01_machineLearning/01_linear_regression_sgd.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting Data with a Line\n",
    "\n",
    "Many of you have probably used Excel to fit data with a line.\n",
    "\n",
    "![excel_linear_regression](img/excel_linear_regression.jpg)\n",
    "\n",
    "We're going to review the math involved in this process to help understand how training an AI works.\n",
    "\n",
    "First we will load some tools that others wrote and we can use to help us work.\n",
    "* [Pandas](https://pandas.pydata.org/docs/): a toolkit for working with row vs. column data, like excel sheets, and CSV (Comma Seperated Values) files.\n",
    "* [Numpy](https://numpy.org/doc/): a toolkit for managing arrays, vectors, matrices, etc, doing math with them, slicing them up, and many other handy things.\n",
    "* [Matplotlib](https://matplotlib.org/stable/index.html): a toolkit for plotting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import IPython.display as ipydis\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dataset\n",
    "In the [previous notebook](00_make_slimmed_dataset.ipynb) we used a realestate dataset from Kaggle to produce this reduced dataset. This dataset contains the _sale price_ and _above ground square feet_ of many houses. We can use this data for our linear regression.\n",
    "\n",
    "We use Pandas to read the data file which is stored as Comma Separated Values (CSV). and print the column labels. CSV files are similar to excel sheets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Unnamed: 0', 'SalePrice', 'GrLivArea'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('slimmed_realestate_data.csv')\n",
    "print(data.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now pandas provides some helpful tools for us to inspect our data. It provides a `plot()` function that, behind the scenes, is calling into the _Matplotlib_ library and calling the function [matplotlib.pyplot.plot()](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html). In this case, we simply tell it the names of the columns we want as our _x_ and _y_ values and the `style` (`'.'` tells `matplotlib` to use a small dot to represent each data point)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='GrLivArea'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(x='GrLivArea',y='SalePrice',style='.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "\n",
    "If you have data, $(x,y)$, that you think can be fit by a line, $y = m x + b$, then there are [simple equations](https://en.wikipedia.org/wiki/Simple_linear_regression) one can use to calculate the slope ($m$) and intercept ($b$).\n",
    "\n",
    "They are:\n",
    "\n",
    "$$m = { n (\\Sigma xy) - (\\Sigma x) (\\Sigma y) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\n",
    "\n",
    "$$b = { (\\Sigma y) (\\Sigma x^2) - (\\Sigma x) (\\Sigma xy) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\n",
    "\n",
    "We'll break this calculation into a few steps to help make it easier.\n",
    "\n",
    "First lets define $x$ and $y$. $x$ will be our _above ground square footage_ and $y$ will be _sale price_. In our equations we have a few different values we need, such as $n$ which is just the number of points we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = len(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we need our $x$ and $y$ by selecting only the column we care about for each one. Note about data formats: `data` is a Pandas [DataFrame](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.html#pandas.DataFrame) object which has rows and columns; `data['GrLivArea']` is a Pandas [Series](https://pandas.pydata.org/docs/reference/api/pandas.Series.html) object which only has rows; then we also convert from _Pandas_ data formats (in this case a _Series_) to _Numpy_ data formats using the `to_numpy()` function which is part of the Pandas _Series_ object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = data['GrLivArea'].to_numpy()\n",
    "y = data['SalePrice'].to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will calculate $\\Sigma xy$, $\\Sigma x$, $\\Sigma y$, and $\\Sigma x^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_xy = np.sum(x*y)\n",
    "sum_x = np.sum(x)\n",
    "sum_y = np.sum(y)\n",
    "sum_x2 = np.sum(x*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The denominator in the equation for $m$ and $b$ are the same so we can calculate that once:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "denominator = n * sum_x2 - sum_x * sum_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate our fit values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 87.688145 * x + 34754.077892\n"
     ]
    }
   ],
   "source": [
    "m = (n * sum_xy - sum_x * sum_y) / denominator\n",
    "b = (sum_y * sum_x2 - sum_x * sum_xy) / denominator\n",
    "print('y = %f * x + %f' % (m,b))\n",
    "\n",
    "# saving these for later comparison\n",
    "m_calc = m\n",
    "b_calc = b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the fit results with our data to see how we did. \n",
    "\n",
    "First we define a plotting function because we're going to do this often and we want to reuse our code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(x,y,m,b,plt = plt):\n",
    "   # plot our data points with 'bo' = blue circles\n",
    "   plt.plot(x,y,'bo')\n",
    "   # create the line based on our linear fit\n",
    "   # first we need to make x points\n",
    "   # the 'arange' function generates points between two limits (min,max)\n",
    "   linear_x = np.arange(x.min(),x.max())\n",
    "   # now we use our fit parameters to calculate the y points based on our x points\n",
    "   linear_y = linear_x * m + b\n",
    "   # plot the linear points using 'r-' = red line\n",
    "   plt.plot(linear_x,linear_y,'r-',label='fit')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now can use this function to plot our results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(x,y,m,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stochastic Gradient Descent\n",
    "\n",
    "SGD is a common method in AI for training deep neural networks on large datasets. It is an iterative method for optimizing a loss function that we get to define. We will use this simple linear regression to demonstrate how it works.\n",
    "\n",
    "# The model\n",
    "\n",
    "In AI, neural networks are often referred to as a _model_ because, once fully trained, they should model (AKA predict) the behavior of our system. In our example, the system is how house prices vary based on house size. We know our system is roughly driven by a linear function:\n",
    "\n",
    "$$ \\hat{y_i}(x_i) = m * x_i + b $$\n",
    "\n",
    "We just need to figure out $m$ and $b$. Let's create a function that calculates our model given $x$, $m$, and $b$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(x,m,b):\n",
    "   return m * x + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# The Loss Function\n",
    "\n",
