{ "cells": [ { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "(conditional_autoregressive_priors)=\n", "# Conditional Autoregressive (CAR) Models for Spatial Data\n", "\n", ":::{post} Jul 29, 2022 \n", ":tags: spatial, autoregressive, count data\n", ":category: beginner, tutorial\n", ":author: Conor Hassan, Daniel Saunders\n", ":::" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import os\n", "\n", "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import pymc as pm\n", "import pytensor.tensor as pt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ":::{include} ../extra_installs.md\n", ":::" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# THESE ARE THE LIBRARIES THAT ARE NOT DEPENDENCIES ON PYMC\n", "import libpysal\n", "\n", "from geopandas import read_file" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "RANDOM_SEED = 8927\n", "rng = np.random.default_rng(RANDOM_SEED)\n", "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditional Autoregressive (CAR) model\n", "\n", "A *conditional autoregressive CAR prior* on a set of random effects $\\{\\phi_i\\}_{i=1}^N$ models the random effect $\\phi_i$ as having a mean, that is the weighted average the random effects of observation $i$'s adjacent neighbours. Mathematically, this can be expressed as \n", "\n", "$$\\phi_i \\big | \\mathbf{\\phi}_{j\\sim i} \\sim \\text{Normal} \\bigg( \\alpha \\frac{ \\sum_{j=1}^{n_i}w_{ij} \\phi_j}{n_i}, \\sigma_{i}^2\\bigg)$$\n", "\n", "where ${j \\sim i}$ indicates the set of adjacent neighbours to observation $i$, $n_i$ denotes the number of adjacent neighbours that observation $i$ has, $w_{ij}$ is the weighting of the spatial relationship between observation $i$ and $j$. If $i$ and $j$ are not adjacent, then $w_{ij}=0$. Lastly, $\\sigma_i^2$ is a spatially varying variance parameter for each area. Note that information such as an adjacency matrix, indicating the neighbour relationships, and a weight matrix $\\textbf{w}$, indicating the weights of the spatial relationships, is required as input data. The parameters that we infer are $\\{\\phi\\}_{i=1}^N, \\{\\sigma_i\\}_{i=1}^N$, and $\\alpha$. \n", "\n", "## Model specification \n", "\n", "Here we will demonstrate the implementation of a CAR model using a canonical example: the lip cancer risk data in Scotland between 1975 and 1980. The original data is from [1]. This dataset includes observed lip cancer case counts $\\{y_i\\}_{i=1}^N$ at $N=56$ spatial units in Scotland, with the expected number of cases $\\{E_i\\}_{i=1}^N$ as an offset term, an intercept parameter, and and a parameter for an area-specific continuous variable for the proportion of the population employed in agriculture, fishing, or forestry, denoted by $\\{x_i\\}_{i=1}^N$. We want to model how the lip cancer rates relate to the distribution of employment among industries, as exposure to sunlight is a risk factor. Mathematically, the model is \n", "\\begin{align*} \n", "y_i &\\sim \\text{Poisson}\\big (\\lambda_i),\\\\\n", "\\log \\lambda_i &= \\beta_0+\\beta_1x_i + \\phi_i + \\log E_i,\\\\\n", "\\phi_i \\big | \\mathbf{\\phi}_{j\\sim i}&\\sim\\text{Normal}\\big(\\alpha\\sum_{j=1}^{n_i}w_{ij}\\phi_j, \\sigma_{i}^2\\big ), \\\\\n", "\\beta_0, \\beta_1 &\\sim \\text{Normal}\\big (0, a\\big ),\n", "\\end{align*}\n", "where $a$ is the some chosen hyperparameter for the variance of the prior distribution of the regression coefficients. \n", "\n", "## Preparing the data \n", "\n", "We need to load in the dataset to access the variables $\\{y_i, x_i, E_i\\}_{i=1}^N$. But more unique to the use of CAR models, is the creation of the necessary spatial adjacency matrix. For the models that we fit, all neighbours are weighted as $1$, circumventing the need for a weight matrix." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "try:\n", " df_scot_cancer = pd.read_csv(os.path.join(\"..\", \"data\", \"scotland_lips_cancer.csv\"))\n", "except FileNotFoundError:\n", " df_scot_cancer = pd.read_csv(pm.get_data(\"scotland_lips_cancer.csv\"))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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CODENONAMECANCERCEXPAFFADJWEIGHTS
06126Skye-Lochalsh91.3816[5, 9, 11, 19][1, 1, 1, 1]
16016Banff-Buchan398.6616[7, 10][1, 1]
26121Caithness113.0410[6, 12][1, 1]
35601Berwickshire92.5324[18, 20, 28][1, 1, 1]
46125Ross-Cromarty154.2610[1, 11, 12, 13, 19][1, 1, 1, 1, 1]
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" ], "text/plain": [ " CODENO NAME CANCER CEXP AFF ADJ \\\n", "0 6126 Skye-Lochalsh 9 1.38 16 [5, 9, 11, 19] \n", "1 6016 Banff-Buchan 39 8.66 16 [7, 10] \n", "2 6121 Caithness 11 3.04 10 [6, 12] \n", "3 5601 Berwickshire 9 2.53 24 [18, 20, 28] \n", "4 6125 Ross-Cromarty 15 4.26 10 [1, 11, 12, 13, 19] \n", "\n", " WEIGHTS \n", "0 [1, 1, 1, 1] \n", "1 [1, 1] \n", "2 [1, 1] \n", "3 [1, 1, 1] \n", "4 [1, 1, 1, 1, 1] " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_scot_cancer.head()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# observed cancer counts\n", "y = df_scot_cancer[\"CANCER\"].values\n", "\n", "# number of observations\n", "N = len(y)\n", "\n", "# expected cancer counts E for each county: this is calculated using age-standardized rates of the local population\n", "E = df_scot_cancer[\"CEXP\"].values\n", "logE = np.log(E)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# proportion of the population engaged in agriculture, forestry, or fishing\n", "x = df_scot_cancer[\"AFF\"].values / 10.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below are the steps that we take to create the necessary adjacency matrix, where the entry $i,j$ of the matrix is $1$ if observations $i$ and $j$ are considered neighbours, and $0$ otherwise." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# spatial adjacency information: column `ADJ` contains list entries which are preprocessed to obtain adj as a list of lists\n", "adj = (\n", " df_scot_cancer[\"ADJ\"].apply(lambda x: [int(val) for val in x.strip(\"][\").split(\",\")]).to_list()\n", ")" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# change to Python indexing (i.e. -1)\n", "for i in range(len(adj)):\n", " for j in range(len(adj[i])):\n", " adj[i][j] = adj[i][j] - 1" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# storing the adjacency matrix as a two-dimensional np.array\n", "adj_matrix = np.zeros((N, N), dtype=\"int32\")\n", "\n", "for area in range(N):\n", " adj_matrix[area, adj[area]] = 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizing the data \n", "\n", "An important aspect of modelling spatial data is the ability to effectively visualize the spatial nature of the data, and whether the model that you have chosen captures this spatial dependency. \n", "\n", "We load in an alternate version of the *Scottish lip cancer* dataset, from the `libpysal` package, to use for plotting." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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CODENOAREAPERIMETERRECORD_IDDISTRICTNAMECODECANCERPOPCEXPAFFgeometryPROP
061269.740020e+08184951.011Skye-Lochalshw61269283241.3816POLYGON ((214091.875 841215.188, 218829.000 83...2.264207
160161.461990e+09178224.022Banff-Buchanw6016392313378.6616POLYGON ((383866.000 865862.000, 398721.000 86...0.006762
261211.753090e+09179177.033Caithnessw612111831903.0410POLYGON ((311487.000 968650.000, 320989.000 96...0.526184
356018.985990e+08128777.044Berwickshirew56019517102.5324POLYGON ((377180.000 672603.000, 386871.656 67...0.716931
461255.109870e+09580792.055Ross-Cromartyw6125151292714.2610POLYGON ((278680.062 882371.812, 294960.000 88...0.211835
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" ], "text/plain": [ " CODENO AREA PERIMETER RECORD_ID DISTRICT NAME CODE \\\n", "0 6126 9.740020e+08 184951.0 1 1 Skye-Lochalsh w6126 \n", "1 6016 1.461990e+09 178224.0 2 2 Banff-Buchan w6016 \n", "2 6121 1.753090e+09 179177.0 3 3 Caithness w6121 \n", "3 5601 8.985990e+08 128777.0 4 4 Berwickshire w5601 \n", "4 6125 5.109870e+09 580792.0 5 5 Ross-Cromarty w6125 \n", "\n", " CANCER POP CEXP AFF \\\n", "0 9 28324 1.38 16 \n", "1 39 231337 8.66 16 \n", "2 11 83190 3.04 10 \n", "3 9 51710 2.53 24 \n", "4 15 129271 4.26 10 \n", "\n", " geometry PROP \n", "0 POLYGON ((214091.875 841215.188, 218829.000 83... 2.264207 \n", "1 POLYGON ((383866.000 865862.000, 398721.000 86... 0.006762 \n", "2 POLYGON ((311487.000 968650.000, 320989.000 96... 0.526184 \n", "3 POLYGON ((377180.000 672603.000, 386871.656 67... 0.716931 \n", "4 POLYGON ((278680.062 882371.812, 294960.000 88... 0.211835 " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_ = libpysal.examples.load_example(\"Scotlip\")\n", "pth = libpysal.examples.get_path(\"scotlip.shp\")\n", "spat_df = read_file(pth)\n", "spat_df[\"PROP\"] = spat_df[\"CANCER\"] / np.exp(spat_df[\"CEXP\"])\n", "spat_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We initially plot the observed number of cancer counts over the expected number of cancer counts for each area. The spatial dependency that we observe in this plot indicates that we may need to consider a spatial model for the data." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scotland_map = spat_df.plot(\n", " column=\"PROP\",\n", " scheme=\"QUANTILES\",\n", " k=4,\n", " cmap=\"BuPu\",\n", " legend=True,\n", " legend_kwds={\"loc\": \"center left\", \"bbox_to_anchor\": (1, 0.5)},\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Writing some models in **PyMC**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Our first model: an *independent* random effects model\n", "We begin by fitting an independent random effect's model. We are not modelling any *spatial dependency* between the areas. This model is equivalent to a Poisson regression model with a normal random effect, and mathematically looks like\n", "\\begin{align*} \n", "y_i &\\sim \\text{Poisson}\\big (\\lambda_i),\\\\\n", "\\log \\lambda_i &= \\beta_0+\\beta_1x_i + \\theta_i + \\log E_i,\\\\\n", "\\theta_i &\\sim\\text{Normal}\\big(\\mu=0, \\tau=\\tau_{\\text{ind}}\\big ), \\\\\n", "\\beta_0, \\beta_1 &\\sim \\text{Normal}\\big (\\mu=0, \\tau = 1e^{-5}\\big ), \\\\\n", "\\tau_{\\text{ind}} &\\sim \\text{Gamma}\\big (\\alpha=3.2761, \\beta=1.81\\big),\n", "\\end{align*} \n", "where $\\tau_\\text{ind}$ is an unknown parameter for the precision of the independent random effects. The values for the $\\text{Gamma}$ prior are chosen specific to our second model and thus we will delay explaining our choice until then." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [beta0, beta1, tau_ind, theta]\n" ] }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
