREWFkZQUJBH6z2VCn3mB1YYWImI1BVeE8w3b97M+PHj6dy5M127duUvf/kLu3fvrnCNWXeRO1n34+0sO4/kkZFv7CYaIiI1ITc3l4kTJ7Jt2zbGjRvHM888Ux7KAcLCwoiJiWHLli2VXrt161Y6duzoyXKr5AqMoKRBBwB8D/5mcDUiUhd4RTDfvXs3t99+O9u3b+fuu+/mL3/5Cxs3bmT06NHlT/ebeRe5k5WtZw7we4r6zEWk9nnmmWfYtm0bY8aM4dFHHz3lNQMGDGDlypUkJSWVH1uxYgXJyckMHDjQU6VWq2zW3PfweihRn7mI1Cyv2PlzwYIF5Ofn895773HRRRcBcOmllzJy5Ejmz5/Pww8/bOpd5E7WsUkY/j5W7CVO1qZkEt8+0uiSRETcJikpic8//5zQ0FAuvPBCPv/880rXDB06lDvuuIPPP/+ccePGMWHCBOx2O3PmzCE2NpahQ4caUPmpFTXtReCm+aV95ofXURxzmdEliUgt5hXBfP/+/dSvX788lANccsklhIeHs2PHDqD6XeTMEsz9faxcEh3Gmn2Z6jMXkVpn9erVAOTk5FQ5Wz506FAiIiJYuHAh06dPZ9asWQQEBBAfH8+0adPw8/PzZMmnVbHPfKWCuYjUKK8I5i1atGDFihWkp6cTEREBQGZmJjk5OTRq1Kh8F7lrrrmm0mtjY2NZvny5hys+vR7Nw1mzL5N9GQUczi6kcViA0SWJiLjFLbfcwi233HJG17Zu3ZrZs2fXcEXnxxXYgJKI9vikb1efuYjUOK/oMZ80aRKNGzdm6tSpJCYmsn37dh588EF8fX25/fbbvWIXuZP1OKnPXMsmioiYW3HT433mqeuhpNDgakSkNvOKYB4dHc2dd97JmjVrGDp0KNdffz0rV67k3//+NxdddJFX7CJ3sg5RoQT72QBYq3YWERFTK4o+vp65w671zEWkRnlFMH/55Zd58skn6dq1K//617+YMWMGl1xyCffffz/Lli3zml3kyvhYLXSNqQeUrmfucrkMrkhERKpSsc9c7SwiUnPMk1arkJ2dzdy5c+nYsSPz589nyJAhDBs2jHfffZc2bdrwxBNPeM0ucicrW888LbeIfRlagktExKxcQQ0pqd8OAN+DKw2uRkRqM9MH8z179lBUVMTgwYOx2Wzlx319fRkyZAhHjx4lOzsbMP8ucieLa16//OfqMxcRMbfipqXtLL6H16nPXERqjOmDedmyWQ6Ho9K5shaWkJAQr9hF7mStGwZRP9AXUJ+5iIjZFTU9uc98vcHViEhtZfpg3rZtWxo1asRnn31WoVXFbrezaNEi6tevT9u2bb1mF7kyVouFbs3CgdI+c6f6zEVETKs4umf5z7VsoojUFNMHc5vNxj/+8Q92797NiBEjWLBgAfPmzWP48OHs3r2bxx57DF9fX+644w7q1avHuHHjmDdvHm+88Qb33nuv6XaRO1mPFuEAZBWWsOtInrHFiIhIlVxBkZTUbwuUbjQkIlITTB/MAa6++mrefvttwsPDmTlzJv/5z38ICwvjrbfe4vrrrwco30WuQ4cOzJo1iwULFhAfH8+cOXNMtYvcyXocnzEH9ZmLiJjdiT7z38FRebEBEZHzZXFprT4AiosdZGZ6dq1zl8vFkNmrSc2x06d1BDNvMF8vvIh4h8jIUKNL8Cgjxmz/nf8jbOndAGTe8EmF9hYRkbNR1ZjtFTPmtZXFYinfBXRdShYljurXYxcREWMUVVjPXO0sIuJ+CuYGKwvm+cUOtqbmGluMiIhUyRXciJL6FwAK5iJSMxTMDdb95D5zLZsoImJqZbuA+qaqz1xE3E/B3GCNQv1pUT8QgBXJ6QZXIyIip1P2AKilpBCf1I0GVyMitY2CuQlc0aYBABsPZnM4WzvKiYiYVfFJfeZ+B9XOIiLupWBuAgM6RJb//LsdRw2sRERETscZHEVJeBtAfeYi4n4K5ibQvlEIzY+3syxNTDO4GhEROZ3yPvNDa7DYsw2uRkRqEwVzE7BYLAxoXzprvi01l30ZBQZXJCIiVbG3vhYAi8OOf9IXBlcjIrWJgrlJDOjQqPznmjUXETGv4mZX4AiOAiAg8f8ZXI2I1CYK5ibRqkEQbSODAViaeARtyCoiYlJWG/Z2NwLge2g11sxkgwsSkdpCwdxEytpZktPz2XU0z+BqRESkKoUdRpb/PGC7Zs1FxD0UzE2kYjvLEQMrERGR03FEtKO4USfgeDuLy2lwRSJSGyiYm0h0vQAubhIKwNLtamcRETGzwg6jALDlHtDSiSLiFgrmJlM2a34wq5Ath3MMrkZERKpib3s9LqsfAAGJCQZXIyK1gYK5ycS3a4jVUvrzb9TOIiJiWq6A+hS1uhoA/6QlWIpyDa5IRLydgrnJNAzxp2uzcAC+234Eh1PtLCIiZlX2EKilpAC/pC8NrkZEvJ2CuQmVrc5yNK+I9fuzDK5GRESqUtSsL87A0jE7IPFjg6sREW+nYG5C/ds2xHa8n2Xpdm02JCJiWjZfCtuXrmnud/A3rNn7DC5IRLyZgrkJ1Qv0pVfL+gAs23GUEoeW4RIRMavCDiPKf66dQEXkfCiYm9TVx9tZsgpLWLU309hiRESkSo4GF1IceTFwfLMhrWkuIudIwdyk+l7QAH+f0j8etbOIiJibvX3prLktex++h1YbXI2IeCsFc5MK9vOhT+sIAJbvPEZhscPgikREpCqF7W7AZfUFwH+b1jQXkXOjYG5iZZsN5Rc7WJGcbnA1IiJSFVdgBEUt+gPgn/QFFOcbXJGIeCMFcxPr3bI+wX42QJsNiYiYXWGHUQBYi/Pw3601zUXk7CmYm1iAr41+FzQA4NfkdHLtJQZXJCIiVSlqcSXOgNIWRK3OIiLnQsHc5K4+3s5iL3HyU9Ixg6sREZEq2fwobHcDAL77f8Wac8DggkTE2yiYm1zP5uHUC/ABYKnaWURETK2sncWCi4DtnxhcjYh4GwVzk/OxWbmqXema5r/tzSCzoNjgikREpCqOyFhKGlwIgH/ix+ByGVyRiHgTBXMvMKBDaTB3OF0s23nU4GpEROR0ymbNfbL24HN4rcHViIg3UTD3Ap2b1iMyxA+ApYnabEhExMwK2w3DZSldUSsgUWuai8iZUzD3Ajarhavbl86ar0vJ4kiu3eCKRESkKq6gyBNrmu9aDCUFBlckIt5CwdxLDDgezF3At9v1EKiIiJkVdhgBgLUoB//d3xhcjYh4CwVzL3FR41Ca1gsAFMxFRMyuqGU8Tv9wQO0sInLmFMy9hMViKX8IdPOhHPZn6qNRERHTsvljbzcUAN/9P2PNPWRwQSLiDRTMvciA9o3Kf65ZcxERcytf09zlxF9rmovIGVAw9yIXRAbTukEQoGAuImJ2JZGXUBLRHoCA7f9Pa5qLSLUUzL1MWTvLziN57D6WZ3A1IiJSJYuFwvalD4H6ZOzCJ3W9wQWJiNkpmHuZk9tZliZq1lxEzO/xxx/n9ttvr3R8xIgRtG/fvtKPe++914Aqa4a9/Y24LKV/1eohUBGpjo/RBcjZaVY/kAujQtiWmsvSxDTu7N0Ci8VidFkiIqeUkJBAQkICcXFxFY67XC6SkpKIj49nwIABFc41bdrUkyXWKGdwFEXN+uK/7wf8d/2P3D5Pgk+A0WWJiEkpmHuhazo0YltqLimZhSSm5XJhVKjRJYmIVOBwOHj99dd59dVXT3l+//795Ofnc9VVVzF06FAPV+dZ9g6j8