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"display_name": "Python 3",
"language": "python",
"name": "python3"
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"file_extension": ".py",
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"name": "python",
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"name": "Principal-Component-Analysis.ipynb",
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"source": [
"\n",
"\n",
"\n",
"*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
"\n",
"*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
]
},
{
"cell_type": "markdown",
"metadata": {
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"source": [
"\n",
"< [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) | [Contents](Index.ipynb) | [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) >\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "WjHXmOiobDY2"
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"source": [
"# In Depth: Principal Component Analysis"
]
},
{
"cell_type": "markdown",
"metadata": {
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"id": "X97hc5UHbDY4"
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"Up until now, we have been looking in depth at supervised learning estimators: those estimators that predict labels based on labeled training data.\n",
"Here we begin looking at several unsupervised estimators, which can highlight interesting aspects of the data without reference to any known labels.\n",
"\n",
"In this section, we explore what is perhaps one of the most broadly used of unsupervised algorithms, principal component analysis (PCA).\n",
"PCA is fundamentally a dimensionality reduction algorithm, but it can also be useful as a tool for visualization, for noise filtering, for feature extraction and engineering, and much more.\n",
"After a brief conceptual discussion of the PCA algorithm, we will see a couple examples of these further applications.\n",
"\n",
"We begin with the standard imports:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "Y04aZfpAbDY5"
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"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns; sns.set()"
],
"execution_count": 1,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
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"id": "fGdMsFqgbDY8"
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"source": [
"## Introducing Principal Component Analysis\n",
"\n",
"Principal component analysis is a fast and flexible unsupervised method for dimensionality reduction in data, which we saw briefly in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb).\n",
"Its behavior is easiest to visualize by looking at a two-dimensional dataset.\n",
"Consider the following 200 points:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "ZyqJruDzbDY-",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 268
},
"outputId": "845b4625-8bc7-4338-e008-53d2ffda4a3e"
},
"source": [
"rng = np.random.RandomState(1)\n",
"X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
"plt.scatter(X[:, 0], X[:, 1])\n",
"plt.axis('equal');"
],
"execution_count": 2,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "8AMp0QM7bDZC"
},
"source": [
"By eye, it is clear that there is a nearly linear relationship between the x and y variables.\n",
"This is reminiscent of the linear regression data we explored in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), but the problem setting here is slightly different: rather than attempting to *predict* the y values from the x values, the unsupervised learning problem attempts to learn about the *relationship* between the x and y values.\n",
"\n",
"In principal component analysis, this relationship is quantified by finding a list of the *principal axes* in the data, and using those axes to describe the dataset.\n",
"Using Scikit-Learn's ``PCA`` estimator, we can compute this as follows:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "dRpow328bDZD",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "b30fb5b9-2278-4ddc-eb38-36ddd6211a3d"
},
"source": [
"from sklearn.decomposition import PCA\n",
"pca = PCA(n_components=2)\n",
"pca.fit(X)"
],
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
" svd_solver='auto', tol=0.0, whiten=False)"
]
},
"metadata": {
"tags": []
},
"execution_count": 3
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "wHFkNyLIbDZF"
},
"source": [
"The fit learns some quantities from the data, most importantly the \"components\" and \"explained variance\":"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "rtHLN2iBbDZG",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "e4335dd7-61f7-42d8-d432-e2564ca155f1"
},
"source": [
"print(pca.components_)"
],
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"text": [
"[[-0.94446029 -0.32862557]\n",
" [-0.32862557 0.94446029]]\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "mFJe8nUlbDZI",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "ea756cdc-4428-4cec-8c70-c3e7012b3d68"
},
"source": [
"print(pca.explained_variance_)"
],
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"text": [
"[0.7625315 0.0184779]\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "Ik0SkXjzbDZK"
},
"source": [
"To see what these numbers mean, let's visualize them as vectors over the input data, using the \"components\" to define the direction of the vector, and the \"explained variance\" to define the squared-length of the vector:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "87_F9hs5bDZL",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 268
},
"outputId": "dceec585-b769-45a7-dbc1-20d600d1864a"
},
"source": [
"def draw_vector(v0, v1, ax=None):\n",
" ax = ax or plt.gca()\n",
" arrowprops=dict(arrowstyle='->',\n",
" linewidth=2,\n",
" shrinkA=0, shrinkB=0)\n",
" ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
"\n",
"# plot data\n",
"plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
"for length, vector in zip(pca.explained_variance_, pca.components_):\n",
" v = vector * 3 * np.sqrt(length)\n",
" draw_vector(pca.mean_, pca.mean_ + v)\n",
"plt.axis('equal');"
],
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "DIyvUom3bDZL"
},
"source": [
"These vectors represent the *principal axes* of the data, and the length of the vector is an indication of how \"important\" that axis is in describing the distribution of the data—more precisely, it is a measure of the variance of the data when projected onto that axis.\n",
"The projection of each data point onto the principal axes are the \"principal components\" of the data.\n",
"\n",
"If we plot these principal components beside the original data, we see the plots shown here:"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "QBvo-rJ_bDZM"
},
"source": [
"\n",
"[figure source in Appendix](06.00-Figure-Code.ipynb#Principal-Components-Rotation)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "CGzRZrKKbDZN"
},
"source": [
"This transformation from data axes to principal axes is an *affine transformation*, which basically means it is composed of a translation, rotation, and uniform scaling.\n",
"\n",
"While this algorithm to find principal components may seem like just a mathematical curiosity, it turns out to have very far-reaching applications in the world of machine learning and data exploration."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "TX-aiP5DbDZN"
},
"source": [
"### PCA as dimensionality reduction\n",
"\n",
"Using PCA for dimensionality reduction involves zeroing out one or more of the smallest principal components, resulting in a lower-dimensional projection of the data that preserves the maximal data variance.\n",
"\n",
"Here is an example of using PCA as a dimensionality reduction transform:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "RSIZ5xGIbDZO",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "e6b7d335-850d-45da-d946-3cd79a3811ff"
},
"source": [
"pca = PCA(n_components=1)\n",
"pca.fit(X)\n",
"X_pca = pca.transform(X)\n",
"print(\"original shape: \", X.shape)\n",
"print(\"transformed shape:\", X_pca.shape)"
],
"execution_count": 7,
"outputs": [
{
"output_type": "stream",
"text": [
"original shape: (200, 2)\n",
"transformed shape: (200, 1)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "YYH_ishgbDZP"
},
"source": [
"The transformed data has been reduced to a single dimension.\n",
"To understand the effect of this dimensionality reduction, we can perform the inverse transform of this reduced data and plot it along with the original data:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "Jdr1I2CkbDZP",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 54
},
"outputId": "5880c0c9-29bd-4c97-85a5-481008d18541"
},
"source": [
"X_new = pca.inverse_transform(X_pca)\n",
"plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
"plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n",
"plt.axis('equal');"
],
"execution_count": 8,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "9vq1_l62bDZQ"
},
"source": [
"The light points are the original data, while the dark points are the projected version.\n",
"This makes clear what a PCA dimensionality reduction means: the information along the least important principal axis or axes is removed, leaving only the component(s) of the data with the highest variance.\n",
"The fraction of variance that is cut out (proportional to the spread of points about the line formed in this figure) is roughly a measure of how much \"information\" is discarded in this reduction of dimensionality.\n",
"\n",
"This reduced-dimension dataset is in some senses \"good enough\" to encode the most important relationships between the points: despite reducing the dimension of the data by 50%, the overall relationship between the data points are mostly preserved."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "NVasdzrvbDZQ"
},
"source": [
"### PCA for visualization: Hand-written digits\n",
"\n",
"The usefulness of the dimensionality reduction may not be entirely apparent in only two dimensions, but becomes much more clear when looking at high-dimensional data.\n",
"To see this, let's take a quick look at the application of PCA to the digits data we saw in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb).\n",
"\n",
"We start by loading the data:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "0szOgGLIbDZR",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "fef43ef8-f567-46bb-8b32-15a94c9697fd"
},
"source": [
"from sklearn.datasets import load_digits\n",
"digits = load_digits()\n",
"digits.data.shape"
],
"execution_count": 9,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(1797, 64)"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "5K6Ng2HdbDZS"
},
"source": [
"Recall that the data consists of 8Ă—8 pixel images, meaning that they are 64-dimensional.\n",
"To gain some intuition into the relationships between these points, we can use PCA to project them to a more manageable number of dimensions, say two:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "6FYycKmWbDZS",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "5f01539b-e3f9-4a25-fbfc-b06e47be3bce"
},
"source": [
"pca = PCA(2) # project from 64 to 2 dimensions\n",
"projected = pca.fit_transform(digits.data)\n",
"print(digits.data.shape)\n",
"print(projected.shape)"
],
"execution_count": 10,
"outputs": [
{
"output_type": "stream",
"text": [
"(1797, 64)\n",
"(1797, 2)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "ZaktSrtnbDZU"
},
"source": [
"We can now plot the first two principal components of each point to learn about the data:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "jZqzHR7jbDZU",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 54
},
"outputId": "451e94fb-cae6-4d5f-8ec2-9ae0f974e510"
},
"source": [
"plt.scatter(projected[:, 0], projected[:, 1],\n",
" c=digits.target, edgecolor='none', alpha=0.5)\n",
"plt.xlabel('component 1')\n",
"plt.ylabel('component 2')\n",
"plt.colorbar();"
],
"execution_count": 11,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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L4/P5SKczvLX3Xfbs2QuAIgQDA4OsrZQlHhkdIxQM0t3VSX19HT/92S+rr/vI0RN87rOPnU2qWphBFPMQOXs3IaRETAwiPYH/0CFKWSjlVt7/Hht+GIYxpev6nwA/0HV98eSvG4axPM64gifwHleMU6f6lvQ7PXXqJA8/9BBr1lzYxZDL5fjZz59nbGwCgO6uTu6481b27TtIfV28KvDpVIbZ2Xna2lrZsWMLBw4c5sjRY4yPT5BMpEimUgSDASzLJhgMkM12Eo/Xkk6lmBifJJlKIYRAOhLHcXBwKBRKqBGN2toa4vFaCoUi3/rrv0MIwdGjJzD6BiiXTYrFIqqi4A/4yefcxiO5fB7HcejoaGfv2/uZmpqiq6sDgDVrVlEqlRkcHGFVdyc7d2zlyT/4KpFImG9889tLXr/j2Ozd++5lZc16fPiQWhBpX0TEteDK+1bAMIx/Av7pco/3BN7jivH6G3uXhC3atsOeN99eUeBffvm1qrgDjIyOsfCc63qMx2vp7GxnfGIK6TiUymU++ciD1NfV0dhYTz6XJ+D3UygUURTFdb8gKRZLZLNZiqUSP/rJc1i2jWmaSCmRUuI4EiEE5bKJE3LYuqUXRRGk0xny+TyKojC/kEA6rivHtm1M08KyHTSfD9t2CAb89G7sYe3a1WiawujYOHV1caLRCH6/n1gsysTkFIlEFCEEP/v5L3nssUeqFS9TqTQzs3MIBLZzjgDUNyNDEcCsbpJCINvPLj57fIjwMlk9PirYtk0qtTxe/NyEofMZOD24bNvIyBiFQoFAMEBnZwdtba2USiUeffTjbNzYA4DP5+Omm7YxMztHMpWmXC6TzxdwHId4vBbHkQR8PoZHxmhsqKdcLpNKpigUSwQCfhoa6lEUgWNLBgeH2blzGxKor69jYnIaVVWRUmJbdvUCUSqV0DSNQMBPPN7I6tXd1fj5unicbDZHNBohl8tz6PBRfJqPVMp1F83OzbNR78E0LY4cOcbs7DyRaBhVcasJnjxp0Nurg6Li3HQPysRJ5PAwhKPItVs8//uHlctcZL2aeALvcUVQVZXW1pZlHZY6O9tXPCcUCiypQTM6Os74+CS1tTUkhkeJRMJs3tzL2rWriUTCPPO9ZzlxwmBwaBjHcaiL17qCbjtYcZvWlmY0TWXrlk3Yjo1pWSiKQktzM0JAeWaempoaGhvq0Xwqc3MJZmbmaGxo4InHH+WXz/+KgD9BIV8AQSX6xf0RSimxLAshIJ3O8OZb73D37jsJhYKsXbuaeF0thXyB8fFJhFCojddWX1c2k+WfvvN9YrEoI6PjbjniXI41q7vp7u5g79v7XIEHiNTgv/NBnA3XZ+9Tj/eAV2zM46PEgw/cww+f/RmFQgGAWCzCPffcteLxu3bt5LXX9gCuaO7bf4hwKIRt2wQCAWI1Mdas7qa3V+cHP/gJb+zZSyKRRCBwHAehCFRFIZFMIaVkfn6e2poaorEoM9OzFIpFJiemyOXy1fo1hUIRKSW5bB6BoK29hc9//gkikQjJ5C28/fY+yuUyAKqqUC6blQVagaqqaJpGLp9namqGI0eOc9ttu9i+bTOf+tQnSCSSvPTyq8zNzS95nWXTZHZ2jvb2VpqbGykWSgghaGpqxO/3k0p5Yv5RRJQyUFz5s32vi6zvB0/gPa4Yra0t/OGTX2VwcBihKNx26xYSicKKx996y02EQkFOHD/Fr156hWgkUnV7lMtlBG77vX37D3LkyHESC65/3nIsstkczc2N5PNFVFWlUChQLCo4TpL9+w+5Bb6kJJVKYzs2fr+fcDiE4ziMjU8SDPoBQTaT4//9xrf5X//dv2JsfIIdO7ai6xuYnZ3j5V+/Vg1xdBwHpOvjVxSBpmkMDJxh69ZNPProxwGoq4tz2627ePnlVxg4PejWvRGCYDBAbW0N+/YdZH4+gaIIamtqKJXcsgbd3R1X70PxuGZIX+jii6y+0FWfgyfwHlcUv9+Prm8AuKwyvlu3bKJnw3r6B86wkEgsaVO5sJCgqbmRQ4eOUqpY1eDWfJFSks3kKJZKbnw6Ak1VcWyHTDrjRtWYFgjw+fy0t7cSjUQYHhklnytQqvjjU6kMb731Ds8+200i6UbbhMMhxsYn8GkaRSHw+TRKpTKWbaMoCqqqEg6FiMWiHD12guHhUVav7gagu7uTjXoPwyNjBENBfJqG7ThMTk6Tz+cpl03y+TyZdJaWlmbq6uLcf9/dV/ZD8Lg+uA4WWZWr/gweHpdA01RisSjtba1LttfGa9m+bQtd3Z34NA1/pYaLqrhf27JpVurUUPW5S8CRDolEEkVVUBQV0zQZH59kanrGdddU3DumZTE3P0+xWGT/gcPU19cBbt35ZDKN3+8nHq8lEnGbeC+6aYKBAD6/j5raGLZlc+bMUHXOUkoUVeGO22/hlptvYuvWzdTEYpRLJWzbRlUUotEIjU0NrF7dze999UvEz/HX41zmj75YQBx9C+WVH6HsfQGmRy99jsdvF8nZrk4X/Lv6U/AseI9rjqqq7NyxDdM0qauvI51KEwgE+PLvfp5QKMjvfO4x3n57H5Zlk0gmsW2bsmnS0FBPsVjEsty+l1JK10eeK6GqWiV71cJxnIrFn8WybFRVdePipaRYKJLJ5tA0ja1bepmdnSOdThMOhchlc7S0NGOZFiOjY6iqiqIIFFUhHo/j03yomkq5XOaXz79EXV2cLVt6sSyLcDhEOBxifjGKSAja2lopl0qomkZ3Vwd+v49cLk9tbQ1i7DTizDFEscBCQwNvJQQ5NHp61tPd3bnsPVMOvYZIV8Yul1COvImz6z6ob152rMc1wnEufsG+3Iv5B8ATeI/rgt2776CmJsYpow9V1dixYytr16zijTf2cvJUH1u2bKS9vRUhBG2trYyOjZHL5UkkU/T3nyaTzlA2TYLBAD6fiiJUcvl8VdBVRSUciRAMBimVzUo2rKRsmqRSKQ4ePExnZwdPPP4IiUSKcDhMf/9ppqamOX7CQEpJvLaGfKFAsVgimUwRjYRpamjg2PGT1ddx9OgJuru7GBoaBiBeW4NQFDRVJZFIEotGCfj9NDY2EAwGifg1mBpGOeGWEslksvQdOEjZlBwKdXLo8FHuu3c3u3btOPtmpebPinsFISVi/DTSE/jrB68nq4eHixCCHTu2smPH1uq2l19+lYOHjlQfh0JB7r3nLm6+eSdvvvk2b771Di0tTbQ0N7F//yFC4RD5fB5NVZmcmiYYCGCaJoqiUFsTo6OjnYnJKQLBIJqmMD09i2maIN2QyNdeewMBfOlLn6W3V2dwcNi9Wyi7YwhFIRDwUyqV0VSFP/6jr7P37XdJpdJEo1G3Zn1fP3rPBjRN4/iJUxTyBRYWEmRzOTKZLLOzc+j6BuprojzWFcX/xs8Q06MIx0Y2dTA2Po7jOAQdi1qnyFje5ufPvcCmTTqhUGVRbiXLb9GnK+VlVDXzuNqIYhry6ZX3e1E0Hjcqtm1z9NjJZdsPHznGzTfv5I47bkUoCseOnWR4ZIyennW0trawb//BquHk87lf73K5TDKVJp8vEAqHiNfWYlkmlmUTCgbx+X2Ypsn8QoIf/uin/Oy555mbnSccCZHL5THLZRCicvHQUDWVYqnEa6+9wfETBuC6U23LQtM0RoZHmV9I0NbaSqFQJJvJUhOL0dLSTLFQpFwq8ZneDtb6rLNWXC4DYpJCwc12LVs27x45xcDUHKVSmYnJKf74j36fnTu2QW0DMhxB5JfWOZENrSiH98DMGGg+ZHcPcu1mT+yvEdIXRvovFkVz8UYzVwJP4D2uS9yyAsu74ZimxeTkNIePHKNULHHXx24jHq9leHgEgPq6OuYXEqiqgqopxGJRcrm8m6hk23R2driWvVUmnckiHUm5bDI5OYWqamia5vrogcnJaQKBABKJWXbLBziOiSYdNM3HwcNHyWRyOBUr35EO8XicVCqFdNwon1K5jCIE2VyOmpoYgUpBNWV2DNori8o1dZBNInJptECQvqExTk0nGBxLkinZqJrGzMwcTz/93/m//+uf09BQj7PzHpQT7yASc0h/ALlmE8rUKGJ+qvJGlRGnj+H4/Mjunqv+eXlcAC/R6Sy6rjfg9htcB5SBfuCPDMOY1XX9duCvgBAwBHzZMIyZazXXGxXbtnljz16OHz+FELB1y2buvPNWFOX9B2ONjo0zNTlNQ0M9a9asQlSsTU3TWL9uLX39A0uOb2io47vP/MCNSwf6B07T1Hg2lX/NmlVMT89gmRbZbBafz41/VxWVWE0UVRGApFgooaoqC6kEQghs20ZgEgj4q81DbNvGtiwURQUsFMXtcxyNRrEsk5npOWKxKOl8nmw2V+08lcvlsSrWfCDgp1Qso6oqjiNxHItiscjw2CTCLNPR0YYvGEE2dzHQP8DzZxIkZ6Y4ML6AXSqzLhamUNuAAPL5AnvefJvHH3sEIjU4tzwItgWKCqUiinFw2fsrJoc8gb9WeD74JUjgLwzDeAVA