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@jessegrabowski
Created January 26, 2023 19:51
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Solving Economic Models with Reinforcement Learning
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{
"cells": [
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"cell_type": "code",
"source": "import matplotlib.pyplot as plt\nimport numpy as np\nimport numba as nb\nfrom numba.experimental import jitclass\nfrom quantecon.distributions import BetaBinomial",
"execution_count": null,
"outputs": []
},
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"metadata": {},
"cell_type": "markdown",
"source": "# Basic Model"
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"cell_type": "markdown",
"source": "The McCall (1970) search model of unemployment was influential in providing a microeconomic framework for understanding how people decide to work. \n\nWorkers seek to maximize the present value of their lifetime utility, defined as a the discounted sum of all one-period utilities:\n\n$$U_t = \\mathbb E_t \\left[ \\sum_{s=0}^\\infty \\beta^s u_{t+s} \\right ]$$\n\n(Note that in the Economics literature, the discount factor is always $\\beta$ (not $\\gamma$ like the RL literature).\n\nOne-period utility, $u_t$, is just the income of the worker. This can be either a fixed-value unemployment benefit, $c$, or a wage $w_t$:\n\n$$u_t = \\begin{cases}c, \\quad \\text{if reject} \\\\\n w_t, \\quad \\text{if accept}\n \\end{cases}$$\n\nGiven this, we can say something about $U_t$ in each of the two cases. If the worker accepts, he locks in wage $w_t$ forever, so $u_{t+s} = w_t \\forall t$, and $\\sum_{s=0}^\\infty \\beta^s w_t = \\frac{w_t}{1 - \\beta}$ is the result (since $\\beta < 1$)\n\nIf he rejects, he's going to have to keep playing. We can evaluate the decision to keep playing by re-writing the inter-temporal utility function $U_t$ recursively:\n\n$$U_t = u_t + \\sum_{s=1}^\\infty \\beta^s \\mathbb E_t[U_{t + s}] = u_t + \\beta \\sum_{s=0}^\\infty \\beta^{s+1} \\mathbb E_t[U_{t + s + 1} = u_t + \\beta \\mathbb E_t [U_{t+1}]$$\n\nGiven that the worker has rejected on this branch of our analysis, we also know that $u_t = c$. So the intra-temporal problem becomes:\n\n$$U_t = \\max \\left \\{ \\frac{w_t}{1 - \\beta}, c + \\beta \\mathbb E_t[U_{t+1}] \\right \\}$$\n\nNote that this is itself a Bellman equation and a value function, and we can solve it via value function iteration. The last piece is just to say something about the source of randomness in the model, $w_t$. Assume $w_t \\sim F(\\cdot)$, so that:\n\n$$\\mathbb E_t[U_{t+1}] = \\int_{w^{\\prime} \\in \\mathcal W} U(w^\\prime)F(w^\\prime)dw^\\prime$$"
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"cell_type": "markdown",
"source": "# Discrete Approximate Wage Distribution\n\nIn approach 1, I follow QuantEcon's first lecture on McCall and use a discrete grid approximation to the distribution over $w_t$. \n\nThis will also transform the state space from $\\mathcal S \\subseteq \\mathbb R^+$ to a finite set of integers $\\mathcal S := \\{1, 2, \\dots, n \\}$, where $n$ is the size of the grid.\n"
},
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"cell_type": "markdown",
"source": "## Small State Space\n\nStart with n = 10"
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"cell_type": "code",
"source": "n, a, b = 10, 200, 100\nwage_probs = BetaBinomial(n, a, b).pdf()\n\nw_min, w_max = 10, 60\nwage_grid = np.linspace(w_min, w_max, n+1)\n\n# plot distribution of wage offer\nfig, ax = plt.subplots(figsize=(10,6))\nax.plot(wage_grid, wage_probs, '-o', label='$q(w(i))$')\nax.set_xlabel('wages')\nax.set_ylabel('probabilities')\n\nplt.show()",
"execution_count": 2,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1000x600 with 1 Axes>",
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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Value Function Iteration\n\nTo get a value function, initialize the 10 states with arbitrary values, then iterate on the bellman equation.\n\nHere's a class to handle it."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@jitclass(\n {'β':nb.float64,\n 'c':nb.float64,\n 'n':nb.int32,\n 'w_min':nb.float64,\n 'w_max':nb.float64,\n 'w_grid':nb.float64[:],\n 'q_grid':nb.float64[:]}\n)\nclass McCallModel:\n \n def __init__(self, q_grid, β=0.99, c=25, w_min=10, w_max=60):\n self.β = β\n self.c = c\n self.n = len(q_grid)\n self.w_grid = np.linspace(w_min, w_max, len(q_grid))\n self.q_grid = q_grid\n \n def action_value_function(self, i, v):\n β, c, w_grid, q_grid = self.β, self.c, self.w_grid, self.q_grid\n \n accept = w_grid[i] / (1 - β)\n reject = c + β * (v * q_grid).sum()\n \n return np.array([accept, reject])\n \n def value_function_iteration(self, max_iter=500, tol=1e-8):\n v = np.zeros_like(self.w_grid)\n v_history = [v]\n \n for i in range(max_iter):\n v_next = np.empty_like(v)\n for j in range(self.n):\n v_next[j] = np.max(self.action_value_function(j, v))\n \n v_history.append(v_next)\n if ((v - v_next) ** 2).sum() < tol:\n return v_history\n v[:] = v_next\n \n return v_history",
"execution_count": 3,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "mc = McCallModel(wage_probs)\nv_histroy = mc.value_function_iteration()\nprint(f'Converged after {len(v_histroy)} iterations')\nV_10 = v_histroy[-1]",
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"text": "Converged after 122 iterations\n",
"name": "stdout"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### VFI progress\n\nWe can see it converges to a solution where everything below a threshold is rejected (the flat line part), and everything above is accepted (line with slope $\\frac{w}{1 - \\beta}$)"
},
{
"metadata": {
"trusted": true,
"scrolled": false
},
"cell_type": "code",
"source": "fig, ax = plt.subplots(figsize=(14,4), dpi=100)\nfor i, v in enumerate(v_histroy):\n ax.plot(mc.w_grid, v)\nax.set_title('Progress of VFI')\nplt.show()",
"execution_count": 5,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1400x400 with 1 Axes>",
"image/png": 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AD/Xwg/+orByn+kSOaYL/PT2gY1J7tBY2DS371t16aOkTqW3yKuhU8BOJRDRhwgQtXbpUkjRu3Djt2LFDTz75pG6//fb4OsMwkr7ONM2zXjvTmWvOtf587/PQQw/pvvvui3/e3NyssrKyj74oAAAAAADQIyz/53uV5WjWcP9+PejcJZcvEK+FTIvetVRqq7NS9ZE8udLzU9jp1dOp4KekpETDhw9Pem3YsGH63e9+J0kqLi6WFJ3YKSkpia+pra2NTwEVFxcrEAiosbExaeqntrZWU6ZMia85ceLEWd+/rq7urGmiU5xOp5xOZ2cuBwAAAAAAdGOP/O8Fysy3qSx8VNcFdmqxTki+WNGQaswcbXSM0EF7mdq90re+91Ndm9KOr75OBT9Tp07V7t27k157//331b9/f0lSeXm5iouLVV1drXHjxkmSAoGA1q5dq+XLl0uSxo8fL7vdrurqas2dO1eSdPz4cW3fvl0rVqyQJE2ePFler1dvvfWWrrvuOknSm2++Ka/XGw+HAAAAAABA7/LbH/+HDnu3yGP3arh/nxanv6c0XzBeD5pW/c06WFudlWoK5qivZ0y33sT5cuhU8PNP//RPmjJlipYuXaq5c+fqrbfe0tNPP62nn35aUvTxrIULF2rp0qWqrKxUZWWlli5dqvT0dM2bN0+S5PF4dOedd2rRokXKy8tTbm6u7r//fo0aNUqzZs2SFJ0iuvXWW/WVr3xFTz31lCTprrvu0uzZsy/oRC8AAAAAANAzPPLgArlzrOoXPqKpgZ3qpzopFCsa0lHl6U3HCH1g7auWZkP/55EnNPG879i7dCr4ufbaa/X888/roYce0ne/+12Vl5frX//1X/X5z38+vuaBBx6Qz+fT3XffrcbGRk2cOFEvvfSS3G53fM1jjz0mm82muXPnyufzaebMmVq5cqWsVmt8za9//Wvde++98dO/5syZo8cff/xSrxcAAAAAAHRhv/3xf+hw81Zl2xo10r9HDzrfl9MXitf9pk2brIO13VmpplCOyrJG9/qpnvMxTNM0U93EldCZM+0BAAAAAEDq/PO375Y7y1S/8BFNDOxUH51Mqh9Wgd50DNcH1r5qbYzoO9//aYo67Ro6k3l0auIHAAAAAADgUv32x/+hI97NyrY3abR/jx60vS+7Lxyvd5h2vW0dqp3OQfIGPSpjr56LRvADAAAAAACuuKX/5x653EGVBw9rRmCnSoyGpL16DqpIbzmG64i1VC0nw3r4B0/p+pR23DMQ/AAAAAAAgMvutz/+Dx1u2aI8S71G+/foAcse2doj0aIh+UyH3rIO007nQDUHsrT4//xfDUhpxz0TwQ8AAAAAALgsln3760rPCqs8dEgzAztVaDQlioa0TyV62zlMRy2laqv36Tsrfq7pKeu2dyD4AQAAAAAAF+Vfl39XwXCd8qz1Gtvxvh6w7ZXVFztDypDaTKfesg3TLucgNbdn6MElP9ag1Lbc6xD8AAAAAACAC7b0/9yjzMyABoYO6guBnco3mhNFQ3pfffWOc6iOG8VqaQpoySM/042pa7fXI/gBAAAAAAAf6nvfWiinO6x8o07j/O/rQct+WU6b6mkxXXrTNly7neVqbXdp8ZLHNTi1LeM0BD8AAAAAACDJsiX3KiPdp4rAIX3NvkO5/tZE0ZB2qZ/+5hyqGqNILfV+LfnBzzQrde3iPAh+AAAAAADo5b774N1K91hUaNRpnH+3HtIBqT1WNKRmM10bbcP1vqNcbb40LV7yuIaltGNcKIIfAAAAAAB6oe8vuUeZLp8qggf1TecOefztSfUdGqBNaUNUpyK1NPq1ZPnTujlFveLiEfwAAAAAANALLFl8lzKzHSo2Tuiajt16UIckX6xoSE1mhjbaR2iPY4B87Q49sOQnGpHSjnE5EPwAAAAAANBDfX/JN5Tp8mlI4IDuS9upLL8vXouYhrZZyrXZOUR1kXz5mk39n0d+oltT2C8uP4IfAAAAAAB6iCX/+yty5zlUbJ7QBP8uPagjSVM99aZbG+0jtM/RX742hxY//LjGpLRjXGkEPwAAAAAAdGPff+QeZbnaNMS/X/en71JmR0e8FjENbbEM0mbnYNWbBfK3WPXtRx5LYbe42gh+AAAAAADoRpY8+BW5sx0qNY9rgv89PaijSSdw1ZlZ2ugYqf32fmpvtuqhR57QuJR2jFQi+AEAAAAAoItb8cg9cqe1aph/nx5wvqf0Dn+8FjYNbbZUarNzsBoiebJb87Vw8XdS2C26EoIfAAAAAAC6mO8+8GVl5qapT+S4rgvs1AOqSdqr54SZrY2OETpgL5OvyaqHlj6h8SntGF0VwQ8AAAAAACn2p1/9l3bsX6csZ7OG+/fpAdcupXUE4/WgadW7lgptTRusxmCu+nrG6HP33JnCjtFdEPwAAAAAAJACjzy4QO4cq8rCR3VdYKc+rtqkqZ7jZq42OkbooL1MvhabvvXIj3VdSjtGd0TwAwAAAADAVfDbH/+HDjdvVrbNqxH+fVrs3K00X2KqJ2Batck6RNudFWoM5qiMqR5cBgQ/AAAAAABcBr/91b/r4N6tsjokmzUkh/zKMH3KirQoN9ys68NH1FcnpVNZjyEdUb42OkboiLWvmhtD+s73n9bklF4FehqCHwAAAAAAzuPFVb/Tu2+vls1hl9UWksMIKN1sV1akVTnhZuVHmlUQadRn5JXdCEuBD38vv2nTO9ah2p5WIW8wS2VZY5nqwRVF8AMAAAAA6JXWV6/R2lf/R1aXVVZ7WE755TJ9yoq0KjvcovyIV4Vmk24yG3WrJSyFFP04FyP6S8Q0dFIe1RrZOmnxqMGapWZrptosGeow09TaGNLD339KU6/WRaLXI/gBAAAAAPQom15bp5f++ltZ022yWsOyW/xKN31yh9uUE25WXizQucZs0hR78PyBjhQPderMLNUZ2TppyVaDNUteq1ttlnR1mE6Fw3aFAxE11dUpKytPlnBIvtw0TSwcqk/feffVuGzgnAh+AAAAAADdwsE9e/SblY/Jlm6T1RqR3RKQy/TJfWpCJ+xVvunVcLNR4+2B6F46wfO8YSzQaTAzVWvkqO70QMdIl99IUzBsU8Rvqs3rlcuZKSkkX5ZLnpBbucdaFQ6fVENhu5pKypQfcWmcLUc3fu52FQ6qvAo/EeCjEfwAAAAAAFLu+9+5Rxa7IYs9IrslGAt02uQJtygvHJ3QKTQb9S27/4IDnSYz44xAJ1MtRoY6jDSFQzaFgoZafK1KNx1Ks6TJ0e5TfXqH2vIz5XTmqajZooKasMLeNvksPrVl1aimIFf1OYU6nOHS0OKg+h7pr2sGDdXUO26/Gj8moNMIfgAAAAAAV8zyJQsla0Q2uymbEVSafMqMtCk73KK8iFcFkSYVmk160OKTwop+fJhYoNNspqvWyFadJVv11ix5LVlqsaarQ2kKRRyK+KWOtjZJFlnSnXKF0pVV55Mv7FWjp0ONBTaZnlxlmmkqa8mRp9Yqo86mQEej7JYWmY275PO06ainvzaVj1Rj3gAVuzI1rKVRo49kKONYlq7/x7nK719+5X+AwCUi+AEAAAAAdNpj310sf6RdNqcpmzWkNLMjGuhEWpQb9io/4lWR2ajFRvsFBzptplMnjFzVWaIbIzfFNkX2yaVgxK5wyCJfm1/WcEhWm02BzDRlhjOVV9chR2uzOhwNavOE1ZjrUUdhgSxOt/IjYRU1B+QJZ8jd1F+Fx4MK7mtQu3FcQdcJhbMP64THqqbs/jpmH6P9niql5bZpqH2f+jU1a3hNq2zb7KocP1LXfvm2q/GjBS4rwzRNM9VNXAnNzc3yeDzyer3KyspKdTsAAAAA0C385IdL1NpyUlanRVZrUGmmT5lmuzzhFuWGm+MTOjlG6wW/p8906ISRo1ojWw1WjxqtbrVaMuVTmoKmQ6GQRf7WDoWCPrlt6WpzRhTxuJXpz1RBQ1DWxg51ROrU7vKqNUuqz85Wq7tYwTS3HA5D/cIdKm2OKKvBLrMpU5EOi0I+v8zWZkUiTWpNOymf54gcnpMys9LVESlTjTFc29wj1JDnVkX2Pg0x96uwoUUZJwtlPVEsT7pVN351vrKKi6/gTxu4OJ3JPJj4AQAAAIBe4OdP/otqTxySzWnIZgnKKb/SzTZ5wq2nBTqN+rrREv0C/3neLDah02Hao49cGTk6afWo0eJWizVTPiM2oRO2KOSLqLZuv/p6yhVWQM0eiwxXjrICGSpoDMjREFHI51WHtVGB9Ba1ZobV5syT15Ypv9uhQFmGPLZ29QtZVdJcqr5NLhn1GdJhQwG/FAgGZbaZSgu0qc1Wr/rM4+rIOa70og6luZwKh/roRGCItmbeqB3ZlcrNbdLIrJ0aFDyof2hYJdUXyb6rv1z+cg2dMkRj7/hfV/yfBXA1MfHThT2x4sua0f52qtsAAAAA0I1ZFVGu2aI8NctiXNhf/wKmVbVGjmqNnNgjV261WDLUbklXIOJQOGRTuD2o2pMHVJxXIVdHQI1pfrXnpMnqypU74FRxU1jOBkPhNr/84ZMK2esUcrWoIyOoRneuGlxlak8rVntmuoy0sIqtDSruaFdRq0XZzVmyeLNktBmK+IPyBSPyhU0Zvg5ltftkRBrUmF6j49nHFM5tU1Z2QPk2q8yOUtV2VGirc6g2Zw9VS45H/bMPa1T6Ng0KHFROfbt8TYWynxyotNY05WQZmv61+XIXFF7hfwrA5cXETw+RHmnXcH2Q6jYAAAAAdHexCZ2gaY1N6GSr3uJRgzVLzZbohI7fdCoSsijol07W7VNB/kCl+w2FA21qygqpLc8tmyNHWUG7ipojymi3aECwUIEPWuRXk4rSGhVqaVIgPaCWjBxtzuwjb04/taSXyu/uqyxni0osJ1XQ0a7yFkNjW7Jlr8uQ9YBD8rcr4M9UWzhdbWGr6gMRuTualNneKL/tmOqzjutYvlfqH1KeO6B+pqnsjiIF/cO0zajUi5ahOuoplaN/RIM9ezXcvkNfC7yhrEa/Wo4UKtIwQJnNk5Ue9uu6m0ZrxDf+LrX/PICriOCnCzsRLNQPXV9IdRsAAAAAujNTioStCgciajp+RJn5fZRuOuVsbVeLo03ebEO+nAzZbR65QzaVtIRU7r5ORq1dZrtfvrCUfvKkzGP7ZaY3KpjuV226Wy1FJWoq7a+Tzr7yZg6VxR1UseOkio2Tym5v14hmU+62dqXVuWU/4JYl4FbEZ8gX9KslYqom4pAtHJC7o1XZrV6lhY6rPf2YGvPqVNM3IltOUEXpAQ0JhlTZkads/xBtC1Xor21DtCd7gEJFLmV62jUsc7duMl7XoNAeZTSG1XywSK2NfWRvmSFLR0QDc6264e4vKj0nJ9X/JICUIPjpwvzpmTqSEUp1GwAAAAC6M8OQXS55wobK3TnyNFik5jQZbWFl+9uUf7RBQesJRdJ2yZJ+Uh3pfnkz3WrLKVCzUaZae3/Vusao1Z2mnMwmlThOqChcrxyfT+WtNXK1+eWsKVH6/gLZ/aWSP1tBf5NaQwG1RKRa0yebaVGGP6jstlZltx2X03ZMwazj+qAwqNpyU2nZQQ2wBTQsENCAjizVBgZqW1uFNrRX6GeZFeoozFQk26E8T6OGO3Zpip7T4PBuObySd3+JmpqK5WuuksNvV14koBm3jNOQqptT/ZMHugSCny7Mc3CfimszUt0GAAAAgG7NVMjWrnDaSYUyTupkul/BwnT5bLlqN0vUYO2vw2nXqC7DIzPTVElGrUodx1UQalSpr0WDWzbL0ZYtx7FiZbSXyhWolDXQX6a/Re3+RrWE/aoPN+mYEZTV8CgjYCqr3aKc1iYV+I+qIf2YDue36P1SQyfzI8ryBDU4HNBwf0AT/WmqDZRrS0OF3jUHaaWjQk05uYp4HIrkONQn47gmWbZqqHZqcGS3rM02NR0rVlNTsY4236z8gFuZHSENKLJr2gNflsvtTvUPG+hyCH66sP1jJ8h6rC7VbQAAAADoxkwZqnMW6JCrRE2ZbrkzWlSSXqMyx1HlBrwa7NunsS3vyfB55DhSJFdbidzBkXKGTBkBn4IdXrUGG9QSataRSItCFo8slhylhVzKag8rp61GZW3HFNBRHcs+qQ8KTb0xwFBTfkQFaUENDwY02h/QbL9FdR39tNVXoc2RQXpOg3TcXaxIgVORbIfksarceVDX6XUN0U4NNnfLbHHI21SspqYS7fbeorxQtrL8Vg2IdGjcnEkaeMOMVP94gS6P4KcLuyazTcfH1qS6DQAAAADdmClTA/37Nb01rEh7hqz1hUprL5E7MFpZYZdsgaBMf6vag41qDtarJbRHxyNWmdYcWax5sofzlNXhUnZbjfq2HlOab7saXcd1uCCod4sNHSyS2nIj6m8Narg/oKmBgL7YEVJ9U19tjYzQlsgg/d4cpH2OPgrnpimSHQ16bFmmKow9GqpdGqqdqtD7CrelqakxOtGzzft3Sgu6VRBMV0lHUGP6ODX17jvlSE9P9Y8U6FYIfrqwfvuHqG/rsFS3AQAAAKCbc4YssgQ6FAx41RJsUHPgsGrC+7TfdMiw5sliyZPV6KvMjgJlt51Q37Zjymx7Vwod05HcFn1QKB0sM3So0FAwO6whoeh+PB/3R39tri3SZnOItkQG6aXIIL2nfvK5MxTJdsQ/0tL8GqbdGqqdGqqdGqh9CvnS1NRULG9TsTY3zVYkkKHCsFv5HYb6GX6N/V/TNGDK1FT/+IBujeCnC2v0Nejogc2pbgMAAABAN2YaUthwxQMew1Kh9HC5ctprowFP6y5lth1TU1qdPiiUthYZOlgoHSoy5EwLa3gwoGH+gD4XCGhYR0Cho1naHKnQlsgg/dQcpO2RcnkdbkVyHPG9ecwsu9zWVg01d2pILOjpp0MK+51qaopO9LzbNFx+f6Y8kXTlBdNU2BFQUf8MTbrrDqZ6gMuI4KcLyzesCgZGpLoNAAAAAN2cy3dSGW2HlNm2XnZ/jY7mBXSwyNDBwYYOFRk6VCAVWCIa5g9oeCCgW/xBDW8MyBp2aktkoLaYg/RsZJA2RwbphHIVcdvjkzxmtkOmy6o8o0FDzb9pqHZpiHaq1DyqcNChJm+RmhpL9G7TKPl8WbKbNhWFs1TeIWUYHRr32RvVd/y1qf4RAT0WwU8XVlu4U77Nq1PdBgAAAIBuzJS0v0A6NMLQwSJDx3OlfiFTwwJ+jfIHdFsgoKE1AaVFrNoZ6a/NkUH6f7GwZ79ZItltCmXb4yFPxOOQbBaV6oQGm2/H9+gpMOsUCdvU7C1UQ1OxNjeNUWtrjiSLciOZ6hNwytXhV1GFWxPv+pLsDkeqfzRAr0Dw05X1a9NfPx5KdRcAAAAAujGLKfULhTTVH9A/BgIa+kFA6aZ0wCzVu5ERWhUZqEcjg/Se2U8B2WVx2xXIskdDnmyHzAybDEMaYBxTZWRzdI8ec5c88sqMWNTqLVCDt0Rbmq5RS0ueTNMqp2lXccitfh2m0m0duubzN6t09OhU/yiAXongpwsb5yvWZ46dSHUbAAAAALq5WiNfm0JDtSYySD+M7cvTonRZbRaZOQ4FshKPbslukVURVVqOqDK8KXa0+nvKMNtlmpKvOV8N3r76wDtBzd4CRSJ2GaZUEMlSScAhp79DpcNyNP5L85nqAboAgp8u7I+eeXqq45pUtwEAAACgGzMl+ZQmSUrLtMvvsSvgiU3zZNokw5DTCGu45bAqw29riLldFXpfznBAkuRvzVZTU38d8hbK6y1SKOSUJKWbTvUPupXREVGGo0PX3HGrioYNT9VlAvgQBD9d2EG3Q97KwlS3AQAAAKCbMzNtingc6nBaJUmZlpCGWz7QoNCbGmJuUbl5QLZIdJuJkN8t78n+OthcpMamYgWDLkmSxTRUFPEo22+XM+BTyah8XTN/HlM9QBfXqeBnyZIleuSRR5JeKyoqUk1NjSTJNE098sgjevrpp9XY2KiJEyfqJz/5iUaMSJxM5ff7df/99+u3v/2tfD6fZs6cqSeeeEJ9+/aNr2lsbNS9996rP/zhD5KkOXPm6Mc//rGys7Mv9jq7paJCi8J+d6rbAAAAANDN5VqDGmE9oEHBjRoc+ZvKwodlCUeixYhb3tp+qm8q1snmQvk7En8HyYq41D+UqXRfWBkuv8Z/ebbyKypSdBUALkanJ35GjBih1asTJ01Zrdb471esWKEf/ehHWrlypQYPHqxHH31UVVVV2r17t9zu6P94LFy4UKtWrdJzzz2nvLw8LVq0SLNnz9amTZvi7zVv3jwdOXJEL774oiTprrvu0vz587Vq1apLutjuZrb+rMHmM6luAwAAAEA3ZsiUO9QsI3ZujMXIUFtDP9XXFulEc6HafR5JhiTJZlrVN+KRp8MmZ6BdfSaUaPz8z6eueQCXrNPBj81mU3Fx8Vmvm6apf/3Xf9W3v/1tffrTn5Yk/eIXv1BRUZF+85vfaMGCBfJ6vfqP//gPPfvss5o1a5Yk6Ve/+pXKysq0evVq3XLLLdq1a5defPFFbdy4URMnTpQk/exnP9PkyZO1e/duDRky5FKut1txGVbl2SypbgMAAABAt2Yo6KvUiUNZOuEtlrctW1Li7xk5kUwVhtLlag8p3e3XhLs+qdyy/inrFsDl1engZ8+ePSotLZXT6dTEiRO1dOlSDRw4UAcOHFBNTY1uvvnm+Fqn06np06dr/fr1WrBggTZt2qRgMJi0prS0VCNHjtT69et1yy23aMOGDfJ4PPHQR5ImTZokj8ej9evXf2jw4/f75ff74583Nzd39tK6nA8+GKa1a2enug0AAAAAPYjDtKk0nK2sDovswTaVTS7T2M/eluq2AFwhnQp+Jk6cqF/+8pcaPHiwTpw4oUcffVRTpkzRjh074vv8FBUVJX1NUVGRDh06JEmqqamRw+FQTk7OWWtOfX1NTY0KC8/e0LiwsDC+5lyWLVt21v5D3Z1hGDIMI9VtAAAAAD2feYW/8KLf/3IwlG+6VRBMl7M9oPTsgCbe/b+UVdonlU0BuEo6Ffx87GMfi/9+1KhRmjx5sgYNGqRf/OIXmjRpkiSdFVSYpvmR4cWZa861/qPe56GHHtJ9990X/7y5uVllZWXnv6Au7vprpmhK5YRUtwEAAABcnIgpMxyRGYrIDJtSKCIzFH1NoVO1U59H15ih6Hqd+n3sV52zdvb7miFTCkdSHLRcuLAZVsQMKWJGFDFDsc/Diij6a/xzM6zwqXUKnfaaqYiM6IdpUUSGFInIiIQVMQMyLQHZMizqe/0Ajfr7T6f6cgGkwCUd556RkaFRo0Zpz549+tSnPiUpOrFTUlISX1NbWxufAiouLlYgEFBjY2PS1E9tba2mTJkSX3PixImzvlddXd1Z00Snczqdcjqdl3I5XU7rm8fVsuaDVLcBAAAAdH82Q4bVIsNmkWE1JJtFRuw1xV4zDVOmIgorrEgkrHAkpFAkqHA4oFAooGDIr2DQr0CgQ8GAT/6AT4GOdgUC7WcENInfRxRSOBbqnFVXONqbYZHV6pIMpyKmU4aRJhlpsV+jnxtGmmRJk2G4ZAuFle5vk6ujVekdjXJ1nJRp1qvWU6+mIq+yK0s1fNqnNPaar8juzEjtzx1Ayl1S8OP3+7Vr1y5df/31Ki8vV3FxsaqrqzVu3DhJUiAQ0Nq1a7V8+XJJ0vjx42W321VdXa25c+dKko4fP67t27drxYoVkqTJkyfL6/Xqrbfe0nXXXSdJevPNN+X1euPhUG9hcVplyXKkug0AAADgohiGIcNmxIMVw2aRrInAJVE7PYRJBDSKfc2ZAU3y155aE10fUUTBYIf8HW3q8LXJ39GqjrY2dbS1qqO1RR1tLfK3tkY/bzz1Wqs6WlsVCYcu6XodLpfSMt1ypmfKZs+UxeqSjDRFwnaFgg4FO6zqaLfJiDhkM9JkWKIBj2RPerrBajWVYbQrra1OjvpDcrUfU5rvpFwd9UrrqJdMvw4VSu/3MXR4kJTVL1tjh03Rx0Y/qsKikZf4Tw1AT9Op4Of+++/XJz7xCfXr10+1tbV69NFH1dzcrDvuuEOGYWjhwoVaunSpKisrVVlZqaVLlyo9PV3z5s2TJHk8Ht15551atGiR8vLylJubq/vvv1+jRo2Kn/I1bNgw3XrrrfrKV76ip556SlL0OPfZs2f3qhO9JMl9Q1+5b+ib6jYAAACAq8o0TQU7fOpobZXvVGDT2qKO5mhAkwhrWuRva5WvNfH7gM93Sd/bYrUpLTNTaRmZSst0n/F7t5wZmXKmZygScSgcdMjfYZO/zaI2r6HWxoC8J31qaf7wAMmwSjablJmTJneOQxmWNqW1nJC9Zp+sezfLeeKA7MEWnb7JRWNGNOR5v4+hPX0MOQodmpg/WDMGfUKjh8+VzZ52SdcMoGfrVPBz5MgRfe5zn9PJkydVUFCgSZMmaePGjerfP3rU3wMPPCCfz6e7775bjY2Nmjhxol566SW53e74ezz22GOy2WyaO3eufD6fZs6cqZUrV8pqtcbX/PrXv9a9994bP/1rzpw5evzxxy/H9QIAAAC4SsKhYDSoaUsENv625Cmb00Ocjra2+JpIOHxJ39uZniFnRuZ5Q5y0WN0Ze82V6ZYttn1Ee3NAzSc71HzSF/2o71DNIZ+a631qa/TLNAOSAh/6/dMy7crKS1NWgUtZeS5l5TnlCnllP7ZXlvc3y7/lXfn37JEikaSvC1mkPaXSnj6G3i+Nhj3BTFNTHHmaVjpF9426Q/kFwy7pZwOgdzFM0+wm2551TnNzszwej7xer7KyslLdzkXZ8P9+q43/81yq2wAAAAA6zTRNmWeEGp1ltdmSJm0uOMTJyJTltP+wfC6BjtBZwU709x1qOelTKHj+3m12i9z5LmXlpykr3xUNefJdsY80WYM++bZslW/LZvk2b5Fv61ZFvN6z3qc1y6KdpaZ2xSZ6DhZJIas0wrRravYQTauco1FDPyOrjS0gACR0JvO4pD1+cGWZZuSS/0sHAAAAkGrOjIyzHpdynTZp82Ehjs3h/MgTgj9MOBxRa4M/Eeyc7FBzvU/NddGQp6M1eN6vNwwpI8cpT74rGvCcEeykZznivZmRiPx798q35U35/nuzDm/ZosC+/dIZ/43dtNvUWGrX9iK/3uor7Sk11OiOvkdOxNQUR4G+VDpVU8d8Ubm5FRd13QBwJiZ+ujB/e7sCHe2pbgMAAAC4KDa7Q86MDFks55++uRimacrXEkwOdk76YuFOh1obO87MXc6SlmFXVn6a3HkueQpiv+a75M5Pkzs3TVab5ZxfF2psVMfWrWrfvFkdW7bIt3WbIq2tZ62zlBSqodSqbXlerSnu0O5iQ2FrNOgxTFOjTIem5QzTtMpPafiQTzLVA+CCMfHTQzjT0+VMT091GwAAAEBKBDpCajntEawzH8sKBc7/OJbVbklM6py+305BmrLyXHK4PvqvQ2YoJP+ePfJtjj2ytWWLAgcPnrXOSE+Xc/gwNZZI293H9decWm3NajhthUW5EVPT7AWa1ucGTR59h7Jzyjv5EwGAziP4AQAAAJASkXBErY3+6ElYJztivyaCHV/L+R/HkiFlZjvjj1/FH8WKhT3pWQ4Zls49Khaqr5dvyxb53t0c/XX7dpntZ0/hOwYMkGvsWHX0c2urY7fW2HbrTXOzfKd9P4tpaoycmpY7XNMG/72GVs6WxcpfwQBcXfyvDgAAAIArIv44Vn1ysOM92aGWep9aGvwyI+d/HsuZbjs72MmPTuy4c9NktZ/7cawL6i8QUMfu96PTPFu2yLd5s4JHjpy1zpKZKdfo0XKNHSPr0EHaZd2p1+tf0xutf9TB059iMwwVhE1NTSvWtLLpmjT6Dnk8/S66PwC4HAh+urAtaw5ry5rDqW4DAAAA6DRTpjraQgr5z39YidVmkTu+cXJa0qNYWflpcqbbL1tPwRO1SSFPx44dMv3+5EWGIWfFIKWNGSPXmDFyjR6jGvtxvb77Ob1e+2u9c7RN/lNTPVbJZpoaozRNyxup64d8RoMr/k6G5eLDKAC43Ah+ujB/e1AtDR2pbgMAAAC4eLHHsdxnnIoVfSTLpQxP5x/HuhCRQEAdO3bEQp7o3jyh48fPWmfxeOQaM1qusWNjQc9o+a1+vbPtWb1+8Bmte+Owjpw+1WMxVBQ2Nc1VqmllN2ri6Nvlzupz2fsHgMuF4KcLGz6tj/qPyk91GwAAAMBFcbpsl/w41oUwTVOhY8eiIc+WLWrfvFn+nbtkBs/YI8hikXPwYLnGjpFrTDTocZQPkExTBw69or/s/IXW/c9mbTLbFTCSp3rGGy5NyxujqUM/o4qBNzPVA6DbIPjpwjJznMrMcaa6DQAAAKBLifh8p03zRE/bCtXVnbXOmpubmOQZM0auUSNlyciQJLW31uqNrSv1xlsva137UR07Y6+e0rA0Lb2PpvabqYmj5ysjs/gqXR0AXF4EPwAAAAC6LNM0FTx8OOmkrY7du6VQKHmhzaa0oUOjAc/YMXKNHSt7374yYpM7ZiSivftf0rr3/ltv1G/VJtOn0GlTPXbT1AQjXdMKxmrasM+qvP8MpnoA9AgEPwAAAAC6jEhbm3zbtic2Yd6yReGGhrPW2QoKotM8sZAnbfhwWVyupDWtLce1cctKrTv8itb5jumE9bS9hAxDfcPStIwyXT+gShNGzVd6OtssAOh5CH4AAAAApIQZiShw8FDSSVv+PXukSCRpnWG3K2348HjI4xozRraSkvg0z+nv9/7eP+v13f9P6+q3a4s6TpvqMeSMmJpgydD1hddo2vB56lc2lakeAD0ewQ8AAACAqyLc0iLflq3ybTk1zbNVEa/3rHW20hK5xoxReizkcQ4fLovDcc739Ho/0Matv9C6w2v1RkeN6k5N9RjR/9M/LE3LHKBpA27WhFFfUJor58pdIAB0QQQ/XZgZCskMh1PdBgAAANB5pqnABx/EH9fybd6swL79kmkmLTOcTqWNHBk7aSt62pa9qPBD3zYSDmnXnj/ojfef17qGndoqv8KnTfW4Iqaus7o1tXC8po2Yp7KyKVfyKgGgyyP46cJOPvlTnfzJT1LdBgAAAHDZ2MvKEidtjR2rtCGDZdjt5/2apsYDWr91pd44+rrW+WvVYEme6hkYNjTNXa6p5bdo/MjPy5nmueLXAQDdBcEPAAAAgCvCSE+Xa9SoeMjjGjNatry8j/y6cCignbt/r3V7nte6xve03Qgocmqqx2IoPWJqotWjacUTNHXE59Wnz3VX+EoAoPsyTPOMWcseorm5WR6PR16vV1lZWalu56JEAgGZgWCq2wAAAAAuisWVJsNqvaC1DQ179caWlVp3bJ02BE6q0ZK8cXNFxKLr3QM1deDf6ZoR82R3ZlyJlgGgW+hM5sHETxdmcTikD9nEDgAAAOjOwqGAtr33/7Ruzx+0ruk97TRCMk+b6smMmJpky9a04omaOnK+ikvGprRfAOiuCH4AAAAAXBUn63bpjW2/0Lpj67U+2KDmU1M9FkkyNCRi0bSsSk0bNFtjRsyV3Z6eynYBoEcg+AEAAABwRYSCHdqy8z/1xr4/ap13j3ZZTjux1mLIHTE12Z6jaSWTNXXk7SosGpm6ZgGghyL4AQAAAHBRImZEDR0NOtF+QnXtdaptr9WJxn2qrd2qE95D2h5qVkvSVI80PGLVVM9gXV8xR6OGfUY2e1rqLgAAegGCHwAAAABnaQ+2q7a9VnW+Op1oP6Ha9tr4x6nPT7afVMgMffibWAx5Iqam2PM0rXSqpoy+Xfn5Q6/eRQAACH4AAACA3iQcCauho0G1vlrVtiUHOad/tARbLuj9DNNUXjiiwnBIhaGwisIRFaYXqrBwtAaWz9SIoZ+W1caBJQCQKgQ/AAAAQA/RHmyPP3Z1rjDnRPsJnfSdVNgMf/SbSXLZXCpKL1KhK1+FpqHCtkYVNhxSUdMxFYbDKgyFlRcOy56eL1XMlCqqpEE3Shn5V/hKAQAXiuAHAAAA6OLCkbDqO+rPGeSc/nlrsPWC3s9iWJSflq+C9ILodE56YTTgOf33gQ5lHlov7Vkt7fyrFGxLvIFhkfpMkCqrpIpZUslYyWK5MhcPALgkBD8AAABACrUF25I3Rz7Hfjr1vvoLntLJsGdEAxxXYTzIOTPYyXPlyWY5468CwQ7p0Dpp6x+kPdVS/Z4z3rgwGvJUzpIG3iil516mnwAA4Eoi+AEAAACugHAkrJO+k+fdHLm2vVZtp0/SnIfFsCjfla+i9CIVuKKTOkUZRWeFOxn2jAtvsn6ftHd19OPA61LIl6gZVqlsYvQRrsoqqWgUUz0A0A0R/AAAAACd1BpojQY3vtPCnLbkcOdkx0lFzMgFvV+mPTMpwDnXpE5eWp6sFuulNR5olw6uk/ZWR8Oehv3JdXdJdKqnYpY0cIbkyr607wcASDmCHwAAACAmFAnppO9k9Bjzc2yQfOrz9lD7Bb2f1bDGp3ROBTkF6QVn7aeTbk+/MhdkmlL93uijW3tXR0OfsD9Rt9ikfpMTYU/RCMkwrkwvAICUIPgBAABAj2eaplqDrR+5OXJ9R/0FT+m47e6PnNLJTcu99CmdzvK3SgdfT4Q9TYeS61l9o/v0VFRJ5TdIaVlXtz8AwFVF8NOF7Ti5Qzvqd6S6DQAAgG4lGAmeM+Dxnb5/zXnYDJvy0/PP2hC5wJU8qXPFpnQ6yzSluveiIc+eaumDDVI4kKhbHdGpnsqqaNhTMISpHgDoRQh+urC1R9bqyS1PproNAACAHsPtcCeFN6fCnQJXgQozor/PTcuVxejimxh3NEsHXovt1bNG8h5Ormf3i4Y8lVXSgOslZ2Zq+gQApBzBTxc20DNQM/vNTHUbAAAA3YrNYoufenXmh8vmSnV7F8c0pRM7EidwfbBBioQSdatTGjA1EfbkVTDVAwCQJBmmaZqpbuJKaG5ulsfjkdfrVVYWzy0DAACgm/E1SftfjYU9a6SWY8n13IGxTZmrpAHTJEcXefQMAHDFdSbzYOIHAAAA6ApMU6rZGtuUeY10+E3JDCfqNpdUfn3iBK68QanrFQDQbRD8AAAAAKnS3iDtf0Xas1rat0ZqPZFcz6uMbco8S+o/RbJ300fVAAApQ/ADAAAAXC2RiHR8c+IErqPvSKcfH2/PiB6xXhmb6skZkKpOAQA9BMEPAAAAcCW11Uv7Xk6cwNV+MrleMDQa8lRWRY9dtzlT0ycAoEci+AEAAAAup0hYOvq32KbM1dHf67TzVByZ0sAZib16sstS1SkAoBcg+AEAAAAuVWttdKpnT3X0V19Dcr1opFQxM3oCV9lEyeZITZ8AgF6H4AcAAADorHAouj/Pqb16jm9Orjs90qAZiamerNJUdAkAAMEPAAAAcEFaamKPb62OTvV0eJPrxaMTJ3D1vVay2lPTJwAApyH4AQAAAM4lHJQOvxXblHm1VLMtuZ6WLQ26KRr2DJopuYtS0iYAAOdD8AMAAACc4j2a2JR5/1rJ35xcLx0X3aenskoqvUay8q/TAICujT+pAAAA0HuFAtLhjdF9evaulmp3JtdduYlNmQfdJGUWpKZPAAAukuVSvnjZsmUyDEMLFy6Mv2aappYsWaLS0lK5XC7NmDFDO3bsSPo6v9+ve+65R/n5+crIyNCcOXN05MiRpDWNjY2aP3++PB6PPB6P5s+fr6ampktpFwAAAJCaPpDe+bn023nSinLpF5+Q1v/fWOhjSH0mSDMekv7xZel/75X+/t+lMbcR+gAAuqWLnvh5++239fTTT2v06NFJr69YsUI/+tGPtHLlSg0ePFiPPvqoqqqqtHv3brndbknSwoULtWrVKj333HPKy8vTokWLNHv2bG3atElWq1WSNG/ePB05ckQvvviiJOmuu+7S/PnztWrVqottGQAAAL1RyC8dekPauyY62XNyd3I9oyBx+tagm6T03NT0CQDAFWCYpml29otaW1t1zTXX6IknntCjjz6qsWPH6l//9V9lmqZKS0u1cOFCLV68WFJ0uqeoqEjLly/XggUL5PV6VVBQoGeffVa33XabJOnYsWMqKyvTn//8Z91yyy3atWuXhg8fro0bN2rixImSpI0bN2ry5Ml67733NGTIkI/ssbm5WR6PR16vV1lZWZ29RAAAAHRnDQcSJ3AdeE0KtidqhkXqe51UGQt7isdIlksahAcA4KrqTOZxURM/X//61/Xxj39cs2bN0qOPPhp//cCBA6qpqdHNN98cf83pdGr69Olav369FixYoE2bNikYDCatKS0t1ciRI7V+/Xrdcsst2rBhgzweTzz0kaRJkybJ4/Fo/fr15wx+/H6//H5/0g8BAAAAvUTQJx18I7Exc/3e5HpmcTTkqZwlDZwhuXJS0iYAAFdbp4Of5557Tn/729/09ttvn1WrqamRJBUVJR9lWVRUpEOHDsXXOBwO5eTknLXm1NfX1NSosLDwrPcvLCyMrznTsmXL9Mgjj3T2cgAAANBd1e9LbMp88HUp1JGoGVap36TEI1zFoyTDSF2vAACkSKeCn8OHD+ub3/ymXnrpJaWlpX3oOuOMP1RN0zzrtTOdueZc68/3Pg899JDuu++++OfNzc0qKys77/cEAABANxJokw6uS4Q9jQeS6+7S2ONbVdLA6VKaJzV9AgDQhXQq+Nm0aZNqa2s1fvz4+GvhcFivvfaaHn/8ce3eHd0or6amRiUlJfE1tbW18Smg4uJiBQIBNTY2Jk391NbWasqUKfE1J06cOOv719XVnTVNdIrT6ZTT6ezM5QAAAKArM03p5J7oo1t7qqVD66Vw4tF+WexS/8mxqZ4qqXAYUz0AAJyhU8HPzJkztW3btqTXvvSlL2no0KFavHixBg4cqOLiYlVXV2vcuHGSpEAgoLVr12r58uWSpPHjx8tut6u6ulpz586VJB0/flzbt2/XihUrJEmTJ0+W1+vVW2+9peuuu06S9Oabb8rr9cbDIQAAAPRA/tboZsx7Y1M9TR8k1z39Epsyl98gOd2p6RMAgG6iU8GP2+3WyJEjk17LyMhQXl5e/PWFCxdq6dKlqqysVGVlpZYuXar09HTNmzdPkuTxeHTnnXdq0aJFysvLU25uru6//36NGjVKs2bNkiQNGzZMt956q77yla/oqaeekhQ9zn327NkXdKIXAAAAugnTlGp3JTZlPrRBigQTdatD6j81tjFzlZQ/mKkeAAA64aJO9TqfBx54QD6fT3fffbcaGxs1ceJEvfTSS3K7E/815rHHHpPNZtPcuXPl8/k0c+ZMrVy5UlarNb7m17/+te6999746V9z5szR448/frnbBQAAwNXW0SztfzUW9qyRmo8k13MGRB/dqpgllV8vOTJS0SUAAD2CYZqmmeomroTOnGkPAACAK8g0pRPbY5syr5EOb5QioUTdliYNmJYIe/IGMdUDAMB5dCbzuOwTPwAAAIB8TdL+V6Q9q6OTPa01yfXcQdFHtyqqpAFTJbsrJW0CANDTEfwAAADg0kUiUs3W2Alcq6Ujb0tmOFG3p0c3Y66YJVXMlHIHpq5XAAB6EYIfAAAAXJz2Bmnfy4m9etpqk+v5Q2KbMs+S+k2R7Gmp6RMAgF6M4AcAAAAXJhKRjr2bOIHr6CbJjCTqjkypfHp0oqdilpTTP3W9AgAASQQ/AAAAOJ+2k9Fpnr2rpX1rpPb65Hrh8NjjW7OkfpMlmyM1fQIAgHMi+AEAAEBCJByd5NlTHQ17jr0r6bRDYJ1Z0sDpsRO4ZkqevilrFQAAfDSCHwAAgN6utTb2+Nbq6J49vsbketGo6D49FVVS2XWS1Z6aPgEAQKcR/AAAAPQ24VD01K29same41uS62keaeCN0ePWB82UskpS0ycAALhkBD8AAAC9QfOx2F491dK+VyW/N7leMjZ2AleV1GeCZOVfEwEA6An4Ex0AAKAnCgelDzYmHuE6sT257sqJTvNUzIru1ZNZmJo+AQDAFUXwAwAA0FN4j0RDnj3V0v61UqDltKIh9bkmtinzrOjvLdaUtQoAAK4Ogh8AAIDuKuSXPtgQC3tWS3W7kuvp+dFpnooqadCNUkZ+avoEAAApQ/ADAADQnTQeim3KvCY61RNsS9QMS3R/nsrYVE/JWMliSVmrAAAg9Qh+AAAAurJgh3TojcRePSffT65nFMY2ZZ4VPYkrPTc1fQIAgC6J4AcAAKCradgffXRrb7V04HUp5EvUDKtUdl3iBK6iUUz1AACAD0XwAwAAkGqB9uhUz57qaNjTsD+57i6Jnb41Sxo4Q3Jlp6JLAADQDRH8AAAAXG2mKdXvTZzAdegNKdSRqFtsUr/JibCnaIRkGKnrFwAAdFsEPwAAAFdDoE068Foi7Gk6lFzP6hvdp6eiSiq/QUrLSk2fAACgRyH4AQAAuBJMU6rbHTuBa7V0aL0UDiTqFrvUf0rsBK4qqWAIUz0AAOCyI/gBAAC4XPwt0SPWTx237j2cXM/uFw15KqukAddLzszU9AkAAHoNgh8AAICLZZpS7c7YpsyrpQ82SpFgom51SgOmJsKevAqmegAAwFVF8AMAANAZHV5p/6uxsGeN1HIsuZ47MLYpc5U0YJrkSE9JmwAAABLBDwAAwPmZplSzNbYp82rp8JuSGU7UbS6p/PrECVx5g1LXKwAAwBkIfgAAAM7ka5T2vRyd6Nm7Wmo9kVzPq4xtyjwrukGz3ZWaPgEAAD4CwQ8AAEAkIh3fHAt6qqUjb0tmJFG3Z0SPWK+MTfXkDEhVpwAAAJ1C8AMAAHqntvrYVM9qad8aqa0uuV4wNBryVFZJ/SZLNmdq+gQAALgEBD8AAKB3iISlY+8mTuA6ukmSmag7MqWBMxJ79WSXpapTAACAy4bgBwAA9FytddFpnj3V0ekeX0NyvWikVDEzegJX2UTJ5khNnwAAAFcIwQ8AAOg5wqHoJM/e6mjYc3xzct3pkQbNSEz1ZJWmoksAAICrhuAHAAB0by01iU2Z970idTQl14tHJ07g6nutZLWnpE0AAIBUIPgBAADdSzgoHX4ruk/P3mqpZltyPS1bGnRTNOwZNFNyF6WkTQAAgK6A4AcAAHR93qOxoGe1tP9Vyd98WtGQSsclTuAqvUay8q84AAAAEsEPAADoikIB6fDG2Alca6TaHcn19LzoNE/FrOh0T2ZBavoEAADo4gh+AABA19B0OLYp82rpwFop0Hpa0ZD6ToievlUxSyodK1msqeoUAACg2yD4AQAAqRHyS4fWRx/f2lMtndydXM8oSJy+NegmKT03NX0CAAB0YwQ/AADg6mk4kNir58BrUrA9UTMsUt/rpMpZ0cme4tGSxZK6XgEAAHoAgh8AAHDlBH3SoTeij2/trZbq9ybXM4tjmzLPkgbOkFw5KWkTAACgpyL4AQAAl1f9vtimzKulg+ukkC9Rs9iksomJE7iKRkqGkbpeAQAAejiCHwAAcGkC7dLB1xNhT+OB5HpWH6liZvTxrYHTpTRPavoEAADohQh+AABA55imdHJP7ASu6ugGzWF/om6xS/0nJ07gKhzGVA8AAECKEPwAAICP5m+Nbsa8NzbV0/RBct3TL7Epc/n1ktOdmj4BAACQhOAHAACczTSluvdij29VS4c2SJFgom51SP2nRvfpqaiS8iuZ6gEAAOiCCH4AAEBUR7N0YG0s7FkjNR9JrucMiIY8lVXSgGmSIyMlbQIAAODCEfwAANBbmaZ0Ynv00a09q6XDG6VIKFG3pUkDrk+cwJU3KHW9AgAA4KIQ/AAA0Jv4mqT9r0TDnr1rpJbjyfW8isSmzAOmSnZXStoEAADA5WHpzOInn3xSo0ePVlZWlrKysjR58mT95S9/iddN09SSJUtUWloql8ulGTNmaMeOHUnv4ff7dc899yg/P18ZGRmaM2eOjhxJHiVvbGzU/Pnz5fF45PF4NH/+fDU1NV38VQIA0FtFItKxzdJrP5D+4xZpxUDpv78ovfuraOhjT5cG3yr93b9I926W7tkkfez70Y2aCX0AAAC6PcM0TfNCF69atUpWq1UVFRWSpF/84hf6wQ9+oHfffVcjRozQ8uXL9b3vfU8rV67U4MGD9eijj+q1117T7t275XZHT/f42te+plWrVmnlypXKy8vTokWL1NDQoE2bNslqtUqSPvaxj+nIkSN6+umnJUl33XWXBgwYoFWrVl3whTU3N8vj8cjr9SorK+uCvw4AgG6vvUHa93JiqqetNrmePyS2KfMsqd9kyZ6Wmj4BAABwUTqTeXQq+DmX3Nxc/eAHP9CXv/xllZaWauHChVq8eLGk6HRPUVGRli9frgULFsjr9aqgoEDPPvusbrvtNknSsWPHVFZWpj//+c+65ZZbtGvXLg0fPlwbN27UxIkTJUkbN27U5MmT9d5772nIkCEX1BfBDwCg14hEpOPvRvfp2VstHd0kmZFE3ZEplU+PHbc+S8rul7peAQAAcMk6k3lc9B4/4XBY//3f/622tjZNnjxZBw4cUE1NjW6++eb4GqfTqenTp2v9+vVasGCBNm3apGAwmLSmtLRUI0eO1Pr163XLLbdow4YN8ng88dBHkiZNmiSPx6P169d/aPDj9/vl9/uTfggAAPRYbSejUz17qqV9a6T2+uR64QipYmZ0sqdskmRzpKZPAAAApFSng59t27Zp8uTJ6ujoUGZmpp5//nkNHz5c69evlyQVFRUlrS8qKtKhQ4ckSTU1NXI4HMrJyTlrTU1NTXxNYWHhWd+3sLAwvuZcli1bpkceeaSzlwMAQPcQCUcnefaujoY9x96VdNrQrjNLGjgjOtFTMUvy9ElVpwAAAOhCOh38DBkyRJs3b1ZTU5N+97vf6Y477tDatWvjdcMwktabpnnWa2c6c8251n/U+zz00EO677774p83NzerrKzsI68HAIAuq7U2tk/P6uh0j68xuV48KnECV9l1ktWemj4BAADQZXU6+HE4HPHNnSdMmKC3335b//Zv/xbf16empkYlJSXx9bW1tfEpoOLiYgUCATU2NiZN/dTW1mrKlCnxNSdOnDjr+9bV1Z01TXQ6p9Mpp9PZ2csBAKDrCIekI29H9+nZu1o6viW5nuaRBt0UC3tmSu7i1PQJAACAbuOi9/g5xTRN+f1+lZeXq7i4WNXV1Ro3bpwkKRAIaO3atVq+fLkkafz48bLb7aqurtbcuXMlScePH9f27du1YsUKSdLkyZPl9Xr11ltv6brrrpMkvfnmm/J6vfFwCACAHqP5eGyqp1ra96rk9ybXS8bGTuCqkvqMl6yX/Ec3AAAAepFO/dvjt771LX3sYx9TWVmZWlpa9Nxzz+nVV1/Viy++KMMwtHDhQi1dulSVlZWqrKzU0qVLlZ6ernnz5kmSPB6P7rzzTi1atEh5eXnKzc3V/fffr1GjRmnWrFmSpGHDhunWW2/VV77yFT311FOSose5z549+4JP9AIAoMsKB6XDb0b36dm7WjqxPbnuyo1O9VRWSYNmSpkFqekTAAAAPUKngp8TJ05o/vz5On78uDwej0aPHq0XX3xRVVVVkqQHHnhAPp9Pd999txobGzVx4kS99NJLcrvd8fd47LHHZLPZNHfuXPl8Ps2cOVMrV66U1WqNr/n1r3+te++9N37615w5c/T4449fjusFAODq8x5JbMq8f60UaDmtaEQneSpmRcOe0nGSxfqhbwUAAAB0hmGapvnRy7qfzpxpDwDAZRXySx9siIU9q6W6Xcn19PzE6VuDbpIy8lLTJwAAALqlzmQebBQAAMDl0HgotinzmuhUT7AtUTMsUt9rE5syl4yVLJaUtQoAAIDeg+AHAICLEeyQDr2ROG795PvJ9cyixFTPwBlSem5K2gQAAEDvRvADAMCFatgffXRr72rp4OtSsD1RM6xS2USpclZ0sqdoJFM9AAAASDmCHwAAPkygPTrVs6c6+hhXw/7kurs0+uhWZVV0qifNk5I2AQAAgA9D8AMAwCmmKdXvTZzAdegNKdSRqFvsUr9JiRO4CodLhpG6fgEAAICPQPADAOjdAm3SgdcSYU/ToeS6p+y0vXqmS053avoEAAAALgLBDwCgdzFNqW537ASu1dKh9VI4kKhbHVL/KbETuGZJBUOY6gEAAEC3RfADAOj5/C3RI9ZPHbfuPZxcz+4ffXSrokoaME1yZqamTwAAAOAyI/gBAPQ8pinV7oxtyrxa+mCjFAkm6lZnNOA5FfbkDWKqBwAAAD0SwQ8AoGfo8Er7X42FPWuklmPJ9dxBiU2Z+0+VHOkpaRMAAAC4mgh+AADdk2lKNVtjmzKvlg6/KZnhRN3mksqvj070VM6ScgemrlcAAAAgRQh+AADdh69R2vdydKJn72qp9URyPX9w4gSu/lMle1pq+gQAAAC6CIIfAEDXFYlIxzdHQ569q6Ujb0tmJFG3Z0SPWK+YGQ17cgakqlMAAACgSyL4AQB0LW31same2F497SeT6wXDoo9uVcyS+k2WbM7U9AkAAAB0AwQ/AIDUioSlY+8mTuA6ukmSmag73NGpnsqqaNjj6ZuyVgEAAIDuhuAHAHD1tdZJ+9ZEw559L0u+huR60cjECVxlEyWrPTV9AgAAAN0cwQ8A4MoLh6KTPHuro2HP8c3JdadHGjQjegJXxSwpqyQVXQIAAAA9DsEPAODKaKmJnb5VLe17RepoSq6XjImdwFUl9b1WsvJHEgAAAHC58W/ZAIDLIxyUDr8V25R5tVSzLbnuypEG3RQNewbNlNxFqekTAAAA6EUIfgAAF897NHbUerW0f63kbz6taEil4xKbMvcZL1msKWsVAAAA6I0IfgAAFy4UkA5vTJzAVbszuZ6eF53mqayKTvdk5KemTwAAAACSCH4AAB+l6XBsU+bV0oG1UqD1tKIh9Z0Q3aencpZUMpapHgAAAKALIfgBACQL+aVD66MTPXuqpZO7k+sZBbFNmWdFp3rSc1PTJwAAAICPRPADAJAaDsT26lktHXhNCrYnaoZVKrtOqpgZnewpHi1ZLKnrFQAAAMAFI/gBgN4o6JMOvpHYmLl+b3I9szj66FbFLGngjOiJXAAAAAC6HYIfAOgt6vclNmU++LoU6kjULDapbFIi7CkaKRlG6noFAAAAcFkQ/ABATxVojwY8p8KexgPJ9aw+ib16Bk6X0jyp6RMAAADAFUPwAwA9hWlKJ/fETuCqjm7QHPYn6ha71H9ydJ+eillS4TCmegAAAIAejuAHALozf2t0M+a9samepg+S655+sce3qqTy6yWnOzV9AgAAAEgJgh8A6E5MU6rdldiU+dAGKRJM1K0Oqf9UqbIqGvbkVzLVAwAAAPRiBD8A0NV1NEv7X42FPWuk5iPJ9ZwB0ZCnskoaME1yZKSiSwAAAABdEMEPAHQ1pimd2B7blHmNdHijFAkl6rY0acD10X16KqukvEGp6xUAAABAl0bwAwBdga9J2v+KtGd1dLKntSa5nleR2JR5wFTJ7kpJmwAAAAC6F4IfAEiFSESq2Ro7gWu1dORtyQwn6vZ0qfyGxHHrueWp6xUAAABAt0XwAwBXS3uDtO/lxF49bbXJ9fwhsU2ZZ0r9pkj2tNT0CQAAAKDHIPgBgCslEpGOvZs4gevoJsmMJOqOTKl8euy49VlSdr/U9QoAAACgRyL4AYDLqe1kdJpn72pp3xqpvT65Xjg8sSlz2STJ5khNnwAAAAB6BYIfALgUkXB0kmdPdTTsOfauJDNRd2ZJA6cnNmb29ElZqwAAAAB6H4IfAOislhPRaZ491dE9ezqakuvFo2KbMldJZddJVntK2gQAAAAAgh8A+CjhUPTUrb3V0bCnZmtyPc0jDbopcQKXuzg1fQIAAADAGQh+AOBcmo/F9uqplva9Kvm9yfWSsbETuGZJfSZIVv7nFAAAAEDXw99UAECSwkHpg42xE7hWSye2J9ddOdKgmdGwZ9BNUmZhavoEAAAAgE4g+AHQe3mPJDZl3r9WCrScVjSkPtdE9+mprJJKx0kWa8paBQAAAICLQfADoPcI+aUPNiTCnrr3kuvp+VLFzGjYM+gmKSMvNX0CAAAAwGVC8AOgZ2s8FNuUebV04DUp2JaoGZbo/jyn9uopGStZLClrFQAAAAAut079DWfZsmW69tpr5Xa7VVhYqE996lPavXt30hrTNLVkyRKVlpbK5XJpxowZ2rFjR9Iav9+ve+65R/n5+crIyNCcOXN05MiRpDWNjY2aP3++PB6PPB6P5s+fr6ampou7SgC9R7Ajuinziw9JP54g/dto6U+LpPf/Eg19MgqlMfOkz/xc+t/7pH+slqY/EH2si9AHAAAAQA9jmKZpXujiW2+9VZ/97Gd17bXXKhQK6dvf/ra2bdumnTt3KiMjQ5K0fPlyfe9739PKlSs1ePBgPfroo3rttde0e/duud1uSdLXvvY1rVq1SitXrlReXp4WLVqkhoYGbdq0SVZrdA+Nj33sYzpy5IiefvppSdJdd92lAQMGaNWqVRfUa3Nzszwej7xer7Kysjr1QwHQzdTvS5zAdeB1KeRL1AyrVDYx+ghXZZVUNIqABwAAAEC31pnMo1PBz5nq6upUWFiotWvX6oYbbpBpmiotLdXChQu1ePFiSdHpnqKiIi1fvlwLFiyQ1+tVQUGBnn32Wd12222SpGPHjqmsrEx//vOfdcstt2jXrl0aPny4Nm7cqIkTJ0qSNm7cqMmTJ+u9997TkCFDLusPAUA3E2iXDq6LncBVLTXsT667S6KPblXMkgbOkFzZqegSAAAAAK6IzmQel7THj9frlSTl5uZKkg4cOKCamhrdfPPN8TVOp1PTp0/X+vXrtWDBAm3atEnBYDBpTWlpqUaOHKn169frlltu0YYNG+TxeOKhjyRNmjRJHo9H69evP2fw4/f75ff74583NzdfyqUB6EpMU6rfm9iU+eA6KZy432WxSf0mJ8KeohGSYaSuXwAAAADoIi46+DFNU/fdd5+mTZumkSNHSpJqamokSUVFRUlri4qKdOjQofgah8OhnJycs9ac+vqamhoVFhae9T0LCwvja860bNkyPfLIIxd7OQC6Gn+rdPD1RNjTdCi5ntVXqowFPeXTpTQm+wAAAADgTBcd/HzjG9/Q1q1btW7durNqxhn/pd00zbNeO9OZa861/nzv89BDD+m+++6Lf97c3KyysrLzfk8AXYhpRo9X37s6GvZ8sEEKBxJ1qyM61VNZFT1uvWAIUz0AAAAA8BEuKvi555579Ic//EGvvfaa+vbtG3+9uLhYUnRip6SkJP56bW1tfAqouLhYgUBAjY2NSVM/tbW1mjJlSnzNiRMnzvq+dXV1Z00TneJ0OuV0Oi/mcgCkSkezdGBtbK+eNZL3cHI9u1805KmskgZcLzkzU9MnAAAAAHRTnQp+TNPUPffco+eff16vvvqqysvLk+rl5eUqLi5WdXW1xo0bJ0kKBAJau3atli9fLkkaP3687Ha7qqurNXfuXEnS8ePHtX37dq1YsUKSNHnyZHm9Xr311lu67rrrJElvvvmmvF5vPBwC0A2ZpnRiR3RD5r1rolM9kVCibnVKA6ZFH9+qrJLyKpjqAQAAAIBL0Kng5+tf/7p+85vf6Pe//73cbnd8vx2PxyOXyyXDMLRw4UItXbpUlZWVqqys1NKlS5Wenq558+bF1955551atGiR8vLylJubq/vvv1+jRo3SrFmzJEnDhg3Trbfeqq985St66qmnJEWPc589e/YFnegFoAvxNUn7X02EPS3Hk+u5A6NTPRWzoqGPIz0VXQIAAABAj9Sp4OfJJ5+UJM2YMSPp9WeeeUZf/OIXJUkPPPCAfD6f7r77bjU2NmrixIl66aWX5Ha74+sfe+wx2Ww2zZ07Vz6fTzNnztTKlStltVrja37961/r3nvvjZ/+NWfOHD3++OMXc40AribTlGq2xjZlXiMdflMyw4m6zSWVX584gStvUOp6BQAAAIAezjBN00x1E1dCZ860B3CJ2huk/a9Ie1ZL+9ZIrWfs0ZVXGduUeZbUf4pkd6WmTwAAAADoATqTeVz0qV4AerFIRDq+OXEC19F3JDOSqNszpPIbEset5wxIVacAAAAA0KsR/AC4MG310r6XE3v1tJ9MrhcMkypmRid7+k2WbJyyBwAAAACpRvAD4NwiYeno32JHrVdHf6/Tngx1uKWB0xN79WSXpaxVAAAAAMC5EfwASGitjU7z7F0dne7xNSTXi0ZGp3oqqqSyiZLNkZo+AQAAAAAXhOAH6M3Coej+PHuqo2HP8c3JdadHGjQjMdWTVZqKLgEAAAAAF4ngB+htWmpij2/Fpno6vMn14tGJE7j6XitZ7anpEwAAAABwyQh+gJ4uHJQOvxXblHm1VLMtuZ6WLQ26KRr2DJopuYtS0iYAAAAA4PIj+AF6Iu/RxKbM+9dK/ubTioZUOi460VNZJZVeI1n5nwIAAAAA6In42x7QE4QC0uGNib16ancm19PzotM8FbOi0z2ZBanpEwAAAABwVRH8AN1V0+HoRM+e1dKBtVKg9bSiIfWdENuUuUoqHStZrKnqFAAAAACQIgQ/QHcR8kuH1kcnevZUSyd3J9czChKnbw26SUrPTU2fAAAAAIAug+AH6MoaDiRO4DrwmhRsT9QMi9T3OqkyFvYUj5EsltT1CgAAAADocgh+gK4k6JMOvpHYmLl+b3I9szi2KfMsaeAMyZWTkjYBAAAAAN0DwQ+QavX7EpsyH1wnhXyJmsUmlU1MnMBVNFIyjNT1CgAAAADoVgh+gKst0C4dfD0R9jQeSK67S2OPb1VJA6dLaZ7U9AkAAAAA6PYIfoArzTSlk3tiJ3BVRzdoDvsTdYtd6j85cQJX4TCmegAAAAAAlwXBD3Al+FujmzHvjU31NH2QXPf0S2zKXH6D5HSnpk8AAAAAQI9G8ANcDqYp1b0Xe3yrWjq0QYoEE3WrQ+o/NbpPT8UsKX8wUz0AAAAAgCuO4Ae4WB3N0oG1sbBnjdR8JLmeMyD66FZllTRgmuTISEmbAAAAAIDei+AHuFCmKZ3YHn10a89q6fBGKRJK1G1p0YDnVNiTO5CpHgAAAABAShH8AOfja5L2vxINe/aukVqOJ9fzKhKbMg+YKtldKWkTAAAAAIBzIfgBTheJSDVbYydwrZaOvC2Z4UTdnh7djLkitjFzbnnqegUAAAAA4CMQ/ADtDdK+lxNTPW21yfX8IbFNmWdK/aZI9rTU9AkAAAAAQCcR/KD3iUSkY+/Ggp5q6egmyYwk6o5MqXx69Lj1QTOlnP6p6xUAAAAAgEtA8IPeoe1kdJpn72pp3xqpvT65Xjg8+uhWZZVUNkmyOVLTJwAAAAAAlxHBD3qmSDg6ybOnOhr2HHtXkpmoO7OkgdOjmzJXzJI8fVLWKgAAAAAAVwrBD3qO1trYUevV0T17OpqS68WjEidwlV0nWe0paRMAAAAAgKuF4AfdVzgUPXVrb2yq5/iW5HqaRxp0U+IELndxavoEAAAAACBFCH7QvTQfi+3VUy3te1Xye5PrJWNjJ3DNkvpMkKz8vzgAAAAAoPfib8Xo2sJB6YONsRO4VksntifXXTnRk7cqq6LTPZmFqekTAAAAAIAuiOAHXY/3SGJT5v1rpUDLaUVD6nNNdJ+eyiqpdJxksaasVQAAAAAAujKCH6ReyC99sCEW9qyR6nYl19PzpYqZ0bBn0E1SRl5q+gQAAAAAoJsh+EFqNB6K7tOzZ7V04DUp2JaoGRap77WJTZlLxkoWS8paBQAAAACguyL4wdUR7JAOvZE4br1+T3I9sygW9MyUBt4opeempk8AAAAAAHoQgh9cOfX7EidwHXhdCvkSNcMqlU2UKmNTPUWjmOoBAAAAAOAyI/jB5RNolw6ui53AVS017E+uu0ujEz2VVVL5dMmVnZI2AQAAAADoLQh+cPFMU6rfmziB6+A6KexP1C02qd/k6ERPZZVUOFwyjNT1CwAAAABAL0Pwg87xt0oHX0+EPU2HkutZfWOPb1VJA6dLTndq+gQAAAAAAAQ/+AimKdXtjp3AVR09dj0cSNStDqn/lNjGzFVSwRCmegAAAAAA6CIIfnC2juboEet7q6ObM3sPJ9ez+0cf3aqYJQ24XnJmpqZPAAAAAABwXgQ/iE71nNgR25R5dXSqJxJK1K1OacC0RNiTV8FUDwAAAAAA3QDBT2/la5L2vxoLe9ZILceS67kDo49uVVZJ/adKjvRUdAkAAAAAAC4BwU9vYZpSzdbYpsxrpMNvSmY4Ube5pPLro2FPxUwpb1DqegUAAAAAAJcFwU9P1t4g7X9F2rNa2rdGaj2RXM8fHNuUeVZ0qseelpo+AQAAAADAFUHw05NEItLxzdHHt/ZUS0ffkcxIom7PiB6xXjEzGvbkDEhVpwAAAAAA4CqwdPYLXnvtNX3iE59QaWmpDMPQCy+8kFQ3TVNLlixRaWmpXC6XZsyYoR07diSt8fv9uueee5Sfn6+MjAzNmTNHR44cSVrT2Nio+fPny+PxyOPxaP78+Wpqaur0BfZ4bfXS1v+S/ucu6V8qpZ/dKL3yPenIW9HQp2CYNOUe6fbfS4sPSJ/7rXTtPxL6AAAAAADQC3R64qetrU1jxozRl770Jf393//9WfUVK1boRz/6kVauXKnBgwfr0UcfVVVVlXbv3i232y1JWrhwoVatWqXnnntOeXl5WrRokWbPnq1NmzbJarVKkubNm6cjR47oxRdflCTdddddmj9/vlatWnUp19v9RcLS0b/FjlpfHf29zETd4Y5O9Zw6gcvTN2WtAgAAAACA1DJM0zQ/etmHfLFh6Pnnn9enPvUpSdFpn9LSUi1cuFCLFy+WFJ3uKSoq0vLly7VgwQJ5vV4VFBTo2Wef1W233SZJOnbsmMrKyvTnP/9Zt9xyi3bt2qXhw4dr48aNmjhxoiRp48aNmjx5st577z0NGTLkI3trbm6Wx+OR1+tVVlbWxV5i19BaG92QeW+1tO9lydeYXC8aGQ15KquksomS1Z6aPgEAAAAAwBXXmczjsu7xc+DAAdXU1Ojmm2+Ov+Z0OjV9+nStX79eCxYs0KZNmxQMBpPWlJaWauTIkVq/fr1uueUWbdiwQR6PJx76SNKkSZPk8Xi0fv36cwY/fr9ffr8//nlzc/PlvLTU+Nuz0ts/k45vSX7d6ZEGzYidwDVLyipJSXsAAAAAAKBru6zBT01NjSSpqKgo6fWioiIdOnQovsbhcCgnJ+esNae+vqamRoWFhWe9f2FhYXzNmZYtW6ZHHnnkkq+hS2mtSYQ+JWNiJ3BVSX2vlazsyw0AAAAAAM7viqQHhmEkfW6a5lmvnenMNedaf773eeihh3TffffFP29ublZZWVln2u56RnxayuojDZopuYs+ej0AAAAAAMBpLmvwU1xcLCk6sVNSknj8qLa2Nj4FVFxcrEAgoMbGxqSpn9raWk2ZMiW+5sSJE2e9f11d3VnTRKc4nU45nc7Ldi1dQt6g6AcAAAAAAMBF6PRx7udTXl6u4uJiVVdXx18LBAJau3ZtPNQZP3687HZ70prjx49r+/bt8TWTJ0+W1+vVW2+9FV/z5ptvyuv1xtcAAAAAAADg/Do98dPa2qq9e/fGPz9w4IA2b96s3Nxc9evXTwsXLtTSpUtVWVmpyspKLV26VOnp6Zo3b54kyePx6M4779SiRYuUl5en3Nxc3X///Ro1apRmzZolSRo2bJhuvfVWfeUrX9FTTz0lKXqc++zZsy/oRC8AAAAAAABcRPDzzjvv6MYbb4x/fmpfnTvuuEMrV67UAw88IJ/Pp7vvvluNjY2aOHGiXnrpJbnd7vjXPPbYY7LZbJo7d658Pp9mzpyplStXymq1xtf8+te/1r333hs//WvOnDl6/PHHL/pCAQAAAAAAehvDNE0z1U1cCZ050x4AAAAAAKC76EzmcVn3+AEAAAAAAEDXQfADAAAAAADQQxH8AAAAAAAA9FAEPwAAAAAAAD0UwQ8AAAAAAEAPRfADAAAAAADQQ9lS3cCVcuqU+ubm5hR3AgAAAAAAcPmcyjpOZR/n02ODn5aWFklSWVlZijsBAAAAAAC4/FpaWuTxeM67xjAvJB7qhiKRiI4dOya32y3DMFLdzkV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},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Reinforcement Learning\n\nFollowing [this quantecon lecture](https://python.quantecon.org/mccall_q.html), I'll use a tabular Q-learning approach first. We will see that it craps the bed as the states pace grows.\n\nUnlike the quantecon lecture, I will use an object-oriented approach to setting up the RL problem that closely mirrors the Gym API. We will be able to re-use the `McCallEnvironment` in several experiments.\n\nThe agent, environment, and training loop are compiled with numba `jitclass` to make the simulations run extremely fast."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Environment Class"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@jitclass(\n {\n 'w_grid':nb.float64[:],\n 'q_grid':nb.float64[:],\n 'q_cumul':nb.float64[:],\n 'c':nb.float64,\n 'max_steps':nb.int32,\n 't':nb.int32,\n 'state':nb.int32[:],\n }\n)\nclass DiscreteMcCallEnvironment:\n '''\n RL Environment for the McCall (1970) model\n '''\n \n def __init__(self, c, q_grid, w_grid, max_steps=100):\n self.w_grid = w_grid\n self.q_grid = q_grid\n self.q_cumul = q_grid.cumsum()\n self.c = c\n self.max_steps = max_steps\n self.t = 0\n \n # Element 0 is the wage state (discrete), element 1 is the accepted wage (-1 if unemployed)\n self.state = np.array([0, -1]).astype('int32')\n \n def _reward(self, action):\n '''\n Compute agent reward based on action:\n u_t = w_t if accept, c if reject\n '''\n # If employed, action is irrevelant\n if self.state[1] > 0:\n return self.w_grid[self.state[1]]\n \n if action == 0:\n # Reject offer, collect unemployment\n return self.c\n else:\n # Take the job forever\n self.state[1] = self.state[0]\n return self.w_grid[self.state[1]]\n \n def _draw_wage_state(self):\n '''\n Use the CDF transformation to draw discrete random states\n '''\n x = np.random.rand()\n i = np.searchsorted(self.q_cumul, x)\n \n return i\n \n def reset(self):\n '''\n Reset the environment\n '''\n initial_state = self._draw_wage_state()\n self.state = np.array([initial_state, -1]).astype('int32')\n self.t = 0\n return self.state\n \n def step(self, action):\n '''\n Update the environment based on agent action\n '''\n reward = self._reward(action)\n\n if self.state[1] == -1:\n n = self.w_grid.shape[0]\n next_w = self._draw_wage_state()\n else:\n next_w = self.state[1]\n \n self.state[0] = next_w\n self.t += 1\n done = self.t == self.max_steps\n \n return self.state, reward, done, None",
"execution_count": 6,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Agent Class"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@jitclass(\n {\n 'α':nb.float64,\n 'min_ε':nb.float64,\n 'max_ε':nb.float64,\n 'dec_ε':nb.float64,\n 'ε':nb.float64,\n 'β':nb.float64,\n 'n_actions':nb.int32,\n 'n_states':nb.int32,\n 'Q':nb.float64[:, :]\n }\n)\nclass Q_Agent:\n def __init__(self, n_actions, n_states, α, β, max_ε=1.0, min_ε=0.1, dec_ε = 1e-5):\n \"\"\"\n General agent for tablular Q-learning, adapted from:\n https://github.com/philtabor/Deep-Q-Learning-Paper-To-Code/blob/master/q_learning/q_learning_agent.py\n \n Parameters \n ----------\n α, float\n Learning rate for temporal difference updating\n β, float\n Agent's intertemporal discount factor, 0 < β < 1. Larger beta indictates that the agent thinks\n more about the future when making decisions today.\n min_ε, float\n Minimum allowed value of ε\n max_ε, float\n Maximum allowed value of ε\n dec_ε, float\n Slope of the ε update schedule. Larger value produces a shorter explotatory \"burn-in\" \n period.\n \n \"\"\"\n self.α = α\n self.min_ε = min_ε\n self.max_ε = max_ε\n self.dec_ε = dec_ε\n self.ε = max_ε\n self.β = β\n \n self.n_actions = n_actions\n \n self.Q = np.zeros((n_states, n_actions))\n \n def learn(self, state, action, reward, next_state):\n '''\n Update Q-table via temportal-difference learning.\n '''\n greedy_action = np.random.choice(np.flatnonzero(self.Q[next_state, :] == self.Q[next_state, :].max()))\n \n self.Q[state, action] += self.α * (reward + self.β * self.Q[next_state, greedy_action] - self.Q[state, action])\n \n def take_action(self, state):\n '''\n Choose an action in ϵ-greedy fashion. Break ties randomly.\n '''\n if np.random.rand() < self.ϵ:\n return np.random.choice(self.n_actions)\n \n return np.random.choice(np.flatnonzero(self.Q[state, :] == self.Q[state, :].max()))\n \n def update_epsilon(self):\n '''\n Linearly decrease ϵ, probably of taking an off-policy exploratory action, over the course of training\n '''\n self.ε = min(max(self.ε - (self.dec_ε * self.ε), self.min_ε), self.max_ε)",
"execution_count": 7,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Training Loop"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@nb.njit\ndef run_env(env, agent):\n '''\n Perform one iteration of the RL training loop\n '''\n wage_state, employed = env.reset()\n done = False\n game_score = 0\n while not done:\n if employed == -1:\n action = agent.take_action(wage_state)\n agent.update_epsilon()\n else:\n action = 1\n \n next_state, reward, done, info = env.step(action) \n next_wage_state, employed = next_state\n \n agent.learn(wage_state, action, reward, next_wage_state)\n \n wage_state = next_wage_state\n game_score += reward\n \n return game_score",
"execution_count": 8,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "env = DiscreteMcCallEnvironment(c=25, q_grid=wage_probs, w_grid=wage_grid, max_steps=100)\nagent = Q_Agent(n_actions=2, n_states=11, α=1e-2, β=0.99, min_ε=0.02, dec_ε = 1e-5)",
"execution_count": 9,
"outputs": []
},
{
"metadata": {
"trusted": true,
"scrolled": false
},
"cell_type": "code",
"source": "reward_history = []\nn_games = 1_000_000\n\nfor game in range(n_games):\n game_score = run_env(env, agent)\n reward_history.append(game_score)\n \n if game % 1000 == 0:\n print(f'Game {game}, average score: {np.mean(reward_history[-100:]):0.3f}' + ' '*30, end='\\r')",
"execution_count": 10,
"outputs": [
{
