Praktikum-Machine-Learning/ML0101EN-Reg-NoneLinearRegression (1).ipynb

888 lines
316 KiB
Plaintext
Raw Permalink Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p style=\"text-align:center\">\n",
" <a href=\"https://skills.network\" target=\"_blank\">\n",
" <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
" </a>\n",
"</p>\n",
"\n",
"\n",
"# Non Linear Regression Analysis\n",
"\n",
"\n",
"Estimated time needed: **20** minutes\n",
" \n",
"\n",
"## Objectives\n",
"\n",
"After completing this lab you will be able to:\n",
"\n",
"* Differentiate between linear and non-linear regression\n",
"* Use non-linear regression model in Python\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression since linear regression presumes that the data is linear. \n",
"Let's learn about non linear regressions and apply an example in python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"importing_libraries\">Importing required libraries</h2>\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although linear regression can do a great job at modeling some datasets, it cannot be used for all datasets. First recall how linear regression, models a dataset. It models the linear relationship between a dependent variable y and the independent variables x. It has a simple equation, of degree 1, for example y = $2x$ + 3.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"y = 2*(x) + 3\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"#plt.figure(figsize=(8,6))\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Non-linear regression is a method to model the non-linear relationship between the independent variables $x$ and the dependent variable $y$. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$). For example:\n",
"\n",
"$$ \\ y = a x^3 + b x^2 + c x + d \\ $$\n",
"\n",
"Non-linear functions can have elements like exponentials, logarithms, fractions, and so on. For example: $$ y = \\log(x)$$\n",
" \n",
"We can have a function that's even more complicated such as :\n",
"$$ y = \\log(a x^3 + b x^2 + c x + d)$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at a cubic function's graph.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"y = 1*(x**3) + 1*(x**2) + 1*x + 3\n",
"y_noise = 20 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other types of non-linear functions are:\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"source": [
"### Quadratic\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = X^2 $$\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"\n",
"y = np.power(x,2)\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exponential\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An exponential function with base c is defined by $$ Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable. \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"\n",
"Y= np.exp(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Logarithmic\n",
"\n",
"The response $y$ is a results of applying the logarithmic map from the input $x$ to the output $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n",
"\n",
"Please consider that instead of $x$, we can use $X$, which can be a polynomial representation of the $x$ values. In general form it would be written as \n",
"\\begin{equation}\n",
"y = \\log(X)\n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAkMAAAHFCAYAAADxOP3DAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAABj4ElEQVR4nO3deVhU1f8H8PewDfuw74vgCu6CKa6ouaCZZotmmVv+8luWSrZY31LbNK2+tlqWiqaVlUu5ZFqKlmKuiCKSKAqyiLIN6wAz5/cHMYmgMjjDZZj363nmeZx7z537YQTmzTnnnisTQggQERERmSgzqQsgIiIikhLDEBEREZk0hiEiIiIyaQxDREREZNIYhoiIiMikMQwRERGRSWMYIiIiIpPGMEREREQmjWGIiIiITBrDEBm9mJgYyGQy7cPCwgJ+fn6YOnUqMjIytO1iY2Mhk8kQGxur8zkOHTqEhQsXoqCgoEHtFy5cCJlMhuvXr+t8LqlFRkYiMjJS+7y0tBQLFy5s1PvWVIYMGYKZM2dqn9f8X//444/1tp81axZkMllTlWdQU6ZMgUwmQ8eOHaFWq+vsl8lkmDVrlvb5pUuXIJPJEBMTo91W8zN06dIlnc/f0GMb+nOqTzKZDAsXLtQ+P3v2LBYuXFhvrVOmTEGrVq1qbcvLy8OECRPg4eEBmUyGsWPHIj8/H05OTti6datBaiZpWEhdAJG+rFmzBh06dEBZWRkOHDiAxYsXY//+/Th9+jTs7Ozu6rUPHTqERYsWYcqUKXByctJPwc3UZ599Vut5aWkpFi1aBAC1QlJz8dNPP+HgwYNYt26d1KVI6uzZs4iJicH06dNv287b2xtxcXFo3bq1Xs47atQoxMXFwdvbu0HtDflzerO4uDj4+flpn589exaLFi1CZGRkneDz2muvYfbs2bW2vfnmm9iyZQtWr16N1q1bw8XFBc7Ozpg7dy5eeOEFjBw5ElZWVnqtmaTBMEQtRqdOnRAeHg4AGDRoENRqNd58801s3boVjz32mMTVNX+lpaWwtbVFaGio1KXo5J133sEDDzwAX19fqUuRjJ2dHXr06IEFCxZg4sSJsLGxuWVbuVyO3r176+3c7u7ucHd3b3D7pvw51eXrrC8cnjlzBq1bt65T18yZM/HWW2/hxx9/xMSJE++6TpIeh8moxar5RXj58uXbtvv5558REREBW1tbODg4YOjQoYiLi9PuX7hwIV544QUAQFBQkLabXx/DRnc6d42ffvoJXbp0gVwuR3BwMD788EPtUNyNPv30UwwYMAAeHh6ws7ND586dsXTpUlRWVtZqFxkZiU6dOuHAgQPo06cPbG1tMW3aNO2+mh6gS5cuaT/oFi1apP3ap0yZon1vZDIZEhIS8PDDD0OhUMDFxQXR0dGoqqpCcnIyRowYAQcHB7Rq1QpLly6tVUd5eTmef/55dOvWTXtsREQEfvrppwa9fydPnsSRI0cwadKkBrW/nY0bN2LYsGHw9vaGjY0NQkJC8PLLL6OkpKRWuylTpsDe3h4pKSkYOXIk7O3t4e/vj+effx4qlQoAIIRA27ZtMXz48DrnKS4uhkKhwDPPPAPg7t+DGu+++y4yMjLw4Ycf3rZdfcNk9dmzZw/GjBkDPz8/WFtbo02bNnjqqafqDP3ezRAbUPfntLy8HPPnz0dQUBCsrKzg6+uLZ555ps4Q9d69exEZGQlXV1fY2NggICAADz74IEpLS7Vtbhwmi4mJwcMPPwygOoTVfC/XvA83DpPVvEe//fYbkpKS6vzMe3p6YujQofj8888b9TVT88MwRC1WSkoKANz2r9ZvvvkGY8aMgaOjI7799lusWrUK+fn5iIyMxJ9//gkAePLJJ/Hss88CADZv3oy4uDjExcWhR48ed1VfQ84NALt27cK4cePg6uqKjRs3YunSpfj222+xdu3aOq954cIFTJw4EV9//TW2b9+O6dOnY9myZXjqqafqtM3KysLjjz+OiRMnYufOnXj66afrtPH29sauXbsAANOnT9d+7a+99lqtdo888gi6du2KTZs2YcaMGfjf//6HuXPnYuzYsRg1ahS2bNmCwYMH46WXXsLmzZu1x6lUKuTl5WHevHnYunUrvv32W/Tr1w/jxo1r0LDX9u3bYW5ujgEDBtS7X6PRoKqqqs5DCFGn7fnz5zFy5EisWrUKu3btwpw5c/D9999j9OjRddpWVlbi/vvvx5AhQ/DTTz9h2rRp+N///od3330XQPWH8LPPPos9e/bg/PnztY5dt24dlEqlNgzd7XtQIyIiAg888ADeffdd5OXlNfi4W7lw4QIiIiKwYsUK7N69G6+//jr++usv9OvXr064vhs3/pwKITB27Fi89957mDRpEnbs2IHo6GisXbsWgwcP1obNS5cuYdSoUbCyssLq1auxa9cuLFmyBHZ2dqioqKj3PKNGjcI777wDoPqPhprv5VGjRtVpWzOU2L17dwQHB9f7Mx8ZGYmDBw82eB4hNXOCyMitWbNGABCHDx8WlZWVoqioSGzfvl24u7sLBwcHkZ2dLYQQYt++fQKA2LdvnxBCCLVaLXx8fETnzp2FWq3Wvl5RUZHw8PAQffr00W5btmyZACBSU1MbVNOCBQsEAHHt2rV69+ty7p49ewp/f3+hUqlqtXN1dRW3+xFWq9WisrJSrFu3Tpibm4u8vDztvoEDBwoA4vfff69z3MCBA8XAgQO1z69duyYAiAULFtzy63z//fdrbe/WrZsAIDZv3qzdVllZKdzd3cW4ceNuWXNVVZWorKwU06dPF927d79luxpRUVGiQ4cOdbbX/F/f6XErGo1GVFZWiv379wsA4tSpU9p9kydPFgDE999/X+uYkSNHivbt22ufK5VK4eDgIGbPnl2rXWhoqBg0aNAtz63rezB58mRhZ2cnhBDi3LlzwtzcXDz//PPa/QDEM888o32empoqAIg1a9Zot9X8DN3q+7vm/bh8+bIAIH766acGH3tzu9v9nO7atUsAEEuXLq117MaNGwUAsXLlSiGEED/++KMAIOLj4297zpu/b3/44YdavwNuNHnyZBEYGFhr28CBA0XHjh3rfe09e/YIAOKXX365bQ1kHNgzRC1G7969YWlpCQcHB9x3333w8vLCL7/8Ak9Pz3rbJycnIzMzE5MmTYKZ2b8/Cvb29njwwQdx+PDhWl3u+tTQc5eUlODYsWMYO3ZsrYma9vb29fZYnDx5Evfffz9cXV1hbm4OS0tLPPHEE1Cr1fj7779rtXV2dsbgwYP18vXcd999tZ6HhIRAJpMhKipKu83CwgJt2rSpM2z5ww8/oG/fvrC3t4eFhQUsLS2xatUqJCUl3fG8mZmZ8PDwuOX+d999F0ePHq3zeOSRR+q0vXjxIiZOnAgvLy/tezdw4EAAqFOLTCar8/536dKl1tfm4OCAqVOnIiYmRjvUtnfvXpw9e7bW1V13+x7cqH379pg+fTo++eQTpKWl6XTszXJycjBz5kz4+/trawoMDARQ9/3Qxe1+Tvfu3QsA2mHYGg8//DDs7Ozw+++/AwC6desGKysr/N///R/Wrl2LixcvNrqexqr5vjPUlXDUtBiGqMVYt24djh49ipMnTyIzMxMJCQno27fvLdvn5uYCQL1Xwfj4+ECj0SA/P98gtTb03Pn5+RBC1Bvobt6WlpaG/v37a+eN/PHHHzh69Cg+/fRTAEBZWVmt9g29+qchXFxcaj23srKCra0trK2t62wvLy/XPt+8eTMeeeQR+Pr6Yv369YiLi8PRo0cxbdq0Wu1upaysrM45bhQcHIzw8PA6j5uHTouLi9G/f3/89ddfeOuttxAbG4ujR49qh/Rufu/q+9rkcnmdmp999lkUFRVhw4YNAIBPPvkEfn5+GDNmjN7eg5stXLgQ5ubmdYYydaHRaDBs2DBs3rwZL774In7//XccOXIEhw8fBlD3/dDF7X5Oc3NzYWFhUef/RyaTwcvLS/tz07p1a/z222/w8PDAM888g9atW6N169Z3nC+lTzX//3fzXlDzwavJqMUICQnRXqXSEK6urgCq587cLDMzE2ZmZnB2dtZbfY05txACMpkMV69erdMuOzu71vOtW7eipKQEmzdv1v4FDwDx8fH11tAc1tlZv349goKCsHHjxlr11MwNuRM3Nze9zI/Zu3cvMjMzERsbq+0NAnDX80HatGmDqKgofPrpp4iKisLPP/+MRYsWwdzcXNvmbt+Dm3l7e2POnDlYsmQJnn/++Ua9xpkzZ3Dq1CnExMRg8uTJ2u0183vuxu1+Tl1dXVFVVYVr167VCkRCCGRnZ6Nnz57abf3790f//v2hVqtx7NgxfPzxx5gzZw48PT0xYcKEu67zTmq+79zc3Ax+LjI89gyRyWrfvj18fX3xzTff1JpQW1JSgk2bNmmv8gKq/+oH9PdXYEPPbWdnh/DwcGzdurXWxNDi4mJs37691mvWfJDW1ApUf4h8+eWXd1Wrvr/2G8lkMlhZWdUKAdnZ2Q2+kqpDhw56GSKp770DgC+++OKuX3v27NlISEjA5MmTYW5ujhkzZtQ59928B/V56aWX4OLigpdffrlRxxvy/bidIUOGAKgOiDfatGkTSkpKtPtvZG5ujl69eml7QE+cOHHL19fn93LN952xLUVB9WPPEJksMzMzLF26FI899hjuu+8+PPXUU1CpVFi2bBkKCgqwZMkSbdvOnTsDAD788ENMnjwZlpaWaN++PRwcHG57jm3bttXb5qGHHmrwud944w2MGjUKw4cPx+zZs6FWq7Fs2TLY29vX6hUZOnQorKys8Oijj+LFF19EeXk5VqxYcddDfQ4ODggMDMRPP/2EIUOGwMXFBW5ubnUWrWuM++67D5s3b8bTTz+Nhx56COnp6XjzzTfh7e1d5yqs+kRGRmL16tX4+++/0a5du0bX0adPHzg7O2PmzJlYsGABLC0tsWHDBpw6darRr1lj6NChCA0Nxb59+/D444/XmeN0t+9BfRwdHfHqq69i7ty5jTq+Q4cOaN26NV5++WUIIeDi4oJt27Zhz549jXq9hho6dCiGDx+Ol156CUqlEn379kVCQgIWLFiA7t27a5dQ+Pzzz7F3716MGjUKAQEBKC8vx+rVqwEA99577y1fv1OnTgCAlStXwsHBAdbW1ggKCtL21Ori8OHDcHV11f5uIOPGniEyaRMnTsTWrVuRm5uL8ePHY+rUqXB0dMS+ffvQr18/bbvIyEjMnz8f27ZtQ79+/dCzZ08cP378jq8/bdo0PPzww3Ueupx7xIgR2LRpk7ZddHQ0HnjgAYwZM6bWatgdOnTApk2bkJ+fj3HjxuHZZ59Ft27d8NFHH931+7Rq1SrY2tri/vvvR8+ePWvd4uBuTJ06FUuWLMEvv/yCkSNH4t1338XLL7/c4IXsxowZA3t7+7vqRQGqh2d27NgBW1tbPP7445g2bRrs7e2xcePGu3rdGjUTtm+eOA3c/XtwK08//TSCgoIadaylpSW2bduGdu3a4amnnsKjjz6KnJwc/Pbbb3dV053IZDJs3boV0dHRWLNmDUaOHKm9zH7v3r3anp1u3bqhqqoKCxYsQFRUFCZNmoRr167h559/xrBhw275+kFBQVi+fDlOnTqFyMhI9OzZE9u2bdO5TiEEfv75Z0ycOLFZDDfT3ZMJUc+CG0TUrFVWVqJbt27w9fXF7t27pS5HUs8++yx+//13JCYmNtsPpvDwcMhkMhw9elTqUkgPfv/9dwwbNgyJiYno0KGD1OWQHjAMERmB6dOnY+jQofD29kZ2djY+//xz7N+/H7t3777tsIApuHr1Ktq1a4dVq1bhoYcekrocLaVSiTNnzmD79u1YvHgxtmzZgrFjx0pdFunBoEGD0KZNm7uej0fNB+cMERmBoqIizJs3D9euXYOlpSV69OiBnTt3mnwQAqqXGNiwYYPBlkForBMnTmDQoEFwdXXFggULGIRaiPz8fAwcOLDeFdvJeLFniIiIiEwaJ1ATERGRSWMYIiIiIpPGMEREREQmjROo70Cj0SAzMxMODg7N9rJdIiIiqk0IgaKiIvj4+NS6IXZ9GIbuIDMzE/7+/lKXQURERI2Qnp4OPz+/27ZhGLqDmlsppKenw9HRUeJqiIiIqCGUSiX8/f3veNskgGHojmqGxhwdHRmGiIiIjExDprhwAjURERGZNIYhIiIiMmkMQ0RERGTSGIaIiIjIpDEMERERkUljGCIiIiKTxjBEREREJo1hiIiIiEwawxARERGZNIYhIiIiMmkMQ0RERGTSGIaIiIjIpDEMERERkSQ0GoHU6yXIKSqXtA7etZ6IiIgMTlWlxt/ZxTibVYjETCXOZiqRlKVESYUaL0d1wMyBrSWrjWGIiIiI9KqwrBJnM5U4m6VEYmYhzmYqkZJTjCqNqNNWbmGG4vIqCar8F8MQERERNdq1IhUSM6t7exIzC3EmQ4m0vNJ62zrZWqKjjyNCvR3R0UeBjj6OCHKzg4W5tLN2GIaIiIjojoQQyCosx5mMQpzJqA4/ZzILcVWpqre9r5MNQn0c0dHn3+DjrbCGTCZr4srvzKjC0IEDB7Bs2TIcP34cWVlZ2LJlC8aOHXvL9rGxsRg0aFCd7UlJSejQoYMBKyUiIjJeQghcyS9DYmYhTmcU4nSGEokZhcgtqajTViYDgtzs0NFHgU43BB9nOysJKm8cowpDJSUl6Nq1K6ZOnYoHH3ywwcclJyfD0dFR+9zd3d0Q5RERERkdIQQyCspw+kohEv7p9TmTUYj80so6bc3NZGjrYY9OvtXBp5OvAiHejrCTG1WcqMOoqo+KikJUVJTOx3l4eMDJyUn/BRERERmRmqGuhCvVgSchoxCnrxTUG3wszWVo5+mATj4KdPJToLOvAh28HGBtaS5B5YZlVGGosbp3747y8nKEhobiv//9b71DZ0RERC3NtSIVEq4U4NSV6tBzOqMQ14vrDnVZmsvQ3ssBnX0V6OSrQBdfJ7TzsofcouUFn/q06DDk7e2NlStXIiwsDCqVCl9//TWGDBmC2NhYDBgwoN5jVCoVVKp/J4MplcqmKpeIiKjRCssqcSajEKeuFCAhvRAJVwqQWVh3MUMLs+oen86+CnT2U6CLnwLtvRxMJvjUp0WHofbt26N9+/ba5xEREUhPT8d77713yzC0ePFiLFq0qKlKJCIi0ll5pRpJWUqcSq/u9TmVXoCL10vqtJPJgDbu9uji54Su/tVDXSHeji1yqOtutOgwVJ/evXtj/fr1t9w/f/58REdHa58rlUr4+/s3RWlERER1aDQCF68XIz698J/wU4CkLCUq1XUXMPR3sakOPn4KdPFzQidfBeyNfHJzUzC5d+jkyZPw9va+5X65XA65XN6EFREREf3rWpEK8ekFiE/PR3x69ZBXkaruCs2udlbo6u+Ern5O6OKvQFc/J7gY0eXszYlRhaHi4mKkpKRon6empiI+Ph4uLi4ICAjA/PnzkZGRgXXr1gEAli9fjlatWqFjx46oqKjA+vXrsWnTJmzatEmqL4GIiEirvFKNxEzlP+GnACfT8nElv6xOOxtLc3T2VaCrv0IbgPycbZrlAobGyKjC0LFjx2pdCVYznDV58mTExMQgKysLaWlp2v0VFRWYN28eMjIyYGNjg44dO2LHjh0YOXJkk9dORESmrWYhw5PpBThxOR8n0wtwNrOwznBXzTyf7gFO6ObvjK7+CrT3dJD8lhUtmUwIUXfQkbSUSiUUCgUKCwtrLdxIRER0O2UVaiRcKagVfq4V1b11haud1T/Bpzr8dPFXwNHaUoKKWxZdPr+NqmeIiIioORJCILOwHMcv5+P4pTycSKue5HzzXdotzGQI9XFEjwBndA9wQo8AZw53NQMMQ0RERDqqVGuQmKnE8cv5OHE5H8cv5yNbWXdNHw8HOXoEOKNHoBO6Bzijs6+Cl7U3QwxDREREd1BYWonjaXk4eqk6+CRcKUB5paZWG3MzGTr+0+vTI9AZYYHO8Gmmd2mn2hiGiIiIbiCEQHpeGY5drgk/efj7anGddk62lgi7Ifh08VPA1oofq8aI/2tERGTSqtQaJGUV4eilPBy7nIdjl/KRU89E52B3O4QHOiM80AVhrZwR7GbHXp8WgmGIiIhMSnmlGqfSC3D0Uh7+Ss3DybQCFN+0qKGluQydfBXo2coFYYHOCA90hqs9F+RtqRiGiIioRVOWV+L45XwcSc3D0dQ8JFwpRIW69nwfB7kFwlo5o2crF4QHOqOrvxMnOpsQhiEiImpRCkorcCS1utfnr9RcnM1U4qYr3OHuIMc9rVzQs5Uzega5oIOXI8zNOORlqhiGiIjIqF0vVlWHn4u5+Cs1D+eyi+q0CXS1rQ4/QS64p5ULAl1tOd+HtBiGiIjIqFwvVuHwxdx/HnlIyal7pVcbD3v0CnLBPUEu6BXkCi+FtQSVkrFgGCIiomYtt1iFv1LzcPhiLuIu5OJ8PeGng5cDege74p5/ApAbJzuTDhiGiIioWSkorcDhi/+Gn+SrdYe9Qrwd0TvYBRH/BCAnWysJKqWWgmGIiIgkVaKqwtFLeYi7kItDF3JxJrMQN99CvKbnp3ewK3oFucDZjuGH9IdhiIiImpSqSo2TaQU4dCEXcReu42RaQZ0bmrbxsEef1q6ICHZFr2BXuDD8kAExDBERkUFpNALnsovwZ8o1/JmSiyOpuXXu6+XrZIO+bVzRt40bIoJd4eHICc/UdBiGiIhI767kl+JgynX8mZKLQynXkVtSUWu/m70cfVq7/vNwQ4CrrUSVEjEMERGRHijLKxF3IRd/nL+Ggym5SL1eUmu/rZU5egW5oG8bN/Rv6452nvZc54eaDYYhIiLSmVojcOpKAf74+zr+OH8NJ9MLoL5h3o+5mQzd/J3Qt40b+rVxQzd/J1hZmElYMdGtMQwREVGDXMkvxR/nq8PPn+evQ1le++amwW526Ne2uuenV7ALHK0tJaqUSDcMQ0REVK/ySjX+Ss3D/uRriP07Bxev1R76crS20Iaffm3c4O/CeT9knBiGiIgIACCEwKXcUsQm52D/39dw+GLtq77MzWTo7u+E/m3d0b+dG7r4KmBhzqEvMn4MQ0REJqysQo1DF64jNvka9v99DWl5pbX2ezlaY2A7d0S2d0efNm5Q2HDoi1oehiEiIhOTlluKfck52HsuB3EXc1FR9W/vj6W5DD1bufwTgDx41ReZBIYhIqIWrqJKg2OX8rQB6MJNc398nWwQ2b46/ES0doW9nB8NZFr4HU9E1ALlFquw91x1+Pnj/HUUq/698svcTIawQGcM7uCBwR080NaDvT9k2hiGiIhaACEEzucUY8/Zq/g96SpOphfUutmpq50VBrZ3x+AOHujf1p1zf4huwDBERGSkKqo0OJKah9+SruL3c1eRnldWa3+otyPuDfHA4BBPdPFVwMyMvT9E9WEYIiIyIsrySuw7l4M9Z69if/I1FN0w/GVlYYY+rV0xJMQTQzp4wMfJRsJKiYwHwxARUTOXXViOPUlXsTsxG4cv5qJS/e/4l5u9FQZ38MCQEE/0a+MGO05+JtIZf2qIiJoZIQRScoqx+2x1ADp1pbDW/jYe9hgW6ol7Qz3Rzc+Jw19Ed4lhiIioGRBC4NSVQvxyJgu7E6/Wuuu7TAb0CHDGsFBPDA31RLC7vYSVErU8DENERBJRawSOXsrDrjPZ+DUxG1mF5dp9VhZm6NfGDUNDPTEkxAMeDtYSVkrUsjEMERE1oYoqDeIu5mLXPz1AuSUV2n12VuYY1MEDIzp5IbK9Bxc/JGoiRvWTduDAASxbtgzHjx9HVlYWtmzZgrFjx972mP379yM6OhqJiYnw8fHBiy++iJkzZzZNwUREAFRVavx5/jp2nM7Cb2evQln+7xVgChtL3BviiahOXujX1g3WluYSVkpkmowqDJWUlKBr166YOnUqHnzwwTu2T01NxciRIzFjxgysX78eBw8exNNPPw13d/cGHU9E1FgVVRr8mXINOxKysftsNopuCEBu9nIM7+iJEZ280DvYFZa88zuRpIwqDEVFRSEqKqrB7T///HMEBARg+fLlAICQkBAcO3YM7733HsMQEeldRZUGB1Oqe4B2J2bX6gHycJBjZGdvjOzsjbBAZ5jzCjCiZsOowpCu4uLiMGzYsFrbhg8fjlWrVqGyshKWlnWXo1epVFCpVNrnSqXS4HUSkfGqUmtw6EIutp3KxK83BSB3BzlGdvLCqC4+CA905iXwRM1Uiw5D2dnZ8PT0rLXN09MTVVVVuH79Ory9vescs3jxYixatKipSiQiI6TRCBxPy8e2U5nYeToL14v/nQTt7iBHVCcvjOrsjfBWLuwBIjICLToMAahzJ2bxz50Lb3WH5vnz5yM6Olr7XKlUwt/f33AFEpFREEIgMVOJbacyse1UJjJvuAze2dYSIzt7474uPrgniAGIyNi06DDk5eWF7OzsWttycnJgYWEBV1fXeo+Ry+WQy+VNUR4RGYHU6yXYejID2xIycfHavwsh2sstMKyjJ+7v6oO+bdw4CZrIiLXoMBQREYFt27bV2rZ7926Eh4fXO1+IiAgAcotV2J6QhS0nMxCfXqDdLrcww5AQD9zf1QeR7T14GTxRC2FUYai4uBgpKSna56mpqYiPj4eLiwsCAgIwf/58ZGRkYN26dQCAmTNn4pNPPkF0dDRmzJiBuLg4rFq1Ct9++61UXwIRNVNlFWrsSbqKrSczsP/va1BrqofUzc1k6NfGDWO6+WBoqCccrPmHFFFLY1Rh6NixYxg0aJD2ec3cnsmTJyMmJgZZWVlIS0vT7g8KCsLOnTsxd+5cfPrpp/Dx8cFHH33Ey+qJCED17TAOX8zFlpMZ2HUmG8Wqf68E6+KnwNhuvhjd1QfuDhw6J2rJZKJmRjHVS6lUQqFQoLCwEI6OjlKXQ0R6cPFaMTaduILNJzJq3Q/M18kGD3T3xdjuPmjj4SBhhUR0t3T5/DaqniEiosZSlldiR0IWfjx+Bccv52u3O1pbYFQXHzzQ3ZdrARGZKIYhImqx1BqBQxeu48fjV7DrTDZUVRoAgJkMGNjOHQ+F+WNICCdCE5k6hiEianEu55bg+2PpdYbB2nrY46EwPzzQ3RcejtYSVkhEzQnDEBG1COWVavyamI2NR9Nx6EKudrujtQXGdPPFQ2F+6OKnuOWCq0RkuhiGiMionctW4rsj6dhyMgOFZZUAAJkMGNDWHQ+H++HeEE8OgxHRbTEMEZHRKVZVYdupTHx3NB2nblgU0UdhjUd6+uPhcH/4OtlIVyARGRWGISIyGqevFGLDX5fx86lMlFaoAQAWZjIM6+iJ8T0D0K+NG+8LRkQ6YxgiomatrEKNbQmZ2HD4Mk5dKdRuD3a3w4Se/hjXww9u9lwUkYgaj2GIiJqllJwibPgrDZuOX4GyvHplaCtzM0R19sLEewJwT5ALJ0MTkV4wDBFRs1FRpcHus9lYf/gyDl/M0273d7HBY70C8XCYH1zZC0REesYwRESSy1GWY/1fafjmrzRcL1YBqF4YcUiIJx7rFYABbd25MjQRGQzDEBFJQgiBk+kFiDl4CTtPZ6Hqn7vEezjIMeGeAEzo6Q8fXhFGRE2AYYiImpSqSo0dCVmIOXQJCTdMiA4PdMaUvq0wvKMXLM3NJKyQiEwNwxARNYmrynJsOHwZ3xxJw/XiCgCAlYUZ7u/qgyl9WqGTr0LiConIVDEMEZFBnckoxFd/XMT2hH+HwrwV1ni8dyAm9PTnhGgikhzDEBHpnUYjsPdcDr7682Ktq8LuaeWCKX1bYVioJyw4FEZEzQTDEBHpTXmlGptOXMGqP1Nx8VoJgOoVou/r4o0n+wdzKIyImiWGISK6a9eKVPg67hLW/5WGvJLq+UAO1haYeE8ApvRtBW8FrwojouaLYYiIGu3itWKsPHARm09moKJKAwDwc7bBtL5BeKSnP+zl/BVDRM0ff1MRkc7OZBRiRewF7DyTBVE9JxrdA5wwo38w5wMRkdFhGCKiBhFC4PDFPHwWm4I/zl/Xbh/SwQP/iWyN8FYuElZHRNR4DENEdFsajcBvSVexYv8FnEwrAACYm8kwuos3Zka2RgcvR2kLJCK6SwxDRFSvKrUGP5/KxOf7L+Dvq8UAqhdJHB/uj/8bEAx/F1uJKyQi0g+GISKqpVKtwZaTGfh0Xwou55YCABzkFng8IhDT+gbB3YGLJBJRy8IwREQA/glBJzLwyb4UpOVVhyAXOytM7xeESRGBcLS2lLhCIiLDYBgiMnEVVRpsPnEFn8amID2vDADgZm+F/xsQjMd7B8LWir8miKhl4285IhNVUaXBj8ev4NN9Kcgo+DcEPTWgNR7rHcAQREQmg7/tiExMpbo6BH2y98YQJMfMgcF4rFcgbKzMJa6QiKhpMQwRmQiNRmD76Sz8b8/fSL1efd8wdwc5Zg5sjYn3BDAEEZHJYhgiauGEENiXnINlv/6NpCwlgOqJ0U9HtsbjvQNhbckQRESmjWGIqAX762Iulv2ajGOX8wFUXyI/Y0AwpvUL4n3DiIj+wd+GRC3QmYxCLPs1Gfv/vgYAkFuYYUqfVpg5sDWc7awkro6IqHkxurspfvbZZwgKCoK1tTXCwsLwxx9/3LJtbGwsZDJZnce5c+easGKipnM5twTPbDiB+z7+E/v/vgYLMxke6xWAAy8OwvyRIQxCRET1MKqeoY0bN2LOnDn47LPP0LdvX3zxxReIiorC2bNnERAQcMvjkpOT4ej47/2T3N3dm6JcoiZTUFqBj/emYF3cJVSqBWQyYExXH8wd2g6BrnZSl0dE1KzJhBBC6iIaqlevXujRowdWrFih3RYSEoKxY8di8eLFddrHxsZi0KBByM/Ph5OTU6POqVQqoVAoUFhYWCtQETUHFVUarIu7hI/3pqCwrBIAMKCdO+ZHdUCIN79fich06fL5bTQ9QxUVFTh+/DhefvnlWtuHDRuGQ4cO3fbY7t27o7y8HKGhofjvf/+LQYMG3bKtSqWCSqXSPlcqlXdXOJEBCCGw60w2luw6p71/WAcvB8wfGYKB7djzSUSkC6MJQ9evX4darYanp2et7Z6ensjOzq73GG9vb6xcuRJhYWFQqVT4+uuvMWTIEMTGxmLAgAH1HrN48WIsWrRI7/UT6cvJtHy8vSNJe4WYu4Mc84a1w0Nh/jA3k0lcHRGR8TGaMFRDJqv9y14IUWdbjfbt26N9+/ba5xEREUhPT8d77713yzA0f/58REdHa58rlUr4+/vroXKiu5NRUIbFO5OwPSELAGBjaY7/GxCM/xsQDDteJk9E1GhG8xvUzc0N5ubmdXqBcnJy6vQW3U7v3r2xfv36W+6Xy+WQy+WNrpNI38or1fjywEV8GpuC8koNZDLgoR5+eH5Ye3gprKUuj4jI6BlNGLKyskJYWBj27NmDBx54QLt9z549GDNmTINf5+TJk/D29jZEiUR6JYTA70k5eGP7WaTlVc8L6hXkgtdHh6Kjj0Li6oiIWg6jCUMAEB0djUmTJiE8PBwRERFYuXIl0tLSMHPmTADVQ1wZGRlYt24dAGD58uVo1aoVOnbsiIqKCqxfvx6bNm3Cpk2bpPwyiO4o9XoJ3tiWiH3J1Ysmejla49VRIbivi/cth4WJiKhxjCoMjR8/Hrm5uXjjjTeQlZWFTp06YefOnQgMDAQAZGVlIS0tTdu+oqIC8+bNQ0ZGBmxsbNCxY0fs2LEDI0eOlOpLILqt0ooqfLI3BV/9kYoKtQaW5jI82T8Yswa14bwgIiIDafQ6QxUVFUhNTUXr1q1hYdFyf0lznSFqCkII7Didhbd3JCGrsBwAMLCdOxaMDkWwu73E1RERGR9dPr91vh1HaWkppk+fDltbW3Ts2FHbE/Pcc89hyZIljauYyISlXi/B46v+wqxvTiKrsBx+zjZYOSkMMVN7MggRETUBncPQ/PnzcerUKcTGxsLa+t8rWe69915s3LhRr8URtWSVag0+3ZeC4csP4GBKLuQWZphzb1v8Fj0Qwzp6cW4QEVET0Xl8a+vWrdi4cSN69+5d65d1aGgoLly4oNfiiFqqk2n5eHnTaSRfLQIA9G/rhrfGduJ9xIiIJKBzGLp27Ro8PDzqbC8pKeFfskR3UKyqwnu/JmNt3CUIAbjYWeG1+0Iwtpsvf36IiCSi8zBZz549sWPHDu3zml/gX375JSIiIvRXGVELs+fsVQz9YD9iDlUHoXE9fPFb9EA80N2PQYiISEI69wwtXrwYI0aMwNmzZ1FVVYUPP/wQiYmJiIuLw/79+w1RI5FRy1GWY8HPifjlTPXq6QEutnjngc7o19ZN4sqIiAhoRM9Qnz59cPDgQZSWlqJ169bYvXs3PD09ERcXh7CwMEPUSGSUhBD48fgVDPlgP345kw1zMxlmDmyNX+cMYBAiImpGGr3OkKngOkPUGDlF5Xhl8xn8lnQVANDVT4HF47og1IffQ0RETUGXz+8GDZMplcoGn5yBgUzdztNZeHXLaeSXVsLSXIa5Q9vhqQGtYW7GeUFERM1Rg8KQk5PTHSd4CiEgk8mgVqv1UhiRsSkorcDrPyXi51OZAIAQb0d88EhXhHjzDwQiouasQWFo3759hq6DyKjtO5eDlzYlIKdIBXMzGZ6ObI1nB7eFlYXO0/KIiKiJNSgMDRw40NB1EBmlYlUV3t5xFt8eSQcAtHa3w/uPdEM3fydpCyMiogZr1B1W8/PzsWrVKiQlJUEmkyEkJARTp06Fi4uLvusjaraOpOYh+vt4XMkvAwBM6xuEF0e0h7WlucSVERGRLnTuw9+/fz9atWqFjz76CPn5+cjLy8NHH32EoKAgrjNEJkGtEfjwt/OYsDIOV/LL4Odsg29n9Mbro0MZhIiIjJDOl9Z36tQJffr0wYoVK2BuXv2LX61W4+mnn8bBgwdx5swZgxQqFV5aTzfKLizH7O9O4q/UPADAgz38sGhMR9jLG9XJSkREBqLL57fOYcjGxgbx8fFo3759re3Jycno1q0bysrKdK+4GWMYohp7z13FvB8SkFdSAVsrc7z9QCc80N1P6rKIiKgeel9n6EY9evRAUlJSnTCUlJSEbt266fpyRM1eRZUGS3edw1d/pgIAOvo44uNHuyPY3V7iyoiISB8aFIYSEhK0/37uuecwe/ZspKSkoHfv3gCAw4cP49NPP8WSJUsMUyWRRC7nluDZb08i4UohAGBq31Z4OaoD5BacG0RE1FI0aJjMzMwMMpkMd2raEhdd5DCZ6fr5VCZe2XwaxaoqONlaYtlDXTE01FPqsoiIqAH0PkyWmpqql8KIjEF5pRoLf07Ed0er1w66p5ULPny0G7wVNhJXRkREhtCgMBQYGGjoOoiahcyCMsxcfxwJVwohkwHPDm6L5wa3gYU5V5ImImqpGn098NmzZ5GWloaKiopa2++///67LopICocv5uKZDSeQW1IBZ1tLfPxoD/Rr6yZ1WUREZGA6h6GLFy/igQcewOnTp2vNI6q5kWtLmzNELZ8QAmsPXcJbO5JQpREI9XbEF5PC4O9iK3VpRETUBHTu+589ezaCgoJw9epV2NraIjExEQcOHEB4eDhiY2MNUCKR4ZRXqjHvhwQs3HYWVRqBMd18sOk/fRiEiIhMiM49Q3Fxcdi7dy/c3d1hZmYGMzMz9OvXD4sXL8Zzzz2HkydPGqJOIr27cX6QmQx4ZWQIpvcL0vZyEhGRadA5DKnVatjbVy825+bmhszMTLRv3x6BgYFITk7We4FEhnDz/KBPJ/ZAnzacH0REZIp0DkOdOnVCQkICgoOD0atXLyxduhRWVlZYuXIlgoODDVEjkd4IIRDzz/wgNecHERERGhGG/vvf/6KkpAQA8NZbb+G+++5D//794erqio0bN+q9QCJ9qVJr8NpPZ/Dtker1g8Z288HicV1gY8XVpImITJnON2qtT15eHpydnVvkXAuuQN0ylKiq8Mw3JxCbfI3zg4iITIBBb9RaHxcXF328DJFB5CjLMW3tUZzJUMLa0gwfP9qDt9UgIiKtBoWhcePGISYmBo6Ojhg3btxt227evFkvhRHpw/mrRZiy5igyCsrgameFVVN6opu/k9RlERFRM9KgMKRQKLTDCQqFwqAFEelL3IVc/N/Xx1BUXoVgNzvETL0HAa6cKE1ERLXpNGdICIG0tDS4u7vD1laaD5XPPvsMy5YtQ1ZWFjp27Ijly5ejf//+t2y/f/9+REdHIzExET4+PnjxxRcxc+bMBp+Pc4aM00/xGXjhhwRUqDUIC3TGV0+Ew9nOSuqyiIioiejy+a3TCtRCCLRt2xYZGRl3VWBjbdy4EXPmzMGrr76KkydPon///oiKikJaWlq97VNTUzFy5Ej0798fJ0+exCuvvILnnnsOmzZtauLKqakIIfBZbApmfxePCrUGIzt7YcOTvRiEiIjolnS+mqxjx45YtWoVevfubaiabqlXr17o0aMHVqxYod0WEhKCsWPHYvHixXXav/TSS/j555+RlJSk3TZz5kycOnUKcXFxDTone4aMR5VagwU/J2LDX9XheEb/IMyPCoGZGa8YIyIyNQbrGQKApUuX4oUXXsCZM2caXWBjVFRU4Pjx4xg2bFit7cOGDcOhQ4fqPSYuLq5O++HDh+PYsWOorKys9xiVSgWlUlnrQc1feaUaM9cfx4a/0iCTAQtHh+LVUaEMQkREdEc6X1r/+OOPo7S0FF27doWVlRVsbGxq7c/Ly9NbcTe6fv061Go1PD1rXxLt6emJ7Ozseo/Jzs6ut31VVRWuX78Ob2/vOscsXrwYixYt0l/hZHBlFWr839fH8Mf565BbmOGjR7tjeEcvqcsiIiIjoXMYWr58uQHKaLibF8kTQtx24bz62te3vcb8+fMRHR2tfa5UKuHv79/YcsnAilVVmB5zFH+l5sHWyhyrp/RE72BXqcsiIiIjonMYmjx5siHquCM3NzeYm5vX6QXKycmp0/tTw8vLq972FhYWcHWt/wNTLpdDLpfrp2gyKGV5JaasPoITaQVwkFsgZlpPhAVyAVAiItKNznOGblRWVtZk82usrKwQFhaGPXv21Nq+Z88e9OnTp95jIiIi6rTfvXs3wsPDYWlpabBayfAKSivw+Fd/4URaARQ2ltgwoxeDEBERNYrOYaikpASzZs2Ch4cH7O3t4ezsXOthSNHR0fjqq6+wevVqJCUlYe7cuUhLS9OuGzR//nw88cQT2vYzZ87E5cuXER0djaSkJKxevRqrVq3CvHnzDFonGVZusQoTVh5GwpVCuNhZ4dsZvdHFz0nqsoiIyEjpPEz24osvYt++ffjss8/wxBNP4NNPP0VGRga++OILLFmyxBA1ao0fPx65ubl44403kJWVhU6dOmHnzp0IDAwEAGRlZdVacygoKAg7d+7E3Llz8emnn8LHxwcfffQRHnzwQYPWSYaToyzHY1/9hfM5xXB3kOObJ3uhraeD1GUREZER03mdoYCAAKxbtw6RkZFwdHTEiRMn0KZNG3z99df49ttvsXPnTkPVKgmuM9R8ZBaU4bGv/kLq9RJ4K6yx4cleCHa3l7osIiJqhgy6zlBeXh6CgoIAAI6OjtpL6fv164cDBw40olyiO0vPK8UjX8Qh9XoJ/Jxt8P1TEQxCRESkFzqHoeDgYFy6dAkAEBoaiu+//x4AsG3bNjg5OemzNiIA1UFo/BdxuJJfhlautvj+qQj4u/CGq0REpB86h6GpU6fi1KlTAKonLH/22WeQy+WYO3cuXnjhBb0XSKYtp6gcj6/6C5mF5Wjtbofvn4qAj5PNnQ8kIiJqoAbPGZozZw6efPJJdOrUqdb2tLQ0HDt2DK1bt0bXrl0NUqSUOGdIOoVllZiw8jCSspTwd7HBppl94OFoLXVZRERkBAwyZ2jXrl3o2rUr7rnnHqxcuVK7plBAQADGjRvXIoMQSaesQo0n1x5FUpYSbvZyrJ/ei0GIiIgMosFh6Ny5czhw4AA6d+6MefPmwcfHB0888QQnTZPeVao1eOabEzh6KR8O1hb4evo9CHS1k7osIiJqoXSaM9S3b1+sWrUK2dnZ+Pjjj3Hp0iVERkaibdu2WLJkCTIzMw1VJ5kIjUbghR9OYe+5HFhbmmH1lJ4I8ebwJBERGY7O6wzd7MKFC1i9ejVWrFiB4uJiVFRU6Ku2ZoFzhpqOEAKLtp1FzKFLsDCT4csnwjGog4fUZRERkREy6DpDNyopKcH+/fuxf/9+FBQUoHXr1nfzcmTiPvo9BTGHLgEA3n+kK4MQERE1iUaFoQMHDmDq1Knw8vLC7Nmz0a5dO/zxxx9ISkrSd31kItYeuoT//fY3AGDR/R0xppuvxBUREZGpaPC9ya5cuYK1a9ciJiYGFy5cQK9evfC///0PEyZMgL09VwKmxvspPgMLfk4EAMy5ty0m92klbUFERGRSGhyGWrVqBVdXV0yaNAnTp09HSEiIIesiExGbnIPnv69exHNyRCBmD2krcUVERGRqGhyGvv/+e9x///2wsND5RvdE9UrJKcKsb06iSiMwppsPFozuCJlMJnVZRERkYhqcbMaNG2fIOsjEFJZW4sm1x1CsqsI9QS5Y9lBXmJkxCBERUdO7q6vJiBqjSq3BrG9P4FJuKXydbLDisR6wsuC3IhERSYOfQNTk3t11Dn+cvw4bS3OsfCIMrvZyqUsiIiITxjBETWrT8Sv48o9UAMB7D3dFRx+FxBUREZGp0zkMTZs2DUVFRXW2l5SUYNq0aXopilqm+PQCzN9yGgDw7OA2GNXFW+KKiIiIGhGG1q5di7Kysjrby8rKsG7dOr0URS1PjrIcT319DBVVGtwb4om597aTuiQiIiIAOlxNplQqIYSAEAJFRUWwtrbW7lOr1di5cyc8PHj7BKqrvFKN//v6OK4qVWjrYY//jeeVY0RE1Hw0OAw5OTlBJpNBJpOhXbu6f9XLZDIsWrRIr8WR8RNC4NUtZxCfXgCFjSW+mhwOB2tLqcsiIiLSanAY2rdvH4QQGDx4MDZt2gQXFxftPisrKwQGBsLHx8cgRZLxWn3wEjaduAIzGfDpxB4IdLWTuiQiIqJaGhyGBg4cCABITU2Fv78/zMx4IRrd3p/nr+PtHWcBAK+OCkW/tm4SV0RERFSXzvfWCAwMREFBAY4cOYKcnBxoNJpa+5944gm9FUfGK7OgDM98cwIaATwU5odpfVtJXRIREVG9dA5D27Ztw2OPPYaSkhI4ODjUupeUTCZjGCJoNALPf38KhWWV6OqnwNsPdOI9x4iIqNnSeazr+eef1641VFBQgPz8fO0jLy/PEDWSkfnyj4uIu5gLWytzLJ/QHXILc6lLIiIiuiWdw1BGRgaee+452NraGqIeMnKJmYV4b3cyAOD1+0IR5MYJ00RE1LzpHIaGDx+OY8eOGaIWMnLllWrM/i4elWqBYaGeGN/TX+qSiIiI7kjnOUOjRo3CCy+8gLNnz6Jz586wtKy9Zsz999+vt+LIuCzemYSUnGK4O8ix5MEunCdERERGQSaEELoccLtL6mUyGdRq9V0X1ZwolUooFAoUFhbC0dFR6nKarX3JOZi65igAYO20ezCwnbvEFRERkSnT5fNb556hmy+lJ8otVuGFHxIAAFP6tGIQIiIio3JXKyeWl5frqw4yUkIIvLTpNK4Xq9DO0x4vR3WQuiQiIiKd6ByG1Go13nzzTfj6+sLe3h4XL14EALz22mtYtWqV3guskZ+fj0mTJkGhUEChUGDSpEkoKCi47TFTpkzR3k+t5tG7d2+D1WiKvjuajt+SrsLK3AzLx3eHtSUvoyciIuOicxh6++23ERMTg6VLl8LKykq7vXPnzvjqq6/0WtyNJk6ciPj4eOzatQu7du1CfHw8Jk2adMfjRowYgaysLO1j586dBqvR1Fy8Vow3tlXfbmPe8HYI9eGcKiIiMj46zxlat24dVq5ciSFDhmDmzJna7V26dMG5c+f0WlyNpKQk7Nq1C4cPH0avXr0AAF9++SUiIiKQnJyM9u3b3/JYuVwOLy8vg9RlyirVGszdGI+ySjX6tHbFk/2CpS6JiIioURq16GKbNm3qbNdoNKisrNRLUTeLi4uDQqHQBiEA6N27NxQKBQ4dOnTbY2NjY+Hh4YF27dphxowZyMnJuW17lUoFpVJZ60F1ffjbeZy6UghHawu8/0hXmJnxMnoiIjJOOoehjh074o8//qiz/YcffkD37t31UtTNsrOz4eHhUWe7h4cHsrOzb3lcVFQUNmzYgL179+L999/H0aNHMXjwYKhUqlses3jxYu28JIVCAX9/Lhx4s+OX8/BZbAoA4J1xneGtsJG4IiIiosbTeZhswYIFmDRpEjIyMqDRaLB582YkJydj3bp12L59u06vtXDhQixatOi2bY4erV67pr4F/IQQt13Yb/z48dp/d+rUCeHh4QgMDMSOHTswbty4eo+ZP38+oqOjtc+VSiUD0Q2q1Bq8uuUMNAIY190X93XxkbokIiKiu6JzGBo9ejQ2btyId955BzKZDK+//jp69OiBbdu2YejQoTq91qxZszBhwoTbtmnVqhUSEhJw9erVOvuuXbsGT0/PBp/P29sbgYGBOH/+/C3byOVyyOXyBr+mqfn68GWcyy6Ck60lXrsvVOpyiIiI7prOYQiovj/Z8OHD7/rkbm5ucHNzu2O7iIgIFBYW4siRI7jnnnsAAH/99RcKCwvRp0+fBp8vNzcX6enp8Pb2bnTNpuxakQof7P4bAPDC8PZwtrO6wxFERETN310tuthUQkJCMGLECMyYMQOHDx/G4cOHMWPGDNx33321riTr0KEDtmzZAgAoLi7GvHnzEBcXh0uXLiE2NhajR4+Gm5sbHnjgAam+FKO25JdzKFJVobOvAhN6BkhdDhERkV40qGfI2dm5wTfdzMvLu6uCbmXDhg147rnnMGzYMADVN4T95JNParVJTk5GYWEhAMDc3BynT5/GunXrUFBQAG9vbwwaNAgbN26Eg4ODQWpsyY5fzsOmE1cAAIvGdIQ5rx4jIqIWokFhaPny5dp/5+bm4q233sLw4cMREREBoPrS919//RWvvfaaQYoEABcXF6xfv/62bW6856yNjQ1+/fVXg9VjStQagde2JgIAHgn3Q48AZ4krIiIi0h+d71r/4IMPYtCgQZg1a1at7Z988gl+++03bN26VZ/1SY53rQe+jruE135KhKO1BfbNi4SrPSeYExFR86bL57fOc4Z+/fVXjBgxos724cOH47ffftP15aiZyy1WYdmvyQCAecPbMwgREVGLo3MYcnV11U5SvtHWrVvh6uqql6Ko+Vi6KxnK8iqEejvisV6BUpdDRESkdzpfWr9o0SJMnz4dsbGx2jlDhw8fxq5duwx6o1ZqeifT8rHxWDoA4A1OmiYiohZK5zA0ZcoUhISE4KOPPsLmzZshhEBoaCgOHjxY695hZNzUGoHXf6qeND2uhy/CW7lIXBEREZFhNGrRxV69emHDhg36roWakY1H03E6oxAOcgvMjwqRuhwiIiKDaVQY0mg0SElJQU5ODjQaTa19AwYM0EthJJ38kgos/fUcAGDu0HZwd+CkaSIiarl0DkOHDx/GxIkTcfnyZdx8Vb5MJoNardZbcSSNZbuTUVBaifaeDngigpOmiYioZdM5DM2cORPh4eHYsWMHvL29G7wyNRmHhCsF+PZIGoDqSdMW5kZxxxYiIqJG0zkMnT9/Hj/++CPatGljiHpIQkIILPw5EUIAY7r5oFcwl0ogIqKWT+c/+3v16oWUlBRD1EIS++P8dZxIK4DcwgyvjOSkaSIiMg069ww9++yzeP7555GdnY3OnTvD0tKy1v4uXbrorThqWp/srQ65E3sFwNPRWuJqiIiImobOYejBBx8EAEybNk27TSaTQQjBCdRG7PDFXBy5lAcrczM8NaC11OUQERE1GZ3DUGpqqiHqIIl9vPc8AOCRnn7wUrBXiIiITIfOYSgwkJdatzTHL+fjYEouLMxkmDmQvUJERGRaGnXd9Ndff42+ffvCx8cHly9fBgAsX74cP/30k16Lo6ZR0ys0rocv/JxtJa6GiIioaekchlasWIHo6GiMHDkSBQUF2jlCTk5OWL58ub7rIwM7faUQscnXYCYDno7kcglERGR6dA5DH3/8Mb788ku8+uqrMDc3124PDw/H6dOn9VocGV5Nr9CYbr5o5WYncTVERERNT+cwlJqaiu7du9fZLpfLUVJSopeiqGkkZSmx++xVyGTAM4PYK0RERKZJ5zAUFBSE+Pj4Ott/+eUXhIaG6qMmaiKf7KteV2hkZ2+08bCXuBoiIiJp6Hw12QsvvIBnnnkG5eXlEELgyJEj+Pbbb7F48WJ89dVXhqiRDCAlpxg7T2cBAJ4dzF4hIiIyXTqHoalTp6KqqgovvvgiSktLMXHiRPj6+uLDDz/EhAkTDFEjGcBn+1IgBDAs1BMdvBylLoeIiEgyMiGEaOzB169fh0ajgYeHhz5ralaUSiUUCgUKCwvh6NgyQsPl3BIMfn8/1BqBbbP6obOfQuqSiIiI9EqXz2+de4Zq5OTkIDk5GTKZDDKZDO7u7o19KWpin+27ALVGILK9O4MQERGZPJ0nUCuVSkyaNAk+Pj4YOHAgBgwYAB8fHzz++OMoLCw0RI2kR1fyS7HpxBUAwLOD20pcDRERkfR0DkNPPvkk/vrrL+zYsQMFBQUoLCzE9u3bcezYMcyYMcMQNZIefbH/Iqo0An3buCIs0FnqcoiIiCSn8zDZjh078Ouvv6Jfv37abcOHD8eXX36JESNG6LU40q+rynJsPJYOgL1CRERENXTuGXJ1dYVCUXeeiUKhgLMzexqasy/2X0RFlQb3tHJB72BXqcshIiJqFnQOQ//9738RHR2NrKws7bbs7Gy88MILeO211/RaHOnP9WIVvjlSfVPdZ4dwXSEiIqIaOg+TrVixAikpKQgMDERAQAAAIC0tDXK5HNeuXcMXX3yhbXvixAn9VUp35cfjV1BeqUFXPwX6tXGTuhwiIqJmQ+cwNHbsWAOUQYYkhMAP/8wVmtgrADKZTOKKiIiImg+dw9CCBQsMUQcZ0Mn0Aly4VgJrSzOM7OwtdTlERETNis5zhgCgoKAAX331FebPn4+8vDwA1UNiGRkZei3uRm+//Tb69OkDW1tbODk5NegYIQQWLlwIHx8f2NjYIDIyEomJiQarsbn64Vj1ukIjO3nDwdpS4mqIiIiaF53DUEJCAtq1a4d3330X7733HgoKCgAAW7Zswfz58/Vdn1ZFRQUefvhh/Oc//2nwMUuXLsUHH3yATz75BEePHoWXlxeGDh2KoqIig9XZ3JRXqrH9VCYA4KFwP4mrISIian50DkPR0dGYMmUKzp8/D2tra+32qKgoHDhwQK/F3WjRokWYO3cuOnfu3KD2QggsX74cr776KsaNG4dOnTph7dq1KC0txTfffGOwOpubXxOzUaSqgp+zDXoH8XJ6IiKim+kcho4ePYqnnnqqznZfX19kZ2frpSh9SE1NRXZ2NoYNG6bdJpfLMXDgQBw6dOiWx6lUKiiVyloPY1YzRPZgDz+YmXHiNBER0c10DkPW1tb1BoTk5ORmdbPWmmDm6elZa7unp+dtQ9vixYuhUCi0D39/f4PWaUgZBWU4eOE6AOChMA6RERER1UfnMDRmzBi88cYbqKysBADIZDKkpaXh5ZdfxoMPPqjTay1cuFB71/tbPY4dO6ZribXcfBm5EOK2l5bPnz8fhYWF2kd6evpdnV9Km45fgRBARLAr/F1spS6HiIioWdL50vr33nsPI0eOhIeHB8rKyjBw4EBkZ2cjIiICb7/9tk6vNWvWLEyYMOG2bVq1aqVriQAALy8vANU9RN7e/15OnpOTU6e36EZyuRxyubxR52xONBqBH49XD5E9zInTREREt6RzGHJ0dMSff/6JvXv34sSJE9BoNOjRowfuvfdenU/u5uYGNzfDrIYcFBQELy8v7NmzB927dwdQfUXa/v378e677xrknM