1/W/BP5c1/U/BP4R+JphGG/ouv5/AH8OfP2azfQG5dXX3uTAgUPVx3vffhcpJbt33/G+xnvhxV+zf/9BBgdHSCSStLQ28+QffMV1QwAPPXQfUkoGTp9BUVQ2bdJJJpNVcS+VyszMzDI8PMqtt+5ibm6B6ekxamtr2LlzO2++9TYLCwmKxRKtLc3U1tSQyebckgNQrTmzGP4YCgUJBt0Kf47tuOGYQuDzqfj9UTfMUVWpramhUCygaiq1tTVEI2Ey87MkM26cu1KJ0FmMphGKwOfz0RN0aDFT1HfUUnYkE5VqmNt710NilhcH56BQwBeJYIk0WbNIg23TI3LM25D1hZb3oFUrP2HhFiZb3sjZc89cMzyBP0ulpvEr52zaC/wJsAsoGobxRmX7N3GteE/gf8scPXp8+bZjJ96XwE9OTnP06HFOnuonl3V9yZMTU3zve88SjUbZsH4toVCQJ574pJvVKlyR/Nu/cyul5vIF3t67j2w2i6IoRGMRHn7wPkLBINmc272sd2MPY+MTTE/PEo1GKJZKpNMZamIx6htqsadmicViSMehp2c9UkqSyRSOY7uRNtJxx45EqG+oZ3bWPb4mFiWZShEJhxGFDO2yhK/WR1qoJBzB6Yxr/WuqhmVZ3HLLTXxiy2oaJ/uxrAg1sRiKY1JUfGSLFrmxYcxghKzwMZOY4vRCFk1RsCyL0USW7rBKbVhhR0uMjT3rLvyGBkLQ2A6z40s2y4617/mz8bhCyEsUG7uRBP5cdF1XcMX9p0A3MLy4zzCMOV3XFV3X6y9W6P58GhqiH3heTU2xDzzG1eC3Na9w2I9pKsu2Xez5m5piSCl5a+8+9u8/gmmabNnSSywaQUqLcqmIz6dWjzfNMiPDg9x5x/YLjrdtm86ePW/z/At7mJiYQlEUIuEwg4ND7Nu/n54NaxmfcP3lGzeuIxj0Ew4HsSwLmZcEAj6CQR+RcJjNm3WMUwOEwkHuvfd28vkiQ0MjxGpiDA+5iUOrVnWyfv1qBgdHqau7nWKxVBl7PT/4/k+pmZ9HSgcRCLCmq43bRJnv98+TDsardwn/5l9/nVtK0xzdVyKXTKBU3FCKEJyMtGM3+WluaiR6fJT96SJICGHREfWDdJCOw+dW19C7cyMb1jairvB+y/sexDq2D2diBHw+1HW9aOs2Xd6He5lcr78BuP7mJvJJyC2vsFrdz/I1pivNdSnwwH8DssB/Bz5zJQacn8/ifIDynE1NMWZnr7+iUL/Nea3qXs2R86z43t7eFZ9/cW779h3klVffqG6fnt5DR3sb+XwZ01z6JVc1H+lMYcUxN2/ayrf/9p+ZmJimXDaxbZtSqYw94GDbsHv3bgZOj1ZdGS0tLdy0cwfjE5MAGMYA8/MLpNMZ6usb2NCznnKpzPx8mrHxCerq4kxNzhAIBGlpaaK+voFEIsvjj3+qsvDrsFHfwPPPv0RbJITMBdyIHUXQUxOAgsmD61p5ZcFGUQTxeC0vPP8qr06dIZ/JkEkmuX11C601YSSCgs8iGIhjlmx2re7khXeOowDSsgj7VLY01lIfi3D3xjUoGiQmZ5H+hpU/pM6t7t8iV/C7cb3+BuDKzU1RxBUxBgGcQAxpr6w5IvDeLtCTSLAAACAASURBVEi6rq8GfnzOpjhQYxhG/UrnXHcCr+v6fwE2AI8ZhuHouj4CrDpnfyPgvBfr3ePKcHdbK9bbBzg5No6I17LtwXvYfdel3TOHjxxbtm1qepYd27cyMHCmWjI4VhOlsaGezZt7VxwrkUjS0tJIfX0d09Mz+DQfCCgWS0xPTdPR3sZnPv0pDh46SqlUomfDOhBUBX7Nmm5KpRKlUpFcPs+tt9zExo09/PRnv6S5qZFjx08yNjqBoiokEkna2zOsXbuaocFhvvCFs7bGxOQUGzaspadJZS6VhlIBK5/FNE3m0gVC4Qbq6+PU1tRg9A2wuTVOoFymFAqz58wUT2xbTS5cx12PPIq/MAELM9zW080DOzfSPzYJhRwtPkFAU+muCaEUMlDKg30Jqy+bQjEOwMIMRGI467ZCy/voGOU4YJXBF/DCLN8vVziT1TCMIdzG2wDouv5fuYSGX1cCr+v6f8b1uT9qGEapsnk/ENJ1/a6KH/6Pge9fqzneqNgn+xD7j/JAVxf3d7qp81qs5rIKitkXqKgnpcMjjzzImjWr+MXzvyKZSCKEwJGSkycMQqEgXZ3LqyyWy2VCwSDx2hrm5xeq1R6RkjVruhk4fYb77t3N2rWryWSyJBJJLOusKPr9frZt2wzY9G7cxNj4BN///o85c2YI07Sq4ZRWqcTc/AII6Ohox5EOxWKJt/a+w+DgCG+/vY9CoYgZh7idr/aJLTuSwwmTxm4/mzdtpK9vwK1xU9eEtC1qEESjEWIbt3Hr41/AF4nhmGsRA0cQc5N8/pH7+Hn/BIlTJxGzY9RIi/vjINILyIY2lL5DOJaJ7Nmx7L3BtlEOvIIoVip4ZtNuCYNbH4Tai1j95yEmBhH9hxGlIjIcwdl4MzS04sxOIsamkXVNEKm57PFuWC5zkfVb3/pW59NPP33+3qRhGMmVTtV13Q/8LvDxi03huhF4Xdc3A/8e6APe1HUdYNAwjM/ouv4V4K90XQ9SCZO8ZhP9iOMkU+BIlPr4ku32qbPhiouhjPbAIOotOxCqysXY1KvzwosvMzo6Tr5QIBaLcv99d1fFdtu2zTz3ixc5edJNGuofOM3pM4N84QufobNjacOQjo42IpEIa9euZnZunnKpjCMl69atYdOmjWiVqJLvfPf7vPTSq5TLZZqamli3bnW1ZR5ATU2M5194ya1SWfkNJpJJLNOqtupLp9NYlkUmk2HTpo386Mc/58iR4xw+coyJiSnMcpmfNDfSLbO0+QX+2jpOFRXywo3VLxZL9GxYj6SSWdrciWxsR0hJ832fwhep3KL7/Mjem5FAM/Dvvhhk3zf+G74zAVarZbRyHiwLkUvD0CmU5Bz26l7wn9PQ3LYQx95GjPS5VndNPahapWn3EPJyBT6TQBx/pxqNI/I5lEOvQ7SWsp3Dmc9jFSy0nbsQPVsvMdgNzmUK/DPPPPP6Bfb+GfCnFxn9cWDcMIwDF5vCdSPwhmEcZ4WYLsMw3gS8b9NVRBaKmL95AznjNqsQ9XF899+FiEbcA6wLuAZs57IiAXR9Pd/75x+RzeWQjkRRFBbmFzBNE5/PRyaT5dSpviXnOI7Dgf2Hlwm8pml8+olH+YXPx/TMLPlcnvb2NjZsWIuqamzevJHXXnuTH/zwp1XhHh4eIZfL8b/82z8mk80zNDjM8Mgw4+Ou28ayLErlsltWIJFA07RK/Xf3/Pb2NpqbGnnW6Mfo6yexkMCnaQghyOQLHHUE78wWCCfcr28gGGDDhnV88pMP0d3dxT/+4z9jWZU+q4pCV2cHra0tK75fPp+Pno5mRI0fMXgCkiUI+Nyd5SLKaD889/c4G7Yj12+FQAjlwKuIsTOITGVRL5NEdq5zY+QvhGPD3BTCtpCNbeBzK3WKqdFloZYiOYdMzDI3rzLfnwApEQemqf1yiPDW9Su+jhsdkUtAdkUjHCHd39QXv/jF3U8//fTYebtXPtHl68C3L3HM9SPwHtcW691DVXEHkAtJrLf24XvoHgCUNd3Yx04tOUfp7kBchoumr2+AVas66e7ucMvpKgqlcpkzZ4bQ9Q0Ui8Xl8d1AvpC/wGjQ3t7Kk09+lYcfvp/9+w8xNT1NfV0dd37sNurr63jl1T3LSrHOzc+TSme5aec23nzzHfx+X7WipKZpbi16AUIomKaJqmogBI2N9fh8PgYHhxkZGXPHXUzGUlVCwSCKqpBKpgkE3Dh527IwTZOuzg4aG+r50hc/y7vvHiCVzrCqu4tbbrnpku8ZoShMDEG5DOWSK8CqhsimkIqKSM2jjJ9GTo/gbLoVkZiFUAQ0H1gmmGVX5OONyPbVS8cu5FD2/waRd8NJpebD2XEX1LfAhT7PYo5CViM9VK5e0KVpk3jxHQLru1BDgeXneCCDNRddZCXourmeeuqpsaeeemrocsfVdb0DuAf4yqWO9QTeAwBnbGL5tolppOMgFAV15xYolbHPDLkunM42lI3rMF/Zg0xlUJobUXdsRoSWd6mxKn7yxUzPRRZ9842NDdTW1i5r2r1u7ZoV57uwkODI0eMkUym6u7u4845bqatz3UqadgGrVUIwEHAbd1gm4XCA5pYmpqdmsCwL23bo6upEEQqW7friw6EwSPjVS6+QyWRcF1M+TzgUIm1mKsNKstkcwVAAy7bwB/w0tzQRDoer3amamhrZsXMbWqVv7TJyacSwQTGdYrSsUL7tZoLlEmJyCJFPu4udZhkZjoLmh0gMykXE0ClEqQiDJyBcA41tyNp6102TzyKKeZz1WxDzU4j9vwHLRK7b5rphRvsRuQyoKtQ2opzch3PnJ5Ftq5GDJxGLdxwA0VqKU8Vl05aKRnlintC6lfvu3tBcvUSn3wOeMwxj/lIHegJ/wyERSCRu2j2AzOWR07M4cwuIUBDR0oTw+RABf9VaFaqK9rFbUG/b6SZvlMuUf/oCVGq02IkUztQMvic+gTivdMFGfQP79h1cYqX7/X7Wrl3tji0Ej33q4/zs5y+QSrldlTZu7OGmmy4cC18oFHnme8+Sz7sW/vz8AiMjo/z+175MMBjg7rvv4MiRY5TLZ0Wqta2F7du3IISgsaGBfCHL2jWriIRDzMzMgYB4vIbh4VGKxRJ+nw9FVUhnsjQG/CiKwvbtW9jz5tvYjk1dfRwpJfl8nsbGBnw+H6ViCdOy6OzoYO3aVSiKytz8Aj/60c+rF6+WlmY++5lPEYlUXF+5NKXXf8HwxDTPHzQwbRv/L5+nXZh8PGZiFUwCtsCnKPgdByUWdz+TQg5RzLkLq5bpWvuDJxDlgvv5+PzIcgn1+e+41n8g5F4czpxAWmWEWnH5mCCKoyAUKBchGMbZdR+KsR+yGWRjK3KVjjL3U5g7235RxurAH0QJB9/7V/BGwblEotP7D9v+GvBvLudAT+A/ksjK31kRB1Cw8FGuCryFzzUOf/EyUkpkLo+QDiKxgNPUhFYXxz5wBNHYgNLVjlCUqkvGOn6qKu7VZ01lkONTiK6lFl1LSzOffOQhXn9jL+l0mqamJh544G6CwbO39q2tLTz5B19hbm6eUChINLpyLLLR118V90VyuTxGXz/bt23hzjtuY2Ehxa9e+g25XJ7u7k7+6A+/Vr17ePjh+/j23/4DRt8ZVFVl164dTE/NcsroIxgMIITAsixaW5qxbZtYLFqZYzP33H0nk1PTbN7Ui8+nkclkyWZzDAycQatY7I502LRpI8FggGd/9LMldybT0zO8+tqbfPKRh5iamubFf/g7ps4McGhwgra6GtrranCmxzmdWOBAncaWllpSSpAANr6yTa2mua6ahWkol5CqCj6fK+y2w6JvSjo2QuKGVgrhinwwjPT53cXa+jbXel8kn3aPMcsoZ45DasH1xZtlZChC6LOfxX7mecqzSWQoApEaAh2NBNpWDMH2uEoWvGEYl11cyBP4jxgqJhpmRcTBRgUEEoGG27uUyhYfZcyhCWQuj1JfR3BDB1os6NZnCfgpz+exjk4DoHS143tg99knOk/cF5Hn9E6Vto0zPYsIBunt1dm4sQfTNPH7/Rc8VwjhNsu+BKVS+YLby5XtiqLw+GOf4OGH7qNcLlNTszSh5PjxU9TVxVmzejWappLPF7Adm9bWFizLYn5+gWi0gVAoSNk0WXVOR6XGxgZuumkHX/j8pxkdHeN7//wjwmG3RszU1DS2bbN92xYeevBeyuUyE5X4+3MZHh7Bsix+9OOfk5+ZI1ssUzQtBmcWCEmLRs3BLJcZTZvc1BhCKD6Kqo8JNUzXqm3U97/rulCEQKgapBKAAqoA6VAwHcxyiVKhRFwDH8ItSmZbCC0Atom0y6AEoFQEx0a2doOiIk7uR5xT7kDMT6Gc3I+2/WOs+jdfZPjXR7BSOQIdDUS2ruxC8wC4hMD/Fnr2eQL/EUJg42NR/CQaNhplbHwIHBRkVfCr51RiptV4BF9XpRtQsQi2TaCzATudR5o2zugEzuQ0SpvrQ1ZWdcLEOP72OpSAHydfojSVQOloA8CZmiH18/2Yc+nq8drdt68o7u+F9evX8sYbby1x+SiKwrp1SwUnGAwsuUsA9+Jw9NhJgkGNmhrXMjdNk6npGbZu6WXt2lUUCkXm5uapq4tz1123c+jQ0SXPc9utuwDo7Oygs7OdsbEJWlqaaG5uolwus27tagxjgA0b1hIKhSgUCkvmEI1GGR0ddxO8wlECvgUErhbMz81TE1HJlC1CUbdOPcIhEw4zpUVZm0tUF1xZ9JNLG4SK9AcoFEski2VqNVAlOBZITSIcG0oFd/FVUQABuYzr4xcCMTWCOPoWYm75WgwzYyAl/roY8bu9YLbLJp2AzEXyMb2WfR7vBfWc2hauze5U/t8BBAIbgUBWe60LlM42OHgKNXaOL9WyEMEgCIEaDWIl3GJgMpmCisCrrY0EP7YNZ3oWbAc1HiGyeQPloB9p21iv7cUnzs7HGR7DPtmPtmXjB36dDfV1fOLjD/Lqa3vcRc9wmHvvuavaNPtimGa5Umf+7Fff5/NRe46VHwoF6erq4O67P8att9xEd3cXfUY/Pr+f7ds2VxdKhRB89jOPcejwMcbHJ+gfOANIDh85xuEjxzhwsJmbbtrOnj17q2MLIbjttpvPLgTX1BEo5mmuTTI9O4/QbEq2IBrwsSoeYbSsYErYp0VZ29ZOtJwHBDLeiJidgGLe9Z8LAAXbkQQ1CCgQAJTzA4+lBNUHqTl3gVYooGkoM2OIF5/BWbPJXcQV56yjaD4vm/V9IMM1yIuJePjqJ4t5Av8RYukNn4PAqSymLi6tgorFogVvoyLrG9Bu3YkcHXJPUxWUznZk0rW8nbJVHVE0nk2WUbFQmhsRjfVgmuD3I4RAwcZKpJH5AkSWWuvO8ChOYz0iFkVEPlg3m82bN7Jx4wYymSyxWBT1EslWi0SjUdraWkmllvY0ffzxR8hkspw5M4SmaWzfvoWbK31Qezasc0seXAC/38+tt9zEVFcHp08PEgicvWOYnp5h69ZNPPHEo5w8YaBqKtu2baar0w0XbWxoYG5+Hlo6WVtTT/zEQTZENBrsPL31YYIKLBRNXklrlLo6+frWdZCah/QCFAsQDIFtIX0BhFVGKAI/DgFt6WX8LIor1qrqnu84LFg2tl2kKexDLBRRbAtCEeS6Le6iLHj15N8vXrlgjyuJjYaGhYKFil2x4iVgYeGDiqPGbXkB1tQCpCdR2tth3SoUM4MI+UAoOHIUa2wGJ+dWjFA3rEVpWp4NKRQFAkvdICIUXGbxOQsJGJtAzi6AIlD19Wi3XUY8+EVQVZV4vPY9n/foJx/mlVdfYWBgBEVR0PUN3HvPXWiaVu3herkXjEVm5y4csTY3O8+O7VvZsH5p2V4hBL/zO4/z+ht7GR4eJd7cyL9YHaMp5GPq2EEC5QIC8AVrULp1Hn34AQLWHBRzyHAUZWrEDZ8UCviDSF8ALBMnFEXJJc+5Rzv3wi+rbgHLcfjBmSQj2TJIh6agxmdX1RIPFqBUQJ45jrzpPmTnWmTXhvf0XnhUuHpRNJeNJ/AfKRTKBAhhIlEqsTISBQeNMhIVBw1pO5R+sxd7bAqJwBZ+1B2bKW/vRcNC4OCsWY8drEdrbHOjaM4TdxsNFXNJ6rGsXEDUiB9tXSdMLLaPKyHGx1HXdyMwcRwV+2Q/SlsLSvfyejNXm3i8lj988ssMDIzj8/sInxO77/P53teYbStkpl4sYzUajfLIJx6sPlbeeh6RSRLoXM3oqOsLHwnU09TWxqZeHSfVgDI6gJJJIRXFjQpSVUQm6frVhSCkqJXldZfFWCrA9dv73BLEpzIWI/mzd2ezBZMXxjP8i6Ym1ydv2zg+n2e9fyC8RVaP83Al0vVduwui77UdnsBBQ8GquGeW/thBYg+OYo9NnT1FSqx3D0GhgCUUlK52lPZWd0G17cICJVEwCaLaRUQ6hW062LX1+AMlRKmAuqYZRbNQp9MIU0Ou7wZNhVwORQisQBRnYuqaCPwitbVXzge6GF1zbser7q5OensvXyCdrXegvPMS62sD1JtxZoJ11Nz8ID29G907isY2ZDQO5cpiqeOAUvl8pUQKFWGalUip88RDKMhAEIJhkJJRHAhZNMgiDarEdBwmTYHpSDRVgOZDTA27C9me//394bloPM5FwcZHsWpxaUCZIBKBDxMFuxK/7sfhwi4EWXHMuBeKpQs8Cg52uYQ1NF45FhxUZLGEMzCImcmi1MWxT/aj7thMYIeOglO55GicXyrITucpvvAbZM6NEvF1NsD2HuzJaTfbtSZCpKEWy3Qo/WYOmciAENhli+TUCCOpEjHFT8+uTRd0ieSyOY4dPM7C3AINzQ1s2bnFDUl0HCiVIBhckhl7wffDtnH6TuNMzSKiEdTeDWfr61xh7r9vN70bexgfn6C+vm5Jj9nLwrZBOij1zUTC9azRfDha0Y11B3AclPlJCEbchdBSsRoVI31BhGOBdBdNcZxKw2fh7q9tRAiQ/iBofjQnyar6KJ1aCGGWwDTpUhXXnAjH3EJmwct7nxzTQmjqe3utNwAiveCumay0/2INua8QnsBfR7hx6mcRUA17VM6JiAmQc4UZgZWzCJJHomLhw0ZDQuUuYNFmV3AklN45RqFvHGdqFrmQROluh5CKnJ0Bq4wS0KpdZgK5WYK2mwzjoFYCLoOcK/LWgSNVcQdQAz7svtOIyDnCINyLjRoLIqWNVbYwBsd5bWSa9EQKjg3Qur6LL/yr3yVWezaSpVQq84tnf0k240bwTE1MMzo4xmO3bIPDx5H5AiIaQbvtJpSulVPlrVfexBk9G/rnnB7C99jDpPyS/oFBGhvqqyUOzkdKedG4/QvR1tZC2wp3PZfC7D/MyKk+stk0jiNob2+lTVGQa7e4gpuady1wAfhDFQtehXIBoakgfEizjNDc74Co7JeiYtFbNmg2+Px0924maByHYAgZqYFykU6/gxIIQm0DsrENGY4iTh2ASAzZvjzm3ZxPk3zlCKWpBdRQgNjNG4hu81oELuKEapHWRRp+hN77+tF7xRP4a4KsWuOyYokLLNSqW+Xc7FO7+njRfeM6YSxAIgsF/EgcFDRMbBTcy4FArQi8wME0RiidHMLBh6ivQ84ncIbG8G1cjSwWEPEovrCKxESJhlB8CuUTAyi1MYTfhzOdwJ5JI3o3oXS6gipn5lFjIbS6iOtudKRrVYZCrk9YQmkuhSNAvX07YmyK+X0DvJ0ukvEHkIUiIhZl+vQY77z+Dg986oHq6x7sH6yK+yKl6Vnmf/4r6hvccEiZzWG+8ib+zz2KCC+vgePMLWAfN5DJtPtOaBpCEez9u+9yQpNkswWEEOzcuZ3779u95Nz+gTO8+uobJJMp6uvruP++u1m9uvvCH2dqHjE2gLAsZEuXmzR0mZw4YXD06HEkksb+/cTsAj6fhmlaDA0No6kqDaWCK/CaD4IRZHMXYmHa9bUXC4hQxF1kVTVEqYBUFKhtRM5PIFChvhmRmENKB2JxZOtqeiyL5pkBprNFHKtAY22U5vZ2pM+PbOl0SyBkU5Cr1NwZG0B+8mzDE+k4zP/iHay0m1FsF0okXz+GWhMhtPriFzhp2WQPn6EwOIUS8hPdtpZgV9Nlv2cfGiSXcNFc/Sl4Av9bRsHEz2Ivk8X0I1BxUHAXvdxCA4tCvfjfxTh2dylTnPftcC8YDgJw0Cp+2EVfrMAama4GzikqKBtWIxMJfJ3NaE1xnNkEIhTA1xQHv0a5f5hyKg+pLIptEdi6ATmVoPTCHnxfeAKlsQ6tuRZ/PEQ1CFMRyIKoBl8Xk1lmDwzg72giGAiitrYwE5hiJuXWUJEoMDsP9XHGh5ZWSy3klyYHAdRkMtjnJS5h2zgj46gbl5ettQ4dwz4zDI6DXEiA7TATDPDK5ASh7TqiuQUpJQcOHGL9ujV0VzJWE4kkP/vZ85V4ebew2Y9+/Bx/+ORXlpdQWJhG2f/K2frp06M4ubQbZngJDh06yksvvwK4dywnTw5yV2uEhoaz8fxjC0kaIjU4joOI1iLrmhBSulZ5TT2k55ENbRAMI84cRza1u0XFAgFEJO6KupTu+ofwIRvb3WNHDOpUSX1TzE2YsoowOgDhKKKQc8dYvQnCUXBsRCaJPXoGYh04pkV670nyfeNo8QhK8OwdTqFv7JICn/jNIfJ9Z7NlS8MzND5+B4HOS2cxf7jwFllvICQ+SvgpVmvB2KioFbF2FsW3IuJnU5WUc+z5RYt88V/O+3dxu1WJnVHOXgh8PmzUs/cHqoLSWEfw9m0In0rxlXfRmuuRAuzZJP4NXSjJHMVX9+M4kvLAKFa6iL2QwPn2P+G7/WZCPa3ITAY1VolplxLR1UapbwKnUGT+QD/ZmTT+7m7+f/beO0iy7Drz+91n05vypsu1y3bTMz3eYBzMDEAQJEiCIqgVwQhtBLRSBBkhxW7oD61WWv2pIFYhhVax4oZ2l1pql1qRxDIAgiTczGAwGD89M22zu7q6urzLqvSZz92rP26W66ruHozBDEh8Ed0V9TLzvVf5Ms897zvf+U5Y9VG1dawbC7gKPCG0r41SiEaT7oHdGdzI+AHefv2dXdukYZLO7TPH0t77MVZRhFpY1vxzrYEKI8Iw5NLyMutBG/nGOfyDVQ4VDiOEYGZmbivAF69MbgX3TURRyNWrU5w5c3rXduP6xb3+6Tcuo8aPadXKbfDGm2d3/X6pbdJfbm0F+ECYLKSGWPzec1y6dAUhBKeOjPOZdg17fQksG2XaukM1mdb6dgW4FqTzoAQ0ayzVWry72CZo1Sn45zh030NQr0Aqh2o3EGGo+f8oQgQBlEu6sHr1XegbglYdhEGYSRKeyLH2Fz/BW9ygPbuCmBPEJgawu3XBWpi3FwVEjTatq7u7ZZVS1N+d+tsX4H9RZP27A7NDwYgdQdrs0DQCbQRmdDJwoCN1E7ucH3Umv12Y2SWB2wHRKZ+qDk8fYWIcPQivXkDW6yjHwuzrwToyhpFOAor4M49AvUlQqYMXgDAwU3FwLKKFNe1ZEylot1HpFAiBkYghogAjm0K4LiKfQcRjqP4DVIsLVCbLVPMHsKsRB4ZiCM+jL6jxdDbOhWqDBSBSioz0OLW+TvDDH2HffQK6u+jp6+GBR+/n7GtvE4Yhtm1T+MLTxK5e2+WDIxLx/ZU4bU8XJUeGiNb1oPBWq0XctgikiYmivLzCSj5Hf38v2dy2osY09g9Sxn7Bq73Xs16EoS5+3iHAt1rbFryu65DIZPhBpU48PULUbFMxXVKhSe38xa3nvf3yK9g5i0/f1VHnVNcRN4o6YINW02S7daG0vMqNcoM/vbZOJHWwOT9Z4vGuBR5JZhD1iu5qtbRPDabRsTEAlERU18BrdO4AbKLZKVpLzxHWJGYqhhl3iVpt/JlFnclbFokTt6enpBfs8f5XkaR9Y5n6uevExvux0h+sCe6TAlEuQXnt1o//wqrgbw82bQRUJ2gDW8FbdfJt0SFntomVjgoCgxAL3Z26aRd2+9Vf3xVolUwUKWpnL1JZLBFzTW07W6thnTmxleULQ2FkEpiOjT+zrBuTpCJaXie8sYgShraGlQohJSqKiBpt7KSDiMcwB3T2JREYJsSOH8K+vgpzq8hmk5V3pumeu07MgONDeQZSMZaCiLoJhZ48/Qd6cPIuLExjpi0iJ8GpMyc5cuIIjWqFrlwCy7YJDo8QvnUBtVFB9HRhnbkLsZ92PRFHZNMYgDpykPa1aRq+TyabJr9eohIEhKZJuVzhxIkCxwrbzTzHjx/l5Vdex99hnBaLxTh6ZC8NpLoGtK/6zm2prC6G3gGHDx/kwoVLW78XCodpNtv4bgJpJ3nszN28/PLru1/ktbg41+TTdx3WXjJrC9ol0upo3Df9aXwPlczwysIkkdfWxdZECiyb186e54GnzuDMXdteoJTSTVOdoKMMAxH429ujkGhlHlFvQlr70eQnYlgr8wivjR0aWE88izt469GAzckFmlfn8Jc3MBIuVjqB9AKal2dx+vOUf3QO8eML5D97hsSRvYv25sLw86LWUcnc7Qd+JPcv7n+Y+EWAf59QStFY1u3uyf78rg9dfWmd5XNTBE2P3Fg/fXcdRJk6C1cYW0qVTbdHg910gFbB7MzQZSfDV1uPs7Uw7IUAIgwiTEJPMvlnLyBfPUvPw3eRONCN05XBMgVRaYN2V5++qy/NQ7kMQUDUaKEaHtIPac+uYQYRhoW+jbcsyOeh2cKfLWEe6sVyOy3tWi+jFw0hOPaFB3jrT76PXwsR80uoUOIcGCC8OEnOC8kqhUimcE4cxhnq2M5GErVRxurXlFLcNcj0JjrvQ4CZdwk+8wjyDh9dIQTWow+w9s3vsFKr4QYBdSVpJOM8mTzAWcfEC0POnDnNb3/1K7sanFKpFL/5lS/z4o9fZnV1jf7+Pp54/BHi8b3e5+rwKVRtA9HJ1JQbR558CNVqI+cXwbExhgf3AG526wAAIABJREFUnVv71JOfol5vcOPGDADj42N86ZefZWJikNXVGkopXn31DaKdHw83hhHq+oSorOkAHAZ6kamXtXVB/xjkExAGVIJOgO54y4hWAy+WwCuXcKJOo9OmXE9F0G6AG0cEEco0EbarqR/DhFYLS8ZAKayoTjJYhHwCYaZInRiEjSIyLOhi8E2ovXmVyit6MbPSCVpTizDcQ1htYmUSOP25zqlIKi+eJz4xoJVBaBlm5aULNItzCCFIHB8h+8iJrcc/sfgFRfPziXalweRfvUa7okeexfNpDn/hQdx0gvryBle+/TKyM62ovrROc63Coc/eg0G4JW8UyE5/aRwLH/ChU2Q1dmX7uuBqdrxlduJ2eYyBREQBK+dn8Mo1eu85jN2TIXFoCCumfWMsYRAQ4q/VafzVSzjDXVhdGRzLwJMRzdcvYqhI0zgCSKe09tyxwbKI2j7Nywuo3l7sRApcF4VBiA746f4893z1UzTXqqiz5xHzi4SXpzBSSSLLR3ja8tbMbcsqZasNlRpGfy+iXsUorSFliEgnEd15hDAwpMeVqRmiKGJ8fAzX3V/GOFmt8u16hXTcQR4eZXZyim4DnLERUvk0d0Xw1d/6jT2Ok6Dljv/Jb375zh8G20U++FntDxOGkOtGLiwTPP/DrTm2IpPCfvbpPf478XiM3/zKr1Kt6mB+c+OVEIK77jq5q3mKdJ67RjpZsox0Fu+3dea96f3erKK8JkIYjPXmKc935ux6LUDQrXxSa7NbuvubsRl2BGL7jsAwQUncsQFMz8EubY8MdUd6tWVFECDWFveoiFQkqZ3dHtpuJFySp8axMglAEFZ3q6WilkdYa2Lndb2l8tIFGhdubJ1b/d3rCMMg+9jJfS/JJwZKaWXZLXBz7ea9oFAoxID/Bfgs0AZeLhaLX7/V838R4N8HZl86vxXcAVobNWZfusDhzz/AyrmpreC+iY2pRdq145COdawAtG3vZvOQbvuPCHcWRaGjsDE6efEO06/OT7Xj583BXgB+pYZlSjKHh3Fli9ThIQzb0n7vhnaKBI9mcRIjighnlgkXS0TzK3hvX8aybVQ6gaq3wHUwclkdkE8VMA+Noa5Moiyb5vNvY1gG1hMPayHnu5eg0aRxfBx5ZIxUX5bw6BitS5MoP9Dt9ckkpPRM1HBhFWekD/+dInK9jOjOY5y7StTwiZ8+qImrSg1Ra+AP9nHu3CW++yNdoIzFYvzal3+Z4Y5N8U68+uobBFJxtdnE8zxS4yOsRJL7CocZGxvk8KGjWxp45Qc64zYMjAN7M25VqYFp3LpJKqPvQJSUhC+/uWtIuarWCd8+j/3Yg/u/NLNP4biDJ594FNM0uHSxCEJw+q4TPPzAGeTqvCbvGp2Rfl5LB2Mh9HxW24FcD4+dPMhiZLFc6txt+g1+OW/qRSEK9x5QGAg3rl/fqHVuB0OU42L0D2MeO0n/ycfwXxBYiworl8ZMbC+Qap+6gwojpLd3foCSCneoa0+AN1xb13/Qd8qt4s3zqKFZnPs5CPDcnkl9fwn8/4wO7EeLxaIqFAq3lSz9IsC/D1TnVvdum9fbwvbeYRRKKcK2j0onCPbpQJVYBCgsAkARYW8VVjclkbvV8Rq3yuA3PzeWZZDpSxPPxrGExMlqqkNJiXBtDMsEQszA61BFElWpEUzOgFIYCRfl2ChDaC5RSozRA8Se+RTG8iK+AXK9pAu5uS7k917UA6E7dJVXnMJfLuF87n7ciQGCiSHCmXmU1AoaY3SYSsvnytVl6sUF0jKkcHCALssiKE4TtQPcQ0MYSU2NqEqNuXqd5dVtj+12u833f/ACv/u1r+55HzY2Kpw7d4HmDsnl0NAAv/KlLzA83M3qqubO5WqJ4Ps/gs7AEJGMYz3zFEY209Hav4Ra0wHSODCI9cTDiFs1PzVbqMbewqtauXWxbftJCtpNVLhNBZmmyZNPPMaTTzy2+6lDE/q5M1dgYxURbg7EFuC1EF4TwoBUMsvvHs6zMJDALy0xkurFDm4R3AGU1Fx3Qi86IuxYIiSzGH2DUC5hvfhNLMdBZCyQbfCVNjxLpqF7YM8uDdfG6c/jdyhNJRXhRg1hGti9GYwZm6jlE1UaSC+g69n7MXYqo/bj3H8eePj3qIP/wz/8wwPf+MY3bn60XCwWyzs3FAqFFPA14ECxWFQAxWJx+XancNsAXygUBoB/DTwKXAD+YbFY/MmOx6vFYvGjNzX+hMFJxfFqzT3bALJj/VTnd3+Z7bhLPJ/qKGn8TgHUJMTZYtGjTheqhiJGE6Nj/EUnzBuo2wb17Vtr/c+K2YRegJOKEbR9IsPAcixM08B07K3n2mODhNMLyJZHtLCim1wyKcw+TYkg0AE+l0OcOoTbn0CuSeyeFKIvTbReoz05jVQGxtgwuNpNUsQd3J4kUdPDSLjEv/A4YblB1Agg5hJEkjeuLiMPTiAnr1NS8Np0iScyGcx6G7m4TPPHZ0k8dBIjlwYElbV11s5d48jSGkoI1jIpVtE68pupGoXaFdwB6vXGnm3hq29uBXcA1WgRvfEOxmceJ/zJ61vBHUDOLRK9dQ7r4fv2vxDxGLjOrv0BiDu5XpbXMC68imjU8LJJRM/EbbX0Yvoy4vJbiHplm6IRhqZtlO5JoNVAtOrgxBhOZiET05Og4kldXL05yHcMy3Bi0KjqLtcogtBHoZBL84hoHtGsItpNvRA4MUhlUQNjyE99cUuFE1YalH90Dm92FTMdJ35kGNnyCco1msU5UGBlklReuogzkCesrhI12lj5FPW3r2HGHNL3Hdni3OvvXt91qsk7qHU+EdhYhY3bLOwdKe6f/MmfvLjPo/8U+B9v2nYIKAH/Q6FQeBqoA/+4WCz++FaHuFMG/78CC8BTwJPAtwqFwu8Vi8V/13n852AZ/fAxeO8Rpl94Z882gL6T47RKVUpX5giaberLZRI9Ga78xYsc/tQRUv1a47wpm/RxtwqGeluAid8J+7psuRnW98xuYFNIydZCsbNgazkW8XyS0AuREXjNACfhYnayIy2mFNgTw8jSBt6f/TWyXNVNSKaJX28jbAtiLtKxOCdNKq9NEpsvc3AgzbETE/jTi1iDDomuDN47V4k/WMDKJFFBiB23CfwIpNIdu45J4vOfovnKReRGleW6jxweIHJs6s0WUbOBbdvMzS4zur4Bnk+0uEbtWy9iHxzBGBli8do0A1OzW39jttFkJTaK4+wt7B0YGiCVSlKvawogFnM5eGic1bUSR45ozbuKol0BfBNyeRUVBMiFvQmSnJmHWwR4YZpY95wifPWt7Y2OjXn3iX2fDxD5PvPf/QusMOBAdxbCAOPaeaJUFvpH9r6gUUVcfUfz3s3adjFvk083zW2JpowQwth2nzSMzgLQKZxKqZ9rmiAEKteHyvdoh8paBdHu8PqlJaQBxtqyLqL6bb34GyYy26MLs6uLqK4IZbus/IfnaVyeRTZ9jGQMf6VM71cex5tdRbZ9zB3DuutvT2EmXdzhbR189bUiicIBzFRcF1QNQy8MQpA8MUr6gU++y6VKd6OiW4dIlda03le/+tXHv/GNb9zMQ5X3vgITOAicLRaL/6hQKDyEjsmHi8Vidb9j3CnAPwWMFYvFNnC2UCj8EPhOoVBIFovFf8nPpNn2k4eeY6M4qThrxVmEEHQfPUDmgG7UEYbB+FP3MHjfUc7/yXNkx3RBM562qc6tYrk28Vx8x/QlhcTqWA2EHUY+2tH8JDp6+d1c+3bGLggDiRASwzL38PGmZWKYBqZjgTAxrM3XakXPpkDTipkEPVnMniwykoQ3FhGVOqo7R2javLIRIlNtQsvF8AKKF+ZIxWwGEjFks43VnYF7j+H0Zjrn4ehb8JyNTDpbun6zvwfnV5/hyvlJ/ubP/obrb1+lUW/Q59gMGeAZPjeuXGekP4sY6CUMIir1Buqdy3Q/eD+nF1a5JAzdoYle4B7OZPeVzo2OjnD69Enq9QZSSdKpFIZh0Ldj7qswTUQqiarv5oFFNqODoWPvnT+7T1F2J8zjRxDdeeSNWXAczEPjt+Tu19ZK/Om//WMaV7XWvTud5GufvR8bA7Eyh9onwIv1FV2gq5f1tY4lNAcPneDdycQ3g3mnnqA2R/0ZHQ7edjqUGnpRtxyiJ76EqG0gLryu31PL1hYIfgtVWWdL0qM6/wU+1Da0uufl70DXAM1r89T+al4b4lk2UTJNVGnQuHADM+GivJCI9laQjxotPSNgh/5dSYm/WiGeiiMsk+xjJz/5nPvNeI8c/Ne//vW5r3/969PvYY8zaCXGvwcoFouvFgqFNeAo8MZ+L7hTgLd2PqdYLL5bKBSeAr5XKBRuXRl6nygUCn8A/AYwDtxVLBbPd7YfBf4I6EbfonytWCxe/bCP/9Mgc6B3K6jvB7/e0lz3TYGnvVEjmdsdILSgMUBh7iqy7texqrb+GYSBJAo9okAbi5m2hR3f5O9hawkQAtO2thT2OnO3ANUxKLOJZpf1oA5PD5Ewx4dgo4YcGaSU7Wb6m69g2yYqkSDVaJPOx5lfrjJ4pB/DsTF78xjjDmZXGlVvYsQczfHHYhgi2nLQUQgW5ld47nsvcu36NM16A6/VZq7tE6ZiDKVcsCNWMims3l5+fP4qIlS0LIHz49f5Jdvk7rtPsbqyipSKnp5u0rcwCzt9+hSXLhVJNVs4oaIWRtz3qQf3qFXMe+8ifPHVbb7UNLDOnEKYJuaxI0TvXtz9/JOFW173rWva14PRd+fOzO9+7znqTW/ripVqDX747lWevatwy0YptamxD3wdoEF71IiOUsay9TQmKbezdSH0z0QGlUihUhntYTN0EKYu6DuBVA5jfQXWl8A0UYk0otnR+JvWFqWgJZfRrvMTy7OodB7qFaLrM8SMBr6KE4YgahWkYWmaRUqak9qmwM6liB8ewoi7uzJ60J9ZuytN/dw0tTeL+MsV4gcH6Pr8/T83jVBK3l5Fc7vH9kOxWFwrFArPAZ8DvtuJi33A5K1ec6cA/ybwLPBnOw4y2QnyPwA+bN/V/4imhW7mpP4F8M+LxeIfFwqF/wz4P4FPf8jH/lBxc9djfa1JujuJYW8H8Z2lU9EJvLuV7Xs/ANtNUNBYrRJL2DhxCwSEfkQUGJi2td3AhNx1tM3OVo8YEruzqEhtEJZIoIIIFQQdLtbGH+xn5dVrtNfrWAM5hCFo1z1s10IYBpFhEzgOtjBxu7IYCQeVcLXCQxhIpTq6fkmEwsflRrFIeW0FiIjiAtkGoSRlFF0H+1lO2PSbBtPT8zQRYNtgWwS2zbVqjdNDfYyNbXOwm+ZnN8MxDX6rp4/S6gZtzyebyZLr27somwfHEJk08voNraI5NK4VQ4B55hQiGUdOzYBlYhw9hDl24I7X/70gCAIWFhb16D03oWWOwPTyBupuAzWyt7EK0L7wuR5EvQyJNKpRQVg2ZPIopVCZLt0AFUXgdukg73uo3mEYGIPAQ1kWyo0jZq4gyrqeQeAjFq6j8n26A9NxtS5eSlQmj2EIZLWiA7ul/Y6UaWm/mloF0jnEtfPEzDrZnI9UAQ1PUm8mIPAI18q44wNY2RRhpU5QrmOuVsg9eZpgtUJY3lamJU+NE6xVWfv2K7SuLWiDsvPXqbx0gdF/9Ju76JxPLD4aHfw/AP5VoVD4BhAAv3NzMXYn7hTg/3tgzyTjYrF4o1AoPAn8/fdzhrfCZrGgUNjOkAqFQh9wL3rVAn178r8XCoXeYrG4V87yCUGyL0+iJ0tzTbeQt2oeq9c36D5yALUVek02A/ymT4wOwAaminShErUnzAtAKkWr0sJxDKJQIIQg9ALCdkiiJ7OjDUoHdrljMVEYnXYrc/v348eIZpYQ2Qx+qUJ7tUJprcFy8WXqNZ9MwkXZlpZ4+iGNikd+eIjVhsKrNdk4v0yqZ4UTz9yFYW6fqFKiowoyCHExiTCEJOrc6rspl1qriVAQzzlYCQejO8eBsSHe+tYLej+2hTF2AITgajrF3d3aDRPA6O/Fuv/ufa+BvDwJK2t0d293V4avntX7YvcNqNHThdHTtWcfQujxgmbhFsH2A8CyLJLJBI1GEzU4BhsriFad3MAg8r6ntZ/MfhACee+TiN5BDCGg1UTZOmtX48cpjZ3CW7hO/+o0ZqPW8Xv3INujF243jvA9pFIY5ZIO0smMDtztJoQ+0enHMOav6QEjUQCGifPgp6jXmhiLM9Coo9p1VPcgavQoxuJ1XZgNfKy4gZ0wCX1B0mzTlglEXw5noEvTlUeGiGpNZNMneXyU7mfuI6jU2fjeWYJynfTpg2QeLLD27VdoTy0SbtQJNuqolkf7+jIzf/Cn5J+6m9xT2kfp5uz/E4PdziL7P/5TolgsTqGp8/eE2wb4YrH46m0emwf+p/d8Zu8fI8B8sViMOseNCoXCQmf7JzbAAxz5woPMvXqJyuwKKpQkhvuJEl14RB1JpIbsjNqz8WmvlKgtlpBBgBVz6SsMYNmGljB2nq/Q39NMbxLTNjBtExUpQj/Cb4XEezJsulFu2pZtB3exFfh3QvYPY3/+KdTFy7TKbWY8m1bvEMkxmySKHIKVSpNKtYGbiNM70M/s6/O4KRcZKdy4TaPUYOHiIkN3DetjCu2es2mJLDFxCDh67CBnX7/AytIajmOTTidptTxisRjZfJYzD91D7wP30VNuU1pa3TXjNTPYj/OlZ5DlCkIYiB0e8sgIw68BAummkftJEzeLqp8AYyshBI888iDf//7zmifvGQQhePp3fxPyd7DPtWzUxEmiseOwOo+oVwiTWf7q9Qtc/uEfAxCPx/niLz3DhL+OMX15+7WBj1iYwognwbYRzRqqWdteULwW6ujdRPc/jVjWBW01MEpsuJfaag35zksYk+9qg7NMDvoPoKJAe8e7MUy/TaLLou05KCXID3dhf/HT1N6c3Pq7rUwSlU7gjvbSvL7Iyv/zHEoprFyK6utFMARRrUVYbhBUGsiW1+naDWlNLaIiSfWNIu5gN+5YH11ffeLDvjwfHOtrULpNiPqFF82Hh+7u1J2fdAf09v60ZYc03d0pzv35j2mWqtSvzXN9scTJLz9KqqcbFYVaCWHqQuz69SUmf3gJlEJGSrvsLdc48exJkB1Jm2GA0mYEsXQcGQTIUOLV2pQml4nlkqgQYt09CNNCCQvVKqNkCGgeVgCGm0RYOxpUZIhM9BEd6Ob8tTLDXyqQyGrpp2EZFL9/gQHTojeVxLAtBo70E+/NIANJPBfHsnUQt10bK5ZEKJ2hO66j7x3sGGknQdSCg4eG+cpvf55vffMHXLk0RVd3liMnj/HAo/dy15kTJDsFyWd//XP85Z//zVa2b1kWz3zxcX0dbroWsl0nWpnZ5om9MsFgjvZNXzAhBJmJgfd5PT98fO6zj3JwYohz5y5hmib33HOSkZG9PiyytEx49QK0mxh9w5hHT2laBqBf00mvvvYWM3MzJLYajyTPv/ACd3/t15CrU9v7Wi0hLQOjfwDpN1Ayg2rWESJC2A7WsVO4xwu6fnSgDwAV+CivTbfRxK8vw85Zs9Pv4Dz9ywS2Ijz/Biqbw5IRcQAnwfBXv47VP8SigNqlWZRSNG+sEK7XaKxXWZleRgihvwulKonxPjb+wws4XSnCtQpGh+ZDCIRpoJptqDcx4zaJhAOrZdaef5f+z9//oV+fDwKV7UbJ26hosnvvGD9s/DwE+FlguFAomJ3s3QSGOtvfM0qlOvIDTDHv7U1vNcb8NLj+w7OUZraDTKPh8dY3f8KJ39jOOEwamIRMv/oujUp9axyfScjKZJ1YT4rcQIpkTxZlmh1VjYHh6gHKrXKD0AsxHYvIDzn/3XNM/NJTQAR4CExswi3P+AiLsLlpj6AhIg9TeZgmJLpTpHvThL5eVOyYw+GnjrF2bZVmpc3o/eP0TPTit0NMyyAKJI2NFn4rwMmlabQlAXF6uhJsrNc6HbkRUMMkwsZneGSIf/D7v0MURdRbEieplTDNRkB75l2i189iLa/zrJtirqePcKCfiSPjOPHkvtfB2pjCCNs7tvhEOYeWMlE7dO9m4RChD73wvq7nB0E4dYPwBz/WFstHD2F/5nFEPEYm081jj31q13NXi9d0ltyogO1q10iro/OfX0TNziPvfXLXa86evUyz6e3a1mx6XFioMjJ6GnHtHML3NHPbNQTSRAQS0WwABtJJog7dRevuT1Nb6/DhYYC4+DpieZZkwqFRqWl55E0F4PrkddTJJzCagZZYdiBHj9A20rBaw3zgGE42Tfm5d/D8EOtAL9VLM/grZYRpYHWlUetVGvMljKQLvVmMTBx/pQJK6bGAMQcpFUEQYShBo6H/XvPqAsZ9H/x6Gob4UJJB4COhaH5afOIDfLFYXCkUCm8Dvw38cefn2Y+Cf1dKUV9aRwYh6aGeTqfnB0NtYS9N0FyrEHoBlmtjEmyP5TPFlmWwQiB9n7Wri3h1Dzfl4iZdDn/hQdLdmyqCiNCLdK3GMLZGtdVWmzRLVRIdj+7qwjqNFa3HTw/36C9oB1JKLr96ntlL1yD0GBztpnD3CK5rISNJdamC12iT6kmT7M2BEMQzehaq6dhYtsAwJfGMS+hLkn059FwogTC1QmcnNn/ftF6QpoObNBFBAyFDhFcl+P6PkBv6yxprtTnYbGOdOYWRSmJs2S6zbfeg1E3BXcOwFfaXniG6OgWNJmJo4GMb8h1dm8b/F3+ECjp/98w88sYc7n/5uzpz3QFZr2KcfQGxKUmcv65plNGjbBY4xNoilJZ1gTOu73hS+0gxhRCkkklUbgg1PAG+B+US5rsvIRantV9KojP0I51Hnnxol1mYmHwXY2lGNzsFCtGoIlpN7TfjtzVn77idWa828sHPalqnWUd19UHXdqYvDIPksRFqb17F7RiNKaUwHFsb3EmFbPnIdoCZTWDEHFL3HKZx8Qaqk2yYqThRvaW7Ywe21VOGu4+j6MeMT4DX2HsL8IVC4R8Wi8U/2Gf7f1MsFv/Zh3UyhULhfwN+HRgAvl8oFErFYvEkunL8R4VC4Z8AG+h23Q8VQcvj6l++SrOki6JWzOHwsw+QGvhgt1FOOoHf2B187LiLaW9n6ZvoO3aAtSsLul0cg8qcHrwQzydAgdfwuf7iZY5/+RFsfKQUBO0Av+GxPreOMEykMvHbkR5MDVx/7iylK9s9FPmJfg599t5OoBBMvXuVqXevEvkBlmyzOL2MiiIeePw47XIT0zFprNVxky6mo0jkU1id4B9PJ1FhgAojhGkR6+3BdJ3b9NtqROwI/DLCqkzrAK0kanEWWdronJ/ekxE0ia5cwxro2jENa3s4SogefCGiHT7xQQuhIhwxizzYTZQ8tuWo+HEgeO6lreC+CTk1radRje/Wusu5qe3gDgiph3FsShmREWJ5FvOlv9RWwfle5NEz3JezuFxaJHDikNK+QYWjh8ltdtEaptbMp0NdlVntTFWyXVT/CKJVx/zB/4sq3Ic8cloXY4tv64VARkSujRA2KvRheRaxMoeIQlQsjjEwiuwdBtPad37rTmwqh82O6Z2ZjiN39BoYjkVstA9hGDh9OW1R7VoYpolwHaxMnLDWxHBsZBASluvYJ0aRfoCxT8Pbx4afowz+nwB7Ajzwj4EPLcAXi8XfB35/n+2XgYc+rOPsh4XXi1vBHbSnzPQL73Dqt57+QPsdvPcIk3/9+lbA3dx2c9YGkB7Ic+Rz9zD/1hTNeoCbjnHsmbtI5OIoBc2NJsvTFYLQQFkupYtXaS2tMnd2iupCGb/lYyaT9B4ZZPXcJJNz6yyevYqbTZLqz9MzlifTZaGqJWK5NAEO81dnqMys0FyrkBtMIwQE1SbHD/ajFCQyMVrrTRbOzxHPJug9LLDjDm4mgSEUyrZRhoFXruFvtLATCeyuLjDfW5Oz2VrblX1HpQpyaRViccxcsvM+SayotaswvfV6AkJhEyX7Matzmu8PW4igjnSzCBlgtkogQzy3j8W3rlCdniffnSBdGCf9IUke74hafc8mFck9DVbAnuKbsl1EuL69vbSkM3FX10jE6gLm1Xfo7xnid+49yJvX5qjZIeOPf4a7777J7mBtEePtF3Vw9tqARFk2YvYqJHOIdBZW5jCWZ8F2MK5fQDTrKGGgurp0jcMwOkFfdmbBOhjvvowaPqzvEnadvNJzeh1n6+4jcXyMyk8uIBwLZ6ALb7FE4tgIdlcGYRkYMWeXFbCZjpM8MYqZjJE4NoIz0EXj/DSVVy7hXZnHzMRZe+Fdmt9+Vatrnjzdcar8eKFKa6i1WxMN6uMushYKhU2tudnxPtj5rT0I/GxJzI8Q+1Ep7XIdv9HGSW7LsKrza6xduoGMJF2Hhug6fPtb/uxIH8e+/Bhrl2dQkSR/aIjsSN/W4xEWxg4uvGuin+zEEAEu62+e1eoZpQi9ECfh0D3WhTANmpUmV18oslGcoV6q4jfapHuSZFImg0d7kGEdGmX8WhO/0Saedsj2a+140GgTz6Ww8fArdRqrmjOVkcRQkna9SatUQ0YKr+FR/OFFRh89SqvaorxYoWeit/PhVEQhzLw2RbI7hWmb1BdXaU6uMPjIPXveCxWGyOlZVKOJOdCNmY0h2tuLanBhmuDcHLLahPUGqlTFmhiAeAJr4sCuAeSb2PytRYyFsknKjBhOWKhYF9t6TTC8KlPPX6c+fQMReayXTFYuXqXwK48SP1jYsT9t4rx5rJC9NNP7gVE4RHRjRzd620P5AdHbF1DlCtZ9d2u1EGAcmEC9/RYiDBFL09Csa8fI8qrOwANPd7hupsLVEqK6juoeoDeT4vNnjgEQHR3f6mLdOo+r7yACvzPNSTcviXpVjzb0mqgBfTdhLF7XjUubPvJKoho1UAai3dAaeCG0541haGXOjcu7A/zGCsbF1xGNmh7mffAkaqxA6p6DICWNC9OYR4bIPFTA6c1hZpMkjg4TlKpUXrqIv7wg5oemAAAgAElEQVSx5URZe0P3NTbOTdP1hQdI3TVB48IN4keGaFy4gQwjgiBk/ftvEaxV6futJ3e5XH4cULkelLz1XaPKffxF1v+r8zMG/Ksd2xWwBPzeR3FSHwecdIJ2ZXc2Zbk21g5ub+P6IlPfe3Nrskx5egm/3mLgnttrpJO9Oc1f74MIrS03O9mpxCRAfzC7Dg2zVpyhVap2LIgFdipBe6NG5Id41SYqktjJOLmhHMlcDGEaNNaqDJ8eRUYR63Pr1FYbuAkLGUYYlokd1/sXwEBfnk0bp3bNIxET9PZloR2CbVKZ3yBoBUReiJuOk8y4yPUyvpnHcF2WpjYQlkW74WM5FkIIXEfSWi3tUrqotkfwnR+gqjWsjMBcAWOgDzOvh3bLyCG4fAMsF3O0H7lcQbY8ZEsS+/T9WOPD+9oiSwympm7w7/74/6O8toFpmZw+3Mff+/ITODsCfLPcoDa7iBFtUzxKKdbeLTI6Mgq2i4WP3aGAZEdmauN3ehY+WLnK/vTjyNkFouI1Pfaw0cQ4WYAwRE5OE1RqOF/8LABGJo888SDmX/4bzbWbFqqrHwbHddDNduvB2JsI/C3KbRdadU3V7EStDPWq1s4LEH5LS0edONV1k3q5ATRIiQqpuzKIZFrbS3st3QDnxCGW1I6VAI0qKgz1YrGTVA4DfacQ6M+1CHxE8SxROofo6id93xHS9x1hP7iD3fR95XGUUsz/H9+i3aENAdqzqwjXJjbeT1CqElYaRC1vy18parSJmm2axTnSZw69z6v14UBJ9rPb3/X4R4076eAnAAqFwv9dLBY/dN77k4TBe49QXyzt8nIfuOfwrkLr0tnJPfMkl96+Rv/pg/tSLu8NghCHcCtL3LYZcHMp7GQcv97GBKy4SxQqZn9ygcNfeAg3HacBmKaBm3S0jMwwsBwbYQhS3WlyQzlqq1plo6TCTSeI5bdVAv3jw4yMDrK6so4MJAlTMJRI4NgGM+dmaZTqmiJC0RvWMF+cwg8jcB3sZx8hEXdotS2S3QmMTSfBICIMdqs5oktXUNUawgI73ZlTtbKGyB/EjOrIclMHCCFQ2V7MnmHMSGKODWKf0sZSAQ5mp7QqKzWChTU8N8W/+Zf/lsXZpa1jvbiyymBPhs8//cDWtpCY5rJvQhREiLCJbW+2mG163CiiTnOYSbh/gFcK4dcwghbKcpFu5pY8v4i5xP6LrxHNLxE+/xKy3cbYoURRqyXkehmjSycCoqZrKirXqzP1MECUlvSAkcN3ISbPbe88nkTZ270CAMo0IXeT1t9vI9aXEKVlKK9ont80wXLw6pJqzULGdEAu1yJEtkaqy0bYDso0MSIfLFd30c5PaYVPGCB8T48DrJSgsg7ZLigtbQX3Xe/D0oxerN4DhBA0L81sBXflh4SNOhs/OEv6wQJIRbBegx3qOLOTvMjm3qL7zxwfjR/8T4X3lJbsDO6FQsG46bGfwTr00SM92M2xX3tc0y9hRG5ikNzY7g9isONDo6TCr7fwjRYyjDCd9x7glZSUbyzTLtdJ9edJD/Wwn9t7hI30Q2K57YC8cGmWtcllTNcm2Z9n7dyU1okLgWEaWK5N71Gt8zYsAyebpuvwMBKT3MQgsWx861ASk9zBAwyPDjDQm9UGZ15A8/o8xvEhDt87xvpShcRYH97MEswuga19TYJKk/l//R38B+4hO9oNkfY9MaIIxxDEunZ3F6p1TQMZOx19pQI/RCbz0APKSSCFDaaDJMIwwex0l4ZYHVM2m9ZrbxKdPQ9ujNn1dRbfvgT57JZVbaRMXnt3mmc//ZAu3DppYhP92JnrhOu7bZ7zI10I09rlAaTffW3DtrPb+GZY1blOY1Xnz2lvEGbHblvMNYcHkIP9MDO/98GdhdXlWZ0Vix22w80ayjBQY8eQsQRifgrph5QrGdqTM5jBHOmxLImxHOr4/VpeuRMX36JV8gmurpEwPCwzQpgGIpVBqIBYUtKMAMsg3W/DygIikdHTqgCRyUHHxkK5MS2HFEIvEqkswjQxpi4gzzyuRzvu+6b9dHSXiiSypb3uw3JDWzFEktl/9mdE1aamudoBxoFuhG3jdhrYYmPvbRH5SKFEp2flNo9/xHivKpp7gX8OnEbTNbBti/IJH4z43pHozjD6qbtu+XjmQC9rxVn8RpuNawtEQYiTinPl269w+AsPblEfm5CRxK81sZOxrVtIGUZc+uaLLLx1lfZ6FTvucvBz93P0iw/vOV6ITW3DQ8iAdqXO/NkbrF1fxUknuPTnL6KUYujUOIuXZgjaAT0TvQyeOkAsk0AGIV6rjudBZrgH07W59N3zZPtTxPNJuo9PYKYTxFIRd//a/Syeu0GzVKW6sEE4PMCFl6eIp2Oc+PL9JEZ6adXKeKu2bn6JJI21KjKUhEsl5HCeoFon6Zpbxmbh5DSye7vWILrzMLfQGULcCaaGQSNS1FbKZEaOIB5+FN7QNswKE5nPI48dpx05YNqoZovgu88T/PDHEEaIbAazK6vVKc2WdmyUCtVuIysenurF6NE8sogCjn/mGOV3PBobTbyWQe/RfrqOjYOdQPcEaAuJm4N9tM9HXPiNXcEdwAhaGF4VGbv9MGVjYlRbDu/cXyaN2GmVYNk6U16e2c70hIEaLWgjsKEJ1NAEa996hfbKCuSHCL0W3lpA1yP3k9hUsqwvY1y/iGo38V56heZyHSM0wIYoMvVdl50AN8RxYtSzx0l4cxi+h4o54Nq6mBtPYRw7ARfPIeYmdS0gntR3Cum8poiadWh2XGvz/ahkBtHQvyulwLJQwwdv+97sROWlC8gwIqw2iOptEGAm4zq5WtrQMw+6M2A0kQ2P5GOHsVJx0mcObwX6jxs/Cynk7fBeicU/Ar4F/OfA3nE1f0cw/NBx2uU61587SxSEWK5NbqyfxmqZhTeK9B4fo3R1rqMRt1g5P43faCPDiAMPHWf4wWOUrsxy7Xtv0lje2KKDqvN/TXdhhO49BVuBmc3x+j//C1rrVdqVOkIInEYL09YSsdlGG0wTz9YZuuE4eA2P5PAA+YFx0idCSlfnWOrMxFyd3oDpDdZmapz4yhPagz4dZ/zRY8y8UqS6sIGZiBElknhErC3VGRvtx0jEoVInXFojqLewpMBPplicXMVPJOkdTBPrz+K6JrLWRm7U8c5dhoOHQUa4I0moudBqIUwJEl5bqnLx7A0iTMzMDA89/iCHfvXzqIUlSMSR5QreN78LfoAx2IcKAsKX39iyIBDlCr0yYqQrx2yjqQd2r29gSMV9ySTBX34f877TWCePYpensR0fCqNk2g1yvRna6QmieB4EWPiIjlnztvzSIMLZl54RkbdnG4AI99++E+bEKKrRJDp3CTwf0duNcWCQ6I13EN15VNdx1MgRXZwcHEdUtYImOnoP6ui2705Ya9KeWdnesRsHN07zyhKJ4xNQKWG8+TxCKaJaE1Er44YN2iqmi6OAlAJVbWAIkM0WpEIsrwKtGnY+oQdvx1MgI+TUFUBoNU+rjoonIJbapoZkhMp2Aqth0Oy/i/V//x2Ca1MkkwHxQ4PEM+cwzjx4x0zeW1yn9vY14hMDqCDEl+tIP8TKp4g26tv22YbA7s3ixh16f+UR3AM9WzTNxw25WkKu3FpFIz5A4+V7xXsN8GPAf7c5JurvKuy4y6Fn7mdjegklFU4yhlIKv9Fm7uWLrF2aQSlF5AesXrxBsi9Hc7VCFEasnJuiurBG5Ac0VjZ2cf1By+fKt17mkf/6K3uO2SpVEYbAsE1M20KYJq1SFScZx7Atmus1LVszBdffmiXVnSYKIsaf7sF0GjRLVVbOXd+z32apgldr4qS36YSNmVXd3LSwTqvSxrBNlAndx4Yx3TjR0jpBw0MGIUGlRaPU5Jrv0fYj4veNETcEVjoOSuEvl3GdOBwEs7GEJRsYR8dQlRoq8LlRDbiwskxkJ1BmHBmE/OT5Vxj6nV8nebJANHkd+c62Ta9cWCZ86x1A6ICilLZjnl/i7z10L//xxjxr5QpWMsmJoQEePTwOQPT2BezRbqTfYu7KDF5LB+DSapX4eJbchM6aA2Id9YwkwibE2TFhay+Utb/BlbTjt/4A7YB16hjmiaOoICB6/ieacuqgvrSAfPghbSsxfw3VdwA1OKaz910H2//ruCm/E3OTW4OdVRgRmElMUUUI8CMX2/BRoUKYCqu/C6ORwrhxCWlWiacjYvFIz3cVhp7+5NqaBktmt/3mDbFljqS6+7emUHmL66x88xWC66vkEi0EimB2EfHc8ySFj7r/9vJjf0EPCreySVKnD9KKu/grZWIHemg22voOzjT0QBo0Xx8b79896u9jhsrfQUWT//hVNJv4JvAM8Dcf4bn8XMB0bGLZFJEfELQ8Nq4tEHoBXqVB5kAv+YODeJUmURixeuEGsS6tJFHA4ltXSfblkOHeskV9qUTxWz/Birt0HRoiP6GHSNfmVxGmQTyfRgYRYWcUXBSGGLaFaZuEoSTyIyzXwWv4KKWYfeUiXkcVVLoyh2GbW/sEOkNAbCI2p0ApnITD7NQi7WqLdqhYLpe5ODnNbL3BKB4nDo2ipuZoLPqUqwFNFI4jWbi0RDLwGPzSfQReQFiqIVs+Vq+2qjW8qh46aAhEXnfXzk9dBieJwNxqjJJSsji3xOFjh5BTN/a8R6reRCQTiGQCVa3pjB0Y6eni9/7+f8rct76Ls1GhL7Oj1TyKoFahtLK2Fdw3j3XjnUtkRicwTBOJic/OoH17flTZCaJYHrO9Y5yfk0Y5793fRhgGcnkVubiya3swv4ScW0CMHkIduLUSxMomd8063UT8iL4TFOF2Y5WVSUAsiSdytEOLdhgnpmqYriCZTSNyXaSPjZKanUIlhjGbZf3eOTGdrbsJaksBlUUf3BiZgxkSVgPVdwBMi+jo3XD0ni1pauP8NP7KBgnWEEFbO2AqRdRsE01dwzhx/9bc1/1gZnVXrooiVBSRODaCEXex0gnckV5a1xaxc8mty5R/+NgnKrjDz4GKZgdiwDcLhcKP0fLILfxtV9fcDMMyGbjnEPOvXaY8vUToBZoLjDl4tSa1xRJOMq6te2+aBGSYBsm+HFbM2R7OrRQyjFi7PEd5ZgXDMOg5PsrBz9zLyCMnSQ/3ApdACGK5FI3lDQzLwrQtTMci2ZWmvl5j5N5xukdytOse9bUG7XIdr9qkvrSOV23g15rEsininQWn59golmsTdUSADm16xru4VNW+LSvlDTw/wEnGqCyWmcHHTrsMxFK0o4oe5OGFdA3F6To6wNFHjhFeX0FtzoTIpnFPH6deDwBDc7BKbhVCk8k4yisRrde0r053HhyHRLKTAe9UhEQRtD1EJqMzSaU6CgWJcBxEbzd2Ns3YiSNE53a4JoLmq/MDtK5d2drkWJBNKmTkw8IFjK5BZHy3bv6WUBLDq+rOzngXMpZDhC2U6aKcn348girvO2kNtVGB0Ts3YXU9ex/l59/Fm11FOBap0xMkT47pffQf2HKDFKZJ/NAQDcOmOp9B1lq4WYP+MYl1ML81RMSQASrmorqPaEmljFDJw1QWIppzk0TtEJoN1t5skBtzSQ85enhIKofqvH8qjIhaHmJjFcNvgdNZaKIQos6wlXCvwmYn4hMDSC+gcX5a36mZJqnTEwz8zmeJ6i0qL1+ifnYSFUYkT45z6L/6Euv1O9NjP1P8vBRZgYudf78AMHjmCFbMYWNqETsRI9mbpTKzgl9v0VqrEjY9vHKdsOURNNrYyRiGaZLozpDsyXLomQeYefEdZBjpQmyjRRQEyJqOjguvX8FOxBi4+xATT9/D3CsXqXS41sxIL0HTo/fEGKZjE49Z9BZ6SffnUErhphJ4nuTSX7/DxuR8h6c0sGIOjZUN+k6Ok5sYoO/keOevEWwOAU8M9NJ1ZJDK4hphSRLLJnASLiIKEL15lmbnGLcCgrgF0iZ/pJvDnzpE9r5T2IkYcjSPV9EDIIyxAxjxGNR8UBGiWUHEXIQZB9PmyMQI5167Rq3eQLV8wuVV+scG6H/nVVjqxpzoQ84v4Zc2MBeWUFGEcB2UNKFaRyTiEI9hDA+gVlbhWhFnootgKUm4uq0Rt86cgniCmkpjyja2CekEtHyBZUE82kCsbRDFu4lS/USxbtTcIsrzMIYH9XE2EQXYlektSwTVWCZKD+nF4X3C6Olir3gTjJ7ufbbuhZVO0POlh5FBqCmLHXJdNTCGrFcRM0VEGGIOD5L87K8wEVoY0sNwDMw3ntuicQBUMr3tDb8ps+zup3Z9FSMM8RoSGSgs4VMzItIPWYjAh0tvEMUzVN6Zp3lljmhpEaNVpe07OE5HCy/AtCTWQD/yVl73HQSlKsI2cQ/0EDU8zKSr7wBNg9hoH7HRPnp+5WFQYCZczLgDn7AAr7iDF8372GehUJgG2p1/AP9tsVi8JbPyXmWS//R9nMvfWsgwIjfWT09hhCgIaW/UCJoe9eWN/5+9Nw2S7DrP9J5z19zX2veqXrIXNJZugCBAEgBBUkNR+1CW6JnROGKsoWVHyPYve8Lh9YeXcMTYDodmYixNxHhCmtBiUSGKWiiIAneAAAGi0UAv2UtV175l5Z5593P842ZXdaHRzQbI5jLiG1FRUTfvzbx5697vnPN97/e+yCAkPVoiO1Em6Hv4nT7JUo7S0Yk4N395FaELhk7MxI1HpsHm61cJvdv04aOI5uImXschM1pk5iNnuPaXr+C1e9i5DEc/+QR+16V5c4uR2XHGzsyRHT8ICG6zS9jvH7qBdNuiOD/K0WdPYudTRLcZidzq2kyVcxSnhxBCYm7uoqRESUmymEErZDE7OUTQIVfSKJ4eI/3ERKwn4jeQdhktaWGV4kB5C5qzh1AKFZq431lBOi7a2Aj27Aw/89zjnH97kX6rQ+HGCieUg1pZJ1xZZ0XTeL0d0njlAgVd5wOz44zPj8dNOikRMzKSGSgPo7lNxPJVjPxR9MfniFoevp9CGx/BMvqIvSpT40m+8eU+pWISqQSWBeMjydg/S4EWOqjdVZwv/jlytwm2jTZUwnjuafT5uANYd2qH9W4Avbt9T/77d4M2MYa2MHsoJWUfXyCceG80v7ulJ9T8ydgZSilIpNBWr2NfexMRBkhNp9dUyM1NDBFiLMyiP/dLaEuXEG68klOJJM7cQ7z+O7/F8vVNkiGcTmTJi4GrcK8NuRJCKTp/8zK9vcF3yFtQ0ujVk7ihIGk7JIcSJI5OIs9+5NAK7d3g3tyKtWhGi+/Yvk3y+CRhvYNRzPzomn0AcmcPuf0ungQDfA9F1l++ZWf63XDfSatKpfIJ4DPASLVa/blKpfI4kKtWqy++z5P8sYNSivVXLrN7aZkoCIm8AKfRoXZlJU6h5NNEXoAQMPrQPELX6e00YuOOM/PUr67t39ipoYMOQ90yDgX4eBdFqpyjtbpD/do65WMHy/XW8g56wiI1lCddSlO7vEJns056uEBmrIidT5MdK9Jc3ds/pjBVYu7cdPwgE/8EWIM2/IF+pRAMHR1l9ZUqViRoO3Hu1EzGmu7zj1bQu230JNgjGnpi8JAO0hYyWUbId6SlvDZRs0P49beJ/IDQ8TC2W6y9fo1vdFxCxyPvB5wsp7EGQ06j7/LVizdhuIhWKtIJXb5Wr/Orp0ewczbBzR6iEC/1lddGyBBt4NMpNA2jmETlp9HcFpoXUxkLpTQf/alTbG20yCQUIyMZDHl7M4zA+fzXia5toPSYrK/26mCZaDOTsTl3cGfzjFARIvLvWnS9H5jPfBB54ihqr4EoF0mfnqf/XqSMXQexfAXRbaJyJdTsidhS78p39jVjGBpHzp5AXHl9f8buVleIml06mQqRZiOWDYYeLWJ/6GdjvRsBlMb4/Of+jLe3Vgl6PaRS3HR7/Hx+BEsZ+J0Qa5B16a82IBUHZD+yyaYUdkKRefQ0djkDUiLPPhO7RAH96xt0XrtK1HNJTA+Tf/oUembgQXCrYckLQEr87SbS9ZGej/b1t+Nau66RPXeM3BPf3SP3h4LSMMh7pP1K8crvt3/7t6f++T//5+98tXkvK777xf3y4H8T+C+Afw3cono4wP8NPP29nsSPC3Yv3mTrzRv7f7udHruDxighBJpuxukY08DrOCRLWTJjJUpHJhh7+Aj1a3c2t1jZFOmRIqEXEN3SX08nGX34CP1aaz81czva6zWSxSzJUpaNt5YZPjpC6PooKXFbXYZPzTH3/Dm6e714FdF1KM8U8Fs96osbFGZGSZayCK+PH5joGTNuyZeS7SsbjJyYpDA/xnatSavdRTgBj/3SBxmzJOLNVzFzsD/11TUwjThoyABpvkPkSehE19ZQUhJ5PqDodl22qqtEY2X8SNFsd/iy0+fvV6axgKV6J7aTkzK2i1OSIIKepUjlU6iyj+9HaJqGCPtopSL69OEZrwjcOFd+a40sBOlskoVKCjSdlBHgN1wUCrnXpn/+MsHrV1CmBZlBgHc95MY2qtVBlAoow4bQOfQ5Smj7A8L3Am1kCO7DpPsOBD7aq3+DcGP2stjbRu2uo4Ym0NYO7lV2N9BqG4jB5ZCeT9jsIgAzbBMZY7Fc9ls3Y7/TkbhQu7GxxcrqGsZImWi3ifRCfBTXZZ9nChlCEliAMgxEKQtuRNR16FfXCUSCfKKJu7QJagzz7DnUQA/JW6vReOFA9qN/bZ2w0WXkV2ONey1h0b+yStDsEtbaaOkERi5F581FjHSS1MlpwmaX2he+hZ5JMjx8+n1d9weK7yIXfGsJ/Qd/8Afv9KAG+J+A//EuR/67SqUigG8A/829BoL7XVf+l8DHq9Xq/8aByOUV4Ed06HwwqF8/CNBKKrrre0A8c08Us+gJ+2AmftsKdOjEzCAP/y4KkuMlzvzDj1GYHSU/PczIQ3MU58bw+y5XPv9NVr75Nn73cFAJXQ/dMnAaHfYWd+nUOjHtUikiL6Cx3qJ4ZIojn3icZCmL33VIFtIkSllUJGksbrB7ZYWdtxd5+w+/zKUvfJteHzwfvF5IiIlhW0xOjnDq5AJzszOMz4xi2X2MuVFUEMV5eVOgZ2200EGEDtJIIROHl9RRsoRyvLgDUcbnuFdvxzLAXoBha2i5BH4UseU58WpAEMsujAyjpQ6Cp25oSE3QOzPBRsFiTUT058awn3tsX31QKUWz3uTy1WW81i5avxanibxO/LRpOkF+Fi03gjQswq02zhtryO1GfI5dB9W7XeclQGTiQStKDaG0w3OiKD3yQ5UhFlvL+8F9f1u3HZuFvHPfdmPf8UrdRtOV4jbJBO/wCqzXj9/bKOVJTI9hD2WxS0miiRJMzmJODqGGJ5Dnnif96HGk69O7tELYc3DCFM30SbqZY9SccWTl3P4KtjegFN8Ov9bC324QNDps/PZfErZ6BHttZBCiogg9m0IIQdRz6L5xg/61ddyVHbZ+90vUv/WO4vqPAGI9eHGPn3i/z3zmMx8B5t/x83/d5W0/Uq1WHwGeII4yv3Wvc7jfFE2WAwelW/8Vk9stgf4O4HZdGhlGRGEUpy8GhS0xSNOkhvIkC1n6u000y2DpxTcYPj3H0MlZdt4+4KTrpkHkBay+fAk7l8LKxkVNK5dCG6gAWukEe1fXyYwV0C0TK5MkPVpET1h4PQcpFde+UiU7mmP80QXCQDH6aI70NEycO47fddAMHSOV3u+mdVs9Ascn8EK620262w32qqsMn57D9xW6ZSDRB