{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Modelling with local GP experts (Part I): A 1D case study\n", "The main intended use case of ``GPSat`` is to model complex looking fields from a large set of data points, a situation commonly encountered in the geosciences, namely optimal interpolation (OI). The strategy that we adopted is quite simple: to model local chunks of data using different GPs and then gluing their predictions together.\n", "\n", "In this tutorial notebook, we will see how this method performs compared to a single \"global\" GP. We note that ``GPSat`` has an automated API to carry out this whole workflow, which we will see in the second part of this tutorial. However for the sake of understanding, we will hard-code this method here." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2023-08-03 15:49:14.356855: I tensorflow/core/platform/cpu_feature_guard.cc:182] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.\n", "To enable the following instructions: SSE4.1 SSE4.2, in other operations, rebuild TensorFlow with the appropriate compiler flags.\n" ] } ], "source": [ "import scipy\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from GPSat.models.sklearn_models import sklearnGPRModel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we generate noisy data as follows:\n", "\n", "\\begin{align}\n", "\\tag{1}\n", "y = \\sin(1/X) + \\epsilon, \\quad \\epsilon \\sim \\mathcal{N}(0, 0.05^2 I),\n", "\\end{align}\n", "\n", "in the region $X \\in [0.1, 0.6]$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set random seed\n", "np.random.seed(0)\n", "\n", "# Generate data\n", "N = 100\n", "noise_std = 0.05\n", "\n", "X_grid = np.linspace(0.1, 0.6, 100)\n", "X = np.random.uniform(0.1, 0.6, (N,))\n", "f = lambda x: np.sin(1/x)\n", "epsilon = noise_std * np.random.randn(N)\n", "\n", "y = f(X) + epsilon\n", "f_truth = f(X_grid) # Ground truth\n", "\n", "# Plot\n", "plt.plot(X_grid, f_truth, 'k', zorder=1, label='Ground truth')\n", "plt.scatter(X, y, color='C3', alpha=0.6, zorder=2, label='Noisy observations')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function is tricky to model well as the variability of the curve varies depending on where you are (shorter lengthscales near 0 and longer lengthscales near 1).\n", "\n", "Let's first see how a standard GP fits on this data." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "'__init__': 0.067 seconds\n", "'optimise_parameters': 0.122 seconds\n", "'predict': 0.002 seconds\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Initialise sklearn GPR model\n", "gpr = sklearnGPRModel(coords=X, obs=y, kernel='RBF', likelihood_variance=noise_std**2, verbose=False)\n", "\n", "# Train model\n", "_ = gpr.optimise_parameters()\n", "\n", "# Predict on test locations\n", "pred_dict = gpr.predict(X_grid[:,None])\n", "\n", "# Extract mean and variance of predictions\n", "f_mean = pred_dict['f*']\n", "f_var = pred_dict['f*_var']\n", "f_std = np.sqrt(f_var)\n", "\n", "# Plot results\n", "plt.plot(X_grid, f_truth, 'k', zorder=0, label='Ground truth')\n", "plt.plot(X_grid, f_mean, color='C0', zorder=1, label='sklearn GPR prediction')\n", "plt.fill_between(X_grid, f_mean-1.96*f_std, f_mean+1.96*f_std, color='C0', alpha=0.3)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the model fits quite well near 0.1, however as it approaches 0.6, we start to see some spurious fluctuations that does not exist in the ground truth field.\n", "\n", "Checking the learned lengthscale," ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lengthscale: 0.0364\n" ] } ], "source": [ "print(f\"Lengthscale: {gpr.get_lengthscales():.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "it is quite short, which explains the rapid fluctuations.\n", "\n", "Let us also check the mean squared error and the log-likelihood loss from the ground truth field for future reference." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error: 0.0005\n", "Mean log likelihood: 2.3388\n" ] } ], "source": [ "print(f\"Mean squared error: {np.mean((f_truth - f_mean)**2):.4f}\")\n", "print(f\"Mean log likelihood: {scipy.stats.norm.logpdf(f_truth, f_mean, f_std).mean():.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Local GP experts\n", "Next, let us consider a natural idea to solve this issue by fitting different GPs (called *local experts*) on different regions of the domain. For simplicity, we will use two GP experts: one to model the data for smaller values of $X$ and another to model the data for larger values of $X$.\n", "\n", "We assign the following data to the two GPs (call it GP1 and GP2):\n", "\n", "- GP1 gets assigned data points within the interval [0.1, 0.4] and makes predictions in the same region.\n", "- GP2 gets assigned data points within the interval [0.3, 0.6] and makes predictions in the same region.\n", "\n", "Note that we deliberately let the two regions overlap, which will be useful later." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# Data points assigned to GP1 and GP2\n", "Data1 = np.array([[x, y] for (x, y) in zip(X, y) if x < 0.4])\n", "Data2 = np.array([[x, y] for (x, y) in zip(X, y) if x > 0.3])\n", "\n", "# Prediction points assigned to GP1 and GP2\n", "X_test_1 = X_grid[X_grid < 0.4]\n", "X_test_2 = X_grid[X_grid > 0.3]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By convention, we will associate each region ([0.1, 0.4] and [0.3, 0.6]) by their mid-points (0.25 and 0.45 respectively), and refer to them as the *local expert locations*.\n", "\n", "The distance from the local expert location to the boundary of the region where data points are assigned is referred to as the *training radius*. In this case, we can check that our two experts both have a training radius of 0.15.\n", "\n", "Likewise, the distance from the local expert location to the boundary of the region where prediction points are assigned is referred to as the *inference radius*. In our case, we have set the inference radius to be equal to the training radius." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# Set expert locations\n", "xpert_loc_1 = 0.25\n", "xpert_loc_2 = 0.45\n", "\n", "# Set training and inference radii\n", "training_radius = inference_radius = 0.15" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we train GP1 and GP2 in their respective regions and make predictions." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "'__init__': 0.031 seconds\n", "'optimise_parameters': 0.122 seconds\n", "'predict': 0.001 seconds\n", "'__init__': 0.017 seconds\n", "'optimise_parameters': 0.041 seconds\n", "'predict': 0.000 seconds\n" ] } ], "source": [ "# Train and predict with GP1\n", "gp1 = sklearnGPRModel(coords=Data1[:,0], obs=Data1[:,1], kernel='RBF', likelihood_variance=noise_std**2, verbose=False)\n", "_ = gp1.optimise_parameters()\n", "pred_dict_1 = gp1.predict(X_test_1[:,None])\n", "f_mean_1 = pred_dict_1['f*']\n", "f_var_1 = pred_dict_1['f*_var']\n", "f_std_1 = np.sqrt(f_var_1)\n", "\n", "# Train and predict with GP2\n", "gp2 = sklearnGPRModel(coords=Data2[:,0], obs=Data2[:,1], kernel='RBF', likelihood_variance=noise_std**2, verbose=False)\n", "_ = gp2.optimise_parameters()\n", "pred_dict_2 = gp2.predict(X_test_2[:,None])\n", "f_mean_2 = pred_dict_2['f*']\n", "f_var_2 = pred_dict_2['f*_var']\n", "f_std_2 = np.sqrt(f_var_2)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we plot the predictions from the two GPs over-layed on top of one another." ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot results\n", "plt.plot(X_grid, f_truth, 'k', zorder=0, label='Ground truth')\n", "plt.plot(X_test_1, f_mean_1, color='C0', zorder=1, label='Local expert 1')\n", "plt.fill_between(X_test_1, f_mean_1-1.96*f_std_1, f_mean_1+1.96*f_std_1, color='C0', alpha=0.3)\n", "plt.plot(X_test_2, f_mean_2, color='C1', zorder=1, label='Local expert 2')\n", "plt.fill_between(X_test_2, f_mean_2-1.96*f_std_2, f_mean_2+1.96*f_std_2, color='C1', alpha=0.3)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, we find that GP1 fits the data with a shorter lengthscale and GP2 fits the data with a longer lengthscale." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lengthscale of GP1: 0.0321\n", "Lengthscale of GP2: 0.1632\n" ] } ], "source": [ "print(f\"Lengthscale of GP1: {gp1.get_lengthscales():.4f}\")\n", "print(f\"Lengthscale of GP2: {gp2.get_lengthscales():.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now use the ``glue_local_predictions_1d()`` method from the ``GPSat.postprocessing`` module to glue the two predictions smoothly to yield a single prediction.\n", "\n", "This is achieved by a gating mechanism, which considers a Gaussian-weighted average of the two predictions.\n", "\n", "First, we record our results into a pandas dataframe as follows. This dataframe should have as columns (1) the prediction locations, (2) local expert locations, and (3) any results we wish to glue such as the predicted mean and variance." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " pred_locs xprt_locs f_mean f_var\n", "0 0.100000 0.25 -0.501423 0.003268\n", "1 0.105051 0.25 -0.080115 0.000920\n", "2 0.110101 0.25 0.310646 0.000572\n", "3 0.115152 0.25 0.635114 0.000698\n", "4 0.120202 0.25 0.866515 0.000760\n", " :\n", " :\n", " pred_locs xprt_locs f_mean f_var\n", "115 0.579798 0.45 0.985532 0.000255\n", "116 0.584848 0.45 0.988731 0.000312\n", "117 0.589899 0.45 0.991786 0.000402\n", "118 0.594949 0.45 0.994677 0.000536\n", "119 0.600000 0.45 0.997378 0.000728\n" ] } ], "source": [ "from GPSat.postprocessing import glue_local_predictions_1d\n", "\n", "# Prediction locations for GP1 + GP2\n", "pred_locs = list(X_test_1) + list(X_test_2)\n", "\n", "# Expert locations for GP1 + GP2\n", "expert_locs = [xpert_loc_1 for _ in X_test_1] + [xpert_loc_2 for _ in X_test_2]\n", "\n", "# Predictions from GP1 + GP2\n", "f_mean = list(f_mean_1) + list(f_mean_2)\n", "f_var = list(f_var_1) + list(f_var_2)\n", "\n", "# Put these information together into a dataframe\n", "results_df = pd.DataFrame({'pred_locs': pred_locs, 'xprt_locs': expert_locs, 'f_mean': f_mean, 'f_var': f_var})\n", "\n", "print(results_df.head())\n", "print(\" \"*20 + \":\")\n", "print(\" \"*20 + \":\")\n", "print(results_df.tail())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now glue local predictions by running ``glue_local_predictions_1d()``. This returns a dataframe containing the results of a single *glued prediction*." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " pred_locs f_mean f_var\n", "0 0.100000 -0.501423 0.003268\n", "1 0.105051 -0.080115 0.000920\n", "2 0.110101 0.310646 0.000572\n", "3 0.115152 0.635114 0.000698\n", "4 0.120202 0.866515 0.000760" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Glue predictions\n", "glued_preds = glue_local_predictions_1d(preds_df = results_df, # The dataframe where results are stored\n", " pred_loc_col = 'pred_locs', # The column in dataframe corresponding to the prediction locations\n", " xprt_loc_col = 'xprt_locs', # The column in dataframe corresponding to the local expert locations\n", " vars_to_glue = ['f_mean', 'f_var'], # The columns in dataframe corresponding to the predictions\n", " inference_radius = inference_radius) # The inference radius (by passing a single float, it is assumed to be equal for both regions)\n", "\n", "glued_preds.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we plot the results of this glued prediction." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PH8+KovQPEc6l4fm3Mwasff55pmW/yHzTZ4Bt4zpKF+G8qiqqFy6kbdMmLEVBS6WyU0Kjx2xMJIQQI51j21jhMGZnJ3pjU7ZVRAwUFTUvL3MbJ7sN5FgmRlMTem0t6QMHie/bhxqP97+vvs2ilG3RYJj0eL24J06kYtFCZp5xBtOKT/z7qWOamS2eVCq73ZNt3OY4me0brxfV70erqkIrKkINZFYz+kLKyQ5KFBJecsJxHPa/8QZnZ5O1Z9JEsB3UgoJ3PVZRFJZcdSV/3bSJkONQCRjt7Vhy40gIMQo5hoHZ1YURCmVaRPT04KRSKF4fan4+7tJSFFXFMQ30Qw2k9+/PPB08CH3TlAEVMB2HZsPgkK4T9vvImzWb6ctPZ+n8+RQWFh1fPY7Tv83Tt9WDZQKgaFp/SNEqK3GVFKMGg0euoPh80lR0EEh4yYFQczNOUxPu0jIIBjNNhhwH7ShX7AAuuuEGHrvvfprjcSqDQcyuLqzu8NAWLYQQg8QxDMzOToy29mxgCeNYFkogiFZckrnhgoPZ1Exi3TpSu3e/K6wAxC2LOl3noK7TpEDxnNNYsHQJFyxaRGVl1bFr6DvL0XdQNZ3O3LJxnMwKiseLmp+Hu6YGrbAgG1CCqMFsSDmBAYfi1El4yYHVzzzDlOyBL/+M6TiJJK7x49/z8FNpVRUl8+fRfbAWACsUwuzuylxXG4b374UQ4v04ppkJLK1t6IcOZea8OTZq8O2zK1YsRmr7dpI7dpDesyezXX6YqGWxP53mQDrNvnQad3UVS1ecyQeWLWPO7Nm43uN6smMYmYCSne6MkzkHo3i8qD5vf4t9rSD/7ZWUYDCngwjFkSS85MDLzz3H1dmg4pk6DSedxl0x7phvc8bVV3Pwe98DQG9tzXzRxeNo+fnHfDshhBguHMfB6u7OBpZ6rK5uHMtEzcvHXVUFbhdmczPRFzeQ2rETva7u7aZqQNpx2J9KsTudYm8qTbttM3fePM448wxuOn05FRUV7/p4h1/1dfR0ZiXF5Ubx+1AL8vFMnYJWWJgJJ31PchZl2JPwkgN7t27lzv7+LpNBVVALjj0p+pLrr+ez//YtAJxIJDMYLBaT8CKEGPbsRAKjtZV0XX3mSnMqiRrMQxs3DsXlQq+rJfbKKyS3bsV6Rx+rNsdhSzTKrnSK+rSO6nGzdOlSPrZiBcuWnU7eYaNS+ic9JxKZbR+c/kOzrspKXOVlaPn5aHl5qHl5R70KLEYGCS9DzDRNvKEQwerx4HKhlZWBrqMVHTu8TJw0iY5ggLBpUuxyYba1y5gAIcSw5dg2ZkcHekMjxqFDWNEIituTmXjsq0CvrSX20kskN28+YjvIUlVqbZv14W52pVKELRuP18Ppp5/OdWedzbJlS/H5/JlVlVQqOzgxAbaN4nKhBvy4KipwjSvHVVCAWlCAlpcnN3tGGQkvQ6ypqYl5nsy+qWfSJEjrqNl91WNRFIXqufNo2b+fYpcLIxTC7O1FdmCFEMOJnUxiNDeTrq3FbGvDMS20oiJcEydiNjUTWbWKxKZN2D09/W9juVzUqiqvtLayM5VEd8Dl0liydCkf+MAHWL58OV6vL7P9E42Rbm9HcRwUvx8tGMQzaSKu0tJMUCkslLMpY4CElyFWW1vL3GyDH++0adjJJN6ZM47rKt2cpUto2rmTuX4/Zmfnu5ZXhRAiV8zubvRDDei1B7F6ejPXh8vH4aSSJNZvIL52LWZra//jHY+HhoCf5xoa2RGJYGZfPnfuaZx//vmcddZZBDxe7GgUu70dA1B8PrSCArwzpmcO1RYVZaYuy02fMUfCyxCrq6tjSv9h3alg22hFxe/zVhmLlizh5V/8kkshs28cjWGnUqjDoNuhEGLscWwbs72ddG0tekMjdiKBVliIa8J4Ujt20vPkE6R37X770K3LRbi8jJfbO3ilrhYz++LKygrOv+ACVq5cybhgHnYkghPqxPK4UfML8M2dh6u8DFdxMWpBgdyyFBJehlr9vn0syf6WoBYXobhc73vepc+SJUv471QSyF6XjkYzYwIkvAghhpBjGBjNzaQOHMRsacGxLLTSUlSXi9jfXif+5pvYkcPOsVRVsdVx+P327UTq6wFwu12sPPtsLr7wQmbXTMSJRSGVxtFcuCeMx11dnVldKS4etq3yRe7Iv4gh1nngAL6+8JJtfHS8N4amTZtGl8dDwrIIaBpma2vm0G5Z2WCWLIQQADi6jt7URHrfPoy2NlA1tLJSjLo6Is88Q2rHjv7Hqnl5dI4fz58bDrFuw4b+l0+aPInLL76YcxYtxmdbmVb/qoJ7zhzcFRVoZWVoh90gEuJoJLwMMb2uHgDL68XRDVw1NUdMPT0WVVWZfNpptLa0Mk3TMDs6sKJy40gIMbhsXcdoaCC1dy9mezuKx4urtJTE5i3EHnroiLMs2rRp7PC4eXTDBrr37AEyh2/POessrjzvPCaXl6OoGlpBAZ6JNbgrK9HKy6W3ijghEl6GmBrqgGAeSkkJmAauE1w1mb14MU2HGpjm9WJ2dmJ2yaFdIcTgcAwDvbGR1O7dmdDi86MWFRP/2+vEX30Nu2/woceDPW8eL/SE+csbb2CameO