3J0Ut5SMsrhb3cAiM6eUldDhERUbOlcxiqMXjwYAwePFiftdxWWloa8vLykJaWBrVajfj4eABAmzZtYG9vDwDo0KEDFi9ejAceeAAymQxz5szBO++8g7Zt26Jt27Z45513YGtri4kTJzZZ3VL54Z9eoVGdvWFr1ej/ZiIiohZPp09JjUaDmJgYbN68GZcuXYJMJkNQUBAeeughTJo0yaC3eXj99dexdu1a7fOa3p59+/YhMjISQPUk7sLCQm2bF198EWVlZXj66aeRn5+PXr16Yffu3XBwcDBYnc1BiaoKO09X30iXQ2RERES3JxNCiIY0FEJg9OjR2LlzJ7p27YoOHTpACIGkpCScPn0a999/P7Zu3WrgcpueUqmEQqFAYWEhHB0dpS6nQb4/lo4Xf0xAsJsdfn9+IO9FRkREJkeXz+8G9wzFxMTgwIED+P333zFo0KBa+/bu3YuxY8di3bp1eOKJJxpXNenNjzVrC4X5MQgRERHdQYMvrf/222/xyiuv1AlCQPX8oZdffhkbNmzQa3Gku0vXS3DkUh7MZMC4Hr5Sl0NERNTsNTgMJSQkYMSIEbfcHxUVhVOnTumlKGq8TSeqe4X6tXWHt8JG4mqIiIiavwaHoby8vNuuz+Pp6Yn8/Hy9FEWNo9YIbKpZW4grThMRETVIg8OQWq2GhcWtpxiZm5ujqqpKL0VR4xy6cB2ZheVwtLbA0NBbB1ciIiL6V4MnUAshMGXKlFuuzqxSqfRWFDVOzU1Zx3TzhbWlucTVEBERGYcGh6HJkyffsQ2vJJNOYVklfk2svgEtb8pKRETUcA0OQ2vWrDFkHXSXtidkQlWlQTtPe3TxU0hdDhERkdHQ+a711DzVDJE9HObPtYWIiIh0wDDUAqTkFCE+vQDmZjKM7c61hYiIiHTBMNQC1NyUdVB7D7g71D/BnYiIiOrHMNQC/J6UAwAY291H4kqIiIiMD8OQkcsuLEdKTjFkMqBfGzepyyEiIjI6DENG7s+U6wCALr4KONlaSVwNERGR8WEYMnJ/nr8GAOjXlr1CREREjcEwZMSEEPgzJRcA0JdDZERERI3CMGTEkq8W4XqxCjaW5ggLdJa6HCIiIqPEMGTE/jxfPV/oniAXyC14LzIiIqLGYBgyYn/8E4Z4FRkREVHjMQwZKVWVGkdS8wBw8jQREdHdYBgyUicuF6CsUg03eyt08HKQuhwiIiKjxTBkpP5Mqb6kvm8bN96YlYiI6C4wDBmpmkvqOV+IiIjo7jAMGaHC0kqcvlIAAOjf1l3aYoiIiIwcw5AROnThOjQCaONhDy+FtdTlEBERGTWGISP0RwovqSciItIXhiEjdJBhiIiISG8YhoxMel4pLueWwtxMht6tXaUuh4iIyOgxDBmZmlWnu/s7wV5uIXE1RERExo9hyMhoh8i46jQREZFeMAwZEbVG4OCF6jDUn2GIiIhILxiGjEhiZiEKSithL7dAVz8nqcshIiJqEYwmDL399tvo06cPbG1t4eTk1KBjpkyZAplMVuvRu3dvwxZqQH/+M0TWO9gVFuZG819HRETUrBnNJ2pFRQUefvhh/Oc//9HpuBEjRiArK0v72Llzp4EqNLw/z3OIjIiISN+M5nKkRYsWAQBiYmJ0Ok4ul8PLy8sAFTWtsgo1jl3KB8DJ00RERPpkND1DjRUbGwsPDw+0a9cOM2bMQE5OjtQlNcqRS3moUGvgrbBGsJud1OUQERG1GEbTM9QYUVFRePjhhxEYGIjU1FS89tprGDx4MI4fPw65XF7vMSqVCiqVSvtcqVQ2Vbm3deOq0zKZTOJqiIiIWg5Je4YWLlxYZ4LzzY9jx441+vXHjx+PUaNGoVOnThg9ejR++eUX/P3339ixY8ctj1m8eDEUCoX24e/v3+jz61PNYoscIiMiItIvSXuGZs2ahQkTJty2TatWrfR2Pm9vbwQGBuL8+fO3bDN//nxER0drnyuVSskD0bUiFZKyqnuo+vJ+ZERERHolaRhyc3ODm1vTfbjn5uYiPT0d3t7et2wjl8tvOYQmlUP/LLQY4u0IN/vmVRsREZGxM5oJ1GlpaYiPj0daWhrUajXi4+MRHx+P4uJibZsOHTpgy5YtAIDi4mLMmzcPcXFxuHTpEmJjYzF69Gi4ubnhgQcekOrLaBReUk9ERGQ4RjOB+vXXX8fatWu1z7t37w4A2LdvHyIjIwEAycnJKCwsBACYm5vj9OnTWLduHQoKCuDt7Y1BgwZh48aNcHBwaPL6G0sIoV1ssR+HyIiIiPROJoQQUhfRnCmVSigUChQWFsLR0bHJz5+SU4x7P9gPK3MznFowDDZW5k1eAxERkbHR5fPbaIbJTFXNJfXhrZwZhIiIiAyAYaiZ4yX1REREhsUw1IxVqTU4fDEXAOcLERERGQrDUDN2KbcUxaoq2FqZo6OPQupyiIiIWiSGoWbswrXqZQNau9vD3Iy34CAiIjIEhqFm7N8wxBuzEhERGQrDUDOWkvNvzxAREREZBsNQM3bhWgkAoLUHwxAREZGhMAw1U0IIXPynZ6gNwxAREZHBMAw1U9eKVChSVcFMBgS62kpdDhERUYvFMNRMpfwzeTrAxRZyC648TUREZCgMQ82Udr4QJ08TEREZFMNQM3Wh5koyzhciIiIyKIahZoprDBERETUNhqFm6gKvJCMiImoSDEPNUImqCpmF5QCAYDeGISIiIkNiGGqGUq9XT552tbOCs52VxNUQERG1bAxDzRBvw0FERNR0GIaaIe3kaQ9OniYiIjI0hqFm6N8rydgzREREZGgMQ83QhRzeoJWIiKipMAw1M2qN0E6gbsOeISIiIoNjGGpmruSXokKtgdzCDD5ONlKXQ0RE1OIxDDUzNVeSBbnZwdxMJnE1RERELR/DUDPz75VkHCIjIiJqCgxDzUzN5GnOFyIiImoaDEPNDHuGiIiImhbDUDPDu9UTERE1LYahZiS3WIX80koAvEErERFRU2EYakYuXKueL+TrZAMbK3OJqyEiIjINDEPNSM0QWRvOFyIiImoyDEPNyAXerZ6IiKjJMQw1I7xbPRERUdMzijB06dIlTJ8+HUFBQbCxsUHr1q2xYMECVFRU3PY4IQQWLlwIHx8f2NjYIDIyEomJiU1Ute5q5gyxZ4iIiKjpGEUYOnfuHDQaDb744gskJibif//7Hz7//HO88sortz1u6dKl+OCDD/DJJ5/g6NGj8PLywtChQ1FUVNRElTdceaUa6fmlABiGiIiImpJMCCGkLqIxli1bhhUrVuDixYv17hdCwMfHB3PmzMFLL70EAFCpVPD09MS7776Lp556qkHnUSqVUCgUKCwshKOjo97qv1lSlhJRH/4BhY0l4l8fCpmM9yUjIiJqLF0+v42iZ6g+hYWFcHFxueX+1NRUZGdnY9iwYdptcrkcAwcOxKFDh255nEqlglKprPVoCjcutsggRERE1HSMMgxduHABH3/8MWbOnHnLNtnZ2QAAT0/PWts9PT21++qzePFiKBQK7cPf318/Rd9BzT3JOERGRETUtCQNQwsXLoRMJrvt49ixY7WOyczMxIgRI/Dwww/jySefvOM5bu5lEULctudl/vz5KCws1D7S09Mb98XpiPckIyIikoaFlCefNWsWJkyYcNs2rVq10v47MzMTgwYNQkREBFauXHnb47y8vABU9xB5e3trt+fk5NTpLbqRXC6HXC5vQPX6lcI1hoiIiCQhaRhyc3ODm5tbg9pmZGRg0KBBCAsLw5o1a2BmdvtOraCgIHh5eWHPnj3o3r07AKCiogL79+/Hu+++e9e165NGI3DxOm/QSkREJAWjmDOUmZmJyMhI+Pv747333sO1a9eQnZ1dZ+5Phw4dsGXLFgDVw2Nz5szBO++8gy1btuDMmTOYMmUKbG1tMXHiRCm+jFvKLCxDeaUGluYyBLjYSl0OERGRSZG0Z6ihdu/ejZSUFKSkpMDPz6/WvhtXBkhOTkZhYaH2+YsvvoiysjI8/fTTyM/PR69evbB79244ODg0We0NUbPYYitXO1iYG0U+JSIiajGMdp2hptIU6wyt/jMVb2w/ixEdvfD5pDCDnIOIiMiUmMQ6Qy0J70lGREQkHYahZoBXkhEREUmHYagZqJkz1IZrDBERETU5hiGJFZZW4nqxCgAQzJ4hIiKiJscwJLEL/6wv5OVoDXu5UVzcR0RE1KIwDEnsQg4nTxMREUmJYUhiKdc4eZqIiEhKDEMSq7lbPSdPExERSYNhSGIX2TNEREQkKYYhCVVUaXA5rxQAwxAREZFUGIYklJZXArVGwM7KHJ6OcqnLISIiMkkMQxLSrjztYQ+ZTCZxNURERKaJYUhCNStPc4iMiIhIOgxDEqpZY4hXkhEREUmHYUhC2rvVu3PBRSIiIqkwDElECMFhMiIiomaAYUgiOUUqFKuqYG4mQ4CrrdTlEBERmSyGIYnUXEkW4GILuYW5xNUQERGZLoYhiVzgytNERETNAsOQRIpVVbC2NOPd6omIiCQmE0IIqYtozpRKJRQKBQoLC+Ho6KjX19ZoBFRVGthYcZiMiIhIn3T5/GbPkITMzGQMQkRERBJjGCIiIiKTxjBEREREJo1hiIiIiEwawxARERGZNIYhIiIiMmkMQ0RERGTSGIaIiIjIpDEMERERkUljGCIiIiKTxjBEREREJo1hiIiIiEwawxARERGZNIYhIiIiMmkWUhfQ3AkhAABKpVLiSoiIiKihaj63az7Hb4dh6A6KiooAAP7+/hJXQkRERLoqKiqCQqG4bRuZaEhkMmEajQaZmZlwcHCATCZr0DFKpRL+/v5IT0+Ho6OjgSukGnzfpcH3XRp836XB910ajXnfhRAoKiqCj48PzMxuPyuIPUN3YGZmBj8/v0Yd6+joyB8WCfB9lwbfd2nwfZcG33dp6Pq+36lHqAYnUBMREZFJYxgiIiIik8YwZAByuRwLFiyAXC6XuhSTwvddGnzfpcH3XRp836Vh6PedE6iJiIjIpLFniIiIiEwawxARERGZNIYhIiIiMmkMQ0RERGTSGIYM4LPPPkNQUBCsra0RFhaGP/74Q+qSWrQDBw5g9OjR8PHxgUwmw9atW6UuySQsXrwYPXv2hIODAzw8PDB27FgkJydLXVaLt2LFCnTp0kW7+FxERAR++eUXqcsyKYsXL4ZMJsOcOXOkLqXFW7hwIWQyWa2Hl5eX3s/DMKRnGzduxJw5c/Dqq6/i5MmT6N+/P6KiopCWliZ1aS1WSUkJunbtik8++UTqUkzK/v378cwzz+Dw4cPYs2cPqqqqMGzYMJSUlEhdWovm5+eHJUuW4NixYzh27BgGDx6MMWPGIDExUerSTMLRo0excuVKdOnSRepSTEbHjh2RlZWlfZw+fVrv5+Cl9XrWq1cv9OjRAytWrNBuCwkJwdixY7F48WIJKzMNMpkMW7ZswdixY6UuxeRcu3YNHh4e2L9/PwYMGCB1OSbFxcUFy5Ytw/Tp06UupUUrLi5Gjx498Nlnn+Gtt95Ct27dsHz5cqnLatEWLlyIrVu3Ij4+3qDnYc+QHlVUVOD48eMYNmxYre3Dhg3DoUOHJKqKqGkUFhYCqP5gpqahVqvx3XffoaSkBBEREVKX0+I988wzGDVqFO69916pSzEp58+fh4+PD4KCgjBhwgRcvHhR7+fgjVr16Pr161Cr1fD09Ky13dPTE9nZ2RJVRWR4QghER0ejX79+6NSpk9TltHinT59GREQEysvLYW9vjy1btiA0NFTqslq07777DidOnMDRo0elLsWk9OrVC+vWrUO7du1w9epVvPXWW+jTpw8SExPh6uqqt/MwDBmATCar9VwIUWcbUUsya9YsJCQk4M8//5S6FJPQvn17xMfHo6CgAJs2bcLkyZOxf/9+BiIDSU9Px+zZs7F7925YW1tLXY5JiYqK0v67c+fOiIiIQOvWrbF27VpER0fr7TwMQ3rk5uYGc3PzOr1AOTk5dXqLiFqKZ599Fj///DMOHDgAPz8/qcsxCVZWVmjTpg0AIDw8HEePHsWHH36IL774QuLKWqbjx48jJycHYWFh2m1qtRoHDhzAJ598ApVKBXNzcwkrNB12dnbo3Lkzzp8/r9fX5ZwhPbKyskJYWBj27NlTa/uePXvQp08fiaoiMgwhBGbNmoXNmzdj7969CAoKkrokkyWEgEqlkrqMFmvIkCE4ffo04uPjtY/w8HA89thjiI+PZxBqQiqVCklJSfD29tbr67JnSM+io6MxadIkhIeHIyIiAitXrkRaWhpmzpwpdWktVnFxMVJSUrTPU1NTER8fDxcXFwQEBEhYWcv2zDPP4JtvvsFPP/0EBwcHbY+oQqGAjY2NxNW1XK+88gqioqLg7++PoqIifPfdd4iNjcWuXbukLq3FcnBwqDMXzs7ODq6urpwjZ2Dz5s3D6NGjERAQgJycHLz11ltQKpWYPHmyXs/DMKRn48ePR25uLt544w1kZWWhU6dO2LlzJwIDA6UurcU6duwYBg0apH1eM448efJkxMTESFRVy1ezfERkZGSt7WvWrMGUKVOaviATcfXqVUyaNAlZWVlQKBTo0qULdu3ahaFDh0pdGpHeXblyBY8++iiuX78Od3d39O7dG4cPH9b7ZyrXGSIiIiKTxjlDREREZNIYhoiIiMikMQwRERGRSWMYIiIiIpPGMEREREQmjWGIiIiITBrDEBEREZk0hiEiuiOZTIatW7dKXUaDLFy4EN26dZO6DL2LjIzEnDlzGtw+NjYWMpkMBQUFt2wTExMDJyenu66NyNgxDBG1YFOmTMHYsWOlLsPoNSQ0vP/++1AoFCgtLa2zr7y8HE5OTvjggw8aXcPmzZvx5ptvNvp4Iro1hiEiIj144oknUFZWhk2bNtXZt2nTJpSWlmLSpEk6v25lZSUAwMXFBQ4ODnddJxHVxTBEZEIiIyPx3HPP4cUXX4SLiwu8vLywcOHCWm3Onz+PAQMGwNraGqGhodizZ0+d18nIyMD48ePh7OwMV1dXjBkzBpcuXdLur+mRWrRoETw8PODo6IinnnoKFRUV2jZCCCxduhTBwcGwsbFB165d8eOPP2r31wzz/P777wgPD4etrS369OmD5OTkWrUsWbIEnp6ecHBwwPTp01FeXl6n3jVr1iAkJATW1tbo0KEDPvvsM+2+S5cuQSaTYfPmzRg0aBBsbW3RtWtXxMXFaeuYOnUqCgsLIZPJIJPJ6rxnAODu7o7Ro0dj9erVdfatXr0a999/P9zd3fHSSy+hXbt2sLW1RXBwMF577TVt4AH+HeZbvXo1goODIZfLIYSoM0y2fv16hIeHw8HBAV5eXpg4cSJycnLqnPvgwYPo2rUrrK2t0atXL5w+fbpOmxtt27YNYWFhsLa2RnBwMBYtWoSqqqrbHkNk9AQRtViTJ08WY8aM0T4fOHCgcHR0FAsXLhR///23WLt2rZDJZGL37t1CCCHUarXo1KmTiIyMFCdPnhT79+8X3bt3FwDEli1bhBBClJSUiLZt24pp06aJhIQEcfbsWTFx4kTRvn17oVKptOe1t7cX48ePF2fOnBHbt28X7u7u4pVXXtHW8sorr4gOHTqIXbt2iQsXLog1a9YIuVwuYmNjhRBC7Nu3TwAQvXr1ErGxsSIxMVH0799f9OnTR/saGzduFFZWVuLLL78U586dE6+++qpwcHAQXbt21bZZuXKl8Pb2Fps2bRIXL14UmzZtEi4uLiImJkYIIURqaqoAIDp06CC2b98ukpOTxUMPPSQCAwNFZWWlUKlUYvny5cLR0VFkZWWJrKwsUVRUVO/7vWPHDiGTycTFixe121JTU4VMJhM7d+4UQgjx5ptvioMHD4rU1FTx888/C09PT/Huu+9q2y9YsEDY2dmJ4cOHixMnTohTp04JjUYjBg4cKGbPnq1tt2rVKrFz505x4cIFERcXJ3r37i2ioqK0+2vev5CQELF7926RkJAg7rvvPtGqVStRUVEhhBBizZo1QqFQaI/ZtWuXcHR0FDExMeLChQti9+7dolWrVmLhwoX1f4MRtRAMQ0QtWH1hqF+/frXa9OzZU7z00ktCCCF+/fVXYW5uLtLT07X7f/nll1phaNWqVaJ9+/ZCo9Fo26hUKmFjYyN+/fVX7XldXFxESUmJts2KFSuEvb29UKvVori4WFhbW4tDhw7VqmX69Oni0UcfFUL8+2H+22+/affv2LFDABBlZWVCCCEiIiLEzJkza71Gr169aoUhf39/8c0339Rq8+abb4qIiAghxL9h6KuvvtLuT0xMFABEUlKSEKJuaLiVqqoq4evrK15//XXtttdff134+vqKqqqqeo9ZunSpCAsL0z5fsGCBsLS0FDk5ObXa3RyGbnbkyBEBQBvUat6/7777TtsmNzdX2NjYiI0bN9b7dfXv31+88847tV7366+/Ft7e3rf/womMnIVEHVJEJJEuXbrUeu7t7a0dXklKSkJAQAD8/Py0+yMiImq1P378OFJSUurMXykvL8eFCxe0z7t27QpbW9tar1NcXIz09HTk5OSgvLwcQ4cOrfUaFRUV6N69+y3r9fb2BgDk5OQgICAASUlJmDlzZq32ERER2LdvHwDg2rVrSE9Px/Tp0zFjxgxtm6qqKigUigadp0OHDmgoc3NzTJ48GTExMViwYAFkMhnWrl2LKVOmwNzcHADw448/Yvny5UhJSUFxcTGqqqrg6OhY63UCAwPh7u5+23OdPHkSCxcuRHx8PPLy8qDRaAAAaWlpCA0NrfV+1HBxcUH79u2RlJRU72seP34cR48exdtvv63dplarUV5ejtLS0lr/n0QtCcMQkYmxtLSs9Vwmk2k/SIUQddrLZLJazzUaDcLCwrBhw4Y6be/0AX7z+Xbs2AFfX99a++Vy+S3rraml5vg7qWn35ZdfolevXrX21YQTfZznRtOmTcPixYuxd+9eANXhZOrUqQCAw4cPY8KECVi0aBGGDx8OhUKB7777Du+//36t17Czs7vtOUpKSjBs2DAMGzYM69evh7u7O9LS0jB8+PBa87Ju5eb/0xoajQaLFi3CuHHj6uyztra+4+sSGSuGISLSCg0NRVpaGjIzM+Hj4wMA2onENXr06IGNGzdqJ0bfyqlTp1BWVgYbGxsA1UHA3t4efn5+cHZ2hlwuR1paGgYOHNjoekNCQnD48GE88cQT2m2HDx/W/tvT0xO+vr64ePEiHnvssUafx8rKCmq1ukFtW7dujYEDB2LNmjXaic+tW7cGUD2ZOTAwEK+++qq2/eXLl3Wu59y5c7h+/TqWLFkCf39/AMCxY8fqbXv48GEEBAQAAPLz8/H333/fsrerR48eSE5ORps2bXSuiciYMQwRkda9996L9u3b44knnsD7778PpVJZ64MbAB577DEsW7YMY8aMwRtvvAE/Pz+kpaVh8+bNeOGFF7RDbBUVFZg+fTr++9//4vLly1iwYAFmzZoFMzMzODg4YN68eZg7dy40Gg369esHpVKJQ4cOwd7eHpMnT25QvbNnz8bkyZMRHh6Ofv36YcOGDUhMTERwcLC2zcKFC/Hcc8/B0dERUVFRUKlUOHbsGPLz8xEdHd2g87Rq1QrFxcX4/ffftcN/txsyunFY7quvvtJub9OmDdLS0vDdd9+hZ8+e2LFjB7Zs2dKgGm4UEBAAKysrfPzxx5g5cybOnDlzyzWI3njjDbi6usLT0xOvvvoq3Nzcbrn21Ouvv4777rsP/v7+ePjhh2FmZoaEhAScPn0ab731ls51EhkLXlpPRFpmZmbYsmULVCoV7rnnHjz55JO15o8AgK2tLQ4cOICAgACMGzcOISEhmDZtGsrKymr1FA0ZMgRt27bFgAED8Mgjj2D06NG1Lkl/88038frrr2Px4sUICQnB8OHDsW3bNgQFBTW43vHjx+P111/HSy+9hLCwMFy+fBn/+c9/arV58skn8dVXXyEmJgadO3fGwIEDERMTo9N5+vTpg5kzZ2L8+PFwd3fH0qVLb9v+wQcfhFwuh1wurzXkNGbMGMydOxezZs1Ct27dcOjQIbz22msNrqOGu7s7YmJi8MMPPyA0NBRLlizBe++9V2/bJUuWYPbs2QgLC0NWVhZ+/vlnWFlZ1dt2+PDh2L59O/bs2YOePXuid+/e+OCDDxAYGKhzjUTGRCbqmyRARHQXpkyZgoKCAqO5hQcRmTb2DBEREZFJYxgiIiIik8ZhMiIiIjJp7BkiIiIik8YwRERERCaNYYiIiIhMGsMQERERmTSGISIiIjJpDENERERk0hiGiIiIyKQxDBEREZFJYxgiIiIik/b/K6OUpWaxaosAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"X = np.arange(-5.0, 5.0, 0.1)\n",
