{ "cells": [ { "metadata": {}, "cell_type": "markdown", "source": [ "# Function-on-Scalar Regression\n", "\n", "In previous examples, we have examined regression when the outcome is a scalar value. But what if the outcome is a function rather than a scalar? This is an interesting challenge that has led to functional data analysis. In the described context, one can consider using function-on-scalar regression. While there are various ways to implement this regression approach in the literature (see Gunning et al.), we will review one method here that is straightforward to implement with estimating equations. This method is based on a series of regression models that can be pooled together.\n", "\n", "For illustration, we use weather data collected from 35 locations averaged over the period from 1960 to 1994. Our interest is in modeling the average temperature (a function) by latitude (a scalar). The corresponding data for this example can be obtained from the R package `fda`.\n", "\n", "## Setup" ], "id": "bf06330b78c82f33" }, { "metadata": { "collapsed": true, "ExecuteTime": { "end_time": "2026-03-17T15:30:01.321682900Z", "start_time": "2026-03-17T15:30:00.241736100Z" } }, "cell_type": "code", "source": [ "import numpy as np\n", "import scipy as sp\n", "import pandas as pd\n", "import matplotlib as mp\n", "import matplotlib.pyplot as plt\n", "\n", "import delicatessen as deli\n", "from delicatessen import MEstimator\n", "from delicatessen.estimating_equations import ee_regression\n", "from delicatessen.sandwich import compute_confidence_bands\n", "from delicatessen.utilities import spline\n", "\n", "print(\"Versions\")\n", "print(\"NumPy: \", np.__version__)\n", "print(\"SciPy: \", sp.__version__)\n", "print(\"pandas: \", pd.__version__)\n", "print(\"matplotlib: \", mp.__version__)\n", "print(\"Delicatessen: \", deli.__version__)" ], "id": "897af89761f8e8da", "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Versions\n", "NumPy: 2.3.5\n", "SciPy: 1.16.3\n", "pandas: 2.3.3\n", "matplotlib: 3.10.8\n", "Delicatessen: 4.2\n" ] } ], "execution_count": 1 }, { "metadata": {}, "cell_type": "markdown", "source": "The data was extracted as two parts: the average daily temperatures (in a 365 column by 35 row matrix) and the corresponding latitudes (a 1 column by 35 row vector). The following code loads these objects and does a bit of pre-processing for our question.", "id": "ebc073ca6046943d" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:01.342355600Z", "start_time": "2026-03-17T15:30:01.321682900Z" } }, "cell_type": "code", "source": [ "# Loading the data\n", "dy = pd.read_csv(\"data/CanadianWeather_temps.csv\", index_col=0)\n", "dx = pd.read_csv(\"data/CanadianWeather_coord.csv\", index_col=0)\n", "dx['x'] = dx['x'] - np.mean(dx['x'])\n", "dx['C'] = 1\n", "\n", "# Converting to arrays for regression steps\n", "y_matrix = np.asarray(dy)\n", "X = np.asarray(dx[['C', 'x']])\n", "y_s_vals = y_matrix.shape[1]\n", "n_obs = y_matrix.shape[0]" ], "id": "8d79092dd6d66df8", "outputs": [], "execution_count": 2 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-16T20:42:53.660617600Z", "start_time": "2026-03-16T20:42:53.620088600Z" } }, "cell_type": "markdown", "source": [ "## Function-on-Scalar Model\n", "\n", "Letting $Y_i(d)$ denote the average temperature at day $d$ and $X_i$ indicate the latitude of the weather station. The regression model of interest in then the following function-on-scalar linear model\n", "$$ E[Y_i (d)] = \\beta_0(d) + \\beta_1(d) X_i \\;\\; \\forall \\; d \\in \\{1, 2, ..., 365\\}$$\n", "Note that the intercept and coefficients are defined for each $d$. Therefore, we have a whole collection of objects that need to be estimated.\n", "\n", "One simple and popular method for function-on-scalar regression is to use a series of linear regression models. This is the approach we will take here. While we could fit separate linear models, save the coefficients, and then collate them; this approach makes it difficult to draw valid inference. Instead, we are going to jointly estimate all 365 linear regression models. This is a little computationally burdensome, but it can be somewhat mitigated by cleverly choosing the initial values. Alternatively, we could solve each regression independently and then stitch those results together at the end. Since it doesn't take too long, we take the simultaneous solving approach here." ], "id": "e2c586b7c3f499b9" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:01.352812600Z", "start_time": "2026-03-17T15:30:01.342355600Z" } }, "cell_type": "code", "source": [ "def psi(theta):\n", " # Organizing coefficients that will be estimated\n", " beta0 = theta[:y_s_vals] # Time-varying intercepts unique for d\n", " betaL = theta[y_s_vals:] # Time-varying coefficients unique for d\n", "\n", " # Looping over all individual days for each regression\n", " ef_ols = []\n", " for d in range(y_s_vals):\n", " # Extract outcome vector for regression model\n", " y = y_matrix[:, d]\n", "\n", " # Setup corresponding coefficients for the day\n", " beta_s = np.asarray([beta0[d], betaL[d]])\n", "\n", " # Linear regression for temperature at day d\n", " ef_ols_d = ee_regression(theta=beta_s, y=y, X=X, model='linear')\n", "\n", " # Stacking together outputs\n", " ef_ols.append(ef_ols_d)\n", "\n", " # Returning stacked estimating functions\n", " return np.vstack(ef_ols)" ], "id": "519be87498db40fc", "outputs": [], "execution_count": 3 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:01.361740800Z", "start_time": "2026-03-17T15:30:01.352812600Z" } }, "cell_type": "code", "source": [ "# Using means as starting value for intercepts to speed up process\n", "init_vals = list(np.mean(y_matrix, axis=0)) + [0., ]*y_s_vals" ], "id": "521be71baec4fdd2", "outputs": [], "execution_count": 4 }, { "metadata": {}, "cell_type": "markdown", "source": "Given the defined collection of 365 linear regression models, we can now jointly solve them with `MEstimator` quite quickly (less than 30 seconds on my laptop)", "id": "e3e56fcc0f084243" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:10.582976400Z", "start_time": "2026-03-17T15:30:01.363486600Z" } }, "cell_type": "code", "source": [ "estr = MEstimator(psi, init=init_vals)\n", "estr.estimate()" ], "id": "540b0415e4114eb0", "outputs": [], "execution_count": 5 }, { "metadata": {}, "cell_type": "markdown", "source": [ "As before, I mention the difficulty of inference. The main challenge here is that the parameter of interest is actually a collection of parameters (or more specifically, the functions $\\beta_0(d)$ and $\\beta_1(d)$ over a year-long period). In these settings, confidence intervals are not appropriate to report, as their coverage only corresponds to a singular parameter in each vector. Instead, we should report the confidence *bands*. These bands provide correct coverage for functions. See the References and corresponding Applied Examples for further details on confidence bands.\n", "\n", "Here, we compute the confidence bands using the sup-t method. This requires that we have the complete sandwich covariance matrix for all our parameters of interest. This fact is what required us to simultaneously estimate all linear regression models and thus compute the correct sandwich covariance matrix. If we fit separate linear regression models, we would no longer be able to compute the confidence bands using this approach.\n", "\n", "Once we've estimated the sandwich covariance, the confidence bands can be straightforwardly computed using `MEstimator.confidence_bands` but this function may take a bit of time again due to the dimension of the sandwich covariance matrix being quite large (a 730 by 730 matrix)." ], "id": "272c4db9a52db44e" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:21.382682100Z", "start_time": "2026-03-17T15:30:10.614550600Z" } }, "cell_type": "code", "source": "cb = estr.confidence_bands(method='supt', seed=3810841)", "id": "85f35b5c44dc7ed2", "outputs": [], "execution_count": 6 }, { "metadata": {}, "cell_type": "markdown", "source": "Examining the results (730 coefficients) is unlikely to be helpful. Instead, we can plot the $\\beta(d)$ functions by $d$ to get a handle on our results. For statistical inference (i.e., expressing our uncertainty), we plot the aforementioned confidence bands as a shaded region around the point estimate of the function. Code for this is given below", "id": "8c2f1c99be2458f9" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:21.564036500Z", "start_time": "2026-03-17T15:30:21.400150200Z" } }, "cell_type": "code", "source": [ "s_range = list(range(1, y_s_vals+1))\n", "\n", "plt.subplot(211)\n", "plt.plot(s_range, estr.theta[:y_s_vals], color='blue')\n", "plt.fill_between(s_range, cb[:y_s_vals, 0], cb[:y_s_vals, 1],\n", " alpha=0.4, color='blue')\n", "plt.title(\"Intercept\")\n", "plt.ylabel(r\"$\\beta_0(d)$\")\n", "plt.xticks([])\n", "plt.subplot(212)\n", "plt.plot(s_range, estr.theta[y_s_vals:], color='red')\n", "plt.fill_between(s_range, cb[y_s_vals:, 0], cb[y_s_vals:, 1],\n", " alpha=0.4, color='red')\n", "plt.title(\"Latitude\")\n", "plt.xlabel(r\"Time since January First ($d$)\")\n", "plt.ylabel(r\"$\\beta_L(d)$\")\n", "plt.xticks([1, 60, 152, 274, 365-30],\n", " ['Jan 1', 'March 1', 'June 1', 'Oct 1', 'Dec 1'])\n", "plt.show()" ], "id": "cf763f058f6700c8", "outputs": [ { "data": { "text/plain": [ "
