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@ChadFulton
Created June 24, 2019 08:24
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Statsmodels state space: time-varying regression
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"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": [
"## Model\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"y_t & = d + x_t \\beta_{x,t} + w_t \\beta_{w,t} + \\varepsilon_t \\hspace{4em} \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2)\\\\\n",
"\\begin{bmatrix} \\beta_{x,t} \\\\ \\beta_{w,t} \\end{bmatrix} & = \\begin{bmatrix} \\beta_{x,t-1} \\\\ \\beta_{w,t-1} \\end{bmatrix} + \\begin{bmatrix} \\zeta_{x,t} \\\\ \\zeta_{w,t} \\end{bmatrix} \\hspace{3.7em} \\begin{bmatrix} \\zeta_{x,t} \\\\ \\zeta_{w,t} \\end{bmatrix} \\sim N \\left ( \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} \\sigma_{\\beta, x}^2 & 0 \\\\ 0 & \\sigma_{\\beta, w}^2 \\end{bmatrix} \\right )\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"class TVRegression(sm.tsa.statespace.MLEModel):\n",
" def __init__(self, y_t, x_t, w_t):\n",
" exog = np.c_[x_t, w_t] # shaped nobs x 2\n",
"\n",
" super(TVRegression, self).__init__(\n",
" endog=y_t, exog=exog, k_states=2,\n",
" initialization='diffuse')\n",
"\n",
" # If the design matrix is time-varying, it must be\n",
" # shaped k_endog x k_states x nobs\n",
" # Notice that exog.T is shaped k_states x nobs, so we\n",
" # just need to add a new first axis with shape 1\n",
" self.ssm['design'] = exog.T[np.newaxis, :, :] # shaped 1 x 2 x nobs\n",
" self.ssm['selection'] = np.eye(self.k_states)\n",
" self.ssm['transition'] = np.eye(self.k_states)\n",
"\n",
" @property\n",
" def param_names(self):\n",
" return ['intercept', 'var.e', 'var.x.coeff', 'var.w.coeff']\n",
"\n",
" @property\n",
" def start_params(self):\n",
" exog = sm.add_constant(self.exog)\n",
" res = sm.OLS(self.endog, exog).fit()\n",
" params = np.r_[res.params[0], res.scale, 0.001, 0.001]\n",
" return params\n",
"\n",
" def transform_params(self, unconstrained):\n",
" constrained = unconstrained.copy()\n",
" constrained[1:] = constrained[1:]**2\n",
" return constrained\n",
"\n",
" def untransform_params(self, constrained):\n",
" unconstrained = constrained.copy()\n",
" unconstrained[1:] = unconstrained[1:]**0.5\n",
" return unconstrained\n",
"\n",
" def update(self, params, **kwargs):\n",
" params = super(TVRegression, self).update(params, **kwargs)\n",
"\n",
" self['obs_intercept', 0, 0] = params[0]\n",
" self['obs_cov', 0, 0] = params[1]\n",
" self['state_cov'] = np.diag(params[2:4])\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulated data: drifting coefficients"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nobs = 1000\n",
"\n",
"rs = np.random.RandomState(seed=93572)\n",
"\n",
"d = 5\n",
"var_y = 5\n",
"var_coeff_x = 0.01\n",
"var_coeff_w = 0.5\n",
"\n",
"x_t = rs.uniform(size=nobs)\n",
"w_t = rs.uniform(size=nobs)\n",
"eps = rs.normal(scale=var_y**0.5, size=nobs)\n",
"\n",
"beta_x = np.cumsum(rs.normal(size=nobs, scale=var_coeff_x**0.5))\n",
"beta_w = np.cumsum(rs.normal(size=nobs, scale=var_coeff_w**0.5))\n",
"\n",
"y_t = d + beta_x * x_t + beta_w * w_t + eps\n",
"\n",
"plt.plot(y_t);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fit with our model class"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Statespace Model Results \n",
"==============================================================================\n",
"Dep. Variable: y No. Observations: 1000\n",
"Model: TVRegression Log Likelihood -2336.846\n",
"Date: Mon, 24 Jun 2019 AIC 4685.692\n",
"Time: 09:20:18 BIC 4715.139\n",
"Sample: 0 HQIC 4696.884\n",
" - 1000 \n",
"Covariance Type: opg \n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"intercept 5.0548 0.202 25.050 0.000 4.659 5.450\n",
"var.e 5.1240 0.249 20.571 0.000 4.636 5.612\n",
"var.x.coeff 0.0468 0.022 2.097 0.036 0.003 0.091\n",
"var.w.coeff 0.4092 0.096 4.243 0.000 0.220 0.598\n",
"===================================================================================\n",
"Ljung-Box (Q): 40.12 Jarque-Bera (JB): 0.98\n",
"Prob(Q): 0.46 Prob(JB): 0.61\n",
"Heteroskedasticity (H): 1.05 Skew: 0.07\n",
"Prob(H) (two-sided): 0.63 Kurtosis: 2.93\n",
"===================================================================================\n",
"\n",
"Warnings:\n",
"[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
]
}
],
"source": [
"mod = TVRegression(y_t, x_t, w_t)\n",
"res = mod.fit()\n",
"\n",
"print(res.summary())"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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rraXgZzlS2ndZJuAFrXUjoB3wlFKqcSmfU4ird2oHfNsFVrwIFWrAgwvgyS2XTV7kFph5ccFe3lx2kMCqHjTwc2dE+1r8r09jvnqo5a1JXlzKoyo+w2eyNnQuR/HnLfuZrLB7kd3LZ4DFcuvjEUIIIYQQ4jZhY2NDxYoViY6OxmKxsGjRoqL3unXrxpQpU4peR0RElEWIwqpU77S01me01rutzzOBKECqDIqyd+4kLHkKZnSDrEQYMAMeXQH1e4BSl931g9+j+HV3HKM71ub7R41hZ0opHu0QQAO/sp2y0aVbb1q8EQ4P/YKdowt9Y/5Lwmft0cfWl2lcQgghhBBClGcffvghvXr1omvXrvj7+xdtnzJlCps2baJp06Y0btyYb7/9tgyjFLdsGVWlVC1gA9BEa51xwfbHgccBatSo0fLkyZO3JB5xh8jPhEPLIekgpB6FtJOQnQqZ8WBjB+2ehE4vg+PVJR5MZgut311NaD0fJg9tXsrB35j4s1msnDeJ7okz8FcpEHgf9J8K9k5lHZoQQgghhLgDlKdlVEX5Ue6XUVVKuQG/As9emLwA0Fp/A3wD0KpVq1uTTRF3hsO/w6IxkJcGtg5QqTZUrAW+TcA3EBr1hYo1r+mQm4+mci6nkHubVimdmG+iqpXcGD7mVR6bHkqr+J8Yd2C+kdAZOr/YoqRCCCGEEEIIUZ6V+l2MUsoeI3kxW2u9sLTPJwRaw7p3YcPHRpHLu3+Gai1v+KY9r9DMxysPU8HFnk71fW5SsKXL1kbx/N1N6TelH8HB9el46G1Y8SKnQ9+jsocT9rZ/zyL7IzKBVxfuY8V/OlLFU6oqCyGEEEIIIcqX0l6FRAEzgCit9WeleS4hADCb4Lf/QMRP0HwY9P70hqdMZOQVkppVwLi5u4k8ncG3w1vhZG97kwIufc2qV6Bd7Uq8fLw54e2fxXbzF/y4vYCjdR/D1dGWUaG1CfL3ZNqGo5zLKeS78OO8fo/U2hVCCCGEEEKUL6U9AqMD8DCwXyl1vlzra1rrFaV8XnEnKsyDX0fCoWXQaTx0Hn/FgpxXEh6dwrAZ23C0s8HFwZapw1rQvbHvTQr41nmiUx0e/X4HHxYOoq3Ndl7Rcxh7uDJLLK3ZdfIc/YKrsic2DU9ne+ZuP8WTnetS0VWWihJCCCGEEEKUH6W9Ckm41lpprZtqrYOtD0leiJsvPxPmPGAkL3p9CHe9esPJC4Cv1scAUN/XnbmPt6NXk/Jf+6I4nev7EFy9At9sPMGbtk+TU7kZkx2/4vNQM+k5hUxZd5TQut58/2hrcgpMfLkupqxDFkIIIYQQQoiLSCU/cfvLToXZA+HMXrhvGjQb8o8mp87msP34WTo38MHLzfGKhwyPTuH936M4EJ/Bq3c35IlOdUoj8ltGKcW8x9txOCGTAB9X3ExtYHoX7ot6gXvG/UmuazU8ne0BGNDCnxnhx/ltbzx3NajMBwOCUDchGSSEEEIIIYQQN6JUR2AIUerMhTDvQUg8AENmF5u8iDqTQddP/+KFBXu565P1JGbkXfaQyZn5PPrDdnIKzLzeuxGPdggorehvKSd7W5pVr4CHkz24+cBDv4ApH4f5Q/BUOUXt3u7fhLf7BRJY1YP5O0/xe2RCGUYthBBCCCHE9Xv33XcJDAykadOmBAcHs23btlI714kTJ5gzZ07R6x9++IGnn376uo+3fv167r333huO67333rvodfv27W/4mGDEt3nz5ptyrKslCQxxe1v3HpzaCv2/ggZ3F9tk3vZYUPD1Qy3IyDOxJirpsofcciyVQrPmi8HBjA6rjYPdv/TPxKcBDJ4FqdGwaCxYLICR6Hg4pBbTH2lNQz93Jq2JLuNAhRBCCCGEuHZbtmxh2bJl7N69m3379rF69WqqV69eaue7NIFRXlyawLhZSQdJYAhxLY6sgvDPoMUjEDSw2Cb5JjNL9sbTM9CPXk38qFbBmb+OXJzA0Fozb3ssn6w8zImUbLYcTcXd0Y7Aqh63ohdlq3Yn6PEuHF4O4Z9e9JatjWJgS38OJWQSm5pTwgGEEEIIIYQon86cOYO3tzeOjsYUcm9vb6pWrQpArVq1eO211wgJCaFVq1bs3r2bnj17UqdOHaZOnQoY9wkvvfQSTZo0ISgoiPnz5192+/jx49m4cSPBwcF8/vnnAMTHx9OrVy/q1avHyy+/XBTbqlWrCAkJoUWLFjzwwANkZWUB8Mcff9CwYUNCQ0NZuHBhsf0ym8289NJLtG7dmqZNmzJt2rSi/oaFhREcHEyTJk3YuHEj48ePJzc3l+DgYB566CEA3NzcACMB0alTJwYNGkT9+vUZP348s2fPpk2bNgQFBXH06FEAfvvtN9q2bUvz5s3p1q0biYmJnDhxgqlTp/L5558THBzMxo0bSU5OZsCAAbRu3ZrWrVuzadOmm/ST/JvUwBC3p9O7YMEI8A2CXh+U2GzdoSTScgoZ0KIaSinC6vswd3ssbd9bzZKnQsnMK+StZQfZGJ2CUvDr7jhslKJNQCXsbO+Q/F7bJ4zrufZdqBIM9boXvdW9sS/vLI/iz6hERoYGUGCykGcys/VoKov2nGZUx9q0rFmxDIMXQgghhBC3hd/HQ8L+m3tMvyC4u+R7gR49evDWW29Rv359unXrxuDBg+nUqVPR+9WrV2fLli0899xzjBgxgk2bNpGXl0dgYCBjxoxh4cKFREREsHfvXlJSUmjdujVhYWFs3ry52O0ffPABn3zyCcuWLQOMKSQRERHs2bMHR0dHGjRowLhx43B2duadd95h9erVuLq68uGHH/LZZ5/x8ssvM3r0aNauXUvdunUZPHhwsf2aMWMGnp6e7Nixg/z8fDp06ECPHj1YuHAhPXv25PXXX8dsNpOTk0PHjh358ssviYiIKPZYe/fuJSoqikqVKlG7dm1GjRrF9u3bmThxIpMnT+aLL74gNDSUrVu3opRi+vTpfPTRR3z66aeMGTMGNzc3XnzxRQAefPBBnnvuOUJDQ4mNjaVnz55ERUVd70+3WJLAELef1KMwexC4esGwX8DBpcSmv+yKw9fDkY71fAAY2qY6sWez2X0yjdE/7iT2rDGyYEKfxrSqVYkBX2/GZNH8955Gt6Qr5YJS0GciJEUZy9CO/NOYXgLU9HKlURUPPvrjEPa2iinrYkjMyAfARsGaQ0ksHNse/4rOVHAxll1NzconPbeQ2j5uZdYlIYQQQggh3Nzc2LVrFxs3bmTdunUMHjyYDz74gBEjRgDQt29fAIKCgsjKysLd3R13d3ecnJxIS0sjPDycoUOHYmtri6+vL506dWLHjh0lbvfw+OcI7q5du+Lp6QlA48aNOXnyJGlpaRw8eJAOHToAUFBQQEhICIcOHSIgIIB69eoBMGzYML755pt/HHPVqlXs27ePX375BYD09HSio6Np3bo1jz32GIWFhfTv35/g4OArXqPWrVtTpYqx0mKdOnXo0aNH0TVZt24dAHFxcQwePJgzZ85QUFBAQEDxNQJXr17NwYMHi15nZGSQmZmJu7v7FeO4WpLAELeXrGSYdR+gYdgicPcrsWlsag7rDyczsmMAtjbGKhpN/Sswe1Q7lu6NZ8LSA7g62DL/iRCqVzKSICufDcPF0ZbK7k63ojflh4MLDPkJZvQwru9jK6GCMT/wm4db8p95e/i/JQcAGBkaQIe6XgRW9aTnFxt48Nut5BSYWTAmhEZVPHjpl33sOHGWv166i0quDmXZq7JnsYC5AOzvsN8nIYQQQohLXWakRGmytbWlc+fOdO7cmaCgIGbOnFmUwDg/tcTGxqbo+fnXJpMJrXWxxyxpe3EuPK6trW3Rcbt3787cuXMvahsREXFVq/9prZk8eTI9e/b8x3sbNmxg+fLlPPzww7z00ksMHz78quO78DqcvwYA48aN4/nnn6dv376sX7+eCRMmFHssi8XCli1bcHZ2vmIfrtcdMkZe/CtYLLBwNGQlwoMLwLtuiU0PxKfzyq/7cLSz4bFiVhHp26wqO1/vxvqX7ipKXgDU8na985IX51WsBcN+hfwsI4mRlQxA9UouvNKrofW5M6/3bkSXhr74ejjxZOc6ZOQZH2yDp22l7XtrWH84icw8E5PWRJNXaMZkNoqDrj6YSEpWfpl0rVQV5MCuH2DxkzD7ASMJNKUtfNIA3vaGd/2MbRs/NVbLEUIIIYQQt8Thw4eJjv67IH1ERAQ1a9a86v3DwsKYP38+ZrOZ5ORkNmzYQJs2bUrc7u7uTmZm5hWP265dOzZt2kRMTAwAOTk5HDlyhIYNG3L8+PGi2hOXJjjO69mzJ19//TWFhYUAHDlyhOzsbE6ePEnlypUZPXo0I0eOZPfu3QDY29sXtb0e6enpVKtWDYCZM2cWbb+0vz169ODLL78sel3StJUbISMwxO0j/FM4tg76TAL/lsU2iTiVxtGkLMYv3EehWfN2v0B8PYpPSNjYKBxsrpzhvKP4BcGD82DW/TCjO4S9CI360iagEoNa+RNSxwubC67ZqNDatK5Vifi0PD778zCJGflYNHSs581PW0/y58FE6vm68WTnuoz6cScDW/rzyQPNyrCDN5GpAHbPhL8+guwkcPMFj6rg6AHevuDkCW6VjbYxq2HNW8aj2YPQbQK4+5Zl9EIIIYQQ/3pZWVmMGzeOtLQ07OzsqFu3brFTMkpy3333sWXLFpo1a4ZSio8++gg/P78St3t5eWFnZ0ezZs0YMWIEFSsWXyvOx8eHH374gaFDh5Kfb3zB984771C/fn2++eYb7rnnHry9vQkNDSUyMvIf+48aNYoTJ07QokULtNb4+PiwePFi1q9fz8cff4y9vT1ubm78+OOPADz++OM0bdqUFi1aMHv27Gu+jhMmTOCBBx6gWrVqtGvXjuPHjwPQp08fBg4cyJIlS5g8eTKTJk3iqaeeomnTpphMJsLCwooKot4s6lqGv5S2Vq1a6Z07d5Z1GKI8OhEOM/tAkwFw/7dG3YZL5JvMBE1YRYHJgrebI8vGheLneYeOprhRJzbBihch6SDYOUH9nlD7LqgRYtTHKGFo27pDSeyOPcfDITXp/PF6cgrMAPi4O5KcaXw4P9etPv4VnUnMzGNkaACOdra3rFs3xGKBtJPGNTm2HiIXQk4K1AyFu16Dmu1LvC4AZCXB1q9gyxRwcIOBM6BOl1sWvhBCCCHErRYVFUWjRndQbTlxVYr7vVBK7dJat7rSvpLAEOVfVjJM6wgOrvD4enAsvgjMsn3xPD1nD70C/Xjyrjo09a9wS8P819EaTm2HyF/+vlkHqFTbeDh6QMN7IPA+sPlnEmJjdDIWDVPWxpCclc/QNtX54PdDWC74yJk4JJh+wdWKP7+5EJQt2JThTLesJNg7D6KWQuJBKMw2tts5Qf1e0PIRI7FzFXMViyQfgQWPGEVTu/wXQp8v2z4KIYQQQpQSSWCI4kgCQ/x7WSwwe4AxImD0GmOKQzHScwsZ8s1W0nMK2PhKl6KineImOT/64OhaiP7TmDKRcQYy442fSYdnoVFfsLt80c6YpCycHWzJsP68Qut6M+WhFlCQDQmRcGav8UjYa9zg2zoa0zJcvcHFy/ivc0UjuVGYY9SfcHSHpoPAv/W1JRIuJzsVNnwMO6aDpRCqtTSOX7kx+AZC5UZGQu16FWTD0meM5FCNEOj6f8YIDiGEEEKIfxFJYIji3EgCQ2pgiPJt0+fGTfO9n5eYvAB4Y3EkMUmZTB3WUpIXpcHGBioFQKWR0Hqksc1igYOLYO07xvKrjp5QvQ2EPFniqIS6lY2lVatVcKZ3kB8HIrZjnvcZtoeXgzaKfeLiDVWaQUhXMOVD5hnISYWzx+DUNsg5a4yAsHc2Vk/JToEd3xr73P0x1Gh7/f00F8KWL2HjZ1CQBc2HQcjTRcvK3jQOrjBgOgR0hHXvwfd3Q52uxoiMai1u7rmEEEIIIcqQ1vqqVtYQd4YbHUAhIzBE+XVyM/xwLzTuBwO/K/Hb9dwCM83fXsXAlv6807/kJIcoJRaLkWSKWgrRq4yEQ5Vg6Pi8MSrj0p+b1hC3k4Q1X+JzfAna3gW7NiONEQhVmoF7lWsbSZGfCZG/GsU0M05D0yHQ9Q3w9L+2fqREw8LHIX431L/bKLRZueFG+VnCAAAgAElEQVS1HeN6FOQYCZjwzyH3nFFTo+UIaNRHll8VQgghxG3t+PHjuLu74+XlJUkMgdaa1NRUMjMzCQi4eKVImUIibm/ZqTA11LiBe/wvcPIosekfkQmM+WkXs0e1pUNd71sYpPgHUz5EzDFGMaTGgE8jo1Bl7U7gVddISm2fBgn70XbOfF/YndhGo5gwpNONnzs/y5j2sfVrIwHSbiyEPmesBnI5OWdh1/fw18fG79u9nxt1PW61vAzYOcNYkvXcCWOqTPBD0O5J8CyhTogQQgghRDlWWFhIXFwceXl5ZR2KKCecnJzw9/fH3t7+ou2SwBC3L7MJ5gyCExth1GrjW/nLeH5+BGsOJbHzv92wt5ViiOWCxQx7ZhkjI2K3gTn/7/d8GkLbMdBkAM8sOkp4TArbX+uK3c362aXFGtNa9s036mZ0esWYCnJpzYrMBNj4KeyeBaZcY9RFny/A3e/mxHG9LBY4/pexRGvUb6BsoPnDRjKmQvWyjU0IIYQQQohSIAkMcdtZeSCB48lZjMmcbHwL3WeSscrDZRSYLLR650+6N/bj00GXT3SIMlKYC3E74NxJo/hltZZFU0SW7zvDU3N2M3d0O0LqeN3c88ZHwJ9vwPENRs2Mut2gblcjuZKw30hwWEzQbIiRULlMjZXi/LorjuwCEw+2qcGD07cRVs+b4e1r4eZgh83NqsNy7iSEfwZ7rOt1N38IOr4oiQwhhBBCCPGvIkU8RZnLKzSzdG88B+Mz6BtclRY1Kha9l51vYsq6GH7aepIaXi7MHtmOD38/RM9zc8F+nrG0ZDHJi1Nnc6heyaXodXhMMhl5JnoG+t6SPonrYO8MAWEQ8M+3OjfwwcHOhpUHEm5+AqNqMAxfCrFb4MBiYzTDoWXGe3bOEDQQOr5gLAl7jcKjU3jxl70oIDY1h+3Hz3I4IZOpfx3jqbvqMrZznYvarz+cxLztp2hXuxIjOvzzQiRl5uHl6vjPArQVa0KfiUbSIvxzY1TL3vkQ9iK0Hwd2jtccuxBCCCGEELcrGYEhbqpCs4XsfBO/Rybw2Z9HSM40pg60DajE/CdCAOOGr++UcNJyCunWyJfVUYl0qOuF17GlTHKYwmbnzuT3ncaSvWcA6NOsKp3q+zBneyz/t+QAE4cE0y+4GrO2nuSNxZF4ONmx/fVuONnbllm/xfUbNXMHB+MzSn/5W4sF0mPB3sWoL2Frf+V9gP1x6Xy08hDv3