35WWlXH3hhXxg8RLyAn60oiI8kyZJYBGnTMLLEIrFYhSkUhDMw1NWlllyLTy+8y59Fi5dys7Hfs95eXmZlZdwdgaInLYXQgwQx8xMaE7t2YPR0pIJLXl5RF9+mfgbb/bPFNJKSojNmc0f9+9nzdNP97/9aTNn8MHzz2fhrNm4iwpxV1fjqanBVVEhZ/TEgJDwMoTq6+upys7a8JaUoAYDaEeZJH0sixcv5rHsoV2jrQ07kcx02j3BECSEEO/kOA5mSwvJ3XswmhozbfR9PqKrV5NYvx4sCwBXTQ3tU6fw242b2P3Y7wFQVYULTj+dy845hynTpuMaV45n6lTc1dVyhkUMOAkvQ6i2tpbq7PkWNRjI9CgIBE7ofZx22mnU2ja6beMxjEyAkfAihDhFZlcXqT170A/W4uCgerxEX3yR+Jo1YGcGF3pmzKBhwnh+9eprHFqzBgC/28WV55zDReecQ8W0abgnTcYzsQZXeblcaRaDRsLLEKqrq+O07JU/1R/A9Y4hYsfD4/EwftYsQj29jPd4MNvasGJxju/IrxBCHMmKxUnv20t63z7sZBLF6yP+SnZ7KLvS4pkzh7rx1fz6xRdpfPllAEqDAa4+9wOcd94HKJk2Hc/0aXjGj3/fbuFCDAQJL0Oo/sABzsmeTdGKCnGd5GrJzEWLaF69OhNeQiHsWPT930gIIQ7jmCZ6fT3J7TuwurtQgkGSW7cSffElMAwAPLNmUT+xhodWr6Z59WoAKvPyuGblSs696CKKZs3CM2Uy7spK6cUihpT8axtCnfsPEOgLLyUlJ7xl1GfB0qXUPrOK5UEyM44OmxEihBDvx2hvJ7VjB/qhQyg+H+n6Q0RXreq/PeSZOpXW2bN4cPVq6l58EQWoKcjnqvNWcs6ll1I4dy7eKZPRSkuPa7SJEANNwssQMhoOAWB5PKiBIMpJnrpfvHgx308lgWLM9jbsaBTHtmV/WQhxTHYiQXLXLtL79uEYBmY4TORPT2GGQgC4KiroXbqE/371Nfa89hoKMD4vyNUrz+cDV19N4fx5eCdNkjN2IuckvAwRx3FwhTqhtDRzUNfrOekrgwsXLmR3Oo3tOKixOGZXF3YiiZYne81CiHdzbBujoYHk9u2YHR04DkT++lfSO3cCoObnY599Fr/cuo11P/9fFKDS7+Pycz/ABR/8IKVLluCdMlnOs4hhQ8LLEOno6KA8O5zMU1qC6vMfd2fddwoGgxROnkK3YVDmdmM0NOIkEyDhRQjxDlYkQmrHDlL794PjkNiyhdhLL2cO42oarrPP5qlQiL8++BC2bVPqdnPpWSu4+CMfoWL5cryTJbSI4UfCyxCpra2lKhtWtMIi1ILjm2f0XmYsWkjLm2sy4aW1FTuVGogyhRCjhGPb6LW1JLdtx+zuxuzqpPfJP2Fnz8h5TpvD+sJCfv3kE6SSKQpUlQ8sXsQV11/P5PMvwDt1ykmfyxNisEl4GSJ1dXX9PV60vDzUE2xO907zly6l6bXXWABY4TB2IjkAVQohRgMrGiW5bRvp/ftxdIPoiy+Q2roNAK2sjI6FC/nx88/R1tpGQFE4d9pUrvzoR5l/xRV4Z8w47mGxQuSKhJchUltby/K+Hi8F+Wh+/ym9v8WLF/NkOtOi2+zuxk7ET7lGIcTI5jhO5vrz1q2YoU70uloiz6zCSadBVeGMM/jf/fvY+Ktf4QbmlpZy1bXXcPbHPoZ/zhxcxcW5/hSEOC4SXoZIfW0tl/Vdky4sOumbRn0WL17M94xseAmHscI9p1qiEGIEsxMJktu2kdq7Fzsao/evqzAO1gLgmjSJNwsLeeTJJ7BMi2qvl0vPP59Lb/kEJcuW4aqslCvPYkSR8DJEOvfvJ5gNL66SklMeTlZaWkqsuCTzH4kERigk16WFGKOMtjYSmzZhtLSQrq0j8swzmeGJHg+RJUv44euv0dbeQYGqcvbCBVx7661MvuACPJMmSXM5MSLJv9ohYjU1gdeH7fGg5uWhnOK2EUD1wgXEdu8hT9MwW1txkkkUuRUgxJjhmCapPXtJbt+O1dlJ7+rVGPv2AaBOnswf0yle+OMfcQMLysv54A3Xs/yGG/DPmiWHccWIJuFlCBiGgbenByoq3+7x4vWe8vudtWABoe3bM+GlvR07mZQrjUKMEVYkQmLzZvSDB9HrD9H79NM4qRS43bTOnsUPXn2VRCJJhcfN5StXcvknP0nx6afjHjcu16ULccokvAyBhoYGxme3jNwlJaj+k+/xcrjZc+bQbJhM8YLZGcJOyo0jIcYCvamZ5KZN6C3NxP72N1Kb3sq8Yvx4Ho1EeOOvz+JTFM6dPo2P3vZJZlx+GZ4pU2SLSIwa8i95CNTW1r59TbqgAHWAriHOmjWLp7KHdq1wj4QXIUa5/m2irVsxGhvoefrP2N3doCg0T5nC99euIa0bTAgE+NCVV3LhbX9P3sKFaKfYmkGI4UbCyxCoq6ujsi+85Oefco+XPrNmzaJez4QXvaurf6iaEGL0seNxEps3k9q7j+S2rcRWvwC2DYWF/NHQeem11/ApChfPnctHbv8kEy+8CM/kSXKIX4xKEl6GQG1tLedp2R4vhQWn3OOlT35+Pr3ZVRyzuxurp3dA3q8QYngxOjpIbNiAXldH9MWXSO/eDUC4upr/2LaV3lSammCQG677EOd9/OP4FyyQRnNiVJPwMgTqa2v5cHavWSsoOOUeL4fTJk+GjhBqOo3R0SHXpYUYRRzHQa+rI7FpE+mDB+l96mnscBg0jdf8Pv5v/XrcwAVz5vB3t99OzcUX4Zk8Wb4HiFFPwssQCB08SN4A9ng5XPXcuURbXyRf0zBaW3FSKRS5AinEiOcYBsmdO0lu3Upy6zaizz0HloWRl8eP21rZd6iXcp+XG6+5hgtuuong0qVoRUW5LluIISHhZQjYzc1QVIzj8WRWXgZo2whg5uzZtD/7LPmahtV3XVrCixAjmp1IkNj0Fsndu4m/9hrJjRsBaMnP53t795C2HVZMncLNt93G5Isuxjdr5oDcYBRipJDwMsgikQhFySQUFaMVFaF4BqbHS5/Zs2dTZ5hM94IZkuvSQox0ZjhMYv16Urv30LtqFWZDAw7wEvD47t14FYVbL7mYK2+5lYIzluOurMx1yUIMOQkvg6yuro7x2d+IXMXFA9bjpc+sWbN4XT98QGNiwN63EGJoGS0txNevJ7VjBz1PPYUTjWG6XPyso4OdiQSTS0v49N/dyLyrryKwaJE0pRRjloSXQXZkj5eBuybdZ+LEiTQ7NgDpzk4JL0KMQI7joNfWktiwgfjGTURXrQLbJux28/81NtBlWlyyeBE3feIWys8+C9+sWSjZc3RCjEUSXgZZa2srFX3XpPPyB6xBXR9VVdErKsC0sMJhrJ6eAX3/QojB5VhW5mDuW5uJv/EG8ddfB2CP4/Cz+joUVeWz113HhR/9CMFly3BXVeW4YiFyT8LLIOvo6GBZ38pLYeGA9Xg5nGf6DNizB80wMNs7cBxHxtsLMQI4uk5i82aSW7cSXf0Cqe3bAXguFuPpnh4mlJXyhZtvZuYFFxBYtkx6twiRJeFlkHV0dFDW1+OlsHBAe7z0qZk/j8jOnRRoGnpLS+a69CCEJCHEwLGTSeIbNpLcspneP/8Fs7ERC3iku4t1iSTnLVrEbX/3MUqXn4F/4QJUjyfXJQsxbEh4GWQ97e0UDlKPlz6zZs+m3TAoOHy6tIQXIYYtKxolvm49ibc20fvkn7DDYZLAT0MdHEzr3H7NNVx+9dUEli7BO326NJ0T4h0kvAwyu7UVAEvTUAe4x0uf2bNns940mIEPM9SBnUhCyYB/GCHEADC7u0msXUd800Z6n3gSJ5mk07L4UaiDhMfD/Z+5k/nnnEPw9NNxV1fnulwhhiUJL4PM0x0GwAkGUb0D2+Olz8yZM3lcN4DMgEYnKTeOhBhuHMMgXVtHats24ls2E3nqaTBN6nWdn3R2Uj6+mvtvuYXqxYsJLF+Oq7g41yULMWxJeBlkgWgU8vMz06QHuMdLn/z8fHqyXXXTHSEsuS4txLBitHeQ2r4dveEQqX37iTz1FDgOO5JJftHdxYozzuCO666jYO5cgsuWSf8WId6HhJdBZJomgXQa8vNx5Q98j5fDWePHQ1cXTiSC3SvTpYUYDux0mtTu3aR278FJpUju3EX0mWcAWBOP8dtwD3933Ye49ryV+OfPJ7BoIYoczBXifUl4GURdXV2UZm8aeQoGvsfL4fJmz4I33sRlmhitbXJdWogcc0yT5KZNJHftRistIfHmm0RXrwbg2UiEvyYTfOkzd3L6/Pn4lyzBd9ppcjBXiOMkXymDqKOjg5K+a9J5eYPS46XPpAUL6LUsAPSWZpx0etA+lhDi2BzbJrltG6k9e3BVVRJdtao/uDze08Nrqsp3v/xlTl+0mMCZZ+KbO1eCixAnQFZeBlFHRwclWuYbkhoIDkqPlz5916ULNQ2zvSNzXXoQP54Q4r2l9u4luW07akkJPY89RnL9BmzH4Xc9YZrLyvnepz9FSWUlweXL8UyenOtyhRhxJOoPolAoRHHfaICC/EENE7Nnz6bJyNw4Mjo6cGS6tBA5odfXk3zrLRS/j57f/Y7k+g2YjsPD3d3Ep8/gW5//B0prasg75xwJLkKcJFl5GUQdHR1MyS4Fa0VFg9r1tqamhpbsgMZkezt2KjVoH0sIcXRGezvxDRtwbIfe3/+B9M6dGLbNL7q7KT/7LD7z0Y/i8vkInn027nHjcl2uECOWhJdBFGpro6DvzEtR0aD0eOmjqiqpkhIwLYzOTmxZeRFiSJnhMIm167AiUXr/8hf03btJ2zY/6+pi0Yc+xPVXXYkTjRJYtkyCixCnSLaNBlG8pQUAG3CVlg1Kj5fDaZMmAaDEYtjx+KB+LCHE26xolMSatRjtbYSfeqo/uPy0u4uLPnUHH/vwh7G7uvEtWIA7+3UqhDh5El4GUaqtDQDb5UIrGPxpsPnz5gHgsiyM7FgCIcTgshMJ4uvWozccovvpP2Pu20fatvl5Tw8fuecfufiCCzGam/HMmIH/tNOkhYEQA0DCy2Dq6gLA8XpRsx1wB9O0BQuI9F2XbmzCyT4vhBgctq4T37iR9P79dD39Z6wDB0jZFr+IRfn41/6ZM888E6OlGU91NcGlSwZ99VWIsULCyyBSeiOZP/3+Qb0m3WfW7Nl0mCYAVkcHjhzaFWLQ9DWhS+/eQ9czf8GurSVlWzyUTHL7/fczb958jJYW1EAQ/7Kl0vJfiAEk4WUQebPnTlx5QdQhaPk9a9YsWrPXpRNtrXLjSIhB4tg2ya1bSe7YQeczz+AcOEjatnnUNLnr299m6uQp6A2HUIMBgitWyAFdIQaY3DYaJLquk59dBXEVFA7JvJK8vDzC2WXpZGsrdlLCixADzbFtktu3k9iyhdAzq2DfPgzb5g+OzWe+/W3KCovQGw7hmTCBwOmn4yopyXXJQow6El4GSSgUokTTAPAUFQ3ZsDW9uBgSCYyubpyUXJcWYiA5jkNq124SmzcTWrUK9uzBdByeVOCOb32HIq8Xs6UF74yZBJctHZKzbkKMRbJtNEgyc40y4UUrKBiy8KLWTMg8E4vJyosQAyy9bz+JTRvpePZZ2LkLy3H4i6rw99/5DkUuF1Z3N/7Fi8hbcaYEFyEGkYSXQXL4aACtIH/Iwktw5iwA3LqOGekdko8pxFiQrq0lsWE9Ha+8grJlKwDPuzQ+8Z3vUoCCFeklsGwZ/sWL5VaREINMwssg6ejooCi7baQO0ZkXgKrFi7AcBw0wmpqH5GMKMdrpDQ3E162n/Y03YM1aAF5WVf7uO98hYFnYsUznXN9c6eMixFAYkvDyk5/8hClTpuDz+Vi6dCmvv/76ez72lVdeQVGUdz3t2bNnKEodMB3t7RRmw4urqHDIfhObPmsW3dmDwkZzE072eSHEyTFaWoivXUv7urVYL70MwDpV5YPf+TY+3cCJx/Gffjo+aUAnxJAZ9PDy2GOP8cUvfpGvfe1rbN68mXPPPZfLL7+choaGY77d3r17aW1t7X+aMWPGYJc6oHpbWnBlv5FpZWUo6tAsck2bNo22bGBJtch1aSFOhdHeQXzNGto3bMT467NoisI2BS769rfwGyZOMkHgjOX4Zs+W4CLEEBr0n6g/+MEP+OQnP8ntt9/OnDlz+OEPf0hNTQ0//elPj/l248aNo7Kysv9Jy65ijBSJ7FwjU1Vx5Q/+aIA+RUVFdKuZb6LRxkYcGdAoxEkxu7pIrF1LaOs2Ek8/jVtR2Aec9c1vkoeCHY8RWL4c36xZElyEGGKDGl50XWfTpk1ccsklR7z8kksu4c033zzm2y5evJiqqiouvPBCXn755fd8XDqdJhKJHPE0HBgdHQA4bjdKYGg7aybzCwBId4Zk5UWIk2D19BBfu5buXTvpeuwx/IpCIw6L77+fAp8fK9yNf9EivDNn5rpUIcakQQ0vnZ2dWJZFRUXFES+vqKigLTu08J2qqqr4+c9/zuOPP84TTzzBrFmzuPDCC3nttdeO+vjvfOc7FBYW9j/V1NQM+OdxMpTubgAcvw/V7x/Sj+1k/76d3oiMCBDiBFmxGPF16+jdt4+GX/2aQkUhZNvM+OpXKSwowGhrwzd3Hv5582TFRYgcGZImde/8Ancc5z2/6GfNmsWsWbP6/3vFihU0Njbyve99jw984APvevxXv/pV7rnnnv7/jkQiwyLAuKJRcLlRAwEUz9Bem/RNmwqNjWiJBJZsGwlx3OxkksS6dcT272fXz/+XSUDUtqn4/OcprazCaGrEN2sWgcWLUEbYVrYQo8mgrryUlZWhadq7Vlk6OjretRpzLGeeeSb79+8/6uu8Xi8FBQVHPA0HvmyDOFd+wZDMNTpcyYIFAHhsGyu7AiSEODZb14lv2Eh83342/OznTHIc0o5N4O9vpWrWLPSmJjyTJxM4fZn0cREixwY1vHg8HpYuXcrq1auPePnq1as566yzjvv9bN68maqqqoEub9AkEgkKbBsY2tEAfSYvXkzatlEB/dChIf3YQoxEfROiU3v28Oovf8lMw8ByHLjuOiYuPwOjuQlPVRWBM85AHYIJ8UKIYxv0baN77rmHm2++mWXLlrFixQp+/vOf09DQwJ133glktn2am5v59a9/DcAPf/hDJk+ezNy5c9F1nUceeYTHH3+cxx9/fLBLHTChUIjSvrlGxUVD/lvatOnT2WKaTPB4SDY24ej6kAcoIUaK/gnRu3bz0u9+x4JYDIDU+ecz6+JLMFpb0fLzCSw/HS0vL8fVCiFgCMLLDTfcQFdXF9/4xjdobW1l3rx5rFq1ikmTJgHQ2tp6RM8XXde59957aW5uxu/3M3fuXJ555hmuuOKKwS51wIRCIYpd2dEA+UM316hPWVkZIcdhAhCpr6cqlUKT8CLEuziOQ3L7dpJbt/L6M88wt6UFFIXeefOYe/31mOEwAIHly3GVleW4WiFEnyE5sHvXXXdx1113HfV1Dz/88BH//eUvf5kvf/nLQ1DV4Dl8NIBWOHSjAfooikI8EADLItHaip1MoQ2Ts0BCDBeZCdG7SG7ewvo332TS9u1omkZ4/Hjm3fUZ7HgcOxohcMYZeIbBJQAhxNtkttEgCIVCOQ0vAGZpaebPcBgnJTeOhHin9P79JDdtYseOHRS+8ip+TSNcUMC8r3wZRzcw2tvxzZ2H77Dbj0KI4UHCyyDoam7Glx0HoJWW5uRKpTv7m6Iai0mjOiHeITMhegP1jU3oTz5JsctFxOPhtH/9F1BUjKYmvDOmE1i4YMhGewghjp98VQ6CWFMTABbgKi7KSQ0Fp80BwKPr2IlETmoQYjjqmxDd1d1N00MPMcHtJqGqTP/aP6MGghhNTXiqqwksXSYH3YUYpiS8DIJUtq+N7XahBod2NECf6mXLAPCSGS4nhIB0XR3xN98kEY+z+cc/YYbLhQ5UfeHzeMrHYba1oRUWEDhjOVpebr52hRDvT8LLILA6OwGwPV5UfyAnNUxbsICYZQGQrK3FcZyc1CHEcJE+cID4mjVYlsWrP/4x8wHLcci7+WbyZ8zEzDZ0DJx+Oq7smTEhxPAk4WUQqD09mWf8/pwtO1dWVtJhZ8JL+OABHF3PSR1C5JrjOKT27iW+di24XDz/v79gSXZshnPZZYxbsSJzsygWxb9ksdwsEmIEkPAyCDzxOABaXt6QzzXqoygK0WxwijU24ciMIzEG9V2HTqxbh+Lz8/rjj7OgtRWA6KJFTL72Whxdz9wsOm2u3CwSYoSQ8DLAHMfBn0oD4CkqHPK5RodLFxYBoIdCcuNIjDmOrpN86y0SGzai5uWz4803mLx5C5qi0DVhArM/dQeOZaE3NeGdPo3AooVys0iIEUK+UgdYLBajMPu8t7gkp7cVlKrKzDORXmxZeRFjiBWLE1uzhuSWLWglJTQf2E/gL8/gUVXa8vNZ8JUvg0NmZlF1NYFlp8vNIiFGEAkvAywUClGSHQ3gLi7O6fTZwLRpmTqSKRxZeRFjhBkKEX/tNdL7D+AaP4FYZyfxXz5IQFVp0TQW3vd1FM2VuVlUIDeLhBiJJLwMsI6ODoqzTelcBUM/1+hw5YsWA+CzLKxYPGd1CDFU0nV1xF55FSPUgWfSJMx4nMbvfY98RaHNtpn1L/+C2x/I3CxS5GaRECOVhJcBdvhoADVHowH6TD7zDGzHwa0opBoO5awOIQabY1kkd+wg/rc3sE0T94QaHF1n/ze/SZFt02VZlP/D5yisqMjeLIrhXyw3i4QYqSS8DLBQayv5fSsvJSUoriGZfXlUE6ZMIZzt9dK1cxeObeesFiEGi51KkVi3nsT69ah5ebgrKsDQ2f+tb1GYShGxLMyPfIRJc+e9fbNortwsEmIkk/AywHobGwGwAa0st8vRmqbRkw1PvXV1OOl0TusRYqBZvb3E/vYGqV07cVVUohUW4pgGDT/8L4Ld3SQsi9rlp7P04otxbBu9uTlzs0hmFgkxoslX7wBLtLQAYKkqWo5GAxwuGch0+E21tcp1aTGqGB0dxF59FaPhEO6aiah+P45t0/6LX6DV15O2bV6pqODK227LPL65CXdlBYFlMrNIiJFOwssA09vbAbA9npzNNTqcXV6e+bM7LI3qxKhhdnWRWLMWszuMe+IkFLcbB4fu3z6KuW07puPwOA4f/6evoCgqZkcHqt9PYNnpaHl5uS5fCHGKJLwMMKcrMx/F8flyek26j2fSRADUeFxWXsSoYPX0EF+zBrO7G/eECf3bP5E//Ynkm2uwHYdHo1E+9s9fIxAIYkWjOHqawLJluCvG5bh6IcRAkPAywFyRCABKMDAslqaL58wBwGea0qhOjHhWNEr8zTWYHSHcNTX9wSX28ktEn18NwO96wqz8zJ1MnDgRO53G6uzEt2ABnilTclm6EGIASXgZYJ5kAgBXXv6wCC9Vy5cD4HccrL6BkUKMQHY8TnztWoy21iOCS2LTJnr+8EcAnurtpeLSSzn77HNwbBujuRnPjBn4585FUZRcli+EGEASXgZY0DABcBcVobhzH14mL12KYdtoikJox45clyPESXF0nfi6deiHGnDXTETJtiNI7d1L98MPA/BqLEbTxBpu/sQnADBaWnBXjCOwZPGw2MIVQgwcCS8DKJVKUZj95c5bUpKzidKH8/p8hLPPd+/ajZPt+yLESJLatw+9rg5PTU1/cDGam+j62c/AsticSPCcY/OlL30JTdWwenpQ3C4CS5fKAV0hRiEJLwMoHA5TomX6qnhLS3M6UfpwMa8XgHhTE3ZSDu2KkcVobye5fQdacUn/CorVEyb0Pz/CSaXYl07zcE+Yf7z3XkpKSrFTKaxwGP+CBbirq3NcvRBiMEh4GUDd3d0UaZm/Uq0wt3ONDmcUF2X+7AzhpOTQrhg57HSa5JYtOHoaragIAMcw6Pz5/2JHIrSaBj/v6uTD19/AwoWLMudcWlrwzpyJb/bs3BYvhBg0El4GULi7mwI1OxqgsGjY7LMrlVWZZyJRuS4tRpTUrl3ojU24q8cD4OAQfuz/MOrrSQA/6exk+rz5fOxjHwPAaGnGXVWJf/Hi/u0lIcToI+FlAPW0t+PO3oDI9WiAw+VNnw6AN5WURnVixDCam0nt2oWrvLw/iMRf/xuJN9dgA78MhbDz87n33ntRVTV7zsVNYMkStLzcN4gUQgweCS8DKNbaCoAFqMXFuS3mMOWLFgLgtyxZeREjgp1IkNiyBcey0fLzAUjXHqTn978H4KneHvboae75x3+kqKgIR9cz51zmz8ddVZXL0oUQQ0DCywBKZEcDmKqClp0pNBxMXLECgICq0Vt/KMfVCPH+Unv3Yba19QcRq7eHrp//L1gWW3Wd1dEYH/7wh1m4YCGO42C0tuCZOkUmRQsxRkh4GUDpzk4ATFVDzd7wGQ4KJ0wg6dgAtG3enONqhDg2MxwmvW8vWkkpiqbh2DZdv3wQOxKhS1V5ONTBzJkzuOmmmzKPD4XQ8vPxL1o0bM6ZCSEGl4SXAWRk5xpZHs+wuWkEoCgKvdmDxJHagziGkeOKhDg6x3FI796DnUigFRYCEHvpJfQDBzBVlf9paUb1+bn3S19C01zYiQROKoV/yRJcw2irVggxuCS8DKS+9vsez7D7DTCVbdSVam2Tcy9i2DLb20nXHsRVlpmGbrS20vv00wA81tVFh2lx1113UVlRiWNZGG2t+GbPwjN5cg6rFkIMNQkvA0iJxTLP+P3DauUFwC4ry/wZ7pYBjWJYcmyb1O5MF2g1GMSxTLp/9SswTfZZFm/E41xwwfmcd955QCbYuKuq8C9Y0D/nSAgxNshX/AByJzJDGdVAYNitvHgmTQLAFc8sswsx3BhNTeiHGnCNqwAg8txzGA0NpFWVh9rbqays4NOfvhPITJdWNJXAokWow+hwvBBiaEh4GUCedBoALS9v2IWX4tPmAODTdRkRIIYdR9dJ7dqFomUOu+sNDURX/RWAR0MhIjjcc889+P1+HNPEDIXwnXYa7vHjc1y5ECIXJLwMIF/2IKy7sADF5cpxNUeqPv10APKAZDh87AcLMcT0Q4cwWlpwjRuHYxqZ7SLbZpuhszGZ5KMf+QizZ2cCuNHSgqdmAr7TTstx1UKIXJHwMoD82evI3qLiYbfyUrFoEQBeTaNt27bcFiPEYexkktSu3SiBIIrbTeTZ5zBbW0koCo+EOpk2bWp/+3+rpwfF68W/aPGwakcghBhaEl4GSDKZpEDJ/HX6y0qH3cqL5vcTzT7fuWMHjuPktB4h+uiHDmF0hnCVlWGGQkSffx6A33Z2ors07rnnHlwuN45hvN1Ft2JcjqsWQuSShJcBEg6Hyc/eePBXVOS4mqOLZ39TjTc24uh6jqsRIjMGILV7D1p+AagK4d8/BqbJnnSat5JJbrn1VmpqJgKgNzfhmTwJ36yZOa5aCJFrEl4GSLizk2A2vLhLSnJczdHpRUVApiOpDGgUw0G6rg6zqwutpITU1q2kd+7CAv4vHGbRooVcdeWVAJnH5OVJF10hBCDhZcD0tLSgKgoAWunwmSh9OC07J0aNRKRRncg5Ox4nvXcfWkEBmAbhP/wBgNWRCDGPm89//vMoioqt69jRKP4FC3AN068tIcTQkvAyQKItLQDogBoM5raY95A3fTqQudItjepErqXr6jG7u9FKSoj89Vns7jDdlsWz0Qif/OTtlJWV4zgOZksznilT8Gb//QohhISXARJvawPAUBTUYdZdt0/5wgUABGwLM57IcTViLLNicdJ796AVFmYO6a5eDcAfesLMW7KEiy6+KPO4ri7U/AL8ixYOu0PwQojckfAyQFKhEACWpg3bb7LVy5cDUKBqtB48kONqxFiWrqvF6ulBLS6i5/e/B9tmRzLJAVXlHz73ORQU7HQaO5bdLpKhi0KIw0h4GSBmZycAlss1bA8U+iZMwMJBUxQ6pNeLyBErFkPfuxe1sIj0jh2kd+/GcBz+0NvDJ2+/ndLSssx2UWsLnunT8U6fluuShRDDjISXAWL39Gb+9HjANTzDi6JpRFUNgMj+Azi2neOKxFiUPnAAq7cXNT+Pnj/+EYAXo1EmLVrEhRdeCIDV2YlWUEBgwQIUTctluUKIYUjCywBRopHMM34fint4bhsBpPLyAEi3tsiARjHkzHA4c8OouITYyy9jdXbRY5m8bll89rPZ7aJUCjsRx79wIVr2er8QQhxOwssA0WJxABT/8JsofYSyMgCc7rBclxZDynEc0nv2YMdioEAkO3jxT7293PT3t1JaWprZLmprxTNtOp6pU3NcsRBiuJLwMkDcfROlg8FhHV58kzLdSl3xuDSqE0PK7OggXVuLa9w4ep96CnSdunSa5NRpXHzJJQBYoRBaYSGBBfNlu0gI8Z4kvAwQb3aitKtg+E2UPlzRnMxkXr9hYCXkurQYGo5tk9q1G8cwMEMhEmvXAfBkPMbn/uEf3t4uSiZku0gI8b4kvAwQv2UC4CkqGtbhpWrZMgAKVJWu5pYcVyPGCqOxEf3QIbRx4+j83W8BWBOPc87111NVVZW9XdSKd/oMPFOm5LhaIcRwJ+FlgASyQ5r9paXDetsoOGsWAHmaRvOunTmuRowFjq6T2r0bRdNIb92K3dhEyrbYWlzMtR/8IJDdLiouxi/bRUKI4yDhZQAkk8n+idLBysocV3NsrpIS+uZJh3dIeBGDTz90CKOlBbUgn9BjvwfguVicT37h82iqltkuSiXxL5iPVliY42qFECOBhJcB0N3ejq8vvIyvznE1x6YoCnGvF4BEQwN29qCxEIPBjsdJ7dqNEgjS/fSf0VIpWg2DgosvYsqUqTi2jdHaglduFwkhToCElwHQ09gIgOU4aEXDv425mZ3Ma4VCcuNIDBrHcUju2IER6sBOJEi98QYAzytw/cf+Dsh0pnYVl+BfuABFlW9HQojjI98tBkCkuRnITpQO+HNbzHFwT5gAgBaNynRpMWiMhgbSe/fiKh9H+69/hQKsT8S5/M478Xq92MkkTiqFf9FCtIKCXJcrhBhBJLwMgHhrK5CdKD2MD+v2KZg1EwBfOi3XpcWgsGJxklu3guYi8dZbqG3tJCyLplmzWLJkaWa7qK0N74zpeCZPznW5QogRRsLLAEi2dwBgaOqwvmnUp2Jp5rp0oaIQbm3LcTVitHEch9SO7RihEErAT9fjjwPwXCrFzXfeCYAZCuEqKca/QLaLhBAnTr5rDACjMwSArblgGPd46VNwWqZRXYGm0SjXpcUAMw4dIrV3L+6KSkKP/R6XadKg60z76EcpLi7JbBel05lmdPn5uS5XCDECSXgZAFZ3d+ZPjwfF7clxNe/PPWECJqApCt07JbyIgWPFYiS3bkNxe9Bra7G2bMF2HN7Iy+OyK67I3i5qxTtzhmwXCSFOmoSXgRCJZv70eof1ROk+iqoS92RCVqK2DkfX3+cthHh/jmmS3Lo1u10UoP2hhwB4NR7nw5//B1RVxezowFVWKttFQohTIt89BoAaj2WeCQzzidKHMUoyV7qtUEhuHIlT5jgOye07SO/Zi6u6ivDvfoeWTNJqGOhnn8XUqdOwEwkcQyewaBFaXl6uSxZCjGASXgaAK5UCQA0GhvVco8O5qjLN9NRIBDtbvxAnSz9wgOS2rWhlZaS3biW9dSum4/CEYfCxj388s13U3oZv1izckyblulwhxAgn4WUAePTMRGktv2DErLwUZGccedNp7LhclxYnT29qJr5xE2ogCIZO9+/+D4BVkQgX3/IJgsE8zLY23OPG4Z8/H0VRclyxEGKkk/AyAHyWBYC3sHDErLyMW7wIgEIg3C7XpcXJMbu7SWxYD5aFVlJM169+DbpObTpN44QJnH/++VixGNg2/kWLUIPBXJcshBgFJLwMAL9tA+AtKR4RV6UBCubOBaBQ02jctTvH1YiRyIrFSKxbh9nTg6uqitgLL6Dv30/atvl1T5hPfeZOsGysUAfe2bP7OzsLIcSpkvByihzHIZhdBg9UVI6YJXHPpElYgFtV6dy5I9fliBHGisWJr1mD3tKKZ0IN6d276f3TUwD8sbeHMy67jCmTp2C0tuCqrMQ/b+6I+doQQgx/