{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "\n", "##
CSCI-UA 9473 Introduction to Machine Learning
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Fall 2021
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Assignment 3: Convolutional nets, SVM and Robust PCA
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Given date: Thursday November 1
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Due date: Friday November 26
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Total: 30pts
\n", "\n", "Additional readings (To go further): \n", "\n", " - [Ian Goodfellow and Yoshua Bengio and Aaron Courville, Deep Learning](https://www.deeplearningbook.org/)\n", " - [Robust principal component analysis? EJ Candès, X Li, Y Ma, J Wright ](https://arxiv.org/pdf/0912.3599.pdf)\n", " - [Saharon Rosset, Ji Zhu and Trevor Hastie, Margin Maximizing Loss Functions](https://web.stanford.edu/~hastie/Papers/margmax1.pdf)\n", " \n", "The assignment is divided into three parts. In the first part, we will go back to neural networks. You will be asked to build and train a convolutional neural network for image classification. In the second part, we will focus on the max margin classifier and study how such a classifier can be learned by means of gradient descent. Finally, in the last part, we will implement a principal component decomposition of a video sequence to extract moving targets from their background. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Question I: (10pts) conv nets and autonomous driving \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this first question, we will use [the Keras API](https://keras.io/) to build and train a convolutional neural network to discriminate between four types of road signs. To simplify we will consider the detection of 4 different signs: \n", "\n", "- A '30 km/h' sign (folder 1)\n", "- A 'Stop' sign \n", "- A 'Go straight' sign\n", "- A 'Keep left' sign \n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An example of each sign is given below." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib.image as mpimg\n", "\n", "img1 = mpimg.imread('1/00001_00000_00012.png')\n", "plt.subplot(141)\n", "plt.imshow(img1)\n", "plt.axis('off')\n", "plt.subplot(142)\n", "img2 = mpimg.imread('2/00014_00001_00019.png')\n", "plt.imshow(img2)\n", "plt.axis('off')\n", "plt.subplot(143)\n", "img3 = mpimg.imread('3/00035_00008_00023.png')\n", "plt.imshow(img3)\n", "plt.axis('off')\n", "plt.subplot(144)\n", "img4 = mpimg.imread('4/00039_00000_00029.png')\n", "plt.imshow(img4)\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question I.1. (10pts) \n", "\n", "In this exercise, you need to build and train a convolutional neural network to discriminate between the four images. \n", "\n", "- Before building the network, you should start by cropping the images so that they all have a common predefined size (take the smallest size across all images) \n", "\n", "- We will use a __Sequential model__ from Keras but it will be up to you to define the structure of the convolution net. Initialization of the sequential model can be done with the following line " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = Sequential()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### I.1.a. Convolutions. \n", "\n", "- We will use a __convolutional__ architecture. you can add convolutional layers to the model by using the following lines " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.add(Conv2D(num_units, (filter_size1, filter_size2), padding='same',\n", " input_shape=(3, IMG_SIZE, IMG_SIZE),\n", " activation='relu'))\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "for the first layer and " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.add(Conv2D(filters, filter_size, activation, input_shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "for all the others. 'filters' indicate the number of filters you want to use in the convolutional layer. filter_size is the size of each filter and activation is the usual activation that comes on top of the convolution, i.e.\n", "$x_{\\text{out}} = \\sigma(\\text{filter}*\\text{input})$. Finally input_shape indicates the size of your input. Note that only the input layer should be given the input size. Subsequent layers will automatically compute the size of their inputs based on previous layers. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### I.1.b Pooling Layers \n", "\n", "On top of the convolutional layers, convolutional neural networks (CNN) also often rely on __Pooling layers__. The addition of such a layer can be done through the following line " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ " model.add(MaxPooling2D(pool_size=(filter_sz1, filter_sz2),strides=None))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "The _pooling layers_ usually come with two parameters: the 'pool size' and the 'stride' parameter. The basic choice for the pool size is (2,2) and the stride is usually set to None (which means it will split the image into non overlapping regions such as in the Figure below). You should however feel free to play a little with those parameters. The __MaxPool operator__ considers a mask of size 'pool_size' which is slided over the image by a number of pixels equal to the stride parameters (in x and y, there are hence two translation parameters). for each position of the mask, the output only retains the max of the pixels appearing in the mask (This idea is illustrated below). One way to understand the effect of the pooling operator is that if the filter detects an edge in a subregion of the image (thus returning at least one large value), although a MaxPooling will reduce the number of parameters, it will keep track of this information. \n", "\n", "Adding 'Maxpooling' layers is known to work well in practice. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although it is a little bit up to you to decide how you want to structure the network, a good start is to add a couple (definitely not exceeding 4) combinations (convolution, convolution, Pooling) with increasing number of units (you do every power of two like 16, 32, 128,...). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### I.1.c. Flattening and Fully connected layers\n", "\n", "Once you have stacked the convolutional and pooling layers, you should flatten the output through a line of the form" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.add(Flatten())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And add a couple (no need to put more than 2,3) dense fully connected layers through lines of the form" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.add(Dense(num_units, activation='relu'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### I.1.d. Concluding \n", "\n", "Since there are four possible signs, you need to __finish your network with a dense layer with 4 units__. Each of those units should output four number between 0 and 1 representing the likelihood that any of the four signs is detected and such that $p_1 + p_2 + p_3 + p_4 = 1$ (hopefully with one probability much larger than the others). For this reason, a good choice for the __final activation function__ of those four units is the __softmax__ (Why?). \n", "\n", "\n", "Build your model below. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = Sequential()\n", "\n", "# construct the model using convolutional layers, dense fully connected layers and \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question I.2 (3pts). Setting up the optimizer\n", "\n", "Once you have found a good architecture for your network, split the dataset, by retaining about 90% of the images for training and 10% of each folder for test. To train your network in Keras, we need two more steps. The first step is to set up the optimizer. Here again it is a little bit up to you to decide how you want to set up the optimization. Two popular approaches are __SGD and ADAM__. You will get to choose the learning rate. This rate should however be between 1e-3 and 1e-2. Once you have set up the optimizer, we need to set up the optimization parameters. This includes the loss (we will take it to be the __categorical cross entropy__ which is the extension of the log loss to the multiclass problem). " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from tensorflow.keras.optimizers import SGD\n", "from tensorflow.keras.optimizers import Adam\n", "\n", "# set up the optimize here\n", "# Myoptimizer = SGD\n", "# Myoptimizer = Adam\n", "\n", "model.compile(loss='categorical_crossentropy',\n", " optimizer=Myoptimizer,\n", " metrics=['accuracy'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question I.3 (2pts). Optimization\n", "\n", "The last step is to fit the network to your data. Just as any function in scikit-learn, we use a call to the function 'fit'. The training of neural networks can be done by splitting the dataset into minibatches and using a different batch at each SGD step. This process is repeated over the whole dataset. A complete screening of the dataset is called an epoch. We can then repeat this idea several times. In keras the number of epochs is stored in the 'epochs' parameter and the batch size is stored in the 'batch_size' parameter. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "batch_size = 32\n", "epochs = 30\n", "\n", "model.fit(X, t,batch_size=batch_size,epochs=epochs, validation_split=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Question II (10pts): Max margin classifiers and outliers\n", "\n", "Consider the dataset below. We would like to learn a classifier for this dataset that maximizes the margin (i.e. such that the distance between the closest points to the classifier is maximized). We have seen that one can solve this problem by means of the constrained formulation\n", "\n", "\\begin{align*}\n", "\\min_{\\mathbf{\\beta}} \\quad & \\|\\mathbf{\\beta}\\|^2 \\\\\n", "\\text{subject to} \\quad & y(\\mathbf{x}^{(i)})t^{(i)} \\geq 1 \n", "\\end{align*}\n", "\n", "where $y(\\mathbf{x}^{(i)}) = \\mathbf{\\beta}^T\\mathbf{x}^{(i)} + \\beta_0$. We might sometimes want to use a (softer) unconstrained formulation. in particular, when selecting this option, we can use the following function known as the _Hinge loss_ \n", "\n", "\\begin{align*}\n", "\\max(0, 1-t^{(i)}y(\\mathbf{x}^{(i)})) = \\max(0, 1-t^{(i)}(\\mathbf{\\beta}^T\\mathbf{x}^{(i)}+\\beta_0))\n", "\\end{align*}\n", "\n", "For such a loss, we can derive a softer, unconstrained version of the problem as \n", "\n", "\\begin{align*}\n", "\\min_{\\mathbf{\\beta}} \\quad & \\|\\mathbf{\\beta}\\|^2 + \\frac{C}{N}\\sum_{i=1}^N \\max(0, 1-t^{(i)}(\\mathbf{\\beta}^T\\mathbf{x}^{(i)}+\\beta_0))\n", "\\end{align*}\n", "\n", "In short we penalize a point, only if this point lies on the wrong side of the plane." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD6CAYAAACxrrxPAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAT7UlEQVR4nO3db4hld33H8fd3N13ootXgTqXdzeyskqhbMNKMsS2VxgpNYqFBSCFxUAiWJdWID2O71BZkqYUWtES7LCEV2aWhaKoRoqEgasGmzSzkj2tQ1jXZLClkUqWl5kHY7LcP7p119nrnzpk7957zO+e8XzDM3nuPd3453vs5v/8nMhNJUvvtaroAkqTZMNAlqSMMdEnqCANdkjrCQJekjjDQJakjtgz0iHggIl6MiO9t8npExN9HxNmIeCoifnP2xZQkbeWqCsd8AbgP+OImr98KXDv8eRfwD8PfE+3bty+XlpYqFVKSNHD69OmXMnNh3GtbBnpmficiliYcchvwxRysUHosIl4fEb+Wmf816X2XlpZYXV3d6s9LkjaIiOc2e20Wfej7gec3PL4wfG5cQY5ExGpErK6trc3gT0uS1s0i0GPMc2P3E8jME5m5nJnLCwtjWwySpCnNItAvANdseHwAeGEG7ytJ2oZZBPrDwIeGs11+C/ifrfrPJUmzt+WgaET8E3ATsC8iLgB/CfwSQGYeBx4B3gecBV4G7ppXYSVJm6syy+XOLV5P4KMzK5HUNadOwdGjcP48LC7CsWOwstJ0qdRBVeahS5rWqVNw5Ai8/PLg8XPPDR6Doa6Zc+m/NE9Hj/48zNe9/PLgeWnGDHRpns6f397z0g4Y6NI8LS5u73lpBwz0tjl1CpaWYNeuwe9Tp5oukSY5dgz27r3yub17B89LM2agt8n6ANtzz0HmzwfYDPVyrazAiRNw8CBEDH6fOOGAqOYiBrMO67e8vJxuzrVNS0uDEB918CA8+2zdpZHUgIg4nZnL416zht4mDrBJmsBAbxMH2CRNYKC3iQNskiYw0NvEATZJE7j0v21WVgxwSWNZQ5ekjjDQVS4XUUnbYqCrTC6imi8vlp1koKtM7lI4P14sO8tAV5lcRDU/Xiw7y0BXmVxENT9eLDvLQFeZXEQ1P14sO8tAV5lcRDU/Xiw7y4VFKpeLqOZj/Zx64+rOMdClPvJi2Ul2uUjjOE9bLWQNXRq1Pk97fWrf+jxtsFarollDl0Y5T1stZaBPYrO7n5ynrZYy0Dfj8uj+cp62WspA34zN7v5ynrZaykDfTNua3XYPzY6LmtRSznLZzOLioJtl3POlcVbG7DlPWy1kDX0zbWp22z0kCQN9c21qdjfdPWR3j1QEu1wmaUuzu8nuIbt7pGJYQ++CJruH7O6ZH1s+2iYDvQua7B5qurunq1wHoSlEZm59UMQtwGeB3cD9mfnpkddfB5wEFhl04/xtZv7jpPdcXl7O1dXVacutUiwtje/uOXgQnn227tJ0h+dVm4iI05m5PO61LWvoEbEb+BxwK3AYuDMiDo8c9lHg+5l5PXAT8HcRsWdHpVY7tGk2UJvY8tEUqnS53AiczcxzmfkK8CBw28gxCbw2IgJ4DfAT4OJMS6oytWk2UJu4/YCmUCXQ9wPPb3h8YfjcRvcBbwNeAJ4GPp6Zl2ZSQpVvZWXQDXDp0uC3Yb5ztnw0hSqBHmOeG+14vxl4Avh14B3AfRHxK7/wRhFHImI1IlbX1ta2WVSpR2z5aApVAv0CcM2GxwcY1MQ3ugt4KAfOAj8G3jr6Rpl5IjOXM3N5YWFh2jJL/WDLR9tUJdAfB66NiEPDgc47gIdHjjkPvBcgIt4IvAU4N8uCSpIm23KlaGZejIh7gEcZTFt8IDPPRMTdw9ePA58CvhARTzPoork3M1+aY7klSSMqLf3PzEeAR0aeO77h3y8AfzDbokmStsOVopLUEQa6NC33WlFh3G1Rmoa7TKpA1tClabjLpApkoEvTcK8VFchAl6bhXisqkIE+Dw6WdZ97rahABvqseWOC+SjtIuleKypQpRtczENnb3DhjQlmb3RGCQxqwwaoemhHN7jQNjlYNnvOKNEclNbomwUDfdZKHyxr46fYi6RmrKs9owb6rJU8WNbWT3HpF0m1TlcbfQb6rJU8WNbWT3HJF0m1UlcbfQb6PJR6Y4K2fopLvkiqlbra6DPQ+6TNn+JSL5Jqpa42+gz0Punqp1japq42+txtsU/WP61Hjw66WRYXB2He9k+xNIWVle599A30vunip1gSYJeLJHWGgS5JHWGgl6aNKzklFcE+9JJ4WzNJO2ANvSRtXckpqQgGeknaupJTUhEM9JK0eSWnpMYZ6CVxJaekHTDQS9LV9cjSDjjxqzoDvTRuQiVdVuoW/qVeZAx0la/Ub4/mrsSJX6VeZMCbRKt03iC613btGoTmqIhBI7YJTd8H3ptEq71KrKKpNiVO/Cp5drGBrrKV/O3R3JU48avEi8w6A11lK/nbo7krceJXiReZdQa6ylbyt0e1KG3iV4kXmXVuzqWyeZclFajU+8QY6Cpfqd8eqTCVulwi4paI+EFEnI2IT2xyzE0R8UREnImIb8+2mJLaxuUD9dsy0CNiN/A54FbgMHBnRBweOeb1wOeBP8rM3wD+ePZFVWP8ZmqbSl5802VVaug3Amcz81xmvgI8CNw2cswHgIcy8zxAZr4422KqMX4zNQWXDzSjSqDvB57f8PjC8LmNrgOujohvRcTpiPjQuDeKiCMRsRoRq2tra9OVuI+arCH7zdQUXD7QjCqBHmOeG12MexVwA/CHwM3AX0TEdb/wP8o8kZnLmbm8sLCw7cL2UtM1ZL+ZmoLLB5pRJdAvANdseHwAeGHMMd/IzJ9l5kvAd4DrZ1PEnmu6huw3U1Nw+UAzqgT648C1EXEoIvYAdwAPjxzzVeDdEXFVROwF3gU8M9uiNqTpAcGma8h+MzWFkhffdNmW89Az82JE3AM8CuwGHsjMMxFx9/D145n5TER8A3gKuATcn5nfm2fBazG60996dwfU98lcXBy/tVtdNWQX9mhKLh+on9vnTtL0Ppng9rFSC5w6VV+dx+1zp9V0dwfYdpUK1/S8hY3aFeh192eXMiBY2u5Eki5ret7CRu0J9CYugw4IStpCCQ35de0J9CYug3Z3SNpCKQ15aFOgN3UZtLtD0gQlNeTbE+glXQYlaaikhnx7Ar2ky6AkbVBKQ749gV7SZVCSCtSuOxa59EySNtWeGrok7UDT2zLVoV01dEmaQgnbMtXBGrqkzitpNec8Geh16kObTypQSas558lAr0tJO/hIPdOXZSwGel360uaTCtSXZSwGel360uZT6/ShJ7Avy1ic5VKXpu88JI3Rl9kf0I9lLNbQ69KXNp9axZ7AbjHQ69KXNp9axZ7AbrHLpU59aPOpVewJ7BZr6FKP2RPYLQa61GP2BNZr3jOK7HKRes6ewHrUMaPIGrok1aCOGUUGuiTVoI4ZRQa6JNWgjv1kDHRJqkEdM4oMdEmqQR0zipzlIkk1mfeMImvobdSH7fEkbZuB3jbeKEMtYJ2jGQZ627g9ngpnnaM57Qz0Pl/+3R5PhbPO0Zz2BXrpl/95X2z6cnPEjupDXcQ6R3PaF+glX/7ruNi4PV5rlV4XmRXrHM2pFOgRcUtE/CAizkbEJyYc986IeDUibp9dEUeUfPmv42Lj9nitVXJdZJbaWufoROspMyf+ALuBHwFvAvYATwKHNznum8AjwO1bve8NN9yQUzl4MHNQwbny5+DB6d5vliLGly2i6ZKpAHV+PE6eHHwlIga/T56c/d8o+e9v18mTmXv3Xvn/y969ZZYbWM1NcrVKDf1G4GxmnsvMV4AHgdvGHPcx4MvAizu7xGyh5Mu/bU1NUNfHo4SunZUVePZZuHRp8Lv0BmRXWk9VAn0/8PyGxxeGz10WEfuB9wPHJ71RRByJiNWIWF1bW9tuWQdK7nIo+WKjxtX18ehKONWp5J7c7agS6DHmuRx5/Bng3sx8ddIbZeaJzFzOzOWFhYWKRRyj1Mt/yRcbNa6uj0dXwqlOXWlcV9nL5QJwzYbHB4AXRo5ZBh6MCIB9wPsi4mJmfmUWhWwVb/+iCer4eHjj5+07duzKuwlBOxvXVWrojwPXRsShiNgD3AE8vPGAzDyUmUuZuQR8CfhIL8NcKoA9f9vXlcb1ljX0zLwYEfcAjzKYyfJAZp6JiLuHr0/sN5dUr/UQOnp00M2yuDgI87aFU9260LiOwSyY+i0vL+fq6mojf1tS2U6d8oK0mYg4nZnL415zP3RJRVmfdrnen70+7RIM9a20b+m/pE5z2uX0DHRJRXHa5fQMdElF6cqc8CYY6JKK4rTL6RnokorSlTnhTXCWi6TidGFOeBOsoUtSRxjokjQDJdwgwy4XSdqhUhZDWUOXpB0qZTFUNwK9hLaOpN4qZTFU+wO9hPttSeq1UhZDtT/QS2nrSOqtUhZDtT/QS2nrSOqtUhZDtT/QS2nrqAgOp6gpJdzquP2BXkpbR40rfTjFi43mrf2BXkpbR40reTil9IuNusFb0Kkzdu0ahOWoiEEzuElLS4MQH3Xw4KB5LlU16RZ07a+hS0MlD6c4dq86GOjqjJKHU0q+2Kg7DHR1RsnDKSVfbNQdbs6lTil1H+31Mh09OuhmWVwchHmJZVV7GehSTUq92Kg77HKRpI4w0CVdoU8LoLr232qXi6TLSrlRQx26+N/qwiJJl/VpAVRb/1tdWCSpkjoXQDXd3dHFxV4GuqTL6loAVcLeNl1c7GWgS7qsrgVQJWyk1sXFXga6pMvqWm1bQndHySuLp+WgqKTatXVAsgQOiqq3mh5403hd7O4ogYGuziph4E3jdbG7owSVulwi4hbgs8Bu4P7M/PTI6yvAvcOH/wf8aWY+Oek97XLRvNmsVxftqMslInYDnwNuBQ4Dd0bE4ZHDfgz8Xma+HfgUcGJnRZZ2roSBN6lOVbpcbgTOZua5zHwFeBC4beMBmfndzPzp8OFjwIHZFlPavjrmGdtHr5JUCfT9wPMbHl8YPreZDwNfH/dCRByJiNWIWF1bW6teSjWujcE174E3++hVmiqBHmOeG9vxHhHvYRDo9457PTNPZOZyZi4vLCxUL6Ua1dbgmvfAWwmLY6SNthwUjYjfBv4qM28ePv4zgMz865Hj3g78C3BrZv5wqz/soGh7OLg43q5dgwvcqAi4dKn+8qgfdjoP/XHg2og4FBF7gDuAh0f+wCLwEPDBKmGudnFwcbwu7gWidtsy0DPzInAP8CjwDPDPmXkmIu6OiLuHh30SeAPw+Yh4IiKseneIwTWei2NUmkoLizLzkcy8LjPfnJnHhs8dz8zjw3//SWZenZnvGP6MbQ6onQyu8VwcU7Y2DuTvlCtFtSWDa3MrK4NxhEuXBr/rPCd9DKyq2jqQv1NuziW10Ojt02DQavJCO9DlgXw355I6ximTk/V1IN9Al1qor4FVVV8H8g10qYX6GlhV9XUg30CXWqivgVVVXwfyr2q6AJK2bz2Yjh4ddLMsLg7CvOuBtR0rK/07Hwa61FJ9DCxNZpeLOmvaedrO71ZbGeiamyaDcdqFJX1dkKJucGGR5qLphS/TLizp8oIUdcOkhUUGuuai6WCcdmtbt8RV6Vwpqto1vfBl2nnazu9Wmxnomoumg3HaedrO71abGeiai6aDcdqFJX1dkDLKmT7tZB+65ubUKRe+tFHTA9qazEFRSZU1PaCtyRwUlVRZ0wPamp6BLukKTQ9oa3oGuqQrND2grekZ6D3gjAVthzN92svdFjtudMbC+t4k4BdUm3Mnx3ayht5x3ntS6g8DveOcsSD1h4Hecc5YkPrDQO84ZyxI/WGgd5wzFqT+cJZLDzhjQeoHa+iS1BEGuiR1hIEuSR1hoEtSRxjoktQRjd3gIiLWgDHb6HfaPuClpgtRKM/NZJ6fyfp0fg5m5sK4FxoL9D6KiNXN7jTSd56byTw/k3l+BuxykaSOMNAlqSMM9HqdaLoABfPcTOb5mczzg33oktQZ1tAlqSMMdEnqCAN9xiLiloj4QUScjYhPjHl9JSKeGv58NyKub6KcTdnq/Gw47p0R8WpE3F5n+ZpW5fxExE0R8UREnImIb9ddxqZU+G69LiK+FhFPDs/NXU2Us1GZ6c+MfoDdwI+ANwF7gCeBwyPH/A5w9fDftwL/0XS5Szo/G477JvAIcHvT5S7p/ACvB74PLA4f/2rT5S7o3Pw58DfDfy8APwH2NF32On+soc/WjcDZzDyXma8ADwK3bTwgM7+bmT8dPnwMOFBzGZu05fkZ+hjwZeDFOgtXgCrn5wPAQ5l5HiAz+3KOqpybBF4bEQG8hkGgX6y3mM0y0GdrP/D8hscXhs9t5sPA1+daorJseX4iYj/wfuB4jeUqRZXPz3XA1RHxrYg4HREfqq10zapybu4D3ga8ADwNfDwzL9VTvDJ4x6LZijHPjZ0XGhHvYRDovzvXEpWlyvn5DHBvZr46qGj1SpXzcxVwA/Be4JeBf4+IxzLzh/MuXMOqnJubgSeA3wfeDPxrRPxbZv7vnMtWDAN9ti4A12x4fIBBbeEKEfF24H7g1sz875rKVoIq52cZeHAY5vuA90XExcz8Si0lbFaV83MBeCkzfwb8LCK+A1wPdD3Qq5ybu4BP56AT/WxE/Bh4K/Cf9RSxeXa5zNbjwLURcSgi9gB3AA9vPCAiFoGHgA/2oFY1asvzk5mHMnMpM5eALwEf6UmYQ4XzA3wVeHdEXBURe4F3Ac/UXM4mVDk35xm0XIiINwJvAc7VWsqGWUOfocy8GBH3AI8yGJV/IDPPRMTdw9ePA58E3gB8flgLvZg92SWu4vnprSrnJzOfiYhvAE8Bl4D7M/N7zZW6HhU/O58CvhARTzPoork3M/uypS7g0n9J6gy7XCSpIwx0SeoIA12SOsJAl6SOMNAlqSMMdEnqCANdkjri/wElRT6PIwfQEwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from scipy.io import loadmat\n", "pointsClass1 = loadmat('KernelPointsEx4class1.mat')['PointsEx4class1']\n", "pointsClass2 = loadmat('KernelPointsEx4class2.mat')['PointsEx4class2']\n", "\n", "\n", "plt.scatter(pointsClass1[:,0], pointsClass1[:,1], c='r')\n", "plt.scatter(pointsClass2[:,0], pointsClass2[:,1], c='b')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question II.1 (3pts)\n", "\n", "Start by completing the function below which should return the value and gradient of the hinge loss at a point $\\mathbf{x}^{(i)}$. What is the gradient of the hinge loss?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def HingeLoss(x):\n", " \n", " '''Returns the value and gradient of the hinge \n", " loss at the point x'''\n", " \n", " \n", " \n", " return value, gradient" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question II.2 (7pts)\n", "\n", "Once you have the function, implement a function HingeLossSVC that takes as innput a starting weight vector $\\mathbf{\\beta}$ and intercept $\\beta_0$ as well as the set of training points and a value for the parameter $C$ and returns the maximum margin classifier. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def HingeLossSVC(beta_init, beta0_init training, C):\n", " \n", " '''Returns the maximal margin classifier for the \n", " training dataset'''\n", " \n", " \n", " \n", " \n", " \n", " return beta, beta0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Question III (10pts): Robust PCA for video surveillance \n", "\n", "Principal Component Analysis (PCA) retains an approximation of an original dataset $X$ by focusing on the largest singular values. Such an order $K$ approximation can be obtained from the singular value decomposition $\\boldsymbol U \\boldsymbol \\Sigma \\boldsymbol V^T$ by truncating $\\boldsymbol U$ to the first $K$ columns, retaining the $K\\times K$ diagonal matrix $\\boldsymbol \\Sigma_k$ as well as the first $K$ rows of $\\boldsymbol V^T$, $\\boldsymbol V_k^T$, and writing the approximation as $\\boldsymbol U_k \\boldsymbol \\Sigma_k \\boldsymbol V^T_k$. This approach is particularly efficient when each of the feature vectors (or images in this case) are close to each other. When there are sharp variations across images, such as when an object appears, move throughout the images and then disapears, a simple PCA does not suffice anymore and one might want to extend it to something more robust. The escalator sequence below is an example of such sequence (the movie can be found on github). " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(20800,)\n" ] }, { "data": { "image/png": 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MSTMGC29rtRpKpRIAyELyWp1OR1IuLMsS051ChK4or62TCk3risykXcNGoyHVAeZPMBiUgIEG7FmWouvwWGPK0DsDEGQwgsXEVDS2oucVGMyyf0IfHJkpD8OIygrYt+RjsRhisRii0agUmedyOVSrVeRyOen+4vV6EY/HEY1GpR3TW2+9hdHRURFy/X4fpVJJciG/8Y1v4MaNG5iZmQGwHzT72Mc+hsXFRfzu7/6ujIWpHNoIYKCs0+kInszXDqO/NgJNYwW0PrSfr4uGTRyKZILmJJ113+12kc/n4fF4BgSa7s5hhsSJWehr6i4evAaZy7YPkj8Z/WSGtik8aJmRabRWNMlMsTAjpPo7OnTP0itWQ7CelblupCcu5wdDTliV5m3ND+yOMTU1NVBL7PV6kclkJDeRba/MxouFQkF4KBqNCh9WKpUBfI0CMJlMIpFIoFKpIJPJ4NKlS1hdXUWj0UAoFBKLjNdgtJ5K1OVyIRQKIZFIHGku/loJNG5+n883EILmxtPYkCnM9HVMk5iahQKtUChI3SULeMkoTvgTzXlel66ptqa0QOPnSToAYbqmOi9OC1aSUzTXzB/T39W5SDoiy+RL1rW2Wq0H6gafuJwfDOl5JS8ykk5lxPdGRkbg9/sxMzMDn88n1Se2baNQKKDT6SAQCKDdbqPZbCIUCmF0dBTdbheVSkXK6jweD8bGxgRmqdfrorxYxxwKhRAKhSRCWi6Xce3aNaysrAj0wvFb1n67+nq9jkqlIvuTbbGeCLR3iAKIrYHNin8KC/0zLGxMZqH5q79PQB8A7t69i62tLdy8eRPA/mamMOL/GqejQOJ7pvVIMs8Z4Of5m9qRlpX+WwtcHcl0yhczhRpD7VpgMh0FOLC86KZ6PB5JE9EuqLbWntD7R/3+fm89n8+HeDwuln6lUkGj0RBBFo/HEY/HEQ6HhV9cLheq1SpqtZoIwUajgUQigdnZWXH7KpUKPB4PksmkXF+3Q6IQZaPSQCCA27dv4/r163j99dcRDAYRDAaxurqKWq0m+49j4Djy+Tx2d3cB7PPO6Ogo5ubmMDU19UC7Lif6mRNoJsCtQ9IaK9Ob3skiMYWJTmUwrTszYkl8iYsFHFhKlmUNFIN7vV4EAgHEYjHB0DjmcrksyYhmsqrulGE+g35OCi+dGjIsdYPf0e+bgpGfYWBDC0WdTW4qhWEW7/tB5vM+rnRUnOtRiBgnO63omkquWygUgt/vl+4Wo6Oj0kCUAsv0Evg3+Y73obXGqD3f9/v9GBkZQSKRkMglcd1KpYJgMIhoNIp6vQ6Xy4WFhQVEIhEpfeJ+MWuRqQiPisH+TAk0LbQ0wKgxL51gqsuSdFRTb2p+n9qCCbJ6E3U6HRE6uoCX2BjNfuJLLP3o9XoIBAKYmJjAL/7iL2JpaQmjo6PS+fO1117DrVu3cOfOHcnvIWngnQKSz8xrsIe/Fkx6nugq6kirFtx0awn2AwepI91udyA/ibiJuWmd3KFhQRbSUUP0fC6mtTjVpT5OpAX+o2xSYPic+P1+pNNpxGIx+Hw+7OzsyLrz98TEhOBkxDtzuZzgq7TuiFv5/X6xlPheIpGQvxksWFtbw+joKILBII4dO4Z4PI6ZmRlZh1QqNdBGaHd3F81mE8lkEv/kn/wTdDodZDIZrK2tIZfLDURMddG7zo97GP1MCTTiY51OB6FQCCdOnEA4HJYFoiBhsbfeWNvb29je3kaxWHwAAAcwoKECgcDAe6lUCvF4XLKjq9UqMpkM1tfXH8C1Op0Ozpw5I67B6OgoEokEYrEYbNtGNpuVTUmzf2NjY+D8ACcsSgP5+mwDki6zeuqppxCJRBAMBkUY379/X+amWCyiXC7j9OnTcLvduHfv3gPheW11aS1OgWi68Nq91mNzsuSc3tOkBRlPGmJQhIrisHY/phVvWo7vJon4YWTe82GfHRZRBw4ggNHRUckjK5VKsG1b8iAty0I0GhUhxOfkQTvAQeUJMVFGL4vFolhJnF9GyRnFZFAgHA4jFothcnJS8DIKzbm5OYyPjwvOxtZWXq8XFy9eBADBXokBc93Mllacg4fN3c+kQOv3+4hEInjmmWeQTCYRiURw9+5dEQozMzOYmpqSzGcAuHLlinTL4IRqokCjUNOUTqdx4sQJjI+Pw+fzoVgs4vr169jZ2ZFNpi2TU6dO4fjx4wPnAYTDYdGcfJZYLAbLsnDp0qWB/DanzaFdw2FYm9vtxsjICJ566imk02mEw2FhNGDfep2dncXNmzeRy+WwsLCAkZER7O7uSlKttrb0tWmdajdUu8mmpXhYYu5RyLIsmTu/3z/Qy0xDCTrI4yQ8h6UBvF/uq14ffe2jft4JAmFaTTgcFkC/UqmIl0DFEYlEEI/HB7BLnuHKhG+d5gNArCa2x+aP3+9Ho9FAuVweEJiJRALpdBrj4+NyTB/HzHQN3rfRaKBUKqHZbOLKlSvSfl5XpOimmiaMosc5jH6mBBqjipOTk3jmmWfwpS99CVeuXMHKygq++MUvwuVyYXl5GWNjY4hEInjttddQLBaFIXSWMrvNknTyKgUAqVQqYXd3F08//TTGx8dRLBaxt7c3kEbhcrkwMTGBc+fO4ed//ucxMzODP/qjP8Lc3BxeeeUVbGxsoFqt4plnnkEmk8HVq1fxyU9+Eul0Gqurq1hZWcHt27ePnGjopM3IfL/wC78At9uN//E//geee+45nDt3DhMTE2g2m4hEIqjX67h37x5efvllhEIhCXJUKpWBfDQSXU++zkRMc+PqVBOdnKs3rR73MACYgoqRsm63i2AwiMXFRfluNpuVM06ZCKqt9MME1vspzPQa6CjzUa/Pa9D64eEinENaP7a9X4oUi8UGTmMC9qtQgP2gDT2GZDIpsEI+n0c+n5d5icfjgscxv+zWrVuiABYWFhAMBjEyMoJAICDtsIDBE8XI+/q54/G43IOF6oQ2eH3dfYYBON0k8jD6mRJoJBaBT05O4q233sLu7i4ikQhGR0eRzWalhiyXy0lEpVwuP9C4TpPGzMzyoWaziWKxKG2yuUg6WZW1nKlUCpFIRPAOgqL6kJNcLodyuYxgMIh0Oi2ArxYc3ChaCGv80In4TPl8HsD+pu90OuL2tlotAY1drv3jx0Kh0EDElffWY6ELpF14PYf6NW09OQnjYS610+d0oCIYDGJhYQHAAaZI7GZkZEROHjLv6XSfDyqw8KjXpaVlZvSbz0Frila95gMKBnod/JzGR3mICXFaPVe6zTZdz1gsJpFMCkUKShNrNROrub7EE/XrZi814AB3PIowA34GBZoG7wHg5s2b+MY3voHPfvazmJiYgMfjkVYmP/rRj7C6ujrAOMBg73R9XQAPJIsC+wKiUqkIfqHBaQ20xmIxxONxlEollMtlfPvb38bOzg5OnjyJy5cvY319HT/84Q/h9/sxNzcn12OElC6GFl5awPF1yxo84YhUq9VQrVbx5S9/WRhxbm4OExMTA2dVUhjR+tEAtg4oABjQzIx+MWBA4a+1tulCmXl5psB2IgZXeK1wOIzjx4/jV37lV9BsNlGv1/GDH/wA29vbaLVaskG0IDWj2preL4H2flh64XAYgUAAoVBIvANek1ZbKBQSIcODfqmser2eJLASUhgfH8fy8jJyuRxu374t96CgCwQComCz2Sz8fj+effZZpNNpJJNJ2S88vUlb0nrtnKxvttdiEm673ZaIKpuYsscfhSiVOa95GP3UCzTTUjEz/rkhKeX7/f3C21gsht/8zd/E7u4udnd3sbq6ivX1dXz605+Gx+PBD3/4w4GNxnIfRg81RSIRpFIpMePfeOMN1Ot1fOQjH8FTTz2FeDyOXC43kF/GxaLg9Pv9GB8fx5e+9CUJcSeTSSlmZwKk/uGz62itDrubRGHT6XQwPj6Oz3/+8zhx4gTm5+dx5coVWJaFpaUlfO5zn8O5c+ewtLSEVquFmZkZVCoVbG1tifus50WTadlSsAEYwHiYpGu2NdKWnolVatL4GLPL2Z+eCktH8fTZpfqEK00mLnhUgaSFLy2c+fl51Go1FAoF2cT6GfX88Vm0UqJSDYfDkgLB+eQah8NhEUJMy9je3kav15O54/P7fD6EQiF0Oh3cu3cPmUxGIIZwOIxQKCR8RsgAAObn56WjBo9apFJwAu71vOr5JO/RGuT/XC/LssQTCYfDA/MZiUTErf5rIdCoMYDB05+1yauz+UOhEObm5vAbv/EbqFaruHr1Kl599VXU63V88YtfxOjoqIS/Saxxq9frqFarA2OIx+NYWFjA2NgY3G433njjDSQSCbzwwgv4tV/7NczMzODKlSvY3NzE3bt3ZdzUPm63G6FQCIFAAP/4H/9jBAIBdDodbG5uYm1tTTodaGGm8Sj+bbqceuNYljVQNTA2Noa/9/f+nkRm33rrLXg8HiwtLeHkyZPCpDs7O5iensbGxoYjLqaZ2em+5me73a5kjlvWQUkVn4P1hGY1hCbmLGmBRrff5XJJjhQBbwYOmEPFKJ8TH2m32Kxy4N8m6cRoj8eDUCiEc+fOYW9vbwDr4zOyYQDHrnFWuvA8ezUUCmFkZATlclmuz0oXHnVIATYyMoJMJgOXy4Xp6WkRkiMjI4hEIpidnZVM/Wq1CrfbjXg8LrxXLpclCspo/uLiIuLxOMbHxwdOKONcmDyh/6ZVDBwINOaZaUXGpHR2kDEbI/h8PpnDh6W6/NQLNE1mVIsMQixge3sbr776Kv7wD/8Q5XIZLpcLMzMz+M3f/E20223cu3cPv/M7v4NAIPAA49LcN/EzAHJWwJUrV1AqlbCxsYGdnR1sbGzgjTfeECssmUxiZmZG2vIQv7BtG4uLi/B6vbhw4QJu3LiBP/qjPxoIY9Pl0MJMP59JJuZAV5JjWVlZwT/6R/8In/rUp/DSSy+JW3bt2jV885vfxGuvvYZ/+k//KQKBAPL5PBqNxgOC5Ki4BsnJnaTrS9CXuA8jcE5kWgBMP6hUKhK1LZVKUqrDa+vuJno8es4okHRlhN7AVHJm1JKfYwSSSazBYBClUknWjpa++SzAQWPFWCyGsbExzM/PY319XWqDmULBRNl4PA5gPzK5vr6OSqWCSCSCfr+P9fV1TE9PY2pqCgBQLBbxJ3/yJ3IvtgqixcWSIwCYmprC/Py8pF1QAWkLSUMQIyMjktbDLAHt2tNDotDk55gxoOs2dfG8bdtiMbK8SgtCJ3rXAs2yrFkA/x8AEwD6AL5i2/a/tywrAeC/AjgG4D6AX7NtuzDsOu8naX+dvjgZjKa6bdsyORsbG4KxAPsA6fLyMkZHRzEzM/NAhGpY6QUb4W1ubmJ3d1cWoNfrIZPJAIBUAczNzQ1oIGpsug/b29tYWVnBj3/8YwFIp6en5bk0hvYwrMlpnKzBazabuHr1Kk6ePIlnnnlGXOFSqYR79+7h4sWLKBQK4hZqN43MbLqfDyOn8fP7TgGPh6U36E3T7XZRrVZFoFFZUKs7uZAU8vyb4xkGROvAhh4j3SbtNnJuaIEzWZlWqmnZ6KALcaxEIoHNzU0RouRpJnfzProVNmse+/2DU5eI75bLZRGyPKCaFmS32xWXb2pqChMTE0gmkwgGgwAgwQGNeeo5MFN09PrRYtdWF7/PZ6Iy4fybrrg5T8PovVhoXQD/0rbti5ZlhQG8aVnWnwP4nwB827btL1uW9dsAfhvAb72H+zwysZ3JyMgIUqkU5ufnMTExgVgshp//+Z+XzOp/9s/+mTAxzXxugr29vQcYephlwjYsFy5cwOrqKkKhkCwmXTq6UMRFmH2dTCYxPj4uQOjOzo5EITkmninwKMKD2l4D4KlUCpOTk4Id/ot/8S/kpHYCvLTEXC6XpDtUq9UBoP/dZuJzPPoMR24qMzH3sMgWhQg3DxM+V1ZWZIPqYmkzN0+TDk7wf1qhLNPRAimRSAxsTLqwbKBJ4ZrL5dDv9xGPx7G1tSVRY16Ph+XoJF7Oh23b0q2FEWd2s6BF4/f7sbe3N1BaND4+Dtu2MT4+jmeffRarq6vY2dnBpUuXYNs2pqampNh8dHQUtVoN9+7dE2X1sY99DOPj45ibmxMMkgm7GsLR89FqtYQ/AEgeqI56hkIheUZWsfT7fSlg5xowWu71ekXIMnMgHo8jEomg1WpJZoITvWuBZtv2NoDtd/6uWJZ1A8A0gL8D4JV3PvZ7AL6DvwKBZtu2CIBqtYqdnR1cvnwZwWAQH/nIR1AsFrG7u4u//Mu/xLlz53DixAm8+OKLsG0b9+7dQz6fH7AciL8Qo6Dm1K8B+8KtXq9jd3dXus7SpaDVwc2bz+dx48YNTE1NIZlM4qWXXsLExARqtZqcdh4Oh3H69Gl84QtfkM1+//59Kdx1wqzMqCff01of2O9Hlc/nsbm5iX6/j5//+Z/H9PQ0qtUqbt26hW63i4mJCbTbbYyOjqJQKMiGtW1bcpKGBR0eRvyOzqMyI58EuNmCyEkIaaur3+/LaVqrq6uC0+icMwZUzNQC8g1/a2tLW3T6vXq9LlYY76+BdD4XrVvLsuQcCVoeTniQyXvlchnb29vodrviFrrdbjSbTezt7aFQKMhrqVQKwWBQkrrL5TKuX7+OUqmEarUqnTXi8ThqtRrq9Tp6vf0zMSk4mVfW7Xaxt7cnXoaZVwZgAPLQQTjynU4j6fV62NnZketwb/B94MD60229eG/dcKHRaHxwLqcmy7KOAfgQgB8BSL8j7GDb9rZlWeOPcB28870jf14zJIt0iWP98Ic/RDqdxssvv4xMJoP79+/jT//0TyWJ9qWXXkKn08GtW7fECiLA22g0BLfgJNLaIr7Ce1erVaytraFarQrgqZ+Ff2ezWRQKBal3e+WVVwDsJ+bevXsXlUoFzz33HNLpND784Q+j0WigWq3itddew+bmJnK5nCwuhaSuV3WaS00UuMvLy0in0/jc5z6HXq+HQqGAq1evCp7XarXg9/uRzWalegKARNsINDut1WHWm3YvtYWj3T1uBgAyHtNN1HWq3Ji0LnVOFa1BCuRhAk3jQlqImhHPXq8nOBNfM11ICrRsNivAOjtcEHSnQNP30T8sP6KADgQCkkbTbDZlDCyZm5iYgN/vh9frRblcRqFQwP379yX/7tSpUwiFQgiHw5KuoYXI+Pg40uk03G63KD3CK05RXx2A0y42PxeNRmU8zWYT6+vr8ry0OLWVzvNnKSiZ16bXt1qtolKpPJDUbpJ1VOEx9AKWFQLwFwD+N9u2/9CyrKJt2zH1fsG27bjD974E