{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Seasonality in time series data\n", "\n", "Consider the problem of modeling time series data with multiple seasonal components with different periodicities. Let us take the time series $y_t$ and decompose it explicitly to have a level component and two seasonal components.\n", "\n", "$$\n", "y_t = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t\n", "$$\n", "\n", "where $\\mu_t$ represents the trend or level, $\\gamma^{(1)}_t$ represents a seasonal component with a relatively short period, and $\\gamma^{(2)}_t$ represents another seasonal component of longer period. We will have a fixed intercept term for our level and consider both $\\gamma^{(2)}_t$ and $\\gamma^{(2)}_t$ to be stochastic so that the seasonal patterns can vary over time.\n", "\n", "In this notebook, we will generate synthetic data conforming to this model and showcase modeling of the seasonal terms in a few different ways under the unobserved components modeling framework." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Synthetic data creation\n", "\n", "We will create data with multiple seasonal patterns by following equations (3.7) and (3.8) in Durbin and Koopman (2012). We will simulate 300 periods and two seasonal terms parametrized in the frequency domain having periods 10 and 100, respectively, and 3 and 2 number of harmonics, respectively. Further, the variances of their stochastic parts are 4 and 9, respectively." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# First we'll simulate the synthetic data\n", "def simulate_seasonal_term(periodicity, total_cycles, noise_std=1.,\n", " harmonics=None):\n", " duration = periodicity * total_cycles\n", " assert duration == int(duration)\n", " duration = int(duration)\n", " harmonics = harmonics if harmonics else int(np.floor(periodicity / 2))\n", "\n", " lambda_p = 2 * np.pi / float(periodicity)\n", "\n", " gamma_jt = noise_std * np.random.randn((harmonics))\n", " gamma_star_jt = noise_std * np.random.randn((harmonics))\n", "\n", " total_timesteps = 100 * duration # Pad for burn in\n", " series = np.zeros(total_timesteps) \n", " for t in range(total_timesteps):\n", " gamma_jtp1 = np.zeros_like(gamma_jt)\n", " gamma_star_jtp1 = np.zeros_like(gamma_star_jt)\n", " for j in range(1, harmonics + 1):\n", " cos_j = np.cos(lambda_p * j)\n", " sin_j = np.sin(lambda_p * j)\n", " gamma_jtp1[j - 1] = (gamma_jt[j - 1] * cos_j\n", " + gamma_star_jt[j - 1] * sin_j\n", " + noise_std * np.random.randn())\n", " gamma_star_jtp1[j - 1] = (- gamma_jt[j - 1] * sin_j\n", " + gamma_star_jt[j - 1] * cos_j\n", " + noise_std * np.random.randn())\n", " series[t] = np.sum(gamma_jtp1)\n", " gamma_jt = gamma_jtp1\n", " gamma_star_jt = gamma_star_jtp1\n", " wanted_series = series[-duration:] # Discard burn in\n", "\n", " return wanted_series" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "duration = 100 * 3\n", "periodicities = [10, 100]\n", "num_harmonics = [3, 2]\n", "std = np.array([2, 3])\n", "np.random.seed(8678309)\n", "\n", "terms = []\n", "for ix, _ in enumerate(periodicities):\n", " s = simulate_seasonal_term(\n", " periodicities[ix],\n", " duration / periodicities[ix],\n", " harmonics=num_harmonics[ix],\n", " noise_std=std[ix])\n", " terms.append(s)\n", "terms.append(np.ones_like(terms[0]) * 10.)\n", "series = pd.Series(np.sum(terms, axis=0))\n", "df = pd.DataFrame(data={'total': series,\n", " '10(3)': terms[0],\n", " '100(2)': terms[1],\n", " 'level':terms[2]})\n", "h1, = plt.plot(df['total'])\n", "h2, = plt.plot(df['10(3)'])\n", "h3, = plt.plot(df['100(2)'])\n", "h4, = plt.plot(df['level'])\n", "plt.legend(['total','10(3)','100(2)', 'level'])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components (frequency domain modeling)\n", "\n", "The next method is an unobserved components model, where the trend is modeled as a fixed intercept and the seasonal components are modeled using trigonometric functions with primary periodicities of 10 and 100, respectively, and number of harmonics 3 and 2, respectively. Note that this is the correct, generating model. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t + \\epsilon_t\\\\\n", "\\mu_{t+1} & = \\mu_t \\\\\n", "\\gamma^{(1)}_{t} &= \\sum_{j=1}^2 \\gamma^{(1)}_{j, t} \\\\\n", "\\gamma^{(2)}_{t} &= \\sum_{j=1}^3 \\gamma^{(2)}_{j, t}\\\\\n", "\\gamma^{(1)}_{j, t+1} &= \\gamma^{(1)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\sin(\\lambda_j) + \\omega^{(1)}_{j,t}, ~j = 1, 2, 3\\\\\n", "\\gamma^{*, (1)}_{j, t+1} &= -\\gamma^{(1)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (1)}_{j, t}, ~j = 1, 2, 3\\\\\n", "\\gamma^{(2)}_{j, t+1} &= \\gamma^{(2)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\sin(\\lambda_j) + \\omega^{(2)}_{j,t}, ~j = 1, 2\\\\\n", "\\gamma^{*, (2)}_{j, t+1} &= -\\gamma^{(2)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (2)}_{j, t}, ~j = 1, 2\\\\\n", "\\end{align}\n", "$$\n", "$$\n", "\n", "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_1)$, and $\\omega^{(2)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_2)$, where $\\sigma_1 = 2.$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "==============================================================================================\n", "Dep. Variable: y No. Observations: 300\n", "Model: fixed intercept Log Likelihood -1145.631\n", " + stochastic freq_seasonal(10(3)) AIC 2295.261\n", " + stochastic freq_seasonal(100(2)) BIC 2302.594\n", "Date: Tue, 17 Dec 2019 HQIC 2298.200\n", "Time: 23:38:36 \n", "Sample: 0 \n", " - 300 \n", "Covariance Type: opg \n", "===============================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "-----------------------------------------------------------------------------------------------\n", "sigma2.freq_seasonal_10(3) 4.5942 0.565 8.126 0.000 3.486 5.702\n", "sigma2.freq_seasonal_100(2) 9.7904 2.483 3.942 0.000 4.923 14.658\n", "===================================================================================\n", "Ljung-Box (Q): 34.17 Jarque-Bera (JB): 0.08\n", "Prob(Q): 0.73 Prob(JB): 0.96\n", "Heteroskedasticity (H): 1.17 Skew: 0.01\n", "Prob(H) (two-sided): 0.45 Kurtosis: 3.08\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n", "fixed intercept estimated as 4.053\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "model = sm.tsa.UnobservedComponents(series.values, \n", " level='fixed intercept', \n", " freq_seasonal=[{'period': 10,\n", " 'harmonics': 3},\n", " {'period': 100,\n", " 'harmonics': 2}])\n", "res_f = model.fit(disp=False)\n", "print(res_f.summary())\n", "# The first state variable holds our estimate of the intercept\n", "print(\"fixed intercept estimated as {0:.3f}\".format(res_f.smoother_results.smoothed_state[0,-1:][0]))\n", "\n", "res_f.plot_components()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. ],\n", " [ 0. , 0.80901699, 0.58778525, 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. ],\n", " [ 0. , -0.58778525, 0.80901699, 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. ],\n", " [ 0. , 0. , 0. , 0.30901699, 0.95105652,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. ],\n", " [ 0. , 0. , 0. , -0.95105652, 0.30901699,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ,\n", " -0.30901699, 0.95105652, 0. , 0. , 0. ,\n", " 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ,\n", " -0.95105652, -0.30901699, 0. , 0. , 0. ,\n", " 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0.99802673, 0.06279052, 0. ,\n", " 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , -0.06279052, 0.99802673, 0. ,\n", " 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0.9921147 ,\n", " 0.12533323],\n", " [ 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , -0.12533323,\n", " 0.9921147 ]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.ssm.transition[:, :, 0]" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Observe that the fitted variances are pretty close to the true variances of 4 and 9. Further, the individual seasonal components look pretty close to the true seasonal components. The smoothed level term is kind of close to the true level of 10. Finally, our diagnostics look solid; the test statistics are small enough to fail to reject our three tests." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components (mixed time and frequency domain modeling)\n", "\n", "The second method is an unobserved components model, where the trend is modeled as a fixed intercept and the seasonal components are modeled using 10 constants summing to 0 and trigonometric functions with a primary periodicities of 100 with 2 harmonics total. Note that this is not the generating model, as it presupposes that there are more state errors for the shorter seasonal component than in reality. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t + \\epsilon_t\\\\\n", "\\mu_{t+1} & = \\mu_t \\\\\n", "\\gamma^{(1)}_{t + 1} &= - \\sum_{j=1}^9 \\gamma^{(1)}_{t + 1 - j} + \\omega^{(1)}_t\\\\\n", "\\gamma^{(2)}_{j, t+1} &= \\gamma^{(2)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\sin(\\lambda_j) + \\omega^{(2)}_{j,t}, ~j = 1, 2\\\\\n", "\\gamma^{*, (2)}_{j, t+1} &= -\\gamma^{(2)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (2)}_{j, t}, ~j = 1, 2\\\\\n", "\\end{align}\n", "$$\n", "\n", "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$, and $\\omega^{(2)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_2)$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "==============================================================================================\n", "Dep. Variable: y No. Observations: 300\n", "Model: fixed intercept Log Likelihood -1238.113\n", " + stochastic seasonal(10) AIC 2480.226\n", " + stochastic freq_seasonal(100(2)) BIC 2487.538\n", "Date: Tue, 17 Dec 2019 HQIC 2483.157\n", "Time: 23:38:37 \n", "Sample: 0 \n", " - 300 \n", "Covariance Type: opg \n", "===============================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "-----------------------------------------------------------------------------------------------\n", "sigma2.seasonal 55.2934 7.114 7.773 0.000 41.351 69.236\n", "sigma2.freq_seasonal_100(2) 28.6897 4.008 7.159 0.000 20.835 36.544\n", "===================================================================================\n", "Ljung-Box (Q): 165.59 Jarque-Bera (JB): 1.20\n", "Prob(Q): 0.00 Prob(JB): 0.55\n", "Heteroskedasticity (H): 1.27 Skew: -0.14\n", "Prob(H) (two-sided): 0.24 Kurtosis: 2.87\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n", "fixed intercept estimated as 4.468\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "model = sm.tsa.UnobservedComponents(series, \n", " level='fixed intercept', \n", " seasonal=10,\n", " freq_seasonal=[{'period': 100,\n", " 'harmonics': 2}])\n", "res_tf = model.fit(disp=False)\n", "print(res_tf.summary())\n", "# The first state variable holds our estimate of the intercept\n", "print(\"fixed intercept estimated as {0:.3f}\".format(res_tf.smoother_results.smoothed_state[0,-1:][0]))\n", "\n", "res_tf.plot_components()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plotted components look good. However, the estimated variance of the second seasonal term is inflated from reality. Additionally, we reject the Ljung-Box statistic, indicating we may have remaining autocorrelation after accounting for our components." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components (lazy frequency domain modeling)\n", "\n", "The third method is an unobserved components model with a fixed intercept and one seasonal component, which is modeled using trigonometric functions with primary periodicity 100 and 50 harmonics. Note that this is not the generating model, as it presupposes that there are more harmonics then in reality. Because the variances are tied together, we are not able to drive the estimated covariance of the non-existent harmonics to 0. What is lazy about this model specification is that we have not bothered to specify the two different seasonal components and instead chosen to model them using a single component with enough harmonics to cover both. We will not be able to capture any differences in variances between the two true components. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\gamma^{(1)}_t + \\epsilon_t\\\\\n", "\\mu_{t+1} &= \\mu_t\\\\\n", "\\gamma^{(1)}_{t} &= \\sum_{j=1}^{50}\\gamma^{(1)}_{j, t}\\\\\n", "\\gamma^{(1)}_{j, t+1} &= \\gamma^{(1)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\sin(\\lambda_j) + \\omega^{(1}_{j,t}, ~j = 1, 2, \\dots, 50\\\\\n", "\\gamma^{*, (1)}_{j, t+1} &= -\\gamma^{(1)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (1)}_{j, t}, ~j = 1, 2, \\dots, 50\\\\\n", "\\end{align}\n", "$$\n", "\n", "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "===============================================================================================\n", "Dep. Variable: y No. Observations: 300\n", "Model: fixed intercept Log Likelihood -1101.455\n", " + stochastic freq_seasonal(100(50)) AIC 2204.910\n", "Date: Tue, 17 Dec 2019 BIC 2208.204\n", "Time: 23:38:48 HQIC 2206.243\n", "Sample: 0 \n", " - 300 \n", "Covariance Type: opg \n", "================================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------------------------\n", "sigma2.freq_seasonal_100(50) 0.7591 0.082 9.233 0.000 0.598 0.920\n", "===================================================================================\n", "Ljung-Box (Q): 883.25 Jarque-Bera (JB): 0.72\n", "Prob(Q): 0.00 Prob(JB): 0.70\n", "Heteroskedasticity (H): 1.00 Skew: -0.01\n", "Prob(H) (two-sided): 0.99 Kurtosis: 2.71\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n", "fixed intercept estimated as 4.426\n" ] }, { "data": { "image/png": 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NiZMQG8Pe4gO4sYMwYDfry2cWIfEbTHgDITRhwGKo7iQcY7chC124pP77zuULkl/qpnlKDMbj3M6vUCgUSiFSAPpDMBjXkCZmLw7b4YdVvN3CnRe15cUl+oNlWGYqsTYzw7u34peiEE8//yyFcR1IEpruC1IJi8lA5xQDPwW6seDfX1GQn8dzz79ITs5uPvnk41M6v3MBKWWNO4YOlQ8cOJCkJH3ZcuTIkfzwww9cdtllPPzww0yaNImhQ4dy4YUXsnHjRjZu3MjAgQMBCIVCNGjQINLfNddcU+X1Rx99xEUXXcSHH37IXXfdhdPpZPny5YwePTpSz+fT/XuWLVvG3LlzARg7diyTJk2qIqvT7QUMOGxVrTxGo5EY4aW0sBCMJpKaNAQgxmqiOAA5hU79fZSx2vwNBgMGLUDQaMcXCLGnsJyANLC/xEmjJBW0UaFQHB9KIVIAsG7DL5gTG9MhtfoD956LW9EtLYFCp58B7fUAeAPTGzD131vIDcUS3zKLjKaJGAzV2948MJPVH27gvudmECzYSZN73+er79/jwIED1K9f/6TP62RxNEvOySI9PT2ibByivLyc3NxcjEZjNWVJCEGbNm1YvXo1ixYt4tFHH2XQoEGMGDGC9PR0VqxYUeM40dGHFdthw4bx6KOPUlxczOrVq7n44otxuVzEx8fXaiE72jZvtz8IWHBE26qda9G8OW6PB5/XR1xcHAAJMXaKS/z4QxLN6ySlcXKN/doMGm4EuwpdBKQBpKTEHaBhYs1KpEKhUByJsicrAPhh/TaEwUiPdo2rnTMZDfRskcSQjqk4rLr1qFmSnWi8xF94A4a4VMb2Squx38EZTWiVaMbS8zos/e/EYI3B0XM0b82YeRJnc24yYMAA3G437777LqBbdh566CEmTJiA3W7n66+/pri4GI/Hw6effkrv3r3Zt28fdrudG264gYcffpg1a9bQtm1bCgoKIgpRIBDgl19+qXHMmJgYunfvzv3338/QoUMxGo3ExsbSvHlzPvnkE0C3UK1btw6A3r178+GHHwIwa9asav35QxK0ECZj9a8eIQTRdjuJiQkRJcZutyEDuvXJYZJYrdYa5YyLthIsP4A/pCGDAULOIjRhxOU7OY7hCoXi3EMpRAoA1uw8AECfTi1qPG8yGrCaDy9XCCHo2y4VQ1Q0XRrHMqxzwxrbGQ2C6eN74rDbMCc2YnRWY0yOZN5avK7uJ3GOI4Rg/vz5fPLJJ7Ru3Zo2bdpgtVr5y1/+AkCfPn0YO3YsmZmZXHXVVXTr1o0NGzbQvXt3MjMzmTp1Ko899hgWi4U5c+YwadIkOnfuTGZmJsuXL6913GuuuYb333+/ylLarFmzePvtt+ncuTPp6el89pkeiP6ll15i2rRpZGdnU1JSUq2vEAZMHL/DsxACi+ZFcxbTuEHt6TmSkpIwywDBknyCpfk0TIoFqXGg1Fmlnj+o4QuE0FTyYYVCcQTibM9K3q1bN7lq1arTLcZZT5cJT1FSL5Ntf70Ccw2/3mti+fZC7v9wLW9P6EZG4/ij1v1uawE7CpyM69mMrMfnc/DAflY/MzLiuzJ2/AQOFpVww7jxjL165O+ez8lg8+bNtG/f/nSLcVYQCATYsGEDNpuNZs2aYbfbCQQCbN7vxG4M0aphzUtfNeF2u/H5/STEH/0eq6ioYMuWLURHR9OuXTs27NqPwWyhYxPdr8ofDLHtoBOL0UBitIWkmKij9ncuUdO9K4RYLaXsdppEUijOOJSF6DzkzTff4sFHJvLzzz9HyopCVuzBiuNWhgAuaJXMovsvPKYyBNCnVTJjujfFaDQwoEUMlpQ0vv2fPv6+ffv4YleIDSkDmLgol/mLvj7xSSnOKJxOJ8Iej1ea2LptO5qmUe7ygBDYLSeWdd1utx9TGQJwOBw0b96cpk2bIoTAbABNGCMBG8u9QUKaJBDS2FfqxRcIHaNHhUJxPqEUovOMQCDApGdf47V539AtuzsrV66ktLQULTaVhtHHbn8kKY7j+5VtMIjIktvQnvov1W/W7QBg4df/JbbX1TRJa0VUaismv72Is91yeb7g9/vZsWMHW7ZsYf/+/ZHyMpcXY0wixtgURHwDnC5XeIcZOOw1+wHVBUlJSRGncJtZ/3pz+wNhmXzIUBD3/l1IqbG3xHXS5FAoFGcfSiE6R8kv87D9YAUbd+SSk5sXKV++4keiBz9AvdFP0uDW15nxwTy+/OYHTI5kOjVJPCWy9WjTEKlprN+rRyz+9MfNCGFgypUZNLZ4qEjNZM7c+adEFsVvJxQKsW3bNsrKyvD6g+zLz48EcXT59b9JdjPCaKa4zEmFV1dMoq2WUyJftE0fp9ztQ0qJO6Ah/W4aN0xFeitw+jVKyp3H6EWhUJwvKIXoHOSXvBLGPf8pF098i353/4P0Cy9l+/btALzz7xUYoxMY0j4JU2w9/r21nFfnfwPAiH5dT4l8dosJq7+UfJ++dLKxMIQh5OOyTg2ZOLInJkcyT7w1X1mJznB25ewhYI7BXK8FIqERxviGlJeXI6UkKEwYZYj6cTaQknJvEM1kxSJCNYZnOBk47DbQNNy+AN5ACAmY0UhNTaVV43ogJfnKSqRQKMIohegcZPxLC9jitGC22onPHEjyNX/hkb+/BsAPuR5E0MefR2bS0OIl2LgLv/oTsWoeerc+dXGBGkdrhBwNWbduHaHkVjSzBTAZDQzNaESs0U9pSmYkWrLizMPpdOIyRmOwx+GwmomzmRHmKArKXFS43AhzFHazwGQ0YBYaRDnAYCTZYT9lMkZFRSGDfnxBSYnbD0CsXbcaRdusWAgSNFhwebxH60ahUJwnKIXoHOPLVVsoNCbRsGwT/3nqOmbf3huL5udHbyofLPgaT1IbmpqdpDis3HBhG8wJDbGmZXJ5egrGU/TLHaBL00SMMQnc+sQLmOLqM7hzU0D3Nbq5XzuiGrXjz9PfP2XyKE6MPQeKESYL9R1RNIy30TDehpAhPNJEQZkbgMQYPfhivN0CAoTUSHScPP+hIxFCYCRECAOlLj8yGCA+1hE53zAxBoRgb1H5KZNJoVCcuSiF6Bzj8ff/i+b38PpDY2hd30H3tERu7NWEqEbteWjeZoy2WK7uoccaGtu3PYQCoIV4+Mrup1TOQd3aArA3tTcA1/TtFDl304WtMMkg632J7N69+5TKdaaTl5fHlVdeSevWrWnZsiX3338/fr//pI55KM7RISqcTgImOyY0UmKtWEwGzEYDsRYBpihc0gyaRmw46WpynO7kHGMxYDhK1OiYmJhaz/1WooyCm6++gvU/r0G6iqqMERttwxDy49WMdbI8279/fw6FALnssssoLS2tte6nn37Kpk2bIu+feOIJFi9e/LtlUCgUvx2lEJ1DHCgq5YClAU2C++jcvhWg/0p+eFg3GlsDpNRvSL8GGrdfcQEADquZ63s05aouDWgQXz2Vwsnkwk4tMMog9sT63HtxK5qnHH5QOWxmLmkVi71tH75Y8v0pletMRkrJyJEjGT58ONu2bWPr1q04nU6mTJlyUsc9UiEqrvAgjCbqx9mqKDiNkuMwhzxYpY9GcZZItGmz0UCLlBiapsSdVDlrwmE1IUNBAmX7SY6LqZbGI9psAIMRt69mpTIY/G2RrhctWkT8UUIFHKkQPf3001xyySW/aSyFQlE3KIXoHOKr/21EGIwMzmxapdxiMvD5I5cx5w+Defm2IVXSJjwxvDNTR50aZ+rK2Cwm5t7dl9m39+bO/i2rnb/70kyEwch/1ueectnOVJYuXYrVauXGG28E9ISoL7zwAjNmzMDtdjNz5kxGjhzJkCFDaN26NRMnToy0/eqrr+jVqxddu3Zl9OjROJ3Vd1fl5+fTt29fMjMz6dixI99//z1//OMf8Xg8ZGZmcv311wPw0Ucfcd3QAQy4sBe33347oZAezyc+Lo43XnqWa668lKtHXklBQUGk72iLMbIkO3z4cLKyskhPT+eNN96oIsOUKVPo3LkzPXv25