diff --git a/one_neuron/logistic_regression_2d.ipynb b/one_neuron/logistic_regression_2d.ipynb index 2715989..860fe23 100644 --- a/one_neuron/logistic_regression_2d.ipynb +++ b/one_neuron/logistic_regression_2d.ipynb @@ -10,9 +10,9 @@ "\n", "Today, we're going to perform the same exercise in 2D, and you will learn that: \n", "\n", - "* the logistic regression can work in 2D (or more dimensions) as well, depending on the problem;\n", + "* the logistic regression can work in 2D as well, and in more dimensions;\n", "* the logistic regression is **a linear algorithm**;\n", - "* it is often necessary to add **non-linearities**, and thus to go beyond the logistic regression. \n", + "* it is often necessary to add **non-linearities** to be able to describe the dataset, and thus to go beyond the logistic regression. \n", "\n", "**Prerequisites**\n", "\n", @@ -34,23 +34,18 @@ }, { "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "normal = np.random.multivariate_normal" - ] - }, - { - "cell_type": "code", - "execution_count": 9, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ - "from mpl_toolkits import mplot3d\n", "import matplotlib.pyplot as plt\n", - "%matplotlib inline" + "import numpy as np\n", + "\n", + "%matplotlib inline\n", + "\n", + "# in this tutorial, we will generate our samples ourselves, \n", + "# with nsamples in each category\n", + "nexamples = 500" ] }, { @@ -65,15 +60,17 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ + "normal = np.random.multivariate_normal\n", + "\n", "s2 = 1\n", - "sample0 = normal([0.,0.], [[s2, 0.], [0.,s2]], 100)\n", - "sample1 = normal([2.,2.], [[s2, 0.], [0.,s2]], 100)\n", - "target0 = np.zeros((100,))\n", - "target1 = np.ones((100,))" + "sgx0 = normal([0.,0.], [[s2, 0.], [0.,s2]], nexamples)\n", + "sgx1 = normal([2.,2.], [[s2, 0.], [0.,s2]], nexamples)\n", + "sgy0 = np.zeros((nexamples,))\n", + "sgy1 = np.ones((nexamples,))" ] }, { @@ -85,22 +82,22 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 11, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -112,25 +109,35 @@ } ], "source": [ - "plt.scatter(sample0[:,0], sample0[:,1])\n", - "plt.scatter(sample1[:,0], sample1[:,1])" + "plt.scatter(sgx0[:,0], sgx0[:,1])\n", + "plt.scatter(sgx1[:,0], sgx1[:,1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Our goal will be to classify (x,y) points in one of the two categories. To do that, we need to build a single sample containing the examples from the two categories. So we concatenate the arrays of points, and also the arrays of targets for later use:" + "Our goal will be to classify (x1,x2) points in one of the two categories. To do that, we need to build a single sample containing the examples from the two categories. So we concatenate the arrays of points, and also the arrays of targets for later use:" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1000, 2) (1000,)\n" + ] + } + ], "source": [ - "x = np.concatenate((sample0, sample1))\n", - "y = np.concatenate((target0, target1))" + "sgx = np.concatenate((sgx0, sgx1))\n", + "sgy = np.concatenate((sgy0, sgy1))\n", + "\n", + "print sgx.shape, sgy.shape" ] }, { @@ -153,16 +160,16 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 14, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, @@ -207,24 +214,147 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# define parameters\n", + "b = 0\n", + "w1 = 1\n", + "w2 = 2\n", + "\n", + "def sigmoid_2d(x1, x2):\n", + " # z is a linear function of x1\n", + " z = w1*x1 + w2*x2 + b\n", + " return 1 / (1+np.exp(-z))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To see what this function looks like, we can make a 2D plot, with x1 on the horizontal axis, x2 on the vertical axis, and the value of the sigmoid represented as a color for each (x1, x2) coordinate. To do that, we will use a standard matplotlib technique, that I'd like to explain in details. \n", + "\n", + "First create an array of evenly spaced values along x1, and another array along x2: " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "xmin, xmax, npoints = (-10,10,51)\n", + "linx1 = np.linspace(xmin,xmax,npoints)\n", + "linx2 = linx1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, we create a meshgrid from these arrays: " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(51, 51) (51, 51)\n", + "gridx1:\n", + "[[-10. -9.6 -9.2 ... 9.2 9.6 10. ]\n", + " [-10. -9.6 -9.2 ... 9.2 9.6 10. ]\n", + " [-10. -9.6 -9.2 ... 9.2 9.6 10. ]\n", + " ...\n", + " [-10. -9.6 -9.2 ... 9.2 9.6 10. ]\n", + " [-10. -9.6 -9.2 ... 9.2 9.6 10. ]\n", + " [-10. -9.6 -9.2 ... 9.2 9.6 10. ]]\n", + "gridx2\n", + "[[-10. -10. -10. ... -10. -10. -10. ]\n", + " [ -9.6 -9.6 -9.6 ... -9.6 -9.6 -9.6]\n", + " [ -9.2 -9.2 -9.2 ... -9.2 -9.2 -9.2]\n", + " ...\n", + " [ 9.2 9.2 9.2 ... 9.2 9.2 9.2]\n", + " [ 9.6 9.6 9.6 ... 9.6 9.6 9.6]\n", + " [ 10. 10. 10. ... 10. 10. 10. ]]\n" + ] + } + ], + "source": [ + "gridx1, gridx2 = np.meshgrid(np.linspace(xmin,xmax,npoints), np.linspace(xmin,xmax,npoints))\n", + "print gridx1.shape, gridx2.shape\n", + "print 'gridx1:'\n", + "print gridx1 \n", + "print 'gridx2'\n", + "print gridx2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "if you take the first line in both arrays, and scan the values on this line, you get: `(-10,-10), (-9.6, 10), (-9.2, 10)`... So we are scanning the x1 coordinates sequentially at the bottom of the plot. If you take the second line, you get: `(-10, -9.6), (-9.6, -9.6), (-9.2, -9.6)` ... : we are scanning the second line at the bottom of the plot, after moving up in x2 from one step. \n", + "\n", + "Scanning the full grid, you would scan the whole plot sequentially. \n", + "\n", + "Now we need to compute the value of the sigmoid for each pair (x1,x2) in the grid. That's very easy to do: " + ] + }, + { + "cell_type": "code", + "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "Text(0,0.5,'x2')" + "(51, 51)" ] }, - "execution_count": 25, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "z = sigmoid_2d(gridx1, gridx2)\n", + "z.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "numpy applies its magic and calls the `sigmoid_2d` function to each pair `(x1,y2)` taken from the `gridx1` and `gridx2` arrays. \n", + "\n", + "Finally, we can plot our sigmoid in 2D: " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] }, "metadata": { @@ -234,22 +364,10 @@ } ], "source": [ - "# define parameters\n", - "b = 0\n", - "w1 = 1\n", - "w2 = 2 \n", - "\n", - "def sigmoid_2d(x1, x2):\n", - " # z is a linear function of x1\n", - " z = w1*x1 + w2*x2 + b\n", - " return 1 / (1+np.exp(-z))\n", - "\n", - "# create an array of evenly spaced values\n", - "xmin, xmax, npoints = (-10,10,51)\n", - "gridx, gridy = np.meshgrid(np.linspace(xmin,xmax,npoints), np.linspace(xmin,xmax,npoints))\n", - "plt.pcolor(gridx, gridy, sigmoid_2d(gridx,gridy))\n", + "plt.pcolor(gridx1, gridx2, z)\n", "plt.xlabel('x1')\n", - "plt.ylabel('x2')" + "plt.ylabel('x2')\n", + "plt.colorbar()" ] }, { @@ -259,10 +377,47 @@ "The 2D sigmoid has the same kind of rising edge as the 1D sigmoid, but in 2D. \n", "With the parameters defined above: \n", "\n", - "* The weight of $x_2$ is twice larger than the weight of $x_1$, so the sigmoid evolves twice faster as a function of $x_2$.\n", + "* The weight of $x_2$ is twice larger than the weight of $x_1$, so the sigmoid evolves twice faster as a function of $x_2$. If you set one of the weights to zero, can you guess what will happen? try it in the cell above. \n", "* The separation boundary, which occurs for $z=0$, is a straight line with equation $w_1 x_1 + w_2 x_2 + b = 0$ or equivalently: \n", "\n", - "$$x_2 = -\\frac{w_1}{w_2} x_1 - \\frac{b}{w_2} = -0.5 x_1$$\n" + "$$x_2 = -\\frac{w_1}{w_2} x_1 - \\frac{b}{w_2} = -0.5 x_1$$\n", + "\n", + "For the record, if you prefer, you can plot the sigmoid in 3D like this: \n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits.mplot3d import Axes3D\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "ax.plot_wireframe(gridx1,gridx2,z)" ] }, { @@ -271,67 +426,213 @@ "source": [ "## Logistic regression\n", "\n", - "Let's now perform a logistic regression in 2D to separate the two classes of samples. " + "Let's now perform a logistic regression in 2D to separate the two classes of samples. \n", + "\n", + "We take the logistic regression algorithm from scikit-learn. \n", + "Here, the logistic regression is used with the `lbfgs` solver. LBFGS is a minimization method used to find the best parameters for the logistic function. It is similar to [Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method_in_optimization), if you know it. If not no worries, I'll cover minimization techniques in a future post. " ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 13, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n", + " intercept_scaling=1, max_iter=100, multi_class='warn',\n", + " n_jobs=None, penalty='l2', random_state=None, solver='lbfgs',\n", + " tol=0.0001, verbose=0, warm_start=False)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "from sklearn.linear_model import LogisticRegression" + "from sklearn.linear_model import LogisticRegression\n", + "clf = LogisticRegression(solver='lbfgs')\n", + "clf.fit(sgx, sgy)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The logistic regression has been fitted (trained) to the data. Now, we can use it to predict a probability for a given (x1,x2) point.\n", + "\n", + "We would like to plot this probability in 2D as a function of x1 and x2. To do that, we need to use the `clf.predic_proba` method which takes a 2D array of shape `(n_points, 2)`. The first dimension indexes the points, and the second one contains the values of x1 and x2. Again, we use our grid to map the (x1,x2) plane. But the gridx1 and gridx2 arrays defined above contain disconnected values of x1 and x2: " ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 14, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(51, 51) (51, 51)\n" + ] + } + ], "source": [ - "clf = LogisticRegression(random_state=0, solver='lbfgs', multi_class='ovr').fit(x, y)" + "print gridx1.shape, gridx2.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What we want is a 2D array of shape (npoints, 2), not two 2D arrays of shape (51, 51)... \n", + "We need to reshape our data. First, we will flatten the gridx1 and gridx2 arrays so that all their values appear sequentially in a 1D array. Here is a small example to show how flatten works: " ] }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 1]\n", + " [2 3]]\n", + "flat array: [0 1 2 3]\n" + ] + } + ], + "source": [ + "a = np.array([[0, 1], [2, 3]])\n", + "print a \n", + "print 'flat array:', a.flatten()" + ] + }, + { + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "xmin, xmax, npoints = -6, 6, 100\n", - "gridx, gridy = np.meshgrid(np.linspace(xmin,xmax,npoints), np.linspace(xmin,xmax,npoints))\n", - "grid = np.c_[gridx.ravel(), gridy.ravel()]" + "Then, we will stitch the two 1D arrays together with np.c_ like this: " ] }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 1 2 3]\n", + "[4 5 6 7]\n", + "[[0 4]\n", + " [1 5]\n", + " [2 6]\n", + " [3 7]]\n", + "(4, 2)\n" + ] + } + ], + "source": [ + "b = np.array([[4, 5], [6, 7]])\n", + "print a.flatten()\n", + "print b.flatten()\n", + "c = np.c_[a.flatten(), b.flatten()]\n", + "print c\n", + "print c.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This array has exactly the shape expected by `clf.predict_proba`: a list of examples with two values. So let's do the same with our grid, and let's compute the probabilities for all (x1,x2) pairs in the grid:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2601, 2)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grid = np.c_[gridx1.ravel(), gridx2.ravel()]\n", + "prob = clf.predict_proba(grid)\n", + "prob.shape" + ] + }, + { + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "prob = clf.predict_proba(grid)" + "Now, prob does not have the right shape to be plotted. In the cell below, we will use a gridx1 and a gridx2 array with shapes (51,51). The shape of the prob array must be consistent, as the plotting method will simply map each (x1,x2) pair to a probability. So we need to reshape our probability array to shape (51,51). Reshaping works like this:" ] }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 1 2 3]\n", + "reshaped to (2,2):\n", + "[[0 1]\n", + " [2 3]]\n" + ] + } + ], + "source": [ + "d = np.array([0,1,2,3])\n", + "print d\n", + "print 'reshaped to (2,2):'\n", + "print d.reshape(2,2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally (!) we can do our plot:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "Text(0,0.5,'x2')" ] }, - "execution_count": 36, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ - "
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" ] }, "metadata": { @@ -341,16 +642,21 @@ } ], "source": [ - "plt.pcolor(gridx,gridy,prob[:,0].reshape(npoints,npoints))\n", - "plt.scatter(sample0[:,0], sample0[:,1])\n", - "plt.scatter(sample1[:,0], sample1[:,1])" + "plt.pcolor(gridx1,gridx2,prob[:,1].reshape(npoints,npoints))\n", + "plt.colorbar()\n", + "plt.scatter(sgx0[:,0], sgx0[:,1])\n", + "plt.scatter(sgx1[:,0], sgx1[:,1])\n", + "plt.xlabel('x1')\n", + "plt.ylabel('x2')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The logistic regression is able to separate these two classes well. \n", + "💡 **This kind of numpy reshaping operations might seem a bit convoluted. But these operations are very efficient, and I can assure you that you actually get used to it. Always check the shape of your arrays and stay strong!**\n", + "\n", + "In conclusion for this section, we see that the logistic regression is able to separate these two classes well. \n", "\n", "But what about more complicated sample distributions? " ] @@ -371,28 +677,33 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 21, "metadata": {}, "outputs": [], "source": [ - "x1 = np.random.uniform(-1, 1, 400)\n", - "x2 = np.random.uniform(-1, 1, 400)" + "x1 = np.random.uniform(-1, 1, nexamples)\n", + "x2 = np.random.uniform(-1, 1, nexamples)" ] }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 23, "metadata": {}, "outputs": [], "source": [ - "samples = np.column_stack((x1, x2))\n", - "sample0 = samples[x1*x2>0]\n", - "sample1 = samples[x1*x2<0]" + "# stacking the x1, x2 values\n", + "# into an array of shape (500, 2)\n", + "# (all examples)\n", + "srx = np.column_stack((x1, x2))\n", + "# select examples for category 0\n", + "srx0 = srx[x1*x2>=0]\n", + "# select examples for category 1\n", + "srx1 = srx[x1*x2<0]" ] }, { "cell_type": "code", - "execution_count": 94, + "execution_count": 24, "metadata": {}, "outputs": [ { @@ -401,13 +712,13 @@ "Text(0,0.5,'x2')" ] }, - "execution_count": 94, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -419,8 +730,8 @@ } ], "source": [ - "plt.scatter(sample0[:,0],sample0[:,1])\n", - "plt.scatter(sample1[:,0],sample1[:,1])\n", + "plt.scatter(srx0[:,0],srx0[:,1])\n", + "plt.scatter(srx1[:,0],srx1[:,1])\n", "plt.xlabel('x1')\n", "plt.ylabel('x2')" ] @@ -429,46 +740,46 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Obviously, we cannot draw a line separating these two samples, and the logistic regression is going to be of no use. \n", + "Obviously, we cannot draw a line separating these two samples accurately, so the logistic regression is going to be of no use. \n", "\n", "**This is a non-linear problem**. \n", "\n", - "To be able to deal with non-linearities, the classification boundary must be a non-linear function of the inputs $x_1$ and $x_2$. This means that the weighted input of the last sigmoid neuron must be a non-linear function of these variables. \n", + "To be able to deal with non-linearities, the classification boundary must be a non-linear function of the inputs x1 and x2. This means that the weighted input of the last sigmoid neuron must be a non-linear function of these variables. \n", "\n", "To do that, we have two solutions: \n", "\n", - "1. changing variables, which requires some insights of what the dataset looks like\n", - "1. using a more complex model, like a neural network with one or more hidden layers. \n", + "1. change variables, which requires some insights on the dataset\n", + "1. use a more complex model, like a neural network with one or more hidden layers. \n", "\n", "## Changing variables\n", "\n", - "We're first going to try and change variables. Looking at the plot above, we see that the distribution of the samples is done according to the product $x_1 x_2$.\n", + "We're first going to try and change variables. Looking at the plot above (and also at the code used to generate the examples!), we see that the sample categorization depends on the product $x_1 x_2$.\n", "\n", "Indeed, For the first sample, ($x_1 > 0$ and $x_2 > 0$), or ($x_1 < 0$ and $x_2 < 0$). So the product $x_1 x_2$ is always positive. For the second sample, it's always negative. \n", "\n", - "So instead of considering $x_1$ and $x_2$ separately, we will work with $u = x_1 x_2$. \n", + "So instead of considering $x_1$ and $x_2$ separately, we can work with $u = x_1 x_2$. \n", "\n", - "We build the samples as a function of $u$:" + "We build the examples as a function of $u$:" ] }, { "cell_type": "code", - "execution_count": 139, + "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 139, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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mT58HHbXn3CVJM3c0H7lLkmZoTsM9It4aEVsiYn9ETPlO9FQ36K7+G+J7IuLB6gbdiwbQ47KI+Ha1jW9HxNIONa+JiO/Xvn4dEedX826KiIdq817e7x6b9lnV7av1srE2PvB92bTPiHh5RNxVvTbui4i31eYNbH8eyY3gI+KKanxrRLyhXz3NsM/LIuL+at/dHhEvqM3r+PzPUZ/viIidtX7+sjbv4uo18mBEXDx52Vnu86O1Hn8cEU/U5s3a/uxZZs7ZF/Bi4CTgTqA1Rc0Q8BPghcAi4AfAydW8DcC66vEngXcPoMePAJdXjy8HrutSv4z2jUqOraZvAi6YhX3ZqE/gf6cYH/i+bNon8CJgTfX4BOARYMkg9+d0r7NazXuAT1aP1wFfqB6fXNUfA6yu1jM0oP3XpM/X1F5/7z7Q53TP/xz1+Q7g4x2WXQZsq74vrR4vnas+J9W/F/jsbO/PmXzN6ZF7Zj6QmVu7lJ0OjGfmtszcA9wCnBcRAbwWuLWq+xfg/AG0eV617qbbuAD4ZmY+NYBeptNrnwfN4r6EBn1m5o8z88Hq8Q7gUWCGt+5qrOPrbFJNvfdbgbOqfXcecEtm7s7Mh4Dxan1z0mdm3lF7/d1N++5ps63J/pzKG4BvZ+Zjmfk48G3gnKOkz4uAmwfUS1/Nh3PuU92g+zjgiWzfTKQ+3m+/nZmPAFTfn9elfh3PfPL/vvoT+aMRccwAeoTmfT4r2vexvfvAqSNmb1/20icAEXE67SOqn9SGB7E/j+RG8E2W7Zdet7Ue+GZtutPzPwhN+3xL9VzeGhEHbud5VO7P6vTWauC7teHZ2p89WzjoDUTEd4Df6TDrysz8apNVdBjLacZ7Nl2PPa7n+cAptO9adcAVwM9pB9SNwN8A18xhnydm5o6IeCHw3Yj4IfA/HepmfBlVn/fn54GLM3N/Ndy3/Tl5cx3Gmt4Ivm+vxQYabysi3g60gPq9AJ/x/GfmTzotPwt9fg24OTN3R8S7aP9V9NqGy/ZLL9taB9yamftqY7O1P3s28HDPzLOPcBVT3aD7l8CSiFhYHUV1unH3EfcYEb+IiOdn5iNV2Dw6zaouBL6cmXtr636kerg7Iv4Z+OuZ9NivPqvTHGTmtoi4EzgN+BJ92pf96jMifgv4BvDBzLy7tu6+7c9JerkR/EQcfiP4Jsv2S6NtRcTZtP8xPSMzdx8Yn+L5H0QYde0zM39Vm/w0cF1t2TMnLXtn3zs8tK2mz9064K/qA7O4P3s2H07LdLxBd7bfzbiD9jluaN+gu8lfAr2q3/y72zaecT6uCrAD57XPB340gB6hQZ8RsfTAaYyIOB54NXD/LO7Lpn0uAr4MfC4zvzhp3qD255HcCH4jsK66mmY1sAb4rz711XOfEXEa8ClgbWY+Whvv+PzPYZ/Pr02upX2PZmj/5fv6qt+lwOs5/K/hWe2z6vUk2m/u3lUbm8392bu5fDcXeBPtfzl3A78ANlXjJwC31ereCPyY9r+IV9bGX0j7l2gc+CJwzAB6PA64HXiw+r6sGm8B/1SrWwU8DCyYtPx3gR/SDqF/BZ4zoH3ZtU/gD6teflB9Xz+b+7KHPt8O7AW+X/t6+aD3Z6fXGe1TPmurx8+q9s14ta9eWFv2ymq5rcC5A/696dbnd6rfpwP7bmO353+O+rwW2FL1cwfwe7Vl/6Laz+PAn89ln9X01cCHJy03q/uz1y8/oSpJBZoPp2UkST0y3CWpQIa7JBXIcJekAhnuklQgw12SCmS4S1KBDHdJKtD/A6ECILBPQ40CAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] @@ -480,12 +791,14 @@ } ], "source": [ - "u0 = sample0[:,0] * sample0[:,1]\n", - "u1 = sample1[:,0] * sample1[:,1]\n", - "y0 = np.ones(len(u0))\n", - "y1 = np.zeros(len(u1))\n", - "plt.scatter(u0, y0)\n", - "plt.scatter(u1, y1)" + "# category 0: \n", + "sru0 = srx0[:,0] * srx0[:,1]\n", + "sry0 = np.ones(len(sru0))\n", + "# category 1: \n", + "sru1 = srx1[:,0] * srx1[:,1]\n", + "sry1 = np.zeros(len(sru1))\n", + "plt.scatter(sru0, sry0)\n", + "plt.scatter(sru1, sry1)" ] }, { @@ -497,14 +810,14 @@ }, { "cell_type": "code", - "execution_count": 140, + "execution_count": 26, "metadata": {}, "outputs": [], "source": [ - "x = np.concatenate((u0, u1))\n", - "x = np.c_[x]\n", - "y = np.concatenate((y0, y1))\n", - "clf = LogisticRegression(random_state=0, solver='lbfgs').fit(x, y)" + "sru = np.concatenate((sru0, sru1))\n", + "sru = np.c_[sru]\n", + "sry = np.concatenate((sry0, sry1))\n", + "clf = LogisticRegression(random_state=0, solver='lbfgs').fit(sru, sry)" ] }, { @@ -516,22 +829,22 @@ }, { "cell_type": "code", - "execution_count": 141, + "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 141, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -547,8 +860,8 @@ "prob = clf.predict_proba(linx)\n", "prob = prob[:,1].reshape(len(linx))\n", "plt.plot(linx, prob)\n", - "plt.scatter(u0, y0)\n", - "plt.scatter(u1, y1)" + "plt.scatter(sru0, sry0)\n", + "plt.scatter(sru1, sry1)" ] }, { @@ -560,7 +873,7 @@ }, { "cell_type": "code", - "execution_count": 144, + "execution_count": 42, "metadata": {}, "outputs": [ { @@ -569,38 +882,38 @@ "(10000,)" ] }, - "execution_count": 144, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xmin, xmax, npoints = -1, 1, 100\n", - "gridx, gridy = np.meshgrid(np.linspace(xmin,xmax,npoints), np.linspace(xmin,xmax,npoints))\n", - "gridu = gridx * gridy\n", - "us = np.c_[uspace.flatten()]\n", + "gridx1, gridx2 = np.meshgrid(np.linspace(xmin,xmax,npoints), np.linspace(xmin,xmax,npoints))\n", + "gridu = gridx1 * gridx2\n", + "us = np.c_[gridu.flatten()]\n", "probs = clf.predict_proba(us)\n", "probs[:,1].shape" ] }, { "cell_type": "code", - "execution_count": 145, + "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 145, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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cxCW8ufohOgQPNdnezsOTF+mev03w9q3i/2J8Phq+/kvr7zelif6s+rMRjT9oE8DMEGPvU6OTgLiS8f9oQlRmewJAWLjoSuoRXb/Gf9c/oOJJncnTmScf74SoeGQNx3S/kacMrJ43q/Kp2t8/rF+7VybZb6Cb3A5efX+Uzt8H6w3fSBvBAHOn7DFlCM2ZtNNo/GNAfauTXBO+f70745LGE7GytRCAJ7IqyZMbOaNk8nJ7Ocu8nbB9nPXQJMT8ASRFC/lcJuzaWawb/gC8Pgdrtt1mMP6RMGWYZkT/uWk655uz6Ols4F8mL6I0//LF7cGaDnqx3UnFgeJOJ4B443JszH5nylKDEQdjgpnVnkCyrSM8XOTx8cLKmoTx7xIqnw+qafoRyZO/FMqnlYG/pBBSF1g9oSweXcNHko1MnxCvP9mhaPeVggydSDROKZCJa3gQv5ee0Rp2jd5uGeePfLxw12Tmja8Kp3vW3BrCIAoeWvL2TY5XugtZ2hA09t6UkH4mkFNdmk/ZLLB9utdDpvkeghUMqwBVtjjW+kTi/YvefocaZBA5pOBxEtrffPKwjygTNndTJK/hOXzC30DMAfAZ2DvCselTGZGX0cBpU30giV+tn8n04ZsNnnlnLKBLQWAVsPjAOP49io3ZWCeIzhLMrPYE3BbssNqLkR2teOH6Nf6NJ02brTz5WCmfkQz8lQ4hmbF4NA2fGoHrX2Mw/ODn7t+x3+D5L1gzgvn37gynca4dBcDXS7czY8wxZElFUSWW7B7Mq6vHUe9KI7db+ARQ35wW1hYtqk/ko9pl5o5aT3aqi3p3BgtqbqWqdgQkd359vDDDt4tvK5X0ppHapkxeTClncXYhSkpk5lS8kJbWQqsJ779betMVuX9X8GTJu3x/5VzMZtVoksTiiRfXzeh0Y/ZSmTuREsxiFZfr0z1++TKRcP0a/8x+mn5+CFQFVv7gvbBQTKyUz0gGPuoQUhc5/JbjBtqFUE204RydximKtn04iuqaAXy97CNm3fyx7qTbJJVZRUcAWLC+kPnlW8MmjYWbbo7g4Qfff+mgw8wZs8mv4JnBgj2TqD5ZQFXtCM3YA2pArtkWEsO3ma8CDCuCCPF/0/7+4+nSLp5XKkhD2xvopzbyM7eWD/BOyijMoBq8eqnTdsu9AL9HPHrMdrZtnoxPCP3YbR4mj12PR/D2xVWDMcPXyPwxOwajpy2ek8VVgOiZiyF/Cyf9voLN/Ofqz3OxLTxUF0gSu9QsYIgu/h9ANBuzl4O5Y7UnACChogofXqrDxnfuuTLChdev8S//oVY4RQj9qGpQPtksFBML/z6SgbcKIblazZd5l4pAnN9qcRzg5QeOI3H3RVQd6E+VoNEToHfOGHPMNOozo/Aor64ehyTLzJm0U2P7NKexcNPNVB8e1Om3rHTgYeZNWBukdKa7dAXPqjPmBjZW3O3Usnlz7Y3U+TJ5pbGcle7CTq97SqrUDX8AaXh4pq2Sd7qNguZucDEbfA5t0zenDlI6Z/c01eZy/uBQvG0pJKW66TviAL36mYsJDhh4jFS5g41bp9DeroUhbTaPaV8rbDg0lrc3TeN8cw96OS/whYmLubNgU0xjXCq+e8c/eL7yK2FJYvNL3o3L+NFqAEWzMVt7GaShzfYENEioBCYA6JNxge9Om5pg+3QZ/kpYdW9+Kybd/Gg3aiPtEbxROZRn7t9Lkt3IhkhN9lA2+kz4/YRiK2+syo9qAuosW7etw8aC6gJ9tbCgusCg1wP+cM6aEcH4uVVhFn+7LJmzO2RJkyqtPjKI6iOD/I3+6yXjuKEaPgBzxm4xp3SO3kjVWcH4WzF8LLR9Ag71XZm7+V7OUp3Z09veyHM9KkCCpWpRWH8RvTGP5fdRGzXD39A7uJTwJsHpvih2BTnrojam8JEFPHx3XS+aa4bqWb4d7jSO7SxCUSWcg4/o/T2KUIBGlfF67QRc7PaONCrX30my5GXUkP1AkB0ERubPuoPj+O81n9eZPueas3h99ZewSyq35Qc3XA1sH+G9iswf8Sdk+Ob5r11RM4HXNnyGOlcWuRkNPFnyji7+9pv1D+hc/ydL3uW+gi1+9s6lZQEDvLP/Fp6rfFCfWKw0gACembKEZz94yCAbIeYOvHtgLBImhUboWnKZGPvXJhfje1GR9KIzct7Dl3yfWHFlc6CvNIq+wFd+fTv3/ORuywiL6MHHIu/8RuVQ2jqMgwb2CKr29sHdHr4dlmTXNPYN95uxx3i/GXuikpO2ytZVVahrTOVXAfqmH1X7+/HSskLqGlNR/H1eWj5GD/NEA8XMOkZojxaXU8HzrszdPNfv3fBsXtnDN7pVdnr9acx5/7VSpubxh2r5qDLq6d4Rx2w5elOYsqfqs1N7wHq5v2PHeEPYBzTGT/W22yPeC2DR5vsMFE+ADm8Sf9k4q9NrY8GKmgn8fNUjuvTzGb/087Ka8Uwr2MLKuc+x88knWDn3OabHKTtY0wAKpZJqGkChmDV8Gz+782/0yWhAQqVPRgM/u/Nv+iTxwrrphhBMABJql6Wh7x++nQ8f+4nlKv1qFJ25fj3/EETD5ollo7azPYKMNKMnG4A42VgVW3ls6kF9nFjj/Crw8G+n+q8VTkgyVQcGUHUgRHLZavo3ycpdsmsQs8YcNZxSVVi6Z4iW0RtNJq8cXt4xIqVTGCcaDr/467qz+x6+12cpdosVS56t0Vqx09/+K7Wc56UKQ+inFQcvppSD2yKM57HQ+PE/htJuvlvtcafiVcxj+C0mG74QVPoEDPF/kfnT0GxuWM43Z1myfQIx/6qDE3hr4wPUu3qSnXGef520iLsC4SLJ6Jm/tmG2Kaf/1+sf4J4QATkrT94q/m+1Cog1wWrW8G2mISEFxfIalfjJNFxLshU3jPE3Y/MoKmyoCaoVxsr1j7RHEM1k05XcAsvxTWL48cKrq8eBJDGj8KjO9lm6Zwivrh3fpXEX7pjIvImrY1bwnJq9l8cGryY3uQkfEjIqZz2Z/L62jA8ujObxnFVhHr+IM77OlTGXUoRig2/7/Gwfyc/2SSrUaJ6+cC0fHJHj8XJyO0p7OIXYkWr9d09La6a