El5OUaKzE1f2m3LeMJ8ofTjF7SaRPZ+TqKvDMYwcVyRGikxweRP9UAOemhqs7i66HnwQHIc34zF2uj3ceOONWD09KG43gSVLUAOBXJcthBhFJLyconBDAwCGbZNXUZnjak6MUVQEgNneLjeOxHGxYnHia9dmgsvEiTimSecDD+AkEtQbBv/X08Ott95CwO3BCofxz5+Pu6oq12ULIUYZCS+nqLexEYC046D6fTmu5sRo1dnr0r292Anp9SKOzY73BZdDeCZOBE2l+1cPY7a2kdA0fhYKMXXmTFauXInR0oxn6hR82VttQggxkIYkvPzkJz9hypQp+Hw+li5dyuuvv37Mx7/66qssXboUn8/H1KlTeeCBB4aizJMSbWoGwFBVVM/wHw1wuLwZ0wHwptI4SbkuLd6bnUgQX7MWvb4eT00NistFZNVfSW3dhqOq/Ki1hV7b5lOf+hRWZxdaYSH+RYtGTOsAIcTIMujh5bHHHuOLX/wiX/va19i8eTPnnnsul19+OQ3Z7ZZ3qqur44orruDcc89l8+bN/PM//zOf//zneTw7mXa4Sba3A5nwMlJuGvUZt2gxAAVAOPt5CPFOdiJBfO1a0ofeDi6JDRuIPvMMAKtdGvW6wQUXXsD08RNwUin8ixfjKi7OceVCiNFq0MPLD37wAz75yU9y++23M2fOHH74wx9SU1PDT3/606M+/oEHHmDixIn88Ic/ZM6cOdx+++3cdtttfO973xvsUk+KHspMlDY1bcT9lpk/9zQAilSVxj17clyNGI7sVIr4uvWka2vxTKhBcbtJ7d1L969/DUB4xgz+VFuHz+/jEzfdhNnWim/2LBm6KIQYVIMaXnRdZ9OmTVxyySVHvPySSy7hzTffPOrbrFmz5l2Pv/TSS9m4cSPGUW7EpNNpIpHIEU9DyQpnJkrbbveICy+eKVOwAa+m0SHTpcU72Ok08XXr0A8ewFMzEcXtxmhuoutnPwPLwrNwAd/fshmAGz56PcF4HHdNDf6FC2XoohBiUA3qd5jOzk4sy6KiouKIl1dUVNDWdvSurm1tbUd9vGmadHZ2vuvx3/nOdygsLOx/qqmpGbhP4Dg4vb0AWF7viAsvms9HMrvVlThwECfbKVgIW9eJr1uPvn8/7uyKi9XdRehHP8ZJpfBMn85zHi/d4R4qqyq5YsUKXPn5BJYtQ/X7c12+EGKUG5Jfj97ZnMpxnGM2rDra44/2coCvfvWr9Pb29j81Zm//DBUlHs884/ePmNEAh9MLCgAw2tuwk3JdWoBj2yS3bCW9bx+uCTUoHg92Ik7oxz/G7u3FVVWJ9aEP8eSf/wzAp266CZfj4F+6FFdpaY6rF0KMBYP607asrAxN0961ytLR0fGu1ZU+lZWVR328y+Wi9CjfGL1eL16vd+CKPkFaMnPFWA0ERtzKC4BaXQXd3ag9vZkbR3kye2asSx84QGrXLtyVlageD45p0Pmzn2O2tqEWFlL+2c/ynz//X0zTZOnChcyfUINv/nw55yKEGDKDuvLi8XhYunQpq1evPuLlq1ev5qyzzjrq26xYseJdj3/++edZtmwZ7mEYDtxpHQAtP39ErrzkTZsGgCeVwk5Kr5exzmhvJ7l5M2owiBoI4ODQ89hj6Pv3o3g8lH/2s+xta+PNN99EVRVuvfxyvNOnSft/IcSQGvRto3vuuYdf/OIXPPjgg+zevZu7776bhoYG7rzzTiCz7fOJT3yi//F33nknhw4d4p577mH37t08+OCD/PKXv+Tee+8d7FJPitc0AXAXFIzIlZfyRYuA7HTp9ziHJMYGKxYnsXEjdirVv/0Te/El4m+8CYpCye2fxDW+ml/88pcAfPjcD1CzcAGBpUtH5L99IcTINehLBTfccANdXV184xvfoLW1lXnz5rFq1SomTZoEQGtr6xE9X6ZMmcKqVau4++67+fGPf0x1dTX//d//zYc//OHBLvWk+LPncTzFRSOuzwtA/mmn0U32uvS+/VQsX57rkkQOOKZJ4q23MNra8WS/NpPbttGb7a9U9OHr8M+bzyuvvMyB/QeoCga48oPXEjj9dLT8/FyWLoQYg4bkp+1dd93FXXfdddTXPfzww+962Xnnncdbb701yFWdOsc06btX4R9XMSKXzb3ZbSO/plEn16XHrOSuXZmbRdXVKKqK0dxE94MPAhA85xyCF1xAOp3m17/+NUFV5YMXX0zlypW4K0fWPC8hxOggzRhOgZm9Jg0QrB6Zw+e0vDyS2Z4c8f375br0GGR2dpLauQutpATV68WKRQn99Kc4uo5n1iyKbrgeBYWnnnqK3s4uZpaVcfFdd+HJBl8hhBhqEl5OQSJ7RiRtWRSMG5fjak5e/3Xp1lbshMw4Gksc2ya5azdOKolWWIiDQ/jRR7G7w7jKyym7/ZMomotwT5jH//gHJng8XHDLJyhatkwa0Qkhcka++5yC8KFDAKRwCJaM3P4WSnbpX+3pkfAyxhjNzeh1tbgqMv8GEm+uIbV1G2gapXfcjhrMA+DRRx6hxLLInzSJy+6+G2WEDSEVQowuEl5OQaypCQAdBdUzcm9b5E3PTJd2JZNYsViOqxFDxdF1Ujt3oqgaqs+H2dVJz+9/D0DB1VfhnpDpVt3Q0MCGl17GcBxu+Mb9uLIrdUIIkSsSXk5BojWzbaSryoi+Klq+aCEARUBXNpCJ0S9dV4/R0oKrogLHtul+6OHMOZdp08i/6OL+xz360EMUKAplZ53FWVdfncOKhRAiQ8LLKUj3T5R2obhGbnjJmzsXgGJNo0FuHI0JVixOatdO1LxMc8Xo6tXotbUoXi8lt97Sf55l+7attG3fxkHT5PPf/36OqxZCiAwJL6fAzE6UNl0ulBG8beSdORMbCGgaoZ07+2dJidErvW8vZlcXWkkJRmMDkb/8BYCi66/HVVoGgOPY/Pmhh2g3TZbe+HfMmjMnlyULIUQ/CS+nwO6NAOB4PCN620gLBklm60/U1eHIod1RzezsJLV3X39I6fr1b8Cy8C9aSGDFmf2PW7N6NfWHGtinqnz1G9/IVblCCPEuEl5OgZM93Op4vSNyrtHhzNISAOz2DrlxNMqlDx7ESSbQCgtJrF2L2dyM4vdTdOONKGQaLerxOM//8Y9sSyX5xD/+43sOUhVCiFyQ8HIK+iZKK8HAiA8vnokTAXBFoxJeRjGrtxe9/hBaSSmOnqb3z38GoOCyy9Dy3m7z//oTj7OxrY3e4mLuueeeXJUrhBBHJeHlFGjpdObPQHBEbxsBFM2bD0DAMEiFe3JbjBg0emMjdiyKmp9P9KWXsHt70UpKyFu5sv8xsZZm/vT882xPpfh/999PMBjMXcFCCHEUEl5OgdswANDy80d8eClbshiAUk2jac/uHFcjBoOdSpHefwA1vwA7GiX67HMAFF57bf+/X8c0eempp1jf1UXFjBncdtttuSxZCCGOSsLLKfBm5wC5CwpG5ETpw/myN0kKNI2WHXJdejQympqwwt1oxcVEVj2Do+u4J07Ev2xp/2O69u3j/156mQO6zre//W1cI/zftRBidJLwcpIc28abfd5bXjYiJ0ofzl1dTUpVUBWFyL592NktMTE6OKZJ+sABFK8PszNE/G9vAFB43XUoSubbgBWL8dzq59kU6WXJ8uV88IMfzGHFQgjx3iS8nCQrGu3/y/OP4KGMfRRFIZ09sGm0tGDH4zmuSAwko60No60dV2kpvU/+CWwb37x5+GbOBDJhvH33bh568SVaTZPvfve7Iz6QCyFGLwkvJ8nq6gJAt22CoyC8AFBVBciAxtHGcRzStbVA5sBuats2UBQKP/Sh/seYHR088fJL7EjEufTSS1l52AFeIYQYbiS8nKS+0QBpxyG/dOROlD5cMPtbuCeZxJKVl1HD6uzEaGzCVVZG9PnnAQisOBN3Nqza6TRNdbX87KWXSDgO3/72t3NZrhBCvC8JLycp2pgZYJh2bPKLS3JczcAYlz24WQR0NzbmtBYxcNL1h3DSKaxolNT27QDkX3xJ/+vNjnZ+s3o1jYbBDTfcwJIlS3JVqhBCHBcJLycp1toCQMoBt8/7Po8eGQrmZ3q9FGsaTXLjaFSwYnH0+nq0omJiL74IgG/+fNzZjrl2MsnB2lp++8YbqC4X//Zv/5bLcoUQ4rhIeDlJyY7MtpGhqiO+u24f77RpmIBbVenatQsn28dGjFxmWyt2pBdHVYivXQtA/kUX9b/eaG/nF6tW0WKa3H777UyfPj1XpQohxHGT8HKS9OyBXVPTRk14Ub1eEj4fAMmGQ3LjaIRzbJt0fT2K10f89b+BaeKeOBHPjExAsWIxdh/Yz5ObN+Pz+fjXf/3XHFcshBDHR8LLSTJ6wgDYLteIb1B3ODN7+NjpCMmNoxHO6urCbG9Hzc8j/uqrAORfdGH/8EUz1MEDf3mGTsvic5/7HNXV1bksVwghjpuEl5Nk90Yyf3rco2blBcAzZTIAWjwu4WWE01tasFNpklu3YcdiqCXF+LOHca3eXrbu3ceqXTvJz8/nK1/5So6rFUKI4yfh5WTFY5k/vb5RFV5K5i8AIGgYpHt7c1yNOFm2rqPX1aHmBfsP6uaffwGKquE4DkZniB89/TQ9lsXdd99NWVlZjisWQojjJ+HlJCmJZOYZ3+gKL+OWLQMyAxqbd8mAxpHKbGvD6unBaG7GbG9H8fkInn0WAFY4zIbde3hh/z6Ki4u55557clytEEKcGAkvJ0nTdQCUvOCoOvPin3saAAFNo33nDpzs8EkxsugNDYBC7JXMWZfgOeeg+vw4joPe1cl/P/UnYrbNV77yFQoLC3NbrBBCnCAJLyfJbWTCizuYN6pWXlxFRcS1zD+L6P4D2MlkjisSJ8qKRDCam3FMA33fPlAU8s9fCYAdibBm2zbW1NdTUVHB5z73uZzWKoQQJ0PCy0lwHAe3ZQPgKihA0bQcVzSwUtnfxI22NrkuPQIZra1Y0RiJzVsA8M2bh5btAp3s6OCnf/4zEdvma1/7GsFgMIeVCiHEyZHwchLsRAJP9nlPUdGo2jYCUKrHA6D29kp4GWEcy0Kvq0PxekiuWwdA8OyzAbDjcd7csIFNLS1MnDiRT33qU7ksVQghTpqEl5NgdXX3P+8vL0NRlBxWM/DyZs8CwJtKYUUiOa5GnAizsxOzI4TR3JK5Hl1QgG/eXAASra089NdVdFkW//qv/4rXOzrGWgghxh4JLyfBDGca1KUsi0BRcY6rGXiVy5cDUOA49NTX57YYcUL6zrok1q8HILhiBYqqYadS/O2NN9jU0cHUqVO55ZZbclypEEKcPAkvJ8HqzowGSNo2eSWjL7wULVqU+dPlonnXLpzszSoxvNnpNPqhQ2DbpHftAiB41goA4s3NPPL8c7SbJv/v//0/3G53LksVQohTIuHlJKQ6OjJ/AvnZdvqjiXv8eNKAqiiE9+zBisVyXZI4DmZ7O1ZPD4mdmeDimTkTV/k4HMPg9VdfZUtXF9NnzOCmm27KcaVCCHFqJLychFhrGwBp2yZQWJTbYgaBqmkksrdQkg2N2BJeRgS9qQmAxLrM9Oi87EHdWHMzv3/xBVoMg69//eu4RtkBcyHE2CPh5SSkQpmVF11VcHk97/Pokcmqqso8092NFY3mthjxvqxYDKOpCTPUid0dRgkE8C9ahGNZvPr882zt7mbGnDl87GMfy3WpQghxyiS8nIRU9raRpWqj7pp0n7y5mRsqnkQCqzuc42rE+zFbW7EiURJvvQVAYPlyFLebaEsLT7/yMk2GwX333Yc2ynoSCSHGJgkvJ6HvtpHlHl0TpQ9Xfe45AJQqCj0Nh2RMwDDmOA7pQw04lklq+3YA8rJzjF555hl29fYyY+5cPvKRj+SyTCGEGDASXk5CX+8Tx+UateGlZOlSbMchX9No2bVLmtUNY1Z3N2Z7O/qBg2BZuCdNwj1+AtFQBy+89irNhsH999+PqsqXuxBidJDvZiej7we51ztqw4urtJRYdoshsnevHNodxozWNuxUsn/LKLjiTABeeOIJ6mIxJsydywc/+MEcViiEEANLwstJUPqGFfp8oI3O8KJ4PCSzM4707KwcMfw4poleX4cdi2E2N4OmEVi6lEhPmDdee516Xefr990nqy5CiFFFvqOdIMe2UdNpAJSAH8U9OsMLgDppEgBKby9Wb09uixFHZYZCWF1dpPbsBcA/fx5qMI/n/vg4bfE45XPmcO211+a4SiGEGFgSXk6QY5q4TBMALS9v1G4bARQuWghAIK1jdoRwHCfHFYl3MlpasE2T5KZNAATOOINoNMKGl1+iztD5Z1l1EUKMQvJd7QTZuo7LtgFw5+ejjOKrpxPPPx+AElUl3NSI07ddJoYFO5VCP3QIsyOEHYmgBgL45s7lmccfpyeZomjmTFl1EUKMShJeTpATjdK31uIuLIJRPCMmf/Zsko6DS1Ho2L5Dzr0MM2ZbG1ZPD8ldOwHwL1tKLJlk3fOraTUN7v7612XVRQgxKsl3thPU3+PFcfAXFY7qbSMtL4+o1wtArL4eOy7hZThJNzTgWBaprdsACJ5xBk8/+SRGOo1v6lSulRtGQohRSsLLCTKz3XUTto2/oABlFP9mq2gaqbLM4EkjFMLqjeS4ItHH6unBaG5Bb2wCXcdVXk6qtIy//fVZwpbFnf/yL7LqIoQYteS72wmyezIrLynbJlhUlNtihoB7xozMn9EoZldXjqsRfYy2NpxEnOTWLQD4z1jO008/hdswcE+ayDXSTVcIMYpJeDlBfdtGKcchr7g4x9UMvnHLzwCg0LIww2FsXc9xRcKxLNK1tTimhb53X+aF8+bx/J//Qtq2+cS998qqixBiVJPvcCco2RECIG3b5JWU5LiawTf5gvOxHIeAqtJ98IB02h0GzFAIq7OT9IH9AHimTWPVG2/gMwwC46u56qabclyhEEIMLgkvJyjR0QFAGvAVFOS2mCEQqKykR1EA6N61GzsazXFFQm9swjZNEhszvV1cixbx9NNP41dVrv3MZ9BG8SFyIYQACS8nTO/OnPuwNA3V7clxNYNP9fuJ+f