MABPXp6QUEBV111FdnZ2WRnZ7Ns2TIAVq5cyQUXXECXLl244IIL2LJlCwAej4drr72WjIwM7rn7LnweFylJiTRq1KjKWGlpabzw92e4bugA+lxwQWTjwYQJE3jwwQe56KKLmDRpEi6Xi5tuuons7Gy6dOkSicpdeZxrrrkGj8dTpe/CwkIA3n33XTIyMujcuTNjx45l+fLlfP755zzyyCNkZmayY8cOJkyYwJw5cwBYsmQJXbp0oVOnTtx0002RxLlpaWn86U9/omvXrnTq1Ilff/0VgG+//ZbMzEwyMzPp0qULFRUVx7yXFApFdVRy13OI5Zv3AHEM6Nq22rnEaAuJ0dW3O0eZqmcPP1V0ahyPQdScDLRjo3gMvgp+LTt98h2Npxb8wqZ9det70qFhLH+6Ir3W87/88gtZWVlVymJjY2natGnkYb527Vp+/vlnoqKiaNu2Lffeey82m41nnnmGxYsXEx0dzd///neef/55nnjiiSp9zZ49m8GDBzNlyhRCoRBut5sLL7yQV155JZLIdfPmzSxc8Dnvzl1I15ap3HXXXcyaNYtx48bhcrnolpXFC88/z9NPP81TTz3FK6+8AlT9jGfMmEFiYiIej4fs7GyuuuoqkpKScLlc9OzZk6lTpzJx4kTefPNNHnvsMe6//37+8Ic/0KdPH/bs2cPgwYPZvHkz7dq147vvvsNkMrF48WImT57M3LlzefXVV7Hb7axfv57169fTtWtXkpOTa7zPkpMSmb1gMV/O+4AHHniAL774AoCtW7eyePFijEYjkydP5uKLL2bGjBmUlpbSvXt3LrnkEl5//fVq49T0mU2dOpVly5aRnJxMcXExiYmJDBs2jKFDhzJq1Kgq9b1eLxMmTGDJkiW0adOGcePG8eqrr/LAAw/o8iYns2bNGqZPn85zzz3HW2+9xXPPPce0adPo3bs3Tqez1nxvCoXi6CiF6CThC4bIKXTRMN4WSYh6IngDIYKaJCbq+D+iTfvK0KSZnp3anPB4p4OjOXELIWhsdpIT1wyX20O0/dQu6Z2JSFk9c3tI0yKRmEFPAHsoU3yHDh3YvXs3paWlbNq0id69dX8tv99Pr169qvWZnZ3NTTfdRCAQYPjw4WRmZlaTYfHixWzeuJ7rhl2C1WzC4/FQr56eY8xgMETynd1www2MHFlzCpaXX36Z+fP1OFO5ubls27aNpKQkLBYLQ4cOBSArK4uvv/46Mmbl5aXy8nIqKiooKytj/PjxbNu2DSEEgYAe5+i7777jvvvuAyAjI4OMjIxar+kNN9yAM+hn4BUj+NvTj0fKR48ejdGoK+NfffUVn3/+Oc899xygKy179uw5rnGWLl3KqFGjSE7WU5UkJh491teWLVto3rw5bdro/8Pjx49n2rRpEYXo0DXNyspi3rx5gJ5Q98EHH+T6669n5MiRNG5cPUGzQqE4NmecQiSEGAK8BBiBt6SUfzud8gRC2gmlswD9ITNlxn+Ys9VH73pBXrxzGCknsLtG0yRvf78DgWBIpwY0SrAdlyVnv0dg0QojX+RnO31bJbNnp5k5S39i/NC+p1ucKhzNknOiBEMampSYDEe/z9LT05k7d27kfUjT2JZ7kN25e4hNqo+maURFHY4cbjQaCQaDSCkZOHAgH3zwQZX+fvzxR267/XakJpk4aSJjrh3Dd999x8KFCxk7diyPPPII48aNq9LG5/dzxegxPPbY4zRPPfrDXQhBbm4uV1xxBQB33HEH7dq1Y/HixaxYsQK73U7//v3xevVt72azOaKcHZIdQNM0VqxYgc1WVSm+9957ueiii5g/fz45OTn079+/ytjHw6GdaAFMVdocinYN+v/z3Llzadu2uuX1WOPUpMQeq/7ROPT5Vr4+f/zjH7n88stZtGgRPXv2ZPHixbRr1+64x1QoFDpnlA+REMIITAMuBToAY4QQHU6XPLfcdR9N2nbmnocmsWH7HvzB48vSPWX6R3yyLUjI72VZcTSDJ89g277i4x73wxVbeParbfzjq60M/ct8Xp77bbWxi11+vJVyMWmahjcqiXqW3+YEeiZy/YCuSKmxYPXO0y3KSSOkaWzLL2FLbgEbt2xjX/6BWh+KAwYMwEpaFigAACAASURBVO128+677yKlJOdgOVMencSwUWMo1yzsKyghpFW/R3v27MmyZcsiy2put5utW7fSKr0z7y/8llkLv6FT9758+fUSbDYbt956KzfffDMrVqxg48aNmM3miPUlu0cvFi/8HE9FGQDFxcWRnYCapkX8YGbPnk2fPn1o0qQJa9euZe3atdxxxx2UlZWRkJCA3W7n119/5ccffzzmNRo0aFBk6Q2ILN+VlZVF/IJmzpwZOd+3b19mzZoFwMaNG1m/fn2tfX/00UdYTYIvv5hP9x49ATjy6g8ePJj/+7//i3wuh3IAHs84AwYM4OOPP6aoqChyvUDPu1aTr0+7du3IycmJfFbvvfce/fr1q1V+gB07dtCpUycmTZpEt27dIr5FCoXixDijFCKgO7BdSrlTSukHPgSuPB2CfDzvM74obYh11N+YV9KES+79Bw8/+8axGwKzN5RjcBcx+9aetPBtpzi6GUP+PIedeQeO2bbI6eXxuesIFOVRP+9bKgKSV9a4GDbp/yJ19uwv5KJHXuOJGV9ElKKNO/ciouy0S637rcuni/YtmyILc1hfYkLTJEVFxeTn7z92w7OInP0lBDAiTRZw1KPAo7FrT16VOsGQFrE0zJ8/n08++YTWrdvQv0cXzEbBU49Nxiwk0myjtMIdSZ9xiJSUFGbOnMmYMWPIyMigZ8+e/LxuPftKPcigH7PQMNpj+fnXHfTo2ZMuXbowd+5cRl17PUFbEsNHXkWnTp24/vrraZzWkrsfmcKYUcPJyMhg4MCB5OfnA7pV5ZCf09KlS6v5KAEMGTKEYDBIRkYGjz/+OD179jzmNXr55ZdZtWoVGRkZdOjQgdde04OMTpw4kUcffZTevXtHHLsB7rzzTpxOJxkZGfzjH/+ge/faQ0r4fD5GXzmU2W+/zuSnpiKlxBcIVfkB8vjjjxMIBMjIyKBjx448/vjjxz1Oeno6U6ZMoV+/fnTu3JkHH3wQgGuvvZZnn32WLl26sGPHjkh9q9XKv/71L0aPHk2nTp0wGAzccccdR70+L774Ih07dqRz587YbDYuvfTSY15ThUJRHXEmpUcQQowChkgpbwm/Hwv0kFLec0S924DbAJo2bZpV17FqnE4nba+eiDnjcoZ0qMeO/SVsK3AjEXx4fVt6ZbZDSsm4G28mO7s79919+Atr74ECLvjnCjqZD/LF1Fso9waY/OocFuyPobP5AJ8/c0ukbk3m9LtfnsvCfVaGx+7izw/ezrode7lt2iJctlQWP9Cb1k3qM+6v7/Fdmb5ckW4uYOGfJ/D8h1/y8togf+xm4Y5RA+v0epxOht33DOvtXXi4TwrTnrgPJGz++dhWhZPB5s2bad++fZ31V1rhZk+pH0PIS4sGyZR5AhRWeJEhP52a1UMIQTCksetgGanx0Thsh53i95dUcNAVIiUqRGpyIoGQRs7BUryakUYxRpLiHUcZGX7ZfYCQwUxqtIH4WAf+oMaugnJkMEinNN0naP2u/QiLnnrDprlo3awxm3LyCRqtdGocX+3ejYmJqXH32plKWloaq1atwmq1suNgBcYoGw3j7eSVuImxGGhRL/Z0i1hn1HTvCiFWSym7nSaRFIozjjPNQlTTYns1jU1K+YaUspuUsltKSkqdC/HFf3/EnHE5nROCPDMyg9dvvIC/XtYcDAaenLUEgB//t5LFWkeeXrCRzxd9GWn7+XerEQYjF3dqBkCs1cxz91yNuXgX68uthMIOsB5/kHW5pVUcYgFW7SokVFHAPyfdicNqpneHZjw6tBOYzDwy4ys8/iDL9oMsyiG66Fc2+hLZW1DKj1v2ATCoR935tpwJ/N8jEwiW7ucfCzfi7HMf5d1v5pdNm0+3WHVCQZkLBLRITcBmMZLiiCLapIEpiuJyPcfW3qJyPCHB7iIngdBhq4XT4wcpSYzVY+tYTEYaJzpASopdvkg9rz+A/4hYOlJKQsKESQaplxiPxWQkOspEjFmAOYrSChdOlxthtmE1aAgkHs2EpmkENDCinZBfzJmOzWYj5CpBk7C3RI+y7fKF0M6gH4sKheLkc6YpRHlAk0rvGwP7TrUQ36zfBcC9gzqSHBNFi5QYru2fQUxFLpt98RSWuZj6/n+IatiWmMxLuePV/0T8Ab7dkAPAFX06R/qzmo0MbGkHewIz/rMSgCufeo/hLy3l0592VBm7IGjFESiNOEYLIbjh0j4Y9//C2nIbz8xfQ8iWSI8kP3deko4wGHlx7n9ZWyiRJXm0aNLwZF+eU0qzJo3pbC3EEFcfk8mIOaEhL36y5HSLVSf4QxJCAezWKITQ8341DCs1hRVepJRU+ELIUABNGsgtOmx98YUkBP1YLIetRnarBRH04dUMSCmRUrI1v5SteUVVHu4erx8MRmzmw//+QghSE2JAwsFyT0RZS42zYzNKMFvJP1CAMFuxmWt22j+brEMAOTk5JCcnYzQaSXTYkX4PEgi5ypBCUO72HbMPhUJx7nCmKUQ/Aa2FEM2FEBbgWuDzUy3Ehr0VyKCf/hnNI2VCCK7LbozBHs+Nf53JWmcclkAF3ZJDWNIv4eMv9YjKvx70gKeM1o3rVelz8tjLCbnLefObzWzYlc8WXzyYrUycs46cQv1BUlDqRItOpkV81c1/QgiuTY9D0ySzfi4g5Cln4jUXc9uIiwmVH2Tery780fXplnhyUzicLt5+9EY6lP/Ev27IRHjL+W9u6NiNzgJCwoiJqv4+1igLIuDBJ40UOH1owog56EF6y3H6dauFlJIQRkyiuqXGZpRIYaDM7deVGqMZzRRF7sHDTv2lLt0K4rBHVW0bZUEEvfikCVfICFoQhz2KlHDqjUKvBCGoHx/NuUZqaiqB0v0ES/ZhwwdS6tdPoVCcN5xRCpGUMgjcA3wJbAY+llL+cqrl2O83Y/UVV4noDDDxhsswl+awgTRMqa0Z2jaOx67qAcAXP+m7QoqJIYHqu0eaNGpAUukmDhpTuOblxWA0kbrtc/waPP3xcgAW/KDvnunVrlG19o/dM56u+V9Q/J+Xsa79iKzMDCwWC41lISFrPJrXyTM3X16n1+FMIbV+Pea99Dj9u7alY3QFgeRWrNy8q0qd/WVeth2oqLYEeaZwpK+ezx8Ag5EoU/V/QUfY6LO/zAtSkhIXjcNmBgQubwCPPwhCYDVXb5vosIKU7C/zUOj0I0MBCPop84E/oC+dubz6jrH4mOqZ55NsBjSfG2kwEkUIIQSx9ijQQgizFYMWJPo3xNU607FarSTExaL53KQ1a4oIevGGqn5umpT4gxrBGnbynUpCoVCd5F5TKBRVOaMUIgAp5SIpZRspZUsp5dSTOVYwGGTGex9QXHZYgfF6fQRjUmlsr/6lZzab+OHvN5IR48QRKueJ6y8ms3l9DJ4SNhUG2LprDyIulbYp1R80ADMfvobQnrW4oxKxF2/n65nPEcrfyo879BD//92gP+Sv6N25Wlu73c682TNZ/vF0ls6aFrEMjMjWrViJFTto36rF77sgZzDW8DLN3Zfq0YD/FV56BNi8ez+3vvolo6d/x4xlp2eLviZlrT4nFU4XufkHCVbyASp367F3alIuUhLiCBTuRnOXEXIWkRAfR1y0HoOn1Omh1KmniHDYoqq1jXU4CJYdwK9BEAPGgJt6jigwGCko1S2RvhCIUABTDfGqGtRPoWVqAokmP2n1EwDdQmkRuuxx1nMjxlVNNG3alDZt2mC1Wom2GJHCiNsXiJwvcfnZW+xkb2FFlc/yVFJaVs66devYvPlXXGFLn0KhqBvOOIXoVPLc6+/wx8+3kHX59axao8cWWfrTBgxRdjKbJNTYpn6cnXf+MIIlT4wgPlp/IDWO8uBxNOL5979ACAP9OqXV2DYzoyPzplxNUsFa/jKmFw6Hg8ZRbtzmOAoqfPyS70SrKKBTm+Y1tjcYBB3btKRJ48MWpDtHDyZh6xf87YYLf8eVOHsY0KMzIVcJGyulzbj5pc9YX6hRWFjI3z9bg8d3amMxhUIau/cdYPOWrfyyaRO5eXurbH3fU1hBqRbF9r0FEaXJ6dGXN2Ojq0fgjo6Opk3rVhh95TjMYDKZiHPEIIN+nL4g5d4AaBpxNVh4TCYTcTYzgeK9aO5yEuwWUuJjQGo4fQGklGjChEnUrLwJIXDE2GlUP4WoqMP+SQ0SojFpARoknTs7r47EbDYTG6vPz2HXA6lWuHTlU0rJ3hI3FT6NMr9k0669lJWVnVL5issqyDlQgimpCQFrPFt378XrU35OCkVdcV4rRB+szsfeMhvZ53aun/oeAEt+3gbAxV1a1douIdpCvUqRp/u1bYDB6mDh/miE38kNg2uPrZKd3pqlr0xkxMV6nf7tGgAw/8ctFOEgNlR2Qjt4HA4HKz+ZxpCLzg+FyGw2E+U+yH7fYcvKvoCdqJIddGMHAZOdP0yfd0pl2pVfQIW0EoqpT8iRSpHPwP6DutUvpGmEDBbQQvgNUew5UALoqVnQQtiiqueXA3DExNCxY0dattQT35pMJgyhAAGM+KURfBVVHKor07x5c2JtFoLlB0lMiMdoNCJCAfyaoMLtBYMBu+Xolp4j78G4GDttGyfXaFU6FzmkqLrCFiKn1w9CYAk6sRk0sDrYlZcfiRZ9stE0yd5SDwZbLLaoKMxWO6bYFMzmmu8BhUJx4py3ClFBUTHFjpYkBw5SnxI8TXqwJ28va3YXI4N+BmQf//b1sYOyATA6krm1e/1j5i6Lsx0+P2pADzSvk2e/3g72BHo3OfGcXSeaWuRsp6E1hN+aiDcQYvWvuyA6ke7N4vnkxccxluaycLuHvPyDp0QWp9uDWzNj0IKkOKKIs0dhsFgp9uiO30VlTjAYSLAKCPpx+vXyoBQYZPCoyq8Qosp5a9jXXoaCR00FYzAYaNWqFR07doyku7AaQRpM5JfojsIJjpqXdY/G0XLPnWtEWcwQCuILB2gsLteXp1KT4mlePx6zQSBikti//9jBVuuCvUVlSKOFGGOIpknRtEiJoXV9x3n1mSgUJ5vz60laiec+/AqjLZbxvZtzXY80DNYYps1dyi6vnSjXAayW43ccbdOkPlGeApL8B5k0+sRybnXtkkkwfwsBQxT+nSt59t5rT3Qq5x2dGschDEaWb9rDrK9XAXBVn46YzWYmDu2M0ZHM7f+cfdLl2JBXxpJN+9he4KbCH2J/mZcip489BWVsLQmxYvsBVu4qZvuBCgrckt2FFWwt9PHTriK2FfrIKXSxIa8schyLQ87Ns15/kYGXDCA9PZ0XX3wxcj4tLY1OnTqRmZlJdnY2VquVgoIC+vTpwxWD+rP0PwvxYcIQ9DL2umvZt+/kR7R4+eWXad++Pddffz0XXHBBjXWefPLJSOLUU01tMgEYCVFSVsH06dNx+YMQChDniMZkNJAaZ0MYzRSWuyNpTX4vMTE1R5nXNEmJV4OAj2b1E4kyG7GGD4VCUXectwrRvzeXIl0l3DHsQm6/vCcy4OXDX/3gqMcVHWr2HzoaPzxzLV8+fR3GE7TWGI1GWpiKCRTlMqatKeLDoKidvh3TAFiyZis/bD+I5iln6IV6wN3bLu9JjDufDYH67Ni996TKIZGEMGGUAWKsVkwGA2ajkWSHHt25oNyHXxoQIT9mk4noKN3Es7dEj/FzyAfteIlzxLBp+dd8Pm8OK1euZN26dXzxxRds27YtUuebb75h7dq1rFqlK4offPAB48eP54fvf+Cd114GYPX3S+jatSsNG578mFXTp09n0aJFzJo1i+XLl5/08U6Uo8lkMQrKnS6mT59OEBMmGYpY7OLtZixGgYiOp/QIXyIpZbX0Kb+HCrcXhIHYKHHC3y8KheL4OS//uzRNQ/jKaW0swGwyYrWYSAkeRMSlIl3F/PnW4SfcZ4rDSnLMiT3gDnHLwEz49zM89uA9x66soF92BiF3GT9sL+CA5iDOX4jZrCsbQggeH9kVgy2W+1/99KTK4a9l63y0zYrwuwhKAcKALbzUFeeIBk1DwwABH7ExJxbPx2q1EgqF6N27N3a7HZPJRL9+/Zg/f36tbcxmMx6PB5AIIQlUlPDOv97mkUceOepY7777LhkZGXTu3JmxY8cC8Pzzz9OxY0c6duxYxTKVk5ND+/btufXWW0lPT2fQoEF4PB7uuOMOdu7cybBhw3jhhReqWECmTp1K27ZtueSSS9iyZUuVsd9//326d+9OZmYmt99+O6FQqNYxapO1pj5q4pBMNfVPKMBLf32S7Tt2cPWQvrz092cifffo0YPRg/vy5ymPUFLhibS/66676Nq1KzfffDPTp0+PjPPkk0/yz3/+E4Dhw4eTlZVFeno6b7xx7PyIFR7dcbqmMAkKhaIOORTR9mw9srKy5G8hGNJkIBiKvH/01Tmy2aQv5MjHXv9N/f1eNE07LeOerTS6/q+y2aQvZLNJX8hb/jKj2vlWt0+TLe6uXl4bpW6/3FPkkqFQ7Z/Dpk2bqrz/ZmOenLs6V/53U55cn1ta5fhh0x65YPkGuXDFRrlq58FI+bwft8m5q3Plf1Zvr9bmeNi0aZNs3bq1LCwslC6XS/bs2VPec889Ukop09LSZJcuXWTXrl3l66/r93Fpaam87LLLZFZWlpwzd66cOnWqnDlz5lHH2Lhxo2zTpo0sKCiQUkpZVFQkV61aJTt27CidTqesqKiQHTp0kGvWrJFSSrlr1y5pNBrlzz//LKWUcvTo0fK9996TUkrZrFmzSD/R0dFSShnpy+VyybKyMtmyZUv57LPPRuY3dOhQ6ff7pZRS3nnnnfKdd96pdYyaZK2tj5o4JFNN/b/+5lty0fJ1smWbdnLdniLpdLmr9B3SNHn12Jvk1GdflLt27ZJCCLlixQoppZRr1qyRffv2jYzTvn17uXv3bunx+eX69Rvk5s2/ysLCQpmeni4LCwuryHIkW3IPynV7imUwGDzq53Y0jrx3pZQSWCXPgO9wdajjTDlMx9SYzlF0Z8TDDomPTxhK3nOzeOGe0+PDcy7lhjoVNHFtZcvqHFrFBHnlw2nVzneMDfCzoRnrcg7QOa3+Ufty+QKMeXYeu4o8DEouZ/KdN1A/OfGYMngDAcBEtK26g3OsI5ZYRywSiah0n9mMGk53GUkNf1sOvvbt2zNp0iQGDhxITEwMnTt3xmTS/42XLVtGw4YNOXjwIAMHDqRdu3b07duXhQsXAlBSUsLrr73GvHnzuPXWWykpKeGhhx6iV69eVcZYunQpo0aNIjk5GYDExETee+89RowYQXS0btUaOXIk33//PV26dAH0nW2ZmZkAZGVlkZOTU+scvv/+e0aMGIHdrls8hg0bFjm3ZMkSVq9eTXa2vlHB4/FQr149+vbtW+MYJSUl1WSdPXt2jX0ciyP7P5C/jyYd9PAE8aYQ0XZbNfnKKpwkJCQgpaRZs2b07KnvHu3SpQsHDx5k3759FBQUkJCQQFJKfbbmFTD9zX+x9KtFoIU4cOAA27ZtIykpCdCtjpYj/Bf9GiADkXQ+CoXi5HBeLpnVhM0axduPTiApXvnwnA3cOaI//RNK+ffMF4iKqr5UeU3vNgC88Z81kTJvoOZlk3H/+JhN7hjc5jjmFzcge+RtLPvxf1XqfL7oK/xHOM/6gxpoIaJMtf+uEEfkK66XnEhqUixRlt+2vApw8803s2bNGr777jsSExNp3bo1QMQnqF69eowYMYKVK1dWaff0008zZcoUPvjgA7KyspgxYwaTJ0+u1r+UspqCLuXRIyNX/gyMRuMxt6PX9gNASsn48eNZu3Yta9euZcuWLTz55JO1jlGbrLX1cSJzCIVCOMwhTAZokppcY99Ll63krkcew+3xEh0djZQyErRx1KhRzJkzh48++oirr7mGnQfL+WnVGn76cRnvLVjCnK9+oG3bdni93si4G7ftZN/+/VXk0jDUGjdKoVDUHUohqsT5tn39bGbcuHHM+/hDkuIcNZ6/7KLe+PZu5vtd5WiaZGvuAcb/+a1IlOdDLPlpE6td8UQf3MjMm3qQlmTHcMGNjPrz+/j9evDE0rJy7py3nYIyN55KkYtDGDBwYs6zZpOZOMfvU7oPHtRDCuzZs4d58+YxZswYXC5XJMGwy+Xiq6++omPHjpE227ZtY9++ffTr1w+3243BYEAIUeVhfIgBAwbw8ccfU1RUBEBxcTF9+/bl008/xe1243K5mD9/Phde+NtiX/Xt25f58+fj8XioqKhgwYIFVcaeM2dOZI7FxcXs3r271r5qkvVE+zgabZs3xeN2R5SuI/sOeV3sy9ujOz4DO/L2s2lXHpqmce211/Lhhx8yZ84cevUbgDSaCblKSE1JpkVqEjk5Oaxbty7i3ySlxBRXn4MVAUpKwvGqfHoiXmsNKV4UCkXdct4umSnObWJjY0lw5lAu2vPZ2r3884OvyDM25q6X5zN78nWRep8v3wDE8My4i+nXrgHv3BHL/W8uZn2nIbz7+RJuGXUpb372X8zJzZBGCzsOltOhUSIgaVk/jigCtG0cd0rndtVVV1FUVITZbGbatGkkJCSwc+dORowYAegpaa677jqGDBkSaTNlyhSmTtUz4YwZM4bhw4fz0ksv8fTTT1frPz09nSlTptCvXz+MRiNdunRh5syZTJgwge7duwNwyy23RJbLTpSuXbtyzTXXkJmZSbNmzaooVh06dOCZZ55h0KBBaJoWmWNqamqNfdUma019NGvW7IRlTUlOpnfv3nTs2JFLL72UZ599tlrff3jib5iT4wFwa2aw2ti7v4D09HQqKipo1KgRMQkpBENBxl47mvkfz2ZA72waN2tBRtduuNzhaNjhMQ02B7kHi0hISKAsHCk72qoCMCoUJxtxLFP4mU63bt3koS3GCkVl7nvwYeZVtCKuQTNcfo2Q14nRZOb7yYNpkqj7wvR76DV2aYns+McIzGbdd2PTnkIuffl7GgX3sfzFu+nzwDRyjam8M7IRic3a0SjWjNkgyCn1E2/WaFr/2P5GinOXDbsLkECCzUiJX7fkSK+T9LTUiH/X+j2FGGWI9GaH/dkqPAF2Fbmwa26aN6rPxrwSLAaQwkAgpNEu1cHeonKcmpk2KXastUQ1Px42b95M+/btq5QJIVZLKbv95k4VinMMZYdVnLOMGX0VhQuexenxESjeR/qBxUgEE9/9NlJnn9eM1X0wogwBdGiaTHzFLvYaU1mfW0IeiTiceXp0ZykpcXopDf9yj6khwari/CLeZgSjmRKfAC2Ew2JAREVzsFBfxvP5A2AwYTVX/bqNsZoQUsMdhJIyJ8JowmE1E2+3IIwmSsoq8Pj1FC+/RxlSKBTHh1KIFOcsvXr14vknHmL/rElYVrzB/BkvE9q9hp9ynUgp8fgC+O3JNLZX9wO6qnMKwmxlwuvfgjWWPmkxWMxmCHrxhKDcp0EoSPxvSIGhOLdonJKAOegBIYgiQIOEaBCCcq/uWF5Soaf9cFirKs9CCKIMEkxW8ov1ZMXJcdEkOvR0K8UVHkIGCxbD2W3FVyjOFpQPkeKc5q677iLKZqNdmzbYbDbaJZnYbo7W02Zs2YEwmshqkly93dWX8tKwOwhkXIrBYuP26/Wt6RYh8QsjUhixal4MKlzCeY8QgpaNUsjZu58mqclYzUaE1PBr+r3h9PoAS43Kc0pcNLmlXqTVgdBCWC0mfeec1AiY7QiDgZTY2vPWHQ9nu1uEQnGqUAqR4pzn5htvjLzu36ER2/fBop+2smnbDsDOkOx21dokJyfz5fTHee+DTxBIMjuOIScnB03z45M2BFAv/sQiTSvOXSxmE62aNYooyFFGiUez4Pf78QUliBAWc/Wv24QYK8JgoMLjJzpKV3yEEFiN4NGMICUJjhNP+HwIKSVFRUVYrb9PqVIozgeUU7XivOLnn39m2L8207WBlQMFRewNRrPjuVFYLLX7aByKdRMIBNi+fTt7CssxaCEapcSrgJqKGil1eXH6JXHmEGU+MApJg8SaQ0RIKdEkGITg0O1U4fFT5g0RZYSU2N+uEIGe8qVx48ZV/ORAOVUrFEeiLESK84pOnToRzP+UX6yZBM2pxBSuPaoyBIeDCJrNZtq3b8/DV46kR/f/Z+++w6Mq0wYO/96ZdAhptEAgoSeU0EKTJk1swFrALpbFlV3bWlZd7F0/exdXpSyoiK4iogIKIoJAQgmhdxJIh/Q6yfv9cU6GSUijJDNJnvu65mLm1GfOHDLPvDWKJ2adPqihEADRh1KZ8dFGird9j3vfSUztZuX/bh9c6/3Tcwq56oN1vHJ1JBGdguowUiFEGUmIRJPi5uZGW2sOJy0eFGck8ciYsDM+xg/ffXPe4xKNS2SHICi14dbnUiwlRTx2/eVntH9Qc0++v3sEvl7uNW8shDgvpJeZaHKGh7Wg+GQilo3/5fYbnTN3nWjcPNwsBKk8lMXKpN6t8fM+88RGkiEh6tc5JURKqf9TSu1WSsUqpf6nlPJ3WPeoUmq/UmqPUmqiw/KLzWX7lVKPOCzvpJTaoJTap5T6UiklA2+IOnHRBf05PnsGD91yxWntKoQ4X6YM742HVfGvyWc3orcQon6dU6NqpdRFwK9aa5tS6mUArfXDSqmewOfAYKAdsBLobu62F5gAJACbgOu01juVUouAb7TWXyilPgS2aa0/qCkGaVQtzlRJSQmLFi3i6quvloRI1Jn8ohJ2Hs9iYFiAs0OplDSqFqK8cyoh0lov11qXTWv9JxBiPp8CfKG1LtRaHwL2YyRHg4H9WuuDWusi4AtgijJarY4FFpv7zwX+ci6xCVEVq9XKddddJ8mQqFPeHlYGhPrXvKEQwiWczzZEtwE/ms/bA/EO6xLMZVUtDwIyHJKrsuWVUkrdoZSKVkpFp6amnqfwRVM0Z84cRowY4ewwRCMlwzII0XDUmBAppVYqpeIqeUxx2GYWYAMWlC2q5FD6LJZXSms9W2sdpbWOatWqVU1vQTQgYWFhrFy5OaS40wAAIABJREFU0tlhNHmHDx9GKYXNZqt5YyGEaARq7HavtR5f3Xql1HTgcmCcPtUgKQHo4LBZCHDcfF7Z8jTAXynlZpYSOW5frZiYmDSl1JHabOugpXlOV+SqsdVXXH0mTJhwGMg+g33OJbYgoKVSas9Z7l8dV/0soebYPIA+7u7uMfUUTxlXvWauGhecfWyh5zsQIRo0rfVZP4CLgZ1AqwrLewHbAE+gE3AQsGIkYAfNZR7mNr3Mfb4CrjWffwj8/VxiqyHu6Lo6dmONrb7iAg4D46tYdzmwFcgA1gGR5vIEYHGFbd8C3jaf+wGfAInAMeA5wGquuwVYW008I8xzZWBU997icMx5QCpwBHgMsDgc8w8g2dzvIHCBuTweSAGmO5xjjnnPr8BIBH8DQh3WX4DRASHT/PcCh3WrgWfN82UDy4GWDuuHOsS/Dbiw7POsbl/gKEYpbY75GNaY7rPGEperxyYPeTSkx7m2IXoX8AVWKKW2mr3D0FrvABZhJEs/Af/QWpdoo/TnLuBnYBewyNwW4GHgfqXUfoxf7Z+cY2yiEVFKDQA+Bf6GcX98BCxRSnkCJ4BLlVItzG2twDRgobn7XIwq3a5Af+Ai4K+1OGdHjHZx7wCtgH4YCRnmMj+gMzAauBm41WH3IUCeGetCjA4Eg8wYbgTeVUo1d9j+BozkpKV5jgVmDIHAD8Db5rFeB35QSjkOX3y9ee7WGD80HjT3bW/u+xwQaC7/WinVqqZ9gVHmv/5a6+Za6/U1XS8hhGjIzmmkaq1112rWPQ88X8nyZcCySpYfxOiFJkRlZgAfaa03mK/nKqX+jVECUgRsxuiZOA+jx2Ke1vpPpVQb4BKML/Z8IFcp9QZwB0ZSVZ0bgJVa68/N1+lAuplwXQP011pnA9lKqdeAmziVyB8CMrXWJUqpL4FZwDNa60JguVKqCCM5KkuwftBarwF7m7xMpVQH4EJgn9Z6vrnd50qpe4BJGCVLAJ9prfea+y4CJpvLbwSWmf/nwPjhEg1c6vAeq9pXCCGalKY6dcdsZwdQDVeNzdlxhQLTlVJ3OyzzwBjnajbGvXwdRkJ0PadKh0IBdyDRocePhfK9HavSAThQyfKW5rkd264doXzPyGQzFoB8AK11ssP6fMCxhMgej9Y6Ryl1wnxv7Sqcp7JzJTk8z3M4bigwVSk1yWG9O7AK45pdX82+zuLs+6wqrhoXuHZsQjQYTTIh0lq77B8QV43NBeKKB543Sx5PY1YDvaaUCgGuAIY57FeI0TbmTLtMxVN5qWUaUIyRcOw0l3XEaJ9kd4bXzN7ZwKxKC8ToWHCc0xu/dsSoiq5JPDBfaz2jspVKqeur2ffsR2w9By5wn1XKVeMC145NiIZE5jITrshdKeXl8HADPgbuVEoNUYZmSqnLlFK+AFrrVIxGwp8Bh7TWu8zliRiNhV9TSrVQSlmUUl2UUqNrEccCYLxSappSyk0pFaSU6qe1LsFoI/e8UspXKRUK3A/89xze86VKqRHmlDXPAhu01vEY1cvdlVLXmzFcA/QEltbimP8FJimlJiqlrOa1vNBMGmuSCpRitJESQohGTxIi4YqWYVQplT2e0lpHY7Qjehc4iTH6+S0V9lsIjOdUdVmZmzGquHaa+y4GgmsKQmt9FKO9zQMYDbe3An3N1XcDuRg9yNaa5/y09m/xNAuBJ83zDMRov4TWOh2jd90DGG2Y/gVcrrWusZu1mVBNAf6NkeDEAw9Ri//3Wus8jDaAfyilMpRSQ8/iPQkhRMPh7G5udfHA+GJKAeIclgVidGveZ/4bYC5XGD149gOxwIB6juv/gN3muf+H0fgXIAwjGdhqPj50wjV7CqMaqCyGSx3WPWpesz3AxHqO60uHmA4DW+v7mmFUca3C6C25A7j3bO8zjMbRz9VDbE6916qJyxXus6pic+q9BngBGzGGTNgBPG0u7wRsMO+zLwEPc7mn+Xq/uT6srq6ZPOTR2B5OD6BO3pTRZXhAhS/RV4BHzOePAC+bzy/F6FqtMHosbajnuC4C3MznLzvEFea4nZOu2VPAg5Vs25Py40wdwBzXpz7iqrD+NeCJ+r5mGCVMA8znvhiTFvc8m/uM858QVRWbU++1auJyhfus0ticfa+Z90tz87k7RpIzFKPK1nHctpnm879jJmfAtcCXdR2jPOTRWB6NsspMG92XT1RYPAVjPBooP3nsFGCeNvyJMWJ2jdUp5ysuXfUEufWqimtWlaom763XuMxJgacBn1e2vi5prRO11pvN59kYJQvtcY37rNLYnH2vVXPNqlKf91m1sTnrXjPvlxzzpbv50FQ9Gbbj/bcYGKdkQjUhaqVRJkRVaKONBraY/7Y2l1c14awzOE6QC9BJKbVFKfWbUmqkk2K6SykVq5T6VCkVYC5zlWs2EkjWWu9zWFbv10wpFYYx4OMGzuI+01rforV+rB5ic+TUe62SuFzmPqvimjntXjMbxG/FqDpegVFSVtVk2PZrZq7PxBjQUwhRg6aUEFXljCaWrbMgTp8gNxHoqLXuj9GDaWHZSMz16AOgC8YIzYkYVQbgItcMY9whx1/s9X7NzC7yXwP3aa2zqtu0kmV1es2qis3Z91olcbnMfVbN5+m0e00bo/z3wyjRGwxEVLaZ+a+r/N8UosFRWjfs/ystW7bUYWFhzg5DCCEalJiYmDStdauatxSiaWjwAzOGhYURHR3t7DCEEKJBUUpVHAFdiCZNqsyEEEII0eQ1+BKic7E9IdPZIQghxFnpE+Ln7BCEaFSkhEgIIYQQTV6TLiESoinTpTZ0TjqUFDs7FHEWdmUfr9V2Xl5ehISE4O7uXscRCdGwSUIkRBOlc9JpGeiPf0AAMnZfw+PjUfOfb6016enpJCQk0KlTp3qISoiGS6rMhGiqSoolGWrklFIEBQVRUFDg7FCEcHkulxAppfyVUouVUruVUruUUsOcHZMQjZUkQ42ffMZC1I4rVpm9Bfyktb5aKeUB+Dg7ICGEEEI0bi5VQmQOfT8K+ARAa12ktc5wblRCiLrQOtC/zo49f95c7r/3nkrXff/dd7z4/HN1du6qzJ83l8TjpxpCR3TvSlpa2lkf78ILL7QPSjt+/HhOnjx5zjEK0ZS5VEIEdAZSgc/MSRP/o5RqVnEjpdQdSqlopVR0ampq/UcphGiw3nj9VWb87c56P++C+fNITKxdz7AzddNNN/H+++/XybGFaCpcrcrMDRgA3K213qCUegt4BHjccSOt9WxgNkBUVFTDnoxNCBfw4rJd7E7KPq/HDG/ry6OXVjYPadVSU1O5965/EB9/FIBXXn2NIUOH0Su8O+s3RuPvb5Qq9YkIZ+Xq37BYLKdtP+yC4VUef9/evXh6etKyZUsAvvl6MS889xxWqwU/Pz+W/7KK+fPmsnTJEkpKSti5Ywf33HcfRUVFfL5wAZ6ennzz3fcEBgaybdtW7r3rH+Tl5dG5cxc+mP0xAQEBlS5fvepXNsfEcNv06Xh5e7FqzVoAPnz/PZb9sJTi4mL+u/ALeoSHk5ubywP/vJcdcXHYbDZmPfYEl0+eTH5+PnfO+Cu7du0kPDyC/Px8+/uaPHkyI0eOZNasWWd0vYUQp7haCVECkKC13mC+XoyRIAkhmoCHHrifu+65h9/X/cnCLxbxjzvvxGKxcNnlk1jy3bcAbNq4gY6hobRp06bS7auzfv06+vbrb3/94vPPsWTpD2yI3syir/9nX75zxw4+mzef3/5Yx9NPPoGPjw/rN0YzeMhQFv53PgAzbruVZ59/kY0xW+jVuzcvPPdslcuvuPIqBgwcyKdz5/Lnphi8vb0BCAoKYt2GTcy442+89ebrALzy0ouMvnAMv6/7kx+Xr2TWo4+Qm5vLxx99iLePNxtjtvDQI48QExNjjzcgIIDCwkLS09PPw6cgRNPkUiVEWuskpVS8UqqH1noPMA7Y6ey4hGjszrQkp66s+vUXdu869V8+KzuL7Oxsrp46lReff56bp9/CV4sWcfXUqdVuX5XkpCRatjo1wfuwYRdwx19v56qrr2byX66wLx914Wh8fX3x9fWlhZ8fl152OQC9evcmbvt2MjMzyczMZOSoUQDccONN3Hj9tVUur8oU85z9Bwzgu2+NhO+XlSv4YelS3nrDSJAKCguIP3qUP9auZeY/7gKgT59IIiMjyx2rdevWHD9+nKCgoCrPJ4SomkslRKa7gQVmD7ODwK1OjkcIUU90aSmr1qy1l6CUGTJ0GAcPHCA1NZWlS5bw8KP/rnb7qnh5eZGVlWV//fZ777Np4wZ++vFHhg2OYv1Go5Gyp4enfRuLxYKHp6f9eYnNdk7v0VHZca1WKyUlxnG11iz84ku69+hx2vbVdaEvKCio9XUQQpzO1arM0Fpv1VpHaa0jtdZ/0VpL1wkhmoix4yfwoUPj4G3btgJGIjBpyhQe+deD9AgPt5eCVLV9VXqER3DgwH7764MHDjBo8BAef/IpgoKCSEiIr1Wcfn5++Pv788daoy3Q5wsXMGLkqCqXAzRv7kt2dk6Nxx4/4SI+fP89tDaaR27dugWA4SNG8OUXCwHYsSOO2NhY+z5aa5KSkggLC6tV/EKI07lcQiSEaBry8vLo1jnM/nj7zTd49fU32LI5hsED+zOwbySfzJ5t3/7qqVP5YuFCrjKry4Bqt6/MiJEjid26zZ5szHr0EQYN6EdU/34MHzGSyMi+tY5/9iefMuvRhxk8sD+x27bx6KzHql1+4803c+9d/2DooIHlGkRX9Mi/Z1FcXMzggf2J6t+PZ596CoAZf7uT3JxcBg/szxuvvcrgwYPt+8TExDB06FDc3Fyx0F+IhkGV/WFoqKKionTZWBxnantC5nmORoiGo/RkAt0qqZZp7B68/59cetnljB03ztmhnBPHuczuvfdeJk+ezLgq3tOuXbuIiCjfTkwpFaO1jqrTIIVoQKSESAjRpDz08CPk5+U5O4zzqnfv3lUmQ0KI2pGESAjRpLRp04bLJk1ydhjn1YwZM5wdghANniREQjRhDb3KXNRMPmMhakcSIiGaKqs7GSdPyBdmI6a1Jj09HS8vL2eHIoTLky4JQjRRqnkQaSfSSUs9+wlGhfN4uNXu96yXlxchISF1HI0QDZ8kREI0UcrihmrRxtlhiLMUEeLn7BCEaFSkykwIIYQQTZ4kREIIIYRo8iQhEkIIIUSTJwmREEIIIZo8SYiEEEII0eRJQiSEEEKIJq/Jdrt/+vsdbDp0wtlhCCHEWRnUKZAnJ/VydhhCNBpSQiSEEEKIJq/JlhA9OakX2xMynR2GEEKclT4yMKMQ55VLlhAppaxKqS1KqaXOjkUIIYQQjZ9LJkTAvcAuZwchhBBCiKbB5RIipVQIcBnwH2fHIoQQQoimweUSIuBN4F9AqbMDEUIIIUTT4FIJkVLqciBFax1Tw3Z3KKWilVLRqamp9RSdEEIIIRorl0qIgOHAZKXUYeALYKxS6r8VN9Jaz9ZaR2mto1q1alXfMQohhBCikXGphEhr/ajWOkRrHQZcC/yqtb7RyWEJIYQQopFzqYRICCGEEMIZXHZgRq31amC1k8MQQgghRBMgJURCCCGEaPIkIRJCCCFEkycJkRBCCCGaPEmIhBBCCNHkSUIkhBBCiCZPEiIhhBBCNHmSEAkhhBCiyZOESAghhBBNniREQgghhGjyJCESQgghRJMnCZEQQgghmjxJiIQQQgjR5ElCJIQQQogmTxIiIYQQQjR5khAJIYQQosmThEgIIYQQTZ4kREIIIYRo8iQhEkIIIUST5+bsABwppToA84C2QCkwW2v9Vl2dr0+IX10dWgghhBANiKuVENmAB7TWEcBQ4B9KqZ5Ojkk0AGFhYaxcudIp577uuuv49ttvz/k4S5Ys4dprrz0PEQkhhDhTLpUQaa0TtdabzefZwC6gvXOjEg3dqlWrGDNmDH5+foSFhZ22/vDhw4wZMwYfHx/Cw8NPS6zeeOMN2rZti5+fH7fddhuFhYX2dbGxsWzbto0pU6YAsHr1aiwWC82bN7c/5s6da9/+xIkTXHHFFTRr1ozQ0FAWLlxoXzd58mTi4uKIjY09z1egcXBm0iuEaPyU1trZMVRKKRUGrAF6a62zKqy7A7jDfNkD2HOGh28JpJ1jiHXFVWNz1bjAiC0YOAxkV7LeB/DC+AEQDGyvsD4cyAGOAX5AGBCHUWLZAuiEcY8VA10dtgXoCBQBSeZrX3P7WCq/Zp0AZcbqYx5vN1Bgrm8LeABHa/G+z4Wrfp7VxdWHqj/juuaq1wvOPrZQrXWr8x2MEA2W1trlHkBzIAa4so6OH+3s9+gqsQEPY3y5Z2N86Y8zl1uAR4ADQDpwAgh02O8rjCQgEyNx7eWw7lJgp3nMY8CDDutmAPvN4y0B2jms08CdwD7gJPAep5L2LsCvZixpwALAv+yaYXxRjq/hvY4HDldY1h0oBHwdlv0O3Gk+Xwi84LBuHJDk8PogMMLh9YVAQmWfJdAMI3nq7rBsPvCSw+vhwKFq3kMH4Bsg1bwW7zp8Xo8BR4AUjLZ4fua6MPPa3grEm9f2CDAII3HLKDuOuf0twB/AO+bnu7vsvjDXtzM/uxPmZznDYd1TwCLz/NnADiCqwr5fm/EfAu6psO+JyvY1r1MpkI+RkP6rMf+/bCyxyUMeDenhUlVmAEopd4w/mAu01t84O57GTCnVA7gLGKS19gUmYiQWAPcAfwFGY3yJlWAkKGV+BLoBrYHNGAlKmU+Av5nH7I2RyKCUGgu8CEzDKKk5AnxRIazLMb6o+5rbTSwL19y3HRCBkRg8dZZv3VEv4KA2qmjLbDOXl63fVmFdG6VUkFKqGadKjxy1VkolA32UUm+Y24GRfJVorfdWcS4wqonDlFItKgaqlLICSzGuWxhGdXLZ9bvFfIwBOmP8qHi3wiGGYHxm12Bcv1kYSWIvYJpSanSFbQ9ilD48CXyjlAo0130OJGB8FlcDLyilxjnsO9mMyx8jcXrXjN8CfG++5/YYyeV9SqmJDvv6V7av1vomjFKzSVrr5lrrVypeHyGEOBculRAppRTGl+kurfXrzo6nCSgBPIGeSil3rfVhrfUBc93fgFla6wStdSFwHLhaKeUGoLX+VGudba57CuirlCrrtldsHrOF1vqkNtuFATcAn2qtN5v7PQoMM6tHy7yktc7QWh8FVgH9zPPt11qv0FoXaq1TgdcxkrVz1RyjFMRRJkbVV2Xry577YnxpQ/kqnN1mzMEYidJAM9banMvxWP6cbjBGEvKQ1jpXa12gtV5rrrsBeF1rfVBrnYNxba8t+7xMz5r7LMcobflca52itT6GUSrW32HbFOBNrXWx1vpL871cZvYEHQE8bB5rK/Af4CaHfddqrZdprUswSnb6mssHAa201s9orYu01geBjwHHluQ5VewrhBB1yqUSIozqgpuAsUqprebj0jo4z+w6OOb5Um+xaa33A/dhJDQpSqkvlFLtzNWhwP+UUhlKqQyMkoUSjNIRq1LqJaXUAaVUFqdKlVqa/16FUW12RCn1m1JqmLm8HUbpRtn5czCqfRwbzic5PM/DSCJQSrU24ztmnvO/Duc7l2uWg9FOyFELTiUmFdeXPc/GqGoCh4RGa52ktd6ptS7FKN34F0YpSm3O5XisDE7XATiitbZVsq7ctTWfuwFtHJYlOzzPrvA6H/Nam45prR0bGB4xz9EOOFGhRO0I1X+GXmZiFgq0K7unzPvq3xVi3FnFvs4mfzOEaORcKiHSWq/VWiutdaTWup/5WFYH53HZPyD1HZvWeqHWegTGl5UGXjZXxQOXaK39zYeP1trLLE24HpiCUd1S1ggZjGottNabtNZTMKrTvsVoUwJGKVNo2bnNqqQgTjVQrs6LZnyRWusWwI0O5zuXa7YD6KyUciyl6WsuL1vft8K6ZK11utY6F6ONVffKDmzGpcviBPYCbkqpblWcC4zqwMO6QkcCUzzQsYoEody1xWjsbaN80uMot4rlZdqbJbaOxztuPgIrXK+O1O4zjMdoH+Xv8PDVWjv+6Nlfzf5O6wEifzOEaPxcKiES9Usp1UMpNVYp5YnRyykfoxQI4EPgeaVUqLltK6XUFHOdL0ZD5HSMnlIvOBzTQyl1g1LKT2tdDGQ5HHMhcKtSqp95zheADVrrw7UI1xejhCVDKdUeeOgM3qdFKeUFuBsvlZdSygPAbM+zFXjSXH4FEInRjg2MBr63K6V6KqUCMBouz3E4/DIcqu6UUhcqpToqQwfgJeA781y5GA2in1FKNVNKDcdILOc7HG80RvusymwEEoGXzP29zGOA0a7nn0qpTkqp5hjX9ssqSpNqozVwj1LKXSk1FSNRW6a1jgfWAS+a548Ebqd8G7KqbASylFIPK6W8zZLG3kqpQbWMKRmjfZQQQpx3khA1bZ4YX9hpGNUcrTGqMADewmjUulwplQ38idHQFowk4QhGqcBOc52jm4DDZtXWnRilOWitfwEex0g2EjF6jtV2JMKngQEYbW5+wEgsamsURrK3DKM0Ix9Y7rD+WiAKo/fVS8DVZjsltNY/Aa9gtGc6Yj6edNh3NnCDQ2nKAGA9RgnMOozu+/c4bP93wBujjc7nwEyttWMJ0XXAR5W9CbNdzSSMrvpHMRo2X2Ou/hQjsVqD0XurALi72qtSvQ0Y1aRpwPMY1yTdIcYwjNKi/wFPaq1X1HRAh/j7mTGmYbQ/qu2Q8S8Cj5nVbQ/W/q0IIUQt1GeXtvp6YHw5pABxDssCgRUYXbpXAAHmcgW8jVFUHwsMqOe4/g+jIW4sxpdLWVfyMIwv7q3m40MnXLOnMJKeshgudVj3qHnN9gAT6zmuLx1iOgxsre9rhtGeZxVGr7AM4D/nep9hJAuLznNsO4B7z/BeW4XRMLour5ljXK5wn1UVm1PvNYzxszZi9MzbATxtLu+EkbTuM2P0MJd7mq/3m+vD6uqayUMeje3h9ADq5E0ZJQIDKnyJvgI8Yj5/BHjZfH4pRhWFwpguZEM9x3UR4GY+f9khrjDH7Zx0zZ7CYQwhh+U9zT/QnuYf5gOAtb7iqrD+NeCJ+r5mGL3IBpjPfTHaB/V0kfusqthqda9hdN+vi4Soqrhc4T6rNDZn32vm/dLcfO6OkeQMxWiXd625/EOMkkYwSiA/NJ9fi1FtWuf/H+Qhj8bwaJRVZlrrNRgDvDmaApTNoTAXY4ydsuXztOFPwF8pFVxfcWmtl+tT7Tz+BELq4tw1qeKaVWUK8IU2usAfwvg1Ori+4zKrqaZhVD3VK131NDOucJ9VGpuz77VqrllV6vM+qzY2Z91r5v2SY750Nx8aGAssNpdXvM/K7r/FwLgKjeOFEFVolAlRFdporRPB+OOH0V4GjD968Q7bJeC8+dNuo3yD2k5KqS1m1/WRTorpLqVUrFLqU7NRMbjONRuJ0eNrn8Oyer9m5jhK/TF+vbvUfVYhNkdV3mvAAW30PKzPuFzmPqvimjntXjMbn2/FqDpegVFSluGQ3DpeF/s1M9dnYvTkFELU4JwTIqVUB6XUKqXULqXUDqXUvebyQKXUCqXUPvPfAHO5Ukq9rZTab/4BHOBwrOnm9vuUUtPPNbbavoVKltV7916l1CyMbtJlvXUSgY5a6/7A/cBCVcnoxXXsA4yGz/3MeF4rC7eSbZ3RJfo6yv9ir/drZvbo+hq4T1feVd6+aSXL6vSaVRWbs++1SuJymfusms/Tafea1rpEa90Po0RvMEaPv9M2M/91lf+bQjQ45zy5q1nsH6y13myOTRKDUXx7C8YAbi8ppR7BaFz6sDIGWrwbo03FEOAtrfUQZUwLEI3R20ebxxmotT5Z3flbtmypK5vBXAghRNViYmLStEzuKoTdOY8Aa1YLlFURZCulHNtSXGhuNhdYjTGRqL0tBfCnUqqsLcWFwAqt9QkApdQK4GJqqLMPCwsjOjr6XN+GEEI0KUqpIzVvJUTTcV7bEJ1jW4patxdQSt2hlIpWSkWnpqaez7cgztGepCz2JWfXvKEQQgjhQs5bQnQe2lLUuu5baz1bax2ltY5q1UpKfF3F1zEJXP7OWq54fx37JSkSdazYVkpe4dkOxC2EEOWdl4RIKeWOkQwt0FqXjSCcXNat2Pw3xVyegDEIWpkQjBFvq1ouGoAtR0/ywFfbCG/bAner4ubPNnIyt8jZYYlGKDOviNvmbKLfs8sZ+uIvHM/Id3ZIQohG4JzbEJljXHwC7NJav+6wagkwHWMqhOmY8zmZy+9SSn2B0ag6U2udqJT6GXjBocvtRRij1IoG4M+DxlBB824bzKG0XKZ+tJ7nftjFa9P61rCn6yguLiYhIYGCggJnh9Jk5Bba0ICPhxVLLYbLKS3VpOYUcn13K7f1CqbQVsL+vXvI9PWs+2AbKC8vL0JCQnB3d3d2KEK4tHNOiIDhGHNXbTfHygBjPqyXgEVKqdsx5l2aaq5bhtHDbD+QB9wKoLU+oZR6FthkbvdMWQNrUf9SswvJyCuiS6vmWCynvqgKikvYfOQkF3RtWW77uGOZtPf3JqCZBwHNPJh+QSifrj3M9UM6MjA0oOLhXVJCQgK+vr6EhYUhY9nVvRO5RSSczANAWSx0bdMcd6tRaJ1dUExJqcbfx6PcPsdO5lOaV0THQB/8vN1JyynkeEY+bQN8CGjmcdo5mjqtNenp6SQkJNCpUydnhyOESzsfvczWUnn7H4BxlWyvgX9UcaxPMeauEk6SkVfE9R9vYGei0QzM18uNj24caE+A3vl1H++tOsDTk3sx/YIw+36xxzLo0/7UHJ0PTOjB99sSeeGHXXz99wvq9T2crYKCAkmG6kl+kY1jGfn4eLgR1MyD+JN55BTY7ElNYkYBhbZSvNyteLlb7fvlFtlo5mHFz9so7Qhq5kFqdiFZBcWSEFVCKUVQUBDS+USImjWlkapFLXyw+gC7ErOYeWEXHr8sAm93K2/9cmpw3p/Z2VWaAAAgAElEQVTikgB4ZulONh4yCvAy84uJP5FPn5BTCVEzTzeuHdSBLfEnySoort83cQ4kGaofxzMLsCgIC/LB38cdq0WRYzaQtpWUUmArQaNJOJlP2VhpJaWawuJSfDxO/Y5TSuHtbqWguNQp76MhkHtaiNqRhEjYpeUUMm/9ES7tE8zDF4dz+8jO3DgklA2HThB/Io+DqTkcSM3lgQndCfTxYPaaAwDsOJ4JQK925QfqHdYliFINmw5Jzac4JafQRm6hjda+nrhZLSilaObhRq6ZEOUWlQAQ4ONBXpGN7AJjeX6xkST5eFjLHc/bw0qRrYTSUhmQWQhx9iQhEnafrj1Eoa2E+y/qbl92VVQICvgqOp7lO5MBuHJgCKO6tyTmyEm01uw4ZlSv9XaoMgMY0DEAD6uF9QfT6+09iLp14YUXVjoQ6rvvvkvXrl1RSpGWlmZfrrXmnnvuoWvXrkRGRrJ582aSswpws1hYuvgLunXrRrdu3fh+8ecUlZRSbCslp6CYGddMprmlCIWiV4+u9OnTh6GDBnLdpWPsCdGJEyeYMGECFwzowx3XX0FiqnHepUuX8uSTT1b5Hr799lueeeaZ83xlajZnzhyOHz/VcTYsLKzctTpTjp/F+PHjOXmy2kH9hRA1kIRI2P158AT9OwbQpVVz+7L2/t4M7RzEZ+sO8+naQ/QMbkF7f28GdwrkZF4xB9Ny2X4skzYtvGjZvHxPHy93K/06+rNuvyREjd3w4cNZuXIloaGh5Zb/+OOP7Nu3j3379jF79mzunDmT3EIbqiiHZ599hg0bNrBx40Zef/kFsjIyyC2y8cMPP9CzTyQB/v54uVvQwKpVq/hh1Tq+/vk33MyG1y+99BLjxo1j5+7dDB4+ipdffhmAyy67jCVLlpCXl1dprK+88gp///vf6/R6VKZiQnQ+3XTTTbz//vt1cmwhmorz0ctMNAJaa/anZnN5ZLvT1s26LIJ//287+1Ny+MeYLgBEhQUCsO5AOusPptO/g3+lxx3epSVvrtxLZl4xygI3f7KR+yd0Z1R31x5Q8+nvd7DzeHXji565nu1a8OSkXpWuy83NZdq0aSQkJFBSUsLjjz/ONddcQ0xMDPfffz85OTm0bNmSOXPmEBwczMcff8zs2bMpKiqia9euzJ8/Hx8fH7766iuefvpprFYrfn5+rFmzhoKCAmbOnEl0dDRubm68/vrrjBkzhjlz5tgThwMHDnDFFVfwyiuvADBz5kw2bdpEfn4+V199NU8//XS1761///6VLv/uu++4+eabUUoxdOhQMk5mkJqcxOG4TUyYMIHAQOM+mjBhPOt/+4U2rabx7eIv+euMOwDw8XRDa43WmrziEpo5VJd99913rF69Gg+rhb9MvZ6/XjOJt19/lVINQ4eP5Pvvv+eaa64pF8/evXvx9PSkZUujk0Bl12vOnDl8++23lJSUEBcXxwMPPEBRURHz58/H09OTZcuWERgYyNatW7nzzjvJy8ujS5cufPrppwQEBFS6/JdffiE6OpobbrgBb29v1q9fD8A777zD999/T3FxMV999RXh4eHk5uZy9913s337dmw2G0899RRTpkwhPz+fW2+9lZ07dxIREUF+/qnxlyZPnszIkSOZNWtWtZ+TEKJqUkIkAEjLKSIr30a31s1PW9e7vR9L7hrBzmcuZvoFRtfdzi2bEeDjzpsr9pKaXch1QzpWetyhnQPRwNLY47z36362xmfw3qr9dflWGqSffvqJdu3asW3bNuLi4rj44ospLi7m7rvvZvHixcTExHDbbbfZv/CuvPJKNm3axLZt24iIiOCTTz4B4JlnnuHnn39m27ZtLFmyBID33nsPgO3bt/P5558zffp0+1hLW7du5csvv2T79u18+eWXxMcbs+c8//zzREdHExsby2+//UZsbOxZva9jx47RocOp8VbbtmtHSlIiqUmJ5ZZ36NCB3JMpFNpK2Rq9gQuGDAIwEiClGD/hIq6aOIrFC+bY90lOTiY4OBilFB1C2pNm9qRKzymkY4/e/Lp6zWnx/PHHHwwYMMD+urLrBRAXF8fChQvZuHEjs2bNwsfHhy1btjBs2DDmzZsHwM0338zLL79MbGwsffr0sSeNlS2/+uqriYqKYsGCBWzduhVvb28AWrZsyebNm5k5cyavvvqq/dqPHTuWTZs2sWrVKh566CFyc3P54IMP8PHxITY2llmzZhETE2OPNyAggMLCQtLTpTRWiLMlJUQCgH0pxlQbXStJiCqjlCIqNJAVu5Lp3qY5F1ZR4jMwNIB+If48s3QnAM093dhw6ARH0/PoGORzfoKvA1WV5NSVPn368OCDD/Lwww9z+eWXM3LkSOLi4oiLi2PChAkAlJSUEBwcDBhf2I899hgZGRnk5OQwceJEwKi6uuWWW5g2bRpXXnklAGvXruXuu+8GIDw8nNDQUPbu3QvAuHHj8PMz2n717NmTI0eO0KFDBxYtWsTs2bOx2WwkJiayc+dOIiMjz/h9lfUQK1OqwWKxYKmk45Ovtwc9g1uQnZlB25bG2FXeHlbmfvMTwe3akZaayt03X0VUvz6MGjWq3L7e7hbAKEnKyC8mMKgVaxISTjtHYmIijtP9VHa9AMaMGYOvry++vr74+fkxadIkwPicYmNjyczMJCMjg9GjRwMwffp0pk6dWuXyqpSdc+DAgXzzjTHI//Lly1myZIk9QSooKODo0aOsWbOGe+65B4DIyMjTPo/WrVtz/PhxgoKCqjyfEKJqUkIkADiQkgNAt9a+td5ncCejumPm6C5Vdu11s1r4eHoUft7ulGrNZ7cOwqJgUXR8pds3Vd27dycmJoY+ffrw6KOP8swzz6C1plevXmzdupWtW7eyfft2li9fDsAtt9zCu+++y/bt23nyySftJT4ffvghzz33HPHx8fTr14/09PTTkhJHnp6n2n1ZrVZsNhuHDh3i1Vdf5ZdffiE2NpbLLrvsrEfvDgkJsZc6ARw/lkBI+3Z06NCh3PKEhATatWuHxaJwc3OjtNToRu9htdCuXTtKSjXdw9pz5RVXsHHjRgDatGlDYmIiAFknUgkIakVyViEFxSXYigqxuntRUqHnmbe3d7n3Utn1qnhdLBaL/bXFYsFmO3/zp5Udt+zag5FEfv311/bP/ejRo0RERADVd6EvKCiwlzwJIc6cJEQCgH0pOTTztNKmRe2nQJgW1YHHL49gUt/T2x05auXrydczL+C/tw9hUFggw7u2ZHFMQrVf1E3N8ePH8fHx4cYbb+TBBx9k8+bN9OjRg9TUVHt7k+LiYnbs2AFAdnY2wcHBFBcXs2DBAvtxDhw4wJAhQ3jmmWdo2bIl8fHxjBo1yr7N3r17OXr0KD169KgylqysLJo1a4afnx/Jycn8+OOPZ/WeCm0lXD5pEvPmzUNrzZ9//kkz3xaEhrRn4sSJLF++nJMnT3Ly5EmWL19uL+Xq0aMHBw8eBCAvL4/SonwsSuGjbCxfvpzevXsDRruZuXPnAvDtooWMv/gyUrKNZOdk4hG69AgnM7/8GFgRERHs33+qyray61Ubfn5+BAQE8PvvvwMwf/58Ro8eXeVyAF9fX7Kza570eOLEibzzzjv2/x9btmwBKPc5xsXFlavG1FqTlJREWFhYreIXQpxOqswEAPuSc+jaqvkZDeLm5+PO7SM612rbDoE+dAg0qsgm9GzD7/vSSMoqINjP+EX717mbOJlXzA1DOnLlgJAzfwMN3Pbt23nooYewWCy4u7vzwQcf4OHhweLFi7nnnnvIzMzEZrNx33330atXL5599lmGDBlCaGgoffr0sX/RPvTQQ+zbtw+tNePGjaNv376Eh4dz55130qdPH9zc3JgzZ065EpCK+vbtS//+/enVqxedO3dm+PDhNcb/9ttv88orr5CUlERkZCQXX3IJ/3zmdboNHEXH0B/o2rUr3j4+zHrpbTzdrQT6BvL4448zaJDRVuiJJ56wN7C+7LLLWL16NV27diU5OZnr/3IFGk1pSQnXX389F198MQCPPPII06ZN45NPPqFjx47MXfA5J23g4+HGn3/8zoz7Z5GVX0ygwwjWo0aN4oEHHkBrjVKq0uu1devW099gJebOnWtvPN25c2c+++yzapffcsst3HnnneUaVVfm8ccf57777iMyMhKtNWFhYSxdupSZM2dy6623EhkZSb9+/Rg8eLB9n5iYGIYOHYqbm/xJF+JsqYb+Kz0qKkpXNi6KqNr89YfZk5TNVQND6N/RaKsR9dwKLuzRilen9qvz8286fIKpH67n01uiGBvehqTMAoa++Ave7lbyi0uYe9tgRjuhF9quXbvsVRPi3GTmF3MkPReLUigFEcEtyC20cSgtl84tm9Hcq+qJRhMTE7n55ptZsWLFmZ83r4iME2ncNv0mPlu0hLyiEsKDTw0YWlxSyj/vu4/JkyZx0UUTzuq9uaJ7772XyZMnM27cabMlAZXf20qpGK11VH3EJ0RDIFVmTUxxSSkv/7SH/244ypXvr2NrfAaZecWk5RSdUfuhcxHe1jjPrkSjVGPDIaPdxoIZQ2jbwotXftot1WkNRHFJKYfTczmQkmOvrgLIK7KhUIQEeFNSqskrKqGg2BiB2tPdWtXhAAgODmbGjBlkZZ35sAd+Ph6kJB7jtddew9PdSlFJqb0dUUFxCbsTs7jqtrvYdzydfHNE7Magd+/eVSZDQojakYSokSssLiHHYS6xbfEZ5BTaeHpyL9ysih9ij7M53hjhtkfb+kmIfL3cCQnwZpc5zs/6A+n4ernRN8Sfe8d1Y8fxLH7ZlVIvsYizV1qqOZyWS06BjUJbKSlZhfbpM/KKSvByt+Dr5YYCcgpsZObb8HSz2me0r860adNo0aJFjdtVZtCgQfTr188+KWyhzUh8sgqK0UB45w5ceNElHEzLsSdpDd2MGTOcHYIQDZ4kRI2Q1pql244z7rXVRDzxE1HPr+R4hjGI2+/70lDAlH7tGNwpkOU7k/kmJoEWXm4M61J/3XXD27ZgZ6KZEB1MZ1BYIFaL4uqoENr7e/P2r/tqOELdkJKp2juekU9+cQkdArwJCfCmVGtyi2xorckvKsHHww2rxYK3h5WMvCLyimwE+FRdVXa+ebkZf97KJn7NLrDh5WYl2M+bLq2aozWkZJ1d77mGRO5pIWpHEqJG6P3V+7nr8y0U2Uq5eVgoxbZSPv7d6LWzZm8qvdv74e/jwcRebTmSnseyuCQujwzG0636qozzqWe7FhxOz+VwWi5H0vO4wEzG3K0Wbh/RidiETGITMuotHgAvL68au6kLQ0FxCSfyighq7omfjwfNPd2wKEVWfjGFtlJK9alJWJt7ulNUYiQlfvWYEHm4WbAoRUFxib3aztfLaHTs5W4lwMedzAIbNjO2xkhrTXp6Ol5eXs4ORQiXJ10SGpnM/GI+WH2Qkd1a8tktg3CzWjiRW8wXG+O5bbiRaMy80Jh+Y1xEG574bgclpZqrBtZvz66ewb6UanhjhTFA4NDOp0qnpkaF8OryPXy69hBvXlv5lBB1ISQkhISEBFLNEY9F1dJziii0lWBt4UVWotEzMSOnkJQSTQsvN07mFUOGJ0lWC4W2ElKzi/CwKg5m1+8Xc3pWASeVItnLjbScImzNPchINBK14pJSkrMKyU9xw7eaRt4NnZeXFyEhTa/nphBnShKiRubjNQfJKbTx6CUR9kkwZ17YhSXbjnPRG2so0ZoR3Yx5nNr7exMR7EtOgY0BZm+z+hJh9vz5bttxBnT0t78Go43RVQNC+GLTUR6/vCdBzWs/NtK5cHd3p1OnTvVyroZsf0o2N81dw52ju/DwsHD78i83HeXhb7fTwsuNUg2xT16ExaIospVy+Tu/c+foLoyOqN8v5o+/3Mra/WmMCW/Nt1uS2fbkRfa2RQBTP1xHclYha/41pl7jEkK4HkmIGpEiWylz1h1mQs/W9Gx3KsGICG7BPWO7si8lh8gQPwabE7MCvH/9AEpK9RmNP3Q+dAjwISo0gK6tm/P0lF5YK8zlcMWA9sz/8wibDp/g4t7B9RqbqN66A+lo4MZh5We2v6hnW+atP0LL5h5cO6gjFvMz9XCzsPyfo50QKXRv68s3W47x5aZ4LusTXC4ZAhgb3pqXf9pDZn4xft6Nt5RICFEzSYgakYNpOeQU2iqdsf7+iyofmbhTq9rNXXa+WSyKxTMvqHJ9z+AWuFkU2xIyJSFyMXuSsmnh5UY7v/LVXwHNPPjhnpFOiqpykSHGPG3jI1rz2rS+p63v3sboWbk/JZuBoYGnrRdCNB2SEDUie5ON+cjK/sg3ZF7uVrq39WXr0fptWC1qtisxi25tfOu9VPFsXNClJUvvHk7PYD97iZWjsv8re5NzJCESoomTXmaNyL7kbKwWRedWzZwdynnRv4M/249l2se2Ec6ntWZfSg4RwQ0n6e7d3r/SZAiMdnRe7hb2Jtc8x5gQonFzuYRIKXWxUmqPUmq/UuoRZ8dztrILipm95gAncgrr7Zy7k7IJDfSp1+7zdalviD85hTYOpec6O5RGr6SWXc8TMwvILrDRoxGUQoJRddu1VXP2JElCJERT51IJkVLKCrwHXAL0BK5TSvV0Vjxr96Xx3NKdHE7LOaP9jmfk85f3/uCFZbuZ+ObvrD+Qdkb7a615+afd/Pt/29lwsPbj4uxNzm4U1WVlIjsY7T/qezyi+nYwNYePfjvASz/uIjW79gMFaq155afdDHp+JWNeXc1//zxyxudeuy+Vca+tptdTP3PXws1k5BXZ1x1Ky+X1FXvKjdOzxyxJ6dH27EaRdkU92vqyL/nM/o8LIRofl0qIgMHAfq31Qa11EfAFMMUZgaRkF/D3BTH8Z+0hxr72G3cv3ExyZu2+rO5ftJXEzAIeuywCDzcLN36ykXnrD9f63J9vPMoHqw/w+YajXDP7Ty5563eiD58ot83GQ+nlph0oKC4h/kQe3etp+o360LVVc7zcLWyLz3R2KHXmcFoul729lhd/3M2Hvx1kzKu/sWJnUq32ffSb7by/+gBhQT54WC089m0cb67cW6t9tda8tXIvN36ykewCG2N6tGbZ9kQ++u2AfZvP/jjE27/s519fx9qT8rKSlMZSQgRGO6LUnEIy84pr3lgI0Wi5WkLUHoh3eJ1gLitHKXWHUipaKRVdF4Poaa155Ovt5BeXMO+2wVw7uCM/xiUx6d215ZKQbfEnSatQJWYrKWXr0QyuHdSBv47szLJ7RzIoLIAnvtvBr7uTazz3wdQcnv5+J0M6BbL58QnMujSCtJxC7l+0zf6ltOFgOtM++pPJ764l/oRRnbQ/JYdS3bi+qNysFvp18GfFzmSKS0r5YPV+Xvlpt7PDOm+KbKX8fcFmY065e0bw830jCWzmwavLa05qEk7m8cWmeK4Z1IFFfxvG0ntGcFHPNry5cp99mpbqvL96P2+s3MdFPdvw20Nj+ODGgfTvGMCafadKM9cfSMfb3co3m4/x3w1HASMhatPCs15HnK5rZT8i9qYYyV5+oU3arQnRBLlaQlRZy8fT/jJprWdrraO01lGtWrU670HsT8nh190p3D22G6O6t+KFK/rw4Y0DSMkuZMVOI6nJzC9m2kd/MvWDdeQW2k7tm5pDga2Uvh38AfDzdmf+7UMIbObB4phjNZ57ybbjFNlKefu6/gQ082DGqM48fHE4R0/ksfmoMQnr0thEPNwsHMvIZ/qnm8yGrsYf8+5tnNONvq78dURnjmXk8/JPu/m/n/fwn98PkVdkq3nHBuDrzQnsTMzi5asi6dXOjx5tW3DNoA7sScq2J9rHM/IZ99pq+2dfJu6YUWp23eCOKKVwt1q4d3w3ADYcSq/x3Eu2JjKgoz8f3jgQb3OKjdHdW7HzeBbpOYWk5xSyLyWHu8Z2JbytL9/EJACw43hmo6qWhVM9zeISMskttDHilVW846S59IQQzuNqCVEC0MHhdQhwvL6DKJt0dGKvtvZlY8PbEOznxecbjV/KP8QmUmgr5VB6Ho9+s92+XWyC8UXVu72ffZm71cIlvdvy6+5k8ouMEqb9KdksinYsDDu1f6dWzWjT4tQYL5f2Ccbb3cqiTQmUlmp+iktkTI9WPDwxnINpuRxIzWHHsSzcLIqwlo2jh1mZcRGtCW/ry39+P4RFKYpKSvl935m1yXJVsQkZ+Hu7c0nvU/fZiK7GKOJ/7Dfe47LtiRxIzeWhr7ZR7NCWJ+5YFlalCHeoIg1v2wJfLzf+PHCqenXuusMsiy3/X6iguIT9KTkM6xJUrvfVyG4t0cAfB9LZeMg4xtDOQYwNb01sQiZ7krLZm5xTr5MA14d2fl50bd2cBRuPsjgmgfTcIhZFJ8icdkI0Ma6WEG0CuimlOimlPIBrgSX1HcSuxGzcKnRft1gU06I6sP5AOgkn81gUHU/nVs24c3Rnlmw7zv4Uo1Hm9oRMmnlY6RRUPjG5PLIdBcWl/Lo7BYBHvt7OvxbH8sf+8lV+cccyiXRIpgCaebpxce+2LN1+nF93J5OaU8SlfYIZ37MNAMt3JvN97HGGdg7C3epqH+m5UUrxoDmo5FOTe9Hc042VO2uuemwIdicajeAdx/Pp3d4PXy831ppJ34qdyTTzsHIgNZfP/jhk3y42IYOurZuXG3nZalEMCgvkT7OEqKC4hBeW7eLBxbGkODTW3pOUTYnW9Klwn0WG+NPCy401e1NZfzAdL3cLkSF+jOzWihKtefr7HQBc7PBDoTFQSvG3UZ3Zn5LDKz/vxt2qOJaRz5b4xt2YXwhRnkt9e2qtbcBdwM/ALmCR1npHfcexKzGLLq2an5ZcTBtkFF7d/MlGtsZnMHVgCNOijGVljZ5jEzLo1a7FaeOeDO4USFAzD77ZnEBsQgbRR05iVYp//y+OQptRapSSXUBKdiF9QvxPi+nGoaHkF5Xw13kxuFsVY8Nb087fm/C2vnyw+gDJWYXcMKTjeb8WrmB8zzZs/Pc4bhwayujurfh1d0qDb+OhtWZvSvZp4/lYLYphXYL4fV8amfnFRB85yU3DQhnaOZBP1x627xt3LNM+CrOjYZ2DOJKeR0pWAesOpFFoKyWvqISXlp1qe7XdrG7r1a78/laLYnjXlizbnsiSbceJCg3A3WphQKg/Xu4W1h1Ip2vr5nR20ujmdWlKv/a0au5JbmEJj14SgbtV8d2Wmqu4hRCNh0slRABa62Va6+5a6y5a6+edEcOepNO/qMAYxO2Na/uRVVCMm0VxRf8QOrVsRoCPO5sOn6C4pJRdidlEVpLQWC2KqVEh/LI7hRnzovHxsPLmtX05kp7Hl5uMqrOydiEVf7kDDAwN4JuZFzA2vDW3Du9kn517fEQbsgtsBPi4My6izfm8DC6ltVmFOKFnG9Jzi9jWwLviJ5zMJ7ewpNLu66O6tSIpq4Anl8RRUqoZH9GGi3q2JSmrgMTMfJKyCjiRV1yuWrbM4E7GaMsbDp1gxc5kfDys3DwslG+2HONgqlGKGXcskxZeboQEeJ+2/z8ndKdncAvyCkvsU6Z4ulntx720d+MqHSrj4WbhrrFd6dKqOdcP6ciobq34YXsiJS6WeJeWlvL+qv2s2dvwfxQI4WpcLiGqTwkn85j+6UZ7ew2AjLwikrIKys2+7ugv/drz+7/GsuL+0bT180Ipo5pi4+ET7EvOoaiklD6V/HIHeGhiOFf2b09yViHXDOrApL7tCQ30YfUeo9pse0IWCujVrvJz9+sYwKe3DOLfl0bYl5VVm101MAQPt8b/cV7Q1Wi/ssVhSo9Nh09w+9xNPPjVNg6lOW8Qx6PpuexPOX2Av7nrDnHxm2tOq7YCYwyciiZFtiO8rS/fbjmOv7c7/TsGMCA0ADDed9wxo41b7/an3ye92rWguacbn6w9xC+7UhjRtSW3Du8EGEkSQOyxTHq396t06o3ubXxZPPMC9jx3MTcOPTV565gerQG4pE/jnVdu+gVhrLx/FF7uVib2bktaThGHHQYF3XT4BI/9bzv/WLCZ1XtS6j0+rTWPfhPHKz/v4ZbPNvHCsl3ler0KIc5Nk57LbNGmeH7bm8rv+1J5clIvpl8Qxm7ziyq8ioQIwNvDSieHxsuDOwWyfGcyb6zci9VMkCpjtShem9aXS/sEM9xsPDukcyA/xSVRWqqJTcigU8tmNPOs/cfSN8SP/7s6kot6Ns5f7hW1au5JgI97uakW/vP7QdbsTUWhiDlygh/vHXXarOZ1Kf5EHn+dF21PcsKCfJh/+xA6BPoA8FV0AruTsrnh4w18/fcLaOHlbh/gsLJegX4+7iy5awRv/bKXDgE+WC2KnsEt8LBa2HzkJN7uViyKSpN2N6uFpyf35MGvYtEYJWphQT74ebuz5ehJrhoQwt6kbG4f2ana91QxWbphSCh92vtV+UOhsSh73xFmyd2epGy6tGqO1pq7Fm4mNbsQd6uFH7YnctPQUJ79S+96i+2TtYf4MjqeyyODKbSV8vXmBGZe2KVe73UhGrPGX6RQjZ93JtOnvR99Q/x5d9V+tNbsNnuYRZzBAIdRZgK0Ymcy1wzuQDv/06siyiilGN+zjb2r85BOQWQV2NiVlMXW+IwqS5eqO97UqA6NalyY6iil6N7Gl91JxuektWbjoRNM7tuOj28eyKG0PF76sX7HKnriuziOpOdy3/hu/GtiD46eyLP3RszMK2ZnYhbDuwaxPyWHuX8cBox2au38vexVnxV5uFl4aGI41w7uaH/dq30LNhw6weLNCfTvEICPR+WJ81UDO/D8Fb2JCPZlfESb/2/vzMOrqq4F/lsZSCAjgSSAhIQZAS2gTAqCiIhU69Rah2qpra1aq77WV636rLW2fdZqa6t1elqrdaxWpdZWrRVQEXBgUJAhTIKBkDCEhDBk2O+PvW9ycnPHjJfc9fu++91z9j7DOnuvvc86e1qICGMKsvn4872sKqmgtt4wul90etYtKaFBz2GHbd0AACAASURBVOOBofnpJAgNH0ibyvdTuu8QN885mndvOJnTRvXhL4u3BGwRbA8O1tTxx7eLGVOQze/OH8MDF4/jn9eeRK/0lA65v6LEA3FrEG3dXc3aHZWcNaYfF0wooKzyEOtKq1i9fR89eySTmxF5RTOqXyapSQmkpSTyo1OHRSWHb2zG7X9fza79h5tMwVYCM6JPButKqxocje6prmHioF5MG57HBeML+POizazvIGedC9aV8fbaMq6eMYTrZg7jqpOHMGlQL/7xyXaMMSzZtIt6A9eeMowRfTN413XPrt1RyYgo3V8cX9iTT76oYHvFQa46eXDIYy+aWMg/rz2JnmndABg3oCcbdlbx5PtbSE4Upg7t3bIHjhNSkxMZkNODz9wH0qINdubeySPyyM1I5VfnHkNqciJ3vb62Q+R5dunn7K6u4fpZw0lKSiApMYE+WanhT1QUJWLi1iDyLbB46sh8pg7NdWE7eH1VKRMG5gQcXxGM5MQErjt1GL8655iov9j69+xOfmYKSzbtpqhXj7jp+moNw/pkUH24ji/2HmgYFzNpoB1b9OPZI0hNTuS3EbqwaC33/nsd/Xt25/KpgxrCTj+mL1t2VVO8s4pFG3aRmmRX3D5hUC+Wb93L9ooDbCzbz+ggY8WCMXaAHUc0LD+dGSPyojw3GwP8bdkXzDw6n+we3aI6Px4Z3iejoRv0veJy8jJSGrrKc9K6ccnkQt5YVdqw5EZ7UVdveOSdTYzql8mJQ7rWGlCKEkvErUH0+qodDMlLp7BXGv2yuzMoN437395AxYEa5p4QenxFIK6YNpivjGnmZSQsIsJE9zK/avrgZtP1leb43JOsK61k8YZd5GWkUJBjuylz0rpx6eRC/vnJjnbvzqivN6zevo9ZI/NJSWocx3HayHwEu6jie8XlHF/Uk25JCUwa3JtDtfXc8epn1BnDnGOjG6A8YWAOPXskc/2s4VEZ7EDDyukAXx9fEOJIxcfRfTPZurua6sO1LN64i8mDezVJ90snF2IgaufN0bKhrIov9h7gksmFUee7oiiRE5cGkTGGLxVkN1m3Z/qwXA7U1DE0L51Jgzp2rMT5xxcwY0QeZ4/t36H3PVIZ6gyiNTsqWbJpF5MGNX1RfW/aYLolJfDnRdF7f4+GrXuqOVhT38yVRV5mKmMKsvntv9ezfmcVJw6xLZATinIQ4B+fbGd4fkbUXWa901NYdussZrVgYcSs7skM6p1GXkZKQ4uoEpoRfTIwwN9XlLCnuqZhIoSPo7K7k909mU/crL9IMcZENTvM1203pqD5ch6KorQdcTnLTESaTF0HmD48j8fe28xlUwZ2+FfYlKG9maJjOiImq3syfbJSeXDBBvYdqOXkEU1f8Dlp3Rhf1JOlEfj0ag3rSm1XybAAA/DvOGc0ryz/gvRuyVzkBkZn9UhmRN8MPtteyXnHRd+a2Fp+ec4xgJ3tqITHt0bUbfNWk5TQfNyViDCyX2bD+mGRsH5nJb/+11qWfb6Hn545ijO/1C/sOatL9pGcKAzuggtiKkosEZcGUSCmDu3Nk5dNaPYVqMQmw/MzWLCujK8e15+zA3RVji/qxe/+vY6KAzVkdQ8/A+8Pb63nrTU7GVuQzRXTBpGfFXymoA/f1P+hec1fVKP6ZTVbCRrgxCG9WbejirNa0L3aWiZ1MR9k7c2AnB6kJidQW1/PHy4aS98AOnHMUVk8+u4mDtfWh10H7PNd1Zz7x0UcrKkjJ60b1z67jLp6w9ljG3Vhxba9HOu3RtSqksAr5yuK0rZoCXOICFOH5eoYniOESyYVMveEIu4879iALXrji3pioJmX+EDc/3Yxd7+5jp2VB3li8RZm3/sOi4qbjgv516fb2VzedPDsuh2V9M0KPnU+ENecMpQXrpzcxHmvEpskJgj3fG0MT1w2gdNHBx7vNfqoLGrrTYNxXFtXT8WBw82Oq6mr56qnPqK2zvD8dyfz2rVTKeyVxiPvbGw45oPNuznrvvf4+aurm5y7Zse+Lr/+k6LEAmoQKUckM0fmc9tXRgXt/hkzIJtEET7abA2iiuoa7n+7mMO19U2O21hWxV2vr2XWyHze+fEMXv3BFNJTkrj8yQ8bxnlUHqzh+08v45LHllJ1qLbh3DU7KhsGeEdKZmpyw2wxJfaZc2xfJg8O3mrsc5+yusSO8/npvFXM+u1CDhxuOkbouQ+28mnJPm4/exRjC3vSKy2FM4/ty+qSfVRU1wCwwK1Y/9h7m3nxo20AlFcdorzqcNDV6xVFaTvUIFK6JD26JXF03wyWuHFED7+zkbteX8vLy5s67FzuPJpff9pwEhOEo/tmcvtZo9l/qK5hSv/ijbupqzds3X2Am1/6BLAtARvLqwK63lDih8KcHqR1S+STLyo4VFvHvBUllO47xKPvbmpy3OKNdjbk145rnOE3ZWguBljsdPS9DeUM75PB8PwM7n7Drm/kG1CtLUSK0v6oQaR0WSYMzGHltgr2Hazh2Q/sytGPvrsJYxqdYq4q2UdKUgKDPK5YJg/uRWpSAv92a1W9u76M1KQEvnViEa8sL2FT+X4276qmps40m2GmxBcJzoh+b0M5C9aWUXmwlryMFB5euIF9B2sajlu5raLJ0gdgZ42lJifwbnE5Bw7X8cm2CqYN7c354/tTUnGQrburG1qe1CBSlPZHDSKlyzJ7dF8O19Zz1n3vsavqMLNG5rN2RyUfbG4cV/TpFxUM75NBkmfAampyIicM6c1bn5VijOGd4nKOH5jT4Oz0/Q27WO2+3NUgUi6YUMDGsv3c8OJKsron8+A3jmPfwdqGbq+K6ho+313dbNp8t6QEjivsyaLicj7asofaesPkIb0bJnYs2bSb9zfuIj8zhZw0XUhTUdobNYiULsuEgTn88NRhbCrfT9+sVO75+hgyU5P4y+LNgF0PZnXJvoZxIF5OHZlPScVBFq4vZ2PZfqYNzWVQ7zRy01NYtKGc11ftoGePZEbq2I6457xx/Zk2LJc91TXMHt2HcYU9yc9MaTC8V35hu2W/1L/5OkJThvRmQ9l+7n5zbYNj6GF5GWR1T+bvK0p4Z305c46JbgFPRVFahk67V7o0V88YggFG98skPSWJ6cNzWbLJvqi27j5A5aHagANWZ4zII0Hg23/+ALDT5UWEyYN78W5xOYdq6vjysX11TR8FEeE3XzuW655dzmUn2lXuxxRks8KNT1u5za5TdEwAw/ucsf15/sNtLPt8L2MLsklPsVXyhIE5De6FfOtYKYrSvqhBpHRpRIRrThnasD+moCfzVmyndN9BVpXYF1Ugz+/5mak8Nnc8L7hujxFu8PQJg3sxb0UJgH65Kw3kZqTy1OWTGvbHDejJ66tK2VV1iGWf72FATg+yejRfnqFPViqvXTOFxZt2N1nP6oTBvXhzdSnHHJXVsDK7oijtixpESlzhG9i6YuteVpXsI1Ek6Eyx6cPzmD68qRPVyW5xw/SUJE4IMR1biW9844WWb93Lim0VTBwY3B1Q925JnOynZ1OH5iLANyZp65CidBRqEClxxah+mSQlCCu27WXJxt0Myk0jNTkx/ImOATk9GNQ7jfFFOWFXJlbil9FHZZEgcNfraymrPMSMEXnhT/IwJC+dN394krrrUJQORA0iJa5ITU5kWH4GrywrYdveA9wwe3hU54sI834whW7qRkEJQVpKEkPy0lmzo5Jh+ektctUyJE+7yhSlI9FaXYk7xg7IZtveA3RPTuSiCYVRn5+ekqStQ0pYxhbYFcl/euZIHXyvKEcAWqsrcYdvHNH54/sHHOiqKG3BVScP5lfnHsOJQ3I7WxRFUSKgVQaRiNwlImtEZKWIvCQi2Z64n4hIsYisFZHTPOGzXVixiNzoCR8oIktEZL2IPCciuhKZ0i7MGJHHqSPzuXLakM4WRenCFPZK40KdMq8oRwytbSF6ExhtjDkWWAf8BEBERgIXAKOA2cAfRSRRRBKB+4HTgZHAhe5YgDuB3xpjhgJ7gG+3UjZFCUjv9BQeufR4+mSpx3lFURTF0iqDyBjzhjHG5/57MdDfbZ8FPGuMOWSM2QQUAxPcr9gYs9EYcxh4FjhLRASYAbzgzv8zcHZrZFMURVEURYmUthxDdBnwT7d9FLDVE7fNhQUL7wXs9RhXvvCAiMh3ReRDEfmwrKysjcRXFEVRFCVeCTvtXkT+DfQJEHWzMeYVd8zNQC3wlO+0AMcbAhtgJsTxATHGPAw87O5dJiJbgj5AYHoD5VGe01HEqmyxKhfErmyxKhfErmwqV/S0VLbop1gqShcmrEFkjJkZKl5EvgmcAZxijPEZMduAAs9h/YEStx0ovBzIFpEk10rkPT6cfFFP4RCRD40xx0d7XkcQq7LFqlwQu7LFqlwQu7KpXNETy7IpypFEa2eZzQZuAL5ijKn2RM0DLhCRFBEZCAwFlgIfAEPdjLJu2IHX85wh9TbwVXf+N4FXWiOboiiKoihKpLR2per7gBTgTTsumsXGmCuMMatE5HlgNbYr7fvGmDoAEbkaeB1IBB4zxqxy17oBeFZE7gCWAY+2UjZFURRFUZSIaJVBZIwJupCLMeYXwC8ChL8GvBYgfCN2FlpH8HAH3aclxKpssSoXxK5ssSoXxK5sKlf0xLJsinLEII3DfhRFURRFUeITdd2hKIqiKErcowaRoiiKoihxT5c0iETkMRHZKSKfesJyRORN5yvtTRHp6cJFRH7vfKutFJFxHSxXQH9wIlIkIgdEZLn7PdhecoWQ7TYR+cIjwxxPXEBfdR0k13MemTaLyHIX3mFpJiIFIvK2iHwmIqtE5FoXHgt6Fky2TtW1EHLFgp4Fk61TdU1EUkVkqYiscHL9zIUPlAC+H8XO7H3OpdkSESlqD7kUpUtijOlyP+AkYBzwqSfs18CNbvtG4E63PQe7wrYAk4AlHSzXLCDJbd/pkavIe1wnpdltwPUBjh0JrMDOMBwIbAASO0ouv/i7gVs7Os2AvsA4t52B9eU3Mkb0LJhsnaprIeSKBT0LKFtn65rTl3S3nQwscfrzPHCBC38QuNJtXwU86LYvAJ5rbxn1p7+u8uuSLUTGmIXAbr/gs7A+0qCpr7SzgCeMZTF2gci+HSWXCe4PrkMJkmbBCOarrkPlEhEBzgeeaY97h8IYs90Y87HbrgQ+w7qbiQU9CyhbZ+taiDQLRkfqWUjZOkvXnL5Uud1k9zME9/3o1b8XgFOc7IqihKFLGkRByDfGbAdb+QF5LjyYf7XOwOsPDmCgiCwTkQUiMrWTZLradbE85uv+IXbSbCpQaoxZ7wnr8DRz3RJjsV/vMaVnfrJ56VRdCyBXzOhZkDTrNF0TkUTXVbcTeBPbUhbM92NDmrn4CqyvSEVRwhBPBlEwovKj1m5CNPcHtx0YYIwZC/wQeFpEMjtYrAeAwcAYJ8/dPnEDHNsZ6zdcSNMv9g5PMxFJB14ErjPG7At1aICwdk2zYLJ1tq4FkCtm9CxEfnaarhlj6owxY7AtehOAowMd5v5jpWwqyhFHPBlEpb4uCve/04WH8rvWIUijP7iLjTEGwHUT7HLbH2G/Cod1pFzGmFJXGdcDj9DYXRELaZYEnAs85wvr6DQTkWTsy/MpY8zfXHBM6FkQ2Tpd1wLJFSt6FiLNOl3X3H32AvOxY4iynVzQNF0a0szFZxF5V7iixDXxZBDNw/pIg6a+0uYBl4plElDh6/LoCCSIPzgRyRWRRLc9COsPbmNHyeXu6x3jcg7gm+kVzFddRzITWGOM2eYL6Mg0c+MyHgU+M8bc44nqdD0LJltn61oIuTpdz0LkJ3Sirrn7+GYDdneyfEZw349e/fsq8B+f4asoShg6e1R3e/ywTdvbgRrsF9O3sf3obwHr3X+OO1aA+7FfeJ8Ax3ewXMXYPv/l7uebIXIesAo7y+Zj4MxOSLMnXZqsxFa0fT3H3+zSbC1wekfK5cIfB67wO7bD0gyYgu2KWOnJuzkxomfBZOtUXQshVyzoWUDZOlvXgGOxvh1XYg1F3yy3QVjjsBj4K5DiwlPdfrGLH9ReaaY//XW1n7ruUBRFURQl7omnLjNFURRFUZSAqEGkKIqiKErcowaRoiiKoihxjxpEiqIoiqLEPWoQKYqiKIoS96hBpCiKoihK3KMGkaIoiqIocY8aRG2AiMwVkXfb6FoiIn8SkT0islREporI2ra4diwjIkZEhnS2HNEQL3nT3ohIkcv/pPBHxwYisllEZna2HEcqIvKgiPxPZ8sRCSIyX0S+47YvFpE3PHEnish6EakSkbNFJF9EFopIpYjcHfyqbSpfxPVQuGNFZIB7lsQIrjVdRLyrt68SkekRCR0FTp5BbX3dQMSsQeQqnFIRSfOEfUdE5kd4foMSt4Esq1ymVIlInYgc9Ozf1Bb38DAFOBXob4yZYIx5xxgzvCUXEpHbROQvYY65WkQ+FJFDIvJ4gPhTRGSNiFSLyNsiUuiJO19EFrm4+S2R8UjC32hrTd50NY5EoyYWEZHHReSOzpajvTHGXGGM+Xl7XLs9P66MMU8ZY2Z5gm4H7jPGpBtjXga+C5QDmcaYH7WHDAFkirge8j/W37A3xnzunqWuBXKMMsbMj/Y8L4He206eDnFbFbMGkSMJuLazhXAZnW6MSQfeAa727RtjftnGtysENhtj9oc7sI1ePiXAHcBjAa7fG/gb8D9ADvAhHgeXWKeRvwP+tw3kaHci+erpSqhxorQXqlsNFGJduHj3Vxt1AXFk0tm+Q4L9gM3AjdiXbrYL+w4w33PMCcAHQIX7P8GF/wKoAw4CVVgLHmAE8Ka75lrg/BbINR/4jl/YXOBd4DfAHmATHr9LWI/Tj2J9cn2BNUASA1z7207mOif3z4DpwDa/dLkB69voENZovMFdt9I91ynAbOAw1gdYFbAizHPdATzuF/ZdYJFnPw04AIzwO65JvoS4x+VYH0u7sT6r+nniDHAN1kFmOXAXkODihgALXD6XA895zguap1gfVA8ArwH7gVuAHd60xzoTXem2JwDvA3tdXt0HdHNxC52M+116fj1A3hzt9GMvtpL8ip8s9wP/cPm0BBjs4gT4LbDTPeNKYHSQNPwW1rlnpUur73nipmP9vd3gnvNJF34G1jfXXmARcGyIPDLAFVhfbHuczD4XPwkuDbc4WZ8Aslzc5+7cKvebHODaE7BG9T6gFLjHhRe5c7/prlMO3Ow5LwVreJe43+9o9N21ADjPbfv8kfl8kM0ElkdSRiPQ3Uvcc+/C+lfbDMz05O0d/vng2e8HvAiUufteE+Qe38WW18MuDf8eTq9aqB83uTTeDFzsp6MPYstTpUvbQj/d+L7TjU1h6uAcd68z3X46tuxf6p9mHrl+jNWr7cDZWD9367Bl+yY/PYq4nLagDJwKrHHPdJ9Lh+949chtbwDqsXViFdbvojf/ZkagG83qbk9Zu9HdYxfwPM4vYgB5/a+5GbgeW49UYD9iU/2PxfoQ9Mr/YxrLYlKk+uR3X1+Z2EtjXbDfXbMI6Am8ii0Le9x2f3dOsPe2AYa47SxsvVOGLY+30PiemEsryrgxJuYNopnYFgpfwWl48WIL3B5sRZUEXOj2e7n4+XgMF+zLfKvL4CRgHLZSGOXiL8K9GMPI1eS6noyowb7wE4ErsRW370XyMvCQkyEP63Txe0GuPxdX4EIo3XKgAOgODHfP1c/FF9H4or0N+EuE6R3IILoXeMAv7FPcC8gTFtYgAma49B6HfcH9AVjoiTdYD945wABsReirhJ7BvoQSsM4rp0SYp49jK4QTPeduAE713PevwI1u+zhgkrtWEbYiuM5PxiGB8gZIxlb4NwHd3PNWAsM9suzGVuZJwFPAsy7uNOAjIBtrHB2Nx8GpXzp+GRjsjpsGVAPjPPLUAne6NO7u0mQnMBGrm990OpQS5PoGW0llu3woA2a7uMvcMw7CvuD+RqPRVYSnIg1y7feBS9x2OjDJ79xHnMxfwhr7R7v424HF2LKTi32h/dwT9we3fZPL3zs9cfdGUkbD6O5IbAV9kkvXe1w6hzWIsHr3EXCr04tB2BfLaUHu5X+tkHrVQv24xz3HNOzLyqujlZ7nvJemdZHBGks5Lp/C1cGzsIZ5nsvbFwI9p0euW93zXo7Vu6eBDGAU9iU5qIXlNOIyAPTGGuxfdbL8l5OtmUHkqY9nhsi/ULoRqu6+Dqvz/V1ePAQ8EyTPG67pkWkp1hDPcelzRYhjvfIX0dQgCqdPQa/lCf8l1lBNxjq/Pg/o4fL2r8DLnmPn0/z96jWIngBececWYd8TPoffc2lhGW+4V6QHdvSPRoNoNPallktTg+gSYKnfOe8DcwMlLPaL/h2/4x8CfhqlXIEybC5Q7Nnv4TKxD5CPrdy7e+IvBN4Ocv25hDeILvPsD8EW9plAst+1bqN1BtGjwP/6hb3nS2NPWCQG0aPArz376U55izxKP9sTfxXwlqcQPIz7kog0T7GV0RMBnvMxt52BfSEUBpH5OuAlz34og2gqtvJP8MQ/A9zmkeX/PHFzgDVuewa2YE/ynh9hvr0MXOuR5zDua9CFPYAzHjxha4FpQa5ncAan23+eRoPxLeAqT9xwl4e+F1M4g2ghttWzt1+479z+nrClwAVuewOu1cftn4btVgbbGupr4fuX08XFbn8BcG64MhpBGt+KM17dfppL50gMoonA537X+wnwpyD38r9WSL1qgX7UAml++fs/nnt7nzMd+8Ve4NGNGZ74kHWw2/8D8An2xdQr0HM6uQ7gWm6x5dIAEz3HfwSc3cJyGnEZAC716Y/bF2zrVXsYRKHq7s9wrUVuvy+urAWQueGaHpm+4dn/NfBgiGODGkQR6FNIgwhbR28GcoNcbwywx7M/nyAGEdbIOQSM9MR9j0abYC4tLOO+X6yPIcIY8yn2i/VGv6h+2CYzL1uAo4JcqhCYKCJ7fT/gYqzR0hbs8G0YY6rdZrq7bzKw3XPfh7BfTS1lq+dexdgK4TZgp4g8KyL9WnFtL1VApl9YJvYrMlqa5JcxpgrbFOzNr62e7S3uHLBNuQIsdQPcL3PhkeSp95pgvzrPFZEU4FzgY2PMFgARGSYir4rIDhHZh/2y6R3F8201xtT7PYP3+XZ4tqux+oEx5j/Ypvn7gVIReVhE/NMdJ+PpIrJYRHa7553jJ2OZMeagZ78Q+JFfGhXQmLaBCCgnzcvcFqwxlB/iWl6+DQwD1ojIByJyRivu65P/fWCYiORjK9cngAI3/m0C1ghrdn2/MhqOfjQtc/uxuhsJhUA/v/S/icjTLBK9aiAC/dhjmo5P9KYlNH3OKmyrZsB4IquDH8Z+1P7JGBMqzXaZxoG8B9x/qSf+AC6vWlBOoykD/nltaF6HtAlh6u5C4CWPvJ9hjdNI9SZYWYqKCPQp1LljsfXaOcaYMhfWQ0QeEpEtLu8WAtkRju/sjW0l9a8LAtaxUZZxIPYHVfv4KbYZzPvgJVil8TIA2x8L1jL0shVYYIzJ9vzSjTFXtovETe97CPtV7LtvpjFmVCuu2eTZjDFPG2OmYNPDYLtMmh3XAlZhuy8AcDP+BtN0EGGkNMkvd61eNOYX2ErKxwB3DsaYHcaYy40x/bBfBH90s0giyVP/tFqNLUSnY7tJn/ZEP4AdOzDUGJOJfXFJFM9XICLeMuXVx5AYY35vjDkO2z0wDPhv/2OcEfcito883xiTjR0f5ZUxkN7/wi+Nehhjnonwubz4l7kB2BaH0gD3bYYxZr0x5kLsx8CdwAveWaRR3tenG9XY1oNrgU+NMYexXWo/BDYYY8ojuH44tuPRTRHpgdVdH/uxX6M+/A3yTX7pn2GMmRPkXv7pGLFeRagfPf3SvCEtHd7nTMd2uXjjvfKFrIPdS+4hrJF6ZRvO/Iq2nEZTBvzzWmhaL0VLKN0IVXdvxY5/8cqcaoyJqD6JgqDlNkJ9CnZuLvASdgLSMk/Uj7AtyxNd3p3kOyWcPNjhEDU0rwvaLE2OCIPIWdLPYQfd+ngN+2V4kYgkicjXsX39r7r4Umx/vY9X3fGXiEiy+40XkaPbWfbtwBvA3SKSKSIJIjJYRKa1xfVFZLiIzHDKexD7JeX70ioFivwqU//zk0QkFdscmSgiqZ4ZJC8Bo0XkPHfMrdjuiTXu3EQXngQkuHOTg9zqaeBbIjLGyfpLYIkxZrPnmP8WkZ4iUoB9wT3n7vM1EenvjtmDLTR1tDxPn8bq0knYPmwfGdjxA1UiMgLbB+3FX6e8LMFWfj92ckwHzgSeDSMLTuaJLu320ziw3p9u2PEEZUCtiJyOHacRikeAK9z1RUTSROTLIpIRTq4APAP8l4gMdC/LX2IHuNc6meoJnj6IyDdEJNe1dux1wZFM730GuEVEcl3Lz62AdzmJBcDV7h9ss7t3Pyxil6iYHyT6BeAMEZkiIt2wY5O8ZWo5MEdEckSkD/ar38dSYJ+I3CAi3V2ZGS0i44Pcy1/HotGrSPXjZyLSTUSmYgcbe8vAHM9z/hxbRoO1kISrg31LklyGfak+EWFLQDiiLafRlIF/AKNE5FxXD15D63oRgupGmLr7QeAX4pY5cbp/VivkCEaoOq0l9Y1vBuKLwFPGmOf8ojOwz7lXRHKwjR0RyeNaEJ/HpkuGS5sf0rQuaBVHhEHkuB3bdw+Aa349A2tx7sJ2q5zh+SK8F/iq2AUOf2+MqcRm5gXYL5sdNA4+9S241ZKWj0i4FKtcq7Ev9BewfcJtQQp22ns5jQMYfRWRr6LbJSIfBzn/FqyC3gh8w23fAuCaOc/Djv7fgx0PcYHn3Evc8Q9gxzocwFY+zTDGvIWdvv8i9itssN+1wA6W+whbifwDO+4IYDywRESqsLPTrjXGbAqXpyF4Btv//R+/FoTrsa1Gle45/AvzbcCfxTZjn+/3fIeBr2BbnsqBP2Jn1KwJIwvYbshHsGnsm8n0G/+D3PNeg60U9jhZ54W6sDHmCkb/iQAAAZdJREFUQ2zr6n3unGJsX3tLeAw7M2UhdgbHQeAH7j7VWD15z6XPpADnzwZWuXy8FztG6GCA4/y5Azs7bSV2PMrHLszHAmxFuzDIfiQUYMfHNcMYswo7u+pprO7uwY4r8fEksAI7VuINPHrjKvEzsd15m7C68X/Y2TKBeBQY6dLw5Wj0KkL92OHiSrAD+6/wu9bT2JfUbuzg5YuDyBmyDhaR47Avq0tdGtyJ/ZDxH/rQEqIqp9GUAVcffA1bp+4ChhJELyIkqG4Quu6+F5t3b4hIJXaA9cRWyBGMX2E/NvaKyPXeiJbUN47+2PfBddK4Xl+ViAzAzhDtjn3mxdhxf16avLcDXPsH2A+EjdgZZU8TYMmYQIhdDPTBkMe4wUeKoihxi4gsxw5ijXRs0BGHa136izGmf5D4x7GDZG/pSLkUJVbQxbUURYl7jDFjOlsGRVE6lyOpy0xRFEVRFKVd0C4zRVEURVHiHm0hUhRFURQl7lGDSFEURVGUuEcNIkVRFEVR4h41iBRFURRFiXvUIFIURVEUJe75f3nRze8DZUOTAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "model = sm.tsa.UnobservedComponents(series, \n", " level='fixed intercept', \n", " freq_seasonal=[{'period': 100}])\n", "res_lf = model.fit(disp=False)\n", "print(res_lf.summary())\n", "# The first state variable holds our estimate of the intercept\n", "print(\"fixed intercept estimated as {0:.3f}\".format(res_lf.smoother_results.smoothed_state[0,-1:][0]))\n", "\n", "res_lf.plot_components()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that one of our diagnostic tests would be rejected at the .05 level." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components (lazy time domain seasonal modeling)\n", "\n", "The fourth method is an unobserved components model with a fixed intercept and a single seasonal component modeled using a time-domain seasonal model of 100 constants. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & =\\mu_t + \\gamma^{(1)}_t + \\epsilon_t\\\\\n", "\\mu_{t+1} &= \\mu_{t} \\\\\n", "\\gamma^{(1)}_{t + 1} &= - \\sum_{j=1}^{99} \\gamma^{(1)}_{t + 1 - j} + \\omega^{(1)}_t\\\\\n", "\\end{align}\n", "$$\n", "\n", "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "======================================================================================\n", "Dep. Variable: y No. Observations: 300\n", "Model: fixed intercept Log Likelihood -1564.378\n", " + stochastic seasonal(100) AIC 3130.756\n", "Date: Tue, 17 Dec 2019 BIC 3134.054\n", "Time: 23:38:54 HQIC 3132.091\n", "Sample: 0 \n", " - 300 \n", "Covariance Type: opg \n", "===================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "-----------------------------------------------------------------------------------\n", "sigma2.seasonal 3.558e+05 2.96e+04 12.012 0.000 2.98e+05 4.14e+05\n", "===================================================================================\n", "Ljung-Box (Q): 2223.75 Jarque-Bera (JB): 25.29\n", "Prob(Q): 0.00 Prob(JB): 0.00\n", "Heteroskedasticity (H): 0.49 Skew: 0.85\n", "Prob(H) (two-sided): 0.00 Kurtosis: 3.37\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n", "fixed intercept estimated as 4.690\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "model = sm.tsa.UnobservedComponents(series,\n", " level='fixed intercept',\n", " seasonal=100)\n", "res_lt = model.fit(disp=False)\n", "print(res_lt.summary())\n", "# The first state variable holds our estimate of the intercept\n", "print(\"fixed intercept estimated as {0:.3f}\".format(res_lt.smoother_results.smoothed_state[0,-1:][0]))\n", "\n", "res_lt.plot_components()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The seasonal component itself looks good--it is the primary signal. The estimated variance of the seasonal term is very high ($>10^5$), leading to a lot of uncertainty in our one-step-ahead predictions and slow responsiveness to new data, as evidenced by large errors in one-step ahead predictions and observations. Finally, all three of our diagnostic tests were rejected. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison of filtered estimates\n", "\n", "The plots below show that explicitly modeling the individual components results in the filtered state being close to the true state within roughly half a period. The lazy models took longer (almost a full period) to do the same on the combined true state." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# Assign better names for our seasonal terms\n", "true_seasonal_10_3 = terms[0]\n", "true_seasonal_100_2 = terms[1]\n", "true_sum = true_seasonal_10_3 + true_seasonal_100_2\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "time_s = np.s_[:50] # After this they basically agree\n", "fig1 = plt.figure()\n", "ax1 = fig1.add_subplot(111)\n", "idx = np.asarray(series.index)\n", "h1, = ax1.plot(idx[time_s], res_f.freq_seasonal[0].filtered[time_s], label='Double Freq. Seas')\n", "h2, = ax1.plot(idx[time_s], res_tf.seasonal.filtered[time_s], label='Mixed Domain Seas')\n", "h3, = ax1.plot(idx[time_s], true_seasonal_10_3[time_s], label='True Seasonal 10(3)')\n", "plt.legend([h1, h2, h3], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth'], loc=2)\n", "plt.title('Seasonal 10(3) component')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "time_s = np.s_[:50] # After this they basically agree\n", "fig2 = plt.figure()\n", "ax2 = fig2.add_subplot(111)\n", "h21, = ax2.plot(idx[time_s], res_f.freq_seasonal[1].filtered[time_s], label='Double Freq. Seas')\n", "h22, = ax2.plot(idx[time_s], res_tf.freq_seasonal[0].filtered[time_s], label='Mixed Domain Seas')\n", "h23, = ax2.plot(idx[time_s], true_seasonal_100_2[time_s], label='True Seasonal 100(2)')\n", "plt.legend([h21, h22, h23], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth'], loc=2)\n", "plt.title('Seasonal 100(2) component')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "time_s = np.s_[:100]\n", "\n", "fig3 = plt.figure()\n", "ax3 = fig3.add_subplot(111)\n", "h31, = ax3.plot(idx[time_s], res_f.freq_seasonal[1].filtered[time_s] + res_f.freq_seasonal[0].filtered[time_s], label='Double Freq. Seas')\n", "h32, = ax3.plot(idx[time_s], res_tf.freq_seasonal[0].filtered[time_s] + res_tf.seasonal.filtered[time_s], label='Mixed Domain Seas')\n", "h33, = ax3.plot(idx[time_s], true_sum[time_s], label='True Seasonal 100(2)')\n", "h34, = ax3.plot(idx[time_s], res_lf.freq_seasonal[0].filtered[time_s], label='Lazy Freq. Seas')\n", "h35, = ax3.plot(idx[time_s], res_lt.seasonal.filtered[time_s], label='Lazy Time Seas')\n", "\n", "plt.legend([h31, h32, h33, h34, h35], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth', 'Lazy Freq. Seas', 'Lazy Time Seas'], loc=1)\n", "plt.title('Seasonal components combined')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Conclusions\n", "\n", "In this notebook, we simulated a time series with two seasonal components of different periods. We modeled them using structural time series models with (a) two frequency domain components of correct periods and numbers of harmonics, (b) time domain seasonal component for the shorter term and a frequency domain term with correct period and number of harmonics, (c) a single frequency domain term with the longer period and full number of harmonics, and (d) a single time domain term with the longer period. We saw a variety of diagnostic results, with only the correct generating model, (a), failing to reject any of the tests. Thus, more flexible seasonal modeling allowing for multiple components with specifiable harmonics can be a useful tool for time series modeling. Finally, we can represent seasonal components with fewer total states in this way, allowing for the user to attempt to make the bias-variance trade-off themselves instead of being forced to choose \"lazy\" models, which use a large number of states and incur additional variance as a result." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 1 }