    "A _loss function_, or _objective function_, is something we define and is based on what we want to achieve. In the method of SGD, it is our goal to minimize (or make close to zero) the values calculated from the _loss function_. In our example, we ideally want the prediction of our _model_ to be equal to the actual data, though we will settle for \"as close as possible\".\n",
    "\n",
    "So we will select our _loss function_ to be the [Mean Squared Error](https://en.wikipedia.org/wiki/Mean_squared_error) function:\n",
    "\n",
    "$$ L(y_i,\\hat{y_i}) = (y_i - \\hat{y_i}(x_i))^2 $$\n",
    "\n",
    "where $y_i$ is our $i^{th}$ entry in the `data['SalePrice']` vector and $\\hat{y_i}$ is the prediction based on evaluting $m * x_i + b$.\n",
    "\n",
    "This function looks like the figure below when we plot it with $x=y_i - \\hat{y_i}(x_i)$ and we we want to be down near $y_i - \\hat{y_i}(x_i) = 0$ which indicates that our $y_i$ is as close as possible to $\\hat{y_i}$.\n",
    "\n",
    "![loss_func](img/loss_func.png)\n",
    "\n",
    "\n",
    "Here we crate a function that calculates this for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(x,y,m,b):\n",
    "   y_predicted = model(x,m,b)\n",
    "   return np.power( y - y_predicted, 2 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Minimizing the Loss Function\n",
    "\n",
    "We want to use the loss function in order to guide how to update $m$ and $b$ to better model our system. In calculus we learn to minimize a function with respect to a variable you calculate the _partial derivative_ with respect to the variable you want to vary.\n",
    "\n",
    "$$ { \\partial L \\over \\partial m } = 0 $$\n",
    "\n",
    "The location of the solution to this is the minimum as shown in the figure above. We can write down the partial derivative of the loss function as:\n",
    "\n",
    "$$ { \\partial L \\over \\partial m } = -2 x_i (y_i - \\hat{y_i}(x_i)) $$\n",
    "$$ { \\partial L \\over \\partial b } = -2 (y_i - \\hat{y_i}(x_i)) $$\n",
    "\n",
    "We can use this to calculate an adjustment to $m$ and $b$ that will reduce the loss function, effectively improving our fitting parameters. This is done using this equation:\n",
    "\n",
    "$$ m' = m - \\eta { \\partial L \\over \\partial m }$$\n",
    "$$ b' = b - \\eta { \\partial L \\over \\partial b }$$\n",
    "\n",
    "Here our original $m$ and $b$ are adjusted by the partial derivative multiplied by some small factor, $\\eta$, called the _learning rate_. This learning rate is very important in our process and must be tuned for every problem.\n",
    "\n",
    "In our example, the selection of the learning rate essentially defines how close we can get to the minimum, AKA the best fit solution. This figure shows what happens when we pick a large learning rate. We first select a starting point in our loss function (typically randomly), then every update from $m$/$b$ to $m'$/$b'$ results in a shift to somewhere else on our loss function (following the red arrows). In this example, our learning rate ($\\eta$) has been selected too large such that we bounce back and forth around the minimum, never reaching it.\n",
    "\n",
    "![largeLR](img/parabola_largeLR.png)\n",
    "\n",
    "If we select a smaller learning we can see better behavior in the next figure.\n",
    "\n",
    "![smallLR](img/parabola_smallLR.png)\n",
    "\n",
    "Though, keep in mind, too small a learning rate results is so little progress toward the minimum that you may never reach it!\n",
    "\n",
    "A pit fall of SGD that one must be aware of is when your loss function is complex, with many minima. The next figure shows such a case, in which we select a small learning rate and our starting point happens to be near a local minimum that is not the lowest minimum. As shown, we do reach a minimum, but it isn't the lowest minimum in our loss function. It could be that we randomly select a starting point near the minimum we care about, but we should build methods that are more robust against randomly getting the right answer.\n",
    "\n",
    "![local_min_smallLR](img/local_min_smallLR.png)\n",
    "\n",
    "Then, if we increase our learning rate too much, we bounce around again.\n",
    "\n",
    "![local_min_largeLR](img/local_min_largeLR.png)\n",
    "\n",
    "What we want to do in this situation is start with a large learning rate and slowly reduce its size as we progress. That is shown in this next figure.\n",
    "\n",
    "![local_min_variableLR](img/local_min_variableLR.png)\n",
    "\n",
    "As you can see, this process is not perfect and could still land in a local minimum, but it is important to be aware of these behaviors as you utilize SGD in machine learning.\n",
    "\n",
    "So let's continue, we'll build functions we can use to update our fit parameters, $m$ and $b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def updated_m(x,y,m,b,learning_rate):\n",
    "   dL_dm = - 2 * x * (y - model(x,m,b))\n",
    "   dL_dm = np.mean(dL_dm)\n",
    "   return m - learning_rate * dL_dm\n",
    "\n",
    "def updated_b(x,y,m,b,learning_rate):\n",
    "   dL_db = - 2 * (y - model(x,m,b))\n",
    "   dL_db = np.mean(dL_db)\n",
    "   return b - learning_rate * dL_db"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Putting it together\n",
    "\n",
    "We can now randomly select our initial slope and intercept:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_i = 5.00 * x + 1000.00\n"
     ]
    }
   ],
   "source": [
    "m = 5.\n",
    "b = 1000.\n",
    "print('y_i = %.2f * x + %.2f' % (m,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate our Loss function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first 10 loss values:  [3.03421561e+10 3.55511025e+10 1.24579082e+10 1.91656336e+10\n",
      " 1.60604929e+10 2.04432804e+10 1.72410030e+10 1.76517796e+10\n",
      " 1.52769600e+10 2.18152900e+10]\n"
     ]
    }
   ],
   "source": [
    "l = loss(x,y,m,b)\n",
    "print('first 10 loss values: ',l[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_i = 5.47 * x + 1000.00     previously calculated: y_i = 87.69 * x + 34754.08\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rate = 1e-9\n",
    "m = updated_m(x,y,m,b,learning_rate)\n",
    "b = updated_b(x,y,m,b,learning_rate)\n",
    "print('y_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f' % (m,b,m_calc,b_calc))\n",
    "plot_data(x,y,m,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[029]  dy_i = 88.89 * x + 32912.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478200827.641291\n"
     ]
    },
    {
     "data": {