N/3A1Z7Fv7J32JvO8TokkTEpNTK4oXi20dSNkf+zTa1s4iIudjtdm644QZeeeUVhg4dSlRUVKVrdu3aBUCbNm08XZ7H2VtdjdO/HgD+29XOIiJVUzD3QlGh/nSOKR3kv92ehlNP+ouIidjtdnJzc5k5cyYzZszAx6fyh7M7d+4ETgTz/Px8j9boUT4B2C+4HgC/fcux5qUaXJCImJWCuZca0L50dZa03CI2Hsg2uBoRkRNCQkJYunQpAwcOrPKanTt3EhwczPTp0+nSpQtdunQhPj6eJUuWeLBSzynsULo6i8XlxH/HZwZXIyJmpWDupa5q1xDb8X6WpYlpxhYjInISq9V6ylnyk+3atYu8vDxycnJ44YUXeP755wkODmbq1KksWrTIM4V6UElUV0rCSz8dCEhM0JrmInJKXvPwZ3p6Oi+99BLLli2jsLCQ2NhYHnzwQTp37lx+TUpKCjNmzGD16tUA9OvXj0ceeYSIiAiDqq459YP86NGiPr/tyeD7HUd5sP8F+Fi1OouInB+73U5mZiYOh+OU56Ojo93yPqNGjcLpdHLrrbeWHxs0aBCDBw/mxRdfZMiQIdhsNre8lylYLBR2GEnIb/+HT/p2fI5soqTRJUZXJSIm4xXBPDc3l1tvvZW0tDTGjRtHWFgY7733HmPHjiUhIYF27dqRkZHB2LFjKSoqYtKkSTgcDubOncv27dtJSEjAz8/P6G/D7a7pEMlvezLIKChm7b4MLm1Z+/4BIiKekZmZydNPP823335bZSgH2LZtm1ve75Zbbql0LCAggKFDh/Lqq6+ya9cu2rdv75b3Mgt7+xsJ/m0GFlwEJH5MroK5iPyJVwTz2bNnk5yczLvvvkuPHj0AGDhwIPHx8cyZM4cXXniB+fPnc/jwYRYvXlz+MFGnTp0YP348ixYtYtSoUUZ+CzWi3wUNed62k2KHi28SjyiYi8g5+7//+z+++uorLr/8ci688ELDJjPKPuGsjQ+DOkOiKW52BX4pP+K/YxG5lz0BNn+jyxIREzF9MHe5XHz22Wf069evPJQDREZGMm3aNHx9fQFYsmQJcXFxFZbe6t27N61atWLJkiW1MpiH+PtwWasIlu86xg87j/JofFv8fPTYgIicvWXLljFy5EieffbZGn+v1NRUJkyYwHXXXceUKVMqnEtOTgYgJiamxuswQmGHEfil/IjVnonfnu8palP1A7IiUveYPsXt37+f1NRUevfuDZQG9by8PABuvfVWRo0aRVZWFikpKcTGxlZ6fWxsLJs3b/ZozZ40oEMjAPKKHKxITje4GhHxViUlJVx88cUeea+oqChycnJISEggNze3/PihQ4f49NNP6dmzJ5GRkR6pxdPsra7F6Ve6KVxAotY0F5GKTB/M9+7dC0CDBg2YMWMG3bt3p2vXrlx99dUsW7YMKJ19AU65iUVkZCS5ubnk5OR4rmgPurx1BIG+pX+MS7drsyEROTc9evRg1apVHnu/f/zjHxw+fJibb76ZBQsW8N///pcRI0bg4+PDk08+6bE6PM43EPsFgwHw27sMS77GbRE5wfTBPDu7dI3u//znP/z444/8/e9/Z8aMGQQEBHDPPfewYsWK8hn0wMDASq/39y/t36uN/YoAAb42rmjTAICfk45RUFz1Q1siIlV57LHHWLt2LS+88AJ//PEH+/fv5+DBg5V+uEt8fDyvvfYagYGB/Otf/2LevHl07tyZDz74oNbvBlrYobS10uJyELBjkbHFiIipmL7HvKioCCgN6N988w316pXueNm/f3+uvvpq/v3vf/PYY49V+3WsVtP/G+ScDejQiG8Sj1BY4uSnXce45sJGRpckIl5myJAhOJ1O3n77bebNm1fldeeyKkvZp5t/Fh8fT3x8/Fl/PW9X0rg7JfVa4pO1h4DEBAo632F0SSJiEqYP5kFBQQAMGDCgPJQDhIWF0b9/fz777DOCg4OB0vV3/6zsWNk1tVGvlvUJ9fchx17C0u1HFMxF5KzdcccdWCzaC8EjLBbsHUbis+pFfI5txXZkC47Iys9IiUjdY/pgXtY3fqpNgiIiInC5XDRoUNrKceRI5V69tLQ0wsLCygN+beRrs9K/bUM+33yYFcnpZBcWExbga3RZIuJF/vrXvxpdQp1S2G44wateBCBgewJ5CuYighcE87Zt2+Ln58euXbsqndu/fz/+/v5EREQQExPDli1bKl2zdetWOnbs6IlSDTWgQySfbz5MidPF8p3HuP7ixkaXJCJe6Oeff+a7777j4MGD+Pr6Eh0dTb9+/ejTp4/RpdUqzrAYippeht+BXwnY/il5vR4DW+3bCE9Ezo7pG6+DgoLo378/y5cvZ+fOneXHU1JSWLZsGVdddRU2m40BAwawcuVKkpKSyq9ZsWIFycnJDBxY+9eJ7dYsnIig0lnybxLTDK5GRLyN0+lk6tSpTJ48mY8++oiNGzeyevVqFi5cyB133MF9992Hy+UyusxapfDCkQBYC9Px2/OtwdWIiBlYXF4w0u7fv5+RI0sHsDFjxuDr68s777xDQUEBn376Kc2aNSM9PZ3Bgwdjs9mYMGECdrudOXPm0Lx5cz788MNqd7ErLnaQmendK7f8a9kuPlp/EKsFvpjck8gQ7SgnUldERoae1+vfeustXnrpJUaPHs3dd99Nw4YNATh69Chvvvkm7777Lo888gjjxo1zQ7XnrzaM2RTn02BBD6z2LIobdiRz1FegPn+ROqGqMdsrgjmUzpC/+OKLrFixApfLRffu3Zk2bVqFZbV2797N9OnTWbt2LQEBAfTt25dp06adsj/9z2rDIL/lUDbj3t8AwISezbirTytjCxIRjznfYH7ttddywQUX8Oqrr57y/F//+leSk5P54osvzut93KU2jNkAQatfInjNSwBkDZxHUaurDa5IRDyhqjHb9D3mZZo1a8asWbNOe03r1q2ZPXu2hyoyn9gmYVzcJJRNh3L4ZOMhxvdsToCvzeiyRMQLHDhwgLFjx1Z5vlevXvz0008erKhuKOg0kcCNc7AWZRO05iWKWsZr1lykDnN7j/nJ2yuL543uFgNAVmEJX25NNbgaEfEW9evXZ8+ePVWe37NnD6Gh5zcrL5W5/OtR0GkiAL5HNuG393uDKxIRI51VMH/nnXdOe/7LL7/kuuuuO6+C5Pz0a9uQJmGlveXv/34Ap3d0KomIwfr3788HH3xwys2Avv/+ez788EP69+9vQGW1X8ElE3H6lf6jJ2jNTNC4LVJnnVUry/PPP09hYSGTJ0+ucHz//v08/fTT/Pzzz+UPDIkxfKwWburSlJd/3M3ejAJWJKfTp3UDo8sSEZO7//77WblyJffccw9t2rShVavSZ1R2797N7t27adq0Kffff7+xRdZSroBwCi6ZSPDal/FN24jf3mUUtbzK6LJExABnNWN+8803M3PmzPJeb4fDwVtvvcWQIUNYsWIFt956K1999VWNFCpnbujFjQn2K+0tf+/3AwZXIyLeIDw8nISEBCZOnIjL5eKnn37ixx9/xOl0Mn78eD755JMzepBezk1Bp0knzZq/pFlzkTrqrFdlefnll3njjTe48cYb2bRpEzt37qRz5848+eSTXHjhhTVVZ42rLU/4l5m5PIn3j4fyhbd3pX2jEIMrEpGadL6rsnib2jZmAwStepHgtf8BIGvQAs2ai9Ribl0u8Z133mH69OlYrVaeeuqp8jXGvVltG+QPZhVyw9zVOF0wKDaKp65tb