4Evv/Pu86WIMyxI3I3vaCmH0x3ongphKpSRRlBu1WCyKS+r3+2Hb+/Vv1GxaEzMLWuMGNNe5aZrNpnyOjKqZlUyvtRqxjXA4LAvGDh08KV1bdtlsdsDc126ZDuNr0smTmtxu90ChMce3tbWFTqcjJS7EY9xu9wMVD5xzameThvGU7upAS4rMrF1yamrt3vKaDEywhEYHShgh1Z1OdCKq7nln4jwmf+n50vOrcSITM7IsSyydWCyGZDKJ6elpmWfWSOr+eJp0Wg03ts4No6vJde319k9Uun//PmKxmOSShcNhAfSj0ajcr1qtYn19HYVCAa+88gparRbeeOMNrK+vixtnPpe2Rs150r/pIaVSKSwsLODUqVMA9pX1t771LdTrdTQajQfwMl5b39fE6bi+1WoVnU4HjUbjTdu2P+zEY+/JQrMsywvg/wfgv9i2/YfvvLxrWdbkO9bZJIA9p+/atv0VAF955zq2nhz+PQzzMDEWE6C1LEtAfxanM3ufUSBKe61duCHM+zJKRq0zMjIi1hhBc21ya0GiF4fmNJM/ydQ6mqf/5nV04zwNShNQNcFWflenB2hiCoAeIwULW4R7PB5JAWBpCwUNv+NEpkWlyRR+elPotdfPqF1+zqFp0eh7O12Pa2oKR6dxmgLKtA41dndYxBSAYESMmuuuJVRWTvOlBRsFGBUQgwwARKCXSiVRBEyynZ+fx9TUFKLRKJaXl0UZjo2NIRqN4tixYyiXy3C73ajVashkMocaEU6klRsA8ZCIwZL3ye88WJuWs97LlnVwxoZ2x7Xi1k0hh9F7iXJaAP4zgBu2bf8/1Vt/DOA3AHz5nd9fO8r1NHOYTOVw7wcmg9cgE/AzCwsLWFhYwHe/+124XC4sLi4inU5jbGxMIkW9Xg+3bt3C7du3sbOzI+F3+u1Mmv3EJz4hn7948SIymQy63S4ikQjGxsak42ev1xuwkCgwWDZy8uRJKRqmIKJ7lUgk5DlYtEs3YW1tbQBroYB0agbJCKkm7VqZZG4sRtO4EU2BOYzJDwsa6CgxNyytPNPt4xxoAaJdvGH31QpECyDzGd+tZ+J0b5LmS0YiA4GAWEnZbBbFYlHwPdP95XPTRQb2Gx9EIhHEYjGBJqgM2UVjbGwMs7OzSKfTmJ+fRzqdxpkzZ6R9z+/93u/Btm28+OKLeOWVV7C0tITNzU0UCgXcvn1bOsSakdfDiNavJip7ClxdZfJuA0mPSu/FQvsYgP8jgCuWZb31zmv/C/YF2Vcty/pNAGsAfvUoFzPdR9PsNaNN2hUwtSMnNplM4qmnnsL58+dx/fp11Gq1gZOggX0tOj4+jnw+j/X1dalRo4DK5XKYm5vD9PQ0ZmZmZLHa7Tb29vbwxhtvYH5+Hi+++CJ+/OMfDwC2ABCLxeB2u5HL5RAOh5FIJLC0tIRUKiWaU7szHBcBeoLzjUZDXBENyFIAmMmsdOk0OblJJH3iOzB4LN5R3C2SaQWZY9JCSeNJ+jM6H00LKS30nK7vNCZTUQ4b27shEyfVLppl7afA3LlzR6LerBpgBxb9eY7VxPG4jjz3kp4BXXTyaiqVQjQaFV4pl8uIxWIYGRnB3NwcgsEgTp06hW63izt37mBrawtbW1uHtlnSz3hUhWZaxg+7/mH0br73XqKcrwMYlhTyqUe9HgXWO9ceYD4yOBPw+Fu7H1rg9fv77YNOnTqFl19+GS+++CL++3//79IxghYYgf+lpSVsbGwMJC2+8MILuH79OorFIk6dOoXFxUXMzc0N5HJtbm7irbfewokTJ/DLv/zLEorP5/Mybh4s3O12EY1GkU6npbsFGzeamBgtr+PHj2NsbAx37tyRBnicKz43LbSjpHToDWOspdQIcg04j8DgOZ+6vtOJWZ1cO31/4EBYUqBpoc550ImtpoZ3Elxa0Or7O43v/SCumdM1aT1ns1ncvXtXMuDL5fJAzhp5ROOl5rOxXx1rM2u12oAgDAaDmJ+fRyqVgt/vx7Vr1ySSyfMz//bf/tuYnZ3FqVOncPHiRdy6dQv5fB57e3tHEjhO7j1wEBQgmV6VttA45qPSu12nx6JSgDgN85wI4FOTEz8gnqAzi/l9El0V27bl0AUekFqpVFAsFlEqlXD16lVJWl1aWkI2m5Xwsj723rZtifq8+uqr0sPpk5/8pJSeNJtNZDIZETjUwMViEZOTk2LOEwTf2tpCuVzG17/+dTl0gs8RiUQAQFyK8+fPY3NzU07k0fgZ4Nz9g/QowoaCRWNkGquh+2Zmz5tkWhjme8CBQNPpEbqLr6695Zh13SB/mxvNSbBQSGss7ijuj4nLckOyHrTf70tXCvIc14ElRcxn1G42v6tTV4ZhicABFMH5YJ1vIBBAOp2WE5HYIOHevXvwer2YmJjACy+8gJMnT2JychKNRgNf//rXsbW1hUKhIK6hBuffDXFeuC6EWYjHsnpDz6H+nrluFO7aOzMDEIfRYyHQgAcLk/lQJlY0rG5RA7jc5NVqdSCUzwzyer2ObDaLZDKJWCwmuVas0fR4PGLiU6DV63Wsr68LXqatCJr4OoLFU5uYIkJrkAmDdLkYPqdLmc1mpQ8V6xGLxaIkVuoFNzeEpsOsk2HuIAUHn40bX29E/Tmn+zpZGeaYyNy8Bv8GIAnGtD55zWGurpOFoPlBW/B6k+jPH7ZRtJtLXqQA0I0GNP8RQyM/cz4ZbSdEQCBc34tzrgNVhFiYo8e2TmyJZVmW8DfPqBgbG5N0DJfLhWazKYq01WrJ9/S6PIyGza9JGlLQXYQPu4e+linEHkWoPRYCjRqaf9OaMV0KnShpLoIGy3u9HqrVKrLZLJ555hmcOHEC+XwehUIBrVZLAO+Pf/zjWFpaQiAQQKvVQiaTkcLllZUV6dZ54cIFhMNh/M2/+Tdx/vx5PPvss3C73VhbW8Pa2hrS6TRu376Nra0tyd3iBr106ZKMf3p6GtFoFFNTU1haWsI//+f/XJ77z/7sz3Dz5k2srq7izJkz+OIXv4gTJ06g2+3i/v370gBSC3D9zMPmVdNhTKFTTlqtFur1umxYnUKh87+G0bD7aEFmfpbCjZuTYyExwkxcTQsCbi4tsMwNAmDAqtXC9TAy+YzHvLEkiLxGAaSTSonlnjt3DqlUCrOzs4KDMQWB2KUW7vrZmK5htn0HDrrAZjIZJBIJnDhxAq+88oq0G2q327h58yYKhQL6/b4UvHNs9C5YJvYoZAozLXSohFlPy5QkAA+46VoRkJwsNCfr1YkeK4GmGU27BToSpidg2ANqt4oZz7SMer2eMN3Zs2cxMTGBS5cuSc2cbsVDa4Rm/71796TJ3dmzZ6VsQ3dwcErjoJBlwu/rr7+OO3fu4Pbt24jFYjh27Bii0ShSqRTy+TzGx8dx+vRpbG5uYnt7WwSxk/B6N1iD07zp3C8zHcTMCdOYl0nm2j2MtFUDQLpxhEIhnD17FuVyGbdu3RIlpwXgUZ/R5BdzU2m+OwpRsHMcOkihFQ0tqnQ6jcnJScnID4VCUl2gcTUdfOFaU6DpiKI5Xrp6lmVJATdbZff7fSlN0i14COvoCLP2fEw6CgZGl5g/bPvzKO7su3V9SY+FQAMwgEGYxNfNKJ85+WY3BZfLJS4g3Txu2EAggI9+9KPweDz4N//m32BlZUUOV6F7S9yNgvGNN95AoVBAsVjE2bNnkUgkpDMtUxs8Ho/gf0yipZBjlGtnZwc+nw+VSgXnz5/HxMSEnJiTy+UwPT2N8+fP4y/+4i/wne98R9JDmMYBDAqyYcw27DUnbaeFl6kVtUDT+VNOdFgRvxPxOsQZW60WQqEQxsfH8eu//uti+fJwDloqvL5pJTg9tx6rmerD981I6jCiAtOHPg/zFIi3MkLOdWIElzgrIQodEOHfFGgcp2lVMkiWyWRQLpexu7sr7idbCjEBPJvNyvVGR0cF5uC6Os2LOX+Hkdt9cI7B2NiYPKMuNn9UMgX3w+ixEWiAc2IkmUZrEuISprmqF8RJ8PFa1IiMwrDnGPPUZmZm8HM/93N49dVX8Y1vfAO/8iu/gmg0iqtXr8p5BPy+7qhJ14GF3pZl4fOf/zwmJibwxhtviNn/sY99DOFwGP/5P/9nyU2zrINDV3u9HvL5PDKZDAqFAiYnJ8UVIWNooFnPHUkHDvT8DmOswzQjLU6NoR1m0TyKhcbP6uz3M2fO4Ny5c3j66afhcu339mKJlonHmNbXYe63tv7JK1QSOv9tWOBE86WZVmQ+EzPzM5kM3njjDSwvL4tS0h1YWZ2isTbN+7pbh34G/R1d+xiLxaQVN3mTwo3KmvdgsrkJY+jnfRRhQiw4l8vBsiyJYjuVnH1Q9FgJNE0mLmIyGidIT7RO5WDRLdMwkskkSqWSlBFRIPR6PalxpFYNhUKSZe1yuTA3N4d0Oo12u41gMIhEIoF2u41GowG/3y/Z2WNjY/IaNV8ymcTU1BQSiYR0rFhaWsL4+DgWFhakEyiwL5yYLMnM6kajIdFUur5M3KW16WQNOVmw/O5hyaH6s+bcm6+9G43LtQUeFAq0jNPpNKampgb635sKzNwcR8VZ+H0t1HQajI6EHuZmmW6mORcai8xkMnIoL+sruc46idYUZoy46woNp3vTArIsSzp6EP/VAkz3nGOkVVuNR0n9MckE7Kn0aP2Z3Z1NY+UoFvGjCMLHUqCZZrW5YbWw06Q199TUFH7t134Nn/nMZ/D888/jt37rt3Dx4kX8u3/37+SzurkgwegrV67g5s2b+O53v4ter4d4PI6VlRWMjo7iX/2rfyV1ea+++ipWVlZw7NgxfOxjH8MXv/hFfPazn8Xa2hr+9b/+19jd3UWxWMSf/dmfyQEXtAhbrRYmJyfxH//jfwSwbwF9+9vfRjabxcLCAtLptERoG40G9vb2q8ecepLpDan7TtHtNefHtHZJTvlevFYkEpFrs4KCwL3JsByTExPy2jwPlKU73LjJZBInTpzA5OQkAOBrX/sabt26hRs3bghozaJ4faaAvq+T8B22gbS1pvuxcUzms9FKHrYJ9T0Z5WbaUTweF0uz1WrJmGKxmHyfSlBHmsmjus2O+cwul0ui8jr6zygjn4VRUPJLpVJBoVCAz+dDLBZ7IBDHZ9Jrp1+nEcAobCAQQCQSkRSsXC6HYrEoCl5Hd3lNpgeZwpT8pps9/tQEBd4v0qkdvV4P9+7dw3e/+11sbm5iZWUFa2trA67h97//fQAHzfC0pmY0lKczAcC3vvUtwZMuX76MTCaDarWKmzdv4o//+I/R7XYlUxuAtHthsIHA7MWLF6W7aKfTQb1ex+3bt6UPGjdFJpORsWir0nQLdM6WBs2dmJCfOQxf00QX2MRWtEtv0rANz2two/f7fYyPjyMUCmFiYgKTk5M4ffo0ZmZm5JxS1uHeu3cPuVwO1WpVQHATu6KF5eQ2aqtej8UM3tC6oTtnPhfX3yTelwKIn+E1WDDP9Sa/PYyo3J3ahvM5yGf0GsgnWvFx7XWXDSoUXVfppCT0PJLIj4yYMnOAlTY8/JmpRjrIZFraTnxHHntY7fAD8/Fu3Yb3k6x3itMf8TsPvMaJZL5Pu90eOCyVER9qC7Yh1gCqDjFTm+imh7yv2eSP9zI7RehIKd09nmhNhtJRUbpXDDbYti3312VBOh9PCxftghwmWJwYyOnzh13DyaI77L58T2ePv/TSS1hYWMDTTz+N2dlZnDt3ThQTT8i6f/8+vva1r+Gtt97C5cuX0ev1Hjg3lc9NjM2Mkus0EJ3vqPPLGE2kxW5aY6bnwNdoAbFcjcmue3t7WFtbw8LCAqLRKKLRqKRakAec5sd0hwEM7QNGV53NBXgSFHFcCmbmxvEgFB7j+N3vfhfBYFB63ZlkjkPPaaPREEyQZxy8/PLL0lz14sWL2NnZwdramigKp/E73ZfzrjvCsCNxp9P5YLpt/CTJadPoZD5+huY9mZiCyeVySQ80RnzMRE9OpNmyh+Y8sO8C0Zzne9wQHBOvQS3NLge655NOpCRgyzFoIceNqJNsNWhMBhlmbdFFcBJoR9GCGkB2wuO0xnW6P3Bwenen08HHP/5xPP/885IwSnyJOWeBQADHjx/HL/zCL+DkyZPY29uTjiDmfZmUq8fEdA8dedUCzVRemkec3B2nOeL66jNAdatrKhi6dOQfc+60QuLaPwxnogXDltrM1/P5fDLH7LzLNBJW3OigAPeBuWa6KadJzGnjeyMjI9LSXguvbrcrWPMwi97JArRtW4I2dNUfhv/+1Ao0J6JFpEtQTLcEgGxo3WKZuWrM99FWhAZTaToToCf2xjw6bgot0GzblpIZjT2YWA+fQT8LgAGmMwFh/jbBWSetyms4aUrSw9xFfU26HCYNA5j5WZfLJXgie2dVq9WB9kyEBrxeL4LBIJaWluD3+xGNRh2DIDogpIFv/Twck7agzTkDBku0TBfVjBzz8/w+N7g+vVzDABRomk9J+oBdjk9/ZxjRuuR9+Zvf56lK7OBCvNC07vX99Zpp4e50b83zFJJcP/I2KyWOClFw39BTcQqOONHPlEDTuWZ6A3LCdeoBtRlzxAAMWFba/SDuoN0s/VlOtO5bRq1CAckIpwZI9YJroUTm0kypGcJJWJlCzckl5evEPLQ25v/m65q0y31YnpmTa8bXbdtGMBiU5FkWVmezWTluzRQeDM4A++106H7wmtxA+vQhrhPnUhfT63V0aretm0PqORkmqHVeGd03BpsIf2jlxH7+ZtDBLIMy8UAn4rOzBbfOV2TaBJN3i8Wi8JVt73f/oDVKgWGWF+pqET0O5lgCB2kqxK15DzaC4GcZgdUYGskJutCKxePxoNFooN/vSwdlx/kY+s5jTFprOllgptujN6j53WHf1+kC1BLDsCf9Gxg8j1CPQSevAgeH8GqBpqNQWghTEJkCzenZAGcBZYbvOVb+doo2mZaMtiAOWx8nocjvEpTudrtYWVmBZVlYW1vD1NQUJicnpfmAZe3n5tVqNeRyOTm3gcmaulxKW0h8j3NH64JjMtfKKQXIxCpNBcHr8XMck87qpxIiH5ntk4YJfeBAYeighRNpr4QwBnDQIIH3pFDldXj+Ju+px8Wxa97Tc8Vn17Wq2ogwx8XPaytvGByh50EHVojTDbMUST+1As1p05hul958Tm4YXRLTKjHxBIK3Zr6S1rwAhnaIpaAiHWZlsTmlHh+ZRo9DC6JheJX+jP7hBtPjGHadfr8vhxzrTa/HZt6Xgtd8Plo8xEOKxSK+9a1v4cKFC+h2u3jqqaewsLCAWCwm1nOz2cTGxgYuXLiA27dvSya8Xh8t3M0zOOkC0SWl5UMrzSklSM+ZWUFhvseNys3PU5mAfb7RLrLe4E4tuDV2a9JhAs2yLLH2tDLVNaLayur3+yiXy6jVagP3pWWqAxNOitMU6gAcYQyNsfL+TjRMAXJsLLgfHR196JkCPzUCTU+gGQI28Qvzs8MwgMMAT3Py9YRrl0oD+07kxIgmMwwjrTlpdpu4x8OsIc3MpvAy78Xf+trMgdL30u7QMCvXaVNS2BDTcblcWF9fR7PZRLlcxuXLl/EXf/EXgqXxmDS6Z/1+H9FoVDabrsygBcuOJ1wXBmk0psY0GGIz5vhNwcUfKjDe3+Qtl8slrh+/w9OrKFw5tmF40DD3UkMcmrTQYF4g54X30kEy3pMYphZmXHdCHJwzKlMtFPV7AAbcXBJTSUKhEILBIEZHRx1z3WjFms/FMTPZXXfDHUY/FQJNb04ykCnUyDymQONnnQBPMqU5mYdF/LSQoaDh/06beJiwGaaxdD2qFhbDsJzDMC99LydLzHSh9Jj1XDOpU3/OxAD5PZ16YBI3urZOWRu7sbGBfr+PK1euyDrSIu33+5iamkIsFhs445Gbg33JdB87jkeD9LyWZR0kz+rAkaloTOGuI6CcW407adeIOKs+p1Lzx2G8Yr5nWviaNC7I59PBJzP4wM9pPtN4lXa/tTAftk84D9r9ND0MplLpg5Y1mcX3eny0us29PYweS4GmNxQZRTOPPgldu09OQDfpUcx4l8slJ51roqbVm9nU6E7P4vQaBbImDVJrAcn78PlM4eZ0H9OC0/+bQsVJ6OnPOLmWWoPqcXIdnIguJ9s1uVwufO5zn4PH48Hv/u7volgsyrmXrEekJfDRj34Uc3Nzcn6onutGoyGWCJM7aTHo2lMKXILneo4Py4Xi39oyYyKp5kmmnjDCx/mj1URrbVif/cMs7mGuaL/fF17VcAjLrhi91y4350HnuwGDDQq4r7SApJVmCjYaDD6fD+Pj49Jpo9VqIZfLSUAgHA6LUNPkFP0k33Ev8rs/NRiaCRhyYnWyKhlIg8ZOG1svkGnROPn/2uriZ4YJJ0ZIyRT6OtzIpoYf9qzDUh60haavo0F7Ldz0d4cJJv3MJnbmZPHpn8Py1syx6rUABgUFtTCTQAEMCHCXyyXuIwAp/uepU9T2FAhMizh27JjwSKlUQr1el8gen4lj4nh04rJ+Jv1bC21TiPJvfpabWltoJLppDFZQ4DhZYvramsyIpxMEwvd0Eq4pPEwBri1YCjHt/Tjdj99vt9sCD2hByu+yx55OY9Hj4LqbHhcxUOJnbNlFt/UweiwEGhlZTxongWAgNaB2H+jvmwJJYxs6rK0XjBPe7XalcFjn/ThpQ2IQ+rNkdFO4ajDfJG1VmqTBVSfLxynaxns5PbcTXqfHa17XZFy68vybpAWZ+bdOUNbvMbWFJV2jo6PY2NiQdjwulwuxWEyqKur1OkZGRpBOp+XE8GAwKOdyRqNRJBIJfP7zn0cqlUIqlcIPfvADXLt2DT/+8Y+lcaFuwQMctCoyFY4W0vpZiA1xHfhMOvGZ8xkIBATr0Za8njMAjmkbDyNaoXrtaR3yVHHyI4vetRtIoaOFH/cVcSzTQDAtQ9NlZKJuu91Gs9lEPp8X9z+bzaLdbiORSEgKSyAQEGOAVTLkP1q3tHB5fX43FotJIGMYPRYCzbIswUG0VTAyMoJwOOwo0DjxuqBX4yLasqDZTzBWg+u0AjUjczxOzK6Z3tSYTniUk9B6GIamSeMUxAFpDXCuyLgaL9T31mNywuK0IHNyvZysTK1tdXDAVAhacHMNarUaZmdn8fzzz8t5CalUCpVKBZVKZcA6oNanO0k3tNls4sSJE1hcXEQqlZLAxdzcHLxeL+7fvz+QDW/CD3rMJnZlYkt0t5zwH1NYdDodETLkaQoR3RVYR0PNeTaVKQUqS6r0ulHpsywoEAigUqng/v370vGC1lcwGJR0Ec5poVAYqGgweUVboBomIT9qy4ljoaDa3NxEs9mUfctUHSd3l1iZOa/kHZ0beBg9NgLNPJqOpmYoFJLJ4m8t/Kg52SSPQst0pbQ7qfENLdC0RiP4TDI367AIn2nlDMPQnLAIAEO1Nj9PptJuN8fA91n/5uTS0ILTjKSFolNpidO1tItqZoRzroCD6By1Mu8bi8Vw6tQpObgmGo2i3W4jm80OuJ3aGqZ7Qn6ZmJjAwsKCWN/dbhfxeBwej0fOwjRhAP7tlLKhn5e/dfDHBM8pdLWLSoFGHvZ6vSJEtAt7WLTOnGsKUr/fj/HxcdkndMkoVNiglCkZnDMdZGGBPLCfi0Z8ipaTSXzNTMa2LEusJyZEBwIBjI+PS44bO/PShWTxvDY8uPeAAxhAR1k5rzox+TB6LAQaBQijHcymHh0dRTgcHtioppTWWtQ875Cf46EjnCQujiY9gSYOROKm1cEACgOnJE+Ob1hEa1hQwolYDOxkbZnXJLM73ZPzqIWYFtBODKM/q+9jCmYtAFhwz7mhC2lZFj7zmc/g2LFjOHbsGNbX11Gr1TAzM4Ner4fNzU25FjV+KpVCPB6Xg0GAfVdkZmYGU1NT2N7elnWPx+Oi9HRlhUlOoLwWVlqoUdCbEAI/R8uTpXQ8ECcQCAxYNPrEqIdFpzVpOCGfzwuOtLa2Jh5KJBKB1+vFlStX4PF4MDExgampKcTjcWSzWezt7eHtt98WN5wWXbVaFdzPKaWCSkgbCBrT5bjYTZpngfp8Pqyvr6Pb7eL48eOYmprC/Pw8dnd3Ua1WUSwW5V7c8+FwWNaLwn9sbEyEJgv7D6PHQqDR3KQZrks5qK011qOZQVsDZGBTcOm0DX0NvXhmkMGJtPXCxeV1tCWgv++0cUycwpwLJzIBbrqcFNqawYZZaNr6pZWiNxivr0njYMMsT42zmOPXiZXElqanp5FIJAAcYKVaGekfj8eDSCQibg07SszMzGBsbAxerxfFYlGA8GAwKHlLuk22uQamUNbWpZ47/ezmZ8zr0pJiswLyHdebLpW2qo9Ctm1LorEObrEgnZ01GFWMRqMYGxvD9PQ0UqmURAhv374tOXj1el1OQOO4nXrokXSKFAWahm6orACIu10sFtHr9ZDL5SRyWqlU5LQzKgodLdaVHuQfc68eRu9ZoFmW5QbwYwCbtm3/kmVZCQD/FcAxAPcB/Jpt24XDruFyuaQ7AYUa26BoJiATaiYhgEiTXDOq9smpabRbq90ZXmuYSWsC39rHHyaEhgUFNHBv0jA3yLIshMPhATCYr/N5dBRYA7/6vtqi0q4Q59TEdfr9vnS30JaxjrqxU4mJK9q2LU0FmU4RDAZx/PhxeL1e1Go1mYvt7W3pB6etPFobbBpYKpUwOTmJz372s9Jza3t7G/V6HW63G2NjY4jFYpicnITb7RbLyczF4o9pmWuFpIUbrRetCLTg44ZlA0+eBNXv9yUoob0QBj5MftG/NelTn7jmZ86cQSKRwOLiIi5evIjbt2+j0WgglUrhhRdewNLSEiYmJtBqtbCysoJsNovV1VXs7OwMgPe0ZvlsJs9QcXO+tAek+duyDjrmMtDHWtJ6vY7NzU2Ew+GBbioa5tDYmnareW2TB53o/bDQ/mcANwBE3vn/twF827btL1uW9dvv/P9bhw7C40EikRAT3bKsARPfZDwmC+oop2k9aE1m/uZnTetNCyhz4jgWCjTTatRALT8PDM/8HhblHNYexQwEEEvi/fT9OTfmM2gLDcAAdqivY5JpHZgb2+/3D1gtGvj1+XxyYjyjXYyIdbtdOWhmbm4OAMSl4sHSwWBQ+tW5XC5MTk5ibGxsIDv/1KlTkv7BeywuLsLj8eD27dtwu91izZhragp+rikwCNJrBag/zzUwaw0pzDVuyOtT8XCuTKveiQc8Hs8A7/V6Pbz++uuCqaXTaSSTSfR6PSQSCczOzgpAXywWMTIygs9+9rNyrNze3h5WV1fxp3/6p+KG6s4e+tkpZEyrXycZ87OlUmnguxwr9xbXnc+jAyTaaKGybTabsh8JRR1G70mgWZY1A+BvA/jfAPyLd17+OwBeeefv3wPwHTxEoNF8DgQCwiys2SJAaEajtKupxjPwt97k5kbV75tuFplOk8nU+rraVDbJSds6uXD87DBrz+12D0ReneoldRRWR6T0NcyggPldk2n1NXSAxbRy+DwawCWIn0wmMTc3h4mJCbjdbiwvL0vCJ7P/5+bm0Gw2sbq6OmCl89Qibo5EIiFnPZCmp6cHgHNadWzmyYCS01xpTMaJV7Tw5v/kA9Na5nxxDbghCZto5UtLmNE77VY5NXNkonC/v59/12g0cOvWLRSLRZw8eRInTpxAIpFAtVpFKBRCMpmU9JRarQav14tnnnlGnrFUKuHatWt48803sbu7K8E1M8hl8oTJz3oPcj75efKn9oCo7Ii5cd4p4HSAhZYxvTDugcPovVpo/zuA/zuAsHotbdv29jsPuG1Z1vjDLkK3xQkf07gKmY3mvSmktEvFz2hcyenzTm6WCbZzLJrRTBPcSdM/DPR1EmgmM+tNw0iUttD0Z7SV5EQck2k1AAdZ/JphdZTJZGpdNaHXTCsgr9eL5557DolEQk7wBoBnnnnmAQG6uLiI733ve6hUKpJZT/wkGo0iHo8jEolgZmYGiURCBBjvw7FzTRlQSqfTA3xFHuJ9nVw5jRWR2ApHCxY955wjzou2shgQWV9fF55hm3EdXeS1dIMCvRacbwoqPnez2cRrr72GWq2GqakpzMzMDOSUMStAZwAEg0Gk02m8+OKL2NvbQzabxeXLlx8A3Q9Tsg8jnVmg58TEL8vlsnS/1TCTFvT0yh42lnct0CzL+iUAe7Ztv2lZ1ivv4vtfAvAlAAOFr2ZyH6U339O+u9Om1C6gTgXROWnv3F+u79QpwBR+phDQwlWb1NpyeVR8TW8M3oNjMedFBwP097nZeC29kQ8bFz+nhaGO0JmCkhteW4K00Pj/6OgoEomE1II6KSFeNxgMYmJiArOzs8hms+IaaWuWa6Vdbz0H+tk4Z+FweGBTmgJNW0Z6/cwx0lLUSbnkC22RcV60QORa6JQcAuZmram5pppMeEED9blcDvl8HlNTUwN7QH9P80a5XEar1UI8Hkej0UC9Xh9Yn3crxMx54xzpLABgsAaZbigDKkx90bzFtJmH0Xux0D4G4POWZf0igFEAEcuyfh/ArmVZk+9YZ5MA9oY87FcAfAUAotGozSxi5prpiaBgOizDHoCEi7VrpQMAwKDQA46ePqG1L7WjdsFoTWiB6+TO6uuZ72n8ydyc2iLUAtpkVn6Xv01lMGxMGvzWgk+7A2ZEj98zBQtf9/v9mJiYQLvdlhPhdZBHW0KNRgPj4+N4+eWXceHCBQHW2f+MqREcP0HlYZiWy7UfaEqn09KBQ99XB4RMd0o/G78TDu87IU74FteNuA//N2t/dZNJutYAEIlEEIvFHuBNPZfmuRNUHLRoyuUytra2EAwGEQ6HhU80T2hL58aNGyiXyxgbG0OhUBgwJjQ/vBcaJvhpLQIQXA3AQNddQgcaiz3KeN61QLNt+3cA/A4AvGOh/d9s2/4HlmX9WwC/AeDL7/z+2sOu5XIddLTUoWDgoF+73tTaEtEWiE7JMAF7c5OaAsMkc5O4XC4Bv4kN8R5awGlrapgw050O9BzwHvq++tl0twrdTsa06CjQ9Pw4YWHmmAA8MH8cl8ngwzA3EhWU271f7lQoFMRS04KJeMr29jZarRZmZ2dx5coVWJaFUCiEcDiMcDgsh4ywdlCX8Ghtz/ngM4+MjKBWq6FWqw3MpxOZAs2JhlnVuuicr2l+II+Qf8hT2WxW2grxTAXzBDKuj1Yq+hm0wp6ZmUEymRQB2Ov1UC6XJRWKJU7ZbBbFYhEAJCjAtSe+pS12J57R1q1WEJwDvY85F+be4xxqZc7XvF6v8MDc3JzksB1GH0Qe2pcBfNWyrN8EsAbgVx/2BcuyZAMAD0YATcGjTVjthpkVAnpzOgHhvO4wwaM/B0DaKZtj4gJyLOaBruaGN10SfT19D9NE10LMxBr5mhYU2nqiUOJ1zfEQ3DXz9UwrkKRTF0yLBsBAKkCn05HQPTc355w5W7u7u7BtW6w42z5oO+P3+xEIBBAIBGR8tNo0lqTnTGfr9/t9yQszlZo5D1pA6/e1hW++rq0wU8DrddJKgP8Xi0WJ0Gr+cRK+GkumsDGx5VQqhVgsJpn5nU4HjUZDUnn4uXq9jnq9Dq/XK1U2nDcdedXGgx6LHpuO/mqBZhoNpjDTfKV5UFu7wH6UnWfVDjv9ivS+CDTbtr+D/WgmbNvOAfjUo3zf5XIJ8EsmdbJyuIiacbQ7qpvvDbPKNJmaQpN2SSkoWO9mjkn/bVp8ZnEvcGChMbeJz+FyHXQo0JrY1JaWZUlfdS3EOp2OCG/tujs9tyZqUzIlhQGjd6bFwjnmd81rAUA0GsXo6CgymQzu3buHt99+G5ZlIZ1OY2JiQr7faDRQKBRw4cIFJJNJPPvss2g0GpInpS2eTqcj3TQKhQI2NjbkgF23e78wnK7lqVOn5Lt+vx/xeNzROtDnWOrnM11ZPhc3lHZTtUWilQvnmtfSzUC5phTetVoNbrdboqI+nw/hcFhKhXjMXK/Xk+8wmbZarSKRSMjJSszPy+fzKJVKGB8fl33Cc00/8YlPoNFoIJvNYnNzE9lsVqxgt3u/awkDNKZL7kQcm+77Rr40m1Oa/KSL+7lXqSAajcahCb8mPRaVAgR7GRwgbgY82JMKGNzkFARcMH7XyeU0yckd06TdPROINT+nX9Oa3snF0SFq7cJqy4JMz+ubgnSYINGb0YkRh7lbpiY13Tjzs06uj/6fTfkI+DppbFoAurGAFgC6dRSFRb1el6hhNpuVBFa6c5lMBo1GA+l0egBTNS0d3t+pDE7n0TnNsf6b19IdIszP6GejlaSFIHBQ2karTedqUWHTPefzcN4ajYbgcDqQw/MYxsfHJfetUqmgXq/L2EZHRxGNRpFMJpHL5cQyorfA+5iKWXsC/N/EhbXndJjxoBPlyX8aYzNho8PosRBolmUNuBQUSuw7r4kTxEmg8GLxre7rpCNHTlJeu6MmmdgcMGhZmZ/VACYB7G63K2UnmnSNKYWadjnNqJCTqc6xDOte4NSzXrurTs97GO53VCJDsgSJtYLT09MYHx9HPB4fmFf+HhsbQygUGtgg0WgUkUhkoOdWJpPB3t4erl69img0KrWedE3v3LmDO3fu4MSJE5iYmEAikUC5XH6gFz2tIKfmgk7BhsNo2CajICCepRs71ut1sagBiGvY7/eRzWYRiUSQTqcxPT0tz0mhB0BKh5rNJnK5HE6ePImpqSlRhqzEyOfzOHnypOCZa2trWFtbQ6lUgtfrxczMDE6fPo14PI7/8l/+C3Z2dlCpVCRRF9i3SnXtpfnM5D0t5DVfU7GYHWxI0Wj0gUwDCrRAIIBwOCw88DD+fCwEGnBgsurIkMvlkugSybQiqIEp5HSkSGNqThnG+lqabNsWYFS/T23ltCjELIgP6TZFvKa+vokhUIPrEhQyhXb99LMzasXrmILTafG1IBn2WScr76ikv+d2u4VZI5GIuEX6s3R3FhYW0O/3sbOzIy4k54WC2bIs6Vkfi8UGQO5utys1gzyYpNfrDWwEJ4tLYzd6fpwSpYdZ88MCIxw/3TYqn16vh0gkIlaPOd/koUqlIkB4KpUCAElp0Phop9NBNBrF1NSUYLA0BMz+bKVSCZlMBpOTk2g2m3j99dfl3s8//7yc4UCMkvlhTkqfc8f9wvnlXtDHQ7JJo1NwgaVh2mMhvMPut7Rqh5UGkh4bgaalul5Up8xg7XISgKdA0y6KLng1wVzzWpr6/b5ExbTV4wTUApD6vVqtBtu2xdI0a934nPre5us6AZiuGkuUeBCyjpxpc1734Devr8fv5DZTw1IQ6IiT07zpAI1JenPS8h4bG5OOJ2T+breL3d1dZDIZvPDCCygWi1heXpYUGL3ROXZuEnZ1oLBiby9adry/7kev3fJh7gsVyDDec8pZNMF+87o6lUMrawCSoa8VE8/TpGtYq9VEcTNYovP9Op0OgsEgUqkUfD4f6vW6WFQUFpyjWq2GUqmEs2fPIpPJ4M0335T22KdPn5aOwJubm9ja2oLb7ZaGAMPWWeODlmWh0Wig2WxKRJI1vBRo5vyw/ZO+Hi38QCAg2Q/D+E3TYyHQ3O79kpbx8XFhCmoVp01p+tQaTzMz6IcJIeDBqBbJ5XI9kEHOz/N/Avo+nw+XLl3Cq6++iq2tLdi2jeeeew6Li4s4f/68MJMGiXkdraF1qYf+jP7brN/UloQppIZZGHTFh7lJZE5iKdoS0PPGz5rzQoF4//59sdICgYB0l/X5fGi1WiiVStjd3cXIyAhSqRRu376Nzc1NXL16FX6/HydOnEAmk4Hb7RZBaNu2BAuSyaQ8MwUGy5yYpBsMBrG5uYlIJIKnn356oD5Q5zw5KTSui/ncTseoeTwe6VzB4mvtZpVKJekmUq1WUalUxHrXm5iWHHPLCMW43W7cu3cPoVAIU1NTcrAMBc3k5KTknlmWhWKxiB/96EdYWlrCsWPH4HK5UK/Xsb29jVgshvPnz0t32VKpJPx369YthMNhzMzM4Pz58/j4xz8uY2bhO4MWgUAAJ0+elEhqKpVCMBhEIpGQHndvvfUW2u02nnnmmQeUit5XxPc4xxpb5Hz4/X7s7e39dLQPokuozU6nWkVgECA33zusW4YTaWvQJCfXguaudsW8Xi+azSa2t7exubkJ27aRTqeRSqUeKL3iPfVz8zWOQY+fwkQLaQ2ma8FmhsWd6DDAn//ruXgYAKvHyc9rAa0xIrohBPYrlYpsJrqa+Xxe+tSPjIxgb29PMsc55+12Gz6fT+p+KYB16oE+KKVUKiEWi0nrIVpJVH5Ox8M5RTn5nKby0y4qcVzbtrG3tydrX6vV0O/3JfKrFSStYa3ctEtJ+IE91ojJ0VpnBJfWJK/H91laxUAKU2Hy+Tz6/b7keTEHjlYRFRAAhMNhcT/ZPSUQCEgPu263i3Q6jWAwiFgshkajgWq1Ki2JFhYWHN1WDZXovaD3pe5US+PgMHosBJrb7UYoFILf7xewVKcgmJ/VQQGTnHzsYRaaxuw0o9Kq0MQJZpM5TnI4HBZm4YZZWVnB7Oys1NDRHaRrYUZ9dLRNuzTcfLR0dGKtk3XJa3k8HtTr9YEzEh+FtNBzstBMHFMLNK7PzMyMPAOtF27sXC4nWpwb5dKlS3C5XBKR63Q6ePvtt1EqlbC3tyeWCltxj42NoVgsolaroVwuo1KpyAlD4XAY8Xgctm2jWq0O5K5xPOxlP+zEISfF4Ha7EYvFHvAAKAhGRkawu7uL9fV1/MEf/IGUb/l8PiQSCXzhC1/A3NwcFhYWkM/nZeOzk6tOIaFQ4slNrVYLXq9XAhy93kFXjbNnzyISiYgAsG0bExMTkohMd65YLGJ6ehpjY2PI5/Pw+/144YUXpE6WuYMUZJzreDyOU6dODeBq/X5fWjoxaZfWMgXb9PQ0ut0uSqWSKBknl5OKQ6dj6aaZeq5/KqKcJI290Ox0cpuo2UwN6vTA/PxhALmT1nW6DpmD7rDX65UIlNfrxac+9SmEw2G0221Eo1HcunULS0tLiMViA24jcFB4TyJuZAohjoOLrQWafl8LR+ZiOeE9D2MKbfXp+5ik8TYn4njoWoXDYbE0GGm7ceOGbNatrS2pu1xYWMDY2BjOnj2LsbExHDt2THCUaDQqG4PYCzc9e+h5vV4RZIlEQtpD05qgmznMQuPzOT2Tk5XG5GCPx4NMJoNcLicpJQwuMWM/n88jGAxKLaWORuuUHVp3TL3gsXQ7OzuyhnNzc5ibm5OyKa6Jz+fD5OQkAoHAQGApkUjIGR3j4+OIRCKYnZ2VMzs4d36/X4Q/n1tbkXRvzcoHzhuVARtvUhCvrq46Bpr0Xjbnl2kqHo9Hjjk8jB4bgWZGeUimhabxJ5OGuZsmuK9f17+d7kPSuXIMi7P4mZG0T3ziE5ibm8Pq6iqKxSJu3ryJxcVF+P1+CTIw2uQU1dLZ0XS7NV6o3RDNOE7CeljOzzAyLdRhgoyfHZbaQFeT4+P8cJM0m02sr6/jypUr+O53vzuQpzYxMYFQKISzZ89icnIS58+fRywWw/z8vFyXG5L40ujoKAqFgrg3tJxrtRqCwSDi8bhEQynQdPTbqYKEG9kp7cUpCZe4jmVZyGazyGQyKBQKA0XXtr1fEM4+/EyY5ffM1B+OrdPpSFZ/sVjE1tYWAoEAQqEQXnrpJUxNTYmw57p4PB5MTk5KxJOvJRIJAduTySRcrv1Ttki6NTvdWp7ToU+bZ+Ta4/FIAEPPB4VSuVxGp9NBOp1GqVQSBaZ5hoqdz8z3tHvJ9k+sNjmMHguBRpeN0pgYCrWAJgoWTqgmJ1xNf28YuG1Sv993dNdYg0hGoyVEoPjP//zPkU6n8ZnPfAarq6v4wz/8Q7jdbpw/fx7PP/88bHu/CJv9sbjpzWzqYdEyrQk1DXvtMIF2mMDid51STkhOggA46IJLV465hKurq6jX6yiVSlheXhb3kJu91WrBsiwBuWmlcX7ostZqNcnBIm7D8qZisTgQMdNYjO7Oy3V0uVyOh9IMS7gm5KCJvLu7u4utrS1sbGygUCgM5BHyAOKJiQmxQplGRAuNv+k2MspKvnjrrbdQqVRQLpdlDxQKBbzwwgv40Ic+JPvkzp07GBkZweTkpAju7e1tsfp43N2lS5dQKpUGDlPhHHW7XQQCAVFEHCetxmAwiFAohFOnTomrzbUvl8sS+GAOoVbKOqmcvBUKhR6Yax3B5f4wu5I40WMh0DTz8OHNbhIkWiQ6QvWwaCa/Z5KeVHM8ThNHl48btdPpoFgsCh6yurqKcrmMp556Cru7u8jlclhbW0M4HMb58+cHLAOd0a2jlYe5eMO62To921FdS6f7mJark2s/7B78n3gfN2ihUJA5IYbG59HP3O/3BfQHIKU9+Xwe5XJ5QAAyQGCOH4C4T8OSprnBtEDj2PmaDj6ZIDXB+k6ng2q1OtDems9Gq4PYFNdfR/G45pwrE59kOROxWpYCdbtdsQS1e0hhr4mYl9/vlzQRYpgMDvDZOO5QKIRQKCSHPBMSISzCE7pYKqXL7Ih90c3XEIiJWzMI4mS4kOc5J06Re5MeC4Hm9XrldBe9scm4mpifRDOajDLMYjiKW2luWIL9mjTgatv7JTaZTAbXr1/H5cuXcefOHZn4K1euwLb3e2hdvnwZ2WwW58+fl+inxr1IZEon3IvjHxYlcnq2w1zOYcJ9WMT3MHISwFowMxq5t7eHb37zm3JeZKlUkkRYPlu320U+n5fN43K5UKlUcPPmTdy4cQP5fB7nz58XrIxlPHQ1uWb9fh9jY2OIRCIieOjWAxgIBDDSSqXqcrmQy+XEbWZ9Y7VaRbPZRK1Wk6oEWoxra2u4evUqLl68KGdhEsQnqJ5IJKQ43+PxSGdXCgxdi6yTj6enpzE5OYlTp05hY2MDFy9exL1795DP5+VsTf5ouIKAvsvlEiHn8/lQrVbldCo+hxOMQS+Ic0be4N4rlUr44Q9/iGPHjuH48eOSksOAAkuyKPz6/b6cb9DpdAQX1JasJv5Pj8Y8Y2QYPRYCjXlfxKL0hhuWma1BcL7mVAiupbvTdYaF5033jovN+6ytrWFlZQUXLlwQoJeRTmZX8/Qhv9+PTCaDYDAo0T8nephFNUwoOwkVp9cehqk5RfYe9Vq0LJzcVVoq2WxWMBlacjzLkVE8umC1Wk2AcEbyzDQHbjJejxsZwICGJ9FysiwLwWBQrkmLjhFp4pgEv0dHRzE2Nib3JR9SKDGZlO4dI4bRaBShUEjazGu3mJaIDsA4Aef1eh3BYBAf/vCHMTExgXw+j7t378Lr9aJer8tGr1QqMh5ei25qIpEQjI+5cRR0fE7OFZ+RyeLcQ7q5KiPKxPCIJ7KagYKZ0V7imuQDrvkwmEhjxiYcM4weS4FGDU/m0kRLyYxyUtCYmAjNfKfcK24EE+hlpMncBPo+jNJduHABgUAAiURCXAFuDkZBQ6EQdnd3MTY2Js/jlHbB14fRowo0J8xQa2Kna5vM5TTOwwSjzofTz8OoZDAYFBwMOEgAJuBL5mfCJgUa+6LpZo86QMQfWu18jk6nM5BlzzFxnKFQSFw5vWa0+Gn98DvJZBK1Wk1OeHe73RL146bt9XoSjR0fH5exs2pCH4yse+sPC3jRRYxGozh//jwWFxfFBR8dHZWAE61Wbc3rtAlGf3d3d1EqleQ+DK7oIyOZRsLW4+z+wesy4hyLxaTUrN1uy+c9Hg9isRj6/f3ytnq9LkX0xD05Xyy1cuK7h0EnJj0WAo1RFQKG1BDMz9GkAWudWmDbg+2gSaYlp4nm/zCrzmQ0hqDD4TB++Zd/Gc8//zz29vbEpE6n02i323LyTb/fx9TUFFKpFK5cuYJAIICXX35Zrmlq4kddPM245vec5uIo5CRg342QpYVLpcS2NrQG0uk0lpaWYNv7OUcbGxuYmprCCy+8gNnZWREQVA6Tk5MIhUK4evXqQGE5cRkqEi3QGNwhcE0Fpi024l8XLlzA1tYW9vb2kEgkMDk5iU9/+tP40Y9+hB/84Afo9XpIpVL45V/+ZcRiMYTDYWxvb0s7o3K5LM0afT4fpqamMDc3h6WlJXHf7t27h3g8jomJCcmOpxUzTGHw75mZGZlPHrDMbrxbW1s4ceKEnJIVCoUQjUZRKBRQq9Vw7tw5dLtdFAoFVKtVNBoNZDIZsSippMvl8kDFCnPNQqEQ5ufn4fP5JCrq8/nk8GeW5nFeGTCjZTg1NYVisYhMJoPt7W2xdmnxDfMAuIbcJ0fZH4+FQAMwABQChwPS2iRmxIoWnVPe2lFcLfP3sDQPBiympqbQ7++fWE1Xk431iIWFQiFhfh2+f7fkNJ5hzzfMjB/2Huf5qFHUw143n5HuF+/D/K+RkRHR+qOjo5iZmcHS0pJgX8SUCDp7vV7BnjS/ULnpYBHH4eS+mc/darWws7ODTCYjpVVME6AA4EG6rAAIBoMDm4yCWbuhXq9XXF6WXDHKSExIH4jCa+kyORKFBt053oN4VqFQgG3vp0pYliUChFYcn1MngNPSpdDgocPcT5wfLayYduTxeORULq0g6CEx8kxlY1nWgPKhRWwKLL0uGk5wgpOc6LEQaBqQJrM79UMDMLAYuvOFZVmOrXrMe2jSuVRaMLAeUG98Yg168VjDR/P6wx/+MEZHR/G9730PiUQC8/PzmJmZEeuAx63pELZJwxZuWL7ZMBrWFeRh7zm5qcOSkp3IDCzQXRkbG0Oz2US5XEY4HEY+n8e3v/1t/MN/+A/xzDPPSEoDXXfiK7ZtIxaLSdoGAW0qs263Ky4cAHHxufnpCulUDgpJgt9MC3nqqacwPz+PsbExuFz79Y+f/vSn8ff//t/Hj3/8Y2SzWdy+fRv9/n7x9Pz8PLrdLu7duyeCmRnxgUAAOzs7uHHjhngC4XBY3Czm07ECgkJK8zM9EMuypP27ds0oNEdHR3Hv3j20223cvXsXoVAIt2/fliaNV65cQTgcxkc+8hFZI7rb6XRa3ON2u42RkRGk02lxuW/duoV2uy0F7CMjIxLwmJmZGRhXs9nE1tYW0uk05ubmJAp78eJFqWqge3rr1i0JDvE5KLR1GhcFoJmEPIweG4FGcFAXqjoRrTCno+ecar00bmIScRR+XwsqzUz6+3yNGAOz1IkBRSIRvPTSS2KBbG9vo9PpSOscjZkMsyaPavnwO49Kh1lhw7A1p7EMwwD16xTQesPSoqHrs7u7Ky6Nhg60FU7Mh1gr36NS6vX2u7cSiOfhyP1+X7r3aquDxNQEBhQomDqdDjKZjAijyclJyfDX0UEqOo378n+mn7BgPRqNipWUSqWktU8wGJT0Byo67XIxIKLHTsyMwpBKPpFIwOv1IplMSmSVrl+z2UQymZTKCQZX6KqyZQ/hEt7b6/VKrlir1RLBzVxRKg82B+BcNJtNCfCwMzEtzKmpKRHuujccPSBGrGndh0Ih3L9/H+Vy+VDefiwEGqNZACQwMKwkRRcCm+8Pc7OGpSJoxtFgtv5fk74f8QcWWTOBdGpqCq+88grq9TpyuRzefPNN5PN5fP7zn4ff7x/IqnZ6hsNOhnZyv50Afs7FUYWdFqLDosrDIsFOc8uNQDeMFhGtIrotrVZLumG8/PLL8rqOSnOzVCoVcdUogHRhNzPq/X6/CAveS3dh4XNS20ciEQkMeDweKRdqNBqijJrNJp599lmMjY1J14tQKCQBAG5sHRXVwSgmAEciEdn4s7OzEkygNU+rTLuhdNcSicSA8tXrQKXR6/WwsbEx0EiSbmWlUkGtVkM0GsXc3JwIO0bfaSVxzTinXLtQKCQCisX+3KM6h42BBSYhswUSlVepVEIwGMSHPvQhwdnu3r0rxfe0mvVh0xRoN27cQC6XO5SXHwuBxocgM/DvYekWh2Fcw4TgYakN+npOgkyPE9jfZJcuXcLbb7+Nvb09idi9+uqruHjxIv78z/8ckUgEyWQSd+7cEazNzJx2CkY8qoX2k6TD5ptzpdcpFothbGxMolyMdtLqYZmUBvPJzCwN42av1WpwuVyykRgh9fv9SCaTA2e96ui3trgty5I8KZ2Zfu3aNWSzWSwvL2Nubg6tVgvj4+MIBAJ46qmn5OyCSCQCr9eLu3fvSuE9+bdarQ5Yd2NjY0gkEmKtsMuuZe0n9165ckXcuoWFBbHOzE4U+rf+m9jh/Py8BNPa7TaazSYmJycxMjIiFlEulxO3kUXnumSNgtjn80n9MjHDbrcrnYC14mK6yvz8PPr9vuS7tdttgW+4n3u9Hq5evYqRkRH4/X7MzMzAtve7sDSbTVFe7PzBaCtrYw+jx0KgAYMtoHWm9KMC3sPoKNbKw3AlbYpvbGzg/v37EokDgN3dXeTzeezt7SGZTEqGOzUO3Wlt1r+bcT4OdJh1yPeBwXXlJmETQuaAMfue1rdOvwiFQhJNY0kVMRYdDSdWR1xK399M79Fj1Ok/7XYb1WpVop17e3syhmKxCMuyJKoHQEB/ClW6i3TvmApBtzMSiQiexyRyy7JE8DC1ggm4hFG06+lExJ51yRaxWiYcNxoNEZ61Wk2qLIg3Oil3PqMOuPA7tJK5FzmPzMfUGBjz22hYUKhT0NFS5efJAzphmKk8PxUYGv10mur8zYc3PztM0B1Gh7lgjyLsWq0WyuUyvv/97+PixYsDWpN5aJa1fyrT2toaOp0OJiYmJNpJfMYp/03jJ073fzeC/FHoUa/vZGUOS0dh8myz2cTc3Jy4N9xkdGf0sx87dgxTU1M4fvy4WDsUhplMBtlsFqVSSdyYc+fOYXJyUqKhwEEeou5nrxUTLbNWq4X19XU5gSqXy4myajQaiMViSKfTmJycRDKZHMC89GZnUm8mkxFXk8qM42DAoVarCSbIszQ7nQ7eeOMNBAIBjI+PS/PGYWVvxCsp0NiHDIAc/8fT0Xu9npRlFQoFOT1rcXERMzMzGB8fh9vtFgGtc/harRb8fr+czmae/6BTqCg0aSVqiIBYKKEV4qOMLNNCZb0vD8HhOjyMRx8LgUYzd2xsTHosAe9uE2tA2tQ6wGBemo4o6gx3raVM4dJqtST5U3cg0GA4NxP/53d4lJoGyDkGvTEOezb9XboATm7y+y38zCRjCgN2XOBzbG5uYmVlBcePHx9onczxu1wuSctg11QWdzNJVZfEENfi2vB/lth4PB5sbW0NuJJUFIxwEsIwha+2CnVU/cSJE0ilUrh//z663S52dnZw9+5d1Ot1RKNRKX8CDrA4rjWTRLlOhBj4LMSlmCvH9wiKM7+LVh6xJd2fT1tF2ioEDpol6tpLRpgjkchA8i+tqt3dXbF4KbgZIaUQoWDW5ziY/EChRbcWgLi6nB/OGy1U3dSVQqtYLMLr9SIWi4l12uv1sL6+7tgxWNNjI9C8Xi8mJiYGmMNJoJFxD8ul4vd1nZgGaSkAtCBidEVfl/fXwqrZbA60hjHz55yqFRqNBnK5nHSP0IW8TESkaT8s7YS4kq6xoxZ9mCA051rPFelRLFiOmeOlC9Pv93H9+nX8yZ/8CT7/+c9jfn5eQv1kZLfbLaCyZVnS4+r+/fsYGRnBwsKCYClO1hUASQNhHtfy8rIIBf5w/avVqmM3B849PQPCAS6XCy+++KLUGm5vb4uwpTWj3Tu6QeRbCoF4PC7Yk7bkmGoSjUYxMjIi1lCtVpO8rkQiITxTrVZhWZYEOahILOvgBHp9lgRThBqNhvBFOp1Gr9eToMbu7q40qvR6vdje3sbt27dlraanp2FZlmBXABCJRCT/jl1AtFDk3wT6t7a25IwDJpozuMD5437kHHLtKpUKYrGY3JNreeXKlZ+O9kHEUXSiH4WMU0H2MPypUCigUqnI6duBQOCBMimtpXU2OzeMxgVIWujt7OxIVjkLm4/yfAxfkxF5by4smcKpxz2f2+VyYXl5GcViETMzM9Iq+SeBu2mrUKcOMA1hfX0d3W4XL7/8sghgbgQK52KxiGg0im63i8uXL8O2bREYwWBQLGBtcdMCzuVySCaTGBsbQywWQ6VSwdraGvx+P5rNpnSspXVgHj3IzcQN4/P5pNPq4uKiWBw3btzAzZs3pf70zp07WFpaQiqVgtfrFSuQViGTpxm0SCQSkgPHoAaFGYURhQHHQywtEAgIxNFsNiVvjHMyrPsELSr9fzqdxi/+4i9ic3MTu7u7ePPNN1GpVAT47/f7uHbtGtbX17G1tYVjx45hYmICmUxGoBQWn1OQ6+JzCkfdBoxEXGwYbzsp02q1KnNIizwSiSAajR7Kl+9JoFmWFQPwuwDOA7AB/J8B3ALwXwEcA3AfwK/Ztl142LW02fqw7G6SKXgoFPgeGUl/lv/r5ErtwlFY6mtri69YLOL+/fuSqqHmYuiYdShcj9Pj8Uj9GwBh5mECyuVyIZvNYmNjQ6wUHc7/qyTt4uk5ZI4SC81pfWoXXs87sRhdNB2Px8UCMHmCOFA2mxVXlNatzobXBdrD0k403se5p8DxeDw4fvy4tPamtbS1tYV4PI7JyUnpRGwqTG2l092l8KFVaQL4Gh4h//EEJn0uZjQalbk8LGhGJUnFyQOFeaTg/fv3AUAiqV6vV1qaM/iRTCYFy6YVq2urmTbDcyAYNdbJ43ruh3kBTlisPkeCQYLDMgBI79VC+/cA/sy27V+xLMsHIADgfwHwbdu2v2xZ1m8D+G0Av3XYRTRmpSOAw2ozyRzme8zloZakCU78gUXI1CZmP3l+h+Pga3RnMpkMbty4gddff11azByF+v2+JN6aG+D69ev46le/KrV5X/jCFwbax+jn9vl8WFtbw8WLF9FsNnH8+HEcP378SGN4P0mvF5mduA07UvDYszfeeANzc3M4c+aMRK0YIOHZlPV6HXfv3sW9e/dw6dIlPPPMMxgbG0M2mxU3RFvw1WoVOzs72NraEuuafe/ZlZXRxLm5OceNpL0ArjcFDseWTqcl6bRcLmNvbw9//ud/jtu3b+Pq1av41V/9VYRCoYHus1xXwgGdTgdjY2MYGxuTaGOxWJRj+DiX5Otud/9MCpYWMZWFKULb29s4duyYYIhOjU7N/EC6urlcTk5mCgQCWF9fx7e+9S0AGIBgisUiLly4gOvXr2NhYQGpVArnz58faKmloQC32414PA4A2NzcBPBgq3lCJU7kFAijQstmsxIEWltbw87OzqG8+a4FmmVZEQB/A8D/9M7A2wDalmX9HQCvvPOx3wPwHRxBoOnwsHbx9GJRAzAVwuv1yiGkTtLbtvf7ltG05uEafI8CTOepaU0JDB7gkM/nJQGYgHe5XHbMDzJJR0DNlAZqqMNC0toiYmNJ4itHJQpnzu17IW39aBggFAphdnYWOzs7qFarUra0vr4uc72+vg6/3y/Jky6XCxMTE/B4PLh79y4mJydlfU1LkNqf7p5Ojk0mk1JSxDwrHegxx6/TTmhVMT2g3+9LpHFxcRGnTp1CJBLB1tYWGo0G7ty5g7fffhvRaFQafOooKsfo9/sl7YBCX0MM3MzkQcvarwogb3LOJicnZQ7YGZY5duaBPuZzUklTcDJVIp1O4/z58+KGaheS7bsZRMjn8+IKcwyFQkHGSOyuUqlIfzodgaWV6sTjGr7Q+4+WJZU5+eUwei8W2iKADID/t2VZzwB4E8D/DCBt2/b2O4Pbtixr/GEXorTXrokmPpxlWahUKrh7966EuxkS10JFa6d79+7h1q1biEajmJiYwPz8vGh6mrG0xrg4HAOZjjkyOzs74s5MTEwMnNSjkwxNYtKgxnHonvEYMpbBHEZaGLJ9jN7wDyPtVh/l8w+7FgDJ7AcgBfrnzp3DrVu3UCgU8Mwzz6Ber+Pq1auCsb399tuYnJzE6dOnBVc7deoUMpkM3nrrLczMzGB0dBTJZFLmXxc20+pmoTXdRFpUXq9XcB3g8IAHAwGMsHk8+4eusLEAu3zUajVsbm7i8uXLWF1dxbVr1+D3+wUjY3mRDkKx9TbxQh4YTMxKY00cg23vn63AhGMKwLNnz0oEsVgsIpfLSX0oo4FOQlv/TWHQ6/UkWplMJvH222/j1q1b2N3dlXMELGv/NCu2A2JKBfdap9PB1taWCG5ihNlsVhQ3LT6usY4kO0EWJK0kI5GIlI3FYrEPtFLAA+A5AP/Utu0fWZb177HvXh6JLMv6EoAvAUAymRTgVh/9BhwUR9u2jdXVVdy6dQt//Md/LAz3D/7BP8DY2NiA+0hh1W63cfPmTbz22ms4deqU+OXAg8Xe2o0CHuxJ5ff78fTTT2N+fh6f+cxnpOXyv/23/xblclkKqR2eEwCk8R2Ft3Z5dC3dsLbRwAHewQghMSNaIkelYUJ32HvDnkm76Azs+Hw+pFIpOSh4Z2dHsJdPfOITkmzK5ygWi2g2mxgfH5dzTXd3d9HtdvFzP/dzss5ULqzjPH78uKwn+3lRmOk0Bu1Sms+r8VRiQZxPbn4mkk5PT0sPLwq6QqGAQqEAt9uNYrEoAQ9uSLqvc3NzUjupi+6p6Bg00W48I4p02TY3N8UiZU+1crmMWq2Gu3fvSt+1ZrMpeKAuidKRfq4h6yRPnz6NqakpaYl05coV+Hy+gaMk5+bmpA04sJ8eMjc3J2OixZxMJiWnkMES8rWO8Gs+cjJgND2KN/FeBNoGgA3btn/0zv//DfsCbdeyrMl3rLNJAHtOX7Zt+ysAvgIAx48ftwEMMIN+KJdrv+EizzxkR4F4PI5arYZIJCKbnCY2NS5BdBbDckF4D36epO+rX/d4PEilUkin03C59g+eYJ3ZYaFkXo9Wod5ofFa6w6YwN+ZLmEtnmTPn6VFomLXybq02nQrC8aXTaQBAsVhEOByWw08SiQRisZhkgjNfismXhAh2dnbQarWkKSI3JudBb1idya7BdtKwDeGEn9Li1JYThVq73UYymRRg/c0330S9XheXUkMmOooaCoXEUrMsS/iQ93S5XKIMtBXNgAFxQ+4P8h2VZLValfQQ8oO2hsz6WO3WEf+KRCIol8sIBALY29sbUOgaotA5fgAeSDXSHTMY1WdKDPfbo9CjRvDftUCzbXvHsqx1y7JO2bZ9C8CnAFx/5+c3AHz5nd9fe9i1NChrBge4SPV6HX/2Z3+G7e1thMNhMdFzuZwcJKGvU6vVcO3aNeRyOXi9XiwtLeHYsWMiVMzJpcbkeKjRyGB8j+CvjuhR8zlFZ8m0uuc7v098gYXLxOWGLTqtEdaE8tCLw6y6v2qiC/Lss89iZ2cH/+E//AcsLS2JhVwqlSSHj+4Nv3PixAmcOXMGv//7v4/l5WVcu3YN8/PzOHv2rGj3ZDIp7hpwkGxMgWZa3sNIWwfkG+0yapwTgJRipdNpnDlzRjp63L17F5cuXRJ3kbAJ02lyuZycWE4hzP5rLFJvtVrIZrOIx+MSAdXj5Nj4vBzX7Oys5LAx8v70008jEAhIo0nuHz7PMF5xu9145plncOrUKZw9exbLy8tYWVlBsVhEpVLB17/+dbz00ksimLPZLL75zW/i3Llz+NCHPiQ8vre3J+upW5rryKu5R0zjRWPKOoJ+FOH2XnfBPwXwX6z9COcKgP8TABeAr1qW9ZsA1gD86lEuZIKWeiErlQr29vaQyWQkAZE+vU4u5UNzkdkjKhqNIpVKIZFIiAYj0wybJCfQm68TF6BQYRtkM9eJRLfBqdSJ+BCvNSxySqFKayYajUrG/eNEHCdxrlAohE6ng+3t7QF3igJNzwkje+xpxigmD8UlUK3nQt+X1s5hG8YkLcAOE4a0RKh4IpEIFhYWBAoBICkLpnvHaCf5mZgfBToAKYvjs2mlbtu25JXRoidEA0BaJvl8PkklIgSjAw4MQgwjWr7JZFLAfeJpHJNu+QMA2WwWN27cwMzMjOP+