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Created March 23, 2022 03:03
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Interpolation.ipynb
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{
"nbformat": 4,
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"metadata": {
"colab": {
"name": "Interpolation.ipynb",
"provenance": [],
"authorship_tag": "ABX9TyMLSSYVRYmXIoN6/bpCi5T9",
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},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
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"source": [
"<a href=\"https://colab.research.google.com/gist/DianSano/4206311b9bd88dda5d335def5c52aeb2/interpolation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"Interpolation"
],
"metadata": {
"id": "ZxTCAUWg9YF5"
}
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 833
},
"id": "lxECnMPY6fZK",
"outputId": "b40d7d15-c901-4f83-b7fb-522e1686a26f"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" hours temp\n",
"0 0.0 22.0\n",
"1 1.0 20.5\n",
"2 2.0 19.0\n",
"3 3.0 18.5\n",
"4 4.0 18.0\n",
"5 5.0 18.0\n",
"6 6.0 18.5\n",
"7 7.0 19.0\n",
"8 8.0 21.0\n",
"9 9.0 23.0\n",
"10 10.0 24.0\n",
"11 11.0 24.5\n",
"12 12.0 25.0\n",
"13 13.0 26.0\n",
"14 14.0 27.0\n",
"15 15.0 28.0\n",
"16 16.0 28.0\n",
"17 17.0 26.0\n",
"18 18.0 24.5\n",
"19 19.0 23.0\n",
"20 20.0 22.0\n",
"21 21.0 22.0\n",
"22 22.0 21.5\n",
"23 23.0 21.0\n",
"24 24.0 22.0"
],
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" <tr>\n",
" <th>0</th>\n",
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" <td>28.0</td>\n",
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" <td>24.5</td>\n",
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" <th>20</th>\n",
" <td>20.0</td>\n",
" <td>22.0</td>\n",
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" <td>21.0</td>\n",
" <td>22.0</td>\n",
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" <th>22</th>\n",
" <td>22.0</td>\n",
" <td>21.5</td>\n",
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" <td>23.0</td>\n",
" <td>21.0</td>\n",
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" <tr>\n",
" <th>24</th>\n",
" <td>24.0</td>\n",
" <td>22.0</td>\n",
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"</div>\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a7aecaf2-4988-4f5b-b73b-89b7f6c4b3f2')\"\n",
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"\n",
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" [key], {});\n",
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"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
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" element.appendChild(docLink);\n",
" }\n",
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" "
]
},
"metadata": {},
"execution_count": 10
}
],
"source": [
"# Python code in case you want to follow along\n",
"\n",
"# Importing Python packages\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Creating the data\n",
"hours = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.]\n",
"temperature_celcius = [22, 20.5, 19, 18.5, 18, 18, 18.5, 19, 21, 23, 24, 24.5, 25, 26, 27, 28, 28, 26, 24.5, 23, 22, 22, 21.5, 21, 22]\n",
"\n",
"# Creating a pandas dataframe\n",
"data = pd.DataFrame({'hours': hours, 'temp': temperature_celcius })\n",
"\n",
"# Printing the data\n",
"data"
]
},
{
"cell_type": "code",
"source": [
"# Creating a scatter plot from the temperature per hour\n",
"plt.figure(figsize=(12, 10))\n",
"plt.scatter(data.hours, data.temp)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Temperature')\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 606
},
"id": "9tgZGs5562nk",
"outputId": "590c78f8-a123-40a9-cad2-f1c2ea1e69fb"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"Linear Interpolation"
],
"metadata": {
"id": "ciFnhTCS8Skm"
}
},
{
"cell_type": "code",
"source": [
"# Import Python packages for interpolation\n",
"import numpy as np\n",
"import scipy.interpolate as interpolate\n",
"\n",
"# Create a linear interpolation function based on the original data\n",
"linear_interpolation_func = interpolate.interp1d(data.hours, data.temp, kind='linear')\n",
"\n",
"# Create a list with 10 'time' values per hour (6-minute interval) \n",
"in_between_hours_scale = np.linspace(0., 24., 24*10)\n",
"\n",
"# Interpolate the temperature on the 6-minute scale\n",
"linear_interpolated_y = linear_interpolation_func(in_between_hours_scale)\n",
"\n",
"# Plot the result\n",
"plt.figure(figsize=(12,10))\n",
"plt.scatter(data.hours, data.temp)\n",
"plt.plot(in_between_hours_scale, linear_interpolated_y, 'red')\n",
"plt.legend(['Linear Interpolation', 'Original'])\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Temperature')\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 606
},
"id": "-vCXD7oi7RT0",
"outputId": "a989f392-f842-4903-a13b-bbbc5625dae0"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"NN Interpolaton"
],
"metadata": {
"id": "veVB9fhv8le2"
}
},
{
"cell_type": "code",
"source": [
"# Create an interpolation function for Nearest Neighbors interpolation\n",
"nearestneighbors_interpolation_func = interpolate.interp1d(list(data.hours), list(data.temp), kind='nearest')\n",
"\n",
"# Use the 6-mitue scale from before to interpolate values using the Nearest Neighbors interpolation function\n",
"nearestneighbors_interpolated_y = nearestneighbors_interpolation_func(in_between_hours_scale)\n",
"\n",
"# Plot the results of the Nearest Neighbors interpolation on top of the Linear interpolation\n",
"plt.figure(figsize=(12, 10), dpi=80)\n",
"plt.scatter(data.hours, data.temp)\n",
"plt.plot(in_between_hours_scale, linear_interpolated_y, 'red')\n",