3RJIlKDzjaYHzx4kIiICAICAsp/fSaio6PPuraaUNvGbABLYQYR7/TCWpxLcaPOZI5YrBVaRGqpc1ousaqBOj4+nry8PP7zn//w+++/06dPnwo7wpll4K7LousFcGXbhny/4yjfbEtjSp+WNNSGQyJy3FVXXcULL7zAkCFDgNKHPy1nEAK3bdtW06XVWa6A+hR0mkjw2v/gm7YB333LKW5xpdFliYgHnTaYn8lAvWjRIj7//PMKxzRwm8PobjF8v+MoJU4XCRsOasMhESl3zz330L59+wq/PpNgLjWroNMkAjfOxVqcS/Cal8hs3k+z5iJ1yGlbWV555ZVzGqinTJlyXkUZoTZ+LAow4f31bDqUQ70AH76Y3FMbDonUUp7oMS8qKsLPz6/G3+dM1NYxGyDotxkE//4KAJlDFlLcvJ+xBYmI27m1x/zPSkpK8PHxmk1ET6m2DvLfbT/Co1+UfoLxaPwF3NhJbUYitdH5BvOrrrqKxx57jKuuOvUDh1988QXPPvssq1atOq/3cZfaOmZDWa/5pViL8yiO6krm8M81ay5Sy5xTj/mpLFu2jDfeeINZs2bRuHFjAJ5++mm2bNnCtGnTuPTSS8+vUnGrsg2HDmXbef/3Awy7pAlWDfAidV56ejpJSUnlvz5w4ACbNm0iLCys0rVOp5Nvv/2WoqIiT5ZYZ7kC6lN48XiC1r2Kb+o6fFN+orh5X6PLEhEPOKtg/t133/HXv/6VZs2aYbfby49369aN9evXM3HiRObNm0dcXJzbC5Vzow2HRORU/P39efDBBzly5AgAFouFN998kzfffPOU17tcLgYOHOjJEuu0/M6TCdg0D2txHsFrZpLZ7ArNmovUAWfVyjJixAgCAwOZO3dupT7DkpISxowZg8Vi4b333nN7oTWtNn8smmsvYfBbq8grctC9eTivj7zE6JJExM3OpZVly5Yt7NixA5fLxWOPPcaoUaPo0qVLpeusVisRERH06tXLNG2LtXnMLhO8cjpB614DIPP69yludoXBFYmIu7illSUpKYlHHnnklA//+Pj4MHjwYP7973+fW4VSY0L8fRh6cWPe//0Aa/dlsiMtl3bacEikzouNjSU2NhYoXR53wIABtGvXzuCqpEx+5zsJ/GMelpL80lnzmMs1ay5Sy1nP5uLg4GD2799f5fm0tDTTPLEvFd3UpSnW4+P5++sOGFuMiJjOlClTKCoq4oEHHuDYsWPlx2fMmMG9995boR9dPMMVGEHBJeMA8D20Bt/9vxhbkIjUuLMK5ldccQULFy5kw4YNlc5t3bqVhQsXcvnll7urNnGjsg2HAL7ZlsbRXHs1rxCRumTt2rWMHj2aX3/9lYyMjPLjkZGR/P7774wYMYLExEQDK6yb8jvficsnEIDgNTPh/BdSExETO6se87S0NEaOHElaWhqxsbG0aNECq9XKvn372LRpEw0bNiQhIYGoqKiarLlG1IV+xT8OZjPxgw0ATOjZTBsOidQi57tc4u233052djYLFiwgPDy8wrmsrCxuv/12oqKimD179nm9j7vUhTG7TPCK5wha/zoAmUM/ojjmMoMrEpHzVdWYfVYz5o0aNeJ///sfEyZMoLCwkGXLlvHNN9+QmZnJbbfdxmeffeaVobyuuCQ6jIublN4In2w8RGGxw+CKRMQstm3bxk033VQplAPUq1ePUaNG8ccff3i+MCG/y1/KZ82DVr+kWXORWuysH6+vV68eDz30EA899FBN1CM17JZuMWz6YhtZhSV8uTVVGw6JCFD6AP/JLSx/lpubi9Pp9GBFUsYV2ICCi8cStP4N/A6twvfACs2ai9RS57TuVVJSEt9//z0HDx7E19eX6Oho+vbtS+vWrd1dn7jZlW0b0jjUn8M52nBIRE7o2bMnCxcu5Prrr6dZs2YVzqWmprJw4ULtUWGg/M5/IXDTAiwlBQSteYksBXORWumseswB/vWvf/H2229XmjmxWq2MGzeOadOmubVAT6lL/Yrvrd3Pyz/uBmDmDbHacEikFjjfHvPdu3czcuRInE4nV1xxBS1btsRisbBv3z5+/PFHLBYLH330EW3atHFTxeenLo3ZZYJ/fZagDaUbQGUO+5jipr0NrkhEzlVVY/ZZBfOEhASeeOIJ+vXrx1133UWbNm1wOp3s3r2b2bNns2zZMp5//nluuOEGtxXuKXVpkNeGQyK1z/kGc4C9e/cyc+ZMfvrpJ/LzS8fDgIAALrvsMqZOnWqaUA51a8wuY8k/QoN3e2EpKaSoaS+yhiUYXZKInCO3BPOhQ4cSHh7OggULTnl+7Nix5Obm8sknn5xblQaqa4P8Sz8k8cHx9czfu72rNhwS8XLuCOZlXC4XGRkZOJ1O6tevj81mc9vXdpe6NmaXCf7lGYI2vgVA5rAEipv2MrgiETkXblmVJTk5mQEDBlR5fsCAAezevfvsKhND3NQ1WhsOicgpWSwWIiIiaNiwYYVQvnXrVgOrEihboSUAgKA1Mw2uRkTc7awe/gwODubIkSNVnk9LS8Pf3/+8i5Ka17ReIFe2bcj3O47yzbY0pvRpScMQ/dmJ1FXFxcW89dZbLF26lPz8/ArPETkcDvLy8sjNzWXbtm0GVimu4EYUxN5O0MbZ+B1Yge/B3yiOvtToskTETc5qxrxPnz4sXLjwlLu/bdu2jYULF3LZZXpS3FuM7hYDQInTRcKGgwZXIyJGevnll3nllVfIysoiMDCQAwcO0KRJE3x8fDh8+DDFxcX8/e9/N7pMAfK73IXLVjqRErRas+YitclZzZg/8MAD/PLLLwwfPpw+ffrQqlXpzpG7d+/m119/JTQ0lPvvv78m6pQacEl0GB2bhLL5UA6fbDzE+J7NCfA1Xy+piNS8r7/+mri4OObPn8+RI0fo27cv//jHP2jXrh0//vgj99xzD76+vkaXKRyfNe94O0Eb5+B34Fd8D66iOLqn0WWJiBuc1Yx5dHQ0CQkJDBgwgDVr1jB//nzmz5/PmjVriI+PJyEhodL6t2JuZbPmZRsOiUjdlJqayoABA7BarURFRdGgQQPWr18PQN++fbnhhhv4+OOPDa5SyhScPGuuXnORWuOsNxiKiYlh5syZOJ1OMjIycLlcREREYLWWZvyioiL8/PzcXqjUDG04JCJQuiziyTPizZs3Z8eOHeW/vuSSS/jmm2+MKE1OwRkcRUHsbQT9MRe//b/gc3A1JdHaAErE253VjPlVV13F999/X/pCq5UGDRrQsGHD8lD+xRdfcPnll7u/SqkxPlYLN3dtCsDejAJWJKcbXJGIGOHCCy/kp59+Kv9169aty2fMoXRG3aJ/tJtKQdcTs+bBmjUXqRVOO2Oenp5OUlJS+a8PHDjApk2bCAsLq3St0+nk22+/paioyP1VSo0aenFj3lqxl/xiB+//fkA7gYrUQbfeeiv3338/o0eP5q233mLQoEF88sknPProo7Ru3Zr58+fTuXNno8uUkziDG1MQeytBf7yN3/6f8Tm0lpIm3Y0uS0TOw2k3GMrLy+O666477RKJJ3O5XAwcOJCXXnrJbQV6Sl3drKKMNhwS8W7u2GAoISGBefPmsXjxYmw2G//+97+ZPXs2UPqM0ezZs02z+2ddH7PLWPMOE/HuZVgcdoqa9SXr+veMLklEzsA57/y5ZcsWduzYgcvl4rHHHmPUqFF06dKl0nVWq5WIiAh69eqFj89Zt64brq4P8geyCrhx7hqcLhgUG8VT17Y3uiQROQvnG8x37tzJBRdcUKld5eDBg2RlZdGmTRtTPT9U18fsk4X89DiBm+YDkDH8c0oadzO2IBGp1jkH85O9+uqrDBgwgHbt2pUfy8rKIiAgwOs3FtIgD48s3sr3O47iY7Ww+I44bTgk4kXON5hfdtll3HDDDfztb39zU0U1S2P2CdbcQ6Wz5s4izZqLeImqxuxqH/4sLi7mww8/5NFHH2XKlCnloXzt2rUMGjSISy+9lC5dujBp0iRSUlLcW7V41C3HHwItcbpI2HjI4GpExJPy8/OJiYkxugw5B86QJhTG3gKAX8qP+Bz+3eCKRORcnTaYFxUVMXbsWJ566im++OILSkpKANizZw8TJ05k9+7dXH755YwbN47k5GRuuukmjh496pHCxf3KNhwC+GTDQQqLHQZXJCKeMnbsWN5++23Wrl1rdClyDvK73oPLWtpqpBVaRLzXaYP5ggULWL9+PQ899BBr1qwp7x1/5ZVXsNvtDBo0iLfeeotp06bxySefYLPZeOONNzxSuLifxWLRhkMiddTmzZs5cuQIt99+O126dOHKK6/kqquuqvAjPj7e6DKlCs6QaAovOj5rvm85PofXGVyRiJyL0wbzr776imuuuYaJEycSEBAAlM6iL1u2DIvFwsSJE8uvDQ8P58Ybb2T58uU1WrDUrLINhwDe//0AzjN/BEFEvJjdbqdjx450796djh07EhMTQ3R0dIUfTZo0MbpMOY2TZ821G6iIdzrt8il79+7lxhtvrHBsw4YNFBQU0KhRIy688MIK55o3b05aWpr7qxSPKdtw6OUfd5dvOKR1zUVqv3fffdfoEuQ8OUOjKbzoZgI3v4P/vh/wSV1PSVTlVdRExLxOO2PudDqx2WwVjq1cuRKA3r17V7o+JyeHwMBAN5YnRhh6cWOCfEv/3N9asVez5iJ1wJgxY8rH91NZtmwZgwcP9mBFci5KZ819Ac2ai3ij0wbz5s2bs23btgrHvvvuOywWC/369at0/S+//ELz5s3dWqB4Xoi/D6O7la7Qsi01l6+26lMQkdqmoKCAgwcPlv9YvXo1u3btqnCs7Mf+/fv56aefznnlrccff5zbb7+90vGUlBSmTJlCXFwccXFxTJs2jfT09PP91uo0Z2hTCi+8GQD/vcvwSd1gbEEiclZO28oyaNAgXnvtNa644gouu+wyPvroI3bu3EnDhg3p379/hWv/97//8euvv3LffffVaMHiGbf3aMaiTYc5mlfEa78k079dQwJ9bdW/UES8QkFBAcOGDSMnJwcoffj7+eef5/nnnz/l9S6Xi8suu+ys3ychIYGEhATi4uIqHM/IyGDs2LEUFRUxadIkHA4Hc+fOZfv27SQkJJhqMyNvk99tCgHbPsTiLCZozUyyBy8wuiQROUOnDebjxo3j559/ZsqUKVgsFlwuF76+vjz33HPlg+a3337LwoULWb16Na1atWLcuHGeqFtqWJCfjbv7tOSZb3ZwJLeId9ekMLl3S6PLEhE3iYiI4MUXX2TTpk24XC5ee+01rr76atq3r7zrb9nOzoMGDTrjr+9wOHj99dd59dVXT3l+/vz5HD58mMWLF9OmTRsAOnXqxPjx41m0aBGjRo06t29Mjs+a30TgloX47/0en7SNlDTqZHRZInIGThvM/fz8mD9/Pl9++SUbNmwgODiY66+/ngsuuKD8ms2bN7Nu3Tquv/56HnnkkfLVW8T7DYqN4uP1B0lMy+WdNfsZenETokK1G6hIbdG3b1/69u0LwMGDB7n55pvp1On8A5zdbmfkyJFs376dYcOGnbJ3fcmSJcTFxZWHcih9dqlVq1YsWbJEwfw85XedQsC2j47Pmr9M9qB5RpckImeg2p0/bTYbQ4YM4YknnmDq1KkVQjnAX/7yFzZu3MiMGTOoX79+jRVaJjExkY4dO/LKK69UOK5eRfezWizc3681APYSJ//9JdngikSkpgwaNOi0obyoqIgXX3zxjL6W3W4nNzeXmTNnMmPGjPI9MMpkZWWRkpJCbGxspdfGxsayefPmsyteKnGGxVDYYSQA/nu+xSftD4MrEpEzUW0wr05gYCBW63l/mTNSUlLCo48+SnFxcYXjZb2KGzZsYNKkSYwfP55ly5Yxfvx4ioqKPFJbbdWtWTj9LihdLvHLrWlsPZxjcEUiUhMmTZrEM888Q2FhYaVzZZ+Kvv3222f0tUJCQli6dCkDBw485fnU1NLNy6Kioiqdi4yMJDc3t7z3Xc5dfre/4rKW/qMoaM3LxhYjImfEM4naTd5880127txZ6XhZr+KCBQuYPHkyd911F7NmzSIxMZFFixZ5vtBa5t4rWuNjtQAwc3kSLi2fKFLrjBw5kvfff5+hQ4eyceNGAAoLC3nuuee47bbbyMzM5J///OcZfS2r1VpplvxkeXl5AKdcXtffv7RdLj8//2y/BfkTZ1izk2bNl+JzZJPBFYlIdbwmmG/fvp3XX3+du+++u9K56noV5fw0qx/ITV1Kl0/ccCCbZTuPGlyRiLjbs88+y9y5cykqKmL06NE888wzDBkyhIULF3LjjTfy9ddfM3z4cLe8l9PprPYaT30SW9tp1lzEu3jFyFfWwtK7d2+uv/76CufUq+gZEy9tTr2A0sF91k/J2Euq/4tVRLzLZZddxmeffUZ0dDTvv/8++/fvZ9q0afzzn/8kPDzcbe8THBwMlPai/1nZsbJr5Pw4w5pT2H4EAP7J3+BzRH8nipiZVwTz2bNns3fvXp555plK59Sr6BmhAT7lyyUezCrko3UHjC1IRNzu119/5aabbiIlJYUBAwbQtGlTXnzxRZ5++mlyc3Pd9j7R0dEAHDlypNK5tLQ0wsLCCAoKctv71XX53f6Ky1K6D4V2AxUxN9MH8507d/Laa6/x8MMP07hx40rn1avoOTd2akKriNK/LN9etY/0fD1YK1JbPPDAA0yaNIn8/Hz++9//MmvWLBYvXszo0aP56KOPuPbaa93WGhgWFkZMTAxbtmypdG7r1q107NjRLe8jpZz1WlDY4cSsue1I5d93ETEHUwdzh8PBo48+Srdu3apc01a9ip7jY7Vw3/HlE/OKHLy1Yq/BFYmIu3z11VcMGzaMJUuWlO/sHBgYyOOPP867775LSEgIf/vb39z2fgMGDGDlypUkJSWVH1uxYgXJyclVruYi5y6/273ls+bBazVrLmJWpk6sc+fOJTExkQcffJD09HTS09PJzs4GSreTTk9PV6+ih13WKoJLW5auV//ZH4fYdTTP4IpExB1mz57N9OnTCQsLq3SuW7du/O9//2PSpElue7877riDevXqMW7cOObNm8cbb7zBvffeS2xsLEOHDnXb+0gpZ70WJ3rNd3+N7ehWgysSkVMxdTD/+eefKS4uZuTIkfTq1YtevXpxww03AKWhvVevXuVL96lX0XPu69saqwWcLvjP8t1aPlHEC02ZMoW1a9eW//ryyy/H5XKRmJhIQUFBpeu//vpr5syZ47b3j4iIYOHChXTo0IFZs2axYMEC4uPjmTNnDn5+fm57Hzkhv/tfT5o1f9nYYkTklKpeaNYEHn744fIZ8jJHjx7loYceYujQoQwbNozWrVurV9HDLmgYzA2XNOGTjYf4bW8GK5IzuKx1hNFlichZ+O6777jmmmsqHMvMzOSGG27g7bffplevXm57r2XLlp3yeOvWrZk9e7bb3kdOz1mvJfb2NxKQmIB/0pfYjm7F0fAio8sSkZOYesa8Y8eO9