Chapter4.ipynb

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   "source": [
    "# Chapter 4 - Training Models"
   ]
  },
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   "source": [
    "## Signs Used in This `IPythonNotebook`\n",
    "- I have Used **Exit** Heading for Writing a Paragraph or a Text That Does't Fall under any Heading.\n",
    "- I have Used **Bold** Font to Highlight a Name or an Important Text.\n",
    "- I have Used `This` Type of Highlighter for Programming name or a Small Code.\n",
    "   - For Example :- `python`, `numpy`, `ndarray`, `pandas`, `DataFrame`, `loc`, `iloc`\n",
    "- I have used *Italic* Font For Some Important but not so Important Text."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"4.Training_Models\"\n",
    "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
    "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)"
   ]
  },
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   "source": [
    "So Far We Have Treated Our Machine Learning Models Like Black Boxes and Many of You Have Wondered that What We Can Do Without Knowing Even a Little Thing about How Things Work Under-The-Hood However Knowing How Things Work Can Help us in Many Different Ways One of Then is *Fine Tuning* Models. But in This Chapter Finally We are Going to Look at **How Things Work Under the Hood**."
   ]
  },
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   "metadata": {},
   "source": [
    "## What We are going to Learn.\n",
    "- Linear Regression\n",
    " - The Normal Equation\n",
    "  - Computational Complexity\n",
    "- Gradient Descent\n",
    "  - Batch Gradient Descent\n",
    "  - Stochastic Gradient Descent\n",
    "  - Mini-Batch Gradient Descent\n",
    "- Polynomial Regression\n",
    "- Learning in Curves\n",
    "- Regularized Linear Models\n",
    "  - Ridge Regression\n",
    "  - Lasso Regression\n",
    "  - Elastic Net\n",
    "  - Early Stopping\n",
    "- Logistic Regression\n",
    "  - Estimating Probabilities\n",
    "  - Training and Cost Function\n",
    "  - Decision Boundaries\n",
    "  - Softmax Regression"
   ]
  },
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   "source": [
    "# Linear Regression\n",
    "This is the Main Equation in Which **Linear Regression** Model Relies on.\n",
    "$$\n",
    "\\hat{y} = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\cdots + \\theta_n x_n\n",
    "$$"
   ]
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    "### Equation 4-1\n",
    "Let's say we have a dataset of housing prices in a certain area, and we want to predict the price of a house based on its size (in square feet) and the number of bedrooms. We can model this problem using linear regression, with the price of the house being the target variable and the size and number of bedrooms being the input features. \n",
    "\n",
    "Using Equation 4-1, we can express the linear regression model as:\n",
    "\n",
    "$$\n",
    "\\hat{y} = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2,\n",
    "$$\n",
    "\n",
    "where:\n",
    "\n",
    "- $\\hat{y}$ is the predicted price of the house,\n",
    "- $x_1$ is the size of the house (in square feet),\n",
    "- $x_2$ is the number of bedrooms,\n",
    "- $\\theta_0$ is the intercept term (representing the base price of the house),\n",
    "- $\\theta_1$ is the weight of the size feature (representing how much the price of the house increases per square foot),\n",
    "- $\\theta_2$ is the weight of the number of bedrooms feature (representing how much the price of the house increases per additional bedroom).\n",
    "\n",
    "To train the linear regression model, we need a dataset of labeled examples, where each example consists of the input features (size and number of bedrooms) and the corresponding label (price of the house). Let's say we have the following dataset:\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "| Size (sq. ft.) | Bedrooms | Price ($) |\n",
    "| --- | --- | --- |\n",
    "| 1500 | 3 | 220000 |\n",
    "| 2000 | 4 | 300000 |\n",
    "| 1200 | 2 | 180000 |\n",
    "| 1800 | 3 | 240000 |\n",
    "| 1600 | 3 | 210000 |\n",
    "\n",
    "</div>\n",
    "\n",
    "Using this dataset, we can estimate the values of the parameters $\\theta_0$, $\\theta_1$, and $\\theta_2$ that minimize the difference between the predicted prices and the actual prices of the houses in the training data. We can then use these parameters to make predictions for new houses.\n",
    "\n",
    "For example, let's say we want to predict the price of a house that is 1700 square feet and has 3 bedrooms. We can plug these values into Equation 4-1 and use the learned values of $\\theta_0$, $\\theta_1$, and $\\theta_2$ to compute the predicted price as follows:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\hat{y} &= \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 \\\\\n",
    "&= 150000 + 100 \\times 1700 + 50000 \\times 3 \\\\\n",
    "&= 425000\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "So according to the linear regression model, the predicted price of the house is $425000. Of course, the actual price may differ from the predicted price due to factors not captured by the input features, but the linear regression model provides a useful estimate based on the available information."
   ]
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   "source": [
    "### Exit\n",
    "In *Chapter2* We Saw a Most Common **Performance Measure** which is `RMSE` so Now According to *Equation 4-1* We have to Find $\\theta$ Values Such That We Can Reduce its `RMSE` But it is Simpler to Minimize `MSE`(Mean Squared Error) and We can Compute `MSE` by Using *Equation 4-3* Which is Explained in Next MarkDown."
   ]
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    "### Equation 4-3 \n",
    "It represents the mean squared error (MSE) cost function for linear regression. The MSE measures the average squared difference between the predicted values y_hat and the actual values y in the training dataset.\n",
    "\n",
    "$$\n",
    "\\text{MSE}(\\mathbf{X},h_{\\boldsymbol{\\theta}}) = \\frac{1}{m}\\sum_{i=1}^{m}\\left(\\hat{y}^{(i)} - y^{(i)}\\right)^2\n",
    "$$\n",
    "\n",
    "- $\\text{MSE}(\\mathbf{X},h_{\\boldsymbol{\\theta}})$ is the cost function that we want to minimize. It takes as input the training dataset $\\mathbf{X}$ and the linear regression model $h_{\\boldsymbol{\\theta}}$ with parameter values $\\boldsymbol{\\theta}$.\n",
    "- $m$ is the number of instances in the training dataset.\n",
    "- $y^{(i)}$ is the actual value of the target variable for the $i$-th instance in the training dataset.\n",
    "- $\\hat{y}^{(i)}$ is the predicted value of the target variable for the $i$-th instance in the training dataset, based on the model's current parameter values.\n",
    "- $(\\hat{y}^{(i)} - y^{(i)})$ is the difference between the predicted and actual values for the $i$-th instance.\n",
    "- $(\\hat{y}^{(i)} - y^{(i)})^2$ is the squared difference between the predicted and actual values for the $i$-th instance.\n",
    "- $\\frac{1}{m}$ is a scaling factor that averages the squared differences over all instances in the training dataset.\n",
    "\n",
    "In other words, Equation 4-3 computes the average squared difference between the predicted and actual values for all instances in the training dataset. This cost function is commonly used in linear regression because it is a convex function, meaning that it has a single global minimum that can be found efficiently using gradient descent or other optimization algorithms."
   ]
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   "source": [
    "# The Normal Equation\n",
    "To find Value of $\\theta$ That Minimizes Cost Function There is a Direct *closed-form* Solution in other Words This Mathematical Equation Gives the Result Directly.\n",
    "### Equation 4-4 \n",
    "$$\n",
    "\\hat{\\boldsymbol{\\theta}} = (\\mathbf{X}^T \\cdot \\mathbf{X})^{-1} \\cdot \\mathbf{X}^T \\cdot \\mathbf{y}\n",
    "$$\n",
    "\n",
    "It represents the gradient vector of the mean squared error (MSE) cost function for linear regression. The gradient vector is a vector of partial derivatives of the cost function with respect to each of the model parameters $\\theta_0, \\theta_1, \\dots, \\theta_n$.\n",
    "\n",
    "The gradient vector of the MSE cost function is used in optimization algorithms such as gradient descent to update the model parameters at each iteration. The direction of the gradient vector points in the direction of the steepest increase in the cost function, so the negative gradient vector points in the direction of the steepest decrease in the cost function, which is the direction of the fastest improvement in the model's performance.\n",
    "\n",
    "Here is a breakdown of the terms in Equation 4-4:\n",
    "\n",
    "- $\\mathbf{X}$ is the design matrix containing all the training instances with added bias terms.\n",
    "- $\\mathbf{y}$ is the vector of target values for the training set.\n",
    "- $\\mathbf{X}^T$ is the transpose of the design matrix.\n",
    "- $\\mathbf{X}^T \\cdot \\mathbf{X}$ is the dot product of the transpose of the design matrix and the design matrix itself.\n",
    "- $(\\mathbf{X}^T \\cdot \\mathbf{X})^{-1}$ is the inverse of the dot product of the transpose of the design matrix and the design matrix itself.\n",
    "- $\\mathbf{X}^T \\cdot \\mathbf{y}$ is the dot product of the transpose of the design matrix and the vector of target values.\n",
    "- $\\hat{\\boldsymbol{\\theta}}$ is the estimated value of the model parameters $\\boldsymbol{\\theta}$ that minimize the cost function.\n",
    "\n",
    "In other words, Equation 4-4 computes the partial derivatives of the MSE cost function with respect to each of the model parameters. This gradient vector is used to update the model parameters iteratively in order to minimize the cost function and improve the model's performance on the training dataset."
   ]
  },
  {
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   "cell_type": "markdown",
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   "source": [
    "Now Let's Create a Linear Looking Dataset With Numpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "x = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * x + np.random.rand(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(x, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now Let's Compute $\\theta$ using *Normal Equation* We Will use `inv()` from `np.linalg` Function to compute Invers of the Matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100, 1)), x] # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.45640353],\n",
       "       [3.04520045]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Till Now We Have Computed Our Best Theta Value so Let's Make Predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.45640353],\n",
       "       [10.54680443]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new] # add x0 = 1 to each instance\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's Plot Our Models Predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\", label=\"Predictions\")\n",
    "plt.plot(x, y, \"b.\")\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Doing The Same With `scikit-learn` is very Simple:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.45640353] [[3.04520045]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(x, y)\n",
    "print(lin_reg.intercept_, lin_reg.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.45640353],\n",
       "       [10.54680443]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.45640353],\n",
       "       [3.04520045]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If Don't Know What Does `1e-6` means? So It means That 1 and 6 Zeros = `1000000`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.45640353],\n",
       "       [3.04520045]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b).dot(y)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computational Complexity\n",
    "There are Two Ways to Compute Inverse of a Matrix:\n",
    "## 1. Singular Value Decomposition (SVD)\n",
    "\n",
    "Singular Value Decomposition (SVD) is a matrix factorization technique that decomposes a matrix into three separate matrices. The purpose of this decomposition is to simplify the original matrix and identify patterns or relationships within the data.\n",
    "\n",
    "For a given matrix A with dimensions m x n, SVD breaks it down into three matrices:\n",
    "\n",
    "1. `U`: An m x m orthogonal matrix, which contains information about the relationships between the rows of the original matrix A.\n",
    "2. `Σ`: An m x n diagonal matrix, which contains information about the importance of each dimension of the original matrix A. The diagonal values of Σ are called singular values.\n",
    "3. `V`: An n x n orthogonal matrix, which contains information about the relationships between the columns of the original matrix A.\n",
    "\n",
    "Mathematically, the SVD can be written as:\n",
    "\n",
    "$$\n",
    "A = U \\sum_{V}^{T}\n",
    "$$\n",
    "\n",
    "where T stands for transpose.\n",
    "## 2. Normal Equation\n",
    "\n",
    "The Normal Equation is a mathematical method used to find the optimal parameters for linear regression problems. It works by finding the set of parameters that minimizes the sum of squared differences between the predicted and actual values of the dependent variable.\n",
    "\n",
    "In simple linear regression, where there is only one independent variable, the Normal Equation can be expressed as:\n",
    "\n",
    "θ = (X^T X)^{-1} X^T Y\n",
    "\n",
    "where θ is the vector of parameters (including the intercept term), X is the matrix of input features, Y is the vector of output values, and T denotes the transpose of a matrix."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exit\n",
    "- Both **Normal Equation** and **SVD** appproach Get Very Slow When Number of Features Increase But After They Got Trained Once There Prediction Speed is Very Fast But this also means that Making Prediction on Twice Features Will take Twice as much time.\n",
    "- Now we Will Look at a Very Different way to Train Linear Regression Model, which is Better Suited for cases where Large Number of features or too many training Instances to fit in memory."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Descent\n",
    "- Basically Gradient Descent is a technique to minimize the cost function.\n",
    "- In Gradient Descent You Start By Filling **$\\theta$**  with Random Values and then It Starts `Decreasing Cost Function(Mainly MSE)` Gradually by taking one step at a time and at the end it ends on the Minimum Value of `Cost Function` Possible."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hyperparameter - `Learning Rate`\n",
    "`Learning Rate` is Basically Size of The Learning Step if it is too Low then it will take so Much Time to Compute even Smaller Datasets but if `Learning Rate` is too High then It Will take very Less Time to Compute but it will be very `Error Prone` so `Learning Rate` should be in a Balance Between High and Low."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Batch Gradient Descent\n",
    "- It is a type of Gradient Descent Where We Use Whole Dataset to take that Baby Step about Which we Talked Earlier.\n",
    "- **Advantage** - Chances of Error are Nearn to Zere or Very Less.\n",
    "- **Dissadvantages** \n",
    "  - Takes So Much Time to Compute Even Smaller Datasets.\n",
    "  - Less Probability of Reaching `Global Minimum` instead of `Local Minimum`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1  # Learning Rate\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "\n",
    "theta = np.random.randn(2, 1) # random initialization\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.45640353],\n",
       "       [3.04520045]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now You can See that it is Exactly Same as `The Normal Equation` so This Means that Batch Gradient Descent Worked Perfectly."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's Understand Seriousness of The Learning Rate with This Example :-\n",
    "- If Learning Rate too Low then it will take so much time to complete the work.\n",
    "  - **Learning Rate** - `0.02` then this will take almost twice as more time as `0.1`.\n",
    "- If Learning Rate is Normal then it will be Perfectly Fine.\n",
    "  - **Learning Rate** - `0.1` this is a Perfect Example of a Balanced Learning Rate.\n",
    "- If Learning Rate is too High then it Will Jump the Actual Point.\n",
    "  - **Learning Rate** - `0.5` then it Will Jumps the Actual Point and with Every Iteration It will Go far from Minimum Cost Function."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stochastic Gradient Descent\n",
    "- `Stochastic Gradient Descent` is a Type of of Gradient Descent where We take a *Random instance* and then **Compute `Gradient` of the Whole Step through that Random Instance**.\n",
    "\n",
    "### Advantages\n",
    "- `Stochastic Gradient Descent` is very fast Because it dosen't Takes Whole Dataset to Compute each `Gradient`.\n",
    "- It takes Very Less Computing Power to Computer even Larger Datasets.\n",
    "- There is a High Possiblitiy of Reaching Global Minimum if Compared to Batch Gradient Descent.\n",
    "\n",
    "### Dissadvantages\n",
    "- `Stochastic Gradient Descent` is Error Prone.\n",
    "- Normally it Jumps and Forth Between the Minimum Gradient So Many Times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50 # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta = np.random.randn(2, 1) # Initializing Random Values\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.45427635],\n",
       "       [3.04149437]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `Stochastic Gradient Descent` in Linear Regression - **`Scikit-Learn`**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SGDRegressor(eta0=0.1, penalty=None)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SGDRegressor</label><div class=\"sk-toggleable__content\"><pre>SGDRegressor(eta0=0.1, penalty=None)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "SGDRegressor(eta0=0.1, penalty=None)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-3, penalty=None, eta0=0.1)\n",
    "sgd_reg.fit(x, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.43777145]), array([3.05739498]))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mini-Batch Gradient Descent\n",
    "You have learned about `Batch Gradient Descent` and `Stochastic Gradient Descent` up to this point in time. While `BatchGD` uses the entire dataset to compute a single learning step, `StochasticGD` uses one random instance to compute the entire learning step. Both have advantages and disadvantages. **Let's move on to `Mini-Batch Gradient Descent`, which is sort of present between the other two.**\n",
    "- **Defination** - `Mini-batch gradient descent` is similar to batch gradient descent but uses mini-batches(smaller subsets) of the entire dataset at each iteration. The same idea as batch gradient descent applies here too: updating parameters towards reducing the loss on the mini-batch.\n",
    "\n",
    "### Advantages\n",
    "- Reduces memory usage by processing smaller portions of data at once.\n",
    "- Allows for faster adaptation to changing conditions through incremental adjustments based on small sets of data.\n",
    "- Increases stability and reliability by smoothing out fluctuations that may arise from working with limited amounts of information at any given time.\n",
    "\n",
    "### Disadvantages\n",
    "- **Noise sensitivity** - Mini-batch gradient descent is prone to being affected by noise in the selected mini-batches, potentially leading to suboptimal results.\n",
    "- **Variance of gradients** - Randomness in the selection of mini-batches causes variations in the gradients calculated, resulting in increased instability and uncertainty.\n",
    "- **Higher computaional cost** - Evaluating gradients for each mini-batch incurs extra computational expense compared to traditional batch gradient descent, particularly with larger mini-batch sizes."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison of Algorithims for Linear Regression\n",
    "\n",
    "|    Algorithim   | Large m | Out-of-Core-Support | Large n | Hyperparameters | Scaling Required |   Scikit-Learn   |\n",
    "|-----------------|---------|---------------------|---------|-----------------|------------------|------------------|\n",
    "| Normal Equation |   Fast  |         No          |   Slow  |        0        |        No        |        N/A       |\n",
    "|       SVD       |   Fast  |         No          |   Slow  |        0        |        No        | LinearRegression |\n",
    "|     BatchGD     |   Slow  |         No          |   Fast  |        2        |        Yes       |   SGDRegressor   |\n",
    "|  Stochastic GD  |   Fast  |         Yes         |   Fast  |       >=2       |        Yes       |   SGDRegressor   |\n",
    "|  Mini-Batch GD  |   Fast  |         Yes         |   Fast  |       >=2       |        Yes       |   SGDRegressor   |"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Regression\n",
    "- What if Your Data is more Comples than a Straght Line ? Surprisingly, We can use Linear Model to Fit Nonlinear Data By adding Powers to each feature as a new feature and this technique known as Polynomial Regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After Plotting This Data its Clearn That a Straight Line Will never fit this Data Properly So Here We are Going to use **Scikit-Learn**,s `PolynomialFeatures` class to transform our training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=True)\n",
    "X_poly = poly_features.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.43159986])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        , -2.43159986,  5.91267788])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`X_poly` now Contains the original feature of `X` plus the square of this feature. Now you can fit a `LinearRegression` model to this extended training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2.16219223]), array([[0.        , 0.96930786, 0.44870455]]))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning Curves\n",
    "The Graph Which is Plotted Below Shows that How Well `Linear Regression(1)`, `Quadratic Model(2)` and `300-degree Plynomial` perform on a DataSet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = Pipeline([\n",
    "            (\"poly_features\", polybig_features),\n",
    "            (\"std_scaler\", std_scaler),\n",
    "            (\"lin_reg\", lin_reg),\n",
    "        ])\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After all of This You can Conclude that :-\n",
    "- `Linear Regression` Underfits the Data.\n",
    "- `300-degree Polynomial` Overfits the Data.\n",
    "- `Quadratic Model` Generalizes Mostly Well Because this Dataset Was **Generated** With `Quadratic Model`."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, How do We Know that `Linear Regression` is **Underfitting**, `300-degree Polynomial` is Generalizing and `Quadratic Model` is **Overfitting**. There a Two Ways to do This.\n",
    "\n",
    "\n",
    "### First Method\n",
    "- If a Model is Performing Well on Training Set but not on Testing Set then it is **Overfitting** the Dataset.\n",
    "- If a Model Performs Worse on Both Training Set and Testing Set then it is **Underfitting** the Dataset.\n",
    "- If a Model Hits the Sweet Spot Between these two then it is **Generalizing** the Dataset Very Well.\n",
    "\n",
    "### Second Method\n",
    "We can use `Learning Curves` Here to Check if Our Model is not **Overfitting** and **Underfitting** the Dataset.\n",
    "- To Generate Plot we can Train the Model on Several times on different sized subsets of the training set. The following code difines a function that given some training data plots the learning curves of a model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
    "    train_errors, val_errors = [], []\n",
    "    for m in range(1, len(X_train) + 1):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train[:m], y_train_predict))\n",
    "        val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "    plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"train\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"val\")\n",
    "    plt.xlabel(\"Training set size\", fontsize=14)\n",
    "    plt.ylabel(\"RMSE\", fontsize=14)\n",
    "    plt.legend(fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure underfitting_learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)\n",
    "save_fig(\"underfitting_learning_curves_plot\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can See that this Model Underfits the Data Because :-\n",
    "-  In The Starting of **Training Data** `RMSE` Was Zero Because **Model Fit them Perfectly** but as the number of Instances Grow `RMSE` Starts Increasing Because **The Model is unable to Generalize Well** and at last It Ends With a Plateau.\n",
    "-  In The Starting of **Validation Data** `RMSE` Was So high Because **Model is Incapable of Generalizing Properly** which is Why The Validation Error is initialy Big Then as the Model is Shown More Training Examples **It Starts Learning** and `RMSE` Goes down and again **Ends With a Plateau Very Close to Other Curve**."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a Typical model that's Underfitting Both Curves have Reached a Plateau; the a Fairly Close and Very High."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### **Note** - If a Model is Underfitting the Training Data Adding More Example Won't work You Have to come up with a more Complex Model or come up with a Better Feature."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing a `10th-degree Polynomial` on the Same Data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "polynomial_regression = Pipeline(\n",
    "    [\n",
    "        (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "        (\"lin_reg\", LinearRegression()),\n",
    "    ]\n",
    ")\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "save_fig(\"learning_curves_plot\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### **Note** - One Way to improve an overfitting model is to feed it more training data until the validation error reaches the training error."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Bias/Varience Trade off\n",
    "An Important Theoretical result of statistics and Machine Leanring is the fact that model's generalization error can be expressed in three very different Errors.\n",
    "\n",
    "### Bias\n",
    "This Part of the Generalization error is due to wrong assumption such as assuming that the data is linear when it is actually quadratic. A high-bias model is more likely to underfit the training data.\n",
    "\n",
    "### Varience\n",
    "This part is due to the model's excessive snsitivity to small variations in the training data. A model with many degrees of freedom(such as a high-degree polynomial model) is likely to have high varience and thus overfit the training data.\n",
    "\n",
    "### Irreducible error\n",
    "This part is due to the noisiness of the data itself. The only way to reduce this part of error is to clean up the data (e.g., fix the data sources, such as broken sensors or detect and remove outliers).\n",
    "\n",
    "### Exit\n",
    "Increasing a model's complexity will typically increase its varience and reduce its bias.Conversely, reducing a model's complexity increases its bias and reduces its varience. This is Why it is called Tradeoff."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized Linear Models\n",
    "We can Solve the Problem of Overfitting By **Regularizing the Model**.\n",
    "- A Simple Way to Regularize a `Polynomial Model` is to **reduce Number of Polynomial Degrees**.\n",
    "- In a `Linear Model` Regularization can be achieved by **Constraining the weights of the model**.\n",
    "- Regularization in `Ridge Regression`, `Lasso Regression`, and `ElasticNet Regression` are complex so we Will **Regularize them Seperately**."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **Resources** - `Hindi`\n",
    "  - Youtube Playlist - [Regularisation in Hindi by CampusX.](https://youtube.com/playlist?list=PLKnIA16_RmvZuSEZ24Wlm13QpsfLlJBM4)\n",
    "  - **Regularisation** with `Ridge Regression`.\n",
    "    - [Ridge Regression Part 1 | Geometric Intuition and Code | Regularized Linear Models](https://youtu.be/aEow1QoTLo0).\n",
    "    - [Ridge Regression Part 2 | Mathematical Formulation & Code from scratch | Regularized Linear Models](https://youtu.be/oDlZBQjk_3A).\n",
    "    - [Ridge Regression Part 3 | Gradient Descent | Regularized Linear Models](https://youtu.be/Fci_wwMp8G8).\n",
    "    - [5 Key Points - Ridge Regression | Part 4 | Regularized Linear Models](https://youtu.be/8osKeShYVRQ).\n",
    "  - **Regularisation** with `Lasso Regression`.\n",
    "    - [Lasso Regression | Intuition and Code Sample | Regularized Linear Models](https://youtu.be/HLF4bFbBgwk).\n",
    "    - [Why Lasso Regression creates sparsity?](https://youtu.be/FN4aZPIAfI4).\n",
    "  - **Regularisation** with `ElasticNet Regression`.\n",
    "    - [ElasticNet Regression | Intuition and Code Example | Regularized Linear Models](https://youtu.be/2g2DBkFhTTY)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **Resources** - `English`\n",
    "  - `Ridge Regression` - [Regularization Part 1: Ridge (L2) Regression](https://youtu.be/Q81RR3yKn30).\n",
    "  - `Lasso Regression` - [Regularization Part 2: Lasso (L1) Regression](https://youtu.be/NGf0voTMlcs).\n",
    "  - `ElasticNet Regression` - [Regularization Part 3: Elastic Net Regression](https://youtu.be/1dKRdX9bfIo).\n",
    "  - `Ridge v/s Lasso Regression` - [Ridge vs Lasso Regression, Visualized!!!](https://youtu.be/Xm2C_gTAl8c)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ridge Regression\n",
    "- Ridge Regression is Regularized Version of Linear Regression.\n",
    "$$J(\\theta) = \\text{MSE}(\\theta) + \\alpha \\sum_{i=1}^{n} \\theta_i^2 \\$$\n",
    "- As You can See there is a `Regularisation` Term added to the `Cost Function` at the end of this `Equation` Which **Increases the Bias and Reduces the Varience** Which is Good for `Preventing from Overfitting` and `Generalisation`.\n",
    "  - This forces Learning `Algorithim` to not only **Fit the Data** but Also Keep the `Model Weights` as small as Possible.\n",
    "- **`Note`** - The `Regularisation` Term Should only be add to the `Cost Function` Only When You are **training the Data**. You Will not Want to Use it While **Testing the Data**."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use `hyperparameter` $\\alpha$ to define how much you want to **Regularise the Model**.\n",
    "- if $\\alpha$ = 0 then `Ridge Regression` will remain `Linear Regression`.\n",
    "- if $\\alpha$ us very large then all `weights` will come **close to zero resulting a flat line through the data**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55071465]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\")\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.46619232])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(penalty=\"l2\")\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `penalty` **hyperparameter** sets the type of Regularisation tern to use."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### **Note** - It is Important to Scale the Data(eg.using StandardScaler) Before performing Ridge Regression as it is sensitive to scale of the input features. This is true of most regularized models."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importance of $\\alpha$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure ridge_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
    "    for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
    "        model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
    "        if polynomial:\n",
    "            model = Pipeline([\n",
    "                    (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "                    (\"std_scaler\", StandardScaler()),\n",
    "                    (\"regul_reg\", model),\n",
    "                ])\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        lw = 2 if alpha > 0 else 1\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    plt.legend(loc=\"upper left\", fontsize=15)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 3, 0, 4])\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "\n",
    "save_fig(\"ridge_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `Linear Model` **`(left)`** and a `Polynomial Model` **`(right)`** with Various Levels of `Ridge Regression`."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lasso Regression\n",
    "- `Lasso Regression` - Least Absolute Shrinkage and Selection Operator Regression.\n",
    "- It is also a `Regularised` form of `Linear Regression` and Just Like `Ridge Regression` it **adds a Regularisation term to the cost function**.\n",
    "- The Only Difference Between `Ridge Regression` and `Lasso Regression` is that `Ridge Regression` uses `l2 norm` but `Lasso Regression` Uses `l1 norm`.\n",
    "- If You dont know about `l1` and `l2` norms :-\n",
    "  - `l1 norm` means that `Absolute Values` of the vector **w** will be used in the `Cost Function`.\n",
    "  - `l2 norm` means that `Squared Values` of the vector **w** will be used in the `Cost Function`.\n",
    "- One More Difference Between `Ridge` and `Lasso` Regression is that `Ridge Regression` Don't Set Parameters to `0` but `Lasso Regression` Does."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cost Function\n",
    "$$\n",
    "J(\\boldsymbol{\\theta}) = MSE(\\boldsymbol{\\theta}) + \\alpha \\sum_{i=1}^{n} \\left| \\theta_i \\right|\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/praddyumny/MachineLearning/Hands_On_Machine_Learning/venv/lib64/python3.11/site-packages/sklearn/linear_model/_coordinate_descent.py:631: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 2.803e+00, tolerance: 9.295e-04\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), random_state=42)\n",
    "\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note** - One Important Characteristics of `Lasso Regression` is that it tends to Eliminate Less Important Features(set them to 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elastic Net\n",
    "- `Elastic Net` is a Middle Ground Between `Ridge Regression` and `Lasso Regression` . The **Regularisation** term is a simple mix of both `Ridge` and `Lasso's Regularisation` terms and you can control the mix ration `r`.\n",
    "$$\n",
    "J(\\theta) = MSE(\\theta) + r \\cdot \\alpha \\sum_{i=1}^{n} |\\theta_i| + \\frac{1 - r}{2} \\sum_{i=1}^{n} \\theta_i^2\n",
    "$$\n",
    "- `Elastic Net` also performs `Feature Scaling` if `r` is between **0 and 1**.\n",
    "- When `r = 0` `Elastic Net Regression` is Same as `Ridge Regression` and if `r = 1 ` is Equivalent to `Lasso Regression`.\n",
    "  - `r = 0.5` is a Balance Between `Ridge` and `Lasso` Regression.\n",
    "  - No Matter What is Your Goal it is always Preferable to have `r` more than `0` even if it is `0.1`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Early Stopping\n",
    "- **A Very Different way to `Regularize` Iterative** Learning `algorithims` such as `Gradient Descent` to Stop Training as Soon as the `Validation Error` **Reaches its Minimum Point**. This is known as `Early Stopping`.\n",
    "- **Fun Fact** - `Geoffrey Hinton` Popularly Known as the Father of AI called it `a beautiful Free Lunch`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.base import clone\n",
    "\n",
    "\n",
    "# prepare the data\n",
    "poly_scaler = Pipeline(\n",
    "    [\n",
    "        (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
    "        (\"std_scaler\", StandardScaler()),\n",
    "    ]\n",
    ")\n",
    "\n",
    "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
    "X_val_poly_scaled = poly_scaler.transform(X_val)\n",
    "\n",
    "sgd_reg = SGDRegressor(\n",
    "    max_iter=1000,\n",
    "    tol=1e-3,\n",
    "    warm_start=True,\n",
    "    penalty=None,\n",
    "    learning_rate=\"constant\",\n",
    "    eta0=0.0005,\n",
    ")\n",
    "minimum_val_error = float(\"inf\")\n",
    "best_epoch = None\n",
    "best_model = None\n",
    "\n",
    "for epoch in range(1000):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)  # continues where it left off\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    val_error = mean_squared_error(y_val, y_val_predict)\n",
    "    if val_error < minimum_val_error:\n",
    "        minimum_val_error = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = clone(sgd_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure early_stopping_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(\n",
    "    max_iter=1000,\n",
    "    tol=1e-6,\n",
    "    warm_start=True,\n",
    "    penalty=None,\n",
    "    learning_rate=\"constant\",\n",
    "    eta0=0.0005,\n",
    "    random_state=42,\n",
    ")\n",
    "\n",
    "n_epochs = 500\n",
    "train_errors, val_errors = [], []\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)\n",
    "    y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    train_errors.append(mean_squared_error(y_train, y_train_predict))\n",
    "    val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "best_epoch = np.argmin(val_errors)\n",
    "best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
    "\n",
    "plt.annotate(\n",
    "    \"Best model\",\n",
    "    xy=(best_epoch, best_val_rmse),\n",
    "    xytext=(best_epoch, best_val_rmse + 1),\n",
    "    ha=\"center\",\n",
    "    arrowprops=dict(facecolor=\"black\", shrink=0.05),\n",
    "    fontsize=16,\n",
    ")\n",
    "\n",
    "best_val_rmse -= 0.03  # just to make the graph look better\n",
    "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(\"Epoch\", fontsize=14)\n",
    "plt.ylabel(\"RMSE\", fontsize=14)\n",
    "save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As You can see in the figure that The Best Model that Stands here is in between of `100` and `200` (Probably `150`) so we should **Stop all the iterations there** and it will become kind of te perfect model."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression\n",
    "- As We know, some `regression algorithims` can be used in `classification` tasks and vice-versa.\n",
    "- `Logistic Regression`(also known as `Logit Regression`) can be used for `classification` tasks with a Technique known as `Estimating Probabilities`."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating Probabilities\n",
    "- Basically `Estimating Probabilities` is a Technique where a `Regression Model` is Trained to Estimate `Probability` that an instance belongs to a particular class or not and if Estimate is Greater than `50%` then model predicts that the instance belongs to that class.\n",
    "$$\n",
    "\\hat{p} = h_{\\boldsymbol{\\theta}}(\\mathbf{X}) = \\sigma(\\mathbf{X}^\\top \\cdot \\boldsymbol{\\theta})\n",
    "$$\n",
    "<p align=\"center\"><b>Equation 4.13 - Logistic Regression model estimated Probability</b></p>\n",
    "\n",
    "- The logistic $\\sigma(.)$ is a `Signoid` **Function** Which outputs a number between `0` and `1`. It is Defined in the Equation Below.\n",
    "$$\n",
    "\\sigma(f) = \\frac{1}{1 + \\exp(-f)}\n",
    "$$\n",
    "<p align=\"center\"><b>Equation 4.14 - Logistic Function<b/></p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_function_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-10, 10, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot([-10, 10], [0, 0], \"k-\")\n",
    "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-10, 10], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\", fontsize=20)\n",
    "plt.axis([-10, 10, -0.1, 1.1])\n",
    "save_fig(\"logistic_function_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Once `Logistic Regression` model has Estimated the Probability of the Instance **X** having in a Positive Class We can use Equation 4-15 to Compute The Final Result of all the Computation.\n",
    "$$\n",
    "\\hat{y} = \\begin{cases}\n",
    "    0 & \\text{if } \\hat{p} < 0.5 \\\\\n",
    "    1 & \\text{if } \\hat{p} \\geq 0.5\n",
    "\\end{cases}\n",
    "$$\n",
    "<p align=\"center\"><b>Equation 4-15: Logistic Regression Model Prediction</b></p>\n",
    "\n",
    "- **Note** - The score *t* is often called the *logit*. The name comes from the fact that the logit function, defined as `logit(p) = log(p / (1-p))`, is the inverse of the logistic function. Indeed, if You compute the logit of the estimated probability *p*, you will find that the result is *t*. The logit is also called the `log-odds`, since it is the log of the ratio between the estimated probability for the positice class and the estimated probability for the postive class and the estimated probability for the negatice classs."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training and Cost Function\n",
    "$$\n",
    "c(\\theta) = \\begin{cases}\n",
    "    -\\log(\\hat{p}) & \\text{if } y = 1 \\\\\n",
    "    -\\log(1 - \\hat{p}) & \\text{if } y = 0\n",
    "\\end{cases}\n",
    "$$\n",
    "<p align=\"center\"><b>Equation 4-16: Cost function of a single training instance.</b></p>\n",
    "\n",
    "- If You Don't Know about `log()` is a Mathematical Function Named as `Lagorithm` which Determines the Exponent Needed to Obtain a Given Number by Specified base and has bases like 10 or e.\n",
    "  - For More Info Checkout - [Lagorithm Wikipedia](https://en.wikipedia.org/wiki/Logarithm)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "j(\\theta) = \\frac{1}{m} \\sum_{i=1}^{m} \\left[ y^{(i)} \\log(\\hat{p}^{(i)}) + (1 - y^{(i)}) \\log(1 - \\hat{p}^{(i)}) \\right]\n",
    "$$\n",
    "<p align=\"center\"><b>Equation 4-17: Logistic Regression cost function for Whole Dataset.</b></p>\n",
    "\n",
    "- $j(\\theta)$: This represents the cost function.\n",
    "- $m$: It denotes the number of training examples in the dataset.\n",
    "- $\\sum_{i=1}^{m}$: This is the summation symbol, indicating that the following expression is summed over all the training examples.\n",
    "- $y^{(i)}$: It represents the actual binary class label (0 or 1) for the \\(i\\)th training example.\n",
    "- $\\hat{p}^{(i)}$: This represents the predicted probability of the positive class (class 1) for the \\(i\\)th training example.\n",
    "- $\\log(\\hat{p}^{(i)})$: It calculates the natural logarithm of the predicted probability.\n",
    "- $(1 - y^{(i)})$: This represents the complement of the actual label for the \\(i\\)th training example (i.e., 1 if $y^{(i)}$ is 0, and 0 if $y^{(i)}$ is 1).\n",
    "- $log(1 - \\hat{p}^{(i)})$: It calculates the natural logarithm of the complement of the predicted probability."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\partial j(\\theta)}{\\partial \\theta_j} = \\frac{1}{m} \\sum_{i=1}^{m} \\left( \\sigma(\\theta^T x^{(i)}) - y^{(i)} \\right) x_j^{(i)}\n",
    "$$\n",
    "<p align=\"center\"><b>Equation 4-18: Logistic cost function partial derivatives.</b></p>\n",
    "\n",
    "- $\\frac{\\partial j(\\theta)}{\\partial \\theta_j}$ denotes the partial derivative of the cost function with respect to the j-th parameter $\\theta_j$.\n",
    "- $\\sigma(z)$ represents the sigmoid (logistic) function.\n",
    "- $\\theta^T$ denotes the transpose of the parameter vector $\\theta$.\n",
    "- $x^{(i)}$ represents the feature vector of the i-th training example.\n",
    "- $y^{(i)}$ represents the actual binary class label of the i-th training example.\n",
    "- $x_j^{(i)}$ represents the j-th feature of the i-th training example."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Boundaries\n",
    "- Let's Use `Iris` Dataset to illustrate `Logistic Regression`. This is a Famous Dataset that Contains the `sepal` and `petal` length and width of 150 iris flowers of three different species: `Iris setosa`, `Iris versicolor`, and `Iris Verginica`.\n",
    "- Let's Try to Build a Classifier to detect the `iris virginica` type based only on the petal width feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data',\n",
       " 'target',\n",
       " 'frame',\n",
       " 'target_names',\n",
       " 'DESCR',\n",
       " 'feature_names',\n",
       " 'filename',\n",
       " 'data_module']"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, 3:] # petal Width\n",
    "y = (iris[\"target\"] == 2).astype(np.int8) # 1 if iris virginica, else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "log_reg = LogisticRegression()\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regresion_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", label=\"Iris Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", label=\"Not Iris Virginica\")\n",
    "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.legend()\n",
    "save_fig(\"logistic_regresion_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After Seeing This Figure we can say that the `Decision Baundary` Lies a little after `1.5`(probably `1.6`)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now Let's Predict an Instance with `predict()` methode rather than `predict_proba()` methode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0], dtype=int8)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As You can see that now this doesn't predict Probability now it gives the result according to probability of the instance having in a Class if the Probability is Greater than `50%` then it returns `1`(Iris Virginica) and if it is not then it returns `0`(Non Iris Virginica)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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YjgnCetg45Jb6bZlW4l5KDNGRoWWj5+b1aNF1Mq17Tse6nn7nqTKoNcUcvbuBzfFh5aLnQzyCCHB+CxODmr9IIAiCIAiCIAiCKLprVMnJ/+UfZ3ljZnPqu1b9PbrqwuIH0fMIUk/8JXrexQtfhT+NR7TBwNhQr9covB5XGj3PLImHW2A14XUmXjjI9gP7KzxWLpczdOhQgoODCQgIKB89v3VNGz1fv6g0em5pjfWISdiMCcLYo5FeYy+Rn5vBpWN/EH0ojKx07XmSyeR4tx5Km4CZuDQuH4uvCbeyotkcH8q+lHBd9NzayJ6B7lMZ6DFVRM8FQRAEQRAEoYaJorsGlZz8PqzFxNCSniOdCFR40KyLbbUUdKmn4okKjeT6qrO66Lm5kzWtp3Wn5fvdsXCqhOj50o3a6PmVWACyULOlWQOWqhKJvZ3y2ONbtWpFcHAwo0ePLh89z84ka/0SlMtCKYq7rm2UyTAPGIjtWAXm3V8rE2t/7u9BoybuwlaiIkNJurZP127v0hrfnkE07TgGI2Pzx/RQPVSF99idtJCtCfO4m6+9SCCXGdDVYRjDPGfS0q5HrbhIIAiCIAiCIAgvG1F016CSk6/ouo/rxwp17Y3bWROo8CDgLWeMTfVb8Oxp5KZmcuG3o1yYf5ic25nAg+j5m23xDQ7AqZOe0XNJInfPEVSh4eRsOwiShAaJoy6WLLMuZv+VC4893s7OThc99/LyKtu3RkPu4d0ol4aQG7lD127k3VQbPR8+vtKi5+m3LxEVGcKVU+EUF+YCf4me95iGtb3X4zuoBmpNMcfvbmZj/Jwy0fNG1m0Z4hFEL+e3RfRcEARBEARBEKqRKLpr0F9P/t2bsDk0noiVtynM1+61bdPAmAHvuzFwqgcN3Konen5zfRRRIRHcORana3fs5Imvwh+fkW0wMDHS6zUKbyagmreczD/WolFp7y2/ZW7An42sWX3zItm5ORUe26tXLw4cOFDh44Vx11Etn0vm2oVoch7ct25hhfUbE7XRcy8fvcZeIj83g8vHFxF9KIzM+9rF45DJ8G4VSJteH+DauHwsvibcyophS3wY+1KWUqjJB8DKqB4D3N5nsMd0Gpi51/AIBUEQBEEQBOHFJ4ruGvSok595v5CdvyexZW4C95K0hZLcQEaPEY4MDfakedfqiZ7fPZNAVEgk11adQVP4IHruaKVd9XxqD/2j59k5ZIZvQhmyVBc9z34QPQ/PTOZGSlK5Y9atW8frr7/+FH1nkblhCcplYRTduqprN/cfoI2e9+xXqdHz6ENhJF7dq2u3d26Fr38QTTuMwcjEQu/X0Vdm4X12J2uj56l5cUBJ9HwogZ7BtLarHfenC4IgCIIgCMKLSBTdNehxJ7+4SMOxTXfZEhZPTESGrr1xO2uGBHnQ6+3qi55fXHCMmPmHyUlWAdroeeMRbfAL9sexs5deBZskSeTtO4oyJJycrQd00fPjzpYss1Wz93IMAO7u7sTGxmJoWH6RN41GQ2Ji4qNXPT+6F+WSOdro+YO3pZGXD7ZjFFi9Ph4Dy8p506ffuUxURAhXTi3VRc9NzO1o2XUyrXtMrx3Rc0nNibtb2BQ/h+j0g7r2hlZ+BHoGE+D8FqYGNX9/uiAIgiAIgiC8SETRXYOe9uTHRmWyKSSegyvKRs/7v+fGoGnVFD0vUhO7IYqoORHcPnpL1+7Q0QM/hT8+b7bVO3peFJuAct4KMhes0UXP48wMWN3YmpZD+/PB17MfedzOnTsZOHAggYGBKBQKevfuXX7V8/gbqJbPI3PtH2iytfetyywssX59IrZjgjD2bqLX2EsU5Cq5dGIRMYfmorp3U9sok+Hdcgh+AcG4NSk/tpoQl3WBLQlh7EsJp0CtvUhgaWRHf7f3GOwxHUezmt8aTRAEQRAEQRBeBKLorkHPevIz7xey648ktoQlkJZYGj3vNtyBoTO9aNm9mqLnZxOJDo3k2sozqAuKATBzsKLVlG60ntYDC2cbvfrX5OSStWwzytBwCi9e17Wbv9Ydm+BxWAwMKBMPHzhwIDt2lC6i1rJlS4KCghg7diwWFhYP9Z1N5salKMNDKYq9Utp3z/7Yjguu1Oh5/MXtREWGknh1j669tkXPs4oy2JW0oGz0HDldHYcxxCMI33q9asVFAkEQBEEQBEGoq0TRXYOe9+Sri7XR882hZaPnDdtYEajwpNfbzpiYVUP0/G4WFxcc48L8w2QnKQGQG8ppNKINfgp/nLp66x89P3Ac5Zyl5GzZXxoPb+SBzfR3sJ40gti0VJo0efQsta2tLZMmTWLGjBk0bNiwXN+5R/eiWhpCzsFtZaLnNqNnYP3GxMqLnqdeIToyjCsnFlNUqF0ozsTMluZdJuHrH4SNvXelvI4+1JKaU2nb2Bg3h6j00n3UvSxbEegZzCsuo0X0XBAEQRAEQRCew0tRdH/33XesX7+eK1euYGZmRrdu3fjhhx9o2rRphccsXryYiRMnlmkzMTEhPz9f97UkScyaNYvff/8dpVJJ9+7dmT9/Pj4+T7dKdmWc/FsxWWyaE8+B5Sm66Ll1fSMGvOfOoGnuNHCv+u2hNMVqbm6I1kbPj8Tq2h3au+MbHECTUZUQPb+VWBo9V5bEw8053KMpM49sJzM7u8JjZTIZgwcPJjg4mFdffbV89DzhJqplc8lctxBNlupB35ZYDxuvjZ43aqbX2EsU5Cq5fHIJ0YfCUKXdKBkc3i0H4xsQjHuT8mOrCfFZF9mSMJd9KUvJV2svElga2dHP9V0Ge0zHybzmLxIIgiAIQmXYG7uX4B3BhAwIoU/DPjU9nBpRVedAnFtBKPVSFN39+/fnrbfeomPHjhQXF/PJJ59w4cIFLl26VC5+XGLx4sXMnDmTq1dLV7+WyWQ4Ojrqvv7hhx/47rvvWLJkCd7e3nz++efExMRw6dIlTE2ffJ91ZZ78rPRCdv2RzJa58dyNL42edx3qwNCZnrTqaVctBV3auUSiQiO5tuIv0fMGlrR8Xxs9t3S11at/TU4uWcs3owxdRuGFawBko2F7U3uW5tzhWlLCY49v3rw5QUFBjBs3DktLy4f6ziZz8zJUS0MovHlZ127eoy+2Y4MxDxhQKdFzSaMh7vIOoiNCSLiyW9du59gcP38FTTuNxdjE8jE9VI/sIiW7kv5ga8Jc7uRp7+OXI6ezQyCBngr86r1SKy4SCIIgCMLzkCSJzgs6cyrlFB1dOnJi8omX7vdaVZ0DcW4FoayXouh+WFpaGg4ODkRERODv7//I5yxevJgPPvgApVL5yMclScLFxYUPP/yQjz76CACVSoWjoyOLFy/mrbfeeuI4quLkq4s1HN98l82hCUQfTNe1N/TTRs8D3nbG1Lzqo+d597K5+PtRYuY9FD1/ow2+Cn+cu1VC9PzgCZQhS8nZvB80GiQkTjhZstxOw+4rMTzubWhjY8PEiRP58ssvsbEpew+6JEnkHduPMjyEnP1bSqPnHo200fMRkzCw0u++9RIZqVeJPjSXyycWUVSgna03NrOhReeJ+PYMwqZBo0p5HX2oJTWn03awKT6Ec/dL70/3sGzBUI9geruOFdFzQRAEoc7ZdWMX/Zf31329c/RO+jXuV4Mjqn5VdQ7EuRWEsl7KovvGjRv4+PgQExNDq1atHvmcxYsXM3nyZFxdXdFoNLRr145//etftGzZEoDY2FgaNWrEuXPnaNOmje64gIAA2rRpw5w5c8r1WVBQQEFBge7rzMxM3N3dK/Xk/1XchSw2h8azPzyFgjxt9NyqnhH933Nj8HQPHDyqJ3oeuzGaqJBIUg7d1LU3aOeGX3AAPqPaYWiqZ/Q8LgnVvBWoFqxBk6GNhyeYylnjY8uquEuosrIeeZyTkxPx8fEYGxtX3HdCLMoVD1Y9z1QCIDO3KI2eN26u19hLFOSpuHxiMTGH5qJMe7B4nEyGV4tB+PoH4dH0tUqZZddXRdHzvq6TGOwxHWfzhk/oQRAEQRBqXslM7NnbZ1FLagxkBrRzbvdSzchW1TkQ51YQynvpim6NRkNgYCBKpZLDhw9X+Lxjx45x/fp1fH19UalU/PTTT0RGRnLx4kXc3Nw4evQo3bt3JyUlBWdnZ91xb775JjKZjD///LNcn19++SWzZ5ff9qqqiu4SWemF7FqYzNa5CaTG5QEgl0PXYY4EKjxoHVCveqLn55OIDovk6vIzqPOLgAfR8/e60Xpadyzd7PTqX5ObVxo9j9HeFpCDhu1N7Fmae4erD0XPZ8+ezRdffPGUfeeQuSkcVXgohTcu6drNu7+GzbhgLAIGVlr0PP7KLqIiQki4vFPXbuvQFL+AYJp1Glcrouc5RSp2Jy9ic3yILnouQ0YXh0CGes4Uq54LgiAItdrDM7ElXqYZ2ao6B+LcCkJ5L13RPW3aNHbs2MHhw4dxc3N76uOKiopo3rw5b7/9Nl9//fVzFd3VPdP9MLVa4sQW7arnUftLo+fevlYMDa7m6PmCY9roeaJ29XWZgZxGb/jhp/DHuXtD/aPnESdRhoaTs3FvafTc0YKV9jJ2Xo7C0NCQxMTEMvfo/9WCBQvo1asXjRs3Lt/38QMol4aQc2ALaLQJAiP3hqXRc2vb5x77X2XcvUbMoblcOr6IogLtbL2xqTXNO0/E1z8I2waNn9BD1VNLas6k7WRzQihn7u3StXtYtmCIRxB9XMZhaljzW6MJgiAIQomHZ2JLvEwzslV1DsS5FYRHe6mK7qCgIDZt2kRkZCTe3s++AvPIkSMxNDRk5cqVzxUvf1hVnPynFX8xi81hCexbmkJBrvZD0dLOiH7vujIkyBNHz2qKnm++QHRIBMkRN3Tt9du44hccQJO32+sfPU9IQTVvOarf16BJVwKQaCLnavfmTJrzAyatym83duvWLRo3boxGo2HgwIEEBwfz2muvIX9oJrsoKQ7l8rna6LnqwcUDM3Osh4/HZvQMTHxa6jX2EoX5WVw+sZjoQ2Eo72oXj9NGzwfi66+oNdHzxOwrbIoPeWT0fJDHNFzMa/7+dEEQBEGoaCa2xMswI1tV50CcW0F4tJei6JYkCYVCwYYNGzh48OBTb+n1V2q1mpYtWzJw4ED++9//6hZS++ijj/jwww8B7cl0cHCo0YXUnlVWRhG7/khi27wE7twqjZ53GerIkCAP/F6ppuh5VDLRoRFlouem9ha0fK8rraf3xMq9EqLnK7eiDFlKYXTpivRmr3TBVjEGi8BXkRloZ/n/8Y9/8NNPP5U5vkmTJigUCsaPH4+VlVXZvvNyydq8HGV4CIXXLpT23fVVbMcFY9FrkK5vfUgaDQlX9xAVEUL8pe26dluHJvj6K2jeaTzGplaP6aF65BSp2Ju8hE0JIdzO1d7HL0NGpwaDGeo1kzb1eour3IIgCEKNKJmJPZNyBg2aco/LkdPepf0LPSNbVedAnFtBqNhLUXRPnz6dFStWsGnTpjJ7c9vY2GBmpp3RHTduHK6urnz33XcAfPXVV3Tp0oXGjRujVCr597//zcaNGzlz5gwtWrQAtFuGff/992W2DIuOjq6RLcP0pVZLnNqexqY58Zzfd1/X7tnSkqEzPXlltEu1RM/z03O00fO5h8hK+Ev0fLgvvsEBuPTQP3qef+g0ypClZG/Yo4uHG3q6YjP9HQzfHoinb6sKV623srJi4sSJBAUFlbt4I0kSeScOogwPJWffptK+3byxLYme2+h38aCENno+j8snFlGYr9233MjEiuadJ+DrH4SdQ/kZ/OpWsur51oS5nL5Xen+6u0VzhnjMoI/reMwMa/7+dEEQBOHlUVBcgOfPnqTmpFb4HCdLJ+JmxmFiaFKNI6s+VXUOxLkVhIq9FEV3RUXaokWLmDBhAgC9evXCy8uLxYsXA/C3v/2N9evXc+fOHezs7Gjfvj3ffPMNbdu21R0vSRKzZs3it99+Q6lU0qNHD+bNm0eTJk9X8NSmovuv4i9msXVeInuXJJOf8yB6bmtI30luDAnywMm76reH0hSrubXlAtGhkSQduK5rr+/niq/Cn6bvtMfQrOJVx59GUUIKqvkrUP2+Gs19JQCZpkYs8LFiVdxllFmZjz1+wIABKBQK+vXrVz56nhyPavlcVGsWlImeWw0di+2YIEyaPHrV/GdVmJ/FlZNLiYoMKY2eA54tBuLnr8CjWd9aET1Pyr7K5oRQ9iQv1kXPLQxt6Of2LoM8povouSAIglBtElWJpOWmVfi4g4UDbtZPv+5PXVRV50CcW0F4tJei6K6tamvRXSJbWcTuhUlsmZvAndjS6HnnIQ4MUXjSpnf1RM/vxaQQFRLBteWnKc57ED2vZ06L97rhO70HVh719Opfk5dP1qptqELDKTinXZk8Fw07fOxZmp/K5cT4xx7v4+NDUFAQEyZMKPfvqMnLJWvLCpThoRRejda1m3XprY2evzK40qLniVf3EhUZStylbbq9xW0b+ODrH0TzThMwNqv591hOcSZ7k5ewJT6U5FztxRQZMjo2GEigZzDt7F8TkTNBEARBEAThhSKK7hpU24vuEhqNxOkdaWwKiefs7tLouUcLS4YGe9B7jAumFoZVPo789BwuLTxOzNxDZMZpV1+XyWV4D21Nm5kBuPg31j96fvg0ypBwbfRcrUZC4pSDOSvqy9l5JRqNpvw9SiUsLS1ZuXIlgwcPfmTfeScjtNHzvRv/Ej33wvad6ViPeBcDW/0uHpRQpt14sOr5wvLR854zsHNs+oQeqp5G0nD63k62xIdx+t4OXbu7RXMGe0ynj+t4zA1r/v50QRAEQRAEQdCXKLprUF0puv8q/lI22+YlsHdJMnnZZaPng2d44NywGqLnao02eh4WSdK+0ki1va8LvkH+NB3dASNzPaPnibdR/bKSzN/+RH1PGw9PNpaxpqkdK+Mvk5FZPnpuYGBAXFzcE7eiK0pJQLV8Hqo1v6NRPrh4YGqGVeAYbMcqMGnaWq+xlygsyObqyXCiIkPISL2ia/do3h+/gGA8m/WrFdHz5JzrbI4PZU/yIvLU2QCYGVjR120SgR5BuFjU/NZogiAIgiAIgvC8RNFdg+pi0V0iR1XE7kXJbA6N10XPZTJt9DxQ4UGbV+2rJSZ8/+JtokMjubL0pC56bmJnrlv13NpTz+h5fgHZq7ahDFmqi57noWGnjz1LC+5yMSFO99w333zzkfuzV9x3Xmn0/EqUrt2scy9sxyiweDUQmaH+CQJJoyHx2j6iI8O4dXGLLnpuU78Rvj2DaN5lIiZmNnq/jr5yijPZl7yULQlhJOWUrjDfof4AhnoG065+X+Symr9IIAiCIAiCIAjPQhTdNaguF90lSqLnm0MTOLPrnq7dvZkFgcGe9BlXTdHzjNzS6PktbQReJpfhHdgav2B/XHv56B89P3pWu+r5+j1QXIyExJn6Zix3MGDHlWgiIiLo0aPHI4//7rvvSEpKIigoiObNm5fv+/QhlEtDyN67EdTaBIGhiwc2o2dgM3JypUXPVfdiiY4M49KJhRTmqQAwMrGkWafx+PoHUc+xWaW8jj40koaz93azKT6EM/d2IqH9OHGzaMoQjyARPRcEQRAEQRDqFFF016AXoej+q8Qr2WwJKxs9t7AxpO8kVwZP98ClsUWVj0Gj1hC39QJRoQ9Fz1u74BvUUxs9t9Bvm4qipDul0fM0bTz8jokcn7eHYRs8DtO2Lco8Pz8/H3d3d+7d016UeO211wgODmbAgAEYPLSIWtHtRFQr5qP68zc0ygcXD0xMS6PnzXz1GrvudQpyuHIqnOjIUNLvXNK1ezTri6+/Aq8WA2tF9Dwl5wZbEuayK+kP8tRZgDZ6/prrBAI9Fbha+DyhB0EQBEEQBEGoWaLorkEvWtFdIiezmL2Lk9gcmkDKjVxAGz3vOKgBQ4M9aduneqLn6ZduEx12iMtLTlKcWwg8iJ5P7krr6T2w9rLXq39NfgHZf25DGbqMgjMXdO2mPdpjGzwOy2F9kBkZsWTJEt3WdH/VsGFDgoKCmDhxIra2tg/1nUfW1pWoloVRcOmcrt2sUwA2YxVYvjq0cqLnkkTi1b1EH5rLrQuby0TPW/ecQYvOEzExt318J9UgtziLvclL2Jowl8Sc0vvTO9TvzxBPBR3q9xfRc0EQBEEQBKFWEkV3DXpRi+4SGo3E6Z332BIaz+mdZaPng2d48NoEV8wsqz56XqDM5dKiE0SHRZIZWxo99xrSCj+FP269m+gfPT92DmVoONlrd0FxMQCGro7YTH+H/usWcOrs2QqPt7CwYNy4cQQFBdGiRdlZckmSyD9zBOXSOWTv2VAaPXd2L42e2+l38aCE6v4tYg7N5eKxBaXRc2OL0ui5U/Mn9FD1JEni3P29bIz/mVNp23XtruY+DPFU0Md1PBaGL97PkiAIlWtv7F6CdwQTMiCEPg371PRwhKfw45Ef+fzA53z9ytd83P3jmh6OIAjCMxFFdw160Yvuv0q6lsOWsHj2LCqNnptbG9Lv3eqNnsdvv0hUaCSJe0oX6qrX0hk/hT9Nx+gfPS9OSUX1yypUv65CfVdb4N82hjVN7VmZcIX7KuVjj+/Tpw8KhYJBgwaVj57fSUK18hcyV/2KOkN7EUNmYorVkHewHRuMSXM/vcaue52CHK6eXkZUZCjpty/q2t2b9tFGz1sOQi7Xf29xfaXk3GBrwjx2Jy8kp1h7kcDMwJI+ruMZ3fhLbIzr1/AIBUGojSRJovOCzpxKOUVHl46cmHyiWtJXwvPTaDRYfW9FblEu5kbmZP1fFvJacAuUIAjC0xJFdw16mYruEjmZxexbmszmkHiSr+fq2jsObMDQYA/avlYfubwaoueX7xA99xBXFp+gKOdB9NzWjBbvdqX1jJ7YeOsZPS8oJHv1du2q56e10fN8NOxqXI+lRfeIib/12OO9vb2ZMWMGkyZNws7O7qG+88netgpleCgFF0tn0E079MR2XDCWfYZVWvQ86foBoiNDuRWzGUnS7i1ubd+Q1j2n06LLJEzN7Z7QS9XLK85mX8pSNseHkphzBUsjO8IDEjE1rPoLOYIg1D27buyi//L+uq93jt5Jv8b9anBEwpN8G/ktnx34TPf1N698w6f+n9bgiARBEJ6NKLpr0MtYdJfQaCTO7LrH5tB4zuy8V3IrMW5NtdHzPuNdsbCunuj55cUniA47hOrmgwi8TIb3kJb4KgJwf7USoufHz2uj52t26lY9P1ffjJWOhmy9Eo36QWT8UUaOHMnq1asr7vvsUZThoWTvWlsaPXdyw+ad6di8+R4G9Spntjfzfhwxh+dx8dgCCnK1+5YbGpvTrOM4/PwV1HNu8YQeqp4kSZxP3096fgqvuo6t6eEIglALlcxyn719FrWkxkBmQDvndmK2uxb76yx3CTHbLQhCXSOK7hr0Mhfdf5VyI4fNYQnsXphEXpa2cDSzMqDvJDcCFZ64NDKv8jFIGg1xOy4THRJBwu7ShbrqtXDCV+FPs7Ed9Y+e376L6tdVqH5ZhTpVW+DfMYK1zexZkXiVe8qMcsfs27eP3r17P7nvO8moVv2CatWvqNPTAJAZm2A15B1sxiowbdFWr7GXKCrI4eqZFURHhnI/JUbX7takN77+CrxbDakV0fPqIEmS+CNdEOqYh2e5S4jZ7trr4VnuEmK2WxCEukQU3TVIFN1l5WYVsz88hc2h8SReyQFA8UsLBk7xqNZxpF9JJWbuIS4vPkFRdgEAxjZmtJjUGd8gf2wa6jd7rCkoJHvNDpSh4RScjAagAA27G9Vjqfo+UXGxALRs2ZKYmJhHFnaFhYXk5OQ8Onq+fTXK8BAKLpzRtZt26IntWIU2em5kpNf4QVtwJt+IICoihFsxm/4SPffWrnpeS6Ln1eFO7i2czL1rehiCIDzBw7PcJcRsd+31qFnuEmK2WxCEukQU3TVIFN2PptFInNtzjx2/J/Hh4tbVssL5oxSo8kqj5ze0s8fIZHgPbomvwh/3Pk31/gMt/0QUytBwslbvgKIiJCTO25uxwtmIgZPG8v7fPnjkcStWrGDy5MmMHTsWhUJBq1atyjwuSRL5549ro+c71+hWVDdwcMF29HSsR72PYb0Geo29RGZ6PDGH5nHp2ALyc7X7lhsamdG041j8AoKxd25ZKa9T22yJn8vB2ytRFaYBEiO8P6a/++SaHpYgCBWoaJa7hJjtrn0qmuUuIWa7BUGoK0TRXYNE0V17PC4qLGk0xO+6QtScgyTsKo2e2zVz1EbPx3XC2FLP6PmdNFS/rCwTPZcZG2E5aiC2irGYdvQt8/yuXbty/Phx3devvPIKwcHBDBkypNyq58WpKaXR8/t3H/RtguWgt7AdF4xpy3Z6jb1EUWEuV08vJzoyjPsp0bp2tya98e0ZhHfrwBcieq7WFLMq9luW35iNb71etLDrgaowjQMpyxnv8w1DvYJreoiCIDykZJb7TMoZNGjKPS5HTnuX9mK2uxZ53Cx3CTHbLVSmxecXM3HTRBYNXcSENhNqbByy2TICPAM4OOFglb1GZX2vEzZOYEnUEm7NvIWXrVelje9FVBV1n/jkE+qckj+y7twq/8tdJpfjNaAFQ3dOZ8yVT/FV+GNkZULGlVQiZqxhkevnRH6wDmXJbPhzMHRqgP2XwXgnHMRx+X8w7eyHVFhEVvgmEjuNILHLSDJXbEEqLOTUqVNlCm6AAwcOMHz4cBo1asS///1v0tPTS/t2dMF+5ld4RSTg+O9wTFp1QCosIGvDEhKHtyfxrR5kbfsTqajouccPYGRsTqtu7/H2P8/zenAEjfxeRyaTk3RtP9v/eJ2lXzXi7L6fyM9Jf3Jntdjh1HWsufUjA92n8n2n/Yzz+YrxPt/Qrn5fNiWEkFVYt78/QXgRFaoLSVAlPLLgBtCgITEzkUJ1YTWPTKhIdmE2+UX5j31OfnE+2YXZ1TQioa6IU8Yhmy2j/7KKky2C8CIQM91PScx01x5b5sZzcOVtVGmFIMGIj73pP9m9wucXZuZxeclJokMjUV4vjZ57DWqBX0n0XM8r7/mnorXR81Xb4UFBbODUgHXtXflk1waKH0TGH8XMzIwxY8agUCho3bp1mcckSaIg+iTKpSFk7VxT2reDC7bvTNNGz+0d9Bp7iaz0BGIOz+fisd/Jz9HuW25oZEaTDqPxCwimvkvrJ/RQu+Src5lyqAX1TV35tuMeTA3MdSsg70xcwK9XPiCk62ncLZvV9FAFQXhIoiqRtNyKL446WDjgZu1WjSMSnuRE0gluZNyo8PEm9ZrQ0bVjNY5IqAvilHF4z/GmX6N+7Byz86mPU+WruJ19G2dLZ2xMbapwhI935d4VzI3M8bCpujWNKut7vZ11G1WBikZ2jTAy0H/NoBeZiJfXIFF01zx1sYZV38ayfPYNfHvVo0UPO1RphRxYnsL4b3wYGuz12OMljYaE3VeICokkfsclXbttEwd8Ff40H98JYytTvcZYnHpPu+r5/JWo72j/YEw1hPXN7FmefI27GY+fWe3VqxcKhYLAwEAMH9q/u/jubVQrf0H156+o76UCIDMyLo2et2qv19h1r1OYp1v1/F5ylK7dzecVWvsH0bBVIHKDmrl3/1msvfUTa2/9yNTmIfRyfktXcKslNZvjQ1lw9SPCup3D26puXUwQBEEQhBfF8xbdglCVRLxceKkdXpfK2n/fYsAUd77f34lxX/kw/hsf2vWtz+bQBDLvPz5qKJPL8ezfgsDtUxlz9TP8ggMwsjJBee0ukYq1LHL7gsiZ68i4dve5x2joWB/7L4Lwjj+A04r/YtqlDY7FMO3CffZn2PG/hh1o6924wuMPHjzIG2+8QaNGjfjhhx8oKCgo7dvBGfuZs/E+mIDjT8sw8e2EVFRI1salJL7egcQ3u5K1daXe0XNDYzNadn2Xtz4+x+szI2ncZiQyuQFJ1w+w4483WPpVI87s/bFWR88L1HlsjPuZFrbd6O74OqC9DxRAkjTczDyHg6knnpYv5sJxgiAIglCXTdg4AdlsGbEZsfzn6H9oMbcFJt+YMGHjBEB7n7NstozF5xeXOe7s7bOMWD0Cj/95YPKNCQ3+3YCOv3fk28hvn/ia7256F9lsGZHxkY98/L/H/otstozfz/yua5PNltFrca9nGjtARFwE/ov8sfiXBfY/2jNq7SgSVYn0WtwL2eyya1VU9L2WvHZqdirjN46n/o/1MfvWjC4LunAw7mC58ZeMK04ZV+6xyPhIhq0ahuNPjph8Y4L7/9x5/c/XOZxwWPeclKwUZh2YRZcFXXD4twMm35jg9bMX07dN527O8//t/LIQRbdQJxTkqVn4z6s09LPivf9o48BqtYS1vTEd+tcn/XaBNm7+lOyaOOA/5w0mJX9NQNgIbJs4UJiZT1RIBMuafsPmgb8Qv/MSkubR9xQ+iczYGKu3B+N+bDXup9ZhNW4YJsYmDIpVseoWrLVrxRut25ebzS6RkJDAH3/8gdEjtgyTGRtjHTgaj7UncF9zHKvA0WBkRP7549z5+zvcesWT+2FfUfxgNvx5yWQyXBv1ZMCk1Yz/IpYOfT/B1KI+WRkJHN38TxZ+4cq+FZNJ+8tseG1x4u4WCtQ5dHUYhpHcGLWk1q0FkF5wmxN3N9PFIRC1VHHs/1ZWNDsSf2fJtc84lrqpuoYuCIIgCMIDih0K/nX4X3Rw6cAHnT+gtUPF6bTzd87T7Y9u7Lixgx4ePfh7l78zovkIzI3M+e3sb098rbF+YwFYFr3skY+HR4djYmDCyJYj9Rr77pu76RPeh5PJJxnRYgTvt3ufeGU8PRb1QJmvfKq+SyjzlfRY1IOLdy8y1ncsrzd/ndMpp+m3rB8X7l54qj7mHJ9Dr8W92BO7h9cavsaHXT+kt3dvolKjWHtpre55kfGR/OfYf3C0dOTtVm+j6KSgUb1GzD89n65/dEWVr3qmsb9san9GVBCArfMSKMjVMCTIA1NzA9RqCQMDGWq1RF62msJ8DcVFz36nhLGVKb4z/Gk9rQeJe68SFRJJ3PZLxO/Q/s+2iQO+M3rSfGLn546em3ZojdOSHyn+9z/J/O1PlPNX4JtyF9+MAv5m6M36VvYsS7nO3fT7ZY5TKBRPXOXV1K8zTn6dqf/Pn1Ct+hXVql9Q371Nesgs0ud/g9XAt7Adq8DUV7/76KzqedB18Ld07Pc5186sJCoihHvJ57l0/A8uHf8D18YB+PoraNh6aI1HzyVJIir9ADKZnACXtwGQUXrVeHvirxRLRbSv3w8jufEj+9gcH0b4jS/IKVLiYt6YDXH/xdOqFcEtf6ORdZvq+DYEQRAE4aUXnRrNuSnnnuqe6fCocArUBWwcsZGhzYaWeex+7v0KjioV4BmAh40Hay+tJXRAKCaGpbvdXLh7gfN3zjOixQhsTW2fe+xqjZr3t7yPWqPmwMQD9PDooXts/MbxLI1a+lR9l4hKjWJ6h+mEDgxFLtP+zdjbqzeTt0wm7GQYvwz+5fHH34ni77v/jrOVM0cmHSmzqrkkSdzOvq37urd3b+58dAdLY8syfSyNWsr4jeMJOxkmtgV8DDHTLdR6BXlqNvwvjhbdbOn+hhMAJbWopJG4eS4TB09TvFpZVtiHWi2Rm1XxrKZMLsejb3OGbJ3C2Guf4TczAGNrU230fOY6Frp+TkTwWv2i5w721PtsOt5xB3Ba9T9Mu7XDoRimXrjP/nRbfm7YgfYNfQCwtLRk/PjxFfYVHh7OvXv3Svtu4IS9YhbeB+Jx+u8KTP06Q1ERWZvCSRzRicSRXcjcsgKpUL/Vfg2NTGnRZSJvfXyWN2YewqfdKGRyA5JvRLBj4QiWfNWQ03u+Jy/nyb/cqopMJiM17xYNrfwwlptQpCnU/SKKz7rI1oS5dHd8g8bW2u3XHl7W4lLGURZe+yeNrdsxt/t5vuu4j/9r8yc5RSrWx/2n2r8fQRAEQXhZ/aPbP555kTIzI7Nybfbm9k88TiaTMbr1aDLyM9h2fVuZx8KjwgEY03rMU4/jUWM/nHCYeFU8Q5oOKVNwg3YvewPZs23XamFkwQ+v/aD7OwdgfJvxGMoNOZVy6onH/3rmVzSShm9e+abcNmIymQwXKxfd1w4WDuUKboCxvmOxNrFm7629zzT2l40ouoVa78SWuxTkqOk6zAEjYzlqdek+3em3Czix+S5dAh0eO9N9fu89wqZd5PcPr3B2z70Knwdg27gB/j+/wcSkrwiYOxK7Zo4UZRUQHRrJsqbfsKn/POJ26BE9NzLCatQg3I+swv30eqzGD8fE2ISBsSpWxsI6u5b8+OpQzLPzHnl8VFQU48aNw93dnXfffZfz58+X9m1sjNXgt3Ffcxz3tSexGjoWmZEx+VEnSP1wtDZ6Hjqb4rQ7zzV23evIZLg06kH/CauYMCtOFz3Pzkjk2Jb/x6Iv3Ni34l3Sks4/sa/KJkkSpgaWpOUnoixM081mp+TcIPzGF5gaWNLfbTK2Jg667wVAI2n/PXcnL8TKqB7jfb7F28qXBmbudHEYQoDzWxxIWc6trJhq/54EQRAE4WXUybXTUz/3zZZvIpfJGf7ncCZtmsTKmJUkZyY/0+uN9dVGzMOjw3VtGknDigsrsDezZ6DPwKfu61Fjj0rV3pLXw71Hucfcbdyf+QJDE/sm5QphQ7khjhaOTxVVP5l8EoC+jfo+1eutv7yefsv60eDfDTD8yhDZbBnyr+RkFmSSkpXyTGN/2YiiW6jVJEki6kA6MrmMgLe1V9tkf1lfYvuviRQXSbTvVx8j40e/nYsKNeTnajiz6x57lyTzWb/TTG4aifIJ94AbW5niO70noy/+P4bumobX4JYgk5Gw6wpbBv5CeNNvOT/nIIWZjy6On4Zp+1Y4Lf4Br8RI7L/9G4aujrTOKKTPppPc8nyF22//jbxj58rMxoaGhgKQn5/PwoULadu2Lf7+/qxZs6bM1mSmvh1x+vdSvCISqBc8GwMHZ9Rpd0gP/ZJbvTy489FY8qNOPvfYS1jaudF18LdM/CqRPmOW0MCtHeqifC4dX8iqH9uybo4/N86tRaOuOGlQmWQyGa+5TiCnWMW+5KXEZ10kJecGv175gKOpG5jQ5F+0sOsOlJ3llsvkqCU1J9O20cSmo26RtQK19t/Xx6Y9MpmcYk1huWMFQRAEQah8jhaOT/3czm6dOTj+IP6e/qyIWcE769/B7X9udPq9EwduHXiqPpo3aE575/Zsv76djLwMAA7GHSQpM4lRLUc901Zbjxp7ZkEmoJ01fuQxlk///QJYmzx6ZW1DuSFqjfqJx6sKVMiQ4Wzl/MTn/ufof3hj9Rucu32Ovo368mHXD5kVMItZAbOwMbGhoLjgiX28zETRLdRqMpmM1Ft5NPSzwthETlGhBrlcW3XHX8xi69wEur/hSON22g+dRxVCRsZyug935M+0V5n0Y1MsbAyxtjfGqt7TfXDqoudbpjDuxue0+VsvjG3MUN1I49AH61no+gURirVkXH3+hcsMHeyp98k0vG7tx2n1HEx7tIfiYrJXbSOp2ygSO75B5tINpKXcZvny5eWOP3ToEG+++Sbe3t7861//Ii2tdH9bw/qO2Ad9gff+OJz+uxLTtl210fPNy0gc2ZmENzqRuWkZmkL9PiwNjUxp3mkco/5xmjc+OIxPu7eQyw1JuXmIHYtGsmS2N6d2/4u8rIr33q0MkiThW68XAU5vseja//HZmf68d7gZNzPPM87nG/q4jtPFsGSysiuEZhdlYGVUj9ziTMwMtVeOTQy0MbUDKSuQIydPna07tlCdT/T9gyy/MZs5F97nTNquKv3eBOFltDd2Ly3mtmBvbOVGF6ui37o01rqoLp2HujRWqL3jffj39JP09OzJjtE7yPhnBgfGH+DvXf5OzN0YBq0YRGxG7FP1MdZ3LIXqQlZfXA2UznqXLLSmz9hLiuSKVvtOzdZvEdxnZWtqi4TE7azbj31esaaYryO/xtnSmQvTL7D89eX88NoPfNnrS2YFzKJQrd/ti8+rtr5vH0UU3UKtJkkSppYG3E3IR5lWqJvNTrmZS/gXNzC1MKD/ZDdsHbSLXTzuw1mjkcjPUZOjKuadLxphYFD63KedtbRpWJ+e/32diUlf0Wv+m9g1d6Qou4DosEiWNfuWTf3mcWvbRf2i5yMH4H5oJe5nN2I98Q1kJsYUnLlA6vh/cq31QAJ9Wj1yVXOApKQkPv30U9zd3Zk4cSJnz54t7dvYGKvBb+H+51Hc153SRc8LYk6R+o+xxPXy5H7IlxTfffwH7xO/B5kMl4bd6T9hJeO/jKNjv88ws2xAtjKJ41s/ZdEsd230PPGcXq/zuNc3M7RkWosQ5nePYYjHDD72Xc6/O0cy0vtjANIL7qCWyl8BtjGuTys7f25mniM6PQKAYk0RMemRHLqzGmvj+jSz7QJo42bzLwfz5dkhbIoP4WbmWWafG8q/o8eSVZRRJd+bILxsJEnik32fcPneZT7Z90mlJUyqot+6NNa6qC6dh7o0Vqh7430aZkZm9PLqxX/6/YdPenxCXnEee27ueapj3279NoZyQ5bFLCOvKI/1l9fTuF5jurh10Xtcfo5+ABxJPFLusaTMJBJUCXq/xrPo5KKNwO++ufuxz7uXew9VgYqu7l3LzdKfTjlNXvHzpz6fV11734qiW6jVZDIZr01wJTezmH1Lk4m/mEXKjRx+nXmZoxtSmfBdE1p0twMqLpxL2mOjstjxayIte9rRoX+Dh56j/e+WufGc2f34e74BjC1NaD21B6MvfsLQPTPwHtJKGz3ffYWtg3/VRs9/PkCBSo/oedsWOC78rjR67uaEQ3oO38SoiNB48Y9WXXCyr//IYwsKCli8eDHt27enR48erF69mqK/7N9t2rqDNnoemYj9B19j4OCC+l4q6WGztdHzD0eTH3XiucdewtLWlS6Dvmbi7EReG7MUB48OqIsLtNHzf7dj7c89uH52dZVFz90tm/Fmw/8jwHkUzuYNMZAbklOcyQ9Rb/NT9DhddBxK3ydvN/oMbytfPjnVh1lnhvDZ6f58c0671/drrhMxlpugLExj2Y0v2ZW0gCEeQfzR8zqz2m1mctOfOJ22kwvpj97jUxCEZ7P75m7dYkCnUk498Q/Dmuy3Lo21LqpL56EujRXq3ngrcizxGPnF+eXaU3O0s8emhk+3C42DhQN9G/XlSMIRfj7+M5kFmc+0gNrj9PDogYeNB1uubeFY4rEyj31+4PNHTghUpakdpmIgM+CzA58Rr4wv85gkSbr7tB0sHDAzNOPs7bPkFuXqnpORl4Fih6Jax1yirr1vRdEt1GqSJOHbqx4Bbzmx6P+u8Vn/M7zX7DA3z2cy7hsf+oxz1cXNK5rllslkFBVqOLvrHgmXshn1/xqWeVyjkZDLZaQl5fP7h1f5vP9ppvke5uS2J69ULpPJ8OjTlMGb32fczS9o+2FvTGwfRM//toFFrp9zcMZq0q/oET1vUK80er4mBNOeHaivhvcu3GfvfVtCvTrQqVHTCo8/cuQIo0aNwtvbm+PHj5ft296BetM/w/tAHE7/W4Vpu+5QXEzWlhUkjuyijZ5vDNc7em5gZEKzTmN588OTjPjgiC56fjv2CDsXj2Lxl16c2vUNuVnPvzr807qZeY6Y9AgScy7rouNQ+v6pb+rK52038LdWC6lv6oajmRfmhjYYG5jR120SAKfTdrA+7j8MdJ/KGJ/ZWBnXw97UhX5u72JqYM7pezur/RenILxoJEni8wOf61bzNZAZ8PmBz/WezaiKfuvSWOuiunQe6tJYoe6N93F+OPIDjj85MmTlEIJ3BPPxno/ps7QPc0/NpaFdQ4Y3H/7UfY31HYuExKyDswAY41s5RbeB3IBfBv2CXCan99LeTNg4gf+39//R7Y9u7L+1Hz9HvzLbnFa11o6t+bn/z9zOuk3LeS0Zs34Mn+77lHc3vUuTsCb8eORHQLvuzfSO04lTxuH3ix9/3/V3Jm+eTKv5rZDL5GVWOa8OdfF9K4puoVaTyWSYWRoyLaQF82O6M2SGBx8v9+XfkZ0Z+bE3AOl3ClCrH/9DFn8xm33hKfj2qldulrvEhv/ewtTCgMBgTzxbWjI78CzTfA9zeufT3YNs421Pj5+GMTHpK175ZRT1WjpTlFNIzLzDLG/+LRv7zuXWlpjnj54bGmI1oj/ukSvwOL8J60kjMDE1pV+cimU3NWywacGbrTtgbPzovaczMjJo2vTRxbnMyAirQaNwX3UY9w1nsBo+vjR6/vE44gI8uD/nC4pT9VuZUiaT4dywG/0nrGTC7AQ69v8CMysHclTJHN/2OYu+cGfPsgncTTz75M6ek2+9AOZ1j2ZWu826thuqsxxJ3UDRg0XSLI1sedV1LIqW87EzceJuXhz93SbjYt6IO7m32Ju8GCOZMe83+y9GcmMkSUKtKUaSNFgb1ye9IOWZt/0QBKGsklmMkgtYakldKbMZVdFvXRprXVSXzkNdGivUvfE+zrQO0xjWbBjX719n8fnFzD89n9vZt/mkxyecmHyiwkXHHmVo06FYm1hTpCmiq1tXGtVrVGnjHOAzgN1jdtPBpQOrL67mt7O/4WbtxuGJh1FL6mcaZ2UI6hTE/vH7ecX7FXbc2MFPx35id+xu/Bz9eLPlm7rnfffqd3zb+1tkyJh3ah57Yvfwdqu32T12N0byp19grjLUxfetTKrNlwRqkczMTGxsbFCpVFhbV+8Pg1CxnMxivhp6lnouJnywoBUmZqWFjiRJulnudT/dYuln1/l6Zwfa9y2NZJfMct9NyOODzsdp1tmGvy1qDcDFQxls+yWBhIvZTAttQZfAR680WRFJkkg6cJ2okAhubb6gy7DbNKpP6xk9aTGxMya25np9/+p76agWrEE1bwXFidp7se/LJTa0qM/S2ze4c780Kj9lyhR++eWXp+67OD2NzD9/Q7ViPsWpD7bcMDTEst8IbMcqMG3b9ZkXOHnk91BUwPXza4iKCOFuQumeks7e3fANCKaR3+sYPMNqoU+r5P0BcOLuVpbdmEVPp5EEOL+No5knaknN/uRw/ndhEl5Wrfm560mM5SZsT/yNuRenMaHJd4xs+DFqTTFymQEymYx8dS7v7Hfida+/M8bnyzKvIQjC05Mkic4LOnP29tkyqREDmQHtnNtxYvKJ5/rZqop+69JY66K6dB7q0lih7o33RZdVkIXjT460dmzNicn63+L3oqqO921V1H1ipluo026eyyQmIp3EyzmYmBmUiZWU/MDFxWSxf1kKfr3tyxTc2udo/7vx5ziUqQXYOhpjZWeElZ0RXQId+NvC1ny2vi2t/B9/3/ijyGQy3Hs3YfDG9xh38wva/eNVTOzMUd28x+G/b2Ch6xccmPYn6Zeef+Eyg/r1qPd/U/CK3YfT2lDM/Dtir5Ex+cJ99t23JcyzPZ0ba2e3g4KCKuznyy+/5OuvvyY1tTQGb1ivAfWmfYrX/ls4/fwnpu17aFdU37aKpLe6k/hGRzLXL0FTUP7+qWf6HoxMaNZxDKM+OsnIvx2jSfu3tdHzW0fZtfgtlnzpzcmdX5ObWbkrev71A7mZbRe8rXxZfmM2P0WP5ZtzI5h2uBX/uzCJLg6BKFr+qr2Xu+AuUff3Y2ZoxQjvfwAglxmg4cEe30kLKVDn4GbRtNxrCILw9B6exSih72xGVfRbl8ZaF9Wl81CXxgp1b7wvipzCHLIKssq0qTVq/rHnH+QV5zGs6bCaGVgdUVfft2Km+ymJme7aK+5CFha2RjRwM6W4SIOhkRxlWiG2DbQx61X/usnSz67z7e4OtO1TfuGx/Fw1YVMvkptVTNT+dGwdjJn8U1O6Dn22vRKfRlFOAVeXnyY6NJL7F0qLbbdXm+Cn8MdrcCvkBvpdCyuIuowyNJys5VuQ8rX3Yt+yNaHd1PHYTB+NkXvZvRhVKhWurq7k5ORgbGzMqFGjUCgUdOzYsXzfl86jDA8ha8sKpAf3eRvUa4D1qPexfXsahk6ueo29RE7mHS4c+ZWYw/PIe3Cft9zAGJ92o2gTMBMHj/aV8joPu5xxjHVx/6FIk4+ZgRVt67/GKy6jMZZrV8dPy0vk7ye60d3xdaY2n4NaUiNHriuupx/xw1BmxP/5rcLForGY6RaE51Ayi3Em5YzugtZfyZHT3qX9M89mVEW/dWmsdVFdOg91aaxQ98b7Ijl/5zw9FvagX+N+NLRtSFZhFocSDnEp7RItG7TkxOQTWBhb1PQwa6Xqet9WRd0niu6nJIru2u2vxY3qXiE/vBNFm1ftcfI2I/yLGzh6mfHNzg66OPmjKNMKuROby9LPr3PtpIp/rvSj44BH3/9dGeNNjrhB1JwIbm2OQdJofwytve3xDepJ84ldMLXTM3p+P6M0ep7w4F5sAwMsh7+GrWIspj07IJPJ+Pnnn/nb3/5W7vguXbqgUCgYMWJEufvEi9PTyFy9ANWKeRTfSdI2Ghpi+drr2I4LxrRdt0qLnt84v5aoyFBS40ujVk5eXfD1V9C4zQgMDB99D7s+8otzMDUs/YWnltQYyAy4lRXDjCN+/NNvJf5O2vucNJIaA7khWxPms+DqR7zu9SHjfL6q9DEJwsuioLgAz589dSsOP4qTpRNxM+MwMTSp0X7r0ljrorp0HurSWKHujfdFkpaTxsd7PyYiLoLUnFSKNcV42HgwrOkwPvX/FFtT25oeYq1VXe/bl6Lo/u6771i/fj1XrlzBzMyMbt268cMPP1S4ABTA77//ztKlS7lw4QIA7du351//+hedOnXSPWfChAksWbKkzHH9+vVj586dTzUuUXTXHel3Cvh8wGluRWVhamlAfraaD/5oRd+Jbo98/l8LcY1GIvFyNv/wP0mHAfX5eJlflc9WZsbdJ2b+YS4tOEZ+unYbBkNzY5qO6YCfwh/7VvqtCCkVF5OzZT/K0GXkHShdvdzYrxnWQWPo+N3/42ZsbIXHOzk5MXXqVKZMmYKTk1O5vrP3bkQVHkreqdJtskxatsN2rALLQW8hN3m6LTqe5E78SaIjQrh+bjUatXb7MwtrZ1p1n0rL7u9jYe30hB6ezaP+3S9kHOaz0/2Y0WIer7mO17XnFmcxKbIRruZN+FurP3CzbCpmuQVBD4mqRNJyK17E0sHCATfrR3+mV3e/dWmsdVFdOg91aaxQ98YrCFA979uXouju378/b731Fh07dqS4uJhPPvmECxcucOnSJSwsHh21GD16NN27d6dbt26Ympryww8/sGHDBi5evIirqzbuOmHCBFJTU1m0aJHuOBMTE+zs7J5qXKLornuunFCybNYNzu6+h7efFa+MdqHbcEdcGpXOIJe8/WUyWZki6bP+p4m/mE3o2W66mHpVK8otLI2ex5SuEu7Wuwm+Cn+8h1RC9DzmqjZ6vmwzUp72XuxLNkascjdnw/UYCgoq3hrMyMiIN998k+Dg4DIXtHR9X45CGR5K1pblSA/u8zawq4/1qPexeWcaRk6V84s7NzNVGz0/Mp/czDsAyA2M8Gk7Cr+AYBw9y8fiK0tWUQb/ONETN4tmTGsegr2pCyk5N/jj2sdEpx8kqMV8ApxHVdnrC4IgCIIgCFXrpSi6H5aWloaDgwMRERH4+/s/1TFqtRo7OzvCwsIYN24coC26lUolGzdufKo+CgoKyhQgmZmZuLu7i6K7Drp0NIOF/7zGpSMZfLKmDT3ecCI3q5iiAg029bUF9V8L7uIiDV8PP8fdhDzmR/eo9vFKkkRK5A2iQiOJ3RCti55bedbDN6gnLSZ1wbSefvf6qNOVZP6xFuXc5RTHa1cmT5dp2NC8PsvSbpGc9vj9sjt16kRwcDAjR44sFz1XZ9xHtfp3bfT8dqK20cAAy9eGYzs2GNMOPSonel5cyI3za4mODOVOXOkMvqNnZ/z8FTRuO7LSo+eSJLElYS4Lr/2T1nYBWBvbE51+EGVBKh+2XkI3x+EYG5iKWW5BEARBEIQ66qUsum/cuIGPjw8xMTG0atXqqY7JysrCwcGBNWvWMHjwYEBbdG/cuBFjY2Ps7Ozo3bs333zzDfb29o/s48svv2T27Nnl2kXRXXddP6OicTtrZDIZl45msGzWDQZN96D78NIF00ri5R90Pk6/d92Y+H2TMtuQVbfM+HQu/HKYi78fI/9+DgCGZkY0HdMRX4U/9VvrGT1Xqx9Ez8PJ268tXIuROOhhTbhJLseuX3ns8TNmzCAsLOzRfRcXk7NvM8rwEPJORujaTZq3wWZcMFaD36606HlqwmmiIkK4fvZPNGrtXtvmVo606jGNVt2nVHr0/Oy9PayO/R6NpMbVwodujq/TscGASn0NQRAEQRAEofq9dEW3RqMhMDAQpVLJ4cOHn/q46dOns2vXLi5evIipqfaP+lWrVmFubo63tzc3b97kk08+wdLSkmPHjmFgUL6oEjPdL6aSt3tsVBY/jo7GzMqAYTM9adrZFueG5lw9qWTJp9eJv5jNR+G+tH310RdlqltxXiFXV5whOjSSe1HJuna3V3y00fPA1vpHzy9c00bPwzfpoudXrI1Z5WnO+mvR5D8ien7mzBnatWv35L6vRKNcFkbW5mVI+XkAyG3tsSmJnju76zX2ErmZqVw89jsxh+eTo9JG9OUGRjRuMxK/gGCcvDpXyuuUyCrKwMqo9BYVMcMtCIIgCIJQt710Rfe0adPYsWMHhw8fxs3t6e4H/f777/nxxx85ePAgvr6+FT4vNjaWRo0asXfvXl599dUn9ivu6X7xXDutYsFHV7h8VIm3rxVFhRqSruagLpL4aKkvPUY6YWwir1WFlCRJpBy6SXRoJDfXR5VGzz3saD2jJy0nd9U/ep6hInPhg+j5Le3K5OkyDZuaNyD83i2S7mpXjOzevXuFF8Py8/ORyWSYmJRdOVKtTEe1ZgGq5XMpTknQNuqi5wpMO/SsnOi5uoib59cRFRHCnbhjunZHz074+ivwaTMSAyOxGqsgCIIgCIJQ1ktVdAcFBbFp0yYiIyPx9vZ+qmN++uknvvnmG/bu3UuHDh2e+PwGDRrwzTffMGXKlCc+VxTdL66ze+6xZ1EyGrVEPRcT2r5Wn04Dq2arsMqUlZBOzPzy0fMmo7Wrntf31W/PbEmtJmfrAW30fJ+2cC1GIsLdmmVmeQR99glvjR3zyGPnzZvH7NmzmTJlClOnTsXFpWwMXiouJmf/FpTLQsk7fkDXbtzUF9txwVgNeQe5qZle4y9xN+EMUZGhXDuzskz0vGX3KbTuMa3So+eCIAiCIAhC3fVSFN2SJKFQKNiwYQMHDx7Ex8fnqY778ccf+fbbb9m1axddunR54vOTkpLw8PBg48aNBAYGPvH5ouh+8RXkqcvcv12bZrgfpzi/iGsrzxA1J6JM9Nw1oDG+wQE0DGyF3FC/+9ILLt1AFbaMzCUbkHK18XCZrTU2k0diO2M0Rl6lSRRJkmjRogVXrmjvBzc0NGTkyJEoFAq6dOlS7pwWXI3RRs83hZeNno+cjM3o6Ri5eOg19hK5WXe5ePS3stFzuSGN247E11+Bk1f5sdUWkiSxLXE+3Rxfp56JuEggCIIgCIJQVV6Konv69OmsWLGCTZs2ldmb28bGBjMz7czXuHHjcHV15bvvvgPghx9+4IsvvmDFihV0795dd4ylpSWWlpZkZ2cze/Zs3njjDZycnLh58yYff/wxWVlZxMTElIvAPooouoXaTpIkbh+JJSokgpvro5HUGgAs3e1oPa07Ld/vjpm9ntFzZSaZi9ahCltGUeyDlcnlciyGvIJt8DjMXunC3r176du37yOP79ChAwqFglGjRj0yep65biHKZWEUJ8eX9t1nGLZjFZh1Cqi86HnUeqIjQrh966iu3cGjA37+wfi0fbPWRc8vZxzj7ye6YSgzIsD5LYZ4BNHUtvy2bYIgCLXB3ti9BO8IJmRACH0a9qnp4TxWXRqrIFQH8TPxkhTdFf1RvWjRIiZMmABAr1698PLyYvHixQB4eXkRHx9f7phZs2bx5ZdfkpeXx7Bhwzh37hxKpRIXFxf69u3L119/jaOjY7njHkUU3UJdkp2UQcz8I1z47Qj597TRcwNTI5qObo+vIoAGfpUQPd8egSo0nNw9R3Ttxi19CPMw5qcdGx97vIODQ8XRc7X6QfQ8jLxj+0r7btoa27EPoudm5g93+VzSEs8RFRnCtTMrURdrF4ozs2xAq+5TaNVjGpY2+q0OX1kuZRxlwdWPuKwsvT+9iU1HhnrOpKfTSIzk1bOXvCAIwpNIkkTnBZ05lXKKji4dOTH5RK1OEdWVsQpCdRA/E1ovRdFdW4miW6gsyrva4s7WoepnU4vzi7i+6ixRIRGknUvStbv0bIRfsD8Nh/nqHT0vvHwDZegyMpduRMrJBeC6lRGrvCxYez2GvPz8Co81NDRkxIgRKBQKunbtWj56fv0iyvBQbfQ8T9u33LYeNiPexead6Ri5eek19hJ5WWlcOPobF478QrZSe5500fOeQTh5lx9bTbiqPMnmhFAib6+mWNLen25n4sQAt/cZ6D4Fe9PacZFAEISX164bu+i/vL/u652jd9Kvcb8aHFHF6tJYBaE6iJ8JLVF01yBRdAuV5be/X2bL3AQCRjkzROFJ0442Vf6akiRx++gt7arn686jKX4QPXezpdW0HrR6rytmDaz0eg21MpPMxeu10fOb2pXJlWjY3KIBS+/HkZB657HHt2/fHoVCwdixY5HLy25/plZlkLluEcploRQnxWkb5XIsXh2qjZ537lUpRbFGXUxs9EbOR8zhdmzpyuwN3Nrh12smTdqOqhXRc2XBXXYk/cbWhHmkF9wGwEBmSE+nNxnmOVNEzwVBqBEls2Rnb59FLakxkBnQzrldrZwtq0tjFYTqIH4mSomiuwaJoluoDJIk8Wm/05zbc1/X1ryrLYHBnnR/3REjY/322n4a2clKLvxyhJhfDpdGz00MaTq6A74Kfxq0ebrt+SoiaTTk7ohAGbqM3F2HAFAjEelmzXKLAiKvXqzw2I4dO3Ly5MmK+1aryTm4DeXSkLLR8yatsB2jwGromEqNnkcfCuPq6eVlouctu71P6x7TsLTVL6JfGYo0hRxJXc+W+DAuKUtj/j7WHRjqGUxP5zcxltf8RQJBEF4OD8+SlaiNs2V1aayCUB3Ez0QpUXTXIFF0C5Xp6kklW8ISiFh1m+Ii7Y+gnZMJg6a6M3CqO3aO1RM9v7HmHFEhkdw9naBrd+7eUBs9H+6HgZGe0fMrN1HOXU7m4g1I2doC/4alIasaWrHmWnS56Hl4eDhjxjx6G7KHFdy4hCo8lMyNS0uj5zZ2WI94F9t3pmPk/nRbDT5JXvY9bfT88Pwy0fNGbd7At2cQzg2714orwNdVZ9gUH0LE7VWl0XNjRwa6T2WA+/siei4IQpV6eJasRG2cLatLYxWE6iB+JsoSRXcNEkW3UBXS7xSw/ZcEtv+aRMYd7WyqobFMGz0P8qBpJ9sqH4MkSdw5Hqdd9XxtafTcwtWG1tN60PK9bpg76Bk9V2WVRs9vaBc9VKFhc/MGLE2PJz71Ng4ODiQkJDxyNwFJkli3bh2DBw/G1NS0bN+ZSjLXLUK1LIyixFhto0yGRe8h2I4Nxqxr78qLnsdsIioihJSbkbr2Bm5t8QsIxqfdWxgamT6mh+qhLExjZ+LvbE2Yy/0C7dZoBjJDejiOYKjXTJrbPnlLRUEQhGdV0SxZido0W1aXxioI1UH8TJQliu4aJIpuoSoVFWo4sj6VjT/HcfWEStfetLMNQ4M96THCqVqi5zm3VcT8coQLvxwh724WAHJjA5q+0wG/YH8atHXXq39JoyF3ZyTKkPAy0fNDrlaoX+3M+3N/Qm5ZfluzyMhIAgICqF+/Pu+99x7Tpk3D3b3sWCS1mpyI7ajCQ8k9skfXbuzTEpsxQVgPHYvcXL8t00qkJZ0nOjKMq2eWoy7SztabWtSnZbf3aN1jGlZ2+p2nylCsKdJGzxPCuJhRen+6j3UHAj0V+DuPEtFzQRAqRcks2ZmUM2jQlHtcjpz2Lu1rxWxZXRqrIFQH8TNRnii6a5AouoXqcvWUii2h8UT8eZviwtLo+cApbgyc6kE9p6ovlNQFRVxfc56okAjunvpL9LybN77BATR6vRKi51djUc5dTtbi9WiytNFzubUl1pNGYDNjNMaNPXXPHTFiBOvWrdN9bWBgwPDhwwkODqZHjx7lfgkU3ryCMjyUzI1LkHJL+rbVRs9Hz6i86HnOfS4e/Z2Yw/PIztDuWy6TG9DI93X8AoJrTfT8RuY5NseHcCBlhS56bmPcgIHuUxnoPoX6pjV/f7ogCHVXQXEBnj97kpqTWuFznCydiJsZh4lhzV7sq0tjFYTqIH4myhNFdw0SRbdQ3TJSC9j+ayLbf0kk/faD6LmRjJ5vOjE02LNaoucAd47fIiokkhtrzpWNnk/tQcv3KyF6nplN1pL1KEOXUXQ9Ttsok2E+MADb4HHca+JGw0aN0GjKX30F8PPzIzg4mLfffhszM7OyfWepyFy/GFV4KEUJN3V9W7wyWBs97/Zq5UXPL2wmOiKU5BsHde31Xf3w8w+mSfu3MTQ2q7iDaqIsTGNX4gK2Js7jXr72/nQDmSHdHV9nqOdMmtvWjq3RBEGoexJViaTlplX4uIOFA27W+i3UWVnq0lgFoTqIn4myRNFdg0TRLdSUkuj55pB4Lh9T6tqbdHwQPR/phLFJ9UTPL/yqjZ7nppZGz5u81R6/YH8c2nvo1b+k0ZC7+zDKkKXk7ii9Z/qWVwO+N83kwJULjz3e3t5eFz338Cg7FkmjITdiB8rwEHIP79a1GzduURo9t7DUa/wl7iVHExUZyrXTyykuygP+Ej3vPhWrevqdp8qg1hRz9O4GNseHciHjkK7dx7oDQzxmEOD8FsYGNX9/uiAIgiAIQnUTRXcNEkW3UBtcO61ic8hD0XNHYwZMcWfgFHfsXaq+UCqJnkeHRpJ6Ml7X7tTVCz9FAI3e8MPA2FCv1yi8dgvVvBVkLlyri57HmhvwZyNrVt+8QE5uboXHyuVyhg8fjkKhwN/fv3z0PPZqafQ8J1t7jJUN1m9MwnZMEEYeDfUae4n8nHQuHf+D6ENzyUrXnieZTE5D3+H4BQTj0qhnrZhVjs2MYlN8CAduL6dIo01UWBvVZ6D7FAZ5TBPRc0EQBEEQXiqi6K5BougWahNlWiE7fk1k2/wE7qdoCyUDQxk9RzoxdKYnTTvZVEtBd+dkPNEhEVxffQ5NkXaLCQtna1pN60Gr97th7qjfz4omK5vMJRu00fNrtwDIRM3W5g4sVSYSezv5scf7+vqyZs0amjRpUu4xdZaKrA1LUC4LoyjuurZRJsOi1yBsxgVj3q1PpUXPb13YQvShMJKu7de127v44uevoEmHdzAyrpy9xfVREj3fljiftHzt/ekl0fMhHkG0tCt/77wgCIIgCMKLRhTdNUgU3UJtVFykjZ5vCUvg4uEMXbtPe2sCgz3xH+VcPdHzO5lc/O0IMfOPkHsnE9BGz33ebItfcACOHT2f0MPjSRoNuXuOoAwNJ3d7BEgSGiSOuFiy3LqY/RVEz+vVq0dSUlK5e73L9X1oF8qlc8g9tEvXbtyouTZ6PmxcpUXP76dcICoyhKunlpVGz83r0eLBqufW9fQ7T5VBrSnm2N1NbIqfUyZ63si6LUM9gvF3HoWJQc3fny4IgiAIglAVRNFdg0TRLdR218+o2BwaT8SqOxQVaBcds3UojZ7Xd62G6HlhMTfWalc9Tz3xl+h5Fy98Ff40HtFG/+j5jXhUYcvIXLQOTaY2Hn5LFz2/SPaD1coB/vnPf/L9998/fd+xV1Eun0vW+sVoch7ct25pjfWISdiMnoGxZ2O9xl4iPzeDS8cXEnNoLpn3tTP4Mpkc79ZD8QsIxrVxQK2YVY7NjGJLwlz2p4RTqNFujWZtZM8A9/cZ5DGdBqYvz6IqgiAIgiC8HETRXYNE0S3UFcq0QnYtSGTrvETuJWkLJbmBjB4jHBk205NmXWyrpaBLPRVPVEgE1/8sjZ6bO1nTamp3Wk3pjoVTJUTPwzehDA2n6EosAFmo2dKsAUtVicSl3iE2NhZPz0fPHn/++ed4eHgwevRozM3LxrvV2ZlkrV9cLnpu7j8A23HBmHd/DZlc/wSBRqPWRs8jw0i6tk/Xbu/ii69/EE07jK4V0XNV4T12JS1gW8J87uZrt5CTywx00fNWdrXj/nRBEARBEAR9iaK7BomiW6hrios0HN2gjZ5fOFQ2ej4kyIOAt5wxNtVvr+2nkZuayYXfjnJh/mFybj+Inhtpo+e+Cn+cOnvp1b8kSeTuPYoqZCk52w7qoufX3O3p8eE0rCe+gYF12Xh4SkoKnp6eFBcXY2dnx+TJk5k+fTpeXmXHImk05B7ejXJpCLmRO3TtRt5NsB2jwHr4eOSW+m2ZViL99iWiIkO5cnKJLnpuYm5Hy67v0brn9NoRPZfUHL+7mY1xP3Mho3SF+YZWbRjqGUyA81siei4IgiAIQp0miu4aJIpuoS67eT6TTSHxHFxxWxc9t2lgzMAp7gycWn3R85vroogKjeDOsThdu2MnT/yC/Wk8sq3+0fObCajmLiNz4To0Km08XGZpgfWE4dgGjcG4qXZl8lmzZvHVV1+VOVYulxMYGIhCoeCVV14pv+p53HVUy8LIXLeoNHpuYYX1GxOxGROEsZePXmMvkZ+bweXji4g+FPZQ9DwQX38Fbj7lx1YTYjOj2Jowj/0p4RRotBcJrIzq0c9tMkM8ZuBgVvNbownCi2Jv7F6CdwQTMiCEPg37iH4rud+qUJfGKtRN4j1WdUTRXYNE0S28CFT3Ctn1RxJb5yaQllgaPe/+uiNDZ3rSols1Rc9PJxAdGsm1VWfQFD6Injta0XJKd1pP7Y6Fs41e/Wuyc8gM34QqNJzCyzd17eZ9e2A2bRQtpo4nNTW1wuNbtmyJQqFgzJgxWFhYPNR3Fpklq57fulrat/8AbMcqMO/Zr9Ki5/EXt3M+Ys5D0fPW+PZ8ED03sXhMD9UjqzCdHUm/P4iea+/jl8sM6OYwnCGeQbS2K79tmyAIT0+SJDov6MyplFN0dOnIicknKuVnSvRbderSWIW6SbzHqpYoumuQKLqFF4m6WMPRDXfZHBbPhcjS6HnjdqXRcxOzaoie383i4m9HiZl/mJwUFaCNnjce0UYbPe/ipdcvEUmSyNt3FGVIODlbD+ii58edLVlmq2bv5ZjHHm9ra8u7777LjBkz8Pb2Ltu3RkPu0b3a6HnEdnjwUWrk5YPtGAVWr4/HwLJyPivSb18i+tBcrpxcQlGhdqE4EzNbWnR9F9+eQVjbe1XK6+hDLak5eXcrm+JDiEov3RrN28qXoZ7B9HJ+R0TPBeE57Lqxi/7L++u+3jl6J/0a9xP9VlK/VaEujVWom8R7rGqJorsGiaJbeFHdis5ic2g8+8JTdNFza3sjBkxxZ9A0Dxq4VUP0vEhN7IYoouZEcPvoLV27Q0cP/IID8BnZBgMTI71eoyg2AeW8FWT+sRaNUntveZyZAasbW/Nn7EWycnIqPFYmkzFkyBCCg4Pp3bt3+eh5/A1Uy+eSuXYhmuwH961bWGH1+gRsxwRh7F1+n/DnUZCr5NKJRcQcmovq3s0HY5Pj1WoIfv4K3JqUH1tNuJUVw9aEuexLCadAnQuURM/fZbDHDBzNav7+dEGoC0pms87ePotaUmMgM6Cdczu9Z7VEv1WnLo1VqJvEe6zqiaK7BomiW3jRlUTPt81P4G58afS823AHhgZ70rKHXbV8mN89k0B02CGurTyDuqAYADMHK1q9341W03pg6aJn9Dwnl6xlm1GGhlN4UbsyeTYatjWtz9LsFK4nJz72+G+//ZZPPvmkgr6zydy4FGV4KEWxV3Tt5j37a1c9r8zo+aUdREWEkHh1j669nnNL/PwVNO0wpnZEz4sy2JX0B1sT5pKaFweAHDldHYcR6KGgdb3asTWaINRWD89mldB3Vkv0W3Xq0liFukm8x6qeKLprkCi6hZeFuljDsU132RwaT0xEafS8UVtt9LzX29UTPc9Ly+JCSfQ8+UH03FBOoxFt8AsOqJzo+f5jKEPDydm8vzR67mTBinoSuy9FlztGJpNx/fp1GjVq9MS+c4/uRRUeSs6BraXRc8/G2IwJwvqNiZUXPU+9QnRkGFdOLNZFz43NbGjR5V18e87Apn7DSnkdfaglNafStrE5PpRz9/fq2r0sWzHEU0FvlzGYGtT81miCUJs8PJtVQt9ZLdFv1alLYxXqJvEeqx6i6K5BougWXka3YrTR8/3hKRTma6PnVvWMGPC+G4One9DAverv0VUXqYndGE10aCQph0oXRXNo745vcABNRrXVP3oel4Ry7nIyF6zRRc8TzAxY7WPDqtiLZGZnAzBo0CC2bt36yD4KCgowNjYuHz1PuIlq2Vwy1y1Ek6W9eCCzsMR62Hht9LxRM73Grnv9PJV21fPDc1Gl3dA2ymR4txyCb4AC9yav1opfxPFZF9mcEPro6Ln7dBzNvWp2gIJQS1Q0m1XieWe1RL9Vpy6NVaibxHuseoiiuwaJolt4mWXef7Dq+byy0fOuwxwIDPKgdUC9aino0s4lEhUaybUVf4meN7Ck5fvdaD2tB5autnr1r4uehy2j8MI1QBs93960PktzbhPy2y/0GzDgkcd+++23LFu2DIVCwbhx47C0LLs3uCYnm8zNy1CFh1J445Ku3bxHX2zHBmMeMKBSoueSRkP85Z1ERYSQcGWXrt3Osbk2et5pLMYmlo/poXpkFynZk7yIzfGh3Ml7sDUaMro4BDLUcya+9XrViosEglATSmazzqScQYOm3ONy5LR3af/Ms1qi36pTl8Yq1E3iPVZ9RNFdg0TRLQigVksc33yXzSHxRB9M17U39LMiUOFJr3eqKXp+L5uLvx8lZt5hspOUwIPo+Rtt8Av2x6mrt/7R84MntNHzTftAo0FCwtDLDbugMVhPGoGBXem95UVFRXh7e5OcnAyAtbU1kyZNYsaMGTRu3Lh830f3oVwWRs7+zaXRc49GpdFzK/3uWy+RkXqV6ENzuXxiMUUF2r3FjU2tadFlEr49g7Bp8PiYfHXQRs+3syU+jLP3d+vavSxbMcQjSBs9N6z5+9MFoToVFBfg+bMnqTkVb23oZOlE3Mw4TAxNRL/P2G9VqEtjFeom8R6rPqLorkGi6BaEsm7FZLElTBs9L8grjZ73m+zGkBkeOHhUffRcU6yNnkeFRpISWRo9b9DWTbvq+VvtMDTVP3qumrcC1R9r0aQrAZCZm2E1dii2QWMwadWE1atXM2rUqHLHymQyBg4cSHBwMH369EH+0Ex2UeItlMvCyFz7R2n03NyiNHreuLleYy9RmJfJ5ZOLiYoMLRM992oxCD9/Be7NXqsVV8UTs6+wMX4O+1KW6qLnloa29HObzGCP6TiZez+hB0F4cSSqEknLTavwcQcLB9ys3US/z9lvVahLYxXqJvEeqx6i6K5BougWhEfLSi9k18JktoTFl0bP5dB1uCNDZnjg26uaoufnk4gOjeTqijOo84sAMK1vQav3u9Nqanes3O306l+Tm0fWii3aVc+jr+razXp34WPNbVYe3PuYo6Fp06YEBQUxfvx4rKysHuo7h6zNy1CGh1J4/aKu3bz7a9iMC8YiYGClRc8TruzmfMQcEi7v1LXbOjTFz19Bs87ja1H0fDFbEsK4nftgazRkdGowmGFeH+BX75VacZFAEARBEIQXjyi6a5AougXh8dRqiVPb0tg4J46o/aXRc69WlgQGe/LKaBdMzashen4/pzR6nqhdfV1mIKfR6774BQfg3L2h/tHziJPa6PnGvbro+QlHC1bay9h5OYrHfaxaWVkxceJEgoKC8PHxKd/3sf2l0XONNkFg5N4Qm3emYz1iEgY2+l08KFFR9Lx554n49pyBrYPPE3qoehVFzz0sWzDEI4hXXcZiZljzFwkEQRAEQXhx1Lqiu7i4mKtXr6JUKlGr1Y98jr+//3MPrjYRRbcgPL24C1lsmZvAvqUpFORqPxss7Yzo964rQ2Z44OhV9dtDaYrVxG6KITo0kuSIG7r2+m1c8VP40+Tt9hiaGev1GkXxyajmr0D1+xpd9DzRRM6apnasvHURVVbWY48fMGAAwcHB9O9ffiXSoqQ4VCvmoVr9O5pMbd8yM3Osh4/HZkwQJo1b6DX2EoX5WVw+sZjoyFCUadd17Z4tBuIXEIxH09cqZZZdX0nZV9mcEMqe5MXkq7Vbo1kY2tDf7T0RPRcEQRAEodLUmqJbkiS++OILQkNDyXrCH5UVFeN1jSi6BeHZZSuL2L0wic2hCaTG5QHa6HmXoY4EKqoven4vOpmo0EiuLjtdGj23t9Cteq539DwvvzR6HnUFgFw07GhSnyV5t7mSmFDhsX379mXXrl0VPq7JzSFrywqU4SEUXrugazfr+iq244Kx6DUImYH+CQJJoyHh6h6iI0OJu7Rdt8CbrUMTfHsG0bzzBIxNrZ7QS9XLKVKxN3kJWxLCSM7VXiSQIaNjg0EM9QymrX0fET0XBEEQBOG51Zqi+6uvvuLLL7/E1taWoUOH4ubmhqGh4SOfO2vWLL0HWRuIolsQnp9aLXF6RxqbQuI5t+e+rt2jhSVDgz3oPda12qLnlxceJ3ruIbLitRF4mYGchsNa4zezFy499I+e5x86jTI0nOwNe0CtRkLilIMFy+vDzsvR5aLnW7ZsYfDgwU/Vd96JgyjDQ8nZt0kXPTd088Z29HSsR7xbadFzZdoNoiNDuXxiMYX52n3LtdHzCbTuOQM7hyaV8jr60EgabfQ8IYwz90ovWmij5zPo7TIWc8Oav0ggCIIgCELdUmuKbi8vL2QyGadPn8be3r5SBlLbiaJbECpH/KVsNodqVz3PzymNnved5Mrg6R44N6ye6PmtLReICokg+eBfoud+rvgG9aTp6A76R88Tb2uj57/9iea+EoAkY5k2eh53GWVWJo0aNeLatWvlVjUHbUpo//79vPrqq+VXPU+OR7ViPqrVv6FRPbhv3cwcq6FjsR2rwMSnpV5jL1GYn8WVU+FERYSgvFu6eJxH8/60CZiJR7O+tSN6nnONLfFh7EleRJ46GwBzQ2v6ub7LEM8gnM0b1vAIBUEQBEGoK2pN0W1qasq0adP43//+VymDqAtE0S0IlStHVcTuRclsDonnzi1t9Fwmgy6BDgQGe+L3SvVEz+9fSNFGz8NPUZz3IHpez7w0eu5RT6/+NXn5ZK3ciio0nILzlwFt9Hynjz0Og15hwr+/QfaIpNCmTZsYNmwYPj4+BAUFMWHChHKfPZq83AfR81AKr0br2s269MZ2rAKL3kMqOXoeRtylbaXR8wY+tO45gxadJ2JsVvOfizlFKvamLGVLfBjJudcAbfS8Q4MBDPUIpl39viJ6LgiCIAjCY1VF3fdcUxTe3t5kZmZWygAe9t1339GxY0esrKxwcHBg2LBhXL169YnHrVmzhmbNmmFqakrr1q3Zvn17mcdL7kN3dnbGzMyMPn36cP369Qp6EwShqlnYGDH8Ay8WXPfnyy3taN+vPpIExzbd5f+9eoqprY6wdX4C+TnFVToO+1Yu9P71LSYmfUX3fw/F2qse+em5nPl+L0u8Z7P9jT9IOnj9sSuSP47czBSbSSNwP7sRt8jlWI4cgLmBEa9fz6DHz+uJa9SH9B9+Q30/o8xxISEhAFy/fp2ZM2fi6uqKQqEo83koNzPH5s3JeGw+j+uyg1j0fR3kcvKO7+f2jOHE9WlExoJ/o1amow+ZXI5n834MmbKFcZ9dp02vDzA2tUaZdp1D6z9g4ReuRKwNJiP1yZ/VVcnCyIahngp+63mZr9vvoEP9/tp4f9p2PjvTnymHW7A1YR65xY9fi+RFtzd2Ly3mtmBv7OO3uRP9CoLwMhGfCVriPFSN55rpDgkJ4dtvvyUmJgYHB4dKHVD//v1566236NixI8XFxXzyySdcuHCBS5cuYWFh8chjjh49ir+/P9999x2DBw9mxYoV/PDDD5w9e5ZWrVoB8MMPP/Ddd9+xZMkSvL29+fzzz4mJieHSpUuYmpo+cVxiplsQql7ilWw2hcSzb+lfoue2hvSd5MbgGdUUPVdriNt6gaiQSJL2X9O12/u64BvkT9PRHTAy1zN6nnQH1fwVZP72J+p7D+LhpiZYjR6CrWIs1w3UtG7dusLj+/Xrh0KhYMCAAeWj5ykJpdHzB8W2zNQMqyGjsR0XjEnTivt9FoUF2Vw9GU5UZCgZqZd17R7N+uIXMBPP5v1rRfQ8Oec6WxLmsjtpIXlqbbFtZmBFX7eJBHoocLFoXMMjrF6SJNF5QWdOpZyio0tHTkw+USmz/6JfQRDqMvGZoCXOg1aNxcsTEsquvCtJEh999BHnzp3jiy++oF27dhUOyMPDQ68BpqWl4eDgQERERIXbj40aNYqcnBy2bt2qa+vSpQtt2rThl19+QZIkXFxc+PDDD/noo48AUKlUODo6snjxYt56660njkMU3YJQfXJURexdksymkARu38wFtNHzToMbMHSmF216V1P0/OJtosMiubL0FMW5hQCY2JnT8r2utJ7eE2tPPaPn+QVkr9qGMmQpBecu6dqjfT2ZpbzBxYS4xx7fuHFjZsyYwcSJE7GxsXmo77zS6PmVKF27WZdXsB3zIHpewQKYz0KSJBKv7CH6UBi3Lm4tFz1v3nkCJmY2T+il6uUUZ2pXPX9E9HyIRxDt6/dDLqv5iwRVbdeNXfRfXrpF3c7RO+nXuJ/ot5L6FQShbhKfCVriPGjVWNEtl8sf+QeuJEmP/cNXJpNRXKxfNPTGjRv4+PgQExOjm7V+mIeHB3//+9/54IMPdG2zZs1i48aNREVFERsbS6NGjTh37hxt2rTRPScgIIA2bdowZ86ccn0WFBRQUFCg+zozMxN3d3dRdAtCNdJotKuebw5N4Myue7p2jxaWDJ7uTp/xrphZ6l84Pkl+eg6XF58geu4hMmO1q6/L5DK8A1vjq/DH7RUf/Vc9P3JGu+r5ut26Vc/PNjBnuYOc7Zej0TxYrfxRLCwsGD9+PEFBQTRv3rx836cPowwPIXvPBniwjaOhiwc2o2dgM+JdDOwqZ0FM1b1Yog/N5dLxPyjMUwFgZGxBs84T8PUPop5js0p5HX1oJA3n7u9lU/wcTqWV3obkau5DoGcwr7qOw8LwxfyML5nBOHv7LGpJjYHMgHbO7fSeyRD9CoJQl4nPBC1xHkrVWNE9YcKE5z7ZixYteq7jADQaDYGBgSiVSg4fPlzh84yNjVmyZAlvv/22rm3evHnMnj2b1NRUjh49Svfu3UlJScHZ2Vn3nDfffBOZTMaff/5Zrs8vv/yS2bNnl2sXRbcg1Iykq9lsDk1g75Jk8rK1haOFjaF21fMZnrg0qqbo+baLRIVEkLTvL9HzVs74KvxpOqaj3tHz4uQ7qH5ZherXVajTtPHwFGNY29SeFQmXSVepHnv8a6+9xtKlS3Fycir3WNHtRFQrf0G16lc0ygcXD0xMS6PnzXz1GnuJwoJsrp5aRvShMNJvX9S1uzd9Db+AYLxaDKw10fOtCfPYnbyQ3GLtOiVmBlb0cR1PoKcCN4ua3xqtMj08g1FC35kM0a8gCHWZ+EzQEuehVK1Zvby6TJs2jR07dnD48GHc3NwqfF5VFN1iplsQaqeS6PmWsASSr5dGzzsObMDQmZ607WNfLVdk0y/dJjrsEJeXnCyNntua0eLdrvgG9cTaS7/ZY01+Admrt6MMCafgzAUA8tGws3E9lhbd40L8rUce5+7uTmxsLIaPiY5r8vPI2roSVXgoBZfP69rNOgVgM1aB5atDKy96fm0f0REhZaLnNvUb6VY9NzG31ft19JVXnM2e5MVsSQgjKad0MbgO9QcQ6Kl4IaLnD89glNB3JkP0KwhCXSY+E7TEeSir1qxenpCQ8MTVy7OyssrdC/4sgoKC2Lp1KwcOHHhswQ3g5OREampqmbbU1FTdTE/Jfx/3nIeZmJhgbW1d5n+CINQ8CxsjhgZ78duVnny1vT0d+mtXPT+5LY1P+55mSsvDbJkbT25W1a56Xq+FM73mvcmk5K/o8Z9hWDe0p0CZx7n/7Gdpo6/YOux3Evddff5Vz01NsB43HPdT63A7+ieWbw3C1NCYYTeUrIs3YFUDX4a0bFtuIbUZM2Y8tuDW9m2GzYhJuG88i9uKQ1gOGAkGBuSdjOCOYgRxrzYk/dfvUWfcf66xl5DJZHg07cPg9zcz7oubtO39ESZmtqju3eTwhr+z6As3Dq6eTvqdy0/urAqZGVoS6BnErz0u8W2H3XRqMBgZMk7f28EXZwby3qGmbIoLIae4anbtqA67b+7mVMqpMn9MAaglNadSTrH75m7Rrx79CoJQN4nPBC1xHqrec810GxgYMGvWLL744osKn/Ptt9/yxRdfoFarK3zOo0iShEKhYMOGDRw8eBAfH58nHjNq1Chyc3PZsmWLrq1bt274+vqWWUjto48+4sMPPwS0VzAcHBzEQmqC8AJIvp7D5tB49ixOJi9L+5ljbq2Nng+Z4YFL40fvfFCZNGoN8TsuETUngsS9pbOl9Vo646fwp+mYDhhZmOj1GsUpqdro+S8rddHz28aw5kH0PLeggKSkJOztHz3L/vnnn9OxY0cGDRqEwUP7dxfdSUK1Yj6Zf/6GOkN7/7w2ev4OtmODMWnup9fYda9TkMPV08uIigx9KHreB19/BV4tByGX67+3uL5Scm6wJWEue5IXkVOsjfRro+fjGOIRhLtlzd+f/rRKZjDOpJxBQ/m1AeTIae/S/plnMkS/giDUZeIzQUuch/JqTbxcLpfz5ZdfPrbo/uabb5g1a9YzF93Tp09nxYoVbNq0iaZNm+rabWxsMDMzA2DcuHG4urry3XffAdotwwICAvj+++8ZNGgQq1at4l//+le5LcO+//77MluGRUdHiy3DBOEFkpNZ/CB6Hk/ytdLoeYcBDQhUeNCub33k8mqInl++o131fMlJinJKo+fNJ3XBd0ZPbBrW16t/TUHhg+j5UgpOl0bPr7bypN9nf8fy9b7IjIzKHHPt2jXdZ6q3tzczZsxg0qRJ2NnZPdR3Ptnb/kS5dA4Fl87p2s06+mP3/v9hETBAr7GXkCSJ5OsHOR8xh7gLW5Ak7S96a3tvfHsG0aLLpFoRPc8vzmFvylI2xc95KHren0DP4DoRPS8oLsDzZ09Sc1IrfI6TpRNxM+MwMXz6C0OiX0EQ6jLxmaAlzkN5daronjp1KqtWrUKpVD7bgCq4grJo0SImTJgAQK9evfDy8mLx4sW6x9esWcNnn31GXFwcPj4+/PjjjwwcOFD3uCRJzJo1i99++w2lUkmPHj2YN28eTZo83UI5ougWhLpDo5E4u/sem0LiOb2jdNVzt6YWBCo8eHWcK+ZWVb/qeYEqj0sLjxMz9xCqmw/GIZPhPaQlvooA3F9tov+q5yeiUIYsJXvNTniwW4SBiwO2097B+v1RGDpoZ71nzpxJSEhImePNzc0ZO3YsCoWCli1blu/77FGU4aFk714HxcXYf/A19aZ/9tzjrUjm/ThiDs/n0rEF5OdqZ/ANjc1p1nEsvv4K7J1bPqGHqidJEufv72NzQign7m5BQvur09m8EUM8gujrNqlWr3qeqEokLTetwscdLBxws378rVyiX0EQXjTiM0FLnIeyarTo/uqrr3T//8svv6RXr1706tWr3PPUajWJiYmsWrWKLl26sH///koZaE0TRbcg1E0pN3LYMjeBXX8k6aLnZpYG9JngytBgT1x9qj56Lmk0xO24THRIBAm7r+ja7Zo7aqPnYzthbKln9Pz2XVS/rkL1yyrUqQ/i4cZGWL41CPmk12k8pC9ZWVkVHt+7d2+Cg4MZPHhwueh58Z1kVKt+wWasAkN7B73G+ThFhblcPb2c6IgQ7t++oGt3b9oH355BeLUaXCui57dzY9kSH8bu5IXloueDPWbgYdn8CT0IgiAIglBb1WjR/dfFemQy2RMXB3JxcWHDhg107NhRvxHWEqLoFoS6LTermD2Lk9k2L4HEKzm69g4D6jMkyJMO/aspen4ltTR6nq3dIcHYxowWkzpro+eNGujVv6agkOw1O1CGhlNwMhqAQjTsalSPper7RMXFPvZ4Ly8vZsyYwbvvvlsuel5dNBoNKTcjiY4MJTZ6Y2n0vJ4Xrf210XNT85oZ21/lF+ewP2UZG+PnkJhTuhhcW/vXGOY5kw4NBtT66LkgCIIgCGXVaNEdEREBaCN2vXv3ZsKECYwfP77c8wwMDKhXrx7NmjUrt6puXSaKbkF4MUiSxLm999k0J56T20qjVK4+5gxReNJnvCsW1lUfPS/MzOPSohNEhx1CdePBOGQyvAa1wC84APc+TfVesKQkep61ZicUFSEhcd7ejBXORmy9HPXYNTfMzMx00fOStTGqW1HiLfLMZcQc+YVLR38vEz1v2mEMfv4K7F1qZmx/VRI935IwlxN3N+sWonEya8gQjxn0dZuEpZFtzQ5SEARBEISnUmvu6Z49ezavvPIK/v7+lTKIukAU3YLw4km5kcO2+Yns+iOJHJX2fmgzSwP6jHclUOGBW1PLKh+DpNEQv/MyUaGRJOwsnS21a+aIb1BPmo3vrH/0/E5aafT8jrbAv2ME65rWY0XyNdIyMh57/F/X1KgOymVzydq6EnVGGkgSdpM/xmLYaK6eXk5UZAj3U2J0z3Vr0htffwXeLQcjN6j6iyVPkpobx+aEUHYnLSS7WAmAqYEFfVzHM9hjBp6WLWp2gIIgCIIgPFatKbpfRqLoFoQXV152yarnD0XP+9dnSJAHHQY0qJboeca1u0SHRnJ58Ymy0fOJnWk9oye2jfWLnkuFhWSv241yzhLyT0QBUICG3Q3tWKrJICruZrljjI2NSUhIwNHRUa/XfqrxFReTPv9b0sNmY9a5F2bte6BOTyNr83Ls//YNtuOCkSSJlJuHiI4M5WbUel303MrOg9Y9Z9Cy62RMLepV+VifJL84hwO3V7Apfg7x2aVbo7W170OgZzCdGgwS0XNBEARBqIVqrOiOjIx87hd4UWbDRdEtCC8+SZI4vz+dTXPiOLk1jZJPR5fG5gQqPOgzwa3aoueXl5wkOjQS5fXSCLznwBa0mRmA+2vN9I+en4rWRs//3KGLnkfVM2WlizFbrkRT/GAl9DFjxhAeHv7IPtRqdblF1/SRte1PUj+ZhPXw8Th8OU/7Ghn3ufvFFAoun8d97UkMbEsL6sz0+NJVz3PuA2BoZEbTjmPw9VdQ36V1pY3teUmSxPn0/WyJDysXPR/kMY1+bu9iZVTz96cLgiAIgqBVY0W3XC5/7j/wnnWf7tpKFN2C8HIpiZ7vXphEtrI0ev7qOFeGBHng0byaoue7rhAdFkn89ku6dtumDvjO6EnzCZ0xtjLV6zWKU++VRs9v3wUg1RDWN7NnefI1tu7aWeGCmP/4xz84deoUwcHBBAYGYmj4/BckNHm5xA9sgaGjK66L9iA3M0dSq5EZGKBavYC0f32Ax7rTGDdqVv57KMzj2pmVnI+Yw/2UaF27a+Ne+AUE491qSK2Jnm9JmMuupAW66LmJgTmvuowj0CMIT6ua3xpNH3tj9xK8I5iQASH0adin0vr98ciPfH7gc75+5Ws+7v5xpfVbFarqHAhCVRPvXUEoVWNF95dfflmu6D5+/Di7du3Cx8eH7t274+joSGpqKkePHuXatWv069ePLl26MGvWrEoZaE0TRbcgvJzyc4rZuzSFzaHxJF4ujZ6362tPoMKTjgOrJ3quvH6X6LBDXFp0nKIsbfTcyMqEFhO74BvUE1sf/bby0kXPQ8PJP3YOgEIkrDr5YRs8DquR/ZEZG+uen5OTg5ubG0qlEgB3d3emT5/O5MmTqV+//jO/fsYf/yHj9x9o8NkcrAa/rSu4JbUaZXgo9374CI+N5zBpWvHstSRJpMQeJjoilJvR65E02ou+lnbu+PaYQYtukzGzsH/msVW2fHUuB1NWsDkhlFtZpRcJ/Or1JtBTQWeHIRjIan5rtGchSRKdF3TmVMopOrp05MTkE3qnMUC7kr3V91bkFuVibmRO1v9l1dpFWqvqHAhCVRPvXUEoq9bc033o0CFee+01wsLCePfdd8v8YEqSxO+//87MmTPZs2cPPXr0qJSB1jRRdAvCy60ker4lNJ7jm+/qoudODc0IDPKk7yRXLGyMqnwchVn5XFl6kqjQSJRX7+raPfo3p83MADz6NkOmZ1GSfzoGZWg42au2IRUWAWDgWB+bqW9hM+UtDJ0d+O2335gyZUq5Y01NTXnnnXdQKBS0adPmqV5Pk59H/Gs+mLTqgPOc1ciMjZEkSbs9ZVERqZ9OJv/MYTz33qjwD8GS55fIykgk5tA8Lh5bQH6Odt9yAyNTmrYfjW+Aggaufs94ViqfJEnEpEewKSGE46mb/hI992aQx3T6uU7Cyrjm709/Grtu7KL/8v66r3eO3km/xv307vfbyG/57MBnuq+/eeUbPvX/VO9+q0JVnQNBqGrivSsIZdWaortXr17Y29uzbt26Cp/z+uuvk5GRwYEDB/QaYG0him5BEErcjs1l67wEdv9RGj03tTDg1XEuDAnyxLNF9UTPE3ZfITrsEHHbL1FyFcC2SUn0vBPG1mZ6vUbx3fsPoucrUac8KPCNjLAa2Z+3rx7m4JmTjz2+Z8+eBAcHM2zYsMdGz7O2r+buF1No8Mn/sH59gm6WG6AoJYGEQD+sX59A/Y9+KDPb/jCpqAi1Kh1NphLjhk2130NRPtfPruL8wTncSz6ve65LI3/8AoJp2HporYie381LYFvCfHYk/UZWkXZrNBO5Ga+4jGGY58xaHT0vmSU7e/ssakmNgcyAds7t9J4t++ssd4naOttdVedAEKqaeO8KQnm1pui2srJi5syZfPPNNxU+59NPPyUkJISsrCy9BlhbiKJbEISH5ecUs39ZCptCEki4lK1rb9vHnsBgbfTcwKDq/2hR3UzTRs8XHqcwMx8AI0sTmk/sjG+QP3ZN9IyeFxWRvf5B9PzIWQAK0bDH245lMhVnYq8/9ng3NzemT5/Oe++9Vy56LkkSaV9OJ2vHarwPpyA3NkHSaHSz9ff++ynKpXNwDlmLhX//ssc+eJ5UXEz2vk1k/vkbBddikJtZIDOzwD5oFpZ9h+teJyX2MNGRYdyMWlcmet66+zRadnsPM8tnj8VXtpLo+ZaEMGKzonTtfvVeYYhHEF0cAjGQ1/xFgr96eJashL6zZQ/PcpeojbPdVXUOBKGqifeuIJRXa4pue3t7unTpwrZt2yp8zsCBAzlx4gT379/Xa4C1hSi6BUGoiCRJRB1IZ3NoPCc230WjTQnj5G3G4P/P3n1HRXXtfx9/z9A7KKDSxood7F1QY2KJqNEkaqyxFwbzy82Tm2pMcnPTboqANSYxYkmxYo8NsNcI9i5dRWTodeY8fxwZRMAGQ9H9WsuVuOecPZsjynzP/py9Z3nQb5Ib1vaVFD0POUZUUAQpF27p2z36NcM7wBdV/+blj56fPIsmcDkZqzfro+enHUxZ7WrOxotR5Ofnl3mumZmZPnretm1bfXv8pP5I+Xm4Ld+DlJenn83OvXyWuJHdsXphCI7//hbj2s4lYuQASV//PzS/fIdV36GYe3VCaW1LzskDZIZtwWbIWGq//QVG1kX/bmekxHH6wELOHFhSFD03NqNph9F4+ahxcmtTrmtUESRJ4kzKPjZGz+PQrQ366LmzuQo/lX+1iZ4/OEtWqLyzZaXNcheqbrPdhroGgmBo4ntXEEpXbYruUaNG8eeff/LFF1/w9ttvY3pf3C8vL4/vvvuOjz76iBEjRrBq1aoKGWhVE0W3IAiP4+Z1OXq+Y2lR9NzM0oi+4ysxei5JxO68QGRQBDe23Bc9b+JE63urnpvZlTN6nnSXtJ/+IHXBKgri5QI/yQjWNa/NisQr3Eq+U+a5r7/+On/88Yd+rDcDXiP3QiRufxzEuJa8F3le9BXufPtvciOPUPf71Vh07Fnia1QoFKT8+gPJ8z7GZuAI6vz3Z/3r+YmxpK1bhvbOLRymvYdJXbeSX0N+DpdP/kFkeCBJcSf17fUa9sDbN4BGXq9Ui+h5UnYsW2IXsi12CWn58o1sU6U5vV1GM0Q1mwY2Vbc1WlmzZIWedrasrFnuQtVptttQ10AQDE187wpC6apN0R0XF0eXLl1ITEzE2dmZDh064OzszO3btzl+/Di3b9/GxcWFQ4cO4eZW8oNOTSSKbkEQnkROlpawVQlsnBfNjTNF0XPvPrUYEqCi0yDnyomeX7tD1Px9nPv5MHmp2QCYWJnSbEJnvNU+ODStU67+pfx8MjbsQhO4nJz9JwB51fPdDexZoUzj2NVLJc7Zv38/3bt31/8+Y+9mbr8/EYcp/8bSpz8KUzOSvniLrPCt1PlqGTZDxsgx8gdmuQtuJRDt1xqFqTlWvQehNLfA2LU+DhPe0h+Td/0SJqrGpZ6v/xokicTrB4mKCOLqqbXodPLNEn30vOtkLGycynWdKkKuNpuwxFWERgdzLf2Uvt27Vm8Gecyiq/OQSo2eF86SnUg4oZ+Jv58SJe1d2j/xbNnDZrkLVZfZbkNdA0EwNPG9KwhlqzZFN8DNmzd57733+PPPP8nJydG3m5ub8/rrr/PVV19Rt27dChlkdSCKbkEQnkZh9HxTcAyHN94qFj1/eaYcPbdxqIToeUYuF0OOEhW8j7vnburbPV5qhpfah/oDW5Q/ev7POVKDQkhftQkpNw+Asw5mrHYzZ/2FSPLz82nbti0nTpzQf4iTJAkpK5M7339A6uqF6Oxqo9TcwdixLnZvzKTWjA9KvE/hs9zJwZ9xN2guSrtaGNk5YNa8DZkR2zDxaEy971dj2ri5/j0UCgW63BxyIo+QfSSMgtsJWPcbjlWPl4r1nZGawJn9CzlzYDHZGUmAHD33bD8Kb58AnNzblhhPZZMkibOaA4RGB3Lg1jp092KhTubuDFap6ec6qVKi57kFuah+VHEr81aZx9S1rsuN2TcwMzZ77H7TctJw+Nqh1EKgkFKhJOXdFGzNq/bnsaGugSAYmvjeFYSyVauiu1B+fj4XL14kNTUVOzs7PD09i8XNnxWi6BYEobxux2SzeUEM25bEkZEiP/tsZmnEC2NdGKz2QNXSxuBjkCSJ2N2XiAoK5/qms/rouV0jR7z8e9L8zS7ljp5r79wl9ac/5eh5nFzg3zGC9c1r02bEUEZ9+G6pMyd//O9L9vz3A6waeuIz2Z+B4ydjamFBQdJNjGo5yft237eV2PUeLmg1ydT53wqse/uBsTFZ4du49d4E7Ce9Q23/OcX6v/XRVNK3rEZhYoqJWwPyLp3Buv9rOH0ciJGdQ7FjC/JzuPzPn0RFBHE75ri+vV7D7nj5qGnkPQwjI8PfLHmUpOxYtsYuZlvcElLz5JsEpkpzetV7gyGqABraGnZrtNjUWJKyksp83dnKGTfbJ0+8HYk7wpWUK2W+7lnLk46uHZ+4X0Mw1DUQBEMT37uCULpqWXQ/L0TRLQhCRcnJ0hK+OpHQoGiuRRbt8ODVqxZDZqvo7Fd50fPTC/Zz7udD5Grui56P74SX2pdazcoZPS8oKIqe7ysqXM3atcQ+YCzWI15GaS7PoEiSRPv27fnnn3/0x7m6uqKe9CavX9iLhZsK5y+WojAzR6FQkLZpFbfeGYPVi6/gElx8+8qYIW1RWttSb8EGjOwc0KZp0Pz6PXcX/AeHKf/GYfL/Q8rNIePvddwN/hTnL5Zi3XdImV/HzeuHORU+j6un1hRFz+3daNV9Oi27TcHSpnyrw1eEPG0OYYmr2Rg9r9iq560dfBmsUld69FwQBEEQaipRdFchUXQLglDRJEnidEQKoYHRHNp4G51W/ue4Tn0LBs304KWJrtjWNnxyKD8zl4srjhMZGF4yeu7fE9XAliiNyhc9zz11Dk3QCjl6npMLgJGjA7ZTR2A34w2ORl+lR48eJc7raAEhrnDbuhaWS/+mffv2ACT/+DF3F36Ba8heLDv56lc912rukjBtENq7Sah2XEShVJK2cQW350zD9pXxOH3wo351dF1ONtH9m2HlOxCnOcH6vcHLkpGawJkDizlzYBHZ6fK+5UojUzzbj6KN7+xqEz0/pzlIaHQQ+2+t0UfPHc3d8POYRX+3Kdia1q7iUQqCIAhC9VVlRXefPn1QKBT89ttvuLm50adPn8frXKFg9+7d5R5kdSCKbkEQDCkpNpstC2PZujiW9Lv3oucWSnqPcWFIgIr6rSoneh639zKRgeFcDz2jj57bNqiNl39PWkzsgpm9ZbneQ3vnLqk/ryF1/koKYhPlRiMj9nVuxEeXjpJ4p2TUsYkppOngVgH4dO3CjIDZvHD7AmnLfkC1/QLGzvX0z3lnnzxIono4Vn0GU+fzxeRFX+H2x1PJPfcPDQ4kojQzR5Ik0GqR8nKJG+2DcV03XBZufPyvIT9Xjp7vC+ZW9FF9e72G3fHq6U+jNsOrdfTct95IBqsCaGxb9TcJBEEQBKG6qbKiW6lUolAoOH/+PJ6eno+9WqhCoUCr1T76wBpAFN2CIFSGnCwt4b8nsik4hqv/pOnbvXrVws/fg65DnDEyNvyKzanXkzmzcD9nlx4iN0VeRdrY0pRmYzvipfahdst65epfKiggY+NuUoNCyA6XC9d8JPaq7FhhksHhKxcfev4UDzveMUvD4l9f4T7tXQC0d++QHDiHtL9+xm31fsy9OpL6x0/c/mQ6tf/1JbWmvItUUABGRvLCatlZXO9WF/s336Z2wNwyVzd/mJs3jhAZHsiVf/7UR8+t7Fxo3WMGLbtNrTbR84ibf7Ih+keuphXF91s59GSwKoCuzkMwVlb9TQJBEARBqA5EvLwKiaJbEITKJEkSZ/ensGFeNIc2FEXPnVXmvDzDg/6T3Sover7yOJGBEdw9m6hvd+/bVF71/OUKiJ5HXUATFEL6ilB99PycnQm/e1iy/tJpcnNzS5xjo4SfXcDCSMHFZl0YP9OfvG1/krknFPvxb+H0wfdoU1O4PWc6Wft30PB4irwAmySBTofCyAjNivkk/SeAOt+GYOv3Rrm+hszURM4cXMKZA4vISpMj+kojU5q0fR3vXrOp49GhXP1XBEmSOK85xKaYYPbd/AutJN8kqG3myiCPmfR3n4K9adVvjSYIgiAIVUkU3VVIFN2CIFSVpLgctiyMYdviWNKS5ei5qbmS3qNdGDJbRYPWlRM9jw+7TGRQBNc3nkbS3Yue169F61k9aTm5a/mj58kpRdHzmAQA7iolNjR3ZPntayQk3S52fBNT+NgJ2loqsLCzR6E0wu6NGdRSz0WhVJKfGEvciG5YvzQMp4/mIWm1cC+5BRDt543CxIS6P/yOqarxU810l/gaCvK48s9fREYEcSv6iL69bv2uePn407jNqxgZV/0OH8k5CWyOWcD2uJ/Q5MnX1URpRq96oxjsoaaxXbsqHqEgCIIgVI1qU3THxsbi7u5eIQOoKUTRLQhCVcvNlqPnoUHFo+etfR3w81fRbWjlRM/TbiRzeuF+zi09RM7douh50zEd8Fb7ULuVS7n6lwoKyNy0B03QCrL3Hgbk6HmYyo4Vppkcunyh2PEr/jOHYS8PwKSuO8Z1XfXtuRdPEzPYm7o//I71gNfkRq0WhbExmlULufP1OzhM/Be1Z39WrvGW5Vb0MSLDA7n8zx/otPLNEivberTqMYNW3aZiaVtydfiYGLhzp+w+HR3Bw6Pixpiny2Vf4p9sjA7kclrRCvMt7LszRBVAtzqviOi5IAiC8FypNkW3UqmkUaNG9OrVi169etG7d29cXMr3Iau6E0W3IAjVhSRJnDuoYeO8aA6su6WPnju5mzNoVuVFzwuy8/TR8+TTCfp2tz6eeKl9aODXqvzR89MX0QSvID1kI1J2DgDn70XP1106jYWFBXFxcVhZWZU4N/v4fm6M7UPupPdp886n+nZdRjo3+jbCpL4ndf77M6YNm1bILHdZMtNucvaAHD3PTJMj+kojE5q0fR0v3wDqqjoBcsHdtCnk5Nw7sfs30Ptj2Ps5HJCfWzc3h4sXy1d4f3PgGz7e+zGf9/6cd7vL/UqSxAXNYUJjgh6Inrsw0H06A9yn4mBWvi3kntaua7sI2BZA4IBA+jbsWyVjeFaV9r1QEWrSn1lNGivUvPEagrgGgqFVm6J7woQJhIWFERMTo/+Q0rhxY3r37q0vwuvUqZofzoYiim5BEKqjpLgcti6KYduSOFKT8gA5eu47qh5DZ6to6G34f68kSSIh4gqRQRFcWx+lj57bqGrhNasnLSZ3xdyhnNHzuxrSflmLJngFBdHxANxV6Iju3opB//kAC5+OJYrm42G7uTW+L9fyYIt7W8bO/hdDO7cl9YePyD4ahvPchdi8PKJc43qir6Egj6uRazkVNu+B6HkXvHr6k85rdOxUeLNEBx/YgGkW5FnCf9MB+QbGiRPQ7inT3zqdDpuvbMjKz8LSxJL099JLLI56NyeRzbEL2Ra7WB89N1aYytFzlZomdu2f7s2fgiRJdF7amWMJx+jo0pEjk48Y7ObI8+ZxvheeRk36M6tJY4WaN15DENdAqAzVpugudP36dfbu3cuePXsIDw8nPl7+IKRQKGjatCm9e/dm/vz5FTLQqiaKbkEQqrO8nKLo+ZWTRdHzVj4ODFar6DrEGWOTSoieR9+Vo+c/HSwRPffy98GxdTmj51qtHD0PDNFHzwFMvZpirx6LzRt+KC0tABg3dixsWsG/HOFoNqRqoYu1EkdjsPwwCLfXJ+q3EKvsD223Yo4TFRHEpRO/o9PKN0tMLOqyMWw6B85MI73dz9D3o6ITdv0H9n8IlK/o/iLiCz7aW9Tvf3r/hw99Piz12DxdLvtvriE0OpCLqUVbozWz68KQ+rPpUWe4waPnO67soP/K/vrfbx+9nX6N+xn0PZ8XT/K98CRq0p9ZTRor1LzxGoK4BkJlqHZF94OuXLnC+vXr+d///kdSUpLYMkwQBKGSSZLEhcMaNgZGs3/NLbQF8j/xtV3N8JvlQf8p7tg5Vk70/NLqE5yaF05yVFH03LVXY7wDfGkwuHX5o+dnL5MavIK05RuQsrIBUDrYYTfldXJee5FG3TuTl5dHd0uY6gBGQHQ+7MiAQ/kmvPbaawQEBNC5c+dyjaM8stJuyaue71+oj54XaE04ZaYj3FJLtAkgAflFs91PW3TfP7NZ6HFnOM9rDhMaHcT+m39RIMnPpxs6el44o3Uy8SRaSYuRwoh29dqJma0KUJ7vhYepSX9mNWmsUPPGawjiGgiVpVoW3VlZWezbt4+9e/eyd+9e/vnnHwoKCrCysqJ79+5s3769QgZa1UTRLQhCTXMnPoeti2LZtiQWze17s6lmSnqNqsdgtQeN29kZfAySJJGw7ypRQRFcXR+FpNUBcvS89YzutJjcDYvaJZ/HfhLalFTSflmDZv5KCq7HAZCukFjT3JGQO9eJu30LAFslpOlKnt+xY0fUajWvv/46ZmZm5RrL09Jq89m1YR3bVwfS0OWgvj3aCMIt4JQpFOyWZ7uftuh+cGaz0JPMcKbk3mJr7CK2xCwkJU++rsYKE3zrjWKIKqBCo+cPzmgVEjNb5VcR3wulqUl/ZjVprFDzxmsI4hoIlaXaFN179uzRF9nHjh0jPz8fc3NzunbtSp8+fejduzedOnXC2Ni4QgZZHYiiWxCEmiovV0fEH4mEBkZz+URR9LxlDweGBKjoOrRyoufpsSmcXrCPsz8dIic5EwAjcxP9queOXq6P6OHhJK2WzC1haIJCyN4lF64FSIS727LCIpsDl84/9HxnZ2emTZvG9OnTq2Rx0JMnoX17He7/tsKnIIf2eVD4UzRNAQdNjNm/8AZ797k+cdFd2sxmoaeZ4czT5XLg5lpCo4O4kFoU829m14XBKjU96r6KifLpExUPzmgVEjNb5VfR3wuFatKfWU0aK9S88RqCuAZCZao2Rbfy3j6nXbp04cUXX6R379507doVU9Oq33vUUETRLQhCTSdJEheOpBIaGM2+v24WRc9dzHh5hgcDprlj71RJ0fPfTxIZGM6dU/H6dhefRngH+NJwSGuUxkbleo/cc1dIDQopFj2/aGPCHw2sWHMxipzc3DLPNTY2ZtOmTfTvX3JGxZBOnoT2s7/QP8ttrYNuOdAjB+zv/aQu0BlRt/EIeg3xp279Lo/9IbOsmc1C5ZnhvKg5yoboeSWi5wPcpzHAfSq1zOo+cZ9lzWgVEjNbT89Q3ws16c+sJo0Vat54DUFcA6EyVauiG8Da2poePXrQp08fXnjhBdq0afPM3mUSRbcgCM+S5IQctiwsPXo+aJYHnh0qJ3qeeOAakYHhXF13X/Tcw4HWM3vQYlJXLByty/UeWk0aab+sIXX+SvKvxQKQopAIbV6b5XduEHsven4/Gxsb4uLinvrf+pwzJ9BlZWDR0eeJfiYeP66j43obMMmC+05TSuCdBz450KigqN3ZvT3evrNp0vZ1jEzKjsU/bGazUEU8z5uSe4ttsUvYHLuAlNybgBw971n3dYbWfwtPuw6P1U/hjNaJhBPoKPk8gBIl7V3ai5mtp2Co74Wa9GdWk8YKNW+8hiCugVDZqk3RnZKSQnh4uD5ifvbsWQDs7Ozw9fXVR8xbtWpVIYOsDkTRLQjCsyg/T8e+P2+yMTCaS8dS9e3Nu9ozZLaK7sPqVEr0PCMuhdMLD3BmyQFy7twXPX+jPV4Bvjh5V0D0fGs4msDlxaLnEe62rLDIYf+lc/pj1Wo1gYGBpffzGCudx095mazwrZg29cJ+jD82g0ejtHj0lmlnr6TRKsQBlKU8eH6PW56C793eIOnyGrQF8my9hY0zrbpNpVX36Vjbl7xOaTlpOHztUOqH1UJKhZKUd1OwNS//z7d8XR77bv7F5pj5nNcc0rc3teuMn8csfOqNeGj0PLcgF9WPKm5llrwhUqiudV1uzL6BmXHVPINfUxnqe6Em/ZnVpLFCzRuvIYhrIFS2alN0P+jOnTvs3btXX4hfuHABACcnJ27evPlEfUVERPDtt99y4sQJEhMTWb9+PUOHDi3z+AkTJvDbb7+VaG/RooX+ZsDcuXP59NNPi73etGlT/Tgfhyi6BUF4lhVGzzcFR7Pvz5sU5Ms/GmrVM2PgdHcGTnPHoY7hP8wU5ORz+feTRAaFk3QyTt/u0rMR3gE+NBzqVe7oed75K2iCV5D22wakTHnG77KNCb/Xt2LtlTP8c+oUnp6epZ47Y8YMUlJSUKvVdOvWrUQBLul0JH3mT9r635Cy5b6V9rWwe3USdqNnYeKqeujYNh4/wumEK2W+7u3qiV/7jmRn3OHMwSWc3reAzFQ5oq9UGtOozat4+6ip26BrsbEdiTvClZSy+/Ws5UlH144PHdvTuJR6nI3R84hI/EMfPXcwq8vL7tMZ4DaVWub1Sj0vNjWWpKykMvt1tnLGzdatwsf7PDDU90JN+jOrSWOFmjdeQxDXQKhM1bboBrh58yZ79+5l9+7dbNq06am3DNu2bRsHDhygffv2DBs27JFFd2pqKtnZ2frfFxQU4O3tjVqtZu7cuYBcdK9Zs4Zdu3bpjzM2NsbR0fGxxyWKbkEQnhd3b+ayZWEM2xbHknJLjp4bmyruRc9VNO1YOdHzm4euc2peOFfXRuqj59buDrSe0Z2Wk7ti4WRTrvfQpqaT9utaUoNXkH81BoBMJJwH98U+YCwWfYoXrsnJybi5uZGTkwNAu3btUKvVjBw5EnNz8wf6TiFtzS9oVs6nIO663KhUYtVnMPbjArDo3KtCYpBabT7XojYQFRFEwtV9+nYnt3Z4+wbQpN0IjE3MH9JD5dDk3mZb3E9siVlAcq68hZyRwpiedV9jiGo2zeyrbts2QRAEQbhftSq679y5Q1hYmH4l80uXLgHyB6W6devSu3dvevfuzeTJk59+cArFI4vuB23YsIFhw4Zx/fp1VCp5RmHu3Lls2LCBU6dOPfVYRNEtCMLzJj9Px/41cvT84pGi6HnTznYMfas+PYZXUvQ8XsOZRQc4s/gA2UkZABiZGeP5Rnu81T44tXUvV/+STkfWtnA0gSFk/b1f327avBF2AeOwHTsEpZUlX3/9Ne+9916J8x0dHZk6dSozZszAza34TIuk1ZIZtgVNSBDZB4tu/Jp6troXPR+D0rJ8W6YVSor9h8iIQC6dWF0UPbd2omW3qbTuPh1rh6qfBSrQ5bP/5ho2xQRzTlO0NZqnXUf8PPzxqTcCU6WIhwqCIAhVp9oU3V5eXvrotiRJODk50atXL32h3bRp04oZ3FMU3X5+fuTm5vL333/r2+bOncu3336LnZ2dfmuzL7/8Eg8PjzL7yc3NJfe+1W3T0tJwd3cXRbcgCM+lC0c0bJ4fQ/gfiRTk3Rc9n+bOgGnu1KpbSdHzP04SFRTB7ROx+vZ6PRri5e9Do2HeGJmUM3p+4WpR9DxDfrZcaWeDzZvD8Nn0KxevXi3zXCMjI4YNG4ZaraZHjx4lZrJzr5wjdUVw8ei5rT22r03GfvQsTNzql2vshbIzkzl78CdO75tPhkaO6CuURjTyHo63bwD1GpSMxVeFK6kn2RgdSFjiagokOVFhb+rMQPfpvOw+vczouSAIgiAYUrUpumvXrl2syG7ZsmWFDOZBT1p0JyQk4OHhwapVq3j99df17du2bSMjI4OmTZuSmJjIp59+Snx8PGfOnMHGpvR4YmnPgQOi6BYE4bmWciuXrYti2bIolpSb8o1JYxMFPiPqMVjtQdNO9gYfgyRJ3Dx8Q171fM0pdAVy9NzK1Y7WM3vSakoFRc+XrZOj51eiAUhFR2hzJ5bfjSb6VuJDz2/Tpg0BAQGMHDkSCwuL4n2naUhb8wupK+eTH3tNblQoiqLnXXpXSFGs0xZw7fRGoiKCiL8Srm93dG2Dt28Anu1HVZvo+fa4pWyOWUByrvx8upHCmB51XmWwSk1z+67V4iaBIAiC8HyoNkX346zeWhGetOj+8ssv+e6770hISHjonuEajQaVSsX333/PpEmTSj1GzHQLgiCULT9Px4G1NwkNiuH8IY2+vWknOwYHqOj5Wl1MTCshep6QypnFBziz6ADZt9MBUJoa4TmqPd4Bvji3q4Do+fYINEEhZG2Xn5nWIrHP1YaV1nmEXzz70PNr167NlClTmDlzJu7uxcci6XRkhm9F89u84tHzJi2xH6uu2Oh5fCRR4YFcPLEKbb78TLq5lSOtusurnts4lO86VYQCXT4Hb61nY/S8YtHzJrYdGKxSi+i5IAiCUCmqTdFdWZ6k6JYkCU9PTwYNGsQPP/zwyOM7duxI3759+fLLLx9rLOKZbkEQhNJdPJbKpqDoYtFzh7pmDJzmxsBp7tSqZ/jZVG1uPpf++Ieo4AhuH4vRt9fr3hAvdQVFzy9dRxO8gvRl69Cly9HzK9bG/NHAhr+unCbrvkU9HzRt2jQWLVpUdt9XL6AJCSJtw29IWfdi7bb22L46SY6euzco19gLZWcmc+7Qz5zeN5/0FPk6KZRGNPJ6BS/fAFwalozFV4WraafuRc9Xka+Tb4DbmToxwG0qgzxmUtvcpYpHKAiCIDyrRNH9EGFhYfTu3ZvTp08/cn/wjIwMPDw8mDt3LgEBAY81FlF0C4IgPJzmdi7blsSxeUEMdxPlQsnIWEHP1+syJEBFs872lTKOm0fk6PmVP/8pip672NF6Rg9aTu2GpXM5o+dpGaQvW4cmeAX5l28AkIaO0OaOhGhiuZ6YUOKcx/nZBKBNTyVt7a+krggmP+be8+MKBVa9B2E3Vo1lt74VFz0/E0pUeBDxV8L07Y6ubfDy8adp+zcwNrUou4N7YmLgzp2yX3d0hIcsn/JImrwktsf+xJbYhdzJkZ9PN1IY073OcAar1LSwrx7PpwuCIAjPjuei6M7IyODKFXn/yLZt2/L999/Tu3dvatWqhYeHB++//z7x8fEsX7682Hljx47l8uXLHD58uESf77zzDn5+fqhUKhISEvjkk084deoU586dw8nJ6bHGJYpuQRCEx5Ofp+PAultsCo7m3AGNvr1pJzv8/D3wGVHvkdHzXdd2EbAtgMABgfRt2PepxpGZeC96vvggWTfTADl63mREO7wDfKnToRzVIPei53/vl6PnW+VnprVI7He1ZpVNAXsvnAGgT58+7N69u9Q+0tPTSUlJKbGwp6TTkRW+DU1IIFn7ixYGNW3UHLuxamyHjEVpZV2u8Re6k3CayPBALh5fcV/0vDYtu06hdY8Z2NQq/TrFxEDTpnBvB7VSmZvDxYvlK7wBtLoCDt7ewMboeZxNKVphvrFtO4aoZuNT93VMjar++XRBEASh5nsuiu7CGesHjR8/nmXLljFhwgRu3LhBWFiY/rXU1FTq1avHvHnzmDJlSolzR44cSUREBMnJyTg5OdGjRw+++OILGjVq9NjjEkW3IAjCk7t8IpWNgdGE//740XNJkui8tDPHEo7R0aUjRyYfKddspjavgCt//UNkUAS3jkTr2+t2rY93gC+NhrepkOh56vyVpP26Vh89v2ZlzB+NbBniP40hU94s9bwff/yRf/3rX7zyyiuo1Wp8fHxKfK151y6iWTmftHW/ImXKW6YpbeywHT4R+zH+mHg0LNfYC+Vk3uXc4Z+J2jef9LvydVIolDT0Goq3TwAujYuP7eRJaN/+0f2eOAHt2lXIEAE5er4pJpi9CSvJ08kVv62JIwPcpzDIYxaO5q4V92aCIAjCc+e5KLqrK1F0C4IgPD3N7Vy2L41j8/wYkhOKouc9Xq3DkNn1ad7FXn/sjis76L+yv/7320dvp1/jfhUyjptHo4kKCufyH/+gy9cCYFXPllYzetBqajcs65Tv33ddegZpyzegCQoh/+J1fbvlAB/sA8Zh+VIPFEp5ll+r1eLp6cm1a9f0x3l5eaFWq3njjTewtLQs1rc2I60oeh4tJ8L00fMx/lh2f7Fiouc6LddPhxIVEUTc5b36dkdXb7x6+uPZ4Q1MTC2rrOgulJp3Rx89T8qRt5ArjJ77ecyipUP1eD5dEARBqFlE0V2FRNEtCIJQfgX5cvQ8NKh49Nyzoxw97/laHXqu6MbJxJNoJS1GCiPa1WtX7tnuB2XeTNOvel4ieq72oU5HVbn6l3Q6snYeKIqe3/tRa9KkPvbqMdiMH8a2iDD8/PxKPb9WrVpMnjyZmTNnolIVH4uk05G1bweakCCyIrbp200aNsN+rBrboeMqLHqenHCGqH3BXDi6nIJ8eaE4c8tatOg6GaXDLLr5Pjo3bqiiu5BWV8Dh26FsjA7kdErR1mgNbdowtP5b+NYdIaLngiAIwmMTRXcVEkW3IAhCxbryTxqhgdHsXZWgj55b1ILTrVYR22ELubZ39cdW5Gz3/bR5BVxZc4qooAhuHr6hb6/bpT5eah8av9oGI1Pjcr1H3pVoOXr+yxp0aYXxcCvWtXfns6N7yLi3WnlplEolQ4YMISAgAF9f3zKj5+nrlqHLvLdlmrUttsPfxG6MP6aqxuUaeyE5ev4Lp/fNJ+3uDblRoSTyyhAiItVcju8FlH5TxNBF9/2upUXqo+e5Ovkmga2JI/3dJjPIYyZOFlW/NZogCIJQvYmiuwqJolsQBMEwNEl57Fgay+YFsdyJk5/R1SkLuNX8ANGdN5LucYl2LhU/2/2gW8eiiQyK4PIfJ9HlydFzyzo2tJrenVbTe2BVt5zR84zMouj5BTlSno6Wzc2cWJ4Wx9WE+Iee37p1a9RqNaNHjy41ep6+fjmakEDyb1yWGxUKLH0HYj9WLUfPleXfN12n03Lj7BYiw+cRd2mPvj3+TmsiotQcvzia/ILiY6vMortQWl4y2+N+YlPMfP2q50qFEd3rDMPPw59WDj1F9FwQBEEoVZUV3Uql8ql+OCkUCgoKCp5qYNWNKLoFQRAMa+v57Uz85AvqHx6KQ2xLfXuqyyWiO21iyX/+xcst+z+kh4qRdSuNM0sOcmbhfjIT70XPTYxoMqItXv4+1O1cv1z9S5JE1s4DpAaFkLklDCQJHRKHXGxYYVvA7gunH3q+g4MDkydP5r///S/GxsVn4SWdjqz9f8vR8/Ct+naTBp7Yj1Fj+8p4lNbl2zKt0P7dZwn6TzAdmy3HzCQLgMwcBw6fm0RElD8p6XIsviqK7kJaXQGHkzaxKTqIyLtFz6c3sPFiiGo2veu9IaLngiAIQjFVVnT36tXrqe8I792799EH1QCi6BYEQTCcwhXLTyScQIcOm8SGeBz1wyWqD0ZaUwB01pmMCmiN3ywParsYvlDS5hVwdV0kkYHh3Dx0Q9/u3NED7wBfmrzetvzR86sxpC5YSdrPa9ClyvHw65ZG/NnIlj+vnSU9s/ToeY8ePdi3b9/D+75xmdSV80lb+yu6jHs3D6xsiqLn9ZuUa+yFC6lZmKXQpcUv9Gw9H0c7efE4nU7J6etDiIjyZ/WG3rRvX/WzyqVHz2vzktskBnnMpI5F+Z7jFwRBEJ4NIl5ehUTRLQiCYDi5BbmoflRxK/NWsXaTTDvcTr6Ex7FBWKQ5A/Kq591eqcPgABUtu9tXSkz41vEYooIjuLT6RLHoectp3Wk9vTtW9ezK1b8uI5O0kI2kBoWQd/4qABn3ouch6fFcjo8rdvwff/zB66+//ph9p5O24V70/PolfbulzwDsxwVg2eOlp4qeP7hPt0KhpaVqK75t5tHUvWhfcpvaLenQN4CmHUZjYmb1xO9T0dLzU9gRt5RN0cHczokBQImSrnVeYYgqQETPBUEQnnOi6K5CougWBEEwrNjUWJKykkp9TVsgkRBmzv6fMjizL0Xf3ridLYPVHviOrIepefn22n4cWbfTObvkIKcX7CuKnhsrafx6W3nV8871y1WwSZJE9u6DaIJWkLlpjz56frieNSvtdew8H4WrqyvXr1/HxMSkxPk6nY6vvvqKUaNG0aBBg+J963RkHdhJ6opgMsO2FK2o3sAT+9GzsBk2ASPrJ/v5FhMDd+6UbM/SnCPxfDBJ15ajzZdn680s7GnRdRKte87CrnaDkidVMq2ugCNJm9kUE8yp5KKbBPWtWzNEFUAvlzcwN7J8SA+CIAjCs0gU3VVIFN2CIAjVw7XINDYFx7BnRQJ5OToAbGubMGCqO4NmeeDoWgnR83wt19ZHEhkYQeKBon22nTt44KX2wXNEW4zMShbFTyL/Wgya+cWj59EWRqT07cCQrz/BtHnJlcn//vtv+vXrh0KhwM/Pj4CAAPr06VNy1fPoK6SuCC4WPVdYWWM77E3sR8/CtGHTco29UG6WhrOHf+b0vgWkJcvXSaFQUr+VH94+atw8S46tKtxIP8PG6ED2Jq4kVys/n25jUov+blN42WOGiJ4LgiA8R6pd0X3o0CF27dpFQkICubm5JTtXKPj555/LNcDqQhTdgiAI1UvqnTx2/BzHlgUx3I6RM85KIwXdh9XBz9+DVj0dKqWgu30ylqggOXquzZUXD7VwtqHV1G60mt4da1f7cvWvy8wifUUomqAQ8s5e1rdbvtgdO/VYrAb6ojCSZ/n9/PzYvHlzsfNbtGiBWq1m7NixWFlZPdB3BmkbQ9AsDyT/2oWivnv2w35sAJY+/Stk1XNJp+PG+W1EhQcSc+FvfXutui3w9g2gaYcx1SZ6vjPuV0JjgriVfQOQo+ednQczVDWb1rVKbtsmCIIgPFuqTdFdUFDAqFGjWLduHZIkoVAouL+bwt8rFAq0Wm2FDLSqiaJbEAShetJqJQ6H3mbDjzc4E1EUPW/YxoYhASp8R9bDzMLw0fPspHTOLj1E1Px9ZManAnL0vNGrbfAO8KVulwqInu89jCZwOZmhe4ri4Q3dsfMfQ1KvtjRr346yfqzb2dkxadIkZs2aRcOGDUv0nXVwF6nLA4tHz+s3wW70LGyHTcDIpnzPrRe6e/M8Ufvmc+HIMvLz5Oi5qYUdLTpPxMvHHzvHho/owfC0kpajt+Xo+T/Ju/Tt9a1b4adS06feaMyNq/4mgSAIglDxqk3R/fXXX/P+++8zceJEZs6cSYcOHXjrrbcYMWIEERERfPXVV/Tt25evv/6a+vXrV8hAq5oougVBEKq/61HphAZHs3dFArnZRdHzfpPd8JvlgZO7hcHHoM3Xcm1DFFFBESTsu6pvd27vLkfPR7Yrf/T8eiypC1eTuvQvdClygX/bwoTljW34/fpZ0jIyyjxXoVAwaNAg1Go1ffv2LXEjID/mGpqV80lb8zO6dLlvhZU1tq9MkKPnjZqVa+yFcrNTOX/4V6L2BZN652rh4GjQ0g8vXzXuni9Ui1nl6IxzhEYHsTthuT56bm3iQH+3KQxyn0Edy/pVO0BBEAShQlWbotvLywuAqKgoQN7He+7cucyZMweAs2fP0qlTJ77//numTZtWIQOtaqLoFgRBqDnS7+axfWkcm+cXj553e8WZwWpVpUXPk/6JJTIogkurDBQ9z8omfWUomnnL9dHzDHRsaerISu1dLly5/NDzmzdvjr+/P+PGjcPa2rp435kZpIWuIDUkiLwr5/Ttlj1ekqPnvgMqLHoefX47kRFBxJzfrm93qNMMLx81zTqNw9TM+iE9VI6MfA07438lNDqYm9ny8+ly9NyPwaoAvGv1rhY3CQRBEITyqTZFt6WlJZMnTyYwMBAAIyMjPvjgAz7//HP9MSNHjuTChQucOnWqQgZa1UTRLQiCUPNoC3Qc2ZxEaGA0kXvv6tsbeMnR815vVFL0/E4GZ5ce4vT8fWTEaQBQGClpNNwb7wBf6nVrUP7oedgRffTc2MUZ1bXd7A4LIzAwkC1btpQZOwewtbVlz549tG/fvvS+D+5GsyKIzD2biqLnqsZF0XNb+6ce+/1Sbl0kal8w548sIz9Xnq0vjJ637jkTe6eSi8dVNq2k5VjSFkKjg0pGzz386eMyRkTPBUEQarBqU3Tb29szffp0vvrqK0B+TmzkyJEsXrxYf8y///1vgoODyczMrJCBVjVRdAuCIBhWWdtPFXJ0BA+Pp+//+ul0QoOi2bsykdwseb0Rm1py9HzQTA/qqJ4sev4049UVyNHzyKAIEiKKoudO7dzwVvvSZGQ7jM3LGT2Pjif/agyWfbrq265evcr8+fP5+eefSUtLK3GOs7MzMTExmJmZPbzv2OtF0fM0DQAKSytsh47Hfow/po2bl2vs+vFeTuP8kWUkng8iJ/3KvVYFDm4DcWkxm0at+6JSVf2sckzGeTbFBLMzfpk+em5lbEd/tyn4ecwS0XNBEIQaqNoU3a1bt8bLy4uVK1cC0LlzZ9LS0jh37pz+Tr2vry/Xrl0jNja2QgZa1UTRLQiCYDgxMdC0KeTklH2MuTlcvFi+whsgPSWfHUvj2DQ/mtvR96LnSug6tA6DA1S09nl09LwixpsUGU9UYDgXV51Am5Mvn+NoRaup3Wk9ozvWbg5P9fU9TEZGBiEhIQQFBXH+/Hl9+5w5c/j0008fux9dVibpoStJCQkk//JZfbtFt77YjwvAynegfkX1J3X/tVWgo5lqBz5ewbSsv1V/zG1NU14Y5k+3/uMxNbd5qvepSHL0fBmbY+aTkCXfJFCgkKPnHmra1K4ez6cLJe26touAbQEEDgikb8O+VT0cQRCqgWpTdPv7+7Nx40ZiYmJQKBR8//33vPPOOwwYMICBAweyf/9+/vzzTyZOnMhPP/1UIQOtaqLoFgRBMJyTJ6GUZHMJJ05Au3YV855arcTRzbcJDYrh1O5kfXv9Vtb4qVX0GeOCuWXphWNFjjc7OZNzSw9yesF+0mPk1dcVRkoaveKF92xf6nVvWOEFmyRJ7N69m6CgIHbs2MG1a9dwcXEp9diJEydiY2ODv78/TZo0KdFP9pEw7gZ9S/aJHaCTF68zcW8oR89fnfjE0fOyrq2T/SV8vILp3HwZ5qbyvuWm5ra06DKR1j1nVYvouU7ScSxpKxuj5xWLnqusW+qj5xbGVf98uiCTJInOSztzLOEYHV06cmTyEXFzRBCE6lN0nzx5kp9++okPP/wQNzc38vPzGT58eLG9QTt16sSWLVuoXbt2hQy0qomiWxAEwXCqoui+X/TZdDYGRrNnxQPR80luvDzDnboNLA0+Xl2BlmuhZ4gKDCc+/Iq+3amtm37Vc2ML08f+mh7XnTt3cHR0LPW1mJgYGjRogO5eMT1gwAACAgJ46aWXUCqVaOavIH31ZrRJKUj5eZi0dSI3emdR9NzCEtuh47Abq8ascYvHGs+jrq2ZSTqdmi1n7OBActIu6dtVLQbg7ROAR7OXKmSBt/KKy7hIaEwwO+N/JUcrP2pnaWxLP9dJDFapqWvZoIpHKOy4soP+K/vrf7999Hb6Ne5XhSMSBKE6qDZFd1mOHz/O1atXUalUdOrUCWU1+KFXUUTRLQiCYDhVXXQXytDk8/cvcWwKjuHm9WxAjp53HuzMkAAVXr1qoVAoDD7eO1HxRAZFcHHF8aLoeW0rWk7tRusZPbBxr/joeWnee+89vv766xLtTRs34fsmnWiy/RgWvTpj0aM92qS7pK8MxWHOTIzcJDQrgsi7dEZ/jkXXF7Afq8aq96CHRs8f99oeP66jtsUOoiKCiT6/Tb/Am71zU7x6zqJ5p/GYWlT9z+vCVc83xywoFj3v5DQIP5U/7Wq/KGZXq0DhLPfJxJNoJS1GCiPa1WsnZrsFQaj+RfezTBTdgiAIhlNdiu5CWq3EsS1JhAZH88/Ooui5qqU1g2Z54OjlQtcexo/sp7zjzU7O5NzPh+ToebS8+rrCSEnDoa3xVvvg4tPYYAVCQUEBLi4uJCUllXhtINb8lzpsMcnh5vRh+Pv706i2E7enzSH31Hncj65B6WBH9tFwNMsDydy9UR89N3arj/1ofzl6blfy5sHTfC9okq4QFRHMucO/kJ8rR89NzGxo0eVNvHr6Y+/c5CE9VQ6dpOPEnR2sv/ED/yTv1Le7WzVnsErNCy5jRfS8Ej04y11IzHYLglBtim4jIyPmzp3Lxx9/XOYxX3zxBZ988gkFBQXlGmB1IYpuQRAEw6luRff9Ys5nsDEwmt3LE/TRc3MbY86luxOLO9lYlnluRY1XV6Dl+qYzRAaGEx9WFD139HbFO8AHz1HtDRI9v379OgsWLGDp0qVoNBoAzFGwFRW3KOBN4slBQgm81L8/H3l2pM7PoXgcX4tps0b6fvLjbpC6eiGpfy1Fp7l388DCEpvBY7Afq8bMs5X+2PJ8L+TlpHPh6HIiI4LQ3L6ob/do3h9v3wBUzfpVm+j5ppj57IxfRrZWvklgaWzLi65vMlilxsWy0SN6EMrjwVnuQmK2WxAEqEZFt1KpZO7cucyZM6fMY7744gvmzJmDVqst85iaRBTdgiAIhlOdi+5CGZp8di6LZ1NwDIlX5e2hJCAJJ25Qn7vUAop/UDfEeO+cTiAqKIKLK45RkH0vel7LkhZTuuE1swc2HrUq9g2BzMxMVq5cSVBQEJ3OxDEFB/5DElvIQAnoACUwFnvew4mD745k+Af/ws7Orlg/uuws0jetQhMSSN7F0/p2iy69sR8bgFUfP/6JNCr394Kk0xFzcSeR4YEPRM898eo5i2adxmNmYVf6yZUosyCNnXG/sjlmPvFZlwE5et7R6WUGe/jT1vFFlIqqv0nwrClrlruQmO0WhOebIeo+g/1LnpSUhIXFk+15KggVRaGAXr2qdgwTJsjjuHHDsO9TEV9rWJjcz9y5FTAgQXhGWdub8Mpb9fnpYk/G/NCOO9RGATiTRCeO0Z0DuBODEYZNeDm2dqHPkpG8GfcZ3b8Zgm39WuTczeLk17v4rcGnbB3+M3F7L1GRT49ZWVkxdepUTh05yjuOTbhZz4FdCvnGg+7eMUqgBWbEk8ekbz7nm2++KdGP0sISu9cn4xEaieuKMKz7DQelkuzDe0mc9Qo3XmyMyaZvsVPeLdd4FUolqub9GDx9C+M+ukybXv+HqbktmtuXiFg7m1/nuBG+Rk3K7UuP7syArIxtGVp/Nkt6XuDz9tvo4DgACYmjSZv56ER/pu1vwabo+WQXZFTpOJ8lkiTx8d6PUZbxEViJko/3flyhf38EQRAee6Z7+fLl+v+fMGECQ4cOZejQoSWO02q1xMbG8uOPP+Lp6cnhw4crbLBV6Vmc6b5xAxrcWzz1pZdgx46Sxxw+DF27wvjxsGzZ079Xr14QHq6fbHji8xIToW7dxz9PoQBfX7mYrCoTJsBvv8H161C/vuHepyK+1rAw6N0bPvlEFN5C1ajMfborQuF4jXIy8CAGV+IxRk525WNMHG7cMvUg8rKlwcer0+q4sfkMkYERxO0pKiJre7ngrfbB840OmFhWTPQ8/c+t3J42B6cfPuBur3Ysmr+AJT8vJSUlhXoYE4oH60jje8VdLt24jsdDvnhJp0OhVJKfEEPqygWk/vWTPnqerbMgNH0MIRo1l/Jalzj3ab4X8nLSuXhsBZERQaTcKtqj3KNZPzl63rx/9YieZ15ic8x8/o77VR89tzCy4SW3N/Hz8MfVquqfT6/JcgtyUf2o4lbmrTKPqWtdlxuzb2BmbFaJIxMEobqo0ni5Uql8rOdbCruzsLBg7dq19O9fdnynJnnWi26A3buhT5/ix9TUovvCBbC0rNoP54mJkJoKjRqBiYnh3qcivtasLLmIcHSUfwlCVYiJgTt3yn7d0bF6FNyF7h9vTno+JzfFc/ivGJJj5BlghQI6DXJiSICKNi/UrpRnRJPPJBA1fx8Xlh+jICsPADMHS1pO7krrWT2xVT199FySJJJmziX9z200SNiP0swUSacjOyeHVatWceeD7+iflE8AiTgPH8CaNWtK7Sfl7l2URkbY2dmhy84h5cvFmHXywrJvl3vR8yDyLkTqjy9o2Zv8fmoK2vuBkbx4XXm+FyRJIvbSbiLD5nHj3Bb9DyY7p8Z49fSneecJ1SJ6nlWQzq743wiNDiI+q+hmSienl/Hz8Ked40siev6UYlNjScoquUBgIWcrZ9xs3SpxRIIgVCdVWnT/9ttvgPzDauLEiQwdOpQhQ4aUOM7IyIhatWrRtWtXHBwqZ0uTyvAsF93168sfHtu1g6NH5Q+KhWpq0S0IglAVdDqJ49uSCA2K4cSOojsI7s2tGOyv4oVxLlhYP3rV8/LKScmSVz2fv4+0G/cWLlMqaDBEXvXctVeTp7oJEN9/ElJePm57liPl5aEwlWfQc89eJq77SDK6tOI7Iw2T//0vevbsWep7fPLJJ3z33Xd81fUlXjR1QLltPwDOP/0Hu0mvIUkSOcf3owkJJGPneri3Noyxiwd2b8zE7rXJGDnUftpLU0zqnWuc3r+As4eWkpedCoCJqRXNOk/A20eNQ52mFfI+5aGTdPyTvIvQ6CCOJW1BQv5B6mrZBD8Pf150exNLY5sqHqUgCMKzwyB1n/QUJkyYIG3cuPFpTq2xUlNTJUBKTU2t6qFUmOvXJQkkqV8/SRo/Xv7/338vfsyhQ3L7+PElz79xQ5ImTpQkFxdJMjGRJFdX+ffR0cWPk0vtkr9K6/NBvr7ysYmJRW1798ptn3wiSQcOSNKLL0qSnZ3cdv97+voW70ujkaSPP5ak5s0lycpKkmxsJKlRI0kaN07+Wh4mIkLu8803S3/91i1JMjaWpG7ditoKr+n160829qQkSZoyRZKcnCTJwkKSOnSQpHXrJOnXX+Xjfv21+HuX9rUWvve1a5I0b54kNW0qSaamkuThIUlz50qSVlv8+PvHVdrX9vbbkuTpKUnm5pLk4CBJnTpJ0rffFj/u558lafBgSVKpJMnMTD7upZckac+e0q+ZIDzrYi+kSwvUZ6VXrP+W+rNN6s82aZjtTmnx/52T4q9kVsoYtAVa6VpolLS+b7AUiFr/a2Wr/0qnlxyQ8jJzH7svnU4nJQz3l6437ivl307Wt+deviHFD5slXXPtIWVFHC393Hv/6OTk5EhtateR3qG2dIpG0gwcpNNKT+kf74FS1tFI+dj8fP15eQkxUtK370lXOtaWLjVButQE6XIrc+nm+5OknHOnnuaSlCo3J12KilggrfiihRSoRv9rw/yXpGunN+nHX9XiMi5JC8/NlobttJX6b0Pqvw3plb9tpAVn1VJs+oWqHp4gCMIzwRB131Plkn799VcGDx5cMVW/UC189hmYmcFHH0F+/qOPv3QJOnaEX36RVxz+17+gbVv59x06yK8X+uQTUKmK/r/wVylLAjyRgwflmXCFAqZOhREjyj5WkqBfP/j8c6hVSz5+6lR5zKGhcPnyw9+rRw85EbB2benPnK5eDQUFMHZs+caekSE/n/3TT9CkCcyeDc2awciRsG7d4/V9v//3/+SvuWtXmD5dbps7Fx6y218xFy9Cmzbw/ffg7AwBAfDGG3Kc/b//LX7srFlw6xb07Qv/938waBAcOiT/fuPGJx+7INR0bk2tmRHYgpC4Xkz7sRmuTSzJSitg/Q/RTG4SwSd+Jzjx9x2DLtikNFLSwK81Q3fOYvTZ92k9owcmVqYkn0lk79Tf+dX1Y/b/vw2k3Uh+ZF8KhQKbCcPQpaaTvnw9uWcvk3clmqS3viBz/U5q//dtzLvLy44/+DUVPiu95//m8HWyOR2xYBoJnCMXE52ORZGHaD1qGD/88IN+a7Lkz+eTe/wyju98SYOIWJy//AWz5m2QcnNIW/MzMUPaEDfal4wd65DKuT2pqZk1rXvO4I33zzDUfzcNWg0GhYKYC3+zeYkfIf/x5NTeH8nN0pTrfcrL1aoJ05v/yIpe8cxqMR83q6Zka9MJjQliyv5mfHx8AMeTtqOTdI/uTBAEQag85anY161bJ7322mtS69atpUaNGunbz58/L3399ddSXFxcOe8JVB/P+ky3JEnSO+/Ivw8KKjqmrJnu3r3l9sWLi7fPny+39+lTvL1wxvpJPWymGyTpl19KP+/B2d+oKLlt6NCSx+bkSFJ6+qPH8tFHch9//FHytfbt5Znk5KLJn4fOdJc19sL3mDq1ePuuXUXnPclMd4MGkpSQUNSelCRJ9vbyLH/ufRNcZc10d+ggty9ZUnKssbHFf3/tWsljEhLkJESTJiVfE4TnjVark45uvS19NOCYfua7P9ukKc0ipE3zo6XMtPxHd1IBclIypZPf7ZaWNZyrn/kOUgZIm4YskWJ2XZB0Ol2p5+l0OkmbniHdUn8mXTJuLl1z6yldMmomXXPtISV/seDh7xl5Xro57WPptHlL6T+KOpIpCgmQtqOSQvGQGmEqAZIJSFZWVtJ7o8dLFxWe0iWFp3TDa5CUsXmPfgxZx/ZJCQGvS5eaGelnv6/5uEvJi76UCpKTKuw6ae5ck/atf0da/K69fuZ74b+spL1/zJCSE89V2PuUh1anlY4n7ZA+Oe4nDdim0M9+TwpvIq2//qOUkf/sfGYRBEGoLNVmplun0zFixAheffVV1q5dy7Vr17h+/br+dQcHBz788MNiK54L1d8HH4C9vTwzmvGQ3UliYmDvXmjRAqZMKf7a9OnyzOyePRAba9Dh0q4dvPnmk51T2i52ZmZgbf3ocwtnsVesKN5+/ry8X+zAgfIs+uMoa+wrVoCpqZw8uN8LL8grzD+pjz+GevWKfu/oCEOGQHq6PIv9MEePwvHj4ONT8s8ZwO2BNWbuX5SvUL16MHy4nCSIjn7y8QvCs0SpVNBxgBOfb+3ATxd7MiRAhYWNEbEXMpk/6xxjXPeyaPZ5Eq5kGnQcZvaWtH27D2MvfcygTVNxf7Epkk7i+sbTbOg7n1WtvuT0ov3kZ+YWO0+hUKC0tsI58GNUpzdhN2s0dVf+D7eIlTi8K/8jUXAzCeneM9gAUl4e6X9tI2HgFPLOXqb+n4GMvX6Ef73/HuOt6lEfEzaSxlXkRd+0yHuC1125g1SpgNAGttyxMSNhyEyiWw8ia8c+LDr0oN68P6i/9wYO0z/AyMGRgsRYkr97n+u+7tz6YDK55yMpL7vaDegx9Fve/CyO3iMWUateS/LzMjm9fyEr/9uCDfNf5NrpUHQ67aM7MxClQkl7x5eY2z6UpT6XGap6C0tjW+KzLrP4wluM3evKwnMBxGU84h98QRAEwaCequj+4Ycf+Ouvv5g2bRopKSm88847xV6vU6cOPXv2ZMuWLRUySKFyODjAe+/B7dvwv/+VfdypU/J/fX2LL7oGoFTKRdr9xxlKx46Pf2zz5uDlJcfAfXzkuPTJk6B7ggSepyd06gTbtxdfYbmwCH/caDmUPva0NHlxu8aNoU6dkq937/74/Rdq375kW2GxfC/BWaajR+X/Pm6xf+2aXJw3aiRv56NQyL+CguTXExIerx9BeB64eVoxfV5zQuJ6Mz2wOa6elmSna9kYGM1kz318MugEx7YlodMZOHo+qBVD/57F6HMf0HqmHD2/e+4mYTP+5Fe3Oex/ZwOp10ouKW/arBG13puGzYiXMWnogcLYGG1aBjdHvc2tce+iy5afw8n95zx35waBiQkuGxdi7dcHD5WK//73v8xx9CRTVY+bzeRlyE2Q9/xWYUJ/rFlPGh9fO0HfA+v5pHYecfnZ3Pn3t2Qf+kc+vq4bjm9/Qf2IWOp8tQyzlu2KRc9j3/AhffuackfPTcysaNV9Gm+8d5pX/PfQ0OsVFAolsRd3seWnIYR83oSTe76r8ui5i2UjpjX/gRW94vFvsRB3q+ZkazP00fMPj/XjaNJWET0XBEGoAk+1hOqyZcvo2LEjCxYsACh1ddLGjRuLorsGCgiA4GD47juYObP0Y9LS5P+WVhhC0cxq4XGGUtb7l8bYWJ59nztXfi77X/+S252cwN8fPvwQjIwe3c/YsXIx+scf8jPMkgQrV8o3LF5+uXxjL7xezs6Pf86jlLbgovG9v/XaR0zOpMoL+eLq+uj3uXJFviGRlibv9+3nJ7+3UinvAR4eDrm5j+zmuVbTtssyhK++klMjZWnfXr4x+KQMdW0rol8rW2OGqFX4zfLgn5132BgYw7GtSRzdIv9y9bRksFpF3/GuWNo8/arnhw7JN8bK0rBhXXrNf52u//Xj/K+HiQyKIO1aMv98t4d/vt9LA7+WeKl9cX/Bs8xVz3P/OUd2+FHM2jRHaWGOJEkY1amNZf+epM5fSWz3kdj7j8F+1hjSVm1CG5NIg2/eZdO/JnLgwAGCAwNZs24daq0cGcpHIvver9W3ryF5e/LbvB8w9nAp9r5KM3Nsh43H5pVx5Jw8iGZFMBk71pBzfB83j+/DuK4bdqNmYDtiCsa1nJ76GioUCtw8e+Pm2ZvU5Ouc2b+Qs4eWkpZ8nQMb3uHI1jk06zgWLx81teu1fOr3KS8LY2te9pjOQPdp/JO8i00xwRy5vYmTyX9zMvlvXCwbM8hjJi+5TsTKpOq3RhMEQXgePNVP8CtXrjBr1qyHHlO7dm2Skx+9MItQvVhYwKefwqRJ8n9Lm70tLORu3Sq9j5s3ix9nKE+6203t2vKsa2CgvLf1nj3y7z/5RN5H+/33H93HyJHw9tvy7PasWRARIcemp02TY+rlGXvh9bp9u/RzyrrehmJvL/83Pv7Rx/7wA6SkQEgIjBlT/LXp0+WiWyhbTAw0bVr6In2FzM3lRwKe1cL7q68e/XewcNvnJym8DXVtK7pfpVJB+35OtO/nRPzlTDYviOHvX+KJv5TFQvV5ln1wib7jXRmsVuHmafX4A0UuuLt1e/RxBw9C164WtHmrN94BvtzYeo6o4AhidlzgeugZroeewaF5Hbz8fWg2rhOm1sX/0Tvonsb/3lfy74Gj8QDQ6TCp70atD6Zj5deHtJ/+5M7bX6IJCkF7JwWz9i2xfq0/CoWC7t2706NHD2IvXuay3xTCom8wKs+OfljzBUmEkUWbMb0wbd64zPErFAos2nfHon13Cm59R+rvi0hdvYiCm3Ek//Ahd+d/ho3fG9iNVWPeou0TXcMH2dVuQPch39BpwFwuHl9JZPg87iae5cyBxZw5sBg3zxfw9g2gfsuXUSof446uASgUCto5vkg7xxe5mXWdTTHBbI9bSkLWFZZceJuQy3Po6zoBP49ZuFs3q5IxCoIgPC+eKl5uYWFBauE0WBmio6OxL/zU/gQiIiLw8/PDxcUFhULBhg0bHnp8WFgYCoWixK+bhZXfPfPnz6d+/fqYm5vTuXNnjhZmZ4USxo+Hli3lFbSvXCn5eps28n8jIkruuy1Jcvv9x0HRLPKjZlcrg0Ihx81nzYKdO+W20NDHO9fREfr3l/cvv3KlKFr+YKH5NGxt5RXSr1wpvfA+eLD87/EkOnWS//v3348+9upV+b9DhhRvlyQ4cKBix/UsunPn4cUbyK8/bFa1pnvYDPfTHFfIUNfWkH9mrk2smPZDc0LiejEzuCh6vik4hilN9zHn5SeLnj9shrus4xRKOXo+ZPtMRp//EC9/H0yszUg5f4vwWX/xq9sc9v1rPalXkwB5tfIPdn/ADtML/PvsN0iShOLeP/xGtR2w7NUZp3kf4n5sLUo7G3SadPKvxpJ94KT8fvfuRLo3bUKfS2GMvXGUax9NJNPagv9SBy87M9bkrCl1pff8/HyCgoJISUnRtxnXcaH27M+oHx5Dna9/w6xVe6S8XNLW/krs0HbEjuxB+tY/kR5nu46HMDG1pFW3KXL0XL2XRt7DUCiUxF3aLUfPP2vMyd3fkpOV8ujODKiuZQOmNPuOFb3iUbdYhMq6JdnaDDbFBDN1f3M+OPYiR25vFtFzQRAEA3mqortt27bs2LGDnDI+cdy9e5ft27fTpUuXJ+47MzMTb29v5s+f/0TnXbx4kcTERP0v5/syun/88Qdvv/02n3zyCSdPnsTb25t+/fpxu6wpxeeckZG8HVR+vhzHfpCHhxwhPntW3iLsfkuWyAuL9ekD7u5F7YULjBl6cbWy3Lgh/3pQ4eyxufnj91U4+790Kfz1l7yA2NM8b12a0aMhL0+efb9fWBjs2FEx7/G4OnaUf0VEyDdgHnT/DHjhlnD79xc/5quv4MwZw41REJ5lljbG+M1SseR8T/6zowOdBjmhUMCxrUnMGXiCKU33sTHwBplp5Xtm+VFqNauDb9CrvBn3GT7zhmPX2Im81GxOfb+X5U3+wya/xaz/bSXH4o8BcCzxOH9fLXm3zsixFmZezdDeSsa0aQNMWzUhc9MeCm4m6Y8pXITNsp4zwz99H9vf/g87hREv17PheBn9rl+/noCAAFxdXZk2bRpn7vtHR2lmju0r43Bfewy33w9g/fJIMDYm5+QBbr41ght9GnB34RcU3E0q0e+TUCgUuDXpxcBJaxn3yTXavfAu5pa1SLt7gwMb3+XXOW7s+X0adxJOl+t9ysvC2JqBHtNY2P00/+2wky7Og1Gi5J/kXcw96cfkfZ6su/49GfmaKh2nIAjCs+apiu6AgADi4uIYPnw4cXFxxV67evUqr7zyCqmpqQQEBDxx3wMGDOA///kPr7zyyhOd5+zsTN26dfW/lMqiL+37779nypQpvPnmm7Ro0YJFixZhaWnJLw9WjPfJzc0lLS2t2K/nyeDB8t7UhTOYD1q4UJ71nTJF3m/7gw/kWc7p0+XnpBcuLH58nz7yf4cPl/cC/89/YNMmg34JxZw6BQ0bQpcuMHGiPN7x4+VVwZVKeV/px+XnB3Z28mJsqanyLPeTRt3L8u9/y6u/L1oEPXvK4xw3Tp5d9/OTj1E+1d/ap7NyJbi4yHuJ+/jI45s9W95728ur6Ljp0+WI/vDhMGGC/Mx89+7yKuxP8qy7IAglKZUK2r/kyKeb2rP0Uk9e+T8VVnbGJFzJYtHsC4x128sC9TliLzxk24kKYGZngXeAL2Mvfojflml49G8OksSNzWeJf/MoH84fQ8+jrbHMM+fjvR+XOiutCQ6hICYB26kjcN36E07zPsKojiNwr+C+9w+cJEmgUPDv5KVcc86jQ6oFNnnGpfYbdG+1xuzsbJYsWULr1q3p06cP69evR3uviFcoFFi060a9H1bTYG80tWbNwai2MwW34kn+4SNu+Lhz898TyDl7stzXybaWiu5DvubNz+LoM2optV28KMjL4uzBJaz+yov1QX24FrWxSlc9VygUtHXsyyftNvKLz1WG138Ha2N7ErOu8tPFfzEmzJXgszOJyThfZWMUBEF4ljzVx/chQ4bw73//m23btqFSqfjuu+8AufD19PRk3759fPTRR/QprLQqQZs2bahXrx4vvvgiB+7Ls+bl5XHixAn69u2rb1MqlfTt25dDhw6V2d+XX36JnZ2d/pf7/dO2z4mvvy77taZN5e2kJkyQFxb79ls4dkzeBuvYMXml7/tNmQLvvitHLb/+Wt7Kau1agw6/mA4d5IJRoYAtW+SF4sLC5OLxwAH5JsPjMjeH116TkwBQMdHyQjY28szypEnyc+c//ADnzsmrrvv6yscY+ln5+zVpIq/yPnu2PLP9449ypD4jQ755UqhtWzmG3q4drFsnJyDs7eVr26FD5Y1XEJ51Lo2tmPp9c1bE98J/YQvcmlrpo+dTm+/n4wHHDb7quUKppP7AlgzZNoMxFz/Cflx9ckzzqHPHgde29uKT78bh9osZm/esL3GuRY/22KvHYtW/J0prK4yda6O7q6Hg1h0URkYoFAp9Uf331b+JvnCSfKVElqmOdNMCjsUfKzbbffLkSfY/GLEB9u7dy7Bhw2jUqBHffPMNd+/e1b8mR88/laPn34Zg1rojUl4u6et/I/aV9sSO7E765t/LHT03NrWgZddJjPr3KYapw2jkPRyF0oi4y3vZsnQoyz9rxIld35CTeffRnRlQHcv6TG72LSG94ghouYT61q3J1WaxJXYh0/a34P1jfTl8OxStVA2eDxMEQaihFFJpt6If086dOwkODubIkSPcvXsXW1tbOnfuTEBAAP369Sv/4BQK1q9fz9ChQ8s85uLFi4SFhdGhQwdyc3NZunQpISEhHDlyhHbt2pGQkICrqysHDx6ka9eu+vPeffddwsPDOXLkSKn95ubmknvfcstpaWm4u7uTmpqKbWVWPYJwz5gx8szzuXPyM+nCs+PkydK3d3vQiRPyjY1n0WuvFS2U9jCvvio/1vG4DHVtq8ufmSRJnNqdTGhQDEc23davs1GvkSV+/h68NNGNDZuMH+vm4IoV8iMuT/r+nZd25uz107Q/5YnPUS/qJDvIrykk6g9oiXeALx4vNkVRRkwn/a9tpC5cjcO7k7Hs11NfeHdd3AnrfReZ94cz/+ubzLKuGowURrSr144jk4+gUCi4cOECn376KWvWrKHgIVuDWVhYMHr0aNRqNV73x3TuyT51mNSQINK3/6W/o2rk7IL9GzOwHTEV49plbCvxhNLvxhC1fwHnDv5ETpZcbBubWNC041i8es7C0bXk2CqbJElE3Q1jY/Q8jtzehA75Oe+6Fg3w8/DnRbc3sTFxqOJRCoIgGE5aWhp2dnYVWveVq+g2tMcpukvj6+uLh4cHISEhT110P8gQF18QSpOYWLTtWqHwcDkK37ixPAMuPFuqSwFXlUTRXX4JV7PYPD+av3+JJzNVLkAtrI1w7+rKzzs9yMT6oec/TdG948oO+q/sr/+9QgdNr3nge8Sblpfr69vtmzrjNasnzcd3wtTWolgf2fuPc2vShxjVtsf+rfGYtWvJXi7w1Zzh/Gt3bZQS+I9I5Lpj0czz9tHb6de46OZ+fHw8ixYtYvHixSQlPfz5bF9fXwICAhg8eDDGxsU3cSm4nUjqH0tIXb0Q7R150Q+FiSnWA0dgPy4A89YVE90pyMvm0snfiQyfx534SH27a2NfvHwDaNh6SJWten6/W9nRbIlZyLa4JWTky4vBmRlZ0qfeGIbUn43KukUVj1AQBKHiGaLue6J4+aFDh+jTpw82NjbY2try4osvVstVwDt16sSVe8tuOzo6YmRkxK0H9lu6desWdevWrYrhCcJDDRwob+8zcyb8v/8nPxPdp4/8qOO9RxcFQRBKcGlkqY+eqxe1wL25FdkZWi7tjKEn++nAMZy4DVTMvXZJkvh478co7/soISnhQuMYFo/exH/UKzj/QiImNmZoLt4mImAtv7jNIWL2WjRXigpjix4dqLviWzA24uaY/0fiq2psOwewaHU93FNM+HxAUrGCW4myxLPdrq6ufP7558TGxrJ8+XI6POS5lvDwcIYPH07Dhg259sDS7sbO9ait/oQGYTHU+d8KzLw6IeXnkb4xhNjhHYkd0Y30zauR8vLKde2MTS1o0eVNRr77D8MCwmnc5jUUSiPir4Sz7efhcvR859dkZ1bt1qt1LFRMbPoVIb3iULdcrI+eb4tbwvT9LXn/WF8O3togoueCIAiP8Ngz3adPn6Zz584lViy3sLDg6NGjtGzZsuIH95Qz3S+++CI2NjasW7cOgM6dO9OpUyf9Yis6nQ4PDw/8/f157zE3fBUz3UJl+fFHOUZ+9Sqkp8vPRnfvLu9h3LlzVY9OMASxT/fj7dMN8OWXz+Y+3YYgSRKn9tzlt0+jubDvNoXrPWZiSQwexONKASb64+V9uh+//9yCXFQ/qriVeavMY+pa1+XSmxe4tiqSqOAINBeLdg1RDWiBl9oHVb9m+uh51q4DaEI2sOriX1y1SiOicRbnXHLl+wSK4v3emH0DM2MzSiNJEkeOHCEwMJC//vqr1Oh5o0aNuHTpUrGFV0uTE3kUTUgg6dv+vC96Xg+7UTOwGzEVY8c6Dz3/cWWkxBG1fwFnDy4h516xbWRiTtP2o/H2Dag20fPTKRFsjJ7H4Vsb9dFzZ3MVg1VqXnJ9ExvTWlU8SkEQhPKp0nj56NGjWb16NR9++CFqtRqQ977+/PPPGTNmDMuXL6+QAWVkZOhnqdu2bcv3339P7969qVWrFh4eHrz//vvEx8fr3+/HH3+kQYMGtGzZkpycHJYuXUpQUBB///03L7zwAiBvGTZ+/HgWL15Mp06d+PHHH/nzzz+5cOECdeo83g9LUXQLgmBIMTEP39PZ0fHZLbgLffXVw/fhbt/+yQruQoa6tjXpz2zr2ix2/RLD1bA48rLkAtTYzIiGPV1p+qIHbXtaP1HBXSg2NZakrLLj3M5WzrjZugEg6XTE7rrIqXnhRG87T+ED6Paeznj5F4+ex9y9wZ3cshcYu7/fR0lISGDx4sUsXry4WOrt+++/5/+eYOuKgqSbcvT890VobycC96LnA16Xo+deHR+7r4e+T34Ol0/+TmR4IElx/+jbXRr1xNsngIZeQ1EaGT+kh8pxKzuarTGL2Ba3hPR8+c/KTGlBb5cxDFapaWDTuopHKAiC8HSqtOj28PCgfv36REREFGv39fXlxo0bREdHV8iAwsLC6N27d4n28ePHs2zZMiZMmMCNGzcICwsD4JtvvmHJkiXEx8djaWmJl5cXc+bMKdFHcHAw3377LTdv3qRNmzYEBgbS+QmmDUXRLQiCINR0OZkF7FmZSGhgNNFni7YYa/NCbYbMVtFxoBNGRhW0B+JDaK4kcXr+Ps79cpi8NDkuYGJtRvMJnfFS++DgWTELl90vNzeXv/76i8DAQM6dO0dcXBz29valHjtu3DiaN2/OlClTcHR0LPaalJdH+o41pIYEkXPqsL7d3LszdmPV2PR/DYWpabnHK0kSidcOEBkeyNWodUj3thizdnCndY+ZtOw6GQtrx0f0Yni52mz2JqwkNCaI6+lR+nbvWn3wU/nTxckPI2XV3yQQBEF4XFVadJuZmTF79my++eabYu3vvvsugYGBJWLnzxpRdAuCIAjPCkmSiNx7l9CgaI6E3kYnp4Sp29CCQTPlVc9tHEwe3kkFyEvP4ULIMaKCIki5UDQL7dG/Od5qH1T9m5e56nl5xMTE4FFGDOHMmTO0bi3P0pqZmfHGG2+gVqtp27ZtiWNzTh9HszyQjK1/IOXLz3kbOdbBbuR07EZNx9ipYtaOydDEc+bAIk7vX0ROphyvMDI2w7P9G3j7BuDk1qZC3qc8JEnibMp+NkYHcvDWuvui5x4M8phFf7fJInouCEKNUKVFt1KpZO7cucyZM6dY+6effspnn32GVvtsL6Ihim5BEAThWXTrRhab5sewY2kcGRo5em5macQL41wYrFahavHwVc8rgiRJxO66SGRgODe2nCuKnjdxwsvfh+YTSq56XiHvq9Nx5+0vsR4xEPMubVAoFEyfPp3FixeXOLZHjx4EBAQwdOhQTEyK35AouHOLtD9/QrNqgT56jokJNv1fk6Pn3hWzIEdh9DwqIpjbsUXPYtRr2ANvHzUNvV/ByMjwN0sepTB6vj1uKWn58k0COXo+Gj8PfxraelfxCAVBEMomiu4qJIpuQRAE4VlWGD3fFBzNjdNF0XPvPrUYrFbR2c+5UqLnqVeTiJq/j3O/HCEvNRuQo+fNxnXEO8AXh6YVs3AZQObWMBJengqAWftWKCcPo+m/ppGVlVXmOa6ursycOZMpU6bg5ORU7DUpP5+MHWvRhASS888hfbuZVyfsx6qxHvAaStPSF397EpIkcfP6ISIjArl6ai06nXyzxNrerSh6buP0iF4ML0+bQ1jiajZE/1gseu5VqxeDVQEiei4IQrVU5UV348aNady4cbH2K1eucPXqVfr161fiHIVCwZYtWypkoFVNFN2CIAjC80CSJE6H32XDvAei5w0sGDTLg5fedMWmVvmfWX6UvIxcLoYcJTIogpTz90XPX2qGl9qH+gNblDt6nnfhKinfLCV91SakXDkefsbelNVu5my4GEV+fn6Z55qZmTFq1CjUajXtStmMPefMCTl6vuX34tHzEdPk6LlzvXKNvVBGagJn9i/izMHFZKfLq8PL0fNRePsE4OReMhZf2SRJ4qzmAJuig9h/ay26e1uMOZm7M8hjJv3dpmBrWruKRykIgiCr8qL7iTtXKJ6ZGXBRdAuCIAjPm9sx2WxeEMO2JXFkpMgFqJmFkt5jXBgSoKJ+KxuDj0GSJGJ3XyIqKJzrm87qo+d2jRzlVc/f7IKZXfmi59o7d0ld8gepC1dTEHcTgCQjWN+8NisSr3Az+SHL1APdu3dHrVYzbNiwktHz5Nuk/bEEzaqFaG8nyI0mJlj3exX7sWrM23RBoSh/gkCbn8ulk78TtS+Y2zHH9e31GvbAy8efRt7DqkX0PCk7ls0xC0pEz3u5vIGfhz+NbNtU7QAFQXjuVWnR/bSrk6tUqqc6r7oRRbcgGEZN2nZJkB06BNeulf16w4ZPtt+zoRnqe8wQ16G6/n3IydKyd2UCm+fHcC0yXd/u3bsWfv4edBlSp3Ki59fucHrBfs79fIhcTfHouZe/D7Wal2/hMqmggIwNu9AELidnn1y45iGxp4E9K5TpHL168aHn//DDD7z11lul952fT8bO9WiWB5Jz8oC+3axVB+zHBWA98PUKi57funGEyIhArvzzlz56bmXnQuseM2nVbWq1iZ6H3/yDDTd+5Fr6KX17Kwcfhqpm08V5sIieC4JQJaq06H7eiaJbECpeTAw0bQoP2/zA3BwuXhSFd3Vx6BB06/bo4w4erB6Ft6G+xwxxHWrC3wdJkjizL4WN86I5tOGWPnrurDLHz19Fv4mVEz3Pz8zVr3p+99xNfbv7i03xDvBFNaAFSqPyRc9zI8+jCQyRo+c5uQCctTNhtYclGy5GkZeXV+x4c3Nz4uLiqF370THpnLMn0YQEkbF5NVKe3LdRbWfsRk7DbuR0jOu4lGvshTJSEzh7YAlnDiwiK12O6CuNTPFsPxJvnwCcPdpXyPs8aNe1XQRsCyBwQCB9G/Z96LGSJHFOc5DQ6CAO3FqLVpJvEjiau/Gy+wwGuE/FzrTqt0YTBOH5IYruKiSKbkGoeCdPQvvH+Mx34gSU8sikUAVWroQxYx593IoVMHq04cfzKIb6HjPEdahpfx9ux2SzdVEs25bEkpYsR89NzZX0GePC4AAVDVpXTvQ8PuwykYERXA89jaSTP9LYNqiNl39PWkzsgpm9ZbneQ5ucQupPf5K6YBUFsfLK5MlKifXNHQm5dZXEO0kATJo0iaVLl5bah0ajwdLSEtMH9u8uuJtE2h8/kbp6IQU34+RGY+Oi6HnbrhUWPb986i8iw+c9ED3vjpePmkZer2BkXDE3SyRJovPSzhxLOEZHl44cmXzksb+GOznxbI5ZwLbYJfrouanSnF713sBP5U9j26p/Pl0QhGefKLqrkCi6BaHi1bQiQxBFdyFRdBfJzdYStiqR0KDoYtFzr161GKz2oMtgZ4yMK36v7QelXk/m9Px9nPvlMLkp8urjJlamNBvXidazelK7ZfkWLpMKCsgM3Y0mMITs8KMA5COxV2XHCpNMFqxcTttOHUs9V61Ws3btWmbMmMHUqVOpU6f4CuxSQUFR9PzEfn27Wav22I8NwPrlERUSPQe4eeMIURFBXD75R1H03LYerXrMoFX3aVjaOJer/x1XdtB/ZX/977eP3k6/xiUX232YPF0uEYl/EBodyOW0oq3RWjr0YIgqgG7Or4jouSAIBiOK7iokim5BqHg1tch4nomiWyaK7pIkSeLsAQ2hgdEcWHcLnVb+eOHsYc6gWR70n+xWOdHzrDwurjxOVGA4yWcS9e1ufTzxnu1L/Zdblj96HnUBTeBy0lcWRc+NHB2wnfI6djPewMS9qMBPS0vD1dWVjAx5GzZTU1NGjBiBWq2mY8eSRXrOuX9IDQkifdOqouh5LSdsR0zFftQMjOu6lmvshTJSEzh78Cc5ep4mR/SVRqY0aTcCb98A6nh0eOI+C2e5TyaeRCtpMVIY0a5euyea7X6wv3Oag2yKDmb/rTX66HltM1de9pCj5/amVf98uiAIzxZRdFchUXQLQsWr6UXG80gU3TJRdD9cUmw2Wwqj53eKoue9R8urnjfwqrzoeVTwPq5tiCqKntevRetZPWkxqSvmDhUQPf95jRw9j46XG42MsH7lRezVYzHv2YHg4GACAgJKPb9Lly6o1WpeffXVEtFz7d07pP75E6mrFhSPnr80XI6et+tWMdHzgjyunFpDZPg8bkUf1bfXrd8Vb98AedXzx4yePzjLXehpZrsflJyTwJbYRWyNXURqnhzpN1Ga0aveGwz28KexXTX/SyEIQo0hiu4qJIpuQah4z1KR8bwQRbdMFN2PJy9Hy97C6Pmpouh5a18HBqtVdB1SOdHztOi7nF6wj3NLD5FzV46eG1ua0nRMB7zVPtRuVb6Fy6SCAjI37ZGj52FH9O2m3s143yqN1QfDH3p+3bp1mT59OtOmTaNu3eIrsEsFBWTs3khqSBDZR4v6MWveBrtxAdgMGoXSzLxc4y90M/ooURHBXD75OzqtfLPE0rYurbvfi57b1inz3AdnuQuVd7b7QXm6XPbf/IuN0YFcSj2mb29h343BqgC61xmGsbLqt0YTBKHmEkV3FRJFtyBUvGexyHjWiaJbJoruJyNJEucOytHz/WuLoueObub4zfKg32Q37BwrJ3p+afUJIueFk3w6Qd/u1ruJHD0f1Kr80fPTF9EEhZC+IhQpW16K/rytCb+rLFl36TS5ubllnmtiYqKPnnfq1Klk3+cj0YQEytHzXLlvIwdHbEdMxe6NGZjUdSvX2Atlpt3kzIHFJaPnbV/Hy1dNXVXJsZU1y12oIma7H3Rec5jQ6ED231xDgSTfJJCj59MZ4DYVe7PyPZ8uCMLzSRTdVUgU3YJQ8Z7lIuNZJYpumSi6n15Z0fNeb9TDz19F47aG/xkrSRLx4VeICo7g2voHoucze9JiUhfMa1mV6z20dzWk/bwGzfyV+uj5XYWODS2cCLl9jfik2w89v3Pnzrz99tu8/vrrJftOSSb1r6WkrpxPQWKs3GhkhPVLw7Afo8a8Q48Ki55fjVxHZPg8bt44rG+vo+qEt08Ajdu+hpGxqX6W+0TCCXToSvSjREl7l/YVNtv9oLs5iWyNXcyW2IVo8uTraqwwxbfeSIaqZovouSAIT0QU3VVIFN2CUPFqwr7EQnFin27Z87pPd0XKy9ES/sdNQgOjuXIyTd/eqqcDgwNUdBtaOdHz9Ji7RC3Yz7mfDhZFzy1MaDqmI15qHxxblzN6rtWSuXkvmsDlZO+RC9cCJMI8bFlhns3BS+fLPHfs2LEsX7687L4LCsjcHYpmRRDZR8L07WbN22A3Vi1Hz80tyjX+QreijxFZuOq5Vt6j3NKmDq26T8ezywSa/9KFW5m3yjy/rnVdbsy+gZlxxazCXprC6HlodDAXU4ti/i3su+Hn4U/3usMxURo+USEIQs0miu4qJIpuQTCMmBi4c6fs1x0dn40C41ly6BBcu1b26w0bVo+Cu5ChvscMcR2ex78PkiRx/pCG0KBo9q+5hbZA/lhS29WMl2d4MGCqO/ZOhi+UCrLvRc8DI7gTGa9vd+3VGC+1Lw0Ht0JpbFSu98g9cwlN8ArSQzYiZWUDcNHGhN/rW7H2UhQ5D0TPjx49WuoK56X2ffE0muWBpIeu0EfPlfa1sSuMntdzL9fYC2Wl3dJHzzPT5NXhlUYmuLQcRK02Q7BxbV3qec5WzrjZVkz8/XFc1BxlQ/Q89t/8677ouQsve8ygv9sUHMzKfj5dEITnmyi6q5AougVBEATBsO7E57B1USxbF8eSmiTPppqYydHzwf4eNG5nZ/AxSJJEwr6rRAVFcHV9FJJWjkvbeDjoVz23qF3O6HlKKmm/3IueX5dXJk9RSGxs4UhI0g1ib9+kS5cuHDp0qNTzMzMz2bBhA6+++ipmZsVnjrWau6St+RnNyvkUxEfLjUol1i++gv24AMw79KyY6Lk2n6uR64gKDyTx+kF9u7NHR7x91DRp+zpGJoab1X5cd3Nvsi12MVtiF5GSKz+fbqwwwafeCIaoZuNp9+RbowmC8GwTRXcVEkW3IAiCIFSOvFwdEX8kEhoYzeUTRdHzFt3sGTJbRbdX6mBsUgnR89gUTi/cz9klB8lJzgTAyNxEXvU8wLdioudbwtAEhZC9Sy5cC5CIcLel3qsDGPSfD1FaloyHL168mOnTp+Ps7Kxf9dzFpfhY9NHzlcFkH96rbzdt5o39WDU2fm9UXPQ85jhREcFcOrG6WPS8ZfdptOo+DWu78l2nipCvy2PfzT/ZFD2fC6lFz6c3t+/KII9Z9Kz7moieC4IAiKK7SomiWxAEQRAqV2H0fFNwDPvX3KQg/77o+XQPBkx1w97Z8LOphdHzqOB9JP0Tp2939W2Ml9qHhkNalz96fvYyqcErSFu+QR89VzrYYTvpVexnjcakvhzNliSJ1q1bc/bsWf25xsbGvPbaa6jVarp06VJiJjv30hk0IUGkbwxByrnXt30t7F6bgt3omZi4VMwzC9npSZw5uITT+xeQmSqvDq9UGtO47Wt4+wRQp35ngyyk9qQupR5nY/Q8IhL/0EfPHczqMsh9JgPcp4rouSA850TRXYVE0S0IgiAIVeduYg5bFsWydVEsmtv3Rc9H1WOwuvKi54kHrhEZFMHVtZH66Lm1uwOtZ/ag5eSuWDhal+s9tJo00n5ZQ+r8leRfu7cyuUKB1eA+2AeM45CURd++fcs8v0OHDqjVakaMGFF69HztL3L0PO6G3KhUYvXCEOzHBWDRybfCoufXItcTGRFE4rX9+nZn9/Z4+ajxbDey2kTPt8f+xJbYhdzNlZ9PN1aY0KPuawxVzaapfcmt0QRBePaJorsKiaJbEARBEKpeXq6O/WvkVc8vHk3VtzfvKkfPuw+rnOh5RlwKpxcd4MziA+TcuS96/kZ7vAJ8cfJ2LVf/klZL5rYIUgOXk7XzgL79dANHfjRNZd/Fcw8938nJiWnTpjF9+nRcXYuPRdJqydyzCU1IENmH9+jbTZt6FUXPLSzLNf5CSbH/EBkRyKUTq9EWyAvFWdg406rbvei5ffmuU0WQo+d/sSk6uFj0vJldF/xU/vSo+yqmyqq/SSAIQuUQRXcVEkW3IAiCIFQv5w/fW/X8r/ui5y5mDJzuzoCp7jjUqYToeU4+l38/SWRQOEkni6LnLj6N8Fb70GCIF0Ym5Yue552/giZ4BWm/bUDKlLc1u2xjwu8NrFlzKYrsh+wzZ2xszPDhwwkICKBr164lo+eXz5K6Ipi0DcuRsuW+lXYO2L02GbvRszBxVZVr7IWy05M4c+gnTu9bQGaqvDq8UmlMozbD8fadTd36JWPxVeFy6gk2RgcSnvg7BZKcqHAwrcNA9+kM9JhOLbO6VTxCQRAMTRTdVUgU3YIhPI/bA1WW9evhvkceS2jZEl555cn7NdR2WYbo11BjNdT3bU3rV6g+7t7MZdviWLYsjCHlllwoGZsq8B1ZjyEBKpq0r6To+cHrRAVFcGXNqaLouZu9HD2f0q380fPUdNJ+XUtq8Aryr8YAoEHHphZO/JZ8g5hbNx96frt27di5cye1atUqpe8U0tb+imZFMAVx1+VGpRKrPoOxH6vGokvvioueR20gKiKYhKsR+nY5eu5Pk3YjMTYxL/f7lFdK7i22x/3ElpiFJOfKz6fL0fNXGawKoLl9lyoeoSAIhiKK7iokim6hosXEQNOm8JAJCszN4eJFURA8qfXrYdiwRx+3bt2TFd6HDkG3bo8+7uDBJytmDdGvocZqqO/bmtavUD3l5eo4sPYmoUHRXDhcFD1v1sWOwWoVPV6ti4lpJUTP4zWcWXyAM4sOkJ2UAYCRmTGeo9rjHeCDU9vy7Zkt6XRkbQtHExhC1t/yM9NaJPa527LCMpeIi6XfcWzXrh3Hjx9/aPEsabVkhm2Ro+cHd+nbTT1bYT9Gjc3g0Sgty7dlWqGkuFNEhgdy6cSqoui5tROtuk+jVbdpWDtU3r7eZSnQ5XPg1jo2Rs/jvKZoC7emdp0YrFLTo+5rInouCM8YQ9R9hv/JIwhCqe7ceXghAPLrD5uhE0r3sBnupzmu0MNmjZ/mOEP2a6ixGur7tqb1K1RPpmZKer/hwg+HuvLjkS70Hl0PYxMFFw6n8s3oKCbUD2flZ1e4ezPXoOOwdrWny2cvMyHmU/r+Ngandm5ocws4v+wIv7f7lrU+87j850m0+dqn6l+hVGL1cm9cd/yC6vw27PzHYGxtTa/YdJZezGOrdXPGte6IhXnxGWO1Wv3I2WqFkRHWLwzGbdlOPLaexe6NGSgsLMm7dIbbc6Zx3ceNpK//H/mx159q7PdzcmtD39G/8OZncXTz+wprB3eyM5I4tuM/LPu0Ptt+eZ2EaweoyvkhY6UJvvVG8H2XgwR1PcGLrm9iojTjYupRvo0ay/gwD5ZfnsPdnMQqG6MgCNWfKLoFQRAEQXjmNO1kz7srvPktphdjP2uMQ10z7ibmsuKTK4z3COPbsVFcOp766I7KwdjchObjOjHi+P/j1YP/h+eo9iiNlSTsu8r2Ecv4rf5cjn2xg+yk9Kd+D9NmjXAOmkOD+H04zfsIkyb1aZxRwEenNUTkuPJx8y6o6tTD0dGRkSNHltqHJEmMGzeOX3/9lezsbH27WeMWOM9dQIN98Ti+9x0m7g3RpWnQ/Pw/bvRtRMKMoWQd3F3uotjC2pH2L/6b8XOuMeDNv3Bt7Iuk03Ll1F+s/bEHf3zbnnOHf6Ug/xF30AyssV073m79C8t7xTKuyefUNnNFk3eb1Vc/Z1y4B19HvsG5lINVepNAEITqSRTdgiAIgiA8s2rVNeONjxvzW7Qv/17lRfOu9hTkS+xZkcDsjod4q8sh9qxIID9PZ7AxKBQK6nVtQL9V4xkf/Skd5/THso4NmQmpHP5oC7+6f8LOCSu4fSLmqd/DyNYa+4BxqC5sx2XLEiz798QOJWPPJ7P9lhW/2zQj5+c16DIyS5x78OBBQkJCmDhxIu7u7nzwwQfExsbe17c9DhPfRvX3Jeot3oRl9xdBksjcvZH4CX2JebkVmtWL0GWV7PtJKI2Madz2VYYFhDHq35G06DIJIxNzkuL+Yfeqifw6x42Dmz4gIyXu0Z0ZkL2pE6MafcQy3+t80OZPWth3RysVEJa4mn8d6c7sQx3ZFb+cPJ1hExWCINQcougWBEEQBOGZZ2KqpNcoF74/2IV5x7rywlgXjE0VXDySyrdjoxivCmflp5UQPXexo8unA5kQPZcXQ8bi3MEDbW4BF347yh8d/sea7j9w6Y9yRs8H9sJ128+oLmzHTj0WExtrPK7fIsn/M6679iTp//5L3pVo/TmBgYH6/09OTubLL7+kQYMGvPbaa0REROhnbhVGRlj3HoTrr3+j2noOu9GzUFhZk3flHEmfzOB6T1eS/vs2+TFP+NxKKRxdvXjhjaW8+Wks3QZ/jY2DBzmZyZzY+SXLPq3P1p9fJf5KRJVHz3vWfY3vuuwnqOsJXnKdiInSjMtpJ/ju9HjGhbmz7NKH3MmJr7IxCoJQPYiiWxAEQRCE54pnBzveWe7F8phejPu8CbVdzEi5mcuKuXL0/Os3Irl4VGPQMRiZmdBsTEdGHHuH1w6/jecbcvQ88eB1doxcxm+qTzj6+Xaybpcjet60Ic6BH1M/bh9OgXL0XJeWgebHZUR7vkT8y1O4vHIda9euLXGuVqtlzZo1+Pr60rZtW37++edi0XPTxs1x/iSYBhFxOH7wAyYejdClp6JZ9gM3XmxMwowhZB3YVTHR877vMm7OVQZMWquPnl+NXMu6QF9+/6Yd5w79QkFe9qM7M6DGdu34v9Y/E9IrjnFN/kNtM1dS85L449p/mRBen69OjeJsStU+ny4IQtURRbcgCIIgCM8lhzpmjPqoEb9e9+Xfq7310fOw1Ym81fmwPnqel2u46DlA3c716bfygeh5YhpH5mzlV/c57By/glvHyxk9V9+Lnm/9CcsBPiBJZG0NRzvm3yyu60XvZq3KPD8yMpLJkyfj5ubGe++9R0xM0ViMbOxwmPAWqr8v4bJ4M5Y9+92LnocS/+aLxAxsiWbVQnSZGU89frgXPfceJkfP34uiZbepGJtYcCf+FLtXT+LXT9w5GPo+6Smxj+7MgOxMHRnV6EN+873Bh23W0MrBB61UQPjN33nnSA/8D7ZjZ9wyET0XhOeMKLoFQRAEQXiumZgq6TWyHt8f7ELQia70Hf9A9NwjjJBPLnM30bALeemj5zGf8tLKcdTppEKXp+XC8qP82fF//NXtey79fqJ80fMBvrhuXYrq0t/Yzx6PiY01PvEZLL6Qy3bLZrzZuhNWlpalnn/37l2+/vprGjRowPDhwwkLCyuKniuVWPV+Gdeft6PafgG7Mf5y9PzqeZLmzpRXPf/v/5EXc/Wpr08hR5fW9Bm5mDc/i6P7kG+wqaWSo+e7vuK3Txuw9efhxF8Or9JZZSOlMT3qDufbzuEEdTvJS64TMVWacy39FN+feVMfPU/KrtqbBIIgVA6xT/djEvt0CxVN7B9sOGKfbrFPt6H7FZ59mtu5bFsSx5ZFMSTHy7OSRsYKerxahyEBKpp1sX/k9lsV4eaRG0QFRXD5r3/Q5cnFtlU9W1pN706rad2xrFO+zyS69AzSlm9AExRC/kV5G7A0tGxu5sTy1DiuJT78eeRVq1YxatSoUl/TZqSRvm4ZmpAg8qOvyI0KBVa9XsZurBrL7i9WyDXU6bRcP7OJqPBA4i7v1bfXdvHC2zcAz/ajMDEt/UZCZUrLS2Z73FI2xQRzJ0deDE6pMKJHneEMVgXQwr5bpXxPCYLwcIao+6pd0R0REcG3337LiRMnSExMZP369QwdOrTM49etW8fChQs5deoUubm5tGzZkrlz59KvXz/9MXPnzuXTTz8tdl7Tpk25cOHCY49LFN2CIcTEPHx/YEdHUQg8rfXrH74Pd8uWT1ZwFzp06OF7Wzds+GRFrCH7NdRYDfV9W9P6FZ4PBfk6Dq6/xcZ50Zw7qNG3e3a0Y7Dag56v18PUzPDBwcybaZxZfIAziw6QdTMNAKWpEU1eb4t3gC91OqrK1b+k05G16yCawOVkbQ0HSUKHxAEXa1baFrDnwpkS59jb2xMXF4eVldWj+963A83yQLL2bde3mzRshv0Yf2yHjkNpbVOu8RdKTjhD1L5gLhwLoSAvCwBzy1q06DqZ1j1nYlurfNepImh1BRy+HUpoTBBRd8P07Q1t2jBEFUCveqMwNTIvuwNBEAzquSi6t23bxoEDB2jfvj3Dhg17ZNH91ltv4eLiQu/evbG3t+fXX3/lf//7H0eOHKFt27aAXHSvWbOGXbt26c8zNjbG0dHxscclim5BEARBeL5d+SeN0KBowlYlkn/vOW87J1MGTnPn5Rnu1HYxfKGkzSvg6tpIIgPDuXn4hr69TmcV3gG+NH61DUamxuV6j7wr0aTOX0naL2vQpcnPYl+3NOKPRrb8efUsGfe2BnvnnXf49ttvS+0jIyMDKyurEjO3edcvoVkRTPq6Zegy5UXilNa22L46EbvRszBVNS7X2AvlZKVw7tDPnN43n7S7NwBQKJQ09BqKl48a18a+1WJW+VpaJBujAwlLXEWeTo7k2Jk60d9tMgPdp+NsIe4ICkJley6K7vspFIpHFt2ladmyJSNGjGDOnDmAXHRv2LCBU6dOPfVYRNEtCIIgCAKAJimPbUti2booljtxcqFUGD3381fRolvlRM9vHYsmMjCcy38Wj563nCZHz63qVkD0PGSjHD2/IMdm0tGyqZkTKzMS2BEeRoOGDUs9d+zYsZw6dQq1Ws2YMWOwfOA5cTl6/hualcHkX78kNyoUWPoOxL4weq4sf4JAp9Ny4+wWgUdoAgAAWhNJREFUIsMDibu0W99eu14rvH1n49nhjWoRPU/Pu6uPniflyM95K1HSrc4whtSfTUv77tXiJoEgPA9E0f0YdDod9evX591338Xf3x+Qi+5vv/0WOzs7zM3N6dq1K19++SUeD8kT5ubmkptbtLJkWloa7u7uougWBEEQBAEAbYGOgxtus3FeNGf3p+jbG7ezZchsFT6v18XU3Mjg48i6nS5HzxfuJzPxXvTcRI6eewX4UrdTOaPnkkTWroOkBi4nc0sYSBISEqaN62PnPwbbCcMwsiuKh9+8eRMPDw/y8/MBcHBwYNKkScyaNYv69esX71unI2v/32hCgsgK36pvN2ngif0YNbavjK+46HniWaIigrlwbHmx6HnzLhPx6jkL29r1H95BJSg7eu6Nn4c/vV1GY2ZkUXUDFITngCi6H8M333zDV199xYULF3B2dgbkyHpGRgZNmzYlMTGRTz/9lPj4eM6cOYONTen/kJf2HDggim5BEARBEEq4eiqNTcEx7F2ZQF5OUfS8/xQ3Bs30wNG1kqLn6yKJCoog8eB1fbtzRw+8A3xp8nrb8kfPr8aQOn8Fab+sRZcqx8MV1lbYTngFe/8xmDZtyGeffcYnn3xS4lylUsngwYNRq9X07t27ZPT8xmVSVwSTtvbXoui5lQ22w9/Ebow/pvWblGvshXKzNJw7/AtREUHFoucNWg/By8cftyYlx1YVrqefJjQ6kL0JK8nVyfuQ25rUZoD7VBE9FwQDEkX3I6xatYopU6awceNG+vbtW+ZxGo0GlUrF999/z6RJk0o9Rsx0C4IgCILwpFLv5LH9p1i2LIwlKbYoet59uBw9b9m9kqLnx2Pk6PkfJ/XRc8u6trSa1o2WU7tj7WJXrv51GZmkrQglNXA5eeeLtgGz7NeTkfEn2H8m8qHnt2zZUh89f3AhNl1GOmkblsurnl+/WNS3zwA5et6zX4VFz6PPbiUyIpDYi0Xr/tSq1xJvnwCadhxTbaLnO+J/YVN0MLdzogE5et61zlAGqwJo7eBTLW4SCMKzQhTdD/H7778zceJE/vrrL15++eVHHt+xY0f69u3Ll19++VhjEc90C4IgCILwuLQFOg6H3mbDvGjORBRFzxu2sWHobBW+I+tVWvT87E8HOb1gP5kJqQAojZU0fq0t3gE+1Olcv1wFmyRJZO8+iCYwhMzNe/Wrnh+uZ81Kex07z0c99Hx7e3t99LxBgwbF+9bpyDqwsyh6fu8jq0n9JtiP8cdm2ASMrCvmM1ly4llO75vPhaPLyc+TF4ozs7CnRddJtO45C7vaDR7Rg+FpJS2Hb4eyKTqYyLt79O0NbLwY7KGml8sbmBtV/U0CQajpRNFdhtWrVzNx4kR+//13hgwZ8sh+MzIy8PDwYO7cuQQEBDzWWETRLQiGIbaJktWk8daksRqSuA7C4yqMnoetSiA3W46e2zqaMGCKvOq5k7vhn9HV5muLoucHivYSdO7ggZfaB88RbTEyMynXe+Rfi0GzYBVpP69Bp5GfLY+2MOLPxnb8fu0M6ZmZZZ6rUCjw8/Pj7bffxtfXt8TreTFX5ej5ml/QZch9K6yssX1lAvZj/DFt2LRcYy+Um51aFD1Pvl44OBq0Goy3jxo3zz7VYlb5RvoZQqOD2JMQoo+eW5s40N9tCoM8ZlLHouq3RhOEmuq5KLozMjK4cuUKAG3btuX777+nd+/e1KpVCw8PD95//33i4+NZvnw5IEfKx48fz7x58xg2bJi+HwsLC+zs5OjUO++8g5+fHyqVioSEBD755BNOnTrFuXPncHJyeqxxiaJbECpeTAw0bQo5OWUfY24OFy8+WfFiqH4NpSaNtyaN1ZDEdRCeRlpyHtt/imPzghh99FxppKD7sDoMVnvQsodDpRR0t0/GEhkYzqXVJ/TRcwtnG1pN60ar6T3KHz3PzCItZCOpQSHknZM/02WgY2szR35LT+ByfGyZ5wYEBDBv3ryH9J1B2oblpK4IJu/qeX27Zc9+2I8NwNKnf8VFz89tIyoiiJgLf+vbHeo0x9tHTdNOYzE1sy73+5RXet5d/o7/lc0x87mZLd8kUKKks/NghqgC8KrVq1rcJBCEmuS5KLrDwsLo3bt3ifbx48ezbNkyJkyYwI0bNwgLCwOgV69ehIeHl3k8wMiRI4mIiCA5ORknJyd69OjBF198QaNGjR57XKLoFoSKd/IktG//6ONOnIB27aq+X0OpSeOtSWM1JHEdhPIojJ6HBsUQFXZX397Q24bBASp6jaqHmYXho+fZSemc+ekQpxfsIzO+KHreaHgbvGf7UrdLBUTP9x5GE7iczE17QadDh8SRulasdJDYeeE0D34MvXjxIp6eno/Vd9bBXaQuDyQzbEtR9FzVGLsx/tgOm4CRTfluHhS6e+sCUeFBXDj6mz56bmphR4suk/DqMRM7p8f/PGkoWknL0dubCY0J4lRy0dZo9a1bM1ilpne9NzA3tnpID4IgFHouiu7qShTdglDxRNEtq0njrUljNSRxHYSKcj0qndCgaPauvC96XtuE/lPceHmGB84elRM9v7Y+kqjgfSTsK1oUzbm9O15qH5qMaIexeTmj59dji6LnKXKBH1MYPb9+lrSMDAYMGMDWrVtLPT85OZmTJ0/St2/fEjcC8mOuoVk5n7Q1P6NLl/tWWFljO3S8HD1v1KxcYy+Um53KhaO/ERkRRGqSPIOPQkH9Fi/j3Ws27p4vVItZ5eiMc4RGB7E7YTm5WnlrNGtje/q5TcZP5S+i54LwCKLorkKi6BaEiieKbllNGm9NGqshiesgVLT0u3ns+DmeTcHR3I65Fz1XQtdX6jAkQEWrnpUTPU86FSdHz1edQJtbAICFkzUtp3aj9YweWLval6t/XVY26Ss2oglaQd6ZSwBkomNL09p0GD+Kl95VozAqOcv/9ddf895779G8eXP8/f0ZN24c1tbF4926zAzSNobI0fMr5/Ttlj1ewm6sGivfgRUSPZd0Om6c30ZUeBAxF3bo2x3qNMPLR02zTuOqR/Q8P4Wdcb+yKWY+N7Pl5/jl6Lkffio1bWpVj+fTBaG6EUV3FRJFtyBUPFF0y2rSeGvSWA1JXAfBULQFOg5vSmJTcDSRe4qi5w28bBis9qD3aJfKiZ7fyZBXPV94gIxYefV1hZGSRsO98Q7wpV63BuWPnocflaPnG3eDTp7lN27ghv2s0dhOfBUjBzkeXlBQQMOGDYmNLXoW3NbWlokTJzJr1iwaN25csu9De9CEBJK5Z1NR9NyjkRw9H/5mhUXPU25dJGpfMOePLCM/NwMAU3NbOXrec1a1iZ4fT9rGxuh5/JNctDWayrolg1UB9Kk3WkTPBeE+ouiuQqLoFoSKJ4puWU0ab00aqyGJ6yBUhhtn5Oj5npCi6LlNraLoeR2V4aPnugIt1zZEERkUQUJEUfTcqZ0b3mpfmoysgOh5dDyp81eSuvQvffRcYWmBzdgh2PuPYculMwwfPrzUcxUKBQMHDiQgIIC+ffuifGAmOz/2OppVC0j7aym6NM29vq2KoueNm5dr7IXystM4f2w5URFBaG5fKhwc9VsMxNsnAPdmL1aLWeWYjPNsjpnPzvhl5Gjl59OtjO3o5zYJPw9/6lpW/dZoglDVRNFdhUTRLQgVTxTdspo03po0VkMS10GoTOkp+fz9SxybgmO4dUPeHkqphC5D6jAkwIPWvrUqJ3oeGU9UUDgXVxzXR8/NHa1oNbU7rWd0x9rNoVz967KySV+1CU1QCHlRF/Xt+71c+fruNS7GxTz0/KZNm6JWqxk3bhw2NjYP9J1JeugKNCFB5F0+q2+37P5iUfS8lFj7k5J0OqIv7CAqIojoc9v07Q51mtG65yyadxqPqbnNQ3qoHBn5Gv6O+4XNsQtIzJJvphRGzwd5zKJt7ZLPzgvC80IU3VVIFN2CUPFE0S2rSeOtSWM1JHEdhKqg1Uoc2XSbTcExnNqdrG9v4GXDoFke9BnjgrllJUXPlx7i9IL9xaPnw7zwUvvi0qNh+aPnEcfk6PmGXaDTISFxtI4Vq2rD9vNRJVY9v5+trS1vvvkms2bNokmTJiX7PrwXTUgQmXtCi2Ltbg2wH+OP7asTMbK1f+qx309z+zJR+4I5d/hX8nPTATAxs6FFl4l4+fhj79T4ET0Ynk7ScfzOdjbemMfJ5KKt0TysWzDEI4A+LmNE9Fx47oiiuwqJolsQKp7Yp1tWk8Zbk8ZqSOI6CFUt+lwGoUHR7F6eQG6WvNe2tYMcPR80sxKj56FniAoMJz78ir7dsY0r3gG+eI5sh7GFabneIz8mgdQFK0n96S90dzUAxJop+cvTnt9vnEeTnvbQ8wcOHMi6deswMzMr2XfcDVJXLSD1r6XoUu/dPLCwxHboOOzGqjFr3KJcYy+Ul53G+aO/EbVvPprbRTP4qhYD8PYJwKPZSxWywFt5ydHzBeyKX0a2Vn4+3crYjpdcJ+Kn8qeeZcMqHqEgVA5RdFchUXQLgmHExMCdO2W/7uj4dEWLofo1lJo03po0VkMS10GoDtJT8tn5axyb5sdw81pR9LyznzODA1R4966c6PmdqHiigvdxIeQY2px8AMxrW9FySldaz+yJjXs5o+fZOaSv3oxm3m/66HkWOrZ5OrI8+ybnY6NLPa9Pnz7s3r271NeK+s4ifeMKNCuCyLt0Rt9u0a0v9mPVWPV6ucKi5zEXdxIZPq9Y9NzeuSlePv407zgOU4uq/4yZmZ/K3/G/sClmvj56rkAhr3ru4U+b2i+gVFT9TQJBMBRRdFchUXQLgiAIglBdabUSx7YksTEwulj0vH4ra/z85VXPLayNDT6O7ORMzv18iNPz95Eec1/0/BUvvPx74uLTuNzR85x9x9EEhZCxfidotUhIHHO2YqVjyej5hg0bGDJkyGP3nX00XI6e79pwX/S8PvajZ2H76iSM7Mp386CQJukKp/fN59zhX8jLkWfrTcxsaN55At4+auydmzyiB8PTSTpO3NlBaHQgx+9s17e7WTVliCqAF1zGYWFc9VujCUJFE0V3FRJFtyAIgiAINUHshQxCg2LYuSxeHz23sjOm/xQ3/GZ5UKe+pcHHoNPquB56mqigCOL2Xta31/ZywTvAl6ZvtC9/9Dw28V70/E90yRoA4kwV/NXUgdU3zmNfuxZXrlzBqJRZaq1Wy5QpU3jttdfo169fyVXP46OLoucaees2hYUlNoPHYD9WjZlnq3KNvVBeTjrnj/7G/2/vvsOjqPY/jr83mx7SSUIghSo9oXdCEQSkKgLSu0hJ8FrRa8Ny1Z/3qiQgIIhIrwqEjkDoSAkQegkhPQHSe9md3x8LG2NCTdlEvq/n4bmXszNnzs44D/lmPnPO+UPzSIq/om/3bNQHr84z8GzYu0JEzyPTrxAYMY8/on8lS6N7P93K2JYeNcYxwGMG1a0M/366EKVFim4DkqJbCCGEEJVJenIee5ZGEzg3gtjQTABUqnvRc18Pmj3vWD7R8/MxhMw9yNXlJ8nP0kXPu8wbgte0zqXSvzYrm7Q120jxX0bO2cuALnp+u8VztPtgJlUGPo/KuPBT/q1bt9K/f38A6tWrx4wZMxg3blyRn/G0WZmkBa4iebk/uVfP69st2nXDbrQfVt37l070XFGIvPoH5w7M4dal7fq1xe2c6uHl46ub9bwiRM/zU/kjailbIgKIydS9x69CRWunFxng6Udzxx4SPReVnhTdBiRFtxBCCCEqI61W4eR2XfT8zJ6C6Lln4yoM8C2/6Hl2UiaXfj7GlWUneeXIG5ham5dq/4qikH3ktC56vnE3aHRP+Y3dXbGdPhLbSUNQO+ri4S+88AJ79uwptH+VKlUYN24cM2bMoH79+kX6zjp5kJTlAaTv+b0gel7DsyB6budQKt9DFz3/kUt/LiE3S7duuYlZFRq2HYdX5xnYu9R/RA9lT6toCb67m8CIuZy4s03fXsPyOQZ4+tKjxlgsjQ2/NJoQT0OKbgOSolsIIYQQlV3klXQC5+qi59kZBdHzXhPd6D/Dg2q1yj56rihKmT9hz4uKI2X+KlIWrkWbcO/dcnMzrEf2J75fR7xf6vfQ/V944QX8/Pzo06dP0eh5TAQpK+9HzxPu9W1RED2v37RUvkNuTjpXTiwj5GBAoei5R8PeePnMoGbDPhUieh6dcZ0t4QH8EfMrmfm699MtjW3oWWM8/T2mU8PK8O+nC/EkpOg2ICm6hRBCCPFPcT96vnVeBDE3CqLnbfo5McDXk+Y9yid6Xta02Tmkr9lG9H9XYXwxBIAstOys58iynNtcjLj10P3r1KnDjBkzGD9+PLa2tn/rO4u0ratJXuZP7pVz+naLNl100fPnBxSJtT8NRVGIvLaXkAMBhF0M1EfPbZ3q4tV5Bo3ajq8Q0fPM/DT2xSxn0605RGde07e3qtqHQZ4zaV61p0TPRaUgRbcBlebJl2VmRGUkS3sJIcQ/j1arcGrnXTbPuUXw7oLouXtDKwb4evL86PKJnpeVkHkHubY6mKw76Wgzs6lXLQ2nM7v1s54HO1mw0lnN9sshaO9FxotjZWXF2LFjmTFjBg0bNiz0maIoZJ86RPL96Pn9WHt1D2xHTMN2yCTU9o6l8n1S7t4k5NA8Lh3/uSB6bmpFgzZj8Orih4NLg1I5Tkn8NXp+8s52FHSlRg3LevT3mEEPt3FYGRv+lwRCPIgU3QZUWic/IgLq14fs7AdvY24OV69KoSEqjrL671buByGEqDiirqYTOC+CPb9Ek5WuKxwtbYzpOb4GA3w9qV6n7KPnpUWbr+Hkl7s5MXsnbl3r4tqpNll30rm68hRt3vbBMy+UlIVr0NzRzUweYwob6juyKuIyiSkpD+173759dOvWrdjP8mIjSVk1n9R1i9Ak6X6jrDIz10XPR83ArKF3qXy/vJwMrpxcTsjBABLjLunbPRq8gJePL56N+mBkVPIJ3koqJjOULeEB7In+RR89t1Bb84LbePp5TMfN6jkDj1CIoqToNqDSOvnBwdCy5aO3O30aWrR46sMIUarK6r9buR+EEKLiyUjJ449fo9kSUHz0vNnzjhgZVezo+bW1weydsIqGY9vQ9cehgG4N8f1T1nD3bDRDT7yFqaUx6eu2k+y/nJzTFwDIRsvOug4sz7vL+fCwIv3WqFGDsLAwTExMHnp8bU426dvWkLzMn5xLZ/TtFq19sB3jR5XnB5Za9Dzq+n7OHfAn7MIWffTcxrE2Xj4zaNRuAmYWto/opexl5aezN2Y5W8IDiMy4rG9vWbUXAz1n0rJqL4meiwpDim4DkqJbPMuk6BZCiGePVqsQvPsum+eEc2pnwXtAbvWtGODrQY+xNSpk9Dw/K5cVDf9DlRq2DNwzHRNLU7QaLUZqIy4uPsqhN35j6Kl3cGjgAtyLhx8/q5v1fP1OyM9HQeFMVQtWuRiz7UoImnuR8S+++IJ///vfxR43NzcXU9PCa48rikL26SMkL/cnffdvhaPnw6fqoucOVUvle6fcvcn5w/O5dGwxOVnJwF+i551n4ODaqFSOUxKKohCcsIct4QGcvLOtUPS8n8d0etYYh5WJ4X9JIJ5tUnQbkBTd4lkmRbcQQjzb9NHzpdFkpRWOnvef7kGNelYGHmGB4P/tI/ibP/CZM5jnhrfUF9xajZaQgAMcfnszr555l6pNqxfZNz8mnpSFa0hZsAbNbd077nGmKtbXd2BjfBhnL5zHycmp2OP279+frKws/Pz86Nu3L+q/rd+dFxdFyuoFpK5ZWDh63n+kbtbzUoyeXz21knMH/UmMvahvd6/fA28fPzwbv1hhoudbw+exK/rnv0TPq+hmPfecIdFzYTBSdBuQFN3iWSZFtxBCCIDMtHz2LI0mcG440dcKouetX3RigK8HzXtWNWj0PD8rl2X1Pse5lQd91o1HbWqsX6JMk6dh36TVxBwOZcyNj4vMzn5/u+ykTLLvpGJ04k+S5/xKzild9FyDglXHltj5jqbKyy+g+kvEPDQ0lHr16nH/x+patWoxffp0JkyYgL29faHj6KLna0leEUDOhdP6dvNWnbEb40eVHoNKNXoecnAuYec3oyi6ieJsHGvRtPN0GrWbgLml/SN6KXtZ+ensi1nBlogAItIL3k9v4fgCAzx9ae30okTPRbmSotuApOgWzzIpuoUQQvyVVqtwZs9dtgREcGLbHX17jXqW9Pf1pOe4Glhal3/0/Pq6YPZPWUvn71+m4bi2+qfcAGkRiaz2/oaG49rS4ZsBqE2LH9+Z7/Zxa9sljIyNaDSpPW7uKlIClpO2fifk5QGgru6M3dQR2Lw2DGNnR958802+//77In1ZWloyevRofH19ady4caHPFEUh+8wxkpf5k757I+TnA2BczQ3bEdOwGToJY4fin6o/qdSEW/pZz3MydeuWG5ta0qD1GLx8ZuDo2vgRPZQ9RVE4m7CXTeFzikTP+3pMo2eNcVQxsTPsIMUzQYpuA5KiWzzLpOgWQgjxINHXMwicq4ueZ6bqCkdLG2N6jK1O/+keuNWvUi7jUBSFoGnruLHuDBNiPkdtZoKi1aIy0hXdx/69lXNzguizYQKevR/8fnP0oVBuBV4gJfQu4Tsv49Tcjc7fv4Sjm0VB9Dz+Xjzc1ATLYS/iE7SO0MiIh46ve/fu+Pr60r9//yLR8/y4aFLWLCBlzUI0iXfu9W2Gdf8R2I72xbxR85KcGr283EyunVrFuYP+JMSc17fXbNyPfq9tqTBrs8dlhhEYMY9dUYvJyNfNJm+mtqRnjXEM9PDDrUp9A49Q/JNJ0W1AUnSLZ5kU3UIIIR4lKz2fvcti2OwfTtTVDH17qz5VGejnSYsXyj56vrn3j2hzNby0zxdNbr7+aXbCxVg2dPyB2gOb0vHbgVg6W+vj5A+SEZfK7ZPhnPh8F5bO1ry4cYKukM/NJW39TpL9l5FzIgSAHLTsru3Acm0iZ2+FPnSMNWvWZNq0aUycOBEHB4dCn2lzsknfvo7k5QHkXDilbzdv0VEXPe/5UqFY+9NSFIXo60GEHJrLzZBNNGo/ke6v/lTifkvb/ej51oh53Eq/oG9v7thTHz1Xqwz/frr4Z5Gi24BknW7xLJN1uoUQQjwurVbhzB8JBM4N58TWO/dXsaJ6XUv6TffghQluWNmUfvRcURR2DFnC3bPRDDn2LyycrAFICb3DkXe3EHf8Fr3WjKNG5zpP1O+NDWfYMXQpfdaPp+7gZoU+yz5xjmT/5aSt2wF5eSgonHO0YJWrCYGXz+lnPS+OhYUFo0aNws/PjyZNmhT5Ltnn/iT51zmk79pQED13qYHtiKnYDHut1KLnaYkRoFJhbe9eKv09zKN+0fGw/c4l7mfTrR84cWerPnrualmH/h4zJHouSpUU3QZUmic/IgLu3n3w51WrSoEhKp6y+u9W7gchhPjnignNZEtAOHt+KYieW1ir6TmuRplEz8O2XmDvhFW0eK8Hnr0bojYz5tAbv3Fr+yV6LB1Jg1GtUBkZFVv83W+7cyYSp+YFBWhK6B2W1fuC7j8No/GkDsUeNz/uTkH0PE4XD483gY31HVkZfZU7SUkPHPPHH3/M7NmzH/h5fnwMKWsWkrJmAZqE2wCoTEyp0m84dqN9MW/yGJGxCiYlIQxbx1pPtW9cZhjbIuezM2ox6Xm682qmtuT56mMY4OmLZxXDL40mKjcpug2oLE6+EEIIIcSzICs9n30rdNHzyMsF0fMWLzgycGZNWvUuefRcURTyMnI59kEgF+YfxrKaDRmxqVhWs6bptM60/uCFR/aRHpPCutb/xdzBkuZvdQcjFWe/2096dDI9fhlJrX66J9JajZbka7eJ2n+dlNC7ePZuiEfPBrro+YZdpPgvI/vPc4Auer6ntgPLlCTOht0odDxjY2MiIiJwdXV95Ni0uTkF0fPzJ/Xt5i06YDfKlyq9BpdK9LwshRycx7Xg1WSl3wFFocXz79K4w6Sn6is7P4N9MSsIjJhbTPR8Bq2d+kr0XDwVKboNSIpuIYQQQoiSURSF4D0JbJ0XwZ+Bt4tGz8fXwMq25IVj4pV4bm4KwaaWIy6tPbD2sMfIWE1GXCoWTlX0M5r/nSZPw+2T4Zz9IYgbG85h42mP2sKEJlM64jW9M0bGuiLu+MfbuLDgCDlJmdjWcyL1ZgI1+zWm67whWLrofk7MPhlCcsBy0tduR8nVRc9DHCxYVd2EwCsh5OfnM2LECFauXFnsWGJjY7lz5w5eXl5FPss+9yfJy/xJ27m+YEZ15+rY3Y+eOzqX+ByWJq0mn5O7v+TEztm41e2Ka+1OZKXf4eqplbTv9wXeXfyeum9FUTifeIBN4XP48/YWtOiWRqtmUUsXPXcbj7WJ4ZdGE5WHFN0GJEW3EEIIIUTpiQvLJHBuBLt+jiIjRRc9N7e6Fz2f4YF7g9KNnuemZrF14CKsqtvy/OLhGFuYPnDbtIhE9k1Zi6WzNe2+6EuVGraojIzIz8rl2ppg9k5cTb1hzen030EoWoWovdc48u5mOv7fQBqOa1uor/z4uwXR81hdPDzeGH5r4Mjgt33pOHZEsWOYNWsW33zzDV26dMHPz48BAwZg/Lf1u/NvxxZEz+/GA/ei5y8Ow26MH+ZNW5XklJWaa8Fr2btqAg3bjKXr0B8ByMpIYP+aKdyNPsvQt05gbuXwiF4eLT7zFlsj57MrajFpeYmALnre3XUUAzx9qWnd5BE9CCFFt0FJ0S2EEEIIUfqy0vPZvzKGLQERhF9M17c37+nIoJmetOrjVCqznkcfuM5v3ebi1KwGrwa/W+RzRasFlUr/rvfNzSGcX3CEAdum6Jcdi9p/jT1jVuDc2oMu/oOp4qZ7gqrJyWN9h++xrGZD398mojYr+rReyc0l/bfdJPsvJ/vYGX27WRsv7PzGYD2kNypT3S8CsrKycHNzIzExUb+dh4cH06ZNY9KkSTg6OhbpO23nelKWB5B97k99u3nz9tiN9qXKC4P1fZe3vNxMVv6nEVVsazBw+h5MTC3RajUYGam5eHQxh357g6HvnMLBpUGpHTNbk8n+mJVsCQ/gVnrB0mjNHJ+nv8cM2jr3l+i5eKCyqPuKz9YIIYQQQghRDiyqGPPiFA/mn+/If/a0ot0AZ1QqOLMngU/6BTO5/iF+/+EW6cl5JTpOjS71GBHyHv22TNa3nfl+P4ff3qRfz1ulUqHN1804nnA+ljvBUdw5Gw1A1t10Li89QXZCBh2+6l+o4FabmWBV3ZacpMxiC24Alakp1q/2w/3oWtxPbsR6zCBUpibknAghftTbhHl0JeGTOeTH3mbVqlWFCm6AiIgIZs2ahZubG5MmTeLcuXOF+rYZMBL39cdxX/8n1gNGgYkJ2WeOEffmCMK61yRh7mfk33saXp7OH55Pfm4mXj6+hQpurVZDXk46+fnZaDUlu7Z/Z662pI/7ZH7seI5v2gTR0eVljDDibMJePj/zEhMO1GFD2Lek5T14gjshSpM86X5M8qRbCCGEEKJ8xN/KJHBeBLsWR5GeXBA97zFWFz33aPj00fO/zlx++J1N3Fh3hiZTO1FvWAtsPO1RGRmRfOMOeyeuIvnqbcZFfobaRM2t7RfZ+epSGk/uQOf/vVSkryXVP8SjV0O6/fQqapPHe4qafzuB1J/Wkjx/FZoYXfQcY2MCW7rxf9eDiU9MeOj+Pj4++Pr6MmjQoKLR8ztxBdHzO3HAveh5n6G6Wc+92zz2OXta+blZLPu8Hs4eregzfh1qY1P9OdNo8ti3ehIxoYcZ89F1fZrgvvvb3QzZTG52Kg3ajC7RWOKzwtkWoYuep+bpzquZ2pJuriMZ4OlLLeumJepf/HNIvNyApOguXceOwc2bD/68dm1o3778xvMolWm8sgSXjixxJoQQlV92hm7W88C5Edy68JfoeQ9HBvh60rqvE2r100fP02NS+PPjbVxbHYxLaw/cutfDyERN6O8h3D4VScdvBtDinefJy8jhxOydhMw7xKjLH2DtoXv/WKvRYqQ24vo63XverT7oSav3Hz1L+t8peXm66HnAcrKPBAOQi8Ifte1YoUrlVOi1h+7v7u7O1KlTmTx5MlWrVi3cd24u6bs3krzMn+yzx/Xt5t5tsR3jh3WvV8osen49eB37106h88vf07DtOP1TbtCtD776G28ath1HhwHfoDYufgwndnzGiZ2zsXaoSft+X/Bcy+ElGlOOJoug2NVsDp9DWFqIvt3boRsDPWfSxrmfRM+fcc9E0X3w4EG+/fZbTp8+TWxsLL///juDBg166D5BQUG8+eabXLx4EXd3dz788EPGjRtXaJt58+bx7bffEhcXh7e3NwEBAbRp8/i/4ZOiu/QcOwYdil/mspCjRytGIVuZxhsRAfXrQ3b2g7cxN4erV//ZhWFZnQc5v0IIYRiKonBufyJbAsL5c8tttLoJqqlW24L+0z3oOd4Na/unn/U89lgYf36ynaQrt8nPyMGkihnN3uyGt68PKiMjNHka1rb8FvsGzvReOx6VSlXoKffWQYu4ExxF302TcG7hXuw64I8rO/giyf7LSF+9FSVXF7s+b2/K6hrmbL4aQl7eg6PYZmZmjBkzhoULFxZ7/Ozzp0he5k/69rUoebkAqJ2qYTtsCrbDX8fYqdpTjbk4iqIQtG4aN86sY8LnMahNzPQxfoBjW//NuaA59JmwAc9GvR/YT05mMrejgrl8/Beun1mHtb077fv9h3othpZ4fBeSDhEYMZcj8b+hVXSvFTibe9DXYyp93F7D2rTkk7uJyueZeKc7IyMDb29v5s2b91jbh4WF0bdvX7p168bZs2d54403mDRpErt27dJvs3btWt58800++eQTgoOD8fb2plevXty+fbusvoZ4iIc9MX6a7cpaZRrv3bsPLwhB9/nDntT+E5TVeZDzK4QQhqFSqWjW3ZGPf2/BklAfXnm3FlXsTYi7mcWit64yusZ+Al6/SPil9Ed3VgzX9rUYtHs6Lx/wY1jwu7x69j2azeyqLxAzYlJIuhyHc0t3FI2u4r//vzc2nCHu2C1qdK2Lcwt3/XiflnmLxlRb+g01ow7h+OW/MK7hQtOkXP5zIZUgbU3eatwWl79NpHZfTk4OiYmJDzy+edNWVPt2GTUPRODgNxu1syuaO3Ekzp1NWFcP4t4eVWgitpJQqVSkJoRRtYY3ahMzNPm5+vOZEHuRkEPzqNNsME7uLQBdEVwcM0s73J/rTufBPzDg9e1Uq9WBnb++yupvmhN5bV+JxtfUwYcPmq1jqU8YQ2q9h42JI7ezI/jl2vuMDnLD/8KUQk/DhXhaFa7o7tOnD1988QUvvfTSY22/YMECatWqxf/+9z8aNmzIjBkzeOWVV/j+++/123z33XdMnjyZ8ePH06hRIxYsWIClpSVLliwpq68hhBBCCCHKgEtNSyZ+U5/lUV3xXdiYmk2rkJOlZfvCSF5vfJj3e5zk6KZ4NJonD3Pa1nLExtMBc3vLQu3aPA0m1uagUunX6jYyVqNotZz+Zi+mNuZ4+/oA92ZBLwXGTg44fDCVmmH7qLZuDuadW+GkgSkXE9mbYM+cWq1oVbtekf18fX0f3XdVFxxnfEytfbeo9t1qzFt0gLw80rasJHJIOyJeaUvq5hVoc3OeevyKomBiVoW05Eiy0u7o4+PJd27w5/aPMTGtQqP2k7C01q0p/qBfFNwvxi2sHHGv/zwNWo/G2t6DxNgL3I0+V+w+T8rJwp0J9b9medco3mzyC7Wtm5GjzWJH1E9MO+LNO3924Uj872juPQ0X4klVuKL7SR07dowePXoUauvVqxfHjh0DIDc3l9OnTxfaxsjIiB49eui3KU5OTg6pqamF/gghhBBCiIrB3FLNi6+58+O5jnwT1IYOL7lgZARn9ybw+UtnmFj3IBv/F0ZaUslnxrZytcG+vjPhOy6RFqmb8To3PYcDvhtIOB9D48ntcWntCVBkQrCSUpmYYD2kD+4HV+EevAnrcS9jZmZGn7AUVt2E3+waM6RJS0xMTPDy8sLHx6fYfnJycpgxYwbBwcEFfZuaYt3vVdzXHMF940msXxqLytSMnJATxL8zmltdPUmY8zH58TFPPm6VioZtx5GblcLlk8tIiL1I8p0bHPrtDUJDfqd9//9QvVZH4MFPue/3c1906CEOb3qbnKxkeo1djXcXP/1nJ3Z+Ttj5wCce51+Zqs3p6TaOuR2C+b82B/CpNhQjlZoLSQf54szLTDhQm3U3vyY19+ET3Anxd5W+6I6Li8PFxaVQm4uLC6mpqWRlZXH37l00Gk2x28TFxT2w36+++gpbW1v9H3d39zIZvxBCCCGEeHoqlQqvLg589FtzloT6MOS9Wlg7mBB/K4vFb+ui53MmX+DWhbSnPoaJlRlNp3fm9qlIDsxYzwG/DWzs/APn5x+h7ew+NJ6km9SlrKdKMm/eiGq/fE3NyIM4/udNjN2q0SQ5ly/vRc//z6Ux2UeDix3HunXrmDdvHi1btqRTp06sXbu20Pvh5k1bUe2bpdQ8GInjv75A7Vwdzd14Eud9Tlg3T2LfHEHWmWOP/R0VRaFGva7Ua/Eqx7bMYsv83qz4sgF3os7Sru8XNGwzRv8Likc95VYUhbhbf7Jn+WjSkyPpPuwn6jZ/BZVKt3/K3Zv8ueMTti4eyKqvvQi7sPWJzuvf3Y+ev99sLUu73GJorVlFoudzLkzmZmrpPGkX/3yVvuguK++//z4pKSn6P5GRkYYekhBCCCGEeAiXmpZM+FoXPZ+5qCB6vnNxFFObHmHW8yc48ns8mvwnj4A3GNWaF3+bSHZiJrGHb2Ltbk/3Ra/S8r2emDtYASV7l/tJGDs54PD+67ro+Xp/LHxa46SB2ntOEdVpOJGtXiZ16W9os3XxcEVR8Pf31+9/5MgRXn31VWrWrMkXX3xRaJ4jYwcnHKb+m1r7b1Hth7WYt+gI+fmkb11N1LAORA5uQ+qm5Y+MnqtUKkzNqtDlFX+Gv3+epp2n88KYlQyeeZCWz78LQEZqHFrtgyPb989naMjv7F42Eq0mjx4jftFPoqbc2/do4PuYWdjR7sXPsHduwLbFg1j1VVPCL+18irNbmJO5G+Prf6WLnjddSl2bFuRqs9kZtZjpR5vx9p+dORS3AY02v8THEv9cxo/epGKrVq0a8fHxhdri4+OxsbHBwsICtVqNWq0udptq1R48Q6OZmRlmZmZlMmYhhBBCCFF2zCzU9J7kTq+Jblw4lMSWgHCO/hbPuX2JnNuXiLOHOf2me9B7khvWDo+/XJZHzwZ49GxAZnwqli4FsxqXZLbyklAZG2P9Sm+sX+lNztlLJM9dQdrKQHKCLxI/fhZ33/kGm9eGcaVtfU6dOlVk/5iYGD766CM+//xzXn31Vfz8/GjZsqWubxMTrF8civWLQ8m+cJrkFXNJ37qanAuniH93DHe/eRvbYa9hO3wqxi7VHzpOB5cGOPScVagtNyuVXUuHY2VbneeHL8bY1EL/2V/X8o4NPcz+1ZNRG5vxwpiVuD3XDQCNJg+12oTk29e5cXY9zbq8QbOu/yI/P5sGrUcTcmgeRwNnYWphi2utki8vY6o2p2eNsfSoPoaLSYf1s55fTDrMxaTDOJm709d9Kr3cJ2Fn6lTi44l/lkr/pLt9+/bs3bu3UNuePXtof2/tJlNTU1q2bFloG61Wy969e/XbCCGEEEKIfx6VSkVTHwf+vb45v4R1Ydj7tbGpasLtiGyWvHeN0W5BzJl8gbCQJ4ue/7Xgvn8cQzNr1giXxf+hVtRBHL9+G2OP6mjuJpH0nwWYvPQG7zZuh2vV4ovB3Nxcli1bRqtWrejQoQNr1qwpHD1v0pJqX/9yL3r+JcYuNdAk3Cbxxy900fN/DScr+OgTxevvRJ0hOvQASfGXCxXcf3XlxDJ2LxuJpU01ug9frC+4AYyMdM8O/9zxqe7vxqaYmFlhYeVIrab96TnqV3qNXU3V6l6PPabHoVKpaOLQmfebreXXLuG8Wvvf2JhU5U52JEuvf8CYIHe+Pz+R0NSzpXpcUblVuHW609PTuXHjBgDNmzfnu+++o1u3bjg4OODh4cH7779PdHQ0y5YtA3RLhjVp0oTp06czYcIE9u3bh5+fH9u2baNXr16AbsmwsWPHsnDhQtq0acMPP/zAunXruHLlSpF3vR9E1ukuPZVp3WuoXOOVdaR1ZJ1uIYQQD5KbrSFodSybfggvVGx7d3Ogv68n7fo7oTau9M+lUPLzSd+8l5SA5WQdOAFAHgr7PW1ZbpLOnzeuPnR/V1dXpk6dymuvvVbk52UlP5/0Pb+TvDyA7FOH9O1mTVpiN8qXKn2HYWRm/sgxJsRcwMzCjir2bmg1+ahURvfWRc8h4sputi8ZjLW9B30nb8bRtbHu2H9JFeTmpLP715Gojc2IuLILc6uq+AyeQ60m/Z7oXJVUriabg3Hr2BIewPXUgkRBI7uODPT0o4PLSxgbPf068qJ8lUXdV+GK7qCgILp161akfezYsSxdupRx48Zx69YtgoKCCu3zr3/9i0uXLuHm5sZHH33EuHHjCu0/d+5cvv32W+Li4mjWrBn+/v60bdv2scclRXfpOnbs4eta165t+AL2ryrTeCMiHr5OdNWqz0ZBWFbnQc6vEEL8MyiKwsXDSQTOjeDwxni095YYc3I3p980D3pPdsPG8fGj52UhLyMHtbkJRuqS/RIgJ+QKyQHLSVuxBeXee96XbE1Y7WHJ71dDyM3NfeC+pqamBAcH07hx4+L7vnSW5OX+pAWuQrn3nrfawQmbYa9hO/x1TKq5PXRsxUXzzwbN4eSuz7F3aUC7Fz/H7bluKFrtA2eGz85MIjn+Kke2vEfS7Sv0m7yFajUf/+f80qIoCpeTj7E53J8j8RvRKLr3vKuau9HXfSq93SdL9LwSeCaK7opKim4hhBBCiH+mO5FZbJsfyY5FkaTe1cWqTc2N6DayOgN8PajtbZif/Y7M2sKNdWdoOq0TjSa2L7J++JPSJCSR8vMGUuatJD9CtwxYgpHCpoZVWX77JjF3bhfZp2HDhly8ePGREXpN4l1S1i8mZdWP5Mfem4BYrabKCy9jN2Ym5i06PFYMPy78BOu/a4etY20Gv3EYKxvdHEzFFedarQYjI9266YpWy+3I02z4vgNePr50fvm7Rx6rLCVmx7ItcgHbIxeQnKs7r8YqU7q6DmdgzZnUtWlu0PGJB5Oi24Ck6BZCCCGE+GfLzdZwYE0sm+aEc/NsQfS8iY89A/08aT/Qudyi54pWy/L6X5Jy4w4AxhYmNBjTBi9fHxwbu5asb42GjC17SQ5YQdb+48C96LmHDSvNMjl2/Yp+23nz5jFt2rRi+9FqtRj97emzkp9P+h+bSFkeQNbJg/p2s0bNsR3ti3W/4Y+Mnt+NDkFBwamGd6HCutBxtFpQqVCpVIUK8lVfe6FWm/KS735Mza0f74SUoVxtDgdj1xIYMZdrKSf17Y3sOjLA05eOLi9L9LyCkaLbgKToFkIIIYR4NiiKwqWjyWwJCOfIxng0+QXR875T3ek92R3bqmUfPc/LzOXaqlOcCzhIQkiMvt2tWz28/LpQq3+TkkfPz1/VzXq+fDNKlm7Sksu2JqzxsGRfXDg3bt6kSpUqxe7bvXt3qlevjq+vb7GvbeZcPkfy8gDSAlei5Oj6VttX1UXPR0x9ZPT8r+4X1lkZCSiafCxtXPTtoJvgLD0lhm0/DcDErAov+wUZbFb5B7mcfJwt4f4ciluvj547mlWnr8c0+rhNxs7M2cAjFCBFt0FJ0S2EEEII8ey5G53N1h8j2PFT4eh51xGuDPD1pE6zsv+5UFEUYg7e4Jz/QW5uCkHR6n58t6npQNNpnWk0sZ1+rfCnpUlMJnXJRpLnrST/VhQAuSqwf+kF7PzGYOHTulABGxwcrF9eDKBNmzb4+voyZMiQIsvuapISSNnwMykr55EfE6FrVKup0vMl7Eb7Yd6q02MXx9fPrOfC4fk0f/4dPBv21u+n1eQTfnkn238eTIcBX9O8279KcjrKVGJ2LNsjF7I9cgFJubpljY1VpnRxHcYATz+es21l4BE+26ToNiApuoUQQgghnl252RoOrotj85xwbgSn6tsbdbRj0MyadHipfKLnaRGJnJ9/mIuLjpGdkAHooufPjWyFt18XqjZ9+JrZj6JoNGQE7iM5YDlZ+47r202b1sfObzTWI/pjZGnB+PHjWbp0aZH9XVxcmDJlCq+//jquroVj8Ep+Phl7t5C83J+sEwf07WYNmxVEz82LXz7svpjQw+xdPRFzS0eadX0DJ/cW2DnVJezCVo4Fvo+iaHlx4m/Yu9Qv0XkoD3naXH30/GrKCX17I7sO9PeYQcdqgzExMuxkfs8iKboNSIpuIYQQQgihKAqXjyWz2b9o9LzPFHf6THbDztnsEb2UXH5WLtdWn+ac/0HunovWt9foWhcv3y7UHtAEI+Oi70I/iZwL1wqi55lZABg52GE6ZiBeS74lOTXlgfsaGxszZMgQ/Pz8aNu2bZEn2TlXQkheMZe0zcv10XMjOwdsh76G7chpmLi6P7Dv+PCTHN70NnG3jmHv0pDcrGTSkiMxNrGg32uBuD/XvUTf2xCuJp9gc7g/B+PW6qPn9mbV6Oc+jRfdp0j0vBxJ0W1AUnQLIYQQQoi/SojJZtv8SLYvjCTljm7ZLRMzI7oOd2WAnyd1m5dT9PzwTUL8DxD6ewiKRguAtaeDftZzC8cSRs+TUkhdsoHkuQXR8ySVwuZGVVl2J4yo2/EP3b9Vq1b4+fkxdOjQotHz5ERSN/xM8sp55EeH6xrVaqr0GITdGD/MW3V+YPQ88uperp5aidrYlCr2HtRs2Acn9+YV7l3uJ5GYHcuOqEVsj1xAYk4soIue+7gOZYCnH/VtWxt4hP98UnQbkBTdQgghhBCiOLnZGg6tj2OzfzjXT/0let7BjgF+nnR82QVjk3KInkcm6aLnPx3VR8/V5ibUH9lSFz33qlGi/hWNhoxtQST7LyNr7zEA8lE46G7Dcossjly7/ND9nZ2d9dHz6tULx+AVjYaMfYG66Pnx/fp20wbe2I32xbr/iAdGzx80w3lllqfN5XDcBjaHzykUPW9o154BHr4SPS9DUnQbkBTdQgghhBDiYRRF4cpxXfT88IaC6LljDTP6TvWg9yQ37F3KKXq+Jphz/ge4e/Yv0fMudfHy9aH2wKYlj55fukHK3BWk/vq7Pnp+zdqYNTWrsOFaCNk5OQ/c9/vvv+eNN954cN/XLuhmPd+8HCX7XqzdzgHbIZN10fPqHiUae2VzNeUkgeEBHIhdQ76im8zP3tSFvh5TedH9dezNXAw8wn8WKboNSIpuIYQQQgjxuBJjs9m+MJJt8yNJvq2LnhubqujyqiuDZnpSt4VtmY9BURRij9zknP8BQn8riJ5XcbfHa3onGk3qUPLoeXIqqUs2kDJvJXk3IwFd9HzLveh55N+i51ZWVkRHR2Nr++jvr4+er/qR/KhbukYjI6yeH4jdGD8s2nSptDHyp6GLnv/E9siFhaLnnasNYYCnLw3sii7bJp6cFN0GJEW3EEIIIYR4Urk5Wg6tiyVwXgRX/yyYeKxhezv6z/Cg0yvVMDEt++h5elQS5+cf4eKio2TdSQfuRc9HtMTL1wenZo+/ZnZxFI2GjO0HSAlYTuaeI0BB9HylZTaHrl4CYNq0acybN6/YPqKiolCpVNSoUTgGr2g0ZARtI/nXOWQd36dvN63fFLtRvlgPGImRhWWJxl+Z5GvzOBy/kU23fuBqyp/69vq2bRno6Uenaq9I9LwEpOg2ICm6hRBCCCFESVw9kcymH8I5tD6uIHpeXRc97/NaOc16np3H9bW66Pmd4Ch9e3WfOnj7+lB7kFeJo+e5l2+QPHcFqb9uQsnIBOC6tQlralrx9n+/wuuF54vdb8qUKSxZsoTBgwfj5+dH+/bti856fv0iKSvmkrppGUqWrm8jW3tsh0zCdsQ0TNxqlmjsD5MQc4ETuz7Hu4sfrrU6VIin7NdSThEYPpeg2NXkK7pEhZ2pM33cp9DPfSoO5q6P6EH8nRTdBiRFtxBCCCGEKA2JcTns+EkXPU+K0737bGyqwmeoKwNnevJcq/KJnscdv8W5OQcI3XgWbf696LmbHU2mdqLJax2wqFqlRMfQpKSR+stGUuauIC80QteoUmHVrxt2fqOxeL6gcE1KSqJGjRpkZWXp92/RogV+fn4MGzYMc3Pzv/WdROqGJaSs+pG8yJu6RiMjrLoPwG60LxbtupV6Ubx/7VQuHFkAgLN7S7x8fKnXYhjGJuaP2LPsJeXEsz1yITsiF5KQEwOAscqETtWGMMBjBg3s2lWIXxJUBlJ0G5AU3UIIIYQQojTl5Wo5tC6OwHnhXDleED1v0M6WAb6e5Rc9j07WzXq+6BhZt9MAXfT8ueEt8Jrhg3OLB6+Z/TgUrZbMHQdIDlhB5q5D+nbThnWw9R2NzeiBfLdgPu+8806x+1etWlU/67mbW+EYvKLRkHFguy56fmxvQd/1GmM32g/rgaNKLXp+NzqEcwf8uXpqBZp83S9LzK2q0qTjFJp2mkoVu5LNDl8a8rV5HI3/nc3h/lxKPqJvf8629b3o+RBMjco+UVGZSdFtQFJ0CyGEEEKIsnLtVAqb54RzcG0s+Xm6H88dXM3oO9WdPq+5l8us55qcPK6tPUOI/wFun47Ut7t2rI33zC7UHuSF2qSE0fOrN0kOWK6LnqfrljUzsrXmp0b2zD17lMy/POn+O7VazeDBg/H19aVjx45Fo+c3LhVEzzPv922PzSsTsRsxDRP3WiUa+31Z6Xe5eGwx5w//SHqS7jwZGRlT2/tlvH18ca1ddGyGcD3lNIERuuh5nlb3SwJd9Pw1+rpPxdG8+iN6eDZJ0W1AUnQLIYQQQoiylhRfED1PjL0XPTdR0XloNQb6eVK/jV2Zj+F+9Dwk4CA31p/RR8+tatjS9H703Mm6RMfQpKSR9uvvJAcsJ+9GOAApaAls5MSyxHBuxcU+dP/mzZvj6+vL8OHDi0bPU5NJ3fgLKSvmFkTPVaqC6Hn77qVSFGs1+dy8sIVzQXOICT2ob3dya4F3F1/qNR+GsWnxa4uXp+TcO+yI/IltET/qo+dqlTGdqw2hv8cMGtoVfXf+WSZFtwFJ0S2EEEIIIcpLXq6Wwxvi2BJQOHpev60uet55SDlFz2NSuLDgMBcWHi2InpsZU+/VFnj7+uDcsmRrZitaLZm7DpHsv4zMnbrouQaFQzWsWVUll6CrFx+6v6OjIzNnzuSjjz4qtu+MA9tJWR5A5uHd+nbTuo2wHe2LzcDRGFmWbMm0++5GhxByaC5XTi5Hk5cNgLmVI407vIZXp2lUsS/Z7PClIV+bx7Hbm9gSHsCFpIKYf12bFgzw9KOL66sSPUeKboOSolsIIYQQQhjCtVMpbAkI58Dqgui5vYupbtbzKe44VCuf6Pn19Wc553+A2ycj9O3V2tfEe2ZX6rzsXfLo+bUwkueuIG3pb2jTdPHwUCs1a+vYsP7GBTIyM4vdb+LEiSxevPjhfd+4TPKKuaRu+rUgem5tq4uej5yOiUftEo39vqyMBC4d1UXP05J050llpKaO10t4+fhSvU7nCvFU+UZKMFsi5nIgdjW5Wt0vCWxNnejj9hp9PaZS1dzw76cbihTdBiRFtxBCCCGEMKT70fPtCyJJiCmInncaUo0Bvp40bGdX5mNQFIX4P29xLuAgN9afRZunAcCqui1NXu9Ik9c6YOlSsp+VNanppP36G8lzV5J3LQyAVLQENnRiWXIEYbExhbY/e/Ys3t7ej9d3WkpB9DwiVNeoUmHVrR92o/2w6PB8qUXPwy4Ecu6AP9E3gvTtVWt44+3jx3Mth1eI6HlK7l12RS0mMGIed7N1S8gZqdR0chnMQM+Zz2T0XIpuA5KiWwghhBBCVAT5eVoOb4xni384l48l69ufa23LQD9POg2phqlZ2UfPM2JTOL/gCBcXHiEzXhc9NzJV89yrLfHy9cGlVSlEz/ccIXnOr2Tu0L0zrUHhSHVrVtnkse/KBXx8fDhw4ECx+6empvLNN98wZcoUPDwKj0XRask8uJPk5QFkHtqpbzet07Agem5VsiXT7rsfPb96cgX5ebqJ4swtHWjUYTJenaZh7VCy81QadNHzzQSGz+V8UsH5rGvTgv4eM+jqOhxTteGXRisPUnQbkBTdQgghhBCiorl2KoXAueEErY4lP1f3Y72dsyl9prjTb6o7Dq5lXyhpcvK4seEs5wIOEv9nuL69WruaePt1oc5gb9SmxiU6Ru71W6TMXUHqLxv10fMwSzXqAd3o/Nm7mNarWWSfgIAA/Pz8MDIyYtCgQfj5+eHj41PkyW3uzaskLw/QRc8z0oF70fPBE7AdNR1TjzolGvt92RmJ+lnP0xJ150mlMqK210t4+/hSvW7RsRnCzdRzbAqfUyR6/qL7FPq4T8HJ3PDvp5clKboNSIpuIYQQQghRUSXfzmHHoii2/Rihj56rjXWznvef7kHD9nblUtDFnQgnJOAA19eeKYieu9rQ5PWONH6tI1bVSvZztDYtndRlm0ieu4K8Kzf17ZZ9fLDzHY1lr86ojIzQarU0aNCA69evF9q/adOm+Pn5MWLECCwtC6/frUlPJe23pSSvmEverXv7qVRYdnkRu7EzsezQo3Si51oNty5s5dxBf6Ku7dO3O1b3wtvHl/qtRlaI6HlqbgI7oxazNWIed7LvLY2mUtPB+SUG1XyDRnYdKsQvCUqbFN0GJEW3EEIIIYSo6PLztBz9PZ7N/uFcOpKsb6/X0oaBMz3pPNS1fKLncalcWHiECwuOkBmXCoCRiZp6w5rj7dcFl9aeJepfURQydx/WzXq+4yDcK2lM6tXEzncUR2pY02/wyw/c397ensmTJzNt2jQ8PQuP5UHRc5PaDbAbNQObQWMwqlKyJdPuuxtznvOH5nHl5HLyc3UTxZlbOtCo/SSadp6GjUPJzlNp0GjzOXr7dwLD5xWKntexaa6PnpupDf9LgtIiRbcBSdEthBBCCCEqk+unUwicF0HQqljycnRrbds5m9J7sht9p3pQtUY5RM9z87mx4Swhcw8Sd+yWvr1au5p4zehM3SHNSx49vxFOyryVpC7ZgDZVFw+PsjJmRW1r1oVeJP3ebOXFMTIyYuDAgfj6+tK1a9ei0fOwa6SsnEfqxl/QZtx7b72KDTavTMB25HRMPeuWaOz3ZWcmcen4Es4fnEtq4i3gfvR8EF4+vtSo26VCPFUOSzvPlnB/9sYsJ0+rS1TYmDjSx30Kfd1fx8nC3cAjLDkpug1Iim4hhBBCCFEZpdzNZeeiSALnRZAQXRA97/SKi27W83KKnsefiiAk4CDX1pxGm6uLnltW00XPm0wpheh5eoYueh6wXB89T0PD1gZOLEuNIjQm+qH7N2nSBF9fX0aNGlV89Pz3ZSSvCCAv7Jq+3bLLi9iN8cOyY09URiVPEGi1Gm5d3EbIwQAir/6hb3d0bYKXjy/1W4/CxNTyIT2Uj9TcBHZHLyEwfB63s3Xvpxup1LR3HshAz5k0sa8YS6M9DSm6DUiKbiGEEEIIUZlp8rUc3XSbLf7hXDiUpG+v01wXPe/yavlEzzPjU7m46BjnfzxERuxfoudDm+Pl14VqbUohev7HUVIClpOxdT8oCloUjrlWYYWdhr2Xzz90f3t7ey5evIirq2vRvrVaMg/v1kXPD2zXt5vUqq+Lnr80ttSi54mxlzh30L+Y6PlEmnaaho1jzVI5TklotPm6Wc8j5hKSGKRvr23djAGeM+jiOhxzteF/SfAkpOg2ICm6hRBCCCHEP8WNM6m6Wc9XxZKbrYue2zrpoufDP6yDmYW6zMegyc0ndOM5QuYeJPZomL7dpY0nrT7oSe2BXiU+Rm5oBCnzVpC6ZCPaFF08PMxSzbo6NqwLu0RaenqRfdq1a8exY8ce3fet6wXR8/R7vzywssZm8HgcZnyC2s6hxOMHyMlM5tLxJYQcmktqgu48qVRG1Go6gLYvfkbV6k1L5TgldSvtAlvCA9gXs5wcrW5pNGsTB/q4vcbwuh9VmuJbim4DSklJwc7OjsjISCm6hRBCCCHEP0JqYi5//BrNjp+iSIzJxrWOJf6nOmBkVL7R4DtnIjm/8Cg3NpxBm6el9Ue9aPn286XWvzY9g9Q120hduJa8azdR2VjjcGIdazZv4qeffiI0NFS/7aJFixg6dGix/SiKUiQ2rU1PI3XbalLW/kR+2HVUdvbU3HEZI/PSnVxMq9UQcXk3F44sJOrGfgBemr4XF89WpXqckkrNTWRfzAp2Ri3iTlYErpa18e9wGiNV2acoSkNqairu7u4kJydja2tbKn1K0f2YoqKicHev/BMDCCGEEEIIIYR4uNDQUGrXrl0qfUnR/Zi0Wi0xMTFYW1uX6qQA93+TIk/QKw+5ZpWPXLPKR65Z5SPXrPKRa1b5yDWrfOSaVT4pKSl4eHiQlJSEnZ1dqfRZsvn5nyFGRka4ubmVWf82NjZyI1Yycs0qH7lmlY9cs8pHrlnlI9es8pFrVvnINat8jEphNnp9X6XWkxBCCCGEEEIIIQqRolsIIYQQQgghhCgjUnQbmJmZGZ988glmZmaGHop4THLNKh+5ZpWPXLPKR65Z5SPXrPKRa1b5yDWrfMrimslEakIIIYQQQgghRBmRJ91CCCGEEEIIIUQZkaJbCCGEEEIIIYQoI1J0CyGEEEIIIYQQZUSKbiGEEEIIIYQQooxI0V2G5s+fj5eXFzY2NtjY2NC+fXt27Njx0H3Wr19PgwYNMDc3p2nTpmzfvr2cRivgya/Z0qVLUalUhf6Ym5uX44jF33399deoVCreeOONh24n91rF8TjXTO41w/r000+LnP8GDRo8dB+5xwzrSa+Z3GMVQ3R0NKNGjcLR0RELCwuaNm3KqVOnHrpPUFAQLVq0wMzMjLp167J06dLyGawAnvyaBQUFFbnXVCoVcXFx5TjqZ1fNmjWLPf/Tp09/4D6l8e+ZFN1lyM3Nja+//prTp09z6tQpunfvzsCBA7l48WKx2x89epThw4czceJEzpw5w6BBgxg0aBAXLlwo55E/u570mgHY2NgQGxur/xMeHl6OIxZ/dfLkSRYuXIiXl9dDt5N7reJ43GsGcq8ZWuPGjQud/8OHDz9wW7nHKoYnuWYg95ihJSUl0bFjR0xMTNixYweXLl3if//7H/b29g/cJywsjL59+9KtWzfOnj3LG2+8waRJk9i1a1c5jvzZ9TTX7L6rV68Wut+cnZ3LYcTi5MmThc77nj17ABgyZEix25fav2eKKFf29vbK4sWLi/1s6NChSt++fQu1tW3bVpkyZUp5DE08wMOu2S+//KLY2tqW74BEsdLS0pR69eope/bsUbp06aLMnDnzgdvKvVYxPMk1k3vNsD755BPF29v7sbeXe8zwnvSayT1meO+9957SqVOnJ9rn3XffVRo3blyobdiwYUqvXr1Kc2jiAZ7mmu3fv18BlKSkpLIZlHgiM2fOVOrUqaNotdpiPy+tf8/kSXc50Wg0rFmzhoyMDNq3b1/sNseOHaNHjx6F2nr16sWxY8fKY4jibx7nmgGkp6fj6emJu7v7I5+Ki7Izffp0+vbtW+QeKo7caxXDk1wzkHvN0K5fv0716tWpXbs2I0eOJCIi4oHbyj1WMTzJNQO5xwxty5YttGrViiFDhuDs7Ezz5s1ZtGjRQ/eRe82wnuaa3desWTNcXV3p2bMnR44cKeORiuLk5uayYsUKJkyYgEqlKnab0rrHpOguY+fPn6dKlSqYmZnx+uuv8/vvv9OoUaNit42Li8PFxaVQm4uLi7zjUc6e5JrVr1+fJUuWsHnzZlasWIFWq6VDhw5ERUWV86ifbWvWrCE4OJivvvrqsbaXe83wnvSayb1mWG3btmXp0qXs3LmT+fPnExYWRufOnUlLSyt2e7nHDO9Jr5ncY4Z38+ZN5s+fT7169di1axdTp07Fz8+PX3/99YH7POheS01NJSsrq6yH/Mx7mmvm6urKggUL2LhxIxs3bsTd3Z2uXbsSHBxcjiMXAJs2bSI5OZlx48Y9cJvS+vfM+GkGKB5f/fr1OXv2LCkpKWzYsIGxY8dy4MCBBxZxwvCe5Jq1b9++0FPwDh060LBhQxYuXMjnn39ensN+ZkVGRjJz5kz27Nkjk/5UEk9zzeReM6w+ffro/7+Xlxdt27bF09OTdevWMXHiRAOOTDzIk14zuccMT6vV0qpVK/7zn/8A0Lx5cy5cuMCCBQsYO3asgUcnivM016x+/frUr19f//cOHToQGhrK999/z/Lly8tl3ELn559/pk+fPlSvXr3MjyVPusuYqakpdevWpWXLlnz11Vd4e3szZ86cYretVq0a8fHxhdri4+OpVq1aeQxV3PMk1+zvTExMaN68OTdu3CjjUYr7Tp8+ze3bt2nRogXGxsYYGxtz4MAB/P39MTY2RqPRFNlH7jXDeppr9ndyrxmWnZ0dzz333APPv9xjFc+jrtnfyT1W/lxdXYv8gr9hw4YPfS3gQfeajY0NFhYWZTJOUeBprllx2rRpI/daOQsPD+ePP/5g0qRJD92utP49k6K7nGm1WnJycor9rH379uzdu7dQ2549ex76PrEoew+7Zn+n0Wg4f/48rq6uZTwqcd/zzz/P+fPnOXv2rP5Pq1atGDlyJGfPnkWtVhfZR+41w3qaa/Z3cq8ZVnp6OqGhoQ88/3KPVTyPumZ/J/dY+evYsSNXr14t1Hbt2jU8PT0fuI/ca4b1NNesOGfPnpV7rZz98ssvODs707dv34duV2r32FNP9SYeadasWcqBAweUsLAwJSQkRJk1a5aiUqmU3bt3K4qiKKNHj1ZmzZql3/7IkSOKsbGx8t///le5fPmy8sknnygmJibK+fPnDfUVnjlPes1mz56t7Nq1SwkNDVVOnz6tvPrqq4q5ubly8eJFQ30FoShFZsKWe63ie9Q1k3vNsN566y0lKChICQsLU44cOaL06NFDqVq1qnL79m1FUeQeq4ie9JrJPWZ4J06cUIyNjZUvv/xSuX79urJy5UrF0tJSWbFihX6bWbNmKaNHj9b//ebNm4qlpaXyzjvvKJcvX1bmzZunqNVqZefOnYb4Cs+cp7lm33//vbJp0ybl+vXryvnz55WZM2cqRkZGyh9//GGIr/BM0mg0ioeHh/Lee+8V+ays/j2Td7rL0O3btxkzZgyxsbHY2tri5eXFrl276NmzJwAREREYGRWEDTp06MCqVav48MMP+eCDD6hXrx6bNm2iSZMmhvoKz5wnvWZJSUlMnjyZuLg47O3tadmyJUePHpV39isYudcqH7nXKpaoqCiGDx9OQkICTk5OdOrUiePHj+Pk5ATIPVYRPek1k3vM8Fq3bs3vv//O+++/z2effUatWrX44YcfGDlypH6b2NjYQtHlWrVqsW3bNv71r38xZ84c3NzcWLx4Mb169TLEV3jmPM01y83N5a233iI6OhpLS0u8vLz4448/6NatmyG+wjPpjz/+ICIiggkTJhT5rKz+PVMpiqKUeORCCCGEEEIIIYQoQt7pFkIIIYQQQgghyogU3UIIIYQQQgghRBmRolsIIYQQQgghhCgjUnQLIYQQQgghhBBlRIpuIYQQQgghhBCijEjRLYQQQgghhBBClBEpuoUQQgghhBBCiDIiRbcQQgghhBBCCFFGpOgWQgghngFdu3ZFpVI99vYqlYquXbuW3YDKwdKlS1GpVCxdutTQQxFCCPEMk6JbCCGEeEq3bt1CpVIV+mNqaoq7uzsjRowgJCTkqfuWgvHx/BN+OSCEEOKfzdjQAxBCCCEquzp16jBq1CgA0tPTOX78OKtXr+a3335j7969dOzY0cAjFEIIIYShSNEthBBClFDdunX59NNPC7V9+OGHfPnll/z73/8mKCjIIOMSQgghhOFJvFwIIYQoA76+vgCcPHmyUPvmzZt5/vnnsbe3x9zcnCZNmvDf//4XjUaj32bcuHGMHz8egPHjxxeKr993+vRpZsyYQZMmTbC1tcXCwoKmTZvy9ddfk5eXV2bfKzc3l++++44WLVpgZWWFtbU1nTt3ZsuWLUW2HTduHCqVirCwMPz9/WnQoAFmZmZ4enoye/ZstFptkX0yMzN59913cXd315+fRYsWERQUhEql0v9y4/7fAQ4cOFDoHBUXyd+9ezcdOnTA0tISR0dHxo4dS0JCQqmeGyGEEKI48qRbCCGEKEN/LZTff/99vv76a2rUqMHLL7+Mra0thw4d4p133uHPP/9k/fr1AAwaNIjk5GQ2b97MwIEDadasWZF+Fy1aRGBgID4+Prz44otkZmYSFBTE+++/z8mTJ9m4cWOpf5ecnBx69+5NUFAQzZo1Y+LEieTl5bFt2zYGDhxIQEAAM2bMKLLfO++8w4EDB+jXrx+9evVi06ZNfPrpp+Tm5vLll1/qt9NoNPTr14/9+/fTtGlTRowYQWJiIm+99VaR97Zr1qzJJ598wuzZs/H09GTcuHH6z/5+vrZs2cK2bdvo378/HTp04ODBgyxbtozQ0FAOHz5cmqdICCGEKEoRQgghxFMJCwtTAKVXr15FPvv4448VQOnWrZuiKIqye/du/bbp6en67bRarfL6668rgLJhwwZ9+y+//KIAyi+//FLsscPDw5X8/PxCbVqtVpkwYYICKIcPHy70WZcuXZQn+WcfULp06VKo7YMPPlAA5aOPPlK0Wq2+PTU1VWnVqpViamqqREdH69vHjh2rAEqtWrWUmJgYffudO3cUOzs7xdraWsnJydG3L168WAGUPn36FPpuFy9eVMzNzRVA+eSTTx45zvvun0NjY+NC5yM/P1/p2rWrAijHjh177HMihBBCPA2JlwshhBAldOPGDT799FM+/fRT3nnnHXx8fPjss88wNzfXP8mdO3cuAD/99BNWVlb6fVUqFV9//TUqlYrVq1c/9jE9PDxQq9WF2lQqFdOnTwfgjz/+KOnXKkSr1TJ//nzq1KnD7NmzCz3Bt7a25uOPPyY3N5fffvutyL4fffQRrq6u+r9XrVqVgQMHkpaWxtWrV/XtK1asAODLL78s9N0aNWrEmDFjnnrsI0aMKDSZnVqtZuzYsUDR+L8QQghR2iReLoQQQpRQaGgos2fPBsDExAQXFxdGjBjBrFmzaNq0KQDHjx/HysqKJUuWFNuHhYUFV65ceexj5ubmMnfuXNasWcOVK1dIT09HURT95zExMSX4RkVdvXqVpKQkqlevrv+uf3Xnzh2AYr9Dy5Yti7S5ubkBkJycrG87d+4cVlZWNG/evMj2HTt25KeffnqqsT/u8YUQQoiyIEW3EEIIUUK9evVi586dD90mMTGR/Pz8YgvW+zIyMh77mK+88gqBgYE899xzDBs2DGdnZ0xMTEhOTmbOnDnk5OQ8dl+PIzExEYCLFy9y8eLFB25X3HewsbEp0mZsrPsR5K8TyKWmpuLu7l5svy4uLk803qc5vhBCCFEWpOgWQgghyoGNjQ0qlYq7d++WuK+TJ08SGBhIr1692LZtW6Eo9vHjx5kzZ06Jj/F39wvXwYMHs2HDhlLv//4x7j8x/7v4+PgyOaYQQghR1uSdbiGEEKIctG3bloSEBK5fv/5Y298vpIt7EhsaGgpA3759i7zXfejQoRKOtHgNGzbExsaGU6dOldmSZN7e3mRkZHD27Nkinx09erTYfYyMjORptRBCiApNim4hhBCiHPj5+QEwYcKEYteHjouL4/Lly/q/Ozg4ABAZGVlkW09PT4Aiy11dvHiRr776qtTG/FfGxsZMnTqV8PBw3n777WIL7wsXLnD79u2nPsbIkSMB+PDDDwut4X3lyhV+/fXXYvdxcHAgKirqqY8phBBClDWJlwshhBDloHfv3nz00Ud8/vnn1K1bl969e+Pp6UlCQgI3btzg0KFDfPHFFzRs2BCA9u3bY2FhwQ8//EBSUhJOTk6AriBt06YNbdq0Yd26dcTGxtKuXTsiIiLYsmULffv2LbP49+zZswkODsbf359t27bh4+ODs7Mz0dHRnD9/nnPnznHs2DGcnZ2fqv/x48ezfPlytm3bRvPmzenTpw+JiYmsWbOGnj17EhgYiJFR4ecF3bt3Z926dQwaNIjmzZujVqsZMGAAXl5epfGVhRBCiBKTolsIIYQoJ5999hk+Pj74+/uzd+9ekpOTcXR0pFatWnz66af6J72ge4K7YcMGPv30UxYtWkRWVhagK7rVajVbt25l1qxZ7Ny5k5MnT1KvXj3++9//0qdPnzIrus3MzNixYwc///wzy5YtY+PGjeTk5ODi4kKjRo14/fXX9bO1Pw21Ws327dv55JNPWL16NT/88AN16tThf//7Hw4ODgQGBhaZFO3+++v79u0jMDAQrVaLm5ubFN1CCCEqDJXy1/VFhBBCCCEqoA8//JAvv/yS7du306dPH0MPRwghhHhsUnQLIYQQosKIjY3F1dW1UNulS5do164darWamJgYLCwsDDQ6IYQQ4slJvFwIIYQQFcbUqVO5desWbdq0wd7entDQUAIDA8nLy+Pnn3+WglsIIUSlI0+6hRBCCFFhrFy5kgULFnD58mVSUlKoUqUKrVu35q233qJXr16GHp4QQgjxxKToFkIIIYQQQgghyois0y2EEEIIIYQQQpQRKbqFEEIIIYQQQogyIkW3EEIIIYQQQghRRqToFkIIIYQQQgghyogU3UIIIYQQQgghRBmRolsIIYQQQgghhCgjUnQLIYQQQgghhBBlRIpuIYQQQgghhBCijPw/w+iZHvmMZuIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int64)\n",
    "\n",
    "log_reg = LogisticRegression(solver=\"lbfgs\", C=10**10, random_state=42)\n",
    "log_reg.fit(X, y)\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "        np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
    "\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "\n",
    "\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
    "\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.5, \"Not Iris virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notes\n",
    "1. Just Like other `Linear` Models, `Logistic Regression` can also be regularized using `l1` or `l2` penalties. Scikit-Learn Actually adds an `l2` penalty be default.\n",
    "2. The `hyperparameter` controlling the `regularization` strength of a `Scikit-Learn LogisticRegression` model is not alpha(as in other `linear models`), but its inverse C. The higher the value of C the less the model is regularized."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Softmax Regression\n",
    "- The `Logistic Regression` Model can be generalized to be able to support multiple classes directly without having to **train and combine different** `Binary Classifiers`. This is called `Softmax Regression` or `Multinomial Regression`.\n",
    "- **The idea is simple**: When we give an Instance `x`, `Softmax Regression` model first Computes `Softmax Score` for Class `k` and then **Computes the Probability of each class by applying** `Softmax Function`."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "S_k(x) = x^T\\theta^{(k)}\n",
    "$$\n",
    "<p align=\"center\">Equation 4-19: Softmax score for class k</p>\n",
    "\n",
    "In this equation:\n",
    "- $S_k(x)$ represents the softmax score for class $k$ given the input features $x$.\n",
    "- $x$ is the input feature vector.\n",
    "- $\\theta^{(k)}$ represents the parameter vector associated with class $k$.\n",
    "\n",
    "The equation calculates the softmax score for a specific class by taking the dot product between the input feature vector $x$ and the corresponding parameter vector $\\theta^{(k)}$.\n",
    "\n",
    "- **Note** - Each Class Has its own dedicated Parameter Vector $\\theta$."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\hat{p}_k = \\sigma(s(x))_k = \\frac{\\exp(s_k(x))}{\\sum_{j=1}^{K}\\exp(s_j(x))}\n",
    "$$\n",
    "<p align=\"center\">Equation 4-20: Softmax Function</p>\n",
    "\n",
    "In this equation:\n",
    "- $\\hat{p}_k$ represents the estimated probability or predicted probability for class $k$ given the input $x$.\n",
    "- $\\sigma(s(x))_k$ represents the softmax score for class $k$.\n",
    "- $s(x)$ represents the input vector containing the scores or logits associated with each class.\n",
    "- $s_k(x)$ represents the $k$-th element of the input vector $s(x)$.\n",
    "- $exp(\\cdot)$ represents the exponential function.\n",
    "- $\\sum_{j=1}^{K}\\exp(s_j(x))$ represents the sum of the exponentiated values across all classes."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note** - The `Softmax Regression classifier` **predicts only one class at a Time**(*it is multiclass but not multioutput*), so it should be used only with mutually exclusive classes, such as different types of plants. You **cannot** *use it to recognize multiple people in one Picture*."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross Entropy\n",
    "- `Cross Entropy` is the Cost Function of `Softmax Regression Classifier`.\n",
    "- It is used to know that the Model is working Correctly or not(Giving High Probability to true class or not)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "J(\\boldsymbol{\\Theta}) = -\\frac{1}{m} \\sum_{i=1}^{m} \\sum_{k=1}^{K} y_k^{(i)} \\log(\\hat{p}_k^{(i)})\n",
    "$$\n",
    "<p align=\"center\">Equation 4-22: Cross Entropy Cost function.</p>\n",
    "\n",
    "Where:\n",
    "- $J(\\boldsymbol{\\Theta})$ represents the cost function.\n",
    "- $m$ is the number of training examples.\n",
    "- $K$ is the number of classes.\n",
    "- $y_k^{(i)}$ is the target value (0 or 1) for the $i$-th example belonging to class $k$.\n",
    "- $\\hat{p}_k^{(i)}$ is the predicted probability of the $i$-th example belonging to class $k$, given the model parameters $\\boldsymbol{\\Theta}$.\n",
    "\n",
    "This equation calculates the average `cross-entropy loss` over all training examples and all classes. It measures the dissimilarity between the predicted probabilities $\\hat{p}_k^{(i)}$ and the true target values $y_k^{(i)}$ for each example. The model aims to minimize this **cost function** during training.\n",
    "\n",
    "I hope this clarifies the **multi-class cross-entropy** **cost function** mentioned in the book. If you have any additional questions or require further assistance, please let me know."
   ]
  },
  {
   "attachments": {},
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   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "\\nabla_k \\theta &= \\frac{1}{m} \\sum_{i=1}^m (\\hat{p}_k^{(i)} - y_k^{(i)}) x_i^{(i)} \\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "<p align=\"center\">Equation 4-23: Cross entropy gradient for vector for class k.</p>\n",
    "\n",
    "Where:\n",
    "- `∇θk` is the gradient vector for class k\n",
    "- `m` is the number of training examples\n",
    "- `i` is the index of a training example\n",
    "- `ˆpk` is the predicted probability for class k for the ith training example\n",
    "- `yk` is the ground truth label for class k for the ith training example\n",
    "- `xi` is the input vector for the ith training example\n",
    "\n",
    "he equation shows that the cross entropy gradient vector for class k is the sum of the products of the difference between the predicted probability for class k and the ground truth label for class k, and the input vector for the ith training example. The sum is taken over all training examples.\n",
    "\n",
    "This equation can be used to update the parameters of a neural network during training, in order to minimize the cross entropy loss for class k."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "Let's use `Softmax Regression` to classify the `iris` flower ito all three classes. `Scikit-Learns Logistic Regression` uses one-versus-the-rest by defaultwehn you train it on more that towo classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
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      ],
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       "LogisticRegression(C=10, multi_class='multinomial')"
      ]
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     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][:, (2, 3)] # petal length and petal width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "sofmax_reg = LogisticRegression(multi_class=\"multinomial\", solver=\"lbfgs\", C=10)\n",
    "sofmax_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
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     "data": {
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       "array([2])"
      ]
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     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "sofmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.38014896e-07, 5.74929995e-02, 9.42506362e-01]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sofmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercises"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Which `Linear Regression` trianing algorithim can you use if you have a training set with Millions of features.\n",
    "- You can use `Mini-Batch Gradient Descent`, `Stochastic Gradient Descent` or even `Batch Gradient Descent` if You Have Enough Compute power but Make Sure to not to use `SVD` or `Normal Equation` in this case because if you use it `Computational Complexity` will take place."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Suppose the feature in your training set have very different scales. Which algorithms might suffer from this and how?\n",
    "- We can use `Polynomial Models` here and `Normal Equation` and `SVD` will also work just Fine. but make Sure not to use `Gradient Descent` But You can use them after **Scaling the Data**."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Can Gradient Descent Stuck in a Local Minimum While Training `Logistic Regression` Model.\n",
    "- No, Gradient Descent cannot get Stuck in a Local Minimum While Training `Logistic Regression` Because it is a `convex` Model."
   ]
  }
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