{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction about PCA\n", "\n", "PCA (Principal Component Analysis) is a technique used to emphasize variation and bring out strong patterns in a dataset. It's often used to make data easy to explore and visualize. PCA is also a technique widely used in the field of bioinformatics for the analysis of gene expression data, and for the analysis of data from other high-throughput technologies.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "PCA is a powerful statistical technique that helps in understanding the underlying structure of large datasets, particularly useful in fields like bioinformatics, genomics, and other high-throughput technologies. Let's dive into the basics and apply PCA on a real dataset.\n", "\n", "## What is PCA?\n", "\n", "PCA is a dimensionality reduction technique that transforms a large set of variables into a smaller one that still contains most of the information in the large set. The goal is to reduce the dimensionality of the data by finding a new set of variables, the principal components, which are uncorrelated, and which are ordered by the amount of variance they capture from the data.\n", "\n", "## Why use PCA?\n", "\n", "- **Data Visualization**: Simplify the complexity in high-dimensional data while retaining the trend and patterns.\n", "- **Feature Extraction and Engineering**: Reduce the number of variables in a dataset, by combining them into a set of principal components, without losing much information.\n", "- **Noise Reduction**: Eliminate noise by focusing on the components that maximize variance.\n", "- **Efficiency**: Improve computational and storage efficiency for high-dimensional data.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Important concepts in PCA\n", "\n", "### Principal Components\n", "\n", "Principal components are the new set of variables that are obtained from the original variables by linear transformation. The first principal component captures the most variance in the data, and each subsequent component captures the remaining variance in decreasing order.\n", "\n", "### Eigenvalues and Eigenvectors\n", "\n", "Eigenvalues and eigenvectors are the mathematical concepts behind PCA. Eigenvalues represent the amount of variance captured by each principal component, while eigenvectors represent the direction of the principal components in the original feature space.\n", "\n", "### Variance Explained\n", "\n", "Variance explained is the proportion of variance in the data that is captured by each principal component. It helps us understand how much information is retained by each component.\n", "\n", "### Scree Plot\n", "\n", "A scree plot is a graphical representation of the eigenvalues of the principal components. It helps us visualize the amount of variance captured by each component and decide how many components to retain.\n", "\n", "### Loading Scores\n", "\n", "Loading scores represent the correlation between the original variables and the principal components. They help us understand the contribution of each variable to the principal components.\n", "\n", "### Biplot\n", "\n", "A biplot is a graphical representation of the loading scores and the sample scores in the reduced space. It helps us visualize the relationship between variables and samples in the reduced space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Hands-on Example: PCA in Action\n", "\n", "Let's apply PCA on a dataset to see how it works in practice. We'll use a gene expression dataset as an example, which is common in bioinformatics.\n", "\n", "### Step 1: Import Necessary Libraries\n", "\n", "First, we need to import the libraries necessary for our analysis." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from sklearn.decomposition import PCA\n", "from sklearn.preprocessing import StandardScaler" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 2: Load and Prepare the Dataset\n", "\n", "For this example, we'll simulate a gene expression dataset. In real-life scenarios, this data might come from high-throughput sequencing experiments." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

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	Gene_1	Gene_2	Gene_3	Gene_4	Gene_5	Gene_6	Gene_7	Gene_8	Gene_9	Gene_10	...	Gene_41	Gene_42	Gene_43	Gene_44	Gene_45	Gene_46	Gene_47	Gene_48	Gene_49	Gene_50
Sample_1	0.548814	0.715189	0.602763	0.544883	0.423655	0.645894	0.437587	0.891773	0.963663	0.383442	...	0.359508	0.437032	0.697631	0.060225	0.666767	0.670638	0.210383	0.128926	0.315428	0.363711
Sample_2	0.570197	0.438602	0.988374	0.102045	0.208877	0.161310	0.653108	0.253292	0.466311	0.244426	...	0.318569	0.667410	0.131798	0.716327	0.289406	0.183191	0.586513	0.020108	0.828940	0.004695
Sample_3	0.677817	0.270008	0.735194	0.962189	0.248753	0.576157	0.592042	0.572252	0.223082	0.952749	...	0.896547	0.367562	0.435865	0.891923	0.806194	0.703889	0.100227	0.919483	0.714241	0.998847
Sample_4	0.149448	0.868126	0.162493	0.615560	0.123820	0.848008	0.807319	0.569101	0.407183	0.069167	...	0.398221	0.209844	0.186193	0.944372	0.739551	0.490459	0.227415	0.254356	0.058029	0.434417
Sample_5	0.311796	0.696343	0.377752	0.179604	0.024679	0.067250	0.679393	0.453697	0.536579	0.896671	...	0.863856	0.117532	0.517379	0.132068	0.716860	0.396060	0.565421	0.183280	0.144848	0.488056

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5 rows × 50 columns

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" ], "text/plain": [ " Gene_1 Gene_2 Gene_3 Gene_4 Gene_5 Gene_6 \\\n", "Sample_1 0.548814 0.715189 0.602763 0.544883 0.423655 0.645894 \n", "Sample_2 0.570197 0.438602 0.988374 0.102045 0.208877 0.161310 \n", "Sample_3 0.677817 0.270008 0.735194 0.962189 0.248753 0.576157 \n", "Sample_4 0.149448 0.868126 0.162493 0.615560 0.123820 0.848008 \n", "Sample_5 0.311796 0.696343 0.377752 0.179604 0.024679 0.067250 \n", "\n", " Gene_7 Gene_8 Gene_9 Gene_10 ... Gene_41 Gene_42 \\\n", "Sample_1 0.437587 0.891773 0.963663 0.383442 ... 0.359508 0.437032 \n", "Sample_2 0.653108 0.253292 0.466311 0.244426 ... 0.318569 0.667410 \n", "Sample_3 0.592042 0.572252 0.223082 0.952749 ... 0.896547 0.367562 \n", "Sample_4 0.807319 0.569101 0.407183 0.069167 ... 0.398221 0.209844 \n", "Sample_5 0.679393 0.453697 0.536579 0.896671 ... 0.863856 0.117532 \n", "\n", " Gene_43 Gene_44 Gene_45 Gene_46 Gene_47 Gene_48 \\\n", "Sample_1 0.697631 0.060225 0.666767 0.670638 0.210383 0.128926 \n", "Sample_2 0.131798 0.716327 0.289406 0.183191 0.586513 0.020108 \n", "Sample_3 0.435865 0.891923 0.806194 0.703889 0.100227 0.919483 \n", "Sample_4 0.186193 0.944372 0.739551 0.490459 0.227415 0.254356 \n", "Sample_5 0.517379 0.132068 0.716860 0.396060 0.565421 0.183280 \n", "\n", " Gene_49 Gene_50 \n", "Sample_1 0.315428 0.363711 \n", "Sample_2 0.828940 0.004695 \n", "Sample_3 0.714241 0.998847 \n", "Sample_4 0.058029 0.434417 \n", "Sample_5 0.144848 0.488056 \n", "\n", "[5 rows x 50 columns]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Simulating a gene expression dataset\n", "np.random.seed(0)\n", "gene_data = np.random.rand(100, 50) # 100 samples and 50 genes\n", "samples = ['Sample_' + str(i) for i in range(1, 101)]\n", "genes = ['Gene_' + str(i) for i in range(1, 51)]\n", "\n", "# Creating a DataFrame\n", "df_gene = pd.DataFrame(data=gene_data, index=samples, columns=genes)\n", "\n", "# Display the first few rows of the dataset\n", "df_gene.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 3: Standardize the Data\n", "\n", "PCA is affected by scale, so we need to scale the features in our data before applying PCA. We will standardize the gene expression data to have a mean of 0 and a standard deviation of 1." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-8.99280650e-17 4.83640905e-17 1.17683641e-16 -3.01980663e-16\n", " 2.77555756e-17]\n", "[1. 1. 1. 1. 1.]\n" ] } ], "source": [ "# Standardizing the features\n", "scaler = StandardScaler()\n", "df_gene_scaled = scaler.fit_transform(df_gene)\n", "\n", "# Checking the standardized data\n", "print(df_gene_scaled.mean(axis=0)[:5]) # Should be close to 0\n", "print(df_gene_scaled.std(axis=0)[:5]) # Should be close to 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 4: Apply PCA\n", "\n", "Now, let's apply PCA to reduce the dimensionality of our gene expression dataset from 50 dimensions (genes) to 2 principal components. This will allow us to visualize the dataset in a 2D space." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