1NXzTNBrGT5bzoukE0LOT7N6qgxP4ddXDtPsN+llXL16segQgOAEIsCr5aCUJHQ/E05hajdUnjoa5s5yAK4nrO+wjoGpvH1Z81MdQWUuW4N5bavUwixWn/1Lknd9YlW8eFlqV3+m49Y0pSLJknbkLvFk9nLYOY+hAjPNLshTk8IfGvMTKWkJFLEmW9ZcB/vOlBceZNOg0kqRy1pXGC+9P5NV1E0zHMrxki5f/fPXxfF7aVkZdS4YWkmrN4KUdd1JVOwJVkvSXOObUnL18u2A5eSlNSBLYJRVZgrykRr4zYCnlPfaQ67Dm3rsVB6+4yq2rgAmvJbYiypKeYnjSj7i923zN8IPG75dCQ28qZDSiqvhfkv5S0F6pg44jyUbarWTzkltwUO+jhFTaKhqzDZvNuJoMKH16VBse1YZPlfWXIrxmjF+JI6TKVZK9g89NXEqHatNfPmThJbFww2zd8AfQ7k3mDxtno6Dx/wMvBcjJMN/ozs1o0Kp9CS+xqlegAtjiA8Xc+eZPGP3yb7nzzZ+w+MDYsIpdYKwI9nTJYlJCKpCl2Nt5umQxPlUxMIM6wzNTlpBymauB3T98Oz+78+8hoae/XxUNoBvG8weYXHAurJKgGNaJp7yzHhaKsJn7xqp8Q4H1wP3erMoPGy9sfIG/L1biqj7Qr5MrLw2afMNWg3zD/KlbkGRJY/R0EdUnC/TavKq986/lY4NWk2IzD62lyh7+rU8VdZ5MeieFTwBeVeInjTNZ0VYEXamW6WyCtlRoETfxJLjQEyW9Vd/0DUVK7jlS7R4uHB6Mr01T9swtOEiPvtaVTQcO+hjQsn1bW9Nxpjcz/uaNjBhSY3lNAOOH7QTQa/1mOS8we8JyPevXCpZicBYefkD6uT2E1fNEySLT/stqxuubwJkpLTS3J+NVtZBZQAMIYIZJFnDFgWJeWj+T064sMpNbSLF7aGxLp3fGBZ4uWRwmCxENAuEgkTl0OaSZr5WiMzeU8e8szNJleecQD7sz6qjZBPFmVb51cfXQ8f1a/ZFWCGUjTjL3DoGzv2aEKY1T+4dFzF6WmFuy21q+4chgk2uiyOq1Wd1buInI3hGOc5IjhztyHI38+PRs/k/eEkPoR1E13vo3Myo1tg+R2T6R2gFocxJGcldlONMbsi4auP3icXrvetL88s4Zjnb/s0mGGLwY//eqNvoNPE6/gcfpZgtSdsV9ATHmH8r8GTdsN+OG7SZF6jC0izBoDCHTy9lAfXO4oc/OOO/fEzDy/+8s2ISCsRTkN0re4T6TgjHLasYb6J8X28L3NNq8yby0/v4w419xoJgfCoqfF9udpNjbeeGet0yNfix5AWZ7AoGr46kRdC3o/99Qxj+aOPyV1toP3C+SAb9UlI04yfz7dhrLMd67EyRJZ/mUFhxn7m17yc7w6/J/ONq0Dq+lfIPTvP1yo8mbSneHdRr8WU8m77m08Mzj2avIs2tSzYGPuY+9kR90q0Bx07XqXb7YNn0/TfjypHd5tfrLBk8+2d7Oo5PMPXmAuws2GYy9w4LG+Zv1D4RtDpvhtCuL0S//lt4ZDcwvqWDm8K28tH6m6cbyL9fPitnjD+QI1Lp6YJMUfKpMn8usIBopi3h23mW5pSluKON/Wap2dUF7PyqDbzF+NEqec++wKLR+2z6qDvSnbPgJ5t+9QwjluJl/13YtDi9IMUuSHEG+IT3otVvy+YW9CZG9Y7nSMO8TcEyn5uwlzWa9OepWHLx2pgxVhpUthaxsKWTRoJfDJJxTZQ/fS10eFHMTP1L/8XR28XS7ttl7mkxekMuDMX+IvOmrGjnjBmaNInrm5t6+2O4zKH/aTI9Fb9+K+eMw1PM1foeMWb0yChIOWwftfiOVkdLME7f9jbL8zdremfC3CdX/Dz638AkI7dFLO2iJULWunvyw8ouoKJy2uPa0q4fOCrJiE4mrgKU14w28f5//c7LKFXjnwC1xCQlFyiKeXRrzcJeMG2bDFzQv+5cVI6m7mKJtLF5MuSy1c68VdCbpMPe2feaTw5Q9Ydcs3DiGNk/IBnNAvuEK47HBa0iSw+mbqgpnOjL5z5PT+aDRmL2bazPf/O0uubnPscv03HR28VMq6EsjMtAXTdphVsduYQCTTV9JgTzr+H08cPTjwby96EF+98dv8Mf/fYSDR4fFdfy1B4t5rfpLNLdnENgFD80V6ApyL6H+byAM1NviWqt2K7y4bkZYneDgvYy5AosPjOPZDx6i1pWFiqR76+8eGBvTPaFr+v/xxA3l+UOcwjrXsLcvwkrSQQL++LWV5GRYTA4ZrWH6+tVHBoGEJt/gFOQbjg0Npn1GE+c3rAgssnQ70fy3iverwGcPzfP3Nd7XqniLJKGVbjSRcn6aSlItpB1079/pf5bGbK2gi90DvU8j9whk+Iox/+A4xti++SrAI8b8heMjnwxh0+Zb9aSv5pZuVG+Yil3y6RvAPgulUI+/7OPWQ2NYuuUuGpq7k+W8yAMTlnOHIO/8l42zLMo+fibYLwr9f6NgUjALuLUjCfziBgE4ZA9pjjaa2p3+EcK/72dcWfz8ngWGAjEQkIuoCOsfCZ0ZW/G82URxqZo/1wrX/4Yz/jEhTuUUr6TBF42lWaF10Axebjc3imqux1XvSjMtw1h9ZDDVx0I8TKuCLFahHqsJwmYxKZhMEGfbu5GXEj4BnPVkGiWdhVu90ljOT7PeDtMmAqF0Y0jYp7caQdpB3O9Mb0LtGWT2yMk+g9HXnydWkTcxTCQ83I6d5tm+67bfSsHgQ0CEsI/qZdvhIv6x9gE8fmPW0NyDP635HDZJYfIwzZBZl33M0gvOVB0q5q0Ns6lvziI74zyPTlpEecFmQwgIyTgRrPRnARsppCqZKc18546/A/DK+tmWYaG8jAZ9Azi0NOTMTkpDhiKS4FrgfACRvPVYhekic/0T8g4JxAFVB/rz0sqbqWtMNXidAcgSYe1tHhsLNnRhA/QK4PVjpbT5jH6LW3HwX7VlltesdBdyUTFPgLMq3RhR2uEqwkrf39USXZGbZVvu0g0I0DvCAAAgAElEQVR/AB3eJN7eNE3/dy+nuRfay58YtvrgeH5d9TBnmzUph7OuXvyq6hEqayZEvPdrJrkDIJHq0FhIP618mDOunpi5JSn2dp70i8HNGL6VDx79AXvmfYMPHv0BAOVv/piRL/+G8jd/TMWB4ojPAZjmCATvZawXbOWVX4q3fq1w/ROefwjKRp+5JKG1UMTL2y8bcZK5pUEu/4LVIwyaPUBIYZPgsSTLeqH1ZU+9bakr0uhOIiOlQ6+7u/rwQMsxrYq5aM8RLt0Q9nyinLLFisAg3SB68v5VQGXDaJRjEl/rV0VOUhNnPZm8dqYMZPjfYS9ryp3eTH53oZyVLYX6mC823cdzmSalG9vL9cQuEb+knJ9SYQj96NIO0UKYXKPx9r0hYm7B9uBnm5rWgttE7sGZ7tI9fuOmsF049nGhubvpo55v7qFf99mJS1mw+kFDnD/J3s6XJ72LD4n/3viAaQLYmxtmc7eY/Wtw/FXORsgCfmV9uDxEYJDeGQ18q+Qdvxhc8POySVJYneDA5jDAzOFbLctNinWCQ9k+T5csZnrBNgJf2M5E4QIITUgLIHRFcC1w/RPGX4AmtBZSoGWGtvl5NTaFy0acNChx5ma6mX+flrATNgF0gnpXKrkmG8CSBG0eOw/+4QGkUNnTaxiVDaOpbNCKuPuSZe7svpvv9ROUOx2NPNtLiwEHJoAVbm1F841uQunGDuvSjUulIlC12L/O9kktZ3Fy51LQlxOjij7ioy2T8QmrH5vNw6RbNkR1fXdnIxdNJoAsZzB0VeIP//xz03QamnvQ09nAQxMruN0f77cOC5kb9wByMs5T5+oV1p6b0WApAyEBy+f+u+WYVnWCX1o/M6Y6wRUHxukF43+5XhO9e2CEVibTLAHsWi0oHy0Sxh90D9xS2E0QWgu/NEZ+fgyx/bmlNeZsnDv2U1UjqHF2IsUMsGBdId+7d7NpzFvf4LXy9q3i9GBM1JLNr1Gtkr9sxhVBWe/9PJq/luwUF/Vt3Xjj6O1Unh8tjBPsbtgLkOHxvCpT5c4nsipZ4S7UvfrlbUUsEWSclSQMybn6mP7jJVIRi5OC/X3JnRctj8bbV6NaEYgbtcHjvjd9goLE/l03425NJy2tmZvHbGXQoKO6525M8gqO2aHauHPcKt79cAYegaLqsHcwa8IK/Tqfvzj8xGEf4SD4HQyc7+ls4JyJoZckhfJX/kC28zxzJy/inpBVwFcnLeLFqvAs4Mcnv81rG2ZzxmJiEGHw5FVr2uhpVxYKimUcXhxn6YFinhMSx2pdWTynrx40A28lChcNrmRB+WiRMP4C4l3Evau41GLqZqg+eBNfL91BZmpH2Ll616WXWowXynrv56lR7wULuqQ28fTwFagHJVbVd17QJcdCx8eK4vlpR/+bjtH/pmM4beYx60gYM3QvAJXbyrjQ3J0ezotMG/8+E4btiHqML01azH9Vfyls41bxTz5nm3vxUtUj2MBQNCYgCPf6xmAW8NcnL+Jef2LYz1c9Esbi+aaFPEQAVnWC82KgfppLQ19a4tinBTeW8e+EvRNtEffL6e2L/SNW34rC2w/12F9dfYt5qcWNY8IlmS3YOgZPX3jWsH5RxPnF+z2a/2F4QRebl8cGrdbDO9YyzhJnPZnkmej41Pkyg4Jten/heaz+lNH0EWHhyRs9/OCxIbFLjO1bHFvJOBiSvCz6dAgxf4ek/e0Lh+5n/DBjfoO4N2BDlERQhT7aPSb5w0J/2TiL881ZSJKiG/4A2r3JvL5xNmV6xq82TnnBJu4dHpwQbEgowN3+fq9tmE2dqye5GQ08UbKIewo2G9hONkOpS5VvlbwTsVJYNF53NNz7Sy0fGYprZRVwbaw/rhFEo8R5JbFg9QjTxKoFa0Zc0njVB2/ipcpi6prStCS3pjRerppgyOa9Wsg2oW5C5xo+AbxWNxW3YqQ/uhUHv70Yw+ZsAgZsOnQL3//zs/zLa7/k6T/9gPWHjAlNt+Vv5dVHfsg/nvgmamhRGz+sROCscG/BZt6Z833+4+7XAfiPlY8xc8H/x/Iaa9nwaQVb+GH5n+idcR4Jld4Z5/lx+Z9NBeGsYJ04duV19q8Urn/PP4YZOpISZ1fYO8Yu0fP2q/b3AymkmPrakVTV9I/a2w+2+7n6hweyOiDEBponbzPpH81x4HqTc9HE+cW4fX1bN3JTTbj77d2CHr8hzm9cBbzXXIh6Gh7PWaWzfV5p8tfplawLvlgem2Cmdxffbqukj6rp+v/CWcbi1Og3f614/pFYQA0ne1N7oACPO5XkVDcDRu1l0MCP9T4e2XwVEM2xHMJMcajBlde6Q+P469rP6JTQ881ZLFj9IBKqrgZqE5Y7liJwzvNBGXULOYjOcgHOuHry08qHUSBMJC6wCphWsEUvF6m9Nwmff1ixTKSV1z2/pMIgFgdBaWgzWElFx7oiCGUHXUlv/Po3/jHiSgu7dYaqA/2DpRYtRLKsUJr/CXNLdmsF1V1pLNhQRPWhm4Lnhx1jzmQxY/eWYA1eoHTwUeaM3062s4X6lnQWbh1H9SfxlREI4I3Dt/P0yBUGmeY2n53Xj5dGPcb7TYWsaBc2Z+OorTbTu4v/6wlW9OqnNvJzl6bzvtg3BWqFDN/cM9C963sNDSd7c3xXIaqf1dPuTuPIR7eQLHvpM+BEl8ePhIot95jmAvzPphmmUtBWInBzJ0eO15vBLBegzZvMD1c+xu/Wz+abJYu4L05lIAOYqSeOaTLRQSG56zPeDwnjH4Z4xfOjGjOKLN1Lie2Duf7+d+/eyHfv3kh9cxqbjvXl7uFHg+czWpl3x0aQZaqPDqZ06MfMm7I+eN7Zwrxb14HdZszytZJotpmvAqyOV50bBQc03Z7slCbOtnfj9WOlmkaPv5tq4aWLoWZjhq9k3t/izxEptv+Mt9JQyhE0qYfvulazuO3zSIEbeJOgtp8W3u7e2KWs3toDw3XDr5/32Tm8p4i8ASe12wn8f8MqQBG4/VJwj8cs/q/3E85FzAUILBUFh33ysO14VZm/bZrJ+eYsejkb+PKkd7k1fysd/j9gkuAte0JrgQYQIRcAf13g51Y+xgurH+Tbd/zdUAs4dC8gOL7VcEave/rwzUwfvjmkfGQQVpnCIuK1L3AlkDD+nzKYSjCbxOzN9PcDtjA3o5UZow+FF7Zx+JgzfjvVRwczp3hbOM3U7mPOzVvCJR7ihFVnR7Hq7CgUu/Cj6aKW2L2puzRev03j9f+mpZylauwZzNZSDxcw1fM/m9dl79/jNq8009YaX3bWzsMjqdxaRmNLJt2djdxTXEkP50UumJZ+tI6B35a/ldvyt4ZNKrHCKhcgCInGtgx+VvkwMsR9FXCjIGH8CffMy0ae4tGykAIr+/tbXG09jnDCvN2yv7m3Xzr8BPPv+ihcgtmfySuOaaW/39mts50tIElkp7eYn09vtmT/qDaL1YiFbg+GuL35XoCB2284tsgCFvrcm7bLkNHbx9bIDzP8Gv7+xC6r1YQBEpyWMulrMgHUqhZGyusIeziDvLOghCbKO4vHjpQ2PG3hkhTJqa266FuSHAyTeWOM+XtUG3uOjGDph9Pw+GNkF5u78/bamRTnb2frobGG0I/D3sH9E1boY4gsIJ9FLN0mePUdwu8g0irALBfADG3eZF5ZPzusOHwkiN67zyBD3fm+gFWmcDTy0SKulRVBwviHoGzkKZ6avseQ5fvU9D0gydYVtq4Q5t66xzzpq2R30Pj7YaW/3xnqmzXdmPqWdHKd4ROAq73zAhzXCr6RURme+CV5NBXPZmvv/zmW8KBvGzZUfEj8tW0cL9rLDTF/gFY1iV94v2A+iD1yEfdokFNwkNrdo1GF0I5s8zJo1N4ujx1A1dZS3fAH4PElsf/EcD5327ss33IXF5sz6eG8yMzxK5k47KO43dsKYi5AnYXOTwDR1wWIH8QSkr0zGng6xr2BQAGZq50pfEMZ/2ji+Y+WHTTN8n20rMbU+F9ub19sz45Cgjmgxrlw4xjmlW0OmyxEKKrxcdq8NhZuLwabzMLtE3hqSjVJNqO3k+bwUDroMNXHNfqrFatHtYz5W3n4Ft5+NH0sYvt5FgleuopnSH9V0gz/l9iqN9tR+YqibQb+u2Mm3/YKbB/vgyxWbjW5gwo5dYBkmclrKfUsPJCzz1ly1X2cOzgUb1sKjlQ3fYbX0LN/rZ4DYIj5C+EWuxRd/L+xpZvJ88PF5kwKh+yncMh+Q+lHcc9AtgymC/kawuebpAqZwhYx/8AqoLRgM3cVbOL9mokRVwGypAQ9eENqieDhR+GxR7MKAPw6Ql806Ag9V/lFFAiTkjBbEVQcGMdzlQ8aMomf/eBBFFVh5vBtV9Qg31DGPxpYZvlGmVUblRDbJcKympZJhm71oYG6/n6Os9VQwhC0fIH3Dg5h4oBTGpunOZ2F24up/niIdv2xoTw+YT1JIRmkDpvCnKKNuvG/lnHGl0kfEw1/KxVPgIfYFq5dB3xR2caPU2bwbnqQ2ql0OOGCYpiJVFSk7g1xYfsAZPY9Q2bfM6TFYSVhhm7pTTS1hH8e3Z1XNzO6smYCC/xZwBkpzf5qYuHGVLHIL7hc6IqOEFxbmcTXvfGPlZ+vqlII7zjY3tlYZSNrmX+fiRCbRKd0TStvv3T4CeZO2UN2RisutwOPV8ZhF8pQihm6YIjBVx8dQvVRzZiXDjvGnPEfBQ391rFUHx3Cq1tEz90WJBrbZDKSzaUDstOag968hYcfDbc/5lWAYUVg0S5q+LeU84MMExXPjvLg+wxNW7DwEk3bhUIuqs9P88w6C70uhvcFQ9DfwPARPVBR1dPyWGT4BNvtBt1+IaYeIeZfMnYdH6y/C68Q+rHbPEwdVxWM7QtmYtvhIpZtuYsL/iIwsyas0GQhLCWPzFcBRrVPwbtWVVYdnMBLgrff1JaB1Q1yM84HfXOLkpExw+K92CQpoo5QKMxqClwrVbwgTsZfkqR7gZfR0oVeV1X15yHn5wAvAKf8Ta+oqvp6PO4db8gmhj9SuwirmrlfL98dnqh1IHwDOZTJs/FIHveMPq6PmZnmocMrGSSYF2wo0iSYO0H1kcFUB5K75Oi8pfoWJ7nO5vD21uh0460wNXefgdL5xtE7+OBi/JUyV7Rpcf1vOoMqnr92l7MM63i/Dwm7ya8/tN6tDmeT9kqKQvDtGkSg8te67bfiasmgW3oTpePWMGbovrC+2w8X8vaHMw1FYP6y5rMAptz/WFF1cAJvbXiAs81mcX6J0MpfyfZ2Hr+EPIKuwEpHKNoSktdKFS+Ig/GXJMkG/Ba4CzgJbJEkabGqqqHfnr+rqvrNrt6vS4hil/2shZ7O2SaBdWExjlVoqFuqh8w0zfvMzXQz/54dIElU1wzQ+5gxeWbe/HHYFkGSXeVCq52H3vxssNEiy9agz2PFxxc1+G1Gz33hronMm7DaoLmjqJCd5uKtaW+xYO9kqmsFqQkrD18YtyxvH08XBJO58lKa+HbBcpSPZV3BU7VbrQJii/+rMizvKGJ5QxGi8oMqHoewff7GOL4sxPxBMzl/tY3TVoSGE8I+jSG4j+mxVZzfp8i0HLoJz5k8/aLUPqfJG12j9zFo/lvo/Hv9HnTt8f4c2VOIuzWd1LQWxozZysBBWlawGP9v9z/c4EFHGTzoKGlycKVnlgm8Yku5aeLXu5vvNYjCibpAsvCs4uqpQxKXblpxmN9Wf6VThk9OxjnqXT3JzjjPVyctoix/Ex16Jm+wnyJ8voZfa4wrgtB9gSdL3uXHJiUk55W8a5KtG84Uml+yOKZM4suJeHj+E4DDqqoeBZAk6W/A/UC46/ApwILqAoOGPvj1dKoLOr3WsmauCZ9+7m17DcbfjMljScfshMYZCkOmbkhsPxKqP9Hi+nPGbCInrdmwb5Cb7mL+2FXaJHZqeMRxynL38dhQzdNXVAl7SPH1FJuXf+1fZZBvvlr4KVrR7ocQ2D62cfw4Zfplu2fQ8Af+4BLu2j7UywrZIw/FNFbt8f7s2zYexZ8c5m51smWztikdmAAuFY0mewNgnRAWC8yKw4QiJ+M8f/6X71uG5q4EAkllvw4pIRmtjlB4JrFWOOZqZBLHw/j3BcRc85PARJN+n5Uk6XbgIPCUqqqXNz89gBgzcAObs2Gbtgf6BX+bFlbZrGauqpqH+bMz3AbP3IrJY4b65rSovf3SwUeYd6uQqZvRwrwp60CS/cXXreL02nH1yeFUnR7BW/e+RW66y/AcKXYvc0etp6pupPZeheSsgLdflrePp0eu1D19q/BZTlITU3vtMVTn+q/aMt5rLhTGDPa35v93ftyZts9PmcHz9hl6s9KFkI61wmew3Wj4gw/TfLIvWSOOAKHevkzDyd6cqSnA404hKdXNgJH76D/wGId2F+mGPwCfz86uncX0G3jc4NHbQnjobcKSSDap+5mZ3mQ6AXR3NloqglrF+UP7WBWHCSDZ3s7cSYs0j16yGFQ4fO/gBH6/ISgb/fhkTR00HvsC9xVsNmQWA53qCImYOXxr2Oawec/Li3gYf7OPMPSbUwH8VVXVdkmSHgfeAqaGDSRJXwO+BjBgwIDQ01cMVfv7+UXVYmMSBOL4c2/bp08cKQ4fmWlmGvqpIf82Z/KE0TH9G7zRYk7xdpNMXS+PT1jPnLFbyE5vpr7FycIdE6g+Yb26yU5zmbenmrcH8NjQtQa9His0eVP47sClwXBQUiPfHbAU9RS833h1K2ddPZhbp4aTvTm5e7Qu/dDhTuPojptxyD7a3ebZv1Z1f2NBWXE1Sz+8L6wIzH3j3+/y2FbFYUAl29nAo5PfZmp+dMlcofTQOlcvfr7qESBcGC6A5TUT+N362dS5ssjNaLgs+kHXGuJh/E8C4u5lP6BW7KCq6nnhn38A/tNsIFVVfw/8HqC4uDjua7vLwck3DhOsmatr7BQcZ/5d28PDSOsKDeMs2FDE/Klbwvq9d2AQEwfWku1sxdWWDCh8584NzJm0i4VbbtE2ca10fmRJy9g1QbfkdjJTtBhvrrOZeZPWgM1G9Qk/f99mXE3UuzPINZkA6t0ZOstHNeH5W0k1i9CKsUthk0Sq7OHfcqt4z1UU9kzR8PwNmb+Yt1tq/sSLLRIFzz/SQAH2z4WTvWk4NARvW4p/UON3VvHZObqnkORUt+kEkJrWgkeRkYWfvC1E20YWVgLt4iaJ/1b5gw8hAau2ltLY0o20ZI1C/Neqz7F8y13cN/59xg7djVGTQ3B8DDF58fm9fGFiBa+v/iIdIcJwXy/9M7fnb8EhKbpGkJg1LL4Dh39V+YeN4cJw7d5kXttgzAZW/OOsrJnAf656WI/DiyqioR5+p4jAFAo+89Xw88MRD+O/BRgmSdIgNDbPQ8CXxA6SJPVWVfW0/5+zgP1xuG+XcDn5+CICcf25t+7xs3jSWLButH+CEPr51TbnTt6lq3Au3DiG6iODePVDNKG10s3G8M1tWs3WAJ3TDFaZumH7EHYvc4o26MY/FAv2ljD/lkrD5m+b186bNbdFfP9WUs1eRUKWVM52dOMPJ8r49yHvml6fa1Gh63qCPbcOb10uoTGS1D7aT6bldDaNB/KFTF/ziaPdnUpB8VYOfXSLIfRjs3kZURRepevIx0PYvmMCLS1O0tObmXjLBoYNjrzHUDhkH4VD9rH7yEiWCKuAi83d+efa+wGYFENFsABuzddi3v/wC8P1dDbwlUnv6jWDY4FVDYGzrp6srJnAayHhoNc2hBeOb/Mm87v1s2M3/p8idNn4q6rqlSTpm8BKNKrnm6qq7pUk6Xlgq6qqi4EnJUmahUb6bQDmdPW+0cLg7fs9/LIRJ3l62k6S7No0nZvp5ulpHxn5+BAdJ99wwtwDrz48iOrDg/zt/j62YDZuoH310cGsPhrqyWvHcybtMqWRzhn/kVFozbAXoGXqzitZazDalvsQac1B71rYO1BtElVnRsBOibkj1pGd6qLencGbNbdpJRb93yIDS8f/HK9/fAffLlgeJtX8wtFpfNAUpFx+y/ce3e3h+x513kw91h9NDN/QbnE8zbaL+fZKektaUfZfqX6xN6tVQ3ROuukFqsVAInsnefAJVFXCdzZHHywpr47uw4+iqBJNRwYZJB6skJTqJqtfLYNViRP7RtDuTiM5tZWCwp3k9D9Ju2LX91x2bBnPx0cKCLzplpYMVm8ow6fKDBl0BJuwKS+uCAKx+sqtpYbwD4DHm8TyLXf5vX/9qfQjn8D5F+sCBzBx2E59Evjw4Dj+tPF+Xv5gbthEoKCy+uB4/nvjA5xrziLb2cC/TF7EnfmaLES28zxnm8M1l5zJLkOdgEA4qN1rrh5Y58rCY1Dp7MJyMIoVwZVGXHj+qqouA5aFtP1QOP4+8P143Cse+Pqdu3XDH0CSXeXr5btN+ffXAqzCN1btAVQfGwpgiO+n2D16yEdEZ/z9qtrhrKoLqafbyTdoVf0oVJvEV2+qJie5SfP0j5dqzB5/ZKG8xx4DzTCADsXGa/VhW0NdwjT7Ln7kqCBV0qi3fWnkJ1QAUBGB/x/ArPbdPNNWSR+lkVo5k1+kT2VxSnR7EkpDd9TTvcHjwJfUga1vLbZeGr87ZchxGHKcZEf4/ogShZ6SZPMyYKRGsMvuf4r+A4/p55Jl45gnjg00GP4AfD4HW3dMZMigI4b2/UcKwvIAmiLIQnQVHx4cZwgBnWvuyavVXwbg9vwtYbTQs809+XXVw8ioTM3fzNzJiwxJYqCFkCRJMg0HyZIvrAQlaAlk1zOu+wxfQrxr0Hj3ZuiW6rHW2CEKOWWrWVxYfYR6+6bXmvDz65vTyc0IN/T1LekhOvrhtXerTxZQfTrIx7/jpkPML64KC+Es2FeiX2/k6QurAHvIqicKHv4HF0bzwYXRxnFtQS/9a/2qSJLD46AtShIrW4v0SmMxM3xMnO55SZW64Q8gVfLwFJWdGv+Znt38rF0o6KI08nPXEgAWOzopMn8xE7W2X/ABO5LxfaKFBO255/RuPhO1Tzm5HaXdTN5ZASQcKW3kFBwks28dHX4ev8iqEtU32xWVPbvGYhU6amlx0i7kAhz5eAjrNt6hZwA3tWSybN29JCe5ae8I31vITG8yMH8sYZXtC/x90yxD7B80I/2njfczedh2/mhCC233JvPmhs9wa/5Wbs3fioLEWxtmU9+cRbbzPHMnL+IX73/V9FEUVSbZ3h42Wfzr5EXG6Hy8MogNY8ZpnEvA9W/844TSguPMv9tETlmSwhQ1LwcWbhnLvNvWGzeEvTYWbiuOeawAq2du4Uay01zUt2b4