"output_type": "stream",
"text": "Game 999000, average score: 5157.700 \r",
"name": "stdout"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Learning Plot\n\nFrom the learning plot, we can see that the agent converges to a good policy after about 150,000 games. "
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "k = 1_000\nsmooth_hist = np.convolve(reward_history, np.full(k, 1/k), mode='valid')\n\nfig, ax = plt.subplots()\nax.plot(smooth_hist)\nax.set_title(f'Learning Plot for McCall Q-Learner, 50 States, {k} Game Rolling Mean')\nplt.show()",
"execution_count": 11,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Approximate Value Function\n\nWe can recover the value function from the Q table by taking the row-wise maximum, and compare it to what we got from VFI. We caan see that the agent learned a very good approximation to the true value function."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "fig, ax = plt.subplots()\nax.plot(wage_grid, np.max(agent.Q, axis=-1), label='Learned Value Function')\nax.plot(wage_grid, v, label='Analytic Solution')\nax.set_title('Comparison of Learned and Analytic Value Functions, 50 States')\nax.legend()\nplt.show()",
"execution_count": 12,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Increase the number of states\n\nTest the ability of the Q-learning agent to generalize to a more finely binned state space, by setting the number of states to 50."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n = 50\nwage_probs = BetaBinomial(n, a, b).pdf()\n\nw_min, w_max = 10, 60\nwage_grid = np.linspace(w_min, w_max, n+1)\n\nfig, ax = plt.subplots(figsize=(14,4))\nax.plot(wage_grid, wage_probs, marker='o')\nplt.show()",
"execution_count": 13,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1400x400 with 1 Axes>",
"image/png": 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S5ny6T8VnKk1OBACejyIPAAAAcA5//WSfTpVXKbF7iK67qJvZcbzKjRd3V7/IYJWUVWnO2n1mxwEAj0eRBwAAAGhEVuFpvfr5IUnS4+MGyGq1mJzIu9isFv1mbPVW9P/ccFB5xWdNTgQAno0iDwAAANCIP/53t6pchi7rF65RF3Q1O45XuqJ/hIb3ClV5lUuzV+81Ow4AeDSKPAAAAEADtmSf0Iod+bJapEfH9Tc7jteyWCx65Ju/3zc352hfQanJiQDAc1HkAQAAAL7HMAzNWpEpSfppUg/1jwoxOZF3S4rtotSESLkM6bmVe8yOAwAeiyIPAAAA8D2rMo7qy4MnZPe31u4Ahbb1m7H9ZLVU/93/a+NBvbctV2n7j8vpMsyOBgAew8/sAAAAAIA7qXS69IcPd0uS7h0Tp2hHB5MT+YYLIoKVHB+mDfuPa/qyXbXHox12TR+foLGJ0SamAwDPwEgeAAAAQJLTZSht/3E9/u4OHSg8rS5B/vrFpb3NjuUzVu7M04b9x+sdzy8u05RXt2jlzjwTUgGAZ2EkDwAAAHzeyp15mrE8Q3nFZbXHnC5DG/cVMoKkHThdhmYsz2jwnCHJImnG8gxdnRAlG9vYA0CjGMkDAAAAn7ZyZ56mvLqlToFHkkrLqhhB0k7Ss4rq/f1/lyEpr7hM6VlF7RcKADwQRR4AAAD4rJoRJA0t7VtzbMbyDBb/bWMFpY0XeFrSDgB8FUUeAAAA+CxGkLiHiGB7q7YDAF9FkQcAAAA+ixEk7mF4XKiiHXY1ttqORdW7bA2PC23PWADgcSjyAAAAwGcxgsQ92KwWTR+fIEmNFnqmj09g0WUAOA+KPAAAAPBZw+NCFRXSeAGHESTtZ2xitOZOHKIoR/3/Hz8b2oNdzgCgCdhCHQAAAD7LZrXo2oFRWrThYL1zNWNGGEHSfsYmRuvqhCilZxWpoLRM23JO6h8bDmrToRMyDEMWC/8fAOBcGMkDAAAAn2UYhtIPVi+q3Cmw7uefUQ675k4cwgiSdmazWpTcO0zXD+6uX6f2U6dAPx04dlob9h03OxoAuD1G8gAAAMBnfX6gSDtzS2T3t+rThy/TvoJTKigtU0Rw9RQtRvCYq1Ogn34ypLsWpx3S4rSDGtOnq9mRAMCtUeQBAACAz1qw7oAk6aYhPRQeHKjw4ECTE+H77kyO1eK0Q/oo86gOnzijHl2CzI4EAG6L6VoAAADwSfsKTunj3QWyWKR7x8SZHQeNuCAiWKMvCJPLkF77ItvsOADg1ijyAAAAwCctXJ8lSbqyf6TiwzuZnAbncsfIXpKkpV/mqKzSaW4YAHBjFHkAAADgc46fKtc7Ww5LkialMIrH3V01IELdHHYVna7QB1/lmR0HANwWRR4AAAD4nFc+P6TyKpcG9XBoeFyo2XFwHn42q24fGStJWpx20NwwAODGKPIAAADAp5RVOvVK2iFJ0n0p8bJY2EHLE9wyLEYBNqu2Hy7WtpyTZscBALdEkQcAAAA+5d2tuTp+ukLdO3fQtYlRZsdBE4V1CtSPB0VLYjQPADSmRUWeOXPmKC4uTna7XUlJSVq3bt05269du1ZJSUmy2+2Kj4/XvHnz6rWZPXu2+vXrpw4dOigmJkZTp05VWVlZS+IBAAAADXK5jNpt0/9ndC/52fjM05PcOaqXJOn9r/J0/FS5uWEAwA01+11t6dKleuihh/TEE09o69atSklJ0bhx45Sd3fB2hllZWbr22muVkpKirVu36vHHH9cDDzygt99+u7bNa6+9pkcffVTTp09XZmamFi5cqKVLl+qxxx5r+SsDAAAAvmfN1wXaf+y0ggP9NGFYjNlx0EyDYzprUA+HKqpcWropx+w4AOB2ml3keeGFF3Tvvffqvvvu04ABAzR79mzFxMRo7ty5DbafN2+eevbsqdmzZ2vAgAG67777dM899+j555+vbZOWlqbRo0frtttuU69evZSamqpbb71VmzZtavkrAwAAAL7n5c+qt02/ZXiMgu3+JqdBS9yZ3EuS9Nrn2XK6DHPDAICbaVaRp6KiQps3b1Zqamqd46mpqdq4cWODz0lLS6vX/pprrtGmTZtUWVkpSRozZow2b96s9PR0SdKBAwe0YsUK/ehHP2o0S3l5uUpKSuo8AAAAgMbszC1W2oHjslktuns026Z7qh8PilaXIH/lnjyrjzOPmh0HANxKs4o8hYWFcjqdioyMrHM8MjJS+fn5DT4nPz+/wfZVVVUqLCyUJN1yyy165plnNGbMGPn7+6t37966/PLL9eijjzaaZdasWXI4HLWPmBiG2wIAAKBxNWvx/GhgtLp37mByGrSU3d+mCcN6SpIWf7NLGgCgWotWmvv+NpOGYZxz68mG2n/3+Jo1a/Tss89qzpw52rJli9555x29//77euaZZxrt87HHHlNxcXHtIyeHObkAAABoWF7xWb3/VZ4kaVJKvMlp8EPdPqKnrBZp/b5C7Ss4ZXYcAHAbfs1p3LVrV9lstnqjdgoKCuqN1qkRFRXVYHs/Pz+FhYVJkp566indcccduu+++yRJAwcO1OnTp/Xzn/9cTzzxhKzW+rWowMBABQYGNic+AAAAfNQ/NxxUlcvQiLhQDezhMDsOfqCY0CBd0T9SH2Ue1aufH9Jvr7vQ7EgA4BaaNZInICBASUlJWr16dZ3jq1ev1qhRoxp8TnJycr32q1at0tChQ+XvX73Y3ZkzZ+oVcmw2mwzDqB31AwAAALTEqfIqvZ5evRMso3i8x12jYiVJb20+rFPlVSanAQD30OzpWtOmTdOCBQu0aNEiZWZmaurUqcrOztbkyZMlVU+juvPOO2vbT548WYcOHdK0adOUmZmpRYsWaeHChXr44Ydr24wfP15z587VkiVLlJWVpdWrV+upp57SddddJ5vN1govEwAAAL5q6Zc5Ki2rUnx4R13RP8LsOGglo3t3VXx4R50qr9K7Ww6bHQcA3EKzpmtJ0oQJE3T8+HE9/fTTysvLU2JiolasWKHY2OpKel5enrKzs2vbx8XFacWKFZo6dar+9re/qVu3bnrxxRd100031bZ58sknZbFY9OSTTyo3N1fh4eEaP368nn322VZ4iQAAAPBVVU6XFq2v3jb93jFxslobX0cSnsVqteiOkbGasTxDi9MOaeLI2HOuEwoAvsBieMl8qJKSEjkcDhUXFyskJMTsOAAAAHAD7391RL98fatCOwZo46NXyO7PKHFvUlJWqZEzP9aZCqdenzRCo3p3NTsSALSJptY8WrS7FgAAAODuDMPQy+uqR/FMHBlLgccLhdj99ZMh3SVJr7CdOgBQ5AEAAIB32nTohLbnnFSAn1V3JseaHQdt5M7kXpKkVRlHdeTkWXPDAIDJKPIAAADAK7382QFJ0k8u7q6unQJNToO20jcyWCPjQ+V0GXr9i+zzPwEAvBhFHgAAAHidrMLTWp15VJJ0X0qcyWnQ1mpG8yz5MlvlVU5zwwCAiSjyAAAAwOssWp8lw5Au7xeuCyKCzY6DNnZ1QqSiQuwqPFWhD3fkmx0HAExDkQcAAABe5cTpCr25OUeSNCkl3uQ0aA/+NqtuH9FTkvSvtIPmhgEAE1HkAQAAgFd57YtDKqt0KSE6RMm9w8yOg3Zyy/Ce8rdZtDX7pHYcLjY7DgCYgiIPAAAAvEZ5lVP/+mYr7UmXxMlisZicCO0lPDhQ1w6MliQtZjQPAB9FkQcAAABe471tR3SstFxRIXb9eFA3s+OgndUswLxs+xGdOF1hbhgAMAFFHgAAAHgFwzC0cF2WJOnu0b3kb+NW19cM6dlZF3YLUXmVS//elGN2HABod7zzAQAAwCt8trdQe46WqmOATbcO72l2HJjAYrHorm9G87zy+SE5XYa5gQCgnVHkAQAAgFdYsO6AJOnmYTFydPA3OQ3Mct3gbuoc5K/DJ85qzZ4Cs+MAQLuiyAMAAACPl5lXonV7C2W1SPeMjjM7Dkxk97fp5qExklS7CDcA+AqKPAAAAPB4C75Zi2dcYrRiQoNMTgOzTRwRK4tF+uzrYzpw7JTZcQCg3VDkAQAAgEdyugyl7T+uxWkH9Z9thyVJ96UwigdSz7AgXd4vQpL06ufZJqcBgPbjZ3YAAAAAoLlW7szTjOUZyisuqz3mb7PoaEnZOZ4FX3Jncqw+2V2gf2/K1iV9u6r4bKUigu0aHhcqm9VidjwAaBMWwzC8Ysn5kpISORwOFRcXKyQkxOw4AAAAaCMrd+Zpyqtb1NBNrEXS3IlDNDYxur1jwc24XIZGzPxIx05V1Dke7bBr+vgE/o0A8ChNrXkwXQsAAAAew+kyNGN5RoMFnhozlmewdTa0KiO/XoFHkvKLyzTl1S1auTPPhFQA0LYo8gAAAMBjpGcV1Zmi9X2GpLziMqVnFbVfKLidmmJgQ2rKfxQDAXgjijwAAADwGAWlTVtzp6nt4J0oBgLwVRR5AAAA4DEigu2t2g7eiWIgAF9FkQcAAAAeY3hcqKIdjRdwLKpeWHd4XGj7hYLboRgIwFdR5AEAAIDHsFktmj4+ocFzNZtiTx+fwBbZPq6mGNjYvwKKgQC8FUUeAAAAeJSLe3ZRQzWcKIed7dMhqW4xsLFCD8VAAN7Iz+wAAAAAQHMsTjsolyENi+2iaan9VFBapojg6lEZ/NKOGmMTozV34hDNWJ5RZxHmQD+r/nLLYIqBALwSRR4AAAB4jLMVTr32RbYk6d6UeCX3DjM5EdzZ2MRoXZ0QpfSsIu3ILdbMFZmqqHJpUI/OZkcDgDbBdC0AAAB4jHe2HtbJM5WKCe2gqxMizY4DD2CzWpTcO0w/vyReI+NDZUha+mWO2bEAoE1Q5AEAAIBHcLkMLVqfJUm6e1QcU7PQbLeNiJUkLfkyW1VOl8lpAKD1UeQBAACAR1i795j2HzutToF+unloD7PjwANdc2GkwjoG6GhJuT7ZXWB2HABodRR5AAAA4BFqRvFMGBajYLu/yWngiQL9bPrpNwXCmrWdAMCbUOQBAACA29uTX6p1ewtltUh3j+pldhx4sFuH9ZQkfbb3mHKKzpicBgBaF0UeAAAAuL2aUTzXXBilmNAgk9PAk/Xq2lEpfbrKMKrX5gEAb0KRBwAAAG6t8FS53t2WK0m6d0ycyWngDW4bXj2aZ+mXh1XJAswAvAhFHgAAALi11z7PVkWVSxf1cCgptovZceAFrkqIVHhwoApPlWt1xlGz4wBAq6HIAwAAALdVXuXUK58fkiTdMyZOFgvbpuOH87dZNWFojCTptS8OmZwGAFoPRR4AAAC4rWXbjqjwVLmiHXZdOzDa7DjwIrcMj5HFIm3Yd1xZhafNjgMArYIiDwAAANySYRha+M2Cy3cm95K/jVtXtJ4eXYJ0Wd9wSdIb6SzADMA78E4JAAAAt5S2/7h255eqg7+tdqFcoDXdPiJWkvTmphyVVzlNTgMAPxxFHgAAALilRRuqR/H8NKmHHEH+JqeBN7qsX7iiHXadOFOplTvzzY4DAD8YRR4AAAC4nazC0/p4d4Ek6X9G9zI3DLyWn82qW4ZVjxJ77QumbAHwfC0q8syZM0dxcXGy2+1KSkrSunXrztl+7dq1SkpKkt1uV3x8vObNm1evzcmTJ3X//fcrOjpadrtdAwYM0IoVK1oSDwAAAB7uHxuyZBjSlf0jFB/eyew48GIThsXIZrUoPatIe4+Wmh0HAH6QZhd5li5dqoceekhPPPGEtm7dqpSUFI0bN07Z2Q1XvrOysnTttdcqJSVFW7du1eOPP64HHnhAb7/9dm2biooKXX311Tp48KDeeust7dmzRy+//LK6d+/e8lcGAAAAj1R8plJvbjosSbp3TJzJaeDtohx2XdE/QpL0OgswA/BwFsMwjOY8YcSIERoyZIjmzp1be2zAgAG64YYbNGvWrHrtH3nkES1btkyZmZm1xyZPnqzt27crLS1NkjRv3jz98Y9/1O7du+Xv37L51iUlJXI4HCouLlZISEiL+gAAAID55q3dr99/uFv9o4L14YMpslgsZkeCl1uzp0B3/+NLhdj9lP7EVbL728yOBAB1NLXm0ayRPBUVFdq8ebNSU1PrHE9NTdXGjRsbfE5aWlq99tdcc402bdqkyspKSdKyZcuUnJys+++/X5GRkUpMTNTMmTPldDa+wn15eblKSkrqPAAAAODZKp0u/WvjQUnVo3go8KA9XNInXD26dFBJWZXe/yrP7DgA0GLNKvIUFhbK6XQqMjKyzvHIyEjl5ze8Gn1+fn6D7auqqlRYWChJOnDggN566y05nU6tWLFCTz75pP70pz/p2WefbTTLrFmz5HA4ah8xMTHNeSkAAABwQx/uzFdecZm6dgrUdYO7mR0HPsJqtejW4dULML/+xSGT0wBAy7Vo4eXvf6JiGMY5P2VpqP13j7tcLkVERGj+/PlKSkrSLbfcoieeeKLOlLDve+yxx1RcXFz7yMnJaclLAQAAgJswDEML11dvm37HyFgF+jFlBu3nZ0N7yM9q0Zbsk8rMY5YAAM/UrCJP165dZbPZ6o3aKSgoqDdap0ZUVFSD7f38/BQWFiZJio6OVt++fWWzfftGPmDAAOXn56uioqLBfgMDAxUSElLnAQAAAM+1JfuEtuecVICfVbeP7Gl2HPiYiGC7rrkwSpL0OtupA/BQzSryBAQEKCkpSatXr65zfPXq1Ro1alSDz0lOTq7XftWqVRo6dGjtIsujR4/Wvn375HK5att8/fXXio6OVkBAQHMiAgAAwEPVjOK5cXB3de0UaHIa+KLbRlQXF9/dmqvT5VUmpwGA5mv2dK1p06ZpwYIFWrRokTIzMzV16lRlZ2dr8uTJkqqnUd1555217SdPnqxDhw5p2rRpyszM1KJFi7Rw4UI9/PDDtW2mTJmi48eP68EHH9TXX3+tDz74QDNnztT999/fCi8RAAAA7i6n6IxW7qwe/X0P26bDJMnxYYrr2lGnyqu0fPsRs+MAQLP5NfcJEyZM0PHjx/X0008rLy9PiYmJWrFihWJjYyVJeXl5ys7+dnhjXFycVqxYoalTp+pvf/ubunXrphdffFE33XRTbZuYmBitWrVKU6dO1aBBg9S9e3c9+OCDeuSRR1rhJQIAAMDd/WvjQbkMacwFXdUvKtjsOPBR1Qswx2jmit167Yts3TKcaYMAPIvFqFkF2cM1dc94AAAAuJdT5VVKnvmxSsur9I+7h+ny/hFmR4IPKzpdoZEzP1aF06VlvxytQT06mx0JAJpc82jR7loAAABAa/n3lzkqLa9SfHhHXdo33Ow48HGhHQM0biALMAPwTBR5AAAAYBqny9A/NlYvuHzP6DhZrRaTEwHS7SOql6JYtv2ISssqTU4DAE1HkQcAAACmWZ1xVDlFZ9U5yF83DelhdhxAkjSsVxddENFJZyqc+s82FmAG4Dko8gAAAMA0i77ZNv224T3VIcBmchqgmsVi0W3fLLr82ueH5CXLmALwARR5AAAAYIodh4uVfrBIflaL7kzuZXYcoI6bhvRQoJ9Vu/NLtTXnpNlxAKBJKPIAAADAFIs2VI/i+fGgaEU57CanAepyBPnrx4O6SZJe+5wFmAF4Boo8AAAAaHdHS8q0fHv1Wif3jok3OQ3QsNtHVk/Zev+rIyo+wwLMANwfRR4AAAC0u8VpB1XlMjS8V6gG9nCYHQdo0MUxndU/KljlVS69veWw2XEA4Lwo8gAAAKBdOF2G0vYf11ubcvTPjQclSfeMiTM3FHAOFotFt4+s3k799fRsFmAG4Pb8zA4AAAAA77dyZ55mLM9QXnFZ7TGbxSKXi1+a4d5uGNxNs1Zkal/BKaVnFWlEfJjZkQCgUYzkAQAAQJtauTNPU17dUqfAI0lOw9D9r2/Ryp15JiUDzi/Y7q/rB1cvwPx6OgswA3BvFHkAAADQZpwuQzOWZ+hc43VmLM+QkxE9cGO3Da+esvXhjnwVna4wOQ0ANI4iDwAAANpMelZRvRE832VIyisuU3pWUfuFApppYA+HBvVwqMLp0lubc8yOAwCNosgDAACANlNQ2niBpyXtALPcNrx6O/XXPj+kjfsK9d62XKXtP84oNABuhYWXAQAA0GYigu2t2g4wy/iLuum3y3bpUNFZ3bbgi9rj0Q67po9P0NjEaBPTAUA1RvIAAACgzQyPC1W0o/ECjkXVvyQPjwttv1BAC6zbe0xlVa56x/OLyzTlVRYQB+AeKPIAAACgzdisFk0fn9DgOcs3f04fnyCb1dJgG8Ad1Cwg3pCayVosIA7AHVDkAQAAQJuKCQ1q8HiUw665E4cwzQVujwXEAXgK1uQBAABAm/rrx/skSeMHReu2EbEqKC1TRHD1FC1G8MATsIA4AE9BkQcAAABtZnd+iVbuypfFIj1wZR/1iQw2OxLQbCwgDsBTMF0LAAAAbeavn1SP4rl2YDQFHnismgXEGxt3xgLiANwFRR4AAAC0ib1HS7ViR/WOQ7+64gKT0wAt990FxBsr9LCAOAB3QJEHAAAAbeKvn+yTYUhjL4xS/6gQs+MAP8jYxGjNnThEUY66U7IC/awsIA7AbbAmDwAAAFrdvoJTWv7VEUnSr65kFA+8w9jEaF2dEKX0rCLtzivR0+9nqLzKpdiwjmZHAwBJjOQBAABAG5jzafUonqsTInVhN4fZcYBWY7NalNw7TP8zJk7XDqoevbNgXZbJqQCgGkUeAAAAtKqDhaf1n225kqQHruhjchqg7fw8JV6StGx7rvKL2T4dgPko8gAAAKBVvfTpPrkM6Yr+ERrYg1E88F4XxXTW8LhQVToN/XPjQbPjAABFHgAAALSe7ONn9O7Wb0bxXMkoHni/mtE8r31xSKfKq0xOA8DXUeQBAABAq5mzZp+cLkOX9g3X4JjOZscB2twV/SMUH95RpWVVWvpljtlxAPg4ijwAAABoFYdPnNFbmw9LYhQPfIfVatGkb0bzLFqfpSqny+REAHwZRR4AAAC0ijlr9qvKZWjMBV2VFNvF7DhAu7nx4u7q2ilAuSfPasXOfLPjAPBhFHkAAADwgx05eVZvbqqeqsIoHvgau79Ndyb3kiTN/2y/DMMwNxAAn0WRBwAAAD/YvLX7Vek0lBwfpuFxoWbHAdrdxJGxsvtbtTO3RJ8fKDI7DgAfRZEHAAAAP0h+cZmWpDOKB74ttGOAfpYUI0l6ed0Bk9MA8FUUeQAAAPCDzFu7XxVOl4b3CtXIeEbxwHfdOyZOFov0ye4C7T1aanYcAD6IIg8AAABarKCkTG+kZ0uqHsVjsVhMTgSYp1fXjromIUqStGBdlslpAPgiijwAAABosfmfHVB5lUtJsV00+oIws+MAppt0SfV26u9uzVVBaZnJaQD4Goo8AAAAaJHCU+V69YtDkhjFA9RIiu2ipNguqnC6tHjjIbPjAPAxFHkAAADQIi9/dkBllS5dFNNZl/TpanYcwG1MSqkezfPK54d0pqLK5DQAfAlFHgAAADTb8VPlWpxWPUrhwSsvYBQP8B1XJ0SqV1iQis9W6s1Nh82OA8CHtKjIM2fOHMXFxclutyspKUnr1q07Z/u1a9cqKSlJdrtd8fHxmjdvXqNtlyxZIovFohtuuKEl0QAAANAOFq7P0tlKpwZ2d+jyfhFmxwHcis1q0b3fjOZZsP6AnC7D5EQAfEWzizxLly7VQw89pCeeeEJbt25VSkqKxo0bp+zs7AbbZ2Vl6dprr1VKSoq2bt2qxx9/XA888IDefvvtem0PHTqkhx9+WCkpKc1/JQAAAGgXJ05X6F8bD0piLR6gMT8d0kNdgvyVU3RW/92Vb3YcAD6i2UWeF154Qffee6/uu+8+DRgwQLNnz1ZMTIzmzp3bYPt58+apZ8+emj17tgYMGKD77rtP99xzj55//vk67ZxOp26//XbNmDFD8fHxLXs1AAAAaHOLNmTpdIVTA6JDdNUARvEADekQYNMdyb0kSX//7IAMg9E8ANpes4o8FRUV2rx5s1JTU+scT01N1caNGxt8TlpaWr3211xzjTZt2qTKysraY08//bTCw8N17733NilLeXm5SkpK6jwAAADQtorPVOqfGw5KYi0e4HzuTI5VgJ9V23NOatOhE2bHAeADmlXkKSwslNPpVGRkZJ3jkZGRys9veAhifn5+g+2rqqpUWFgoSdqwYYMWLlyol19+uclZZs2aJYfDUfuIiYlpzksBAABAC/xjY5ZKy6vULzJYqQlRZscB3FrXToG6aUgPSdL8zw6YnAaAL2jRwsvf/8TGMIxzforTUPua46WlpZo4caJefvllde3a9K03H3vsMRUXF9c+cnJymvEKAAAA0FwlZZVatD5LUvVaPFYro3iA87kvJU6S9FHmUe0/dsrkNAC8nV9zGnft2lU2m63eqJ2CgoJ6o3VqREVFNdjez89PYWFh2rVrlw4ePKjx48fXnne5XNXh/Py0Z88e9e7du16/gYGBCgwMbE58AAAA/AD/2nBQJWVV6hPRSeMSGcUDNEXv8E66akCkPso8qoXrszTzxoFmRwLgxZo1kicgIEBJSUlavXp1neOrV6/WqFGjGnxOcnJyvfarVq3S0KFD5e/vr/79+2vHjh3atm1b7eO6667T5Zdfrm3btjENCwAAwA2cKq/Sgm9G8fzyigsYxQM0w88vqd5Y5u3Nh1V4qtzkNAC8WbNG8kjStGnTdMcdd2jo0KFKTk7W/PnzlZ2drcmTJ0uqnkaVm5urxYsXS5ImT56sl156SdOmTdOkSZOUlpamhQsX6o033pAk2e12JSYm1vkenTt3lqR6xwEAANB+nC5D6VlFKigtU9r+4yo+W6n48I768aBuZkcDPMqwXl10UUxnbc85qVfSDmnq1X3NjgTASzW7yDNhwgQdP35cTz/9tPLy8pSYmKgVK1YoNjZWkpSXl6fs7Oza9nFxcVqxYoWmTp2qv/3tb+rWrZtefPFF3XTTTa33KgAAANCqVu7M04zlGcorLqtz/NK+XWVjFA/QLBaLRT9Pidf9r2/RK58f0uRLe6tDgM3sWAC8kMWoWQXZw5WUlMjhcKi4uFghISFmxwEAAPBYK3fmacqrW9TQTaJF0tyJQzQ2Mbq9YwEercrp0uV/WqOcorP63Q2Jmjgy1uxIADxIU2seLdpdCwAAAN7J6TI0Y3lGgwWeGjOWZ8jp8orPCYF242ez6p7R1TttLVyfxTUEoE1Q5AEAAECt9KyielO0vsuQlFdcpvSsovYLBXiJm4fGKMTup6zC0/oo86jZcQB4IYo8AAAAqFVQ2niBpyXtAHyrY6Bf7TStlz87YHIaAN6IIg8AAABqRQTbW7UdgLruHtVL/jaLNh06oc2HTpgdB4CXocgDAACAWsPjQhXtaLyAY5EU7bBreFxo+4UCvEhEiF03DO4uSVqwjtE8AFoXRR4AAADUslktemxc/wbP1WycPn18AtuoAz/ApEviJUkrd+Xr0PHTJqcB4E0o8gAAAKCOrMIzkqTv13GiHHa2TwdaQd/IYF3WL1yGIT37Qabe25artP3H2XELwA/mZ3YAAAAAuI+Dhaf1tzX7JEkv3DxYkSF2FZSWKSK4eooWI3iA1jG4R2et2XNMqzKOalVG9U5b0Q67po9PoJAKoMUo8gAAAECSZBiG/m/ZLlVUuTTmgq66fnA3WSwUdYDWtnJnnv7y8d56x/OLyzTl1S2MmAPQYkzXAgAAgCTpw535+uzrYwqwWfX09RdS4AHagNNlaMbyDDU0Mavm2IzlGUzdAtAiFHkAAACgU+VVenp5hiRp8mW9FR/eyeREgHdKzypSXnFZo+cNSXnFZUrPKmq/UAC8BkUeAAAA6M+rv1Z+SZliw4L0v5f1NjsO4LUKShsv8LSkHQB8F0UeAAAAH5dxpET/3HhQkjTjugtl97eZGwjwYhHB9lZtBwDfRZEHAADAh7lchp78zw45XYauHRily/pFmB0J8GrD40IV7bDrXCteRTuqd7MDgOaiyAMAAODDlm7K0Zbsk+oYYNP//fhCs+MAXs9mtWj6+ARJarTQ838/TpDNysLnAJqPIg8AAICPOn6qXL//cLckaerVfRXlYHoI0B7GJkZr7sQhjV5zFHgAtJSf2QEAAABgjt9/uFvFZys1IDpEd4/qZXYcwKeMTYzW1QlRSs8qUkFpmSKC7Vr7dYHmrT2g332QqUv6hrM+FoBmo8gDAADgg748WKQ3Nx+WJP3uhkT52RjgDbQ3m9Wi5N5htV8P6uHQu1tzlV10Ros2ZOl/L7vAxHQAPBHv5gAAAD6m0unSk+/ulCTdOjxGSbFdTE4EQJI6Bvrp0XH9JUkvfbJPR0vYRh1A81DkAQAA8DGL1mdpz9FShXYM0G+u6W92HADfcf1F3XVxz846U+HUH1buNjsOAA9DkQcAAMCH5J48q9kf7ZUkPTquv7p0DDA5EYDvslot+u346p3u3tmSq63ZJ0xOBMCTUOQBAADwITOW7dLZSqeG9eqinw7pYXYcAA24KKazfppUfX3+dtkuuVyGyYkAeAqKPAAAAD7i48yjWpVxVH5Wi353w0BZ2aYZcFu/GdtPnQL9tP1wsd7Zmmt2HAAegiIPAACADzhb4dT0ZbskSfeOiVO/qGCTEwE4l4hgu351RfXuWn9YuVunyqtMTgTAE1DkAQAA8AEvfbpXh0+cVTeHXQ9c2cfsOACa4O7RvdQrLEjHSsv10if7zI4DwANQ5AEAAPBy+wpKNf+zA5Kk6dddqI6BfiYnAtAUgX42PfXjBEnVu+IdLDxtciIA7o4iDwAAgBczDENP/menKp2GrugfodSESLMjAWiGK/pH6NK+4apwuvS7DzLMjgPAzVHkAQAA8GL/2Zarzw8Uye5v1YzrLpTFwmLLgCexWCx66scJ8rNa9FFmgdZ+fczsSADcGEUeAAAAL1V8plLPfpApSfrVFX0UExpkciIALXFBRCfdNaqXJOmZ9zNU6XSZGwiA26LIAwAA4EWcLkNp+4/rvW25evjN7So8VaHe4R01KSXe7GgAfoAHruyjsI4B2ldwSq+kHTI7DgA3xap7AAAAXmLlzjzNWJ6hvOKyOsfHX9RNAX58tgd4MkcHfz18TT899s4O/fmjr3X94G4K6xRodiwAboZ3ewAAAC+wcmeepry6pV6BR5L+8tFerdyZZ0IqAK3p5qExurBbiErLqvT8qq/NjgPADVHkAQAA8HBOl6EZyzNknKPNjOUZcrrO1QKAu7NZLZo+/kJJ0pIvs7XrSLHJiQC4G4o8AAAAHi49q6jBETw1DEl5xWVKzypqv1AA2sTwuFCNv6ibDEOasSxDhkHxFsC3KPIAAAB4uILSxgs8LWkHwL09Nq6/7P5WpR8s0gc7mIoJ4FsUeQAAADxcRLC9VdsBcG/dOnfQlEsvkCTN/CBTZyucJicC4C4o8gAAAHi44XGh6hTY+KapFknRDruGx4W2XygAbeoXl8are+cOOlJcpnlr95sdB4CboMgDAADg4f67K1+nyqsaPGf55s/p4xNks1oabAPA89j9bXr82gGSpHlr9yv35FmTEwFwBxR5AAAAPNiOw8Wa9u9tkqQr+kco2lF3SlaUw665E4dobGK0CekAtKVrB0ZpRFyoyqtcmrki0+w4ANxA4+N6AQAA4NaOlpTpvsVfqqzSpcv6hWv+HUmyWCxKzypSQWmZIoKrp2gxggfwThZL9ZbqP/7rOn3wVZ7uHHlcI+LDzI4FwEQtGskzZ84cxcXFyW63KykpSevWrTtn+7Vr1yopKUl2u13x8fGaN29enfMvv/yyUlJS1KVLF3Xp0kVXXXWV0tPTWxINAADAJ5ytcGrS4k06WlKuCyI66cVbL5afzSqb1aLk3mG6fnB3JfcOo8ADeLmEbiG6dXhPSdL0Zbu0YV+h3tuWq7T9x+V0sb064GuaXeRZunSpHnroIT3xxBPaunWrUlJSNG7cOGVnZzfYPisrS9dee61SUlK0detWPf7443rggQf09ttv17ZZs2aNbr31Vn366adKS0tTz549lZqaqtzc3Ja/MgAAAC9lGIYefmu7vjpcrC5B/lp411CF2P3NjgXAJL9O7acO/lbtzi/V7Qu+0INLtunWlz/XmD98opU72WId8CUWwzCaVd4dMWKEhgwZorlz59YeGzBggG644QbNmjWrXvtHHnlEy5YtU2bmt3NEJ0+erO3btystLa3B7+F0OtWlSxe99NJLuvPOO5uUq6SkRA6HQ8XFxQoJCWnOSwIAAPAosz/6WrM/2it/m0Wv3juC6RmAj1u5M0+TX91S73jNOD7W5QI8X1NrHs0ayVNRUaHNmzcrNTW1zvHU1FRt3LixweekpaXVa3/NNddo06ZNqqysbPA5Z86cUWVlpUJDG9/ms7y8XCUlJXUeAAAA3u79r45o9kd7JUm/uyGRAg/g45wuQzOWZzR4rubT/BnLM5i6BfiIZhV5CgsL5XQ6FRkZWed4ZGSk8vPzG3xOfn5+g+2rqqpUWFjY4HMeffRRde/eXVdddVWjWWbNmiWHw1H7iImJac5LAQAA8Djbc07q1//eLkm6b0ycJgzraXIiAGZLzypSXnFZo+cNSXnFZUrPKmq/UABM06KFly2Wugv4GYZR79j52jd0XJKee+45vfHGG3rnnXdkt9vrna/x2GOPqbi4uPaRk5PTnJcAAADgUfKLyzRp8SaVV7l0eb9wPXbtALMjAXADBaWNF3ha0g6AZ2vWFupdu3aVzWarN2qnoKCg3midGlFRUQ229/PzU1hY3eHFzz//vGbOnKmPPvpIgwYNOmeWwMBABQYGNic+AACARzpb4dR9i79UQWm5+kZW76TFrlkAJCkiuPEPxlvSDoBna9ZInoCAACUlJWn16tV1jq9evVqjRo1q8DnJycn12q9atUpDhw6Vv/+3u0D88Y9/1DPPPKOVK1dq6NChzYkFAADgtVwuQ79+c5t25pYotGOAFt41TMHspAXgG8PjQhXtsOtcZd9oh13D4xpf7xSA92j2dK1p06ZpwYIFWrRokTIzMzV16lRlZ2dr8uTJkqqnUX13R6zJkyfr0KFDmjZtmjIzM7Vo0SItXLhQDz/8cG2b5557Tk8++aQWLVqkXr16KT8/X/n5+Tp16lQrvEQAAADPNfvjvVqxI1/+Nov+fkeSYkKDzI4EwI3YrBZNH58gSY0Wei6I6CQG/wG+odlFngkTJmj27Nl6+umnNXjwYH322WdasWKFYmNjJUl5eXnKzs6ubR8XF6cVK1ZozZo1Gjx4sJ555hm9+OKLuummm2rbzJkzRxUVFfrpT3+q6Ojo2sfzzz/fCi8RAADAM723LVcvfly9k9bMGwdqWC8+iQdQ39jEaM2dOERRjrpTsroEVY/6W7e3UIs2HDQhGYD2ZjFqVkH2cE3dMx4AAMATbM0+oQnzP1dFlUu/uCSehZYBnJfTZSg9q0gFpWWKCK6eovWPDVn63QeZslikBXcO1ZUDGl5LFYB7a2rNo0W7awEAAKDtHDl5Vj9/ZbMqqly6akCEfjO2v9mRAHgAm9Wi5N5hun5wdyX3DpPNatG9Y+J06/AYGYb0wBtblZlXYnZMAG2IIg8AAIAbOVNRpUmLN+lYabn6RwVr9i3spAWg5SwWi56+PlGjeofpdIVT9/7zS7ZTB7wYRR4AAAATOV2G0vYf13vbcrVxX6GmLtmmXUdKFNYxQC/fOVSdAv3MjgjAw/nbrJp7e5Liu3bUkeIyTVq8WWWVTrNjAWgD3DUAAACYZOXOPM1YnqG84rqfqvtZ2UkLQOtyBPlr4d3DdOOcDdqec1K/fnO7/nrLxbIyUhDwKozkAQAAMMHKnXma8uqWegUeSapyGSo8VW5CKgDeLK5rR82bmCR/m0UffJWn2d/s3gfAe1DkAQAAaGdOl6EZyzPU2BanFkkzlmfI6fKKTVABuJGR8WF69saBkqQXP96r/2zNNTkRgNZEkQcAAKCdpWcVNTiCp4YhKa+4TOlZRe0XCoDPuHlojH5xabwk6TdvfaVNB/lZA3gLijwAAADtrKk727ADDoC28sg1/ZWaEKkKp0u/eGWzcorOmB0JQCugyAMAANDOQoMCmtQuItjexkkA+Cqr1aLZtwzWhd1CdPx0he7555cqKas0OxaAH4giDwAAQDs6Vlquv3z89TnbWCRFO+waHhfaPqEA+KSgAD8tvGuYIkMCtbfglH75+lZVOV1mxwLwA1DkAQAAaCdfHT6p615ar02HTsruV30b9v3Ni2u+nj4+QTa2NgbQxqIcdi24c5js/lZ99vUxPfN+htmRAPwAFHkAAADawTtbDutn89KUV1ym3uEd9cGDKZo3cYiiHHWnZEU57Jo7cYjGJkablBSArxnYw6HZEwZLkv6Vdkj/2njQ1DwAWs5iGIZX7M1ZUlIih8Oh4uJihYSEmB0HAABAklTldGnWh7u1cH2WJOmqARF6YcJghdj9JVVvp56eVaSC0jJFBFdP0WIEDwAzzF2zX39YuVtWi7To7mFK6RPOzyfATTS15kGRBwAAoI2cOF2hX76xRRv2HZck/eqKCzT1qr6y8ksSADdkGIb+31tf6a3Nh2X3s6qT3U+Fpypqz0c77Jo+PoGRhoAJmlrzYLoWAABAG8jMK9F1f1uvDfuOKyjAprm3D9GvU/tR4AHgtiwWi2beOFAXRHRSWZWrToFHkvKLyzTl1S1auTPPpIQAzociDwAAQCtbsSNPP5mzUTlFZ9UzNEjv/O8ojRvIJ98A3J/NalHJ2Ya3Uq+ZAjJjeYacLq+YEAJ4HYo8AAAArcTlMvTH/+7W/762RWcrnUrp01XLfjla/aOYSg7AM1SvwVPe6HlDUl5xmdKzitovFIAm8zM7AAAAgDcoKavUQ0u26ZPdBZKkSSlxemRsf/nZ+EwNgOcoKC1r1XYA2hdFHgAAgGZoaDesg8dPa9LiTTpw7LQC/az6w02DdMPF3c2OCgDNFhFsb9V2ANoXRR4AAIAmWrkzTzOWZyiv+NtPsLsE+etshVNlVS51c9j19zuGamAPh4kpAaDlhseFKtphV35xmRpbdSfAZlH3Lh3aNReApmH8MAAAQBOs3JmnKa9uqVPgkaQTZypVVuXSBeGdtOxXYyjwAPBoNqtF08cnSJIa2wuwwmnoRy+u0/LtR9ovGIAmocgDAABwHk6XoRnLMxr9VFuSTldUqUtQQLtlAoC2MjYxWnMnDlGUo+6UrGiHXc9cn6iLe3ZWaVmVfvXGVj385nadKq8yKSmA72O6FgAAwHmkZxXVG8HzfTW7zST3DmunVADQdsYmRuvqhKh6a5DZrBbdMjxGf/14r176dJ/e2nxYXx4s0l9uuViDYzqbHRvweYzkAQAAOI8jJ880qR27zQDwJjarRcm9w3T94O5K7h0mm7V6Ape/zappqf205OfJ6uaw69DxM/rp3I2as2afnK5zjXkE0NYo8gAAADSiosql1744pJkrMpvUnt1mAPiS4XGh+vDBS/SjQdGqchl6buUe3b7gc+UVnzU7GuCzKPIAAAB8T0WVS69/ka3Ln1+jJ97dqeOnK2VtbAVSVS9OGu2onsoAAL7EEeSvl269WM/9dJCCAmz6/ECRxs5ep5U788yOBvgk1uQBAAD4RqXTpbc2H9ZLn+xT7snqT6LDgwP1v5f1VljHAD24ZJsk1VmAuab2M318Qu1UBgDwJRaLRTcPjdGwXqF6cMlWfXW4WJNf3aJbhsXo/8YnKCig+tdOp8tocI0fAK3HYhiGV0yaLCkpkcPhUHFxsUJCQsyOAwAAPEil06V3thzWXz/Zp8Mnvi3uTLm0t24b0VN2f5uk6m3UZyzPqLMIc7TDrunjEzQ2MdqU7ADgTiqqXPrzR19r3tr9MgwpvmtHvXjrxTp84gw/P4EfoKk1D4o8AADAq53rk+NKp0vvbsnVXz/dq5yi6uJO106BmnxpvCaOjK0t7jS1PwBAtY37CzVt6Xbll5TJZpWcrvptan5yzp04hEIPcB4UeQAAgM9rbOTNEz8aoDMVTr30yT5lF1XvnNW1U4AmX9pbt4+IVYeA+sUdAEDznDxToUfe+kr/zTjaaBuLpCiHXesfuYKCOXAOTa15sCYPAADwSit35mnKq1v0/U+z8orL9MvXt9Z+3bVTgH5xSW9NHElxBwBaU+egAN09utc5izyGqn8up2cVKbl3WPuFA7wURR4AAOB1nC5DM5Zn1CvwfJfVIv1mbD/dmdyrdlFQAEDrKigtb2K7svM3AnBebKEOAAC8TnpWUZ0pWg1xGdJFPbpQ4AGANhQRbG9Su9UZR7X3aGkbpwG8H3c1AADAK1RUubTpYJE+3VOg97YdadJz+OQYANrW8LhQRTvsyi8uO+foyve/ytP7X+XpopjOunloD42/qJtC7P7tlhPwFhR5AACA22nqDlb5xWVas6dAn+4p0Pq9hTpd4WzW92nqJ8wAgJaxWS2aPj5BU17dIotUp9BT81P9F5fGa/+x0/p0d4G255zU9pyTenp5hsYlRulnQ2OUHB8m6/feA9jpEGgYu2sBAAC30tiOWNPHJ+iqAZHalnNSn+4p0Ce7jykzr6TOc7t2CtRl/cJ1aZ9w/W5FhgpKyhv85JjdXACgfZ3rZ3vN9unHSsv1n625enNzjr4+eqq2XffOHXRTUg/9LKmHYkKDmtQX4G3YQh0AAHicxnbEqhEUYNOZ74zWsViki3p01uX9InRF/whd2C2k9tPemr6khj85njtxCL8MAEA7auroG8Mw9NXhYv17U46WbT+i0rKq2nN9IzvVKQDV4Gc7vB1FHgAA0G5aY9i802Vo1O8/1tGSc+/EEmL302X9InR5/3Bd0idcYZ0CG23Lp70A4NnKKp367658vbnpsNbvKzxn2x8ySpPpX3B3FHkAAECjWvNmtrmFFMMwdLSkXPuPndKBY6e0/9hp7T92SplHSlR4uuK83+/Ve4drTJ/wJufjxh0AvMOy7bl64I1t52039ao+Gn9RN8WGdWzSz3s+EIAnoMjjYVr7BrQ1+3PnbO7enztnc/f+3Dlba/fnztncvT93zubO/bXmzWxj06tqUj3x4wGKDulQp6Bz4NipZi+Q/F1/uWWwrh/cvcXPBwB4pve25erBJdua3N7ub1WfiGD1iwpW/6jqP/tFBis8OFAWS92pvY29j7V0+hf3O+7Rnzd90NPUmge7a7mB1q4ct/bNu7tmc/f+3Dmbu/fnztlauz93zubu/blzNnfur7Gb2fziMk15dUuTbmYNw9DpCqcKS8v1xH92Nrh+Ts2x372f2WAfNqtFsaFBig/vpN4RHdW7ayedrazS9GUZ530N7IgFAL6pqT//47t21JHisyqrdGlHbrF25BbXOd8lyF/9ooLVNzJY72070uj7mEXSjOUZujohqlmFAe533KM/Xx2h1aKRPHPmzNEf//hH5eXl6cILL9Ts2bOVkpLSaPu1a9dq2rRp2rVrl7p166bf/OY3mjx5cp02b7/9tp566int379fvXv31rPPPqsbb7yxyZk8dSRPa1eOW7M/d87m7v25czZ378+ds7V2f+6czd37c+ds7tyf02VozB8+qXOz832hHQP0xLX9dfJslU6eqVDR6QqdOFOhE6crdeKbr0+eqVSF09Xk/BdEdNTgmC7qHd5J8eEd1Tu8k3qGBinAz9pgvvziMnbEAgDU05z3CUnKLjqjPfkl2p1fqj3fPA4ePy1XM38D/sUl8UqK7aLOQQHqHOSvzh38FdLBX3Z/W7223O+4R39tNULLTG02XWvp0qW64447NGfOHI0ePVp///vftWDBAmVkZKhnz5712mdlZSkxMVGTJk3SL37xC23YsEH/+7//qzfeeEM33XSTJCktLU0pKSl65plndOONN+rdd9/V//3f/2n9+vUaMWJEq75gd3K+m+3m3sy2Zn/unM3d+3PnbO7enztna+3+3Dmbu/fnztma09/qqZfKkCGny1CV6zt/Og1VuVy1X1dUuXTPP7/U8XOsVRNi99PPL41XRZWh8kqnyiqdKqt0qayq+r/PVrpUVunU8dJy7S88fd7X0FR+VouqmnCn3JzpVeyIBQA4lx/6PlFW6dTeo6e0O79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},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Value Function Iteration"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "mc2 = McCallModel(wage_probs)\nv_hist2 = mc2.value_function_iteration()\nv2 = v_hist2[-1]",
"execution_count": 14,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "As before, the true value function is piecewise linear -- constant where the agent should reject, then increasing with slope $\\frac{w_t}{1 - \\beta}$"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "fig, ax = plt.subplots()\nax.plot(wage_grid, v2, marker='o')\nax.set(title='True Value Function')\nplt.show()",
"execution_count": 15,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Reinforcement Learning\n\nUse a longer random exploratory period, since the state space is much larger (`dec_ε = 1e-6`)"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "env = DiscreteMcCallEnvironment(c=25, q_grid=wage_probs, w_grid=wage_grid, max_steps=100)\nagent = Q_Agent(n_actions=2, n_states=n+1, α=1e-2, β=0.99, min_ε=0.02, dec_ε=1e-6)",
"execution_count": 16,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "reward_history = []\nn_games = 2_000_000\n\nfor game in range(n_games):\n game_score = run_env(env, agent)\n reward_history.append(game_score)\n \n if game % 1000 == 0:\n print(f'Game {game}, average score: {np.mean(reward_history[-100:]):0.3f}' + ' '*30, end='\\r')",
"execution_count": 17,
"outputs": [
{
"output_type": "stream",
"text": "Game 1999000, average score: 4716.700 \r",
"name": "stdout"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Learning Plot\n\nConvergence takes longer by design since I increased the exploration phase, but we still see convergence to a fixed policy."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "k = 5_000\nsmooth_hist = np.convolve(reward_history, np.full(k, 1/k), mode='valid')\nfig, ax = plt.subplots()\nax.plot(smooth_hist)\nax.set_title(f'Learning Plot for McCall Q-Learner, 50 States, {k} Game Rolling Mean')\nplt.show()",
"execution_count": 18,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Value Function Comparison"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "fig, ax = plt.subplots()\nax.plot(wage_grid, np.max(agent.Q, axis=-1), label='Learned Value Function')\nax.plot(wage_grid, v_hist2[-1], label='Analytic Solution')\nax.set_title('Comparison of Learned and Analytic Value Functions, 50 States')\nax.legend()\nplt.show()",
"execution_count": 19,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "The agent simply doesn't visit the rate states enough to get a good approximation of their value, even with 2 million runs. My adjustment of the exploration space was actually pointless, because the problem is with the *environment*, not the agent's exploration.\n\nA quick look at the probabilities for the wage states reveals why. Wage states under 30 have probability less than 1 in one-million, so we can only expect to visit these states extremely rarely."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "np.c_[wage_probs, wage_grid][:21, :]",
"execution_count": 20,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 20,
"data": {
"text/plain": "array([[1.17916374e-21, 1.00000000e+01],\n [7.91385058e-20, 1.10000000e+01],\n [2.63322684e-18, 1.20000000e+01],\n [5.78951642e-17, 1.30000000e+01],\n [9.45852331e-16, 1.40000000e+01],\n [1.22425907e-14, 1.50000000e+01],\n [1.30715161e-13, 1.60000000e+01],\n [1.18361860e-12, 1.70000000e+01],\n [9.27411020e-12, 1.80000000e+01],\n [6.38444655e-11, 1.90000000e+01],\n [3.90773732e-10, 2.00000000e+01],\n [2.14682757e-09, 2.10000000e+01],\n [1.06680218e-08, 2.20000000e+01],\n [4.82546790e-08, 2.30000000e+01],\n [1.99734835e-07, 2.40000000e+01],\n [7.59880083e-07, 2.50000000e+01],\n [2.66702315e-06, 2.60000000e+01],\n [8.66281202e-06, 2.70000000e+01],\n [2.61087529e-05, 2.80000000e+01],\n [7.31758378e-05, 2.90000000e+01],\n [1.91073370e-04, 3.00000000e+01]])"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Here is the comparison again, this time only for states with probability greater than 1e-3"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "prob_mask = wage_probs > 1e-3\n\nplt.plot(wage_grid[prob_mask], np.max(agent.Q, axis=-1)[prob_mask], label='Learned Value Function')\nplt.plot(wage_grid[prob_mask], v_hist2[-1][prob_mask], label='Analytic Solution')",
"execution_count": 21,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 21,
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x13392c910>]"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Patching?\n\nThe Quantecon lecture proposes to use deep Q learning to approximate the continuous state space. This wouldn't actually solve the problem of rare states. Having finer and finer bins for wages between 30-55 would be nice, but the agent will still never encounter states below 30 or above 55, so the neural network wouldn't be able to learn anything about them.\n\nOne hacky solution is to assume there is a continuous, smooth value function over all of R that the agent is estimating. In this case, we can just use the value function learned by the agent as data in a piecewise linear model."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "trunc_wage_gird = wage_grid[prob_mask]\ntrunc_scaled_wage = (trunc_wage_gird - trunc_wage_gird.mean()) / trunc_wage_gird.std()\nall_wage_grid = (wage_grid - trunc_wage_gird.mean()) / trunc_wage_gird.std()\n\nV = np.max(agent.Q, axis=-1)[prob_mask]\ntrunc_scaled_V = (V - V.mean()) / V.std()",
"execution_count": 22,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "import pymc as pm\nimport arviz as az\n\nwith pm.Model() as vf_model:\n intercepts = pm.Normal('intercept', 0, 1, size=(2,))\n slopes = pm.Normal('slope', 0, 1, size=(2))\n \n wage_data = pm.MutableData('wage_grid', trunc_scaled_wage)\n \n switchpoint = pm.Uniform('switchpoint', 0, trunc_scaled_wage.max())\n \n mu = pm.math.switch(wage_data < switchpoint,\n intercepts[0] + slopes[0] * wage_data,\n intercepts[1] + slopes[1] * wage_data)\n \n sigma = pm.HalfNormal('sigma', sigma=1)\n obs = pm.Normal('obs', mu=mu, sigma=sigma, observed=trunc_scaled_V, shape=wage_data.shape)\n \n idata = pm.sample()",