"plt.plot(in_between_hours_scale, nearestneighbors_interpolated_y, 'green')\n",
"plt.legend(['Linear Interpolation', 'Nearest Neighbors interpolation', 'Original'])\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Temperature')\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 669
},
"id": "R0RGbgvq8oc_",
"outputId": "9b370861-4ace-4a64-bde7-9b423fbaf092"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 960x800 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"Polynomial Interpolation"
],
"metadata": {
"id": "6Xk5IgaL-bZx"
}
},
{
"cell_type": "markdown",
"source": [
"An example of a polynomial of degree 2\n"
],
"metadata": {
"id": "rqKXhPE4-bMh"
}
},
{
"cell_type": "code",
"source": [
"# degree 2 is a parabola\n",
"x = np.linspace(-3, 2, 1000)\n",
"degree_2_polynomial = lambda x: 1 + x + x**2\n",
"plt.plot(x, [degree_2_polynomial(i) for i in x])"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 282
},
"id": "D7S4O26dCP7t",
"outputId": "ef1a7325-41d9-4cc5-b10a-8105a9476623"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f31be8c9210>]"
]
},
"metadata": {},
"execution_count": 14
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"An example of a polynomial of degree 3\n"
],
"metadata": {
"id": "bIUu6VsNDJeb"
}
},
{
"cell_type": "code",
"source": [
"# degree 3 is a cubic\n",
"degree_3_polynomial = lambda x: 1 + x + x**2 + x**3\n",
"plt.plot(x, [degree_3_polynomial(i) for i in x])"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 282
},
"id": "U_xWZz0nDJKB",
"outputId": "61955d34-24e9-45e7-a0bd-cf0873b580c2"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f31be943790>]"
]
},
"metadata": {},
"execution_count": 15
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"An example of a polynomial of degree 6"
],
"metadata": {
"id": "yMMgUGtoDwrA"
}
},
{
"cell_type": "code",
"source": [
"x = np.linspace(-5, 6, 1000)\n",
"degree_6_polynomial = lambda x: 1/100 * (x**6 - 2*x**5 - 26*x**4 + 28*x**3 + 145*x**2 - 26*x - 80)\n",
"plt.plot(x, [degree_6_polynomial(i) for i in x])"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 282
},
"id": "R77-wPn0Dw8m",
"outputId": "8541ede9-faea-4bf2-a400-27122549b5b8"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f31c85ccd10>]"
]
},
"metadata": {},
"execution_count": 16
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"Newton Polynomial Interpolation in Python\n"
],
"metadata": {
"id": "3TYPv6b-KuXI"
}
},
{
"cell_type": "code",
"source": [
"# Credits to stack overflow for this code\n",
"\n",
"def _poly_newton_coefficient(x, y): \n",
" \"\"\"\n",
" x: list or np array contanining x data points\n",
" y: list or np array contanining y data points\n",
" \"\"\"\n",
"\n",
" m = len(x)\n",
"\n",
" x = np.copy(x)\n",
" a = np.copy(y)\n",
" for k in range(1, m):\n",
" a[k:m] = (a[k:m] - a[k - 1])/(x[k:m] - x[k - 1])\n",
"\n",
" return a\n",
"\n",
"def newton_polynomial(x_data, y_data, x):\n",
" \"\"\"\n",
" x_data: data points at x\n",
" y_data: data points at y\n",
" x: evaluation point(s)\n",
" \"\"\"\n",
" a = _poly_newton_coefficient(x_data, y_data)\n",
" n = len(x_data) - 1 # Degree of polynomial\n",
" p = a[n]\n",
"\n",
" for k in range(1, n + 1):\n",
" p = a[n - k] + (x - x_data[n - k])*p\n",
"\n",
" return p"
],
"metadata": {
"id": "cK6GoqnGKvRw"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# Computing the Newton Polynomial Interpolation\n",
"newton_interpolation = newton_polynomial([2., 4., 6.], [4., 16., 36.], np.array([0., 1., 2., 3., 4., 5., 6., 7.]))\n",
"\n",
"# Plotting the Newton Polynomial against the original data\n",
"plt.figure(figsize=(12,10))\n",
"plt.scatter([2., 4., 6.], [4., 16., 36.])\n",
"plt.plot([0., 1., 2., 3., 4., 5., 6., 7.], newton_interpolation, 'red')\n",
"plt.title('Newton Polynomial Interpolation solves the simple example')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 624
},
"id": "J01ss9HtK6M7",
"outputId": "b834c4b2-f09a-4897-8cb3-71d6efe4a049"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Newton Polynomial Interpolation solves the simple example')"
]
},
"metadata": {},
"execution_count": 18
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"# Computing the Newton Polynomial Interpolation\n",
"newton_interpolation = newton_polynomial(list(data.hours), list(data.temp), in_between_hours_scale)\n",
"\n",
"# Plotting the Newton Polynomial against the original data\n",
"plt.figure(figsize=(12,10))\n",
"plt.scatter(list(data.hours), list(data.temp))\n",
"plt.plot(in_between_hours_scale, newton_interpolation, 'red')\n",
"plt.ylim(0, 100)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Temperature')\n",
"plt.title('Newton Polynomial Interpolation finds a very complex polynomial that fits the data')\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 638
},
"id": "3WpCGucALjm8",
"outputId": "bd2c9be1-2b3f-4ff9-bdf8-5669015a547a"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Newton Polynomial Interpolation finds a very complex polynomial that fits the data')"
]
},
"metadata": {},
"execution_count": 19
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"Cubic Spline Interpolation in Python\n"
],
"metadata": {
"id": "wSZxs6J-S85d"
}
},
{
"cell_type": "code",
"source": [
"import scipy as scipy"
],
"metadata": {
"id": "KZ5nf7jjUWjK"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# Computing the Cubic Spline Interpolation\n",
"cubic_spline_interpolation = scipy.interpolate.CubicSpline([2., 4., 6.], [4., 16., 36.])\n",
"\n",
"# Show the interpolated values: x squared has been found correctly\n",
"plt.figure(figsize=(12,10))\n",
"plt.plot([0., 1., 2., 3., 4., 5., 6., 7.], cubic_spline_interpolation([0., 1., 2., 3., 4., 5., 6., 7.]))\n",