E7Yi8/WtUJa7j28UfEA3h6aL1OhJ5ZWjd2khoSiQYxHXz7SFh4HuSd/NEz0qybU1UufL5JXGcpZ7otfn7y1Z6PKjtc9QdvG0WklvnxYSetFWzmKH5tl/p8OioEvLKhZndPJez+aFxKQAxYbvVB8QjL8Z0gd/QnPNUEPoR5J9ZI/aT3b/UxGuNEekegBpacaM7q07JhqkHwC8Pgd2uwe7zWM457B1MLW4OubnEbH+0FjOm9QRAK2UpPj/UIh00bL8zZT52UGBvIAFG2abhoNyMs7zr5MW8frG4F7A1yYv4u6CTcTPyl97uP6Nv4l33eROMqVfNrmTLDV25t62z1xOecqeoPcfq4cfTTau/7j62FCwy8wZu5Xs9BaNnrl9PNWfaO3mY5pXzcImUV07XDP2IkPHbt7f4O2HMKBK++zjmeFLSRJixN2T3Hw3fynIUHl+tHFFIOwLKP5VwFlPJnlJ4Ua5zptpsJd3O3fzbFZQq6e3vZHnelSguNDLN1p5/oHfcCT5hhnKLn6qVpBKMCT0f30VqB6ocBRaF3RRjO2m5Wk9FjUlO5JQBN0eVYgx+/xvICnnPN0kFdeRgSjtydhS2ugx9ChpefVh/H/9WMigbRfer4xKSlorbabUT5XRYz6iXXXoPP+WFqfpY7e1p3LvbcvDwkHDB9fQJjCFRPVORfhNiO0+f/uWQ2P429rPYGVws5wX6FBt9HReMM0L6OVswOP/PAza+35W079MfodfVz0c5uE/OmkR5QWbKPdLSQee0qdi0PkSf/1WGcSigujVjOdHg+vf+Jvg1VWFfPve7TiEuL/HK/NqlbUHaZVVG2u2bVdQ/fFQqj/WYvix5iBcLjw2eI3B8AeQJPv46oDqqLJ2XztTxvf6LTUKsCkOXjtnjPd/o7uJPr/s4VvOSkPt3kiwkiGWUXlardQNfwBpeHixXdOPsSzoImeCqxtcyAnW8e1VB90ElpPdo5V4DEVSdGqdaXn1pOXVA5AcRd5EJAwdvcuQBaxBZfDQAwwQ9goA0tOaaTHZC3KmuxgxpEbXBkqRuq46WrHlHjosNl+T7B18fqIWYvvCxMVhtFBQqW/O4t/++FO+POld3esXUZa/GRmVBRtmU9+sSURohj/6YjDXE65/428Sw68+eBPIskC/9MfvDw6wzJyNJKcsBbz2aDz8Turwlg4+wpzibX7vPp2F2yfom7aG8a3GiaKyVugqQG+39PzNY/kAOcnWPP6c5CYUm2St1eO/9/uuItQzEo9nryLX3kidN5PfNZTzXmshQviZXCt9frkx6PGLj2eyF3BazaSvSejntJRJb8zHt6Pys/YK/mkbw+d8O8MLurR/EVr76DeUvEmodf7aD1n+MXPq4HRf49JE8iH1rjVMR6Kqpyy4lz7BA/UKfxubwdsPHovaObIk8vft9Ox3mnxlO8f2jaKtNY2UtFbyR+9k0KCjeAL7DH7TMHrMdrZuLsEnhHdsNg/jbt5smgsA4DNo2kTv/VrLRKh0eB38Y9MMPKqN2/O34sPGPzdNF0JEgb2xnvyu+ssoSNyWr2XR+oQlYGBPAILhII8qGWv1GvIRxFWT+B5FDz/YbjNQxlSL/iLn/+oF/a9/42+B6poBBm2dzrBgfaGhIDrEnm3bGUoHH2HelHXGouklaygZJwsAACAASURBVLXnDUwAsYzXr4a5o/1xfXcGC/aWUH2yc42iaDE1Zy+KKllKNjR5zWvQmuE9VyHvubTYumI3Nxh1vkx6m+nzK9EzTF7ylvO8wPYBcOPgl5TzNJX0tZgA0vBQrhzi2bSZPNO6ij7qRWrVXvzC+wXTgi6SKqOey9UsxtlcbUVg84GqgGIDhwepTy22nldezREgd8BJBg462mm/mwZ+jF3ysWPHeFpatXyA4ps3hTGCAth/pID126fQ1NKNbulNTC2uZvSQ6NJ6rOoGBwx7Q3MW/73m89glhZJh2ykZtp2n//SDsD2ADm8yf9k4Szf+CZjjujf+kgn7JbyTPxs3/xPmluw2Jln54/mrjwxGkmXmTNqpnW/2nz86WGejxOLha8fG1YF50XQvc8Zu0ZKvLK418+RL+9Uwf2yQ0ZOb5mL+LZUgS1SdGRm81kJ907Ldf9+p2Xv59rAVYSJtRmhevziWYqXPE0Xd3t+4yvlBZrg+/6/d5Xq/zmL+y9QiVBWeopLeNHJayuSXlLNELkIFfqpUhG3qBtBbbWRxciHvXLwfg0yoFbwOo7fvs2vx534nsGVrEsCqKkXQ/wkei96roeavpbcvKmjaTdtFVk8k9L3pOH1vOg4EaaMe1RYmSHPw6DAq15Wj+tk+TS2ZvLtmOl7VxsghBwx9FcGPDqwU7ixexTuCZLQZOrxJ/M+mGYwdugsg4uZwMP4vfHZifWHhDTiE1ZFVBrFs8PCFPuLfyWJF8EHNxLDksnsKNmNhka4Irnvjb9hIFRGyOVs67BjzyrYKbJ5W5pVtBlnSErQkieqPh2hqmKKxtRsNuOlxlJTOSEXTFz7wZ7LTmjVmzu5JVJ8SPHiTkM7c0RsMVE7wC7GNWMeqc8E4vKXB72ST9quDqjvV7Olmd6PaJKPBFycC4dtn7CMcC8+xoqMIXEZ9/t+0lrPcV6Svya2KuYvHS6QilhCQjBDaZa3tF8oi003h01KmtgEYpdEMu3Hg33V5qILHrwr0TnFTtK2uBx3H+6O2JyEld5Ay8DjJOectQ0CSIhp8i4mgiz950WgrIXH+NZtv1w1/AKpq5/2NUxk46CiKySaveDxi8EFUdQnvb50qCMiFrwIbmrvTpmoTRJbzIg0mE0CW84IuVCcaaoeQaBbNpGAL2SyvPjieP26YbZpcBuYhow9qJvL/TLSGFPAziq4Orn/jHyXmTNppnkE7cUcwO/cyw6p4CkBuerP//y7mF1eBRMQQjpXgWk6qi7K8fQbv/1KQk9S5Zs9ZT9cTfkKxoq2IFW1FRvvbefJr1Fhi0yaA0BVAKw5eSCr3388Lvsievyop1qnBVswfAd5zPfAeu0mfFdX2ZNyHBgOQ1Ptsp9dfDXR0mIf52jtSTdvNMGboXsYM1QrU/7+/f4uLJvsAPZzBSmmzJqzgL2s+a9goTrJ38JmJy8Ku6yqqD47nFYEtFJpcFoqXqr/Ekr13+HWMjN+Fdm8yP3nvq/x+w2yBVnplcd0bf2PYx+LHKEnWbB5nq+ahW3n1Vh6+bHHfCCGghbsnMW98dVjxlNDHTrF7mVu4kaozfm65SSlFKyE2SYKnRr+HapdZVTfSuIEri165uJoIdgl47mc7upEXYbPXrTh4ra4MxWbt7VuFehRDyAnTPvGQbg6Dv32JXQsNPeOtpLeqhYZeSC6nIqkQUCHjLDT2DrmZArIWz1cD5RwbcswZPnZPiOCbMIp/wvCe7GtcDgEoNtqODdBZPwBen7mH77VYBXQViigDLQx75Ejk+hDtisOwqkkWQndWG8RTx1VR8eF0o4qorYO7i1fpdNKiIXvxqDa9tGQP50VmjH+fW4buFjx/gT4rjG/w6oX3lSQUuRdXWX/cYC4YF0gug2DI6LerH2LpnjIi5wlI1Ll68YtVj+BT4c4rPAFc98Y/WtQ3p5FrMgHUN3ddCjdaBIqizynapCdf5VyilPKbNbfxVNF7pqGZFJuXxwavYVXdpXv/vz9ZZpBgBm2iktB+YMmSh8dzqwB4rzn6JKxrBRWOIioc/tBQiBSInObSzIkrR4vj27zQ42ywpq9dhaZu4JMhpPQgkgI5Zzp/gA7zuLfabh0Pv1o4fmwg2zaXYGXokpPbLmncQCnJyq1lNLZkkpneyF3Fq0K0g2Dc0F2MG7rLkMl8OWBVc8CsffneO4g2Qazdm8zrG2cnjH/cYULdLB3yMXMm7ghWttoyloVbxoVn0HpsbDrRj4Vf/N8g9XJbsZF5I/LtrQqsWFExDe3acdXpEYaQzFv3LLCUUg4kd6kmnv+q+lGo+2S+P3qJuYhbShOqTY6uZKI93EP/oKkQTkh8rU8VOY5GmnypOCQvabIHu/9HmJfUyPf6LkWpk/SiLJabv5YbwZj3t5JxiHFFYCng1okhkdNcqM7g30WcIKSmblDfJ+Smqsb2yT0N3ZuMm7yKuAL0f/+SOqAjXNNHSuow0kEF79Xji2P8S4Aov6wIOkEBL3rXznH4fOamRJZ9FI/bQJviMMb5hT+CQ/C0PcIqxSH5GDr4CEMHHyFJEqRIhKIzHcIXxOixCx6+IVErOI6h3KS4gSusRMQVgVVyWU9nA23+vY7AmEroXk8nqHf1xBOVgmD8cG1kCl1BlA75mHl3bCQ3owVZCkgjrwfg5bUl1LnSUVSoc6Xz3qGh3D3sMLlOf19nC/OmfEjpoMNX7HkX7JtCm9f4w2rz2llQE04vDEVV3UjOtpkLcJ1tN2+PBR9cGM3nDjzJ8yceIFn2km7zhE00qbKHr/daxd3O3Swa+DIbBv2Yd/q/xN3pu80HjQH3OXaxIuNX7HT+iJXpv2KafVeXx4wLGnLCN3qRNK+/e3QS1ba+tcGJIADZh2PAyfg8YxxhLRehMmTIAQZHQSn9NOALExeTZDcKECbZ2/nSpPD6u7IUrlWlwdypyHZeeRG569/ztwtvUZKYM3GH+cbuhO3M+eeDBj37hZ/9uwn10secsduoPuHXwYlA3QzAkGxlEfM3WwUArDo7CnW3zBOjVunaOe2KDcUmozjCk8tCGTtWksqvHy9FccjWFEurYuxh8jQS/5ZXFZZ5KyLX3sj3c5cEZRkcjTybXYFyAVa6C/VxgvcTnkO8n3B8n2MXP0oN8vX7SI38KKUCxQvLlKKw/tYevsWxgJgdMq/Fhq7XEfztW8X8/cwfqcdFbKBp/3QkISV1YO9/ClvPC/h8gmcqeLWW9uYSIMbek2QxtBdsT/b3sZaLkDh6tIAevc4zYOAxPIJn7lCNHr5+LNwr0opAfzZhRSAKyjkk8xVBh0W7LKwCPMJmhig9XTxsFx7svL1pGuebe9DTeYHPTVzK+KE7aPNvZgUK5Ewd8SEf7LudUAW7wr77OVg3JExi4iuT3qXNRFn0cuL6N/4hsJRGNqFZZqebM2+s2i8nkmWvPm9kJrXz9KiVAJ2ydgLiao8NXq1JKrd34/XjpVSei1+x9M4KrihIprIM38ys1I1/rJiXYq7OOd9eybKOq7zHYCXlYI9NAsHW64Iu+WwzUT29VjBk9G72bysOqx0MWv3gPTvHhslGXA1sP1zIyq3lXGzOpLuzkZnj36N42M6Yxpg8bDuTh23vtIj8o3f8Ewmo3H8riiojSwp3jVzLV+/4H9YdHMefN97PueYsejkbeHjSO9xxCUVruorr3/jbjVx6q8pW9S1OcDiMkg6tTp1iaejb6gSH9tFZevWi529YHQgDReH5q7LEo8M/DOfs27w8Nmwtq0KF00xWAR9cLOT9HYXGPmYFWAwx8s5XBNq/NQG23hYTgFtxWOq+5NoadY9ftYr/izF/4TnyLNQ5e9Ooe+pRefjRxP+jgWgLepyFc8aYvyopSNl1ej+R2298BuM1ARg48sK1ki9+kVvRq285mUNdTT4edwqOVDd9hteQ1e80SUIoKrA66N73DAXqNvZvmYDZ8qm1NZ1WnwOH8N68AhsuXisCY9KWcXyzymN/W/MAbaqNW4buNcb/JSPzZ+uhMSwR2EQzx69kUv5HwXsJqwNxnK/c/g5fuf0dbUx/e5tiZ8Kwj5gw7CN/f+0L0RaNDHacccPF/BduL6bNa1xetXntLNwxIbzvzomm8faFuyZf1mcMhVUd3Gjq414JvHZuKu6QjFdVhQveVH52biZnfOZ8f6v2aHBGNb/2NPHPLYgZGU3QqxbsHaioqPYOyDkFmZ+OkpSNp/I4tXsUHncqIOFxp3F8VyENJ3tbXpM34ATJqeZ06ZS0Kyd+aIVVZpXHfEm8v7U84nVbD43hz9Wf8ctOSFxo7sGfqj/H5kM3X8anvTK4/j1/h2CUJInqkyNgk505N2/yZ8w6WbhrMtW1+eAweuBVp0egbpOD+jgB3fu6EXp1OoPHHqtXb5EjYIixS9rmbJ6JoVdUidI++6lsEDJ2o/DYo/LwDc9jPk7gmhXuIpR6iSd6GnX2V7b64/lN8Fz3ijDVzt+0lhNweKwYPlYx/1+ZafSoDl5SyoPZvlbMn654+NEio0l72cTgvtWmgmp2aDwWs4BFaYQ4Pn/A868/OBQ1JISj+uzU7h9O975BmqpdZAGpEv1H7ufojpsN4R/Z5mXQqD24fQ6DzLRHFbz6LqwIxCL0hpWCGM+XFBojVB5z+VIsx/zn+ukoIV65otr5+7pZjPJrFhn2DgxlH8PLX2p9VNM+VxrXv/H3o/SmQ8y5ZXPQ4O+cSPUn/s1dm/UCqPpkgZZJa2XkrwDeOHo73y5YEcbZt8sqzwxdBkeISjr5cuK9lkJWtImhpeC5FW4tBv+NbpXk2Ro548vkleZyVsRQhCUUy3zatWIt3pd85SyNohRjApHhazPP1PVYtAcQKCxzYt9I2t2pJKe6GTx6N3kDTsT9GWNFRroLl8kE0C098urZ3W7OZLJq7wybDt3CO5vvpaG5B1nOC3x24jImD9t+SWN1Fde98VeTHJT2r2Fe8ZqgyFl6M/MmrEa128INezQsnSj6qFEwfwyOoGy+IlBtEh9cLEI9IvN/hlXoHPoAUmxevnrTat53FYWNGS8P35IvH+GcyN5BhuWeIpafLwrpg6GP3m7h7Yv9p9n9RdjxG35FM/yWBdxjjP9HlREswqKAu5HVIzBzDO1Cf8ERFOP/inhCfJ4YY/6q1X0Bu03zYG0p7aYTgD2ljTa/V994Ko/zB4fiaUvBkdJGnxEHyOp3mow+ZykSVweyjza/FIZX8HLFVYPVisAmmCe7bO7VGz181byP7GX8LRtZs6HMUHnMbvMweex6WpVkQ5xfvDYSWhWNsdMmagGJ5TMNexBeth0u4h9rH9CF6xqas1i4+gu0K3bGx7jxHA/cEDH/uYUbzUXORm24Sk8UOyrPjbYsRJJjUgXresY02y6et1fQV2pElqCv1MjzcgXTpWuE598ZmrrBoXzYP0r7/8Urs0/RXteT8xvHUb+6hPMbx9F6JrykYcvpbFQ9MzkISfaRNUyTcW48lUfdnpF42vx7Am2pne4JXG0MG3yI2ydX4UxvAlSc6U2Ul3zA8MEHI16XmhxeSjRSeyQs23JXmGKpx5tExZZ7Yh4rHrgBPH872VYSCWku1CR7dJ68VXze4F1aef7C81jE/K28cfHasx2Z5CWHG/qznkx8Din8Xpbx/yj6RJMpG+310ejzSJ33D7gq8x0WNM//n703D4+juvO9P6d6Ubd22dZqW953SwaMwRBCbEQChCVhntxMZvImA5O8JDcLOARIZiYTMkzIcAlJIAOZJJMEZu6de5O8cwN4wWyyxHIxxmaTzOJ912pLbm29VtX7R/VyqqtOq7XZxDff5/Hj6upTp051t37nt35/WjObRKPrtarMH/n89Yk27ohLfD7+FJ/P+CGyffgDpdAj0Twn/NAxy1pIeQjTpvnLAlhhBcjWk2QFZGv4sd5pRA/MS5tPRjTAwJ5F6KZGINlDeLirksE9C7NMMhPhjVO+ZD/+6lNEE14rJpDFO2TqXk68t5RAzUm8soYv+fC9Urqq15DH6K7nfdJ5zRjdClBq/slra+uPcWOSmjo1ZlC3LBxV7OCyi16k+f9ciSHdX9MSrL+oJX2tptD2s+dUNavpHypn0Mif/G6ycM4Lf1CTnPWGne3pPsj4Zcd67qrfQsCT1e6wa/1ZXNWZh6rjlup8uil70kX0I09Tmr0zhesTbdwbzzB5zjRD/CC6CYCNwYltADacqka4+c56qvOu/h0PYkdnuxLFhQ/VZ4T/wTnOMQg0r0FRbYZMThUTSIwSEzgbOHJ4Hu1vX8DISDGFhUOcf97OMVUcL0laBq++cSmDwyWUFA1y6QX/x9GfIB+UFYUIDTs3gPLis2O5n/PC3wx4+c2+D/ONlc86qlx/feByjIIszV+pgY9fk1fNr7IgTIX2/sxwA0YHfLna4tPpiZfx8+4reHa4AXyp9Yw+T34avuJ58/T5q3zvY+bkcYkLdFLm2nGrU5Q51ufWlP37+iZMYbF3pp7tjkSzo4lLIXHujDWPXfibqmORX/VvarhcC0AeVoD8uSFbAaaSEM6IFhBPeNLHbtAjBcSSKc+6ZqAVRDGiTkHvCUSIJrwkZA3fdNf2ZW3ZZh0Id4vANt5wz8n3ZV174sgc2nddlM4+Ghkp4dUdlxM1fMyee9jmn/cK91x9TZjU1B/nk/W/t1kEIb1QGuNuNdhYQ4XBJRe8wvOvfNQRd7jsgpc5rY8vgDwRnPPCHzJVsH+9+GUqAwP0Rkr59f4PT5jT/mzguVADz4Uazmr20dnGg0YT92jurRizoWrKfkei2RL+SdS6NGbPdX7cmKTq37FC+GOYbkRxBTHbsemyAWgFdj6bkgWHCb2/yOEeMnUPQ51VlM3Mg7X0DGBP+ypH1bGue3mn7Xxmj7Pi+MChBex662KGh4spLhpizXmvsnhB7rhBCqlm93Kby8tXvzQuK2IycM4Lf73A+oE+39/A869Jpr4Akr9zlfau9J+r/McexbUCrizfzZfqJI29az3Ph7Kqbl3mt2m++WjyKi19jFlA6vHYkNc1+cyl8s+7jN9MI4aA28m4clKtGLPXUKuPUgmc1P46RRkzXQR9hyhzfJfmcImdzrm0BySGT7vDXarGNU2L5z+b8VMYMKMbDGF/XmUK+OhWgJBZQzUTbWYH+pF6u8DWdLyzjpNIxgr89cdscYHUmIK5x4glGUM9psBb2UeRcYDhfXOTTW0EIDDifk6+u5SEoaXdRDIthewDt2v+ksZuG+N1HWO7VrhbAV5hKAnnwiNFDCYCtgQK2crI1thT6Dxaz+uvXZpmMB0aLuHFV9cTNnzMnXcoea0iZpGcs27OMf587v+0zR/Sz7y/H/4vEP4fBFxZvpu76reki5xq/CG+NWsLgG0DmCxcVdTOVyqaqfZaBVeP9DeNm0Png4otNKZz+nOx5+ZyEcl4wNfEvTFn964HAnZrwhwusTdy0X1wutaSf0W5eywAVuEXYPZVWa4ebxwxoxvKprZaO8URlCKKwx/DN/s4vmQvYQB/8tjWOnKO1ToyG4Hqk4QP1WNkV5kZHgYPzrPFCM4WCoJhomHnBjDeiuPdb1/goK7WdS9tb1+YFv5/TDjnhb8esHP7pKD0vScPr6zYzS0zM5r6LzrX8/zpBtsYa04c11rzZ17cUudkvQxqcb5U28LT0caca0vNeVVRO1+ZlqmgfeR0poJWvu9VRe38rVRNW+sN8XfTN2EMWC0QHWvOwx+v1MrzHJePdZDXtcnja802u9ZvNqX772Y/zwOeJu7VXYS6twlE5l4b/Q2YAu6MWdk+HaKMBwJNbMzO9hl0oWs2NQhVjS78Uwpl8QCUZoS9qZnp94Ts51dYAWa2NZE+zlxgM2CTF4uK0/il3sEIeycwwzARFSEKKkJokqYdl+hQDLnbW84YgSe5Dol7R6G9p84PdVYR2j8vGVC2muB4AxGmLTpgcyWpNX+7NVGzdA9H2xps1cqaJ0Ht0j2EYkFlTEFlEYy4Mpda55944tNERgoJFo6wtOEtZs05YrMabM9ru9efKnw/ULiyYrctq6bGH+K79U9w28xneOjEVZbPfQxQsV5We/PzJ19V1M7fzsgS6NOsTJTUBpDCV0ub3Rk0i5szwv+PGNeabXyfrACuuQmMTAN2GSm//h16ZrN4wNeU7tIlY5O/IZ3aqbQmFE1LlOfPYahiBACnXl1N0bwjBGtO5jXXUGcV/e8ukVJIrU0mEQnS+84yhDAprese0/qmzeoEoPP9JcTCQfzBMDOXvc+MWR1jmicFNXU16fPhkSLadl0MQP3cD7Y1cM7/YvWghyvL2/lSrd3f/tyAJDSFXfP/f2e22NIpU0PKvWHumr0Fwy94djAlJEaPBahYL7v1MvQCkfPaq4raubv8cUdlb1CL873pj3PP9D/QZZTxz0NNPB1tpMbjvqHUeEKkea1UlostW0RCDs1fqcmPNfaQx5oQcLvuDOAGiXO72cwmrdH1Xpt9jWwqkOM9JhlV2/2+yqpeVfN2mXpDle2Du8YuZ/WYmszPP3pQ3xYXUNAIyRaBPF5k0UTL8S6Z4VPInbCkWgJRdhqzpwrnhyUwogEG9y4kYWj4k24jpRWAyel98x21A5k1ezi5dxHeyn7HemTNXz6f0rS9VX3MqX4lM14zGEoG3DWc43Md1y7dw5G3G7OCyFltOrFcQe+2nU9xXY9iTvcMpTONcz5P5Mrydu6avYUav1UNmvK3f7RM3UkqFz99UIvz5RnbxrSGn/U3OVgvw4aPR07nZhS8KtjOd8qclA4peIWJJqDOE+K7pZu4uqCNLkPBoKk4/8eGseb4TzpKepxdU4QBZT3u4/8IoJ+qING+gvjr5xFvX4F+qiKv68zT5eTkvjA8RI7U5zWXyoWUXmMk9/tnAjNmdTBnVRv+4Ahg5uyeEw2fnSDuWHDOa/5Kf3tNC1tjq6wTWX77XPz0YLlrEgHBVYXtfLVcYrIcaEqTmMlzbtEb0UPwtZIsYjO9MZNx5KJ1frXc6cJRISjifL24mYeiTbYOV2A1Vq/RQmwt/wkPRZoyna4U9815PltdyCv+Mbbxuc536ooALmWYHvU8cqltPv18bZC7ZRUNWvqinO1T0oMoHExr3rZ5VD0/ZE5+TWEFCHdVXh6vrEK3mQGu0yAMDaO/HI7PznwoMT/G4TnEjs1CzDqONu10WqPWT1VgdtZBzAf+uPX/KDCjfmJxb3Kp0ucoWQGaMHO6kMBKNw3HfY55ZO3dXoQvn3fX5LOtj9HGa8LEW9VHReIAPbuXKy0VAF8gwulY0HbtaMdnGue85q/yq+fyt7tp6jK69TKuKmzn76ZtotZrWRS13hDfKd/E1UE1v0xQxBBArSfEnSVbuTqQm4umRhubNlurhbgt0MwTsVV0GGWYpiX4NWH9q9NCfC+46YPT63Yc+JHWxAj27yYdwJ1C3BBt58XTD3Hg1D28HPs+nyh/AjFzD6LmACKfLJ8PKrpq3Xd03Yt5tB6jz6pI1U9VYB6dbWUKIZL/jw7hj40+CCvN1NGzOAVNJzj3qPt7ZwGnXOgtZAhNp2pJfrn/ZxPnvObfpZdR5yLou/QyEkF3f7vutzrrBExLe5Y1irDp46cjTXy9wj2w+tWyZraYjbY5r/G38b2iJ/BLZmKFJ8z3Sp9E91mMlzYNNLVGs4w6l45VpmlfU3rpwupl+0n/29wdu57bfM3MzNpAgiLOrQXNbBZOFtBrtTY2eLKYMrOeRV7ntbTxDSFl3Ygm9/RLhUadT6et7DGbPI2YiWQAN8nB84BXCuDKGv445nc7viHazg+GN6czhmYZIf5peDMAGwMuwf+8VH8JshUgVFq9NKM8pXAdbn9Gm7ovr8yEeA7t3dQwO+rQSwcwO+qyik5Skzl93pm3DcyEh/CO1eCLo83swDPd6bdHAOUDeOYczaSipuCP4Z11AqN8gHDUqfnno+2Pdfxo1oSaxsLEE4hSMv8QzAjRH1Vo/gor40zjnBf+jww0uTYSeWTQXVO8OtDG35fax6f+2DpTgdVYI/eW/MH1ejdt/dZgs03wp+AXOrcFmi3h74KHIk4XjmlarL+5Wj0HRZwNvuacrQ6zca3Wxj2ezL1mYjFlYlhFVY7xtPGPwj7++1gZSFPNqb/Z22jP1snhdp4M3BHe5k79EN7mLvz/mKCqOE4h7sPsL8+9Sfhi1vuabn0Xugc8ukU0l2qEEvdjHJkNkN4AsuGZ0Y9XqjuYiq812jOdyOF6zKgfrSBKcO5RCqqddQy5odrwTGo+9NokrPLM4JwX/ptFI/qIJYBrtBBdRhk/jTSxVTRCsv5DVoy+VuLU6IWw3CcPRZt4SjRCQK2Vd5llJLIUg1zumxoRQs92daayVGhklXGUz2i70qUIQuQW/PK8ygInyhyZPxtwyaIRcTZ4mtnocQrzb6iybmhmk7dR/Zc7Vj+/4tq8NPwx3lc1f53h/v2pztswVivAzQQkT4tAqEwC10ut85Xd0DUTZW6rR4cTs1B+sL44LN5jfwJhYu5Z6kx/NT0Yh+dgHJ5jXVdjpWLSVWttHr44orYTbdrp5ESja8j2NhtZ1kQW9JMVtipnIxpgeN8ConGvrdht9Hupf2SDUmBaZXHIOJs+/3Ne+EOykUg8h0CSoNKWNQG3BZp5asgShA9Fm/hewKWNYMxpUag2CoBORS/aFD6i7ZNr0PJGJ2X8xGziH3Gu0Y0DZ6xZNGc96+YMokMrY5aLoO