"X_positif = X[X > 0] # Filter agar hanya menyertakan angka > 0\n",
"\n",
"Y = np.log(X_positif)\n",
"\n",
"plt.plot(X_positif, Y)\n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.title('Plot Logaritma (Hanya Nilai Positif)')\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmoidal/Logistic\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"Y = 1-4/(1+np.power(3, X-2))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"ref2\"></a>\n",
"# Non-Linear Regression example\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For an example, we're going to try and fit a non-linear model to the datapoints corresponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year. \n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2025-10-20 14:43:18 URL:https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Year</th>\n",
" <th>Value</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1960</td>\n",
" <td>5.918412e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1961</td>\n",
" <td>4.955705e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1962</td>\n",
" <td>4.668518e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1963</td>\n",
" <td>5.009730e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1964</td>\n",
" <td>5.906225e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>1965</td>\n",
" <td>6.970915e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>1966</td>\n",
" <td>7.587943e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>1967</td>\n",
" <td>7.205703e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>1968</td>\n",
" <td>6.999350e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1969</td>\n",
" <td>7.871882e+10</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Year Value\n",
"0 1960 5.918412e+10\n",
"1 1961 4.955705e+10\n",
"2 1962 4.668518e+10\n",
"3 1963 5.009730e+10\n",
"4 1964 5.906225e+10\n",
"5 1965 6.970915e+10\n",
"6 1966 7.587943e+10\n",
"7 1967 7.205703e+10\n",
"8 1968 6.999350e+10\n",
"9 1969 7.871882e+10"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"#downloading dataset\n",
"!wget -nv -O china_gdp.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv\n",
" \n",
"df = pd.read_csv(\"china_gdp.csv\")\n",
"df.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](http://cocl.us/ML0101EN-IBM-Offer-CC)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting the Dataset ###\n",
"This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerates slightly in the 2010s.\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,5))\n",
"x_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\n",
"plt.plot(x_data, y_data, 'ro')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choosing a model ###\n",
"\n",
"From an initial look at the plot, we determine that the logistic function could be a good approximation,\n",
"since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAGwCAYAAABVdURTAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAABRkElEQVR4nO3dd3xT5eIG8CfpSLqS0k2hk1kos4Wyl9iCyhDvBRXZ8LtcB6OKilym3FtEURQFRYSCIvYqQ5EKFJkyLrRQZhlt6aCD7qZ7JOf3RyVaW6CBtCdJn+/nkw/tyUnyNFrycM573lciCIIAIiIiIhMhFTsAERERkT6x3BAREZFJYbkhIiIik8JyQ0RERCaF5YaIiIhMCssNERERmRSWGyIiIjIp5mIHaGoajQbp6emws7ODRCIROw4RERE1gCAIKCoqgru7O6TSBx+baXblJj09HR4eHmLHICIiokeQmpqK1q1bP3CfZldu7OzsANS8OQqFQuQ0RERE1BAqlQoeHh7az/EHaXbl5t6pKIVCwXJDRERkZBoypIQDiomIiMiksNwQERGRSWG5ISIiIpPCckNEREQmheWGiIiITArLDREREZkUlhsiIiIyKSw3REREZFJELTfHjx/HqFGj4O7uDolEgj179jz0MceOHUNAQADkcjl8fX3x+eefN35QIiIiMhqilpuSkhJ069YNn376aYP2v337Np566ikMHDgQFy5cwDvvvIM5c+Zg586djZyUiIiIjIWoyy+MHDkSI0eObPD+n3/+OTw9PbF27VoAgJ+fH6Kjo/HBBx/gueeeq/cxFRUVqKio0H6vUqkeKzMREREZNqMac3P69GkEBwfX2hYSEoLo6GhUVVXV+5iwsDAolUrtjSuCExERmTajKjeZmZlwdXWttc3V1RXV1dXIycmp9zELFy5EYWGh9paamtoUUYmIiJoVQRBQUlGNu6pypOaViprF6FYF/+tqoIIg1Lv9HplMBplM1ui5iIiIjJ0gCCirUiOvpBIFpVXIL635s6CsCoW/f11YVnNTlVehsKwaqrIqFFdUo7iiGmpNzWdyK3srnHx7mGg/h1GVGzc3N2RmZtbalpWVBXNzczg6OoqUioiIyHAJgoD80ipkF1Ugq6gc2UUVyC6qQE5xBXKLK5FTUom8kpqv80oqUVGteazXM5NKIBX5vJBRlZu+ffti7969tbYdPHgQgYGBsLCwECkVERGRODQaAdnFFUgvKENGYTnSC8qQXlCOTFUZ7qoqkFlYU2Yq1boVFkszKRxsLGFvbVFzs6r5WmllAYXVH38q5ObaP+3kFrCTm8PKwuy+Z1Oaiqjlpri4GPHx8drvb9++jdjYWDg4OMDT0xMLFy5EWloatm3bBgCYPXs2Pv30U4SGhmLWrFk4ffo0vvrqK+zYsUOsH4GIiKhRqcqrkJJbiuTcUiTlluBOfhnu5JfiTn4Z0vLLGlxcWlhbwMVODmc7GZztZHCytYSjrQyONpZwspXBwcZSe7O2FL+gPA5Ry010dDSGDh2q/T40NBQAMGXKFISHhyMjIwMpKSna+318fBAZGYn58+fjs88+g7u7Oz755JP7XgZORERkDKrVGiTlliIhuxiJ2SVIzC5GYk4JbueUIK+k8oGPNZNK4GonQ0t7K7jbW8FdKYebUg43hRwuCjlcFTK42MlhaW5U1xA9Folwb0RuM6FSqaBUKlFYWAiFQiF2HCIiakYEQUBaQRniMopwPUOFm1nFuHW3CInZJQ88AuNoYwkvR2t4OdrAw8EaHi2s0LqFNTwcrOCmkMPczPSLiy6f30Y15oaIiMhYqDUCbucU49KdQly6U4hrGSpcz1BBVV5d7/5WFmZo42IDXydb+DrbwNfZFr5ONvBytIadnONKdcFyQ0REpAd3VeU4n5yPC6kFiE0twNW0QpRUquvsZ2EmQRtnW/i1VKC9qx3au9qivasdWtlbQSo13nEuhoTlhoiISEeCIOBWVjH+l5iLs0n5OJ+cj7SCsjr7WVuawd9dCf9WSnR2V8CvpQJtXWyb1fgXMbDcEBERPYQgCEjILsZvt3JwOjEX55Ly6wz0lUqADm4K9PS0Rw/PFujWWglfZ1uY8WhMk2O5ISIiqkdeSSVO3MrGiVs5OBmfg4zC8lr3yy2kCPBqgd7ejujl3QJdPexhK+PHqiHgfwUiIiLUHJ25nlmEw9ezcPh6Fi6k5EPzp+uJLc2l6OXdAv3aOKGPrwO6tLLn6SUDxXJDRETNllojICY5H79cycDBq3frjJvp6GaHQe2dMaCtE3r7OEBuYSZSUtIFyw0RETUrao2A/93Oxc+XagpNTnGF9j65hRT92zhhaEcXDOvoAnd7KxGT0qNiuSEiIpMnCAKupqvwY2wa9l7MQKbqj/EzCrk5hndyxYjObhjU3plHZ0wAyw0REZms7KIK7Dp/B9/H3EF8VrF2u0Jujqe6tMTILi3R19eRY2dMDMsNERGZlGq1BsdvZSPiXCp+jctC9e+jgmXmUgz3c8WY7u4Y3MEZMnMeoTFVLDdERGQScosr8N25VGw/k4z0P1223d3DHhN6eeDpri2h4DIGzQLLDRERGbVLdwoQfioJP1/M0C4+2cLaAs/2aI0JvTzQwc1O5ITU1FhuiIjI6Gg0Ao7ezMLnxxJx9naednvX1kpM6euNp7u25MDgZozlhoiIjEZltQZ7L6bji+MJuHm3ZoCwhZkET3dpiSn9vNHDs4XICckQsNwQEZHBq6zW4IeYO/jsSLx2oj1bmTleDPLEtP7eaKnkfDT0B5YbIiIyWFXqmlLz6eE/So2znQzT+/vgxSBPKK04QJjqYrkhIiKDo9EI2BObhg+jbuJO/h+l5p+D2+DFIE+Op6EHYrkhIiKDcuJWNsIir+NahgoA4GQrwz+HtMFElhpqIJYbIiIyCHEZKoT9ch3Hb2YDAOxk5vjn0DaY1s8HVpYsNdRwLDdERCSqwtIqrIm6gW/OJEMj1Fz9NKmPN14d1hYONpZixyMjxHJDRESi0GgE/Dc6FasP3EBeSSUA4OkuLfHmiA7wcrQROR0ZM5YbIiJqclfSCrFo92VcvFMIAGjnYovlYzqjXxsnkZORKWC5ISKiJlNepcZHh25i04nbUGsE2MnMMe/J9pjc1wsWZlyZm/SD5YaIiJrE6YRcLNx1CUm5pQCAZ7q2xJJRneBiJxc5GZkalhsiImpUxRXV+E9kHL79XwoAwE0hx8qx/hjeyVXkZGSqWG6IiKjRxCTnY35ELFLyao7WTAzyxFsjO0Ih58zC1HhYboiISO+q1Bp88ustfHYkHhoBaGVvhQ/+3g192ziKHY2aAZYbIiLSq8TsYsyLiMWl36+EGtejFZaN6cyjNdRkWG6IiEhvfoxNwzu7LqOkUg2llQX+82wXPN21pdixqJlhuSEiosdWXqXGuz9fw/bfBw0H+Tjg4+d7wE3JK6Go6bHcEBHRY0nOLcHL28/janrNQpevDWuLuU+0gznnrSGRsNwQEdEjO3z9LubuiEVRRTVaWFvgowndMaSDi9ixqJljuSEiIp0JgoANxxLw/oEbEAQgwKsFPn2xB1oqrcSORsRyQ0REuimrVOOtnZfw08V0AMALvT2xfHRnWJrzNBQZBpYbIiJqsPSCMvzf19G4kqaCuVSCpaM7Y1IfL7FjEdXCckNERA1yJa0Q08PPIauoAg42llg/sSf6+HJSPjI8LDdERPRQx25m4+VvYlBSqUYHVztsmhIIDwdrsWMR1YvlhoiIHui/51KxcPdlqDUC+rVxxOeTAjjbMBk0lhsiIqqXIAhYe+gWPv71FoCaZRRWPdeVA4fJ4LHcEBFRHRqNgMU/XtHOOPzq0LZ4Pbg9JBKJyMmIHo7lhoiIaqlSa7Dg+4vYE5sOiQRYOdYfE4N4RRQZD5YbIiLSKq9S47UdFxB17S7MpRJ8NKE7RnVzFzsWkU5YboiICABQUlGN//s6Gifjc2FpLsXnL/XEsI6uYsci0hnLDRERobiiGlM2n0VMcj5sLM3w5ZRA9GvjJHYsokfCckNE1MwVV1Rj6u/FRiE3x9bpvdHDs4XYsYgeGcsNEVEzVlJRjelbziH692KzfWYfdGmtFDsW0WPhZAVERM1UaWU1poefw9mkPNjJzfH1jCAWGzIJLDdERM1QWaUaM8Kj8b/bebCTmWPb9N7o5mEvdiwivWC5ISJqZiqrNfjn9hicTsyFjaUZwjnGhkwMyw0RUTOi0Qh44/uLOHojG3ILKcKn90aAF4sNmRaWGyKiZkIQBCz96Sp+upgOc6kEG14KQC9vB7FjEekdyw0RUTPx0aFb+PpMMiQSYM34bhjawUXsSESNguWGiKgZ2HLyNj75fXXvFaM7Y0z3ViInImo8LDdERCYu8nIGlu+9BgAIfbI9JvX1FjcQUSNjuSEiMmExyXmYFxELAJjc1wuvDWsrbiCiJsByQ0RkopJySjBrWwwqqzUY7ueCpaM6QyKRiB2LqNGJXm7Wr18PHx8fyOVyBAQE4MSJEw/cf/v27ejWrRusra3RsmVLTJs2Dbm5uU2UlojIOOSXVGJa+DnklVSiSyslPnmhB8ykLDbUPIhabiIiIjBv3jwsWrQIFy5cwMCBAzFy5EikpKTUu/9vv/2GyZMnY8aMGbh69Sq+//57nDt3DjNnzmzi5EREhqu8So1Z26JxO6cEreyt8NXUQFhbcilBaj5ELTcffvghZsyYgZkzZ8LPzw9r166Fh4cHNmzYUO/+Z86cgbe3N+bMmQMfHx8MGDAA//jHPxAdHd3EyYmIDJMgCHh75yVEJ+fDTm6OLdN6wcVOLnYsoiYlWrmprKxETEwMgoODa20PDg7GqVOn6n1Mv379cOfOHURGRkIQBNy9exc//PADnn766fu+TkVFBVQqVa0bEZGp+uJ4IvbE1kzS98VLAWjvaid2JKImJ1q5ycnJgVqthqura63trq6uyMzMrPcx/fr1w/bt2zFhwgRYWlrCzc0