\n", " \n", " 100.00% [16000/16000 00:18<00:00 Sampling 4 chains, 0 divergences]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 2_000 tune and 2_000 draw iterations (8_000 + 8_000 draws total) took 32 seconds.\n" ] } ], "source": [ "with pm.Model(coords={\"area_idx\": np.arange(N)}) as independent_model:\n", " beta0 = pm.Normal(\"beta0\", mu=0.0, tau=1.0e-5)\n", " beta1 = pm.Normal(\"beta1\", mu=0.0, tau=1.0e-5)\n", " # variance parameter of the independent random effect\n", " tau_ind = pm.Gamma(\"tau_ind\", alpha=3.2761, beta=1.81)\n", "\n", " # independent random effect\n", " theta = pm.Normal(\"theta\", mu=0, tau=tau_ind, dims=\"area_idx\")\n", "\n", " # exponential of the linear predictor -> the mean of the likelihood\n", " mu = pm.Deterministic(\"mu\", pt.exp(logE + beta0 + beta1 * x + theta), dims=\"area_idx\")\n", "\n", " # likelihood of the observed data\n", " y_i = pm.Poisson(\"y_i\", mu=mu, observed=y, dims=\"area_idx\")\n", "\n", " # saving the residual between the observation and the mean response for the area\n", " res = pm.Deterministic(\"res\", y - mu, dims=\"area_idx\")\n", "\n", " # sampling the model\n", " independent_idata = pm.sample(2000, tune=2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the residuals of this first model." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "spat_df[\"INDEPENDENT_RES\"] = independent_idata[\"posterior\"][\"res\"].mean(dim=[\"chain\", \"draw\"])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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KSsLHx4eAgACSkpLq9eCXX36Zn3/+mU6dOnHnnXeSmZnJ2rVr2blzJz/++COdOnWqV71CWKpTmCdnzuVWuqbRKOnc3otunXzw8tRQWKTnjw3xFBUbKpWToCuEqA+rg+7ChQsJDQ0lODiYZcuW8d///tfqh+7Zs4eff/6ZQYMG8cUXX6DRlA3TTZkyhdmzZ/PKK6/w7bffWl2vENZoHeCGu5uawiIDfq1c6N7Jm/btPCstpHJ3c2Ls6BDWbIqvNAcsQVcIUR9WB93hw4c3+KHLly8H4NFHH60IuADDhg1j5MiR7Nixg/Pnz9O+ffsGP0uImigUCoYMCMTD3Qk/X5cay/n5unDVsKCKRVYARSWGGssLIURNmmRvRFRUFG5ubgwYMKDKayNHjgRg37599m6WuAKFtdXWGnD/KefJgD5+ACgU0KOLT2M3TQjRAtl99XJRURHp6el06dIFlapqmr2wsDAAWVAlHE7fHq3IzdXh4eGEr3fdgVoIIS5n96Cbn192eouHh0e1r5dfLygoqLUeLy8vlEpJYlATHx/piTWGG8Z5A9g9gYb8PIVoGZrtPt3c3Ny6C12hfHx8yM6u/SQd0Xw0l5+nfDAQom527ypqtWV7I2vqyZZfr6knLIQQQjRXdg+6bm5u+Pv7k5iYiNFY9bzS8rnc8rldIYQQoqVokknR8PBwioqKOHjwYJXXIiMjARg8eLC9myWEEEI0qkYNullZWcTGxpKVVfl0lxkzZgDw3nvvodPpKq7v3r2byMhIBg8eLHt0hRBCtDhWL6Ravnw5Bw4cAOD06dMV1/bu3QvA2LFjGTt2LADfffcdS5YsYd68ecyfP7+ijqFDhzJ9+nSWL1/O1KlTueqqqyrSQHp4ePDKK6809H0JIYQQDsfqoHvgwAFWrlxZ6drBgwcrhoqDg4Mrgm5tXn31Vbp27cpPP/3EN998g5ubG1dffTWPPfaY9HKFEEK0SAqz2Vz1UNFmoDlsoWgqzWWLibBMc/l5ypYhIeom2SWEEEIIO5GgK4QQQthJs81IJYQQNTGbzVxyEiMqRdmpUkI0NQm64opgNpvll+4VwGQ2YzCZMV123WAGJWbUSgVKB/17kJ2dzYYNG9i6dStnzpwhNTUVd3d3evfuzcyZMxk1apTFdT377LNVFrxebsGCBTz88MNA2b+Pt956i5iYGM6fP09ubi5arZZ27doxbdo0pkyZgpOTU4PeX12++eYbjh8/TkxMDLGxsRiNRr7++muGDBliVT0bNmxg9erVnDx5koyMDMxmM23atGH48OHMnTuXwMDASuWTkpJYunQpMTExJCcnU1BQgL+/P507d2b27NkMGzbMlm9TFlK1RM1l4Y09/fDi91yISaD7qB50H9WD9v3bo1JXPeXKETWXn2dTL6Qyms3oTXX/OnNSKlA5YOD94YcfeOWVVwgMDGTo0KEEBgaSkpLChg0bKCkp4emnn+aee+6xqK5NmzZx4sSJal/7/PPPKSoqYvny5fTp0wcAg8FA//796dWrFx07dsTX15fc3Fx27NhBUlISI0eO5JNPPmnUQ2a6du0KgL+/PwDp6en1CrpPPfUUR44coXfv3hV1nThxgqioKLRaLd9//z2dO3euKL9r1y4eeeQR+vXrR0hICB4eHqSmprJ582YKCgp47LHHeOCBB2z0LiXotkj1/SX91+L9OHto6HpNKL6hXo3Qsqaz8s0V/PbmP5/8XTxc6Dqsa0UAdvNyw9XTDTdPN1w8XBwqIEvQrZvJbEZnQcAtp3HAHu/u3bspLS1l9OjRlYLbuXPnmDFjBiUlJWzevLlKT80aMTExTJs2jS5duvDHH39Ueq20tBRnZ+dK1wwGA3PmzCEqKoqlS5cyZsyYej+7Ln/99Rc9e/bE39+fl156iZ9++qleQbe69wFl+SReeOEFxo0bxwcffFBxXafToVarq3ygSE1NJSIigtzcXHbt2oWnp2f93thlZHhZAJByMpPTWxMAiP7jLH4dvelydSidRoXgoq36F7i58Qqo/CGipKCEIxuPcGTjkWrLv398Md6tve3QMmELBisCbnl5jcqxgm5Nw5gdOnRg4sSJ/PTTTxw6dIjx48fX+xnLly8H4Oabb67yWnWBSq1WM3bsWKKiooiPj6/3cy1hq4Be3fsAmDBhAi+88AIJCQmVrms0mmrLBwYG0r9/fzZu3EhycrLNgq6sXhYA7P/+eKWvM2Jz2PXpEb69Zx3H/zzXRK2yHU9/y3vuXoFeEnCbEbO56hxuXUx/39dcqNXqSn/WR0lJCWvWrEGj0TB58mSL7jGZTOzYsQOALl261PvZjuCvv/4CqDS0XJvs7GyOHDmCq6srISEhNmuH9HQFSUfTSI5Jr/Y1k8FE9oX8Wu8vLdChcXdyiIVK2RezuXgmGfNlPZ+MhOrfX3XC+kpGtObEWM/YaTKXrWp2dAUFBfz55584OzszcODAetezfv168vPzmTRpEt7e3jWWW7x4MVAWdHbv3s25c+eIiIiw+YKixlY+r11cXMzZs2eJjIwkJCSEBQsWVFs+MTGRlStXYjQaSUtLY8uWLeTn5/PKK6/Y9KhZCbpXOLPZzL7vjtVaRl9iYOsH+/HwcyWkXyCBXXxRqssGSUwGE+te20lA11YMm93broG3MLeQuEPnOXfoHOcOnuP8wXNkX2z43GdYn7CGN044vObSz3355ZfJyMhgwYIFDZo3//XXXwGYPn16reWWLFlS8d8KhYI5c+bwxBNP1Pu5TWXTpk2VVnD36tWLd999l7Zt21ZbPikpqdJ7d3Nz4/XXX7d4VMBSEnQbkdlsZuuXWwjpHkKXoV2bujnVStifQtqZ2gOVvthA4uFU9MUGDv1yCic3NcF9Arjm0cEc+OkEaWeySTuTjclgYsTcviiUdQdes8lMcU4JBRnFFGQUUZBe9md+ehEF6UXoigxo3NRo3Jwu+Z8ajaeKA1siOX/oHClnU2z1bagktG9oo9QrHEtTdHLLe5GXmjlzZo3zhe+88w6rV69m1KhRDVpBGx8fz759+wgJCWHo0KG1lj116hQmk4m0tDS2bt3KO++8w+HDh/nkk0/q3eMr70VeSqvVMmvWrHrVZ4lFixaxaNEi8vPzOX78OO+++y4REREsXry42l77kCFDOHXqFHq9nqSkJH766SeeeeYZoqOjeeGFF2zWLgm6jURXouPrJ79ix/fbmfHyLQ4ZdM0mM/sum8utTkF6EfpiQ8XX+iIDTi5qUo5ncGTl6Yrrx9efw2Q0Mer+/pUCb/rZbOL2JlcKsIWZRZgM1vc1vEJd2L18l9X3WUOGl5sXlaJsH661LPhsaHOX9qTKTZ06tdqgu2TJEpYuXcrQoUNZsmQJKlX9V9T/8ssvmM1mpk2bZtFolFKppHXr1tx22214e3vz6KOP8tFHH/HUU0/V6/mX9yKh7HCcxgy65bRaLUOGDOHTTz9l/PjxPPPMM2zevLnGfcdOTk6EhYXxzDPPUFJSwjfffMOoUaO46qqrbNIeCbqNIDMxgw/u/oC4w+cBOHcgtolbVL1zu5LIis+ts1xWQl6lr5VqJT3Hd+DPN3ZXKXtyYxwmg4nRDw1EqVJQkFHEuoW7KMkrtUmbdfoim9RTE20rLb7Bvo36DGFbCoUCJdYtplLSNBmqTp06ZVG5JUuWsHjxYsLDw/n4449xcXGp9zONRiMrV65EpVIxbdo0q+8fOXIkQMXxrfVR3otsSh4eHvTt25dNmzaRkJBAx44d67xnxIgRfP/99+zdu1eCrqM6tu0YH839H/mZ/yw+OnfQMVf/no28YFE5o85Y6ese49qz7/vjFOdWH0hPb03Ar4MP3a8PY+N/omwWcAFys7JsVld1QvuEOcSCMGEdtVJh1T5ddVN0cy20ePFilixZQnh4OMuWLcPV1bVB9W3bto309HTGjBlTrz2+aWlpAA3qaTsKa99LefmGrBq/nGwZshGz2czaD9bwn2lvVgq4AFnJWTZZ4GNrV88fRHAff6vucXJTo1QrSTqaVnMhBbQbGMiuz4+SXsd8sbVS45NsWt/lwvqFNWr9onEoFQqcLAykTg6YGKPcBx98wJIlSxg0aBBLly6tM+Dm5+cTGxtbERyq88svvwDV780tFxsbS2ZmZpXrxcXFvPHGGwCMHj260mtRUVF07dqVu+66q9Y2Npa0tDRiY2PJz//n961Op+Pw4cPVlv/11185evQooaGhhIWFVVw/evQopaVVOwZJSUksW7YMwKoUnHWRnq4NlBSU8On8T9j3e83DL+cPncMnqP7L/RuDxt2J8c+PYPtHBznzV0LdNwBBPfyI/uNsrWVCBwdx8XgmJ/48b4tmVlCoFCSdadwN+rJyuflSKRQolFSbexnKehiOnHt5xYoV/O9//0OtVtOnTx8+++yzKmXCw8MrZWjauHEjzz33HFOnTmXRokVVymdkZLBt2zb8/Py4+uqra3z2jh07ePvttxkyZAghISFotVpSU1PZvn07OTk5DBgwgNmzZ1e6x2Qq+y7bqge8bNkyzp0rGxU8dOhQxbXyBVg333wzgwYNqij/zjvvsHLlSt544w0iIiKAsr3It9xyC126dKFbt24EBgaSn59PdHQ0x44dq1iRfKmPP/6YAwcOMHjwYIKCglCr1SQkJLBt2zb0ej2zZs2q9NyGkqDbQClnL/L+Xe+TfKr2Hti5g+cYMNGxgi6AyknJmPkDcfV25uhvZ2ovq1GSdjq7yh7YywX19CNy6SFbNhMAd19njAZj3QUbILRvWKPWLxqXUqFAo1KUJcwwl20LUlC2aMrRpw2Sksp+hxgMBj7//PNqy8ybN8+qtIgrV67EYDAwZcqUWodIhw8fzs0338yBAweIjo6msLAQDw8PunTpwsSJE5k+fXqV+8+cKft9MWnSJIvbU5sdO3ZUmTeOjIys+O/w8PA6g5+rqyvz588nKiqK3bt3k5OTg1qtJjg4mJkzZzJr1izatGlT6Z7p06fj4uJCdHQ0O3fuRK/X4+vry5gxY5g+fbrN5nLLSe7lBji47iDLHviY4vziOsv2vKonT6981g6tsjxXb1J0Gud3JZF2NpvMuFzM9c0ycAkPP1cUSgX5abZf8OTVzpW1X39v83rLuXm58eG5jx3ul7PkXhaOaMGCBRw+fJhNmzbVmEpRVCU93XowmUz89uZKfv/Pbxbfc/7QeUwmU6Oe0mEtbYA75/ck17ggqj4KMosbLeuAwVj3h5v6Ujmp6DO2r8MFXCEc1YEDB7j33nsl4FrJcSJAM2A2mzm66SivXf8vqwIuQFFeEamxqY3TMCsZ9Ub2fBmNSq1k/PPDUTvbcFViI46b5OfmNFrdGhcNDyx7sNHqF6Kl2blzp1322bY00tO1gNlsJnpzNL+9uYLYBuy5PXcwlqDOQTZsWf2onFQcW3+OmLVn6XxVOwbf3pM9X0XXOVfb1NIuJDda3fpSvfRyhRCNToJuLcp7tr+9uaLBe201rhq0rWxzNJQtuHpqKMgo5tTmeFCA2lmFoaRxFyk1iAISz8Q1WvUGncHhhv+FEC2PBN1q2DLYAviH+jP/60cI7e04OX1dvJwpyPh7jtSMYwdcwM3HmdIi2809V8dQakDjKvNTQojGI0H3Mrlpubx3+zs2yyLV+5rePPDJQ3j42O5oKFtw9WxeB9M7eTRuD9Q3uFWj1i+EECBBtwptKy15GXl1F7TAjU/cRMSz01CqHG/I0qWZBV2jufF6ueFThjDrndnSyxVCNDrHiwZ2kHEho8ahSqVKybVzxjaofidnJxZ88wg3Pz/dIQMugItn8wowBXl1H8xgLRcPF+798H4e+uxh3L3dbV6/EEJczjEjQiMym80svf8jXrzqBU7vOV1tmdF3XYWTS/XHPlnijjfuZOAk26UNawyuXs2rp5uZbNvtVh0HdeLVbQsZeetIWbUshLCbKy7o7l0Zxek9p0mNTeH1SQv57rlvKcguqFTGw8eDYTcPr1f9w24expiZZTlOdSU6EmLiSYhp3HzBljIZyw6Oz4zLpSRP19TNsUrCadvkcVYoFUx+agr/t+Z5Attbf+KKEEI0xBU1p6sr1vHTKz9WfG02m9mw9E+2f7eNcQ+MZ9xD4yuGGcfOHcv2b7dZVb9SpcTNy433bn+H5NPJpMenYzaZmfXObNr1st/K5eNbYkmISaY4p4TinFKKckooyi6hJE/n8Htxq+PipaEot6DugnVoFdKKB5Y9RJehXWzQKiGEsN4VFXTXLVlLZmLV46tKCkr4/e3f2LhsA+MeGs/1D4wjtE8YnYd04UxU9UPQ1XFycWL3L7spyq2cd7jnmF4Nbrs1irJLOLLS8nY7OqPORNtuYVw4GVfvOgI7BPLsqv/Dt40cUC+EaDpXzPByVnIWq9//o9YyRXlFrFy0gif7Pc6q//7OyFtHWvWMRXve4v0Ti3nwk4foeVVPAALaBxAQFlDvdtdH30ldm91Cqdroiw107TYUv7at63W/BFwhhKO4Ynq6y1/9GV2RZfOYhTmF/PrvX3DxcLHqGVlJmfgG+zJ02jCGThtGenwayacv1qe5DeLkoqbXDZ3Y//1xuz+7sRTnlDJw6NXsLlpHXmaOxfcFtA/g2d8l4F5pSvVGsgpKMZrMqJQKfD2ccXayYY7xRrJlyxZ27tzJsWPHOHnyJMXFxcybN4/58+dbVc/Jkyf56quviImJIS0tjaKiIgIDA+nZsydz586ld+/elcqbzWbeeustYmJiOH/+PLm5uWi1Wtq1a8e0adOYMmUKTk71X1xqqR07drBs2TKOHTuG2WymV69e3HfffVYdIr9hwwZWr17NyZMnycjIwGw206ZNG4YPH87cuXMJDKy8liMpKYmlS5cSExNDcnIyBQUF+Pv707lzZ2bPns2wYcNs+h6viKP9Yvef5dXr/9WIrSnzwLIH670Ay5Z8fHxISUzl+/vWoy82NHVzbMqzjStbV62kpKDuE4cC2gfw3Krn8Q1u3gFXjvazXF6xjoT0AjLzSiudvaEAWnk6087fA08H3o991113sXfvXjw8PGjVqhXx8fH1CrrLly/n3XffpV+/fgQFBeHq6sqFCxfYunUrOp2ON998k8mTJ1eUNxgM9O/fn169etGxY0d8fX3Jzc1lx44dJCUlMXLkSD755JNGTZO6atUqnnrqKXx8fJg0aRIKhYJ169aRkZHBf/7zH2666SaL6nnqqac4cuQIvXv3xt/fH4ATJ04QFRWFVqvl+++/p3PnzhXld+3axSOPPEK/fv0ICQnBw8OD1NRUNm/eTEFBAY899hgPPPCAzd7nFRF0L565yEtXv2BxT7e+pj1/Mzc9Mbnugo2s/Jd01DcxLWput5xXW1c2