8bdgtzYEJrXihUQt2uxE5AhwPWJlI5WzMWzW904lFsNltfxv/oaqu5Cs4MUAikh8iI8IfDTNrqpoaULSC/AMAxE5LMwXOSibiGtNPrMGGp3j0QYkRsaomNLAgXuUAFrDBoCkp06mXSSyEhx4+oSixsdNAGpYYPRcpp8PocIXaQQhJmFWNBsaI5A5Qhe/QIyFIhMOmbp1Fuofh/SKUCgP3YGYQ0GGd0iKB6Jr4WMUFYGdZ+89wcG7y6aK+8iRauyRbASCN9FS9lotkkYQKinSPduokc9EhyPNWXycU1nemoSwzBR5RxazyFQ8b0+fexhcj/3HNq5Ywey5laLsNkjrHeQYcx2klLQXu5gFCSR62HcYkndRSpXScnuH3wVf7cJmkCzTaIgrlXJgbZN1PPiFXN6IJpnGex98yLZsTJ6+kcnJ3+/hh+f/exn1z772c/evJ/3rFarq4PfXqVS+ZfAn91r//sN8F8D/hnwP9+27T8Hvnyfx/97gaGTs7TXayip6O02cOsd9IRJdnKIoOcSuj7FhQnO/vqnWH/1yv4sPnA8Nl6rMvXUKSaeOMHSl76D3+uTKOZY/sZb+wOHEIIeiuLCxL7+jNfuE/Qd3KaJDENkIDHTNjtrS6AUbq1FGMZ88P5XLpIeLjB0ap6bXzlPopCJXaNMg/p6CzttYSYMAsfDbfdZemWJ5nodr9klUchgZVOEro/b7JIeKaAQWOkkE49XABe1W0OF8Qww6vhotiBqtdCHxiCRi3XdIz/WktnaofuNl5BdD2WmUW6ToN6iE0lkJHnbB8NzMa0ECkHp1Dxzz58lavdZq9ukX3+Tjesr6JbGyYfGeeSRE6z1AmR3DwwDQ4OsLdjrKXYbDul8iWa9ySvVFj1f8ficSdtVyFqPZDqDaVko3UQmy2hESKeFpYWImQmCZgd/cQshFSqdRNM09OEinDyB+feeO3wTaPr3xJr5bhBIZOCiEd5TB+cW1NA4LF4EIGz38dZ2idwAOb5ANu8dksxVU0dQC6cRS5cQ7Qb2hyfpXO+RXT2PCBwMCdrVKtH2Otqn/wGiPEQiYfOpT32CF154Ee3ULNpQi9Mzczz1i5/EKh7w2KUX0HnpEtZYkeTxSfztBv5Ok27jRuy3ahps/dsvMfkbP4PQNJKVafrXNw59FyOfRksl8Lbqse5MJOMGqkgS1NpoKRvZ9wnrHbSUDbqGkU9hlrKxfMFui+SPUoAnnqnf6/X3gkqlkgaMat7aTCYAACAASURBVLXaGqRoPgOcv9cx9xvgfxP4QqVS+adAtlKpVIm14H/2PZ3hjzlKRyZQkeTi//cVnHqH7PQwQc+lt9OktDBObmqE4z/3FIZt0lrevuP4vSurRH6AnU9h51NsX1ikv9skWc6jWwZKKbx2H6/TJ1HIICNJayU2JE6Vc9SurNDdaWJnU1iZRBy8LROzmEA3Yl2R/l6LlW+8jTl4sI2EhWbohH7E6sUtUrkEtSvLtLbbqEgRdJ3Yk6HjoKTEzqVIFjNMP/0QumVQmBtDM3RkZCFuaxRSEUSdAG+tR2JBoKViHZdb6Yro6o39JbgQAjEzhT0+ivnIScxem+eaDdb3tmi7EePjQzx+9jhGJsnlpSar19ZJ24JjU8OoMMTflbz21Sq9yOTqtVU0w2BsyKZcTDA2U6JQ1kA36fXc28U4QUDXUzQDk3K+GKdXBLEksIpb5YNrK8idPbSEiXQFGhrmqQVSv/Qx/InKDzT9ohNi4KH8CLNfR+1uERhp1Ojs3Vv7C0PIo2dQl8/Tv7aGUgInMYHXzeB3mww9nEEIhRqbRS2cBk1HnXwcRZyfHZlfhZe2CS4sxcJebQfV7KN+948w/5N/gp5McPzYEebnZogihzDUyGTu9CwN6h3kYPC3p4boX41z6iiFnk5glbJ0Xq1SPz5J6flHSc6NUnjmDJ3XrhH1XezJIQrPPUzUdfDWakgvdgpTkUT2XDTTIGz3idp9hGVAKJGejzUSF8ARYBYPn5e7uou/WccopEkemUC8S4r0QSLcrhNu3Z1Fc7dO5HtgFPjcwJdaJ6au/2f3OuB+aZKblUrlCeADwAxxuubVf1+UJN8L8jMjpIcL+yyYKAjxmj2SQ3ke+sxH42Dqvnvmyml0uZXhcls9utuN2M5PCDKjRRBiEJDjf0voeMhIkirn6O008QdqlpEfgEjiNnukhnIkR0tYmWSs/35tPebeDwJ86PqMPDSPimSsXjlWolvr0tyIjTbU4CYzkxaB42OlE8hIUj4+ddiTVrcI7FG0xiKaCVGoE213YiXGgXuOtHNwK0f9Dns6AGGaJObnSA2XGQUeclvozSUMpw6yhuqarN6sEbp95N4eZhjRaDssrzeZmS+TP1rBabk4XQcryhP1PRq1HpWTcbdnMp0kk7LIdVuoxQbZ0RROMklywGWXieJATiz+zrLbR7keImGhhQFSgF7OY04NY5XTENQJreK+CfqDQHRtMaZIahr6sQnE3ATR2k14/VugVKyMc+Mi8omP73uvvhNq4TTtLUkvJZB6AjXIqTsU6I08SqoyFTcZeW4sEnZbGk1EIbLVQw26q/2mi1d3URse4W99jtzPPRO7LZkmYyN5djffvZ5nFNIIQ4+bnLpuvNKTA/lnqQgbXUKtz87v/S3+Wo38U6fInJlHWAbNr72Nv9uk+9YShBI9ZWMN5Qg7fcJ6F2HqpM8ewd9sgCA+V0ODIMLfbmCNFSmeOwb5g+vT+Mqb9C4eUE+tC0sM/cJTP9BuV22ojKbuPqhoQ/fuBXgnqtXqIvDYeznmvr/tQIfmlUql8u1b2yqVivZ3LchHQXioOKSbBqnhPKlSbj8gGgmLwtwYjaXNQ8cmijGlUYYR3a16PLMVgtDxcBtdEqUs6aEcZ3/9p6lfW6exuImmaUReSL/eik2JgxBp6LEWCwol45y5lU7Q34u7Io3kYVaHDCPmnj0QqYr8ALfdi5uyXB8VSaxMct/cJDteflfDcXH6DP5ajXBrAz3qoBsSrVQgavUR0wtEqQMWiDY3DfXDsxeRSceqkrfOy0hiDbpCQcPr+TRvLLKx0yVjSeodh3rDIQoUy2s1tLpPOpVGKIHjKYaHTNKZNLXtDqWREiMz0zzRlIhCCq/dxVlbZ2xSkEAjsjJEVpZbipEAmgrRhIJCFjIJ9NFSLLs8GGAN6aPhEmDfU5fm/SJ88+JtGjQKf30FnnoEo3b1YPWDQrgOYvEi6vQH7v5muklk3DmzVkrFKZmly4gwQKXSyFNPQilW+lRDEwOFT4jcEG+vRyLloKc8ZPM88k8Wkc9+kG5N0Gwrum0He6JM8flHMW4FVM/B2LhBrhzRvtHC32oRuV6sl2/oKD8k6LkY5RzCtoh6Ltu//2XCdp/+pWUwdYx8mu7bN+OeiQFZQNgmei6FljAxyzmc6hoxPxKMUg4VBAhdY+jnn2L47AK7A2ppUGsfCu4A/naD/pU1Mmfm3vf/673iVjH1Xq8/aPxELvg9ws6mSI8U6O0cnskUF8YP/T377CPolkFjcRPdivPe9esbtNd2cRqduOs0l47NrpM2KEV2vMypT3+E/NQIKpTUr62TLOfo7TZx6nEzlYpk7Nq02yQzViY7WiSRjx9sK5MkWcxiZQ4X/rITh7siRx9eoLG4Saqcp3hkgvqNDaxMEs3QSRazzD7z8Lt+d5Gw8U4uIF5ZRviCSLNRbRf99UtYqWm09MFsRT8yR1KL6L90HoIQUS5ifOgDhzot9d52TK/ULfZWW1z++iKi4xPW+zSVZC9wiEKJLjSiQBJ0XaKERq6QY2x+gnzOQvN7eH0fLZkBM8V4Ksl6q8ul7QbdtuSIcMhtbmOnbHS/i7SyhLmR+MbNJtBHSoQ7dUAhtIHBx+xYzPgZ+Mrq+N/3AK+UIrp09fA2ILxwGTUU3rZNoHwfbt5Ajc0jCqU7bPgg1p/pfOc6hB5G1CPSbEjmSGUV2sUDRo3o99De/DryIz8fp30sG575GKz/MWHdIZl20RM6aAKLNsLp0P3bb9JtWlhDw5AfxdvYo/7XrzHyK8+C66C98gLCcyjkIDkf4S71MMs5IiWIXG+fsaPZJtZogbDZpX91jaDRjV+LJGHUIWz3ka6PcnyEZSAsAz2TRE8l0AwNdC1WvFTx6kvPJrGnR0hMDx+6FkGtxbsh2Hv37Q8KSgnkj0OA5ydywYew8LGzLL14nu52HU3XKFemGX34sM61YZvMPfcoc8/FUgNv/Jsvoga6M6F7q3VbMPlEZbBd8sivfYLS0UmUlFS/8BJ7V9fiGZimEXo+kRdgFwZsGAXFuVE++d/+Q25eXMFtdEiPFvFaPda/Xd1XFCwujFM6MnHo3OxcmlO//Ay16ipB32PkgyfYXt/G80PGH1kgUcjQ3arTvLmFkbAoHZva96V1Fq+TVhJpHuSEpfSJrl5Fmzksd5z8wKNY07MQBCjXR7XaKNtCpAdNSTIOZDKS3Hx9jdD3GS0k6PbSrCzuoojQMvGS3On6WHmDMPCwk2WyuSQijF2gRqaHwEqiQkWj3eVLr75NGEZoKGQmYnltg+NHYv615ncInRRaaRzVd7CeexL58gXk8gpeGHBD01g9f43y2g5nZmZIbLyFCkLk7BG0k7FZunJc5M3YY1efnUJk75w5H4ZCJ9yXhJDoMYvkkFaRQKKjhQphWhA4gCDc2EVtrMVuVJcvI2am4ZmfQo3NHvoEs5Rl+NES4UtfQ7keejqBWXkMrXGwivR3m/ib9VgNdC9F9pPPoWeSaMdOon/6VxBf+CLaVhelaWi2QGjR4LgumCVUuwHpEhgm/m6LoNnF2l1EeE6cAhIadiFBbszA6yn0mWHCRoeo1UdKiT09jDlSwL2xifTDQxSTyA2QXg/lhzHlNQgRvoGeSmCNFREJC8Io1v7XNIJBETbzyDtMvgFzOH/HNgDrLraZDww/Lo5O/EQu+BDsXJoTv/ghgr6LZujo1uECWBSE7F68SXerjpG0Wf7ahf0lt2YaJPJxgMuOl0gNbrpEIUNxEIg3Xr/K3tU1Qi9ABiHd7QYqlFjZJHY2hW4ajJ89Rm5qmGQxw1Bl+tDnl45O0t2qY+fTd/WCNVMJxh87xvbNDV574Vv759d48dusn7+OVj/ggm+dv0HlF56OFS29O0WilIpTR7ejudtg5UKVRr1DaXuboV4HTYtNmo2zD6M/dIIoNYxRv4m7uYNfbyMGg5Jtm1QmSqx327RTIYYUBD4oEXHm0VHS5Qnwu2hCcezhGUbHC2heB5nIcWVlk3BQ7EsldAxDoysl/V6f1GBg0YIemmETYiKSGlplgYZl82dffxVXShKpBM5qDfOvX+PUmeMI3UDunEfvdNGOLRD89Zf3g3P0xluYzz59x+B2AImNe5uJSBC7U+k62sQwcv2gkU2hI2dmMU6P4X77JWS7h9zcQvd7sW69lMjlFfTXvob62N8/nJN3eiS6q4gzc/GkQAhw68hO/LlBs4t786Dw767V8f/i1f3GIv10hcRwkeB3/iVSgR7EnHmh62gJm1iXQMUiYYOCr9A1RGMntu9z+7Fxd65E8XSZVrND0PYxyzkSs6PInktifhitu4cIXTTbROhabLkHqCBE+SEIEVMdB2Jy1miB3OPHMSdKtL95CSXVgF0Tf493kyowyzkyD8/TvXBASbbHS3Et4geIH5sUDT+RC35XmO9ycymluP5Xr9LZjGUCvFaP1uo2MlL7jU5mKi5k3kqlJEtZFj52dl/ed/fiMol8hvZGjd5uK05NDKRflVTotkno+vvKkLfD7zo0b24NBpLvrm54/Y0q0dYOqtlG6BqqWODiW0ucPn3swGPV89l64zrzzz+GGJnEa26hRQHmreaiQGAcPYIMIxqLm6xdXuJ6dQnb0tm6sIjWblKZHebo9DCFQobw9Qt08jl6jkvx0jaB3qHvBchQslvvMTqcRVoa1rDJSthB1wTdZkAuneI/+JXHEVaSjmuQyiSwE3GwkUGAMH38XC6eZUuJ0+ijpjJolkV42wCktPgY3wP5wldoVpfY3akzubHLBSNBb6LMrOcQBCGNeovCcJyvjq4tIRvN2FDaBhmA8n38z38R7aEK2lAZvXLkgDcPGIOZ+y0IImwCIgyMpx7C+cq3CXebgECbGEN//DHMqSFCo4D82ldR9nascnmLzaMUqtNB1DZQ0wem1aKxExt7OB7hIGiaQzkYSqD6+qG0RagnCY0Mcm2X+guvo2eTpI5NYY6MoD/3NMHFS9AM0aVAz6bITIzgXunFBXQ7GacJLYPGl94gt/EmSdmJazZSIpo1rNEEY7/2U7S+fQ3pBehJGzsrcL7+MkHLQZMCy0qjhobjomzHQejaIOjrSD+MZ+pK4W3UUZFEOT56NoV0/X13J+DQoHU7Ch85Q/LoJP7mHkYhQ2Ju9HvwTX5/CHbqBJt7d9/hB2D39BO54O8j/K7D4otvsPzVNzHTCTKjRXQ71nrRLf2ge1AIRs/Mc+6f/ixKSjTT4MYLr9HdqqOkZOO1q0SeT6/Wxu/24wdK09AsI25cMnV022T8scOu9M2bWyx+6fV9M5H1V20qP/c0iUIGgYz532io28om/cvXUQM9cgWEzQ6BG+ula7c9EE6jQ+B51ENFRyshu01Eo85CMUPm0ScQ87Nc/fOX6W43uHL5Or1Oj+kxk2efHaKQH8fpBogwQmYDLq/WuPFHn6PVdNm6foOFUpa8sOhsOeiWTtLSkZrG0RNjPKxFbO51iRzFwuwwyXQK7BR2MYWM5H4qSoYhKpTMnDzG9ZVtomaXYLtFbavDmFIkt3dQmRSYFtGAxx5eqNK9ucPORoNmq4vf81jQAl7d1HH1iKRtEqtHxHlwtVNDLN/AHE5ilIfB1PAvbuMvNyCVRC2vI5dWMH/m4zF1jzjxcoDY51UM1u7CVKTmEoQEKKHBqIm8NanLFFDzJ5E31+L+gtsgTDOWVLj9nZMZgkYH58bmfuDwturYo8cxzn2UcOULRK2AwMjiJsYIOw7O1bU4zZRO0D2/SOmnzpJ88qPYpTJiexWxuw6aTjJboJR2icwJgnaEu7SFt9OgF7royU08S5GdSGFmLSIvIgxMUmcWSD20QNjsoqctav/7v0JLJLASCaQf4NX64PfIPLKAkUlijBVovPAdnOoaUd+Li90JEy1l4W3VscaLRF0HGUSIARlABSHu2t0dk+zxEvb4gzfVuBu04e/Cohl+byya94OfyAV/nxC6Plf+9Js0V7bxOjGX3Wt2GTo1i5VJ4ja76IaO0DWKC+M89k8+RWdzj83Xr7F94TpREJGbHqG1vI3T6OC1enEuUgEIhK7HLk6GTrKQ4ex//Cns7IHui1KKlW++fdgpqh83WB3/+EMYHMxgY6kxGxUElAL3UFFF1zUyhBjvME3OjBbZunqNdEqQPjUf1xKCiB1shj90jr2ra3QHxhOeFzA7ZTMxnqA8nEBIRbZgk8/Z6AmNY8UiM5rJleoONy+FXNms88TcGOnxBFEEhck0pz44S7fWx+04FDMJIqUx9dg8WjqLMlMgDDS/S7C9GztalUuEVpGpoxOc3Onw9h//BSjFxkqXk8OjyLpLYDXh7JNgDISstncJg5AgiEgKjXwYEAlBNgyo2QmKQK6YR0Uh8voSGAJrPIFqtvDrHcyTk5hDNlE7va9zr+pN5Mr6vgKlQmOQ39inaCol0RobqKUqcmUJXao4BbOzhqYUTH4KAO3IHNGFCejvwqBeIVJJGBlFDb8j3VAcprsboN+e18akedNh6ANDaM9+ksZf7RPg8NY20RLWfuenkpLWy5dJHplAnTyHOnku3rHXBs8hkS8zPFbk2p9+i351DRXERu8ICEONvmujC4PI1fH9Ns7/+zcUP3GW5PwY/tXr0O2QEW3w+wSORGpJkD2M8TJDv/R0LDnwr79IFITcEnERuk769BzawMlMT9tEPXcw4RExw8bQ3jVt+KMA+V2KrPd67fuFHxu54Eqlcpy42FsG9oB/XK1Wrz3Iz+zXWrTXa9i5FEPle6c76tfX8XsOdjaJEAKlFIHr099pEvTdmOdO7AiVGSvjd3rc/PJ5lFI4jS4yknjt2NxAt83YAccP4hm+oaPpAr/do3hkgtLRCRa/9B2yE2Xyz8eMl9Dx7tCsAejvNg4Fd4jTBhKDKJIcnyjR7bk0O/GxqaTFwyfmaera/mCRyGcYf+woW9WDMV4zdCxDp9+I00pO/cC4IptNMzIGicSg8UlEpNMGuq3RbLqEgJ7WWZjLMzOZJwgjcsMpRCDp+xHJ0QyWoVEqW8iyFWve2Am0XAE0A2mkCZc30bUApQQXvvom7cBg+hfyTM1N88S5h6lcuorj++RTSTQh8OsK4bWwPnDQ2SlyGZK5NAnXJdFpkTF0HM/nTKfFXi7JaD6Ntb0DIkIzApLnZtBsHRwX2fOJ9jrotoaxMEYU3WZQ0jsYMkNMNCI05D4DX/W7EPqo3UF6IQrQOjVkcRJqG6gg7qMQloX5858kOj+OtnQJzdIQx08gjz98B5NGRZI2E1jJBEbURWoJPKuM2u3Q/PpbBLU2RiGDdDxUEKEnLazb2FXSD+lfXaP79k1SxybRBrNk0rn4Z4Cg1iLqDfox1MAZynAI2g5SptBMHd8aQgYhjRfPY376w7irNZLBDroJke9jaIqM6bPXShFt7tH+9lXa33gbBmmaeE4T2zJKx4dCnGvPPHqU7ltLqCCMJzxjRYxSbt9f9kcNg3XaPV9/0HgvcsHPAf8YmATWgd+tVqs/SKmCfwX8i2q1+nuVSuUfAf8P8PyD+rD1b19h8zsH40fvxhrjzz62r+fyTgT9uMtTt0zyMyO0VndQUtHfa5Eq58lND8eFLyDou6x96/JB4dXQkZEkcGKNDd00MBImMtSIBjMlI2mTLGbpbTeIgpCdi8sYSYudb1+h/PAREsVYliB8x2wmVXp3hodGhEzYJKbH+aBp0O65RFKRzyQwHznFVOU47dUddNskPzOKrsc1hCg8bE+RGHDu0yMHxdzJqTGsRJ0o9BHEKYW+F7G528ILJZGCpAtDYzk+8uEj1HbajBeymIZOsxdRsmxk142leKUk6Ck4OY6wUshkCdXqYBgBfiS5sLLLi2/cQA81Lvf+lNPPPMkHnjqHmbQJoii+xoMBd6XbY+fLL5FKp/jQs2fRHzqJsbzGkCnoCQ3LMlG5PI8KSXGkhDE9hujUUK0OyafmY858FKBsC80yEXYK0KEtDnHLtPHblS0FfszER6CI0DGdAbNF0+KcenDLpUrGee7bG5GSSYynPghPfRC4e1AQuoY1UsTf1fCJ+xFUJPHfoUZq5NOM/EfPUv/ia/uG3WGrh3N9Ay1p0fzqBTqvXmHo55+Oc/gMzL2XtrBG8xjFDFrSJho03bW8MpIOSRmCnaGfGCMwYxaLt7HHxu/8FUm9hakgankIIYncWFpDtxTOYnwtgr32fnOUkvFQKEXMmtEMneSxiZg6qWuE7T7CNmJVycrUj5xV3z7uU03yQeJ+efC/DvwvxHLBrxB3s/5+pVL576rV6u88wPO79fkjwFngE4NNvw/8VqVSGa5Wq3dPwr1PeJ0+W29cP7Sts9XAvLxyBx3yFvIzI2y+EQ8IqaE8iUKG0PEoHZuku9W4Y/8oOAiU6dEirZWdmI0jZTyTMQ2cvQ6gUFLgdx2MhIUc5OMBuht7XF/dpdvukSrn92WLb7VkK8BLGFx+rcrkwji50sFMTCIQSIwPP0n49W+R267F4k5zM+iPnMbQdYZOzOzvr1Dkhoo03tF6nR2Kg0lhbozC7BjN5S0sy4SeQbpgEgWCzdUWG/Umq3stel5APpfg0ZMTzEzlODYw9DbRELrO/FiKVCPArw/Os+kStVzUjIWaHEMTICIHBSxvNVhe3iIgYrfZI7+1x+ULV0hn0lxY2aS/tIouNB6fn6Led7iRSiIGA3Ft7SYfev4j2M99iMTqJtboMIFlUZQSsVtDeB4ijOsdqpSGvkvk+mhWzAQSuo55ZIJQpjGzAts2iXoeUXk0th88BIEcPGoRBsLx0KSPzBWh1UCz7f1ZqxqbRRgmB4Y994/8R86w9+evIG8xfHouxtBhymDY6uEubpF/+hRBrU3Ud/FWdmI/g5l4YIocn9Yrlxn6mSdxbmxS/5vXYz2YtB2vsOZGiVq9uO6Bhj9yDP3IGFHvNikLqfBWdkmfmgGpMIaHiBotwkYHDA1h2WjSghCiVh+jlEV54X5zFJEEqUhVpih/8gmMbApruECw16J/eQ1hG2QfO0rmkbt71v6w4W818O9VZH3/hh/3jfsd+v4r4BPVavXNWxsqlcofAp8DHniAB6aB9Wq1GgFUq9WoUqlsDLZ/3wN8v9a6Q8oUoLd7d/39zFiJySdOsPmda8gowkzazD//GHYuzdU/f/nQvrppMPXBk9x44TUA0sOFWOKg78UUx+06yzsNNHOwDB/MQp29NkbSor/bJPRDQsfDStp4rT52Po3TcRg5M0dhbIh+p8fV6iLbV5bRCbn2xjXOPX+WySPjCBQmXhziMxraT38U2fdA1xC2/c6vNoAgNzGJrut06jHrw85myU/FFE2haRz95BO012vsvL1I7ZJHPm3zre9cpb7X5vziCkOjKXJ5myCMePXCKsVCmmPHp3j47HG6noGVTKDV9nC3d/FaA7UUkUErZJCYqPYemh4hTOiHIbVak8XLi0SRxLA19po9kt0+X/7iV7BMi4Y0CVpdbu5dxRovMDE2gqnD8VGDYsant/gGuZlZoiNTaE6AAcjNLSRxrnvfyk43BgVyhfQihGWiZRNEToh5ah7dzIHrYSRsRNAnvPkdlGEhyzOoZO6O6xgUpjBW38KYXYBEArW1DmYSfXqe6Mi5e92a94Q9XmLs1z6Gs7SFt1ajf3UNb20XoRcOUi5A1PdIlXOM/qPn6V9bJ9iL0ze3a7UE202UlDS/8fYhaWEVhCSPjZN/5iGc6jpGKUPmkQWErrP7uW/sDy7KDzAKaTA02osumtdCIFGmjWYZKDSctk3Y7UEkEclY3VJJiRysWvVimqjdx1uv0b2wxN5fvoK/24oL60GEv1mn+eJ5hj/94fd9zR4k9NEyurh7H6g+8uB5+fcb4MvcWWStAj+8EvV7RLn83ZpRDpAxBVsv2XcsoSaOjDE8fHcn+OG/d5aTz5zGaXZJlXL7rf92GLD8ymUiPySRS3Hs42cpzo6Sz9isvHIZt91n6tQMR59/lGQhw86VFRpX18iUc7RWd4nCKE516BrRwOFGG8gVBH2XMAyofvMCoeeztrjM6V/8EGbSJjmQU1XKAhVx7c1Fjj58BGS4ny4CELpAG1AB7wYVBahQo5ibQWjzCMNE3KaN7rb7uM0usycmUY0WwW6T69d3qe1K9tqSVjMgjFxMQ0c3DKQSrNZcTj9sITRJqZxFNto4ro8eSpJDNloWhBGhggjT2kYLfISWQvodws4eN9+8wrXVXVw/IJQ66YJJr91ifGaC7YurCMvCGi4ROA6bWzV6MuTs8RL4WUI/jZIBaSsk8dQ8zis3AZDjwwT9Ptb8BBCh+iHS9dFEEq1sQyjBthFKoGoBtqUhsklEIYNsbKGCDrbhQ9BF7LTQT34wlkPu7CF78bJEGy6hhj6E7NSgPIQ496FBuge0we93u89irfsWyVSCRPLuqonbV5bx13exlcSttQmaPfIPz6EnbRAweXYBeyh+fzVegOoqQat36D1SsyMUUyZNJSF9MOin0zamGzD/8Ufh448eOmboP/0UrfM3CLsuiekhNv/0ZTqXVwnbfZpRjrSoYeghgTRQkycwvD5GMomm69hjRTTHQ/oB7mYdkbKwMkmC6+vsXlnFyKVwLq4QeT5GOoESAs/1EUfHKST0u16zHyZ+BPqc7jvAfwP4PyqVyn9drVb7A9nK/xV46cGd2iGsApOVSkUfzN51YIIDjfrvir29LvI9LIky85Nsv7W4//fwzDDG+PC+3sU9YVh47QNfXHt2nKOTIwR9N5bkFYLd3Q7acIm5n/3Q/mFtJ2T9xnW8dh8jk8Lr9BCWGTNahMDKxLP1yA8RRtzNaqRtVi4t7dPywr7P6194mfT0MNlyfsDciKl5ruPTrHew7fjf3t1psfX2MpEfkp6bplyZPRT4b0EnwLxN+l8BATaSWAFz9aWL7F68iVIK3TRIjxbp9Twcx8PzQ9rNLqbS8LshtfU+/a6kOJYmaSeRISjps/Gt17nw9gbthseJZWTAQwAAIABJREFUE8McPXWMdFoNHJ1C+v0+muei54YRUqIM2B1cBxkpvEjgN9s8MjxCt9HD6R2kOKRU7NWb9H2P3Jki3WYLr9tlajhJ0Izz0MYTU3gNSZQbhQ+cw3nzEngeWjKL9fAY3neqaL0QLZOAvk/YCTCPlPADiXQCkC5auxn3AjkByouvl7x6GVUaw+jd1tBUq6G0NHqpHP/fIqAf7x/0oTRs33GfbW9u8/UvfZNOu4Ou65w4U+GJpx+/4/8VdR22Xh50MgsNbayEt16jubhN6tgkuadO0VaC8MZ2LGaWT6M/fITWC6/HxV2hoSVs0qfmaPQCXCX28+3ptE2v55EcLd1xfkop/PU9IsPEOj3G1lfforPTon1jA+nGypCdVAGjnCHaczH89sAkXJCYGkFmk4SAt92MBfC8EK/Rxe97WCMF3HZ/oJsUEbo+wjKJ+h6t5R3qTYfRbOr+ns3vAk0T72kyeC/crx78g8T9BvjfAP4QaFUqlTrxzP0l4D98UCd2O6rV6k6lUjk/+LzfG/x+40Hk329h+unTFOZG6WzsYWVTHH/yOPXmnSyV+4Vm6Ni5uzNxOhs1brzwOuEgMBi2SeDosYtRpNBNnezEEELUUUphZVNousDt9JB7LXRdB8sgiEKivTahlGSKWQwtIq72QK6YJWkLJIrV167zxr/7GkHfx8rYZKa2ceo9pp++0/rM4KBw22126NTb+H6Eni1jBPKQiUkUhLRXdzDTSTLZFK7jIRQkUgmUrhFJCb4kbZqcmCwhuz6tSzt869VlfE+SySWYfPIEoR6hDA2sBK7rsbW5TaPl4EUbpEpldjd3uby0g53KoCV0EmHE+NQ44zPj7G3WuL1S4PkB5XKJYk5jvJQglTDwQ4VlgHA7KMNCNxSpEgSpPjJRQE1+ACltVL6EUhFEGYLLVbR6J15NWQbaaBF/pYYY0tHzyXjkkxH4scwACEToozn1/XORjSZyfROkgOFptLGR2K7v1uvvIu0URRFf/quv4Dju/t8Xz1+iVC5x9MThHHQ4kH2+BWusiDmcxyxmGPnVZ1GRZPfzL+Gt1fB3mhBEpI+PkUu10PptMA2S5x5CG86DppF/6iSNF88fEAISFqmT03TeuIFmGSSPTqCUYu3//BPar12NVzu2gT09Sur4JPbkEO7yDkpKjELcdKaPJLAmyygvxJoo7RdJVRjtSwQLXUNFEbjE8gWmgTB1VBQNirDxitYcKaElvnfLxAcBOZha3ev1B437lgsGnqlUKlPEM+eNarW69kDP7E78BvBvK5XKfw80iBk9DxTZiSGyE/HDdzf2zPtF6PpsX1hk7/o6fqdHc2kbBCSKWRK5FLmZEYZOTNPdatBa20VJid918Tp9UKAbsQJferhAXUVgGfQ7PaJOXLzN57J423XI2/gdByHg5MlZ/L5PFIRc+KOXYqliwO24+NfXMFM242ePYRx6YA7kdRs7dXZXY2pfFEneevEthlMZjFut8bcgBBPnjlFJnWZpYwcXScos0Oq00WREVodHp8bJKYP21S5X/uo87UDDTuiUjpcHXHFBJBVhECAVJFNJ6k2Hy1c3sDJdRkZLhFaGbt9lbCTPyHCWXNYiLbs8+5lP8scdj+7uLieOFGh2uzRbHR5/ZALbEhQLCQxdwxQSlIx1XqREyRCztULkd2O3JgRhYKPsLPpTTyImJlHLSzE903FxXrkOhoXGZcy5cRKVPKpTR8MHAZEykYksRr8R67CjI1c3QCr6ns+Fr58nOzNMbm6K8SPzmKncgDd/GDtbu/vB/XasLK3cEeDNoRyabR7ihgtdI31qFs0yqX/pjf38vLuyE68g1q5iDUekJzMkJyZhdxm5WkLNVmKp4OE8/Wvr2D0HZ7XG1r95gVQ2xJIdgkQKxyjSfOkSciCTHXUcgloHs5QlMTNCUIsptLdy+eZwHnssDsy3jlFBiOr7WBMlolY/nsVLFef0hSBZmSQYUHGFETf6JY6MU/zoI/wo44et7fJeaJIF4FkGAb5SqfzF98P1+35RrVavAE/+oD7vQUKGEVc+/02aN7doLG7itXt0txqYKTu2/BsuUD4+hZVJ8eF/9kmu/vnLrLx0kf5eC6Ug8vxYCkHXmH70KB1NUdvei6maQmDZJrPHZhiaLiKNCGEYDI+VsGyT2vUNQmUQ+iEHrTeCKIhwGh1C139HgBcD+76Q+mY8L1ZKsb60xY03r7HmSYYzGcbmJ0hmDhqvEoUM04/M87HP/iIv/9lX8V2fo5kUxm4Ntddg2shQv9bgWxdWoecjlcSLNLoNByUVkYhnOFEUQaRwW326zR4bux1EWxJYWSwNGt0etcBDdrOEo3l++hPnKMga/+A3f5XOpVfxel0CzaTb3sMiIAhCWr2QTMpgJBF3GaObqDBEeQ5YFiJ0UWYaIUDv7xLa2Zi+OjcNc9PIepPgz/4ajFhqIkJDXl1CS09jZiQM7Oo0W4faTQQhQkTIfghSEkaS166scaW6h3FxieTsKowu8ouf+QXsd0mt23cpfNuJO7drpkHxo4/Q+NIbhww40g/HolzuzS3c5e24WSmSJCyXrNXAUmnCzT5uq0HbySLfaJL55RzJI+MYxQz+Zp1gp0H9b98ka9YwCyHmWBkRNAlXLqCH9j5TCE0g3QB3bZf0iWns6WHcxU2MfBp7oow5WsAaKVD+2Sdpv3IFbyWmFCcqkwQ7TdA1orYDYYSRTJM+M4+RTZI+MUPQ7JGYH8HIprDHy6RPz9xxDX5U4G038Dbqd9/hfeZoKpXK/0BsyH2mWq2+fa9975cm+TzwJ8SF1WVimuS/qFQqn65Wq3/7vs7y7zCaN7dwm919aQKv66CUJHR9en6AlBIzZVM+FncryjAiVcrSWa+h6RpaKgGouNkobTM9NY630UBGYBoao6Uy6Wya9soeC08t7GvehG5AZ7VGr6swsxm8/mHOvJ1JYr+Lfk2AhSGjfQ58q97mwktXUEqRwMduNdm70GHi8YfQTJ1cySafdpHdOhPzk0wdn2VvI86mqaTN9EKesaNpthsdpitZ6gmJu1nD9SJ2bmxQ3z5KeaaInk7R7Xr4fY+L317k4tVtbjZcMiMRBEtEzTZJIkzdREpJbavJF7/4CiePT/CBhSWyoou+MAHJLJ1Wmn67TWOviR9ElEdH0K24gzParCObPVQUImwLbWYcEhLRbWC4XcTWCrI4QTRyNBbU2nmnS49ARAFRow//P3tvGmNXep/5/d737Hff6tZeRVaRLK7dYi9Sr5IswZFlSbAUZ2a8DSaDGWgSBBkgX4J8CAJkgDGMAAqCySAI7GAAzww8ih0vsRzJlm1ZrV6k3slussnLpfa96u73nn3Jh1Mskk2qRcmS1W31AxBk3XvOuad47vmf933e5/88kY5wXaQmkK4NapbYzCBJEEmICDy2Wx43bqbS2TAIGdg+cuiwdGOZk2fvzbGv1MpMTI2zuX7bGVJRlPtuC2DNT2BM1vA2mmma0tjdss1gtwtRhAh8CsUeJDGRGxKHaSi6kXTo9mu0/uI1al96itgNcJZ38K+uEnW7WPU+YQ+E0kEfLSOSiFzWod1NFzmFpiLCiKA9SEM8AHOmTvb0LEohg5q3KDxzBsUyKHzsJOHxSZRiFv5Q0HOuEex2SYIQxdKp/8rPUfn583gbTaqffRxUSbDd+amlNP0wUEerRO+holF/BBXNgXX7E6R1+AefwwMe998CX240Gr9/xwf9A1KP+JM/7En+LMLr2zQba4RecJj4FPkhcZhyinEYE/lpU4ffd2jf3OLRf/EFIHWv9PrO3Q0wQiIVid3s4doe84+dYr+xhpBpiMhwr0Pkh7S3+4zMGfQ222y8ucSw7WBVSzitHrEfELoBasZIaaGHj/Jn/+cfsnplEUVVGZ+bZPL4DGeefhgza7Gza9Nrdrn51iKu4zNp95ghxMxnGQw8jLUlxj99hvFzkyh+j2jfRYstPva5Z9hZ2WLQ7lOxPEZaq2C7eH6I1ARe2YLMBPFOl1gR7Ld6jJ+oI72EnettvvvCWww7PVSRyhCD/SH7fRdFxFTzFtOlLJnmgJznEb/c453Fm3TmKnz2c0+jShU8h3zWImcqVEcqgIKuS5ydAcE7iyiJi7AMhKqShAl+YwvtrI5wByllEofI/VUSIYlrM4j8fdZSpAKBB06IklG5xbDKYZfENIgTncRU8PbabK3ZhAcJSqgKslJCVSWmLlAI7yvR/bnPfpIXv/US6ysbjE2O8fCj56iOVO/ZLnZTL3Vp6ljz4/e8b8yOkjx3MdXhhyGqEiGlIHY8hJHO3KSISPJlor5D94XLmEfHCHY7JFGMqt5hhWCnyU3GZA3XbsMdduvGZA19oopi6ShZC7WUJWj1iFyfsDfE/39eQFp6Gs13wLlrtSKJF6DVCiRxjFYrEvWGKFmL/EduU1HWzJ2NZO9fxAd/3uv9HwYLCwsGac39VeDbD7LPgxb4CVLN+534Y/5uNPAfeNj7XRpf+24atUdqK+D2hhj5DL7tEgxdkig6HI1IXaU4O4Kz36V8ZIyxj8yz+fo1FF1F0VSiIETLmYcNT1algJ6zyI+VGe51iaOIztI2hekRVl9ZpLnSor++R+gFKLp2+BBBCLSMgbR0jIdm+ZPf+UM6u238g47a7eVNEILm1j6GZdDabrK9vIHv+GhxxETkkSkXkIqkVDSo5yLixeusDXYpmBr+SBEvW0SdLzN+dBKOgnPzAle6CUE3QCQqV1eaOF5IHCbIrIlu6VRHc6y/c4Ph1T3GopAzpSw3/JClHY+qmsEOIgZ9l5iE4ydHGNveQfFCojjBSGKmujZLKxAlcerhIpVU1mhkCR2X/dYApeegLHYRN/bQShJtJEGUCiRuQLhvo9b3oJAhTm7dIjFa6yaJ9Il1QVK1CJsOt9YoxMgYIpsg9VtqI0HsRxBFyMgnUlSEVNA/8SRHl7pcbHZIDA1ZH0EqgtnJIl6/xeZihKUdQWAc8vGe5/Otr3+L7c10/aO5u0/yLnbX22zSee4tglYfJWNS+NgC2dN3e8YDlJ4+Q/+bz+N7Jn7XI8RA00OEmhBHCf4wIspXGa50iGwXf7eNv90m7A1RhCDJFojjLlLGh8qt3Efmiecz9P5qhbBnY0xWyRw0ON2Cv9uh9/JVlIKFWsii1Yr42y2s+Qm0Sp6g1af/+nXUch61nEXqGtLU06jJpW2yZ+79Xd7veFCZ5G//9m9PfeUrX3n32537UOD/CviPjUZjeWHh/rO3d+NBC/x/AP4b4N/c8dp/Dfz7B9z/Zxpbb14/LO4AqmWgOD7WZJHexh5SkcSKgqIpqJaBAAqTI+mCKmkBf+Sf/SJv/ruvMyjlCL2AJIrIVIs89l9+hrf/v1dIkoTizChWrcje5RWy40UKUyN43SHt5W0iLyBTLZCfqrH3zipxHGMWc+SPjXPj+jIXvvZt2q0eoRcgpUBISb/dY2txHc/xmDoxi2EZzJw8Sne/gzkYULJuj0HCIMS3B+RiQWLkaA1tdpodhFDYvLjHqU8+jZCCV7/xBvGB10prt8tgr0tZFwx3higFAzujs7LSJREKQSBhvcmxhQlEYrCxu4OlQcZQSArQ67rQdjGCiCBJEAIMXYEkpDj0GfYGqNk8ihIjLZOVrsLKSpfXX2lgrG1jSMlni3mStT7+Wh+RH6LMzyIMjUTPECU6t4LLFBEA8iCsOsH86Bz+fozo9VFKedT5GeLVdZLdm8S+TxyAjGXqgX+QDJWoOvHEMSpHTD49O82rL77G7vYus5U8hWKeOI5pNdtElwNmjx8nECm19vbrbx8WdwDHcXn+r17kl3/jSwghGLR77P/R86i3As9tl9Y3XydoD7BmR9Enq4eL4ErGYOSpo3RjG6YSCAvIeA9VT/A9SRBr7N2ESOmiZAy0aur1Ig0N/BCZMeknE1RyXbSSRe78MeTUDIWHn6HwGyqR4yFUheGlFbovXQYg9oJDzl8oaW6re2MTYWhE3SFRz8bf66SLs80++liZzMnbZmrvZxrmvfCgBf6rX/3q8/d5+38m5dkBWFhYeBJ4DPgffphzeNACfx74rxYWFv57Uh+aSaBOmtH6nVsbNRqNj/8wH/6zAu9dTSSQesCf+tIzaFmdwVaL3cvLt6eqlgFCUJgcuWv7j/3L/5y9K6s4zR6ZWpHaqRnGJsrsru2zffEmQDobiGOsatpBaRSzjJyeZbDdojhdp7+5z/7yJkEYofT6rLWayJyJM3BSc7MkJgpBURLiJKGz30bX9QN5ZDfNiI0irEoJQ/rIKMLMZWjvNMlO5TAnC3gKZDIaZKG/79Pd7XDxudfJFLKE0kxVJqRrC27fRZYy5DMagePjNYesFfvkZycRFYPXN9t8+ztX6DsRPT+hUK8hYxchIF8w0FRBLmPS9QL6tovmhwgloVow2V3apDdUMMsZeqrgxsoujStLrC1uUtjvUCqXuJHLcvrAq4YggCTGqRRpupKi3aVQKiJEDESgmYjAIVHT2ZM1VwbrNnUgx+rEgw7R3hYkEVGiQKVCN9JYbCYUZ6eY0tIH+OzcDDNHp3nhWy9Qy8tD+k0ObeIrN+ldaKBNHkF5+DQba5v3fH/6vT6t/RYXXr3I7usN8jf3yeWzzM7PkrSHeKu7eFstzJk6xniF6heeOJQj5p54mIzoMljrI02F3jUdL/GJp6bob7r4w02k7mOemkHJWXibTeIgojA3hhi4qKUjuFkD6/wEnD1GnL/NJStWuvCbPTXN8NISYc8mbA8QBw8Joae9E3EUw9AliROCVsrtSMsgCUIi2yXY66GPlVEsA3Nu7Ee99X6qSIQgvk9fyZ3vA/zKr/zKs1/5ylferUp89+j9E8ApYOlg9D4F/MXCwsI/bTQa3/x+n/GgBf53+JCO+ZGRHS0fBmLfgp61yNSKlI+OEwcR9TNH6K7ukiSpqdfI6Vkqx+6O2lN0jbH7eG9MPXGawtQI1//8FfyBi5SS5rV1siMlijN1FE2lNFMn9ELWr65g+z5RkhCEgu5Ol5JfJAmi9KZLbk/+BWCaBnbfobm5R+B69Nt9VF1jemGWrVKZc5bEtEyGwx5xxsSRWipxAwQCux/gDAXdpU1y5QJSMYiNIiJ0sXSN0IuQfohqqkhLQSvpPHRU0CvCm69vcuXSEhlNRSLoOT5Rs02hXMDrDSCKGJ0uMjdW5a13NoiiGCkF2bzFQMmz+HobRe3jqwY3VcloTTBfFMw9NIK/a3DjWpO9uIKcP0LSbqLVswwLARvaELpDOq6NtrHHqTPTaYiHqiD8AUnoEpulNFjkjusgclnkseNErU2U2EdkTa7vNnlx0cdLVLiyxan5azz10RNIKdP/ByFxvQDT1BF+QObVS6hRRFgsIu1F4q0d8hmTd2sxFFXhnbeusLq4iuwMCDsDugOH1Tih7nAY9QjgbbUYXlohfz797gRWldZKQrDaJXJCeksdZKmE7A0wJqpYcUISROj1EvbVNcK+jVAVjNEyYcam/ImHsUYMVKcN3SaJlT1MeboFaeqM/PKzDC8tM7i0DAKCVp+g1Sds94mDCCkEYaefDmUFCCnQp0aIhy5EEebsKMUnTyHflZj2QYG73cbZeg8VzcF98uUvf3n9y1/+8vJ7HavRaPwW8Fu3fl5YWFgGPv9jUdE0Go3ffZDtPsT9MfHoCfqbTdzOAEibnmaePYeQkvHzx9m9tIzTSlNxpKZy6kvPcOQTP6S+VwiSKKY0O4rfHxIFEcO9DlYlDeE+9tmPsXN1BeeFN5DVHJ5zYAyVQLvVIVfI4QepjFAAilTIZU1mF46wvrRB4AXYfZskSQj9AM3Q6BVKvBrHfOTYDGHOoqsPcTaaxCJGUSWqUNhp2qyudZGagt0fIqWkPjNGougY+Zjx4j6aChgKiQIjRZ1EgZLhkQmaiDhB1xQEYGkK/b6NkBpKmKCpCv1hxLe9hIppcTRjMnuyxiBbYGt9CAJ0IYjDgMzAIcpq2Ae9anpeY3LMombqaGNZjMfriIrJcK/FaJyw14sI3ZDVm00qhsXYTAVZ1hFSSbNkQ49Izd6jWheJi1KvAAl7rR7PffcGiWZCeYJ6XpKP2/R3tyhXy8jA5vTRKt956RInjo+jb+0hgzSTVDuwLEgGQ85OT7C+sZNKRg9w+twpbjRuYl/fIOwMMD0fdRjT7NlUR8dTR9JKjiSMEKqSml4dFPj2c2/hqyWYyWK/tUgkM8R2iGoEOMvbGOPVtCO3bxMe0ITGWCVdwFdVkqUG+m4Pr+3SvdEmCCTaYx+l+OxDqHeosJSMQeGjC+TOz7Pze3+DWhsQfvcKSZguQBvTIyQCkjgi8QJiNyDsDpGWQeUXHqX2+fdWRUdDl+HlFaKBg3FulqRWum8n9k8L2liZ6D2sjLX3kRcNCwsLz5JSNXf18TYajd/8cZ/U3zdoGZMz/+ATqa+MH1Ccrh9qzaMgRKoSo5hFz5oYpdxd3uoPir3Lywx32qgZg8qxKborO/i2S+SHzDx9luJ0nV63D8UMCpAtZgjdgFAVDMMAo5ChHEZ4ro+hqkxMjnLuyYconp9DGjrNzT26u210Q8fKZYjDmLXGMqoiqM3WcBIwW73UHySKSBCUyznWuhFIQWWsRqFaZOP6Kk7fxspn0Os1Pl2IyXgDVpQITVcwBg5c34LLG5whZsXS8eOEKI7JmCoBEZPTdbR+n+7AxRtG7KgxzkiJLQGFM0eINm3yukdk+0ihEGgaJgnSjcFMS7KfJOSnyjz69DmyYzqCGM9zIYlQScglDh3Xo1q1cPyAsO3h2AFdRaFSKWKWKsRK5sC07Tbi1l6qb+536a+sYyUBTgDEEWPFdCRq2w7lA8fJ0bzgxLnTNN6+ykSrRc2LmBofgzvkddVCns/98mdpXL6G53rMzs0wd2KOpQtXCbtDEIK9qkGxF2D5B+lfORP7ylraQVrIkjnI7Y2DEG89lXlGbkgcgXpg6gXprEstZRn9tU+x90fPp52pB7RLEqeZrNHyKv5Ulq2/WSL2Q6ShEb55Gb85YOzXP5W6Qd4BqamMfOlp2t+6QP/lBkrGQMlnbnfcxglhZ3ioHkqiiN5r16l85rFDyufdiAYOu3/w/KGNwvbqDkzXKX/6/A997/yk8JPsZG00GkceZLsH1cH/78A/BJ4H7uzX/2k3an1gIKSkNHuvvGvvnRWElIeBIADD3Q7D3TbZ+oNFei196002X79G9yC+zCrlqJ2aIYli5j/zGJX5NBB67Pg0uXqJwW4HISVaxiBnqFTrRVRNxc91MfwYTVUZnZtk4XNP4iURiqpQnxnDczycQVoIHNvFNFUe+8QZitUcW8MeamUUM9/HHThEQcjl5QEdV2H86Cj5A6vi2dNzjB2dYPrELNXJOmq/SfMbf4466LC12sJeaZG1NGZrWSoDh+OhyyueJBsrqElCVTOYmp/FX11jcODfgkwwVQ0vjthvOoxKsFSJKyQiisF1iKKEfEZDKhIvTJu8zp09glYQaRhTkmCICEMFL4jRlQShQXvLYa6U4/KLl7mx1aI3M0Gia5x9QmdszmLl+k1yWY3xyTGq4xOo3Rbi0stg29T9hEeUPl65yt6ITkZLA/wsy7p98ZKI0+dOcfLsSfztXcQ3nyOT1bGHt343gZyeoJrL8tQnn7zruh+fmmTzlXQhM1IlrYrBwvgklp7DXbntfRO7PsGBE+qt7NO7Ol1VBWOyhnVsAqQkd2oK5dqrlHtvkam2sf0szlIXp7mKyOpYRzSa390mPLDuiG0P4m0oj9B54RJatYAxVUMr3zb/UgsZKj//CK1vvIrQ7n4AhO0BSjUPB7MXYWj4Wy38rRbW3L1ST4DBW0uHxf0WhlfXyD16HK304/GS+dvig2Q29uvA2Uajce9qz4f4oZEkaTK8VBXiILzvNpF//9ffjc7aHs3r65ilHHrWxB+6OJ0BVndI7cQ05aO3bxDN0HnmNz7Lq1/7Dm5niGpqTJ6ew7VdXNuByTpxEJIEEXM//zjtbo/95S1i2yOSkvr0KKtXl1F1lcD1OPXwMXKlPIEfEEcxwxA8z+KVv36H/e0WcQRmLoPd7XPisdMYByHlE3NTjB6ZIApDNls+W4UJrry5grrfQ0fgejHdrSEPj5UYMVuMOgl+IjAVlWwhT7exSXF+FG27RRBGGLpKVlMII4nvRpSqOva+BpbEdwMiO8YcyzJaKdDuDxGKRrGQIZO16DshmqWgSBCKQi5r4HVsgjDG9UKS7QHhbp/eXpM6gpGVHVZmJvn2t19Hf+kilqmDogLv8NGzM5z312HQgwTyumSilsGOPaQVkrdUhGFRqtz2aE/0fJo/KgTmxBjRE48iGw0Y+gjTQPnYI4jc/T2Mzjz9CPaFRZb2donjmOlqjfn6KEIIpK4Rdm2krqLViin33bdR8xlyD8/Re6WBkrNQLIPI8dDHb3u6FPQm0eXLCCnQSlkKrX00VcXvZynOTSA7ayT23eRUMAjwLi4StPpo1QJCCIpPnyH3cJqf4O93Gbx+nbBnE7keSs5KzcaEQGZ0pK4eZq2mN0CMML8/9x7eR7gAEHWH75sCj4D3TOX7O2CTHrTArwHeD9zqQ/xAbF+4wfaFm4SeT2GyRnF2lNbNu5+bWsYgN35vEwtA5Ae0bm7RW99FNXX0JD5YUBNUT0xhN3sEtkdlfpwTn3+CwPboru2iWQaF6TozJ48wOjtGc3MfK2dRHq1i94c0Xn2H9k6TYXdAEEb8ze99k0FjHeEGhH5ACJhH6+QrecxsqpopVguomooXRnRbfbp7XVZvbLG+uJ0apCkSzQgZdAfsrW3xqS+cp1bNUK9FDFs7vPjnb2L3h/TbPRrX25woKugHdSOIYD+WVGanqMZ93DBByVmY5RyKIokTlYnHztJaWqeY13CViJn5KvOzZaKdXSCgkM0jMyrF+Sz7BYPr3SZ0XOI4YbcdcvyUhtA0XD8mo0eARDdM8iWdwVAyVRKcGfPYurmAY5p+AAAgAElEQVRH4ieIjIFQdGpdl4utDUqmIFfNgxQkmSKXXtrgoXMVpGIikhA0SdFQ0WSGq+t7vNQJ0RUYu77N6YUZSmMTZCp3K0SUk8coPnEOf2UXcplDrfn9oFULnP3MU8y+fv2Q3sgcnyQ8iG5U7yh0aRBMeqzC4wso+QzOtXX00TTMOvEClLxF/iNz6BsvYx90LSuWilGRGEVIcnkyJ2sM3upjmPvYpAU4FiqeI5CJe8jBJ0lC93tXsI5PkgQh+3/8ErEfYExWcZZ3iIcuxmwdY6ySZh3c2Dz0kgcw58fRxyrEfnDfRVZjsnqYBnX4O6oK+uhPPsj6QWHvtLHfY5H1fg1tP248aIH/Z8DvLCws/Cdg5843Go3Gd+6/y4d4N5rX11l/+crhz52VHfYba+g5C3u/i1nKka2XOPKJh5H30f4O9zpc+9p32Xl7EX/oIlWFkSOjdPe6lOcnEFKSHUkXbsbPH6e9uMXycxcPuU6rnOfEF57EsEwm5m/rjDP5LOc/9Tj9do/nfv8vUVSFwdI2QWeIZ7soqkKSJLTeXsYtmYxMjpAtFdhd30c3VC597yqdvQ5bK7v02v205R2I4xh36DA7U+fJnzvJqbMTGJaJkNBbW0SLDkZhCWSLOXZdhwkZI6IAqUhC1yaKExxDI1YTojAkbPY48fhpjn36USoL0+QrBS6/eIHO0nWqBcGLlxbZbayg64KTCwqPn53B7Ue4gUV2ZIGL3+qB63JyYQyZL0HiMnBi3CDB0qDb88gU8hxbmCQe2rhhSFkL2LvQAxmBZ2OREAz7GLkSQkRpCpHdxB8OCXYC9E6fRApkOQdSYWunw2aQx3Y8trpD3mjscWllQHlkn5///AgT0xNIt4N026mKyRhHFHJ3dS5/PxQ+dhJrYYpgu41ayafKl+sbtN5VWKz5cZTMHb7uJ6fJnpy+94BRCJuvoJZyhH2HaGCDE4CioY+ZqdSxPorTN9DmTZwtmyBSEKGHdWr6Lv49CSOCZg9vY/+weBszdZIwIuwM0UdKZE/NUHjmDO1vvMawsUbsh+gjRQpPnGL3P/41Yd9Bq+QpPXsOY+q262b29Czuyu5h7KBQJKWPn3tfOUvqo2Ui8f01/Hq9+H3f+3HhQQv8o8BngY9zLwf//nX7eZ+hdWPj8N9JHNNsrBG4PiOnZrEqBYxChlNfejYN87gP1l68TH+7degCGYcRdjv1wPb7DkYhVV4UJmsUpkZ4+/f++i7rWKfdZ+fiTaaeOH3Xcd2hw9LbN1i6dIPWdhPDMsDxCW55msdpcVUSkH2XaKVJd63FSneA3R9iDxysnEXgh/juwSjsoDiFQcj4dJVKLYeZvc09q7rBSEnStWMyhSxmxmJoO9ga6F6E8EOkiNDOTWB2trGHKWUllVQzPn726KH9cqleYfmywitv3eSdxg0sxeczH52lOpLh5m6TmakqedvhyhvL1JKApz59mvxIFncwxCgaDPt9/CBmpzXA7bQ5d2Icc3SE9V4IrossWwSWhgwSFFKP9MnREsV86gkEQBRRs3TMSoFoOEQEPjgeoVRZciCIYXJ9l1knoBlJNtd3KFZrXLrwDlM1E3WwnV6rOCFqbaBQIMq+dwjLLWil3F20ROb4JEkUM3xr8SBmUCOOYjovXiZ39shdSpd7oKgk47Nono/dWCca+hAKHF/DaAuMKCY3lcdWakSOhjmeYCWg1gqErbv92IWUaOUc7h0jbaHIg1F9RPlTD5M7iMCs/9rP4W+10kVbS2f/j148/O4GrT7Nr7/C6D/+9OGiq1AVal94Iu2yHThMPjRL+13eSj9tJD+AonlP+ubHhAct8L8JfKHRaPzVT/Jk/r7jli4ZwGkPCA48aYQUCJnmrnaWt6kcm7zv/sPdNqFzN1PmD1yqZ45QmhvHKuWxqgXKR8ewm717ArgBBjupyVVnr80rX3+B9m6bzk6TfLWIlJL9jV2MjElyIO9KEg79ciDB9kISQFUUBo01tjb2qM6NIaQg8KM0VEXAobgZQb6QYXy6dtd5qJqKbkgUfFQ1YWS8RH9zg7BoEWcN6vUswUiWKImYfmyapTe2UYQkW85TO3/sLm/98blJLrzwBu80rhP4LuNjGfScScsNyWZ0vERQES6na9AyNNprS1hykriQpbG5wf7Q5/nXVuh0+pydq1It5+n5kn7fRtcVCmFIeaRAf6tLoZyneGacJ07P853vXmSv2QUhyVsmT585QqKHMDJGPBgSJQJ/8gSrW8scXdzEtn3sIKGcxFQ6XXp+gDO0UZwWwTtLhNfW0gDu6To8dAIyI/eM4oPOAHdxC6EqWMcm7xqV34lbI/T2ty8yvLxC0OwRDV26L1xi9B9/GnOidt/9AJKTj+KttyCfQ8lk8ZQSzkaf3tv7dDaHVD71EJVf/zxBa0DUtzEmqiAFe3/4ImHvNjee+8hcSqsdHUu18HdAsXQyJ+7oVhUiPQ7Qe/nqXQMTSNU/7tL2PfYL+lgZnTJq1oT3WYH/cXvR/Ch40AI/BD6kYv6WGDk1Q2d5G+DQukDPWaimjj908ToDdt5apDA18i7L3hRmKYfT7sPO7RBvzdLTEe3544f0DICRzyAVhfgO7TSkHbGbi+v8yb/5Kq7t4vRtht0+umlQmxpNOXXbpTBbx2/1iYI0LhAhcJKIGAiiNNxbSkEcRvQ7A4yMxS3dgECAEKl1QMYiP1KhUCtDfAfHmrXoD8JDr3kBlEoW8/MVDENBURXiMKbTG7LRsRnkNCQCpZLhxEfnUPrpbCg2SyhalvxUjWKtRLfZIp+3UDWVIIwIoxhLSdByOmZBoaAZqFLy6uVFnvncxwnbewjfodls0+na+FMFcgbY/T4iTgg0STtvsa3rDGolHv9Hz6IX8ijNdb54vk6zlyWMEkbKBSKRI0ZgN/MIDRIU1KlHmFv2UFaa+IkNSToTyVkmotdj/InzhDdXCS7fDk0Jt5uEg4soM3f3Qjg3N2l9843D4td7pUHti0+h1+4/1Y96PfybK2l37o0tgoM+jNXf+n3yjx7HGCtjHZvAmr+7oS4Rkv3lmNYbMZHtAdskro+iKdhDj+7vvkbmu9vUf/kZik+fOaRl6v/o49iNDaKBjTldP6RUzJk6xSdO0X/9OnEQouQsyp986PvTKd/HmuC91iPer/hpywwftMD/T8D/trCw8K+A3TvfaDQafxcPor8XKM6MMvfpR9i+cIM4jIi8gMLUCMOd9qHE0VzZ4fIffJuTv/T0PQlQkx89yWC3TeQHOK0+iqpQna1TP3PkruIOoJo6448cZ+PVq4evRX5IZ2WXS//+G4StDqJgMuwNcIcuYRDR2t4nX8pTqBTJIcmdm2fx0k3iIMSRCX6sokQRfhwhkGiaTuwH9Jtdmpv7+K6HlAqIBFXX0HUNM5eh1XRYWmwzPZ1DUw6izDSLh37+WUrXN1Ov+Ifm+NN/u4LjBFTKJooU9PsRa2t9BiJHEMR4jksYuLz6R9/gmc98BCtrIN0uUX6SQbvH+GidMAxpDQNi0hCSjGWQNVVaHZv+MPXLN3WV0ZEsL796lZm6hW232d3tAoJq0SIII2SSWsgUShnCKCI/V2Ww20PDI8lMk7gDIKFWlqCpYGUQAUSOwBxV8fYThJ5BHp3lfBCytrJFFCV02l0M0yCTzZAZqfLwYw8Rfv3Pbl+4JCGJAuJ2H9ncRVTraRNbktB98fJdI9vYC+i9fJXa5+5tCFIG28jmBsXxCHu1iz1Mi3vsBrjNbaKBQ/ahOewbmxSfOEX+0eOH+w7evMng4iLhgTY+7AwgTkgsPVW6SIlzc5P+hZugSErPnMVd26P38lXCZg/t4MFxJ/KPHid77gjRgZXG8MIivVevYYxXyD1y7C69e+bEFIM3btylMFMy5gfOsuCDRNH8u4O//8Udr6UuTNwnY+xDfF9Ujk0eUjAbr15l8/Vr9DebCCHIjVfQMgaB7bF94SazH3/orn2LM3X0jEFxZpTsSAnVNMiNlKgu3GexDBh/5Di58QrdlR2SOGb74iK97SZeq0/SHkLXJhbpqDqOolvJfoSdAbNnFtB0DY+E4cBGqgpOGLB2bQVN1cjks3iOhxcExHFEfBClli1m0QyNKIxQVYXKeA3NNHj1+QbXq3me+sUnkZYJUmXljQssvrVI4AdUxirMnpwmo/bQdYllabheQJAYTJw4wsb1VXTNRIYuNy8toYqIT/7SE8QJvPKnf0V7qYu71ycfaTR7Ni++uc7TH5lmYmIEx/PZ2esztAPyGQMpBZalsXlthxm9xo2rO8R+jNQ1xuoFMhmLTs/G0gS26+P4EbmMypPnZ1BGRsHvgIC4OEZMgpLYCGLIFUFPEJqNXs2TnHwcoWuY80eYPTHHTL1K3Orgez5ipEL+V7+I1DQCqwTKHoQeMnQQuo4xmkVvvU0c1giLMwRkCfv3RkbeSku6E8LpoPR30oKsKvgdGz2bEHUF0cBBGlrqgz9wkOUcnRcvYx4dRTvoVRheWSV2PNRChqhvp8U9TtKuWEsnCSMiPyDoDrEb6+TOHaX59VdIDpQ33vo++3/6PcZ+49OpSdkBpK6R+CE7//dzh0lO/k4bb32fkX/48cMuVLWQofqFJ+i9cpWwNUAfLVF44tShl84HBcOdDsMPiIrm6E/0LH5GMfn4SXKjFfyenTpM6rcvx/26WfubTaIgojCZTn3tocPqxjarv/tnLHzyEeYePoH6rpsgP14lP15l8/VrCCnor+wivRCZpCN6PYmJDQUQGBkDKQS5bBbtQJpWLhdYXVpnaDsolpHmbWp6OvVUBEJXEXGCoihEByHDZjYDJOTyWcaO3B7JdZp9Vpd2OXJmnrWry1x59XpaGIHmVovR6TIT5QrdnRaRLbAqNcbndHa29kgCFykTSGIUCYN2j9bGNj0b9jb2KZVr1Mfr3HjjbSY9nxMa+NeGvCIHPPXEUcRKl2oONEUSB4KuE2O1u2RWNDZv7FMEoiQ1LlOJmaikmv399hBdJuRrVaZmJkA3SGIQ7R2SW6POW3F8Zp7mYEB3GBJ1W7Q7lzj7zHl0y0TOHyH4f/+cxPXQdR2BJOn1oVxELhwn3NxF0CMhQZ0sQNZC6BrS66H2N4mLs6iFTDqqPnDjRNPRR+6mZ2RzFW33KiL2QSpYk0X6jT1ggKKC1BSU7EFslCBt9bddiBOsuTHyjx7HW90l7NvIjIHMGMR+mPrMqwqx7aWmeJqKc3MTESfY19YPi/stxK6Pu7RN5l1KneE7q4fF/Rb8/S7e2h7mzO1FZWO8wsgvPXXPPfBBgjFaInoPJZTxflHRNBqNFYCFhQUJjAI7H1IzPx7kJ6pk66V7FkQz9+FV71LE2C7Xri2hKgI1CLj2+hVa202e+Pyzh9vEccze6jbdZhd/q83+6jb72/vEisA0DYTvI4MIXdU4cv4EhUoRI2NSz+fBCRn0h1x96zqD/pAoigiTBM00KNbL6BmT7l4Hb799yNELKQg8jzAIMUyd8miFXCntZgyDkJ3VLXZWt6jUq+ysbhN4Ptm8SW2iiqZr9DtDJp8+z5GHJYHnI6Rkde0lWtv7iNAlUtKRfamSUlex79DaD0iU9GFkqgpHVQWkQTGfo+T7hO8ssXFmgRPPfJSbb19JF+uikK3vLfJQ28HsbvBrozk2QoO9OKG52WSqopNIhXLepJKvIEno2yG+66LrWULNZN+RWJFDPmsSOCFKIU+7bdPeSUdsjg97m+usqjYLj57EX1lGOXk8DZKWaYNPdPEyyuwUyuwUPPsxePUlZCRQR4okB81QIkkgCgka14ldF/HGm2hqnPLe5TL5L90ugsLuoGxdIyFO12bjCF0MGPnsOcI/fgsZZ5ClIf5eJ/Vg324T2S5KxkRoCr03rtN54RJKziJ2fKK+g1YroI+VCZt9BAlB30n15vXU9yX2AqLBvXmxcP8R6ruL++Hrzv1f/yDjA9PJurCwUCBNdfqVg32ChYWFrwL/stFodN9z5w/xnpCqwtSTZ1j5zluHBdwsZhk7f/yebfMTtUMKZ3e3SdwZEnkhqhPhCsleHNPd71CslYjjmNf+4rvsrqaLultXV/Aam8gwRlEVkFAoFYhjn3bgsbe6jaqpnHj8NMfPHuPa177Hyo1VHMdFAJplIA0Nz3ZJgFwpz6DdQwiBZmr4ro+iKOimTrFW5PFfeIrQcRj0XQLP5+aFa3T22uTKBZbeukEcx1i5DIGfwx56zJ6eQ5EaQpGYWQsza7FyZZHjpydZ30vob21gGAr10RymkQZ01+p5mk5ArKdcrej2UvMvKTEUSeIHKH6AaA7Qn/wU9dhkc3mFTOTxhaxFf7+PKSIyXoDSd3HDiOSVm7QqOrNz9cPZkCDBNBQip8/GEL710jWcAIJhTK3n8ejoBLrexS4IxHgWGQXEQ4/ToxqR0yTp7SJb28RaBrQsSRKT+AH0BofXVpk/gjJqovQ2UMIuURgDkkRI7OU9BitDlJsrCDUm8UPM6RH0sQpi8SYcKGJkb5eNnQ5vvrPMxIhJMWcxOVYik0sY//Vn6K6lo2VnMZVkDt68gdQ1zKOjaXTk+j5CCMzZUfLnj6VUjRuQPTlN/tdOIjab7H7vKsQx0tDQakWMySpKMYOQgtgLD20IpK5hHb2XMzePjB7G+N2CUBWM6ZF7tv2gI+G9lTLvmwJPGvSRBc6SZgHOAv/64PV/8pM5tZ8d1BamyY9X6K6m3amlI2P31cJLVeH4Zz/G6gtv475yGeEE6HkLrzvA3u0gl7fZOXOc7JNnWb+2ws7KFkII3IHDztImRD45P0bxBDJrsOs5BMRkynkSRdLc3qdUK5OtlTj1pWe4+NZVFFNDipgwinB7QyAhjhNqk3VyxRw3Llxj2BsgDySgQkpGJuvkSnnGzh7l8stX2F3bxu4PUz94P0itGuIYd2CTyWfwXR+7N2R2YYZsIZtmhIYRnu3RHCpMLcxSXMjT290nCCJKlSwfOT+O1A1mHl5gefMC9sAml83iCEFJlxj7+8Seh0ig+NKr/PWNBuHODqEqKRYsjpQzZPYNhGPTcnxMRTKTVRFFgzEJuqYQBiFSSqQiUDWVMIx44YULeE5EbI5gL6+yEseUrBLH6nXaF5fIRTam4TNughlCkKSNXbJWIt7cI+7sEveHEIGs14hXN5Az6ZpMIhRkYEMcIqIQ4pBQFghaTby+QBn0QFVQtQTF6yDthOR6DM+ki6w9J+AvX7xMFMV0ujajtQw7zSGPjJ9EGTtOYeL2d8rbakIYEnZtvPVm6tFue4fdr/p4BX28gpq3qP/qzyE1FWV5Cze6t2QlYUxk+zg3NkjihPyjx6h+/mP3VcmYM3UKjy/Qf/MGSRihWDqlTzz0feWeH2R8kBZZfwGYazQa9sHP1xYWFv4pcPMnc1o/ezAKWepn77/U4XYGuJ0BmZESmVqRk198hu3ra2xeW8Vt9m771gw9rvzVq1x5/R06nR79do/R2Qn6W/tpYLamEOQzJH6I54cM/YDCSOkuBcPFb7/GkbPzmKUc80+fo9nv0Vvewh06hyOOzk4TIQXnPvEI+5t7+I6Llc2knaZ+yMrVZZpbTaycwbHzp/Ecj8AP8B2POE6Tl6SiYGYtNEOHJGF0doxHPvMsgSaQbockDlnvLNPp+wgBk1MVTp4okzUFtVqGRCokSUwmavOJ/+wUy5s+g81RTmgR7uV38GwHXUpGMybejZuMNyKGY9V0NrLdYqeSZ2JmhOG1VRCCXEElP54hLBlYRYPI81K1kJQouoEbghsKAlTcIGT75jW8zS6WobGlCo7nDLKlLOawTaRlUA+Ufjk9QbG7+IFLfLlBMvBSt8d6Gaplgue+i/5ffC71nXGaxFYFqfiEB342UQC9HUnoC6RUUGMbXXWQQYBwFaTwke0N4vIkN3cdooOL5AURq1t9EkUj31I4OXn3gMEYr6LkswzeXgZSOiVs9+/iwSHNVr21uFl86Cja9xoEd2QbmLN1Bq9dQ5oa2bNHUtuMhPdspip8dIHcQ0cJBw5aKXeP++TfF3xgKBrABUa4O8m7xof+ND9RJElC409fYuX5txACzFKe47/4McbPH6dUr7B3bZ1u3yaOYjRDJ5PPsrO9TybwMUtZmlv7bC2ukzcMxIHUzjANjFKeuD9Ej0KUvHXXZ/p3cKSPffYplq8ssnF9NR11kzYoSUXyva89z1vPvZ6OvrtDhLQxLBOkwD5odmlv77P09iJmzko5dSFTeiKOMS0dVQG72yNTyHPisTPoByO+OJtO16fOnabzwgUUCVKC7QsqYxUSTaSrub5NaDuIGKYmz2A8fILw2ATuby4SkSBVFXIZdtc2MUhwkgSkoFqxMD0bdaqEXsxgEmPkVIKCiSDBDiIyUYTQNUQiEPt9tI5HsuehbXZo+z5hGKDEAdJzifsCaXeomSH6SJ6uVIiSiFw2vSbh9UWSK1eRWQmRArqKUGOkERBHEfHaFurcBCKJU+MxM08cH3RsCp0o6gIBUXUEq3Ud4HB0rB4dQ+4uEZcnQTWIShNIuwOhD5pJnC3d1/Igsj2IYswjY4TNHkiBUS8TB7cXS9W8Rf7x29mfiqEx8svP4NzcIuoO07Dt9b27nCuFSHsj3OV7m5LuhDT1w+v99xWDnQ79D4iK5v8C/nJhYeF/5TZF898Bv/2TOrEPAZe++jdc+uq3iKMYIQVGMYvXHVKZn0CqCqofUTQtwihCkZKB79Fp28SaZGJ6BF1T6e93UQs5dEVh0B3Q80JM06A2VsPKKLh3dMYKIZh7+MThz357gOaEiAQ0TU0LvKEjpDwo6iINbsiaJFFCEASH6hunbyMF+J6PoqkIBFEYoqoyddGMY7r7XRRVQUrJn/4ff8Av/vMvMnPq9izmyJl5csU869dXyeaGVOs5MtIncW2izW389oAgTIhzFvtrHeKJs0yfWUBOTUC3lyYu+X4aFq1JsgWdSkbFVCVCyyIMBf3IBLm1DfyygrA0EkVhYHvUxiuoVoZgs4MMIkTfQ5M6R4c2zTCirankdVAiwbRpEgQhqqFQGctQqU9DEiO9LiIKCBc3IYoglghNQhJDEKJEfbByoKkkik4iZFrkgWFvwPLyDuQr1J89zfCFd4hqoyjZFjII0GpFlJkR1MkahC4kCUePH+XCaxfx7ZDQcZCxRqZscmT+3kIbOx5JHKOPFO9S4milHNmHjqbc/NzYPdJEqal3edh42/cvYOJvKWmMgxCS5AOb5gRg/gAVjfkjqGgWFhb+hFTVGAMD4L9tNBoXvt/2D3oV/jWwCfwaMHHw7/+F2/r4D/FjQmd5m/2rq/S3Wyx96800Ro80bMHrDBjqGnvvrJBEMcWZOpHjgevTdB3WOj0SRdId2uxt7lHJ58kZBokfEnVtCoZB6pkomBqrM/aJs7zy7dcYdvpohsaRs/OcezYNTPAHDt/7D39Od6+NaRq4rkcUhEQyNQKTikgdCg/OW6iC0En5dSEESRyTKJI4ivFsF90yiOKYfDlHrpAlCAKcgYsQAkUR2P0hbz//JlMLs4d8/s7KFle+9zaDTh9vtECpJkk0jbCxRhx6hH6q3RfdIYoq2L5yhbFjR1Ef/wjBt14AIIhisnM1lPkaei2PqQm8nT5hJU9/tkboRmQ+eQq5uUl/2EfXJHUZoDo2u/s2yUoL+i6xE2NURpgYK3Oi47Aaahw5I5kOdfKBwBwzqT00jrCidOotJLFZIrY9goEGPiSKCgQIU8U4NY4yVSIxDUTBJ4wjokwVtb3C9WvX+eOvv05/4NOxYezoNF/69S8yohqE2yVWV5fRNIUjB4lASTZ1ZMwXcnx0ZJKXL76E49iUszkenTiCfp8OULWcQ81b92jrrROT5M4dJWj1cZe20UaKd/m6vxuZhSkGb968ywlSyVmYR+7NPngQxEFI57m3cW5sQJxgHh2j/KmP3KWn/6Ag4Qdw8D/aYf/JLWHLwsLCL5HW4Ee+38YPKpNMDg70YUH/CaJ1Y4PFv34DgO7KDm5nQOQFKAdf7iQ5sDgQgsgPKUyNMDJb5+prDXYa19FUhdhQ8W0Xp90n6btUK0WEoWFmzTTGzTRQTQ1XScgIld/4H/956j9jGVTGa2wtrnP9jQbuXofF68tsbOwQBCFRmPrMiChG1zV0QyeO41TjrQicgUOhViKJEwzLYNgbEIcRUpGIA18bVVWIo4R8Ocfuxv5hIY/jBAVwhg7D7oD/n703C5LsPNPznv/sJ0/uWZW179WdvaC7se8gQYBDDjnkcKixJM545LAlBxS6si4mFPKNYxThcDhsM8K2dOFgyNLYmrDomZjwrBwOSXADib1BAI1esveqrjUrs3Jfzvr74lRXd6Grmw0QHBFkvxV1kWfLk3lOfv9/vu/93nft0grVlQpX37u4q5Gztdnixe91ee63nkRrvo20gIGHcD0CL8KkQ9issPXv/5jhI4ton3ic8L1zNGoVMg8uIAwF04oNQKzZAr1MgkhIFFPhSqXG4bEshbpCuFVHuD16lS4eFgw8WtUOW6ttlESXkfkpVM/jacdiblhBJnUyaZ2pEQMR1YhEnmB0ESXwkKZD0AEvUUETWyiKj7QtjIUh1FwCCiMoY2N4vTbV9TewDQXF93jtjfO4rkdnAEEIa5dW+PH3X+GRpx/hh69eQm6vIQKPk+8ZfP7XHiVxIE6j+PU2yfU2zx89duOm8iS9s9dInpgncn2CZgdvo46atMk+/wD1b721a5xhz42SvH+Bxg/e3aMdk7x/gexTR/e9Z7VUguwn7qP2N28QtPs4R2fIP//Ah25Kar16ll752u7r/uV1hKaQ/7WHPtTx/lPi58GieR9rMfNT3uKuaZL/O/D1crn88k3LngT+Qblc/ucf4jzff/zfA/4FcAT45+Vy+d/ctC4B/HtiRcsA+P1yufxX+x7oY46Nd27UrBVdw0zZeJ0+itR2u/zsbJKR4/N47R7bl9ZiHRtbQ3dsdNvA93x6bkC0oxWT1iAJ59sAACAASURBVC1qnS4Q64EbOzn3wcBF1TUMy9iVDn75z7/Pa9+IVfzq61XqlTpSRgihxNruuoaTS3LiUw/T3GqwdOYyqq7g9lx0Q2fmyBxPf/k5Tr30Ey69XWZzeX2Xahh4PkMTRXRdYWx2lGatRc+PZ4+KqmKYBtnhHG/8zcv02l2Wz15h4+oamazJg4/OksrnaPRhY63FiMwgWhtEOx6xQkrMMKJ3tkbisTzyyjKiWKD3T36X6ivfJjduIqREVSUSiVRA80I8z8f3IyqbLQxfMl9tx3Q/kUQUTLKaRrfrkUkn2Rqss3FpGyOEyclRKr0endWQxfmArGPHbd2qhjQd1Po6wYEnOP36u7z4ly8yd+UqRVNlIW+RSmmoM6OIo/ch0hmqlSpryyuMOyHewMP1Qja3GgQhOBYMfIikZOPaOi9/7xVCFMhPIvwBHeCNmsknzbiguV9XK8BguUL/8jqtN8/jrW9jjOQwJ4cwRnIUf+dZgnoHxTbQs0ncleotwmCdty+RWBiH4Vtn8v0rG9S/+w5C12JufaVB0OjcWbHyDuhfuNVTqH9pHfl8tEes7+OAuMh6+zB+fc3Xvva1ya9+9avvX90ol8uN/fYrlUr/FvgMsZrAr9/pHO52mP0d4Pfft+wk8GfAzxzggbeJOfb/cp91vw+0yuXyYqlUOgC8VCqVFsvlcmefbT/WCG5q9kgMZWL1SNdHUdW4MJlL8fA/+xK6bTL11H0EA4+w0Sbh2OiWgZl28DfrJBwbDyikUjiWSbXTRtW1PZ2yyVSS4ZuKYFsrm7z7w58gpWTQHdBt94h2G6siwjDO0R948DDHP/kQhmnQa3d58Y++AXlBfrRAeijLd/+fb5IfH4otCoey9JodUpqCbWhkRnII2yaZz3L4kYOc+vEZglBiZ1JMHpimMDHM6vllOvU29co2qYRC2gLcPnqgsTCaRVdDlNFR/G/8hKigo6dNpBvQvlRjwvWwen1IOshKDRsoZAxAIIWgL8BQIkLXo9P1CANJ+WKVK0vbzMy5RBEIBdThJCJnEwUhwjRQez6L949T3+gQCYk2lOfoUI4ojHDMOtKLiNJxYViEAbgdLrz6Fn/6f/8F/cGAnlBxqg2qDYVobgp7dAaRzhAEIavX1hhSB1iKRk9INEKypqTbj+KGKMDzfer1BvVmi1whRzLlxEbeQG2rtnsNrzcfvb9417uwCgK8tZgO6a7XEDv3Qu/sNVI7ZtwA7lqN/eCuVeHYNGHfRdG1XebL+5UfZRjRevUc1sxIbAso+EB5dKHdGsSFqt6VNv4vGjqVOq07FFnZuU5f//rXX9pn7b8C/mC/3crl8n8NUCqV/hHwPwOfv91b3G2Al3CLgby6z7IPhXK5/B5AqVTa73HjH7LDtS+XyxdKpdKbxNr0f/JRvPcvEjIzRbbOxEQl1dAYPjxDfnGCzFQRI2kz/cwxzFSs+a7bJge/8AQpU2XiWpXBv/sz1i+vxgqPEaQyKUYyGTRVpZjP4WVMdNvE6/TJFQs89nuf3dMtW1vbItjJo/quRxRFu08NiiIQQsFIWBSmRgj8gJXyErX1LTLDORKpBL12j/VLq7TrTYSqIKUknTBRt2pkhIbuhYgryzz0O59n/jNP0dlu8cRvf4HG1jaqqjI8Pcr5N84A0KzWsWyTlB7/ADwvQO0PcFpNhuvXCMankFKF8iauKogUgZM0yc1laPd6tC4sg+fhIBnO9iEShJZOdxDR9lzUKOT1t66xWe0CKroCE1kFY8d0W00miFQPXUoSiqBv2SRn88xnkpgnl3FED4UsiqYhUZEDF6Vd3f3BRrrJmbc36A/i4udiv8dAUVlWNaRhUFiqo2RTuJqGJgN0IjrdAYqioBka980PUX1nnbYHfdel3e0yMj/BxuoGta0aU7OTFIZjad3r5t0QUxOT9y/Q/snF3WVq0o51Z1q9PYE/2G5jFLP4lRvKpEGrh7tew9uooxVSe9MsQrD8R9+ldnE9LrQenyP92KFbNOAB3Eqd6l+/hrtUASGwF8fJPnv8rtI2zn2zNF85u3fZkende/HjBLuYu2OR1d4RCPzKV77yzFe/+tWV963ed/Z+M8rl8n8olUpfK5VKhXK5vO/IfLcB/iXgvy+VSv+iXC5HO5IFf7Cz/OeNafbSM5eB/dW17oBC4Wf3aRze5xH1Z0XoB1QvrOJ1Byw+WsIkor5UQUpJhxAxlqVnQ/HQGOOzw7t565uxcHSaf/zf/WPeevENzv7oFFGzx4EDsyhSMmj1+ORnH6Z4fJat1S1M2yRTyJDMpnZ/NO7AJZ22yQ6laVTq6IaGpqkEikBRlJirLsBKWKTTNpsXl/AHLqvlJTaurhEEAYZpoJk6AsHY7Ch9Q8OqNXGSJsWkhWNqTE8VOWgEJIppol4XGXrc93Bply4nB7NUrlzDMDXshEHCjCULxlI6RekxnHBQL5fx334RXQAjKYSux2mVvossJOn7EX7TxWo2qbwdkLyvQKQJNF3iagI/iuidXadaaREqCilT8PhCjlqtgS4j8rpEuj10O00gYjHjlCkJgVwugXpwmCQmmuyj2BkIk2i0Yk/XKCDwPBodF3Xgo2sKyTDAiUJc36Pb72FubFK4lmV8cozMiWmi196h06jgWwb5qRyqqrC4OMbIzDSvLUVoF1dI5dOk0kkcx+TKxSVqW1WmZsawbIvnf/0pCjfdl8NfeozBowfoXdtCzyYxh9Nc/bd/S6irBEvabl5Atw0cx6QwP0JhOEX38jprf/4Kqh+gdHr41QapI9PoqQTWWJ5wucKg3sZxYvpmdG4Zc2aYwoEx+qvxk4G31cRvdgkHPsLUSSR2aJCrW4hzSww/d/9P/T0MfeYBGvkkzVNXkVFE+ugM+cdKd5We+Xn8Pn8W3K0e/AsvvLDywgsvXP1pxyuVSkkgVy7HRYpSqfRFYHvnf1/cbYD/b4C/AtZLpdIScdBdB754NzuXSqW3uL3z00i5XA5vs+4jQ63Wic0oPiSGh1Nsbd06W/lZ4PcGlP/iZQY3GQhPPXmU+RMHOH/yLJXzS7AzQ9pcrVGrtjj06H23Pa8Dj99PdmKMznoV2Rqg6Rozh6ZJTw5T3Wryg//vJVbOL2EmLBKpBMlcmma1ju/65EbytJtd/CBEt0x0yyAIQoQSP/IrikpqKMOZ18+RKqTZuLxKq96i2+oipcR3/TgNpGl0Wn2S+Qxyc5MokmQtjVwywfDoEOtXN3nrf/tjXM+n3WiDhGd++zmmSrPoqTRDMxOsl5epb7dJFk1Kx6aYTESYwscI2gyurBL5PkrWQagGUbuPMA2UqRF6hSRs9OjhEVg2Vyp1rFMD5u4bo9kc0Hc9hB9gv7vM/YOQQS6Jpgr0oM9gSGNFV4mA1HYDJ2ERaSYiEmiKJJIhuiZQFoYJah16567AUgdFVTDmU9huH9cSrLY93DCiGAW0m12kotNstXE9b8cUxWN7q8LglMnYegP7Spdgs4IuJFtbbawDo4yMjaONn+Czz4zR+MM/odft0e262E6S+YMLNOpN5g4eYHxyFM8XbG214z6FIIxnyZoOc+OEwCCAcCjLYGkTcim8HS8BLePg6jr+ZJGtrTYX/+i7VC4uE0URmWwGJ0zQ77gknn0AZThN7U9/hOOYdLs3aLVrb1wg/fhhBteqdN5bwt9ugaogXZ9Bux/PvHdm7YOTlxDHFrgrzI7hzMZm8RFQre1vsH2738HPAkURH8lkEPh5mG47wJ+USiUHCIkD+xd3SDD74m5ZNCulUulB4FHi2fM14PW7FRwrl8u3pfHcBZaJefdbO6+nge/9DMf7hcHmu5f3BHeA1dfPUTgwyca1jVu2Xz579ZYAfx3bGzXe/ObLeDs2e04myWO/8TSJlEO/0+Ob/+7PuXZ+GYB6ZZtBt08ql0bRVIQQBF7A+MIUnUabiQPTRGHE+TdOU1neoN/pYacdJg/OcPEnZS6+XSbwfHzPj/PUO4NAGIRYjk2/3aM4PUrUGcPpdpifGyU1lEHTNN7ZqNLLm6yUl3bP9a/+jz/lc//kt5g5Os+hsM/ERIpyOETXdxlOqCT0gJQ+gI6LZkWo4wpe28d6/DByEKKM5NEPzLF1+ipXpYsvWyyulvHcPv1rPYLeAMNW6bZc1lbqHMQnh2S4UqdvWWyoGpmkRWbgU1U0Ik0gN7YILZtAKuhpC8/RUVQwZITImIjxDFun1hku5InqHQYZm9PXmhTHkqRtGEqY/KNHDb5xqkFNStKqwshIgYnxIZARotZgcHmZomEyGJ1GcQIKqsSensMqPUJPiVMwI2NFrly8unudLdsiHUace+8cp98+jWEaHBubZLjSJ+wNMEZyZJ89vscEJP+ZB2m9dg4tZRMujKMXUjiHprEPTqDoGtcuL1N+/d3dFE6j3mRscoyx4SLJY7MEzf0D7HXRsfyvP8pgpYqWdVAzDt13LhN5Pl6liTkRf46flRf/cUSEJLpDkfVO6/ZDuVzeBB7/IPvc9be+E8xf3fn/u8SfEOvQv7lTZH2EuOj7sUeveqtOWxSEMT1yH82Pm92ZfNfj9Mvv0NqoMvDCOG/t2Ltpl26zw7nXTvPgpx9l5fwyjZtyrW5vQBiEdOotEpkkumnQrrcoTo+SGcpSeuQIK+UlJkszFKdHuXrmMgAbV9Zwe7F4mIxiPZnYvEmgalrMyjENdMugvlGjMDrMXM8gPZQhCCS9gUsjkaK+ub0b3AF67R7vfvsH9C+cJl+rkk04PHhwR5/Fl9iWh+wGRP0d3rsQGMMaQhFoow7C0RChx1DepnJlE73gY9UiTE0wiBQGbY/GapuBByYCw1RwQ4k6lCfz0BGEqZHQe/SWrhK6Es+K2K736bh9DEMDo4hwJIoQaIEkKm8QXq0SdXsgJJudiG3LiY3BXRcPHaGpOJbg0QWHtzIFwgtLHMqm8VWNgaGSvLqCVFVETpIZT6JkhxAJCyVXQKRysYca8NDjD1Kt1Gi3drx3PQ9JPJgC9LYa/ODH7/HZY/eTME28zTq1v3qN0d97frcQqhg62WeOwTM36JNLl5d598++SbfdZWNtkwkN7JsETSvrFaYeOgTEs31rahhukrAWQuDcNxvfl30XvZDeXacPZ/A260Q3XePkzra3g7u+jV9txgJmY/k7bvtxwcdJquDnilKp9DvE1eAc8KVSqfQvgc+Uy+UzO8v/sFQqXSR+LHmhXC5/tLmS/0SwC2laq9U9yxRNxcomGV+YZPnsXtW963RGgHd+8BYbl1cIW12212usr2wyujBJce6G/vr2Rnxs3/X2iJddn6lJxI3cprxxOxqWSW0tfmC6PtBIKdm6tkng+URRhIxkvO9OMVZG0Y4gV8Do7BiGZeI4JufbSTYrbSxFR6TTeOsruM3mbnk+iiJSmkdrbY0LjSrqwGVuIsdCdhjizn2UpIP0ewg9IhTxWVqTaSKhEg1AG88gaxukgOmigb/dIFFKsxgIzlf82DpwPIu63WchazA1k8ZMOuRL89S6Ei+UBDLB0LxN5+RPqLci3OEkipRs+zoTQ3k8BKqqEG11cK/W8DouKhGRGaKqEZOmQtOKrQp7gwBdg05PYKkKWq2Bvw2DTy6gF1IMnTtPsGNpqE+m4++x14NkAmEZRPU1MOJrncqk+PLvfom1a+uEYcjG2gbvvPEuWxtbKKqC1XKJpGSz1WRuONaRCbsD3LXaLboy17FavsK3/vivUSwDJWGyem2NrSDkMZFG2Yk6ARL7Jpen/K8/jDi3jPvOVdSESfL+hd3jG2O5uLC+c6+YU8MITUUvpDGGMiSOzJA8NrvvuQDUX/wJ3XM3uO+Jg5PkPv3Ax7KwejNalW2ad5Qq+Pkrrv9CBPhyufwfgf94m3Vd4O//3Z7R3w1Gji/QuLqB2+rtLht/uIRmGRx54jhRGLJ2KS6uj81PcuTJ2KPTdz02r67RWNokaHXxvYDIC9goL5MdymLsMG2cTJxLHJ0bJzOco1VrIqVEN3QCz6cwNoRE4vZdbMdGSsiN5MmPFkikHVq1JpZjoRs6zWqDKIqlhjVNQ9EUfNdHRgqqppDMpsgM5ciPDWNYN8TLgs6Ay+fWyAxnkZsNdMtA7/pgC9BUlNDHSmkIAaphwMDl6mqdqXwGI4opjgyNwugwlVNnGTgRji6RUkNL2JhTY3H7f7cBhsPIzBhBPoHaqZI/fJCxlsq19W1Eu0l6bZvR6QxG2sYoFhCOSTYrcDd9Mv0QVXdotXXs1Q6zYQLvxCxaWielg4ek43rIgYeiK/SbPXIFi0CDKBL4nYBkzokHoDCi0Q8ZhDpzkwVW37xKXVOoXlpnKPJIVOtg6Kx4HvXVGpZlcHAsS3ZkCKHrSH8A+g5nE1BVlanZOOBfOHuRs6fO7Q7Sdttj2HYwtb0/5dsVJVuvneONP/kbetV4ADeGMqTSSWpb26wsZsm7AqmAc3CS1PQIkR/grtYQqsLkp44jjt+aR1cTFpmn7qP5o/eQOwN+9qmj5D/7MOI2/qrX4a5U9wR3gN75FRKlydsOUB8XOMUc0R0GqffbbP488AsR4H9VYTgWR/6zT1K/tIbfc8lMF3epi5qucf+nHuHYMw8CEvV9P+DQD+hvt9E1JVZDTDr0en06mw3yqQSKqnDwocMA5EeHePD5RxFCcOGts4RhRLaYRwqIgghFCFRNpVVt8OCn4+0OPHSYt779GhA/OdQ3a6Ty6R1VybioqggF3dGxnQTTR+d4/PPPsH55hUFvQKvWZONSi9blTZT2IGbYCEG/22d4qohFCI5OMOihBj3slINiW8jBAOn5dFyPVqXDRiRIZjOMyw0GkQZOBsVUGGSGyaRTmJYJ7vUBUiIRqMksStCHKGB4YoiRiSQoEJxbQsgQ6foIXUVJ2lhCId/poLgKoaKgZtOkFA1qLbTTF0idGEY2LExNQUqFrhnhIXEcEzsVK0sKP0CkzXiQDDy2WiEdqbM4XUC10szk8yieoLC6jhH20DSV05UaZ/0QQwfF6FN2I37zEzY5QBj2bnC/GVEUUVmvoGqxlDGAa8ZFzdHMjWCh55JoYznKp8+zurxKwklw+PghEoGg9eb5m/obYn344blR+r0BoabQzyVJphye+uwn4nTPX78ey2EA4U8uYD33AGoybpaLXD929BKC5LFZ7PlR3LUaWsbBKN45ePUvrdMrX6N/ZYOg0UXL7m2M8jbrH/sA/3HSg7+HnxNUXSO/OMHW2SXW3ixjJG2Kx+axdjoB1X2kVHXToDhR3NP5mnBspqbHSOTTzJw4yFRphlTuRl50/vgBBr1BnBYwDIQiqK1t0ao1dwcCgLOvvsf4whRjcxM8+aVPcq28BFKSymfotTr4fsDldy7QqtVRhMrCgyVS2RSmbXHw4cNYSZvXv/Fj1q+sYhoa3V6fjAC/1cTKpIlQwO3yxf/iSfQEXDizyvLFjXj2DohcBsXzadgZLiptRC5Fe7PL25caTBVNxsZT9AyLIVWhWe/iZNMYmolQNEI1gex0ke0u0rCIxufBySBFCJV1RDqBlojtCYVpggC1kMcJLQa9LVip4NSa6EEftaChGT7K5XWCuo06nMQwTeyUymAuTZC2wPdISIVADlCKFhHQDhQCKREy5Dunq1jZiIO5JCMDl3xrQL/aogW82+xhpGzCjo8ylcd3krz73hU+8cz9KLkJ1s6u8cbLJ6nX6hSG8zzy1COkMyk8z+PA4UUq61sM+gOcZIKZ4VGssQJhq4c5OUT6icO8/L1XuFi+cX9cKl/i2SNxgX4yP8S17Ru0adH3ePDxB/jkrz1DFEmKozEdd/Pr398N7gDedpved35C5Pq0T15AqAJ7cYLsJ4+TWBxHdSwSByZ+6j3fOXWFxg9PARDUO/QurmLPjaLfVBi+7g/7cca9HPw9AHD5OydpLG3uvt6+uMbhv/c0Zvr27d4Pfu5Jtt67SqNSQ0cwPJxnZHSYyccOM7aPGxTA9np1T/qk3+nFOu0Dd3e5N3BpbzfJFvPkRgrkRmIWRHFmjTf/9hU0QyeZTaGbOrlinqHxG048bt/FcmyqaxXatSaBYzE5bVH0AyJvgKko+KpJZjhNfiKFqirc/0SKXrtHfXsQ08aE4MCTJ7hwsY7I3viRz8ykODSjky8k8AJwAzDDAdXyOp4rCXyLEdYwew0EEX7k4NdTqCdGkNeuYjXOoeAizGSc2O+7SN9HOAnE0DDRX75KcHkNzeujJiRKEKKmNNSdGXIkA1RfItGxDo0QtnzCagORdEjoXfpeiBtIqm0fdBvPlVR6ErpVpuZmOZgwCS4O8EMINR0za6JqQDKNnFwkCl3qroafX6TrC77zje/uFlKrlRrf+asX+fLvfglFUdhY3aTf65NwbArFAoXDsxQ/d8Oqsd1sc+n85T3X3vN8LqytsgiM53KcmJrh3PoabuBTnBjl2U9/An29Rdjq4vZDjPHCHt13gND1d821r3evBs0ekeuj51Po+RRhz8Vd2UJ1LIzxwp48uowi2m+cZ/3/+vbuPsbkEFrawV3f3g3w5sQQ1tyHEyv7RcK9AH8P9KrNPcEdIHA9ts4sMfn4kdvuZ5gGz/3T36Ly6mlqa9sIIcjNjzFybJ4wCDjz6ilWL1xDEYLpw3McfOQIVsLacwzd0HcZMNehKApWMkEYhDE9Mmmjahqjs+M8+rmnuHr6EoPugEG3R7Z4g+2QSDt4A4+3v/sGmqaRHspi6wItqJGfSTBoxD6thfEEk48fxFDjNhBFFzzzuYdYrSv0ux75yXHsfIFz5/5i99j5FEzm0yT0mOZhaCBkRGPdx/c1ti/W4yJlapuZkoMiVBTfQ6ycI1w+jzWXRvG7CEJkT0UkbJSETaQYREGAt7VGOHDRcjoinUQQIL0ABhHSUBCqQIQRiiYQQYBERRnNogznCA0HZfMySROkB6YVoUiJpupkLA9VU+jbfcY+f5Tu3/SRqs3kqMa5d8/R9wOE6UG7SpQepjgzB4rGxfLl3eB+Hb7vc7F8iU67S2O7EUtK9Af0ewP+3u/81p5tu93eLXIFAJ6pYU5mcFeqLI6OMT8yippLUvzC49T+4hV6O7WgzntXSRycRLXNPTN4d7OxKz9wHWFvQNDo0L+4hp91qH/37RvF1tE8hS8+titV0D55IU4R9VwkEm8r/hz2gQmido/U/QvoQxnsxfGPne7MfmhWtmncK7L+asPr7m9Y7HX6+y6/Gc5wlkf+q8+yfG4VzTIwdnKj7/7gJMvnru5ud/HtMkJVmD9xkMq1jV0J4txoAd009qSBZu9boLa2xekfv4M3cNFNnUOP3sfMkXmK06MUp0d54LlHeOObr+yydAzL5MSzD7N28RpSSlL5NP1uH134oGj4UpCfSJAeyjIykcMxBG7Xw3QMBBJD8ZmemwAzSYSCh8LQZJGta/HAl0nEFnrpgo2qqURhhBlGBClB/cwGcrNJsRhSnFCJwhDVVjHVLrrTQ5oOSuDGQmCDADFwUSbmEEIBM4WSzmJ01ghzGjKdRTbqiFDE3qKKipZzAIkwNUQUIiOBcLtAhExkiIZmEUGA0muiCo9kv4Ll+WxvDlhsCzZH0yQsHTsZIH77ObxTl7HkBk8eGOGHS3VC24ZBm6HJSY49sH+Pw3WsLa+RcGwO3VeiUW+iKAq5QpZmo0lx7Ea+emi4gGmZuIO9fjwT0xMM3VeiV17Bq9TRcimcI9N03r5McFOhH+JCZ/LEAp2b0oAyijCKWbytvV30MggBSeMHp3aDO8Ra8Z13r5B+OPYY6J2LCQNqxiFoxlJSQa0FMyOkHjpA5jaKlR9XOD9FquBekfVXAMnRPKquEe4Uza4jPXV3BSYhxB5NmSiKWL1w7ZbtVs5dpfTwEZ780rNcPX0Jf+AxMjtGYXyYa+eu4vZcijOjZApZvv//fmu3EOe7Pu/96G2yxTyZofiG1E2DE88+ROXaJnbSZnhyBFVT2bi8CkC2mMf3AsJmDRHB0HiR0vEZwgBW3l2j+XqD/kYPE5g+MEzhoWmcJxZ3BI8idDyOf+JB3n7xddzKKo4isJ00TiaJcl1eodtHduv4zSaa2mV4NokQPgxcBC4oEmEIMBRAokQekW0j8lmEFfcLKJoC3Tp6SsdNWdBvI3M2Uc2Pm3jmCigZE1SFyEwQbG+jGjvCV75LqJqEQ7Mo26tIt4fhdkgGkmvLXdZWerEOS7PPxNMnCKWJUsxjPj+EcuUU84d1xp8SrFUaWKZO8cgJ5E6aLJtLU6/VMUwDJxmn6QxDpzBcYGNtE9MyGbkpoHvuTQR24gL9M88/zXf++kWajRa2bbF4aJHSfaWYn390BufoDFJKmo0W/a39Z5nmeB5rpkj/4ipCUylMD3H1z18jqHeIgh2jc0VBL6TR86k9mvC757Zag4evv4qfKqyZIv0L/u7TgVHMkHn6zoPbxxE72qV3XP/zxr0A/58Ymqkz++wJrv7gXULPRwhB4eAkhbsoVn0YZIdz3P/sw3uW3dwde+W9i3tYFhBz4DevrpEZyhKFEW9/741d+qZhmTzw/CMMT44wWZpm6cxloihieLIYP2pvr3LssUUUReH8q8u06gHddZ+w7eMTsXalgRQJGNkisTAKgEKInTB55kSKcDuPokp0LYIoRKoaAtCcJP3KeXr1LsjYO1UI0BUQRHEsEQJUFRQBYfykJBJO/FpKROAhvD5oGvaUQbDkgq0QJZJgmmijKaJIIs0EoW7RMQMShoqpGyAEMpFF2ziP8PqI0Ed2XWzNoNdWMA0DTVVI2RYrby8xk1dRrBRhfgqxE7QtYH4qrmGEVhIJvPz9V1i5uoRuGKwur2EnLB56/EEeefJhdEPnzLtn96RfFEVhau5Gf8R1VCvVHYmJuMs4m8+g3fSkVq1U+cG3XqLVbBFsNRntSk7MzO4OoEJVMEZyqI4VNzkB+eEU9Y0mhBGDpU0i1yf14CJDv/kEatKOHbTed+/czI5JlKZovVFGMWP/1rA3wF6coPjlp+54z36cDoJ1fwAAIABJREFU8XeRZ78T7gX4XwDk5sdJTxXpVhqYKfuOxdWfBkVRmDgwtSdFAzB5aPau9tdvI+2q7wiCLZ25vBvcIS7K/uTFN3j+P/8cmaEcDz33IOffPEO36zGxMMnkbzyDjOqE3Sb19hqBNUTQXwYtPl67GzIqVDrnVncDPAiU5gaiU0fbOZ9IhlBvEwQG0o0IzQxDwwlkBXxfEnkBdlZFkZJYoxYEAkI/Vn0UBtJMEJk2QjMRSBj04lmU76IoA/TJNNKXCEtH5LL0pUYoFBRFRSGCTIqrW30ODA8hOjWUTh2lcwmpapytC86e3aa/3SKTSjBi2ygywlQjdKdHUF3D8Lqom5diaeGbaJDSThOli2ysbVI+fR7HMUmmHA4eiYvlJx45sZuCeepTT/DmK28x6A+wbYtHn36EdGYv46RaqfL2G+8ghCCVjgW43j15iqmZSYpjRaIo4nvf/D6ddtwuqxXSLG+vkt6qsFAcQQhB5okjqM7emg1A+rFDOMfnCDt99Fxqj2G2c2yWzjs3iruqbZC8/wZvPvXwAWQY0j2zDGGE80jply4tczM+aqmCD4N7Af4XBKqukZ4YuuM2UkrW37pA9dwySEl+cYLC5x+5ZbujT51AqMqeIuuBBw/d1XmMzU9QfuMM/c6NnKxpm0wsxgKelX00cryBS3Nrm2Kiz1S6y9RzM0hVJzN3iK1tj6AaIrMFlNwWNNpI4rSJQCI0Dfk+1aUQDdHf26wc9gLcH5WJEgWklYJwi7SzSf6IAKmA7CJVG3R7pynXQ4QSYZtIRSNKFRDDo4TpYZTmJiQSoKjgDZBrl6DbRpgWwtIACWFEqBu756kJiSl90n4dpaki7dRukK5UtlldbrIlddx+wEqnTtvKcsCxsPIRTlZHM3TarQ7bzQ2ktkHi6JPkCzmklSTKjoGisrWxxX7Y2thicjp+ojtw+ABzB+bpdbs4SQd1Hzu+tZX1fY+zvrpBcazIdnWbysYWlY0tfM8jmU5RXByjZTrouSxaykbL3V5wS7VNVNu8ZXn26fswxwsMliuoCQvnyPQuZx7idE7miSNknrg9eeCXCfdYNPfwgbB+8jxrJ8/vvt545xKppEnmvr3dhaqmcezpBzj29AMf+D1UTePJL32SC2+do1Gpky6kWXzg0C6N0krYt+xjGZBlG2XgxUETEKGPd/k0/ovnkb24YFzwFDZNA5EwcRsdhBAMTRYI0UgcmiJCIUQjREOVEqW5AYGPFApys4Wi+ISajvA66DRQwj7C2LEqkIDXQwYRkZlFc3QIA4RhIA0bNB3RrEF2jND1EGsXke4Aui0IdzRTXBepC6RmgFRRYyUGNCEJw4jN+gBdT4IMiZwcYidVUtlukdQlQtfRhgp4/QaXBi4jpUXSkx6OE9DoeixdN9NQ+lx87STjz3yehfEb6ZVsfv+iWya315xZ09RbZu03I5naPzhfX97v9bl47tJuKq7b6dHZblJIFfFnbfytBv3L66QfO7RbIL1b2PNj2PNjH2ifX1Y0KtvU1/c3UIF7LJp7eB+q524tnm6eXiJ9dP4j1e2wkwmOf2J/AdC5Y4usXVoh3CmyjedhZiZNwq9CFCANB6knYgnhCxfBvcEGKhoRoaLSMA28SKIj6fYGTD7+ONrCHLvSVIMOSn0NogBvu8a18y2amwNUoTA6s4WjmQgj2jH5Udh5IIi/AxmgTYyhZncMqQc96LVRwy5STcHWMn51BZo1ROQjUBCKhgwDpB8hfQ/0CGE66IqLHwZ4oaTZGtDsweLBeehVUHp1pJNHWknCUDLYqZGr2RzO0CzNrQbBoRLp9BYprcWZS/GsWkpJre2zEW5z7aXXWCjN734/kzMTjE+O0azfKHqOjBWZmb+d0vat8H0fTdexbYt+/wZDK1fIMrMQO3itLK2SSqdoNm6I3TXXtxgandtzrM7JCySPz30gR6Z7uIHUT5EqSN1j0dzDzdhvxJdRFAuF/R0JM6ULGZ7+8rNcOXURxeswP66SGc6B24oTLV4XqRrghUSDWHVSFQOEiAgjk9alFbKLE2QXb4iitfouN9/qaj1m40ROgfL3luh1IlB03EHE5XKNAwsZNF2PP7OuAzKeakuJGF9AGZ9CRHFRFmMnZdOtI/ttOpUN/F6PZKGImswShBKjuolobxFJFaQgGJiorkDRQPd9+l6EmhnlyISF7nfi/H7kIdwm0jBIF4c5fbEBlolM5LA1k7lD8xx67ARpS8Kpv8HzQ8Iw4vWL29T6knrUY3CxxYlHTnD0RJyyEELw6S88T2u7yoXTFxlSe8yPJFE3zxMOzYJx69PTdURRxPKVZX783ZfxPJ8wDNENncnpCYZHhindV9otsg76A2YWpqmsV2g12+i6RlKxSBh70y5REBJ2B3cd4GUQxoXdX0Fp4P0gJdzJgmKfVoWPHPeuxMcIhQOTe+QJAIZLUx+6KURGEZunrlC/tIaiqwwfmSW/ML7/xl4fdaOM0qmTMyzS98+jqBK1H882I91GiTyEjNMzUtORfYmp1lBE3Bwjggi3F93ic9BaeV/uOYqbfDrVNr2eBEUD6aMYIP2ARqtFMj+GzI2AW99hzCgQhYjsMARBzDSRMp7Zmw7RxirS62N3m6THZ1BzxTj3HwnExALyGkStAYrioQqPsBPC9ALICLuzTSIKEM01RBDPiqPiLCRSiGDA2P0PUPCv0FvdQrhN6nVBEARsrG6ScBI894knMda6XDq/TLUv6EY6vUglnU1y8pW3mDswRyJhM+gPeOPlkzSrmyzKCsOjeXRPwHYX0a4SLD5B3P56A67r8eoPX+Xy+SuceecM2XyOsclRVDXuF5iYGufQsb31l6nZKa5eWmJ0YpTRibiwLdfrFJJ7HZHUpH1X5tkyCGn88BS98ysgwZ4fJfvsCRTzV3vm/1HTJEulUgH4D8AC4AEXgH9aLpf3L97wEXmq3sPfDcYfLlE8OouiqSiqylBpisVP/XQbtNvh2itnWHn1DN2tBu21Gpe/c5LahfdbQwIyQrv6FkqrGgfRQRdt5RS4NzVpqQaRmSXSTEIzRZidQh/KoQgfxRBojkBPq1iOj/D2+qXrjgWBi9LbQunViJJxh2yo7ASIKEREIRgmwknA0BDWkSEYmSJ08kjNQGoGkZNCKCr0ezGlMhLIMJ5GeZUOQbWJCCVK9rq8gkQXEYIQURgl2pnvCCKEFkLgIQZtIicb0y2FgMAHKVG2lqDbhEQCyzb5zKcf5nf/wXMcPTxDPmWg7XQH97o9fvDj9xj69d/jnJdjPbBpRgamZTE5PUEYhtQqcZ72e9/8PhfPXcQeNAj7HZavLO+mUYTvorT2djwDvPy9l7l8/gqtZhvP86lsVKisV3bXr167teC6UJrnyPHDuwXahJPgM//ll0mM3OhMVnSN3LPH72ry0HztHN2zy8gwQkYRvYtrNH747k/d75cd8i7+P8Qh/6dyuVwql8vHgEvA/3inHe7N4D9GUDSV6aePMfVkTC0TioJqfLhLGAUh1bPLtyyvnLpC4cBeXrXoNmK++M2QQL+DTFiI60VKVSe0MgSZGRACfWEct1dBHdRBUdBtm7FFg2trTULNBkVFKApjR8bQ65dj6iLEzJZ+g6zcwjDB60VIzUCEPiAZHtXBD2JfV7VIZKfQlD4CSeS6CMMi3GwTRQpCVQmuXMZ9/QrCECgJA3XKQ8nGUsQSgVRUpGrvvL9EEQHCCBHb15CqjuINEF4P4XYRgRcPHprO1QtXOLdVRhsa48jRA4yN5tmqtni/hmC71UZGkk994TO8/P3YLyeZimfGQggyuTS1ap2lK8sYhoEqbuxf26qRye4UWYO9jUSe57F0Ob6Gxk1plO1anZHxkT3vs+d6CsFjzzzK8YeO0e8NyOYzKIqCXJjGXakSuT7W1PBdz8D751dvXXZpHflc9FPlgn+ZEd9Nd5rBfzCUy+Vt4Ps3LXoV+Gd32udegP8Y4qPQ6YiCcI9D1HWE+3Qj3uFE8LNzKIM6InCRuk1kZXfrAUoijZq2EbaM0y5hwORiGnNhlOrqAGE7DB8YJd89hdjuIS0Hmcig1lcg8JCqSunBIS6Xe3TrfXRDYXwhRTZvxIOLZxCpAk31wR9AFBKuXkEZmSFs+0RSYbBeY/DSO+hahG6oyF6fYKuFpucQjo4UAjWZwPfaqGaAECbSdBCqRCoqUW4C0WsiOrX4M4iYW7+y2eDVKy4ddGTP4OrKNp/99MMkEiY0faSUuAMXVVOxLAvLtjhy/DCXL1yh0+rguR7b1W3GpsY4++5Zvv+3P+Sdk+8ihGDz0DRfOJrZaVK6/l1DlNpLoxVCxGYrUmLZFtl8lsZ2Y7fgbpgGh4/fSM+0mi3WVzZIppKMT41hJ2zsm1hRQojdpqYPAqHdej8KRfkwnqO/VNiu1Ni+A4sm2qmpfe1rX5v86le/+v7VjXK53Lhlpx2USiWFOLj/xe22gXsB/lcWmmWQGi/QXtt7A2ZnR2/ZVjpZpGEhvL26Odf521Fif/6+MjpLdPEUWn0Nek2EjIh0i2FnQOHAKFJ2UdZ+jDANUDVEv4OyvQqmHT/uBxFOyuC+xxyifgdVV1GEIKw2CPoh6DZCNhF2gDACkKAEEdHVM/TPbVO9GsHARe96eEJgSwUrq+CdOoOSOIGeyiM0ncjrIwbbiHwupmSaNmLQRdxc1BYKSD8unHke9fYATQZIucPjl5JTp69y4pEHOLfyCpfOlXe1YO574Ci6oaOqKr/597/Am6+c5Ifffgk7YdPr9Pg///UfxqbZkWTgurx96hIZY56nDhbIF3KgaoQjB8DaS3/UdZ35A3O7ssDTc1MkUw7F0SKH7itx+PihXTrl6XfO8MaP39ztgh0ZK/KZL/4a2kdQEHWOztB85eyeZYkj078UgmE/C9LF/B1ZNOnhHABf//rXX9pn9b8C/uAOh//XQAf4N3c6h1/tK/Arjtln7yc5Et9kQgjyC+OMP1y6dUOhEMw8gEzmYqd4wyKcOIJ0crc/uJREzQ1wHBi0YqMNVUfxXUR9ExkGiEEHEYUIf2fgiCJot4kqVcLVKsGlVcJmF6GCmskhjARhy8VdbuGtDoha3VjC0e0iXRcGXQhdlMilW4+IghCpq3FwFoJBUxIJDdntEb73NtHGFaLGJrSqqFqEzA8RFSaRiTxEfpwS2Zm1SztNZKchDAgR+CEsDpnM5gyQgtDO01EyDB08jp10cJwE6UyaqdlJNE3j9NtnADAtk36vz+jEKJlchlajRa/bo1ap4QcBge/T7fb50TvLeAeeIvnY5/BLzxDl95eueOKTj3Pk+OHYjDuT4rNf+gy/9oXn6Xa6vPz9Vzl76hy9bo+Tr7y1R+Jgc71C+fT5fY/5QZF8YJHMk0fRskm0tEP6kYO/Ms1Md4a849/1JM1XvvKVZ4C59/3/r7c7aqlU+l+AA8A/3PHKvi3uzeB/hWGmEhz6radx2z0UTUXfpzvxxsYOwexDd03JVAZ1omgbpbUNqh7n2+XOLS0UlE49bkAC/JaL31TQgy5q6CEVnXCrgZpNolg6qDoilYHtKsHqNmGtA0iCgY5eUCATm3igip2BRBCiIGSAUCEyNBQ/RApBhI5qqOjj6VjKIPBBhiAjFK+DNHVEcwuCABH6KM11ouQQUjfBdsDro4c+lmnQR2PIEKy1B/SFyuTcNM1GkzAImX4fd335yjLHH4pNr5v1GzrrqqYShiGu65LQHeyEjVAETtJB0XXeee8yQRAwuzhLYehWM2pN17j/kRM8+PgD6LrOyvIq3/rL7+wG8/WVdS6eu0S4TzquslHhKD97IBZCkHpggdQDt9r5/SrjbjtZX3jhhZUXXnjh6t0cs1Qq/Q/AQ8BvlMtl96dtfy/A3wPmjofrXeEu+faK2wYdUBRAIIW6k5MNYpGv3jZEabbf3aS9PCAyHGg0yIwp2EmBZisoaSfuTBUJhK+g6QoibYFogVDBdxFKIp6gq9fPSyCiECuv4Q8EMggIcylwPVQk5rCKMeKgGiGyVUW4NiSS8Xl6fRQ/gDBAJtKEdgYRBgjTRBaPotaWEDKPHLgsTGm0uwMiIQjzaXpDYxx/6BiBH6Aoyi2CbaZ1Q9elODpMt9lAEZJcPodpGDtiafFnuN6p+q2//A6jO8XSU2+9xzPPP72nMarb6fLSiz9mfWUdVVM5cGiRZr15ixb8xuoGiqqgvC9lcrvO2Xv4aCCR++ry37z+g6BUKh0F/lvgPPByqVQCuFIul798u33uBfh7uDuEAUp1CaW7jdQtoqEZpH37dnmpaICPzI/D5hUIA5ARyOsSSwru8gatKx3QDES/iYwC6hdD1AM26CaiHyEjgVrwEfUGUg1RRwqI1QFRzwffjztJFLGjCxMfWQqFzKzGoDnA76pITSeybQrH01i5nQYofxA/jXgDMC2kanF5o8up8xt0tQzTE0UePOqg2wqqcIlMhyg3iSIlgiam72JpklAKsiNF1LlJgrCHnsgwf3Cei+cu7n4XQgiOHN+xRYxCHp+xGKl06Pd6dDQD7/FjvHvqEp1WGylheKRAFEV71B+llJx89S3mDszuBuoffvslNtY2iaKI+madlasrCKEwMl7c09ms6Roz8zMsXV7aXZZMJzl03z7puHv4yFDbrFFdr952ffQBpQrK5fJpPmDp+l6Av4e7grb8zv/f3plH13Vd9/m7w5tHPDzMIMAJvBxEUtRIS7IkRrblyEPjOMuxm6TpalM3XU3T/JE2HVfStInTQWmb2l2p445xaqduWjv1GA9xbEm2NUukSB5OGIgZeADew5vv1D/OAwiQAAgOGESeT4tr4d1z731bFxf7nrvP3r+NVpoFQCOPPj+NvfvBaxb+FvAiGbDHIBjG3XkEfewiWmUePxzEizWjl+eozNEo3PGlho3pgebjlGtEUj44EfSgieEVoDoHnofmaET2RKmO1vCqQWiNoYVr+BqyktW1QdMwQxqdDycpz3q4hAnt6iRUHpX6MYk4GCmpPVOtgA+DkyW+9cpl2fQ7GeHUuWHmSxXe/YglbdQ0fDMgHw66IR8KaGjRFAFcvHoFvZLDC6d45MnjpJtSDPVfJhQOcvDIATp3yAIyfaoffW4MXQfHdgi6NR7ozBCM3ccFcZFyqYxhGEyOT5NIJci2XlnALhVL2HWbUDhEuVxZdO4XxSVKxRKu61KaLzGbm+HAkSt9dpua05x47xMMD44wOjxKPBFn7/69hELBjbpdFECqbe1F1lTrGmtYtwnl4BWrUpmdxwiYhAx70bkv4rkYs8O4HSurVPqej5HpxnUm0bJRnPYDaOOX0MsF0HV8p4oZD6FHdAgEG1rvRXyqBJt19KCPFvAJtEWhXJCzdMfGq9rga4RadGjtwk+34s9cRqsWwXPwwnG0elXmtAeDRLsjaPUynl+SbxCJhJzdaroMvQSC+K7PqYs5fNuV8f6yzE4b6i9TvreXaEcHWqWANj8tQ1S6Dp6PH01DuBHecl00X8a5DcPg8H33cPi+e/B9nzdfOcnz3/0B+D6PtruUcpPUqzUMQyc/W8DPzzM8GWE2N0s6k6a7p51ILEZ+Nk+xUCSelA/RVDpJMBhAzw0RyY1wIFxATNUoFUuUSxUK+QKmaTI+NonjuBy69yBNmTSPv+txNE1jx85uduy8Vjt+Pbiuu2IcX7E6quGHYltSnSty8ZsvU5mRkr1NbVH6dnoYV+c7OyvkzNermJffRKsUcGJB0JM43ffINMgWD/3yKcBHCwRJHdlJaXYcu1iX44k0oXiexN4Qmu+AbuOXS2h2VUoMOw56ONSYRWu4sSSE47gdFvrcBFp5FjwHAuAbJngOWr2Eb4bQPAdi8UazDxqO2pDdmnQD2/bkLD3YKMCya+Da1Go2YTNMYOqiDOkYAfxqGa1cBOahnsRPZCAcxQsmrrkcr7/0Bq+/9Mbi50ulKYzaPMlUgmKhiO97uB5MT88SjoTxPI/W9hYCwTCVUoVyuUI8Gcc0TY4//jD1gVOUL52SvUy9Em2VcSK1PJenSgQCJrF4lEg0QnNLBuvgPh79sUduSYjOtm1++L0X6T/fTzQWpK2zi+OPP0QgcHfLEKwLf+0Y/GaI0SgHr7iG/j9/bdG5A8yOFxmpl+k5uLwIxktcWxRjjp5Gq1zJEtHnp2HyAm7HfvxUO269QmDqIlrAxEjE6Xyqh/yFPPZclVAmTLytBaaH8PUwml1Bq8gCKU3TZF/VSEw6X01HqxTw483y52oedB3N9cC10epl/IXsHbsmhdoCETCD+L6HFgzhaya+GcCNtLPTMph4+bTUvdE08Bya40Ey1XE4PYVvaGiBINg1KBcXc99pLKR5wQRuqAlcW2YNNTh3+vyy6zPpRkiXp0ikEti2i+/5XJiqyYwL32c2N8ubr76F43hkW5t54t2P09zSxI6dO5gan+T8976N5rvMzsxRr9UJhcPsy5Z5a8gmnogtFi6lmlJUKtVbVhl96flXFtcTPNfjwtkLGIbBI08ev6Xz3g0oPfgGlmV9CngKqCGT9/+uEOLlxlgbUmBnJ1ABPi6E+NEWmXrHY5erlCavKqDTdGaqCXYEQg3nquFluvFTbcv3cx204rX9PbXCFDRCOV7LTrTaDGgOfjCMgUbmcKucPXseXnkeL7jQjKOMr/kQCIFbR/M8KStQKePXXJjN4w7N4saaCZRnMJOaTPLxXKlfA1LbHR+MIL7XWKEyAmhmUMoURFJQr5JKxUlHDHL5PIZp0poM8+SRTinREE6gzTeuiWsDGpgB3GQHflOHdPSTlwnY0pl7yTbczgNgmNdk0+S1OJPVGBE3wPR8jdfOjfPmcIloo42fruukm5LYtku5XCEUDtJ3oA/f93n5+ZfY57t4nrdYRBUIGnR1thA9W8RrSBdmshli8RjJ9LVvFDfKpXOXVtymHPz1USGaK3wN+BUhhG1Z1vuBP0YqpgF8AvieEOI9lmU9BnzWsqx9Qoitbnd4R6IHTHTTwHOWx1uNVBPOvndArQRmaLHl3jI0XS5IussbiGMs2dd1YHYcSnOgZ/HxGzruPhgmflmeX3NqYBh4oThaKA61Ir5r4xcKUKmDD/WxCrWRKQiP4QU87BBED6QXu+H5ZhA32YpmV9E0HT+cxKvN4JsBbM/HCASpl2p8/fnzjE/lQYpect+OGPcf7Glk27hyo+81MnU0NN/D13Q0M4Cvm+iFSTzPhYBMhdTzE6AbuF0H2b1vF6ffWF7leeCxExSqFb78p28yN1snFJFNwEulMjt27aBrRwe26xOJhHnrjdMce+hebNtmLl+kEApg1grUa3V0w0DXHczmHvbs1ynMFug7sJdYXM7kF2SIQb4dDF0aYmJ8klQ6xZ59u9dVxWqYBrZtX7NNcX2mJ3JM3cYsmpthWzh4IcSXl3z8AdBtWZbeqNL6CHL2jhDiOcuyasg+7S9tuqF3AUbApOVgLxNvXpm5aZpG+9E90sGF15gV6jpuphtjamDZZi/bKPrxXPSpQbSxi2iAVyujN7Xgh8KyrV5+Fr9UkG33PBctGEcLxnDjGTQziDEzjD9fAg3cqkd9tCxtqtuU0ajN15gUGqmdCZrCupztJ1rwdR2tVsJNd3LytQJvnB0CDSKRKO3BGuM5r6EtL3u1vjEwx/6+LiKJFFrNlJk5uoEfToJTw3dtCMXRynMYdhUqBXS7JsM/oSh+KI5emKTa2sfuvbupV+v0XxwAH3bt3cnDjz/EC9/9IelMimQ6QbVSlVIFNOQKqjXGR6fwfZ96rY5dq5PKpCnNl/jOxRz7Y2VCnkutVmds3kVLxujbv5ede3oJR8LE4jH2HthLdInOzF988/v0n+9f/Hz25Fme+fCPXzeWvu9gH2++cvKabYrrk27L4K0RIUu3Xlu4drvZFg7+Kn4J+IoQwmvoH2tCiKWPwSFgB8rBbxjdxw8SSsaYvTQqHf6hnaR2tK7rWK91DwRC6HMT6MkoTqZZhnJcB7P/Zdmpyanj1uuMnp2mMDdAMKjRcriXyIFjGI4n9eSjSfTSHOCjl2bRq/NgmDhlH03zcYqeXHg1Q1Trdc5P1EgHXMx8Db0cwPMCNAdd9MIEXqoNt3kHU4MDXDg/gG2DGQ5TKFY5c3mMjvYMeqBRxRsIY0cSTIQ66U3GpIZOcRo/FGs4+QReLI0xMwyajmcG0V0HfX4SPxxHq5XwIjVO5eCl575AvW4TCAQWJQscx+Xkq6fQkGJg9VqdaExm4lTKVeZm5qhWKgSDQRzbwfU8Tr1+moNHDzA3m2dwaJLJeJSwblAoVNFDAQ531HjosYc49tC9K8bcpyamlzl3kIqTF85e5MDhtXv1HnvoXgzD4PzZC8RjIfoO7ufoA0fWdS/c7fjXWWRdcwH2NrEpDt6yrFeB1fqOtQkh3MZ+HwX+MvD47bahuXn1JsLrpaXl1mOaG8FG2NXaehiePHyTBx+ERgn8Qha3OzGAa9TxgxpePIl47jJzUxUZ0jFM5l4vcLRtgkhrh9S7qZXx6gX8Ur6hB6OjxZMYMRe/NI8Z0nB0DXSNWVsuWM3WIOh7VIo2s2WP7K7dBJtawa6g+yXGxy6wL15nxvAYKFQxIwkC0QgVF9KxRthBNzCy3fSeeIakX8K3a2iBMO7kEN7kgMz7d218N4OW7cIvTOPVIrI1oe+gBcPkZqZ59YJPIN1CtWJz6q2zfOfr3yGZTJBMJbAO9RE0dXraEwz2j4BuUrY9TEMnGgtTmi9Rq9bkm1NnK5rmg+8Si4XIZNN09XSgaTqZbBOGofPIkw9z/8Or9wWYnhgjFrtWhsJ3a+u6d979zGO8+5nHbuwe2AK249/nVseRN8XBCyFWbvC5BMuyPgT8FvCUEGKicVzOsiwsy8oumcX3ANc2J70OudyVRaiboaUlwdTU/PV33GS2yi7f83Bq9pr6NUttM8an0Et1NC9ANVdhdrre6GnmAS71qs3gmWl6H4ijOVWM3DB44Ecy4NTRnSr/diCWAAAecElEQVSe40NrGueyQ2muTDUYIWJ7uLpPNqJR0zS09jCubuLoJnaphFc+j+bU8WcmwZfyu01hjYmSS7E0TzzTgt7URs2XWvN+MIrVZ2H7AXKkpdwCQOthSPehF6fBrmLUNah66OUqmhYEQwrt+J7BhRmfKkH8Uo1zZy4xXyhSmi+j6wY+GgPnB3h6f4LDB5o5HdMZHMkxWahhveM+5mbyzOZyzEznmcnN4Ps+sVgM2/bQdBPH8UikpMRAve4CLoYZWfMeMAMRSqVrZUuC4fgN3Tvb9W8Abp9tuq7dlskgqCyaRRoLq78LvFsIMXDV8BeAXwT+RWORNQK8srkWKpYydXqQ0ZcFdqVGOB2n952HSXSuLBm8gB9Nwcww1ErY1brMRvF9QMM3gmh2Fbtcxdl1P8boWfTClOzUFEmhFyaxR8vUL1zGLrtcnHSpJNLQ2kFgdpRMcxnbsPGCkI3rzNoBkrEgpl1GipCZaNUiLTGdXD6E7ziEghonRwpUoxF2Neu4eoS9+/eya+/O1YuBgmG8TLfs6JSfQKtX8AMRKaMcCOOl2vBDMYL5Kfx8Ddt2qFaquI0F6wWJgSZKRPQIyWiAn37mQQA+9+UfUQyHCASyDF0apFatYug6ruNSqVS4cPYiqaYkXb3LVSV7d/fQuaNjzWufzqQ5fN89nHz11OK2rp4udvXtXPM4xa3h4eOt4cbXGrtdbAsHD/xXZI/B/90Q0AE5k88B/wCZOfPzyDTJn7ueRKZi4yiOzzD4/Svt2KpzRS5842WO/MxTGGs0Z/aSbWihfgKTl4hFdExDw7F9fNcDzQHDJN2ZgnAcL9uLV76SqukEUtTPCXwtyOi8y7ztQzmAWaviOzWKFYPeAwFK5Rrluk9TCDoTmpy5N1IaQSNi+uztaWF8psjkRBE9FGVX3+7F9nq1ao2eXTuufxE0Daf3XszRM1Jbx3PwjYCM0xsmvcef4NXc8xTnSximIbs0mSbhhuBYOiq/L5G8MlPc0ZHhzLRNIBAmFo9SLJYJhkOYpkmtWmNibIJEMk5TJs09x+4hGAzQ3JKhq6drXbnuD7zjfnb37WZybIJUU4qO7rUfCopbZ2p8ismxVdulysyrDWZbOHghxKptZIQQ48C7NtEcxRrMXBy9Zptbt8kPTZLZu7JmOSDlCTI7cGfGYXyWPftiXDxfxa47YNu07kzTvLcDRs+AI2f4Mh3RwJss4IXieOlOCrlJCDfSMOcL4HvUqhANxklFAlKkKxpDcx18z8UPJ2T+vGmg2S7xSIjdLZ1kZwbQoi6UpihV6sw7OnMzc7zzqUeXdTlalVAMZ9cDV9YHqkWZYRNNEzRMnvnQe3nz1ZO4jsPE2ASdPZ1MjE3IlPxUM+lMgqbmK1kUDx7ZyZSo8dorbzE8NIbjOCRScWqVGoZp0tbRtihBfO70OQ4dPYjnyUW89RYzZbJNZLIbr3+ikGTamvHX+N1k7tIsGsU2Rl8lB1pfR061H4rhV108P0Qi5XLvMY3KfB1DMwimffSR0/hVWQWrzY1L8TDTBF/DS7dDIEQwFKRakQ5eC5j4toGheQSCOoYRwvA9vGgKTzPQnTropqw0DcfxIwm8dKc8TzyHNjfO6OQc49ON74wm+doXv8H7PvzMdYW4zp48yxsvn6RWq1EpVwhHwjS3ZLj/+H10dHeQSCV49MQjPHriEUaGRum/0I/v+aQzabp2dNJcGuDcydNcHpslGg3S98DDuAwRDAfxXIdatUa9Vgd8AsHgYs76wIUBisVSY0yGWt71vh9D13UmxyZ57cXXyc8VaG1v4f7j95FIbb+Fx7sFVeikeNuRtXYwebJ/WT/XUDJKsvv6vTz9eAYv1QLDI7huGMOpEAmbOFUNv+ag18v4M8P4uonm+/iajtfUjRH30KfH8IC2zhTzhYqcGcXi+I5JRxfo0RC+GcAPRfGS7bLatpxHq0gVSi/bg7P7IVkV69gc3nWGof5hJqavyCpkE0Hys3nEKbHYnGMlvvInX+WbX/k2ruOSm5ohnozTtaMTz/P45le+zYc+9hPLwi9dPZ109XQuO8f33jzDxYslcDX8qsEPv/gCpmkwPDhKtVrDcWQLQk3T0HT5QJsvzDM3m1+m4z4yNMLl/ss0ZZv4xp9+Ux4H9F8oMTU5zYc+9hPLZIcVm4jSolFsNyozBSbevES9WCHRmaXtyO5ls/ZwOs6+9x9n9JVzVOeKJDqa6XzQQjfW1/3RPfJO3Mtz6DPjOHNl3BoYfpVQR1BKHVQKaLqBH0qgIbXbtWCA0P17qE1rxHOz7N/RwWw4iedUaAnN0tSRwHUdWT3asgu9MCkXQKMp+S8cl85d09DmxtBnx9iXNRjua6d/OIfn+zQlo7S2pfGBmelr5RYWGBka5bnvvCALkio1XMehMJsnFAouOvH+8/3XPCAK+QITY5OkUkmi8SgXxUUqrsb4cI5SqYxdr+P58rtd11tspq3rGhpg1+tUShVC4RCdV8XPZ3Kz5KZnFp37AsVCkZHBYXr39K7rd6O4vTSUitYcvxEarfo+jCz8PCyEOLX2EcrBK5ZQnSty9ksv4NZlaXphZJr50Rz73r9cdyTenmHf+25Oi0TTDYz3vg/3zHn0kz8gQJlgJgNaXQp5GQGZYeM5+KGoFP8CtOZmAkcPARAEFlqNaMUc3swI+C5+qh0v3YHX3IPekBD2I0m8zA7QdYzRM7KpN0C1zENdAQb2tVFpVOJ7IakHk1mhNd4Cw4PDS/RlGg1GfJ9atYbneRiGcY3+zJuvnORHz73IyNAI8/kiyXSSWDzG+Mj4ogyAY7uMj44TjUbRdR27LtM2PV/DNAN093Zz4uknePXF16+JuWeyGRnfXwHHURK/W8Xk+BQTY5Orjl99n6yDLwL/HlipSfeKKAevWGTq9OCic1+gMDJFeTpPNJu6bd+jBQKYRw6i7ekk8Na30Isz4OvSXQbCUgkSTapVNvTXveY1slsCIfxACC/evPjZa9u7fB+7ij47svhRb2onWLvM8V1xvvvmGL4RQPNc0k1JrDU6HYUjYdJNKcYrVcKRMIX8PI5tY5omhmFiGAa79+1a3H8+P8+rP3qNi2cvUqnI5uK5qRwDFwcIh8MEG7F+XdcJBALMzc7hOg4+PoYhM3Cask2YpsnBew8yN5un/8LA4vm7e6XGezQW5fQbZ5aFBILBAN03qf+uuHWa25plI5rVxlubb+h8QojnAJZkGl4X5eAVi9jl6orb66XqbXXwC/ixNPb+xwmc/4HMsgmEZWqj5+G275NNsM0QXnPPiu0B9YkLy3Rv9OkhnN0PQvDaLBjNri5/Jw6G8BNZ9u7QiHf0MporkYiF2LF/B9oaC6x9B/bSs7uHet1mcnwS3/MW+6kOXBjgo3/tIyRTV2ydHJ+iOF9adO4g4+rxRJzifIlgKLjYicl2HAzDwAwE0D0PXddJpOLs3N1DLBGjUq7wxHsep+9AH7mpHE3NTXT3yjTJlrYsj554B6/88DUq5QqpphTveOK46tq0haw3D/7Tn/5097PPPnv18JwQYu6ag24Q5eAVi6R6265JgzSCARIdG5fO5SdbcboPYUwPykWpUAy3w5KhlrUOtGvymCVoTh0jN4Tbce0Mxw8nroR/gMmxKUbPn2di3iPd0cnR/d0y9FGew65XVnxIAERjUZ75yR/nrdff4s/+37fwPJ9wOEQsEaOju52RwZFlKo7JdHLFhbaOrg7q9TqZ5iamp3LYdfkWsNAIpFyqkEgl6N3dw869O4kn4yRTSTRNW3HRFqDvQB97rD3Ua3XCkfA144rNZb2VrJ///OdXCrn8M+A3btUG5eAVi2T2dlGamGXqzBC+52GGg+x88t41C5huB17bXrzmHrkw2igWuh5avbJiFoJWK618gG7gdB3EHD7F1Og4kxMT5PJ1LuYcvKl+anWHBw7vbBjkrHiK+UKRH/zFDxm9PIqu64yPjBOJRvA8j/n8PBdK5Wty6Fvashw6eoCh/qHF1MZQOERrewvHHr6XwYuDTI5PEQwGSaWTRKIRmjIp2ZM1mSCRTBAMBXnsxPo6M+m6rpz7dmGdWTQf/ehH3/nss88OXzV6y7N3UA5esQRN0+h57DDtx/qwSxUimeSqee+3HTPYaM6xPvxwXDYFuaoa0IumVzkC/GQLtvVOXnz1f1Fzm8nVTXRkpeGZS2Pcf0+vFBMLraxF8p2v/flihs34yDjFefkwWXDqruNSr1/bxvDJp58gk83w3Lefo1yqkM6k0QydM2+eJZNt4p3vepThwRHOnT5PtVJF13Va2lrYvW8XJ55+EuuefapF3tuQ9ebBf/zjHx/++Mc/PrARNigHf5fh+z7lqTk0wyDafG1cGyAYCxOMbfNZoGHidlgYo2cWZ0J+JLH2YmzjuFzdwNB1ub9no5cL2I6LF07g9RyWC7tXMdg/xFD/ZaKxCLqu4/k+iWScSrmy6OA1TWPfgSuLu7Ztk5uaIZGMc++DR7n3waMUC0W++PkvYdsOtm0zMTaJpmkk00n27NvN2Mg4lXKJA0f28b4PP0N7Z9s1tijeHkyMTzI+ulYWzY1lOFmW9XvATwLtwLcsy8oJIQ6tdYxy8HcR1bkiF77+EtV8EZDpjnuffhAz/PZciPOaOvFiGfRSDt8M4cczLLZzWoPe3b0MDwwA4McyuNEmdu3egdcnUz9r1RovPv8yQ/1DBIIB6jWb+XxB9iM1DXp395BuShGJRkhn0iRSCTQg29rCsYeOMT05zdTEFK/+8DXqdRtd19l/j8V9Dx/j61/6Bq+9+IZULWzN0tbRiu/77L/HIhAI8MJ3f4BpaoDBpXOXaGnLYhiqUOntSLYtu6ZUQfbGs2h+GfjlGzlGOfi7iIHvvrHo3EEKh428eJbex9/GDRyCYbzgGho4K/Dgo/cTDum8+dpZALp3dnP8xKOL43/xZ99j5LJcbB69PMrw4Ag9u3uIxaOUimUGLw1x6OhBdu7pJZaIYZomqXSSju4Ovvp/v0ZpvsSZk2fJtjbT0d2B53mcfvMMw4PDXDrXj+M4eK7HpXOXKBdL9O7pRUOj/3w/mqYRDocolWqIt84RjUW598Gjt+96KTaNhUbqa41vNMrB3yW4dZvixLUVmvmh1V8hr4fnuMxcHKU+Xybe0Uyya23J4O1CIBDg6Q8+xaFjR/F9f9miZHG+uOjcAQp5qTE+MzXDzr07Gb08RmGugGmavO+nnmGvtWcxZfJ//P5n8VyXes2mUqkyMTZJLBEjmUrieR5nTp6lpb2F/gsDzOZm8X2fUrFEvW7zrvc/xfjoBPV6nXJxHteFRCrBwMUB5eDfpigtGsWmoRkGZiiAU1u+CBhYodPPenDrNuJPX6Ccu6Ll0npoJz2P3WQXqE2mUq4i3jpHfjZPa0cre6w9mKZxTWLOwuKmj08gEKApk8ZzXdIZWRegaRoToxP8yWf/DyNDI8zm5rDr9cUHRyQaoTRfplarUatUaetswwyYGKaBYzuYpklndwcDFwaZmZ7l8sBlTFPHtl2isSjHn3h4sy+N4jahHLxi09ANnbYjexh56eziNk3TaL937xpHrc7UmaFlzh1g8q0BWu/ZRTh9ezribBS1ao1vfPGrjI7IDJoL4iKDl4Z4zwfeRSIZp72zjfFRWfrf0pZlNjdLprmJ2Zk5Bi8Oks6kmZme5blvP0+xUGTo0hC6YZCfzVMtVxoLqHWKxRKFuQLRWJRYPEZ7Vzvi1Dk0TSPbmsX3fTobypOT45NUyuVlr/TlUplQ8O25PqJAiY0pNpeO+/oIJaPMXBhFN3Wy+3vWpQK5EpWZworby7nCtnfwF85eJD+33P6RoRHGRydo72zj0NGDvPWGjJnHE3FOvPcJsq1Zvv/t5+nq6Vq2OHb6zTPkpnJcOn+J6cmc1KM3TTzPR9PAceVMPBqLynh9wKA8USYcCdHc0kxrh2xmbhgGHd0d6IZBpVQi4Hhk27IYpvoTfbsyNjbB2OjKGkEA7t3S8EOxeWT2dq3dmGOdxFrS5M4tr83QNG1DJA1uN4X8yg+n+XyBpkya73/7OZpbMmSyTWiaxtxMnieffoLhwRFKxeWFVFPjU1w4e4HJiWl8z8NzPWyvjhkwCYXD+L4vs2w0jWKhyL6DfRx76BhzM1fqWILBAA8++gDf+eqf09HVTiwWWuyhmm7a/tdTsTIt7S1rZtG0tG38mpVy8IpVWVhEXRAby+zpXCx8yu7vYebCCMWJ2cX9247uIZyKbZW566a9q53L/QPLtmmaRntnO4OXhhaLlRYqR13X5dK5frp7uxFviWXHVatVNF3HMAwM08T3bdA0zECgEb+/8hq+0LTjHU8cR9Ng4OIgwWCQvgN7iSfiHDiyn7deP724fzQW5eDRAxtwBRSbgX+dEM2a4ZvbhHLwihXxPY/zX/sR86O5xW05cZl97z+OpuvopoH1wUeYG5ygViiT6Gwm1rJ6Fel2YueeXvIz07z20luALO+/7+FjJFIJxkfHVzxG0zTuP36MQr7A2PAYIJtZG4bB2PC4zFc3DYr5eTzfJxKNkMk2EQgGWZjDtba3cPDogcXipbaO5UVMDz36IJ3dHRTzs9iORt+BvUp24G2MWmRVbFvyQ5PLnDvA/FiOuYFxmnZLoStN12na9fZr3qxpGu9+3wl6du8hP5enpS1LPCHXDXp29RAMvbyoGwNgmAa7+3YRCod47196D/m5PI7j0pzN8OqPXuPU629Rq9bINDcRCARwbBvrHovdfbtIJOKgabR1tLLv0L7rhly6e7tpaTnA1NT8hl4DxcazXrGxjUQ5eMWKVGZXdjCV2SJ3StvmlZpQh8Ih3vOBd/PyCy8zNTlNUyZ9TW/TVPqKkz5y/xGGB4f5i29+H8d2aGtv4b7j9/HBj7xfzb7vcsbHJhgdWfmNEG5cquBmUA5esSLxtpXd+Grb7yRa2rL8+Ifeu659TdPggx/5ACfee4KRyyNkmjO0tt9cZpLizqK1rWXNWXpr28bfJ+trpKm460h0Zsnu71m2LWvtuOm0yjudRDLO/kOWcu6KRXz/+v82GjWDV6zKzieO0nKwV2bRNCeJtd75s3eF4nahFlkV255YS/ptkx2jUGwnPN/HW2OavtbY7WJbOHjLsv4x8NOAC2jAJ4QQf9wYiwL/FbgfcIBfFUJ8eatsVSgUivWgZvBX+KQQ4rcALMvqBM5alvVnQohZ4FeBghBir2VZfcD3LcvaK4QornVChUKh2EpGxyYYGRlbddz11uw6fFvYFg5eCJFf8jGOTBFdWAD+aeDnG/udtyzrZeDHgS9sqpEKhUJxA3S0t7BWF932m1iQtyxrH/DfgWYgB/wVIcT51fbfNlk0lmX9omVZZ4HXgI8LIRaqbHqAwSW7DgHX6cumUCgUW4ssdFrrv5vi94FPCSH2AZ8C/tNaO2/KDN6yrFeRjnol2oQQrhDi94HftyzrMPBHlmV9a4mTvxUMgObmW1c4bGlJXH+nLWC72gXKtptlu9q2Xe2C227bLfdJzGab10yFzGalKumnP/3p7mefffbq4TkhxNzSDZZltQL3Ae9ubPoc8EnLslqEEFMrfcemOHghxH03sO9Jy7JGgSeBP0HO2HuBhf+BHuDPb+Dr33619AqFYqvpAC7e5LEFYPY/fuoT180rrlar1c985jPfX2HonwG/cdW2HcCIEMIFEEK4DV+5gyv+cRnbIgZvWdZBIcTpxs+7gGPAgqzeF4C/CbzcWGR9EPjYDZz+JeCdwBgyS0ehUChWw0A695du4RwzwF4geb0d/+iP/oh8Pr/S0NxKG28UbTMkK6+HZVn/CzgE2Egn/K+WpEnGgP+GdPou8PeFEF/aIlMVCoViS2iEaM4BzY3Zu4FcaO1bLUSzLRy8QqFQKK6PZVnfBT4jhPisZVk/C/x1IcSJ1fZXDl6hUCjeJliWtR+ZJtkEzCLTJMVq+ysHr1AoFHco2yYPXqFQKBS3F+XgFQqF4g5FOXiFQqG4Q1EOXqFQKO5QtkWh03ZlO8sYW5b1KeApoAYUgb8rhHi5MdYG/CGwE6ggtX1+tIm2/Szw94GDwK8IIT65ZGyrr9sNiTVtsC3/Bvgw8vd0WAhxajvYaFlWM/L+2QPUgfPA3xRCTFmWdRypfxIBBoCfFUJMbpZtDfu+COwCPOS9/3eEEK9v9XXbjqgZ/Np8UghxRAhxDHgG+APLshbKjxdljIEPAJ+xLOvWBW/Wz9eQTuEo8Angj5eMfQL4XkOQ6G8Dn7Usay1hu9vN68BHgf+5wthWX7cbEmvaYL4IPM5yMT3Yeht9ZLGhJYQ4jCzZ/x3LsnTgs8Dfbtj2PeB3Ntk2gJ8XQhxt/F3+G+C/NLZv9XXbdigHvwbrkDH+T439zgMLMsabZduXhRB24+MPgO7GHyDAR5A3O0KI55Cz/Ac20bZTDemJlQSvt+y6LRFr+lxj0+eA+yzL2pJGqkKI54QQl5du2w42CiFmhBDfXbLph0g9qPuBauOeAnmPfWSz7Frgqr/LFOBth+u2HVEO/jq8TWSMfwn4ihDCa7xea0KI6SXj20lieSuv2zViTcCCWNN2YVvZ2Jg0/C3gT7nqd9e4x3TLsjJbYNdnLMsaAn4L2S9iW1237cJdHYPfYhnjW7atsd9Hgb+MfNXfFNZrm+KO4D8g49yfBD60xbYsIoT4BQDLsn4O+NfAP91ai7Ynd7WD32IZ41u2zbKsDyFnME8JISYax+Usy8KyrOySWXwPcHm182yEbWuwodftOlwGuizLMpaINXVyG6/NbWDb2NhYBO4DPtB4O1z43S2MZwFPCDGz2bYtIIT4Q8uyPg0Ms02u23ZChWjWwLKsg0t+Xk3GmCUyxl/fRNveD/wu8LQQYuCq4S8Av9jY7zFkxsMrm2Xbddiy69bI9nidK3LTHwNeW02JbyvYLjZalvXbyJj7Twghao3NrwCRxj0F8h7b1NaZlmXFLcvaseTzB5DyvNvium03lBbNGmxnGWPLsqaQKWxLb+CnGjP4dmS2Qy8yTfIXhRAvbKJtH0O+Njc1bCwB7xFCnN4G1+2GxJo22JbfA34SaAemgZwQ4tBW22hZ1iHgFFKattLY3C+E+JBlWY8gF8nDXEmTnNhE29qALwEx5P0zg0y1fXWrr9t2RDl4hUKhuENRIRqFQqG4Q1EOXqFQKO5QlINXKBSKOxTl4BUKheIORTl4hUKhuENRDl6hUCjuUO7qSlaFYiOxLGsA+AUhxLdWGQ8iFTcfQNYsnLhK5EuhuCXUDF6h2FqeA34WGN9qQxR3HqrQSbGhNMrK/z3wTuSE4nNCiF9qqBT+I+BvIKUUvo5s3JC3LGsn0A/8NeA3kVLN/xBZKv+fkfo1nxVC/FLjO/5q4zyvAT8HjCE1y7/dGO9ESts+hqx8/JdCiD9ojP0GsjFJFSmmNYTUG395ybH/ASnmVgT+rRDi9653rGVZfwj8DFKq2QV+Uwjxr9a4TsPIqtDv3uAlVihWRc3gFRtGQ/Dpy0iJ2Z1AF/D5xvBfbfw7AexGOvFPXnWKh5FiVz8N/DvgHwPvQspHfMSyrCeu2vcikAV+Hfg/S2RsP48Uo+oEfgr4bcuyfmzJsR9s7JNGyuJ+smG/Dvw/4I2G7U8Bv2JZ1tPXO1YI8XNIh/8BIUR8LeeuUGwUysErNpKHkE717wkhSkKIpc0ifgb4XSHEJSFEETlD/6hlWUvXhf5545g/Q+rZfE4IMSmEGAG+j9SzWWAS+HdCCLuhFySA9zXeIB4Ffq1xrteBzwB/ZcmxzwkhvtqQOf5D4Ghj+4NAixDiN4UQdSHEJeAPkN2qrnesQrHlqEVWxUayAxgUQjgrjHWyvPHHIPJ+bFuybamIVWWFz0tb/Y0IIZbGGwcb39EJzAgh5q8aW9rhamn8uwyEGw+aXqDTsqy5JeMG8uGy5rGr/D8rFJuKcvCKjeQy0LOKwxtlibY4Mq7uIJ149018V5dlWdoSJ9+DDJmMAhnLshJLnHwPMLJO+/uFEH03YQ/IFo8KxZahHLxiI3kRueD5O5Zl/TpysfF+IcTzyJ6Zv2ZZ1teQkse/DfyxEMKxLOtmvqsV+GXLsv4j8BPAAeCrDfnkF4BPWJb1q8A+4K8jQ0TrsX/esqxfA34PKX18AIgIIV5ax/ETyPWFVbEsKwQsNEQPWpYVBmpXvY0oFDeFisErNoxGXPoDwF7kguMwcsEU4L8gY9bfQ2bMVIG/cwtf9yPkguw0ssvVTy1prfgx5CLvKPB/gV9fLTd9BfvfD9zbsHEaGb9PrdOmTwD/xLKsucbDZcWvQYabuoBvNH7uXWVfheKGUGmSirc9jTTJXxBCPHa9fRWKuwk1g1coFIo7FOXgFQqF4g5FhWgUCoXiDkXN4BUKheIORTl4hUKhuENRDl6hUCjuUJSDVygUijsU5eAVCoXiDkU5eIVCobhD+f9LbYARxp5RRwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