N9vb2WLdu3X1fJywsDEqlUnvz8PDQ689BRGQojlzPwnv7rwMAlo7qhH5tnURORCQO0QcU/3XkviAI9x3Nf+3aNcyZMwdLlixBTEwM9u/fj9u3b2P27Nn3ff6FCxeisLBQe0tNTdVrfiIiQxCfVYw5Oy5AEIAXenvipT5eYkciEo1oI8ycnJxgZmZW5yhNVlZWnaM594SFhaF///5YsGABAKBr166wsbHBwIEDsXLlSrRs2bLOY2QyGWQymf5/ACIiA1FYWoVZ26JRVFGN3t4OWD6al3xT8ybakRtLS0sEBAQgKiqq1vaoqCj069ev3seUlpZCKq0d2czMDEDNER8iouZGrRHw2ncXtFdGrX+pJyzNRT8oTyQqUX8DQkNDsWnTJmzevBlxcXGYP38+UlJStKeZFi5ciMmTJ2v3HzVqFHbt2oUNGzYgMTERJ0+exJw5c9C7d2+4u7uL9WMQEYlm7aGbOH4zG3ILKTZODoCTLY9UE4k68cGECROQm5uLFStWICMjA/7+/oiMjISXV8254oyMjFpz3kydOhVFRUX49NNP8frrr8Pe3h7Dhg3De++9J9aPQEQkmsPX72Ld4XgAwHvPdUVnd6XIiYgMg0RoZudzVCoVlEolCgsLoVAoxI5DRPRIUvNK8fQnJ6Aqr8bkvl5YMcZf7EhEjUqXz2+emCUiMjLlVWr8c3sMVOXV6O5hj0VP+4kdicigsNwQERmZ5Xuv4kqaCi2sLbB+Yk/IzM3EjkRkUFhuiIiMyA8xd7DjbCokEuCTF3rA3d5K7EhEBoflhojISMRnFWPxnisAgPnD22NgO2eRExEZJpYbIiIjUF6lxqvfnkdZlRoD2jrh1aFtxY5EZLBYboiIjEBYZByuZxbB0cYSH47vBqmUMxAT3Q/LDRGRgTt4NRNbTycDANaM7wYXhVzkRESGjeWGiMiApReUYcEPlwAAswb6YEgHF5ETERk+lhsiIgNVrdZg3nexKCyrQtfWSiwI6Sh2JCKjwHJDRGSgPj+WgLNJebCVmWPdCz24ICZRA/E3hYjIAF2+U4i1h24BAJaP7gwvRxuRExEZD5YbIiIDU16lxryIC6jWCHiqixvG9WwldiQio8JyQ0RkYFb9ch0J2SVwsZPh32O7QCLhZd9EumC5ISIyIMdvZiP8VBIA4P2/d0MLG0txAxEZIZYbIiIDUVBaiQU/XAQATO7rhcHtubwC0aNguSEiMhCLf7yKu6oK+DrbYOFIP7HjEBktlhsiIgPwy+UM7L2YDjOpBB+N7w4rSzOxIxEZLZYbIiKR5ZVUYvGPNat9/3NwG3TzsBc3EJGRY7khIhLZ0p+uIqe4Eu1dbfHaE1ztm+hxsdwQEYlo/5U/Tkd98PdukJnzdBTR42K5ISISSX5JJf61p+Z01D8G+aJra3txAxGZCJYbIiKRLNtbczqqnYst5g5vJ3YcIpPBckNEJIKoa3fxY2w6pJKayfp4OopIf1huiIiaWFF5FRb/fjpq1kBfdOfVUUR6xXJDRNTEVu+/gUxVOTwdrDFveHux4xCZHJYbIqImFJOch2/+lwwACBvXhZP1ETUClhsioiZSUa3G2zsvQxCAvwW0Rv+2TmJHIjJJLDdERE3k86OJuJVVDEcbSyx6imtHETWWRy43lZWVuHHjBqqrq/WZh4jIJMVnFeGzI/EAgCWjOqGFjaXIiYhMl87lprS0FDNmzIC1tTU6d+6MlJQUAMCcOXOwatUqvQckIjJ2Go2Ad3ZdQaVagyEdnDG6m7vYkYhMms7lZuHChbh48SKOHj0KuVyu3T58+HBEREToNRwRkSn44fwdnE3Kg5WFGVaO9YdEIhE7EpFJM9f1AXv27EFERAT69OlT6xe0U6dOSEhI0Gs4IiJjl19SibDIOADAvOHt0LqFtciJiEyfzkdusrOz4eLiUmd7SUkJ/zVCRPQX7+2/jvzSKnRwtcP0AT5ixyFqFnQuN7169cK+ffu0398rNF9++SX69u2rv2REREYuJjkP351LBQCsfNYfFma8QJWoKeh8WiosLAwjRozAtWvXUF1djY8//hhXr17F6dOncezYscbISERkdKrVGizaXbPEwvjA1ujl7SByIqLmQ+d/RvTr1w8nT55EaWkp2rRpg4MHD8LV1RWnT59GQEBAY2QkIjI64aeScD2zCPbWFnh7JOe0IWpKOh+5AYAuXbpg69at+s5CRGQSMgrL8FHUTQDAwpEd4cA5bYiaVIPKjUqlavATKhSKRw5DRGQKVu6LQ0mlGgFeLfD3AA+x4xA1Ow0qN/b29g+9EkoQBEgkEqjVar0EIyIyRqfic7DvUgakEuDdMf6QSnkVKVFTa1C5OXLkSGPnICIyelVqDZb+dBUAMKmPFzq580g2kRgaVG4GDx7c2DmIiIzettPJuJVVDAcbS4Q+2UHsOETN1iMNKM7Pz8dXX32FuLg4SCQS+Pn5Ydq0aXBw4KWORNQ8ZRWVY+3vg4jfDOkApbWFyImImi+dLwU/duwYvL298cknnyA/Px95eXn45JNP4OPjw3luiKjZeu+XGyiqqEa31kqMD+QgYiIx6Xzk5pVXXsGECROwYcMGmJmZAQDUajVefvllvPLKK7hy5YreQxIRGbKY5DzsPH8HALCcg4iJRKfzkZuEhAS8/vrr2mIDAGZmZggNDeXCmUTU7Kg1gnYQ8YRAD3T3sBc3EBHpXm569uyJuLi4Otvj4uLQvXt3fWQiIjIa30en4kqaCnZycywYwUHERIagQaelLl26pP16zpw5mDt3LuLj49GnTx8AwJkzZ/DZZ59h1apVjZOSiMgAqcqr8P6BGwCAecPbw8lWJnIiIgIAiSAIwsN2kkqlkEgkeNiuxjCJn0qlglKpRGFhIWdTJqLH8p/IOGw8nghfZxscmDeIq34TNSJdPr8bdOTm9u3beglGRGQqbueUYMvJmr8bFz/TicWGyIA0qNx4eXk1dg4iIqPy733XUKUWMKSDM4Z2cBE7DhH9ySNN4gcA165dQ0pKCiorK2ttHz169GOHIiIyZMdvZuNQXBbMpRL86+lOYschor/QudwkJibi2WefxeXLl2uNw7m3sKahj7khInocVWoN3v35GgBgcl9vtHWxFTkREf2VzieJ586dCx8fH9y9exfW1ta4evUqjh8/jsDAQBw9erQRIhIRGY7tZ2rWj2phbYG5T7QTOw4R1UPnIzenT5/G4cOH4ezsDKlUCqlUigEDBiAsLAxz5szBhQsXGiMnEZHoCkursPbXWwCA0GCuH0VkqHQ+cqNWq2FrW3MY1snJCenp6QBqBh3fuHFDv+mIiAzIp0duoaC0Cu1cbPFCL64fRWSodD5y4+/vj0uXLsHX1xdBQUFYvXo1LC0tsXHjRvj6+jZGRiIi0SXnliD8VBIAYNHTfjDnpd9EBkvncvOvf/0LJSUlAICVK1fimWeewcCBA+Ho6IiIiAi9ByQiMgSrfrmOKrWAQe2dMYSXfhMZNJ3/6RESEoJx48YBAHx9fXHt2jXk5OQgKysLw4YN0znA+vXr4ePjA7lcjoCAAJw4ceKB+1dUVGDRokXw8vKCTCZDmzZtsHnzZp1fl4iooc7ezsMvVzIhlQCLnvITOw4RPcQjz3PzZw4ODo/0uIiICMybNw/r169H//798cUXX2DkyJG4du0aPD09633M+PHjcffuXXz11Vdo27YtsrKyUF1d/TjxiYjuS6MRsHJfzaXfz/f2RAc3O5ETEdHDNGhtqXHjxiE8PBwKhUJ71OZ+du3a1eAXDwoKQs+ePbFhwwbtNj8/P4wdOxZhYWF19t+/fz+ef/55JCYmPnKh4tpSRKSL3RfuYH7ERdjKzHHkjSFwtuPimERi0OXzu0GnpZRKpXaSPqVS+cBbQ1VWViImJgbBwcG1tgcHB+PUqVP1Puann35CYGAgVq9ejVatWqF9+/Z44403UFZWdt/XqaiogEqlqnUjImqIsko1Vu+vuQr05aFtWGyIjESDTktt2bIFACAIApYtWwZnZ2dYW1s/1gvn5ORArVbD1dW11nZXV1dkZmbW+5jExET89ttvkMvl2L17N3JycvDyyy8jLy/vvuNuwsLCsHz58sfKSkTN0+aTt5FRWI5W9laY3t9H7DhE1EA6DSgWBAHt2rVDWlqa3gLcOyL059f467Z7NBoNJBIJtm/fjt69e+Opp57Chx9+iPDw8PsevVm4cCEKCwu1t9TUVL1lJyLTlVNcgQ1HEwAAC0I6QG5hJnIiImooncqNVCpFu3btkJub+9gv7OTkBDMzszpHabKysuoczbmnZcuWaNWqVa3TX35+fhAEAXfu3Kn3MTKZDAqFotaNiOhhPvn1FoorquHfSoHR3dzFjkNEOtD5UvDVq1djwYIFuHLlymO9sKWlJQICAhAVFVVre1RUFPr161fvY/r374/09HQUFxdrt928eRNSqRStW7d+rDxERPckZhfj2/+lAADeecoPUmn9R5OJyDDpXG5eeuklnD17Ft26dYOVlRUcHBxq3XQRGhqKTZs2YfPmzYiLi8P8+fORkpKC2bNnA6g5pTR58mTt/i+++CIcHR0xbdo0XLt2DcePH8eCBQswffp0WFlZ6fqjEBHV673911GtEfBERxf0a+Mkdhwi0pHO89ysXbtWby8+YcIE5ObmYsWKFcjIyIC/vz8iIyPh5eUFAMjIyEBKSop2f1tbW0RFReG1115DYGAgHB0dMX78eKxcuVJvmYioeTt7Ow8Hrt6FVAK8PbKj2HGI6BE0aJ4bU8J5bojofgRBwLPrTyE2tQAv9PZE2LguYkciot/p8vn9WDMUl5WVoaqqqtY2FgYiMlb7LmcgNrUA1pZmmP9kO7HjENEj0nnMTUlJCV599VW4uLjA1tYWLVq0qHUjIjJGldUa7YR9/zfIFy52cpETEdGj0rncvPnmmzh8+DDWr18PmUyGTZs2Yfny5XB3d8e2bdsaIyMRUaP79n/JSMkrhZOtDLMG+oodh4geg86npfbu3Ytt27ZhyJAhmD59OgYOHIi2bdvCy8sL27dvx8SJExsjJxFRoykqr8Inh+MBAPOGt4ONTC9rChORSHQ+cpOXlwcfn5ppyBUKBfLy8gAAAwYMwPHjx/WbjoioCWw8noi8kkr4OtlgQi8PseMQ0WPSudz4+voiKSkJANCpUyf897//BVBzRMfe3l6f2YiIGl2WqhybTtwGALw5ogMszHT+a5GIDIzOv8XTpk3DxYsXAdRMsndv7M38+fOxYMECvQckImpMHx26hbIqNXp62iOks5vYcYhIDxp8YnnevHmYOXMm5s+fr902dOhQXL9+HdHR0WjTpg26devWKCGJiBpDfFYx/htds5juwqf87rtoLxEZlwYfudm/fz+6deuG3r17Y+PGjVCpVAAAT09PjBs3jsWGiIzO6v3XodYIGO7nil7eui0fQ0SGq8Hl5vr16zh+/Di6dOmCN954A+7u7pg8eTIHERORUYpJzsPBazXLLLw1ooPYcYhIj3Qac9O/f3989dVXyMzMxLp165CUlIQhQ4agXbt2WLVqFdLT0xsrJxGR3giCgLDI6wCAvwd4oJ2rnciJiEifHumyAGtra0ybNg3Hjx/HrVu3MH78eKxevRre3t56jkdEpH+/xmUhOjkfMnMp5j/ZXuw4RKRnj3XNY0lJCY4dO4Zjx46hoKAAbdq00VcuIqJGodYIWH2g5qjNtP4+cFNymQUiU/NI5eb48eOYNm0a3NzcMHfuXLRv3x4nTpxAXFycvvMREenVrvN3cPNuMZRWFvjnYP6DjMgUNfhS8Dt37mDr1q0IDw9HQkICgoKC8NFHH+H555+Hra1tY2YkItKL8io1Poy6CQB4ZWgbKK0tRE5ERI2hweXG29sbjo6OmDRpEmbMmAE/P7/GzEVEpHfbTicho7AcLZVyTO7rLXYcImokDS43//3vfzF69GiYm3NBOSIyPoVlVfjsSAIAYP6T7SG3MBM5ERE1lgY3lXHjxjVmDiKiRvX5sQQUllWhvastnuvZWuw4RNSIuEIcEZm8u6pybDlZszjmgpCOMJNymQUiU8ZyQ0Qmb+2hWyiv0iDQqwWG+7mIHYeIGhnLDRGZtITsPxbHfGtkRy6OSdQM6Fxupk+fjqKiojrbS0pKMH36dL2EIiLSlzUHb0CtEfBERxcujknUTOhcbrZu3YqysrI628vKyrBt2za9hCIi0oeLqQWIvJwJiQRYwMUxiZqNBl8tpVKpIAgCBEFAUVER5PI/pixXq9WIjIyEiwvPZRORYRAEAe/tr1lm4dkerdDRTSFyIiJqKg0uN/b29pBIJJBIJGjfvu5CcxKJBMuXL9drOCKiR3XiVg5OJeTC0kyKUC6OSdSsNLjcHDlyBIIgYNiwYdi5cyccHP44d21paQkvLy+4u7s3SkgiIl1oNH8ctXmpjxdat7AWORERNaUGl5vBgwcDAG7fvg0PDw9IpbzQiogM08+XM3A1XQVbmTleHdZW7DhE1MR0XkvBy8sLBQUFOHv2LLKysqDRaGrdP3nyZL2FIyLSVWW1BmsO3gAA/N8gXzjYWIqciIiams7lZu/evZg4cSJKSkpgZ2dXa84IiUTCckNEooo4l4Lk3FI42cowY4CP2HGISAQ6n1t6/fXXtXPdFBQUID8/X3vLy8trjIxERA1SUlGNj3+NBwDMeaItbGRc6JeoOdK53KSlpWHOnDmwtuYAPSIyLJt/u42c4gp4Oljj+V6eYschIpHoXG5CQkIQHR3dGFmIiB5ZXkklvjieCAB4Pbg9LM150QNRc6XzMdunn34aCxYswLVr19ClSxdYWFjUun/06NF6C0dE1FCfHYlHcUU1OrsrMKorp6Ugas4kgiAIujzgQZeASyQSqNXqxw7VmFQqFZRKJQoLC6FQcMZSIlNwJ78Uwz44hkq1Blun98bg9s5iRyIiPdPl81vnIzd/vfSbiEhsH0XdQqVag76+jhjUzknsOEQkssc6KV1eXq6vHEREj+RGZhF2XbgDAHhrZMda01MQUfOkc7lRq9V499130apVK9ja2iIxsWYA3+LFi/HVV1/pPSAR0YO8f+A6BAEY6e+G7h72YschIgOgc7n597//jfDwcKxevRqWln/M/NmlSxds2rRJr+GIiB7kXFIeDsVlwUwqwRshHcSOQ0QGQudys23bNmzcuBETJ06EmZmZdnvXrl1x/fp1vYYjIrofQRCw6peav3Mm9PJAG2dbkRMRkaF4pEn82ratuxCdRqNBVVWVXkIRET1M1LW7iEnOh9xCirlPtBM7DhEZEJ3LTefOnXHixIk627///nv06NFDL6GIiB6kWq3B6gM1i2POGOADV4Vc5EREZEh0vhR86dKlmDRpEtLS0qDRaLBr1y7cuHED27Ztw88//9wYGYmIatl1Pg3xWcWwt7bAPwa3ETsOERkYnY/cjBo1ChEREYiMjIREIsGSJUsQFxeHvXv34sknn2yMjEREWuVVanwYdRMA8OrQtlDILR7yCCJqbh5pydyQkBCEhIToOwsR0UOFn0pCpqocreyt8FIfL7HjEJEB4spyRGQ0Ckorsf5IPABg/pPtIbcwe8gjiKg5atCRmxYtWjR41s+8vLzHCkREdD+fHYmHqrwaHd3s8GyPVmLHISID1aBys3btWu3Xubm5WLlyJUJCQtC3b18AwOnTp3HgwAEsXry4UUISEd3JL8XWU8kAgLdHdoSZlMssEFH9dF4V/LnnnsPQoUPx6quv1tr+6aef4tChQ9izZ48+8+kdVwUnMk6hEbHYdSEN/do4YvvMIK4hRdTM6PL5rfOYmwMHDmDEiBF1toeEhODQoUO6Ph0R0UNdTS/E7tg0AMDCkX4sNkT0QDqXG0dHR+zevbvO9j179sDR0VEvoYiI/mzVLzWLY47q5o4urZVixyEiA6fzpeDLly/HjBkzcPToUe2YmzNnzmD//v1cOJOI9O63Wzk4cSsHFmYSLAjm4phE9HA6l5upU6fCz88Pn3zyCXbt2gVBENCpUyecPHkSQUFBjZGRiJopjUbAqv1xAICJQV7wdLQWORERGYNHmsQvKCgI27dv13cWIqJafryYhitpKtjKzPHasLoL9hIR1eeRyo1Go0F8fDyysrKg0Whq3Tdo0CC9BCOi5q28So0PDtQss/DPIW3gaCsTORERGQudy82ZM2fw4osvIjk5GX+9ilwikUCtVustHBE1X+GnkpBWUIaWSjlmDPAROw4RGRGdy83s2bMRGBiIffv2oWXLlrwkk4j0Lr+kEp/9vszC68EduMwCEelE53Jz69Yt/PDDD2jblue/iahxfHL4ForKq+HXUsFlFohIZzrPcxMUFIT4+Hi9BVi/fj18fHwgl8sREBCAEydONOhxJ0+ehLm5Obp37663LEQkvuTcEnxzpmaZhXee4jILRKQ7nY/cvPbaa3j99deRmZmJLl26wMLCotb9Xbt2bfBzRUREYN68eVi/fj369++PL774AiNHjsS1a9fg6el538cVFhZi8uTJeOKJJ3D37l1dfwQiMmCr999AlVrA4PbOGNjOWew4RGSEdF5bSiqte7BHIpFAEASdBxQHBQWhZ8+e2LBhg3abn58fxo4di7CwsPs+7vnnn0e7du1gZmaGPXv2IDY2tsGvybWliAzX+ZR8jFt/ClIJEDl3IDq68XeUiGro8vmt85Gb27dvP3KwP6usrERMTAzefvvtWtuDg4Nx6tSp+z5uy5YtSEhIwDfffIOVK1c+9HUqKipQUVGh/V6lUj16aCJqNIIgYOXP1wAAfwtozWJDRI9M53Lj5eWllxfOycmBWq2Gq6trre2urq7IzMys9zG3bt3C22+/jRMnTsDcvGHRw8LCsHz58sfOS0SNa9/lDJxPKYCVhRle5zILRPQYdB5QDABff/01+vfvD3d3dyQn1wz8W7t2LX788Uedn+uvl5LfO731V2q1Gi+++CKWL1+O9u3bN/j5Fy5ciMLCQu0tNTVV54xE1LjKq9R4b/91AMDswW3gqpCLnIiIjJnO5WbDhg0IDQ3FU089hYKCAu0YG3t7e6xdu7bBz+Pk5AQzM7M6R2mysrLqHM0BgKKiIkRHR+PVV1