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b/doc/LectureNotes/_build/jupyter_execute/Clustering.ipynb new file mode 100644 index 000000000..2c1c48b1e --- /dev/null +++ b/doc/LectureNotes/_build/jupyter_execute/Clustering.ipynb @@ -0,0 +1,917 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Clustering Analysis\n", + "In this chapter we will concern ourselves with the study of **cluster analysis**.\n", + "In general terms cluster analysis, or clustering, is the task of grouping a\n", + "data-set into different distinct categories based on some measure of equality of\n", + "the data. This measure is often referred to as a **metric** or **similarity\n", + "measure** in the literature (note: sometimes we deal with a **dissimilarity\n", + "measure** instead). Usually, these metrics are formulated as some kind of\n", + "distance function between points in a high-dimensional space.\n", + "\n", + "There exists a lot of such distance measures. The simplest, and also the most\n", + "common is the **Euclidean distance** (i.e. Pythagoras). A good source for those of\n", + "you wanting a thorough overview is the article (DOI:10.5120/ijca2016907841\n", + "Irani, Pise, Phatak). A few other metrics mentioned there are: *cosine\n", + "similarity*, *Manhattan distance*, *Chebychev distance* and the *Minkowski\n", + "distance*. The Minkowski distance is a general formulation which encapsulates a\n", + "range of metrics. All of these, and many more, can be used in clustering. There\n", + "exists different categories of clustering algorithms. A few of the most\n", + "common are: *centroid-*, *distribution-*, *density-* and *hierarchical-\n", + "clustering*. We will concern ourselves primarily with the first one." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Basic Idea of the K-means Clustering Algorithm\n", + "The simplest of all clustering algorithms is the aptly named **k-means algorithm**\n", + ", sometimes also referred to as *Lloyds algorithm*. It is the simplest and also\n", + "the most common. From its simplicity it obtains both strengths and weaknesses.\n", + "These will be discussed in more detail later. The k-means algorithm is a\n", + "**centroid based** clustering algorithm.\n", + "\n", + "Assume, we are given $n$ data points and we wish to split the data into $K < n$\n", + "different categories, or clusters. We label each cluster by an integer $k\\in\\{\n", + "1, \\cdots, K \\}$. In the basic k-means algorithm each point is assigned to only\n", + "one cluster $k$, and these assignments are *non-injective* i.e. many-to-one. We\n", + "can think of these mappings as an encoder $k = C(i)$, which assigns the $i$-th\n", + "data-point $\\bf x_i$ to the $k$-th cluster. Before we jump into the mathematics\n", + "let us describe the k-means algorithm in words:\n", + "1. We start with guesses / random initializations of our $k$ cluster centers / centroids\n", + "\n", + "2. For each centroid the points that are most similar are identified\n", + "\n", + "3. Then we move / replace each centroid with a coordinate average of all the points that were assigned to that centroid.\n", + "\n", + "4. Iterate this points 2, 3) until the centroids no longer move (to some tolerance)\n", + "\n", + "Now we consider the method formally. Again, we assume we have $n$ data-points\n", + "(vectors)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

\n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:kmeanspoints} \\tag{1}\n", + " \\boldsymbol{x_i} = \\{x_{i, 1}, \\cdots, x_{i, p}\\}\\in\\mathbb{R}^p.\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which we wish to group into $K < n$ clusters. For our dissimilarity measure we\n", + "will use the *squared Euclidean distance*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
\n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:squaredeuclidean} \\tag{2}\n", + " d(\\boldsymbol{x_i}, \\boldsymbol{x_i'}) = \\sum_{j=1}^p(x_{ij} - x_{i'j})^2\n", + " = ||\\boldsymbol{x_i} - \\boldsymbol{x_{i'}}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we define the so called *within-cluster point scatter* which gives us a\n", + "measure of how close each data point assigned to the same cluster tends to be to\n", + "the all the others." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
\n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:withincluster} \\tag{3}\n", + " W(C) = \\frac{1}{2}\\sum_{k=1}^K\\sum_{C(i)=k}\n", + " \\sum_{C(i')=k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}}) =\n", + " \\sum_{k=1}^KN_k\\sum_{C(i)=k}||\\boldsymbol{x_i} - \\boldsymbol{\\overline{x_k}}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $\\boldsymbol{\\overline{x_k}}$ is the mean vector associated with the $k$-th\n", + "cluster, and $N_k = \\sum_{i=1}^nI(C(i) = k)$, where the $I()$ notation is\n", + "similar to the Kronecker delta (*Commonly used in statistics, it just means that\n", + "when $i = k$ we have the encoder $C(i)$*). In other words, the within-cluster\n", + "scatter measures the compactness of each cluster with respect to the data points\n", + "assigned to each cluster. This is the quantity that the $k$-means algorithm aims\n", + "to minimize. We refer to this quantity $W(C)$ as the within cluster scatter\n", + "because of its relation to the *total scatter*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
\n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:totalscatter} \\tag{4}\n", + " T = W(C) + B(C) = \\frac{1}{2}\\sum_{i=1}^n\n", + " \\sum_{i'=1}^nd(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\n", + " = \\frac{1}{2}\\sum_{k=1}^K\\sum_{C(i)=k}\n", + " \\Big(\\sum_{C(i') = k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\n", + " + \\sum_{C(i')\\neq k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\\Big)\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Which is a quantity that is conserved throughout the $k$-means algorithm. It can\n", + "be thought of as the total amount of information in the data, and it is composed\n", + "of the aforementioned within-cluster scatter and the *between-cluster scatter*\n", + "$B(C)$. In methods such as principle component analysis the total scatter is not\n", + "conserved.\n", + "\n", + "Given a cluster mean $\\boldsymbol{m_k}$ we define the **total cluster variance**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
\n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:totalclustervariance} \\tag{5}\n", + " \\min_{C, \\{\\boldsymbol{m_k}\\}_1^K}\\sum_{k=1}^KN_k\\sum||\\boldsymbol{x_i} - \\boldsymbol{m_k}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have all the pieces necessary to formally revisit the k-means algorithm.\n", + "If you at this point feel like some of the above definitions came a bit out of\n", + "no-where, don't fret, the method does get a whole lot simpler once we start\n", + "programming." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The K-means Clustering Algorithm\n", + "The k-means clustering algorithm goes as follows (note in my opinion this\n", + "description is a bit complicated and is lifted directly out of ESL HASTIE for\n", + "deeper understanding purposes)\n", + "\n", + "1. For a given cluster assignment $C$, and $k$ cluster means $\\{m_1, \\cdots, m_k\\}$. We minimize the total cluster variance with respect to the cluster means $\\{m_k\\}$ yielding the means of the currently assigned clusters.\n", + "\n", + "2. Given a current set of $k$ means $\\{m_k\\}$ the total cluster variance is minimized by assigning each observation to the closest (current) cluster mean. That is $$C(i) = \\underset{1\\leq k\\leq K}{\\mathrm{argmin}} ||\\boldsymbol{x_i} - \\boldsymbol{m_k}||^2$$\n", + "\n", + "3. Steps 1 and 2 are repeated until the assignments do not change.\n", + "\n", + "As previously stated the above formulation can be a bit difficult to understand,\n", + "*at least the first time*, due to the dense notation used. But all in all the\n", + "concept is fairly simple when explained in words. The math needs to be\n", + "understood but to help you along the way we summarize the algorithm as follows\n", + "(try to look at the terms above to match with the summary).\n", + "\n", + "1. Before we start we specify a number $k$ which is the number of clusters we want to try to separate our data into.\n", + "\n", + "2. We initially choose $k$ random data points in our data as our initial centroids, *or means* (this is where the name comes from).\n", + "\n", + "3. Assign each data point to their closest centroid, based on the squared Euclidean distance.\n", + "\n", + "4. For each of the $k$ cluster we update the centroid by calculating new mean values for all the data points in the cluster.\n", + "\n", + "5. Iteratively minimize the within cluster scatter by performing steps (3, 4) until the new assignments stop changing (can be to some tolerance) or until a maximum number of iterations have passed.\n", + "\n", + "That's it, nothing magical happening." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Writing Our Own Code\n", + "In the following section we will work to develop a deeper understanding of the\n", + "previously discussed mathematics through developing codes to do k-means cluster\n", + "analysis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Basic Python\n", + "\n", + "Let us now program the most basic version of the algorithm using nothing but\n", + "Python with numpy arrays. This code is kept intentionally simple to gradually\n", + "progress our understanding. There is no vectorization of any kind, and even most\n", + "helper functions are not utilized. Throughout our implementation process it will\n", + "be helpful to keep in mind both the mathematical description of the algorithm\n", + "*and* our summary from above. In addition, try to think of ways to optimize this\n", + "while reading the next section. We will get to it, take it as a challenge to see\n", + "if your optimizations are better.\n", + "\n", + "First of all we need a dataset to do our cluster analysis on, for clarity (and\n", + "lack of googling beforehand) we generate it ourselves using Gaussians. First we\n", + "import" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import time\n", + "from IPython.display import display\n", + "\n", + "np.random.seed(2021)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we define functions, for ease of use later, to generate Gaussians and to\n", + "set up our toy data set." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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IZ5wWvLY9eigBrUXGfX8sAvljgI86rvwocML1vbDcmv8sKapP9ZDFverGH+da3iu43hmIXtkaMs3KecPvo1BFbw2U7y8Sw9tG7VfbIXGg2B6mjLOSZujRCL0HXix+6flT/MYbuxxMc5YaPheWmxhr+NoTS7Qjn51RyjevHCCATuhRacswKR6wDLJEUZn5e59kJa9uDWlF/n3VDk8y+muHU75yfmkx+HYfLAL5Y4BPsnTxKCcNf1S41zl/3Gt5tyz0zkBUaehEPtvDlGfX/dvO4V74sPIC8KHZqpKCtNTzchu4RTbwHrz1dWG5yZ/+2rn5a57qRozTEiUF47Tgm1cOMNrw3EaXysCN44TzS416UeSepZA7F82rB1MsYl7KuTVYWwTPnWoDzIeKQk8ikXMmziI7vzsWgfwxwSdVujihqQ2Sgmle0QpdMLmzBvuopQM+zvHuVz75KNfyYUfrW6GiqAzTvJr/7GCSczjN+cbl/YcarFJS8GE7jJNRe/h4O7U7r8fJe31te4QAntvo0grfLz0dz3KOZjkvXh+gjWGpHggaJgWXVlscz4r5dTr59yApKLTmS2e6tCP/A8Ha8wSvbg350tn+LaqLglb00XYznzUsAvljjJMv3PYwZZpVtCKPjV78SLehS82A37q8Tzf251/ArUHCn/rq2dvO46PWNx8mA33QjOxRl6Ie5P3duXhs9GJ+sDmkHTplwYNJzmtbQ75wpveBY4ALUi/dOCZQikurLaZ5xfYw5WiWszfK+UOfu30qMvYVWal/KDu1k8C+PUwZzArePZjSjQJW2yGNQHHjeMYwLVhrR+SlYWc0QckJT622ePdgyhdveY9XD6a3cdePpwXvHBzz4vVjtIa1TsjFlSaXVlr8YHPI1YPpfLw/rzQXltvz9/tp3gV+0lgE8scUJ8FlklW8fHNAXllCJajO9R+ohvmgOJ4VfOFMj0FSMMk1rcjn3FKT41kxlzZ9GH71nQ3BUVqydkdD8G4Z6INmZI+6FHXvmjvzxXRnlHJxuUXkS64dzRhnJaEnuDlImGYVXzjTY60T3XaMVzaHaGNpBB4SSVZW/N2XbnI0K2h6Hhu9iFlRzbPVW1UIhbh3aePjLPQnjJhGoMiKirSoeO+oYqnhM0xLsIK3dsZzrnngSb71zgFPr7Xvet+WmgH/9LUdxlmF1hZPCW4cz2iFHk+ttfnSmS6X98ZYBAbLs+vt+6ouLuCwCOSfctzLkssY+MHmEE8Iuu2AWaZ5ZXPIzzy58si2oScNtZMABMypj7c+50Hq6B9oCG4OmeQVy3c0BF/bHvETF5bue7x74VGWou72/m4OEoZJQSPwONdvEHmKN3bGJEXFmV7Mzz25gqfkvPwR+ZLLu+N5iep0N+LK/pQvbHRdIJfwzu6MzeOUwBPEDcWN44TQV7y1M+F77x0RBR7N0GOlGbHc8gk8xTipGGUFhTac68ec6sS0I49RWtLwPd47nHE8K0iLilPdmG9dOeBUJ8JaaEUe7chd91tZKdcOZ6y2Ql7ZdJriaVEwSkvek4InVhrcPErxPUUndg3QcVY6iqqxH7hOJ/fteFaw1AooKstmpjFYluJgvvs4t9SYNzYfVHVxAYdFIP8UY5gUH+Bwbw4Sfv7pVcZpyfEsRxtLpxEgEDRDxSA1HM9yPPVhJMGHx4PQ9R6U0veBhqCxdD+kISiwn6pJ0bu9v2lWsdIK5z+PA8U0L0kLTeSr+eI0zSpevH7ENNMst0LO9GJKbXh1a0hluG3I6HBSMExKSq0ZJRpPWkLfw5OCpKhYUYpJUjJOK24OJM+stRmmJUVp2BrOKCsDFraGFm0cdXR/nNGOfARweXdMHCh2hylPn2pzOM0ZZyVJXnG6F+NJybeuHDJMCqy1LLUClCw5mOREvuKptRZFZZnlFW0pqLStz81gLXjy9s/drfdtnJZUFUgp6tfOEEJw/XBGUrhg/sL5HsCnbi7h045FIP8U45XNIZuDlF4c0IgleWXYHKS8sukoaG/tjulGPmVlCDxFqS3dyOM4KXmqZgB8XFxcafKtKwd1cDH4StJr+PzcLQNBD1qT/mBD0KOoNNP8/QnGtNQ8tdYmKSqmWcXxLOc4KVBS8kvPn3ok7+lhcbf314q8D/hb5qUhUIJSGy7vjjnTb7B5PCPJNXGg0Nry3uGU070GFkEzkPNFYpprCq3JS40QgkBBUhrGWUY39rmw3OLCcpOi0nz/xoDV2p5trR1xlORUxvLu/tT1MvKK59c7fPvqEef6MYGnOJzmSCnAwiit8JTizZ0he+OUM90YIVIEgkq7Jm2/ETBKSqQUPLfeoagsWanJSkNWGaqkIAoUaWGQQvL0qTatyCcpqg/9HHRin1FWIBG0Yo/Ak2wOZgyykk7D52sX+nhKznsHJ/2DBe6PRSD/EeGjsDDe2Z/Qjfy6gw+Rr+han3f2J/zrXz3Ht64ccDTL59lSJ/Y53YlQkgcaj3/Qc7IAAoT7zwfm/B60Jv1hDcFXNge0Iv+2LfRXzvcZpSW/8cYu2sBSI2CpGXL1YEo39n/kmdnd3t+1w9n8/ZwwLRrByb1yUq7/7I09Qk+SFIaLqy2S3DDKCoZJwU9fWmaYlvNF6+rBxN3LQNGJXHM5G2cUlSEtDKttJwlbWcs4LSi1xlOSZqDYPEqoKjduvz/JOJ4VPLHUYJpX7I4zjIXtYULse2xnBUVlSSrN4TgjChS+L7myN+XzG108JXlrd8okryg1pGXJE0tO18dYwVo74NlTLd7enzJOS55abdJtBASe4peeP8XxrOCt3TFv7Y4YpZpvXtnn608s8/mNLlIKZkWFXwmksKSFYanh4yvFzihjoxfPJRMWDJUHxyKQ/wjwUVkdSWE4GM9ICkNauu16M5A06wbQajtkf5yz1AjItGacFqy1Q37p+fUHambdeU7fvHJAN/Y/UCtda0c8cZeBoDsXgy+f6z2w6JGSgrP9Bp3YZ5AUCAFKCn5wc8juKOPicuu22vydg0h3Y7w8ageluy14F1eYv58Tf8tW6IFwFL3tYcLRJOXJ1TZhK2B7mPH0WpsLyw3GWYmnJBu9mKVmwH//8hb745yi0vi+pNKWrKqotEZJQ+j7bA5SAiXZn6RM6gAdKMn+OEcK8KVkrRthjEAJwavbIxCWaVailGSUliSFJskrSm2Y5AVJbmhFHpGv2J/kDN49xJcCgcWTAVlRsj/OAYGwgmdONdnoN0iKiqfX2qSV5p2DGeeWDP/GV8/RjX3e2B7zjcv7VNpwph+jhOJfvLXPOC350pkeNwcz9sc5WanR1nCu16Df9Cm15fLuhGdOtT4g0rXAvbEI5D8CfBTVvJMa5f7EfeB9T5HkJUmgaIQer2wOubjS4vxSszYG0HgKzi815mySk+PcrVl65yTd5iBllJRcXGny+vaIb769j5SSr5zr3XZuJw2sh12gPiyz/bmnV2+bjDTGBcHv3zimGXh88UwPbS3TXNMMJI3Q4yu1ycLJa3tS8PrWiH/2+i6NwOP50x1W2+HHpkE+yOj4yftx/paKF873mWYVv/HGDoezAqQk9BWVsdzYnzDJSp4/3a4zdld2eGVziK8EXzjTnZs+DJOCwPd5fqPH5jCh4SusNVw/nHFjkOJ7gsCTSATbw4R25HO6zmaNNZzuxtwczPjKuSVuDmYcTgtOd2N2RimltWjAR2Bw4mtH04JTnYiirEApKmMYZSWzXNMIFHlpwFoOZzl5qWlHgbuHkcdyI+D3PbnCe0czrh/NeHVzjJKCwPMZzCrWez5Lcci1wxk/+1TM02ttvny2z42jGaHnrs1qJ57vPK8dzfj8RvdBvloL1FgE8h8BHoTVcWcgcV/4LnvjrGYCWJSSRL7i+dNd3tmf8PULywgh5o3CO9kkdwbHt3bHvHh9wC89f+oD57Q9TOlGjlr29t6UyFestEKuH6W8sjXiy2d7H6CCfZQF6l6TkcbAjeMZka9Y78TcHCT8je/e4Km1FqutgKRQBFk1v1aNwEMbO3eDx8IoyblxPCMO1Px8HySLv1uwflCZ2JNewmvbQ947mDHOHHOlGwe8tjXkwnKTJ1ebXD9K+P6NIZ/f6NCvNbpf2Ryx1PBphQGTvMICq+2AUhsakeKFc46XvTlIeH17jK8Eoac43Y3RxpJXhlJbelFAK/SQAqZFSaktG72Iz53u8HvvHSERZKVGJIUb4MkcBVS4ohlZpTEW/Lo2f7g7phMHnOqESCGoKs3OKOMHN4d0Yx9jDYOJRknL1jAhKw2NQDErSqRwzd+TQaFTnZDDSY617zcy98YZ55ZiDqcFW8MEXVmkAiEEf+xLG/f/Yi0wxyKQfwQ8bL37fqyOD8v6Xr4x4GsXljjTb5AVmrTUxL4kCjxW2yHvHc/uesyT83vpxjGVsVTa0m8ErLYixmnBb7yxyzOn2rf9/jTXVFpz7WBKM/ToNXxWWiG9po/AcvVwypfO9G5rYP3g5vCBx/cfZDLyeOZq/ZHv0Qo9to5naAvGWNJCczDJ+emaWnmyEJ0E8cj3qIxFCrfYnTBhbj2fB52cvHN0/Gwv5uZxchtt8MO2/hY4mhYEnqIZukWmMpYLy03yyiCl4OxSg2bo0W0EnOs3SEvN1iAh8lostyKePdXh5nHC5iCh0pZT7YiNbsS1wwSAZqCIlPscdOKAUmu6sc9xUlBaw1NrTbaGGUrC86fbzPKKg0mOAApjEFLSCDwKbWhhiesmqNYGJQWRFAgp5kJpnchDSslKMyDLNeO84GiW8d1rR2SVphV5XFhq8VtvH5CVmvVejLCQV5bAc4yWtDQkuaEZeXTqHsfJwno8LUgKzSSrsFjKCvqNhw9Lj3qy+HHDIpA/JD5Kvft+rI4Py/qWWuGcy1tqQ+R7rsSiRP3FtHzn6hFLTZcNnvCV17ut+flJJMezlKzQdOIAIQSdOOBgmgPcNt7tHNXHeDUrZZpVXNmb0G8FPL3aYpiUH2hk3j6+r2mFaj6+f7fBH0+KednmhfN9vnS2Nz/WW7tjVluuJj4rKlpx4Lbz0xwLSAFv705QUtCOXHnprd0xy82Q1U6ErwTgstXxhzgo3S27vpW3PslKfvfdIzaPE4ZpQex7fM8e8fWLy4Se5N2DKb937YjnTrd5YqU5H0ffHWWstEJOdxt0ItfovLI/Zus44cm1JqOs4sJSAykFvhQUmjk9cb0b873rA9Y7Ed3YY63jFtDPb3SY5Zp/8uo2hbYkuWZSaI5mKWc7DQrtczx19e/lpk9eaP7JaztobVGe5Fy/wTAtMQbakZswDZXgIC1ACOK65FMaiyclSoAUktBT6MDirqYgzSpGQtAIJNrA5nGKxiKEoCyd7njkKUZZSV5pnjnV5ejIKTK2Iw+s4DjN+fqF/m1N+BP1xUa9A8srQ1bquZbLgzY7F8qJC2OJh8ZHMSY4qaXeTRD/wwwLLi67INFvBKRFxSjJScsKX0m3VV9q8bULfRDw4vVj8kpzabXFt9894u29CTePE6SErLA0Q4/DSQZAXjmWwMkW9+ScfCXY6DeIfMW7+1N+sDniMClRCGaF5miS36Yb4ib/Uv7BD7Z4c2eMqptqr20N8aS4zX7sxlEyr7+/vTdFCclKK+TGUTI3Gri40kRJyTh1vYFhUtIMPFbaEc3QY7UVcaoTMUgLrh1M2R66hl879Enykiu7E5SUtEKPcVrQDNQHDC7uZgxxwlsHeGVzxJs7Q0qjWeuEYC2bg4Q3d0a8dzhF13rdk6zi731/k+Opu0fDtOD68QwpXKkDIPIUB9OMy7sTPCl4dr2DrSlArfB92qKSzBe717fHfPe9YyJP8qWzPa4dTDmYFQzSEouhGSqsge1xzvZxgrGWpq+4tNKm2/RJS4MG1jsRlTbsTwpGacGs0Fxaa/NTl5bpNkLyyu1yrIVWoNDGMkhKCu2aoYfTHF+peudh0cbtKAptWO3GdKKAhq/wPME0L9kaJSRZyc4o4zjJWW0HSAGDtKQVSX7xuTV+35MrvLI55P/1rav8v7/1Lq9sDvEkHM4Kvn/jmO1hwplezGo7fCibwM+SZ+zd8EgyciFED/h/Al/A7TD/V9ba330Ux/604aOqAd5r0vDDSi+ekrxw3tWlsyqej1jfOer95bMBSVGRV07XYpiWrDRDCm3Yn+TsjBKEhTCQtCMfKQTnlxof2OICZKXmm28fcHOQgIVISF7ZHHJ21uBzGx2SvKKoDN+6coDFBZ4vnOlymDi62TPrHb5wpscb22OeWGneNvjjS8FvvLFDMwzoNTxWWiFVPZp+Ii97phfzjbf3CZQk8CQXlhtc3p2w3o2orOHmYUpWajwhCTzFl8/2eGd/4oZcfEUjkCgpeGtvwtl+g1PdaM5FfunGgHcOpoSe5NKKY+C8cnPED7YGZKXmyt6En760yutbQ0JP4kvFUjOiqDLO9mPe3pvy1Qt9uqHHuXaD60cJZ3sRg6RgrROx3AyZ1ruAwaxgb5IRKMHnTneYFRXNWnPFk4JRVvLlsz3ATea+ujliZ5yx1HD16Hbozbn17x5OERamWck0r1BC0ot8BmnJ3jTn0orHc+tdEJZASYyxFJW7rsdJweEkp9/wCT1JM/CY5ZrlVsDuOGOalbSjgH4joBEYtgYJx8biS0kn9BECTnXfv09l5QSyIl8xmpXEgUepNYNpBdbV9YWQXD+cISSstSP+zNfPz5k5r24O2RwkdCIfELx4fcD1o4Rn1lpcOr9EXmm2hglKigcyxjjB46jQ+ajxqEorvwr8E2vtnxZCBEDjER33U4cfhsnD3UovtzIjTvCNy/t4UtSj3nruqXgy6r3cDCi0RVvmzaXjWY5MJa1gwk9eWkF+CM+8E/vcHCRcXG1x/TghKSomWUVeWcZ5hScFP9gacnlvwtbQDaGsd2NaoUcgFb6nOJzkPLXa4mCS8bnTnfmxpYCbg4RBUnGm36DScGV/yqXV5m2j7kvNgD/+pQ2uHc7YGqYEnuTSahNjLO/sTQg8xdcu9NkaZrx3OOULZ7p85fwST621ubI35gc3h3z1whJ//Esb81LTKC25ejClEXg8d6rNq1tDvn31iKRwpaPIl1xcbjLKSn7z8j7744wzSw1OdWJiXxH5EmM9AuWoc0KIeZZ6MngzyUpmRcXbe2N8T3G6E+MpN4n5zHqH052Y/WnGSzcHNAJnw+bOSfE77xwwSiqEsOyOUg4mGb//6TUCT/DK5pBxUlJog7VuDL4oLYEnWG5ENCNFI/B4dr3FNNcMZjkCwfEsY3OQYowhN6amG1rWOxF7EzfJmRYVseeRl4bdIiNQigvLTQ6mOXGg8KTAGMt7BwmtyMOT4EvFLHPURSlhlmlsna17SlAZWGn5dGOP/VHG8bTgcOLOZWeU0G+ErLVDIt99d8rK0AoVR7OCfjOsjTE0145mfO2JBx8G+qSNVz4N+NiBXAjRBX4/8L8EsNYWwI/tUvjDMHl4kIGak5rzq1sjJzQUeCgp8ZXgyv6EaVagEEgJ00xzOM04muVMMk079ogDj2nhGmv9Zpcf3BzewYlu8s2399kdpgyTAm0h9BRxKBgnJb/9ziGt0OOJlSbSCrYGKUmuUVLQjHzSvGJrkDBMS7qxzytbQyrt5FyT3FBpQ7vhPCAFUJQVm8eO6TBKS752vo82lp2RY+mc6cUst9wW+/XtEU+vtznTa9AMPIZJSSGZNzTbkY9Skq9eWOLL526/D99+9+i23cGXzvb5xuV9XtseuUZiv0HsKRqBT1aWaB0RexIlnM5HM/DYGSasdUKysprblp1fajDJSkS9qEa+4snVNvuTnFe3RvSbHkIK3tmfcGVvQl5p9iY5Xzvfpxv5XNmf8MbWCOkJpkVFO1R4QjDNK/7hqzv8yRc2eGVzxHI75O39CUfTAiXBV5JKGwgsG70YIQRSCFZbAduDxMnFVpaqMpTWkBUVk7RkmJV1zV8xKzRSCkprUPXCVGmLks7qzRaaaeaGiJqRxxOtmFB5NEJHgd0fZUxLt9BX2mIM7ncrTehLRmnFMKsQacU/e32Pz5/pMs00W4Mhv/DM+yqOpTbEvmKpFVJqzbsHE7DQbz5cAP4kjVc+LXgUGflF4AD4r4UQXwZeBP68tfa2ApUQ4leAXwE4f/78I3jZTwYPOsV4L9zZYV9qBrdpON/acR8mBa9sDnn5xpClZkBZafZHKePA54llN7l39WDK2aWYyhiOJwV7k5z3DqeUlWW5HfDMegdPSA5nGVcOpnztiaX5B/7WptBTp9r81tsHhL6kKC2VgYNZiq4M+xPJ184vYaxAKkFeuBH0cVahpGumrbcjkqLieJqjpOBUO6SoDG/ujsmKksNpySs3hiy3Ak53YqTS+BICJXhrd+Tqu9bOaWhbo5Q/+xPn2Ru7RmJUS7e2Ig9rPY5mOeO04NrRjBffO+aFcz0mWTmnHca++sDuoB35nO7GvL035uJKEylcm8hXgrwSnOpG+FKQlSV5JQDLxZUmnz/TZXuYstQK64EVw2tbQ+JQ0Qo8QCCl5GsXlhiku+yPc84tNbh57KRoLW5R+ObbBzRDj+fW24SB4qAeAtorNZFyC8g0L/kXbx2w0vL5+gV3b44mOVlpafiSyPdoRz6FNlxcaTo1Qiybo5S80kzzEoubmhQCPCmxxrA9SGnHHu3QRwiBMYYokJSVITOGvNIoIUi1Gy4y1pXE3j2YcX65RRx4+J5HaXOSUuNLia8sFou1AmPh+uEMY01d3lFcP5qxN86JfEkz9tkapTyz5tfXXFJUmmag0AaeXG1jrcFYHrkt3o87HkUg94CvAv+BtfY7QohfBf4PwH9665Ostb8G/BrA17/+9Q+6uT5G+LB694PSn+7ssB9Mcn7r8j5fONP7wBALuA/01jBlpRVyPCv4jTf38RR4mabUlpWWy6bzyvKDm0MOpznDrGRnmNFteHzxTBeB4HCac2XfZYa//c4h1roGW14aXrw+4Fy/wY1BggX6cUDqaSZpidaGSVGiK3h585i39id0Qg8pLdvDDGMNIBgkJYfTgksrbhpzqelGtm8cJ7x3OGWUlpxfarDaanFzmPL2/pSfeKLPc6ddgHz55oDjpGSjGzHNKoZJCRJe3x7xwvkeN44TxllFK1S8cK5PWmhuHDv3+KVmwJfP9bAWLu9O5vKnaalZbUcf7D94gk4jJMkrWpG7R6W2WGt5+lSHn35ymW+/e8TBJGO1HfHTTy5zYbl52z0+TnI2B65ZG3iKL5zp8Ic/d5pxVtLwFUfA/rjgaOYGuo6nBRYIPEmca+LAJysMe5OM2JMYC5mxFFrTiQKKskLJgLd2J2hjWe/GHM0KZL1ohp5iZ5Ryrh+DtfzExWWK0vIvxlntvelkbmPPNQADzzV1LTAr3PWYpCVZZQiVohSasrJ4gUBaKK3BGJjlGmst0zSnGyle2x6Rl67UhhR0osA1Tsuylllwr+15kqRw/9dUJIXlYJZhKk2Saxq+wmDxlXQ0xsAHXKP42fXOPU2aH/Q7+VnCowjkm8CmtfY79b//Ni6Qf2bwMPSnOylwg6SgW4+or3Wi2wZOwFHkKg15VfLq1ghrDT6KKFBsHk+pdIOVVsD+pKAyhkmm8YXAk4KsMLy0OaAbB1TasDfK6DV8Lu+M6TUdRbAb++zXutPDacGFlSavb41oBIqk0OSlIcvB81wAyCpLlldoYymNQRtnAhAGHr3Y573jmRsKyTVPr7V5c2dEHKg5jzrTjnmhjWGYFry9N0EK2BqkSOGolVIIpABj4G/93k3+zE+epxv7rLWj+U5CSljvxvjKiUUJ4UoUTV+xNUg4v9wkKSp++sllrh5MAai0mdffl5s+e+MMay2+pxjVmdxJ0L51OvYEJ8Hi1c0hf/P3blBozdl+g0wbLu9N6cbH9JsB1sLZrmuQpqXBk4JZqcFCr+FTGsO7B45GaY0lLW19vSuUEEShRzNwVBZtLIEUNFoBVkCSueeU2rDUCDG4EoU2lrSsaIYBZ/uwPc7wEFgBWekeb/iKaVG5EohyE8IAjVAyLS1CWLLSIIBcg6qPLYB3DmbcHGQUlbv2FldKmeQus1fCKSEWWqMNUBqkrxDWHUNaQRQoJnmFNppZYVltR/yBZ1f5xtv7vHE4ZJxpOg0PJQVPrt59TP+zzhn/MHzsQG6t3RVC3BRCPGutvQz8IeCNj39qjw8eZsLxzg77NK/qptn7H9qTBuDeOEUiOZrl9WsoTnVjdgYpuYXQ95ikBZ6EnVFC5Cs8JfGlZKMbkRSa3aFTtIt8SSN0ComTomR/6sarZ0XKSsOVQLoNn7BUtGOfw3HOcZKTlYbAh8Bz9e2qqpgal4Uv1YuWxTJLS/KywhiYZE77enuYoq0bsFnvhISeZFa4bbexlp1hynY7xVOCtNJI666d8gAhiDyBNpqXbwyREg7bOWudiI1ezHq3xd9/aZOVVkgn8skr7YZYBOyNM5461Z5vr7uxX5enBiy1Qn7uqRWy0vDijWOGSYEoNE+davOLnzv1oQH8Tvzj13YpjcEiqKxjiQRS8vbehOfW2xjAk04UrJEqNgepm0LVhiTXNCN3LadZxVIz5HCWkxQWK5xkbagkS42Apu+x3oupjOVgnOEDvifBOhnZpWbAwbSg6St+sDnk3YMpx9OUXFt0qalwNW8lIQ4DZkWJ0YbQE1TGkFQlq80YrQ0WhfAFw6SgqMB3L8OJvLjWUOmTLF8ghEQqSOtZhFbk0Qx9pmlBrl2JzBoocAuBtbDSCek3fPqNiOVWgCcFm4MUa93j55YaYJ2C49GscPTaW3BnmXG1HXLzOOGbbx/wwvnefCbhzt+5W9D/cVoQHhVr5T8A/puasXIV+Hce0XEfCzwM/enODnsr9JhkJa3o/QbPwSRnZ+SGLKRwmeD14wMuLjfohh77UoA2tBo+aeFcyitjSbKKpVZAqS1R4JFrg1Kyns4TNEOPrUFKmhuyyk1ybg8zLq0acm144XyP/b0JOElrlJRI3DCSAMrKUhmDNRAFzvi3Mm5QRSkw9TDOO/sJ610nrHQwdouBmxSNaFeal4czBklJJwrYGiRYLJO0QgCf2wiZFRXWwix3wy651jyz3MbgMtelZsC33z3icFqQlYaNvmuChp4T1VJC8tKNYyZZOf9ytyOfn7q0Mr/unRh+4Zm1Oaf/QXDyxf/ee0fM0pKVTkQrdFovg1lOMtW04z6XVt2gSzdWTDIYzgqkcAF1kJZU1hJ5glJrGqHPV8/12RmnjFKnQ96O3KDOOC+wY1ip7+n2MCErKrwwoB16nOqE7IwyvnnlgLyWMl5q+kxzwyQra40ed09muUZKyXIzQEjJIM0JpGCWlzRDj/VmAymcMqG2rraeV07P/KQOaoBQCcrKEvgWTwgm2gV9JQWnOxF7wrFRxlmJwCKlROAWBIlBa8PhNEMKGKUF//LyPk+vtfGUQiDwfUmoDcezDzclOSkzpqXmG5f3eXKt7WYSjhO0sbftgu+1U4aPZyf4acMjCeTW2peBrz+KYz2OeBj6050d9n7DBbNzS825lOu1oykXl1toa/nOtSO0gXbkZD6XWwEbvQadSHE4K9C24uZxQlKWlFrQin1W2yFaW45nllOdiKVWgK8ku8MMYyxbw1md8Xr0YqcJPs5Krh3MiH1FJ/IYJgWxp9CVIS0qjAVP1KYBAhq+R64r8tIgRZ29GcFKK8JTgtd3Rnz5XI9O5NGJPN7dm9XZnmGQlHQjn6W2z5X9Gb2mx5MrTd7YHfP9GwOkEJzuhiglWW25TH5vnHI0K0iKite2RgSe4um1Fu8cTLmyO2ajH3PtYMbmIOGnLi5zMC54a2ebH9wc8Sde2PjAYnviPbo3zub35V5f4FuDQjP0mOTVXNNbSYmuo91qy9XUZ0XFe4cJvWZAP/bItSUpKpZin07DfV4qXbHaCjnVjVnphOwMM3bGKZOs4ivnexgN2+OUq/vOGMJXEitglBdUeHz3vQH9RoA2rnyRa0NSaCJP8fSpNnvjjHFWUlaWvNK4nqyiqCragc8kL6ikZakZsFYHx9D3MKZyRhFA7EmkgEK7+6yNRQoIPEVVWQLldlGdMKATeRgTsTNOXPO4NChhWW4EeJ5knDmZ3Td2xhxPC1qRR1ZWfOfaIUs1bbYV+qy23MDaKzeHtKP3VThPyoydSLE/yeZJUL8RMM6q+UzCyS74Xjvlk39/VDvBTxsWI/qPAA9Df7qzw77UCvhTXz3L8ayYezvujjJ2RynDxA1shApOtSPe3JlwcaXJOK24duiC0Fo7xJOwFAZsT3IOJhm+dFtwbZxWRyNwI+P7kwxtDXlp8DxJaTQrLZc5L3uS944TAiWJPFjvRgzTiqysSEuXUSnfIi1IJaisoRMHpEUGwpUSTnfdNCEIQiVZ78QcjDOeXG3SChSX96fklaEXhzy93nRThaHBGMvRrOBcr0EcKo6mOcZYGoELeAfTHGstndpNaJYbvnimg6cUZ3oN3tod8y/e2sOX7jWdV6ZitR0xSvIPaMucmEAI3EJXVOa+2ditQeGp1TZH04KsqDiYuKZzURnOL7UYZQX/v9+7Tit0AT/2PX7x+XV+990jfE8RKjGvV7eWYrSBvXGKNpZu7HO6EzLMKma54er+mFlpSPOK7VFC5PtYK8gLTV7mnCg/SikwVuArp2Y4LUryY0c7VJ4gUJLKQFq62YLKup0gForScO0w4WhasN6N3LCOtaSVwTP1mxfUw0YGbSAKJb4QaGFYbgYgBKUxrqErcEbdoYenJAf1hGgnkkyEYDzL6TUDNgcpkS/JKkOaa9qBz6lexDipuHaUcH6pcdu9SQrNuX6DVuh2uu8dzdxWYZrTjny6sf+BXfD9dso/TkNEi0D+gLhXPe1h6U8f1mHv1mJXkae4vDdmd+S2n73Y0bqeXG25L2mmGSQ5u6MUC+TacJRUtEKfp1ZbDJKSUVbRDBTPn+7Qa/i1MXCGtk5TY7UdkZSupqytYb0bUWhDqASd2CPyFHmZsdoKGCeObTEtNMZA6DtVQWsNKy2nijfJCwLluQzOV0S+IvQE33r7gE7sow34Hqw0A5qhj8GVZ2alwZdwYzCjrCwbXZfNZ6Vma5QRyALfAyHcxGKgXL15qeHz6uaIceZYFyvNgMhzk5Obw4RJ7tNvhPQaPlI4fRB4X1tma5DMGRxn+o3bsrETM+UPqiMeI5G0Io9zSzGBt8KrmyOuHkzpNwPOr9Za6AcJo3qB7jZ83t6bkJUuW+43nABVqARR4BEox8xQ0qfUhsNJTmkM/aZrTi+3IpLjGYfTnLy0lKGjSap62KnQpeOCIxHCLbaBklgrGSQ52oJfQWYqCu1KI7V6AFXiroXvuSx7f1K4Zmngoa1FWEBAUbmaehwqjJHYvCIKPHwl8JSPMSeaK5p3jqZ4QrDWCWjHAbHv8aWzPaZZRb8Z8sbOkFle4SsP3xNUlaXUBqRhP8nRAmZ5hbUGaNx2b/bHudvlRj7fvz7AWoGrAQre3Z/wB5499dAWhD9OQ0SLQP4AeBBWysehPw2Tgn/62i7DtGSalSw1QraHGYHnPCA7UcDlvQlfPtvjvaMZq52Q0lhGs4JJWqGUMwLoN31n2hs4v0gpJcO0ZJJpksIJbnXiwNViK7d1nqQljUBSVtAK3fj64bTg/HKTceasvGZ1SQAJTd8Da5nmhqK0PH/aDRdlVYXCGRpUxoBVTHOnzNdvemwep0gpCH3B0cyp3RXaMWBmhabfCLBY3jtK6DU8nllr8/LmiNGo4HQ3IvAkV/bH7I9zVtqhyyhxgQbjJFjdFKajsB1MM64eTVlrhZzpRx+QTz3ViTjTb9zGOb/VTPlWsw0BBMr1K0ptmeYu4P3ic2s8farF6W7M7107phEq3tlzE7dX9iesdSKsdQ1bISwGWG0GCOlUEiNf0o19Ql85Kz1jSDI3zr8/yYk8ibbC6bOIutmIojTOj1MJ0NoyzUuMZS4sFipX35aAUM6R3tzxmTtpresKfGf8RJobyqpgqR0ReoppViKEIPQEae5ecKMXs9oJGeUVk6R0x64Ms8JNj/pKMM40S03Xm7m40uS9wxnPnGry3mDKRi+k4fuEvmRrkIIFgWS5GaIQZEVV90GcG9Ll3fF8crYRKkZpyaXVJlvDhGsHCRdXm5zpRexPMnxP3LYLvt9O+cdpiGgRyB8AD8JKuV8H/F7GBd+6csDr2yMCJZzmRjNkvRMyySpGWUU39pkVFZuDhPcOE55db7PcDLG19+Jyw9VgdeWysllW0fA9jO+y2EbgpF0neYW1JWlZkWlDUWpGScneJKMZeKy2I64eTNnoxexPcsZZxXPrHd47nFJUhihUCCO4MXIj/OODMVcPJ87KrNSkhaZVeWwsNTia5YSBYm+SM6oDQjtyAcrigtL+OKfQhn4cstQMmBUaYw1podkeZzRChScdM8PUxPduFLAzTDndjVlph273UFWcW3JKf2mp68cjFxhKzXFSclHcvtgeT4vakGM6V22800y5ETgneixcWm3VE5yCXu38XlnoN0MOprnznzxOGSYVpa4YpBVHScmZXkiSOQ9OH81rWyM8JelEiiR3O4LDaU479mkHip1xxtEkJw499kdlzcO2WOuCc6m1m/CUUBjXWKTOxi0gLMxuaVJmpalt+j5o0XeC0rrHfQUnFJNu5GHqZrm10G8o2nHAaidke5iyN8koS42vFKUxSCEIlCvzlJXhaOrkAv7Ht/Yx2k2SrrZCwk7M1cMZe5OMSerkB3ylOL/UwFqLto7xMkiK+cRs6Cl8zzVNnZia4vMbPX7fpVXGWck0qyi0/kBp7H475R+nIaJFIH8A3K/Wdr+M/W6PX1pt8c/f3OWtnQmltSzFAXHgcTDOWO86RkQ3FmSVphm8L7r05s6E0BPMco3Whrym83kerDcjitJw/TjhtBLEzZB+M+Ld/RmjNOdAQ6Dc97XSzL04tXEGAFcPLQfTjG7k0/AdQ+SNbactEnoBWVFRltqZFFQWXSsHRj70mwGRp9geJoSeR1E46mJRSVqhYJKVBJ5yVEEraAYeLSEotXMn0tq5zCslmeaaWaYZzgoKrWlEHnmpSYxjQkS+JC00vdjH9zwqbZ1fKZJxVlEaV+ePfEnsvy/yOUwKdkcZ//T1HVaaAavtiM3jKYezgjP9Br2GX2uPOx2bE8XEduTz7HrHqS5mJUoJ/vDnTnH9aMbf/L0bvLkzpqgcJTEpKxRut7AzzGkGisCXHKfO3m256ZOXGoRA4sol5/tNKmOxOArgJCuZlZoG4EuBFk4/R1t33wLpmn66HrM3xjFN4rruXJ6k4PXv3G8Cz/J+Fn88dYyXRuBxph9z/XBG4LtyyPE0d0827rg+YKzFGIuSjtHSCBQHk5yDac5Gp8EXzrQZpQVCSCrr1B7BWRXujJx2+hvbIza6zuEoqyreO5pyYakBCPJK8+x6GyXdZ/5WyYXTxCRFReDJe7hSPZzJyeOIRSC/Ax+WOd+v1na/jP3DHnd2YLvcOEpYaQXkGjaPE1bbAYkQ7IwyvnS2x/44Iy01n9/oMssrPC9z/5eStbbP9siwPU5ZaQRcWm2yNy7oNVzWejjJ2Z8WRMplzNq4IRuhBKVxNWJfUgsfuXr5zijjYCr42SdXWW2HHE5dbdJXrsm2M0qRysmZGtz2XlgoSpctCVGiK4OOLQ3f53w3ptSOBz3JCqLA43Q3ZnU5YpQWHM8Kd6zKYD1VB1DwA49RVjItSgIlwLrFpqycwUYceLTDgKSsKHTF0TSfqz7+5BNLNAJFVhnaoc8Xz/So6oXqpRsDbg5m9Bo+148Tvn9jwHPrHb6w0eXmccpvvLnH59Y79BsBeWXYGWacW44B6mDusz/OuH485e+/tEkUqPlrZWWF1u877SgBU+149vnMmSo/1++w3A7ZGqbkpcvQQ9+N5rdCn/VehKfc8FXkKZJaB6W6IxJboBEo8kqgfKiModTM2SYnGfjDOF/W8dkxYEonKZAVhrQ0zMoCUcsia2sIfOXq3Aaqwr2eq5MIplmJtoJ2pFhq+Sy3Yuw0Ayx7owprBef6MZ04YLkVMMwq0kIzzTWfO92hHXm8fHPAKzdHrHVDVpoR7+y7CVenJOka2Sclkf1JRjf2+cbl/U+ED/5p4KMvAvktuFfmfDId+GH1tPtl7Lc+PslKtocpb+6MnOAQrpnXjRQsNZjWdem9cUpSaJSU/KHPrbDRa/D9G8ecyxsYM2MwK5C13OeFpZjn1rtc2Z8AdQZnYW+So40bmbYWpBA0AqfXPMtLtHZ6KkJYWoHCGkc1bEWeK7ukJVuDlPV2xKx0DavLe2OwbvJPwrz2WuEyUCVBKkmWa7qRM6jIK402hlYQYIHBNGcwK4gDRVHWI+CF408XpWFWQDu2xJ4klRKlHCOj1wiYZiUNvy55AO3QQ+P0y2dFxdl+g9Bz9+hUO+KF833nABTKuZ3c9cOZ45aHPkmhefdwhq8kN4cpRmteN5av1r+31PTJS0NSVLV2S+40VgJnhbc5yFBSEnmSvHC9Cilc1mxqWmbDdw3FNNe8czhlkBS0I4+yFskCj6R0AmRL1k2wXt2fMEhyRqnBw31RT9TgT/TLI09RVrW6oXE/U8I1NB13qC6ZyPd/di8I3O+D6wXM8opCGwLP/X5RWSeXKyWFdp+pSjttFAMYDc3Q7bCMMfjKpzKgsSy3nOjYpTWf/UlGWTsSfelsnze2R6im4Ey/wRMrTQYzZw2HEKy1Ql7ePCbXlvO9Bqf7Ub170M62ri4bhZ76UP2gHzY+LaYWi0B+C+6WWR/PinvW0+6WsQtxuw72Witia+gmMLV2GdUk1xzNclaaEe1QkeSSylQ8tdpmpRWwO8p4Y2dMO3JBxxjDcFayNcpZavicaoeMkopvvXuIEK62+d3rUyZZUXO7DUlh5xla7LtzK0pnwIsFoSHwBNoqpHAc76NZzv4kY5xrF4grww09Q0lBWlgUuAbcLZliYdxWu+FJ8rJib1wwTSuUJ3l+vUvgC97emzJISyJfUmpDszaC8KWkGwcopclqZT03Pu94zHmlOdWJajcjx2tfbvl0ooBprvlXvtgn9j12RylJURH5imaoUFLcZk13PMvpNAJGWcnbBxMkoI1zCRJC8PnTHY6mBW/ujHlmvc1PXlxmmJZzA47Dac4XzvS4OUjQ1ikwlsZQWRDSce21FVSyVgUUuEzdQBS593xjkLDeiTHWzq9Dkrkm3+4oZ5g4it4o00Sq4GToV+GCuJTQCF3PoxE6k4uToRtbB9V6wn+OoC5n5Ob9Movi9ow9VG6wx+nOQKYNSalphz6Bet/ZaJy5ec1+7Ne1cHcsT0FauGvhS7fQRL7TJ5fCcjxzA0/aWOLA0R/HmXOeOpoW3BymDJKcjZ5jrGwPM17edDMDgRLsjXNWOyGNWjTsK+f7vHRj4ByNau/WaS25rKTg99+itPjDwkfxrf1hYBHIb8FHFaj/sO74/iSbZwonOtiXdydcWIoBD6UEK+2IlTZcO5yiMUxnmlHiHHJk0w2IlNawc5ghheDm8Ywr+1MqbVlqOJrYW3tjlpohrVCxOcy4eZQCTsa0qNkNJ1ttJZ2XIrjx7fn228LuKCP0Be3IJw48hrkGY6m0+6pr3G5CG7cASN4f374Vxrix7civ9VQSl7ofTFN+5qlVZpnmPa2xxh0kKzVx6HGmG6OUQCYFp9o+OyMXcOPQOEf31A3gKAHPn+mipOTzpzu0I5+Dac6ptjPaUFLwzKn2fNgn8ORt1nRv7Y7pxwEvXR+gBCghyUrXdLu00nKTpkKQTQxFZejFAeeXG/OhlFc3h0jhFsPdkZMX8JQkkBIv8tHWMh1XBEpQOUoGUgpagaSsXKZqrOV46hqaWEHkO2bQs80O7x1MaYSK1XbM0bRkkhbzYHvibWQtxL5HN3KGEUmhGafVXAgtcIO/VEDDd01Ix3V//4YJbg/ivnTWc5WxyPpzUVYGa90wUNNzNXJjndJhoNzfBYLAc7TUrDT4nsUzbo7hOCk4oxuMkoxR3diMfXcdBon7LDlFSydTcarWKn/xxoAvn+1ytt9gMCsQOLZTtxHSb4Qcz3K8euuwPUw5nGS8vTehGwec7sVIAS/fGHzoyP6jxqfF1GJh9XYLhIBXtoa8eH0wpz3dmlmfWJedDCkM65t10h3PK813rx/z+vaQg0lG7LuVuhMHfOlsHwHsjnJ8Jfipi8vI2jex3wgwdaYzzkuSeghmnJUoIYh9ycubA64fzkjSal43HSSF42NnmpvHKZNMM84qhqlmWlpy7TLmk1rpiXaGG5eGyHNfeomjrTUDD1XrXbd8ySwrmZVOS3xcM0IagYcv775NlwJCT5JXmqS0FHVzbm+c891rxygFnzvdqXU3Ajcxihv3NxZGSclbu1Py0mlVr7cjrKHO0ktOdyJ8JVlrh5xfavLseofVVkheORnWVuiytaVmyGo7YpyWXDuc3WYntzfO6EQ+7dgnKQxSSk61Q2Z5wWs74/q6avYnKb/51h5pUc3v/6lOxCyvuLo/ZXvoJid3hjmhLwl9p2WjhERKiaeEC6yewgLN0CMMFYEn54urkK6mLqVknJWYmoGi6nRaCclJYq2p75+BaVqyP87q1xMo6XZVnnTHVKrOyrHMCkOpLaW9PRs/Oa6oP/uVcaU+W+usgJMYFlDLCDsjCiEsjdBzzdXAvc+s0HQij1bg6JS+lCzHIdePp063vd4telK6ngCOVrk7SikNXFppoaTg+tGMstK18bXlqbUWZ3oxK62YXhwQepLjpJybjF89mPG994aMkor9Sc7bexPS0sw9b3/YONmN34pPgo++COQ1honTA59mJYFy9d4fbA7Zr70uG4E33769uTNma5DyyubwtmNoY/nCRpevX1im1HD9yH2IwTXKvnimy2on4tn1Dqd7MWd6MZd3x7yyOQJh+bmnV8kKJ/MJlu1RyrevHnF5d8KNwwTfk6x0QgLltuNVzVYZpjmTrELWjUfLXVgK9v2GVhy4r7HvSzzlvvxSShqeorKw0g7ptwICKZnmFcbWqniVqbm/7+Pk7x4uACSFcep5wgUTW1/frUHC9cMZu8MUgNWO20kczuqmZ6VZbkcY63wxlXTOQsPU+Xe2AsVyO0TVqoBv7IxJiorT3Yhh6rwpT3cj9scZr20NWWmFc7Pnv/Y713hlc8hPXVwiKZz36alWxNcv9Flthfie4L2jlF7kYw1sjTIOpyXWwt/+/ibG1HXuUvP9m0NeuTnkcJI69x4sceDYJtY6lxxrcYM11HVk4/S3m7WwWVZW7I4zDqcZw6TEGMPuMEUJQVEa3juakmtDVhm895URqKwL0kiJJwX7k5TjWUlaubp2oR37BOHs/ZyImit7nUDWB5Pi/X/LeuHQ2tW6VT16H/qK0JNM0pLrhzMOJzlFqZlmFYNZSVo66mGpHdXR8yRLrZD1fsxGP8KTkudOtXlqrY2UYq6cOC40gZIIIcC6HddhvUt54VyPaabZHqZ4UnA4y7l6NGEwy3l9Z0RRaS6uNHllc0hlDGlZEQUKIeBgnHPtYMrF5eZD+X5+VFxcac69Ya21H/CJ/VFhUVqpce1wxmo7YqkZ1vziinbo0Y39eVPn7b0Jka/oRD5ZWd22fbuzVrbcdI25ExcbgKVmyChzmdTmYMbr22PGWcnXn+iz0op4fXtM6Ev2xjlXj5wxhJAWaQXtOOA4KejFAWf7DY6mOdpakkJTVgZRj2nfk2Ym3PCHNhAqxbSqUNLVoU+aZpEnGCUVZzoRa+0IbMZglmMMlMbQjDysNdiqDipA6AmEgjy380VEApGjxGCFY1IMkoJjZwdKO1RMs4qDaQ7W0gjiejEStAKPQeKoirrePfjSBaWdcY4UEE9yOg2ftXZIK/L4/IYzj6iMndex40Bxedfds0bg8dtXjmiGinP9BmXHsj/J6MQ+P/f0Ct9+9xBtDKudBgJBPtXEgZuYPJxkvLU7rrf4zgwh8J2S47kln17f53hWECrJ3qQgq1zj1lM+aeF8Tq21VEZjrWCcVpT1jdIGQl+TFa6o7QalHJc6LXSdKbvrLOtsXQD9yGdSlHOxMV+4EtktU/VkudNH8ZT7optb/thbsnNZSyxUmvnz45ruCoJcG8qspLLO2FlXUJqSyHNUR2Mg9CAKJEU9MRxIwe44w5OCOPI4XcslH6UlnnTj/uPMfXZLT3IwdbsLYzOEgF4zZLUV8t7RDKVc09Nal2Cttd2w0Dv7E061I7I1zdGsoNLQDN0wnKckjfCHn6c+7FT3DwuLQF7jpNYlhJgHXlsPJnRin9e3RkS+mvsNCiHn27evnA+4sjfhxnHCMCnpN3wurbiR+rmLzeGM41nBRi/mjZ0Rm4OEUluywnBlb0roK5LcUbCOp86iLfAEHtJJplrLOKncsIjvpvtmuRvswUKv1nq+VyA/Kako4cbVZT0ZKAREvqId+IzSEm1hZ5zRiQOOZgW9elGyBrJaZa/QGh+3nQeotHP1qepdZh3D547yEjd4IqFmQVh2Ril5ZTjVjZASxmlFVrop1LTQLDV9Yk8wMIbJtORMv0noCQ6mOTuZ5qtP9HmizohurYd+4/I+/UYwX3i1teyOnYXchZZzVSp1xec3umyPUq4ezDicORGnw2nhAmUjIA4UO5Occ/0Gx0lBqBSFFnhKcbbfYHPghLx8JdzYv4Snas/TqDZyOBSCUBlOdUKOZgX7k+y2e2SArAQltFu0JHQCj1RbBqUbRvLUSRPVad1YC9PSDVlp466nkyIwVI6eTlG54CylYxhV3I5bzyH0XA2dumEb+hIpoSgtwoOlOMRYy+FE0w7d9XSlLOOs54ShHbtxfcdGgXp95nQ/ZpiULDcDksrp2+fCoK2ptXac8cUsr+YSCqttyzOnWzQCyele7My3a9vAjV48N504aeGfW3K+rqGnMNZRFO82pfnDoAp+Gvjoi9JKjXvVui6uNDmeFbVusiUrHfXpZPt2/cg51UzT0nHCS8t33zsm8hS+Erx4/RgEfO1Cn6x0IkvaugEaTwl2Jxm/+eY+V/bHHExyCm0JPOcUL4TA8xSl1swKN7ExSEsmqctYV1shnnJZm68UzVuyEHXLe5FQ61JLug0P33OWYS54WDwJx2nGrND0Gj6+EuyMEipjKSpNVdPFepE/n7JDuOap84h0EqftyIlulabmNNs626uzRSXB85y1V2nc6+alxhhBUbkdxiyvWOu4uvcgKTHWEvqKceLq3dNaCvZolnPzOOHtvamTOKh7Fp3Y52CS89bumKsHU17dHNaNS5/IVwSe4omVFlf2JrQjj8+dbtOLA061I5qBq/068+mSotD87JPLpHlJUpTM8gphLYeznDO9GE8I8sowzSuywtCOfNY7kTtGaehHPl+90GepHTLOq3nGe3JP4P0JzKTQZIXG96RzEvJdeUlaVzYBF5iFqCWF60WyrNzPZF0fNzVrpOFLd5PuaGjc+qV3dXq3GAe+a9R5StHwfJqBhzGCWeWYJkZAYdznQJ1Mk9ZDas3Q0SaVgrSWO750qsW5pQZSwLsHs7rh7HatCqeUeaobsdwMyLWhqr9bn9/ocqb/vqzul870+NqFPs+uu+Z27LtBrafXWnUfCS4sN9HW7cYuLDc+lP53QhW8W6/rccYiI69xL12GXiP4gN3YheX2nJ/87XePuLDsOuyVtjQjR5F7e3/MLz53ak6P2h6mvLU7Zpa7YDVJS4rKMElLZllJaU62uRKL+8Kc1DHTUuNLRSAkfujcZBqhIvIk/dhNzikpOZhkrlaNG7nWJ9S1euqvHfpEvsQvTE1dE4zSClsPDHlKUtWTlo3AY6MTsj8tUMrVSkvtsuXAcxngSWYXex6n2gFSCopKM0oqSq3J6qbryfMKA2Wm8RV40g2UHM9KhrMBUjrRJykFfq1tkuJ6AZ6yTCtDUrrG3mo7ZGuQ8cb2qHYYSmiGip97ehVPCn7jjR32JjnWGIapJvQEP/vUKnnt3F5UmvVexM88ucrl3TFPrTXZGWa0QjhMYJJWVAZ+8bk1nlprczDNOJoUzjDBwlIjJA4UvaZPp6ZQjtKKtHSiV1k9udkOJSutWmbVV8h6EjaQ1OPsjgV00nD0lWJzmICQc/5/ecILr6+jL0AIA8ISei77NsbSCH3Hy8exSASghcGXruF5kqYYwBPv18qNdtz3vIQEjZdr8lDXAlyuTJIWZu5mlKHn5+zV1nOqrmVbI4iUdCqTaUXsSSprOdtrcLYfo40l9CTfuXZMpQ3rnZi80jRCj1lW1nTUkuNZjhBOaO1uw3hOCbR0OjXacKYX8/mNDj/39OqHZtmfFqrgDwOLQF7jfrWuL53tOfnRwPtAoP/tKwec7rpJtcOJm7zsxL4bjb6jvr7cDDmcjNgbZ0ghnSuPpyg8zWhWOEqZLx1N0Fq6jYCjaY6SkmaoagMBOeeiy0BythfjeYLIc+JL3YYL9Gmh8XBB3PcE3UaAr4TjBsduTNwCgZRoo1HCqTDm2vHYlBRMC4PyJKu+ZFpqWn5AVuUESjDJnJTtNC/QWrM/y3l2pY1o+JRVxuGswlMgjQvgJ/Vzi9vu5/r9DX5UMyVybWkFHsMkB1wJCwmz3BAGjh7pBJ0MobK8eGPg9EaA946mvHxzgNbQiQKGSclBUqCNq/m+tTvGU4IXzvV5dWtE6Eku7455+eZgbp82zjQrrYBe7Xjzk3VzdKMbc7ob0/A9/vmbOyjpBJwEAg18+Zzbbe2OMyaZphEodFZy/SilqCxfvbDEk2struxNmeR63jw9Ca4Ct4gLCVlmkUJTam6jHooT3r5wu59pbvGUoBm5BcHgmsS9RjDve+SVriduXSNcCbfAx6FCV86TUws7V0c8oaROcoMvDL4S7I4q6p7kh4hvWaSQSGCSVa5RHTptlEGSkxUVaW2wHAc+o8SVF7+40eXq0ZTD2tEoKZxFYT+OqKzLnl8418f3xLzk8mEJ1s89vfrApZJPC1Xwh4FFIL8F99dl+PBAv9qOmGQl3UZIc7kFwCjJiQPvA/X11U7Elb0pRWVZaXu1foSTBm2VFq0t653ISZdWbqLQWEHsSXqxz6wwjpnigdZOZ+Pa8YyVZsjTp1rkZcUs16y2nMZLqS2z0gVpYyyHSUEYeDxzqk3kK7577YijievuKwmDWU5l3La81IbSGBq+otCGQhumWeqybAGBL+eWZ8JaPCsYZiVSwKluiMWQVoaicE5CdxsXP8lGg3rnUlmLMM6mTGAIpMQoS8PzWG4GaOBwWlB4gmlZESuFkIKbRynDtOKZtRZFZTi71ODiapvNQcLBOCP0oBmoWhNEkxSurtoMPK4fzbAWzvQies2QJC+5sNygMpZGKPm5p1cBl71t9BtM0orTvZi1dshGL3aTvwL+4HOneOXmiG9fPWS1FfHcepsbxxmvbg5RgtrQ+n32ELhBnLDWoHG1cFcqu7WOrQF1S4N0mps6uFry0pXivnSmx/mlmK1Bys1Byt44o9IGIYRr3MItjCCJ8qQL5NYtIidTndhbRLhwg00nzdmTQA8uo499hRKQ1l6fgZJ1n8PtGCbWKSReO0zoxD5nerHbKVlD01cMZiWdyKffCJhkmlxXnK6nOqV0CdTJdb/1eweOEnwSwL987v6c8YcxgHncsKiRPwROgvkvPLt2Ww3up59cZpSWjJIcYwyjJGeUlpxbinnpxjH/6NVtfu/aMfsTRy97cq1JHDhN6W7k0W8GiDqItCKP0JP0ms7TUAjJ+aWY5053kEJirGE/ccpx06wizata4sLyzsGMC8stVtohvlIsN6PaasviqzoYVwZrDFd2p87MGQh8gV9P9RnjgsiscLQu50BjGcxKkqwiUAq/rslLnMlzqCSeUoS+Ypo7loY2lk4c4EvpZFfvcV0t1INL1k0HZhXT3FmONWqDhkaoyLVhb5zT8pUrtWRuSz0uKsZZyTir2B9mNR3OMM3cWP1Tqy0urjZ5eq3F/iTnvcMZWeWMEJLC7UqwzuG+E/tzka04UDyx0mSSlfyd72/yd79/k51RyqXVFs1Q0Yk9p7IoBb2GjycFVw+nvLE9ohlKltshz5zu8cRyq3Z+SljrRvSbLnCcTET6dYMx8ATTQtMI5FzY7FbcWhqZKxb6AimkmwGQjt1kwKkXWkNWWseVx5WyWpHTaM9LzfE0w1Mu0/bq+x94Tv8+kK5sYgCp3u+3yPqPhzNtrowl14ZQSdqx201W9VBYVTr6JEBZl9te3XTTtbPMFWdOtQNHkVSS8/0GzVDx8s0hvdjn0mqLa4czfnBzCMCXz/Vus2l72Fr3p4Uq+MPAIpA/AlxYbvKnvnqWOPDYGaXEgcdPXFziu9eOkQi+sNGhqCp+990jRmnB73tyhV945hSr7YhppvHrLGZWVFxYarLcCgmV4BefW+PzG22eOV1T66yhMk5fRCnBUivECjdFt9aJOb/UwFj4qYvLtCKP4zRH1Y0obazz4JSucRb5kqDWxdbaIiX0Y/elOmlkhcrDGMtxWpAUhqJiPkGolMvuikq7L7YSLLdck7QRKFqRRyNwzd67mKHPIe741/tDMZJCW/LS1JmzotsI3E6h7p46GQJb/zFzxovvSYZZicWxexqBsz/rN0OeWGmy3Ax4YrnB9jBlkBRcWHGONDeOExDwxTNdxqnmb3znOi9eHxB7EmvgN9/a462dCc+ud0iKiv/hlW2+994RUrrBmaNpztu7I64dJry5PeL1zRH709SVtAon+HUixhgoZ2RcaPc+PCUJlKDhu0XxftooutY/EdKSaSfA9Ztv7RH7HtNCs9Ft0Gl4+Mrd86VmWEsCaDwlWavNkJVyfRkXxN3dMDhuuakXbFmf80lt3OAmP8vSLfjGGlqB78p9uN6Otk4RsRn4FJUgLSqmWUVWe7weJXltVO0Git7aG/Hq5oj3jmacW3K7nA8L1rfWuoUQ87+fDACdNDW/cXn/Qwf3TuQWTvxaH1fp2luxKK3cAw9KVRombqBlvRvxzHqbiytN/ulru3Rjn24jxPMUFqfTPM0rlBRcWmvSiT2+deWAXqyAiLzUZFpjK+HG5FOnKbLSDJjlJcezgmbg1Xz0iuVmSFG5BeB0N6YyhveOZiRFxXrHie0PZyXW2tqEwCBw2erhtEApRxsUgLCCcV5igMgXtX9oydH+7SPilQVTc9l0ZRASerHPM+ttvnJuic1BQl5W3Bgkjq5XWXzPMSvuFpgsUFgoclPLGtQ6HZ6iwjF8qsKVEry8xFrPTUcaW4+luwEhay2BL7l6OOPJ1RaTpODm8czp3HQivn31kIurTbSxtCPnyvPUWpurBxOUlBxNM5aaAWd6DZQQzPKE3XGGNTUvu9T045BKW/bGGX497NIMPY6nBVf2J9w4SlCeG04ZZxUvbw4422sQKklWVOwM3dUMPUfVzIXzvexGnitLSTdyX1TmNqEsuL2sIerHjHbMkVJrCmHIS81wlmOsm7hUQhCHkqqEtNZ7D5Wjt1QGtHFywnktgmWMJajvlxUWIetavrn9fp3solzT2k2unuqEzuTCWIrKeTCFyj2GNGhtnV5+rvGU233EgWKWVhwnuVtMlMIYy9/63iZ/8Nk1VlpOeuGkHPLK5pAr+1MkbshuoxfPmSyDpLiviNWngSr4w8AikN8FD6pqdrfn3TiecWnF1cubgceFlRb7o5StYUrgSX7+6VVe2RyyO8rJtebcknQ2bbOCg2leb4sd3/ZoWjgPTguV0WwNde0E47KrUsPmIOHagQvipbG8sz8h9BXWuixV1/oYzdCjrAyj1KkPhr5wTJvQJ6knOKvqJGA4euDJl3juKnPLdfLq8fnLO2P2xintwDV5A08R+7VK3v1Sy1vgmnGSMHBfaF051xkt3Lj7qV4MuIGPg4mrAVe1IbA2IIxld5hSak235sGf7oQst0J8JZEI/vlbezQDj1lR0Yt8BonL3PfGKf1mwO+8c8CZXoNBUmG0xQrYHKS8sz+lEznq5ubA48vnevQbAXuTjO1BynevHxFIxbl+zFt7TokyRrqMXDophlHh3Jl0XXcW1i2ck7wizTWd2Ck7mrqpKW8Z8rm1Nn3yb1VPaGoLfr0DOk5KQuVq4EWhySpbl8NMvfBZmrX87rSoMFqQz6qawipZagRuUa957dNUz6eGT+69J6AZeVxYihmljlZ5MM3dbk66spRzJrIMZi77hZoTrwWTzM0SXNuf1YtAhBDOsHmtE5AWzmXp0mpr/tmotOHlG0OWWgGyTkgu7455dr2DkoJO7D80M+XTIEH7KLAordwFH7Z9Mwb+6Wu7t23Z7rbNs4i5RdX1oyk3jhJmpebzZzrzxcBa+P3PrHBhqcGF5SahJxmkJdujlKSwzoCgME6FMC1p+ophVlEZSxRIlJKM6kGKb76zzzSvjRtKzdE0p9JOHlbU3OVZUTFISgqtKbRrpGrjMt5pWpCUBl2ngLLmI5f3CMInJZGkcIMgk6Rkd5IhpWW9EzIr9Dybu1csF0DsuaafV9eG08Jt4qO6DtEKPM72Yy4st/ClYKMTstx0+h+eEISedHRNKQh8yXIrchOA1lIZwaWVFhLJ928csz1wmXbkKX776iFbw5Rppuk3A6eLYgSvbA4ZpwVHScnhNKc6EbuaOW/LtKjYGaVsDxMOJzmzwulsC2GZ5E5LvKgso7wEnBdqaUwtAVxbteG+gLPcMkpKKmMZpyWekMShnE9q3lp6OpnwPIG2UNTR1fG5PSRuArIoNCcEUWMhKTSdho+QkihwzjutQFFoS+x7rHVi/sjn1/nCuS4rLWenJ2t+euhL/PoeBd7JJKhmf5LjK8nTp1rMssI5QYVOx2a5EbqSl3WUQwtkdePbl4J27NFrBCRF5ZyMsLQjhdZ27oh123fyaMZSM+DSSqseNHP3/erBdF7rPjECuRUnvPM78ePEK19k5HfBnVSlSVZy/XhGqQ2fO92ZZ94n7t63IvYVF1cavLs/ZZxV9GJnVjxOC55ZazFMirkaX1EZzvQb/N61I16+OUAIyXPrbfIKtkcZUrovaFlp+s2QaVERewKso2V1QvdFUFpirBPe0tYSBR6H0xyw5JWdC2YJYFbWDSsBYSixhcUIg3TfJRC15sZ9rpGlHkQR4HmSWanpeR7TTFO2rNNbN8YJOVk+YI5wUjoIFYSBIlKuWVppg5SCZhBQaIuxuqY7at7cGTnzYj/g6VMt3twe0Yt9As+JfJXWccyLyjDK3JTsrKj4x6/usD/OqbSh3woYTguOJzlKCFaaIac6EanW5EVFkrsBqMATZKXzFr12MKMsNdN64rQRelSV4fLehBfO9d2uQDpWyihzmXwn9ubOOePUyavGnkIKVy8X1s77B5VxkgbaGrQ2UGvVKMltrBFTX/iTpuPJPYprXr4xrryUFgYPgdauVHLCQpmmlXO8nxWcarvMt9SG88uu1Of6EdJJ3BqD1qIuvVl85cpZ7r268ps2lnFeMskqQt8n8lw5RwvB7jBFSjeR2Qo8jC2JwtAxXZTAaNdgXm1FdBseSroBpl7T7Q4nWVXXyTXHddL0B59dqw0+2k5KI7MYzLwx+u7BhEApLq225n6sd2Om/DjxyheB/C64k6q0PUyRwHIznGfe8L67952UpqfWXO30BzeGHEwzsNBvhFw9nPHr377Ozz61wlIz4NXNIZuDBE8JLi632BymxIFPK4Srh1Oy0rkBrXcifE8RKBcwW1Ky0vB5fqPHt97Zpyt9R/HTJ/6OTsfiZOpTSadKiHWa4UVhyCqL8py5bmEgip3HpTCQ3uf63Dkd6MoyMMoL0lISjTwq4wKVMa45Ku37Lu7iluN4dbCSnqAT+SSlU31qhh6BsRyOK7aHKb4vHfc+9hASzvYbXFptM8lLxmlJhUAJy9E0J/IVceAWBq0NhzOn4RH6iqK0ZJVmqRHSjH2S3Fm3pUnF1tAxOfw6g7y40mJrMGN/VtIJFRuNgIbvUVSGw1nB0TRnlBROWz1QTNLKqUNay/44JfQUvYZHWhhakc84q2hKUZsm67rZd3JNLIGSGGHIKld/llKihcWrFc9OAv9JWeVWzZSicuyUZhAQKo2QAlVnuko4HZ7KGgQWbQyz3JVdzi01+Or5Xq1XYslKw9GsZJyV86GhylpiKTFS0PQUuhb0EjilxmuHKZEvGaUV4yxHSWdDFypFv+HjK8WS57RrrHVBMwoUS42AwcwF6Y1uxHI7JC8Nndjn+Y0OL9085nS3wVIjQKwIrh1OaUf+3K0pKZxxydWDKY3A49lTHV7ZGvHK5oAvnunhKXnXcf0fJ175orRyF9xJVTqaOQPgjV48f06lDQfTnO9cPeIHNweM04L9ccarWyO2hym7o5Rn19t0IscG2R1lJLlme5BwPC14ZXPI9aMZ28OMy3sTSu2+ZLujhLd2xsS1LKnBsjVMmWXOWSb0vLrZ5IKWYzzANC/JKkPoy3nJpNCudmw084ZgN/bxPPc7xji97zQ3JLkzyQ0jdfcLU8NSB+C6blrUxs9J5lgMe9OMrUFC6AkasayplI6pIRW0I0UjlLRCJ/laac1xkjNJS3wl6MY+03pMvnTUCSdXIB0z5L1DZyDxwrkuT6222ejGBEowTp3OdewpdoYpoa9oxQHjpKLXCOYj7hdXWzyx2qDhK5QQXN6dcDR1gVlry3LTTW4OkgIpBJ1Qsd5p8NULS6x1narf86c7nOnHHCUlx9Occ/0mT59q0Y6cGXYzCDjbj7E4nZQnVlq0Isc4ktLpeMeey3ixIJXzBvU8xzTRtbqVkxxWICWBB+3YNRBL63ZVCkhKN5CTaJfpa2PpxgFPLLnrYq3T1JG4xcEXAk8Jnlx1bJ2qHqI6u9TgxtGMvKrcc+v8xDVa3fLrS0Gr4dNtBCgpscb1XNwWzaKN0zUP6uZl7PtklZtlCJSk3/A51Qm5tNIk8hV/8itn+eoTTsYgrwznlmL+yOdP04l8TncbfPFMd66VvjXMeG17eBt9EJhn1p044Mtne7Qin7f2JvdkpnxaJGgfBR5ZRi6EUMD3gC1r7R97VMf9pHDnAFAv9llphfPt2iQreXVrSK/hc3G5ybWjGd9695Cmr/jc6W49Qp7wD36wzdnaIVwpwSApWGuHbA0TZoVzkn96reUCiLE8s97mW+8eMU0LTndi4tCj1JajacbeOKPfCunFHrPSMEwK4lDx+Y1u3bEvEVCXJ1yDKyvd9ltbMKXb/ud1JuWMyRw1Tdbqd54EjMAD7qwqenU25Su3QHi1jIepWR1zCV0LRVG5EX7rtuWelBjrasMCJ7blS8cN13W9wAUAQ5pDK3Db7uNpwSw3xKGbNC0qV6roxR7HSYE9Ejyx1GCcuQWgsk7FcVRTOtc6EU+uthhnBaKuoTcCRS/2Gc4Kt1MJPN7ZHuJLRcNXtEO/NlgOCJRkat34e6ldqWZr6CiKR7OAn31ylWFaApam7zLOSVpxabXJ2V7saJTSaYZMspKNbkwn8nj3cOr0xI1lllVEgcSXgspaQk+gpCIrnINSUWmyely/GfkYa2+TLD6xeFMSAuWonzpzC56q/U6lxJlYhB6R59x+Rnnl7r0QlMaw3grRymn5BJ6iEdTerNKZOysBpzpOtKrQlkBapnmFsBJPGpKywhhLO3Zm2HFt2Fwa1ytphh6B55GVFUopAqU41YnpxB5/8oUzhJ66bWd77WhKVE/fRr5ivRMRKHj3YMqZXmMuDfCdq0cI4XZwqy03oPWlMz0GSTHnnX8Y7iXL8bjhUZZW/jzwJtB5hMf8RHErVemkMXLi3fja9pCtYcbprjNKPmGoYGGt4yhTkf++GpsxjmtdaIunJDeOEwJP8tLNAb9z9YjYd8MorcojVhIvDhBScHG5yf4kZ5Y5ZcNLy008JdgepmSloRMG/MQTSwyTks3jhElWEkqFDJxV10kedesXfpqXtQqh6/wb6+Q/T5zdLU7JMBbvb9t96dgtFY6R0BTOwDkKHD/YuKl+Yglx4FNpNz6ujcGTgmnuIrhzeld04xAENAy0Yo9JLYR1YmIxLSoaVlFWThbVaCiFq9OGnmCYlOj9hIurTsAp8hWnuw2y0mWHuqYlVtrQDBWXVvuEnqy/rK4BPMrcVOHBOKUfBWTaEIcelbUU2rAzSDi35LLotXbIweT9IH66E7PRa7AzTslLw/XDGdO84otnemz0Go5pYw2elDQCZ3k2SUtWmj6VhSR3PQ9fCEZBOTeASAvtpmqNoN8ICJRgZJ3rTq/hY3G9kdCra+d1X+OE7dMOPed12Q5qLe+SYVHg1dOjvhIEniLJ3WvFvsdS0wdjeWV7wkY3QgKNwCc3BmkdO6qqnClz5At2Rjmt0KdV9wkO84KGr9yiLZ0FnGPICFQ9VyCF4HQv5oVzfZK84p3DGXvjlLVOyKXVFt3Y/0BQVVKSV06I7ER1tBkGfP5Mj3bk/AGcI5XGGEtWa5xPsorzSw2WWveuc39aJGgfBR5JIBdCnAX+NeAvA/+7R3HMTxtuvek3BwnXDqY8udpiqRkxSHLe3Bkxytyk5kmjxVjBM6dabA1zfE849/ClJllpGE5zrh1NiQMPY5yy4s4gnUfOE/fwZ051yKsho8jVnEPfI/Il3Vhzqi25tNqiMpb1bsTPPrXK23sTRmnJ7ihF17Zdop7Ss0I4kwLphI00FiEkvnKlFBU615bQc2JJZeVmySvjZFQDX7IUerQiD2Fhf5LTjX1akarLI071Liud2YKQzv1HWyd05SlXIjBAWrqmZqAUDePq2XnpTOTi0OnIFBp8Tzm1KOHqzlprKiHR1qIxbA8TZkWF1o7dvNwMqLQh8iVGMFcnrIxhoxWzP8m5sNxkoxfzzv6EV246E+xWrDgTNRyTxxqwTrSs2/CZpAWr7cgZIUjXR/CU4GCSsT/JyUrNpZUWB9MMXWfUCMvRuOTiWpMnV1q1N2XJUiuiNKZukBrSXM+bk5UpWG0HRL7HzjBxxtlC0Yp8wobk0mqTysDrO6N6AXaSsXV/ei56llWaae6cjza6EbEn2R6nzPKcng2YFSWzTCOFW4TTUHGmFyOVAms51Q3ZHCROf11JrLVOPbIZ8Ln1Luf6Fa9tjzmY5gRK0ot8kE7+IC3cDivyPTqRGxBrRT5VZfn8Rpf3DmfsTVL6jYA/8eWzZKXhN97Y5XQ3diWp2lS5E/v80vOn+PsvbdEKHVc+rwxZqXnmVIvLe2M+v9Hj5nHCmX6D3VGK4KTu7XPtaMrXnjj3gN/rxy9w34lHlZH/FeA/Atp3e4IQ4leAXwE4f/78I3rZHy7u5JguNd0N3xundKIAIdzwxu44Rwnp2AaIObe1FSp6zRCNYKMbszNKyfIKqQR7kwxPSc4tNTmaOi3xrDAcTnOeO93hxvEMbdyXNa+cqt5Sw0NJp543SgtEw2el7WiMs6LieFYwnOUcpaVrbNXlv5avCHxJUTnPRGOpx9BPsiWn3eF8QN37toDveUS+IC2cdkYkJO3I52w/ohV6dBoewkrS2mLNGR+7ycpW6CMFBIHkaFYQ+AKJJA48ZrnTpU6risizdK0PdcC1OCVFLxC1o4xlnDr2S6k1QgkqI+jGAetdZ+VWlJpZoZ3XqXTCWoESzKxFCzjfbyKky9z+9NfOzjOul24c87nTHRqBx+bQ7ZBGmQuuSy1nRdeNPbJK8+buhCQvkULw3OkOw6RgZ5Q5S7/aSeer55c4TgoGSU7k+/z819bcKHxSEHiK//UvPMl3rh3jCWrzDNdUe6bdZlYYOpHicJrz7uGMUjujhmaoiH2PcVZwc5ByuhPy9GqTK/szpllZO+4ItDa0axXGonK7oE7kjJmzyrn4KCEYpoVjt9QlH4vAaMfwWW357E1y2nHAhnWMnaNpwTTXgGOzTAvXa2hFHiuepBN5HE4KdicpcTPkbDcgN26b4EnBMK04nBY8tdp0HPWm78pAyum8bA1TPCFI8oqVVkhSVLfVtO+mOmpxNonTXNNvBIS+4mCccTTLOduPaYTepy6z/mFy1j92IBdC/DFg31r7ohDiD9ztedbaXwN+DeDrX/+6vdvzPi24c9DnYJLzW5f3+cKZHhLJajvg3Xro5qSup6RguRUgcLKqS01XJ//y2R55qZnkPqNZwXPrHS7vTVhrhEicc1CSVyjlygH9ps/WAA4mOYGagRV87nSb9W7smkrAmVqw39b0tpc3h7yxM3bCSwgqIWgELtMrK0ffC6SoZUSdhsj2IGWcVu7LGfustCJsPVq90YsxCKZ5yc4gJfBgKfaojOHlm0M6cVBvY10gO5xmdBshjVpnRQpLI/AZ5wVe7cCupKQROueZtNC0Q49IOVkDY53qoSclnieJal54WS8+UniklSH2nFnxc+ttokBRGYMnnOfnrDSc7kVY6+QGzgZO93ylHfDMqbbrddzyxXnfmKBBUjra4TQrUUpypt9kZ5QyLWZgXDaYlpovne1xpteg1wjmwmZRYLmw0qQZeCy3QkZpyFonYqMXM05LnjrVnn9pbxwnJHlFUhqMsSzVmjr7kynnl7pkpcZo52+ZasPeKCMOnFOSJwWnejGXdyc0fYlSPlldjrGuGUGpDdoKytIgpUanhTP0EMKZJ5eOkeOmLK3T0xGuTJFXltWWo3yGSnDj2EkddIS7fxbL1iBhf5TTChRZZYh8n0unAp461cJXko1+zCAp2TxKOJjkSOWGgrbGGfl7xzQCxVIz4HQ35tWtIRu9BqHn/Eo/jP53N9XRp9ecfk2rVgRtBh6qG3FuqcG5pcZ8AOnTggcdMPyoeBQZ+c8Cf0II8UeBCOgIIX7dWvvLj+DYnxju5JgOkoJu7DsWg4TjiatZX9mbcHGlRSv2+OLZHk+vve/g/tSpNn/qq2c5nhUf+EK/d5QwmOVY69xZ4sAjLzWFsQgheH6jy944Z1ZWPLPeptfwXWaW+oyykoNJxsXVFlIK/uXbB2yNUsZ5iS+gHQWUSY5Ugrw2dXAsCUllodvwafgeZ/sN9mcFQS5pRx5FXc/OS4MxFVnpsrlGqOh5AWmusaWhrNkyrUBhhWCSFnhK0goUgQgJPMn+NKcyBRZHb5zlFctNpzVtMXWt3Q2vrHcjJrlG4jjKvVCRlIayqAg9yXK7STv0wVpWOiHvHsxqJ3nFc+sdSm1pzzLeO0j44kaPWV6SV5ZSW872Iqa5/lA2wuluxO++c4hSkoavMNpirHAOPUWFL91iMi6cbvw011zeHdNrBPQbARvdmKI0dOOAZv05ySunnbPRi7m40pxnYNcOZ1xcgY1eTFG539keJs4T1rhy1v4kczs9BNOiZJprhDwxlbCM0gpPCJ5cafKOsZSzAl9ZwthDSsE4c9LFjcCdtzWWWems4Dzl4UmFF4CQjqKqtSXXmnFS0o4CkkLw1FqLzeOErWFG6EnO9RsczkqSvCT2PZRSbr5BuHPeG6dUxvL86TZfPt/nl55f56UbA660p7x7MGGUlBibE9aTuL6UXFpp0W8EvLU7RgrBKCtphx6TrKQVerfR/+5WxwYnnNVvBFw/npGXTkJ3bbn1qWxY/rA56x87kFtr/2PgPwaoM/K/8LgHcfggx3SaV7Qjt/WkFmLqNwJGaYExhnbg8fRam3bkc365yVOn2vOO+YXlD6qr/atfWOf//pvvOAU7T8yHWX7m0gpCQDMKWGqGHE4yKmNYboa8czBFG+hGvlP+qzQHk4JRWnKqGTCaFVTGzJkgSklWW5JRWpKVhshTrHcCXjjb5+rBjHbk80TodEtmeeUWoWFKVmq0cbzoYVJihCXQBl86pyJPuOnEwjj5VFUbCZzuRuyMUvzKBYCictliVjnVxMo4Jo0UzvoiKwyr7YCn1tqMU83+OHELGbU8a2VptRTnlpp85VyP9U7M1jAlVIqjpKAdBhhruLgSM84iOmHguNie4nCagnD3EZGw3PL5+VqKFlyGZIxlqRWSl5pRWrI3zvjCmQ5r7YhXbg7xlKDfDJnkFWd7DTaHCXujjJdvDLi40mK9G6GNIakMaVEBlnFWcrbfYKkZfGgGdmm1xaubQ75z9cg1fZdb9WfL4+YgwRMlnnK6Lr4SeJ7jnPdjnyBQTGqLu2muOZhltdiVpN8IKE1C6Ek6kV9LDhRY4+iGgSfwZO3NmmmakU8QSI6TjGFaslZpnlrrMZiVTu/ek3ieIpQCTzjWUVoajqYzskqjtWuWtyOPtVbI1jBFW7fRzivD928MyEtNpxHQb7ifb3RjhqkrPeWVM1ceznLiQLHS7HB5d/KhTcq71bFPAnxWOTPoVuSx1Ao+lWP2P2zO+mIg6C64cyCoVWcMaVGx0WvgKcmbu2PSymKSkrWOpRV6c27rs+v9e9bEzi01+MLZLr979ZDR0IkldUI3jamNpRU5q61G6DNOC/75W3tcWGry5GoTr3a2zyvN1sBJ484qg7ACq6FShkA5dkNibW3Y7JpZS01HX1tq+ZzpNfCkpBN7bI9SlpoB//LtAzoNn8E0J/Q8orouOi01F5Ydc2OW69ruS9S6IU6NcHuYuYk/YKkZUFYa2wo5mmRIIKk0wjqKXSOQJLmbmtyb5JR1fVwbw1Gi6UU+S62QRm2cAbA9SlHSDWW9vT9hkBTEnqLUhuc3Ovzhz53iO9eOmGaO+lhUxvHsgeuHM55Yfj9D3h1lrLRCfuri8ty56eJqiwtLDZ5aa3N5d0KhNdujlI1OXCsoStL/P3t/9mvZled3Yp+1533me8+db8xkcCaTOagyS6rKVlsqlFqCBNmQXzy89rMBv/lfMGCgAT8J6Ac3bNgNuBsCZKlVlapSVWVNmVk5cQ4GY77zcMY9D2v54bfPYUQwgoxMMlPJFBfAJPMO55x7zt6/9Vvf33fwbAnWzku+dnHAaltSkY6mKQY5Sb1xYfDUDmwUS1dpWUIAdW3F9c2ueHoXFffOE1qeTVpJcLJvxB7WshS7/YCkLGl7DrsrLfKy4iwuyCqBzzqewyQtSPKata7HWgdmWQnGLKl5t06jJg5O0/Zd2r5cy5O04KPjiPWuj0Hx6k6fW6cx50nJLJNNZW8UYzebgrJkMx/HJWUNG12PuoZ/+/MDvnt9ncC2pBuPc3qhy1lU0A2MuD/aNu8dzhi2fVByfU7SEstSzzykhI8L/KdRDH9T1q/aC/0LLeTGmD8D/uyLfMz/XOtxjulKy2N/nGBbiqqu2R8n9DyHb1xcoShrbp5GPBgn7AzCR45+T8PE3tqbYCn4p6/t4Ds2t04j/sM7h5zMc66uiR3t8TylH3hs9QIRWNiKDw6nXFzpsN71+cHtc7kBlORDdlsuswTGDX+47cuR228CiB2E3vfW3oStbsB5lHN9s4Ol4LWdPj+5PybLKwYtB78fSsG2LXTjjdHxHWZJwbzhho+TAkcpbEdRVBXvHZYM2z7rXdms1nshnm0ROoo4q9kObO6PU/KipqUksSgua8K8ktQiz1m6Lw7aYlc7jkve3htzdb3L67sDxknOnVHM9iBkux+Q5ZpaGQxys7yw2eXPPjil0kK3+/ZzfVZaHnfPYv67//ghr+322R2EHM4y4qLipa0eL271pCv2HeZ5TTdw+eaVFW6fzNmfZpRaWDOWsnhpu08/dDmapZxFOX/42tYTu79ZOvnUDuy1nX4jyxfGUJyXjJKCe6MEZQwbXZ+slDAPjGGjJxa0vtN4mSuYF1K8LwxcbpzMqbSYYdnKYpJWtD0by4JB4NEKbKpasGbHkqH1Vj/kwkrI6TxlmslkvBM65FGxFGMZY/AtJS6QBrq+hVaKeVrhucLV7wQejmUxL0pCxxb5fz/kNBa7iLioGuxdqISWpXh9t8+l1TZJWXM2l1NBktdcHv7mddNfxPpVc9a/6sifsh7H5lY7Hv/yGxf421vnvHswpeM77Ky0aHsOmaV4bafPziB8xPj+0zCxmycRvYYfe/885i9vnlJrzSyv6Mxt+qEU7rwSHvRZBJO0bDxfTtjoBmhtmKUVri0Ebde2cF05jnu2zWY/5NKwha0sjucpeVmz5QeEzYD23ijGKHh5SzIpV1oeV9baSxhpEGrunidcXGlRahgnwtpwbeGUg3RlupLsSFtBnMsR99Iw4MIg5HCW0g0cQk8Gahsdn7SoOItKkrLEsRVbHa9h/Igicdj1sJRFkheM4hLX8tgfpby+O+A8KsmKmt3VkBc3+4DAELOs4HvvHfP6bp+LqyEns5ykrPEdm6SsuTuSBJ+0qMWT4yyS4GpL8fVLq8sTV6cRfF3f6DKKJYfzPJL5yGrbW3bPF1ZCNnrBU4vOwx3YPCs5mKScxyIs2x4EeI7NB3sTai2WtmdxQVpIWHNa1ijLwrGlUFuN940xivWuz3mUsTcWJodvW7R9h0HgcjTLKLRh4CuGoYsGTG7Y6HpcXmtzFouVwVSXdEOba+tt5lmFZdm8eaFDbWC9EzCJS/YmKbsrIeO44KQ5UbUCB8t2UIifva0UrmOz2fPxXZuTecYr25Ife229w04S8OA8IUoLLl1q02+5XN/ooBqWymJI2R52uGQMp1H2iHL609aXzbXwV81Z/6qQf8p6EjbXD12OZylrHZ/AtWUgWNa8sNl9xGHtszAx1bB/749i/vi9I+ZZScu1cSxFWmr6oeDyvjb83b0Rw7Yv9L68ZhTnIi23Ff3QZpqUrLY9uoFLVtSstX22+iG7K60m7V6BNry4Jcf+aVKyN4kJXJv9UYIykNeaFze6fOPKCj+5NxZetpIjeOh5/Ks3dtmfSGRZWs6ZVzW2JfJ8S4Ft2Qy7Lj3fx3fkRhvHBbdOxfp1ZxByFolzYNYIclZCD2MMh9O84X7bWNAwRMTXuuVZDDs+53Ephaqu2ez5uOpjVkKlNe88mBH6EodnWYq00nR8h9N5jlKGstJ0PId7o4Tn17uyyUxT3tk3PLfeWZ64Lq62RYVrKXb6AZ5j8cPbI4pK8+JWC1vJxnFptf2JY/HDxUUpmKYlLVc2TAtJAlrr+BxOMu6eRQybkOYPj2cUteH5jS5FVWM7irwUD3nhhNdsdOF/9fJFwPB398ZkZc3fuzSg1vD24RRlYKsfSv5rXTNJBev+3efWmCQFqvGo+ccvb/GT+yOySvPWgwm2rbi61mGjF+LainvnCa6tKMqaKaBRbPVDTFd/TE01IrVPyppuU9TLusZzZKZwcVUamKtrHVquMIsuDltc3+jwxoUBb+1N2B8n3DtP6Icu24OQutYUlWGelfz5jZPP9P//6f0xWsMozvngaM6P7434g1e2lvOo38RC/6vkrH9VyH/BNWh5vHlphfvnCbNmyn552Ma2FC3/4+LyWZjY8xtdfnxvzA9vj8REyHckLNlSdALxpK6NqEBf2OoxS0tc22aSZdRGMitbgc3RVAQpo7TkyrDNes+jatRww7bPvSZYoRM4DEJXoImziHkiwRTzVMyRoqzk79KS37myyqXVDrdPI9KyZrsXsNoNyCvNB4cTsWtFrE1RTbCALdL0sjJYIcyzmrvjlI2Oj20MWVnzwcEM15Gbv9aGtmuz0vYYxQVGC92x7TsU2vDgPKbf8uj5No7joQ28utNjo+uz0fV5/3CG7YjvR1xUfHQcUdQVV7o9yloT5xVVXVOUhlJZFFoUoYsO0HMsXMdjklTM84r/4a/usLva5pWdLq4jNgpKQdt3uLLW4fn1Dn/50Rkfncx5ZafHpdU2lsUjEWFPopcpSu43jpnDtr/sNm+fRkzTEscWXv2F1TZbvUAKf5M+b9lgSknu6fpKYKSyZpwU/MHLW4ybPNbAtUlqoSyud33unkUMWgHbfckT/RdvXuBklvFXt86oasM4zRm2ha9tW0LbrGoJaX55e4XTeSEeNY5I4gdtnxuHM+K8ZBIV2JZFrTVZIe5n/UBUvOtdn+vtHmWl2d1ssd71ubja4nQe0gtdgWUCVyIR05LayPt3HuW8vTdhvetzabWN79hL6OFp9Lw7ZzFaw/1RQuDarHd8ZqmcyP7VNy8Anw5r/jaurwr5L7Gexm19GO/6LEzsjQsDfv5gQlFVeI10v9aGru/gKJgXmq2ex6DtEToWYy1FPW1sc7Oi5u5JTF5KcUrrmigt2ex1OJpm3B8l7A5CXt3ucTLPsC3FStsjcEXE1A09Sl2T1ZpV38MKFQ/GCX9965QLK202uh6TVNEOXLqezbv7E/nDmo7UApFtA6rWhA5MU+gEFaM4B2VxNpf8zCwt0bVBlY1NQanp+Danc+Fh90MHx1ZkVc319S5RWmJbsrlt90PysmZnEBJllXCEbYVnW6RFyf4opapr1joB/ZaoIldawpu+fRYxX9jHujbnUcrOIMAg9MnzOGezFxA6Ps9vtDlrXBMXyewL74+W5/DfvLbN7bOIvNJPZEY8abi53pWUpt+9toZS4k9/42hOVgqHfmfQarp7GToXtSH0LLTWhK5DaSuSUhN6Nps9yQZ9MEroBQ7XN4XlAeAqxe1xRJwL9XGjF2Ap+bxB7HEncc6rO31uHM/Ja5l9bHR9pmlJnNfcP4+XBXHQFhjgZJ7jOzbDjsvts4iu71DUFVqL4dabFwbsDkIur7XJiprnNzsoFHdHMfdGkXTy8Ehx/t57R1wddvjahQEHkxTHttldbVFUNVfW2s9Ez5ulJaM4bwLNZcbQCz1Oo2wZ9/bbYk/7rOurQv5LrGfBux7/GaVEMPTzB5PlUW+zF9BreYyiglIbNrseKBksYRQXVweNig2ySnM0TfFcm2lWcR5nKIQ9kJQlg5aP7Vh8dBzxzSurRLlAEWlV81+9sMErOz1un0Z8eBzhKDEyGiciZ7aU4mSek2QVcVayP8l5cavDpWGbvKiYZKWYJDkO4zihQV1wbLFVNUBSQcupmSSFBAg7hsqAUdByHRItgpt+6OA4FpOkAsvQ81wc2yIuNKEjmaJvXhowigpevzhgveNjW4oPDudEmaQa/dM3dhgnBTdPIvF43+qy3W8tqZOLJPdhy+P5jQ5VbTicZqx3fXSD9Y+Sgt1+SNt3afkWoeeilHi4LI7kjiUq3SgX4cnVYZtKmyeyJBZQ2gIPj3IZNiZFvTyZHUxSAtem5TugPh50lnXd+L44XB12cZTi9nlMnGu2+h7XN3u4tkXgOqy2PW6fxVzf7GFb8N7hhBvHc9CGqCiYJjVn85zfubZGx7f56f0Rf3PrnLMoY5ZV2Eqx2vHISs3BJGWrF/DGbpuDacooKZjnFdt9CQEPPZv9adowtUJarohveoHLoO2glIQv9wOPP3x1uLSS3R2EpGXN2/tTrg4fLc51A4e81Ovz4pacTo0x/MWHJ08MhHgSPa8XunxwNGe94y+/lle1JBs18OZviz3ts66vCvkvuZ4F71r8zMPH7kVn8v2bp8Jb3unz4dGckygnq2qyQoKGL622GEUFea1Z72nOZxmHk5SWa1MgxlKdQPwsZmlB4IiZ1KwWT+/XdvvUGl7e7uI5FpeHbfqhy8ksJ/RtZmlN6AqT4YOTKdOkEPWeEh+UvbHMAS6vtfmLm6f0A5fQawaqjZ92aQT3RX/slBi6DlmpyWtDN5SAAKVEjGTEgYWWaxMVBR3XZZZXeI5NP5CMyff2Z3z3xQ02eyHfuLRCVWtxmWy7fPeFNRzb4izK+fqlFb77wsYy4aXliQfMwSTlLC4oasO3rgyXBmbzrOSdgwl3TmNe3emz0fU4mUmk3lpXgkF8x2aaFkuM+639KYPQoxc45JXmrf0pr+482ROuF7qcznNuHM+YZ+Ijow3LIeBGNyDKqiX32iAReVWt+egkoh04+I7CoIUGOezyZzeOMSjOo5zVtjBvpknJ4TThB3fO6TVZoUlRNfBGwMZGwL3zhL+7d84buwNRkRYiCrp7FuM1m2XHd5mkJRdXW7R8h5e3+7y41aPdUGgFiqp4bq2D79hUteTNroQeqjFWGyclr2532egFjOLiE11wrTWjhicum1stFN6y5qXt/vK9S8ua9W7wzPS8q2ttfnxvxCwt6IXe0p/l4bnFr5Lq95u4frN0rL+l60lxcIdToa+N4pxhx6MTSFqQ61q8sjvg6noHxxHDor+7M0ZjGLQ8fN+irBVd38GzbYYdj52VFr5ncxqVDFoul9faDYc6472DKT9p4qsGLY8/fG2L33t+neubHWzgw+M5UVERuDbKFndAz1aMk5IPjufcPY/pBy6nUc7JLMMYQ9u38TxhS/iOTSuw6fkWw27AZjegF7hUDW3OArJK7FI922K14/Ha7oB+4GGQPFPHUeKRbYth9geHU8ZxznsHU376YEwncPnahQG90Fu+j4sj9MO+8R3f4eJqixc2O1xdazGKc358b8SNoxkA37m6xu9dX+fV3T6+a+O7FtuD8BOqzMUNr5YxwyCC/qc7S1xda/Pe4ZT9cdI4S8qQz7VYinY0UtzfvLjC1y+uUNaat/enhK7DmxcGeI7NeVTy8wcTbp7OWOt4FGXN3bOYW6cR41iyW7cGYhL1/tGcSVKy2fPZ7IWcJwXawKXVFnVt2BvLCS70HCzbZmcQYtkWd04ToqJkrS3D5qyBrgCuDtuM45KsrJffs5WweBasJIMhzgT+8hybo2nGX9085f55zDz7eOC/2vLYn6TcOJpT1oZe4NByxSd+cS0tPrvvPDd8xP9/8d8PzyEWa9Dy+INXtqgMnEYZjqUemVs8niXwaY/127K+6sh/DeuJsXGnkgr00nafw0lKoQ2OEj+NC4MAhcVq22eWlCKaaLm8fmGFSVywP0vRtcN5JEk6F1dCjuc5tqX4nSur5GXNrZM5z21IN6Uxjwx7fu/6Or3QZX+SYrRBGYlqsy2YpYCj8CxRhL6zP+PiagujoRfaaKMZJxK2u9lxmTYd90ZHsOeoEJViVrkYDa5rkZcaZYHBYrcfcnE1ZKvn8fbBjNC1Gpy2YpxouoHDoO3z/EZXwnszw3rHbzq6OR3fWQ7+FsyEpPF17zTsmK1+h1unAiEtOrYbRzMurbaXFNGra22+f/OUvXH6CVXm1bU2P38w4fXdAR+dRtw6jQChHM6z6omf8aAlnWovcCm1mJJd3+hhKcPBNOW/eX17OTexG8zeshTX1ttcWxNFbeDaeI4MIEdJgUKRVJqi1FRRQa+V88p2T2TtifirV1pzNi/ohzZJIRuGgibaT+PaiguN58s8r8BoOqGN1mJHPElKNvsCs+wMICs1LU+CU5X8D+tdH9uCNy6s8PMHYx6MY7JCPqt/+/M9nt/oNW6QOVFe8+KWKJxX2z7vHkoUn+9Y5FVN6Nn8/efWOItyHFstIce7ZzG2pR5xP/w0et7lYZt/9c0LT2Wm/LbY0z7r+qqQ/xrWgsFSa7NUEc6ykrWeT8d3ub7pcnG15oPDKadRRlkZWj68sNXlcJpyZa3dDPE8AtdmnpeczGv+3tUV8rJmltdsdH2+frFPWtb8+Y0TlBJcfXfQ4nefG2JbajnsGbQ83rgw4Gf3x3Q8hx/fHzOJZfDY8iTswbNr2rbcwFVZc2G1xQdHM1ZbPsrALBe1Zz90RWrecvFtxTgVJ8SVtkelDaN5TqsrRSstpZtbFIabZ+LgV2vDZs8jboy0+qFDbQwfHs84mKT88bvH9FvyPL3QZb3j8eal1SVcdXGltRwmL/xNrg473B8l5JVAVXlZc+c85ptXBN8etDx+//o6b+1N+Ohk/ogqc9DkqY4ikfE/ty4b4iwtOJymy9PN46vlWay22oQPH+mLatnJPz43ySvN67sDDqfZcnAX5xXTtGCzJ8Pdy8M2984ifFtRVZqdXsjts4iPTiI6nsOgLZBO3DCeHowShi2PrX4oA9/TmIurYugldgWiUq5qTVkLnDVNCzxLcdoEdr+y3V9CUsAyTq0buORVzfsHM9Y6NnujhPVuQFVrOr7L3jjhwkqL/XHCpaF0yK9s98Ve9iGG18JP5cpam++9d0ytNastsaSwLJ6ZXfJp8OZviz3ts66vCvmvYV1da/OXN0/ZGycN7GBoeTazRKbvKy0PY8Sc6uVun67vNJ2k+Gq7lk1aau6dx9RaIrsGLZc/fHWb9a6/LGJrHZ9//9YBoStBBrU2HEwToqzPVj94ZNhz5yxmtePT9l0ejBNmaYHVmER1bBvHslBK3AELbTBFKZ2V69BrsO95UYnjX9fDMkJDfG13QNt32OwHfHA4W4qLLq226PouP3kwZm+c8Ppunzd2+9w4nmGj6IUuniPUxvujlPcPpxS1ZE2eRimztKTl2/RTl71JiucIu+RJzIRZWrLe9ZfY7CyraPvOJ6xNBy2P776wwXdf2HjiZ/bje2MJqHbsxmJXgj6exn54fqPLuwczlFJNB6qZZuUjuPrDc5Nbp3P++N0jjmYZV4YtLg47Mij2HIE2UKyEHnHHxxjD7iDknYMpKy2PKK84nmWYU8F/y1rT9W1Wuj6Djsdax0cBN47m3DyesdYk51iWwmk64EFHM2x53DqNuXMa88pOH9tSBK71yJB3uy+Okg97Bz0YJWRFzUrbo6zE7Oy5DXGYXBjGvbglm9ZihrFYSVGhFHzvvSMcpVjtBORVzf1RzKXVp7+/X62nr68K+a9hLTq8TupS1NANBMsFmCQldnNz/e5za1wetvnee0ecRjmrLZffvbbGX948xbFlwJSVgl9eXm3z/tGUeyOb5zfEoOuP3jlisxfgN0PMGjgYJ/z/3jrgd66ustoRI6dZWnLrdM7uoMXBJGOr6zOOcg6mKUlhuLDSIsqEix26FudxziguWO+Igq8fulwattjuhfzw7ojNbkBS1LQ8m5bv8s/f3OHysM2f3zhhpYEcFmuj5/OzB2Pmeck0LXh9e8AoyblzHjNNKozRGKVoezbrnYCf701wbUfCJrRE1vVdm3f2JvzBK1sAHzNFsgqN5vmNLmlZLwN6QYrHL2JtOmh5bPcDkrx6xAv7cXe+h9cbFwZLnvQsrXEcxWpLnn9xSpLXK+nw8yb1KXBs7p4nkjdaG7b7IbdOInotl6LWeI7QTrNSjKaiom6eo6Tr2QSezVbP58E447lNj5e3e1zfkGiAlmfz798+lPzOtTa9wOWtBxNW24K/W817HTg27+1PmKYV33v3GN9VDNs+2/2Q+6OEbzUnmQVMGDUMpLLSuI54i19alVPY71xdXRb9q2t8goZ7Mhcf95vHEVs9H8exl3OKUSyQyy+6PksA9JsoEPoi11eF/BdYn+diMAbe2B08wif2HQurDS9v90iKanms/1ffvPjI83iO4uZxTFyIl0ng2QxbLm3f4dKwvQygPZ1nbPdDHMfmw6MZo7jAdxTTtOJknrM3TvBtm/Wuj2fb3D6LeW6tw/4kkQFk6PFgnDCKhGlQ1YYM8TGxLcFAPcdhsxvw+u6AH909Z5pWtOOClZYnjoe15k/eP+K59S5H00yyGz2bj07m3DyZczDJqGvN339+nWHb5/2jGVFeNukvFXFR0/ZcQkeCCYpK4JbVtk9RaTqBQyd0OJxkS7jqZ/cnRHlFUpT4TVFo+Q4b3eBz+VosLGcf7iZPZhlnUf5U9WE/dDmdZxgUm+2ASusl6+Ot/SkKQ+gKNl1pw8WVFi0v56OTmKjQbPYEYpimJdoYyrrmwkqLXiCnmdNZxkbPp6wFrvIshesId7zbnPYWRbEbuHzj8iq+a8nwtYbzKGPY9bg/islqwziRnM20FOpmVtaAoqiEYlpUNZ3A4eJqyE/vj7l1OsezbSxl6IUeR9OUoqoJPQm1sB8TSg1aHtfWO/ztrXN5zrLGGMH2+4FDWhjuncVcXmvTcm1OI+nmf5H1WV7fv2ov8N+E9VUhf8b1eS+GBT1tnBREeYVtiQTftoWa9/Aw5nF8b5aWvLDZQynhNZe1eaIZ/3o3YJ6V9FsCKwSlTZRWrLRc1joeWovR1UYv4Np6h7f2xtw9j1EYHkwSpg0dLW660GlWstH1KWvxDp8lBVFeMElsbhzN+Nvb52x0fTAQ5zU/uT+mH7pMEpcXN3tMs4I///AE1xbzpiQrmSQFYPizG8dERY2n4CQqJRBBi6zetiQAdJaVDDsSulFUejkYy8qaS2viO33zZM79UUxa1WSNM+XBNOPFLaFdfp5h1+OirtN5zjv7E17bHXziGoCP1YTfujz8BI/6xtGMQegBhlunEVaDVcdFxYtbfXZXWtw7ExWu59j8szd2loIqDZI96jp4Ky02uwGTdCa0yFI3KseUnX7AKM6JspIPjkouN0yOf/Ty1pLj/f6ByOCnqbB8HAXjsuRkmtENXJSy2OoHpEXjRe9JmtFP7o25tNrmxc0eP7w74rCJEgxdG2MMrUCySP/gla1PdMK3TyPWOj5xUYndbS15nLOsxHVsQseR3NSWh21ZvzC75LO8vn/VXuC/CeurQv6M6/NeDKttj7+4cUI/dOkG7tIS919+48IT/cofXg/L/aO8bnjNMlSEj8UO33luyL/5yR4Ada1ZCT08y+IfvrjBwTSjGzjCXEC6tatrHf7o3SNqbUiLirWuxzgpqeuaohbFZVGLj3le1by2MyCramZ5xcGDMRtdj41uIEET04ykrDifF7yw0+XD4zld32Wz63PzJCavaoaN5WvbdcSGt6gY5bUEWihJ/qkBzxFrXQvF9iDg3llCWlS0fBvPsfAsxT96aYOvX1rhP753xNk8Y9D22VnvYivFOC64fRrzT1/f+WU/buCTw8mzKOe13cFyEPjwNbD4/4uv1dpw/zzmaJLy0naP0yhns/vxANG1LcCQFDIIdSyLK+ttXt3pLwe2tqWWPtvHs5QXNrvcPYtJy5rAUSR5zTwXj57tgagoO427YF7WS3dGkA3w3YMJD8bSeW/1A3zbpqw0cV5jWarxRRGaaKvtk1UyzJ6ksqEuDMB8WyyXs1IvHTa/cWmwPFE+vBb3zYNRIsEUyiIIREiktd1g8oqjWU43dD+xETzL+ixfo1+1F/hvwvqqkD/j+rwXwygueG13wDgpmOc1ncDl4mqbUVx8ZiF/uDNsexZHM3HSW+v4cDRjpeWx2vG4PGwvHRrjsqYXSBEHeHd/zFlUMOxKBNl2P+R0nrPe8bmy1uaDozl5WZOUNeOyxndtAkcxTUsC28axLXzPYncYMksrbhzOGbbFR7rWMpSsak1ZauaJyL4nScXhLKfUNSuhR6VFFYgR10RjFIXWBLZNJ3BoBw6nswwbsFHsrITMsxJno41jKVqe+MdcW2/zu88NhVfvOFxda9MNZeh7FhVMkkzyS5/CLvlF1sOnowXm//B6+BpYfG8BnbU9h6SsKWvD2VyCilueiL2iXHDy2hiKBwIRvbrbW0I1j/ts//T+mHcPptTG8NbehLzUnEUZLd/FsiwCV+Cb13f7tDyH59Y7fHA8568+OuNwmnF12OZbl4dcXs35t2/t88Jml1unEbNCHC3X2z61kdjBk1mGUeDZQpPM65pr63KNHkxSfNem7TtkVcn1jS4rLTFse9J7/TCm3gscWp5FWRuMMTy/2eXeeUw7cPjGSuuplsCftT7L1+hX7QX+m7C+KuTPuD7vxbBgUjxM6zKNp/dnrYc7QwPcO0+4PGyx0fGZZyW3Tua8fnHA7IZg6n/42hZ/+NpWM9is+NvbZziW2M+6Fvyn94/43efXGcViz+o7Nistl6p2GLQ9fnR7RK/lEGclVWXIa83FFSngiyT5jZ54UJ/Mc4FObEOpYaPj4do2P7hzTtuzOZllxEVNkmksC57f7HI8k8Dd0laohpznOBZlZWgHDrZlUdaaf/TyJm9cGAA8dTax2vGk8GQFZ5Fwry1L0Q6cz42DPj4TUerTFYOPS/HXuj4H0xQwbPcD7o5idvsyXziLCj46nuO5wt/fWQmXJ6wnratrbW4czTieZ1wZthnFOeO0IC+qJtNU8fXLKww7PsfzjLMooxMIu8hRcH8UE3o2G72AV7b77I0TuoFL23W4vKo4meXMsoJZVpBWNXkzHHZti1d3elxckUJ+GuWcRzkWFsO2R1kb7o0kpedJ1gVKwd/ePuOd/Rm10ay3Q2Z5AUZODYFrszsI+b3r68/0OT1pTvVZvka/ai/w34T1VSF/xvV5L4bPuxE83BkO2/6ys19kcY7ign7g8u7+lO9/eMqblwZcW+/wP/7oAZalWO8EXN3oEmc151HKB0dzvnNtlfvnCXlVs9YNuHcWoVBs930sJayFK2sdTuc5xkA/tHluo8N5VLDZDfjoZE7o2dgKlKXo+zbDjs/Nkxm1gWHLxbYsQg+K2jBNSubpx3a9VSQBCrU2+LbVuAR6tHyXf/G1nUdogU+Dr9640OfH9zQPRokENXsWvcDjle3eUgH6y+CgT5qJTNMSRbnkTt85jxlFOW9eWuHysM3tRjh0MsuZZwWzrOTiaoey1tiWYrMb8MpOn0qLYvKfvbH7Cb72017voOWxMwi5OMt5/3DGySzn4qC1TIzPS7kWsrJmEovx1bW1Dh8eR/RCj3GS8ze3zhh2AnxHEeUVb+z2lzTXcVxw82TOndNY/HfaLt3QY7Xl8vJ2T2YcRUWcVVSVxnUV692AwLUZxznvHszo+M4jG+0kKTiYpHx4EtEPXUZxzu3zGfOkYqXtMk4Ul4ZyOvllP5PFZv1pAqBn8Ub6sq+vCvkzrs97MXxRXcHjnf2NoxlOTzHNKj48nksn2PG5P0qEcw584+IKliXUu5YnFL/9SQoIVnswldCJKK8YJyXDlsvWoMUr2z3WuxLvduc8YhyXrHd8nl/vsj9JCN0BP7k/4iwu2O74XLzQQmvD6SznLM6IcsWV9Q5Gw1mU0fbkpn9uo8PL2z1c2+ZHd0dkZUXgCI3OcSxe3e7x959be6b3Y0H5G8cFw7Z0kB3f4fmN7ufCQZ80E9noCt85r2p+dl8ofN+8vIpjW9w+jbi23uHeecyDsfzuS9t9HMta+oCsdj6GSxYwzeMmWy3feSS0eUFZNAbe3p9gWxIa3fFs5nnF3bOYC6ttXt7ucjLLafs2vdDhjd0+3cCl48t7sPB8v7om7JK80uxPEj5qCvfruwMOpjFrPTlRxVmFY1mEns3RLOMfv7K1PBFaFmz1fFqezf444ed7Y9q+y8lMWEqTpFjeK5U2vLzVY56VYkqWlmS1RqO4tNqi7bkcTDLe2ps8kc//WZ/J4utSzJ9+L/62C4S+KuS/wPo8F8MX1RU83tlHucAdSV7h2S5H05y0qNDAdk8GYAsmS1xU3DuLKCvN9kBCCMBQ1pq0rJuu0aflOzy30V56c692PL555SJv7U24f55wME2xLEU3dHjj4gqTJGenL9DAhycxu4OQfuiABeO4IHRtbMvi4iCgH7q8sNlbyun/wfU17p3H3DyJUEi4wpOGZp/2vv7+9XWSvGaSFkvf727gkhTVIyeeZ6WPTpKCn9wfYyFD4cXjha69lI9/+9rwkdMVyBykG7j845e3uD+KcaxGGFRWn8ii7IUud89jfr5ICbIhLjRxUXL7NOKV7T6Bay0pi6/vDpinFWdRzjgVGmoncDmb5/z43phxkrPdD/nffecSo7igqMQvfGcQ8v7hjLrW+K7QQPfGiYSUFBVv7A7ohS5vH0z56YMpeV7TDmw6gcs8LcmKkmljS7DYhEZRIcKfecaN4zlrHZ+NrsQRPizqmaUCza00qs3LQzibZ+RlTceXeUdZG6ZpwdvPUMj/Sxha/rLrq0L+a1wPq/runMWPWNr+sp29YymmWQkoDqc5gWPj2uI0eG8Us9H1mCZiZDSKC8pKU9SGN3YHtDyHspZQh2trHW4czZYy8Z8/mND2bN5sfElAEm/meUU/cFl4kzy/3ub1C7v8yftHFJWh69ustbvcPJlT1pokr7GVotZa3BWNpOQsDI4GLRnSftZN/Ph6vCh/5zmxUdUa9scJo0RCEP7glc3lzz8LfXTxc75jYaEoa82NoxkvbvWwLVGgPqmgVLXmnYMpaV6x2QvYHbSYZRLa8SRV6Wrb4//zw/uEjoXv2dw7iylriWWbJBJIYVtqSVk8nGb0W55ASHVNUVUczQrSUrPW9eh6wh55e2/C6xcGS5in4zt0A4fTeUaU1PR8YSKttX1Oo4xxXDBKCvZGCVVZYzsWSokAqeXbpKXhkv8xRHV1rc0kKcR/xxj6gU3gOnR8h+OZZG+eRwUv7/TYGYQ4jmoUymJRO81KPMem4zuNK6bCqyzO4s8uxv8lDC1/2fVVIf81r8/LR3+8s780bIm51d506elR1JrLa22qqiZ0Hf7rb2zyt7fO2d+fsj0IeWN3wHbjdlfWGoXiYJKiDdw7j7lzluDY8PWLkoRUa4k+2+gGDNv+0pK0E7j0QpfLwzZfv7RKUWlqbbhxNOf6Rpe//OiUShvisuLKWptOE/g7bgrBF4lfL7jKP7hzTq1ZenfcPhV89lnpo4ufk41NoCrfEehkdyVcys4fLijzrOTt/QmdwMVRwhlPS82LW11e2OxiN3OMh9coLlhpuYzighvHEYFnsdtvEeUlnUC8ym+dRo0cPub+KMGzbeJCTmDH85yy0Ky0G0MqrbkybDNJSkZx8cg1st0PaXkO3UBiCg+mGaWpcR3xG7eUYOubg5Akr1EYSm1I85pey2WzGy59vh++/u6ex2SVJi0LYUB1fQahy2kknjSv7fYpqpof3j2T1KpQ7IBD16YT2Bgkgq+oatYfmhUsPuOHN+rVtsBQP7s/ZrXjc3XYxrGt37qh5S+7virkv+b1tILy1t6EbuB+4tj/JDjg4dUNpJDeO485GCc4jsXloWRLFsbQCcSo6PKwzQtb3U8oFV3bAiWxWXfPYkZJgaUUA8fjaJYt+cPvHkz41uUhSqlHAgEWx9qFm+DhNOX+Wcp5kqON4aWtDnkFW72A9V5Ay7WZZdUXjl8DvHcw4/XmpLFYiwHisx7LFz8nf2e3kf4bNHq52T4uO799GmEQB8iPTsWyteVaHE6EsXNhJeT3r68/8jwHk5Si0gxCj6IndLz7o5h5JkPLS0NDXmrePZhyMsvQBrSGw6koOy+vttkfp2SV5J8Grphi+Y71SHZslFfERcmP7o7o+DbncckoynFtyfCcxAVZWWFZFkPXF7jDaIpKvMStXPHjeyPOYsHxdwbhkimy0vZp+w4fHM7QBs6inKIyBI7F1WGHdw+mPDhPMNowiXMOJilVbVgZShB3lEnc3aDtL9lJ8MmN+nSe8xc3Tnhtd8A3L69y5yzmx/fGvHlp8Fulzvw866tC/mteTzuW/+z+mG9fW3ukS7+23lkq8hZf//7NUxSw3g0e6UbfuDDg5a0+46TgNMoF0rAV7axa8qlX294n3OYGLZcol0GprQwYqI2m0pqirElyCaAwqKemwk+aYpjkFQ9GKbYFl1dbdAOHYSdgte3hNQk3WSlGTJ/nSPy0onw6z3h5u/eJry9mEs9yLH/45xZeLQuflqexIIq65o3dPofTjJWWL7Fjs4yDqRTgWhv64QSQoWWvCfBu+w73zxOOZxlJKeHFli0d/p++f4Tv2ERFRVLUXBy08ByLrZ7PJK0InIx+6OAVipYvjpD3zmJmhThMzrMSbeBnD8bMsorzeUZZu5zPcxwbJllJ1LBQaq2xFGz1QtJSLIonSSEDSpRs/r7N3bOIwLGZJAW2JQZi90cxbd/BGLg7Snh7f8paN2CaFkRZxbDtcXGlTejaTQJTTl6LydZ615e0oZb7SCF/fKPenyTM8oq/uX3GS1s9rq13uL6pHvlM/ktfXxXyX/N6UkFZOBE+3mH+7a3zT+QYTtMSDFwedh752byqsSwRpczSgrDtohE8+uFN4WrDQR4lJdOs5A9e2eLeeUy/5TKNC1xH0Q08bKWYpBXbjUXs9Q2RxEdZ9YlU+IXHdqlNM6QTPHQUZ9w9T2j7NnWtycsaDWx0xR9mq99Zmng9y6xgcTpZ+H1cW+/QDT7mcH9ayszDs4Wq1tw5ixnFBW9eGjwiHHoau+hJr3Ux/OuFEgoS5TW2BedRzkmUM08L2r7F+XnO8Sxjte3xO1cEgnowTjmdZ9S1IcoFS3dsi9W2h2NbTOKCk6ogyyv5bNKSla7Hq7sDGVTmNadRzjyv6JUVt04jsqpCGSNWth0fx5ITW5rXuK7NPKsYdj3OoxJlDOdRQce3CRyXyhiKuubCIOT9oymTuGCl7eFYCseyOZ6JzfE4kZDvSVry3evr1Mbw7uGc++cRh+OUlY7P1WHIJC756d6Y339+HY2kQLm2uGuO4pwXt7rklebV3f4nPveHN+qFuKofupS1ZpqWvH80Y9j28F37CzO/+rKban1VyH/N60mFYn+SstXz+fG9ER1f2Bwd33lih1lVprGx+niFrs1ZlNMNHL5/85i6huc2Oryw0V2yN/7k/aOlcdIif/IkyviP7x8D8PJWl1qL8dbd84S2Z+N7Nt0m+mtRtP7onaNHUuEXj//uwQQLi1b4MRa80vLJS01RGQrkqL7aDnAdteRdP+usYHHc1hpspXhrb8qN4zm/9/wag5a3TJlZDPkep3guuui/vnXG9z88wXNsrq21KatHQzeexC7a6j/5ZNQPXeZZxfEs5XQukWtZVdP3XcZxTqk1RxPxGg9Dl0lccOs04uuXVtHaEGUVa52AbugyaHscT3NGcUk3dOm3POaTFGMa6mMvIMpL7pzGQuX0HZSBstK8vz/DsiD0XdqeTVpUnM0087xi2JZcS9e2iPOKuKg4mxc4toWtFBu9EKUU4yjn1qmYWlUaLq21sZWirA2hpzibl0RZyVYvwFKwN06azTDn5a0uH+xPMEo2sXcOJA2o47l8eDznuY0eoSvXRVULY+WNRuW8uK4eLqQLs7WNXsDBJKUfelS1xrIUR9MUG5inwkj6IsyvfhtMtT53IVdKXQT+B2ATycX618aY/+7zPu5v63q8UCglVqOLI/fDaTZP6jCLWnMeFY8U/bSoOZymrHUGXFrp4DVMgcWqas3bezP+3pVVeoFADT+5N+a59TZW4553Os/xm2zPCyst7pzHJHnJpWHrETrgVj/g5e3eI9a0C+jlcYZCXomVq6UUr+8OHimu7x5MGcUF86wiyStCz6EXONiWeoTBsrjBf3J/TK21YKwtn9cv9Ll3FvGfbpzwT1/fXt50i8Hm0yieB5OMFzd7SyHM/VHCpccGrw/TTCdJwR+9cyR+I21vGYm2N045nIpC1VJK7G3jnP1JRnujcR/0XSotYqh24OKWNfdHCV+/tEqtNbZSbPUCnCYZ52Sa4SjFejvgcJLgWopZpbl9FtMNPCZJzjSrWW05zLOKKK8IPZt24JKXNXmlUUY+z1lWUWmhltrKYlIUJGVNFWlKrVGVottsOHll6IcOriMOl5O0oJ0ItFFps0x6shTklSYt5dr6f/7NHVY7Pps9n7O0oCg0rqOYpaIL6AYOZ1HONS1MqVoborzitd0Bb+1NKGo5LTmW4gd3RkvIL/RsMSdjQJRVrLYdbp/G+K5Ny7WhCcn+/bXOI4Epv+z6bTDV+iI68gr4PxtjfqKU6gI/Vkp9zxjz3hfw2L+V6+FC8dP7Y17Z7nPjaM7JPGpCe+WY/i/e3Hmkwzyd54zjnMCz8WyLoqp5a29M2aS6LAKIj6YZt84ifnDnnOsbXRxb0Qsc9sYJlZbiFLgWZ0nBdi9Aa8PhJCNwxQskrzTb/ZA/eOXKJ3xgnoY17/RDPjqJeDCKGbZ9hh3xVnn4tYHcJFFW8f0PT3l+vcP5PMNSFmlZ4Nnws/vj5cbxcKdkAWdRSVLU9EKPju/yys6A0yh7xOfjca7/4jEWnV6UV1xaaaEaky54ugf24ncnacFa26eohZFjW9APXG6fRTy33iFwHWqTkxSaCwPxh4nyqmFoOER5yTyt8N2PTyuWsri42sKxFb5rM81KsroGrYSlMhY3wNC1OI1zfnT3TOx5Q5eO71LqknXP52iaYbQmLSVyr7Y1W2HA8UzMrZK8AqXIipq0qKhBQrHTksSqmGUynPQsRVLVaC3/X7xqKnzPRhlNy9gEnkOcl7x3OMW1oOW5dHyHt/amZEXdJBZ5FE3QBMBGP6Df8rg3iuj6HleGbdE2NMrSUVTwvfcOuTRss9ULyauaKMq5ut7hLMrRaALX4R++uMn3b56yH6cNZTZY3hefl0f+28BP/9yF3BhzCBw2/z1XSr0P7AK/dYX8V4GjzdKSwLVASdCvAVzbJikq+qG79HI+nWckpeblnT5rnUcpgJNE1J4gsMOP7p7TCRwUiltnEe8fztjo+gSOxVqT5h7niklS0PUd6XB3e9w8iZilJW9eWnmkmD5OA3scvhD/bQn9naYFH57MUafwT17dIvSc5WtbrFEsBlJncUHgOniO3bAkKnZWgifaj3YDl3ujhI7vcDbPaA875FXNast7hKXx8Gf11t5kqcC8uia47iwtGDf+5gC+Y3Ea5U/0wL5zFqM1RFnN4VSyJ7uBy/4o5VrDHvId4d0fTjNqo1ltB4yTCteS7EzPtugHDnfOIlFQXuiL/0xecRrldIOctXaApRR1ZaiN4e55gsIwSyXQw1YK17JIi4o4r+Tca8TnvKw1SVmDAaUU2hiOZzkWCpTCdizirMQ0drieLXms2nMotcEYOTGcxTlZoRl2fDzXgkSGplkh720v9NjqhkzSmj6KRBscR+CzTiD4f5LXZLnG80Q3EBcV/9tvXeQ719aWwR+nUSYe5Wsy3ziczuREUtbN5trMfBqHxq9d3FpCaq6jGIQuNTJA/ndv7XN52OGl7V/Mv/zx9dvAT/9CMXKl1BXg68APnvC9/xb4bwEuXbr0RT7tr2U93B06lnrE0+QXUSI+vnqhy7sHU1ZaPtt9SQ3Kyopai8tdrY0IaBT83b0xP3tQ8Z1ra7y4Jdi5MYa/uHnKW3sTKm14d3/KVj8kKSrOE+H2uspintUMhz5lZZikJb3AIbQcfMfmeJYySUv6ocerO4Nlh/s0vva19Q6juFjCF73QpawM90cJz613eWW7zywtmKQVG71PwkOjpODaepsPjyMGLQ+D0O+macE/eH64LMwPd0qiUJxS1DVlrcjKail9f/yGW7zu/UkqkWcKfr43YRwXzLKKkwdjvn5xZTkYfjwMYbEOJinH05RByyUtBQJadNvio9Iir2pO51I4L660SAqR8F9caXEwTUV80/Hpt0BrTct3eO9wSidwmCYlZ/OcD48iXFtxZa3TODhmjXukhDy4rsU0E5fCbuByOkvRgGUUoWfjOhaWBUWp0drCQmMwFGVNVtgYI0Is37HpBi4rHY/jaUKcCx5uKWgHYi+blBV5DbUxaG2oDbRcC4yhHdhM04q60vie+Oo8GCcSPuE7tD2XrCipaovAt3lpu893rq0tvVAA/t1bByR5xYfHER3f5mSeN0Ea9fJ9952PAyYWUOQfvXNEL3A5mxfiotnxsRU8GCfsDILP5XT522Cq9YUVcqVUB/ifgP+TMWb2+PeNMf8a+NcA3/rWt8zj3/9NWk/qvBfdYa3N0tOk7dn81c0zfnZ/8sSC/iwd/Grb4539Kb5jM2iKoqXghc0uP30wxnMs7p3FeK4ECJ9HOafzA/75GztsD8LG0MosFZeCuxvGaYUN7I2yJulFOjjftXgx7HA4y5ow6ARbSdTcoOVy7zwiq8Iljv8k7HAhOFmsP79xwijOlwHCIB3caZQBLBOMFjeJbVlcWGmDUhzNpGg5Fry41cWxLVq+1TzGo1TAb19d4/sfCf3SsRSXmuCEx4vw4nVXNfQCm6SsOZllKEsxCFwmxrA/SZjnEq7wNA/sKKuwlKLfkoi7s3nG3jghqzTTtMKyFKezjJunEWjYWQ1xG5FKnJc4tuKNC/3ltdJqZhoH44yzeY5lWXQDh1FcAIqLqy1hoqQluSUMn9CxqI1GG/BdC200cV7Rch1KrTGlYTX0GCcFlmdhNBR1Lc6FlkXgWcyTmrQQfnqUV9S6Zp5KBFDggmPZy+COopKgCscSD3NlDMpSVLXhcJzSbTlklcTxtTzNRtdnnheYQtMJbH7nyiqBZzOJc/ptgX7+7396k1GcEXoOh9MMG0VRyyZS1ZpLqy1sC7KybnjwxSMBE4OWt5zN/OzBmKNpJlx932XVs1nvBk/Fs5/lHvyi7DP+c64vpJArpVykiP+/jDH/8xfxmP+51tMm2EkhXdaiiNcGDqcplYENz+ZP3jvmf3n7kN2VkDcuDJ6JlbFIT7m21mEcF0wbbu+3rw7JSs3+OKEfegSuzfGsoKhqXNsiLWv+/MYxl9c63D6T378ybDcUNsXxTJz3VkKXaSpDrrbvoDBM04oXNjq0ApeTeUZWGdY7LmvdgLbnME1yosZb42mc93cPJo/cGL3Q5YOjOesdXyCDec40K+j4MpR7bbe/hIfWuwHfvrrKWZRzYdCirvUyBWd30OJknuFYFv/9X94mLWqMYWne1W+5/M7VVfqhuxwOP+nGXLzuji94/9lcWB5lDZs9SU+yLYui0mxvBEs738cfpxNIgk9W1rRc6WZdy2JtENALHH54e8TeJKXj2VxqZgmjuGB7EOIoC9cWr5WFuvM8zvn//t0DfnD7jMB1GLQkkac2Bs8yHEwy2oFAHq5t4zsyJE3LirqWBKSseW2rLRfbVkSFllg+7eJ7NvOklKmVMaz1AmylKEpNVtW0fIeiqhglhqqWThxb4bsWSSKF1SARb5UGZQyuLcZZlgWlNvRDl7QwjGOxva0qTakN3UAgutN5TuhbDDs+6x2PDw6nTNISreGtB+dMkhKNRNzZluJkXrA/TvmXX9/FscQm17Y+mTS02NS1UTy/0UUpOZW5tvVUPPsXYaM8Plt5+DG+DLTEL4K1ooD/HnjfGPN/+/wv6T/veloXejLLSRuHwF7gcn8UU9TiN3LvPGKe1byy1SPKK947mPLWgwkvPzTkq7Vhf5Jy+yzmG41/yeK5rgzbHM8yMOBairvnEZayuLre4WCcyU3o2bQ8m6ys8FybB+OUTuBxabVFx3fYn6S8uNXlxc0eN472GUUFaVahLIVChChpWfPCZk+8xw1cW2tzOs+J84p7ZzGurWj7zlIu/Th2OM9K3tqfNrj6o8Il24KjacooKSkqMbCK8orRXDaGK2ttXt7uNdBBvoRnsipcpuC4jiKJasZJQi9wCR2b43nGe4dTrlUduoHzmUX84de9Mwi5cTRnkpS0PBvHYsmg2ZsklLXmYsOTf9INvjMIqWrDRydzxklBXupGQFWSFjX90MN3LfJSowCMFNjaQFxUPLfRWcr7HVuJYCeVeL9ZVnLeyPSl281wLZthx5WBtzasN3bFudaNUAsWM9njuOTSashrax1O5hkd3ybONdOsRBlJWaqqmgrB6JWSYnUeKbQuMcY0A15FWmoagS9ayz5QA54C21ZM44LYUdQGPjqNaTkO53FOVJTYymKz6/OtK0OivGwG0Q47g4BRVFDWBteyOZyljJOSpKjwHYu75wnbvYD1jjB79scp24OQ5ze7T/xcF/CHY0vnrpT8+/Kw/VQ8+/OyUb5MtMQvoiP/B8D/EXhbKfWz5mv/F2PMv/8CHvvXvp42we4Ewqd2LOkETuY5h5OUUmsmSYlriV+J59pkPd1kIAr/93CSNh4gBtuCK6tiPJQUNYPQ5aPTOdoYxnFBqTUnUc53rg7ZHYQcT3OmSckglOJb1LDdcdnpBWz2A1SDE6ZFzcEk4WiWU9ca11YkpYQ5hK6FMoZbpyKscG3FP39zl3vnMXvjFJbxDkIf7AZyWTyOHd4+E4fCa+sdorxq1J05J7Ocb18d8j/9ZI9RXDShzwKPWLbNOwdTLq4KU+RxeObxFJz79eIUIj+31QupjbymWhtanrOEaJ52Uy1ed8tzeGGzw9E05TQqeH23x/MbIru3EF/3h1/T4zf4Ip5v2Ba2xU8ejLl7FrPRDem2XWaZbOpzZDB9FhVs9sTL/R++uMYsKzmZZ+yPE87mOaDIas08rZk1mHelJUoPFHFRU9SG3UHA6bzEdRUtz6bKNZmRLhpLYI+8qjieZvQCh7SqsZRFUWscS4acpdaMk4r1nk9WaAaNaGmt4xE1ea8GwcLzUmiiCqEaKkB8MQFjZKiqDQfjDMuGQShOkC3HZp7XPJjE/PWtU7a6oisIHIu/+vCUoAnwnmUVs1z+XoVw32sUSSkNSsez2RpIctWTwingY/jDttRygL046TwNz/40NsqzdNpfJlriF8Fa+Uvks/+tWE+l1zUeE3IhjZnEJWCoNGAMgeewN8lY67q8sNnhZJby7sGM7X6LH9w5l6xCT26OBXc5yir2Jwkns4yO7zLY8IizirSsiPKSrPRZ7wS8sz9mnJastz22Bz5FWbM7CFGKJj2+pu3Z3DuPOZxmlBp2V1u4lsUkKWSjcWC7J1SwuKy5dx4T5RUtzxLBhTYcTlKOphkfnYg/yyiWzeZkltMJxPDo9d0BwNIpca3tcxZLnuWVYZuzmSTTDAKhQu6NEgaWDA4XHi1POwrPUglhbnkf3ySCmdZ8dDLn1Z3BM91UD2OeWVnzD66vMU1LNroBoWtzHhe4FktO+NNe073zmNBz2JukZGVMlJakleb+KKbbcvAda2k54FgWGz2f3UFIJ3DZHoR0Mof7owTLsqgNhK7iznkqcnxLURtDWtS4lsWg5TJoOewOWlwYtDieptw6S3AdjVMpnNrCGE1thODkWLL13jmLsJXF7iAkcSrcymKeVxgjG3Nda8q65vpGm1FcYVkL7F94/rWGQkNdGDxHMWgLXVI3MgSlED8XA7Ytat4ol8LsIJuH7wqGvjdJeOdgwqs7faZZiWtbZKUWdlHo0Qkc5nlJUQrMk+Y1qSehG8FjHjGL9XjBfeOCzKIWX2v51lPx7Kfdy0rxTJ32l4mW+JWy87H1aRPsQcvjuy9s8MaFAf/X//ABxazCscCxLY5nOWgoKulCNnshlTb8+P6IujYEgQySLq91sJXIlJWCv/ronLyo8VwZdgaehQ386QcnWOqUS6ttfvfaOu8dzhgnBa/s9LAti0prXCxWWx790ONgnJCUmqSssJXcrP3QwbEVgS8KzcvDDhvdgNN5xn9875ii1vzOlVWivFrKoF/f7XOelPybn+zx2u6AQegyjgtunUR0AimCN48j5nnFIJQh5LDt0fIcTuY5/bYEMqtmbw+cgrw2j6TAPO0o3AtdXNuSAmPEu3qSiBFUN5RO/OH1aTfVk/jkb+1NePdgwvE0Y6v/qNve469pkhT87P6EtY5P6LX56Dgi9BzaZc0oLmWDarlMkopuEGBb0PZc3j+as90PG0OxknGcc2VNUpVuHM+ZpBVlVdEOXDyllkNG17UJbbkdA9fGsRW2JUKaqoZKy8+FjvDO86LGGINBMUlzeR8MtAKHlZZLlFWkRc15XNL2bSZpxXrHY1aUeI5FqG00UBU1EgMNShlcW8npM6+ptKGqNEaD7YA2EJfgKOEqVGiMgbo2zcnO4CiLD0/mDAKXwzijNIZ5WhJ3hM8uUXyWPKcyjR+PR16Zp7KPnpYI9Fnrafeybaln6rS/TLTErwr5Y2vRzS1ueoPi+kbnEz9zbaPDVi/g3aMZSV6hMbRdi3lWcRbnXFpt8dx6hz/78ISWa6MNrPcCTmcS/DDNSoYdD200nm2htWZ/HBMVmroW06rnNjocTTOysubrl1ewlcK25fUcTqTj9x0L15bh3e4gIC0q2q5DVkkh0bWhHwpFbbsfcDRN8RxLfMsdi5/eH3N9s8truwMCVzD4qDl2/9mNE9KyIq00eSH0MINhpe2z2w9Ics3JLOIfvrghpkhIZFucVVi24myeMc1L6lpT1FJ4Po3adXWtzf444eZJxCTO8RyxOvVdUb6ezvNHotF+0Zuq1oZXdwa8uKl5e3/Cz/cmvLHbf6Id6p2zmNW2h1JwPs/pBi5dhFGEksCNeVqy1vU5mecM2y4t3+HvP7dGUdWMmk5yoxNQac0ozhjHObURY7JJXNIJHC4MQrSBkyhju+vT8ixGcc4P7o3JigKtFZWWjrjUQjdF1WgEPgmUK4O/QtKg6qxcWuZaCuq6ZqMjc4CDWUreZLCihMFjK/nbtZbXNc9KfMcm9GwwCqVglpUUlRTyRdGv5cfxLena87qmKkXZGU0q/DWbVuAwTQqKqmJ/VrPWCXAthaUsklLjOTL32emHZGX1VPbRp82ZPg2rfhob5ecPJs/UFHyZaIlfFfKnrMVN/zQ89vpGh++9d8ylQciVYZt39iaczgv6oZjsv3lR8Lw3L6yw1vG5cTRjf5zQ8YWFcG+UiMTbUsRljaUUo7hknpV0AvHMyEpNx7fwbEXS+GZEhUiz754nTLOK0FGsti3GScFWL+BomhOZkgurMig7mclAzXMcbh7PcRuaY8d3GHZ83tqbcusk4vmNDh+OYk7nOedxzk4v4MbxnHFSEro2l4ctzuICW4Frl0x9h37gsdn3mWUl/ZbLpdU22hj+7MYJx7OclZbLelfer6LUDec3fOpReNDy+L3r65zMMyZJgUHx3HqH5ze6pEXNnfOYTuD8UjfV40XhjQsr3D6NuHE84/kNwVofDvqYpSVX19p8eDzneJZhjKgRK635/evrvH8442iWMWi5SwOoV7b71HoxHC3JypqTecr4sCDKa1qey6yJPJPO16XX8phnBVfXOg07KWOclMRpQV7V+K6DNgrLAqMl4DpQwobJak1a1WgNGsE3LQNJLsNX31XU2nA4E65L27PIS1FdurZayuZtS4REdcNaETAetDGUNcvH10ghf9hZXVlgUFSVbrB5g63EsXCjK/DfStunrMWHvLI006Sg7UsnblmKkyjnd58bAjxiTHYwSbm4ItqKhXmWBH7I6fazBo9Pw8GftdP+MtESv5SF/FdNCXqWIcflYZs4rxhFNY5tcXm1xWY/4JWtHpallkOYV3Z6/ODOiHvjhKLUxLmE+O72Q+aZiGqqGgwis660wXMs1gchaGE/TJIClGKelzw4T/jp/REbHclMPJvnXFhpkxQ1UVHx0naXo1lOlleiRPQ9jDGstiWAVymLvVHKKzs9Dicpvm1xNM2YZCU7g5Bh2yUuKt4+mHE6a2h7WnPrNMJ1bNquOPO9cWHASstbKjSHHY9Xdnr86fvH9EKxq51lJXFjNXB9s4vnWJ95JB60PJ5b7y69zxer4ztklfCjf5mb6nG8sxsI3vpgnDxxiGpbCse22F1p8eP7YyptaLs2vdDnzpmETHz90spSmPXXt065eTzn/ijBsRVlVTNPS94difBmrSu2wdoYYkuxFrrM8pIHo4SsrLk2tOm3PEoNx7NUiqpRDZ/bIivEWREQuMMyKBRJJiyYpbNOLQVdWaL0LGpNnJVooxnHojRdaXuErs0oLcQ6t7ZQisb/xZAWUrRtQNnCYgEp4LaSzlw2dPl66NnYQF5rktzgeUrcM+OCuBBIxxihzRYNXVFnFUcm48E4ZbUt4rN392f0Ww6uJdmr46QgcOyleZZoFAzdwP3MweOnwTK/SKf9NFrib9r60hXyXwcl6LOGHAv+90tbXcZxQVpJF/KtnT5xKR4bnmOx1e/w1t4EbTTTWDycaw1fuzCg0pqfPchwbYfdFY+75wmh52BbEvzQ9Vz2RgmjOCf0HU7mGZ5js9LxeevBhP1JxitbXYZtjw+OZwxClyQ3/N71VdanKQ9GCUWlcWz42oVVpmnBX32U4xjDsOPxwdGM9W7AlbUQ21KM04JZUi67yUlakpcVtm1hSrP0U/Fci7TUGGCaVhxMJE3o5e0u46TgylqH9w5mdAOX7X6IZ9t8cDSj1pp5w0//rI330wbOz4KNPutjns4l/b0fOgSuTVKI4KqsNJv9kIurIdOk5M0LAx6MUlBwbb3DjcMpZ1HOmxc/fi2rLY8/vXHCesdnlkmKz2rHZ5ZWTNKYotT4nmK142HFBWeJhDBcXm0TeGIx+6O7I17Z7tHzXfotl8NJxiiW96wy4BgZNmoDRWmwlEEbKOuP9XU1DePEQJoLrTAuZEhqIQPLogbHhrqGsq6XuLXWhrI2WA1+YsyyOQearr8Z2lq2hW8LB76qDHWTgtT2HOaZGHg5lgxQzxMRIQWOjWNbKANRUzy1AW0kWWoUFVwctnhtp49tKSpteL9RwUZZtTSDW/j/fNqM5HEBX5TXODZLU7ZFp/1gnCzpr3fOYq6u8SvpuH/VzeeXrpD/KihBj7/JSvHEm/4syvnzGyccTTPWOj6v7Q6W7A1jRMxgWbDdFzbEuwdT9sYpg9Djxa0eaaG5fTZnnhVcHHbQBlCNFLo2y+l9UpTcG8XkhYQiW7YFRuHbFnvjBICsqLk/Ttno+vRDt/E5EbvaeVrJAM22qLRpjrkB/+S1bd7Zn3A0zVBGsd7xOZyJ2900yTmcJHiOTVbUOECuLPKqarIVLSpjiLOKrUGIrg0/fnAGSrHT9/ngcM44ydnqBTy30cFSCs+xGSc57x/MOZ0XXN/sMIqKZcr60y7kXwU2+fhjns5z3tmf4NmKlmvzk/uTpeFXO7CZHIvb4TQtaHsuz21I8ag1DNo+jm0tvdABVts+SV4RuTKzAInRW+/65GWNZStc20IbQ8sTafpaN+DCsE1VG05mOY6leP9wimNZ1BoWbsVKNSIdwFHgOha61BQfG1ziNJ3yAgJp5pEY5OsGwcwdpUjykqvDFusdj/eP5hgMgQ2lckjLmsCCpNB8PJ5uXgdgWWBZirquieuatufSCR2GbY95UdIPPNIqxlYWjiWUxqwocRxhuBggLiXo27IsvIY2OYpzVkKHqjacRTmXhx02uz6jpMBzLDQabWxe3Oo94kH/tBnJLC1xLMWHxxGBa9ML5JT4s/uTpQL76prc+2sd/zMprZ9n/Tqazy9dIf+iKUFPepOnaYmiZL2hqy1u+td2BU744GhOnJe8tN3nxa0eB5OUk3nG/VHCH7y8xXrXF8/qD094fr1L4IqM+N4opu053DqNsC3xg7YtoSMGrsV6t808KzmcCLfbVrA7CAk9m62+zzv7M86jnMARg/44r7mVRlgKbp3EKDRJqWl5NhhDXMrJoOvbrLQ85lnNt6+t8Vc3T6mMYZwWrIQeN49n3GuyOV/d7qMsKcKu2xyHS42lDGdzjdUNOI8L/s1P90DBd55box947I9T0rJmHBe8ujvg/nlMVtV8eDzDUzI0W2l5T7SNfXw9CZvc6neazfYXD6x+0mOeRTmvNZ7Y7x1MOZlnBJ4tflTGoqxqplnBWid4JNwD4GSWic1vUS2vjzvnMetd8R5Zawf0QoftbouDccJWP2BvlnE8TShqodtZCjzLcDTN2Or5OLZCl1oEQxbEeUXg29SVpjQGFxkwai0bdFk3wHWzqodML8R4TTrvRbFXgGlsaG0FH51GXFptcWk1xLEllk5XFb4tPHRtHnrw5vctRPGZ1xoLGgtaCw2cpQWuZVFpeGGjyyQRC4IoL3FtG88WnrzRQn1URjB/z1cN1VERFcKUSZY7lPDoH4ZD0qJuwrXLpQL0SWvhYfSwbYRSog14kikb/Op44r+O5/nSFfIvmhL0pDd5oxuQP4THLm76BWNi2PaImrizBRf5aJrRD11CzybKKz46mXPzOObuecqLGz0CTzFLSx6ME/bGCfO05Mpam5O5yMP/wXNr2LbFD2+PyCtNP3R5ZafPsO3xw7vn3Dyek+TiqlcZ6d5nqagoHdsir3UTuSbYrmcrur5DWht+/GDM7kqbwFX8+O6IvNb4jsVK6HE8y4hS4RMbbfjweEZR1RgjOH8v8IiVGEZVWlNWInZKioqW63I8y+kFHt3AxVJCQ5unJUWl+fGDCaMo58JKyGbPZ7Xtk5X1U21j4ZOno69dHADPxvv9rPUw3vnnN05YaXnU2vDuwYxpVtLzbarK0PIdtvsBx9OM3UHrE14xlgV/8Momo7jgwViG1leHHS6uhPyPP7pPXtX0wpC6MmhjsCwlql3HwrYtaq0JPLGu7RcVxgTS5TbGVr674FTXWK5F3xJBTlbKYLOo9GcKN7JaIJbFsgGjIdcG34Gyqjmc5rQ9i9CVf9LSgBHcfSHVV8jG4Nhgaggd2RBankPoSU5onFe0fZuW53Beata6PsOuT9f3+PB4Sj90KbTBsWuSXARNNQbPlo2z36hhi0pjjCF0JQx6mpW8utNbfnbX1jufiCpchGs/SRT2/Q9PWOv4GCOU1qyseWGz+0RTtsX6VfDEfx3P86Ur5F/0sftpb3JW1ks8dnHTL9bOIOSDo5K9ScoslbDiqtasd1r87MGYtNDMspKtfsD984S390f0Qg8QTu1618dxbG4cR2htuLTa4p2DGRs9n42+x+VhSFEbLq62OJtnovpMSgyK9Z7LJK0Yx5mYQoUORWWIspo4k4JsW4KVpkHNetdHGcV/+uCQXuiz2ff5r1/c5E/eP+a9gym1FuZDlFXYtnR8fuNJ3gs8Alex0nLZn6RLtZ/WkFeGbgB3T2PSoubiSggYBm2PP37viEkT4rzZ8ahrTVrUxEVFy7WXtrFPs8h9vGBnpeY8yqm0WYZptDznc3U0vdDldJ6zP0npBxIjFhca14aVtkfQUEkXKtcFFXWnH9L2bd7Znza2rLkoHT2bbhDwz9/Y5Y/ePeSDgznrPU84yy2X9DgiL0W5uYBK4qLm1omcqKxG2Xtx2MZWMIpsorKm71j0fI/a1OyNBLBOCv0pf5ksg1wDi7WAXFqO6B58x8axDJZtERc1dhMAUmrByFX90MDTEjzdAHkF3cCi6ztkpSYr5ARR1oY4r+iGHi3fFggtLrEbNWtalIBC2Ya6EqxeTj/yXvQDl9C18F0L37WpjeZC41u0WKO44PXd/iNN3CJc+0misDcvrXD/PGGWlXR8EbnZlnqiKdti/Sp44r+O5/nSFfLPSwl6uHgoBbdO55Q1y/SXbuB+4k1WCt7anyxj0nYGIZdX2/z4/pjStRm2XV7a7uHaFqNRwtEsY6cvhlB3jSGtDJNRQujZBL5D27UIXHmcvVHM0Szj+maPV7b7fHQScTxPsZTi5tGMThPp1Q8cYSA0Ks6iFM8PWykKXVNWgj8u/kHDOKlICpGRTxLoZQK1KKV4dbfPn31wzINRSlGJ61ypNaUyeMZgjPRi2kBlDIOWR1ZU1I2daaklazJwbNJcNoKzOMeyFOtdn9WWy2lUMs9LWp7D/VEMSnFlKCHCq23vE13299474uqw88jpKMoq/vzDE97Y7dMLPk5QemGzS1bWT/iEn21dXWvz43sjHKW4ut6mMjKM3ej6zNKCorQYtPylIvRbl4dLiO3KWoe9ccI4znlrfypYsFK8vN3jd64O+V9/4wL/6cYJV9c6nM4yDIZxUlBrLUwcDRpDx7fJKsO9ccqw5bK9EqKNZtL4sYRa0fU9amPwbQdNjkGKq2WxVF8ur9OH/v0QxL5crhK2iWUpPNcWx8G8ZJrVXB62aK3aHE5yQtcIs6TWVBqySoamntiUE2UaVEle1RS1fD2rNO3AIXQsHKVY63i8ezAFBRaKsnE6tBQUQNg4PxptSIqafujy2oUBKy0XrQ2uZX3CTfRgkpLkFXFRPxKJ+LTO9o0Lg08wkh5u+n5dPPFfx/N86Qo5/PKUoMc9xd/an5KVNa6tiLKSD45KLjfWqIs3eZIUzFLJK+wF4lfx870JF1ZCXt3pcbFJmxE/lTPeP5pzMEn5wJ2RljWeLarEvBRYYtjx8BybWiPhA8oiqwoOpykfHM4ojaTqhI3PxtFc0tjXugFbgc3d80RuIC22tJ3QZZRKco6lpHuCpnNGcFWUTPtnWc7xzOb//cN7fPvqEM+2mt9R9EIZdFVNiLDvSgpRPxQHwH7gUBtDz3No+w5ZmZKXoLA4T9KGDaHp+fJ9SSuq+PBohjbg2TansxQF/B++c5lRXHwC0qq1hE48LPpZhFAoZT0SPHDnLObV3f7nuoa2+yFJXtFveWwPQraaHM1JUvLiVo+2Z3MwychLzc4gZJwIDPbO/mTJwZ6lEprcDz32Jyl/9sGxRM4FLr5jkVeav7t7jmMp0lzL52PAd21s2+ZrW2I4NknFr0X8d+SEt9r2yEpxh3Qci15gM89qOTnVH8Mei7Uo5I8XcEsuAbSBtIRAGbJCNu9pWlABB5OEtudSaWFNlXmB61hQG4JGjGQ7FgNX0oYmjX+4BeRN9260XDv5OGG1JWHik6RooCWZ3WhtcG0j/HMDtqP4xsVVXtruopRw0t/Y7ZOVmu+9d8R2P2RnELLa9pbReo5tces04qf3x1xea/HSVo/H16Jhe9hi4nENw6+LJ/7reJ4vZSF/lrWQZH90Mn9EnbkoHjeOZgxCD0JDUWvanji6nUU5f/iaDFB+en/MT+6P8R2La2tdZk2oQNcXF75usDieJ9w4mjNPxUUwK4VDvNLyKesajAh8Wk22YpxXKGVhYYiLEs+y8GyLrIE4jDGczHM2uyFFZXhpq8fRNOXmacrhJKMXuGitCR25UdwGg7WUwrYMNaB0cyw20gk5SqiPaaEpqox39qacJyWz5vksTzaOzFKUqcazLGxHkZaGo2mOb1nkWuNbFp6r6QaWHKm1YRgE7A5CPjqNOI9ykZ/bhryq2ej5nEcF3dDl2lqbNy+uUDUF8HFIK3AUb+9PH+m4RolAVB+dzKm1aWwHLPYnKStt+f1flsq1MwgpKs1L233mzczjPC5wbVjvCnd5re0tI97Ssmaz63N/dM7zG10+PJ4x7ATM0hLXgjgTE7S/vHnGNy4PuH0a8c7+hINZjkJTarCaIIfK1BSVFKU0ryV707M5meW0XJt+4BJ4NistsW29cSR/v2tB6DoUVi2YdrM8Sxg1D59RHPUx40XSgWjYMJpZWkiXbAT3LiqFUrXEsGWSSmSMoahqdOM2KZmymij7+FkMLLv1qtacxxkd32GrFzAI5Z6qa3AtG9+xiYqq2VikiegELkfTDCzDd66ukRQ1f3bjhKSoCV0L11KsdXy+994R652A/UnC8VlMp2kWHoxTtvvhI8ESDzdsC3fLpKg+xYv8V88T/1U/z29lIZ8kBd+/ecreWPBPMLx3MGWaVvze82sARHlNr8E/80rz4lav8ceQY9rDWZF5UfPH7x8RpRUow4WVEK8JKv6LGyfMcrHm/OlpjO9atD2bcVqSlhUtz+bBKKHlOczzirSsWev4DAKbaVqQFYbrm20urITUGrQPd88jzuY5aanp+w61Jb1WlmvKWjNOctq+I1imsXBtg2OJd4WtBM+saYZUSgZoaVmRFcI+GbZ9Dmcp2hjWu36jxMto4+AohVGGQmsC12KWlPi2YJYSsiydaF4bQs9m3XcIHJtKS4xYYeDuWUTLs6mNInAU/ZbLq9s93ry0sjwKP8kidxQXGMUjeaSzTE5MO4OAWVpxMs84nkmAcpJX/PDOiB/fG/EHr2x9Il/0s9bDR96O73BxtcWwI7i279jkpaao9fIUMIpz5pklzo5G+NmOEsvYUSJy+rZnLQd5p1FOWmmUkdBoz266VwO6gF5HotrSsmboOXR8j61e3QQrSFF/aavHzeM5986Fi64VpIWEWriWsEhcCwLfYpp+jLUoGkm9EdqiBZQGwsAizfUj3uNZBbqu6QYOZSmfrbEEBmj7FmleMUlLilovC/tiEKoQd02tNVnZnBI8UY8WtaHtCQSYVTVZo0K1LXBNTWYptlyHaVZy/CBnuxdyMMk4mmVLRedff3ROUmqOGhV0x3eIfIdSS2j5iivePg/j5F8m18Ivav1WFvI7ZzHTtGTQhDIApKXmYBrxR+8e8caFAZYyTdK8DNDkZwQbf/hCsCzpEu+ex3R8l42ux92zmFFU0Gkc/v70xgnnUU5W1GwPQtKyxrVEVl/WYl27uxpwNMloew5lWZN7FhvdkNAT3+6i0uSV5sOTCEcpdgchZ3HB/iim7bsYYzhPclzLQiuwlUVeG9qehbJstgYhJ9OURnODhTANLAVJWckN39AJD6YZq22fK8OQ43lObcSatKg1s6zCtW06nkNeGdY6AZFXMk9rtgcBLU+8rd+8uMIHRzNmmTjleY5Qz07mOR3PZSX0mozMmu9eX6cTOHx4HOHYku35CYvc04jAc/j9nUFz8pE8Uq0F+ml5bnPC0RSVZp6VVBoR4KQF33vvmH/1zQu/8KzkSUfvhReH+JlL2JVnC+VzmpbsDlrcOZszinLiomKnH+LYLq6l+PAkYrXlklaSZdr2bGzbkkGvZ4OqyRvfkmmaE+cB612Pja5PXIpHjUbRC23A4ecPxiRlLScwT05IRcMwAjl1eZ5I5BcslcUGXvMxLbHZeyhyqeBO4z9ujBT40oCuG2xcG1qBC8aQFiWxhAmRl/WySXAaXMeyISvFPMtxZOPACJ6tkE3GNLRJx2qGrhrqhuieVZrQFVbJn7x/LHz8ouRkLhmfw7bHndM5cS4WD6/tDB4KlpBN/nEGyJfJtfCLWr+VhXyWlkIjCwUwjouKw2lK6FpUtSbKSuKiJq8KWp7F67sDkqJaDiB+/mDyyIVwOMsIXenOLWURuA4t3+E/vH3ENCno+jYYn+M65VbDuuiHrnhQ1JqNbsh6J2CeVQSO4jQqyQpNEQjLpDI1o7jgznlMpQ3Dtke/JZvQ0TQjbcKNS60bPq/iPMlRwMRWOJbFWsfHdixsLYbStgWDVkBR1+Rlja41ukb44Y4EAx9OU0otRSora0qtwYK2a1MZwzQuMbVQ6FxbfE9un0Zs9AO2+gEHU1HFGQxHM6FfWkbgkP2pBAWs2x7H85y1rr8MKX5vf8rxLGOzFyxpYUVdy0Az9NhGKJ3GGP7iwxO+vjvgcJoxyyqKWjNsexQ1n4iV+2UCAxZH79N5xjwr+fkDEUxVtWGjF/DiVo+PTua8fzjDsSxe2ely+yzBdWx6vkNaVYySgpZn0++GSwYGsJyD6EZqXzfTSQsapgecRzm90CGpDHvnMRdX21y93OGjk4iTqKRuim5tOdS6bnDkj5dtgWNZzHOJhrObAlssxER8TENcDEhrA74tNroAbvO9USqpTrYtsFlaGVAK3zZCe2yYKzYs23mtP5bsdzw5mRXaUBUlm52QeV7S7Dl4roXX+GIqJQ3OJM7pt2SeMIpKqtrQCR0Zwjcw5LzQDEKbSVzywzsjgVu6QRMs0f0EOeEXYYl8WRKAPmv9VhbyXujiNHLeoMlatBAZ9VZfuspJVhHlBZ7jL42TFrzkhy8EY6DlOuhabhRLKS6stqiqmh8dThl0fZSG87ggLUVqnJc1upnIayP49DQrQBvBNbV4N++PBed1bMXpTGxtd3oB2kiXow20PcXhtBK5tF440BlcR+IgklyIZtpkWFh0AoU2iqKuKOsKW1nUTYhu2YDnEntWM8s0hTZ4SkyZWp5DUpQczzNqI256cdunF7g8v95BoZYnnV7g0vZdbCvDwtD2HbFcNYphx8exwXMUcVYxTUuitOTSWote6GID7x/OWG35WBZ8/dIKvSb44OGVljXr3QDHtpaeJh3f5mf3Rww7/vLn8qpmteU90c/6SetJrnp744RO6vLG7oCqNryzP+Fq0WEci4zfd22+fW2V03lON3D4Z6/v8MO750RZxYfHcwBW2i7fbK9yNM04n+fM8lLsZrXBUuC7Dk6tsS2D0RqnkbiP44LTeQ7A3iQl8Bzavs1mz+f+aUwNtFzFJDXUtdy0C7jEtkUYtiiWtiWQwzytqWBpnqVQaK0f2QQCRyAztJHQkgoSI3az8UIeakwTviEznEUxtyzoBjaTpG5ojYqWL2Zsx7MMrQ3zomrgFRttjCQ7tVyMltNn13NwHRttFFFe4rmKwLNxm5NPrWvBt0vNLHV4ZavHKMn50b0Rv/f8OpeHLW6fRYyinDcvrSxx8mdliXyZEoA+a/1WFvKra232xolg5MYVJ7qqwrEsOoEryjcLNnstfvfacPlBP/z7iwuh7dm4CiaVbhJlhNlwNssYZaUYZNlW03GJ4ZUcgx0spQgcD9+3SYsa33G4P46ZpGIG5DniS+65FoPQIy00p3HO8+tdtIGbxzNOo4KiAs9pbEkbzNNUYFsy/a+aIWboSVq6No2wI6+xVI1jKVylMEY8rZNCIJ9ai4VuquVoPE0lEq1uCk9RSReZNaeVn+2NsRSkZckP7pxz/zym1nCaFGz3A+paBlRRUaELw2lcSsGyJMMxLWp2BwGV0eyNEv7m9hlXGm7vGxcGT7z5vvPckNun0fLrKy0JwRBrW7Ps6C+ttp+Zl/v40ftgkgojqRajqY1ewJW8w0/uj9FaZgprXZ+DSUpWafqBuBi+tNWjrDW95pp6ZafP/jhhf5xwHlf4lkVpy6zBGBnc5aW870UFgRKYKMpLxnHFhdUAozU3jyL2pwmerbBdi7qqySsZdFYPQRu2JRBb0TQZClF9tv2FnzgfKzBtizivyIqqoQIaHFvjWoq4Mni2wrUMtuPg25AVmlrr5rkMcVEvYRqLhVzfwrdriYXzBLvp+C6nKifXNTRwUtuTxqisDJdXQpKiYm+cMUpLOr7h0rBFnIt/fjdwifOKldDjJJaufKXt0QscjmYZr+32CD0H11bcOJqz2vb45uVVHNtaFmEQT5WHbagfL86TpOCP3jlikpaPUI/hy4mlf+kK+bOmYv/+9fUla6WsJcT32lqblZbPzdM5s6TgxSZjc8FWOJkJY+VhuhAKkU9rwywvOJqljKOC1Y7H1dUW47RkGheklfhHKAxrXTH+WW27fP/mGVlRE2UllTaczwtKRFk3oyZwhNc7z0pWWx6TpOKDozn90GaSliijGHYaauBDHZWtPh40pYVuvKclQssoTVULZUwpGvMi8b4AGfTqhuGQNl3wgpscZaJcDDwHZdUoo8ThMMrZXQmxULx/NOOFDdjuB9w5jYjyiqrWkv5eGbK6xrMsQtehshAxUF4xyyo2+yF75wmBa0sxUPCz+2PeuDB4KkWr38wtxom87//771zhB3dGnEYZqy2PYcfnTmMJACx9rZ92nTx+9I7yqqFiam4czYjyirMoZ9DymtOHQ1KKNHxvkrA7COmHHl+7IF472mhcW7zcx2nB5WGbKK8EV641WVHz/tGMNK+bTVY+P9koS/JKXC/vj1Khe2bCla5raIU23cBjlhRLm1kHYaDYTUdv0ZhlKWkmziLxk194h5eVJnRsLDkMstbxiPOCvDQU2tCyJXHItW0sx2Kt5UnKUG04i3Oy6lE4p2YxJNVYtqLl2LiW1SiaZ3JtacNq2218YwyWUvgOjBPhn19ZazGJSwZtFwtFLxBF9HovIM6FVOBZNkGgGHZ98T/XQs19fiCQzbevDR8Zlt88jvjee0cYY7i63uHV7Y+95h+vId+/ecq7B1OhYCYlJ7OcNy8NPpWX/pu8vlSF/BdNxf7uCxt894UN/uLDE949mNHyGrOdXDcfcM2No3kTWeZxFuePPN5iV/Zsm7/86IT9SUZe1Ay7gl8/t97hf3nnEGNEmVcZTVoY+qFmHBfcO5tjKcVq2+feuQTvLg7/C553VkFZVWB9rHI7iUrS0sFvbpCyqhsTKqBAHsMSbFgBaVFQ1osuyyxNkmwFgacoKoOFotCavPok/xjk5qwbZKNtKcpa0w1coqLiWqdFK3C5ut7hZ/fHXBm2ySvDPM+Z59Lx3z2P2egG2LZhOi1ITI3vOQxbPiOVE+diw3o4SSlqyRI9jTRuozL8o3eO2OoHS1n+w5/nk6hbFxu/loNJupTILz1ubp6iEArhk66Tx4/ejqU4nmf4ttin9gKXj45neK7Nasvl9mnEz/cm5JVw9dEQtwTTv7TaJsrl9FA3842TKhdnyWGbj05m3DyZ0/YcdG3wsJjEJVaTLOU073VVSQgERj4/1Qwry6rG8SU5CQXK1ihU49OjUNpgu4qqNDL4tBWVMVSVfP62Eh/1aVbJUNqWE5uyLZTWy03AUXKya2nDKC7ExsGyaAcOaeOBYhq+uCe0cLK8xlZgXANNExOXNaaW0wLGoBrhk+8InfEsylnrCHzZD13GsQjJjIGNnuDe/dBFG+iGLlH6Mdvq4mqbvNKstn1mebUMh5hnJT97MOb+KOHeWUw/dJmlU+Zpze8+N/yECvitvQl741TEdsgp7Hie8dHJnBe3er+RCUCftb5UhfyXpRUZA2/s9pcDs25g0w8DjmYZzzWmVlkpwQ2Pf+gLP5NvXBrytYuGv7s7AsSt7iwquLDS4mCcMis0vq3Y6EnK+0/ujdgaBLyx22eUlBhE+mzVD6kv+Vg6jRZHw8C1qSrNtC7o+i5RJnxfu2mvlAWukSxLhWGalsvBWY0cvbuuwnVsPNeiqDRVLQNJZQmP+bME3kVt8JRg8F3PldQiSrxm86vrxpJWKfK6JnQVtRbY452DCZU2tFzxFFnAKXvjlM1uKIpaxPZ0rRswiguirOJgmvLyVg/HUeyNE37/+vozpL/I99c6/kN2pRWHk5Rh1+Py8GPtwMPXyeMCjUvDFuNEYCXfEXsC35Xgg/Oo4K8+OsV3HTq+TVHKYFcD/4+/vsPuaou/d2WVV3f6jGL52UlaELo2e2OxSS0rQ+BYOB2PoqyZ5SVo8F0ZOtdGLTfgotKNgEoRBqKInKQFW72QV3f7jOKM87hgf5JhGjylVoauLza0caFRpinOgFZSpBciWKOgqGTDQH5daK8GlNJkWvjdvqUa7rkC18a1hfGktWDdIvzVdAOPvK6bsAdDaNu4vtUkD9UYauyi4lK/RTu0ubhqcW29zZ+8f4xqaJ4YQ1Fp2r2ACjlhTPMST1lcXA3ldKMs1joCgViWBLssTlUHk5Szec4kLrBtxUojpLp1GrHe9Xjz4sojXfZHJ3P6gehA7p1F+I6i7dl8dBJxcbX1G5kA9FnrS1XIf1la0WKQthiYzbOSn+9NKCuNZyuysmom4O1P+I4fTTN+cn/MIHRIS4PT0AotZfj5g4mo1TAMOz790MGzxLp10HLpBS4PxsKLLSuzhBIq83HSysMCjmlWkxTCTMhqKOuCauGdUgv04dqKti+ez5OyXLIHbAtCi0bkYeh5NpaCcXPELyrxpF4EA8CTlYALL+u6NlS1ZqsfkFUV2/0Of3vrjDSv2E9KqlqqyGrbJS2FX/zB0QxHWWilqY0MrHq+gzYWr11Y4WsXetw6mTNLNW3fJs5LzqOCSVqwqYKl4GRvnPLW3oTvvrDxTNeE2JXOG7tSl7tVxN3TiNd2Bkvc8/Hr5PEuf56JMdgsq+j4Nt++OmRvkvD2/oSVtgsoskKz2vGZpjnnkXC8d/shf3PrnLf3prx+oU/Ls/Eci9MoZ2+cch7nBK5NURuyqqYXuGy0DbPmc1FIfmRWyWBPLbrxpi3vNsEegWsx7Hji521ZTfOhxYPHGC6utNgfJ4zTkrz8mIroNbxD19Liw6NkjhJ6LklUCKvFagy1ao3nys9sr7Q4TwraroMdKBGrFTW2MvieiLJcx2Kz67M/zmh5tpheAW3fwXMsokLR8W1macUsrzAK3tjtcH+UUBuI45KWb/CaGUrRHAmNgufXxAl0kpb4tmJnJWSallwatri23qEfuvz0/pgoq/jgcMZb+xMxgmsF1Fo+77LW3B+ln+iyTXMmbXsul9c6nM0llcmxrC/loBO+ZIX802hFn4adP36Uti3FhZUQ31GcxTnDts/lYZtu4HIyyziLcv7dWwccTlPWOwFtz+LBJMVCEXoSx9ULPdq+TVHKBL7tSifebdn4boDC8GCckpXVcnhYGbEX9flYGPLw0ojt6IJvm9fgO8KUWbBVVts+tmWx0vJ4MIpFLajkd1qeQ8t1GGclcVFiYeHaiqoyy0GV74CuWAYNPO5W4jTD07IW8yzHVmyEAeMkZ5J87BpnCw+SSWooSoPvWqSVxkbERCttyYNMq5qu0vz9a0P+8LUt/uqjM+6eRZzORdS0N0pxLIusNCRlTdtz6BuXj07mj6SlP20e0gtd3t1f2JUuTmoutm1xMEl5ceuzvavhY5Xnw9eWbSm+f/OUqpZueWsQUFSaNNdM0oJJv6TWIpTCwA9unROXNVdWW6y0XH50Z8w0LWh5LV7c6nE8TYmKitB1ME16j6413cDBKRV5WWOa2UdlEAtbx2DbYjzlOzZQNjx6cSjcHQSUtWZeVJRaYzdSzsCRKDejBTpYZGwWpcGyDeTlEt5bCVziTE52xhi6bZ9OKIKzWVqCsnEsi5YrFgGaCk87DFpywrAsESn1Q4HiqsaJ03EUU63p+y6v7vTohi73xwkns6JhwzSBzkWFmyt0ahiEHv/VixuUtWGSFpxHOdOsZKMb8t0X1nBsi9unEV+/tNK4IR5R1DKjEEhGzLs8x8JzLMr6k4yV6xsd3juYChvHtdnsBQSuxSs7/S9lEYdH4/d+49fVtfaS722MWf73woCpqDQrLW+Z5zdpOrDFUXphS+s5Fr9/fZ3/zTcu8sJml4urLTq+w+3TiD9+74g7ZzH/4Z0D/urmKf/+7QNcu8EJK815nPP8lnBXW66D5Vj0AofAk+5Eaxle3jlPGcU5AmzK8XVh9q+N/LfdHHsfXsIX/xh+qSrISoOjBC7R2pCW8nc7jkOTs0tdy9BukktWZF7IE1q2Ra3A92SgZFnWsgV/vIgrpINb6dgM2w5bXZ+u73JpJSQpNbatiPKa0LMIG+/uWVoT+rY4+1U1ugmUiHLNStuj4zpc3+gsh8g7gxDXsQh9h7KWGLPVlsdKy+Nsni3fhaTQn/qZPnxNjOJCjvtGrF47vsNqy+M8zh+5Th4P9/3Ma6us2O4FXBiErHc88lJz82QuYRO+jdbSEdu2DPo+OJoRpSUPxikXhx2ub3V4dWfQBCzAxWGLbuBIULdn0/VsAs/BUhZpUbPV85dB3QCeK3h3L3CZ5xX/80/3eXtvyjguJLtSwYWVFrU2HE0ystJQmxpHCTxmKwm3KJphv+uIgKfSEJcGAwRKYDrbsVnvh2z1Q17fGfD8eqdh64jUfpJIhqiuoe05bPd92q7AJ0GjS3BdG1cpCi3S/iSrlurYW6cxUVZyFhXUGGaNck3cJQyTRE5vIAV8vefz5sUVnltv89xah+1BQC/0ltDqnbO4cUMc8E9e2+a59bbMIGzhqOdVTa0Nl4etT3TZl5swjw8OZ7x7MGGelVxYaT3itPhlW1+qjvxp5jPPgp0/aWA2SYolTSkpag7HKZvdgFGaczDOm4IlDonSJRmmScl646tdaUNgW7Rdj8NpTuDZdDybs6ggLsrlgCctNJ6j2GjJ8THKKlzHLCljuno6bl0jF3tRa9JKbszNfoA2ikEI51HdyOahrCS6q+NZGISL3gtcPMtikpQUql52+48vBwhcOXImuRYaWZSz2jbcG2tCx6KsFG3PLB30Au0winKirKQUyJyqEpw/LytmWc2VYchLW/1HTkff//CUi4MWgWtT1jUPzmO2BwFJLl7ld89jtDYMQpdr652Gx/zkecig5fH8ZoefP5gQ5zUrLZfXdwfYluIsyp/ZpOhJ11Y/dPn2tTV+cPuMXuCyP02Wc4FX1vtMk5JKayZ7JaEnAQt5WXO38dtZhCz3QofQU8zSmq1ewOW1DpdXWvzd3TOO5wVlw3gqa8OFlTYPRjGurQhcW8zLnCbp3hjyuiYvjGwkxnB/lKCUoh+4ZFXFNLVwHYWrNFluKIy4Hirk+nBs8O2P5zKWDVlV4yjFeZQzbPmcxymdoENlDB3PZpaJd/5pnGO3PEZpyTSrCHyHF7Z6jJOCru/w/tF8OeC0LAtlDP3AwbKkgfroVHE+y8CS92UR+tzxZHOzbKF+WsDZPKM97DBNhdKqFEtGUduzafkScr7S8lBK8d3rG3zv/UP2xxl5UfHahQGv7PT4w9e2P0E7vH0a8fJ2n81ezigpsCyL1x9zWvyyrS9VIYcnF+RZOnkqdv40yOVhBsyLmz3+4uYp98dy9NXAoO1Ra01c1qR5zbAToIxmre1x4zgiKWo8RzHsBOS15vlNZ5mUk+QVXd9FK6graHsiBrEtaDkuu/2Qbmhz6zQRwyVbNwrPT/69hiaqS4gBWLZCaQVK/DJc26IqheNrml9YHMO7vsNKy+U0KpbwS9kwsWwAJSwG17bIGnzTtS1ats1K22WcSlpRr+WJn0gsQ7zQd6gqTa5rlCWOer4lwQkoUfZ5luCqnm1xPMsfMTXqBDY3jme4tmDag47P3igFpZlmBVv9cNlx/uzBmLYvwqzFDbzgCi+M0d7em5IUNVeGLVqew62ziAsr4fIU8MteW39+44SrazI3eXt/woMJvLQpLBUJNBY20PE8Y7XjE7oOcSn5jwsmxFrL4/KwzUrbl0LZ8TiPcg4mCVFes90PSIv6/9/em/5Icub5fZ8n7oiMvCvr7uquPtgkh8cMh7OzMzurtbS71q4kS4K8ECRbNiS9EARYtmwYECzrHzAgw7AACQYEWX4jwTKwXq8F6xiN1qvdtaSZ3eFwyCE5bDbZd1XXmXfGHfH4xROZXdXsJvsostnN/ALETDeLWRGREb94nt/ve2AYKYMgxncNlUhkqx64LFSkW5pLKo5avXu2mvNEWcHuKGS56tLyTQ4mBW1NDR+DpEDoYBalPF5X7TJZgDA1DCGRomSwILB1SHKB0GAS51zZG1FxDGUfkast5DjKqbs65zsVBEpg1wsSoiRnremyuVChKCSX90fUy/vfNnU0IXBNg71hoGyPM/VddScp3UlKrOcsVR00oawYBnFKnEsWqxk5BQW6apeUjKJhmDCIUp5bqs5arb5jsLngK99/Kdlc8KnYHy9vRxd9U5fNIMnoTpKH9ur5IuFECrkQ4leAv4OqD/9ASvk/nMTnPiju1zufJBm//satWaJIlisFX901ubw3xjY0Fn2HrX5InEo6VYvtMs+yXbUYhQXdccJC1VZFVNORsmB3GOKaakUwKlsZVdtE1wS+a1J3lUHWIEwZpCmWJpjEKYYQuLaBRHLtIMDUS8/tOFUPy30wbbOYgMwlu5MQ1zAYRumUfIDGkZW2pPTIRnmpFEr2nOdF6S9zx9a0KJThUlEonw0bQZLn2IZDw1Ey/jCLcXVBmBZkuRrYGYaGlgksTSPXCuqesqGdJBm6ENR9i8Wqhe8YbPUm/J3f+oB2xUZKqR4YqXjINw8DVmqO4mrHyjvjKyt1hlHKIEzZG0a4tsGFTnX2AE/bK2/e6LHVD2cy++1ByIJvz9wpH3eFddSH/nS7Qqdqz1ooUVKQZpkaYLoGLU9R5kxNyfK744hJlGNpKd86t4CpC5KsYG8UYWgal3ZHLFVdskJ5feukuJbqVbc9m2GSUrV1XNOmFyQcotwVqxZMskJFwZk6jmkxTlQmaMM1GYUZFdsiy8E2JHEpJnAtjTgpyKSKmvNMZU9M6RNeq1g0DR3f1svwEKkyYoMEWSi/dSEkoyinYheYQsO1lFe+8lQRKlmp5qiVuyjFS4VUrSRTrcwvLFXZH8f4loVtmuT5RHnW2wYrDYfTLY8bvQlpnhNlGd862+ajvTGeeYdRJBFslkV3yhG/vDssIxdjlmo2uZS45sfDR55VH5bHLuRCCB34e8AvA7eAPxBC/FMp5XuP+9kPintJcvdGEdcPJmilF/ftwZBJlJIUkrpjKke9ussPrh6y2nBpeAZZnjMK1bCmGyg70XGcqZQdVLiDYeicDmP6oWI4VCydpmsxjlM+2InJpJJI26XCLsoKBpOEOJPUXJ2qozynw0S1PaqOYpTEaTbrWQtU/1zKO0IPszSVLgrV24yyfNZ3l4Ijyj41yIyyHF3X1KCuKKiYBoeRUnYi1c9YutriDssIOYEkTjMkgq3+RKn5MvBtgVUOEpOiwCr7u0GsDLZavk2QKk8XUR7HIMjIZcw4VgZiL6zWmOgpe+OY3aEy7doeRDMa3C+9sMwHu2MsHYZRymrD5ae3h2rHkcljD/DVgwmgXoJZrhSuw1ANlYM445W1Otndk+QHxHQHt90PubI/JiskS1WbJCvY6ofcPAzwHIPNdoUwkRwGEV7piePZOi+sNPlob4wQguWag2cbvHWrz0rDZa3h8PJanfduDzB1wSRK2Z/EJLnysun4NrquFhHJsGCp5rI7jAnSTFE1xxFBmpEUBZqmYejKDmHKvfbKfrvv6Ir9pKlWWJgW6nqURi1CSqSmZPta2U/uTpLy3sxmrpiHEyVICzM1hNUQaAjGYYZtqXtLCkHLd3h+pc6VgzG3egEt12IcZwR5NvMG6k4SbENRA9eaXrmSL3BtHV0XLFVt2hWb/VHMSt3l66ebM9bSP3t7+xij6HS7OhPunO34/NZPd/gXP9lB1wTnOz41x+LK/oRRlLK54M92cPD5pQJ93jiJFfnPAB9KKa8ACCH+CfCngM+tkN+vv5kVzFJsHFPn/dtDJJK6bWKZOjd7gQpcCBN82+SNbh9TF3THCZM0x7cMmhWL7WGk/LirNqahjLeiNKfumDQrJoaumCxV18DRdXZHMf00wTY1glipHS1DCYM0DYbjDENXvVZyqDvKZlbmd5zrOEITVHJsNfhCU25vlq7hGAX9QPmw6CjpflxmNea5GvxVLJ0gU0HMUKa5lMIOTSgJfpqB5Qgc3SAvVOjA4URxg01DDc56E3U+SNgdRASOia1rrNRtNE1jux9RdQT9IEeWxVmTkv1RhGUa7I2U6CNKciVcEhrbvaDM8Eyo2AYHY+XuWHVNVhsucZbTmyg2xamWy8Xl6jHlXdOz0ITkw70JVduk4Zr0g5S3twazrMeHwVTxNwhTru1PkKKksRVSnZMUXFyukRUFgyij7li8WK9j6gI0gcwlt3oTklwlMW20fQZhgq5pjKMUUQZp54XEtQyCRJmFgUDXNJJc8upyFd3Q2B2qot2p2Xi2ck9My4KrBpcC37KQSGxDw7d01XYT4Bo63zrX5o1rfQZpQsUxmEQ5Qi+IUonn6mhFodwMpWq7BLFKmbItHdvQmMQ5UZqUL/0CzzAIC4ljKFqfnmtlzCH0w5gfXFG73k7N4cyCzr95f08ponNl0eCYBusNj+1+yM+eXeD8orJAMHWNsws+661KaS+hVMBv3+xTdVQr9F6MoiDJEAKu7I+xDJ31pkeaK4pk1YOqraw5OtFxVefnlQr0eeMkCvkacPPIn28B37z7h4QQfwX4KwAbGxsn8GuPQyn27siyP9wfM4kTNNSw6HAQYZQr1DjPOeV6vHkQsD8My7g3ySBUtCXXMvBK69hx6RJkuwLH1LiyHzCK1aolSDKGYUKO8kmuOyqWq+Ya9GQ5mRfg2QJNaOwMAnRNxzYFRS5m3imurWMaAssQ2IZWSt5L17uiZLwIxWGvlFtfQxOcXvB5++aAJJPHBpi6WnjhWwadqsWVw3TGGY/zO14ZU1dDS1c9bd816AcZlgl5UnqaZ6CJgkwqnrEoeetZVlB1LfqTFDSBjqAXxKSZekFYomAcZ+QShMjoBQlprlR54yjlVjfEdwzyomBnGPEH17q8vFZnbxRzGCi2iW3otH3B6XZlpjo9unoKZyoX9T9pXuBaOuJjutUHw1Tx13AtNCEwdZXb2anafP10ix/KQwSC55arXNoZ4pQv1INJwmbb451bA3pBSt01SLKcf3/1ECElzy356EJnEKb8dGfIrW6AkHCmpdgTvUnEMJK4ZsH+JEEWBWGaUS9MPFPndNPjpztDxk5eKhstsmIaYqxe3LeHMec6Pn/+Zza4PYjJi4KqOyJINfJM7UINw8LWU0xDMIoybFMrKYkFiYQ0k8RFRqdiqUKJahN5jhJcVXUdTSgWja4p7r0KzBBcDkYs+jbnFn2CJOdnz7XpT1IGUYquCRqeScuz0DSPUaTCmn3b4JX1Omc7Pq2KwyTJuLY/IkoylpaqdMcJb1zvqr54lLFZtremxVfXxGxX5ts6o0gxxHvjiLbvEMU5vnO8xH0eaT1PAp/bsFNK+feBvw/w+uuvP9qT9gm4W75vG1rpVGdiGUqVpiMohJI4741iWhWTG90JYZyRFpLFqs3eOMY1dS4u1RgnGTuDkIZjcnsU8dHhhCwvqJThxHFekGUFjmny/JJPnBVcO5yw2nQxdcFWpnofcUkBEyXVKorVltQxDZqOzs4wRkOAUH3UUt1MAbi22gIL1GoLIfB0A9dR+YrIO+yXMlNWeW4ASaG211NFpSygyFXcmDHN/0JgGMyogXkxYW+YzUqhRA1hBarnSfm7pC7pTxIcSydIVK8+zZQlgJQQJ4qvXC8DMHrjhN5E+c0Mg5i259CoWHy4G+PZyizpRjfg3KLP3lCFR5xb9BnHynhJSrhyMGat9AwH1SMP04LzixW2hxHDIOG55RrnO/4jtVamij/H1HEttTvxbYOb3YDXNlozmXzVMbm4XFOKwklMw7XK/q7Pv79ywLWDgIZnoWspgyBjux+xXHfZGUTolP1nUycpCgwdmp5NlheEecFHe2MWazaGrpMUkv1RzChKOdWsKK8bIbh+OGGrHxIkOaahzyiXizWbX3pRpVtdPZgwijKuHIxndEVZttOGUabsCEr15iS+swzQUAPvSZwhNFhsOYpdguRMu8LeMGIYZriWwUGQoAEd3yLJVZDGSsPFMXXOLlSQC4KaYyLKtKFhlHFhscKl3SFnOyqb1TF1upOYKM3YHyr7YNs0qLsWN7oBSVZw4zDA0AW/9+E+X1mtcX6xesw33rdVy3KaQDQIM1oVON3xWG24H/ueP69UoM8TJ1HIt4BTR/68Xv7d54q7KYhnF3wu3R4hUb7HWSYxDUHbddXWV9fYG2VUHZOvrjd5e6unhn26WmXFacEwSDgcqu1jxdYJ44I0z6k5Gos1FcxrOGoFvdWPcAydZsVGFjCKcsJMydnjcjlZFCjVna62daYuiKaKP9fEEIJeqAITTEMVTsvQSBLlTZKVjoW5LhlnKcmRqK8CtXLXdcVDN3WwdR1dlDanqBt4oudICpJU0vQsnlv2uXE4YRhltNMcz1TcZpJsNgydpg1Nf5uGomIamiAvJGkOji7wK0rxN45SbFNxxdWMIkfTpJKnBymHk5R2xcEzdRZrNrrQkLIgSAu+dqrJBzvqe3ttozWLYBtFKQUc4wR/baPJ3jCmHyacW/BnDnZBks2S0h8GU8UfQKdqc707ASlnvPKGp1wOgySbJQrZpkbdNXn7Zp+lmkPbV0XZt01u9jJ0Q9EgD4OEjaaHayo631rToztOcE2Des3EMTXeuTXEs5SJk2PpDMOEumtx9XCCZahgiwVfeaRrwOX9CQuuyeJilVbFZBRlM0XstFB1xwlb/YAbXSVOm8Q5P90dEqbFLORYE3dM01zTwDA0KkInSAtaVZuKZRDEGTuDmDMLFYRQQ8OFqsX1w7B081SCoWGodiTv3R6xWLUV0aDiEGcFvq1j6Bpf22jxtdJ29s0bPXzboDuJ2RmGVCyDb262VWCJVL4vWSF5Za1BI0wYhOmMeTbtd682XJUcNYioljOrqmuwUnc/UTvwLOEkCvkfABeEEJuoAv7ngP/kBD73oXD3NLrqmHznwgL/5tIenq3z+maTXqlMPBzFTJKUKMnZaLl0ajbnE1/Z3tYtDkYh3SBifxRj26ov3PQcxuGkdH2TrJQrt/1hqIQXRQ6ZZBymFJpGP0yomDqpXir4johw9EL1dy1T0HBsHEPQHWdolo5r5tiOQYHimxfF1CZX4NnKOyXNc1zdIEO1PKZhAgUgczUYVfa6gu1+RFA6ZclCEmYZnYqNdAQrdWUqhYSf7gzZHUcqKCAvZlmP98qpL4AgBZ0CQ1OsCzTBcsNlEqYMUS+nimOW7AedSZSpAuHoWJoyR6rYOjXXpOPbaGjYpqDqKC95ZeYxXf2q4myV6qc3b/RmdNKpze00Kf1oQMjD4pjiz9JZrtlcO5iwVHewDI3vXOgAzLbl02tkG0odOIkzbnUDTrc9giRnEKYcTFI6FYvtfsjVfMwwyjnVdJX3u5khZcGFRZ9LO2M0HSaJmk0YmskgSAhTFTjsmTqGodHwTLYHIVGe8+qpOqdbyk8mydTi5AdXu9zuR+yP1PAVVJjIesMlKXK2eyFfXa9zaWfM9YMxaOBaGkmZ8qMJNVcyhaBi6tQdg07NYbXm8M62WkknqeSjvT11jwnFZmp5NllRcDBWPXnHUKKxD3fHnGrdobZu94Nj3uHTNoehC17baLHg2yzWHLavR6oHj0qvEkKUASLxjIky7Xd7lsGr6w3e1YZcORiz3rT5ymqNV55ybvjD4LELuZQyE0L8NeC7qBf7P5RSvvvYR3YXPs2+9l7T6IZn8asvr1B1TIZhytmyUfzh3ghL19ns+DMflKbvEKYqXWcY6cSpxLV1PFNXk/mKwf5IJ0gKao7O+UWf92+PsAwdz1K0woPxlM2i6FSGIYgyiaHrpcWsxNFVPmSS57imhWVqrLoeWR6o1baU9MOYJCvl8nmGa+nUXGXnGmc5ozhVx1yx0cKkHJqpc1MrcY0cJZO2TeU8N2U3OqbOKM5plkEMHyQTfFvnhZUqN3shO+MQTWhoQq22DXFvfjuUhl8S7PJnR6XvScU0SYui5L1T7gZM1pouG60K1w8nXD8M4NaAi0tV+kFCkkteXK7x7z46IMlyFqs2QZIdG0gt1/2PuV9e2R9ztuPTnSSznudy3S/vlf5Dpb68st5gGKb0g5RBmKi+cNmPf/NGl1GUzux21d/1sA0dzzJYa3qzvnlvkrBQdZS3eUWttnVd0J2o65MWyofc0DXSQmXGvrhWIytyPtyfULWVQRcYXNsP2Fjw0HWNlbpL07OIs5w3rqUqjLgXqOIvlD3th7eHdCoWK3WXa4cTfnitS9O30UE5IMqCV9ebvLSq+v/9IKYo1C7R1NXANM0kmiFYrDp4ls7Nw4B3bg1ouCaOoRMlKRVbZxRlRGlKmGSM4wxNU2yXqm2wXPdY8FVw9eEkxjJ01houX1mtHfMOP9rmmK7QgySjYmlc3ktxTY2KZXD9cEw/yPAdne1+eOS/VS+CKM35xmaLP/uNU1+a4n0UJ9Ijl1L+c+Cfn8Rn3QsPYl97v2n0vUxwpiEGRUG5dY8wdcGLKzX2xjErZQQZQq1mZC7pRykNT/V7VxouWV6QFDn9MMUqpfPDIEUIJb92yi20JgTIsqghaPsWaa4EQHYp74/SgvWmxzvbfZJSn2+WBTDLgSTHsTLCRA2oTKER5ClCaFi6TlDKsqeRW46j0/ErfLSnkmtUNKlUYh5DL6lgGmEiSQvFM19veqSZ+plRlGFoAs0QaMCwzA2bNiumHVWJMlzKpMQrTYqqjgVIGp7LesvjRjdgEmW0qzbNisXhJMHQBM8vVbEsxdwppGTBt4gypZY1NMH+KEbTVD9XIDm/WOX64b0VvN1Jckwk9KipLw3P4jsXOsfoh6auLARA8O72kEGoinl3kvBvL++zVHNYa3qzvrkQ8NbNPgWwVHWo2Drv3h5hCA3JdPgmGIaK7vfCQg1DF7Q85dhXsXUqthLiBHGurBVsa9ZuGEYZHd/mpbU6W4MQRzeouTq2bvDjW32arsVvX1KWy0GcUrENhlHGRsvjcByxWLW51Qt4abXOzW5ImKRYuo1nl/L6PCfNlfHV+Y5q/2S5ZLXhsNrweOtWn9Ol4+PvX+1yMElYqDhomihFZQLL0JBILi7XeG6pyh9c7/LSav3YIgvurdKdFmbPNiiKgkGYcbOr/OtrrolnWtweRFw/VBL96cLubuvjLxueCmXng0vwH2wa3fAsznZ8vv/RoUrWMTUcy8BzDL61pCLNfv/aIf0g5WAU06o4nG5V2GhWuNmb8MJKnawoZu6AaS7Z6k4QmkbVsRgESnadS0AqS9esUENP09Q4v1QlKwo0NOUVrqn09YppkOYSKQWFVEVNE6rnPQxTXFO9IIIsI8sUXQxUb1MW4FlqJZ2VDoJJhkoFAqW4zCVhosyMKrZOkhekiZKS3+gFdEp14jBUw19NU74pdqYoXEIILFNjHJWxdyj2TCYluVSWunGWU7MNznYq+I7B7lAjM3UqpaFXfxySFDlLbYevn25xcbmmAoaTHFNXrn62obEzDPnhtR7/4YvLM6bCD64c8PXTrWPf5d1ijsdNUD+6QuxNlIXD1IxLCMHtfsTucJeX1+qzdsqlnSEXl2uqMK8oFsblvTFZqbBteianGi7745iDSYIhlIOlEALTENweRKS5Es5cXKyS5AW3ehGebdDxLYSQbPVDLi5XATX0LaSk49tUbANTaOiGGpR/dDDGtQwVXJEXdLsBlqnRqarV8c1uQN1NcUwdz9ZZa3gEac5STZlv9YOEXMIvv7DEtcOAfqR2f5O0oJACTZN0g5j1ZoWff67DmW5Ab5JwsxfQ9iyiNOej/THuIOJc6VIokDPv8Pt9b3df/83S/fDfvL+PEAJDF2Tl4mqxavO993Z4ea1xz5f1s5LD+TB4Kgr5g6qx7jeNvvuLbVUsruyPObNQYb3pcvVwQnccs1J3GIUZvSCm5VrcOJgQpAX9yYibvQmOofPHX16hFyb88FqfOJW0Koay9jR1dE1jECQYusYgjEkyRe8rpA5C0PEdPFNN6s+0a4zijDhTA8ZrhwGmpaMlGWmufJ8NTQ0B9dJWtlAfg2+ZUKi0lbyUXwtUYIZrK9lGUmrxs0L1zF3boMgVh9wUSkCjCYEmBLqAOFGh1Mq9rowR05Ujn2PrpFkx6x2nqUpqqbqqrTB14zMNFavlWTpX9gNeP9PkG6db7I5irh+MZwZJjqHjWfqMUZDmBXvDiHOL1Vmgcpyq1kMvSFisqZzVlm9z9WDCq6fufMd3izk+6V55mAd8GKakuXpdXdoZsDOMZtFyzy/XZ+2UH9/scThOuNUL2FzwaXjmrJee55LrhxMGQYqpCSqWQZRknF/yKQrJtW7A2cLjl55fmiXZHIyVQGij5dKsKGGNUYY2XN4dEqQFAjkzy/pgd4xjChquzTjOGUUpnqmTFVJlvBaQpgXbvYgoy5WvixB8sDtkEKQYukanaiuVqKFRdyzqpXAtSnPaFYtBoAzE4jRToQ5hxnPPV6k6Jit1l//9B9cVvVHXOBgrZ0PfNviNp5CX7wAANBhJREFUH91kc8FnsaqEPlNJ/L2+t7tx9WDC5oJPbyMlSjLCVKLraqcQp0oMd/RlPY4yvvvODr5jfCxo5GnN4XwYPBWF/HFSsadF++hW+3vv7bLZrhx5EHQWfJu3bvQJ0pwz7QpRmrLScLlyMEYTSgW6VHP43cv7bLQrrDRcqo5yhRvFKRKhRD2owjEM1cOHFPiO8ptolmnhFUvn3a0BF5ar5EVBzTXxHYMLHZ+KpXP9YEKmqYchiJV4SNOUTNrQNGWelBUlLU8SZcUsoCLJCvJcmWhN7VBlDmmQlTalqJT1vMA09JnyUxdq0CalkmIXEsXiKZ37ypQ4JrGKJZNCORdObVPVoNJis1Pl6sGEQZjwu5f3WWu46JrG6Y6PLKOLhCb45ubCzCvc1DWSvMA27jBNBlFK2zMZx3fGrZvtCm9c732sd350sHm/e0UIHqrlUnNVn//SjgqrcC2DNMvZG8S0KxGjqMx6Kil9o0itFiUq+3QYphSyYHOhQj9MuHYwYbHm8K1zC8RZwaX9IaeaHq+sN2fX4esbLd67PeBgFGPqise+0fI4v1hlECS8ebPHi7MV/4ir++NZG3CrHzAKE7JcCX2GsXIenMay9cMUXZOkmaK+Ukw9dnKqtoGlaxQSRnGi6Jz9EEfXGQQJWSl3X6w5anht6Lyzrdo4P9kaKIFTuZA51XKZRDm7g5i6Z7Jcs1lvVnhnq8+Z2CfJcrqBEkn98otL9312P9ofcXGpRse3SXOVyKUojCndICnbXQqjKOV6d0KaqxamIQQ3ugGupT/VOZwPg6eikD9OKvb33tths+0fe3vnRUF3EiMCUfpV6Eip1HO6JhiGqcrIzNX2tT9JGcUZDEMGQUpSL2h6SuYfZQW1XFKzDd7aHpbxWbL00BDUKhZpVtD0TTUYddTgcrPj0/Ft4lwVi+eXa+wNI6I0Z0sPsMt2jGkoKXbHtzkYJ2gaCCmUwrRQftOuqRNn+SyAohCqkFuGEvQIlPCoyJV9ALIogyGUz0ZeSDzbIM0KHF1TFruaktWYpgoMrjrKbx0BSZZglXTIRCvoBymOqbjCe4OIm90AmRdouoZoKJ+Z3iRC03Q22xUuLPnUPSW4CtOchmfSqdoMw4Saa5XnohLVffvOltzQNb660ZjZEd+rfXa/e2UqHnnQlsvmQoX/7/I+3UlS/qxa4bZ8NcTc7ocANCsWzYqNqSvVZ5BkfP+jQ84sVJQNQT/kpTWVBekYOnXXwjDUtf3O+Tsvs1GUlnxqxfaRUu3IhFD3o106IaZ5wXY/JExyorTgYBxzeXdEx3fwXVOZmeWUIQ8FnqVRyEK1AkvPnaWai2UIanlOP8zwHZNTLY8kzdkaSHRNsYd0AVe7YyqWwfllH9vQ2R1FrNQc/u3lQ860PQopOdfxudkLON+u4FkG24MAocHFpSoS5Wi4mfj86EaXlbpHy7NoVWyu7I9nnjh3P7uWrvP21oBzCz5b5bWWslCtPE2jVbFn39V2P0QD2hXlhaPuoWLmR/8seKl8Gp6KQv6g/e+3b/XZ6oXqhrWNUuAC3cnxbV3Ls+gGKbahUyuVX3GmmBxZLhlEGQ3X4Ho3YBKn6EJxhQdByiRO6U4Smp7JrV6EqSnbzsMgoeWaOIZge5gor+cy8DbKVbZhdxLz3FKb84tVbENTniJ1l9/u73LzcEKc5eyPklLNWSiv7jKdZjqA3BtG+LZJ3TGJ84LDcQJS0RtdSyfXCoJEiYSm1rICoHRHnAqBikJQFAVxpkIhTA2EoRLZ665JWqgQiyjNMbWcOC/U8M5SNgS9IFEycdsgSlWoQSHh8v4YUxNouvI+L1BtGyngVMPhF19YUtv0LCcqd1XfudDh5fUG33tvdxao/Op6g6v7Y5qeNSv49xteP8i9MhWPHMUnPeDTOcruMCptejXWmw6tis21gzGHkwRLF6WRU87ptupfZ3nBW7fUrqHqKKuBi8s1Xlmr8/7uiM1OhZprstHyMHS1AxlFKZd2RohSdGMZOr/9/i7PLVdZ9G12RxEf7IzYXFDFNM0LPtwbo2uCQZQiyrSetYbDrW6EZ2qECeiWQZZLHFO5VU5psOcXlff6R3sT6o4yz5qULZyvnWqwUHUYRxm3h0p9GqY5/SBRL/ryJdqqWAhNMBinbLQ8LF3j9iDkbMdnUHr+11wTv3QgjNOclbrHt88tzK5xkGSzF+nHdCAdn7dv9dgbRzy35M/an1/daHK6XeHK/ni2MzucJJiaCgfZ7ofEWY5t6DPP82fBS+XT8FQUcvh0NVY/SPjxjR4Lvk3NUTS9H9/o0QtiruyPCEo5t5SoyXymGAJRue2O0pyzHaXMOxzF0PbojiKKQrJUd/EtkzDJcS2dG92AqlPDNTVudifsjRLWWi6nWga7g5iOD0VhEqaZ8lPRBP0gnRXlrCi4uTdhf5zwO5f3uLo3YX8U4ZoGnqWz1nQZRSlSCjzTRDME272ANJdKjm9JbEMwigtMXSClwNEVh7oo7gh3clCtDO7EuqVFTt21ccoCJESG0CSFFBilJe0gSqnaBkkZFuEYKs4uzSS3wxBDV62ZJM+RKC/sIJe0Smm3usaS9ZpFkedqkGzpnO1UWaw5M074UTMjgOeWfD7cGzGMMy7UHf70a+vHaIUPKqW+173yKGZJqw2X51dq6EKb9e6jNONMp0K9DKYukFxcVv3iUaR8Xqq2OSu400GooWu8ttH8GLsGYKsXECYZh5OYhapDEGecanmESc7eOObq/gTD0BS/2xA0PZswzuiWebJLvk2ttBXwTDWz2B7GCCGZRhG6rql88DXBD691ObdYLSmH6iW+VFM2sutNj5Zv0apY/OaPbnFxuapEOXnBrX7I2QWfD/ZGKm6t1Alc3htxvuPz0d6YvVGErmmcaftogtkc5O52CBx/kd5LB/LyWoP3d0dkheQrq/VjM426a85e1g3XVK6XjslqQ/mWx2lOxTYeS1fwNOGpKeSfhqsHE1q+jRBqO5oXsDuKyHNFZ/tgZ6h6tS1PDUps5X3x4e6YxarNxeUqu8OQ5ZrL2bbP7WEIAmqepVR2UVK2XdQy93Y/nBXMmmPgGhptz+bmYYBlaCU/V1J1DCxdZxBlZXLQmL1hiOeYHA4jbvVDBqEyQoryHJlIap5Ju2Jxux+R5DqioORVq+10lOYYVZumB8MQekFOxRLkuk5KQVEmsesoGqNEsVosQ1EgVWiDwThREXIVx6A3jpGApWuqjzlJqXuSqqNaVA3HUuG+pVlLxTZUKICt064ov/JxlFHkEt3QWGu6LNVcbg9CNE2y2qiwWFXb4buHj9v9kNuDiM12hddPt2er75PEo5glbS5UuNULlFBMmoDq0a43vdlA880bvfK+UDOB3kQ58vXDhKZnYxsqmmyt6R77XUd3DtcOJyqkuulhGRrvbPXJsoJaxWTT8qk4BnXHYBDlIAWDIKUfp2RZxmrdI5eS7X5Iw1W70OW6o0zXioKdQUJRSHRDUPcsJnFGkhV0RzGnGpWSAQM7g4CfPdtB09R5Xz2Y8NJaQxVaIQiTDGscc3l/pBwzy3ZP27fJCkleSF45VWfBd5TyM8rYaFXUnCdRv7MXJrxxvYdvq0G3ronZi/ReL9q7X35HcT/+uW8bbLQqXD1UFEbL0J4JL5VPwzNTyIdhyma7wge7YwDluqfrBHnGeqvCKEwVAyVMeXmtwUcHY+qOya+8tMyPrvf5zbe22GxX+LlzHVYaakXsGMrJMM0ktq2z0rTI8oLdQUiaF0RZwWrTo8gLbg8jmp7NZqfCwUT1O3VNwzVNNA3avsVi1VGeJ6bBKErZHaniiVAMEV1XYpH+JOVnzrYYRhkSyZLvkklJksU0PI1cKu/r1YaL0JRHyzQF3bN0jLwgStXgR0qVpF6xDVxLw9Q0gjRlHOekhXppDIMEy9QpsoJCSAxDR2Y5aemgiFTMkrzkoqcyp8jVbsC3VAbqc0tVRpEyx7J0jWbFol2xyPOCKMlY8O3Z6mx/FHO9O+atmz1avk2eFxgCbnQnswHVOMo+kWL2sHgUs6SGZ/HzFzq8favPh3sjJIIXV+vHFINf22jy9q0+P77RJ0xyXl6rY+hKFKTYR1BQ3PO4p8Xog50RYZJhGDrXD8a4pkFIzv4woWJG2KZOmBSloVrKrV5Iy7WotipUHYPrhxMWqhY6qpW2N4r41ZdWeON6j95E6RyEANtSdMaDUcyNfsBCzeYXLnRUQMUwxDTE7NyGYR/HVK0fz1ICpe44IkwLznZ8tnohN0vVa81RO67/9GfPzM5x+pKeKmAXq8pXPSPno72Q37/a5VTL5U9+dQ14PFfCu7/blm/x9TPPfvE+imemkNdckyQruLhcZbsfcjhJ8B2d55arSKnEGaBWCsMope6YDCJFMTuz4BGlGZ5pzAYrW/2QxarN1YMRbV/xhfdGihmy3PA40/YI04KKbfDR3lj1SnMl7BlFI+quhS6g6pmM45SGZ7Jcd2l4Jq+sN/n+R4cMgoSaZ1GxTLoTdcPnmSTUFeNgsWax04tZqFlIlHpyqzfBcwxMTXCuU2V/nCiRUSbZSTKitEAIZW06Ex7ZGhstxR7JC0mlMFiuOQzDhNvDmEGQUnMN5V9tGkzSHF3TQSpu8jSJPc4KxaDJNbCUt7SUECY5W33lk1F3Lb652SLOcq7sT9B1wbnlGheXa/i2wd4w4p2tPghBL0i4tDNhZxDw0mqDjQVvNqDqTuKPUczg3sPJB6UVPopZUsOz+EPPLc68se/176uOyTfPtrnZDUjzAsfUaVYsTF1wqqVW2Z9UVHzHYBKnbPWC8mdNRocplN72YVowjFRASbNsX7UrFnGac67jc6rpcasXsDuM+cUXlhhFGaeaHoMwLXvJOVXHwNY1pVNAstmusFp3GScZy3WXtabyqZkepwrVGNBwLWqOwYd7I6JMJd7LQrDe8tjpB9zsKZrp88u1Y+d49Fq/eaOHvaDTDFN+cPWQvJC0Kxa2oR8beD6OK+GzaIT1MHhmCvlR34XnlqpEWc44SrmwWJ0NQEDg2zrjOMcqPZgbroljGjQ8U+UQlrFeqw0P0GiU9ppJXuAUGs8v1XjrZpetfshaw1NhFXnB5oJHVigflrpn4lvKDS7LcoJYRZ4FScZqXXkrV2wDXdNUoG0hKWRBkiner4xz3tsZ8NX1hmrLhKmyHTU0Njs+k0Sp/n54rUu7YuEYGu/fHpIWEqGp+LG6a9KPMnRd0nQtRe/TBIs1Sw1CywQlS9ewdME4UnFxFUtRAQ1No+oYajVeSBaqlgqW1gVRUmCbGp5lcDiK2RlFRFnBLzzX4eyCOr6Vusurp5oz06LpA3owjtns+PzuB3tEaYFn61Rsk/f3hhRCquEgn95TneJxlJxHP+NxBCTT/u5qw+XHN3uMooA0yxnH+WwAOL1H7yVYqToGjuGzPThAKy2RX16vc/1wQm+SMklybFMnKgp6k4ymZ/Lccq089pS2b7He9Pj2+QX+0HOLvHmjx/4oppCS0wsVbh4G6Lqm5jCWwTiWLFbhYBJjaYLtQcgfubjIMEyPnZc4YpUWlD3n9aan4t8S2GhV0HSNC4vVTwwunl6fm92A8x0fxzRmbohFAd99Z4fluvOlEe98Fnh4i7gvKKZv9Ck1baPlsd700DVlDjUIE/phwkrdwShTaDxbxUcB1MoVtJQFvUmClKoXXXMMlqsOLyzXaXg2a02P51fqhGmBKFWNC76Frmk8t1TldMvlhZUapzsV0rxgue5xdsHDMnQ+uD2m6hh8tDciL5R3dncS0w1iTF0jzylDAzSVBTmMeHWtyf44UvmNUiXFNxyTV0/VaXrKXXB7GKFpgrMLHgsVB0PTiHOJqQmqlo6hC8ZxzlLVxtA1ruyV6T859MKEDJBC8cmTPKcoV23N0mGu4Vp0qjY1T5kXgURDpRD1woTlmsNKzaEo4N3tAUUBVceYFdPpd/MLFxfxHYMPdkZs9xUXWyLoVC0KCYeTmINRxFs3e6rwh8kdvjb3Hk4eZTtMQ5qnKesPgmmYxLvbA67uT3h3e8DvXd6fxck9CKb9XWDWKpskJdMjVyHSSVbw5o0e1w8nvHmjR5IVND2LJCsYhClhmnGmXeHMgsdSzaVim3z7XIe0TOupOzoLno0Q8O1znTIHU6dVMXlhpcZa050V082Fskds6ry20eS5JV9lf+aSMM5YbzpIJL1xQj/MqFjKtfLotZUSXl5rYOqKXVW1FdOmWbH55mabqqPajkmmWi1HWypv3ujxO5f2ePNGj365ug7TnHGczZ63OCvQhFQeKmWhn16jh7n2cyg8Myty+Pj2arryidKcF1frAGSFZKPlzcyRojRDlCZR39xc4FpX3Vjv74w4t6j450HJKBiGqWKPZAWnFlxe22gwijL2hoo7vTeMqXsGgyDj8v6Q55ZrCARJljOJExCSf/nubRZ9ZbtZcwzCxKQfpkxi5SI4NQlSAiKLbpiwUvOwdMHNnurNn1+sEiQ5dpmZWHMMhkFKL0iJs4Kqp2hfk0jlhi6Wgo9JnGOXdqi7wxhDV8OmIMpUAk5pG5AjlXdMlOKZBqtNm0IK4ryg7VnspHkZH1YaP+WS/XFMIZVT3U+TIb0g+Zj7XD9IuD0I2RmGQMH+KKUfZqw2XFaqNqMkY2eoVux/+OIiVw/GvHWrzytr9Zny8e6e6eNmMB4Nk/Bcjbi0N5jawT4IprvBrV5I0zVpeTZJWnB+0cezTG4PIi6WK+gpx1yJ0UYz5WbLt9hoe/z4hpobTCl3aw2XVkWtZg1DcK7uk0vFlLlyMKZAWR3fbRRWcwwEMEkKXjvd4j+4uMQ/fWuLOM1Ya1X4cHdEkCS0hMUgTI5d236QsDOI6IcJ7YrNc0tVWIK3b/UoJNzqB7QrFk3P5HTbn7VH4N6iq7Md9TOGJmbPW5Qq3YMmBO2KOXsJw7Mv3vks8EwV8rvxSX2z64cTfuunO/zk1oDFmsNrG010TRDGOb/84jKHkxhZSMYlj/xmNyjNnRyaFZM4U0wBNcBz1GrD1LA0HcPX+NH1jDMtDctU4coLvkUQZ+yOIjzTVDFlpVyyH6VoKBMthFrpupZigXRqDpsLissb54rHK4DuJKMXqOFTrXTLG0ZKvp2mBaMiVSvBvKAfpehCCSZqZTh0L0iw0ZE51Eo5tmMas/DdYZShSSXV1xAs1mycSAUGdIMYkUsG4wzPUi+MaVSbocF4mBOmOf/uowP+2Murs2t+9WBCx3f4/bCLEDrtqsYwzLi6P+K1000aFYvnlqu8uq4KStUxubI/5tLukK9ttI4FSkzbEkLwWBmMR8MkQLlD1qXJh3ujBy7kd/q7YzQ0fEdlaTY9xdKZ8pldU2d/FLHedPlgd6SMoByTKM34cHfEf/7tTU63K3z/o0PevNGjO0n55tkWqw2PC4sqlcgu2UG6JlhruMecGI8W0GmizvMrajZ0aWeIY+nKanYU0/Yt+pOM/bEK9piuqqcr6gXfZpJkjKOU928nnG77rDc99kcxSV7QrtjH/N+P5qjez9QsSgt+54M9LF3jXKdCd6K+w6PhD18G8c5ngWe6kN8P/SDhyv6Yr6w2uLhU4+rBhEs7I6qOwUtrDRZrDp2qUuXVHJPLe4o+VnctBEo8VHct3r09VIkmhkbVNpBlDFjVMdnqB+yPEnQ9nRlBVSwd3zGxdI1+oCKwRpGyIFXGVwUIDVEaUEFIs2Jh1RyuHU6o2yaFlGwNQlqeSZQZZJlyxKu6Kp7ONg2GYYIudOJC9ZyDJCfOVKF2Sj6ia+oIIJA5Wi7RygDcVsXG1DX2h0omjlAiou1ewPmlGofjmMWqy1Y/QGgaYZJRCBVoEaeS7kQNdju+ze99sMe3zy3MVuXDkvf8ynqDd7cHHI4TWp6JECa6psKqp+nooAr5K+uKAnc0iOBYwQpTJCmLVeeRMhiPhkkc/Vs5Y94/GFQxbx3Jlhwem8uAesF0qg5XDyalonhqxqXR8m3evtUnLyRnFiq8sFLj7a0+Vw/GM/Wnpgne3xlh6HB2sTJrXU2vydECutmucPVwjO8YpWgmpuaonVmSF+Q5rDQMNM3lzILH9z865NrBhJ1BNPMEdy19Rhw4GMf80ZeWeetmn6ZnlS02haPF95N2R46p8csvLJftxIRBoMKRp+c3vUbPunjns8Az0yN/GBztq9Zci1dPNfnm2TYS1Y+EO3Fe3zjTwjHVoOhWNyArCk4v+CqAVgqyQnIwSegFKdcPA/79RweMopRvn1soMzZN1hoOk0TR+V5db2BqKt/ycBJzexgSp3KW31kAjmUgJWRFQdu3VMiChLpnsj2IcUzBZsenahlIUZAXBZoUvLbRYNG3Wag6VG3lHX2q6bLWUGyZzbZLL0jQNDELjXYNxU7J8gJDCIIkZ6Fq8/MXO3RqDr5j8NxSjYpjMQwTorQoV5ESVxdkucQSgjDJ0Q0VHXZ+sUrNUZYEVw8mswL84f6Yn2wNqHsmP3e+w9c2mni2ScU2Wao5fOtce6Z2nOLog32vfnin6lB3zdlsZCo0etCB2YVFn2GkWmxSSqJUsZouLPoPfV9tLlRmApS75zLTv//Zc+1ZgLL6fUrhutmucHlvfOz8zi74SATvbPd5//YAWRb5nzu3SH4kym7qjHkUnarNSt2dXZeGa/HqehOBYnCdaXvUHAsNldWpeO9W2VYc8KMbXT7YVTbIL63WWK47x1J57vUd1VyT/VHMpZ0hb1zvcWlnyP4oplaKdzxL+bU8v1Ln2+c6fOdCh/1xVIrI5OwafVlSfU4SX8oV+f36qsr46s42farUW6g4dHxbxZ6Vg/xBlOHYGkLAwThGBxqeQT/MuLQzYqPl8csvLfPO1pCdYUzVNjjdrrDW9IjznB/f7DOK1RZZ1yDNwdQFrqER56r3fKY09srIWanZ7AwjpaaMBT+8dsggSGn7Du2KRXei+ppSSFbrDmlWkEsIM4llaKw1XHZHMTvDCKtMW3csjbZp0g0SpBQYhjqfG2XeY8MzOVupsFRzkAi6QYxtCPphim9rxClYvk5vEiMLqDkWq2X6zShKOdtR5kv9QPmVPL9U5drBhPe3Bzy/WufMgsdy3WajVaHlW5/KJb7f9xal+T1FIw+Cu8MkTF1jvel9jIXxIMyWoxS6u+cynn1HmPLVjQY3ugHDKMO3dU63q+ilw+HRglx1TF5Zq/Nb7++wVPNoV8yPtTO+tmHdU0wzjUC7W0l6uu3RmyT0EmUbsd6s4JgCv8zWdE2NS4djal7OhU6VOMv5yVZ/di6f9B0NwpTfvbRH3TVnStetXsCffm2daweTj313napNlOWf6J0zx4PhS1nIj97400zIw4lqJeyNotk2/crBGIHk62eafLg3Ym8YYeoaW72APC+wXXXDrdZddgYhQZxTdwwEkquHY37t66f49rmFWYjF9cMxgyAmjHM6Zc9ZFij1o6lCITIpEQW0fAPX0lmue0gk720PuNULcAydUZQSZ8rnfFrIVHo8eKaOb+lcGyc0XZPVmqJPpkXB88s+aaEGmXFWYJvK3a7hWTQ9i2bFpGIZbPdD3t8Z4hoaL6zWsAyNl9frfP/KAdu9gHOLNTpVmysHY5Cw0nA4HMVIAUGSEyQpS3Xlencwjlnw7VmR+fkLHX7v8j7vbPXpVB2MUu16fmn5U7nEjyKz/zQ0joRJ3K9IPwzF8UH4zK+sN5RRWRlPNy2G5xer91Q3rjUrfON0i3Gcsd0PGccjKpaOZytm0IOIaabXVtcEP77RY61ls9mu8M72kELKY31qQ9cIZ4HM4lib6ZO+o6Nq0FE8NeOq0J0kD/SymePR8aUs5NMbfxxlXD9UNrWmrnG6VVH+KKWhU5wVvLzWoOZa+LbB5b0RNw4nDKKE71zoUBTK8H+hdGLbLmX7N3sB/TDjN350k/OL1VkUWZS5jKNpdJvJYtUmyaFZUQnygzABdFbqNit1m2+caatgXE2ZdnV8h/1RxKD0yi5yE9FUmZFRmuNYGkFaEGaSTtUiTgu6UcJixSZOcyZpxstrDYIkR0PgWoJBqFgTUaYsV/dHEQWKutiqqNQaiYqn++qpJjcOA8ZxRsM1Wa459IO09LexsAz1OcNIFcSrh2NqjnlslblSd/nO+QV++9IeVce4pxPe/Qrh46j/PgmfVnwfN6zi3r/v48UQuOf5XVj02R/F3OhOZgPSYZgwiNKPZV9+0sp2Km56Zb0xe3Ed9SkBlTI1FRNNdwyvrNXJjrRy7ne9hmE6U4NO4ZgawzDl1VONz+S7m0PhmSrkD6fwa/Ldd3ZICz62ZZ32Wadq0SkqZY+v4VozF7fvvrPDwSShXbE41fT4cH/E4Thn0bdwDGMWD/bzFzrHGAZZIekHCZd3x8Sp4pRbukPdMznTrtAtg6JtQ+PSzohbvQBKD5mao9gFwzjjxkHAn339FJf3J3imwHNM8kxiGsoPQwrUZ0kJaYFnGjRckzQvOCxdHF1T5/YwZBgm7AwjarbBxmkPQ1d+5U3XnPmF/Jmvr6v4r0IySTJeXKmjaxqmLqg5Jt+/csCkTJxP8ju84DMLPsMwZRxn3O6HnO1U+NbZzuzaHm0V3A+Pq/57VDwuxfFeuF8xvF+B//U3bqn81EJyc2/EIMw4veDOaJIPo2y8n0+Ja+oYmiBMJd86d8diN0gyPPvTx2lCwE+2+tRda2ZcN23LPKnv7suCZ6aQP6zCr+FZLNcdXlip3XcCf7+V+4Jvzz77j760PPu9Nw4nHI6T2XbYLYdWgzA9VqQ2Fyos1Wze2R7imjp5UWAXGjEFF5aqKg80z/nt9/c4s+Cq/rUG/TBjXJpJuZaOluUkecHtQaiUhFLgWgZ74whD0/AslfoiZU4vSLE0jXGSst1PWS0HoLomuLw3Is4KhkHG7WGIqQts0+CUr0ILkkzO/ELgDtWtYulM4ow0l5xuKwXtRstDaMqYq2qbnO/4XNobcXl3xMXlGp5l0A1Sqq5qa02LxYMUxicV4fVZtHTuh/sV5JW6w83DgDevHGLoOusNBw3Bj2/0Hyst/u4Cu9FWq3FdE8fsgx+OBTR9nu7VlpkX7s8Czwxr5VEUfkIoQcgb17tc2hkyilL2RzE7g4jfubTH1YMJZzs+B+OYtADfMXl+uTaLHrt6MDmmKN0dRlAGBVdKH2bb0MgyeUz+3PAszi9W+ZkzLaquyTguWKjabLZdrh9MuD1Q5v0qfEGxVXRNUcFMXSX4pLlEFxp2yQxpV21kISkKZUk6LgdNuyMVVhCnBS3fxjNULNbvXd7nVi8ky5XV6fXDCT/Z7tMdJyRZwcEo4np3Qqeqwi8qljk79un5erZBJpXAyrcNDicJhVRb8Cm9rllRDoB111SDVkPj5bUaftmLn+LTCuP0RX1UEfl5qQCPslGeFLui6hhsDUNOt3yeW/QxdZ2bvQDH1B5YxXo/HFXevrLeoO6avLvd5w+ud4mz/IFZQFLCK2t15Y4YZZi64JW1OvJuduccJ45nZkX+sNvffpAoD5M4o+6YJFnOD64eEqc53zjTnq3qr+wrLu4nrdyPrjTe3Rqga3d+Ls4KDEN8rEhJCX/44iJ/5PklfnSjy84w4tr+mMkw4dyCj20YSCSGrtPwTBZ8E9fSQUpsXcexBFLCQsXi9c02Hd/m0LOIM7WKOt32mcQJH+xNeHGlim+ZdMdqCLXVm2AZytLXNDTefH9AWvLMTU25E3YnKbeHEXVH7XAWfP/YDmcakPv2rT6X98Zc744xdTjdUmkxR6XYtmHwwnKVUZxxcbnGKEp5f2eoRFcPuOo76T71w+Bx2wIntZOIk4xa1TiWFGIb2sc8Uh4Wx+2EVd7lo9gJ3zGuq83+7kHbMnM8Hp6ZQv6w29+rBxMWqw7tMo5rHOdESU67as3ShKaftTeMH+izNxcqbPUCbvUCJXlHJbisN92Prd6OHu+FxaqSxJcPpGPqjOKU5aqLbcD1gwlxJnlppc7uKMLQBZauYeiKtfLKep1RlDFJMpoVA9tQUvMwtRlEORJFZfMsne0bPcZxjlsUvLXVpz9J2RuFeJaBpkk0ISikSg+yCqEsUDWBW9rVTgvn0VbWN063CNOcvVFEmGYfk2JvtJQtsF+2UaqOyemWYrQ8aGH8LPrUD4NHbQuchKkXqBf/i6t1docxkzjDs3TOLymrhsdp8Rw9viDOHivv8rMaRj8KnlQb7knhmSnkD3sTTQuDEIKLy+qG/aEsEHcp+lxTx3eM2crkkz674Vm8vN5gbxTxk+0Brqnx+pn2MXXjvY53aoZ/4zCg5pq0KzZNr8reKEJKNdwspFTBD6ZGkOQYGlQdi6WaPWMhOIYqbMMoQxMqNzRJc273c8y2xuEkYRilaEjyXImM+kEMoOK5qhqG1LE0QT/KuLBY5cJSjSjN2e6HrNQd3tkeMAzTmQLw6Ap5sap66jXX5Mc3ejimgW0IupOUnUHIt851ZitwTYM/+tLyAz9cn2ef+iRxUjuJmmtyqllBSkqlsK4UvGUQxEkc3yTJHyvv8osy0Dypl+fThGemkD/MTTQ1BXp/Z0S7Ys0YK6aucbcye8p1naamfNJnH5X+f9rW9O7jbfkWf/E7mzMTp+4kASkZJSqIuFWx2RmG6ELQ9AwOxymTJOP84kJpc5vy7naflq+oi1cOJggkF5dr7I5CtvsRu6NQDT9tVfwMTcPUNQqpQp6FLpQrnVb2uMv2iG1o7I4iDsYRvqN8Yt7fGTGJ02Mrtymn/RcuLnK6XeF77+0SZQVrDZezHZ+9kTLqUjmWD/dQfZFWew+Dk9pJbC5U6AcJG60K3UnM/jgqk+gf/GX4acfn28Yj5V1+0Va/T7IN96TwWIVcCPG3gf8ISICPgL8kpeyfwHE9Ej5p+3t3rNhi1WYSp8oUaCfldKtCwzORMKNiHS0WD7K1ftgb6F6fWXdN3r7V57s/uY3QQBeCzQUVyLs7jLg1CFjyHVZLV7wkK/jNH93ipbUGXz/d4urBhO++u0PVNlhuuEgkp5oekzTncBKxWlMBtZ6toaGKOWis1h00TSUNpbnkbN3FtfRSug79SUKjYnF2wUcIQbtiMS7FVNMdzdGHvjtJeHmtfmwFvVRz7pnV+aDQNcG7230kgguL/lOxwjqpncTRF7+hC84vVWmVit5rBxNqrjn788MU1KPHt9pwHzrv8ou4+n3SbbgngcedQnwPeElK+QrwAfA3H/+QTh5HGQ+qDwiH45j1VgXfUZzqg3HMdy50+PkLnYf27Zh+/r+9vM+Nw8kxD23X1B9qGDUVbfzaNzZ4frnOV9bqtCoOB6OEumOx6Dss1hxeWmvQqtjKvc81y52CSn43NMXaWaoqf4ztfsSCZ3Gh41NzDJoVi7prY1k6ay2XF1drtHyVVq8LZaX7/HKNl9Zq5IXkYBxTcw1eWavPVt+rDZcCZgPLu5kc9/L/eNhrcff1tQ2d10+3eWm1fsxr5IuMk2S8HGWXbC6oJPkpi6c7TvjNH92iO04eitVz9PimLb5MMsu7/LT7/1H94O/lW35S+CQ/mGcVj7Uil1L+qyN//D7wa493OJ8NjvcBi7IPqJzzLi7XkFIqYyFvmsP44CuJoyuSpZqKhLu0M5olqz/qDbS5UOH3PthnwbeRUjKIUgyhtr9ZrkRKdvnCOdOuMIrVjbvdD2lXbMKsQAjVkmFR5TguN1ykhMWay94wwrF1mp6Pa+r8zqV9LizVWK07gGB3FHHe8rmwVJ21lY6Koz5tYHmSPe23b/XZ6odkObPg3mmx+KJvlT+rvvHdu79ekMxe6FN67PTnHkZk9bB5l4+y+v2sV/FPaxvucXCSPfK/DPwf9/uXQoi/AvwVgI2NjRP8tZ8MddN0S59oA02UPiOGzrBcOT/O2/roA7XW9Li0M0Qgubw7RNc1uuOYr5YWrA9zkzbuMleq2joNz+JgEs9cV+NyNXaUEbI3ignTjNvDCM/UWGm4ZViFzl/42TOzY97uh4yjDN9RvPJffXmF7X5EN4hpejY/d36BUy1v1gbZXPi4fPzowPJOn7Q/2+Zf2R8f+/lHeZj6QcKPb/RLGwCdOCu4tDPiuSVfBUPf9bNfpF7tFJ+FEObuAjqOM2VUFd+5Jg/aTnic43uUF/b9WpBv3+pTdczH/v6+KEPXzxNCfgpbXwjxr4Hle/yrvyWl/L/Ln/lbwOvAn5Gf9oHA66+/Ln/4wx8+wuE+HKZv/q1eiAqb1+gFMUiBZyn/64222lo+6Grg7mKx3Q851fRmHPNRlHJ5d8hbN/u8drrF5kJllm7zsCuOoyuXLC94e2tAlOZYuqBiGRSosIhrB2NeWmvgmBr/8r0dirzgdLtSOvqlnG57PL9Su29Qwj97e5vdQYhrGSpEOssJk4ylussff2X12PFMz31KqZdSCauGYUrnLk/wqcfM4zyYb97ozbj5U//uKM3JZcFXVusfc/e724jqaeijPwqmrcJpEby0M2RcvtCnPO6jdhOfFR7luv/Opb2PeZoPw4Q3rnf55tmFL8X396gQQrwhpXz97r//1BW5lPKXPuWD/yLwJ4BffJAi/nli+uY/2/FVQoopaLgW4zgjk3LWB3zQt/W9toS3ByGOoc+451XHRNc1Xjvd4tVTxx+gh20FHF1ZRGnOV1bVAzqKstlqerXh8tWNBt2J2nmcarpkuaTqmCz4DsNQiYBAPUB3F9R+kMz8YDq+xULVoWIZxGnOOMrucTzWxx7et7f6jKOUVsU+Ftk1TYZ5HAzDlM2Fyswb2zZ0pCzojuNjfeYvG1Ph7vZB07PY6gWcalUeSVr/qHiU1e+9VvFXDyZKefwl+f5OGo/LWvkV4G8AvyClDE7mkE4Ox7niNbb7IaMoRdcF//Fr6w/9pr9Xsdhsq2zFaRJLmOZ0xzFfP9069t8+6tT8Qbe9p9uV2flO7U6HUQplFFqaSbqTmPd3Rrxxvcsvv7hM3TV580YPq/RBD+KCa9GYlYaLEOA797497r4OWRkXd5TBclIsgaNqwek5GZrgq3et1L5sTIV79bb/9GvrdCfJ595OeNjWzL162N1JwtdPH3/pPMvf30njcXvkfxewge+V26TvSyn/6mMf1Qnh6JtfJf7ccTd8lBv8XsXibnP8aQF8Z3twLNfw85iaT893eq4Ab93s0fCUTa5j6nR8m2GY8L33dnluSYVLrzc9BmHCMMwZRAX9IOGrp5q0/Htfo7uvg2/rJFnBOL6zgj+p850+9J5l8NxSdbbSvDv44WkVDD0O7lVAT7e/+Ok691rFf3Wj8YnpUHN8Mh6LfiilPC+lPCWl/Gr5zxemiMPJmx3dj9Y0Ncd/9ZQKDDjd8jF1rQyuHbA3jD4Xk6V7nW93kmDrWmlipSOEoOZa5EXBh3sjXFOxQDQhWK7bvLxaw3dMtE9QDN59HVYbrmLVlI55J2kqNX3oP40S+kUwtprjwXGUSvm1jSavrDfm399j4Jl2s3nQIvCg+LRicSyXcFkVxLRQUXCfx9DmXuf71Y0GUaYCoqeIs5yWZ82i7ab5pKaucTCJabjmJx7v3ddB1wTrTZeNtnci1/l+5zV96O/1uSf9Xc/x+WL+/T0ePpW18lng82KtfBb4JIrb/abxl3aHnOtUH4q5cT+GyMMq+PpBwq+/cROjXIlP0482WhVMQ9wzcuxBRVBfRKrfHHM8y7gfa2VeyE8Qd1PCRlHKW7f6VG2DV9YbD1wo+0HC713eV3FbYcrtfkizYvPNzRZRWvDOVp+X1hp0qvYDfeb1wwnfe2+XvChm0WqaxoxRMi/Ic8zxdOCR6YdzPDjunsZPw5vPdvxjtLxPo1RNjbMarkWc5rimwSBM+Wh/jGcZD63gO92u8GtfX79vwX5QxsF8FT7HHF9MzAv5CeLuafw0vHnqTwIPRqn6cG9E3TFxTJ0wLag4BmZWcKMbst70SgXfHYbIg3zm46oLv4jmSHPMMYfCvJCfMI4WzLvDm+HBKFUq51C1vDxLJ82K8o8S39aPSfIf9DMfF182wc0cczxNeKZZK08ad7M79oYRP9kasN0PP9Hx7cKizzBKidKMBd9mHKf0woRTTZemZzEoedyfJ03rJN0M55hjjpPFvJB/hjhKqbrZC7h6OGazXeFU0/tEm9FX1husNz3yQpLmBatNl5W6w0LVmSn4Wr71udK0vozWoHPM8bRg3lr5jHG01XJ3NBrcuzXR8Cy+c6HziYPFz1vB92W0Bp1jjqcF80L+OeFhvUA+C+vTx8GX0Rp0jjmeFswL+eeEZ8EL5Iv2cpljjjkU5j3yzwn3kvfvjSJGUfqZxF3NMcccXx7MC/nnhLu9JOIsR6D8tR8mY3GOOeaY427MWyufI462JqZhwnNe9hxzzPG4mK/InxDmvOw55pjjpDAv5E8Ic172HHPMcVKYF/InhHkQwhxzzHFSmBfyJ4S5kf4cc8xxUpgPO58g5rzsOeaY4yQwX5HPMcccczzlmBfyOeaYY46nHPNCPsccc8zxlGNeyOeYY445nnLMC/kcc8wxx1MOIaX8/H+pEPvA9c/9Fx/HAnDwhI/hs8D8vJ4uzM/r6cEX4ZxOSyk7d//lEynkXwQIIX4opXz9SR/HSWN+Xk8X5uf19OCLfE7z1socc8wxx1OOeSGfY4455njK8WUu5H//SR/AZ4T5eT1dmJ/X04Mv7Dl9aXvkc8wxxxzPCr7MK/I55phjjmcC80I+xxxzzPGU40tdyIUQf1sI8b4Q4m0hxP8lhGg86WN6HAghfkUIcUkI8aEQ4r970sfzuBBCnBJC/LYQ4j0hxLtCiL/+pI/pJCGE0IUQbwoh/p8nfSwnBSFEQwjx6+Vz9VMhxLee9DGdBIQQ/015D74jhPjfhRDOkz6mo/hSF3Lge8BLUspXgA+Av/mEj+eRIYTQgb8H/CrwIvDnhRAvPtmjemxkwH8rpXwR+Fngv3gGzuko/jrw0yd9ECeMvwP8Synl88CrPAPnJ4RYA/4r4HUp5UuADvy5J3tUx/GlLuRSyn8lpczKP34fWH+Sx/OY+BngQynlFSllAvwT4E894WN6LEgpb0spf1T+/xGqKKw92aM6GQgh1oE/DvyDJ30sJwUhRB34Q8D/CiClTKSU/Sd6UCcHA3CFEAbgAdtP+HiO4UtdyO/CXwb+xZM+iMfAGnDzyJ9v8YwUPQAhxBnga8APnvChnBT+Z+BvAMUTPo6TxCawD/xvZcvoHwghnvrsQinlFvA/AjeA28BASvmvnuxRHcczX8iFEP+67Gvd/c+fOvIzfwu1jf/HT+5I57gfhBA+8H8C/7WUcvikj+dxIYT4E8CelPKNJ30sJwwDeA34X6SUXwMmwLMwq2midrebwCpQEUL8hSd7VMfxzEe9SSl/6ZP+vRDiLwJ/AvhF+XST6reAU0f+vF7+3VMNIYSJKuL/WEr5G0/6eE4IPwf8SSHEHwMcoCaE+EdSyi9UcXgE3AJuSSmnu6Zf5xko5MAvAVellPsAQojfAL4N/KMnelRH8MyvyD8JQohfQW1v/6SUMnjSx/OY+AP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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/Clustering_18_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def gaussian_points(dim=2, n_points=1000, mean_vector=np.array([0, 0]),\n", + " sample_variance=1):\n", + " \"\"\"\n", + " Very simple custom function to generate gaussian distributed point clusters\n", + " with variable dimension, number of points, means in each direction\n", + " (must match dim) and sample variance.\n", + "\n", + " Inputs:\n", + " dim (int)\n", + " n_points (int)\n", + " mean_vector (np.array) (where index 0 is x, index 1 is y etc.)\n", + " sample_variance (float)\n", + "\n", + " Returns:\n", + " data (np.array): with dimensions (dim x n_points)\n", + " \"\"\"\n", + "\n", + " mean_matrix = np.zeros(dim) + mean_vector\n", + " covariance_matrix = np.eye(dim) * sample_variance\n", + " data = np.random.multivariate_normal(mean_matrix, covariance_matrix,\n", + " n_points)\n", + " return data\n", + "\n", + "\n", + "\n", + "def generate_simple_clustering_dataset(dim=2, n_points=1000, plotting=True,\n", + " return_data=True):\n", + " \"\"\"\n", + " Toy model to illustrate k-means clustering\n", + " \"\"\"\n", + "\n", + " data1 = gaussian_points(mean_vector=np.array([5, 5]))\n", + " data2 = gaussian_points()\n", + " data3 = gaussian_points(mean_vector=np.array([1, 4.5]))\n", + " data4 = gaussian_points(mean_vector=np.array([5, 1]))\n", + " data = np.concatenate((data1, data2, data3, data4), axis=0)\n", + "\n", + " if plotting:\n", + " fig, ax = plt.subplots()\n", + " ax.scatter(data[:, 0], data[:, 1], alpha=0.2)\n", + " ax.set_title('Toy Model Dataset')\n", + " plt.show()\n", + "\n", + "\n", + " if return_data:\n", + " return data\n", + "\n", + "\n", + "data = generate_simple_clustering_dataset()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we are our, albeit very simple, dataset we are ready to start\n", + "implementing the k-means algorithm." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "n_samples, dimensions = data.shape\n", + "n_clusters = 4\n", + "\n", + "# we randomly initialize our centroids\n", + "np.random.seed(2021)\n", + "centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :]\n", + "distances = np.zeros((n_samples, n_clusters))\n", + "\n", + "# first we need to calculate the distance to each centroid from our data\n", + "for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + "# we initialize an array to keep track of to which cluster each point belongs\n", + "# the way we set it up here the index tracks which point and the value which\n", + "# cluster the point belongs to\n", + "cluster_labels = np.zeros(n_samples, dtype='int')\n", + "\n", + "# next we loop through our samples and for every point assign it to the cluster\n", + "# to which it has the smallest distance to\n", + "for n in range(n_samples):\n", + " # tracking variables (all of this is basically just an argmin)\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot and see" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/Clustering_22_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_subplot()\n", + "unique_cluster_labels = np.unique(cluster_labels)\n", + "for i in unique_cluster_labels:\n", + " ax.scatter(data[cluster_labels == i, 0],\n", + " data[cluster_labels == i, 1],\n", + " label = i,\n", + " alpha = 0.2)\n", + " ax.scatter(centroids[:, 0], centroids[:, 1], c='black')\n", + "\n", + "ax.set_title(\"First Grouping of Points to Centroids\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So what do we have so far? We have 'picked' $k$ centroids at random from our\n", + "data points. There are other ways of more intelligently choosing their\n", + "initializations, however for our purposes randomly is fine. Then we have\n", + "initialized an array 'distances' which holds the information of the distance,\n", + "*or dissimilarity*, of every point to of our centroids. Finally, we have\n", + "initialized an array 'cluster_labels' which according to our distances array\n", + "holds the information of to which centroid every point is assigned. This was the\n", + "first pass of our algorithm. Essentially, all we need to do now is repeat the\n", + "distance and assignment steps above until we have reached a desired convergence\n", + "or a maximum amount of iterations." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Converged at iteration 5\n", + "Runtime: 0.476909875869751 seconds\n" + ] + } + ], + "source": [ + "\n", + "max_iterations = 100\n", + "tolerance = 1e-8\n", + "start_time = time.time()\n", + "\n", + "for iteration in range(max_iterations):\n", + " prev_centroids = centroids.copy()\n", + " for k in range(n_clusters):\n", + " # this array will be used to update our centroid positions\n", + " vector_mean = np.zeros(dimensions)\n", + " mean_divisor = 0\n", + " for n in range(n_samples):\n", + " if cluster_labels[n] == k:\n", + " vector_mean += data[n, :]\n", + " mean_divisor += 1\n", + "\n", + " # update according to the k means\n", + " centroids[k, :] = vector_mean / mean_divisor\n", + "\n", + " # we find the dissimilarity\n", + " for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + " # assign each point\n", + " for n in range(n_samples):\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index\n", + "\n", + " # convergence criteria\n", + " centroid_difference = np.sum(np.abs(centroids - prev_centroids))\n", + " if centroid_difference < tolerance:\n", + " print(f'Converged at iteration {iteration}')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + " break\n", + "\n", + " elif iteration == max_iterations:\n", + " print(f'Did not converge in {max_iterations} iterations')\n", + " print(f'Runtime: {time.time() - start_time} seconds')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And thats it! We now have an extremely barebones, un-optimized k-means\n", + "clustering implementation. Lets plot the final result" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/Clustering_26_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_subplot()\n", + "unique_cluster_labels = np.unique(cluster_labels)\n", + "for i in unique_cluster_labels:\n", + " ax.scatter(data[cluster_labels == i, 0],\n", + " data[cluster_labels == i, 1],\n", + " label = i,\n", + " alpha = 0.2)\n", + " ax.scatter(centroids[:, 0], centroids[:, 1], c='black')\n", + "\n", + "ax.set_title(\"Final Result of K-means Clustering\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now there are a few glaring improvements to be done here. First of all is\n", + "organizing things into functions for better readability. Second is getting rid\n", + "of the small inefficiencies like manually calculating distances and argmin. And\n", + "finally, we need to optimize for better run-time. It's like we always say: the\n", + "best way of looping in Python is to not loop in Python. Let us tackle the first\n", + "two improvements." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Towards a More Numpythonic Code" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Converged at iteration: 5\n", + "Runtime: 0.41599512100219727 seconds\n" + ] + } + ], + "source": [ + "\n", + "def get_distances_to_clusters(data, centroids):\n", + " \"\"\"\n", + " Function that for each cluster finds the squared Euclidean distance\n", + " from every data point to the cluster centroid and returns a numpy array\n", + " containing the distances such that distance[i, j] means the distance between\n", + " the i-th point and the j-th centroid.\n", + " Inputs:\n", + " data (np.array): with dimensions (n_samples x dim)\n", + " centroids (np.array): with dimensions (n_clusters x dim)\n", + "\n", + " Returns:\n", + " distances (np.array): with dimensions (n_samples x n_clusters)\n", + " \"\"\"\n", + "\n", + " n_samples, dimensions = data.shape\n", + " n_clusters = centroids.shape[0]\n", + " distances = np.zeros((n_samples, n_clusters))\n", + " for k in range(n_clusters):\n", + " for i in range(n_samples):\n", + " dist = 0\n", + " for j in range(dimensions):\n", + " dist += np.abs(data[i, j] - centroids[k, j])**2\n", + " distances[i, k] = dist\n", + "\n", + " return distances\n", + "\n", + "\n", + "\n", + "def assign_points_to_clusters(distances):\n", + " \"\"\"\n", + " Function to assign each data point to the cluster to which it is the closest\n", + " based on the squared Euclidean distance from the get_distances_to_clusters\n", + " method.\n", + " Inputs:\n", + " distances (np.array): with dimensions (n_samples x n_clusters)\n", + "\n", + " Returns:\n", + " cluster_labels (np.array): with dimensions (n_samples)\n", + " \"\"\"\n", + " cluster_labels = np.argmin(distances, axis=1)\n", + "\n", + " return cluster_labels\n", + "\n", + "\n", + "\n", + "def k_means(data, n_clusters=4, max_iterations=100, tolerance=1e-8):\n", + " \"\"\"\n", + " Naive implementation of the k-means clustering algorithm. A short summary of\n", + " the algorithm is as follows: we randomly initialize k centroids / means.\n", + " Then we assign, using the squared Euclidean distance, every data-point to a\n", + " cluster. We then update the position of the k centroids / means, and repeat\n", + " until convergence or we reach our desired maximum iterations. The method\n", + " returns the cluster assignments of our data-points and a sequence of\n", + " centroids.\n", + " Inputs:\n", + " data (np.array): with dimesions (n_samples x dim)\n", + " n_clusters (int): hyperparameter which depends on dataset\n", + " max_iterations (int): hyperparameter which depends on dataset\n", + " tolerance (float): convergence measure\n", + "\n", + " Returns:\n", + " cluster_labels (np.array): with dimension (n_samples)\n", + " centroid_list (list): list of centroids (np.array)\n", + " with dimensions (n_clusters x dim)\n", + " \"\"\"\n", + "\n", + " samples, dimensions = data.shape\n", + " np.random.seed(2021)\n", + " centroids = data[np.random.choice(len(data), n_clusters, replace=False), :]\n", + " distances = get_distances_to_clusters(data, centroids)\n", + " cluster_labels = assign_points_to_clusters(distances)\n", + "\n", + " start_time = time.time()\n", + "\n", + " for iteration in range(max_iterations):\n", + " prev_centroids = centroids.copy()\n", + " for k in range(n_clusters):\n", + " vector_mean = np.zeros(dimensions)\n", + " mean_divisor = 0\n", + " for n in range(n_samples):\n", + " if cluster_labels[n] == k:\n", + " vector_mean += data[n, :]\n", + " mean_divisor += 1\n", + " # And update according to the new means\n", + " centroids[k, :] = vector_mean / mean_divisor\n", + "\n", + " distances = get_distances_to_clusters(data, centroids)\n", + " cluster_labels = assign_points_to_clusters(distances)\n", + "\n", + " centroid_difference = np.sum(np.abs(centroids - prev_centroids))\n", + " if centroid_difference < tolerance:\n", + " print(f'Converged at iteration: {iteration}')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + "\n", + " return cluster_labels, centroids\n", + "\n", + " print(f'Did not converge in {max_iterations} iterations')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + "\n", + " return cluster_labels, centroids\n", + "\n", + "\n", + "# quirk of numpy / Jupyter need to set seed again\n", + "cluster_labels, centroids = k_means(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: the start of the timing is after the random initialization, and first\n", + "'cycle' of our algorithm. This is technically not the correct way to time it but\n", + "due to this being in a Jupyter notebook and the way it is structured this way of\n", + "comparing our algorithms will produce a more equal result. When timing code we\n", + "should always encapsulate our whole computation block.\n", + "\n", + "So we see an improvement from just switching to numpy's argmin function. There\n", + "is a very nice tool (or category of tools) called profilers. These can be\n", + "utilized to make clearer which improvements to our code we should care most\n", + "about here is an [excellent source](https://ipython-books.github.io/42-profiling-your-code-easily-with-cprofile-and-ipython/)\n", + "on the topic. Even before optimizing we can understand which parts of our code\n", + "will be taking the most of the run-time. It will be the longest Python loop,\n", + "i.e. the loop over all the samples. Nonetheless, let us do some profiling!" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Converged at iteration: 11\n", + "Runtime: 0.8284149169921875 seconds\n", + " " + ] + } + ], + "source": [ + "test_data = generate_simple_clustering_dataset(n_points=10000, plotting=False)\n", + "%prun -l 10 cluster_labels, centroids = k_means(test_data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we can see the reason for profiling. We now know for certain a lot can be\n", + "gained just by vectorizing our distance function. Ideally we wish to perform\n", + "most of our loops in numpy, i.e. C. To do this we need our array shapes to match\n", + "and clever reshaping will let us do so." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def np_get_distances_to_clusters(data, centroids):\n", + " \"\"\"\n", + " Squared Euclidean distance between all data-points and every centroid. For\n", + " the function to work properly it needs data and centroids to be numpy\n", + " broadcastable. We sum along the dimension axis.\n", + " Inputs:\n", + " data (np.array): with dimensions (samples x 1 x dim)\n", + " centroids (np.array): with dimensions (1 x n_clusters x dim)\n", + "\n", + " Returns:\n", + " distances (np.array): with dimensions (samples x n_clusters)\n", + " \"\"\"\n", + "\n", + " distances = np.sum(np.abs((data - centroids))**2, axis=2)\n", + " return distances\n", + "\n", + "def np_assign_points_to_clusters(distances):\n", + " \"\"\"\n", + " Assigning each data-point to a cluster given an array distances containing\n", + " the squared Euclidean distance from every point to each centroid. We do\n", + " np.argmin along the cluster axis to find the closest cluster. Returns a\n", + " numpy array with corresponding labels.\n", + " Inputs:\n", + " distances (np.array): with dimensions (samples x n_clusters)\n", + "\n", + " Returns:\n", + " cluster_labels (np.array): with dimensions (samples x None)\n", + " \"\"\"\n", + " cluster_labels = np.argmin(distances, axis=1)\n", + " return cluster_labels\n", + "\n", + "\n", + "def np_k_means(data, n_clusters=4, max_iterations=100, tolerance=1e-8):\n", + " \"\"\"\n", + " Numpythonic implementation of the k-means clusting algorithm.\n", + " Inputs:\n", + " data (np.array): with dimesions (samples x dim)\n", + " n_clusters (int): hyperparameter which depends on dataset\n", + " max_iterations (int): hyperparameter which depends on dataset\n", + " tolerance (float): convergence measure\n", + " progression_plot (bool): activation flag for plotting\n", + " Returns:\n", + " cluster_labels (np.array): with dimension (samples)\n", + " centroid_list (list): list of centroids (np.array)\n", + " with dimensions (n_clusters x dim)\n", + " \"\"\"\n", + " n_samples, dimensions = data.shape\n", + " np.random.seed(2021)\n", + " centroids = data[np.random.choice(len(data), n_clusters, replace=False), :]\n", + "\n", + " distances = np_get_distances_to_clusters(np.reshape(data,\n", + " (n_samples, 1, dimensions)),\n", + " np.reshape(centroids,\n", + " (1, n_clusters, dimensions)))\n", + " cluster_labels = np_assign_points_to_clusters(distances)\n", + "\n", + " start_time = time.time()\n", + "\n", + " for iteration in range(max_iterations):\n", + " prev_centroids = centroids.copy()\n", + " for k in range(n_clusters):\n", + " points_in_cluster = data[cluster_labels == k]\n", + " mean_vector = np.mean(points_in_cluster, axis=0)\n", + " centroids[k] = mean_vector\n", + "\n", + " distances = np_get_distances_to_clusters(np.reshape(data,\n", + " (n_samples, 1, dimensions)),\n", + " np.reshape(centroids,\n", + " (1, n_clusters, dimensions)))\n", + " cluster_labels = np_assign_points_to_clusters(distances)\n", + "\n", + " centroid_difference = np.sum(np.abs(centroids - prev_centroids))\n", + " if centroid_difference < tolerance:\n", + " print(f'Converged at iteration: {iteration}')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + "\n", + " return cluster_labels, centroids\n", + "\n", + " print(f'Did not converge in {max_iterations} iterations')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + "\n", + " return cluster_labels, centroids" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When working towards becoming a data scientist using Python this last step is\n", + "arguably one of the most important. Thinking of ways to avoid explicitly looping\n", + "by adding dimensions to our arrays in such a way that they become broadcastable\n", + "using numpy (also tensorflow and many others). Let us take a look at our the\n", + "fruits of our labor." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Converged at iteration: 5\n", + "Runtime: 0.003773212432861328 seconds\n" + ] + } + ], + "source": [ + "cluster_labels, centroids = np_k_means(data)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/Clustering.py b/doc/LectureNotes/_build/jupyter_execute/Clustering.py new file mode 100644 index 000000000..36885f47b --- /dev/null +++ b/doc/LectureNotes/_build/jupyter_execute/Clustering.py @@ -0,0 +1,600 @@ + + +# Clustering Analysis +In this chapter we will concern ourselves with the study of **cluster analysis**. +In general terms cluster analysis, or clustering, is the task of grouping a +data-set into different distinct categories based on some measure of equality of +the data. This measure is often referred to as a **metric** or **similarity +measure** in the literature (note: sometimes we deal with a **dissimilarity +measure** instead). Usually, these metrics are formulated as some kind of +distance function between points in a high-dimensional space. + +There exists a lot of such distance measures. The simplest, and also the most +common is the **Euclidean distance** (i.e. Pythagoras). A good source for those of +you wanting a thorough overview is the article (DOI:10.5120/ijca2016907841 +Irani, Pise, Phatak). A few other metrics mentioned there are: *cosine +similarity*, *Manhattan distance*, *Chebychev distance* and the *Minkowski +distance*. The Minkowski distance is a general formulation which encapsulates a +range of metrics. All of these, and many more, can be used in clustering. There +exists different categories of clustering algorithms. A few of the most +common are: *centroid-*, *distribution-*, *density-* and *hierarchical- +clustering*. We will concern ourselves primarily with the first one. + +## Basic Idea of the K-means Clustering Algorithm +The simplest of all clustering algorithms is the aptly named **k-means algorithm** +, sometimes also referred to as *Lloyds algorithm*. It is the simplest and also +the most common. From its simplicity it obtains both strengths and weaknesses. +These will be discussed in more detail later. The k-means algorithm is a +**centroid based** clustering algorithm. + +Assume, we are given $n$ data points and we wish to split the data into $K < n$ +different categories, or clusters. We label each cluster by an integer $k\in\{ +1, \cdots, K \}$. In the basic k-means algorithm each point is assigned to only +one cluster $k$, and these assignments are *non-injective* i.e. many-to-one. We +can think of these mappings as an encoder $k = C(i)$, which assigns the $i$-th +data-point $\bf x_i$ to the $k$-th cluster. Before we jump into the mathematics +let us describe the k-means algorithm in words: +1. We start with guesses / random initializations of our $k$ cluster centers / centroids + +2. For each centroid the points that are most similar are identified + +3. Then we move / replace each centroid with a coordinate average of all the points that were assigned to that centroid. + +4. Iterate this points 2, 3) until the centroids no longer move (to some tolerance) + +Now we consider the method formally. Again, we assume we have $n$ data-points +(vectors) + + +
+ +$$ +\begin{equation}\label{eq:kmeanspoints} \tag{1} + \boldsymbol{x_i} = \{x_{i, 1}, \cdots, x_{i, p}\}\in\mathbb{R}^p. +\end{equation} +$$ + +which we wish to group into $K < n$ clusters. For our dissimilarity measure we +will use the *squared Euclidean distance* + + +
+ +$$ +\begin{equation}\label{eq:squaredeuclidean} \tag{2} + d(\boldsymbol{x_i}, \boldsymbol{x_i'}) = \sum_{j=1}^p(x_{ij} - x_{i'j})^2 + = ||\boldsymbol{x_i} - \boldsymbol{x_{i'}}||^2 +\end{equation} +$$ + +Next we define the so called *within-cluster point scatter* which gives us a +measure of how close each data point assigned to the same cluster tends to be to +the all the others. + + +
+ +$$ +\begin{equation}\label{eq:withincluster} \tag{3} + W(C) = \frac{1}{2}\sum_{k=1}^K\sum_{C(i)=k} + \sum_{C(i')=k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) = + \sum_{k=1}^KN_k\sum_{C(i)=k}||\boldsymbol{x_i} - \boldsymbol{\overline{x_k}}||^2 +\end{equation} +$$ + +where $\boldsymbol{\overline{x_k}}$ is the mean vector associated with the $k$-th +cluster, and $N_k = \sum_{i=1}^nI(C(i) = k)$, where the $I()$ notation is +similar to the Kronecker delta (*Commonly used in statistics, it just means that +when $i = k$ we have the encoder $C(i)$*). In other words, the within-cluster +scatter measures the compactness of each cluster with respect to the data points +assigned to each cluster. This is the quantity that the $k$-means algorithm aims +to minimize. We refer to this quantity $W(C)$ as the within cluster scatter +because of its relation to the *total scatter*. + + +
+ +$$ +\begin{equation}\label{eq:totalscatter} \tag{4} + T = W(C) + B(C) = \frac{1}{2}\sum_{i=1}^n + \sum_{i'=1}^nd(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) + = \frac{1}{2}\sum_{k=1}^K\sum_{C(i)=k} + \Big(\sum_{C(i') = k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) + + \sum_{C(i')\neq k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}})\Big) +\end{equation} +$$ + +Which is a quantity that is conserved throughout the $k$-means algorithm. It can +be thought of as the total amount of information in the data, and it is composed +of the aforementioned within-cluster scatter and the *between-cluster scatter* +$B(C)$. In methods such as principle component analysis the total scatter is not +conserved. + +Given a cluster mean $\boldsymbol{m_k}$ we define the **total cluster variance** + + +
+ +$$ +\begin{equation}\label{eq:totalclustervariance} \tag{5} + \min_{C, \{\boldsymbol{m_k}\}_1^K}\sum_{k=1}^KN_k\sum||\boldsymbol{x_i} - \boldsymbol{m_k}||^2 +\end{equation} +$$ + +Now we have all the pieces necessary to formally revisit the k-means algorithm. +If you at this point feel like some of the above definitions came a bit out of +no-where, don't fret, the method does get a whole lot simpler once we start +programming. + +## The K-means Clustering Algorithm +The k-means clustering algorithm goes as follows (note in my opinion this +description is a bit complicated and is lifted directly out of ESL HASTIE for +deeper understanding purposes) + +1. For a given cluster assignment $C$, and $k$ cluster means $\{m_1, \cdots, m_k\}$. We minimize the total cluster variance with respect to the cluster means $\{m_k\}$ yielding the means of the currently assigned clusters. + +2. Given a current set of $k$ means $\{m_k\}$ the total cluster variance is minimized by assigning each observation to the closest (current) cluster mean. That is $$C(i) = \underset{1\leq k\leq K}{\mathrm{argmin}} ||\boldsymbol{x_i} - \boldsymbol{m_k}||^2$$ + +3. Steps 1 and 2 are repeated until the assignments do not change. + +As previously stated the above formulation can be a bit difficult to understand, +*at least the first time*, due to the dense notation used. But all in all the +concept is fairly simple when explained in words. The math needs to be +understood but to help you along the way we summarize the algorithm as follows +(try to look at the terms above to match with the summary). + +1. Before we start we specify a number $k$ which is the number of clusters we want to try to separate our data into. + +2. We initially choose $k$ random data points in our data as our initial centroids, *or means* (this is where the name comes from). + +3. Assign each data point to their closest centroid, based on the squared Euclidean distance. + +4. For each of the $k$ cluster we update the centroid by calculating new mean values for all the data points in the cluster. + +5. Iteratively minimize the within cluster scatter by performing steps (3, 4) until the new assignments stop changing (can be to some tolerance) or until a maximum number of iterations have passed. + +That's it, nothing magical happening. + +## Writing Our Own Code +In the following section we will work to develop a deeper understanding of the +previously discussed mathematics through developing codes to do k-means cluster +analysis. + +### Basic Python + +Let us now program the most basic version of the algorithm using nothing but +Python with numpy arrays. This code is kept intentionally simple to gradually +progress our understanding. There is no vectorization of any kind, and even most +helper functions are not utilized. Throughout our implementation process it will +be helpful to keep in mind both the mathematical description of the algorithm +*and* our summary from above. In addition, try to think of ways to optimize this +while reading the next section. We will get to it, take it as a challenge to see +if your optimizations are better. + +First of all we need a dataset to do our cluster analysis on, for clarity (and +lack of googling beforehand) we generate it ourselves using Gaussians. First we +import + +%matplotlib inline + +%matplotlib inline +import matplotlib.pyplot as plt +import numpy as np +import time +from IPython.display import display + +np.random.seed(2021) + +Next we define functions, for ease of use later, to generate Gaussians and to +set up our toy data set. + +def gaussian_points(dim=2, n_points=1000, mean_vector=np.array([0, 0]), + sample_variance=1): + """ + Very simple custom function to generate gaussian distributed point clusters + with variable dimension, number of points, means in each direction + (must match dim) and sample variance. + + Inputs: + dim (int) + n_points (int) + mean_vector (np.array) (where index 0 is x, index 1 is y etc.) + sample_variance (float) + + Returns: + data (np.array): with dimensions (dim x n_points) + """ + + mean_matrix = np.zeros(dim) + mean_vector + covariance_matrix = np.eye(dim) * sample_variance + data = np.random.multivariate_normal(mean_matrix, covariance_matrix, + n_points) + return data + + + +def generate_simple_clustering_dataset(dim=2, n_points=1000, plotting=True, + return_data=True): + """ + Toy model to illustrate k-means clustering + """ + + data1 = gaussian_points(mean_vector=np.array([5, 5])) + data2 = gaussian_points() + data3 = gaussian_points(mean_vector=np.array([1, 4.5])) + data4 = gaussian_points(mean_vector=np.array([5, 1])) + data = np.concatenate((data1, data2, data3, data4), axis=0) + + if plotting: + fig, ax = plt.subplots() + ax.scatter(data[:, 0], data[:, 1], alpha=0.2) + ax.set_title('Toy Model Dataset') + plt.show() + + + if return_data: + return data + + +data = generate_simple_clustering_dataset() + +Now that we are our, albeit very simple, dataset we are ready to start +implementing the k-means algorithm. + +n_samples, dimensions = data.shape +n_clusters = 4 + +# we randomly initialize our centroids +np.random.seed(2021) +centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :] +distances = np.zeros((n_samples, n_clusters)) + +# first we need to calculate the distance to each centroid from our data +for k in range(n_clusters): + for n in range(n_samples): + dist = 0 + for d in range(dimensions): + dist += np.abs(data[n, d] - centroids[k, d])**2 + distances[n, k] = dist + +# we initialize an array to keep track of to which cluster each point belongs +# the way we set it up here the index tracks which point and the value which +# cluster the point belongs to +cluster_labels = np.zeros(n_samples, dtype='int') + +# next we loop through our samples and for every point assign it to the cluster +# to which it has the smallest distance to +for n in range(n_samples): + # tracking variables (all of this is basically just an argmin) + smallest = 1e10 + smallest_row_index = 1e10 + for k in range(n_clusters): + if distances[n, k] < smallest: + smallest = distances[n, k] + smallest_row_index = k + + cluster_labels[n] = smallest_row_index + +Let's plot and see + +fig = plt.figure() +ax = fig.add_subplot() +unique_cluster_labels = np.unique(cluster_labels) +for i in unique_cluster_labels: + ax.scatter(data[cluster_labels == i, 0], + data[cluster_labels == i, 1], + label = i, + alpha = 0.2) + ax.scatter(centroids[:, 0], centroids[:, 1], c='black') + +ax.set_title("First Grouping of Points to Centroids") + +plt.show() + +So what do we have so far? We have 'picked' $k$ centroids at random from our +data points. There are other ways of more intelligently choosing their +initializations, however for our purposes randomly is fine. Then we have +initialized an array 'distances' which holds the information of the distance, +*or dissimilarity*, of every point to of our centroids. Finally, we have +initialized an array 'cluster_labels' which according to our distances array +holds the information of to which centroid every point is assigned. This was the +first pass of our algorithm. Essentially, all we need to do now is repeat the +distance and assignment steps above until we have reached a desired convergence +or a maximum amount of iterations. + + +max_iterations = 100 +tolerance = 1e-8 +start_time = time.time() + +for iteration in range(max_iterations): + prev_centroids = centroids.copy() + for k in range(n_clusters): + # this array will be used to update our centroid positions + vector_mean = np.zeros(dimensions) + mean_divisor = 0 + for n in range(n_samples): + if cluster_labels[n] == k: + vector_mean += data[n, :] + mean_divisor += 1 + + # update according to the k means + centroids[k, :] = vector_mean / mean_divisor + + # we find the dissimilarity + for k in range(n_clusters): + for n in range(n_samples): + dist = 0 + for d in range(dimensions): + dist += np.abs(data[n, d] - centroids[k, d])**2 + distances[n, k] = dist + + # assign each point + for n in range(n_samples): + smallest = 1e10 + smallest_row_index = 1e10 + for k in range(n_clusters): + if distances[n, k] < smallest: + smallest = distances[n, k] + smallest_row_index = k + + cluster_labels[n] = smallest_row_index + + # convergence criteria + centroid_difference = np.sum(np.abs(centroids - prev_centroids)) + if centroid_difference < tolerance: + print(f'Converged at iteration {iteration}') + print(f'Runtime: {time.time() - start_time} seconds') + break + + elif iteration == max_iterations: + print(f'Did not converge in {max_iterations} iterations') + print(f'Runtime: {time.time() - start_time} seconds') + +And thats it! We now have an extremely barebones, un-optimized k-means +clustering implementation. Lets plot the final result + +fig = plt.figure() +ax = fig.add_subplot() +unique_cluster_labels = np.unique(cluster_labels) +for i in unique_cluster_labels: + ax.scatter(data[cluster_labels == i, 0], + data[cluster_labels == i, 1], + label = i, + alpha = 0.2) + ax.scatter(centroids[:, 0], centroids[:, 1], c='black') + +ax.set_title("Final Result of K-means Clustering") + +plt.show() + +Now there are a few glaring improvements to be done here. First of all is +organizing things into functions for better readability. Second is getting rid +of the small inefficiencies like manually calculating distances and argmin. And +finally, we need to optimize for better run-time. It's like we always say: the +best way of looping in Python is to not loop in Python. Let us tackle the first +two improvements. + +## Towards a More Numpythonic Code + + +def get_distances_to_clusters(data, centroids): + """ + Function that for each cluster finds the squared Euclidean distance + from every data point to the cluster centroid and returns a numpy array + containing the distances such that distance[i, j] means the distance between + the i-th point and the j-th centroid. + Inputs: + data (np.array): with dimensions (n_samples x dim) + centroids (np.array): with dimensions (n_clusters x dim) + + Returns: + distances (np.array): with dimensions (n_samples x n_clusters) + """ + + n_samples, dimensions = data.shape + n_clusters = centroids.shape[0] + distances = np.zeros((n_samples, n_clusters)) + for k in range(n_clusters): + for i in range(n_samples): + dist = 0 + for j in range(dimensions): + dist += np.abs(data[i, j] - centroids[k, j])**2 + distances[i, k] = dist + + return distances + + + +def assign_points_to_clusters(distances): + """ + Function to assign each data point to the cluster to which it is the closest + based on the squared Euclidean distance from the get_distances_to_clusters + method. + Inputs: + distances (np.array): with dimensions (n_samples x n_clusters) + + Returns: + cluster_labels (np.array): with dimensions (n_samples) + """ + cluster_labels = np.argmin(distances, axis=1) + + return cluster_labels + + + +def k_means(data, n_clusters=4, max_iterations=100, tolerance=1e-8): + """ + Naive implementation of the k-means clustering algorithm. A short summary of + the algorithm is as follows: we randomly initialize k centroids / means. + Then we assign, using the squared Euclidean distance, every data-point to a + cluster. We then update the position of the k centroids / means, and repeat + until convergence or we reach our desired maximum iterations. The method + returns the cluster assignments of our data-points and a sequence of + centroids. + Inputs: + data (np.array): with dimesions (n_samples x dim) + n_clusters (int): hyperparameter which depends on dataset + max_iterations (int): hyperparameter which depends on dataset + tolerance (float): convergence measure + + Returns: + cluster_labels (np.array): with dimension (n_samples) + centroid_list (list): list of centroids (np.array) + with dimensions (n_clusters x dim) + """ + + samples, dimensions = data.shape + np.random.seed(2021) + centroids = data[np.random.choice(len(data), n_clusters, replace=False), :] + distances = get_distances_to_clusters(data, centroids) + cluster_labels = assign_points_to_clusters(distances) + + start_time = time.time() + + for iteration in range(max_iterations): + prev_centroids = centroids.copy() + for k in range(n_clusters): + vector_mean = np.zeros(dimensions) + mean_divisor = 0 + for n in range(n_samples): + if cluster_labels[n] == k: + vector_mean += data[n, :] + mean_divisor += 1 + # And update according to the new means + centroids[k, :] = vector_mean / mean_divisor + + distances = get_distances_to_clusters(data, centroids) + cluster_labels = assign_points_to_clusters(distances) + + centroid_difference = np.sum(np.abs(centroids - prev_centroids)) + if centroid_difference < tolerance: + print(f'Converged at iteration: {iteration}') + print(f'Runtime: {time.time() - start_time} seconds') + + return cluster_labels, centroids + + print(f'Did not converge in {max_iterations} iterations') + print(f'Runtime: {time.time() - start_time} seconds') + + return cluster_labels, centroids + + +# quirk of numpy / Jupyter need to set seed again +cluster_labels, centroids = k_means(data) + +**Note**: the start of the timing is after the random initialization, and first +'cycle' of our algorithm. This is technically not the correct way to time it but +due to this being in a Jupyter notebook and the way it is structured this way of +comparing our algorithms will produce a more equal result. When timing code we +should always encapsulate our whole computation block. + +So we see an improvement from just switching to numpy's argmin function. There +is a very nice tool (or category of tools) called profilers. These can be +utilized to make clearer which improvements to our code we should care most +about here is an [excellent source](https://ipython-books.github.io/42-profiling-your-code-easily-with-cprofile-and-ipython/) +on the topic. Even before optimizing we can understand which parts of our code +will be taking the most of the run-time. It will be the longest Python loop, +i.e. the loop over all the samples. Nonetheless, let us do some profiling! + +test_data = generate_simple_clustering_dataset(n_points=10000, plotting=False) +%prun -l 10 cluster_labels, centroids = k_means(test_data) + +Here we can see the reason for profiling. We now know for certain a lot can be +gained just by vectorizing our distance function. Ideally we wish to perform +most of our loops in numpy, i.e. C. To do this we need our array shapes to match +and clever reshaping will let us do so. + + +def np_get_distances_to_clusters(data, centroids): + """ + Squared Euclidean distance between all data-points and every centroid. For + the function to work properly it needs data and centroids to be numpy + broadcastable. We sum along the dimension axis. + Inputs: + data (np.array): with dimensions (samples x 1 x dim) + centroids (np.array): with dimensions (1 x n_clusters x dim) + + Returns: + distances (np.array): with dimensions (samples x n_clusters) + """ + + distances = np.sum(np.abs((data - centroids))**2, axis=2) + return distances + +def np_assign_points_to_clusters(distances): + """ + Assigning each data-point to a cluster given an array distances containing + the squared Euclidean distance from every point to each centroid. We do + np.argmin along the cluster axis to find the closest cluster. Returns a + numpy array with corresponding labels. + Inputs: + distances (np.array): with dimensions (samples x n_clusters) + + Returns: + cluster_labels (np.array): with dimensions (samples x None) + """ + cluster_labels = np.argmin(distances, axis=1) + return cluster_labels + + +def np_k_means(data, n_clusters=4, max_iterations=100, tolerance=1e-8): + """ + Numpythonic implementation of the k-means clusting algorithm. + Inputs: + data (np.array): with dimesions (samples x dim) + n_clusters (int): hyperparameter which depends on dataset + max_iterations (int): hyperparameter which depends on dataset + tolerance (float): convergence measure + progression_plot (bool): activation flag for plotting + Returns: + cluster_labels (np.array): with dimension (samples) + centroid_list (list): list of centroids (np.array) + with dimensions (n_clusters x dim) + """ + n_samples, dimensions = data.shape + np.random.seed(2021) + centroids = data[np.random.choice(len(data), n_clusters, replace=False), :] + + distances = np_get_distances_to_clusters(np.reshape(data, + (n_samples, 1, dimensions)), + np.reshape(centroids, + (1, n_clusters, dimensions))) + cluster_labels = np_assign_points_to_clusters(distances) + + start_time = time.time() + + for iteration in range(max_iterations): + prev_centroids = centroids.copy() + for k in range(n_clusters): + points_in_cluster = data[cluster_labels == k] + mean_vector = np.mean(points_in_cluster, axis=0) + centroids[k] = mean_vector + + distances = np_get_distances_to_clusters(np.reshape(data, + (n_samples, 1, dimensions)), + np.reshape(centroids, + (1, n_clusters, dimensions))) + cluster_labels = np_assign_points_to_clusters(distances) + + centroid_difference = np.sum(np.abs(centroids - prev_centroids)) + if centroid_difference < tolerance: + print(f'Converged at iteration: {iteration}') + print(f'Runtime: {time.time() - start_time} seconds') + + return cluster_labels, centroids + + print(f'Did not converge in {max_iterations} iterations') + print(f'Runtime: {time.time() - start_time} seconds') + + return cluster_labels, centroids + +When working towards becoming a data scientist using Python this last step is +arguably one of the most important. Thinking of ways to avoid explicitly looping +by adding dimensions to our arrays in such a way that they become broadcastable +using numpy (also tensorflow and many others). 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- "[ 0.93335357 -1.39959184 0.49879283 0.86425016 0.73260395 -0.58027265\n", - " -0.11924306 -0.40279866 0.63314635 0.01601298]\n" + "[ 0.52767404 -0.32617572 -0.84692682 0.35650759 -2.05926228 -0.91335551\n", + " 0.68132045 -0.31279832 -0.35453393 -0.0157447 ]\n" ] } ], diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb index 85d81c6c5..7654bacd0 100644 --- a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb @@ -2284,34 +2284,24 @@ "Learning rate = 0.1\n", "Lambda = 1e-05\n", "Accuracy score on test set: 0.9111111111111111\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ + "\n", "Learning rate = 0.1\n", "Lambda = 0.0001\n", "Accuracy score on test set: 0.9222222222222223\n", - "\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ "Learning rate = 0.1\n", "Lambda = 0.001\n", "Accuracy score on test set: 0.9111111111111111\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ + "\n", "Learning rate = 0.1\n", "Lambda = 0.01\n", "Accuracy score on test set: 0.9305555555555556\n", - "\n", - "Learning rate = 0.1\n", - "Lambda = 0.1\n", - "Accuracy score on test set: 0.8388888888888889\n", "\n" ] }, @@ -2319,6 +2309,10 @@ "name": "stdout", "output_type": "stream", "text": [ + "Learning rate = 0.1\n", + "Lambda = 0.1\n", + "Accuracy score on test set: 0.8388888888888889\n", + "\n", "Learning rate = 0.1\n", "Lambda = 1.0\n", "Accuracy score on test set: 0.9055555555555556\n", @@ -2336,48 +2330,38 @@ "Learning rate = 1.0\n", "Lambda = 1e-05\n", "Accuracy score on test set: 0.09166666666666666\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ + "\n", "Learning rate = 1.0\n", "Lambda = 0.0001\n", "Accuracy score on test set: 0.11944444444444445\n", - "\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ "Learning rate = 1.0\n", "Lambda = 0.001\n", "Accuracy score on test set: 0.1361111111111111\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ + "\n", "Learning rate = 1.0\n", "Lambda = 0.01\n", "Accuracy score on test set: 0.1527777777777778\n", - "\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ "Learning rate = 1.0\n", "Lambda = 0.1\n", "Accuracy score on test set: 0.16666666666666666\n", - "\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ + "\n", "Learning rate = 1.0\n", "Lambda = 1.0\n", "Accuracy score on test set: 0.1111111111111111\n", - "\n", - "Learning rate = 1.0\n", - "Lambda = 10.0\n", - "Accuracy score on test set: 0.05\n", "\n" ] }, @@ -2385,6 +2369,10 @@ "name": "stdout", "output_type": "stream", "text": [ + "Learning rate = 1.0\n", + "Lambda = 10.0\n", + "Accuracy score on test set: 0.05\n", + "\n", "Learning rate = 10.0\n", "Lambda = 1e-05\n", "Accuracy score on test set: 0.08888888888888889\n", @@ -2394,15 +2382,15 @@ "Accuracy score on test set: 0.08611111111111111\n", "\n", "Learning rate = 10.0\n", - "Lambda = 0.001\n", - "Accuracy score on test set: 0.08888888888888889\n", - "\n" + "Lambda = 0.001\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ + "Accuracy score on test set: 0.08888888888888889\n", + "\n", "Learning rate = 10.0\n", "Lambda = 0.01\n", "Accuracy score on test set: 0.08888888888888889\n", diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb index 344f752d3..3ff3900d1 100644 --- a/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb @@ -1681,6 +1681,13 @@ "editable": true }, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial cost: 457.256\n" + ] + }, { "name": "stderr", "output_type": "stream", @@ -1689,13 +1696,6 @@ " return array(a, dtype, copy=False, order=order)\n" ] }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Initial cost: 457.256\n" - ] - }, { "name": "stdout", "output_type": "stream", diff --git a/doc/LectureNotes/_toc.yml b/doc/LectureNotes/_toc.yml index eabbf4dd5..823ac3ef8 100644 --- a/doc/LectureNotes/_toc.yml +++ b/doc/LectureNotes/_toc.yml @@ -26,6 +26,7 @@ numbered: true chapters: - file: chapter8.ipynb + - file: Clustering.ipynb - part: Deep Learning Methods numbered: true chapters: diff --git a/doc/src/How2ReadData/Git.do.txt b/doc/src/How2ReadData/Git.do.txt new file mode 100644 index 000000000..f57fdf7f2 --- /dev/null +++ b/doc/src/How2ReadData/Git.do.txt @@ -0,0 +1,28 @@ + +===== Git and Github/GitLab and more ===== + +Git is a free and open source distributed version control system designed to handle everything from small to very large projects with +speed and efficiency. _Git_ is a version control software (VCS). + +Without a VCS in place, you're probably working together in a shared +folder on the same set of files. Shouting out to your team mates +that you are currently working on file "xyz" and that, meanwhile, your +teammates should keep their fingers off is not an acceptable +workflow. It's extremely error-prone as you're essentially doing +open-heart surgery all the time: sooner or later, someone will +overwrite someone else's changes. + +With a VCS, everybody on the team is able to work absolutely freely - +on any file at any time. The VCS will later allow you to merge all the +changes into a common version. There's no question where the latest +version of a file or the whole project is. It's in a common, central +place: your version control system. + +Other benefits of using a VCS are even independent of working in a team or on your own. + +"Git":https://git-scm.com/" is one of the more popular version control softwares, and combined with repositories like "GitHub":"https://github.com/", "GitLab":"https://about.gitlab.com/?utm_medium=cpc&utm_source=google&utm_campaign=brand_emea_pr_rsa_br_exact&utm_content=homepage_digital_x-pr_english_&_bt=363211725518&_bk=gitlab&_bm=e&_bn=g&_bg=75294586319&gclid=EAIaIQobChMI1uiRi6288gIVFJ_VCh1dSgu8EAAYASAAEgKKxfD_BwE" and other, we have an efficient way of organizing our documents and always be able to keep updated versions across platforms and devices. + +The videos here give you a brief introduction to both _Git_ and repositories like _GitHub_: + +* Introduction to Git and GitHub/GitLab. Watch the video at URL:"https://mediaspace.msu.edu/media/t/1_8mgx3cyf" +* "Introductory videos on YouTube":"https://www.youtube.com/watch?v=SWYqp7iY_Tc&ab_channel=TraversyMedia" diff --git a/doc/src/How2ReadData/add.do.txt b/doc/src/How2ReadData/add.do.txt new file mode 100644 index 000000000..08f6118ad --- /dev/null +++ b/doc/src/How2ReadData/add.do.txt @@ -0,0 +1,505 @@ + +===== Simple linear regression model using _scikit-learn_ ===== + +We start with perhaps our simplest possible example, using _Scikit-Learn_ to perform linear regression analysis on a data set produced by us. + +What follows is a simple Python code where we have defined a function +$y$ in terms of the variable $x$. Both are defined as vectors with $100$ entries. +The numbers in the vector $\hat{x}$ are given +by random numbers generated with a uniform distribution with entries +$x_i \in [0,1]$ (more about probability distribution functions +later). These values are then used to define a function $y(x)$ +(tabulated again as a vector) with a linear dependence on $x$ plus a +random noise added via the normal distribution. + + +The Numpy functions are imported used the _import numpy as np_ +statement and the random number generator for the uniform distribution +is called using the function _np.random.rand()_, where we specificy +that we want $100$ random variables. Using Numpy we define +automatically an array with the specified number of elements, $100$ in +our case. With the Numpy function _randn()_ we can compute random +numbers with the normal distribution (mean value $\mu$ equal to zero and +variance $\sigma^2$ set to one) and produce the values of $y$ assuming a linear +dependence as function of $x$ + +!bt +\[ +y = 2x+N(0,1), +\] +!et + +where $N(0,1)$ represents random numbers generated by the normal +distribution. From _Scikit-Learn_ we import then the +_LinearRegression_ functionality and make a prediction $\tilde{y} = +\alpha + \beta x$ using the function _fit(x,y)_. We call the set of +data $(\hat{x},\hat{y})$ for our training data. The Python package +_scikit-learn_ has also a functionality which extracts the above +fitting parameters $\alpha$ and $\beta$ (see below). Later we will +distinguish between training data and test data. + +For plotting we use the Python package +"matplotlib":"https://matplotlib.org/" which produces publication +quality figures. Feel free to explore the extensive +"gallery":"https://matplotlib.org/gallery/index.html" of examples. In +this example we plot our original values of $x$ and $y$ as well as the +prediction _ypredict_ ($\tilde{y}$), which attempts at fitting our +data with a straight line. + +The Python code follows here. +!bc pycod +# Importing various packages +import numpy as np +import matplotlib.pyplot as plt +from sklearn.linear_model import LinearRegression + +x = np.random.rand(100,1) +y = 2*x+np.random.randn(100,1) +linreg = LinearRegression() +linreg.fit(x,y) +xnew = np.array([[0],[1]]) +ypredict = linreg.predict(xnew) + +plt.plot(xnew, ypredict, "r-") +plt.plot(x, y ,'ro') +plt.axis([0,1.0,0, 5.0]) +plt.xlabel(r'$x$') +plt.ylabel(r'$y$') +plt.title(r'Simple Linear Regression') +plt.show() +!ec + +This example serves several aims. It allows us to demonstrate several +aspects of data analysis and later machine learning algorithms. The +immediate visualization shows that our linear fit is not +impressive. It goes through the data points, but there are many +outliers which are not reproduced by our linear regression. We could +now play around with this small program and change for example the +factor in front of $x$ and the normal distribution. Try to change the +function $y$ to + +!bt +\[ +y = 10x+0.01 \times N(0,1), +\] +!et + +where $x$ is defined as before. Does the fit look better? Indeed, by +reducing the role of the noise given by the normal distribution we see immediately that +our linear prediction seemingly reproduces better the training +set. However, this testing 'by the eye' is obviouly not satisfactory in the +long run. Here we have only defined the training data and our model, and +have not discussed a more rigorous approach to the _cost_ function. + +We need more rigorous criteria in defining whether we have succeeded or +not in modeling our training data. You will be surprised to see that +many scientists seldomly venture beyond this 'by the eye' approach. A +standard approach for the *cost* function is the so-called $\chi^2$ +function (a variant of the mean-squared error (MSE)) + +!bt +\[ \chi^2 = \frac{1}{n} +\sum_{i=0}^{n-1}\frac{(y_i-\tilde{y}_i)^2}{\sigma_i^2}, +\] +!et + +where $\sigma_i^2$ is the variance (to be defined later) of the entry +$y_i$. We may not know the explicit value of $\sigma_i^2$, it serves +however the aim of scaling the equations and make the cost function +dimensionless. + +Minimizing the cost function is a central aspect of +our discussions to come. Finding its minima as function of the model +parameters ($\alpha$ and $\beta$ in our case) will be a recurring +theme in these series of lectures. Essentially all machine learning +algorithms we will discuss center around the minimization of the +chosen cost function. This depends in turn on our specific +model for describing the data, a typical situation in supervised +learning. Automatizing the search for the minima of the cost function is a +central ingredient in all algorithms. Typical methods which are +employed are various variants of _gradient_ methods. These will be +discussed in more detail later. Again, you'll be surprised to hear that +many practitioners minimize the above function ''by the eye', popularly dubbed as +'chi by the eye'. That is, change a parameter and see (visually and numerically) that +the $\chi^2$ function becomes smaller. + +There are many ways to define the cost function. A simpler approach is to look at the relative difference between the training data and the predicted data, that is we define +the relative error (why would we prefer the MSE instead of the relative error?) as + +!bt +\[ +\epsilon_{\mathrm{relative}}= \frac{\vert \hat{y} -\hat{\tilde{y}}\vert}{\vert \hat{y}\vert}. +\] +!et + +The squared cost function results in an arithmetic mean-unbiased +estimator, and the absolute-value cost function results in a +median-unbiased estimator (in the one-dimensional case, and a +geometric median-unbiased estimator for the multi-dimensional +case). The squared cost function has the disadvantage that it has the tendency +to be dominated by outliers. + +We can modify easily the above Python code and plot the relative error instead +!bc pycod +import numpy as np +import matplotlib.pyplot as plt +from sklearn.linear_model import LinearRegression + +x = np.random.rand(100,1) +y = 5*x+0.01*np.random.randn(100,1) +linreg = LinearRegression() +linreg.fit(x,y) +ypredict = linreg.predict(x) + +plt.plot(x, np.abs(ypredict-y)/abs(y), "ro") +plt.axis([0,1.0,0.0, 0.5]) +plt.xlabel(r'$x$') +plt.ylabel(r'$\epsilon_{\mathrm{relative}}$') +plt.title(r'Relative error') +plt.show() +!ec + +Depending on the parameter in front of the normal distribution, we may +have a small or larger relative error. Try to play around with +different training data sets and study (graphically) the value of the +relative error. + +As mentioned above, _Scikit-Learn_ has an impressive functionality. +We can for example extract the values of $\alpha$ and $\beta$ and +their error estimates, or the variance and standard deviation and many +other properties from the statistical data analysis. + +Here we show an +example of the functionality of _Scikit-Learn_. +!bc pycod +import numpy as np +import matplotlib.pyplot as plt +from sklearn.linear_model import LinearRegression +from sklearn.metrics import mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error + +x = np.random.rand(100,1) +y = 2.0+ 5*x+0.5*np.random.randn(100,1) +linreg = LinearRegression() +linreg.fit(x,y) +ypredict = linreg.predict(x) +print('The intercept alpha: \n', linreg.intercept_) +print('Coefficient beta : \n', linreg.coef_) +# The mean squared error +print("Mean squared error: %.2f" % mean_squared_error(y, ypredict)) +# Explained variance score: 1 is perfect prediction +print('Variance score: %.2f' % r2_score(y, ypredict)) +# Mean squared log error +print('Mean squared log error: %.2f' % mean_squared_log_error(y, ypredict) ) +# Mean absolute error +print('Mean absolute error: %.2f' % mean_absolute_error(y, ypredict)) +plt.plot(x, ypredict, "r-") +plt.plot(x, y ,'ro') +plt.axis([0.0,1.0,1.5, 7.0]) +plt.xlabel(r'$x$') +plt.ylabel(r'$y$') +plt.title(r'Linear Regression fit ') +plt.show() + +!ec +The function _coef_ gives us the parameter $\beta$ of our fit while _intercept_ yields +$\alpha$. Depending on the constant in front of the normal distribution, we get values near or far from $alpha =2$ and $\beta =5$. Try to play around with different parameters in front of the normal distribution. The function _meansquarederror_ gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as +!bt +\[ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n} +\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2, +\] +!et + +The smaller the value, the better the fit. Ideally we would like to +have an MSE equal zero. The attentive reader has probably recognized +this function as being similar to the $\chi^2$ function defined above. + +The _r2score_ function computes $R^2$, the coefficient of +determination. It provides a measure of how well future samples are +likely to be predicted by the model. Best possible score is 1.0 and it +can be negative (because the model can be arbitrarily worse). A +constant model that always predicts the expected value of $\hat{y}$, +disregarding the input features, would get a $R^2$ score of $0.0$. + +If $\tilde{\hat{y}}_i$ is the predicted value of the $i-th$ sample and $y_i$ is the corresponding true value, then the score $R^2$ is defined as +!bt +\[ +R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2}, +\] +!et +where we have defined the mean value of $\hat{y}$ as +!bt +\[ +\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i. +\] +!et +Another quantity taht we will meet again in our discussions of regression analysis is + the mean absolute error (MAE), a risk metric corresponding to the expected value of the absolute error loss or what we call the $l1$-norm loss. In our discussion above we presented the relative error. +The MAE is defined as follows +!bt +\[ +\text{MAE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n-1} \left| y_i - \tilde{y}_i \right|. +\] +!et +We present the +squared logarithmic (quadratic) error +!bt +\[ +\text{MSLE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n - 1} (\log_e (1 + y_i) - \log_e (1 + \tilde{y}_i) )^2, +\] +!et + +where $\log_e (x)$ stands for the natural logarithm of $x$. This error +estimate is best to use when targets having exponential growth, such +as population counts, average sales of a commodity over a span of +years etc. + + + +We conclude this part with another example. Instead of +a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn. + +!bc pycod +import matplotlib.pyplot as plt +import numpy as np +import random +from sklearn.linear_model import Ridge +from sklearn.preprocessing import PolynomialFeatures +from sklearn.pipeline import make_pipeline +from sklearn.linear_model import LinearRegression + +x=np.linspace(0.02,0.98,200) +noise = np.asarray(random.sample((range(200)),200)) +y=x**3*noise +yn=x**3*100 +poly3 = PolynomialFeatures(degree=3) +X = poly3.fit_transform(x[:,np.newaxis]) +clf3 = LinearRegression() +clf3.fit(X,y) + +Xplot=poly3.fit_transform(x[:,np.newaxis]) +poly3_plot=plt.plot(x, clf3.predict(Xplot), label='Cubic Fit') +plt.plot(x,yn, color='red', label="True Cubic") +plt.scatter(x, y, label='Data', color='orange', s=15) +plt.legend() +plt.show() + +def error(a): + for i in y: + err=(y-yn)/yn + return abs(np.sum(err))/len(err) + +print (error(y)) +!ec + + + +===== The Boston housing data example ===== + +The Boston housing +data set was originally a part of UCI Machine Learning Repository +and has been removed now. The data set is now included in _Scikit-Learn_'s +library. There are 506 samples and 13 feature (predictor) variables +in this data set. The objective is to predict the value of prices of +the house using the features (predictors) listed here. + +The features/predictors are + o CRIM: Per capita crime rate by town + o ZN: Proportion of residential land zoned for lots over 25000 square feet + o INDUS: Proportion of non-retail business acres per town + o CHAS: Charles River dummy variable (= 1 if tract bounds river; 0 otherwise) + o NOX: Nitric oxide concentration (parts per 10 million) + o RM: Average number of rooms per dwelling + o AGE: Proportion of owner-occupied units built prior to 1940 + o DIS: Weighted distances to five Boston employment centers + o RAD: Index of accessibility to radial highways + o TAX: Full-value property tax rate per USD10000 + o B: $1000(Bk - 0.63)^2$, where $Bk$ is the proportion of [people of African American descent] by town + o LSTAT: Percentage of lower status of the population + o MEDV: Median value of owner-occupied homes in USD 1000s + + +We start by importing the libraries +!bc pycod +import numpy as np +import matplotlib.pyplot as plt + +import pandas as pd +import seaborn as sns +!ec +and load the Boston Housing DataSet from _Scikit-Learn_ + + +!bc pycod +from sklearn.datasets import load_boston + +boston_dataset = load_boston() + +# boston_dataset is a dictionary +# let's check what it contains +boston_dataset.keys() +!ec +Then we invoke Pandas +!bc pycod +boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names) +boston.head() +boston['MEDV'] = boston_dataset.target +!ec +and preprocess the data +!bc pycod +# check for missing values in all the columns +boston.isnull().sum() +!ec +We can then visualize the data +!bc pycod +# set the size of the figure +sns.set(rc={'figure.figsize':(11.7,8.27)}) + +# plot a histogram showing the distribution of the target values +sns.distplot(boston['MEDV'], bins=30) +plt.show() +!ec + +It is now useful to look at the correlation matrix +!bc pycod +# compute the pair wise correlation for all columns +correlation_matrix = boston.corr().round(2) +# use the heatmap function from seaborn to plot the correlation matrix +# annot = True to print the values inside the square +sns.heatmap(data=correlation_matrix, annot=True) +!ec +From the above coorelation plot we can see that _MEDV_ is strongly correlated to _LSTAT_ and _RM_. We see also that _RAD_ and _TAX_ are stronly correlated, but we don't include this in our features together to avoid multi-colinearity + +!bc pycod +plt.figure(figsize=(20, 5)) + +features = ['LSTAT', 'RM'] +target = boston['MEDV'] + +for i, col in enumerate(features): + plt.subplot(1, len(features) , i+1) + x = boston[col] + y = target + plt.scatter(x, y, marker='o') + plt.title(col) + plt.xlabel(col) + plt.ylabel('MEDV') +!ec +Now we start training our model +!bc pycod +X = pd.DataFrame(np.c_[boston['LSTAT'], boston['RM']], columns = ['LSTAT','RM']) +Y = boston['MEDV'] +!ec +We split the data into training and test sets + +!bc pycod +from sklearn.model_selection import train_test_split + +# splits the training and test data set in 80% : 20% +# assign random_state to any value.This ensures consistency. +X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.2, random_state=5) +print(X_train.shape) +print(X_test.shape) +print(Y_train.shape) +print(Y_test.shape) +!ec +Then we use the linear regression functionality from _Scikit-Learn_ +!bc pycod +from sklearn.linear_model import LinearRegression +from sklearn.metrics import mean_squared_error, r2_score + +lin_model = LinearRegression() +lin_model.fit(X_train, Y_train) + +# model evaluation for training set + +y_train_predict = lin_model.predict(X_train) +rmse = (np.sqrt(mean_squared_error(Y_train, y_train_predict))) +r2 = r2_score(Y_train, y_train_predict) + +print("The model performance for training set") +print("--------------------------------------") +print('RMSE is {}'.format(rmse)) +print('R2 score is {}'.format(r2)) +print("\n") + +# model evaluation for testing set + +y_test_predict = lin_model.predict(X_test) +# root mean square error of the model +rmse = (np.sqrt(mean_squared_error(Y_test, y_test_predict))) + +# r-squared score of the model +r2 = r2_score(Y_test, y_test_predict) + +print("The model performance for testing set") +print("--------------------------------------") +print('RMSE is {}'.format(rmse)) +print('R2 score is {}'.format(r2)) +!ec + +!bc pycod +# plotting the y_test vs y_pred +# ideally should have been a straight line +plt.scatter(Y_test, y_test_predict) +plt.show() +!ec + + + + +Many Machine Learning problems involve thousands or even millions of +features for each training instance. Not only does this make training +extremely slow, it can also make it much harder to find a good +solution, as we will see. This problem is often referred to as the +curse of dimensionality. Fortunately, in real-world problems, it is +often possible to reduce the number of features considerably, turning +an intractable problem into a tractable one. + +Later we will discuss some of the most popular dimensionality reduction +techniques: the principal component analysis (PCA), Kernel PCA, and +Locally Linear Embedding (LLE). + + +Principal component analysis and its various variants deal with the +problem of fitting a low-dimensional "affine +subspace":"https://en.wikipedia.org/wiki/Affine_space" to a set of of +data points in a high-dimensional space. With its family of methods it +is one of the most used tools in data modeling, compression and +visualization. + + +Before we proceed however, we will discuss how to preprocess our +data. Till now and in connection with our previous examples we have +not met so many cases where we are too sensitive to the scaling of our +data. Normally the data may need a rescaling and/or may be sensitive +to extreme values. Scaling the data renders our inputs much more +suitable for the algorithms we want to employ. + +_Scikit-Learn_ has several functions which allow us to rescale the +data, normally resulting in much better results in terms of various +accuracy scores. The _StandardScaler_ function in _Scikit-Learn_ +ensures that for each feature/predictor we study the mean value is +zero and the variance is one (every column in the design/feature +matrix). This scaling has the drawback that it does not ensure that +we have a particular maximum or minimum in our data set. Another +function included in _Scikit-Learn_ is the _MinMaxScaler_ which +ensures that all features are exactly between $0$ and $1$. The + + +The _Normalizer_ scales each data +point such that the feature vector has a euclidean length of one. In other words, it +projects a data point on the circle (or sphere in the case of higher dimensions) with a +radius of 1. This means every data point is scaled by a different number (by the +inverse of it’s length). +This normalization is often used when only the direction (or angle) of the data matters, +not the length of the feature vector. + +The _RobustScaler_ works similarly to the StandardScaler in that it +ensures statistical properties for each feature that guarantee that +they are on the same scale. However, the RobustScaler uses the median +and quartiles, instead of mean and variance. This makes the +RobustScaler ignore data points that are very different from the rest +(like measurement errors). These odd data points are also called +outliers, and might often lead to trouble for other scaling +techniques. +