BQ7O++TedMrd1Lgan5MW6qPw+HsSaLZtvwXgww5vfepRr6VNdDIPH2Rvbw937tzB9vY2+v0+jh8/jlQqhXg8LhtDZ/m3223k83lcunQJ/f7+aTNMFKRFYOIspvWktYmTG0irKh6PS88pJ6HFjca0A9O9pQbjIRrEHhzmWiJe2n0blov0kyKOk4mhk5OTaLfbuHr1qmwmHjrMaKKOxPl8PkxMTKBUKuH27duoVquIRqNYWlqS79GloXXMnv+615ymYUEBU5iZf/Mz5E3d/cPv9+Opp55CIpHAysoKLMuSOkrbPjh4hAEl1qmyvIupJTzmcHJyUoIc2tMwS6gotNguaWRkBNFoFCdOnIBt27h586aUaOl0EI23Oq0ZcHDubCKRELwyn8+LohkZGZGgBCswNjc3cePGDXz+85+XygASPRxCBhqz1EQ+0MKWikl7U0dxWR8PP+Ud0laRLqlYWVnBlStX0Gq1EA6HMTU1JXk9xBh0QODmzZu4desWstksJiYmMD09LS4CI1n09Ul6snSEhmRGUfk/Be+w9trcGBRoJhEfoSBjdrRJ1Ny0EsikhUJBTHx9v/eLDrue+bw6h5BA8QsvvIDl5WVcvHgR09PTA9nmPp9PhDcVUrvdxuTkJFqtFi5evIher4fbt28jlUpJi3O6n7yXUx7WUYjjp4uYSCQwNjYmSaKEFzR+qS0PdrZ9+umnpc315uam4FrlchmlUgmNRkNOTGd9JmuWFxYW0O/3B/Ijzc1LHuf8UsgxAklw3+12I5VKiQDlNaempiQIo7FXWkUE9nVdpde7f1jMhz70IekaQyin2Wyi3+9L00mPx4Nr164hGAxibm5OAlyZTEYqCjTGabrPulGBNh5Mr+0oa/vYCjRuikajgZ2dHaytrcHlGiyDcGqT3ev1sLm5ic3NTWnhQibVxcHAweTo8iOS/ltjazprXadAPKy6QZd0aSHByBfNe1qQJunFp8Zjp1yexk3SUcj3g0yhNkxwO0Wn5+bmsLu7i1arhVKpJOA6u2cQHOcmte39bPjx8f1sn3q9jp2dHRQKBYyNjQ103dAWlR6bE45pPgPXghZiKBRCIpFAOp2WhFGtxEwYxOVySRRyZmYG9XpdynWq1aooJ9aqMhLLCgpaXfF4XFI0zM2s8Vt6IRov5DMw70uXS+kDiXVpEklX1HCv6R/mlk1MTIgQY94beZkWc6/Xk2DOxMTEQIMJnQplBiN0np2JX5OGBcmG0WMl0IBBC6hSqWB9fR1vvfUWLl68iDNnzmBhYQFLS0sicGipMXJUr9fx2muvydFnMzMzOHHihPSuonbkvbRrYWIyfF1XD5hWJA+7HYafmVFOfV0A0mkiFApJBOswnIO9o27fvi3/M+JrPtMHRRpT0a4a01GAg4aDTOH4yEc+gjt37uD+/fsIhUIYGxuTeki32y1YZDAYFGvh7/7dv4uVlRX86Ec/Qq1Ww8zMDH7pl34JsVjsgWoR4pT82xyvSeQzy9rv188WOlNTUwPttU0hRkHNao5QKISnnnoKS0tL+OQnP4lvfOMbuH37Ni5cuIDV1VU57m52dhbj4+MDNZAUCLxXsViUxpHEIFnMrjuQ8DtM2tUpQYx2plIpsezW19clSs+AGq/F53K73VILvbq6iomJCbkGAGlPHo1GpVQvGo2i3+9Lp+B+v4+3335bGnkS645Go9K4kRb13Nwc6vU6isWiY9WPVijD1tCJHhuB5hTNYI5NqVQCACwuLmJ2dlYW2rZt0QYULDTxKWBY0KsB16PQMMyFv9mC+zBhBjyY+axD4MC+BuN1dJsVp+v0+32xTHjkGPE5Cl5e868CVzNxJt2ih2vJmtOTJ09ia2sLxWIR2WwWo6OjmJ6eFmbWidU8DerEiRMCIbCP1t27dzE1NYWlpaWBeRmWejOM9Bp4PJ6BDiB8Hg3ks/wKwACwzd8c/9zcHGzblk7GzWYTt2/fRqFQwMmTJyXoQaiB86ZTGwjIc/NrYWryGueb+KHuHsJn437JZDLodDqSIKu9Eh3l1WOi9afP7kwmk9KJg9/nOjAjQbfozuVyGBkZQSwWQ6FQkKMe+XzDFI65Xj9VGJqTQMvn81I3yTMtk8mk+P0ApLh5d3cXOzs72N3dFayK4ChbGuti8sNIb1T9mv6/XC4jn8+jUCg8cHaoE+mDNLQZ3e12kc/nUalUpOTFiSi4eC4in5MJxNrNJK7yqDk/j0LmHFmW9UAUEthf15mZGUxOTmJlZQXNZhP37t0TnEWfT8n1p7XGhOl79+7hxo0bUpT/9NNP48SJE7KZmN91WMqLSXR1KASo9Gg58TO0INmQkXgVQf5WqzVQAcAmky6XCysrK7hx4wb+8i//Eh6PB6+88gqeeeYZnD17FisrK6hUKqhUKuLuMtXj+vXr8Hg8iEQicj4CPQy2+gYOcEeOW5dV6dPjJycnkc/ncfHiRelQcuLECbjdB4ee8Ln6/T7i8ThisRhisRiy2Sy8Xq80ddT5nxcuXBDDQjdfYMCCzThzuRxOnjyJM2fOoFwuS0JwJBLB2NjYQ09z0pbkw5TVYyHQdLRJC45isYg333wTk5OTOH78OGZmZuTkbUZ6uMDNZhN7e3tYXV0VvGFiYkLM92EdP4eRxjL0a7R+Njc3sbq6imq1eqigpNtCUFhHzRh5yufzA8mWw67DDqIej0fuy/725mffTxqmQblWOlWBpBmUm+7UqVPweDy4fPmyYEbDajb5DKlUCj/3cz+HVquFGzdu4M033wQAfPrTn5ae/joJ1lQ8AIYGbPge14etodmpg3W7LpdLNiLvR8uC1gYPzKFlND8/j1arhd3dXRSLRalaIebEIBVTV2jZeDweHDt2THLtOCamKPGzxB35DEzOZnkUI6AsGfP5fDh//rwIjzt37sDv9w+0I6KFSreUp2jR/eUzM+Dz9NNPI5fLSfI6hTyhA/Z7Y0E5Mw7Gx8exsbExgKMd5pU8imf1WAg0PWAyY7PZRKlUwubmpria7FDAhQYOcn9YsL23tydHZbGrAMFMff2jkGmh6d+5XE7A7sO0C7+js/u1+0lGJpMOA0F5X6a08LtMUj0swnoUMuf/3ZCZ7mBai0zh+P73v496vY5WqzVwpibHwbH0+/s96peWlvD2229jfX0d165dw8TEBIrFomxYfn7YGpvpNGaKBtMsmGNFa5FCl32+aInplkDEZfP5PLa3t+UwlWQyiVwuh3g8LsXyu7u7Em08f/48xsbGBly1ZrMpuCPPN6AFzjkiL+vaYQoYNttkIEALBObzMVGWngUjtVQuAGTPdLtdUTZa4dBV5OErnB+mrZDXyaOVSkXuMTU1JTmF9FgYlDD5wIz0HkWoPTYCTVsZzWYTX/3qV3H9+nXE43GcO3cOH/3oRyVdQTMSteTu7q4Uoo+OjmJ8fBzPPvssEomELC7BXEZ7HpZRrgF2czJv3bqFq1evPlSgmbl11ODEUFjcTguHzf9MYlE2heJHP/pRbG1tYWVlZSAKBeChrtcwoWUCsYeRvr5uh6QrPvg5Cqnp6Wn5f2VlBV/72tfwyU9+EseOHRNQWZdEMcUmEong2WefxejoKC5fvoz79+/jK1/5Cv7W3/pbOHv2LDqdjrQ5d3pu7dL4fD7EYjFEo1E5edzl2u89trKygtu3b0sfsu3tbZw9exZnzpxBo9EQTCyfz6PT6WBxcVEs72AwiHg8Lof2ptNpaafd7/exurqK3d1dZLNZKWaPxWJ44YUXJFLJjhwUmOFwWCKmrBllrzl+lvNPS5l1qMxzozdDi9Pr9SKRSEj+5JtvvikBAK5dKpUSnNCpYQTXs9VqIRKJIJFIYHR0FNlsFpcuXRK8k3uDjQSWl5dRKpUwNjaG559/XmAYpnewIoRBEGLG7AenKx6G0WMh0IADt5OW2b1795DL5SR5VXcU4MbTG6BQKIh24kKw+wKZlniJZvphE6RTMvTnuJiNRgO1Wu2hAoBaxsTQgINkYn1aESsQTKKlw5SC8fFxEeicB1OYDBvbsIDHsAjpUZ9Rp0LwRzdppNJikfPa2ho2NjYwMjKCqakpuTeLxGmxMGLKk9W73a4ICLYd0ikH5njNvv+6M7Lmp1qthmw2K5YF+66NjIxI11jLsuT7WqhwjYkPEUKgW8fcNGAfSmH9J0970vPItdTrwd7+VFbEu3SkWcMA7IrBH64DBR5fY1S5VCqJxatrYnXU2olXqKjpEicSCTm4hnPM9aE34na7sbq6ikgkglgsJueCMlLL+QQGU6qOkl/4WAg0Chq32418Po/19XW8/fbbaLfbmJ2dxcTEBJLJpDwYGYqmdaVSwf3799FoNKSVyejoKE6ePCmhcS4I+2+9G9L+PFsHHWWzs1zJ5/OJSc48pGAwKBuV7aSH9XwiE/V6PalLvXLlygCuoYMNpuV41EjRsHubc8Fr6pwjukhcI7rTzOZn+sXm5iauXbsm/cReeeUVyRVk1JcgNw/GYORzZ2cHd+7cwZ07dxCJRDA1NSVCj0LNXAMt+Im/kk+AfaFXKBSwvr6ObDYLy7IwNjaGmzdv4vbt2wLM61wuFozTRRsZGcG1a9ekXnV2dlbqWFOplHS/3dvbk4BSoVCQYncqPW5+rhUtOj7bzMwMQqEQ9vb2YNu2HHTMZ2T1CZVlrVYTK5YZ/zwv8/Tp09ja2sL29rY0AmACrtfrHQi4mHOq8UsNB927dw/lclkEGd1XYmblchnf/OY3MT8/j/Pnz+PMmTMIhUK4e/euBCd0IEDz28P222Mh0JjLUqvVcP36ddy4cQOlUgnhcBiLi4vSkpnaH9gPkxMUzmaz2NzclJDwyZMnpaun1lIMP1MwPurG5nWIiekzEw+LTlqWJS2beR2SthCoNZ1cWH5On0HJzV4ul1EsFkUgDMvH4uEhTpalrsxwegZzLLRICDq3221ks9kHjqPTlhHfi8fjctrT5cuXsbGxAdu2pUaSLifxG5fLJak4S0tL8Pl82Nraws2bN1Eul/GJT3xC6j+HYYkU+uQ1zh8tQAZsiGf1+31pfMC6SEIXtKLL5bK4c/QC5ubm5OATWtrJZFLO5GTHGKYi3bx5E51OR87BoNLjOjP9gYKu0+lgd3dXDiExXUKO3VQ4nAOeoM6WPm63W/ZRPp9HNptFr9dDOp1GKpU6NLFV15pSEE1OTkrJ28rKCvL5PFZXV0UAssrAsixkMhm8+eabyGQySCQScjgLzym1bVsscipsJ+9F02Mh0Mjs1WpVep41Gg15yHA4/EAfJX2KkGVZ0k222+0inU7LmYjMwKdA0z2r9PUeJvlNsJqbgAD9MJOYAjAWiw24vxpb4ue022QSmZb5UGSyRqMhETZm1w8rcOeGJlNp4kZwyqkzP0tBQGHVbrdRr9exsbGBWq0mWI12kVwul5x8TWu13+9jfX0du7u7UnpES9ztdktBNuep3+8jnU6jWq3C5/Nhc3NTUgIADHRuNddTu0/andWuk07SZdWGbllEZUGXj1YkBWm/35eTvXQ0kqdO2fZ+kbllWdje3katVsP29rbUJPMeXANm49MypKW7tbUl6+1Uy2sG2XTEnsEYXTjO1lX3799HvV6XUi1ajcPmk/elgGK5VDAYRCqVEg+G5xe43W7BjInpMcKfTCYxMTEhiqPRaKDf7ws8QUvvg+xY+76RZVkoFAr43ve+h9dffx1Xr15FMpnE4uIiPvrRj2JiYkKwI+IDxB0YWqZZ7Xa78dxzz+HEiRPCqLqtzDC3hAyptZG5iLa9f+Q9XQqPx4OZmRlxYfL5vLhWJB0MYJdPalwmBLMN0s7OjqSh6GihZVlSOsToVCAQwPb2Nm7cuCHWKLPEH3bUF69r/q/dR3Ne9DNRMNKN6Xa70oee5zkybM/8pVgsJgC3Ze13In3++edx6dIlZDIZfPvb35YKgmPHjkklAfEcKoxud//cgoWFBdy4cQNbW1t4/fXXcebMGczPz4vQIr6orRPddYKWld6M8Xgc09PT2NvbE7e5Xq8jn88LFKBb4dCa0GVI8/PzGB0dRblclrQcrj/z6uLxOHZ2dlAsFrGysiKpDbyOjoRr5QcceDOFQgF37tyR1uPMyicxN5Lzxn0TCoXgcu0ftqO7dfh8PkkXabVayGQyuHDhApaWlqRCwIz0AwedRKgYqMh8Ph+ef/55nD9/Hk899RRu3ryJixcvimXs8XjkLAY2k/j2t78t54IyrYU8qINrh9FjIdD6/b60lC4Wi+j3+5icnMTExITUYepF1QzFcxDp5tAVZQSLWJtZn6fJDEkDeCC3TKdJNJtNpNNpwSTYEplVAzrkTLOeVkypVBIBqwVavV5HpVJBJpOR5+UzsiiYTEhXhDlHhUIBu7u7mJubk/QDrUH1cw7D0Di/Tlamk8XIVABaFnQLGSzh9+iycZ2pNNhWWeegcTMxh4rFz9olp/XJ/ELbtpHP55HL5SStQjO+ngcNtJuCmlYYPQGtVGjV2rY9YCnR3eZ8u1wu4Tcd9eU4uGbsacfncLvd4r6yq4bpBnOOtUXGeS0WiyL4dWBgmKWvG0DquSWsQwuUGJpO66CFpF1RbQ1qoccABHGzvb09gSWo2GiBUmmzcw0NFu4f4pQPo8dCoHU6HaysrODu3buoVCoIh8N48cUXcfr0aYyPjw8A3Zw8Plwmk8Hu7i7y+TzGx8flgFKez8i6Oc0cZDYdIQIOFqbdbmN7e3tgjP3+fokSme0jH/kIXnzxRdi2Ld0kstksqtWqbHZGL0dGRlAqlSQzWzPA1taWHF7s8/lw5coVSc/gYnq9XlQqFWxsbCCZTIq1QPN8bW0NPp8PCwsLCAaDAxnumg4TaMMSGCnIh5HL5ZIIl/4+N73ZGoafYUQtHA6jXC4jlUqJ5U13Ix6PC15JovXJeSiVStjb20MkEsHGxgZSqZQc18b76VwsPW797Pr4Nb6vP885YDIscAB3UJCOjIxIwjNzIXVd6OjoqASoCKPQEtzZ2cH4+LhYS16vd6AFN/O9AAiGt7CwgHK5jMuXL6Pf70vqBV1Uyzqo+6SAY4oH8Vz9fLqbB7ubEMphcwDi0tpypNKlwOW8c47YVCCZTOLrX/86yuUyqtWqHNSihXS328Xu7q6cQ3rixAkEg0GMjY0N1AoPo8dCoLVaLaytrUlDv3g8jomJCenLRG2pNw2F09WrV7G8vCyahFqQLU+YC0OG1uY8F11jJnSlCoUHjxJ1uw96W+XzecGystksCoWCWBUUau12G2NjY1LESyuN99zc3MTa2pokOmqAvVarDZjktDaZ2sH8IuIihUJB2iuxGNjE0ijMnHCXRyUtHCnk6Y6xSQAjf8yL0vlSvH8sFpP6QgoTPnu9XhfLgJuH4LPf70cymUStVsPo6ChisZgIccuypKU3I6Qm0fVk3SSDJfpEeHOONDBPa4zzwLmmBU7rw8R8KGD5Hu9bLpexu7uLSqUi7cs5N6aFRmXncrkQiURw+vRpCXYxT5OJrRw3MHgWrSa68vr7/JvtiLgme3t7cjAMBRn3pg5EaIyYey2RSODFF1/EsWPH8Pbbb8sp6aFQ6IE+bey55vP5MD4+LsrtYXz7WAg0Rm4KhQImJibkJBvmpmimMa2Au3fvYn19XRiRhbisISOj6XY1dEkYHrZtW1r4dLvdgZwhEkFqRmB4uIfL5UKhUBCzn00aeR2mZtBdajQaUoq1traG3d1daTmje+ezE0GtVkOpVILX60UoFBJAWwu0Vqsl+BTTCHgvTdptfz9IYzwUAhRo3CDMvGefNw3OW5YloK8+kYiuO4F7WjVagLL1DpmeBdd0vbQ76ESM6BIk7/f7A4C1U9E0n43PR14CDgIJFBrM5+JzmtfSZXAul0tOhiqVSlIE7hQoIu9yfIFAADMzM5JrZ+JvwEEO2bDIvs5TM4WnPuyYilYHCyjUaMEyOq2vTVed5W/pdBqZTEaiqk5WF8+wzWaz0ibsp0agUWsRZD927JgAk1qg6b5OLA7//ve/j2w2i2QyicnJSSnEzefz2NraEvO7UqnIYcE0mc+cOYNYLCbgs7YGzQRNaimCoFzIvb09bG1tSb+2YDCIYrEIYH8DpNNpTE1NidDkmYdutxtra2tyHBkXlVgB3SBuFJ/PJ4KKmN3m5qakFNAqZU8ublRNWnO/VwsNGAwk0L3WjRdpzRB3pBVB5ne73ZiYmJCeYKFQCBMTE9je3h5IiSAOp3uBud1uzM/PIx6Po1KpYGFhAR/+8Icl/43KaVhKDTdvPp8XZVMqlSQC6HSCvXa/uS7kR31fl8s14Pbqe2qX2+VyoV6vi1V9+/ZtFItFrK2todVqSYcKlk5RYdJCI9/UajWxUN9++23BLqemppBIJMQrIC5lzofmeRNPptJMpVKieHkQMjFbnf/ohEfzf0Z8A4EAfvEXfxEbGxtYXl5GsVh8gFfZRisajSIcDks7d33YsRM9FgKNzBUOhxGPxxGPxyXCpCefwKzL5ZKi2Gw2KykejKwx4ZHpAxSAFJKc6KmpKWFcmt3UdKZAI9NrTcZFI85DrcYwvmVZkgWtEwS56LTkdCSP/bOIIxFMBg66GBCM14mSDPc3m03U6/UBjQ0Mgr9OWBlJf47PredARwxN/JHuh3ZBmOzMwm1ttVBYUcgSJ4rH4xgZGcHa2hosy5KIsploGQqFpKMDNx+vzfUkTDFMgOvoKYAB15kF2VRctORoxfF+TObWOBVz0bQVRr7T0AcVADcvLW42guThPxwnLTVeUwee6J5zfCwf05aknh8dvHIKvOjPc160kCOcQ0/ECbQ3eY17hHucglqXAepAE/eY3neH0WMh0Gj1HD9+HAsLC5iamhIMRZvdxDuq1SoymQxyuZxkOE9PT0tTOVp2zFZ2uVxYW1uTCByZb35+XiJldCOBg1O0nTY9GYeRGhbBHz9+XDQNTWSWXxEjINNwc2ltToF048YNYVAKgGg0Ko0gmQFO5jl27Ji4OI1GQ4IPJO2m8X8nq0V/h0xkRgFZQOxyuQZOu6Lg0IKOARnmpTWbTVE42kXVKQ+WZaFYLGJychJutxs3btxAo9GQyCUAEX71eh3j4+MYGRnB8vIydnd38dZbb2FqakpadTMqTaGkSQtm/u33+6Vnl2VZWFxcRCwWQzgcxh/8wR+Ie8sNRrDetm34/X4EAgEp0K7VaojH47KOLOAmdEHBHIlEBLc9deoUer0eLl68iHa7jb29PSSTSZl/CigAoqiZEsL1WVxcFP5l7znWlTI4poNTVMaMaBKz5bV1XTCfkXlzxJE7nY6cPaqJwszMveQ9Z2dnMTc3h+XlZWQyGdy7d++B7jUsei+Xy6hUKg9AQSY9FgKND5lIJABgAIOipcJcrWq1ilwuh1wuJ+UgOmoEHAhI4OAABnYD1f69jsyQYbRW0JueWkovDF0sai+2idHfj8fjcigGBVU6nUavt38oa7fblcgktZ4OYPA6uuMtx+xyuZBKpTAzM4NEIiGChidvM2ihwWQnDEU/oyaNdZlzQQGho5kakKZ7w3sToNfWFrEXyzqoTS0WiyJQOI+6Pz4TU5lR3+/3JfJ2584dVKtVJBIJOUCGFs4wC43JtdoVjsfjksYQi8UwPj6OsbGxga6x5FuOjViptvAogGi9cu50oIPXYYSX0UryPvmJp0QRKyXf0yKjR0Eec7vdElRgwGl8fHwAJtA5bxybOU/6NVMJUlH4/X7s7OzA6/Vifn7+gWtwvbU1qImVQIFAQKAUduEllryzsyNtmg6jx0agsauCbdvCBARKKeUzmQxKpRK2t7cFMCfjMZ+FgokLTI1DN5QAvc7zooAioOnkllGgUTAAEDCbYfRwOCyWHc1pfYYmUzjGxsbQ6/UQi8VE6NG6o7vCe3IM2hUGIIAtu8HOzs7i5s2bEk1ikTQFn2aqYe2GzDXhZ5wYmi4UlQDTFJh7pDuGaEyw2WxKG3ENJicSCRSLRVljKjkdsNH5SHTz+v0+YrGYpLVwrdlAktHOYa6KdoFZmcDDd4hZsXSJCdVcA1pC1WpVzkidmJgQQB+A4Gy0BLkWtLQ10fpLJpMolUrIZDLCy6FQCLVaDblcbiAgQWVM4a8TUBlQ2dzchM+3f6I9n9Up0q0DCoDzuRqaJ7gXPB4Ptra2YFkW5ubmHuAVbQU74ZLEyBKJhBx7mM1mUa/XpSQyn8/LYUKH0WMh0CjliR1psHV8fFzyVkqlEorFooR02+02pqenMTk5KXkqJE4es8KZZxONRgcA44f55Jqo0XS0iFqVTMaaM76mTzUicM5DTdhq+syZM6KBCoXCQN4XGYOWgQ6Te71eSUBOpVK4evWqJOgyCkrmJrO/H8EAzi+FL6OJwWBQ+oER7CUmSHeSPfM5Lo6Hm5yRXH6OETbmn7GEjHWMwL4rVCqVJDjClBueMUnhrolWPK9LN4wH9Ha7XWmD4/P5kM1mkcvlMD4+LmvLzaWTeScnJ5FKpZBOp+XZiO8SI6Mbagq0ZrMp7lYmk5E6XWA/746BCM4P94kOflBAM8LM52s0Grhx44akQDCYRBeeCkQLHxoS+rp6/RnJ9Xq9WFxclC4orAxhJFdbtYfxoMvlQjKZFNedZ+uyhxyAgb3hRI+FQGN0kKa6NoFpGuuTkWiV0SUIhUIADrqPklm5+Dq5kyb6UQSZOfFcXB2tcvpf/5DZ2G1WEwMC7NlmWfslYBS0+gfAA8xGhtPlJ4x2UtCYz6KB9fdKmuGZzMvTuDY2NqTlDgBpW226XhwXIQJdfEyLRUdMTewLgDA8Twyni6etRXO9db4V/2d+G7vX1ut19Ho95HI5yXFk6RzXQycN0/J1u92CfbFUS2fxO6UgaMuHWBXThLievD7ngzW55HuOSe8fwhC6XTsDNXx+zWOmi3lYAEkHhpguRcjEBPZ5badrcZwaPqKCy+fzst5OOXQmvSeBZlnW/xXAPwJgA7iC/ZPTAwD+K4BjAO4D+DXbth/MUlXk8/mkGwUHTMuG4fRMJoNyuYx2uw2/34/x8XGEQiFMT09jdHRUoiQul0uAWWpcWmRsJUyBZoaW33mmATeURLyEm1gvPKNSTA2hC6axDvr+brdbNko+n8fY2BimpqYkOfT+/ftyfTIFx6uFEV3zra0t6eQAQFwMXW2gBa6OsL2HdRdLlYENzi971t+9e1fOeWBjTh151YKEQsPr9SKZTAr+R8HBedUJotri4tww/YNuDCOojJw7kS410sKTnTHu3r2LV199FclkEuFwWKwjRjkp6AiPZDIZBAIBSQUiVtjr9eRgECpkvs71JL+xyHtubg737t0TcJ/vU0FmMhmZP33IDAF9prpw3hms4TkBrEogOQWG9Pg0z9DY4HhoYPh8PnHDNcZGQeskIMkPOipMQ4WVPtz3NF6G0bsWaJZlTQP4ZwDO2rbdsCzrqwD+HoCzAL5t2/aXLcv6bQC/DeC3DrsW8SAKi36/L8Cwz+cToLhSqSAej+PDH/7wgJnNtiK6bpOTzcgI3T0AEoViedPs7KykddB11CkjpmYlIzLSRQtQt9lmf3e6EOz/z6TadrstlgMTKumeETDWOBU1PwWBbitDN5UWEPOO3G63WD50uamx6dLrCKi2uDQDm1ZFv98Xq0F/JxAISAY8FQVbwmjrud1uy+lHTH5mtC4SiaBSqaBcLgtfECao1WrY2trCxMQEjh07JlYGLaVOp4PV1VWpCyYQrnjW0QLRVqbmyVAohEgkgnA4jHa7/YCFbGJNlrV/1gSrFwj083M60TmZTErFB/mXPMt78YR2Cggq1Ugkgmg0KvekwCDvMLhE4cbcLbfbLQmyuVxOhA2DVtr61Z6HnrdhliV/040lz9N74P7j9ejq6pQS8rb+zfZBxL9N19ek9+pyegD4LcvqYN8y2wLwOwBeeef93wPwHTxEoDHqo900YgfERxgEmJubw9/4G38DmUxGirK5qEzJoKDgD0PonFAme2YyGclp022Nac5rl5I5U1rT0ELRWhd4sCCam41umQ6N27YtAo2CV+MEfAYKIBJdKrfbLRgjAx5MytQup3YByLQ6WmpqZK6L/k2y7YOealoI0F3THVjT6bS0OKJgo4VDoJ1zwZY19+/fR61WE4uaz9RsNuUMU2JpIyMjUvEBYED5mblRThtWl+zoubVtW9zYcDgsCo5K08zB4zwxnYgVEsxBNPGpY8eOIRAIoFAoCCBO4cfDo+l96HSjer2OsbExBAKBAZeS46bFxkJ31oRSuFGh7OzsoNPpCJans/G1F6Bz0rT3YvKDGQTQqU1M9NVpG1pZ8zucd16Tlhr3G69xGL1rgWbb9qZlWf8PAGsAGgC+adv2Ny3LStu2vf3OZ7Ytyxo/9EIYLBsBDgDHVqslnRTK5TJOnjyJp59+Gs899xy+/e1vY3d3V0LTjOToCKQ+M5P4R6FQkBo1Ci6Nz5FJKWBJdC20laQXRTO3FmiMsvE7zA9iRwkAEpbmoRhHpV6vJycC8flGR0clZcEEnTl2s1cZLUodwSUxOdaM+OpIpSamXpw6dQqxWAzLy8viHlMAZbNZOVvz5MmTD1iAhUIBXq8Xs7OzyGazuH79utyL2BbXkekyOuhBQcGNRHdMW1TaEtelTBQaTLngQc537txBJpPB/fv3BwQ5rUhuulqtJoEJWmpmuozL5UKxWMTo6ChmZ2clV4994li0zhb0IyMjuHv3rihECnMeskIsjfxgki7Upzu6tLQ0kLyezWYRiUSEp8kfTiVgDyMqYSaYUxltbW0hHA4/sLecrC6N+Wr6wASaZVlxAH8HwAKAIoA/sCzrHzzC978E4EsABkLrZm5YrVYTYceyCZ30aVpFpvukr0trjSY2D17QP9xc5kLyNS0UgME6OSfi+1xA7QLqDaa11aMQ54BJjRybiY/wPW5AHd6nq0KrT5PTc9FlcBKA3GDEmyg8Keht2xa8k/AA15rAP6O/LGw3XT1uDubwEZ/0eDyS/kKwnuVgHButZd3vjHNP90hnrE9NTUk/vpGREbm2Hg/xKUYv6f4TiyP/aaIAZaY8LRqOm2OiC8lx6rMEGJllQjgAEdzEKhl116C6ZVkScOBz65I8DS28G7zVtIT1vtFJ60785nQdbdU9jN6Ly/lpAPds2868c/M/BPAygF3Lsibfsc4mAew5fdm27a8A+AoAJBIJm8AlH54HU2xvbwvjMgP84sWLaDabGBsbE402NTUlyafEt+hGEuthfksikcD8/LwEGfg5BhW0ma6tMW4uMgUZkUJKW5j8Te1NXIt4kU7kJI4BQGoLj0J0Q9kMcXd3V8YxPj4uXRtIfB7e37SMhtEwQF0/K4nXZtsZulHMUgcgJ3S9/fbbMr86ApdIJDA+Po5SqSTtsnkfj8eDTCaDP/mTP5EiaZ72RPzO4/FI59tarSZdcQkwU6CyI4kWaLo10OjoKM6ePQvbtnHy5ElMTExgZWVFQHbyVrVaFfdUu4KcHwoJHU2kO7i3t4doNCr99er1+oBy4jPpZHEteHd2dvCDH/xAsD6NSfHZmArBtBHyAN064pO01HVrITMYcBiZUAuxX0YuQ6EQCoWCBO14lsbDBJW21j7IKOcagI9alhXAvsv5KQA/BlAD8BsAvvzO76897ELUchqboAYls+kOGrdv3xbsgAyi88HIQDpSxrytSCSCxcVFPPfcc6hUKgOteTRepd0x/uiaOeDgJCZaG2aaBQDJ1qc2YhkUhTZTBWju7+3tPaAZtdXpNG9sikcBOjY2Jk0uTdLXPYow43eAgw4VvCeTHjnH+jo8CCQWi0m3XW095HI5XL9+XZ6JbggtCgDSNJPPyhQIzme/3xdLiBYJLRwqx1QqhZ2dHYEWKDT12Qw6CkzyevfPx6xWq7h27ZpYo6dPn0Ymk8He3t7AEYR0UXXliPYkaBURvzXXUQdt9GlXtG5DoRDq9bq