8wp2MOl0ytz3+wFPorrfRSb9xqDl86idXAqb7CXbVJt44tImyZmaqNQRhQpeDxUVoKyfnj/mSgGdKhx7gf89hsDMhsAJMI/USdK7Np4vhMm/AfDfnwJP0x4JwX/gk54yoP7VKlLQPUihBPl/yEB40mNpmNGAZs0DI+75+YTWzxNVoMm9L8PxJN/JP5hMP1E8PDj7Um9GwXonTteIjFwvj4sWZVvZoGdjpjLYvOOHmvzrjaSjBcfiU5s268Y9feZeR1reL8RK5VreeHEGPpYAAAIABJREFUwSv4J8nnDzBi+rk//ucQq7WcANIGYNP11S9cD20XD5VCnxSQTfjhZJ01T5ImwvZYY3z2dHZQ0SAsGITBEjhVnaadYHo3dM9SODhMRPUJi9MoIW0OoVLMk9WKhWRP4rKpmBpmRy16cdYGpworjKLt28aogtQxP9GITxqvWG9qntpOODrbHgMROtR0Eo6430Pp259il2UunPPCP4WPa21s8EnBTL2JLYbTnfGg3sR/8/zBVdsWwu4L32I2stlljmykfOB/Z26lAqsDUD9B7hXXjOofz7UZpRBDY4gCygmnA6+patfNWiObaVQLxSRaWMRn2UW2eGoRi1zH56RNOMeQ8uvfOfQidfTRYU7n/sSn2WhcZg0YzIPaYTw4XelOJdFfmRb+k4rSAadVcSoHC2k2H1GoFLpzuJDyhYr2eqLwxS2Lw+38GKBNO20ZRB11GXdVXYcylvFBxaQIfyHE1cBDWO7oX5mmeV/W+wXAvwOrgVPAn5umeXgy7j0aEkUWp/s9WZzu93g3YQhLOMqC8UkaWZU4yl+yS5kHm/KFP5lNEZBDwG6ikU15COHseR5INHFvwi5kY3gYwm8J+1S2i9dlE8nrXpZGsj6xz6H4CuAz5uvsop5NPntgc6OvATOe4cKxd77K4cfMJ/NnjNeOfczoftbs9WwMNPDkqU+530D3JgnfqjPaoNChrBtRrNgUZNZNVVjArZI4dd4tK1KlsuZ72u368l44lZUOKgxERQ/Es8afrFYI/tRD5afmmt44xDzj+p7ckH6s6d0um5MJwUGMaB6RNPlehUOwMJPOaQKJsM8ac7rMas6TsqCqurMa9Zw9P7+MCQt/YVVrPAJ8FDgO7BRCbDRN811p2BeAftM0FwohPgP8N+DPJ3rvfOHG6Z6iBHDLZLnHex1v6PV802ymjpDrT/ZM+bbT3DQJiZvG685NMxGo3EtezHRHq+wNYJOvwX7uLJqwuWCMlMBgJRhe0CwKZk3R2jMnVNQOAKfrsPufvHC6FlMw/piAkkpiarn/bUhZGNlxBzfLI5fGXnXCQWVtJknNhNx4RhgW7fVUoGwARgphYBqZ70rAYAWERjLxj4ngdBl0ZrXp7JxpHU9hp7bxYDI0/4uA/aZpHgQQQvwW+AQgC/9PAN9LHv8n8LAQQpimOeVbYKLIpHZAHZxMFFlLMMIlmMMZAfF4UTFPBht4cfBBJc97onCKlp8lRJ+kgSfJTil0v7cxUgJDkqAr7s0t6JL36gi7BzUh2fwk3szGwnGmNSY1OEsI2ytjxyWEc8DBOjpcAgM1mT9GwwehWgzGIZRLepxCHlxep6DBQBWM8owqBdcs7bHoorO5/0t77bw/kwSlFh0ctP7JiLto+Ll4jwqGoKLTYj/VveCJI8qStM+hSm4wX+Mu3++oE6foGCrjfnP95LXPlJ9ruATH95Vqo+kfmvj83S7Wj6lZ58c7/xRhMoT/TOCY9Po4cLFqjGmaCSFECJgO5Ef5NwHohQYdQ4psDa0MvdCwAmtDdgFhDtWgF5j8t5L13DewxeHbvr9kPUZgikiZxrunnKqG4QrSv0bDB4M1GF7TohF2vZc19v6iK7hvcLMjnz2FOiNkzTNeuPHgh2oxJqIZjwYTNQXzOPz0omgQc6xJKBNg+xSFg1aNSfaGGRxkKpiAbSIxLz+cHUZxL4RqsBMHGJYCkhDWBlCVFIDST+mG0u38ILzJVkR33+AWtITGxoJJ2ACkexk5XGlaZOKEB7nm94x8sAgVJmM17skAYx+DEOIWIcQuIcSu3t7JawZxf/F6V0qA+4vXWy/61YG1jYUNfLv0Wo5rZRjAca2Mb5deO7lNvScDQ6V2wZ+CqUGoctTLNwYa+HbJdSQUWmyHNkFiuJBCCA9UTWze0TDZFMwye+dUjM+CKBpE1BxAq9uDVn1g0i2lyYRWOAhlXaDFAdP6v6xr1DXfEXHvn3xHpHkKFpn5Pm7QXuZl/60cLPhLXi64lRtiarLH8cyf1/mziMnQ/I8Ds6XXs4BswuzUmONCCC9QBjgSa03T/CXwS4ALL7xwcnwqhQk2Fi6DAoO7+lupSwzQ4S3l/op1bCxZBuTw4+o+KNTZWLicjdOz+/26RNzyWXEeGpXDGTZQagXTUgGkGd1On2tHJUIhuE3dB35F4Yp0s43+FeAxuS+0hUJTsnSEj/tL14NvFHUz17PlEMJmtkWh+hzH+vkK1K6IVDWqch7F+ZIeuwUDWGq4wDmhYZG+yVputJ07wtuoM0J0aGU8ELyCjf484jd5Pbv6rRti7dwRaaYuFZwvaEr3LpisewB4fIOIiixh75b+Ln1PdYp4U50ZQovm/nvJq0ZKHlNwEiNczQ3aK9zn+xWFwlrcLE7xg/AmtBj2VGjVPArovpPo0WqyrR+P7ySeEZH/ms8AJkP47wQWCSHmASeAzwB/mTVmI/BXwHbgU8C2M+Hvty2gZAUbS1a4v3mWmmrnhQErfU5IASSze6b1Q5TT8nIF28bwHBuLVgJw12ALdXqIDk8Z95esZ2PhynEsXoInTqasOOv8VKKsx8qVzzZyDW1cBVoqVk/ANdtH1nrdOIJ+MLwZTDE57g0Fboi129wqM80QP4gkg/jZG8BZgKp/cnarzcmAx299H3cZv0sL/hQKifMdfata+Oczv8+aX4/NsIL+IoHHfzJ9/oOECQv/pA//a8AzWKmevzFN8x0hxD3ALtM0NwK/Bv67EGI/lsb/mYneN1/4ixTCRdp69NknnM2thY42qwNP0LpetVWZ9vp6xRjF4vKY0zzlDCAJU4O+apghOaBVOcyYiKou8Cu0dpc1bPQvZ2O5ZOmYQrlY+7MpCpfAslZ6ZtoaiyAMmN4Dnnw1f1WeqHJBloXU75aCqMFAJaYiFdPu/856r2gwHS+4IdLOnSlNPljGD4NXsEkhyFUcQXeEmzPtIlW1QLZndB+jOn+nwq1yZ7TZ3v0sn3vncb+xrvVHNPF97OnMYaxKdM9oRbNyjVee6/QwSJ1w5/OpMMPcEGnL1N+M4zPxMgia9LtKAHEX4kS9iaf0s9ddb1Ly/E3TfAp4Kuvcd6XjCPBfJuNeU4FUcUamuXUc7SwUbRj95TaeE6q71GXy2eeruqBjljOHWRjQMRt63PKNpwDZLqrp3RkLRRiZjU3oiMquqSlWyoaDjTIJlbsvT9wQabdV/qbYPgW4avJKjqBxVHHng+vj7dwZa1bOP57q8anAZk8j6PBN084Q69aWU8Z1Rputev3HNLElyVbr6PNMk62gUlU8KQR8A4uZdzLhSpzo2QQmtv4aZxLnfIVvSWEkfSxr1Ea2FjmrG2Z12xRHmwau0DoN2xj3NajmkYcneqdZBFop6yPuh46Zap+1L463QAoiVZ9C9xqZqkNNtzaClOBL5Rt7DDtviuJ5leezYNOATpfbi2gSfuiZCdFCCFVkbUwaaCYk/f3mGLVFpXbpttZcLidFwxQFC7LtXncqNfltGeFvCsvPH2lWhhg6RVmmKdSYn939O7s+0ca98U3K7C2wBKAtDjnWe6uQ1/dkv+QpGnmKRtt4eW3Z81wrnML0++am9DX3ep7EL/T0e/9kPokWzwjaB7Um7vf9wbWurZYQ18fa2OBPkkGaZTwYa2JrQmEl5cHc8I3iZhvHFljFot/Qmnl2+E/Cf8oQ6Z5B+FA9RrQgTePqq8qfyOlMQEU6hcewBHmWS0rUOZtQe6b3YyYFu757OcSzWRU1y7KYAtIswMqVdsvoOS0X1UjnT1Y7KQKmAhXuVaqUTyyjLB+2zxui7fxgRC2ER/Dxw4LJp8S4I+F09WTf90eeP14qjg0ed2G6wdNMIbG04E/BL3T+1reVp6KWoH3KaORvzK1ME2HH3CEzyD8UZDaWOhHiHwo2IYCnEuMT1CrCyLE2bJpMnPPC39NXysjeBenOO0Y0wPCeRWgH40xbso/i2h4GOqsJ7Z+PHinAE4hSuuAgRbW9uS2FJFRjZE3WwF3zl8dHVaRTupeCRQeIHZ2NGfUj/DF89cfxzshsXm6WhZ7DXeT16Y7x2WtWxTIc1o38nGPlZEn40v7+fDR5OUfAVIyRs5cYKIX+Kus+QgfNSG6ocWtDKB6w32uoxEqL1X2WxVXWk/btW8Vi9iCvku1TK0uv6Y6wuxA2sQoFf1jQZFVJm9Ib6Wdxf8Z8NGuVS8cEOijjR8nGO0LRPMt2D0WTeNW989H2xzwma221ik58tYqKfIBywniimdf369dwd6GT9RZw3Vhu8zXzTJLVd6zP3lWobirlHVEseIpxzgv/vn0LXFquCYy4n1PvLiVyupThjrr0GD0S4PR7SwAorJnyGrTMihQ9TEVBDH9lH/7KvrxcTACJkzkacOfZVm9cUAadFZjKbKrB0iQDZlLbN72AATM63AvehkqhP6sIrb/WutTEXmmbLFC7v+jj3Gf8p5PcLpDRqFX+dhO4vGRD5sUkQ+XT7qCM9d5vAB+clMPxIFc/jVqFlp2NrfFGGIFbA1Kvj3ATPyjKv1FTvnh4sIm/L8u/qdSZwDkv/NUt18A0PAydcLIQmoaHoYPzqJuTKVyWtXdDob2rjm3avjSPbkicJgsOEXp/kd29o+kUzz9M0O/MOMplTYROzERVV1cw51iW5i+9q1qzQut0XFPXYfV5tVHdGlBxCvqnO90uNV0Ij+GY11RQF6i0KlPSTNPP01dlzyyCpAtKwYipYtAMVQLC9b2N4asR5ZFMtk8qb1/S5DtEGbNUaYzJMXbNenQNX6WJy8c/Fk18XyIzhEwGTbpVbg4rTr5HXlr6RKwD+V6q9WTN81OzibuLnFr7Pw81cVfxVipc3DmnzSDeiH2eZyONPDvYaLvXrYFmVy29Wy/DG0laqmN83uaRBjwxuH3GVso1a20Rw4snCr6Rs7MLn/PC3x8MEwsXqgco3DnxsHrTmAoU1vQSO11CuKMWkr1RAzVdBKvHbn2YUbX2nW1BTCY80/vRwUF1K8pDGEUj9kymmk7EVGYeqVxQqvO5Cv1U0L1sDDSwMdCQ/qO/IdrOi6EHqTNDdIgytnkX8an42w7r4If+qdX4NmuNkNXLQc6Gyca12LNjfiKaJj3jZTKxNd4Iw/YOff883MTWWCMMwT+U2PtnxEyN+wevyWvuRwab+I6Llv5waOLfWUAk0kHmCm+Yv6my6i2eHTrz9RbnvPBf2vAWu1+/CENVYSpM1w2gIBimvCCjPdi1es31fCJ5vu94LR3vLyUeDuALRqhespeKmZ3OeSQ9p+94LZEumRdFEO2qwZh2mpK6bsCuZSekNWRr6QMFUYyoc/PSCqIEfHGH9SH3NRUFMQJzjuKXOhvZLJQsJcWQ3wM81aeg+pTdIjAEnqo+qOqzWxqqeW0Ux7Kf3z0OYWuUkbIaFIV7pjeO0FzG5yxCE2rCMmk9VnBXSv00Q3wq/jb/6V1Fk77PRn292dsgZfhIz6LSKKXz1yXa3NMis8ZvodFKb1Rp9Mnja0Ub92j2zJl/ZBNCT2bHjFXDV2jy+Vgs+VgcqTHPRpNauzTeAzwba0SLw9fKmqn2hOjWy3g41MRzIw14bD9A9/s+H25Ai8FXpjVT7Q3RnSjjZ31NNA82pAWmMEafJ/vz+eosZ4vYoBbnK9Oa2dajKECdQpzzwr9uzlEA3n3zAhLxAuSfo+ZJUFN/mK6jc22bg+ZJMHfFO+O6X9/xWo62NWAm54uHg5xot77Y1AbghlN7FzpiE6bhoX///LTwd8NwZyUDBzLB6uL5hylZcNjVhVQ074jj+mjPdML75qfHmtECwvvnY5oCf9VYG1t/gDCjG7PbXlSWky5YlRGUYp7sd3mvxD6XiqOmSd9n+fdVQiJPXKe38R3DagiU+hWnUhwxrH7V48EGTZE5423mqVh+c37c28Zt/mZqhJUa+VCkadyZMePF1cE2vlrSTI0k8J8JN+Bwb+WBZ4cbeHbYfu1E7eUqn7ulqzo/1TjnhX+5L0z5wj0sX7iHQ4fm0/72akZGiigsHGblqjeon3uYw9WdvNN2PuGRIoKFwyxrfIvZcw7bNPy4TduXjmUt2hS8+/7itOBPwdS99O5ZxJx5h+yWgiScVbEJPRKg2BdL3teu+YdO1HD6vSW2YPXA+4sorutA8+hprVx441Qs3U9xrSWsZE2+//Bs1xTT2NFZ6U1Hl55Xz/LHm5LDPdI9g/jRWZgxKyvJO/s4vso+DOFuKWWcz2BI85rCbhEYfS7Fbyru9dSlFcmsj2TBmZniRCodsMUU0lZDaXK+FG+9J26lghYPZKyDkD3bJ5saQpX6WWuGLCGiylDKQ9u/PtHm8OGnkOpNIXemU2rQLpp/rSdH5kwix/XJ89f42vheVmrk94KbEMPwdFSxpjye2X4+88LNIriqsJ2/k1w1td4Q36mw8v6fG5RcKpLmn996ct83+/xHy9q5pa6FKl+InlgZv+xYz/P9KxEm9MTKqClwftY9sVK84SliCM6Bc174y5gz9xBz5h4CwJC4XmbPPczsuYet8xP0h0cV8YVoOGh73XtsJkffXU4sHMQfDOPxxdDjzmwfXzDiOJfCSYW1MHh8FjY9xZHtJL3lkmGU67wKsZ7pxA7OzVgQsQLih+YC4JmeqSvQT1ZIldQxPDNzV1IbfeXJRt+ZJt+cmGX98Y0WMygbyNQR5KP9lQxkgsHZf4tJSodcGrsq9XMyOGrcGhLJmEhzoU6zjJmKzJl8cFvA3XK4NdhsE/5Tia9WqF0qNuE/hbiyvJ27Zm0hkOSrqikIcVf9FgCa+1byyxPruWtO5n2AiO7lX4+tPyPry8Y5L/yneYfTx7otY0fSZhWafFwSmjru2qu8icQNjWDhMOGRYsc6AoUjlPnCJAwPHUdnc/Ct89Kupli4EKHpVi66lCmjeRLMWf4Oxb6oY80JU8uRyZSlnRseBvbPo3L2CetaSfP3BCLoEfvGZJ2P4vfqyftmJJ5sNYBl7QAMHZ3lakEkjs8iUG25j2K90+wcSrEC9CP1CGGiSRuEKUlYvSubQRPrdU8NWnLTkDV5OfMHm5dGtixktU2dyeQKWzzC/tYDgSZHQZcc3B1r1ox8PJpwFyY08xMeNJKB2jFo/g/FmmxFTWBlzjwUsTKDRtPScxUwyfLY/mzuGng+/n+3eaoV1ku1N4QnajrGO++Vh4avK65NHn+pZptNsAMEPHFuqd1Ga8cyWjuXocUNvjinlaqCAXqipfz64Edo7V2Gx7Uv59TinBf+ZxrLGt/i7Z1r0bNiCEsa3k6/3r+70RGANg0PXn8UjydCNFxIQTDM3BXvMG2Ws5I3hVEzmSSoNoqKhQc59e5SmwUhNJ2S+YdyzhfunsHwwTnpqmmVpSBnHsWOuruYEsdn4p+uqDrOl9tosjBY6nT95Mmhn6J0uCPcnM72ecDvQp08Dqjy9lMQIskXo1n+/y0u7UlVeEpvhCgWnYHks9+a5bO/xtdmy4n/5xEru6bLKKPORfh2GRnL4epAG18rtvzxXXoZj6T88ZOE7kQZtS6+8+745DODqlDld69WryrInN92cgUt3RnSxCtmvMN/XPyz9GZA2wJo/PSUrxX+LxD+07yZ1mkxM/O4svZu1+oli8BjjdlzcDHb37iUoeESiosGWXPeDhbO32+NkeMCmocVC94nqMV48601jIwUU1g4ROOq15k7zxKmCdNDZMRdYCdifq759P+2WShyXCA77jB/xW72vnlB1kZi4haa8gXDFCaLqmTNP1B/nAJPgp49i4lHAngDEWYs3k9RbSaYKWv7CU1juLOSoT0LbVXTKrVZK4jiSebyK1NQY348WkadM2Rt3B+DmMvG4osjNMstZHba4wGi3NpIbFbAYFZT7ZT/X+bwGSqxB311v0UHbZIpDLNVE0vzJ483+hvY5JWEmpF5T772+nibrS/zj7QmNnsalVrwj5PMl7LrxzRxcNMERZwNmj1QK895rdbGbQWWkA+ZlsVXJsJ0mVaB09Z4Y3rdQrr+Gn8b35WqYes8Ib5bZGUEPTzYxN+XuhQwhZrQ4iZXFbbzHen9upQ/XodnhhvUFoFN65bHyJ+RNegXXev51swtjjX8smM9npjhfq3S+lDEBeTzLlZAT7SUmoBzA+iNlOIJSw+QnGd9zbvcvuQZAsmssZrAAGy61RpzBjaAc174TxR7Di6m5ZUmEslUv6HhUl56dR1AegPIxvx5B5k7N6M561lc8oWFw4y4uIaChWOr866uPw7AoXdWEg0HKQiGKavu4uSxekf2Ut3SPcp5ymd2UT6zy5Y+mshy78gYODDftWrasfFoOsF5RzMjFFXMAJE3G/DOPmGjrQDwzOxwpdsWtZ2W4D/mjAeYkN4AAEdTbZHqiQAgUzr3K7qNhSrVbTDHgevjbdybkPj1CfF9w8r3VuXhpzT522m2UkYpU1IZqFxEH/fYA7NyIVSdCHF34SYYIbMBSPh6kYtfX4vzteJmrjv5DSuVsUTS7AeaeDrciMDka2UKf3xFM88MT472/1zIysz5ck0y2Bov4xcd63n+9MoJZ+nki18f/AjfXLI1LczB8un/+uDltnHra97lCwtfoiow4CSWi4eh+Z4/Cf/JQIlmBUzf2N/AM7uaOD1URnlxiCtXb2PVQiud0+a3l3zuuqmx441L0oI/hYTu4/W3LmL1ojbikjWhiilkz7nm/Fd5+dWPoEvzejxxzl/1GqXesG18XMscy9ZKasz8+QeoTwarrWcRdFb1cGB3A5GRQgqCI8xb8Q7TZ2fcR7YsI4XATwi7tp9ep6GhR9TBYCuGYLmCShYcprCmN205FM8/zOCehS4BaJEMEM9B0wxbAFhU9iGESeL4TFuQWFScJtG+wl1Yd9cgpvVn6gJ6axzjRJJYzizJoyGO7rPoH/LdAEap+Pz7+FbXlNBvGs1s8aizY9LMl0kl8jnvT1xdQZ1mmf3a5PgNQacAlxEUcW4NNPN0pNGhaauoDWo8IbSEybOxBp5NBlZT9/ZgIoxR/PFxU6nV5+Wfl8a3dK+gpXuFbbyGqRw/mibvXIPCUkiOaT2+FC2u89eLX6YyMEBvpITf7P0wrZ1LaKpu5+YlL1MZtJQNLdeOFDqe483Jwzkv/MES/H946XriySKe00PlPPnydQDpDUCFgeHSMZ3PBwvmHQBg15sXMzxSTFHhEKtW7WLevIPjnlNGbf0xauuP2QLWiWwhOQ6ETtRwcu9C5fueQJTay3YAzsAwQLD6JIYp0gyrDveU4SF2dDbBrOwf74x+vDP67YF2XeQfD1CNk4X9QK7vU6R5fvL1/6twfaKNCpzUAzD2jJ0H9SYbrTFYgdoHE+6VqKrArG2MQsh36e7EZN366D51pT8+ceb88WcKLV3LaelK+vRT7p3a99iw4jkC3jz7+JbNmqLV2XHOC/8ST5jndl2RFvwpxHU/za+v58NLXk9nrABZmrxGeXGI00PljnnLikKUeCIOrV6+NjOnrL1b589b+A4rFrwvjZezjLyKa52aP9itA1mr90uE6LbYgaa5nk+ozpsafcdr6X5nmaOGIQWh6UxftJ+CpMmrJy2Hoc4q+vcvSBehFc07TNWlu+hq+ZDrPGbUj9eTUat0eX/QpQ3FgzoeABhtjZmaABXhnDee2X9OVZOzjCfl/hmr8M+KEdwRz8HrT5lD2891/BRWVs8GbzO1qUBtrImnE/bYgWZYwVoDgTZKSlOXkeT4l6/XTR4JNfGdCqdf/2f9TWiJHGvVTX7eewXfrtnsuPYXXevRYmZeWUA2C0o3Rx8vj7GRYqliCioNX3FeMd5tzF8veil/we8LQtN3Rx83CTjnhT9An4vwBuhXnJfx0QubeUKyGgB8nhhNF7ZM2vo+6Og7XsuRt1Y5XSwAmK5BYrAEv5xJpEcCDOxZBJDMEHKnoMgXrvEAOe6Qqgko77N6CmRX6FZJldP50FFPsPMXqLV7E4uMbax4Sm9MtwLUFNmC1/jauLtwE95RaDzDho+Hh9zXkMrMkSkTftbflJfPPuUO+vKMbVT7QnTHy/hF93rLT58DV1bstgqm/MmCqRPrae6fYC9pCVdUvcMX5r+YdNGU8uv9l9sycSYLKVdPLpgm9IyUUP25H/8p22eyUCRiTC/u59TQNMd704r7KRRRW3aJLvlidVPj8sW7CIo4m3ZeRf9QORXFp7l6zfNcsLAdyMoOyhE7cD2vsg5EwvV8PnParAD5vORY9UrnE5K6JGcTpc73HJvFsbYGheC3sOLKVusaydUTEx5O73cJDBsehg/NpXzRQfreXeKkoJh/xKb5K6FraNnxAMChvZua5a+feRy6aywXkDfT0lKkTAsFF5ANuZrN55HDj6lO2ewnyGbh9LWnoTjWlP7yzPGtLsFasBToASNImRZOB2mfCTcicNeonx1q4HlJYAtDYqKSNW3bmqzzz/etpPnkStv5lBXiprE3TdvNXfVbMpkwBSHumrMZLWGwrXeFY7z1ueSh1RtSps3STKZNdXCA25c9jUgYtHYslcZLi1PEC2xj7NS7APSOlFBdpN4ATBM27V3Ov7x+OVt/eGYEP/xfIPxf2XcBkbif7EwUvzfGjRdtzWuONYveZvWi9vTrmKon7DmIw++sUJPiYVUg9x2vpWvPEovILhChasleCmt7c1BWFFBc24NuaAwemJuuFSiaf4Rg9cmcmUbZ8M7oT7eljO06331Q3Gdl/6RTQF3md+ECsmESOn8BPOBp4l7d2az8XvJjnBwPVH58ATT1fivz+szXGSlxy6wWW9YMQMCT4O8WbeSL9a386sg6tp0cPxnaFxa95Jzfm+Cvl7xkF/6TgEfb17Lhwhal60cIuHjWUf7l9Um97ag4p4X/E2+e4NEXPk0sIfuFTUoCw3zuQ//JZYutT9te4Stp8rJFII3xCXcNXL425uLnh7FbB/lYCrZjKV6w5+Ai3nprDcMjxRQWDtO4ahdz5x3CJyXAj2YRZNNSyNA8CSqqOjnRvjKoTmyFAAAgAElEQVS9QcQjQTp2r2CmeAdfMELc5XpvIIJP0ymb2UXZzC7rOn1sG6qdnDH5ueSoCVATxSf/L7f4d8xTVi2A0PQkH4/HzvOjjz9xUJiwxWNp1t/Unc3FrzPstMoP0pTm68nHInDL8AHURVh6WXrc1cE2vlYquXT6Mi4dkeX/d7uHTfPPx4efyO23VxVMCWHlw9+x8CnLCpDcNEIRC8DF/1/pko8PlotGxDJCet3M97l5xXYqCwfpHSnh0d1raT2+JH2vdbP3clPjdioLh+gdKeaxty+m9chi6+LkvV44uACR0LnpvNeoKhpy7RtcWTgE8SlsbuSCc1r4//CZPVmCH0BQ4I2mBf+5igOHFvDqjg+n00lHRorZ+dplAMyaezTXpTYECkeIjBQ53xAGC85/kyMuloGpe+nes5jqJXs50b7CFiQWms60RQfG8USjwzPrBPqhOWQ3kxG1ajZVG0oHrH9gF/ITEPhu2OxptFXgCt3i0/8+dlrlezzJ3H9DXa37cW8btwWSlblGGT+NNNny9K/xtxEUMUdBWNjw8ciA5d+/OtjGd8rtpGh/O8O692Tl4Y8VqoKpFAKeBF+Y/6JN+I8FveESql2C973hkvTxull72HD+trTGXl00yIbVVqzvhSOLWTd7L7etaZHeH+K2i14AyGwASbQeWUTrkUU89on/oLp4iGz0Drv8jU0xzmnh33HaPaXu1NA0ApJfXVewTsoZOLLW7Zd4OKbCOojZtHqpKllaj1ytHHfx7b/x1kW2OgIAXffS3raaRVJxmldap5tFsLzxTd7audZRNLZs9S5q64+xb9eFuCEeDlBdfxyvZnDivUxvg8rF+9La/kRg7zpmaVj+yj5ipsgQxyWbyXim92PImUKm+zx28nnFcR6w+ZvzjAXcjroh+VN6o6tW/3FvG98L2qtu7y7chBiCp2ONXF3QxneL7amgpgmnjSAPnL6GZ4ca0DD5Wqm6COu5gQalP19Tafu28WMdYx27FUxlozIwgBaTFmSzOKQXLpr/o+9cyobzm22umEjCy6PtaxFxa86bl/8fh6sm4E1w88rtvLB/Pjc1bHd9/6bGHbTun49bi7nHXl/NbZe