"execution_count": 23,
"outputs": [
{
"output_type": "stream",
"text": "Auto-assigning NUTS sampler...\nInitializing NUTS using jitter+adapt_diag...\nMultiprocess sampling (4 chains in 4 jobs)\nNUTS: [intercept, slope, switchpoint, sigma]\n",
"name": "stderr"
},
{
"output_type": "display_data",
"data": {
"text/plain": "<IPython.core.display.HTML object>",
"text/html": "\n<style>\n /* Turns off some styling */\n progress {\n /* gets rid of default border in Firefox and Opera. */\n border: none;\n /* Needs to be in here for Safari polyfill so background images work as expected. */\n background-size: auto;\n }\n progress:not([value]), progress:not([value])::-webkit-progress-bar {\n background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n }\n .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n background: #F44336;\n }\n</style>\n"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<IPython.core.display.HTML object>",
"text/html": "\n <div>\n <progress value='8000' class='' max='8000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n 100.00% [8000/8000 01:45&lt;00:00 Sampling 4 chains, 0 divergences]\n </div>\n "
},
"metadata": {}
},
{
"output_type": "stream",
"text": "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 105 seconds.\n",
"name": "stderr"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "with vf_model:\n pm.set_data({'wage_grid':all_wage_grid})\n idata = pm.sample_posterior_predictive(idata, extend_inferencedata=True, )",
"execution_count": 24,
"outputs": [
{
"output_type": "stream",
"text": "Sampling: [obs]\n",
"name": "stderr"
},
{
"output_type": "display_data",
"data": {
"text/plain": "<IPython.core.display.HTML object>",
"text/html": "\n<style>\n /* Turns off some styling */\n progress {\n /* gets rid of default border in Firefox and Opera. */\n border: none;\n /* Needs to be in here for Safari polyfill so background images work as expected. */\n background-size: auto;\n }\n progress:not([value]), progress:not([value])::-webkit-progress-bar {\n background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n }\n .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n background: #F44336;\n }\n</style>\n"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<IPython.core.display.HTML object>",
"text/html": "\n <div>\n <progress value='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n 100.00% [4000/4000 00:00&lt;00:00]\n </div>\n "
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "post = az.extract(idata, 'posterior_predictive')\nhdi = az.hdi(idata, group='posterior_predictive')\n\nfig, ax = plt.subplots(figsize=(14,4), dpi=100)\nax.plot(wage_grid, v2, label='True Value Function')\nax.plot(wage_grid, post.obs.mean(dim='sample') * V.std() + V.mean(), label='Predicted Mean')\nax.fill_between(wage_grid, hdi.obs.sel(hdi='lower').values * V.std() + V.mean(), \n hdi.obs.sel(hdi='higher').values * V.std() + V.mean(), \n color='tab:blue', alpha=0.50)\nax.legend()\nplt.show()",
"execution_count": 25,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1400x400 with 1 Axes>",
"image/png": 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5hssuu4wRI0Zw7rnnEhQUxIIFCzwuLZozZw4JCQlceOGFXHjhhfTo0aPW463l6OLj43nxxRd54YUX6NmzJytXrmTixIkebf7xj3/w6quvMnPmTBISEujfvz8zZ848ao8fqLzcKycnh0GDBhEbG+sa/sADD3DWWWcxePBgBgwYQEREBJdddtkR5zV16lRiYmL485//zOjRo5k4cSJBQUGu8UFBQXz33XfExsYyfPhw4uPjufbaaykuLvYIsurj9ddfp7y8nL59+3LbbbfxyCOP1HseAwYM4P3332f+/Pn06tWLv/zlL6xYscI1/r///S87duygY8eOh70k7bLLLuPZZ5/lySefpFu3brz88su88cYbDBgw4LjWS0REREREpCnall3Au6t2UVLuICu/lIqdy3nZ9xn8DAcbwwbxVcd/w1HuQdzYGGbNm6o0Enl5edhsNux2e61QoKSkhO3bt9O+fXsCAgK8VKHIyaX9XEREREREmpIMezGvfb+dvfZiyiuc7P59Ne/6/RebUcT25snMj5+K0+JLTlEZZRVO/m9oV5r5n573+j1S5lHT6bmGIiIiIiIiIiKHHCwsY/bynaTnFONjMdj0+zre93sMm1HEnpAefHrm4zgtlbcSqXCYGAY0lX4/9brUS0RERERERESkISkoreCdFbvYklVAgNXC2vW/8ZbvZMKNXLKDOvFJ12eo8Kl8GnN+STkHC8voE9eCIL8jP8m6sVDwIyIiIiIiIiKnpZJyB++t2sXP6bk087ey7NfNzLJOJtaSTY5/NB91e55Sa+WlUIWlFezJLeZPZ7RiWM+2rqdSN3YKfkRERERERETktFPhcPLxT3tYse0gtkAr367bwSs+j3GGZQ/5vq35qPt0ivwqn6pcXO5g98EikjuGccVZ0fhZm04c0nTWVEREREREREQaBafT5PN1mSzZlE1okC+Lf03nWZ6gl2UrxdZQ5nV/nryAtgCUljvYsb+Qvu1aclXfWAJ8m8YlXlUU/IiIiIiIiIjIacM0Tb7dmMWXv2XSzN/KN+v3Mtk5jfN81lNqCWJe1+c4ENQRgLIKJ9v2F9IrpjmjEmMJbCL39XGn4EdEREREREREThurd+aw4Je9+FstLNmYxd3lL3GRzyoqDF8WxD/FvpBuQOWlYFuzC+gWFcqYxLjT9tHtf1TTXGsREREREREROe2s32vn/dW7MU1Ysf0A15W8zgjrEpxY+LzLZHY3PxuACqeTLdkFnBERwtikOGxBvl6u3HvU40cOa9KkSfTq1cv1/pprruGyyy475XXs2LEDwzBIS0s75csWERERERGRhmH7/kLmrtxNUVkFv6TbuTR/LtdZPwdgUaf/Y2vYAAAcTpNt2YW0bxXM1UlxhDXz92LV3qfg5zRzzTXXYBgGhmHg6+tLhw4dmDhxIoWFhSd92c8++ywzZ848pranOqwZMGAAhmHw2GOP1Rr317/+FcMwmDRp0impRURERERERE6sDHsxb6/Yyf6CErZmFdIv52Pu8n0PgG/b385vbS4BwGmabMsuILpFICnJ7QgPDfBm2Q2Cgp/T0JAhQ8jIyGDbtm088sgjvPjii0ycOLHOtuXl5SdsuTabjebNm5+w+Z1oMTExvPHGGx7D9u7dy9dff01kZKSXqhIREREREZE/4mBhGXNW7GLngUL25pbQOSuV/1pnArA8ejw/RY0GKm/6vC27kPDQAMYmxdG2eaAXq244FPychvz9/YmIiCAmJobRo0czZswYPv74Y6D68qzXX3+dDh064O/vj2ma2O12rr/+esLDwwkNDeUvf/kLP//8s8d8H3vsMdq0aUNISAjjx4+npKTEY3zNS72cTiePP/44nTp1wt/fn9jYWB599FEA2rdvD0Dv3r0xDIMBAwa4pnvjjTeIj48nICCAM888kxdffNFjOStXrqR3794EBATQt29ffvrpp2PaLkOHDuXAgQP88MMPrmEzZ87kwgsvJDw83KNtWVkZd999N23btiU4OJjExES+/fZb1/gDBw4watQooqOjCQoKIiEhgXfeecdjHgMGDODWW2/l7rvvpmXLlkRERKhXkYiIiIiIyAmUX1LO2yt2sSkzH3txBS33fstU3/9hMUx+ihzBj7E3AJWhz/b9hbQM9mVsUixxYcFerrzhUPBTxTShrNA7L9P8Q6UHBgZ69OzZsmUL7733Hh9++KHrUquLL76YzMxMPv/8c9asWcNZZ53FwIEDOXjwIADvvfceDz74II8++iirV68mMjKyViBT07333svjjz/OAw88wG+//cbbb79NmzZtgMrwBmDx4sVkZGTw0UcfATBjxgzuv/9+Hn30UTZs2MDkyZN54IEHmDVrFgCFhYUMHTqULl26sGbNGiZNmnTY3kw1+fn5MWbMGI9ePzNnzuTaa6+t1fbvf/87P/zwA3PnzuWXX37hyiuvZMiQIWzevBmAkpIS+vTpw6effsqvv/7K9ddfT0pKCitWrPCYz6xZswgODmbFihU88cQT/Pe//2XRokXHVK+IiIiIiIgcXkm5g3dX7eaX9FyKyx04dyzjJd9p+BoONrQewrft7wTDwDRNdh4sopm/ldGJcXQKD/F26Q2KnupVpbwIJkd5Z9n37QW/40sjV65cydtvv83AgQNdw8rKynjrrbdo3bo1AF9//TXr1q0jKysLf//Km1o99dRTfPzxx3zwwQdcf/31TJs2jWuvvZZ//OMfADzyyCMsXry4Vq+fKvn5+Tz77LNMnz6dcePGAdCxY0fOO+88ANeyw8LCiIiIcE338MMPM3XqVIYPHw5U9gz67bffePnllxk3bhxz5szB4XDw+uuvExQURLdu3UhPT+ef//znMW2P8ePHc9555/Hss8+yZs0a7HY7F198sUdPnK1bt/LOO++Qnp5OVFTlZz5x4kRSU1N54403mDx5Mm3btvUInG655RZSU1N5//33SUxMdA3v0aMHDz74IACdO3dm+vTpfPXVV1xwwQXHVK+IiIiIiIjUVu5w8sGadFbtOEiFw+TgllW84/ckAUY521qcx5edHgSjsi9Lek4x/lYLI8+JJT4y1MuVNzwKfk5Dn376Kc2aNaOiooLy8nIuvfRSnn/+edf4uLg4V/ACsGbNGgoKCggLC/OYT3FxMVu3bgVgw4YN3HjjjR7jk5OT+eabb+qsYcOGDZSWlnoETkeTnZ3N7t27GT9+PNddd51reEVFBTabzTXfnj17EhQU5FHHserRowedO3fmgw8+4JtvviElJQVfX8/H9q1duxbTNDnjjDM8hpeWlrq2kcPh4LHHHuPdd99lz549lJaWUlpaSnCwZ0DXo0cPj/eRkZFkZWUdc70iIiIiIiLiyeE0WfDzXpZu3o9pws7Nabzr9zihRjHpob35tMsUnJbKOGNvbjEYcGXfGHrGNPdu4Q2Ugp8qvkGVPW+8tex6OP/883nppZfw9fUlKiqqVrBRM5xwOp1ERkZ63MOmyvHerDkwsP43yXI6nUDl5V7uvWYAfHx8gMrrMv+oa6+9lhdeeIHffvvNdclZzTp8fHxYs2aNa7lVmjVrBsDUqVN55plnmDZtGgkJCQQHBzNhwgTKyso82tfc9oZhuNZTRERERERE6sc0TRb9lslXG7IwMNnw+2/M9Z1CKyOPfcFn8kn80zh8Kp/UtS+vhDKHkxF9Yzi7XUsvV95wKfipYhjHfbnVqRYcHEynTp2Ouf1ZZ51FZmYmVquVdu3a1dkmPj6e5cuXc/XVV7uGLV++/LDz7Ny5M4GBgXz11Veuy8Pc+fn5AZU9Z6q0adOGtm3bsm3bNsaMGVPnfLt27cpbb71FcXGxK1w6Uh11GT16NBMnTqRnz5507dq11vjevXvjcDjIysriT3/6U53z+P7777n00ksZO3YsUBkWbd68mfj4+HrVIiIiIiIiIsfu+837+eyXDExM0jZuYbZ1Mm2NAxwIiGNet+cos1b+z/r9BaUUljm4vFcU/TqGHWWuTZuCnyZg0KBBJCcnc9lll/H444/TpUsX9u7dy+eff85ll11G3759ue222xg3bhx9+/blvPPOY86cOaxfv54OHTrUOc+AgADuuece7r77bvz8/Dj33HPJzs5m/fr1jB8/nvDwcAIDA0lNTSU6OpqAgABsNhuTJk3i1ltvJTQ0lIsuuojS0lJWr15NTk4Od9xxB6NHj+b+++9n/Pjx/N///R87duzgqaeeqtf6tmjRgoyMjFq9caqcccYZjBkzhquvvpqpU6fSu3dv9u/fz9dff01CQgJ//etf6dSpEx9++CHLli2jRYsWPP3002RmZir4EREREREROUnW7DzIxz/twemE1Zt28rplCh0tGdj9Ivio+3SKfVsAkFNYRm5ROcN6RnL+meEYhuHlyhs2PdWrCTAMg88//5w///nPXHvttZxxxhmMHDmSHTt2uJ7CddVVV/Gf//yHe+65hz59+rBz586j3lD5gQce4M477+Q///kP8fHxXHXVVa7721itVp577jlefvlloqKiuPTSSwH4xz/+wauvvsrMmTNJSEigf//+zJw50/X492bNmrFgwQJ+++03evfuzf3338/jjz9e73Vu3rx5rUve3L3xxhtcffXV3HnnnXTp0oVhw4axYsUKYmJiXOt21llnMXjwYAYMGEBERITHo+xFRERERETkxFm/1857q9MpLnewaks603mM7pYdFFpb8FH36RT4Vz40yF5czv7CUgZ3i+CCrhEKfY6BYZ6Im6o0QHl5edhsNux2O6Ghnnf1LikpYfv27bRv356AgAAvVShycmk/FxERERGR08G27ALe+GEH2fklrN2exePlj3G+z8+U+DTjg+7/I7tZFwDyS8rZm1vCoK7hXNarLVafptuX5UiZR01NdyuJiIiIiIiIiFftyS3m7RW7yMov4ZddB3ig/FnO9/mZcsOfT7pOc4U+haUV7M0tpv8Zrbm0iYc+9aUtJSIiIiIiIiKn3P6CUuYs38mug0Vs2GPn5uL/cYnPcioMKwvin2BvaE8Aissc7M4pIrljK4b3aYuvQp960dYSERERERERkVPKXlzOnOU72ZKVz9bsAkYXvMFo69c4sZB6xsPsbNEPgJJyBzsOFHJ2u5aM6BuDv9XHy5WffvRULxERERERERE5ZYrKKnhn5S5+3WNnT24JFx58hxt9FwDwVcd72dxqEAClFQ627y/krNjmjDonlkA/hT7HQz1+REREREREROSUKKtw8sGadH7amUN2QRm9sz7iHt+5AHzX7lZ+jbjM1W57diE9opszOimOYH/1WzleTTr4cTqd3i5B5KTR/i0iIiIiIg2Jw2nySdoelm05QE5RObF7Pudh6xsArIj+O2vapgBQ4XCyLbuArlGhjE2KJTTA15tln/aaZGTm5+eHxWJh7969tG7dGj8/PwzD8HZZIieEaZqUlZWRnZ2NxWLBz8/P2yWJiIiIiEgTZ5omX6zL4Jvfs8gvKSd411dM9X0Ji2GSFvE3lsX+E4AKp5Mt2YWcERHC2KQ4mgfpfOaPapLBj8VioX379mRkZLB3715vlyNyUgQFBREbG4vF0qQ79omIiIiIiJeZpsm3G7NIXZ9JQWkFFduW8prfNHwNBxtaDeabDneBYeBwmmzNKqRj62BSkuIIa+bv7dIbhSYZ/EBlr5/Y2FgqKipwOBzeLkfkhPLx8cFqtaonm4iIiIiIeN3K7QeZ//NeCkorsG9dxWy/pwgwytna4jy+7DwJDAtOp8nW7AJiwwJJSY4jPDTA22U3Gk02+AEwDANfX198fXW9oIiIiIiIiMiJti7dzodr08ktKidjy8+87fsYIUYxu0PP4rMuU3BarDjNytAnqnkAKUntiLQFervsRqVJBz8iIiIiIiIicnJsycpn7qpdZBeUsnPr78y2TibMyCcjOJ758VNx+ARgmibbsgsJDw1gbFI7YloGebvsRkfBj4iIiIiIiIicULsPFjFnxS725hazdcc2ZlkeIco4yP6Adnzc7TnKrM0qQ5/9hbQM9mNsUiztWwV7u+xGqV53fZ00aRKGYXi8IiIiXOMLCgq4+eabiY6OJjAwkPj4eF566SWPeZSWlnLLLbfQqlUrgoODGTZsGOnp6R5tcnJySElJwWazYbPZSElJITc39/jXUkREREREREROiay8Euas2MnOA4Vs2bmH/5mTaW/ZR65fBPO6T6fEtzmmabLzYBGhAb6MToylU3iIt8tutOr9uJ9u3bqRkZHheq1bt8417vbbbyc1NZXZs2ezYcMGbr/9dm655RY++eQTV5sJEyYwb9485s6dy9KlSykoKGDo0KEeN1gePXo0aWlppKamkpqaSlpaGikpKX9wVUVERERERETkZMotKmP2ip1s2lfApt37eMY5ma6WnRRYW/JR9xcp8G+DaZrsOlhEgNXCqHNiiY8M9XbZjVq9L/WyWq0evXzc/fjjj4wbN44BAwYAcP311/Pyyy+zevVqLr30Uux2O6+99hpvvfUWgwYNAmD27NnExMSwePFiBg8ezIYNG0hNTWX58uUkJiYCMGPGDJKTk9m4cSNdunQ5zlUVERERERERkZOloLSCt1fsYv2ePDbvPcCjZU/Q12cTxT4hzOs+HXtgDAB7covx9bFw1TmxJETbvFx141fvHj+bN28mKiqK9u3bM3LkSLZt2+Yad9555zF//nz27NmDaZp88803bNq0icGDBwOwZs0aysvLufDCC13TREVF0b17d5YtWwZUhkc2m80V+gAkJSVhs9lcbepSWlpKXl6ex0tERERERERETr6ScgfvrdrF2l05bNtn59/FU+nv8wtlRgCfdJ3G/uDOAGTYizFN+FufaM6KbeHlqpuGegU/iYmJvPnmmyxcuJAZM2aQmZlJv379OHDgAADPPfccXbt2JTo6Gj8/P4YMGcKLL77IeeedB0BmZiZ+fn60aOH54bZp04bMzExXm/Dw8FrLDg8Pd7Wpy5QpU1z3BLLZbMTExNRn1URERERERETkOJQ7nHy0Np3l2w6yI7uAG/Kf52KflVQYvizo+hQZoT0A2JdXQmmFkyv6RJPYIczLVTcd9Qp+LrroIq644goSEhIYNGgQn332GQCzZs0CKoOf5cuXM3/+fNasWcPUqVO56aabWLx48RHna5omhmG43rv/fLg2Nd17773Y7XbXa/fu3fVZNRERERERERGpJ6fT5NOf9/LdpmzSDxYyIncGI63f4sTCF2c8wq7mlVfzZOeXUlTm4LLebenXUaHPqfSHHuceHBxMQkICmzdvpri4mPvuu4958+Zx8cUXA9CjRw/S0tJ46qmnGDRoEBEREZSVlZGTk+PR6ycrK4t+/foBEBERwb59+2otKzs7mzZt2hy2Fn9/f/z9/f/I6oiIiIiIiIjIMTJNk0Ub9rF4wz4y7CWcnz2b630rO4gs6nQ/W1r9BYADBaXklZQzrGcUA85ofcROHXLi1fseP+5KS0vZsGEDkZGRlJeXU15ejsXiOUsfHx+cTicAffr0wdfXl0WLFrnGZ2Rk8Ouvv7qCn+TkZOx2OytXrnS1WbFiBXa73dVGRERERERERLxr6Zb9fPbLXjLtpfTIeJ+7fN8D4Nt2t/Nbm2EA5BSVkVNUzkXdIxgU30ahjxfUq8fPxIkTueSSS4iNjSUrK4tHHnmEvLw8xo0bR2hoKP379+euu+4iMDCQuLg4lixZwptvvsnTTz8NgM1mY/z48dx5552EhYXRsmVLJk6c6Lp0DCA+Pp4hQ4Zw3XXX8fLLLwOVTwcbOnSonuglIiIiIiIi0gCs2XmQeT/tYV9eCdHpC3jYbyYAy6PH81Pb0QDYi8vZn1/Khd0iGNI9EotFoY831Cv4SU9PZ9SoUezfv5/WrVuTlJTE8uXLiYuLA2Du3Lnce++9jBkzhoMHDxIXF8ejjz7KjTfe6JrHM888g9VqZcSIERQXFzNw4EBmzpyJj4+Pq82cOXO49dZbXU//GjZsGNOnTz8R6ysiIiIiIiIif8D6vXbeW7WbjNxiQnYtZqrv/wD4KWIEP8beAEB+STmZ9hIGxocztEckPgp9vMYwTdP0dhEnQ15eHjabDbvdTmhoqLfLERERERERETntbc0uYOYP29mWXYC54wfesD6Gv1HOb60vYmHnSWBYKCitID2niAFnhPO3vtH4+vyhu8xIHeqTefyhmzuLiIiIiIiISNOwJ7eYOct3sn1/EcU71/Cm9Un8jXK2tPgzizr9BwwLRWWVoc+5nVoxvE9bhT4NgIIfERERERERETmi7PxSZi/fwZasAnJ3ruNNnyk0M0rYGdqHz8+cjNNipbjcwa6DRSR1CGNE3xj8rT5Hn7GcdAp+REREREREROSw7EXlzFmxk9/25rFv1yZmWR6hpVHA3uCuLIifisPiT2m5gx37Czm7XUuuOjuGAF+FPg2Fgh8RERERERERqVNhaQVvr9xJ2q5c9u7ewQzzYSIsOWQFduCTbs9Sbg2mtMLBtv2F9I5tzqjEWIL8FDU0JPo0RERERERERKSW0goH76/ezaodB9m9dw/THQ/TzrKPHL8oPu42nRLf5pQ7nGzLLiQh2sboxDia+StmaGh0lyURERERERER8VDhcDJv7R5+2LKfnXuzeLLsEeItu8m3hjGv+wsU+remwuFka1YB8ZGhjE2Mwxbo6+2ypQ4KfkRERERERETExek0+WxdBt9szGJbZg4PFj/GWZYtFPmEMK/7dOyB0VQ4nWzJLqRzRAgpyXG0CPbzdtlyGAp+RERERERERAQA0zT56vd9fLk+k+377EwseII/+6yj1Ajkk27PcSC4Ew6nydasQjq0DuLqpDhaNfP3dtlyBAp+RERERERERASAH7ceYMHPe9melc8/cp/lIp9VlBu+LOj6FJkh3XE6TbZmFxAbFkhKUjvCQwO8XbIchYIfEREREREREWHtrhw+XJvO9uwChh/4HyOsS3Bi4Ysuj7K7+Tk4zcrQJ6p5AClJ7YhqHujtkuUYKPgRERERERERaeJ+z8zjvVW72ZpVwIB9s/iH9QsAFnV+gK1h52OaJtuyCwkPrQx9YloGebliOVYKfkRERERERESasJ0HCnl7xS427cunZ8Z73On7AQDftr+D38KHVoY++wtpGezH2KQ42rUK9nLFUh8KfkRERERERESaqEx7CbOX72TD3jza75nPQ76zAFgWcx0/RY3CNE12HCgkNMCXMUmxdApv5uWKpb4U/IiIiIiIiIg0QTmFZcxZsZNf0nMJS1/M49ZXAFgTOZIVMddhmia7DhYR5GdldGIsZ0aEerliOR4KfkRERERERESamILSCt5euYs1Ow4SkP4Dz1qfw2o4+bX1UL5rfzsYBuk5xfj6WBh5Tizd29q8XbIcJ6u3CxARERERERGRU6ek3MF7q3bx49b9ONLXMMPyJP5GOZta9Gdx5/vBsLAntxjDgBFnx9Arprm3S5Y/QMGPiIiIiIiISBNR4XDy8U97+G5TNoXp63jdmEKwUcr20L6knvkopmEl016Cw+nkyr4xnN2upbdLlj9IwY+IiIiIiIhIE+B0mny+LpPFG/axf/cmXjMfoYVRQHpwNz7rOhWHxZ+s/BJKyh1c0Sea5A5h3i5ZTgDd40dERERERESkkTNNk69/38cXv+5lz67tvOh4iDZGLvsCOjC/27OU+wSxv6CUgpIKhvWK4k+dW2EYhrfLlhNAPX5EREREREREGrkV2w8yP20v23al81z5Q8Rasjng15ZPEl6g1NfGwcIy7MXlXNIjkr+cGa7QpxFRjx8RERERERGRRuyX9Fw+WL2bDbsyeLzkv3SxpGO3tuLjhBco9GtFblEZBwpKGdItggu6Rij0aWQU/IiIiIiIiIg0Uluy8pm7che/7NjHpMJH6WXZSoFPKB8nvEBeQFvyisvJyi9lUNc2XJQQicWi0KexUfAjIiIiIiIi0gil5xTx9opdrN62n4n5j3Ouz3pKjEDmd3uOg0EdyC8pJ8NewvlnhjOsZxQ+Cn0aJQU/IiIiIiIiIo1Mdn4pc1bsZNnmLG6wT+VCnzWU48uCbs+wL6QbhaUV7Mkt5k9ntOKyXm2x+igeaKz0yYqIiIiIiIg0Ivbict5esZPvN2Zz1cGXuMJnKQ4sfB7/GOm2PhSVVbA7p4hzO7Xib32i8bMqGmjM9OmKiIiIiIiINBLFZQ7eWbmLb37P4oLsN/i7dSFODBZ2nsS2ln+mpNzBzgNFJLZvyYi+MfhbfbxdspxkCn5EREREREREGoGyCifvr9nN4t/20TfzHW6zfgTAN+3vYmP4RZSWO9i+v5C+7Vow8pxYAnwV+jQFCn5ERERERERETnMOp8n8n/fwxbpMOu+Zx/9ZZwOwNOZGfom6krIKJ9v2F9IrpjmjzoklyM/q5YrlVFHwIyIiIiIiInIaM02Thb9mMj9tL612p/KIzwwAVkWOZlXMtZQ7nGzNLqB7WxtjEuMICfD1csVyKin4ERERERERETmNfb95Px/9lI7vziU8ZXkeH8Pk59bDWNp+AhVOk63ZBZwZGcLYpDhsQQp9mhr17RIRERERERE5Ta3ZeZC5q3ZRsm05rxhP4W9UsKHFQL7pfB8VpsmW7AI6hTcjJakdLYP9vF2ueIGCHxEREREREZHT0G9783h7xS6yN6/lVSYTZJSyJTSRL898mArTwrbsAtq3Cubq5Ha0DvH3drniJfW61GvSpEkYhuHxioiI8GizYcMGhg0bhs1mIyQkhKSkJHbt2uUaX1payi233EKrVq0IDg5m2LBhpKene8wjJyeHlJQUbDYbNpuNlJQUcnNzj38tRURERERERBqRHfsLmb18B1t//4UXzYexGUXsDO7BF12fpAIrW7MLiG4RSEpyO9qEBni7XPGiet/jp1u3bmRkZLhe69atc43bunUr5513HmeeeSbffvstP//8Mw888AABAdU72YQJE5g3bx5z585