0qmeALBgMYmFhQVpnr62tiYW+sbGBYrGIs2fPIpFIyDi73a54Op1ORwIY2mJjUTjHr61srvXDFC+/o7/H2mNaaAya6X1F/jfpsBQS0nvB0H5kWdZ/A3ARQBfAJexbXCEAX7Us6zexL/R+9SjX0+Fy4CBCAkAmmVYOE2oZpteYG4ABgcbFYM5XJBLBwsICnn32Wdy/fx+FQkEsO52cqHEPalnTdCemAUCY4Z25GXBvgINTcZhjQ+3LVjHELfr9vpQRaRCf13WaMwLuvB5TDHQLY36eQkOto7muD7iZOleJeCOxTbar5jwzerm7u4tSqYREIiGfJwTAMjZaOgAQjUZlbuPxODwej5x/ybFzXMwvY40oN4wuO6NASyaTEoghH+lmjpx7uoU6WXd8fBx7e3tYW1vD+Pg4kskkTp8+LYEkziUFKAUuFQvvx3uxtZQ+M4CbXhd4NxqNAbyWAo1rza4XfP348eO4e/eudIQdGRlBIpHAzZs3sb6+LjmA4XBY5iyZTAomyfbdW1tbonzYPt3sgkF+cCLyvZlepBU0qzG4x1nfqgWYKQQfhd5TlNO27f8VwP9qvNzCvrV2ZHK5XBJNouYl0EuAttfrSaE3JzsSiQyUnzB4AGCg/o9nDpCRqOGq1arkDlED0+WlG8F76YgVTXZaWU4RQh32BiA5YQwEVKtVnD17Fs1mE2tra9LgkJYpv6NxBCftxO/U63XE43Fx9ziPtER0Tl6lUnlgrHoey+WypJHoDUk3jH8z/07nh01NTWFhYWEAo6Jrx2egu8OortvtFrfR4/FILS/vy9IyCnpiq8BBXzE+K+tFy+UyMpkMbty4gVarhXg8LtFTRoH5XZ/PJ5t6dHRUkrxjsRjm5+clBaLX6yGVSkn7Jqb6tNttSYQlrEBBNzo6KjhaLpcTPtnZ2UG325XUjHA4LLmVPPnq1q1bOHbsGKLRKJ566ilkMhlcu3ZNhGY2m5Vi8RMnTiCZTOK1116Dx3PQ2ocHyACQvC4KWo/HIx2h3e79Kge2yapUKigWi5iZmZGUEgpD1k2b+JeTANK4tkmEB2hd8kwMKlDyt1boH5iF9n4SmYoLpXEwmuI+n0/OF9DBA+0OkYEoBGkxUUjpBErmhVEoUtiwmoAnmI+MjCAajYprCAziafoMQXPitemsXVeOjVEgAr5aCJqL58QsfA4dzm6329jY2ECj0ZDSIVq+xF40sK2v1ev1RPvzNzcjmV4XoWvMic8RCoXEagIOGg0QU+Gz0M1izp22xqmdNc7DDaTnhvPOuWcSMcfTbrdFwVHgkJeorPhsrChgd10z2EFMkCVXU1NTWF9fl0g6LTAKYuaSaYCfTS6pDChUAIgSBfY7cNCFrVQqgpMyuZQCgnPFBpd8TgZa4vG4RHx1MbxWvjpPTudvEuKhUcDr87vDhJTejw8jjS8CB8cs6p56XMuj0mMj0ILBoPRI4kLSrE6lUhgbG8Ozzz6Lbne/Sy1NYQq3QCCAqakp+P1+vPXWW2J1cTOkUinJNCbzvPDCCyIotdDTkRXgQZeNYybRwjGjlsRoNCMBBxYiQVidUPko1Gg0kM1mEY1GJYS/vr6O733ve2Jt8LmI37G6Qnd3pavIXDAnjcjcOW5gFgrXajXs7u6iWq2KxUA3z+/3Y2trC/1+XwrwzWfkOFnnydQVJsU2m03p4srqCuIvwIH7wzI43ZeO68wa0YmJCVFCtH4rlYr0kKN1xxY2pVIJOzs7ckKTx+PB5cuX8elPfxpf+MIXsLW1JadCjY+PY3JyUg6K4TkPDBQ0m03cu3dPit01X1Ewb2xsSFoGFd+dO3fg9/vxS7/0S2i324K1UhmYFQLPPfcc6vU6tra2MDU1henpaRk74QJalVTkWkF4vV4Rin6/H2traxgZGcG5c+cGMgqOIrCOSlQE+Xxe+IZrpKPjJj7tRI+FQPP5fJiZmcH09DRyuZzk4DBznhEk4kqBQABzc3NIpVIDpim14ZUrVwYAZgYDyFy2baNUKmF6elqsG1qEGmjXmJMGeLUlpSNkOijAH24cul3Ek5hsSgFTKBQGLJujEOeCnTxpvc7Ozg7MLeeQEWEGEHRQgIKATATA8fn5nNraKxaL4nq2222USiUkk0n0+31pjDisw4cGun0+n+A2xWJR+okx658WO5+LxHWgQAL2rXKmIhCfy+fzIpg5FlqrOnWHeCgDDro4OpfLYWVlBZcvX5YoMptXAhBYgtZ8tVqVbh3PP/+8XHt8fBy2bQuwTyGmhYVlWcK3rPFdWFjA5uamBI9SqRQSiYTACRMTE2i1WtIcklZrq9VCoVAQhcRKDP3s5AdaScFgUFp68cwMQizvBt86jDS+plOYDkvrcKLHRqDNzc1hdnZ2oDEdtSvdPUYfQ6EQFhcXceLECbGomHPErgum68IzCqjpi8UiFhcXpbSEJSFkaJ4gzc2rM8oJ4nLiqeGp9bRgdLv3y6QqlYpEI3d3d9FqtXDs2DEsLS3h/PnzEtFzAun1b02cCwo0pjGcOHFCxkMhxkOOKcx1EEQLaLr7GhckhqTz83QEiwe0sDqhWCzi9OnTGBkZwfXr18UqcEoaZk+7druNeDwufccKhQLm5+flvhQYuhZUzw03pRZCXG/WGO7u7qJYLGJ7e1vWifxDPI0CxYzMUVgXCgUsLy+j3+/jqaeeQiqVwsrKilShEH9jfW2lUsHc3BySySTOnTuH3d1drKysIBaLwePxIJ1OIxKJYGxsTLqwvP3225KnmEgkEI1Gkc1mEQ6Hcfz4cWxsbMiBKt1uF0tLS5KGMjc3h263K4nHtPSInersfbPxA4UxFTFd5larhWw2i7GxsYHDbpzo3Qg7foetgwhTMECnP/dTgaH5fD7pOHvz5s2BFjqcVGrYcDiM2dlZbG1tYWNjQ4DnnZ0dWdSNjY2BGk6PxyM5Z8zG9ng8eP3111EoFPAXf/EXgjHRFWObHx2V8Xg8snEoPCjc9KZn4IL1pbZtI5lMCj63ubmJYrGI9fV1VKtVEXTlclkOpaAlxygUsR1aFDMzMxI8WV5exvr6Ol588UXZdNlsFuVyGS7X/jFz8/PzMnadakEGqVQqACBCgG6gbdti+bEImpgX3T22ytGdU3kdCmnWaDJ/UAP5lrXfs55Z8Xx+9u+qVqtiqYTDYelYrKsjKLTcbre4wnS1mZM4NzeHcDiMXC4nykoXp5Mo7Jkw2+/3BZc6e/as8AhPLj937hw8Ho9YZW63G6dPnxYFOzc3h6mpKSwuLool+dprryGfz+Ps2bNiHbPUKRAI4Pbt23j99dcll67ZbGJiYgJTU1MiANnFdWtrS/LM6MWwEy4VVLVaxc7OjuCHOtGcipEWmvYwGFRLp9OoVCq4fv26HJislRoVg04yPkywacHEz/NvClpg8EzYnxqXs9vtYm9vD36/H7u7u9L3nwKCeAh76IfDYWxubiKXy6FUKg3gOHQ5uFFs+6D0gtYWXc9MJoOdnR1cu3YNAERLsPMFcJAfo90xjZGRAZgWovNzqNXNAlxuPkY+zWx4YDA3jxFXhtkBiIXR7/dRKpWk5xcTPikkyXTUerrMR4ffqSVZP8k0AR2dtG1bGJl5fbr2lNpcu+v65C6OmxuF1zQtQh0I4pxTGdDi5DrrTcM10h1GWL9o2/ZAoEdb+2YJF+fW/HG79/vp0WplvebExMRA6ZQW7jr4QozP7XbjrbfeEn7mBmaj0rGxMezs7IgwYwCG+BzdaNbBsmyKz8U9o/lQRw4JxtN7oMFAPtCpOzoBW5/V0ev1hBe0YNPP+zBriu/rgBrHq8difv4weiwE2vr6Ov7lv/yXWFhYkDbbZGBqPnYqZdZxpVLBysoKLly4AMuyJOrEE6BGR0cFk8tkMmJZ7OzsiAWxsrKCUqmEqakpTE5OYmZmZuDAWxZbE4eLxWIiFDOZjBRVFwoF7O3tyULQ3Wu1WmKFMaGT3Vi9Xi/Onj2LxcVFnDt3TjplbGxsiCXEDPH19XWxOBnpvXHjhmhPbn6G5Inp0QXrdrvIZDIDCbVkYjIrAWZaADolplwui5CrVCqw7f32PMlkEul0Gnfv3hVrgS7/zs4OQqEQPvGJT2BzcxPLy8vSDnt7e1tSXjg32WwWsVhM3H6mGNA64nwQZ5uYmBC3v1wuy/NyzSqVivAOu+BOTk7Ctm2k02lMT09jfHx8wKoBDsq6aHkzgMPe9svLy1J7ubOzg3Q6jS984QvY2dnBysqKCLJcLodQKISFhQUsLy9jdXUVTz31lERXT506JZFL295v9lmpVKRudnJyEp/61Kdw+/ZtbG5uYnp6GvV6HVeuXEEqlcKpU6ewubmJbne/EWU6nZZW7lw3ClieHKVbZ2lLDXjQEiLp9ycmJjA9PY0f//jHYiQkEgmMjY0NlDM9LJufdFhElBYkiQr3Ye7sYyHQGGnUCZzaLKak1t06uWB0X4LBoKQMMMHx6aeflgNSCbpOTU3h2LFjmJ6eRiAQQLFYxM2bNwWcnZmZkZKU+/fvI5PJyJFkugElrZXTp0+L5UThMD4+Lljc9PS0FGw3m03B7Lg4xIuI/TBA0e12ceLECcRiMUSjUbF2EokEAoEA7t+/D7d7/1RqWkjxeFxC/CsrK9ja2pKEzfn5eQAH/es1c1AwAhgoDVpYWBjQ7o1GY+AoOh7fx+4SbJvM76dSKXzsYx+TPDPOCyOavV5PcpqYzMkUmWAwKHleqVQKtm3L/SnkotGoVEMQJ6LbOjc3h5GREczOziIWi6FcLovbODs7K+7qrVu3JGDDza4tBp0MzP5ztBRoia6urorLSOiD32XAg5HPdDqNyclJiQRns1lxjYnj8v/x8XFsbm5KRQu9AR4EQy9C47fkTV2LTBeeSay0zGj1UbnpEjOSFiq0vpLJpARzmBbDVJejVp84kbYK320U9bEQaKOjozh27JgkH9L1YwIlhRxNbpauEEsCIBZUt9tFpVJBMBjExz/+cdFY+XweLtd+f6VYLCaMT2FC4Hxubg6WZWFtbQ1vv/02vve972FmZkaKjqnZpqenMT09jU984hNiSZGRpqenUSqVsLe3h3Q6jX6/j/X1dWFYJqzy+dhpg8xMgXb27FmcPn1aDu0IBoNSv0rw+dixYyiVSmg0Gkin04hGo5ienkYikcDy8jKA/az32dlZcZ2Il3Bu+v2+HFJy6dIladX01FNPyTkPuVwOhUIBi4uL8Hg82NzcxL1797C8vCwCfXt7W55xd3cXs7Oz+PVf/3X4/X7U63U5O5IF47lcDk8//TTi8TjW19fF9ZycnMTo6ChWV1cB7B83uLm5KS2SaEWdOHECU1NTEkjgKUmRSEQSb4mf8nRyn8+HqakpObv1Rz/6EXZ2dkRosOMqqwh0j7dut4vt7W1pX0RBfuXKFZw6dQpnz57F2toaCoUCwuGwwAWlUgkAcPPmTYlMplIphMNhbG9vi+uucV6v1yuHbhcKBeH5er0Or9crlhFzxZiKQXdT8ySFcbFYlAYPDMTQpdXQCvBg3iMVbafTkVPZ7t69K1bssWPHBgIrj0qm4AQeLf+M9FgItHq9jtu3b2N6elpcERaKs5RnampK8m2YH7S2tiYPrev5iBGMjIzg2rVrYrYDwPj4OD760Y/i6aefxn/7b/9NDjv96Ec/ijNnzmB1dRXFYhEXLlxAJBLBF7/4RQAHC0xLja2mNzc3cffuXVy6dAmlUgnhcBhf+tKXUKvVsLy8jKWlJYRCIcmzY8/8druN7e1tySRnMTwBbB5A2+/38Z3vfAfdbldC9LRGG40G3njjDQHxaQH2ej2srKzghz/8oSTezs7OylzpZErSmTNnBHcplUrY2trC17/+dSm2Zn96nupz5coVlMtlwecAYG5uDpVKRYISvV4P9+7dk7MN2Mr62LFj6PV6KJfL0qqbQQlaYrZtI5/PC55JdxPYL5NaWFjA9PS0dDmuVCq4ffu2PB+DGteuXZNzStkUslqt4uLFi7h69aokrqZSqYGyNuBBV4gtjWq1Gvb29gQGeeONN8T6X1hYQCwWwxtvvIFkMonZ2Vnpp3blyhX5HF1dBiV0bhghiVgshmeffRYzMzO4fPmypL8Ui0Xpl1YsFrG5uSkWLk920rlbbNnDgBiTnAnfOOFm5HlaXVRa3GN+vx/Hjx+XBOzt7W2MjOyfOEYc86j0bgTXMHosBBqjMDqHiD69CZwDkHwjXRdnAuqcpEajgUKhIJYfI2/NZhMrKyuiUZm1zaBEsVhELBbDzMzMwBmGxHMYeWTUkF1SiSPojU7BTDCX7hHTB5gDpAFtMhfzuojXcR4YPmd0ldE9lnyxrIuuli6jIpgLHLgRs7OzEmGklcVW3nTr9Mar1WoSGCDj67pJRjcrlYq4cZwPulS6WJ1uONdeKyiNofV6PamzpMvJuWIuFk9h73Q6kgdH69ntdsvpSWxBxDw9jol8RgtHR/wY9W61WlKqx/52VGi0fmnp8ZrsxEsPggKNFRqcG/72+Xwyp8vLy8JrxCp5yhiAgftbljVQhK/XnUXv5HcN6GtQ37S0zL8ZzddpH/3+fqkihTT34Lu12t4NPRYCjVpxe3tbolhkaF01wGPfaIkkEgncuXMHHo8Hk5OTchoULZxyuYx4PI5z586JlmfGMzGmWq2G06dPw7Zt3LhxAxsbG2g2m5KKwA6p1GrcWHQZIpEIms0mCoUCYrGY1H2yJzyP6NLRWjLc7du3MfH/b+9NYyNNr3u//1vclyKrikWyuDXZZPd0z/QsmlHP2KNl5JFGsSMolgMkgi98bSdXgRHgAjcLgtgDG7nIBwN2rmHkwwUSGLm+SyLb1/ASCQYkzdiyLEOzj2bpnumV3WQ396VW7izyzYfi7/DU20V2z0jTQyl8AIJkLe/7vM9ylv/5n/NkMlYCvFAoWGWHRCJhTPRz586ZO/HEE0+or69Pb775puLxuD71qU9Z/f7p6Wlls1kTIgMDA4ZDIdhwrT0/ztfCoix5T0+PucY7Ozv65Cc/qfPnz+ull15SLpdTf3+/zR9A/IkTJzQ/P6+JiQk7PWltbc2CDmBV8/Pzamxs1JNPPqkTJ06ooaFBL7zwglpaWtTf329RPzhaPT09hlfhcvX399tYshZGRkYsiNLf369isWiFFFtbWw1vvH79ukULvXuJ+8RceQXC/4lEwv73mOrGxoZlEXR3d+vRRx+1ze7zX8vlyslIra2tSiQSGh0d1c2bN/Xmm2/q8ccfV3d3t3knwAwNDQ06e/asJiYmNDExoQsXLmh+fl5f+tKXFIvFdPPmTc3MzGhmZsbyTF999VXjqT3zzDPq7Oy0g5T9aexra2sm6OG+eQsPfJb3PM4Glkmx1M3NTV29elU9PT0aHBw0SxvyuucO+uaDCJ7MHRWwKMbD2pEQaAD+PvxP5zFdPVgLtwtGdjTsS+WNixcvmsaDqkEkaHt7W0NDQ8pkMjp16pRSqZThatSuBysBPCUtp76+3tJhmpubVSgUzIpZXV3VxYsXze1C+5MDSd88F4zNQkI0CcK4Ej7fEeyJsjozMzOWKE1gxV+XQyWam5stoZ/GhvWaFJehsbGxCrwHBvDRJgQFwpgoMweF7O7uanp6WolEQul02koJFYtFdXR0GE5aLpetGgnPSvQOCw6CNJYZddKwMrAQEdCsIzZyS0uLJYfHYpUDVYaHh81y9UqUNVmLeEyUV9oPGJBZAo0DiAThnsvlDB8l+Z/DdaEhpdNps8aJStIPSVYfrq6uzqLlKDnOF9je3rYCBUNDQ1aNF8G9srJi1qJnDWBQRL2cWsLEW3OMlc+nTaVS2tnZ0fT0tDo6OqpSqw4C+v14Rq1DTz3x/x/UjoxA80ecRXk50n7OJtYNg0PSrLRvFoMn/eM//qNhLRw8y3thGBpJ8sEHH6yqhJHL5czi6uvr08TEhOEEmOqLi4s2oWxsAOArV64YdQKBRGHHlpYWFYtFi4SxwFjAJ06c0PLysm7duqUbN24Y+E0qz8LCglXCILpFYKOvr6+qnj9BEFylwcFBex5cN0Bi2ujoqEVWSWlaXl5WY2Oj5ubmTEuD+2UyGc3MzCibzWpiYkKFQkHLy8s6efKkJOnatWsaGxvTyMiIpAoEcPv2bSPE4oZmMhmzlBASUGxwGRsaKueQImw9JoSVjjtfV1c5AKS3t9fyAqenp81igLbB6UyeK0cUnYOFcWXX1tY0Pj5ur5Gb6vNAb9y4oZMnT+r555/X8vKyLl26pGw2ayfGQwcigs0p76Ojo1paWrJzM4Ae4LcRaOKMAQJKdXV1lgK4vr6uwcFB9fb2Gv/Oezq5XK7KqvXrTrrTUmIdsZaiexaoBMMD7HJqakrXrl3TY489Zm5pFJ/zDWWxvb1trra0rzA8T/AngljrwUdwJCwhLDQwEDhLCwsLWlxcNEyAAUETplIpfepTnzIsaWFhQZlMRs8++6wuXryoK1euqKOjQ8ViUa+88oqam5vV3t6uz3/+8zZ4/f39On/+vLHTH3nkEbPyqGghSbdu3dLLL78saf+M0aGhIZ05c0Y//OEP7URvqnsMDQ2pra1Na2trymQySqfTZmWNjIwok8mop6dHMzMzlijNddPptDo7OzU2NmZuAYKN9C74TY2Njcpms+ro6NCTTz5prjuVTUknW1tb02uvvWbPc/r0aY2NjSmXy6lYLOratWs2tmy0UqmkZ599Vp/73Oe0sbGhbDarQqGgZDKp7u5u3bx50yKvGxsbevnll9XT02OLPgxDFYtFO5gYPGh9fd2EC9gZmQAkjCOgpGriM+49G76pqUknT560YpPQOh566CFdunRJ09PTunz5ctVmxxIGB2R9SjLl4S0O3GncSpLQf+/3fs8q8/p6cbD833//fUkVy6u+vt7KEtF3FCLWYxiGFiS4fPmySqWSrl69qq6uLvX29ur27dt21CPuP0L25s2blm1AxY+uri5Jsr3jsV8EkLfc6UOUG8bnwOqwUJuamjQ/P6/5+XllMhkL6tTC08ABCfpJ+0KO/Y/wjJaVj7YjIdAkmUDzYLE3h1kQbGBC/5SHjpq1zc3NGh4e1s2bNy2jgATutbU1zc7O2hFZk5OTluq0sbFhi5NKsrhGQRAYwXR+fr4qOkmyL2lTzc3NymQydi0PgLNZ29vbzfWQKpNIKWXcVCwitFRHR4dpdSxbsClJRung2erq6hSPx9XZ2WlcN48b4X4DNO/u7laV9M7n85aFsb6+rs7OTosqbm9vmxDZ2NgwPGVgYEDz8/Pa2dmxirEQnn15Gk6O8tZaNG/U5xSSeeET3T2XDlyLKrT19ZVDnEmlQ9uTR7mxsWFu/dLSkilQBBouHWsTK4h7emIy65bSS2+88YadYh9lxDc1NWl2dtaO58P191YVa9pTKcAYb926ZUq6oaFBJ0+eVBAExjfzng2N9YvVR7+jnC+UZJT1H7WwPLUCrBAYorGxUR0dHUY+B//knvTDY3X0j2tHX4vO94Fy5C5y5r40IiaeX4Umwf30aUarq6t2XBlHt7HxYZsHQaCuri4D+REm8/Pzunz5st5880199atftZC6F6BSxTpbW1vT22+/ratXr2ppaUnXrl3TQw89pCeffFLXr19XuVzWl7/8ZSWTSYuGbm5uam5uzjCkL3zhCxYen5ub0+XLly1i9Su/8itqbm42/Ath0d7erlOnTqmrq8swFSqQnDp1ytyocrlsHKv19XXNz88btkH2w+zsrG7cuKHf+Z3f0cDAgDKZjLLZrLHYcXmJCvo8zJdffln5fN6sKNxnUoCam5uVzWb1+uuva3NzU7/2a7+m8fFx/fVf/7UReilA2NfXp0cffVTt7e365je/qXw+r3w+r97eXiWTSRM43hoAIpD2T0cHb8SiILgh7SuExsZGy/UcGRmxiOv8/HxVClpDQ4NhX9AYsPSw1NhI9M9XI8Ed9MKEfGI2scedSBoHQ9zc3NRXvvIVNTU1aWNjwwjEvuSRh1lYFzMzM9ra2jJe29NPP62uri5TCLijuJvgjhymgrIm6unTtqKYIQLEu5eebO3T8/g8r5ESNj09bbmmPT09ltXiXV6UhRfgjBkKDQv+sHYkBJq0T22AVEiAwGsEBM7Ozo5pIXLhoonEyWTS0n26u7utZhgRsb6+PgVBYAdNMLhgHalUynIGqSG/vLxsGrCvr8/64bG/WCym/v5+9fT0KJFIWN15+E6jo6MW5ifsjztQLldOGcKS7OjoUBAESiQSWl1dVaFQsDFg4SGQWAhoQJ/RQH/7+vrU3d1tY0yV27a2Ni0uLioM93M1SSuC7Q725Nng/M7n88pms7py5YodRkIVkPr6euVyOb399tsaGBiwyCVKyVez9cEMihY2NDQYVkRmBxvG0zX8WiEw4oUemwKltrOzYxQMLCGsVW9Vs9E9DYOGVejTzVBq3oqsZYFgAfq6eGTGeHeP6/A6yioWi+l73/ueWc6sv1wuZ94GDeudkvUIMLBC+u8jjPTbRzuZ81ruKY2/sZZ3d3ct/zWfz1s9N8abKHj0+36ceDae/7B2pAQakUj4RgwWD0JUCysC1ygWi1lER6oA201NTbp27ZpZImQHJJNJjY6OanV11XhKb7/9tmmQRx99VG1tbXZA7tramqampjQ7O2t18dvb2/XII49I2q/AQfibUkgU/Lt27Zqy2azy+bwGBgb0xBNPGM0jlUrZooYl3tPTYxwlIn8tLS22iNgULGIfoQJP9DgFFJfPfOYzFrJnId26dcsOw4BxTl6e52Bls1nDDrGOcDEIkNy4cUPf+c53zH2CwtLY2KjJyUl94xvfUCKR0Llz59Tb26u5uTlNTExYgIQ5BytFqYRhaJzAtrY2LS0tmTXFGqF8NwERqRpQppHtcf36de3u7hoFg/WHoKSyLfgNr6NAGF82LK68LxTpXaSoy4lgIDMG5j/4IYUUcOV2dnbMHV1dXdWZM2c0OjqqF198UYVCwc4gra+v1+zsrHk5uPecvtXf36+lpSWVSiULnMDlRKhFo4gIOE6FQqBxfaxAXmfM4diBe83OzmpyclKpVMpc+42NDZVKJVN8jJdP4QJ/jEahD2pHQqAFQWB10dmg3d3dRlPgYYjG4aaQRrK+vq4bN25oaGhI3d3dymQyFnGamJjQ+vq6PvvZz2plZUU/+MEPdOXKFd26dUvvvPOOdnZ2NDw8bATS9fX1qhN9SMolZ7SlpUWvvPKKRVrr6+stssdgkw4EToOp3NTUZGVjmpqa9Nxzz0mqPsQYzIUqFR4M7ejoMEDca1ZcRZLTV1dXTShykMm1a9dMUIDZbW9va25uzqgskqrOicSi8guX78JY/7u/+zulUik1Nzdb1VwilAsLC7p+/bpu3LhhBR99eXSft4hg8ZhYT0+PcrmcJicn1dXVZVkBWBf19fU2TtK+cpH2o8dUV+nq6jLKA2WoSE+CksN9wc68xYeF4nMk2bz9/f322sLCgpXq8XXg2OwEhvr7+5VOp00AUWqKa3ql4bMkUOpBENi5AePj4+rs7NTQ0JBu375twQkUEJYoLl1LS4sJT+4BHSra8ED8KVakTTHujBFCKHo9oICTJ0/q1Vdf1cbGhh5//HHDi2tFPqO0Ef/6Ye1ICLRYrHLk+8DAgAkFn/6E+4MGpgIpVgwHYlAxI5lMqlAoWDWNpaUlk/ZXr1610kOTk5O2KVg0VDwg/44FRU4fFhsLlcnFzeB/flh8/vSc3d1dsz4Q4FgDCBSEOH3wbHaPy7BZPLjKePkoKGd2SjKhWF9fKYpZV1dnpwARHUXDYvkRfCBSRWCgWCwa3ws4YHd313JTOeW8tbXVMgx8FI8x47m8pia6jLDxbpkXMHDpEDxYeawdrDfoJryGEmHTeEjDg+D0y7vZ0j5vCsoCwYimpiZL2vYuI6B5KpVSMpm058Pa9vfiu/DyWCfe4uzt7bW8Wa6JYoUsTaqep0V44Yn146OdNC9MGHfvkvIZD3Xs7OyXymIMoWAlEglNTU1pcXFRp06dsnGrlYoXDQJE+3ZQOxICraWlRU899ZS++MUvWvQslUppcXFRFy5c0OTkpCU3h2GF3AjgTN35np4ejY2Nqb+/X2EYmktz8+ZN45StrKzoW9/6lllXN27cMHwJjX7jxo0qwi7aA4GCIGUhLi0tWUVdNCtAJhUjyNGjWgYlhBAqgPBQGTDh+Z4kI2GywFlc9fX1dnIQwslXHn3wwQeVSCTMbSSyiZsMvgSrfGtr/+QkNhabYXt724QH5cPBw9jIjBkCH6FWLpeteOcDDzxgnK7Lly9Lkh555BFTKljH8XjcKqVIFdpEd3e3isWiWUBhGJobLclAedjwS0tLplwKhYLRYFCWIyMjZr1hBaIkmEusuI2NDS0sLFj+ouehQT1hfH3NNdymxsZKNeEnnnjCzrig3PjU1FQVdoo7xiZmLcRiMcMRn3vuOd28eVMvvviizp07p76+PhUKBXNDEdYclpPNZpXJZJRMJrW0tGSKDwvxIHcO0N+nOLF2ie4CGXCuBBZwEARWUqqhoUHZbFa5XE7JZFLT09P61re+peeee04nTpyouqd31T9IOxICzeMfaFYWtxcukoxigPkLHYFIFu4Y+AMaCWGDtvduhD+nETPaYyu4AX4i0bgwrtEkPszPcxGdxSXyDGtoHuSFskDAqjyW6Cvk0nyf/AEnaE4sKiwmT1r0FAkEEMA4loXX0h5shx3vI30+OuXLPGGdEtiAyU8QBga8j1h696WhocGyK7D0eHbuzf+eIgNvDDY+Al+SWS0Is8XFRTvHAosKK8YTXMll9WMJX41nj8ViRskgpxJh1NTUZK4ga5DSS74GHs/Cc/GsCEhJ9lw+MAWFBo/BXwcBTbn0WCxWBa0cRInwyhyryluq9M17HH4+ouljnlrU39+vUqmk6elp9fb2VvVV2nd5vTV+WDsyAs1Lcm+BhGFoqR3QFG7dumXMf1zT6elpDQ0NVWEi+XxejY2NymQy5tMDQHs3AlDXR0tZ1FhzbGYmjABGPB43lzPqMuAisGCwirw7Q10vXziRZ6P0NZEwqBo+546y4WBsXliyEDY2NqwUj9/wvrHBvODG0vTVV3kWoo/z8/NmmXB2pufGUaQxFovZ4SxEtsA/s9mszYnHdHyQwOenMldsUOYLhcBcraysaGJiQg8//LBlIlCUkEyLoaEhNTY26sKFC8rlcsrn83dE4FA6VFkhWESNfSKjvmJsT0+PWahEc7e2tqrSuyTZ+5OTkxZxBoBnnlAQzB3PiIVMylu5XK4K8HjogfthTVOGigR2cNtaQi0Wi1VFTWlYjZ6zRwSd/QYcIcms6e3tbXV1damrq0v9/f16+eWXNT4+bhQnH1GGAFwul40FcVi7q0ALguCPJX1Z0kIYhg/vvZaS9B8ljUiakPTVMAxze+89L+lrknYk/YswDL9zt3vwsPz2/jJSmUXe0NBgZXgAWCkQiYWCZbCxsWFEWB8xQaB4ygP3YfN58Dca9geU9vwdhEw0xM51+A4Lk2dBsyKoPmhjsfoqHX6s0OLUwIJ+EdWEHpj1VimcJl7n2pzCRbSL+/OcXqP64MbOzo4mJiZs8/lKtDTPR4OCwBjWqtKBu84coERw+xF+uIOlUsnWFJgl1gVKQ9oH4D0Qj6vKISisgZGREZ0/f15nzpxRU1OTxsfH9d577+nVV1+1sxmGhob0+OOP6ytf+YpmZ2cteBAEgQlYyj3552ENeiucXNetrS2l02nl83mNj4/bEYUoY1IKCYxwdgWUGM8B/CCN/jE+WOHgnNHGvkEweg/m7NmzKpVKeuutt5TJZOx/BCX3Yo4Oa/diof07Sf9a0n9wr/2WpL8Lw/D3giD4rb3/fzMIgock/bKkc5L6Jf1tEAQPhGF4eKz1gMbi9NwnXEhoBBDzwJck3WFJ4NqQVsJP9Npsau8