"plt.xlim(0,7)\n",
"plt.ylim(0,50)\n",
"plt.title( 'Cubic Spline has found the x-squared polynomial')\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 607
},
"id": "QmyzS-KxS-Ox",
"outputId": "0d671579-bc79-4087-e56e-357664e83768"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"# Computing the Cubic Spline Interpolation\n",
"cubic_spline_interpolation = scipy.interpolate.CubicSpline(list(data.hours), list(data.temp))(in_between_hours_scale)\n",
"\n",
"# Plotting the Cubic Spline against the original data\n",
"plt.figure(figsize=(12,10))\n",
"plt.scatter(list(data.hours), list(data.temp))\n",
"plt.plot(in_between_hours_scale, cubic_spline_interpolation, 'red')\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Temperature')\n",
"plt.title('Cubic Spline Interpolation finds a perfectly fitting function: smooth and simple')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 638
},
"id": "_nMRjwmRVtpt",
"outputId": "a79a6584-6cae-4101-e029-572445f00a58"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Cubic Spline Interpolation finds a perfectly fitting function: smooth and simple')"
]
},
"metadata": {},
"execution_count": 23
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
],
"image/png": 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V3/fye/zzfAw/WkNxXsO/Zr/h+y72iFpeNuBf22OieT0MnOGc+7qQefwTfxDTUnzh/U6B6fcDfzd/EooHCnn8pfiC9Dv8iBEvAE+UkDseLsHvYv0Jf3DPk/mm1cR/of2G3+W7DD8iy1ai9/wy/A+C34Be+P7BxfkU2AP/+t0G/N05tyyadga+cMgbeeYVfJeLmERfzN3wXXjytsX+/Pm53gdfHHyN73t9RfS4r/HF0HfROlZUF6ZngOaU7cfOy9H1MjPL64tb0jpTJOfcUvxxBXfh36dm+H7e62N8/Fz8gWdjgP/h18lYl70S/9lyPH49+h/QMZpc2PPM7wn8Z+OH+G14HX7bKJH5k0etKuYufYAfzHeruhC/x2BbDMG/ll/iR5yZFt2Gc24McBO+hXgx/uC+/P10BwFPR+vTKaVZ6DZuV/kVt20XtDN+O1uBH91jPOXXJekFfOPCr/gDEXsXcb/r8AePToreszEUfbyLJCnbujueSPoxM4cfhSNjxn42s0H4g2KK+gCXODOzs/BH75f5BEIhmNkZwPnJnD9q6V0AnO6cGxc6j2QmM3sKP4LNjaGzSGKo5VlERLZiZtsBFwP/DZ2loKibSk7UfWAgvm/spMCxRCSDqHgWEZE/RP0vl+D7sb4QOE5hWuO7ey3Fd6Ho7gofyk9EJC7UbUNEREREJEZqeRYRERERiVFZT3aREHXq1HGNGzcOHUNERERE0tzUqVOXOueKPHlNShTPjRs3ZsqUKaFjiIiIiEiaM7PizlSpbhsiIiIiIrFS8SwiIiIiEiMVzyIiIiIiMVLxLCIiIiISIxXPIiIiIiIxUvEsIiIiIhIjFc8iIiIiIjFS8SwiIiIiEiMVzyIiIiIiMVLxLCIiIiISIxXPIiIiIiIxUvEsIiIiIhIjFc8iIiIiIjFS8SwiIiIiEiMVzyIiIiIiMVLxLCIiIiISIxXPIiIiIiIxUvEsIiIiIhIjFc8iIiIiIjFS8SwiIiIiEiMVzyIiIiIiMVLxLCIiIiISo4qhA4iIiKSUpUvhqadg5kz49lvYsgU6doSjjoI2baCC2qVE0pm2cBERkVgsWwYDBkDjxtC/P7z7rr990ya4/XZo3x46dYIFC4LGFJH4UvEsIiJSkilTYP/94c474fjjfavzwoXw4YcwaZIvrB955M/7vfZa6MQiEicqnkVERIrz3HPQrh1UrAiTJ8Pw4dCs2db3ycmBCy6AadN8y/SJJ8LbbweJKyLxpeJZRESkKA8/DH36QKtWvnA+6KDi77/nnr41ev/9oWdPmDMnMTlFJGFUPIuIiBTmhRfgkkvghBN8/+a6dWN7XLVqkJsLlStDt27w++/xzSkiCaXiWUREpKC33oIzz/QHAb74IlSqVLrHN2oEr7ziR+O4/PL4ZBSRIFQ8i4iI5DdnDpx2GjRvDq+/DlWrbtt82reHq6+Gp5+GqVPLN6OIBKPiWUREJM/q1XDSSb7LxWuvQc2aZZvfgAG+u8fVV4Nz5ZNRRIJS8SwiIgK+uL3wQpg1y4+o0bBh2edZqxbceiuMH6/h60TSRNyKZzNraGbjzGyWmc00s8uj2w8ws0lm9rmZTTGzQ+KVQUREpCS50xfSZuhY+h93JTz3HLMvvBo6dy6/BfTty4rd9mR+30vYo/9rtBk6ltzpC8tv/iKSUPFsed4EXO2cawa0AvqZWTPgLuAfzrkDgJuj/0VERBIud/pCBoycAfPmcfP7/2VSw305qXbHci1uc2f8zPUte9Jw2UK6zP2YhcvXMmDkDBXQIikqbsWzc26xc25a9PdKYDbQAHBAXieyWsCieGUQEREpzrDRc1i3YSN3vf1PDLjm2CtYs8kxbHT5jc88bPQc3ml0IPNyduaMaW8AsHbj5nJdhogkTkL6PJtZY6AF8ClwBTDMzOYDdwMDinjM+VG3jilLlixJREwREckwi5avpc+0N2kz70uGdDyXBTk7/3F7eS5jS4UsnmlxHIcsmEWzn78r92WISOLEvXg2s+rAq8AVzrkVwEXAlc65hsCVwOOFPc4591/nXEvnXMu6sQ5MLyIiUgot3AquH/8UHzQ5iBH7d/nj9vo52eW2jLx5vbxfZ9ZWrEKfqPW5PJchIokT1+LZzCrhC+fnnXMjo5vPBPL+fhnQAYMiIpJ4zvHQpCcBuKFLPzADILtSFv27NC23xfTv0pTsSlmsqFqd/9vncLrPGs/Om9aU6zJEJHHiOdqG4VuVZzvn7s03aRHQIfq7E/C/eGUQEREpUm4u9T58j+/69YdGjTCgQU42d/RoTvcWDcptMd1bNOCOHs1pkJPNswd2JXvTeh7b/GW5LkNEEsdcnAZtN7O2wEfADGBLdPNAYAVwP1ARWAdc7Jwr9tRLLVu2dFOmTIlLThERyUArV8Lee0OdOjB5culPv10Wbdr45X/5ZeKWKSIxM7OpzrmWRU2vGK8FO+cmAFbE5IPitVwREZES3XorLFoEr76a2MIZoFcvuOQSmDkT9tknscsWkTLTGQZFRCSzzJ0L998P55wDhx6a+OX//e9QoQK8+GLily0iZabiWUREMstVV0F2Ntx2W5jl77QTdOwII0b4U4KLSEpR8SwiIpnj7bfhzTfh5pt9ERvKaafB//4H06eHyyAi20TFs4iIZIaNG+HKK2HPPeHSS8Nm6dEDKlb0rc8iklJUPIuISGZ44gmYMweGDYPKlcNmqV0bunTx/Z63bCn5/iKSNFQ8i4hI+lu9GgYN8sPEHX986DTeqafCjz/CZ5+FTiIipaDiWURE0t/998NPP8Gdd/5xJsHgjjsOsrJ8H2wRSRkqnkVEJL0tXeqL5m7dfMtzsqhd2+d5443QSUSkFFQ8i4hIerv9dli1yl8nm65d4fPPYcGC0ElEJEYqnkVEJH3NmwcPPQRnnQXNmoVO81fHHeev1XVDJGWoeBYRkfR1883+bH6DBoVOUri994YmTdR1QySFqHgWEZH09OWX8Oyzfkznhg1Dpymcme+6MWYMrFkTOo2IxEDFs4iIpKeBA6FWLbj++tBJite1K6xbB+PGhU4iIjFQ8SwiIunn4499P+Lrr/ejWiSzDh2gWjUYNSp0EhGJgYpnERFJP4MGQd26cMkloZOUrEoVOPJIeOcdcC50GhEpgYpnERFJLxMnwnvvwbXX+hbdVNC5sx8Z5NtvQycRkRKoeBYRkfQyaBDsuCNcdFHoJLHr3NlfjxkTNoeIlEjFs4iIpI8JE3wBet11qdPqDLDHHrDrrr7FXESSmopnERFJH7fcAjvtBBdeGDpJ6Zj5fs9jx8LmzaHTiEgxVDyLiEh6+PBDX3xedx1st13oNKXXuTMsXw5Tp4ZOIiLFUPEsIiLpYdAg3+p8wQWhk2ybTp38tbpuiCQ1Fc8iIpL6xo/3Jxm5/vrUbHUGf5DjAQfooEGRJKfiWUREUt+gQbDzzqnb6pync2c/1N7q1aGTiEgRVDyLiEhq++ADf7n+esjODp2mbI48EjZuhI8+Cp1ERIqg4llERFLboEFQrx6cf37oJGXXpg1UrOi7oYhIUqoYOoCIiMg2GzfOF5oPPJD6rc7gx6Zu2dKPHCIiSUktzyIikpqc8+M6168P550XOk356dABJk+GNWtCJxGRQqh4FhGR1DRunO8bPGAAVK0aOk356dDB93v+5JPQSUSkECqeRUQk9eRvde7bN3Sa8tWmDVSooK4bIklKfZ5FRCT1jB0LEybAgw+mV6szQM2a0KKFDhoUSVJqeRYRkdSS1+rcoAGce27oNPHRoQNMmgTr1oVOIiIFqHgWEZHU8v77/kQiAwemX6tznvbtYf16f+CgiCQVFc8iIpI68lqdd9klfVudAdq1AzN13RBJQurzLCIiqWPMGPj4Y3j4YahSJXSa+KldG5o310GDIklILc8iIpIanPNnE2zYEM45J3Sa+Gvf3v9Q2LgxdBIRyUfFs4iIpIb33vPF5MCB6d3qnKdDB1i9GqZODZ1ERPJR8SwiIskvf6vz2WeHTpMY7dv7a3XdEEkqKp5FRCT5vfuuP+NeprQ6A+y4I+y1lw4aFEkyKp5FRCS5ZVpf5/w6dPAng9m8OXQSEYmoeBYRkaSUO30hbYaO5cxTB8OkSXzepx9Urhw6VmJ16AArVsAXX4ROIiIRFc8iIpJ0cqcvZMDIGSz8bQ1XTHiBBTXrcoZrRu70haGjJVZev2d13RBJGiqeRUQk6QwbPYe1GzfT4ftptFg8h4dan8qKLRUYNnpO6GiJ1aAB7L67imeRJKLiWUREks6i5WvBOa6c8DwLau7IK82P+PP2TNOhA3z0EWzZEjqJiKDiWUREklD9nGw6fjeFAxbP5cHWp7Axq9Ift2ec9u3h119h5szQSUQEFc8iIpKE+nfeg+s+fIYfcurxatTqnF0pi/5dmgZOFkCHDv5a4z2LJAUVzyIiknS6zx7PXr98zxNHn8OmrEo0yMnmjh7N6d6iQehoideoEeyyi++6ISLBmXMudIYStWzZ0k2ZMiV0DBERSYT166FpU6hdG6ZMgQpq56FXL3/Q4IIFYBY6jUhaM7OpzrmWRU3XJ5KIiCSXRx6BefNg6FAVznnatoVFi+CHH0InEcl4+lQSEZHksWIFDBkCnTpB586h0ySPdu38tbpuiASn4llERJLHPffA0qW+1VndE/60zz6w/fYqnkWSgIpnERFJDj//7Ivnk0+Ggw8OnSa5VKgAbdqoeBZJAiqeRUQkOQwZAuvW+Wv5q7ZtYc4c+OWX0ElEMpqKZxERCe/bb/2Bgn37wp57hk6TnPL6PU+cGDaHSIZT8SwiIuHddBNUqgQ33xw6SfJq2RKqVlXXDZHAVDyLiEhY06fD8OFwxRVQv37oNMmrcmU49FAVzyKBqXgWEZGwBgzwJ0S59trQSZJf27b+x8aqVaGTiGQsFc8iIhLOuHEwejQMHAg5OaHTJL927WDzZpg0KXQSkYyl4llERMJwDq67Dho2hH79QqdJDa1b+2Hr1HVDJJiKoQOIiEiGevVVmDwZnnjCHwgnJatZEw44QMWzSEBqeRYRkcTbtAluuAGaNYMzzgidJrW0beu7bWzYEDqJSEZS8SwiIon3xBMwdy7cfjtkZYVOk1ratYO1a/2BgyKScCqeRUQksdasgUGD4LDD4IQTQqdJPXknS1HXDZEgVDyLiEhiPfAALF4Md94JZqHTpJ6ddoI99lDxLBKIimcREUmcX3+FoUOha1ffd1e2Tdu2MGECbNkSOolIxlHxLCIiiXPHHbBihe/rLNuuXTv/Q+Trr0MnEck4Kp5FRCQx5s+Hf/0L+vSB5s1Dp0lt6vcsEoyKZxERSYxBg/yJUW69NXSS1Lf77r7vs4pnkYRT8SwiIvE3axY89ZQ/k2CjRqHTpD4z3/qs4lkk4VQ8i4hI/N1wA1SvDgMHhk6SPtq1gx9/9BcRSRgVzyIiEl+ffAK5udC/P9SpEzpN+sjr9zxhQtgcIhlGxbOIiMSPc3Dddb5/7pVXhk6TXvbbD2rUUNcNkQSrGDqAiIiksbfe8sXdQw9BtWqh06SXrCx/lkYVzyIJpZZnERGJj82bYcAA+Nvf4LzzQqdJT+3awcyZfsxnEUkIFc8iIhIfL7wAM2bAkCFQqVLoNOkpr9/zxIlhc4hkEBXPIiJS/tavh5tuggMPhJNPDp0mfR18sP9hoq4bIgmjPs8iIlL+HnkE5s2DRx+FCmqniZvsbF9Aq3gWSRh9oomISPlascJ31TjiCOjcOXSa9NeuHUyZAqtXh04ikhFUPIuISPm67z5YuhSGDg2dJDN06ACbNsHHH4dOIpIRVDyLiEj5WboU7rkHTjoJWrYMnSYztG3rh60bNy50EpGMoOJZRETKz513+u4Dt94aOknmqFHD93tW8SySECqeRUSkfCxcCA8+CH36QLNmodNklo4dYfJkWLkydBKRtKfiWUREysfgwf7EKLfcEjpJ5unY0b/2Gu9ZJO5UPIuISNl98w08/jicfz40aRI6TeZp08aP96yuGyJxp+JZRETKbtAgX7zdcEPoJJlpu+3g0ENVPIskgIpnEREpmxkz/Km4L7sM6tULnSZzdewIU6fC77+HTiKS1lQ8i4hI2dx0E9SsCddeGzpJZuvYEbZs0dkGReIsbsWzmdja4ksAACAASURBVDU0s3FmNsvMZprZ5fmmXWpmX0e33xWvDCIiEh+50xfSZuhYup9xL7z2GrNOvwBq1w4dK7O1bs3mylUYMfQpmlz/Jm2GjiV3+sLQqUTSTjxbnjcBVzvnmgGtgH5m1szMOgLdgP2dc/sAd8cxg4iIlLPc6QsZMHIGC5ev5bKJw/k1uyZ9qh2qQi2w3NnL+LRBMw6YMwUHLFy+lgEjZ+h9ESlncSuenXOLnXPTor9XArOBBsBFwFDn3Ppo2i/xyiAiIuVv2Og5rN24mf0Wz6XTd1N47ODuLKtQhWGj54SOltGGjZ7DB40OYK+l89hx5TIA1m7crPdFpJwlpM+zmTUGWgCfAnsC7czsUzMbb2YHF/GY881siplNWbJkSSJiiohIDBYtXwvAZROH81vVGjx9YNetbpcwFi1fy0dNWgDQ7ofPt7pdRMpP3ItnM6sOvApc4ZxbAVQEauO7cvQHXjIzK/g459x/nXMtnXMt69atG++YIiISo/o52ez70zcc+e1kHju4O6urbPfH7RJO/Zxsvq7bmCXVcmj3w7StbheR8hPX4tnMKuEL5+edcyOjmxcAI533GbAFqBPPHCIiUn76d2nKlZ+MYHnV6jx90PEAZFfKon+XpoGTZbb+XZpStXIlPmrcgrY/fI65LXpfROKgYrxmHLUmPw7Mds7dm29SLtARGGdmewKVgaXxyiEiIuWrO7/A3Ek8euRZrK6yHQ1ysunfpSndWzQIHS2j5b3+X845lB4zx9Fh7SK6n9ZV74tIOTPnXHxmbNYW+AiYgW9dBhgIjAGeAA4ANgDXOOfGFjevli1builTpsQlp4iIlNKJJ8IHH8APP0CtWqHTSEGLF0P9+jB0KFx3Xeg0IinHzKY651oWNT1uLc/OuQnAX/oyR3rHa7kiIhJHX3wBubn+dNwqnJNTvXqw337w7rsqnkXiQGcYFBGR2N16qy+aL7+85PtKOEcdBRMmwOrVoZOIpB0VzyIiEpsvv4SRI33hnJMTOo0U5+ijYcMGeP/90ElE0o6KZxERic3gwVCzJlxxRegkUpJ27aBGDXjjjdBJRNKOimcRESnZV1/BK6/AZZfB9tuHTiMlqVwZunTxxXOcBgYQyVQqnkVEpGSDB/uWzCuvDJ1EYnX88X7kjenTQycRSSsqnkVEpHizZsHLL8Oll0Lt2qHTSKyOOQbM1HVDpJypeBYRkeINHgzVqsFVV4VOIqVRty60aqXiWaScqXgWEZGizZ4NL74Il1wCO+wQOo2UVteuMHky/PRT6CQiaUPFs4iIFG3IENhuO7j66tBJZFt07eqv33orbA6RNKLiWURECjdnDowYAf36QZ06odPItmjeHBo2hNdfD51EJG2oeBYRkcINGQJVq8I114ROItvKDLp3h9GjYdWq0GlE0oKKZxER+au5c+GFF+Dii/2BZ5K6evSAdevgnXdCJxFJCyqeRUTkr4YMgSpV1OqcDtq29d1uRo4MnUQkLah4FhGRrc2dC88/71udd9opdBopq4oVoVs3P2Td+vWh04ikPBXPIiKytcGDfavztdeGTiLl5aSTYOVKeP/90ElEUp6KZxER+dOcOb6vc79+sOOOodNIeenUCWrWVNcNkXKg4llERP6UN8JG//6hk0h5qlLFj/mcmwubNoVOI5LSVDyLiIinVuf01qMHLFsG48eHTiKS0lQ8i4iIN3iwxnVOZ8ccA9Wr+9Oti8g2U/EsIiLw9dcwfDhccolandPVdtvBCSfAq6/Chg2h04ikLBXPIiKiVudMcdpp8OuvMGZM6CQiKUvFs4hIpsvf6qyzCaa3o46CnBwYMSJ0EpGUpeJZRCTT3XKL36WvVuf0V6WKP3AwN9efsltESk3Fs4hIJpsyBV56Ca66Sq3OmeK00/wJU95+O3QSkZSk4llEJJNdfz3UqaNW50zSsaP/oTR8eOgkIilJxbOISKZ67z1/uuYbbvBnn5PMULEinHoqvP46LF8eOo1IylHxLCKSibZs8a3OjRrBRReFTiOJdtZZsH69xnwW2QYqnkVEMtFLL8G0aX6IuipVQqeRRDvwQNhnH3j66dBJRFKOimcRkUyzYQPceCM0bw69eoVOIyGYwZlnwiefwNy5odOIpBQVzyIimebRR+Hbb+GOOyArK3QaCaV3b6hQQa3PIqWk4llEJJOsWgW33grt28Oxx4ZOIyHVq+dPmvLss74PvIjERMWziEgmufde+OUXuPNOv+teMttZZ8H8+TBuXOgkIilDxbOISKaYP98XzT16QKtWodNIMujWDWrVUtcNkVJQ8Swikimuvdbvnr/nntBJJFlUrerHfH71VX/WQREpkYpnEZFM8NFHMGIE9O8PjRuHTiPJ5MwzYc0aeOWV0ElEUoKKZxGRdLd5M1x+OTRs6E+MIpJf69awxx7quiESIxXPIiLp7t//hunTYdgw2G670Gkk2eSN+Tx+PHz/feg0IklPxbOISDpbsAAGDIAuXeCUU0KnkWTVp48vop95JnQSkaSn4llEJJ1deqnvtvHvf2toOinarrtCx46+64bGfBYplopnEZE0kzt9IW2GjuX8HjdCbi5fnXclNGkSOpYku3PP9d02PvggdBKRpKbiWUQkjeROX8iAkTNYs+gnhrz7MLN2bELPaq3Jnb4wdDRJdieeCDk58NhjoZOIJDUVzyIiaWTY6Dms3bCJO0Y/SK11K7nquKtYucUYNnpO6GiS7LKzoXdvP+bzsmWh04gkLRXPIiJpZNHytZz01ViOnvsJ97Trw9c7NvnjdpES9e0LGzbA88+HTiKStFQ8i4ikkYO2LGfQmEf4tOG+PHZw9z9ur5+THTCVpIz994eWLeHRR8G50GlEkpKKZxGRdLF2LY+NGsqWCllcfdyVbKmQBUB2pSz6d2kaOJykjL594auvYPLk0ElEkpKKZxGRdHHJJeR8/RWzhj6Ia9QYAxrkZHNHj+Z0b9EgdDpJFT17+pPpPP546CQiSali6AAiIlIOHnsMnngCbryR1pefycTQeSR11azpT6jzwgtwzz1QvXroRCJJRS3PIiKp7oMP4OKLoXNnGDQodBpJB337wqpV8PLLoZOIJB0VzyIiqWz2bD8+7x57wEsvQVZW6ESSDg47DPbaS2M+ixRCxbOISKr6+Wc49lioUgXefNOf4EKkPJj51uePP4ZZs0KnEUkqKp5FRFLRsmW+m8Yvv8CoUdC4cehEkm769IFKlXTgoEgBKp5FRFLN779Dly4wdy68/jocfHDoRJKOdtwRunWDZ56B9etDpxFJGiqeRURSyfLlcMwx8OWXMHIkHHFE6ESSzvr2haVL/Y80EQFUPIuIpI5ffoGOHWHKFHjxRd/fWSSejjwSGjbUgYMi+ah4FhFJBfPnQ/v2MGeObwU88cTQiSQTZGXBOefAe+/BvHmh04gkBRXPIiLJ7vPPoVUrWLQIRo+Go48OnUgyydln++snnwybQyRJqHgWEUlmb78N7dr5FsCJE/3fIonUqBEcdZQ/g+XmzaHTiASn4llEJBk5B3ffDV27+hOgTJoEzZuHTiWZqm9f33XovfdCJxEJTsWziEiyWbMGeveG/v2hRw/48EOoXz90KslkJ5wAderowEERVDyLiCSXr7/2/ZuHD4fbbvOn3K5ePXQqyXSVK8OZZ8Jrr/lRX0QymIpnEZFk8eyz0LIlLF4Mb70FAwf60ySLJINzz4VNm/xJU0QymIpnEZHQ1qzxw4GdcQYceKAfXUMjakiy2XtvaNPGd91wLnQakWBUPIuIhDRrFhxyCDz1FNxwA4wdCw0ahE4lUri+ff1Y4xMnhk4iEkzF0AFERDJF7vSFDBs9h0XL11I/J5t/rf+CA++6EapV8+M3d+4cOqJI8U4+mY2XXMp7lw+mX+fLqJ+TTf8uTeneQj/4JHOoeBYRSYDc6QsZMHIGazduJnvDOq58/j4O/Op9lrRsTd3XX4V69UJHFClR7tzlrGvanm5fvk/19ueycDkMGDkDQAW0ZAx12xARSYBho+ewduNmdl86n9xnr6LHV2O5/7Ce9DjxHyqcJWUMGz2H5/ftTPam9Rw/+0MA1m7czLDRcwInE0kcFc8iIgmwaPlaTpg1ntefuZId1vzOGafcyn3tTmfBig2ho4nEbNHytczY+W/MrtuYU794d6vbRTKFimcRkXhbv557PvgvD4waxsydduO4s+5nQpMWANTPyQ4cTiR29XOywYwR+3dh/5/+R7Ofv/vzdpEMoeJZRCSe5s2DNm3o8enrPN767/Q67XZ+rlEHgOxKWfTv0jRwQJHY9e/SlOxKWeQ2O5z1WZU45ct3tR5LxtEBgyIi8fLRR3DSSbBhA7z2Gjs0PIid8o22oVEKJNXkra/DRs/h7aaH0WPWB9R+8D5O0HosGUTFs4hIPDz6KPTrB02awOuvQ9OmdEcjEkjq696igV+PDzXo1IkTvp0Erf8WOpZIwqjbhohIedq4ES69FM4/Hzp1gk8/habapS1pqEMH2G03ePrp0ElEEkrFs4hIefn1V39a7QcfhKuvhjffhJyc0KlE4qNCBejdG95/HxYtCp1GJGFUPIuIlIf586FtW5gwwZ9q++67ISsrdCqR+Dr9dHAOhg8PnUQkYVQ8i4iU1VdfQevWsHChP832mWeGTiSSGHvuCYccAs89FzqJSMKoeBYRKYuPPoJ27WDLFv/34YeHTiSSWH36wOef+x+RIhlAxbOIyLbKzYXOnWGnneCTT2C//UInEkm8U0/1XZTU+iwZQsWziMi2ePJJP4bzAQf4fs6NGoVOJBJG3br+QNnnn/d7YETSnIpnEZHSeuIJOPdcOPJIP9JAnTqhE4mE1bs3LFgAH34YOolI3Kl4FhEpjSefhL594aij4LXXoFq10IlEwjvhBKheXV03JCOoeBYRidVTT/kW586dfX/nqlVDJxJJDttt57sxvfwyrFsXOo1IXKl4FhGJxVNPwTnnqHAWKUrv3rBiBbzxRugkInGl4llEpCTPPbd14ZydHTqRSPLp2BHq14dnnw2dRCSuVDyLiBTn3Xfh7LN9YaDCWaRoWVnQqxe89RYsXRo6jUjcqHgWESnKtGm+H+c++8D//Z8KZ5GS9O4Nmzb5vs8iaUrFs4hIYb7/Ho49FmrX9i1pNWuGTiSS/PbbD/bdV6NuSFpT8SwiUtDSpf6kDxs2wDvv+H6cIlIyM9914+OPYd680GlE4iJuxbOZNTSzcWY2y8xmmtnlBaZfbWbOzHR2AREJLnf6QtoMHcveV7/KVwe2Z/O8eTBqFOy9d+hoIqnltNP89YgRYXOIxEk8W543AVc755oBrYB+ZtYMfGENHAX8GMfli4jEJHf6QgaMnMGi31Zz3xv30Gz+11xxfH9yt2scOppI6mnSBFq3hhdeCJ1EJC7iVjw75xY756ZFf68EZgMNosn3AdcCLl7LFxGJ1bDRc1i7cTOXTRzB0XM/4bZO5zJq91YMGz0ndDSR1NSzJ3z5JcycGTqJSLlLSJ9nM2sMtAA+NbNuwELn3BclPOZ8M5tiZlOWLFmSgJQikqkWLV9Ll7kfc+XEF3hl3yN4vGW3P24XkW1wyilQoQIMHx46iUi5i3vxbGbVgVeBK/BdOQYCN5f0OOfcf51zLZ1zLevWrRvnlCKSyQ5b/zP3vnEv0+s15YYu/fxBT0D9HA1NJ7JNdtoJjjjCF89OO5klvcS1eDazSvjC+Xnn3Ehgd6AJ8IWZ/QDsAkwzs53jmUNEpEirVvHv14aytnJVLjhxIOsrVgYgu1IW/bs0DRxOJIX16gXffQeffRY6iUi5iudoGwY8Dsx2zt0L4Jyb4Zzb0TnX2DnXGFgAHOic+yleOUREiuQcXHghNed9y9f3/IdKDXfBgAY52dzRozndWzQocRYiUoQTT4QqVXTgoKSdinGcdxugDzDDzD6PbhvonHsrjssUEYndo4/C88/D4MG0veAUJobOI5JOatWC446DF1+Ee+/1p+8WSQPxHG1jgnPOnHP7OecOiC5vFbhPY+fc0nhlEBEp0qxZcPnl0KULDBwYOo1IeurZE37+GcaNC51EpNzoDIMiknnWr4fTT4caNeDpp/2oACJS/o47zm9nGnVD0oi+MUQk89x0E3z+OTz+uB8VQETiIzvb931+9VX/o1UkDah4FpHMMn483H03XHABHH986DQi6a9XL/j9d3j77dBJRMqFimcRyRxr1kDfvrDbbnDPPaHTiGSGI46AunU16oakDRXPIpI5brkFvvkGHnsMqlULnUYkM1Ss6M84OGoUrFwZOo1Imal4FpHMMHmyHy7rggvg8MNDpxHJLL16wbp1kJsbOolImal4FpH0t2kTnHsu1KsHd94ZOo1I5mndGho10qgbkhZUPItI+nvwQZgxw1/XqhU6jUjmMfNjPr/7LixZEjqNSJnEVDybWSMzOzL6O9vMasQ3lohIOfnpJ9/X+eijoVu30GlEMlfPnrB5M7z8cugkImVSYvFsZucBrwD/iW7aBVCnJRFJDdde6/taPvCAb/0SkTCaN4d99lHXDUl5sbQ89wPaACsAnHP/A3aMZygRkXIxcSI8+yxccw3ssUfoNCKZLa/rxoQJ8OOPodOIbLNYiuf1zrkNef+YWUXAxS+SiEg5cA6uvhoaNICBA0OnERHwxTPAiBFhc4iUQSzF83gzGwhkm1ln4GVgVHxjiYiU0auvwqefwuDBGtNZJFnsthsceqhOmCIpLZbi+TpgCTADuAB4C7gxnqFERMpkwwa4/nrYd18444zQaUQkv1694IsvYNas0ElEtkmxxbOZZQGznXOPOudOds79Pfpb3TZEJHn95z/w7bdw112QlRU6jYjkd8opUKGCDhyUlFVs8eyc2wzMMbNdE5RHRKRsVq2CW2+FTp388HQiklx23tlvn8OH+2MTRFJMLN02tgdmmtn7ZvZ63iXewUREtsnDD8PSpXDbbRqaTiRZ9erl9w5Nnhw6iUipVYzhPjfFPYWISHlYtQqGDfMtzq1ahU4jIkU58US48ELf+nzIIaHTiJRKicWzc258IoKIiJRZXqvzLbeETiIixcnJgeOO80PW3X23jk2QlBLLGQZXmtmK6LLOzDab2YpEhBMRiZlanUVSS8+e8NNP8MEHoZOIlEqJxbNzroZzrqZzriaQDZwEPBz3ZCIipfHvf6vVWSSVdO0K1atr1A1JObEcMPgH5+UCXeKUR0Sk9DZsgH/+0x/Br1ZnkdSQne37Pr/yCqxfHzqNSMxK7PNsZj3y/VsBaAmsi1siEZHSGj4cFi2Cxx8PnURESqNXL3j2WXjnHejWLXQakZjEMtrG8fn+3gT8AGgNF5Hk4Jw/4Kh5c+iinWIiKeWII6BOHX+6bhXPkiJiKZ4fc85NzH+DmbUBfolPJBGRUnjnHfjqK3j6aY3rLJJqKlXyZxx88klYuRJq1AidSKREsfR5/leMt4mIJN6wYdCgAZx2WugkIrItevaEtWvhtddCJxGJSZEtz2bWGjgMqGtmV+WbVBPQgIwiEt6XX8K4cXDXXVC5cug0IrItDjsMdt3VH7vQu3foNCIlKq7luTJQHV9g18h3WQH8Pf7RRERK8PDDULUqnHtu6CQisq0qVPB7jkaPhiVLQqcRKVGRLc/RmQXHm9lTzrl5CcwkIlKy33+H557zR+vXrh06jYiURa9efg/SK6/ARReFTiNSrFj6PK8xs2Fm9paZjc27xD2ZiEhxnn4aVq+Giy8OnUREymq//aBZM50wRVJCLMXz88DXQBPgH/ih6ibHMZOISPGc8102Dj0UDjoodBoRKSszf+DgRx/Bjz+GTiNSrFiK5x2cc48DG51z451z5wCd4pxLRKRoY8fCnDlqdRZJJz17+usXXwybQ6QEsRTPG6PrxWZ2nJm1ANTBUETC+c9/YIcd/PiwIpIedt8dDjnEnzBFJInFUjwPMbNawNXANcBjwJVxTSUiUpRly/x4sL17+5E2RCR99OoFn38Os2eHTiJSpGKLZzPLAvZwzv3unPvKOdfROXeQc+71BOUTEdnaCy/Ahg1w9tmhk4hIeTvlFD90nQ4clCRWbPHsnNsM9ExQFhGRkj3xBBx4IOy/f+gkIlLe6tWDjh198exc6DQihYql28ZEM3vQzNqZ2YF5l7gnExEpaPp0v0tXrc4i6atnT/jmG5gyJXQSkUIVeZKUfA6Irm/Nd5tDI26ISKI9+aQ/DXevXqGTiEi89OjhR9IZPhwOPjh0GpG/KLF4ds51TEQQEZFirV8Pzz8P3bvrjIIi6Wz77eGYY2DECBg2DLKyQicS2UqJ3TbMbCcze9zM3o7+b2Zm58Y/moiIlzt9Ideddxf8+itXb3cAudMXho4kInH0WeujYfFievW+kzZDx2qbl6QSS5/np4DRQP3o/7nAFfEKJCKSX+70hQwYOYN2k99jWXZNXqvTjAEjZ+jLVCRN5U5fyAW/7cyqytmc+NU4Fi5fq21ekkosxXMd59xLwBYA59wmYHNcU4mIRIaNnoOtXsUR33zGW3u1ZVNWRdZu3Myw0XNCRxOROBg2eg6/UYk39mrHsXMmUG39Gm3zklRiKZ5Xm9kO+IMEMbNWwO9xTSUiElm0fC2d/zeJ7E3rea1Zh61uF5H0k7dtv9S8M9U2ruPYORO2ul0ktFiK56uA14HdzWwi8AxwaVxTiYhE6udkc8LsD1lYoy5TG+y91e0ikn7ytu1pDfbi29q7cPKMMVvdLhJaicWzc24a0AE4DLgA2Mc592W8g4mIAAw8dEfafz+NUXu3w5n/yMqulEX/Lk0DJxOReOjfpSnZlbLAjJebH8khC2ax94rF2uYlacQy2kZV4DJgMPAPoF90m4hI3B03dyKVtmxm0qFHYUCDnGzu6NGc7i0ahI4mInHQvUUD7ujRnAY52YzctxObKlTg/nWfa5uXpGGuhNNfmtlLwErgueimXkCOc+7kOGf7Q8uWLd0UnWlIJDN16gSLFsHs2WAWOo2IJNrxx8O0aTBvHlSM5dxuImVjZlOdcy2Lmh5Ln+d9nXPnOufGRZfzgH3KL6KISBGWLoXx4+Hkk1U4i2Sqs8/2P6DffTd0EhEgtuJ5WjTCBgBmdiigZmARib/XX4ctW/zpekUkM3XtCnXqwBNPhE4iAsRWPB8EfGxmP5jZD8AnwMFmNsPMdOCgiMTPq69C48ZwwAGhk4hIKJUrQ58+/sf00qWh04jEVDwfDTTBj7jRIfr7aKArcHz8oolIRvv9dxgzxrc6q8uGSGY75xzYuBGefz50EpGYhqqbB6wAagE75F2cc/OiaSIi5e/NN2HDBjjppNBJRCS0ffeFli19140SBjoQibcSD1s1s8HAWcC3RGcZjK47xS+WiGS8kSNh552hVauS7ysi6e+cc+Dii2H6dDjwwNBpJIPF0m3jFGB359zhzrmO0UWFs4jEz5o18PbbcOKJUCGWjykRSXs9e0LVqvDYY6GTSIaL5VvpKyAn3kFERP7w3nu+gNYoGyKSJyfHD1v53HOwalXoNJLBYime7wCmm9loM3s97xLvYCKSwUaNgpo1oX370