	Principal Component 1	Principal Component 2
Sample_1	-1.261112	-0.944955
Sample_2	0.675727	0.685626
Sample_3	0.799683	2.153984
Sample_4	0.604753	0.734807
Sample_5	-0.316385	0.306273

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" ], "text/plain": [ " Principal Component 1 Principal Component 2\n", "Sample_1 -1.261112 -0.944955\n", "Sample_2 0.675727 0.685626\n", "Sample_3 0.799683 2.153984\n", "Sample_4 0.604753 0.734807\n", "Sample_5 -0.316385 0.306273" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Initializing PCA\n", "pca = PCA(n_components=2)\n", "\n", "# Fitting PCA on the standardized data\n", "principalComponents = pca.fit_transform(df_gene_scaled)\n", "\n", "# Creating a DataFrame with the principal components\n", "df_pca = pd.DataFrame(data=principalComponents, columns=['Principal Component 1', 'Principal Component 2'], index=samples)\n", "\n", "# Display the first few rows of the PCA transformed data\n", "df_pca.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 5: Visualize the PCA Result\n", "\n", "Finally, let's visualize the result of PCA using a scatter plot. This will help us understand the distribution of our samples in the reduced space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Score plot\n", "\n", "A score plot is a graphical representation of the samples in the reduced space of the principal components. It helps us visualize the distribution of samples in the reduced space and identify patterns or clusters in the data.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Score plot\n", "plt.figure(figsize=(8,6))\n", "plt.scatter(principalComponents_full[:, 0], principalComponents_full[:, 1])\n", "plt.xlabel('Principal Component 1')\n", "plt.ylabel('Principal Component 2')\n", "plt.title('PCA of Gene Expression Data')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "plt.scatter(df_pca['Principal Component 1'], df_pca['Principal Component 2'])\n", "plt.xlabel('Principal Component 1')\n", "plt.ylabel('Principal Component 2')\n", "plt.title('PCA of Gene Expression Data')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.05625045 0.04943072]\n", "0.10568117624076481\n", "[5.62504539 4.94307224]\n", "10.568117624076482\n" ] } ], "source": [ "# Explained variance ratio\n", "print(pca.explained_variance_ratio_) # Explained variance of each principal component\n", "print(pca.explained_variance_ratio_.sum()) # Total explained variance\n", "# Understanding the explained variance ratio\n", "print(pca.explained_variance_ratio_ * 100) # Explained variance of each principal component in percentage\n", "print(pca.explained_variance_ratio_.sum() * 100) # Total explained variance in percentage\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Variance explained by each principal component\n", "\n", "Variability explained by each principal component is an important aspect of PCA. It helps us understand how much information is retained by each component. The cumulative variance explained by all the principal components can be used to decide how many components to retain.\n", "\n", "Values close to 1 indicate that the component captures a large amount of variance in the data, while values close to 0 indicate that the component captures very little variance.\n", "\n", "**Components are usually ordered by the amount of variance they capture, with the first component capturing the most variance, the second component capturing the second most variance, and so on.**\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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k1KlTdnEVdN3+/fsb/fv3t93O6//h4eFGVlaW7fjIkSMNk8lkXHPNNXb37927d76fW977b+PGjbZjhw8fNnx8fIybbrrJdmzChAlGSEiIcfr0abv733777UZAQIDt558XU8uWLQvsaxf77rvvDEnG888/b3f81ltvNUwmk10/6d+/v9GxY8dir5nXtn379sapU6eMU6dOGX/99ZfxwAMPGJKMiIgIu+fv4eFh7Ny5M981Cvvcv+uuu+za3XTTTUa9evVst/ft22d4eHgYN910k+19l+fCz4vCfp6OfJ45+j7Oi7koixcvNiQZb7zxRpHt8syePduQZMybN892LCsry+jdu7dRu3ZtW+x5fb9BgwZ2n2vTp083JBmdO3e2+zwfOXKk4eXlZWRkZNiOOfoefeihhwxJxm+//WY7lpqaaoSGhhotWrSw/RzyXuMOHToYmZmZtrZvvvmmIcnYvn27YRi5P6c2bdoYQ4YMsfuZpaenG6GhocagQYNsxxztF4ZR+O/kgIAAY/LkyfmOo+phqh4qrLypIY58g1ZSEydOtP3bbDarR48eMgxDEyZMsB2vU6eO2rVrp4MHD7rscS8cRTl79qySk5PVr1+/Eg/r+/v765prrtHChQvtphEtWLBAl112mZo1ayYpt8iA1WrV8OHDdfr0adt/wcHBatOmjVavXu3Q47399ttasWKF3X8//vijXZvw8HBFRUXpo48+0pAhQ3T69Gl98sknBS7WHjNmjN3P+dZbb1VISIh++OGHIuMo7et4zz332C3079evnywWiw4fPixJWrFihZKSkjRy5Ei718tsNqtXr1621ys+Pl5btmzR2LFjFRAQYLveoEGDFBYW5lAsgwcPVoMGDeym68XFxWn9+vUaOXKkbX3Jhc85LS1Np0+fVp8+fWQYhjZv3pzvupMmTXLo8Z15LQcOHGg3+tmpUyf5+/vb3iNWq1XfffedIiIiClwLl/eaf/XVV+rXr5/q1q1r9/oOHDhQFoulwOlmF2vUqJHdt9H+/v4aM2aMNm/erBMnTkjK/SbZx8dH8+fPt7X76aefdPr0aacKbuSNOm3dutWllbXGjBljN72qV69eMgxDd911l127Xr166ejRo8rJybE73rt3b3Xv3t12u1mzZrrhhhv0008/yWKxyDAMff3114qIiJBhGHav9ZAhQ5ScnJzv5zx27NgiR3vz/PDDDzKbzXrggQfsjj/88MMyDCPf54Izdu/erQYNGqhBgwbq0KGD3nrrLV133XX5RjT69+/v8PtMyh0duFC/fv105swZ2++c7777TlarVc8880y+dV2OFAZx5PPM2fdxUZz9XfnDDz8oODhYI0eOtB3z9PTUAw88oHPnzumXX36xa3/bbbfZfa716tVLkjR69Gi7z/NevXopKytLx44ds7u/I+/RH374QT179tTll19ua1e7dm3dc889OnTokHbt2mV3zfHjx9uNgvbr10+SbJ9BW7Zs0b59+3THHXfozJkztv6elpamq6++Wr/++mu+6cDF9Yui1KlTRxs2bNDx48eLbYvKjal6qLD8/f0l5c4dLit5CUWegIAA+fj4qH79+vmOnzlzxmWP+/333+v555/Xli1b7NYslKZa14gRI/Tdd99p3bp16tOnjw4cOKBNmzbZTXfat2+fDMNQmzZtCryGo0UDevbs6VBxiEcffVRffvmlYmJi9OKLLxb6x83F8ZhMJrVu3brYfapK+zpe/POvW7eupNzEQcp9vSRpwIABBd4/r4/mJVoFva7t2rVzKJGrUaOGRowYoXfeeUfHjh1T48aNbUlU3jQ9STpy5IieeeYZLVmyxBZnnuTk5HzXdGSqoOTca3nx6yblvnZ58Zw6dUopKSm2aWKF2bdvn7Zt26YGDRoUeD4hIaHYuFu3bp0vxrZt20rKXaMRHBysOnXqKCIiQp9//rmee+45SbnTjxo3blzoz7Ywo0aN0nPPPacZM2a4rLJWQZ9DktS0adN8x61Wq5KTk21TIqWC+13btm2Vnp6uU6dOycPDQ0lJSfrggw8KrUB68WtdUNXMghw+fFiNGjXK90d73jS8vPdGSbRo0UIffvihTCaTfHx81KZNGwUFBeVr52iseYp63/v7++vAgQPy8PBwKhm7kCOfZ868j4vj7O/Kw4cPq02bNvmSwsJ+Zs70T0n5no8j79HDhw/bErLCYrrw88TRz+6xY8fmu2ae5ORk2/2Ku2bea1yYV155RWPHjlXTpk3VvXt3XXvttRozZkyha49ReZE4ocLy9/dXo0aNtGPHDofaF/bHssViKfQ+BVWmK6xa3YUjOSV5rDy//fabhg0bpiuuuELvvPOOQkJC5OnpqY8//rjA4gCOioiIkK+vrxYuXKg+ffpo4cKF8vDw0G233WZrY7VaZTKZ9OOPPxb4PGvXrl3ixy/IwYMHbb/Atm/f7tJru+J1LO5nnfeN5Geffabg4OB87Vxd6nj06NH673//qy+++EKPPPKIvvjiC4WFhalLly6ScvvXoEGDlJiYqMcff1zt27dXrVq1dOzYMY0bNy7fN6je3t4OVUJz9rV05D3iCKvVqkGDBumxxx4r8HzeH1euMGbMGH311Vf6448/dMkll2jJkiW6//77na4UlzfqNG7cOC1evLjANkV9PjjzmePK11nK7V+F/SHZqVMnu9uOjDaVtVq1amngwIHFtnM2Vle9riXl7Pu4OO3bt5fk+s/YPGXdP0vC0c/uV1991fb5ebGLf9+V5vkMHz5c/fr107fffqvly5fr1Vdf1csvv6xvvvlG11xzTbH3R+VB4oQK7frrr9cHH3ygdevWqXfv3kW2zft2KCkpye54ab7xLIvH+vrrr+Xj46OffvrJrkz2xx9/nK+tMyNQtWrV0vXXX6+vvvpKs2bN0oIFC9SvXz81atTI1qZVq1YyDEOhoaEu/aO0IFarVePGjZO/v78eeugh2/4XBS2qz0uu8hiGof379+f7Y+5CzryOJZU3HS0oKKjIP+CaN28uKf/zkHL3kHJUr1691KpVK33++ecaNGiQdu7cqRdeeMF2fvv27dq7d68++eQTjRkzxnZ8xYoVDj9GQVz9WjZo0ED+/v7FfunRqlUrnTt3zqE/jguzf/9+GYZh917Zu3evJNkVCRg6dKgaNGig+fPnq1evXkpPT9edd95ZosccPXq0nn/+eUVFRWnYsGH5ztetWzffZ4OU+/lQFt9AF9Tv9u7dK19fX9tonp+fnywWS6le64I0b95cP//8s1JTU+1GnXbv3m07X9m0atVKVqtVu3btKvSP7qIU93nm6vdx27Zt1a5dOy1evFhvvvlmsV+ANW/eXNu2bZPVarX74qCsfmaOvEebN29e4GdlSWPK++z29/d3aZ8v6ndySEiI7r//ft1///1KSEhQt27d9MILL5A4VTGscUKF9thjj6lWrVqaOHGiTp48me/8gQMH9Oabb0rK/YCsX79+vnUR77zzjsvjyvtQvvCxLBaLQxvxms1mmUwmu9GpQ4cOFbhmolatWgX+AVaYESNG6Pjx4/roo4+0detWjRgxwu78zTffLLPZrKioqHzfohmG4dLpiLNmzdIff/yhDz74QM8995z69OmjSZMm5avGJ0mffvqp3TSTRYsWKT4+vshfOM68jiU1ZMgQ+fv768UXXyxwD5S8ksghISHq0qWLPvnkE7tpNitWrMg3N784o0aN0ubNmxUZGSmTyWS3YWXeN6IX/uwMw7C9B0rK1a+lh4eHbrzxRi1dulQbN27Mdz4v/uHDh2vdunX66aef8rVJSkrKt5anIMePH7cr+56SkqJPP/1UXbp0sRslrFGjhkaOHKmFCxdq7ty5uuSSS4pMzIuSN+q0ZcsWLVmyJN/5Vq1aaf369XZl17///nuXlvy/0Lp16+ymgx49elSLFy/W4MGDbXu+3XLLLfr6668LTGYLKsHvqGuvvVYWi0X//e9/7Y6/8cYbMplMlfKPxhtvvFEeHh6aMWNGvtEfR0Yfivs8K4v3cVRUlM6cOaOJEycW+L5Zvny5vv/+e0m5P7MTJ07YVQ/NycnRW2+9pdq1a6t///4ljqMgjrxHr732WsXExGjdunW2dmlpafrggw/UokULp6dNdu/eXa1atdJrr72mc+fO5Ttf0j5f0O9ki8WSb3plUFCQGjVqVOj2Aai8GHFChZb37Xte2fAxY8YoPDxcWVlZ+uOPP2wlVPNMnDhRL730kiZOnKgePXro119/tX2z5UodO3bUZZddpunTp9vKR3/55ZcO/aF33XXXadasWRo6dKjuuOMOJSQk6O2331br1q21bds2u7bdu3fXzz//rFmzZqlRo0YKDQ0tcB54nrz9eh555BHbH0sXatWqlZ5//nlNnz5dhw4d0o033ig/Pz/FxcXp22+/1T333KNHHnmk2Ofw448/2r4JvFCfPn3UsmVL/fXXX3r66ac1btw4RURESMrdO6lLly66//77tXDhQrv7BQYG6vLLL9f48eN18uRJzZ49W61bt9bdd9/tktexpPz9/fXuu+/qzjvvVLdu3XT77berQYMGOnLkiJYtW6a+ffva/mCcOXOmrrvuOl1++eW66667lJiYqLfeeksdO3Ys8Bd3YUaPHq0ZM2Zo8eLF6tu3r92oSfv27dWqVSs98sgjOnbsmPz9/fX111/nW1PgrLJ4LV988UUtX75c/fv31z333KMOHTooPj5eX331ldauXas6dero0Ucf1ZIlS3T99ddr3Lhx6t69u9LS0rR9+3YtWrRIhw4dyrfe8GJt27bVhAkT9Oeff6phw4aaM2eOTp48WeBo2ZgxY/Sf//xHq1evtis9XRJ5a522bNmS79zEiRO1aNEiDR06VMOHD9eBAwc0b968QrcTKK3w8HANGTLErhy5lPvHdJ6XXnpJq1evVq9evXT33XcrLCxMiYmJio2N1c8//5xv/x1HRURE6KqrrtKTTz6pQ4cOqXPnzlq+fLkWL16shx56qMyec1lq3bq1nnzyST333HPq16+fbr75Znl7e+vPP/9Uo0aNbOXUC1Pc51lZvI9HjBih7du364UXXtDmzZs1cuRINW/eXGfOnFF0dLRWrlxpm3Z7zz336P3339e4ceO0adMmtWjRQosWLdLvv/+u2bNnu7wgkyPv0SeeeEJffPGFrrnmGj3wwAMKDAzUJ598ori4OH399ddOT6n18PDQRx99pGuuuUYdO3bU+PHj1bhxYx07dkyrV6+Wv7+/li5d6vRzKeh3crt27dSkSRPdeuut6ty5s2rXrq2ff/5Zf/75Z749IFEFlEfpPqC09u7da9x9991GixYtDC8vL8PPz8/o27ev8dZbb9mVPk1PTzcmTJhgBAQEGH5+fsbw4cONhISEQsvSXlhC2DByyzTXqlUr3+MXVEb3wIEDxsCBAw1vb2+jYcOGxr///W9jxYoVDpUj/7//+z+jTZs2hre3t9G+fXvj448/LrDs7O7du40rrrjCqFmzpiHJVga1sHLohmEYo0aNspXaLszXX39tXH755UatWrWMWrVqGe3btzcmT55s7Nmzp9D7XPi4hf338ccfGzk5Ocall15qNGnSxK6ErWH8UzJ2wYIFhmH8U1r2iy++MKZPn24EBQUZNWvWNK677jq7krylfR0LK0d+cansgsrJ5x0fMmSIERAQYPj4+BitWrUyxo0bZ1cCOu917dChg+Ht7W2EhYUZ33zzTYFxF+fSSy81JBnvvPNOvnO7du0yBg4caNSuXduoX7++cffdd9vKgV9Yir+wvpx3rqSvpaQCy+4WVIL78OHDxpgxY4wGDRoY3t7eRsuWLY3JkyfblRFOTU01pk+fbrRu3drw8vIy6tevb/Tp08d47bXX7Ep0F6R58+bGddddZ/z0009Gp06dbLF/9dVXhd6nY8eOhoeHh/H3338Xee08F5Yjv9iF74eLP0tef/11o3Hjxoa3t7fRt29fY+PGjYWWr7443sL6Z0GfW3k/j3nz5tl+fl27ds3Xhw3DME6ePGlMnjzZaNq0qeHp6WkEBwcbV199tfHBBx8UG1NRUlNTjalTpxqNGjUyPD09jTZt2hivvvqqXRlow3C+HLkjbQvrj3nnHPncL+zzdM6cOUbXrl0Nb29vo27dukb//v2NFStW2MVY0M/Tkc8zR9/HjpQjv9DKlSuNG264wQgKCjJq1KhhNGjQwIiIiDAWL15s1+7kyZPG+PHjjfr16xteXl7GJZdckm8rj8L6vjP91pn36IEDB4xbb73VqFOnjuHj42P07NnT+P777x167MK2I9m8ebNx8803G/Xq1TO8vb2N5s2bG8OHDzdWrlxpa+NMvyjod3JmZqbx6KOPGp07dzb8/PyMWrVqGZ07dy7w8xuVn8kwymk1JABcZM2aNbrqqqv01Vdf6dZbb3V3OKgGunbtqsDAQK1cudLdoaCK4fMsvxYtWig8PNw2TRCo7FjjBACoFjZu3KgtW7bYLcgHAMBRrHECAFRpO3bs0KZNm/T6668rJCQkX9EUAAAcwYgTAKBKW7RokcaPH6/s7Gx98cUX8vHxcXdIAIBKiDVOAAAAAFAMRpwAAAAAoBgkTgAAAABQjGpXHMJqter48ePy8/OTyWRydzgAAAAA3MQwDKWmpqpRo0bFbrZc7RKn48ePq2nTpu4OAwAAAEAFcfToUTVp0qTINtUucfLz85OU++L4+/u75JrZ2dlavny5Bg8eLE9PT5dcE9UH/QelQf9BSdF3UBr0H5RGReo/KSkpatq0qS1HKEq1S5zypuf5+/u7NHHy9fWVv7+/23/4qHzoPygN+g9Kir6D0qD/oDQqYv9xZAkPxSEAAAAAoBgkTgAAAABQDBInAAAAACgGiRMAAAAAFIPECQAAAACKQeIEAAAAAMUgcQIAAACAYpA4AQAAAEAxSJwAAAAAoBgkTgAAAABQDBInAAAAACgGiRMAAAAAFIPECQAAAACKQeIEAAAAAMUgcQIAAACAYpA4AQAAAEAxSJwAAAAAlAuL1dCGuERtOm3ShrhEWayGu0NymFsTp19//VURERFq1KiRTCaTvvvuu2Lvs2bNGnXr1k3e3t5q3bq15s6dW+ZxAgAAAPiHxWpo3YEzWrzlmNYdOONQAhS9I16Xv7xKo+ds1Kf7zBo9Z6Muf3mVonfEl0PEpVfDnQ+elpamzp0766677tLNN99cbPu4uDhdd911uu+++zR//nytXLlSEydOVEhIiIYMGVIOEQMAAADVW/SOeEUt3aX45AzbsZAAH0VGhGloeEih95k0L1YXp1cnkjM0aV6s3h3drdD7VhRuTZyuueYaXXPNNQ63f++99xQaGqrXX39dktShQwetXbtWb7zxBokTAAAA4ASL1VBMXKISUjMU5OejnqGBMnuYirxPSRIgi9VQ1NJd+e4jSYYkk6Sopbs0KCy42Md3J7cmTs5at26dBg4caHdsyJAheuihhwq9T2ZmpjIzM223U1JSJEnZ2dnKzs52SVx513HV9VC90H9QGvQflBR9B6VB/6lYLFZDGw+fVUJqpoL8vNWjed1iE5Cfdp7U8z/s1omUf/5ODvb31lPXtteQjg0LfZxnl+wsMgGKXLJTrev7qlEdH3mac1cF/d/aQ3ajUwXdNz45Q+v2J6hXaGAxz9a1nOnDlSpxOnHihBo2tP9BNmzYUCkpKTp//rxq1qyZ7z4zZ85UVFRUvuPLly+Xr6+vS+NbsWKFS6+H6oX+g9Kg/6Ck6DsoDfqP+209Y9I3hzyUlPVPolTHy9DNLazqXK/gdUdbz5g0Z29eqYN/7nciJUNTvtyiu9r+c1+rIZ3LllKzpdRsk06kmAuNxZB0MiVTA2ev1fTOOQr+35/aP+zxkCOlFZb/tkFn/irfYhHp6ekOt61UiVNJTJ8+XdOmTbPdTklJUdOmTTV48GD5+/u75DGys7O1YsUKDRo0SJ6eni65JqoP+g9Kg/6DkqLvoDToP2XD2ZGjn3ae1MfrtuYbAUrOMunjvWa9dXvnfKNHFquhma//KilT+eU+1rwDnvo9qaZOp2XrbHqW8uo+PD6kjfTXvmKfRw0Pk7r26qOuTetIko77H9K2n/YWe7/B/XqV+4hT3mw0R1SqxCk4OFgnT560O3by5En5+/sXONokSd7e3vL29s533NPT0+Vv9LK4JqoP+g9Kg/6DkqLvoDToP67jbMEFi9XQCz/uKXLa3As/7pGvt6dW7zmlhNQMJaRm6uiZdJ1OyyoyliyLVXsS0my3TSYp0NdLtX28HHoun03oqZ4t69tu39O/tT5df0QnkjMKjNckKTjAR71bB5X7Gidn+m+lSpx69+6tH374we7YihUr1Lt3bzdFBAAAAPyjPAou7D6RooV/HnVo3dCPO07oq01/O/087uvfShGdQ9SgtrcCa3mphtlDFquhd9YcKDYB6hlaz+642cOkyIgwTZoXK9P/YrvwPpIUGRFWoQtDSG5OnM6dO6f9+/fbbsfFxWnLli0KDAxUs2bNNH36dB07dkyffvqpJOm+++7Tf//7Xz322GO66667tGrVKi1cuFDLli1z11MAAAAAJJWsTHdxFeckacrnm/Xjg7XVpqGfJGn5zpOa8/shh2IKqVNTU65qrSB/bwX5eetkSqYil+ws9n792zZQx0YBdsdKkwANDQ/Ru6O75Xt9got5fSoStyZOGzdu1FVXXWW7nbcWaezYsZo7d67i4+N15MgR2/nQ0FAtW7ZMU6dO1ZtvvqkmTZroo48+ohQ5AAAAXMrZkSNHRo0GtG+o40nndSQxXUcS0zU0PFj7Tp4rcuRIknKshlbuTrAlTh0b+atbszqKPZJU7PPo3bKeerf6ZwTIYjX03i+OjBoVvNaoNAnQ0PAQDQoL1rr9CVr+2wYN7tfLLdPzSsqtidOVV14pwyi8csbcuXMLvM/mzZvLMCoAAABUZyVZb1TcqNHk+bGyGvajNM0CfXU2vej1Rnn8ff75s/3qDg11ZbsgXf7yKqcTIFdMm8tLgJydkpj3+L1CA3XmL0O9HLxPRVGp1jgBAAAAjiqr9UZXd2ioI4npijuVpoOnz2n9wTPFjhpZ/ndBH08PNa3rq2aBvqrpZZan2ceh5xJav7bdbXdPmzN7mOxGsqoDEicAAABUOWWx3sgk6Ylvtiv1fKwtEXLGczd21OhezWUy/ZPMWKyGQgJ8SjR1zhXT5koyalRdkTgBAACgSnG2St25zBxtPZqk5TtPFFupLik9W5JU09Os0Pq11LJBLXmZTfpm8/Fi42rdwM8uaZJKP3WutNPmqtuoUWmQOAEAAKBCc2bKnSPrjR5btE31anvr0ha5ozjbjiZp1EcbHI4naliYxvRuYUuCLFZD6w4muqXggkQCVF5InAAAAFBhOTvlLiYusdj1RikZOfp03WFb4tSmoZ9a1PNVvdre2nT4bLExtW3obzdy5O6CCygfJE4AAACokIqbcvefkV3UOshPe06kaveJVHUI8XP42hdWqWvg5601j14li9UoUaU6iYIL1QGJEwAAAMqFq6fc/euLLXbHh3YM1tg+LRyK5fpOjfIdc+d6I1R8JE4AAAAoc85MuTublqUv/zxS7JQ7SfL19FB44zpqG1xbvULrqWdoYImr1EmsN0LhSJwAAABQpoqbcvfIkLbyrmHW1r+TtfVoko4kpjt87Zk3d9INXRvbHWO9EcoCiRMAAAAcZrEa2hCXqE2nTaoXl6jerYOKTCgc2Rtp1op9sljtW4T4+yg+pfgRpyD//BvIst4IZYHECQAAAA6xn25n1qf7NhZZ4S4hNUMLYo4WuzeSxWqoe/O6GtA+SJ2aBKhT4zqq7VOjxIUaJEaN4HokTgAAACiWIxXuIjr/M2Vu2sIt+ib2mMPXH9O7uW7o4topd4wawZU83B0AAAAAKrbiptsZyq1wF5903na8WaCvTCapad2aDj1GkF/hU+6CA+zPBQf46N3R3Ryacge4CiNOAAAA1ZAzpcEd2VRWkr6O/VtTBrSRJI3r00ITLg+VrxdT7lA1kDgBAABUM8WVBrdaDe0+kaoNcWfUv20DJaQWnzRJUtO6vrZ/1/H1sv2bKXeoCkicAAAAqpHC1irFJ2fovnmx6tTYX4fOpCslI0eS9O9r2+uSxnUcunZBFe4k11S5A9yNxAkAAKASc2bKXVFrlfJsO5YiSarlZVb3FoFqUte31JvKSky5Q+VH4gQAAFBJFTflLo/Famjn8WR9GXPEobVKz98Yrtsvbaoa5n/qiJV2up3ElDtUbiROAAAAlVBx5cGnX9teHiaT1h88ow1xiUr939Q7R/j51LBLmiSm2wEkTgAAAJVMceXBTZJe/nG3LBc08POpoTZBtRV7JKnY6xdUGlz6Z7rduv0JWv7bBg3u10u9Wwcx3Q7VAokTAACAmzmzTkkqvjy4IcliSJ2bBuja8BD1blVPHRsFSFKpSoNLudPteoUG6sxfhnqxRgnVCIkTAACAGzm6TkmS4k6n6aedJ/TVxqMOXfuuvqG6oUtju2OuWKsEVEcexTcBAABAWchbp3Tx6FHeOqUlW44pK8dqO75o01G99ONuHTiV5tD1C5pyl7dWKTjA/lxwgI/eHd2NtUpAIRhxAgAAcIPi1ilJ0gNfbtEHo80aHB4sSRrYoaF2Hk/RVe0a6L+rD+h0amaJptxRGhxwHokTAACAGxS3TinP4q3HbIlT12Z1NXd8T0lSQ3+fUk25ozQ44Bym6gEAALiIxWpo3YEzWrzlmNYdOCOLtfCtZhNSi0+aJGlwWHCBx5lyB5QvRpwAAABcoLgiD+ezLPp13ykt33lSXjU8NKxzI4euG+RfcGlwiSl3QHkicQIAACilojajvW9erDo3CdCek6nKyM4t9ODrZdZT13VQSIBPqUqDS0y5A8oLU/UAAABKwZEiD1v/TlZGtlWN69TU+L4tNGfcpfLxNCsyIkzSP+uS8lAaHKh4GHECAAAoBUeLPLx4U7hG9mwmk+mfRChvndLFU/yCC9nHCYD7kDgBAABcwGI1HFozlJaZoxW7TuqDXw84dN1a3jXskqY8rFMCKgcSJwAAgP8prsBDVo5Vv+07pcVbjmvFrpM6n21x+NoFbUabh3VKQMXHGicAAAD9U+Dh4ml3J5IzNGlerKJ3xOtkSoYmfLJRS7Ye1/lsi1rU89WUAa1Vv7ZXvnVKeUzKTb6KK/IAoGJjxAkAAFR7xRV4MEmKWrpLax8foGvCgxUSUFM3dGmkTk0CZDKZFN7Iv1Sb0QKo+EicAABAtVdcgQdDUnxyhmLiEvXu6O75zlPkAaj6SJwAAECV5GiRB0lasyfBoWsmpBaeXFHkAajaSJwAAECVU1yRhxyLVRbDkHcNsyQpy2J16LpFFXiQKPIAVGUUhwAAAFVKUUUe7psXqwlz/9RlM1dp0aa/befuv7K1ansX/n0yBR4AkDgBAIAqo7giD5K0cneCTp/L1M+7TtrONfDz1mu3dZJJylcdjwIPACQSJwAAUIUUV+QhzyOD2+qDMT3sjuUVeAgOsJ+OFxzgo3dHd6PAA1DNscYJAABUCYZhaMexZIfaNg30lac5//fHFHgAUBgSJwAAUKEVVx3vzLlMfbfluL7aeFS7T6Q6dM2iijxQ4AFAQUicAABAhVVYdbynruugml5mLfzzb63cfVLZltwVTJ5mk2p511ByenaB65xMyp16R5EHAM4icQIAABVSXnW8ixOg+OQMTf58s92xTk0CdFv3JhrWubHWHTytSfNiZZLs7kuRBwClQeIEAAAqnKKq4+UxmaSxvVtoxKVN1SHE33Y8r8jDxSNVwRfs4wQAziJxAgAAFY4j1fEMQxrSMdguacpDkQcArkbiBAAAKgyL1dDKv07q9RV7HWqfkFp4ckWRBwCuROIEAADKXHGV8STph+3xemHZXzqWdN7h6xZVHQ8AXInECQAAlKnCKuM9c32YBoY1tO2n5OPpoWNJ51XX11