+Fubk5zM3NsWLFCly8eBHm5uY4fPhwva8jk8mgUChq3YjIsGw9lYTUvDK4KeSYNYgT9hHR49G53Kxbtw5ffvklFi1aBDOzPybWCgwMxOXLlxv8PJaWlggICEBUVFSt7VFRUejXr1+d/RUKBS5fvozY2Fjtbfbs2ejQoQNiY2O5aCeRkcotrsCnh2uml1gQ0gHWlo+0KgwRkdYjDSju0aNHne0ymQwlJSU6PVdoaCgmTZqEwMBA9O3bFxs3bkRKSgpmz54NoOaUUlpaGrZt2wapVAp/f/9aj3dxcYFcLq+znYiMx9pDt1BUUQ3/Vpywj4j0Q+dy4+Pjg9jY2DoDi3/55Rd06tRJp+eaMGECcnNzsWLFCmRkZMDf3x+RkZHa587IyEBKSoquEYnISNy6W4Rvz9b8ji96qhOknLCPiPRA53lutmzZgsWLF2PNmjWYMWMGNm3ahISEBISFhWHTpk14/vnnGyurXnCeGyLDMW3LWRy5kY3gTq7YODlQ7DhEZMAadZ6badOmobq6Gm+++SZKS0vx4osvolWrVvj4448NvtgQkeE4djMbR25kw1wqwcKn/MSOQ0Qm5JFG7s2aNQuzZs1CTk4ONBoNXFxc9J2LiExYlVqDd3+fsG9KP2/4ONmInIiITMkjX5aQlZWFGzduQCKRQCKRwNmZa8AQUcN8cyYZ8VnFcLCxxJwn2okdh4hMjM6XgqtUKkyaNAnu7u4YPHgwBg0aBHd3d7z00ksoLCxsjIxEZELySirxUdRNAMAbwR2gtLJ4yCOIiHSjc7mZOXMm/ve//2Hfvn0oKChAYWEhfv75Z0RHR2PWrFmNkZGITMhHUTehKq+GX0sFJvTyEDsOEZkgnU9L7du3DwcOHMCAAQO020JCQvDll19ixIgReg1HRKbleqYK2/9Xs2TLkmc6wYyXfhNRI9D5yI2joyOUSmWd7UqlEi1atNBLKCIyPYIg4N2fr0EjACP93dC3jaPYkYjIROlcbv71r38hNDQUGRkZ2m2ZmZlYsGABFi9erNdwRGQ6oq7dxcn4XFiaS/EOL/0mokak82mpDRs2ID4+Hl5eXvD09AQApKSkQCaTITs7G1988YV23/Pnz+svKREZrfIqNd7dV3Pp96yBPvBwsBY5ERGZMp3LzdixYxshBhGZso3HE7Wrfr88pK3YcYjIxOlcbpYuXdoYOYjIRKXmleKzIzWrfi962g82Mq76TUSNS+cxNwBQUFCATZs2YeHChcjLywNQcwoqLS1Nr+GIyPj9e18cKqo16OPrgGe6thQ7DhE1Azr/E+rSpUsYPnw4lEolkpKSMGvWLDg4OGD37t1ITk7Gtm3bGiMnERmhE7eysf9qJsykEiwb3RkSCS/9JqLGp/ORm9DQUEydOhW3bt2CXC7Xbh85ciSOHz+u13BEZLwqqzVY9tNVAMDkvl7o6PbgVXyJiPRF53Jz7tw5/OMf/6izvVWrVsjMzNRLKCIyfuGnbiMhuwROtpaYN7y92HGIqBnRudzI5XKoVKo622/cuMHFM4kIAHBXVY6PD90CALw5oiPXjyKiJqVzuRkzZgxWrFiBqqoqAIBEIkFKSgrefvttPPfcc3oPSETGZ8XP11BSqUZ3D3v8rWdrseMQUTOjc7n54IMPkJ2dDRcXF5SVlWHw4MFo27Yt7Ozs8O9//7sxMhKRETl+Mxv7LmVAKgFWjvWHlOtHEVET0/lqKYVCgd9++w2HDx/G+fPnodFo0LNnTwwfPrwx8hGRESmvUmPJj1cAAFP6ecO/Vd116IiIGtsjz6Y1bNgwDBs2TJ9ZiMjIbTiagKTcUrgqZAh9koOIiUgcOpUbjUaD8PBw7Nq1C0lJSZBIJPDx8cHf/vY3TJo0iXNYEDVjt3NKsOFoAgBgyTOdYSfnIGIiEkeDx9wIgoDRo0dj5syZSEtLQ5cuXdC5c2ckJydj6tSpePbZZxszJxEZMEEQsOTHK6hUazCovTOe6uImdiQiasYafOQmPDwcx48fx6+//oqhQ4fWuu/w4cMYO3Ystm3bhsmTJ+s9JBEZtp8vZeDErRxYmkuxgjMRE5HIGnzkZseOHXjnnXfqFBugZvzN22+/je3bt+s1HBEZvsLSKqz4+RoA4JUhbeHtZCNyIiJq7hpcbi5duoQRI0bc9/6RI0fi4sWLeglFRMZj1f44ZBdVoI2zDWYP8RU7DhFRw8tNXl4eXF1d73u/q6sr8vPz9RKKiIzDmcRc7DibCgBY9VxXyMzNRE5ERKRDuVGr1TA3v/8QHTMzM1RXV+slFBEZvvIqNd7ZdRkA8GKQJ3p5O4iciIioRoMHFAuCgKlTp0Imk9V7f0VFhd5CEZHh+/RwPBJzSuBiJ8PbIzuKHYeISKvB5WbKlCkP3YdXShE1D9czVfj8WM2cNivGdIaCc9oQkQFpcLnZsmVLY+YgIiOh1gh4e+dlVGsEBHdyxQj/lmJHIiKqReeFM4moedt6KgmxqQWwk5ljxRh/seMQEdXBckNEDZaUU4LVB64DAN5+qiPclHKRExER1cVyQ0QNotEIePOHSyiv0qBfG0e82NtT7EhERPViuSGiBtl6Oglnk/JgbWmG957ryiUWiMhgsdwQ0UMl5ZTgvf01p6MWPuUHDwdrkRMREd0fyw0RPZBGI+DNnX+cjprI01FEZOBYbojogb4+k4yzt/84HSWV8nQUERk2lhsiuq/E7GKs+uX301EjO/J0FBEZBZYbIqpXlVqD+RGxKKtSo39bR0wM8hI7EhFRg7DcEFG9PjsSj4t3CqGQm+ODv3fj6SgiMhosN0RUR2xqAdYdjgcAvDvWHy2VViInIiJqOJYbIqqltLIa8yNiodYIGN3NHWO6txI7EhGRTlhuiKiW/0TG4XZOCdwUcrzLtaOIyAix3BCR1pHrWfjmTAoAYM34blBaW4iciIhIdyw3RAQAuKsqx+vfXwQATO/vg/5tnURORET0aFhuiAhqjYD5EbHIK6lEp5YKvDWyg9iRiIgeGcsNEeHzYwk4lZALa0szrHuxB2TmZmJHIiJ6ZCw3RM1cTHIePoy6CQBYMcYfbZxtRU5ERPR4WG6ImrHC0irM2VFz2ffY7u54ricv+yYi48dyQ9RMCYKAt3ddQlpBGbwcrbHy2S6QSDgLMREZP5YbomZq88kk/HIlExZmEqx7oQdsZeZiRyIi0guWG6JmKDopD2GRcQCAfz3dCV1b24sbiIhIj1huiJqZ7KIKvPLteVRrBIzq5o7JfbnaNxGZFpYbomakWq3BnB0XcFdVgbYutlg1juNsiMj0sNwQNSNrom7idGLNfDafv9QTNhxnQ0QmiOWGqJk4eDUTG44mAADee64r2rrYiZyIiKhxsNwQNQM37xZhfkQsAGBqP2+M6uYubiAiokYkerlZv349fHx8IJfLERAQgBMnTtx33127duHJJ5+Es7MzFAoF+vbtiwMHDjRhWiLjk19SiZlbo1FSqUYfXwcsetpP7EhERI1K1HITERGBefPmYdGiRbhw4QIGDhyIkSNHIiUlpd79jx8/jieffBKRkZGIiYnB0KFDMWrUKFy4cKGJkxMZh2q1Bq/uOI+UvFK0bmGF9RMDYGEm+r9piIgalUQQBEGsFw8KCkLPnj2xYcMG7TY/Pz+MHTsWYWFhDXqOzp07Y8KECViyZEmD9lepVFAqlSgsLIRCoXik3ETGYtlPVxF+KgnWlmbY9XI/dHTj//NEZJx0+fwW7Z9wlZWViImJQXBwcK3twcHBOHXqVIOeQ6PRoKioCA4ODvfdp6KiAiqVqtaNqDn477lUhJ9KAgB8OL47iw0RNRuilZucnByo1Wq4urrW2u7q6orMzMwGPceaNWtQUlKC8ePH33efsLAwKJVK7c3Dw+OxchMZgzOJuVi05zIAYP7w9hjh7yZyIiKipiP6yfe/TiAmCEKDJhXbsWMHli1bhoiICLi4uNx3v4ULF6KwsFB7S01NfezMRIYsPqsI/7ctGlVqAU93aYnXhrUVOxIRUZMSbQYvJycnmJmZ1TlKk5WVVedozl9FRERgxowZ+P777zF8+PAH7iuTySCTyR47L5ExyC6qwNQt56Aqr0ZPT3usGd8NUilnICai5kW0IzeWlpYICAhAVFRUre1RUVHo16/ffR+3Y8cOTJ06Fd9++y2efvrpxo5JZDTKKtWYuS0ad/LL4OVojS8nB0JuYSZ2LCKiJifq3OuhoaGYNGkSAgMD0bdvX2zcuBEpKSmYPXs2gJpTSmlpadi2bRuAmmIzefJkfPzxx+jTp4/2qI+VlRWUSqVoPweR2NQaAXO/u4CLqQVoYW2B8Gm94WjLI5ZE1DyJWm4mTJiA3NxcrFixAhkZGfD390dkZCS8vGpWKc7IyKg1580XX3yB6upqvPLKK3jllVe026dMmYLw8PCmjk9kEARBwIq9V3Hw2l1Ymkvx5eRA+DjZiB2LiEg0os5zIwbOc0OmZu2hm1h76BYAYN0LPbi0AhGZJKOY54aIHt/WU0naYrN8dGcWGyIisNwQGa0fY9Ow9KerAIB5w9thSj9vcQMRERkIlhsiI3TkehZe/+9FADWrfM99op3IiYiIDAfLDZGROZ2Qi39uj0G1RsDY7u5Y8kynBk18SUTUXLDcEBmRM4m5mB5+DuVVGjzR0QXv/52T9BER/RXLDZGROHs7D9PDz6GsSo3B7Z3x2cSesDDjrzAR0V/xb0YiIxCdlIepW86itFKNge2c8MWkAM4+TER0Hyw3RAYuJjkfUzbXFJsBbZ24rAIR0UOIOkMxET3YqYQczNwajdJKNfq1cWSxISJqAJYbIgN16NpdvPzteVRWazCgrRM2Tg6AlSWLDRHRw7DcEBmgny6mIzQiFtUaAU92csW6F3rwiA0RUQOx3BAZmB1nU/DO7ssQBODZHq2w+m9deVUUEZEOWG6IDIQgCFh/NAHvH7gBAHipjydWjPbnPDZERDpiuSEyANVqDRb/eAU7zqYCAP45pA3eDOnAmYeJiB4Byw2RyEoqqvHqt+dx5EY2pBJg2ejOmNzXW+xYRERGi+WGSERZReWYHn4OV9JUkFtI8cnzPRDc2U3sWERERo3lhkgkV9ML8X/bYpBWUAYHG0t8NSUQPTxbiB2LiMjosdwQieDnS+l44/uLKK/SwMfJBlum9oK3k43YsYiITALLDVET0mgEfBh1E58eiQcADGrvjHXP94DS2kLkZEREpoPlhqiJFJVXYX7ERRyKuwsA+L9BvnhrREeY8VJvIiK9YrkhagJX0wvxyvbzSMothaW5FKvGdcG4nq3FjkVEZJJYbogakSAI2HE2Fcv2XkVltQat7K3w2cSe6O5hL3Y0IiKTxXJD1EhKKqrxzu7L+DE2HQDwREcXrBnfDfbWliInIyIybSw3RI3g0p0CzIuIRWJ2CcykEiwI6YD/G+jLpRSIiJoAyw2RHlWrNfj8WALWHrqFao0AV4UM617oid4+DmJHIyJqNlhuiPQkJbcU8/8bi5jkfADAU13c8O+xXdDChqehiIiaEssN0WPSaATsOJeC/+yLQ0mlGrYycywf3RnjerbiwpdERCJguSF6DInZxXh712WcvZ0HAOjt7YA147vBw8Fa5GRERM0Xyw3RI6hSa/DliUSsPXQLldUaWFmYYUFIB0zp581J+YiIRMZyQ6SjmOQ8LN5zFdcyVACAge2c8J9nu/BoDRGRgWC5IWqg7KIKrPrlOnaevwMAUFpZYPEznfAcx9YQERkUlhuih6hSa/D16WR8FHUTRRXVAIAJgR5YMKIDnGxlIqcjIqK/Yrkhug9BEBB17S5W7b+OxOwSAEDX1kosH90ZPTxbiJyOiIjuh+WGqB7nU/IRFhmHc0k1c9Y42FhiQUgHjA/04IBhIiIDx3JD9Cc37xbho6ib+OVKJgBAbiHFzAG++MdgX9jJLUROR0REDcFyQwTg1t0ifPzrLey7nAFBAKQS4G8BrRH6ZAe4KeVixyMiIh2w3FCzdutuEdYdjsfeS+kQhJptI/3dMG94e3RwsxM3HBERPRKWG2p2BEFAdHI+vjiWgENxWdrtIzq7Yc4T7dDJXSFiOiIielwsN9RsqDU1Vz9tPJ6A8ykFAACJBAjp5IbXnmiLzu5KcQMSEZFesNyQycsvqUREdCq+Pp2MtIIyAICluRTP9WyNWQN94OtsK3JCIiLSJ5YbMkmCIOByWiG+OZOMH2PTUVGtAQDYW1vgxd6emNrfGy52HChMRGSKWG7IpBSUVmL3hTREnEvF9cwi7fbO7gpM6eeN0d3cIbcwEzEhERE1NpYbMnpVag1+u5WDnefv4ODVu6hU1xylsTSXYqS/Gyb39UJPzxZc/4mIqJlguSGjJAgCYpLz8WNsOvZdzkBeSaX2vk4tFZjQywNjurvD3tpSxJRERCQGlhsyGmqNgPMp+fjlciYOXM3UDg4GACdbSzzT1R1/C2gN/1a86omIqDljuSGDVl6lxumEXByKu4sDV+8ip7hCe5+NpRlC/N0wtnsr9GvjCHMzqYhJiYjIULDckMFJLyjDkRtZOByXhZMJOSiv0mjvs5Ob40k/V4zwd8Og9s4cHExERHWw3JDoisqrcCYxD7/dysaJ+BwkZpfUur+lUo6hHV0Q0tkNfX0dYWnOIzRERHR/LDfU5FTlVYhJyseZ27n4X2IeLqcVQq0RtPdLJUB3D3sM6+iCYR1d4dfSjlc6ERFRg7HcUKMSBAGpeWU4n5KvvV1LV+FPXQYA4O1ojf5tnTCwnRP6+jpBaW0hTmAiIjJ6LDekVznFFbh8pxCX7hTicloBYlMLaw0Cvsfb0Rq9fRwQ5OOIIF8HtG5hLUJaIiIyRSw39Eg0GgFJuSWIyyhCXIYKcRkqXMtQIaOwvM6+FmYSdHZXoqdnC/T0skeglwPclFz6gIiIGgfLDT1QtVqDO/llSMguxs27xbh1twg3s4oQn1Vc6yqmeyQSoI2zLbq2UqJLayW6tlais7uSVzUREVGTYbkhqDUCMgrLkJxb+vutBLdzSpCYU4Lk3BJUqYV6Hyczl6KDmx06tVTA7/dbJ3cFbGX834qIiMTDT6FmoEqtQWZhOTIKy5FeUIa0gjLcyS9Fal7Nn2kFZfctMAAgt5DC29EG7Vzt0N7FtuZPV1t4Olhz4jwiIjI4LDdGTK0RkFtSgeyiP25ZRRXILCxHpqocWaqaQpNdXAHh/t0FQM24GA8Ha3g5WMPL0QbejtbwdbaFr7MN3JVWkEp5KTYRERkHlhsDIQgCSivVKCirQkFpJQpKq5BXUomC0krklVQhv7QSuSWVyC2uQG5xJXJLKpBXUlnnkur7sTSXoqVSDnelFdztreDhYIXWLazRuoUVWrewQkulFcxYYIiIyASw3OiJWiMgt7gCRRXVKKmoRnF5NYor/rgVlVdDVV6FovLfvy6rgqq8CoVlVVCVVaOwrPKBp4buRyoBHG1lcLaVwclOBlc7GdyUcrgo5HBTyOGqkMHd3gqONpacCI+IiJoF0cvN+vXr8f777yMjIwOdO3fG2rVrMXDgwPvuf+zYMYSGhuLq1atwd3fHm2++idmzZzdh4vplFJZhwHtHHvt5LMwksLe2hL2VBRxsLOFgYwl7a0s42FjA0UYGR1vLP/78/WsecSEiIvqDqOUmIiIC8+bNw/r169G/f3988cUXGDlyJK5duwZPT886+9++fRtPPfUUZs2ahW+++QYnT57Eyy+/DGdnZzz33HMi/AR/sJWZQyqp+dNWZg5buTlsfv/aTm4OO5kFbOW/fy23gNLKAgq5ORRWFlDILWBvXXOzsjDjERYiIqLHIBGEhw01bTxBQUHo2bMnNmzYoN3m5+eHsWPHIiwsrM7+b731Fn766SfExcVpt82ePRsXL17E6dOn632NiooKVFT8MUOuSqWCh4cHCgsLoVAo9Paz3HsbWUyIiIj0T6VSQalUNujzW7TreCsrKxETE4Pg4OBa24ODg3Hq1Kl6H3P69Ok6+4eEhCA6OhpVVVX1PiYsLAxKpVJ78/Dw0M8P8BcSiYTFhoiIyACIVm5ycnKgVqvh6upaa7urqysyMzPrfUxmZma9+1dXVyMnJ6fexyxcuBCFhYXaW2pqqn5+ACIiIjJIog8o/uvRDkEQHngEpL7969t+j0wmg0wme8yUREREZCxEO3Lj5OQEMzOzOkdpsrKy6hyducfNza3e/c3NzeHo6NhoWYmIiMh4iFZuLC0tERAQgKioqFrbo6Ki0K9fv3of07dv3zr7Hzx4EIGBgbCwsGi0rERERGQ8RF0YKDQ0FJs2bcLmzZsRFxeH+fPnIyUlRTtvzcKFCzF58mTt/rNnz0ZycjJCQ0MRFxeHzZs346uvvsIbb7wh1o9AREREBkbUMTcTJkxAbm4uVqxYgYyMDPj7+yMyMhJeXl4AgIyMDKSkpGj39/HxQWRkJObPn4/PPvsM7u7u+OSTT0Sf44aIiIgMh6jz3IhBl+vkiYiIyDAYxTw3RERERI2B5YaIiIhMCssNERERmRSWGyIiIjIpLDdERERkUlhuiIiIyKSIvrZUU7t35btKpRI5CRERETXUvc/thsxg0+zKTVFREQDAw8ND5CRERESkq6KiIiiVygfu0+wm8dNoNEhPT4ednd0DVx9vLlQqFTw8PJCamspJDZsA3++mw/e66fC9bjrN+b0WBAFFRUVwd3eHVPrgUTXN7siNVCpF69atxY5hcBQKRbP7RRET3++mw/e66fC9bjrN9b1+2BGbezigmIiIiEwKyw0RERGZFJabZk4mk2Hp0qWQyWRiR2kW+H43Hb7XTYfvddPhe90wzW5AMREREZk2HrkhIiIik8JyQ0RERCaF5YaIiIhMCssNERERmRSWG6pXRUUFunfvDolEgtjYWLHjmJykpCTMmDEDPj4+sLKyQps2bbB06VJUVlaKHc0krF+/Hj4+PpDL5QgICMCJEyfEjmRywsLC0KtXL9jZ2cHFxQVjx47FjRs3xI7VLISFhUEikWDevHliRzFYLDdUrzfffBPu7u5ixzBZ169fh0ajwRdffIGrV6/io48+wueff4533nlH7GhGLyIiAvPmzcOiRYtw4cIFDBw4ECNHjkRKSorY0UzKsWPH8Morr+DMmTOIiopCdXU1goODUVJSInY0k3bu3Dls3LgRXbt2FTuKQeOl4FTHL7/8gtDQUOzcuROdO3fGhQsX0L17d7Fjmbz3338fGzZsQGJiothRjFpQUBB69uyJDRs2aLf5+flh7NixCAsLEzGZacvOzoaLiwuOHTuGQYMGiR3HJBUXF6Nnz55Yv349Vq5cie7du2Pt2rVixzJIPHJDtdy9exezZs3C119/DWtra7HjNCuFhYVwcHAQO4ZRq6ysRExMDIKDg2ttDw4OxqlTp0RK1TwUFhYCAP8fbkSvvPIKnn76aQwfPlzsKAav2S2cSfcnCAKmTp2K2bNnIzAwEElJSWJHajYSEhKwbt06rFmzRuwoRi0nJwdqtRqurq61tru6uiIzM1OkVKZPEASEhoZiwIAB8Pf3FzuOSfruu+9w/vx5nDt3TuwoRoFHbpqBZcuWQSKRPPAWHR2NdevWQaVSYeHChWJHNloNfa//LD09HSNGjMDf//53zJw5U6TkpkUikdT6XhCEOttIf1599VVcunQJO3bsEDuKSUpNTcXcuXPxzTffQC6Xix3HKHDMTTOQk5ODnJycB+7j7e2N559/Hnv37q31IaBWq2FmZoaJEydi69atjR3V6DX0vb73F1R6ejqGDh2KoKAghIeHQyrlvzceR2VlJaytrfH999/j2Wef1W6fO3cuYmNjcezYMRHTmabXXnsNe/bswfHjx+Hj4yN2HJO0Z88ePPvsszAzM9NuU6vVkEgkkEqlqKioqHUfsdzQn6SkpEClUmm/T09PR0hICH744QcEBQWhdevWIqYzPWlpaRg6dCgCAgLwzTff8C8nPQkKCkJAQADWr1+v3dapUyeMGTOGA4r1SBAEvPbaa9i9ezeOHj2Kdu3aiR3JZBUVFSE5ObnWtmnTpqFjx4546623eCqwHhxzQ1qenp61vre1tQUAtGnThsVGz9LT0zFkyBB4enrigw8+QHZ2tvY+Nzc3EZMZv9DQUEyaNAmBgYHo27cvNm7ciJSUFMyePVvsaCbllVdewbfffosff/wRdnZ22jFNSqUSVlZWIqczLXZ2dnUKjI2NDRwdHVls7oPlhkgEBw8eRHx8POLj4+sURx5MfTwTJkxAbm4uVqxYgYyMDPj7+yMyMhJeXl5iRzMp9y61HzJkSK3tW7ZswdSpU5s+ENGf8LQUERERmRSOXiQiIiKTwnJDREREJoXlhoiIiEwKyw0RERGZFJYbIiIiMiksN0RERGRSWG6IiIjIpLDcEBERkUlhuSFqhiQSCfbs2SN2jAZZtmwZunfvLnYMvRsyZAjmzZvX4P2PHj0KiUSCgoKC++4THh4Oe3v7x85GZOxYboiMyNSpUzF27FixYxi9hpSANWvWQKlUorS0tM595eXlsLe3x4cffvjIGXbt2oV33333kR9PRPfHckNEVI/JkyejrKwMO3furHPfzp07UVpaikmTJun8vFVVVQAABwcH2NnZPXZOIqqL5YbIiA0ZMgRz5szBm2++CQcHB7i5uWHZsmW19rl16xYGDRoEuVyOTp06ISoqqs7zpKWlYcKECWjRogUcHR0xZswYJCUlae+/d8Ro+fLlcHFxgUKhwD/+8Q9UVlZq9xEEAatXr4avry+srKzQrVs3/PDDD9r7751W+fXXXxEYGAhra2v069cPN27cqJVl1apVcHV1hZ2dHWbMmIHy8vI6ebds2QI/Pz/I5XJ07NgR69ev196XlJQEiUSCXbt2YejQobC2tka3bt1w+vRpbY5p06ahsLAQEokEEomkznsGAM7Ozhg1ahQ2b95c577Nmzdj9OjRcHZ2xltvvYX27dvD2toavr6+WLx4sbbAAH+cVtu8eTN8fX0hk8kgCEKd01LffPMNAgMDYWdnBzc3N7z44ovIysqq89onT55Et27dIJfLERQUhMuXL9fZ58/27t2LgIAAyOVy+Pr6Yvny5aiurn7gY4iMnkBERmPKlCnCmDFjtN8PHjxYUCgUwrJly4SbN28KW7duFSQSiXDw4EFBEARBrVYL/v7+wpAhQ4QLFy4Ix44dE3r06CEAEHbv3i0IgiCUlJQI7dq1E6ZPny5cunRJuHbtmvDiiy8KHTp0ECoqKrSva2trK0yYMEG4cuWK8PPPPwvOzs7CO++8o83yzjvvCB07dhT2798vJCQkCFu2bBFkMplw9OhRQRAE4ciRIwIAISgoSDh69Khw9epVYeDAgUK/fv20zxERESFYWloKX375pXD9+nVh0aJFgp2dndCtWzftPhs3bhRatmwp7Ny5U0hMTBR27twpODg4COHh4YIgCMLt27cFAELHjh2Fn3/+Wbhx44bwt7/9TfDy8hKqqqqEiooKYe3atYJCoRAyMjKEjIwMoaioqN73e9++fYJEIhESExO1227fvi1IJBIhMjJSEARBePfdd4WTJ08Kt2/fFn766SfB1dVVeO+997T7L126VLCxsRFCQkKE8+fPCxcvXhQ0Go0wePBgYe7cudr9vvrqKyEyMlJISEgQTp8+LfTp00cYOXKk9v5775+fn59w8OBB4dKlS8IzzzwjeHt7C5WVlYIgCMKWLVsEpVKpfcz+/fsFhUIhhIeHCwkJCcLBgwcFb29vYdmyZfX/D0ZkIlhuiIxIfeVmwIABtfbp1auX8NZbbwmCIAgHDhwQzMzMhNTUVO39v/zyS61y89VXXwkdOnQQNBqNdp+KigrByspKOHDggPZ1HRwchJKSEu0+GzZsEGxtbQW1Wi0UFxcLcrlcOHXqVK0sM2bMEF544QVBEP74cD506JD2/n379gkAhLKyMkEQBKFv377C7Nmzaz1HUFBQrXLj4eEhfPvtt7X2effdd4W+ffsKgvBHudm0aZP2/qtXrwoAhLi4OEEQ6paA+6murhZatWolLFmyRLttyZIlQqtWrYTq6up6H7N69WohICBA+/3SpUsFCwsLISsrq9Z+fy03f3X27FkBgLZ43Xv/vvvuO+0+ubm5gpWVlRAREVHvzzVw4EDhP//5T63n/frrr4WWLVs++AcnMnLmIh0wIiI96dq1a63vW7ZsqT2dERcXB09PT7Ru3Vp7f9++fWvtHxMTg/j4+DrjP8rLy5GQkKD9vlu3brC2tq71PMXFxUhNTUVWVhbKy8vx5JNP1nqOyspK9OjR4755W7ZsCQDIysqCp6cn4uLiMHv27Fr79+3bF0eOHAEAZGdnIzU1FTNmzMCsWbO0+1RXV0OpVDbodTp27IiGMjMzw5QpUxAeHo6lS5dCIpFg69atmDp1KszMzAAAP/zwA9auXYv4+HgUFxejuroaCoWi1vN4eXnB2dn5ga914cIFLFu2DLGxscjLy4NGowEApKSkoFOnTrXej3scHBzQoUMHxMXF1fucMTExOHfuHP79739rt6nVapSXl6O0tLTWf08iU8JyQ2TkLCwsan0vkUi0H4yCINTZXyKR1Ppeo9EgICAA27dvr7Pvwz6Q//p6+/btQ6tWrWrdL5PJ7pv3XpZ7j3+Ye/t9+eWXCAoKqnXfvbKhj9f5s+nTpyMsLAyHDx8GUFM2pk2bBgA4c+YMnn/+eSxfvhwhISFQKpX47rvvsGbNmlrPYWNj88DXKCkpQXBwMIKDg/HNN9/A2dkZKSkpCAkJqTWu6X7++t/0Ho1Gg+XLl2PcuHF17pPL5Q99XiJjxXJDZMI6deqElJQUpKenw93dHQC0A2vv6dmzJyIiIrQDhe/n4sWLKCsrg5WVFYCaD3ZbW1u0bt0aLVq0gEwmQ0pKCgYPHvzIef38/HDmzBlMnjxZu+3MmTPar11dXdGqVSskJiZi4sSJj/w6lpaWUKvVDdq3TZs2GDx4MLZs2aIdCNymTRsANYN7vby8sGjRIu3+ycnJOue5fv06cnJysGrVKnh4eAAAoqOj6933zJkz8PT0BADk5+fj5s2b9z0a1bNnT9y4cQNt27bVORORMWO5ITJhw4cPR4cOHTB58mSsWbMGKpWq1gcxAEycOBHvv/8+xowZgxUrVqB169ZISUnBrl27sGDBAu0prcrKSsyYMQP/+te/kJycjKVLl+LVV1+FVCqFnZ0d3njjDcyfPx8ajQYDBgyASqXCqVOnYGtriylTpjQo79y5czFlyhQEBgZiwIAB2L59O65evQpfX1/tPsuWLcOcOXOgUCgwcuRIVFRUIDo6Gvn5+QgNDW3Q63h7e6O4uBi//vqr9nTbg07R/Pk02KZNm7Tb27Zti5SUFHz33Xfo1asX9u3bh927dzcow595enrC0tIS69atw+zZs3HlypX7zoGzYsUKODo6wtXVFYsWLYKTk9N95z5asmQJnnnmGXh4eODvf/87pFIpLl26hMuXL2PlypU65yQyFrwUnMiESaVS7N69GxUVFejduzdmzpxZa/wFAFhbW+P48ePw9PTEuHHj4Ofnh+nTp6OsrKzWkZwnnngC7dq1w6BBgzB+/HiMGjWq1iXU7777LpYsWYKwsDD4+fkhJCQEe/fuhY+PT4PzTpgwAUuWLMFbb72FgIAAJCcn45///GetfWbOnIlNmzYhPDwcXbp0weDBgxEeHq7T6/Tr1w+zZ8/GhAkT4OzsjNWrVz9w/+eeew4ymQwymazWKZ4xY8Zg/vz5ePXVV9G9e3ecOnUKixcvbnCOe5ydnREeHo7vv/8enTp1wqpVq/DBBx/Uu++qVaswd+5cBAQEICMjAz/99BMsLS3r3TckJAQ///wzoqKi0KtXL/Tp0wcffvghvLy8dM5IZEwkQn0n5YmI/mTq1KkoKCgwmiUbiKh545EbIiIiMiksN0RERGRSeFqKiIiITAqP3BAREZFJYbkhIiIik8JyQ0RERCaF5YaIiIhMCssNERERmRSWGyIiIjIpLDdERERkUlhuiIiIyKT8P7Gd3MhYXCfAAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"Y = 1.0 / (1.0 + np.exp(-X))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"The formula for the logistic function is the following:\n",
"\n",
"$$ \\hat{Y} = \\frac1{1+e^{-\\beta_1(X-\\beta_2)}}$$\n",
"\n",
"$\\beta_1$: Controls the curve's steepness,\n",
"\n",
"$\\beta_2$: Slides the curve on the x-axis.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building The Model ###\n",
"Now, let's build our regression model and initialize its parameters. \n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def sigmoid(x, Beta_1, Beta_2):\n",
" y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look at a sample sigmoid line that might fit with the data:\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x71146b73f310>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"beta_1 = 0.10\n",
"beta_2 = 1990.0\n",
"\n",
"#logistic function\n",
"Y_pred = sigmoid(x_data, beta_1 , beta_2)\n",
"\n",
"#plot initial prediction against datapoints\n",
"plt.plot(x_data, Y_pred*15000000000000.)\n",
"plt.plot(x_data, y_data, 'ro')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our task here is to find the best parameters for our model. Lets first normalize our x and y:\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# Lets normalize our data\n",
"xdata =x_data/max(x_data)\n",
"ydata =y_data/max(y_data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### How we find the best parameters for our fit line?\n",
"we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. Optimize values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.\n",
"\n",
"popt are our optimized parameters.\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" beta_1 = 690.451712, beta_2 = 0.997207\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"popt, pcov = curve_fit(sigmoid, xdata, ydata)\n",
"#print the final parameters\n",
"print(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we plot our resulting regression model.\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(1960, 2015, 55)\n",
"x = x/max(x)\n",
"plt.figure(figsize=(8,5))\n",
"y = sigmoid(x, *popt)\n",
"plt.plot(xdata, ydata, 'ro', label='data')\n",
"plt.plot(x,y, linewidth=3.0, label='fit')\n",
"plt.legend(loc='best')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Practice\n",
"Can you calculate what is the accuracy of our model?\n"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error: 0.04\n",
"Residual sum of squares (MSE): 0.00\n",
"R2-score: 0.92\n"
]
}
],
"source": [
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(test_y,y_hat) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python \n",
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(test_y,y_hat) )\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Want to learn more?</h2>\n",
"\n",
"IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems by your enterprise as a whole. A free trial is available through this course, available here: <a href=\"https://www.ibm.com/analytics/spss-statistics-software?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">SPSS Modeler</a>\n",
"\n",
"Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at <a href=\"https://www.ibm.com/cloud/watson-studio?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">Watson Studio</a>\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Thank you for completing this lab!\n",
"\n",
"\n",
"## Author\n",
"\n",
"Saeed Aghabozorgi\n",
"\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"\n",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
"\n",
"<!--## Change Log\n",
"\n",
"\n",
"| Date (YYYY-MM-DD) | Version | Changed By | Change Description |\n",
"|---|---|---|---|\n",
"| 2020-11-03 | 2.1 | Lakshmi | Made changes in URL |\n",
"| 2020-08-27 | 2.0 | Lavanya | Moved lab to course repo in GitLab |\n",
"| | | | |\n",
"| | | | | --!>\n",
"\n",
"\n",
"\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python",
"language": "python",
"name": "conda-env-python-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.12"
},
"prev_pub_hash": "f873d3177bf529d2d648c46bab1627042a257e5ec6ce42ca68028520459f817e"
},
"nbformat": 4,
"nbformat_minor": 4
}