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IXC+CBU7deAJR9QMsTFvh5usGkaVuvJkQn1NgqdKYMkKiB7rtouDkE0LCjbEa9UHave320seugjhwsxwWmR6wwExEcLQ/aiMTLQGB2POR0r8nikVnM7jlDkYl9BLEManoPA/uPn+o4HoLIkyF6wdW82NCIh+Kpyg4+YSQcJGEWJ6TEXO0ElYTI5pOR+FJI5RmY1+1PH2MOCZ/mJpOu+Ceaob3nImq4zmwskSDxSkYEiCUzkBAumkg3ANWva4IPt+B57IRJ5aO8zsSwe27ER+mjxES+VA8RcHJJ4SEiikX0BxWn0RYgHQy72Cl4QtcUddbjXL3wJ30BSwqiRAJgQRPM8QF5UE47YJo2ow4oJoqeFkddLRKM/xhxTElwNVpBKo5T/da2Xz/g5tvB1ygc2NIXJJYheIpCk4+ISQUmmMiL4F1qbE1Ge+C9cNM5poJNgwlCopQRXuyn6KR3miM99R0/J/hltO6TAWWJSYeUJF6AepGrffRqiUBwlatTdehbpQKp5etdjW/RFE8GIlX0tgYmBASG9RC4crjMTnvhBVJxYw3VDhdA+G0A+1S1GoUiNqwRhXC0pSO2KdZEGZi/YwnNBbsDbjlTNPiNXDJ1YbArIe/1ZX5EJoNqxv1BhF5BbWnjrLa06ysRN8+QiJjVCKEkAjF9GLri4l3SQDLRRrapnSE5eN1L8KpFtxQ+xBQXh/xUIV4rC7+53M08CX7z5OWH5gDEdsTbru9EEKz4cY8BnW13sC5PAwCSq1Ok/D8MXi9yUHEmhESmVA8EUIijDTUSNJq20fA0rHCR1FKG7WA3IxsMXXjvYQ4HZskWLGyYTXpi32nYYI3hTBVCLCP24GsQTZdJ2TgqQhabAnabbDYaQzaO4gHOwqCqSV6/xXjf8/Hd6DtXgiJLljnqQpgzBMhFaUjMrw6wnKxA3E23gouJmHyrW9lhtVFAcfnvLjYVIx1RubX2/jfXkiv1xgmFnUMD83wXfRFmYNMWAPrI15qNiyImyCUJ+B3fY6CldQsDBiPgpNPCLE5AiUFasPS5Ms91xgBzL28FLdcBouTHRieAeuVB/3oPsdkTaqOFHyXx6EieyMIKM1WNKzEd5EAobwTVijNiKSQJTUDA8YJIVFEPzTgLbKa4LqtTKfD5ZYJK4ZhD8TQD4ihKXVZQRoi3mYNxFUslxaIFIohjPagRU4Byhj0QkXyASgtodXLn0WMWWNYrDwQUIRELox5IoTUIAnoQXcKShC4LULqhjsbAcoqhAyrEVOzzo+VIhW1nsYxrqZGKIVLLg+Zel2RIfk7shj/gdinx2B1Uqvg1xBbmxFLRUhkQvFECKkBUhFY3B0Wp21e4l2aIgBcXW6CwO5xSHFfCLHliyQENet+U6vwcxD/eBCIvxg1urrDApgPi9NQ1I+qj9IGWl5iLCxQW1ztdQiJHCieCCHVRBpqATWDYGqD2Bi7eW8qLFFNkPKehgn0IwQZ6/8HQl+zC2Jqvgwgskj1oMHg76MlzkGwONWyimi2RW2uTMRJ7UVc2ypcLxoDNwOxUYTUPBRPhJAqRgXRiaj5U4Jq0w0Q22QChQWWoutdQcXqnnshhIKKtSCc5kNwsRBjZAkobRT8I4pqdoKLzoMMyKdF5J9w0c5H/Ft3XDOHIEbqZ1iuCKlZKJ4IIVWIWhkGogjlFrjTvJUf6IVsrFooMTAbVqYpIQR4pyCuZhGFU0Rj4tpWoKL70ajRpUL6KxE5V0TOEZFHLItkPVgie+DaWA1LpLpyCal+9MqNK4455hj5/PPPZcOGDeLxeOTsszUYtTwPPfSQbNy4UXbv3i2TJk2STp10hUQICQ0VTOfB7bIU4ikb1iBbOGka+9UQTrMxaX6KoOJiP4HmzWGl6IGf7WGxUPcQLU6RjwcB5S+hifAMWCNXoFzFPSJyB+LemkEU56Ho5pUosukuVUFI9RB3lqd69erJ3Llz5Y033pBPP9UBujx333233HLLLTJkyBBZtWqVPPLIIzJx4kTp0aOH7NmjabeEkMDUQVuVNFgIfKHC6RYEDKs1YVQQjWMTYWFSN9AXqDzuwd8a58RSBNGDBxmTuv0Ga2NDXBcZKGsgEMc/QGwthrg6FLFRP+KnZugRUj3EdYVxtTydc8458tln2rNpP2pxGjlypLMpWugyOztbhg4dKh98oP76wLBIJolfWiNmqQUyphZjYvOGCqthCA5Xi8ITIrLVy35JeM1aqAWUhEDij1CAkcQO9RH31sz63nuhgKohB9/7p7gedkJwfwXrFSEVh0UyK0D79u2lefPmMnmyNqzcj1YKnzFjhgwYMMCneEpJSZHU1NRyJ5+Q+EOz5AZBFBXDEuBNOKWhuWwfCKds9DzTrDs3ybAybcNr/QQrxQpYmkhsoULoWxG5HN+zunt/RbmJMxFk3hSbWqj+azV6PgsWqRkINiek6og7t50/srL215NRS5ON/m2e88awYcPkwQcfrPLjIyRyyURG3V5MePVhTTJ0hRCqgxR0newELrcXfAinJPzfAlgZNNCcLrnYZy7cdIfDwrgb15S5rtS6eS1i6u6G2245BNN5sHrqQpdlDUjVQfEUBkaMGCFPPvlkOcuTBqQTEj8cDUGkQkcs4dQR2VNaPsBmo4jMFJFZrliVVEyOqRieNEj4QwaAxxUaSfINMuzaQXDvg5DaCVewCu6bUCvscrjtnkHM26GIn5tW0x+ExDAUTxabN+8fxDMzM8t+N3/PmTPH50ksLi52NkLiE3W/9ffSk+58tF1RimFd8kAwaSadOwGjDtwy8yHCEmFtYOZc/JGD5IEWcM8diazKIlw3arEcATdxe4isG5BpuRaCvTXcfVzIkvBD8WSh2XWbNm2SgQMHOhl5xorUv39/eeklTaclhOynqRV/0gvuOnWr2ZYoI5x+QjCvN9ecnbvSEfEqn2ByJPGNB8JHtz9E5GAI9TqwTLaCe05F9m2wbl6NDMzvIbh6QqhrixhCwkdcliqw6zZpkHifPn1k+/btsm7dOnn66afl/vvvl2XLlpWVKtAMvHHjtKcWIWR/wPclEE8qmgrgJjGxT6l4XtH7ZnwQJ60l3He6L4UTcVOCwHHdBC7ioYiJW4aEg1PRRPp0xEAtRC2wc2G9moM4uo1BlMMgxD9xJ54OPfRQ+f57XZXs56mn9KYTefPNN+Wqq66SJ554whFYr776qjRs2FB+/vlnOfXUU1njiRCHZFiUOiEeyUxCGntyFUSQYWGQwqkp4lvUOsUMOhIMuShVcY4VTzcZ15JanG5HwdUvUP7iVBTXTHJVsM+D+CIkNOK6zlNVwTpPJPZoDPdcS8Q3rbZ60qmgegC1efbBjaKxKQ8GcNUJLAKZmOS0CCIhoaCiu7OI9BWRfihhcTEy9RIh7kejAGdtTHdNYT1NgAgbg2B0QoR1nggh4aI2UsD7Ilh3JVbthlMhnHLRWqUNfg8U45SOuJVJFE6kguyCO241BJEKqY9Rifw8xEhpHJRYLj87saEL6ke94iWBgRDfxF1vO0JIKKIpCzEjveGmW+wSTu3RhkVQUmAn9jPNX71RF4G86bAI/FmUlpCKkQcL0ncQ71pU9UUEjiciPupSuO70uha0f1mFa9hdSoMQ/8RdzBMhJBh0QvkLVvPpcIfY5Ti6QACZOBJTs8kbdeDuS4XFqRhZdZPRLJiQcLADMXaNYSVdg4bD6to7DFXtlSuQlFAPVqspyOTTEhmEBAfFEyHERXO4PJohM2mdKzTyIhEZaP2tVqZ3fJzFTlj5/4EGwWlwsejvrABNwo0K889gHe0Jt/D7SF7IhKhqDuEk+LsEYqoT6kupyKeoJ/6heCKEWHREccssCBx3PskhlnCajlYa8zABuekMd8pncOUxN4VUB1thcWoFy+iRuE53oc1PA2yarPB/uKZno8xBAlrAzMS1+7vLTU3IfiieCIlr6kMolWBlfgqsQ27hpK65g6zg2wmYiNwkY98GyLj7EDV3CKlu1uMaVQvnMaha70HF+nwEjv8BF3RTiKs9+HmS1VtxLKvckwOgeCIkbjkCk0RDTCrJCPh2173JQt0c08xX40Q+9/J6HUQkBZNVCiqFUziRmnbjTYZLrh1c0FrY1TAN4knvha+tx7fgGu6Lnx8GUXaDxBMUT4TEHXWQPXcWLE7LEZfkzfWmbowrIZx2wZ3xgZcKzU0xKX2A+BHtScaWGCQSyEWj4dPgSvbgWq8Nl1wxrte7EA/1CyxWxcgu7Y7aUaZtEHstEoonQuJMNB2PzKImEEPq2hAvYigRrrcTsWpXF9zDPiqAp8Llp61YTANtbehLSKQwC9dkO4ih2rj2TY/GgVa5glOQnTcLIkpd2N1E5HpYVb9CjBSJZ2h5IiRu0LiPwcgoWuZyX9jo6vtW1MExfOxDOCVhNa+BtT9X0XETEg52Iu5JN3tBYbLsOqO8wem49gehZMfzsEClYzsHCw8uEOIZiidC4iaL7miUFdBsJF+0QnyTBo0LJon3UZfJm7UpHYUGv/Lh9iMkkimEmFILlOl5+j1aEV0BYaUZeU9j8ZCLx05HI2u68OIViidCYpoE9Pk6FatsDZj1RTtYnOqhFtOzEE/uEgPJcHEsR2uVWdiPkGhErbDHYTrci1in2WggfBfE0q0oybETQeY9EQc1wdXuhcQLFE+ExCQas9QD8R39MehrWrY3wdQQboqzIbBWQDjpqtybGOuMooNv+diHkGhiFRYL3RH7V4z+jRtwH9yGa143wb0yEWUMGuE+0GKyJJ6geCIkJm/rUxEcngRrU4GX/nJXohO9zVLEeOzx4/7bjFIFFE4kFiiCADoOVtZOWHishrD6D3rjleD6PxOLkSkQXBoD9SaLacYZFE+ExBRHYWuBbKJ8H9ajaxHXUYpJYjcsU1NcPezsYprtIZw+CdD4l5BoI9+qXZaJxUcPZNepgBqO5wajUfZFyEb9Dhao4+H+2werFavpxzoUT4TEDO0x6CcgHmmPj0y6cyCcirGq1gyjQKh7byoKDmrHekJiFY11GoO4prPgrjMu7wko83EM6kZpvbRXROQElPUoRYNhLXHAOMBYhuKJkJigCTKA6qIujbcYqMvR5ysRK+S3ghROjbEy/5HCicQRC+Ga1qy7trhX6qAJtj53qYi0Ro2oidjXJGgko+6Zt/IeJBageCIk6slC5k87P7VnTkCpAkEm0ZdWgUxvaKxUM4ispqjQTFcdiTdWQgSdi+KypiL5bFh2b8W9NdNqRfQH2rpkIEOvCe6j71BPisQCFE+ERC0avNoSXeHboJCfDtJumsL9IFg1qwXJH3Xx2puwgv4O4omQeGQuAsS1d2MeLLwdYH3Se+lYEbkbwuonEflMRBbBKjUY92QyqpRvhBijiIp2ql081apVS7KysqRu3bqSk5Mjubk0axISGp1QZ+loCJ09cNV5E04a23SNVYJAB3d/JEM4/YLCl/swKTAAlsQzK7AJhNQFuLemwcqUjnvxFLj4nnW5xBNgieqNBsNja+hzkKgST/Xr15fLL79cLr74Yjn88MMlJSVFEhISxOPxyPr16+Wbb76RV199VX777bfqOBxCopjDEPBdD5lvmgnkjW6o7zQAMU468L8cQAQlI3NIKy5/wYBXQryyGPGCXVHe4HXUSitBfFQ3LFhGW5mrHiRa7IWl+He4BEm0UuXi6fbbb5f77rtPVqxYIV988YU8+uijsnHjRiksLJSMjAzp1auXHHPMMY6AmjFjhtx8882yfLnxHRNC/kQtQmdgkFaXgZsEuPH6Wm46027iQx+97GqjrEEq4pz0dT+icCLEL2uwJSLrbibuL7XS3my50udCOC3GoiQf99sRFE9RTkJV2+Pfe+89GT58uCxapD5g36g16qqrrpLi4mIZPVoVe/SSlpYmO3bskPT0dCkocBcnJKQiqEvg6gBB4ecixsLwC9wKvvavj9fTQX0LYpwWwS1BCAnuvvwrkjaMJakrLE9qjbLZg1Yub8JyrCUO2NolWufvKhdP8QjFEwk/J8GatNiHBUlXs/+0Kor/ECAwvBaqI3+PzDtvhTEJIYE5CNX6k1CuYBUsun2wOElG+QJ9TFArbQF6QrIeVLTO31Xutps6darMmTOnbJs3b57s2eOr9QMhxLuFSAffrX5cb1dh8J6N2CZ/JFqF/7Q+DYUTIRVnAe4jE5PYBffWDGzKBwgWvwHFNGfjnlYLFJsLRyNVLp7Gjx8vBx10kNx5553SsWNHJ0h82bJl5QSVbpp5RwjxRi+0jPDm+k4Tkb8hw2cnYpv8kYG4qFVIqWYVZEIqh2akTsLvy2GFaonGwoYSCCZNijoUluQ34OJrCUvxdN6PUUS1uu0OO+wwGTdunPz8889SUlIiBx98sHTr1s0RVNnZ2dKypV5E0Q/ddiR8pKMPXYYr9bktgsc7wjKlgapPBoihaAaxNR097Lz1vSOEVA61KJ0Pi+461xSr7ZEewu8PIM6wKWKmNqMF0i8QWySu3XY2L730ktx0002OgDIMHjzYKVMwZoz2EiKE7KcJBtTuiJtYaLnc+qM1hGbICQbdF/HT362u4mkchBMhpGqYiR53g9AfrxhWYd0KYIHqB1f70yiYuR3357kowPkLLFdM3ohUqlU8de/e3XHR2UyYMEFuvPFGp6QBIaSViByFQTcdxuHVcA2oWLoTYsrEWnyNLB9vsVCGJMRhLIPViRBSdXgQDL4M93EbVBtvoHnluAe74D7WeW+kiBTBCpULN73+3w4RmYOkDv2dxK3b7vvvv5cpU6bIQw8Zs+V+2rVrJwsWLHCKacYCdNuR4DGVh5uhd1YPuOE2wK1m357XwOq0CwGqk7DC9UcdVCT/A1WN2Z+OkOonCYshFU1/wWLnb3hMS4k8j1IGhhQ81wJdAQLFMpLqnr/VB1Bt3HHHHY6F6Y033pDevXs7VcZTU1OdYPKtWzWTKHJQa9iqVaucYp7Tp0934rUICS8pMNPfhrimQ9A7ayF+2sJpAISTiqUXYHHyJ5zqQ4i1RcaPVkSmcCKkZiiFVelXuPVqo4VLEYLG74HF2bji1dW3FTFTvbC4IpFEtYqn2bNnS//+/aV169aO+06FiSq7a665RoYNGyaRwoUXXihPPvmkYyHr16+fzJ07VyZOnChNm2pgHyHh4nS0d9iJLJ0lPoK4G4nIxfhdM+T8VeBvC9HUGnETryNNmmZ/QmoeDwrX7sK9PhI/NVlqiIiMEJFTrZpQuSi2qW48EknUWJFMFVB9+/aVffv2yaxZs2TzZn/BrtWLWppmzpzptIpR1EK2bt06ee655+Txxx8P+P9025HAtENl4jxs/rgcndu1P90Tfm7Z+sjmmYI+WrOCcOsRQqqfi2BpWogM2KPRskVLkgjE1STcyw1xH78mItn8suIl205FkgoPN/qYt8dbtGjh9L6rKZKTk+WQQw6RESN0BbAfLaUwefJkGTBAXSfeW8uo+9E++YT4ucowcNZBMLg/6mNQFcQs+VvrtEEdGXXpsXEAIZHLd4hn6oquAV+hWOahKEGShQbgg+CmT0UPvamwPGsCCYlpt51acF5++WU59FC9KLyjCu/aa6+V+fPny/nna32MmqNJkyZSq1Ytp+6Ujf6dlaUX9IGoy1GVqtk2bLCLoxFi0wCD4uGuuk2+OBaxUauDcNdtR7E9CidCIpscBIHnQkQJBNGvqP80SkQ2ogL52bj3D0JspC68SE1T5ZanHj16yH333SeTJk2SoqIix0WnliX9vVGjRs7zPXv2dOKh7r77bqd0QbShViqNkbItTxRQZD+aMXMBsudKIZqy4ILTwpb+yMRq0/TD8rb2Scd+2lPrcxFZzxNPSFSgY8K3GmULEaX3sGDxMxOlDh6DdaohOgyoW/4EPBc5oS7xSJWLp+3btzvZdCqgTj/9dDn66KOlbdu2UqdOHSfD7t1333WCsRcuNEUAaxY9pr1790pmpvE970f/9hWXVVxc7GyElEctRueJSF80CRXEIi0IYB2qjyy8vniNRRhM3bduNwy6i9EEWAdUQkj08CviH9U1r2EsBVacosZCzsfYoRboj5Ax2wPjw4cYT0hMF8lUS9PYsWOdLZLRtjFqHRs4cKB89tlnZQHj+vfzz2stDkKCpSdM7VpjKdhm2F1Rz0lXmoLB8U2X2KqNxr4qmj6GC4AQEn3sRdV/jYNsD8uSKYy7G4siFU/Ho97TZown3ZBI8lkQcZMk6iuMRwvqgtN2Mb/99pv8+uuvctttt0m9evVk9OjRNX1oJKqK4h2BHlWBhFM9BIl2w+CZiHiHD2FNKnHt2x6ZdF9y5UlI1KMiaQwWTFlo3XII3HgLYanuhXYuzyITbzGK316DfTSQ/MAELBKD4qlhw4Zy8sknlzUD1jgodd/l5QVK2656PvzwQ6em08MPP+wEiWtNqlNPPVW2bNlS04dGooYeaNrrLyhczfVXIGBUxZbhJ9RmcruCEyGctH7T2AAtWQgh0YUpW/IHqo4PxDgyEWOJ3vv3ich/4K5fihpwR6AH5jRk20ZWwelYpUbqPF199dXy97//XcaPH19WlkBFlAqU//73v04F8miGdZ7iHY2XG4qVpPad89XD7k5YkgSrxi8R8O3LDdceGXWvY/AkhMQuWvJmAIrp5qGdS1O46f7jskg3hdVqAxJH1DJFqnL+rhHxtGTJEqdy9+7d5bON1DWmWXddu2rcR/RC8RTP6ArxLNRcWuzj9lIL0j9RVXgZ0pIDWVzTMTi+hSBSQkjso5alWyzX/31IKNEx4CWX9TkB488+dCtQEcVFVkz0trOLTnorJKmP6XOERCcdRORSuOF08PJ1LR8P4aRtWV4MQjgJxJh2Y6dwIiR+yEW2bTMkj7wId35vWKLsyBsP6kHlIGbqZAgqEjMxT3fddZf88MMPsmDBgrJ6SK1atXLqPWlZA0KiC3XPHYYtDTEL3khCyrF2VRdk2WjwZyDSsJ+7XAEhJPaZh7GlPsTRs7BGqYC6Exl3ulgzqLVkFf5HH59bg8ceu9RYb7vExEQ5/PDDnXYsisY+aWab9rqLdui2iyeyUASzC+KRNrpuqXMRzKmD2cFWCYJpXkoQ+KIrLE6akUMIib9pWgtpHonMO8F4o71XTVuwb7AY2+uyhGtpg1etApwkatx2gwcPltWrV8u2bduc/nCnnHKK87gWzbz//vulS5cu8tNPPznNeGNBOJF4ojZarXSCaX2DSwxpd/TByKo7AcIpHyUIRgcpnBqhaJ4W0yOExB8e9MLLRhsmgXX7QRH5Hn+ri2446soZ1kJAaTsXuu/CTZWLJ82e++STT+TCCy+U33//XcaNG+eUAtBWLGvXrpUzzzzTebxzZy36R0g00AiC6WSkEv9hVQU2mMaegkJ3UxEYfo+PVituElDzqSX61TF7hpD4ReOYJqDjQBM8pjFQ74nIy4iNyhCRG63ed3theToNnQ60ECeJGrfdzp07nVimNWv217u55ppr5JVXXpE77rhDnn1WfbciTz31lFOqQAVWLEC3XSyXIDgWlcPrI2Rwg4+A76uQZjwHQZ6h3pbdMDjOQN2nYCuUE0JilxNhzd7h6m2nY9ElInIM/h6L+lCCsaot/o6+3rFx67ZTl53GNhm0l522O5k6VVfi+3nxxRednneERCaJ6DOn1Xz1Ot2Nxr4LfQgntTqZa15rN4UqnLpiYBwDKxWFEyFE4L77FKVLGlunRK1Mb1vi6Hxk3Amyejeg6KYu/khUZNv95z//kddff126desmEyZMkLlz5zpCSWs9GerWrevUeCIk8kiD+60PRMzCAMZaNY3/FZl1cxF3EKxVKxPiSQtmvo+CmYQQYqMdBurCHadlC2zryKdY7J2C3ncr4dLLw9h0BhZ/WomcRLR40h5xavq6/fbb5V//+peUlpY6wkmLYeq2ePFi5/Fp0zT7iJBIQcWPZoKehCw5tTSVL+p6ILoavE5EWsOs/k6Q9ZvSMLh9jMFQBdf+Eh6EEOLdAlUPbjzN8t1kLerGIRtPOxJcrd1a8VwOsvMGw7LNxVnUlCpQ61KfPn2kb9++ZZvGQ9WuXdspVTBjxgyZN2+es2lgebTCmKdopiEy47pBDNVFFfA9QWTeDUOQt6YFv+Cn3pPt3qsN195KZNMQQkgwJKN8wdFw4dmFeZuii0Ft1IH6yvq/7rBGmSQUHXd+h3uPpEVyexZ3vSd16dmC6qCDDnIa8kYrFE/RLJyGIr03B9ajQNYmYz36C2KVdFAaKSKBmkjXQQkDDez8M/6PEEJCQzNyL4Slab3VkmUAElcEi7m51rTfFFnDHgis7zEWkbRoEU+xCMVTNFIPDTiPRlxTsDXH+qBNQiJcbtqwc39mqX+XYHfEHbznpcwBIYSEQgbGLg0I34pMXUEG3gmwKt3no1hmOtq/vA8LlIYR9MNzi4NYCMbn/F0j7VkIiQwSIJh6wQTeFJXAgxVOTbCyS8SqbpyPWCWzRkmEeT0LMVSaOkzhRAipLNvRCHg3xrQ9EEwfwiLeAgHm3qxLOyC+/oIMvcawZiWiNczrHKcipTEwITVPAuIFToDZugSrrFD8/lcgJmoFCtVt8OGeOwi1obrB6jQFrVnia0VHCKmOQPJpcOElYXH2EZ47CYV9vbEa7r4OCCpfhBiqruihR9zQ8kTijFRYmvphYMhHpkqoHAPXm7rq3vCxMktCJfJfYNEqRhC5b1MwIYRUnH2o9aSJKx0x3ixEod1j0IezISxSbvJcdetKMWYdAzGlvxMDxROJI2qjTcFhGAjWBRkQbkjDQNIHKzvBQKXB5d5oDdH0BQUTIaSaKEAG71CECGxGAU0d7y6FBSoBFqlAIQrrsQBU69Osajr+6IDiicQJB8NNp9am5RXoMq6Cawh6S5mKvlr9+2sf+6fApfczhRMhpJpZgbHpLFihNllNhC9FtXENJVgKd52v+MtijJVHw423q5o/R+RC8UTigOaoEl4bZuxQ2p1o1e/jERuVCEuSmsAX+GjNYmiPAcykBxNCSHUy1WrVkgcR9D0CxI1VypQEKrV64blZhxCFc0VkIzL55kq8Q/FE4oAj4edXwSMhCqd7EfSt/KjdGYOo7pGFgUpdeowTIITUFNNFpDOSVkxRzNn4vQ8s8UeJyKkY37xZ5PfCWn8o3H06pmlIwniMkdkhZCjHDhRPJMZpDZddKK0IWmBAOQTCaTUq9Aaz2mqL2+orWJ4IIaSmUIvSD2jXUt/KJi6EsJqBYr1amuAG1HoyyTA5aBm1Bftr4LlgIXoiYkBVmE1Chl98QfFEYoAk1ClpCT/+ZKvVyQAUwAxUuNJwDuqh2PVTngsybkkLzQkGoDkhfgZCCKkKVsFy1A2tpmzUiv4/EbkZgukh67mWGFt1/LNRF2AKRFYRQhr+sApzxgcUTyQKsQvj14Pg6YEA7drYfkOs08EhNNkdZAmnWRBA84PIyEuAqy4DXc0pnAghkcRvKNFiW58MKnweRTXyTijfMgF/90btJ+29abMFWwJedxDKH8SP+47iiURZjaZTIIp+hivuAvju1+BvDeruixtaMBDoFox7T8sYCAYBtV4FSzuYtVU4sU8dISTSWIqwg+4IS1jhyq7TbLwnrcKaJgThGFQsd1ufDB4Iq8Ngpd+ImlCxL6IonkiUoIKoPyxMJfC168qnFQYGOzDb9KYLFNhdB2KsF5pkJmGFFopwqgNR9xH6QhFCSKShGcZvwbJ0KkTUYi/lCey/v0bsZ2+rXpQ3dsGVNxj/Pw2Wq90YU/tg/J4CF2JsQPFEooBD0XdJ4LPfA9HSDCZnd0ZbsP3irsaNbdiJeKVQaAuxpj2gCCEkUvFg/NTGwVciiPwPP+NlDsa1vohr0tgoX2zGpm7B4xDCMBnC6zjESDVFOYTYqFZO8UQinCzEIRW5MuYKQwgCNyTgZs6D+OqDgWMMXm8DaqAESwMMAprNwga/hJBoIBdZdBciwWYfEmy8dUr4FuLpKFiOfFmf7AXoUngIOiL+dB0SbtpDtGlM6Ach1tuLPCieSITTHV2+Q63R5CYNxeK05pPNVKTsVuTWaYPaKCxJQAiJJjagJ6cKoyawDnkTT0thWe+JmneCXp2f+enSUAzrUh2rP54gNqo2SsCoq29cVC86KZ5IBJOMBr7+KnkHw5VoLyC4WfciTikbfedCIQnm56aIGdDVGCGERBv5sJo3gUW+sY9yA2+KyL+wABXUeMoSkVeQ4eyrRIE3cVWEunlH4/29xZf2RkjGDgi3UPqPVh8UTyTCaIBVyV6YfZtXMsiwvSWctiCwewGy8jTwPBSaI7A8Bzf9D0Fm8hFCSKSyFVXHT4Lg2Q2hlAB3m45xjyMjWcfM6+GWewL7PIosu2DZiYXrKXi9H63knqPQj08Xt4Kxf1wFQjSqHp1B4oZ7771Xpk6dKrt27ZLcXPX7Hkjr1q3lyy+/dPbJzs6WJ554QpKS1NpAKk9biA9vl2EdpMXeKiK3QzgdYrUDqCjnWe65+5GuWxqicKoN4aQ1pT4RkadF5HMKJ0JIjGCqhLdHqEQmFrLavsUsPGchgNz0wEtFILhm74WKWqtyIZQux/sMwN8FsDgtQWjERZbVK3KIK8tTSkqKfPTRRzJt2jS55pprDng+MTFRvvrqK9m8ebMceeSR0rx5c3nrrbekpKRE7rvvvho55tihOwIU92GVsxvlBtYgfTYDZf93QKicCdNtsAUuvdELN2VJBdxzhgaotLsdg4Y2BSaEkFiiEEHka5Hd/B3GzaFeCmtqCYMWGLO1xt3hWEyqBSsUcvC+fdF7z2NZpQSL3GXICmyHgsWRWao5bhgyZIg8/fTT0qhReSvIqaee6lidWrRoIVu2qNIWuf766+Xxxx+Xpk2bOiIqGNLS0mTHjh2Snp4uBQXBtPWIVNJxieRXUp8fjgq0tSGaMvC6hXisCHFNe+CyqwWxVYrAw2BRy1ASBFhT9GpSU/M3GBhCIQXCKQsZJ5NxbIQQEsvYsuAKiBu1AnnjFixS1Wo1uhLvWQdjrre5pjtCJDRIveoJdv6OK8tTIAYMGCDz588vE07KxIkT5eWXX5aePXvKnDlzfFq0UlNTy538qmMQhMbviAsKJ0m4gAshRC5DMOHPlQiMVh/22RA0psR/oHTXvQHqj7ipi2DHO3D8K9DHSfBZtGBbKGRgZZUNM7WKJwonQkg8YNtTZqKkS4qP8IlxEE/9UUpmdgV73BX6yd7LhYBSy/8RmJM+q0DManiheLLIyspy4pxszN/6nC+GDRsmDz74oFQP/TCxq2VlfBhftzWEWTPEB7XEBbsNdZZ24kYK9TVPgMur/HkNjK8aIA2xOjE3+AnowWTTDcJLxdqXIQofE9+kgut7WMUIISQeWYFg8GauOnsGdfPNgHjSQsZniMhIPB4utsN1dz3mlGQIue9DrMsXXqI+YHzEiBHi8Xj8bl27dq3yY1ATn9latlThUdUcgUk+HLRH0F5vWJwuwM2wEjfObjTfPR1iRWOV/Onxw2BxugSuv1CFk6/XvRwZHvfBB34wggkNa1EFV2/mf4vIf1BOIBS0CeYcBFBSOBFC4pkSWJN00eqLD7Hg3gD32y1Y3AuEzmEI3aioraYYc1ETzCXrkBl4g/U+1U/UW55Gjhwpb76pdSh8s3KluyO0dzRQ/PDD9Uv+k8zMzLLnfFFcXOxs1cdWXEjHI/urMpVaO0KAZPiJL1qP9xsEvZ2PoMHpLtdaEgSWHpdAfPjylYfCAGTNaQySIAPjHvyeiFTXL2Ed21sJF2MzuES/ieribYQQEj6WYsz3VQeqAF0a1Gp/F8bn2zAOn4oFtFihG+NCLG0gWMCvdR1TW4i1miHqxdPWrVudLRxoFp5m1WlweE7O/mqrgwYNkvz8fFm0KJTA5epgJaxPiRBQvvzFblJhaUrCxX46sin0YvSHnmNznrNQrbsLAvmMOO2PSrXrw2hObYEil0lWW4FeEFQC4fS/Sogd+3zoufy0Ajc2IYTEKpsQED4Yc4Vao7K9jLm6WH5GRP6BhahmVwsEl46tjRB83gaegcokU9V8nlvUi6dQ0BpOGRkZ0qZNG6d2U58++5vCLl++3Knr9M033zgi6e2335a7777biXMaPny4vPDCC9VsWQpWiS+HYNH0/7FB1EPqgPil9riY9+F1NB00FDbDQtMLLrx5qBp7ElYo4fRDXwxhMwcVbUsRe/UDAsUr27alM1Jgl0IUVqRVCyGExDJTMVaWIrSjh4/SAQUIrVCLUx+EUHyFDL52WAjrOHsN6uVFL3FVqmD06NEydKjWrSjP8ccfLz/8oJOxOMLqpZdech5TQTVmzBi55557pLQ0eMtG1ZYq+AcyH4wbsQ5Ekfqdf4Wg8CZeDoLrqx6qtu6Ddq5sc0Y1ybbEpWSy5MJFW8Q3laA9QEWyONw0hv9erWVpcFe+WMl6UoQQEuukYoGuIRw3Ye5Igkci2PkxC8WKdQ57E33ybDpgcb8BC1pf8iQZYuz5MAenBz9/x5V4qi6qVzwprWBBysYF9QdceSbguTuCtxMjssy9b86FqVgtTaMq8ToJWDUl44bfjps4ASUf1F9PCCEkOM5GIeMtEE6hCJiTkZSkWdAPYLGfCDef9s0zLEbz4vyIFE9Rn21HBCq9JcoY7EEslLrQjPXmXFxs0SScBJ9HkO1R2bipfNQJ0fiod7CqyQnDaxNCSLzxG1xyM6yA8GCZjDAPU0tQrU1/s4TTYsxjuugfhrkt8oirmKfYxYMLrhS/70XGW21YXDKCCAiPBFohqHAVMusy4bKrTFxTCtx0H8Fvb3gZ71FzdUIIISR6F+yjUCrgEIyxGgcbDBoy8hZCMg7GJhjrX0X/0SwIquYofTAM/xc5UDzFDHa1cXMRHwPXXTjjkCrKsbjJPnTFF7VBcGGJlUFXiFoeAuG0p5KCbLmPAp+VaTtDCCHxTg7K0RwSgngSZGSPwdhfH8U4v8bCWRCW8riIDMeCuqvVKNhbsc7qh+IpqngUF9vPQbQ4yQvxYvZmsekJi1ZRGNxmlyC48C64zzpDMHVwFWDLxc2iZRAEN1RFqYsgR7U4RVq2JCGExAKzYD2qE0LJHEFms7/s5t0IqzgWC+vjEMoxH56DmoXiKWpQ//D/IUOsDy4e7732wsMQVIZVMfNaBcoZGFJRGTwJYqkesv5sNiMeS821Wk/rQQiq2dZKJBQSsFJRa9zCMJQzIIQQ4p1lsO4fhIxo4zUIV2zVsYjjNfTG3LS/FmNNQfEUNezCRfQ/9G47H/WVqsIP3B4Xp8AKdC1KBeypgOXnTvQjKoLlrDvqQ2UjpkmLqb2EQmyGFxCz9VkFhFoHBMdrQOLnEF/hbqBMCCFkPzoHfYcwiC4IlQiXa+0PeFAaYiGvQk27gAzF3z+FPdsuWCieogq1NL2HcgWZiGnaX5+qcmRAjPVBzQ61DgnihNohKPAMFOIMhQshnPJRS2kztkDtU9aEWD4gFW7GVnAzLsVNF8i1SQghpPIsw9Yf7b7qhdiQ3Z8wexqB4+qZECRF9YOgqrn6fBRPUUcxYp5OQZpnJoKwK0pd9CHS7AYTnyQwiX4EK9Tf8H5HwCz7Piw73ugMa5UKmiNx8b9UQfebryKXta2bJhGrnR3YJvk5NkIIIVXHTCy4j8JCdi88AemQG8nWWB0sG10ts14XkQ8wH4WnNVtFoHiKSqbhqxuIek7r8FhFuBbCaTvSRJshNmkOSh/8jkaOpyC1vwFir5700gNOMy7+6iofpjU9gmvM7J86sGIVIyixBzI02sJSNQ5xVRROhBBSM+wTkfFY5HbH33vhetuL5u3tMCeEElzuZk+N1y2keIpK9kF570ABzEsQaB1q6v1xiD9SQfIcrDnehM54+LTVKnUp0kUfhFvMVDPPhBBLxE2hYucLEfkyDJ9XrVgdEfz9Iz7nGTj2zXgPFVKEEEJqlgIReRuutXpw563HvJCEOeTQqE/koXiKar5GnFIHWKACxSQdjpTPRNTMOB2PfxKE77gIwup5ZM/1gsUqCyuMBNwYs5Gdp+IpXK1pWuF437CCv9/CMaxE4CAhhJDIoMBHPG4pStV0QCxtzWbMVQaKp6jGg47VN8OtpvFG33opCFkL1ikNMDeo4BFk7AUK4LbJg4BKQzzUxbgJBK6/tyBwwiWcasHyNMOVNbcH9UUIIYRED1vQxH4wYpZMe91EeDfS4FXZFHFVxW0onqKeBVZvuw7YMqDulU4QOG1wIZqik6cgiPvVCvaGLoDwWo6yBi3hUtPCZuGkCcoaqMuOEEJI9DMDrrumEFPJqM23Ht6L7ohrNW3HIg+Kp6hHhc+bInICfj8KcVDLEEytFicjdl7DxSgQUXsqKJxsdoepXIIvGiK7sDItWgghhEQO21EA8xT83hVxux8jo3sqFv3dEbIRebX6KJ5igjUQUILYIy0RcIPV7XoqstHsgPLKtlypDhJgyg1XmQNCCCGRwWzUheqGxKMPrfjVrSiJ8xc8vyjiXHgUTzHHh1DrWmvJCKdQCk5GEumwmIWz3D8hhJCaJxtdJBKQLe3OFt+K+exGlD7YjrCUxDCVv6kcFE9RSSNcWHt9uNEeRlPf5ACNF6ubTIghd1xUUxzrXtSZKkW9pma4qdSMSwghJLb4PcDz2xDveizmj1WYL+xm8jWDXc2QRAXfwU2nVbV9sQvZDFMrGWzXCnFTujKoLHVxwXd0afYkiKRiZNVNRBn+LnhfjXcihBASnyzCPLYWXpR5VieMmoOWp6hjJmpjXI+UznCVBHCTjNffCiGj/eIqQ0sE/tWGW7EYtaD2IlvQxGxtQRXzhvhdbxxCCCHxyUrER81ETNQvyB5PQjeMmoHiKSpZDVFxGEoFVKbMvS+ykDY6QUSuqKRQq4sLfQYqgg+ACXYtfp8OoWTIR72ocGQDEkIIiV6KReRd62+NgX3WWtzXDBRPUcsUlL7vBjEVjg7WpnFjMiw/k1DaYDEqmVfE+lQHQX4/W40iP7eeXwJB5YZVwwkhhHhjT42Xr2HMU9SyHgUuZyIuqbJ0QTxSFjIbfoKpVFCPoxi1OLIgroIhAa/5GwSTtwB3jd9iDSdCCCHRAy1PUY3WvfgeoiYDqZwVoQW6XY9FdkMS4pCMy0wtRu/B+tQK77fQh0utFvzRmxEIvgVB4BRIhBBCYgOKp6hnA7IPjqygeEqBi+7DAF2uF2BrjGD1jug/VBv1OvZAdHXDMXWA6+1LVzwTIYQQEt3QbRcTzIMVSlP9Q6UNgs7VtRYMapkaj58e/OwCV15nvNYYVId9G2UHCCGEkNiBlqeYYAWCxrvBCuQtANvEILXETy13YC6Bn0NM+ZwDUVQLAeGX4r3zENuUjY0QQgiJPSieYgItIPapiPQSkRPhhlMhY1MbrrZN6GvXCYbH3wK463zhgeAqgaWpC37XAHBCCCEkdqF4ihk2YNMYpkGoyVQKwZSK3+eLyFdwtZ2DuKSJlaxCLqgzRfccIYSQ+IDiKSbbt3RCLFM+YqE+QPD2cksojYOFyrjvCCGEEBIMDBiPOXahfEEKGij+ggreS10WJnWxUTgRQgghoRI34qlt27by2muvycqVK2X37t2yfPlyefDBByU5uXzBx969e8uPP/4ohYWFsnbtWvn73/8u0cdcxEC9ISJf1/TBEEIIITFF3LjtunXrJomJiXL99dc7wqlXr14yatQoqVevXplASktLk2+++UYmT54sN9xwgyOk3njjDcnLy3P2jR7UVTe1pg+CEEIIiVk88brdddddnhUrVpT9fcMNN3i2bdvmSU5OLntsxIgRnsWLF4f0umlpaR5Ff9b0Z+TGc8BrgNcArwFeA7wGJKzzd9y47bzRoEED2b79z6rcAwYMcFx2JSV/1jyaOHGiY7Vq2FCDq72TkpLiWK3sjRBCCCGxSdyKp44dO8rNN98sr7zyStljWVlZkp1dvrij+Vuf88WwYcNkx44dZduGDVoygBBCCCGxSNSLpxEjRojH4/G7de2qjWz/pEWLFvL111/LRx995ASRh+MY0tPTy7aWLbWKNyGEEEJikagPGB85cqS8+eabfvfRDDtD8+bNZcqUKfLLL7/IddddV26/zZs3S2ZmZrnHzN/6nC+Ki4udzQ3dd4QQQkj0EOy8HfXiaevWrc4WDGpxUuE0a9YsueqqqxyrlM20adPk3//+t9SqVUv27t3rPDZo0CBZsmSJk3EX6smn+44QQgiJPnQeLyjQTh3e0Q6x5RVEjKLC6fvvv5c1a9bIkCFDpLS09IC4JnW5LV261ClX8PjjjzvlDLRUwe233x5yqQJ9P38nnhBCCCGRKZw2btwYcL+4SGEcMmSIxxf2fr179/b8+OOPnsLCQs+6des8d999d40fOzeeA14DvAZ4DfAa4DUgEXMO4sbyRAghhBASDqI+244QQgghpDqheCKEEEIICQGKJ0IIIYSQEKB4IoQQQggJAYonQgghhJAQoHgihBBCCAkBiidCCCGEkBCgeCKEEEIICQGKJ0IIcfHAAw8c0PuyKtH30vckhEQHFE+EkKhCe1Oq2DjkkEMq9Tp16tRxBMtxxx0X1P7Dhg2Ts88+u1LvSQiJDSieCCFxSd26deXBBx+U448//oDnhg8fLrVr1y732L333ivnnHNONR4hISRSqVXTB0AIIZFGaWmpsxFCiDdoeSKExBTJycny0EMPyW+//SZ5eXmyc+dO+fHHH8tZmNq2bStbt251flfrk7oB7bgjd8yT/l6/fn0ZOnRo2b6jR492ntOfq1atCipuKiUlRZ588knZsmWL7NixQz777DNp2bKl18/RokULef3112Xz5s1SVFQkCxYskKuuuipMZ4kQUhloeSKExBTp6ely7bXXyv/+9z8ZNWqUpKWlyTXXXCMTJ06Uww8/XObOnSs5OTlyww03yMsvvyyffPKJsynz5s3z+pqXX365vPbaa/Lrr7/Kq6++6jy2YsWKkI9NX+OKK66Qd999V3755Rc58cQT5auvvjpgv2bNmsn06dMd8fX88887xzt48GB54403nM/3zDPPhPzehJDwoksjbjwHvAZ4DUTFNTBkyBCPcsghh3h9PjEx0ZOcnFzusQYNGng2bdrkee2118oea9y4sfM6DzzwwAGvoY8p9mMFBQWe0aNHH7CvPrZq1aqAr3HQQQc5fz///PPl9nvnnXcOOI5Ro0Z5NmzY4MnIyCi373vvvefJzc311K5du8a/B248BxLH54BuO0JITLFv3z4pKSlxfk9ISJBGjRpJrVq1HDdev379auy4TjvtNOfns88+W+7xp59++oB9zz//fPniiy+c42/cuHHZptazhg0b1ujnIITQbUcIiUGuvPJKufPOO6Vbt25OnJFh5cqVNXZMGmelQehud9/SpUvL/d20aVNH8F1//fXO5g116xFCag7GPBFCYorLLrtMxowZI59++qn85z//cYKzVbRonaaOHTuG/f18FdNMSkqq0OslJu53CLz99tvO5/CGr9gsQkj1QPFECIkpLrjgAse6c95555V7XDPwbEKtIO5r/9zcXMeV5s3SZLNmzRpHUKmA++OPP8oe79q1a7n9NDhcM/F032+//TakYySEVA+MeSKExBSmPpPGCxk0y27AgAHl9tu9e7fz05vw8cauXbu87qtCTR/v3bt32WNZWVly7rnnlttvwoQJzs9bbrml3OO33XbbATFbY8eOdeKeevbsecD7NWnSJKjjJYRUHbQ8EUKikquvvlpOPfXUAx7//vvvHeGhbjstA9C+fXunLMGiRYucWk0GrZ20cOFCueiiixxL0Pbt251aSvqYN2bNmiUnnXSS3H777bJx40antpOWLnj//ffl8ccfd95Pg8G1cvnf/vY35zXtFjJaIuG9996Tm266SRo0aOCUKhg4cKB06tTpgPe655575IQTTpAZM2Y45Rb02DMyMpxAcT0GDR4nhNQsNZ7yx43ngNcAr4FQSxX4olWrVp577rnHKR9QWFjomTVrlue0007zWlLgiCOO8MycOdNTVFRUrlyAt1IFXbp08Xz//feeXbt2Oc/ZZQtOOukkz7x585zXWbx4sefSSy/1+hqpqamep59+2pOTk+OUPvjss888LVu29FoyoWnTpp7nnnvOs2bNGs+ePXs8Gzdu9EyaNMlz7bXX8n7h/cJrQGr2HKhdOzTHPyGEEEJIHMOYJ0IIIYSQEKB4IoQQQggJAYonQgghhJAQoHgihBBCCAkBiidCCCGEkBCgeCKEEEIIiacimTfeeKP8/e9/dyr6ahG6m2++WWbOnOm3dcMjjzwi7dq1k2XLlsk//vGPssq/dhuHv/71r07V4KlTpzoF75YvXx7ScbVo0UIKCgoq/LkIIYQQUv2kpaU5hXADEbXFti688EKnKN3QoUM93bt397zyyiue7du3O8XlvO0/YMAAT0lJieeuu+7ydOvWzfPwww87xed69uxZts/dd9/tyc3N9Zx11lme3r17e8aNG+dZsWKFU9wu2ONq0aKF3yJ+hBBCCIlcdB6P2SKZ06dPd6xMam0yvazWrVsnzz33nNMuwY22UahXr56ceeaZZY9NmzZN5syZ41iXFFWbI0eOdDYlPT1dsrOzZejQofLBBx8ErVq1sWfLli1pfSKEEEKiBJ2/N2zY4Mz9/rxHUeu2S05OdvpGjRgxouwx7YQwefLkAxqAGvTxJ598stxjEydOlHPOOcf5XXtgNW/e3HkNg4og7S+l/+tLPKWkpEhqamq5k6/oiafrjhBCCIktojZgXDuL16pVy7EK2ejfGv/kDX3c3/7mZyivqQwbNswRWWZT1UoIIYSQ2CRqxVMkodYvNfGZTd11hBBCCIlNolY8bd26Vfbu3SuZmZnlHte/N2/e7PV/9HF/+5ufobymUlxcXOaio6uOEEIIiW2iVjyVlJTIrFmzZODAgWWPacC4/q1B4N7Qx+39lUGDBpXtv2rVKtm0aVO5fTR+qX///j5fkxBCCCHxR1SXKigsLPRceeWVTumBl19+2SlV0KxZM+f5MWPGeB599NFypQqKi4s9d9xxh6dr166eBx54wGupAn2NM88809OrVy/Pp59+GnKpgrS0NCfVUX/W9DnixnMQr9dAfxFP+wg4Dm48B7wGJGrOQQjzd80fbGW2m266ybN69Wqn3tP06dM9hx9+eNlzU6ZM8YwePbrc/hdccIFnyZIlzv7z58/3DB48+IDXfOihhzybNm1yhNmkSZM8nTt3rqqTz43ngNdAFVwDCSKeO0Q8p/L64vXFa4DXgIR//o7qOk+RiqnzFKhOBCGkamgiIreKiOa9vsyTTAgJ8/wdtTFPhBDii6Y6CIpIMxGpV4WnKYVfASFxCcUTISTmUNGUbAmoquAQEblFRE4TkTpV9B6EkMiE4okQEnO0EZGdaKGgVqhw00ubjMM9eKqIHFMF70EIiVwongghMYMGcfYUkbbaWklE9olIuzC/Ry2IpSQRWSEiOSJyaBW7BwkhkUXU9rYjhMQnfWBVUuFiD2TdRKQ/fmoWzHIR2SMih4nIMhH5vRLv2QpCrJGIdBaRLtb75+A9e4jITNfKVI+ruBLvSwiJTCieCCE1gsYktRaR1RAmwdAJ7rKVLvF0uogci9dZLyK78Xi+iDQQkXNFpKGI/CgipV5il9Zo1wIRSReRU0Rkm4jMEJFd2jBcRK4QkboiYtp/b4YwE7yevt8RIjLPelytU0eJyDrs/5OIFFXifBFCIge67QghNUI/EblaRIaKSH0v7rfzYOExqLA5U0QyIGhMLFMqXHV5IvKHJZwMayFoTod1yEaF1Uki0h1/Hy0ix+G91RUncPs1RtmDxSKySES2u15nHYTdIdbx98Yx9sR797SeI4RENxRPhJAaMXkfDuHTxxIWtptMxcsg7JMEi5CKpvkQUh2xb0u409yCxmaLJdhsOsL61Q7vOQCWq+3YNxXB4TtgNfJVFG8vxNuxVoZfFkSVWsgK8XkugJAihEQ3dNsRQqqdLhAsq0SkBYTKTMt91x0iROOLzkApgEOxfynEyMEiMhuiJzmI2KJNeN+BeI1dsETVQXbeYRBlaqkqgFA7QUSaW+LLHxshAvvi+NLgDjTv3RnP62svgLuSEBKdUDwRQqqdtrAm7UE8UDuIlRWILeqHQOxCxA0J4pz0b4F1SIO0j8f/uV113tgBa5CKMeM+S8DrNoBg07gngRDbhzIEiRBtgdgHi9VREEgl1nOFiL/aCUuXCrivIaqCjffyxgBYxObD+kUIqR4ongghNSKeVEgYYZEC8bICgqA54otK4Q5zUwxxdRrEjR087g+NiTKocKqN928KV9sS63nN0AuVTYh9agALlo2KRIFY6w3RlysinwQpzmzS4e48GyJ0qoh8XIHjJYRUDIonQki1UgdixYgngcXmIJQXOAZuMndWnJts/J9t4QkFj2XJyoeYCvSegdjnEmjeUGvbQgigdnDnhSKeVGSejyD27bC6HYZMv0DvTQgJDwwYJ4RUK02RXWeLpxw8fgZERTAxRlIJ4eRmPYK7q5MdED89QxiI0+BKTIdQ2ozXSUIm4l9YrJOQaoHiiRBSrTRBFpuphySw+BQheHxpHH0f2yEa1U0pqFJ+kVU6wc1AuPtWumKcVsBVOADB74SQqoXiiRBSrTT1kfK/EnFOlQmgjjZ2QzC1RQzFWcjwuwAiyaYPgtHXeHEv7oXlLBFB8YSQqoXiiRBSbdSHVUXLBJD9FKA6+bGofbUYhUCPxc/BCKg/CiJJ3XT+xJgGrBuSEZyubj1CSPhgwDghxCe9Ub9I25WEgxNFpAOqdJM/4616oERDPgSQWpG6Ioi9CwLbWwYRC7YDLkATU3YS+v2VuDIJ66BY5zRUTieEhAYtT4QQr9RFKQBTZ6myZCErbH0YstpiiVII1Ib4aaxR9WCly0BNK3eQvTfyEUyeZdXBykSVdEMCqrUf76VdjbisVirgDAPQI1ChJYvEOxRPhBCvtMMkfDCCvIMlBfE57h5unTGxa20jUp5tCJS3Y8HWwAq1FkHgwTQV3gvR0xHCKxmv0xMtbASPHwVrVC/XJJDosjqeg9irFIinw9D/73pYwgiJV6JWPDVq1Ejeeecdyc/Pl9zcXHnttdekXr16fvd/9tlnZcmSJbJ7925Zs2aNPPPMM5KersP5n3g8ngO2iy7S/BdC4gsVOwLLh7v3nD86wWKllg+B+DoXbUvUokKCo8BymdazimwGYhsqtPfE79tRE+owxGkcA5G2Claplpal8TpYpGqhyXE3iKXeaINTH7FYh+D7JCReidqYp3fffVeaN28ugwYNkuTkZBk9erS8+uqrctlll3ndv0WLFs521113yaJFi6Rt27by8ssvO4/95S9aHeVPhg4dKl9/rc0T9pOX563GMSGxRXu4hXIwkfbAxFsfE2ewtILwOhaxOoNhOdkTQiVw8if70AsvWLZA9Hgsa9YmiKbGsDwtx/dRB0IrG9bCHnDVdYL1agWEUme4F1cjpmoNRPGPFMQkTknw0yg8YunWrZssXrxYDj30UJk1a5bz2CmnnCLjx4+XVq1ayaZNOlQE5oILLnCsV2qxKi3dH4WhlqZzzjlHPvvsswofX1pamuzYscOxahUUcK1Nao56cNGsDxCkrRPiNRgQvkYdpr8g80tdd7p8eDqI99P/vxnWjLqwfDTC6+jfvBuqh7ZeevJ1hhtvA2KjlHQI20UQyQ3R36+NVS09FW1sdlqxaokQWu+JyIxq+kyEVAfBzt9R6bYbMGCA46ozwkmZPHmy7Nu3T/r319yS4GjQoIFzkoxwMrzwwguSk5MjM2bMkKuuuiqsx05IdaFCRu2w5yHLrZafQWAwrBK1UGPoGMQmmeKV9TGBBsL0iMtGC5JdmID1dSicqo81Xlq+LINIMsLJZOcth9hqCWG1G5l5ptXLHvyPPUruw379vMS2ERIPRKXbLisrS7ZsKZ+0qwJo+/btznPB0LhxY/nnP//puPps9LHvvvvOiYs6+eST5cUXX5T69evLc8895/O1UlJSJDVV12d/KldCapqGcKGthUuuCybPZFdbkxZ4bjUmxGauJrmF+Ds9iKDl1mghopO3Qod35FNUgcbEghisdtgq8v+ERDMRZXkaMWKE14Bte+va1U6erRgqbr766isn9unBBx8s99zw4cPll19+kTlz5sgTTzzhbH//+9/9vt6wYcMcC5bZNmxg5RRS82TAVaZxSwIrQR0EBQ+00s1b43EVTsoWiKx9luVBrU7lUyu8o0HKxVXwWUjkoddLqpUYQEg8EVGWp5EjR8qbb77pd5+VK1fK5s2bpVkzXQv/SVJSkmRkZDjP+UOtSBoMrr7Mc889V/butTtEHYi67v71r3851qXi4mKfou/JJ58sJ84ooEhNY9xwpRBEHREU3AG/65X/AwKE/VmUSrHKMvbUPrAsua1KTRBoHGxTXxL9FOBaIiTeiCjxtHXrVmcLxLRp05zSA/369ZPZs2c7j5144omSmJjoiB1fqKiZOHGi7NmzR8466yznZyD69u3ruAN9CSdFn/P3PCE1JZ6M9SgXAb4HQQhtRzbcFsS7GOuUP9Lx/xfCpfceXIOavfUrhFMDBKeT+BFPjSGsqzqmLSqzm0jMElHiKVi0VtOECRNk1KhRcsMNNzilCp5//nl5//33yzLttATBt99+K1deeaXMnDnTEU7ffPON1K1bVy6//HInkt7UeNLgcA02P+OMMyQzM1OmT58uRUVFThmEe++9V/773//W8CcmJHRaIV5JMOmUwjqkwb+bUSDxQkx+gdqllCK2ZQBcNf3g9muK92mGbC6dQDnBxQ8FVoxcVYqnU+GG/phuYRIhRKV4UrSekwomFUgqfMaOHSu33HJL2fMqqLSkgYolRa1URxyh7TdFVqwoX22mXbt2TtHMkpISuemmm+Spp56ShIQEWb58udxxxx2OSCMkmkjBhGY34N2GwPF5+Hs5ShkstCxUviiCZakuagelw92nrr9NsGLtc/VPI7HPXkwizaqohlcLCP5jcM1puYTPq+B9CAkVWkKrANZ5IjWNpp3fhJIBJhBcEPgdTJsPN7VhZVrvw7JUD1auQCIsFqljWfjika5oMDw2zK+redNXo0xGClzLKtRGuhYFhISTmK7zRAjxTycIGls4SQWFk/m/dX5ccrviUDhprNgwEXkSrU/ilZ1w6Ya73tNBEFDZqFGVC+uTtpQhpKaJWrcdIcQ7Seg7pgUQSdWcXy2de7j12OWaCQzXaLyxA1XkNXYucLpPcNSHIM2xFgD7MGFl4lwTUpPQ8kRIjNEOQdwsGVA1nAbhpJP5dMT6qOuufIfMP8s63CgiQ2J4sN0JsePNIpRYCateYy/XcAnqkhFS09DyREiM0R5VxCvqootXEhBjo/FdnyAQ3uZQETkXk7rymoj8hr6AD8Ha1wwTfi20xtG+goZVsJhsiLGMRA9EUiaSDwzaOPhIH+cyEE3xfbhdwQW4vtX6V76pFiHVS6wuhgiJSxJQ5Tve+8hpTavrUXcqWNRK1B8/70eml0HrWV2BSV0HzZkQTgJhMBePD8Jjp0M47bMEgLr2/iUil0jssRuixnA0ymD0FpGTrWr2waKWU2+V8/LxnWbh/Vigk9QUFE+ExBBZsH4EU/QyVtGJ+koROUREzgjh/7R5siEZ/6uvdZGI3AvXnLroHhaRN1z/+w1+DsB3oO1vBPv9nysW6HgcW6zFPTVHKQsVjWcjiWARxKjWBQuWWnDNFfgQafXQi/FkiFT9rqqSOpYljBAD3XaExBBtMLlok9945XAUVFSOQ5bgMh+uo+awXqxGjzZ1Bb0gIrdYvQDVkmdie97y8TrL4JZrD3ElaMisldeVZ/D6LSGe1Co2By4tu6FUF4gv7ZMQqP/BYBE5AvtOcjV7rm7y8PkGw9q0A1lyAhF1IlbqDfHcdD+uy8aIofIVs1eA76YZhFN3q3ZZVXAOLJl/iMjbVfg+JLqgeCIkRmgKd0m81hwyQuc8/F0Ky9HlmMAfRrq7vf/tmNDN4ypoFojIbEzQPfE6Y/CcvziybyCKDJ9Zv2djqwXRcCxipHRSHo7nrrRipM6CiFNBZkjA8ydYdbfM5J7lxRpW3cUyN+L4ElwV69fhPF6C53ZCWPpqn94UFixf1/EWLBKS8L5HINYq3DFQddEHsi++s7aorh+4qReJByieCIkB6kE0tA6i1UoschKCuY0LR605X4vIUEyq9RAMbtp394eLTYWTINVe+RY/34QYaAUryf4Omv6ZDbdeFiwU873so5P9/0RkCo6nHQTvIitGKg+Ws7+KyCMQEQnI2NMAbJsf8f9HQKToe/pvjV51bMfnc9cWU+GxGL+XQki1hHg6CNa/SVZsmMna82WZKoSA2Y64qC4Qod7Ot00LCM9pQZQ6aA93bW1YzDZA1Gm8FbNYiULxREiU0wrtK3pikoqlTK5gOEVEzsfv2QjknoCJdS6E0/2ohH0KhIgKLdsNlAZriLasEViYQm0Douf9vxABgb4DFTjjUcbgMCs4XUXVOASWN0UW35coDnkkxIdx9RXBXZgE4fUXfK7/uCxW3kjBplagUGkGC4yKNTe+aovZVqESWHS2QvA3gGXwZzzfNYgK4qtdr30MWgP5cl0mIUbqSBSQfcvPOdJr4Uyc/2xLjNbG90DxRBSKJ0KigI6wqrh7x+mK+2JYUFZg5R9PJMLqpHwK0WSzC9v7sEKpi8vwM2JliuFSUlFSWUJxHS2AlaYRNhVd38Gq8qqI3Izv9VLre31HRKa6XmccLCUNIBTVdfgYgql7o9Dk0zi2BFwvaq0SuAZDsVTqcd4H8fREBYtV5uF6NvF52yFs1uK7ysI+wbIWgkjvhTU4Z0ZcGnrhXCzAuTrEj3g6Cq+3yPV9qgDb30qeEIonQiKeZrAqeOBKslf3rTGgB3JZxAp9YBV4F5Nfb4iGHVbGmzd+EZHOVkzRdFgfDP+U6mcvrGQa/ySIqVKhIxAB94jINZjoU2DpcQsnk77/ICwj98HtdZ9VpiEDNZd+Q1C3uq4MKrRGeHH1JUFQNoL1JQlWGxVNhqsRR+atpIA/8iB09mAx4EHQ90m4jtPRQzFYiq3YpxPgElzsigFrDuFYiM+q7sKfrKB2Q0t8zk0+hDDFEzHQ8kRIBHGYFT9jBu+TMfibWB2NDzG0r6DrJRqoj5igjVZ8kmbPCYKrh1tCYFoQVp8xcJU1CMKtVV18AlG0zYtVUQXBx5jok3Hs/iiCZepOSziZukgDIZ7UvSUQDpmIF7rM6s+XgevrMEvU9fZyXDsh6o+Cq1FCFDt/4HiNe3MlBF5GkG5PN+vhtjYLjPZWwVKzyDAB6NvhJu3sRTwdjPPlzSVZYhVIJYTiiZAIIQETVhsM/F8hI6w9VssJSHPfiOyiNEyAsVgQU1PbL/CzulMLwQNw8ZRa8TKByLGsO5GAuu1+8PO8iqpXcD0EE7S+FBasvhAor8Ky1BFCUx8XCJ7dsBx1xXsYulgtUDZB1KnFZRauzZUQORfD2jOlgp/bxlihWuD6DpVCxEHtxvXQAtlxW2Aty3QtMopx7djUhnvPV38+FXtsSkwMFE+ERAiNsOothRtjAgb4dEwMxbDG/AUTwzYIqGgOYE1A3JJtNWqAAPBacPE0xIS2E8/NgosnC1aQ17xYEGKJUGsYvQ1LzE9wZ36Pyuemsvlyyy02AQUtxUrBVwEhuN6ecAVvm6rqabgO3RaeylBcyfpkBa7X6oRK8E0QW2XX59rlpUdeewSJm6QBbwKtIa7LeIstJAdC8URIhNAU4mgjBukmWOkmW3Elq/DYqdgvmgfyTFTfTsIknWe5KZORSfYfnJc8VybVHxCVK/zUC4pXClyZgp/AEtMT7qjXrecm4NwaV1ojWPy6IHh9l5/3WASXnrqSv5DIYjvEUz242uq46kYZId4Ark3BgiXBz/1UiHuyWQWtYyS2oHgiJEIwfdN2oPxAJn66B/Nsq1CgWp+iEZ2E/gGxqFyLuJtjrDYp6rYUH242dU2R4DBV0zvDqmKL0H2uIPR8lFuoE0Rj6dkQTz0iUDzlQTy18hGnZLL6GuMzHw4XpL8GxjsRg3ckYtFIfEPxREiE0BITmwmWbY16ON5q53iQkRWNJCKLrD4sIU1g6bgbn9cEgMdjsc+qYq9VqDIYgqlSb16vXQRW3t4Li2YbiKjdXp6vBfGUA2tnYRAlErQswqEQjhUp00BiBzYGJiQCSMNAb+I2diP2pFUUW5d8cSQCmAthETElA4xwUpfT6Bo8PhK8a2wLRIqK30hjJ+6hdj5i4vbB2tsKAfD+rE6GHQgs1/goEt9ErXhq1KiRvPPOO5Kfny+5ubny2muvSb166uH2zZQpU8Tj8ZTbXnrppXL7tG7dWr788kvZtWuXZGdnyxNPPCFJSTo8EFI1pCP1vpWV6ZODv5dXoI5OpKOp98pETMCzUOByH9LktaI2iQ5MeQXN2HOTghiiytwXqRA4V4nIrYivCpY8WDVTvFieBAuV7rBMJYRQ4HSnFR9F4peoddu9++670rx5cxk0aJAkJyfL6NGj5dVXX5XLLtOqJb7Rff71L21+sJ/du/+8rRITE+Wrr76SzZs3y5FHHum8/ltvvSUlJSVy331ado6Q8NMZK/fF1gC+M0YLXyZZE61We7YDl011bRJd4ulYCGI7DqgOWuJo4P/zcHc1hGAJJFLUsnMXLLEliE9qaFknZwWZJLEDFk5fGXybLYtZKLXStiMesWmUZ7qSOLQ8devWTQYPHizXXnut/PrrrzJ16lS5+eab5eKLL3YEjz9ULKlFyWwFBX8muJ588snSo0cPufzyy2Xu3Lny9ddfyz//+U+56aabHIFGSLhoi8Dojlj5llRBV/hI/dx1MFm5CxFSOEUfCxBYnuVy3Z0AcdEQQuhMtIzRSu7+R+j9QkyFk5KM1zBJA3W8FO30hQexSSp2vLEX950ee64Ez0642d2lDkh8EZXiacCAAY6rbtYsXYPsZ/LkybJv3z7p39+/YVctUzk5OTJ//nx59NFHpU6dOuVeVx/fsuXP9cTEiROlQYMG0rOnJvoSUnnqoOaOdm0fDMuTrwE+1tDMLLHacpDoRoXTr/jdVH+vZ/UbNJakMzHZaMmE22CB9EVPy637PxH5Hb35vsbjmhkXLtZXwPLkwUJHFwIkfolKt11WVlY5gaOUlpbK9u3bned88d5778maNWtk48aNctBBB8njjz8uXbt2lfPP39+TXf9XrVE25m9/r5uSkiKpqX92fUpL03UJId5pino6S2B52uenMF+soX3aFGbSxQ7fw3V3GOKUTL2yzajTdS+y2lZbTZB7wPIzFKUSTF2qBEs8zUftKVPB/FfUNzvIS92milKI9wiVfFiMo7nOGokhy9OIESMOCOh2byp2KsqoUaPkm2++kQULFjhC6sorr5TzzjtPOnQweT4VY9iwYbJjx46ybcMGlu2zSUfAp+m3VRVEU/CmTi6pWO3mYhUbDwNwF5RjUPfcnzZjEu2sR989XQR0ReZaNlq+aFDEc2hB87JVofwU1PZSIXWG1dPRNLouQgFU9/tshCtPW8P822o3U93k4XP6XlKTWCeiLE8jR46UN9980+8+K1eudAK6mzXTOq9/ohlxGRkZznPBMmPGDOdnp06dyl738MPLG4UzM/d3M/L3uir6nnxSS/z9aXmigPqTbjBxN7Wq+YaTY1B7RSfkHyu5ktAJoCroZVVxzrLeJ5j06FjBNPGdESarAYkcxonIdIinIhQxNTFsKnjetaxHA634qCK49a6AWDJiyE6esJmJdjLaKFoZgqr7VTGu+KMQx90CGbIn4bMxgDx+iCjxtHXrVmcLxLRp05xSBf369ZPZs/e3yzzxxBOdbDkjiIKhb9/9t+qmTZvKXlez6po2berERSmazaflEBYt8u1oKC4udjbi3SKkZ7lZFVmeUlEZWOuupEFA+Wop4Q89vrNE5KMqFHgeuOfaV/AYo4WWmBTt+lQNXU1pSeyhy8tAS9dVEFMt4MZ7Da67ThBCpvGusVC5+dXqxWfiqzS/+kWpfvZaC8Mjcb1TPMUPEeW2C5YlS5bIhAkTHDfcYYcd5pQVeP755+X9998vE0ItWrSQxYsXO88r6pq7//77HcHVtm1bOfPMM50yBD/88IMTJK6oS09F0ttvv+3ERGn23fDhw+WFF16gOKrERNoOAaJVIZ66IntnmdXHqiJkInC7n4Sfhnh9FU0H4xjtJqaRirpTRmBiC5bGiHG5B+4VWzwmwfJGp3Z88zQy7x6F2FBfQzFqJ2XAquOr/U6OFR/4DaxTfa1EhOpkM8aLo1FLSuuyeUPvA/8VCEnciadatWpJq1atpEuXLo4lqDrRrDkVUd9++62MHz9efv75Z7nuuuvKntfSAlrSoG7dus7fahk66aSTHIGk/6cuwrFjxzoiyqDZemeccYYTfK5WKC3CqQLLrgtFQqMJgjvVmlPe0RoeDsIAuhNWqIqKpwwc61FVIPKaI46jDlwWjX20XIkk6sIS1xhtU1QEB8OhmCwaWHEsnRBQrNDqRPJcrU22WFXmBdl1dv89NxpL9QzqSpnr6SIIGC1j8Ih6DKrhNOuYthDlGrKtRWKi635Rq9S51XA8JMLddvXr13fqIGlNJY0P0kyzhIQEJ5h7/fr1jjjRQpS//ebL8BoetFSBv4KYmlWnx2XQYzv++OMDvu7atWvl9NNPD9txxjsm73B3EPVdKnLxtnb1owpFPGnQ6lysIJsjeLsxYpLC6bpTF0UC3BQZfuI5Igkd8G0GYoJrhnM+K0A2nXI8JrRL8fe2GG3om4IYtngI+q8qfoVgP9YqSeCLfOv+/BIivTmKcpoA7nMhrKrrOynA4qspFnQq4kZhUdfHWjwx1i9OLU+33367rF69Wq666iqnrtI555zjxA2p5UlrJD300EOONUoFlLrVNBCbxDcNEetTiPTlP6tqVZ5GMIebGvGFIRSuqwuTez9L4JhaL/ttlZUnGSKkB46xAM18I32STbWCu00V8HaYGNQdd72PWjtNsN8+WA7aWcJJg4lHRoForGjF9M4BrHPhvO5jFS158HAQcVM2u5HFt9eV+VYLSRrmftZl9g0icjNqrAWyGiRAAJ0EcRyIXRiLBqHJcBYWSq0xtqRb8VwkDi1Phx56qBxzzDFOLJGbFStWyMyZM502KTfccIMjsHTf5cvjpYINER8TahGETQMMLhvClKqegYHRVKreiUErmNorDWAV6wfrUzoGwAZhFE8a33QBxISKpkgnDQN/Jysz8kOrQfFtEMDKmYhTOQmWv9GowaMsRcCvmaQ0peMNiU1aIoV+Js5JtuvaS0AtrxS4ak1RRn8LgmT8364QizfGKyvQYFpjpjRdqD+u48Nh6TzTKuBp0EzAT6y/e8Ji9AWE/2343owr+vkA34UH3/th+I6b47tsiKw8gXjy1SqGxLh4at++vfzf//2fzJkzx9nmzZsne/Yc2FRB44teeUU90yTeaQzxVARRcgKCu8MlnhKstP9dmPQzgsh6aQBrQD3EOdWzWkDU9SGEcoKY/Az14ILYhb5ekY6eR40YNFXUipHBtBkiqgHO7S7sqxPBja6BxGTT6QS0HJtmI/0i0UVqEK1iUpBllYQaR7PhssxyXSPGrfw7hGZPnM/1Pu6VRtjfg/NtkiGIfxZiE1yfJ8Nd1t6Kt/sC5/UsPP87sv9UZF0NN0wz7NMRCz4dW7QK4D8Q6G5nkLrRRYOhOcah7rA418G1EHwuOIkp8fTll19Knz595M4775SOHTs6cU7Lli0rE1NmM2n+JL6pi20PBqQ8TDZZmCj8DUTBYAY6cdWMSQ9SPAn2OwI3QjFWj+6A8QSsXDfCEhOI1shUaxNFlbQHWzV6voMYMKJvNSYiweCvsWHnw5KyGCv9ftbzxta8KQrrWDWEuzHXh7WwMYRTY3z22VaA82+ItTHCKBmWui9xXvLx+gNwbaxzXb9NsKj4AI/3QP2j+hFmgUqBKDYiMNJcsWuR1am1pIZZwkbFkxE2h8GitAYuPRO/Yqqb61jwJMauW7FYuFJEngryGIrx/pm4lkog5KqylhyJYPGkveAMWgJg3LhxTrVuFVFDhw51stv0d21p0rJlsPk5JFZJg5gxwZ0bIES6Q2BUVjy1dtVLKsXgFExzHFs8FVg3gg6W7rzRhlhFNsBzBRh85/uY1I7AxLckAicWXyLUpEhoL7FprufthkXTMOEYMeCBQOoFC8kEiW6a4XttBZFvx98kYOLdhM/6gauh7GI0e26I66gDhKQJkjfndTPEdS+4nHbjtZNwzZjJdRHepyt+JiB+JhX30h4Iq31W3J85Tn99AxPxOXLwGfV//VXXa4j7rMS675bhONq6Mucihc9E5O+WkNH6bYY5uH+74Huug883Bd/LVpRPMOJZXXYPwBoVrPjZhUVcfSuswLSmqey4R6K8SOZLL70kN910kyOgDIMHD3Yy7caMGROu4yNVRDoG9znVIJ5sF4gHW9tKvncdDES7fHy2QGTByiKuDJhiL5anJhgEa2HFvROmf10ejMU+tfE6ibBc6MQULWVTL4GVZIEX4SR4/GScLzOh2BmO47FFO4n4jmfABXQBGjab77ER/h4Nq1uhF5G5BOJZcH1P8uIC/B3WkUGwQq3E9eNO4ffAstUT13QrTOzZCFAXWEr3QTAtx/H3xHeVg/9b5xLxTfF9d4c1tbkf8dQYWy0Ixe2wPP2Ie1BLBEQiKu5+wv36ust1/oclAjUoXHDeP0f84ybXvbvRsmpnBmlN3Q3RuQ/f426MFxRP5TkZ99qGeBJP3bt3d1x0Npphd+ONNzpZeSSyaY8LN6cKL9w0DOpu64tOPJXNwzSpv+56SfswaAVjYTDiyaYYg6Qd99IEE2s+Yra2Q0wdifevhVXsuxgo010WiUgmE5NtKaxO3liC1Xew8V7RSmN8t8vx3XeDdWgnRGNTuNXKtw4vz1zExy3C9eBLQG9DwHIKXKIJCDp3l8hYCDF3JATBR/jfvhBp0/Ael0D0N8N+tfF3LkTSEiuQPQP/txHX7wW4xktd120iLF0TIezOxuvPgqA2xV7TIrTo69s+Hs+H9S8L5UrE6qPnzVXrwbXfCYIrGPG0C9ePEW2lsCxWbzXEyCYNFsDEKBVPFS6SqZl1Q4ZoQf3yaLVud384EnnUh4DSeBXBAHs4bvBw4ct9VmjFQ1WUdEwQbgFUhEku0Ge3SxzYFGNCs4+tOSaetZgwjItKXX6nwYLQEdao1hEYo+IP8/3rZO8vUnEehEUsk4nPWYDr4EMIygJYKPYFEcO2DDFjXwZheSyGYDKZWr/52EdF1vsi8p6VzfcbBO0suBlnY3IvQuXtd2BxGQWriinhYe5vFVNT8b+LMRY0wDhg9mkB0fAj9v0O9Zg+wjFkw6oV6H4zZOE8hnOMqSjG+mQy4dxNiN0Y11uwpVD24lqx3b77vNShS0I8ZTALvli83xrhmrC7EcS85emOO+6Q7777zml18tRTTzmxT1owU4PJg+lPR2qW+hAJB2MgPgmDb28MrNPCENhoRIebIoifNB8CJhjSXZl29mtnBIj7aARxtC2AeNoNodTWEkNLrWJ3hVa8yl6kOhv8xZxUF3UwsWV7cR2Z83OEVYcpnknHd7y/U+afForpsDQcg/vC1L3yRXGIcV9/IONL/89XUZcSH+5Ud42kfLyGvp7NVARFJ+Paz3XtMw33whpYo7vhOm8It6OxKn3t5b6a76c1ionR2g3LVVMsQDpEQAbhTCsLT4IoIRCqeBIv1rgiLy1cWmHsbQehHi2u/nCQBfHaDJ8/2GuiMVrifFnDMaUVFk/akLd///5OTzl135WUlDiNeffu3SvXXHNNeI+ShB0102/FpHESsn82YuBsj0HYn3siEAkYaLxZYIowsadV4j18xTWZkgj1/bgSmvpJR7fFUxfEdNS2VqYmfsFgx73kQmj5ay1RndxsWSNexko4CYUr+2NCMHW41N0UbyRAaDfCdzzDmiRt1lRhna5STAJ7Kym4t0LoeGMerMrdsNj4xnVf2p8vFy7AHhCN7uvCfYwrcZ+le3GhN8H1Vt+KA5yGoGyzf20r3qs6WYrSA5di0g5UmsJcF3pe7kRD41C7EOyCUEi2xogWsPj1hYu2avtyRBbtcE5qW0kIvjgEFlITO9YDCx1v92vEiydl6dKlMmjQIGndurVTaVx7w82aNUs2bw6lRiwJJ3VgTdqDQbMkQP2lXKwEa8Etk4fsnvRKiqdGeA1vA4wJcA0mK84XGX6sWhkB4jDcJQ5sPDi2uhBCel72t40OzEa4PSIhPT/diiurDcuDZgwNsVx1HfFdxPqKtxEG6nnWSrUervttGJQXW3WCqpuqLqBaDJffaRD7Kp58kYNMMyO6A8UyZeP4O3oRT41hufsVi5A1sIK1QazLTgS+l+C+s8eKVNynVTk5LkJLl2DYYFUR1/HxchTmDIXdEJSNrFIq5jwn4bzEi3hKwefdgdghf7FgGbASFuEebQQB1SqaxZNh3bp1zkZqnh4IAN2LQUknDG9fen0IrG24oXXiF0ymiWHwwTfFe2wIMME3gWALtWWJr4DvPRAL/oRZhwAxSQkwKXcNcXXpiaC6Tl2tya02vo+LIZz2IY6mLSwBgVxR0U5LCNpmlrBtBdfNl1EU3F8Z8iCggmGHy30ZiAVw97fD2LIZQiMRFuw1qDBvFnK/Ikj+IFiu1mByXGyNA+2wfzNXzbZAZRiqCj2uRyESr8Tx9wvxPO2CYMjEZ6qDezAP560jRFQ0lDepLI0xP2zGQtVfM/YW2FRECc6fWRwGcmdHTMC4WphCoUUL/cikOjGZU4lWwTc39Vxuq6VezObBpPv7w2So+Yqb2oeYqL9YE32w1MLqo8iP5chXEGt9POdPPG1DCrnJvopG1EUjcLuYYiImxmMerA+jYlQ41YI4aoABdyfcrnpNCiYoY1GMB+FU1WjO9aewAqyE278ZFh6rLbeiWYisQB2mCfi/8RBOtqVU8FimNUm1hXtLx6+aIAeWNOMe1bibUDCirw2E4//hPOXh3DTC3/FAQ4jHIojkBgEWP02tc9MSFtF2NXgthCyeNMPu5Zdfdnrc+SI9PV2uvfZaJ+vu/PO1DjGpDroj+LcjVjU5ECVGrbsFhL8WFHvCcBP7ChY3FMG607YCVi5TP8pXh/JCP4LMWMT8uSM2QzzW9SHQokk8LUV7FJNdJMieikWawvLaHYKpISakBcgU24IFRVdM5uy6GR6KELD+MlzAq3D/zPUjTqfB6rcS7qzx+M6aWfEvXyDAvD3GiiRYC02YQU2hrkfBdVYXImpokBlj+bg3j8dnWgPxsBuvpeNmPNDQEpTFEFK+zl8XLLZbYuxOxxhd38f8Vl2EdA326NFD7rvvPpk0aZIUFRU58U0bN250fm/UqJHzfM+ePZ1g8rvvvtup+0SqB5OxkWy5ylrCtDzZh3gq9iM+7A7lodIIA0tugAG3Pt7H26qjNUTcFj9lCnyJv1z8f3+8vq5yDe6ATV8sjZCU6orQCkKiFJOQB6nrw2BVq6nYnqrEBH5Pxvf/O66rJFxD+n2PwT3SFxaRaCknEU2oy+9j3J+hiNM1KGp5DtxbP+J7/ArxRakQWLMsK4QJNahutqCEQyu0NTK1opZZwsoXubCmpUI42mOwCoQWIboCo/l+9eD3YswFdb2ESTTB970JgqsV9tts1RGMCvG0fft2pxSBCqjTTz9djj76aKdUQZ06dZzyBO+++65MnDhRFi6MxeE5cmlkxQ7ttC5KveAGQmSssAYbvVDFT+xAIfYxKfmhcggu+AUBxFMHK67BzakYTN70EgOQgYBDX+IvHyu44yC0frViXbKCjCnYF8U9qMxgPtuynOlgc58VnBtLpGDS+coVDO2+dtdhCzTBkcpR0ejXaYid2gCXneDnR7AUm4zX+SipsBOuk+rO1BOIuFbWvSYQ5YGurd0Yk4q8jF+7vZQyiFWaW/enneHsFk+m/tgK3OOdsG+g7MjqoELWT7U0jR071tlIzZMFFb7UNeFvhQA6D2681xFAbMSTLwpxwTasgHjS7Jmj8H7+Jul8CJpEKxbF0BBWs4YYkHSgsmkS4LWN8GmF/TpY4qldjFscGiOTydTlsYnVz90ek+wPQe4fraI41tkFC6m75ZK7jdNyLApbYRJNd7VfqQ5+tCzbhj6owt4fls1XffzvHz4s37uxMAzGMh7NJGFxvdslnnSuctMbQrMQ1sxuERRQX+EK4yRyyPITnL0OGWCZVsBwmwA3p+njFGrQeBtkdGkQX6BiFaah7G7sbwf+tYR4K4YVy9v7BBJ1y/C5d+EGTLBiYCKxlUS4OB7Xgn72eMh/zcAE6q2HHIk+coIonLsa1/Y0uAhrueImW1r3fFVRgNIfT4nIw9bi7HQs7g7100Gh0Ec8qBkLY72FSwOXV6MU32FdL/Naeyt0Yy8sVjVdYLVaxNP772tTARLuyfFsBCkai02HIMTEWtR/6malx/rCZKy5xVNv3NwJ8Nnb1qZ26PuWEeLFXYTXst+rFd4jFy49k32TgBVKZhBWlFJsW/F6zbDaMZWkY5FasPoJOsTHyirVxJ7pd+8evFpiEg3UXoPEDiXoG/gZ6iJNQ4xjBiblBojtq+pgYg8snhr/9C0esxs7h5abvn8MNw3PY5mGEEqFrnNZ12VBH+wqvroUVf4jxXJcpUkLhx1mHAgkXPSH+NmLC+kdTCCB6hHtgMXmCAwugdoRuMVTGorsLcSklYUA3H3o6WYa9QZ6XV/VxtNRFuAgtETZAZHTEjfSBgSTmhpVwRbw3InP3QyfITGCzL7hZgDOzXYf9b2ikS74zhIgokyQrQeieE0MZw8S39gNwKZYdX9aQNBsxQIzL8j7PQ0LwC0VLA78IwLe9bq8AYk6rTHhB4spHhxrfe7quIRSJ7gm3dY3WzydgnMYyvmLOsvTI488IhdddJGTZZeUVH35SZrd984770h+fr7k5ubKa6+9JvXq+a76oIHtHo/H63bBBVpWcj/entfPF0lsQjpwS7RdaBRk0OQ2iJ7kIJuW2rWSsmDxGYA+Xz0h5NpYfv+dFehVZ2KX1CJ2DdolmEwaY5VqjEGlI2Kg6oTwPh5smVaAeizRHoNOL7hMzWQSC0HhdfF9TUSpgd8wIXXBtZCI59yVrUl8UYBF5NOIMxqHkgZbca109WK1tKkF4bS0ktYqTyX64NmvUZPp9+HmUBG5EV4PwVh+hJcsav3cZvZuAG/G+gh3xVfa8rRt2zanRcvtt98unTt3dkoXaLadNgquXz9QaHLF0cy+5s2bO++dnJwso0ePlldffVUuu0wbURyIVkDPyiqfgH/dddfJ3//+9wNKKgwdOlS+/vrPcNu8vJrI5/DPTligOuLCKw0ynqBXkG6rQlcWnImrSsBg5UF5hCUYmOw6QqHiQTzWXrj8bIGTgBuuIVaXDSpwQ+1G6QR9nVhqWa0ruLthaaoHUfybnx5n0UYWLJlf4xrphaDcVXDVpMRokU9SMXSUtkfql7BoOgohBwt9uHzSrbpfplBnZVhriadmCLWYGqDbgj3u6qK4MiRgUT2/Eo3Xw0ETZEVqnNL5WOR0xOMLvCzWjcWtHQwCJuMyZsXT00+r3v+Tdu3aSa9evZxN60FVBd26dZPBgwc7xTq11pRy8803y/jx4+Wuu+6STZsO7C6mffeys8sbZM8991z58MMPZdeu8vkdKpbc+0YixRgcgm0hshdujmBuqCIMKqYkQDuIFrsbe0eYVitbpXkZbnhvVqE9GEzWwhKxsAKtXHbgZmxYg7VhqgJ1cYq1Ul2IjMpIiQmoDMmwMM62VvRLUXhRBSJFEwnG0r4NoqU+LM/eak+ZMIC1YWoBYyxP6lYejt+7WL/7Iw/H2b0S4qEXREthDbvvD8ECaD4+zwArANzjZZw3MbydYQyI9HEsJLedCpbVq1c71qbJkyfLKafsr3Lxz3/+U7788kv5xz/+4QgR/f2xxx6Tyy/X8mbhZ8CAAY6rzggnRY9HBVL//qbtqX/69esnBx98sLz+uk435XnhhRckJydHZsyYIVdddVXA10pJSZG0tLRyW3WQA+uTDhDBkhuk5cYO5E6Fe84t0lbgvSvbCNf04fOGiXtqBqUfqnAy4qlJDNY4MlXEjbB4NQbiuUzD6I74THaauil0SeFEQkHHrQm495vi2mroEk+rMTaalPjKkOfFldwGC9Bg/leDX86ElTXUuJo6qG/XsYZrRtWCiNuO874ZArKpj8LHBfAMtIKbNRraYoX03fz3v/+VTz75RC688EL5/fffZdy4cY7lRquJr127Vs466yzncXXfVSXqftuypfxXUFpa6hTxdLvmfHHNNdfIokWLZNq08q0FVQjq51N3oNaxevHFFx2rlj+GDRsmO3bsKNs2bAjGQFt58rAKrwq/sMn8SEcQZgMfsSVbq3iFkGu13aio8NmL11EfeqxQFwOy8ncRGVnBgqaRKAgbQZR/4+XajiXxS6qPJWhTlAUrUyNLXCTgsVyrTYqhTgUDg9+Au/kF9MMTiJpgWAFr8iWI8bQFyVCIEIO9TG+E/+kCC3vXGqzA3RpeERMmsR3HutnHPbwDz/fHZ48G8RSS206Drp955hlZs2aNfPvtt7JkyRJ55ZVX5I477pBnn33W2eepp56Sf//7344ACZURI0bIPffcE9BlV1lq164tl156qRPs7mb48D+Nq3PmzHGC0DUu6rnnnvN73E8++WTZ32p5qi4BVRFLTDCUYgWUjpuyMlVdD4EbxgwioWDes2klxUG0CietG6P23S1Ih57mykLbFILbNhJJQpxJMeK2dBL7AFZVBoKTcPIdJuXfMSadb7Xu2YqxJhcCaxvGnCxYRULNIl6EzVjPj8B7vusas8+HFewda6zzQEB1hmt+MSzn9WHNKUWMaWd0YngXn+skiK2lVqKNL0tPVdPOy5xhzoc3PK6G8lU1r9WYeFKX3eGHH+6IJxO0rUHaU6f+WZReLTU//BBsrd/yjBw5Ut58Uxty+GblypWyefNmadasfFMPzfTLyMhwnguEZtfVrVtX3nrrrYD7quvuX//6l+OaKy72nqOmj/t6LppJwOqhcyVqI+kNfD1+X1rB+Kh1GDTsGirxQEOUh0iGlekqWOAmWpl1kR5UGYhMCCUTnzLHFVdHSLjQMexn677JRwxOgWUhWY/xrhnuv1lWplhFWQFxk4HYH40BMgugU6xx8ilX+MIWuN8uRHjGJiwwTK2+I/F6+vdmxJ/qzFyM12kDr0F1iacEiKCWiG8KdVFnQjSiZdEUknj6z3/+48QIqfVHM9Tmzp3r9LdTC5RBRYm/kgH+0P54ugVCXW1aqkDjlrQJsXLiiSdKYmKiI3aCcdl9/vnnQb1X3759HXdgLIqjQJhaKYmVyFLT/zd08NJqJRh2Y8CJBbdUKJwK4ZSDGjJnwax9GL4TNc1He+ttnTQ+jaGiniQ6yIH1RgXHVKvrwErEGukM9jmCzXvCklOZ8Ii5KCLcFxaYPq6+eJ0ghmyzQz7cX31hbcqEEFOBcRk8AnvwGUpxjDtclhy73Ey4LcatINbMON8R4tRUWf9TFQRHLs61nquYE09jxoyRgoICpyyBWmM0zkiFkwoY3RYvXuw87o4jCjf6nireRo0aJTfccINTquD55593KpqbTLsWLVo4rsUrr7xSZs7Uqh/76dixoxx77LFy2mm6pi/PGWecIZmZmTJ9+nSnf5/GPd17771OrFc8ko2bum4FzNaCCd5UvK6MeJI4EU71MXhswSpM62kpb8Fqp5aZv+K8atD0azWcilzZwbctVuQMACc1wU8QUH/ODvsXaRsx+S+F62k7hEpgn4Zv5kA89cHr/AWPl6DA5kC49X7wYnVPQHxrbSTy7IQo2gGB1QViaUkFGg0H0/y9FoRdDyxylqIUwpGI7UpAOYZWEHtGOIUan1iAGN5ocNlVqFSBBozrptalPn36OJYZ3VSkaKFMjSfSWk8ff/yxzJs3z9k0sDzcaD0nFUwqkDTLToO7b7nllrLnVVCphUwtYTZXX321rF+/Xr75xu6/vp+SkhK56aabnLithIQEWb58uRPPpSItXlleiaDDTq6sFhVPxDd/hRneZrFVZVcH+V0YRPfbW6OXTpikpsAKQEh1s8aynNgYF7JSjPvvuEqKpz9w72oM6RnW4+/guYEQQWmu3pu260uFk8DKZB/Laggld6btLtRY8tVouDmaxn8UwLXXGVbvFFjkUiAEM2EFawsxtxCW5EWVTO6JFipb0qIc6jZTwWIElW4HHXRQ0BlwsYIGjGvWXXp6umOpCyf/wMVbmRu5ujgJ/vr11gpIV3tfVUE2RaJVTTyaC17aaBajpjRUT+pB9ZGKgNLXYyBmi8Q+eq1eC4tPKGVh3Ki1aRB+L0WWrIklvRfv804Y2w3Vg6h5FparCyAWf4MQuwDW7TEQPuLDNXkWxNISLO5MG5kEuOm6YdwNNbaqF7bPKuBZSMb5et6qz1Xd83dYe9upBUjT/3V77733wvnSJAoxgul3mHJr42ZNhcspHKRhUDoU7xOtNkKzGv0BKc5nIv4i1oSTWfGujaDu6IT4YzXiogZXUjxNgYUpEdYZOwlnNsRAnzCKJ1N2oTFKzfSDuy0d914/jMmtYD1S4TTe9Rq1EUqwHaLJ9Dbdh/9rB4HmL5POF1fAHaoLx39H4cK30r3tCAkkntRvb4fx9w6Tam+A1dsReD0NpK66hkBVRxbiCfZBOOkA/WYMN7ytBxdkNJnoSXwz26pFlIIQhFD9KVutmM8/89P3YyqBB+rDFwoeq71VO8QZbsJ4eTreZxPe8yBkHrppj4WvnTBk6vrlwW23uwK1/mpBOAmyAu3Y2GiB4olUCUmwMBjxpLVI/g83nAYpVr5a1/6ME1OTxd2yJJLQWIa7/ARvHmMFq1ZmZRsN6Kq3AFlDhEQLWxAq0RRiIxuiJAmTaG+rvYg/dFE03EvM4kbc+yl4/XBRgvGnJ+KntkEAmlY1+YhLzUIphfIRwvvH6QQfC52diKuqSA09jZeyMQV/owmKJ+IMCJdbYiccZMEvXegKvjTtNipbO6UO/OWCKr6aViwwe1eEnkG2T6gI12AAu9PHCkxrokgMW5psmkBM10ThPkIqY8VZiPpPWofsbbjUm0MIbMGYVyeA5ajET4yOqf+kQixcrMGY2NqKM10MN1spBFAGftaHIHRn//orU7MG43qoaP0pGzuxKFqgeCJyjogcKyJ3BLl6CgZjZVnvY4DQmiCV4SAIj414DyPKelTAJaji8VYEbWo8VjhJsszT9bwI1F4YpHKjKGW/RSXOU90o+pyE2KyFcPoZC8LpsKQ2Q7zlUoiUNhAsoY5DZmw8NIzj0B5k822zypp4XJl58xADleoa/zvh76qwhjd3ZRNqCEa0QfEUp/TFBZxqWWv0Ar4NA0JlaeFDPJkswcqKNA12FMv8vR43omliHAo6SEglLVe+cB/LQJxfzV45zXLZzYySgMnOVo0mf4OKt++3Ib4juuxINKJWlknWQm06MofV/fUr2gq9iAbdWyowji6EO7A+xgcJo4DyZ+nda409xvJUBxbx4irqXdoCPxcHYXnqicxtQ2aExLaGNduORAcaBHgjfs+BmXkrbiBdRf1NRB6v5HuYYEp3SQWTtZECsVaRvmyJsDAJVnyGVRCFHUJs5WJbwQ7HQBguTPzCDgymR0KguVdaFS0eWp2kw+2gqc4nQkTVwZbjGhibYNAucD0+FRMEIdHGXlfii94Lk2GJMjWYjJUmB8HUoZRk2QcxdjWyb/V+G+ulflNVUYi5IQ3irXsVlhJpgZ+LEcCe7qNuUiK8AsbypyLwXzhWLXVSk9DyFIfYrqOm1irqadzAHcNgRvUlnkqtAaWi1idjMSt0WbZMTzRvWSP+6OBa5VSsudCfGJN7gmXJGo+BohbO7VbXOYmGfm7pGLym4Pj74jusY1nYEuCmXOZqDVEfYirai3sS4sYIJ5tVFRxHfsU4kQJrixbn9DXG3InCuqaIcUWLGRu2IIzgb7CQr62ijNha1tiwFHNOEkSbG3WD2handoilTbe8DzUFLU9xiDHN7kLMUH2snrZbgY/NK2gVMorc3BzerAw5mHSbVtCFY1xGa10rlYqIpzrWKqjQEgL2iqs33GvvIVvQH5pyOwTn0jQe3Yu4grVYzalYehnxP0NQniBSaQWxl4fB7TdYk36HcP0Wg9rF+D5rYfW93PU9tMPEEA0ikZDKkl1BMbMPDYK17935qGGXifspG8Hdc/B4V2uBmoax51cEs1fE1bYT8VFZ+FlV3VxbQyztwDi5A267hl6aAttZ2ZkuQdof/xPuIpnBQvEUh+gNKPDfu4uibcLN06ICjR0NTXBh7UEgtJutlbQ8GfG0xksxu314XXebA29Vc7vA4pYIQbcB1pRmlnjSAfBSCM4CDEy9sPJzu9oS0MzXnOMMHM/r+My6vQSRZm74YRK5NMQqbyoG5gSIbUFDYlPRfT0E1vH4+wcEhfeHFaoePvukKInrIqSybLEWYxXpyzkFAsrEP9kxUKtcCxMtqGs4ClaZtyq4+C2uBjHSHj9Nv9Q8jDXevB122YYWrjHdA3FlamRVNxRPcSyevGVRbEIZgeZhcNll+5gscywB0xPtAwrDIJ6KcPwtkY3nLkRnr3xMRW8VUILJvthLDZJelqXuGKyYNG5JIITsmKsu+N9SPNcY58CuvmvvH8nUwnn6HkKpPa4b44a1V7YeWKCW4PFNVhD8SfheAvXPIiSW2AIrSoMKiqdi3Hd/QWmPLCvGxoiP8Yj9bId7bz4yp9VSfr+IPBChjcPb4aexQuf7CBqvhQQVWzwZy9TnEF+6+K0pKJ7iECMGvAUzbvRRhyMUjPjwFRhsx/t0hLVnWpCvnWT5wb019ZwOc/dFeP91Xvo1nev6Oxf9lfq5jv94bDZGOJkinSVYIaZZ2TU/1eBqKBw0h1BaidpThRBC/QIIIHcrma/R3mGLq3M9IbFOCQTNMZXoQzoJbvI8iDAP3OjHYYyZDwFVxxIgi5EM1AQlD36MYPG0Gj9NKITb8nQmLPxFGEeMNV/gutTPXZMwYDzKqOwFYwJ6fVmewiGefAWLG3J87B8Mpkv4bi+vo3wHUVgbjXa1qrlNb1iT1Do0DgLrdbzeFks8dYG7rgX2fQsm45WoErwBYukWmJZbwMReBJN7tGKC8T+C9cwIXRU/X/jozu5v9fwhrFeExBvLMd5WZpLNhWjKg0BaiHII8617zHbPrbfuN21XFWnUt8b71X4sT22wKBWMz/ZnLPUx9lc3tDxFkWj6LyqBa0XtipIO8bHPR/BzNp6rF0TcUCC3mnHfuHFf+Opms6kHt9uvXtJ0O1kmX28uQZ3c/yci1+FzdrVKFyQjsFmQYjzeFfNlLGVNXC1TPoeVS4PqxVrhXQfL2QrsUwTx6a0zebSQgc8y1UcwKSEkOFZD/DTyslBNgBW9FJl14Rwz1Fp1AVxeFS0HUxV0skrkbEHCki/L0ykQnToHzEVplAbW/1ZF7alQoeUpSiiFuTYdxRUDdau+3WoTYJpZimX2zPNxAZZY4qYi1qc0K21d01C9oVaeVxAnI156vqmf/yorLslbTSZd1flCb7abLAFwkuVyawrL1Jde/i8fAigRwc6Cuive3IO5ELOP4ediCLpoFk6pOP5QamQRQrxTYGWveRvHOiL7ti0WeeGajLdjQZdYBUV/K0qiiFwJy9NW1K8SV/iIydBuZIVQaNyXuNz+NZVd54biKUpQ8+xQCJ4+iNsxgqgZgq9T4ZI6BjflYXA/PYbK4Xa8k7+S+5sqKJ7qW4151wSwWs2y+tHZDSntG/5YL6ZRI56CmeDVuiS4Eevg9ZRv/IicLS5L1MoAgnZlNRaxq2oycF24Y5cIIRXjByy03GNpKmICtWTJaFisK9uyymaRl+4JNUECFrIvQ0TqnPCwK3FmszWPJVqJOUussehnZCa/4xJeNQnddlHEb4jpUUvKYFihxqAibQeru7fhbHzBybiJ2gcIFjdstNq3BEsXxP8YQae++UCYpsGNMbgsx+eoZ1mxDkUQ+ImWy21fkOJpA1Y5TWC1aw3Lmr8MjXWW5exjiS8aIl4ilLgmQoj/heg3sKJ3gyuvFlxWC62FahIWx7V9FN0MFVM/L5yCrCIc5rJ+fenl8+ViMWt662kGtvKLa79tVgC8zmk1DcVTlDEZ6ZrnicghEAKmQvYgXFSmvog79fNY3KQSIAMkVMuTXvA3uLqJByOeTIBjY9xgZ8JiZixt+npH4zPqZzPkhOAeW4PjO92yePlL3/0EpvZ5lk8+HqgPCxrjmggJL9Mw3p6AxW0SxM1ml6VoCYTD0jBU9l6FRWZTLLLdxSergySrBtUfsMKpAcCNB1b+NsjEM4vXSB+L6LaLQuZCrde2+v7Yavxby7qiF+Br+N248cRHHI9bPAVjeUqHS7A+VlU/ov/TihDNy6dYwsnEGgksZs0ti5kgTTdYVrtapgTqW1eAwS6ehJMg7mKOnzg1QkjlxMwYZPgWIEbSTngpRfLKcoyDlW21UmhlTnew3PKHI77qLhG5N4j42cpwETKX9fM+F6D5+SYrLjUJnpFQ+gLWBFErnu69916ZOnWq7Nq1S3JzvdWx9s5DDz0kGzdulN27d8ukSZOkU6fyXuFGjRrJO++8I/n5+c7rvvbaa1KvXmW7nYUXDwSUMR3us0TCHrj2NLX+EREZCcGwGZYcEzBu9vfGZrxmmo9+QwIx0xrirRmsQS/AJ/16CNkQ31vBgDsR5D0LAnAtLlANIBf8/TeYwYPF/pxFlaiaHss0xLlX4csK4IRUDaWwvrzlo+7ZBmQKb7fKyVQGs4DtBC/FgyJyLXridYGV5xxXD0pfNAgxjOMI1Mjbh88byFNgxFOPKLE6RbV4SklJkY8++kheekmr0QTH3XffLbfccovccMMN0r9/f0d4TZw4UVJTjV1C5N1335WePXvKoEGD5IwzzpBjjz1WXn31VYk01Epg0NXM+7hAv8REuBfxO2YyNGJLEAek+/ii2AooNzdMb6xSEnAzqjD7JwRUPpoKVyQl1oOAyTEIbB+DTLxi6zNqELxA+IQanG1nZiyookaX0U5LBHDq9UIIqVrUuutrub8N1nhdkFYWbc4tiF+9Cp4Kk8Tzu+V9sKt4u0mABWmEGh4gigJRC6JMkBRkzz2+cIeR+MumjhSiNubpwQdVR4sMGaKtVYPjtttuk+HDh8vnn+/P87ryyislOztbzjnnHPnggw+kW7duMnjwYDn00ENl1qz9nctuvvlmGT9+vNx1112yaZOvykXVzxK45lQETYQIudnP/nOtomP+rE6GjViRtERw9rWIoypCsLqxeO2EcKpM0bK9Plqp/I4sQsPSSpivW7gEJ9lPI3yHgdyZhJDqYSFKpWRVsqbRAiw2jRDT2UtnzXq458+Bu76zl+BsgyYnDbT+HoLjWYU4Km8WpePg4dgegpfAnlmLoqRDQ9RankKlffv20rx5c5k82SSwi+zYsUNmzJghAwYMcP7Wn+qqM8JJ0f337dvnWKr8WcHS0tLKbVWNXsBvoIKzJ0gTbkEQ8U7i6jvUB0GMprL5xTDhbkCs0z+qMLV9Az6jDiazrWa9oTIGFbPZIqQ8SaixpTFqtDoREhmY4OrSAKUGmmB89tVgfbfL/fUr5oqdLutOZx8xVlmWBek9LNaTsJD+t4j83cv/6KL6ZPz+ZQiW/s0Y33WB/KiPAs6RRtyIp6ys/aXK1NJko3+b5/Tnli3lu3eVlpbK9u3by/bxxrBhwxwhZrYNGyKvUo4HdUWyfWQ8uNEJVZBea4pMGkoR11RUDTWO9IZ9BnVCKupyW4U+UYzn+ZO6CExdjhg5QkhkoKVCPkc9I5MxZ2cym5jTDFjs62KB28nLhG67zGb6iIlqhlAJdzuXU5GEtACxqaNdHRnaICa2NsriaGhHf1izc0PoVyoYm59CjG5FewHGtXgaMWKEeDwev1vXrporEFnocaenp5dtLVu6G45EBpMQp+SvQKZhG1YteoGYM26yNyajxACJXjpiJfpBHGYWEhINLMUitg7ca73xexJiUSchwPwlBGWr6HDPjrNgaZrrpal3oeVhUPq7kkg0M0+sYsYexNfebPW8bI3QitPx+BBrjoiV4sFREfM0cuRIefNNbbvqm5UrK9Y8YvPm/Xo2MzOz7Hfz95w5+6Nh9PFmzcqH6iUlJUlGRka5/3FTXFzsbLHGVKu0gQqnx/F3NPijiW/MynCiNQgSQiKPcbD6pCF7rR9EyWqr1+ZGbHpPXw9LlKlllw/32j4/IQ2nw+pkShpkofByLSyg3TGyeyC6msDld5Tr+c0hlpPJgBfDX/29SCSixNPWrVudrSpYtWqVE/A9cOBAmTt3vzFTY5M0lslk7E2bNs0pVdCvXz+ZPVujbEROPPFESUxMdGKj4o1pMCHvhnunOMjMCRIZJEDsZrtiCJphRUrhREhks8+qeTQe924her65xcYaeASauwSPPwvQRsSV9kGtvq6IaWqA1/fVCmUdBNfplmAaDquYHl+wdIXlO7MSMa01RUS57UKhdevW0qdPH2nTpo1jHdLfdbNrMi1evNjJpDM8/fTTcv/998uZZ54pvXr1krfeesup+TRunOp7kSVLlsiECRNk1KhRcthhh8mRRx4pzz//vLz//vsRlWlXnfyG1NniSk7iWWEo/EZCoxmSBJpbHclTcdNrHAMhJHrQjOZRiE9a4UNo/Q4RFAqlVkmXOzFWqDh6wOXWEz/Neb/FHBGKcErCnLAySueGiLI8hcLDDz8sQ4dqN6D9GNfb8ccfLz/8oLkK4pQeaNDATBsiTzzxhCOutG5Tw4YN5eeff5ZTTz1V9uz5M+HysssucwTTt99+62TZjR071qkNRSpOEwQ96g0SnxK0ZmiKFWoygv4LURhPYylYLJSQ6CMviNpOOyrQkmWlldmnMVIvBqjbt876fbvlQgyFVLjroiVA3I3OZ0xCCjPqDtSsOw0eLygwBQLCwz+QeRFNF1wP+M41c48Wj+ohEyu7FzGIXi4iB2FAfCtKitARQkLnOjSBDyU6WN12N+H3x4L830cwzmjrlfkVOM4MzGWfI9B8aQg1rZKxEHzeixWsuubvqLU8kehAgxf3IMi8BaqFb7cy90j4SYHV6ROreOnHMOnrUEDhREjssgClC0JhHmoGLguyDqDyLCxcwfYxdWMqnudYjeDVEhUtUDyRKiUTN+MvSLPV+iQDrP55pGrKECy2mkMLLE77UyAIIbHMSogSzdAL1u+h7qc/y0cHR04lO0vURkzVLiywjRsvWojagHESXtrC1Btu6mFVY27OCaghpSKKVJ50VxXiLAyYE4JoxkkIiT02I6ZRuwdEMrVRe8qIJ3ch0EiH4ok4gW/18VOLo4VzYne7iXbAPx5MJ28SmBYQpqbreTqK5wVreieESEzW6FMrzp/pUpHJDnSO2AnLUzRB8UScGywfNZxahzFttAkm8Wwf3b6jMT01kkjADbwWxerqILapIpkvhJDYYRVin3w3FYuM8avAyiJM8bNfX7ghIwmKJ+K40Nag991mWDDCZZb1lrWRF6Vm2kijoRXLtAZF9OKvlCshxBtLkZUWiYvUZBRgNuUUtvmxPKUjoDycXpFwQPEU5yTBYrEYouYnpJDq4+HAdPC22YGaQ/q+pHKWvdUQTO/S4kQIsVhr1XyKNOoh1infmid8ibyGqA+omduCz9MTFdBrss4SxVOc0xluNFOnYz56JIXLROqtUNtOiCe1TIWLhij1Hy7RF+kkwnK3AAOIWp5YsI0QYtBMuA1YDHuz/NSk5b8JxixT9HOXH/FUD3NSkiWe/kBphZosecNSBXFKCvqebUaRMmMhyrNWK4Gq2fojFaZWb5YnD/qq2VliFXU3ZuL1ElH1tiusaLEgJBJQCK4QWSn7XIPPNpjmCSHEG4tRnNgeU7piLKmN59V9Vl10gQjSbaH1+E6M2e6q3cn42652XheLRm0bVpPQ8hTHfc/U5fOalwqtulr5s0NgxTA1O3zVGdlSSctTfQiIKSIyEy6rDxGcrkHvsUATCNBSL0KzCQL8w1u/nhASa9YnI0qMeNHmwa8jC1qzdauLJlY7lnxX37ydVqFMQwt4RjZDaBVjXqlVyfpS4YKWpzilNvzI3i7CTVD8lX19f+Ipr5KBjFmoZfKFa6WiafqX4sbbFuW1jpogBk1XWVdjIKkF4VmI+lmEEOKL7VZ8qang/SkWzg0wViZhgVaVJCER6QuItvauuWenVShzjxWKoQ2Hp0E47cbnSAjQd6+6oOUpyigJk+JNhbjwdcNJGMRTvp+bcgdugi4V6AKehIFgthf3nD72PQaMLhFUO6RWiPFYqTCtL0BM2q+wqmn2YgdY23QAJIQQX2yDMKmHopmzrHFjIcInqiOLrQ0sTb/g53eu53dC2Jnx2oyVK/EZCrBPA8yBlQkpCRcUT1HGojAVPvP4sQrZq5XKVo8VP+KpCIGAzSsQ65QDy5O3z/UF+i7NhrUmElJ1uyDWIFiawn1qTNtfoAnmRxCHP1bRcRJCYocSjMMtMebaLZt2wstQ1dl4KZgPvkdguDf2Yj4y4ikdi28dAw3rMS7q3ETxREJmOW6I1DAWKPMmnnZVMu4pGcLIFzmI2ZlfgayPDGRbqBnXFyrMPsPNp61ngqGqsk+SYEUqCiGLsSHccjqoCH7ugfXpPT9WQ0IIEZfoqIfgcBVLNiusEgBVRTrmFG+LXZttVhxsQ2TS2e65WXgdHffptiMhswYBdJVpb5ICH7Iv8VSESbqy5Qr8BTOrOPsfBILxdQcr+pJ8FN90o+LtG9yQqUEIsn5V5OZrgFXfMqwAfVEPn8/4/e2ASkIIqQhbkRQ0x8tz2Va2sq9wgwzMN70rWEA5DaKtMIjjNAvYulYnCttwMAuvFQlN5em2izJKEO9SDxlzVZEJV9kVSS1YSoKxjmyEyGnkJSA8w8txN4EQcWcI+nNzbgvCNN0Ur+k+jlDRrLgecNMlWKuo9fjeEny4EVPxvz0RTJkdwmckhBBfbIDVxy1GBAvxAj9xp52x+ExGRnNKBRoO1wlyIWjK2phyBd7CPiagk0IkwGy7KOQnWF/OsVJRg2n8W+DKhPNWg8mwyVqRhKry6+G1dSURjBjUFcUA3MjmeDWuyQ5eN8HlRbA6BfPaAgvbZgiTFFiBEmDCNp8rATdCtpUaK9Zz6Qh8d9/cbhpjdaV1s44WkY74bHUwcG223KHuc98AQjIbovUny2VHCCEVZRNc/d7YDpHS2lXQuBnmDB2n3sF4m49g80usOSQQZqHoL/7VYMbEOnDNeVt87/ITN1Xd0PIUhejE/Tsu/GAsJS0RrJxiWTl2BCiOZlYkobjumkKkpOFGC9YvvRQXYl1kkjWFNarIClrPxA04GrFMobAOr63najL+1uKTtnDJg7XNzojTz9EL4qkJPltzPNbDS4xUcwSpT4WAMoNQEd5zG86JNytYAwxMWn/lOR8mdkIICTffW4tEwc90CKbJGBfNWD4LcaodQmzDEqx4KoWlflcUxHVSPEUpebDA6KQeiIaYmI01p3YQlptc7JMeQipqHcTqtAzR5bQcFpdeuGk6w8y7CUIqAT+n+wh6DMRWmJ134uafCEuTEWaNcbzzsI8RjG1hAXoaBTgTse8EHIc9gLTEOfsNfy+BKOyMfVfD0rXahyBVIcbSA4SQ6mYB+mMad1xrhBiM9JLVW4rxMycIAZWMeWFzkJ6CPIy/zTHGV2fl87gST/fee69MnTpVdu3aJbm5/vK69lOrVi157LHHZN68ebJz507ZsGGDjBkzRpo3Lx8Ct2rVKvF4POW2f/zjHxKJLMak669+UH0Ikk1WPY+UICu0LgvB8qQi62srQywUgVOIzLv1sNosRazSXFhk2uMGVKtORdiKm3IzRNoiuMiaWGJyKVZH2bBQGevXj7DwzYO17w/UKJkMi5JaxJpDiH1l9VryoDbTYog+4+Zb78VXnoKBIlRRSAgh4UDHKcHisADjsL8Yqi8wjvlKsGkMb4cuIj8IMvRjO8bYxCiJ94zamKeUlBT56KOPZNq0aXLNNdcE3L9u3brSr18/eeSRR2Tu3LnSqFEjeeaZZ+Tzzz+Xww47rNy+//znP2XUqFFlfxcURGYTjD8gcHrg4syBADA90TbAbbQWFpGDILQSgiyEuTFAjI9YQd0mmywH7q1gY5IM03GcC/FzHURFR8Q6TapE8c6tEEKL8Dk8EENn4Xj3QNR4sAo7G2LwG4gpwXOf4Zj2wOqnxzQQz4/Das1mEUSRfk+GLVapCbuSbp4r1ooQQqqLDRiDOkA4BVrIrcaC1HgbbBKwoJwAl2AwsVGGXys4f9QEUSueHnzwQefnkCFDgtp/x44dcvLJJ5d77P/+7/9k5syZ0rp1a1m3TqfrP8VSdraZNiMXFSxvIzhZrSWHYHJOgzWlDX7OhhssF5aS4iCFyCY/Ac61sLIowI3yC957G1xdoa4c9NiM/VB97ILj/Ajvo+62ilKI/7frjKzC6zfHMW+0SkGUYFPfvr9gxe/xOok+skn2eWncuxafr4OV/WJ69AVK5SWEkKogH2NgM1fDXl/stNqluAtWNsJYPj1E4WTmHI0X/XM2jlyi1m0XDho0aCD79u2TvLzyX/8999wjW7duldmzZ8tdd90lSUmhNNao/ov+K5hdEy1Lhmnuuw2iYRcm7hb4PRjxlIP/91bRvClutjEQEWpuNT7xqRW4afwJxJlhqOsxyVWtdi1WT/UgYox/fR0+9/IgBeCaEOsx7YW4TIQobIP3DmbAIoSQquIPWODN4tUfHljlTdxoHcR9NsVicGUlqoAvC+P8UZVEreWpsqSmpsrjjz8u//vf/8q55Z599llHNG3fvl2OPPJIGTFihBMXdeedd/p1IerrGdLSKlteMnS2wnyqbqU0WFqScCGaTIkVsFKpICkI8gbR/zneJTwEgmoBRIZu0YaKmDdhAbIzQUogBgNH0VWcxRBzKty6QYSyICYhpCZZBGt8sGPfZhE5GL+3h/CqDyEVqJp4LBBR4kmFilp9/NGtWzdZutTtDAkNDR7/8MMPJSEhQf72t7+Ve+6pp54q+33+/PlSXFwsr7zyigwbNsz53Rv6nHEj1hQmKDodoucPTNLbvfi1QzGJroMP213vKSlKTKv+2OXFNWf87lXJPmSsCL4v076FEEJqipwgE4kM+ZgbUjB+fYXH+nsJV4hFIko8jRw5Ut58U+0Bvlm5MpjGHIGFU9u2beXEE08MGAw+Y8YMSU5Olnbt2skff9ihv+VF35NPPlnO8qTZfNWJccX1gDl1oxez6UYroyxYVuB1s+DyW4nYHDWrMsC58tiF6QghJFrIx0K9KeYUnRuKkTwTD0SUeNI4I92qCiOcOnfuLCeccILjmgtE3759pbS0VLZs8V3mSy1SvqxS1claxNFM8+Fv3oMS+xqnE8rkrhasM2DWzYRZV28ciidCCIlP8rGQboZM5JqfAeNYPIWCZshlZGRImzZtnIDuPn36OI8vX77cqf2kLF682HGpjRs3zhFOH3/8sVOu4IwzznD+JzNTpYA4IqqkpESOOOII6d+/v0yZMsWxSA0YMMBx473zzjsHBJVHIhoA/QPqEPlChVWoLEb66EpkpzVF0HOkFzEjhBBSNeRhIb20gvNKLOCJxm306NEebxx33HFl+yhDhgxxfm/btq3X/e3/Ofjggz3Tpk3z5Obmenbv3u1ZuHCh55577vGkpKSEdGxpaWnO6+rPmj5P4diSRDzdRTwZIp4HRTyPiHhaRsBxceM54DXAa4DXQM1dA61FPKkxdg0GO3/7q39IKojGPGldqfT09IgtsFlRLkOmnundRgghhMTb/B21bjtSM3yKNH9CCCEkXqF4IiGhVWUJIYSQeCauK4wTQgghhIQKxRMhhBBCSAhQPBFCCCGEhADFEyGEEEJICDBgvAqpiQbBhBBCCKnaeZviqQpPfnX3tyOEEEJIeOZxf3WeWCSzimjRokXYC2SahsMtW7aMueKb4YLnKDbg90h4bUUG8XgvpqWlycaNG/3uQ8tTFRHoxFcGvYDj5SKuKDxHsQG/R8JrKzKIp3uxIIjPyYBxQgghhJAQoHgihBBCCAkBiqcoYs+ePfLggw86PwnPUSzDa53w2ooMeC96hwHjhBBCCCEhQMsTIYQQQkgIUDwRQgghhIQAxRMhhBBCSAhQPJG4wuPxyNlnn13Th0EIISSKoXiqZkaPHi2ffvpplb7HX//6V5kyZYrk5+c7YqFBgwYSCZ9bj+Wll1464Lnnn3/eeU73iUTOPfdcmThxomzdutU5zj59+tT0IcXttR2I1NRU5zjmzZsnJSUlNX48pGpo1aqVvP76607la80GW716tTz99NOSkZER9Gscd9xxQY2P0XpNmTFXt+LiYtm8ebN88803ctVVV0lCguaKVR1ZWVny7rvvytKlS6W0tFSeeuopiTUonmKQunXrytdffy2PPvqoRBJr166Viy++WGrXrl1uYLr00ktlzZo1lX79WrWqpmB+vXr15Oeff5Z//OMfVfL6JHwkJSVJYWGhPPvsszJ58mSe2hikffv28ttvv0nnzp3lkksukU6dOskNN9wgAwcOlGnTpkmjRo3C+n7RfE1NmDDBETLt2rWTwYMHO4vqZ555Rr788kvnc1UVqampkpOTI8OHD5e5c+dKrOLhVn3nYPTo0Z5PP/3U+f2UU07x/PTTT57c3FzP1q1bPV988YWnQ4cOZfu2bdvWo5x77rme7777zrNr1y7PnDlzPEcccURQ73Xcccc5/9+gQYOI+dzz5s3zXHrppWWPX3LJJc5n0ud0H/N4sOfmwgsv9Hz//feewsJCz5AhQ5znrrrqKs+CBQs8RUVFno0bN3qee+65sv9TrrnmGs8nn3zinM8//vjDc+aZZwb1Gcx79unTp8bPZ6Rf26tWrfLceuut5Z7//fffPQ888EBI30XPnj0948eP9xQUFHg2b97seeuttzyNGzcO+Xi4xc450Oth7dq1ntq1a5d7PDMz07Nz507Piy++WPZYSkqK57HHHnP21/Fg2bJlnquvvrrsXraxx59YuKZ8HesJJ5xQdu+Zx3SOGDVqlGfLli2e/Px8z7fffus56KCDyv3fGWec4fn111+dsTYnJ8e5b4M5jilTpnieeuqpGj8f4d5oeapB1KLx5JNPyqGHHuqsmvbt2+eYhN0m1X//+9/y3//+V/r27St//PGH/O9//6vSVUNV8sYbbzhmY8PVV1/t1V0X7Ll57LHHnJVU9+7dHdearkBfeOEFefXVV6V3795y1llnyfLly8v9zwMPPCAffvihHHTQQTJ+/HjHvBzu1SoJDn/fhbpTvvvuO/n999+d6+DUU0+VzMxMZ38Sn+i1ccopp8iLL74oRUVF5Z7Lzs52rp+LLrqo7LG33nrLsU7dcsstzhhx/fXXy86dO2XdunVy3nnnOft06dLFsc7ceuutEg+o9WnOnDlln1/56KOPpFmzZo516pBDDpHZs2fLt99+W3Yvnnbaac74q/fowQcf7IzJv/76q8Q7Na7g4mnzt3LRFbWiq23926yOdKVk9unevbvzWNeuXaPS8tSkSRNn5dKmTRtn2717t/O53ZanYM/NLbfcUm6/9evXex555BGfr6M8/PDDZX/XrVvXeUwtXYE+Ay1P4bc8+fsu7rvvPs/XX39d7jVatmzp7NO5c+dK3WvcovMcHH744c73f/bZZ3t9/rbbbnOeb9q0qXONKAMHDgzb+BhN15S/Y/3f//7nWbhwofP7UUcd5cnLy3OsdPY+aqX761//6vw+depUz9tvv12h45hCyxMJN+qrf++992TFihVOcLcGPSpt2rQpt58GKho2bdrk/NRVQjSiQddfffWVDB061LFA6e/btm2r8LnR2AdD06ZNpWXLls6KyR/2+dy9e7fz+tF6PqMdf9+FBuafcMIJZd3cdVuyZInzXMeOHWvsmEnNE0zAs1rq9+7dKz/88EO1HFO0nT8NJDf3Wf369Z1x2L7XNLbM3Gd6LgONq/FG1UTYkqD44osvnEBpzY7buHGjJCYmysKFCyUlJaXcfprhYTAXvO4brajrTjPslJtuuqlS52bXrl1lv2tQZzDY59Oc02g+n5GIulndE1xycnJI34UO6HodeAvUN4sIEl+oC16vLXXBjRs37oDn9fHt27c7wcrBjgfxiJ6nVatWld1nej8df/zxB+yXl5fn/OS5PBDOGDWEptR269bNyUbQuA5dUcdL3I1mAqoI0slU45TCdW40lkEHBPXHk5pFJ6/mzZuX/Z2WluasZENB4y569uzpWB3VAmlvaqUi8YcKo0mTJsmNN95YLmtX0Xi4yy67TD744APn7/nz5ztCXEsSeEPT95VojR+tKGrN1RjDsWPHlt1nGvOlVjr3fWa8Amoh5rhaHoqnGiI3N9dxYV133XWOaVQvaA2QDgc6iKgpVl1figZO69+RIs7MyrFHjx7O7+E8Nw8++KDceeedcvPNNzufX4Mb/+///q9Sx6vnTc+fHq/StWtX5289z8Q7KnqvuOIKOfroo6VXr14yZswYp95LKGjgvwppTZDQgPEOHTrIySef7Fgu/VkK9drS70f/V4PO9XfW5ood9H7WVHhdeB1zzDFOzScNIldRpXWf7rvvPmc/tVzrdafXixbG1XR9FVJ/+ctfyp7X8eeMM86QJk2aOEkqsXZN6XnScapFixbOWDhs2DD57LPPHIuuBtMrWn5BSzyoJW/QoEHStm1bGTBggLN41eBx5aGHHnIC73V81YVtr1695O677/b73uYcqWVLQyr0dz2PsUSNB7bF0zZmzBjPRx995PyugYwatKcB1Jquf+yxx5YLhvQWoKzBjYoGO/p6Dw3K9YZJ5a+JLVCgpTtgvCLnxmzXXXedZ/HixZ49e/Z4NmzY4HnmmWfKnvMWbKrlEPydG33OG3bwM7fy13ZaWpoTlKqBqGvWrPFceeWVXgPGA30XnTp18owdO9azfft2p5zBokWLPE8++aTf863B6t7gdxQ716kmm+h4sWnTJuc+12tM7/OMjIxy+6WmpnpGjhzpjANaqkDLYQwdOrTs+fvvv98pZ1JaWuo3YSUaryn9PIbi4mJPdna255tvvnE+f0JCQrl969ev75w/Tbgx51MDxFu1alW2j5bMmT17tnMet2zZ4vn444/9vr839DzW9HkJ15aAX0g1Fi1Tv71aRgiJJXhtE0LiBbrtqomGDRvK6aef7gTlRVuVWkL8wWubEBKP1Lj5Kx42rca6bt06z/Dhw2v8WLjxHPDa5jXAcYDXAK8BqfA5oNuOEEIIISQE6LYjhBBCCAkBiidCCCGEkBCgeCKEEEIICQGKJ0IIIYSQEKB4IoQQQggJAYonQgghhJAQoHgiJIaZMmWKPPXUUxJpROpxxRvV+T1oX7js7Gynd1ogtD+d9ltTtLfhHXfcUQ1HSEhosFAWzwGvgSi8BgKhfeQaNWrk9K2q6WN1b5FwXIH6LcbCZvc3s+nYsWPYvocpU6Z4nnrqqYD7aY+5V199NajX/PDDDz0vvfSS83vPnj0927Zt86Snp9f4+eTGcyA4B7Q8ERKlZGVllW233nqr5Ofnl3vsv//9r+Tm5srOnTsl0ojU44pEkpOTK91z0L4udFu1alVQ30Nl39tQp04dueaaa+T1118Pav8+ffrInDlznN8XLlwoK1askMsvvzwsx0JIOKB4IiRKUReI2VQ4aZN3+7Fdu3Yd4JbRv5999lnnse3bt8vmzZvl2muvlbp168obb7whO3bskGXLlsmpp55a9j8JCQlyzz33yMqVK2X37t3OpHb++ef7PTZ9ft68ec7+W7dulUmTJjnvYR+HOS79/ZlnnpHHH39ctm3bJps2bZIHHnig3OvpMfz97393jq2oqEjWrFkj9957b6WO0c0pp5wiP/30kyMo9Ji/+OIL6dChQ7ljDnScKkpUyNr8/vvv5fYL5n2ee+455/zk5OTIxIkT5YorrnD2TUlJKffan376qbz11lt+P9eePXvKXRe67du3r+y93NeH+739fZejR492+nXedtttzvWnmze33GmnneYcx4wZMw54rl+/fvLDDz84rz979mw5/PDDpWPHjmXiSdFzdPHFF/v9nIRUJxRPhMQZQ4YMcSZBnaR0onzppZfko48+kl9++cWZyL755ht5++23HWuBMmzYMLnyyivlhhtukJ49ezoT6zvvvCPHHnus19dXy4bGqagY6969uzO5fvLJJ47A8XdMKvb69+8vd999t/zrX/+Sk046qez5ESNGOOLokUcekR49esill17qiABDqMfojXr16smTTz4phx56qAwcONARGCpO7OMOdJzhfJ/i4mI56qijnM+k309SUpKcddZZZfs0bdrUaTau5zmc2O/94IMP+v0uVSjqdfPqq6+WWbXWrVt3wGsec8wxMmvWrAMe79q1qyPYVDz16tVLhg8fLuPGjXOeU8Fm+PXXX53r1S0eCalJ6MflOeA1EOXXwJAhQzy5ubkB41H07x9//PFPv31ioqegoMAzZsyYsscyMzOduJj+/ft7UlJSPDt37vQcccQR5V531KhRnnfffdfrsRx88MHO/7dp0yaoOBn3Mek2Y8YMz4gRI5zfNSansLDQc80113h9rYocYzAxT40bN3Y+h8bcBHOcuq1atcpz6623ltvn999/d+LPQnmfWbNmHbDfCy+84Pnqq6/K/r799ts9y5cv93td6GcsKSlxvmOzaTyRv+vDfu9Qv0tfm57n11577YDHJ0+eXO7a002Pb/HixeUe6927d8Dj4MZzINV4DmrVqGwjhFQ79operR7qgpo/f37ZY8ai06xZM+nUqZNjKVFXjY1aANQd5Y25c+fK5MmTnddUt49asj7++GPJy8sL6pgUdYnp+ytq8ahdu7Z8++23Xv+3Isfo63Uefvhhx6rUpEkTSUzcb5hv06aNE3cT6DjD+T7erDSjRo2SmTNnSosWLWTjxo0ydOhQefPNNwO+n1p2/va3v5X9rZYzf9jvXZHv0htqxVR3q41+XrW8HXzwweUeLykpKeeyUwoLC52ftuuXkJqE4omQOEMnJxuNU3E/puikXr9+fed3dQ9t2LCh3PMaw+INFWSDBg2SI488Uk4++WS5+eab5d///rcjFlavXh30MRlRYSZOX1TkGL2hcTUaS/XXv/7VESf6/ipmbFeRv+M0n93tnnQHXQfzPt4EjgoKFTPqnlQRo+5J/cyB0NfSgOtgsd+7It+lN9RN3KhRo3KP9e3b1zmftnBXVEyNGTPmgDIHisZhERIJMOaJEOKTRYsWORYDtRLoBGxv69ev93vmNBZGY2Z0MtQYmnPPPbdCZ1qDxDWYWK0U4T5Ge3Lu1q2bE3Pz3XffyZIlSw6Y7INBJ/fmzZuX/Z2Wlibt27cP2/u89tprjsXpqquucixCwX6+yuLvu9S/NR7LH2oB1Fg1GxVmKhxt0Th48GDH0ui2PGk8lMZSqZWUkEiAlidCiE80jV1LHmgAtk50P//8szRo0MAJJtbMPG+ZXhrYq0JHrSNbtmxxrBQa3Lx48eIKnWm1HmmG2xNPPOFM1FOnTnVeTy0vGshckWN0YzLfrrvuOscVp0LsscceC/lYVRCpuFHrkrq21D1XWloatvd57733nM+qViu1QFU1wXyXaoHSxzXLTr8LzeJUi5yNuvw06L9hw4ZlLj91D6rl6T//+Y+MHDnSEUiavKC4xZMGnOsxEBIpUDwRQvzyz3/+07GoaEabptTr5Kcp5Y8++qjX/VWwaJabpq+np6c7Lqo777xTvv766wqfac2y27t3ryNGNOZHhcfLL79c4WNUVGjpayo62WsqvJZxWLBggSxdulRuueUWJwssFFQgqKXpyy+/dMpH6HHZlqfKvo+e27FjxzruOpOVVpUE812qmFM3m1oANSapXbt2zn42+ln1+7jwwgudzDxFv0Mtk6Hn7Oqrr3Yy6lToqlXNzqRMTU2Vc845p1z5DEIiAWYp8BzwGuA1EHfXwIQJEzzPPfdcjR9HqJtmqD3zzDM1fhyhbqeddppn4cKFnoSEhJD+74YbbvBMnDixxo+fG8+BWOeAlidCSFyhriN16WnNItt6FQ3Hrces24033ijRxvjx46Vz587SsmXLkGK11LWngeqERBpU1DwHvAZ4DcTNNfDJJ5941q1b5xk+fHiNH0som9aQysvL89x55501fizceA4kzs9BAn4hhBBCCCFBwFIFhBBCCCEhQPFECCGEEBICFE+EEEIIISFA8UQIIYQQEgIUT4QQQgghIUDxRAghhBASAhRPhBBCCCEhQPFECCGEEBICFE+EEEIIISFA8UQIIYQQEgIUT4QQQgghEjz/D3DHEHfo8eHyAAAAAElFTkSuQmCC" }, "metadata": {}, "output_type": "display_data", "jetTransient": { "display_id": null } } ], "execution_count": 7 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-16T20:33:15.212333700Z", "start_time": "2026-03-16T20:33:15.184217900Z" } }, "cell_type": "markdown", "source": [ "As we would expect, the Intercept plot indicates that temperatures steadily rise as time moves on from January, peaking a bit after June 1. Around September, these temperature decline. Regarding the latitude plot, we see that increasing latitude creates the largest temperature differential in the winter months. This temperature gap by latitude is closed somewhat during the summer months.\n", "\n", "## Smoothing\n", "\n", "Looking at this plot, you might notice that it is quite jagged. One might think that we can smooth over these jumps because they are most likely statistical noise. To do that, function-on-scalar regression generally takes the point estimates and applies some smoother at the end to even out this jagged-ness.\n", "\n", "Since post-processing step provides a slight challenge to inference, we describe how the smoothing step can be done within the estimating equations themselves as an alternative. This directly provides inference for the smoothed functions." ], "id": "b81be64170217900" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:21.573459500Z", "start_time": "2026-03-17T15:30:21.564036500Z" } }, "cell_type": "code", "source": "x = np.asarray(dx['x'])", "id": "b80dceadd1c2685f", "outputs": [], "execution_count": 8 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:21.580334300Z", "start_time": "2026-03-17T15:30:21.573459500Z" } }, "cell_type": "code", "source": [ "def create_spline_time(d):\n", " # Function to generate spline terms for a given day\n", " d_knots = [15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180,\n", " 195, 210, 225, 245, 260, 275, 290, 305, 320, 335, 350]\n", " intercept = np.ones(shape=n_obs)\n", " linear_term = np.ones(shape=n_obs) * d\n", " spline_term = spline(linear_term, knots=d_knots,\n", " power=2, restricted=True, normalized=True)\n", " return np.concatenate([intercept[:, None], linear_term[:, None], spline_term], axis=1)" ], "id": "92723c90334b9cae", "outputs": [], "execution_count": 9 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:21.587045600Z", "start_time": "2026-03-17T15:30:21.582343300Z" } }, "cell_type": "code", "source": [ "def psi_smooth(theta):\n", " # Looping over all individual days for each regression\n", " ef_ols = 0\n", " for d in range(y_s_vals):\n", " # Extract outcome vector for regression model\n", " y = y_matrix[:, d]\n", "\n", " # Processing the design matrix\n", " time_matrix = create_spline_time(d=d)\n", " lati_matrix = time_matrix * x[:, None]\n", " design_matrix = np.hstack([time_matrix, lati_matrix])\n", "\n", " # Linear regression for temperature at day d\n", " ef_ols_d = ee_regression(theta=theta, y=y, X=design_matrix,\n", " model='linear')\n", " ef_ols = ef_ols + ef_ols_d\n", "\n", " # Returning stacked estimating functions\n", " return np.vstack(ef_ols)" ], "id": "cca6ee6b6282cef9", "outputs": [], "execution_count": 10 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:30:21.593575300Z", "start_time": "2026-03-17T15:30:21.587045600Z" } }, "cell_type": "code", "source": "init_vals = [np.mean(y_matrix), ] + [0., ]*23 + [0., ]*24", "id": "132c93c8d669b106", "outputs": [], "execution_count": 11 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:02.195720300Z", "start_time": "2026-03-17T15:30:21.593575300Z" } }, "cell_type": "code", "source": [ "estr = MEstimator(psi_smooth, init=init_vals)\n", "estr.estimate()\n", "estr.print_results(subset=[0, 1, 2, 3, 4])" ], "id": "ffc954b81368cab3", "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "==============================================================\n", " Estimation Method: M-estimator\n", "--------------------------------------------------------------\n", "No. Observations: 35 | No. Parameters: 48\n", "Solving algorithm: lm | Max Iterations: 5000\n", "Solving tolerance: 1e-09 | Allow P-Inverse: 1\n", "Derivative Method: approx | Deriv Approx: 1e-09\n", "Small N Correction: None | Distribution: Z-stat\n", "==============================================================\n", " Theta StdErr Z-score LCL UCL P-value S-value \n", "--------------------------------------------------------------\n", " -14.21 0.98 -14.46 -16.13 -12.28 0.00 155.09 \n", " 0.01 0.02 0.51 -0.03 0.05 0.61 0.71 \n", " 71.76 74.35 0.97 -73.96 217.49 0.33 1.58 \n", " 496.32 110.57 4.49 279.61 713.04 0.00 17.09 \n", " -626.31 90.87 -6.89 -804.41 -448.20 0.00 37.41 \n", "==============================================================\n" ] } ], "execution_count": 12 }, { "metadata": {}, "cell_type": "markdown", "source": [ "This code may take a little while to run (0.5-2 minutes), as the fitting process above is not the most efficient coding (we will return to this later).\n", "\n", "As before, it is more helpful to look at a plot of the results rather than the numeric values for the coefficients. This process involves a bit more work on our part relative to the un-smoothed version. To simplify the following code, we define a function that computes the point and confidence bands for a given day based on the intercepts and coefficient" ], "id": "eeca801b97061d16" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:02.222926600Z", "start_time": "2026-03-17T15:31:02.214117900Z" } }, "cell_type": "code", "source": [ "def predict_at_times(beta, covariance, days, x_value=0, include_intercept=True):\n", " # Processing the design matrix for predictions\n", " days = np.asarray(days)\n", " intercept = days*0 + 1\n", " d_knots = [15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180,\n", " 195, 210, 225, 245, 260, 275, 290, 305, 320, 335, 350]\n", " spline_term = spline(days, knots=d_knots,\n", " power=2, restricted=True, normalized=True)\n", " time_matrix = np.concatenate([intercept[:, None], days[:, None], spline_term], axis=1)\n", " lati_matrix = time_matrix * x_value\n", " if include_intercept:\n", " design_matrix = np.hstack([time_matrix, lati_matrix])\n", " else:\n", " design_matrix = np.hstack([time_matrix*0, lati_matrix])\n", "\n", " # Generating point predictions\n", " yhat = np.dot(design_matrix, beta)\n", "\n", " # Computing the covariance matrix\n", " cov_p = design_matrix @ covariance @ design_matrix.T\n", "\n", " # Computing confidence bands\n", " cbands = compute_confidence_bands(yhat, covariance=cov_p,\n", " method='supt', seed=23210177)\n", "\n", " return yhat, cbands" ], "id": "9f5d9eaa935eed3f", "outputs": [], "execution_count": 13 }, { "metadata": {}, "cell_type": "markdown", "source": "Now we can create the range of days and then generate the predictions for the smoothed $\\beta_0(d)$ and $\\beta_1(d)$ separately", "id": "80bb938d6c907889" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:03.229151200Z", "start_time": "2026-03-17T15:31:02.222926600Z" } }, "cell_type": "code", "source": [ "day_range = np.asarray(range(0, 365))\n", "\n", "# Prediction for intercept\n", "y0hat, cb0 = predict_at_times(days=day_range, beta=estr.theta, covariance=estr.variance)\n", "\n", "# Prediction for latitude\n", "y1hat, cb1 = predict_at_times(days=day_range, beta=estr.theta, covariance=estr.variance,\n", " x_value=1, include_intercept=False)" ], "id": "dd5c77268a9c7a63", "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\pzivich\\Documents\\open-source\\Delicatessen\\delicatessen\\sandwich.py:568: RuntimeWarning: covariance is not symmetric positive-semidefinite.\n", " mvn = rng.multivariate_normal([0., ] * k, cov=covariance, size=n_draws)\n" ] } ], "execution_count": 14 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:03.335007700Z", "start_time": "2026-03-17T15:31:03.247011300Z" } }, "cell_type": "code", "source": [ "plt.subplot(211)\n", "plt.plot(day_range, y0hat, color='blue')\n", "plt.fill_between(day_range, cb0[:, 0], cb0[:, 1],\n", " alpha=0.4, color='blue')\n", "plt.title(\"Intercept\")\n", "plt.ylabel(r\"$\\beta_0(d)$\")\n", "plt.ylim([-20, 20])\n", "plt.xticks([])\n", "plt.subplot(212)\n", "plt.plot(day_range, y1hat, color='red')\n", "plt.fill_between(day_range, cb1[:, 0], cb1[:, 1],\n", " alpha=0.4, color='red')\n", "plt.title(\"Latitude\")\n", "plt.xlabel(r\"Time since January First ($d$)\")\n", "plt.ylabel(r\"$\\beta_L(d)$\")\n", "plt.xticks([1, 60, 152, 274, 365-30],\n", " ['Jan 1', 'March 1', 'June 1', 'Oct 1', 'Dec 1'])\n", "plt.tight_layout()\n", "plt.show()" ], "id": "7c3e2765e225f54", "outputs": [ { "data": { "text/plain": [ "
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" }, "metadata": {}, "output_type": "display_data", "jetTransient": { "display_id": null } } ], "execution_count": 15 }, { "metadata": {}, "cell_type": "markdown", "source": [ "At the end of this process, we have a smoothed plot for each of our coefficients. We see the general shapes are the same but the bumpiness of the functions has been ironed out. Provided that we think the jaggedness from before was statistical noise (which seems reasonable to presume), we might prefer to present this plot.\n", "\n", "The smoothing was controlled through our specification of the spline term. How many splines and where they are located control the smoothness of the corresponding regression coefficient functions. An advantage of this approach is that we can straightforwardly compute the confidence bands at the end of the process.\n", "\n", "## Vectorized Smoothing\n", "\n", "One difficult is that this process can take a bit of time to fit. While not a problem here, it can become more of an issue with larger data sets or more granular functions. To close this section, we review a vectorization of the previous estimating function. This is based on the underlying algorithm used for pooled logistic regression in `delicatessen`. To do this, we will (1) avoid creating a new design matrix for the day terms in the `psi` function, (2) avoid creating an individual-level design matrix for time, and (3) avoid having to loop over each day." ], "id": "e8b82486725149a7" }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:03.414067200Z", "start_time": "2026-03-17T15:31:03.335007700Z" } }, "cell_type": "code", "source": [ "# Creating a spline design matrix for all unique times (note subsetting)\n", "d_matrix = np.stack([create_spline_time(d=d)[0, :] for d in range(365)], axis=1).T\n", "\n", "# Covariate design matrix (no intercept)\n", "X = np.asarray(dx[['x', ]])" ], "id": "9d52a1ed48aeace2", "outputs": [], "execution_count": 16 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:03.422895400Z", "start_time": "2026-03-17T15:31:03.414067200Z" } }, "cell_type": "code", "source": [ "def psi_smooth_fast(theta):\n", " # Setup dimensions\n", " theta = np.asarray(theta)\n", " n, p = X.shape\n", " q = d_matrix.shape[1]\n", " alpha = theta[:q]\n", " Gamma = theta[q:].reshape(p, q)\n", "\n", " # Fitted values\n", " yt_hat = alpha @ d_matrix.T + X @ Gamma @ d_matrix.T\n", "\n", " # Residuals\n", " residual = y_matrix - yt_hat\n", "\n", " # Scores\n", " score_alpha = residual @ d_matrix\n", " score_gamma = np.einsum('nd,np,qd->npq', residual, X, d_matrix.T).reshape(n, -1)\n", "\n", " ef_vals = np.concatenate([score_alpha, score_gamma], axis=1)\n", "\n", " # Returning stacked estimating functions\n", " return ef_vals.T" ], "id": "11ede670c4b39ce", "outputs": [], "execution_count": 17 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:03.428016200Z", "start_time": "2026-03-17T15:31:03.422895400Z" } }, "cell_type": "code", "source": "init_vals = [np.mean(y_matrix), ] + [0., ]*23 + [0., ]*24", "id": "a24e52d9d18c0c27", "outputs": [], "execution_count": 18 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:03.733125100Z", "start_time": "2026-03-17T15:31:03.428016200Z" } }, "cell_type": "code", "source": [ "estr = MEstimator(psi_smooth_fast, init=init_vals)\n", "estr.estimate()" ], "id": "86a04d1461e24c0b", "outputs": [], "execution_count": 19 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:04.730993600Z", "start_time": "2026-03-17T15:31:03.733125100Z" } }, "cell_type": "code", "source": [ "# Repeating the plotting steps for the updated version\n", "day_range = np.asarray(range(0, 365))\n", "y0hat, cb0 = predict_at_times(days=day_range, beta=estr.theta, covariance=estr.variance)\n", "y1hat, cb1 = predict_at_times(days=day_range, beta=estr.theta, covariance=estr.variance,\n", " x_value=1, include_intercept=False)" ], "id": "33fe1286c5658e02", "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\pzivich\\Documents\\open-source\\Delicatessen\\delicatessen\\sandwich.py:568: RuntimeWarning: covariance is not symmetric positive-semidefinite.\n", " mvn = rng.multivariate_normal([0., ] * k, cov=covariance, size=n_draws)\n" ] } ], "execution_count": 20 }, { "metadata": { "ExecuteTime": { "end_time": "2026-03-17T15:31:04.837020400Z", "start_time": "2026-03-17T15:31:04.746720900Z" } }, "cell_type": "code", "source": [ "plt.subplot(211)\n", "plt.plot(day_range, y0hat, color='blue')\n", "plt.fill_between(day_range, cb0[:, 0], cb0[:, 1],\n", " alpha=0.4, color='blue')\n", "plt.title(\"Intercept\")\n", "plt.ylabel(r\"$\\beta_0(d)$\")\n", "plt.ylim([-20, 20])\n", "plt.xticks([])\n", "plt.subplot(212)\n", "plt.plot(day_range, y1hat, color='red')\n", "plt.fill_between(day_range, cb1[:, 0], cb1[:, 1],\n", " alpha=0.4, color='red')\n", "plt.title(\"Latitude\")\n", "plt.xlabel(r\"Time since January First ($d$)\")\n", "plt.ylabel(r\"$\\beta_L(d)$\")\n", "plt.xticks([1, 60, 152, 274, 365-30],\n", " ['Jan 1', 'March 1', 'June 1', 'Oct 1', 'Dec 1'])\n", "plt.tight_layout()\n", "plt.show()" ], "id": "4ec6233244dc27bc", "outputs": [ { "data": { "text/plain": [ "
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" }, "metadata": {}, "output_type": "display_data", "jetTransient": { "display_id": null } } ], "execution_count": 21 }, { "metadata": {}, "cell_type": "markdown", "source": [ "This vectorized version takes less than a second to run on my laptop, so we can really see the benefits of vectorization here. These benefits would compound as the dimension of either the function measurements or the number of observations increase. Therefore, the vectorization is probably the preferred implementation to use in practice.\n", "\n", "You may notice that the functions look slightly different between the two approaches. This is not due to a difference in the algrebra between the approaches but is rather due to floating point errors. Some of the usual mathematical properties (associativity) no longer hold with floating point errors. In high-dimension problems (like this one), it can lead to an accumulation of floating point errors that can modify the results. This is a limit of computation that we persist with.\n", "\n", "## References\n", "\n", "Gunning E, Warmenhoven J, Harrison AJ, & Bargary N. (2024). *Functional Data Analysis in Biomechanics*. Springer." ], "id": "a6f34479b5ec9b1f" } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 5 }