O7du8KPrl27AtCsWTN69+6Nv7+/ehUNcGfvFgT7lc68vPxjEiUOLZ8oUhvoE7DaLa9Cr/l/DK5GRP7M1MH8TKlX0fPqB/kx8dLmAOxJL+DTPw4bXJGIiFTHGd4Ke7vSllD/pCXYjm0zuCIROVmtCObqVTTGTV2aEl0vAIC3Vuwhu7DY4IpERKQ6+d3vxWUp/es/aI1mzUXMxNQ95qcSExPD9u3bKx1Xr6Ln+flYufeKVjyyeBtZhSXM/W0fD/RrY3RZIiJyGo7w1tjb3UDA9k/wT1pC/rFEHA06GF2WiFBLZszFOP3bNqRL09Ll1T5ef5B9GZVXcxAREXPJ734fLosVCy6C1GsuYhoK5nJeLBYL9x+fJS9xunjlp90GVyQiZyozM5ODBw+W/zh8uPRZkfT09ArHDx48SEZGhsHVijs5wltjbzsMAP9dX2A7VvmTaBHxPItLj+ADUFzsIDMz3+gyvNZTXyWyZGsaAG+MuoRuzcKNLUikjomMDD2r6zt06IDFYql03OVynfJ4mW3bzPGwoMbs82fLSKL+B1dicTkpvOB6cq75r9ElidQZVY3ZXtdjLuZ0V59WfLfjKPYSJzOX72bBrV2wWav+y11EjFW2WZvUXY76bbC3HUrAjs/w37WY/B7344hoZ3RZInWaZsyP0+zL+XtrxR5mr9wHwBPXtOP6jo0Nrkik7jjbGXNvpzHbPWwZu6j//pVYcFHYdig5A14zuiSROqGqMVs95uI2t/doRmRI6fKU//1lD/lFDoMrEhGR03HUvwB72+sB8N/5P2zpOw2uSKRuUzAXtwn0tXFPn1YAHMsr4p01KQZXJCIi1cnvfj8uLFqhRcQEFMzFra67qBEXRoUAsHDtfg5nFxpckYiInI4jou1Js+afY8vYZXBFInWXgrm4ldViKd9kyF7i5LVf9hhbkIiIVCu/+32aNRcxAQVzcbsuMfXo37YhAF9vS2PLoWyDKxIRkdNxRLTDfsEQoGzWPMngikTqJgVzqRF/vaIVvrbS5RJfWr4bLf4jImJu5bPmLqdmzUUMomAuNSImPJCbuzQF4I+D2Xy346jBFYmIyOk4GrTHfsFgAPx3LsJ2dKvBFYnUPQrmUmMmXNqc8EBfAGb9uJucwhKDKxIRkdPJ734/LosVi8tJ2Dd3QVGe0SWJ1CkK5lJjQvx9+MtlLQA4nGPnqa+341RLi4iIaTkatCe/xwMA+GQmEfrTY6BxW8RjFMylRt1wSRMubx0BwE9Jx1iwWmubi4iYWX63eylqehkAAds/wT/xY4MrEqk7FMylRlktFp6+rgMx4QEAvPHrHlbvzTC4KhERqZLVRvbVr+AMjAQg9Ke/Yzu23eCiROoGBXOpcaEBPswYchH+PlacLvj7kkRtPCQiYmKu4EZkX/1K6SotJYWl/ebF+UaXJVLrKZiLR7RrFMKj8W0ByCwo5tEvtlFU4jS4KhERqUpxsz7kd78PAJ+MHYT89ITBFYnUfgrm4jGDYqMY3qkJAJsP5TBzuTawEBExs/weD1DUtBcAgYkf4b/9/xlckUjtpmAuHjW1XxtiG4cC8P82HuLLrakGVyQiIlWy2si5+hWcgQ0ACF3+GLaMXQYXJVJ7KZiLR/n5WPm/IRdSL8AHgOe/3cnOI7kGVyUiIlVxBjcmO37W8X7zfMK+vhOKC4wuS6RWUjAXj2scFsBzgy/EagF7iZNp/9uqzYdEREysuHlf8rtNAcAnfTshv/zD4IpEaicFczFEzxb1+ctlLQHYn1mozYdEREwuP+5Bipr0BCBw6wf47/jM4IpEah8FczHM2Lhm2nxIRMRbWH3IGfAKzoD6AIQsfwRb5m6DixKpXRTMxTDafEhExLs4Q6LJif8PANbiPMK+/guUaF8KEXdRMBdDafMhERHvUtSiP/ld7wbA59hWQn552uCKRGoPBXMxnDYfEhHxLnlxD1HcuDsAgVvexX/nYoMrEqkdFMzFFLT5kIiIF7H5kj3gvzj9wwEI+eEhrJnJxtYkUgsomItpaPMhERHv4QyNJif+ZQCsxbmELb0bHHZjixLxcgrmYhplmw+FB/oC2nxIRMTsilrGk9/5TgB8j2wi5NdnDa5IxLspmIupNA4L4J+DOpRvPvSwNh8SETG1vEsfoTiqCwCBm+bjl7TE4IpEvJeCuZjOyZsPpWjzIRERcyvvN68HQOiyh7Bm7TW4KBHvpGAupqTNh0REvIczrBk5/V8CwFqUrX5zkXOkYC6mpM2HRES8S1Hra8jvNAkA37SNBK943uCKRLyPgrmYljYfEhHxLnm9HqO4UScAgv6Yi9/urw2uSMS7KJiLqWnzIRERL2LzI/ua13H6hQEQuuxBrNlqRRQ5UwrmYnp/3nzoMYVzERHTcoY1J6f/vwCw2rOo//+G4Jf0pcFViXgHBXPxClP7teHiJqUzMD8mHeNvn2+hsNhhcFUiInIqRW0Glq9vbi04Sr2vJxO69B4shXpWSOR0FMzFK/j5WJk1vCOXRJeG85V7Mnjgs83kFymci4iYUV7vx8m++pXyZRQDdn5OxPv98dv9jcGViZiXgrl4jRB/H14ZfjHdm5UO8mtTsrj3k03k2rUBkYiI6Vgs2NvdQMYty7C3HACAteAI9b6aSOi3f9XsucgpKJiLVwnyszHzho70alkfgI0Hs7nn/20iq6DY4MpERORUnMFRZA+cS3b8f07Mnu/4jPofXIVf8lKDqxMxFwVz8ToBvjb+NTSWvm0aALD1cA53JfxBRn6RwZWJiMgpWSzY2w8n45bvsbeMB8CWn0a9LycQ+t19WAozja1PxCQsLpf2OgcoLnaQmZlvdBlyFkocTp74cjvf7TgCQKuIIP478mIahvgbXJmI50VGhhpdwjkZMWIEmzZtqnT8mmuuYdasWVW+TmO2F3O58N/+CSE//wNrUTYAjuAocvu9QFHLqwwuTsQzqhqzFcyP0yDvnRxOF89+s50lW9MAaBYewH9HXkLjsACDKxPxLG8M5i6Xi65du9K7d28GDBhQ4VzTpk3p3r17la/VmO39rLmHCFn+MP57l5UfK+wwitw+T+I63vIiUlspmFdDg7z3crpczPhuF5/+cQiA6DB/Xht5CTHhgQZXJuI53hjMU1JSiI+PZ/r06dx4441n9VqN2bWEy4V/4seE/PIU1qIcABzBjcm98gWKWvQ3uDiRmlPVmO01PeY///wzo0ePplOnTnTp0oVx48axYcOGCtekpKQwZcoU4uLiiIuLY9q0aaSnpxtTsHiM1WLhkfgLuLlrUwAOZtu586ON7EnXX9oiZrZr1y4A2rRpY3AlYhiLBfuFN5Fx8/cUNe8LgC3vMPW+GEPIsgex2LMNLlDEs7wimK9evZo77riDnJwcHnjgAe655x727dvHbbfdxh9//AFARkYGY8eOZcOGDUyaNInx48ezbNkyxo8fT1GRHgqs7SwWC1P7tWZsXDMA0nKLuPOjjew6mmdwZSJSlZ07dwIngnl+vv4xXVc5Q6PJGryQnCtfwOkbAkDgto+o/+FV+O770eDqRDzHK1pZhg0bRlZWFl9++SWBgaXtCUePHmXgwIHExsYyb948Zs6cyezZs1m8eHH5IL9ixQrGjx/Ps88+y6hRo077HvpYtHZwuVzM+W0fb63YC0C9AB9eHXExHaK872N+kbPhja0sDz30EN9//z3XXXcdX375Jfn5+TRr1owHHniAQYMGnfa1GrNrL2vOAUJ/eAi/lJ/KjxVcdAt5l/0Dl5/33ecip+K1rSxZWVkkJiZy7bXXlodygIYNG9KjRw/Wr18PwJIlS4iLi6vwkWjv3r1p1aoVS5Ys8XjdYgyLxcIdvVpw7xWtAMgqLOGuhD/YfEgfh4qYza5du8jLyyMnJ4cXXniB559/nuDgYKZOncqiRYuMLk8M4gxtStaQ98jp9384fYMBCNz6AfU/uhZL/lGDqxOpWT5GF1CdkJAQvv766wqhvExGRgY2m42srCxSUlK45pprKl0TGxvL8uXLPVCpmMntPZrh72PlxWVJ5Nod3JOwiZk3xtI1Jtzo0kTkuFGjRuF0Orn11lvLjw0aNIjBgwfz4osvMmTIEGw2m4EVimEsFgpjb6OoWT9Cf/gbfvt/wZa9l7Dv7iNryLtgMf28osg5Mf2dbbPZaNmyJVFRURWOJyYmsm7dOrp06UJqaipApWsAIiMjyc3NJScnxyP1inmM6tKUv1/dFguQX+zg3k82s2qvtoAWMYtbbrmlQigHCAgIYOjQoRw9erT84VCpu5xhMWRd/wGFbYcC4JfyI0G/v2ZwVSI1x/TB/FTy8vJ4+OGHAZg8eTJ5eaUP+J1qVt3fv3SzGT1UVDcNu6QJT13XHqsF7CVOpn62mV92HzO6LBE5jYiICEDjthxnsZDbbwYl9UpbFINWv4jvwVUGFyVSM7wumBcUFHDXXXeRmJjI5MmTiYuLw+l0Vvs6q9XrvlVxk4EXRfHcoAuxWS0UOVw89PlWlu1Un6KIkVJTUxk0aBCvvvpqpXPJyckAxMTEeLosMSmXXwjZ176Jy+aPxeUkdOk9WAo0ySK1j1el1ezsbCZMmMCqVasYPnw4DzzwAADBwaUPh9jt9kqvKTtWdo3UTfHtI3nh+ovwtVkocbp4bPFWvtyaanRZInVWVFQUOTk5JCQkkJubW3780KFDfPrpp/Ts2ZPIyEgDKxSzcTS8iNw+TwGla52HfXcfuKqfmBPxJl4TzI8dO8aYMWNYt24dN910E8899xwWiwWA6OhoAI4cOVLpdWlpaYSFhREUFOTResV8rmjTgH8Pi8Xfx4rDBU9+tZ1XfkrG4TT9iqEitdI//vEPDh8+zM0338yCBQv473//y4gRI/Dx8eHJJ580ujwxocLY2yi8YAgAfvuWE7j+dYMrEnEvrwjmubm5TJw4kW3btjFu3DieeeaZ8lAOEBYWRkxMDFu2bKn02q1bt9KxY0dPlism1qtlBP+5sSOh/qULEr2zJoX7P9tMdmGxwZWJ1D3x8fG89tprBAYG8q9//Yt58+bRuXNnPvjgA+0GKqdmsZB75Qs4wloAEPzbC/gcWmNwUSLu4xXB/JlnnmHbtm2MGTOGRx999JTXDBgwgJUrV5KUlFR+bMWKFSQnJzNw4EBPlSpeoFuzcBbc2oXWDUo/RfltTwZj31tPknYJFfG4+Ph4EhIS2LRpE2vWrOG1115TKJfTcvmFkn3tG7isflhcDsKW3o2lUCtuSe1g+p0/k5KSGDhwIKGhoTz22GOnXNN26NChpKenM3jwYGw2GxMmTMButzNnzhyaN2/Ohx9+iJ+f32nfR7vI1T15RSU8/fUOfjj+IGigr5WnrutA/7YNDa5M5Ox5486f50NjtgT8MY/Qn58AwN4ynuyB8+CkT9NFzKyqMdv0wfyDDz7gqaeeOu0127dvB2D37t1Mnz6dtWvXEhAQQN++fZk2bVr50luno0G+bnK6XMxbtY83f91L2f8IEy5tzp29W2DVAC9eRMFc6hyXi7CvJ+O/+ysAcns/QUGXOw0uSuTMeG0w9xQN8nXbz0nHeOLLRPKKHAD0aR3BswM7EOJv+s1xRQAFc6mbLPYs6n98HbbsfbisPmTe8AkljbsZXZZItaoas72ix1ykpl3epgHzb+1Ci/qlm1T9sjudse+tZ88x/cUvImJWLv96ZF/zOi6rLxZnCWHfqN9cvJuCuchxLSOCmH9rFy5vXdr6tC+jgHHvr+fHXdrEQkTErEoadSKv998BsOUeIPT7B0HNAOKlFMxFThLi78O/hsVyR6/mAOQVOfjb51uYvWIvTg30IiKmVHDJROytrgHAf89SAv+Ya3BFIudGwVzkT6wWC5N7t+TF6y8iyLd0FaC3Vu5l2udbybWXGFydiIhUYrGQ0//fOEJjAAhe8Rw+qRuMrUnkHCiYi1ShX9uGzLu1M83CAwD4MekYE97fwN509Z2LiJiNKyCc7AH/xWX1weIsJuybu7DYs4wuS+SsKJiLnEbrBsEsuLUrvVvVByA5PZ9x76/n193pBlcmIiJ/VtK4K3mXlm5EaMtJIXTZ39RvLl5FwVykGqEBPrw0rCPjezYDINfu4IHPNjNv1T602qiIiLkUdJ6MvWU8AP67vyJg03xjCxI5CwrmImfAZrVwd59W/N+QCwn0teIC/vvLHh5ZvI3842ufi4iICVgs5Fw1E0dINAAhvz6LT9ofBhclcmYUzEXOwlXtInn7li40rVfad75s51HGv7+eFcnpmj0XETEJV0D90n5ziw2Ls+h4v3m20WWJVEvBXOQsXRAZzIJbu9CzRTgAu4/lc9+nmxn73np+2HlUyyqKiJhASZPu5F36MAC27L2E/DBN/eZiehaXpvkAbe8sZ6/E6WLeb/tYuHY/+cUn2llaNwhifM/mxLePxMdqMbBCqUuq2t65ttKYLWfE5STsi7H47/sBgJy+z1PYcYzBRYlUPWYrmB+nQV7OVVZBMR+tP8BH6w+SXXhinfOY8ADGxTVj4EVR+Nr04ZTULAVzkVOzFKRT/6MB2PIO47L5kzH8fzgiY40uS+o4BfNqaJCX85VXVMInGw7x3u/7Sc8vLj8eFerPmB4xXN+xMQHHNywScTcFc5Gq+R5cRb1Fo7C4HJTUa0V+z78B5/+JZnFUZ5xhzc+/QKlzFMyroUFe3KWw2MHnmw7zzpoU0nKLyo9HBPlyW/cYbuzUhGA/HwMrlNpIwVzk9ILWvkLwqhlu/Zouqy/5Pe4nv8vdYPN169eW2k3BvBoa5MXdih1OlmxJZcGaFPZnFpYfDwvw4eauTbmpSzRhARrIxT0UzEWq4XIS9uVE/Pd86/YvXRx5CTlXvYSjQQe3f22pnRTMq6FBXmpKidPFt9vTmLcqheRjJ+6xYD8bIzpHM7pbUyKC/AysUGoDBXORM+B0YMveC87z33/Cmp9GyE9P4JOxAwCX1Y+8uKkUdPkLWPWpqJyegnk1NMhLTXO6XCzfdYx5v+0jMS23/Li/j5UbLmnCbd1jiAr1N7BC8WYK5iIGcNgJXj2TwPX/xeJyAlDcqFPpBkcR7QwuTsxMwbwaGuTFU1wuFyv2ZPD2b/v44+CJDS98rBaGdIxiTI9mxIQHGliheCMFcxHj+KSuJ/T7B/DJ2AUcnz3v+SAFne/U7LmckoJ5NTTIi6e5XC7W7c/i7d/2sXpfZvlxmwWuubAR4+Ka06pBkHEFildRMBcxWEkhwav/TeCGN0+aPe98fPa8rcHFidkomFdDg7wYafOhbOb+to9fdqeXH7MA/ds1ZHxcc9pHhRhXnHgFBXMRc/A5/Duh30/FJzMJAJfNn7y4v1HQeTJYtWSulFIwr4YGeTGDHWm5zFuVwvc7jnDy/5iXtYpgwqXNuSQ6zLDaxNwUzEVMpKSA4FX/InDDW1iOj+bFjbuR0/8lHPXbGFycmIGCeTU0yIuZ7DmWz/w1KXy9NRXHSf+Hdm9WjwmXNqd7s3AslvPfHENqDwVzEfPxObS2tPc8Kxk4PnvecxoFnSZp9ryOUzCvhgZ5MaMDWQW8u2Y//9t8mOKTEvrFTUIZ37M5fVpHKKALoGAuYlrFBQSveoHAjXNOmj3vXrrueXhrg4sToyiYV0ODvJjZkVw7C9fu59ONhygscZYfbxcZzPiezbmybUNsVgX0ukzBXMTcfA6uJnTZVHyy9gDHZ897PUrBJRPAYjW2OPE4BfNqaJAXb5CRX8SH6w7w0fqD5BWd2CCjZUQg4+Kac02HSHxsGuDrIgVzES9QXEDwb/9H4B9vn5g9bxJHdv9/4wxvZXBx4kkK5tXQIC/eJKewhIQNB3n/9/1kFZaUH4+uF8DYHjEMjm2Mn48Cel2iYC7iPXwP/kbo9w+W7kJ6nMvihp5zi5Wi5v3IveKfOEObnv/XkxqjYF4NDfLijfKLHHz2xyHeXbufY3lF5cfrB/rSr20D+rdtSPdm4ZpFrwMUzEW8THE+wSunE7Rpntu/tNM3hLw+T1J44c2g55BMScG8GhrkxZvZS5ws3nyYBatTOJxjr3Au1N+Hy9tE0L9tQ3q2qE+Ar1YCqI0UzEW8k8/h3/Hb+wO4nNVfXA1b1h4Cdv2v/NdFzfuRc+ULOEOiz/tri3spmFdDg7zUBiUOJ0u3H+GbxDRW782kxFnxf+8AHyuXtS4N6b1bRRDir62iawsFcxEB8Nu7jJAfHsKWlwqA0y+M3D5PYu8wSrPnJqJgXg0N8lLb5BSW8EvyMX7YeYwVyenYSyrOxvjaLPRsUZ8rL2jIFW0aEB7ka1Cl4g4K5iJSxmLPIuSXpwlI/Lj8mL1Ff3L7zcAZ0sTAyqSMgnk1NMhLbVZY7GDFngx+2HmUn5OOVVjRBcBmgS7NwrnygoZc2bYBkSH+BlUq50rBXET+zG/P94T8MA1b/kmz55c/jb39CM2eG0zBvBoa5KWuKHY4Wb0vkx92HuXHXcfILCiudM3FTcK4sm0DrmzbkJjwQAOqlLOlYC4ip2IpzCTklycJ2P5J+TF7y3hy+/0fzuDGBlZWtymYV0ODvNRFJU4XGw9k8cPOo/yw8yhpuUWVrmkXGcyVbRtyZduGtG4QpJ1GTUrBXEROxy95KSHLH8GWnwaA078euZc/g73djZo9N4CCeTU0yEtd53S52HY4h2U7j7Js51H2ZxZWuqZF/cDykH5hVIhCuokomItIdSyFGYT89AQBOxeVH7O3uoacvtNxBTcyrrA6SMG8GhrkRU5wuVwkHc1n2c4j/LDzGLuO5lW6pnGof3lIvyQ6DJtVId1ICuYicqb8dn9N6PJHsBYcBcDpH07uFf/E3naoZs89RMG8GhrkRaq2L6OA5cdn0rcczql0PiLIl37HHxzVhkbGUDAXkbNhKUgn5OcnCNj5efkxe+trS2fPgyINrKxuUDCvhgZ5kTNzOLuQH3cdY9nOo2w4kMWflkon1N+HK9pEcKU2NPIoBXMRORd+SUsI/fExrAXHAHAG1Cf3iuewXzBEs+c1SMG8GhrkRc5een4RP+06xg+7jp5yQ6NAXyuXtToR0usFaq30mqJgLiLnylJwjJCfHidg1+LyY0UxfWrtqi0umz+FHUZQ0qSHYTUomFdDg7zI+aluQyMobXlp1SCIlhFBtD7+31YNgmgY7KcHSc+TgrmInC+/XV+Uzp4XphtdSo1zYaGg00Tyej4Mvp5fFljBvBoa5EXcp6DYwcrTbGj0Z8F+tvLA3up4WG/VIIgmYQF6qPQMKZiLiDtY8o8SsvI5fA+ugloaEa15qVicpcsDl9RrRc5VL3l89lzBvBoa5EVqRrHDye8pmSSm5rInPZ/k9AL2HMsnv/j0YR3Az2ahRcSJwN7yeGBvHh6In48eMD2ZgrmIyJmxZSQRumwqvod/B8pmz+8g79KHwMczs+cK5tXQIC/iOS6Xi9Qce4Wgnpyez55j+WScYifSP7NaICY8kJZlob1BYHlwD/bz8cB3YD4K5iIiZ8HpIHDjbIJXvYjFYQegJLw1OVfNpKRxtxp/ewXzamiQFzGHzPxiktNPBPWy/x7OsZ/R6xuF+J1oiznpv/UDfWt1H7uCuYjI2bNl7CL0+wfwTV0PgMtipaDzZPLi/gY+ATX2vgrm1dAgL2Ju+UUO9qTnl86yHzvx3/2ZBTjOYBSrF+BzysAeFeqPtRYEdgVzEZFz5HQQuOFNglf/+8Tsef0LyOn/EiWNu9bIW9aZYJ6SksKMGTNYvXo1AP369eORRx4hIiLitK/TIC/inYodTlIyC0g+VjGw780oOOXKMH8W6Gs9qSXmRD97THiAV22U5K3BXGO2iJiFLX1H6ex52kbg+Ox5l7vIi5sKNn+3vledCOYZGRkMHz6coqIixowZg8PhYO7cuTRt2pSEhAT8/PyqfK0GeZHaxelycSi7kD3HCth9LO94YC9gT3o+OfaSal/vY7XQLDywNKw3OL5aTEQQLSICTblpkjcGc43ZImI6zhIC179B8OqXTqzcUr9d6cotUZ3d9jZVjdm16imp+fPnc/jwYRYvXkybNm0A6NSpE+PHj2fRokWMGjXK4ApFxFOsFgtN6wXStF4gl7U+Mfvqcrk4ll9c3r+efFIf+9G8ovLrSpyu8l53dp74uhagSZj/8bAeTKsGgeWz7WEB2kDpbGjMFhHTsfpQ0G0KRS3jCf1+Kr5H/sAnYwfhnwwlv+vd5Pe43+2z5yerVTPm8fHxxMTEMH/+/ArHr732WqKioliwYEGVr9Xsi4jkFJYcXykmv0JwP5hVyJkMlBFBvhU2TvLkBkreOGOuMVtETM1ZQtC61wla8xIWZ+mKYSUR7UtXbml0yXl96Vo/Y56VlUVKSgrXXHNNpXOxsbEsX77c80WJiFcJDfDh4ugwLo4Oq3C8sNjBvoyCCg+e7j6Wz76MAkqcJyJ7en4x6flZrE3JqvD6EH9b6XKOfwrsdXkDJY3ZImJ6Vh/yu/8Ve6uy2fNN+KRvJ/z/DSG/2xTyu98Htqpb7s5FrQnmqampAERFRVU6FxkZSW5uLjk5OYSGet+skogYK8DXRrtGIbRrFFLheInTxYHMyoF9b3pBhQ2Ucu0ONh3KYdOhnAqv9/ex0rz+iTXYWzcI4rJWEabsYXc3jdki4i0cDS4kc/j/CFr3GkFrX8biLCF47X/wT15aOnse2dFt71VrgnleXh4AgYGVd2zy9y/tBcrPz9cgLyJu42Mt3Zm0RUQQfS84cbyqDZSSj+WTedIGSvYSJzuP5LHzSF75sU7RYcy5pbMHvwtjaMwWEa9i8yW/x/3YWw0oXbnl6BZ8jm2j3uc3kX7bL7gC6rvlbWpNMHc6q18WzWr1nqXPRMR7WSwWGocF0DgsgEtbVjxX3QZKdaW1RWO2iHgjR8OLyBzxBUG/v0LQ77PAYgWr+x78rzXBPDg4GAC7vfLugGXHyq4RETFKeJAvXYLq0SWmXoXj+UUOUnPsNAuvuZ3mzERjtoh4LZsv+XFTKeg0EVxOXH4h1b/mDNWaYB4dHQ3AkSNHKp1LS0sjLCyMoKAgT5clInJGgvxstGpQd8Yojdki4u1c/vWqv+gs1ZrPCcPCwoiJiWHLli2Vzm3dupWOHd3XmC8iIudHY7aISGW1JpgDDBgwgJUrV5KUlFR+bMWKFSQnJzNw4EADKxMRkT/TmC0iUlGt2mAoPT2dwYMHY7PZmDBhAna7nTlz5tC8eXM+/PBDbe8sIrWWN24wpDFbROqqqsbsWhXMAXbv3s306dNZu3YtAQEB9O3bl2nTphEREXHa12mQFxFv5o3BHDRmi0jdVGeC+bnSIC8i3sxbg/m50pgtIt6sqjG7VvWYi4iIiIh4KwVzERERERETUDAXERERETEBBXMRERERERNQMBcRERERMQEFcxERERERE1AwFxERERExAa1jLiIiIiJiApoxFxERERExAQVzERERERETUDAXERERETEBBXMRERERERNQMBcRERERMQEFcxERERERE/AxugBvlZKSwowZM1i9ejUA/fr145FHHiEiIsLgymqnESNGsGnTpkrHr7nmGmbNmmVARbXT448/zt69e3n33XcrHNf9XnOq+j3XPe9euoc9S/ev52jc9qyaHrMVzM9BRkYGY8eOpaioiEmTJuFwOJg7dy7bt28nISEBPz8/o0usVVwuF0lJScTHxzNgwIAK55o2bWpQVbVPQkICCQkJxMXFVTiu+73mVPV7rnvevXQPe5buX8/RuO1ZnhizFczPwfz58zl8+DCLFy+mTZs2AHTq1Inx48ezaNEiRo0aZXCFtcv+/fvJz8/nqquuYujQoUaXU+s4HA5ef/11Xn311VOe1/3uftX9nuuedy/dw56l+7fmadz2LE+O2eoxPwdLliwhLi6u/GYH6N27N61atWLJkiUGVlY77dq1C6DC77e4h91u54YbbuCVV15h6NChREVFVbpG97t7ncnvue5599I97Fm6f2uWxm3P8vSYrWB+lrKyskhJSSE2NrbSudjYWDZv3mxAVbXbzp07gRM3fH5+vpHl1Cp2u53c3FxmzpzJjBkz8PGp+CGa7nf3q+73HHTPu5PuYc/T/VuzNG57lqfHbAXzs5Samgpwyn8xRUZGkpubS05OjqfLqtV27txJcHAw06dPp0uXLnTp0oX4+Hj9q98NQkJCWLp0KQMHDjzled3v7lfd7znonncn3cOep/u3Zmnc9ixPj9nqMT9LeXl5AAQGBlY65+/vD5T+Syk0NNSjddVmu3btIi8vj5ycHF544QWys7N55513mDp1KsXFxQwbNszoEr2W1WrFaq363+e6392vut9z0D3vTrqHPU/3b83SuO1Znh6zFczPktPprPaa6v4A5eyMGjUKp9PJrbfeWn5s0KBBDB48mBdffJEhQ4Zgs9kMrLD20v1uDN3z7qN72PN0/xpL97znufOe15/MWQoODgZKe47+rOxY2TXiHrfcckuFmx0gICCAoUOHcvTo0fKHLsT9dL8bQ/e8++ge9jzdv8bSPe957rznFczPUnR0NABHjhypdC4tLY2wsDCCgoI8XVadVLZJgh4sqjm6381F9/zZ0z1sHrp/PUP3vHmcyz2vYH6WwsLCiImJYcuWLZXObd26lY4dOxpQVe2VmprKoEGDTrl2aHJyMgAxMTGeLqvO0P3uebrn3Uv3sGfp/jWe7nnPcvc9r2B+DgYMGMDKlStJSkoqP7ZixQqSk5NP+9SunL2oqChycnJISEggNze3/PihQ4f49NNP6dmzJ5GRkQZWWPvpfvcs3fPup3vYc3T/moPuec9x9z1vcblcrpootDZLT09n8ODB2Gw2JkyYgN1uZ86cOTRv3pwPP/xQW9262Xfffcc999xD27ZtGTlyJHl5ebz33nsUFxfzwQcfaBMLN+rfvz9Nmzbl3XffLT+m+71mner3XPe8e+ke9izdv56lcduzanrMVjA/R7t372b69OmsXbuWgIAA+vbty7Rp08r7icS9vvvuO958800SExMJCAggLi6OqVOnaoB3s1MNOKD7vSZV9Xuue969dA97lu5fz9G47Vk1PWYrmIuIiIiImIB6zEVERERETEDBXERERETEBBTMRURERERMQMFcRERERMQEFMxFRERERExAwVxERERExAQUzEVERERETEDBXOQ07rvvPtq3b88HH3xQ5TUffvgh7du355///KcHKxMRkT/TmC3eThsMiZxGamoqAwcOxGaz8fXXX1faMS09PZ3rrruOwMBAlixZQnBwsEGVioiIxmzxdpoxFzmNqKgo7rvvPrKysnjxxRcrnX/hhRfIzMzkySef1AAvImIwjdni7RTMRapx6623Ehsby2effcbvv/9efnzt2rV89tlnDBw4kCuvvNLACkVEpIzGbPFmCuYi1bDZbDz99NNYLBaeffZZnE4nDoeDp59+mnr16vH3v/8dgKysLJ599lkuv/xyOnbsyHXXXceCBQv4c7fYli1b+Otf/0rv3r2JjY2lV69ePPjggxw+fLj8mldeeYWLL76Yb7/9lssuu4wuXbqQkJDg0e9bRMQbacwWb+ZjdAEi3uDiiy/m5ptv5v3332fRokUUFBSwY8cOnn/+eRo2bEh+fj633XYbhw4dYvTo0TRu3JjffvuN559/nj179vDkk08CsH37dkaPHk2LFi2YPHkygYGBrFu3js8//5y0tDTefffd8vcsKSnh8ccfZ+LEiRQVFdGtWzejvn0REa+iMVu8lYK5yBmaOnUq3377LS+//DIlJSX07NmT4cOHAzB37lySk5P55JNPaN++PQCjR4/mpZde4s033+Smm26iQ4cOvP/++1gsFt555x3Cw8MBuOmmmyguLmbJkiVkZmaWH3c6ndx2221MnjzZiG9XRMSracwWb6RWFpEzFBoayiOPPEJqaiq5ubk8++yz5eeWLl1Ku3btiIyMJD09vfxHfHw8AD/88AMATz31FMuWLSsfyAFyc3Px9/cHID8/v8J79unTp4a/KxGR2kljtngjzZiLnIXBgwfz4IMP0qlTJ1q0aFF+fN++fRQWFtKrV69Tvu7QoUMAWCwWMjIyePPNN9m+fTv79u3j4MGD5T2NTqezwusaNGhQQ9+JiEjtpzFbvI2CuYgbOBwOunXrxpQpU055vlGjRgAsX76cu+++m0aNGnHppZdyxRVX0LFjR3755RfefPPNSq+zWvWhloiIu2nMFrNSMBdxg6ZNm5KXl0fv3r0rHM/KymLlypXlMzXPPvssLVq04JNPPiEoKKj8usWLF3u0XhGRukxjtpiV/mkn4gb9+/cnMTGR5cuXVzj++uuvc99997Fz504AMjMziY6OrjDAHzp0iKVLlwKlszgiIlKzNGaLWWnGXMQN7rzzTpYuXcqUKVO4+eabadu2Lb///juff/45V1xxBVdccQUAV1xxBV9++SX/+Mc/uPjii9m/fz8ff/wxBQUFAOTl5Rn5bYiI1Akas8WsFMxF3CA8PJyPPvqIWbNm8fXXX/PRRx8RHR3N3XffzeTJk8v7Dp966imCgoJYtmwZn3/+OY0bN2bYsGFcffXV3HLLLfz2229cdNFFBn83IiK1m8ZsMSuL689bXImIiIiIiMepx1xERERExAQUzEVERERETEDBXERERETEBBTMRURERERMQMFcRERERMQEFMxFRERERExAwVxERERExAQUzEVERERETEDBXERERETEBBTMRURERERM4P8DilDYf1n+2bQAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = simul.plot(subplots=True, layout=[1,2], legend=None)\n", "for i, lab in enumerate(simul.columns):\n", " ax[0, i].set(ylabel=lab);" ] } ], "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": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 }