ElEJJlcdBGsXKkDByWoWE7V8zRwJzAD2BLfOCKS8bZsgTfegKOP9kNUiYjkadUK9t8f/v1vOP98jcQjQcRSPK9xzj0Q9yQiIgBTpsDPP/tT8oqI5GfmW58vvBAmTYLWrUMnkgwUS7eNj8zsDjNrbWYH5l3inkxEMtOoUf4gwWOOCZ1ERJLR6adDjRrw8MOhk0iGiqXluUV0nX+8KA1VJyLxMWoUtGkDO+wQOomIJKPq1f0ZBx97DO69F+rWDZ1IMkwsJ0npWMhFhbOIlL/58+GLL9RlQ0SK16+fP4nSo4+GTiIZqMTi2cx2MrPHzezt6P9mZnZu/KOJSMZ54w1/reJZRIrTrBkcdRQ89JAvokUSKJY+z08Bo4H60f9zgSviFUhEMtioUfC3v0HTpqGTiEiyu+IKWLQIXnkldBLJMEUWz2aW1x+6jnPuJaJh6pxzm4DNCcgmIplk7VoYNw6OO07DT4lIybp08T+077sPnAudRjJIcS3Pn0XXq81sB/xBgphZK+D3eAcTkQwzfjysW6dRNkQkNhUqwOWX++EtP/kkdBrJIMUVz3lNP1cBrwO7m9lE4Bng0ngHE5EM8847ULWqziooIrE74wx/2u577gmdRDJIcUPV1TWzq6K//w94C19QrweOBL6MczYRySRvvw0dO0J2dugkIpIqqlWDiy+GO+6Ar7+GvfYKnUgyQHEtz1lAdaAGUA1faGcB20W3iYiUj+++g7lz/Sm5RURK4/LLoUoVuOuu0EkkQxTX8rzYOXdrwpKISOZ65x1/rf7OIlJaO+4IffvCI4/AP/4BDRuGTiRpLpY+zyIi8fX227Dbbn6YOhGR0rrmGn+tvs+SAMUVz0ckLIWIZK7162HsWN/qrCHqRGRbNGoEp58O//0vLFkSOo2kuSKLZ+fcr4kMIiIZasIEWLNGXTZEpGyuv97/GL/zztBJJM3FcoZBEZH4ee89qFQJOnQInUREUtlee0GfPvDgg7BgQeg0ksZUPItIWO+/D61aQfXqoZOISKq75RbYsgWGDAmdRNKYimcRCefXX2HqVDjyyNBJRCQdNGkC558Pjz8O334bOo2kKRXPIhLOuHHgHByh45NFpJzccIPvCnbzzaGTSJpS8Swi4bz/vu+uccghoZOISLqoVw+uvBJeeAE+/jh0GklDKp5FJJwxY+Dww30rkYhIeRkwABo0gEsugc2bQ6eRNKPiWUTC+PFH+N//1GVDRMpf9epw990wfTo89ljoNJJmVDyLSBjvv++vdbCgiMTDqaf6ITAHDoRly0KnkTSi4llEwhgzBnbaCfbZJ3QSEUlHZvCvf8GKFXDppaHTSBpR8Swiieecb3k+4gidkltE4qd5cz/qxvDh8OKLodNImlDxLCKJN3Mm/Pyz+juLSPwNGOBH9Lno+uOGGAAAIABJREFUIli0KHQaSQMqnkUk8dTfWUQSpWJFePZZWLcOzjpLo29Imal4FpHEGzMG9tgDdt01dBIRyQR77gn33w/vvQfXXBM6jaS4iqEDiEiG2bgRxo+H008PnUREMsl55/kuY//8JzRtChdeGDqRpCgVzyKSWJMnw8qV6rIhIol3zz1+fPlLLvFnIuzWLXQiSUFxK57NrCH8f3t3Hq/1nP9//PHutDi0CROFEBpLKR1ryJ5MJWX/IuP7ZcyXGds0o5n5zvId38HkN4uZwZhhym5GSYSEpI6UNqImOzmRDIfiSMvn98f7lCzlVOc672t53G+3btfpOsv1rE/XOc8+1+vzfnMz0BbIgBuyLPtDCGEo0Bf4FHgZ+HaWZdW5yrEhRs2sYujYeSyorqFd63IG9+pE/27tU8eSisMjj8QVNg47LHUSSaWmrCyuvHHkkTBgADN/ciUXbNo9pz/v7RTrpxD+vkKWZbn5wiFsA2yTZdmMEEILYDrQH9gWeCzLsuUhhKsAsiz70bq+VkVFRTZt2rSc5PyiUTOrGDJyNp98uozuVXOZtu0elDcp44oBnfPu4EkFqWdP+OgjaKDntCR9yZIlLOzVl7ZPPs41B5zMNT1OZXlZ443/eb9sGcydG1f1eOcdZr74Nn+f+yELmzZn7jd25MNNmtsp1mFVB/vGO/P5pHFTFrbYMsnfVwhhepZlFWt7f87OPGdZ9hbwVu3bi0MIc4H2WZY9vMaHPQWckKsMG2Lo2HnULFvBmTPG8L+P/IU+g37Pc1vvzNCx8/yHLm2sjz6CyZPh4otTJ5FUypo358Rjh3DB4sZ8f/Jd9H7hSX55xLlM2rHb+v28r6qCKVPgqafir2nToKZm9bu71f4CWB4aMatdJx7ruA9/oYb+3Y6v9z9WoVvVwS6edBsHvv4s+55/MzXLVuRdB2uQmecQwg7Efz9TvvCus4GvXLU8hHAucC7A9g14Rf6C6viP/p49D+eSSbdxycRbOfvEX6y+X9JGmDgxnplx3llSYvMXL+OHvS/koV0P5GeP/pVb//E/PLP1Lozd9QDovQV06ACtWsUxs6VL49r0zz8Ps2fHkjx5Mrz5ZvxiTZtC9+7xIsR9942fu9VWHPjbSbT8ZAlbflTNvvOf45DXZvDDJ27m/Mn/gI++Cz/6UdxpVUBtB8sy9n9jNk9t33n1Jlr51sFyXp5DCM2BEcBFWZZ9uMb9PwGWA7d91edlWXYDcAPEsY1c51ylXetyqqprWNxsM/6y30B+NGE4e1fNZeEeezdUBKl4PfYYNGkCPXqkTiKpxK36ef/YzvtSuUNX/mPmg/SbO4EfPnEzdL05flB5edwR9ZNPPv/JHTrAQQfB/vvDAQfAXntBs2Zfeoyw/Rv8q7b4TdqxG7895Ax2XfQal8wYxTHXXAPDhsXVP844w91WicekySsvsfWS92J5XuP+fJLT8hxCaEIszrdlWTZyjfvPAvoAR2S5GrreQIN7dWLIyNnULFvBsL37cvbT9zJ40m0svOTU1NGkwvfEE/GszKabpk4iqcSt+fN+aeOm3LTPcdxx4AB+12MLjnn/pTi3/NZbsdRuvjlsuSXsthvsuWf8/Xo+xirz23XkkwuGQfli+K//gkGD4M474eab42OUsMG9OjH9f0YD8NR2sTyXNyljcK9OKWN9SS5X2wjAjcDcLMt+u8b9xwA/BHpmWfZxrh5/Q62aqYlXesLth53GhWOuheoXgPyZt5EKzpIl8aXOH63z+mBJahCf/3n/2coOx3RrD+yT08dYPb/7xBPw5z/D4MGwzz4walQ8i12i+ndrT/eVb/Buiza82qY97UtwtY2DgInAbGBl7d0/Bq4BmgH/rr3vqSzL1rlSeUOutvEln3wCHTvG3YnGj0+TQSoGDz8MvXrB2LFw9NGp00hS/nj6aTj+eHj/fbj11vh2Kcoy2G67OBJz553JYnzdahs52547y7JJWZaFLMu6ZFnWtfbXA1mW7Zxl2XZr3JffW/xssklcGeDxx2H69NRppMI1YUJcY/XAA1MnkaT8ss8+8ZW5Ll3ghBNg+PDUidJ4+eW4gsmhh6ZOsk45K89F5ZxzoEWLuDORpA0zYQJUVEDz5qmTSFL+2XrruInU4YfDWWfBtdemTtTwHn883lqei0CrVnGo/x//gDfeSJ1GKjwffwxTp8Ihh6ROIkn5a7PN4L77oF8/OP98uO661Ika1uOPx6X7OuXXBYJfZHmuqwsvjLfXXJM2h1SInnoqru/cs2fqJJKU3zbZBO6+G/r2jQX69ttTJ2oYWRbL86GH5v2yfZbnuurQAU48EW64AT788Os/XtJnJkyARo3iRSCSpHVr0gTuuiu+WnfmmXD//akT5d6qeecCOMlieV4fl1wCixfDLbekTiIVlieegK5d4wiUJOnrlZfD6NHQrRucdFK8oLCYPfhgvO3VK22OOrA8r4999oG994brr48vL0j6ekuXxrGNAjibIEl5pWXLeNb5G9+IYxzFfN3VAw/EWeeddkqd5GtZntfXeefBc8/FPe0lfb2pU+N66ZZnSVp/bdvCmDHxwus+feIr4MXm44/jXhrHHps6SZ1YntfXqafGZeuuvz51EqkwTJgQbw8+OG0OSSpUe+wRLyKcMwe+/e3ie/V7/Pj4KqXluUg1bw6nnx6XrXvvvdRppPw3YQJ07gxt2qROIkmF66ij4KqrYMQIGDo0dZr69cADcZm+AjnJYnneEN/5TvwfUqnuACTV1bJl8OSTjmxIUn245JJ48eCQIfDoo6nT1I8si+X5yCOhWbPUaerE8rwh9toL9t8f/vrX4nvpRKpP06bFWTbLsyRtvBDgxhvjhXWnnALz56dOtPHmzoXXXiuYkQ2wPG+4s8+OB7zYl46RNsaqeWd3FpSk+tG8OdxzT3wF/IQT4m0he+CBeNu7d9oc68HyvKFOOinuAjRsWOokUv6aMAF22y0usyRJqh+dOsXR0alT4fvfT51m49x3X7wuZrvtUiepM8vzhmrVCvr3hzvuKPz/9Um5sHw5VFY6siFJuXD88XDZZXHn40I9kbdgAUycGM+gFxDL88YYNAjef780ts2U1tesWXE9UsuzJOXG5ZfDYYex/Lv/zX9cfBM7XjaGHlc+xqiZVamT1c0//xmvHTv55NRJ1ovleWMcdRS0a1e4/+OTcsl5Z0nKrbIyHrzsaqrLmvGzW39Js2WfUFVdw5CRswujQN91V1yEoVOn1EnWi+V5Y5SVxTWfH3wQFi5MnUbKL5MmxW1W27VLnUSSitblM6q56FuXssu78/nluL8AULNsBUPHzkuc7Gu8/nrcrfmUU1InWW+W5401aBCsWAF33pk6iZQ/sizOO/fokTqJJBW1BdU1TNqxG38+4CROnj2O/s+PX31/XvvHP+LtSSelzbEBLM8ba/fdoUuXeOGgpOill2DRIsuzJOVYu9blAPz+oNOYsu0e/N/YP9Px3/NX35+37rwT9tknvkJZYCzP9eG002DKFHj11dRJpPxQWRlvLc+SlFODe3WivEkZKxqV8f1+g/mkcVOuHX0VP+q5fepoa/fiizBjRkGObIDluX6sOviObkhRZSW0bh1fmZEk5Uz/bu25YkBn2rcu550WW/J/Jw+h0zuv0W/Y0NTR1u5vf4vXjRXYKhurhKwAtpeuqKjIpuX7Tn49esRluZ59NnUSKb3dd4cddvhs5yhJUsO57DK46qo4UppvZ3eXLoVtt4WDD4aRI1On+UohhOlZllWs7f2eea4vp54Ks2fD88+nTiKl9d57cet6RzYkKY1f/QoOPBDOOSeOSOSTu++Gd9+F7343dZINZnmuLyeeCI0aeeGg9OST8dbyLElpNGkSR0mbNo2rWXzySepEn7nuOth5ZzjiiNRJNpjlub60bRv/Idx5Z1ymSypVlZXQuDHsu2/qJJJUurbbDoYPj7u9Xnpp6jTRs8/GnxHnnRdPOBaowk2ej048EV5+2blnlbbKSujWDTbdNHUSSSptffrE4nzttXFcIrXrroNmzeCss1In2SiW5/rUv3/8n9SIEamTSGl8+ik8/bQjG5KUL664AvbbD/7zP+MJvlTeeguGDYvXiG2xRboc9cDyXJ+22goOOcTyrNI1Y0acrbM8S1J+aNIE7rorntwbMAA++ihNjquugmXL4Mc/TvP49cjyXN8GDoQ5c+Bf/0qdRGp4bo4iSfmnQ4e4oMFzz8G3v93w12YtWADXXw9nngm77NKwj50Dluf6dvzx8dazzypFlZWw446wzTapk0iS1nTMMXGE45//hCuvbNjHvuIKWLECfvrThn3cHLE817f27WH//fN24W8pZ7IslmfPOktSfho8OM4c/+QnDXeSb/58uOGGeMZ7p50a5jFzzPKcCwMHxtnPV19NnURqOC+/DO+8Y3mWpHwVAtx4YzzJd/rpn43a5UqWwfe/Hx/3Jz/J7WM1IMtzLgwcGG89+6xS4ryzJOW/8nIYPTquA92vH8ybl7vHGjECRo2CX/4yzl0XCctzLuy4Y1zn1rlnlZLKSmjVCvbYI3USSdK6bLklPPRQ3NDqyCNzs4Tde+/B+efD3nvnzyYt9cTynCsDBsDkyVBVlTqJ1DAqK+GAAwp61yhJKhk77QQPPww1NXDYYfDKK/X3tbMMLrwwFuibboolvYj4Uy5XVo1ujBqVNofUEN57Ly7R6MiGJBWOvfaCRx+Naz8feijMnVs/X/fqq+HWW+Oc81571c/XzCOW51zZbbf4y9ENlYLJk+Ot5VmSCsuqAv3pp/HVw3HjNu7r3XEH/PCHcPLJ8LOf1U/GPGN5zqWBA2HCBFi0KHUSKbeefBLKymDffVMnkSStr65dYerUeFFf797wu9/BypXr/3Xuuw8GDYKePWH48KId4yvOP1W+GDAg/uO7997USaScGDWzih5XPsZTt4xm7tY7M+qF6tSRJEkbYvvtYdIk6NMHLrkEDjnkS7slr/qev+NlY+hx5WOMmll7Xdfy5XHb7X79oHNnuOceaNYswR+iYViec6lr17jyhqMbKkKjZlYxZORsFv57MXu99SKTt+7EkJGzP/tmKkkqLC1axOI7fHi8jmWvveCcc+DZZ1d/z6+qriEDqqpr+PGIZ5h8zc3xTPMVV8SPnTQJNt889Z8kp4rr8sd8E0Ic3fjDH+CDD+IyXlKRGDp2HjXLVrDXwpcpX76UadvuTs2yFQwdO4/+3dqnjidJ2hAhwJlnQq9ecWb5llvgb39jj2068qstduDFLbdj00+X0nbJvzngjWfpUP02bLMN3HwznHFG6vQNwjPPuXbccbBsGYwdmzqJVK8WVNcAUFEVr86e1n63z90vSSpgbdvCX/4Cb74Jv/kNbzdrySGvzmDI48P43pN3ctgr05jfqi0X9PsRvP56yRRn8Mxz7h1wAGyxRdzN56STUqeR6k271uVUVdfQ/c05zG/VlndabLH6fklSkWjTBgYP5rIV3amqrqHF0o+oadyM5WWxQrZvXQ5NmiQO2bA885xrZWVx+H7MmHgGWioSg3t1orxxIyqq5q4+61zepIzBvTolTiZJqm+De3WivEkZi5tttro4l+r3fMtzQ+jXD6qr4w5sUpHo3609f9ivFd/46H2mb7s77VuXc8WAzs47S1IR6t+tPVcM6Ez71uUEKOnv+Y5tNISjj45LtoweHXfwkYrE0dUvA3D50O9Aly6J00iScql/t/YlWZa/yDPPDaF5czjiiFiesyx1Gqn+VFZCy5awxx6pk0iS1CAszw2lXz94+eX62zdeygeVlfGi2LKy1EkkSWoQlueG0qdPvHW3QRWL6mp4/nno0SN1EkmSGozluaG0bw8VFXF0QyoGkyfHMSTLsySphFieG1K/fjBlCrz9duok0sarrIzjGvvtlzqJJEkNxvLckPr1i2fqxoxJnUTaeJWV0LUrbLZZ6iSSJDUYy3ND6tIFtt/e0Q0VvmXL4qsojmxIkkqM5bkhhRDPPo8bBx9/nDqNtOFmzYKaGsuzJKnkWJ4bWr9+sXQ8+mjqJNKGW7VbpuVZklRiLM8NrWfPuKmEoxsqZJWV0KFDXEVGkqQSYnluaE2bQu/ecN99sHJl6jTS+suyWJ496yxJKkGW5xT69oWFC+Hpp1Mnkdbfa6/BW29ZniVJJcnynELv3nF9XEc3VIicd5YklTDLcwpt2sBBB8XRDanQVFbGuf0990ydRJKkBmd5TqVfP5g9O74ELhWSykrYf//46okkSSXG8pxK377x1rPPKiTV1fDcc45sSJJKVuPUAUrWLruweIed+dc1wzipaifatS5ncK9O9O/m0l/KY089FVfbsDxLkkqUZ54TGTWzin9s05W9XnmW5ks/oqq6hiEjZzNqZlXqaNLaVVbGcY399kudRJKkJCzPiQwdO48Hd9qHpiuXc8grMwCoWbaCoWPnJU4mrUNlJey1FzRvnjqJJElJWJ4TWVBdw4x23+S98pYc8fLUz90v5aVly2DKFEc2JEklzfKcSLvW5axsVMb4jhUc/vLTlK1csfp+KS898wx8/LHlWZJU0izPiQzu1YnyJmU80nFfWn+yhO5VcylvUsbgXp1SR5O+mpujSJLkahuprFpV48+Nl7P0/sb0nz+d035wuqttKH9VVsL228O226ZOIklSMpbnhPp3ax/L8pOHc9prz4DFWfkqy2J57tkzdRJJkpJybCMf9OsHL7wA81xpQ3nq9ddhwQJHNiRJJc/ynA/69Im37jaofDVpUry1PEuSSpzlOR906BDXzrU8K19NnAgtW0LnzqmTSJKUlOU5X/TtG8/u/fvfqZNIXzZpUjzrXFaWOokkSUlZnvNFv36wciU8+GDqJNLn/fvfMGcOHHxw6iSSJCVnec4X3bvD1lvD6NGpk0ift2re+aCD0uaQJCkPWJ7zRaNGcXTjoYfg009Tp5E+M3EiNG0K++yTOokkSclZnvNJ376weDFMmJA6ifSZiRNh331hk01SJ5EkKTnLcz454ggoL3fVDeWPjz6CGTOcd5YkqZblOZ9suikceWSce86y1GkkmDIFli+3PEuSVMvynG/69o27uT33XOokUhzZCAEOOCB1EkmS8oLlOd+s2m3QVTeUDyZOhC5doHXr1EkkScoLlud8s802cVUD556V2rJlMHmyIxuSJK3B8pyP+vWDqVPh7bdTJ1EpmzULPv7Y8ixJ0hosz/mob994weCYMamTqJRNnBhvLc+SJK1mec5HXbrA9ts7uqG0Jk6Ejh3jKJEkSQJyWJ5DCNuFEMaHEOaEEJ4PIVxYe3+bEMK4EMKLtbeb5ypDwQohnn1++GGoqUmdRqUoy+K23G7JLUnS5+TyzPNy4NIsy3YH9gfODyHsDlwGPJpl2S7Ao7W/1xf16xeL82OPpU6iUvSvf8G77zqyIUnSF+SsPGdZ9laWZTNq314MzAXaA8cBw2s/bDjQP1cZClrPntC8uUvWKQ3nnSVJ+koNMvMcQtgB6AZMAdpmWfZW7bveBtqu5XPODSFMCyFMW7RoUUPEzC/NmsExx8D998PKlanTqNRMmgTf+AbsskvqJJIk5ZWcl+cQQnNgBHBRlmUfrvm+LMsy4Cv3oc6y7IYsyyqyLKvYaqutch0zP/XtCwsWwPTpqZOo1EycGM86h5A6iSRJeSWn5TmE0IRYnG/Lsmxk7d0LQwjb1L5/G+CdXGYoaH36QOPGMHLk13+sVF/efBNee82LBSVJ+gq5XG0jADcCc7Ms++0a7xoNDKp9exBwb64yFLw2beCww2DEiLj6gdQQnHeWJGmtcnnmuQdwBnB4CGFW7a9jgSuBo0IILwJH1v5eazNwILz4Ijz3XOokKhXjx0OrVtC1a+okkiTlnca5+sJZlk0C1jYweUSuHrfo9O8P3/1uPPvcuXPqNCoF48fDIYdAWVnqJJIk5R13GMx3bdvGl89HjEidRKXgzTfhpZfiuJAkSfoSy3MhGDgwjm288ELqJCp248fH20MPTRpDkqR8ZXkuBAMGxFvPPivXHn8cNt8c9tordRJJkvKS5bkQbLst7Lef5Vm5N3583N2ykd8aJEn6Kv6ELBQDB8bNUl57LXUSFavXX4dXX3XeWZKkdbA8F4qBA+OtG6YoV1bNO1ueJUlaK8tzodhpp7ju7t13p06iYjV+PGyxBeyxR+okkiTlLctzIRk4ECZPhqqq1ElUbLIsludDD3XeWZKkdfCnZCFZNbpxzz1pc6j4vPACzJ8PRx6ZOokkSXnN8lxIdtst/nLVDdW3cePi7VFHpc0hSVKeszwXmoED4YknYNGi1ElUTB5+GHbcETp2TJ1EkqS8ZnkuNCecACtXuuqG6s+yZXFzlKOPTp1EkqS8Z3kuNF26wDe/CXfckTqJisWUKbB4sSMbkiTVgeW50IQAp50WRzfefDN1GhWDcePiChuHH546iSRJec/yXIhOPTUuLXbXXamTqBiMGwcVFbD55qmTSJKU9yzPhWjnnWGffeD221MnUaGrroapUx3ZkCSpjizPherUU2HGDJg3L3USFbLx42HFCi8WlCSpjizPherkk+P8sxcOamM8+CC0aAH77586iSRJBcHyXKjatYtbKd9+e5x/ltZXlsGYMfGsc9OmqdNIklQQLM+F7Iwz4MUX4amnUidRIZo1CxYsgG99K3USSZIKhuW5kJ1wAmy6KQwbljqJCtGYMfH22GPT5pAkqYBYngtZixaxQN95J9TUpE6jQjNmTFy1pW3b1EkkSSoYludCd9ZZ8OGHMGpU6iQqJIsWxZ0F+/RJnUSSpIJieS50PXtChw4wfHjqJCokDz4YLxh03lmSpPVieS50jRrBoEFxl7iqqtRpVCjuvx+23hq6dUudRJKkgmJ5LgZnngkrV3rhoOrm009h7Nh4oWAjvwVIkrQ+/MlZDDp2hCOOgBtuiLvFSevy6KNxTv7441MnkSSp4Fiei8V558Ebb8BDD6VOonx3993QsiUcdVTqJJIkFRzLc7E47rg4w3rddamTKJ8tWxZXZunXD5o1S51GkqSCY3kuFk2awH/9FzzwALz+euo0ylfjx8N778X1wSVJ0nqzPBeTc86BEOCvf02dRPnq7ruheXM4+ujUSSRJKkiW52Ky/fZx3d6//Q2WLk2dRvlm+XK45564MUp5eeo0kiQVJMtzsfne92DhQrj99tRJlG+eeALefdeRDUmSNoLludgceSTstRdcfXVc+1la5c47YdNN4ZhjUieRJKlgWZ6LTQjwgx/AnDkuW6fPfPxxLM8nngibbZY6jSRJBcvyXIxOPhm23TaefZYARoyAxYvh299OnUSSpIJmeS5GTZrARRfFZcmmT0+dRvng73+HnXaCQw5JnUSSpIJmeS5W55wDrVrB5ZenTqLUXn01/kfq29+OYz2SJGmDWZ6LVcuWcOmlcTe5p59OnUYpDR8eS/OgQamTSJJU8CzPxeyii1jaug1TT/suO142hh5XPsaomVWpU6mBjJpZxUG/foQ3f3cdUzvuzah3fbpLkrSx/GlaxEa99CG/qxjIvi9NZ783nqWquoYhI2dboEvAqJlVDBk5m92nPc62H77D8N2P9NhLklQPLM9FbOjYefy9yzG83bwNP3jiFsgyapatYOjYeamjKceGjp1HzbIVnDt1JG+0astDnQ702EuSVA8sz0VsQXUNS5s04w89TqOiai795j6x+n4VtwXVNXR/cw4VVXP52z79WdGobPX9kiRpw1mei1i71uUA3NXlKJ7Zehf+57G/0vKTJavvV/Fq17qc86aM4L3ylvyz81Gfu1+SJG04y3MRG9yrE+VNyljZqIwf9zqfNh9/yJBJtzC4V6fU0ZRjv9y1jKNemsLNe3+LmqabAFDepMxjL0nSRmqcOoByp3+39kCcf53Dzow4oD+nTL6H8OmbQPu04