O39mii72KP6/S5TKrjAagQSJwAAECZKaoy3qT5sbomPFjvju4uSerfNkhv3t5FQzoGy8fTrO7N6lIdD0CFkX/LbAAAABdwpDLe8p0nlJ1jlZS7JumGLo3l42mW9E91vOAA++l4wQE+end0N6rjAShXjDgBAIAy4UhlPIshbTx8ttAiDlTHA1BRkDgBAIAyUVTFO2faUR0PQEVA4gQAABxWXHW8o4np+mz9YV3fKcThindUxgNQGZA4AQAAhxRVHa+Or5c+/j1OP/91UlZDSkjJ0OvDuygkwEcnkjOojAeg0iNxAgAAxSquOt6F+rWprxu6NpbZw6TIiDAq4wGoEkicAABAkRypjidJI3s21V19Q9WmoZ/tWF5lvItHqoIDfBQZEUZlPACVBokTAAAokiPV8SRpWOfGdklTHirjAagKSJwAAEChrFZDq3afdKhtUdXxqIwHoLIjcQIAoJqxWA1tiEvUptMm1YtLVO/WQflGfzKyLfo69m/939o4HTyV5tB1qY4HoCojcQIAoBqxr4xn1qf7NirkgvVGFquh/6zcp8/WH1ZiWpYkqba3WYYhpWVZCrwm1fEAVAce7g4AAACUj7zKeBevVzqRnKFJ82IVvSNeZg+Tft9/WolpWWpcp6aeuT5M6/89UK8P7yyT/qmGl4fqeACqC0acAACoBoqqjGcoNwGKWrpLg8KC9fDgdjqTlqmhHYNVw5z7HSvV8QBUdyROAABUA8VVxjOUuydTTFxioUUcqI4HoDojcQIAoBooquKdM+2ojgegumKNEwAA1UC9Wl4OtaMyHgAUjMQJAIBqoHer+qrpaS70vElSCJXxAKBQJE4AAFRSFquhdQfOaPGWY1p34Iws1n9KP2z7O0njPo7R3pOpknKn2D0bESaJyngAUBKscQIAoBKy348pV0iAjyZcHqoNcYlaseukJKmWVw29PaqbJGlEz2YK8PWkMh4AlACJEwAAlUzefkwXlxaPT87Q88v+kiR5mKQbuzbWg1e3sWuTVxlv3f4ELf9tgwb366XerYMYaQKAYpA4AQBQiRS1H1MeH08PLZ7cV+2C/Qs8b/YwqVdooM78ZagX5cQBwCGscQIAoBIpbj8mScrItioxLbucIgKA6oHECQCASuTvs+kOtXN03yYAgGOYqgcAQCWQbbFq4cajeiV6j0Pt2Y8JAFyLxAkAgArMMAz9tPOEXoneo4On0yRJZpNkKWSRk0m5VfLYjwkAXIvECQAAN7NYDcXEJSohNUNBfrlJj9nDpC1HkxS1dKc2H0mSJAXW8tK/BrRW/dreeuCLzZJkVySC/ZgAoOyQOAEA4EaF7ccUGREmD5NJm48kqaanWRP7heqeK1rKz8dTkuRpNrEfEwCUIxInAADcpLD9mE4kZ2jSvFi9M6qbnrimvW7u2lhB/vZrlvL2YypopAoA4HokTgAAuEFR+zEZyp12N+P7XVr7+IBCkyGzh0m9W9UryzABAP9DOXIAANyguP2YDEnxyRmKiUssv6AAAIUicQIAoJwZhqGVu0861Jb9mACgYiBxAgCgnB06k67/+y3OobbsxwQAFQOJEwAA5eBcZo7t36H1a2n0Zc1Uy9uswko5mJRbXY/9mACgYiBxAgDABSxWQ+sOnNHiLce07sAZWay5ZR/OZebo1Z9267IXV+rAqXO29s/deIlev62zJOVLntiPCQAqHqrqAQBQSgXtxRTs76Or2jfQil0ndfpcliTp29hjemRIO1uboeEhend0N/ZjAoBKgMQJAIBSKHQvppQMfRFzVJLUsn4tPXFNew0Ka5jv/uzHBACVA4kTAAAlVNReTHn8fWrohwf7ycfTXGgb9mMCgIqPNU4AAJRQcXsxSVJKRo42H0kqn4AAAGWGxAkAgBI6lpTuUDv2YgKAyo+pegAAOMkwDP2w/YRe+nG3Q+3ZiwkAKj8SJwAAnLDt7yQ99/0u/XnorCTJwyRZC1nkZFJuhTz2YgKAyo/ECQCAC1isRoEV7k4kZ+iVn3brm9hjkqSanmbd17+VWtT31UNfbpEkuyIR7MUEAFULiRMAAP9T0H5MIf/bU0mSLWm6uVtjPTakvYIDcqfgedfwYC8mAKji3F4c4u2331aLFi3k4+OjXr16KSYmpsj2s2fPVrt27VSzZk01bdpUU6dOVUYGi24BAKWTtx/TxVXyTiRn5O7TZEh39Q3V4sl9NWt4F1vSJOXuxbT28QH64u7L9ObtXfTF3Zdp7eMDSJoAoApx64jTggULNG3aNL333nvq1auXZs+erSFDhmjPnj0KCgrK1/7zzz/XE088oTlz5qhPnz7au3evxo0bJ5PJpFmzZrnhGQAAqoKi9mMylDvtbsb3u7T28QGFTrtjLyYAqNrcOuI0a9Ys3X333Ro/frzCwsL03nvvydfXV3PmzCmw/R9//KG+ffvqjjvuUIsWLTR48GCNHDmy2FEqAACKUtx+TIak+OQMxcQlll9QAIAKxW0jTllZWdq0aZOmT59uO+bh4aGBAwdq3bp1Bd6nT58+mjdvnmJiYtSzZ08dPHhQP/zwg+68885CHyczM1OZmZm22ykpKZKk7OxsZWdnu+S55F3HVddD9UL/QWnQf1zj+NlzDrWLT0pTdrZ/GUdTPug7KA36D0qjIvUfZ2JwW+J0+vRpWSwWNWzY0O54w4YNtXt3wfti3HHHHTp9+rQuv/xyGYahnJwc3Xffffr3v/9d6OPMnDlTUVFR+Y4vX75cvr6+pXsSF1mxYoVLr4fqhf6D0qD/lFyOVXplq1n/1MEr3MGdW/TD35vLPqhyRN9BadB/UBoVof+kpzu2kblUyarqrVmzRi+++KLeeecd9erVS/v379eDDz6o5557Tk8//XSB95k+fbqmTZtmu52SkqKmTZtq8ODB8vd3zbeG2dnZWrFihQYNGiRPT0+XXBPVB/0HpUH/cY112Tv0dezxAtc4SXn7MXlryogrqkxpcfoOSoP+g9KoSP0nbzaaI9yWONWvX19ms1knT560O37y5EkFBwcXeJ+nn35ad955pyZOnChJuuSSS5SWlqZ77rlHTz75pDw88i/Z8vb2lre3d77jnp6eLv9BlcU1UX3Qf1Aa9J/8CtuPyTAMLd0Wr85NAtS8Xi1J0lPXd1SPFvU0/Zvtkgrbj6mjfLy9yvdJlAP6DkqD/oPSqAj9x5nHd1vi5OXlpe7du2vlypW68cYbJUlWq1UrV67UlClTCrxPenp6vuTIbDZLkgyjsO8JAQDVTWH7Md1zRUut2HVSfxw4o6vaNdCccZfKZDKpjq+Xbu/ZTHV8PdmPCQBQILdO1Zs2bZrGjh2rHj16qGfPnpo9e7bS0tI0fvx4SdKYMWPUuHFjzZw5U5IUERGhWbNmqWvXrrapek8//bQiIiJsCRQAoHrL24/p4q/T4pMzFLV0l6TcDWu7NasrqyGZL5h5NzQ8RIPCggscqQIAVG9uTZxGjBihU6dO6ZlnntGJEyfUpUsXRUdH2wpGHDlyxG6E6amnnpLJZNJTTz2lY8eOqUGDBoqIiNALL7zgrqcAAKhAitqPKY93DQ/99NAValG/VoHn2Y8JAFAQtxeHmDJlSqFT89asWWN3u0aNGoqMjFRkZGQ5RAYAqGyK249JkjJzrIpPzig0cQIAoCBu3QAXAABXSkgtOmlyth0AAHlInAAAVUa2xbFCQUF+PmUcCQCgqnH7VD0AAEor22LV+78c0Js/7yuyXe5+TLkFHwAAcAaJEwCgUtv2d5IeW7RNu0+kSpI6NvLXzuMpMqmw/ZjCqJIHAHAaiRMAoFI6n2XRrBV79H9r42Q1pLq+nnomIkw3dmmsn3aeYD8mAIBLkTgBACosi9UodE+lx77epqVbj0uShnVupMiIMNWr7S2J/ZgAAK5H4gQAqJCid8TnGzUKuWDU6F8DWmvb30mKjAjTgPYN892f/ZgAAK5Uqqp6hmHIMByrYAQAgKOid8Rr0rzYfHsyxSdnaNK8WEXviFfbhn5a9fCVBSZNAAC4WokSp08//VSXXHKJatasqZo1a6pTp0767LPPXB0bAKAaslgNRS3dpcK+ljMkRS3dJYvVYOodAKDcOD1Vb9asWXr66ac1ZcoU9e3bV5K0du1a3XfffTp9+rSmTp3q8iABANVHTFxivpGmi8UnZygmLpGpeACAcuN04vTWW2/p3Xff1ZgxY2zHhg0bpo4dO+rZZ58lcQIAlEpCatFJk7PtAABwBaen6sXHx6tPnz75jvfp00fx8fEuCQoAUH3Vq+XlULsgP58yjgQAgH84nTi1bt1aCxcuzHd8wYIFatOmjUuCAgBUX71b1Ze/T+ETIkzKra7XMzSw/IICAFR7Tk/Vi4qK0ogRI/Trr7/a1jj9/vvvWrlyZYEJFQAAxVm1+6RqedVQr5b1ZPYw6eVbOun++bGSZFckIq8URGREGIUhAADlyukRp1tuuUUbNmxQ/fr19d133+m7775T/fr1FRMTo5tuuqksYgQAVHIWq6F1B85o8ZZjWnfgjCzW3HQoJSNbj361VXfN3ahpC7cqNSNbknTNJSF6d3Q3BQfYT8cLDvDRu6O7aWh4SLk/BwBA9VaiDXC7d++uefPmuToWAEAVVNhGtrf1aKJFG//W8eQMmUzSNeHB8jT/833e0PAQDQoLVkxcohJSMxTklzs9j5EmAIA7OJQ4paSkyN/f3/bvouS1AwAgbyPbi/dkik/O0H9W7pckNa/nq1dv7VzgmiWzh4mS4wCACsGhxKlu3bqKj49XUFCQ6tSpI5Mp/7d9hmHIZDLJYrG4PEgAQOVT3Ea2kuTrZdb3/7pcfj6e5RYXAAAl4VDitGrVKgUG5n4TuHr16jINCABQNTiykW16lkU7jqUwqgQAqPAcSpz69+9v+3doaKiaNm2ab9TJMAwdPXrUtdEBACotNrIFAFQlTlfVCw0N1alTp/IdT0xMVGhoqEuCAgBUfvVrezvUjo1sAQCVgdNV9fLWMl3s3Llz8vHhlx8AQDqamK5Zy/cU2cak3PLibGQLAKgMHE6cpk2bJkkymUx6+umn5evraztnsVi0YcMGdenSxeUBAgAqD8Mw9NWmvxW1ZKfSsizyqeGhjByrTGIjWwBA5eZw4rR582ZJub8Ut2/fLi8vL9s5Ly8vde7cWY888ojrIwQAVApJ6Vl6/Ott+mnnSUnSpS3qatbwLtp5PDnfPk7BAT6KjAhjI1sAQKXhcOKUV01v/PjxevPNN9mvCQBgxySTtv2dLE+zSVMHtdW9V7SS2cOkpoG+bGQLAKj0nF7j9PHHH5dFHACACs5iNfIlP9kWq7xreMhkMinA11NvjewqH0+zwhsH2N2XjWwBAJWd04mTJG3cuFELFy7UkSNHlJWVZXfum2++cUlgAICKI3pHfL7pdvVqeamGh0kPD2mn4T2aSpJ6tKDQAwCganK6HPmXX36pPn366K+//tK3336r7Oxs7dy5U6tWrVJAQEDxFwAAVCrRO+I1aV5svs1sz6Rl6WRqpl5fvkc5FqubogMAoHw4nTi9+OKLeuONN7R06VJ5eXnpzTff1O7duzV8+HA1a9asLGIEALiJxWooaukuu4p4BSlomwoAAKoSpxOnAwcO6LrrrpOUW00vLS1NJpNJU6dO1QcffODyAAEA7hMTl5hvpOliJ1MyFROXWE4RAQDgHk4nTnXr1lVqaqokqXHjxtqxY4ckKSkpSenp6a6NDgDgVgmpRSdNzrYDAKCycro4xBVXXKEVK1bokksu0W233aYHH3xQq1at0ooVK3T11VeXRYwAADcJ8vNxaTsAACorpxOn//73v8rIyP1m8cknn5Snp6f++OMP3XLLLXrqqadcHiAAoPxlW6x6a9V+DevcSCEBPjqRnFHgOieTcjez7RlKNT0AQNXmdOIUGPjPL0cPDw898cQTttvnz593TVQAALc5dDpNDy7Yoq1Hk/TLngQ9fV2YJn8eK5NklzzllYOIjAhjM1sAQJXn9BqngmRmZmrWrFkKDQ11xeUAAG5gGIa+2nhU1/3nN209miR/nxq654pWurZTiN4d3U3BAfbT8YIDfPTu6G4aGh7ipogBACg/Do84ZWZm6tlnn9WKFSvk5eWlxx57TDfeeKM+/vhjPfnkkzKbzZo6dWpZxgoAcAGL1VBMXKISUjMU5Jc7ze5cRo7+/e12LdseL0nqFRqoN0Z0UaM6NSVJQ8NDNCgsON/9GGkCAFQXDidOzzzzjN5//30NHDhQf/zxh2677TaNHz9e69ev16xZs3TbbbfJbDaXZawAgFKK3hGvqKW77EqMN6jtrRyrVWfTs1XDw6Spg9rqvv6t8iVFZg+TereqV94hAwBQITicOH311Vf69NNPNWzYMO3YsUOdOnVSTk6Otm7dysaHAFAJRO+I16R5sfmKPJw+lylDUoPaXvpo7KXq3LSOG6IDAKBic3iN099//63u3btLksLDw+Xt7a2pU6eSNAFAJWCxGopauqvAynh5x8weHgpvHFCeYQEAUGk4nDhZLBZ5eXnZbteoUUO1a9cuk6AAAK4VE5doNz2vICdSMhQTl1hOEQEAULk4PFXPMAyNGzdO3t7ekqSMjAzdd999qlWrll27b775xrURAgBKLSG16KTJ2XYAAFQ3DidOY8eOtbs9evRolwcDACgbjs6qDvLzKb4RAADVkMOJ08cff1yWcQAAysjq3Ql66tsdRbYxKXdfpp6hgUW2AwCgunLJBrgAgIrpbFqWpnweq5SMHDWv5yspN0m6UN7tyIgw9mUCAKAQJE4AUIXVreWlF266RGN6N9fyqVfovdHdFBxgPx0vOMBH747upqHhIW6KEgCAis/hqXoAgMph/cEzquFhUo8WudPubuzaWDd2bSxJGhoeokFhwYqJS1RCaoaC/HKn5zHSBABA0UicAKCSslgNbYhL1KbTJtWLS1Svlg300do4vfrTbtWv7a1lD/RTAz/vfPcze5jUu1U9N0QMAEDlReIEAJVQ9I54RS3d9b+9mcz6dN9GedfwUGaOVZJ0eev6quVtdm+QAABUISVa4/TZZ5+pb9++atSokQ4fPixJmj17thYvXuzS4AAA+UXviNekebH5NrTNS5pG9Wqm14d3lq8X340BAOAqTidO7777rqZNm6Zrr71WSUlJslgskqQ6depo9uzZro4PAHABi9VQ1NJdMopos2p3gqxFNQAAAE5zOnF666239OGHH+rJJ5+U2fzPNJAePXpo+/btLg0OAGAvJi4x30jTxeKTMxQTl1hOEQEAUD04nTjFxcWpa9eu+Y57e3srLS3NJUEBAAqWkFp00uRsOwAA4BinE6fQ0FBt2bIl3/Ho6Gh16NDBFTEBAApxMiXToXZBfj7FNwIAAA5zeuXwtGnTNHnyZGVkZMgwDMXExOiLL77QzJkz9dFHH5VFjABQ7RmGofd/PaiXf9xdZDuTcje07RkaWD6BAQBQTTidOE2cOFE1a9bUU089pfT0dN1xxx1q1KiR3nzzTd1+++1lESMAVGtpmTl6bNE2LdseL0nq3bKe1h88I0l2RSLytrCNjAhjQ1sAAFysRLVqR40apVGjRik9PV3nzp1TUFCQq+MCAEiKO52mez7dqH0J5+RpNumZiI4a3auZftp54oJ9nHIFB/goMiJMQ8ND3BgxAABVk9OJU1xcnHJyctSmTRv5+vrK19dXkrRv3z55enqqRYsWro4RAKqlNXsS9K8vNis1I0cN/Lz13uhu6t48dwre0PAQDQoL1rr9CVr+2wYN7tdLvVsHMdIEAEAZcbo4xLhx4/THH3/kO75hwwaNGzfOFTEBQLVhsRpad+CMFm85pnUHzshywQZMvl41dD7Lou7N62rZvy63JU15zB4m9QoNVPf6hnqFBpI0AQBQhpwecdq8ebP69u2b7/hll12mKVOmuCQoAKgOonfEFzjd7tn/TbfrGRqozyb0UvfmdeVVw+nvuQAAgAs5/ZvYZDIpNTU13/Hk5GRZLBaXBAUAVV30jnhNmhebbzPbE8kZum9erKJ3/K8QRKt6JE0AAFQATv82vuKKKzRz5ky7JMlisWjmzJm6/PLLXRocAFRFFquhqKW77CriXSxq6S67aXsAAMC9nJ6q9/LLL+uKK65Qu3bt1K9fP0nSb7/9ppSUFK1atcrlAQJAVRMTl5hvpOli8ckZiolLVO9W9copKgAAUBSnR5zCwsK0bds2DR8+XAkJCUpNTdWYMWO0e/duhYeHl0WMAFClJKQWnTQ52w4AAJS9Eu3j1KhRI7344ouujgUAqoUgPx+XtgMAAGWvRIlTUlKSYmJilJCQIKvVanduzJgxLgkMAKqqnqGBCvb30YmUgkeUTMqtrtczNLDA8wAAoPw5nTgtXbpUo0aN0rlz5+Tv7y+T6Z99Q0wmE4kTABTCMAxZjdz9l54dFqZJ82LzFYjI+0SNjAhjXyYAACoQp9c4Pfzww7rrrrt07tw5JSUl6ezZs7b/EhMTyyJGAKj0MrItmrpgi2Ys3SlJGhoeondHd1NIgP10vOAAH707upuGhoe4I0wAAFAIp0ecjh07pgceeEC+vr5lEQ8AVDnxyed1z6ebtP1YssweJt3Zu7laB/lpaHiIBoUFKyYuUQmpGQryy52ex0gTAAAVj9OJ05AhQ7Rx40a1bNmyLOIBgCpl0+FE3ftZrE6fy1RdX0+9PaqbWgf52c6bPUyUHAcAoBJwOnG67rrr9Oijj2rXrl265JJL5OnpaXd+2LBhLgsOACoLi9XIN3K0aNNRPfXdDmVbDLUP9tOHY3qoaSCj9QAAVEZOJ0533323JGnGjBn5zplMJlksltJHBQCVSPSOeEUt3WW3qW0tb7PSMnM/D68JD9Zrt3VWLe8SFTIFAAAVgNO/xS8uPw4A1Vn0jvgCq+PlJU0RnUL05u1d5cG6JQAAKjWnq+oBAHJZrIailu7KlzRdaOPhs0WeBwAAlUOJ5o2kpaXpl19+0ZEjR5SVlWV37oEHHnBJYABQ0cXEJdpNzytIfHKGYuISKQABAEAl53TitHnzZl177bVKT09XWlqaAgMDdfr0afn6+iooKIjECUC1kZBadNLkbDsAAFBxOT1Vb+rUqYqIiNDZs2dVs2ZNrV+/XocPH1b37t312muvlUWMAFAh1a/t7VC7ID+f4hsBAIAKzenEacuWLXr44Yfl4eEhs9mszMxMNW3aVK+88or+/e9/l0WMAFDhpGXmaM7ag0W2MUkKCcgtTQ4AACo3pxMnT09PeXjk3i0oKEhHjhyRJAUEBOjo0aOujQ4AKqBTqZka8cE6rdx9SjX+Vy3v4pp5ebcjI8JkpqIeAACVntNrnLp27ao///xTbdq0Uf/+/fXMM8/o9OnT+uyzzxQeHl4WMQJAheLrZZYkBdby0odjeuhUaka+fZyCA3wUGRGmoeEh7goTAAC4kNOJ04svvqjU1FRJ0gsvvKAxY8Zo0qRJatOmjebMmePyAAGgoqnlXUP/N/ZSZWZb1ayeryRpUFiwYuISlZCaoSC/3Ol5jDQBAFB1OJ049ejRw/bvoKAgRUdHuzQgAKiIPlt/WCnnszX5qtaSpIb+9gUfzB4mSo4DAFCFlWgfJwCoqixWw27kqHvzunolerc+WhsnSbqsZT11b17XzVECAIDy5lDi1K1bN61cuVJ169ZV165dZTIVPv0kNjbWZcEBQHmK3hGfb62Sdw0PZeZYJUmPDmmnbs3quCk6AADgTg4lTjfccIO8vXP3K7nxxhvLMh4AcIvoHfGaNC9WxkXH85KmCZeH2qbpAQCA6sehxCkyMlKSZLFYdNVVV6lTp06qU6dOWcYFAOXGYjUUtXRXvqTpQj9sj9e/r+1AwQcAAKopp/ZxMpvNGjx4sM6ePVtW8QBAuYuJS7SbnleQ+OQMxcQlllNEAACgonF6A9zw8HAdPHiwLGIBALdISC06aXK2HQAAqHqcTpyef/55PfLII/r+++8VHx+vlJQUu/8AoLJpUNvboXZBfj7FNwIAAFWS0+XIr732WknSsGHD7KrrGYYhk8kki8XiuugAoIxlZFv02fpDRbYxSQoOyN3UFgAAVE9OJ06rV68uizgAoNydPpepiZ9s1JajSTJ7SBZrbpJ0YZGIvK+HIiPCKAwBAEA15nTi1L9//7KIAwDK1f6EVI2f+6eOJp5XQE1PvX9ndyWlZ+Xbxyk4wEeREWEaGh7ixmgBAIC7OZ045UlPT9eRI0eUlZVld7xTp06lDgoAytIfB07rvs82KSUjR80CffXx+EvVqkFtSdKgsGDFxCUqITVDQX650/MYaQIAAE4nTqdOndL48eP1448/FnieNU4AKjKL1VDk4p1KychR9+Z19cGd3VXvguIQZg+Tereq58YIAQBAReR0Vb2HHnpISUlJ2rBhg2rWrKno6Gh98sknatOmjZYsWeJ0AG+//bZatGghHx8f9erVSzExMUW2T0pK0uTJkxUSEiJvb2+1bdtWP/zwg9OPC6B6MnuY9MGYHhrZs5nmT+xllzQBAAAUxukRp1WrVmnx4sXq0aOHPDw81Lx5cw0aNEj+/v6aOXOmrrvuOoevtWDBAk2bNk3vvfeeevXqpdmzZ2vIkCHas2ePgoKC8rXPysrSoEGDFBQUpEWLFqlx48Y6fPiw6tSp4+zTAFCFWayG3XS7Tk0CtOVokvq2ri9JCq1fSzNvvsTNUQIAgMrE6cQpLS3NltTUrVtXp06dUtu2bXXJJZcoNjbWqWvNmjVLd999t8aPHy9Jeu+997Rs2TLNmTNHTzzxRL72c+bMUWJiov744w95enpKklq0aOHsUwBQhUXviM9X4MHTbJLFamju+J66om0DN0YHAAAqK6cTp3bt2mnPnj1q0aKFOnfurPfff18tWrTQe++9p5AQx6tOZWVladOmTZo+fbrtmIeHhwYOHKh169YVeJ8lS5aod+/emjx5shYvXqwGDRrojjvu0OOPPy6z2VzgfTIzM5WZmWm7nbdJb3Z2trKzsx2Otyh513HV9VC90H9c56edJ/WvL7falROXpGxL7pE/406rd2idco+rLNF/UFL0HZQG/QelUZH6jzMxOJ04Pfjgg4qPj5ckRUZGaujQoZo/f768vLw0d+5ch69z+vRpWSwWNWzY0O54w4YNtXv37gLvc/DgQa1atUqjRo3SDz/8oP379+v+++9Xdna2IiMjC7zPzJkzFRUVle/48uXL5evr63C8jlixYoVLr4fqhf5TOlZDioo1/y9pKqgKnqHPfj+gluf3qioWyaP/oKToOygN+g9KoyL0n/T0dIfbOpw43XrrrZo4caJGjRolkyn3r47u3bvr8OHD2r17t5o1a6b69es7H60TrFargoKC9MEHH8hsNqt79+46duyYXn311UITp+nTp2vatGm22ykpKWratKkGDx4sf39/l8SVnZ2tFStWaNCgQbYphICj6D+usSEuUUnrNxbRwqSkLKlB2GXqFRpYbnGVNfoPSoq+g9Kg/6A0KlL/yZuN5giHE6ezZ8/quuuuU6NGjTR+/HiNGzdOLVu2lK+vr7p16+Z0kPXr15fZbNbJkyftjp88eVLBwcEF3ickJESenp520/I6dOigEydOKCsrS15eXvnu4+3tLW/v/FWzPD09Xf6DKotrovqg/5TOmfQch9tVxdeZ/oOSou+gNOg/KI2K0H+ceXyHy5GvXLlSBw8e1IQJEzRv3jy1adNGAwYM0Oeff263hshRXl5e6t69u1auXGk7ZrVatXLlSvXu3bvA+/Tt21f79++X1Wq1Hdu7d69CQkIKTJoAVB9Bfj4ubQcAAHAhp/Zxat68uZ599lkdPHhQK1asUKNGjXT33XcrJCREkydP1qZNm5x68GnTpunDDz/UJ598or/++kuTJk1SWlqarcremDFj7IpHTJo0SYmJiXrwwQe1d+9eLVu2TC+++KImT57s1OMCqFpyLFZ1ahKgkACfAlc3SbmrnkICfNSzCk3TAwAA5cfp4hB5BgwYoAEDBig1NVWff/65/v3vf+v9999XTo5j02UkacSIETp16pSeeeYZnThxQl26dFF0dLStYMSRI0fk4fFPbte0aVP99NNPmjp1qjp16qTGjRvrwQcf1OOPP17SpwGgksvItmjK55tlGIaeuq6Dpny+WSbJrrJeXjIVGREmc1WsDAEAAMpciRMnSYqLi9PcuXM1d+5cJScna+DAgU5fY8qUKZoyZUqB59asWZPvWO/evbV+/XqnHwdA1ZOUnqUJn2zUpsNn5VXDQw8ObKN3R3fLt49TcICPIiPCNDTc8S0TAAAALuR04pSRkaFFixZpzpw5+vXXX9W0aVNNmDBB48ePV9OmTcsiRgDI53jSeY2dE6N9Cefk71NDH429VJ2a1FGnJnU0KCxYMXGJSkjNUJBf7vQ8RpoAAEBpOJw4xcTEaM6cOVqwYIEyMjJ00003KTo6WldffbWtPDkAlIe9J1M1dk6M4pMzFOzvo0/u6ql2wX6282YPk3q3qufGCAEAQFXjcOJ02WWXqXPnznruuec0atQo1a1btyzjAoACbTyUqLvm/qmUjBy1alBLn07opcZ1aro7LAAAUMU5nDht3LixRPs1AUBJWaxGvil3NcweyrYY6tasjv5v7KWqW4utCAAAQNlzOHEiaQJQnqJ3xOcr8hDyvyIPX9xzmdo19FNNL3MRVwAAAHAdp/ZxAoDyEL0jXpPmxdolTZJ0IjlDk+bF6kTyeZImAABQrkicAFQoFquhqKW77PZhypN3LGrpLlmsBbUAAAAoGyROACqUmLjEfCNNFzIkxSdnKCYusfyCAgAA1R6JE4AKJSG18KSpJO0AAABcwaHiEF27dnV4r6bY2NhSBQSgevOp4dj3OUF+PmUcCQAAwD8cSpxuvPFG278zMjL0zjvvKCwsTL1795YkrV+/Xjt37tT9999fJkECqD5+23+6yPMmScEBuaXJAQAAyotDiVNkZKTt3xMnTtQDDzyg5557Ll+bo0ePujY6ANXOk9eG6a/4FG06nCSTZFckIm/cOzIiTGYPx0bBAQAAXMHpNU5fffWVxowZk+/46NGj9fXXX7skKADVy5Ez6TKM3BSpppdZX0/qq/dGd1NwgP10vOAAH707upuGhoe4I0wAAFCNObwBbp6aNWvq999/V5s2beyO//777/LxYc0BAOf8sveU7vtsk+6+oqWmDWprOz40PESDwoIVE5eohNQMBfnlTs9jpAkAALiD04nTQw89pEmTJik2NlY9e/aUJG3YsEFz5szR008/7fIAAVRdS7Ye18MLtyjbYmjL0STlWKyqYf5nINzsYVLvVvXcGCEAAEAupxOnJ554Qi1bttSbb76pefPmSZI6dOigjz/+WMOHD3d5gACqpk/XHVLkkp0yDCmicyO9fltnu6QJAACgInE6cZKk4cOHkyQBcIjFathNt7u0RV29tWq/3ly5T5I0pndzPRvRUR5MwQMAABVYiRKnpKQkLVq0SAcPHtQjjzyiwMBAxcbGqmHDhmrcuLGrYwRQSUXviFfU0l2KT/5ns1pfL7PSsyySpIcGttGDV7dxeJ84AAAAd3E6cdq2bZsGDhyogIAAHTp0SBMnTlRgYKC++eYbHTlyRJ9++mlZxAmgkoneEa9J82LtyolLsiVNt1/aVA8NbJv/jgAAABWQ0wsKpk2bpnHjxmnfvn12VfSuvfZa/frrry4NDkDlZLEailq6K1/SdKFf9p6SxVpUCwAAgIrD6cTpzz//1L333pvveOPGjXXixAmXBAWgcouJS7SbnleQ+OQMxcQlllNEAAAApeN04uTt7a2UlJR8x/fu3asGDRq4JCgAlVtCatFJk7PtAAAA3M3pxGnYsGGaMWOGsrOzJUkmk0lHjhzR448/rltuucXlAQKofIL8HNsM29F2AAAA7uZ04vT666/r3LlzCgoK0vnz59W/f3+1bt1afn5+euGFF8oiRgCVTLtgP3maC6+UZ5IUEuCjnqGB5RcUAABAKThdVS8gIEArVqzQ2rVrtW3bNp07d07dunXTwIEDyyI+AJVMcnq2xn0co2xLwYUf8tKpyIgwmdm7CQAAVBIl2sdJki6//HJdfvnlrowFQBXwxDfbtO3vZNX19dT9V7bWnN/j7ApFBAf4KDIiTEPDQ9wYJQAAgHNKlDitXLlSK1euVEJCgqxWq925OXPmuCQwAJXTv6/toONJ5/XyrZ3UPthfd10eqpi4RCWkZijIL3d6HiNNAACgsnE6cYqKitKMGTPUo0cPhYSEyGTiDyCgurNYDVsy1DTQV99N7mv7bDB7mNS7VT13hgcAAFBqTidO7733nubOnas777yzLOIBUMkkpmVp7JwYTb6qlW36HV+oAACAqsbpqnpZWVnq06dPWcQCoJI5cy5Td3y4XtuPJWvG0l3KyLa4OyQAAIAy4XTiNHHiRH3++edlEQuACsxiNbTuwBkt3nJM6w6c0cmUDI38cL12n0hVkJ+3PpvYSz6eZneHCQAAUCacnqqXkZGhDz74QD///LM6deokT09Pu/OzZs1yWXAAKoboHfGKWrrLrjpeDQ+TcqyGGvp764u7L1PLBrXdGCEAAEDZcjpx2rZtm7p06SJJ2rFjh9051jUAVU/0jnhNmheri3dlyrHmHrn/ytYkTQAAoMpzOnFavXp1WcQBoAKyWA1FLd2VL2m60Hu/HNDoy5pTYhwAAFRpTq9xAlB9xMQl2k3PK0h8coZi4hLLKSIAAAD3cGjE6eabb9bcuXPl7++vm2++uci233zzjUsCA+B+CalFJ03OtgMAAKisHEqcAgICbOuXAgICyjQgABVHkJ+PS9sBAABUVg4lTh9//HGB/wZQtbUL9rNVzyuISVJwgI96hgaWb2AAAADljDVOAAqUmpGtu+b+WWTSJEmREWEUhgAAAFWe01X1JGnRokVauHChjhw5oqysLLtzsbGxLgkMgPukZeZo/Md/asvRJNXx9dSUq1rr/9bG2RWKCA7wUWREmIaGh7gxUgAAgPLhdOL0n//8R08++aTGjRunxYsXa/z48Tpw4ID+/PNPTZ48uSxiBFCOzmdZNOGTP7Xx8Fn5+dTQvAm9FN44QOP7hiomLlEJqRkK8sudnsdIEwAAqC6cTpzeeecdffDBBxo5cqTmzp2rxx57TC1bttQzzzyjxERKEgOV3e4TKdp8JEm1vWvo07t6KrxxbkEYs4dJvVvVc3N0AAAA7uF04nTkyBH16dNHklSzZk2lpqZKku68805ddtll+u9//+vaCAGUq67N6urj8ZfK0+yhrs3qujscAACACsHp4hDBwcG2kaVmzZpp/fr1kqS4uDgZRsGLyAFUbNkWq/4+m2673adVfV3agkp5AAAAeZxOnAYMGKAlS5ZIksaPH6+pU6dq0KBBGjFihG666SaXBwigbOVYrHroyy268e0/tPdkqrvDAQAAqJCcnqr3wQcfyGq1SpImT56sevXq6Y8//tCwYcN07733ujxAAK5lsRq2Ig/1a3tr4Z9HtGx7vDzNJh1POq+2Df3cHSIAAECF43Ti5OHhIQ+Pfwaqbr/9dt1+++0uDQpA2YjeEa+opbvsyopLkodJevuObrqyXZCbIgMAAKjYHEqctm3b5vAFO3XqVOJgAJSd6B3xmjQvVgWtRLQakpU1igAAAIVyKHHq0qWLTCZTscUfTCaTLBaLSwID4DoWq6GopbsKTJokySQpaukuDQoLZm8mAACAAjiUOMXFxZV1HADKUExcYr7peRcyJMUnZygmLpG9mgAAAArgUOLUvHnzso4DQBlKSC08aSpJOwAAgOrG6eIQkrRnzx699dZb+uuvvyRJHTp00L/+9S+1a9fOpcEBcI0gPx+XtgMAAKhunN7H6euvv1Z4eLg2bdqkzp07q3PnzoqNjVV4eLi+/vrrsogRQCmlns8u8rxJUkiAj3qGsuktAABAQZwecXrsscc0ffp0zZgxw+54ZGSkHnvsMd1yyy0uCw5A6cXEJepfX2623TZJdkUi8kpBREaEURgCAACgEE6POMXHx2vMmDH5jo8ePVrx8fEuCQqAa+w6nqIJn/ypzByrBnYI0n/v6KrgAPvpeMEBPnp3dDcNDQ9xU5QAAAAVn9MjTldeeaV+++03tW7d2u742rVr1a9fP5cFBqB0Dp9J05g5MUrNyFHPFoH67x3d5ONp1jXhIYqJS1RCaoaC/HKn5zHSBAAAUDSnE6dhw4bp8ccf16ZNm3TZZZdJktavX6+vvvpKUVFRWrJkiV1bAOUvISVDo/9vg06fy1SHEH99OLaHfDzNkiSzh4mS4wAAAE5yOnG6//77JUnvvPOO3nnnnQLPSWyGC7jTyt0JOpp4Xs3r+eqTuy5VQE1Pd4cEAABQqTmdOFmt1rKIA4ALjezZTGYPky4LrUeJcQAAABco0T5OhUlPT5evr68rLwnAQdkWq7JyrKrlnfu2Ht6jqZsjAgAAqDqcrqp39dVX69ixY/mOb9iwQV26dHFFTACKYbEaWnfgjBZvOaZ1B84oO8eqR7/aqjs+2qCzaVnuDg8AAKDKcXrEycfHR506ddI777yjESNGyGq1asaMGXrxxRft1jgBKBvRO+IVtXSX4pMzbMd8vcxKz7KohodJu+JT1Ld1fTdGCAAAUPU4nTgtW7ZMb7/9tu666y4tXrxYhw4d0uHDh/X9999r8ODBZREjgP+J3hGvSfNi7TawlaT0rNxCLGN6NydpAgAAKAMlWuM0efJk/f3333r55ZdVo0YNrVmzRn369HF1bAAuYLEailq6K1/SdKEfd5zQk9eFsS8TAACAizm9xuns2bO65ZZb9O677+r999/X8OHDNXjw4HylyQG4Vkxcot30vILEJ2coJi6xnCICAACoPpwecQoPD1doaKg2b96s0NBQ3X333VqwYIHuv/9+LVu2TMuWLSuLOIFqLyG16KTJ2XYAAABwnNMjTvfdd59+/fVXhYaG2o6NGDFCW7duVVYW1byAsuLofkzs2wQAAOB6TidOTz/9tDw88t+tSZMmWrFihUuCApBfz9BABQf4qLDVSyZJIQE+6hkaWJ5hAQAAVAsOJ06vvPKKzp8/b7v9+++/KzMz03Y7NTWVcuRAGUrLypGvl1mGlC95yrsdGUFhCAAAgLLgcOI0ffp0paam2m5fc801dhvhpqen6/3333dtdAAkSVk5Vk2at0kHT6Wprq+nGvp7250PDvDRu6O7aWh4iJsiBAAAqNocLg5hGEaRtwGUDcMw9Niirfp9/xnV8jLrswm91CHEXzFxiUpIzVCQX+70PEaaAAAAyk6J9nECUH5e+WmPvttyXDU8THp3dHeFNw6QJPVuVc/NkQEAAFQfTheHAFB+Plt3SO+uOSBJmnnzJbqibQM3RwQAAFA9OTXi9NFHH6l27dqSpJycHM2dO1f169eXJLv1TwBKb+OhREUu2SlJenhQW93Wo6mbIwIAAKi+HE6cmjVrpg8//NB2Ozg4WJ999lm+NgBco0vTOhpxaTNJhqYMaO3ucAAAAKo1hxOnQ4cOlWEYAC5Ww+yhF28Kl9WQTCYKPwAAALgTa5yACuRUaqZe+2mPcixWSbkJE9XyAAAA3I+qeoAbWayGNsQlatNpk3z3nNJ/Vh/Q9mMpOpuepRduusTd4QEAAOB/SJwAN4neEa+opbsUn5whyaxP922WJNXyMmtiv5buDQ4AAAB2mKoHuEH0jnhNmhf7v6TJXlqWRXtOpLghKgAAABSGxAkoZxaroailu2QUct4kKWrpLlmshbUAAABAeStR4nTgwAE99dRTGjlypBISEiRJP/74o3bu3OnS4ICqKCYuscCRpjyGpPjkDMXEJZZfUAAAACiS04nTL7/8oksuuUQbNmzQN998o3PnzkmStm7dqsjISJcHCFQ1CamFJ00laQcAAICy53Ti9MQTT+j555/XihUr5OXlZTs+YMAArV+/3qXBAVVRkJ+PS9sBAACg7DmdOG3fvl033XRTvuNBQUE6ffq0S4ICqrLwxv5q4OetwnZnMkkKCfBRz9DA8gwLAAAARXA6capTp47i4+PzHd+8ebMaN27skqCAqspqNfTYom06n2WRIeVLnvJuR0aEsfEtAABABeJ04nT77bfr8ccf14kTJ2QymWS1WvX777/rkUce0ZgxY8oiRqDKmP3zXv2444Sycqx6ZHBbBQfYT8cLDvDRu6O7aWh4iJsiBAAAQEGc3gD3xRdf1OTJk9W0aVNZLBaFhYXJYrHojjvu0FNPPVUWMQJVwuItx/SfVfslSS/efIlu7d5Ek65srXX7E7T8tw0a3K+XercOYqQJAACgAnI6cfLy8tKHH36op59+Wjt27NC5c+fUtWtXtWnTpiziA6qEzUfO6tFF2yRJ9/ZvqVu7N5EkmT1M6hUaqDN/GeoVGkjSBAAAUEE5nTitXbtWl19+uZo1a6ZmzZqVRUxAlXI86bzu+WyTsnKsGtghSI8Nae/ukAAAAOAkp9c4DRgwQKGhofr3v/+tXbt2lUVMQJXyxoq9OpWaqfbBfpp9e1dGlQAAACohpxOn48eP6+GHH9Yvv/yi8PBwdenSRa+++qr+/vvvsogPqPRm3BCuO3o104djeqi2t9ODvAAAAKgAnE6c6tevrylTpuj333/XgQMHdNttt+mTTz5RixYtNGDAgLKIEajUanqZ9eJNl6hpoK+7QwEAAEAJOZ04XSg0NFRPPPGEXnrpJV1yySX65ZdfSnSdt99+Wy1atJCPj4969eqlmJgYh+735ZdfymQy6cYbbyzR4wJlZfGWY3pjxV5ZrYa7QwEAAIALlHje0O+//6758+dr0aJFysjI0A033KCZM2c6fZ0FCxZo2rRpeu+999SrVy/Nnj1bQ4YM0Z49exQUFFTo/Q4dOqRHHnlE/fr1K+lTAFzGYjUUE5eohNQMpZzP1ozvdynbYii0fi3d2JWNoQEAACo7pxOn6dOn68svv9Tx48c1aNAgvfnmm7rhhhvk61uyaUizZs3S3XffrfHjx0uS3nvvPS1btkxz5szRE088UeB9LBaLRo0apaioKP32229KSkoq0WMDrhC9I15RS3cpPjnD7ninxgEa1rmRm6ICAACAKzmdOP3666969NFHNXz4cNWvX79UD56VlaVNmzZp+vTptmMeHh4aOHCg1q1bV+j9ZsyYoaCgIE2YMEG//fZbkY+RmZmpzMxM2+2UlBRJUnZ2trKzs0sVf56867jqeqg8ftp5Uv/6cqsKmpC3/Viyfth2TEM6NizyGvQflAb9ByVF30Fp0H9QGhWp/zgTg9OJ0++//+7sXQp1+vRpWSwWNWxo/4dlw4YNtXv37gLvs3btWv3f//2ftmzZ4tBjzJw5U1FRUfmOL1++vMSjZIVZsWKFS6+His1qSFGx5v8lTflLjBsy9NQ3W5R9yCJHKpDTf1Aa9B+UFH0HpUH/QWlUhP6Tnp7ucFuHEqclS5bommuukaenp5YsWVJk22HDhjn84M5KTU3VnXfeqQ8//NDh0a7p06dr2rRpttspKSlq2rSpBg8eLH9/f5fElZ2drRUrVmjQoEHy9PR0yTVR8W2IS1TS+o1FtDApKUtqEHaZeoUGFtqK/oPSoP+gpOg7KA36D0qjIvWfvNlojnAocbrxxht14sQJBQUFFVnBzmQyyWKxOPzg9evXl9ls1smTJ+2Onzx5UsHBwfnaHzhwQIcOHVJERITtmNVqlSTVqFFDe/bsUatWrezu4+3tLW9v73zX8vT0dPkPqiyuiYrrTHqOw+0c6Rf0H5QG/QclRd9BadB/UBoVof848/gOlSO3Wq22CndWq7XQ/5xJmiTJy8tL3bt318qVK+0ea+XKlerdu3e+9u3bt9f27du1ZcsW23/Dhg3TVVddpS1btqhp06ZOPT5QGkF+Pi5tBwAAgIrL6X2cPv30U7tiC3mysrL06aefOh3AtGnT9OGHH+qTTz7RX3/9pUmTJiktLc1WZW/MmDG24hE+Pj4KDw+3+69OnTry8/NTeHi4vLy8nH58oKQ6Nw1QQ3/vAlY35TJJCgnwUc8ipukBAACgcnA6cRo/frySk5PzHU9NTbUlO84YMWKEXnvtNT3zzDPq0qWLtmzZoujoaFvBiCNHjig+Pt7p6wJl7cUf/lJ2jiFD+UtD5N2OjAiT2ZHKEAAAAKjQnK6qZxiGTKb8fwj+/fffCggIKFEQU6ZM0ZQpUwo8t2bNmiLvO3fu3BI9JlAa38T+rXnrj8hkkqZc1Upfxx6z28cpOMBHkRFhGhoe4sYoAQAA4CoOJ05du3aVyWSSyWTS1VdfrRo1/rmrxWJRXFychg4dWiZBAhXJ7hMp+ve32yVJDwxoo6mD2mrqoHaKiUtUQmqGgvxyp+cx0gQAAFB1OJw45VXT27Jli4YMGaLatWvbznl5ealFixa65ZZbXB4gUJGkZGRr0rxYZWRbdUXbBnrg6jaSJLOHSb1b1XNzdAAAACgrDidOkZGRkqQWLVpoxIgR8vGhUhiqF8Mw9OhXWxV3Ok2N69TU7BFdGFUCAACoJpxe4zR27NiyiAOo8OZtOKKfdp6Ul9lD74zqpsBaVHEEAACoLpxOnCwWi9544w0tXLhQR44cUVZWlt35xMRElwUHVCQRnUK0eneCBrQPUuemddwdDgAAAMqR0+XIo6KiNGvWLI0YMULJycmaNm2abr75Znl4eOjZZ58tgxCBiqGOr5c+GtNDo3o1c3coAAAAKGdOJ07z58/Xhx9+qIcfflg1atTQyJEj9dFHH+mZZ57R+vXryyJGwG2yLVZF74iXYRiSJA8PU4Hl+AEAAFC1OZ04nThxQpdccokkqXbt2rbNcK+//notW7bMtdEBbvZK9G7dNy9Wzy7Z6e5QAAAA4EZOr3Fq0qSJ4uPj1axZM7Vq1UrLly9Xt27d9Oeff8rb27ssYgTKhcVq2O3FdDYtUx/+FidJlBoHAACo5pxOnG666SatXLlSvXr10r/+9S+NHj1a//d//6cjR45o6tSpZREjUOaid8QraukuxSdn2I7lTci754qWGhoe4p7AAAAAUCE4nTi99NJLtn+PGDFCzZo107p169SmTRtFRES4NDigPETviNekebEyLjqed7tzk4DyDgkAAAAVjNOJ08V69+6t3r17uyIWoNxZrIailu7KlzRd6Pllf2loeAib3QIAAFRjDiVOS5YscfiCw4YNK3EwQHmLiUu0m55XkPjkDMXEJbLOCQAAoBpzKHG68cYbHbqYyWSSxWIpTTxAuUpILTppcrYdAAAAqiaHEier1VrWcQBuEeTn49J2AAAAqJqc3scJqEp6hgYqJKDwpMgkKSTARz1DA8svKAAAAFQ4TheHmDFjRpHnn3nmmRIHA5Q3s4dJ114Sov9bG5fvXF4piMiIMApDAAAAVHNOJ07ffvut3e3s7GzFxcWpRo0aatWqFYkTKpUjZ9K14M+jkqTa3jV0LjPHdi44wEeREWHs4QQAAADnE6fNmzfnO5aSkqJx48bppptucklQQHnItlj1ry8361xmji5tUVfzJvRS7JEkJaRmKMgvd3oeI00AAACQXLCPkyT5+/srKipKERERuvPOO11xSaDMvbZ8j7YeTVJATU/Nvr2rvD3NlBwHAABAgVxWHCI5OVnJycmuuhxQpn7de0rv/3JQkvTyLZ3UuE5NN0cEAACAiszpEaf//Oc/drcNw1B8fLw+++wzXXPNNS4LDChLn647JEkafVkzDQ0Pdm8wAAAAqPCcTpzeeOMNu9seHh5q0KCBxo4dq+nTp7ssMKAsvTOqu+b+EacxvVu4OxQAAABUAk4nTnFx+cs2A5WNVw0P3XNFK3eHAQAAgEqCDXBRbWw9mqRXoncr22J1dygAAACoZJweccrIyNBbb72l1atXKyEhQVar/R+hsbGxLgsOcJXUjGz964vNOpKYrhoeJk0b3M7dIQEAAKAScTpxmjBhgpYvX65bb71VPXv2lMnEPjeo2AzD0JPf7tCRxHQ1rlNTE/q1dHdIAAAAqGScTpy+//57/fDDD+rbt29ZxAO43Feb/taSrcdl9jDpPyO7KqCmp7tDAgAAQCXjdOLUuHFj+fn5lUUsgEtYrIZi4hKVkJqhbIuhZ77bIUmaNqitujev6+boAAAAUBk5nTi9/vrrevzxx/Xee++pefPmZRETUGLRO+IVtXSX4pMz7I63a1hb9/Wnih4AAABKxunEqUePHsrIyFDLli3l6+srT0/7aU+JiYkuCw5wRvSOeE2aFyujgHN7Tp7Til0nNDQ8pNzjAgAAQOXndOI0cuRIHTt2TC+++KIaNmxIcQhUCBaroailuwpMmiTJJClq6S4NCguW2YM+CwAAAOc4nTj98ccfWrdunTp37lwW8QAlEhOXmG963oUMSfHJGYqJS1TvVvXKLzAAAABUCU5vgNu+fXudP3++LGIBSiwhtfCkqSTtAAAAgAs5nTi99NJLevjhh7VmzRqdOXNGKSkpdv8B7hDk5+PSdgAAAMCFnJ6qN3ToUEnS1VdfbXfcMAyZTCZZLBbXRAY4oWdooOrX9tLpc1kFnjdJCg7wUc/QwPINDAAAAFWC04nT6tWryyIOoFSyLVZ51yh4ADWvFERkRBiFIQAAAFAiTidO/fv3L4s4gFJ57ac9OpaUIT+fGqrpaVZCaqbtXHCAjyIjwihFDgAAgBJzOnH69ddfizx/xRVXlDgYoCTW7jutj9bGSZJmj+iiK9sFKSYuUQmpGQryy52ex0gTAAAASsPpxOnKK6/Md+zCvZxY44TytnzXCUnSqF7NdHWHhpJEyXEAAAC4lNOJ09mzZ+1uZ2dna/PmzXr66af1wgsvuCwwwFFRwzrq0haBGvi/pAkAAABwNacTp4CAgHzHBg0aJC8vL02bNk2bNm1ySWCAo0wmkyI6N3J3GAAAAKjCnN7HqTANGzbUnj17XHU5oEhHzqTr4YVblZRecPlxAAAAwJWcHnHatm2b3W3DMBQfH6+XXnpJXbp0cVVcQKFyLFY9tGCzYo8kKSPHorfv6ObukAAAAFDFOZ04denSRSaTSYZh2B2/7LLLNGfOHJcFBhTmnTUHFHskSX7eNfTE0PbuDgcAAADVgNOJU1xcnN1tDw8PNWjQQD4+Pi4LCijMlqNJenPlPknSjBs7qmmgr5sjAgAAQHXgdOLUvHnzsogDKFZaZo4e+nKzLFZD13cK0Y1dGrs7JAAAAFQTDheHWLVqlcLCwpSSkpLvXHJysjp27KjffvvNpcEBF3p+2S4dOpOukAAfvXDjJXb7hwEAAABlyeHEafbs2br77rvl7++f71xAQIDuvfdezZo1y6XBAXmS07O1Zs8pmUzS68M7K8DX090hAQAAoBpxOHHaunWrhg4dWuj5wYMHs4cTXMZiNbTuwBkt3nJM6w6cUW2fGop+8ArNHtFFfVrVd3d4AAAAqGYcXuN08uRJeXoW/i1/jRo1dOrUKZcEheoteke8opbuUnxyhu1YSICPIiPCdAPrmgAAAOAGDo84NW7cWDt27Cj0/LZt2xQSEuKSoFB9Re+I16R5sXZJkySdSM7QpHmxit4R76bIAAAAUJ05nDhde+21evrpp5WRkZHv3Pnz5xUZGanrr7/epcGherFYDUUt3SWjgHN5x6KW7pLFWlALAAAAoOw4PFXvqaee0jfffKO2bdtqypQpateunSRp9+7devvtt2WxWPTkk0+WWaCo+mLiEvONNF3IkBSfnKGYuET1blWv/AIDAABAtedw4tSwYUP98ccfmjRpkqZPny7DyP3W32QyaciQIXr77bfVsGHDMgsUVV9CauFJU0naAQAAAK7i1Aa4zZs31w8//KCzZ89q//79MgxDbdq0Ud26dcsqPlQjQX4+Lm0HAAAAuIpTiVOeunXr6tJLL3V1LKjmeoYGqqG/t06mZBZ43iQpOMBHPUMDyzcwAAAAVHsOF4cAyprZw6QbuzQq8Jzpf/+PjAiT2cNUYBsAAACgrJRoxAkoK9OvDVMtb0998schnUnLsh0P/t8+TkPDKXkPAACA8kfihArngavbaPJVrRUTl6iE1AwF+eVOz2OkCQAAAO5C4gS3MwxDr/60R7d2b6KWDWpLyp22R8lxAAAAVBSscYLbLfjzqN5Zc0A3vfOHzmXmuDscAAAAIB8SJ7jV4TNpmvH9LknSlKtaq7Y3g6AAAACoeEic4DY5FqumLtii9CyLLmsZqAmXh7o7JAAAAKBAJE5wm/d+OaDYI0ny866h127rLA+KPwAAAKCCInGCW2z/O1mzf94nSYq6oaOa1PV1c0QAAABA4Uic4BYfrT2oHKuhay8J1k1dG7s7HAAAAKBIrMSHW7x2W2e1beinO3o2k8nEFD0AAABUbCROcAtPs4cmX9Xa3WEAAAAADiFxQpmyWA3FxCUqITVDvl5m7T6RqnuvaCWvGswSBQAAQOVB4oQyE70jXlFLdyk+OcPu+Oo9CfpmUl83RQUAAAA4j6/9USaid8Rr0rzYfEmTJMUeTlL0jng3RAUAAACUDIkTXM5iNRS1dJeMQs6bJEUt3SWLtbAWAAAAQMVC4gSXi4lLLHCkKY8hKT45QzFxieUXFAAAAFAKJE5wuYTUwpOmkrQDAAAA3I3ECS4X5Ofj0nYAAACAu5E4weV6hgYqJMBHhW1ra5IUEuCjnqGB5RkWAAAAUGIkTnA5s4dJkRFhkpQvecq7HRkRJrNHYakVAAAAULGQOMHljiWdVx1fL707upuCA+yn4wUH+Ojd0d00NDzETdEBAAAAzmMDXLiUYRh64utt+m3faUUN66i1jw9QTFyiElIzFOSXOz2PkSYAAABUNiROcKkFfx7Vb/tOy7uGhy5vU19mD5N6t6rn7rAAAACAUmGqHlzmeNJ5vbDsL0nSI4PbqVWD2m6OCAAAAHANEie4hGEYmv7NdqVm5qhrszq66/JQd4cEAAAAuAyJE1xi0aa/9cveU/Kq4aFXb+3EOiYAAABUKSROKLUz5zI14/tdkqRpg9qqdZCfmyMCAAAAXIvECaUWWMtLUcM6qn/bBprIFD0AAABUQVTVQ6mZTCbd3K2JburaWCYTU/QAAABQ9TDihBI7fS5TyenZttskTQAAAKiqSJxQInkb3Q564xetO3DG3eEAAAAAZYqpeiiRxVuO6+e/EuRpNimwlpe7wwEAAADKFCNOcFpCaoYil+yUJD0woI3aBVNFDwAAAFUbI05wiMVqKCYuUQkpGfps/WEln89Wx0b+uu/KVu4ODQAAAChzJE4oVvSOeEUt3aX45Ay74zd1bSxPM4OWAAAAqPoqxF+9b7/9tlq0aCEfHx/16tVLMTExhbb98MMP1a9fP9WtW1d169bVwIEDi2yP0oneEa9J82LzJU2S9MKyvxS9I94NUQEAAADly+2J04IFCzRt2jRFRkYqNjZWnTt31pAhQ5SQkFBg+zVr1mjkyJFavXq11q1bp6ZNm2rw4ME6duxYOUde9VmshqKW7pJRRJuopbtksRbVAgAAAKj83J44zZo1S3fffbfGjx+vsLAwvffee/L19dWcOXMKbD9//nzdf//96tKli9q3b6+PPvpIVqtVK1euLOfIq76YuMQCR5ryGJLikzMUE5dYfkEBAAAAbuDWNU5ZWVnatGmTpk+fbjvm4eGhgQMHat26dQ5dIz09XdnZ2QoMDCzwfGZmpjIzM223U1JSJEnZ2dnKzs4u8D7OyruOq65XUcQnpTncLjvbv4yjqbqqav9B+aD/oKToOygN+g9KoyL1H2dicGvidPr0aVksFjVs2NDueMOGDbV7926HrvH444+rUaNGGjhwYIHnZ86cqaioqHzHly9fLl9fX+eDLsKKFStcej13O5hskmQuvt3OLfrh781lH1AVV9X6D8oX/QclRd9BadB/UBoVof+kp6c73LZSV9V76aWX9OWXX2rNmjXy8fEpsM306dM1bdo02+2UlBTbuih/f9eMkmRnZ2vFihUaNGiQPD09XXLNisBiNbTg1V906lxWgedNkoIDvDVlxBUye5jKN7gqpKr2H5QP+g9Kir6D0qD/oDQqUv/Jm43mCLcmTvXr15fZbNbJkyftjp88eVLBwcFF3ve1117TSy+9pJ9//lmdOnUqtJ23t7e8vb3zHff09HT5D6osrulOnpKaBvoWmDjlpUmRER3l4+1VrnFVVVWt/6B80X9QUvQdlAb9B6VREfqPM4/v1uIQXl5e6t69u11hh7xCD7179y70fq+88oqee+45RUdHq0ePHuURarX0x4HTij2SJJOk+rXtk6PgAB+9O7qbhoaHuCc4AAAAoBy5faretGnTNHbsWPXo0UM9e/bU7NmzlZaWpvHjx0uSxowZo8aNG2vmzJmSpJdfflnPPPOMPv/8c7Vo0UInTpyQJNWuXVu1a9d22/OoanIsVkUt2SVJurN3c0VGdFRMXKISUjMU5OejnqGBTM8DAABAteH2xGnEiBE6deqUnnnmGZ04cUJdunRRdHS0rWDEkSNH5OHxz8DYu+++q6ysLN16661214mMjNSzzz5bnqFXafM3HNGek6mq4+upaYPayuxhUu9W9dwdFgAAAOAWbk+cJGnKlCmaMmVKgefWrFljd/vQoUNlH1A1ZxiGFvx5VJL0yOB2quPLGiYAAABUbxUicULFYjKZ9M39fbRw41GN7NnM3eEAAAAAbkfihAL5eJo1pncLd4cBAAAAVAhuraqHisUwDP24PV4Wq+HuUAAAAIAKhcQJNku2Htek+bEa+cF6GQbJEwAAAJCHxAmSpLTMHL34w1+SpP7tGshkotQ4AAAAkIfECZKkt1fv18mUTDUL9NWEy0PdHQ4AAABQoZA4QYdOp+mj3+IkSU9fHyYfT7ObIwIAAAAqFhIn6Pllu5RlseqKtg00sEOQu8MBAAAAKhwSp2pu9Z4E/fxXgmp4mPTM9WGsbQIAAAAKwD5O1VyQn7e6Nauj7s3rqnVQbXeHAwAAAFRIJE7VXMdGAVp0Xx9lW63uDgUAAACosEicqhGL1VBMXKISUjMU5OetnqH1ZPYwycPDJG8PCkIAAAAAhSFxqiaid8QraukuxSdn2I7V8jLr+Zsu0U1dG7sxMgAAAKDiI3GqBqJ3xGvSvFgZFx1Py7Jo6oItqunpoaHhIW6JDQAAAKgMqKpXxVmshqKW7sqXNOUxSYpauksWa2EtAAAAAJA4VXExcYl20/MuZkiKT85QTFxi+QUFAAAAVDIkTlVcQmrhSVNJ2gEAAADVEYlTFRfk5+PSdgAAAEB1ROJUxfUMDVRIgI9MhZw3SQoJ8FHP0MDyDAsAAACoVEicqjizh0mREWEFnstLpiIjwmT2KCy1AgAAAEDiVA0MDQ/Ru6O7KSTAfjpecICP3h3djVLkAAAAQDHYx6mKs1gNbTmapKHhIRoUFqyYuEQlpGYoyC93eh4jTQAAAEDxSJyquC//PKInv92h2y9tqpdu6aTereq5OyQAAACg0mGqXhWWkpGt15fvlSS1C/ZzczQAAABA5UXiVIW9tXKfEtOy1KpBLY2+rLm7wwEAAAAqLRKnKirudJrm/nFIkvTU9WHyNPOjBgAAAEqKv6arqBeW/aVsi6Er2zXQVe2C3B0OAAAAUKmROFVBa/ed1s9/nZTZw6Snruvg7nAAAACASo+qelVQtsWqkAAfDekYrNZBFIUAAAAASovEqQq6qn2QVj18pXKsVneHAgAAAFQJJE5VVE0vsySzu8MAAAAAqgTWOFUh/121Twv/PCqL1XB3KAAAAECVwohTFXHg1DnN/nmfcqyGmtfzVa+W9dwdEgAAAFBlMOJURbyw7C/lWA0NaB9E0gQAAAC4GIlTFfDL3lNatTtBNTxMepLy4wAAAIDLkThVcjkWq57/fpckaWyfFmrVoLabIwIAAACqHhKnSm7+hiPal3BOdX099cDVbdwdDgAAAFAlURyiErJYDcXEJerY2XS9+tNuSdK0we0UUNPTzZEBAAAAVROJUyUTvSNeUUt3KT45w3aspqdZgb4kTQAAAEBZIXGqRKJ3xGvSvFhdvEtTRrZFUz7fLLOHSUPDQ9wSGwAAAFCVscapkrBYDUUt3ZUvaZJkOxa1dBeb3wIAAABlgMSpkoiJS7SbnncxQ1J8coZi4hLLLygAAACgmiBxqiQSUgtPmkrSDgAAAIDjSJwqiSA/H5e2AwAAAOA4EqdKomdooBr6exd63iQpJMBHPUMDyy8oAAAAoJogcaokzB4mdWlap8Bzpv/9PzIiTGYPU4FtAAAAAJQciVMl8ffZdK3ec0qSVPeiPZuCA3z07uhulCIHAAAAygj7OFUSO44ly8MkXdYyUPMm9NKfh84qITVDQX650/MYaQIAAADKDolTJTE0PESrm9ZRRrZVNcwe6t2qnrtDAgAAAKoNEqdKJCSgprtDAAAAAKol1jhVcH/sP60/D7GpLQAAAOBOJE4VWFaOVdO/3a7b3lunxVuOuTscAAAAoNoicarAPl13SIfPpKuBn7cGdmjo7nAAAACAaovEqYI6m5al/6zcJ0l6ZHBb1fJmORoAAADgLiROFdR/Vu1TSkaO2gf76dbuTd0dDgAAAFCtkThVQAdPndNn6w5Lkp66Low9mgAAAAA3I3GqgF76cbdy/r+9e4+Kss7/AP4eLgMIwx0HCLlsIjcBE0TIFEsSdSOtjpqa620v6ngh0MpONoimYFpeImt1T3Ks1NwNU0tdFxHNVBBFxRVEwmR1lFVRLgoi8/394Y9nnUCGW85Q79c5c848z/eZ73yeZz5nznzO9/t8RyvwrJ8LnvF1NnQ4RERERES/eSycjIwQArFBrvBwsMLbIwIMHQ4REREREYF/gGt0ZDIZXgnzwKinnuAUPSIiIiIiI8ERJyMihJCes2giIiIiIjIeLJyMxN17DRj18Q/YdrwMWq3Q/wIiIiIiInpsOFXPSGw49CNOld3C9ao6xIW6w9LE1NAhERERERHR/2PhZEANWoGc0pu4UF6Fj7IuAADeHO4PS3MWTURERERExoSFk4HsKdBg0c5/Q3O7VtpnbiqDOe9tIiIiIiIyOrzHyQD2FGgw4/MTOkUTANQ3CMz84gT2FGgMFBkRERERETWHhdNj1qAVWLTz32hp+YdFO/+NBi4QQURERERkNFg4PWY5pTebjDQ9TADQ3K5FTunNxxcUERERERG1iIXTY1Ze9eiiqT3HERERERHRL4+F02PWXWHZqccREREREdEvj4XTYxbh4wg3O0s8au08GQA3O0tE+Dg+zrCIiIiIiKgFLJweM1MTGdRxgQDQpHhq3FbHBcKUy5ITERERERkNFk4GMKy3G9a91heudrrT8VztLLHutb4Y1tvNQJEREREREVFz+Ae4BjKstxueD3RFTulNlFfVorviwfQ8jjQRERERERkfFk4GZGoiQ9STToYOg4iIiIiI9OBUPSIiIiIiIj1YOBEREREREenBwomIiIiIiEgPFk5ERERERER6sHAiIiIiIiLSg4UTERERERGRHiyciIiIiIiI9GDhREREREREpAcLJyIiIiIiIj1YOBEREREREenBwomIiIiIiEgPFk5ERERERER6sHAiIiIiIiLSg4UTERERERGRHiyciIiIiIiI9GDhREREREREpAcLJyIiIiIiIj3MDB3A4yaEAABUVlZ2Wp/19fW4c+cOKisrYW5u3mn90m8D84c6gvlD7cXcoY5g/lBHGFP+NNYEjTVCS35zhVNVVRUAoEePHgaOhIiIiIiIjEFVVRXs7OxaPEYmWlNe/YpotVpcuXIFCoUCMpmsU/qsrKxEjx49UFZWBltb207pk347mD/UEcwfai/mDnUE84c6wpjyRwiBqqoquLu7w8Sk5buYfnMjTiYmJvDw8PhF+ra1tTX4h09dF/OHOoL5Q+3F3KGOYP5QRxhL/ugbaWrExSGIiIiIiIj0YOFERERERESkBwunTmBhYQG1Wg0LCwtDh0JdEPOHOoL5Q+3F3KGOYP5QR3TV/PnNLQ5BRERERETUVhxxIiIiIiIi0oOFExERERERkR4snIiIiIiIiPRg4URERERERKQHC6dOkJaWBm9vb1haWqJ///7IyckxdEhkhA4ePIi4uDi4u7tDJpNh+/btOu1CCLz77rtwc3ODlZUVYmJiUFxcbJhgyagsW7YM/fr1g0KhQPfu3TFq1CgUFRXpHFNbWwuVSgUnJyfY2NjglVdewbVr1wwUMRmTdevWISQkRPqjyaioKOzevVtqZ+5Qa6WkpEAmkyE+Pl7ax/yhR0lKSoJMJtN5+Pv7S+1dMXdYOHXQ1q1bkZCQALVajRMnTiA0NBSxsbEoLy83dGhkZGpqahAaGoq0tLRm25cvX441a9bgk08+wbFjx2BtbY3Y2FjU1tY+5kjJ2GRnZ0OlUuHo0aPYt28f6uvrMXToUNTU1EjHvP7669i5cye2bduG7OxsXLlyBS+//LIBoyZj4eHhgZSUFOTl5eH48eN47rnnMHLkSJw9exYAc4daJzc3F59++ilCQkJ09jN/qCVBQUHQaDTS4/vvv5faumTuCOqQiIgIoVKppO2Ghgbh7u4uli1bZsCoyNgBEBkZGdK2VqsVrq6u4v3335f23bp1S1hYWIjNmzcbIEIyZuXl5QKAyM7OFkI8yBVzc3Oxbds26Zhz584JAOLIkSOGCpOMmIODg9iwYQNzh1qlqqpK+Pr6in379ono6Ggxd+5cIQS/e6hlarVahIaGNtvWVXOHI04dcO/ePeTl5SEmJkbaZ2JigpiYGBw5csSAkVFXU1paiqtXr+rkkp2dHfr3789coiZu374NAHB0dAQA5OXlob6+Xid//P394enpyfwhHQ0NDdiyZQtqamoQFRXF3KFWUalU+P3vf6+TJwC/e0i/4uJiuLu743e/+x0mTJiAS5cuAei6uWNm6AC6suvXr6OhoQFKpVJnv1KpRGFhoYGioq7o6tWrANBsLjW2EQGAVqtFfHw8BgwYgN69ewN4kD9yuRz29vY6xzJ/qNGZM2cQFRWF2tpa2NjYICMjA4GBgcjPz2fuUIu2bNmCEydOIDc3t0kbv3uoJf3798fGjRvh5+cHjUaDRYsWYeDAgSgoKOiyucPCiYioC1GpVCgoKNCZJ06kj5+fH/Lz83H79m38/e9/x6RJk5CdnW3osMjIlZWVYe7cudi3bx8sLS0NHQ51McOHD5eeh4SEoH///vDy8sJXX30FKysrA0bWfpyq1wHOzs4wNTVtsgLItWvX4OrqaqCoqCtqzBfmErVk1qxZ2LVrF7KysuDh4SHtd3V1xb1793Dr1i2d45k/1Egul6Nnz54ICwvDsmXLEBoaitWrVzN3qEV5eXkoLy9H3759YWZmBjMzM2RnZ2PNmjUwMzODUqlk/lCr2dvbo1evXrhw4UKX/e5h4dQBcrkcYWFhyMzMlPZptVpkZmYiKirKgJFRV+Pj4wNXV1edXKqsrMSxY8eYSwQhBGbNmoWMjAzs378fPj4+Ou1hYWEwNzfXyZ+ioiJcunSJ+UPN0mq1qKurY+5Qi4YMGYIzZ84gPz9feoSHh2PChAnSc+YPtVZ1dTVKSkrg5ubWZb97OFWvgxISEjBp0iSEh4cjIiICq1atQk1NDaZMmWLo0MjIVFdX48KFC9J2aWkp8vPz4ejoCE9PT8THx2PJkiXw9fWFj48PFi5cCHd3d4waNcpwQZNRUKlU+PLLL/HNN99AoVBI87/t7OxgZWUFOzs7TJs2DQkJCXB0dIStrS1mz56NqKgoREZGGjh6MrQFCxZg+PDh8PT0RFVVFb788kscOHAAe/fuZe5QixQKhXQvZSNra2s4OTlJ+5k/9Cjz5s1DXFwcvLy8cOXKFajVapiammLcuHFd97vH0Mv6/RqsXbtWeHp6CrlcLiIiIsTRo0cNHRIZoaysLAGgyWPSpElCiAdLki9cuFAolUphYWEhhgwZIoqKigwbNBmF5vIGgPjss8+kY+7evStmzpwpHBwcRLdu3cRLL70kNBqN4YImozF16lTh5eUl5HK5cHFxEUOGDBH//Oc/pXbmDrXFw8uRC8H8oUcbO3ascHNzE3K5XDzxxBNi7Nix4sKFC1J7V8wdmRBCGKhmIyIiIiIi6hJ4jxMREREREZEeLJyIiIiIiIj0YOFERERERESkBwsnIiIiIiIiPVg4ERERERER6cHCiYiIiIiISA8WTkRERERERHqwcCIiIiIiItKDhRMRURd08eJFyGQy5OfnGzoUSWFhISIjI2FpaYk+ffp0at/e3t5YtWpVp/U3efJkjBo1qtP6A4ADBw5AJpPh1q1bndovEREZBxZORETtMHnyZMhkMqSkpOjs3759O2QymYGiMiy1Wg1ra2sUFRUhMzOz2WMar5tMJoNcLkfPnj2RnJyM+/fvt9h3bm4u/vznP3darKtXr8bGjRs7rb+2OHnyJEaPHg2lUglLS0v4+vriT3/6E86fP2+QeIxVZxfLREQdxcKJiKidLC0tkZqaioqKCkOH0mnu3bvX7teWlJTgmWeegZeXF5ycnB553LBhw6DRaFBcXIzExEQkJSXh/fffbzEeFxcXdOvWrd2x/ZydnR3s7e07rb/W2rVrFyIjI1FXV4cvvvgC586dw+effw47OzssXLjwscdDREStx8KJiKidYmJi4OrqimXLlj3ymKSkpCbT1latWgVvb29pu3Ha2NKlS6FUKmFvby+NwsyfPx+Ojo7w8PDAZ5991qT/wsJCPP3007C0tETv3r2RnZ2t015QUIDhw4fDxsYGSqUSEydOxPXr16X2wYMHY9asWYiPj4ezszNiY2ObPQ+tVovk5GR4eHjAwsICffr0wZ49e6R2mUyGvLw8JCcnQyaTISkp6ZHXxMLCAq6urvDy8sKMGTMQExODHTt26FyL9957D+7u7vDz8wPQdPRBJpNhw4YNeOmll9CtWzf4+vpKfTQ6e/YsXnjhBdja2kKhUGDgwIEoKSnReZ+fX4dZs2bBzs4Ozs7OWLhwIYQQ0jGbNm1CeHg4FAoFXF1dMX78eJSXlz/yPH/uzp07mDJlCkaMGIEdO3YgJiYGPj4+6N+/P1asWIFPP/1UOjY7OxsRERGwsLCAm5sb3nrrLZ1RucGDB2P27NmIj4+Hg4MDlEol1q9fj5qaGkyZMgUKhQI9e/bE7t27pdc0TiX89ttvERISAktLS0RGRqKgoEAnzn/84x8ICgqChYUFvL29sXLlSp12b29vLF26FFOnToVCoYCnpyf++te/6hxTVlaGMWPGwN7eHo6Ojhg5ciQuXrwotTde/xUrVsDNzQ1OTk5QqVSor6+Xzu+nn37C66+/Lo1QAsBPP/2EuLg4ODg4wNraGkFBQfjuu+9a/RkQEXUECycionYyNTXF0qVLsXbtWvznP//pUF/79+/HlStXcPDgQXzwwQdQq9V44YUX4ODggGPHjmH69On4y1/+0uR95s+fj8TERJw8eRJRUVGIi4vDjRs3AAC3bt3Cc889h6eeegrHjx/Hnj17cO3aNYwZM0anj/T0dMjlchw+fBiffPJJs/GtXr0aK1euxIoVK3D69GnExsbixRdfRHFxMQBAo9EgKCgIiYmJ0Gg0mDdvXqvP3crKSmekKzMzE0VFRdi3bx927dr1yNctWrQIY8aMwenTpzFixAhMmDABN2/eBABcvnwZgwYNgoWFBfbv34+8vDxMnTq1xSmB6enpMDMzQ05ODlavXo0PPvgAGzZskNrr6+uxePFinDp1Ctu3b8fFixcxefLkVp/n3r17cf36dbzxxhvNtjeOgF2+fBkjRoxAv379cOrUKaxbtw5/+9vfsGTJkibxOjs7IycnB7Nnz8aMGTMwevRoPP300zhx4gSGDh2KiRMn4s6dOzqvmz9/PlauXInc3Fy4uLggLi5OKljy8vIwZswYvPrqqzhz5gySkpKwcOHCJtMaV65cifDwcJw8eRIzZ87EjBkzUFRUJF2n2NhYKBQKHDp0CIcPH4aNjQ2GDRum8zlnZWWhpKQEWVlZSE9Px8aNG6X3+frrr+Hh4YHk5GRoNBpoNBoAgEqlQl1dHQ4ePIgzZ84gNTUVNjY2rf4MiIg6RBARUZtNmjRJjBw5UgghRGRkpJg6daoQQoiMjAzx8FerWq0WoaGhOq/98MMPhZeXl05fXl5eoqGhQdrn5+cnBg4cKG3fv39fWFtbi82bNwshhCgtLRUAREpKinRMfX298PDwEKmpqUIIIRYvXiyGDh2q895lZWUCgCgqKhJCCBEdHS2eeuopvefr7u4u3nvvPZ19/fr1EzNnzpS2Q0NDhVqtbrGfh6+bVqsV+/btExYWFmLevHlSu1KpFHV1dTqv8/LyEh9++KG0DUC888470nZ1dbUAIHbv3i2EEGLBggXCx8dH3Lt3T28cQjy4DgEBAUKr1Ur73nzzTREQEPDIc8nNzRUARFVVlRBCiKysLAFAVFRUNHt8amqqACBu3rz5yD6FEOLtt98Wfn5+OrGkpaUJGxsbKUeio6PFM888I7U35sfEiROlfRqNRgAQR44c0Ylvy5Yt0jE3btwQVlZWYuvWrUIIIcaPHy+ef/55nXjmz58vAgMDpW0vLy/x2muvSdtarVZ0795drFu3TgghxKZNm5rEX1dXJ6ysrMTevXuFEP/L+fv370vHjB49WowdO1bnfR7+zIUQIjg4WCQlJbV4/YiIfikccSIi6qDU1FSkp6fj3Llz7e4jKCgIJib/+0pWKpUIDg6Wtk1NTeHk5NRkalhUVJT03MzMDOHh4VIcp06dQlZWFmxsbKSHv78/AEhT1gAgLCysxdgqKytx5coVDBgwQGf/gAED2nXOu3btgo2NDSwtLTF8+HCMHTtWZ2pfcHAw5HK53n5CQkKk59bW1rC1tZWuT35+PgYOHAhzc/NWxxUZGamzsEdUVBSKi4vR0NAA4MFoTFxcHDw9PaFQKBAdHQ0AuHTpUqv6Fw9N+2vJuXPnEBUVpRPLgAEDUF1drTPi+PD5N+bHwzmjVCoBoMWccXR0hJ+fn/Q5njt3rtnP+eHr8PP3lslkcHV1ld7n1KlTuHDhAhQKhZR3jo6OqK2t1cm7oKAgmJqaSttubm56pz7OmTMHS5YswYABA6BWq3H69OkWjyci6kwsnIiIOmjQoEGIjY3FggULmrSZmJg0+cHcOC3qYT//gS+TyZrdp9VqWx1XdXU14uLikJ+fr/MoLi7GoEGDpOOsra1b3WdnePbZZ6U47t69i/T0dJ0YWhtPS9fHysqq8wIGUFNTg9jYWNja2uKLL75Abm4uMjIyALR+QY1evXoBeHBfWmfQlzONhVdbcqYj7934PtXV1QgLC2uSd+fPn8f48eNb1cej/PGPf8SPP/6IiRMn4syZMwgPD8fatWs76ayIiFrGwomIqBOkpKRg586dOHLkiM5+FxcXXL16Vad46sz/Xjp69Kj0/P79+8jLy0NAQAAAoG/fvjh79iy8vb3Rs2dPnUdbiiVbW1u4u7vj8OHDOvsPHz6MwMDANsdsbW2Nnj17wtPTE2ZmZm1+fWuEhITg0KFDzRapj3Ls2DGd7aNHj8LX1xempqYoLCzEjRs3kJKSgoEDB8Lf379NC0MAwNChQ+Hs7Izly5c32974/08BAQE4cuSITs4cPnwYCoUCHh4ebXrP5jycMxUVFTh//ryUMwEBAc1+zr169dIZHWpJ3759UVxcjO7duzfJOzs7u1bHKZfLdUa5GvXo0QPTp0/H119/jcTERKxfv77VfRIRdQQLJyKiThAcHIwJEyZgzZo1OvsHDx6M//73v1i+fDlKSkqQlpams9JZR6WlpSEjIwOFhYVQqVSoqKjA1KlTATy4kf7mzZsYN24ccnNzUVJSgr1792LKlCnN/iBtyfz585GamoqtW7eiqKgIb731FvLz8zF37txOO5fONGvWLFRWVuLVV1/F8ePHUVxcjE2bNkkLGDTn0qVLSEhIQFFRETZv3oy1a9dK5+fp6Qm5XI61a9fixx9/xI4dO7B48eI2xWRtbY0NGzbg22+/xYsvvoh//etfuHjxIo4fP4433ngD06dPBwDMnDkTZWVlmD17NgoLC/HNN99ArVYjISFBZzpneyUnJyMzMxMFBQWYPHkynJ2dpRUGExMTkZmZicWLF+P8+fNIT0/HRx991KbFPiZMmABnZ2eMHDkShw4dQmlpKQ4cOIA5c+a0aREVb29vHDx4EJcvX5ZWgoyPj8fevXtRWlqKEydOICsrSyr6iIh+aSyciIg6SXJycpOpRgEBAfj444+RlpaG0NBQ5OTktOlHqD4pKSlISUlBaGgovv/+e+zYsQPOzs4AII0SNTQ0YOjQoQgODkZ8fDzs7e3b/AN8zpw5SEhIQGJiIoKDg7Fnzx7s2LEDvr6+nXYuncnJyQn79+9HdXU1oqOjERYWhvXr17d4z9Mf/vAH3L17FxEREVCpVJg7d670p7suLi7YuHEjtm3bhsDAQKSkpGDFihVtjmvkyJH44YcfYG5ujvHjx8Pf3x/jxo3D7du3pVXznnjiCXz33XfIyclBaGgopk+fjmnTpuGdd95p38X4mZSUFMydOxdhYWG4evUqdu7cKd1T1rdvX3z11VfYsmULevfujXfffRfJycltWj2wW7duOHjwIDw9PfHyyy8jICAA06ZNQ21tLWxtbVvdT3JyMi5evIgnn3wSLi4uAICGhgaoVCoEBARg2LBh6NWrFz7++OM2nT8RUXvJRGvvViUiIvqVGjx4MPr06aPzX1G/NgcOHMCzzz6LiooKg/z5LxFRV8cRJyIiIiIiIj1YOBEREREREenBqXpERERERER6cMSJiIiIiIhIDxZOREREREREerBwIiIiIiIi0oOFExERERERkR4snIiIiIiIiPRg4URERERERKQHCyciIiIiIiI9WDgRERERERHp8X/5DW/OKJELGgAAAABJRU5ErkJggg==", "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Step 1: Perform PCA without specifying the number of components\n", "pca_full = PCA()\n", "principalComponents_full = pca_full.fit_transform(df_gene_scaled)\n", "\n", "# Step 2: Calculate the cumulative explained variance ratio\n", "cumulative_explained_variance = np.cumsum(pca_full.explained_variance_ratio_)\n", "\n", "# Step 3: Plot the cumulative explained variance ratio\n", "plt.figure(figsize=(10, 7))\n", "plt.plot(range(1, len(cumulative_explained_variance) + 1), cumulative_explained_variance, marker='o', linestyle='--')\n", "plt.title('Cumulative Explained Variance by Number of Principal Components')\n", "plt.xlabel('Number of Principal Components')\n", "plt.ylabel('Cumulative Explained Variance Ratio')\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Loadings plot\n", "\n", "Loadings scores represent the correlation between the original variables and the principal components. High loading scores indicate that the variable contributes significantly to the principal component, while low loading scores indicate that the variable has little impact on the component.\n", "\n", "A loadings plot is a graphical representation of the variables in the reduced space of the principal components. It helps us understand the contribution of each variable to the principal components and identify the variables that are most important in explaining the variance in the data.\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

	Principal Component 1	Principal Component 2
Gene_1	0.485469	0.050651
Gene_2	-0.157812	-0.338372
Gene_3	0.081259	0.346014
Gene_4	0.090567	-0.028143
Gene_5	-0.201834	-0.225091

\n", "

" ], "text/plain": [ " Principal Component 1 Principal Component 2\n", "Gene_1 0.485469 0.050651\n", "Gene_2 -0.157812 -0.338372\n", "Gene_3 0.081259 0.346014\n", "Gene_4 0.090567 -0.028143\n", "Gene_5 -0.201834 -0.225091" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Loading scores\n", "loading_scores = pca.components_.T * np.sqrt(pca.explained_variance_)\n", "df_loading_scores = pd.DataFrame(data=loading_scores, columns=['Principal Component 1', 'Principal Component 2'], index=genes)\n", "\n", "# Display the loading scores\n", "df_loading_scores.head()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Loading plot\n", "plt.figure(figsize=(8,6))\n", "plt.scatter(df_loading_scores['Principal Component 1'], df_loading_scores['Principal Component 2'])\n", "plt.xlabel('Principal Component 1')\n", "plt.ylabel('Principal Component 2')\n", "plt.title('Loading Plot')\n", "plt.grid()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "Congratulations! You've just performed PCA on a gene expression dataset. By reducing the dimensionality of the data, we were able to visualize the distribution of samples in a 2D space, which can be incredibly useful for exploratory data analysis in bioinformatics and other fields.\n", "\n", "Remember, PCA is a versatile tool and can be applied to various types of data. The key is to understand the assumptions and limitations of PCA to make the most out of this powerful technique." ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 2 }