x+Ef0UjeTbw680kZOQRdy4XgMrujiRZf9erVXBm48t3FY3CWHkggafn7MbJzpbMfBNzRrelfZ2/a7Vk5BXSdMIqegf58cXg5szfEUuPQD98PYop4Jl2Cla+ZhRM9aoHbR43Vi3xbSIFP4UQQgghxG1LRmCIMvHyL/tYtOc0AG0CKjFxcDA7TpzjizVHOJOeSxVPZxbtOU16biE/PxFCm4BKPD1nN8n71/KxwzRi3Vsw+txIsmfuwtHOBid7WxZHxNPQz51jydkA/GdeBH9EJhAek0LbgEp8MKCpJC9uY/e38Gd11G7m7YjlgZbVcbArpTomNjZQsVaJb5vMFgZ/sxVXRzs+uD+IqhWcySs089zPEcQkZfHeiii+eqgl8Wm57Dx5jhe616emtytx53IY2roGT8zahZODLRuOJPPXkWTualiZ3bHneGr2bppU8+Tb4a3o92U4by+LYunTHYrqtayNSgJgxf4EXB32s2BXHG8tO8hLPRswKrT2xdNRKlSHwbMg+k/4/RX4/SVr3+zAN5C4Fi9RteW9N28KixBCCCGEEOWIJDDETWG2aH7dHceiPafp2rAyXRpVZmjrGtjYKKpUcObz1Uf46I/DvH9/ECsPJNCyRkXaBFQC4OPOTtgen0ihc01qjF3IDlt3th5LpZaXK/4VXVi6N573VkTRvbEvofW8eXXhfsKjU8gzmXmnfxMCvF2vEJ0oz3oF+tHU35PXF0UyeU0Ms0e3pY6PG2aLZvPRFBr4uVPZvfjRBXHnctgYnULnBj5U8XQu8Rx5hWYW7DzFA62qFyW7cgvMpOcW4ufpRHpuIb/simPXyXMAvLs8iikPtWDSmmhikrLoVN+HFfsTOJqcxdKIeADubVb1ot+9n8eEkG8y0+2zv5jw2wFqerkwI/w4ro52/DiyDR5O9vxfn0DG/LSLT1YeZkBLf9yd7Fix/wzuTnZ4OtuzYFcc7k52BFevwHsrDuHj7sjx5GyOJmczeWjzvxMT9bobNT0yTkP8HojfQ1bEIvyXD2Pf2jY0vu8V7Gp3lCkmQgghhBDiX6XUp5AopXoBEwFbYLrW+oOS2soUEkjPKeTLddE807Ue7k5XN8S9PPhs1WEmrY2hXmU3lj4dirPDxSMiPvrjEF+tP0qXhpVZeyiJ13o35PGwOsbSl992gdyzMGqNMee/GFrrorWjU7LyqeBsz9mcghJvbMXt5WhyFn9EJvBd+HHO5RTQsmZF4tPyOJ2WS20fV34d056Krg7/2O+pObtZvu8MXq4OhNX3wcnelvfv/2cxzm83HOPdFVGMv7shYzoZ9SleWrCXxRGn+V+fQL7bdJxjydk0quJBu9qV+H7TCdrX8WLrsVQGtvRnXJd6dPxoHR3rebMxOoWegb5Me7j4EW5bj6UybPo2TBbjs/XRDrX4X5/AovdfXbifudtjAfD1cCQ1q4CHQ2oyoIU/j/+4k/fuDyKsng89v9hATHIW5z+iZ41sQ8d6Pv84X26BmYlrovn+ryget13GI3ar8FYZYOtoTC+p0Q5qhBiPyyxHLIQQQgghRFkpF6uQKKVsgSNAdyAO2AEM1VofLK79nZDAOJSQwbZjZ+ncwIeaXv8cOfDKL/uYv/MUb/ULZHhIrVsf4HU4m11A6Idr6VTfh8lDm5e4HOZ/F+/np62xeLs5sPLZMLxcHWDRGNj/Mzy8GGp3usWRi/Lm1Nkcft55inWHk6jg7ECn+j58vPIwni72fPdIa4L8PYvaZuYV0uqd1dTycuVwYiYA9raKXW90x+OC5F+ByULYR+tIyMjD3dGOFjUr8tHApnT+eD02CrILzAC80qshvYP8KDBZ6P75BgBGdwzg2W71cXW0o/PH6ziRmkMDX3eWPN3hstOWzvdjccRpZj7ahto+bkXvWSya7zYdJz4tj1lbT+Dr4cTycR3xdLG/KFG3JiqRN387yAs96jNh6QFC6njx1UMt0Vrz7vIoAqt50KdpVV7+ZR8LrdO2Xu/diF+3RxOm9vFqkzRU7FY4E2GstmLvAi0egbCXwPUmF0wVQgghhBDiBpSXGhhtgBit9TFrUPOAfkCxCYzbkcWiWX8kCTdH+6IpESXRWvPM3D0cSczC282BVc91opKrA4kZeVRwscdk1qyINApX7olNY3jIrejBjZu24Si5hWZe6FG/xOQFwAvdGxCflseojgF4uTnC7h9h3zzo/JokLwQA1Su58EKPBrzQo0HRtna1vRj9405e+XUfHw1sysu/7CPPZKZnoB/5JgvvDwji2w3H2H78LKnZBaw7lES/4GpF+6+JSiQhI48Xutdn+f4z/HUkmVEzd5JbaObnJ0IIj07GztbmopVD5oxqS20fN/w8/x7hE1rPmxOpsYztXOeKNVeK68d5NjaKUR2NlU/6BlfFx90RTxcj4XI+eQHQtZEvXRsZq+scjM9gevhxTqRkszE6menhx6noYs+sLSfZHZvG03fVpVn1CnRu4IOTgy1vLDaRl1eTN0e9gzq/jO3eebB9GkTMgbAXoM0TUvhTCCGEEELcVkp7BMZAoJfWepT19cNAW63108W1vx1HYFgsmrCP11Hbx40fH2tz2babY1J4cPo2RoYGMHPzCVrVqoiNUmw+mkr1Ss50rl+ZWVtPUtXTCbPWbH2160U3NOVRSlY+HT9cR89AX74Y0vzqd0w+AtM6GsPbhy0EGynCKUq2dG88z8zdg4OdDRWc7cnON5FdYKZ5jQosHNsei7aOtPh4HQ183Zk1sg1KKSJOpfHG4kiSMvPYPL4rtjaKh2dsY2N0CiG1vZgzuu1V/40dScxk7vZYXuvdqKgA562SlJlH2EdG3w7EZ1DL25WYpCxsFHw2KJh+wVWL+mGxaN5dEcWM8OM8260e9X3d6R1UxXqgQ/DnGxC9Cu1elWXVXyKoy2BqSR0ZIYQQQghRhq52BEZp/194cXcGF2VMlFKPK6V2KqV2Jicnl3I4N5+NjaJ/cDXCo5NJyswrtk2BycKpsznM23GKii72vNSzAe/fH8Tu2DQOnsngma71MJk1s7aepKGfO093qUdiRj5749JLJeYTKdnkFZqv2O6PyATmWefql2TaX0fJN5l5pmu9awtizZtg6wD3fyvJC3FFfZpW4e3+TWhcxYNpD7fk1d6NqOBiz4cDmqKUwtZG4exgy9hOdQiPSWHBzjiOp2TTf8om9p9O577m/kVLtE7oG8i4LnX5bkTra0oQ1vd15399Am958gKgsrsTL/dsyJHELJpU82Thk+15sG0NPri/Kf2bV7uoHzY2itd6N6JRFQ++WB3Nk7N388Om49YDNYSHFsDwpSSbXbnnwPMs/vZNYpKySvz8EkIIIYQQorwo7REYIcAErXVP6+tXAbTW7xfX/nYcgQEQk5RJt8828Ma9jRkZGnDRewfi03nrt4Psjj2Hva0NvYOq8MkDzQCIT8vF1cEOTxd7Nh9NYdj0bbzVrwl9mlWlyyfrCfB2ZcGYkJs6CmP94SRGfL+DgS39i+IozpajqQybsQ2tNfMeD6GBnzuezhcXFU1Iz6PzJ+voHVSFzwYFX30QcTthelfo/Cp0Hn+9XRF3OJPZ8o8pSxaL5sHpW4k8nUH3xr4s2nOax8NqM7ZTnWKLgN5uzBaNjeKqPhNikrJYdyiJHSfOsupgIhOHBBdNrdkfl86Qr9Yy0/1rWuVv4z8FT7LEEkrHet58Pawlbo6yQJUQQgghbkN56XBoRdES83jXA9vbZ2GEO1l5KeJph1HEsytwGqOI54Na6wPFtb9dExgAfSaHo9EsG9cRMBIXKyMTmLQ2BhsFNkphsmimDmtBryZVij1GfFoufh5O2NgoZm05wRtLDrBsXChNqnkW2/5apecUEvbxOtJzC7GzUUS93avo22SzRbM79hxOdrbY2yke/HYbFZztOXk2B7NF4+JgrO5w/gao0Gxh6DdbORCfwR/Pdiy2IGmxLGZj1ZHMBBi3Exzdb0rfhDjv1Nkc7p64kax8E6F1vflpVNuyDqlM5RWaGfrtVuLTctkyviv7T6fz3PwIsgtMrBoXgvP8gdjE72JB0+m8ts2WkR0C+O+9jcs6bCGEEEKIq1eQDasnwO5ZYMr9e7uNPVRuBO3GQuD9Uv+rHCsXU0i01ibgaWAlEAX8XFLy4nbXv3k1Ik9nEJ2YyextJ7lnUjiT1sbQp1lVNrx8F/e3qIazvS2hxSyDeF7VCs7YWIe59wj0A4yREDciJSufX3bFEXUmgynrY8jIK+SF7vUxWTSrDiQCxrfWz/8cwQNTt9Dny3B6fbGRQrOFbx9pxeeDg3mmS13qVXZjwtIDZOebAJi/4xQ7T57j/fuDrj55AbB5krEqQo93JHkhSkX1Si4sfqoDw9rV4Pke9cs6nDLnZG/L8JCaJGbkE/i/lfSbson03EImDmmOp7srDkNnYedemaHHxjM62JnvN5/gZGp2WYcthBBCCHF1EiJhWifY/i0EDYRRa2DsFmOqesiTgIbFY+GTerDqDSjMveIhRflVqiMwrtXtPAIjKTOP9u+vpbK7I0mZ+bQJqESvJn4MalUdJ3tbcgpMJGbkE3ANxfK6fLqeWl6ufDei9RXbnjqbQ7ULEiA5BSYcbG24d3I4hxIysbMxRoAMauXP2/2b0OPzDZw6m8OUB1uQkpXPG0sO8PRddWng505SZj73Nq2Cr8ffGco9see476vNhNX3oWYlF5bvP0MdH1d+fuIapric3g0zukPDe+CBmVDOC5QK8W+RnlNIs7dWAfB89/oMD6lJBZcLptSc2Qff9aKwQi3axr9Az5b1ef/+oDKKVgghhBDiKp0Ih7lDjeXi7/+m+JUNLRY4tg4iZkPkQqjcGLq8Dg16y/1IOVIuppBcq9s5gQEQHp3Cl+uiqe/rzgvdGxQtjXhVspKNPyxXH6gVCrb2vL5oP0si4tn1Rjcc7f5Z6FJrTWJGPluOpfDc/L0MbVOdt/o14fM/j/DV+qM429uSW2jmvfuCWBOViL2tDROHBuNoZ0tGXiFDv9lKalYBeSYzjfw8rrgiw5R1MUzfeAyLhhqVXPhgQBCBVa9yektBjrHqSGEujN0EzhWv/toIIW7Y8/MjMFk0E4cEF/93HrMa5gzmmEsQ/VKfon3jAAKrevJEp9rFfv4IIYQQQpSpTRPhz/+BVx0YvgQ8/a+8z5GVsOIlSDsJdbpA70+M/UWZkwRGeWQqgNM74fhGOBlu3NRrC1gKIfGA8RzAswa0H8dWz7sZ8sM+3u4XyMMhtYoOo7Vm5YFEPvg9ihOpOQBUdLHnXE4hjnY25Jss9Ar0w8fdkQou9jzfvX6xNyzbj59l8DdbqOLhxMzH2lDPtxSndPzxKmz9Ch75DQLCSu88Qojrt+9n9KIxnLP3ZYalDzOy2hHaqDrTH7nyKDAhhBBCiFtmwyew9m0IvA/6Tr62qelmE+ycAWvfAVOecYwKNcGjCjh5gp0T2DqCnaPx3M7B+K+jO7hXkVEbpUQSGGWhIAcOLYOo38BiAgdX8G4AzhXg2HrjUZAFKPALAhcv4w9A2UCVZtCoD6THwebJcGob2rkSv6tQZheE8fig/pgtFs6k5zF3eyyRpzNo4OvO4NbVScstZEjr6kSdyWBjdAq1vFwY1q7mP1ZoKE58Wi6V3R2vqu11O7kFvr8bWo+Cez4pvfMIIW7ciU2w6nWI30OunQff5XXmgbFvU7larbKO7KbLzjeRkVdIFU/nsg5FCCGEEFfrr49h3TvQdDD0/xpsrnOkaGYCrH7TuEfLSvj7y+TLcXAD7/pQoYZxH5efaRQQrdYS2o8Dd7/ri0VIAuOWWvk6nDsBx/6Cgkzw8AeXisYyPmmxRhsPf6jfA+p2g5rtrzyF4uQW2DYVy+HfsTHns8TcnimmfhzVVWlUrSIPtKzOQ21rlG7i4WYoyIGpocYok7FbwNGtrCMSQlyJ1hC7laz1E3E59gfaxg7blsONf5grBVx5/9uA2aIZPG0LEafSeLlXAx4Pk+GjQgghRLmWnwV/jIc9s6DpEOj/1fUnLy5lNkFWovFlsynPGDlvygNTPpjzjee55yAlGpIPQfppQIOjhzFS49R2Y+nW0Geh44vGqA1xTSSBcSvN6AE5qVC9LQQ/CDXag401sZCfCdkpULHW9Q03yk3j2NIPqX5oOva6gHOOVfEY/A22tTve1C6UmvNTR4YvLb6ojhCiXBv5+c/0TJvH/eovbDCTXaEh7nXbGyOqfG/f5VZnbzvJ64siaVLNg8jTGXw0sCmDWlUv67CEEEIIUZwz++Dn4caXxqHPQZf/3rzkxc1w9hisew/2LwCfRnD3h8a0eZluctUkgfFvk34ajq6BjZ/BuePQdix0/T9wcCnryEq2exYsfRraPA69Py7raIQQ1+HU2Rw++/MIUUeO0DXvT+5yPExL2xiUOR/aPwNhL5Xvz6ESDPlmC+eyC1n2TCiP/bCDLUdTmTWyLSF1vMo6NCGEEEJcaP8vsORpYwT7wBnGaPby6sgqWP48pJ8Cr7rQuD80GXBbf+lzq0gC49+qINuotrvjW2NaSpf/QtNB5SsDCXBoBcwfZmQeH1oAttewIosQolz6I/IMY37azQONnZngNA/Xg/ON0WX3fGpMj7PSWl/98so3ycnUbPJNFupfRTHinAITzd5cxaMdAnitdyPScwsZ8PVmkjPzWfRke2r7yFQ3IYQQosxlJcMfr0Dkr8YI90Ezwa1yWUd1ZYV5sG+esWTriY1GbY3ad0G/KeBZrayjK7euNoFRzgsoiH9wcDUKYY5YAa7esHgMTOsEMWuMeetlTWs4/DssGGEUJh38kyQvhPiX6NHYj2HtarAsuoChScMpHPYb2NjDTwPgl8eMuaHAG0si6fDBWjbHpACQkJ5HboG51OLKzjcxeNpWBk/bQna+CYBCs4XP/zzC+yuiSMrMK2p7ID6dLp/8RaFZ07GeNwCezvZ890hrbG0Uz/+8F4ulHHyW3ua01ry3Ioqv1sdctp3ZojmRko3JfBWF04QQQtwZCvNg1w8wpbWxOMJdr8MjS29Z8iImKYu8QjMxSZnX9++TvRO0HGHE/MIR6P4WxO2AaR2NezZxQ2QExu3MYoEDC2HNm0ax0Eq1jWFKjfuCX7O/63Ccb5uXZhSXUTZGQRqXSjd3XtaJcGPu18lN4NPQmmSR4dhC/NusPJDAE7N2cW/TKrjYmHnTaxXOWz4Dj6rk3fc9Db9OBMDbzZE1L3Qi7KN19GlWhXf6B930WDZGJ/PZn0fYE5sGwKt3N+SJTnV45Zd9zN95CqXg8Y61ebV3IyJPp/PErF2cTsulkqsDm8d3wcn+79Frv+6K44UFe5nQpzEjOvw7ipWWld/2xjNu7h5sbRRrX+hETS/XYtt9svIwX66LIcDblSfCanM6LZcXejS4xdEKIYS4pbSGuJ1w5HfjnkQpcPE2Vm5MiYa9c631BdtB30ngc+v+XUhIz6Pd+2tQygizjo8rc0e3o7KH040dOCXaqOGRFAWdXoFOL/PJnzE0qeZBryZVbk7wtzmZQnInMeXDvvnGMKXjG0CbjbWKHVyN/1pMRiFRfck3oH5NIexFaNjn4mTHhbJTYe8cY1RFTqqR/FC2xgeNrT24+hiVd+N2QUYcuPlBx+ehxSNG9lEI8a/0xuJIZm09CcCbfQN5pHoyLBiBJTOBFaaWBFY0Y0k7DU4e7Mv1Jsa2Ls88/RyO3jcvMbBoTxwv/LyXKp7OjOoYwKoDicSn5zJpSHP6TdnEE51qE5OYxcEzGYzqWJu3lx3ExcGWOaPb0dDP/aLkBYDFonls5g7+OpLMNw+3ontjXwDScgqo4CLVxK+WyWyh08frcXey43hKNj7ujuQWmBkdVpsxnf5e7eXU2Ry6fvYXjat4EHEqrWj7fc2rEVLbi0GtpaiqEELc1kwFkHTAWK40L8O4l4jbbnzpmZ1s3FPYOxv3KibraElbB6jXA9qMhoBOt7wI5pxtsby2aD8AvYP8+D0ygbsaVCYxI4+2AV68fk8jbG2uM6aCHKM+xt65ZPuH0THmQSpVrsqfz4Xd8qm35ZEkMO5U2akQvQoSI61L/+QZSQcXb2PKibYY6URtMZYgSo0xRkuEPg+B9xlL/pzPiu6cYSRFzPnGdJCKtcBitu5vBnOB8eGTnwlVgo1VRpoNNT6IhBD/anmFZhbtOc2nq45Qt7Ir8x4PgZyzbPpyFHVy9uJbLYDwRHvsC87hr5LxV8Z0EvyCoEFv8KpLkq7AqlgY1LUdDi4e13T+A/Hp3P/VZprXqMB3I1rj4mDHvO2xjF+4nyqeTmTnm9g0vgtrDyXxn3kRAHRr5MsnDzS9bDIir9BM74kb8XC2Z/FTHfhtbzzPzo9g+vBW3NWwMueyC/ho5WGSMvL45IFmVHQt3cTGppgUFu4+zUcDm7Ji/xlMFgv3NfdHa82rC/fTrHoFhrapUaoxXKtl++J5es4evnm4JfZ2NszYeJzTabmcTsvl1bsbMqClPx5O9oz9aRfrDyez7sXO/N+SSDZEJ1PF05njKdnY2ypWPdeJAG9Xlu87Q+uAilR2v4OT4hnxsGMGHF0LhTlQvyd0flX+vRVClD9aG9MkIn+FQ8shP/3i9z2qQa1Qo05e437gaK1dVZANuWng5AmOZVeLatTMHRxKyGTVc2G4ONjx4P+zd9/RUdRdA8e/k957SCOFEHoLEELvRUVpggICNhQLir2/dkV9bIiKBSyIgkpXQQRC7zV0UkgP6b1tts37x8RgNECAQALczzk5mN2Z2d9yxmXnzi1zd7HjVB4ONpaU6028e2sHPBxtsLGyYECriyhpUVU48AOGP56mxGzDC4b7eGLGU7T2vbDvQaqqMnPVMfq38qVDgCuuDlUl+0b9VTvCVQIY4vzMJji+ArZ8ANnHwcYJHDy1oEdplvZ7pwkQMVU65wohavXh2hg+3xjP++M6kZJfzidRcTxzQyumDwwjq1jHJ1FxdG/mwXe/b+B2p8Pc4XoEUnYBZ/7tMSo2WHWdAkNfP/NF5hyKdQZGfLqNSoOZVTP64OlkC0B+mZ4ub64D4NkbW/HwgDB0BhPv/xWDp5MNd/cKwcHG6rzH/257Iq//fpylD/XisZ8PklZQgb+rHZ2D3InLLiEhpwwLRaFrsDuLpvW4uL+4Ohrw/kaS8srp19KbLbE5WCjw2R1daOJsy7gvdwLw3tgOjO92aUGMw2mF7E7IZ0rP4P9kplwIVVUZPWcHReV6op4aUH2XKrtYx6jPt5NRpKNHqAf39G7GAwv28+TQlswY3AKdwURemR5bKwtS8su585s96I1mJkQG8sPOZCZGBvHOrfVfgtToqSpEL4Q1z4O+VEuntnGE+HXazYdb54Jfx4ZepRBCaH0rErfAjtla40p7D63Bd+vh4BasBSbsXLVrjUaYbbBkfxrFFQbeW3OSCd0CeX1UewBWRqfz2M/RfDWlK7PWx3Eio7h6n9sjmjJzTAesLC+srWRMZgmPf7qQOU7fEqyLYY//ZHrc8TI4+5x9p7JciPkTw+kjWJRlos+MwTI/jkKcOWYOJqRlR5qZkrReG4/sBbfGdXOjLiSAIerObNbu6sSugcpiLWMjqIc28qcOFxNCiOtXZpGO27/aSUp+OQDuDtZsfnYgLnY1m/d+vjGe9/+KYeF93ekVaMtvW/ezcMNeOrpWEFoazXirjSgeoTB5GbgHn/M1P42K48N1sSx5sCcRIR41nvtkfRy21hY80C/0otMxi3yC/sMAACAASURBVCoM9H53AzZWFuSX6bm/bzN+3pOKrbUFJToj397djT2J+czeEMfBl4decHmJ0WTG0kI57/rMZpWub62joNwAaKUVuxPyOF10pilp+wAXTmWXsfqxvjTzqr3PxPnsSshjwte7ABgV7s8Ht3XC+gK+jGUUVfDsksMcTS9CBQrLDbw5qh1TeobU2M5oMrP8YDrPLDkMQGtfZ1ZM711rwORIWhFv/HGMvUlaY1gPe0t2PxSKta5A6/fk5H1R7/WqUpIJvz+m/dsc3BtGfgqeVSU48VGwcjqU58PoOdBhXMOuVQhx/TJWajdDd34OhjItQNH/eYi456pp5J9drCNyptZc09PRhlUz+uLrqmX9qarKqZwywpo4EZ1ayPIDaQxq48O+pHw+3RDPpO5BvD2m9gB7ZpGOn/emYDSpDGztTddgD1RVZdyXO0nMLWP9o92ImTuV7mVRKJbWKB3HaxnxiqJ9vpdkQNYxyDyi3WxWzZQr9hRZelLqGMSGPHcCbcpoZjxFmGUm1r5tIbgP9HgI3K6+MkwJYAghhLgiCsv17DiVR0SwOzZWFrVe0BdVGLhp1hYyinVM6BbI1rhcvJ1tefaG1kycu4slN5qJ2DUdrB1g8lLwaVfra6mqysAPNuHraqeVrVwmH6+L5ZOoOPq28GLB1O6AdgFeojPi7mjD3qR8bvtyJ19O7nLBzbee+CWagykFrJze50zK57+UVhqZtS6WedsSmdYvlFAvR8Z3CyS/TM/qIxm8vPIYrX2d+f6eSIZ+vJkuQe58f083iiuMrDyUzh2RQXW+IzRj0UE2x+ZwV89gZm+Ip0uQG78+0PO8+xeU6XFzsOa5pYdZGX2aWzr6s/ZYJrbWFmx5duBZs122xOaw7EAaTw1rRaCHw1mPfzS9iFs+3coE+/08bv4OX6XgzJNeLbWLep92WiaCd+trJ6ihqlrq9aqntIzIwa9C9wf/26uqLFdrCJeyE0bNgfCJDbNeIcT1K2UX/P445JzQLrzDJ0FI34vugzdnUzwxmSW8PaYDTrbnz5isDzvic3l68SFOF+m4v28zRoUH0D7AtU77vvbbMX7YmcSCqd3pHORW/e9ecl4ZMxYdJDG3jJJKIxaKgsmsMqSND/1bevHyymO8e2sHJkQGEXUiizd++IP5bfYSkrICjBU1X8TZD3zaQ9MIEr36M/DHPEC7ATKkTRPm3dWNF5Yd4bfodA6+Mgwbq6t3yGhdAxhX5swQQghxzXJzsGF4h3NfxLvaW7PmiX7MWhfH/J1JmMwqr49sR+cgN2ysLPiztBkR9/wJC26FrwdC/2eg12P/qePcn1xAUl450weGXcZ3BPf1bUZibhkzBp95HStLi+qeF52auuFgY8n2+Lw6BzCKKgyk5pez/GA6AP+38iifTuxc67afb4xn3rZEAO7sGUxTd+1C39PJlik9Qwhr4kywpwO+rnY8NrgFb606wddbEiirNDJ7QzwudtaM7nz+WfMlOgN/Hcvk9ohAnhzWCm8XO15ecZQNJ7MZ1s63ejtVVXlvTQzdQtwZ3MaHjSezuXf+Xm5s50vUyWxu69qUt8d0oELfHp3BdM5SnX4tvenX8vzBhvbO5WwP+ZaAzChiLcP43DweZ09/ejjnYpO6jQ55v+Colp/ZwdIGnH3BNRAsLLWpWxZW2qhfRy9wbQr+nbUJXE6+4Hr+v58rwqCDojStEXZBEsSuhZhVEBABY74Erxa17+foBZOWwM8TYcVDWuln78caZWq2EOIaU1EIa1+Cgz9qPS3u+FXrzXMJiioM/G9NDADb4nJ5ZURbRoVf/s/pF5Yf4XSRjiFtmvDSzRdWMj99YBiL9qQwad5ueod50iXInbAmTizZn0Z8dikDWjfhiSEt8HW158ddyXy4Nob1J7Jo5+/CbRFahkT/lt7YeIdxe2owa6bPxCM/GqzsiM614KX1mTg5+fDTxO4UlBv46I/jWFpYYKoa9/7kUG06y+DWTVi0J4UJX+/kqykReDvb1u9fUiMjGRhCCCGuqKIKAzklOsKaaCVqt3+1kz2J+XQIcGXlnc2xWPsCHFsOXq1gxCwI7lW97wvLDrPi4Gn2/t+QK3Z35mweWLCPnafy2PTMQDz+1czTZFZrdCk3m1XGfbmDA1XjXls0cSIxt4wdLwzC28m2RjmJzmCi5ztRNHG249WRbenV3Ouc6zCYzDy68CBrjmVWPxbgZs/Qtj60D3BlXNemZ93373Gnf5fjGE1mer27gXb+Lsy8tQPv/XkSgPBAN177/TiONpb0DvNiT1I+VhYWFJbrsbJUWDWjL82966npWlWDM9a+rDWRHvgiKS3v4fkVx0nMLSOjSEf7ABdS88pp5VDKotGuWObFQGm2FgAoy9U62puNWsNpY1XD6bIc/tl7hcDu0HkKdLxdm6Z1uZhN2vi8v4MUJVln1lOWA+n7z3TfBy0Lqd8z0GsGWNbhHDdUwPIH4PhKaDNCy8awu7BmcEIIUWfJO2HZNChOh16PQL9nL7rpZqXRxOG0IiKC3fluexJv/HGcl29pyy97U6gwmNjyzMDLOp3jVE4pgz/czLM3tuK+PqEXlb2wOTaHqBNZ/LAzucbjtY1kP5hSQExmCSPD/WsE+o+dLmLEp9u4s2cI1pYKt0UE8vnGeFZGnwbg/XEdmbU+jvTCCsZHBDKpRxBu9jYEeWo3N8xmlblbE3h3zUkeHRjGk1fpOHIpIRFCCHFV+Ht6CMCPU7vTp4WXdhd61VNQlAKtbobu09A17UO3mVEMbePDR+PDG3jVEJtVwk2fbKVHqAdvj+5ASFUPiiNpRYz7cgc9m3vyyfjOxGaX8NXmBNafyKred9WMPtw8exv39m7GtvgcxnZpygP9m1OsM3Df/H3sSczn52k96BHqWae1mM0qY77YwaHUQm7u6MfuhHx0BhOllUa+vTuCQa1rbwz25K/RbDiZzf7/G1odcPlkfRwfr4+libMtxToDZjPoTWZCvR3JL9PjaGNFqLcjLw5vQ6i3IwpK/aWs5p3S+j4kbdXqeEfOPtP3Aa2B69pjWdzS0Y/VRzJ48tdDLJgaycLdKZhVlS8nd63xZTe7WIeiKHy0LoZH+/jhXx6rTc7KOQGHfoack1p6bs/p0PWeS+t8bzZrNcppe7UgSmWRNj3k1EaoyK+5rZ2bNobc0Uub8uXfGVz8tWlfLgFaBsmFUFWt/nzdK9oxRn8BQd0v/r0IIcS/VZbAtlmw7SOtQeTYb6Dpea81z+mLTad4b81JhrRpQnRqIc28HFn8YK/q7wV/PtaXNn41A7Ims0pqfnn1v7mX4ustp5i5+iTbnx9EgNvFT3VSVZXPNsTTPsAVO2tLnO2s6lyG8rcp3+xma5w2sc3aUsFgUrm5gx9rj2diMKk421kx/95IOge6nTWoc893ezh2upjtzw+6oF5WjYUEMIQQQlw1dAYT3WdG0dbPhY/GdyK9oIKNR5Jol/gdQ0p/x0ZfQLZtCLNLBzLizqfp3ursWQVX0oJdybyz+gR6o5nJPYJ5YmhLHvpxPztO5QHQsakrh9OK8HS0YUQnf7oGu5NVrOO+vqHc/8M+1h3XghpWFgojO/lTUmkk6kQW74/rxNhzZE7UpqBMz0+7k7mvbyh21pZUGk3cMnsbqQXlPDGkJQ/0b15j+0qjiV7vbKBPCy8+mXCmlEVnMHHz7K0k5ZWz6P4e+LnacSClgC5B7ng722JjaYGFRT3fEasshV1fwNYPtaZvQ9+ALnf9t+/DP+SWVhLx1voaj4UHuhEe6MaTw1py3/f72JOUj4ejDfllesZ2acqHt3c6s7GqQsJG2PqRFjBxC9Iu/EP61H3dmUe10eUpOyFld81xgVZ2WjO7kL4QOkALLLg21cpcLldju6TtVXdG07Rxxf2fA/+GD/YJIa5SqgonftcCvgmbtCadnSbC8PfrpdH/nd/u4VBqIRUGEwaTmd8f6UP7AFdySiqJnLmeGYNa8MTQloDWh+q3Q6dZfjCdrXG5/PFoH7ycbInNKqFvC68LztQwm1Vu/GQLNlYW/PFo30t+L5dqxcF0Hv8lmgGttKljZhW+nNyVWetjOZlZwmd3dOaWjv7nPEbUiSwe+vEAvzzQg85B7ldo5fVHAhhCCCGuKl9t1u7E+Lnak1dWiVkFFzsrSkpLud8jmmGlK+lokQgOXtDjQeh2P9i7NfSyyS7W8fH6OH7Zm4KXky3ZJZW8NqIt+5IL+ONwBn1bePHVlK7/6QtRWmnkqV+j6RToxu+HMkgvKKdYZzxnR/MLlZpfzvPLDrM3qYB9/zekejpMYbmeWz7dRlpBBV9N6coN/+h3AdpkkdOFOroGX+YvQJWlWrnI1g+hPBda3wI3/a/O/SlCnl8FwIzBLVh7LJPE3DIqjWY8HW0oKNczopM/K6NP4+dqR3ZJJRufGlCdcltD0nZY/qCW8dN8sFZWEjpACzb8k6pq5SApO+Dwr5C8XXvcq5U2vSu4l1aa4hLwn/4tF2NrXA4/7Ezm04md6z7etrIEds6BXXNAVwSR98PgV2SqmBDiwphNWkD06BJwaQqtboROd0DTrvVyeKPJTKfX1zKmSwB39wrhdKGuRn+kSfN2kZRbzpZnB2JpofDNtkTe/ON49fN9W3hx7HQx+WV6bmrvyxeTu1JWacTSQsHWyoIvNp+iXwvv/2RCqKrKx+vjmB0VB8Cs8eF16hl1uekMJt5ZfYL7+oZiMqssO5DG9EFhnMouY19yPnf+a7JXbUxmlcJyffV4+auNBDCEEEJcdbbG5TDlmz1YKLD+yf74u9nzSVQcG05kc2tnf6Y1y0bZ9rF219vGWbs4i5ymXWjWdvdFVwy5sVpvBHt3CIy8bBdyUSeyeGDBfkZ08ufD2zqRXljBF5tP8dTQlnX6MlFaaWT5wXRGh/vjbFd/d+gPphQwZs4OHh0UxoP9m+Noa8V7a07y5eZTzJ0SwZC255g7fzmU52sj4WLXwL7vtI7rzfrBoFcgsNsFHep/a04yZ9Mpjrw2DLMKqPDn0Qy+35HErV0CmNavOYm5ZdhbW9Lv/Y2M7RLAO7d2rP1g+nLYOxfT1o+x1BUAijbppPXNWklH8nYt0FGupfjiFqSdex0nXLYJKMM/2crxjGJmDG7Bk1V3IetMVwQb3oY9X2vlKTd/pF2ACCHE+eiK4LcZcHwFDHgR+j194aVt57EpJpu7v9vL7ImdGdnpv5kFqw5nMH3hAb65K4JWvs7cPHsb7QNceH1ke55efIjo1EIC3OwZ2NqbH3elsOj+Hry0/AhleiMTI4OYtT4OP1c71jzWr8bEr78zHfxd7XB3tGHl9N51ntolLi8JYAghhLgqvfbbMdwcrHl8yDku2DIOa3W4x1YAKti5go0TqGYtQGHjCCWZ2gz1f7Kw1u6SNx8IfuHg2xEc69Znoi7+Hi16OZuOXShVVen//iZS8svp1dyTZ25oxcS5uxjW1pfZZ5mC8q8DgK5Qa5JpZatN8DjXiLy8U1ppRmkOlGVr+5XlgGIJhcla4zcAFOg0Qes9cZH9GsxmFb3JXKfshJdXHOXnvSn8PK1njcySzCKtgaavqx1H0ooY/dlmng5Xecj3BBxdBrlaV3xcmmrlJcG9tMCGZ/PLOvHDYDLT+Y11lFYaAbi5ox8f3d4JW6sLvIhI3Qu/PXpmzOGN74HzFQ5aCSGuHsWnYcEYLdts8CvQ5/F6O7TRZGbBrmSCPR2YOn8fLnbWRD3VH69agvwGk5kB728CtI/aogoDyx/uRVgTZ5YdSOPpxYdYOb0PIV4O9HxnA6DdCAj0sCc1vwIXOyvK9SZu7uhXo0xyyje7Sc0vZ8NTA+q/HFJcEglgCCGEuPblxGrZGAWJ2jQGxQL0pVoavaM3eLUE71bg3ky7mI6Pgrh12sXc3+zdtW1RtP0srbXHQvtrtb7era/60ZRH04v4aXcyi/ak4mBjiaeTDUsf6kUT56pAhFGv9XFI3g5Zx7SfymJtIkZptjYN5J/s3LS7+j7twL+Llo2QfQIyoiH2LzAbtO0cPMGxidasUjVrpRW+7bWZ9n6dtMevkJySSm77cge5pXrWPdkPP1d7Vh/J4KlfD+HmYM1rI9vx2m/HyCjSYW9tybHXb8BCoSoIptTI8jmQUkBGoY6bO9ZthO7ZqKrKt9uTSMkr44b2vng42jDx6118PqkLCgoT5+7ikwnhJOaWMWt9HCM6+Z919O45GfWw/RPY8j+wtodhb0PnyVf9eS2EqGd5p2DBaC1TbsJC7d/BehR1Ioup8/fhZGuFyayy9bmBtQYv/hadWsjtX+0kwM2eWePD6RSolY2qqkql8Uzw+pttiSzdn8bIcH/GdW3KQz/uZ1R4APllej5aF8vcOyMY2taHwnI9EW+tZ2rfZrxwU5t6fW/i0jV4AENRlPeBEYAeOAXco6pq4bn2kQCGEEKIK6IsD7KOaJkchclVIzbRsjdMBu2iNWm7NobT3l3L1PDrCL5VEyM8Qs/ZYPKyUVWtJCZxC6TsgtMHtKwSpybg5KNdZHuEaiUZnmE1LlB1BhPDPt6Cg40lc++MIJBMLQCUshP2fgP6Ei0A5BkGTdpqWS1G3ZnjOjbRfi/N1LJbitIg41DNLBeP5lrviF6Pag0rL1ezyouUklfO4I82ATCmcwArok8T6uXIycwSAEK9HBnYugnfbEtk8YM96RbiUetxbvpka3XjOGc7a94b2+E/PU7q4te9qTy79DC2VhZUGs34uNiSVVxJqJcjVpYKWcWVbH9+EE62VnwaFceH//giflFy47QpL8nbteaiIz6pMeVFCHEdyzwCC27VRlBPXgoBXQCtZ5KlhVIvpY3PLTnML/tSARjSpgnz7jp/2WBuaSWu9tYXNVXDaDIz7OMt2Flb8tSwlkxfeACdwcyyh3vR5SpscnmtawwBjGHABlVVjYqivAegqupz59pHAhhCCCEajdIcOPk7nI7WLtSzj4NJrz3nEqCVP3g016ZLuAeDs78WMDDqtB87t5p3uI16iPsLohdqF/2uTbWL/fDJZ0oyVLXmPmYTpO2D+PVQlAqpuyE/QXvO2Q+aVn35K82G0iztuEatJALXIAgbpDWVNFRAQSLG4iwsy7JQitIg/9SZ12k3BjqO1y5qL3SUaHGGFszwbgV2LuffvoG9svIoP+xMrs5EWTm9DysOplNhMDG1TzMMJjN93tuIl5MNyx7qjauDNWkF5fy4KwVfF1te+/14jeNZKHBzxwvPjNgUk80DC/bTOciN7+6O5MXlR1h+MJ2IYHeOpBehKDDvzm7aWGG0dOpbZm8jq0THovt7/Ge0YJ2ZzXDwB1j7inauBHTRAk6tb7644wkhrn7pB+CH0drn/5Tl2uc5UKIz0OG1tUQ28+DXB3qedfddCXl8vz2JD2/vRE5JJcU6Ax2b1myyrTOY6P3uBnQGE2V6E2+Nbs/kHsGX9W0BLN2fxlOLD2FnbUFTdwfu6R3CHZFBjarUU2gaPIDxr8WMAcapqjrpXNtJAEMIIUSjZTJoZRKnD8LhXyB5B/CPf0MtrLXfzVrPAhy9tfIK71ZQlgvx67RMDydf8GmrNRbNT9B+d/HX6o5Ls8DSRvsSaeOklcOU52mZES4BWqlGh9vOjOX89xcwVdXKaU5tgPgNWqaGXssuwMpOy6Zw8tEyNkL6aAEQ92b12geksas0mojPLqWNrwtmVa21edvuhDzumLebqX2a8eLwNtVBj3+aNT4cSwuF4xnFfLn5FFFP9ifUu27Bn40nteBFWBMnfryvOx6ONugMJn7Zm8ro8ABsrCxQUf+T1ZGSV87YL3cQ5u3Eomk9aj12sc7AqyuPcSS9iBXTe+Nke5bMkJJM2PaxVlaVFwdDXq/XWnchxFUiJxa+uwlsHODu1eAWWP3U/604wo+7UgA4+eaN/+k3tD0+l1nrY8kpqSQpr5y+LbzYn1yAyazy0e3htPJ1IqyJM4Xleqb9sJ89SfnMmdSFY6eLeLB/83ptWH02JrPKR+ti+GVvKnPvjLgqx4teLxpbAON34BdVVX8813YSwBBCCHHVMFZqmQcFSVoZSkGyFmiwddZKJ7KOayUeeae0ca/BvSH8Dm1Mp6WVFmxI3AK7vtB6TLj4a8EFk0ELXOjLwMIKmg+CsCEXNzLWZIDCFG09roHS8+ACPP7zQdYez2L9k/25efZWCsq1vh7vje2Ar6s9/avG/eWUVNLnvQ1VTTbD63Ts4Z9sRW8ys/TBXjW649fFe2tOMndLAgdeGVo9Frdcb2TOxlOM7xbIB2tjWBl9GoA3R7dnyvnucJoMsPwBOLoUhn+gTfZBG8FraaHg72Z/QesTQlxFMg5rDTsVRQteeJ9pnl1Yrqf7zCi8nGxJL6xg/r2R1Z97x04XYTbD+K93Uq43AdCiiRNx2aVENvPg+OliSiuNeDnZMntCOP+34ihpBRV8eHsnRtQycUQIqHsA48ILNmu+yHrAt5anXlJVdWXVNi8BRuCnsxxjGjANICgo6FKWI4QQQlw5VrZa/4CL7SGgKFqDtHpuklaDpbX0OLhIDw8MY/XRTAZ+sIlKo7m6z8W/v3x7O9tyd68Qvt6awL29m9E+wJW0gnJeWn6U1PxyOge509Tdnik9g8ks0tHCx4nYrBKm9Qu94OAFwMBWTfhi0ym2x+VyUwetiejS/Wl8tjGezzbGA/D4kBasP5HFt9sSuaGdz5lmrbWxtIYxX2llRqufBhtH3kgN59vtifi42LL9uUEyYlCIa1HaPvjxVrBxxjxlJdEVnmQfzWT+jiRGhvtTVmmk0mjm0zs6M+HrXXyzLRFnOyt0BhN3zN2NlYWCi701C6ZGEp1axOQeQRRVGGjibMf2+FyiUwv5eF0sd8zbjbezLT/e153IZrX3FRLiQlzWDAxFUe4CHgQGq6pafr7tJQNDCCGEEI3F0fQivt2eSHigG1N6BJ+1ZrpYZ6DPuxsY2LoJb4xqz/ivdpJeUEHXEHcOpxWRX6bH0caSMr2J7s082J2Yz2d3dOaWjhd+J9JoMtPlzXV0CnRj/j2R7E3K567v9qAzmLmhnQ+tfV2YPjCMnQl5PLBA+041oVsQr45oe+6ab4MOFt6OmriVR/SPsMu+H3ller65K4LBbWTsqhDXlKTtsPB2bRLUXb/zU4zKS8uPAlR/VjnbWtHGz4VfH+zJV5tP8f5fMRjN2nWjvbUlFgq8f1snhnc4+zSmDSezyCqu5IZ22pQlIc6lwUtIFEW5EfgI6K+qak5d9pEAhhBCCCGuRi8uP8KyA2mEeDpyKqeUeXd1q063fvzng6w6kkHvMC82xWhfiTY8VfeeGf/2w84kXll5jMhmHuxJzAfgjVHtuLNnSI3t4rNL+XxjPMsPpvP6yHbc1SvkP8eqQV/GifeH0sJwEvO4+fRaYYfeaKZrsDs3tPPlhna+uFddhJTrjcyOiuehAc1xtW9c02aEEOdwagMsukPrdXHnSnDxZ8yc7RxMKWRoWx9eG9mOCV/vJK2gghUP964eXZpZpGP9iSzeWnWcF25qw+QewVhaSFmiqD+NIYARD9gCeVUP7VJV9cFz7SMBDCGEEEJcjfYl5TPuy5042Fjy1ZSu9G3hXf2cyaySV1oJQOTMKABOzRx+0V/+VVXl3TUn+WpzAv1bejNjcAvCA91qPZ6qqkz5Zg8nM4vZ9cLgs5aDmMwqm2KyeWz+FtZ7fYxveSy7un/GgtyW7EvOJ6u4khZNnFjyUC9c7a1ZGZ3OYz9H8/ItbZnap9lFvQ8hxBVUmg0b3oQDC8CnHUxZAU7eJOaWMfCDTbw4vDXT+mklh7FZJSTklHJj+/9mV+iNZmyspKxM1L8r0gPjXFRVDbtcxxZCCCGEaEy6Brvz4vDW9Az1okNT1xrPWVooNHHR+lCM6RyA3mS+pDuXiqLwwk1tGB8RSIC7PbZWlufcdlL3IB766QC7E/PpHeZV/dzuhDxmrY/jrTHt2ZWQV5VC7oBu/K+waiI99jxKj7HfYJ44gs2xOdz/wz4GfrCJmWM6sD+5AIDVRzIkgCFEPTGZ1XrPalALU9j8yywiMhZhr1SS0/ZeKno9TTMnLci685R2r3lY2zNtDVv6ONPSx7nW40nwQjS0KzKFpK4kA0MIIYQQon7pDCa6vrmOG9v78eHtndAZTEz/6QBRJ7MBuL9vM46mF7MzIe/MpIHyfFg4HtL3wcjPoPMkolMLeXXlUY6kF2H+x9fHJ4a05MEBoecMpAghzu3Y6SImz9vNW6M7cHPHs/eVqBNDBcSthf3fo57aiILKbutIXii9nQRV670zqHUTZo7pwKz1saw5lsnBl4eeu0+OEJdZg2dgCCGEEEKIhmdnbcm4rk35cXcKDw9szuJ9aUSdzGbGoDC2n8rjx10pVBpNPDoorLpvBw4ecOcK+HkS/PYI2LkQ3mYEC+/vwYhPt5GQW8btEU3JLK7k4/WxbInL4cep3bG3kSCGEBfj199+5wX9r5Qvt0OX3QU7z6bgEQqB3cHCEoPJzG/Rp/FztaPXPzKpqhWmQMwaiFkNydvBpAeXpsy3mcAulxuY8/Bo7tieiIONFVnFOr7cfIoP18Zw9HQxHQJcJXghrhoSwBBCCCGEuMY9MqgFS/an8djPBzmRUcKEboE8OawVvrtT2J98BOC/U1FsHGHCTzB/JCyZClOW4xjSm7l3RTD9pwPc2TOE9gGu/HboNDMWHeSNP47zzq0dGuDdCXEVK0giZ+XLvJ75GxU2juhMCnbb/jrzvLMfdBjHnMQAfk20J8fKh4MvD8XRUEB5bBT2eSdQ4qMgS/v/2OQRhmXkNAgdSKJrJK99tJXX+rfFwkLhvr6h1YfNKa1k4e4UAKYPlHHb4uohAQwhhBBCiGuct7Mt/3dLW15YdoQmzra8MLwNAKM7+5NdomNQ6ya08q2l5t3GESYthm9vgEUT4Z7VNPdtz5rH+1VvMrKTP0fTi/h6SwK3RTSlS5D7lXpbQpybeL4IHAAAIABJREFUyQj5CWDvBo7e0FiyDApT4cTvcHwlaupuXLDme4uxTHjiQ+ZsyeCHrTEsnxKKIXU/DieXErJ9Do8pJh61U0g0+2L62BJVl44DKmYsqfCL4Hirp3j5eFPiMn1ZOa437fxdWb42BqDWUch39QypDmBEhHhc0bcvxKWQHhhCCCGEENcBVVX5YWcynQLdCK8ajVhnhanwzTBQzXD3KvCq2au9rNJI//c3EertyK8P9KzHVQtxAfRlkLYPUnZByk5I2wv6Uu05K3ttdKhbMLiHaJM42o7SyqWuhOLTcPgXOP4bnD6gLderHZ9ntmWZOoDnxw/m5o5+5JRUEjlzPW721hSUGwDwtSqlo20Wn/coZN/+PRRWwnG9D5vM4cQQhF7V7kn3CPXg+OliinVGPBxtyC/T07eFFwumdq91San55RRVGGjn7yIlJKLBNfgY1YshAQwhhBBCiEYq6zh8PxyMehj+PwifVOOO9rfbEnnjj+P88Wgf2ge4nuNAQtQTkxFyYyB2DcT+pQUvVBOggE97COoBAV2gshQKk7WfgqqfyiKwsNa2cQ0E16ZapoaVrRbscGoCLgHg4g92rhefvVGSCZvegeiFWl8K/y7QdiS0GclLW8pZvC+NTc8MwN/NvnqXcV/sYF9yAe38XZg1Phx/N3t0BhOeTrb8ui+VZ5ccRlHg27u6cd8P+xjSpgm3dQ2kX0tvvtmWyHtrTnJzRz96hHoyoVsg1mcZnyxEYyIBDCGEEEIIUb+K0mD5g5C0Vbt7PfwD7UIPKKow0GNmFKPC/Xl3bMcGXqi4JqkqpB+A2D+1LIukbUDVtYxfODQfBMG9oGk3LRhxLhmH4dAiLehRnA4lGVqGUW2s7LSsjbajoON48Kxjz4gTv8NvM7QskM6TKen8EIX2TVl2IJ2MogoW709jYmQgb42u2Ttm7pYE3l59goX3df9Pw84SnYFub6+nW4gHC6Z2J72wAl8Xu+rxq6qqklNSWT26WYirhQQwhBBCCCFE/TObYMensOEtsLaHgS9C5ANgYcHzSw+zIjqd3S8OwdXeuqFXKhoZo8nMzoQ8eoZ6YnUhWQEGHRz5FfbOg4xDoFhWBRRGgmcYNB8MLpc4etRk1AINxkowlEFpjhbYKD4NpZna6yZuBVRo0labEOLRTFuHe4j2u2sQWFpB5hGIehPi/tICK2PnUercjFGfbSOtoIJKoxYo8XGxZe3j/XF1qPn/is5gYmdCHgNaetda2rE/OR8fFzuaujtc2nsWohGRAIYQQgghhLh8cuNgzfMQvx5a3gS3fs3RPJVbPt3GqyPack/vZg29QtGIGE1mHv7pAGuPZ/HMDa2YPjDs/DuV58Peb2DPV1CWA95toNtU6Hi7VtZxpRWlw5HF2pjSgqqSFKPuzPOKJTh6QWmWtr4+T1DUaRoZZSY+jYrnz6MZ+LrYYWdtyf/d0oZAdwda+NTSPFeI65AEMIQQQgghxOWlqrBnrhbI8AyDSb8yamE6lQZTjUkl4vqUVlDO1rhcOgS4klZQzoM/HsDP1Y5SnZGtz/TFrTJDC4QVJEHJadAVA6r2Z3G6Vi5iNkDYUOg9A0L6Np5JIgBms5adUZCkTTvJT8RYkEKyTRgfZUdgsHFlw8lsjGbteuuFm1pzV68QjGYVJ1sZBinEP0kAQwghhBBCXBmJW+GXyWBpzco2H/HYNku2PDOQIE9Jcb8emc0qs6Li+GJTPAaTiqKAp6MtTpYmFkbEUbT1K1paZmCpGs7sZGlTlVWhgK0TOPuBf2etWaxP2wZ7L7VRVZV5WxPZlZCHt7MtozsH0CPUk0OphdwxdxdlehNeTjYA3NLRn5Y+zpRWGri/b6hM+xDiLCSAIYQQQgghrpzcOPhpHOaSTB4pn0aXm+7hvr6h/9msWGfAxU76Y1yrdAYTTy0+xKrDGYzpHMC0fqH8vCeFXbu3scRlFs66DOKsW7NHbcPtNw7CukkrrX+Eo1fjyq74B6PJzPc7kohOLWRKj2D2JRfw/l8xNPNyJL9MT4XexJxJXXjjj+OYzCqPD2nB8A5+OEqWhRB1JgEMIYQQQghxZZXmwM8TIW0vW+0G0nfGt+DgUf30nsR8Js7dxdw7uzKotU8DLlRcDjqDifvm72NbfC4vDm99JuPgxB+Yf3sUxdIGZcwXrNO15f4F+/F1sWPmre1p4+eCn6v9+V+ggXy+MZ73/4rB2dYKndGEjaUFvcK8+HpKV4orjIz9cgeJuWWYzCo/3ded3v+aHCKEOL+6BjBkKLAQQgghhKgfTt5w92p2NL2PHhVbMM0dok1xqPLxulhMZpVZ6+NoTDfRRP34eF0s2+Jz+eC2Tkzr11wLXhxbAb9MxsItEOWe1dB8EEPb+bLo/h7YWltw7/f7GPLhZvJKKxt6+bXSGUx8uy2RAa282fjMAOysLSnTm5gxqAWKouDqYM1rI9phMqv0au4pwQshLjMJYAghhBBCiPpjZYPTjS8zUf8S+sLTVM67CYrSicksYWdCHuGBbhxOK+Lu7/airxonqaqqBDSucqqqsvpoBoNaN2Fc16Zag9edc2DJvRAYCff+BZ7Nq7fv2dyT3x/tw/vjOlJuMPHt9sQGXP3ZLdmfRl6Zngf7N8fLyZb3xnbkoQHN6dD0zBSUPi28mD2xMx/c1qkBVyrE9UECGEIIIYQQol51CHDltEs4k3TPYSzOQv1+OPsORQMwZ1IXZgwKY3NsDofSCgH4cG0skTOjiE4tbMhli0uQkFtGan4FA1s3AX0ZLJ0Kf70ALW+ESYvB+r8lIi521twWEchN7X35fnsSmUW6Wo7ccExmlblbE+gU6Eb3Zlop1PAOfjx3Y+v/bDuykz/+bo23DEaIa4UEMIQQQgghRL1SFIWf7u/BiFtGM6nyBQwledy8+05u9szA382eCZFBAMRklqCqKt9tTySnpJJ7v9/LgZSCRnchK85v48lsAIZ4F8O8IXB0GQx6Gcb/WDVd5Oyeu7E1RrPK8NlbeWbxIYwmc72uTWcwsWR/GqWVxjrvo6oq//vrJMl55TzYT6aHCNFYSABDCCGEEELUu2ZejtzdKwTr4G5MVt+g1GTBrIoX4cQf+Lna4WxrRWxWCccziinTm7i7VwiF5XpunbODUZ9vY3dCHu/+eZKTmcUN/VbEeRhMZn7aHsfbHn/it3AwlGTA5KXQ72mwOP/lRrCnI2+MakcrH2cW70/j5ZVHMZvPX1JkNquU6Azn3W7OplM8vfgQt8zeWqcghsms8sHaGL7anMCk7kHc2N73vPsIIa4MmUIihBBCCCEum/3JBYz9YgetnCpY6fEZdtnR0HkSM5L78Ntpl+rt9rw4mD+PZpKQU8qyg+mU6LQLzYmRgbxza8eLeu0tsTm8/vsxAtwd+N/Yjvi62tXLexL/YNSza/V8vPd9SHOLDGg3Bm54B1z8LupwH/wVw2cb42nu7YijrRUPDwirNYBQrjdy93d7ScgpY8PT/UnIKcPG0oK2/i41tsstraT//zbi42JHQm4ZX03pyg3tzh6QKK00ctuXOzmRUcyEboHMHNMBCwvJvhDicpMxqkIIIYQQolHYEZ9LmI8TTexU2PAW7PkaTHr2mFuxwXkUTXpM5N6+odXbZxRVsDepgHdXn8DbxY6V03tf8GvuTcpn4te7CPJ0IKNQR7dmHsy/p5uUAtSXgmTKds7D4dgilLIc0i388J/4KUqLoZd0WFVVWbgnhQ0nsjmSXoS9jSWLH+iJt7MtiqJgNquk5Jfz9dYEft6TglmFUC9HEnLLsLRQeHNUe+7orpUomc0qM34+yNpjWfz2aG9Gf76dCd2CeG1ku7O+/uyoOD5aF8sHt3Xi1s4BErwQ4gqpawDD6kosRgghhBBCXL96/XO05A1vQ58n2LH0U3zjf+b5sv9B6mEo/RScmgDg52rPyE72HEkrZP7OZAwmM9aWda98LtcbeWThAZq627P84d6sOJjOq78d469jWVIOUAcFZXoW7ErG18WO27sFag+azVCcBqej4eCPqHFrsVNhu2UE8/T3MH7C3QS0CLjk11YUhUndg5nUPZg1RzN58Mf9RM6M4qmhLXl0cAtmrj7BvG3axJJ7eoeQU1LJhpPZPDGkJXuS8nhr1XHis0uxsbJg1ZHTpOZX8MSQlrT2dSEi2INdCXm1vq7OYGLGooNEncxmWFsfbZKKEKLRkQCGEEIIIYS4shy9iLjjVVLynoLEhbDuFZjTE279CsKGVG/WPsAVvdHMqZxSWvu6nOOANS3el0ZWcSW/PtATV3trJnUPYv7OJD5YG0OXYDeaOEspybm8tmwfoTFzCbU4SsU2E4bSfJzMJVioWllPpZ03mz2n8Fp6BM4+zbiply83tPev93UMa+vD9IHNOZBcyKyoOIoqDMzblkiHAFdUVB4b3AIHGysMJjOOtlYk5Pgx9OMtfL8jEbMKLX2cmD2xM7d00MpZeoV58r81MXy0NoYnhrZkw8lsDqUWcltEIO//FcPa41nc37cZDw0Iq/f3IoSoH5e9hERRlKeB9wFvVVVzz7WtlJAIIYQQQlyHsk/AkqmQFwd3r4LASADis0sZ8tFmHugXyvM3tT5r+UdOSSVGs5lVhzM4drqYLbE5BHs6sOzhM6UnUSeymLZgP852Vmx+eiCuDtZX5K1dVVSVyuOryfj1SUKUTPaprck0u1GkOlKqODF6UE9WZbgw87ATRqy4sZ0vX07petmXVaIzMHHuLo6mFxPZzIMf7o3Eztqy1m03x+bg6WiDj4sdbg7WNTJ3yiqN/N+Koyw/mM7MMR34YnM8qfkV1c8/e2MrHpbghRANolH0wFAUJRCYB7QGukoAQwghhBBC1Ko8H+YOAn0p3L8B3IJQVZVHFh1k1eEM3hzdnm4h7syOimNqn1Da+DnjYGOF3mhm6MebKdUZyS/X42JnTSsfZ14Z0Zb2ATXHd+5OyGP817t459YOTKwa5Xo9KyzX89PuFO7s5ETe/uWY93xDqCGOBLMv5cPeJ9mlGzFZJfRv6c198/diZ21JRpGOADd70gsrmDmmQ3W/icutRGdgxcF0RncOwNnu4oNPZrPKXd/tYcepPExmlaeHtaSk0kiolyPju8k5IURDaSwBjCXAm8BKIEICGEIIIYQQ4qxyYmHeELB3g0mLwbsVqqoy4etdnMopxdHWiuS8cgAsLRRuau9LeKAbb606AYCNpQXbnhtIE5faS0RUVWXIR5txd7Bh8YM9z9nQM79Mj4ejTf2/x4u09lgmm6syS+7oHoyT7bkrwc1mlQW7kskpqeSJoS1JyiujoEzPuuNZDG9hTxvrDBYtXUpk0V+0skjDAjOnzH58aRrBDochbH5+KFb/yF5YcTCdx3+Jpq2fC8se7sW641nc0M4XG6u69yZpLLJLdNw0ayslOiP7Xh6CyyUERIQQ9aPBAxiKoowEBquq+piiKEmcJYChKMo0YBpAUFBQ1+Tk5MuyHiGEEEIIcRVI2weLJoBRD+N/gNABRKcWMu6LHTjYWPLBbZ3IL9NzPKOYH3YmoyjQt4U3LZo44e5gzSODWpzz8N9sS+TNP44ztktT7KwtMKtqjTGtJrPKyyuPsnB3CnPvjGBoW5/L/IbP76N1scyOisPZzooSnZGbO/jx+aQu59znf2tOMmfTKQAmtoTglKW0M8XQwiIdX6WgertjFq1YW9medeau9OkzkCeHtcKsqjjY1AyQqKrK4v1p9Az1JNDDof7f5BV2OK2Q9IIKbupwceNehRD164pMIVEUZT1QWyvnl4AXgWHnO4aqql8DX4OWgXEp6xFCCCGEEFe5phFaCcnC8fDjWLhhJuGR0zjy2g3YWllUj7VUVZXkvHIOJBfwzq0dCHCzr9Ph7+0dQonOwKz1cdWPjQoPoEeoJwAfr4tl4e4UAFYfyWBoWx+yinWsO57FpO5BV3QMq9FkZtnBdD7dEMetXQJ4b2xH3vvzJN/vSCKvtBJPJ9ta98srreS77Uk82KqCsbolNEv+CwWVIo+2pFn35LsMV+LUAAb06UfPrl34/sudlFYa+SQi8Ky9JRRF4faIwMv5dq+ojk3d6NjUraGXIYS4QJclA0NRlA5AFFBe9VBT4DQQqapq5tn2kxISIYQQQggBgK4Ylt0PsWvALxz6PAFtRoDFmQvsSqOJ4goj3s61X8ify5qjGaQVVDBvayJGs5nJPYLp1dyL8V/vZFyXpuhNZrbG5bLj+UE8vfgQfxzOYOlDvega7F6f7/Kcnl58iCX702jj58LSh3riYGNFTGYJN8zawiu3tOXePs1q3e+bv/bite0VRlnuABsnTgWNI6vNPfTqGo7eaOaJX6PpE+ZV3QfEaDKTW6rH11WmswghGkaDl5D8azFJSA8MIYQQQghxIcxmiP4Jtn0E+Qng0Rx6Pwbhk8DykhKJq53IKOa1346xJykfBS3TYPtzg9idmMdjP0fX2HZKj2DeHN2+Xl73fKJOZDF1/j4e6B/KM8Na1ehHMeLTbRhMZjoHuTO2SwARIR7aE6oKR5dSvPxJ7M1lWPd7Eno+DPZXLugihBAXQwIYQgghhBDi2mA2wYnfYdvHkBENXq2g+SAI6AJ2rlCWA9b2YO0IbkHg3apGpkZd/B0wGNrWh7l3RqAzmPhqcwIF5XqOnS7CztqSI+lFbH12IDZWFthaXdjxzyW7WMfYL3cwJjyAcV0DWbI/lSX707CzsuCve5thnXsS8uKhMAUcvVls6ssza/MA8HGxZd6d3ciN30vvtHnYxP/JYbU5W9q8xiMTRtbbGoUQ4nJqVAGMupIAhhBCCCGEOCtVheMrYfeXcDoajBW1b+fkCyG9oUlb8Gmv/bet83kP/8fh03QMcCPI879NKqNTCxkzZztOtlZ4Otrwx4y+550EUldztyTw9mptkoqlYqYT8dxouZc7nKNxqkg/s6GNM+hLUW0cebFiMni1xDt3N8OVHbS2SKVCtSG+3QxGH+jErIkRjOjkXy/rE0KIy00CGEIIIYQQ4tplMkLOSagsARd/MFSAvgxyYyFmtRbgKNKacWJlB50mQs9HwCvsol/y1ZVHWXYwndJKI3f2COb1UZdeTmI0mRnx2Xa8lSJed/8Lt6TVuJtyMSlWKM0HYtHqRvDpAF4ttFKQgiRYOR2St1cfI9stnOKwUdy1L5hcowN6k5ldLwzG5yzjZIUQorGRAIYQQgghhLi+6Yoh4xAc+RUO/QKmSnANAvdgaD4QWo8A75Z1PpyqquhNZl5deYzlB9PZ89IQXO2t/7NNXSeVbDyZzZurjtMybyOznH7AzlgCLW+AtqO0P+1ca9/RbIbjy8HCGoJ6gpM3AN9uS+TNVcd59Za23N279gafQgjRGEkAQwghhBBCiL+VZsORxXD6IOTEQOZh7fGgXhBxD7QZCdZ1y1g4nFbIyM+289bo9kzuEQyA3mjm+WWH+eNQBp/d0Zlh7Xxr31lVobKEnKMb+GnF7/SwTaSHaT+qXyeU0V+CT9tLepsFZXrcHW0u6RhCCHGlSQBDCCGEEEKIsynO0DIz9n+vTTixc9P6ZVjZag1Bg3qCZ3Mt8FGUBgWJUJYL7iGoHqE8t8OCTRXN+eKu7nQN9uDzjfEsWruVARaHGOSQwMA2fijerSCkr9ZYNGkrnNqg/ZRkVC/D5OSPZbd7tDGxltZnX68QQlzDJIAhhBBCCCHE+ZjNWnAheqEWqDDqoKIA8k+d2UaxAJcAcPSCgmSoyK9+qgRHiu0DMJYXEqxkA3Ba9cDT0Qbb8syar2XvDqEDiLFozlv7rejaZziPD+90Bd6kEEI0bnUNYNRP62QhhBBCCCGuRhYWENpf+/mnonQoydSCFi7+NbMjyvMhaRuxR3az60gMIaWZeHm2Rdf1MZQWQxnw2SkmtwnhlUE+kLhZC4yE9Aa/cNKKKrntk60083fk4WEdrux7FUKIq5wEMIQQQgghhPg31wDtpzYOHtB2JM1bj+D5vB208XPhrdHtq5t3RoYUsi0+B0a0hfa3ArDiYDrfLd9JQk4ZKvDpxC7YWFlcoTcjhBDXBvnUFEIIIYQQ4iJYWigsfagXb4/pUGPySJ8WXsRmlXLf/L0UlOmpNJp4e/UJ8sr03NzRjx/v606Qp0MDrlwIIa5OkoEhhBBCCCHERaptZOotHf1YdzyLzbE5jP1iB0azSk5JJQumRtK3hXcDrFIIIa4NkoEhhBBCCCFEPWrq7sDSh3rxxqj25JXpaeblyMTIIPqEeTX00oQQ4qomGRhCCCGEEEJcBhMjg5gYGdTQyxBCiGuGZGAIIYQQQgghhBCi0ZMAhhBCCCGEEEIIIRo9CWAIIYQQQgghhBCi0ZMAhhBCCCGEEEIIIRo9RVXVhl5DNUVRcoDkhl7HRfICcht6EUJcAXKui+uFnOvieiHnurgeyHkurhdX67kerKrqeedMN6oAxtVMUZR9qqpGNPQ6hLjc5FwX1ws518X1Qs51cT2Q81xcL671c11KSIQQQgghhBBCCNHoSQBDCCGEEEIIIYQQjZ4EMOrP1w29ACGuEDnXxfVCznVxvZBzXVwP5DwX14tr+lyXHhhCCCGEEEIIIYRo9CQDQwghhBBCCCGEEI2eBDCEEEIIIYQQQgjR6EkA4xIpinKjoigxiqLEK4ryfEOvR4hLoShKoKIoGxVFOaEoyjFFUR6retxDUZR1iqLEVf3pXvW4oijK7Krz/7CiKF0a9h0IcWEURbFUFOWgoih/VP3eTFGU3VXn+i+KothUPW5b9Xt81fMhDbluIS6EoihuiqIsURTlZNXne0/5XBfXIkVRnqj6/nJUUZRFiqLYyee6uBYoivKtoijZiqIc/cdjF/w5rijKXVXbxymKcldDvJdLJQGMS6AoiiXwOXAT0BaYqChK24ZdlRCXxAg8papqG6AHML3qnH4eiFJVtQUQVfU7aOd+i6qfacAXV37JQlySx4AT//j9PeDjqnO9AJha9fhUoEBV1TDg46rthLhafAKsUVW1NdAJ7ZyXz3VxTVEUJQCYAUSoqtoesAQmIJ/r4trwPXDjvx67oM9xRVE8gFeB7kAk8OrfQY+riQQwLk0kEK+qaoKqqnrgZ2BUA69JiIumqmqGqqoHqv67BO1LbgDaeT2/arP5wOj/Z+++w6OqtgYO//akk5AESIAUIPSaEHov0hVEQRHBhoBiL6joxXJRL17x0yuiCFbAAqJIFUGk906oCSSBNJKQ3vvM/v44QwiQUAMJuN7n4cmcM/vss87MZMis2Xtt6+17gB+0YSfgrpTyuslhC3FNlFK+wGDgW+u2AvoAi6xNLnytn/0dWAT0tbYXolJTSrkCPYHvALTWBVrrNOR9XdyebAEnpZQtUAWIQ97XxW1Aa70ZSLlg99W+jw8E/tZap2itU4G/uTgpUulJAuP6+ADRJbZjrPuEuOVZh1K2AXYBtbTWcWAkOYCa1mbyOyBuZdOBSYDFul0DSNNaF1m3S76ei1/r1vvTre2FqOwaAInAHOt0qW+VUs7I+7q4zWitTwMfA1EYiYt0YB/yvi5uX1f7Pn5bvL9LAuP6lJallXVpxS1PKeUC/A68pLXOuFTTUvbJ74Co9JRSQ4AErfW+krtLaaqv4D4hKjNboC0wS2vdBsjm3DDj0shrXdySrEPh7wHqA96AM8ZQ+gvJ+7q43ZX12r4tXvOSwLg+MUCdEtu+QGwFxSJEuVBK2WEkL37WWi+27j5zdgix9WeCdb/8DohbVTdgqFIqAmP6Xx+MERnu1qHHcP7rufi1br3fjYuHcgpRGcUAMVrrXdbtRRgJDXlfF7ebfsAprXWi1roQWAx0Rd7Xxe3rat/Hb4v3d0lgXJ89QGNrdWN7jEJByys4JiGumXXu53dAsNb6fyXuWg6crVT8GLCsxP5HrdWOOwPpZ4eyCVGZaa3/pbX21Vr7Ybx3r9daPwRsAO63NrvwtX72d+B+a/tb7lsL8c+jtY4HopVSTa27+gLHkPd1cfuJAjorpapY/545+1qX93Vxu7ra9/G/gAFKqWrWEUsDrPtuKUp+T6+PUuoujG/tbIDvtdZTKzgkIa6ZUqo7sAU4zLm6AJMx6mD8CtTF+ANhhNY6xfoHwhcYBYBygMe11ntveuBCXAelVG/gVa31EKVUA4wRGdWBA8DDWut8pZQj8CNGXZgU4EGt9cmKilmIq6GUCsQoVmsPnAQex/gSS97XxW1FKfUuMBJjVbUDwHiMOf7yvi5uaUqpBUBvwAM4g7GayFKu8n1cKTUW4297gKla6zk38zrKgyQwhBBCCCGEEEIIUenJFBIhhBBCCCGEEEJUepLAEEIIIYQQQgghRKUnCQwhhBBCCCGEEEJUepLAEEIIIYQQQgghRKUnCQwhhBBCCCGEEEJUepLAEEIIIYQQQgghRKUnCQwhhBBCCCGEEEJUepLAEEIIIYQQQgghRKUnCQwhhBBCCCGEEEJUepLAEEIIIYQQQgghRKUnCQwhhBBCCCGEEEJUepLAEEIIIYQQQgghRKUnCQwhhBDiKiilJiulvq3oOMqbUuqoUqp3RcdxpZRSTyulziilspRSNZRS3ZRSodbte5VSq5RSj11BP7fUdQshhBD/ZEprXdExCCGEEJWGUiqrxGYVIB8wW7cnaK1/vvlRiZKUUnZABtBZa33Qum8dsFxr/VkFxTQFaKS1frgizn81rAmbn7TWvhUdixBCCHE1bCs6ACGEEKIy0Vq7nL2tlIoAxmut11ZcRNdPKWWrtS6q6DjKUS3AEThaYl+9C7aFEEIIcZuRKSRCCCHEVVBKTVFK/WS97aeU0kqpx5VS0UqpVKXUU0qpDkqpQ0qpNKXUFxccP1YpFWxt+5dSql4Z5+mslIpXStmU2DdMKXXIerujUmqH9RxxSqkvlFL2JdpqpdSzSqlQIFQpNVMp9ckF51ihlHrJejtCKdWvxDX+qpT6QSmVaZ1m0b7EcW2VUges9/2mlFqolPrPJR6zJ6zXnKm3nqozAAAgAElEQVSUOqaUamvd31wptdF6DUeVUkNLHOOglPpYKRVlnSoyWynlpJRqAhy3NktTSq1XSoUDDYAV1ikkDtZ+x19BDCWv26SUekMpFa6USrY+BtUveK4fs8aUpJR603rfIGAyMNJ6/oNlPA6Xut651udopTXGXUqphmX0M08p9Yr1to81rmes242UUilKKVXGsc7AKsDbGmuWUsq7rOdOCCGEqEwkgSGEEEJcv05AY2AkMB14E+gHtAQeUEr1AlBK3YvxQXc44AlsARaU1qHWeieQDfQpsXs0MN962wy8DHgAXYC+wDMXdHOvNbYWwDxglFLKZI3Fw3pMqecHhgK/AO7AcuAL63H2wBJgLlDdevywMvpAKTUCmAI8Crha+01WxjSQFcAaoCbwPPCzUqqp9dBpQBMgEGgE+ADvaK1PYDyuAO5a6z5a64ZAFHC31tpFa51/JTGUEu4L1sesF+ANpAIzL2jTHWiK8di9o5RqrrVeDXwALLSev3Upj8PlrhdgFPAuUA0IA6aWEiPAJqC39XYv4KT1J0BPYIsuY46w1jobuBOItcbqorWOLeM8QgghRKUiCQwhhBDi+r2vtc7TWq/BSDos0FonaK1PYyQp2ljbTQD+q7UOtk7p+AAILGsUBkZyYBSAUqoqcJd1H1rrfVrrnVrrIq11BPAV5z7EnvVfrXWK1jpXa70bSMf44A3wILBRa32mjHNv1Vr/qbU2Az8CZz+Ud8aYgjpDa12otV4M7L7EYzMe+EhrvUcbwrTWkdZ+XIAPtdYFWuv1wB8YSRYFPAG8bI0/0/pYPXiJ81xKWTFcaALwptY6xpoEmQLcr5QqOeX2XevjeRA4yLnH5XLKvN4SbRZrrXdbXxs/YyRvSrMJ6GFNRvUEPgK6We/rZb1fCCGEuO1IAkMIIYS4fiWTALmlbJ+tq1EP+Mw6hSANSAEU4KOM1U3ODumfbW0/HxiulHLAGLWx/+wHb6VUE6XUH9ZpJhkYH/A9Logr+oLtecDZIpMPYyQmyhJf4nYO4Gj9IO8NnL7gG/4Lz1NSHSC8lP3eQLTW2lJiXyTGSAtPjAKq+0o8Vqut+69FWTFcqB6wpMQ5gzFGutQq0ebCx8WFK3Op672qvrXW4UAWRoKjB0YiJNY6mkMSGEIIIW5bksAQQgghbp5ojJVM3Ev8c9Jab9daf1BiSP9TAFrrYxgfcu/k/OkjALOAEKCx1toVY2rKhXUPLpxG8BNwj1KqNdAcWHoN1xCHkXApea46l2gfDZRWyyEWqHN2SotVXeA0kISR+GlZ4nFyK1lg9SqVFUNp7e684PlxtI6kuZzLLet2qeu9FpuA+wF7a3ybMKbIVAOCrjNWIYQQolKSBIYQQghx88wG/qWUagmglHKz1me4lPkYtRl6Ar+V2F8VYynRLKVUM+Dpy51cax0D7MEYefG71jr36i+BHRijEp5TStkqpe4BOl6i/bfAq0qpdsrQyDplZhfGdJtJSik7ZSzteTfwi3WUwjfAp0qpmlBcrHLgNcR7qRguNBuYevY+pZSn9fquxBnA74IERUllXu9VXck5m4DngM3W7Y0YdTW2Wqf9XC7WGkopt2s8txBCCFEhJIEhhBBC3CRa6yUYxSl/sU77OIIxuuJSFmAUbFyvtU4qsf9VjFEZmRgf9hdeYRjzAH8uPX2kTFrrAozpLOOANIypKH8A+WW0/w2jGOV8a6xLgerWfoZiXH8S8CXwqNY6xHro6xiFLHdaH6u1GMUzryXmUmMopelnGAVL1yilMoGdGEVQr8TZ5FKyUmp/KTFc7nqv1iaMJNbZBMZWjGk3m8s84lwsIRivq5PW6TKyCokQQohbgiqjSLUQQgghbkNKqZ4YU0n8LqjHcD197gJma63nlEd/QgghhBClkREYQgghxD+EdSnPF4Fvryd5oZTqpZSqbZ1C8hgQgFFkUwghhBDihpEEhhBCCPEPoJRqjjHlwwuYfp3dNcVYQjQdeAW4X2sdd519inJ0wao2Jf+tqujYhBBCiGslU0iEEEIIIYQQQghR6ckIDCGEEEIIIYQQQlR6thUdQEkeHh7az8+vosMQQgghhBBCCCHETbJv374krbXn5dpVqgSGn58fe/furegwhBBCCCGEEEIIcZMopSKvpJ1MIRFCCCGEEEIIIUSlJwkMIYQQQgghhBBCVHqSwBBCCCGEEEIIIUSlV6lqYAghhLixYlJzqOpox1tLjzCqYx26NvSo6JCEEEIIcZsqLCwkJiaGvLy8ig5FVBKOjo74+vpiZ2d3TcdLAkMIIf4h0nIKuPOzLdStXoWjsRmsOBjLqf/ehVKqokMTQgghxG0oJiaGqlWr4ufnJ39vCLTWJCcnExMTQ/369a+pD5lCIoQQ/xCzNoWTmVfE0diM4n2bTiRWYERCCCGEuJ3l5eVRo0YNSV4IAJRS1KhR47pG5EgCQwgh/gFmbQznq00n8XZzBMDH3QmTgn2RqRUcmRBCCCFuZ5K8ECVd7+tBEhhCCHGbKzRb+HJjGHc09WTps90wKejZxIN6NZwJS8iq6PCEEEIIIYS4IlIDQwghbnO7TqaQmVfEqI51qenqyPdjOtCstiuJmUckgSGEEEKI21ZycjJ9+/YFID4+HhsbGzw9PQHYvXs39vb2FRmeuAaSwBBCiNvc2uAzONqZ6NHY+A+7d9OaADSq6cKmEwkUmS3Y2siAPCGEEELcXmrUqEFQUBAAU6ZMwcXFhVdfffW8NlprtNaYTPK30K1AniUhhLjNHTmdTmtfd5zsbc7b36imC4VmTWRKDjtPJnPXZ1vIzCusoCiFEEIIIW6OsLAwWrVqxVNPPUXbtm2Jjo7G3d29+P5ffvmF8ePHA3DmzBmGDx9O+/bt6dixIzt37qyosAUyAkMIIW57cel5dKpf/aL9TWq5ALAsKJZvt5wkp8BMcFwmHUtpK4QQQghxPd5dcZRjJVZCKw8tvF35990tr+nYY8eOMWfOHGbPnk1RUVGZ7V544QUmTZpE586diYiIYMiQIRw5cuRaQxbXSRIYQghxGzNbNPEZeXi5O150n7+PG0MCvJixLrR4X1x6LnO3nWLejkh+Gt8JH3enmxmuEEIIIcRN0bBhQzp06HDZdmvXruX48ePF26mpqeTm5uLkJH8jVQRJYAhxG5AaBv8s6TmFONiZcLSzuWzbxMx8zBaNl9vF/8kqpZg+MhBXJzvm74oC4HRaLisOxnEqKZtnft7Psme7nXeM2aKZujKYhzrXpaGnS/lckBBCCCFue9c6UuJGcXZ2Lr5tMpnQWhdv5+XlFd/WWkvBz0pEPvEIcYs7nZaL/5Q1bD6RWLwvr9DMa78dpMdH61kfcua6zzF97QkW7omioMiCxaIvf4C4YcwWzdCZWxk3b895/9GWRmtNdGoOAN6ljMAAsLUx8cEwf0LeH4R7FTtOp+YSm5YLwMHoNBIz889rH5aQxffbTrHAmvAQQgghhLjVmUwmqlWrRmhoKBaLhSVLlhTf169fP2bOnFm8fbYoqKgYksAQ4ha3LvgMuYXm8xIYP+2M5Ld9MVgs8Pz8AxQUWa65/+C4DKavDeVfiw/T5K1VzNsRcf1Bl2L2pnDGzt1zQ/q+HlprIpKyKzqMYtvDk4hMzmFbWBJ/bd0JQfNh63TY8gmkxxiNLGYIWsC2zx7jz2/e4SGbtTSLWwZnjpXZr6OdDb7VnNh5Mpn03ELua+sLwAd/BrPxeEJxuxNnMgHYeSr5xl2kEEIIIcRNNm3aNAYNGkTfvn3x9fUt3j9z5ky2bdtGQEAALVq04JtvvqnAKIVMIRHiFrch2BhhcTAmrXjfsbgMvNwceefuFkz4cR8HolLp1KBG8f1mi8bGpC7bd0RSNu8sO4KzvQ2Na1UlKDqNQzHp5X8RwNIDpwmJzyQtpwD3KpVniN7fx87w5I/7WPJMV9rUrXZTz621Jq/QUrx6iCVyJ7krvuY3xxCaEoHrugsSK5s/hiYD4cxRSDpBe21HdzvrqiKbgM0m6PQU9H4DHN0uOp+PuxN/HTVeT6M61uH3/TEsOXCaJQdOc+q/d6GUItSawDgam0F6biFuTnY37PqFEEIIIcrLlClTim83atToopEUI0eOZOTIkRcd5+npyaJFi250eOIKyQgMISqh3AIzyw/GXnaKQMH++XwaOYxl9m/RJvYXLOs/gN8eZ0zoCywyv0j/NQOYaTedLd+9zpKF30FRPuk5hTSc/Cc/7Ii4ZN8RSdncN2s7x2IzeHtIC5Y+243Wvm4kZxeU34VapecUctz6wfhAdNplWt9cq4/GA7DqSPxNP/fsTSdp/s5q0rPzYOOHqDmD6Jm+nLpVYZdTL752fR6e2QmTY+GFIGg5DKL3oB1c+U+VN7jT+Rfa5s2mY95M9PP7od0Y2DkLPm4Kvz8BCcHnna+GiwMATnY2tPJxo5WPa/F9B62Jq9CELGxMCq1hW1jSTXsshBBCCCGEKJcEhlLqe6VUglLqSIl91ZVSfyulQq0/b+5Xl0LcwhbuieKFBQfK/jCfnQzLnsV++dOc0l7UdNJMNs1Dbfk/dOwBigrzSHNugMm3LW1tT/Gq3W8MC56I5dNW7Fn4ATaYmbc94pIxfPBnMEUWzfLnu/Ngx7oA1HR1JCEj75LHXYu9kSmczdU8PmcPAz/dzIqDseV+nqtlsWg2HTem5vx1NP6yCaXytnh/DKDJ/GU8bPwvS83d+dB/JbVe2c7KepP4obAP1GwO9s5QvT7c+yVMPMquvr/ybUoAE3o3oWtAU2r7+qFqNIQhn8KEzdDmITjxF3zVEw78VHy+Fl5GwmLa/QE42tkw9/GOrHqxB7YmxbRVIWw+kciBqDR6N/HEx92JLzeGcTIx66Y+JkIIIYQQ4p+rvEZgzAUGXbDvDWCd1roxsM66LYS4AvuijMTFzpMX1BnISoDlz8OnLdBBC9hU8xEe1u+S9tgmeuR/yu8Dd5IybhfD8/7Nrg6fwYi5ZEw4wIxOmxlT8BpJTvXpF/k/ltu/RXPziTLPX2i2sD08mcEBXuetNFHL1YH4G5DA2BGejJ3NuSktsem5zN4UXu7nuVqbQxNJzi6gS4MaRCbn8MX6sJt6/urO9oyz+RPf6BWsrT2eSZanmdA/AABvdyfi0/Mwl1JUdc62U1SrYse9bXz4fFQblj/X/dydXgEw+BN4YT/U6wbLnoXdxlzOkR3qsGXSHQxt7Q2Ah4sDzb1ceeaORhw5nc6j3+8mPiOPlt6uPNmzAUdOZ9Dnk00cvkHTioQQQgghhCipXGpgaK03K6X8Lth9D9DbensesBF4vTzOJ8TtSmvNkdMZ7ItIAWDXyRSe6W29syAb5twJqZHoNg/z8OE2bIvyoHdTT5rWdiXdwYe1oVksPWLM56vvaSwN1bR2VRoPDKDrgSSGZXahdcFG3nP4iRnZk4j84CsO1LqPw55DSM4x4+XuxIGoVJ7v05is/CJ6NPI4L77aro6k5RSSV2i+oiU8r/Sa14Uk0LlBDe5v50tEUg5FFgszN4SRnV+Es0PFlOrJKzQzZflR/GpU4dvH2vP674f45O8T3N/el6TMAuxsFc1qu553zIbjCbT2dae687XV8LiwNokp6QSTbH9lnW7PhKg+jO5Yr3g5VG93J4osmqSsfGq5GiuMZOcX8eveaP4+doanejW89HPk7AGjf4XfHoM/XwU7J+zaPEyd6lUuajqxfxOevaMhq4/Ek5VfxGB/L5zsbYhOyeHbrafYH5WKv+/FNTWEEEIIIYQoTzfyk0EtrXUcgNY6TilV8waeS4jbwoHoNIZ/uR2AKvY27I1IodBswc6kYPUbkBwGjy4juWYXtm1bC8AjnethMikCfN2L6zUANCoxcsJkUgxv68OXG8OJVZ3p2fdBYlZ9Sn+9j3ujp+Ef9SMzGM2s/DaAIqcgBKWgS8Ma58VX0/pBOTEzv9QPutciPDGLU0nZjO1en3sCfQAjEWDRRmHSrg09LtPDjfHbvhgiknOYN7Yjzg62jOtenz8OxfHCggPsiUjFw8Wecd0bYGOCJ3s2JD23kMfn7KGVjyt/PN/jqs8XnpjF/bO283L/JjzaxY+8tDN8kD+VQrsqzLR/Bpc8O17u36S4vY+7kcg4nZZLLVdHolNyeP33Q2wPT6aqgy2PdKl3+ZPa2sP9c2DBg8bInvxMo8inurjAq4OtTfHzc9abg5uz+MBpDp9OJyo5h7o1yuc1IYQQQgghRGkqvIinUupJpdRepdTexMTEyx8gxG3sRHxm8e2RHeqQXWAmKiUHtn0G+39ga+1HOebYli2hxu/KnDEd6Nu8FgAtrQUXG3g4882j7S9KMIzqWBelwN/HjbaN6/KFeRj3FLwPD86noacLn6mPCfKaxliHDUTHRNO7iedFq4Gc/ab/p52RZOUXlcs1bwgxrqW/9ToA2tYxSubsOZVKZl4hllKmSZyVnltIZHL5LnNaZLbw9eZwAuu407OxkUBp7uWKrUmxJyIVgKSsAmasC+X7rREAxbUgjpzOuKZzfr4ulNScQt5dcYyw6Fj0ggfxUins6zqLn1++l78n9jxvZIeXu/FcxKblEp6YRb//bWLnyWT+7/4ADrzTv3ikxmXZOcKD86HpXUaS7KfhcHo/JIVC0aULtiqlaOntyqJ9MfT8vw0kZeVf07ULIYQQQghxJW5kAuOMUsoLwPozobRGWuuvtdbttdbtPT09b2A4QlR+p5Kysbc1sWXSHQwJ8MKeQmzXvQNr/83fpm48EjGAu2Zs4eWFBwHw83AuPraltzGE/5k7GtG/Ra2L+q5TvQqv9G/CM70b0sDDmaGtvfn96a7QbDA8vQOGfo67KZd31DfscXiGGeb/GLURUk4V91HL1Vil4qvNJ5m5oXzqQYQlZOFZ1YHabsYHciwW3Gzy6OTnzhcbQvGfsobvt50675gNxxO487MtxKbl8sqvB7ln5jbyi8zlEg9ASHwm0Sm5PNa1Hso6GsHRzoamtasCcJd/bQByC83EZ+RZkwjnkihx6blXdb6krHyWH4xlsL8XgToE75964ZgQxIuFz+HWpBtO9jbUrOp43jHe1hEYz80/wNSVwRSYLax+qScj2tfB1uYq39rtq8ADP8JdH0P0bvjmDviiPUytDTPawM8PwOrJxuth5aswqxssGgdHl9Cs6rmkRUhc5iVOIoQQQghx802dOpWWLVsSEBBAYGAgu3btumHnioiIYP78+cXbc+fO5bnnnrvm/jZu3MiQIUOuO64PPvjgvO2uXbted59gxLd9+/Zy6etK3cgpJMuBx4APrT+X3cBzCXFbOJmUjV+NKtSpXgWXzJMss3+beiFRpLV4mKf2D0RfkHP0rXbuW/a7A7zwcXekbd2yF/x5rk/j4tszRrU5d4eNLbR9FNo8QkLoXrL2LaTBmTVGbQQbB7jjX9Dlebxcz51vezktoRmRnE296lUgLx2OLoGt0yH1FL/YV2WR9xhei+7C6iPxjO/RADBWBvlgZTChCVnc/fnW4mVdNx5PZGDL2uUS0yFrUcp2dauftz/A152jsRk807sRq4/Ec3ZgyL7I1PNW49gWlsz97Xyv+Hy7TqZg0fCqz2F8TkwlEy/+bjePv7baMK2MaRmujnYMb+vDhpAE1ock0L5eNZrUqnqVV1qCyQQdnzBGYkRsBW2BlHBj2lJSGJzaDEW5YFcFfDvAyQ1wZBGTUXS0a8Of5k4cj29Od+uIlVWH49genszwtj60ucRrUgghhBDiRtmxYwd//PEH+/fvx8HBgaSkJAoKLj3C9HqcTWCMHj36hp3jWnzwwQdMnjy5eLu8kg4bN27ExcWl3BIiV6K8llFdAOwAmiqlYpRS4zASF/2VUqFAf+u2EOISTiVl41fDGU6swX3+ndQ0pfGy6Q0C99+FGRtGd6pbvNQlgF2Jb9qVUrSrV714xMA1UYqaTTrQYNTH8OJBeH4/NBkAa6fArC64xW5i9sPtGNPVj4Mx6SRkXv+KJPFJqTzKCuOb/hUvGkuC9puC8g5kRPJs3umoCYpOIzOvEIBNJxIJTchiYMtaJGcX4OJgS7UqdszfFUWR2XLd8QAcPp2Om5MddaqfPw1jTFc/Xh/UjFY+bjT0dKGKvQ2Odia+23qKZUGx1Pdwpoq9DUdOX92qHEeOH+cjh++ov/EFTtg14W2P6ewpqo+bk91F03hK+t8DgXzyQGsABrUqn+QNbj7QeiQEjoI+b8GIufD0VpgcCxND4PUIeGw5vHICxv4F3V+mr1ssn9rPot6h6WCxYM7LJGzJf6i7dyr/nbek+LkTQgghhLiZ4uLi8PDwwMHBGEXs4eGBt7ex2pqfnx+TJ0+mS5cutG/fnv379zNw4EAaNmzI7NmzAaPY/GuvvUarVq3w9/dn4cKFl9z/xhtvsGXLFgIDA/n0008BiI2NZdCgQTRu3JhJkyYVx7ZmzRq6dOlC27ZtGTFiBFlZxpdhq1evplmzZnTv3p3FixeXel1ms5nXXnuNDh06EBAQwFdffVV8vT179iQwMJBWrVqxZcsW3njjDXJzcwkMDOShhx4CwMXFqJW3ceNGevXqxQMPPECTJk144403+Pnnn+nYsSP+/v6EhxurAq5YsYJOnTrRpk0b+vXrx5kzZ4iIiGD27Nl8+umnBAYGsmXLFhITE7nvvvvo0KEDHTp0YNu2beX0TJ6jtC57bvnN1r59e713796KDkOICmG2aJq/vYrZDbbSJ/pLqO3P2LyXWR9vvOHe0dSTOY93JC2ngMD3/gYg4sPBNz4wrSHkD1j3PiSHQrcXifLsxZ+/fUfX2hYC6taAonzoOQk8Gl22u4SMPB6fu4fU7ALmjGnP6S+H0scmCOr3hD7vgG97o4hkdjLM7Eih2cLYzCd55KHHGdCyNlOWH+WXPVEc+vdAcgvM5BWZWbQvhv/76zh3+dfmy4faXfclD/l8C+5O9vw0vlOZbb7dcpLErHyKzJqFe6LJyi+ilY8rdjYm7GxM/Dqhy/kHJJ6A4yshNQKUDfi0hWp+cHQpBXvmYoMZmy7P8HLSUPaezqZedWcy8wpZVnIJ1DLsjUghwNcde9sKKmukNRs/eoDeuWvIdqyNykujCnkUKTtyLHb80fpLRg8fVjGxCSGEEKLCBAcH07x5c2Nj1RsQf7h8T1DbH+4s+3vyrKwsunfvTk5ODv369WPkyJH06tULMBIYr7/+Ok8//TQvv/wy69atY9u2beTl5dGyZUsSEhL4/fffmT17NqtXryYpKYkOHTqwa9cutm/fXur+48eP8/HHH/PHH38AxhSS9957jwMHDuDg4EDTpk3ZunUrTk5ODB8+nFWrVuHs7My0adPIz89n0qRJNG7cmPXr19OoUSNGjhxJTk5OcX9nff311yQkJPDWW2+Rn59Pt27d+O2331i8eDF5eXm8+eabmM1mcnJyqFq1Ki4uLsUJEqB4e+PGjdx7770EBwdTvXp1GjRowPjx43n33Xf57LPPOHXqFNOnTyc1NRV3d3eUUnz77bcEBwfzySefMGXKFFxcXHj11VcBGD16NM888wzdu3cnKiqKgQMHEhwcfNHzct7rwkoptU9r3f5yT3nFrE8ohLhITGoOw1lHn+hvoeUwuOdL4mftAzJ4e0gLxnWvD4B7FXtGdaxz84blKwXN74aGfWDlK7B1OnX5lPF2tiQmulKYpbCzFMCx5TBwKnQYd8nuVhyK42isUegybOEbDLYJ4lDrtwgY9tr5DZ1rwNi/sP1lND/mf8j2vw6yIGkyfx1NpH296tjbmrC3NeGGHc/e0YicgiJmbggnOC6D5l6upZz5ymTlF3E8PrN4ykpZSt4/ulNd+n6yib7NapGYlc+Kg7Foixl15gjEBkHsftj/I2gzVKkB5kLY+x0A2mTHoqLuqO4vMWpgb+qtPcHSI0nkFljo1qhGWac/T3u/6pdvdCMpxaZm77BybyN6Z+8nWVfld3MPFk68l/zZ/RhxaDw0M0GLeyo2TiGEEEL8o7i4uLBv3z62bNnChg0bGDlyJB9++CFjxowBYOjQoQD4+/uTlZVF1apVqVq1Ko6OjqSlpbF161ZGjRqFjY0NtWrVolevXuzZs6fM/a6uF/8N2rdvX9zcjFp1LVq0IDIykrS0NI4dO0a3bt0AKCgooEuXLoSEhFC/fn0aNzamfT/88MN8/fXXF/W5Zs0aDh06xKJFiwBIT08nNDSUDh06MHbsWAoLC7n33nsJDAy87GPUoUMHvLy8AGjYsCEDBgwofkw2bNgAQExMDCNHjiQuLo6CggLq169fal9r167l2LFjxdsZGRlkZmZStep1THO+gCQwhKgkTh3bw9u2P5Ll3Q2X+74Hk4mW3q4ci8vg7gCv89r+d3jAzQ/Q3hmGzYZek+D0fnJqdWL0D+Gk5hSw9okmeKydCCsngqUIOk0otYuEzDz+OhJP01pVuc9mE4NT5jO/6A5atR9f+jk9GqEmbGb9V6/QM3E+DdfvYGPhGFp1eOiipk/0aMCcbRF8sT6MmQ+1JS49l+rO9jjY2lzVZS7ZH0OhWTOglEKopdKahum7CG05B9uIVFIys3nckoGeloXKt04lMdlCh/HQ81VwqQkWCw/89wca2qXi7NuKn4KL2NHDmDvYwNMFrY3CnvVqOF/ixJXL0Da+vH5yEPssA3mhT2OetDHh6OnFnHY/0XXnUzT6/QXC7VoT0NivokMVQgghREW4xEiJG8nGxobevXvTu3dv/P39mTdvXnEC4+zUEpPJVHz77HZRURFlzVa4mlkMJfu1sbEp7rd///4sWLDgvLZBQUFXNB1ca83nn3/OwIEDL7pv8+bNrFy5kkceeYTXXnuNRx999IrjK/k4nH0MAJ5//nkmTpzI0KFD2bhxI1OmTCm1L4vFwo4dO3ByusLV8K5BhS+jKkRld6klPMtNRhxtNj9JNlVwGPGVUVARmDK0JX+91JOaro6X6eAmqt4A/O/HtWYdZj3clrScQpaFa8RdvUMAACAASURBVBj9KzQbAqteh8OLLjpsQ0gCHaeuY3dECi967mV86mdsNbfkI5snaFDzEllZO0fsB77LPQXvk2Fy5yv76UwIGg7B5w+lc69iz4SeDVl5OI4/DsXS/3+b+XJD+FVf3k87o/D3cSOwjvvlG4euha97wU/DsUs4gnJ0xcbVixPah1ifO+He2fBCEEw6CXd9ZCQvADOK3ZmeLEhpwg9HixjRrg7VrEukdm5wbjSFXxkFPCujNnWrseblXqx/pTf3tvFhsDXpFtCkIW8UPoFjUTqRS9+t4CiFEEII8U9y/PhxQkNDi7eDgoKoV6/eFR/fs2dPFi5ciNlsJjExkc2bN9OxY8cy91etWpXMzMuvyta5c2e2bdtGWJixql9OTg4nTpygWbNmnDp1qrj2xIUJjrMGDhzIrFmzKCw06oydOHGC7OxsIiMjqVmzJk888QTjxo1j//79ANjZ2RW3vRbp6en4+PgAMG/evOL9F17vgAED+OKLL4q3g4KCrvmcZZEEhhCXEByXQYPJf7I9vHxW3DiP1pB+GsLXw0/3YV+Uwcce72NXrU5xE2cH2+KlOyujZrVdaentyoqDscZKJvd9B/W6wpKnjOuyWhZ0mmd+3k+z2lWZXn8Xd4W9i6luJ1q8uJTtbw7ExeHSg8G6NarBuBH3UuvVHeQM/hJ7F3dY+BCsfRfMRcXtnu7dkPoezvxr8WGy8ovYHJp4VdcTl57L8TOZ3BPoXXr2OzcVonZB8ApYNBZ+vg/yM2Ho50bR00eWYPvIbzxb+BKLfV41CmFWrw+Obud1E52SU3y70GIpnh4EULOqI23rGsmTOtVvnQRGWdrUdSdY12OxuQcDslZwPPQ4QLkueyuEEEIIUZqsrCwee+wxWrRoQUBAAMeOHStz9EBphg0bRkBAAK1bt6ZPnz589NFH1K5du8z9AQEB2Nra0rp16+IinqXx9PRk7ty5jBo1ioCAADp37kxISAiOjo58/fXXDB48mO7du5eZbBk/fjwtWrSgbdu2tGrVigkTJlBUVMTGjRsJDAykTZs2/P7777z44osAPPnkkwQEBBQX8bxaU6ZMYcSIEfTo0QMPD4/i/XfffTdLliwpLuI5Y8YM9u7dS0BAAC1atCguhlqepIinEJfwxfpQPl5zgoaezqyd2Ov6Vvgo6dhyWPeeURQT0FVq8HjGBJp2Hcq/7mp+mYMrl1kbw5m2OoQd/+pDbFouQSeiGBf2rLH8Zt93yPYMpPucOBr6evNd1xTclj4CTQbBAz8aSY9rYS406nHsnwc+7YyRDp5NAPhkzXE+X29ks21MikP/HoDzZRIkZ/15OI5nft7P0me7nRuBYTFDyEo4tBBC14DZuvSWUzUIfAj6vA1254+Q6fV/G2jh5cqsh0svKLrmaDxP/rgPgMH+Xsx8qO1596dkF7BgdxRP9WqIjamcXnMV6O9jZ/DhDA0X3sGZam1Z1HQ6s7ZG8suTnWlXr4LrdwghhBDihimtWKMQUsRTiBskJN4YEhWemE1oQhZNapXDaIiYfca3955N4c6PoHoDQuyasXH2Ie7zcbv88ZXM2UKT+yJT+XBVCDGpubR/fB6tNz8Jf03GGThgBwUZntgvTTGqRQ//5tqTFwA2djB0BjToZSQyvu0Ljy4Fn3b0b1GLz9eH4WBrIr/Iwr7IVHo28byibvdHpuJgazq3VG3EVqNi9pnD4FwT2o+DBr3BoSrU6VTmNbTwciU4LoPYtFy83S+eAxiaYFSB3vr6HXi4OFx0f3Vne5694/Irutwq+reoBdTiA/unmJz2BSN33k0rkx9JixvA2Cng5lvRIQohhBBCiFuATCER4hIOxqRR1zqM/2Ri9vV3GLYWfhwGVb1gzB9GscvG/TmeavwqlkuC5CZr7uWKg62JA1Fp2NsY1zFjRyqMWwsvHmKe34d8qkdj26Q/dH8JHvodHFzK5+St7oOnthqjIX4cDvGH8fdxo6W3KxN6NcTWpNh5MvmKu9sflYq/jxv2JmD9VJg7GPLS4P7vYWKwUXyq6SDw63bJBExzL1ciknPo+uF6ftgRUbx/9ZE4nv5pHx+vOY6PuxO+1argaHd1RUZvZaHe9/B4wWscs/jhXyWV3mlLsHzeHrbNMKZUCSGEEEIIcQmSwBCiDMlZ+USn5HJ3a6MYYVTKdSYwDi+Cn0eAex0jeeFUjcTMfAqKLIQmZGJjUtT3uHVWnTjLzsZEgK8b+yJTiUvPA2BbeBJFGr4+XMSH4fUJbTIe07BZ0PcdcLmy0RBXzM0XHlthrJLy4zBUyklWvtCDif2bEODrdsUJjNwCM0dOZ9C5jgP8+ghs/gjaPAzP7jYSJVcxYqRk3ZJ3VxwjLj0XrTXTVh9n1ZF4XBxsi4tc/pM0qunCBksb3nZ6E8cXdnG/7Qx2qwD4+23YN6eiwxNCCCHEDVCZShaIine9rwdJYAhRhg9XhaAUDPb3xs3JjqgShRevWn6msTqHTzsKx6wiz8WXnIIiBk3fzJg5uzken4VfjSrY296av5Jt6lYjKDqN3EIzbeq6k1do4amf9vHBnyF0a+TB20Na3NgAqtWDR5YaS7jO6gorXoKkMDo3qMGhmHRyCs4V+swpKGJ/VOpFXeyJSMHBnMWE8Gfh+J8waBoM/QLsr76QZs/GnjzVqyFzxnTAbNEERaWxPyqNU0nZfHR/AIenDGTyLVbrpDw0tq424+/rRjVne54d1odRmc8TWa0LrP4XZCVUcIRCCCGEKE+Ojo4kJydLEkMARvIiOTkZR8drX2FRamAIUYqIpGx+2xfDU70a0sLblXo1qhCZfB0JjB1fQk4SjP6VJ38JYV9kKq8ObEpydgHbw40RAoNa1i6n6G++fs1r8fXmkwDcHeDNgag01gYncHdrb2Y8GFh+xU8vxbMJPLEetk6HoPmwby5jffux1HI3eyJS6WWtg/HmkiMsCzrNrsn98Kx6rv7EtrBEPrP/Epf0UBi1EJoMuOZQnOxteOPOZuQVmo1CoqfTObI7iir2Ntzl/88beXFWo1rG1KHWvkatl0GtvLgrwIfxRx9gjf0u1I4voP97FRmiEEIIIcqRr68vMTExJCZe3cpw4vbl6OiIr++11z+TBIYQpTgamwHAEOsw/zrVq3D0dPq1dZaXDjtnQtPBaJ+2bDj+J2CM8AjwdcOvhjPLD8ZW6uVSL6eDX7Xi24Na1ea/q4IpNGvuLWs50hulegOjuGeft2D3N9TY+SUzHaOYs7clvZp4svtUCksOnAYgKDrNWlzSUBCyhj6m/dBv6nUlL0pytLOhcU0XZm001vL+73D/yy4Zeztr5e3GQ53qck+gT/G+4W18GHcojlS/wVTf8x10ewmqyMokQgghxO3Azs6O+vXrX76hEFfo1hyvLsQNFhKfgY1J0aim8Y1xvepViEnNpchsodBsOW9KwmXt+spIYvSaRHRKbvFue1sT0+4L4LMHA5n/RCee6NmgvC/jplFK8fP4ToxsXwcvN0caerrgYGuia0OPyx98I7jUhD5vogb/jzYcp1HwTMISMnln2RG83RyxMSmCoktMI8nP5JGMr0mx94aOT5ZrKHWsRWB7NPbgwQ51yrXvW429rYmpw/yLHxOAFt7Gii/bvB6Dgizj96WcRSZn3zpDV81FELMXdsyEjR9CysmKjkgIIYQQotL4534VKMQlBMdl0MDDuXiFCH/HBLoSxPH4Liw7GM+ao/FseLX35UcX5GUYH0Sa3AnegRwIMr79/35Me1p6u1HL1Zj/VWEf9MtRt0YedGtkXMejXfxIzsrHyb6CV9gIeIDs4+t54dgvPPeZLyHmzsx+uC0z1oURFJ1mtMlOpujXx6ir41jdfCZDbO3LNYRO9avz97EzTBrY7OaORrlF1HZ1pFoVO7Zn1eLupoNh12zo+pyxVG052HUymZFf7+T/7g9gRPtKnEA6cww2TIWTm6Ag89z+TdOMpXt9O0KXZ8HRtaIiFEIIIYSocJLAEMIqK98YVeHiYEtwXCZt61WDghz461/cuW8ud9rDyV83sbvwKSJS7DmTkU9tt0sUoNEaVr9hLMPZaxIA28KScLKzoWdjT2xtbt8BUKM71a3oEAxK4Tx8Brkp4fzvzFc81LcXXVp5sTk0iT+CYjBv+BCb7TMwmQt5tfBJ+jTsXe4hjOnqx53+Xvi4O5V737cDpRQtvF05FpsBw16Bb1bCnm+h+8vl0v+yg7EAHD6dXvkSGFobIyyOr4J17xor6QSMAL8eUK8baAvsmgUn1hiJjIML4JElxlQpSYYJIYQQ4h9IEhhCAHmFZu78bDMxqbmM7liX02m5jG1XDb7tCwnHoMtz/Bxi4b6Ub/ial3jR9CxHTre/dAJj5ywI+hl6vQ4+bdkRnsxv+2IY1bHubZ28qHRsHXB6eAF8cwdddj4Lpue4t1p9Blk+xGbTYWhxD3vqjmfx0kwevgFJBlsbkyQvLqOVtxtztkVw2rkdhe6d8dr4CQ6BDxlTga5DkdnCmqPxAMSm5V6m9U0WGwSLn4CkEwBYGvThlzpv0a9dS2q6lnhf6f+e8S9yB8x/AD5vCzUaQcBI8G4LdTrKqAwhhBBC/GPIpyghgF92RxGdkkuAjxs/74rCxcGWB80rjOTF6F9h4FR875zIPQXvk6GrMNfuIxKO7yi7w7B1sOZNaDYEer0BwNebw6nt6shbg/95y2dWOBdPGL3Q+LnmLTpufIhOphB+8JxI3IDZnNDGiBFfSTRUiAc71sWsNf0+2cS4M/dBYS5Zv78AFst19RuemE1SVgEAIfGZl2l9EyWegHlD0flZfGCawOdN5vCe2/tM/iueib8eLL1eR70uxio7A6aCo5sx3eTn++CjBrBv3s2/BiGEEEKICiAJDCGABbujaVvXnR/GdSKwjjvvDqqLc9C3RgKiyUAAejXxZNzwIcxrNos0kxsDj7wG2ckXd5ZyChY9Dp7NYdhXYDKRmVfItrBkBvt7UcVeBj5ViFot4amt8EIQjFrItKYLeSe6PQ9+s4uYtFzsbBQeLg6X70eUu/oezjzWxQ9nB1ueuf8uPmM0LqdWGdMmrkNogpG0uMu/NjGpucXTxCpUTooxksLWnr86z+PrnF58ccyJuTsiae7lytawJJ7+aT9Z+UWkZhew+kjcuWM9Ghv1QZ5YD29EwaPLjMTGylcgZt91hWW2aPZFplznxQkhhBBC3FiSwKggWmt+3xdzrpCgqDB5hWbCErPo2tADNyc7lj7bjfssa4yVQ7pPPK/tAx3q8P7o3vxU9z9UNafAwocht8RzWJgHvz1m3H7wZ3AwVjHZeDyRArOFga1q36zLEmWpXh+aDuLl4T0ZHOBFZHIOO0+m4OXmhMkkdQUqyttDmrN7cl/ua+dLfIuxLFd3wKYP4cjia+4z9EwWSsGdrYzlkEPiMsor3GtTVAALH0FnxBI14Ftm7M3Hyc6G/CILNZzt+XVCZ14b2JS/jsUzbVUIU/8M5qmf9rMnopTEgqObUdxzxDxw9TLed3KuPQHxy54o7pu1g/DErGvuQwghhBDiRpMERgWZvjaUV347yPML9ld0KP94YQlZmC2a5l7WeeSFubD9C2vl/3alHuPWqBMTC55GR++CafXg8/aw6SNY/jzEHTRGXlQ/t+b13ogUnO1taFu32o2/IHFFqjra8XK/xgAcjE6jTnWZPlKRlFLFCaTODTx4NXcMubU7wNKnIXr3NfUZlpBF3epV6NbIA5OCzScSyzPkq6M1rJwIkVv5ptpEei7IJjg+g08eaE2Pxh68Obg5VR3tePaORjzetT4/7oxk0b4YAGZtDOej1SE88cPe4u4SM/N5Z9kRpm1OYG/H6eisM7D4yWuedrPqsFErJCol5/qvVQghhBDiBpGx7BVk/q5IAGJSc0nNLqCac/ku3Siu3DHrt7LNvazLNh74CbIToMd3ZR7TyseN/1i6MLZfD9oWBkHkNmNOOkCPV6Dpnee1D0vMolFNF2zkG/5KpaGnS/HtRzrXq8BIREmdGlSnADv+aDaNEQfHwryhcP930GzwVfUTmpBJ45ouVDdl06GeG2uOnWHigKY3KOrL2DETDvwIPV9j9rZ2QAEzR7flLn8v7vL3Oq/ppEFNMVssbA5NomdjD+btiGR9SAIA0Sk5FJotjPpmJ6nZhZi1ZpZFs7DNa3QKngrbPjXeg65CWk4BO04a0+Hi0/PK5XKFEEIIIW4ESWDcbFqTveod1hZ+S5p7PZ5PH02b9+GrR9oxsKVML6gIwXEZONnZUK+GM5gLYdsM8O1gLGVYhhbexmiN7fkNaNvHqJFByiljacNqfhe1D0/IpmujGjcifHEdlFK81K8xcWl58vtXidStXgVvN0fWRGlGjPsb5o+EXx4yEhg9JoLPxSOjPllznISMfKbdHwBAodlCRFIm77gshWnfM8feg9eyRhOd0p461avc8GtISstg/bYduPk0o5/ajc2at9At7iG/++ukrFnDxP5NLkpcnOVoZ8O797QCjJVUolNzORCVSmpOIS8tDOJUUjYKWPpsN3yqOXHn9M38UNiXTi2PwfqpUK871O1U3N8POyKIS8/j9UHN0Fozdu4e/DycmXxXc+xsTKwNTsBsMQqHxkkCQwghhBCVmEwhuYnyc9IpWP4SzrtnsNvSHG99huUOb/Nv23n8Z+UxiszXV3FfXJsjp9Np5lXVGB1xeBGkR0GPV41kRBlcHe3wq1GFHSeTi//wp3r9UpMXmXmFxGfk0aimy0X3iYr3Ur8mTLs/AHWJ51vcXEopBrXyYtPxRNJN1WDMSuj6PETtgG/6wG+Pw4m/oODcdIe1wQksOXCavEIzAOERp5hp+oTup7+HlsOwqVaHmfYzCF/3/eUDMBdBQogxnexCuWnGKkOnyyiamRZN9rJXqTK9MQ/seYB+S1pjs2Q80S4BjIh/lLBEI2Y/D+creixsbUx891h7tr7eh4aezuyLTKVmVQcWTuhCC29X3Jzs6Fi/OrsjU9FDpoN7Hfh9nFHDBygosvC/v08we1M4p5KyOZmUzYbjiczZFsF//jgGwOoj8Xi7OVKzqgPx6ZVsuVkhhBBCiBJkBMbNErOX3B8ewr0gnr3eDzPh1J0cfbYbasO7PH5gDhkZzmzdBr279QQbeVpulpyCIoKi0xjbvT4U5cOWj6FWq+KVRy5laKAPM9aF8u/lR/jPvf5ltgtPzAagkackMIS4UvcEevP9tlP8eSSOUR3rwoD3oedrsG067JwNRxeDjQP4dUO71+OVlKNgKqToy/ehIIFm2YnUN9mS3OM9avR5AQdzIQf/ewddjr1H4ekeJDo3wbvksrlaw55v4dgyIzlRmAO2TtCgF7j6gL0zpEdDyJ9gzjeOca9njNoqzEHXakVMngO+iZtw1Jrl5q607X0P+QlhLA3O5Luk/uSTz/dbTwHQ4AoTGGAkdJwdbPl8VFuiUnLo17wmtjbnvn9o71edpUGxRGbbYbrjc+ouuQfWvgtD/sfG4wmk5RQC8PLCIGq5Givt9GlWk3k7IunbvBabQxMZ096TopNbqBeTBDl1oEr163wGhRBCCCHKn3xSvhnST8OCB8ktNDEu/9+YCzvRuKYZJ9dqcPcn6KJsXjz8K6xfjN7rjRr2FdTvWdFR3/YsFs3Ok8kUmjXdGnoYSzYmh8Ho3y45+uKsl/s1Jjwxi1WH43n/nlYXfYOfkl3A4v0xHIs1amw0lBEYQlyxAF83mtWuyhfrw7g30AcnextwdIW+70Cv1yFyO4T+DWF/o2P2Uke7YlY2JGhfXJq2Z+1pG74404olfcYav8+29mwL/D9q7R2NzfcjeCLnBZa8/wz2tiaj8OWqSbDnG6jlD20fhdr+EBsEJzcaRUQLso3zt30UWgw1ivWe3g/2VcDGntTDa1B5efysBjDHMpgWLVoyrG8bADocTyD2wGm2hSez+MBp4MpHYJTUwtu1ePpaSZ0bGMmGV347yL7ITLYFjsFn73do/xF8vw08XOx5vFt9vt96qnjlqy9Gt6Hj1HW8/vsh7tXreP3wj9iYrdNHPv7KmEbXfAh0eAJs7ckrNGNrUuclToQQQgghbjZJYNxo+Znw6yPowhweyZ9CmPaB6DTub+dr3G+yQd33DRtch7Jsw3aeTVtGwx/vw/TA3KsuWCeuzrS/Qvhq00kAOtqfgq2fQuDD0GTAFR2vlKJXY09WHoojLCGLxrWqFt+XlJXPsP9n7z6joyjfBoxfs7vpvZPeA2mEHnovIh1EaQooqNhfsfe/vWHBhgqIiAhKVXqREnpPQkJCEtJ7z6ZutrwfJoYSQBBCKM/vHM5JdmdnnskJm5177vLtXjJL5HTsu8Nb4eNw9RcsgnCnkiSJ/40M5b4fDvBj1BmeGhB49kmVCfj3w+DXl/qB73Iyp5yx3+5DqZBoZ2LLypHd+XxuFHYexucFFjuHt+GRff/Hj3zGGuM3qNpchHG3B2DL65CwDro/BYPePhvAbD/l0gs8J8hcW6+j877NDGjjjLpWi4dKwfPnNAvt19qZfq2d+WZHMp9sTgTA0uT6/fkNcLais48dh9NKAZhTfw+f2WylZvkMnMpGM2L4NCZ3D2B8Jw+6vr+dyZHemBurGBRgQdvEuUw32ozBux+LFaP5M6mOFV2zqEvagcnmV2Dvl+SaBbEnX4mxRwdGPfB/ciBHEARBEO4g62JyeHfdKbbN7nNd/4YLV0/89JvT4QWw5TWoryau17ckb7VtfKqth815m/bsP4xdNX6M3xfBJpu5tFo2GVrfDZEPy80kFcobvfrb3obYXAAe7emJ6fqZYOUKQ967qn1ENtz5PJBacl4AY8XRLDJLavhtZldCXK2xMTe6fgsXhDtEpJ8DA9o48/O+NB7u7Yep0fnvgz/tTePtdfG8PjwEkMsidiQUkFFcTUKemsf6+p+3fVsPGxJVQQyq+5g3jRYz9vDncPhzuRRl8LvQ7Ykm2VexWeWEuVsjSRIarZ7iqjpcbeTSky+3JbEpLo8wN2t0egNjO7hzV9jFG3MCPNbXH38nS5pjGNGMXn4cTjuKn6MFfyWU06PTG/SIfY2vjL/GsHMRHPfE2d6X+PvvR+VqCyk7+CDrIUxVxexxHE/PyfOo2ZPOkZMJlPSYToe/u9JXcZyF3imUxh2nr1SCU85O9D/vRDF9vZx5IgiCIAh3iF2JheRV1HLwTDEDgl0uuk1ueQ3vb0jg8X7+tGklgv3NRQQwmoNOCxufhyMLwX8A9H2ZzaesUUjJGCkV1Gn1hLmfH8AwUip4a2QoOxML+NDpY75ot0N+feJ6sPeHaevA2u2qlqHV6anV6kWU8AIGg4GUwkoyS2p4bVgwMwwroTABJv0OZrb/voNzeNmb42FnxsebErA3N2ZYW/niZc3xbNp72dLNX0weEYRr8VAvXyb9eJDVx7PlXhhAcWUdDpYmLGkYR/1OQzPKezt5sjU+n9fWnkSnNzAi4vz3TBOVkg5eduxL0fNs/WPYR06ir10xhIwCO29KqzSYGSsxUSmYuz0ZVxtTXlgZw3ODg7inoydPLD1GdFYZax/viYe9Gd/tSqa2Xs+phlHMF76vX0huTto8026GhLZi3ZM9cbY24fk/Yph90IDEHL7vVs5g1XFQ50HmIUwTNzS+xsjWhxfNXmHy6HtAqWp8vxr59R4Adurbs8J3Ki8cjWFCJw/Kjq3iu9wvYc2jcM8iUIhyEkEQBOHOEJstN8eOSiq6aABjZ2IBT/12nIpaLUHOlv8awMivqEWSwNnKtFnWezsTnz6uN60GVkyTgw89nobJf4BnZ3YmFtLBy45AF0uUCokQ14v/Uoe4WXMsr56ybi+ytOcm9GN+hMoCWDIOasrYGp/PzsSCK1rKR5sSGDhnl5hu0kCj1bMnqYgfdp9h4Ge7AejjWAG7PoGQ0VfUuPNCkiSxcFpn/BwteH5FNGlFVcTnVJCQp2Z0O/frfQqCcMfp5udAqJs186POoNcb2HW6kM7vbSMpX011na5xO0sTFT0DHAHYfbqQth42BJ2TFXXu/v5x2Kgj9HgK7LzRaPW0f2crTyw9TmpRFZ9vO80LK2MAmLP1NL0+/puYrHLMjVW8tCqG9TG51NbrmdbdBwA7cyPcz20K2gLC3G1wtjJl0fTOTOzihZ2FKZGD7oNhc2DCr/BsPExYCsO/gDE/oHx4Bx89M4O2HnLgtq2HLT0CHMgqrcHR0hiAr/5OQiHBc3e1Yb9JDza4PiY3Ov3zSbmBqSAIgiDc5mrrdSQVVAKwNT6/sZ/UP+q0Oh5dchQXazkYkXMFE72mLjxEl/e2s7EhI1y4ciKAcT3VVsDyKXDqLxjygVxLrVCSX1FLbHY5/YOd6RngRK9Axyap0P8IdbMho6SauduTeeWvZPZb9IcJS6AoCf1nweiXT+GpXw+RV157yWXsTynmw40JLNqXRl5FLXuSiyip0jTXWd8ylhxIZ8qCg4016K2dzQk4+JpcT3/Xh/95v0EuVsy7vyMqhcQzy0+waF8qpkYKRrW7uowZQRCakiSJmb38SCmsIiq5iB0JBegNsOJYFnkVtbw2LJiVs7rxy0NdMDNW8khvP3oFOvLWyNCL7u/Bnr788lAXPO3NyCip4Y21J3n29xNsic8DYNupfNKLz45ntTBW4mptyqQuXmyf3YdXhwUTk1XOhxsTCHKx5NnBQRgpJcLcbW6aUbySJPHB2HD2vdT//PI1pZHcW6nTdIi476KTRj4c25bXh4ew58X+AGSW1NDByw5HSxOCXCz5WT9cbqJ6YgmsfUKe3iIIgiAIt6kajY6XVsag0xsYFu5KYWUdE37Yj7r2bBA/IVdNbb2eZwcFEeFp29gD71LqtDoS8tQALD2U0azrvx2J2oLrJfsorHgQyjJh2GfQ+aHGp3YkyBkTA9q40LpV0zuC5wpt6DC/9JCcGr3meDY9xveFScuIWz+PIaVbyTP8wtc7vC86unNnYgHTfjp83mPTfjqMnk5bkwAAIABJREFUr6MFPQIc8HW05KGevtdyprestSfk7v9avYHP74tgdP0mpA1RMOJLsL503fqVcLUx490x4Tz123FOZJZxXydPbM2Nr8eyBeGONzS8FS+uVLD7dCEHU0sAmB8ljyMNd7eho/fZC/GX7w6+7L4sTFT0CnTCw9acDbG56PTyBfjOxEIAFBKczlc3bv/0wEAe7n22l4aLtSmfbTlNXkUtc8ZHYG1qxHujw/FyuPl6QlwqUH45nvbmjX8jrE1VVNRqeWWY/DP1d7Jka3w+9HsFFEaw411wawddZ13XdQuCIAjCzWJdTA5rTuQA8PrwEB7s6cO47/azNT6fsR3koQz/lJeEudvgYWfGyYbvLyW1qAoAc2MlJ7PLMRgMN81NkFuByMC4VloNrJwBPw6Qe19MWw+dH0Kvl/ssABzPKMPO3Iggl38fo9nd3xFfRwtq6/WYGSnZdDKPGo2OPKeejCt8iN0O9zJVsQnP0z9f9M7X9lMFWBgr+f7+jjzVPwAve/lDdWpRFUsOZPDOungMd8Ads/UxuZxp+PmD3IgvOqucYW1dGRjszFD3eqStb4BfP+gw9bocc2SEG19Pas/0Hj48OSDguuxTEAS5d0V7L1u2xueTkFeBQgKd3oCJSkHov/SduBQPOzN0egPTuvvQ2ccOI6XEvZ080BtgS3w+liYqPhoXzqRI7/NeZ6xS8MaIEB7p7ceAYGcA7u3sSVe/26/fzU/Tu/Dd5A508LID5ABGcZWGsmoN9H4OAofAtreg8HTLLlQQBEEQmklMVjlKhcSBlwfQysaUDl52uNua8Wd0TuM2sVnl2Jkb4WFnhqedOTllNY03SC7mdL58jTKmvTul1fXkXCazXmhKBDCulcoYtHXQ8xmYtQe8u6HR6pn60yEGzNnFppN5xGaXX3F6sbFKwRvDQ7A0UfG/UaGo67T8FZ3DvF0p6PUGfCfOIcmmO49U/4hhXg/Y9xVUnK2dOpxWQgdvO4aEtuLZwa1ZMLUT39/fEScrk8Zt0s5Jj74dncwu5/Glx5i5+AjHMkrJLqth6k+HcLYy4X8jQ5k/MRTT1dNAUsDIr5pMHbgWw9u68eaIUDzsbr67sYJwK+viY09GSTUGAzw/pA1uNqb8NK3zf25SPCnSi9mDgnhjeAi/zezKvpcGMKuvHHg8ml6Kr6MF93X2uuj+7w535eW7g2/7uyUdve0YGn42O83PSR4FnVJYJb9vjvwKjMxh9SOiH4YgCIJwW4rJLqezjx2tbOT+FpIkMSS0FftSiqnTyr24zr3W87Q3o15nIL/i0kGJ9Jx8pik381raVN5SLeJk1jk9NfQ6SNwI29+B8uyrWuvBM8Xc+/1+ymtu77/JooTkerh38XkXwTsTC4hKKgJgzpZEUouqmNna74p316+NM7FvDQZgQVQqX25PIr+ilpHt3PB0tOb3HvP4ce1XvM0RTLe8BlteR+fVnbgyIzoU++PTZmLjvgJdrAh0scLR0piMkmr+b3k0OxMLOJKmok+QEwl5arr6OWCsun1iWV/9nYSxSkFKYRVjv92Hq40pJVUaNj/TG8fqVFj+NORGw8RlYOvZ0ssVBOEKdPaVy0Q6edsxq68/sy4YkXq12nvZ0b4hs0CB/P7tbW+OvYUxJVUa3GxFV/AL+TvJWYTjvtvHLw91oVegCwz/HP6YCutny81BxWQSQRAE4Tah0cqTxv5p2P2PSD97Fu5NJTarnDau1iTkVfB4P/kmiGfDTcy04irc/mnubTDI1x45xzFkH2N69GosjdToJR+mqbaQv2EkJLYDEytI3ADqhpvTB76DjlNhwJtgdPnPJSezy5nw4wE87czJK6/FxszostvfykQA43q44C7cvpRiTI0UvDE8lFdWxwJynfbV7VLe59MDA3ns12MATO8u1yUHudrwgq4fA3o/xxCXSoj9HfWJtdiXF/G+0U44sABO2ICRBVg6g5kdHZVGdHSN4FfnDry3/hRavQE7cyNKq+t5bnAQT/QPvMYfws1BpzewM7GQSV286OBtx9t/xZNbXksXX3tapy+FjS/IdwzvWQit72rp5QqCcIW6+zvy/phwhkdcW7+ay1EoJN4dHcZjvx47+6FDaORhZ4azlQkF6jp+PZBBr0AnCB0NebMhag5UZMOAN8A1oqWXKgiCIAjX7K/oHDRafZPruM4+8k2VpYcy6OrngN5w9rFgV2vMjZU8uzya3x7uiq+NElbNkIc8AFUKK3bWh1DWdiZT7rmH3z5/loDKozhn7EeqLgafXjD0I3AOhahP4cC3kLGfNZ4vcbDGnffHhJ2XARqfU0GgiyW7ThdiMMCqx7rjaGnC7azZAxiSJN0FfAkogfkGg+G/j3u4RexLKaKzjz0Tu3iy7HAGMVnltPX4b3Xad4e7Mndie5ILKglv2Eegs3wXLDFPzZDQQOj3CnPKR/LLgTRWjbGifd0RJHUu1NdAZR7UlIFOA0lb+d3YigPmbcitM2ZezUhK8SC16PYpKUkvrqJOqyfEzZqREW74OVow6pu9POOdDhtfhNbDYORcsHBs6aUKgnAVlAqJSZFezX6cu8NdWToz8pKjru9kKqWCqBf78ebaOJYdzmTw57t4a2Qo3fu/DpatYPvb8H1vubdQ35fBK7KllywIgiAIjfR6AwrFlZV/phZV8dyKaCI8benXxvm85+wtjHG3NWPVsWxWHZPLPNp7ySPJnaxM+OPRbty/4BCfLlzCV6ovUVRkQ7/XeCzGj91FFkzu7s2LQ9qAJKHq/SzjV8Sw4oFudPK5YDrYmHny9LC/nmZ49kQqdf342/Vlvj1RTwcvWwJdrHhhRQxP9AvgZE45gc6WOJpdfQPvW43UnA0dJUlSAqeBQUAWcBiYaDAY4i+2fadOnQxHjhxptvXcCMWVdXR8dxsv3tWGWX39qdPqSMxT09bD9roeZ9jcKMqq62nvZcuwcFfm/p2Mg4UxS2Zc5gNj3knY/QkUp6AtTiFJ48hwzXu093Zkxazu13V9LWVjbC6zfj3Gn0/0aPyZF+dnYb+4H5KFI8z8G4zEnVVBEIT/alt8PjMWy3+rHSyM2fx/veW7PbXlcOQnOeW1uhgmLYOAgS28WkEQBEGA3w9n8r+/4tj0TG887f+9V936mFweX3qM9U/1JNSt6Y3orfH57Ews4NeD6YxTRDHn7lbgGAQOgWDnw7E9G/DfMQuVpSOJnd/hhWN2JBdUMntQEE8OOJv5XlmnpceHf2NpomJ6Dx8mdGnaf6uwIJcNc59kovJvajDlxfqZlEk2lGPBab0bNuam1Gh0vBiQwbTyefDA2luyTF6SpKMGg6HTv23X3BkYXYBkg8FwpmFRy4BRwEUDGLeD9BI5m6F1KzlLwkSlvO7BC4C3R4Vxz7x9ZMfUsC5GrpN6ZuC/lIG0CoN7fwZAH7OK4FXTme2wn4/TezI/6gxTu/tgpLz16pfrdXrqdXrMjVUk5KmRJAh0bhhXazDgsH22/MH6gTUieCEIgnCNegU5MrOXLyFu1vzf8mjWHM9mRi8/MLWRG1p3nAY/D4dlU+D+1eDdraWXLAiCINyhKuu0fP13MvN2pQCwOS5P/psFfLQpgaT8SuZPbXrNnFokTwrxcbC46H4HhbgwyNeYiTkfEFa4Hrad/3wHIBVXVvt8zvEUK5IL5P6Iw9qeXwpraaJiyUORPLrkKO+uPwXQuL5/HMqDN7XTcRv6PL5bH2Ke8ReNz9WrLNlb508RNoxLjZKv925zzR3AcAcyz/k+CzgvRUCSpIeBhwG8vJo/Pbi55TeMwXGxbt4GcB297fj9kW44W5mw4mgWUUlFDAu/8tpw4/AxcGwhD2X/yg9E8O76U7hYm2JhoqRfa+dbqrv+9J8OczyjlLi37yIxT42PgwVmxg3pU0cWwOlNcNdH4BLasgsVBEG4DZiolLw6LASABXtS+Ss65/wPW2a2MGU1/DQUlt4LU/8Et/YttFpBEAThTlWormPSjwdIKaxkYLALJzJL2XYqnxm9/FDX1rNobxo19ToS8ipo0+r80tEzRVW0sjbF4lLTzvLjYel9hFVkQe8XoPsTUJwMRUlQmg4Wjrx3wp+MLImquipMVAoe6eOPX0ND7HOFe9iw96X+DPl8d+P6/qHV6Vl+JBNzYyV9u3amIuwAVRk7KK+ux1ZRjVneESISdmNTfRJ9uwdQDv0AjC8edLldNHcA42JXwefVrBgMhh+AH0AuIWnm9TS7vIaROa2aOYABZ5vFzB7cmtmDW1/diyUJhn6E8fd9+MZoLtPqX+TNP+MoqdLw1cT2jIhwa4YVX3/FlXXsSZYjmjllNRzPLKWTd0P9mDofNr8mpzBHPtKCqxQEQbg9jYxw4/0NCWSX1eB+buNTSyc5hXXhXfDrvTBzO9je+jcpBEEQhFtDbb2OGT8fJqu0hiUPRdI9wJGPNyXw/e4zVNTW81d0DjX1OiQJXl19kmcGBsrNqRukFlXh63hBIECvh5xjEPM7HFkI5vbw0FbwaMjgcO8o/2vQoSqZbZsSAXhtWHCTzIoLDQxxZt6uM6w8mkV6STWTunix7HAGu08X8r+RoRgpFTjYWEL4CM6ubAp2I5DHrypu//4XAM1dL5AFnFuA4wHkNPMxW1ReRS3GSgX2FsYtvZR/5xKKNHIuPZRxfGn5MyVVdQC89WccpVWas9sZDJC8DYpTGh9KLaoi/K3NRGeWXbjXG2rF0azGr3+MOkN+RR2DQlzkB44uAm2NnH1xC2WUCIIg3Cr+KZFMLaxq+qSNO0z+A7R18PsDoNU03UYQBEEQmsEnmxOJzirniwnt6B4gN+/vEeCITm/geEYZa4/nEORiyaQuXhxNL+WzracBOePh400JHM8ow9fpnABG9jG5UfX8AXLwou198Oies8GLixjb3qPx6w7edv+65qFhruj0Bmb/Ec3c7UkM+WI3vx7MoE+QE1MvGOXaxB0SvIDmD2AcBgIlSfKVJMkYmAD82czHbFH55bU4W5vcOiUY7SZBnxe5W7udT1Tf08/PgvKaet5ZHw/VJbDzI/iuOywZBz+PlB8D1kXnoK7Vsi+luMkuD6eVsC7mxsSpNp7MI8TVGiOlxE970zBWKugf7Cx/UD6yUM6+cAy4IWsRBEG40/yTdZFTVnPxDZzbwKivIOe4PGpVEARBEJpZSZWGn/amMrGLF0NCWzU+3tbDBkmCLXF5HE4v4e5wV94bE86Url4kF1RiMBhYdTybb3fKN2297c3lIHzUHDmjsKYERn0DsxNh9Ddg6XypJQDQysaUxQ92YWCwM2EXaQR6oTB3G/a82I/Vj3Vn0zO90Gj1FKrrGNfR419feydp1hISg8GglSTpCWAz8hjVhQaDIa45j9mSDAYDeRW1uNo0f/nIddX3ZQ6llTE+/XuGl6UQ592LIzFVaFL2YFxXCt495JF4uz+FNbNgwm9sPZUPQFxOeZPdfbI5keSCSoa3bd4ylIKKWqKzynh2YBD2qcbsSS5iVDs3rE2NIHaFPEK2y1fNugZBEIQ7mYu1KZIEOeWXCGAAhIyCsHGw9wtoP1mUkgiCIAjNak9yEXoD3Nvp/At/K1MjWrtY8evBDEDOeAAIcLJEXavl250pzI86Q7i7DUNCXZjYKgfmTYCi09B6GIycCxaOV7WW3kFO9A5y+vcNG3jYmeNhJ09JeeXuNizcm8agYJerOubtrrl7YGAwGDYAG5r7OC2tXqcn8v3tlFRpGN72yptp3hQkCcfhb/DpqkCeMV5Dx6zVRKh0xNcHEf7IXyhcw+XtzOxg4wtsmv8qMVk9kSSIz604b1danZ6YrDJq6/WUVGmuaylNbnkN0xYeZmQ7N5QKiQ83JgAwINiFMR3cySuvpeM/6VmHfgR7PzHCTxAEoRkZqxQ4WpqwJ0n+sPh/AwORJInc8hq0OsPZUXUD/weJG2HFgzB1HRjdYoF+QRAE4ZYRdboQGzOji06CDHKxIiFPTa9AR4Jc5IaagS7y9MJPNicS5m7N3AFm+J58B3avBRtPmLwSAm/8NcX93Xy4v5vPDT/uza7ZAxh3AoPBQExWOSUNfSOsTI1aeEVXz8/JkucemQnMBIOBjdHZPLUsmkUVLvRpZeDRJUcpUofxsnlvBmbP48WQUEocOjB/TyrVGi3mxvKvUkKemtp6PQDJBZV08bW/bms8nFZKYr6aTzbLzXAiPG3p6GVHsKsVkiQ1RivJjYbMAzDkA1DcemNhBUEQbiVutmYcSS/lSHop4zt6YKJSMOrrvVRrdCx7uCth7jbyPPox8+ReGFFzoP+rV7z/Oq2Op387weP9Agj3+PcUXEEQBOHOZTAYiEoqomeAI0pF05L+qd19UCok/jcqtLHkP8BZDmRI6FkYsBfnPz4GI3Po/Tz0eAZMmk4OEVqOuLq7RlqdnuFf7eGBBQcbH3O4FRp4Xo4kMSTMFQcLY5YezODAmRI2x+WTV1HH9JIHKDdxZVbhe/RwkzAY4ETG2UaexzNKG79OKlBf12WlFFQiSfDd5A5M7OLJLw914Y0RIU37jRz8AYws5P4egiAIQrNyO6dsMqlAzbvrT6Gu1WJmrOS9hpn2gFxKEjoG9n8DFblXvP9TuWo2xeWxeH/a9Vu0IAiCcFtKKqgkr6KWXoEXL/Xo6G3H5/e1k0vOGzhbmeBAOYuMPsb54AcQPAKejob+r4ngxU1IZGBcI5VSgbeDOXE5FZgbK/nloUiCXa1aelnXzESl5J5OHsyPSqVAXYeDhTHbZ/ehRqPDpiwAFgyiZ+pcrExHs/xIZmN3373JxbhYm6Cu1ZKUX3ld13SmqAp3WzOGhrsyNPwSZTpVxRD7h1xnbdY0bUwQBEG4vsyMznY+P5FRxpb4PO7t5IkE/HE0C53ecPYuWP/XIXETLJ8sl5IYm//r/k81lCpuTyg4f1+CIAiCcIHdpwsB6HUVfSekkyvZa/UyRvoaGPo5dJwuJhjexEQGxnUwqYs3ANUaHR297RrLKW51Ezt7odMbOJFZxmP9AjA1UmJnYYzCvT10ewxVzFKeal3Oxtg8iivrqKit5+/EAoaGuRLgbElywXUOYBRW4u/0L1HQ44tBVwddHr6uxxYEQRAurl5vaPz6250p1NbrGRHhRlsPW6o1OlIKz/lb4OAP4+bL4+hWzYT6yzT/bJDQEMAoqdLQ7u0tpBdfZGSrIAiCIABRSUX4O1k0Tsm6rLIMOPg9rJqJqUsQyod3QqcHRfDiJicCGNdBd38HBgY789m9ES29lOvKx9GCQSEudPGxZ9qFs4d7Pw+Wrbi/5Cu0Oi2/H8lixZEsNFo9I9u5EeBsedUlJFml1ZzILLvoc3q9gTOFVfidO4/5Quo82Pc1+PYG5+CrOrYgCILw37w8tA1P9AugvZctWr0BT3szOnrZEeEp96uIvvB9PXg4DHkfEtbBVx2hOOW8p7/+O4n5UWcavz+VqybUzZr+bZxR12r5O6Gg2c9JEARBuPXo9QaOpZfSzd+h6ZMGA5SkNoz1/gzmdoAvwmHjC9AqHO5fDS4hN37RwlW7PVIFWphCITF/aueWXkaz+H5KRwzQNGXXxAoGv4vpqhm85HKY9zfJsbAuvva097Tl4JkSVh3LprymHhuzizc1PZpeyiurYvn90W7YmBnxf8tPcDitlLkT23N3WCtUyrPxtbyKWmrqdfhdKgNDr4fVj4CmCu7+9HqcuiAIgnAF3GzNeG5Ia7KX13A8o4wPx7ZFoZDwc7TE0kTF/KhU7C2MifC0Zcr8g8zq68+obo+Ba1u5qeeScTB9I1i7klZUxWdbT2NnbsyDPXyRJDiVV8Godm68Ozqcru9v53hGGdN7tPRZC4IgCDebrNIa1HVaQt1s5IBF5kE5wyJ5G6hMoeqcALhvH7nkPOgucAwC5a03hOFOJQIYwmUpLldrHH4PHFnI9PzFbLANJzIijP8bGIQkSQQ2dPNNLqg8O9r0AnuTi0jMV3M0vYT+bVyIz5HThJ/67ThRHT34ZPzZjJYzhXLKsL/jBRkYOi3s+Qzi/4T8WBgxF5xaX8MZC4IgCP/Fq8OCGd/Jg+7+ck8khULiucFBzN+TykM/H2ksLXxpZSxtPWzx9ekJk36HxaNg0TCYtp55uwrRG6C4SkN8bgWmRkrUtVrC3ORsjnaetpfM1BMEQRDubPG55SjQM+jMR3DwIBQngaktBI+US8y9uoKVq/yYd3dRKnKLEgEM4b+TJBg2B6MFg1lj8QG0/REamrkFuvwTwFBfMoCRViQHJV5cGYtWF02VRscLd7UmNqucLfH5fKQ3NAZQzhTJNdT+DYERNNWQsQ+iPof0PeAaAb2egw4PNOcZC4IgCJfgaGmCo6XJeY9N6+HL5K7evLgihlXHs4nwtCU5X82nmxP5ZnIH8OgEU1bBkrEY5vWkU1UErTx6szDLjaikImzN5Ttika0MoNfR3suWTXFy3yWHC44lCIIg3JkyS6qp0miJz1XzlGo1jgkrwb8/RD4iTyU0vkwJunDLEQEM4dq4hMCUFfD7VPhxALSfAt2ewMOxNSYqxWUnkZxpCGAUqusaH+viY4+jpQkbT+ZxpqiSAGd5osuZwiosjJU4VyXCX+9B+l7QVMozmkfPg3YTm/c8BUEQhP/ESKng/bHhWJiouK+zJ1vi8pj7dzJP56sJcrECr0iYto78DR8ypGoXVkXbecYUynbboVea0MMUvBbmgUdnenX/gg+AdTG5TL2wN5MgCIJwRxr9zV6KqzTM8MzhZdVqaDsBxn7f0ssSmolo4ilcO6+u8MRhOcoZsxx+7Iey8BR+TpYkF146gJHW0Enekmr6Ko4zRbmVcHUUHb3k8adH0krlDfU6KnKTeNpyO9L8QXLznfDxcrOdZ0+J4IUgCMJNztRIyTujwwhzt2FKN3ly17ZT+Wc3cGvPexYv0V+xAO2UNezxeYLNmgh21wVSbOEP3Z6AwtMEbxjHGNcSFuxJRXfO9JPbnf4OOldBEISrYTAYKK7SYEYt0wo+pNTEHYbNaellCc1IZGAI14epNQz9CLo/BT/0hV/H08f6FbaUuF9087JqDZpqNV+3+psB5aswM1TLT6z8CT+fnrxm6kTInu/hSCH64hQ+0zVkaQQMhDHfg4XjjTkvQRAE4bpytjKlTSsr9iQV8VjfAACqNVq2xeczur0XqoBwHC07MuWLKAC+u6sDhLtCu8lIS8bxsfolhlW9ztJDfpwprOSN4SFIt2kds15v4OVVsRxOK2HtEz2wMhVN5gRBEM6VXSaP435ctRYPqYiqe9aBySWa/gu3BRHAEK4vG3eY/Acsm8SLWY8TpO+FPssahUsIGJk2bpaXeIidJs/iXFYGIaOh8wxwCICEdUi7P2Ea+8lVu1BlH8qSHF/OGNzo2LEr944eCwqROCQIgnAr6xngyOL96dRodCgU8HdCATX1Oka0dQWgtYsVHb3tCHWzZmi4/BguITBjK4rv+/KV5ismbnCjRKPkkd7+tLIxvczRbl0/709j+ZFMAD7bepo3R4S27IIEQRBuMrFZ5VhRzSzTbWiDxmIR2KullyQ0MxHAEK4/t3Ywax/xy99kWOqvKOb3A0kpjyhyCQVze1xj1lONgoJ71+Eccs4bTZeZ0OlB5u88zYdbzjBQcmabtoDu/g7M7BkmgheCIAi3gUEhLszfk8qQL3aTX1GLhYkKd1szIv0cAJAkiZWzujd9oY0H0uh5tF46jme0i3mD6aQUVt62AYzlhzNp52lLmLs1i/alMTikFd38HVp6WYIgNLOyag1/Recwpav3bZthdr3EZpczSbUDpbYKej7d0ssRbgBxNSg0DzNbCru9Ss+6L0ju+w27XO6nxMQNsg5hiPmd+rpqvnd85fzgxT8UStr7OAOw7VQB07r7sHRmVwKcRTqYIAjC7SDSz4Gn+geQXVZDhIctZkZKfn6wM8rLje5uoAgayJ/mY3lAtZW7FQdILrh0r6VbWWKemoQ8NaPbufHy0GB8HSx47o9oqjXall6acAfYl1LE74czW3oZd6yFe1J5fW2cGBt9BQ6nFjPFZDd4dpVvogq3PZGBITQbT3tzCrFjWaUv89Ps6ORtx4pnunMkrYTx8/bzRc9Lv8lEeNo2fv3MwMAbsVxBEAThBnp2cGse6eOPhYkKg8FwVXcZjwY8iceJGD42+oEFGV3hJp9IUluvo65ej435lfWw0OkNvLs+HmOVgmFt3bAwUfHRPW0ZP28/X/+dzAt3tWnmFQt3slO5FTy46DC19XpC3KwJc7dp6SXdUQwGA+tjcwE4llFGey+7Fl7Rzatao6Uy6ySeRpkQLrIv7hQiA0NoNu62ZgDM35MKwJH0Uu5fcJDfDmagkKB/sPMlX2tqpOTtUaEsnRmJrbnxDVmvIAiCcGNZmMj3Ua42Rbp7azdeM3oercKYUQmziY6La47lXRc7EgsIf2szPT/+m9IqzRW9Zl1MDlFJRbw1IhQnKxMAOvvY06+1E5tO5jXncgWBRXvTMFIqsDU34vW1J6mqE1k/N9Lp/EpSCuVJfcfSS1t4Nf/OYDCQVVqNTm/gaHop86POcDit5IYc+1BqCUOlfRgkBYSMuiHHFFqeCGAIzcbUSIlrQ11yuLsNFsZKopKKWHU8m7Yetlj/Szf1B7r50N1fTBsRBEEQzjcktBUbXp/Az57v4mAow/H3EVRlxrbIWooq6yiurLvk89vi86nXGVDXavn1YPpFt9HrDRxNL0Gj1QOwJS4fZysTJnT2PG+7CE9bUourRBmJcM02x+VRdInf25M55bTztOXd0WFEZ5bxwsqYG7y6O9v62FwUEnT3d+BQWglJ+eqWXtJFabR6Fu1N5allJ+j50Q78X9nAuO/28e76U8xacgyDofnHP+9OyGW8cjd6375geekbo8LtRQQwhGb1yT0RPNrHnw/GhrP/lQFM7+EDyB3oBUEQBOFaDB46hs/cP8cYLWYL+8DqWVCRe942OxIKiM+paJbjl1fXc/eXUXQQzGpLAAAgAElEQVR6bxuL9qZedJuT2eV083Ogd5ATvx7MaPJ8tUbLuHn7GPfdfhbtS0Wj1bPrdCEDgp1RXNATJNjVGoMBEvJuzgsa4daQV17LI78cZcGepr+zGq2epPxKQtysGd7WjWndfdkal4+6tr4FVnrnMRgMrI/JoYuvPWPau1OormP4V3uo0ehaemlN7Ews4K2/4vkrOodJkV480S+AD8eG88zAQIoq68gqrWnW41fVack/th5XqQRlp+nNeizh5iJ6YAjNqmegIz0DzwYrHuntz/GMMkZEuLXgqgRBEITbQbCrNW/MnMB9nxrzgOEvhsf+ATHLwLc3uLYj0yqCmWuUaFExOdKLd0aFNQkKXK2K2noKKmrxc7TktbUnKa7S4GRpIjed7uF73rYarZ5TuWqm9/DB1tyY3acLqazTYtlQOlOt0fLq6pONjfq2xRcQ5mZDZZ2W/m1c5J1UFcPB7+DUXwyoreRNVSjJGd50EHXxwn90tKEsISaraYPI5IJKNDo9oW5y34uh4a1YuDeVXw6kM6OnH8Yqce+zOSUXyOUj07r7ML6TJwpJYvYf0cTllNPJx76ll3ee+Fw5MPzbzK509bNvLAWMzSrni21JnMgsw9PevNmO/1d0DoP1UdSb22PUemizHUe4+YgAhnBDtbIxZc3jPVp6GYIgCMJtQpIkurcP58ntpvhMegrvzLVYpayHtL146us5aGLFXttRvHiwP0NCW9E7yOmajvfs8hNsO1VAVz97Dpwp4fkhrckormbrqfwmzUhP56vR6PSEe5xtgphZUt2QSWFg3Hf7OZVbzpP9A9EbDMzbdYadMclMV22mT8rfkO8ARxdBZQH49UXpZM0DFX9y5kAJ9Nx2Tech3LmOpMv9CWKyytHrDecF9eJyygEIdbMGoIOXHY6WJny8KZHMkho+GBt+4xd8h0jKV3PgTDFA4/tUryD5JuCJzLKbLoCRkKvG19GiyWjnNq5WKBUSr6yOxdrMiD7X+J57KYdS8nlLGY0qeBQor6xBsnB7EGFUQRAEQRBuaQPauGAwwPBfcxl9qh88eQT17HR+9vmQE1IbRpYv4U/j10mLO3TJfbz1Z9xFx0YaDAbSiuSGennltWw7VQDIZRyzBwXxWF9/QtysKanSkF9xfk+BnYnythEetnjayXciy1IOweJR1Hzdg9GF3xFn8yyzjw7kwfwPeF7xKw9Hj+dN1c8YxyyFXR+BjSc8shseWIN072JW2D9MYOVhtKl7r8vPTpAzZR795Sg/7E5p6aVckdp6HQv2pF51aVShuo7F+9P4aW8aAOpaLWnFVedtcyyjFCtTFT4OFgAoFRI/PtARa1MVW+Pz0OvP9jWo1mhJLTr/9cJ/c6awksFf7OajTYnYWxjj1ZC54GxlirutGTsSCyhUX7rXTks4lVdBsKtVk8eNlApCXK1R12p59JejZBRXN8vx9RkHsaYKKUhkX9xpRABDEARBEIRbWpi7dePXKYVVzPj5MOHv7OTNBC9+8ngPHliLo7KKB6InwQdesGAIlJ3tR5FcoGbRvjR+OdC0yebW+Hz6frqTo+klvLgyBkmCXc/35fjrg3hyQCCSJDXerY7PLW98XW29jkX70ugT5ISnvTne5PCD0Ry6bRuHITeWololM5QbMLWyg5BR2Gdu4WHVemL0fvzY5id4JQdezYOZ28G1beN+nfo9RqHBmrKN75JZUk2d9uarjb+V1Ov0PL8imk1xeXy65XRLL+eKzFx8hHfWxfPFtitfb3lNPSO+2sMba+WJPf+U8l44LWJPchHd/BxQnpOV0d7LjrdGhlJUqSGuIWiy6lgW7d/eSr9Pd7L0YIZoLHuNtsbnY2zQ0LH+KEOdy5DOaYAZ4WnD3uRiRn+z97wAUlpRVYv1xqiq05JeXE1wK+uLPv/5fRF8M6kDSoXE51fxe3qlymvq6aDeiVYyBv9+133/ws1NlJAIgiAIgnBLkySJeVM68MuBdPYmF7PtVAE+DuakFVfj7WAOfpH8EPoLxjG/8nRbaxSxy2HhUHhgLTgGNDbXjMspP69HBcD+hpTuJ5YeJ6+ilrdHheHdcHf6H21c5Q/xsVkVjb0r/jiaRVGlhkf7+MPJVdj8+SRdFXo+q7+HXVbjyKw2ore/KV9M6QEKBdLwL1gXk8WTy+NYENEJJAmMzJqca58wb779cyxPFixiwmc/0KbLIN4aGdosP9c7wRtr41h7IgcACdDpDeddvN9saut17EuRfyczG5okphRWMvbbfXw9qT0qhYJIX/smvV7mbEmkQF3Lsoe7EuxqjaWJitN5ar7bmcLYDh6UVGmordeRWVLDw738mhy3d5ATkgTbTuVjZqzg2d+j6ebngM5g4JXVsby9Lo7FD0bSxffmKnO42SXkVfD8HzFU5CSyy+QdWkmlkAt8NBs8OoJvHx7vOZFTuWpSi6o4llGKjZkRX2xLYn1sLtO6+7TI//+T2XKwNsTt4gGMAGcrApyt2HAyl0Oplx6pWlxZh4OlyRUft06rY110Ls5mOkYr91DsPRQXk6ZZIMLtTWRgCIIgCIJwy7srzJVX7w4B5Gv/JTMimdnLlwd7yo0127YO5EvNSD6SHoSp60BbC4tHYqhTszE2D0dLE/QGOJFRRlWdlmeXnyC5oJJjGXKjw9zyWtp52nJ/V+8mx7Y0UdHWw4a/EwtYciCd5IJKftx9hnaetnTN/w1WTEdyDmG4/lPm6sYSXWigpErDhJ4hoGj4KKZUMaK9D7uf70f/NpceB6hUSJh2m0mRwZrHpBX8dijjpkstv1WUVGlYeTSLyZFefDo+gjqtvklJxc0mIU+NTm/Ay96clMJKdHoD86NSKa+pZ+biI0z88QAfbDzVuP2ivak8+/sJ1sfkMiLCja5+DtiYGaFUSLw4tDVpxdVMXXiIyPe38/wKeVxqj4tMinO0NCHS1541J7L5KzoXSYIvJ0SwMOwkR+1fY4xFHI/9euymywhKK6pCp2/+cZ7/hV5vYNrCwxQVF/Kj0RysVTretnqdnL5zIGwMqPNh25uEbhrPnw8FY6xSsD42lwd/Psyu04WA3MhS3wLnt/9MMZIEnbzPCVjVN5060sHLjuyyGvIraps8982OZCLf394YDLkSyw5lMvuPaPau+g5rqQaLbjP+0/qFW5sIYAiCIAiCcFsIcrHE1EhBe09bPOzMeXVYCP5OlgAMCW3FpEgvvt99hmej9Dymfw4qsinf9D55FbXM7OWLQoLVx7NZsCeVVcezWbQvlficsx+ue11mBPhoXwNO2dtJ/Osz3v5iLmUlhfwvMAVpy2sQPBKmrSdHJ08O8XW0IMLDhsiL3K32cjA/rxHoxYzrGsRC/Qh6K2MJ1SWwITb3stsLF7fyaBYanZ6p3X1o00q+i5uQe3OPqI1tuNgb094djVZPXE45q45lYWWiorZej4OFMT9GpTLm270M/TKKVcezWXUsm+IqDT38z//97dfamUhf+8aMjkOpJYyMcMOv4f/MhcZ39CS9uJovtycx1KMe53XTsNz6HA66Ij6ofYfna7/iZHLTMqyWUlRZx8DPdrHscNPxxTeDxHw1RRWVrHH8nkBVPiYTf+GN2c/h1ncGjPgSHtsHE5ZCQQJWf9zHkABzlh3KJLOkhteGBfPlhHYUV2nwe2VD42SZG0GvN7A/pZhQN2tszI1AWwd/TIf3WsmZbWl7Grdt72ULwPGM89eXWlTFl9uT0OoNzNt1Zb1nDAYDyw5nokTHBM0qcszbYBnU6/qdmHDLECUkgiAIgiDcFlRKBe9cpMQDQKGQeHloG1Yfky/owIs/jPsx7vg8eimsGRTSh7yK2sYGhwBLDsgXPhEeNkRnldPrYt30y7Nh5/tMP7GUB431jQ8bkJD2K8CjE4z9AVTG/PZwV1KLqhgc4oKE9K+BikuxtzBm1MNvoP91Aw/rN3C8/K7/tJ873arj2bT3siXIxYraeh1KhcSp3AqGtXVt6aVdUlx2ObbmRvRp7cSX25P4aW8adVo9cye2Z0tcPs8NCeKtP+PYHJd/wSsN9NPshKM6CBkFZnZIksSrw4J57NdjPDe4NYn5ap7oF3D2JQUJcHIF5MeDQcdI53BSrKswq85hVskmKFPAoLeh8wxqt3/IuANfo1k5AAa/Cr59wcFfTodqIalFVWgbLrYnRzbNnGpp+5Py+NjoB1yK9sOob1EG9G26UZthcO9iWD6Zj8yf5EN9XxYzhL6tnTE3UWJpoqKyTsufJ7Lp6N38o5VrNDoi399GRa2Wmb18IS8WVs+C/FhoNwXO7IBFwyBwCAx+h1C3AIxVChbuTSPM3QYPO3P0egMvrYzBRKVgeLgra05kU1qlwc7CGIBNJ/OQJDnofPBMMb5OFjhbmXIqV82p3Aq+8juCT04+6kEftujvl9ByRABDEARBEITbxvhOnpd8zsrUiJERbiw/kslTAwJ5c/v9tDNJ4ifjT1CetuCN4U/Sxcee+NwKajQ65u9JRaWQ+GZyB9bF5NLB65wLBIMB9nwuTwox6CFyFqu1kXQMC8NLn4WUeQjK0mDAW429LDr72NP5Oo1CbO3ZCjpMYeC+b9hfnA0EX5f93imSCyo5lVvBG8PlsiNTIyUhrtbsSykCWrfs4i7jZE454e42BDrLWRKrj2djZapiQBtnhoS2AuCbSR04mFrC5PkHkdDTRxHDkybrcdoqN/Bkw/PQ6UHo/zptPWyJeqFf02BawSlYOATqKsEhABQqjE5v5gUMoAKD/1C4+xOwlf+/mQ59hydOBfBMzdcErJ8t70NlCu4doessaDP8hl9sZpbI0y+O3cDshCumzqfH3gdprYyFfq9B+8mX3rb1XTBhKWa7PuHtyp/xs4ZWNsMA2P9yf2b8fKSx1K25pRRWUlGrRYGeR7RL4YfvwMwOJi6X11lfAwe/h6jP4Ke7MXn8IK8PD+H99acYMGcXw9q64m5rxsHUEj4cG46XgzmrjmcTnVVGd39HqjVa3t9wCq1OT2cfeybPP0g3fwd+eSiSHYkFdJYSGJ73LQQOwSpi9A05Z+HmIwIYgiAIgiDcMZ6/qzX92jjTO8iRuduTGF/3Or+5Lid46+tQXcTQ/m8wNNyV/IpadicV8t6YcDzszOVmnP+or4Wtb8Ch7+XykMHvItl5M6ZxA3/w69P8J9PpQVT7vqJtwRpgYPMf7zay5ng2ksR52RYDg134YvtpCtV1OFldurFgVmk1sVnl9Ax0xMrU6EYsF5AbGCbmqXmopx9WpkYMCnFha3w+wa7WqJRnq8JVSgXd/R0YbxnNI5pfCFDkUGvqDP3nyAGFIz/BwXmQuBFGfIHk2RWMzc8eqCgZlowDlRk8EgV2DdkLNaWgqQYjMyTzpoE458DODDv4FnGP+6DKOQKFiXB6EyyfAm7t5WwN397N/WNqlFki92TIKa8lp6wGN9umTXFvOL0eUrZTtWIWXrXl/BX4NiP6PP3vrwsaghQwEPVvDzIt6WdYq4dBb2Nlbk8XX3u+3ZlCVZ0WC5PmvbRLKawE4GCvaBwPfwVtJ8BdH8A/vw9GZtDzGQgcBD/0hdWPcv/EZQxo48yX25LYEJuLuk5LNz8H7uvsSWWdFkmSy5eeXxFDrUaHuk6eaPPlttNo9QaikorYkVBAQnw0P5nOQbLzgTHzzvYPEu44IoAhCIIgCMIdw9HShLvC5DvVHnZmZJWC60NLYecrsPdLOLMTPDrjYu7AlvGDwd1OvquYfQyKkyF1FyRthboKiJwFQ95vuQ/S9n6cNOtCH/V60H0Oyht3MX0rK66sY9G+NAYFu+Bibdr4+KAQFz7fdpoNsblM7e7T+Hh6cRXf/Z3A8z5ncNAVMTc5lN9PqunqZ8+yh7s1zyLrayE3Wg4AnNkJ1UVorPxZoCiiVVkP0H/A+2PCyS6tYeaFU0OqipC2vM4n2qUkSp5oR32PafhYUMkp+oxsDxETYO3j8EtD2M2js3zxWVUMBfFgYgXTN5wNXoB8p93s0mUKwa5W1GkhQ+WNX8eGyRiD3oZji2Df1/KxBrwJ3Z64If9nMkurkSQ5WepoemnLBzDy42D1o5AXQ7HeiUWeX/PKxPFX/nqFEquJC2G7D+ybCydXQY+n6OgxGZ3eQHRmGd0b+vSsOZ7N/pRiPhgb3mQizX/xy4F0vO3NOVNYRUfFaRyPfAZh98iBhItl1riEwtCPYN3/weaXcbv7Ez66py1PDghgflQqM3r5IkkSVqZG+Dla8O3Opn0wft6fjreDOSqFxPRFh1hq9ClGxsD9q84GTIQ7kghgCIIgCIJwR/r9kW5U1WmxtTSD4Z+DTy/Y/jacXAm15XJ5iJWrfOdZ29BF38JJ7iEQMQF8erbsCQDRrmMJO/MSxP4B7Sa19HJuCYv3p1Ot0fLCXeeXigS7WtHBy5YVGzYRFrUG76AIHIO6kbRjG48UbMGhoa/EK5I1xYqZ7EjtiLq2/qqyMPR6A5LExfufnN4Mx3+RL3RL08CgRy8pSTIOISigE9qMk7hLavwT58EWJU53vc+Gpy9oYpjyt9xQUVNJcYcnSfKcQev2Pk2P5d0dHt0Lsb9DWSakRYGuHmw85AkYEZPAxv2Kzwsg0EVuhJpUUHm2EahSBZ1nQPh4WPMYbH0dqgph8DtXte//IrOkmggPWxLz1BxNL2VEhFuzH/Mfheo69p8pZli4qzyWN/MwLBmLXmnCazxOuusgFkzrfV7mzBVRKGHQ/6DtffL7084P6OmxA2/VFDaezKN7gCObTubxzPITAIzt4E6kn8M1nUttvY531sXT1c8BF+M6vjb5BsnGQ37PvFxZUKcHoTgF9n8NXt0gbCweduZNxr46WZmQUljFxC5e/HEkE73BQJi7DSkFlTw7KIi+Qc7sWDaH7hnxFPT8CGdbr2s6H+HWJwIYgiAIgiDckZrckQ0bK/8DOYAR/6d8QWjtJqe+OwSAvd9N1Tiu3KM/x5IDaL/pZST//mDVqqWXdNPbnpBPJ297ApytzntckiQWDTHGZMmb1FYrsYo+CNHz6GtQcFIRwEzNZJ4c3RfV+idZYDyHedrhHE/vTO/WTcfe5lfU8tafcQxr68rwtvKF8zc7kvlmRzKOliZ8Pak9bS3VcmDMxgM2vgjHfpYDZp6REH4vOAcT+Vs9hTXmbOzZiyUH0vkzOpuYTluRDnwLoaPBs8vZg8b8IWdVOAbCuPk4OAcz/HI/CGNz6Djt2n+gDQIa+nIk5asb+3E0MrWB+5bId+T3zZXPMfiyq7tmWaU1dPG1x9RIwbGMG9cHI6+8lq4fbG/8fqS/kVxG8//t3Xd4VFX6wPHvmcwkIb2TnpAGhBYggoQOIk0MKiKgAjbWtoq7dhRxXRXX8sMCulZ0QYqCCCgIgiiChF5CxwAhhJAEQkhCSJk5vz/uEClBIEFSeD/Pk4fcO3funJvnzGHmvee8r4sPr/m/wczUMhbecg3OFoeqv0jDeBj8OWz5GvOcB1lqXsPUjX0p6TWRj5enEeDuxJGiUuZvPlTtAMaG9GOUltv4PbuQkbZ3CNBHYNB0cPa48JOvGwcHUmDuIxDUykjsepa/94jF3/0ALwyIJ6eghNzCEmY/kITGKBtN3n4GZk+C8CQCuo6q1rWI+kECGEIIIYQQZ3P2hDZ3Gj+1mJ+HC4+X3c+PZc+h5o2GodNqVYCltskuOEnqweM80buSRJ3HM/GYcyd4+PNB5CQ+X5PFI60t/GedjXdHdGLx52vxy/BmVsm/mBczn/szvuLXFWHQePw5p5qx5gALUrNYkJpFTIAbe7ILef2HnfSNcyf44EIcPh8DZfakmg5OYC2BTv+A7s+esRTI2/dncg4X8suuHFb+foSEMG9Ur3HG0pK5j8B9S+HkMVj+Jqz5GMKTYMjUGpli7+ZkJsSrAbuzCys/QCljWcGhjTDnAQhoWukX2urQWjN+4Q4a+bpyKL+YMB8Xgr2c+eDnNE6UluPiWPWvPlabNr5QX8BvabkVvy/YcohWv40nuOgIuwbM4cOv8rm3U6OKYE+1tRgEYe3ImfcSw3+fSe4bK7mprDXXe2fybsjzzNl4kBFJEecE6y7Fb2lGmd02x5fQw/Enfgq6l+6hiRf3ZAcLDPoMPugEX42EexaDxfmMQzrG+NHRvvRlwpAErFb9x7KX/AyYPgw0kPye5L0QAEgvEEIIIYSooxp6OJOmgznY5p+wawFsnlHTTarVft6ZA0C3xmeVxC0tgmlDoKQAhs0guXNbCpQb49Y50jwymJ5NGxLi1YCv12VQioWS3v9hqWM3OqW/Dz+MMZIzAtiskPIhfVcMZrPzKD6zvEZWyizW/DSXD9w/YdKhITxvnYhr6VFsPcZC8kRoeasxO+G6F87JY2K1aQDeWbKbvblF9G8RZOSnuOEtyNkOrwTBW02N4EWHh2HE3BrNDxDb0I1vN2bywreplR9gdoJbPzeWQswcbiQFvYx+2JrFf39O4+nZW7Bp6N8iiLYR3lhtms0Z+VU+78w1B0h4cRHZBSfPeWxnVgFjvtnCij1G4GJLxnGcLSaGtguneNtCIrIWMaH0JkZ8fxIfF0ce6Rlb5XZUyiucwDs/YknHLzlm8uZ28xL8TqTx/NFnSXLYxgNT1lf51D/tyObLlP0kO6zgNctHrLfFUNx+9CW2L8zIlZG1GebcD9by8x7q5mTG08X+HijMho96Gsupbv3ssge7RN1VrQCGUupWpdRWpZRNKZV41mPPKKX2KKV2KqV6V6+ZQgghhBDibAH2ahmrAgZD2LWw4EnjA7+o1LJdOQS4OxEfdNr096N7YdpQyNoCgz6Fhs2I9HPl5ZtaYHFQPNQjBoCEMC/KrEZAITrAgzUJr/A/6/XGGv95f4c9P8IXybDgCQrLTRwK6UVThwy6bRjNi3lP0cP2G6r5zfzQ/nO6lbzByqAR5MbeCskTORremzYvLeb7LYcqmqW1JvOY8YW5qNQKQN/m9qopcb2NtnZ/Dnq/Cg+tht4v13gi15taG3kzPv9tP+lHzhOc8I7g5ID/og9vxTr/H0aWzcvk7SV7CPcxEj/2axFI40D3ivLH66pYTjW3sITXFu6goKScuRszz3hsX24Rt7y/kqkp6fzf4l0ApB7MJz7Igzvb+vGq0+fkuUQyzZJMbmEJt7cP/8sq1/Ts1Z+YMWvg4XWoEfOwmGxMsr6EX24K+cVlVTrnhB9SeUp/xtuWiaTqSP5W+g86Nq7CMrXGfaHXS7D1G3gv0Qj6LRsPS/9t5GA5W9lJmH2fMbvorgUQ07NK7Rf1U3WXkKQCNwP/PX2nUioeGAI0A4KBH5VScVprazVfTwghhBBC2MUEuBHl78rbS9No0G4sndNvpXjSDRQN+JDolkk13bxapdxqY/muHPo0DzSSaJ48DsvfgFXvg8kMN0wwAgN2gxPDuKFlUMWyg74tAlm7/yjdGwfg6mSmZ3wQg34Zgc3JkxEbpsCGKeDsxZSAxxl/uB3Lh3XnqZnrKNz9Cx6c4ImHHiI6JACvtCPw8yru+CSF/i2DmDisDav3HuFoUSkPTl3P3lf7oZTi2IkyisusPNe/KS6OZmxa/3F3GqD5LVf6T3hByQkhtGvkQ8fxS5mxNp0nejep9Lj3DkRiKb+JRzdPg4hrL0sujoKTZezIOs7onnH0bxlEiD3HjZeLIzEBbqzYk0t8sAfd4vwrT6Jaie2HjnPzpJWUWm0EeTrz9boM7urYqGIpyZg5W3AwKW5pE8rsDRnGEqXMfO5u4UT8/IGgs2HwfHqv9+SrtQcY2v4vTkBpcgC/GCAG7l9B8aTuvJf/Dnv2DqRtfNzFnyf/INacXYw9+hRt1S7K2z3AsF86UI4ZzwZVDMB0fMSYRbHqfUj5L9jKQJmM6k/X3Gcsn3JyM2ZBTR8Ge38xZigFtaza64l6q1oBDK31dqg0k3IyMF1rXQLsVUrtAdoBv1Xn9YQQQgghxB8sDibG39ySoR+t4uEfikn2HsPY4vFEzurHptXDaHX3u8aXmkpYbZpZ6zLIOFbMqC5RuDnV79RoGw8c4/jJcro1DjBK4c55wKiI0WoY9HzeSNZ6ltNzJtzQMrgiISdA63BvQPFC4UCKAsJ4sE8Ce7w78tzbKTzSIxJvV0cah/jw7s7m3JYYRnSIkezz9PwHKWlH0Vqz8cAfyxs+Wp7GqC7RZOYXA0a53z6nZl7UAUGeDbiuaUMmr9jHkGvCCfNxOePx4lIrU1L2U6ZupbV1N52/fxIV1AqCW1frdbcczEdraBXmeU6Oibbh3sxYe4CVvx/hy3vbV5QbPdvDX66nR5MAbm4TChgVazSaBfe3ZvvBozz67T4e/2oTbw1uRW5hKSt/P8KjPWPpFd+QWeszeHfJHspKSxh5aDwUZsAdsyCyE08HlDG0XRhBnlewlKuzB8XJH+PxRU8Clj4GUdPOn3gzb79RAac4DzI3wMF1OABNcCKlzRu073cfo0w7uCaymsuTmvQ3fmw20FYoyDKqqayaBDu/g27PGL9npcJN/zWqPQlxlr/qf6oQYNVp2xn2fedQSo0CRgGEh0tZHCGEEEKIS9GukQ8z/9aBL1PSeaJ3T8y2wfz8yWh6ZEzFNqsY080fGeUszzJrXQZPztoMGNPkX7mpxZVu+hW11r6EoJN7FkwdDj7RMGwmhLSp0vkcTIrZDybx2IyNTC3tzIPxPZg2fxsWB8XwpEgARiZFEuzVgMGJYRXP83Vzqvg9t7CE/UdOsPFAHs2CPQjzduGV73dw+HgJ7RoZXxav6Jfey2TsgHj6TFjO6z/s5J2hZwYmfkvL5diJMl68sRmPzn2IX13H4TpjONyzCDwuLlBztKiUFXtyuaFlEAtSs9iUcQwP+9KMVqFefxxos0L+ARKCnDiVHeb5b1N5/oZ4I5B1muJSK/M3H+JI6o80Tc0kxNeDZpt2cZf7YeI+XU+ccsA3bhQjN3TgptYhZB4rRmvo3SyQJoHuRPq6MHvVDj6wvIff0Q3GEtWx+wMAABYZSURBVB/70gdPFwstXby40nyjEhhvGslTuZ/B6zEQ3h4iOsHxg8YMh5IC0DYoKUBrKyVmDxx9QjH1eomVxaGM/vEEnyUOAODJPpXPpqkSkwkwGfkxkt8zSkDPeQC++Rs4eRjJiOMkA4Go3AUDGEqpH4HKFjuN0Vp/e76nVbKv0gVuWusPgQ8BEhMTL98iOCGEEEKIq0TbCG/aRnjbt5w53OVVxn/rxtNbpxu5HULaQrtRENoWgDKrjbd/3MUD/lu4jUU4bEgnL7sJ3tHXQHACeEVAcR6phW7gF0dOQQmeLhYmr9jHja2CuS6+Yc1dbBXtOHScYE9nPH4eC46uxt1x9+pdR5twb25tG8obi3ZxpLCE2esz6BXfED97kMLXzYmh7c69QTcyKZLDx0+yIDWLlL1H2JKRz6C2oYwd0IyX5m/jk1/3Mm+TkW/hnHK/dUCotwtd4/zZeODYOY/tPmxUKRmYEML7ywJ4L2AcT2U9DlNuhpHfXVQS0pfmb+ObDQfxdnHkwalGkkoXRwcifF3wdjYZ5Y+3zILt86AknyHKRD/vEI6YfNh2zJlN/wuh1T9ex9vnj5kYGbn5jDV/wd3mhZT+7oA5zcaNNMDBEgJdnoDcXXTa9j6LG8xn0rRb2a1D6edZTJODOahNu5jsuAFXp634qALo/2atWOKjlGJL8GD+UdicCU33ULhzKW57XzGCBI26gFsAJ8rAydWdUTtasyTTkYHRwbTUXvzrx22A0+WrmPJnIpLgwRTI3maUFXY7tzSxEKdcMIChtb6uCufNAMJO2w4FMs9zrBBCCCGEuIwCPZ15xnojQ7q1IjJrMez4DjZPB48QjrlGku2ZwKiiXYwoWYzNJ5pljo0JyzqA1+HfULY/qgQ0B34lgY9L+7PCFg8o9qWm0LppCr6NEowSoH6xENW91pY4zCko4V/zt7FyTy5D/NKMO8+9X6l28OKUuIZGicpx87aRd6KM4R0iL/iccTc2w2bTJPxrEdNWH6Co1EpCuBcOJsULA+IJ8WrApyv28reuUfi5OV6Wdl5pjQPd+W7LIYpKypm7KZOO0X6E+7qwJ7sQPzcnPF0sJEX7MmOXjX8MmYp5+mDUtKEwcv4ZyUhLy208N2cLng0sPNwjFs8GFnZnFwAwesZGAFoFOtO+fDXDXNfB6yON5I+O7tD0BghrjyrIwjN3J675WbiVHaRfyWpKP1oJw6ZAaCLsXkTDhf/mbvNmPi3vw2vlQyjFjLPFwsa/9wKzg5FsdOcCgr97itcL3jIaVwLMB8wNCPaOZpEtHmvivSRfM+jK/rH/RGKkD+8tbciTdw0laVlH3DnBkDaNGdy+EVat6TNhOaHeDcjIK6ZbY3/mbMxkjj1ZaetwL5zMlS9Bu+wszlWeDSWuLn/VEpK5wJdKqbcwknjGAqv/otcSQgghhBCnCbYvO0htOJDIXg8aCSs3zyB98y/kp2+mWeZK4sya8oQ7Md/4Nl4Zx7npk9WUlZygqUqnocrD7OZDfNk2brN9x1THl1nnmIgOaE6rjCnY9phgz+yK19PBbVA3/Rf8jUSBS3ccxqTUOdP0a8KUVfuZtymTrqZN/D13IvhEQdu7Ltv5TwUw5m3KJCnal2ujfC/qeSaTIjHSh6U7sgFICDNm0CiluK9LFPd1ibpsbawJTQKNv8urC7YzZVU6nWP9+N897fk9p5CYAFcAejQNYPaGg7SfDj3KH+CNAxNg6UvQ618V51mVdoSZazMACPd1ZVCbUDKzsnB1sBBUlMbDHlsZUboYdSIXdIARtIi93vixnDl7xQy4lpRz84uTmGx7H+dPeoF7IBQcwsG5IY+UPkR6SH+aAJsOHOPaKJ8/vsArBU364RTTEw6uh4JMI0jiHwee4TiaTDTPLSLEu3bNmOkc68c7S3bz0vxtABTgwmerMpiXmsMwe1LRjLxiRnSI4MXk5uzLLeL4ybKKfi1EbVOtAIZS6ibgXcAf+E4ptVFr3VtrvVUpNRPYBpQDD0kFEiGEEEKIKyPQ0xmArHyjDCfOHuyOGMINc0NxNN+BOplP/9gGvJp8AyhFm3Bv5jzUkR+3HybStwMPTl2H7Thcm3wjyx2eICF7Nm03vA4ZazkU1o++u5MZ0zuK8T/soatpE68dnYn5ox7oEfMxhSRw9+S1AOwb35+fd+UQG+BWI0shrDbN92t38Zr5I24zL+N4gyich38Lji4XfvJFCvNxwdli4mSZjX8lN7uk5yZGerN0RzZeLhYifS9fm2qDJoFGwsgpq9JxcXRg+e5clmw/zJ7sQga0MpKhXh8fiL+7EzkFJXxNO8YmDsdjxdsQ2s4IRADLdubgZi6no3kHJVt+p2DXetZbvsGmzJh0OZQCkX2MJVKNulaa7+V0rk5mTgYk8LTbRD6I+BmO7Ye4vryT3pQfUg6y48EkNmXkM3DiCrrE+Z97ArMTRHSo9NyRfq5V/4P9RRLCvHA0m1iQmkWwpzO/PtWD7VnHGfDur7yzZDfOFhPv396WzrHGcpraeA1CnK66VUi+Ab45z2MvAy9X5/xCCCGEEOLSeTibcXF04NCpAAYw5ptU3JzMfHV/B0bP2Mh1SbHGXWW7mAC3ivXuSdF+bMo4xs1tQnF1MgNPQI97QGu8Hb3IH7uQCSmFHMGT2bYuhMX25vbU+/D5qAelkV0JVclkaH+KSsq5Z/Ia+jQP5L1hF54e/uainZwsszKmf/wlX/Pe3CIsDopQ7z8CAevWr+bT4tGEmI8wsfxGbhz+Nh5e1aykcBYHk+Knx7vh2cByRtWSi3GqqkOrUK+LLu1ZV4R6N8DF0QGtYfqoa7nvi7Xc87kR2DrVzxzNJu7r3IhXvt8BwILgv3NrzgZMM26HhDsgpgftNk3hccsqXPQJOGice7qtBzd3iMcxoj0EtgCfRpfUtoQwLxZuzULfM44yq+a1hTv4ZMVeovxdUUrRKtSTj4cn0im28moldYnFwcRtiWEs353DE72bYDIpmgV7khjhw+p9R2kb4U33JjU/U0qIi1W/62UJIYQQQlyFlFIEeTqTeayYcXO3YlKKdel5PNA1mih/N+Y+3OlPn/+fQS05dqLMHrywsydXdAZCvIw1845mE2aT4u01xcxSz3GHwxLuSl/CEsdf+NraldWbgim3aZbuyOZkmRVny/nX05dZbUxesY+i0nLuuDaCCN+LvxN8ssxK9zeW4eViYePY642dR34nbsEwbKZSykd8xwMRHTCZ/pogQVUrhbQI8cTLxUKn85T1rMtMJsXj1zcmxLsBLUO9WPZ4d6am7OfLlPQzrndUl2ju7RRF1LPf89Tc3Uz2HcM37VfivGYSbJxCknYhI/g69gb2YcKqfE6aXAiLjmdI33ZVblvjQHemrzlATmEJ/56/nbn2hKklZTbAeP/UxUS15/PSwObn7OvRNIDV+44SH3ye0qpC1FK1M9uSEEIIIYSoFj83JxakZjF55T4+XbEXq03TPMTzop4b7NXgT7/YRPsbd9DjGroRH2Qc1yy+Bf+xDqX7ifF8Ze3KIIefabloMP7kcaLUyrKd2X/6muv251FQUo5Nw+SV+y7uIu2mrU4H4NiJMk6WWSFvP7bJA7CVn2Rm/EQcGyX9ZcGL6nC2OPDLk925u9OlzSCoK+7u1IjezYxihg0cHbi3cxRLH+9G7Fn5FUwmVVE2dneeZmzRIBi9hflJX3FNySRMN71PXMeBbNcR7LX606tp9WYMnJoBMmP1AeZuyuT+rtF0ifNnVB3PO3IpesU3xKQ4rXqREHWDBDCEEEIIIeqhUzknAj2cK/Y1D7k8d1uj/I3ZEXEB7jS1BzCSE0LoGudPJn5M8RvNLaXjcC7LZ5rrm4S7Wvl63cHzni8j7wSTF68nzMGY0p6SdvSS2nOq5Ggv01psE6+F9xKxlhRyR+mzxCdUnq+gtvBwtuBQC4MrV9o7Q1rzw+gu9GsRxC+7csEjmG+zfPD39iTa35VGfq787552dI71o1+LoGq91qkAxpuLd+Hv7sQjPWP44u52jEiKvAxXUjdE+7vx8xPd6V/Nv6UQV5osIRFCCCGEqIee6duE29uHE+HryjUv/4i3i4WQy5RIM+rUDIxAd+IaurHy91y6xPnTJtyb/UeKiAlwo+2/C3io7FE+VW/yhcc79N35MIePN6fhaQGVU96auYjnM/9JgONxFrk8wWMZLSiz2rA4XPhem9aaXYcLeTVyA0Oz3iK3NAaXa+5jnq0L236xVgRYRO0W6OlMoKczbcK9mLspkwNHT7ByTy4DW4dU5AfpHOtP59hKEmte6mud1gcHJgRfcu6S+iLMp34ljhVXB5mBIYQQQghRDwV4OJMY6YO/uxPNQzxoE+592RJFxgcZSwCaB3vSo0lDlvyzG25OZgI9nWkf5YuPqyMAy2wJHLnuLSKPr+Fdh7d5e9G2M09kLaNo2QReyhyFj7kUS1gi/fe+zMtqEh8v2UpaTuEF25KZf5LY0u3cdvj/WG9pwwMub0CfV1hRGISfmxP+7k6X5ZrFlZEQbixp+Hh5GkWlVrpWVgmkmk5/H1xvX+IihKgbrs5woxBCCCHEVeSzke0wX8ZlCm0jfPj2oY60DK08p4ZSCl9XR5wtDvh3GglO5Vz33T8p3fQUv7X8gg7R/mxZ+DG+6yYQbDvEj7bWRN42kZiYJuR+9yK3rH2HzBUDmb3lTvJibmbotY2IDXBj+6ECmga5V3wBLbPa2LMvnXcd36XMNZB1rd5izZJM1qfnsT49j6ZB7pW2T9Re8UEeOJpNfP7bfiwOiqS/KMFpu0ijCkebcMkBIURdorTWNd2GComJiXrt2rU13QwhhBBCCFFNhSXlmE2qovJI+Yr3MC8eQ7pLPKHOJZiO/k6qLZKJejC7PJP48Z/dUEpRWm7jzuff4lnLVFqZ0kizBXLYP4m8xrfx4FIrn428hm6N/Xnl++18/GsaH5rfoqtpIyXDF5Dj0Yweb/5c0Ya/dYnimX5Na+pPIKrosRkb+WbDQZoEurNwdJe/5DUKS8o5UVJOQCVLmoQQV55Sap3WOvFCx8kMDCGEEEIIcdm5OZ35MdPc8WE+25hPcs4HHLZEMa70MZaZ2lFSrnmk1R95DhzNJqLb9eY374Es3vgNXY5+RcKR72mwcjaPm5OZtTaAw8dPMnn5bj4OmkfPvHW8WHYnL0S3xx0Y3iECRwcTVq0ZfE1YDVy5qK7XbmlJmI8LSdG+f9lruDmZz+mjQojaT2ZgCCGEEEKIK2L66nSenr0FRwcTnWP98HNzYsbaAyx+rMs5pTVPGTd3K7NWbmOMeQpDzMv4zdaM77xuZ2ThR8TY9nKkye2kth5H18bVK60phBCi5sgMDCGEEEIIUav0axnE0h3Z7M4u5Jl+TXEym2gT4XXe4AVAqzBPJuPCWH0/XbsNoPVPT9Ph+LMUmb1h8Jf4NulP1yt4DUIIIWqOBDCEEEIIIcQV4eFs4cPhZ95gu80n/E+f0zrMSLL4QLdogrr15eU0D9zTvqPj4Odo2yT2L2urEEKI2kcCGEIIIYQQotaK9HPllye6E+bTAIC7bh7A7PWtSWgSU8MtE0IIcaVJAEMIIYQQQtRq4b4uFb8HezXg4R4y80IIIa5GpppugBBCCCGEEEIIIcSFSABDCCGEEEIIIYQQtZ4EMIQQQgghhBBCCFHrSQBDCCGEEEIIIYQQtZ7SWtd0GyoopXKA/TXdjiryA3JruhFCXAHS18XVQvq6uFpIXxdXA+nn4mpRV/t6hNba/0IH1aoARl2mlFqrtU688JFC1G3S18XVQvq6uFpIXxdXA+nn4mpR3/u6LCERQgghhBBCCCFErScBDCGEEEIIIYQQQtR6EsC4fD6s6QYIcYVIXxdXC+nr4mohfV1cDaSfi6tFve7rkgNDCCGEEEIIIYQQtZ7MwBBCCCGEEEIIIUStJwEMIYQQQgghhBBC1HoSwKgmpVQfpdROpdQepdTTNd0eIapDKRWmlPpJKbVdKbVVKfWofb+PUmqxUmq3/V9v+36llHrH3v83K6Xa1OwVCHFplFIOSqkNSqn59u1GSqkUe1+foZRytO93sm/vsT8eWZPtFuJSKKW8lFJfK6V22Mf3DjKui/pIKfWY/fNLqlJqmlLKWcZ1UR8opT5VSmUrpVJP23fJ47hSaoT9+N1KqRE1cS3VJQGMalBKOQATgb5APDBUKRVfs60SolrKgX9qrZsC1wIP2fv008ASrXUssMS+DUbfj7X/jALev/JNFqJaHgW2n7b9GvB/9r6eB9xj338PkKe1jgH+z36cEHXF28BCrXUToBVGn5dxXdQrSqkQ4BEgUWvdHHAAhiDjuqgfJgN9ztp3SeO4UsoHeAFoD7QDXjgV9KhLJIBRPe2APVrrNK11KTAdSK7hNglRZVrrQ1rr9fbfCzA+5IZg9OvP7Yd9Dgy0/54MfKENqwAvpVTQFW62EFWilAoF+gMf27cV0AP42n7I2X391Hvga6Cn/XghajWllAfQBfgEQGtdqrU+hozron4yAw2UUmbABTiEjOuiHtBa/wIcPWv3pY7jvYHFWuujWus8YDHnBkVqPQlgVE8IcOC07Qz7PiHqPPtUytZACtBQa30IjCAHEGA/TN4Doi6bADwJ2OzbvsAxrXW5ffv0/lzR1+2P59uPF6K2iwJygM/sy6U+Vkq5IuO6qGe01geBN4B0jMBFPrAOGddF/XWp43i9GN8lgFE9lUVppS6tqPOUUm7ALGC01vr4nx1ayT55D4haTyl1A5CttV53+u5KDtUX8ZgQtZkZaAO8r7VuDRTxxzTjykhfF3WSfSp8MtAICAZcMabSn03GdVHfna9v14s+LwGM6skAwk7bDgUya6gtQlwWSikLRvBiqtZ6tn334VNTiO3/Ztv3y3tA1FUdgRuVUvswlv/1wJiR4WWfegxn9ueKvm5/3JNzp3IKURtlABla6xT79tcYAQ0Z10V9cx2wV2udo7UuA2YDSci4LuqvSx3H68X4LgGM6lkDxNqzGztiJAqaW8NtEqLK7Gs/PwG2a63fOu2hucCpTMUjgG9P2z/cnu34WiD/1FQ2IWozrfUzWutQrXUkxti9VGt9O/ATMMh+2Nl9/dR7YJD9+Dp310JcfbTWWcABpVRj+66ewDZkXBf1TzpwrVLKxf555lRfl3Fd1FeXOo7/AFyvlPK2z1i63r6vTlHyPq0epVQ/jLt2DsCnWuuXa7hJQlSZUqoTsBzYwh95AZ7FyIMxEwjH+IBwq9b6qP0DwnsYCYBOAHdprdde8YYLUQ1KqW7A41rrG5RSURgzMnyADcAdWusSpZQz8D+MvDBHgSFa67SaarMQl0IplYCRrNYRSAPuwriJJeO6qFeUUi8Ct2FUVdsA3Iuxxl/GdVGnKaWmAd0AP+AwRjWROVziOK6Uuhvjsz3Ay1rrz67kdVwOEsAQQgghhBBCCCFErSdLSIQQQgghhBBCCFHrSQBDCCGEEEIIIYQQtZ4EMIQQQgghhBBCCFHrSQBDCCGEEEIIIYQQtZ4EMIQQQgghhBBCCFHrSQBDCCGEEEIIIYQQtZ4EMIQQQgghhBBCCFHr/T9a4eoOcfxr6QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 1080x360 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, figsize=(15, 5))\n",
"\n",
"ss = pd.DataFrame(res.smoothed_state.T, columns=['x', 'w'])\n",
"\n",
"axes[0].plot(beta_x, label='True')\n",
"axes[0].plot(ss['x'], label='Smoothed estimate')\n",
"axes[0].set(title='Time-varying coefficient on x_t')\n",
"axes[0].legend()\n",
"\n",
"axes[1].plot(beta_w, label='True')\n",
"axes[1].plot(ss['w'], label='Smoothed estimate')\n",
"axes[1].set(title='Time-varying coefficient on w_t')\n",
"axes[1].legend()\n",
"\n",
"fig.tight_layout();"
]
}
],
"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": "3.7.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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