l6dKlFBQUMHToUBwOh6vN6NGjSUtLIzU1ldTUVNLS0khJSfmDqyoiIiIiIiJy+suwF/PWjzv45bcNTHc8RGvDzt6AznzWfRrllgC27S8k0hZASlI72jYP9Ha54mX1vtTLarXW6uVT5f777+evf/0rTzzxhGtYhw4dXD/b7XZee+013nrrLQYNGgTA7NmziYmJYfHixQwePJgNGzaQmprK8uXLSUxMBGDGjBkkJyezceNGunTpUueyS0tLKS0tdb3Py8ur76qJiIiIiIiINGgHCkp568cdLFu3iefKHiLasp9sv2gWJDxPiU8ztmUXEtbMj7FJccSGBXm7XGkA6t3jZ/PmzURFRdG+fXtGjhzJtm3bAHA6nXz22WecccYZDB48mPDwcBITE/n4449d065Zs4by8nIuvPBC17CoqCi6d+/OsmXLAPjxxx+x2Wyu0AcgKSkJm83malOXKVOmuC4Ns9lsxMTE1HfVRERERERERBqsvJJy5qzYydc/b+PxkofobNlDjrU1n/R4iULflmw/UEjzIF/GJsXRoXUzb5crDUS9gp/ExETefPNNFi5cyIwZM8jMzKRfv34cOHCArKwsCgoKeOyxxxgyZAhffvkll19+OcOHD2fJkiUAZGZm4ufnR4sWLTzm26ZNGzIzM11twsPDay07PDzc1aYu9957L3a73fXavXt3fVZNREREREREpMEqLnPw7srdfPHTdiYVPkwPy3byLTY+SXiRPL827DxQRDM/K6MT4zijTYi3y5UGpF6Xel100UWunxMSEkhOTqZjx47MmjWLkSNHAnDppZdy++23A9CrVy+WLVvG//73P/r373/Y+ZqmiWEYrvfuPx+uTU3+/v74++su5SIiIiIiItK4lFU4+WDNbj5Zs4M77I+R5LOBIiOI+QnTORgYx+6cYvx9LYxKjKVrVKi3y5UGpt6XerkLDg4mISGBzZs306pVK6xWK127dvVoEx8f73qqV0REBGVlZeTk5Hi0ycrKok2bNq42+/btq7Ws7OxsVxsRERERERGRpsDhNFnw8x4+WLWLaw9O5QKftZThx6fdniGr2ZnszS3Bx4Crzo6lR3Rzb5crDdAfCn5KS0vZsGEDkZGR+Pn5cfbZZ7Nx40aPNps2bSIuLg6APn364Ovry6JFi1zjMzIy+PXXX+nXrx8AycnJ2O12Vq5c6WqzYsUK7Ha7q42IiIiIiIhIY2eaJl+uz2Tuil1cnjWd4T5LqcCHz858jD22s8iwF+M0Tf7WN4Y+cS2OPkNpkup1qdfEiRO55JJLiI2NJSsri0ceeYS8vDzGjRsHwF133cVVV13Fn//8Z84//3xSU1NZsGAB3377LQA2m43x48dz5513EhYWRsuWLZk4cSIJCQmup3zFx8czZMgQrrvuOl5++WUArr/+eoYOHXrYJ3qJiIiIiIiINCamafLd5v3MXr6TP+19lWusC3Fi8GXnB9kR9if25ZVQWuHkyj4xJLZv6e1ypQGrV/CTnp7OqFGj2L9/P61btyYpKYnly5e7evRcfvnl/O9//2PKlCnceuutdOnShQ8//JDzzjvPNY9nnnkGq9XKiBEjKC4uZuDAgcycORMfHx9Xmzlz5nDrrbe6nv41bNgwpk+ffiLWV0RERERERKTBW7Mzh1k/7KDrrtncav0IgK/b38XG8IvYX1BKYWkFl/duy7mdwo54P1wRwzRN09tFnAx5eXnYbDbsdjuhobq5lYiIiIiIiJwe1u+188LXmwnZ+AGP+7wEwHcxN7Imdjw5RWUcKChlaI8ohnSPUOjTRNUn8/hD9/gRERERERERkRNna3YBry/djmXjFzxqqbz9ycqIUayJuRZ7cTnZ+aVc2C2Cwd0U+sixqdelXiIiIiIiIiJycuzJLeb1pdvIXb+YFy3TsBpO0sIu5ocOt5NfWkGmvYSB8eFcnBCJxaLQR46Ngh8RERERERERL9tfUMrMpdvZ8fP3vMIT+BsVbLD159su/0dhmYM9uSX8qXMrLu3VFquPLt6RY6fgR0RERERERMSL7MXlzFq2nbS1y3nFnEywUcrWZn1Y1PVRiisMduUUktwhjL/1icbPqtBH6kfBj4iIiIiIiIiXFJVVMGfFTr5fuYb/Of5LC6OAXYFd+aL70xQ5rWzfX0jfdi246uwYAnx9jj5DkRoU/IiIiIiIiIh4QVmFk/dX7+aLH3/m+bKHiLDkkOHfns8SnqWIALZlF9AzujmjzoklyE+n73J81EdMRERERERE5BRzOE0+SdvDB0vX80TxJNpZ9rHfGsGChBcosISyNbuA+MhQxiTFEhLg6+1y5TSm4EdERERERETkFDJNk9RfM3jru9+YVDCJeMsucn1aMr/HS+T5tmJLdgGdwpuRkhxH8yA/b5crpzkFPyIiIiIiIiKniGmafLspm9e+3cjEnIfpY9lModGM+QkvkOPflq3ZBcSFBZGS1I5Wzfy9Xa40Agp+RERERERERE6RldsP8r9vNjI+ewp/9llHCf4s6P4s+4M6sm1/IZG2AFKS2hFhC/B2qdJIKPgREREREREROQXWpdt58ZvNXL5nKhf7rKAcK591fZK9IQls319IWDM/xibFEdMyyNulSiOi4EdERERERETkJNuSlc/0bzbTb8d0Rvp8gwMLX5zxMDubJ7HzYBEhAb6MSYyjQ+tm3i5VGhkFPyIiIiIiIiIn0a4DRTz/9RY6bXqVG3wWALCow7/Z2noQu3OK8bdaGJ0YS5eIEC9XKo2Rgh8RERERERGRkyTTXsJLSzYTun42d/m8A8A3sbewIfJy9uQWYzHgqrNj6d7W5uVKpbFS8CMiIiIiIiJyEhwoKOWV77dSlvYBD1leA+CHyHGkxVxNZl4JFQ4nV/SJpk9cCy9XKo2Z1dsFiIiIiIiIiDQ2eSXlvLZ0O5mr5vOs8QIWw2R1q8tZ2f5fZOeXUlzmYPhZbUnuEObtUqWRU/AjIiIiIiIicgIVlVUwa9kONixfyEtMxddwsK75IJaecQ8Hi8rJKynnkp5R9D+jNYZheLtcaeQU/IiIiIiIiIicIKUVDuau3M3yH77mJXMKAUY5v4f04+v4h8ktcXKgoJSLEiK5IL6NQh85JXSPHxEREREREZEToMLh5MM16Xy55Dueq3iYUKOYrUE9+bLb4+SWmWTaixkYH85fEyKxWBT6yKmhHj8iIiIiIiIif5DTabLg573M+2Y5z5ZNIszIZ7f/GaQmTMNebiUjt4gBXcIZ1qstPgp95BRSjx8RERERERGRP8A0TRZt2MfbX6/m8aL/EGUcJMM3ls96TifHEUB6bjHndW7N8LOi8fXRabicWtrjRERERERERI6TaZp8v3k/ry/6iYfy/kMHSyb7fcL5tOcLHDBD2J1TRL+OYfytTzR+Vp2Cy6mnvU5ERERERETkOK3emcP/Fq9j4sH/0NWyk1xLCxb0fIn9ltbsPFBEYvuWjOgbQ4Cvj7dLlSZKwY+IiIiIiIjIcViXbuf5Reu5PmMSZ1s2UWA0Y37C8+yztmX7/kL6tmvBVWfHEuin0Ee8R8GPiIiIiIiISD1t3pfPc4s3cNWuhxng8zMl+LOg2zT2BnRi2/5CesU0Z9Q5sQT765lK4l0KfkRERERERETqYdeBIp5bvIlBWx/jYp8VlGPl0/gn2N0sgW3ZhSRE2xiTFEdIgK+3SxVR8CMiIiIiIiJyrDLtJTz/1SZ6/v40V/l8gwMLn3f+L9ttSWzNKqBrVChjE+OwBSr0kYZBwY+IiIiIiIjIMThQUMqL324h6tcX+YfPpwAsbP9vNoUNZEt2IZ0jQkhJiqNFsJ+XKxWppuBHRERERERE5CjsxeW8+v12rGte53bLuwAsirmV3yIuY0t2AR1bB3N1chxhzfy9XKmIJ91lSkREREREROQIisoqmLlsOzkr5jDZeB2A7yKu4efosWzNLqBdq2CuTm5HeEiAlysVqU3Bj4iIiIiIiMhhlFY4mLNiJ1t/+JCnzelYDJPlra5gVbt/sjW7gOgWgVyd3I4Im0IfaZjqdanXpEmTMAzD4xUREVFn2xtuuAHDMJg2bZrH8NLSUm655RZatWpFcHAww4YNIz093aNNTk4OKSkp2Gw2bDYbKSkp5Obm1mvFRERERERERP6ICoeTD1ans/rbT3nCMRWr4WRt8wv5ofNdbD1QSKQtgJSkdrRtHujtUkUOq973+OnWrRsZGRmu17p162q1+fjjj1mxYgVRUVG1xk2YMIF58+Yxd+5cli5dSkFBAUOHDsXhcLjajB49mrS0NFJTU0lNTSUtLY2UlJT6lioiIiIiIiJyXJxOkwU/7+XrrxfyVMUUAoxyfm3Wj+/OnMS2/cWEh/iTktyO2LAgb5cqckT1vtTLarUetpcPwJ49e7j55ptZuHAhF198scc4u93Oa6+9xltvvcWgQYMAmD17NjExMSxevJjBgwezYcMGUlNTWb58OYmJiQDMmDGD5ORkNm7cSJcuXepbsoiIiIiIiMgxM02TRb9lMn/x10wtfYgQo5iNgb35qvvjbDlYSstgX8YmxdG+VbC3SxU5qnr3+Nm8eTNRUVG0b9+ekSNHsm3bNtc4p9NJSkoKd911F926das17Zo1aygvL+fCCy90DYuKiqJ79+4sW7YMgB9//BGbzeYKfQCSkpKw2WyuNnUpLS0lLy/P4yUiIiIiIiJSXz9uPcDbC5cyufBBWhoFbPfrwpc9nmZrTgWhAb6MSYqjU3iIt8sUOSb1Cn4SExN58803WbhwITNmzCAzM5N+/fpx4MABAB5//HGsViu33nprndNnZmbi5+dHixYtPIa3adOGzMxMV5vw8PBa04aHh7va1GXKlCmuewLZbDZiYmLqs2oiIiIiIiIi/LQrhxlf/Mgk+/1EGgdJt8bxRc/n2Wo3CPKzMjoxljMjQr1dpsgxq9elXhdddJHr54SEBJKTk+nYsSOzZs2if//+PPvss6xduxbDMOpVhGmaHtPUNX3NNjXde++93HHHHa73eXl5Cn9ERERERETkmG3MzOfFL1Zzd/Z9tLfsI8unDZ/3epEtBf74WQ1GnhNL97Y2b5cpUi/1vtTLXXBwMAkJCWzevJnvv/+erKwsYmNjsVqtWK1Wdu7cyZ133km7du0AiIiIoKysjJycHI/5ZGVl0aZNG1ebffv21VpWdna2q01d/P39CQ0N9XiJiIiIiIiIHItdB4p47os0btxzL/GWXRw0WrCg50tsKgrBMOCqs2PoFdPc22WK1NsfCn5KS0vZsGEDkZGRpKSk8Msvv5CWluZ6RUVFcdddd7Fw4UIA+vTpg6+vL4sWLXLNIyMjg19//ZV+/foBkJycjN1uZ+XKla42K1aswG63u9qIiIiIiIiInCj78kqYlvoLV22/jz6WzeQTzIIe09lY1gqnaXJl3xj6xLX0dpkix6Vel3pNnDiRSy65hNjYWLKysnjkkUfIy8tj3LhxhIWFERYW5tHe19eXiIgI15O4bDYb48eP58477yQsLIyWLVsyceJEEhISXE/5io+PZ8iQIVx33XW8/PLLAFx//fUMHTpUT/QSERERERGREyqnsIznFm3ggo3/4c+WXyjGn/ndn+V3M5bScgdX9o0hsb1CHzl91Sv4SU9PZ9SoUezfv5/WrVuTlJTE8uXLiYuLO+Z5PPPMM1itVkaMGEFxcTEDBw5k5syZ+Pj4uNrMmTOHW2+91fX0r2HDhjF9+vT6lCoiIiIiIiJyRAWlFbz4zWZ6/fwQF1lWUIaV+Wc+yQafM8kvLueyXlGc2yms3vexFWlIDNM0TW8XcTLk5eVhs9mw2+2634+IiIiIiIh4KCl38MqSLQR/9zDjLQtwYOHjTo/yS8ifyc4v5a8Jkfw1IRKLRaGPNDz1yTz+0D1+RERERERERE43FQ4nb6/YhfP7ZxhvWQDA5+3+zXpbf/bllzIwPpyLFPpII6HgR0RERERERJoMp9Pko5/SyVg8nQnGOwAsbHsLP7e6hD25xfTv3Jphvdrio9BHGgkFPyIiIiIiItIkmKbJwvUZ/Pz5a9xrvgbAN+HjWNN2DLtzikjuGMbwPm3x9dGpsjQe9bq5s4iIiIiIiMjp6oct+/lq/ltMcTyPxTD5oeXlrGh3Izv2F9K3XQtG9I3B3+pz9BmJnEYU/IiIiIiIiEijl7Yrhw8+eo/Hyp7E13CwOnQQP3S+m23ZRfSIbs7Ic2IJ8tMpsjQ+2qtFRERERESkUdu8L5/X3/+YR4oeJsAo55egJJbEP8TW/cWcGRnCmMRYQgN8vV2myEmhCxdFRERERESk0dp9sIjp73/Og3kPEGoU87t/D77u/gSbD5TSsXUwY5PiaBHs5+0yRU4aBT8iIiIiIiLSKGXllfD0h19zT/a/CTPy2ebbmUU9p7HpYAUxLQIZkxRHeEiAt8sUOakU/IiIiIiIiEijk1tUxtMf/8DNuycSZRwk3SeG1J7T2ZhjEB4awJjEONo2D/R2mSInnYIfERERERERaVQKSyt45tOVpGy5nY6WDLIsrfms5wv8nu+HLciXMYmxtGsV7O0yRU4J3dxZREREREREGo3SCgfTF/7C0F/voJtlJzmGjQU9XuL3YhuBvgajzomlc5sQb5cpcsqox4+IiIiIiIg0ChUOJzO+/p3E1bdztmUj+QTxSffp/F4ejsWAEWfH0L2tzdtlipxSCn5ERERERETktOd0msz+cRvtl97JAEsaJfjxSddp/E47yhxOrjgrmj5xLb1dpsgpp+BHRERERERETmumafLhmt0ELrqHiy0/Uo6Vj894nA2+XSksreDSnlEkdwzzdpkiXqHgR0RERERERE5bpmmSuj6TvM/+j6uMxTgx+KT9g/wWfA65RWVc1D2S888MxzAMb5cq4hUKfkREREREROS0tXTzfjZ/9DDj+QSABTF3s77FQLLzSxnUNYLB3SMU+kiTpuBHRERERERETkurdxxk2XtPcqtzDgCfR/yTdW0uI8NeTP8zWnNJj0h8LAp9pGlT8CMiIiIiIiKnnfV77Xz+znTuKn8FgK/CxpIWM47dOUUkd2zF5We1xeqjU14RHQUiIiIiIiJyWtmSlc/cOa9xb8k0LIbJ97ZhrOzwL3YcKKRvXEtG9I3B3+rj7TJFGgQFPyIiIiIiInLa2H2wiNfnvM39BZPxNRysDP4Ly7rcy/YDRfSObc6oxFgC/RT6iFRR8CMiIiIiIiKnhX15Jbz0zof8O/dBAoxy0gIS+a7bw2zdX0RCtI3RiXE087d6u0yRBkXBj4iIiIiIiDR4BwpKef69L7gj6z5CjWJ+80vgmx5PsPlACfGRoYxNjMMW6OvtMkUaHAU/IiIiIiIi0qDZi8t5ft43/HP3nbQy8tji05FFPaax8WAFncKbMTYpjhbBft4uU6RBUvAjIiIiIiIiDVZhaQXTFyzj6s0TaGscYJclmoW9XmBDDsSFBZOS1I7WIf7eLlOkwdLFjyIiIiIiItIglZQ7+F/qGi7/9RY6WDLINFrzWc8XWW/3I7pFIClJcUTYArxdpkiDpuBHREREREREGpyyCievfr2e/mtuoatlJwexsaDHC/xaEEJ4qD9jk+KIbhHk7TJFGjxd6iUiIiIiIiINSoXDyewfNtNj2c30tWwknyDmdX+en4tb0zLYj7FJsbRrFeztMkVOC+rxIyIiIiIiIg2G02ny4eqdRH19G382fqYYPz7s8jS/VMQSGmBldGIsncJDvF2myGlDwY+IiIiIiIg0CKZp8unPe7B+cSdDjB8pN334sPNj/GyJx9/HYNQ5scRHhnq7TJHTii71EhEREREREa8zTZOvf88iZ/59XMFXOEyDD9o9SJpfX3wMuOrsWBKibd4uU+S0o+BHREREREREvG7FtoNs+vC/jDM/AWBe27tICzkfh2nyt74x9Ilr4eUKRU5PCn5ERERERETEq9J25bDsvSf4Z8VsAD4J/ydrWl1CSbmD4We1JbF9Sy9XKHL6qlfwM2nSJAzD8HhFREQAUF5ezj333ENCQgLBwcFERUVx9dVXs3fvXo95lJaWcsstt9CqVSuCg4MZNmwY6enpHm1ycnJISUnBZrNhs9lISUkhNzf3j62piIiIiIiINDi/Z+aR+u50JpS8DEBqizGsjBxDfkkFw3pFcV6nVhiG4eUqRU5f9e7x061bNzIyMlyvdevWAVBUVMTatWt54IEHWLt2LR999BGbNm1i2LBhHtNPmDCBefPmMXfuXJYuXUpBQQFDhw7F4XC42owePZq0tDRSU1NJTU0lLS2NlJSUP7iqIiIiIiIi0pBs31/Ih++8xp0Fz2AxTL4OGcay2H+SW1TOxQmR/OXMcIU+In9QvZ/qZbVaXb183NlsNhYtWuQx7Pnnn+ecc85h165dxMbGYrfbee2113jrrbcYNGgQALNnzyYmJobFixczePBgNmzYQGpqKsuXLycxMRGAGTNmkJyczMaNG+nSpcvxrKeIiIiIiIg0IHtyi5n97tvclfsovoaDHwLP5/tOd7O/oIwh3SIZ3C1CoY/ICVDvHj+bN28mKiqK9u3bM3LkSLZt23bYtna7HcMwaN68OQBr1qyhvLycCy+80NUmKiqK7t27s2zZMgB+/PFHbDabK/QBSEpKwmazudrUpbS0lLy8PI+XiIiIiIiINDxZ+SW88f48bst6gACjnNV+5/B1/ENk5Jcx8MxwLu4RicWi0EfkRKhX8JOYmMibb77JwoULmTFjBpmZmfTr148DBw7UaltSUsK///1vRo8eTWhoKACZmZn4+fnRooXn3djbtGlDZmamq014eHit+YWHh7va1GXKlCmuewLZbDZiYmLqs2oiIiIiIiJyCuQWlfHqRwu5Mf0eQo1i1lm7s6jb4+yxlzPgjNYM69UWH4U+IidMvYKfiy66iCuuuIKEhAQGDRrEZ599BsCsWbM82pWXlzNy5EicTicvvvjiUedrmqZHF766uvPVbFPTvffei91ud7127959rKslIiIiIiIip0B+STmvzF/CNdtup5WRxyZLRz5PeIYdeU7O7dSKy89qi6+PHj4tciL9oSMqODiYhIQENm/e7BpWXl7OiBEj2L59O4sWLXL19gGIiIigrKyMnJwcj/lkZWXRpk0bV5t9+/bVWlZ2drarTV38/f0JDQ31eImIiIiIiEjDUFLu4LWFK/jbhluIMg6w04jm04Tn2ZZnIbFDGFf2jcHf6uPtMkUanT8U/JSWlrJhwwYiIyOB6tBn8+bNLF68mLCwMI/2ffr0wdfX1+Mm0BkZGfz666/069cPgOTkZOx2OytXrnS1WbFiBXa73dVGRERERERETh9lFU5mfvUzF6z9Fx2MDDJoxccJz/N7vj+9Y1sw8uwYAnwV+oicDPV6qtfEiRO55JJLiI2NJSsri0ceeYS8vDzGjRtHRUUFf/vb31i7di2ffvopDofDdU+eli1b4ufnh81mY/z48dx5552EhYXRsmVLJk6c6Lp0DCA+Pp4hQ4Zw3XXX8fLLLwNw/fXXM3ToUD3RS0RERERE5DRT4XDy9g8b6PvjP+lm7OAANj7sNp31BaEkRNsYnRhLkF+9HzgtIseoXkdXeno6o0aNYv/+/bRu3ZqkpCSWL19OXFwcO3bsYP78+QD06tXLY7pvvvmGAQMGAPDMM89gtVoZMWIExcXFDBw4kJkzZ+LjU53uzpkzh1tvvdX19K9hw4Yxffr0P7CaIiIiIiIicqo5nSbzVm+nwzf/oq/xO/kE8n6Xaawrbk18ZChjE+MIDfD1dpkijZphmqbp7SJOhry8PGw2G3a7Xff7EREREREROcVM0+SzX9KxzruBIfxAsenH7E7PsMaIp0OrYP5+bntah/h7u0yR01J9Mg/dLl1EREREREROuCW/Z1H6yR0M4QfKTR/mtn+UtUY8MS0CSUmOU+gjcooo+BEREREREZETatWOA+z68F6ucH6J0zSYG/1/rPHrS0RoAClJ7Yi0BXq7RJEmQ8GPiIiIiIiInDDr0nNZ+85/ubriQwDei7idlcEDaBHkx5ikOGLDgrxcoUjTouBHRERERERETogtWfl8885T3FA6E4CPWv6D5S2G0czfyujEWDqFN/NugSJNkIIfERERERER+cN2HSjik7df5OaCyicyfx46gh8iUvD1sTDynFjiI/XQHRFvUPAjIiIiIiIif0imvYT33n2DW3Iex2KYfBV0Ed/G/AvThCv7xtAzprm3SxRpshT8iIiIiIiIyHE7UFDK7Pff46Z9D+FnOFjq/ycWd7ib0gqTy89qy9ntWni7RJEmTcGPiIiIiIiIHBd7cTmz5n3GdbvvIcgoZZX1LL7s/BD5ZXBJz0jO69QKwzC8XaZIk6bgR0REREREROqtqKyCWQu+JmXLBGxGEess8XzR9Qn2lxpc1D2Cv5zZRqGPSAOg4EdERERERETqpaTcwazUZQxffxOtDTubjXbM7/o0GUUWLogPZ0j3SCwWhT4iDYGCHxERERERETlm5Q4n73yzlgvW3Ei0sZ9dRPBR1+fZXexH/zNac0nPKHwU+og0GAp+RERERERE5Jg4nCYf/LCBvj/cQCdjD/toyXvx09laEkS/Tq24/Ky2WH10minSkOiIFBERERERkaMyTZNPVm+l49fXkWBsJccM4Z0znmNTaQvOadeSEX1j8Lf6eLtMEalBwY+IiIiIiIgckWmafLluNy0/v4FzWE+BGcjsTk/zW0UkvWObM/KcWAJ8FfqINEQKfkREREREROSIvtuYhfPjmxnAakpNX95qN4V1Zge6t7UxOjGOZv5Wb5coIoeh4EdEREREREQOa8W2/ez/YAIXOZdQYVp4M/oh0qwJnBERwpjEWGyBvt4uUUSOQMGPiIiIiIiI1Onn3Tlsefderqj4HKdp8FbEvawNTKJ9q2CuToojrJm/t0sUkaNQ8CMiIiIiIiK1/J6Zx5p3HmZM6XsAvN3qFlaFDCSqeQBjk+IIDw3wcoUiciwU/IiIiIiIiIiHrdkFfPvOVK4teg2A90L/zvKwy2kV4s/YpHZEtwjycoUicqwU/IiIiIiIiIjL7oNFfPHuS1yX+ywAnwT/jR8iryY0wJcxiXG0bxXs5QpFpD4U/IiIiIiIiAgAmfYS5r0/i+uzp+BjmCz0H8y30f/C39eHUefE0iUixNslikg96Zl7IiIiIiIiwv6CUt776D2u2/sf/AwH3/r+ia863oOBhRF9Y0iItnm7RBE5DurxIyIiIiIi0sTlFpXxziefcc2Oewg0yljucxYLO0+i1GlheO9o+rZr6e0SReQ4KfgRERERERFpwvJLynn7i68Zvek2Qo0ifjK68lmXx8ivsHBJj0jO7RTm7RJF5A9Q8CMiIiIiItJEFZVV8M6iH7nsl5sIM/L4nfZ8HP8UB8p9uah7BH85sw2GYXi7TBH5AxT8iIiIiIiINEEl5Q7e/XYtg1bfQJRxgO1E8X78NPaVBTAoPpwh3SOxWBT6iJzuFPyIiIiIiIg0MeUOJx/98BtJy66ng7GXvWYr3jnjWdLLmtG/c2su6RmFj0IfkUZBwY+IiIiIiEgT4nCafLJyE/Hf/oN4trPftPFm52fZWdGS5I5hDO/TFl8fnSqKNBY6mkVERERERJoIp9Pk85920PbLG+nN7+SZQbzRYSrbnBH0adeCEX1j8Lf6eLtMETmBFPyIiIiIiIg0AaZpsmj9HoI//xfJ5k8Umf68GvsYm4329IxuzqhzYgnys3q7TBE5wRT8iIiIiIiINHKmafL9pmwq5t/OXxw/UGb6MCPyITb6diM+MpTRibGEBPh6u0wROQnqFfxMmjQJwzA8XhEREa7xpmkyadIkoqKiCAwMZMCAAaxfv95jHqWlpdxyyy20atWK4OBghg0bRnp6ukebnJwcUlJSsNls2Gw2UlJSyM3NPf61FBERERERacJWbjtA9rx7uLj8SxymwYzW97Gh2Tl0DG/GmKRYWgT7ebtEETlJ6t3jp1u3bmRkZLhe69atc4174oknePrpp5k+fTqrVq0iIiKCCy64gPz8fFebCRMmMG/ePObOncvSpUspKChg6NChOBwOV5vRo0eTlpZGamoqqamppKWlkZKS8gdXVUREREREpOn5aVcOW+Y9zBUlHwHwaovbWd/8fGJaBDI2KY7wkAAvVygiJ1O9L+C0Wq0evXyqmKbJtGnTuP/++xk+fDgAs2bNok2bNrz99tvccMMN2O12XnvtNd566y0GDRoEwOzZs4mJiWHx4sUMHjyYDRs2kJqayvLly0lMTARgxowZJCcns3HjRrp06fJH1ldERERERKTJWL/Xzk8fPsW1BTMBeL3ZdfzSaijhoQGMTYojqnmgdwsUkZOu3j1+Nm/eTFRUFO3bt2fkyJFs27YNgO3bt5OZmcmFF17oauvv70///v1ZtmwZAGvWrKG8vNyjTVRUFN27d3e1+fHHH7HZbK7QByApKQmbzeZqU5fS0lLy8vI8XiIiIiIiIk3Vlqx8fvjoJa7JfQGAtwNG8lPUKJoH+zEmMZa4sGAvVygip0K9gp/ExETefPNNFi5cyIwZM8jMzKRfv34cOHCAzMxMANq0aeMxTZs2bVzjMjMz8fPzo0WLFkdsEx4eXmvZ4eHhrjZ1mTJliuueQDabjZiYmPqsmoiIiIiISKOx80Ahi+e9ybXZj2MxTOb5XsyKuBsI8rMy6pxYOrcJ8XaJInKK1Cv4ueiii7jiiitISEhg0KBBfPbZZ0DlJV1VDMPwmMY0zVrDaqrZpq72R5vPvffei91ud7127959TOskIiIiIiLSmOzJLeaz+e9zzd4HsRpOUn0GsLTjRKw+FkacHUv3tjZvlygip9Afepx7cHAwCQkJbN682XXfn5q9crKysly9gCIiIigrKyMnJ+eIbfbt21drWdnZ2bV6E7nz9/cnNDTU4yUiIiIiItKUZOWV8MlnC7h6x78JMMr5zjibr854AAcGV/SJpk9ci6PPREQalT8U/JSWlrJhwwYiIyNp3749ERERLFq0yDW+rKyMJUuW0K9fPwD69OmDr6+vR5uMjAx+/fVXV5vk5GTsdjsrV650tVmxYgV2u93VRkRERERERDwdLCzjw4VfMWrTHTQzillFdz7v8iglDgvDekaR3CHM2yWKiBfU66leEydO5JJLLiE2NpasrCweeeQR8vLyGDduHIZhMGHCBCZPnkznzp3p3LkzkydPJigoiNGjRwNgs9kYP348d955J2FhYbRs2ZKJEye6Lh0DiI+PZ8iQIVx33XW8/PLLAFx//fUMHTpUT/QSERERERGpg724nPcXLWX4+ptpYeSzjo583OVJ8h1WhvaI5Pwzw496Cw4RaZzqFfykp6czatQo9u/fT+vWrUlKSmL58uXExcUBcPfdd1NcXMxNN91ETk4OiYmJfPnll4SEVN847JlnnsFqtTJixAiKi4sZOHAgM2fOxMfHx9Vmzpw53Hrrra6nfw0bNozp06efiPUVERERERFpVApLK3j/21VclPZP2nCQLWY0757xDAcd/lzYLYILu0Uo9BFpwgzTNE1vF3Ey5OXlYbPZsNvtut+PiIiIiIg0SiXlDuZ+9wv9vh/HGexkt9maVzu9yD5aMqBLOH/rE43V5w/d4UNEGqD6ZB76BhARERERETkNlVY4+ODHjfRZegNnsJMsszmvt3+GTFrSr1MrLj+rrUIfEVHwIyIiIiIicrqpcDj5eOU2zvj2nySYG8k1g3k59in2WCI5u11LruwTg7/V5+gzEpFGT8GPiIiIiIjIacThNFmQtpuIr2/lHGcahaY/L0ROId23Pb1imjPynFgC/RT6iEilet3cWURERERERLzHNE1S1+0laOFE+lcso9S08nzrh9gV3I0zI0IZnRhLM3+d5olINfX4EREREREROQ2YpslXv2VSnno/g8u+xGEaPN/i3+ywnUOn8GakJMfRPMjP22WKSAOj4EdERERERKSBM02TpVv2s/+LKVxWPA+A6SG3sSXsfGJaBjI2KY5Wzfy9XKWINEQKfkRERERERBq4VTty2PbZNEYWzALgfwH/YGPEMCJtgaQktSPSFujlCkWkoVLwIyIiIiIi0oCl7c7l589fYVzudABm+V7FutjRhDXzY0xSHLFhQV6uUEQaMgU/IiIiIiIiDdRve/P48fO3+HvW4wC87/NXVre7gRB/X0adE0en8GZerlBEGjoFPyIiIiIiIg3Qlqx8vk79gGv3PoTVcPKpMYAfOk7E38/KVWfH0DUq1NslishpQMGPiIiIiIhIA7PzQCFfLPyCv++8F3+jnG84m6/O+D8MHwt/6xNN79gW3i5RRE4TCn5EREREREQakL25xSxY9DVjt95BsFHCcrM7n3Z+BAdWLu3VlsT2Lb1dooicRhT8iIiIiIiINBDZ+aXM+3oZV/5+Ky3I52ezIx+e8QSlhh8XJ0TQ/4zWGIbh7TJF5DSi4EdERERERKQByC0q44NvV3PJLzfRhoNsMqN5u+NUCs0ALujahgu6Rij0EZF6U/AjIiIiIiLiZQWlFXzw/ToGrf0nsWSy22zN6+2fxm6EMuDMcC5OiMRiUegjIvWn4EdERERERMSLSsodvL/sd5JW/JPO5k6yzOa8GDOVHJ8wzu0UxmW92mL10ambiBwffXuIiIiIiIh4SVmFkw9XbiVh6c10d27EbgbxXOQTHPCrvInzlX1j8LPqtE1Ejp++QURERERERLygwuHkk592Efvt7fR1/ESR6c/TrR8lO6gjvWKbM+LsWAJ8fbxdpoic5qzeLkBERERERKSpcTpNPv8lg+Zf3c2fypdSZvrwZIv/kGnrQZeIEEafE0szf52uicgfpx4/IiIiIiIip5BpmizesA9z8YNcULIQh2kwNeQuMsOSiAsLYkxiHM2D/Lxdpog0Egp+REREREREThHTNPl+835yFj7OpYXvAzAt8F+kR15IeGgAYxLjaBMa4OUqRaQxUfAjIiIiIiJyiqzemcOOhdO5Ku91AF7wvYZdcX8jJMCXkefEEhcW7OUKRaSxUfAjIiIiIiJyCqxLt/NL6uuM3f8sADN9rmBbp7/j42NwZd8Y4iNDvVyhiDRGCn5EREREREROso2Z+SxLfYerMyZjMUzeNwazvsstlDtNLuvVlj5xLbxdoog0Ugp+RERERERETqId+wv5ZtEnXJ3+AL6Gg885l9Vd76WwzMmQbhH8qXMrb5coIo2Ygh8REREREZGTZE9uMV8sWsiYrXcRSBlLzN581/Vh7CUOzj8znMHdIzAMw9tlikgjpuBHRERERETkJMjKL+HTr75jxMYJhFDEKvNMUuMf42CpSXLHVgzrFYWPRaGPiJxcCn5EREREREROsNyiMuZ9u5Jh624iDDvrne34qMtUDpZZ6R3TnCv7RuNv9fF2mSLSBFi9XYCIiIiIiEhjkl9Szgff/8zgtTcSyX62OSOZ3elpDjoC6RLZjNHnxBHkp1MxETk19G0jIiIiIiJyghSXOfhw2Qb+tOIG2pl72Gu25JV2U7FbmhPXMoixiXHYgny9XaaINCEKfkRERERERE6AsgonH63cTO8f/kkX51YOmCE83/ZJCgMiadPMn7GJcYSHBni7TBFpYhT8iIiIiIiI/EEVDiefrN1BpyW30NPxK/lmIE+1nkJxaEea+fow6pxYYsOCvF2miDRBf+jmzlOmTMEwDCZMmOAaVlBQwM0330x0dDSBgYHEx8fz0ksveUxXWlrKLbfcQqtWrQgODmbYsGGkp6d7tMnJySElJQWbzYbNZiMlJYXc3Nw/Uq6IiIiIiMgJ53CafPbLHlp/dQeJ5SspMX15rMUkKtok4GMxuPLsGLpEhHi7TBFpoo47+Fm1ahWvvPIKPXr08Bh+++23k5qayuzZs9mwYQO33347t9xyC5988omrzYQJE5g3bx5z585l6dKlFBQUMHToUBwOh6vN6NGjSUtLIzU1ldTUVNLS0khJSTneckVERERERE64knIHH6zehd+i+xhQ+g3lpg+TQ+7FjO1HaYWTy3q35azYFt4uU0SasOMKfgoKChgzZgwzZsygRQvPL7Eff/yRcePGMWDAANq1a8f1119Pz549Wb16NQB2u53XXnuNqVOnMmjQIHr37s3s2bNZt24dixcvBmDDhg2kpqby6quvkpycTHJyMjNmzODTTz9l48aNf3CVRURERERE/rj8knLeXr4Dv+8mc1HRfJymwROBt0HnweQWV3BR90jO69TK22WKSBN3XMHPv/71Ly6++GIGDRpUa9x5553H/Pnz2bNnD6Zp8s0337Bp0yYGDx4MwJo1aygvL+fCCy90TRMVFUX37t1ZtmwZUBke2Ww2EhMTXW2SkpKw2WyuNjWVlpaSl5fn8RIRERERETkZ9heU8ub3W2i79N9cXjAXgGf8rqO86xVk5ZXylzNbc2G3CAzD8HKlItLU1fvmznPnzmXt2rWsWrWqzvHPPfcc1113HdHR0VitViwWC6+++irnnXceAJmZmfj5+dXqKdSmTRsyMzNdbcLDw2vNOzw83NWmpilTpvDQQw/Vd3VERERERETqZffBIt7+/jf+9PNd9HOuxWEaTPO7noKEcWTkFnNu51YM69kWH4tCHxHxvnoFP7t37+a2227jyy+/JCCg7scQPvfccyxfvpz58+cTFxfHd999x0033URkZGSdPYSqmKbpkYbXlYzXbOPu3nvv5Y477nC9z8vLIyYm5lhXTURERERE5Kg2ZuYza9EKxmyZSDdjO8WmHy+E3UdF5yHsyS7krLgW/K1PNH7WP/QcHRGRE6Zewc+aNWvIysqiT58+rmEOh4PvvvuO6dOnY7fbue+++5g3bx4XX3wxAD169CAtLY2nnnqKQYMGERERQVlZGTk5OR69frKysujXrx8AERER7Nu3r9bys7OzadOmTZ21+fv74+/vX5/VEREREREROSamabJm50Fmzl/MPQfuJ8bI5qAZwuwOT+Js05vtWQXER4Yy6uxYgvzqfWGFiMhJU68YeuDAgaxbt460tDTXq2/fvowZM4a0tDQcDgfl5eVYLJ6z9fHxwel0AtCnTx98fX1ZtGiRa3xGRga//vqrK/hJTk7GbrezcuVKV5sVK1Zgt9tdbURERERERE4Fp9Pks3UZvDJnLg8fuIMYI5s9RgTv9nyd/FY92ZJVQJfIEMYkxWIL8vV2uSIiHuoVRYeEhNC9e3ePYcHBwYSFhbmG9+/fn7vuuovAwEDi4uJYsmQJb775Jk8//TQANpuN8ePHc+eddxIWFkbLli2ZOHEiCQkJrkvB4uPjGTJkCNdddx0vv/wyANdffz1Dhw6lS5cuf3ilRUREREREjkW5w8kL32xh25J3eM7yPAFGOVv9uvBlj2fZ5wwl82AR57RvyZV9Y7AFKvQRkYbnhPdBnDt3Lvfeey9jxozh4MGDxMXF8eijj3LjjTe62jzzzDNYrVZGjBhBcXExAwcOZObMmfj4+LjazJkzh1tvvdX19K9hw4Yxffr0E12uiIiIiIhInQpLKrj9vTSiNr7JNOubWAyTDSH9WNztMfYUGuSXlDKoaxuG9ogiwNfn6DMUEfECwzRN09tFnAx5eXnYbDbsdjuhoaHeLkdERERERE4j27IL+MfMFYywv86N1k8B+Cn8cr7teBc7c8qwGAYX94jk/C7hWPT0LhE5xeqTeeiuYyIiIiIiIm4W/LyH//twLQ+bLzDM+iMA38fexIqocWzbX0iLID+u6BNN75jmh33qsIhIQ6HgR0REREREBKhwOHlw/noWrNjAK35Pk+SzAQc+LOr8H35uOYRt2YXEtgxk5DmxdGzdzNvliogcEwU/Ddy6dDvLtx04rmkP9z8fDAN8DAMfiwWLpepnA4th4GMBi8WCxQADo/Jfo/Jfi2FgsVQON6reGwYmJlUXDJpUPurSdf2gCVXvTPPQq2rUoXame2OqlldZS9XPFrflWQywWKpr8zk03HCr0ccwXHUbhoEBrjZV26DqfdV6UmOdq6bBqG5fdWWkR9011tF9O9Rs69oyh/6xWA7Vb6n8DHwO1W+t+gz0f5BERERETok9ucX8Y9YqcjN28L7f43SxpFPqE8SnZz7BhsA+7MouoHtbGyPPiSE8JMDb5YqIHDMFPw3c7pwiftiy/5ieEHCsN2syK5MKVyBR8z2YcCj4qJrvyYwfquo26rksj+nM6porL7GuCnVwhTtVM64admgobqNcgQ+uNlXtPauqzqrMOre7+52zzBoD3du7wqmqZbsFUhbDwHooELL6WKp/PvTe18fAarFg9THw9bEcCrvAx2K41qNq3d23hee2cWvn3vbQ+tbeFobrvWuL1DGu5naruXz3cK1qXavbeW6HY56uxvDqz9bwGOa+P9QVDLqHmgrfREREmoaFv2Zwx/s/E1O2nXn+jxNh5FDg24qPu05jk6U9WTnF9OsYxt/6xtDMX6dQInJ60bfWaSDQz4d2rYK9XUaDZ5qmq0eRe28i9142JoeCl0PD3XvouIa5BtTuuQOewVTNUMCo8cajrVvyVDXc6VZz1c9O08TpBIfppNR9varGua+baeI0a/eeMjGrYphDdR7bNjwS92DueO8IXzPYM6uGuAV3UCNYcguqqsd5BnlVw+sM8/AMoFxzrTPkqzskc/WGqwqEDvU4qwrZLIaBz6H3VW3cQySDyt5d7r3LXL3qLJ7BkyuMcguqPPbrQ5+507WvVO61zkM7t/PQflw5vGqfAdNp4jy0ParCQl8fA18fH3x9qkNFi2Fg9Tn076FegVaLpbJHWh1tqrade889z55v7p91dc+/qmE1Hy9QFV5WLadquVU94qp+ttRoYz30WYiIiNRHaYWDyZ9tYNaPO+ln+ZVX/J+hGcUcCGzPvG7PsbmkOYXFZQzpHsFfEyLxs1q8XbKISL0p+GnItn9H59++4OIDBYSVBmAaBiYGJhaqzm5NLJXDDOPQ+8qzzcphlb+YKiMAy6E2Ve8N1/xwm6ZyHrjGu+YJNdpUj6+ep3sb3OqhjmHVJ2ju86ycnkPzda+hahi166qj1qPVXruNe52Ga1u511NZn6XG+6rPpGqd3Obv+gwOzcNtfPWyLa7t35S5P1zQ43JAt95oVePqHH7oPzWDBPfgr7qN5zLdh1cFaFUhiomzuh63+df1vq75udfqGlfHetQ1DsME03BL3A69x7NXVdUPh+uN5RruNoF7yFi1jQzTcC2uLoeyOUzT9OiV5tGmRnv3IWaNHzzauq14rUs0awVjNXuEVV+C6mMxKnvCufWQq6qjOiyt8Tke2h64xrv97LY/OWuuwBG207GqCq2qLvW0GFSGWRaLK0j0DL0s+FjAeqiHn/uluVU9/tx7xlmM6qDUvVecZ2+6unrYGbW+ko70DXW4wM3waFO9v1RdklvVq66q5rpCU/eed9XDaoS/bnVXLdd9vd1rqHmc1OzdWHvdjn19ReT0sy27gJvf/onfMvK4zLKUJ/1ewZcK0kN788mZT7Ipz4qvxcmIvjGc16mVntwlIqctBT8N2C8/fEqPLS/TGSDH29XIqeDAM1iqzB+MGq/qgMpZM2iqMd6sNdxyxPHuy3VSGRw6XdNYqudzKABzutXrrFGn0z0kdFuOO/faK//1DAmrhtXV1onFtQyn2/Lc63XWqKc6PK2q13N7uNfgvk2qt2/t9fBsW/XefZtRa3vU3FY127pqrBHIHql9VZuqz63m/lBzeUfbx+oa78R9nzPd1sW9/eHmYfHcT4y6lwFgmlXr4vaZmJ7b2bU9TdPjOKgaVzWP6n2mjm1oeA733OfqqO0knfDXlSnVzo+qA6nGpPYmPUIQUzPwrO+yjjrgmKY6vmVVDT/MCOMwjWo2dw9wPbaUW2hr4PlDVTvDY2QdjnffMur80a0mo3bzowWLbiHdYdsdbrknSb03z7FOUMd+XVevVte4WtvOODUbAOpcp7oveD/5jMPsAEcMqetosGN/EcXlFdzsO5+JPu8CsDFsEJ91epAtB8oJa+bLlX2j6RHd/ARVLiLiHQp+GrBtvmfyU8UFrtNt91NU1zDD81TLQu1TOItrmurTKPdTRfdpwP30jep/jdrja/R9cZ0iVQ7znM+xtvM8tat7XFU91Ghf17yoa1rPU8zDTEeNNp7by2KcnD90fHCelPmecKfryefpWrecHPXdH2q0d5q1A0v3ELP6fe1hNQNAp+tlcXvvFrCadbepK8Q8UmBc9bNHQGhWj68ZJtes0T1grB1qeg73eJk1wj23WmuGbNSxHtQY56w1TXUIWVe9VcGh+3S1w/O6g/C6xnn+djtc0FpjfWqEkTXrP9wyqmupa/vW3n7un1ldn/Gx1F/zM6j+zVi7bfV+aPEIhyv3WfdhVfvz4ffzo2/LU5VwSFNhwckTAW8ygi8BWB01hsXR/2J7djHtWwcz6pxY4sJ0uwUROf0p+GnAeg68ig9s/Vix/SBtmwd6uxypi1nHn6dmzT+5DwVuZnUb1zSm55/tnsNrnMqZ7v1FqF6mWcdpgOn+J36NUwoTav5JX7XMutu7n0I5D7X17ONTc92qh3mcernVhtty3Otx/7PedGvrPs5tOYeWAYeCTdd6H1quWeO01XTfTiaGWX0a5V6P+3LrOj2qXpfawyxu2wM8Ty0N0+na5u711L3/1L3vuPYX0+mx71DHMjzn635qTJ3Lq55H3aegh9sHK+dRPa7mPni4/dXjlLLW/lfH9nfbXu77g8XV/tTyDIBPcg063xXx4P7bxRXSGTW/WTy/vSubegZ6uE9/6GfA1Suxetoa8655+fyhYWYddVXWVvWNZvGczlWzW/BlGHDo8tvD9e40D13Cb5qV6+TZy7a6nlrDsLjmW2teNb6xPX7renSXcWvn1nPSqJrOcN++Nev2XO86/3ec22fkdK/To9euj6t2JxZMw+IKGJ2GxRU6mhg4DZ/K8NNtuNOw4DQt/KnwS3oWLcPEYEn72/m+5ZXsPlBEz+jmjDwnhrBm/nXvgCIipxkFPw1Y+1bBdGtrY9v+Qt3cWU666tNpkdNYzWDJtVO7hUamZxhVO3SqY5jpPr5y2sr3QK2A0j24cq/L/XTQ6QrjqoNXpyusrGtYdahnegyrnNfhQzr3ZVcv172tWWOZhx9XM8CrM9A70vyqtlOdNdT4rFzzrLFt3cPKOmo6Ur21x1UFlYfbR2ruJ+7tqNG29v5Ue/ra6+ERP9QV2tcMPD32kaptc5htXiPEPtw61A7ZDxPG1gpfzeoQ+tC+WB3Iu+/Dh/49gb9lLDW2nVv5R6ZfdFJDheFH6hn/ZUXgn9hvL+ZPnVpxRZ9ogvx0miQijYe+0U4DTtOkwuF2CVDV/7Ry+7PUbbDbeLdx7jdT9rh5KRzx8e6H2ns+paf6yVem2zzdzq9c7aqnqa6lrqdpVQ2vXgW36g33/8dU9b56vOHZtNb6uq+z2+Jq3Suj5g2Da9ZXs8ba09f8ofY0dU3n7lhuIVLXfQ9qNHD/p85515rHYaapYh72Te31g7rX8XCftce+QB2fVa3PxG2AUb/jwDXKqD3N4T4W80gfmHudNZdRx/Kq98+qNtVFHmmc+3Zzba+6htWot+YxXtXGOFST4b48t/dV94w40nuPm0gfZhu413E0VftEzWO75jFd88bW7k9nc9XoVq/nDb4P/V90V131/96q3ieP4Ubfbu/r+n51Xw/3fbmudXS9r7Hd69q3jOoNUXs4Rxhex7JrLqcuxmHf1B58tM/Lswa3/c5tJkf9Djyk3vceqWeGUGt8zQF1/G46zOg6Gxzxc3HfX1zvq9oe2/Y5krp+Z3r8zq/xhWJQ+/vkCDP3DIg8Qkz3oKmO8MkjSIRaQa9r/p7hVM1f0LUC3MP0RPV4X0egVjNIrBzm3vuUGuMP9XdxC3Hd533UYPbQulQv11mjDrfemB5BsXvIaUJVX5g6AlvPGvDYvlWbpdY41/aosd1qbofDfKbu26Jm+Fm9XtXjq8NuJxZX+O109fw1cNQIzg/96/7zofmW+wSyPHo8a8wulBSVcXFCJIO7R+Droyd3iUjjouCngfOxGPj5WNh5sKjWU3I83tU4ea49/tBPlY/lqf7j23UyV+NR2h5PR6m7rccfolXDXAOq2wKuR1gfeufx2OqqJ7RULbf6sew1Hs9u1n6yTvVJVyXnoQE1T9ar1sb9b1HPmlwVezztperhDTWfEFPzJNTitr3qbl9dg+cyq9Xx8VLz1KVW2GTWbFF9sgmeTyuq/Nes0cYzSHA/aa3i8Rm6rV/l2nhuB/f27vuH+z7j/vQg3D53y6Fh1U/1MSo7eBtuJ39V01NjHatqr1wlj5Nr9/0H9/c1tpf7Pl1Vd9X6uH9eNfd71zriyem2XOeh5Tmdputx667hh5bv+rnG/u80cT3xyPVUI7cnXVU90cpiUGP4oe1ncX9iUuX6OJwmDqfpetS702niMKuHOZyVy3aY5qGaTRzOqho99yHT9Nxu7jxO5I9yEuw+1P24rlqGeegEx/Ozrn181DXc/buoru+tWsOp2tbU8b116Glah7Zx1SPmqz6fqidwWVz/Uvu9xeLaj933DcehFajaR5xOs8a+Ubl/uD63qmnr3G/c2tQY73BWHwPuv1c8vzs8Pg3Xl0itr6gazQ7z9tAsjvx5uX8Hun8XmW7Tu5VSp+PJPA4XhB++/fGps2zT/cfaLWoH49Xvav7+M90nwMD9SYCuL0233z9V01dts8rvTbdv15q/19ze1NwG1ftS1edkVP25UflvHdNUcf8+rz2mxveCey2HBrpKruPJh7VqrfG7q2bbutrX3D+O90mNpisAqf5vZe3VW8cjUK/5d4T7sKqf3f4mOfLfH56/R+t6ul31/Ku/L2s60v8IOcJhecLV/Lui+m/Iw/xc1b6O9XOaJjsOFBLoC6POiSW5Y5ie3CcijZKCnwbu3E6t6Ng6+DB//FX/oeh+8l7XcPefq34hepxIHvqNf6RH6npMR/Vwagw/3C9ej/HH+Uv1aP8n3TPEqHxT5x9Arp89/3iA469NpCkw3QIFZ42TgFq9rw5z8uV+jHkOrz623R817wo93MLgqvFVQZ8r/KA6IDE58ndQzZD3cCcM7mFkY1MdCFV/tu7fpbXb13jvdrrn8fumruUAptMznKr5/V0zvHL/Tq8OukwO90kcy6Plq9vW1a72wKN97Icbf7RteLRtV7v3mftnVfc2o+Y46gr5av8OBGr9/nZfv7p+j7oCI7fPquo7oSp4rNqncB2jNcJIPKetDrPc1632OtS5HaramdXLqhpWteZOZ9XPh+o6tM2q9ntc86h7/lXbyPV3kMVwBe8YuL5H3EP4qhC58jvH8+8Nj2PP6fnd6jQ9t5n7+OrtWD3M4TbM4awO9V3zclaG+a5t6PrscAXrNcPYWrt2jZ39aN+IRxt/vGGR++d6uO/+mt9t7uNdaeQhEbYARvSNoWtU6HFWJCLS8Cn4aeCa+VvpFB7i7TIajJr/1/7of1aIyIlkGAY+BvicpGOv6tg+WfMXT1UB2KF33ixFRE4B97CoZmjnCuLcHzBa42vhsL2pOHyof9SajqHmmu3NQ0GWe7BV58+H1reqR6vp9nPVdohpEUSELaAeFYuInH4U/IiIiIiINAEnO7wXEZGGSXcuExERERERERFppBT8iIiIiIiIiIg0Ugp+REREREREREQaKQU/IiIiIiIiIiKNlIIfEREREREREZFGSsGPiIiIiIiIiEgjpeBHRERERERERKSRUvAjIiIiIiIiItJIKfgREREREREREWmkFPyIiIiIiIiIiDRSVm8XcLKYpglAXl6elysRERERERERETlxqrKOquzjSBpt8JOfnw9ATEyMlysRERERERERETnx8vPzsdlsR2xjmMcSD52GnE4ne/fuJSQkBMMwvF3OccvLyyMmJobdu3cTGhrq7XJEvE7HhIgnHRMinnRMiNSm40LEU2M4JkzTJD8/n6ioKCyWI9/Fp9H2+LFYLERHR3u7jBMmNDT0tN0hRU4GHRMinnRMiHjSMSFSm44LEU+n+zFxtJ4+VXRzZxERERERERGRRkrBj4iIiIiIiIhII6Xgp4Hz9/fnwQcfxN/f39uliDQIOiZEPOmYEPGkY0KkNh0XIp6a2jHRaG/uLCIiIiIiIiLS1KnHj4iIiIiIiIhII6XgR0RERERERESkkVLwIyIiIiIiIiLSSCn4ERERERERERFppBT8iIiIiIiIiIg0Ugp+GoDvvvuOSy65hKioKAzD4OOPP/YYb5omkyZNIioqisDAQAYMGMD69eu9U6zIKTBlyhTOPvtsQkJCCA8P57LLLmPjxo0ebXRcSFPy0ksv0aNHD0JDQwkNDSU5OZkvvvjCNV7HgzR1U6ZMwTAMJkyY4Bqm40KamkmTJmEYhscrIiLCNV7HhDRFe/bsYezYsYSFhREUFESvXr1Ys2aNa3xTOS4U/DQAhYWF9OzZk+nTp9c5/oknnuDpp59m+vTprFq1ioiICC644ALy8/NPcaUip8aSJUv417/+xfLly1m0aBEVFRVceOGFFBYWutrouJCmJDo6mscee4zVq1ezevVq/vKXv3DppZe6/jDR8SBN2apVq3jllVfo0aOHx3AdF9IUdevWjYyMDNdr3bp1rnE6JqSpycnJ4dxzz8XX15cvvviC3377jalTp9K8eXNXmyZzXJjSoADmvHnzXO+dTqcZERFhPvbYY65hJSUlps1mM//3v/95oUKRUy8rK8sEzCVLlpimqeNCxDRNs0WLFuarr76q40GatPz8fLNz587mokWLzP79+5u33XabaZr6PSFN04MPPmj27NmzznE6JqQpuueee8zzzjvvsOOb0nGhHj8N3Pbt28nMzOTCCy90DfP396d///4sW7bMi5WJnDp2ux2Ali1bAjoupGlzOBzMnTuXwsJCkpOTdTxIk/avf/2Liy++mEGDBnkM13EhTdXmzZuJioqiffv2jBw5km3btgE6JqRpmj9/Pn379uXKK68kPDyc3r17M2PGDNf4pnRcKPhp4DIzMwFo06aNx/A2bdq4xok0ZqZpcscdd3DeeefRvXt3QMeFNE3r1q2jWbNm+Pv7c+ONNzJv3jy6du2q40GarLlz57J27VqmTJlSa5yOC2mKEhMTefPNN1m4cCEzZswgMzOTfv36ceDAAR0T0iRt27aNl156ic6dO7Nw4UJuvPFGbr31Vt58802gaf2usHq7ADk2hmF4vDdNs9Ywkcbo5ptv5pdffmHp0qW1xum4kKakS5cupKWlkZuby4cffsi4ceNYsmSJa7yOB2lKdu/ezW233caXX35JQEDAYdvpuJCm5KKLLnL9nJCQQHJyMh07dmTWrFkkJSUBOiakaXE6nfTt25fJkycD0Lt3b9avX89LL73E1Vdf7WrXFI4L9fhp4KruxF8zcczKyqqVTIo0Nrfccgvz58/nm2++ITo62jVcx4U0RX5+fnTq1Im+ffsyZcoUevbsybPPPqvjQZqkNWvWkJWVRZ8+fbBarVitVpYsWcJzzz2H1Wp17fs6LqQpCw4OJiEhgc2bN+t3hTRJkZGRdO3a1WNYfHw8u3btAprWOYWCnwauffv2REREsGjRItewsrIylixZQr9+/bxYmcjJY5omN998Mx999BFff/017du39xiv40Kk8jgpLS3V8SBN0sCBA1m3bh1paWmuV9++fRkzZgxpaWl06NBBx4U0eaWlpWzYsIHIyEj9rpAm6dxzz2Xjxo0ewzZt2kRcXBzQtM4pdKlXA1BQUMCWLVtc77dv305aWhotW7YkNjaWCRMmMHnyZDp37kznzp2ZPHkyQUFBjB492otVi5w8//rXv3j77bf55JNPCAkJcaXwNpuNwMBADMPQcSFNyn333cdFF11ETEwM+fn5zJ07l2+//ZbU1FQdD9IkhYSEuO77ViU4OJiwsDDXcB0X0tRMnDiRSy65hNjYWLKysnjkkUfIy8tj3Lhx+l0hTdLtt99Ov379mDx5MiNGjGDlypW88sorvPLKKwBN67jw2vPExOWbb74xgVqvcePGmaZZ+Zi5Bx980IyIiDD9/f3NP//5z+a6deu8W7TISVTX8QCYb7zxhquNjgtpSq699lozLi7O9PPzM1u3bm0OHDjQ/PLLL13jdTyImB6PczdNHRfS9Fx11VVmZGSk6evra0ZFRZnDhw83169f7xqvY0KaogULFpjdu3c3/f39zTPPPNN85ZVXPMY3lePCME3T9FLmJCIiIiIiIiIiJ5Hu8SMiIiIiIiIi0kgp+BERERERERERaaQU/IiIiIiIiIiINFIKfkREREREREREGikFPyIiIiIiIiIijZSCHxERERERERGRRkrBj4iIiIiIiIhII6XgR0RERERERESkkVLwIyIiIiIiIiLSSCn4ERERERERERFppBT8iIiIiIiIiIg0Uv8PYqz6zLHJ9OkAAAAASUVORK5CYII=\n"
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"source": "## Next Steps?\n\nObviously, I should move to a continuous state space anyway, and that will be the subject of the next installment. Another promise of RL in this domain is that the model parameters themselves -- c and beta -- can be included as part of the state space. This would allow the researcher to produce an accurate, differentiable approximation to the model's policy function. This would be useful for deep parameter estimation, for example.\n\nThe method of piecewise linear estimation is a bit unsatisfying. It would be nice to instead endogenously solve the problem of rare states in the RL training loop. This could be done by installing a world model into the agent, and allow it to \"dream\" about what would happen if it were to encounter these rare states. This one done in e.g. Hafner et al. (2019) or Hafner et al. (2020). \n\nA continuous state space version with latent dreaming is coming up next."
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"cell_type": "markdown",
"source": "# References\n\nHafner, Danijar, et al. \"Dream to control: Learning behaviors by latent imagination.\" arXiv preprint arXiv:1912.01603 (2019).\n\nHafner, Danijar, et al. \"Mastering atari with discrete world models.\" arXiv preprint arXiv:2010.02193 (2020).\n\nJ J McCall. Economics of Information and Job Search. The Quarterly Journal of Economics, 84(1):113–126, 1970.\n\nhttps://python.quantecon.org/mccall_model.html\n\nhttps://python.quantecon.org/mccall_q.html"
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"description": "Solving Economic Models with Reinforcement Learning",
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