ZRTR466keWbbMK4Q08gLI9nnAf36rT634QkSdowIcuy1Bm+VkVFRTZt2rTUMQrfhx/C7rtD8+YwbVq8VfGZOhX22w8uuwyuuCJ1GkmSCkoIYXqWZRVre79jG6WkZUu4+WZ44QW44ILUaZQLWRa3Zt96a/jxj1OnkSSp6FieS83hh8NPfxp3nbvlltRpVN/uuAMmT4Zf/xpatEidRpKkouPYRilavjyW6Bkz4MknoUuX1IlUH5Ysgd12g298I27J3sj/G0uStL4c29CXNW4cz1C2bg29e8Mbb6ROpPrwve9BVRVcc43FWZKkHPEnbKlq3x4efDCerezdG95/P3UibYzbb4dhw+AnP4EePVKnkSSpaFmeS1nnzjBqFLz4InzrW1BdnTqRNsTLL8N558GBB8LPf546jSRJRc3yXOoOOwzuvDMuXXf44bBoUepEWh/vvw8DBsQxjdtvjyM5kiQpZyzPiuXr3nth7lzo2dMZ6EKxZEl8xeBf/4J//hM6dEidSJKkomd5VtS7Nzz0ULzgrKICnngidSKtS00NHH88TJkSL/486qjUiSRJKgmWZ32mZ8+4O93mm8MRR8Af/xg33VB+qaqKx+qRR+DGG+MrB5IkqUFYnvV5nTrFs5m9esH3vx/PSC9YkDqVVpkyBfbZB+bMiRd7nnVW6kSSJJUUy7O+rHVrGD0a/vSnOL6x555w112pU5W2mhoYMiQuQ9esWdxF8LjjUqeSJKnkWJ711Ro1gvPPh1mzYNdd4ZRT4NRT4b33UicrLVkWL+bs2hWuvBLOPBOmT4/LDEqSpAZneda67borTJoEl18Od98dz0Lff3/qVMVvVWnu3h3694+/HzcObroJ2rRJnU6SpJJledbXa9w47lw3ZQpsuSX07QuDBrkrYS5kWRyZWVWaFy+G4cPjjPORR6ZOJ0lSybM8q+723jtupvLTn8Jtt8Wz0GPGpE5VHLIM7rsvLhN43HHw4Ydxu+25c+OohpufSJKUF/yJrPXTtCn86ldxjeGzzoI+fXij74mc3X0QL9dAu9blDO7Vif7d2qfhSKwpAAANAUlEQVROmtdGzaxi6Nh5LKiuoff7L/J/k4ax+ZxnYKed4O9/h9NPtzBLkpSHPPOsDVN7Fnref11I+/tHcP0157HLoteoqq5hyMjZjJpZlTph3ho1s4ohI2eTvfE6fxp1BdfecDGfzK9ixs+ujrsFnnWWxVmSpDxledaGa9qUszv24/STL6fV0iXce/Ol9JvzODXLVjB07LzU6fLW0LHzOHrWIzx04wUc9so0fnvQf3DYOdfzvfJu0KRJ6niSJGkdPL2ljbKguoaqDl049qw/8qfRV3HNfVezw/tv8ccDT0kdLT8tWcLgW/6X/nMmMK39blzc51Lmt94aiH+XkiQpv3nmWRulXetyABY135zTT/4Vd+95BJdMuo1rx10Dy5YlTpdn5s+Hgw+m79yJXH3w6Zx82pWrizN89ncpSZLyl+VZG2Vwr06UNykDYFlZE35w7EX8oeeZ9J45Dk48EZYuTZwwTzz9NOy7L7z8MlOuGcaNPf+DFY3KVr+7vEkZg3t1ShhQkiTVheVZG6V/t/ZcMaAz7VuXE4D2m29Kh9/9Om7tfe+9cVWOmhIfRxg/Hg47DDbZBCZP5sALzvj831nrcq4Y0NkVSiRJKgAhy7LUGb5WRUVFNm3atNQxtL7++lf4znfgiCNg1CjYbLPUiRre6NFw0kmw885xh8BttkmdSJIkrUMIYXqWZRVre79nnpU755wTN/p47DE49ti4W14pGTECBgyALl1gwgSLsyRJRcDyrNw680y4/XaorISjj4YPPkidqGHccw+ccgrstx888ghssUXqRJIkqR5YnpV7J58M//xn3Nq7FM5A33dfHNXo3h0efBBatkydSJIk1RPLsxrG8cfDXXfBlCnQpw989FHqRLnxyCNwwgnQtSuMHWtxliSpyFie1XAGDIBbb4VJk6Bfv+JbhWPyZDjuONh111icW7VKnUiSJNUzy7Ma1imnxIsIx4+H/v3hk09SJ6ofzzwTR1LatYurarRpkzqRJEnKAcuzGt4ZZ8Df/gYPPxxHHD79NHWijTNvXrwYsnnzOLax9dZf/zmSJKkgWZ6Vxtlnw/XXw5gx8YLCQt3K+/XX4cgjIctice7QIXUiSZKUQ5ZnpfOd78A118QNVE4/HZYvT51o/VRVxeK8eHE8i97J7bUlSSp2jVMHUIn73vfiWedLL4UmTWD4cCgrS53q6739dtw58e2344xz166pE0mSpAZgeVZ6l1wS556HDIkF+sYboVEevyiyaFEszvPnx1U19t8/dSJJktRALM/KD5ddBkuXwi9+EQv09dfnZ4H+97/jqMarr8IDD8BBB6VOJEmSGpDlWfnjZz+LZ6B//WtYsQL+8hdonEf/RN9/H446Kq6ucf/9cOihqRNJkqQGlkfNRCUvBLj88liY//d/oboabr8dmjVLnQzefRd694bnn4d7741nnyVJUsnJw9fFVdJCgF/+En7/exg5Mm48Ul2dNtP8+XDwwfDcczBiBBxzTNo8kiQpGcuz8tOFF8LNN8PEifGCvJdeSpPj+eehRw9YsCBeHNinT5ockiQpL+RsbCOEcBPQB3gny7I9a+/rClwPbAIsB/47y7KpucqgAnfGGXHTkQEDYL/9qLz8T/zwg7YsqK6hXetyBvfqRP9u7ev1IUfNrGLo2HksqK7h5Krp/Grkb2jSojlMmOBydJIkKadnnocBX3x9+zfAL7Ms6wr8rPb30todcghMmcKHm29Fj/8+jTNGXUvZiuVUVdcwZORsRs2sqreHGjWziiEjZ/P2e0u4aOJtXHnrz5nbuj0PDbvP4ixJkoAclucsy54A3vvi3UDL2rdbAQty9fgqIh070v/M33Jb12M4b8oIRtw6mD3ffomaZSsYOnZevT3M0LHzaP/Wq4y49Qdc+OQd3L3nEZx46pX8atbiensMSZJU2Bp6tY2LgLEhhKuJxf3AtX1gCOFc4FyA7bffvmHSKW+9+nHGT3pdwMQduvGrh69j9PCLub3rMfzu4NPr5wE++IBTRt/AuVNH8FHTTTm/348Ys9vBACyorqmfx5AkSQWvoS8Y/C5wcZZl2wEXAzeu7QOzLLshy7KKLMsqttpqqwYLqPzUrnU5AA916sER51zPsO59OeWZsVRef3bc4vvVVzfsC7/zDlxxBey4I9+bfBdjdz2Qo//zz6uL85qPLUmSFLIsy90XD2EH4P41Lhj8AGidZVkWQgjAB1mWtVzHlwCgoqIimzZtWs5yKv+tmkeuWbZi9X27f7CA6xY8SocHR8Ly5XDggTBwYNzI5Jvf/OoNVrIMXnkFJk2KS+E98ED83GOPZfzp3+e/52Sfe4zyJmVcMaBzvV+YKEmS8lMIYXqWZRVre39Dj20sAHoCjwOHAy828OOrQK0qr6tWwmjXupxzTz6WDt3OgaoquOmmuAbzJZfET2jWDHbbDdq0gRYt4s6FCxfGNZsXLYofs/XWcPHFMGgQ7LEHhwFXrLHaRq5W9JAkSYUrZ2eeQwh3AIcCWwILgZ8D84A/EEv7J8Sl6qZ/3dfyzLPq7OWX4amnYNYsmDMHPvgAFi+GJk2gbVvYZhvo3h0OOgj22AMaudS5JEn6zNedec7p2EZ9sTxLkiSpIXxdefa0myRJklRHlmdJkiSpjizPkiRJUh1ZniVJkqQ6sjxLkiRJdWR5liRJkurI8ixJkiTVkeVZkiRJqiPLsyRJklRHlmdJkiSpjizPkiRJUh1ZniVJkqQ6sjxLkiRJdWR5liRJkurI8ixJkiTVkeVZkiRJqiPLsyRJklRHlmdJkiSpjizPkiRJUh1ZniVJkqQ6sjxLkiRJdWR5liRJkurI8ixJkiTVUciyLHWGrxVCWAS8nuChtwTeTfC4Ss9jX7o89qXLY1+6PPalaW3HvUOWZVut7ZMKojynEkKYlmVZReocange+9LlsS9dHvvS5bEvTRt63B3bkCRJkurI8ixJkiTVkeV53W5IHUDJeOxLl8e+dHnsS5fHvjRt0HF35lmSJEmqI888S5IkSXVkeZYkSZLqyPK8FiGEY0II80IIL4UQLkudRw0nhPBaCGF2CGFWCGFa6jzKnRDCTSGEd0IIz61xX5sQwrgQwou1t5unzKjcWMux/0UIoar2uT8rhHBsyoyqfyGE7UII40MIc0IIz4cQLqy93+d9kVvHsV/v570zz18hhFAGvAAcBbwJPA2cmmXZnKTB1CBCCK8BFVmWuWB+kQshHAIsAW7OsmzP2vt+A7yXZdmVtf9x3jzLsh+lzKn6t5Zj/wtgSZZlV6fMptwJIWwDbJNl2YwQQgtgOtAfOAuf90VtHcf+JNbzee+Z56+2L/BSlmWvZFn2KXAncFziTJLqWZZlTwDvfeHu44DhtW8PJ35zVZFZy7FXkcuy7K0sy2bUvr0YmAu0x+d90VvHsV9vluev1h6Yv8bv32QD/4JVkDLg4RDC9BDCuanDqMG1zbLsrdq33wbapgyjBndBCOHZ2rEOX7ovYiGEHYBuwBR83peULxx7WM/nveVZ+rKDsizbG+gNnF/78q5KUBbn2pxtKx3XAR2BrsBbwP9LG0e5EkJoDowALsqy7MM13+fzvrh9xbFf7+e95fmrVQHbrfH7bWvvUwnIsqyq9vYd4B7iGI9Kx8La2bhVM3LvJM6jBpJl2cIsy1ZkWbYS+Cs+94tSCKEJsTzdlmXZyNq7fd6XgK869hvyvLc8f7WngV1CCDuGEJoCpwCjE2dSAwghbFZ7IQEhhM2Ao4Hn1v1ZKjKjgUG1bw8C7k2YRQ1oVXmqdTw+94tOCCEANwJzsyz77Rrv8nlf5NZ27Dfkee9qG2tRu1TJ74Ey4KYsy/4vcSQ1gBDCTsSzzQCNgds99sUrhHAHcCiwJbAQ+DkwCvgHsD3wOnBSlmVeWFZk1nLsDyW+dJsBrwHfWWMOVkUghHAQMBGYDaysvfvHxNlXn/dFbB3H/lTW83lveZYkSZLqyLENSZIkqY4sz5IkSVIdWZ4lSZKkOrI8S5IkSXVkeZYkSZLqyPIsSQUghLBFCGFW7a+3QwhVtW8vCSFcmzqfJJUKl6qTpAITQvgFsCTLsqtTZ5GkUuOZZ0kqYCGEQ0MI99e+/YsQwvAQwsQQwushhAEhhN+EEGaHEB6q3ZqWEEL3EMKEEML0EMLYL+ywJUlaB8uzJBWXjsDhQD/gVmB8lmWdgRrgW7UF+o/ACVmWdQduAtxFU5LqqHHqAJKkevVglmXLQgizgTLgodr7ZwM7AJ2APYFxIQRqP8YtqCWpjizPklRclgJkWbYyhLAs++zClpXE7/kBeD7LsgNSBZSkQubYhiSVlnnAViGEAwBCCE1CCHskziRJBcPyLEklJMuyT4ETgKtCCM8As4AD06aSpMLhUnWSJElSHXnmWZIkSaojy7MkSZJUR5ZnSZIkqY4sz5IkSVIdWZ4lSZKkOrI8S5IkSXVkeZYkSZLq6P8DuxqKx24DbmcAAAAASUVORK5CYII=\n"
},
"metadata": {
"needs_background": "light"
}
}
]
}
]
}
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