      "image/png": 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hISEhZW+5ubkNffgiIiIi4kE6+DlmWKnCSkRExBM1WWD12muvcffdd5fNjKo8pLxyS135401xrLy5c+eSnp5e9hYQEFDtuSIiIiLS/ARd2CUwSxVWIiIiHqlJAqvz588TFxfHjBkzAOjYsSMAJ0+eLDsnNTW1bIB2aGgoKSkpTXZMRERERFqXDpphJSIi4tGaJLBavXo1V155JX369Cn73OTJk1m0aBEAu3btIiMjo2yXwPLHkpOT2b59O+PGjSs79uqrr1JaWsqZM2eIi4tjypQpZceWL1/O+fPnKSws5LXXXmPq1KkATJw4kfXr13PixAkMw2DJkiVlx0RERESkdbF5WWnXxqYZViIiIh7KpbsEOixdurRs2LrDc889x7Rp04iMjMTHx4c333yzrF3wkUceYcaMGURERGC1Wlm0aBHBwcEATJs2jV27dhEVFVV2bt++fQEYPnw4sbGxDBw4EICpU6cyduxYAHr37s3TTz9NdHQ0drudESNGXLImEREREWk9gvx9yDqvCisRERFPZDFqGuYkAISEhJCenu7uZYiIiIiL6Hu9Z3L16zLunwmczi1i57wRLrsPERERqV5N3+ubbOi6iIiIiIgnCfT30dB1ERERD6XASkRERERapUA/b/KKSiksKXX3UkRERKQSBVYiIiIi0ioF+Zs7BebkaY6ViIiIp1FgJSIiIiKtUqC/DwBZCqxEREQ8jgIrEREREWmVAi9UWGVrjpWIiIjHUWAlIiIiIq1SkCqsREREPJYCKxERERFplTo4Zljlq8JKRETE0yiwEhEREZFWSRVWIiIinkuBlYiIiIi0So5dArM0w0pERMTjKLASERERkVYp0M+ssMpRhZWIiIjHUWAlIiIiIq1SuzY2rBZVWImIiHgiBVYiIiIi0ipZrRY6+HmTrQorERERj6PASkRERERarSB/HwVWIiIiHkiBlYiIiIi0Wh38vcnOV0ugiIiIp1FgJSIiIiKtVpC/D1l5xRiG4e6liIiISDkKrERERESk1Qr096aoxE5+cam7lyIiIiLlKLASERERkVYr0M8HQHOsREREPIwCKxERERFptYL8vQHIytMcKxEREU+iwEpEREREWq3AC4FVjiqsREREPIoCKxERERFptQL9zZbALAVWIiIiHkWBlYiIiIi0WkFlgZVaAkVERDyJAisRERERabXKWgLzVWElIiLiSRRYiYiIiEir5Qisss6rwkpERMSTKLASERERkVbLMcMqWxVWIiIiHsXm7gWIiIiIiJS3evVqVq9eTX5+vsvvq62PF95eFrI1w0pERMSjqMJKRERERDzK5MmTiY+Px8/Pz+X3ZbFY6ODnQ7Z2CRQREfEoCqxEREREpFUL8vfWLoEiIiIeRoGViIiIiLRqQf6qsBIREfE0CqxEREREpFXr4O9Ndn4xhmG4eykiIiJygQIrEREREWnVgvy9KbUbnCsscfdSRERE5AIFViIiIiLSqgX6+wCQo7ZAERERj6HASkRERERatUB/bwANXhcREfEgCqxEREREpFULulBhlaUKKxEREY+hwEpEREREWrVAP7PCKlsVViIiIh5DgZWIiIiItGqOGVbZqrASERHxGAqsRERERKRVc8ywUmAlIiLiORRYiYiIiEirdnGGlVoCRUREPIXLA6vCwkIefPBBIiMj6d+/P3fddRcAmZmZjB07lsjISAYMGEBCQkLZbfLy8rjjjjuIiIggKiqKdevWlR2z2+089NBDhIeHExERweLFiyvc34IFCwgPDyc8PJz58+dXOLZ06VIiIyMJDw/nvvvuo6SkxIWPXERERESag4sVVgqsREREPIXN1Xcwb948rFYrBw8exGKxcPz48bLPDx06lM2bN7Nr1y4mTZpEUlISNpuN559/Hl9fXxITE0lOTub666/n5ptvJigoiBUrVrB3714OHjxITk4OV199NSNGjKBPnz7s2LGDlStXsmfPHmw2G9HR0cTExDBmzBiSk5OZP38+3377LZ07d2b8+PEsXbqU+++/39VPgYiIiIh4sDbeXrTxtpKdr5ZAERERT+HSCqvz58/z+uuv88wzz2CxWADo1q0bAPHx8cyePRuAIUOG0KVLl7Iqq7i4uLJjvXr1YtiwYWzYsKHs2KxZs/Dy8iI4OJjY2FhWrVpVdmz69Om0bdsWX19fZsyYwcqVKwFYs2YNEyZMoEuXLlgsFmbNmlV2TERERERatyB/H7I0w0pERMRjuDSwSkpKomPHjixYsIBrrrmGG2+8ka1bt3L69GnsdjudOnUqOzcsLIy0tDQA0tLS6NmzZ5MdExEREZHWrYOfNzlqCRQREfEYLg2siouLOXz4MP369eOrr77in//8J1OnTqWkpKSs4srBMIwKH5c/3hTHylu4cCEhISFlb7m5udWeKyIiIiLNnyqsREREPItLA6uePXtitVq58847Abjqqqvo1asX+/btA+DkyZNl56amphIaGgpAaGgoKSkpTXassrlz55Kenl72FhAQUL8nQERERESahUB/b84WFFNqr/6PmiIiItJ0XBpYXXbZZYwcOZItW7YAZkiUnJzMFVdcweTJk1m0aBEAu3btIiMjg5iYGIAKx5KTk9m+fTvjxo0rO/bqq69SWlrKmTNniIuLY8qUKWXHli9fzvnz5yksLOS1115j6tSpAEycOJH169dz4sQJDMNgyZIlZcdEREREpHUL9PfBMOCsBq+LiIh4BJfvErhkyRJmzJjB73//e7y8vPjXv/5Ft27deO6555g2bRqRkZH4+Pjw5ptvYrOZy3nkkUeYMWMGERERWK1WFi1aRHBwMADTpk1j165dREVFlZ3bt29fAIYPH05sbCwDBw4EYOrUqYwdOxaA3r178/TTTxMdHY3dbmfEiBHMnDnT1Q9fRERERJqBQH9vALLyighq6+Pm1YiIiIjFqGmYkwAQEhJCenq6u5chIiIiLqLv9Z6pKV+Xf+1I4plN+1n3wA1cHRrUJPcpIiLS2tX0vd6lLYEiIiIiIs1BoL9ZVZWtnQJFREQ8ggIrEREREWn1Av3MlsBs7RQoIiLiERRYiYiIiEir55hblaXASkRExCMosBIRERGRVu9ihZVaAkVERDyBAisRERERafUuzrBShZWIiIgnUGAlIiIiIq1eoL9ZYZWlCisRERGPoMBKRERERFo9by8rAb42cvJVYSUiIuIJFFiJiIiIiGBWWanCSkRExDMosBIRERERwQysNMNKRETEMyiwEhEREREBgvx9FFiJiIh4CAVWIiIiIiJABz9vcgtLKCqxu3spIiIirZ4CKxERERERzAorQIPXRUREPIACKxERERERIMjfG4BsDV4XERFxOwVWIiIiIiJAhwsVVtmqsBIREXE7BVYiIiIiIlyssMo6rworERERd1NgJSIiIiICBJa1BKrCSkRExN0UWImIiIiIAIFlLYGqsBIREXE3BVYiIiIiIlzcJTBLFVYiIiJup8BKRERERAQI9FNLoIiIiKdQYCUiIiIiArT388Zigew8tQSKiIi4mwIrERERERHAy2qhfRtvshRYiYiIuJ0CKxERERGRC4L8vdUSKCIi4gEUWImIiIiIXNDB30eBlYiIiAdQYCUiIiIickGQvzfZ+WoJFBERcTcFViIiIiIiFwT5+1BQbKeguNTdSxEREWnVFFiJiIiIiFzQwc8bQG2BIiIibmZz9wJEREREpOU7dOgQjz32GJ06daJDhw785S9/cfeSqhTk7wNAVl4RXTu0cfNqREREWi9VWImIiIi0Ek8//TQWi4UffvihQdeZM2cOYWFhVV7r0KFD3HDDDURFRXHttdeyd+9eADZu3Midd97J4sWLKS4u5vPPP2/QGlwl0N+ssMrK0xwrERERd1JgJSIiItIKfPPNN3z++eeEhoZWebyoqIjk5OQKnysoKCA1NfWScydNmkRCQgI9e/a85Nj999/Pfffdx8GDB3n00UeZOXMmAPfccw9bt27l4Ycf5siRI1Ve1xM4AqsctQSKiIi4lQIrERERkRausLCQ2bNns3jxYiwWS5Xn/Pjjj4wcOZLvv/8egLy8PG677TZWrlx5ybnDhg0jJCTkks9nZmbyzTffcNdddwEwceJEkpOTSUlJITg4mJdffpkXXniBtm3b0r9//2rXu3r1amJjY8nPz6/Pw22Qiy2BCqxERETcSYGViIiISAv3xBNPcNddd9GrV69qzxk8eDBvvPEG48ePZ/v27YwdO5aYmBjmzZvn9P0cOXKE7t27Y7OZY1ItFguhoaGkpaVx9OhRZs6cycyZM+nXrx8DBgyo9jqTJ08mPj4ePz8/5x9kI3FUWGXnqyVQRETEnTR0XURERKQF++yzz9i1axfPPvtsrefGxMTwyiuvMHz4cGbNmsVTTz1V5/urXMFlGAYAPXr0YOnSpXW+XlNzVFhpl0ARERH3UoWViIiISAu2fft29u/fT69evQgLCyM9PZ0xY8bw3nvvXXLuqVOneOyxx/j973/Pli1b2LZtW53u6/LLLyc9PZ2SkhLADKuOHDlS7dwsT9TBMXT9vCqsRERE3EmBlYiIiEgLNm/ePI4dO0ZKSgopKSmEhISwZcsWbrnllgrnnThxgpEjR/LAAw/w7LPPsnHjRmbMmMGWLVucvq/OnTszePBgVqxYAcDatWsJCwsjLCysMR+SS7XzteFltZCdrworERERd1JgJSIiIiIUFBTw+OOPl+3q169fPzZv3lzl4PPZs2cTEhJCeno6o0aNIiIiouzYq6++yquvvkpUVBTPPvtss2gDLM9isRDo5012niqsRERE3MliOAYLSLUcP5CJiIhIy6Tv9Z7JXa/LyBe2YbVY+GDuTU1+3yIiIq1JTd/rVWElIiIiIlJOkL8PWRq6LiIi4lYKrEREREREygn09yYnvwg1IoiIiLiPywOrsLAw+vTpw6BBgxg0aBBxcXEAZGZmMnbsWCIjIxkwYAAJCQllt8nLy+OOO+4gIiKCqKgo1q1bV3bMbrfz0EMPER4eTkREBIsXL65wfwsWLCA8PJzw8HDmz59f4djSpUuJjIwkPDyc++67r2wHGxERERERh0B/H4pLDc4Xlbp7KSIiIq2WrSnuZM2aNQwYMKDC5+bNm8fQoUPZvHkzu3btYtKkSSQlJWGz2Xj++efx9fUlMTGR5ORkrr/+em6++WaCgoJYsWIFe/fu5eDBg+Tk5HD11VczYsQI+vTpw44dO1i5ciV79uzBZrMRHR1NTEwMY8aMITk5mfnz5/Ptt9/SuXNnxo8fz9KlS7n//vub4ikQERERkWYi0M8bgKzzRQT4NsmPyyIiIlKJ21oC4+PjmT17NgBDhgyhS5cuZVVWcXFxZcd69erFsGHD2LBhQ9mxWbNm4eXlRXBwMLGxsaxatars2PTp02nbti2+vr7MmDGDlStXAmZoNmHCBLp06YLFYmHWrFllx0REREREHILa+gCQk685ViIiIu7SJIHVnXfeycCBA7n33ns5efIkp0+fxm6306lTp7JzwsLCSEtLAyAtLY2ePXs22bHKFi5cSEhISNlbbm5uQ58CEREREWkmAv0vVFjlFbl5JSIiIq2XywOrHTt28N133/HNN9/QsWNH7rnnHgAsFkuF8yoPtSx/vCmOlTd37lzS09PL3gICAqo9V0RERERalkA/s8IqWzsFioiIuI3LA6vQ0FAAvL29+c1vfsMnn3xCx44dATh58mTZeampqWXnhoaGkpKS0mTHREREREQcgi5UWGWrwkpERMRtXBpYnT9/nuzs7LKPV65cyeDBgwGYPHkyixYtAmDXrl1kZGQQExNzybHk5GS2b9/OuHHjyo69+uqrlJaWcubMGeLi4pgyZUrZseXLl3P+/HkKCwt57bXXmDp1KgATJ05k/fr1nDhxAsMwWLJkSdkxERERERGHDmUtgaqwEhERcReXbnty4sQJJk6cSGlpKYZh0Lt3b9544w0AnnvuOaZNm0ZkZCQ+Pj68+eab2Gzmch555BFmzJhBREQEVquVRYsWERwcDMC0adPYtWsXUVFRZef27dsXgOHDhxMbG8vAgQMBmDp1KmPHjgWgd+/ePP3000RHR2O32xkxYgQzZ8505cMXERERkWYoyF8tgSIiIu5mMWoa5iQAhISEkJ6e7u5liIiIiIvoe71nctfrkldUQr8ntvDzwT1YOGVQk9+/iIhIa1HT9/om2SVQRERERKS58PP2wsdmJTtfFVYiIiLuosBKRERERKQci8VCkL83WRq6LiIi4jYunWElIiLSmhgG7NwJiYkQEQHR0WCxuHtVIlIfgX4+mmElIiLiRgqsREREGkFqKowZA8nJ4OMDRUXQqxds2QI9e7p7dSJSV4H+3hw8cc7dyxAREWm11BIoIiLSQIZhhlVJSWZQlZtrvk9KgrFjzeMi0rwE+nuTk1+M3a7/gEVERNxBgZWIiEgD7dwJKSlQUlLx8yUlcPiweVxEmpcgfx/sBpwrKKn9ZBEREWl0CqxEREQaKDERvL2rPubjYx4XkeYl0N8HQIPXRURE3ESBlYiISANFRJgtgFUpKjKPi0jzEuhvptDZ+Rq8LiIi4g4KrERERBooOtocsG6rtJWJzQa9e5vHRaR5CboQWKnCSkRExD0UWImIiDSQxWLuBhgebrYABgSY7yMizM9bLO5eoYjUVQc/syUwW4GViIiIW9hqP0VERERq07Mn7NtnDlhPTDTDquhohVUizZWjwio7Ty2BIiIi7qDASkREpJFYLBATY76JSPN2cei6AisRERF3UEugiIiIiEgljgqrHLUEioiIuIUCKxERERGRSjqUDV1XhZWIiIg7KLASEREREanE1+aFv4+XdgkUERFxEwVWIiIiIiJVCPL3ISdfFVYiIiLuoMBKRERERKQKHfy8VWElIiLiJgqsRERERESqENTWm2zNsBIREXELpwOr0tJSUlJSXLgUERERERHPEejvw7mCEkpK7e5eioiISKvjVGD1ySef0LNnT4YNGwbArl27mDZtmksXJiIiIiLiToF+5k6BmmMlIiLS9JwKrB599FG2b99Ox44dARgyZAjffPONSxcmIiIiIuJOQf4+AGSpLVBERKTJORVYlZSUEB4eXuFzPj4+LlmQiIiIiIgnCPQ3K6yyNXhdRESkyTkVWLVp04bc3FwsFgsAP/74I23atHHpwkRERERE3CnwQoWVBq+LiIg0PZszJ82fP58xY8Zw7Ngxpk+fzubNm1mxYoWr1yYiIiIi4jaOGVZZqrASERFpck4FVqNHjyYyMpLNmzdjGAaPP/44ERERrl6biIiIiIjbBLXV0HURERF3cSqwSktLo1u3bvzqV78CID8/nyNHjnD55Ze7dHEiIiIiIu4SWDZ0XRVWIiIiTc2pGVaTJk1y6nMiIiIiIi3FxZZAVViJiIg0NacCq6KiogpD1v38/CgsLHTZokRERERE3K3DhcAqR4GViIhIk3MqsLJYLGRmZpZ9fOLECQzDcNmiRERERETczeZlpV0bm1oCRURE3MCpGVZz5swhJiaGu+++G4A33niDxx9/3KULExERERFxtyB/H7JVYSUiItLknAqsfvnLX9KrVy82bdoEwNKlS7nxxhtdujAREREREXcL9Pfm1DmNwhAREWlqTgVWAMOHD2f48OEuXIqIiIiIiGcJ9Pfh0Ilcdy9DRESk1akxsPr973/Pc889x+TJk7FYLJccj4+Pd9nCRERERMocPQqHDoH+eCZNLMjfm/ziUgqKS2nj7eXu5YiIiLQaNQZWMTExANx2221NshgRERGRMidPwtq1sGoV7NgBXbpAejp4KTSQphPo2Ckwv1iBlYiISBOqMbD62c9+RmlpKXv37uW5555rqjWJiIhIa5WdDevXmyHV1q0YpaXs9rmO+Ki1nAoZxP9pl2JpYoH+PgBk5xXTpX0bN69GRESk9bDWdoKXlxdffvllU6xFREREWqPcXHj7bRg/Hrp0wZgxg+8/Osnjvd/iiq45XF30Oc8emMCHSb0oLHV6/GaL9Oqrr5KTkwPA7Nmzueaaa9ixY4ebV9WyBfqbFVZZeUVuXomIiEjrUmtgBWal1XPPPUdmZiZ5eXllbyIiLZlhQEICLFtmvldhh0gjys+HdesgNhY6d4Y772TvxsM8FfJv+nXL4sqSb/jzoSmcoz0PPWT+N5iUBL6+7l64ey1atIgOHTqwc+dOfvjhB/785z/zu9/9zt3LatGCylVYiYiISNNx6s+Ujh+E/vCHP5R9zmKxUFpa6ppViYi4WWoqjBkDycng4wNFRdCrF2zZAj17unt1Is1UURF88IHZ7rdhA5w7x0GiiO/5EnHFE/jhWEc4bOZXDzxgZlkxMRpZVZ7NZv7o9tFHH3H33XczZsyYCj+fSeNzVFhlq8JKRESkSTlVYWW32y95q2tY9fTTT2OxWPjhhx8AyMzMZOzYsURGRjJgwAASEhLKzs3Ly+OOO+4gIiKCqKgo1q1bV2EtDz30EOHh4URERLB48eIK97NgwQLCw8MJDw9n/vz5FY4tXbqUyMhIwsPDue+++ygpKanTYxCR1sEwzLAqKcn8/To313yflARjx6rSSqROSkrgww/h3nuha1e47TYOr9jJXzo8y+AeJ7iCA8xPvZfjhR257z7YutXcEHDRIrjpJoVVlVmtVlatWkVcXBwjR44EoKhIQYorOWZYZanCSkREpEk5PQji6NGjfPLJJ1gsFm688Ua6d+/u9J188803fP7554SGhpZ9bt68eQwdOpTNmzeza9cuJk2aRFJSEjabjeeffx5fX18SExNJTk7m+uuv5+abbyYoKIgVK1awd+9eDh48SE5ODldffTUjRoygT58+7Nixg5UrV7Jnzx5sNhvR0dHExMQwZswYkpOTmT9/Pt9++y2dO3dm/PjxLF26lPvvv79uz5iItHg7d0JKivl7dnklJXD4sHn8wiaqIlIVu938DyUuDlavhsxMUgklvtt84ntM5auj3SAdgoJgxgyYMgVuvhm8vd29cM/3z3/+k2effZb/9//+H2FhYRw8eJCbb77Z3ctq0YIcFVb5CgZFRESaklMVVqtWrWLQoEHExcWV/Ts+Pt6pOygsLGT27NksXrwYi8VS9vn4+Hhmz54NwJAhQ+jSpUtZlVVcXFzZsV69ejFs2DA2bNhQdmzWrFl4eXkRHBxMbGwsq1atKjs2ffp02rZti6+vLzNmzGDlypUArFmzhgkTJtClSxcsFguzZs0qOyYiUl5iYvW/OPv4mMdFpBLDgF274OGHITQUhg0jfdE7/J3fMrTHEcJI5dHjv+XguW7ccw/897+QkQFLl8Lo0QqrnDV06FDeeecdfv3rX2MYBt26dePll19297JatEC/CzOszqvCSkREpCk5FVg99dRTfPnll6xfv57169fz5Zdf8sQTTzh1B0888QR33XUXvXr1Kvvc6dOnsdvtdOrUqexzYWFhpKWlAZCWlkbPckNiXH2ssoULFxISElL2lpub69RjlZZNA7hbj4gIswWwKkVF5nERwfwf4Z498Nhj5n8Y117L8YVv83L+vcSEJHM56czNnMePOSHceac5tioz0/z/6K23mgGw1M3MmTPJzs6mqKiIQYMG0aVLl0vGI0jjatfGhtWiCisREZGm5lRL4GWXXVYhcAoLC+Oyyy6r9XafffYZu3bt4tlnn73kWPlqKwCj0m//5Y83xbHy5s6dy9y5c8s+DgkJqfZcaR00gLt1iY42X9+kpIptgTYb9O5tHhdp1Q4cMNv9Vq2Cffs4QWfWdphJfMgMdhwNxzhjwb/AbPWbMsWc/ebn5+5Ftwxff/01gYGB/Oc//2Hw4MF88skn3HjjjTzwwAPuXlqLZbVa6ODnrRlWIiIiTcypCquf/OQnLFiwgIyMDI4fP86f//xnbr/9dvLy8sjLy6v2dtu3b2f//v306tWLsLAw0tPTGTNmDF9++SUAJ0+eLDs3NTW1bMZVaGgoKSkpTXZMpCYawN36WCxmGBkebgaUAQHm+4gI8/OV8naR1iElBZ57DgYPhj59OPXkS/zryC2MCtlHd2sGs3Oe4YtTEfz85xbi481KqlWrYMIEhVWNyfEHtx07dnDbbbfRvn17rFanfpyTBgjy99EugSIiIk3MYtRUanRBTT8IWSwWp3cMDAsLY+PGjQwYMIDp06cTFhbGU089xa5du5g4cSKHDx/GZrPx1FNPkZKSwrJly0hOTmbo0KHs27eP4OBgli1bxooVK9iyZQs5OTkMHjyYzZs307dvX7Zt28aDDz7IF198UTZ0fcGCBYwdO5bDhw8TExNTYej6rbfeyqxZs2pdd0hICOnp6U49Rml5EhJg1CgoLLz0mI+PuaOVBnC3TIZhzo1OTDTDquhohVXSyhw9ag5Nj4uDzz/nDEG84/cL4oJnsfV4P0rtVnx84JZbzEqqn/3MDHibo+byvX7MmDH06tWLzZs3s3v3btq2bcv//M//sGfPHncvzSU85XX5+eKdpGfl8+UfR7l7KSIiIi1KTd/rnWoJtNvtjboggOeee45p06YRGRmJj48Pb775JjabuZxHHnmEGTNmEBERgdVqZdGiRQQHBwMwbdo0du3aRVRUVNm5ffv2BWD48OHExsYycOBAAKZOncrYsWMB6N27N08//TTR0dHY7XZGjBjBzJkzG/1xScvjGMBdXWCVmKjAqqWyWMzXVq+vtConT8LatWZ51I4d5Bjt2OA7hbjur/BB5pUU51vxzoRbboXYWBg3Djp0cPeiW4+33nqLFStWMH36dAIDA0lJSakwxsCTHTp0iMcee4xOnTrRoUMH/vKXv7h7SU4L9Pfhh6NnMQzjkrEWIiIi4hpOVVi1dp7y1z1xj4QEGDmy6iHcqrASaf5USQdkZ8P69WZItXUr50r9eNd7EvGXPcDmk1dTVOKFzWZWm8bGwu23Q1CQuxfduJrT9/r8/Hz27NmDxWJh4MCB+DnRczl69GgyMjKwWq20a9eOl19+mUGDBtV7DXPmzOHdd98lNTWV77//ngEDBpQdO3ToEPfccw+nTp0iMDCQZcuW0a9fP/7+97/Tq1cvbr/9dn73u98xadIkhg4dWuP9eMrrMjd+N+u+OcreP43B38epv/eKiIiIExpcYSXSmmkAt0jL1ao3VMjNhXffNUOqzZs5X+zNRq/biev0CZtOX0thsRfWEzBihNnuN2ECdOzo7kXLp59+yqRJk+jSpQuGYXDy5EnWrFnD9ddfX+Pt4uPjCQwMBOCdd95hxowZfPPNNxXOKSoq4ujRoxU22ikoKODEiRMVdloGmDRpEo8++igxVfzF5v777+e+++5j+vTprFmzhpkzZ/LZZ59xzz338OSTT/LJJ5+Qnp5OampqrYGVpwj0M7e0zMorVmAlIiLSRDSlU6QWGsAt0jK1yg0V8vPNdr/YWOjcmbw772Xtf32JDf6QTj45TC19i3dOXM/10V688gocPw4ffAD33quwylPMnTuX1atX8+2337J7925Wr17Nb3/721pv5wirAHJycqqcT/rjjz8ycuRIvv/+ewDy8vK47bbbWLly5SXnDhs2rMpdlDMzM/nmm2+46667AJg4cSLJycmkpKQQHBzMyy+/zAsvvEDbtm3p379/tetdvXo1sbGx5Ofn1/rYmkKQvzeABq+LiIg0If2JSMQJPXvCvn1qGxJpSXbuNDe+K185CebHhw+bx1tEu29RkZk6rVoF77xDQW4xm7mF+E7v8q79Js4XemPJNB9rbCxMmgRdu7p70VKdgoICosuV9t5www0UFBQ4ddu7776bjz/+GIDNmzdfcnzw4MG88cYbjB8/ntdff5358+czYsQI5s2b5/T6jhw5Qvfu3cvmklosFkJDQ0lLS8Pb25snnngCgH79+lVoI6xs8uTJTJ48ucpQzB0C25oVVtl5xW5eiYiISOvhVGB19OhRZs+ezZEjR/j666/ZvXs327Zt4ze/+Y2LlyfiOTSAW6RladEbKpSUwLZtZki1bh1FWbm8z2jiL4tjQ8lIzhb4wkm4/nqz3W/SJOjRw92LFmf4+/vz4YcfMmqUuVvdtm3b8Pf3d+q2b7zxBgDLly/nkUceYdOmTZecExMTwyuvvMLw4cOZNWsWTz31VJ3XWHkouWNcao8ePVi6dGmdr+cJAv3MCqssVViJiIg0GacCq/vvv5+pU6fyt7/9DYABAwYwbdo0BVYiItJsRURUvZkCmJ+PiGja9TSY3W6WhcXFwerVFGeeYSsjiQt+nXfajCG7oA2cgiFDzJBq8mQIDXX3oqWuXnrpJSZOnIivry8Wi4XCwkLWrl1bp2vcc889zJo1i9OnT9OxUq/nqVOneOyxx/j9739PfHw827ZtY/jw4U5f+/LLLyc9PZ2SkhJsNhuGYXDkyBFCm/kXW5C/KqxERESamlOBVUZGBnfddRcvvPCCeSObrazUW0REpDlqERsqGAZ89ZVZSRUXR8nRDLYxnLgO/2Sd3085k+8PZ+Dqq812v9hY8zFL83XNNdeQmJjIgQMHMAyDPn364O3tXeNtzp49S25uLt27dwdg/fr1dOzYkeDg4ArnnThxgtGjRzNnzhxmzpzJ3XffzW233cYrr7zCmDFjnFpf586dGTx4MCtWrGD69OmsXbuWsLAwwsLC6vV4PUWgZliJiIg0OadSJ8dfyByysrKw2+0uW5SIiIirOTZUqLxLYO/eHr6hgmHA99+XhVSlh1PYwTDi2z3HWv/xnMwLgBy48kqYeyGkiox096KlofLy8ip83Lt3bwCKi4spLi6usS0wJyeHiRMnkp+fj9VqpVOnTmzcuPGS1r2CggIef/xxJk+eDJhzpjZv3szevXsvuebs2bPZsGEDGRkZjBo1ioCAABITEwF49dVXmT59Os888wzt27dn+fLlDXrsnuBiYKUKKxERkaZiMYza90F64YUXOHjwIFu3buXxxx9n8eLF3HXXXcyZM6cp1uh2ISEhpKenu3sZIiLiAobRTDZUOHDAbPdbtQr7vv3sJJq4tjNZY/ycE3ntAejXz2z3i42FPn3cvN5mxtO/11utViwWS9kfEB1hk2EYWCwWSktL3bk8l/GU1yW3sIQBT25h4tUhvBB7lbuXIyIi0mLU9L3eqQqrhx9+mJUrV5Kdnc2mTZuYM2dO2XbFIiIizZlHb6iQknIxpNr9HV9wHXF+v2Z12ykcOx8I5yEqCu67EFLVsOmaNHOqbHevtj5eeHtZ1BIoIiLShJweRHXHHXdwxx13uHItIiLSSjWbKqemcPQorF4Nq1ZhfPEFX3ENcb4ziG/7C46c7wj5ZtviH6aY1VRXXtmKnyuRJmKxWAj09yE7Xy2BIiIiTaXGwOrRRx+t8cZ//etfG3UxIiLS+qSmXjpHqlcvc45Uz57uXl0TOXkS1qyBuDiM7TvYzVXEeU8jPuBdknM7QyH07AqPPGCGVFdfrZBKpKkF+nmTpQorERGRJlNjYNW2bdumWoeIiLRChmGGVY6d+oou/C6YlARjx8LevS04mMnOhvXrzUqqD7fyvb0f8V6/IC5gJYm53aAYQrrA3PvMdr9rr23Bz4VIMxDk70PSyVx3L0NERKTVqDGwevLJJ5tqHSIi0grt3GmOaSopqfj5khI4fNg87pGzpeorNxfefdfc4W/zZvYWRxBn/QXx/v9mf+7lUArd2sGcGWZIdf31YLW6e9EiAtDB35vs/OKyQfciIiLiWk7PsFq3bh27d++moKCg7HNqCRQRkYZITARvbygsvPSYj495vNkHVvn5sGmTOTx940YO5ocQZ7mD+Lb/4IfiXmCHzv7wwN1mu190NHh5uXvRIlJZkL83pXaDswUldPDzdvdyREREWjynAqvf/OY3JCUl8fXXX3PHHXewevVqfvKTn7h6bSLSwmnQtkREXGwDrKyoyDzeLBUVwQcfmJVU77xDUm5n4plCXNvv+I5IMKCjL9z3CzOkuukmhVQini7I3weAnLxiBVYiIiJNwKnAauvWrXz33XcMHjyYF154gUcffZR7773X1WsTkRZMg7YFzJCyV6+LM6wcbDZzJ7zoaPetrc5KSmDbNjOkWreOlKz2rGYycW2/5Gv6AhDkAzOnmu1+N99sVpeJSPPQwd/8DzYrr4jQjv5uXo2IiEjL51Rg1aZNG6xWKxaLheLiYrp06cLRo0ddvTYRaaFa9aBtJ7WW6jOLxQwpK4eXvXubn/f4x2y3my9UXBysXs2RTB9WM5l4/218wZUAdLDBPfeYIdWoUeZjFJHmx1FhlZ1f7OaViIiItA5OBVbt2rUjLy+PmJgY7rnnHrp27Yq3/iwsIvXU6gZt11Frqz7r2RP27WtGAZ1hwFdfmZVUcXEcO2pnDZOI83uPT7kagAAr3Hmn2e43ejT4+rp5zSLSYIEX2gCz86rpYxYREZFG5VRgtXLlSmw2G3/7299YuHAhWVlZrF692tVrE5EWqlUM2q6n1lp9ZrGYr7nHvu6GAd9/XxZSnTicy1omEtdmLZ8wBAMr/haDKVPMkGrsWPDzc/eiRaQxBToqrPJUYSUiItIUnAqsunTpUvbvBx98kCNHjhAaGuqyRYlIy9ZiB203AlWfeZgDB8pCqlP7MlnLROJ9l7PNcgN2w4qfxWDiJAuxsfDTn1rw11gbkRYrsNwMKxEREXE9pwKrsWPHsmrVKmw2G1dddRUAd999N3/6059cujgRaZla1KDtRqbqMw+QkmLOpFq1ijO7U1nPBOJ9FrHVMoxSwwtfDMaNtzBlCtx2m4WAAHcvWESaQpAqrERERJqU1ZmTTpw4QWBgIJs2bWL8+PEcOnSId955x8VLExF3MQxISIBly8z3htG413cM2g4PN0OYgADzfUREMxm07UKqPnOTo0fhxRdh6FCyew1i+by93PrDX+liyeRelvKxMZxbfurFm29CZqaF9eth6lQUVom0Io4KK82wEhERaRpOVVgVF5t/SdqxYwdjx47F29sbq9WprEtEmpmmGvjd7AZtNxFVnzWhkydhzRpYtYqzO3bzH24jzusJtlh/QpHdGxsGo8aYlVTjx1sICnL3gkXEndp4e9HG20qWKqxERESahFOB1YABAxg7diz79+/nr3/9K3l5ea5el4i4QVMP/Pb4Qdtu4Kg+qxwa9u6t6rNGkZ0N69fDqlXkfvg5G+23EG+dyybrLRTaffDCYMRIcybVhAkWOnZ094JFxJME+fuQna/ASkREpCk4FVgtW7aMzZs3c9VVV+Hv78/Ro0d59tlnXb02EWliGvjtGVR91shyc+Hdd2HVKvLe286mkp8QZ7mP/1reJR9fLIbB8OFmSDVxooVOndy9YBHxVB38vNUSKCIi0kScCqzatGnD7bffXvZxjx496NGjh6vWJCJuooHfnsOZ6jPDUKhVrfx82LQJVq2iYOOHbC64iTjLL/iPNY7z+GHBICbabPebONFC167uXrCINAdB/j4cO5bj7mWIiIi0Ck4FViLSOmjgd/PRVLPGmpWiIvjgA1i1isL1m3j//A3EE8sGr2Wcoy0YcP21MGUKTJpkQX93EZG6CmrrzdmCEkrtBl5W/YVARETElRRYiUgZDfxuHpp61phHKymBbdtg1SqK177Lh9n/QzyxrPdaTA7tALj2fyA2FiZPhtBQ9y5XRJq3Dn4+AOTkFxPc1sfNqxEREWnZFFiJSBkN/G4eWv2sMbvdfJCrVlGyej0fn+xPHFNY7/U8ZwgE4OqrzEqqyZPNEFZEpDEE+XsDkJ1XpMBKRETExRRYiUgF7hj4rVlMddMqZ40ZBuzaBXFxlK5azY5j4cQxhbVe/8spggG4sj88fCGkiox083pFpEUKvBBYZeVpp0ARERFXU2AlIpdwZuB3Y9EsptpVDvTCw1vJrDHDgO+/h1WrsK+MY2dKd+KYwhqvrzmBuZVfvysMHppitvz16ePm9YpIixfo72gJ1E6BIiIirqbASkTcRrOYaldVoBcWBiEhkJbWQmeNHThghlSr4vl8fwfiiWW1dSfHMLfyiwo3uG+K2fLXv38r/wIRkSYV6Hehwuq8KqxERERcTYGViDitsVv3WsIsJle2M1YX6B0+bFafhYe3oFljyckQF4exKo5d33kTTyzx1i0cIQSA8F4Gj12opLrySkvzfIwi0uwFXZhblZWnCisRERFXU2AlIk5xRetec5/F5Op2xpoCvSNH4MMPzXCq2c7+OnoUVq/GWLmKb78sIo4pxFvfIQXzyQsLNXg01gyprr5aIZWIuJ9j6HpOviqsREREXE2BlYjUylWtexERzXcWU1O0M9YW6CUlwfTpnh3qXeLkSVizBmPlKr7/JJs4Yom3rCAR88UO6W4wN9Zs9xsyRCGViHiWDn6qsBIREWkqCqxEpFauat2LjjYrkhyhj0NzmMXUFO2MzTnQqyArC9avh7g4fvzwOPH2icRZ/sUBrgCgWxeDORdCqqFDLVitbl6viEg1HLsEZmuXQBEREZdTYCUitXJV657FYrbPVW6raw6zmJqinbE5B3rk5sK778KqVRx47zBxJT8nnoX8SH8AOl9m54HJZkgVE6OQSkSaB28vKwG+NgVWIiIiTUCBlYjUypWVPj17wr59rhtc7ipNUf1kscDmzTBsGBw7ZgZhJSXmsHWPDPTy82HTJli1isT/7CO+cBzx/InvGATAZR3t3D/JnEl1001WvLzcu1wRkfoI9PdWS6CIiEgTcPnftEePHs2VV17JoEGDuPHGG9m9ezcAmZmZjB07lsjISAYMGEBCQkLZbfLy8rjjjjuIiIggKiqKdevWlR2z2+089NBDhIeHExERweLFiyvc34IFCwgPDyc8PJz58+dXOLZ06VIiIyMJDw/nvvvuo6RyL4+IVMlR6WOrFHE3VqWPxWJWIznmMXlcEFMFVz8nYA51HzsWTpwww6riYujWDd57D0JDG379RlFUBBs3wrRpJF82hL9O+oL/WTOPyMIf+CPPkBZ4JTNnwvvvw/EMK0uWwIgRKKwSkWYryN9HFVYiIiJNwOUVVvHx8QQGBgLwzjvvMGPGDL755hvmzZvH0KFD2bx5M7t27WLSpEkkJSVhs9l4/vnn8fX1JTExkeTkZK6//npuvvlmgoKCWLFiBXv37uXgwYPk5ORw9dVXM2LECPr06cOOHTtYuXIle/bswWazER0dTUxMDGPGjCE5OZn58+fz7bff0rlzZ8aPH8/SpUu5//77Xf0UiDR7zbl1z1Vc/ZxUHurucOwY3HJL4wx1r7eSEti2DVat4siaL1id8xPieJAvuQ6ADu3t3DPBbPcbOdKKj4+b1iki4gKB/t4cPpnr7mWIiIi0eC6vsHKEVQA5OTlYLwwqiY+PZ/bs2QAMGTKELl26lFVZxcXFlR3r1asXw4YNY8OGDWXHZs2ahZeXF8HBwcTGxrJq1aqyY9OnT6dt27b4+voyY8YMVq5cCcCaNWuYMGECXbp0wWKxMGvWrLJjIlI7R+ve1q3w8svm+717XVPpYxiQkADLlpnvDaPx76MxuPI5cWaoe5Oy2+GTT2D2bI51Gcw/fvIfopf+ktCc73mYhewLGMJdd5ljq05kWlm2zAzWmmtY1Vy+BkWk6QX6+3C+qJSiEru7lyIiItKiNckMq7vvvpuPP/4YgM2bN3P69GnsdjudOnUqOycsLIy0tDQA0tLS6Nmzp9PHvvrqq7JjN910U4Vja9asqfWalS1cuJCFCxeWfZybq7+iicDF1r2GDhOvSWrqpVVLvXqZVUvl/hP2GK56TppiqHutDAN27YK4OE68vZU1GdHEMYUEXsbASlt/O1PHmTOpxo614ufn4vU0keb2NSgiTSvQ78JOgflFdG7Xxs2rERERabmaJLB64403AFi+fDmPPPIIb775JpZKvSxGpT9flz/eFMfKmzt3LnPnzi37OCQkpNpzRZoDw2geQ80rt8E5hponJZmznGpqg2suj9FZTTHUvUqGAXv2QFwcJ996n3Vp/0McU9jOX7HjhV8bOxNvszBlCtx6qxV/fxetw00a8jUoIq1DkP+FwCqvWIGViIiICzXpLoH33HMPs2bNKvv45MmTZVVWqamphF7oowkNDSUlJaXCsVtvvbXCsSFDhlR7Owdnj4m0ZM2pWsSZNriqqoqa02N0lmOoe+UZVo011P2SgO+yA1jiVnHmrfdYd2gA8cTyEX+iFBu+PnbG3WqGVLfdZiUgoGH37cnq+zUoIq1HB3+z11mD10VERFzLpTOszp49y7Fjx8o+Xr9+PR07diQ4OJjJkyezaNEiAHbt2kVGRgYxF34LKH8sOTmZ7du3M27cuLJjr776KqWlpZw5c4a4uDimTJlSdmz58uWcP3+ewsJCXnvtNaZOnQrAxIkTWb9+PSdOnMAwDJYsWVJ2TKSlKl8tUlQEubnme0e1iKfN5XG0wVXF0QZXWXN7jM5yDHUPDzcfe0CA+T4iouFD3VNToW9fmDkimeT7n8W48UaW9/0Ltz41hC6HPuH/8W+22UZx621evPkmZJ60sn69halTadFhFdTva1BEWhdHhVVWXjVlsCIiItIoXFphlZOTw8SJE8nPz8dqtdKpUyc2btyIxWLhueeeY9q0aURGRuLj48Obb76J7cL+8I888ggzZswgIiICq9XKokWLCA4OBmDatGns2rWLqKiosnP79u0LwPDhw4mNjWXgwIEATJ06lbFjxwLQu3dvnn76aaKjo7Hb7YwYMYKZM2e68uGLuF1zqxapTxtcc3uMdeEY6t6YrY5G+lHeGrKaxSff5RjdiWMKf2Euxfhgwc7YsTBlKowfb6XcnhmthttaMUWk2Qi6UGGVoworERERl7IYNQ1zEsCcYZWenu7uZYjU2bJl8NBDZtVRZQEB5s5206c39aqqZxhm5U9VbXAREVXPD2puj9EtTp6ENWvIfWsD/9kZRDyxvMctFNIGC+YuVwZWvL3ho4+ab8DXGOrzNSgtg77XeyZPfF2+Scvi54s/5Q+39OH+m8LdvRwREZFmrabv9U06w0pEmlZzqxZxtMFVnkfVu3f1bXDN7TE2mawsWL+evLff4b8f+xFvn8R/WUc+/lgwKgRVDr6+TbT7oAerz9egiLQu3TuYW6Kmnclz80pERERaNgVWIi2Yqwd3N6byQ8D/7//MzyUl1d4G15weo8udOwf/+Q8Fb63lvS1W4kon8h9WkkdbLBaDmOtLueY6+Oc/LRQXe11y81Yd8JXjilZMEWk5urT3JdDfm/0Z59y9FBERkRZNgZVIC+ap1SKVd6gLCTEHpFe3y59hQEJC1eGBpz7GJpOfD5s2UfjWGt7fWERc8QTe5XXO0R6AG64tIfYXMGmShR49bBgGbNqkgK82FotZadaaq81EpGoWi4U+Xdvxw9Gz2O0GVmtL/0YjIiLiHgqsRFo4T6sWSU29NFwyDLDbobT0YnufY5e/994z3x8+DFareZ4jjOrZ0zMfo8sVFcH771P01mq2vnOOuIJxvMMr5BAIwLWDi5lyF0yaBKGhF/837wgK773XnO2VkdEKAz4RkUbQt1t7Pj98hqPZ+Vwe7O/u5YiIiLRICqxEWgFPqRYxDDOsclT3VDd7CszjSUlm8HTsWMVjBw7AyJFw6FDFSitPeIwuU1IC27ZR8nY8H68+RVzurazj72Rh7qB69cAiptwFkydDr17el9y8clBYWAhdu8KcOTB0aAsP+EREGlnfrmYV677jZxVYiYiIuIgCKxFpMjt3QkpKxVa0mnh5XRpWOSQlwSefwLBhjbY8z2O3w86dlL4dx/aVx4jPGc1a/swpOgFwVd9CfncXxMZCRIRPtZepLig8fhyWLoWHH1ZYJSJSF326tQNg3/FzjO7f1c2rERERaZkUWIlIk0lMBG9vs7rHGTVVYAFMmADffHOxNbAmledmeUJFUZVrwoBdu7CvjCNhRQpxp0awlsc5gfkLUf/IQh66EFL16ePr1P1UFxSWlJitljt3tuDKNBERF4js3A6rBfZnnHX3UkRERFosBVYi0mQiImoPoRxsNmjfHs6cqf6crCxzvtXevTWHT1XNzSo/1N0dKqzJ2+CKwj3MbBdPf+8DrM28kdU8zHG6A3BFWAH3TzOInWKhf3/nQqryagoKfXzM4wqsRESc5+fjRdhlbbVToIiIiAspsBKRJhMdbQZFlXeo8/Iy3wzj4nylyy6DBx6AJ56o/nqGUXuFUHXtcI6h7rWFXa7gWJMtcT+/L42jX9FednEtf8m6nyOEAhAeUsBj0wymTLUwcGCbBq2xpqCwqMg8LiIiddO3a3s2/XCcvKIS/H30I7WIiEhjs7p7ASItmWFAQgIsW2a+Nwx3r8i9LBazqik83AymAgLM95GRcPAgvP02tGtnnpebCwsWmJVWNXFUCFUnIcEMtapqh0tKMo83qeRkUmY9y5MH7uCnpRt4k7u5gzgW8jCZdMbLavDvf8OhtDb8+RkLV17Z8EDNERRWfi5tNnN3wOjohl1fRKQ16tO1HYYBB0/kunspIiIiLZL+HCTiIp7YhubgznlOPXvCvn2X3j+Yz9epU2aYVFxsfs5RfVVaWvX1aqoQSk01Zz05rlVZcbF5/PPPXfyaHD2KEb+aPa99RdwP/YgnliTmAeBLARbsGFgppA0B/ubjbczXwxEUVv567N3b/Ly7Z3mJiDRHfbqZOwXuP36WQZcHuncxIiIiLZACKxEXaMw2tMYOlzwhSLNYzBa+8m18CQlVDwYvLTXX2bGjGWbZ7ReP1VQh5HgNTp6seS0nT7qoNTAzE9au5celnxP3dQTxTOYAvwGgc/sCbLmllNi9KKRNhZvVp0XPma+R6oJChVUiIvXTp6u5U6DmWImIiLiGAisRF2isXdkaO1zyxHlODrUNBn/kEfj3v52vEHK8BtVVZjmUljbiTnlZWbB+PfuX7iT+s8uJMyazl18B0CWwgNlTSphyp40bbmhD//6XzvKqT4teXb5GqgoKRUSkfkKC/Gjna2Pfce0UKCIi4goKrERcoDF2ZXNFuNRYQZor1DYYfOhQePhh5yuEanoNKmvQTnnnzsF//kPi0u3EbetCvH0ie5gBwGXtCrh/cjFT7vJm2LA2eHldvFljtOh5cgApItLSWSwW+nRrx/6McxiGgUX/wxUREWlUCqxEXKAxdmWrKVw6dAheeQV+9au6BRKNEaTVlbMtjdXtIFi+6qguFUI1vQaV1bkNLz8fNm0ieelHxH8QRHzJBL7hFwAEtS1k5oRCptzty803t6l2aLyjRS8hAd57z/zcLbfA5Zc7vwxPDiBFRFqDPl3bsysli4yzBXTr4Ofu5YiIiLQoCqxEXMCZ8KU2NYVLpaXw61/DSy/VrT2wphCnoMDcva8x1bVdrTEHg1f3GlTm9GtSVATvv0/a0g9YvaktcUW3s4tFAHTwK2T6+AJi727DqFG+eHs7t8a0NPh//+/i433hhbq1fLojgBQRkYv6dDPnWO07flaBlYiISCNTYCXiAo0RvtRWIVRSUvfWr5pCnNJSMzxprOHr9WlXc2YwuLMVW1W9BoWF5ucNA3x9K74mYFY7VbhuaQl8/DFHX9vCmg024vLH8Rn/AKCdbyF3/TSP2On+jB7ti6+v65+fyhqjkk9EROqvT1dzp8B9x88xok8XN69GRESkZVFgJeIiDd2VzZkKobq2fjlCnNGj4eDBiscMo3FnH9XUrpaUVL92tboOoa/qNbjhBvj004qvSVoa9O1rXtfX2841hTuZ6L+J0hKDNXm3ksBfMbDS1qeIqaNzmTIzgLFjfWnT5tL7dFZjtPM1RiVfbRp7l0oRkZbkCu0UKCIi4jIKrETKaexfzhuyK1v5CqHExOp3u6tr61fPnuZueyNHQnFxxWONOfuopna1khL4/PNL76OmQCo0tH4VSZVfA8OoeNwwYMxog+CkXfyi9D94FxXzPmN46OyfMbDiZytm4sjzTLm3Hbfe6oO/v0+9n5PyX18HDza8na+x2ygra+xdKkVEWpoAXxuhwf7s106BIiIijU6BlcgFnvjLuaNC6JVXzJlVVVVaVdX6VVvwlpRktsRVDqyg8WYfRURUv0OfYcDLL8PcuRerncLD4d57zcCsqkDqX/9qeEVSSgoMGwbHjoGPt0G/kj1MbvMu03PPs5WR/IknKcWGjWLacY7zXu1557/ejB7t5FCqGlT++srPrz6ErEs7X0Mr+aqjHQhFRJzTp2s7tu7PpKC4lDbeXrXfQERERJyiwEoEz/7l3GIxdwN86SXnWr9qC94MA/LyzCHrVWms2UfR0dC1Kxw5UvXx48fNdWVkXJwvVVWA5gik3nuvYRVJKSkQFQW9i/czlw0ElmbzCcN4PHceJXjjRQkBnCOHQErw5iwdCPAzw62Gqu7rqyr1aedrSCVfdbQDoYiIc/p0a8/7e0+QmJnLgB4d3L0cERGRFsPq7gWIuIphmEO0ly0z31duBSvPmV/O3cnR+hUeboYzAQHm+4iIiq1f5YORoiLIzTXfO4K3lBRzVtNvflN1dU9jzj6yWGDOnOqDvpISM8xyrLOqsMrB50IXXnVBT2GhGcJV91obh5NZdtVCnij+I5Ec4kV+yx/5C+8zmnacA+yUYiOHIODighsrvKvu66s8i6Xq19RdHC2dVXEEhCIiAv26aY6ViIiIK6jCSlqkurb31TRvqbFa5BrKmdav2gad33STWTFU+bjFYj7+xpp95DB0qHndqoKmmgLEyoqK4JZbYN26S6vMvLzM9f72txVf6w+XHyXw4/X8598niE+6mvd4gELaYKWUQLLJIhA7XmQRDIDVCnb7xes2ZnhX09eXg9UKf/+7WU3n7rAKtAOhiIizHDsFao6ViIhI41JgJS1Ofdr7XPHLuSt2V6ut9au2YOTo0aorq1wVljiz02FtHMFRTMylA8YLC831lpaabx2KMpnCBi4/kM6vhw5kEzMpwA8rdjpaznDasGHHxhk6VrgPLy/o0eNie2JjDi6Hmr++HPz8wN/fM8IqaJodCEVEWoLQYH/8vL1UYSUiItLIFFhJi1Of2TuN/ct5Yw5wryr4cjzOymFYTYPOa2q5q29YUlso52hlHDYM0tKcv67NBm3aXBocVa4yy8uDP/02i9Gl79KLFPbTh5X8gjzaYsHO/4Sd5pe/9qJHLx9iYy/DXk1o1KOH+Vo5BsA3VsDo4Pj6qmm3R0+rWnL1DoQiIi2F1Wrhiq7t2J+hCisREZHGpMBKWpz6tPc15i/njTnAvargKyTEPJaefmkY5jhWV/UJSyqvrbDQHLI+Z47ZCugIfHr2hKeegtmzzZ3xatO1Kzz+OHz7LVx9NcyaZVaAOVgsEHPVOYYkbmTF80mMKOrNen5OLuYMkcs4SQk2bP6+zH6yE9Onm69JdYGRjw/s2GHeR2MPLi+/ZsfX14EDlx731KolV+1AKCLS0vTt1o7dR7LJPFdA53Zt3L0cERGRFkGBlbQ49W3va6xfzp2p8IqOrvl+HAPjY2Ph5EkzZHE8psOHKz4eMMOwMWPMf5efw+QML6+6hyXVhXJHjsCjj5qBYfmKssjI6iuLKrNYYO5cM0h6801zd8QtW6Bn53yKNrzHh//cT/xnl/OO/WfkEAjAZWRSghcF+HOKTuaFSi6+1pUDSS8vs+Kse3czrKpr1Vt9OL6+1q6Fhx6CU6fA19dchydXLbliB0IRkZbm4hyrcwqsREREGokCK2lxGtLe1xi/nNdW4fX553DvvdW3Czoqlw4frrmNrzzHUHXHPKe66NSp7mFJTbveGUbFnQn37nVulpWXl1nllJl5MaDzpojIgx+wrN/3pBZ1552S28ji5wD8T2gmk+/J5V9vBZCW1rnW19oTqoUsFpg0CSZOVNWSiEhL0qerY6fAswyL6uTm1YiIiLQMCqykxXH37J3aKrxeegmOH6+6XfDHHytWLtWFxVK3nffADNbi4yE0tG63c2bXu8ozw8q/JjabOX/KYjHnZ5WUmK2AGRlAaQkj+ZhB7OYUndho3MbGvJ8CcFX3k/xu2lli721PRERnAKbOdP619pRqIU9Zh4iINI7yFVYiIiLSOBRYSYvkymqa2gaN11Th5QhlqmsXXLKk+sql2jhbjVV+PeHh9QtNnNn1DirODKv8moSHm+ckJUFEbztZGxPYvvBrztCB//JTtvITwJxJ1ck7i98+HcQf/nDpX609oXJKRERatw7+3nTv0IZ92ilQRESk0SiwkhbLFVUszuz+V1OF1733mgPIqwp7LBbYtKn2yqWGKF/R1JCKs+hoCAuDgwdrPq/yzDCL5WKbXuIhgysLdxHx8efE/TeAtefHcpxhAHTkFMGc4gyXcYpO+FjgxhtrflyqWBIREXfq2609Ow6dpLjUjreXtfYbiIiISI0UWIk4qS67/1VX9bNzZ/WVSYWFsHlz3WdQ1cRmMweLz5kD1157cb0NrUKyWODPfzaHwlfXhljVMPfUFIOHbtpD6JGd5Bu+zGc06cwBIJjTdOYEmXTmNJdVeAyeuIOeiIhIeX26tWPr/kwOnzzPFRdmWomIiEj9KbAScZIzu/+Vr/CpquqntuHjdQ2rrNbqK7J8fc3d9v7854rBVE2VSnWRmwtt25rvq1J+mLuxbz+7/r6D//u3F3uMkfyHBwAI4gxdOU4GXTlDxwq3t1guti166g56IiIiDmVzrDLOKrASERFpBKpXFnGSY9B4VRyzmmrjaBcMD6/+Ws6y2SAkpPoKJ8OAW291XdBT0xwrb2945+/JnHn+NR7rspTIfjau+7/7+Lcxk7O0pzvpgJ0sgsmgG3DpIr284MUXzcq1ug6FFxERaWp9u5kh1T4NXhcREWkUqrAScVJtu/+Vn9VUE0e74B//CAsX1n9eVXAwbN9utiNWNeC9tja62obH16aqarHuHOUnlq342Eu4+45oDjIDgCBLFpcbaRylO1kEk0Vwrddv0wb8/VVZJSIizUNYx7b42Kzszzjr7qWIiIi0CAqsRJxU0+5/zsxYqhwQ3XILPP98/ddz5owZVi1dCjNnXjrgvaY2OmeGxzvzOP73f+GZ32TS//iH+FDAF8Z1LDfuhlLo0iab2SNT6PeTHvz20SCyioLq9PjqEgKKiIi4m83LSlSXAPYdV2AlIiLSGBRYiTippt3/apuxVFVAFBbWsPWUlJjh2b33mm1zn35ae7WUYUBCgjks/eRJc2ZWTcPjq3scWYezGMFWfIvPUcr/8Ba/AKA9Z7nnxsPc81gPhv0kEC+vQJYtu/iYnaVB6yIi0hz16dqeH46mc+Z8EcFtfdy9HBERkWZNgZVIHVS3+19NYVVNuws2dEdAx8D3Tz+9dMB75TWsXQsPPXQxqKruWpWHx5dd4+w5/nfIRww9mcV3XMUqJgHQjrP0JpFj9OC8V3u+ONme18dcfE5qaqUEcxfDNm0gPb1uIaB4roa2m7aWNYlIy9PnwrD1/RlnuSH8slrOFhERkZq4dOh6QUEBt99+O1FRUQwaNIixY8eSkpICQGZmJmPHjiUyMpIBAwaQkJBQdru8vDzuuOMOIiIiiIqKYt26dWXH7HY7Dz30EOHh4URERLB48eIK97lgwQLCw8MJDw9n/vz5FY4tXbqUyMhIwsPDue+++yipaps2kQsc1UjLlpnvHcPNHbv/TZ9uvq/tl97qdhdsaFjl4OV16RrLS02FPn1g8mTIyKj5fi0W2LSp3HXy80l75b/87co3uDbwAEtPjmc50zlEJBEcoi3nOEd7DhNBAX6Ull4MvRwcrZS2auLxtm1h61bz7eWXzfcatN58paZC374wcqQZkI4caX6cmqo1iUjL17fbhZ0CNXhdRESkwVy+S+B9993HgQMH2L17N7fddhv33XcfAPPmzWPo0KEcOnSI119/nTvvvLMsQHr++efx9fUlMTGRLVu28MADD5CVlQXAihUr2Lt3LwcPHuTLL7/kr3/9K/v37wdgx44drFy5kj179rB3717ee+89tmzZAkBycjLz588nISGBxMREMjIyWLp0qasfvjRTjfkLbk27CzaG/Hx4++2q11i+ussZhYXw4l+LuLv7hzw38E2uD/ieng/8lEe/v5u9Rl8iOUB7cjhPAIlEcp5Lt+329jZDL0eIBhd3RqxKcrI5zys62vkQUDxT+a+3oiLIzTXfO9pNq9vRsrWtSURarvIVViIiItIwLg2s2rRpw6233orlwm+fQ4cO5fDhwwDEx8cze/ZsAIYMGUKXLl3Kqqzi4uLKjvXq1Ythw4axYcOGsmOzZs3Cy8uL4OBgYmNjWbVqVdmx6dOn07ZtW3x9fZkxYwYrV64EYM2aNUyYMIEuXbpgsViYNWtW2TGR8mr7Bddur7ryqjq1tcQ1hvx88z4SE+H66+GTTy62QKWk1F7N5UUJN7KdX/AWV5V+zYqMUcz7YRrfM4ArfQ/Q0XqGPNpyiCs4S4car3X+vDlMvnzQB/B//1d1cOdoRUxIqNvzKp6numrC8u2mWpOItGQdA3zp3M6X/RmqsBIREWkol1dYlffSSy/xs5/9jNOnT2O32+nUqVPZsbCwMNLS0gBIS0ujZ7mtylx9rLKFCxcSEhJS9pabm9vQhy7NSE2/4CYlme1tdam8qq4lzmYzq46qa5Urz9sb/P3Nf1ss4Otb9XmlpXD8OIwYYa7r88+rr+6yYOc6PmMKK7mOz0ngRt7mTr5lEFewn25eJ1jwgj8HuILT9uDaF1lOcfGlQV9iYvXrttnMQfAtoWWrulbS1qCmakIfH/N4U/PENYlIy9anW3sOZJyj1N6KvgGIiIi4QJMNXX/mmWc4dOgQS5YsIT8/v6zqysGo9Ftd+eNNcay8uXPnMnfu3LKPQ0JCqj1XWh7HL7iFhZceKymBI0fMEMLZ3fVq213Qbodhw8zrVubYLW/OHPj2Wxg8GAYOhDfeMNsA8/OrfgyOcO3llys/DoPBfEsEiWTQlZ1E8wXX40MhURzgLB04TncO0Ac/H/j+++qfi/L8/c3HVFp6aUDjqGRxVIFVJS/PvI+67lroaaraDbJXL/N1Dg1t+UO/a6omLCoyjzc1T1yTiLRsfbu2Y8fBk6ScPk94pwB3L0dERKTZapIKq+eff55169bx3nvv4e/vT8eOHQE4efJk2TmpqamEXpiyHBoaWjacvSmOiZRX0y+4hlF9IFNTa5Fjd8GqBouHhZlBx+rV0LWrGRAFBJiBR8+eZogzdy7ExZnv77vPDHJqa/MrKTGHrHftYnCl9QcmsoZhbOd7BrKaWD7nOqI4SAhHKMKHA/TlON3Lbp+fDxs31hxW+fiYQ9/btzfX1bZt9ef5+ZmP1cur4jEvLzO4qfx4mlvLVk2tpCNHmoPvW0IFWU1qqibs3ds8rjWJSEvXp9uFOVYavC4iItIgLg+sFi5cyMqVK/nggw8IDAws+/zkyZNZtGgRALt27SIjI4OYmJhLjiUnJ7N9+3bGjRtXduzVV1+ltLSUM2fOEBcXx5QpU8qOLV++nPPnz1NYWMhrr73G1KlTAZg4cSLr16/nxIkTGIbBkiVLyo6JlFfbrnZVcezU98kn5ltV7WA17S5oscCkSXDsGHz0kRlqffihuYbU1IoBSGIi/PGPta8xgoP8rHQ9fTK3s88exVom8SnRRJJIL0syxfiwn76kczlQdanPqVPm2qq7H0dV1alTZrhVUyVLu3ZmCFU5mAoONsOsqjSnlq3aWklbw9BvRzVheLj52jmC14gI8/PuqCjzxDWJtFaHDh1i8uTJPPDAA/zhD39w93Jcpk/XCzsFavC6iIhIg7g0sEpPT+fhhx8mOzubm2++mUGDBnHdddcB8Nxzz/Hpp58SGRnJ9OnTefPNN7Fd+K34kUceIT8/n4iICMaMGcOiRYsIDjZn6EybNo0rrriCqKgohgwZwiOPPELfC1Odhw8fTmxsLAMHDqRv376MHj2asWPHAtC7d2+efvppoqOjCQ8Pp3PnzsycOdOVD1+aqap+wa1tl7/8fLNNb9gw8+1Xv6pfFU35UMtiqToAKS2Fgwfh178211h+baGk8DM2MJyPOUIoa0sn8FFRDDdfnsSTdx5i4YtejP1tX1LoRXUhVXl2uxmodO9+sUqqKiUl5uysrl2rr2T54x+h8tg4Ly/zmsXFVV+3ObVs1bYbZHOvIHNWTdWEWpOIexQUFHD77bcTFRXFoEGDGDt2bIWq8/qYM2cOYWFhWCwWfvjhhwrHDh06xA033EBUVBTXXnste/fuBWDjxo3ceeedLF68mOLiYj7//PMGrcFThXcKwGa1sO+4AisREZGGsBg1DXMSwJxhlZ6e7u5ltHqOXe/qMgPIMQD7vffMj2+5xQyEoPZrlb+/gwfhxRernxlVHS8viIw0fzl25j7LW7YMHnzQ3HWvKt26mXOv/v2nY7z3zLecLfHjM66nAD+slBLFQYKC4J0fIunc3UZqKowebVb21NZOWF7btuYv+ZGR5pqqm50VEABPPgn//vels7oWLIA776y6vdDHB7p0MQOv8uGczWY+T81lhlVCghlS1mVHyIAA87mdPt1lyxIRJ7Xk7/UFBQV89NFH3HLLLVgsFv75z3/y7rvv8v7771c4r6ioiKNHj9KrV68Ktz1x4kSFjWsAduzYQe/evYmJiWHjxo0MGDCg7NiIESO4++67mT59OmvWrOGFF17gs88+48yZMzz55JP4+PiQnp7Oz3/+87Iq+eo019dl7Is7OFdQws55I9y9FBEREY9W0/f6Jhu6Lq1TfUKmqtQ0zLrSz9AVbjNihFnF4vCXv5hVFTYbpKfXfC1HtVNMDKxZU/ewCsxg6PBhWLsWHn/84voLC81qpDlzYOjQS58XwzAHkRcUVH3dy8hkUMY3jPHx4TP7deTxUyzYieIgbWwlHCIKIvqyagt07m5er/Jz4azCQjOscgR9b75Z9XlFReZjefjhS1/z5curH97u42M+D1UFXVu2mOckJHj+sHJHK2lSUsXgzcur+oCwOVWQiUjz1aZNG2699dayj4cOHcqLL754yXk//vgjEydOZMOGDQwcOJC8vDzGjRvHqFGjmDdvXoVzhw0bVuV9ZWZm8s0335SFYRMnTuTBBx8kJSWFsLAwXn75ZQBmzJhB//79q13z6tWrWb16Nfn1+ebrAfp0bcc7u49xtqCY9m1qKdMWERGRKimwEpepT8hUFccueunp5r+d2UXOMMxqoqoCmvJtaZWv9eOP8OmnFcMRMMOm+vLyMgdtnzplBhmO+zxyBB591Axyyj8vjuft8OGKQUcHsriGr7DjxS6G8J4xFgy4gv34UsgBokj06kOny2BzfMU5WQkJ9QurwNwB0DFsvrpQpvwA6/JBn0NtO7VVF3SlpZltlQ39GmoKNe0GWVRkPpbqnjMRkab00ksv8bOf/eySzw8ePJg33niD8ePH8/rrrzN//nxGjBhxSVhVkyNHjtC9e/eyMQ8Wi4XQ0FDS0tLw9vbmiSeeAKBfv34VqrIqmzx5MpMnT262OzX36dYedh/jQMY5hoQFu3s5IiIizZICK3GJ8jumlQ9pagqZqpKSAtddB5mZlx4rPwOofDgCZkCTlOT8eh2DsXv1MnfWKx+OLFhQt2tVVlh4MayqzDAqDuD+8ceKz1tbznENX2HFztdcw1Z+AkAUB2jLefZzBQfoc/GCpXDyJOzZY36YlGSGP5s21X/9RUUwatTFoKi6UKamAdb1Cboa62uoKTlmJVUVvNX1ORMRcYVnnnmGQ4cOsWTJkiqPx8TE8MorrzB8+HBmzZrFU089Vef7sFT6H5tj+kSPHj1YunRpna/XHPXtdmHw+vGzCqxERETqSYGVuERNO6ZVFzJVlpICUVHVD+QG89jnn1e8VmoqxMbWbU6TY21VVXE99FDdr1WeYdR+e8fzsmQJHEvK57qSr/ChmN0MYjs3AxDJQSI5yEGu4CBXVHut0lJz9hWY1VElJeaspPpytCWWD4qqCmVqCl5qqj6qLrRpjK8hd6iqwqy6IEthlYg0peeff55169bx4Ycf4u/vX+U5p06d4rHHHuP3v/898fHxbNu2jeHDhzt9H5dffjnp6emUlJRgs9kwDIMjR44Q2sp2OejbtR0A+zLOuXklIiIizZdLdwmU1qumHdN8fMzjNTEMsw2wprDKcd68eWaw4fh4zBizyqiuDMMMq8orKTGv1ZCtCRztdDWxUcR1xmdsfvQjvEvy2MmNfMwIOnKaa/mCIE5ziCi+ZgjnaO/0feflmcFQTk791+/gqELbubPiboblWw9rUted2hr6NeRp6vOciYg0loULF7Jy5Uo++OADAgMDqzznxIkTjBw5kgceeIBnn32WjRs3MmPGDLY4Bgo6oXPnzgwePJgVK1YAsHbtWsLCwggLC2uER9F8dGrnS3BbH/Zrp0AREZF6U4WVuERtM4tqGzS9dq0548kZpaVmtUp6+sWqnIZURFVW09DshrBSwmB2045z/Eh/Pim+HoqhN0lEcZAkepNIZKPcV2Otv6Tk0oq28mobsl9V9VF1Gvo15OyaXHVbERFPkZ6ezsMPP0zv3r25+WazatfX15cvvviiwnkFBQU8/vjjTJ48GTDnTG3evJm9jq1uy5k9ezYbNmwgIyODUaNGERAQQOKFvyS8+uqrTJ8+nWeeeYb27duzfPlyFz9Cz2OxWOjTtR3fHcnGbjewWvXNQ0REpK4shtGQ2pHWobluqexOhmEOy65qZlFERM3zhwwDunc3Z0nVxT//Cd9+C2+/Xb8d/arj7W0GPpWrr+rHzpXsIYgs9tOXE3QFoCfJ9OAYyYRxnB6NcUeX8PeH9u3h9GmwWs3HEx5e9UDwmoSGXqxoKx/mhISYLYONNSC9IV9DDg0Z/N9YmwaISPOg7/WeqTm/Ln/6z15e25nMjkduJrRj1S2YIiIirV1N3+tVYSWNqnxFyoIF5u56dR00vXZt3cMqgF//2ryfxt4BOzTUXLuzFV+XMujLXjpxkkNEsYdB5nVJJYZPOMLlpNKLVHo11pKrVFIC8fHmc1/TQPDCQvN1rC7AysgwX6PKr62jpbK0tHEGpNdn7lV5DRna3hwHvouIiGfp082cY7X3+FkFViIiIvWgwEoaTVUVKWFh8NZbkJvrXEuVYZhDzuujtLTxwyowd/gbPRqOHq1LlZVBBIfoRgZJhLOP/uwDQjjCjWznGN1JIoI0mq5U5/LLL85Oqm0g+HvvwTPPVH0dHx/zNXLsfFhd2x40fEB6Q4aVN2Roe3Md+C4iIp6jb9cLOwVmnGXsgK5uXo2IiEjzo8BKGkV1FSmHD8P8+c5XpOzcabaseZKcHFi92rlze5JMCOmk0ZNEokgkiu4cZRjbyKQz++lLOpe7dsH1UH62lGHAnXdWf25BgVmF5WwLoWNAen0DnrrMvSrPMbS9sLDua2rIbTX3SkREACK7BGC1wP7j2ilQRESkPhRYSaNorIqUxERzRlFtuwN6ku6k05NUjhJS1trXlePcxMecIZjvGcgxF8ylcsyhctaRI869Djt3wokT1R+328HX1/nXqKYB6a4MdxoytL2+t9XcKxERcWjj7UWvy9qyP0M7BYqIiNSHAiupl8pBw6FDzlWklL9deLh5/NAh+OEHs5KpQwfXtPU1tk6coDeHOUFXUujFMULozAlu5iNy6MBuriKDbi5dw2WXQXZ2zS155Tleh+jomkOimqqLwHwNCwqcu0+bzZw5FR196TFXhzvR0eb1qhraXt2aGnJbzb0SEZHK+nZrz3+/P875whLa+urHbhERkbrQd06ps6qChq5dqw84HBUp5W9ns0FeXtOuu6GCOE0kiZziMg4Tzkm6cBknuZmtnKct33A1HzOiQffh7W1WLxUVQUAAnDlT/bm//KU5EP6hh5yrtCosNK/Zt2/NIVFN1UVgBjMAXl7m3DAHLy/zzTAuPobqBqQ3RbjTkKHt9bmt5l6JiEhlfbu1Z+Oe4xw8cY7BoUHuXo6IiEizosBKnGYYkJAAsbFw8mTF3eCOHTNb1Cq3qXl5QXCw+bnRo81f3Gsb1O1J2pFDFIfIJpAkIviSjgRzmhFspRAfvuIaPmZk2fkzZ8J//2vO4fL2dj6Us9nMirOHHoJvv4WrrzZb+J59tvrbWK3g719zNVR53brBH/946WtQOSRyVBcdOlR9EObvD+3bm4Fa+TBn82Zz3bW1+DVVuNOQoe11vW1D5l6JiEjL1KeruVPg/gwFViIiInWlwEqc4qiOqtwi5VDdAO7SUjh7Fm6+uW7zltzJn1yu4CDnaEcikXzNNQSSxUg+pAQbu7iGj8qFVOUZhrmb4CuvwGOPOX+fISHmTKi5c81w4803oUuX6s+3WOCWW8z35aucajr/Zz+Df/+79pDIUV00bBikpVV9vZISiI83z60c5vTsWXsw05ThTn2Httf1tg2ZmSUiIi1Tn24Xdgo8rjlWIiIidaXASmpVuX2rrppD658v+VzBAfLx4xBX8C1X046zjORDDOArrmEro2q9zoYNsG2bWWVUl8HxR46Y78tXrR09alZeVfWc9+59MUTp3RsOHqz5+t7eZkWUsyFRz55mK1xYmLmO8mGjY46TI9yqTxBU13CnOey815CZWSIi0jJ179CGdm1s7MvQToEiIiJ1ZXX3AsTzVde+1dzZKKIfPxDFAQrxYw+DOEYPRrCV0WzGh0K2MoqPGMVZAp265unTZrVSXXc5LC29tFLKbjefc0cwY7GYLZahofCrX5mvC8D775uBSLWP80JgcsstdQuJrFb45BOIjDQDrYAA831EBCxYAMuXmy2ihnGxXXTZsoufq4kj3LFVisyrCndSU825WyNHmi2TI0eaH6em1nwfTc1RmRYefunzVdvMLBERaZksFgt9u7Zn//GzGLV9cxQREZEKVGEltfr88+Yzc6o2VkqI4hB2LBwiir0MwI88RrCVNhTwDYOrbfdzl/I/31oskJEBTz1VcWB6YqIZFK1aZb6dO3fp4PPLL6+6AshqNYfm33DDpfddeY5TQIA5B+sXv7g4uyokxDw3Pd353f6cHWre3Hbea8jMLBERaZn6dGvHlylnOJZTQI9AP3cvR0REpNmwGPpzT61CQkJIT0939zLcwjDMX8IdLWvNk50IEvHCziEiseNFG/K5gU9py3l2cxVHqCZZ8XBeXtC5M8TFXWzRq659zjBg7VqzSunkSbOCyzDMY47KpppCJsMwK5ucaQ212cz7ri1Qqq3VLyEBRo2qvo1x61YNMheRxtGav9d7spbwurz9RRqPrf+epfdcw8i+NQyoFBERaYVq+l6vCisBqg8Odu6EEyfcvbr6MAgjGV+KSCSCRKLwoZCb2E57cviBAR5XSVUfpaVw/DiMGGG2ojkCp8qDwh1D85OTzTlW5dsPDcNsYaytaqkuraHO7vZX21Bz7bwnIiLNXZ9uF3cKVGAlIiLiPAVWUiHMKN/StXkz/Pe/tc8j8hwGl3MEf/I4TG9S6I2NYm7kEzpyir3042NuBlpef1ZJiRneVBU4VddWV9U1qgqZHGHmsmVm+6CzGiNQai477zWHofAiIuIeV3Rph8UC+7RToIiISJ0osGpl7HZYsgS++Qauvhruv7/qMCMxEaKi6j483B26cYz2nOUwvTlCKF6UEM1OupDBQaLYxnAaM6Tq3h38/CAtzbOen9JS83WsHDjVpTKqcshUPsz08oL8fOfX0xiBUn123mvq8Ki6wLem9koREWk92vra6Bnsz37tFCgiIlInCqxakZ074eabL4YsS5fCr39t/jJfOcyoatc6T9KJEwSRRSphHKc7J+hCNDvpzlGS6cUn3Ijhok0wMzPhgw/MQOK55zyrAq2kBA4dqhhY1dRWV1n5kKlyZVZd1BQo1YWzw9kdmjo8am5D4UVExD36dG3P+3szKCgupY23l7uXIyIi0iwosGol7PaKYZVDXYMIdwriNJdxiiOEcpIunKITN/ApPUkljVA+5QZKm+BLuqTEfC59fDwrrAJzPZWroGpqqyuvcshUW2WWt7d5f6Gh5sfldwmsLlCqD2d33nNHeFTdc+TsDC8REWkd+nRrx+YfM0jMzGVAjw7uXo6IiEizoMCqlViyxLPa15zVnmy6kEk6IWTRkSw6MpTPiCCRo3QngRvZiXsSAWdCoKZmsZjtiuVV11bnOL9t26pDptoqsxw7DHp7m/PO0tNd14ZX23B2cE94pKHwIiLijD5d2wPmHCsFViIiIs5RYNVKfP21u1fgvLacoysZHKc7ZwnkLIEM4Uv6sI9MOrOd4XzO9e5eZp05Bpbb7a67D5sNIiMrfq66trpeveDPf4Zz58wdBgE++uhi4FRbZZYjGEpKgltuMSuY3BnOuCM8ai5D4UVExL36ltspUERERJyjwKqV6ODhf8xrQx7dOc4JunCediTRjv/hK/rzA2cI5mNGsItr3b3MevHzM+eB9e4N//u/MHWqa+aDeXlBt27mDCuoWOVUU1tdTbtEVleZVZ6ntL+5Izyqz1B4ERFpfS4P8sffx4v9GdopUERExFkKrFqJAQPcvYJLeVNID45ymss4R3sOE85VfMtgdpNDez5iJF9zjbuX2WAjRsC8eRfDi4gIOHCg6nO7doW4ODNI+uIL+Mc/4Pjxqgfjl+flZb4dPw5z5lQ9bLyqtrqa5j7dcosZWo0da4ZZFkv17YGe0P4WHQ0hIWZ4Vtnll7smPKrrUHgREWmdrFYLV3Rtx77j5zAMA4u+QYiIiNRKgVULYxhVV9FERZlVH+4esm6jiB4c4wxBnKMDKfRmAN8zhC85T1s+YiTfMZihQyF3F+DBOxU668orKwY5W7aYIVblYCU83GzJcwwxv/FGePhh8/VctgzeegsKCi69vo8PBATA2bPm6+uYVebMsPHa5j6lp1+szNq0CZ5/vupZaK25/c3ZofAiItK69enanm/Tsjl5rpDO7du4ezkiIiIeT4FVC1Jda9eWLeYv0OHh1Vf2uJKVErpzjHO0J4dAUgmjD/u4gTUU4sNHjOR1Zla4zd69rmmbA7MSqTGu7e9vBki1zaS65ZaKH/fsaQYbCQnw3nsXz4mJMUOOqkJHgDffrPr6drs5h6o+w8adnfsUE2OuY906z21/27kTjh6t+tiRI65tWXRmKLyIiLRu/S7MsdqXcU6BlYiIiBMUWLUQNbV2OapsFiyAyZObakV2unOMPNqSTRDphBLBISaxhlKsfMQIXqsUUpV31kUjHmy2hg899/IyW/XatoXz5+HBB6s/t2NHM/SxWCpW3VgsZgXVjTdWPL+u86RsNrjsMsjNrbryqbZWvbrMffL09jft2CciIp6sTzdzp8D9x89yU1QnN69GRETE8ymwauYc1TibNpnVNDVV2eTmXgxZXLQaunKcQtqQRTDHCKEXh5nEGgC2cRNLuddVd+6UxmiJtNnMSp4//9n8eOHCqucmAeTkVD9TqrK6zJMqHxYtWAC/+EXV16ytVa+uQ8M9uf1NO/aJiIgnu6KrdgoUERGpCwVWzVj5ahyLpeoKG7hYXRIRUf059WfQiUxK8CaLYDLoTiip/Jy1eFPMJ9zIv7kX8IBEo5EUFpqznNatMwOojz6C0aPN0MpiuVjBZRhmCJSba35c20ypusyTqtwuWN+d6upTNeWp7W/asU9ERDxZ+zbe9Aj0Y99x7RQoIiLiDAVWzVTlapyaOKpLHL/QJyY2fIZTMKcAC2foyEm60IN0fs462pDPZ1x/oZKq5YRUlRUXVwyg9u+/GCTl5cFvf3tptU9NM6UMw6ySq07leVKVb9+QVj1PrpqqC09vWRQREenbrR3bD56kqMSOj83q7uWIiIh4NAVWzdTOneYv5bWFVVYrdO0KN9xg/sK+ebO5Y2B9AqtAsvCilNNcxhkuoyvHmcFS2nGWL7mW15iBQev54atyAOV4W7bsYlhSWVWzlByVcjWFj7W1tDU0dPLUqqm6ainhm4iItEx9urbnw32ZHD6VS5+u7d29HBEREY+mwKqZOnTIufY+w4Djx6FfP7PKJD29bvfTjhx8KOY0l5FNEJ3IZDqv0ZHTfMPVLOceSlvxl1FVAVRdZik5UynnbEtbSwmdnFHVTorlB9q3ludBRESalz4Xdgrcf/ycAisREZFatN6koZnLzzd/aa+NYVRsX3v0UbPqqiZtycWPfE7RiXN0IJjT3MPrdCGT77iSt7iLYnwa54HUQWAgfPMN3HQTHDnS5Hdfpaoqn+oyS6m6uVUO3t4QHq6WtvKq20mxpoH2IiIinsARUu3LOMvt9HDzakRERDybAqtmys/PDDCcCa3gYvtafv7FoeDltSGPAM5zik6cJwBvipnGG4SQzo/0YxV3UEibxn0QdfSvf5nBxMqVZmhVl7ZGq7Xqx90Q1VU+1WWWUmKiGUoVFl56fV9fmDvX3I1QYZWppp0UaxpoLyIi4gnCOvrja7Oy77h2ChQREamNywcOzZkzh7CwMCwWCz/88EPZ5zMzMxk7diyRkZEMGDCAhISEsmN5eXnccccdREREEBUVxbp168qO2e12HnroIcLDw4mIiGDx4sUV7m/BggWEh4cTHh7O/PnzKxxbunQpkZGRhIeHc99991FS2wAoDxYZaQYmdeHjYwZdvXtf+JgCOnIKgAL8KcSXX7CCP/K/jOID1vFz/sJjvMvtbg+rAObPN0OnmTPrdrvLL4fOnRtnDd7eEBBgPpcREdVXPjlmKW3dCi+/bL7fuxdCQyueV1P7oGHArbcqgCmvtp0Ud+50y7JEREScYvOyckXXduzXToEiIiK1cnmF1aRJk3j00UeJqTRQZt68eQwdOpTNmzeza9cuJk2aRFJSEjabjeeffx5fX18SExNJTk7m+uuv5+abbyYoKIgVK1awd+9eDh48SE5ODldffTUjRoygT58+7Nixg5UrV7Jnzx5sNhvR0dHExMQwZswYkpOTmT9/Pt9++y2dO3dm/PjxLF26lPvvv9/VT4FLREebwVPlHf9qqiQqLIQ9XxfRoeQscBlFtKGQYqbyNlEc5DDh/IefkUNgUzyEOktMhN/9zqxacra6ymKBX//aDJAmT27Y/fv4wMMPm0PrnRnm7cwspbq0D0rNFWlVzRMTERHxNH26tmNPeg6ncwvpGODr7uWIiIh4LJdXWA0bNoyQkJBLPh8fH8/s2bMBGDJkCF26dCmrsoqLiys71qtXL4YNG8aGDRvKjs2aNQsvLy+Cg4OJjY1l1apVZcemT59O27Zt8fX1ZcaMGaxcuRKANWvWMGHCBLp06YLFYmHWrFllx5ojR9tZRIT5i7qj6icqygw6yldfeVFMR05RUmznxUU+/JDkRyxxLO/1JH+7Jo6PrT/hTzzFCqbVK6zy8qp9LpazarpOaSn84x/ODZt38PaG666DiRPhiivMtTp7f5U5Kp6mTzdDkcaofHK8juHhFV/Hmqq3WrO6DLQXERHxRI45Vvsz1BYoIiJSE5cHVlU5ffo0drudTp06lX0uLCyMtLQ0ANLS0uhZbnqyq49VtnDhQkJCQsrecnNzG/qQG4VhQEICLFtmvg8Nrdh29uGH5pynu++GDgGldOQ0FuyU4s152jKB9cRFPk7mX5cTd/RG7j78NG1m38t5/0613ndVAgNh+3azqqW2ljuLxQzRKgdG5fn6wh131Hwdu935uV3lq5SqC/hCQsz3zggPd03Fk7Ptg3KxIq1yO6wq0kREpLkYHBoIwNKEZAxnf6gRERFphdw2dN1SqXSk8jfs8seb4lh5c+fOZe7cuWUfV1Uh1tRSUsxB48eOmVVDpaUXd0aLiYF27WDsGDtFmdlkGx2w44UPAfyM/zC+yxdMeqAz7e++HcImVrhuTRUrtfnvf+GGG8x/x8fDiBFV73ZntUKnTnD6dM2tfIYB118Pb7/tfCjl4OV1MQyrbsi5IxjaudMM2SIi4NAhmDOn5ufAYjGvtWABLF/uXDtgXTnTPih1G2gvIiLiiQaHBvHzwT1Y9+1R3voijbuGaotbERGRqrglsOrYsSMAJ0+eLKuySk1NJfRCSUloaCgpKSkVjt16660Vjg0ZMqTa2zk4e8yTGQasWWNWHjnCHkcodOgQXD/UYFCvbN7/rB2l2PAmgFt4j2gSyCaYPb1v55eJ46v9Rf6GG6BrV0hPrzj7qrYdCC0Wc/i5Y1e2mBizAqmqWUzdu0NGRtVhVvnzevcGf39zMHxeXs3Pi8ViBmF+fhcDi82b4ciRi2FUVaFSVcFQdWGVl5f5vI8bB48/Dr/4xcWAxBEW9tTPmE2uquCxsQNEERERV3p6fH++TDnDgv/uZWjvjkR0DnD3kkRERDyOW1oCASZPnsyiRYsA2LVrFxkZGWWD2csfS05OZvv27YwbN67s2KuvvkppaSlnzpwhLi6OKVOmlB1bvnw558+fp7CwkNdee42pU6cCMHHiRNavX8+JEycwDIMlS5aUHfNUqanQpw/ExlauTDJoTw4WewnHMyy8/1k7RvEhzzCPR/grqfTkMf7CX3mUrUei2Lnz0nZCwzCv37cvHD16Maxy/NJfW4WTYZi7siUkmG/Ll5sVSL17XzqL6a67ap475eV1cWZTZGTNwZaDtze89FLFFrqePc0gqi4zpmpqMYuMNB/X/PnmYy0qgtxc831SEowdW/dKMGkcjuCxMeeJiYiINJV2bbxZGDuIohI7v4n7lqKSanbMERERacVcXmE1e/ZsNmzYQEZGBqNGjSIgIIDExESee+45pk2bRmRkJD4+Prz55pvYLqQGjzzyCDNmzCAiIgKr1cqiRYsIDg4GYNq0aezatYuoqKiyc/v27QvA8OHDiY2NZeDAgQBMnTqVsWPHAtC7d2+efvppoqOjsdvtjBgxgpkzZ7r64debYZhtT0lJFz8XwFny8acUG7kEcDMf8xPeJ+yKNjx/YByP8Reg4m/uxcXw6adw770VW6jCwiA/36xIqny/zrLZzDDtzJmKlUdvvWUGOxERZgVXWFj117XZzEHqv/qVGTpcfrl5jcq7H1bWtevF2zREbS1mn35qtmNWDtFKSswQa+dOtfGJiIhI3V3bK5hfDQ9n0cdJ/GPrQR4Z08fdSxIREfEoFkPTHmsVEhJCenp6k97nhx/CLbeAb0kuhfhSgjcW7AxjB7ewiRJsbOKnfMb1TI61Eh9f/bUcs53KB0BWa8UWwPry8qp4XZvNDKocrYIJCTByZPVtd6GhZiBUPnhKTYWhQ802wqpYLPC3v8HDD5tBWGO0hlV3nWXL4KGHzACusoAAs8Jr+vS635+IiHgWd3yvl9q19NelqMTOxFc+5YdjOcTddz3X9gp295JERESaVE3f6902dF0uVVBgzmGKX5bHO/+1UVLiQwkBRJPAbWzEi1Le4xYe4y/Yubjd3rlzNc+cqqpSqaFhlSPwqnztkhKzKsxReZSYeLFqqTKLxRx4Xjlg6tnTHOI+cmTVrYQ2G1x3nRlsVa6Mqu9sqeqGntc0lL6oyDwuIiIiUh8+NisvTh3ET1/6hN/G7ea939xI+zbe7l6WiIiIR3DbDCsxFRXBxo1wd2w+XYIKmTABVm7w56qSr3mGP/B3fk17zvIEf+JR/sbHjKgQVgF07HjpDCZXCwiovpKppMQcCA81Bz6O4KkqMTFmW15Vs6XCw81WQ0fLpCtnS9U046p3b/O4iIiISH2Fdwrg8Z/242h2Pk9t+NHdyxEREfEYCqzcxDDgvnsK6RJUyM9+Bm+u9iOqYA9/s/2BlJ/O5tO1GayMfJJHbP/gPW6lGJ9qr3XddWZ4Ym2iV9Pb29whsLpQyDDM+VhQc+ATHl594OOYLRUefukQd2dnSzWG2tahYd8iIiLSUHdeF8qIPp1Z9+1R/vPdMXcvR0RExCOoJdBNLBgcif+MsIIOTPFaw+SbTxM+czjc9kczFQH+8z9mFdGhQzW38Pn7m+HJjTdeOkS9Pry9zdCptPTSUMoRNA0YUH0bosUCfn4X/13TUPOaAp+ePWHfvqpnS330kbnOwsJLb+fjY57fWMPQa1qHiIiISENZLBaem3glY1/cwR/Xf881YUF06+Dn7mWJiIi4lQIrd7FYWPe3JPwCvOD2RyAw8JJTHEHJww/D3/9e/aUKCsxzU1LMaqb09PrNqPLygshIc47WkSPw+efmUPGMjEuDprQ0M7yqbsZUZOSlj6M+gY+nzJaqbh0iIiIijaFTO1/+Oul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      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set our initial slope and intercept\n",
    "m = 5.\n",
    "b = 1000.\n",
    "# batch_size = 60\n",
    "# set a learning rate for each parameter\n",
    "learning_rate_m = 1e-7\n",
    "learning_rate_b = 1e-1\n",
    "# use these to plot our progress over time\n",
    "loss_history = []\n",
    "\n",
    "# we run our loop N times\n",
    "loop_N = 30\n",
    "for i in range(loop_N):\n",
    "   \n",
    "   # convert panda data to numpy arrays, one for the \"Ground Living Area\" and one for \"Sale Price\"\n",
    "   data_x = data['GrLivArea'].to_numpy()\n",
    "   data_y = data['SalePrice'].to_numpy()\n",
    "   \n",
    "   # update our slope and intercept based on the current values\n",
    "   m = updated_m(data_x,data_y,m,b,learning_rate_m)\n",
    "   b = updated_b(data_x,data_y,m,b,learning_rate_b)\n",
    "\n",
    "   # calculate the loss value\n",
    "   loss_value = np.mean(loss(data_x,data_y,m,b))\n",
    "\n",
    "   # keep a history of our loss values\n",
    "   loss_history.append(loss_value)\n",
    "\n",
    "   # print our progress\n",
    "   print('[%03d]  dy_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f    loss: %f' % (i,m,b,m_calc,b_calc,loss_value))\n",
    "   \n",
    "   # close/delete previous plots\n",
    "   plt.close('all')\n",
    "   \n",
    "   # create a 1 by 2 plot grid\n",
    "   fig,ax = plt.subplots(1,2,figsize=(18,6),dpi=80)\n",
    "   # lot our usual output\n",
    "   plot_data(data_x,data_y,m,b,ax[0])\n",
    "\n",
    "   # here we also plot the calculated linear fit for comparison\n",
    "   line_x = np.arange(data_x.min(),data_x.max())\n",
    "   line_y = line_x * m_calc + b_calc\n",
    "   ax[0].plot(line_x,line_y,'b-',label='calculated')\n",
    "   # add a legend to the plot and x/y labels\n",
    "   ax[0].legend()\n",
    "   ax[0].set_xlabel('square footage')\n",
    "   ax[0].set_ylabel('sale price')\n",
    "\n",
    "   # plot the loss \n",
    "   loss_x = np.arange(0,len(loss_history))\n",
    "   loss_y = np.asarray(loss_history)\n",
    "   ax[1].plot(loss_x,loss_y)\n",
    "   ax[1].set_yscale('log')\n",
    "   ax[1].set_xlabel('loop step')\n",
    "   ax[1].set_ylabel('loss')\n",
    "   plt.show()\n",
    "   # gives us time to see the plot\n",
    "   time.sleep(2.5)\n",
    "   # clears the plot when the next plot is ready to show.\n",
    "   ipydis.clear_output(wait=True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In Class Exercises\n",
    "1. In AI, datasets are often very large and cannot be processed all at once as is done in the loop above. The data is instead randomly sampled in smaller _batches_ where each _batch_ contains `batch_size` inputs. How can you change the loop above to sample the dataset in smaller batches? Hint: Our `data` variable is a Pandas `DataFrame` object, search for \"how to sample a DataFrame\".\n",
    "2. As described above, learning rates that grow smaller over time can help find and get closer to global minima. In the loop above, our `learning_rate_m` and `learning_rate_b` are constant through the process of minimizing our parameters. How could you change the loop to reduce the learning rates over loop iterations?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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