+TEDqpmeYUFk0zGN/9ltoW/ungO9koK48yAmXDaA4MMSX/v37nByaxoziPv5i7UY+vHjXWVjh1GFwuMT1/PCws7I4F2bPOUzC0Ni7exWRkUIChSMsWNlObb3V4rIgGHZlMvUHrc99+qwOyuoywj6Wg2F0MuCZ0Y9nhlUnYEyyxj5Z+G58M5/hdTyY6Ah+y2plFlCu3H8Vm+bXC5t5OtzI14ud7wsBEdPPM+GG9J6WqwhLhY+WtvNfq7Zlqmk71/P86cmzErb1rkCYJl+Y/6J7JSwWbcJ40XpiKZimu0snuTNXFjo1dPl8ZZHifcV5gNZDC8A0uenC16kqGsYkU/BVXTL8J3qHycKdVy3hW/97B1HJ9ePV4oxEAwxGLOHYOzSdX7T+JT6hs27xTjs/v3w8AesghqThS+N9QvbhZ74Knyln+0jzSBq+T1LBZM0/ZRGUFg0wMOwsoikpGqTQk0mnVNUUaNJPY8H8AyyYb7lqoob9J7Oo4W3efX2NwzKYs+KdNMNhbJJ+ZrZECo97j2FTHiQr+7ISptDq3QRMvlBmUWZp+N9NbOaz7Erf1ovJZ9nFMH6KiTku7zTLLJ4dl5z3XGyaQlcHeqs91vupTKFcpGha3HRo7FeWt/OtugyPTo0/xLdmbUHo0Ny/Moc/XzpWjZG09JYTy2g5sczKzFn+jFNLf/9DiIRCw3fJwFk3a49N2D/Wtpabtnw+ea01XqCnx/eOFFPtIsh7h4shkaB3uIjq4mGX94sgkVDm/7fum0vrvrk89pn/bQl8GWeQ3mHiZZ8fYHzy/Jl8Y/2/U1VyEoFJVfFJgr4wuml3h0QTBfz79hsndK+X965mw/+4m8/9/EE2/I+7eWXfBROab6K4fPVLeLNSE72eOGsveGXccx47PJdtm2/gqd9/hm2bb+DEkTnU1R9j+eqdBAqHAZOC4DCLz3+DqiR99J9gx2d43eFFEgKCxAhn/S5zVeuCmm8/xabZpai+za7K/VlfE2Ej696Gj5/3XuF6/ZdrWhxuooAnzi0zp6b2paVrOT9552N0h0swTOgeKeHB9o/S0rEs7znWzdrDhgu2UV00iCYs//1ta1pYN3uv8prH3rqYSMKuuEQSXh57Y431/hsXEknYLdlI3MNju1bntaZKl40D+BO9w2Th6iU7uHqJRTlgAE0P/6vruJND0wgIw5ZObdfqJdbJLOvgxb1r+PULf5G2ME4NTePRFz6ND50PL96FZrtWs12bgkcaI1sZcs9Ru0UgadrStSmLYM2it/EKnZZd6wgNl1JaNMDlq19i+YL3bRp+VFJNDx2Yz8631jI0XExR0RAXnPcaC+YdIGL4OHxoHm/uvCRNVR0ZKWL3rovQMJk39xDz5h6y1QlkWwiTAVuvYvkz1WTNPzPekJ5TSKyhwtZ32CXzBzAlM2DMBoGC+dPqMetuImjAd43r2SCsat3OZLXuVj2Zd2/jm7H+/+lIE/cUPYlf2K3DhwebEAY8MtBkC+RCsir3VJKnP6kpPzewEmGY/Nfp9iKs50MrEZhZtQSmuh2hP4SIG/bsIFkzV1kBeWTptB5bQuuxJVnnDbuGr8rJNwxuXvGKu3++YTutB+dn/3Csex6YD4kEN63eRWXRML3DRew4OoubLniNOz/cQu9QEc/uWcjF9cepLB6md6iIx3aeT+uBuYCuzv9PWRZDhVSXuJA5/oneYXLgtxVwmVSVnKJ7cIZjXFXJKXyYyF0KZbNIFsJykFdD8B+vfsLmWgKIJQr43Y7ruWLJDjTpL/eFPWv47Y7rOTU0jenF/Xz64o1ctvh1m1CYrE1h9cI2Vi9sc5yX50xRKb97YCkvvbouTWI3PFzC9lcvxyd05s49RHvbaluPArACyHvaV6VdQtoY8vNzwcbhIx17PbrreV1qyC5/LoYkSGRhnldgV9HwRRUfzqvIC+u79bpsADqCLUajre+tlsjcw62AS5gkeZ3l+1luGk03eXbIokv+almmEfm/nLyC54aSQl2Shc+fbqD5VKYIS9MVBVwJk55YKTUFzkycnmgpmm7m5dIReh7uGtX5HEI+c95ehKX03xcNOV000rWt++fRun8eAOvmHeC2D7+SDtZWlwzzscX7eeiFtbQesMZY8+jSsXPOVOvTR19pZMMVO23B3zNJ73BOu33ccMslj1PgtVMIFHijfHHt42Oeq2XvRfz1v/2AXpfqYbCsCRkv7b2QX77wF5wcmo6J4OTQNH71wl/w8t78zMSpxMtvXObKXvram2sBdaB4xC0N9Awh3D2Dk9tXc/qliwm9dj7RnulnbS354resdoh+04TfG2P/DXy9sBm/ZtjO+TWDr5Y2p18/M9LAJ45vYO3hu/nE8Q08OzTxoOwvj60nkqUIRHQvvzqybsJzTxV6Fb/fsaRY3rTmDbugBgI+nZsufmtca2rdN4cHmy+ke6DQcmcNFML1P/1Tts9kwSdr6SZcu+Q1PMC/bL+RnsHpVJWc4suXPM5VS17DCveY0nhJi5S0Kx8mz++5mJ+2fM6h8cuoLO4jIPS0y+h/vXqDo+4glijg9zuu5yNStpFd8x/dIpADqh4hr1/S8E1ZOzYcxyqW0qHhEgJanOKiQYZcxhQVDhHUrEClNoGfk+xK85vuGr7s9hnsmW6jhzajBYT3zSdoHsRfZbWN1DS7BWHrH5xMAxUSpbM5VgfPWPs9m/CP2nVgwGfMTLbP7/XV3Ktfl6RVyAxXtl9Mfjy5aJbtKZnSsaTt22gPssZla/uZMSYtvSvQDJMv1tvbEbb0Lkdg2rR6lbZvp1wY/bzaCsiDZkHXeeyNZIqlN/OQaf+8buSgaMicV/noK4uHIeEsjzZNxTrl4O+eelr31KdfP/3jP9E7TCmuXvIaH1vy2oTm+NWrN+YU/AXeKH91id2ayLYEUnDjHTrTKCsaIKTIDgJYe/52WrdfYbMOPJ44552303W+Y0fm8l7beYRHiggUjrB45dvUzcm/uGw0DB6Y69oSMnKkPi38ZegnK+wkcHE/5tF6mHnc3vjlDOAfteu4N35d+rWKkG00qCp386FZniiaT61kW7fEsWNk2zNTh3X1e7mp8VX3qloFWg9ZVOQ3XZDx3z+2azWtBxfkfV+Vj7530L0z37pFR7j5kjYqS0boHSzk0VcaaN07J+/7TTXOeeGv4e6klcWGLu3E8ngpm9BmEegm9A6qXAxWXOGv1z5OU3KDSWndlcWn6BlyxhtmFPfZUjc1yRvnkThg5FRPm4YvrS2OnK4pafi2Y2ew+KMXNvPky9cTl4S71xPnI6tfpECL07DwXbxC5+U3Lku3s1x7/nZbI5nUsg8emm/rYxwZKeKd1y/CqxlUzc5kMsiFbSn66d5jMzny7nLi4SC+YJiqxfsoTxaF2WIBOXoGp4w92c2vn6hzbhbJxi9UJIX/BAq7ZCgbgKu0ehM+rrVZ1Mx+iZo5rm7sAjnaJ/Y3qQuqFKRwjnFZ2r7beZsmr0zjlMbkk5apsgKS91o3Zy+3rXnBWVVrGLQelHpNGHLxVzKAu38+rXvnZs7L/vlRgrMAj21fxW3rX7O5fiJxD4++0oCp2z/MdYuPsOGKXZn4QOkIG5p2WeuUNH3bvc4wznnhPxY8vecifr79RroHp1Ndcoovpd1BTuQKHP/2r77Ns3su5rP/9k/0Dk6nsvgUN1/yODdf8jgPtnzeZjEUeKN8/pKxxxvywc59q2xspB9f81w6AJyNVQvfIYEnZ3bQsgV7mJ/VcCZiOGmO33prjWtw+L2282zCPxu9x2Zy8K3zMjxB4UI62q0gZHlWVbAnEEV3IY4TBc5ceUBi/czCVDWCHwM+rrVxj0+q1BUhvldg9cd1a6mYQqrjlkyz/Eh/E8+MNJyzwbybVu1wz9o5b6dd+E8BWvfNtdaw9u2MNr+9kda99Y6xN1/a7hofuPmy3XbhfxZxzgt/j81Pbs/8SUETgq171nDfts8RSQrmrsEZ/MOzX+QnL/w5t3/kd1wtbQIeAV++5HHu2+YU5F+65HFa9l7MTyQh3zM0gwdbPs831/8731j/7/zm1Rttm8IVi1+zN3MxTV7Yu4b//uon01XIn137JB+S+IjktEo3DX/7vgv47Ut/RixJU9w/VMHvX/okHgzOW7jb9bPKJzsop1RJDht26U8MEB4pwiepnobkgDZMwbF3lzt5ggwPPXsXM2N2B17Jh1qx8ICtV4C1Np3CeUfSGUxyCmjORvBJNdyW9mmzGBXnbQu1v7wuYW/Q/mPRxBaz0XX8N7zulbq3BprZmmzErqJrfna4gWeT/Dupj1MjXwI2M8OZ7wvREyvll8fW09y3Mn190/TdWb79y9nWsyJ5P/dsFlnDV2r++fjz09r+Pm5atYPKoiGlQZbO2klBob0ja+iqMS6ZOanzLe/PpuX92fabu8QIKt1SOIHKkrDDSjhbOOeFf754+JUb04I/A8FAtJT7tllVgPIGkLIIfi4Fjm+55HE+tmQHn3rsPkc8IJoo4Fev3sh//NXfpN1BKjfpC3vX8Ejr/5Oeo3doOv/S+lkMRN40FH/Y8fG04E8hnvCzaedVSuE/WSgqGmLYhV6isFBR1JKEikE0HnZq+MXJxjH9++ejRwLpnsHeyj7HWADvrBMkDs9xNIKnJk/StzHguoRLg3YzSdKGU5PPVak7lbiyYjd3zd6SrsSuKRjgrnlbAGjpXUHT9N3cseCpDKd+YIBvLnkaIL0BTBbWzd7DzQ2vJqtvi3msbS2thxaybs4+brv4hVE7YZ0NYrQU1i0+ws0f2p20BoI8+vJKegeDVJc6qWV6B9UsuWca57zw13I4b5/as4Z/fuWTdA1Oy9ncLpIo4Ofb/4xrl1rBzZT4uG7pTq6RNoRUgXiPIh7QOzjdXuSTdEo377mI32y/kd4hyxqIJApcN4//9eoNNC3ekbw2854Hk5f2Xshvd1zPyWT9wKmhCtc19A+VE5B8xHIWkCo7yFb5lg0XS+CS81+hZfsVjgb1563amW7zCPbspQKEkkHUHwzj1Qy8klaY0Iw0JXRUshZCJ2oYPjgHI1qAKIgRmHMUf9Up/FWnrMYvx2ZhSo3gzVIpX32SqB7uSDQ7GrQHiXM7zTyV0v6ljzdkBqkQTkFhIniz/Ht0GWU8PNjE05GUFeDuw1dROstWgHx8S+22tOBPIeBJcMvsFlo7l/PF+lZXTv0vznuR1o7lam1f0mzzyd5ZP+t9bruw1e7HX9MKus5Nq3aOKvgjcQ+P7bwgZ7aP6/kcGr4rXDT8dUuOsuHKNyTffpgNH32DZ3bXc9XKo874wIvLz6qfX8Y5L/xVeGrPGu5p/n9ctH13dA/mn5GTKx6QjeY9FzlcRA4fQhKqbKFU/UBMqjBWzTGtuN/1/GRg78FFvPrmJQwNl1BQEMHjSRCLBSgsHOK8ZIP6qKn2sS9Y2c57r19oc/0IT4K6ZXvyuv9wZ6Uz/XP/fGueaafxVfbhq+wjIZXkJ+KTTzQ3HpI2N6SC+nWeEN8re5I7S7ZSpoXp1st4ONSUbq04Xqg486v8A1xR+Q7VLoVcoObCHy9uanxV6cfPRZIGoBuCh16+NJm1c+aF6s2X7Xb17a9d0MWDz5zHzR9+l8rSML0DQR59aXnSZfQn4X9G4FGocP/8yifzFvwA1SV97lZEVnUlwH9NxgMiWfGAL1/yOD65gtg0edQ1ZdR9zZXFfRmfufT7+d2O6137Frh1L/svF2/Bh24fNhpk7V5hBbxzYJktFTQaDeL1xLnysmdtGUG6VAVckJWHP3vOYTwY7GlfRTRcSEFwhNnL36Ny9glHFtD0RQfS1NB6UgsbODDPNf0zemQ2welSOmc+Gn6oFE5ajV3wxqGiB0ryE3qqVo2dlKW/N1lLL3PR+rPhFzp+jzWu1hviH6f9gVWDR/nRyWszz5IPlbJ0rKrUHYgHuGPRU8rPpjdSCoaZn7avPC/lz+eovlWRp6XnFGayAjdHrv5Ytf18WjRiaf1VJe7fXWVJmJb3ZtHyXjZVg6m2LM4wznnhr0KXUpNPfTGZX37AG+Vrl+afkXO1FA/oziok27rnYn4pxQm6c6SMymtwqxtIQWURgJVGemqogmnF/Xzq4i1cuuiNKWlD2fr65a4Vwq++eYk9HXQU1M05yvTZHenXEd3nmgXUvdtq4iH3BnDL/gF1WqgSp8uge2amb3HCDyfrrONAbk0U1K0af2K6k7R1mWXUKfz+KmgCPlWyi/ZwfTrgO1b869F13Dn/KZtrJ6J7QQglj35E9/LrfR8e1/1U6B0uVjY4eeyNCx3FWbYxQ0434boFh7jp4jepLB6hd6iQx15dlaZomCysW3KUDR97U71BDnxwfPsqTEj4CyGmAb8D5gKHgU+bpunwKwghdCDVBPeoaZo3TOS+Y4GcMy+TgdWU9NHpInhrS/q49dIn+ekrn6BrcBo1ydfXLNnFaGqyJv0Srl26Mx0jSNURPL3nIu6XMoQs15C7FlBaMEjQH6NncDqVJaf44trH+chiKe1UUuFmFPfRO+R8lhnFffzL5y2ekLiiN61HUQsAitTI7GmSl+SqED58eB6L5u8DIIBd208f26wAeyN5VRbQqb0LmT6rg0Qyu8cbiJCIOP/otIJoOgMI7BxJupTJk8766alxNqw3Neivglp34S8nBKlaNW41GjNPL41/KNJka8qSLzQBX5nWzHODyXaLqmbuupTV47eyev712Hq29axEmDgqdf9m2SbX+5km/KTtY7R2LkVgTEjblzXqx95Yw22XvpRF2exJFmHNB8Pkyxe/SmkgZhO2kbiHx3asytzPNFm38BC3feQ1iX9nhNvWvYZpmLTum5NTw1+35Cg3X7abypJwOnDbKmX2mNKab77sHYe7R17Xoy8uyxE7yBVEO3OYqOb/baDZNM37hBDfTr7+lsu4sGma503wXpOKDZc+yd3Nn7W5ZgLeKLde+iTXLtnJtUvslauT8XX9fLvKxePU8r9++e/46JIdtvvGFXQCn7/kcR7Oopoo8Eb5y7UbHWNf3rua3+24gVNDFUwv7ufPLn6KSxa9Mf6HSkJVIQyCF7evB0hvAGOFMgsoEuD0iRoCNScBmLboAL3vLHOkfxbNOzK2G6py/xP51wRs9jSy2dOI1DAOlb31VKIRwnBv8HG8ysYA7sjVcCWFKyt2c1e9PavnznlbEIZJ88mVNJ+0aim0uPVr+8L8F1xbKPZESmnpzJ9GOV+0Hk5V3+5Mu3oee/1CS/ADrQcX0Lp/HuvmH+SmNW/YGTT32ytmb1r7tnt+/SVtlvBXYN2So2z4qDNwi2m65uVXumTygLWfPPj0qg+Ub1+FiQr/TwDrksf/BrTiLvw/EJCtgBuWvoFA48FXrqczqeFvuPRJrluq0PDz/B7lDKLqkj6+dmmmUEzt4oHqkpOOlNHs+/psVb0ZfGzxDryYPJrMGJpR3MfnL3mcyxdJaaHCCgz/Kisw/G8vfBoPBh9a9HrWY8vFUgorgAzDqVuFcAoJ3cfON9eyfMH7GEL2+Ut5/rbm9HJTeY2C4AjRsFsqn6Bj9wpK+joY6a0kEQmg+eKg6ZgJH1pBlKL5RwhWnyQqBXmFi7afnM6CLw5xl2f25qmZy1Oqqn2zbrs10cg/8Qf36UxsHZ9kCODxOQ/y894reD6SYeWUM4JuqXPP6vlifSstXcsd1/zmwOXcvvRpuzso4eU3ey+z5+1PQNu3n9dpPTiP1oPz7OdlDVnXad03xxLgOfz5lcWq/PoRSxNX+PNVgdubL3sn47eXru0dCFJd5twAegaCtLw7CzCVGr55jvj8q03T7AQwTbNTCFGlGBcQQuwCEsB9pmk+McH7TgquX7qL65fuwpgUvd6ZQdQ1OJ3vN38OA7hmyWtUl/TR5bIB1JSc4g83/U36tT4OjeGKxa9xxeLXiMlurixL4X+6Esv5+f92XGcJ/wkgVSH8xAs34LZ5qtpK5oP5K3ez543VDtcPWM3iB47NTt/TiPutJvEr38M7Y5yZTdVdcGKW3fUjDJjW4xh6Q7SdOyLN1BkhOkUZD/iaXHP584HK99+pl/FyeBGfKt7l2ACEgFpfiG/XbEboJs+FnP5/ZVaPIptnW88KMEy+sPAlKgMD9EZK+M3eD9PSuQwxSX8rU4XewUKqS/Pn30mhUhW4VWj4j764jA1Xv+1M5Xxh8i2jqcKowl8I8TxQ4/LW343hPvWmaXYIIeYD24QQ7aZpHnC51y3ALQD19ZNTAq3K8zfkCl9F2aq8KaiyhmQ57ZZBFEkU8LNXbuTaJTv52qWP8/3mzzlcTV+59ImsFSiqS217grNeAMAvaRsxScv2m7qSQK5vqMJqCKIoZNVR51nLmvzqhW207PoIoeFyx7jSogECIm4bL/ve45LDWm5vmRAeZs85gkcY7H5tLa5WWdY50/AQ2j+PKongTQiV5o/jvJjWj2EI6JGyfaYls31ikvUYbecHI1Ixlxni3tgmhGa5fazFyAtzP043Zwk3cXeh3fcfNnw8MtjEswMNtEXq+WpFs8XamfUxBLU4X65u4fn+BtucoM7q6YmW2nP15eYpJ5ZafW7J5PALDGWVrtBN1s3ey02N2+2Ea4ckyoUsbX/dvAOZRilDRTy26wKrgUp6vCI/X5onO2Pn0Vca2NC0yymUX15hzafIsVdp8r0Dwcw10mfV8u4sMOHmj7yXSeVsXULLe3W4OYk/KNq+jFGFv2maV6reE0J0CyFqk1p/LeBUjaw5OpL/HxRCtALnAw7hb5rmL4FfAlx44YVn5dPa9P6FClfQ6FBlEKVqBK5JxhEefuVGupNuoa9c+jjXLHlNrnmZMqgCw9OL3atix4OPXriNJ1++jriecZt4PXEuu+DlCc1bV3+MfckU0HygyvyJ9kwncqgeM+ZH+GOIuk48010shLKQ9Q9sAl/GHRFnMVchcb5pNGeE/xiwNd6IGISvFzVTo4Xo0st4ZLCJp8ONaJg8M9LAMyMN7Kj/B9ctUNVh61+PrefOeVscWT2/Pnj5mNeowrrZe7ltTYsL4ZpJ65FFzvHzDnDbhzJZPNUlw9x22Stgkvb1jwcp1sybL23P8O+8vGJUPp1HX1rOhqvecinKUmvy6VRO02D9suPcvG4Pd93wlrQRnJmOXOPFRN0+G4G/Au5L/v9k9gAhRAUwYppmVAgxA/gQcP8E7zsqnnjzBD98Zg8dp39KbUk/t1+6keuXZlwbbhbBpvdX893mv0hr5p2D07m7+bMINK6XNgCVRaDKIKop6UvzCl23ZBfXLbHm0uW0UgXjqNSkSskyKvcdiCusAF0IbrrkcUcPAn8yMKwJ05btI2fc5KoL0LNU0DWL2vAIk6d3NhEaLqOsKMRHVr/EigXvAVAgVRfLFb4+Kf00oWWOZf///JXtLu4fe7A8BW8gYuug5tEMIt0zCO+bnykCixVgHp2NEKa1AShYPU0X6wCgzshRzJUalvz/Wtq43ZfJ/vmp0ZTp2iV9x8+EG3kmbJ3X4klLBHsTdVXD9Z54WdpvLzNrbutZgXDj3+9ahkDW/FX+/NGrdG9q3K4o1HotQ5ssMW3edMEuR/pmwKdz05o3MoFZF21/3aLDdmI1mSY5Ob51Tz2tsuA1TVIfspyxI8MS4iY3Xy5p8i8sSwrw5DoUPvz1y46z4eMZIrfqsjAbrmnHNKHl3ZnOC86RbJ/7gN8LIb4AHAX+C4AQ4kLgy6ZpfhFYBvxCCGFgxSnvM03z3QneNyeeePMEf/OHdsJxHRB0DE7jO81/AWDbAGRsen8133r2c+hZOfCRRAEPvnK9TfircOulT/IPLhlEX7/0AxHiYH0yVfSx7Tf+/+2de3hU1bn/P2smdxLDLYSEmyIJCILITS5eCFhRbvxCXVYAACAASURBVIK/01PbY1Wkp4+t5xyRR622Pud4erFWrVp7+nusR4HW/qq1rWhQBCUXQW6CIvdwEaFAEAJISEgml5n1+2Pvmdl79l4zO8lMiMn+Pg8Pe/asvfY7eybvetd7+b4hwrhvTyx2zBfkFGOG7GT45RWh13bMn61B34FHATi060oa6jNISa+ne58vqTo2EGmsCvb46Vlg2VhS/4WBzz+IgBf/8Xx76z8GKkU2/aWimMuAWezg54TdOf3QWDsBU9tGp3jx9DQeyX3HQuX8+8oi5TXBrJ5gRg8QV/991DaJduejNUZRYGrBYROlcogmGeLCkx8ibVO4aILWvdnN058FU/dZg8Upfu4p2mev/DsI2qT8pZRnAEvlipRyK/A9/XgD0PbecS3A06v36Yo/DF9zKs9umGur/FdUjOWxkm9bFH8QJyLcOaragbnDtuIBnjfUCCzSawTe3TfBpnbAQUMZmwpiyxumuID9LiB4/sbCzaFFACLy/00GtMLPH/F3YfTbm85j79s3nk82+fnDx7H8/wMGHeGCwa2U3rOayoqhNNWnk5Tmo3fhQbL7fUm9ITXTg1QXezWmOKt0jsAzadN5ot5czFVHMr8W5j+Jxdizdt6fUsLKxlExYwGRxx+cGwkBuDdHa7h+qimbF78sovTslYaev6pqX/vzgNLCd9JXN1qhVsjiN+wsqmq7kZtlVfRVtRnhe0dU4yrTOCfv1Nw6impcGaVKN4QYOfnRrHtVULjPJfWsevRdqqrTWFJW2OEWgk5Z4Vt5zv7LOFFjT3b27Ia5Uake8rKc+8RnD9tqiREUV4w37QhO1PTiv0v+BYlk5lD7TliJRtn+Cfxh43yq9B3Adye+xaTCtuf7Xwz07H+Cnv01ds66KLn4ntQGAg32sYDG7SMg90s8PZ139SpO1WyaB30l5Es92ycpgroZNaePis3TCT44P5IPzo8MuYbA3NSnvbHsswncP3FtRKFWEss+GWc/fsvV3H/dRouPfdmmq5T3UNMka+ctRVrrYvv6nSKada8KFgvdm5vb3ccDszQm3Y60AHRK5Z/fPZ3jNgtAXtZXeG0sVdWiAJrbZvHkFaYYQUszhV7YcKttFtBvN8wL+f+NMPnzFZ3I2rILKN033uT7r6rtxe/K7wDghsIt1ntFy/ZRmMzGDCFjXMA4vsmQgZNsyPl34v83MnwmCftjozIUAroNPmIifgtDaFz/xwYgBfoC4EyRFqeOpDh1JJ5GQ9+IBsPMEk4Ie66fL2W2tW+v0RNj2gVI2zFqC9/JGPNnVObwK3cB4ePyQ5dDQFoLtYK8O2D6PZYfuFQbf81netGWTsOw/9LQB4/M5FGncaYzteCwtUjrpm0gpTrw2oIKXJV1n3NJPb96ezQPzNxJWoqapz8tJcA9Rfsp29Ovw2T+dErl/9CMoQafv4a0pEYenPKO7fi8rK+otMnU8Qo/P5/+mjJO4BSqLCA1v1BisdSm0rihOZVXN80LK/+vKc4d78upfYU0+dLwpvnoMeRQiPs/PVerBK49dCmyIQWLr0d6kCfyoAXWvxM8J6fzMyJSOGUyv/HZc/18XVF+eIhWrWtsoRglrlD++WWUf36Z2V0TZdFVp3FeqS7Sum5PXLJuoqWCBq35e4q0eIDAnjAwJ9vXZjniiU6p/OddrX0ZWrZPHXlZX/HglHeYq1DiD055hx+vuR2foflJWlIjP5/+Z1vF39LagWhZQLHmVKINuwC7dE/QCOKCGTJeg/VjtNb9EX/MRl+90Z+fYsgQMub2Bxz4/FX+f2Pv4WRDA9ok/bjqaD8qd40IBX/9vnTO7BmmZTLlaAHdzLxTeHt/xbl110R+fP2GyRFludCaTl7G88Gir8WyhL5C79Hrmx5q0djSnr/O+PwVFr7x2KnP30nFrhOGzLbw6gdpFqTkBzds45J0bSFtaPKClFGLtIqGHjXn4wezeFpQgbukbKjFuvc1elhSWgAyQNnuPMp25wHw6n1l5Ha3Kvqq6rQOY/VDJ1X+oC0A867uR/OXsft6BheFZ9bP5kRNj9BiMWto2yz+IKLxCF0M5GSd4ZRNv4Heccz3vxj4x57hpqwf0Aq+zh64nJwcs3tNpDYi7QLAyS0jV3OKd+UoVjWEYwGexNymSyA1ORCyrLMzGll00zZq6pPJzrA+1Jr6ZBbdsj0iULsdgLI9+Y7vGWndRwviLikr5IFZu0hLCS8uvkYPr5QWOr5fe6DTKn+nKK4Ya1L6v775VcMOwZCl4iA3VxUXiOQRyss6y6LJK5jlgEfIOI9XZXW2cBfwrxOX84xNI/l7Jr1JStCyd7oRMRp2qLJ6wv58I510iuG8E/9/ksHa9wTCP93gbqVRQQDX7Esz5fx7hCTj0iNcOHC5pa2jyK/Ucvnb0MnLCBVPm9ral7Zjbuq205Lds+bcyCg7ApWfX+G/j3ytsvZVlrySw6flVbq24/U5F0yxb4ze0OTF1+S1uISC70eOX3DDXpPyd2KRG617FWRAUrorHylh4bT95GT7qKpO45XSQsp2O19s2gNdWvkXV4w1uXsqa3ry4zW3AyhdRK1FkEfIiMjl5J2KcaY00ch0UDvSuFtakS30DZ007uVN80OU0fdMXG5KAe0oOPTFYD77bDwX6jJJz7jAiFHbGKDoD5CaXm9bAZyUZt2Cp+Zq1A91XwwKVfuSp6j2vci4qdtOHskJ5/X3TanmR/2DvXY1MrfpPXbx/fxSUxFXaZW5z25R7h4WDvmQnLQaqnxZLN07hbLKrw8XDag5eLLSG3nqnTGWIq2H59hnsKkCuPFC2e78DqfsI9HplX+0bJxn1s82+fkBfM0pPLN+tkX522UJgXpHoNoFqGQrrhhjcg0F00EBZg3dwrv7xvNTw/tB0jgPIsQaCjjeBdw8bDM3D9tMk8lyN2SsGK41yu+PMGWNVcEmP7/p8xtiAcJve97O57/vUCGbNl8X6gVcX5fJti2T8IqAqeFLMPPnshG72LdtjKXgq3fhQVsmz7S+p5E9wlk4jY0J+HNQWPjOfPva/z/sWWIq6AKdy6dvGWVfjmB6z108POjdiEbr7yGkDJG0FfXdw+Lhq0NjctNrWDRqDQSgTOfwUWb1KCx2Jbum6riV1r7xvLIxus6mqTFqhrHghr3KQK3S2m9hBW5H8uO3BPYarYtAleIZLfUzUXhekQ76woZbgejpop0Vmz6dbGoCD+D3J7Fz+1jb8bkDjzHoqp2kpNcBkqS0enKv3GPq9vV1hIqzP8jl8/0BZbaN1hcOXht6vbBgnXVMUjMLhq+Ps7SJxdJ1I0LunCCicfAs/fAK+/HlQxMm49cFnd7yV8GDR5nimZflfOtv3BG0dBdgJJFT2Q5f1vTEK0TUdNG2xAL8CnPU9EmMpmmkoEa+IcPnN2cB2ef8x/L/q2ig6+q6meb3GOTLHXCM3AHHAKg1cPJHy/+3PzZkoDjw/6t8+I7GxPD/K7l8GjUuHxVlc07aeZASEQgom673Sa/hj994hZz0Gqrqsli6cyLlR4earXFVVk8L/fxt6ZkbrNIt29sfAgEFB48B+r3K9uSDDJhoGZaUDbUGatvT2u8k3D5fazw05V1+vOZb1EekeKrqAeKJFRXjTCRyKgTTQZ2ki3Y2ZHWrocamPWRycsfKl0407Lh8fP5kXtK5fFSUzVW+SwzHWeSm11jGSCA3Qzuf262GRePKAPjwi9hZchcLIQ4ecNQM3dhI/evqokkEurTyv3WYFgx6ev0sU4pna4O9LdkFPB+DUgK0dNBFejqo03RRp7uAVfsmmBrMf3/ScqYXbg4NSTbVCIQPLT5/w+c0+fMNnEGmPsGG643jm2SSZfx1Y9bx3kczkNL8M/X7Uzh+ZFAo8JtstOpNx1Y/v3ZMzDFtyfZxYuHPTNphS91sV+H7/vmRiCbJvX3L6JOs9eB96VgRJWdH4AlIXj4ylQcvtzZif+XgdVqmTwCWVFzHAyPfN9EvBKS1O1haUjMLRm7kw88HM3XQAe4e/bFesZvJsk/HU37wUoN8sS12VDUGLbD2o85pREs7ZzmwwOO2WHQQa9+ILq38QVsAgosAmGkZEgl1XEEvshIB5l2xKcQTFPw/Mhto1tAtLZZ41b4JPFl6Z2ghOVnTm6dK7yQgw5lAHQHDL6+g9ONp+BrMP9NAwMvuHVcrs346OmYm7eA/08IVv/lJ1TyWrbF8ftBgz4G45txI1pzT3vM2mL/xYA9eI2XzkgPXmVo0Bnvv3jN0nebiqc8ix2YnABpD59RBB0xcPbmZtdw/eZ3ecvHy1n50Fx0IXV75R8IJV48TxNoFqOINQZPTL728tXciY/K/CKWI2pHGgVDWBRhhjDu8uPE2y66joTmVlzfN5+Zh1t7BRuvQK83zqzKBko1+flOMwd7/n2zM8zcc+xREbPUGv78x/9/E8+Ox3wUkwtpXwW4XcH+qDcunp4l/yyoJdeICMGyMzFW6RpH1fPzSkyMoPx4Oenoa/SGu/mDmTvnxoXx4OOzO+cNNS8ntZl0AquoyuXv0x/b8/GM/CXfbitJLN3xaZb271v7FRpdQ/m9XjDG5dh6a8q7J2ncCFY2zE9gtBIsnF/NYDJ9/ZC8BlQymFpOK360xsHtSETw+VdMr7DYyaK2AKe0zAgZl65fGwLYhbdRUqObABWQ4Vvn9MzJqQ8rfOH+kkj9zLJ/KvUNp1OmeexUexNM7zN0jhKTxVC98RwZqfD8pjXj7VSKyzhvGGD+v4bilAVz9fxWbZ663Wp32qSwEsy/mQnVsGL9sxzXcP77cysS5bQIPTSm1lTEn80J4jpYGdjurwu/gSl6FTq/8364YYwrqaoVc3wJo8QIQTwQ5g57dMJcTNT2CNpplXGQvAdCCxc9tmGPqGeC01SSgbCQvgfnLfsm9k5ZzYwdx/0wZ8xFrNnyDZkPKZ5K3idFXxf68Z47lc2T7yFDef7MvnZM7NBeJJ7WBrMsP09jspf5guLsXjan4jwyEfsfw9LAheKu9BM7lgD+ZgKcZMqvwKNwnKqgatZ/0Z9uMThzK/6HRDdw9apPWd/dCJss+m0D5kQLuHr2ZXJvGKlW13dpVRheJQ6dX/k+vn2XK5gGob07h6fWzWq3847ULmDPsk9AiULTkvxVpp+ZsnsgsoWCrScCyAKjI4v5t8nIef/8ummUk973gZE1vflV6J0CoeMxEMR05pcFSMwZeTfQODlxAjQZXjzeCojnJ20SzrsDTUn1cO34teYOOhscY3D5GwrfKvUMtXD/BBTbQkMb5igLwBGy7e/FlHkQq/+pL4Gwec8UGHk55g3xxmkpfL57y38R7SfZ54zM9O1iUVEKeqObLFI3Q7Te+6TyetsLSiet356abnqcTAjdVQNW0I5CKXUBAUn64gPLDeo/dkCUvWfbJOFOPXdD59jePDo+LsNJtWywa+fRb2mDFCNfajzs6fZFXRyrkiobFk4tJS2owndOyfVaYzj2/YY5tsdfzejFYLKzcN56nyr9Fs1Sv+77mVF7cON+h5InD9oPDWbV+Br7GDDSlLWhudm6vqLh+gpABL1I1X5NNU5jTucwVG3gy+WX6e07jEdDfc4Ynm//O7OYdluGz2MFPk1fQz1ONR0C+p5rH07Xv82c1c6j0ZxOQcKI5m1+cncPqunZteBcV5V9czm/WX8vJ2m4EJJys6cZv1k3WKJhtEGyxmHtJHR4RbrE4tfBIO0vuwik6veUfj0KuaIjnLgDCbiBz03ndWkXauoFAK/by4DGZhcUV40ytI6+7dCfFeyfFTDEFzf8fljN8PhBppRkc4sZgsKkZvAP/v53Pv/STIpO7B6DZn8zmbZP4piHTxxg7MBZwpaTX02jD9eMIyU1WL1xzMg+nvEGGaDSdzhCNPOgv4Z0kc0N2ZfvG1BJmn3+AVXqjdm+DvYVvih0orXpsz5v860baBtUYMPvwA5LyzwdrwV2Tb988Jghli8UpOykP5uQ7gSmw7Vr7iUSnV/52hVzpSY08NOXdiyiVPYxuIBXyss5SaeOvj3QPvVMxztI68o2dN+A0paVP1hlnQicQ52rtfeCqyt9IDBy+h0OfjSZgcf0Y4G0C6TW7fjx+6HvCOjapiXxx2nYau1aNyvaNnta3b+yo6KNssZhYAjUXrUenV/52hVytyfZxgnhnBFnnFyyevMKSJWTvHrJyATlV/GlJDfxg0nLDp1HRQYCKEkLl/9+4/2r+unk2Z2p70DPzK+ZPeI+JBdvwGLOA9OPumdWcq+1ukS+rW01EXMDa2AU0rp+asz04efgyA0dD+LMIj5+MgsMA1H8xkEBDKiKlkaQBx/FnGoK4QfM65ySVZ3vRH+vCeIJsC33zCRTtGwPZamI307HC52+kaFZl9Zh2EMYxUXztDnYOdlk9UwuOILH/dVXVpIeuiZXVU3TFMXPTlfKhsStzXWu/1ej0yh+shVwdBZG9BJxUF4fdQ+beAJF00S1vEan9gfTNOssPJy/npgTQO6/bP44lH95Oo74LO1vbk1fXfhOA0UN2WcbPGFfCm+vm0OQ3cPR4m5gy5qOY9zp+ZBC7t42luTGyXaNeRKe3eJS9NOWclnuaOl/4Pn6fjc8/u5qnLtzEkw1/N7l+6kjm115rS8Znmc7PpbV94wv1nat944JJO6yJAGg6fem6EdY3bFB0xTFr05WZOwHi0obRhRVdQvlfDMTaBTjtJWC3C4h0D9m1j1S5h7DYaJLuabU8fMMbJmpoU2N2oy/fku0TPlQVgwUt+dc2zQ0p/iAam1N46+NbGFsQDpgGKRrGFWynSXoo2VpE9YVsLul2nuvHrmP45RXU+tMs82vHkmNHBrFr6wT8tu4egTetnoHXbwSg1tDNq/l0D5qP9kc2pkByEyLvhN7MPYziHkOgfiYP15aRH6imUmTzTNp0VvrDXbqCO4CVjMLbCItS9PaNgWxeqJ/Oe42jSFLk8KM8b1/khSKrR9mMPVoevYp+IQZdQ47C5QNBxR2Iee8FN+y1jxlM3Ufp7paTsLnWfmy4yv8ioLhiLA+t/hf8MoJqVtFLoDVYNHmFhTguLamBW6/YyNrDI0NB4H+f/BYz9YYwftVkccLpWvvdyJladebVVUP2cNWQPQBcCMQOVANU7BytUPwa/D5r1bDvZG+avrg07PtvSkEeHaCprQxzHn9x+kiK00fi8YUX+CSFa3ulfxQrQ4FdR+J/7VBVk0HuJdYFoKomeraVEarmKoluutKV4Sr/doBxF/BWxdX8eM3tFsUfRGQKamspo+eEuIA091B22gWklLyx8wb6Zp3liRlLmRXqAmY251fuG88LG+ZxUu8Ydu+kN7lZ3xVYiOMcVAIHM3wy02qp8VmDtb0yvyLZsPSoqn2NFr6KwM0jAtTXRc/wSUrzha4JJivVGgu9gpAe5Ik8uLxlRVxtoXRW0jgoYwGxK2jVVnzEcu+EfsHmN7h0w0gWTd9qaaHo1OWDDFB1Pl3ZdMUp2mrtF42oZOH0g+HWiyVDOnw3rrbAVf7tDLvuYUbEKwUVwq0j7QrDjF3CjFi5bzw/LbnD1DHsSb3o6+ahrY8DfLh/PHU2PD1Jnma+eU18KbTTMy5QX5dp+57wNtOz4HPTufqTvVuW799BMK3PbhYOXktO2nmqfJewdM9kyiqHJfy+UwuOsGDSDlMx1/MfjGHBtbvIyaqnqiadpetG6AVezlwoS8uHsmimuT+vr9HLkrL2abpSNKKSxXP2hJqu53b3sXiOtuPsrAuAq/zbGdGKy2L1EmjtLkBVGPbChlstyv+3G+bZjn1x423MGrbFkiFitB2NFYNG/78Hyaub5uG3VBRDWrKP6wu34DO855FGH76RC8js2w/C1ALSE2DkVZ/yyceTI1w/Em9yIwNH7iapTzgt1iMkFw4NQpkJZZfvb4cWWvvqXH3DsTGrJ8J6n5a7h8XDVhnaMp5n0VVrQOptGVX+dVMDlijZPorrpw45zKJpYSs/WMz1/PtXc9fLt2iXhnYNAbUcEb/fYFBX2XQlEX54w5wLpx8MKf4g0lICLJx+0FX+LuIDVdGZV/h54sbXY/r7IzOEwoVgakQrDHNyDtRkcE6h8vdfaIg/V8xAvQBsx/ax+OoySMuoI2/YPnr31/r+nms070ACDapYgkTkVyq7rF1MLBy8VtmWMdSTNwFYMHmnbWD2oVu036CJzqGFKNvb3xrcbSfkZNs3CFKd7wwuIlf5tzNURWe/cKj4IzOEHiv5DkDUBUCV+dM366yFEVTVMSw366y2q4iwgk1Gpal613yck3mWU7XWeXtlnsWLNI9XNGcxN3lvth+v7xQuvfQQ3Q29e6ubwr7jSEpnT2oDATvqaI8fb6+vaK637ljm1u/k4Zoy8qWW8fOsmM47Xi2w6yR7RwRgRsZO7uteQq63mpPN2bx4eholdVfaX2vcBQRQtmXMSa9BSInwS6YO2M/dozaaSduM9AzR8vwVfn5VZo/XI1l00zag5amZ7ZrDr5izqjqN3O5WRV9Vbf1dxNtFZFxIeO5KmP6fMOqfWzxPS9HpuX06Gm4d9ilP3PgX8rPOIpDkZ53liRv/4ijDxy5e4GtO4dkNc23Hr6gYx/QQYZz5j8TYJcyI/5j8ti3H0L9NXh5Tvmi4a9JyUiPmTUlq4PZrViiuiI49nw/jpb9+j2eWLea1N+/g4KHWtx3MuvywVtVrhPAj9F7AkZhbv5Mnz79Lf1mNB+gvq/l5YAWz/TuY7d/BB97n2OV9nA+8zzEzycr5A5ri/0nPFeQlabw/ecnV/Fff5awd+TP+NuwFbuy+M6rMxhaNpvP1WkB96oD93D++jNxutRrXTmYt909cy9TLDkadNxaqatTB9LRkPwuu292m+S8WXikZgq/RrA59jR5eKbH+rqK5iFqK4EKS292nuUqrj8KK/4Adb7R4rpbCtfwvAuyLzmJXB7eEpG5FxVhLqqdAIoH8UGHYp5Y7BWMARk6g+yYv55aI2IBV6kgOIMN5JDcWbsaDZMnG2zhd25PemWf59sRirivUexUYm78rMn98BNh+cAQrN82griFI9ga1F7JYt2kqQkj6DDwels1Be0eAjL5VAJz//DJkQwoitRH6nsDbyyb4LuDh2jIyMHP2ZNDEY4H3SKOZDL2oqx/VPJ62AuphZfMo0/p7X48SE6unJpf2f9+Uan7U/128jZKSM/pOIILn55UD17F4xGpz68bmJJbumgSBAHeP2mjfjGXM1nAnrkjLP2CNB0QydW461JcZI45YXD9B5GTVO/bztxZOrf2iEZUsnLbfkWsmeN6JK6elLqJosFtIaKqHkp8m3Pp3lX8UxKMJTDznaQlJ3bM2PYIlgvysMyyavILnN8zhR6vvsu0HMGvoFm4xZPZYKR1ah2mFH3Nt4VbK94/njxvn89s1d/PnTXP5zsRixg/5LOb12w+O4O2PZpsqfoNo9ifz8baJzB7491bJltG3ikD3sCul3q7CV0d+wJ6bpwf1lthwumji/rQSVtaOMp3P9Ubn90n3NPGvA8rCyj8CwRaNC4esDbVlXLprEuXHtOyYnIxa2+tyulk5+lUIMnUag7szRhxh9e5BzB71BV6P9XcRTM0sGnaUBdcbqBo+vIKyPe3nEy8aUcni2bta5Jop253vyG3TEhdRLCgXjGr7XWc84Sp/BeLVBKY186iqgx+c8o7J5w/hDKFgJlAwC0i1S6is6emsH4BDfW/289tzABkzf9buG8//lH2XBv3+p2t78fvy79AsBdcWfsJH+8fyl81zOVPbg16ZXzFr/PuML9gOwJpPptkq/iBqL2SZsoOSVbUAis5fqibvkRq90pNNf8UCYIdg5y7jhuOkP5u8pOhz9Ek5H87jt6nkLT9xBR8eKQifb2wm+MVV1WWS2826AFRd6Ba2xqP5/FEzdU4cfIKnV41j0Tc+tcntH07RsKMsujmCquGW7SADrebqaalvf+G0/QnL3nmlZIjJ5w9qF1EsqBYSshNPaeH6/BWI1gSmveZ5u2IM17/yXxQ8/zzXv/JfADxx4+sR8QL7QLGqXsArAm3qB9BW/GHj/JDiD6KhOZU3Ns/lo/1jefnDb3OmticgOFPbk9fW3caWA1cBapbPILJs+tEmAk9lFlGHeWdQRzIXsN8tVEtrodL//Wo69YHoNQSnGuz9+k6wbPs1+CJqF3zNSSzbOjbmtVOHfMGy774dlamzfN9Ann//ak6eT9f4/qvTeX71aMoqBrDgejVVg1MUDT/Oq/eVserH7/HqfWUUjah0fC3E1zUTibLd+Ty7Yjgnz6Vpn/1cGs+uGN6qRcUu1kByuhb0TTBcy1+BeDWBae089juG23nixtdZu/C/ldcFdwDaLuFbFnoHVYFZy4nggveLzQFkrPytikLx8MbmOTRGLAxNzSm8s2UGEwu3KVk+ATyeZiaPWW/q5GXy8zuy9p1Zl8UZWtOVH9WUkSerOSGy+TXTeUy+BxGxgNDcYNpNra4dCRJ+2KOEvknVSMw7JJ8/mZf/MTV0jVDw7gi/ZGq/ChaM2KC5f+qyWLpzIuWHCkDC3aM369k+3Vj26Tg920e/PpLPX0qmDvmC+2/4WOnThzBTZ9ne/uHMnpBMsuVUDRHWftHw4zwwK8JlM1sj/nOqYOPpmrGDUxeRk3kgHGvwdB/Qbtk+rvJXIF5NYKLNEy0WYLdjaAn3z9xhnxCQAUtzmGc3zHXULrKteH/fNby0cT6nanqRk3WG703U+gLnZJ7hVG1vy/hemWd1i9+Ks7rCnzGuhL+U34Zd1VVyUiPDBu+n2u+cDqAtKM4YybtcFXrtrRM80/ym7dhsYa/0Vl8YyeoLI0mql3zjkp3c26eU3ORqTjVm81JlEWWnh8eUY2q/ChZdXRIK7uZ2q2HRuDKEP0D5kQLKjxRAk3FBis7gZOfqMcIJbUNbqRruKVK4bKbtd6xw4+maMSIR+f3GheSDwF/bNFdL4Cp/BdraBCao2Ctr4eb3SAAADghJREFUeuhZNmGFlZ7USNFlu6PGAuKx81A1h3HSDyAy/98Jgn7+Vfsm8FTpnSH3zqma3vy67E4EcM+k5TxXdqfJ9ZOa1MB3Jhbz501zOW1TC9Az8xxeAlxTsE1X/lY0NKbjEQGlhe/k2PiRne4CjFDy90udv1+V8y9hTfVI1lSPJMlnqGI2dM1S8fkvGLHBPqvnqs2UH9YVnROeH4CAJCfT3tUjJZwy0TaosfTDK0z0zKAtGkvKhjry3bfaZWPYQbQke8cpnOT3f52Kv1zlr0BbmsBEumwkxjRLbR5VLOCn5fN5ev0spb5tK/ePtV1kuB9AvAroX1T49V/eNJ8/3fUoAEs2zaeqphe9M89y56TlTCzQCoReLP+OyfWTktTIvAnvhV73yDzHVzYsoO3l74+GXwuNv9+YBlovk/mNr3X8/dN67+Z7g8rpk6px97xy8HrKTpp3Aznp9p87xybY6wQqhs5TNenc9cpMR83WQ1QNkY1Z9jir3o3lsrGkcJYW2irYeLlmgohFAfF14wdylX8UtLYJjJ1i19Isz/LRwp8BsHjVHbbXfuXrxlc+e1Ky4M7Dg8dRpzAnXEBGtKUTmXY/zXQ+adtHQDv/L3/4JfdMXM7/u+tRmmTY1PZJL1MLP8aD5E+b5oWyfW7VO31p80tmj/+A19fNo6nZ3ODlujHr8BIw8/9EsH2Gj+0zf9SIPUZIeNczChGAxYES8qjmBNn8tm46q5pGae3nlaye1rz46T138eClK03cPYuHrwIkHx4pDA2vqssi12bhq7qQqVX4jtlCTjfd5791LOUHLrW/L1ol79KNo1g0bYs1i+cjLeU0VjcufRBle/Ip25PfqqyeV0oLTWmaoLtsSgvtUzhn79LumWAFG2tH8nXjB2qT8hdCfBN4HLgCmCCl3KoYdzPwG8ALvCylfLIt9+3ocOKyUcUC7FnEJF4R4Lbhmx0tRnYdwoLFWysqxprcPpU1vfjPkm8DWLqBtRa5WWf50nYBEJyq6c1zZRpL6PWF1sKx6wu3MEFX9mDl8B+np30Wf3wT1Reyye5WzZQx6xl+eUVcZG8r3vGM4r2GcE5/sn38Nya+37/Myt3jbWbhkHUm5b909yQWjSk1uX58zUlsPjqA+yevC8cCMi9w/5T1EAhoTdkVKD8wCMDM2vlRbFdPPBFy2dhY93/69/KLpmBj7UgSmWGUCLTV8t8F3Ab8XjVACOEFfgd8AzgGbBFCFEsp97Tx3hcV0YK1ToLFdjEFa5etIAR+6eXNPdcwLv8wtw77VGmlqzqEBWSAOcM+sS3+0lI95yqVv1P/f5BF9IeTl/NEyXdteghraGhOZcmm+RQZWkVGcgGF722w2HVrcULBNq4wKPtz/jDlgMeG5wfUOf9C4f932O7YFk7CBZE8P5HHfVIU3D1p500Wd/nRQpCSBVduIiejhqq6TJZ9dg13X7XJGgtI9nP3+G1m698I3Uov3zeQ8ooB4fN+P44DP3GCymVzMRVsrCBytMWhI8YC2pTnL6XcK6WMlbw7ATgopTwkpWwEXgfaJ6k8QQj69CtreiIRoWDt2xVjAE2xpyc1mq6JDBbbcfx0T41efemkPiAW/0+8Ulij4ZahH/PItD/SN+s0KqVRpXANudBwqlHB3WPD6VN+bCh3rbqLWa/dy91v30H5kQJlJW9OpvMK344IVapmvFI4oyFWfr+KH2jjvt4m/p5gLKCltQvxRnv4/PsBRw2vjwHXtMN9E4ZohVvGOEGsYHFkTCEyUGyHWEo6mnL3Co/jFNbW+P+NvQRmDdvCrGFbmLP0l7YuoD5ZZyyc/3bHpl7AJj7/8HGKkeFTme3Tspz/NkHp2zceGyt2ref/9x9TeWjwSjN3jz+JJfuvNfdHCVivBa2SN9dG0VfVZoTHRcu8Mfj2nfr5w4eJq95VxgPamMLpFNGCyKoMo44aC4ip/IUQa4C+Nm/9REpppYW0mcLmnO23LYT4PvB9gIED28/H2FI4sZ5bEyw2LhqVNT2we3Sxsn1iKXdV8dfiycUtktUpfjh5Ob8o+a4ltfN7E9vGEtrZUXLmSjxNARYOXhvK9lmy/1rKvhyOoDnm9cs+Gcf9Uz4iLckcuF22eXQixU44ynbngwx0OBdKEHaLwyO37bIde7FjAUI6SN2KOYkQ5cCDdgFfIcQk4HEp5Qz99aMAUspfRptz3LhxcuvW+AQg440pT5Zy/Jy1iKVf93TWPzItLvd4a9txHn1zJ/VN4T/e9GQvv7xtJPOuVqfMObnurW3HeXr1PirP1ZPfPZ2HZgyNOmc8Pkt73s+Fjh1vaOyQ1cc0rph2qhx1EYHnrtSomiORPQAesF8Y2gIhxCdSynExx7WD8k8C9gPTgePAFuA7UsqoxN8dWfm3VjG35j6tUZqusnXhogNhxxsaR3+TwWBMToc5LyRkMW4X5S+EmA/8FsgBzgGfSSlnCCHy0VI6Z+rjZgLPo6V6LpFS/iLW3B1Z+YOrYF24cNECtOMurF0t/0Sgoyt/Fy5cuOiIcKr8XUpnFy5cuOiCcJW/CxcuXHRBuMrfhQsXLrogXOXvwoULF10QrvJ34cKFiy4IV/m7cOHCRReEq/xduHDhogvCVf4uXLhw0QXRYYu8hBBVwJE4TNUbOB2HeeKNjihXR5QJOqZcrkzO0RHl6ogyQXzkGiSlzIk1qMMq/3hBCLHVSbVbe6MjytURZYKOKZcrk3N0RLk6okzQvnK5bh8XLly46IJwlb8LFy5cdEF0BeX/0sUWQIGOKFdHlAk6plyuTM7REeXqiDJBO8rV6X3+Lly4cOHCiq5g+btw4cKFiwh0CuUvhPimEGK3ECIghFBGyoUQNwsh9gkhDgohHjGcv0wIsVkIcUAI8RchhLqDesvk6imE+ECf9wMhhKX5rxCiSAjxmeGfTwgxT39vmRDiC8N7bW7A6kQmfZzfcN9iw/m4PyuHz2m0EGKj/j3vEEJ8y/BeXJ+T6ndieD9V/+wH9WdxqeG9R/Xz+4QQM9oiRwtlWiyE2KM/mxIhxCDDe7bfZTvJdbcQospw/+8Z3rtL/84PCCHuakeZnjPIs18Icc7wXkKelRBiiRDilBDCtm+j0PCCLvMOIcQYw3sJeU5IKb/2/4ArgKFAOTBOMcYLfA4MBlKA7cBw/b03gNv14xeBH8RJrqeAR/TjR4BfxRjfEzgLZOivlwH/FOdn5UgmoFZxPu7PyolMQCFQoB/nAyeA7vF+TtF+J4YxPwRe1I9vB/6iHw/Xx6cCl+nzeNtJpiLD7+YHQZmifZftJNfdwP8ofuuH9P976Mc92kOmiPH/jtZdMNHP6npgDLBL8f5M4D1AABOBzYl8TlLKzmH5Syn3Sin3xRg2ATgopTwkpWwEXgduFUIIYBrwN33cH4B5cRLtVn0+p/P+E/CelLIuTvePh0whJPBZxZRJSrlfSnlAP64ETqG1D403bH8nUeT9GzBdfza3Aq9LKRuklF8AB/X5Ei6TlLLM8LvZBPSPw33bLFcUzAA+kFKelVJ+BXwA3HwRZPo28Foc7hsVUsq1aIadCrcCf5QaNgHdhRB5JO45dQ7l7xD9gKOG18f0c72Ac1LK5ojz8UCulPIEgP5/nxjjb8f6Q/yFvg18TgiR2o4ypQkhtgohNgXdUCTuWbXoOQkhJqBZdZ8bTsfrOal+J7Zj9GdRjfZsnFybKJmMWIhmRQZh913GA07l+j/6d/M3IcSAFl6bKJnQXWOXAaWG04l6VrGgkjtRz4mkeEzSHhBCrAH62rz1Eynl206msDkno5xvs1xO59DnyQNGAqsNpx8FvkRTdC8BPwJ+2k4yDZRSVgohBgOlQoidwHmbcY6eVZyf06vAXVLKgH66Vc9JdQubc5GfMSG/pShwPK8Q4g5gHHCD4bTlu5RSfm53fQLkWgG8JqVsEELci7Zjmubw2kTJFMTtwN+klH7DuUQ9q1ho79/U10f5SylvbOMUx4ABhtf9gUo0Ho3uQogk3YoLnm+zXEKIk0KIPCnlCV1pnYoy1T8Dy6WUTYa5T+iHDUKIpcCD7SWT7lpBSnlICFEOXA38nVY+q3jIJIS4BHgXeEzfGgfnbtVzUkD1O7Ebc0wIkQRko23pnVybKJkQQtyItpjeIKVsCJ5XfJfxUGgx5ZJSnjG8/F/gV4Zrp0ZcW94eMhlwO3Cf8UQCn1UsqORO1HPqUm6fLUCB0LJVUtC++GKpRVXK0PztAHcBTnYSTlCsz+dkXovvUVeEQV/7PMA2UyDeMgkhegRdJ0KI3sAUYE8Cn5UTmVKA5Wh+0b9GvBfP52T7O4ki7z8BpfqzKQZuF1o20GVAAfBxG2RxLJMQ4mrg98BcKeUpw3nb7zIOMjmVK8/wci6wVz9eDdyky9cDuAnzrjdhMulyDUULoG40nEvks4qFYuBOPetnIlCtGzWJek6dJttnPtoK2QCcBFbr5/OBlYZxM4H9aCv5TwznB6P9kR4E/gqkxkmuXkAJcED/v6d+fhzwsmHcpcBxwBNxfSmwE02Z/QnIbA+ZgMn6fbfr/y9M5LNyKNMdQBPwmeHf6EQ8J7vfCZobaa5+nKZ/9oP6sxhsuPYn+nX7gFvi+BuPJdMa/bcffDbFsb7LdpLrl8Bu/f5lwDDDtffoz/AgsKC9ZNJfPw48GXFdwp4VmmF3Qv8NH0OLy9wL3Ku/L4Df6TLvxJC1mKjn5Fb4unDhwkUXRFdy+7hw4cKFCx2u8nfhwoWLLghX+btw4cJFF4Sr/F24cOGiC8JV/i5cuHDRBeEqfxcuXLjognCVvwsXLlx0QbjK34ULFy66IP4/BQomW8l2Qi0AAAAASUVORK5CYII=\n", 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" ] @@ -612,9 +925,9 @@ } ], "source": [ - "plt.pcolor(gridx, gridy, probs[:,1].reshape(npoints,npoints))\n", - "plt.scatter(sample0[:,0], sample0[:,1])\n", - "plt.scatter(sample1[:,0], sample1[:,1])" + "plt.pcolor(gridx1, gridx2, probs[:,1].reshape(npoints,npoints))\n", + "plt.scatter(srx0[:,0], srx0[:,1])\n", + "plt.scatter(srx1[:,0], srx1[:,1])" ] }, { @@ -623,8 +936,8 @@ "source": [ "This works in this simple case, but: \n", "\n", - "* the relation between the two variables can be very complicated, and difficult to infer\n", - "* this becomes a nightmare when working in more than two dimensions...