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"Recall what these components mean: the full data is a 64-dimensional point cloud, and these points are the projection of each data point along the directions with the largest variance.\n",
"Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the digits in two dimensions, and have done this in an unsupervised manner—that is, without reference to the labels."
]
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"### What do the components mean?\n",
"\n",
"We can go a bit further here, and begin to ask what the reduced dimensions *mean*.\n",
"This meaning can be understood in terms of combinations of basis vectors.\n",
"For example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$:\n",
"\n",
"$$\n",
"x = [x_1, x_2, x_3 \\cdots x_{64}]\n",
"$$\n",
"\n",
"One way we can think about this is in terms of a pixel basis.\n",
"That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image:\n",
"\n",
"$$\n",
"{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n",
"$$\n",
"\n",
"One way we might imagine reducing the dimension of this data is to zero out all but a few of these basis vectors.\n",
"For example, if we use only the first eight pixels, we get an eight-dimensional projection of the data, but it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels!"
]
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"\n",
"[figure source in Appendix](06.00-Figure-Code.ipynb#Digits-Pixel-Components)"
]
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"The upper row of panels shows the individual pixels, and the lower row shows the cumulative contribution of these pixels to the construction of the image.\n",
"Using only eight of the pixel-basis components, we can only construct a small portion of the 64-pixel image.\n",
"Were we to continue this sequence and use all 64 pixels, we would recover the original image."
]
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"But the pixel-wise representation is not the only choice of basis. We can also use other basis functions, which each contain some pre-defined contribution from each pixel, and write something like\n",
"\n",
"$$\n",
"image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n",
"$$\n",
"\n",
"PCA can be thought of as a process of choosing optimal basis functions, such that adding together just the first few of them is enough to suitably reconstruct the bulk of the elements in the dataset.\n",
"The principal components, which act as the low-dimensional representation of our data, are simply the coefficients that multiply each of the elements in this series.\n",
"This figure shows a similar depiction of reconstructing this digit using the mean plus the first eight PCA basis functions:"
]
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"source": [
"\n",
"[figure source in Appendix](06.00-Figure-Code.ipynb#Digits-PCA-Components)"
]
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"source": [
"Unlike the pixel basis, the PCA basis allows us to recover the salient features of the input image with just a mean plus eight components!\n",
"The amount of each pixel in each component is the corollary of the orientation of the vector in our two-dimensional example.\n",
"This is the sense in which PCA provides a low-dimensional representation of the data: it discovers a set of basis functions that are more efficient than the native pixel-basis of the input data."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "uj6oDXjbbDZY"
},
"source": [
"### Choosing the number of components\n",
"\n",
"A vital part of using PCA in practice is the ability to estimate how many components are needed to describe the data.\n",
"This can be determined by looking at the cumulative *explained variance ratio* as a function of the number of components:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "MCgWMgtjbDZY",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 54
},
"outputId": "b789edc9-c03c-46d3-c410-f218047bba05"
},
"source": [
"pca = PCA().fit(digits.data)\n",
"plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
"plt.xlabel('number of components')\n",
"plt.ylabel('cumulative explained variance');"
],
"execution_count": 12,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "8HuuNkJvbDZa"
},
"source": [
"This curve quantifies how much of the total, 64-dimensional variance is contained within the first $N$ components.\n",
"For example, we see that with the digits the first 10 components contain approximately 75% of the variance, while you need around 50 components to describe close to 100% of the variance.\n",
"\n",
"Here we see that our two-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance. Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in multiple observations."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "Di-sgTnebDZa"
},
"source": [
"## PCA as Noise Filtering\n",
"\n",
"PCA can also be used as a filtering approach for noisy data.\n",
"The idea is this: any components with variance much larger than the effect of the noise should be relatively unaffected by the noise.\n",
"So if you reconstruct the data using just the largest subset of principal components, you should be preferentially keeping the signal and throwing out the noise.\n",
"\n",
"Let's see how this looks with the digits data.\n",
"First we will plot several of the input noise-free data:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "yvXIaAQVbDZa",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 248
},
"outputId": "378aaee9-d636-4b3d-d0d3-4abd0b7c0ad2"
},
"source": [
"def plot_digits(data):\n",
" fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n",
" subplot_kw={'xticks':[], 'yticks':[]},\n",
" gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
" for i, ax in enumerate(axes.flat):\n",
" ax.imshow(data[i].reshape(8, 8),\n",
" cmap='binary', interpolation='nearest',\n",
" clim=(0, 16))\n",
"plot_digits(digits.data)"
],
"execution_count": 13,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "RkLfMKg0bDZc"
},
"source": [
"Now lets add some random noise to create a noisy dataset, and re-plot it:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "eSd42D0_bDZc",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 248
},
"outputId": "480a7aba-2ab1-43c8-d147-cf13fe0a8c0a"
},
"source": [
"np.random.seed(42)\n",
"noisy = np.random.normal(digits.data, 4)\n",
"plot_digits(noisy)"
],
"execution_count": 14,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "dmzWkqdVbDZc"
},
"source": [
"It's clear by eye that the images are noisy, and contain spurious pixels.\n",
"Let's train a PCA on the noisy data, requesting that the projection preserve 50% of the variance:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "_fsxF4p4bDZd",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "35c186fb-59e4-4129-c371-f93cb8db98b9"
},
"source": [
"pca = PCA(0.50).fit(noisy)\n",
"pca.n_components_"
],
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"12"
]
},
"metadata": {
"tags": []
},
"execution_count": 15
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "md6_GNvqbDZd"
},
"source": [
"Here 50% of the variance amounts to 12 principal components.\n",
"Now we compute these components, and then use the inverse of the transform to reconstruct the filtered digits:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "BxBlVDjEbDZe",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 248
},
"outputId": "8d6e2914-6665-402f-8dcf-0117d1d6a7a9"
},
"source": [
"components = pca.transform(noisy)\n",
"filtered = pca.inverse_transform(components)\n",
"plot_digits(filtered)"
],
"execution_count": 16,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "XzUSZgydbDZf"
},
"source": [
"This signal preserving/noise filtering property makes PCA a very useful feature selection routine—for example, rather than training a classifier on very high-dimensional data, you might instead train the classifier on the lower-dimensional representation, which will automatically serve to filter out random noise in the inputs."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "alxnWqgjbDZf"
},
"source": [
"## Example: Eigenfaces\n",
"\n",
"Earlier we explored an example of using a PCA projection as a feature selector for facial recognition with a support vector machine (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n",
"Here we will take a look back and explore a bit more of what went into that.\n",
"Recall that we were using the Labeled Faces in the Wild dataset made available through Scikit-Learn:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "osR5O3hYbDZg",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "f3bbd475-d661-4120-8c3e-2c5632f5aba0"
},
"source": [
"from sklearn.datasets import fetch_lfw_people\n",
"faces = fetch_lfw_people(min_faces_per_person=60)\n",
"print(faces.target_names)\n",
"print(faces.images.shape)"
],
"execution_count": 17,
"outputs": [
{
"output_type": "stream",
"text": [
"Downloading LFW metadata: https://ndownloader.figshare.com/files/5976012\n",
"Downloading LFW metadata: https://ndownloader.figshare.com/files/5976009\n",
"Downloading LFW metadata: https://ndownloader.figshare.com/files/5976006\n",
"Downloading LFW data (~200MB): https://ndownloader.figshare.com/files/5976015\n"
],
"name": "stderr"
},
{
"output_type": "stream",
"text": [
"['Ariel Sharon' 'Colin Powell' 'Donald Rumsfeld' 'George W Bush'\n",
" 'Gerhard Schroeder' 'Hugo Chavez' 'Junichiro Koizumi' 'Tony Blair']\n",
"(1348, 62, 47)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "3LRcKAWAbDZg"
},
"source": [
"Let's take a look at the principal axes that span this dataset.\n",
"Because this is a large dataset, we will use ``RandomizedPCA``—it contains a randomized method to approximate the first $N$ principal components much more quickly than the standard ``PCA`` estimator, and thus is very useful for high-dimensional data (here, a dimensionality of nearly 3,000).\n",
"We will take a look at the first 150 components:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "4YWL0_QwbDZi",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "ff8bda99-de03-4198-b2bb-53541d02f3a4"
},
"source": [
"from sklearn.decomposition import PCA as RandomizedPCA\n",
"pca = RandomizedPCA(150)\n",
"pca.fit(faces.data)"
],
"execution_count": 18,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"PCA(copy=True, iterated_power='auto', n_components=150, random_state=None,\n",
" svd_solver='auto', tol=0.0, whiten=False)"
]
},
"metadata": {
"tags": []
},
"execution_count": 18
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "33jCmfELbDZj"
},
"source": [
"In this case, it can be interesting to visualize the images associated with the first several principal components (these components are technically known as \"eigenvectors,\"\n",
"so these types of images are often called \"eigenfaces\").\n",
"As you can see in this figure, they are as creepy as they sound:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "1fXrqwoxbDZj",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 248
},
"outputId": "453b02ab-91d3-4ce7-d1c9-c4973577b7f3"
},
"source": [
"fig, axes = plt.subplots(3, 8, figsize=(9, 4),\n",
" subplot_kw={'xticks':[], 'yticks':[]},\n",
" gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
"for i, ax in enumerate(axes.flat):\n",
" ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')"
],
"execution_count": 19,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "zb8wkN_fbDZk"
},
"source": [
"The results are very interesting, and give us insight into how the images vary: for example, the first few eigenfaces (from the top left) seem to be associated with the angle of lighting on the face, and later principal vectors seem to be picking out certain features, such as eyes, noses, and lips.\n",
"Let's take a look at the cumulative variance of these components to see how much of the data information the projection is preserving:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "Ry6GoqKNbDZk",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 285
},
"outputId": "a22dc185-728f-483d-dd69-348aa5eceb5d"
},
"source": [
"plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
"plt.xlabel('number of components')\n",
"plt.ylabel('cumulative explained variance');"
],
"execution_count": 20,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"id": "Wr79lWxzbDZm"
},
"source": [
"We see that these 150 components account for just over 90% of the variance.\n",
"That would lead us to believe that using these 150 components, we would recover most of the essential characteristics of the data.\n",
"To make this more concrete, we can compare the input images with the images reconstructed from these 150 components:"
]
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "hKkUXFBYbDZm"
},
"source": [
"# Compute the components and projected faces\n",
"pca = RandomizedPCA(150).fit(faces.data)\n",
"components = pca.transform(faces.data)\n",
"projected = pca.inverse_transform(components)"
],
"execution_count": 21,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"deletable": true,
"editable": true,
"id": "Wk1sHwWBbDZm",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 178
},
"outputId": "53c05bf0-1c4f-4dde-cc25-6aa05d0fb4fa"
},
"source": [
"# Plot the results\n",
"fig, ax = plt.subplots(2, 10, figsize=(10, 2.5),\n",
" subplot_kw={'xticks':[], 'yticks':[]},\n",
" gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
"for i in range(10):\n",
" ax[0, i].imshow(faces.data[i].reshape(62, 47), cmap='binary_r')\n",
" ax[1, i].imshow(projected[i].reshape(62, 47), cmap='binary_r')\n",
" \n",
"ax[0, 0].set_ylabel('full-dim\\ninput')\n",
"ax[1, 0].set_ylabel('150-dim\\nreconstruction');"
],
"execution_count": 22,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
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"The top row here shows the input images, while the bottom row shows the reconstruction of the images from just 150 of the ~3,000 initial features.\n",
"This visualization makes clear why the PCA feature selection used in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) was so successful: although it reduces the dimensionality of the data by nearly a factor of 20, the projected images contain enough information that we might, by eye, recognize the individuals in the image.\n",
"What this means is that our classification algorithm needs to be trained on 150-dimensional data rather than 3,000-dimensional data, which depending on the particular algorithm we choose, can lead to a much more efficient classification."
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"## Principal Component Analysis Summary\n",
"\n",
"In this section we have discussed the use of principal component analysis for dimensionality reduction, for visualization of high-dimensional data, for noise filtering, and for feature selection within high-dimensional data.\n",
"Because of the versatility and interpretability of PCA, it has been shown to be effective in a wide variety of contexts and disciplines.\n",
"Given any high-dimensional dataset, I tend to start with PCA in order to visualize the relationship between points (as we did with the digits), to understand the main variance in the data (as we did with the eigenfaces), and to understand the intrinsic dimensionality (by plotting the explained variance ratio).\n",
"Certainly PCA is not useful for every high-dimensional dataset, but it offers a straightforward and efficient path to gaining insight into high-dimensional data.\n",
"\n",
"PCA's main weakness is that it tends to be highly affected by outliers in the data.\n",
"For this reason, many robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components.\n",
"Scikit-Learn contains a couple interesting variants on PCA, including ``RandomizedPCA`` and ``SparsePCA``, both also in the ``sklearn.decomposition`` submodule.\n",
"``RandomizedPCA``, which we saw earlier, uses a non-deterministic method to quickly approximate the first few principal components in very high-dimensional data, while ``SparsePCA`` introduces a regularization term (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)) that serves to enforce sparsity of the components.\n",
"\n",
"In the following sections, we will look at other unsupervised learning methods that build on some of the ideas of PCA."
]
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"\n",
"< [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) | [Contents](Index.ipynb) | [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) >\n",
"\n",
"\n"
]
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}