/PgzBn3NHyj8wwJ4btX/0Sqk+WeakqBrmfS8Eo5fyKa232gKBfRo64O/p3WjWPayf/9+/Pz8CA0NZe3atTz++OP1CrqlpaU4O1fdFnjmzBmmTZuGh4cHO3furLRdrrp7DAYDc+bMISoqiqVLlzJmzJh6va+65ObmMnbsWFQqFStXriQoqOxgmLS0NCIiIigtLWXTpk14eXnVWVdN73358uW88MILjBs3jg8++KDiuk6nQ61WV/lAkZqaSkREBLm5uezatQtPT9vkzr8i5nSDOgdxx7/vbLT6VWoVXYZ1JbhbcKM9oz5639gJlabl/YhzLxRz/e3Ta3y9JQVcYZm8Yl2dARfAbIbjF7LJK3bMLXODBg0iLCyswXvHqws6AJ07d6Zjx45kZmZSUFBQ5z1qtZqxY8uSBcXHN97Wx/Xr15OXl8edd95ZEXABAgICuPvuu8nLy2P9+vUW1VXTe58wYQIACQkJla5rNJpqe/CBgYH0798fvV5PcrLtTjhreb+Ra3DV3WMYeIPtElYEdQ7iuvuu49HvH+N/Zz/isR8ed7iEGG7eLnS9Jqypm9EocuNLGH/3jCrX/UP9eW7VcxJwrzAJ6QV1BtxyZjMkpBc2boMcVEJCAufPnycoKAitVltneZPJxI4dOwDo0qXxttrt3bsXgJEjqy5eLZ/PLS9TX3/99RdApaHl2mRnZ3PkyBFcXV0JCQlp0LMvdcUspFIoFMx5bw7nDsSSfdH6oTqVWoV/mD+B7QMJ7NAak8lEWlw6x/71MxkX0mkV3IpFUW81Qssbpu+UzpzYcL5Z7s+tS36Cnutun8LG738D/g64f/wfrUL8mrZhwq5K9UYy8qzLzZ2ZV0Kp3tgsFlc1xIkTJ9i0aRMGg4GkpCS2bNkCwL/+VfMal8WLFwNlQWf37t2cO3eOiIgImy8oulRcXBwAoaFV8xmUX7O2p71p0yZOnDhBcXExZ8+eJTIykpCQEBYsWFBt+cTERFauXInRaCQtLY0tW7aQn5/PK6+8goeH7Q6suWKCLoCHr5b7Prqft6a+ibVT2UaDkZSzKaScTQGOVHk9LyPfRq20nbz0XLZ9tw23YDOFF5q6NY2jKFnB6GnjObH/gATcK1RWgfWHYZiB7IJSWvu42b5BDuTEiRMsWbKk4ms/Pz/efPPNanuU5S4tr1AomDNnDk888USjtrN8qLu63rebmxsqlYr8fOt+x27atImVK1dWfN2rVy/effdd2rZtW235pKSkSu/dzc2N119/vdKCM1u4ooIuQI/RPbnmnmvZ/Okmm9ZbmF2A0WBEpW7aT85ms5ljO2L47b3f2P/HPoz6snNyR0y+FkW+V4vs8Xq6BfJ/q1/EN7jpV88K+zPW8++0oQn+LZT3Ii81c+ZMmy3SuVxERETFQqS4uDi++OIL7r33Xp588knuueeeau85depU2UheWhpbt27lnXfe4fDhw3zyySf17vGV9yIvpdVqmTVrVr3qs8SiRYtYtGgR+fn5HD9+nHfffZeIiAgWL15cba99yJAhnDp1Cr1eT1JSEj/99BPPPPMM0dHRvPDCCzZr1xUXdHf/uptdP+1slLoLsgrwCqh7dV1jKM4rZufPkWz5fDNJJ5OqvL7z980MGDsMD1UbjHpTE7SwcQT3DWDsk+E4uzvuNhDRuFTK+i06Utfzvoa4tCdVburUqY0WdMs5OzvTtWtXFi1aRFZWFm+//TajRo2qcZ5WqVTSunVrbrvtNry9vXn00Uf56KOPeOqpp+r1/Mt7kQDBwcEVQbc8mOfn51dZBV9UVITRaLRoDro6Wq2WIUOG8OmnnzJ+/HieeeYZNm/eXOO+YycnJ8LCwnjmmWcoKSnhm2++YdSoUVx11VX1ev7lrpiFVCUFJXzy8DI+vvdDivPr3uNZH/k2Ooe3PtLiUvnhhe+rDbjlDm7aTXreGZzcWsZnre7Xt2fC88Ml4F7hfD2csTZ8KgAfD/uftHXq1Kkq/7PlIh1LjBgxApPJxP79+y0qXz4U3ZCFTOW9yEv/Vz6/DBAWFgZUP29bfq26+V5reHh40LdvX1JTU6usYK7JiBEjgIYv4rrUFRF0k08n89LVLxL5ww6b1qtQKvD09ySkewg9RvdA0Ygbx+sS2ieMGS/fUme5E1FHOR9/CBevZhyoFDB0Vm9G3t8PpfqK+CssauHspKKVp3UBtJWnS4tfRFWTtLQ0oGw7kDXlVarG+34NHjwYgMjIyCqvla+eDg8Pb/BzrH0v1n6vLHFF/MYKaB/AqNtGodY07BunUCh48JOHeHPff/jf2Q/5PPVLFp/6H//e+QbP/PZck+/Tvf6BcfS9vl+d5eKPnSX68A7c/RwzQUBt1M4qrn96KH1u6izn4IoK7fw9sPSvg1IB7fzdG7dBdpKfn09sbGxFcCh34MABDIaqyWNOnDjBjz/+iFqtZvjwf7LnxcbGkplZ9TCY4uJi3njjDQBGjx5d6bWoqCi6du3KXXfd1eD3MWHCBLRaLd9++y0XL/6TOjctLY2vv/4aT09Pxo8fX+metLQ0YmNjKy2w0ul0HD58uNpn/Prrrxw9epTQ0NCKnjXA0aNHKS2tuhgvKSmJZcuWAViVhrIu9YpCR48eZfHixRw+fBi9Xk+nTp2YOXMmN954o8V1pKSk8OGHH7J9+3YyMjLw9vZm1KhRLFiwoNLmaFtQO6m58fGbGDhpIJ/O/5TY/WfrVY/ZbGbt4jW8sO4lNA6YSk6hUDB3yb28fNWLZF3MqrVsWnwyUUXrGT52AnkXG2e43dbcfFwY93/D8O8oC6ZEZZ6uGnq09bEoI1X3tj4Omwpy06ZNbNpUtsgzMTGx4lpSUtm00cCBA5k+/Z/EMBs3buS5555j6tSpLFq0qOL6q6++SlZWFgMGDKBNmzYYDAbOnz/Pzp07MZvNPPvss5WGtXfs2MHbb7/NkCFDCAkJQavVkpqayvbt28nJyWHAgAHMnj27UltNprK1IbboAXt5efHiiy/y9NNPM3Xq1CppIN96660q2ajeeecdVq5cyRtvvEFERAQAJSUl3HLLLXTp0oVu3boRGBhIfn4+0dHRHDt2rGJF8qU+/vhjDhw4wODBgwkKCkKtVpOQkMC2bdvQ6/XMmjWLQYNsl4PB6qAbFRXFPffcg5OTE5MmTUKr1bJhwwaefPJJkpKSLMpRmZCQwK233kpmZiYjRoxgwoQJxMfHs3LlSrZt28aPP/5Iu3bt6vWGatOmazAvrHuRjcs28MvC5ejqkZUm/mg8Xz/1FfcsnuuQPS1PP08e/+5JXrz2+Tq3ReWmZ7P1j5VcM3UquRccO/C2CvNi3P8Nw8OvZW/xEPXn7+lC/w6tSEgvJDOvpJrcyy6083d32IALZT3Ry1f5njx5kpMnT1Z8fWnQrcns2bPZuHEj0dHR/PXXXxiNRgICApg4cSJ33nkn/fv3r1R++PDh3HzzzRw4cIDo6GgKCwvx8PCgS5cuTJw4kenTp1cZYj1z5gwAkyZNqu/brWTy5Mn4+PiwbNkyVqxYAUDPnj1ZtGiRxT1NV1dX5s+fT1RUFLt37yYnJwe1Wk1wcDAzZ85k1qxZtGnTptI906dPx8XFhejoaHbu3Iler8fX15cxY8Ywffp0my2gKmdV7mWDwcCECRNISUnhp59+okePHkDZHqtbb72V8+fPs2bNmkpd9+rcf//9/PXXXzz//PPcfffdFdfXrVvHo48+ysiRI/nss89qraOhuWhTz6fyxaOfcWLHiVrL+QT5VJtMY/a7cxgz8+oGtaGx+Pj48MmTy/jjv6ssKq92UnP97dPJjS9p5JbVT7uBrbnm8cFoXBv/lBNHJLmXrVeqN5JdUIrBZEatVODTTE4Zak4WLFjA4cOH2bRpExqN436QcTRWzenu2bOHhIQEbrjhhoqAC2Wrwh566CEMBkPFJ5SalJaWEhkZiZ+fX5W5gAkTJtC9e3ciIyO5cKFxszkEtg/k6ZXPMuud2bUe4VfdAfROLk5s/WoreU24WrkuU5+JoFO4ZenODHoDa7/6AW1bx1vV3GtSR65/dtgVG3BF/Tg7qWjt40ZIK3da+7hJwG0EBw4cYM6cORJwrWTVb9na8mNaurQ6JycHg8FAmzZtqh2eDQkJ4cSJE+zZs6fGzCG2olQquXrWNfQZ25evnviCIxurZprqMKADXgFe+If607pjawI7tMY7yLtRj7iyBZVaxYOfPMSLo5+nKLfIonvWf7Oca2+7iZKLTf8LSqGEYXP60mtix6ZuihCiGjt3Nk6+g5bOqshRW35MLy8vfHx86syP6enpiUqlIjk5udo5x/LFA+XPsgeVWkX/CQPQ+mnxCvTCVeta8ZpCqWDGy7dw9axr6D6qB77Bvg4fcI2GsixUfm39mPP+XKvu3fzDKhTeBRavBAVw9bLtfkcnFzXjnhsuAVcI0eJY1dOtLT8mlA0zp6Sk1FqHq6srgwcPZs+ePXz//ffccccdFa9t2LCBEyfK5ljryrPp5eVV7+BnNpu5cOICUb/vIer3KE5Hnap4rdvw7vx76+sc236MvauiaN2utUPNVR1Ytx9ndxd6jupZ40Ku1LhUclJz6DqkK9fPvJ6zu0+zfqllx2IBRP62kUmzbyHnvGULzfTFBsJv6U3yiTQSj6Za/JzqaAPcufn16wno2LwPnrc1R/o7KISovyaZxHvuuee47bbbePXVV9myZQtdu3YlISGBzZs307VrV06dOlVnQM3NzbXqmSajiTN7z3Bw7QEOrTtI6rnqg8OZfafJTM8kdGAooQPLevSOtIjlyLYj/PbmSkL7hjHuwfEMmTKkyv7jwLBA/vphK7FHzzLs5uFMe2k60duia81WdTmTFZkiDToje3+OZvicvvS6sSN7vz1GVrx1Px8Av47ejH9uGE6+Cof6njc1WUglRMthVVfx0vyY1SkoKLAoP2a3bt345ZdfmDBhAsePH+frr7/m/PnzvPrqqxUnOvj62qanc3rPaT55eBkLus3j9UkLWf+/dTUGXACj3ljvfbz2FH8kjmUPfMwT/R/nj3dXUZBd+UDqsfddx/bvtvP727/h5OLEQ5/Nw8nF8sVICpOV87pm2PXZEZJj0ol4+2qufmQQ2kDLt/doA9258bXRuPm61l1YCCGaKauCbm35MXNzc8nOzrY4P2bHjh1577332L17NzExMaxZs4bp06dX7P3q1avqquH68A/158KxBPIzLT8W6uTOk3UXsgOT0VTnXtuci9n88tpyHuv9CF89+SUpZ8uyuSiVSu793338+dGffDpvGa07tuaO1++0+Nn6ovqdwHL09zNseW8/HYYHM+OD6xk+t69Fc77DZvfGycXxVk8LIYQtWRV0a8uPWb6SrSH5MQsKCti6dSve3t4Vq6EbyifIh/9b/QJ9xvaxqLy7tztBXdrUXdAOjm4+yrav/7KorK5Ix5bPN/NM+NO8duO/OL79GD5BPtzzwT1E/hDJf25+i/ApQxg8ue6fj0KppDjb+jNKy53bmcjaV3diKDXQa2JHbv1wHINu7Y6Ta/VBNbiPP6GDbZuFTAghHJFVQXfYsGG0bduW1atXVyx4grJg+eGHH6JWq5k6dWrF9aysLGJjY8nKqpySsKSkpEpeUJ1Ox/PPP09OTg4PP/wwzs62WxHr4uHCo98/ztWzrqmxjFKl5Lr7ruOt/f9h2LSqZy02hcjvt/PDi9+TcSHjn4sWdED3rd7Hm1MW8dJVL1CcV8zI20ZxMvIEr417lRsevRG/trUf9N46LKjB5+5ePJbBque3kZ9WhJOrmgEzunPrh+PofWOnSocUKJQwbHYfh8zuJYQQtmZVRiooS5Axd+5cnJycuOGGG/Dw8GDDhg0kJiby6KOP8uCDD1aUXbx4MUuWLGHevHnMnz+/4vr+/fuZP38+w4cPJygoiIKCArZt20ZycjIzZszg1VdfrfOXcH0WlpjNZtZ+sIaf//VTpeu9r+3D7Qtvp03Xpj2w4FIF2QU80n0+Bp2BHqN78NSKZ1AqlaxctILf3lpZdwWXcNW6VhxnqPXTcsMjN/LTKz9iMla/Wqr3qIF4qmyThtOtrQlcixh522hC+4SiUCjITyviwE/HObMtge7jOjDy3n511lOQXUDOxWxCejTu3m1HJAuphGg5rJ5EGzp0KN9//z0ffPAB69atqzjw4JFHHuGmm26yqI42bdoQHh7OgQMHyMjIwNXVlR49evDss88ybtw4q9+EpRQKBZMeuQHfkFZ8+vAy/EMDuG3h7fS9rm+jPbO+olbuwaArGw04vv04W7/YwrX3jK1XXZeeH5yfkc8vC5cT0qMtCdHV76n28muF2Qa/4z38Xdj0w88YDUY2LttISI+2jLx1JMOmD2fM/EH0mdwFN5+aRzQKcwo5uPYAe3+L4uy+s7z612sNb5QQQjQhq3u6jqKhn/wvnrmIf5g/aifHXLzzr7Evc+7guYqvNW4aFu54nV0/7bS6p2utsF6daN+9KxoXF1RKDRiVGIpNlOTrMOos30tUQBJH/qqaoUypUtL72j6Mum0U/cb3x8n5n1XVRXlFHFx7kL2/RRGzNRqjvizRx11v3c3Yudc1/M01Q9LTFaLluGKDriNLPpXEc8OerXK9y7CudB/Rnd/f/s3+jfqb1scT3yB/vP198fDyxMXdHY2TCwrUmPWgKzJSmqfDs60ra7/+vs763L3dGTptKO16h3Fo/UFitkRX9PDLdRvZnWd+e9bhM4E1Fgm6QrQcjtnNu8JF/lh1dTjA6d2nyEjIqPY1e8nPziM/O494Ymsso1AqLR5BKMwpZPNnm2t83dndmbmL516xAVcI0bJI0HVAXYd3Y+uXW6o9qCArKbMJWmQds8mEvtT6s4qrM+PlW/APDbBJXeLKkV9QSnxiLjqdEY1GRWiIF1oP2+YIbyxxcXG8++67REVFUVRURGhoKLfccgu33367xR8+T548yVdffUVMTAxpaWkUFRURGBhIz549mTt3Lr17965U3mw289ZbbxETE8P58+fJzc1Fq9XSrl07pk2bxpQpU3ByatyTvnbs2MGyZcs4duwYZrOZXr16cd9991l8lq7ZbGb79u1s2bKFgwcPkpycjMFgIDQ0lIkTJzJ79uwqu2Li4uJYv349O3bsID4+npycHFq1asWQIUO4//776djR9vnfZXjZQaWeT2Xx3e9z4VjjHnHoyK70YeVyMrxsuZS0AqIOJHEuPhvTJdvelEoFHUJ9GDIwmNYBHk3YwtqdPXuWW2+9lZKSEsaPH09gYCDbt2/n9OnTzJgxg9des2wx4fLly3n33Xfp168fQUFBuLq6cuHCBbZu3YpOp+PNN9+syP4HZWel9+/fn169etGxY0d8fX3Jzc1lx44dJCUlMXLkSD755JNG+7e4atUqnnrqKXx8fJg0aRIKhYJ169aRkZHBf/7zH4sW6ZaWltKnTx80Gg3h4eF06dIFnU5HZGQkcXFx9O7dm2+//RYXl3+Ocn3sscdYu3YtXbp0YcCAAXh4eHD69Gm2b9+Oi4sLn332GYMGDbLpe5Wg68BKi0r54rHP2b18V1M3xe6c3Z1ZuON1AsKklytB1zJnzmWyZuMZjMaaf6WpVAomXdeFzh0c80CNO++8k3379rFs2TKuuuoqAPR6Pffeey+7d+/mq6++YujQoXXWU1paWm2ugzNnzjBt2jQ8PDzYuXNnpa2Z1d1jMBiYM2cOUVFRLF26lDFjxjTsDVYjNzeXsWPHolKpWLlyJUFBZYly0tLSiIiIoLS0lE2bNuHl5VVrPXq9ns8++4zbb78dT0/PStfnz5/P1q1beeqpp5g795+T11asWEGPHj3o1q1bpbrWrFnD448/TqdOnVizZo0N362VyTGEfTm7OXP/xw8w7sHxTd0Uu5vx8i0ScIXFUtIK6gy4AEajmTUbT5OSVlBruaZw/vx59u3bx5AhQyoCLoCTkxOPPfYYUNaDtURNyYU6d+5Mx44dyczMrDg1rrZ71Go1Y8eWbVWs69jW+lq/fj15eXnceeedFQEXICAggLvvvpu8vDzWr6/7lDQnJyceeOCBSgG3/Pr9998PwL59+yq9FhERUSXgAkyaNImwsDDOnj1bJblTQ0nQdWBms5lNn25iyxc1LzRqibqN7M41c65t6maIZiTqQFKdAbec0Whm70HLT9yyl717y7bXjRw5ssprffr0wdPTs6JMfSUkJHD+/HmCgoIsOpzGZDKxY8cOALp06dKgZ9ektvddPp/b0PetVpctX1KpLD/IpXwOu/xeW5GFVA4q+2I2n83/hOgt0U3dFLtydnfmng9st1q5MLeQlW/8Suq5VEK6hxDcvS1te4QQ1LkNGleNTZ4hmlZ+QSmxcdb1RmLjsskvKHWoxVVxcXEA1R4ao1AoaNeuHTExMRQXF+PqatlpXCdOnGDTpk0YDAaSkpLYsmULAP/6179qvGfx4sVA2RTe7t27OXfuHBEREQwb1jjpcWt73+XXGtrL/vXXXwEszul/9OhRzpw5Q+/evav0nBtKgq4D2rdqH1889jmF2Y43BFZfzu7OuGpdcdW64ap1+fu/XXH1dKv4bxetC+37tbfJsLLJZGLnj5H89MqP5GeUnTB1dNPRitcVSgWBHQIJ6RZCSI+2fwfkEAI7BKJSV/00nHgiEV2xjvb920ueaAcTn5iLtStTTCYzCYm59OzmOFMY5cO9NfVALz1a1Zqgu2TJkoqv/fz8ePPNN6vtVZa7tLxCoWDOnDk88cQTFj2vPmp7325ubqhUqhqPk7XE9u3b+emnn+jYsSPTp0+vs3x+fj7PPFOWdvepp56q93NrIkHXwWQlZfHNM1+1mICrUCp4ZuWzdB/Vg/zMfA6s3l/luMLyr0O6h9BlaNcGPzP+aBxfP/UVZ/fVfC6y2WQm5WwKKWdT2L96f8V1J2cngrq0IaR7CCHdQ/D092TX8l0c33YMgNYdW9NjdE/8Qv0I6hRE605BBIQFoNbU/5+S2WwmPzOf7OQssv7+X3ZyNrmpOYx7aAI+w5t+VbAj0+mM9bqvtJ73NUR5L/JSM2fOtHlvqlxERETFYqS4uDi++OIL7r33Xp588knuueeeau85deoUJpOJtLQ0tm7dyjvvvMPhw4f55JNPKgJ/cxEdHc1jjz2GVqvl/fffR6OpfXSrtLSUefPmce7cOR577DGGDBli8zZJ0HUwvsG+vLL5VRbf/X6lNJDN1eSnptB9VA8Sj1/g3dvfqTG5h9ZPy6tbF9b7OYU5hRzffpxD6w+y6+ed9T4lSV+qJyE6vsa81CmxKXi00laaZ1eqlPiH+tO6UxDB3YIZOGkQHQd1rOgRG/QGspKyyEhIJyMhg4yEDNIvpJN5IYOs5Gyyk7OqZOEqt/f3vTz5/VN0Htk482ktgUZj+TzdpZzreV9DXNqLLDd16lQ8PT0r9WSrU94jrE/gc3Z2pmvXrixatIisrCzefvttRo0aVeM8rVKppHXr1tx22214e3vz6KOP8tFHHzVKz+/S9335CviioiKMRqNF88+XO378OPfccw8KhYJPP/2Uzp0711pep9Px8MMPs2fPHu6//34eeOABq59pCQm6Dsi3jS/PrX6er574gsgfqs9O1Rx0G9mdyU9O4dD6g3x830eUFJRUW06hVPDwZ/PwDbZ8G4fRYOT8wXNEb40mZks0sQdiG3wcoaUMOn2lr01GE6nnUkk9l8qRDYdZ+8Ea/Nr50SqkFRkJGWQlZ9W7bSUFJfx78kKmPX8zNzx2owxtVyM0xAulUlFpX25dlEoF7UJq34LSGE6dOlXja2FhYUD185dms5mEhAQCAgJwc3NrUBtGjBjBtm3b2L9/v0WLo8qHohu6mKkmYWFhxMTEEB8fXyXoln8vqpvvrc2xY8eYM2cORqORzz//nD59aj9PvbS0lIceeojIyEjmzp3L448/bt2bsIIEXQdTlFeEq9YVjYuGuUvuI7R3GD+8+H2Nx/A5Km0rLfd//ADr/reW5f/6ucqQ8qVmvHwL3Uf1qLPO3LQ8Dq07QPSWaI5vP1Ztxi57SIhOwN3bncKcwhrLlPdobcFsNvPLwuUkxCQwd/FcnN1d6r7pCqL1cKZDqA9nz1u+mKpjmI9DLaICCA8PByAyMpL77ruv0mtHjx4lLy+P0aNHN/g5aWlpgOWrcsvLW7Py1xqDBw9m9erVREZG0q9fv0qvla+cLv/eWOLYsWPMnj0bg8HAZ599Rt++tZ8id2nAnTNnTqP05i8lW4YczFdPfMmLo59n+3fbMegMXP/AOJ785WncfZrXXMqc9+9h+Ws/8/MrP9UacAffNJgJ8ybWWpeh1MCBn06wYdFuvnjsc/b/sa/JAi6U9WyDu9v/7OW9v0WxcOJCMhObNv+2IxoyMBiVyrJRALVKQfgAxzk7u1z79u0ZPHgwUVFRbNu2reK6Xq/nvffeA6iyECg/P5/Y2NiKwFjuwIEDGAxVpyxOnDjBjz/+iFqtZvjw4RXXY2NjycysmmK2uLiYN954A6BKwI+KiqJr167cdddd1r3Ry0yYMAGtVsu3337LxYsXK66npaXx9ddf4+npyfjxlXMVpKWlERsbW2Uovjzg6vV6PvnkE/r371/rsy8NuLNnz+aZZ55p0HuxhGSkciClhSXM6/owuqKyvMWe/p5cM+darp1zLSWFpbx/53skHnf8tJAjbxvJxTMpxO6veSETQFDnNry86RVctdWvxDSbzcTuSCTqmxgKM4tx8dKw+fefGqPJVgvp0bbJfhbeQT68G/2ew6XHbPqMVFms2Xi6WWekujQN5IQJEwgICGDHjh2cOnWK6dOns3Bh5XUPK1as4LnnnmPq1KksWrSo4vrkyZPJyspiwIABtGnTBoPBwPnz59m5cydms5lnn32WWbNmVZT/8ssvefvttxkyZAghISFotVpSU1PZvn07OTk5DBgwgM8//7zSqundu3cza9Yshg0bxpdfftmg9/3777/z9NNPV5sG8q233qqUshLg2WefZeXKlbzxxhtEREQAkJOTw/XXX09ubi6jRo2qtoer1Worve/yevz9/bnllluqbdvUqVMJCQlp0Pu7lAwvO5BD6w9VBFyAvPQ8fntzJWveW82wm4cx+53ZrPvfOvb/sa+WWpqWs7sz0VuiyU3NrbWci4cLC755BH2hib/e28ng23vg1/GfX9ppp7PY9flR0k7/M2RYkqvDxcOVkoLiRmu/pRKPX8ArwIvctNrfZ2PIuZhN8qlkQrrb7hdBS9C5gy+3Tu3F3oNJxMZVzb3cMcyH8AGOnXu5U6dOFXmTt2/fXnHgwQsvvMAdd9xhcT2zZ89m48aNREdH89dff2E0GgkICGDixInceeedVXqAw4cP5+abb+bAgQNER0dTWFiIh4cHXbp0YeLEiUyfPr3KcPSZM2eAsuxNDTV58mR8fHxYtmwZK1asAKBnz54sWrTI4gMPCgoKyM0t+/e4Y8eOiqHpSwUHB1cKuklJZUlS0tPTq13kBmVD27YMutLTdSDv3fEuh9YdrLVMj9E90BXrat0O0xzM+3IBPUb2YtXz28hPLUKhVNBncme6jQ3jwM8nOLut+l7kxaxjnDt62s6trV7X4V05tavmhTGNafa7cxgz8+omeXZNmrqne6n8glISEnMp1Rlx1qho14xOGWouFixYwOHDh9m0aVOdW3HEP6Sn6yAKcwo5uulIneWObz9uh9Y0ronzJ9L76j788cIO8lPL5mbNJjPH1sZyeks8xbmlNd7r1ybQYYJuU/Ryy53Ze8bhgq4j0Xo4O1Tii5bowIED3HvvvRJwrSRB10Hs/2MfRr39N+vbW/dR3bnpyamsW7iL7At5lV7z6+hNyvHazwvWejtObyrlbAp+oX5kxNt/YdPZfWfs/kwhLrVz586mbkKz5FgrMa5gUSujmroJjc4nyIf7P3qAzW/vI/1M5ekBrzYepJyoPeACaDSWpb+zl1bBrZrkuSlnU8jPrH9qPCFE05CeroPw8HFv6iZU4hPYigHXjCgLcmYwmY0YjXoMej16XSmlJaXoiksoKSqiKL+I4rxCCnLzKC0qReOmwdnVGWc3ZzSuGpzdy/68+cVb2Pf1KZKj06s8T6lUgAWrCxQmx/krq1AoMJQ03ZKIs/vO0H/8gCZ7vhDCeo7zG+wKN3DSIIfo7Yb26EiPwYMpSNZTctFECbpLXlUCzoBz2f8rQesBeAB/H4Op0qjQBrj9/T/3sj8D3fEMcCN6TSxxey9e/khad29lUS8XoDS/+nSJjUHr64lfSGt8Alrh4eWFi6sbapUzZqMSQ6GR4jwdZqOZznf3Y/3XP9utXeXO7JWgK0RzI0HXQfS5ri9qjbrGHLz1Edo3jOykLPIy8uos2+eqwYS060zuhWLy4mteyFQXo85ITmI+OYmWD31akyKxJFeHi7srJYWNu20oqH0wHUL/zoJjAGMmFGIGqqayzE/Qc93tU9j4/W+N2qbLnd0r87pCNDcyp+sgXLWu9BzTyyZ1tevZjpDuIcQfiaOkqISuw7uhdq76+UqtcWLE5GsZd8vtaBUh5F5omv2vmfG5eARYnk82qEPbRmxNGZWTdZ9Hi5IVjI4YX3fBS3j5+xDUof6Zkdp0cbysSkKI2klP14EMnDSQIxsO11lOoVTQ86peDJ8xnFX//Z2UsykA+LXzQ+vnyflLTifSFek4tesk3q29CQgLQKFU0q59d9QqDbqcsp5jQW7TJpswlBhReClQaZQYdXXnmPYLDiQ1IZl2XdrjF9wad60XKjTo8k1otEr+/OEnjIaGrQRXWZiX9lLGbFeGTBhN1LrtFpUfMWECuQnFdO6oxK2VM0pnMzp9Mfk52aRdSOZ8dO092WvnjrW6jUKIpiXJMRxIXkYeC7rNq3G4NaR7CCNuGcnQm4fh28aX3b/s4uP7PkLbSkvrzkGc3XvGoqHaiXffTm5C02d1ulxAFx/STtf+c1U5K9H6uZGTVPN5w56hGtZ91bB0kR36dCHIt6fV9ylVCnINFzi6rfasYV0G98LfvfajxrxCndn44wr0pboqr3Ub2Z3nVv2f1e1rTI6UHEMIRyXDyw7E08+TrsMqH+Lu6e/JuAfH8+q2hSyMfJ2JCybh28YXg87A6nf/oOvwbpQUlXBmz2mL50ZjTxxtjOY3WNrpbFr3qH0Ljm87r1oDLkBevI5rbrmhQW2xdni5nMloxscllM4Daz81qVPX2o8aA8iNL2VsxM0Ehrap8tp1915Xr/YJIZqWDC87mIGTBhG7P5YBEwcw4taR9BzTC/VlASAvPZcNS/8kOyWbxBOJVj/j1L4YOt7Zl9zEpjuppyapp7Lwaasl+0LVhVhBPf24eMyyRBSlaU4MGjeS/X/W7zxilbL+x5gZSo2EtO5FSbciLpyMq/J63zHh5CZaNtKQd7GYXn1H4x9yipidhwDwDW5F/wmyalmI5kiCroMZefsoRtw2Enevyvt2dSU6Dq8/xM6fIjm66WiDz9dNTjyLO1V7UE3NbDRTkqfDRauhJP+fYVW/Dl5cPG5F5iczuJkDCe3Zifhj1uepVqkbdnaorlBP125DKS4sIeNCSqXXglp3Ij/F8uH9krxSvJ3bc/X0NmxdvoZr5lzT4PYJIZqGzOk6uORTSWxYuoGolXtsfobs+FtuJz/V8eZ2AXzDvMiKzwUzuLdyQV9sRFekt7qe9MIznN4XY/V9vUcNxFPVzur7Lufh78LuLevIy8wBYMiEq1AX1/9YOZ+Orox7ZgSefp4NbputyZyuEHWTnq4Dy03L5c2IN8m5aPsPGGG9OqF0snm1NpMVl0vrHn6knclCpVFRmFl1f2xdFAqIP1a/vawqlW3+aRSklzBi3ES2/r4SfakOL/c2FBZb/14AFEoIv6WfQwZcR5OfXkjcgSRKC/U4uzsRNjAYrb9jZX0TVyYJug7KaDDy4T1LGiXgjpxyHcpCT4vnFZtKyvEMArv6knoqq+7C1XD3c6G0qH6JPpQqJdjo/Im85GKuiZhKYXEWhRmWB1wnVzUuns7kpxYCMGx2X0IHBdmmUS3UxVPp7PnuCGd3JWC65DB7pUpBp+HtGHpHX4K6+jdhC2sXFxfHu+++S1RUVMVZurfccgu33347SqVl615PnDjBn3/+ya5du7hw4QL5+fkEBgYyatQoHnzwQQIDAyuVz87OZsOGDWzdupUzZ86QmpqKu7s7vXv3ZubMmRafZ1tf33zzDcePHycmJobY2FiMRiNff/01Q4YMsbounU7HsmXL+OOPP0hOTsbLy4urrrqKRx99FH//un/ur7zyCj/88AMAkZGRFt1jLRledlAndhxn82ebKC0q/ft/OkoLSygtLKUor4iSAut7Sy7urlxz82RyG5Bxyp5a9/AjxZp53Mt4hbqw9qsf6nXvoOtH4Kxr2qPh/Dv7ENjFl5g1sfSa1JHh9/Rt0vbUpamHl0/viGPVa3/VelqXyknFTS+NocvIMHs1y2Jnz57l1ltvpaSkhPHjxxMYGMj27ds5ffo0M2bM4LXXXrOonhkzZnD06FF69+5N3759cXJy4ujRo+zfvx8fHx++++47OnbsWFH+hx9+4JVXXiEwMJChQ4cSGBhISkoKGzZsoKSkhKeffpp77rmnsd42XbuW7dgoD3Dp6en1Cromk4l7772XyMhI+vbtS3h4OAkJCWzcuJHWrVvz888/1xpEd+/ezezZs3F1daWoqEiC7uVaetCtjUFnYPHM9zn852GL72nXvSPde4dTkFa/oU178+voTUZsToPqcA7Qs+Xn1fW6d8iE0aiLm+YEoXJdrm5H5zHtOPVnAmMeG4hSpWjS9tSlKYPuxVPpfDd/jUXHY6qcVNyxeJLD9XjvvPNO9u3bx7Jly7jqqqsA0Ov13HvvvezevZuvvvqKoUOH1lnPt99+y+jRo2nXrvKahGXLlvHf//6Xq666imXLllVc3717N6WlpYwePbpSb/rcuXPMmDGDkpISNm/eXKWHbCt//fUXPXv2xN/fn5deeomffvqpXkH3119/5f/+7/+YNGkS//3vf1EoFJWuT5kyhTfffLPaewsKCrjpppvo2bMnOTk57N27t9GCruzTbSbio+P56skviY+OR61R8/AX8y1OGzn8xmtp37Z/swm42gA3cpIafmxdRkpK3YVqoFQ1/epg72AtQd39uPGFMQ4fcJvanu+OWHwetVFvZM93jrVX/fz58+zbt48hQ4ZUBFwAJycnHnvsMQCWL19uUV133nlnlYALcM899+Dq6sq+fZUTtwwbNowxY8ZUGb7u0KEDEydORK/Xc+jQIWvfksXGjBljk+BW/v154oknKgIuwLRp0+jYsSNr166loKD6Pf5vvvkmhYWFvPzyyw1uR11kTrcZMOgNfDrvExKi49ny+WbaD+jA1TOv5oFlD/K/2Ys5ufNktfdpXJ25dsZU8uJLMdhqgrKRObmpMZnNGEoa3t44C7cKuWrdaNUmAG9/X7TeXri6uePi4kluQdPOeXuHaFGqlWhcnShsHp+XmkR+eiFndiZYdc/ZXfHkpxc6zOKqvXv3AjBy5Mgqr/Xp0wdPT8+KMvWlUChQKpUWzw0DqP9Oh6quR1pUeyotLeXIkSO0b9+e4OCqOclHjBjB119/zZEjRxgxYkSl1yIjI/n5559588038fPza/S2OvZ3UgCw9oM1JETHV3x9/uA5zh88h8vz3zFg4kDcvd0pzCmsdE9Il1B69h9BXrxjL5a6lEIBXq3dyTiX2+C6XL2dK7bp1GbizFsrz3EXQGkBlNL03zfvEG1TN6FZiDuQZNVJVVCWOSzuQDK9x9eeitNe4uLiAAgNDa3ymkKhoF27dsTExFBcXIyrq2u9nrF+/XoKCwsZP96ygzkKCgr4888/cXZ2ZuDAgfV6pr0kJCRgMpkICwur9vXy63FxcZWCbkFBAS+88AJXXXUVU6ZMafyGIsPLDi/xRCK//+e3al8rKShh1887qwRcFzcXuvUcRoGD7sGtSWD3VjYJuAAaz7r/aoePH+Wwi8qUagWegY7RC3N0pYXW79+GssNAHEX5sKdWW/0HLQ8PDwDy8+s37XLx4kX+/e9/4+LiwiOPPGLRPS+//DIZGRncf//9Tb5Iri7l35fy79Pl3N3L/i1dPrz873//m/z8fF599dXGbeAlJOg6MJPRxOcLPrX6jN2SohJiYw/irHXgjbiXCezqS8pxyw6yt4TeUPsHjlZt/HFXOe72G68gj7JtS6JOzu71+3uucdPYuCWOKScnh/vuu4/MzExeffVVOnToUOc977zzDqtXr2bUqFE88MADdmil/W3bto0VK1bw1FNP0bp1a7s9V4aXHdimTzYSeyC2XveeP3oafamObt2HUJzjOJ/oq+MdoiU91rar0bMz0mp9fci11zXZ+cEAvt186fFgOMacYgric8mITiP1UAomQ1l6T+9gGVq2VNjAYJQqRaV9uXVRqhSEDXScNKh19WTLe2g19eRqkpuby+zZszlz5gyvvPIKkydPrvOeJUuWsHTpUoYOHcqSJUtQOcCiwrqUjxDUtFCqsLBsNLD8+1dcXMyLL77IkCFDuOWWW+zTyL9J0HVg4VOGcCLyOAfXHqzX/Ymn4jCU6ug98CqK6pHRyR5cvJwpyddhMth251rCqfM1vjZ62vgmDbgAHW/qil6pBF933Hzdade/DaF3g9poxJBVjJvButGNK5nW351Ow9txekd83YX/1ml4qMMsooJ/5hzj46u+B7PZTEJCAgEBAbi5uVlcZ05ODrNnz+b48eO89NJL3HrrrXXes2TJEhYvXkx4eDgff/wxLi4uFj+vKbVr1w6lUlkxN3658uvl3+fMzExSU1NJTU2lW7du1d5Tvqjtt99+o3v37jZrqwRdB+bd2psF3zzK3pVRfPPM1+RnWj+fkxKXjF63iUEjr6MgzbHmeJVqJS5aDTmJDd8edCmNm5q0+ORqXwvpEgr57kDtB0YoNSpMukZa8a0Ap7beVdaTmwG9SoU60IP2gc6N8+wWaugdfYndk2jRtiG1RsXQO+o+WtGewsPDgbKVtPfdd1+l144ePUpeXh6jR4+2uL5LA+6LL77IHXfcUec9ixcvZsmSJYSHh7Ns2bJ6L9hqCs7OzvTp04fDhw+TlJRUZQXzzp070Wg09O1blmDG3d2dm2++udq6tm3bRnp6OjfccAMuLi54e3vbtK0SdB2cQqFgSMRQuo/uwXfPfcueX3dbXUdmcjq7N69l+PUTyb/oOIHXv6N3vVM81kTtosLgXP1iLIVSSe+BI8ir4Xvg2bUVHj38MHo5k11sRK1S4OmkRJldTMGpTPJs1Nb213fASM37boM81aiUsi/XGkFd/bnppTGserXujFQ3vjjG4RJjtG/fnsGDBxMVFcW2bdsqJcd47733AJg+fXqle/Lz80lLS0Or1RIQ8E/2tJycHGbNmsWJEyd4/vnnufPOO+t8/gcffMD//vc/Bg0axNKlS+sMuFFRUdx9992Eh4fzzTffWPluGyYtLY38/HwCAgIqLTybMWMGhw8f5r///W+V5BixsbFMmTKlYnjZx8eHf//739XWf9ddd5Gens6zzz7rOBmpjh49yuLFizl8+DB6vZ5OnToxc+ZMbrzxRovryMvL44svvmDTpk0kJiai0WgICQlh6tSpTJ8+HWfn2j/pt+SMVAXZBWA24+FbdV7v4LqDfPXEF+Sk5Fhdr5unB1fdeBN5SdUHHYUCtEFl/9jykhs3OLfu0cqmC6cAvNq5sm/rFtIvVJ8U47rbp1CU/E8wc/Zzw6d/IMrWHuSZoKSOnq2zkxKtkxJFdjGFJzPJO12/IDz839dg9Kx+2M5JBd0DnStt7vfx8WkWf98dYYVrWe7lo5zdFV9N7uVQht7Rx+ECbrlL00BOmDCBgIAAduzYwalTp5g+fToLFy6sVH7FihU899xzTJ06lUWLFlVcv+uuu9i7d29FcovqzJw5E09Pz0r1qNVq7r777mqHsMPDwytliNq9ezezZs1i2LBhfPnllw1638uWLePcuXMAHDp0iLi4OEaOHFkR8G6++WYGDRpUUf7ZZ59l5cqVvPHGG0RERFRcNxqN3HfffZXSQF64cIENGzYQGBjI8uXLLQqi5d+/xspIZXVPNyoqinvuuQcnJycmTZqEVqtlw4YNPPnkkyQlJVm00i0vL4+IiAguXLjAwIEDufXWW9HpdGzfvp3XXnuNjRs38sUXX1i1ibsl+e3NFez8aSeTn5zC2HuvQ63558c0YMIAeo7uQWZSFkW5hax5bzV5mXkoVSoUSkXZQhyTmaL8IorziynMKaS0sGxbTFFeAVtW/sq106ZVzGl6BLigcDGQnpzEiX1HKcotQO2k5vrbb2607TSt2nuRcsJ2AdfV25nswgR2fr2rxjKdB/ZAl+2EX3gAzh28KXZWk1dkIAPAwkQcpXoTpXoTODtB39a4D26DVqVAmVVMwclM8s7WHRidfVww1RBwATxdVJUCrrBOUFd/pr567d+nDCWjK9KhcdMQNrCNQ83hVqdTp04sX76cd999l+3bt1ccePDCCy9YNDxcLikpCShL47hkyZJqy0ydOrUi6JaXNxgMfP7559WWnzdvXqWge+ZM2eldkyZNsrhdNdmxY0eVxB+RkZEV/x0eHl4p6NZEpVLx0UcfsWzZMlatWsWXX36Jl5cXU6dOtfjAA3uwqqdrMBiYMGECKSkp/PTTT/To0QMoWzF26623cv78edasWVPjBuVyn3zyCW+//TazZs3iueeeq7iu0+m4/fbbiY6O5ttvv2Xw4ME11tEcPvnXR1pcGs8OebpiiCygfQC3vHIrA28YVOWXceSPkXzy0NI661Rr1Hj4eOCidcXF3RmNqzPevoHEHj5BZnJ6jfddf2cEhYm2WeDk4qnBM8gDBZAZl4uhtOHzpQoFuIeo2LZyDSWXZY9y8Xan7cCuBHRrh7ZtIC4BAeTpzBitWOFqLWeNEk+VArKKKTiRQX41uaN7z+mHW/+aV822b+WEp0vl1aLS0xWOZsGCBRw+fJhNmzah0VwZW69sxaqe7p49e0hISCAiIqIi4ELZMuyHHnqIxx57jBUrVvD444/XWs+FCxcAKuUYBdBoNIwYMYLo6GgyM2079NhcrFy0otKcVNr5NBbP/ICuw7ty28I7aN+vPQA5KTl895xlcykGnYGc1BxIzbnk6qk679vw7QqumjYeQ5Zr2SofK6g0KnxCtKhdVBRllpCXWkhJnu3mb7VBrpw5cZCsc1l0unYArTq3xb2NPyqtB3qFmuLSfxZKFQPFxbUvnLKFUp2JdABXDQxog8fQtmhVQGYR+cczKDifi1fvQC5N5aBUlG2WL/s4ZcbF8XdnCMGBAwe49957JeDWg1VBt7b8oOWptSzJD9q5c1nqtR07djB8+PCK63q9nl27duHi4kL//v2taVqLkHw6md3Lqx8iPbXrFK9c8xIjbh3Jzc9P56unvqQot6jR27Tt1/UMun4EbubWGPW1BC5F2d5SF09ndEU6si/kkXEup1Ha1Do8iNLO3nQY04GQS7YaFQLooK6VyfZSojNSAuDmDIOC0Y5oR9y5LEpKDZQUGyipZlj7lJczV49og7eXrF4Wjmvnzp1N3YRmy6rh5QULFvDnn3/y66+/0qtX1RNuhg4dikKhYPfu2lfYlpSUcOeddxIdHU14eDi9evVCr9ezY8cOcnNzWbhwIWPHjq21DpPJ1OLmfM1mM2f2nWbT5xvZ/sN2ivKqD6pqJzUGvX33cfYc1o/AVl0pLfgn0YY2wB2vQA+MBhOZCTno6pmOzxpKtRK3Kd0oacHTnmFtvZh2Y4+6Cwohmh2rerqW5AdNseA4NRcXF7755hteeuklVq1aVdE7ViqV3HHHHQwYMKDOOnJzbZOj19H4dw7gtjfuIOLFm9m/ej87vtvGiR0nKpWxd8AFOLb7MLldcxg85hoUSiUFaYXk//0/ewroG0BGCw64AN27eFWaw5U5XSFajibZp5uVlcVDDz1EVlYWy5YtY8CAAZSWlrJlyxYWLVrEX3/9xa+//oqXl1dTNM8hOLs5M2LGCEbMGEHq+VQiv99B5A87yEq27b5WaySeiqP30ELy4psurWRpaMv+OxEU6EZQgOVZh4QQzYtVQdeS/KA19YIvtWjRIg4dOsTvv/9ekYJLq9UyY8YMjEYjr7zyCl999RULFiywpnnN1icPL+Xg2oNo3JxxdnPG2VVT9t/lf7o5o3HV0H/iAM7uO0v8kbgma2t+bjbQNFsvWnX2IbcZ5IFtiP69G/88TyFE07Eq6F6aH/TyOd3c3Fyys7MtWgC1bds2vL29q815OXToUACOHTtmTdOarbS4NHb+tBOzyWyXhVENlXwujiDfnk3ybFW3Vk3yXHtp5etCoF/zSb0nhLCeVSuRyvfNXrpxuVz5arbyHKK10el0FBQUoNNVHabMyiobPr1SlqKvW7LW6gO4m9L5mLOoNPZfwOYR6Eamc/M5qrA+unfylsQYQrRwVv32HDZsGG3btmX16tWcOPHP4p6CggI+/PBD1Go1U6dOrbielZVFbGxsRSAtN2DAAAwGAx9++GGl6zqdruLapdlPWqqc1Bx2fLe9qZthFbPJhLu//bezaPsGNllAqkemVKtpnJS0D/Vs9OcIIZqWVcPLarWahQsXMnfuXG6//XZuuOEGPDw82LBhA4mJiTz66KO0b9++ovx3333HkiVLmDdvHvPnz6+4/uSTT3Lo0CE++ugjdu7cWbGQKjIykgsXLtCzZ88qyb1bog0f/4m+tPG32diaWWnfhVQadyeytPYN9GazmValBsznstEX6ikdGFR2FF8j6dTeCyd1y9oCJ4SoyurVy0OHDuX777/ngw8+YN26dRUHHjzyyCPcdNNNFtXRvXt3VqxYwdKlS9mzZw/fffcdKpWKdu3aMX/+fO655546Dzxo7gpzC9n82aambka95GZnosTbbs9rNaA16Xbak+1sNuOZUUhudBppl5xB7GUyQ3gb9IrGaUe3zt6NUq8QwrHU65QhR9Ac9i3WZs37q/n5Xz81dTPqJaRLKKFt6t5L3VAqVxW+g9vg3LUV2UUGSnWNk2mqolcbl0PGsYwa59i92nmia4TAGxTgxoRr29X4uuzTFaLlkKDbRMxmM4U5heRczCY7JYeclGxyUnLILv8zOYtzB881dTNrNGbCdPTFtk/SofF1oVV4G8yBHmSXGisdUODlqcHFWUVJqZHcvIYPcTubTHhmFZMXnUZhhmVHGXq19UQ3xLaB95qRwYS1rXmrnQRdIVoOOcS+iSgUCjx8PPDw8SCkR9tKryWfSuLLJ75oopZZxq2VE7mJtgm67qFeePUPRO/lQk6xgXQzUFS17tw8HeV5yJw1Krw8NZjNZnJyS9EbLPvsaDab8dUZUMTlkH4sg0IrTx3KvZCHF4CNAq+7m5p2wR4NrkdUlpmUweGNhynKK8LN041+1/WjVbBj74HesmULO3fu5NixY5w8eZLi4uIq62Gs8ccff/DVV19x9uxZnJyc6NevHwsWLKB379513rtu3ToeffRRAN555x2bHOFXnbi4ONavX8+OHTuIj48nJyeHVq1aMWTIEO6//346duxocV0bNmxg9erVnDx5koyMDMxmM23atGH48OHMnTuXwMDAau/bsWMHy5Yt49ixY5jNZnr16sV9993HqFGjbPU2K5Gg60B0xTpWvfM7az9YU+mkIUt5+nviFeBFamwqupLGXexkoKTuQrXw6e2PWw9/ipzV5BcbSINqA21NSnVG0v7unSoU4OPljLNGSWGJgfz8qovTNCYTXtnF5EWnk57esP3QZYHXDEOCGxx4u3XyQamUbUK2cmb/GZa//jP7/tiL0fDPvyGVWsXgG8OZ/n8z6DyocxO2sGZffPEFe/fuxcPDg4CAAOLj4+td18cff8y7775LmzZtuPXWWykqKmLNmjXcdtttfPbZZ7XuDsnMzORf//oXbm5uFBU1bu6A999/n7Vr19KlSxeuvfZaPDw8OH36NL///jt//vknn332mUVn6QJs3LiRkydP0rt374qzc0+cOME333zDb7/9xvfff19x2E65VatW8dRTT+Hj48PUqVNRKBSsW7eOuXPn8p///MfidUrWkOFlBxGzNZqvnvyStPNpDarHxcOFQRMH07pLa7SttCSdSiL+aBzxR+MpKWhYoLzUoHEjcS61/FBopUZJq0FBOLX3IV+hoNgG5+nWxNVFhaeHBqPZjCG1EOW5bDJi0jHZ+Cxdr7Za9OHB6Oq5yEulVDBjckdcXWr/7CvDy5bZvXIXb9/2n1p3BDg5O/HUj08zdMowO7bMMvv378fPz4/Q0FDWrl3L448/Xq+eblxcHJMmTSIkJIRffvmlIkvgmTNnmD59Ov7+/qxbtw61uvq/d/Pnz+fYsWOMGzeOzz//vFF7uitWrKBHjx5VEiWtWbOGxx9/nE6dOrFmzRqL6iotLa12Ae7y5ct54YUXGDduHB988EHF9dzcXMaOHYtKpWLlypUEBQUBkJaWRkREBKWlpWzatMnm6Yhlj0ITy03L5eP7PuQ/095qcMAFKCkoIfLnHfyycDk/vvQDhTmFTHrkBpac+ZBHv3/MBi0uE3/8bJ1l1J4aWo8NI+ju3jhP6052sBdpOlOjBlyA4hIjqRnFZGSWYDidSdqRNJsHXIDcC/k4RSWhMdVvgVf7UG2dAVdY5sz+M3UGXAB9qZ7/3PoWZ/afsVPLLDdo0CDCwsIavB99xYoVGAwGHnzwwUppeTt37szkyZNJSEhgz5491d77xx9/sGHDBl599VXc3Bo/B3hERES1mQknTZpEWFgYZ8+erZLnoSY17XiZMGECAAkJCZWur1+/nry8PO68886KgAsQEBDA3XffTV5eHuvXr7f0rVhMgm4T2r96P88OeZrdv9R+FGJ9FecXs/PHSLZ/s43SwhJ+evlHm9WdfiEFF8+qWcPUbmra3NiZgFl9UIzvRIaPG+nFRovnXG1N5d64WaxyE+sfeHt08W2EFl2Zlr/+s8V73vWlen55Y3kjt6jplJ/aVn7G+aXK5yn37dtX5bX09HQWLlzItGnTqj0z3d6cnMr+7dbUI7fUX3/9BVBlaLm28+HLv0+WnA9vLfmY3YQG3TCI7qO6czLyBIf/PMyRjYfJTbXtkYWDbhzMg588xJLZi7l45qJN63b2VlGS98/XKlc1PjN6kFZogEL7Hz9YHZVr46eOzE3Mx4skGGL5UHOAnyt+vi6N3LIrQ2ZSBntXRVl1z95VUWQmZTj84qr6iIuLw83NrWJe81KhoaEVZS730ksvodFoePbZZxu7iXU6evQoZ86coXfv3nh6WpepbdOmTZw4cYLi4mLOnj1LZGQkISEhVQ7QKf8elH9PLlV+rSHz6jWRoGsnBr2BtHOpJJ+5yMXTyST//b+LZ5IpLSxtlGcOunEwD376EGveW82hdQdtWrezhyuuw9tSnB+PLrsUlauKVrf0IMtBgm05pZ2Gb3MT8/EkCYaEoKtjYZRCAX17tuzDG+zp8MbDmIzWjTQYDUYObzrCtTOvbaRWNZ2CggJ8fasfRSk/Ka78bPRyv/32G1u2bOHDDz+0OsjZWn5+Ps888wxKpZKnnnrK6vs3bdrEypUrK77u1asX7777Lm3bVt4lUtv58G5ubqhUqhpP1GsICbo2VlJQwsUzyZWD66lk0s6nVlpN2dgG3zSYBz55iGN/xbBy0Qqb1q1QKrn+7flkGNW439AFt0MpaAYGOVzABVA42+8owLzEfDxJrDXwOmuUXDMymKDApjkesSUqyqvfCtviet7X0qSmpvL6668zadIkrr22aT+ElJaWMm/ePM6dO8djjz1Wrxz8ixYtYtGiReTn53P8+HHeffddIiIiWLx4McOGNf0COgm6NmIymTh/6DzHtx8j5WwKKbEppJ5LIT/D9p+U6jJi+kjmLLmHzAuZfHzvRzZP2D/xv/PIM5YN2xaWGKG7v1XbfexJ4WTf83drC7xenhquGx2Cp/bKOEHLXtw867fgx7We9zk6Dw+PWs88Ly9T7l//+hdKpZIXXnjBLu2riU6n4+GHH2bPnj3cf//9PPDAAw2qT6vVMmTIED799FPGjx/PM888w+bNmyvmii89H/7ylfdFRUUYjUaLzoe3lgRdG1EqlXQc2JGOAytv5i7MLSQ1NpWU2It//1kWjFPOplCcb1kWJGsMnhzOE989SXpKOu/f+W69ewE1ue6VORRobP8XsdE42X+tYF5iPp7mCzCsLbq/V6IGt3bn6hFt0Gjs+yHgStDvun6o1CqrRpJUahX9xvZtxFY1nbCwMA4dOkR6enqVed3yOcrys9EBTp48SXZ2do29wMcff5zHH3+c5557jlmzZjVKm0tLS3nooYeIjIxk7ty5PP744zar28PDg759+7Jp0yYSEhIqEm6EhYURExNDfHx8laBb/n2qbr63oSToNjJ3L3c6DOhAhwEdKl03m83kZ+SRclkgTj2XQuq5VHTF1ie3GDw5nAeWPYhKreKzBZ+SdDLJVm8DgBHzI9D5B9Vd0JE00ck9eUkFeO4uC7yduvoS3j9AkmA0klbBfgy+MZw9Ky3fBRB+05AWuYgKys49P3ToEDt37mTKlCmVXtuxY0dFmXITJ06sdh/48ePHOX78OEOGDKFt27Z06dKlUdp7acCdM2dOveZx65KWVrYdU6X650Pv4MGDWb16NZGRkfTr169S+fLvkyXnw1tLgm4TUSgUePp74envRZehlf8ym0wmci7mkBJ7kWPbjrHv972knkuttb7wKUMqAu6F4wl4BXhy/f3jUCgVKJQKlEoFCqUShVKByWDkwJoDddZ5qX4zxuDUvTvNLZWKuQkDXV5SAb0NBoYOrD79nLCd6f83gwNr91u0bUjjouHm55r/0aH5+fmkpaWh1WoJCAiouB4REcHnn3/ORx99xLXXXlspOcbvv/9Ou3btGDp0aEX5J598str6Fy9ezPHjx7nllluqJMeIiori7rvvJjw8nG+++abe7+HSgDt79myeeeaZOu9JS0sjPz+fgICAivem0+k4fvx4leAJ8Ouvv3L06FFCQ0Mr9fAnTJjA22+/zbfffsu0adMqJcf4+uuv8fT0ZPz48fV+bzWRoOsgSotKSTyRyIWYBC4cv0BCTAKJxy5YNDx8acAFaNczlDsX3V2lXF56Llu/3MqWLzaTk5Jjcdu6TxxCq2tGYmiEBBONrQQFak8NBhsckFAf3ceGNclzrzSdB3XmqR+f5j+3vlVnRqonf3jKIVNBbtq0iU2byo77TExMrLiWlFQ2YjVw4MBK54xv3LiR5557jqlTp7Jo0aKK6+3bt2fevHm899573HTTTYwbN64iDaTBYOC1115r8N5X09/70i/tOdbHyy+/TGRkJP7+/ri7u7N48eIqZaZOnUpISEjF1++88w4rV67kjTfeICIiAoCSkhJuueUWunTpQrdu3QgMDCQ/P5/o6GiOHTuGm5sbr7/+eqV6vby8ePHFF3n66aeZOnUqkyZNqkgDmZGRwVtvvWXzbFQgQbfJ6Ep0HF5/iP2r95MQHU9KbEqNR8rVZsjUIdy/9J+AW5346Hg2fPwnUSv2WJxAoFzna/oTPPm6Jktu0VD5xQY8pnTFuOsC+Wdz7PrskH4BeLdpRvPfzdzQKcNYFPkWv7yxnL2roqrkXg6/aQg3PzfdIQMulOUJvnSrC5TNt548ebLi60uDbm0efPBBgoOD+eqrr/jhhx9wcnKif//+LFiwgD59+jS4rWfOlGX0amh6yPIPFOnp6SxZsqTaMuHh4ZWCbnVcXV2ZP38+UVFR7N69m5ycHNRqNcHBwcycOZNZs2bRpk2bKvdNnjwZHx8fli1bxooVZbs8evbsyaJFixrtwAPJvWxHZrOZs3vPsPOnnUSt3ENRbsMWOQ2JGMr9Hz9QJeD6+PiQmZHJwbUH2LD0T07tOlXvZ9z44ZPkmatPr9acOKkVaBPzSNtxwW7PHPd/wwgd1PA5cMm9bL3MpAwObzpCcV4Rrp5u9Bvbt8XO4TaFBQsWcPjwYTZt2oRGI6vxrSFB105iD8Sy9P6PrJpHrU1NAbcwt5B9v+zljw9WkXEho8HP0Qb4MPL1eRSVNs4B8vYWYDKR/OvJugs2kDbQnVuWXI9S1fA5ZQm6wtGMGDGCe++9t9FWM7dkEnTtxGw2s3HZBn544Xurs+dcbui0Ydz30f2VAm5+Zj6//+c3tn+3zeYZrjqM7E3YnZMrHSjfnPm5qsj45QSGRtxbPHRmb/pMts0wpgRdIVoOCbp2diLyBP+bvZj8zPolzagu4JYz6A1kJWVRlFHE+ZhzpMWlkXY+jfT4sj8bsi942IOT0fTqVe/7HY2nm5qSLXEUXciru7CVVBoVd3wyARcbJcGQoCtEyyFBtwlkJmbw/l3vE38kzqr7rr9/HLctvB2lqva9p9X9kjabzTzac4FVq5YBXLzc6TFxCIEDuqMO8CevwLqFWI5M46TE7WwWGXuTbVpvt7FhjH5ogM3qk6ArRMshq5ebQKsQP15Y+yJfPPY5u37eWWd5hULB7f++g+sfGFfvZ+am5loUcBVqJV2vHUi7EX1wDgqkQK/AZIYiwL0eq6sdmU5vQh/mTZvW7iSvst35qj0ndKi7kBDiiiRBt4loXDXc99H9tO/Xnh9erHmeV+Oq4cFPHmLAxIENel7ckfM1vhYysDOdxg5G2z6EYoUGvcFMKVB62dZWna5lLKa6lNkMaG23Ort1j1a0au9ts/qEEC2LBN0mpFAouP6BcbTt2Zb/zVlSZZ7XK8CLR79/vEoKyfo4f+ifoOvTLoBuE4fSqmdHDK4eFJeaMAN5RoDqe7NKBegNLS/oOjkpyVh71mb19ZzQse5CQogrlgRdB9B9VA9e2fIqH9z9zzxvmy5tePznJ/FvV/Ug6nrx8mLCfx5G6etDQUlZYM0HsHArkLOziuIS+x1NaC8+BaUkZ5dUfO3fyYdBt/XGp60XPz+yFkOx5e/ZzdeF9kOqbsAXQohyEnQdhF/bf+Z5sy9mMf/rR3D3ss2Zq6npRWR7B5d9UVK/eVmNpvag6+HmhLu7GpPJTHpmSY3lHInWVc3FFSfwDfNi8O29CRsUgouna8Xrd306ha9mrsBkYTauHte3R9lEBywIIZoHWb3sYMxmMyajqda0jnW5dLWrwWji9/Vx5DYw93ArX2cys6ru//XzdcFkNpOV/c9rWg8n8h18lbNSCdcObENIx1a4erqiUFSfxCIzPotv5/5e06h7ha7XhjJ8Tl+cXG3/OVZWLwvRckhP18EoFIoGBdzLHTmW2eCAC6BS/tOD0zgp8fF2Jr9AT0ZW1V6tq7PKoYOuSqng1um98Pau+xDzVqG+zFg8kZ/nra32dVdvZ656aADtbJDuUQjR8slYWAuWlV3C0eOZNqlLqQAvrRMBfi4YjGZS04spKq4+o1N6Vgluf/f43N3VBPq74t/KBU8PJ5u0pSFUKgW332JZwC0X1C2QKYvGVrneYXgw098fKwFXCGExCbrNkMlkpqBQT6nOSE2zAyaTmci9KTY5/9bbS0Opzkhuvp60jBJMdezXNZvLgpuri4rCQgOp6cWkZ5bg4my7Hnx93TylO56elgfccqGD2jL++bJTR5w9nLjm8cGMfXIILjbcbiSEaPlkeLkZij6RxYGj6RVfOzkp0Tgp0TipcHJS4up6kcLC0mqHfq3h5qrG3U1dr4VR1Q4vN+GB8uV27k7gxkndUSqt/7zZZUxHSgtKadO7Fe6+rnXfIIQQl5GFVM1MZnYJf2yIw9SIW2bVagV+Pi6kZdbdq7WGu7uawsLGO2TAUu3DvJlwXWcUdQTeskVtRkwGA0ajAbOxabZMyUIqIVoOGV5uRkp1RrbuTG7UgBvg54pSqSAlvdimAdfFWeUQARfgfFwOW7bFVhmaN5vNmAwG9KUllBYWkHj8HD+/8i2FOXlNFnCFEC2LDC83EyaTmW27ksnLb/hK5Nro9aZGSffoqXWipNRxAtfJ01k4a+IYNqQtZqMRo9GAyVD2oSArKYtV7/zO9m+3YdQbOfZXDI/9+ARu9ZgLFkKIS0nQbSYOHk0n8WJhoz9HrW6kedca9sE2FZVSgburgtLCgoo9ujmpOax5bzVbv9yCvvSfOenTe06z6KbXefKXp/H082yqJgshWgAJus3AuYQ8jp7IssuzlDZe7OTirMLbU0NGtuNkqfL0cOLqEcG08nUBIC8jj3WL17Dp003oiqsfSYg/Gs/e36IYO/c6ezZVCNHCSNB1cJnZJUTuudjUzag3s9lMcYkBg4WpFBtbWFstI4e0RuOk4vyhc2z6dCNRK6Iq9Wyr0298f66Zc62dWimEaKkk6DqwklIDm3ckYjDaL2DZcvEUQKnOhNFkxsdLQ3Zu485H10apVBDeP4BO7dzZ/9seNi3bSOyBWIvu9Wvnx30f3l+vbUZCCHEpCboOymQyszUymQI7r/g1Gs14uDuVLajSG22SXMNgMJObr8fP15mMavI320P7EHdOLN/MR19vJS89z7p7+7XHaHCcRWBCiOZL9uk6qPjEfLbvvmj3M2wD/d24OaJ3xddms5kflx8lywZzsgoF+LdyIS3D/vO7JYeOEPXp6nrf7+zuzPX3j2P8wxPw8PGwYcvqJvt0hWg5ZLzMQYWGaLk9ohPXjQ6hc3svnDX2+VFlZBZX2r+al1tsk4ALZekh0zJKCPS3bzYnD11+gwIuQGlhKX+8s4on+z3OyjdXUJRXZKPWCSGuJBJ0HZhKpaRtsAejhgYRMalD423nuYTRZMZ0SfaNQ0dtv4grNb3YboHXw1nBn899bLP6ivOL+e3NlTzZ73H+eHcVJQWOsypbCOH4JOg2EweOpNt0BbCzRklN64IM+n/mL91cG+dkIHsEXie1goPvf4ehxPYLuApzCvnlteU8OeBx1i1ZW+NWIyGEuJQE3WbgYmohp8/l2qy+oEA33FydakwnWVr6z+KtHt0DbPbcy6WmFxPg13iBNy/qIBejzzda/QD5Gfn8+vovpJ1PbdTnCCFahnqtXj569CiLFy/m8OHD6PV6OnXqxMyZM7nxxhstuv+uu+5i7969tZZ58803mTJlSn2a1+IcirHNmbgKBQzo7cfF1CKyc2teRVxUrMfTq+y/3d2dCfB3Iy29ceYw0zKK8fN1ISu7BBvvViJwaF+C9p1o9MB7x+t3EtKjbaM+QwjRMlgddKOiorjnnntwcnJi0qRJaLVaNmzYwJNPPklSUhIPPPBAnXVMnTqV8PDwKtcNBgNLly5FqVQybNgwa5vWYtli76y7m5qrhrUh+kQmyam1B9D8/FJaty77b4VCwdDBwaxae6bBbahJdk4pSqUCk433I+fplXR/+A56Jiey9Y1vMeptv/1q8E2DGTPzapvXK4RomawKugaDgRdeeAGFQsF3331Hjx49AHj44Ye59dZbWbx4MePHjycsLKzWeiIiIqq9/ueff2I2mxk9ejSBgYHWNK1Fa2hOhrZt3BkZHsSu/SlcSK47f3P+ZYcqtGnjhVJJo51u1MrXhbSM4kap22g0YwwMZsKbD3B6+UYwQ1FeEZkXMijOb9gz/dr5Mfv9eypyNwshRF2s+nW+Z88eEhISuOGGGyoCLoCHhwcPPfQQBoOBFStW1Lsxy5cvB+Dmm2+udx0tUX1/qSsUMLifP9eOCmHPwVTiEwssuq9TR99KX6tUKgb2C6pXGyyht0PiiYuHTnN69ylO7zlF4vELFOcX4xXgRVjfMLoO70rnIZ0J6tIGJxfLFo75BrfiwU8ext3LvZFbLoRoSazq6ZbPw44cObLKayNGjKhUxlopKSns3LkTf39/xowZU686Wqr6HELg7qZmzPA2BPi5smPPRc4n5Ft036B+gWg9qy5u6tE9gH0Hbb99yN1NTXaODie1And3JzROKhQKaNfWm949AzGZzJjM5rI/jWXbmVasOolOb3m3W6VSELNyR5XruWm55KZVXqCmUCq47d934BPozblD5zh/6BxFuUW06x1Ku17tCO0dStte7eyeIEMI0TJYFXTj4uIACA0NrfKal5cXPj4+xMfH16shv/76KyaTialTp6JW190sLy+vKyYXrrNzKmD5sX7t23kzYWwnXJzVbNx2jrNx1ac9bNNaS0paQcWcsbenM0PCQ6s9hs/Dw4VAf3dS0217vKDBaMbVRU1xiYGcS3Iz33RDDzSa6v8eBLXWEn/B8tXcXk5mSgvqHkpWO6l55MtHuer2MRbXbS+S7UmIlsGqoFtQUDY8qdVqq33dw8ODlJQUqxthNpsrhqUtHVrOzbXdFhpHZzTUfgJOOYUCBvbxZ/TwjmRnZ/NXZBrHT9ecPtDdVUm7YA/iLuSjUMC1o9vWeu7tkMFtbL6gqrSag+27d21VY8CFsjnguoKuk1qBq1mHWacjZdepOtvh5unGgm8fpfvI7g6XclHSQArRcjjEgQd79uwhMTGR8PDwanvRVzpLhpfdXNWMGdGG1v5uAOw7nF5rwAXQaJR0DPMk7kI+vbr5EtDaq9byjb2gqtyQQSG1vu7rU/3eXpVSgTulpO6NZucPWyqSYnQd1rX2+oJb8cTPTxLSvfbnCiFEQ1kVdD08yuax8vOrnx8sKCiosRdcG1lAVbu6gm5wkDtXDQvCxbnsx7lr7wViTtZ96L2Tk5KgQDfC2moZPCAIpar2vw4qlYoB/YLY3whzu+VcXVW41JEFy8vLpeK/FQrQqk1kRZ9i//ebKMysOpSen1XzArJ2vdrx+E9P4hMkvTQhROOzKuiWbwWKj4+nV69elV7Lzc0lOzub/v37W9WA3NxcNm7ciKenJ+PGjbPq3iuFsYb9qwoFDOjjT5/uvhUrnA/HZHAwOsOiep3UShQKBWOGt8HZ1bLMUD27BzRq0C0uNvL1d0e4aVIXWrWqfrGSu5sTWmcoPBvH4R82kh2fVmudaedTUaqVmC47sannmF7M/3IBrtUsHBNCiMZg1UqkwYMHAxAZGVnltZ07dwJUm/SiNqtWrUKn03HjjTfi4uJS9w1XmDPncom7UHVkwc1VzYRr2tG3R6uKgBt9ItPigAugcVIB4OSssXhbkru7c6OmboSyjFhJSbmUFBVXOnzBbDZz8WwS/7vzbVbP/TdbF31XZ8AFMOgMtO7YutK1q2dfw+M/PSEBVwhhV1b1dIcNG0bbtm1ZvXo1d999N927dwfKhpU//PBD1Go1U6dOrSiflZVFdnY2Pj4++Pr6VlvnL7/8AsjQcnXiE/OJ3Fu1Vxnc2p3Rw4Jwdfnnx3f8dBb7DqdbVb+TU9lnLidnF/QlJTi5uKCoY0W4QqFg+NC2/Lb6tFXPslSbIA/GXdsJN3dnjAYDpQX5qJ1dSI1N4dP5Szm+LaZe9Xr4lk17qNQq7lh0J9fOGWvLZgshhEWs6umq1WoWLlyI2Wzm9ttv58UXX+TNN99k8uTJnDlzhnnz5tG+ffuK8t999x0TJ07ku+++q7a+mJgYTp48Sc+ePSsl2xBlhxz8tTMZ82Ujyx3DPLl+TEilgJucUsieA3X3+C7n5KREqVKhUCoxmYzoSizL0NSmjTc+3s5WP682KpWCSeM6MeXGHri5l9WtUqtBocBQWoJCaaL31b0I7hZcr/pNRhPuPh489evTEnCFEE3G6tXLQ4cO5fvvv+eDDz5g3bp1FQcePPLII9x0001W1SW93OplZBazeUcSLi4qCosq5ws2m6tmqLqQbFmmqctpnJSYjEbMZjNmkxmzyYBBp0Ot0dR6n0Kh4LqrO/DzyhP1eu7lundtxajhYThVs01I7eSEQafDt40vExdMYsL8iSRExxP5YyS7f9lFfoZlST88/Ty5/+MHCAir36lJer2RuMQCWvu7ovWo/fsjhBA1UZjNl/elmofmsG+xPnJyS9m6M5khAwLYeyiNrJzKpwG5u6m5ZXKnStdW/RlHRpb1h6lPndAeH29nNK5u6Ir/OQTB2UNbZ+IRs9nM738cJ+li1YDv4e6ESqkkN7/6k4zUaiV+fq6YDCauvqo9fn41r3g3GQ2UFlafkMOgNxCzJZrIHyM5tO4gBl3VAw16X9uHm564iS5Da982VJvs3FK27Egi9++c1J4eTrQJcie4tTtBgW4Vc+ONRfbpCtFyOMQ+XVGmoFBPzMksxl/TFr3eVCXgAhQWGSgo1OPhXratRq83kpltfcCFf+Z0L0++oS8uQuPmXuviKoVCwdVXtefbH6OrvBba1osxV3VEr9OTlVVEwoVcjp/KwMvHhZAwb4xKFWbKVl+7utfea1Sq1KicnMp65JdtEFY7qek3rj/9xvWnMKeQvb9FsfOnnZyJOk3/CQOY/NQU2vdrX0PNljl7Ppdd+1IwXLKCPK9AT96ZHE6eyUGhgAA/V0JDtHTv7INKJYcfCCFqJkHXQZTqjGRklTAivDUKhYKz52s+Qzcto7gi6KZmFFeZ971UoL8rqenVz9VWBF195aBrMhopLSjAydW1bF61Bl5ebnTp6MPp2Mq9sJLSsh6nk8aJwNZeBLb2YtCgtpxJzCar4J9nmc1wNimXXh38UNXSs9a4uv1d3ozZZMJkMmI2/v2nyYTZZMLd252rZ13D1bOuoSArv2LhVH0ZjCaiDqZx6mxOreXMZkhNLyY1vZgz53IZOaQ1/q1kRbQQonpXRvLiZkClVBDWVlvRu6ztRKDUSw6UT0mrffFT6wA3XJyrH/50Utf84zebTeiKCtGVFFPbDESvnoG4OFeup7ik6jCvQqGgQ5Anl/cDi/VmLqRUnxu6ujqUKhVqJw1OLi44u7mjdnHjYoGZU6mlxGfpSM034OHnXecq7NrkF+hYszG+zoB7uezcUlZvjCfqYCp6QyOn7RJCNEvS03UQ6ksCYGGRvtbzZS997dIAXF6P4ZJf+AWFenp3962ynUitVliUXtKo02EyGNC4ulabsWrv/kRcXNX0GxJEaZGOzPRCigp01dRUtvq9U5AHZy6bB07JLcXLoxgfK/bMmk0m0nOKOJf6z3xvicEMxSZCAr0qDs0wm0yYzSZMJhNmowmjXlfrh4iExHy277lo1SlGldplhmOnsolPLGBkeGvatJaj/4QQ/5Cg64DqOvc2K6cUvd6IQqkgPbPyfG6HUC09uwaxbvMZSkqN5ObrGD6oNUePZ1Gq++dwgZCgsmxPZ7YlcHb7Bdx8XXDzufR/rvi006JxdcJsMlFaWIhKo0Gt0aBUlvWcExKySPx75bRJoUDp5ox/qDPebjX/tfL1ckObXUL+Zb3hcyn59HHT4KSufVGS2WymoKiUM0l56GrI1FV+ahKAQqlEgRKlCnACJxcXjAYDRr2u0rC6yWTmwNF0ok/UnT7TEgWFetZvvUDn9l6EDwjAWdO4i62EEM2DBF0HFJ9Y+zYYsxnSMkpQqRSVAgyAp4eGDmE+TJnQnh1RF0nPKEatVtCzmw8Hj/6TrapXt7JkJSknMrlwKLX6BynAO1hLYDdfBszphxYdRp0OpUqFyknDnn2JFUWVZhPGv2crWmlr3sOrUCjoHOzJwdjKwU1vNHM+KZsuoX413qvT6Tl3MY+coqrD15cyGmvvparUalRqNWYXM0a9nvy8ArZsTySlhrnvhjhzPpfEiwUMGxRIWFtPm9cvhGheJOg6mJJSAylpRXWWS80oQlndubd/L7Byc1Vz/VUhHD+djU5vokdnH2JOZKHTm2gd4FqRyjGntgBvLntd7eXCuUw9WmcjQV5qXAGTsZh+PVuxdWcyBoMJT2c1/v4euDo74aRWYjQYyhJvVNNGjcaJ1iqIj0mjOLWA/KR8cuJyKEopxOnf19J+SLtK5Y1GI8kZBSRZuC3KYLJsF5xCocBohoQcI87uGmiEoAtQXGJkS2Qy7dvl4+KswtfbBR9vZ3y8nCsWswkhrgwSdB3MheTCWlcjl0tLL2ZAH3+On86m5JIzaS/dsqJQKOjZ9Z/0mz26+nA4JpPe3VtVXMtJqju5hE+XsjryS03kp+nwcVXS2lNN2zYeTBrbjo3bEgkN8UajueR0IGVZ4g0TZlTVzAWf/eM0x9adrXJ91fObuenvwGs2m8nOLeJsSgEWxlGgbOVxXcxmMxk5hcSmlM0J+7fzwYyZhDjLFnVZS6lUEJ+YX+VYRK2HEwN6+9MxTHrBQlwJ5GO2o7EwuKRlluDn68IN14Xiqf0n2NW2NKpnV18C/FwJCSpb3KMrNeBsweEF2raVz9nNLjZxMlVHUo4eL09nbrw+FCWmKguUlCoVKpUao9GAyfjPBwOz2czpv+JqfN6q5zdzYstZjp7L4PRF6wIuUOfKYaPByOmE7IqAC2Xf9oB2vrQNbXjwa+3vivNlK8a9PTXVnkOcX6Bn2+5k9h5KqzJVIIRoeSToOhj3GhYhKRTgpf0nkYTBYCI7pxRPrYYbrgutGC6uLaGFs0bFdaNDKso4aVR0fXQ4I9+5nl6z+uDsVf1crLO/W5VrZiCj0MixlFLO5xqJjs/lZHxGtSuDVSo1CqUSo0GP2WRCV1iKvrj2edmNiyLJT8hFpQAXNVSTIbJG+lp6ugVFJRyMzSC7SF/lNTMQGOpL23YNC7ypGcUYDSYC/V0p/3Fo6hhGjjmZxZ9/XajY4yyEaJlkeNnBuLtVPcDdSa2kfaiW07G5la6nZhTRytcFF2c1469py/bdF2vv6kKlHphCoUCtBL2TGveBIfQfGIIiv4TC2CxyzuWQHp1KcUYxKg9naus7Gk1gNJlx1VQ/h1v+LJXaCbPZTPq5yxJ/KMCnky+turVCG+qNS4A7Kq0zRicVRjMYDeCuUaCzcBhAV01P12wykZSeT2Id88JmILC9L2YzJF6wfqjZzVVNUbEBg9FManox7m5OuDgrK00B1ORiahG/r4/j2lEh+PnKMZdCtEQSdB3M5T1ddzc1fXv6EXWg6grj1PRienQp+2+1SsnVI9pYvb9UrVJULDwyA2atC54D26Ad0IagiB6oMGOoK5L/zcej7pOHzGYzpWYY+PhQnP3cULprMCiVlcKp6e//XXpRX8P2oOpc/j3Q6fScvJBDkc6y743ZDEEdyuaxrQ28ri4qii7pxRcW6Smse13cJeUNrN2cwK1TOjZ6TmchhP3J8LKDUauVOGvKfiy+3s5cNawNB4+mY6xmvu/yBBoKhcLq/aBO1STI0P/dKdOowIjC0mlmPFxr/wyn0+k5dj6DdI0adXtfjFoX9JcF3OooAF3dHcUKpYaywmazmazcQg7GZlkccMuZ/g68wSHWpZNU15Lly1IGg4lz8Y2zoEsI0bQk6DogdzcnQtq4M3Z0CDv3ptQ4NPn/7d15dJN1/i/w97NlT9N0b2lLgbZAUVCWgoKDMoigCG4D/FxgLjKKitsZBj2j/s6ZGc44ovNzweOojPO7M1c9ozh4B0GE8c7lsiibrCJlbWmhtnRv0qRJnuX+URKaZn2SdCH9vM7haJ88+T5PmzaffLfPx1v8IB5CiAT9otz1T8tHn8Bfpw0cGu9OkmR0uBXoBXVFATQq7gEAOj0yJElEdX0bTsVY9hDoCrx5I9KRdznwCgKLNCOPbB7IaHEgT5FhNvIwGnjodRy0GhYNYTKJqXGyx1QCISQ50PDyADRuTDoK8kzYtr3GV04umKH5Jhgi9C4jCTeCKSuAW1Sg45muFIthGLUcoMiQZSZkWUDvfK9bVMAxQLQjxjwLBC8SGNzofAs4jkdBVgoYxobaGMoeeskKkMkyaNxzAY6adnQPqYZ0Hdw3DwOiSKepVlNzJ5qaO5FOc7uEJBUKugNQUYEZO/b8GDZDUm62AdNvzIsqf3I4fITnK+jKaWwQGDg8waMkxwKjC1N9FYkUWcallg50uCQwDMCCARhAvrxnRlK6hq4hRxd41VR8HjXEDLOxK1CxLIvCbAsyzDqcuNCmal4YAHhFwflPvseF3TVBH3c0dSLH4UKjKbGBkWGAkSNSkZISvuwhIeTqQ0F3ADr0fSPOhknSkJGuw8ybhoDn4p8dCDW83JPDo8CoYdDhDgxc1xSm+goMAF35jj2Sgkttgf1TvcDA6VHglrp62RxCz9cKkoTm/RdxbNtZGLJMMGYboc8wQJemh2DRgjdqwOp5MBoeMstgeI4ZqSmB25sMBi2uL85AdX076oLUKA7qkg37/utbeDrCb+HpOFQPZVph2K1aao0tS8eEsZkJa48QMnBQ0B1gTp9rxeHvQ9fSTU3RYNb0AggJWtmqV5GGsMOtICtFgCQDLR0eyApQkmuCXh+4alkTYkFR9wQQHqlrkVT3XjQDgGl14PymU6jdW+s719HgROPxBoSTveZWpFuDV/VhWRZFuanISOlExYX2kKkieSi4uLECVf+qDHstL1tdB7KdHjQZEtcr5XphuJoQMjBQ0B1Aaus6sGtfXcjHTUYet91SELI+biw0PAMNx4Ss2NNTbroJep0GiqJAkiQw6Fol3LOnF6oH7ZKu9HaBruFrh0eBgQfaTjSg4u/H4Ygi93QwG1/6Nx5ZvxAaQ+itSyajDtcXC6iqa0dDu/98OdviwIE/fgtXkB56OJ1H66FMzk9Ib9dk5FE6IjXudgghAxOtXh4gOhwe/HvXxZDzlzoth9tuKQyaPCNeJm30vwbeFcoMw4D3VuuRZb80jwDAhynRFyzdYcf5Vhx8a3/MARcAJJeEr17eEbZeLgBwHIfheakoK0gBywAcFDT96zS+/c/tqgMuALTV2JCegExSgsDi1ukFcS+OI4QMXBR0B4iGJmfYxBZjy9L90kAmUrRBN8MsBO3NsRwHluMgiSJkuSv4hlug5e3t+p4P4Oj7B9XddAiV315A1b7qiOcxDIMUkx4TijNQ87+O4MzG03Fd13O8IWKwD38/wIxpQ2ANkYqTEJIcKOgOEG3tobcGMQx6tQpNtEE3PSX8Kl2O58EwXTmWIw21du/tuk43ojOObT1+GCBzRHrk8y7jeA53vnQLjJmRCz+E03KuFVaPigwePUydlIMhOcHnowkhyYOC7gARbj9uQZ4Jel3vDTkKHANdFAkoTPrIPW1vjmVXhADk7e1yUHD0z4np5QLAXX+YCVOGSdVzBL0GD7w7H0K8w7onQy+AC6es1ErzuIQMEhR0B4hwPd3iYZaQjyVKpN6uwDFh52ljIcsKbIdqIToSU1ln0gPXYuiEgpieq7fo8cC6eWCi3EIVTGNFE1JEdb1dk1HAhHG0PYiQwYKC7gDRHqKnq9VwKMhT13OLRZaZhy5MesZsi1bV6txoZjclScH3fz0SdZvh5I/Lxg1LxsfVhiXHgoVrb4+rDf5Mc9TnMgwwrTwHQgLyNRNCrg701z4AdLpEuEIk5B9RlAIujt5XtASOQXGGJmSPN9Wc+AU+rQcuQol9GtRHb9Fi3uqZYEKkn1QjuzQLd66+JebnXzrWANPeC0g/24yspg6kOz0wyrJfWq2iAjNKR1gw8yf5yKN5XEIGFdqbMAD099CyF8cyGJYuoKbFg1an/4cAfYRiBj1FWsjLQ8GJj75Xe4tBLVh7O4Qo5pujNXxKEW5+ajK2v7U3pud3XHKgtdo/oxjLszDnGGEpTMGknxbCnBWYOYsQkvyopzsAhFpEZbVokW7t2y0kLMOg0Cogw9g1f8sxQPPFNmzcXIH6+ra4tsV013qwFnKQYvNqFd9UiNS81PhvqBvJIyIlK/YeaLAFWbIoo+2CDdXfXETNwdAJUAghyY16ugNAe4iebslwS0Jz+kaLYRjkWXgoooTd31xEx+XygZ/97woYjQKmTSnAsKI0cGEWVvUMzgKjwNMpor3VibpaG7iKxoTcqxii7KFaiqKgva4dRzdW4NCGE1BUFkfojteFX3D2zV+OoOTmQgi9uCKdEDIw0V/9ABCsp8swwIihvbc3NxKGYcBJki/genV0eLD1/5wDy57DjeX5sFp1YFkWHMeAZRlwLAuWZWBzuiHaO9Hc6MCPP9oh9kj8kZWnrjh8KJ3t8e3v9bg8qNpbg2/++yBaa2wJuScuQl5sWez6AEJBl5DBh/7qB4BgQTc/1wh9P6cDDHd9WQZOn2lCfYxF22VTYuZgnW2h58NDURQFLdUtOPjZcRzfciYh99EdF0URia9Wf4O5v7kJGmPi03oSQgYuCrr9TJYV2GyegOMlw/tuAVUohgg9sXhmdzviGL7tzqmip+vqcOHs7vP45oOD6GiK7cNCOBqjgLShFrRUt0U8t/FcK77+417MeWlqv0whEEL6BwXdftbh8EDqUQBAq2H7ZG9uJILQNWwshQiQHc7ADwvRcrok6LIN6KyPvcABALg7PEGrHHkpioJLZxpx4OOjOLMzck7mWJhzjDCk6tB4tgV1P0Q/V33h8CW0VLcjbWj/f8AihPQNCrr9LNh2oeFDU8AloEB9vBiGgV7Hw94RGFw1GhYdEQq8R2IemR530AXQtT8pRNB1d7jw98c2xX+NIDJLrJA8Mpqr2mCr64ipjerv6ijoEjKI9P87+yBXF6SUXcnw1L6/kRBClZlLScCcrCYnMb35cNuYXB3q53zDEfQ8csrSYUzXo+F0C5qrIg8lh1NzsD5Bd0YIuRpQ0O1HsqzgTJV/EoVUi6bP9+aGIssKJCn4XtpEZMkS9YlZRCSHmR/utKmvjxuMKcuAnNHpUGQFdT80JWxOuK6iCS57Yj8YEEIGLgq6/ai2rgMOp/8QrVVljuPeoigKvj1Qj6aW4EHL7Y5/f6wssLCOy4q/nRAfDADA0RxfcMwYkYqM4amwX3Kg7kRTwvYFeymygmObziQs6QghZGCjoNuPTlcGDk2ev2CH05mYqjvxOHK8CSfPtgZ9jGHCp66MFssy6BiVieyZRXG1Ey6zle2S+rlWXsshZ3Q6TJl6NJ5tReO51jjuLrKLRy4NiA9ahJDeR0G3n7jcEqov2AOOy7KCijOtfX9D3Zw+14qDx0KvwrWYNZDj7JhZUjRoanFBlhU0WQ0Y8rNRMbcl9yinp8gyJFGEJIqwN6pbqGXKNIDXcqg70QR7Q+K3FQUz4qbYyhESQq4+tHq5n5w73x6wVcjrxOkWjC1L65cVzBdq7di1L3huYJbtKjWo1cZfV7dnObt6sMhdfC3q//4DZJVD1x6XCEmSgMtbh1iOA3e54pDkib4tY7oOkkdCZwJ68ZEMGZeFUTOLoDUKGJKAIXZCyNWBgm4/CTa07NXpknDuvK3PE2Q0Nnfi37svBlQIys7Uo6m5E6KkwNkpwdkZXw8wxSygsTkwqUWDU0Laf4yBbfMZuKLsoWrNAkzpRnBc8A8Cns7ohup1qVoADJyt8aWVjERr0iDvmgzMeLY8qsxVhJDkQn/1/aClzYXGptBv7pYUDdwqemiJ0G53Y9v2GohiYO+7vsGJjHRdwq6l1YTuKbc6RGjnjEBKaVpUbc359XRwQujPjtEEXa1JA0HD9UqWqp5ufW4ybl01hQIuIYNUTD3do0ePYu3atTh8+DA8Hg+Ki4uxZMkS3Hnnnarasdvt+Mtf/oJt27ahpqYGgiCgoKAAP/3pT7FixYpYbu2qcKZHL9do4JGbbUBethG52QYYDX2bj9fZKWLb9hp0hlmZW3fJiewsPeovxReYzCYBDWE+cACAo1OCMCEXmRl6NHxzMeR5WSVpKJyYH7YtMULQ1Rh5aM0C2n+MLbmFWhkDaA82IaTvqQ66e/fuxcMPPwxBEHDHHXfAbDZj27ZtWLlyJS5evIjly5dH1U5tbS2WLFmCmpoa3HjjjZg+fTrcbjeqq6uxdevWpA26sqzgQm0HigrMyMs2IDfHiBST0K+rV//ft7VoD5L/uaf6S05kZ+pRH8cCI52Wg80e+VoeUUFrvgW58wz4cePpoOfMfmF6xJ+bJ8RKcF7Pw5CqBcuxaL2QmOpCkaQNTYEmQXuTCSFXJ0ZRsUFQFEXMmTMHdXV1+OSTT1BWVgagq8e6aNEiVFZWYvPmzSgqKgrbjiRJWLhwIU6fPo333nsPU6ZMCbgOz4f/PNDS0hLtbQ8osqyAYdCrQdZqtUb986mt68BX/7dGVfuxBl6TUQiaUjKSLA2LH//+PZRuHfExc4ox85c3RXyuy97Vq2Z5DizHguEYMEzXP0VR8N8ProetPvG93NwxGZj4H2VIG5qCtlo7Lhy+hFG3FsGQqn6YXs3r2Z+sVmt/3wIhA56qiaU9e/aguroac+fO9QVcADCZTHj88cchiiI2bNgQsZ2tW7fi2LFjWLp0aUDABRAx4F7NWJYZMHsyFUXBd0cbVD+vvsGJrAz1wcOgj23V8yW3jKwHx4I3X049yQA3LS+P6rlakw5akw6CTgAncGBZ1vfzZxgGtzw5OaZ7CkdjFHDL0xORW5YBrVGDrJI0jP/ZqJgCLiEkuaiKbvv27QMATJs2LeCxqVOn+p0TzpdffgkAmD17Nn788Uds374dNpsNBQUF+MlPfgKj0ajmtkiMamrtEedXQ1GbHGPqlCE4dCT4VqRoNDlEmO8eBff2KpTfPRpaY2JSZQ6dmA9ez0F0JmbhmiXPhNkv3AhThiEh7RFCkouqoFtVVQUAGDp0aMBjFosFVqsV58+fj9jO999/DwD47rvv8PLLL8PtvvIGnpaWhjfeeAOTJye+B0Ku6OrlRl+Grie9nofLHTnwFuanYOYtw6E3aGE0aLDt35UxX9PmFKGdVohRtxbH3EZPLM9h2i8mYvtbe+NuK73Igjn/OZV6tISQkFQFXbu9K4OS2WwO+rjJZEJdXeTeTFNTEwBg9erVWLp0KR588EFoNBps3rwZr7zyCp544gl8+eWXyMoKnTTAYrGAZWnbRSiR5tdOnmlES2vsxQAMeg1a20IHXZ2Ox51zRiIr60oloeIRmfh6eyXk0FkbI3J5ZLS2uZGli7/Kkdc1s0fGHXRzRmZg4auzoTP3TrEKmi8lJDn0y+Spd+3WzTffjJUrV/qOP/TQQ6ivr8e6devw2Wef4fHHHw/ZRltbfCXVklmkhTeyrGDnt5FHJMKRpNDDseUTczH+uiEBCSsYlsGUSUPwzd7Q24CisWd/NebNLYt8YpQ4DYfF//NusBwDwSBA0PLgBB6eTg/enf9xxOenD7PgthemwCk64GxJQH3gHmghFSHJQ1VX0WTq6rXYbMG3WNjt9pC94GDtzJgxI+CxW265BcCVIWiSeGer2tBmiy/VoRIkhWVuthE/f2AcJk0oDJkhqmx0dlzXBYCaiza4OhObqtGanwpLrgUGiwGCTgOWYyHootveUzA+B9oE1BcmhCQ/VUHXuxUo2LxtW1sbWlpags739jRs2DAAQEpKSsBj3mMuV2LqoBJ/kqTg0PdNcbfj9lwZIxYEFnfOLsbd88fAaAo/n6nVChgzKiPu65+rao67jUhYjgUfxYprXQoFXEJIdFQF3UmTJgEAdu3aFfDY7t27AQDl5ZG3cni3CZ05cybgMe+xIUOGqLk1EqVT51pj2ivbk/Nypqfi4alYung8CoemR70VasL4vLivv+9AbZ/UoM0oCj9kmluWgTGzh/f6fRBCkoOqoHvDDTegoKAAmzZtwokTJ3zH7XY73nnnHfA8j7vvvtt3vLm5GWfPnkVzs3+v5J577oFGo8GHH36I+vp6v3bee+89AMCcOXNi+oZIaKIo4/Dx+Hu5As/C5e7q6ZZPzAfPq9t/azbrkZ9ninxiGPYOD9rbej9Xcvqw1JCPWfJMuPW5KeCE+KsuEUIGB1VBl+d5rF69Goqi4P7778dLL72EV155BfPnz8fp06exYsUK39AxAHz00Ue4/fbb8dFHH/m1U1BQgFWrVqGpqQnz5s3Diy++iN/+9reYN28eTpw4gYULF+KGG25IzHdIfE6cboEzRFpENdKsWvAcA4YBLBZ9TG3cOKUw7vs4XnEp7jYiseYHToF4TVxUBp2ZhpYJIdFTvXp5ypQp+Pjjj/HWW29hy5YtvoIHTz/9NObNmxd1Ow899BCGDBmCDz74AJs3b4YkSSguLsby5cuxYMECtbdFIvB4JBw7Ed88aF6uERl5ZvAGLfIkGYJHinnbVkaGCRazFm222Ofujxyrx+RJBSEXbSWCOTv4wsDRs4Zh2JT4h8kJIYOLqtzLA8nVsIWivwTbYnL4+0YcPKY+GYbAs8gvMCM12wxWE/gZ7dqhFhgNsSWDqD7fhC++CpzXV+PuO0ciLy81rjbCqT1eh/VPb7lygAGmLhuHMXNG9No1e6ItQ4Qkj+RNckx8XC4JxyrU9XJNRgH5hSkwpBnBcKF7sycutOP6EUJMvc38Ais0Auu3Elqt7w792KtB12C98oEifZgFP3l8PDJHUHAhhMSGUjoNAscqmuFRGdiKRlhhzDSHDbgAIEoKzta2xbSSmGVZzLm1GBwbewGI6gvtCd+z253OpAXDMrh11WTc89oMCriEkLhQ0B0EqmrU14vtUDHX2mz3oLkttkxM+QVW/OJ/TMAtPykEz8cWfCurem/oVdALmLpsHIZNGTJgqkMRQq5eFHSTnMstoT2G7FMtzeqqD53+0Q6XO7b9vxzPoWx0Lpb9fAJm3lwEQVD3a7nvwMVe2bOrKAok0Y0y2odLCEkQCrpJrqHJfy9rmlWH4pLIQ6StbS7IYfIrB3OiuhVyHNUMOI7DyJHZeHjJeMyaMQxaTXTzxLYOD9rbE7tnV1EUeDqdkDzxJxIhhBAvCrpJrqGxq8fKMEBJqRVF12TDlBZdvWJRZeaqTo8MRwLmVzmOQ0lJFpYuHo/ZM4dDq/UPvmyQOeAfTiR2zy4FXEJIb6Cgm+QampwwmwSMnZiHlBwLGIYBq+Gi6kU6bOoL3PMJLLfIcixGjMjE0sXjUT4+13fcEiQhxeFj9ZCl2HrZXb3aToguFyTRA7eTAi4hpHdQ0E0iHsl/XlOWZRjMGhSPywWvvxKoGIaB1Rq87mt2tsG3oKm1RX3Q5SKsdo4Fy7LIyDD4vk61BAZdWQbq69tjap9hGEiiBx5XJ9wOByRP762GJoQMbhR0k0hThwS32C3wMgzMORawQQKh2RI8oUWKRYdry/NRWpoGp1OEorL3GGzoNxGczis9T4Oeh0YT+D19d/jHmNpWFAVKHHPRhBASLQq6SYRngfPNbshRrOTVh6j/2tLkBMtzMOekYNQE9WkOY00LGUlHt/llm92DgiAFE87XtMPlUj8sLEvx56MmhJBoUNBNIlqegcOjoLK+a19uuNjL6YMH3aZmp2/VMsOyEZNjdMcAvbaX1dZxZci33e7G0PyuoKvTcki3alGQZ0Rmug5VQersenuysiRBEkVIHg9Etxuiy+WbyyWEkL5AaSCTiJbvCpA1jR3g0wUYgwzBerEcC0uKBm3t/vOXigJ4OtzQpqivHqQLc714tbdfCYw2uweFQ8xYsmAkOM4/yDucIlwd9q59u4rSJzV3CSEkWtTTTSIC19XbBIDqFg/cUviAY0kNnNcdNswCjSm6AgY9p291vVhXtq1b0JUkBQ6nGBBwga75XlmSoMgyBVxCyIBDQTeJMAwD7eWVx5LcFXjDMZqvrGAWBBbXjM1CWoEVTBSLoRgA+amC3zGtykxS0VIUBfYee4ZjybJFCCH9jYJuktF2y1/c6Qnf09Mau+Z1ralajBmfB22qIez53XEskKpnkaK78ivkHd6OR7AeqiIHfh8UdAkhVyMKuklGq6JoAKvlMXx4KoZdkw1Oq256n2cZMAyD/FQB3lFeIQHDy6LHHZB+UurxtckogEtAgCeEkL5GC6mSTLRB1yAwcHgAa35qTNfxSF2LlASOwZBUAdUtHgiXVzorigLR5QKv1apazawoCiS3G9AAHH/lV1MUJVw7Kg1ZmXpkputh0NOvLSHk6kTvXkkmmiHe/FQeaQYO9TYJ9bbY9qhKCuDwKDBqGKTqWbQ6WfAcA1mW4XF2lfljmOgWZHnJoghFUSCLIqC9nJ7R1QmIbky6Pium+ySEkIGExuiSjE5gYAwzVJyfyiPdyINhGOSk8ChKEwJWIUfL1tmVxck7zKzIMlwddsiSBJZT/3lOvJx+UZYkiG4XOu22rp4vIYQkCQq6SYZjGYwtSoMmyHYab8DtzqLnUJKpCXp+JDbXlblWgWPAyR5fRg6WDwy6ihJ6G48sy1093Ms8nZ3hs3sQQshViIJuEtIKHIZnCOg+0pxp4gICrpdOYFGapYFZq+7XwekOHRRFtysgwEqiGDKQSm7KCkUISX4UdJOUlmcxPEPjGzp2ieF7jRzLYFi6gCxT9CuQw62RkkURbkeHX+CVPWLQnq6iKBCplB4hZBCgoJvE9AKLoWldCSxsLhlykP2u3TEMg1yLgKFRzvNGOkeWJF/gVRQFkugfdBVFgeTxwON00lAyIWRQoNXLSS5Fx8GslWBzybC5ZFj0kXuyqXoOWp5BVVP4VJLR7AaSJQmuDjsErQ6A4kvRKIkevzlcQggZDKinOwjkWbo+W7V1ShHOvEIvsCjJ1MAUZp6XjXIPriLLcF/eRiS6OuHpdFLAJYQMShR0BwGdwCLdyKHdqa4IAM8xGJ4uIDPEPG8v1asnhJCkRUF3kMg281AAdLhlVc9jGAZ5FgElmRoYBKbHYwm8QUIIGQQo6A4SAscg28yjzaku6HoZNCyKMzXIT+XhrWsf7fAyIYSQLhR0B5EMEwenJ/Y6swzDIN3IY1S2FulGDjHk0yCEkEGNVi8PIuzloOn0KDBoYo+YPNuV9lGMsAWJEEKIP+rpDjKpejZhwZKnlVSEEKIKBd1BhmEYGDX0shNCSH+gd99BiKMeKiGE9AsKuoQQQkgfoaBLCCGE9BEKuoQQQkgfoaBLCCGE9BEKuoQQQkgfoaBLCCGE9BEKuoQQQkgfoaBLCCGE9BEKuoQQQkgfoaBLCCGE9JGYqgwdPXoUa9euxeHDh+HxeFBcXIwlS5bgzjvvjOr5e/fuxeLFi0M+/sknn+C6666L5dYIIYSQAUt10N27dy8efvhhCIKAO+64A2azGdu2bcPKlStx8eJFLF++POq2ysvLUV5eHnA8JydH7W0RQgghA56qoCuKIl588UUwDIOPPvoIZWVlAIAnnngCixYtwtq1azF79mwUFRVF1V55eTmefPJJ1TdNCCGEXI1Uzenu2bMH1dXVmDt3ri/gAoDJZMLjjz8OURSxYcOGhN8kIYQQkgxU9XT37dsHAJg2bVrAY1OnTvU7JxpVVVX429/+hs7OTuTl5eHGG29EWlqamlsihBBCrhqqgm5VVRUAYOjQoQGPWSwWWK1WnD9/Pur2Nm3ahE2bNvm+1ul0ePLJJ7Fs2TI1t0UIIYRcFVQFXbvdDgAwm81BHzeZTKirq4vYTlpaGlatWoWbb74ZeXl5aG9vx969e/Haa6/h1VdfhclkwqJFi8K2YbFYwLK04ykUq9Xa37dAEoheT0KSQ0xbhuJVUlKCkpIS39d6vR7z5s3DqFGjcM8992Dt2rVYsGBB2KDa1tbWF7d6VbJarWhpaenv2yAJcrW8nvTBgJDIVAVdk8kEALDZbEEft9vtIXvB0SgtLcW4ceNw4MABnD9/HsOGDQt5Lv2Bh0c/n+RCrychyUHV+Kx3K1Cwedu2tja0tLQEne9Vw/vm0tnZGVc7hBBCyECjKuhOmjQJALBr166Ax3bv3g0AQZNdREsURfzwww9gGAa5ubkxt0MIIYQMRKqC7g033ICCggJs2rQJJ06c8B232+145513wPM87r77bt/x5uZmnD17Fs3NzX7tHDp0CIqi+B0TRRFr1qzBxYsXMW3aNKSmpsbw7RBCCCEDF6P0jH4R7NmzB8uWLYMgCJg7dy5MJhO2bduGCxcu4JlnnsFjjz3mO3ft2rV4++23sWLFCr/MUzNmzAAAXH/99cjOzobNZsP+/ftRWVmJvLw8fPjhhxgyZEiCvkVCCCFkYFC9ennKlCn4+OOP8dZbb2HLli2+ggdPP/005s2bF1UbixYtws6dO7Fv3z60tLSA53kUFhZi+fLlWLp0KSwWi+pvhBBCCBnoVPd0CSGEEBKbftmnm2zq6+uxZcsW7NixA+fOnUNjYyMsFgvGjx+PZcuWYdy4cQHPsdvtWLt2LbZt24aGhgZkZmZi1qxZePLJJ31bs3r64osv8Ne//hVnzpyBIAi47rrr8NRTT+Haa68Nen5VVRVef/117N27Fw6HA0OHDsXChQtx//33B90D7Xa78f777+OLL75AbW0tLBYLpk+fjmeeeQaZmZlBr7Fz5068//77OH78OBRFwTXXXINHHnkEN910k4qf4MC2bt06vPbaawBCl52k15MQEg3q6SbAa6+9hnXr1qGwsBCTJk1Ceno6zp8/j6+//hqKouCPf/wjbr/9dt/5DocD999/P06cOIGpU6eirKwMFRUV2LlzJ0aPHo2PP/4YBoPB7xrvvvsuXn/9deTl5eG2226Dw+HA5s2b4XK58MEHH2Dy5Ml+5585cwaLFi1CZ2cnZs+ejezsbOzYsQOnTp3CggUL8Lvf/c7vfFmW8Ytf/AK7du3CuHHjUF5ejurqavzrX/9CTk4OPv3004A36o0bN+JXv/oVrFYr7rjjDjAMgy1btqCxsRGvvvpq1NMNA9nZs2dx1113ged5OByOoEGXXk9CSNQUEretW7cq+/fvDzi+f/9+ZcyYMUp5ebnicrl8x998802ltLRUWbNmjd/53uNvvvmm3/HKykqlrKxMmTVrltLe3u47furUKWXcuHHKzJkzFY/H4/ecBx54QCktLVW2b9/uO+Z2u5UlS5YopaWlyrfffut3/meffaaUlpYqzz77rCLLcsDxVatW+Z3f2tqqTJw4UZk8ebJSW1vrO15fX69MnTpVmThxotLa2hryZ3Y1EEVRuffee5X77rtPWblypVJaWqocOnQo4Dx6PQkh0aLkxQkwa9YsTJw4MeD4xIkTMXnyZLS2tuLkyZMAAEVRsH79ehgMBjzxxBN+5z/66KOwWCz47LPP/LZUbdiwAaIo4rHHHvPL+FVSUoL58+ejuroae/bs8R2vrKzE/v37MXnyZEyfPt13XBAEPPvsswCA9evX+13b+/Uvf/lLMAzjO37vvfdixIgR+PLLL325twHgq6++Qnt7Ox588EG/PdVZWVlYvHgx2tvb8dVXX0Xx0xu41q1bh4qKCvz+978Hx3FBz6HXkxCiBgXdXsbzvN9/q6qqcOnSJYwfPz5gyFGr1WLixImor6/3y/rlLZfoLZ/YnXeubf/+/QHnByvBOHbsWKSkpPiVYHS5XDhy5AiGDRsWdKvW1KlT4Xa7ceTIkaiu4b0nNWUeB5pTp07h7bffxmOPPeaXJ7wnej0JIWpQ0O1FtbW1+Oabb5CZmYnS0lIAV1JoelNq9uRNo9n9TbqqqgoGgyHo4hfv+d6yi93/P1hKToZhUFhYiEuXLsHpdAIAqqurIctyyHvyHo/2GsG+h6uJKIp4/vnnMWLECDzyyCNhz6XXkxCiBq1e7iUejwerVq2C2+3GypUrfcOT3mIRoVa0BisqYbfbkZaWFvb87kOF0ZRg9F5Dr9dHvCej0ajqGgaDARzHhSyMMdC9++67OHnyJD799FMIghD2XHo9CSFqUE+3F8iyjF//+tfYv38/FixYgLvuuqu/b4lEqaKiAu+++y6WLl2KMWPG9PftEEKSDAXdBFMUBS+++CI2btyIefPm4Te/+Y3f496eRPdeRnfBehwmkylsOUXvOd3PB8KXYOx+XqR76ujoUHUNh8MBSZLiKvPYX5577jkUFBT4pS0Nh15PQogaFHQTyNvD/cc//oG5c+fiD3/4Q0DSgmBzdt155826z60VFRXB4XCgoaEh5Pnd5+/ClWBUFAXV1dXIysryLfwpLCwEy7Ih78l7PNprBPserhYVFRU4d+4crr32WowcOdL37/PPPwcALFy4ECNHjsTXX38NgF5PQog6FHQTRJZlvPDCC9iwYQNuv/12rFmzJug2k6KiImRlZeHgwYNwOBx+j7lcLhw4cABZWVl+b3Dekore8ond7dy50+8c4Ep5xWAlGI8ePYr29na/EoxarRZjx45FZWUlLl68GPCc3bt3Q6PR+GXWClfm0XtP8ZR57C/33Xdf0H/eoDRjxgzcd999vlXB9HoSQlTpxz3CSUOSJOX5559XSktLlaeeeiogsUFPapMpnDt3LmHJFH7+858nLJnChAkTBk0yheeeey5hyTHo9SRk8KI0kAngLWFoMBiwePFi357c7mbOnInRo0cDCEwbOGbMGFRUVGDHjh0h0wb+6U9/whtvvBE0beCf//xnTJkyxe/87mkD58yZg6ysLOzcuRMnT57Ez372M6xevdrvfEmS8Mgjj/ilDaypqcG2bduQnZ2N9evXB2xx+ec//4lVq1YFTRu4Zs0azJ8/PxE/3gHh+eefx+effx5VGkh6PQkhoVDQTQDvG3I4L7/8Mu655x7f1zabDW+//Ta2bt2KxsZGZGRk4LbbbsOKFStCLljZuHFj0AT5Y8eODXp+ZWVl0AT5DzzwQNgE+Rs3bgxIkJ+VlRX0Gjt27PAlyAeAMWPG4NFHH026BPnhgi5ArychJDoUdAkhhJA+QgupCCGEkD5CQZcQQgjpIxR0CSGEkD5CQZcQQgjpIxR0CSGEkD5CQZcQQgjpIxR0CSGEkD5CQZcQQgjpIxR0CSGEkD5CQZcQQgjpIxR0CSGEkD5CQZcQQgjpI/8fObxmGABFeqcAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "independent_map = spat_df.plot(\n", " column=\"INDEPENDENT_RES\",\n", " scheme=\"QUANTILES\",\n", " k=5,\n", " cmap=\"BuPu\",\n", " legend=True,\n", " legend_kwds={\"loc\": \"center left\", \"bbox_to_anchor\": (1, 0.5)},\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean of the residuals for the areas appear spatially correlated. This leads us to explore the addition of a spatially dependent random effect, by using a **conditional autoregressive (CAR)** prior.\n", "\n", "### Our second model: a *spatial* random effects model (with fixed spatial dependence)\n", "Let us fit a model that has two random effects for each area: an *independent* random effect, and a *spatial* random effect first. This models looks\n", "\\begin{align*} \n", "y_i &\\sim \\text{Poisson}\\big (\\lambda_i),\\\\\n", "\\log \\lambda_i &= \\beta_0+\\beta_1x_i + \\theta_i + \\phi_i + \\log E_i,\\\\\n", "\\theta_i &\\sim\\text{Normal}\\big(\\mu=0, \\tau=\\tau_{\\text{ind}}\\big ), \\\\\n", "\\phi_i \\big | \\mathbf{\\phi}_{j\\sim i} &\\sim \\text{Normal}\\big(\\mu=\\alpha\\sum_{j=1}^{n_i}\\phi_j, \\tau=\\tau_{\\text{spat}}\\big ),\\\\\n", "\\beta_0, \\beta_1 &\\sim \\text{Normal}\\big (\\mu = 0, \\tau = 1e^{-5}\\big), \\\\\n", "\\tau_{\\text{ind}} &\\sim \\text{Gamma}\\big (\\alpha=3.2761, \\beta=1.81\\big), \\\\\n", "\\tau_{\\text{spat}} &\\sim \\text{Gamma}\\big (\\alpha=1, \\beta=1\\big ),\n", "\\end{align*} \n", "where the line $\\phi_i \\big | \\mathbf{\\phi}_{j\\sim i} \\sim \\text{Normal}\\big(\\mu=\\alpha\\sum_{j=1}^{n_i}\\phi_j, \\tau=\\tau_{\\text{spat}}\\big )$ denotes the CAR prior, $\\tau_\\text{spat}$ is an unknown parameter for the precision of the spatial random effects, and $\\alpha$ captures the degree of spatial dependence between the areas. In this instance, we fix $\\alpha=0.95$. \n", "\n", "*Side note:* Here we explain the prior's used for the precision of the two random effect terms. As we have two random effects $\\theta_i$ and $\\phi_i$ for each $i$, they are independently unidentifiable, but the sum $\\theta_i + \\phi_i$ is identifiable. However, by scaling the priors of this precision in this manner, one may be able to interpret the proportion of variance explained by each of the random effects." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [beta0, beta1, tau_ind, tau_spat, theta, phi]\n" ] }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
\n", " \n", " 100.00% [16000/16000 00:41<00:00 Sampling 4 chains, 0 divergences]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 2_000 tune and 2_000 draw iterations (8_000 + 8_000 draws total) took 55 seconds.\n" ] } ], "source": [ "with pm.Model(coords={\"area_idx\": np.arange(N)}) as fixed_spatial_model:\n", " beta0 = pm.Normal(\"beta0\", mu=0.0, tau=1.0e-5)\n", " beta1 = pm.Normal(\"beta1\", mu=0.0, tau=1.0e-5)\n", " # variance parameter of the independent random effect\n", " tau_ind = pm.Gamma(\"tau_ind\", alpha=3.2761, beta=1.81)\n", " # variance parameter of the spatially dependent random effects\n", " tau_spat = pm.Gamma(\"tau_spat\", alpha=1.0, beta=1.0)\n", "\n", " # area-specific model parameters\n", " # independent random effect\n", " theta = pm.Normal(\"theta\", mu=0, tau=tau_ind, dims=\"area_idx\")\n", " # spatially dependent random effect, alpha fixed\n", " phi = pm.CAR(\"phi\", mu=np.zeros(N), tau=tau_spat, alpha=0.95, W=adj_matrix, dims=\"area_idx\")\n", "\n", " # exponential of the linear predictor -> the mean of the likelihood\n", " mu = pm.Deterministic(\"mu\", pt.exp(logE + beta0 + beta1 * x + theta + phi), dims=\"area_idx\")\n", "\n", " # likelihood of the observed data\n", " y_i = pm.Poisson(\"y_i\", mu=mu, observed=y, dims=\"area_idx\")\n", "\n", " # saving the residual between the observation and the mean response for the area\n", " res = pm.Deterministic(\"res\", y - mu, dims=\"area_idx\")\n", "\n", " # sampling the model\n", " fixed_spatial_idata = pm.sample(2000, tune=2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see by plotting the residuals of the second model, by accounting for spatial dependency with the CAR prior, the residuals of the model appear more independent with respect to the spatial location of the observation." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "spat_df[\"SPATIAL_RES\"] = fixed_spatial_idata[\"posterior\"][\"res\"].mean(dim=[\"chain\", \"draw\"])" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fixed_spatial_map = spat_df.plot(\n", " column=\"SPATIAL_RES\",\n", " scheme=\"quantiles\",\n", " k=5,\n", " cmap=\"BuPu\",\n", " legend=True,\n", " legend_kwds={\"loc\": \"center left\", \"bbox_to_anchor\": (1, 0.5)},\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we wanted to be *fully Bayesian* about the model that we specify, we would estimate the spatial dependence parameter $\\alpha$. This leads to ... \n", "\n", "### Our third model: a *spatial* random effects model, with unknown spatial dependence\n", "The only difference between model 3 and model 2, is that in model 3, $\\alpha$ is unknown, so we put a prior $\\alpha \\sim \\text{Beta} \\big (\\alpha = 1, \\beta=1\\big )$ over it." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [beta0, beta1, tau_ind, tau_spat, alpha, theta, phi]\n" ] }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
\n", " \n", " 100.00% [16000/16000 00:51<00:00 Sampling 4 chains, 0 divergences]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 2_000 tune and 2_000 draw iterations (8_000 + 8_000 draws total) took 65 seconds.\n" ] } ], "source": [ "with pm.Model(coords={\"area_idx\": np.arange(N)}) as car_model:\n", " beta0 = pm.Normal(\"beta0\", mu=0.0, tau=1.0e-5)\n", " beta1 = pm.Normal(\"beta1\", mu=0.0, tau=1.0e-5)\n", " # variance parameter of the independent random effect\n", " tau_ind = pm.Gamma(\"tau_ind\", alpha=3.2761, beta=1.81)\n", " # variance parameter of the spatially dependent random effects\n", " tau_spat = pm.Gamma(\"tau_spat\", alpha=1.0, beta=1.0)\n", "\n", " # prior for alpha\n", " alpha = pm.Beta(\"alpha\", alpha=1, beta=1)\n", "\n", " # area-specific model parameters\n", " # independent random effect\n", " theta = pm.Normal(\"theta\", mu=0, tau=tau_ind, dims=\"area_idx\")\n", " # spatially dependent random effect\n", " phi = pm.CAR(\"phi\", mu=np.zeros(N), tau=tau_spat, alpha=alpha, W=adj_matrix, dims=\"area_idx\")\n", "\n", " # exponential of the linear predictor -> the mean of the likelihood\n", " mu = pm.Deterministic(\"mu\", pt.exp(logE + beta0 + beta1 * x + theta + phi), dims=\"area_idx\")\n", "\n", " # likelihood of the observed data\n", " y_i = pm.Poisson(\"y_i\", mu=mu, observed=y, dims=\"area_idx\")\n", "\n", " # sampling the model\n", " car_idata = pm.sample(2000, tune=2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the marginal posterior for $\\alpha$, and see that it is very near $1$, suggesting strong levels of spatial dependence." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[]], dtype=object)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "az.plot_density([car_idata], var_names=[\"alpha\"], shade=0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparing the regression parameters $\\beta_0$ and $\\beta_1$ between the three models that we have fit, we can see that accounting for the spatial dependence between observations has the ability to greatly impact the interpretation of the effect of covariates on the response variable." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beta_density = az.plot_density(\n", " [independent_idata, fixed_spatial_idata, car_idata],\n", " data_labels=[\"Independent\", \"Spatial with alpha fixed\", \"Spatial with alpha random\"],\n", " var_names=[\"beta0\", \"beta1\"],\n", " shade=0.1,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Limitations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our final model provided some evidence that the spatial dependence parameter might be $1$. However, in the definition of the CAR prior, $\\alpha$ can only take on values up to and excluding $1$. If $\\alpha = 1$, we get an alternate prior called the *intrinsic conditional autoregressive (ICAR)* prior. The ICAR prior is more widely used in spatial models, specifically the BYM {cite:p}`besag1991bayesian`, Leroux {cite:p}`leroux2000estimation` and BYM2 {cite:p}`riebler2016intuitive` models. It also scales efficiently with large datasets, a limitation of the CAR distribution. Currently, work is being done to include the ICAR prior within PyMC." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Authors\n", "\n", "* Adapted from {ref}`another PyMC example notebook ` by Conor Hassan ([pymc-examples#417](https://github.com/pymc-devs/pymc-examples/pull/417)) and Daniel Saunders ([pymc-examples#547](https://github.com/pymc-devs/pymc-examples/pull/547/))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References \n", "\n", ":::{bibliography}\n", ":filter: docname in docnames \n", ":::" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Watermark" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last updated: Mon Jun 05 2023\n", "\n", "Python implementation: CPython\n", "Python version : 3.11.0\n", "IPython version : 8.8.0\n", "\n", "xarray: 2022.12.0\n", "\n", "pymc : 5.0.1\n", "pytensor : 2.8.11\n", "pandas : 1.5.2\n", "numpy : 1.24.1\n", "arviz : 0.14.0\n", "libpysal : 4.7.0\n", "matplotlib: 3.6.2\n", "\n", "Watermark: 2.3.1\n", "\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -n -u -v -iv -w -p xarray" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ":::{include} ../page_footer.md\n", ":::" ] } ], "metadata": { "interpreter": { "hash": "c007bd38e36c5a2482764074197001a13920a7126fb86cab77c270b2a8e1c2af" }, "kernelspec": { "display_name": "Python [conda env:spatial_pymc_env]", "language": "python", "name": "conda-env-spatial_pymc_env-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.0" }, "myst": { "substitutions": { "extra_dependencies": "geopandas libpysal" } }, "toc-autonumbering": false }, "nbformat": 4, "nbformat_minor": 4 }