0AJJqbsWTlJafsZBKj4RBOIoHZ2gqaxkutrZBMkV8xjstk1UUIMQZIeDlBZk8PAJbLNapHAxzOGF8NgNPdjSWHdnPKaG3D6o2Q3LUbAPfc03hi1TMUaxoX33gj7jFwDksIISS8nCArktk2cVyuUd3j5XDBufMA8CaTmN3dONnxCGJoOY6DfqgeVIXkhg0AbHcgHotTVVHBhTfemNsChRBiiEh4OQGObeMkEpnnvd4xE16qP3AuAAWOgxEOY8m5l5ywenow2toxOzuxo1GUQIBfv/E3ClSV86+6Cm9VVa5LFEKIISHh5QQ4hoGSTgGgeD0wRsLL1DNXELMsNEXJHNrt7c11SWOS2dqa7e2S6ajbWlJMTyTK9MoKzv7wdaiBQI4rFEKIoSHh5QQ4homSzvQ5Uf2BMbPy4i4soDs7gLKnvg4z3JPbgsYgxzBIH6wFl5vkli0APL53Hy7goksuwT9xYk7rE0KIoSTh5YQ4aNnzHmowOKonSh9OcbmIFxYCkGrvwOxoz3FFY4/R3o7Z1YXe0ACGQSrgZ2c4zPTKCpZfeCGuceNyXaIQQgwZCS8nwLFtXLYNgCs/b8xsGwEweRIAak8PVm8vdjye44LGFv3QIcAhsXEjAK9nb71dc+GF+KZNQxnF082FEOKdJLycADse7/8LcxUUjqkfGIVLlgJQoOvYsRhWRIY0DhWrpwejsRFUDX3vXgBe6+5mfHk5S1echUcO6gohxhgJLyfAzv7A1m0bf0H+mDnzAjD9kotJWRYeINXSKuFlCBktLdjxOMmdOwCosyy6TIuPXnopvsoKtNLSHFcohBBDS8LLCej7gZ20bQJ5+WPmzAvAhBkzaHMyW2Zd+/ZhhkI5rmhs6DuoqwSDJNdneru8GemlpKSEMxYtwjN5MooMYRRCjDHyXe8E9K28pByHQDA4ps68qMEgkfx8AOJNjZihEI5h5Liq0S9zULcTJx7HbG3FcBzeSia5/tpr8BQW4KqoyHWJQggx5CS8nIC+5mxpxyFQVIiSHVg4FiiKgjV5CgBqqBM7kZBmdUNAr68HILEpM4RxezKJt6CQlUuW4Cofh1ZUlLvihBAiRyS8nAAjHAYgbdvkFZfkuJqhV3TmmQDkGQZWJIIlzeoGldXTg9HUhJpfQGLdegDWJuJ86IMfRLNtvJMmjqkALYQQfSS8nIBE9pxH2rEJFhfltpgcmHXO2YRNExXQm1uweiS8DCa9uRk7HiddW4sdj9NjmTR6PFz6gXPR8vJwVVbmukQhhMgJCS8nINmZmahsKiqeYDDH1Qy9SaedRmu2z024rg6zvQ3HcXJc1ejkGAZ6bS1qMI/4m28CsDae4Jprr8WVTOGqqkLLnkESQoixRsLLCTC6uwGwXS4UrzfH1Qw9raCAaEEBAMmmRqxIBDueyHFVo5PR1obZ1Q0KpHfvBmALDldccQVYJp6amhxXKIQQuSPh5QQY2TMejsuFOoYa1PVRNA1r6lQA3KFOrEQCOyJbRwPNcRzSBw+CAvENG1CAfek0Z195JT7TQs0vwC23jIQQY9ighpdwOMzNN99MYWEhhYWF3HzzzfRk25q/l1tvvRVFUY54OjN7UDTX+vq82B43aGPnmvThSlaciek4eG0bKxyWZnWDwOrqwmhuQSspofvlVwDYaOhcffU1WJFePBMmyARpIcSYNqjh5cYbb2TLli08++yzPPvss2zZsoWbb775fd/usssuo7W1tf9p1apVg1nm8YvHAHC8XhT32Awvs884g45sfxejrQ0z1JnjikYfvaEBJ53CaGzEHY+TsCzGX3ABQb8fbBv3hPG5LlEIIXJq0H4C7969m2effZa1a9dyxhlnAPC///u/rFixgr179zJr1qz3fFuv10vlMLxJoSaTACg+35gaDXC4aQsXssGyqAai9fXkZZvVjaU5T4PJisXRD9aiFRVz6Be/wA9s1tNcdd11WL29aIVFMkFaCDHmDdrKy5o1aygsLOwPLgBnnnkmhYWFvJm9PfFeXnnlFcaNG8fMmTO544476OjoGKwyT4grlQZADQTHbHhx5+cTyTZGSzY0YicTsnU0gIzmZszeXhxNxV1bC4C2ZCmFBYXYkQjuiTWoY/CwuBBCHG7QwktbWxvjjvIb4rhx42hra3vPt7v88st59NFHeemll/j+97/Phg0buOCCC0in00d9fDqdJhKJHPE0GBzDwGNZALjy8sbsmRdFVbGmTwfA09ODHU9g9Up4GQiOYZA+sB81GOTA03/GBTQbBhd+/CYcXUfRVDzjZctICCFOOLzcd9997zpQ+86njRs3Ahy1+6fjOMfsCnrDDTdw5ZVXMm/ePK6++mr++te/sm/fPp555pmjPv473/lO/4HgwsJCagbpCqmdTtMYDNBuGLgL8sfsmReAijOWk7AsNMfB7OrE7JQhjQOh7wyRq6SE5Jo1APROnkxxcQlmTw9aWRmu8vIcVymEELl3wj+BP/e5z/Gxj33smI+ZPHky27Zto729/V2vC4VCVJzANc+qqiomTZrE/v37j/r6r371q9xzzz39/x2JRAYlwGh5efy0vBzPwYPcnJc3piZKv9Oc00+n4acPMF3TMEOdGC2tOKY5ZrfSBsLh16P3/u1vlNs2huOwJHvA3YnH8MyfJ3/HQgjBSYSXsrIyysrK3vdxK1asoLe3l/Xr17N8+XIA1q1bR29vL2edddZxf7yuri4aGxupqqo66uu9Xi/eIToD0NvbSzkQyMsb0z9EZi9ZwhumwXSvl2h9PYEli7F6e3GVlua6tBGr73q0q7SMlu//gJlAW3ERUyZOxI7HUQIB3NXVuS5TCCGGhUE78zJnzhwuu+wy7rjjDtauXcvatWu54447uOqqq464aTR79myefPJJAGKxGPfeey9r1qyhvr6eV155hauvvpqysjI+9KEPDVapx60326PGHwzCGL5d4y0sJFJUDIDR0ICjG1jZ7sPi5PRdjz6wZw9Ts+e7pnz0owCY4TDuykqZIC2EEFmD2ufl0UcfZf78+VxyySVccsklLFiwgN/85jdHPGbv3r30ZjvXaprG9u3bufbaa5k5cya33HILM2fOZM2aNeQPgzkufQ32Ann5Y3rlBcCaNRMAdyyGresYw+RG2EhkxWKks9ej9/7ud7gUhS6/n8rFS3BsG0wDz6RJMkFaCCGyBvUncElJCY888sgxH3P4YD+/389zzz03mCWdkt7eXvB4CBbko6hje7JCzdKldG3eQqnbjdndhdnejq3rqB5PrksbcfT6Q9iRXhrSaaZFIqBplF9xOQB2JIJWUIB7GPY9EkKIXBnbP4FPQCqVIpVdzg9mt0zGstOWLaOxr9NuUzN2LIYVDue4qpHHTiZJ79+HWlDIht/8hgJNI6FpVK1cCYDV24N74iQZByCEEIeR8HKcbNvm7i9+kXPO/QDBosJcl5Nzpy1fzgFDByCxdy+OaUp4OQl6QyNmVzeNPWFq2jK38wLnnIOiuXAMA1QVj4wDEEKII0h4OU6BQID77r+fj990I6pffgsOFBbSVVICgN3SguM4GK3v3XxQvJut66T37UUNBnnpkUeZ7PViAVVXXgGAFQ7jKi2V3i5CCPEOEl5OguqVcx0Awblz6TZNFMfBDIUwOzuxs/OfxPszmpowO0K0JhKU1tUBoCyYj5aXOZxuxWN4Jk+RuVFCCPEOEl5OlKKiuCW8AMw74wwa9MzWkX6oATsel62j4+SYJun9+1G8Xv782GMs9vsBqLrqagDsRALV78ddffT+RkIIMZZJeDlBiqaO6dEAh1ty3nnUZsNLev9+sC1M6fdyXIzWVozWNtrTabw7dqApCvaECbgnTADA7OrEXV2NViyHw4UQ4p0kvJwoVRvzPV76zFiwgKbs34XR1IQDGNnzL+K9ObadCXuqwhN//AMfCAYBKMtej3YMAxzwTpsmvV2EEOIoJLycKJcGY3iu0eFUj4f8ObPpNAwUwGxvxwqHsePxXJc2rJnt7RhNzYQMA8/WbQQ0Dbu0FP/ChZnXd3XhGlcuvV2EEOI9SHg5QYqmyQHKw0xbtowmM9PvJX3okJx7eR+ObZPauxfHsfnTE09wft+qywevRVFUHNvGTiTwTp8u/86EEOI9SHg5QYqqyrbRYRaeey51fYd29x8ARcHs7MpxVcOX0dKKcegQnZaNunkLQU3DLinBv3gJAFZPD67iIjzZsy9CCCHeTcLLidI0FNk26rfw7LM5YJoAmM3NOA4YLc2ZmTziCI5lkdqzB0dRePLJJ7igb9Xl2mv7x01YPT14pk2TjrpCCHEMEl5OlKaBrLz08xcW4p0ylY6+UQHt7Vi9vVjZYZvibUZzM0ZTE12OA5veIqhpWMXF+JcuBTIDGtVgEM/EiTmuVAghhjcJLydA9fvxVFejDYMJ18PJ5CVL3p5zVFeHnUhihkI5rmp4cUyT1J49oKo8+cQTXJhddSm/9pq3V126u/DUTMCV7VwshBDi6CS8nABF0/DNmSNnXt5hwdlncai/38s+VK8Xo7klx1UNL3pjI0ZzM92KgrNhI3mahlVUhH/ZMiAzKgAUvFOm5LZQIYQYASS8iFN2+gUXsCedAsBsbcNRFMxQB1ZMrkxDpm9LevceFLeHJ/74h7fPulxzDYqaOT9ldXbirqrEJdejhRDifUl4EaesbPx4lIpK2rKrL0ZLM3YsjtUpW0cAekMDRmsrnbaFtmEj+ZqGVVhIYPnpQGZLydH1zPVoOQwuhBDvS8KLGBA1ixfRlL11pO/LdI812ttzXFXu2akUqd27Ufx+nv6/x7goLw+A8o98pH/VxezowF1ZiaemJpelCiHEiCHhRQyIuWeu4JCeBiC9bx9qXj5Gc0v2LMfYlT5wAKOtnQ7ToHTHdryqilVVhX9ppq+Lo+s4poF3zmwUjwz8FEKI4yHhRQyIZeevZE8qjeU4mB0dOHoaKxLB6uzMdWk5Y4bDpHbtQisu5vnf/IYzA5mzLlWfuBmFzMwio6MD9/jxsuoihBAnQMKLGBAz5s8nEQzQkL0ynd69BxwbY4xemXYch9SuXdjRGG3RCFMOHATAmjMHz6TJQGZLCcfGN3u23GATQogTIOFFDAhFUaiev4C6dGbrKLljB6o/gNHYiGNZOa5u6BnNzegHD+KqrOT1hx5iuteLAUy4+eP9jzFDHXgmTsQ9fnzuChVCiBFIwosYMKedeQYH02+fe8HrxerpGXODGh1dJ7VjBw4KTW2tzG5qBkBdsQKtqBgAO5FAUdXMqosqX4ZCCHEi5LumGDBLzjuPRtOgy7LAstDranHSOmbX2BrUmK6txWhuwV1Zydb//QXlbjcJVWXi9df3P8YMdeCZPEX6ugghxEmQ8CIGzJKzz0b3eNifTAKQ2r4DxetFb2zCcZwcVzc0rEiE1I4dqAUF1O3cwZzuTHDzXnYZitebeUwshuL14p01E0VRclmuEEKMSBJexIDxeDxMWrqUeiNzPTq1cwdKfh5WZwg7Gs1xdYPPcRxSO3Zi9vSilZTQ8vDD+FSNkNfLxCuvyDzGtjFDHXinT8c9blyOKxZCiJFJwosYUMsuuIAmw0QH7EgUq6sbO5HAHANXpo3GRtIH9uOurGT/qmeYnNYxHYeKW29FUTJfamZnJ66SUnynnZbjaoUQYuSS8CIG1MprriFiW+xNJgBI7dgBmgujuTnHlQ0uO5EguXUbqBqoCtaqvwJQW15O9cKFmcek0zjJBP4F89GynXaFEEKcOAkvYkBNnDWLQHU1dXqm30tqxw60oiKMllasUbx1lNq9G7OjHVdlJQcefIh8x6HTNFnwmc/0P8Zsa8UzZQqeyZNzV6gQQowCEl7EgJt5zjk09g1pbGjAMQ3sWBRzlM46MlpaSO3Zg1ZWjtHUhHfHDgAOzZlNWVUVAFZPD2oggH/+fBm+KIQQp0jCixhwKy67jLBl0ZRtTpfevRvF40VvbBx1t45sXSe5fTuOZaEGgzT+/OdowOZ0mpWf/CQAjmVhdnfjnTMHV2lpbgsWQohRQMKLGHBnXXopKZeLPYk4AMnt2zNbR23t2L29Oa5uYKX27EFvbMJdWUX0lZfxdneTsCzS555DYUEhAEZrK57qanyzZuW4WiGEGB0kvIgB5wsGqVq0kMbsnKPU7j3gdmPH4xjtHTmubuCYoRDpXbtwlZRg9fYSfvJPADybTnNFtiGdFYuhKOBbMB812+dFCCHEqZHwIgbF4gsuoMM0iQHoOvqBA6h+P/qhehzbznV5p8wxDJLbtmEnU6hFhXQ98giaZbEvnabm2msIBII4to0V6sA7a7bMLxJCiAEk4UUMivOuvZaYbbOrb+toyxa0oiLMUOeomHWUPngQ/dAh3NXVJNauw9i7F8O2eU5VuOqqqwAw29pwjavAP2+udNIVQogBJOFFDIrpc+fiKh/H/lR2yvRbb6G4XTip1Ii/dWSGwyS3b0fNL8BOJgn/4Q8A/CUa4YqP34zb7cGOx8G28S9cgBoI5LhiIYQYXSS8iEEz+5xzaDUNUpqGnUiQ2rMHJRBArz+Ek72JNNI4lkVy+3bsWAytpISe3/8ekkkO6Tp15eP4wAfOxbFtjPY2vLNm4q6pyXXJQggx6kh4EYPmzMsvI2k7bMv2fEls2JjZOurqHLGTpvW6OvSDB3FVVpHcuoXkW29hOQ6Phrv5+0/ehqKomO3tuCsq8M+bJ9tFQggxCCS8iEFzzuWXk1AVtvZkzrgkt25FUcDWDYwRuHVkRaMkt29H8QfAtuj5v8cAWB2NUrlwIfPnL8BOJMAy8S9YgBoM5rhiIYQYnSS8iEGTl59P+bz5dFsWaZ8PdJ3k9h1oeXkY9fU42avUI4Fj26S2b8fs6sZVVkbvE09gRyK0GQbPxmLccuutme2itja8M2finjgx1yULIcSoJeFFDKoVV1yOA2zVMwd3Exs3ZLeOukdUzxejqYn0gQO4KytJ799P/I03AfhtT5jzLryQSRMnYXZ04C4vxyfbRUIIMagkvIhBdfXHP04CeLMts02U2rETxzRAAb2+LrfFHSc7mSS5LTMxWnG7CP/2UQBei8VoROGmm27ETiZxdB2fTIwWQohBJ+FFDKryCROYuGgxCcch5veDZZHcvAWtuAS9sQlzBPR8Se3ejdnejquigshfnsEKddJr2/wp0ssNN1xPcXFJdrtoBp5Jk3JdrhBCjHoSXsSgO/fD16EpsC4WBSCxcSNaXh52Io7e1JTj6o7NaG9/e2J0czPRF18E4Lfd3RRVVHDttR/ECoVwFRdnbhep8iUlhBCDTb7TikF30Q03YLo9bMpej07v3YsViaDlF6AfOIidTue4wqNzdJ3ktm04uoEaDND96CNg27yVTLI9leKO2+9AsyzsVBL/wgVoBQW5LlkIIcYECS9i0OWVlTH9rBVYjkPY7wfHIfnWW2jFxVjd3RjNLbku8ahSBw5gNDTirqoi9uKLmI1NpBWFx8Jhli5dytJlSzHbWvFMnYZn8uRclyuEEGOGK9cFiLFh5fU3UPfKq/ytq4urAwESGzaQt3IluN2ka2vxTJ40rLZczO5uUjt3ohYWYvX00PuXZwD4fVcXSVXhjjtux+7qRssvILBgPoqm5bhiIcCyLIwR1IJAjD1utxttAL5fSngRQ+Lsq6/iN//0Fbb3RrgqEECvq8Nob8NVVobZ2ooZ6sRdMS7XZQLgmCbJrduwozFckybS9T8/AsOgzrZZk0hw3Yevo6qsHKOlheDZZ6MVFeW6ZDHGOY5DW1sbPT09uS5FiPdVVFREZWXlKbWUkPAihoQ7L48555/P9qeepsnvpyaZJPbqaxRffz2maWQmNA+T8JI+WIteW4tr/HhSGzaQ3rMHS1H4VUc7JSXF3HD9DeitLXgnT8I7dUquyxWiP7iMGzeOQCAgfYbEsOQ4DolEgo6OTI+vqqqqk35fEl7EkLnoxhvZ/vTT/KW5mc+UlJBYs4bCa65BKyxCP3QI32lzct4jxQyHSW7bhlpQgKPr9PzhjwCsikToMC3uve02POk0jt+Pf/58FLc7p/UKYVlWf3ApLS3NdTlCHJPf7wego6ODcePGnfQW0vA5ZCBGvfnnnUewspLmdJp0Xh5OOk1i/TrUggKsSASjuTmn9WW2i7ZiRyNoJSX0Pv44djxOp6ryfG8vy5Yt5ZyzzsLs7sY3dy6u8vKc1isE0H/GJRAI5LgSIY5P37/VUzmfJeFFDBnN62XhpZeSr6mstywAYq++CqqCFgyS2rMnM9gwR/q3i6rHk963l8S6dTjAg22tuP0+PvOZuzDb2vDUTMA7a1bO6hTiaGSrSIwUA/FvVcKLGFKX3nQTNvDngwdw3G7M1jbSe/ehlZVhhjpJHTiQk7r6t4vy8lFwCD/6WwD+lkxSrxvccsstlPh8KJqGf/58VI8nJ3UKIYSQ8CKG2KSFC5m6aDFeReVgdu8z/uqrKKqKVlycaWA3xDcmHF0nuWVLZruotJTeZ57B6uwkpqo8Ge5mzpw5XH7ppVidIXyzZ+Ourh7S+oQQw899993HokWLcl0GK1eu5Itf/GKuyxhyEl7EkFLcbq799KfIV1UeO5hZZUlu3YoV7kYrKsLqjZDau3fI6nEch+SOHaQP1uIePwGjoYHYC5kRAL/p6MBUNf7hH/4BqyOEa9w4fHPmDFltQowFbW1tfOELX2D69On4fD4qKio455xzeOCBB0jkcBv5VL3yyisoijJg19cH+v2NdBJexJCbt3Il0+fMJqQbhAIBcBxir7+Ooii4xo0jffAgRvYq3WDT6+pI7diBa9w4UBW6H3kEHIcths72VIqPfexjVJeW4phGZrtIDkUKMWBqa2tZvHgxzz//PN/+9rfZvHkzL7zwAnfffTd//vOfeeGFF97zbUdLMz5d13Ndwogk4UUMOVdZGRddfz2lmsbT2RtG8b+9gWMaaHl5OGmd1O7dOLY9qHWYoRCJTW+heLxoeXlEV7+A2dxMEvhdqJOpU6dy3XUfwmhrxTtjBu6JEwe1HiHGmrvuuguXy8XGjRu5/vrrmTNnDvPnz+fDH/4wzzzzDFdffXX/YxVF4YEHHuDaa68lGAzyb//2bwD89Kc/Zdq0aXg8HmbNmsVvfvOb/repr69HURS2bNnS/7Kenh4UReGVV14B3l7RePHFF1m2bBmBQICzzjqLve9YAf7ud79LRUUF+fn5fPKTnySVSr3n51VfX8/5558PQHFxMYqicOuttwKZbZ7Pfe5z3HPPPZSVlXHxxRe/b53Hen8Atm3z5S9/mZKSEiorK7nvvvuO93/BiCXhRQw5RdNYdPXVzJ42jS3xOEm3GzsWI7lpEwCuigr0+vpBvTptJxIkNm7EjsdwjRuH0d5G5JnMCIDHurswPG6+/OUvQU8vrqIi/HPnDqvxBUIci+M4xOPxnDw5jnNcNXZ1dfH888/z2c9+lmAweNTHvPNWyte//nWuvfZatm/fzm233caTTz7JF77wBf7xH/+RHTt28OlPf5q///u/5+WXXz7hv7Ovfe1rfP/732fjxo24XC5uu+22/tf9/ve/5+tf/zrf+ta32LhxI1VVVfzkJz95z/dVU1PD448/DsDevXtpbW3lv/7rv/pf/6tf/QqXy8Ubb7zBz372s/et7XjeXzAYZN26dfzHf/wH3/jGN1i9evUJ/x2MJNKkTuSEe/x4Lrj2GrZ+/we8GA5zVV4ekVV/xb9sGarPB4pKatdu3JWVA94IzjFNEps3o7e04Jk4CcexCf/mEbAsdqRSrE8kueeeu6ksK8dsaSZ4zjlohYUDWoMQgymRSJCXo4aPsVjsPcPI4Q4cOIDjOMx6R9uBsrKy/lWNz372s/z7v/97/+tuvPHGI0LFjTfeyK233spdd90FwD333MPatWv53ve+179Scby+9a1vcd555wHwT//0T1x55ZWkUil8Ph8//OEPue2227j99tsB+Ld/+zdeeOGF91x90TSNkpISAMaNG0fRO0aITJ8+nf/4j//o/+/6+vpj1vZ+72/BggV8/etfB2DGjBn86Ec/4sUXX+Tiiy8+rs99JJJfJUVOqD4fi6+5htMmTuSlSC+6y4UZChF/4w0A3BUVGE2NJLdtG9DtI8cwSLy1mfSevbirqlE0jfgrr6LX1pJ2HP4v3M0FF17AypXnY7S24JkyBe/UqQP28YUQR3rn6sr69evZsmULc+fOJZ1OH/G6ZcuWHfHfu3fv5uyzzz7iZWeffTa7d+8+4ToWLFjQ/3xf2/q+Nva7d+9mxYoVRzz+nf99It75eZyqw2uHTP0dQ3RuMFdk5UXkjHfSJC644nI2//QB/tLbw3XBPCLPrCKw/AxUnw/XuAqS27ejeH345p52yo2NHF0nsXETqd27cVVUoPp8GK0t9Dz5JABP9vTgr6rizk9/GqunB61vBIBLvkzEyBIIBIjFYjn72Mdj+vTpKIrCnj17jnj51OwvC31t5A93tBWdd35fcByn/2Vqdqv38K2s9zro6z5shbfv7e1BOnf3zs/jROo8Gvc7VqcVRRm02ocLWXkROeMqLmbpVVdx2vjxvBzuIeHzYUejRLM3DNRgEK2gkORbb6HX1p7Sx7LTaeLr15PctQtXZSVqIIBjGHT98kEwTXYkk6zR03z5y1/G6/ZgdnfjPe00XGVlA/GpCjGkFEUhGAzm5Ol4f8koLS3l4osv5kc/+hHxePykPs85c+bwt7/97YiXvfnmm8zJtjQoz47waG1t7X/94YdiT+TjrF279oiXvfO/38mTbWRpZbuJH8vx1Hki728skPAicso3ZSqXXXYZKvDblhYAoi+8gNXbA4BWVITi8xFfvwG9qemkPoadTBJfu5b03r24x49Hzf5G1/OnJzFbWohYFr8Jh7n99tuZMnkKRlsrnvHV+GQEgBCD6ic/+QmmabJs2TIee+wxdu/ezd69e3nkkUfYs2fP+w7t+9KXvsTDDz/MAw88wP79+/nBD37AE088wb333gtkVm/OPPNMvvvd77Jr1y5ee+01/uVf/uWE6/zCF77Agw8+yIMPPsi+ffv4+te/zs6dO4/5NpMmTUJRFP7yl78QCoWOuRJ2PHWeyPsbCyS8iJxyV1aw9OKLuOSM5byVSNDkOKDrRJ5Z1f8YV1kZWBaJdesw2o9/H9exbfTGRmKvvY5+4ADu8RNQvV4AUjt3EH/5FQB+E+7m/Kuu5LLLL8eKxVBQ8C9Y0P9YIcTgmDZtGps3b+aiiy7iq1/9KgsXLmTZsmX8z//8D/feey/f/OY3j/n2H/zgB/mv//ov/vM//5O5c+fys5/9jIceeoiVK1f2P+bBBx/EMAyWLVvGF77whf4r1ifihhtu4P/9v//HV77yFZYuXcqhQ4f4zGc+c8y3GT9+PPfffz//9E//REVFBZ/73OeO+fj3q/NE399opzjHe69thIhEIhQWFtLb20tBQUGuyxHHIb1/Px3PPsc93/tPCmMx/rF8HCgKFf/6L7grMwfnHMfBaGxE9fvwTJ2Gd9pUXNnT90djdHSQ2rMHo74eByVzayl7dsWKRGj5xjdQEglejkVpmTePL3/pS+CAfqge//wFBE5fJoPuxIiQSqWoq6tjypQp+Hy+XJcjxPt6r3+zJ/LzW1ZeRM65x48nv7qKu2+/nYNpnS2JBDgOvX96qv8xiqLgrqlB8XhJbdtG5Lnnia9Zg9HRgRWJYHZ2YrS0oNfXE1+/gegLL5A+eBCtrBzPhAn9wcVxbNp/+UuURIJmQ2fv+PHcc/fdKIqKGQrhKi3Fd9qpHw4WQggxeOQahcg5NRDAM3UaM8M9XHP1VTz112eZ7/eT2raN+Nq1BM88E8gEGK2wEK2wECsaJbVnD+mDB0HTwDBxLLP/fWolpf2rNn0cHNoeeRR7/34M2+avHg//9LV/we32YKdSOOk0/jOWo+W9f48KIYQQuSPhRQwL3qlTSB/Yz03XXMPmrVt5tqeXKwsKCD/6KO6KcXimHNlrRcvPR8vPx06lwHEyKysu1zFXTOp/+zvca9YA8CfD4HP/9l3y8vJwHAezrRXP9Ol4Jk0a1M9TCCHEqZNtIzEsaIWFeGfNQksk+Me77+a5RDyzfWRZdD7wM6z3mKSq+nyofj+K233M4LL1N7/Gnb1S+aKicNN3vk1ZWeZ6otXdjZpfkOnp8j63G4QQQuSehBcxbPimTUMrKWFiQSFf+MIXeSQSocnQsaNR2n/8YxzjxKevOji88MBPKXozs+KyLRDgo9/7T8aNqwDA1nXsSAT/gvm4iosH9PMRQggxOAY1vHzrW9/irLPOIhAIvGsWw3txHIf77ruP6upq/H4/K1eufN/79GJ0UINBfKedhh2L8oFzzuFfv/kNHkmmiFkWdnMzjQ/8DIfjvxy3f/9+fv7Vf2bqlq1oikJTSQmX/vt3Cfjf7gBqtrTgmToF77Rpg/EpCSGEGASDGl50XeejH/3o+96HP9x//Md/8IMf/IAf/ehHbNiwgcrKSi6++GKi0eggViqGC8/kybgqKzFDIebOncfX/vM/eVJVMB0Hdfdutnz723Q2NR7zfdTV1fLv3/wm6775Ta7s7cWjqkTGjeOM++9D094+5mV2d6PmBfEvXCgjAIQQYgQZkj4vDz/8MF/84hfpeY9zC30cx6G6upovfvGLfOUrXwEgnU5TUVHBv//7v/PpT3/6fT+W9HkZ+dK1tcRefRV39XgUt5tYLMpTX7+P85JJAGKWxYaAn6KVK5kzdy7hcA8doQ5CoRCH6g+R2rmDvysqpiQbSJRFi6i+9RYUz9tN5xxdx2hpJrBiBf5sK3EhRiLp8yJGmoHo8zKsft2sq6ujra2NSy65pP9lXq+X8847jzfffPOo4SWdTh8xeTQSiQxJrWLweGpqcI8fj9HWjmfCBPLy8rnh37/Lm48+SuGGjZQC56d1Wv7yDI/97ncoKARVlaCqsszlYmH2IC5FRZTd8gl8s2a/62PorS14J03CN3360H5yQgghTtmwOrDb1tYGQEVFxREvr6io6H/dO33nO9+hsLCw/6mmpmbQ6xSDS3G78c2ZA46NnV1tcbncfOCWW1nw3/+F+6qrMNxuqt1ubikp5RMlJXy4qIjLCgpYGAjgKAp5F17I+K9//ajBxezqQgtkt4veMY1VCDE8KYrCn/70p0H/OJMnT+aHP/zhoH+c47Vy5Uq++MUv9v/3QNQ33D7Hk3HC4eW+++7j/2/v3qOarv8/gD83xmAD5w1FEARkCGJcFNQUY/4Sb3U0U0PFVFJTU7wc08RjBZTx9ZLp8VbWESFU8qRSHj0YZEAqKYIsLyDzAoExUVERkJhj798fynKCwIANP+v1OOfzB5999t6L1/k4Xr4/7wuPx2v0yMrKalVQjW1x/rzVq1ejvLxcexQXNz4egnCDec+esJBK8fiWEuyZXVR5fDPYvvEGnP4XDeugIAidnWHh6QnRwIGwGj4cHd58E7arVqHTpEngNbA3kaaqCpqqKoh8fWnHaEJeArdu3cLSpUshlUphaWkJW1tbDBs2DN988w0ePXrU3uG9dM6dO4d58+Y169rY2NgGJ8vo08bLSu/HRmFhYZg6dWqj1zg7O7comB49egB4cjPb2f27Ourt27fr9cbUsbCwgAVtoGdyeHw+xL6+qC0vx+OSvyF07KXzOl9shU4TJ+rVJnv8GI9LSyHy9oaFGz0uIqS93bhxAwEBAejUqROio6Ph5eUFtVoNhUKBmJgY2NvbY/z48e0dZqupVCoIhcI2aatbt24vRRvtTe+eFxsbG3h4eDR6tHTQmIuLC3r06IGUlBTtOZVKhfT0dAwdOrRFbRLu4ltZQeznD76lJdRlZa1qi2k0ePz3TVj0doHI1wc8/kv1xJSQ/6SFCxdCIBAgKysLwcHB6Nu3L7y8vDBp0iQcO3YM48aNa/B9aWlp4PF4OpNA5HI5eDweCgsLtecyMjIQGBgIkUgER0dHLFmyBFVVVdrXb9++jXHjxkEkEsHFxQX79u1rMubQ0FBMmDABUVFR6N69OyQSCebPnw+V6t91qIYPH46wsDAsX74cNjY2GDlyJAAgNzcXb7zxBqytrWFra4sZM2bg7t272vdVVVVh5syZsLa2hp2dHTZt2lTv859/5PPgwQPMmzcPtra2sLS0xCuvvIKjR48iLS0N7733HsrLy7VPRSIjIxtso6ioCG+99Rasra0hkUgQHByM0tJS7euRkZHw9fVFfHw8nJ2d0bFjR0ydOlVnFvDBgwfh5eUFkUiErl27IigoSCfXbc2g3+BFRUWQy+UoKipCbW0t5HI55HI5Kisrtdd4eHggMTERwJPHRcuWLUN0dDQSExNx6dIlhIaGQiwWIyQkxJChkpeUuW13iHz7Q1NVCU0rupAfl5RAYGMDsb8/+G30PyBCXlaMMWgePWqXo7kTWMvKypCcnIxFixbByqrh/cRas0HqxYsXMXr0aEycOBEXLlzAgQMHcOrUKYSFhWmvCQ0NRWFhIX777TccPHgQO3fuxO3bt5ts+8SJE8jLy0NqaioSEhKQmJiIqKgonWvi4uIgEAhw+vRp7Nq1C0qlEjKZDL6+vsjKysLx48dRWlqK4OBg7XtWrlyJ1NRUJCYmIjk5GWlpacjOzn5hHBqNBmPHjkVGRgb27t2L3NxcrFu3DmZmZhg6dCi2bNkCiUQCpVIJpVKJFStW1GuDMYYJEybg3r17SE9PR0pKCq5fv44pU6boXHf9+nX89NNPOHr0KI4ePYr09HSsW7cOAKBUKjFt2jTMnj0beXl5SEtLw8SJE5t9L7SEQWcbffrpp4iLi9P+3L9/fwBAamoqhg8fDgDIz89HeXm59pqPPvoI1dXVWLhwIe7fv4/BgwcjOTkZHTp0MGSo5CVm4SZF7f17+OfyZZj3ctJ7CX91WRl45uYQ+/vDjKbPk/8AVl2N/AF+7fLZ7uezwROLm7zu2rVrYIzB3d1d57yNjQ3++ecfAMCiRYuwfv36FsWxceNGhISEaAe7urm5YevWrZDJZPj6669RVFSEpKQknDlzBoMHDwYA7N69G32bsXSCUChETEwMxGIx+vXrh88++wwrV67E559/Dv7TXl2pVIoNGzZo3/Ppp59iwIABiI6O1p6LiYmBo6MjFAoF7O3tsXv3bnz//ffanpq4uDg4ODi8MI5ff/0VmZmZyMvLQ58+fQAAvXv/uw9cx44dwePxtEMyXtTGhQsXUFBQoJ3wEh8fj379+uHcuXMYOHAggCeFUmxsrPZv8YwZM3DixAl88cUXUCqVUKvVmDhxIpye7g/n5eXVZB5bw6DFS2xsLGJjYxu95vnKrK5rq657ixAenw+Rjw9qy8uhKi6C0MGxWYvKMY0G6tJSgGkgHjgI5vb2RoiWEKKP53tXMjMzodFoMH36dJ1lMPSVnZ2Na9eu6TwKYoxBo9GgoKAACoUCAoEA/v7+2tc9PDyatRq8j48PxM8UaEOGDEFlZSWKi4u1f7yfbbcuntTUVFhbW9dr7/r166iuroZKpcKQIUO057t06VKvuHuWXC6Hg4ODtnBpiby8PDg6OurM1PX09ESnTp2Ql5enLV6cnZ11OhHs7Oy0vVQ+Pj4YMWIEvLy8MHr0aIwaNQqTJ09GZwNuufJSrfNCyIvwRSKIBw0Czp2DqqgIgi5dYNbIl4xGpYL6778hsLGBaEB/CGkKPfkP4YlEcD//4scNhv7s5pBKpeDxeLhy5YrO+bqeA1Ej7dT1bjz7n9/Hjx/rXKPRaDB//nwsWbKk3vt79eqF/Pz8J/G24tHU855t6/lHYRqNBuPGjWuwJ8nOzg5Xr17V+/May1FzvWg27/PnzZ9bVoLH40Gj0QAAzMzMkJKSgoyMDCQnJ2Pbtm1Ys2YNzp49CxcXl1bH2BAatUg4Q9C5M6yHD4d40EBoamqgKi4Ce+4LCwBqy8uhLvkbQtfesP6/4VS4kP8cHo8HvljcLkdzi4GuXbti5MiR2L59u94DO+tmyyiVSu05uVyuc82AAQNw+fJlSKXSeodQKETfvn2hVqt1lvbIz89vciV4APjzzz9R/XQNKgA4c+YMrK2tG33EUxePs7NzvXisrKwglUphbm6OM2fOaN9z//59KBSKF7bp7e2NmzdvvvAaoVCI2meWmmiIp6cnioqKdJYZyc3NRXl5ebMeodXh8XgICAhAVFQUcnJyIBQKteNZDYGKF8IpfKEQYm9vdHj9dZjb2+PxzWKo/ip8chQ+OTT/VEM0cCCsAwJojAshL7GdO3dCrVbD398fBw4cQF5eHvLz87F3715cuXIFZi8Y3yaVSuHo6IjIyEgoFAocO3as3sycVatW4Y8//sCiRYsgl8tx9epVHDlyBIsXLwYAuLu7Y8yYMXj//fdx9uxZZGdnY+7cuc3qzVCpVJgzZw5yc3ORlJSEiIgIhIWFaXuEGrJo0SLcu3cP06ZNQ2ZmJm7cuIHk5GTMnj0btbW1sLa2xpw5c7By5UqcOHFCO2GlsTZlMhkCAwMxadIkpKSkoKCgAElJSTh+/DiAJ496KisrceLECdy9e7fBdXOCgoLg7e2N6dOn4/z588jMzMTMmTMhk8nqPfp6kbNnzyI6OhpZWVkoKirC4cOHcefOHb2KH33RYyPCSea23SGQyVBTWAio1YBAAN7Tgy8SQWAC6xgQYupcXV2Rk5OD6OhorF69Gjdv3oSFhQU8PT2xYsUKLFy4sMH3mZubIyEhAR988AF8fHwwcOBArF27Fu+88472Gm9vb6Snp2PNmjV47bXXwBiDq6urziyaPXv2YO7cuZDJZLC1tcXatWvxySefNBn3iBEj4ObmhsDAQNTU1GDq1KlNjtO0t7fH6dOnsWrVKowePRo1NTVwcnLCmDFjtAXKxo0bUVlZifHjx6NDhw748MMPdSa0NOTQoUNYsWIFpk2bhqqqKkilUu0soKFDh2LBggWYMmUKysrKEBERUS/OupWLFy9ejMDAQPD5fIwZMwbbtm1rMg91JBIJfv/9d2zZsgUPHz6Ek5MTNm3ahLFjxza7DX0ZZWNGY6KNGQkh/yW0MaNxhYaG4sGDB0bZqsBUtcXGjPTYiBBCCCGcQsULIYQQQjiFxrwQQgghzdTU2mXEOKjnhRBCCCGcQsULIYQQQjiFihdCCDEBdaudEvKya4t7lca8EEIIhwmFQvD5fJSUlKBbt24QCoVtuuQ9IW2FMQaVSoU7d+6Az+dDKBS2uC0qXgghhMP4fD5cXFygVCpRUlLS3uEQ0iSxWIxevXo1unpwU6h4IYQQjhMKhejVqxfUanWTe9kQ0p7MzMwgEAha3TtIxQshhJgAHo8Hc3Pzerv/EmKKaMAuIYQQQjiFihdCCCGEcAoVL4QQQgjhFJMb81K3SfbDhw/bORJCCCGENFfd3+26v+ONMbnipaKiAgDg6OjYzpEQQgghRF8VFRXo2LFjo9fwWHNKHA7RaDQoKSlBhw4d2nyhpocPH8LR0RHFxcWQSCRt2jb5F+XZOCjPxkO5Ng7Ks3EYKs+MMVRUVMDe3r7JNWBMrueFz+fDwcHBoJ8hkUjoH4YRUJ6Ng/JsPJRr46A8G4ch8txUj0sdGrBLCCGEEE6h4oUQQgghnELFix4sLCwQEREBCwuL9g7FpFGejYPybDyUa+OgPBvHy5BnkxuwSwghhBDTRj0vhBBCCOEUKl4IIYQQwilUvBBCCCGEU6h4IYQQQginUPHynJ07d8LFxQWWlpbw8/PDyZMnX3itUqlESEgI3N3dwefzsWzZMuMFynH65Pnw4cMYOXIkunXrBolEgiFDhuCXX34xYrTcpU+eT506hYCAAHTt2hUikQgeHh7YvHmzEaPlLn3y/KzTp09DIBDA19fXsAGaEH1ynZaWBh6PV++4cuWKESPmJn3v6ZqaGqxZswZOTk6wsLCAq6srYmJiDBcgI1o//PADMzc3Z9999x3Lzc1lS5cuZVZWVuyvv/5q8PqCggK2ZMkSFhcXx3x9fdnSpUuNGzBH6ZvnpUuXsvXr17PMzEymUCjY6tWrmbm5OTt//ryRI+cWffN8/vx5tn//fnbp0iVWUFDA4uPjmVgsZrt27TJy5Nyib57rPHjwgPXu3ZuNGjWK+fj4GCdYjtM316mpqQwAy8/PZ0qlUnuo1WojR84tLbmnx48fzwYPHsxSUlJYQUEBO3v2LDt9+rTBYqTi5RmDBg1iCxYs0Dnn4eHBwsPDm3yvTCaj4qWZWpPnOp6eniwqKqqtQzMpbZHnt99+m7377rttHZpJaWmep0yZwj7++GMWERFBxUsz6ZvruuLl/v37RojOdOib56SkJNaxY0dWVlZmjPAYY4zRY6OnVCoVsrOzMWrUKJ3zo0aNQkZGRjtFZXraIs8ajQYVFRXo0qWLIUI0CW2R55ycHGRkZEAmkxkiRJPQ0jzv2bMH169fR0REhKFDNBmtuaf79+8POzs7jBgxAqmpqYYMk/NakucjR47A398fGzZsQM+ePdGnTx+sWLEC1dXVBovT5DZmbKm7d++itrYWtra2OudtbW1x69atdorK9LRFnjdt2oSqqioEBwcbIkST0Jo8Ozg44M6dO1Cr1YiMjMTcuXMNGSqntSTPV69eRXh4OE6ePAmBgL6Cm6slubazs8O3334LPz8/1NTUID4+HiNGjEBaWhoCAwONETbntCTPN27cwKlTp2BpaYnExETcvXsXCxcuxL179ww27oX+5TyHx+Pp/MwYq3eOtF5L85yQkIDIyEj8/PPP6N69u6HCMxktyfPJkydRWVmJM2fOIDw8HFKpFNOmTTNkmJzX3DzX1tYiJCQEUVFR6NOnj7HCMyn63NPu7u5wd3fX/jxkyBAUFxfjyy+/pOKlCfrkWaPRgMfjYd++fdpdob/66itMnjwZO3bsgEgkavP4qHh5ysbGBmZmZvUqy9u3b9erQEnLtSbPBw4cwJw5c/Djjz8iKCjIkGFyXmvy7OLiAgDw8vJCaWkpIiMjqXh5AX3zXFFRgaysLOTk5CAsLAzAky9+xhgEAgGSk5Px+uuvGyV2rmmr7+hXX30Ve/fubevwTEZL8mxnZ4eePXtqCxcA6Nu3LxhjuHnzJtzc3No8Thrz8pRQKISfnx9SUlJ0zqekpGDo0KHtFJXpaWmeExISEBoaiv379+PNN980dJic11b3M2MMNTU1bR2eydA3zxKJBBcvXoRcLtceCxYsgLu7O+RyOQYPHmys0Dmnre7pnJwc2NnZtXV4JqMleQ4ICEBJSQkqKyu15xQKBfh8PhwcHAwTqNGGBnNA3fSw3bt3s9zcXLZs2TJmZWXFCgsLGWOMhYeHsxkzZui8Jycnh+Xk5DA/Pz8WEhLCcnJy2OXLl9sjfM7QN8/79+9nAoGA7dixQ2e644MHD9rrV+AEffO8fft2duTIEaZQKJhCoWAxMTFMIpGwNWvWtNevwAkt+d54Fs02aj59c71582aWmJjIFAoFu3TpEgsPD2cA2KFDh9rrV+AEffNcUVHBHBwc2OTJk9nly5dZeno6c3NzY3PnzjVYjFS8PGfHjh3MycmJCYVCNmDAAJaenq59bdasWUwmk+lcD6De4eTkZNygOUifPMtksgbzPGvWLOMHzjH65Hnr1q2sX79+TCwWM4lEwvr378927tzJamtr2yFybtH3e+NZVLzoR59cr1+/nrm6ujJLS0vWuXNnNmzYMHbs2LF2iJp79L2n8/LyWFBQEBOJRMzBwYEtX76cPXr0yGDx8RhjzDB9OoQQQgghbY/GvBBCCCGEU6h4IYQQQginUPFCCCGEEE6h4oUQQgghnELFCyGEEEI4hYoXQgghhHAKFS+EEEII4RQqXgghhBDCKVS8EEIIIYRTqHghhBBCCKdQ8UIIIYQQTqHihRBCCCGc8v+gkzL7tLCWYAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Extract mean and variance of glued prediction\n", "f_mean = glued_preds[\"f_mean\"]\n", "f_var = glued_preds[\"f_var\"]\n", "f_std = np.sqrt(f_var)\n", "X_test = glued_preds['pred_locs']\n", "\n", "# Plot results\n", "plt.plot(X_grid, f_truth, 'k', zorder=0, label='Ground truth')\n", "plt.plot(X_test, f_mean, color='C3', zorder=1, label='Glued predictions')\n", "plt.fill_between(X_test, f_mean-1.96*f_std, f_mean+1.96*f_std, color='C3', alpha=0.3)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result of the glued prediction looks slightly better than our first attempt using a global GP. This improvement is also reflected in the metrics, with a slightly improved log-likelihood score:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error: 0.0005\n", "Mean log likelihood: 2.5734\n" ] } ], "source": [ "print(f\"Mean squared error: {np.mean((f_truth - f_mean)**2):.4f}\")\n", "print(f\"Mean log likelihood: {scipy.stats.norm.logpdf(f_truth, f_mean, f_std).mean():.4f}\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.17 ('gpsat2')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.17" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "42c89ee418f45ab16d4cd7d85b9f5fd46783f67990f590db7ef8d9e48f3f848d" } } }, "nbformat": 4, "nbformat_minor": 2 }