\n", + "* the relation between the two variables can be very complicated, and difficult to infer.\n", + "* this becomes a nightmare in more than two dimensions...\n", "\n", "The solution is to make a more complex model, able to adapt to such non-linearities all by itself. " ] @@ -635,179 +948,49 @@ "source": [ "## Neural networks with hidden layers: a non-linear classifier \n", "\n", - "We're going to buid a simple neural network with a single hidden layers with 10 neurons (remember: always start simple). \n", + "We're now going to build a simple neural network to classify our samples. \n", + "\n", + "But first, we need to merge the examples in the two categories into a single sample for training: \n" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "srx = np.concatenate((srx0,srx1))\n", + "sry = np.concatenate((sry0,sry1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The neural network will be an MLPClassifier from scikit-learn, with a single hidden layer containing 50 neurons (remember: always start small). \n", "\n", - "For these neurons, we use a ReLU activation function, which almost always works well.\n", - "You can try and replace it with a logistic (sigmoid) activation later on if you want. " + "For these neurons, we use a ReLU activation function, which almost always works well for neurons in hidden layers.\n", + "You can try and replace it with a logistic (sigmoid) activation later on if you want. Learning is an iterative process, and the default number of iterations of 200 was not enough to let it converge. So I increased this number to 10000. " ] }, { "cell_type": "code", - "execution_count": 211, + "execution_count": 72, "metadata": {}, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Iteration 1, loss = 0.69955820\n", - "Iteration 2, loss = 0.63977156\n", - "Iteration 3, loss = 0.60536046\n", - "Iteration 4, loss = 0.56986051\n", - "Iteration 5, loss = 0.52573969\n", - "Iteration 6, loss = 0.48391111\n", - "Iteration 7, loss = 0.44638821\n", - "Iteration 8, loss = 0.40818126\n", - "Iteration 9, loss = 0.37046082\n", - "Iteration 10, loss = 0.33397852\n", - "Iteration 11, loss = 0.29763007\n", - "Iteration 12, loss = 0.26286892\n", - "Iteration 13, loss = 0.22853328\n", - "Iteration 14, loss = 0.19782385\n", - "Iteration 15, loss = 0.16955532\n", - "Iteration 16, loss = 0.14529448\n", - "Iteration 17, loss = 0.12440173\n", - "Iteration 18, loss = 0.10876436\n", - "Iteration 19, loss = 0.09780275\n", - "Iteration 20, loss = 0.08667825\n", - "Iteration 21, loss = 0.08024256\n", - "Iteration 22, loss = 0.07497204\n", - "Iteration 23, loss = 0.07028556\n", - "Iteration 24, loss = 0.06611100\n", - "Iteration 25, loss = 0.06340387\n", - "Iteration 26, loss = 0.05975164\n", - "Iteration 27, loss = 0.05632828\n", - "Iteration 28, loss = 0.05434881\n", - "Iteration 29, loss = 0.05225860\n", - "Iteration 30, loss = 0.05009863\n", - "Iteration 31, loss = 0.04736596\n", - "Iteration 32, loss = 0.04616879\n", - "Iteration 33, loss = 0.04462167\n", - "Iteration 34, loss = 0.04310667\n", - "Iteration 35, loss = 0.04287115\n", - "Iteration 36, loss = 0.04110059\n", - "Iteration 37, loss = 0.04051164\n", - "Iteration 38, loss = 0.03901095\n", - "Iteration 39, loss = 0.03885556\n", - "Iteration 40, loss = 0.03680747\n", - "Iteration 41, loss = 0.03634235\n", - "Iteration 42, loss = 0.03568480\n", - "Iteration 43, loss = 0.03439902\n", - "Iteration 44, loss = 0.03352214\n", - "Iteration 45, loss = 0.03297043\n", - "Iteration 46, loss = 0.03284510\n", - "Iteration 47, loss = 0.03169026\n", - "Iteration 48, loss = 0.03134423\n", - "Iteration 49, loss = 0.03120860\n", - "Iteration 50, loss = 0.03084569\n", - "Iteration 51, loss = 0.02952726\n", - "Iteration 52, loss = 0.02990835\n", - "Iteration 53, loss = 0.02856682\n", - "Iteration 54, loss = 0.02888320\n", - "Iteration 55, loss = 0.02806726\n", - "Iteration 56, loss = 0.02741508\n", - "Iteration 57, loss = 0.02682158\n", - "Iteration 58, loss = 0.02665464\n", - "Iteration 59, loss = 0.02703869\n", - "Iteration 60, loss = 0.02665717\n", - "Iteration 61, loss = 0.02522633\n", - "Iteration 62, loss = 0.02482024\n", - "Iteration 63, loss = 0.02479319\n", - "Iteration 64, loss = 0.02419861\n", - "Iteration 65, loss = 0.02434104\n", - "Iteration 66, loss = 0.02355208\n", - "Iteration 67, loss = 0.02335324\n", - "Iteration 68, loss = 0.02300042\n", - "Iteration 69, loss = 0.02306898\n", - "Iteration 70, loss = 0.02266823\n", - "Iteration 71, loss = 0.02262395\n", - "Iteration 72, loss = 0.02250124\n", - "Iteration 73, loss = 0.02180375\n", - "Iteration 74, loss = 0.02168452\n", - "Iteration 75, loss = 0.02135599\n", - "Iteration 76, loss = 0.02138484\n", - "Iteration 77, loss = 0.02090104\n", - "Iteration 78, loss = 0.02075262\n", - "Iteration 79, loss = 0.02086131\n", - "Iteration 80, loss = 0.02019474\n", - "Iteration 81, loss = 0.02049321\n", - "Iteration 82, loss = 0.02024461\n", - "Iteration 83, loss = 0.01999256\n", - "Iteration 84, loss = 0.02036052\n", - "Iteration 85, loss = 0.02031262\n", - "Iteration 86, loss = 0.01908929\n", - "Iteration 87, loss = 0.01919538\n", - "Iteration 88, loss = 0.01933829\n", - "Iteration 89, loss = 0.01918154\n", - "Iteration 90, loss = 0.01904013\n", - "Iteration 91, loss = 0.01894300\n", - "Iteration 92, loss = 0.01856925\n", - "Iteration 93, loss = 0.01902838\n", - "Iteration 94, loss = 0.01851341\n", - "Iteration 95, loss = 0.01773735\n", - "Iteration 96, loss = 0.01879717\n", - "Iteration 97, loss = 0.01810633\n", - "Iteration 98, loss = 0.01750319\n", - "Iteration 99, loss = 0.01720573\n", - "Iteration 100, loss = 0.01732679\n", - "Iteration 101, loss = 0.01700379\n", - "Iteration 102, loss = 0.01724611\n", - "Iteration 103, loss = 0.01758949\n", - "Iteration 104, loss = 0.01609985\n", - "Iteration 105, loss = 0.01718848\n", - "Iteration 106, loss = 0.01664022\n", - "Iteration 107, loss = 0.01619999\n", - "Iteration 108, loss = 0.01606060\n", - "Iteration 109, loss = 0.01581211\n", - "Iteration 110, loss = 0.01557306\n", - "Iteration 111, loss = 0.01657962\n", - "Iteration 112, loss = 0.01580022\n", - "Iteration 113, loss = 0.01629202\n", - "Iteration 114, loss = 0.01514204\n", - "Iteration 115, loss = 0.01596253\n", - "Iteration 116, loss = 0.01522800\n", - "Iteration 117, loss = 0.01673828\n", - "Iteration 118, loss = 0.01622391\n", - "Iteration 119, loss = 0.01546004\n", - "Iteration 120, loss = 0.01525453\n", - "Iteration 121, loss = 0.01544497\n", - "Iteration 122, loss = 0.01500503\n", - "Iteration 123, loss = 0.01655712\n", - "Iteration 124, loss = 0.01355555\n", - "Iteration 125, loss = 0.01575188\n", - "Iteration 126, loss = 0.01431428\n", - "Iteration 127, loss = 0.01429461\n", - "Iteration 128, loss = 0.01435635\n", - "Iteration 129, loss = 0.01403294\n", - "Iteration 130, loss = 0.01404748\n", - "Iteration 131, loss = 0.01334687\n", - "Iteration 132, loss = 0.01370567\n", - "Iteration 133, loss = 0.01327307\n", - "Iteration 134, loss = 0.01616728\n", - "Iteration 135, loss = 0.01322481\n", - "Iteration 136, loss = 0.01460457\n", - "Iteration 137, loss = 0.01317093\n", - "Iteration 138, loss = 0.01599130\n", - "Iteration 139, loss = 0.01384219\n", - "Iteration 140, loss = 0.01397748\n", - "Iteration 141, loss = 0.01364828\n", - "Iteration 142, loss = 0.01407112\n", - "Training loss did not improve more than tol=0.000100 for 10 consecutive epochs. Stopping.\n" - ] - }, { "data": { "text/plain": [ "MLPClassifier(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,\n", " beta_2=0.999, early_stopping=False, epsilon=1e-08,\n", - " hidden_layer_sizes=(10,), learning_rate='constant',\n", - " learning_rate_init=0.1, max_iter=200, momentum=0.9,\n", + " hidden_layer_sizes=50, learning_rate='constant',\n", + " learning_rate_init=0.001, max_iter=10000, momentum=0.9,\n", " n_iter_no_change=10, nesterovs_momentum=True, power_t=0.5,\n", - " random_state=1, shuffle=True, solver='adam', tol=0.0001,\n", - " validation_fraction=0.1, verbose=True, warm_start=False)" + " random_state=None, shuffle=True, solver='adam', tol=0.0001,\n", + " validation_fraction=0.1, verbose=False, warm_start=False)" ] }, - "execution_count": 211, + "execution_count": 72, "metadata": {}, "output_type": "execute_result" } @@ -815,11 +998,9 @@ "source": [ "from sklearn.neural_network import MLPClassifier\n", "\n", - "mlp = MLPClassifier(hidden_layer_sizes=(10,), activation='relu', alpha=1e-4,\n", - " solver='adam', tol=1e-4, random_state=1,\n", - " learning_rate_init=.1, verbose=True)\n", + "mlp = MLPClassifier(hidden_layer_sizes=(50), activation='relu', max_iter=10000)\n", "\n", - "mlp.fit(x,y)" + "mlp.fit(srx,sry)" ] }, { @@ -831,33 +1012,42 @@ }, { "cell_type": "code", - "execution_count": 213, + "execution_count": 73, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(500, 2)\n" + ] + } + ], "source": [ - "x1 = np.random.uniform(-1, 1, 400)\n", - "x2 = np.random.uniform(-1, 1, 400)\n", - "test = np.column_stack((x1, x2))\n", - "xt0 = test[x1*x2>0]\n", - "xt1 = test[x1*x2<0]\n", + "x1 = np.random.uniform(-1, 1, nexamples)\n", + "x2 = np.random.uniform(-1, 1, nexamples)\n", + "x = np.column_stack((x1, x2))\n", + "xt0 = x[x1*x2>0]\n", + "xt1 = x[x1*x2<0]\n", "yt0 = np.ones(len(xt0))\n", "yt1 = np.zeros(len(xt1))\n", "xt = np.c_[np.concatenate((xt0,xt1))]\n", - "yt = np.concatenate((yt0,yt1))" + "yt = np.concatenate((yt0,yt1))\n", + "print xt.shape" ] }, { "cell_type": "code", - "execution_count": 209, + "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.995" + "0.99" ] }, - "execution_count": 209, + "execution_count": 74, "metadata": {}, "output_type": "execute_result" } @@ -872,27 +1062,27 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The performance seems looks excellent! Let's plot the classification probability in 2D, together with the test sample:" + "The performance seems excellent! Let's plot the classification probability in 2D, together with the test sample:" ] }, { "cell_type": "code", - "execution_count": 210, + "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 210, + "execution_count": 75, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -904,10 +1094,20 @@ } ], "source": [ + "grid = np.c_[gridx1.ravel(), gridx2.ravel()]\n", "probs = mlp.predict_proba(grid)\n", - "plt.pcolor(gridx, gridy, probs[:,1].reshape(npoints,npoints))\n", + "plt.pcolor(gridx1, gridx2, probs[:,1].reshape(npoints,npoints))\n", "plt.scatter(xt0[:,0], xt0[:,1])\n", - "plt.scatter(xt1[:,0], xt1[:,1])" + "plt.scatter(xt1[:,0], xt1[:,1])\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This simple neural network does a great job at capturing the non-linearities of this dataset. \n", + "\n", + "Now [let's go back and wrap up!]()" ] }, {