yYhkxcQyyVA1UYg15NxFrj82HNkND+3veC8emVvOAMdfxY0fWAoA4G52FEcUp/ML2QgNB5oW7x4pQGOAsNMbDV22Ym5uzhe/HAWXghSz5rwgO7k/fvBJACHsX2R/m4V15XCGsHYQoz8U6iApbvovgC4JKMdKenh6dOnVKTz/9tJVtn5mZMWuOwMuJEyf04IMPKhaLWapSuVw2N5GorF8P0XGnP+CtWI1bW1saGhq6Q4kyzm1tbZZeRYS5ubnZXOODXM6DGpCADxjUiljyWZSPV7p1dXVG3L58+bI9u/cIgI/uRejeVaCFYfj9IAhGIi9/RdLP7f397yV9T9Jv7r3+Z2EYbkq6GQTBdUlPSXr5sHugjdG83rSm5I0XPGhttEwYhlYeyIPtWATkKi4sLNjgAtLX1dWZm0Pb3d01TVhXV8kLZdFyXYB3NjHkTp4HYTc1NaWVlZUqwH13d9fcNNxTrLcPAoRiGdEP7gttg42Ha+7B8FoLzwtfb2mC2bHxsYDZrJA1cd35jCdGIlQAtalIATZIpI+sDgirCALSaBDgDQ2VktWcCOUjj8wBVJK6ujoD7qV97G5ra8uUo59/rwwQIJxzMTw8bBvt2WefVU9Pj+FzuVzOPpdKpdTY2GiBiHg8rjNnziiTyWh3d7eqyOPCwoKdPbG6umr8OM+18xYi1jxY2NjYmN544w3Nzc3pk5/8pOX8gs8hvGOxmFUNLhQKRu5mfj5IY3wp2c56o/pz1JIimR9GAZaxtH/S2DPPPKPl5WV973vf0wMPPGBnglLVGUL6Ye3DYmi9YRjOSlIYhrNBEPTsvT4g6RX3uam91+7aPJHRL1rMZw/SY3p7dwLhhBRHIyAg8/l8VWJzQ0ODfQcLhgH2ACYbiwlBGICvYNpjlUS1HNExtKWncngtxd8IwugG8+C8f91bZz7EzW+eH/eKo+Q+SEOwBEFggDBzwf87Ozt3EFujfcCy5ZT7Bx980IiplMf27PyNjY0qXMafJUHwxyeQe8oFAgFXm4AC841F1NbWpng8rvb2dlM49BchTKUNlGtXV5fS6bQRtuvq6izzAeEPURtqBWPGOsBDYDNDco0+D4rFUyE8ROLXKxQdrDbI477h0RAMYJ/41C9veR3UPLUlum6xqOgvsAMBOfiBfBecmiT/1tZWC/I1NTXZ2vJr/aD24w4K1LJZa5ocQRD8hqTfkGSMcrADpD+pTfCG9r5nAHg6nZZUGaCOjg7TaPjcvl763NycVldX7TRuivUhzBCeWCjgLKQIFYtFTU5OVpnWbOio6+MbGtVz1ugDz4OA9YCoF07e/fXNByF4z38vKhiLxaJVaY1agj56yYYGa8PqhY8HhYSCgR6H5Dfj7t1rTmdqaWnRuXPn9PnPf14vvPCCFhYWND09bZkfUF2g56TTaS0tLVm1CAIhuGjSvrXK5uS+sVjMav/DUu/o6LBCmJQmz2Qydk/vYhLgWF5eNivkscces6osFKyknDiuXDwe14kTJ/T4449rdXXV6B3UQ8PKI0UMjmM2m62KXDOHnifmgwXMeVtbm+Wwtra2WoEASptLsiyIeDyuqakpuzY0FK84UPAH8b+8wQAkIMmsNooVENVlDIENCBZBgSKgQ1BsfHxcExMTdqzf8PBwFax0UPuwAm0+CIK+PeusT9LC3utTkobc5wYlzdS6QBiGfyTpjyRpcHAw3N3dNe3sJ7G1tbWKQuB5Vxz9JcmY/NI+AEnBOzgvHN4LrpTNZs0qYwNiwXmgGReYa3sXjO/6ycdVw+VCA0EmBddDwxHp9H3H+gMH9HgbLaoZfZUJNCWajwqua2trVYfK8l0shY6ODktc5vnZZN6dY9z8s2KJeqwLzVpfX6lHRiEAqqQAruOOwM3CMiLoEK2rRbI8oHE0zM/zMRaejuMtcvAcOG+3b9+uUgpYIj/zMz+jkZERfelLX7IimJKqyNqML2cOcBg2ipM8WrIcWGdESHkeH9FkjHlGvwa8RUwF38XFRaVSKT344INV5blhC+AlEEklqAa+1tzcrJ6eHhO8/lQtL9jATKPYrbe8OBeWv32RUwi/KB7WPI3T4G/fvm1HBJZKpar6bbXahxVo35T065J+b+/3N9zrfxIEwR+qEhQ4Lem1u13MT1YU1CYa5V0XJD84ChPik2yxiqjUKsloE5LucBvR5v7k8Kg15muzedcWDNADmd6F9GCmD0b4+1IuiA3kv3uQhebHjut6fIwFiJtE4UYS733/OXyF8x2hYFA9hL/BxhhPOFleYGNRQyVg8+bzeYte5fN5lctls8Ihbnrrzt+LnFb/v6Sqz0jV9dG86+ifFcvbBwA4owHSM/MH/nT27Fk98sgjOn/+vKR9Qb69XSn5TeECxgCCK9Vpk8mk0um0WTM+GIFVu7KyYgKHDU8fogGjaMQPb+XatWtGL0FIE+lsbm6+Iyrva89B2AVmYX/gFtZae9G1jcKGOxiGoUVwWQveffTK17e2tjZbe+vr65qYmLDI+mHtXmgbf6pKACAdBMGUpH+piiD78yAIvibplqT/cu+B3guC4M8lvS+pLOmff5AIp19IUUuHCfQYBBPiw+2A6wDVuElsSADgjY0N05xgZVw/CAKrLR/VlCy4vbGRtE/Cxe0huRkXOIq3SariWwH2UvffW0JMOuNTa8y8QuA+fvMmEgmdPXvWNhmRPxZ3GIbK5XK2AVdWVqxopCSz6MA2sZ6igh1MiFpcYRhW4Yc+kLKzs2PseKqckhHAOGIVECVsaWmpqvyBO4wVfdAY+ZLWbFiOBuQs0ZGREQ0ODprrCeXj0Ucf1SOPPKKf//mfVyaTsVJOBBVKpZJeeuklC0DgtuVyOQVB5YQnzk545plnDM9jvd2+fVvZbLYq75HKJ0T8/PPxmejcU1HmrbfeMsEPeXV8fFybm5saGBiwc0IpdzUzM6N0Oq14PK733nvPuJqdnZ1KJpOanZ1VGIZmFETXXq3GfcEFOZh5fX3dSt17y67WdRiP4eFh9fb2amxsTK+99ppmZmo6fNbuJcr5Tw546wsHfP53Jf3u3a7rG4LBE073rnUHC/0gy8d/xyfO8l2icV4rcw3/2ahW9/3ymAWusf8ezVMLOFORgAUWJBgQZz7Sl1qTGwX7ffPfoR/RMSNkj+bleX2Kj/8uVg+WkqdCIGQQoFGcxYPK/M+1cYlRRHNzc+rq6lJ9fb3Nj4cc6D+ujY+GehzJ/9RqBC5QhJRB4lT1MAytOghnOuCODQ8P65FHHjH8jaorCKGZmRktLi6qt7fX5rKpqUnxeFyDg4Mql8s6c+aMvY8FS7CLSiy4hZKqzh9FoUcFdnTeGA8wJhQyCnxnZ8fItuBwPiJNvTVgGcYbK7EWdlWLZoRXhTvNmtnd3bVDjX3u5kFUDPqGS4oX5t3sWu1IZArQPBEVYUaSLVYUmBKf98KHz0NQlPaFwdLSktEFGGDSfbDkqMHFpEjVZYa9xYbQxJLBRMcF8wzqaJSqubnZzq8Ez6Hhsnqh4KNdvkU3McKDz/E9QGNSgby7Q0OoErRIp9PGQPeVGSCJ+sRnb0lDpfDuGtYqc9LQ0KBSqaR3331X58+fV2dnpxE+YbJ7y5T6ak1NTcpms2aRoyR8xK1W45AUCjy2t7eb+4UVOjQ0pKGhIQ0PD5uF1tLSokcffVTPPvusJdm/9NJLunLliuWgrq2t6fbt20omk3aqfVtbm8bGxnT69GnDgaGOgNe1tbWZK7W6umrlwRsaKqepY+V6Lll0PTLnnk9JkGZ6etpq8pHpwTkYrGWCY8zv2NiYVlZW9MYbb9g9BgcH1dzcfAfcgXvpG/PNHmbOuHcul9OpU6fM4me914JS2D/0sb6+Xr29vXfcM9qOjEADM/PAPgKBMtge3PQ8JTYum8ALBVw5j/sg0BBENCwoXCo+G2VSe+KfDwT4CgY0JoMoLPgGScKA74wBQrNWACD6mrdkeHYPiPOMKAo2hY/s0hAejCmJ2FyfZwQk9ulTPgDiLQqPZWI11tXVGb2BogLd3d1mOcIX85Fbj4kRJOCsASgYvMf9vdUctWoYDzh6kqp4gVTKwIohaEGuJ+42pYJYQ9A3oIjQFywZfwAMJ7kT+VxfXzerzGOVKFAwWv8s3mpj3XZ1dWl9fd3SA6GkQDtiPDEa/EHDnIp15swZu3YulzMGAnPEOB1UJYMf9g57AMHr59Yre9+89c+68WN5UDsyAi0KfNN5BqS5uXISNhrWCzEfNMCKY3Otrq4ql8uZQPJCiMEBvEbrbG9v2+HDEBg9LsUm95vG/0aooOU5no7oIRVzwVvYgP6aUTfW3yP6vxeCLBo/ht599EEVHzHiO54vRyTM589h3XkXFG4Yv73F5NN3EG7kGq6srGhmZkY7O/tJ3+vr6zYu0p30Eza3j5Z5i8qPjR+vqDuKoMClgSYEZ4qGUgVXZAM2NzebUPKBLGgeROe9gPdFCtfX180y8yW7pf1Tp3wqF4o6mg5FH1mfHR0dKpfLmp2dtbMG4OJh3YJR+kAByqS+vnJ61tramkVssazplySjY0SbhzE8J9AHAaICzM+vn79oIKyWlxJtR0Kg1eq8J1AyCfzG3ZD205R8ZHFxcVFzc3NaXFzUzZs3bWKwSjh/k/v5LAQ2LMew+f7xnu9rLQvJR3GWlpbMpCeZW5LhFeA7MLaJEnmhyH2iC4HnReOh/Xx1U1wOQGNfzdSnY3l6CgsMAc9m47MsWNxuonNEN9GsUauNBQ7VQqoURPRZGE888YSSyaSNtW9YFPzNpkLwUgCylguD2y3JaBH0AQHT29urJ598UmEYGoeRA3V2dnaUSqX0S7/0S8rlclpYWNC3v/1t3bhxQ6+//rqNO8x5DkQmSr+7u2vH4lGOHaEOnQGstb6+kow/OzurZDJpFqv3Jjwm6ZVIMpnU2tqalpeX7dpe0aEEfE4oArevr8+CMJKMG8dnWDso4Ki7CB7nI8BALD4rgEKqnnt6EHbMWobP+RMh0A5rUTfMWyJ+wXtcYGVlxSp2SjL8hkicTxliE3Mff102BwLPV6TwE+kFWvR6CBlvIXIPv8m99VdrQzIWtcbGC1d+WFT0z2dCwNhGkGENSLINKMkwRsbOW74IK7BDvzGwnqNgPQKfKBwAPT9BsF/mKMpL8mONsPRsef+8B60h3Bav6dkwa2trxhXDjUVoA2Z7T6ChoUEjIyMKgsAqFK+trdkpUpw9QZqezwSAvEvhTYJEnK8aj8e1ubmpxcVFtbW1HVhhwltqwCe44bxGRLVWdgprB08FoenTi1gPVEqBLnVQVNm7+VH4xEMkKMa7CSjvsR0U9PHtSAi0WhLaCxdMVr/ZcD28O4nGWlxc1Orqqh2a29raqm984xsqFotVeWZYKjDAETLb29taXl42geSFnzefvZbywsa7XDwXn+N+3iKDBhDNKfWtFoZ20GdpXqAhhHd2dsxqpZimF2j+2ei/B/093hedt1oWJBFFKqKgrbnW2bNnLd8ykUhoenpa6XTaskEOekaCQxBVgyAwSyc6Tt7dRjDzGU5hn5+fV3Nzs8bGxvSDH/zA5oYsEc5/uHTpkuVcPvnkk3rwwQc1Pj6u5uZmTU9P22HUU1NTptxGR0eNLQ+NIQwrlJaLFy/agc3gU319fRb9hE8WxQEZA9YjShy+YVdXl9bW1jQzM6NUKlXljqNUifQyJgjw+fl5Ezjnz5/Xzs6OXnnlFQ0MDKi+vt6IxRR78PPt+Zg+wkqU08M8eAAeU/tR25EQaFI1VoJgAVj0f/PwUddPkrlAhHs7Ozurcg9puLJc1y8MSSZ0eM3jRn6jey3kN7O3ImqB1DTM/1rCqlar9ZmDFgL3p/8IIMBhIsE+gOLHx2tzLFv6C3Mf65Mx8KWEPGbi3wdnQpAPDg5qYGDAFj5ZCXdLcZH2S+pA9zhoLDxuyjjybGBdKysram5utvQaXPLr169rdnbWKq1QKXdra0uPPfaYOjo69PTTT5slByMeAUtRS5+8z/0oFJBIJDQ2NqbFxUXrM4LPV5k4yEJhXbCOSRcipSmTyZiw8srNu6Fgc01NTRoaGjJCLsnto6OjFgihsm4t6wz4Bws6Fqs+DhD4h5OgOMTnboTZe21HRqDVah4f8AJCqnavPOgMgFlfXzlvAHoGzWu6WlYHk+LLbXut7yM4fMcD8bwWxZA8gE9j8/vvRIMM/pofRIt5gcYCpt8Avt7c91gdv/3GJ9eVIAcHozBOsVjM3oNA64U81iypVFijqVRKvb29Zm1PTEwcGPnyz+YhhmgubXScogLBK0LIuuBqUCzYmBzqi0ACTwvDSrn0kydPGq42OztrJX3q6uoM8Kdysi9fxcYOggq9YWBgwCK/CB+EYy23LAoz+DHhGMebN29aIK2+vlLp1mOkUe+HJPD29nYVCgU7X6OhoUH9/f1aWFgwIjLKinH1e4f+equYvlFeqrGx0cjJ3vPyc+x/R18/qB0JgQbA6bEVggLebWKxeZIqALx/UOgdg4ODmpyc1Pz8vGlHmrei2AzgSWgqForPDPADH938YEreoqH/0ED84guCCsE0n89XlQH3+JukqkwF3zw4T6IzmFA0cgSmODAwoGKxaAeeYD0RKKEkkxfkPuLoyZh+oXIPggT+WEEfqPA43M7Ojt59910tLy/rV3/1VzU9Pa0rV67YNb3SYK6YH4IvjY2VI9J2d3ctTzWq7T1tIjp30BGo5Q/DvVAo6I033jB3nGf1SvDq1auamprStWvXqigNLS0tGhsbswKk6XRaQRBofHzcDlhmbdy6dcuslM7OTjU2NiqXy9l6p8gCGKPHY1mzkuw4QqkCvJ85c0bT09NV6Wac0u7nF2u7paVFhUJBQVDhySHQSDL35b4vXLigpqYmffrTn7Y14XNbWXtwChHk5KwSbGH85+bmbL1AB/FwEPPuT+c6qB0JgSZVW1xRvzyKpfmN6rVA9LM9PT26deuWFdHjulwnihd5Te4tQS8caoWYvYBiwXmLBO3uQ/TgCbWwqFpj4vtX697erfUAvv8cCxMLCteqrq7OqjVw/gKuPaF97oHFTPgeIRzFeHxE1Ifyo21lZcXOFKCYo9fyXpj5a3hB6p/5IA0enTcPqHsLHGwuFotpZWXljr774ADpdT5BHnwUPh0RSm8d+ufzubupVMqsNElGIfHYKsquFubsg1nkJGOZ7e7u2txGAyjRIJi3trgvVqan1KysrNxR8smT1XlOT5j2VXT99WOxmLnEURqTDzT9xEY5vYBCw3sypw9FSzJzGS5Re3u7Hn/8cb3zzju6deuWTSpCh2iNx874vbu7a9GhaHCi1sb0YW0EGoILsDafzxtviT5QiNEL1w/b/GJkcfDMbP54PK5MJqOJiQlzIz21YGtry8iVLNBYLFbFN2IMfNVextGXCgqCwHhnjBf8QSw5QPJisajl5WWzqsnE8KkzNM+x4z70P5qofi+NsW9qaqo6VAXGvRekrEfvYu3sVE464v9isahsNitJOnnypOLxeBX3TKqQeLPZrP3Pmj537pyampr0/e9/38aeoITf2HfDZrHuqdmP4Dlx4oQRg1G0ZIiEYVg1tmTNQBBeXl62o/LOnDmjzc1NXb9+Xf39/RoaGtLCwkKVhU6ljp2dHU1OTqpUKml1ddXWF1BFXV2dZaVQ/cYLY3iaBHJ+IgTaQdgQVoQ3kaXqSJzXfiwcrA0SrqOJ5lyTBelPupZkCbq0KO4WbQy4xxB8ojwCDrOfo74oGuiPf/ugje/5AIW3Jj1GSNIwFUMZX8/J8644G9e7arzvU5o8LMD3PPDMtVmkAMXgX1SsiMfjGhkZMZqCFyhcgwUe1eLS3aO+tRruKJHucrmskydPanNzU11dXQbeY5Hy7D7/1itXwPC6ujpzFzngBSsHnJFNOjc3p3/4h3/QwsKClfLe3NxUoVCoIoZ7gYYHcNhzd3V1WSpgGIbq7++vSg30FBr6zZiQ0bKwsGCCr1gsVp24Rj4upZ+8h0BNNSqPxGKVg2M6OztNsaEEgSJaW1sVhqEFXYh8sxaiQcBa7UgINKn2pHi3CKFWC9BkwyJEiJAtLCwon8+b3+3D917wrKysVG0c/5oH9j1nzDcEFxaRd119MIFnLBQKpqF9yo13t+9lc0bdEP/DPb1wam5uthLMXiGQ8IsAijYfcfTCEmHosTF+e0XjLSk2Da8hLG7fvq3h4WGNjIwYQO2fg+8gNMDSDsI177Uh0DzRlEoUyWTS3CTveuIBoKyw9rHyPO7oswCwgvAkcMuWlpaMu0aQYXV1tcqCZUx9IMQLdd94HWFw7do11dXVqbOzU0tLS6ZEotggcwa5Ox6Pa3p62k6r4tBn9lBzc7OWl5e1tramsbEx81CYMxT1ysqKUUk6OjrU1tZmY4FyDcNKRQ8I4cwvR/7Vmuta7cgINO/6eaCbzceGjFpI3s3CjH7rrbc0NTWlr3/961YNwbsMXiBKqhJU3MvXf/JRwmik1W86JjMayWSjgBNR8x1Mw1tLTKS/b3Rj+2dn83gMr6Ojw4iVCGJJRktAsGOtUvvMUzi8mxV9nqh7i8CLYmaMBZ/HBaf2GdHWnZ0d5XI5nT59WhsbGxoYGFAqlaqqd+8Xs3f7a1loURyW5r8TxQRbW1tN+fX19Wlzc1NDQ0NVbjj3BXPkbxK4YdZLFZCeEjxkEBAUopRSQ0ODJcOTXjUzM2OnN33xi1/U+++/b0EcrEDWLZQKjwHy7OVy2eCMS5cuWRYHcy7pDiWNkl9bW1NbW5sd1uzPTiWKSj9SqZR6enpUKBS0vr6uBx54wKxHshY48i+dTlvCOpFgT5HyyhiOJM+IYvmJEGhe0HhsAjMbIeLJoVK11eOB8/X1dS0vL2tiYkLr6+t3EFb9wvavsUD531sxHq/zm9ljbD66xsbmep6L4/MG0bZRweGtJQ+URsdNqq6qwYLz+af+erhLHj/zKTR+LBj/KHgr6Y6AA5rd4ztRaxNB5nMYCY6USiXbIJ5G4LHFWgECT/E4KCBQq0UDKf5sBHKH/ZkVXoj6sUKBkKfLXLHpub53FVECzJVXkuVyWQsLC0okElUHEmNRRWk+/pm9y8da5j48M2Rk/o8Gy4BH/MHCPioZXXsISS9o/fNJMqXlg1B+/0S/6z0vv54OC/rQjoxA8wx+pLGPpOFKRnlpfN9rbyaGInte2PiN4DedH0gie2x6iIRYVRxTxnXBRLgHtb18aaHNzU0Vi0VbrDDAm5ubq8rteKHu3exak+mFoBdu7e3ttlC9EKSfnZ2dtrmoZMJG9HmYjK8PWpBZQAQQbGhra0uFQsHu5SOALEZfVslfH7d+ampKb775pr72ta9Zwc6o5R5NfA/D/cNrGeuDsCX/P31CqCcSCeOG8RoCzVutuMm5XM6Y9qlUygRYtJoLLjVKC2GJqx7FOJubm3XhwgXt7u7q9OnThgfDB2tvb7+D+FxrPUj73gHUJpLmY7GYVldXDVpBwYHr5vN5I84mk0kLMrH3PNufscxkMmpsbLTqI7iSpVJJS0tLymQykmTP75tfZ17B0H/WRzRyX6sdGYHmtYgXNrVMzKh28hgarowkq5+ES1ELY6L5wAMDy99RMBvLhc94S02SaVOq5BLh8qRftLn/7mEpIB8UG/JWZBScl/YDKNToWlxcrOL+sYCYC/rJhvWnBvlj7Lg3m9rjNN69qaVpPfbkLYdaz4bghYsoyYQHZM2o9RK9hlcgYGPwnojE+aAH14AThcCDuwdOSOOZPd7FdbDofBVfX7p6YWFBL730ktrb2608OGPnhXEUR/X3RRgASXCASltbmwqFgmFpBAcQVJ2dnZYCBcyTy+XMNWaumpqajKgNTEPl4e7ubnsN76RWuSFpP5PDW27eEPHcTl/yqlY7EgJNql5w0Sib/4lG8fx3ECLgBQMDA8Z2jsfjVcEFNC8b1Z/gzYb07oK0n1rla617q6WWa4Rw4/RxJtYXzYtGC39czffRj6/nxuHCLy4uGgjN8/iyQDwX8+KTi6Ok5WirZVn6/vEaEUB//VrCD4HGZ/zJW/QbRePH1GOm3uXhHuCbXAuBFnWdEdYQvUk+h+6AIPfP7teytB+E8PXwWHs7Ozuan59XPp/X2bNn1d/fX2UlInA94TnqbnoXDWtpcXFRAwMDSiQSJmx2d3ct6ugFWi6X0/LysgYGBkypR90+MF9faXhqakr19fUaHBw0pcde8m6ob36O/LxIMmHM/N0tRepICLTo4pJU9RBRwNAvQr4v7VsdDz74oE6fPq1HHnlE3/3ud/Xaa6+pVCrZhDH5+PQtLS1m0ntLxoOgUQzK9x1rwF8foclkJ5NJEw5EergmxMQPggHdrXlhythRuub999/X1NSUHUpSV1dnFTOiVlQtnIYWdU19q6WJoxZo1HJEqWBlHwTss17YYL6GGRvMJ2NL1QUDowKN/hOkIbNkdHRUly9frlqX/rmjz8GG4weLC8XpI5wcHEKWgSQLXvkgxM2bN3Xy5EnLGwUY97QjAklggKw/1kEqldLy8rKuXr2qRCJh5cAl2XFyROrr6urs1CfIsARB+BzXxYptampSsVhUfX29PvnJT2pqakp/+Zd/qU9/+tP2Pkq8VhSd5/euJwqePeex0sPakRBo0p04mLeO/AIGrPdBA685qXCLlojH4zUFoDdpfZpP1OT1QjRKfvXvS/vAv7+utF/0DkwITMP3Iwq+HxYEOOy1Wq4H48RrEB/9QS3e4qolSKJWVdSyiro+/vn857xw8GO9s7NjlXyxuKLfZ46jc+NxNjb4QVY+z+CVj3f7KRhZLpftcBUsn+jarBUl9GPkMVk/Lg0NDUayhpIBCF4ul5XL5WzNLC0t2fFzKBy/Vg9SPl5Qt7a2qlgsan193bAwxhiKBIKKMYjSpDwJ3c+FFz5YrVhVCEQCYFFYyQth/xrz4v8+DI7x7UgJNOnONCLAd8BnIii4Td4vB4DkrEF/PbSDL91MFMlbgYcJlKi1GASBEQql6tOovZb2Lql3OXluLyyZYEi3PlIWbV7w+msRsfOhbqwDQGU2bdTKrYXJoB2jOF8Uk2RuwIe4p7dCmRM/zru7uyqVShodHdUzzzxTdS8f/ZL2lQaWsaQqpeRxQNzAWpY31rwnNYO/YbUMDg4al8srRcaGE5SWl5cVj8fV0dFhGxOhED1tCmtlenpac3NzWlpaqkoTwl1lzHh+LCYIwN71wnKq5V5LlVOvgDzW19dVKpWsNNPU1JQJ03Q6bXhkR0eH+vr6TEHQb+gjUoVPSZCM/VUsFjU8PKyHH35Y3//+9zU3N6e+vj7j9LEPWN9QhnDxo8rxXuum0Y6EQAvDCjuYJFavcaNSXaqu3MAEeO2USqW0u7ur+fn5OxJyGxsbLbXCC7Soy+sHkEUc1bRsYD7vo7ReS/uGIPbF96IpWFhWUVcvij9EtVjUVWZBsPj9BkMT09gk4ELewuTz3sKKYma85gUcSgjtXAtXAo9ifhAyWBB+PUQtx6i13NraapSQKHThFULUyuT5/DPU19ers7Ozqky6D1ahLEqlksbHx5VIJJRIJOxksXQ6besNkiwBmLq6Ot28eVPLy8smgKNeBH0h4uoP34n23SsHP/a8x7xmMhmVy2XNz89rbGxM8XhcyWRS5XJZpVJJvb29Fg2tr9+vVsOZCihjP+5ewWGlUkUjHo9ra2vL0qJg/0uqsqLJhfUQCILM01SwiA9rR0agUXvJ53hFgVT/MAi0WpZdd3e3VlZWNDk5WVVVwmMYRHvYuN6NiGoEb8Z7V9X7917LRjea73NdXZ0FFlZWVgw38oCn3+i+HeSC1hJsXqCxYUj+ZnwhTnp8sLe31yxYPy4Icb8I2eBYOz666ykazIuPmvKcRH47OjokyU4/am5uts0edVf8XOAOItBIVYoqA+82ejfTY7VY1owFAg2PwFOGfPTy6tWrSiaTVu22o6Oj6uxJIoHUUtve3tatW7esCkYtd4t7UGbcZ6Lw/N5t82uMceJ6CLT+/n4VCgXNzc3p7NmzVgZqcXFRxWLR1sXKyoplPsARJD3QCzRfmZn9F4tVKCFra2tmBXrOoSdhE8RhX/N8nirjo5o/MbSNaKuFd0UxNh8K9wKwXC6rp6dH29vbmpiYsDxOeGWdnZ1mIiM8a0l9f0+PCfk+7uzsGIt7bW3Nasb7tCkmjL5xjkA6ndaVK1d04sQJjYyM2ORGQXi/MD9oQ0AzTi0tLUokEhodHTVrjQ0MhlJfX2/kV7+BohabX4he4NTV1ZkFTP9xvRlD5g46iyT19/crFovpwoULevbZZ5VMJi1QQ3I81pqHBojWSbJAi490H+aux2L7FR7AyhgXLNtUKqXh4WFNTk7WnJ/t7W0tLS2pWCxqdnbWFObCwoLa2trU1tambDZrZwSwVlgTCHI/39I+HvzEE0/oqaeeMl4YVCBc7sMi5B6fbG1t1eDgoAqFghYWFlQqldTe3q50Om1HKnJdLEOwvjAMNTQ0pMXFRS0vL1uZIyK0rG32CidNvf3228rlcurr69Pu7q4uXryop556yhL2fR+9YvXC2ntH0FwOa0dKoPkH84BktEUBUO9qea4KdcYO+i4biw2BpRVdHF6YeZeA77JIEW5RgYbVhxWDZsvn8+rq6rrDnfH9jP79QcYy6qJ6HK29vd1e80Kd5/KWF43FV8v183mynurgBRpCjTFGiEoyi4xTlKBl+M/wXFHl5q0sb90gAA8bHz8/vOYPNmltbVV3d7dmZmaqChbQEDLQYGDVI9jb29vNamR9+Ih61Dtg7fG7vb3dBEgQBFW0FF/tmOf2rmYUhkAYgBPi2tMXhHut65Hd4jMbolSOaJSS11jvu7u7dlhRNKuG60TnBcUEZHE3LO2uAi0Igj+W9GVJC2EYPrz32r+S9J9J2pI0Lum/DsMwv/fe85K+JmlH0r8Iw/A7d7sHA4Q7FATVtaFquVZ+AFnQra2tSqVSkmRnE3JaDBwrX+EC0Bhmv+fNYIF4hrsXjt6d8EKA/mDV1WLsc7pPNps1BnU0kyGKAX1QgRbF5NDoYELlctkOnuX+uCYtLS0GcqNcPEDtxwCrhnljYYJjcV/AY6xBxhkA3mt7b715VnkUgqDhUvuClSirg6gCPsiAVcLnwMLW1tbU09OjJ598UuPj4zWLC0atdtZZqVS6IwpeiyxMBgzH4mHpsJay2awWFxc1NjamWCymXC5nzxy10Pwa9FYsLqEXJMvLy5KkTCajtrY2JRIJLS8vq62tTcPDw/YM3rjIZDLKZDJ6/fXXzWrDCECo8Tytra06d+6clpaW9Oqrr2p0dFSPPvqo3nnnHW1vb+u5556z/bG4uGh7kP6yF1GQLS0tlpd9WLsXC+3fSfrXkv6De+1FSc+HYVgOguD3JT0v6TeDIHhI0i9LOiepX9LfBkHwQBiGhyJ5LGJPkCQXEaGD7+w1jvfhWZSrq6v64Q9/qPHxcc3Ozt5xmDDmqydeekKmt6a8peI1EdfxC6+WxehD6tHn9dkDvpICY+F/e+sh2g5yqbinp22Ai5B6NTc3VyXIyGCAO1Rrc5Dh4HGo6P29u0Cklk3rsT0Evx83T0kAJvDjEMWIoj8I31rjV2vcECAexyIVbG5uTu3t7RobG6uqPnzYePsxYJ5rWZNcy7uxrD/WKIz+ubk5uy7uNBiU7w/f8//7562rq5Tj4YwB71o2NDSoWCyaVYsbCZ5FZgSVfUulki5dumTBEPrjhSiHLoObeSxtYmLClBxBAw7LQTl5w4C1SRDwoHZXgRaG4feDIBiJvPaC+/cVSf/F3t9fkfRnYRhuSroZBMF1SU9JevmweyAsWltbLcseNj5CzmMiCDo0FK/jsrz44ouanJzU9PS0DXQUJ4u6kNFWa9HW+o7H2bzJXQsLi16DgyhwITzojiBi0UY5cAf1MTqufqOy0bu6upRMJiXtV+DwmRT8eCqAdx+g0rDQalke9A1wPAj2y5rTL29Bch9AZy/QmDtvgfjUH4/D8AxeGR3mdnoLjQ1ElY+VlRWrmkEe8UGtluA86DU/NwgOX0mCZ2hra1M+n9fU1JR9z2dx+LXB89R6Vsaorq7OIA4MB1+goFQq2fXoF5kbVOBtaWlRMpnU5uamfvjDH1q+Kf3x5wMUCgWjdgRBUFVl5cqVK0qlUspkMsZGGBoaMiub5/ACmmrLh7UfB4b2zyT9x72/B1QRcLSpvdcObWgnfoiSgfncy/f9JN2+fVvT09NVbqNvBwmrWguvVouCmLyGxeJruEWtmVisclBEW1ubOjo6zAX04ekfR0Oj4dJ56/Ls2bMql8t655131NXVpe7ubrPg4vG4CYaNjY2qCG6U0AmG6AFe7kEp7SAIbBFjobH4gRS2traUzWbNMn/55Zc1OTmpz372szpx4oTS6bRp/2hic7S1tbWZKytV0ngOG1MsUeglnnqzsbGhTCajdDqt0dFRlUolTU9PV2GdtKjCOug93qfAAXQVX/PL42uUFLp69aoGBwc1NjZm5xKAg0ahhbuNz+7url555RXDBzEmSOG6ffu29ddjXYwr32Mdvf/++xoaGrIacUREcRnj8biNM0UmMQBmZ2d14sQJgyMwXlhTEONR6AcpJ9qPJNCCIPhtSWVJX+elGh+rKRmCIPgNSb8hyY6vRyAhhD7o5mYwqN/vNbq77x2/EUwH0S1qYXheUPnvINBwiX2yO0KBelOeQe2FwY+jcX8oDN7Swk0gIucPZPY4prTPBveJ0yggab8yit9MYRhWCXMOt0CgMcfMFdU7sKYnJia0urqqs2fPWjkhrECfvlSroQRXV1fvylmSZBYg1gruJ3PBmFB+GvfPj+m9Nr+OmH8v0Jg3Iq4eDyRjgLQp6B8H5TbyHNHXSChHWYH1sWbDMFSpVDImAN/DBfQFLFOplB2mQrCL/nJ9rs3zYXX74gU+OOJlQK1nuFv70AItCIJfVyVY8IVw/65TkobcxwYlzdT6fhiGfyTpjySpt7c3hGdDWDoanbxLXxSLVdjHy8vLFt7lmLCo9mShYHFQeRXh0tjYaMEFGi4uAsq7c1gbXN9bmV5gcW9cvHQ6bS5ZLeJoLZf1XhvALCWTfXS1o6NDyWTSam75jeX76zFM8I75+Xmtr6/b0W47Ozuam5ur0sq7u7smoFikPlrp3a1aLtj169fV0dFhAs2Pqc/MqNWgXSDQsLwO2vgcVFwsFu18SGgVuEobGxsaGxuzQBObkUoqku5YZ9619o0xPnPmjNLp9B1z1tDQYHAAAiQMKydM7ezsaHh42BRRoVCwYpHc1//mGr7xjIlEQpubmxofH9fg4KC6urrMtVxbW9Po6Ki6urqUz+e1u7urdDptpYXIs81kMurt7dXu7q7ef/997exU8qjX1taUy+WskkcqlTLX1hcyIPB08eJFra2t6Wd/9mctsOIr1fIceBqHtQ8l0IIg+AVJvynpc2EY+spv35T0J0EQ/KEqQYHTkl672/XAyryERmN6K8cD0FHiLXjIxsaGsZ/r6+sNeAez8UfhcW+EGz9euHAPop1gHf79Ws/jI1DekuNabDzv5vj+eIvxIPD9LnNUdU+/MFAesViF1Z3NZqsCEjQCKh4/WVpauqOsdD6frzr5iEXpgwO1hFhUYHuBQIifzePxOua/1rP6dpgLxv28sokGnyipnc/n1dPTo8HBQavGIVVoQXzPt7q6OnV3dxuFxxf3rKurs3Mz0+l0FeWBZwRm8cEoiLmvv/66ent7Defz+G10XP3ekKrJuIlEwnJ6ETzRABjPtrOznz+KBUmgoKWlxY5P9EEeFCg/eAKsE/Dj+vp6c0lnZ2ft6D/gJ7wnTwU6rN0LbeNPJf2cpHQQBFOS/qUqUc0mSS/uDdYrYRj+t2EYvhcEwZ9Lel8VV/Sfh3eJcDLJ/vgyBAdRDS/MvECLAsJgNRRiTCaTymazKhQK5gb19PSYkIxGIRk8CLM+ysdiRzuzCXDHAEM9sOujepLuuA8EVI/beFeVBeSvG92g0eCDb14Q8j1PU4nFYnaMHM8Ge92z/3O5nEU/scy4PoqkVh+iFnEtiyU6Lv66VKTwG4rTxj1/C+vLBwJq4VbRMYsKPJQW89vc3Gw1/cF+yNekL9Fn2t2tcOiGh4fNuiEBnO81Nzerq6vL6vV5gJ9nQ8jhwq2vr2tyclK3b9/Www8/rL6+Pjsfws+tfxaPeUafH9z02rVrliONhR39YVwZawT90tKS1ZBDCCMY2b94NhzQAzUF63J7e1s9PT2SpHfffVeZTEb9/f2mOD2+eNhap91LlPOf1Hj53xzy+d+V9Lt3u25VJ+orZYzBM3zOGma/VJ0SwkT5hcnvZ599VtlsVn//93+vzc1N5fN5A1u5nxeI0R+pupIGAoeID9dggnEj+B595X1PJuX5ENZYaB5ji05idFHeq1Dzz+eF6vLysmZmZnTlypUq/pDHw7y2BxPxmQO8ftgC8/NSC8+MfpY+s2l6enrU0dFhC5v3vKD388McowRRDrWsN9/AhBgHlCsWxdbWllpaWtTT06NPfOITNk/lclnLy8tWmgrhBqzA4SIUHA3D0IQZlWg5FYpDc8DGfGqQpzHt7Ozo9u3bGhwc1HPPPafOzs4q/lbU9fXYrJ8z0sQ8DaS1tVVbW1t2AvzKyooFiXB/gyCwIFFvb6/y+bwmJyfV39+v7e1tffe731UymVQmkzGCOXtjdXXVMMl4PG6KE75bZ2enyuWyrl69amcPUEGYIM3doKgjkSmAixZ1T6Rq1yLaohubyRoeHrbjucBe2ABeA7M5oqxlr/WjQi4aRPACLZoeJe2nBXFfshL4fNQCq2VV+b4d9OyHWUj+f8YAPMSnZR0EdAPk17pf1Lqq1Rf+ryVYvLClf2CgqVTKKqky3rXc7+jfzOtBbnpUEfqN72kezB0YYmtrq1kTdXWVXNjV1dUqwi1rg8OGEcRRIUNmSS6Xs3NJi8WizQ3WcTRYhiuHgKGOmS80UOt5ow1+IM8MRYN6dBCEKf6IW+oxQyy1bDarkydPqr6+Xtlstoqz5y1O1j5WmyRTlmEYWl27hYUFo5IgyH0w6bB2JASaVH0SD67X3UK00Qa7eWhoSGEYanZ21vhsSHwsQY/LecyKBeddyFr98FYV5YBqVeTkur7KBuC2dzcPwoFod7OE7qX555X2S4Xf7dp3W0RRrMb3yb8OIO1bPB430J4fkqbPnz+vnp4e09IHAfu+n2wENgyZIXcr3Ry9FoKVeyYSCTU2NiqdThu/ijplCwsLVd9JJBJ66KGHVFdXZ4c6I9TW1tY0Ozur2dlZwzOjQRP6EMUdPV4GJ7BcLmt2dlaZTMZO+wIeOQg/DIJKYAgMbGNjQ7lczgIwnAm6tLSkRCJRc9x3dnbsSDuCB2EY6rHHHlMul9OFCxc0NDRkVBCsTO9KI+wpInHixAnl83mNj49bhBWlQDWenwgLzWMAmO61LJS7tba2NnV1dRmWhjaLx+N2AAUCzZcNigozb71FcbpaG5UoaS0h7C0w/+PPKbiX54xaMVFc7oM0npnFHA10RO97kGUVtZiizxod21oWLDQRz3znfz7rsZyDgP5yuVxVrQWSKPP8QQQazburJIcT3YQF708Uw9JdXV3VxYsXTaF6ChJBllqWcVQhRANTNNYb9Aqf8lcLZqDVugZWUaFQ0MDAgOLxuHp7exUEgZaXl9Xf319zbIIgsGvgBcViMXV3dxtuSJ6z398+GMPckJlRKpUUhpW6bEEQWFYBeHc066dWOxICTdqP/iHUvCVxr62rq0snTpwwEx48hJONSPvx2NVhGJpfHPSxVkOQ1epvrRI8pBodRic4aIyiC9XjVPfasEDj8bhtKn+96D15Bv+a50/x/P4nysWDqFtrQe7u7qpYLJrQK5fLVeWD+Imm+vi2vb2tbDarZDKp5uZmy/kjKhctye2fxSsIxpINi4KC4EkWS6FQUD6fNx5XEAS26ZaXl/Xtb3+7itTNPXxVlWg/DgO9fT8pfbW4uGhBiP7+/jue4zBF6Qudku988uRJNTU16fTp05qentb09LSGhoYUBMEd40dQC2FcKpVUX19v3hE14HwAzWOuXvl1d3drbW1NN27cUFtbm06dOlVVYquurq7qBK3D2pEQaDzw/Py8wjA0MNZvVMxz7wL6yNnu7q4SiYQGBweN68IBsJACGxsb1dXVVVXr3fv6UeuCBeGFEn3xwhdyqLci+ByWoj98BEwmlUrp3Llz+vSnP23vsXHJlKivrzfsoRau5zegb971KJfLKhaLZhXC8GYsAMFZpFzLlxTimTxZkv4xhj5gwA/Pxfj7wo2eFQ7u4se1UCgYXQT6A8x/b8HRz66uLrOUh4eHbax9QML3zY+bz0AAxCcNKwxDOxWrt7dXExMTunTpkrLZrGE8fi54bn+fe20HCSHGLx6Pq6enx2ghHn+jKi3UEMbWp4j5NdTe3q4HHnhAU1NTWl5e1tbWltrb2zUwMGDzTlFK5ruxsdEYAAh8Anfb29uanZ1VuVxWb2+vuYfZbNaegTHCMg3D/cNp/MHOtIaGBuVyOU1OThop97B2JAQak0i0hk3iUzqk/dN6opw0BoZ6X7Ozs5L28RmiJAycL5cSxYi8m3OQW0ewgYWLC+JTNvgOHC2S0MERWlpadP36dSM0YrbzXXA2H6VCmByk3Q8aV64PbuhPsUYwYIlRnwtrAwuA62A9RwVaVHDwtx9fPo81I+1nIrS0tNj4YNWVSiU7wRuSLHxFeIoIW6wIBH1HR4fNix+fKDmTdcRGCcPQ1iHWNFhVuVw2LI1+I0ARzj4V7LB2N5gh+n4YhmZtMvbr6+sGzhcKBTuohDHxubge3sA6amhoUDqd1vLyst0vFoupo6NDKysrZhiwZr1AxEVmf7W2tlqRVtxIxgl3lPt6weZd0EQioWKxaFFPoBmiyb29vYcGP6QjItBY+IlEQvl8Xtvb28Zgl/YrY7JQfHTQN/Cx1dVVy5HElx8cHFR7e7ulG5HGQ9qN511h0SCgwJkwzflhswJYIuS8pYc1Ep28lpYW3bx5U8PDwxZZ4yBgAFdwP7+hvKA/DEdjjKiJj4sLoTcej6uvr0/19fXK5/NVETYIl9zDCy0vnADfPaDvS5sjuNhUBFq8FdbT02OVOACjyWC4dOmSZmZmqkD3dDptvL+zZ88qk8lUWere4mKNMIbMjy/RDX7jG5V82fA8l6dSdHV1mUKsr6+3aCeWWzabrRJwHwbr9M0HO7LZrI0hNIjt7W1NT0/r9OnTCsPQDl+RKrm77e3tpqzgtkEAbmho0PDwsJ3F0dDQoN7eXrW2tqpQKJgg5J5wyYAGWlpaNDAwYOuWPeTrxKEcWK8+9enatWva2NjQY489ZuuUlD2O3CuVSgfCOr4dCYFWKpX0wgsvWHoFYH5vb68ee+wx9fX1KR6Pa35+Xg0NDeru7pZ0Jw2AcHYqldLIyIg+97nPmaZh8BhwQt746l5Q+dxCn+LiT4/2ri7fYeFG8ZjoYsYCu337tt566y391V/9VZXwxB39xCc+URX295rfYxC1rs8iRCkgeGKxmCUXP/nkk8bYZgHFYjFdv35d4+Pj5nrVorX46LDniBHp9W47AhjL2LPj2UBci5StlpYWK2cDM12SfaepqcmIrR7D8uMThvuH23I/5u8wAeOt/8bGRmPC7+zsWDI3h3swL0QFb926ZeRj1s+PKszoE1yspaUl474x5qlUykqo7+7uamlpyYQWlrZXgN6CJvUNC9d7HlCe/PdZ71hseD+sLWAT1jQwA6/7ecATwD1lHeBVofy7urqs74e1IyHQlpaW9Ad/8AeGhTBwZ8+e1Ve/+lV99rOf1cmTJ/X++++rs7NTyWTyp955FQAACMdJREFUDqBa2ud2nThxQidOnNBTTz1lxMVXXnlFt27d0htvvGGn7aBBEFh+sNksh5FBaWxehNdh3/GUiffee0/Xrl3T3/7t31ZhbMPDw/rMZz5j4G9bW9sd4D3kRq4XnWjeA/j3Vl1HR4eampr01a9+1axASUZyfOGFF/TCCy9YPTmSpT1RlbHxffLChT55axX6hB+nqFDGfWlpadHc3JzNA+44BQQbGxt1+vRpy5eN4q0eZ2XTscm4Fn2OriP/DFHcpqOjQ/39/Xr44YdtzRQKBc3OzpqCisViVYfvMu4/SsPNLhaLJqx8tLCtrU11dXVWdHF6etpcQta3T2/yP62trYYXki2yurqqfD5v9cyAYOBU+nRCX/WWQgfS/oHMGAh4PR5LxmDwp5B57hrX7O/vv6f9GPw4tMeP2mKxWIgGxNR/4IEH1NPTo1OnTimRSBie1NzcrFQqVVWhgObdPEqdXLt2TZOTk5qZmdHKyory+bxZJVFN5X88aPlBm9/EtTS0F0KeUtDU1KTHH39c3d3d6uvr0/DwsCURMy6e0MsC881jRSwOXud5iSSyWBsaGqwu/uTkpBYWFjQ/P2/5mlg5PhKM1eahgBrzWkUhiEauo4uTcSelJ5/P22ZFOHZ1dam1tVWdnZ3KZDJKJBKmTHwGSS0MCosgmq95kBvjhSR/g4XyzGtra3r33Xe1tLSkxcVF3b59WysrK1pZWalSbh9UoEU/jwvt3X+qtvT396uvr0+pVMpcSPh8zc3N6uvrM3oH7iDXwR3k2qwLjs0jfa/WuGIte8uOSLa30Hy5qCjBnD4AJ2xvb1fRb8KwEjFdXl5WoVDQ+vq6XnnllTfDMDxfa9yOhIUmVWvzurrK6c3UY8/lcgrDSnZ/Q0OD5ufnq3xyGi4VuFaxWNRbb72ly5cv26GnUVyn1kLzAugwnOqg93yktJZQ9FYBGozI6+joqOLxuFpaWgyLyeVyZs6z+Xx5nlr9Z9MhLNHMHpAlUBCLxXTr1i1ls1lduXJFUnV2gHejvUAjyOADIV4AeAAaq863KPaF0FlZWbEIm78+9y2XK4UEp6amNDs7W/Vd7wp7BeeVlqcS1BrDWvNJX1lH3KtUKukHP/iBzdNBa+RHbX5N+bFsaGgwnJRkftKrWOdTU1M2dv4MTIQiY1BfX6lOC+Vie3u76tqMSzKZNFcWPJMxoYgjkA4CzUeZfVCNiD/zDY4LHr61taVisaj5+Xkr1X3oOB0FCy0IgkVJq5KWPu6+SErr4+/HUeiDdDT6cdyH/XYU+nEU+jAchmF3rTeOhECTpCAI3jjIjPz/Wz+OQh+OSj+O+3C0+nEU+nBY+2BU/ON23I7bcTvC7VigHbfjdtx+atpREmh/9HF3YK8dhX4chT5IR6Mfx33Yb0ehH0ehDwe2I4OhHbfjdtyO24/ajpKFdtyO23E7bj9SOxICLQiCXwiC4EoQBNeDIPit+3TPoSAI/j4IgktBELwXBMF/t/d6KgiCF4MguLb3O3kf+lIXBMFbQRD8zcfYh0QQBH8RBMHlvTF5+n73IwiC/2FvLi4GQfCnQRA0348+BEHwx0EQLARBcNG9duB9gyB4fm+tXgmC4Oc/wj78q735eDcIgr8OgiDxUfbhoH649/6nIAjCIAjS7rWPpB8fukUZ8vf7R1KdpHFJo5IaJb0j6aH7cN8+SU/s/R2XdFXSQ5L+N0m/tff6b0n6/fvQl/9R0p9I+pu9/z+OPvx7Sf/N3t+NkhL3sx+qHEh9U1LL3v9/Lum/uh99kPSMpCckXXSv1bzv3hp5R5VDgk7urd26j6gP/4mk+r2/f/+j7sNB/dh7fUjSdyRNSkp/1P340P3/OG++NyhPS/qO+/95Sc9/DP34hqQvSroiqW/vtT5JVz7i+w5K+jtJn3cC7X73oWNPmASR1+9bP/YE2m1JKVUyWP5mb0Pflz5IGokIk5r3ja7PvU3+9EfRh8h7/7mkr3/UfTioH5L+QtJjkiacQPtI+/Fhfo6Cy8lCpk3tvXbfWhAEI5Iel/SqpN4wDGclae93z0d8+/9d0v8syecF3e8+jEpalPRv91zf/ysIgrb72Y8wDKcl/YGkW5JmJRXCMHzhfvYh0g6678e1Xv+ZpG99HH0IguAXJU2HYfhO5K2Pfe9G21EQaLWS3e5b6DUIgnZJfynpvw/DsHi/7rt37y9LWgjD8M37ed8arV4VN+P/CMPwcVXS0O4Llknbw6i+oorr0i+pLQiCf3o/+3CP7b6v1yAIfluVc26/fr/7EARBq6TflvS/1Hr7fvXjXttREGhTqvjntEFJM/fjxkEQNKgizL4ehuFf7b08HwRB3977fZIWPsIufFrSLwZBMCHpzyR9PgiC/+c+90GqzMFUGIav7v3/F6oIuPvZj+ck3QzDcDEMw21JfyXpU/e5D74ddN/7ul6DIPh1SV+W9Cvhnl93n/swpoqSeWdvnQ5K+mEQBJn73I97akdBoL0u6XQQBCeDIGiU9MuSvvlR3zSolEH4N5IuhWH4h+6tb0r69b2/f10VbO0jaWEYPh+G4WAYhiOqPPd3wzD8p/ezD3v9mJN0OwiCM3svfUHS+/e5H7ck/WwQBK17c/MFSZfucx98O+i+35T0y0EQNAVBcFLSaUmvfRQdCILgFyT9pqRfDMPQl5m4b30Iw/BCGIY9YRiO7K3TKVWCaXP3sx/33D5OAM+BiV9SJco4Lum379M9P6OKefyupLf3fr4kqUsVkP7a3u/UferPz2k/KHDf+yDpE5Le2BuP/1dS8n73Q9L/KumypIuS/m9VomcfeR8k/akquN22Khv2a4fdVxUXbFyVwMF/+hH24boqGBXr8//8KPtwUD8i709oLyjwUfbjw/4cZwoct+N23H5q2lFwOY/bcTtux+3H0o4F2nE7bsftp6YdC7TjdtyO209NOxZox+24HbefmnYs0I7bcTtuPzXtWKAdt+N23H5q2rFAO27H7bj91LRjgXbcjttx+6lp/x8CFloW94cfrgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import cv2\n", "import matplotlib.pyplot as plt\n", "\n", "# read video\n", "\n", "import scipy.io\n", "movie = scipy.io.loadmat('escalator_data.mat')\n", "#frame0 = \n", "print(np.shape(movie['X'][:,0]))\n", "\n", "plt.imshow(movie['X'][:,0].reshape((160,130)).swapaxes(0, 1), cmap='gray')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The idea of Robust PCA is to add a \"sparse\" component to the traditional PCA decomposition. Given a collection of images that we store as the columns of the matrix $X$, one then looks for a decomposition\n", " \n", "\\begin{align} \n", "\\boldsymbol X = \\boldsymbol Y + \\boldsymbol S\n", "\\end{align}\n", "\n", "Where $Y$ is a matrix which contains the original PCA decomposition, and thus encodes the part of the images that remains approximately constant throughout the sequence (background), and $\\boldsymbol S$ is the sparse part (i.e a sequence of images that are varying through the sequence but only at a small number of pixel positions in the images (foreground), in other words most of the pixels in $S$ are assumed to be zero). To recover each part one approach is to proceed as follows, see [Candes et al.](https://arxiv.org/pdf/0912.3599.pdf)\n", "\n", "We let $\\mu$ to denote the parameter that controls the amount of dara we want to store in the sparse foreground extraction part, $\\boldsymbol S$. A good choice is to take $\\mu = n_1n_2/4\\|\\mathbf{X}\\|_1$ where $\\mathbf{X}\\in\\mathbb{R}^{n_1\\times n_2}$ encodes the video surveillance sequence (each frame being stacked as a column of $\\mathbf{X}$) and $\\|\\mathbf{X}\\|_1$ denotes the entry wise $\\ell_1$ norm of $\\mathbf{X}$, $\\mathbf{X} = \\sum_{ij} |X_{ij}|$\n", "\n", "The algorithm then proceeds as follows\n", "\n", "\n", "__Initialize__ $Y$, $S$ to $0$\n", "\n", "__Step 1.__ Compute the truncated SVD of the matrix $X - S - \\mu^{-1}Y$, i.e. let $X - S - \\mu^{-1}Y = U\\Sigma V^T$. The truncated SVD is then obtained by replacing the diagonal matrix of singular values with the truncation \n", "$$ \n", "\\sigma \\leftarrow \\text{sign}(\\sigma)\\max(|\\sigma| - \\mu, 0) \n", "$$\n", "\n", "and store it in $L$, $L = SVD_{\\mu}(X - S - \\mu^{-1}Y)$ \n", "\n", "\n", "\n", "__Step 2.__ Apply the thresholding operator $f(x) = \\text{sign}(x)\\max(|x| - \\lambda \\mu, 0) $ with threshold $\\lambda\\mu$ to the entries of the matrix $X - L + \\mu^{-1}Y$ and store the result in $\\mathbf{S}$.\n", "\n", "__Step 3.__ Update the matrix $Y$ as $Y \\leftarrow Y + \\mu(X - L - S)$\n", "\n", "\n", "A good approach to initialize the parameters is to take $lambda = 1/\\max(n_1,n_2)$ where $\\max(n_1,n_2)$ is the max number of rows or columns of the data matrix. One can also terminate the algorithm when $\\|X-L-S\\|_F \\leq \\delta \\|X\\|_F$ where $\\|X\\|_F$ is the Frobenius norm of the matrix and $\\delta$ can be taken for example as $10^{-7}$. \n", "\n", "\n", "Additional indications: if computing the full SVD from linalg is too expensive, you can replace it with the fast randomized PCA from facebook (see [fbpca](https://fbpca.readthedocs.io/en/latest/)) or a sparse SVD.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 3.1. (8pts) Complete the code below which separates the sparse part from the PCA decomposition" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", "from __future__ import division\n", "from scipy.sparse.linalg import svds\n", "\n", "\n", "\n", "\n", "def robustPCA(X, delta=1e-6, mu=None, maxiter=500):\n", "\n", " '''\n", " The function should return a PCA like part stored in 'L' with only a few singular values \n", " that are non zero and a sparse sequence 'S' in which the images are black except w very \n", " limited number of pixels\n", " '''\n", " \n", " \n", " # Initialize the tuning parameters.\n", " lam = # put your value for lambda\n", " if mu is None:\n", " \n", " # complete with your value for mu\n", " \n", " # Convergence criterion.\n", " norm = np.sum(X ** 2)\n", "\n", " # Iterate.\n", " i = 0\n", " rank = np.min(shape)\n", " S = np.zeros(shape)\n", " Y = np.zeros(shape)\n", " while i < max(maxiter, 1):\n", " \n", " \n", " # Step 1. Compute and truncate the SVD\n", " \n", " \n", "\n", " # Step 2. Truncate the entries of X - L + mu^(-1)Y \n", " \n", "\n", " # Step 3. Update the matrix Y\n", " \n", " \n", "\n", " # Convergence criterion\n", " err = np.sqrt(np.sum(step ** 2) / norm)\n", " if err < delta:\n", " break\n", " i += 1\n", "\n", " if i >= maxiter:\n", " break\n", " \n", " return L, S" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 3.2. (2pts) \n", "\n", "Apply your function to the escalator sequence and display the result on at least one frame. Use subplot to display the extracted background and its corresponding foreground side by side. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# put your code here" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }